C€S,/j/l '-S/o£ A/&S -<2/ NOAA Technical Memorandum NOS NGS 21 / \ .<.< °' c % Sr *r K o< v ft / HAYSTACK-WESTFORD SURVEY Rockville, Md. September 1979 f^f^OO NATIONAL OCEANIC AND / National Ocean ■ IUQG ATMOSPHERIC ADMINISTRATION / Survey NOAA Technical Publications National Ocean Survey/National Geodetic Survey subseries The National Geodetic Survey (NGS) of the National Ocean Survey (NOS), NOAA, establishes and maintains the basic National horizontal and vertical networks of geodetic control and provides governmentwide leadership in the improvement of geodetic surveying methods and instrumentation, coordinates operations to assure network development, and provides specifications and criteria for survey operations by Federal, State, and other agencies. NGS engages in research and development for the improvement of knowledge of the figure of the Earth and its gravity field, and has the responsibility to procure geodetic data from all sources, process these data, and make them generally available to users through a central data base. NOAA Technical Memorandums and some special NOAA publications are sold by the National Technical In- fo irm^TTonService (NTIS) in paper copy and microfiche. Orders should be directed to NTIS, 5285 Port Royal Road, Springfield, VA 22161 (telephone: 703-557-4650). NTIS customer charge accounts are invited; some commercial charge accounts are accepted. When ordering, give the NTIS accession number (which begins with PB) shown in parentheses in the following citations. Paper copies of NOAA Technical Reports , which are of general interest to the public, are sold by the Superintendent of Documents, U.S. Government Printing Office (GPO), Washington, DC 20402 (telephone: 202-783-3238). For prompt service, please furnish the GPO stock number with your order. If a citation does not carry this number, then the publication is not sold by GPO. All NOAA Technical Reports may be purchased from NTIS in hard copy and microform. Prices for the same publication may vary between the two Government sales agents. Although both are nonprofit, GPO relies on some Federal support whereas NTIS is self-sustained. An excellent reference source for Government publications is the National Depository Library program, a network of about 1,300 designated libraries. Requests for borrowing Depository Library material may be made through your local library. A free listing of libraries currently in this system is available from the Library Division, U.S. Government Printing Office, 5236 Eisenhower Ave., Alexandria, VA 22304 (telephone: 703-557-9013). NOAA geodetic publications Classification, Standards of Accuracy, and General Specifications of Geodetic Control Surveys . Federal Geodetic Control Committee, John 0. Phillips (Chairman), Department of Commerce, NOAA, NOS, 1974 reprinted annually, 12 pp (PB265442). National specifications and tables show the closures required and tolerances permitted for first-, second-, and third-order geodetic control surveys. Specifications To Support Classification, Standards of Accuracy, and General Specifications of Geodetic Control Surveys . Federal Geodetic Control Committee, John 0. Phillips (Chairman), Department of Com- merce, NOAA, NOS, 1975, reprinted annually, 30 pp (PB261037). This publication provides the rationale behind the original publication, "Classification, Standards of Accuracy, ..." cited above. NOAA Technical Memorandums, NOS/NGS subseries NOS NGS-1 Use of climatological and meteorological data in the planning and execution of National Geo- detic Survey field operations. Robert J. Leffler, December 1975, 30 pp (PB249677). Availa- bility, pertinence, uses, and procedures for using climatological and meteorological data are discussed as applicable to NGS field operations. NOS NGS-2 Final report on responses to geodetic data questionnaire. John F. Spencer, Jr., March 1976, 39 pp (PB254641). Responses (20%) to a geodetic data questionnaire, mailed to 36,000 U.S. land surveyors, are analyzed for projecting future geodetic data needs. NOS NGS-3 Adjustment of geodetic field data using a sequential method. Marvin C. Whiting and Allen J. Pope, March 1976, 11 pp (PB253967). A sequential adjustment is adopted for use by NGS field parties . NOS NGS-4 Reducing the profile of sparse symmetric matrices. Richard A. Snay, June 1976, 24 pp (PB- 258476). An algorithm for improving the profile of a sparse symmetric matrix is introduced and tested against the widely used reverse Cuthill-McKee algorithm. NOS NGS-5 National Geodetic Survey data: availability, explanation, and application. Joseph F. Dracup, June 1976, 45 pp (PB258475). The summary gives data and services available from from NGS, accuracy of surveys, and uses of specific data. (Continued at end of publication) ) NOAA Technical Memorandum NQS NGS 21 HAYSTACK-WESTFORD SURVEY