QB
42
119.23
PRECEPT S,
FORMULAS,
TABLES,
CHARTS,
AND
IMPROVEMENTS;
amuel
BY
S DUN N, 4.74
Teacher of the Mathematical Sciences LONDON.
Published according to Act of Parliament, September. 1° 1784. by S. DUNN.
t
Goth
85-35
Mathematica
5-25-1923
10-16 - 24. EHW
LONGITUDE Instructions; By S. Dunn.
1. Gret the Altitude of the Sun's Centre cleared
from Dip & Sanidiameter, the Altitude of the Moon's
Center deared from Dip & Semidiameter, & the Sun.
Moon's nearest Limbs,
Add 32 to the-
observed Distance of Limbs to get the Rough
Central Distance, with this from Ephemeris…….
page 8,9,10 or 11 for the Month, where the Day
of the Month & Sun are together take out the
nearest Hour; this is the rough Hour for...
Greenwich.
2. The Ephemeris has the
Sun's true Semidiameter
Moon's true Semidiameter
--
Moon's Horizontal Parallax -
Three hourly Distances
Sun's true Declination
page.
page...3.
7.
7.
8,9,10,11.
2.
The Requisite Tables have the
Seconds for Moon's Altitude --page-3 .
Refraction in Altitude
2.
Moon's Parallax in Altitude --- 3,4,5.
Time & Degrees-
6.
3. Begin the Formula with the Rough Central
Distance & Rough Hour for Greenwich, &go
on as it directs until you come to the Number
E in it. Then, in usual Cases, the nearer the..
Rough Central Distance in Degrees, comes to
comes to
120, the greater it is; & the nearer it comes
to 20", the less it is. A great Altitude of the
Moon be that above 20°. When the--
may
Rough Central Distance in Degrees is great,
& especially, when the Moon's Altitude is ..
also great; then Number E
may
for the true Distance of Centres.
be written-
4. For small Distances,
4. For small Distances, or small Moon's Altitude;
Take the Moon's Parallax in Altitude from Requisite
Tables page 3,4,5; with this & the Distance take
the Seconds from large Table IV. also with Number
C & the Distance, take the Seconds from the same Table
IV; & the Difference of these Seconds is F.
5. From amongst the three hourly Distances in
Ephemeris page 8,9,10 or 11, take two such Distances
following each other, so that the taue Distance of the
Centres falls between them; then go on by the Formula
till you have the Time at Greenwich; this is past
noon for Greenwich.
6. From Ephemeris page 2. take the Suri's true
Declination for the Hour at Greenwich; & when the
Declination & Latitude are both North or both
South, subtract the Declination from 90; but in
other Cases, add the Declination to 90, to get the
Blar distance. And subtract the Sun's Co-altitude
from the Half sum to get a Remainder. Then go
on by the Formula, 'till you have the Time at the
Ship; this will be past Noon at the Ship in
an Afternoon Observation, &short of noon in
a Formoon Observation.
7. In an Afternoon Observation, subtract one
Time from the other, the Remainder is the
Longitude; & it is West Longitude when the Time
at Greenwich is greatest, but otherwise Fast Longitude.
In a Forenoon Observation, add the two Times together,
the Sum is the Longitude West, & it's Remainder to
either 24 Hours or 360, is East Longitude .
NB. These general Recepts, in several Parts of the
Operation, may be shortened, by attending to the
following Direction's concerning each in particular.
Published according to Act of Parliament May 29th, 1782 by Samuel Dunn, Fleetflreet
LONDON.
8. Dum inv.& delin".
425944
Supplementary LONGITUDE Instructions; By S. Dunn.
of Preparations.
1. When the Sun & Moon's nearest Limbs
have been observed; add 32′ to get
get the
Rough Central Distance. Also, add the Sun
& Moon's true Samidiameters, & Seconds for
Moon's Altitude; to get I.
2. When the Star & Moon's nearest Limb
have been observed; add 16' to get the Rough
Central Distance. Also add the Moon's true
Semidiameter, & Seconds for Moon's Altitude,
·to get L.
get_L.
3. When the Star & Moon's farthest Limb
have been observed; subtract 16 to get the Rough
Central Distance. Also, subtract the Moon's true
Semidiameter, & Seconds for Moon's Altitude,
to get I.
of Contractions.
1. In taking out the Number from large Table 1,
the nearest whole Degrees may be used in the
most ufual Cases.
2. When the Number falls above or near the
Crooked Line in large Table I, you need not
find the Numbers A,B; but take from large
Table III, the Seconds that are to be added to
Number L, to give Number D.
3. When the Sun or Moon's Altitude is
very
small, the Refraction should be taken from the
Altitude, before it is written in the Formula,
next after the Horizontal Parallax.
4. In computing the Time at the Ship; the
third Number or Sun's Co-altitude, is that
of the Altitude lessened both by Dip Refraction.
t
of Operations.
7. The Observations should not be made wher
the Sun or Moon are very near the Horizon.
If the Moon is very near the Honzon, Proportional
Parts should be used in large Table I.
st
2. Four Places of Logarithms with Index, are
used, till the last Cofine; then the fifth Figure is 5
when 1 remains, 0 whm 0 remains.
3. C must not be added to D, unleſs the 1 Are is
least of the two Ares, & at the same time D is leſs
than 90. In other Cases, subtract C from D.
of Observations.
1. In observing for Longitude only, without use of
a Watch, the Sun should not be very near the
Meridian; then Observations will determine Latitude.
Also, when the Moon is near the Meridian,
Observations will determine Latitude.
2. When the Sun is far à Meridian & not near
the Horizon, Observations are best for the Time &
setting a Watch.
3. In the Night, the Watch shews Time at the Ship.
When no Watch is used in the Night, the Right
Afcension of Sun Star, compared with the Star's
distance from the Meridian, either past or short of
it, gives Time at the Ship. In this, the Chart of
Zodiacal Stars is useful.
