(^,/f;^

]Jmagnet. changes in r will be correspondingly small. If r is extremely large the changes in direction and intensity for small changes in r may become negligible in magnetic measurements. We call this a uniform field. 11. Magnetic moment. — Suppose a magnet is suspended or pivoted at its center of gravity so that it is free to oscillate in a hori- zontal plane in a uniform horizontal field,/, figure 2. The force on the north-seeking pole (+m) is +/m and on the pole (— m) it is —fm, MAGNETIC OBSERVATORY MANUAL [Ch. where m is the pole strength of either pole of the magnet. As these two forces are equal and oppositely directed, the clockwise turning moment or couple, i', will be L'=jm (2Zsin 6) =2ml (f sin 6) in which d is the angle between the magnetic axis and the direction of the field,/. The quantity, 2ml, is constant for a particular magnet so long as its magnetization does not change, and is called the magnetic moment of the magnet. That is. U=JMsme. (7) 12. It is thus possible to measure the magnetic moment of a magnet in terms of/, 6, and L\ When 6 is zero, sin 6=0, and the couple is zero. Hence a magnet freely suspended in a uniform field will come to rest with its magnetic axis parallel to the field. When ^=90°, that is, when the magnet is at right angles to the field, sin d = 1 and L'=fM (8) and M=j. (9) If the uniform field has unit intensity, then M=L' , which means that the magnetic moment may be defined as the couple (dyne- centimeters) which will maintain the magnet at right angles to a L ^ 1 ' ' S\ -m — + m»mN h ^ I H Figure 3.— Relation between length of magnet and pole distance; shaded end is north-seeking end of magnet. Figure 4.— Resolution of a magnetic field into two components. uniform field of unit strength. It is expressed in dyne-centimeters per unit field, that is, — — ^—r or simply the cgs unit of magnetic moment. 13. Referring to figure 3, experiments show that, for bar magnets, the pole distance, I, and the length of the magnet, L, are related as follows: Z«0.4Z. (10) 1.] FORCES BETWEEN MAGNETS 5 14. Resolution of fields, — A field has both magnitude and direc- tion and may be resolved into components. The resultant of two fields acting at a point may be evaluated graphically as in figure 4. Let H=0.3 cgs unit at and directed along ON. Let P=0.4 cgs unit, directed along OE. The resultant field, /=0. 5, is directed along OA. A small compass needle placed at would come to rest with its axis directed along OA. The components of / along OE and ON are OE=OA cos e and ON=OA sin d. 15. Field at a point P in terms of magnetic moment. — Sub- stituting M, the magnetic moment of the magnet, for 2 ml in equations (5) and (6), we have the following approximate relations: /«^, parallel to >SiV (11) for the field of a bar magnet at a distance r from the center of the magnet along its magnetic axis produced, and /«^, parallel to iV^ (12) for the field at a distance r from the center of the magnet along the perpendicular bisector of the magnetic axis. Equations (11) and (12) serve reasonably well for estimating the field of a magnet so long as I is small compared to r. For more precise values of these fields, corrections must be applied for distribution, as explained in para- graph 37.^ 16. Estimation of the field from a nomogram, — Corresponding values of/, M, and r in equation (11) are shown graphically in figure 137. The variation of the field with distance, r, is shown in figures 138 and 139. DEFLECTIONS 17. Gauss' first position, — Deflector end-on, approximate A posi- tion (see par. 32). In figure 5, let Ms be a short magnet pivoted at the point and free to turn in a horizontal plane. If H is the only field acting on Ms the magnet will come to rest with its axis parallel to H, that is in the direction of OA. Now place a second magnet, Ma, in a fixed position at P so that its magnetic axis is on the perpendicular to H through 0, and with its center at a distance r from 0. Ma produces a field/ in the direction OB; the resultant of/ and H is OC. Ms will turn through an angle u, coming to rest with its magnetic axis in the direction OC of the resultant field. From equation (7), the clockwise couple on Ms due to H is HMs sin u and the counter-clockwise couple on Ms due to the field/, of the deflector is /Ms sin {90°— u) =fMs cos u. 1 The aim and scope of this manual preclude showing explicitly the permeability of air in each of the many equations that need it under the standard conventions regarding the nature of pole strength. For full dimensional coherence, one may read into the equations the factor fxcts accompanying and qualifying every symbol that denotes a field component as derived from the pole strength or moment of the magnet that produces the field. The equations affected include those for deflection experiments (e. g. eq. 41), so what we really measure in deflections is, according to this approach, the induction B rather than the magnetic intensity H. 6 MAGNETIC OBSERVATORY MANUAL [Ch. When equilibrium is established and the magnet is at rest these couples are equal and HMs sin u=JMs cos u j^_sin u H cos u =tan u (13) (14) but whence H= f / H tan u 2 Ma 2 Ma r^ tan u (15) (16) B -^0°-u ^^_^^----^ t n ^^^ u -^ r H p ^ . Ma Figure 5.— Magnetic deflection, first position of Gauss. Example: Let Ms=472 cgs; f=30 cm; and ^^"=0.175 cgs=175007. Then 0.035 ^ ^^^ tan u^ ^ =0.200 U.l (o ^«11° 19' IS. Gauss* second position, — Deflector broadside, approximate B position. In this position the deflector axis is at right angles to H 1-1 FORCES BETWEEN MAGNETS with its center at P, PO being directed along H (see fig. 6) . The field of Ma at is directed opposite to Ma (see fig. 1) and (17) •a iH5 Figure 6,— Magnetic deflection, second position of Gauss. Example as in paragraph 17: 472 /= tan u 30^ 1750 17500 =1750t = 0.100 Hence, u^^° 43' (approximately one-half the deflection in the A position) . 19. Lamont's first position, — A position, deflector end-on. In this position the deflector is placed (fig. 7) so that its magnetic axis is Figure 7.— Magnetic deflection, first position of Lamont. always perpendicular to the suspended magnet when the latter comes to rest along the resultant. The couple Ms due to H is HMs sin u and that due to/ is /Ms sin v, but z; is 90° so that HMs sin u=fMs (18) 8 MAGNETIC OBSERVATORY MANUAL [Ch. and ■^=sin u (19) H=-X- (20) sm u H^^^ (21) r' sin 1^ Equation (21), with some minor correction factors, is standard in mag- netometer deflections. Equations (16) and (17) are basic in variom- eter scale-value deflections where a permanent magnet is used as the deflector. ANALYSIS OF THE FIELD OF A BAR MAGNET 20. Procedure for short magnets, — Just as a field may be resolved into components, so the magnetic moment may be resolved, enabling us to evaluate the field of the magnet at any point P, or any component thereof. In figure 8, let M represent the magnetic moment of the magnet. We require the principal components of the field, at a point P on a line OP making an angle d with the magnetic axis of the magnet and at a distance r from 0. The various components are de- scribed below. 21. The radial component, fr, is the component of/ at P in the direc- tion of OP. Let Mr = the component of the magnetic moment, M, in the direction of OP. Then Mr=M cos e (22) 2 Mr _2McosJ ^23) 22. The tangential component, fe, is the component normal to OP at P. The component of the magnetic moment normal to OP is Mfl=M sin e (24) Mb h=-,. M^ (25) 1.] FORCES BETWEEN MAGNETS 9 23. The total field, f, at the point P, is the resultant of/r and/^. =[-73- COS ej +[^ sin ^J =^(4cos2 0+sin2(9) = ^'[4 cos2 0+(l_cos2 (9)] =^(3cos2^+l) /=i!l73cos2 0+l. (26) 24. The parallel component, f\\, is the component of/ parallel to the magnetic axis of M. Consider PJ as made up of PA~JA. By construction, PA=Jr cos d JA=FC=RF sin e=fe sin (9 yii=PA— JA=/^ cos d—fe sin 6 Substituting values of/^ and/e, /il^(^-73- cos 0j cos ^-[jj sm ^J sm 2M 2. M ' 2 a = — 3- cos^ 6 3- sm^ 6 M =^ (2 cos2 ^-sin2 d) M =^(2cos2 0-l+cos2(9) M =-^(3cos2 0-l) =^(cos2 (9-0.333). (27) 210111—53 — —2 10 MAGNETIC OBSERVATORY MANUAL [Ch. 25. The 'perpendicular component, fj_, is the component at P, per- pendicular to the magnetic axis of M. Consider the perpendicular component, /j.> as made up of PB-{-BG: PB=jr sin e BG=RC=RF cos d=fe cos 6 J^=PB+BG=Jr sin B+Je cos d 2M . . . , M . , cos 6 sm d-\ — ?- sm 6 cos 6 M =-y (2 sin 6 cos ^+sin 6 cos 6) M =-^ (3 sin d cos ^) (28) 26. We now list the five equations developed above, together with values of the respective components (see fig. 8) based on assumed con- stants as follows: M= 10,000 cgs; r=:100 cm; ^=40°. We have, then Radial /r=^ cos 6 15327 M Tangential /e=-^ sin ^ 6437 Total /^My'3cos2 0+1 16627 Parallel J\\=^ (3 cos^ 6-1) 76O7 Perpendicular /x= — 3- sin 6 cos 6 14777 27. Other axes and components. — It is often convenient to compute a component of the total field,/, parallel to some other direction. In figure 8, suppose the chosen direction is PQ. Then the component of / parallel to PQ is PD, and the component perpendicular to PQ is DF. If PQ is the direction of magnetic north, PD will be denoted by /at and DF by /^. If PQ is in the direction of a suspended magnet, PD=Jj, and DF=jn. If PD and DF are parallel respectively to the X- and F-axes, then PD=J^ and DF=fy. 28. Components of the field for small values of 6. — It is interesting to note the values of the various components for small values of 6 and for values of 6 near 90°. This is of special importance in con- nection with placing the deflector in the orientation tests described in chapter 12. The values of these components are given in table 1. 1.] rOBCES BETWEEN MAGNETS 11 TABLE 1. — Components of the field of a short bar magnet. [Computed for a Uniform Distance of 100 cm, With M=iooo, for Angles Close to 0° or 90^] d fr fe / /ii A o y 7 T 7 7 200. 00 0.00 200. 00 200. 00 0. 00 1 199. 97 1. 75 199. 98 199. 91 5.23 2 199. 88 3.49 199. 91 199. 63 10.46 3 199. 73 5. 23 199. 79 199. 18 15.68 4 199. 51 6. 98 199. 63 198. 54 20.88 5 199. 24 8. 72 199. 43 197. 72 26.05 85 17.43 99. 62 101. 13 97.72 26.05 86 13.95 99. 76 100. 73 98. 54 20.88 87 10.47 99. 86 100. 41 99. 18 15.68 88 6.98 99.94 100. 18 99.63 10. 46 89 3.49 99.98 100. 05 99.91 5. 23 90 0.00 100. 00 100. 00 100. 00 0.00 a 4 ^fe ^ G F C Figure 8.— Components of the field of a magnet at any point P. 29. Direction oj total field, j, at a point, P. — Consider figure 8. Let the angle RPF=(f)=the angle between the total field vector, /, and the radial field vector,/,. tan = 2M (29) cos 6 sin 6 2 cos e and for small angles =-^ B. (30) (31) 12 MAGNETIC OBSERVATORY MANUAL [Ch. 30. Distribution coefficients and distribution factors, — Equa- tions (11) and (12) are based on the assumption that the distance, r, is great compared to the pole distance. In practice this is not always true so that in calculating the couple due to the interaction of two magnets we must apply certain factors to the equations for the couple based on (11) and (12) in order to obtain greater precision. Bergen, Schmidt, Hazard, Hartnell, and others have developed special solu- tions for these factors as they apply to pairs of magnets of different lengths and different orientations with respect to each other. The correction factors take the form 1 + -2 + -4+---' in which P and Q are called the first and second distribution coefficients. 31. Figure 9 represents three mutually perpendicular planes. All axes pass through the center of a suspended magnet, Mg, the X and Y ^. Fieure 9.— Deflector positions. axes being horizontal and the Z axis vertical. The deflector is designated Ma. (Ma and Ms are also used to designate the magnetic moments of these magnets.) 32. Four positions are considered. The axis of the suspended mag- net lies along the X axis for all positions. A Position: The center of the deflector, Ma, is on the F-axis, and the magnetic axis of Ma is parallel to the F-axis; B Position: The center of the deflector, Ma, is on the X-axis, the magnetic axis of Ma is parallel to the F-axis; C Position: The center of the deflector, Ma, is on the Z-axis, the magnetic axis of Ma is parallel to the F-axis; and and 1.] FORCES BETWEEN MAGNETS IS D Position: The center of the deflector, Ma, is anywhere in the YZ plane and the magnetic axis of Ma is parallel to the Z-axis. 33. It should be noted that, although the positions of Ma and M, are described above relative to the vertical Z axis and the horizontal X and Y axes, the axes may be rotated in any direction. The posi- tion of Ma relative to Ms is considered in each case, rather than the positions of the two magnets relative to a fixed set of orthogonal axes. 34. Table 2 gives the formulas for calculating the distribution coefficients in terms of the pole distances of the pair of magnets and also gives the form in which the distribution factors should be applied for the four positions. In the computations in this manual, the pole distance of a magnet is taken as 0.4 of the length of the magnet (see par. 13). 35. Table 21 gives the approximate values of P and Q in terms of the over-all lengths of the deflector and suspended magnet for various combinations of La up to 20 cm and Lg up to 12 cm. This table together with the nomogram, figure 146, will be found very helpful in making a quick and reasonably accurate estimate of the value of the distribution factor. With magnets of odd shapes, the pole distance may be known to be other than 0.4 of the magnet length; in such cases, enter the table with a nominal value of L equal to 2.5 /, irre- spective of the actual length of the magnet, so that / will be 0.4 of the nominal L. (For table 21 see pp. 227-228.) TABLE 2. — Summary of form,ulas A, B, C, and D Positions. Posi- tion P Q Factor A 2Z„2_3/,2 4^ ^=i+^+f? B -- |/a2+6/,2 1 c 4c B=l + '^ + ^ C -^aj+is') ~{ij+L'y c^=i+^^+t D ,,/35 . , 5\ 5,, « = l + ^"+f? If Afa = deflector or its magnetic moment; Af, = suspended magnet or its magnetic moment; la = po\e distance of the deflector; Z8 = pole distance of the suspended magnet; ^ = height of the center of the deflector above center of Ma', r= distance between centers of Ma and iV/,; e = angular elevation of center of Ma above (or below) center of M, (D-position) . (i = horizontal distance for D-position, r^ = h^ + d^, and tan e=-T- 14 MAGNETIC OBSERVATORY MANUAL [Ch. 36. In Lament's first position, the deflector is always in the A position. The couple, Li, tending to turn the suspended magnet out of the magnetic meridian is, L.='-^{l+^+^} (32) The restoring couple, L2, due to the uniform field, H, acting on Ms, is L2=HMs sin u. (33) When Ms comes to rest these couples are equal and ™sin«=^^(l+^+^) (34) and 37. In equation (34), if r is quite large compared to the pole distance, la, of the deflector, and if the pole distance, Is, of the suspended magnet is very small, this relation may be written H^mu=-^{^1 + ^J- (36) And from equation (19), f=H sin u Hence, /=^"(l+f> (37) Equation (37) will yield a reasonably precise value of the field at a point P along the magnetic axis of Ma produced. Similarly, for the B position, the field in the direction of the perpendicular bisector of Ms would be 38. Special values for Pa and Qa. — In the equation Pa=211—31^, by letting Pa =0 and solving for f, we find ^= 1 .225. Likewise, in the 45 I equation ^^ = 3^*— 15Z^/f+-^ It, by setting ^^ = and solving for fj two positive values are found; ^=2.143 for the usual case that la is greater than Is; ^=.641 for the rare case when /« is less than Ig. The long and short magnets of a magnetometer are usually designed with the ratio of these lengths such that Pa or Qa will be practically zero. 1-] FORCES BETWEEN MAGNETS 15 Table 3 summarizes these ratios in form for convenient use. Note that in solving for Pa = or ^^ = 0, la is taken as 0.4 La. TABLE 3.— Special values for Pa and Qa. For Pa = For Qa = and la>la (a) la = (b) ls = (C) La = (d) Ls = (e) Qa=- (f) Qa=- 1. 225 I, 0. 816 la 1. 225 L, 0. 816 La -4. 500 la* -0. 115 La* Condition 1 La la i L-ls la=0.4:La (g) la== 2.USh (h) Is^ 0. 467 la (i) La= 2. 143 L, (j) L,= 0. 467 L„ (k) P4= + l. 35Z„2 (1) P^ = +0. 216L„2 Condition \ La la i Lru la = 0.4:La Examples For Pa-- = FovQa = Casel Case II Equation Case I Case II Equation when La^ Ls = Qa = cm 4. 9 4. -66. cm 9. 28 7. 58 -854. (d) (f) when La = Ls^ Pa- cm 4.9 2. 29 + 51.9 cm 9.28 4.33 18. 6 (j) (1) CHAPTER 2. THE EARTH'S MAGNETIC FIELD (c) The vertical intensity, Z, ZENITH 39. The magnetic elements, — The direction of the earth's mag- netic field at a point on the surface of the earth is the direction taken by a freely suspended magnetic needle (free to turn in any direction in space). (a) The magnitude of the field is called the total intensity and is indicated by F in figure 10. (b) The horizontal intensity, H, is the projection of F on the hori- zontal plane. is the projection of F on the vertical. (d) The true north component, X, is the projection of H on the true north direction. (e) The true east component, Y, is the projection of H on the true east direction. (f) The magnetic declination, D, is the angle between H and X. (g) The magnetic dip or inclination, I, is the angle between H and F. (h) The magnetic meridian plane is the vertical plane through F con- taining H, F, and Z. (i) The magnetic meridian will be used in this manual to denote the horizontal line through a specified point, in the direction of H. ( j ) The magnetic prime vertical plane is^the plane perpendicular to H. 40. The principal magnetic elements are D, H, and /. A knowledge of their direction and magnitude at any point enables one to compute other desired components. 41. The relation between these various elements is shown in the vector diagram, figure 10. Note also these primary equations: Z=H tan / F'=H'+Z' X=H cos D Z=F sin / Y=H sin D H=F cos I H'=X'-}-Y' 42. Approximate values of the magnetic elements for any part of the world may be scaled from world isomagnetic charts^ with sufiicient accuracy for use in designing magnetic observatory instruments for particular regions. 43. General pattern approximated by dipole field. — The accrued results of past measurements show that the earth's magnetic Figure 10. — Components of the earth's magnetic field. 1 Those issued by the U. S. Hydrographic Office, Navy Department, are a standard source. For most areas, adequate values may likewise be obtained from the Smithsonian Physical Tables (see item 14 of bibliography on p. 228). 16 EARTH S FIELD 17 field is such as could be roughly accounted for by supposing a bar magnet at its center with a magnetic moment, M, of about 8.1X10^^ cgs. The field of such a magnet would have a configuration depending on its length — that is, on the separation of its poles. However, it is found that the shorter the magnet the better the fit. As the poles are brought closer together and their strength simultaneously increased so as to preserve a constant magnetic moment, the field pattern at remote points is but little changed, and with the pole spacing very small in comparison to the distance, the field approaches a limiting pattern which we term the field of a magnetic dipole, taking the pole distance as an infinitesimal quantity. The field of a centered dipole is the simplest over-all approximation to the earth's field. Note further that the dipole field would be indistinguishable from one produced by uniform magnetization (parallel to an axis) of the entire earth, or of any smaller portion thereof occupying the volume within a concentric spherical surface. A suitable distribution of electric current, flowing along circular paths in a metallic core, could also yield such a field. 44. The axis of the centered dipole that most nearly duplicates the earth's field is known as the earth's magnetic axis. It pierces the sur- face of the earth at two points known as the geomagnetic poles, where the dipole field would be perpendicular to the surface.^ The places where the actual field is perpendicular to the surface are known as the earth's magnetic poles and do not coincide with the geomagnetic poles, since the dipole field is only a rough approximation to the actual field. The currently adopted positions of the two kinds of poles are as follows: POLE LOCATION Latitude Longitude North magnetic 73° N. 68° S. 78°. 5 N. 78°. 5 S. 100° w. 144° E. 69° W. 111° E. South magnetic North geomagnetic South geomagnetic 45. Earth's field at various latitudes, — In figure 11 the circle represents the surface of the earth and the small bar magnet repre- sents the hypothetical magnetized portion at the center. Since the north-seeking end of a compass needle is called the North end, the magnetically active core of the earth behaves as though its geograph- ically northernmost part were magnetically a South pole. 46. The approximate relative magnitude and direction of the components Je, Jj, and /, at certain points on the circumference of the circle of radius r, where r is very great compared to the length of the magnet, are shown in figure 11, for various values of 0. The angle is the angle between the magnetic axis and the radius through the chosen point on the circumference. If we consider the plane of the circle as a section through the earth and consider that the mag- netic axis lies in the plane of this section, then the components of the earth's field, at the surface, may be computed approximately, using equations (23) and (25) of chapter 1 (p. 8), with M=8.1X102^ cgs. 2 Chapman and Bartels, Geomagnetism, vol. II, pp. 644-45, 1951 (see item 2 of bibliography). 18 MAGNETIC OBSERVATORY MANUAL [Ch. The magnetic latitude at a point is the angle whose tangent is ji tan /, where / is the actual dip at the point. The geomagnetic latitude is the angle whose tangent is K tan /', where /' is the dip computed from the simple dipole approximation. It can be shown (see eq. 30) that the geomagnetic latitude is a coordinate like ordinary latitude but reckoned in relation to the geomagnetic rather than to the geographic poles. Example: Suppose 0=112°. 5, corresponding to a geomagnetic latitude of 22°. 5 N, taking the radius of the earth to be 6.37X10^ cm, Z=-fr = 2M cos 0=0.241 cgs H=fe=^- sin 0=0.290 cgs F=^lH'+Z'=0.d77 cgs 7=tan-^^=39°.6 47. The correspondence between /, /r, /e, , and F, H, Z, / is as follows: Field of Magnet Earth's Field Name Symbol Name Symbol Radial component Tangential component Total field /r fe f Reversed vertical intensity- Horizontal intensity Total intensity -Z H F Direction of/ Direction of F Angle between / and fe 90° -<^ Inclination (or dip) I The negative sign is required in the relation/;.= —Z because Z is taken positive inward and/^ is positive outward. 48. Equation of a line of force. — It has been shown by Chapman and Bartels,^ and others, that a line of force due to a magnetic dipole is the locus of the equation r=C sin^e (39) in which r= distance from a dipole magnet to a point P, 0=the angle r makes with the magnetic axis of the dipole, and (7= a constant for the particular line of force. 49. It is obvious from equation (39) that a line of force (any line of force) must pass through the dipole since r=0 when 0=0°. When 0=90°, sin^ 0=1 and r=0. By assigning arbitrary values to C (such as 1, 2, 3, etc.), and 5°, 10°, 15°, etc. to 0, the corresponding values of r may be calculated from equation (39). Figure 11 shows the pattern of the lines of force about a dipole for various values of C. 3 S, Chapman an4 J. Partels, Geomagnetism, p. 11 (see item 2 of bibliography on p. 228), 2.1 eaeth's field 19 50. To draw a line of force which shall pass through a given point P whose polar coordinates are known with respect to the dipole and its magnetic axis, first solve equation (39) for C using the given values of r and B. Then using this value of C and various values of B, solve for the corresponding values of r. Figure 11 shows the lines of force Figure 11.— The earth's magnetic field at various latitudes. passing through several points on the circumference of a circle of radius 10 units for values of (9-0°, 22^.5, 45°, 67°.5, and 90°, and for the corresponding angles in the other quadrants. 51. Changes in the earth's magnetic field. — The earth's mag- netic field is always changing in direction or intensity or both. These changes are described briefly in the following paragraphs.^ 52. Daily variation. — There is usually a fairly systematic departure of the magnetic field from its daily mean value. This repeats itself * Further details are given by A. K. Ludy and H. H. Howe, Magnetism of the Earth (see item 13 of bib- liography on p. 228). 20 MAGNETIC OBSERVATORY MANIJAL (though with somewhat variable form and ampHtude) day after day. The amount of departure depends upon the time of day, the season, the magnetic latitude, and other factors not wholly understood. This systematic change is called daily variation. 53. Irregular disturbance and magnetic storms. — Superimposed on the regular daily variation, there are usually irregular changes. When they become v^ery large, we say there is a magnetic storm. These storms are associated with sunspots, and are characterized by auroral displays and pronounced disturbances to radio-wave trans- mission and wire telegraphy. A magnetic storm may last many hours or even several days, and the more severe ones occur all over the earth at the same time. 54. Secular and annual change. — In general, the average value of a magnetic element changes from one year to the next, and the change usually continues in one direction for many years. This is called the secular change. The amount in one year is called the annual change. t CHAPTER 3. THE MAGNETIC OBSERVATORY 55. Selection of an observatory site, — The primary objective of the operation of a magnetic observatory is the measurement of the continuous variations in the earth's magnetism in the particular region where the observatory is situated. 56. The site should be free from local disturbances (irregularities of the magnetic field), either natural or artificial. This can be ascer- tained only by a preliminary magnetic survey of a large area sur- rounding the proposed site, followed by a more detailed survey of the immediate site, say over an area of 50 meters radius. Such a survey should consist of magnetic observations made at points uniformly spaced in the form of a grid over the immediate area with, say, 10 meters between stations. It is usually sufficient to test for irregu- larities in magnetic declination only. Anomalies in vertical intensity may be determiaed by a magnetic field balance. A quartz horizontal magnetometer, QHM, is probably the most satisfactory instrument for the determination of anomalies in horizontal intensity. In gen- eral, if tests in the immediate vicinity of the proposed site show that there are gradients in declination, anywhere in the area, as great as 10' between stations 10 meters apart, or as great as 2O7 in horizon- tal or vertical intensity in the same distance, the site should be con- sidered unsatisfactory. AJso, the mean value of the measured element should be about the same as the mean value for the site, as scaled from the latest available isomagnetic chart. 57. Buildings and equipment. — The minimum requirements for a magnetic observatory are as follows: (a) Satisfactory site, as described in paragraph 56. (b) Magnetic variation building, including instrument piers. (c) Absolute observatory building, including instrument piers. (d) Magnetograph, consisting of H, D, and Z variometers, a photographic recorder, time-marking mechanisms, and facilities and equipment for scale-value and orientation observations. (e) Office and photographic darkroom, (f) Magnetometer (or equivalent) for measurement of H and D. (g) Earth inductor (or equivalent) for measurement of /. (h) Mean-time chronometer. (i) Time marking clock or chronometer. (j) True meridian line or true azimuth from declination pier in absolute observatory to a permanent azimuth mark. (Two permanent azimuth marks recommended.) (k) True azimuth line established in the variation room. (1) Miscellaneous equipment for processing records. 58. Figure 12a shows a plan view of a variation building, designed for operation of one or two complete magnetographs. For other types of magnetographs the pier plan would require alteration but the basic requirements would be practically the same as described here. ^ The building and piers are constructed of tested, nonmagnetic materials throughout. The piers should have enlarged bases extend- ing well below the ground surface and should rest on natural, undis- turbed formation. Within the variation room and attached perma- nently to the walls are special shelves of heavy construction for sup- porting deflector holders used in orientation tests and scale-value 21 22 MAGNETIC OBSERVATORY MANUAL [Ch. are observations by the magnetic method. The variation rooms thermally insulated and are suitable for photographic recording. 59. The absolute building is a small, nonmagnetic structure shown m figure 12b. Asjn the variation building, the bases of the piers je|0|!iii*A « Bu|uiOJj |o*d*y- H B B a H B B R 1 — r J_L_L_i_J^ o • r '1° m q::p g \ ^ ^8 B Ta 0,91 •pms.oo.s a a a a Ir ^ I S3 oniA .»-,l »,•-.! tJOOQ iO|D|UU»A •a pj * 5 « Q ■• s should rest on natural, undisturbed formation, well below the ground surface. In routine operations the magnetometer is operated on the central pier and the earth inductor and its galvanometer are operated on the other piers. The windows of this structure are so arranged as to prov^ide an unobstructed v4ew of one (or two) well established true azimuth marks. 3.1 BUILDINGS AND EQUIPMENT 23 60. The three magnetic variometers shown in figure 13 are con- structed to respond to variations in magnetic declination, horizontal intensity, and vertical intensity. A recorder, a light source, and a time- flashing lamp with auxiliary reflector complete the magneto graph ■f" MASONITE , SOFT 2 X 6" FLOOR JOISTS NOTCHED 1^' ON SILL CONCRETE POSTS STORM OOOR 2'e" X6'8'X|i" 5 PANEL 12 MarbK CubM IxS.i SCottofl PocKin^ Section through Piers Figure 12b.— Magnetic absolute building. assembly. If scale values are to be determined by the electrical method, each variometer must be provided with a Helmholtz-Gaugain coil (not shown). The various components of the magnetograph are described in more detail in chapters 5 and 7-9. Descriptions of mag- netometers and earth inductors with detailed directions for their use are contained in ''Directions for Magnetic Measurements," by D. L. Hazard. 24 MAGNETIC OBSERVATORY MANUAL ^ 2 i ^ 1 « ^ I s ■" O 13 a 2 2 .2f 'z CHAPTER 4. INSTRUMENTAL CONSTANTS AND CORRECTIONS REFINEMENTS CONTRIBUTING TO ACCURACY 61. Quality of instruments, — In order to assure the successful accomplishment of accurate measurements of the earth's magnetic field, it is first necessary to be sure that the available instruments are of satisfactory quality and are so designed as to be capable of measure- ments with the required precision. Quality here refers not only to proper design and fine workman- ship on the part of the instrument maker but also to freedom from hidden defects which could and often do introduce the necessity for index corrections that theoretically should not exist. Such hidden defects may often be traced to the presence of minute quan- tities of impurities in the materials of which the instrument is made, such as to cause erratic or spuri- ous deflection of the suspended magnet or to distort the earth's field in the vicinity of the instrument. 62. Test for magnetic parts, — Before any meas- urements or observations are made for the determi- nation of any of the constants of a magnetometer, earth inductor, or other instrument used directly in measuring a component of the earth's field, the parts of the instrument should be tested carefully for mag- netic properties. Any part found to show objec- tionable traces of magnetism should be rejected; if that part is near the moving magnet or coil of the assembled instrument, any detectable magnetic effect should be sufficient cause for rejection. 63. To test a specimen for magnetism, it is usu- ally sufficient to place it near one of the magnets of an astatic moving-magnet system (magnetism tester) ^magn^et^'^'^S'^of such as that shown in figure 14. The two magnets magnetism tester. A and B having equal magnetic moments (10 to 20 cgs units) are mounted about 10 cm apart in the same plane on a stiff brass rod, but with their moments oppositely directed. The system is equipped with a mirror, M, and is suspended by a fine filament, Q, such as a magnetometer suspension fiber. A lamp and scale are provided for visual observation of the deflections of the magnets. A copper damp- ing box for the lower magnet is necessary to reduce undesirable oscil- lations, and a cylindrical shield, with window, not shown in the illus- tration, provides protection against spurious deflections due to air currents. As long as the magnetism tester is not located too near direct-current machinery or cables, it will prove to be quite satis- 210111—53 3 25 26 MAGNETIC OBSERVATORY MANUAL [Ch. factory for use even in a machine shop for testing parts of magnetic instruments. The specimen to be tested is placed near one of the magnets of the tester, and the deflection (if any) noted while the speci- men is at rest. It is important that the specimen remain at rest while observing the deflection of the magnets, since secondary magnetic fields will be set up by eddy currents induced in the specimen if it is moved about in the field of the magnets. Specimens should be tested in several positions. 64. Although the magnetism tester as described does not yield quantitative results, it can be made very sensitive by properly balanc- ing the fields of the two magnets, and a little practice with the tester will enable any observer readily to become skilled at finding traces of magnetic materials in instrument parts. 65. Instrumental constants to be determined. — For measure- ments of magnetic declination, the scale value of the scale in the telescope (or magnet) must be determined as explained in paragraphs 66 and 67. The equations used in the computation of H and M by the method of oscillations and deflections involve the moment of inertia, induction factor, temperature coefficients, deflection dis- tances, and distribution coefficients. These instrumental constants must be determined as explained in paragraphs 69-145. SCALE VALUE 66. Scale in the telescope. — This scale value is determined as follows: Focus the telescope on a well-defined, distant object and determine the difference in circle reading corresponding to a difference of, say, 20 divisions on the scale. The ratio of the difference in circle readings to the difference in scale readings is the scale value, in minutes of arc per scale division. Repeat several times and take the mean. 67. Scale in the magnet, — Proceed as follows: When magnetic conditions are quiet, suspend the magnet with a filament having a small torsion factor, and when the magnet is at rest, with the vertical cross line of the telescope bisecting some even scale division, observe the circle reading. Rotate the magnetometer through precisely 10 scale divisions to the right, repeat the circle reading; then 20 divisions to the left, etc., making several determinations. As in paragraph 66 the ratio of the change in circle reading to the change in scale reading is the scale value in minutes of arc per scale division. Note that there will be a slight restraining effect due to torsion of the filament, but if a fine filament is used, the effect will be neghgible for such small angular displacements. The operation may be simplified and the effects of change in magnetic declination and torsion entirely elim- inated if the suspended magnet is held in a fixed position relative to the ground by a nonmagnetic stop mounted directly on the pier and independent of the magnetometer. MAGNETOMETER EQUATIONS 68. As shown by Hazard,^ the two fundamental equations showing the relation between the horizontal intensity, H, of the earth's mag- Dir. for Mag. Meas. (see item 4 of bibliography). 4.] CONSTANTS AND CORRECTIONS 27 netic field, and the magnetic moment, M, of the long magnet of a magnetometer, are HM= f^ jj^ . (40) Hi(■+$+^)(-|f)].^^. in which M= magnetic moment of the long magnet at temperature t; 7iL= moment of inertia of the long magnet and its stirrup at temperature t'; 7^= observed time of one oscillation (half-period) in chro- nometer seconds; c?=rate of chronometer in seconds per day; A-= angle through which magnet turns when torsion head is turned through an angle /; /= angle through which torsion head is turned to deflect the suspended magnet through the angle h; iLt= induction factor of the long magnet; ^= observed temperature of long magnet during deflection observations ; ^' = observed temperature of long magnet during oscillation observations ; g= temperature coefficient of magnetic moment of the long magnet; r= deflection distance at temperature t; 16= deflection angle for particular value of r; and Pa and Qa are distribution coefficients. 69. The moment of inertia, induction factor, temperature coeffi- cient, deflection distances, and distribution coefficients must be determined by special observations or otherwise evaluated before TT equations (40) and (41) can be used in the computation of ffllf and y^- The time of one oscillation, its correction for rate of chronometer, the torsion factor, and the deflection angles are determined directly at the time horizontal-intensity observations are made. For all prac- tical purposes, the distribution coefficients, induction factor, and temperature coefficient are taken as constants at all temperatures at which observations are likely to be made, but deflection distances and moment of inertia of the long magnet change appreciably with temperature, and corrections must be applied accordingly to these terms. The torsion factor of the suspension filament is usually deter- mined just before or just after each set of oscillation observations. The rate of the chronometer is, of course, an independent determina- tion not involving the magnetometer itself. 70. It is customary to combine some of the factors in equation (41) and treat them as a single constant for a particular value of r at a particular temperature. Thus, equation (41 ) may be written H C (42) in which M sin u c=i(.-#)(.+$+2.). 28 MAGNETIC OBSERVATORY MANUAL [Ch. The constant C may be computed for various values of r and these values corrected for temperature as explained in paragraph 454, appendix I (p. 193). MOMENT OF INERTIA 71. Basic relations, — The time of one oscillation, T, of a magnet oscillating as a torsion pendulum under the influence of the horizontal component, H, of the earth's magnetic field is given by V^ M in which K is the moment of inertia of the magnet and its stirrup and M is the magnetic moment of the magnet. The moment of inertia of the magnet and its stirrup cannot be readily calculated from the dimensions and mass; it must be determined experimentally by the kinetic method. That is, the period of the system is determined with and without a special inertia weight mounted on the magnet system. The added mass is usually in the form of a precision-ground, solid, right circular cylinder of bronze or brass, or in the form of a cylindrical brass ring. In either case the material must be homogeneous and non- magnetic. 72. The moment of inertia of a solid, right circular cylinder, oscil- lating about a transverse diameter through its center, is in which T^=the mass of the cylinder in grams; l=ihe length in cm; c^=the diameter in cm. 73. For a cylindrical ring oscillating about a longitudinal axis (axis through its center normal to its bounding planes), the formula is K,=^{dl+dl) (46) in which di and d2 are the inner and outer diameters. 74. It is important that the inertia weight be constructed with great precision and that the dimensions be determined for several uniformly distributed positions. The temperature at which these measurements are made should be specified. In the United States, the mass and dimensions are usually determined at the National Bureau of Standards. 75. With the inertia weight added to the system, the time of one oscillation is 4.] CONSTANTS AND CORRECTIONS 29 in which Ki is the moment of inertia of the inertia weight calculated from its dimensions. Squaring equations (44) and (47) and dividing. T' K ^ K and K=y^ (48) - — 1 76. Equations (44), (47), and (48) are based on the assumption that K^ Ki, H, and M are constants and remain constant under all conditions and that no other forces are acting on the oscillating system. However, during a set of oscillations both H and the temperature may change. A change in temperature changes the dimensions of the magnet and the inertia weight, thus affecting both K and Ki. The magnetic moment of the magnet also changes with temperature. The directive force of torsion of the suspension filament affects the period and also changes with the load. The chronometer may not have a uniform rate during a series of observa- tions but it is usually assumed that the rate is the same for adjacent loaded and unloaded sets, and therefore does not affect the ratio, T ~- Induction and damping effects may be considered as equal for loaded and unloaded sets and therefore may be neglected. 77. The moment of inertia, Kx, of the inertia weight and the observed times of oscillation, T and Ti, must be reduced to standard conditions in order to evaluate the moment of inertia, X, of the magnet at those same standard conditions. Temperatures are usually referred to 20° C and changes in iJ to a mean value for the elapsed time or simply to the H base-line value. 78. For the unloaded magnet, the relation between the true time of one oscillation (T) and the observed time T is, (^'=^'5^^[l+(20-0«][l+(20-Q2a]-g (49) and for a loaded set, (ri)'=rfg^^^[l+(20-(,)?][l+(20-<02a,]g (50) in which (T)=the corrected time of one oscillation (unloaded); r=the observed time of one oscillation (unloaded); (7'i)=the corrected time of one oscillation (loaded); Ti = the observed time of one oscillation (loaded); ^=the observed temperature of the magnet in unloaded oscillations; fi=the observed temperature of the magnet and inertia weight in loaded oscillations; 2= the temperature coefficient of magnetic moment of the magnet; a = coefficient of thermal expansion (linear) of the magnet; «! = combined coefficient of thermal expansion (linear) of the inertia weight and magnet; 30 MAGNETIC OBSERVATORY MANUAL [Ch. H and Hx are the average values of the horizontal intensity during a set of unloaded and loaded oscillations, respectively; and Bh is the horizontal-intensity base-line value. 79. The correction factors in equations (49) and (50) are explained in appendix I, and their method of application is shown in the sample sets of observations, figures 15, 16, and 17. UNLOADED Oscillations for Moment of Inertia station, Cheltenham, Md., Pier 6 Magnetometer No. 5064. Magnet No. RIC 6 Inertia ring or bar No. A Chron. corr'n on 75 M. Time, +0 10.0 Daily rate (jjj^^ gaTniSg)' +^-^ ^/^^^ Date, Fri., July 21, 1960 Observer, RL V Chron. No. 6666 Number of oscilla- tions 100 106 IIG 116 120 126 130 136 140 146 Chronometer time (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) 12 15 16 12 21.7 41.8 02.0 22.0 42.2 02.3 22.3 42.6 02.6 22.6 (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) 12 22 23 03.6 23 8 43.8 03.9 24.0 44.1 04.3 H.4 44.6 25 04.6 U Temp, t OC 26.5 Extreme scale readings 17.1 44-0 43.0 40.3 Remarks 60=^12 18 42.7 0= 16 21.7 100- 5 21.0 = 22 03.7 Time of 100 oscil. 6 41.9 42.0 41.8 41.9 41.8 41.8 42.0 41.9 42.0 6 41-9 Means 26.60 41.90 FORMULA: (T)2=T2^^^^ [l+{20-t)q][l+(20-t)2a] -^ Torsion observations Tors, circle 293 113 203 Scale div. 28.9 26.8 32.7 29.5 div. 31. S 27.0 35.1 30.8 Mean div. SO. 10 26.40 33.90 30.16 Diffs. 3.70 7.50 3 76 Mean h=S.74 =4'.94 Magnetometer scale value, 1'. 32 /div. (20-0 Log Time of 1 oscil. Log T Log r2 5400 5400 -ft Log a+(20-t)q) Log (1+(20-O2a) Log (T)2 4. 01 900 0.60 41 18 1.20 824 +40 -52 -6 +339 1.21 146 Computed by RRB Checked by RL V Abstracted by AM Figure 15.— Observations for moment of inertia, unloaded magnet suspension system. 4.] CONSTANTS AND CORRECTIONS 31 LOADED Oscillations for Moment of Inertia station, Cheltenham, Md., Pier 6 Magnetometer No. S05J^ Magnet No. RlC-6 Ineitia ring or bar No. A Chron. corr'n on 75 M. Time, +0 10.0 Daily rate (j^f^J. gaSg)' +^-^ ^^^^^ Date, Fri., July 21, 1950 Observer, RL V Chron. No. 6565 Number of oscilla- tions Chronometer time (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) 50 12 52 56.4 17.0 37.7 58.4 19.1 39.8 00.5 21.2 41.8 02.5 (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) 50.0 10.7 31.4 52. S 13.0 33.8 54.2 15.1 55.5 12 58 56.4 58 Temp, t °c 26.8 26. Extreme scale readings 10. 1 12.7 15.3 div. 50.0. 46.0. Remarks ^ = 12 52 23.1 0= 48 56.4 3 26.7 60= 55 49.8 Time of 60 oscil. 53.6 53.7 53.7 53.9 53.9 54.0 53.7 53.9 53.7 53.9 Means 26. 6 53.80 FORMULA: (T)2=r2 5^ [l+(20-t)q][l+(20-t)2a] — 5400 Torsion observations Tors, circle Scale Mean div. div. div. 203 29. 5 31. 3 SO. 40 293 24.9 26.9 25.90 lis SS.8 36.8 35.30 20s 29.4 SI. 8 30.60 Difls. 4-50 9.40 4.70 Mean h=4.65 =6'.L Magnetometer scale value, 7'.5^/div. (20-0 L0£ Time of 1 oscil. Log T Log r2 5400 5400 -/i Log (l + (20-0e) Log {\-[-{2Q-t)2a) Log (T)2 6.89 667 0.83 8639 1.67 728 +49 -54 -8 +347 1.68 062 Computed by RRB Checked by RLV Abstracted by AM Figure 16. — Observations for moment of intertia, loaded magnet suspension system. 80. Directions for determination of moment of inertia, — (a) Read paragraphs 71-78, and paragraphs 447-452, appendix I. (b) Determine the time of one oscillation of the magnet (unloaded) as in oscillations for horizontal intensity. (See fig. 15.) Mark this set unloaded. (c) Observe one set of torsion observations (unloaded). 