On finding the Latitude. 89 
: ee ae : sin ZP cos A 
Sin ZP’P = sinZPP’ x —T aA? 
putting 8A for mP”’, the variation of A: wherefore, if S + @S be 
the true horary angle-of the middle time, we shall get 
ie MOO sl hcl 
and hence 
8S =a x = (D—d) x 
The corrected cay angle is therefore 
cos § tan 2 
BS MT — d) Xs 
By means of these easy formule the change of the sun’s de- 
clination may be allowed for, when this is thought necessary, 
without hurting the uniformity of the general calculation. 
As an example, I shall take the instance in the Quarterly 
Journal, No. 22, p. 372. 
= cosS X 
cos S tana 
cos = tan a x 
sin t 
Example - 
Ist Alt. 42° 14’ eae ©’s declination 8° 15’ 
2d Alt. 16 5” ie ‘wi 22° oo change in 3", +3 
= 6 ho’ 
au == 8° "'165 
Sin kh = 67217 
Sin A’ = 27726 
2A, 94943 
2B, $9491 
A, 47471°5 
B, 19745:5 
Cos D, 9°99545 Cos l, 9:96639 
Sin t, 9°58284 A.C. 10-03361 
Sin 4, 957829 Sin D, 915813 
b = 22° 15%2 Cos. p, 9°19174 
A.C. sin b, 10°42171 $= 81" a2 
Log. B, 9°29547 Cos y, 9:93112 
Sin y, 971718 Cos 4, 9:96639 
y = 31° 256. “9°89751 
A.C. 10°10249 
Cos. y, 9°93112 Log A, 9°67643 
Cos p—x, 9°94594 Cos x, ~9°77892 
Sina, 9°87706 wv = 58° 32 
A= 48° 5374 p—xr = 28 0 
Siny, 971718 
Secta, 10°18210 
SinS,  9-899258 
Sen = 52° 28’ 
Vol, 58. No. 280, Aug. 1821, M 