4. The Stars of first Magnitude out of the Zodiac,
are useful for Time at the Ship; such as Capella, the
principal in Orion, Canopus, Sirius, Procyon, Lyra.
And so may Venus, Mars,
Jupiter & Saturn.
5. The same Stars & Plands may be used for Latitude
by Meridian Altitudes, Elapsed Time, & otherwise.
6. The principal Stars used in the Lunar Method are, Aldebaran, Polluxe,
Regulus, Spica, Antares, Aquila, Fomalhaut. The others are, Capella, Orion's
Sirius, Procyon, Canopus, Arcturus, Lyra; the Bears, Ship & Grofs.
th
Tublished according to dot of Parliament May 29. 1782 by Samuel Dunn, Fleetſteet LONDON --
&. Divin mer. So delin.
A Short Formula for LONGITUDE, having the Linear Tables, &c By S. DUNN,
Distance Limbs =
Semidiam..
> Semidiam..
For Altitude..
Distance Centres L. =
For&) Alt.
Rough Hour at Greenw
Altitude..=
> Altitude._=
Hor Par.
Co-ar
in Table 1-2.
15
1º Hours...-
2 Hours..
Diff.... f=
"
Ditto...
P.
Common Log.
in Table I
m
A=
Side of P.L.a 4. add =
Bottom P.L...
Minutes.
B:
"
Diff...L=
Prop. Log. S=
Prop. Log.f=
in Tate Prop Log-
1. Hours add in Degrees.
Tune at Greenw past Noon.
Altitude.
add to Dist Centres.
D.::
Altitude.....
) Hor Par.... —
First Arc..---
D..=
= Correction for Refrac".....-
=
Sine.
Co-Secant. =
Proper Log
Proper Log =
Tangent....
Co-secant...
6
sub.
Co-latitude
Polar-dist.
Co-ar
Co-ar
Co-alt..
2)
Hor. Par.. ----
Proper Log-
Half-sum-
Remaind
Sine.
Sine
"
SolarTime
2
Second Arc...
Proper Log
at per Watch
= Co-sine
H
Corr for Par...C.-
D..:
Add the Amos together if D.exceeds 95.
Z
Add C to D.only when the first Are is the least of the two &atsame time is less than go
E.-
F.
P..
3.- 45
6.=
= yo
9.135
add "Eis under go.
True Distance of Centres.
In this Formula when riot to add, subtract.
"
sub.
Time at Ship
Longitude from Greenwich.
154. =223.
18.=270
21.-315
12.=180. Published according to Act of Parliament October 24, 1783 by Samuel Dunn Boar's head Court, Fleetstreet LONDON 24.=360
S. Dunn init et dolin
A New Formula for LONGITUDE, having the Linear Tables, &c.By S.DUNN.
N.B. Co. is Rem. to go. Supp.is Rem to 180. Co-ar is Co-secant less Indexx zo. Sine, Tangent Secant or Coar of Degrees more than go is that of Supp. Subtract if not to add
Solar Time is used for the Longitude in Hours & Degrees. Mean Solar Time is that which Clocks & Watches are made to keep nearly at Sea&c on Land,
Distance Limbs =
Semidiam.....
ɔ Semidiam...
For Altitude.
"
Rough Hour at Greenw.
Altitude
> Altitude =
1. Hours..=
2dHours
Diff...-f=
Hor. Par =
"1
Distance Centres L
Co-ar
ForɔAlt
in Table 1.-2.
H
Common Log
A=
in Table I
B=
K
add to Dist Centres-
=
= Correction for Refrac
Dz
Sine.
Altitude
Hor. Par
First Arc
Altitude.
D.z
Hor. Par
m
Co-Secant.
Proper Log
Proper Log=
Tangent...=
Co-secant.
m
Ditto...=
P...
Diffe... £=
Prop. Log⋅ S=
Prop. Lof
Co-latitude =
Polar-dist.=
Co-alt...=
2)
Half-sum =
Remaind."
Solar Time
abper Watch.
in Tab Prop Log-
1.Hours add in Degrees or Hours.
...... Time at Greenw. past Noor.
Co-ar
Co-ar
Sine..
Sine
2)
= Co-sine
=Time at Ship
Proper Log =
"
"1
Second Arc
Cory for Par...C...
D...
Add C.to Donly when the first Arc is the least of the two at same time Dis less than go,
E..=
EE
This
add it. It is undergo Dip, ` ` ` ` ` *g
True Distanc
Fiet
7=1
4.=2
14=4
Proper Log"=
K
Add the Ares together if Daxceeds go
ཅུ སུཝ
Alt. Re
Ref.
- Longitude from Greenwich.
Alt. Ingmare Hows Degrees-
42
Book o che
Dec.
Nov
Oct.
ལ་་བམ།
K
Aing.
72=
15=
8
Sep. Eu
F8
Jul.17
22-
15212.0
F8
Tron
ལམགྲུས
Mar. 17
-22-
1595
7
15=
222.12
Feb. 1z
82
& Hands.
at Day.
Published according to Act of Parliament October, 4, 1983 by Samuel Durn Boar's head Court Fleetsweet LONDON,
Morid"
&
15-
22.
HP 4pr.
15-4
223
Qako
Mar
© or* à Limbs obsa
© Semidiam!
.P.3
D Semidiam!
p.7
Parts for D Alt.
A Formula for the LONGITUDE having the Ephemeris & Common Tables of Logarithms By SDunn Teacher of Mathematics LONDON.
Nearest Limbs:
©or*a)
1.
ά
DAlt
•I
Farthest Limb
* à D Limb
D Semid!"
· Ih
Odlt. It
ditto
Hours o
"
=
Rough Time I
Lat
first Hour & Distance in Ephem.
second ditto.