32 MAGNETIC OBSERVATORY MANUAL [Ch. (d) Mount the inertia weight on the magnet system, center and level it carejully, and repeat oscillation observations as in (b) (see fig. 16). Mark this set loaded. (e) Make one set of torsion observations (loaded) . (f) Observe the temperature at the beginning, middle, and end of each set, also the extreme scale readings at these times. (g) Repeat (d), loaded. (h) Repeat (a), 2 sets, unloaded, etc., until eight sets of loaded and eight sets of unloaded oscillations have been completed. (i) If a magnetograph is in operation at the observatory or in the vicinity, place special time marks on the magnetogram at the begin- ning and end of each set of oscillations. If a magnetograph is not in operation, or if H cannot be determined independently while Computations for Moment of Inertia Station, Cheltenham, Md. Magnet No. RIC-6 Observer, RL V Inertia ring or bar No. A Date 1950 Set 75 M. Time H ordinate (/Imm) Log (Ti) 2 loaded Log (T)2 unloaded h m mm Jul. 21.... lU 12 15/25 54-7 0.00 339 1.21 145 2L 49/59 55 9 347 1.68 062 3L 13 06/16 57.0 353 1.68 090 4U 29/39 60 7 376 1.21 104 Sept. 11... 5U 14 54/64 54-7 339 1.21 115 6L 15 12/19 56.3 349 1.68 078 12^.. 7L 10 43/52 41.6 258 1.68 070 8U 11 01/11 40.3 250 1.21 115 9U 16/26 47.9 297 1.21 109 lOL 12 12/22 43.9 272 1.68 059 IIL 25/32 50.9 316 1.68 069 12U 50/61 48.8 303 1.21 101 13U 13 10/20 52.7 327 1.21 119 14L 26/36 51.3 318 1.68 085 15L 41/61 54.3 337 1.68 083 16U 14 13/23 55.5 332 1.21 128 Fre\.Hs.v. = SH 2.607/mm Log-| L=o.434|^ft_ H Bh Sums 596 136 Frel.H hlv. = Bh 18199y 0.0000 62 h^u^ Means 1.68 074 1.21 117 a (magnet) 0.0000 11 0.46 957 , /inertia bar\ " Wring ; 0.0000 18 a-\-a' 0.0000 14 2.94 829 [Tl]2 ^ 1.94 829 For UNLOADED oscillations: 0.0000 10 0.0000 12 [T]2 Log (l+2a) For LOADED oscillations: Log (l+2ai) (b): LogiiTi.so 0.28 965 031 2.47 FORMULA: K2o=^^f^ (c): LogK2o:(b)-(a) 2.18 066 (d): L0g7r2 (e): Log,r2/f2o:(c) + (d) 0.99 3.17 430 496 Remarks: log KiMfrom NBS, Nov. 1934 2.47 31 K2o=151.6 r^K2,= 1496.1 Scaled by RRB Computed by RRB Checked by /ei^F Figure 17.— Computations for moment of inertia. Scalings checked by RLV Abstracted by AM 4.] CONSTANTS AND CORRECTIONS 33 TT oscillation observations are in progress, ignore the factor ^- in equa- tions (49) and (50). 81. Computation of moment of inertia of the magnet, — (a) From the magnetogram, scale the mean ordinates, hmm, in millimeters, for the elapsed times of each of the loaded and unloaded sets, fourth column on figure 17. (b) Calculate the conversion factor, 0.434 p-= 0.434 ToVvt?!^ 0.000062 (see fig. 17). TJ (c) Calculate log -^~ for each set. (For example, the first line on TT figure 17: log ^-=0.000062 A^^=0.00339.) TT (d) Transfer all values of log ^~ from the fifth column on figure 17 to the appropriate boxes on the observing forms illustrated by figures 15 and 16. (e) Calculate log Ki from the dimensions and mass of the inertia weight and reduce this value to 20° C (=log K^ 20)- (See paragraph 448, page 187.) (f) Calculate log {TY and log (Ti)^ as in oscillation observations for horizontal intensity, using log (1-J-2q:) =0.000010 for unloaded sets and log (l + 2ai) =0.000012 for the loaded. (g) Transfer values of log {TY and log {TiY to the proper boxes on figure 17 and complete the computation of log tt^ ^20- TEMPERATURE COEFFICIENTS 82. Temperature coefficient of magnetic moment, — The mag- netic moment of a magnet decreases with increase in the temperature of the magnet. If the magnet has been properly heat-treated and stabilized, the process is reversible, that is, the magnetic moment is fully restored when the magnet is brought back to its original temper- ature, provided the original increase in temperature is not too great. The rate of change of the magnetic moment with temperature is almost but not quite uniform over ordinary temperature ranges, say from 0° to 40° C. For all practical purposes, the relation between the magnetic moment. Mi, at a standard or reference temperature, ^i, and the magnetic moment, M2, at a temperature, ^2, is given by M2=Mi -Ml CL {U -U) (51) =MAl-{U-U)q\ (52) ^MAl^{k-t2)q\ (53) in which 2 is the mean temperature coefficient of the magnetic moment over that range of temperature. (For a more precise representation of this relation see appendix II.) From equation (53), M,-M, _ M,-M, 34 MAGNETIC OBSERVATORY MANUAL [Ch. Note that g is defined so as to have a positive value in the usual case (M diminished by a temperature rise). It is necessary to have due regard for signs in the above equations; thus, if ti = 20° and ^2=25°, then ^1-^2= -5°. 83. The temperature coefficient, q, may be determined by deflection observations, using a magnetometer. The deflecting magnet whose temperature coefficient of magnetic moment is under test is enclosed by a temperature bath, figure 18, and the deflection angle, u, is ob- served at several temperatures ranging from 0° C to about 40° C. The magnetic moment, M, at each temperature is calculated from the equation, M smu ^ ^ in which H, the horizontal intensity at the time u, is observed, and a constant depending primarily upon the distance r. (See p. 8.) Then M=^^ (56) and log M=log i7+log sin i^+colog C. (57) Since the change in the deflection angle, Au, even for a large value of M and a large change of temperature, will be only a few minutes of arc, any changes in H and D during a set of observations must not be neglected in the calculation of q. It is necessary to observe D and H independently and simultaneously with observations of u or to scale these values from a magnetogram. After the values of log M have been derived for different temperatures, q is calculated from equation (54), or more conveniently by logarithms from equation (53). (See eq. 363, app. I.) Thus, log M2=log Mi+log [l + (^i -t2) q] and by equation (366) log Mo«log Mi+iU -k) log (1+2) (58) and log(l + g)^ ''^g^--;'^g^- (59) log Ml— log M2. (60) Suppose log (l+g)=0.000103, then from tables, 1 + 2= 1 000237; 2=0.000237. We may also write 2=2.30 log (1 + 2) approximately (61) = 2.30X0.000103 = 0.000237, 4.] CONSTANTS AND CORRECTIONS 35 84. Directions for determination of temperature coefficient of magnetic moment, — On a magnetically quiet day, set up a mag- netometer as for determination of horizontal intensity, short magnet suspended, deflection bar attached. 85. Place the long magnet (or other magnet to be tested) centrally in the inner chamber of the temperature bath holder, figure 18, and mount the holder (with magnet) on the bar at such a distance, say r=30 cm, that a deflection of 15° to 30° is obtained. Place ther- mometers, fitted with cork stoppers, C, in each end of the magnet chamber, B, and see that the thermometer bulbs are in contact with the ends of the magnet so that the magnet may not creep or move during the tests. Remove the holder (with magnet) to a safe distance. Figure 18. — Temperature bath for magnetometer magnet. Observations for Temperature Coefficient station, Cheltenham; Pier 7 Mgr. No. 37, Scale value, 1.38' per div. Deflection distance, 30 cm. Magnet No. Colombia I Dimensions, 5.0 cm. Date, Thursday, September 20, 1951 Observer, J. B. Townshend Therm. Nos., 33246 (E.),33257A (W.) Material, Oersted steel i Column . (1) (2) (3) (4) (5) (6) (7) (8) (9) 75 M. time Temperatm-e observed Circle reading Scale reading Middle Line minus mean East West A B Left Right Mean h TO °C °C o / ,/ / // div. div. div. div. 1 12 48 Away 303 30 05 30 15 49.0 51.0 50.00 0.00 2 12 54 -0.2 +0.7 287 48 20 48 20 49.3 50.7 50.00 0.00 3 13 03 + 5.7 6.9 49.2 49.8 49.50 +0.50 4 09 12.2 13.0 48.5 49.4 48.95 +1.05 5 16 21.1 21.4 47.0 47.8 47.40 +2.60 6 22 28.1 28.2 46.6 47.4 47.00 +3.00 7 30 34.9 34.9 49.6 50.9 50.25 -0.25 8 39 42.3 42.2 50.2 50.9 50.55 -0.45 9 40 42.2 42.1 50.1 50.9 50.50 -0.50 10 45 34.9 34.6 50.9 51.1 51.00 -1.00 11 49 28.1 28.1 51.2 51.4 51.30 -1.30 12 53 20.8 21.1 51.8 52.0 51.90 -1.90 13 13 58 12.0 12.4 51.6 52.8 52.20 -2.20 14 14 03 5.3 6.5 51.3 52.3 51.80 -1.80 15 10 -0.5 +0.5 287 48 20 48 20 49.9 50.5 50.20 -0.20 16 14 14 Away 303 30 35 30 40 49.0 51.0 50.00 0.00 17 18 19 20 Notes (a) Thermometer corrections; apply to observed temperatures: East: 0°.0, West: 0°.0; (b) Record corrected mean temperatures in last column of figure 21; (c) Middle division of scale: 50.00; (d) This form is designed for use at observatories where declination is West, and where "increasing declina- tion" means increasing West declination. If this form is used in areas where declination is East, proper corrections must be made for algebraic signs. Figure 19.— Observations for temperature coefficient of magnetic moment. 36 MA.GNETIC OBSERVATORY MANUAL [Ch. 86. Reset the horizontal circle so that the index line of the suspended magnet bisects the central division of the telescope scale. Observe and record the circle and scale readings, right and left, line 1, figure 19. This is the first away position. Note and record the time of the observation of the scale readings and place a special time mark on the magnetogram at this same moment. Temperature Coefficient of Magnetic Moment Computation of Deflection Angles station, Cheltenham; Pier 7 Magnetometer No. 37 Mgr. Scale Value, r.38 per div. Date, Thursday, September 20, 1951 Magnet No., Colombia I Middle div. of Scale, 50.00 Column (l) (2) (3) (4) (5) (6) (7) Scaled ordinates Scale Corrected circle reading (3+4+.5) Line Mean circle reading middle minus means B ordinate Deflection u dmm hmm o / , , o / o / 1 +26.3 +15.4 303 30. 17 0.00 +26.3 303 56. 47 Away 2 25.9 +9.7 287 48. 33 0.00 +25.9 288 14. 23 15 42. 17 3 26.9 +11.8 +0.69 +26.9 15.92 40.48 4 27.5 +9.9 +1.45 +27.5 17.28 39.12 5 27.0 +9.8 +3.59 +27.0 18.92 37.48 6 28.8 +10.1 +4.14 +28.8 21.27 35.13 7 32.0 -3.8 -0.34 +32.0 19.99 36.41 8 32.9 -18.6 -0.76 +32.9 20.47 35.93 9 32.8 -17.5 -0.69 +32.8 20.44 35.96 10 32.9 -7.0 -1.38 +32.9 19.85 36.55 11 31.9 -4.5 -1.79 +31.9 18.44 37.96 12 31.8 0.0 -2.62 +31.8 17.51 38.89 13 30.8 +3.2 -3.04 +30.8 16.09 40.31 14 29.2 +7.9 -2.48 +29.2 15.05 41.35 15 26.4 +12.9 287 48. 33 -0.28 +26.4 288 14. 45 15 41.95 16 +25.7 +17.0 303 30. 62 0.00 +25.7 303 56.32 Away 17 Mean away. 303 56.40 18 19 20 Notes (a) Columns (1) and (2) : H and D ordinates scaled from magnetogram. Use same sign as in scaling ordinates for base-line- values. (b) Column (3) : Mean circle readings from figure 19. (c) Column (4) : Conversion of ordinates in last column of figure 19 to minutes of arc. (d) Scale value of Z>-vario meter: 1.00' per mm. (e) Column (5): D-ordinate from column (1) converted to minutes of arc; these ordinates have the same sign as the corresponding ordinates in column (1). (f) Column (6): Corrected circle readings: Sum of columns 3, 4, and 5. (g) Column (7) : Mean circle reading, line 17, minus corrected circle readings from column (6). Figure 20.— Computation of deflection angles, temperature coefficient of magnetic moment. 87. Replace the holder (with deflecting magnet) on the bar, adjust the circle so that the suspended magnet is centered on the scale as in paragraph 86. Fill the temperature bath with cracked ice and water. Allow 5 to 10 minutes for the magnet to reach the temperature of the bath. Re-center the suspended magnet by adjusting the horizontal circle, then observe the scale readings, temperature by both ther- mometers, time, and circle reading, and again place a special time mark on the magnetogram (line 2, fig. 19). 88. Raise the temperature 5° to 10° by addition of warm water to the bath. Stir continuously, avoiding mechanical disturbance of the magnetometer. After the temperature has been held constant for about 3 minutes, observe and record the scale readings, the tem- perature by both thermometers, and the time, and again make a 4.] CONSTANTS AND CORRECTIONS 37 special mark on the magnetogram. Record these readings on line 3, figure 19. Do not change the circle adjustment for this observation. All of the changes, Au, in the angle u are to he read directly jrom the scale in the telescope. 89. Continue deflection observations as in paragraph 88 as the temperature is increased by regular steps of 5° or 10° up to about 40° C, then reverse the process by reducing the temperature by uniform steps to 0° C. Observe and record the circle reading for this last test (line 15, fig. 19). 90. Remove the temperature bath holder, with deflector, and repeat the away observations as in paragraph 86 (line 16, fig. 19). 91. Computations, — Scale and check the H and D ordinates for the times given in column 1, figure 19, using the same sign as in scaling ordinates for base-line values (see par. 434, p. 178). 92. Convert the I) scalings in mm to minutes of arc (col. 5, fig. 20). 93. Calculate the corrected circle readings, that is, the circle readings corrected to central division of the telescope scale (col. 6, fig. 20). 94. Calculate the deflection angles, u, (Mean circle reading away, line 17, minus corrected circle readings, from column 6), and record the results in column 7. 95. Convert the H scalings to gammas, apply the H base-line values to get the values of H for each deflection observation (cols. 1 and 2, fig. 21). Computations for Temperature Coefficient of Magnetic Moment Date, Thursday, September 20, 1951 from 12h 48°> to 14i> 14°^ (75 M. T.) Magnet, Colombia I Mgr. 37 Prel. H s. V. 2.55 7/mm Prel. H blv. 18281 y Prel. Mgr. log C=5.86000 Column (1) (2) (3) (4) (5) (6) Mean cor- Line H ord hy Hy log Hc«, log sin u logM rected temp. 1 +39 18320 9. 26 293 2 -f25 306 259 9. 43 240 2.83 499 +0.25 3 +30 311 271 165 436 6.30 4 +25 306 259 103 362 12.60 5 +25 306 259 9. 43 029 288 21.25 6 +26 307 262 9. 42 923 185 28.15 7 -10 271 176 981 157 34.90 8 -47 234 088 959 047 42.25 9 -44 237 095 960 055 42.15 10 -18 263 157 9. 42 987 144 34.75 11 -11 270 174 9. 43 051 225 28.10 12 281 200 093 293 20.95 13 +8 289 219 157 376 12.20 14 +20 301 247 204 451 +5.90 15 +33 314 278 9.43 231 2.83 509 0.00 16 +43 18324 9. 26 302 Computation of l OG (l+g) (Data scaled from graph of t vs log M; See fig. 22) h= 0°. C log Mi=2.83 504 Formulas: f2=40°.0 log M2=2. 83 092 log M=log H+log sin u+co logC t 2-^1=40° diff. .00 412 log (1+?)= =^^«f^^=. 000103 (7=. 000237 9=2.30 log (1+?) ogM Af Fo r Ae=40°, AM-=6. 5 cgs. AM=2.30 MoA log M Figure 21.— Computations of temperature coefficient of magnetic moment. 38 MAGNETIC OBSERVATORY MANUAL [Ch. 96. Tabulate log H and log sin u, figure 21, and calculate log M from equation (57).. 97. Plot log M against observed temperatures, figure 22, and draw a straight line through the points in such a way that it will represent the approximate mean rate of change of M with tem- perature over the observed range. Scale the values of t and log M from this graph for high and low values of t and calculate log (l+g) and 2 from equation (60). 98. If the calculated points, figure 22, show a wide scattering or if the magnetic moment does not return to its original value at 0° C after the complete 40° temperature cycle, this indicates lack of care in the observing program, errors of observation (or computation), or that the magnet has not been properly heat-treated or stabilized. 2.83 500 2.83 000 10 20 30 40 50 Figure 22. — Variation of magnetic moment (log M) with temperature (Cent.) 99. Note that the method described above provides for corrections for changes in declination and horizontal intensity. For example, figure 20 shows a change of 3.2 minutes in declination between lines 6 and 7. This is more than half of the change in u due to the change in magnetic moment for the full range of 40° in temperature. There was also a change of 36 7 in ^ during this same interval. Without taking into consideration these changes in H and D, the experimental results would have little significance, since in this case, the changes in scale readings due to changes in H and D were greater than those due to changes in magnetic moment. 100. In this method it has been assumed that the deflection dis- tance, r, does not change during the operation, and log C is taken as a constant. Therefore the change in log H-\-\og sin u is identical to the change in log ^f+log sin i^ + colog C so that C may be given any value and the same results will be obtained for log (I+2) and g. However, it is interesting to know how the value of the magnetic 4.] CONSTANTS AND CORRECTIONS 39 moment changes with temperature. The change in the magnetic moment, M, may be computed for the full range of t as follows: AM=2.3MX A(log M). For the example given, figure 22, AM=2.3X 684X0.00416 = 6.5 cgs. In this case the magnetic moment was reduced by 6.5 parts in 684 for a change of temperature of 40° C, or 1 part in 4200 per °C ( = 0.024% per °C). 101. Proposed alternate method for determination of q. — In this method the magnet, Ma, to be tested is placed in a temperature bath, north end of Ma to the south, at such a distance north or south of a properly oriented H variometer that temperature compensation of the variometer is approximately effected. The temperature bath is mounted on a separate, rigid, nonmagnetic stand, independent of the H variometer and at the proper elevation. Reduce the torsion in the H fiber until the H spot returns to its original ordinate. Insu- late the variometer against temperature changes by a nonmagnetic, nonconducting shield or cover. Take Ma through several temperature cycles, say 0° to 50° to 0°, and allow the H spot to record con- tinuously. 102. For each temperature step of 5° or 10°, observe H inde- pendently, or operate an independent magnetograph so that point scalings of H can be made. 103. Let Ma be the magnet under test; and let Ml = the magnetic moment of Ma at a standard temperature of 0° C; M2=the magnetic moment of Ma at another temperature, say 50° C; AM= change in moment due to a change of temperature =M2—Mi ti = the standard temperature, 0° C; #2= the other temperature, 50° C; A^=the change in temperature = f 2—^1 A/= change in field at recording magnet due to AM; r= deflection distance in cm; 2= average temperature coefficient of magnetic moment of Ma between 0° C and 50° C (that is, between U and ^2)- Then, from equation (11),^ page 5, 2M By differentiating, or and J^~ y.3 dJ=^^dM A/=^^AM AM=i r'A/. (62) [Ch. or Combining (62) and (63), 40 MAGNETIC OBSERVATORY MANUAL But, from equation (53), Mi-M2=M,q (t2-ti) AM=Miq i—At). 1 2 and 104. Example: Suppose: Mi = 100 cgs; r=12 cm; g=0.00024; then AM=100X0.00024X(-50) = — 1.2 cgs (= change in M due to increase of 50° in temperature) ; r^Af=—MiqAt r^Af (63) (64) A/=^AM=^(-1.2) = — 1407 (change in F due to decrease in M). If the H scale value of the H vaxiometer used in the tests is 3^ per mm, then the deflection of the H spot on the magnetogram for 140 — A^=50° C will be —=—4:7 mm, a deflection of such magnitude o that it may be scaled directly with sufficient accuracy. Temperature Coefficient of Magnetic Moment (H Variometer Method)" Magnet No. 20; Solid cylinder, 5 x 25 mm; i^lnico II; Ma=100 cgs Scale value of standard H variometer 3.00 7/mm; (Variometer No. 5) Scale value of variometer used in test 3.00 7/mm; (Variometer No. 7) Deflection distance, r 12.6 cm Time 75MT Temperature H Scalings, No. 7 H Scalings, No. 5 AHn 7 AH, 7 AHi-AIh 7 A B Mean mm y mm 7 14:50 15:00 0.0 50. 0.0 50. 0.0 50. 15 62 45 186 20 25 60 75 Y4Y "15" "im' A/=A//7-A//5 = 1267 = 0.00126 cgs r^Af _ 2000X0.00126 _ ^ 2MAt 2X100X(-50) """"^^ » Observations hypothetical. Figure 23. — Suggested form for observations of temperature coefficient of magnetic moment. H variometer method. 4.] CONSTANTS AND CORRECTIONS 41 105. Provided the H variometer recording magnet is properly oriented, it will not be necessary to take into consideration changes in declination during the tests if magnetic conditions are quiet. However, corrections should be made for natural changes in H during the tests even though these changes are small. Figure 23 gives a hypothetical determination of q by this method. 106. The method is especially useful for determination of 5 for very small magnets since small deflection distances may be used, provided the dimension ratios of Ma and Ms are such that the distri- bution coefficients are small. 107. Sensitivity of temperature-coefficient observations; mag- netometer method, — ^Magnitude of Au: In determining the tem- perature coefficient of the magnetic moment, it is desirable to know in advance about what value of Ait may be expected from a particular magnet, deflection distance, temperature range, and estimated tem- perature coefficient. In equation (55) we have, H C DifTerentiate, M sin u log sin 16= log C+ log M— log iJ (65) cos u du=-^rj dM—jjdH (66) sin u M H J sin u/dM dH\ ,^_. d^= ("iT zj) (67) cosu\ M H / ^ But, since and ^ , /AM A^\ AM=-MqAt -q^At (68) (69) M Substituting in (68), Au (radians) = — tan ul q^M,-\ — jt) ' and A^ (minutes) = — 3438 tani^UA^+-^\ (70) 108. li H remains constant during the test, equation (70) becomes (A^) ' = — 3438 tan '?^ (g A^) (7 1 ) and we may expect, for example, the following results, based on equation (71): If ^=15°; 5=0.00025; and A^=40°, then Ai/=9'.7; if u=30°; 2=0.00025; and Ai=40°, then At^=20'.9. 210111—53 4 42 MAGNETIC OBSERVATORY MANUAL [Ch. 109. Errors of scale reductions: In this method it is assumed that the value of u as represented by the converted scale readings is identical to the angle through which the circle must be turned to bring the index of the suspended magnet to the central division of the scale. In other words, it is assumed that the suspended magnet remains fixed relative to the ground while the circle and deflector are rotated through the small angle, Au. (Equation (55) is based on the assumption that the deflector is always at right angles to the sus- pended magnet.) It can be shown that the error introduced into the calculated value of Au by following this procedure is never greater than 3 seconds of arc for values of u up to 40° provided the scale deflection does not exceed 20^ In this extreme case, the error in Au would not be greater than 3'' in 20' (3 parts in 1200), which is entirely negligible in this work. Likewise the effect of torsion in the fiber is negligible for an angle of 20'. For example: If 90° torsion produced a deflection of 5' (an exceptionally large magnetometer fiber), 20' torsion would produce a deflection of about 0.02'. INDUCTION FACTOR 110. Induction and magnetic moment. — When a permanent magnet is placed in a weak magnetic field its magnetic moment, M, is temporarily changed by induction, the amount of the change being proportional to the magnitude of the component of the applied field parallel to the magnetic axis of the magnet. The magnetic moment will be increased if the applied magnetizing field is in the same direc- tion as the initial magnetic moment of the magnet, and it will be reduced if the magnetizing field is reversed. For a well stabilized magnet and for sufficiently small magnetizing fields, the magnitude of the change is repeatable and is the same for the field direct and reversed. The change in the magnetic moment, AM, caused by a unit magnetizing field is called the induction factor, fi. For any other field, X, AM—ixX. The ratio of the change in M to the original moment, for a unit magnetizing field is called the induction coefficient, h. That is T7^~^- Combining these expressions we have iJL=hM. 111. The induction /ac^or, fjL, is approximately constant for a given magnet regardless of its magnetic moment. It depends primarily upon the volume or mass of the magnet, its dimension ratio, and its ''magnetic hardness," the latter in turn being rather sensitive to temperature changes.^ The induction coefficient, h, changes if M is altered, being almost inversely proportional to M for the ranges of magnetization used in geomagnetic work. 112. In this work we are concerned only with the inductive effect of the earth's field on the magnetic moments of permanent magnets which may be used in geomagnetic measurements. For this reason we shall be dealing with comparatively weak fields. 113. If a magnet, Ma, figure 24, whose induction factor is to be determined, is mounted near a suspended magnet, Mg, so that the magnetic axis of Ma is vertical and remains in a vertical plane which is perpendicular to Ms, the latter will be deflected through an angle u, since there will be a component, /j,, of the field of Ma, normal to Ms. 2 David G. Knapp, Reversible susceptibility and the induction factor used in geomagnetism, U. S. Coast and Geodetic Survey Special Publication No. 301 (in press, 1953). 4.] CONSTANTS AND CORRECTIONS 43 The relation between the magnetic moment of the deflector and the angle u, is given by, M smu ^ ^ in which H is the horizontal intensity and C is a constant depending upon the relative positions of the magnets and the distribution coefficients for that position. If a uniform vertical field, X, is now Figure 24.— Relative positions of magnets for determination of induction coefficient. established around the deflector in the same direction as the magnetic moment of the deflector, the magnetic moment of the latter will be temporarily increased by an amount, AM=hMX= fxX, and the suspended magnet will be turned through an additional small angle, Au, due to the increased magnetic moment (and field) of M«. This uniform vertical field, X, may be either the vertical component of the earth's field or an artificially created field. 114. When the north end of the defiector is down and the magnet- izing field is directed vertically downward, then. H C M+AM sin {u^Au) H ^ C M+hMX sin (u+Au) H C M {l-\-hX) sm{u+Au) (73) (75) 44 MAGNETIC OBSERVATORY MANUAL [Ch. Upon reversal of the magnetizing field, X, —Ji = ^ (74) Dividing (74) by (73), gives, l-^hX_sm (u-^Au) _t€LB. It + tan Au 1—hX sin (u—Au) tan it— tan Au Expanding and collecting, , 1^ tan Alt .„_. X tan u Equation (76) will also apply to the case where the N end of the deflector is up and the field is directed up, then down. Equation (76) gives the induction coefficient in terms of the measured quantities, X, u, and Au. The magnetic moment, M, of the deflector is deter- mined by deflecting a suspended magnetometer magnet, and the induction factor, fx, is calculated from the relation, ^i=hM. Two methods for the determination of jx will be described. 115. Lamont's method;^ induction coefficient, — In this method the magnet whose induction coefficient is to be determined is mounted on a special holder attached to the deflection bar of a magnetometer. The axis of the deflector is vertical and is maintained in a vertical plane at right angles to the axis of the suspended magnet and at fixed distances above and below the horizontal plane through the latter. (See fig. 25.) The deflector. Ma, may be attached to the holder with the north end of Ma up or down. (The reversal is made about a horizontal axis parallel to the magnetometer deflection bar.) Its magnetic moment is increased slightly by the inductive action of the vertical component of the earth's field, when the north end is down, and decreased by practically the same amount when the north end is up. Thus the applied magnetizing field is the vertical component of the earth's field, +Z or — Z, relative to the direction of the magnetic moment of the deflector, and u is the angle through which Ms would be deflected if Z could be reduced to zero. Substituting Z for X in equation (76) gives , 1 tsinAu .„„. h^yy- (77) Z tan u One advantage of this method is that a fairly constant vertical field may be used throughout the test. Since Au is a very small angle the observations must be made with extreme care in order to obtain reliable results. 116. It has been shown by Hartnell * and confirmed experimentally,^ figure 26, that for a constant horizontal distance, the defiection angle, u, will be a maximum when the vertical distance between deflector 3 J. Lamont, Handbuch des Erdmagnetismus (see item 12 of bibliography). ^ Distribution Coefficients of Magnets, pp. 9-10 (see item 3 of bibliography) . » Terr. Mag., 34, 243, 1929. 4.] CONSTANTS AND CORRECTIONS 45 and suspended magnet is just one-half the horizontal distance between them. Since the controlling error in this work lies in the determina- tion of the small angle, Au, the deflector should be set for a position Figure 25, -D. T. M. C. I. W.6 Induction-coefficient apparatus (Lament's method), witli modified magnet liolder. which will give a reasonably large angle for u, whereupon Au will be correspondingly large. Figure 27 gives a typical set of induction observations made by Lament's method. 117. Directions for determination oj induction coefficients by LamonVs method. — Set up a magnetometer, level the instrument, and suspend Department of Terrestrial Magnetism, Carnegie Institution of Washington. 46 MAGNETIC OBSERVATORY MANUAL [Ch. the short magnet. Adjust in azimuth until the index of the magnet is on the central division of the telescope scale. Attach the horizontal deflection bar and mount the induction apparatus on the bar, on the east side of the instrument at a horizontal deflection distance, r, of 15 to 25 cm. (Call the suspended magnet Ms and the deflector Ma-) The induction coefficient of Ma is to be determined. -+12 S c / ^ \ — -T 1 1 1 + + .r^ 00 Deflection angle • — 4 ^-^ / \ V / - \ \ ; ^^ Deflector elevation in cm -30 -10 1 , 1 . 1 . + 10 I.I. +30 1 Figure 26.— Variation of deflection angle with position of deflector. Curves show changes of deflection angles for various horizontal deflection distances: a=22.5 cm, 6 = 26.25 cm, c=30 cm, d=40 cm. Curve e is the locus of the maxima of the other curves. 118. Mount Ma, N end down, on the apparatus so that its center will be at an elevation of approximately Jr above the horizontal plane through Ms- In this position the jy component of the field of Ma at Ms will deflect Ms counter-clockwise looking down. 119. Readjust the horizontal circle until the index on Ms is in the center of the telescope scale when Ms is at rest. Read the horizontal circle. This is the reading on line 1, figure 27. Mg has been deflected through the angle NOF, figure 28. 120. Reverse Ma so that its A^ end is up and above the bar. Ms will now be deflected clockwise, looking down. Adjust the instrument in azimuth again until the index of Ms is on the central division of the telescope scale when Ms is at rest; the deflection angle is now NOC, figure 28. Record the circle reading on line 2, figure 27. 121. Continue observations for the remaining positions on both 4.] CONSTANTS AND CORRECTIONS 47 east and west sides as indicated in figure 27 and record all observations in their correct order on the form. Figure 24 shows the angles and positions for line 4 of figure 27. Induction Coefficient (Lamont's method) Place, Cheltenham Magnetic Observatory, Pier 7. Magnetometer, 37 Magnet, 37L (Tungsten Steel); Magnetic Moment, 874 Temperature of Magnet, 27°.8 C; Mass of Magnet, 27 gm. OBSERVATIONS Date, March 22, 1938. Observer, J. H. Nelson Apparatus, Lamont's (modified). Length of Magnet, 9.28 cm. Line Position of deflector Side Holder N end of Af<, East East East East West West West West Up Up Down Down Down Down Up Up Down Up Down Up Up Down Up Down Horizontal circle 95 58 40 117 05 30 117 12 50 96 02 30 117 11 30 95 59 10 96 06 10 117 15 20 B 59 00 (1) 05 40 (2) 13 10 (3) 02 40 (4) 11 50 (5) 59 20 (6) 06 30 (7) 15 40 (8) Mean 95 58 50 117 05 35 117 13 00 96 02 35 117 11 40 95 59 15 96 06 20 117 15 30 COMPUTATIONS Line Position of Mc East West East West Operation (3)-(l) (8) -(6) Mean: 2 u+2Au = (2) -(4) (5) -(7) Mean: 2u—2Au = 4tt = (ll) + (14) u 4 Att=(ll)-(14) Au Angles 21 14 10 21 16 15 21 15 12 21 03 00 21 05 20 21 04 10 42 19 22 10 34 50 11 02 02 46 Time, 75 Meridian. Began, U^ sO"*. End, 14 44. Vertical Intensity (Z), 0.54000. colog Z log sin Au log cot u log /* log M logM h 0. 2676 6. 9057 0. 7286 7. 9019 2. 9415 0. 8434 6.97 0. 00798 ^ ^. .1 tan Au , ,^ Equations: h=— — ; n=hM Z tan u Figure 27. — Observations for Induction Coefficient (Lamont's method). 122. Computation of h and jjl. (Refer to fig. 27.) Line 9. — Reading 3 minus reading 1, gives one value of 2u-{-2Au. Line 10.— Reading 8 minus reading 6, gives another value of 2u-\-2Au. Line 11. — Take the mean. It is the largest angle, AOF, shown in figure 28 and represents the double deflection angle for the condition that Ma is used with the A^ end down, and its magnetic moment increased by the inductive action of the vertical component, Z, of the earth's field. Line 14. — In like manner the angle 2u—2Au, COD, is the smaller of the large angles, in figure 28, and represents the double deflection angle for the condition that Ma is used with its A^ end up, and its magnetic moment decreased by induction. Lines 11 and 14. — Solve these equations simultaneously to give values for both u and Au. Determine the magnetic moment of Ala by the method described in paragraph 319, page 129, or other suitable method. 48 MAGNETIC OBSERVATORY MANUAL [Ch. Scale the vertical intensity, Z, from the magnetogram, or use the mean value for the month. Compute h from equation (77) and ju from the relation, n=h M. 123. Repeat the whole operation using a slightly different value for horizontal distance or vertical distance or both. 124. Induction coefficient. Nelson's method J — In this meth- od the applied field is produced by a solenoid energized by a few dry cells. Figure 29 shows an observatory magnetometer upon which are mounted a special deflection bar and two solenoids. These solenoids are identical and are suspended from the deflection bar at equal distances from the suspended magnet. The coils are connected in series so that the current (and the interior field produced) in each is the same. The terminals are so connected that the fields in both coils will be directed upward or downward at the same time. By adjustment of the sole- noids along the bar the components of the solenoid fields at the center of the suspended magnet of the magnetometer will be practically equal and opposite as indicated by no deflection of the suspended magnet, Ms, when the coils are energized. A precision milliammeter in the circuit indicates the current. 125. The axial magnetic field at a point on the axis of a solenoid of finite length ^ is, Figure 28. — Deflection angles in the measure- ment of the induction coefficient of a perma- nent magnet. Xs = 0.1 ni (47r 0)1 C02) (78) in which coi and aj2 are the solid angles described by drawing elements from the chosen point to the last turn of the wire at each end of the solenoid.^ By referring to figure 30, coi and C02 may be evaluated in terms of the coil dimensions and the position on the axis of point P, or. X, = 0.2Trni Xs=i Cs + x _V^^+6+^y V'^+S-^J (79) 7 J. H. Nelson, Terr. Mag., 43, 159, 1938. * Nelson, op. cit., p. 161. > It may be noted that the formula, 0.4 ir n i, for the axial field in an infinite solenoid may be obtained from equation (78) by making wi and w2 equal to zero, or from equation (79) by making I infinite. 4.] CONSTANTS AND CORRECTIONS 49 Figure 29.— Observatory magnetometer equipped with apparatus for measuring induction coefficient (Nelson's method). 2 "^ ^^ 2 Figure 30. — Diagram of solenoid, induction coefficient apparatus 50 MAGNETIC OBSERVATORY MANUAL [Ch. in which Xs = axial magnetic field on axis at point P, distance x cm from coil center; n = turns of wire per cm length of solenoid ; i = current in amperes; I = length of solenoid in cm; h =coil radius in cm; X = distance from coil center to point P on axis; x is plus in the direction of the field Xs] X Cs =^=field per ampere at P (the coil factor). C.=0.2Trn I, I 2 + ^ , 2 _V*^+(l+^y V^^+G-^y_ (80) 126. The average value of the field, Xs, over the length of the magnet is related to the average of the coil factor, Cs, over the same distance by Xs=i Cs. When working with one particular solenoid it is convenient and prac- tical to plot the coil factor, Cs, as a function of x, as illustrated in figure 31. The solenoid is the one described in paragraph 128. 127. The average value of the coil factor, Cs, over the length of the magnet to be tested, may be scaled approximately from the curve of figure 31, using the method of equal areas commonly employed in scaliQg averages.^^ 128. The coils used originally are still in use and have the following specifications: Total number of turns in each coil 825 Over-all length of each coil (=1) 23.15 cm Turns of wire per cm of length of coil {=n) 35.64 Radius of each coil (=b) 3.135 cm. Figure 31 shows values of the coil factor Cs for this coil plotted as a function of x. Sufficiently accurate values of Cg or Cs may be scaled from the curve. Example: Suppose the current is 35.0 milliamperes, the length of the magnet to be tested (deflector) is 9.28 cm, and the deflector is centered in the coil. Scale the average of the Cs curve from 2:=— 4.64 to x=4-4.64. The scaled average is 43.0 oersteds per ampere. The average field Xs over the length of the magnet is then, Xs=i'Cs =0.035X43.0 = 1.50 oersteds. '» A solenoid will produce approximately the same field as a magnet at all points at great distances, r, in any direction, e, if (a) the distance r is very large compared to the dimensions of the solenoid and magnet, (b) the solenoid and the magnet are centered at the same point, and (c) the solenoid axis coincides with the magnetic axis of the magnet. The equivalent magnetic moment of the solenoid under such conditions is, M»0,1 irnilb^ in the notation of figure 30, 4.] CONSTANTS AND CORRECTIONS 51 129. Directions for determination of induction coefficient; Nelson's method. — Set up the apparatus as shown in figure 29, using a deflection distance of 25 to 30 cm for each coil. See that the coils hang vertically and are free from pendular motion. Suspend the short magnet, Ms in the magnetometer and bring it to rest in line with the central division of the telescope scale. 130. Connect the east coil in series with two dry cells, a milliam- meter, rheostat, and a reversing switch, figure 32. Keep the lead-in wires and the ammeter well away from the magnetometer. -I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1- -10 45 -5 1 1 5 10 45 — — — 0> E — - (0 1 (A i2 40 . 40 — J) O 35 / \ 35 — o 1 2 — 30/ \j "" /-lO i/ 1 1 1 -5 1 1 1 1 1 1 1 1 1 5 1 1 1 1 II 10 \ ~ 1 1 \l I Distance, x, along coil axis measured from coil center, in centimeters Figure 31.— Relation between coil factor and distance along axis from center of coil. 131. Close the reversing switch and note the direction of the deflec- tion of Ms. If the scale reading increases, the field within the coil is directed upward. Mark this position of the switch up. If the scale reading decreases mark this position down. Repeat this operation with the west coil only in the circuit and see that it is so connected that its field will be directed as indicated by the switch. Note that when the field is directed downward in the east coil the deflection will be in the direction of decreasing scale readings but for the west coil the scale readings will increase. 132. Now connect the coils in series, leaving all other connections unchanged. Close the switch to up. If the suspended magnet is deflected, adjust one of the coils along the bar until the deflection is reduced to zero for both up and down positions of the switch. Adjust the horizontal circle so that the suspended magnet is in line with the center of the telescope scale. Observe and record several deflections for both up and down positions of the switch. Even though these 52 MAGNETIC OBSERVATORY MANUAL [Ch. deflections are as small as 0.1 division they should be recorded together with ammeter and horizontal circle readings; lines 1, 2, 3, and 7 (deflector away), figure 33. 133. Without disturbing the coils or leads, mount the deflector, Ma, whose induction coeflftcient is to be determined, centrally within the east coil, north end down. With no current in the coils readjust the circle until Ms is again in line with the central division of the telescope. 3f^ Down (j Up -@ — 'I'I'h AAAAAAAA/^ AAAAAAA/ — Figure 32. — Wiring diagram for induction coefficient apparatus (Nelson's method), showing solenoids Ci and C2; milliammeter, MA; rheostats, Ri and R2, for fine and coarse adjustment; reversing switch and battery. Observe and record the circle reading; line 7, deflector in coil, and the scale readings in the telescope, line 9. 134. Energize the coils, field directed upward, using suflacient current to produce a deflection of several scale divisions. Bring the magnet to rest, observe and record the scale readings and the ammeter reading. Repeat for current reversed. Repeat these operations several times; lines 10-14. 135. Repeat the operation described in paragraph 133, and record scale readings and circle readings; line 15 and line 8 (deflector in coil). 136. Remove the deflector and repeat the operation described in paragraph 132, no current in the coil and deflector away; line 8 (de- flector away) and lines 4, 5, and 6. 137. Measure the magnetic moment of the deflector by the method described in paragraph 319, page 129. 138. Calculate h and /z, using the form of figure 34. Record all pertinent data such as kind and size of deflector, magnetic moment of deflector, horizontal and vertical distances of deflector relative to Mg. 139. Repeat the whole operation, changing the current slightly for the second set. 140. Additional notes on induction coefficients. — Observations are taken with deflector east, below the bar, north end down. 141. The deflection u, caused by the magnet alone, will be in the direction of increasing circle readings, that is, clockwise, and will be taken as positive (+). 4.] CONSTANTS AND CORRECTIONS 53 station, Cheltenham, Pier 7 Magnetometer No. S7 Induction apparatus No. J Induction Coefficient (Nelson's Method) East coil No. 1 Date, I'ueiiday, August 22, 1960 Observer, R. L. Viets Magnet No. RIC-14 Deflections for Balance Correction Magnet away Before After Direc- tion of field Up Down Up Up Down Up Current in coil ampereo 0.250 0.250 0.250 0.251 0.250 0.250 Mean current 0.250 Scale readings Left 50.1 49.8 60.2 49.7 49.6 49.7 Right 60.4 50.2 50.5 50.1 50.8 Mean 60.26 50.00 50.35 60.16 49.85 60.26 Correc- tion to 2Am (U)-(D) div. 0.25 0.S5 0.80 0.40 Correction for balance -\-0.82 Description of Magnet Material: Alnico II Chill cast Density 7.1 Dimensions: 0.62 cm diam. 4.9 cm long Mass: 10.6 g. Moment: 784 c. g. s. Solid y Cylindrical \/ Hollow Octagonal Other Deflections for Angle u. No Current Before After 75 M. time 14 07 14 16 Magnet away 47 4i 47 41 227 42 227 41 Mean 47 42 47 41 Mean ui 47 42 Magnet in coil, east side, north end down 58 33 58 33 238 34 238 34 Mean 68 34 58 S4 Mean U2 58 S4 u = U2—Ui = 10 52 Deflections for 2Au Magnet in coil, east side, north end down 75 M. time h m 14 10 14 IS Direc- tion of field None Up Down Up Down Up None Current in coil amperes None 0.260 0.260 0.249 0.249 0.248 None Mean current 249 Scale readings Left div 49.1 62.3 46.6 52.3 46.3 62.3 Right 61.0 64.0 47.3 54.0 47.4 54.0 51.3 Mean div. 50.05 53.15 46.90 53.15 46.85 53.15 50.06 2Au un- corrected (U)-(D) 6.26 6.26 6.30 6.30 Mean (U) - (D) (2Aw uncorrected) 6.28 Approx. horizontal deflection distance of magnet 250 Approx. vertical deflection distance of magnet 170 Remarks: Temp. 27° C. Computed by RL V Checked by CB Figure 33.— Observations for induction coefficient. Abstracted by WW 54 MAGNETIC OBSERVATORY MANUAL [Ch. Computations fob Induction Coefficient (Nelson's Method) Station, Cheltenham, Pier 7 Mgr. s. v., 1.S8' per div. Date, August 22, 1950 Induction apparatus No. / Observer, R. L. Viets East coil No. 1 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18). (19) (20) (21) (22) (23) (24) (25) (26) (27) Magnet No Magnet length Magnetic moment- . Coil length Coil diameter Total turns Coil turns per cm... Average Coil factor _ Current in coil log i .(i) XM) -d) -in) XC\) -(0 -(10)+(11) log O^- logX Average field of coil over length of magnet 'xl. Mean 2A^i uncorrected (U) — (D) Correction lor balance (U)-(D) 2Aii corrected (14) -(15) 2A« A?i . = (20) +(21) +(22) log tan Am log cot tt colog X, log ft log M log/iM=logM = (23)+(24) h induction coefficient II induction factor RIC-14 4.9 784 28.15 6.27 8'45 35.6J, 43.1 0.249 9.396 1.634 1.030 10.7 6 28 0.32 5.96 8.' 22 4' 07" 10° 52' 7.078 0.717 8.970 6.765 2.894 9.659 0.000 58 0.456 c. g. cm cm amp. div div. div. e.g. cm cm amp. c. g. s. div div. div. cm c. g. s. cm cm amp. c. g. s. div. div. div. X.=i C. h= 1 tan Am Computed by RL V X, tan u Checked by CB ti=hM Abstracted by WW Figure 34. — Computations for induction coefficient. 142. Under the conditions of paragraph 141, the deflection Au, caused by the applied field must be taken as positive (+) when that field is directed downward, that is, in the same direction as the magnetic moment of the deflector, since the magnetic moment of Ma will be increased by a small amount AM. 143. Note that decreasing scale readings in the telescope (scale in telescope) correspond to increasing circle readings. Therefore when the magnetizing field is applied, decreasing scale readings indicate an increase in the magnetic moment of the deflector or an increase in the applied magnetizing field, /j,, acting on Mg. 144. If the deflection, Au, for field up or field down, with magnet away, is in the same direction as the corresponding deflections when the deflector is within the coil, the correction for coil balance is negative. 145. Correction for lack of balance of the coils. — This correction is obtained while the suspended magnet is in the magnetic meridian but is applied to the deflection angle 2Au, but 2Au is measured while Ms is deflected through an angle u. The effect of the thus unbalanced field on the deflection angle varies from a minimum when Ms is in the magnetic meridian to a maximum (infinite) when the defiection, u, 4.] CONSTANTS AND COKRECTIONS 55 reaches 90°, at which point Ms becomes unstable. The relation between the true correction, c, for unbalance and the observed cor- rection, x, is given by c= ? u being the deflection angle when the cos 111 deflector is within the coil. The correction to x is negligible for values of u up to 30°. Table 4 gives the factors to be applied to x to obtain c for different values of u. These factors are always positive ( + ). TABLE 4.— Correction factors u Factor o 1.00 10 1.02 20 1.06 30 1. 15 50 1. 