W. E. Carter, C. J. Fronczek and J. E. Pettey National Geodetic Survey Rockville, Md. September 1979 rED STATES ARTMEHT OF COMMERCE pita M. Kreps, Secretary i | NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION Richard A. Frank, Administrator National Ocean Survey |j Herbert R. Lippold, Jr., Director 1' m IP CONTENTS Abstract 1 Introduction 1 Background 2 Haystack-Westf ord vector base line 3 NGVD 29 connection 12 Gravity survey 12 References 14 Appendix A. Input data for adjustment 15 Appendix B. Output data for adjustment 29 Appendix C . Listing of orthometric heights 52 Appendix D . Listing of gravity values 56 Mention of a commercial company or product does not constitute an endorsement by NOAA National Ocean Survey. Use for publicity or advertising purposes of information from this publication concerning proprietary products or the tests of such products is not authorized, iii HAYSTACK-WESTFORD SURVEY W. E. Carter C. J. Fronczek J. E. Pettey National Geodetic Survey National Ocean Survey, NOAA Rockville, Md. 20852 ABSTRACT. A special purpose three-dimensional geodetic survey was conducted in the vicinity of the Haystack- Westford Radio Observatory complex near Boston, Mass. The survey included a high accuracy network connecting points of interest within the observatory complex and connections to the North American Datum (NAD) and the National Geodetic Vertical Datum (NGVD) . Extraordinary efforts were made to determine the components AXg, AYg, AZg of the Very Long Base Line Interf erometry (VLB!) vector base line to the highest possible accuracy between the Haystack and Westford radio telescopes. This report contains descriptive information on the methods employed in the collection, reduction, and anal- ysis of the survey data, tabulations of the observa- tional data, and numerical and interpretative results of our analysis. INTRODUCTION The results are given for a special purpose study conducted by the National Geodetic Survey (NGS) , an office of the National Ocean Survey (NOS) , NOAA, in the vicinity of the Haystack-Westf ord Radio Observatory complex near Boston, Mass. The survey had three major goals: ® To determine the locations of the Westford and Haystack radio telescopes relative to the North American Datum and the National Geodetic Vertical Datum. • To determine accurately the relative locations of the Haystack VLBI, Doppler, and intercomparison-validation reference marks. ® To determine in a well defined coordinate system the magnitude and orientation of the vector base line between the VLBI reference points at the Haystack and Westford radio telescopes. Since the survey required expertise within several specialized geodetic areas, it was planned and managed by a special work group. W. E. Carter served as Project Manager and C. F. Fronczek was Special Technical Advisor. Field Operations were performed by geodetic teams G23, G-37, and G-47, under the direction of the party chiefs, H. D. McKinney, D. C. Frazier, and R. S. Cohen, respectively. The final adjustment of the survey was performed by using computer program HAVAGO (Horizontal and Vertical Adjustment of Geodetic Observa- tions). HAVAGO was developed by T. Vincenty (1979) of NGS for special purpose surveys which combine horizontal, vertical, astronomic, and electromagnetic distance measuring (EDM) observations in a three-dimen- sional adjustment. The input for HAVAGO is listed in appendix A. Output is shown in appendix B. Close cooperation was received throughout the survey from the Northeast Radio Observatory Corporation (NEROC) , which operates the Haystack and Westford Observatories. NEROC was directly responsible for all tasks involving telescope operations and facility modifications. BACKGROUND The National Geodetic Survey, NOS, plans to use the Westford Radio Observatory as one of three permanent stations for project POLARIS (POLar motion Analysis by Radio JEnterferometric purveying). The project will utilize VLBI observations for monitoring polar motion and Earth rotation (Carter et al. 1978). The Haystack Observatory has been used for the past several years by VLBI researchers, enabling the determination of very high accuracy base lines between Haystack and several other radio observatories, e.g., National Radio Astronomical Observatory in Greenbank, W. Va.; Owens Valley Radio Observatory, near Bishop, Calif.; and Goldstone Radio Observatory, near Barstow, Calif. These observatories will very likely be used as base stations, in conjunction with transportable VLBI systems, to establish a much more extensive high accuracy network when VLBI becomes an operational geodetic tool. The VLBI base lines have already been used by NGS as a standard to check the Doppler satellite network scale and orientation. The Doppler network will, in turn, be a very important component of the new North American Datum. Comparative