Log.
Diff-
sub.
Parts for D Alt.
Sum sub.
Sum is D=
Remain is D=
E
Altitude
Dip & Semid."cleard.
© or*Alt..
Dip & Semid, cleard.
Diff
Coalt
co.ar.
D
Ⓒor* Coalt
D
co.ar.
co.ar.
co.ar.
Oor *Coalt.
D Coali
i
3.4314
Log
Sum
Log
2
2
Add
12 Sum
Sine]
½ Sum
Sine
first Hours in Degrees
Time at Greenwich in Degrees.
Remain
Sine
Remain.
Sine
Co.arch
Sine
Co.arch
Sine
2
2
M=
S
Co. sine
DCo.alt
Refraction
Sine
add
Co.latitude
Polar dist
Co. altitude
2
co.ar.
?
co.ar.
2
Parin Alt
DHor. Par *Log.
Difference
Log.
½ Sum
Ramain
Sine
Sine
DPar*Alt Log.
B =
Log.
To. arch
Sine
Refraction sub.
A =
sub.if Mis under go
B =
add if S is under go!
Aft noon
Difference Log.
С
C =
is
M
=A
Co.
fine
Log.
D=
E =
For Altitude.
30
60
70
75
2
S.Dunn inv,& delin
allow © Par. in Alt.
Long?
30
12
60 14
880 16
NB. 1th Rough central Distance sheros the rough Hour at Greenwich & thereby the 's Dedin.is had Ephem. p.2.(the Is Semid"
2. Co. ar. is Cosecant les 10 in the Index.
is p.3.) the D's Semid & Hor. Par p.7.
3d Co. ar. or Sine &c. of more than go. is of
4th Refraction to be taken from the truest Tables. 5th When you do not add subtract. 6th Co. alt sub-
the Remain to 180,
-tracted from ½ Sum gives Remainder. Polar Dist. is Decl,"subtracted from 90. if Ded! & Lat. alike, else added to go..
7th If Time at Greenwich & at the Ship are both before or afternoon, their Difference is the Longitude; else it is rohat they are
8th Observe for Time at the Ship when is not near the Meridian. 9 Reasons at large are in Aftronomy p.185 & Lon
apart.
-gitude at Sea p.go. 10th Latitude is found at any Time of the Day by the common Logarithms, as published by the Author, which fee.
„Published according Act of Parliament, March 17*1779 By Samuel Dunn Maiden Lane Coventé LONDON,
Bef. noon
Time at
the Ship
For D'Alatude
10
15
Parts
34
א
For D Altitude
Parts
"
4010.
Change
1.2.4.5.6.
341.26.
α Markab.
343 31.
a Aldebaran..
α Capella
B Rigel
Y Orion.
d Orion
d. Canopus...
d Sirius
& Caftor..
47.17.
65. 54.
75. 12.
76.3.
78.24,
85,54.
94. 48.
98.56.
110.12.
112. 1 .
113. 3
α· Procyon..
B. Pollux
B Ship...
137. A2.
& Hydra
d. Regulus
162 2.
α N.Pointer...
B S. Pointer...
& Cross..
& Spica
a Arcturus...
α Centaur..
& Antares....
& Lyra
a Aquila....
-α· Fomalhaut.
2.3.5.6.8.
2.4.6.8.10.
1 3.5.7.9.
2A7911
1.3.A.6.7
2.3.5.6.8.
2.3.5.6.8.
1.1.2.3.3.
1.2.4.5.7.
2.4.6.8.10.
2.3.5.6.8.
7 2.4.6.8.9.
The Change for Years, added to R.Afc. gives the R. Afc. required.
0.1.1.1.2.
139.16.2.3.4.6.7.
149.14.2.3.5.6.8.
162 3A.
183. 43.
198,29,
211, 29.
216.21.
244 A.
277.25.
295. 5.
3.14 .N.
49. 5 N.
16. A ‚N.
45 46.N.
8.27.S.
6. 8.N.
7.21 .N.
52.35.S.
16.25.S.
32.21 N.
5.46 N.
28.32 N.
68.50.S.
7.45.8.
13. 0 .N.
57.32.N.
62.54 N.
61.55.8.
59.57.8.
25.56.8.
38.36 N.
8.19 N.
30.45.S.
14. 4 N.
The Right Afcensions and Declinations of Fixed Stars, By S.Dunn.
1785.
R.Aſc.
d. Eridanus....
22.25.
a. Whale's Faw.
42. 46.
α. Perfeus..
2.4.6.8.10 Years. Declination.
58.19 .S.
2.4.6.8.10 Years.
change
1.1.2.2.3. rub.
2.4.6.7.9.
2.4.6.8.10.
2.3.5.6.8.
2.3.5.6.8.
1.3.4.6.7.
2.4.7.9.11.
2.4.5.7.9.
1.2.3.4.5.
1.3.4.6.7.
10. 2.S.
20. 22. N.
The Change for Years, applied to Decl" give the Decl" required.
1.1.1.2.2:add.
0.1.1.2. 2. add.
0.1.1.1.1. add.
0.0.1.1.1. add.
0.0.1.1.1.sub.
0.0.0.0.1.add.
0.0.0.0.0.
0.0.0.0.0¡
0.0
•
0.0.1.add.
0.0.1.1.1.sub.
0.1.1, 1, 1, sub.
0.1 1,1,1 .sub.
•
0.1.1.2,3; add.
1.1.2.2.3.add.
1.1.2.2.3.sub.
1.1.2.3.3.sub.
1.1.2.3.3.sub.
1.1.2.3.3. add.
1.1.2.3.3. add.
1.1.2.2.3.sub.
1.1.2.2.3. add.
0.1.1.1.2.add.
0.0.0.0.0.
2.3.5.7.8.
1.3.4.6.7.