56 70 2.92 SUMMARY OF CONSTANTS 146. The constants of a magnetometer should be summarized in convenient form for field or observatory use as shown in figure 35. Critical tables should be prepared in all cases where their use will result in conservation of time and labor involved in routine compu- tations, no matter how simple these computations may be. For TT — — example, in figure 35, any value of log -^r between 5.79587 and 5.83934 will yield the same value of log ( 1 +/a^ j to an accuracy of ±5 in the sixth decimal of logs. ADJUSTMENT OF LOG C 147. Magnetometer, — Comparison observations usually indicate that the value of H determined by a magnetometer differs consistently from that determined by the sine galvanometer or other standard instrument. This difference cannot usually be ascribed to one specific error in the determination of the constants of a magnetometer but is probably a cumulative effect of small uncertainties in measuring several of the constants. When the correction is small and con- sistent it may be reduced to zero (approximately) by readjustment of log C for each deflection distance. Observations for adjustment of log C consist of not less than four complete sets of the usual observa- tions for H made at each deflection distance for which log C is to be determined. The average value of H for each whole set of observa- tions is derived from the magnetograph by scaling average H ordi- nates for those time intervals during which the observations w^ere in progress. The H base-line value is derived from measurements of H with the standard absolute instruments at the observatory. (At Cheltenham Magnetic Observatory the sine galvanometer is used as the standard for horizontal intensity.) Note also that a standard 56 MAGNETIC OBSERVATORY MANUAL [Ch. Constants of Magnetometer 31 Effective Oct. 22, 1941 Moment of Inertia, log w^ K at 20° C 3.58 233 Temperature coefficient of magnetic moment, q 0.00 018 Log (1 + ^) 0.00 008 Induction factor, /j. 3.5 Scale value of telescope scale, min. per div. 1.37 Middle division of telescope scale 50.00 Declination: Reduction to middle =1.37 (50.00 — mean scale reading) Oscillations: Correction to log T^ for temperature; log [1 + {t-t')q]= +0.00 008 (^ -n Correction to log T^ for induction ; log M + nj^ j from table below Correction to log ir^K for temperature; +0.00 001 (^-20°) Deflections: For r = 30 cm; log C=5.86 826+ (0.00 0023) (20°-^ For r = 40 cm; log C=5.49 406+ (0.00 0023)(20°-0 Log ilf2o = log M+0.00 008 (t-20°) ^«^i log(l+.f) ^«^5 IOg(l+Mf) ^«^i logM+ 4) 5. 79 587 6. 00 848 6. 12 990 0. 00 010 0. 00 016 0.00 021 5. 83 934 6. 03 563 6. 15 059 11 17 22 5. 87 885 6.06 119 6. 17 033 12 18 23 5. 91 506 6.08 532 6. 18 922 13 19 24 5. 94 848 6. 10 818 6. 20 732 14 0. 00 020 0.00 025 5. 97 952 6. 12 990 6. 22 469 0. 00 015 6. 00 848 Notes Log (1+0.0000116 d)2=0.00001 (rate of chronometer in seconds per day ) Log y^ =0.00008 (h in minutes) Figure 35.— Constants of magnetometer. value of H may also be determined directly by simultaneous obser- vations with the standard instrument and the instrument being standardized. 148. We make use of the following relationships: M- HM H log M=log ^M-log H log C=\og iJ— log M+log sin u 4.] CONSTANTS AND CORRECTIONS From equation (448) , appendix I, A log C At = -3(0.434)a. 149. The H value from the magnetogram is combined with HMt TJ TJ from observed oscillations to give a standard value of ^- Log y^ is added to log sin u for the corresponding deflection observations to obtain log Ct. Log C at 20° C is derived from log Ct by applying proper correction for temperature. (See eq. (446), app. L) Figure 36 is a sample set of computations for adjustment of log C for Mag- netometer RIC-3626. The computed values are compared with the values calculated from dimensions; lines 17 and 18, figure 36. Similar procedures may be followed in deriving certain constants for other instruments such as the Quartz Horizontal Magnetometer. MAGNETIC STANDARDS 150. International standards, — A new or reconditioned instru- m.ent is not ready for use until it has been standardized. Instrum.ents that are apparently identical yield results that are not identical, despite the exercise of the utmost care in their construction and standardization. For this reason, there m.ust be occasional intercom- parisons to safeguard the accuracy of even the best available instru- ments. It is no simple matter to make correlated measurements of a shifting magnetic elem.ent in such a way that the purely instrumental discrepancies may be isolated from other effects. Programs for such comparisons are described by Hazard ^^ and others. General specifi- cations for national and international standards are recommended and published from time to time in the Bulletins of the International Association of Terrestrial Magnetism and Electricity. 151. Inter comparison of instruments, — In the United States, all of the m_agnetic instruments of the U. S. Coast and Geodetic Survey, as well as those belonging to other agencies both foreign and domestic, are compared (standardized) directly at Cheltenham Magnetic Observ- atory or indirectly by comparisons first at Cheltenham and then at other observatories by use of an intermediate instrument. 152. The Quartz Horizontal Magnetometer (QHM)^^ has proved to be quite useful for international comparisons in horizontal intensity measurements and the Magnetometric Zero Balance (BMZ)^^ holds a similar position for vertical intensity. For magnetic declination com- parisons the ordinary magnetometer is, of course, the most satisfactory instrument for use in indirect com^parisons. 153. The Sine Galvanometer,^'^ figure 37, requires special standard- izations of its standard cells, potentiometer, and standard resistances at regular intervals of one to two years. There is no indication that the coil constant of sine galvanom.eter No. 1, now at Cheltenham, has changed appreciably with time. " Dir. for Mag. Meas., pp. 37-40, (see item 4 of bibliography). 12 D. la Cour, Le Quartz-Magnetometre QHM (see item 9 of bibliography). '3 D. la Cour, The Magnetometic Zero Balance, the BMZ (see item 10 of bibliography). 1* S. J. Barnett, A sine galvanometer for determining in absolute measure the horizontal intensity of the earth's field (see item 1 of bibliography). 210111 — 53 5 58 MAGNETIC OBSERVATORY MANUAL [Ch. Computation of Log C (H known) Place Cheltenham, Pier 6 H. s v: 2.53 Date: Oct. 31-Nov. 1, 1951 Magnetometer: RIC-3626 7/mm Observer: R. L. Viets Long Magnet: 4.9 cm Induction factor: r25 = 24.996 r3o = 29.988 Short Magnet: 4.0 cm m = 0.43 Deflection bar: Duralumin Oct. 31 Nov. 1 Oct. 31 Nov. 1 Line Terms Step Begin 14:03 End 15:49 15:09 16:40 14:03 15:49 15:09 16:40 1 2 3 4 5 6 Distance Set hmm Bh H 4+5 25 cm 1 28.3 72 18287 18359 25 cm 3 36.5 92 18288 19380 30 cm 1 30 cm 3 7 8 9 log HMt log// log Mt 7-8 1.86 547 9.26 385 2.60 162 1.86 626 9.26 435 2.60 191 10 11 12 1 H log sin u log Ct 8-9 10+11 6.66 223 9.44 490 6.10 713 6.66 244 9.4.4 482 6.10 726 6.66 223 9.20 776 5.86 999 6.66 244 9.20 780 5.87 024 13 14 15 16 t 20-t Corr'n log C20 12+15 25.20 -5.20 + 0.00 015 6.10 728 21.90 -1.90 + 0.00 006 6.10 732 + 0.00 015 5.87 014 + 0.00 006 5.87 030 17 18 19 Mean 6.10 730 log C20 (dimensions) 6.10 733 log C20 (adopted) 6.10 730 5.87 022 5 87 013 5.87 022 Notes Line 3. Scaled from magnetogram Line 13. Mean temperature of or taken from standardization cards, deflections (erect and inverted). Line 4. H ordinate in gammas. Line 15. Correction to reduce Line 5. H base Une value. log C« to log C2o=- — .0.000029 (20-0 Line 6. H from magnetograph for duralumin; —0.000024 (20— (same for all distances of same set), for brass. Line 7. Mean value from oscilla- Line 18. Log C20 from dimensions tions (erect and inverted). of magnets and deflection distances. Line 11. Log sin u; mean value from deflections (erect and inverted) . Figure 36.— Computation of log C. 154. Summary of comparisons. — The results of comparisons of certain instruments are usually tabulated as shown in figures 38, 39, 40, and 41. For inclination and declination the final correction is shown as an additive index correction in minutes of arc. In compar- isons for horizontal intensity, difference in results obtained with two magnetometers may be due primarily to errors in the adopted con- 4.] CONSTANTS AND CORRECTIONS 59 stants, assuming of course that the instruments have no magnetic parts. All of these quantities enter factorially in the formulas from which H is derived, consequently the effect on II of an error in any one Figure 37. — The Sine Galvanometer. of them can better be expressed by a constant of multiplication rather than by an additive index correction. The errors in the constants are essentially independent of H. Hence, the correction is assumed to be proportional to H and is given as a factor H 60 MAGNETIC OBSERVATORY MANUAL [Ch. Correction to Declination Observed With Magnetometer No. 19 AND Computed With Constants Dated October 10, 1941 Cheltenham Magnetic Observatory; Pier 6 Observer Sets 1 2 3 4 WEW Apr. 21 11:37-11:46 WEW Apr. 21 12:06-12:15 WEW Apr. 21 13:16-13:25 WEW Apr. 21 13:32-13:41 Date of observation 1947 ._ __ _. . Time interval (75 M. T.) -8.6 7°08.'6 -8.8 7° 10 /I -8.4 7°12.'9 -8.6 7° 13. '8 Observed declination Variometer ordinate in mm.* -13.1 1.00 -13.1 -11.8 -ii.'s -9.0 '-9."0 -8.1 "-s'i Scale value in '/mm. b Variometer ordinate in minutes 7°21.'7 7°22.'2 7°21.'9 7°22/2 7°21.'9 7°22/2 7°21.'9 7°22/2 True base-line value " Correction to W. declination Mean correction -f0.'5 +0.'3 +0.'3 +0/3 +0/4 a Ordinates corrected to 100.0 mm. shrinkage distance. Parallax allowed for. b Scale value for a shrinkage distance of 100.0 mm. Includes pier correction O.'O added to regular base-line value to reduce to pier 6 and instrumental correction 0/0 added to regular base-line value to reduce to International Magnetic Standard. Total correction O'.O added to regular base-line value. Figure 38.— Standardization of magnetometer for declination. Correction to Inclination Observed With Earth Inductor No. 106 Cheltenham Magnetic Observatory; Pier 5 Observer Date of observation 1946 Time interval (75 M. T.) Observed value of inclination Value computed from Mgph. No. 5 ». Index correction Mean correction Sets 1 2 3 4 WEW June 18 15:38-15:47 WEW June 18 15:49-15:57 WEW June 18 16:01-16:10 WEW June 18 16:18-16:26 71°18.'8 71°18.'6 71°19/2 71°19.'2 71°19.'4 71°19.'5 71°18.'7 71°18.'6 -0/2 O.'O +0/1 -0/1 O.'O a Includes a pier correction —0/2 added to dip to reduce to pier 5, and an instrumental correction O.'O added to dip to reduce to International Magnetic Standard. Figure 39. — Standardization of earth inductor for inclination. 4.] CONSTANTS AND CORRECTIONS 61 Correction to Horizontal Intensity Observed With Magnetometer No 19 AND Computed With Constants Dated October 10, 1941 Cheltenham Magnetic Observatory; Pier 6 Sets 1 2 3 4 WEW June 30 12:41-13:46 WEW July 5 10:07-11:21 WEW July 5 12:02-13:07 WEW Julys 14:01-15:03 Date of observation 1945 Total time interval (75 M. T.) M-"("'4).-('°^s). Observed value of log Af2o -f 0. 00024 2. 80660 18235 +0. 00012 2. 80671 18195 +0. 00009 2. 80665 18197 +0.00010 2. 80666 18208 Observed value of Hia y 42.8 2.67 114 27.6 '"74 29.1 ""78 33.4 ""89 Scale value in 7 'mm ** 18121 18120 18121 18120 18119 18120 18119 18120 True base-line value*** Correction to H- (AH) -1 -1 +1 +1 AH ^^j 0.00000 *Ordinates corrected to 100.0 m m . shrinkage distance. Parallax allowed for. **Scale value for a shrinkage distance of 100.0 mm. ***Includes pier correction +87 added to regular base-line value to reduce to pier 6 and instru- mental correction —27 added to regular base-line value to reduce to International Magnetic Stand- ard. Total correction +I7 added to regular base-line value. Figure 40. — Standardization of magnetometer for horizontal intensity. Correction to Horizontal Intensity Observed With QHM No. 48 and Computed With Constants Dated April 23, 1942 Cheltenham Magnetic Observatory; Pier 6 Observer Sets 1 2 3 4 WEW Sept. 6 15:10-15:19 WEW Sept. 7 08:52-08:59 WEW Sept. 24 11:31-11:39 WEW Sept. 24 11:45-11:51 Time interval (75 M T ) Mean temperature in °C 26.2 18234 24.9 . 18190 23.6 18199 23.5 18199 38.7 2.67 103 21.7 ""58 24.9 ""66 24.9 ""66 Scale value in 7/mm.** Observed base-line value 18131 18120 18132 18120 18133 18120 18133 18120 Correction to H; (AH) . -11 -12 -13 -13 Mean correction AH -12 AH 1 nn(M\(\ H ♦Ordinates corrected to 100.0 mm. shrinkage distance. Parallax allowed for. **Scale value for a shrinkage distance of 100.0 mm. ***Includes pier correction +37 added to regular base-line value to reduce to pier 6 and instru- mental correction —27 added to regular base-line value to reduce to International Magnetic Stand- ard. Total correction +I7 added to regular base-line value. Figure 41.— Standardization of QHM for horizontal intensity. CHAPTER 5. OPTICAL SYSTEMS AND PHOTOGRAPHIC REGISTRATION COLLIMATION 155. Both absolute and variation instruments involve applications of simple geometrical optics which are not adequately explained in standard books on the subject. The ensuing discussion assumes a basic knowledge of the elementary principles involved. 156. Simple lens, — In figure 42, let r be the radius of curvature of the convex side of the planoconvex lens, L. The optical axis is defined as the line, CO, perpendicular to both surfaces. Lenses are usually centered, that is, they are cut and edge-ground so that the optical axis passes through the geometric center of the lens itself. 157. Parallel rays of monochro- matic light falling upon the plane side of L, figure 42, at normal inci- dence will converge at a point, P, called the principal focus. The distance, OP, is called the focal length of this simple lens. A plane passing through P and perpendicular to the optical axis, PC, is called the focal plane of the lens. 158. If a point source of light be placed at the principal focus, P, figure 42, the rays will be parallel after passing through the lens. This process of producing parallel rays is called collimation. If an illuminated scale be placed at P and a telescope, previously focused on a distant object, be placed at T and directed parallel to OP, the image of the scale will be in sharp focus in the telescope. Many Figure 42.— Planoconvex lens. For a thin lens, the index of refraction IS l+r/f Figure 43.— Illustration of both the Gaussian ocular and the modified Gaussian ocular in an autocoUimator. magnetometer magnets are made in the form of hollow cylinders with a scale or index lines ruled on glass fixed in one end and a col- limating lens fixed in the other end. Such a system is called a coh Kmator. 159. AutocoUimator; Gaussian ocular. — In figure 43, a tele- scope, T, is provided with a scale, S, ruled on a glass reticle mounted in the principal focal plane of the objective lens, L. The eyepiece is fitted with a thin, transparent glass plate, G, set at 45° to the optical axis of the telescope. Diffuse light, after entering a small window at W, in the side of the eyepiece, is partly reflected and illuminates the scale. The telescope then serves as a collimator and if a plane mirror is interposed at M, normal to the axis of L, a real image of the scale will be found superimposed upon the scale itself. The scale and its 62 OPTICS AND REGISTRATION 63 image may be brought into precise coincidence by rotation of the mir- ror or telescope in incUnation or azimuth or both. 160. Modified Gaussian ocular. — In this type of ocular, only the upper portion of the central line of the scale is illuminated. This is accomplished by using, instead of the inclined glass plate, an adjust- able 90° prism mounted in the ocular close to the vertical line of the scale as shown at P, figure 43. Hence only the image of a portion of the central vertical line would be formed in the focal plane of the telescope. By adjustment of the telescope in azimuth and inclination the image of this central line may be made to fall upon any part of the scale and serves as an index of relative angular motion between the mirror, M, and the axis of the telescope. This type of optical system is used on some magnetometers. MAGNETOGRAPH OPTICS 161. Optical scale value, — If an optically plane mirror is inter- posed at any point, M, figure 44, so that its reflecting surface is normal to OP, the reflected rays will be parallel and will come to focus pre- ^ 5 ^ _J( ^P ^=^ I P P' n \29^ L i Figure 44. — Optical lever. Figure 45. — Planoconvex mirror. cisely at the position of the source, P. This will be true regardless of the distance between the mirror and the lens so long as the lens col- limates the incident light. If the mirror is rotated through a small angle, d, the reflected rays will sweep through an angle 2 d, remaining parallel until they enter the lens. After passing through the lens they will be brought to focus at some point P' , in the focal plane, and the angle P'OP will be practically equal to 2B. The distance PP^=n through which the image moves in the focal plane for a given small value of 6 is directly proportional to the focal length of the lens. For all practical purposes this rule holds regardless of the distance between lens and mirror. If the mirror is translated in any direction without rotation, the image P' will not move. If 26 is the angle through which the reflected ray turns when the mirror turns through an angle d, then tan 2 d- OP (81) and for small angles, 20P The ratio of the angular motion of the mirror to the linear motion of the image (in the focal plane of L) is called the optical scale value, designated by e. That is, 64 MAGNETIC OBSERVATORY MANUAL [Ch. Note : See paragraphs 200-202, pages 74-76, for more exact expressions for the optical scale value and its reciprocal the optical lever. 162. The optical scale value may be halved (optical lever doubled) by allowing the recording mirror, M, to make an angle of 45° with the collimated rays whereupon the rays will be reflected at an angle of 90° to their original direction. These rays are then allowed to fall approx- imately at normal incidence upon a fixed plane mirror after which they will be reflected back to the mirror, M, thence through the lens, to form an image in the focal plane of the lens. Since the light is reflected twice from the recording mirror, M, the reflected ray will turn through an angle 4 6 when M is turned through an angle 6. The final result is to double the sensitivity of the system. The optical scale value is now equal to ^-tt^ instead of ^ ^^ - ^ 4 OP 2 OP 163. Planoconvex mirror, — Suppose the lens is reversed as in figure 45 so that the light is incident on the convex surface of the lens. Some of the light will not pass beyond the lens but will be reflected from the inner surface of the plane side. If the lens is now inclined slightly making an angle d with OP, the reflected rays from the plane surface, now collimated, will pass back through the lens and form a faint real image at P\ such that the angle POP' is again equal approx- imately to 2 6. If the plane side is silvered or aluminized, practically (b) (c) Figure 46.— (a) Origin of ghost images from front and back surfaces of plane mirror; (b) appearance o main image and ghosts on screen; (c) alignment of ghosts with main image. all of the light will be reflected. Planoconvex mirrors of this type are frequently used as the moving mirror on some galvanometers, optical thermographs, and other laboratory instruments. Images formed by unsilvered plane surfaces of lenses or prisms are sometimes called ghost images. 164. Multiple reflections. — Suppose collimated light from P, fig- ure 46 (a), falls upon a back-surfaced mirror (front and back surfaces not quite parallel) . Most of the light will be reflected at and after again passing through the lens will form a bright image at Pi . Some of the light will be reflected at the front surface at A and since the surfaces of the mirror are not precisely parallel, a second faint image will be formed at P3. Also some of the light reflected from will be internally reflected at B back to 0' and again back through the mirror, emerging at C, and forming another faint image at P2. P2 and P3 are also called ghost images. When the light source, P, is an illu- minated slit or a straight-filament incandescent lamp, the three images will usually appear as one central bright image with faint images on either side as shown at b, figure 46. Usually they may be brought into alignment as shown at c, by rotation of the mirror, M, on an axis, XX, normal to M. Ghost images of this kind cannot be formed when front-surfaced mirrors are used.^ 1 D. G. Knapp, Curiosities of magnetographs, Trans. Amer. Geophys. Union, p. 539, 1944. 5.] OPTICS AND REGISTRATION 65 165. Totally reflecting prism, — 90° prisms, figure 47, are used extensively in magnetic instruments for changing the direction of incident hght approximately 90° and, as in the vertical intensity vari- ometer, for changing the plane of motion of the reflected light beam from a vertical to a horizontal plane. Light which falls on the face AB at or near normal incidence is totally reflected by the surface AC and emerges approximately normal to the face BC 166. Planoconvex prism, — If a planoconvex lens, L, be cemented to one of the faces of a 90° prism adjacent to the 90° angle, this com- Figure 47.-90° prism. Fig are 48.- Plano- convex prism. bination will serve as a collimator for light from a source P when P is at the proper distance from the prism-lens combination. When such a combination is made from one piece of glass, figure 48, it is called a planoconvex prism. The la Cour D variometer is equipped with such a prism. 167. Cylindrical lens (planoconvex), — This is equivalent to a right cylinder cut parallel to the long axis of the cylinder, figure 49. Figure 49.— Planoconvex cylindrical lens. Figure 50.— Action of cylindrical lens in bringing a plane light beam to a point focus. Parallel rays incident on either surface will converge in a line focus or line image parallel to the axis of the cylinder. If the incident light is confined to a very narrow plane at right angles to the axis of the cylindrical lens, the rays will be brought down to a point focus, figure 50. Cylindrical lenses of short focal length, 2 to 4 cm, are used on photographic recorders. Long-focus cylindrical lenses and piano cylindrical mirrors are frequently used on variometers and galvanometers. In such cases the axis of the cylinder must be adjusted so that it will be parallel to the filament of the lamp and at right angles to the axis of the cylindrical lens of the recorder in order to obtain a sharp image. 168. Three-faced mirrors. — A convenient type of mirror for use on magnetic variometers to produce regular recording spots and upper and lower reserve spots is shown in figure 51. The three faces, a, b, and c are ground and polished optically flat and then aluminized. In order that the images from all tliree faces shall lie in the same horizontal plane, the faces must be so ground that they will all be perpendicular to a common plane. The areas of the faces are equal 66 MAGNETIC OBSERVATORY MANUAL [Ch. and the dihedral angles are such that when the regular recording spot from face b passes off the magnetogram at the top or bottom edge, the image from a reserve face, a or c, will come on the gram at the bottom or top. The size of the desired dihedral angle is a func- tion of the optical lever of the variometer lens and the width of the magnetogram. For example: Let y=ihe width of the gram =200 mm; a;=the distance between reserve spots=180 mm; 20P==the optical lever=3460 mm (for a D variometer); a=ihQ acute angle between adjacent faces. Then tan a=iw=^TS= 180 20P 3460 and q:=2° 59' and the interior dihedral angle is 177° 01'. In the Eschenhagen ar- rangement of variometers the mirrors have certain specifications for the angles when the width of the drum face is 20 cm. 169. The following table gives a current set of specifications for dihedral angles, together with the approximate reserve distances which are obtained by using those angles: Variometer Approximate recording distance OP Specifications for dihedral angle Approximate reserve distance X Interior 180°— a Exterior a Tolerance H D Z mm 1200 1730 2300 o / 175 45 177 00 177 40 4 15 3 00 2 20 ±2 ±2 ±2 mm 178 181 188 a b c Note: In some of the older variometers, separate plane mirrors were mounted on thin aluminum frames. With this arrangement it was . ^ismm^ necessary to bend the frames relative to each other in ._ order^to^obtain proper adjustment of the spots — a I tedious and time-consuming process, i 170. Auxiliary spots by other means, — La Cour Y devised] a method of producing multiple spots from a i. single recording mirror, by using small, 90° prisms spaced along a rack in front of the recording lamp. Figure 51.— Three- The prisms wcre so adjusted that each one provided a faced mirror. beam of light f OT ouc variometcT mirror — the assembly having the effect of several light sources, with the corresponding number of spots for the recording drum. Schmidt ^ used a system of inclined mirrors to reduce the sensitivity. Both the normal and the low-sensitivity traces were recorded on the same magnetogram, thus eliminating the need for reserve mirrors. 171. Base-line mirror. — A plane mirror attached to an adjustable bracket within the variometer housing and back of the variometer lens reflects a beam of light to provide a fixed reference line, or base line, on the magnetogram. Each variometer usually has its own base-line mirror. 2 Zs. f. Instrumentenkunde, 27, 137-47, 1907. 5.] OPTICS AND REGISTKATION 67 172. Diaphragms, — The quality of an image may be improved in most cases by use of horizontal diaphragms (narrow horizontal windows) mounted directly in front of the variometer lens. The effect is to reduce the intensity of the light leaving the variometer and at the same time confine the reflected light or transmitted light to a small segment of the lens or mirror. Another diaphragm on the cylindrical lens of the recorder serves also as a screen to protect the photographic paper from extraneous light. 173. Character of image, — The light source is usually a straight- filament incandescent electric lamp or an illuminated slit placed at either end of the recorder at approximately the same height as the cylindrical lens of the recorder. It is important that the axis of the filament or the slit be strictly vertical so that images from the variom- eter mirrors will be vertical as they fall upon the cylindrical lens of the recorder. The recording distances should be such that these images will be sharply focused line images on the magnetogram before the cylindrical lens is adjusted. Great care should be used in making these adjustments in order to insure satisfactory photographic reg- istration. If the variometer lens is of the long-focus cylindrical type its axis must be vertical (parallel to the lamp filament). PHOTOGRAPHIC REGISTRATION 174. Recorder, — This is usually a clock-driven drum having a 20-cm face width and so geared as to have a peripheral (paper) speed of 20 mm per hour. To prevent loss of record and to provide space for a paper-clamp the drum makes one revolution in 25 hours. The recorder and accessories are housed in a lighttight case, figure 52. The light spots from the variometers are focused sharply on photographic paper wrapped tightly around the drum. As the drum rotates, these spots trace latent records of the base lines and variations of D, H, Z, and temperature on the photo paper. 175. Parallax, — In figure 53(a) the horizontal line represents a time line across the photographic paper on the drum as seen from the variometers. When properly adjusted the D, 77, and Z recording spots should be bisected on the magnetogram by this time line. In figure 53(b) the H and D spots are not properly adjusted with respect to the time line. 176. In photographic recording this maladjustment of a spot relative to a time line (or time mark) is called parallax. Obviously parallax of the base-line spots is of no consequence. When the centers of all variometer lenses, axis of cylindrical lens, and center of time- flash mirror are all in the same horizontal plane, little or no parallax between any recording spot and the time line would be expected. In practice, however, because of lack of perfect centering of lenses and effects of spherical aberration, the alignment of lens centers is often not sufficient to eliminate all parallax, and the final adjustments must be made by the trial-and-error method. Adjustment of an^^ individaul spot is made by raising or lowering the whole variometer, perhaps by several millimeters, until the recording spot is on the time line. The time line itself maybe adjusted by raising, lowering, or tilting the time mirror or time lamp. 177. Sensitized recording paper, — Photographic paper from several manufacturers has been used successfully for recording mag- 68 MAGNETIC OBSERVATORY MANUAL [Ch. Figure 52. — Magnetograph recorder showing driving clocli, gears, and cylindrical-lens diaphragm and ligh t shield. Figure 53. — Parallax between time line and recording spots: (a) satisfactory adjustment, (b) poor adjustment. 5.] OPTICS AND REGISTRATION 69 netograms. In general the paper should have high contrast qualities, producing a dense black line on a white background. Its sensitivity to red light should be as low as possible, to facilitate handling the paper by red light at the recorder and in the photographic dark room with a minimum of background fogging. Some paper that has been used appears to be quite sensitive to fingerprints, and no uniform specification as to resistance to fingerprints has been found. It has occasionally been necessary to have the observer wash his hands thoroughly with soap and water just before making the daily change of paper on the recording drum, or even to wear thin cotton gloves while handling the paper, in order to reduce the smudging effect of finger contacts. 178. Standard brands of high-contrast developing solutions for photographic prints have been used for satisfactory processing of magnetograms. It has sometimes been found that more uniform results and greater contrast can be obtained with developing solutions weaker (i. e., with more water) than the strengths recommended by the manufacturer of the chemicals. Developing is generally continued until the magnetogram has a satisfactory appearance under the red light, rather than until a specified time has elapsed. The developing, fixing, and washing baths should be warm enough to produce satisfac- tory speed of chemical action, but not so warm as to risk damage to the photographic emulsion by heat; temperatures of 15° to 25° C. are generally acceptable. Magnetograms will have more sharply defined traces if the intensity of the recording lamp is kept relatively low and the developing process is forced somewhat by leaving the gram in the chemical solution longer, although care must be taken that the gram is not left in the solution so long that the white background becomes fogged. Thorough washing in clean running water is, of course, neces- sary for magnetograms that are to be kept on file permanently. CHAPTER 6. QUARTZ-FIBER TECHNIQUES 179. Procurement of fibers, — The manufacture of quartz fibers of suitable dimensions for use in magnetic variometers and astatic galvanometers requires special equipment not usually available at magnetic observatories.^ For this reason it is well to procure com- mercially a supply of fibers ranging in diameter from 10 to 75 microns (1 micron =0.001 mm) and 30 cm in length. A fiber should be reason- ably uniform in diameter over its entire length, and circular in cross section. Quartz suspensions of the la Cour type, figure 54, can be manufactured with a minimum of equipment.^ 180. Uses of fibers, — Fibers ranging from 7 to 12 microns in diameter are used on astatic galvanometers and require special equip- ment for mounting. A frame of mounted galvanometer fibers is shown in figure 55. 181. Those ranging from 15 to 20 microns are used in D variometers and those ranging from 35 to 75 microns are for H variometers. ^^ 2 mm R=^ r* lO — in « — — dinder and calculate its moment of inertia about an axis normal to its long axis (see par. 72, p. 28). Note: The dimensions of the inertia weight used in this work by the Coast and Geodetic Survey are as follows: Length, 49.4 mm; 72 MAGNETIC OBSERVATORY MANUAL [Ch. diameter, 1.66 mm; mass, 0.90 gram; moment of inertia, 1.83 gram- cm^. 193. Select a fiber and with fused shellac attach one end to the inertia weight and the other end to a laboratory stand so that the length of fiber between support and inertia weight is about 15 cm. Surround the suspension by a glass cylinder to protect it against air currents. Using a stop watch or a chronometer, determine the period, T^, (time of one cycle) of the cylinder while oscillating as a torsion pendulum through an angle not exceeding 20°, by timing 50 to 100 oscillations. Repeat the operation 4 times and take the mean as T^. Remount the fiber in a separate wooden frame and label as to meas- ured nominal diameter and period (say 45 microns; T^=9.8 sec). Figure 56.— Apparatus for mounting brass stems on quartz fibers. Repeat this operation with several fibers suitable for H and D vari- ometers. The classification of fibers by this method of oscillations is quite satisfactory and is preferred to the method of diameter meas- urement by microscope. Calculate from equation (85) the torsion constant, k', for each fiber, and record these values on the labels. Compare with the values obtained from direct measurement of the diameter (par. 191). 194. Installation of fibers in H and D variometers, — A simple apparatus for mounting upper and lower brass stems to a fiber is shown in figure 56. It consists of a brass bar carrying two clamps, Ci and C2, for aligning and clamping the brass stems and two small fiber supports, Ti and T2. The bar is attached to a wooden block by a single screw, aS. By turning the bar at right angles to the wooden base, the latter may be used as a holder when the stems are heated for melting the shellac. The stems are slotted and notched as shown in the figure. 195. To attach the stems to the fiber, proceed as follows: Usmg an alcohol flame and hand blowpipe (or an oxyhydrogen torch) , bend the ends of the fiber at right angles, leaving about 15.5 cm of straight fiber between the bent ends. Feed the ends into the stems A and B and adjust the stems in the clamps so that the fiber is drawn taut as the bent ends engage the notches in the stems. Gently warm the 6.1 QUARTZ FIBERS 73 end of the bar near ^ in a direct flame and apply a small amount of dry shellac to the notch allowing the shellac to melt and flow around the bent end of the fiber and fill the slot and notch completely. Con- tinue heating gently until the shellac is free of moisture and air bub- bles. Avoid burning the shellac. See that the fiber is well centered in the stem at the point of emergence from the slot. In like manner attach end B. Before the shellac is entirely set, hold the bar with its long axis vertical, end B down, loosen C2 and allow the fiber to take the load gently. After the bar has cooled and the shellac is well set, tighten C2, leaving the fiber slightly slack. Break off the ends of the fiber which protrude laterally from the stems. In this condition the fiber may be mounted at once in a variometer or stored in the holder for future use. Experience has shown that fibers mounted in this manner give satisfactory per- formance and that there is little or no yielding of the shellac when the fiber is subjected to large torques over long periods of time. 196. Attach the coupler, figure 57, to the stem A, figure 56, and screw it on rather firmly. Hold the apparatus with its long axis vertical, end A down, loosen Ci and allow the fiber to take the load gently. Avoid bending the fiber near its point of attachment to a stem. Remove the fiber and attachments from the holder and while the system is still hanging vertically, attach the stem B firmly to the torsion head spindle of the variometer. Lower the whole suspension into the variometer suspension tube and adjust the torsion head and the foot screws until the suspension swings freely and the coupler disk is centered and parallel to the jaws of the fiber clamp. Then set the clamp and tighten the torsion- head set screw. Figure 57.— Coupler for at- taching quartz fiber to suspended magnet. 210111—53 CHAPTER 7. THE DECLINATION VARIOMETER 197. Function of a D variometer, — This instrument should indi- cate visually or by photographic registration the variations in the direction of the horizontal component of the earth's magnetic field, that is, the variations in magnetic declination. 198. Basic requirements, — The essentials of & D variometer are: (a) A permanent magnet suspended in a nonmagnetic housing by a fine quartz (or equivalent) fiber; (b) An optical system suitable for visual observation or photo- graphic registration of the variations that occur in the direction of the D magnet as the declination changes ; (c) The recording ray and the optical axis of the D lens to be ap- proximately normal to the recording drum; (d) Magnetic damping (recording magnet surrounded by a copper or silver box) ; (e) The magnetic axis of recording magnet to be parallel to the magnetic meridian in the absolute observatory; see paragraph 331, page 135 for effects of exorientation angles; (f) A fixed base-line mirror so arranged that a straight reference line (base line) is recorded on the magnetogram near the D trace. 199. D scale value, — The D scale value or minute scale value, Sd\ of ei D variometer is defined as the change in magnetic declina- tion, AD, in minutes of arc, corresponding to a change of ordinate of one millimeter. An, of the D spot. Then S.'=^. (90) The D scale value is made up of three parts: (a) the optical scale value; (b) the torsion factor ; and (c) the Jield factor. These component parts will be described in detail in the following paragraphs. 200. Terms in the expression for the D scale value, — The var- ious symbols used in the derivation of the general equation of the minute scale value of the D variometer are: Sd' =the minute scale value; minutes per mm; Sd'^ =the gamma scale value; gammas (E'-PT field) per mm; k^ =the torsion constant of the suspension fiber; dyne-cm per radian twist; Ms =the magnetic moment of the recording magnet; cgs units; k = ratio of torsion constant of of the fiber to magnetic mo- ment of suspended magnet t . H = horizontal intensity of the earth's magnetic field; C =the algebraic sum of the north components of the fields of all other magnets of the magnetograph (Note: the C field must be the same in torsion tests as it is in normal operation of the D variometer) ; R =the effective distance from the D lens to the recording drum, in mm ; 74 D VARIOMETER 75 2R =tlie optical lever; _]_ 2R ^-^ =6= the optical scale value in radians per mm; e' =3438e=the optical scale value in minutes per mm; Ari =a small increment in the ordinate of the D spot, in mm; A^ =a small increment in the angular motion of the D recording magnet (or the D magnet mirror) ; minutes or radians ; h =the angle through which the D magnet turns when the upper end of the fiber (torsion head) is turned through an angle, /; / =see h above; /—/i = total twist in the fiber, in the torsion test; IX =the rigidity modulus of quartz; 2.83X10^^ dynes per cm^ per radian; I =the length of the fiber in centimeters; d =the diameter of the fiber in centimeters; / =the moment of inertia of the inertia weight suspended on the fiber and oscillating as a torsion pendulum; T^ =the period of the torsion pendulum in seconds. 201. The approximate value of E is the distance from the D lens to the recording drum. Since a small portion of the path of the refiected ray is made up of the D lens and the cylindrical lens of the recorder, certain corrections must be made to the measured distance, Z, to obtain the effective recording distance, R. Assuming the glass of these lenses to have a nominal refractive index of 1.5, it can be shown that R=L-^+bl (91) o in which i?=the derived effective recording distance to be used in scale- value equations; Z=the measured distance in mm, from the front of the D lens to the point on the recording drum at which the D spot normally falls ; c=the maximum thickness of the cylindrical lens in mm; 2 b=— for a planoconvex lens, plane side out; o 6=— for an equi-convex lens; o b=0 for a planoconvex lens, plane side in; /=the maximum thickness of the variometer lens in mm. 202. The optical lever and optical scale value, — When the recording mirror (and the recording magnet) turns through a small angle A^, the D spot moves through a small ordinate. An. If R is the effective recording distance (optical lever =2R), the small angle, A^, in radians is — ^- Thus A<'=§ (92) J A0 1 An 2R 76 MAGNETIC OBSERVATORY MANUAL [Ch. But the optical scale value, designated by e, is 4 <»« and from equation (91) ' 2(i-.|+w) \VUJ In radians, Ad=e{An). (96) And in minutes, Ao 3438,^ , A^- 2^ (An). (97) 203. Torsion tests, — If the torsion head is turned through an angle /, and the D recording magnet turns through an angle A. as a result of the torsion in the fiber, the system will be in equilibrium when the opposing couples, k' (f—h) and (H-]-C)Ms sin h, are equal. That Jc' (f-h) = {H+ C) Ms sin h. (98) For small values of h, write sin h^h radians. Then ^^=k=iH+C)(j^} (99) Divide by H, K'+i)(/4s) (103) {H+C)Ms 204. Physical picture of the torsion factor, — In figure 58, let OiHi denote the original direction oiHand M, where His the horizon- tal intensity and M is the magnetic moment of the D magnet; no torsion in the fiber. Now turn the torsion head through an angle /; whereupon the magnet will turn through an angle h, and the torsion in the fiber is f—h. Compare figure 59 in which the original line of no 7.] D VARIOMETER 77 torsion remains along O2H2 but the declination, D, changes through a small angle AD and H is now along O2H2 . But the magnet will be restrained by torsion and its axis will lie along O2M2. Since the direction of the field has changed, O2H2 corresponds to OiHi and O2H2 corresponds to Oi T but the torsion is oppositely directed. The change in the direction of the field, AD in figure 59, is equivalent to the amount the torsion head is turned in figure 58, since by keeping H constant in magnitude and direction and turning the torsion head we get the same result. Thus, when D changes, the magnet turns through the angle A^, and Ad=f-h (104) and AD=f. Dividing equation (105) by equation (104) AD / A8 j—h (105) (106) The term / J-h is the torsion factor. "2 M2H2 Figure 58.— Torsion factor, measured by turning tor- sion head. Figure 59.— Effect of fiber torsion on D variometer magnet. 205. If the preliminary optical scale value, e', is near one minute per millimeter, so that h in millimeters on the drum is practically f equal to h in minutes of arc, the factor, 7^77? will not change appreci- ably for relatively small changes in the recording distance. If the preliminary (or final) value of e' differs appreciably from unity, then h must be converted to minutes before calculating the torsion factor since the torsion-head reading w^ill be in minutes. 206. Effect of the C field, —In figure 60: 0H= the horizontal intensity, H; OC=HX, the vector sum, C, of all stray fields parallel to the magnetic meridian OH] 0X= resultant of O^plus 0(7= original resultant. 78 MAGNETIC OBSERVATORY MANUAL [Ch. Now suppose declination changes: AZ>= small change in declination; HH'=XB=esist field corresponding to AD; (=HaD); OH' =new horizontal intensity, approximately equal to OH in magnitude ; CB=OH' and is parallel to OH'] OB =new resultant = vector sum of OC and OH' = vector sum of OC and CB; A^= angle between OX and OB. For a torsionless fiber, the D magnet will originally be aligned wdth OX; when D changes by AD, the D magnet will turn through the angle A^ and into alignment with the new resultant OB. From the figure, AD -44- (107) A^ OX XB OX (108) Dividing" AD XX' XB+BX' Ad~ XB XB BX' XB = 1 + BX' HH'' Figure 60.— Effect of the C field on D variometer magnet. and In the similar triangles H'BX' and OHH', BX'_H'B_ H'B HH' 0H~ H ' Since H'B=HX=OC=C by construction, BX'^C^ HH'~H AD C _ H+C Ad '^H H (109) (110) (111) 207. The D scale-value equation. — Let a small field, AE, act on a prefectly oriented D recording magnet, Mg, as in D scale-value deflections, or as in the normal operation of a Z> variometer, producing a small angular deflection, A^, of the recording magnet. The couples tending to hold the recording magnet in the magnetic meridian are (H+OMs sin A^ and k'AO. The deflecting couple is (AE)Ms cos AS, When equilibrium is established these couples are equal and {H+C)Ms sin Ad+k'Ad=iAE)Ms cos Ad. But sin AB^AO (radians) and cos A0 — 1. Hence, {H+C)MsAe+k'Ad=MsAE (112) (113) 7.] D VARIOMETER 79 ae Therefore '^=H+C + k. (114) From equation (96), A6=( (An). Then also A 7^ Transposing, and substituting {H-{-C-\-k) for — r- from equation (115), Au ^=e{H+C+k) (116) and So^ = e(H+C+k) (117) since -— is, by definition, the gamma scale value, Sd'^, of the D vari- ometer. By equation (301), page 231, Sn'^=Sn'Ht2inV = ^^' (118) Then _3438^z)> = (^)€(^ + C + ^). But « = sp' hence, (119) ^■=(i|f)(.+l4). From equation (101), A: Substituting this value of yj in equation (119) gives (120) 80 MAGNETIC OBSERVATORY MANUAL [Ch. Equation (122) is the usual expression for the minute scale value of the D variometer. 208. Other forms of the D scale-value equation, — From equa- tion (103) J^= ^' . (123) Substituting this value of 7 — ^ in equation (121) gives the D scale value in terms of the torsion constant of the fiber, thus 209. From equation (150), chapter 8, the torsion constant, k', of the fiber is given by, Substituting this value of A:' in equation (124) gives the D scale value in terms of the period, T^, of the fiber and an inertia weight (known value of I) when oscillating as a torsion pendulum. Thus 210. From equation (148), chapter 8, the torsion constant, k\ of the fiber in terms of its dimensions is, " ~ 32Z Substituting this value of k' in equation (124) gives the D scale value in terms of the dimensions of the fiber. Thus 211. Equations (121), (122), (124), and (125) are all useful forms for the evaluation of the D scale value when the effective distance, R, is known, and the C field is negligible or small compared to H (no control magnet). Equation (126ji has limited usefulness because of the difficulty in measuring the diameter of the quartz fiber to the desired accuracy, as illustrated by example (b) given in paragraph 215. 