studies of various "space techniques" are being conducted cooperatively by the National Aeronautics and Space Administration (NASA) and NOS/NGS. Methods with geodetic potential include VLBI, satellite laser ranging, lunar laser ranging, and Doppler satellite observations. The Haystack-Westford Radio Observatory is one of the primary sites being used in these studies. As part of this program a facility suitable for occupancy by transportable laser ranging and VLBI systems has been constructed adjacent to the Haystack Radio Observatory. The measurements made by the various methods refer to different reference points, and the results can be compared only after their reduction to a common reference point. This survey was designed to yield the data necessary to make these reductions. During the past several years Haystack-MIT (Massachusetts Institute of Technology) researchers have repeatedly used VLBI observations to determine the vector base line from the Haystack radio telescope to the Westford radio telescope. Their results are summarized in Rogers et al. (1978) . The only other comparative information available is the result of a survey conducted by a private surveyor, R. Pressey, of Pressey, Inc., Lynn, Mass. Unfortunately, this survey was only designed to yield an accurate length, i.e., the magnitude of the vector base line, and did not address the question of orientation in any meaningful way. The VLBI and survey-determined lengths did agree to better than 1 cm, but the components had differences which were an order of magnitude larger. The NGS survey design was strongly influenced by a desire to determine optimally the components AX , AY , AZ of the Haystack-Westford base EEL line with present operational techniques and reasonable cost constraints. HAYSTACK-WESTFORD VECTOR BASE LINE Basic Formulation The components of a line connecting two stations on the Earth, expressed in a standpoint altitude-azimuth coordinate system are AX, = B cos A cos a A AY. = B sin A cos a A AZ. = B sin a A where B is the chord distance between the stations, A is the azimuth of line B, a is the altitude (vertical angle) of line B. Subscript A indicates an altitude-azimuth reference frame, If the astronomic latitude and longitude of the standpoint (i.e., the direction of the local vertical with respect to the rotational axis of the Earth and the Greenwich meridian) are known, the components can be determined in an equatorial frame of reference. The appropriate equations are AX = B [cos X (cos <{> cos a - sin sin a - sin 4» cos A cos a) + cos X sin A cos a] El AZ = B [cos (J) cos A cos a + sin sin a] hi where B, A, a are as previously defined, is the astronomic latitude, X is the astronomic longitude. Subscript E indicates an equatorial reference frame. The concepts and equations which are briefly presented above form the basis for the methods often referred to as three-dimensional geodesy. Several books and papers have been published on the subject, e.g., Heiskanen and Moritz (1967), Bomford (1971) and Rapp (1975). Survey Scheme Because of local terrain, vegetation, and obstructions associated with the radio telescopes and their enclosing structures, the VLBI vector base line could not be directly observed. It was necessary to use the survey network shown in figure 1. The Haystack telescope (fig. 2) has an altitude-azimuth mount. The vertical (azimuth) and horizontal (altitude) axes intersect (any eccentricity is below the resolution of this survey) and the point of intersection is the VLBI reference point for this telescope. There is no physical component at this point, but rather it is a point in space that can be located only with respect to some auxiliary monumented point. A special marker was designed and fabricated by NEROC and installed on the telescope trunnion. The location of the vertical axis was determined and marked as accurately as the survey techniques would permit. (The uncertainty is estimated to be a few tenths of a millimeter.) This mark was given the station designation HAYSTACK-TRUNNION. It is located directly below the intersection of axes at a location suitable for setting up and operating instruments such as theodolites and EDM units. NEROC cut two 30-cm-diameter holes in the Haystack radome to allow lines of sight from HAYSTACK-TRUNNION to the instrument points on temporary survey towers at stations OUTER CONTROL POINT (OCP) 2 and MILL. HAYSTACK TRUNNION OCP2 WESTFORD ANTENNA MILL t OND MICRO WESTFORD INTERCOMPARISON Figure 1. — Haystack-Westford vector base line survey scheme. Figure 2.