Y Rigafus
0.33
2.3.5.6, 8.
a Bole Star...
12.14.
6.11.17 23.29.
0.1.1
1.1.add.
1.1.2.3.3.sub.
1.1.2.3.3.add.
13.59 N.
1.1.2.2.3. add.
88.10 .N.
1.1.2.3.3.add.
Note,
The Change in R.Afc" is additive. The Change in Declination is as it is written.
A Mmiature Sketch of the Isines in the Chart of Zodiacal Stars.
Frquater
atering
sliptic:
Fauster
Ridiphic
90
th
Published according to Act of Parliament June 29*. 1782 by Samuel Dunn, Fleetſtreet -LONDON.
S.Dum úrv: delin'?
A New Formula for Latitude, having Two Altitudes &Elaps'd Time,
between Nine in the Morning & Three Afternoon. By S.DUNN.
First Operation:
Second Operation:
Greatest Alt.
;
· Least Alt.
Sum......
1/2 Sum......
Diff.....
Co-sine.
:/½ Diff.....
Sine...
% El Time
Co-ar...
:Ded"
Sec.-R..
: Lat. Aco.
Sec-R..
Mid Time
Sine.....
El.Time
• Rem.....
.301030
::½ Rem
Sine...
Ditto....
Sine....
Decl
Co-sine
- Lat Acc
Co-sine
With Indo-6 is
Log...
Nodd
-Greatest Alt.
Sine...
No
• Merid" Alt.
Sine...
N
Dedh
Co-lat....
Latitude
N.B. 1th The Altitudes are deared from Semidiameter, Dip & Refraction. 2 Allow 6 less, -
than the Index in Log-sines,& you have the Natural Sines in Numbers opposite to the Commun
Logarithms. 3 Mid-time, is the Distance of the Middle-time between the Observations from Noon.
Published according to Act of Parliament September 4. 1784, by S. Dunn
A Formula for Latitude, having affumed Latitudes, & Elaps'd Time, By S. Dunn.
1"Lat
1. Lat. L.
2. Lat./.
Co.lat.
91
7.
Bolard.
.lo.alt.
Co.ar.
Co.ar.
Co.lat.
Co.ar.
Blard.
Co.ar.
1.Co.alt.
2
Sum
Sine
áSum
Sine
Rem".
Sipe
Ran.
Sine
2
2
Cofine
Cofine
2
B=
E-
st-
1. Lat L..
Co.lat.
Polard.
2. Lat.l.
Co.ar.
Co.lat.
lo.ar.
lo ar.
Blard.
Co.ar.
d
2. Co.alt.
2.Co.alt.
24
Sum
Rom"
Sine
Sum
Sine
Sine
Rem".
Sine
2)
Cofine
Sine
2
Cofine
D=
A =
B
add or fub. AFB te give C,
E
nearest to Q
LC =
LE
C =
for 1. Lat.
F-
for 2" List
G-= Diff
H-Diff.
H:
G=: H :: I : K.
st
t
Supp to 180".
Q-Elapsed Time.
I = Diff. Q&C or Q&F.
K=Comec for Lorl
add or fub. D&E to give F.
nearest to Q .
1. The assumed Co-latitudes, Polar-distances, & Co-altitudes, must be such, that any two of them together,
must be more than the third. 2. Co.ar. is Cofecant, lefs Index 10. &Log. of more than 90. is Log. of
3" When the true Lat. is between those affumed, the Correction converges fast to Truth
4th When Is is true, Bis trueTime of 1°. Alt. A true Time of 2. Alt. from Noon. The like for E&D.
For Azimuth, work as above, with Co-lat, la alt. &lar dist. this gives Azimuth from North in N.Lat.
& from South in S.Lat 6. When the same Lat. repetes, the Lat. Times &Azimuths are correct.
H
S. Pum inv. delin.
th
th
Published according to Act of Parliament June 29. 1782 by Samwel Dunn, Fleetfreet LONDON,`
5
1
A New FORMULA for LATITUDE, having, Sights of the Sun, Elaps'd Time
and Equal Dedination. By S. Dunn,
1 = Latitude by Reckoning --
d-Destination
11=Altd• far a Meridian...
B= Co-declination
N= Altḍnear Meridian
Q = Elapsed Time...
Farther Calculations.
0=Co-latitude..
p-Polar dist.....
a= Co Alt
lo.ar.
Co.ar.
Co-latitude
Sum
Sine
Rem".
Sine
Cofine
2
t=
Q=
T:
Sine
d=
Coline
G
Sine
d=
Sine
G-
Secant
A=
Coline
N=
Sine
G=
Secant
D-
Coline
A-
B-
C=
add ifp is under 90:
dfo zub.
D=
E=
Zenith dist.
d:
Dedination.
Latitude.
Published according to Act of Parliament July 27th 1782 by Samuel Dunn Fleetfreet LONDON
S.Diam invt & delinª.
1
S.Dunn
A New FORMULA for LATITUDE, having, Sights of the sun, laps'd Time; By 8.Durm.
1=Latitude by Reckoning
d=Dect" far à Meridian
O=Co-latitude
p-Blar dist.....
a=Co-alt..
Co.ar....
Co.ar.....
d
n = Alt"Ⓡ far à Meridian.
F-Deal
near Meridian.
B = Compt. Declination,
P-Polar dist. near Merid?.
N=Alt. near Meridian
b = Co-alt. near Merid
Q-Elaps'd Time
st
n
1. Obs"
2¢
d
4th
5th
6th
th
H
Sub
Rem".
Sum
Sines
Sine
Cofine
2
n
t=.....
1
Q=...
T:....
F= ...
G=
F-....
•
G=....