212. Low -sensitivity D variometer {scale value). — Note that all of the D scale-value equations contain the factor — fj^^' indicating that the scale value might be increased indefinitely by simply increas- ing the field factor, C, by use of a control magnet attached to the D variometer, A^ end to the north, magnetic axis in the magnetic meridian 7.] D VARIOMETER 81 through the D recording magnet, and at such a distance as to give the required field. Suppose a scale value of 5' per millimeter is desired. To obtain a scale value of this magnitude by use of a control magnet attached to a sensitive variometer, for example where aS/)' = 1.00, it would be necessary to make C=^H. If H is 10,0007, C would have to be around 40,0007 at the center of the D recording magnet. A control magnet having a magnetic moment of 100 cgs units properly placed 8 cm north or south of the D recording magnet would supply the approximate field required, but due to the great uncertainty of distribution at such a short distance, the effective C field would be quite uncertain even with the theoretically correct distribution factor applied. The method is not satisfactory and the use of a larger fiber without control magnet is recommended. Note also that a stronger control magnet at a greater distance, though eliminating some uncer- tainty in the distribution effect, would be undesirable because of the large fields it would produce at the other variometers of the magnetograph. 213. Alignment chart for estimating D scale values; the D nomogram, — Figure 140, appendix VI, is a graphic solution of equa- tions (124), (125), and (126) for the special case that 2i?=3438 mm; 1=15 cm; (7=0; 7=1.83 gram-cm^; and /jl is the rigidity modulus of quartz. For this special case, 1-f 47r'I T^'HM. ^"^ 32lHMs = l+[l.85X10^(^3} (129) 214. Note that equivalent values of JL, k\ and d, are read hori- zontally on the nomogram. In using the k' scale in conjunction with the Sd^ scale and the (HMs) scale, it is first necessary to find the equiva- lent diameter (on the d scale) or the equivalent period (on the T^ scale). This is illustrated in example (a) of paragraph 215. 215. Use of the D nomogram. — The following examples serve to illustrate the use of the D nomogram. (Quartz fibers only.) (a). Given: HMs= 1.85 dyne cm; aS£,' = 1.01 minutes per mm; 2i?=3438 mm; C=0; Z=15.0 cm; 7=1.83 gram-cml Required: d, k' and JL. Solution: The straight line passing through *S'o' = 1.01 and 707s=1.85 intersects the d scale at 17.7 microns (0.00177 cm) and the J_ scale at 61.4 seconds. A horizontal line through 17.7 on the 82 MAGNETIC OBSERVATORY MANUAL [Ch. d scale intersects the k' scale at 0.0185 dyne-cm per radian. There- fore, d=l7.7 microns; T^=Q1A sec; and ^'=0.0185. (b). Given: 1=15 cm; 7=1.83 gram-cm^; d=l7.7 microns (±20%) measured. Required: k^ and T^. Solution: 17.7±20% = 17.7±3.5 microns. This means that d lies somewhere between 14.2 and 21.2 microns Opposite d=14:.2, read r~=100 seconds and A:' =0.007. Opposite d^=21.2, read T^=45 seconds and A:' =0.038. Thus if a torsion test were made with this fiber the value of k' might turn out to be any- thing between 0.007 and 0.038. If the period were determined with the inertia weight, 7=1.83, it might have any value from about 45 seconds to 100 seconds. This example illustrates why it is impractical to rely on the measured diameter of the quartz fiber as a measure of its torsion constant or its period, T'-, as described above. (c). Given: 2/?= 3438 mm; (7=0; 7=1.83 gram-cm^; 1=15 cm; r_=4.6 seconds; 7Z=9000 gammas (=0.090 cgs) ; aS',>' = 5.0. Required: Magnetic moment, Ms, of the recording magnet, to give a scale value of 5.0 minutes per millimeter. Solution: The straight line through Sd' = 5.0 and r_=4.6, intersects the HMs scale at 0.83 dyne-cm. Therefore if 7^"= 0.090, , , HMs 0.83 n o ^u -J Ms= j-r = ^ Ann =Q-^ ^S^} ^be required magnetic moment. M U.U9U 216. Evaluation of the recording distance for unit scale value. — From equation (122), for *S£,' = one minute per mm, we have and from equation (91), L=R+^--bL (131) o Then Sd' will be one minute per millimeter when 7.] D VARIOMETER 83 For example: Let C= + 100 gammas; i?« 20,000 gammas; /=3 mm; and c = 9 mm. Then from equation (132), Z=1719 (1.006) (1.005) + 3.0-2.0 = 1739 mm. In the above arrangement, if the L distance (measured distance from the front of the D lens to the drum) is made equal to 1739 mm, the D scale value will be one minute per mm. 217. Since it is desirable to operate at a scale value near unity, the focal length of the D lens should be such that the product of the three factors on the right hand side of equation (122) shall be unity when the D spot is in sharp focus on the recording paper and when the D ordinate is about normal. It is good practice to specify a focal length of 173 to 174 cm for the focal length of the D lens. If it happens that the derived value of the distance, L, differs from the focal length by as much as one centimeter, the variometer or the recorder (preferably the recorder) may be adjusted to the correct distance for unit scale value without appreciable impairment of the character of the D spot, since the depth of focus of a well-diaphragmed D lens of this focal length may be as much as 3 or 4 cm. CHAPTER 8. THE HORIZONTAL-INTENSITY VARIOMETER 218. Function of an H variometer, — This instrument should indicate visually or by photographic registration the variations in the horizontal component of the intensity of the earth's magnetic field. 219. Basic requirements, — The essentials of the instrument are: (a) A permanent magnet supported by a bifilar or relatively coarse quartz unifilar suspension so that its magnetic axis is horizontal and is kept approximately in the magnetic prime vertical (see par. 39) by the twisted suspension; (b) A nonmagnetic housing with suspension tube and torsion head for regulating the torsion in the suspension; (c) An optical system for visual observations or for photographic registration ; (d) A copper or silver box surrounding the magnet to provide necessary damping; (e) A temperature compensation device. Note: See pages 116 and 124-125, chapter 10, for temperature compensation of the H variometer, and page 135, chapter 12, for the effects of an exorientation angle. 220. Operating principle, — To place the variometer in operation, the torsion head is turned until the mechanical couple of the fiber is just sufficient to turn the magnet into a position at right angles to the magnetic meridian through the variometer. In this position the mechanical couple of the fiber is equal and opposite to the magnetic couple or restoring torque which tends to turn the magnet back into the meridian. Any slight change in H results in unbalanced couples, and the magnet turns in azimuth until the torque applied through the fiber again balances the magnetic couple. It is this motion of the magnet that is observed and recorded. 221. Symbols, — The following notation will be used: T =the total torsion in the fiber, expressed in radians; 6 = angle between the magnetic axis of the recording magnet and the magnetic meridian ; k' = torsion constant of the fiber in dyne-centimeters per radian twist ; A:'t= total couple applied to the fiber in dyne-centimeters; H = horizontal intensity; Ms = magnetic moment of the recording magnet, cgs units; e = optical scale value = ^^? in radians per mm; R = effective distance from variometer lens to drum; f^ =the magnetic east field at center of H variometer due to all magnets of the magnetograph, except the H recording magnet; 84 H VARIOMETER 85 V component of the earth's field along Ms when the recording magnet is not precisely in the prime vertical; plus the sum of the components of the fields of all other magnets, including a sensitivity-control magnet, parallel to Ms] p is positive when it is directed from the south to the north pole of Ms] angular displacement of the recording magnet for a change A//; Ai7= small change of H] n = ordinate in mm of the H spot measured from a fixed line (the H base line) on the gram; An =small change in the ordinate, n; k = ratio of torsion constant of the fiber to magnetic moment of Ad suspended magnet = M. Ej: =exorientation angle; the small angle between Ms and the magnetic prime vertical. For an H recording magnet with A^ end east, E^ is positive when Ms is turned clock- wise, looking down, through a small angle from the prime vertical. 222. The H scale value, — When there is no torsion in the fiber and the suspended magnet, Ms, is not acted upon by the fields of any other magnets, Ms will come to rest with its magnetic axis coincident with the mag- netic meridian, ON, figure 61. This is called the initial line of no torsion, and the torsion-head reading establishes the direc- tion of this line. Now turn the torsion head through the angle NOB so that Ms is precisely at right angles to the magnetic meridian, that is, so that 6 is 90°. OB is the new line of no torsion, that is, the new direction the magnet would take if all fields were removed. The mechanical couple in the fiber is now k'r, r being the difference between the angle NOB through which the upper end of the fiber turns and the angle NOE, the angle through which the lower end turns. 223. The mechanical couple A-'/tends to turn the magnet clockwise out of the mag- netic prime vertical. The magnetic couple HMs sin 6 tends to turn the magnet counterclockwise out of the magnetic prime vertical. Then since equilibrium has been established the couples are equal and Figure 61.— Simple // variometer. and since 0=90°, HMs sin e=k\ UM,=k'T. (133) (134) \ 224. Now let H increase by a small increment AH. This will cause the recording magnet to turn through a small angle AB, so that, {H-^AH) M, sin (9O°-A0)=/:' (r + A0). (135) 86 MAGNETIC OBSERVATORY MANUAL [Ch. 225. If there is a fixed field, /^r, say the field of a sensitivity-control magnet, directed along the prime vertical, there will be an additional couple, JeMs sin A^, supplementing the couple of the fiber, and equa- tion (135) becomes, (i7+AiJ)MsSin (90°-A^)-/^M,sin A^ + ^'(t + A Ad. Schmidt, Ergebnisse der magnetischen Beobachtungen in Potsdam und Seddin im Jahro 1908, Veroff. des Preuss. Met. Inst., Berlin, p. 39. 8.] H VARIOMETER 87 229. A detailed analysis ^ shows that it is more accurate to use, instead oifs, the field p which is the component of all fields along Mg. Thus SH=^e{k-\-p)XlO\ (145) The chief difference between p and Je is the component, along Mgy of all north or south magnetic fields. This component arises when Ms is not exactly in the magnetic prime vertical and gives rise to the a factor (change of H scale value with change of H ordinate, para- graphs 254-260), and to the b factor (change of H scale value with change of declination, paragraphs 261 and 262). 230. Equation (144) is useful in calculating the effect of k and Je on the H scale value. 231. Significance of k. — From equation (134) we have H_k^_, r ~Mr^ i_k'_ dyne-cm/radian _ oersted Ms dyne-cm/oersted radian (146) and since angular values are dimensionless numerics, the dimensions of k are those of field intensity. 232. Also, let Ms be the recording magnet, precisely oriented in the magnetic prime vertical, north end east. In this position the mechan- ical couple is just balanced by the magnetic couple (equation 134). Suppose that both of these couples are reduced to zero but Ms remains suspended by a (hypothetical) torsionless fiber and free to turn in any direction in a horizontal plane. It would then take up the direction of any applied horizontal field of any magnitude. To maintain Ms in the prime vertical or to turn it into the prime vertical (if displaced) would require an east field directed along the prime vertical through the center of Ms. Suppose the system had a scale value of 3.00 7 per mm operating at a recording distance of i?=1180 mm (optical scale value, €=^=0.000424). Then from equation (144), since A:=0, XIO^ ^^A^Q5 and JE=hm ^-"^^^^2360 mm)/' 0.00001 ^-^^^ \ mm / \ gamma/ /^=0. 07080 oersted =70807. In other words, if A:' = ik = 0),fE would have to be 7O8O7 to produce the same scale value as if k were acting alone without /^r. Again, if Ms is acted upon only by the field, /s, and a field, x, of 37 be applied normal to Ms, the latter will be deflected (take up the direction of the resultant field) tln-ough a small angle, A^, such that, tan A0=^=^=O.OOO424. (147) 2 H. H. Howe, On the theory of the iinifilar variometer, Terr. Mag., 42, 29^2, 1937, (see item 6 of bibliography) . 88 MAGNETIC OBSERVATORY MANUAL [Ch. But M=-^yr< and An=2RAd, in which An is the motion of the H spot on the gram when 2R = 23Q0 mm. Then An = 2360X0. 000424 = 1 mm. This means that a field of 7O8O7 applied parallel to Mg (no other fields acting, and a torsionless fiber) produces the same scale value for Ms k' as we had in the original system when^^=0 and only y^ (=^) deter- mined the magnitude of the scale value. We can state then, that k is equivalent to the field which will produce the same scale value, and that k has the same dimensions as Je, that is, k may be regarded as an equivalent field expressible in gammas. 233. Evaluation of k' , k, and other constants, — In the preceding paragraphs it has been assumed that Ms, k' , and/^ remain constant. In practice all of these factors change with time and/or temperature. It would not be feasible to determine the values of all of these factors under changing conditions every time the i^ scale value is determined. (Practical methods for determining the H scale value are given in chapter 11.) However, much guesswork may be eliminated in pre- paring a variometer for routine operation, if one has a good under- standing of the meaning of the factors which make up equation (144). 234. Since each of the terms e, k' , Ms, and Je may vary contin- uously over wide ranges, there will be an infinite number of combina- tions of these terms which will give the same scale value. However, various practical considerations make it necessary to keep the ranges within fairly narrow limits. 235. The value of k' may be estimated from fiber dimensions (paragraph 238), from oscillations (paragraph 239), from torsion observations (paragraph 240), or from the H scale value (para- graph 242). 236. The magnetic moment Ms can be determined directly by deflections (par. 319, p. 129). 237. The term Je can be estimated if the magnetic moments and relative positions of all nearby magnets are known. Usually Je is negligible for first-order effects unless there is a sensitivity-control magnet on the variometer. 238. The quartz fiber and the torsion constant, k\ — The torsion constant, k', of the fiber is the torque in dyne-centimeters required to turn one end of the fiber through an angle of one radian while the other end remains fixed. It may be calculated from Cou- lomb's equation,^ in which example ju = the rigidity modulus of quartz, 2.83X10^^ dyne/cmVradian d = i\ie diameter of the fiber, 0.00372 cm / = the length of the fiber, 15.0 cm ^' = from equation (148), 0.354 dyne-cm/radian. Since the diameter enters as the fourth power in equation (148), it should be measured with great precision by a suitable microscope at 3 Max Planck, The Mechanics of Deformable Bodies. London, 1932, p. 77. 8.] H VARIOMETER 89 many equally spaced places along the fiber. The average of the fourth powers of d rather than the fourth power of the average should be used. 239. Torsion constant by oscillations, — (Preferred method). The period, T^, of a torsion pendulum oscillating under the directive force of the suspension is given by T^=27r^Jj (149) and k'=~i, (150) where example 7= the moment of inertia of a sus- 1.83 gram-cm^ pended brass cylinder, T^^the period of the system, 14.3 sec. A:' = torsion constant, by equation (150), 0.35 dyne-cm. The moment of inertia of the cylinder is calculated from its dimensions and mass using equation (45), page 28. Length of cylinder: 4.94 cm; diameter: 0.166 cm; mass: 0.90 gram. The period is estimated by timing 50 to 100 oscillations with a stop watch. 240. Torsion constant by torsion observations. — The value of k' may also be determined by torsion observations as in a Z) variometer. From equation (99), k' = {H+C)Ms(^j^y (151) The values of h and / are observed by the method described in para- graph 203, page 76. Then, knowing H-\-C and Mg, k' may be cal- culated. Table 5 gives some values of k' determined from torsion observations, from oscillations with known moment of inertia, and from the dimensions of the fiber, using equations (148) (150), and (151 ). 241. Evaluation ofk from t and M^.— Let A:'=0.35 and M3 = 5.0. Then from equation (146) , 0.35 dyne-cm r^ r^^ ^ ^ /^ ^^.n ''•— -^ —0.07 oersted. (152) 5.0 dyne-cm/oersted 242. Evaluation ofk from scale-value observations and optical lever, — Suppose that the H scale value has been determined in the usual manner by deflections as explained in chapter 11, and that ^^=2.977/mm=0.0000297 cgs/mm, when e=0.000424 and there is no control magnet (no /^ field). Then from equation (144) k=^ (153) 0.0000297 0.000424 0.07 cgs = 70007. 210111—53- go MAGNETIC OBSERVATORY MANUAL [Ch, 243. If Ms is known, then k' may be evaluated from the relation, k' k=-irr' Suppose Ms=5.0, then ^'=A:M,=:0.07X5=:0.35 dyne-cm. (154) TABLE 5. — Torsion constant, k' , of quartz fibers by different methods. Place: Cheltenham Magnetic Observatory Date: July 31, 1951 Horizontal Intensity: 0.183 Observer: J. B. Townshend Symbol Quantity Fiber No. 10 No. 36 d I I f h f-h h f-h Ms (H-hC)Ms Diameter cm_ _ Length cm_ _ Oscillations: Moment of inertia of weight gm-cm2__ Period with this inertia weight sec__ Torsion observations: Angular motion of torsion head 0. 0018 15. 4 0. 00655 15.6 1. 83 47. 6 5. 798 5.26 1800' 24.'9 1775. '1 0.014 12.0 2.20 100' 88.'2 11. '8 7.48 5.8 1.06 Resulting angular displacement of magnet- _ Twist in the fiber Displacement per unit twist Magnetic moment of suspended magnet cgs-emu- - Magnetic couple per unit displacement dyne-cm/radian __ Torsion constant, computed: From oscillations dyne-cm/radian _ _ From torsion observations_dyne-cm/radian_.. From dimensions dyne-cm/radian _ _ 0. 0319 0. 0308 0. 0190* 9.26 7.93 3.28* ♦Computed k' is sensitive to small error in diameter (d). Example: If error in d is 10%, error in k' will be approximately 46%; if error in d is 20%, error in k' will be approximately 107%. For this reason, torsion constants computed from dimensions and assumed rigidity modulus are not reliable and may be used only for rough estimates in preliminary tests. 244. Scale value from constants, — Let 2/? =2360 mm (€=0.000424), M,=5.0, ^' = 0.35 (/:=0.07), and /s=0. Then from equation (144), the H scale value is given by ^ /0.000424\ ,^ ^^ , ,, / Sh=\^ mm ) ^^-^^ oersted) (^ 10^ gammas X oersted / (155) = 2.977/mm. 245. Thus, it is possible by careful selection of quartz fiber and recording magnet to assemble a system which will have a desired scale value at a given recording distance. 246. The sensitivity -control magnet {scale-value control). — In figure 62 let Mg be the recording magnet of the H variometer, operating in the magnetic prime vertical with its A^ end east. Ma is a sensitivity-control magnet mounted on the variometer with its 8.1 H VARIOMETER 91 axis in the magnetic prime vertical, A^ end east, and at such a distance from Ms that its field, /^, at the center of M^ is equal to 5OOO7 (0.05 cgs units). Then the i/ scale value, from equation (144) will be 5'^=0.000424(0.07 + 0.05)-10^=5.097/mm. (156) If the control magnet is reversed, the /^ field is negative, and AS'^=0.000424(0.07-0.05)-10^=0.857/mm. (157) It is evident from the above that the H scale value may be adjusted over a wide range by simply adjusting the control magnet along its bar. The approximate field of a bar magnet, along its magnetic axis extended, at a distance r from its center is /.-^-^"X10^7 (158) in which /^^ is the field, and Ma the magnetic moment, of the control magnet. If Ma= 100 cgs and r=10.0 cm, then /^= 20,0007 at 10 ^ cm. The change in Je as r is changed is given by dr r and ^ r For Ar=:— 0.1 mm (=—0.01 cm) -3X20,000X-0.01 A/g= 10 h607. (161) Figure 62.— // variometer with sensitivity-control magnet. Disregarding distribution effects, this means that by reducing r by 0.1 mm the effective field at the center of the recording magnet (due to Ma) has been increased by 6O7. The nomogram of figure 138 gives the same result. 247. Variation of the scale value with k and /^. — From equa- tion (144) SH = ke + eU (162) The relation between changes of Sh and/^, when k is constant, is dJE '' and when J E is constant (164) (163) dk ^' and when both/^ and k change, dSH=edfE-\-^dk. (165) 92 MAGNETIC OBSERVATORY MANUAL [Ch. Equations (160) and (163) will be found quite useful for evaluating the distance at which the sensitivity magnet must be placed in order to change the scale value by a desired amount. For example: Let ^^=5.00; €=0.000424; M«=100; and r=10 cm. How far should Ma be moved in order to change Sh from 5.00 to 5.10? In this case, AASV=0.107/mm, A/:=0, and from equation (163) AS' A/^=^^^= AAS'HX2i? = 0.1 X2360 = 2367. (166) An additional east field, A/g, of 2367 will increase the scale value from 5.00 to 5.107/mm. To produce this change in the Je field at the center of Ms, find Ar by applying equation (160), ^r--r(^\=- ^^^^^^ (167) \3/J 3X20,000 ^^^^^ = — 0.039 cm = — 0.4 mm, approximately. 248. Again, what /^ field would be required to change Sh by just one gamma per millimeter, say from 5.49 to 4.49 by means of a con- trol magnet, and at what distance should the control magnet, Afa= 100, be placed to accomplish this change? From equation (163) dy,='^=-^^^l^= -0.02360 cgs=-2360T. That is, a field of — 236O7 applied at the center of Ms and directed to magnetic west would reduce Sh from 5.49 to 4.49. From equation (158), r''=^^-=^r-p-r— -=8474 cm^ and r=20.39 cm, the distance at which Ma should be placed to produce the change of one gamma per millimeter in the scale value. If Ma is reversed it will increase the scale value from 5.49 to 6.49. 249. Use of two control magnets, — The distance between the control magnet and the recording magnet may change slightly as a result of seasonal tilting of the pier (causing the suspended magnet to swing toward or away from the control magnet) . This would cause a seasonal change in the scale value. The effect may be compensated in part by use of two control magnets symmetrically placed in the prime vertical, east and west of the variometer. (A second control magnet on the H variometer in the Eschenhagen type of magnetograph might have an undesirable effect on the D recording magnet. Its net effect would depend upon the direction and intensity of the other east or west fields at the center of the D magnet.) 250. Table 6 gives various values of Sh, determined experimentally for various positions of a control magnet having a magnetic moment of 50.2. The results are shown graphically in figure 63. H VARIOMETER 93 TABLE 6. — Variation of H scale value with distance between control magnet and recording magnet. [2i2=2360mm; e=0.000424; Afo=50.2; N-end of recording magnet east.] Observed scale value Sh Distance, r, between Ma and M. • Control magnet, N-end k fE k+fs 7/mm cm 7 T y 2. 29 11 w 12950 -7540 5410 3.03 12 w 12950 -5810 7140 3.55 13 w 12950 -4570 8380 3.94 14 w 12950 -3660 9290 5.49 Away Away 12950 12950 7.04 14 E 12950 + 3660 16610 7.43 13 E 12950 + 4570 17520 7. 95 12 E 12950 + 5810 18760 8. 69 11 E 12950 + 7540 20490 10 Scale-Value=5.49 Vmni with No Control Magnet Control Magnet Distance in cm. \ I 10 11 12 13 14 15 Figure 63.— Variation of scale value with control magnet distance. 16 251. Alignment chart for estimating H scale values; the H nomogram, — Figure 141, appendix VI may assist in attaining a par- ticular scale value. It is based on the equation Sh — (w+^^) (168) with k' represented by its equivalent in terms of d (eq. 148) or of TL (eq. 150). When a straightedge is laid across this nomogram, the left-hand scale should be taken to represent k alone. A reading so made on the adjacent Sh scale is valid only if /^.^O. However, when Je^O the Sff scale is useful in another way. Any displacement along this scale corresponds rigorously with the identical displacement along the (k-^-fs) scale, permitting additive correction for /^ when necessary. Special conditions assumed in the construction of this nomogram are: 2R=23Q0 mm (c=0.000424); /=:15 cm; 7=1.83 gram-cm^; and 94 MAGNETIC OBSERVATORY MANUAL [Ch. M=2.83 X 10^^ (rigidity modulus of quartz) . For this special case, from equation (144), = (^+A) (0.000424) X 10^ = 42.4(A:+/^). When k-{-fE=^l cgs unit, AS'//=42.47/mm. The S„ scale is placed so that 42.4 on the Sh scale is opposite 1.0 on the {k-\-fE) scale. For any other value of e, the pDsition of the S^ scale should be changed accordingly. 252. Note that equivalent values of T^, k' , and d are read hori- zontally. In using the k' scale in conjunction with the Ms and Sh scales, it is necessary first to find the equivalent diameter, d, (on the d scale) or the equivalent period, T^ (on the T^ scale). 253. Examples of the use of the H nomogram,— The following examples serve to illustrate the use of the H nomogram : (a) Given: Ms =5.0 cgs units; 2i?=2360 mm; €-:^ = 0.000424; /=15 cm; ^^=3.07/mm; Required: d, diameter of the quartz fiber; T~, period when 7=1.83 gram-cm^; k\ torsion constant of fiber. Solution: The straight line from 5.0 on the Ms scale to 3.0 on the Sff scale intersects the d scale at 37.1 microns and the period scale at 14.3 seconds. That is, a recording magnet having a magnetic moment of 5.0 when suspended on a 37.1 micron fiber of uniform diameter throughout its entire 15 cm length and operating precisely in the magnetic prime vertical would have a scale value of 3.0 7/mm. The horizontal line through d = 37.1 microns (7"^= 14.3 seconds) intersects the k' scale at 0.35 dyne-cm per radian. This is the torsion constant of the fiber. (b) Given: r^= 10.1 sec for 7=1.83 gram-cm^; ^=15 cm; 2i? = 2360 mm; €=^=0.000424; 8.] H VARIOMETER 95 Required: Value of magnetic moment, Ms, of recording magnet to give a scale value, *S'h=3.0 7/mm. Solution: The straight line from Sh = ''^-0 on the Sh scale, through 10.1 on the T^ scale {(1 = 49 microns) intersects the Ms scale at 10.0. That is, if M«= 10.0 the scale value will be 3.0 for the given conditions. (c) Given: Sh=(^-0 j /mm.] 2R=2360 mm: __1_ ^'~2R Je=o. 0.000424; Required: Sh=^.0 7/mm; /^= sensitivity -control -magnet field (E-W field at center of Ms) to reduce Sh from 6.0 to 3.0. Solution: On the {k-\-fE) scale opposite Sh = Q.O find k+fE=0.14:l (14,1007), but/£=0, so ^ = 0.141; and on the same scale find k-\-fE= 0.071 (71OO7) opposite &=3.0 7/mm. ThenfE={k+fE) -^ = 0.071 - 0.141= -0.070= -70007, the required Je field. The negative sign means that the field must be directed toward magnetic west. This required field may be supplied by a small control magnet. Ma, having a magnetic moment of, say, 80 cgs, fixed on the variometer deflection bar at a distance r=13.2 cm (center of Ma to center of Ms) in the mxagnetic prime vertical, east or west of Ms, with A^ end west. In this case, from equation (144) SH=42A(k^fE) 42.4X0.071 :3.007/mm. Figure 64.— The a factor in the //scale value. 254. Variation of H scale value with ordinate; the a factor. — In figure 64, AOB represents the recording magnet of the H variometer. It is held in the magnetic prime vertical by the couple of the suspension , A^ end to the east. Ma is a control magnet, A^ end east, so that its field is directed along magnetic east. A magnetic field in the magnetic meridian is produced by other magnets of the magnetograph and is denoted by C. The C field is primarily a temperature-compensating field directed to magnetic south and approximately equal to half of H. 255. When H changes, the recording magnet turns through angle Ex. The field, /e, of the control ma-^net along Ms is now fs cos E^;. But there is also a component of {H-\-C) parallel to the recording magnet when the magnet turns out of the prime vertical. This component is (H-\- C) sin Ej^. Then the total field parallel to the recordmg magnet is p =Je cos £-,+ (i7+ C) sin E, (169) so that equation (145) becomes *S'^==€ [k-\-jE COS E,^ (H+C) sin E,]X10' (170) 96 MAGNETIC OBSERVATORY MANUAL [Ch. For angles of E^ up to about 3°, cos Ej, may be taken as unity without introducing an appreciable error in Sh, but {H-\-C) sin E^ is appreciable. For example: Let i7=27,0007; €=0.000424 (2i?=2360 mm); k= 12,950;/^ = 6,8207; C= -13,500t. When E^=0, ^^=0.000424 (12950 + 6820) =8.383 7/mm. Now let H increase so that E:,=2°, figure 64. The term (H+C) sin Ex must be added to the scale value. The scale value is now &=0.000424 (12950 + 6820 cos 2° + 13500 sin 2°) = 0.000424 (12950 + 6816+471) = 8.58l7/mm. The difference in the scale value is ASh = S.5S1 -8.383 = + 0.1987/mm. But 2° angular motion of the recording magnet =4° motion of the spot, and the change in ordinate is Ari=1180 tan 4°=82.5 mm and the change in H scale value per milhmeter change in ordinate is ASh , 0.198 An ' 82.5 0.002407/mm/mm. This factor, 0.00240, is called the a factor of the scale value. It means that the H scale value increases with ordinate; the a factor is primarily a function of (H+C) and is proportional to (H-{-C). When {H-\-C) is reduced, from H io H-\-C {^y2H), as in magnetic tempera- ture compensation, the a factor is reduced in the same proportion. 256. Thus it is seen that as the H ordinate, n, changes, the cor- responding rotation of the recording magnet and change of Ex change the H scale value through the {H-\-C) sin E^ term of equation (170). The rate of change, -— ^j is the a factor, so that if *S'o is the base-line scale value (value of Sh when n is zero) then S„ = S^^an. (171) 257. It has been shown "^ that the a factor is given approximately by a^{H-^C)e\ (172) In magnetic temperature compensation (see par. 297, p. 115), C is approximately —]{ H, H-{-C^}2H, and a^'AHe'. (173) 258. Table 7 gives the a factors computed from equation (173) (using C= -V^H), and the observed a factors, for the H variometers at four Coast and Geodetic Survey magnetic observatories. < H. H. Howe, op. cit., p. 36 (see item 6 of bibliography). H VARIOMETER 97 TABLE 7. — Computed and observed a factors at U. S. Coast and Geodetic Survey observatories Recording distance, R 1 ^ = 2^ H H Observatory Honolulu San Juan Sitka Tucson 1126 mm 0. 000444 28620 14310 0. 0028 0. 0028 1144 mm 0. 000437 27470 13735 0. 0026 0. 0020 1127 mm 0. 000444 15500 7750 0. 0015 0. 0020 1215 mm 0. 000412 26020 13010 0. 0022 0. 0024 2 a=HHe2 a (observed). 259. Use of the a factor, — The base-line scale value, aS'o, and the point scale value, Sh, at ordinate n, are connected by the relation SH=So-\-an. (174) To obtain the value of the ordinate in gammas from the ordinate, n, in millimeters, multiply the ordinate in mm by the average of the scale values at zero ordinate and at the ordinate n. This average scale value is given by S^=So+y2 an (175) in which >Sff=the scale value at the ordinate -J aS'o = the base-line scale value. 260. To find the scale value for zero ordinate or for a particular ordinate when it is known at another ordinate, use equation (174). Note that a scale value to be used for conversion of ordinates is based on equation (175) but that the scale value applicable to small changes at a particular ordinate is based on equation (174). 261. Correction to H scale value for change in declination, — For greater precision in calculating the H scale value, a correction for change in declination is sometimes applied. By taking the differ- ential of equation (145), with k constant, ASH=eAp. (176) Suppose ^=90° and D changes but H does not change, figure 65. There will now be a component of H parallel to Ms which did not exist when Ms was normal to H. This parallel component is, from figure 65, HsmAD=Ap. (177) Substituting this value of Ap in equation (176) ASff^eHsin AD. (178) 98 MAGNETIC OBSERVATORY MANUAL Let AD=4:' at time of H scale-value observations; iJ= 18316; and e = 0.000424. Then A&=:0.000424X 18316 Xsin 4' = 0.009 7/mm. 262. In paragraph 261, AD is equal to the difference between the mean value of D, say for 1 year, and the D ordinate at the time of the N Ap Figure 65.— Effect of change of declination on // scale value. Figure 66.— Value of declination affecting H scale value. scale value observations (See fig. 66.). Note: Equation (178) may be written (see eq. 381, p. 184), ASh=(AD) eHsin V (179) when AD is a small angle. The value of e ZZ sin T may be taken as a constant for 1 year. In this case it is equal to 0.0023. And A&=4'X0.0023 = 0.0097/mm. To illustrate how large this correction may become even for moderate changes in declination, suppose ;S'^=3.00; and AD=13'; then A^H=13'X0.0023 = 0.037/mm or about 1 percent of the uncorrected H scale value. CHAPTER 9. THE VERTICAL-INTENSITY VARIOMETER 263. Function of a Z variometer. — This instrument should indi- cate visually or by photographic registration the variations in the vertical component of the intensity of the earth's magnetic field. 264. Basic requirements. — The essentials of the instrument are: (a) A permanent magnet (or pair of magnets) equipped with a quartz (or equivalent) knife edge near its center of gravity, a balanc- ing poise for adjustment of the magnetic axis to the horizontal, and a sensitivity poise for adjustment of the scale value; (b) A nonmagnetic housing with suitable agate or quartz supports so arranged that the magnet may oscillate in a vertical plane; (c) An optical system suitable for visual observations or photo- graphic registration; (d) Copper boxes or chambers surrounding the ends of the magnet system to provide magnetic damping; and (e) A temperature compensation device. Note: See chapter 10 for temperature compensation of the Z variometer and paragraph 331, [page^ 135, for the effects of an exlevel angle. 265. Operating principle. — To place the instrument in operation, the magnetic system is balanced so that its magnetic axis is horizontal and (usually) in the magnetic meridian. When the vertical com- ponent, Z, of the earth's field increases, the magnetic couple increases and the south (south seeking) end rises. When Z decreases the north (north seeking) end rises. Thus any slight change in Z causes the system to become slightly unbalanced, causing the magnet to turn slightly in a vertical plane. It is this motion that is observed or recorded as a change in Z. 266. The equation of equilibrium. — In figure 67, NS represents the magnetic axis oi sl Z recording magnet of moment Mg, in a bal- anced horizontal position, N end north. i7= horizontal intensity of the earth's magnetic field; Z= vertical intensity of the earth's magnetic field; iV= north (north seeking) pole of recording magnet Ms] *S= south (south seeking) pole of recording magnet Ms', Opposition of the knife edges; C=the center of gravity of the complete system supported on the knife edges at 0; " mi = mass of the supported system = mass of recording magnet system, hereafter called the mass of the magnet system; a=jB(7=horizontal distance to C from the vertical, OAB; positive toward the S end of the recording magnet Ms] A = OjB= vertical distance to C from the horizontal, OS; positive downward. 267. When the magnet comes to rest in the horizontal position the clockwise mechanical couple, rriiga, just balances the counterclockwise magnetic couple, M^Z sin 90° =M,Z. That is, MsZ=miga. (180) 100 MAGNETIC OBSERVATORY MANUAL [Ch. 268. Now let Z increase so that the Z magnet turns counterclock- wise through a small angle 6. The new positions are shown in figure 67, N having moved to A^', S to S', B to B' , and C to C\ The hori- zontal distance of the center of gravity from the vertical line OB is now AD, the new mechanical lever arm. With the recording magnet, Ms, in the position N'S^, the magnetic couples acting on the magnet system are: MsZ sin (90° — 0)=M,.Z cos d, counterclockwise. MgH sin d, clockwise. The mechanical couple is rriig AD, clockwise, where g is the accelera- tion due to gravity. The clockwise and counterclockwise couples must Figure 67.— Diagram for Z variometer. be balanced for the system to be in rotational equilibrium in the new position. Therefore MsZ cos d=MsH sin d+m,g AD. (181) From figure 67, AD=AB'+B'D', AB' = OB' sin d=OB sin d=h sin d; B'D=B'C' cos e=BC cos e=a cos 6) and AD=h sin d+a cos 6. Substituting into equation (181) MsZ cos d=MsH sin d+niig (h sin d+a cos 6). (182) 9.] Z VARIOMETER 101 269. Equation (182) must be modified if extraneous fields exist and if Ms is not in the magnetic meridian. Let ^ = Magnetic azimuth of the recording magnet = angle between magnetic north and the direction of M^, as shown in figure 68 ; /p=horizontal component in azimuth A of all extraneous magnetic fields; the/p field will be small unless the Z variometer has sensitivity-control magnets; C= component of all extraneous magnetic fields parallel to Z,positive if C is down- -^OT-/^ Figure 68.— View. looking ^* down, of Z variometer mag- When A, /», and C are taken into account, net oriented at an angle A ,• /ioo\ X. with the magnetic meridian. equation (182) becomes Ms (Z+C) cos d=Ms (HcosA+Jj,) sin d+niig (h sin d+a cos (9). (183) This is the more general equation of equilibrium for the Z variometer. Solving equation (183) for 6, tan^= ,,,y'(^ + q,-"'f'^ ■ ■ (184) Ms(H COS A-\-fp) + m]gh Sol^'ing equation (183) for Z, Z=[(;/cosA+/,) + ^]tan9+"^-C. (185) In normal operation 6 is small and tan 6^6. Then Z=e [iH cosA+,f,)+"^]+'^£-C. (186) 270. The scale-value equation. — In the operation of Z vari- ometers at magnetic observatories we are concerned with the Z scale value, that is, the ratio of the change in Z to the change in the ordinate, n, of the Z spot. The rate of change of Z with respect to 6 is given by differentiating equation (186) with respect to 6, dZ=^{H cos A+f,) + '^'jdd. (187) This is the Z scale-value equation in which all quantities are in cgs units and 6 is in radians. In paragraph 202, page 75, it has been shown that ci«=g (188) where c^n= change of ordinate of spot, in millimeters; and i?= effective distance, Z variometer to drum, in millimeters. Hence from equations (187) and (188) dZ d l=^[(HcosA-,U) + ^] (189) Ai/t 102 MAGNETIC OBSERVATORY MANUAL [Ch. In gammas per millimeter: Sz=^[(ffcos4+/,) + ^]xiO^ (190) Equation (190) is the general equation for the scale value of the Z variometer in gammas per millimeter. Example: R =2244 mm; H =0.1875; A =0; /. =0; mi =20 gm; g =980 cm/sec/sec; h =0.00322 cm=32.2 microns; M,=314 cgs; by equation (190): aSz = 8.667 per mm. As explained later (par. 276), /i. may be either positive or negative. 271. Center of gravity and poise displacement. — It can be seen from equation (190) that the scale value can be increased by increas- ing h. Before taking up this point (paragraph 274) it will be convenient to see how the posi- I tion of the center of gravity is affected by dis- ^ placement of each of the poises. SomeZvariom- 1^2 ^ eters have three poises, as shown in figure 69, Gr^ where m3=mass of balancing (latitude poise) on a horizontal invar spindle; m,=mass of temperature poise on a horizon- Figure 69.— The adjusting ^ i i • • ii poises of the z variometer tal alummum spmdlc ; ™*^"®*- and m2 = mass of sensitivity poise on a vertical spindle. It may be shown that when the sensitivity poise, 1712, is displaced upward on its spindle a distance Ay from A to B, figure 69, the center of gravity will be displaced upward from C to C , a distance — ^ Ay where m^ is the mass of the magnet system. Since h is measured positive downward and Ay is taken positive upward, then dh^-'^dy. (191) TYli 272. Similarly when nit is displaced outward a distance dLi, then the mechanical lever arm (a in figure 67) of the center of gravity, C, will be changed in amount da, given by da=-^dLt (192) Ml and when m^ is displaced outward a distance dL^ da= + —'dLs. (193) nt] N-g- mt 4 1 "3 9. Z VARIOMETER 103 When there are no temperature changes and the poises lUt and m^ are adjusted, da- mi rrii (194) 273. When a temperature change dt occurs, it will cause displace- ments dLt of the temperature poise, m,, and dL^ of the latitude poise, m^. Moreover the centers of mass of the aluminum and invar spindles, and perhaps of M,., itself, will also be displaced; if these are neglected, then dt nil dt nil dt 274. Effect of h on *Sz.— From equation (190) l5 dSy niigXlO^ (196) The change in h may be effected by changing the position of the sensitivity poise as shown schematically in figure 69. Substitute for dh the right-hand member of equation (191), obtaining (197) icy ms^XlO^ , Example: m2 =0.0955 gram; g =980 cm/sec/sec; R =2244 mm; Ms=314 cgs; dy =0.1370 cm = 5 turns; by equation (197), o?*^3 = 0.9l7/mm; also, if mi = 20 grams, then by equation (191), rf^=— 0.00065 cm=— 6.5 microns for 5 turns of the poise. Table 8 shows the variation of scale value with h for two typical cases, TABLE 8. — Variation of Z scale value with adjustment of sensitivity poise ^ = 0° ^=180 ° TIVITY Ah POISE SCALE VALUE HCOS^^j^ ^'^'^ X105 '^^'■'xio' SCALE VALUE turns microns 7/mm 7/mm 7/mm 7/mm 7/mm 8.66 +4.18 +4.48 -4.18 +0.30 5 -6.6 7.87 +4.18 +3.69 -4.18 Unstable 10 -13.1 6.97 +4.18 +2.79 -4.18 Unstable 15 -19.7 5.89 +4.18 +1.71 -4.18 Unstable 20 -26.2 5.12 +4.18 +0.94 -4. 18 Unstable 25 -32.8 4.08 +4.18 -0.10 -4.18 Unstable 30 -39.3 3.19 +4.18 -0.99 -4.18 Unstable 35 -45.9 2.23 +4.18 -1.95 -4.18 Unstable 40 -52.4 1.33 +4.18 -2.85 -4.18 Unstable 45 -59. 0.64 +4.18 -3.54 -4.18 Unstable 47.6 -62.4 0.00 +4.18 -4.18 -4.18 Unstable 50 -66.5 Unstable +4.18 Unstable -4.18 Unstable 104 MAGNETIC OBSERVATORY MANUAL [Ch. 275. Equation (190) may be solved for h\ A = [2i?^,X10-^-(iJcos^ + /p)]-^. (198) rriig Example: R =2244 mm; *S'z=8.667 per mm; H -0.1875 cgs; A =0; /. =0; M,=314 cgs; mi =20 gm; g =980 cm/sec/sec; by equation (198), A=0.00322 cm=32.2 microns. Example: Same as above, except that Sz is now instead of 8.66. By equation (198), A=— 0.0030 cm=— 30 microns, that is, the center of gravity will be above the knife edge. 276. The ordinary analytical balance (nonmagnetic), is so con- structed that the center of gravity is very close to the central knife edge, but always below it. Such a balance may be adjusted by means of a counterpoise so that its center of gravity will be at the same height as the knife edge or above it. In either case the balance beam would be unstable. This would be true also of the magnetic balance (Z variometer) if it were operated with no sensitivity-control magnets and with its magnetic axis strictly in the magnetic prime vertical, N end east or A^ end west; that is, if no component of H or fp acts on the magnet. Suppose now the recording magnet is operated with its axis in the magnetic meridian with its A^ end to the north. As stated in paragraph 268, there will be a clockwise couple acting on the magnet and this couple is equal to MsH sin 6. Thus it is possible to operate a magnetic balance with its center of gravity above the line of support {h negative) and maintain stability for long periods of time. It should be noted in passing that the distance h for a Z variometer as it is normally operated, is extremely small, usually of the order of 20 to 50 microns. 277. Effect of fp on Sz* — If /p is positive, that is, if it is directed the same as the Z recording magnet, Sz will be increased, or what is the same thing, the magnet will become less sensitive to changes in Z. If /p is negative (directed opposite to Mg) it becomes more sensitive to changes in Z, and Sz will be decreased. Thus the scale value of a Z variometer may be adjusted over a wide range by use of control magnets properly placed and oriented with respect to the recording magnet. Control magnets have been used on la Cour Z variometers when it was not possible to obtain the desired sensitivity by other means. 278. Differentiating Sz with respect to/p, in equation (190), dS,=^XlO'; (199) 9.] Z VARIOMETER 105 and if /p is in gammas dSz='^^- (200) Example: i?=2244 mm; /S^^ 8.667 per millimeter; 4488 change /p to +44887; then by equation (200) , dSz= r, w no a a ^ ~^ ^ 7/mm and /S'^ becomes 9.667/mm; or change fj, to —44887, dSz is now — 17/mm and Sz becomes 7.667/mm. 279. Effect of H on Sz* — Differentiating equation (190) with respect to H, dSz=^^X10'dH (201) ^^^"^dHy (202) 2R It is seen that the scale value is not affected by H when M^ is directed to magnetic east (^ = 90°) or to magnetic west (^=270°). Example: i?=2244 mm; C^iJ^ = 1007. By equation (202), ^&=^=0.0227/mm. It is evident from the above that the change in Sz due to a small change in H is negligible for practical purposes, 280. Effect of A on &.— From equation (190) dSz=-^^^^XlO'dA, (203) When dA is in degrees (c^^° = 57.3 dA) and 77 is in gammas (i7^=^X 10^), ^o _ Hy sin A dA"" ^^^ 114:0 ^^^^) Example: ^-y= 187507=0.1875 cgs; A° = 90°; i?=-2244 mm; change A to 95°; then c?^° = 5° =0.0873 radians; and by equation (203) or (204), dSz = 0.36y/mm. Table 9 shows the variation of scale value, Sz, with azimuth A of recording magnet for a typical case. 210111—53— — 8 106 MAGNETIC OBSERVATORY MANUAL [Ch. 281. Scale values of a typical Z variometer, — In order to give some idea of the magnitude of the various quantities entering into the Z scale value, results of various tests with a Schulze variometer are given in table 8. In these tests scale-value observations were made first with the sensitivity poise in its lowest position. The poise was then raised by steps of 5 turns (5 turns=0.1370 cm), up to the point of instability (47.6 turns =1.304 cm) keeping A constant at 0°, that is, N end north. The first column of table 8 gives the 5-turn steps. Column 2 is derived from equation (191) for m2=0.0955 gm and mi =20 gm. Five turns upward adjustment of the sensitivity poise decreases h and raises the center of gravity by 6.5 microns. Column 3 is the observed scale value; column 4 is the value of the constant term, — —^ — XIO^, of equation (190); and column 5 is the difference between columns 3 and 4, that is, the variable term, ^1^^X10^ By equation (197), For mi = 20 gm, ^=980 cm/sec/sec, i?