- — The Haystack radio telescope is a 37-meter diameter Cassegrainian type instrument with an intersecting axis alti- tude azimuth mount. It is housed in a 46-meter diameter rigid radome. HAYSTACK TRUNNION is the monumented survey station established during the geodetic survey. The Westford telescope is also an altitude-azimuth mounted instrument, but the vertical and horizontal axes are offset by more than 0.3 meter. (See fig. 3.) The VLBI reference point is located at the intersection of the vertical axis with the plane containing the horizontal axis. Again, this is a point in space that must be referred to an auxiliary monumented point. A punch mark was made in the steel decking of the telescope directly on the vertical axis. This mark was given the station designation WESTFORD ANTENNA. The Westford telescope was NOT enclosed in a radome during the survey. Astronomic Observations Astronomic latitude and longitude were determined at three points in the immediate vicinities of stations WESTFORD, MILL, and OCP 2. The astronomic positions of the remaining stations were considered to be adequately determined because of their close proximity to one of these primary stations, i.e., the deflections were assumed to vary insignificantly for distances of a few tens of meters. Table 1 lists the observed deflections at the three primary stations. Table 1. —Deflections of the vertical Deflections Vicinity 5 (arc sec) n (arc sec) OCP 2 -1.75 +0.08 MILL -1.85 + .52 WESTFORD -2.16 + .79 The longitude determinations were made by the meridian transit method (Hoskinson and Duerksen 1947) using a Wild T-4 theodolite and a Data- metrics model SP-300 digital timing system. All the observed stars were taken from the Fourth Fundamental Catalogue (FK4) (Fricke et al. 1963) The latitude determinations were made by the differential zenith distance method, often referred to as the Horrebow-Talcott method (Hoskinson and Duerksen 1947) . The constraints on zenith distance differences and time between transits of the stars forming pairs require a catalog containing a large number of stars. It is not feasible to form acceptable observing lists from the FK4, which only includes approximately 1,500 stars. NGS presently uses the Smithsonian Astro- physical Observatory Star Catalog (SAO 1966) which contains more than 250,000 stars. This catalog has been related to the FK4 through zonal corrections. Figure 3. — The Westford radio telescope is an 18-meter diameter Cassegrainian type instrument with an eccentric (nonintersecting) axis altitude-azimuth mount. It is housed in a 30-meter diameter inflated radome. WESTFORD ANTENNA is the monumented survey sta- tion established during the geodetic survey. Both the latitude and longitude determinations included observations by two observers to minimize personal biases. Observations were made on two or more nights to reduce anomalous refraction errors. In addition, the sequences of observations were changed between nights to broaden the spans of right ascension covered by the observations. Astronomic azimuths were observed by the "direction method" (Hoskinson and Duerksen 1947) using POLARIS at any hour angle. Analyses of astronomic azimuths have shown that the determinations are contaminated by significant systematic errors such as observer bias and instrumental biases (Carter et al. 1978) . To minimize the effects of these systematic errors, a multiplicity of instruments and observers were employed. Observations were repeated on different nights and the intensities of the target lights were adjusted to resemble (as closely as possible) the star. All azimuths were observed with Wild T-3 theodolites. For the few lines not directly included in the azimuth observational program (very short lines) azimuth orientations were obtained through angular transfer using horizontal angles measured independently from the azimuth determinations . It is well known that the orientation of the physical body of the Earth with respect to the axis of rotation varies with time. This phenomenon is commonly referred to as polar motion. Polar motion causes the components of a line expressed in an astronomic reference frame to be time dependent. If multiple determinations of the components made at different epochs are to be compared, the observed values must be reduced to a common epoch. All astronomic latitudes, longitudes, and azimuths used in this survey were reduced to the Conventional International Origin using polar coordinates and time information published by the Bureau International de 1'Heure. Altitude Observations The altitudes (vertical angles) of the various lines were measured with Wild T-3 theodolites. Because of the shortness of the lines and by the use of surveying towers, which provided good ground clearance along all primary lines, refraction was not a major source of uncertainty in the alti- tude observations. The main sources of uncertainty resulted from measure- ments of the heights of the instruments and targets above the marks and from personal and instrumental biases. As with azimuth determinations, an attempt was made to minimize these biases by using several observers, theodolites, and observing periods. Precise Leveling Precise leveling was performed among the ground marks. These elevation differences can be included in the three-dimensional adjustment if certain assumptions are made about the behavior of the geoid within the survey area. The assumption most commonly made is that the direction of gravity varies uniformly between the endpoints of a line. Rapp (1975) presents appro- priate observation equations for this simple model. 