DEGREE 
Te will oe festa ey — hae of A is 
direGly given, but e pie ie 
from the ae ae hae n is Geena may be converted 
into degrees, by taking the radius of siane of its middle 
<< 
point, recurring to the general expreflion ak of ee . 
This method, which fuppofes the latitud ae A ce own 
by eee is exact enough for every poffible practi 
cal purpofe. 
The following oS is ftill more accurate ; 
latitude of the known ftat 
L = latitude required of a aan on the fame meridian, then 
dl af 
Fey iy plied 2 
Lalt (Get h aa) 
ty 
which will kerea‘ter be fhewn to be equal to ave — ?R’ 
let 7 = 
4 2 
{Saas 
1 
r aes = normal. 
radius of curvature to the latitude 7. 
And if the value of ¢ =2— be known at any central 
spoint ‘as a principal flation, its value at any diftance x from 
“that ftation is equal ¢= Rro—3 é* fin. ale 
Example I. 
Let B(P/. VII. fig. 66.}be the tower of Dunkirk, A A’ the 
eer an of Greenwich; let the latitude aie be fuppofed 
regia”. L pe aemerecen Ler S 
A! B= y= 547058 Log. =5.7350334 
ag the latitude of B? 
Firft, find the oe of normal=a=p (1+ $¢ fin.’ L.) 
fol ia1® 
=F. 
herman 
cae k 
Jv 
‘Log ne 45 
Log. 0.5 - 6989700 
Log.e - = -9.4766329 
———-—= 1.0000000 
7 25713992 0018085 
Log. (1 +4 ¢ fin.? L) 0. 2.007844 1.001808 5 
Log. p - $205367 
Log. « or normal . 7:32: 3213211 Log n® - ==4.6426422 
Co, log. 0° =5.3573577 
Log.o.5 9. 6989700 
aa 4760668 
R’ - 53144281 
Co.log. n= 33573577 
Tang. L 0.0925 566 
Log. of firft.corr™. 1.9393762==86".97 
Log. 3 7 1.84683 
Sin. L a L 9.68918 
e° 7.77063 
Log. of 2d corr’. 9. 31264 0.205 
Diff. of latitude ecuwed’ 87. 1375 
which taken from the latitude of A. 
- 51° 3! 39" 
leaves for the latitude of Dunkirk . 
51 2 9.83 
Example 1. 
Let the latitude of A (Greenwich) = 51° 28° 40", 
A 
ag. = §.0945489 
Log. = 5.4825500 
"= we a5 124322 . 
A'B = y =303775 
~ Required the latitude of B, Dover-caftle ? 
Firft, find A’ B’, or difference of latitude between A’ and B, 
Log. 9.5 = — 9.69897 
R’ : 31442 
7 0.g0510 
Co. log. n? - —-5-35735 
Tang. L - 0.09376 
1.42960 = 26".89 == 1ft corr, 
1 "y? ; . 
2 me 1.33584 
_ - 7-4 7063 
Sin. L cof. L 9.68918 
8.80165 = 0.06 = 2d corr. 
A! RB ~ - — 26.95 
Se eneeauameend 
‘The latitude of A’ may be deduced from the value of x by 
LON ‘ : 
the formula x” = ; + denoting the radius of curvature 
- 
o the meridian, at the middle point of x, which may be ob- 
ae bias this equation. 
=(i—a(2— 3 fin? L) Log. r = 7.32031 
fret whence wom 1226".5 = 20 26.5 = AA! 
iS = A! B 
Difference of latitude - 20 §3.45 
28 40 
Latitude of Dover-caftle st i ae. O55 
‘To find the SS of — ae 
_ P= : or Fe u-48 — tang.’ L.) 
Log.b + 9. 52288 
2 
Log. re - - 6.32247 
Tang.’ L » . 0.18510 
; —_——- 1.000000 
ot - 6.03045 = = ©.000107 
Log. (1—¥fe tang") 99999524 - > 0.999893 
Log. “ - 53144251 
Log. 2 - - 8.1612280 
Comp. ae L - 0.2023792 
3+0779845 = 4764" = 1° 19! 24" 
Example II. by the Tables. 
Given lat. A. st 28! 40" 
pe ck anal 0945485" 
03775 = §-4025500 
Required lat. BI Bone! caftle. 