=2244 mm, and Ms=314 cgs, by equation (205), —7-^=— 6.64 7 per mm, per cm of upward displacement of the poise. Since 5 turns=0.1370 cm, 1 turn=0.0274 cm; and for one upward turn of the poise, dSz= -6.64X0.0274= -0.1827/mm. 282. Suppose now that the variometer described above is operated with the A^ end of the recording magnet to the south and with the magnetic axis in the magnetic meridian. For this condition, ^=180°, cos ^= — 1, and the term — ^P — XIO^ becomes — 4.187/mm (column 6 of table 8). Then for the first position of the poise (0 turns), the scale value would be &=-4.18 + 4.48 = 0.37/mm, as shown in column 7. This means that the magnet would be ex- tremely sensitive, almost to the point of instability. In fact it would require an increase of only 0.45 mm (1.64 turns) in Ay to make it unstable. 283. Table 9 gives the computed values of Sz for all azimuths in steps of 30° from 0° to 360°. i 9.] Z VARIOMETER 107 TABLE 9. — Variation of Z scale value with azimuth of recording magnet A Cos A 2R ^^^ Z Scale value o yimm y/vam 7/mm + 1.00 + 4. 18 4.48 8. 66 30 + 0. 866 + 3. 62 4.48 8. 10 60 + 0. 500 + 2.09 4.48 6. 57 90 4. 48 4. 48 120 -0. 500 -2.09 4.48 2.39 150 -0. 866 -3. 62 4. 48 0.86 180 -1.00 -4. 18 4. 48 0.30 210 -0 866 -3.62 4.48 0.86 240 -0. 500 -2.09 4.48 2.39 270 4.48 4. 48 300 + 0. 500 + 2.09 4.48 6. 57 330 + 0. 866 + 3. 62 4. 48 8. 10 360 + 1.00 + 4. 18 4. 48 8.66 284. Adjustment for latitude, — The vertical intensity varies from zero at the magnetic equator to approximately ±70,0007 at the magnetic poles. If the variometer is moved to a site where Z is con- siderably different, it will be necessary to rebalance the magnet by adjustment of the latitude poise, ma, figure 69. If nii is the mass of the magnet system, m^, the mass of the latitude poise, and dL^ the distance it must be moved outward along the invar spindle in order to keep the magnetic axis horizontal, we have by equation (193) mi By equation (186) when only Z and a change, dZ= qr-^ da Ms and, combining equations (206) and (207), Example: ^ By equation (208) dZ^^'^dU m3=2.444 grams; ^=980 cm per sec^; M,= 1225 cgs; dLs= one turn =0.04 cm. dZ=0.0782 cgs=78207. (206) (207) (208) I That is, one turn of the poise on the latitude spindle is equivalent to 78207 change in Z. 108 MAGNETIC OBSERVATORY MANUAL 285. Adjustment of both latitude and temperature poises, — For very large changes in Z, it would be necessary to adjust the tem- perature poise, nit (see par. 292, ch. 10) and also to adjust the lati- tude poise to keep the magnet balanced in the horizontal plane. Combining equations (194) and (207), dZ=^-'gdLt+^fjL, (209) and dL,^^ dZ+^' dLt. (210) m^g ma The term — - dZ is the adjustment of the latitude poise needed to bal- ance the change in Z and the term — ' dLi is the additional adjustment TYl^ of the latitude poise needed to balance out the effect of the shift of the temperature poise. Example: Z changes from 0.538 to 0.200 cgs; pitch of temperature thread 0.06 cm per turn; pitch of latitude thread 0.04 cm per turn; dZ=-0.33S; mi=2.030 grams; c?Zj= — 1.074 cm to maintain temperature compensation = — 17.9 turns; m3=2.444 grams; Ms=1225 cgs; ^=980 cm per sec^. By equation (210) dL^=— 0.1729 cm=— 4.3 turns to balance dZ; and c?Z3=— 0.8921 cm =—22.3 turns to balance dL(. Therefore the total adjustment of the latitude poise is c^Z3= -0.1729 cm-0.8921 cm=- 1.0650 cm = —4.3 turns — 22.3 turns=— 26.6 turns. 286. Further details on the adjustment of the temperature poise are given in chapter 10, pages 111-112. CHAPTER 10. TEMPERATURE COEFFICIENTS OF VARIOMETERS 287. Meaning of the variometer temperature coefficient, — As stated in paragrapli 267, page 99, wlien ^=0, the magnetic axis of the recording magnet is horizontal, and MsZ=miga. (211) Suppose that Z remains constant and the temperature of the recording magnet increases, resulting in a decrease in Ms- Then the product MgZ will be less than ruiga (a is assumed to be constant in this example) and the A^ end of the magnet will rise, indicating on the magnetogram an apparent decrease in Z. Now let Z increase by an amount sufficient to balance the effect due to the change in Ms- Then we may say that the change in Z is related to the change in Ms as follows: dZ m,ga ^^12) dM, M and since miga=MsZ dZ M.Z Z (2^3^ dMs Ms' Ms But, by definition, — ^r— per degree centigrade change in temperature is the temperature coefficient of the magnetic moment. That is, i,fj = — gi. Transposing equation (213) and dividing by dt, dZ dMs , /r.-. 4\ Zdt—Mjt=+^^ (21^) and '^=+g,Z=Q,. (215) The term q^Z is the temperature coefficient, hereafter called Qz, of this Z variometer. In general the temperature coefficient will contain other terms in addition to qiZ. 288. Qz may be defined as the temperatu? e coefficient oj the Z spot, always expressed in gammas per degree C. It is equal to the negative of the apparent change in Z, as recorded on the magnetogram, caused by a change in temperature of 1° C. It is also equal to the real gamma change in Z that would be required to return the Z spot to its original position after a temperature change of one degree centigrade causes the spot to be deflected. The temperature coeffi- cient, Oh, of the H variometer is similarly defined. The temperature coefficient, Qd, is defined as the declination change, in minutes of arc, per degree centigrade. It may be noted that this definition of Q leads to the correction term Q (t—to) in the derivation of values from the magnetogram (par. 424, p. 165). 109 no MAGNETIC OBSERVATORY MANUAL [Ch. 289. Mechanical compensation of the Z variometer, — Figure 70 is a plan view and side elevation of a Z recording magnet equipped with a device for mechanical compensation. Let mi =the mass of the recording magnet system in grams; m2 =the mass of the sensitivity poise; Ms =the mass of the balancing (latitude) poise; rUt =the mass of the temperature poise; Lt = effective length of the temperature compensating arm (aluminum) ; the latitude adjustment arm (invar); a =the lateral distance of the center of gravity of the magnet system from the center of support when ^ = 0; 6 = angle between the magnetic axis of Ms and the horizontal; Ms = magnetic moment of the record- ing magnet; Z = vertical intensity ; i = temperature of the magnet sys- tem; qi = temperature coefficient of the magnetic moment Ms ; temperature coefficient of the variometer in gammas per degree C; g = acceleration due to gravity =980 cm/sec/sec; a = coefficient of linear thermal expansion of aluminum = 0.000023 per degree C; p = temperature coefficient of the distance a. The bronze mass rrit is threaded on the aluminum spindle of effective length Lt', the bronze mass, rris, is threaded on the invar spindle of effective length L3. The two masses m, and rris, are approximately equal. The coefficient of linear thermal expansion of aluminum is taken as 0.000023 per degree C and that of invar as practically zero. 290. If the temperature of the aluminum spindle increases by an amount A^, the mass rut moves outward through a distance aLtAt, and the increase in the mechanical couples on this side of the magnet sys- tem is rrit gaLtAt. The product of rrit and its horizontal displacement due to a moderate temperature change is approximately equal to the product of the total mass of the magnet system rrii and the horizontal displacement of the center of gravity of the system due to the same temperature change. That is Figure 70.— Vertical-intensity recording magnet, Schmidt type. ft mtOiLi rriiap (216) or ^ nil (217) in which the minus sign is required because a and Lt are taken positive in opposite directions. The temperature coefficient ^ is a complex function of the masses, lever arms, and temperature coefficients of the various parts of the recording system.^ If both the change of M, J C. A. Heiland and W. E. Pugh, Am. Inst. Min. and Met. Eng., Tech. Pub. 483, p. 13, 1932 (see item 5 of bibliography). 10.] TEMPERATURE COEFFICIENTS 111 and that of a with t are taken mto account, equation (215) becomes <2z=2,Z+g'a?'. (218) Substituting for ap from equation (217), Q,^q,Z-'^iaL, (219) and ^^?=2,. (220) It should be noted in passing that the coefficient of linear thermal expansion of invar is only about Ke that of aluminum and even though the change in the mechanical moment on the invar side of the system (due to a temperature change) is extremely small, it is appreciable. This effect is almost exactly balanced by the change in the mechanical moment of the aluminum spindle itself for the same temperature change.^ 291. Compensation for moderate temperature changes will be achieved when Qz=^, that is, Cz=giZ-^g^'=0 (221) Z.=^^^. (222) amtg Example (a) : gi = 0.000 138 per degree C; Z=:0.538 cgs; then by equation (221), Lt=0 (uncompensated variometer); ^2= 0.000 074 cgs per degree C; = 7.47 per degree C. Example (b) : Z=0.538 cgs; M,= 1225 cgs; 2i = 0.000 138 per degree C; a=0.000 023 per degree C; m«=2.030 grams; ^=980 cm/sec/sec; then by equation (222), Z, = 1.99 cm. If the center of m, is set precisely at 1.99 cm along the aluminum spindle and the latitude poise, rriz, is adjusted along the invar spindle so that the magnet is just balanced in the horizontal plane, the vari- ometer will be compensated for temperature at a site where Z is 0.538 cgs (53,8007). It is apparent from equation (222) that Lt must be 2 J. W. Joyce, Manual on Geophysical Prospecting with the Magnetometer, U. S. Dept. Int., Bur. of Mines, 1937, p. 42 (see item 7 of bibliography). 112 MAGNETIC OBSERVATORY MANUAL [Ch. increased or decreased in direct proportion to Z in order to preserve perfect temperature compensation. That is, L/ 7J (223) 292. If Q is of the order of d=l7 per degree, it will be satisfactory for all practical purposes. What change in Z would be required to change Qz by I7 per degree centigrade if gi =0.000 138 per degree centigrade? By equation (220), ^Qz=q^^Z (224) and AZ=^. (225) Then ^Z= ^ 0.000138 = 72007 approximately. That is, Z may change by approximately 72OO7 before Qz will change by more than I7 per degree for this variometer. This variometer, compensated for temperature where Z= 53,8007, would be considered practically compensated for values of Z ranging from 46,0007 to 61,0007, a range of 14,4007. Beyond this range it would be necessary to adjust the temperature poise in accordance with equation (223) in order to preserve compensation within one gamma per degree C. For very large changes in Z, for example when a Z variometer is moved from a place where Z is 0.538 cgs to a place where Z is 0.200 cgs, both the temperature and latitude poises must be adjusted, as explained in paragraph 285. It is important always to make latitude adjustments with the latitude poise only and not to adjust the temper- ature poise unless one wishes to change the temperature coefficient of the instrument. 293. In south magnetic latitudes Z is negative, and the A^ end of the recording magnet will move downward when there is a small increase in temperature and there is no compensation. In order to achieve compensation when Z is negative, the aluminum and invar spindles should be interchanged, or what amounts to the same thing, the magnets should be removed from the central block of the system and reversed, so that the aluminum spindle is on the same end as the S end of the system. Under these conditions giZ is negative. For an uncompensated variometer, Qz is always positive in north mag- netic latitudes and negative in south magnetic latitudes. Qz then will have the same sign as Z; and Qz(t—to), the correction for temper- ature, is applied algebraically to observed Z in order to obtain the true Z. 294. Temperature coefficient and scale value, — Heiland^ has shown that the temperature coefficient of a variometer compensated as described above is practically independent of the scale value of the instrument. In other words, Qz is independent of Sz when Qz is ex- 3 Heiland and Pugh, op. cit., p. 21 (see i tern 5 of bibliography). 10.1 TEMPERATURE COEFFICIENTS 113 pressed in gammas and not in arc or millimeters of ordinate. Heiland has shown also that the temperature coefficient of the scale value itself is negligible.'' These conclusions are based on the assumption that the axis of translation of the sensitivity poise is precisely perpendicular to the magnetic axis of the recording magnet. (It will be shown later, paragraph 310, that for optical compensation the temperature coefficient is dependent on the scale value.) 295. Magnetic compensation, — Temperature compensation may be accomplished by use of an auxiliary magnet (or magnets) to reduce the component of the vertical field acting upon the recording magnet. An increase in temperature reduces the magnetic mo- ment of both magnets. Reducing the magnetic moment of the recording magnet causes an apparent decrease in Z. At the same time the field of the compensating magnet is reduced numerically, causing an increase in the resultant field acting on the recording magnet, an apparent increase in Z. When the proper relation exists between the temperature coefficients of the two magnets and the amount of reduction in the field acting on the record- ing magnet, first-order temperature com- pensation is effective. In practice the temperature magnet is fixed relative to the recording magnet as shown in figure 71. The position of Ma is reversed in south mag- netic latitudes, that is, the A^ end of Ma is down. Equation (182) may be written, for 6=0°, Mr Figure 71. — Magnetic temperature compensation of Z variometer. or Ms{Z+C)=m,9a MsZ+MsC=m,ga (226) (227) in which C=the amount by which the vertical field acting on the recording magnet is altered; Ms==the magnetic moment of the recording magnet; and mi^a=the mechanical couple balancing the magnetic couple Ms{Z+C). (It is to be noted that Z and (7 have opposite signs. In north magnetic latitudes, Z is positive and C is negative.) Let the temperature of the whole system rise by an infinitesimal amount, dt. This will cause a change in C, Ms, and a, and the result will be an apparent change in Z (increase or decrease) . C decreases as a result of a decrease in the magnetic moment of the temperature magnet and because of the increase in the distance r (fig. 71), due to the expansion of the material separating the magnets (usually this material is brass). 296. Now let Z increase by an infinitesimal amount, just sufficient to keep the magnetic axis horizontal. Then from equation (227) we have (M,+AM,)(Z+AZ) + (M,+AM,)((7+A(7+A'(?)=mi^a + m,^Aa. (228) Heiland and Pugh, op. dt., p. 11. 114 MAGNETIC OBSERVATORY MANUAL [Ch. In this equation ACis the change in Cdue to a change in the magnetic moment of the temperature magnet and A'(7 is the change in C due to the change in the distance between magnets. Expanding equation (228) and neglecting second order terms, MsZ+MsAZ+ZAM.+MsC+MsAC+MsA'Ci-CAMs =miga-\-migAa. (229) By equation (227), MsZi-MsC=miga. Subtracting equation (227) from equation (229), MsAZ+ZAMs+MsAC+MsA'C+CAMs=migAa. (230) Dividing by A^, MsAZ , ZAMs , MsAC , M.A'C , CAMs _ m,gAa At "^"aT"^ A^ "^ A^ + A^ - A^ ^^'^^^ A '7 Let — 7 =()2= temperature coefficient of the variometer in gammas per degree C ; — 71-/- Af ~Q.^ = temperature coefficient of the magnetic moment of the recording magnet ; AC —-pXi ~9^2 = temperature coefficient of the compensating field at constant r; A'C —yyir, —^3 = temperature coefficient of the compensating field at constant Ma] — — =gi = temperature coefficient of mechanical couple = p (par. 289). Substituting these values of the g's in equation (231), having regard to signs, and noting that MsZ-\-MsC=miga, MsQz-ZMsgi-MsCg2-MsCq,-MsCg,=m,gaq,=q,{MsZ+MsC) (232) from which Qz=Z(q,+q,) + C(g, + q2+q.z+g[4)- (233) When compensation is effective, Qz=0, and Z(q^ + g,) = -C{q, + g2 + q^ + qi) (234) or §= J't^\ • (235) Z qi+q2+q3 + qi Let S^=9:i + 9'4 10.] TEMPERATURE COEFFICIENTS 115 and S'?=£> = — 0.078 minutes of arc of east declination per degree C, which means that a temperature increase of one degree G will produce an apparent increase of east declination equal to 0'.078. This example shows that Qd will usually be negligible. 304. Optical compensation of the Z variometer, — In the optical system of temperature compensation, described by la Cour and Peter- sen,^ the motion of the Z spot caused by a temperature change of the Z recording magnet is compensated by passing the incident and reflected light through a 90° prism attached to a nonmagnetic, bimetallic strip of silver and platinum. The strip is assumed to be at the same temperature as the Z magnet at all times. Let the prism be clamped and let Z remain constant while the temperature rises a definite amount. The magnetic moment, Ms, of the recording magnet will decrease. The Z spot will be displaced, indicating an apparent decrease in Z. Now let Z continue to remain constant but with the Z magnet clamped and the prism undamped and let the system be subjected to the same temperature change as above. If the strip is properly faced and is adjusted to the correct sensitivity, the displace- ment of the Z spot caused by the bending of the strip will be just equal and opposite to that caused by the change in Ms described above. The resultant motion of the Z spot, when both magnet and prism are undamped, will be zero. Under these conditions the variometer is optically compensated for temperature. 305. In the la Cour variometers, a portion of the light which passes through the reflecting prism is intercepted by a fixed mirror and reflected back through the prism to the drum, forming the temperature spot. The bimetallic strip then serves two purposes, to provide optical compensation for the variometer and to act as an optical thermograph for recording changes in the temperature of the instrument. 306. The constant, Ct, of the bimetallic strip. — In order to adjust properly the length of the strip for a particular instrument, one should know the sensitivity of the strip to temperature changes. The strip constant, Ct, is defined as the motion of the T spot in mm on the drum, per mm length of strip, per degree change in temperature, at a recording distance of 1 cm. The constant may be furnished by the manufacturer, or determined experimentally by subjecting a known length of the strip to a known temperature change and noting the motion of the T spot at a known recording distance. If the length / mm of the strip is subjected to a temperature change tz—ti when the effective recording distance is R and the ordinate of the T spot changes from Ui to 712 millimeters, then the strip constant, Ct, is given by Also, n2-ni = CTRl(t2-ti). (266) 7 D. la Cour. La Balance de Godhavn, p. 17 (see item 8 of bibliography). 10.] TEMPERATURE COEFFICIENTS 121 307. The sensitivity and scale value of the bimetallic strip, — The sensitivity, Tg, of a strip is defined as the change in the miUimeter ordinate of the T spot caused by a change in temperature of one degree C. Using the same notation that was used in equation (265), rp_n^ni pg^j and by equation (265) T^^'^^—^ = CtRI (268) The reciprocal of the sensitivity, that is the change in temperature in degrees C represented by one mm change in ordinate of the T spot, is the scale value of the T spot, and is designated St. Thus if St is known, variations in temperature may be scaled directly from the temperature curve. By definition, (269) ^» and by equation (268), / /, 1 (270) Example: A platmum-silver strip was tested at Cheltenham Observatory. It was found that the angular displacement of the end of the strip was proportional to the temperature change over a range of 15° C. In these tests, St- 1 iS'.,- t2- -ti 1 Or 712- -Ui CtRI I R=231 cm; 1 = 22 mm; n2—ni = 20 mm; ^2-^1=8° a equation (265), Cr^ 0.00049 per cm per degree. equation (267), r,=2.5 mm/°C. equation (270), ^r=0.4°C/mm. 308. The temperature coefficient with optical compensa- tion, — For effective temperature compensation the ordinate of the Z spot should not change when Z is constant and temperature changes. Let AZi= apparent change in Z due to A^ change in temperature with recording magnet free, strip clamped, and Z constant; AZ2= apparent change in Z due to A^ change in temperature, with recording magnet clamped, strip free, and Z constant; q_i=--irf —17^= temperature coefficient of magnetic moment of Z magnet; 210111—53 y 122 MAGNETIC OBSERVATORY MANUAL [Ch. $^= temperature coefficient of the variometer, 7/° C; aS'z== scale value of the Z variometer, 7/mm; i?= distance from Z lens to drum; Cr= strip constant, or motion of T spot in mm, per mm length of strip, per degree C, for R=\ cm (furnished by maker or determined from equation (265)); /= length of strip in mm. Now let Z remain constant while the temperature of the Z recording magnet changes by A^. This will cause the Z spot to move as a result of the change of magnetic moment of the recording magnet, and the apparent change in Z is, by equation (214) (p. 109), AZi=-(7iZA^. (271) Again, let the temperature of the strip change by A^. With the strip facing properly, the Z spot will move in the opposite direction due to the bending of the strip and the motion of the Z spot, An, will be, by equation (266), Au^RICtM (272) and AZ2=+SzAn=RlCTMSz- (273) The net apparent change in Z will be AZa = AZi + AZ2 = -qiZAt + SzRlCTM; (274) and by definition of Qz (par. 288), Also and Q^=-^=q,Z-RlCTSz. (275) l=^W^ (276) ^^=-^%- ^277) Also, from equation (275), ^_ ^z I x..^.^z . (278) Qz ~h RICtSz When the two apparent changes AZi and AZ2 just balance each other and there is no motion of the Z spot resulting from a temperature change, the variometer is compensated and ^^=0. When Qz=^, q,Z-RlCTSz = (279) and 10.] TEMPERATURE COEFFICIENTS 123 309. Estimation of strip length for optical compensation, — The following examples illustrate the application of the equations of paragraph 308: Example (a): Let qi =0.00030 per degree C; z =232007; R =225 cm; Cr= 0.00049 per cm per degree; Sz =3.007/mm. Z=21 mm. By equation (280): This variometer, having a scale value of 3.007/mm and operating where Z= 23,2007, will be optically compensated for temperature when the length of the strip is 21 mm. It is seen from equation (275) that the temperature coefficient of the variometer will change if the Z scale value changes. Equation (280) shows that for Qz=0, I will vary directly as Z and inversely as R and Sz- For a constant recording distance and scale value, I must be made longer as Z increases and shorter as R and Sz increase. This condition is expressed in the following equation: 1^ = 1 ~y o/e /' (281) Example (b): Let Z =53,8007; R =231 cm; ^, =3.607/mm; Cr =0.00049 per cm per degree; I =22 mm. By changing the temperature artificially, or by comparing with another variometer, it is found that &=7.37/°C. What is the strip length for Qz=07 Let A0z=-7:SyrC. By equation (277) A/=18 mm. Then, for Oz=0, 1=22 mm + A/=40 mm. Also, what is the value of qi in this case? By equation (278), ^1 = 0.00030 per degree C. Example (c): Suppose it is desired to move a Z variometer from Cheltenham where it is properly compensated for temperature to San Juan. What should be the new length of the bimetalhc compen- sating strip? At Cheltenham /=40 mm, Z=53,8007, i?=231 cm, 124 MAGNETIC OBSERVATORY MANUAL [Ch. and S^=3.Qy/mm. At San Juan Z will be 35,5007, R will be 240 cm, and the required scale value S^, will be 2.557/mm. By equation (281) /'=40x|Sx^4ix'-' 53,800'"240""2.55 =36 mm. 310. Optical compensation of the H variometer. — This may be accomplished in the same manner as that used for the Z instrument except that we must now take into consideration the changes in the torsion constant of the quartz fiber with changes in temperature. Let qi ==— TT --7T^= temperature coefficient of the H recording magnet ; 1 dk^ gs =-p -7^ = temperature coefficient of the torsion constant of the quartz fiber=0. 00016 per degree C; Sh =H scale value, in gammas per mm; Ct = bimetallic-strip constant; R = recording distance from drum to H lens; I = length of the strip in nam; Qjf = temperature coefficient of the variometer, in gammas per degree C; A^i= apparent change in jFZdue to change in temperature. At, with recording magnet free, strip clamped, and H constant; AZZ2=apparent change in H due to change in temperature, At, with magnet clamped, strip free, and H constant. With the prism clamped and the magnet free, and assuming that the extraneous fields at the center of H are negligible. AH,= -mq^ + q,)At, (282) and with the magnet clamped and strip free, AH2=lCTRSHAt. (283) The net apparent change when both the magnet and strip are free is AHa=AH, + AH2 = -H(qi + qs)At+lCTRSHAt, (284) 10.] TEMPERATURE COEFFICIENTS 125 and by definition of Qh, paragraph 288, QH=-^=H(q, + q,)-mCrS^. (285) For temperature compensation, Qh=0 and It is seen that in this system of temperature compensation the value of Qh will depend upon the // scale value. The formulas developed for the optical compensation of the Z variometer, paragraph 308, will also apply to the H variometer if qi is changed to ^i + Ssj ^ to H, and *S'^ to Sh- CHAPTER 11. DETERMINATION OF SCALE VALUES USE OF DEFLECTOR MAGNET 311. The H scale value, — For small angles, the angular displace- ment of the recording magnet is approximately proportional to the field applied in the magnetic meridian through Ms. Then the H scale value is St=^ (287) in which aS^ = observed H scale value in gammas per mm; /n= applied field in gammas; 7/^^= deflection of H spot in mm on the magnetogram. 312. The field, /„, is supplied by a small magnet mounted on the deflection bar of the variometer, or by a large deflector of high magnetic moment placed 2 or 3 meters from the variometer (in the magnetic meridian through the center of Ms and at the same elevation as M^ , or by a Helmholtz-Gaugain coil. When a small deflector is used at short distances, a correction must be applied for distribution by means of one of the formulas in table 2. When a large deflector is used at distances which are large compared with the dimensions of the magnets, corrections for distribution may be entirely negligible. 313. In practice, three deflections are made with the deflector in the ^position, figure 118 (p. 204), top, first with the N end to the north and then with the A^ end to the south, the reversals being made in the manner shown in the sample set of observations, figure 72. For a double deflection, 2 Uh, equation (287), may be written S*=|£. (288) 314. In gammas, the field, /„, of the deflector is — ^XIO^, Ma being the magnetic moment of the deflector and r the deflection dis- tance in centimeters (center of Ma to center of Ms) . Substituting this value of /„ in equation (288), and including a distribution factor, a^r, calculated by means of the top fine of table 2 (p. 13), we have ^^ maOH , (289) This is the observed scale value at the away ordinate, that is, at the ordinate, hmm, of the undeflected H spot. 126 SCALE VALUES 127 374d OePAm-MtNT OF COMMCNCK COACT AND OEOOmC SURVCY DIV: OftS Observatory TUCSON Date Mi4. 1951 S^^ y^UES OF INTENSITY VARIOMETERS Deflector ^-^1 cm Deflection distance 3^6 cm Observer J B Campbell (Die l»*»> H VARIOMETER (Deflector face up) D VARIOMETER (Deflector face up) Z VARIOMETER (Deflector face East) Nend 2u, N end 2Ub Nend 2u, I i I Mean( ! > "7.5 E > ?«-5 Mean(E-W)-2uo 26.7 u -■" > .«9.o i > ^7v.^ N-S)=2ue 67.4 u ^ ^9.0 Mean(U-D) = 2u, 29.0 Away onl. Before 16.4 Away Old.' Before 4« 1 Away Before -6,1 After 14.7 [After 5.4 ord. After _ ^, fi Mean ^ 15, 6 Aim Meand L. 4. 8 mm Mean z„ - d.o"™"™ S, «-97 r/mm S; 0. 50 /mm 105 M.Time K 46 r d 2' Began 18 '22 Prel. Hblv. ^593^ 7' Prel. D blv. 13' 21 Ended i5 53 H^ 25975 r D 13' 23 Mgph. Temp. 20. 4*C D 13 24'" Remarks (D-D) _ 1' S;-S^H^tanl' S: = 4M(10)yH/'2uH S, = 2M(10)»ot,/r'2u, log ton r 6.4637 log 4(10)' 5.6021 log 2(10)' 5.3010 logSp' 9.6990 log eX-a 0.0006 lo«o<-r 9-9 9 91 logH^ 4, 4146 cologr* 2, 54^9 colog r* 2. 5429 logSS 0. 5773 log 4(10)»oC^/r' 5. 1456 log2(10)'oL,/r'7. 843^ ^ 3. 75 logM 4. 1603 logM 4. 1603 M = r'2u„SS/2c=Co(10)' colog 2Uh 8. lyi 3 colog2u^ 8. 5376 logr/2(10)» 2. 1561 log S^ 0. 4112 logs, 0. 5415 cologoi„ 0. 0004 Sh' 3. 00 1 s. 3.45 log2u„ 1.4365 -0^0390-5) ■'■.003 Sh=S;- 0» 0030 (D-D) S. = Se- 0. 0024 h_ logS^ 0.5113 s, 3-004 logM 4. 1603 -0.0024^^ -.031 Sh=S, + 0. 001 a h_ h,= Seh„ M 14460 s. a. 9 7 Scaled to lpp,p™n Scalings by ^M eheck^ by M-?. Computed . by RLR itioa (or 195-'- ^^ " ^3 ^4 (to nmrml minut Computations Abstracted checked by Mp by Mp Figure 72.— Scale-value observations and computations. 128 MAGNETIC OBSERVATORY MANUAL [Ch. 315. The H scale value of a unifilar variometer depends on the ordinate of the H spot at the time the deflections are made and on the magnetic declination, in accordance with the equation, Sl=S^+ah+h{P-B) (290) where a =the a factor described in paragraph 255 (p. 95) ; h =the h factor = eHsuiV (see par. 262) ; h =the away ordinate of the H spot, denoted kmm in figure 72; D == standard declination value, such as the mean for one year; I) =the declination at the time of the ZZ" scale-value deflections; 5^0= the H scale value that would be observed when /i=0 and Sh = the observed H scale value when the H ordinate is h and the declination is D. Also, if Sh is the H scale value at ordinate h and declination D, then SH=So+ah (291) and S*=SH+b{D-D), In figure 72, Sh and So are calculated from the observed i? scale value, Sh, as follows: SH = S*-b{D-D) (292) So=SH-ah. (293) If the terms b{D—D) and ah are negligible, then Sh and So may be taken as equal to Sh- This is usually the case for low-sensitivity H variometers. 316. The Z scale value, — For the Z variometer, the deflector is used in the B position, figure 118, center, that is, the center of the deflector, Ma, is placed in the magnetic meridian through the center of the Z recording magnet, Ms, axis of Ma vertical and with its mag- netic center at the same elevation as the center of Ms. In this position, the field of Ma at the center of Ms is Substituting this value of /„ in equation (288), changing H to Z, and including a distribution factor az, we have &=^^X10'. (294) 11.] SCALE VALUES 129 in which 2 Uz is the double deflection of the Z spot in mm on the magnetogram, the deflector being reversed in making the deflection observations in accordance with the example in figure 72. 317. Equation (294) gives the Z scale value at the observed ordinate, Zmm, which is the away ordinate. The Z scale value varies slightly with ordinate, but the variation is usually negligible ajid will not be considered here. 318. The D scale value {gamma scale value), — The deflector is used in the B position, figure 118 bottom — that is, it is placed with its center in the magnetic meridian thi-ough the center of the D recording magnet, at a distance, r, and with its magnetic axis in the same horizontal plane as the D recording magnet, at right angles to the magnetic meridian through Mg. The field, /„, producing the deflection is — 3^X10^, and for a double deflection it is — 3-^x10^. Substituting this value of /„ in equation (288) , changing H to D, and including a distribution factor ao, we have ^-^XlO^- (295) This is the intensity scale value (gamma scale value) of the D variom- eter. The relation between the gamma scale value and the minute scale value is described in paragraphs 321-23. 319. Com,putation of scale values from, deflections. — In the case of a sensitive magnetograph, the D scale value is usually known quite accurately, and is quite constant since jt is small compared with unity (see eq. 119). It is then advantageous to derive Ma from the following equation, based on equation (295) : , , _ 2unr^S l ^«-2a^> " > U 2uz 4. 8 mm. N end ' > W > E 2u 8.5 mm N end N > ^ > N 2uh 14. 1 mm 4.8 8.6 14;1 Mean (U-0) ^. 8 Mean (E-W) g. 6 Mean (N-S) j^. , Away Ordinate Before 14> ^ After 14* Away Before 13. 6 Ordinote After I3. 2 Away Before $0. 3 Ordinote | After 30.4 All scolings corrected for shrinkage to..??.?.^.mm. H from sensitive magnetograph...l55?P...T Mognetogroph Temperature X^ .'c Sj- 2Mltfotj/r*2u2 Sj « 2MIOi'e»o/r'2u So • S; cot I'/h S„- 4Mltfoc„/r»2uH log 2 10^ log M log o-j colog r' 5.3010 4. 0849 0.0000 2.795S log 2 10' log M log oto colog r' log Co log 2 u log So log cot 1 colog H log So 5.3010 4.0849 9-9993 2.7958 log 4 10' log M log > B 1 T /« +/?/"^^^^^:::^;^^ y 1 1 fo H-fa ^i^^ ^a H Ms r w Figure 77.— Test of orientation of Z)-variometer magnet; deflector placed A^ end south The equivalent west field that would produce this deflection if /„ were zero is Ay 2. Then, Ay2=Slu2 and By similar triangles and For small angles and tan (a— ,82) = y H+fa y _A2/2. tan (a— /32) H^-fa fa A2/2=/a tan {a—^2) = SlU2. tan (a+iSi)«tan a+tan ^i tan (a— i32)~tan a— tan ^2- r — 1 ^ ^^ i 5: ~~~^~--^_^ ?7?^^^-^ -^^ ' /T" y Ma , '« H ^ ^ ^ H+fa ^ r w Figure 78.— Test of orientation of Z>-Tariometer magnet; deflector placed A^ end north. Then from equation (315) fa ■ and from equation (319) 210111—53 10 fa ■ tan a+tan ^i tan a— tan ^2- (316) (317) (318) (319) (320) (321) (322) C323) 138 MAGNETIC OBSERVATOKY MANUAL [Ch. Adding equations (322) and (323), la 2 tan a+tan /3i — tan ^2 (324) and tana=^^^%'t^-i(tani8i-tan|82). (325) Let Mi+U2=2u; 2ja= ^ — — ; tan i8i = i8i; and tan i32 = i82; then tana=^|g^,-J(ft-&). (326) 337. In normal operation oi a, D variometer, it is evident from an examination of figures 77 and 78 that larger values of /3i and ^2 will be obtained when /« increases with respect to H. An extreme case might be when ZZ"=80007 and /„=1000t. From equations (313) and (317), tan {a-{-M=jjziJ^ (327) and tan {a—^2)=i-rr^' (328) ^-rja Applying equations (320) and (321) and assuming that tan a=a; tan i8i = i3i; and tan i82=i32, and q:-/32=y7t-7- (330) J^ -Tja Adding equations (329) and (330), y , y 2a+i8,-^2= H-Ja ■ H-^Ja Since tan «=-^' Q _R- y I y ?i Divide both sides by 2a, y I y 2^ 2a 2y 2y H H (331) i Hh^.^h^j)-' ^'''^ ^ 12.] ORIENTATION 139 which simplifies to i \ /2 1 Thus if /a= 1000 and //=8000,'^=- and the ratio 7^2 ^2 =^ — ^ = -^ ' // 8 H^—ja 64-1 0.016. This shows that in equation (326) the term |(/3i— i^o) may be safely neglected in computing tan a and tan E^. Then tan a=tan E,^^^, (334) in which Ex=a and 2i^ is the double deflection of the D spot in mm. Note: The scale value of the D variometer will be changed as a result of the large component of the deflector field parallel to Ms. This component enters as the term C in the general equation of the gamma scale value. That is, In orientation tests the C field, practically equal to fa, may be of the TJ_\_ n order of 5OO7. Suppose //=20,0007. Then the factor, -^j- = 1+Yt==1+ 7^777^77?,= 1.025 for the A^ end of the deflector north and rl zU,UUU C 1 —yj= 0.975 for the A^ end south. As a result of this change in scale value, the deflections will be unequal by a small amount; in this case, by 5 percent. Through the use of the mean gamma scale value in the computation of Ex by equation (334), these effects will cancel each other for all practical purposes. The foregoing proof disregards torsion in the fiber, but even for a stiff fiber the important results (eqs. 326 and 334) still hold. 338. Z variometer. — In making orientation tests of the Z recording magnet the deflector is placed in the same relative position as for the D variometer. Figures 76, 77, and 78 apply except that they now represent side elevations as seen from the west side of the Z variom- eter, and the line marked magnetic meridian is now the horizontal plane through the center of the deflector and the center of the Z magnet. The development of the orientation equation follows the same steps as for D, and in which Sz is the mean Z scale value and 2u is the double deflection of the Z spot in mm. 339. H variometer. — In figure 79, let a: be a small field or its equivalent that is deflecting the recording magnet, Ms, out of the magnetic prime vertical by a small angle a. Then since k (par. 232, p. 87) may be treated as an equivalent field, tan a~ (337) 140 MAGNETIC OBSERVATORY MANUAL [Ch. and if there is a sensitivity magnet having a field, p, at Mg, parallel to and directed the same as Ms, then tan a= k-\-V (338) Figure 79.— H-variometer magnet not in magnetic prime vertical. 340. With the deflector in position for orientation tests, M, will be deflected through a small angle jSi, figure 80, such that (339) Figure 80.— Test of orientation of /7-variometer magnet; ' deflector placed iST end west. in which ja is the field of Ma at the center of M^, and ^x^ is the com- ponent of ja practically normal to Ms and causing the small deflection /3i. When the deflector is reversed, figure 81, tan (a +182) = Aa:o Jc + p—fa fa (340) H^ ^p^~"" m r Ma -^ ^X2 \ X ^^-^^^^ST V^ ■^ k + p-fa fa Ms k^p Figure 81.— Test of orientation of H-variometer magnet; deflector placed N end east. 12.] ORIENTATION 141 For small angles, tan (a— i3i)«tan a— tan /3i, and tan (a+/32)~tan a + tan ^2- Then tana-tan^i = ^=%^ (341) and tan a+tan ^,=^=^ (342) J a J a in which Sh is the H scale value, and Ui and U2 are the deflections in mm of the H spot corresponding to ^i and ^2- Putting Ui-{-U2=2u and adding equations (341) and (342), 2 tan a=?^+ (tan ^i-tan ^2). (343) Ja Neglecting the term (tan /3i — tan ^2), which will always be small compared to a, 2uSh tan a- 2/« tan a=tan E,-^^^,^ (344) since 2/a= — s-^XlO*^ (deflector in B position). DIRECTIONS FOR ORIENTATION TESTS 341. Critical adjustment, — Read carefully appendix III, giving special attention to those parts dealing with critical adjustments of the deflector. Table 18 of appendix III gives a summary of critical adjustments. 342. Orientation bench, — If space in the variation room permits, construct a permanent bench or table similar to that shown in figure 82. Use nonmagnetic materials throughout. Adjust the bench plates (wood, brass, or aluminum plates upon which the deflector rests) in elevation so that when the deflector is in proper position for deflections, its geometric axis will be horizontal and at the same elevation as the recording magnet to be tested. 343. Adjustment of the deflector to correct elevation, — Place a short piece of glass tubing in each end of a long piece of flexible rubber tubing and fill the tube with water, free of air bubbles. Hold one tube vertical near the recording magnet to be tested and the other end near the bench plate opposite the variometer. When the water surface, bottom of the meniscus, is at the precise elevation of the center of the recording magnet and the water is at rest, mark on the bench-plate support the height of the water meniscus in the adjacent glass tube. Adjust the bench-plate supports in thickness until the deflector is at the correct height when resting in proper position on the plate. Check carefully. (Note: The recording magnets may not 142 MAGNETIC OBSERVATORY MANUAL [Ch. all be at the same elevation; the three bench plates must be adjusted separately.) 344. If it is not feasible to construct a permanent bench as de- scribed in paragraph 342, use a small nonmagnetic plane table for supporting the deflector. 345. Establishing magnetic meridians through the variom- eters, — If magnetic meridians have been established previously, proceed as outlined in paragraph 348. Otherwise establish these magnetic meridians as outlined below. 346. Using a transit or theodolite, run a traverse from the declina- tion pier in the absolute observatory to the variation room. This line, preferably about parallel to the magnetic meridian, should be Figure 82.— Orientation bench. marked with permanent vertical lines inscribed on brass plates on the north and south (inside) walls of the variation room. The plates should bear the inscription: True Bearing, (For example: N 14° E.) A simple computation will then, at any time, furnish data for establishment of the magnetic meridian by offsetting one end of the line established by the two permanent marks. An illustra- tion of this is given in figure 83. The line AB, established by traverse, has a true bearing of N 14° E. If the mean magnetic declination in the absolute observatory is 13°48' East, then the desired magnetic meridian in the variation room will be AB\ making an angle of 12' with AB. If the length of the line ^5=300 cm, the offset distance, BB' will be 3000 tan 12' or 10.5 mm to the west of the point B. 347. Make a sketch of the traverse, showing all turning points, courses, and angles on the sketch. Furnish also a record of all circle readings. Check carefully. 348. At approximately the same elevation as the marks described in paragraph 346, mount two wooden strips horizontally on the north and south walls of the variation room. A convenient size for the strips is 2 by 10 cm in section by 3 meters in length, and they should be held away from the walls by spacing blocks 2 cm thick. 12.1 ORIENTATION 143 349. Stretch a white linen or cotton thread between the wooden strips and attach a small weight to each end of the thread to keep it taut as it passes over the top edges of the strips. Attach a light- weight plumb bob to the thread in such a way that the point of the bob can be precisely centered over the top of the D variometer. By moving the thread along the wall strips so the two ends of the thread are the same distance (within \ mm) from the points A and B' , figure 83, the thread can be made to lie in the magnetic meridian passing through the center of the D variometer. Now file small grooves in the wooden strips directly beneath the ends of the threads and mark these grooves with a label; such as, D, Jan. 1, 1951. B B North Wall D =13°48'E "\\4- 12' A 0) 2 Variation Room \ H \ 'z D \ Magnetograph Pier \ South Wall Figure 83.— Establishing the magnetic meridians through the variometers. i4i?= established true bearing; ^iV= true north; yiB'= magnetic meridian (for magnetic declination of 13°48' East). 350. In like manner establish magnetic meridians through the H and Z variometers. (Note: Center of variometer means center of recording magnet.) Label and date each mark. 351. Suspend a light-weight plumb bob (perhaps a suitably sharp- ened copper nail or brass screw so tied to a piece of thread that it will hang straight with the vertical) from the meridian thread of the D variometer and carefully mark a point on the bench plate. Move the bob along the meridian thread and mark a second point, making the two marked points as far apart as possible. These two points then mark the centerline of the orientation deflector. Prepare a wooden strip and fasten it to the bench plate with brass screws (preferably in a way that will permit final adjustment of the guide strip after the screws are started) making due allowances for the size of the deflector magnet or its case so that the deflector will be centered on the meridian and parallel to the meridian. Fasten a 144 MAGNETIC OBSERVATORY MANUAL [Ch. second wooden strip to the bench plate to form a stop that will determine the distance between the center of the deflector magnet and the center of the D recording magent. Both wooden strips (guides) should be well made, with straight sides, so that the deflector will fit firmly and positively in one position only when placed against them on the bench plate. All markings of points and lines should be done as precisely as the materials at hand will permit. 352. Mark a meridian line on the bench plate that will be used for the H variometer in the same manner as that described for the D plate. With a draftsman's triangle having a true 90° angle, mark a line on the bench plate perpendicular to the meridian line at the desired distance from the center of the H recording magnet. This prime vertical line will be the guide line for determining the position of the guide strip that should now be fastened to the bench plate as was done for the D position. Fix an end position stop, also, to the bench plate so that the center of the deflector magnet will be pre- cisely in the magnetic meridian through the H variometer. Check the work carefully. It is important that the work be done with great precision. 353. Establish the meridian line on the Z bench plate in the manner described for H and D. Make a second check on the Z bench plate to see that the center of the deflector magnet will be at the same elevation as the Z recording magnet, and to see that the deflector will be level. (Test the level of the deflector with the sensitive stride level of the earth inductor.) Fasten wooden guide strips to the bench plates to serve as guides or stops against which the deflector may be placed in making orientation tests. 354. The deflection distances, r, need not be the same for all variometers. Measure and record these distances to the nearest millimeter. 355. It cannot be emphasized too strongly that every effort should be made to obtain precisely fixed positions for the deflector magnet for orientation tests, particularly to insure that the deflector shall be accurately parallel to the established magnetic meridian for Z>, accurately parallel to the established prime vertical for H, and accu- rately level for Z. 356. The procedures described above have been outlined in detail. There are, of course, other ways of accomplishing the results with equal if not greater precision, and the observer may adopt whatever methods seem to be most desirable. Experience has shown the author, however, that in any event a complete, detailed record of the methods and procedures followed will inevitably be highly useful at some later time. 357. Orientation deflections, — On a magnetically quiet day, make orientation deflections precisely as outlined in figm-e 84, making certain that the deflector is always against the guides. Begin with the D variometer and see that the first deflection is made with the deflector /ac6 up, N end to the north. 358. Complete all of the deflections indicated on the form, in pre- cisely the order indicated and with the deflector oriented properly for the indicated deflections. 