7:
NB! The Observation far à Meridian may be at any
time of the Day; the other should be as near the-
Meridian as it can be judged of & taken. 2ª
Co-ar is Cofecant lef's Index 10. & Log. of more
than 90 is Log, of Supplement to 180°.--
3. When d&F are equal, then p & Pare
equal. 4th If Decl". & Lat. are both North -
or both South, fubtract Decl. from 9o..
but if otherwise, add Deal". to 90 to get_-
Polar distance .
Az....
Nz...
•
G=...
D=..
Sine....
Cofine..
Sine....
Sine....
Secant
Cofine
Sine
Secant
afine
A=...
B..
l=...
add if P is undergo.
efe sub
D=...
E=...
Zenith dist.for F.
F-...
Dedination.
Latitude.
L =...
Co-latitude.
Ref.
Height Dip Height Dip Alt. Ref. Alt. Ref. Alt. Ref Alt. Ref. Alt. Ref. Alt.
Ft
F
= 1
34
22
IP IPTV I
7=33
12=32
43-30
27 1.33-21 2.50-15 5:20-0 17.03
40=26743-20 3.7:746.75=8 24.0=2
歹
​18=31 50=251.54-10 3.27=137.15-747.0
24-307.4-24 2.7-18 3.50-728.35-6 90.0
30=207.13=23|2.10=17 4.20=77|10.15=5
·.50:10 13.0 =4
36=287.
7.23-29 33-184.20=-11
Published according to Act of Parliament May 20.1782 by Samuel Dunn Fleetflreet, LONDON .
S.Dunn ine↑ & delin'
A New FORMULA for LATITUDE having Sights of STARS, BY S.Durn.
* L = Latitude by Reckoning.
d=Decl" far à Meridian
•n_Alt. far à Meridian ----
F-Decl near Meridian__.
B= Compl. & Declination--
P: Polar-distance of
N-Alt.
near Meridian
· b = Complement of Alt.
*'s Right Afcension
's Right Afcension
O=Co-latitude...
p-Polar dist
a= Co-alt.
sub
2
Rem".
0
Co-ar...
Coar...
Suan
Sine
Sine
Cofine
2
t = .....
Q=.....
T………..
Sine...
F- .....
Cofine
Q=* & Equator, distance...
2
G
Sine..
F.....
Sine..
NB./.
should be observed as near the Meridian as -
Ge.....
Secant
d
th
possible. 2. The Altitudes of& should be dear'd_
from Dip & Refraction. 3.C is the Difference of A&B.
4th When I is the true Latitude,t is the true Distance -
of from Meridian &T that of. 5. When tu..
less than Q the Altitudes were on different Sides of the -
Meridian. 6." When t is greater than the Altitudes
A=....
Cofine
N=....
Sine...
G=....
Secant
th
Da....
Cofine
Az....
th
th
were on the same Side of the Meridian. 7. As 0, p, a,
are used to find t; so use I, p, a, to find t correct -
& then I correct. 8. So use 1, a,p, or rather use
I,a,p,
I, a,p, to find 's true Azimuth; & l, b, P, or. -
B....
rather L, b, P, to finds tave Azimuth. 9th
Co-ar is Co-fecant lefs Index 10. Log. of more
*
than go. is Log, of Supplement to 180°
add if Pis under go
affe sub.
Zenith distance.
Dedination.
Latitude.
Co latitude.
Height Dip. Height Dip. Alt. Ref. Alt. Ref. Alt. Rg: Alt. Ref. Alt. Ref. Alt. Ref.
Bet...
st
Feet
143 =
57
8
72.
14472
22
89
O
Q
•
7=33
•
12=32
.18=31
O
7
•42=277.33=21 2.50=155.20=9 17.0=3
.49=26 1·43=20 3.7-146.15=8 24.0=2.
.15=7 47.0 = 1
.56=25 1.54 19 3.27=13
24-30.4-24 2. 7-18 3.50-128.35-6 96.0=
.30=291.13=23 2. 19-17 4.20-11 10 . 15 =5
36=281.23=22 2.33-164.50=10 |13.. 0 =4
th
Published according to Act of Parliament May 20, 1782 by Samuel Dunn, Fleetfreet LONDON.
C=....
D....
E=....
F.....
L.....
S.Dunn inve” & delin
'
Samid. Dip
Rep?
is
MULA for LATITUDE having Sights of Sun & Moon; By S. Dunn.
A New FORMULA
'મ
1 = Latitude by Reckoning-
d=Deal" or> far à Merid"
N=Alt. • or> far à Merid"..
F-Ded or
near Maid".....
B= Comp") or Declination.
P-Polar dist. > or ● near Merid”. .
N-Altitude ) or near Merid"
b. Co- alt.) or near Merid"
or
R*Afe".• or> far à Merid".
R*Afo > or • near Merid".
Q=&) Equator? distance.
Preparations.
d
Obs & Alt. Lower Limb…….
0
•
•
·
O = Co-latitude
p=
Blar dist...
a=Co-alt.
Sub
Co ar.
Co ar.
Sine
Ram".
Sine
Cofine
t......
Q.....
T=...
Sine
F....
Cofine
G =..
Sine
F=
Sine
True Alt.
Centre
G =....
Secant
Obs Alt. lower or upper Limb.
Semid" 'Dip 'Ref" is
Cofine
Hor For
A ....
Cofine
N...
Sine
M
G..
Secant
"
D =
Ꭰ -...
Cofine
d
Obs Alt.) Centre.
True Alt.) Centre.
I true Dedination.-
> true Blar dist.-
● true Right Afoension
Par Alt
M=
add
A =..
B
C =...
D
E
or
> true Right Afcension .
• &) Equator. distance.
•Declination...
F...
add if P is under 90'
dfe sub
Zenith dist.
) or @ Declination.
Latitude.
I-....
Co-latitude.