10 The Haystack-Westford survey is very limited in extent and the terrain is not unusually rugged. The deflections listed in table 1 do not suggest any anomalous geoidal behavior in the area. The simple model appears quite appropriate and was used in this survey adjustment. Electromagnetic Distance Measurements Electromagnetic distance measurements were made over all lines of the survey scheme. Three different instrument models were used: Tellurometer MA100, Hewlett Packard 3800, and Ranger IV. All were calibrated immediately prior to their use, and their frequency standards were checked frequently during the survey. Meteorological measurements to determine the atmospheric index of refraction were collected at regular intervals throughout the EDM observing periods. Experience has shown that, even after the application of all known refraction corrections, scale biases as large as a few parts in 10 6 often exist between EDM made during daylight hours and darkness (Carter and Vincenty 1978) . Since the source of bias is not clearly understood, it is not possible to state definitely what relation- ship exists between the correct scale and daytime or nighttime observa- tions. With the absence of better guidelines, the EDM observing schedules were divided almost equally between daylight and nighttime periods. For this particular survey, the primary sources of errors in the EDM observa- tions were probably instrumental biases and setup (centering) . Comparison with VLBI Results The components of the Haystack-Westford base line (extracted from appendix B) are given in table 2, along with the values derived from the VLBI experiments. The differences between the AY E and AZ E components are larger (by a factor of 2 to 4) than would be expected from the esti- mated uncertainties associated with the values. If these values are Table 2. — Comparison of NGS and VLBI components of the Haystack-Westford vector base line in an equatorial reference frame Difference Components NGS VLBI NGS-VLBI m m m AX E -198.139 -198.139 -0.000 AY E -863.983 -863.999 + .016 AZ E -866.234 -866.223 - .011 B 1,239.390 1,239.394 - .004 11 transformed to a Haystack altitude-azimuth frame of reference, the discrepancy is almost entirely in the AZ^ component (table 3) , which Table 3. — Comparisons of NGS and VLBI components of the Haystack-Westford vector base line in a Haystack altitude-azimuth reference frame Difference Components NGS VLBI NGS-VLBI m m m AX A -1,149.592 -1,149.594 +0.002 AY A -462.196 -462.200 4 .004 AZ A -30.024 -30.005 - .019 corresponds closely to a disagreement in the difference in elevation of the two observatories. To ensure that no undetected blunders had been made in the NGS survey, a special team verified the connections between the Haystack VLBI reference point and OCP 2 and Westford VLBI reference point and station WESTFORD 1978. Both connections checked to ±1 mm. Later, the difference in elevation between OCP 2 and WESTFORD 1978 was also verified by the leveling team which made the connection between the Hays tack-West ford scheme and the NGVD. During the reduction, adjustment, and analysis of the survey, tests were run to determine the sensitivity of the solution to the selection and weighting of individual observations. For example, adjustments were made with only the zenith distances, only the leveling, and both the zenith distance and leveling observations included. The a priori uncertainty estimates of the observaions were also varied. The components of the base line varied by only a few millimeters for the solutions based on what we considered plausible data sets. It appeared very unlikely that the base line components deter- mined by the survey could be in error by enough to explain a significant portion of the 0.019 meter discrepancy in AZ^, Rogers et al. (1978) had pointed out very explicitly that little was known about the gravitational flexures of the two radio telescopes. Because of the disagreement between the NGS and VLBI results, NEROC personnel measured the flexures. They found that the Haystack telescope did exhibit significant flexure. The effect of this flexure on the VLBI base line orientation is qualitatively correct, and quantitatively of the correct order of magnitude. The final numbers were not available in time for inclusion in this report, and will be published elsewhere in a joint NGS-MIT-NEROC paper. 