359. Measure and record, as in figure 84, the deflection distances for each variometer. Record also the magnetic moment of the deflector (in terms of colog M, line 19), and the gamma scale value of all variometers (line 15). 12.1 ORIENTATION 145 360. From the magnetogram, scale and record all deflections and the away ordinates, and complete the computations for the numerical values of the orientation angles. Orientatiok Tests (Deflector North or South of Variometer) Magnetograph:{f «gf«;^«f^« ^ ^ ^^- Magnetic Observatory: Cheltenham Observer: S. O. Townshend 1. Variometer 2. Date 3. Approximate time 4. 5. Away 6. Face up; N end of deflector 7. Face up; N end of deflector 8. Face down; N end of deflector 9. Face down; N end of deflector 10. Away 11. Mean, N end (A) 12. Mean, N end (B) 13. 2u (A) -(B) 14. r 15. sy 16. Log 2u 17. 3 1ogr 18. LogSy 19. Colog Af 20. Colog 2X105 21. Colog 4X105 22. Log tan Ex 23. Ex (to nearest minute of arc) 24. A'' end of recording magnet 25. Formula tan Ez = D June 2k 19S7 15 20 Ord. mm -S.O : +2.8 -9.5 -9.5 I +2.8 -3.0 r +2.8 -9.5 +12. S 129 cm 5. SO y/mm 1.090 6.SSS 0.72j^ 6.129 I'm 8. 674 2° 42' EofN 2uT^ Spy 4MX105 H June 24 1937 15 40 Ord. mm 4.6 W 6.1 ; 4-3 : 8.7 V 7.0 10. o V +6.6 ; +6.5 +0.1 129 cm 3. 30 y/mm 9.000 6. 3SS 0.519 6.129 4.699 6'.680 0° 02' SofE 2ur^ Sny 2MX105 Z June 24 1937 1610 Ord. mm 34.8 36.6 32.6 32.9 36.7 34.4 36.6 32.8 +3.8 134 cm 5. 54 y/mm 0.580 6.381 0.549 6.129 1398 8.037 0° 37' Up 2ur3 Szy 4MX105 Record all ordinates to nearest 0.1 mm with same sign as in scaling an ordinate for Colog M derived from: Regular scale-value obser base line value. Figure 84. — Observations for orientation tests. I 361. Prepare a tabulation similar to that shown in table 12. 362. By means of table 13, identify the quadrant in which the N end of a recording magnet lies for the away position of the deflector. Record the results on line 24, figure 84. 363. Adjustment of recording magnets, — If a calculated E^ angle for any recording magnet is in excess of 1°, the recording magnet should be adjusted for correct orientation and the orientation tests repeated. Adjusting and testing should be continued until satis- factory orientation is indicated by the recorded deflections. TABLE \2.^Miscellaneous data Observatory: Cheltenham Date: Dec. 31, 1951 D variometer (a) Declination is West. (bj D spot moves up on the magnetogram for numerical increase in declination. B variometer (c) N end of H recording magnet is toward the East. (d) H spot moves up on the magnetogram for numerical increase in horizontal intensitv. Z variometer (e) N end of Z magnet is toward the North. (f) Absolute value of vertical intensity is positive ( + ). (g; Z spot moves up on tne magnetogram for numerical increase in vertical intensity. 146 MAGNETIC OBSERVATORY MANUAL [Ch. TABLE 13. — Orientation of variometer magnets LINE D Variometer West Declination East Declination 1 2 3 4 When N end of deflector is toward.. . The field of the deflector at the D variometer is directed If the D spot moves in the direction of The N end of the recording magnet lies in Magnetic north Magnetic north Magnetic north Magnetic north (a) Increasing West!) (b) Decreasing West 2) (c) Increasing East D (d) Decreasing EastD NE quad- rant NW quad- rant NW quad- rant NE quad- rant 5 H Variometer N end of recording magnet east N end of recording magnet west 6 7 8 9 When N end of deflector is toward.. . The field of the deflector at the H variometer is directed Magnetic west Magnetic west Magnetic east Magnetic east If the i^spot moves in the direction of Increasing H Decreasing H Increasing H Decreasing H The N end of the recording magnet SE quad- rant NE quad- rant NW quad- rant SW quad- rant 10 Z Variometer N end of recording magnet north N end of recording magnet south 11 When N end of deflector is toward.. . Magnetic north Magnetic north 12 The field of the deflector at the Z variometer is directed ... . - Magnetic north Magnetic north 13 If the Z spot moves in the direction of numerically Increasing Z Decreasing Z Increasing Z Decreasing Z 14 In North magnetic latitudes, the N end of the recording magnet is Too high Too low Too low Too high 15 In South magnetic latitudes, the N end of the recording magnet is Too low Too high Too high Too low 364. The D recording magnet can be brought into correct orienta- tion by sHght adjustment of its corrector magnet (see par. 381, p. 152). If a corrector magnet is used the E^ angle should not exceed 20'; if a corrector magnet is not used, an E^ angle up to 1° may be per- mitted. In any event, when acceptable orientation of the D magnet is achieved, if the D ordinate on the magnetogram is not correct (too large, too small, or even negative in sign), it will be necessary to adjust the D magnet relative to the mirror frame, in the manner described in paragraph 377, page 150. Recording of orientation deflections must, of course, be repeated after any mechanical adjust- ments are made. 365. In like manner the H and Z recording magnets may be adjusted to correct orientation by slight adjustments of the tem- perature-compensating magnets. In the case of H, for example: Let £'a:=l°, L (recording distance) = 1200 mm, and A7i=change in ordinate corresponding to 1° change in orientation. Then and tan E^=2Z A7i=0.0175X2400=42 mm. 12.] ORIENTATION 147 If the H scale value is 5.07/mm, this would be equivalent to a change of 21O7 in the field of the temperature-compensating magnet, an amount which would not appreciably affect the temperature coefficient of the variometer. In like manner the change of ordinate of the Z trace corresponding to an angular motion of the Z magnet may be computed. After proper orientation of the recording magnets is obtained, if the H or Z ordinates on the magnetogram are too large, or are negative, it will be necessary to adjust the recording mirror without changing the orientation of the magnet — for H, by turning the magnet relative to the mirror; for Z, by rotating the whole variom- eter and then readjusting the base line mirror, or by adjusting the prisms if the variometer provides for such adjustment. 366. In ordinary routine operation, readjustments of a recording magnet should not be made without the prior approval of the adminis- trative authority responsible for the processing of the results. CHAPTER 13. DIRECTIONS FOR INSTALLING A MAGNETOGRAPH PRELIMINARY STEPS 367. The variation room, — These directions apply to the instal- lation of a complete magnetograph, in which the instruments are arranged as shown in figure 13 and schematically in figure 85. It is assumed that the absolute values of D, H, and Z on the observing piers in the absolute observatory are practically identical with the respective values on the variation-room pier; that the magnetograph pier and scale-value and orientation shelves and guides have been con- structed in accordance with the general specifications in chapter 3; and that a line with known bearing has been established and perma- nently marked on the walls of the variation room. 368. Comparison observations. — If there is any doubt about magnetic materials having been introduced into the piers or the structural parts of the buildings, compare the values of D and H on the variometer pier and the piers in the absolute observatory by making one or two sets of horizontal intensity with a magnetometer or a Quartz Horizontal Magnetometer and at least two sets of decli- nation with a magnetometer or a compass declinometer at both sites. Differences of more than a few minutes in declination or 5O7 in horizontal intensity should not be tolerated. 369. Constants of component par ^s.— Prepare or have on hand several D and H quartz fibers, calibrated and mounted as explained in chapter 6. Determine the dimensions and magnetic moments of all of the magnets to be used with the variometers. The magnetic moments may be determined by deflections, using a magnetometer, at a place where H is known. Label these magnets by number and by magnetic moments for future use. Determine the temperature coefficients of magnetic moment of the H and Z recording magnets and of the temperature compensating magnets for the H and Z variometers for use in the computations which follow, or use the temperature coefficients furnished with the magnets. 370. Record all available data on the appropriate lines in tables 14, 15, 16, and 17, as the work progresses. 371. Calculate the approximate distances at which the temperature compensating magnets for the H and Z variometers should be placed on these variometers for effective temperature compensation, and mount the magnets at those distances on their respective variometers. The H temperature magnet should be mounted with its N end to the south and the Z temperature magnet with its N end up in north mag- netic latitudes and with its A^ end down in south magnetic latitudes. 372. Test of the optical system, — Set up the three variometers, the recorder, time flasher, and thermograph at the approximate posi- tions they will occupy in routine operation of the magnetograph. See that the recording magnets are in the instruments and that the A^'end of the Z recording magnet is to the north; also that the temperature magnets and sensitivity magnets are attached to their deflection bars 148 INSTALLING A MAGNETOGRAPH 149 or holders in approximately the same positions and orientations in which they will be operated later. Details regarding the methods of leriving this information may be foimd in the chapter on temperature '^efficients and in paragraphs 387, 390, 393, 394, and 401 of this chapter. Adjust the D recording distance to 174 cm (D lens to record- ing drum) and adjust the D base-line spot to the desired ordinate on 5 Pq S 3 1 g CONCRETE WALL -=f m } « I CONCRETE BLOCKS 4=' 3=J I I I i 4 t-^^^'i C CONCRETE BLOCKS the drum. In like manner adjust the H and Z recording distances so that the fl' base-line spot and the Z base-line spot are in good focus on the drum, axes of all variometer lenses approximately perpendicular to the face of the recorder. See that the Z base line is not eclipsed by the D or H v^ariometers when the Z variometer is rotated on its vertical axis for the full aperture of the recorder window. In like manner see that the D base line is not eclipsed by the H variometer. Using marble 150 MAGNETIC OBSERVATORY MANUAL [Ch. blocks or nonmagnetic metal spacers, adjust the heights of all of the variometers so that the centers of all lenses are in the same horizontal plane as the axis of the recorder when all instruments are resting on their footplates and when each foot screw is approximately at the middle of its run. Also adjust the axis of the cylindrical lens to this same elevation. Mark on the pier top the positions of the three vari- ometers and then take the H and Z instruments several meters away from the pier. INSTALLING THE D VARIOMETER 373. Removal of torsion. — Consult the nomogram, figure 140, appendix VI, and select a D fiber and D magnet combination that will give a D scale value close to one minute per millimeter at a re- cording distance of approximately 174 cm. Make preliminary vis- ual tests for the torsion factor. Level the instrument and install the D fiber and the mirror frame without the D magnet but with a small torsion weight attached. Adjust the torsion head in azimuth and the mirror in inclination until the regular D spot (from the central mirror if a triple-faced mirror is used) falls at the desired ordinate when the suspended system is centered in the magnet chamber and is at rest. Clamp the torsion head in this position and set the fiber clamp. Remove the mirror frame from the hooks, then replace it, release the fiber clamp, and allow the system to come to rest. If the D spot comes to rest at approximately the same ordinate as before, the mirror frame is in good adjustment and probably hanging evenly on both hooks. Always set the fiber clamp before removing or replacing the mirror frame. 374. Record the torsion-head reading, Rq, when the torsion- weight axis is approximately in the magnetic meridian and the regular D spot is at the desired ordinate. Record also the position of the D spot on the recording-box scale, figure 86. Call this original scale reading Uq. Clamp the fiber. 375. Replace the torsion weight with the D magnet, N end to the north. Release the fiber clamp; carefully raise the damping chamber around the magnet. See that the magnet is weU centered within the damping chamber by slight adjustment of the level of the instrument. Test the damping by deflecting the magnet and allowing it to come to rest. The system should be so adjusted that it will be somewhat underdamped. If the regular D spot comes to rest within 10 mm of the original scale reading, Uq, the D magnet is practically in the mag- netic meridian and there is little or no torsion in the fiber. 376. If the D spot does not come to rest within 10 mm of the original scale reading, no, the magnet is not properly oriented with respect to the mirror, the mirror frame is not properly suspended on the hooks, magnetic conditions are not quiet, or there may be some magnetic material near the instrument. Observe the spot for several minutes. If magnetic conditions are not quiet, postpone operations. If magnetic conditions are quiet, remove the mirror frame and readjust the magnet in azimuth relative to the frame and test again. Repeat this operation until satisfactory^ adjustment has been obtained. If available, use the mirror-adjusting apparatus described below for adjusting the magnet relative to the frame. 377. Mirror-adjusting apparatus, — This apparatus, figure 87, is used for turning the mirror frame and the attached mirror through 13. INSTALLING A MAGNETOGRAPH 151 a small angle relative to the magnetic axis of the recording magnet. The lenses have focal lengths equal, respectively, to those on the H and D variometers. The whole apparatus is mounted on a non- magnetic laboratory stand. To turn the mirror through a small angle relative to the magnet, proceed as follows: Place the stand on the variometer pier so that the longer focus lens is parallel to and at the same height as the D lens, also at the same distance from the recorder. Clamp the magnet so that the frame stands vertically and the triple- Figure 86. — Magnetograph recorder showing scale on front of cylindrical-lens window. face mirror faces the lens. Find the image of the lamp filament as reflected from the regular mirror and adjust the stand in azimuth and the apparatus in elevation until the image of the regular D spot falls on the recorder scale. Then by means of a long adjusting pin, turn the mirror frame in azimuth until the image has moved through the desired change of ordinate. 378. Adjust the D base-line mirror to correct position in azimuth and elevation so that the D spot has an ordinate of about 20 mm and so that numerically increasing ordinate corresponds to increasing magnetic declination. Note that in some cases it may be necessary to have the D base line above the D trace in order to accomplish this. 379. Establish the magnetic meridian through the D variometer, adjust the guides of the orientation bench for D, and make orientation tests as described in chapter 12. Record the observations as in figure 84. 380. Measurement of stray east fields. — When magnetic condi- tions are reasonably quiet, record D and the D base line photograph- ically for one hour. Close the recorder window and quickl}^ replace the H and Z variometers in their correct positions on the pier with temperature magnets, sensitivity^ magnets, and recording magnets all in place, as described in paragraph 371 . Cover the H and Z lenses 152 MAGNETIC OBSEKVATORY MANUAL [Ch. with paper screens. The D spot may be deflected away from its original position, Uq, because of the resultant east (or west) com- ponent, Je, of the fields of the magnets of the H and Z variometers. Record D and the D base line photographically for 30 minutes. Close the recorder window. Develop the magnetogram and scale the change in ordinate, A?i, of the D spot due to the resultant field, /^, at D. Then fE={^n)Sl. (345) Compute Je, noting the sign. It may be as large as ±1507. 381. The D corrector. — If the deflection, An, is large, attach a short deflection bar to the D variometer on the side nearer the Z variometer, axis of the bar in the magnetic prime vertical through D. Attach the D corrector to this bar and adjust the deflection distance until the D spot returns to its original position, Uq, on the scale of the recorder; that is, make An=0. AD corrector having a magnetic moment of 5 cgs units at a distance of 20 to 25 cm would furnish the required compensating field at D. If the field, /e, deflects the D spot only a few mm, the D corrector is unnecessary, since an exmeridian angle this small would introduce no appreciable error in the recorded changes in declination. 382. Determine the torsion factor, tt^; by turning the torsion head 30° clockwise, then 60° counterclockwise (that is, 30° counter- clockwise from its original position), then 30° clockwise. Record the torsion-head readings and the corresponding ordinates of the D spot. Record photographically or observe the ordinates of the D spot on a paper millimeter scale attached to the drum. TABLE 14. — D variometer; miscellaneous data Observatoey Variometer: Cheltenham, Md. Date: December 12, 1948 Schulze No. XI Observer: J. Q. P. Line Symbol Items Examples 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 c b I f c H+C H L f R e M. Ma T SECTION I, the optical SCALE VALUE 9 mm 2 3 3 mm 1.006 183007 +1007 1.005 1739 mm 1.011 1748 mm 1747 mm 0.000 2862 8. 8 cgs 5. cgs West Factor in equation (91); plane side of J) lens out Thickness of D lens at center. Estimated torsion factor (or derived from preliminary visual tests) . . . Horizontal intensity Estimated north field or caculated (see appendix V) Estimated distance, D lens to drum, for imit scale value, equation (132). Torsion factor, mea''ured; see Section IV below Calculated from equation (132) using new torsion factor Optical scale value, — , in radians per mm ... 2R SECTION n. variometer MAGNETS Magnetic moment of D recording magnet (Alnico II; cylindrical; 2 by 10 mm). Magnetic moment of D corrector (Alnico II; 2 by 10 mm) 13.] INSTALLING A MAGNETOGRAPH 153 TABLE 14. — D variometer; miscellaneous data — Continued Line Symbol Items Examples 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 I d I- k' k' f n h h f-h f f-h C H H+C H no ni An 'A- So' Soy D H 7 DR-D D-Dr e Li «i no n n— no 50 s s—so h f f-h f f-h h f-h SECTION III. QUARTZ FIBER Effective length of fiber 15 cm 0. 0017 cm 63 sec 0. 0155 0. 0182 0.0181 -I-IOO7 183007 1.005 47.5 60.0 12.5 667 7O7 1.000 5.32 0.1 mm 0.0 0.0 187. 1 mm 186. 2 mm 0. 000 2862 1000 mm 0. 000 500 Diameter of fiber; several measurements uniformly spaced ; calculated diameter as described in paragraph 188. Period of system with torsion weight, 7=1.83, attached _ Torsion constant from dimensions; from equation (148) . . Torsion constant from period; from equation (150) Torsion constant from torsion tests; from equation (151) SECTION IV. TORSION OBSERVATIONS; SENSITIVE VARIOMETER Torsion head readings 30° right 30° left Angular motion of torsion head 1800' 3600' 1800' Ordinate of the D spot 42. 2 62. 1 22. 1 42. 2 Displacement of the Z> spot 19.9' 40.0' 20.1' Mean h for/=1800' 20.0' Twist in the fiber 1780.0' Torsion factor _ _ . . , _ .1.011 SECTION V. FIELD FACTOR Resultant N or S field at D magnet due to stray fields Mean value of H at the variometer pier Field factor; equation (111).. ..... SECTION VI. EAST FIELD AT D VARIOMETER D ordinate on magnetogram, H and Z variometers in place Change in Z) ordinate due to resultant east field, /b . East field from equation (345) East field, calculated from equations in appendix V (Item 42 is op- tional) . SECTION VII. COMPUTATION OF D SCALE VALUE From equation (122); minute scale value. . .... From equation (301); gamma scale value SECTION Vm. PARALLAX TESTS Correction in mm between time line and Z> spot... Correction in mm between time line and H spot Correction in mm between time line and Zspot SECTION IX. RESERVE DISTANCES Distance in mm on magnetogram, regular spot to upper reserve Distance in mm on magnetogram, regular spot to lower reserve SECTION X. LOW-SENSITIVITY VARIOMETER; TORSION TESTS Optical scale value, D variometer (from line 13). Recording distance, auxiliary scale D ordinate, no torsion in fiber . 46.0 46.0 D ordinate, magnet deflected by torsion 116.6 188.2 Change of D ordinate 70. 6 142. 2 Auxiliary scale reading, no torsion 1.5 1.5 Auxiliary scale reading, magnet deflected by 52. 1 103. 3 torsion. Change in scale reading 50.6 101.8 Angular motion in radians of the D magnet = 0.0202 0.0407 «(n-no). Angular motion in radians of torsion head= 0.0253 0.0509 ei (s-so). Torsion in the fiber 0. 0051 0. 0102 Torsion factor . ... ... 4.96 4.99 Mean torsion factor.. 4. 98 3.96 3.99 383. Adjust the time flasher apparatus in elevation until there is no parallax between the D spot and the time line. The parallax may be examined visually while the D spot and the time flasher lamp are activated simultaneously. 210111—53- -11 154 MAGNETIC OBSERVATORY MANUAL [Ch. 384. Computation of the effective D scale value, — Compute the D scale value (minute scale value) from equation (122) having regard for the direction (sign) and magnitude of the (7 field (see app. V) H-\-C in the factor — yy— • If (7 is directed to magnetic north it is positive (+) ; if directed to magnetic south it is negative (— ) . If the calculated D scale value is (1.000 ±0.002) minutes per mm, the installation of the D variometer may be considered satisfactory in this respect. If the scale value differs from unity by more than 2 parts in 1000, adjust the D recording distance by moving the recorder directly away from, or toward, the D variometer by the required amount. For example: Suppose the effective recording distance is 1720 mm, and the D scale value, calculated from equation (122), is 1.005. Then the distance should be increased approximately 0.005 X 1720 = 9 mm. In that case move the recorder away from the D variometer 9 mm. Check this distance by direct measurement. 385. If the recorder has been moved as above, repeat torsion obser- vations, recording several tests photographically, at the new recording distance; then make a final computation of the D scale value using the new torsion factor, the new effective recording distance, and the field factor. Calculate also the gamma scale value from equation (301). INSTALLING THE H VARIOMETER 386. Torsion and compensation, — These directions apply to H variometers designed for magnetic temperature compensation. Ob- servations for the torsion constant, k', of the H fiber are highly de- sirable though not strictly necessary. 387. Examine the H nomogram, figure 141, appendix VI. Select a combination of size of fiber, magnetic moment, Ms, of the recording magnet, and a suitable sensitivity control magnet. Determine and record all of the constants and miscellaneous data for the H variometer as outlined in table 15 as the work progresses. 388. Kemove all magnets from the variometer, install the H fiber, and remove torsion as for the D variometer. Adjust the damping chamber for proper damping as described in paragraph 375 for a D variometer, and then make tests for residual torsion as described in the same place. Adjust the mirror face (central mirror if a triple- face mirror is used) approximately parallel to the axis of the torsion weight as for a D variometer, and then adjust the torsion head until the H spot falls near the center of the recording drum when the system is at rest and the axis of the torsion weight is in the magnetic meridian through H, as judged by eye. Note the scale reading on the recorder scale, or on a paper millimeter scale attached to the drum. Replace the torsion weight with the selected H recording magnet and allow the system to come to rest. Note the position of the H spot. If it is close to Tio the H magnet is in the magnetic meridian with practically no torsion in the fiber. If not in the magnetic meridian within 2°, readjust the magnet relative to the frame by use of the mirror adjust- ing apparatus, figure 87. When this apparatus is used with the H variometer the shorter focus lens should be installed. Continue adjustments until the H spot falls near the original ordinate, Uq, with no torsion in the fiber, magnetic conditions quiet, and no appreciable stray fields. Read the torsion head. This is Rq, table 16. Deter- 13. INSTALLING A MAGNETOGRAPH TABLE 15. — H Variometer; miscellaneous data 155 Observatory Variometer: : Cheltenham, Md. Date: December 14, 1948 Toepfer No. XII Observer: J. H. D. LINE SYMBOL items EXAMPLES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 L t M, Ma Ma 'A Sh* qi Qi Qi Qh ^q = S'(/ = H C/H~ C T\ ro I d I- k' k' k' k' n 2uh Sh* An ASh* An L f U «i no n n—m so s s-so ft ,u f f-h h f-h HR-H H-Hh section I. OPTICAL SCALE VALUE 1180 mm 0.000 424 5.0 cgs 78.5 cgs 50.0 cgs -0.0677 1.52 2.66 0.000 50 0.000 48 0.000 06 0.000 16 0.000 66 0.001 20 0.183 cgs -0.55 -0.101 11.58 cm 11.63 cm 15.0 cm 0.0040 10.5 0.474 0.655 0.641 0.652 0.655 1180 0.000 424 1000 0.000 500 15.0 112.2 97.2 0.2 200.2 200.0 0.0412 0.1000 0.0588 1.70 1.70 0.70 182.0 181.5 Approximate optical scale value — radians per mm SECTION II. VARIOMETER MAGNETS Magnetic moment of H recording magnet (Alnico II; cylindrical; 2 X 10 mm). Magnetic moment of H temperature magnet (Alnico II; cylindrical; 5x 25 mm). Magnetic moment of sensitivity magnet (Alnico II; cylindrical; 5 X 25 mm). Field of sensitivity magnet at 11.4 cm; A^ end west -. Distribution coefficient (temperature and recording magnets) SECTION III. TEMPERATURE COEFFICIENTS Temperature coefficient of H recording magnet Temperature coefficient of temperature-compensation magnet 3 times the coefficient of thermal (linear) expansion of the bar Temperature coefficient of the torsion constant of the quartz fiber qi-\-qi (see equation 251) 9l+?2+?3+95 - ------ - - Temperature coefficient of the i/ variometer (from equation 249) Temperature coefficient of the H variometer (by test) SECTION IV. TEMPERATURE COMPENSATION Ratio of compensation field to H (from equation 253) Estimated correct distance for temperature magnet (equation (346))-- Calculated distance for temperature magnet (from equation (347)) SECTION V. QUARTZ FIBER Effective length of the fiber Diameter of fiber; give several measurements at uniformly spaced intervals. Calculate mean as explained in par. 188. Torsion constant (approximate) from dimensions (equation (148))..-- Torsion constant from torsion observations (equation (151)) Torsion constant from scale value observations (equations (153) and (154)). SECTION VI. a FACTOR DETERMINATIONS Ordinate of undeflected spot in mm —37. 8 +15. 75. 6 Double deflection of H spot in mm 135. 5 130. 4 126. 1 Observed ii" scale value in 7/mm 2. 56 2. 66 2. 75 Increment in /i scale value 0.10 0.09 a factor in 7/nim/mm 0.0019 0.0015 Mean 0.0017 SECTION VII. TORSION OBSERVATIONS (OPTIONAL) Recording distance, H variometer, in mm Recording distance, auxiliary scale, in mm Optical scale value, auxiliary scale //ordinate, magnet deflected by torsion Scale reading, no torsion in fiber Change in scale reading Angular motion, in radians, of torsion head, «i(5— so) Torsion in the fiber Mean torsion factor SECTION Vm. RESERVE DISTANCES Distance in mm on magnetogram, regular spot to upper reserve Distance in mm on magnetogram, regular spot to lower reserve 156 MAGNETIC OBSERVATORY MANUAL [Ch. mine the torsion factor by the method described for low-sensitivity variometers, paragraph 417. Adjust the H base-Une spot so that increasing H ordinate corresponds to increasing horizontal intensity and so that there may be few negative ordinates on quiet days. Test the H spot for parallax. If the amount is appreciable, reduce it by raising or lowering vertically the entire H variometer (see par. 176). If this adjustment results in reflecting the recording spot too high or too low in relation to the cylindrical lens of the recorder, the variom- eter mirror must be tilted slightly by adjusting the mirror screws, or by bending the mirror frame in older instruments. Figure 87.— Mirror-adjusting apparatus, for adjusting mirror relative to recording magnet. TABLE 16.— i^ variometer, torsion in the fiber Figure Estimated torsion (t) C field Magnet (6) m Torsion-head circle R=Ro+e+r Remarks about M. 88(a) 88(b) 88(c) o ro = ri=145 r2 = 65 7 10100 o 90 90 o 75 75 75 o 7?o = 75 7?i = 310 /?2 = 230 N end N. A^ end E. A^ end E. 389. Calculate the torsion constant, k\ of the H fiber from its dimensions (eq. 148) ; from the period observations (eq. 150) ; from torsion observations (eq. 151); and from scale-value observations (eq. 153 and 154). Compare the results. The torsion constant determined from oscillations is quite likely the most reliable. 390. Calculate the factor, -^; from equation (250) or (253), or esti- mate its value from table 10 (p. 117), and then compute C, the value of the compensating field necessary to make the temperature coefficient, 13.] INSTALLING A MAGNETOGRAPH 157 Qh, of the variometer equal to zero. From the nomogram, figure 137, appendix VI, estimate the magnetic moment of a temperature compensation magnet that will provide the required C field at a distance, ri = 12 cm, along its magnetic axis produced, and select a magnet of this approximate moment. Assuming P^ = 0, calculate the approximate value, ri, for the temperature-compensation magnet from the relation, =[!^»]'- (346) Calculate the distribution coefficient. Pa, from the dimensions of the magnets or estimate its value from table 21a, and then the distribution P factor, \-\ — Y' Finally, calculate the more precise value, ro, from the relation Tq [l+^]*- (347) 391. Uncompensated H variometer, — Clamp the fiber, remove the mirror frame, and turn the magnet until its long axis is approxi- mately perpendicular to the regular mirror face, N end to the rear of the mirror face. Suspend the mirror frame and turn the torsion head clockwise,- looking down, until the magnet is in the magnetic prime vertical as estimated by eye. If the H spot does not fall at the de- sired ordinate repeat the adjustment of the magnet relative to the frame until satisfactory. Use the mirror adjusting apparatus for this operation. Preliminary orientation tests may be made at this point if desired. If these tests indicate that the H magnet is closely in the prime vertical (say within one degree), and the H spot is at the desired ordinate, the variometer is adjusted for routine operation but it is uncompensated for temperature. The torsion-head reading is E^, table 16. 392. Compensated H variometer, — Attach a variometer deflec- tion bar to the north or south side of the variometer parallel to the magnetic meridian and set the temperature-compensation magnet (center of magnet) at the calculated correct distance, Vq, to give the required C field to make Qh=^. A more uniform C field may be obtained by using two temperature-compensation magnets as shown in figure 88 (c). In this case the deflection distances should be equal so that each magnet provides half of the C fleld. The A^ end of the compensation magnet should be to the south to make C negative. Reduce the torsion in the fiber by turning the torsion head counter- clockwise, looking down, until the H spot comes to rest at the desired ordinate, tiq, making allowance for possible change of H during the interval. Observe the torsion head reading, i?2- The variometer is now compensated for temperature. The example given in table 16 is shown graphically in figure 88. Make orientation observations as described in chapter 12. 393. Adjustment of the sensitivity- control magnet, — If the scale value is too high or too low, attach a variometer deflection bar to the H variometer on the side near the recorder. Note the scale reading of the H spot. Mount a sensitivity magnet on the bar with its A^ end toward the variometer, say in this case A^ end west, and 158 MAGNETIC OBSERVATORY MANUAL [Ch. then move it slowly along the bar toward Ms until r is about 10 cm. If Ms shows no appreciable deflection during this operation, the bar is closely parallel to Ms and the sensitivity magnet remains practically parallel to Ms throughout the range of r. If Mg is deflected through an appreciable angle for small changes of r, it signifies maladjustment of Ms, or of the bar, or that the axis of Ma is not parallel to the bar or to Ms. 394. Determine the H scale value by deflections with no sensitivity magnet attached to the variometer bar and for several equally spaced positions along the bar, first with the A'' end of Ma to the west and then with the AT^ end to the east, noting the away positions of the H 310 255" (a) 0) Figure 88. — Torsion in H variometer fiber: (a) 75°, line of no torsion; (b) uncompensated H variometer; (c) variometer with two temperature compensation magnets. spot before and after each setting of Ma. When Ma is directed the same as Ms the scale value is increased (sensitivity diminished) and when it is directed opposite to Ms the scale value is decreased (sensi- tivity increased). Plot a curve showing variation of scale value with r. (See ^g. 63.) From this graph estimate the correct distance at which Ma should be placed to give the desired scale value. If the H spot is not at the desired ordinate (within a few mm) adjust the tem- perature magnet by a very small distance, just sufficient to bring the H spot to the desired ordinate. (See par. 301 regarding the effect of this adjustment on the temperature coefficient of the variometer.) Some sensitivity-magnet holders are equipped with a slow-motion de- vice for making fine adjustments of the sensitivity magnet. De- termine the scale value again and if satisfactory, clamp the control magnets in place. Note: For most precise work the observations with the sensitivity magnet in different positions should be made with the away position of iheH spot the same for all cases, since the scale value varies with ordinate. However, since these observations are made for the purpose of simplifying the process of adjustment of the sensitivity magnet, the change of scale value with ordinate may be ignored for that particular operation. 395. Computation of the Je field (optional), — Compute the /^ field from equation (11), omitting a distribution factor, and then compute the scale value from equation (144) and compare the result with the observed value. 13.] INSTALLING A MAGNETOGRAPH 159 396. Experimental determination of the a factor. — Change the H ordinate by 50 to 75 mm by deflecting the //recording magnet by means of a large (auxihary) deflector placed in the magnetic meridian on the opposite side of the variometer from the scale value shelf. The deflection distance should be quite large, say 2 or 3 meters. Make scale-value observations at this ordinate. Reverse the auxiliary deflector and repeat the scale-value deflections at low ordinate. The difference in the scale values divided by the difference in away ordi- nate, in mm, is the a factor. Some experimental determinations of the a factor are given in section VI of table 15. 397. Damping, — Adjust the damping chamber in elevation relative to the H magnet so that the system is rather highly damped but not critically so. INSTALLING THE Z VARIOMETER 398. Preliminary work, — The directions in this section apply to vertical-intensity variometers equipped with assembled recording- magnet systems (Schmidt type) as distinguished from those made from one piece of steel (la Cour type). 399. Instrumental data, — From table 11, page 134, select a scale value at which the variometer should be operated. Determine and record as in table 17 all of the constants and pertinent instru- mental data, as the work progresses. C 400. From table 10 estimate the value of -^; or estimate the value of this ratio from the g coefficients, and then calculate C, the required vertical field to be applied opposite to Z, for effective temperature compensation. 401. From the nomogram, figure 137, appendix VI, estimate the magnetic moment of a temperature-compensation magnet that will provide the required C field at a distance, fi, along its axis for r^ equal to approximately 13 cm. Select a magnet that has approximately^ this moment. 402. Determine the magnetic moment, il/j, of the recording magne-t by deflections on a magnetometer at a place where H is known. 403. Unless such data are furnished with the instrument, determine the temperature coefficients of the magnetic moments of Ma and M^ C and calculate more precise values of -y and C. 404. From the equation ri^= — -^^ calculate the approximate value P Q of Ti and then allowing for a distribution factor, l-\ — f +^j calculate l-\ — ^+-^ )^; with due regard for the signs 'of Pa and Qa. This value, ro, is the dis- tance at which the temperature magnet, Ala, must be set vertically above or below the center of Alg, N end of Ma up, to provide the nec- essary C field for effective compensation. For south magnetic lati- tudes the A^ end of Ma should be down. 160 MAGNETIC OBSERVATORY MANUAL TABLE 17. Z variometer: miscellaneous data [Ch. Observatory: Variometer Cheltenham, Md. Toepfer No. XIII Date: December 15, 1948 Observer R. X. R. Ms Ma Pa Qa (li Qi Oz Qz Sz ZR-Z Z-Zr 39 mi 40 rm 41 vn 42 mt 43 TOi 44 45 46 section I. OPTICAL SCALE VALUE Center of front of Zlens to Zspot on the magnetogram Optical scale value, — radians per mm SECTION II. VARIOMETER MAGNETS Magnetic moment of recording magnet (cobalt steel) Magnetic moment of temperature magnet (Alnico II) Magnetic moment of A?" sensitivity magnet (if used) Magnetic moment of S sensitivity magnet (if used) Length of recording magnet Length of temperature magnet Length of A'" sensitivity magnet (if used) Length of S sensitivity magnet (if used) Distribution coefficient, recording magnet and temperature magnet (from table 21a). Distribution coefficient, recording magnet and temperature magnet (from table 21a). SECTION HI. TEMPERATURE COEFFICIENTS Temperature coefficient of magnetic moment of recording magnet.. Temperature coefficient of magnetic moment of temperature magnet 3 times the coefficient of thermal (linear) expansion of the bar Temperature coefficient of mechanical couple (lever arm a) qi+qi qi+qi+Qi+qi Temperature coefficient of the variometer (calculated) (Eq. 233) . . . Temperature coefficient of the variometer from tests SECTION IV. TEMPERATURE COMPENSATION Vertical intensity at the Z variometer Ratio of required compensating field to vertical intensity (Eq. 238) Required compensating field to make Qz=0; C=— 0.507 Z Calculated approximate distance (see par. 404) assuming Pa=0 and Oa=0. Calculated distance (see par. 404) when Pa = -28 and Qa = +S20-- SECTION V. SCALE VALUE Z scale value from deflections, at average ordinate; 7/mm SECTION VI. RESERVE DISTANCES Distance in mm on magnetogram, regular spot to upper reserve spot Distance in mm on magnetogram, regular spot to lower reserve spot SECTION VII. SHRINKAGE Shrinkage gauge ; distance between points SECTION VIII. MISCELLANEOUS DATA (OPTIONAL) Mass of Z recording magnet including sensitivity poise but without balancing poises. Mass of sensitivity poise (without set screw) Mass of south latitude poise Mass of north latitude poise Mass of temperature poise Mass of assembled magnet system Pitch of sensitivity thread, ^^o-inch (nominal) Pitch of invar spindle thread, ^V inch (nominal) Pitch of temperature spindle thread 2322 mm 0.000 215 877 404 100 100 8.1 cm 3.5 cm 4.0 cm 4.0 cm -28 +320 0.000 34 0.000 28 0.000 06 0.000 01 0.000 35 0.000 69 0.538 cgs -0.507 -0.273 14.36 13.72 4.52 175.6 175.2 100.0 mm 37.55 grams 1.397 grams 2.396 grams 2.396 grams 2.921 grams 42.34 0.0638 cm 0.0397 cm 0.0397 cm 405. Installation and major adjustments. — Set up the Z vari- ometer at the Z position on the variometer pier and mount the tempera- ture magnet in its holder at the calculated distance Tq. This is the distance in cm from the center of Ma to the center of Ms, when Mj is in operating position. The center of Ms may be taken as the knife-edge 13.] INSTALLING A MAGNETOGRAPH 161 (or pivot) support. Level the instrument and adjust it in azimuth so that the axis of the Z lens is approximately normal to the drum. With a camel's-hair brush remove any dust particles from the recording mag- net, knife edges, bearings, and the damping chamber. Clean the opti- cal parts and the magnet with lens cloth. Set the sensitive poise quite low (large scale value), and the counterpoises at their midpositions. Place the magnet in its cradle and lower it carefully by means of the cradle mechanism so that the knife edge (or pivots) will take the load gently. Quite likely the magnet will not be balanced. Lift the mag- net by the cradle mechanism, adjust one or both counterpoises until the recording magnet remains horizontal (as estimated by eye) when it is resting on its bearings, N end to the north. Turn the whole variom- eter, slowly, 180° in azimuth so that the A^ end of Ms is to the south. At this azimuth, Ms is more sensitive. Rebalance if necessary, and continue these tests until the magnet remains practically horizontal (as estimated by eye) for any azimuth, N, E, S, or W. Finish the test with the A^ end to the north and with the Z spot at the desired ordinate. Readjust the Z base-line spot so that increasing Z ordinate corresponds to numerical increase of Z. 406. Examine the Z spot and time line, and if there is appreciable parallax between them, raise or lower the Z variometer until the parallax is negligible. 407. Determine the scale value by deflections. Raise the sensitivity poise several turns, rebalance if necessary by adjustment of a latitude poise so that the Z spot is at approximately the same ordinate as in the first test. Make scale-value deflections for this position of the sensi- tivity poise. By interpolation or extrapolation, estimate the number of turns of the sensitivity poise that will be necessary to produce the scale value desired. Make this adjustment, repeat scale-value deflec- tions, and continue this process until the deflections show that the proper sensitivity has been attained, say within 5 percent. (Note: By observing the period of the system for each position of the counter- poise and then plotting a curve of period or turns of counterpoise vs. double deflection or scale value, the value of a period which will cor- respond to a desired scale value or value of 2 Uz may be easily determined.)^ 408. Make orientation tests, and calculate the exlevel angle. If necessary, readjust the latitude poises to correct for a large exlevel angle. Small adjustments in level may be made by slight adjustments to the temperature-magnet distance. Continue orientation tests and adjust- ments until the exlevel angle is 1° or less. 409. Unless the variometer is provided with extra prisms or mirrors for independent adjustment of the ordinate of the Z spot, turn the vari- ometer in azimuth until the Z spot is at the desired ordinate for routine operation. Again adjust the Z base-line mirror so that increasing Z ordinate corresponds to numerically increasing vertical intensity and so there may be no negative ordinates on quiet days. 410. Repeat orientation tests and scale-value observations, record- ing final values as in figures 72 and 84. The variometer is now ad- justed for routine operation. 411. Final check, — Remove all tools and superfluous magnetic materials from the variation room. Examine all of the recording spots and the time line for parallax. Also, see that all of the spots are record- > H. E. McComb, The sensitivity of magnetic variometers, Terr. Mag., 33, 65, 1928. 162 MAGNETIC OBSERVATORY MANUAL [Ch. ing at the desired ordinates and positions on the magnetogram, when magnetic conditions are quiet. If the instruments seem to be operat- ing satisfactorily, attach the foot plates to the marble blocks or metal spacers with plaster of paris and attach the spacers or blocks to the pier in the same manner, exercising great care not to move the foot plates or blocks from their proper places. 412. Make scale-value deflections and orientation tests for all the variometers, recording all deflections photographically. 413. Report on the installation. — Furnish a complete, detailed report of the project including sketches that show all pertinent dimensions (see fig. 85 and fig. 131, page 211) and, if possible, a photograph of the complete magnetograph made ready for operation. LOW-SENSITIVITY MAGNETOGRAPHS 414. Object. — In high geomagnetic latitudes, where daily variations are large and the amplitudes of the recording spots may be very high during magnetic storms, variometers must be operated at low sensitivi- ties. Even in low latitudes, many observatories operate both high and low-sensitivity instruments to guard against loss of record during magnetic storms. 415. Procedure. — From table 11, determine the approximate scale values at which the variometers should be operated. Using the D nomogram, figure 140, appendix VI, select a combination of size of quartz fiber and magnetic moment of recording magnet that will give the desired D scale value. (The use of sensitivity-control magnets on a Z) variometer is not recommended.) Using the H nomogram, figure 141, appendix VI, select a combination of size of fiber and magnetic moment that will give the desired H scale value. A sensi- tivity-control magnet may be used if necessary for final adjustment to the desired value. The sensitivity of the Z recording magnet may be adjusted to any desired low value by means of the sensitivity poise. 416. In estimating the C fields for effective temperature compensa- tion of the H and Z variometers, and in measuring the magnetic moments of the temperature magnets and other magnets of the magnetograph, follow the same procedures used for sensitive vario- meters. 