NB. When a zodiacal Star or any other is used instead of the Sun, the Star's R.Afcension
must be compared with the Sun's R. Afcension at the time of Observation, to get the Solar
Time of Observation. Either or) may be nearest to the Meridian, but the Time is
best computed from the Sun when is farthest from Meridian. Coar. is Co-faunt
lefs Index 10. & Log. of more than 90 is Log. of Supplement to 180°.
lower Limb is taken add Semid. & sub. Dip & Ref"
sub. Semid. Dip & Ref.
When
When
upper Limb is taken,
Published according to Act of Parliament May 20. 1782 by Samuel Dunn, Hotplnost
S.Dunn og delm".
A New FORMULA for Latitude, Time &Azimuth; having Sights of Sun, & Elapsed Time; By S. Dunn ·
་
For Alt. fur à Merid.
a.
Account
By
Latitude
Correct
For Alt fur à Merid.
For Alt. far à Merid.
Co.ar.
Co.ar.
Colat.
Polar dist.
a-lo-alt
Co.ar.
Co-lat.
Co.ar.
Co.ar.
Co-alt
Co.ar.
Sum
Sine
2
$2
2)
Rem!
Sine
[Sine
2/
Sine
Cofine
2
Sum
Rem
Sind
2
2
r
Sine
Cofine
Cofine
Azimuth far a Merid
For Alt.near Maid.
t t =
}
Sine
Cofire
-
Q
-T
बक्ष
Q=
T:
Colat.
lo.ar.
Sine
Co-alt.
Co.ar.
Sine
Sine
F F
=GG=
=F
Cefine
Sum
Sine
Sine
Rem".
Sine
F=
Sine
2
Secant
GG=
Secant
Cofine
Cofine
=▲ ▲=
Cefine
2
Sine
-N
N=
Sine
Secant
=G
G=
Cofine
D D=
~A ; A =
=B ¦ B=
add ifP is undergo, elſe sub.
= C
C =
=D ¦ D=
Zenith dist.
-E
Declination
E-
FF=
Latitude
Secant
Cofine
Azimuth near Merid.
1. Q is the Elaps'd Time meas" by Watch.
d
2. Com, or Comp. is Rem to go.
3". When Lat. & Ded" alike, fub. Ded".
th
n
add if Pis under 90, elfe sub. from 90. Elje, add Dec. to 90, to get
Bolar dist. 4" Log. of more than 90,
is Log. of Supp. to 180. 5. Co-ar is
Cofecant lefs Index 10. 6F is Ded
&N Alt. near Merid. B is Co-decl"
7th t &T,correct; are Times from Merid", &
on one Side when t exceeds Q; elfe not.
NB. If two Stars are used; Q is the Diff. of their R.Afcen". or Equatorial Distance ·
8 Dunn inr': & delin
th
Tublished according to Act of Parliament May 29.1782 by Samuel Dunn, Fleetfreet LowDON·
Zenith dist.
Dedination
Latitude
A New Formula for Latitude & Longitude, having Sights of Sun & Moon, or Moon & Stars ; By S Dunn ·
0
"
Altitudes
Distances.
For Alt. far à Merid.
Co.ar.
F
Co.ar.
Co.lat.
Dist-Lambs.
Hours
Polar dist.
a=Co alt.
Rough Central dist.
Rough Hour
Hours
1.Diff.
fPLog.
d
• &Limbs obs.
LSine.
2)
Sine
Sum
Rem.
♦ true Semidiameter.
Hours
Р
> true Semidiameter.
2.Diff.
2. P.Log.
Cofine
For Altitude
d
L= Obs.dist. Cautres,
t Least Alt=
=Q Great Alt =
1. Hours
TableI. 2.
1. P. Log
Rom.
add
Time at Greenwich.
Sine
=T
I =
Cofine
F
A=
Sme
= G
B
lo.ar
ComunonLog.
Tablett
Co-lat.
Blar dist.
Co.ar.
lo.av.
Sme
= F
Secant
= G
-L-
add
Cofine
=A
D=
20
Sine
=N DHor.Par.=
Serant
Cofine
= G Alt
D D
st
Arc....
Hop. Log.
Cofecant
Sine
1
Co-Alt
Sum
Rem
•
•
1
Sine
Sine
2
Cofine
=B
HorPar=
add if Pis undergo, elfe sub.
= C DAI
Prep Leg
Prop Log
Cofecant
15)
=D
DD
Tangent
Tune at the Ship
d
Zenith dist.
Delination
Latitude
Q=El.Time
E2 Are
Prep Log
FC.
D.
E
F• Ded.
N=Alt.near Maid. B= Co-Deel"
S. Dunn inr. & dein*.
P
add Ares if D cxreds go.
add Cto D, only when
1*Arc in lecat, &27) is under 90-
elfe sub.
_add ifD) is undergo°.
True distance Centres.
-th.
Published according to Act of Parliament May 29.1782 by Samuel Dunn, Flestflrest Landow
Time at Greenwich, past noon
+
Longitude
The Points & Degrees of the Compass Card, to Halfquarter Points; By S Dunn.
Points D. MD. M.
Points D. MD. M
North South 0
0
010 0 North South
N. E. S. EA
45, 0
N. WS W
0
0
0
0
0
Yoo Yd rexo Yes Papa ett yo
1
24
4 ㅎ
​2.49
4.13
5.37
8.26
7
2
. 51
N.by E. S.by E 1
11
15
N.by W. S.by W.
NEBE. SEBE,
1
12.40
1
A
14. A
1 품
​15.28
1
16, 52
1 %/
18.17
1
19. 41
ગગગગગગG+++
1
21 6
N.N.E. S. S.EĮ 2
aaaaaaa
22.30
N.N.W. S.S.W.