12 NAD 1927 CONNECTION The connection to the North American 1927 Datum is shown in figure 4. Both EDM and horizontal directions were observed. WACHUSETTS 2 1896 and TADMUCK (MAGS) 1936 are transcontinental traverse (TCT) stations. This net- work was included in the survey adjustment performed by program HAVAGO, and all pertinent data are given in appendices A and B. TADMUCK (MAGS) 1936 WACHUSETT2 1896 Figure 4.— Connection of Haystack-Westford vector base line survey scheme to NAD. NGVD 29 CONNECTION In addition to the precise leveling accomplished as an integral part of the Haystack-Westford vector base line survey, a first-order, class I level line was run to connect the local scheme to the National Geodetic Vertical Datum (NGVD). The spur line is 24.4 km in length and connects to the first-order network at Lowell, Mass., at bench mark Z33. Figure 5 shows the path of the survey. The field work was completed by a subunit of Party G-37, under the supervision of R. Taylor. An adjustment was performed by the NGS Vertical Network Branch, holding the elevation of bench mark Z33 fixed at the NGVD 29 value of 46.410 m. The resulting normal orthometric heights are listed in appendix C. GRAVITY SURVEY Gravity measurements were made along the level line that connects to the NGVD 29 and at several survey marks within the observatory complex. Ties were also made to the U.S. National Gravity Base Network (USNGBN) . The field work was done by L. M. Johnson, and the data were reduced and adjusted by the NGS Gravity, Astronomy, and Satellite Branch. Results are listed in appendix D. 13 NEW HAMPSHIRE Haystack-Westford radio. Observatory complex First-Order Leveling Line ' MASSACHUSETTS 43° 42°N 71 °W Figure 5. — Connection of Haystack-Westford Radio Observatory complex to National Geodetic Vertical Datum. Heavy dashed line indicates route of new leveling. 14 REFERENCES Bomford, G., 1971: Geodesy . Clarendon Press, Oxford, third edition, 731 pp, Carter, W. E., Pettey, J. E., and Strange, W. E., 1978: The accuracy of astronomic azimuth determinations, Bulletin Geodesique , 52(2), 107-113. Carter, W. E. and Vincenty, T., 1978: Survey of the McDonald Observatory radial line scheme by relative lateration techniques. NOAA Technical Report NOS 74 NGS 9, 33 pp. Carter, W. E., Robertson, D. S., and Abell, M. D., 1978: An improved polar motion and Earth rotation monitoring service using radio interf erometry. Proceedings of the International Astronomical Union Symposium No. 82 , Spain, in press. Fricke, W. , Kopff, A., et al., 1963: Fourth Fundamental Catalogue (FK4) . Veroff. des Astron. Rechen-Instituts Heidelberg, No. 10. Heiskanen, W. A. and Moritz, H. , 1967: Physical Geodesy . Freeman and Co., San Francisco and London, 364 pp. Hoskinson, A. J. and Duerksen, J. A., 1947: Manual of geodetic astronomy. Special Publication 237, U.S. Coast and Geodetic Survey (now National Ocean Survey, NOAA), Department of Commerce, Washington, D.C., 205 pp. (National Technical Information- Service accession #PB267465) . Rapp, R. H., 1975: Geometric geodesy notes, vol. II, Ohio State University, Columbus, pp. 111-134 . Rogers, A. E. E., Knight, C. A., Hinteregger, H. F., Whitney, A. R., Counselman, C. C, Shapiro, I. I., Gourevitch, S. A., Clark, T. A., 1978: Geodesy by radio interf erometry— determination of a 1.24 kilometer base- line vector with ^5 millimeter repeatability, Journal of Geophysical Research 83 (Bl) , 325-334. SAO (Smithsonian Astrophysical Observatory) (staff of) 1966: Star catalog. Positions and proper motions of 258.997 stars for the epoch and equinox of 1950.0. Publications of the Smithsonian Institution of Washington, D.C, No. 4562, Smithsonian Institution, Washington, D.C, vols. 1-4. Vincenty, T., 1979: The HAVAGO three-dimensional adjustment program. NOAA Technical Memorandum NOS NGS-17, 18 pp. 15 APPENDIX A.— INPUT DATA FOR ADJUSTMENT Program HAVAGO produced the following computerized listing of input observational data for the survey. 16 a. 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CO CO 10 CO 0. 0. >• CD ll o 3- O O e» cs o • • • • » i* e HOKIO u sr a 3 M 1/3 K a a u o 3T £ £ £ £ > h- £ X £ £ £ £ o CJ LJ o o o o o o CO > * • • • • • to o HOK) o o LJ * 3 *" CO LI co _) K 19 10 o Z LJ K < J a CO Id J z < < CO CO o CJ U LJ lC « _l o u < h- < z z a eu<< 2 u >-> t- t- < > »- C0 CO t~ ee 1-4 9-4 xr, CO 2 _SuJ < > o a ** O CO u k> LJ ce ** X O O (- > o h- k-e jo-i M U 3 0. Q. _l h- X bl X « 3 o < 0. PC ►h U O CO J M M LJ (K CO LJ < D «ri5 cr a: 29 APPENDIX B.— OUTPUT DATA FOR ADJUSTMENT The following computerized listing, using program HAVAGO, shows the output of the three-dimensional adjustment. 30 o IX id w a id co o • CO CO s s: o Q 2 2 O * ix O •J id t- 2 < Id CJ X CO 2 a. LJ 2 2 *■« U. E31 U. U. 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