417. Auxiliary optical lever. — The torsion factors of large fibers may be determined as follows: With a piece of laboratory wax, mount a planoconvex mirror (fig. 45) centrally on the torsion head of the D variometer so that the reflecting surface is vertical. Set up a straight-filament incandescent lamp and a millimeter scale at the same elevation as the mirror and at the proper distance for sharp focus of the image. Using this optical lever as a means of estimating accurately the angular motion of the torsion head (in radians) , make torsion observations as described in paragraph 382, page 152. Record aU observations and data, as shown in table 15, section VII, for the sensitive H variometer. Calculate the torsion factor, . , ? H-\-C and the field factor, — yj^' ^^^ ^^^^ ^h® ^ scale value from equation (122). It is desirable, though not strictly necessary, to determine likewise the torsion factor for the H variometer. 13.] INSTALLING A MAGNETOGRAPH 163 418. Make orientation tests, scale-value observations, parallax tests, and all other adjustments in the manner prescribed for sensitive variometers except that the deflectors for scale-value and orientation deflections should have larger magnetic moments or should be used at shorter deflection distances. 419. Record all pertinent data as in tables 14, 15, 16, and 17. Furnish a complete report of the installation with sketches showing all pertinent dimensions as in figures 85 and 131, appendix V, and if possible, a photograph of the complete magnetograph as it will be operated. THE LA COUR MAGNETOGRAPH 420. Description of the instruments, — Complete descriptions of the instruments and directions for their installation are contained in publications of the Danish Meteorological Institute.^ Only a brief Figure 89. — La Cour vertical-intensity variometer equipped with sensitivity-control magnets, as operated at Honolulu Magnetic Observatory. summary will be given here. The general principles involved in the selection of quartz-fiber suspensions and magnets are similar to those outlined elsewhere in this manual. The use of adjustable prisms on the la Cour D and H variometers simplifies many of the problems of installation, such as adjustment of the azimuth and inclination of the rays reflected from the miiTors of the recording magnets. La Cour's method of attachment of fibers to the torsion-head stem and to the magnet mirror frame is indicated briefly in paragraph 179. The Z recording magnet, magnet mirror, and knife edges are fabricated from 2 La Cour, Danske Met. Inst. Pubs, (see items 8 and 11 of bibliography). 164 MAGNETIC OBSERVATORY MANUAL one piece of magnet steel. The magnet is ground, polished, and balanced by the manufacturer for a particular magnetic latitude and sensitivity. Final balancing and/or adjustment of the sensitivity may be accomplished at the observatory where it is to be operated, by the simple process of careful honing of the magnet with a fine-grained carborundum hone. To increase the sensitivity it is honed below the longitudinal axis of symmetry that is normal to the knife edges, and for balancing it is honed on one end. The knife edges are ground and polished to a definite small radius, and at the same time the two edges are made collinear by a simple and ingenious process. The polished steel mirror is on the upper side of the magnet, and an adjustable 90° prism mounted above the mirror affords a means of controlling the azimuth and inclination of the incident and reflected light. The magnet is balanced on a pair of agate cylinders and is in a sealed chamber which is partially evacuated. At the Honolulu Magnetic Observatory the la Cour Z variometer is equipped with a pair of sensitivity-control magnets (see fig. 89.) Its performance for a number of years has been quite satisfactory. 421. Optical compensation, — The 90° prisms on the H and Z variometers are mounted on bimetallic (silver-platinum) strips. As the temperature changes the strip bends, causing angular motion of the prism. By proper facing of the strip and adjustment of its length, the linear motion of the recording spot due to a change in temperature of the recording magnet (and the resulting change in its magnetic moment) may be just compensated by the angular motion of the 90° prism through which the incident and reflected rays pass. 422. Reserve spots, — By the use of a series of 90° prisms mounted in front of a straight-filament recorder lamp, two or more reserve images are produced for each variometer, as mentioned in paragraph 170, page 66. CHAPTER 14. PROCESSING OF DATA AT THE OBSERVATORY PROGRAM OF OBSERVATORY WORK 423. Routine duties. — After the observatory has been estabUshed and the magnetograph and other instruments are functioning satis- factorily, most of the regular magnetic work is of a routine nature. However, to carry on this routine and to achieve continuously the objectives for which the observatory has been established requires great care on the part of the observer in operating delicate instru- ments, considerable skill in the observing programs, and perseverance in keeping the routine work on a current basis. Some of the principal items are: (a) absolute observations for magnetic declination, usually with a magnetometer, (see fig. 90) ; (b) absolute observations for horizontal intensity with a magnetometer, sine galvanometer (fig. 37) , Quartz Horizontal Magnetometer (fig. 91), or other equally precise instrument; (c) absolute observations for inclination (dip) with an earth inductor (fig. 92), or (d) observations for vertical intensity with a standard magnetic field balance or Magnetometric Zero Balance (BMZ),^ or some equally precise instrument; (e) scale-value observa- tions; (f) time observations for comparison of chronometers and pendulum clocks; (g) changing the traces daily on the magnetograph recorder and developing the magnetograms ; (h) applying legends on the magnetograms (see fig. 93) ; (i) scaling of hourly ordinates of H, D, and Z, from the magnetograms (see fig. 100); (j) computations of absolute values of D, H, and / from absolute observations; (k) com- putations of D, H, and Z base lines; (1) estimation of character figures; (m) scaling of K indices; (n) tabulation of times of sudden commencements of magnetic storms, times of natural disturbances of the variometers (seismic or other) ; (o) solar flare studies; (p) observa- tions for orientation of variometer recording magnets; (q) operation of auxiliary magnetographs, such as low-sensitivity variometers, photoelectric magnetographs,^ etc.; (r) abstracting of pertinent records and monthly transmittal of data and magnetograms to the home office. 424. Conversion to absolute values, — In order to determine the absolute value of D, H, or Z for any moment from the magnetogram it is necessary to know: (a) the base-line value, that is, the absolute value of the element when its trace and base line coincide; (b) the scale value ; and (c) in the case of H and Z, the temperature coefficient of the variometer. Let d, h, and z denote the ordinates in mm at the temperature t, corrected for shrinkage of the magnetogram (increasing ordinates corresponding to increasing D, H, and Z). Let Sd\ Sh, and ' La Coiir, Danske Met. Inst. Pub. 19 (see item 10 of bibliography). 2 R. E. Gebhardt, T. J. Hickley, and T. L. Skillman, A photoelectric magnetograph, Trans. Amer. Geoph. Union, 32, 322, 1951 (abstract only). This arrangement is illustrated in figure 94. 165 166 MAGNETIC OBSERVATORY MANUAL [Ch. Figure 90.- Observatory magnetometer (Ruskatype) with telescope having modified Gaussian eyepiece. Sz represent the scale values of the D, H, and Z traces respectivelv, and let i^ J; *So=the base-line scale value for H; a=the a factor for H; SH=So-\-i a h (see par. 259); ^o=the standard temperature, usually 20° C. 14.1 PROCESSING DATA 167 a Figure 91.— Quartz Horizontal Magnetometer (QHM) mounted on a special base with divided circle and verniers. Finally, Qh and Qz are the temperature coefficients of the H and Z variometers (par. 288) ; and Bd, Bm, and Bzo are the base-line values for D, H, and Z (in the case of H and Z, reduced to the standard temperature ^o). Then D=Bj,+Sn'd =B^o + {So + iah)h+QH(t--to) Z=:Bzo+SzZ + Qz(t-to). (348) (349) (350) (351) 168 MAGNETIC OBSERVATOEY MANUAL [Ch. 14.] PROCESSING DATA 169 ^ ^-^ 2 N N 510H1— 53- 12 170 MAGNETIC OBSERVATORY MANUAL [Ch. Figure 94.— Special light source and photoelectric ce.. ^^d „.»h » h^ visual-recording magnetograph. ll'^^J.ftOll'J =r for 425. Base-line values, — For the determination of base-line values, absolute observations are made at least once a week. From an inspection of the above formulas it will be seen that if the ordinates d, h, and z be read for the times at which absolute observations have been made, the base-line values may be computed, provided the scale values and the temperature coefficients are known. Generally the absolute value of the vertical intensity must be computed, however, from values of H and /. It is, in general, not feasible to make simul- taneous absolute observations of H and /, but the value of H at the time of the absolute observations of dip may be determined from the magnetogram after a preliminary H base-line value has been com- i A 14.] PROCESSING DATA 171 DEPARTMENT OF COMMERCE ' U. S. COAST AND CEODCTIC SURVa Form No. 3«7 Ed. July 1048 Magnetic Observatory ..S9M.?.91t.JM?JA. JAIf.r..J.SliP:. (Month) (Ymt) DECLINATION BASE-LINE VALUE Maineto^raph MCMNMGM Magnetometer Xo ?3.. Date .A5g. M. Mian SCAUNO • Computed OBDlNATKt OsaCBTED D Basb-une Valob Observer Remabes Jan 3 -f. mm. 11,6 11,4 39 U.5 2g 03.: VAT 3 3 3 "-4 o8.8 o8.8 12. 1 _o8,6 o8,6 i6.o 12.1 11.8 03.9 03:5 03.2 ..JAL. _JLC_ MLC 8 "it 11,3 11, 1 14.9 03.8 MLC 8 -?| 13-5 13' s 17.4 04.2 MLC 8 >3?l og.g og,n 13.6 03.9 7AT 8 '4^ og.8 og, 6 13.1 04.1 7AT ~ Mean ^.9.03:1 ♦Corrected for shrinkage to ...1?.?.. :?.... mm. t Assigned scale value = 0.«..9.9- '/mm. at zero shrinkage. Scaled bv Y.J...Thomas Checked by .LL.Q.h.V.^J}.... Computed by f.A.T. Checked by ...K..k..Q. Abstracted by ...H...k.^.. u. s. eovMNHCNT miNTiNS orricc 1»— 50307-1 Figure 95.— Declination base-line computations. puted from equation (355). Z is computed from this value of H and the observed / by the relation Z=H tan /. (352) 172 Department of commerce u. s. coast and geodetic survey Form No. 368 Ed. Oct. 1042 MAGNETIC OBSERVATORY MANUAL [Ch. Magnetic Observatorij .TUCSM,...ARIZOIfA... Sept 1951 (Month) (Year) HORIZONTAL INTENSITY BASE-LINE VALUE Madnetodraph }.9. 9.9.V:V. Magnetometer ^o 3^. ... -2 V CO H O 0) =5S Date 4 1 4 i 11 i 05. M. TIME Mean Time ^rKAN Scaling Time Mean Begin End SCAUNG mm. Becin A. m.^ ..13.38 End h. 171. i.a.45.. Bigiu End SCAI.INO Oscill. E ft. m. .09.30.. ft. m. .09.57.. mm, 21..$.. A. m. .09.37.. A. m. .09.. 44.. & Defl. E .^.0.03. ,10 13 .^3.'.4 ..^3.5.4. M.O.8., 94.'.^.. .P9.53. 10 07 ?5r.4 Dcfl. I _ipj6 _ip,26 .13!.9 .1.4..IJ?. 14..^... 95.'.o. .1P..1.2_ .10.. 26. .^f.O. Oscill. I. .. 10 33 10 40 14.1 H 35 14 42 24.1 10 38 10 4*5 1Q.4 Mean Ord i<^8t ^r7A 24.00 100,6 -.06 .100,6 100. 2 -. Of^ Corr. Ord.* . 13^8 2^.6 24.0 *A (7/mm.).* 2! h (7) ^32 2,98 2.q8 .4^... 70... .79... H (Observed)... sf)98s a6ooq 26001 H Base Line.. .. .^9.^... .259.39... .^59.^9.. Observer ...l.B.Camt^.en L R Southwick G^EM.k^r. Dati 1 Time Mean SCALI.\G Time Mean SCAUNG Time Mean Begin End Begin End Begin End Set UNO h. m. ft. 771. mm. A. m. A. J7I. mm. A. m. A. m. 77J7:. Oscill E. Defl E Defl. I 1 Oscill. I. Mean Ord \ 1 Corr. Ord.* 1 h(-Y) H (Ob.served).. H Base Line Observer... ^ ?^ • Ordinate corrected to ...?P?.».P. mm. shrinkage distance. ? Scaled by L..R..§. E..li..R. Checked by 9...?...A. Computed by ..9.^.4.*....?.^.^... Checked by ...l?.^.'....^!!^... Abstracted by GEA u. s. NTINS orrict 10—50430-1 Figure 96.— Computation of horizontal-intensity base-line value. We have for the computation of the base-Hne values from the observed absolute values, Da, Ha, and I a, Bo=DA-S'^d BHo=HA—SHh—QH (i—to) =HA-{S,^hh) h-Qn {t-k) (353) (354) (355) 14.1 PROCESSING DATA Magnetic Observatory ...MfiQMMj...L'J: J.^.h...J95j (Month) (Yet) VERTICAL INTENSITY BASE-LINE VALUE Ma$neto$raph 4 Earth Inductor ^o 4.. 173 Department or Commerce U. S. COAST AND CCOOCTK SURVIY Fy>nn No. 359 (Rev. Oct. 1042) Date T i *! 1 10 ..1<55.M. Tim Mian scalinos Time Mean scalings Time Mean scalinos H z H z H Z lat half h. m. 10 Jg mm. 17. £ mm. 3P,o '3^" mm. 12,7 mm. 32.7 ft. ffl. "48 mm. 27.8 25.0 OH hftlf ^'t^ 17,0 29.9 «^3 12,7 32-9 "S 28.1 25,0 Mean Ord 17-10 29.95 12,70 32B0 27-95 25X>0 99-5 ,01 .1' ..9M . Ol ' .16 ..99.S V06 x>5 O .: fJorr Ord * 17,^ 30,1 12.8 33.0 ~^o 25,0 ° «2 «fc and €, 3..?<5 .2-.i?9 2,76 ^.?9. 2.7^ 3-29 •S^"** At and Ah i; o a ? **. ! H base line 47 35 78 28504 i 28504 28504 5 ac^i ° S d! ~ H ! 28^51 ! ^539 28582 8:1 Icrj ! I ^ 51,81 ....53: 4.4 2n 48.38 1di| 4., 4 jii^^ 1544... 10663 4.456og g. g 10625 1 9.? 9. 90552 inates separately aled interval time flashes 3 CSJ N a. ...4:.3^.i8l.. 22008 ..4.'.^.20X.. 22018 ...4-..3^i§.i.. .^.^9.9.4.. a . a ^t and Az la 1 99 log 82 1 « - 1 ? Z base line .?2.9.9.9. ! 2i?9?.9.L... 229 12_ rt " Observer T H Pearce R F White D C McGowan ' Ordinate corrected to '.... mm. shrinkage distance. Scaled by .P.S...^. Checked by D C M Computed by Checked by Abstracted by Z revised 194 R F V using differential formula AZ- AH+ AL «. eOVHMMCNT PRIMTINfi OmCI 10 — 60438-1 Figure 97.— Computation of vertical-intensity base-line value. and Bzo=H tan h-Sz z-Qz {t-to) (356) = [BHo+{So-^icih)h+QH{t-to)]tein I^-Sz z-Qz (t-to), (357) Figures 95, 96, and 97 will illustrate how D, H, and Z base-line values are computed for the cases where the temperature coefficients of the H and Z variometers are zero. Note: In figures 96 and 97 the symbol e is used in place of S for the scale value. 174 MAGNETIC OBSERVATORY MANUAL [Ch. IMPORTANCE OF ADEQUATE CONTROL 426. Control observations for deriving absolute values. — Di- rections for making absolute observations with a magnetometer and earth inductor are given by Hazard.^ Directions for operating the magnetic field balance are well covered by Joyce* and by Heiland and Pugh.^ A complete description of the sine galvanometer is given in the Researches of the Department of Terrestrial Magnetism.^ The publications of the Danish Meteorological Institute ^ give com- plete details on the operation of the la Cour instruments. 427. In making absolute observations at a magnetic observatory greater care must be exercised in the operations and a greater degree of accuracy is required than is the case for work in the field. How- ever, it IS not possible, as a rule, to achieve in the individual observations an accuracy on a par with the short-term stability of the variom- eters. Usually the base-line values resulting from a series of observa- tions, when plotted against time, will show more or less spread due to accidental error in the absolute observations, or to the application of temperature or other corrections that are made with faulty coeffi- cients. They may also show a progressive change or drift with time. This drift may result from loss of magnetism of the suspended mag- nets, from the seasonal effect of error in the adopted temperature coefficient of the variometer, or (for ET) from changes in the elastic properties of the quartz-fiber suspension. Hence, in determining what base-line values to adopt, it is necessary to adjust the observed values with due regard for these progressive changes. For any par- ticular set of instruments it can be determined only by experience how closely the adopted values should correspond to those resulting from actual observations. 428. Time observations, — Chronometers, pendulum clocks, or other timepieces used in any part of the observing program should be compared daily with radio time signals broadcast by the U. S. Naval Observatory, the National Bureau of Standards, or other reliable source. Where a time-flashing mechanism is used to place time marks on the magnetogram, it is convenient to keep the time correction of the time-marking clock small so that it will not be necessary to allow any time correction in scaling values from a magnetogram. The method of keeping a record of the performance of a chronometer or clock is shown in figure 98. DIRECTIONS FOR PROCESSING RECORDS 429. Producing the magnetograms. — Change the paper on the magnetograph drum daily at the same hour, on the hour, noting on the magnetograph record (fig. 99) any pertinent facts, however trivial, regarding any adjustments of the instruments, natural or artificial mechanical disturbances, or other unusual events related to the operation of the magnetograph and of the absolute instruments. Develop the traces as soon as possible after exposure, and examine them carefully for quality and for possible malperformance of any of 3 D. L. Hazard, Dir. for Mag. Meas. (see item 4 of bibliography). * J. W. Joyce, Manual on Geoph. Pros, with the Mgr., U. S. Dept. Int., Bur. of Mines, 1937 (see item 7 of bibliography). « C. A. Heiland and W. E. Pugh. Am. Inst. Min. and Met. Eng.. Tech. Pub. 483, 1932 (see item 5 of bibliography). « Barnett, DTM, CIW, Pub. No. 175 (see item 1 of bibliography). 7 La Cour, Danske Met. Inst. Pubs, (see items 8-11 of bibliography). 14. PROCESSING DATA 175 DEPARTMENT OF COMMERCE U. S. COAST AND GEODETIC SURVEY Form 698— Ed. Jan. 1950 18— 29fl5.V.> TUCSON, ARIZONA Chron. 1.^95 (Cbron. or Clock No.) Jan, ^95a TIME RECORD Date BnoAD- CA8T Station -_/*°-i_ Mer. Time OF Signal ^°5 Mer. Time BY Chron. or Clock 1 WW7 h. m. s. 09 00 00 h.» in s. 09 0^ 49. 2 2 II 52.8 4 II f^^.8 4 II 68, g 5 II 04 02, 5 6 II 06. ^ 7 II OQ, 4 8 II 1^.2 9 n 16.0 n ^9' 3 , Figure 98.— Time comparisons between chronometer and continuous time signals from Station WWV. U. S. National Bureau of Standards. 176 MAGNETIC OBSERVATORY MANUAL DEPARTMENT OP COMMERCE US. COAST AND GEODCTIC SURVEV Form 247 Re.. Feb 1938 MAGNETOGRAPH RECORD [Ch. Oct 19_5Li TUQSOlf Magnetic Observatory. Magnetograph No-^omt S5 TiMK BY Chron.' No. 1"*^ ch Tkmpkb- ATUBI RXIIABXS 02 Stop Begin Othert Chion.' Clw5k H z A. TO. ft. m. ft. TO. 10 04 10 00 m. t. m. 1. Parallax Test 10 08 10 49 Scale Value IS 05 00 26,^ 08 02 13 08 00 26.6 08 02 14 08 00 26. i 08 09 ^5 57 Check Operations ifi 26,Ji 16 02 16 10 Visitors 16 oR 00 3iJ3 08 02 17 08 00 a^/i 08 02 iH f^S 00 ^ ^ nR n^ 10 2'y ^ Cleaned jJoPer clamp bar 08 05 20 08 00 ^f'4 08 02 t Thto coloaa la to b« DMd fei fiagb Hm* anblM, uraollx whm Ih* photograpUe trao* to not iBtoiraplad. w. •. ceviiNMNT raiNTiNC omci 10— 41W(hl Figure 99.— Magnetograph Record, Tucson Magnetic Observatory. the variometers or of the time-marking system. Estabhsh a systema- tic and fixed routine for this part of the work. Carefully apply all necessary legends on the magnetograms as shown in figure 93. This work should be done neatly and accurately, because the magneto- grams are subsequently reproduced for publication.^ « U. S. Coast and Geodetic Survey, Magnetograms and Hourly Values MHV-Ch50 (in press, 1952). 14.] PROCESSING DATA 177 SCALING OF ORDINATES 430. Types of scaling, — Three varieties of scaling are customarily done on the magnetograms at the observatory, namely, those con- cerned with: (a) hourly values, or mean ordinate over each of the twenty-four hourly intervals during the day; (b) base-line scalings, or mean ordinate for the time interval during which an observation has been made for absolute value of a magnetic element; and (c) scale- value deflections. 431. Hourly values, — For measuring the average ordinate for an hour a special scaling glass is used, accurately engraved with rulings sc w » » w 16- ."S Figure 100.— Magnetogram reading scale superimposed on magnetogram for scaling ordinates. Cut-out portion, upper left, shows method of averaging hourly ordinates. Parallax test and scale-value deflection on right. and graduations as shown in figure 100. Vertical or lengthwise lines on the scaling glass are 20 mm apart, corresponding to a time interval of one hour on the magnetogram. Horizontal or transverse lines are 1 cm apart, with finer divisions of 1 mm. The scaling glass is laid on the magnetogram with the ruled surface next to the paper, and with the vertical lines coinciding with the hour marks on the gram. The space divided into millimeters on the glass should be placed across the base line. The scale is then moved up or down until one of the traverse lines is set for the average ordinate of an hour-long interval. With a little practice this can be done rapidly and accurately by making equal the areas between the trace being scaled and the trans- 178 MAGNETIC OBSERVATORY MANUAL [Ch. verse line, as illustrated by the shaded areas in the figure. The number of whole centimeters is read at the end of the transverse line, and the fraction of a centimeter is read to tenths of millimeters at the base line. The tabulations are ordinarily made directly in tenths of millimeters for the whole ordinate. Thus, for the example illus- trated the tabular entry would be 257. 432. Occasionally during disturbed magnetic conditions it is difficult to judge accurately the proper setting of the scaling glass for the mean ordinate of the whole hour. It is then easier to use half-hour or quarter-hour intervals, calculating the mean of the two or four values thus scaled for use as the hourly value. One section of the scaling glass is divided into half-centimeter (quarter-hour) intervals. Under extremely disturbed conditions it may be found desirable to divide the hourly interval into even smaller time intervals by drawing auxiliary time lines directly on the magnetogram, but it is seldom that the increase in accuracy thus obtained for the hourly value can justify the extra time required by this procedure. 433. Tabulations of the hourly values may be made in any con- venient form. Figure 101 illustrates the form now being used by the Coast and Geodetic Survey. This style of scaling sheet expedites the step of transferring the values to punch cards for further processing of the data at the Washington office, where the publications are compiled. 434. Base-line settlings. —The same procedure described for hourly value scalings is used for base-line scalings, except that the interval of time is determined by the duration of the absolute observations with a magnetometer or earth inductor. Extra time lines are placed on the magnetogram, through a push-button circuit from the absolute building, when an observation is begun and again when it is finished. For instance, observations for declination usually require 9 minutes. The extra time lines would thus be 9 minutes, or 3 millimeters, apart on the magnetogram, and the mean D ordinate for that 9-minute interval would constitute the base-line scaling for that declination observation. Base-line scalings are customarily tabulated in milli- meters, to the nearest tenth-millimeter. 435. Scttle-Vttlue deflections. — Figure 100 also illustrates a typical set of scale-value deflections for all three elements, D, H, and Z. In the illustration, deflections of the Z trace are made first (two deflec- tions with the deflector magnet placed N end up, separated by a deflection made with the A^ end down) , followed by deflections of the D trace, and finally deflections of the H trace. All three variometers are disturbed, of course, when the deflector magnet is in place for any deflection, so that care must be used in selecting the proper deflection spots on the magnetogram. 436. Scalings of the deflected spots are made, not to the base line but from one spot to the immediately succeeding spot — that is, from an up spot to a down spot and then from a down spot to the next up spot. (All measurements should be made in a direction perpendicular to the base line^ — ^it is the difference between ordinates of deflected spots that is being measured.) This is a measurement of 2Uy the effect caused by a complete reversal of the deflecting magnet, and the quantity used in computing the scale values of the several element traces on the magnetogram. The sample scale-value computation shown in figure 72 is derived from the deflections of figure 100. 14.1 PROCESSING DATA 179 DEPARTMENT OF COMMERCK U. S. COABT AND OlODBTIC SUIVIT Cto & Stis gOJJi^GE^ ALASKA 1951 (Obiirytiori', (i'mt) OCT, "■"(MoiHh) HOURLY MEAN ORDINATES FROM MACWETOGRAMS Average values for successive periods of one hour beginning at midnigh t 150 M.T. Tenths Signs of mi are as llimeters corrected to shrinkage distance follows unless otherwise noted: D + Signs reviewed by of ; H_ + •> 100.0 mm Z + Char. 1 *Shr. 99.0 99.0 99.0 Day- 25 26 27 Hr. D H Z Hr. D H Z Hr. D H Z 01 101 375 71 01 02 lip 197 26.. 199 8.2. 14 01 02 53 94 .447 475 98... 95 02 97 372 72 ...P.? 04 .....1.9.?... 103 364... 366 .71... 69 03 106 446 51 .....03 04 121 528 82 04 109 383 75 130 241 52 05 110 .....3.67. 69 05 146 362 73 05 110 292 5 06 113 368 70 06 153 352 65 06 135 567 ■ 40 ...07 08 ...1.2.5... 130 .....3.65... 368 .7.0.. 70 ...0.7 08 .1.4.4. 163 .3.61. 363 .6.2... 61 07 132 362 61. 08 125 358 64 ..0? 10 ...1^1.. 112 .....3.6.8.... 362 .6.7.... 68 ....0.9 10 .1.5.8.. 146 .57.2... 356 .5.8... 62 .....09 10 .1.11. 98 .5.5.2. 345 67., 68 ...i.l 1? .....102... 89 .....3.63... 366 .6.7... 65 ....1.1 12 99 48 332. 311 59 77 11 92 538 70 12 83 345 72 ...1.2 14 82 ....368... 67 13 -115 278 63 .....13 14 .7.2. 71 .552.. 551 7.5. 71 90 363 70 14 -62 341 68 ..15. 1*1 81 365 70 ....1.5 16 10 578 89 ....IS 16 .71. 70 .5.55. 560 ...7.2.. 70 82 363 70 31 391 104 ...17. IR SI.. 84 .....3.7.Q... 373 .6.9.... 69 ...17 IR 50. -15 4.Q2.. 441 92... 95 ....1.7 Ifl .77., 3:7.0. 71. 74 577 72 ..19. ?0 86.. 75 37.4 376 69... 69 ...19 20 12. 49 543.. 510 126.. 131 ...1.9 ?0 71 53 3,81 510 .7.6. 122 ..21 ?? 42 78 450 521 90 102 ...21 22 40. . 61 473 396 127 109 ....21 22 .162 98 .458 422 145. 124 .22. .6.5.. ....16.7.... 452 94... 65 ...25 ?4 67. 68 3.8.7.. 422 9.2... 91 ...25 24 .6.7. 68 .4.1.6. 587 Ill 100 Sum 2182 9246 1733 1735 8825 1926 2256 8985 1859 Mean 91 385 72 72 368 80 95 574 77 « Seated 6y W.H.S, K.H..S.., W.H.S, »CK,ek»d 6v 1 V.A.T. V.A.T. V.A.T 2 tThis entr y refe rs to magnet Figu ogram w re 101 — hich Tabi 1 begir ilation ( IS on t >fscale log (r)2=log T2-log (l+2aA^). By equation (367), log iTy=los T'-0MSa{t-20) ^40(3) and, for a=0.000 Oil, log (r)^=log r2-|_o.OOO Ol (20-^f). (407) The factor 0.000 01 (20 — ^) is the correction that must be apphed to log T^ to give the value of log {Ty at 20° C. In this case a= 0.000 Oil the coefficient of thermal expansion (linear) of steel. The coefficient is slightly larger for aluminum -nickel-steel alloys. 450. Correction for change in (K^Ki) due to temperature change (loaded system), — It may be shown that the treatment is the same as for changes in the dimensions of the magnet (or the inertia weight) due to temperature change, except that in this case the effective coefficient of expansion is taken as approximately the mean of the coefficients for steel and brass. Taking ai = 0.000 014 as this mean coefficient, and letting AK{=Kt—K2Q) represent the total increase in the moment of inertia of the magnet, stirrup, and inertia weight combined (due to an increase in temperature A^(=^ — 20), with all other coefficients equal to zero), and substituting in equation (406), log (ri)2=log rf-0.868X0.000 014 (^-20) (408) =log Tf +0.000 012 (20-0, (409) 190 MAGNETIC OBSERVATORY MANUAL [App. in which (Ti) is the time of one oscillation at 20° C (loaded system), and Ti is the observed time of one oscillation at t° C (loaded system) . The term, 0.000 012 {20— t), is the correction that must be applied to log Tf to give the value of log (TiY at the standard temperature, 20° C, under the imposed conditions. 451. Correction to T^ for torsion factor, — Let / =angular motion of torsion head in minutes, in torsion test; h = angular deflection of magnet in minutes, for (f—h) minutes of twist ; (T) =true time of one oscillation (torsionless fiber; H, Ms, K, chronometer rate, etc. constant) ; T = observed time of one oscillation, torsion effective ; (ii/, A/^, K, etc., constant). For a small amplitude and torsionless fiber, HMs' (T)'=^y (410) and with torsion effective,^ HMs+t T'=^ rTL ir (411) By equation (151), when (7=0 j-h k'=HMsTK (412) and T'= — Divide equation (410) by equation (413): T' ^j-h f-h HMs-\-HM, J^ (413) (414) Letting /== 5400', the usual angular motion of the torsion head in magnetometer work, / _ 5400' _ h , . /-/i"'5400'-/i,"" ^5400'-/i ^ ^ Since h is usually small compared to 5400', equation (414) may be written: ^«l+j (416) > Dir. for Mag. Meas., pp. 16, 17 (see item 4 of bibliography). I.] APPROXIMATIONS 191 By equation (362), log {Ty^log r-hOAU ^, (417) '--+'(°Jr) «log T^+OmOOSh. (418) Note: Even when h is as large as 60', which is unusual, equation (418) holds with sufficient precision in this work. 452. Correction for change in H (all other factors constant) . — Let (T)^ be the time of one oscillation, reduced to a standard H {=Hq) ; Then (^)^=|§; (^19) Now let H change by AH, such that AH is small compared to Hq; H is now Hq+AH, and Divide equation (419) by equation (420): (D^=r(l+^ (422) log {T)'=\og 7^+log (l +^- (423) From equation (362), aTT log (T)'^\og 7^4-0.434 ^. (424) When the observations are made at a magnetic observatory it is proper and convenient to choose the H base line value (Bh) for Hq. Then AH becomes the mean ordinate of the H trace during the time of a set of oscillations. Thus H=Ho+AH (425) becomes H=BH+hy (426) =B„+hrr,^S„ (427) and ^HKnA (428) 192 MAGNETIC OBSERVATORY MANUAL [App. Then, from equation (424), log {Ty=\og T2+0.434 ^ hmm- (429) Example: Let 5^=18,200 &=2.60. Then 0.434 ^=0.000 062. Bff It may be shown that any value of Bh within about one-half percent of the value of H is sufficiently accurate to reduce T^ to the value (TY that would be observed if the H ordinate were zero. 453. Correction for induction in oscillations. — Let AM=the change in the magnetic moment due to induction; M=the induction factor (see par. 110, chap. 4). r^, AM .AM H Then M^-^, and ^j^=M^- In oscillations, iTy=TfTr (everything constant, fjL=0). (430) When induction is effective and everything else is constant, ^'^HiM-hAM)' ^^^^^ Divide equation (430) by equation (431), (Xy M+AM AM As explained in paragraph 110, AM may be replaced by yiH, and equation (432) becomes {Tf , , H. then log (T)^=log T^+log (l+M^) (433) From equation (362), log {TY=\og r^+0.434M ~ (434) I.] APPROXIMATIONS 193 In practice it is convenient to use a table of log ( I+m t>) against TT / TT\ log Yf ^or a given value of /x, to get log ( 1 H-/z ^r? )• In the lower part of figure 35, page 56, such a table is illustrated, showing critical TT / TT\ values of log ^ for values of log f 1 +/x ^ b for ju=3.5. 454. Variation of log C with temperature in magnetometer deflections, — In the deflection equation ^ ^ (435) M sin u ture because r varies with temperature. That is, ^=1 "20 ~ dC 3(7 dr r2o and dC= ^^dr. ^20 2 . the constant C is made up primarily of -3; which varies with tempera- (436) (437) (438) But dr=r2oadt (439) in which a is the coefficient of thermal expansion (linear) of the deflection bar, and dt is a small increment in the temperature. When everything is constant at 20° C, C^=^- (440) '20 When the temperature changes by A^ and everything else remains constant except r, Divide equation (440) by equation (441), C20 (r2o + Ar) (■+47 (442) log C2o=log C,+3 log (1 + 7)- (443) 194 MAGNETIC OBSERVATORY MANUAL From equation (362), hence and log (720 «log 0,+ 1.30 — (444) (439), j=otM', log (72o«log Ct^-l.^OaM (445) «logO,+ 1.30a(^-20) (446) log Ct—\og ^20= A log C «-1.30a(^-20) «1.30q!(20-0 (447) A-/ (448) Examples: For brass, «=0.000 018; log C2o=log C'.+O.OOO 023(^-20). (449) For duralumin, a=0.000 022; log C2o=log C. + O.OOO 029(^-20). (450) APPENDIX II. TEMPERATURE COEFFICIENT OF MAGNETIC MOMENT 455. In Chapter 4, the temperature coefficient of magnetic moment was taken as a constant over a temperature range of 50° C. However, the relation between temperature and magnetic moment is not strictly linear. A more precise expression is given by Mt=Moil-qt-qr) (451) in which Mt=the magnetic moment at a temperature t° C, ilio=the magnetic moment at ^o° C, and q and q' are coefficients which must be evaluated from experi- mental data for each magnet. Differentiating equation (451) with respect to t, ^^=-Mo(q + 2q't) (452) AM= -Mo{q+2q't)At. (453) Equation (452) gives the rate of change of the magnetic moment at the temperature t° C. In general we are concerned with the change in magnetic moment for a particular change in temperature, hence the average rate, -— -; between the reference temperatures must be used in calculating AM from equation (453). 456. It may be shown that the average rate of change over the range, ^o to ti, is AM At '~ Mo(q + 2q^ ^^) (454) (455) and AM= -MJq-{-2q' ^-^)^^' 457. Example: Let A/o=1000 cgs at fo; ^0=0° C; ^1=50° C; 2=0.000329; and g'= 0.000 000 91. 195 196 MAGNETIC OBSERVATORY MANUAL Then from equation (454), ^=_1000r0.000 329+2(0.000 000 91)(' ^^°^^° ')1 = —0.3745 cgs units per degree C, for Mo=1000. When Mo=l, ^=-0.000 3745 = 2- Then q is the mean temperature coefficient between 0° and 50° C. From equation (455) AM= — 1000X0.000 3745X50 =-18.7 cgs. Equation (451) will give the same result. 458. Summary, — This analysis may be summarized as follows: (a) Equation (451) gives the magnetic moment at a temperature t° C when Mq and the q coefficients are known; (b) Equation (452) gives the temperature-rate of change of magnetic moment at the temperature t; (c) Equation (454) gives, for the mean temperature between ^o and ti, the temperature rate of change of the moment of the magnet whose moment is Mq at fo or 0° C. (d) Equation (455) gives the approximate change of the magnetic moment, AM, when the temperature of the magnet changes by A^; (e) The process is reversible ; that is, to go from a higher temperature to a lower temperature, change the sign of A^. APPENDIX III. ORIENTATION ERRORS 459. Errors in the computed value of Ex. — The formulas for computing E^ for D, H, and Z variometer recording magnets assume that the deflector is placed properly and that the deflection, 2u, if it exists at all, is due entirely to the misorientation of the recording magnet. However, if the deflector is improperly placed, there will be a deflection of the recording spot despite correct orientation of the variometer magnet. If the usual orientation formula is applied, using the 2u recorded on the magnetogram, the apparent (computed) value of Ex will be made up of two parts: first, that due to the real misorientation of the recording magnet; and second, that due to improper placing of the deflector. There is no way to separate these two parts. It can only be assumed that the second part can be kept small by using great care in properly installing the stops or guides that hold the deflector in place while the orientation deflections are being made. The effects of improper placing of the deflector are summarized in table 18, page 203. 460. Discussion of errors, — In this discussion it is assumed that: (a) The deflector, or its holder, is a rectangular parallelepiped; (b) the deflector is symmetrically magnetized with its magnetic axis approximately coincident with its geometric axis or with the geometric axis of the holder; (c) the test deflections are made by placing the deflector (or holder) against the fixed stops or guides which definitely i^x the direction of the geometric axis of the deflector (or holder) and the geometric center of the deflector or holder with respect to the stops or guides; (d) a sufficient number of deflections are made with the deflector in the four positions shown on figure 84, lines 6-9 (see p. 145) to eliminate the residuary effect of nonco incidence of magnetic and geometric axes; (e) errors in fixing the guides or stops are small, say of the order of one degree or less in azimuth and level ; and in any direction normal to the magnetic meridian the departure of the geometric center of the deflector does not exceed H of one percent of the value of the deflection distance, r (5 parts in 1000); and (f) the recording magnet is in perfect orientation. Note: It can be shown that the error equations derived below also hold approximately for the condition that the recording magnet under test is improperly oriented by a small angle of the same order of magnitude as the error angles introduced in setting the deflector. 461. A perfectly adjusted deflector will not deflect a perfectly oriented recording magnet. Imperfect adjustment of the deflector, Ma, will cause a deflection of the recording magnet, Ms, when Ma produces an effective field perpendicular to Ms, in the plane of rotation of M,. Let /p= component of the test field parallel to the recording magnet; 197 198 MAGNETIC OBSEEVATORY MANUAL [App. /„= component of the test field normal to the recording magnet (in the horizontal plane for D and H) in the vertical plane for Z) ; 'Ui = the real ''up" deflection of the spot (taken as +); ^^2=the real ''down" deflection of the spot (taken as -f"); 2u=Ui-\-U2', iS^the normal scale value (gamma scale value); (£'a:)c==the calculated exorientation angle of M,; and Sj^the real exorientation angle of M,=0. Then from equation (334), page 139, (456) tan But by definition of S Jn=u, S; and upon reversal of Ma fn = U2S. Hence 2uS=2fn and tan jp (457) Therefore, part of the analysis reduces to a comparison of /« with/,. 462. By introducing small known errors of placement of the deflector, the effect of such errors on the calculated exorientation angles may be computed. In the following paragraphs the errors (Ex)c in Ex, for critical and noncritical errors of placement, are derived for 5 possible cases for each variometer. The results are summarized in table 18, page 203. 463. D variometer, — In all the cases, Ms is assumed in perfect adjustment. Case (a), figure 103. — Ma is in perfect orientation except that it makes a small horizontal angle, p, with the magnetic meridian through Ms. fp=fr=~^ COS p (458) Jn=Je=^ sin p; (459) Ma . tan {Ex),=^-f=^^ =i tan p (460) ^ :r COS p r {Ex)c^hp (for small values of p). (461) III.] ORIENTATION ERRORS 199 Case (b), figure 104.^A/a is in perfect orientation except that the geometric center of Ma is displaced a small distance, y, east or west of the magnetic meridian through Mg. Angle A0B=8. Jv=h Ma (3 cos2 5-1) = 2M„ since 8 is small; fn = h = SMa sin 8 cos 8- SMg SMa sin 8, since 8 is small; tan {Ej:)c- sin 8 (EA 8^ 2Ma 2 r sm 8 (462) (463) (464) (465) Figure 103.— Looking down. Figure 104.— Looking down. Case (c), figure 105. — Ma is in perfect adjustment except that it is above or below the horizontal plane through M^ by a small distance, h. There is no component normal to Ms in a horizontal plane, hence no deflection of M., and (Ex)c=0. Figure 105.— Looking east. Figure 106.— Looking east. Case (d), figure 106. — Ma is in perfect adjustment except that it is tilted in the magnetic meridian plane through a small vertical angle, p'. There is no component normal to M^ in a horizontal plane, hence no deflection of Af,, and {Ej:)c = 0. f- w Figure 107.— Looking down. Case (e), figure 107.^ — Ma is in perfect adjustment except that the deflection distance, r, is uncertain by a small distance, Ar. Ms will not be deflected and (£'x)c = 0. 200 MAGNETIC OBSERVATORY MANUAL [App 464. H variometer, — In all the cases, Ms is assumed in perfect adjustment. Case (a), figure 108. — Ma is in perfect adjustment except that it makes a small horizontal angle, p, with the magnetic prime vertical through the center of Ma. r r 2Ma 2Ma •>3 sm p; (466) /p=/e=-3- sm e M„ ^ cos p; (467) 2Ma sm p tan {E^)c cos p (468) tan {Ex)c=2 tan p (Ex)c^2p, since p is small. E S M, M. W Figure 108.— Looking down. B (469) o s M. W Figure 109.— Looking down. Case (b), figure 109. — Ma is in perfect adjustment except that its center lies to the east or west of the magnetic meridian through Mg, by a small distance, b, such that the angle A0B=8. , , ZMa . . . j^=j^=-—- COS 6 sin 5 3ilf„ 6, since 5 is small. (470) /.-/ii=^M3cos^^-l) M ■' =-^«(3sm2 5-l) III.] ORIENTATION ERRORS —Ma . ^ . ,1 « — 3— J Since 8 is small. ^=tan iE,\ Jv (^x)< 35 3M« 201 (471) (472) (473) Case (c), figure 110. — Ma is in perfect adjustment except that it is above or below the horizontal plane through Ms by a small distance, h. There will be no component normal to Ms in a horizontal plane, hence no deflection, and {Ex)c=^> Up I^s w A/. Figure 110.— Looking east. Down Figure 111.— Looking south. Case (d), figure 111. — Ma is in perfect adjustment except that it is not level — that is, it makes a small vertical angle, p', with the hori- zontal plane through Ms (in the prime vertical). There will be no component normal to Ms in a horizontal plane, hence no deflection, and {E^)c=^. Ma Ar W Figure 112.— Looking down. Case (e), figure 112. — Ma is in perfect adjustment except that the deflection distance, r is uncertain by a small distance, Ar. There will be no deflection and (£'a;)c=0. 465. Z variometer, — In all the cases, Ms is assumed in perfect adjustment. Case (a), figure 113. — Ma is in perfect adjustment except that it dips through a small angle, p, in the magnetic meridian plane through Ms', that is, Ma is not level. r r Ma . Jn=j6=-:^ sm p Jv=Jr- 2Ma COS p /»_ = tan (E,)c- Ma sin p /, 2Ma ,»,3 cos p J tan p 210111—53- 14 (£'^)c~ Jp, since p is small. (474) (475) (476) (477) 202 MAGNETIC OBSERVATORY MANUAL [App. Case (b), figure 114.— il/^ is in perfect adjustment except that it is above or below the horizontal plane through Mg by a small distance, h, such that the angle AOB=b. /.=/!! = = -^ (3 cos2 5- 1) ^ — ^> smce 5 is small. Tn=J± = ^ Sm 5 COS 8 « — 3- 8, smce 8 is small. iE,).4j-l7 M u p B u P — 1^ . N_— ^s h ^ -n 1 ^5 ^""^S "^•^--J^ ^ 1 wn r" MR r "" t P r Figure 113.— Looking east. (478) (479) (480) (481) Figure 114.— Looking east. Case (c), figure 115. — M^ is in perfect adjustment except that it is displaced in the horizontal plane through Mg by a small distance, y, such that the angle A0B=8\ There will be no component normal to Mg in the vertical plane, hence no deflection, and {Ex)c=0. Figure 115.— Looking down. [Figure 116.— Looking down. Case (d), figure 116. — Ma is in perfect adjustment except that it makes a small horizontal angle, p', with the magnetic meridian through Mg. There will be no component normal to Mg in a vertical plane, hence no deflection, and (E3:)c=0. Case (e), figure 117. — Ma is in perfect adjustment except that the deflection distance, r, is uncertain by a small distance, Ar. There is no component of Ma perpendicular to Mg, hence no deflection, and {E,)c=0. I Ill] ORIENTATION ERRORS 203 466. Practical applications, — It is estimated that the deflector stops or guides can be set to an accuracy of 1 mm in 200 mm, so that p=0.005 radians=17'. Also, it is estimated that the guides can be placed so that the center of the deflector wiU be on the magnetic meridian or at the proper elevation within 2 mm. At r=100 cm. 5 Up Down Figure HT.— Looking east. should not exceed 0.002 radians or approximately 7\ Then referring to table 1§ for these critical errors, assuming the recording magnet is perfectly oriented, the apparent exorientation angles would be: YorD: E, (apparent)=|a+ip=| X 7'+ix 17' = 19' For^: Ex (apparent)=:36+2p-=3X7' + 2X17' = 55' For Z: Same as D. It is obvious that the utmost care must be taken in fixing the posi- tions of the stops or guides for the critical adjustments, otherwise the calculated ~QXOv\QnLi2iiion errors may be quite large even though the recording magnets may be in excellent adjustment. TABLE 18. — Critical adjustments of the deflector in orientation tests. APPENDIX IV. VARIOMETER SCALE-VALUE ERRORS 467. Errors in scale values arising from maladjustment of the deflector, — In order to simplify the analyses and to concentrate on the physical picture, it will be assumed that the undeflected variometer magnets are in perfect adjustment, that is, that the D magnet is in the magnetic meridian, the H magnet is in the magnetic prime vertical, and the Z magnet is level; that there are no appreciable errors in the magnetic moment of the deflector and in the values of 2u (these errors are not relevant here); that operational procedures in scale- value observations are performed in the manner described in chapter 1 1 ; that the deflector is an ideal magnet; and that all other conditions fare ideal, aside from maladjustment of the deflector. From the definition of scale value, the deflecting fields should be directed as fol- lows (see fig. 118): For H: Magnetic north or magnetic south. For Z: Vertically upward or downward. For D: Magnetic east or magnetic west. 468. Maladjustment of the deflector will, in general, change the magnitude of the component of the field in which we are interested. At the same time this mal- adjustment will introduce a small field parallel to the recording magnet which will affect the scale value ; however, this latter effect will cancel out on reversal of the deflector. 469. Therefore, under the assumed con- ditions, the maladjustment of the deflector will affect the calculated field, fc, insofar as this field differs from the real deflector field, / (/ being the effective field — the field which actually produces the deflection), as described in the last part of paragraph 467. In computing scale values we assume ideal conditions and compute a deflector field, fc, as in the examples which follow. 470. In this discussion, the deflection, u, is the deflection of the recording spot on the gram caused by the deflector in one position only, and the double deflection, 2u, is the sum of the deflections caused by the deflector direct and reversed. 2u is always considered positive (+). 471. Magnetic meridian and prime vertical, — The magnetic meridian plane at a point is the vertical plane containing a magnet freely suspended at the point and acted on only by the earth's magnetic field. In this discussion the magnetic meridian will be taken as thei horizontal line in the magnetic meridian plane and passing through] the point. 204 Figure 118.— Positions of deflector rela- tive to recording magnet in observa- tions for scale values by magnetic method. H deflections at top, Z in center, D at bottom. SCALE-VALUE ERRORS 205 472. The magnetic prime vertical plane at a point is the vertical plane perpendicular to the magnetic meridian plane, and containing the point. In this discussion the magnetic prime vertical will be taken as the horizontal line perpendicular to the magnetic meridian at the point. 