H.N.E. H.S.E
2 ㅎ
​2 3
N.EbN. S.Eb S 3
3
3
3
too te mbo y'ap roko raft sto
♡ ng ng ng mg mo m
3
3 t
too you rato yep 30,00 mot yo
23, 55
25. 19
26.43
28. 7
29.32
30. 56
too te coloo
molt too
too the rope toy RD mit 100
too ++ roko tog Roko natt He
46.25
47. 49
Ag. 13
50. 37
52, 2
53, 20
54.51
56. 15
N.WbW. S.wbw.
57.40
59. A
00.28
61 52
64. A1
67, 30
63.17
66.6
W.N.W. W.S.W.
68.55
70, 19
71.43
73, 7
32, 20
33. 45
N.WIN.SWb S.
E by N E. by S
35,10
36. 3+4
39, 22
37.59
N. E.S. EA
40.47
42. 11
43.36
7
45. 0
N. W. S. W.
Bast.
East. 8
too the cabo ter saba matt #100
75. 56
78. 45
81. 34
74.30
77.21
80.10
82.58
W. by N. W.by S.
84, 22
85.47
87. 11
88.36
90
0
West. West.
S. Dum in! & delint.
Published according to Act of Parliament July 27th 1782 by Samuel Dunn Fleetſtreet LoND or
N.
哭
​Month Day
A TABLE OF EQUATION OF TIME;
Shewing the SUN's Southing, in MEAN SOLAR TIME..
JANUARY
h
1776 77 78 79
1780 81 82 83
FEBRUARY
MARCH
79.17776
1776 77 78 79
1780
BYS.Dunn.
APRI L
7777 78 79
8 79
1776
77 78 79
81 82 83
81 82 83
83 1780 81 82 83 1780
//
"/
h
!!
//
//
h
"/
86
4
1 12.4.1 21 14 7 12.14.3
|
12
212.4.28 49 42 35 12.14.10 15 14
412.5.24 44 38 31 12.14.23 26 25 24
6
12.
24
| |
6.17 37 31
812.7.9 28 22
10 12.7.59 1711
12 12.8.46 458
14 12.9.31 28 42
16 12.10.14 29 24
1812.10.53 7
12.14.32 34 33 32
16 12.14.37 39 38
12.12.31 34
12.12.18 21
12.11.51 54
//
"/ h
"
"1
37 40 12.3.45 47 52 577
24 27 12.3.25 29 34 38.
58 112.
12.2.49 5358 2
12.11.23 26 29 33 12. 2.14 18 22 27
16 12.14.37 39 38 38 12.10.52 5659 3 12.1.39 43 48 52
12.10.20| 24 | 28 | 32 | 12. 1 . 6 | 10
512.14.40 40 40 40
22
2012.0.3
6
14 18
10 14
| |
40 44
11 1511.59.5 8 1215
3539 |
35 39 11.58.39 42 45 48
58 2 | 11.58.14| 147 | 20 | 23
52 12.14.40 39 39 39 12.9.48 52 | 55 | 59, 12.0.34 38
5559 41 45
37 12.14.36 34 35 35 12.9.13 18
19 12.14.30 27 28 29 12.8.38 42 47 51 11.59.33 37
|
358 12.14.21 16 17 19 12. 8. 2
7
2012.11.30 43 38 34 12.14.9 3 5 6 12.7.26 30
22 12.72. 3| 15 11 12.13.54 47 49 51 12.6.49 53
24 12.12.34 44 41 37 12.13.36 29 31 34 12.6.12 16.
26 12.13.1 10 7 4 12.13.17 911 1412.5.3439
33|30
28 12.13.25 33 30 27 12.12.55 46 49 52 12.4.57
30|12.13.45| 52 | 50
525048
MAY
JUN E
212511.57.51 54 57 | 59
4348
43 48 11.57.30 33 35 38
13 11
11 11.57. 11 14 16 18
12.4.20 24 29 33 11.56.55|56|58
2.
JULY
AUGUST
О
111.56.474951 53 11.57.27 25 23 21 12.3.26 23 21 18 12.5.50 51 52 53
35|32|29
211.56.40 42 43 45 11.57.36 34 32 30 12.3.37 35 32 29 12.5.46 47 48 50
4850
411.56.27 29 30 32 11.57.56 54 52 49 12.3.59 57 54 52 12.5 36 37 39 40
611.56.17|18|20 21 11.58.17 15 12 10 12.4.19 17 15 13 12.5.24 25 27 29
12 11.58.40 37 34 32 12.4.38 36 34 32 12.5. 911 1315
611.59.3
1 58 55 12.4.56 54 52 50 12.4.52 54 56 58
2 11.59.27|25|22|19|12.5.119 8 6 12.4.32 35 37 40
0 11.59.52 49 46 44 12.5.25 23 | 22
|
22 20 12.4.10 13 16 19
9 12.5-37 35 34 33 12.3.47 50 53 56
811.50. 9 10 li
10 11.56.44 5
12 11.56.0
14 11.55-59 1
16 11.56. 1 1
1
4 3
0 12.0.18 15 12
18 11.56.4
312.0.44 41 38
2011.56.109 9.