473. The magnetic meridians in the variation building and absolute building are assumed to be parallel. 474. Calculated scale value,— -The calculated scale value is 2/c 2u The real (true) scale value is e_2/ The difference is ^c-^^ 2u _2_ 2u _2/ 2u (482) (483) (484) The fractional error in the scale value will be 2 Sr-S 2u^' ^^ _jc-j. and the percent error will be Sc-S 2/c 2u 100 fc-f Jc xioo. (485) (486) 475. D scale value. — (a) Consider first the deflector correctly oriented (fig. 119); deflector level; center on the magnetic meridian Ma Ms w Figure 119.— Looking down. Ma Ms W Figure 120.— Looking down. through the recording magnet, M^; axis normal to the magnetic meridian through Af,; same elevation as Mg. In figure 119, the effec- tive field is fE=Je = fc] 61 = 90°; sin ^=1. , Ma . ^ Ma ic=^ sm e=^ (487) 206 MAGNETIC OBSERVATORY MANUAL [App. This is the value of /c in the following cases. (b) Deflector correctly oriented except that it makes a small angle, p, with the prime vertical. In figure 120, 6 is positive. d=90°—p. Effective field: fE=fe. /,=M?sin (90-p) Ma , = — ^ COS p^c COS p Jc—Je=fc(l — COS p). The fractional error is -^-l-cosp. Jc (488) (489) (490) (c) Ma is correctly oriented except that its center is horizontally displaced from the magnetic meridian through Ms by a small amount, y (fig. 121). Effective field: /^=-/|,. Angle A0B=8; 6=90-5. cos^ (90-5) = sin2 5. /ii = +^"(3cos2^-l) = +^«(3sin^5-l) = +/c(3sin2 5-l) Jc -f=fc 4-/,, =/c (1 + 3 sin^ 8-1) =M3sm'8), ^''+•^'1 = 3 sin^ 6. The fractional error is (491) (492) (493) Figure 121.— Looking down. Down Figure 122.— Looking south. (d) Ma is correctly oriented except that it makes a small angle, p', with the horizontal but remains in the magnetic prime vertical through its center (fig. 122). Effective field: Horizontal component of the fe field; call itfe. fE=fe=je COS p'==—^ COS p'=/c COS p' (494) fc — fe=fc{l—COS p'). The fractional error is j-f. 1 — cos p' , (495) (496) IV.1 SCALE-VALUE ERRORS 207 (e) Ma is correctly oriented but its distance, r, from M, is uncertain by a small amount, Ar (fig. 123). Effective field: /b^/o. Af=-^ Ar by eq (160). (497) But and h f [Ma Ar=r — rc, hence Aj=Je—jc fe-fc=-%'Ar fc-Je Jc 3 ^ — Ar- r Tf- = measured distance (498) (499) Up Ms W Figure 123.— Looking down. f tA/o A N "Mi ■ r^. = measured distance Down Figure 124.— Looking east. (f) Ma is correctly oriented except that it is above or below the horizontal plane through Ms by a small amount, h (fig. 124). The effect is merely to increase the true deflection distance, r, by a small amount, Ar. In figure 124, OA is the measured distance, Vc', OB is the true distance, r; AB—h, the displacement above the horizontal plane. Effective field: Je=J%' Ar r—r cos 6' = r(l— cos b'). As in case (e) above Jc-Jb 3 . 3 /c - Ar=- [r(l— cos 5')] r r = 3(1— cos b'). (500) If the measured distance, r^, is OB rather than OA, then jc=ji and Ar=:0. 476. H scale value; maladjustment of the deflector, — (a) Ma is in perfect orientation with deflector axis in the magnetic meridian through the center of Ms (fig. 125). Effective component producing deflection: jN=Jr=Jc' /c=^- (501) This is the value of /c in the following cases. (b) Ma is in perfect orientation except that it makes a small horizontal angle, p, with the magnetic meridian through M, (fig. 126). 208 MAGNETIC OBSERVATORY MANUAL [App. Effective component producing deflection is the radial component: Jn=Jt- r 2Ma . Jr=—^ COS p=jc COS p fc—jr=jc{^—GO^p). The fractional error in the scale value is je (502) (503) (504) Ma Ms W Figure 125.— Looking down. Figure 126.— Looking down. (c) Ma is in perfect orientation except that it is east or west of the magnetic meridian through M, by a small horizontal distance, y, such that the angle A0N=8 (fig. 127). Effective component producing the deflection is the parallel component: fN =J\\- Ji\=^ (3 cos^ 5-1)=^ (3 cos2 5_i) fc-fn U2-3 cos2 g^i)_y^(3_3 ^os^ 8) (505) ^ 3/c(l-cos^ 8) ^ Sjc sin^ d 2 2 The fractional error is fc—J\\_^ „• 2 sin=^ 5. (506) (507) Figure 127.— Looking down. Figure 128.— Looking east. (d) Ma is in perfect orientation except that the deflector is above or below the horizontal plane through Ms by a small distance, h, such that the angle A0B = 6' (fig. 128). Effective component producing the deflection: Jn=J\\- The result is the same as in case (c) . The fractional error in the scale value will be •^V^=| sin2 8\ (508) IV. SCALE-VALUE ERRORS 209 (e) . Ma is in perfect orientation except that it dips through a small angle p', while its magnetic axis remains in the magnetic meridian plane through M, (fig. 129). Effective component producing the deflection is the radial component: Jn=Jt as in case (b). The frac- tional error in the scale value is /c-/. /« 1— cos p'. (509) Ma — Ar — Tf. s measured distance Ms Down Figure 129.— Looking east. W Figure 130. — Looking down. (f). Ma is in perfect orientation except that the deflection distance, r, is uncertain by a small distance H-Ar (fig. 130). Effective compo- nent producing deflection: Jn=Jt- The fractional error in the scale value is J-Jr_ , 3 Ar. (510) 477. Z scale value; maladjustment of the deflector, — In Z scale-value deflections the deflector is used in the B position, just as in the D deflections. In deducing scale-value errors for the Z deflections, figures 119, 120, 121, and 123 may be taken as side elevations of the Z recording magnet and its deflector, looking east. Figure 122, if rotated 90° so that E means uj^, represents the condition that the deflector makes a small angle p' with the vertical in the magnetic prime vertical plane. Figure 124, if taken as a view looking down, represents the Z recording magnet and its deflector when the latter is displaced horizontally to the east by a small amount but its mag- netic axis remaining vertical. In all cases the pertinent functions and estimated fractional errors are the same for both I) and Z variometers. 478. Sum,m,ary of errors.— Tables 19 and 20 summarize the errors in the scale value deflections for all variometers due to small maladjust- ment errors of the deflector. It is assumed that with reasonable care the deflector holder can be adjusted to the accuracy indicated in each case. For example: It should be possible to adjust Ma (length 20 cm) parallel to a magnetic meridian or to make it level to an accuracy of 1° or better. For a 20-cm deflector this would be equivalent to 3.5 mm in 200 mm, a maladjustment easily detectable by eye. Also, it should be possible to make lateral or vertical adjust- ments to an accuracy of 2 or 3 mm by the methods described in paragraphs 343 to 349. As indicated in the tables, an error of 1 cm inhory will not cause appreciable error in the deflections. 479. The controlling error is in the deflection distance, r, assuming that the other adjustments are made to the precision indicated in the tables. In the tables, r is taken as 100 cm. Ma as 10,000 cgs. Usually r is much greater for scale value deflections. The scale- value error 210 MAGNETIC OBSERVATORY MANUAL TABLE 19. — Summary of possible errors in D and Z scale values due to maladjustment of the deflector. DEFLECTOR ORIENTATION INCREMENT OF VARIABLE ERROR FACTOR ERRORS Position Figure fc-f % Error, •^j^lOO a b c . d e f 119 120 121 122 123 124 y "o.il" 0.3 0.15 3.0 0.15 p = l° y—1 cm; 6=0.01 rad... 1-COSp 3 sin2 S- - 0.015 0.03 0.015 0.3 0.045 p— 1° ..._-. 1-COSp' +:-- - +3 (1-cosy) r=100cm;Ar=0.1cm h=lcm;5'=0.01rad TABLE 20. Summary of possible errors in H scale value due to mal- adjustment of the deflector DEFLECTOR ORIENTATION INCREMENT OF VARIABLE ERROR FACTOR ERRORS Position Figure fc-J % Error, a b c d e f 125 126 127 128 129 130 Perfect orientation y '"6.3" 0.3 0.3 0.3 fi.O p=l° 1-COSp -|sin25 ^sinU' 1-COSp' 0.015 0.015 0.015 0.015 0.3 y=l cm; 5=0.01 rad /i=l cm;5'=0.01 rad p'=l'' r=100 cm; Ar=0.1 cm due to Ar may be positive or negative; all the others are always posi- tive. Assuming the most unfavorable condition where all have the same sign, the maximum possible error would be the sum of all the individual errors, and in the examples given should not exceed 0.4 per- cent. Assuming that the angular and linear displacement errors will be the same for values of r up to 300 cm, the percent error in the deflec- tions due to error in r would decrease as r increases. 480. Secular change in D and its effect on maladjustment of the deflector. — After a number of years it may be necessary to readjust the stops laterally and in azimuth because of possible large secular change of declination. For example: Suppose r=200 cm and the declination changes 30' over a period of years. Then the east- west displacement of the magnetic meridian through the center of Ms, at a distance of 2000 mm, would be ]/=2000 taa 30'=2000X0.0087 = 17.4 mm. Unless the stops were readjusted to the new magnetic meridian, a small systematic error would be introduced into the calcu- lated scale values as a result of this large secular change. It is obvious that a similar error would be introduced if deflections were made at a time when the declination differs by 30' from the mean for the day, assuming that the deflector stops had just been adjusted to the mean value of D for that particular day. This question of readjustment of the stops is discussed further in paragraph 346. APPENDIX V. CHANGE OF ORIENTATION AND SCALE VALUE OF D VARIOMETER CAUSED BY OTHER MAGNETS OF THE MAGNETO- GRAPH 481. Assuming that the D variometer is constructed of nonmagnetic materials, and that there is no gross torsion in the D fiber, an isolated D variometer will always be properly oriented. The H and Z variome- ters, however, contain magnets whose fields can modify not only the orientation but also the scale value of the D variometer magnet. It is possible to compute these effects, if the magnetic moments of the several magnets are known, with an accuracy probably greater in all cases than that obtainable by direct measurement. I „ Magnetic I. ^ 1 — ^f-.^.^ h 65.4 -j- 53.6 Ul2.(>-j Pier Top PLAN Horizontal Center Line , _D i through D magnet Ji \r ^ i I b^ ^ All Dimensions in Centimeters Figure 131.— Plan and elevation showing relative locations of all the magnets in the regular magnetograph at College, Alaska. 482. The example shown below applies to the sensitive magneto- graph at College, Alaska, installed in February 1949. Figure 131 shows the relative positions in plan and elevation of all the magnets of the magnetograph. Dimensions are in centimeters. The following symbols are used, and the magnetic moments are as specified: H is H variometer magnet; moment =8 cgs units; Ht is H temperature-compensating magnet; moment =85 cgs units; 211 212 MAGNETIC OBSERVATORY MANUAL [App. Hs is H sensitivity magnet; moment =83 cgs units; Z \s> Z variometer magnet; moment=215 cgs units; Zt is Z temperature-compensating magnet; moment =450 cgs units ; /„=that component of the field of a magnet that is parallel to the axis of the magnet; /x=that component of the field of a magnet that is perpendicular to the axis of the magnet; /b= eastward horizontal component of the field of a magnet; /ivr= north ward horizontal component of the field of a magnet. 483. Values of /^ and Jn at the D recording magnet will be computed separately for each of the five magnets; the resultant field will be the algebraic sum of the individual components. Magnitudes of /g and Jn will be computed by means of equations (27) and (28) ; signs may be Figure 132.— Position of the H-Tariometer recording magnet relative to the D magnet. determined by examining the relative physical positions of the D magnet and of the magnet whose field is being computed, as illustrated in figures 132, 133, 134, 135, and 136. The figures are not drawn to scale. Slide-rule computations are used. Distribution coefficients (see par. 30) are neglected because the other magnets are far enough away from the D magnet that the effects of distribution will be small enough to ignore. 484. H magnet, — From figures 131 and 132, it is evident that the H magnet is 5.8 cm south and 53.6 cm east of the D magnet. Then, from equation (27), /^=/ii=^(3cos2^-l) (511) _ 8X10^ r./ -53.6 Y -.1 (53.8)3 L \ 53.8 ) J v.] INTERACTION OF VARIOMETERS 213 and from equation (28), -5.14(2.978-1) = 107 (eastward); M Jn=J'x=-3- (3 sin d COS 0) = —27 (27 southward). (512) Figure 133. — Position of the H tempsrature-compensating magnet relative to the D magnet. 485. H temperature-compensating magnet, — From figures 131 and 133, the H temperature-compensating magnet, Ht, is 7.3 cm north and 53.6 cm east of D. Then from equation (28), /b=/i.=^- (3 sin 6 cos 6) 85X10^^^3^^53.6^, 7.3 (513) and from equation (27), (54.1)3 54.r^54.1 = 53.7X0.401 = 227 (westward); Jn=A=^ (3 cos' d-1) (514) ==53.7X (-0.945) = 5l7 (northward). 214 MAGNETIC OBSERVATORY MANUAL [App. 486. H sensitivity magnet, — From figures 131 and 134, the H sensitivity magnet, Hg, is 5.8 cm south and 65.6 cm east of D. Then from equation (27), ^^=A=^ (3COS20-1) (515) _ 83X10^ r / -65.6 Y 1 (65.8)3 L V 65.8 / J = 29.1X1.982 = 587 (eastward); and from equation (28) , /iv=/jL=-^ (3 sin d COS d) = 29.1X3Xg^X-g^-g- = — 87 (87 southward). (516) Figure 134.— Position of the H sensitivity magnet relative to the D magnet. 487. Z magnet, — From figures 131 and 135, the Z variometer magnet, Z, is seen to be 11.5 cm north, 65.4 cm west, and 6.0 cm higher than D. The east component, which will affect D, is the horizontal projection of /x- :fE=J± cos a =—r (3 sin 6 cos 0) cos a (517) v.] INTERACTION OF VARIOMETERS 215 215X10^ 65.7_-11.5_65.4 X3X.^„X X (66.7)^ ^'^^66. 7^' 66.7 '65.7 = — 377 (377 westward); and from equation (27), M /a^=/ii=7^(3 cos^^-l) ^ 215X10^ r. / -11.5 Y -] (66.7)3 \jy ggy ) A J = — 667 (667 southward). (518) Figure 135.— Position of the Z- variometer recording magnet relative to the D magnet. 488. Z temperature- compensating magnet, — From figures 131 and 136, the Z temperature-compensating magnet, Z,, is 11.5 cm north, 65.4 cm west, and 7.7 cm lower than the D magnet. Again, as in the case of the Z magnet, the elevations of Zt and D are different. Je is the eastward component of/j., and is therefore equal to/j. cos /3 (fig. 136); similarly /^^ is the northward component of/j., and is equal to/x sin jS. Je— — 3- sin 6 cos 6 cos /3 (519) 3X450X10^ 66.4 7.7 65.4 66.8 66.8 66.4 (66.8)= = 52X0.985 = 517 (eastward); 216 and MAGNETIC OBSERVATORY MANUAL Jn= — 3- sm B cos B sm /3 (520) = 52X 11.5 66.4 = 97 (southward). Figure 136.— Position of the Z temperature-compensating magnet relative to the D magnet. 489. The following table, then, summarizes the resultant field at the D variometer of all the other magnets in the magnetograph, west- ward and southward components being given a negative sign: Field component H H. H. z Zt Total In + 10 -2 -22 + 51 + 58 -8 -37 -66 + 51 -9 + 60 -34 490. When Je is positive, therefore directed eastward, it causes the N end of the D magnet to lie in the northeast quadrant; the ex- orientation angle (par. 338) is arc tan =16 minutes of arc. (Hori- zontal component of the earth's field at College is I26OO7.) 491. When /at is negative, therefore directed southward, it causes a change of scale value of the D variometer according to equation (122), where the (7 of the equation is equal XoJn derived above. APPENDIX VI. NOMOGRAMS 492. The nomograms given in tliis appendix will be found useful in the preliminary studies associated with the establishment of a magnetograph. Beneath each illustration is a brief note explaining how it may be used and referring to the pertinent text paragraphs. Figure 137. — Field of a bar magnet at a point on[its magnetic axis produced. The above nomogram represents graphic solutions of the equation f=— — ; — -, in which 3/ is the mag- netic moment and/the field in gammas at a distance r along the magnetic axis produced. Example: Given M=1000 and r=lOO cm. Then a straight line from iV/=1000 on the M scale through r = 100 on the r scale intersects /= 200 on the /scale. The field is 20O7, the required field. Conversely, if it is desired to know the magnetic moment required to produce a field of 2OO7 at a distance of 100 cm along the magnetic axis, simply reverse the process (see par. 16). 210111—53- 217 218 MAGNETIC OBSEEVATORY MANUAL [App. figure 138. -Change in the field of a bar magnet, along its axis produced, with change of distance; magnetic moment known.^ The above nomogram represents graphic solutions of the equation — A/= 2 MX 105 3^,=6MX10^^^_ t3 r ri Examples: Given JVf=140 cgs, r= 11.62 cm, and Ar=l mm. A straight line from Af=140 on the M scale through ?■= 11.62 on the r scale intersects the —A/ scale at 46O7. That is, when r is increased from 11.62 cm to 11.72 cm the field will be smaller at r=10.1 by 46O7. Likewise if M= 10,000 cgs, r=200 cm, and Ar = l mm, then A/= — 0.887, approximately (see par. 16). In this nomogram Ar is fixed at 0.1 cm. VI, NOMOGRAMS 219 Figure"139.— Change in the field of a ir magnet with change in distance along its magnetic axis produced; field at a distance r, known. I The above nomogram represents graphic solutions of the equation in which / is the field at a distance r from the center of the magnet, Ar is the increment in r, and a; is mo corresponding increment in /. Example: Given: /=10007 at a distance r = 10 cm. Required A/ when Ar = l mm. A straight line from /= 1000 on the /scale through r = 10 on the r scale intersects the —A/ scale at 30. This means that if a field is IOOO7 at a distance of 10 cm from the magnet and along its magnetic axis, the field will decrease approximately 30 gammas between the points r = 10.0 cm and r = 10.1 cm. (See par. 16). In this nomogram Ar is fixed at 0.1 cm. 220 MAGNETIC OBSERVATORY MANUAL [App. Figure 140.— The D Nomogram. An alignment chart showing the relation between the product of the horizontal intenrfity and the mag- netic moment of the recording magnet, the dimensions of the quartz fiber suspension, and the min-ate scale value; based on equations 124-128, with optical lever 2R taken as 3438 mm. See paragraph 215 for complete explanation and examples. Figure 141.— The H Nomogram. An alignment chart showing the relation between the magnetic moment of the recording magnet, the dimensions of the quartz fiber suspension, and the H scale value. See paragraphs 251, 252, and 253, for addi- tional details and examples. 222 MAGNETIC OBSERVATORY MANUAL [App. Figure 142. — Nomogram for conversion of D scale values. This chart represents graphic solutions of equations (301) and (302). For example: Given a D scale value approximately equal to 1.00 minute per mm at a place where H= 18300t. Required the gamma scale value, Sdt, of the D variometer. A straight line from So' = 1.00 on the So' scale to H= 18300^ on the H scale intersects the Sd^ scale at 5.3 vv^hich is the required gamma scale value, approximately. Likewise the minute scale value may be evaluated if the gamma soale value is given (see par. 323). VI.] NOMOr.RAMS 223 Figure 143. -Nomogram showing spurious effects on recorded magnetic declination due to changes the horizontal intensity (see par. 331). This chart represents graphic solutions of the equation, ADs- AH H tan Ex, in which H is the horizontal intensity in gammas; AH is the change in Hin gammas, and Ex is the exmeridian angle of the D recording magnet. Example: Given, H=183007, AH=1007; and £'x = 18.6 minutes. Then from the above equation, AD, (in radians) =--,-—X0.00532= 0.00029 radians=0.1'. The straight line from 0.00546 on the -^^ scale through 18.6' on the Ex scale intersects the AD scale at 0.1', the spurious change in recorded declination due to A//. 224 MAGNETIC OBSERVATORY MANUAL [App. H^D Figure 144. — Nomogram showing'spurious effects on recorded horizontal intensity due to changes in magnetic declination (see par. 331). This nomogram represents graphic solutions of the equation AH. = HAD tan Ex in which AHs is the recorded change in H, in gammas, due to a small declination change, AD, in radians, when the ex-prime vertical angle is Ex. Example: Given, H=10fi00y; Ai)=10' =0.00291 radians; and Ex= 10°=600'. Then AHs = 10,000X0.00291 tan 10°=5.1'y, the spurious effect. The straight line from the HAD= 29.1 on the appropriate HAD scale through ^i = 10° = 600' on the Ex scale intersects the Alls scale at 5.I7. VI.] NOMOGRAMS 225 150 a; =1 30 < m 6 = 1 3 ■i2^r Figure 145. — Nomogram showing spurious effects on recorded vertical intensity due to changes in the horizontal intensity (see par. 331). This nomogram represents graphic solutions of the equation AZs = AHtanEx in which AH is a small increment in H: Ex is the ex-level angle of the Z recording magnet. The equation applies ;to a Z recording magnet operating in the magnetic meridian. Example; Given A/7=1007 and Ex=&0'. Then from the above equation, AZs = lMy, the spurious effect. The straight line from IOO7 on the A// scale through 60' on the Ex scale intpi^iects the AZ. scale at I.847. 226 MAGNETIC OBSERVATORY MANUAL [App. --.000000 5 Figure 146.— Nomogram for distribution factors ( l-\ — ^-f— ^ ] • P This nomogram represents graphic solutions of the terms -^ and — for different values of the deflection distance r, for the conditions that P and Q are known. The coefficients P and may be calculated from the equations in table 2 or interpolated from the values in tables 21a, 21b, and 21c. Example: Given, for P position A, P=10, 0=5000, and r=40 cm. Required: the factor 1+ —„ + -.• The straight line from 10 on the P scale through 40 on the r scale intersects the - scale at 0.0064. The straight line from 5000 on the scale through 40 on the r scale intersects the -^ scale at 0.002. Then the distribution factor is 1.0000+0.0064 +0.0020 = 1.0084. VI. NOMOGRAMS 227 TABLE 21a. Pa Approximate distribution coefficients for position A. Px = 2ia2-3i.2=0.32 LJ-QA8 L.2 /o=0.4 La Z.=0.4 L, \ La L. \ 1 2 4 ' 8 10 12 14 16 81.9 18 104 20 128 0.00 +0.32 1.28 5.12 11.5 20.5 32.0 46.1 62.7 1 -0.48 -0.16 +0.80 4.64 11.0 20.0 31.5 45.6 62.2 81.4 103 128 2 -1.92 -1.60 -0.64 +3.20 9.60 18.6 30.1 44.2 60.8 80.0 102 126 4 -7.68 -7.36 -6.40 -2.f6 +3.84 12.8 24.3 38.4 55.0 74.2 96.0 120 6 -17.3 -17.0 -16.0 -12.2 -5.76 +3.20 14.7 28.8 45.4 64.6 86.4 HI 8 -30.7 -30.4 -29.4 -25.6 -19.2 -10.2 +1.28 +15.4 32.0 51.2 73.0 97.3 10 -48.0 -47.7 -46.7 -42.9 -36.5 -27.5 -16.0 -1.92 +14.7 33.9 55.7 80.0 12 -69.1 -68.8 -67.8 -64.0 -57.6 -48.6 -37.1 -23.0 -6.40 12.8 34.6 58.9 QA=3h*- Qa la = OALa -0.384 La^ Z.2+0.144 L,* l,=OA Ls V- 1 2 4 6 8 10 12 14 16 18 20 '■\ 19.7 O.CO +0.08 +1.23 99.5 315 768 1.590 2.950 5,030 8,060 12, 300 1 0.14 -0.16 -0.16 +13.7 85.8 290 730 1,540 2.880 4.940 7,940 12, 100 2 2.3C +0.84 -2.61 -2.61 +46.5 +219 617 1,370 2.650 4,640 7,570 11, 700 4 36.9 30.8 +13.5 -41.8 -84.8 -41.8 +190 +745 1,780 3,500 6,110 9.870 6 187 173 133 -14.9 -212 -384 -428 -212 +427 +1,680 3,770 6,950 8 ~ 590 565 493 +216 -195 -668 -1,100 -1,360 -1.280 -668 +689 +3, 050 10 1.440 1.400 1,290 845 +157 -703 -1,630 -2.500 -3, 140 -3, 360 -2,940 -1,630 12 2,990 2,930 2,770 2,120 1,090 -238 -1, 780 -3.380 -4, 900 -6, 140 -6.870 -6,840 TABLE 21b. — Approximate distribution coefficients for position B, Pb Pb=-^ ?a2+6i2=-0.24 i„2_(_o.96 L,2 Za = 0.4 La ls=OA L, \ La \ 1 2 4 6 8 IC 12 14 16 18 20 L. \ -3.84 -24.0 -34.6 0.00 -0.24 -0.96 -8.64 -15.4 -47.0 -61.4 -77.8 -96.0 1 0.96 +0.72 +0.00 -2.88 -7.68 -14.4 -23. C -33.6 -46.1 -60.5 -76.8 -95.0 2 3.84 3.60 2.88 0.00 -4.80 -11.5 -20.2 -30.7 -43.2 -57.6 -73.9 -92.2 4 15.4 15.1 14.4 +11.5 +6.72 0.00 -8. 64 -19.2 -31.7 -46.1 -62.4 -80.6 6 34.6 34.3 33.6 30.7 25.9 +19.2 +10.6 0.00 -12.5 -26.9 -43.2 -61.4 8 61.4 61.2 60.5 57.6 52.8 46.1 37.4 +26.9 +14.4 0.00 -16.3 -34.6 10 96.0 95.8 95. C 92.2 87.4 80.6 72.0 61.4 49.0 +34.6 +18.2 0.00 12 138 138 137 134 130 123 114 104 91.2 76.8 60.5 +42.2 Qb pB=yZJ-^Z„2Z.2+15Z.< 0.048 La^ 0.4 La h- -0.576 L<,2 L,2_|.o.384 L,* 0.4 L» \^i>a 1 2 4 6 8 10 12 14 16 18 20 +0.77 0.00 +0. 05 12.3 62.2 197 480 995 1.840 3.150 5,040 7.680 1 0.38 -0.14 -1.15 +3.46 +41.9 160 423 913 1, 730 3, 000 4,850 7,450 2 6.14 +3.89 -2.30 -18.4 -14.6 +55.3 +256 +670 1,400 2. 560 4.300 6,760 4 98.3 89.1 +62.2 -36.9 -171 -295 -343 -233 +136 +885 +2, 150 +4. 090 6 498 477 415 +178 -187 -633 -1,100 -1.490-1,720-1.670 -1,180 -117 8 1.570 1.540 1,430 995 +308 -590 -1,630 -2.740,-3.810-4.720 -5. 330 -5.490 10 3.840 3.780 3,610 2,930 1,830 +350 -1,440 -3,460[-5,610 -7, 760 -9.780-11,500 12 7,960 7,880 7,630 6,650 5,040 2,850 +148-2,990-6.450-10,100 -13,900-17,500 1 228 MAGNETIC OBSERVATORY MANUAL TABLE 21c. — Approximate distribution coefficients for position C. Pc Pc=-\ {laHU) = -QM {LJ+L,i) Zo = 0.4 La ls=OA Ls \ \ i^a L, \ 1 2 4 6 8 10 12 14 16 18 20 0.00 -0.24 -0.96 -3.84 -8.64 -15.4 -24.0 -34.6 -47.0 -61.4 -77.8 -96.0 1 -0.24 -0.48 -1.20 -4.08 -8.88 -15.6 -24.2 -34.8 -47.3 -61.7 -78.0 -96.2 2 -0.96 -1.20 -1.92 -4.80 -9.60 -16.3 -25.0 -35.5 -48.0 -62.4 -78.7 -97.0 4 -3.84 -4.08 -4.80 -7.68 -12.5 -19.2 -27.8 -38.4 -50.9 -65.3 -81.6 -99.8 6 -8.64 -8.88 -9.60 -12.5 -17.3 -24.0 -32.6 -43.2 -55.7 -70.1 -86.4 -105 8 -15.4 -15.6 -16.3 -19.2 -24.0 -30.7 -39.4 -49.9 -62.4 -76.8 -93.1 -111 10 -24.0 -24.2 -25.0 -27.8 -32.6 -39.4 -48.0 -58.6 -71.0 -85.4 -102 -120 12 1 -34.6 -34.8 -35.5 -38.4 -43.2 -49.9 -58.6 -69.1 -81.6 -96.0 -112 -131 Qc Qc=Y (^a2+Z.2)2=0.048 (LJ+Ls'^)i la = OA La ls = OA Ls \l. \ 1 2 4 6 8 10 12 14 16 18 20 Ls \ 0.00 0.05 0.77 12.3 62.2 197 480 995 1,840 3,150 5,040 7,680 1 0.05 0.19 1.20 13.9 65.7 203 490 1,010 1,860 3,170 5,070 7,720 2 0.77 1.20 3.07 19.2 76.8 222 519 1,050 1,920 3,240 5,160 7,830 4 12.3 13.9 19.2 49.2 130 307 646 1,230 2,160 3,550 5,550 8,S10 6 62.2 65.7 76.8 130 249 480 888 1,560 2,580 4,090 6,220 9.120 8 197 203 222 307 480 786 1,290 2,080 3,240 4.920 7,230 10, 300 10 480 490 519 646 888 1,290 1,920 2,860 4,210 6,080 8,630 12, 000 12 995 1,010 1,050 1.230 1,560 2,080 2,860 3,980 5,550 7,680 10, 500 14, 200 BIBLIOGRAPHY 1. S. J. Barnett, A sine galvanometer for determining in absolute measure the horizontal intensity of the earth's field, Department of Terrestrial Magnetism, Carnegie Institution of Washington, Publication No. 175, vol. IV, pp. 373-394, Baltimore, 1921. 2. S. Chapman and J. Bartels, Geomagnetism, vols. I and II, Oxford, 1951. 3. G. Hartnell, Distribution Coefficients of Magnets, Special Publication 157, pp. 9-10, U. S. Coast and Geodetic Survey, Washington, 1930. 4. D. L. Hazard, Directions for Magnetic Measurements, Serial 166, 3rd ed., corrected 1947, U. S. Coast and Geodetic Survey, Washington, 1947. 5. C. A. Heiland and W. E. Pugh, The American Institute of Mining and Metal- lurgical Engineers, Technical Publication No. 483, New York, 1932. 6. H. H. Howe, On the theory of the uniular variometer, Terr. Mag., 42, 29-42, Baltimore, 1937. 7. J. W. Joyce, Manual on Geophysical Prospecting with the Magnetometer, U. S. Department of Interior, Bureau of Mines, Houston, 1937. 8. D. la Cour, La Balance de Godhavn, Danske Meteorologiske Institut, Communications Magnetiques, etc.. Publication No. 8, Copenhagen, 1930. 9. Le Quartz- Magnetometre QHM (Quartz Horizontal Force Mag- netometer), Danske Met. Inst., Comm. Mag., etc., Pub. No. 15, Copenhagen, 1936. 10. The Magnetometric Zero Balance, the BMZ, Danske Met. Inst., Comm. Mag., etc.. Pub. No. 19, Copenhagen, 1942. 11. D. la Cour and V. Laursen, Le Variometre de Copenhague, Danske Met. Inst., Comm. Mag., etc., Pub. No. 11, Copenhagen, 1930. 12. J. Lamont, Handbuch des Erdmagnetismus, Berlin, 1849. 13. A. K. Ludy and H. H. Howe, Magnetism of the Earth, Serial 663, U. S. Coast and Geodetic Survey, Washington, 1945. 14. Smithsonian Physical Tables, Geomagnetism, Tables 495-511, 9th ed. (in press, 1952). INDEX a factor, 87, 95, 97, 128, 166 — significance of, 96 — determination of, 159 — at C. & G. S, observatories, 97 Aberration, spherical, 67 Absolute control, importance of, 174 Absolute observations, 174 Absolute observatory, 21 Activity, magnetic, 181, 182 Alignment charts (see Nomograms') Anomaly; tolerances in selecting site, 21 Approximations, 183 Aurora borealis, 20 Autocollimator (Gaussian ocular), 62 Auxiliary spots (la Cour), 66 Axis, magnetic (bar magnet), 1 — optical, 62 — of centered dipole, 16 Azimuth of Z magnet; scale value, 105 — true. 21 b factor; if scale value, 87 Balance, analytical, 104 Bar magnet; components of field, 8 Base-line mirror, 66 Base-line mirror, D, 74 Base line, scale value at, 165 Base-line value, H, 30 — drift of, 174 — scaling for, 178 Bench, orientation, 21, 141 Bimetallic strip, 120, 121, 123, 164 — on la Cour variometer, 164 Bifilar suspension, H variometer, 84 BMZ. 57 C^ FIET D* D variometer, 74, 77, 80 H variometer, 95 elTective compensation, H variometer, 116 computation, H variometer, 156 Z variometer, 101 evaluation of; Z variometer, 159 estimation of; for if and Z variometers, 117 C figures, 181 ^ ^^ C (instrumental constant of magnetometer), 27 — adjustment of, 55 — computation of, 58 Centered dipole, 16 Charts, isomagnetic, 16 Chronometer, 21 — rate of, 27 Clock, time marking, 21 , . ^. Coefficient of thermal expansion, magnet and mertia weight, 29 Coil factor, induction tests, 50 Collimation, 62 Comparison observations, 148 Comparison of fields, bar magnet and earth, 18 Comparisons, summary of, 58, 60, 61 Compensated variometer, H, 167 Compensating field, variometers, 114, 116 Compensator distance, evaluation, 118 Components of field: of a bar magnet, 8, 17 for small angles, 10 Constants: ofmagnetograph, 148 of magnetometer; summary, 55, 56 Control, absolute; importance of, 174 Control magnet: D variometer, 81 H variometer, 86, 90 Z variometer, 104 Conversion factors, 30 Conversion to absolute units, 165 Corrections: index, 25 instrumental, 25 Corrections to //observations, 59 Corrector, D, 152 Coulomb's equation for k', 88 Couples: in H variometer, 84, 85 in D scale value equation, 78 Coupler, in variometers, 73 Cylindrical lens, thickness,. 75 D nomogram, use of, 81 D scale-value, 74, 82, 83 D scale value equation, 78 D spot, 74 D variometer: C field of, 74, 77, 80 control magnet, 80 depth of focus of, 83 east field at, 77 effect of cylindrical lens, 75 effective recording distance, 75 evaluation of recording distance, 82 field factor, 74 gamma-scale value, 74 la Cour, 65 lens, thickness of, 75 lens, specifications, 83 line of no torsion, 76 loM^-sensitivity, 80 magnetic moment of recording magnet, 82 measured distance, 75, 83 nomogram, 81 optical axis of D lens, 74 optical lever, 75 optical scale value, 75, 77 orientation formulas, 136 recording magnet, 74 stray fields, 77 torsion constant, 74, 81 torsion factor, 76 torsion in fiber, 75 torsion tests, 76 Damping, 29, 74 — i/ recording magnet, 84, 159 — test, D, 150 Darkroom, 21 Declination, magnetic, 21 — standard value, 128 Deflection angle, u, 27 Deflection distances, 26, 27 — for orientation tests, 144 Deflection, double, in scale value, 128 — exmeridian, 135 — orientation, 144 Deflections, positions of magnets in, 5-8 — for //scale value, 126, 158 — for Z scale value, 161 Deflector orientation, 197 Deflector positions, effect on distributioncoelTicients, 12 Depth of focus, D variometer, 83 Developing processes, photographic, 69 Diaphragms, 67 Dip, magnetic (inclination), 16 Dipole, centered: representing earth's field, 16 Directions for performing operatiors {see supple- ment, page 232). Distribution coefficients, 12, 13, 15, 26, 27, 227, 228 — formulas, 13 — special cases, 14 — corrections for,* 5 Distribution effects, // scale value, 91 Distribution factors, 12 Disturbance, irregular, 20 — local, 21 Diurnal variation, 19 D>Tie, 1 Earth inductor, 21 Earth's dipole field, 16 Earth's field: changes in, 19 east component, 16 at various latitudes, 17 229 230 INDEX Earth's magnetic moment, 17 East field; at D variometer, 77, 151, 152 — at iJ variometer, 84, 86, 87, 88 Elements, magnetic, 16 Equivalent field; H variometer, 86, 87 Errors in orientation tests, 197-202 Errors in scale- value observations, 204 Exmeridian deflections, 135 Exorientation angles, evaluation, 84, 85, 145 Fiber, torsionless, 77 Field, magnetic: at a point; distribution considered, 14 around a bar magnet, 2, 17, 18 C, evaluation of, 159 dipole, 16 equivalent, 86 estimation from nomogr'am, 5 factor {D variometer), 74 in terms of magnetic moment, 5 of magnet, direction of, 11 p, at // variometer, 87, 158 resultant, 5, 8 strength, 1 uniform, 3 Focal length of lens, 62 Force, magnetizing, 1 Gamma scale value, D, 74, 79 Gauss, 1 Gaussian ocular, 62, 63 Geomagnetic latitude, recommended scale^values for, 134 Geomagnetic poles, 17 Ghost images, 64 H magnet: magnetic moment, 84, 87 effect on D variometer, 212 H nomogram ; for H scale value, 93 i7 sensitivity control magnet; effect on D variometer, 214 — reversal of, 92 H spot, adjustment of, by temperature magnet, 158 H temperature compensating magnet; effect on D variometer, 213 H variometer, 84 — orientation formulas, 85, 139 — scale value, 85 Half period, in oscillations, 27, 29 Heat treatment of magnets, 33, 38 Helmholtz coil; external field, 134 Helmholtz-Gaugain coil, 132 Horizontal intensitv, de'inition of, 16 Hourly values, publication of, 176 — scaling, 177, 178 Housing, nonmagnetic, 84 Image, character of, 67 Impurities, magnetic, in instruments, 25 Inclination (magnetic dip), definition of, 16 Index corrections, 25 Induction coefficient, 42 — Lamont's method, 44 — computations, 47 — Nelson's method, 48, 52, 54 Induction factor, 26, 27, 42 Inductor, earth, 21 Inertia cylinder, 71 Inertia weight, 29 Installation of magnetograoh, report on, 162, 163 Instrumental corrections, 25 Instruments, quality of, 25 Intensity, horizontal, definition of, 16 Intensity, magnetic, 1 Intensity, vertical, definition of, 16 Intensity, total, definition of, 16 Intercomparison observations, 57 International standards, 57 Invar; coefficient of expansion, 110 Inverse square law, 1 Isomagnetic charts, 16 k, evaluation and dimensions of, 87-89 K indices, 181 Knife edge; Z recording magnet, 99 — care of, 161 La C our fibers, 70, 163 — magnetograph, 70, 163 — variometers, optical compensation, 120 Latitude adjustment; Z variometer, 107 Latitude, geomagnetic and magnetic, 18 Lens, cylindrical, 65, 75 Lens, D variometer; specifications, 75, 83 — focal length, 62 Lenses, centering of, 62, 67 Lever, optical, 63, 64 Line of force, equation, 1, 18 Local disturbance, 21 Low-sensitivity variometers, 66, 80, 162 — orientation tests, 163 — scale values, 129 Magnet, length of, 4 — poles of, 1 — axis of, 1, 74, 85 Magnetic activity data, 181 Magnetic compensation, 116 Magnetic elements, 16 Magnetic field strength, 1 Magnetic impurities, 25 Magnetic meridian, 16, 74, 204, 205 — D variometer, 151 — in variation room; establishing, 142 Magnetic moment, 3, 27 — D magnet, 82 — equivalent for a coil, 50 —H" magnet, 84, 88 — of the earth, 17 — temperature coefficient of. 195 Magnetic observatory, buildings and equipment of, 21 Magnetic prime vertical, 85, 87, 204, 205 — at /-/ variometer, 87, 90, 95 Magnetic poles of the earth, 17 Magnetic standards, 57 Magnetic storms, 20 Magnetic temperature compensation, 96, 113, 117 Magnetism tester, 25 Magnetizing field, 42 Magnetizing force, 1 Magnetograms, 67, 69, 176 Magnetograph, 21, 23 — constants, 148 — installation, 148 — la Cour, 5 — optics, 63 — visual, 165 Magnetometer, 21 — equations, 26 — Quartz Horizontal (QHM), 21 — constants, 55, 56 Magnetometric Zero Balance (BMZ), 57 Magnets, fields of, 8-15 — bar; forces between, 1 Maladjustment: of deflector in orientation tests, 198-202 of deflector in scale-value observations, 205-210 of deflector due to secular change in D, 210 of recording magnets, 135 Meridian, magnetic, 16 — true, 21 Milligauss, 2 Minute scale value, 74 Mirror-adjusting apparatus, 150, 154 Mirrors: base line, 66 front surfaced, 64 planoconvex, 64 time-flashing, 67 triple-face (three-face\65, 150 Moment of inertia, 26, 27, 28, 30, 31 — directions for observing, 31 — corrections for change of temperature, 187 — of cylinder, 28, 89 — of weight, 29, 75 Moment, magnetic {see magnetic moment), Monochromatic light, 62 Multiple reflections, 64 Nomograms: I) variometer, 81 H" variometer, 93, 94 for estimating field of a magnet, 5 Observations, absolute, 174 Observatory, absolute, 21 Observatory, magnetic, 21 Observatory site, selection of, 21 Oersted, 1, 87 INDEX 2:u Optical axis, 62, 74 Optical compensation, 120, 164 — H variometer, 124 — la Cour variometer, 120, 123 Optical lever, 63, 64, 75 — auxiliary, 162 — double, 134 Optical scale value, 63, 75 — D variometer, 74, 75,77 — 27 variometer, 84, 87 Optical system; 7/ variometer, 84 — magnctograph, 63, 148 Orientation, 135 Orientation bench, 21, 141 Orientation deflections, 144 Orientation errors, 197 — critical adjustment of deflector, 203 Orientation formulas, 136, 139 Orientation of variometer magnets, 135, 146 Orientation tests, 141, 145 — effects of maladjustment of deflector, 141, 144, 161, 198-202 — evaluation of Ex angles, 145 — low-sensitivity variometers, 163 Oscillations, 28, 29, 33 Oscillations, corrections to: for all effects, 184 for change in H, 191 for change in moment of inertia, 188, 189 for change in magnetic moment, 186 for torsion factor, 190 for induction, 192 for rate of chronometer, 185 p field at H variometer, 85, 87 — computation of, 158 p field at Z variometer, 104 Paper, recording, 67 Parallax 67 Parallax'te^ts, 156, 161, 163, 177, 181 Parallel component; field of bar magnet, 9 Parallel rays, 62 Period, torsion pendulum, 75 Perpendicular component; field of a bar magnet, 10 Photographic registration, 23, 62 Piers, 21 Pivots and knife edges, care of, 161 Poises, Z recording magnet, 161 Pole, unit, 1 Poles, earth's magnetic and geomagnetic, 17 Poles of a magnet, 1 Positions of magnets, 5-8. 12 Potentiometer, precision, 57 Prime vertical, magnetic, 85, 87, 204, 205 Prisms, 65, 163 Processing of records, 165, 174 q coefficients, 115, 116 QHM (Quartz Horizontal Magnetometer), 21, 57 Quality of instruments, 25 Quartz fibers: 70 classification, 71, 72 dimensions, 70. 75, 88 galvanometer, 70 installation, 72, 73 la Cour type, 70 measurement, 71 modulus of rigidity, 70 period of oscillation, 72, 75 procurement, 70 selection, 72, 154, 162 torsion constant, 70, 72 Quartz Horizontal Magnetometer (QHM), 21, 57 Radial component; field of a bar magnet, 8, 10 Radian scale value; //variometer, 86 Rate of chronometer, 27, 185 Recorder, photographic, 23, 67 Recording distance, 82, 84 Recording paper, 67 Recording magnet, D, 74, 82 Recording magnet, //, 87, 88, 90, 95 — damping, 159 Recording magnet, Z: azimuth and scale value, 100, 101 balancing poise— center of gravity, 99, 100 knife edge, 99 la Cour, 163 magnetic axis, 99, 104 scale value, 101 sensitivity poise, 99, 104 supports, 99 Recording magnets, adjustment, 135, 145 Registration, i)hotographic, 62, 67 Report of installation of magnctograph, Ifi", I 13 Reserve distances, 155 Reserve spots, 65, 164 Resistance, standard, 57 Resolution of fields, resultant field, 5 Resultant field, D, 77 Resultant field, //, 87 Rigidity modulus of quartz, 75 Routine duties, 105 Scale value: a factor, significance of, 96 a factor tests, 128, 159 adjustment by control magnet, 90 bimetallic strip, 121 calculated, 205 computations, 129 correlated with geomagnetic latitude, 134 double deflections, 128 electromagnetic methods, 132 errors due to maladjusted deflector, 204 Helmholtz-Gaugain coil, 132 low-sensitivity variometers, 129, 162, 163 optical, 63, 75 recommended, 134 scale in magnet, 26 scale in telescope, 26 scahng of deflections, 177 sensitivity-control magnet, 90 shelves, 21 temperature coefficient, 112 Scale value, D variometer: adjustment, 83 computation, 154 equations, 78, 82 gamma, 74, 79 gamma and minute, 129 minute, 74, 231 optical scale value, 75, 77 Scale value, H variometer: a factor, 87, 95 adjustment by control magnet, 91, 92 average, 97 b factor, 87 base-line, 97, 128 cgs tmits per radian, 85, 86 control magnet, 157 correction for change in D, 97, 128 deflections, determination, 126, 158 dimensions of k , 87 distribution effects, 91 equation, 71, 128 from constants, 90 gammas per mm, 86 graph, 158 graphic solutions, 93 optical, 86, 87 reversal of control magnet, 92 selection of, 90 use of nomogram, 94 variation with/a, the east field, 91 variation with k, 91 variation with distance of sensitivity magnet, 93 variation with ordinate, 97, 128 with control magnet, 93 with two control magnets, 92 Scale value, Z variometer: azimuth of recording magnet, 105, 106, 107 center of gravity of recording magnet, 103 deflections, 101 equation, 101, 128 example, 106 effect of //, 105 latitude and temperature compensation. 108 A'' end south, 106 parallel fields, 101 p field, 104 sensitivity poise. 99, 103, 106 Scaling, base line, 177, 178 — during a storm, 178 — hourly values, 177, 178 Scaling base line, — low sensitivity magnetograms, 180 — ordinates, 33, 177 — scale value deflections, 178 Secular change. 20 Sensitivity, bimetallic strip, 121 — control magnet. 90, 91 232 INDEX Sensitivity— Continued — double; D variometer, 162 — Z recording magnet, 104 Sensitivity magnet, adjustment of, H, 157 Sensitivity magnets, two, 92 Sensitivity magnets, la Cour Z variometer, 164 Shelves, scale value, 21 Shrinkage, 180 Sine galvanometer, 57 Site, observatory, selection of, 21 Solar flare effects, 181 Solenoids, axial field, 48 South magnetic latitude; temperature compensation, 112 Spherical aberration, 67 Spots, reserve, 65, 66 Spurious effects, 98, 135 Stabilization of magnets (see heat treatment) Standard cells, 57 Standard resistance, 57 Standards, International Magnetic, 57 Storms, magnetic, 20 Stray fields at D variometer, 77, 211, 212, 216 Stray fields at Z variometer, 101 Sudden commencements, 181 Tangential component; field of a bar magnet, 8 Temperature bath, 34 Temperature coefficient and scale value, 112 Temperature coefficient, mechanical, 110 Temperature coefficient: of D variometer, 119 of H variometer, 167 of magnetic moment, 26, 27, 29, 33, 195 of magnetic moment, alternate method, 39 of magnetic moment; directions, 34, 35 of magnetic moment; errors of scale reductions, 42 of magnetic moment; graph, 38 of magnetic moment; sensitivity, 41 of variometers, 109 of variometers; errors, 118 of variometers; meaning, 109 of variometers; optical compensation, 121 of Zspot, 109, 111 Temperature compensating field; C field, i7 variom- eter, 96, 156 Temperature compensating magnet; adjustment of Hspot by means of, 158 Temperature compensation: device for H variometer, 84 estimation of compensation distance, 118 H variometer, 154 H variometer by two magnets, 157 magnetic, 96, 113, 116-118 magnetic; south latitudes, 112, 113 magnetic, Z variometer; evaluation of q coeffi- cients, 113, 115 mechanical; examples. 111, 112 mechanical; south magnetic latitudes, 112 optical, 120 Z variometer; evaluation of C field, 159 Temperature, effect of, on log C, 193 Temperature magnet, adjustment of, 119, 148 Temperature, standard, 166 Thermal expansion, coefficient of (magnet and iner- tia weight), 29 Time comparison, 174 Tune flasher, 23, 32, 67, 153 Time signals, 174 Tolerances in local anomalies at observatory sites, 21 Torque, applied; //variometer, 84 Torsion constant; Coulomb's equation, 88 Torsion constant: by oscillations, 89 by torsion observations, 89 calculations, 71, 72 D fiber, 74 equation, 71 evaluation from k' and Ms, 89 from nomogram, 94 from scale- value observations, 89, 90 H fiber, 84, 94 k', for D variometer, 81 definition, 88 estimation of; H variometer, 88 per unit magnetic moment; H variometer, 85 Quartz fiber, 70, 90 Torsion factor: D variometer, 74, 76, 152 //variometer, 154, 156 low-sensitivity variometer, 162 Torsion head, 150 Torsion in H variometer fiber, 84, 156, 157 Torsion, line of no; in variometer, 76, 85 Torsion in fiber, magnetometer, 27 Torsion observations, 30-32 Torsion pendulum, 71, 75 Torsion, removal of, 150, 154 Torsion tests, D, 76 Torsion, total; in D variometer fiber, 75 Torsion weight, variometer, 150 Torsionless fiber, 78 , 87 Total field of bar magnet, 9 Total intensity, definition of, 16 True azimuth; true meridian, 21 Unifilar suspension, 84 Uniform field, 3 Unit field, 1 Unit pole, 1 Variation building, 21, 22 Variation, daily, 19 Variometers, 23 Variometer data, miscellaneous, 145 Variometer, D, 74 — installation, 150 — miscellaneous data, 152 Variometer, H, 84 — installation, 154 Variometer, low-sensitivity, Schmidt, 66 Variometer, positions on pier, 149 Variometer, Z, 99 — installation, 159 Vertical intensity, definition, 16 Visual magnetograph, 165 Z magnet, la Cour, 164 Z recording magnet, effect on D variometer, 214 Z scale value, effect of H on, 105 Z spot, adjustment of, 161 Z temperature-compensating magnet; effect on D variometer, 215 Z variometer equation, 99, 101 DIRECTIONS FOR PERFORMING OPERATIONS a factor, H scale value; determination of, 159 Damping, H variometer; adjusting, 159 Disturbance, local, testing for, 148 Impurities, magnetic, testing for, 25 Induction coefficient: Lamont's method, 45 Nelson's method, 51 Magnetic meridian marking in variation room, 142 Magnetograph, installation of, 148 Mirrors, variometer; adjusting, 150 Optical lever, auxiliary, use of, 162 Optical system of magnetograph, testing of, 148 Orientation tests, 141 — critical adjustment of deflector, 141 Parallax, removal of, 67 Parallax test, recording of, 181 Processing records, 174 Quartz fibers, 71, 72 —•installation of, 72 Recording distance, D variometer, evaluation of, 82 Scale values, coil method, 133 Scale value: D, 129, 154 H, 126, 157 7, 128, 161 low-sensitivity variometers, 129 scale in telescope, 26 scale in magnet, 26 Scaling ordinates, 177 Sensitivity-control magnet, adjustment of, 157 Shrinkage, determination of, 180 Stray east field, D variometer, determination of, 151 Temperature coefficient of magnetic moment, 35, 84 — alternate method of determination, 39 Temperature compensation, optical method, 164 Time flasher, adjustment of, 153 Torsion constant, determination of, 71 Torsion, D variometer; removal of, 150 Torsion, H variometer; removal of, 154 Torsion factor, D variometer, determination of, 152 Torsion factor, H variometer, determination of, 156 Variometer installation: D, 150 //, 154 Z, 159 low-sensitivity, 162 U. S. GOVERNMENT PRINTING OFFICE: 1953