812.1.9
6 3
2211.56.18 17 16 15 12.1.35 32
24 11.56.28 27 25 24 12.2. 158
26 11.56.40 39 37 36 12.2.26 23
28 11.56.54 52 51 49 12.2.51 48
29
2
2
31
35 12.5.46 45 44 43 12.3.21 24 28 37
0 12.5.54 53 52 52 12.2.53 57 0 4
|
26 12.5.59 59 58 58 12.2.24 27 31 35
55 52 12.6.2
20 17 12.6.3 3 3
45 42 12.6.1 1
2
212.1.5256 0 4
9242832
312.1.1924 28 32
2 12.0.45 49 54 58
30 11.57.9 86 4 12.3.14 12 9 6 12.5.57 58 58 59 12.0.9 14 18 22
SEPTEMBER
OCTOBER
496
NOVEMBER
DECEMBER
111.59.32 36 41 46 11.49.24 29.33 38 11.43.46 46 47 47 11.49e
47 47 11.49.43 37 | 34 | 25
18|22|247
2 11.59.13 18 22 277 44 49 6 10
19.11.43.46
15 19 11 43.40 46 46 46 11.50. b 0 55 49
4 11.58.34 39 44 49 11.48.30 34 38 43 11.43.49 48 48 47 11.50.55 49 43 37
6 11.57-55 59 4 9 11.47.5559 3 8 11.43.54 53 52 51 11.51.47 40 34 27
811.57.14 19 24 29 11.47.22 26 30 34 11.44. 3 2 159
10 11.56.33 38 43 48 11.46.51 55 58
59|11.52.40|33|27| 20
211.44.10 14 12 11 11.53.35 28|21|14
|
1211.55.52 57 27 11.46.22 25 29 22 11.44.31 29 27 25 11.54.31 24 17 10
14 11.55.10 15 20 25 11.45.55 58
45|43|11.55.29||22
4 11.44.50 48 45 43 11.55.29 22 15 7
33|36
1611.54.29 33 38 43 11.45.30 33 36 39.45.13 10 7 4 11.56.28 20 13 6
15 11.45.39 35 32
29 11:57.27 2012
57 11.58.27 20 12
28 11.59.27 20 12
18 11.53.46 51 56 111.45.7 10 12
20 11.53.49 14 19 11.44.47 49 52 54 11 46.84 1
22 11.52.23 28 33 38 11.44.30 32 34 36 11.46.40 36 32
56 11.44.15 17 18 20 11 47.16 11
20 11.51. 1 0 11 16 11.44. 35 6 711.47.5449 44 40 12.1.27 20 12
28 11.50.22 26 31 36 11 43.55 56 56 57 11.48.36 30
24 11.51.42 47 51
7
2 12.0.27|20|12
5
G/G G
5
5
25 20 12.2.26 19 12 4
3
9 3 12.3.24 177 10
85 86 87 1784 8586.87
89|90|91| 17788
89
89 90 91
939495
30 11.49.43 48 52 57 11.43.49 49 50 50 11.49.2014
1784
85 86 87 1784
85 86 87 1784
1788
89 90 91 17788
89 90 91 1788
1792
93 94
94 95
1796
97 98 99
99 1796
1792
1796
93 94 95 1792
97 98
93 94 95
97 98 99 1796
9798.99
1796
The Hours & Minutes read with the Seconds which do not beling
to
Bissextile Year.
th
1792
17.92 93 94
1796 97 98 99
Published according to Act of Parliament January 24, 1777 By Samuel Dunn Maiden Lane, Covent Garden, L ONDON.
A VARIATION CHART of the ATLANTE ETHIOPICK INDIAN OCEANS for the Year 1770
Delineated according to MERCATORS or WRIGHT'S PROJECTION agreeable with the LATEST & BEST OBSERVATIONS BY S. Dunn.
I
Teacher of Mathematics LONDON
N
80
NORTH
AMERI
CA
40
J
30
20
10
RSt Lawrence
Jamaica
10
HISI
I
I
N.B. This is the First Variation Chart of those eas that has ever been drawn by a Theory and found to agree nearly with Observations.
4
1
1
1
+
Loud!
ENDL
10
DEGREE S
10
I
1
}
60
50
40
30
20
Nfd
10
20
I
1
20
RHUMB S
J
1
1.
310
2
30
land
FRICE
3
40
EXEL. THE HE BEAST THE
TERRA FIRMA
SOUTH
Equinoctial Line
J
AMERICA
PERU
:
1
GUTANA
:
20
Tropic of Capricom
30
40
7
CHILI
Į
19
1
1
BRZIL
"
80
PATAGONIA
60
50
7:
Falkland I.
1
Terra Fuego
15
DEGRES of EAST
1
+
་
1
VARIATION
310
1
PORTUGAL
1
SPAIN
MOROCCO
08
60
40
7/0
12
So
19
19
FOL
**
3-
|
1
เ
1
•
I
I
F
I
510
60 70
T6
|
17
17
8lo
08
9
09
3
40
15
50.
60
40
3
30
2
20
10
1
10
2
20 30
GUINEA
18
72.
[
20
10
No Variation
LONDON
Merialia of
J
20
13
4
↓
AFRI
16 15
1
CA
"
1
ZANGUEBAR
NATAL
SOFALA
MOZAMBIQUE
19
18
17
200
-
-- h
24
NVL V
20
70
MADAGASCAR
ARABIA
28
1
USE
1
At Sea, having the Latitude & Variation, find_
the Longitude in both Charts D & E and the Medium:
is the Longitude of the Ship.
S.D. inv†
PERSIA
H
26
1
J
INDIA
I
MALABAR
O MANDÉL
COR
to
Ceylon I
ކ
BASE THE. THE OPENED I
DEGREES of WEST VARIATION
10
20
30
40
5/0
60
+
70
810
r
4
|
Tropic of Cancer
PEGU
+
This ART is designed for finding the LONGITUD by the FTTON and LATITUDE, within a Degree and half or go Miles, in many of the Seas that are
much frented where the Lines run
agreeably for that Pose The Annual Change of the Variation is delivered in the general Description of these CHARTS.
.
JAPAN WINE TOUT
+
4
|
Pished according to Act of Parliament November 6.1776 amuel Dunn, the Author, Maiden Tame Covent Garden toxvox; where his other Publications
Lane forDon;
may be had.
1
IVA
PATHO
COCHIN
MAZAYA
UNATRÁ
12
13
1
78
19
20
CHIN A
15
14
20
Ainah. I
BORNHO
10
CEZNBE
*
10
1
1
20
NEW
}
30 南
​HOLLAND
40
100
110
320
5.9
}
6.45