the Trigonometrical Operation . toy 
affumed for the purpofe of exemplification, becaufe its degrees, 
in the direction of the meridian, differ fo little in thefe latitudes 
from thofe of M. Bouguer’s fpheroid. 
Art. IV. 'The fame pole far ohfervatlcns applied to computations- 
on a fphere of greater dimenfons . 
Let us fuppofe, in the iecond place, the earth to be a fphere 
of fuch magnitude as to have degrees of a great circle con- 
taining 61253! or 61254 fathoms, we ill all then get the lati- 
tude of B or Botley Hill 1=51° i6 ; 46 /r , the latitude of ft = 
51 0 f 1A2, and PR = 38°52 / 5 8 ' 8 ; alfo RG = 1 f 19A9. 
Now, BP— 38° 43' 13A9, and the obferved angles will give 
the angle BPG, or the difference of longitude — zf 3 6 A/ .7, the 
fame as before, and the arc PG or co-latitude of G = 38° 53' 
2 // .05 *. This la ft fide, with the angle RPG:=: 27' 36.7 of 
the right-angled fpherical triangle PRG, will give P R ^38 1 
5 2 / 58" 8, and RG — if 19V9; that is to lay, the obferved 
angles PBG and PGB, at Botley Hill and Goudhurft reflec- 
tively, are nearly the fame as they would be found on a fphere of 
fuch magnitude as to have degrees containing 6 1 253 J 01*61254 
fathoms. But fince the value of RG as an arc of a great cir- 
cle was before found by the triangles BPG and RPG to be 
17' 20", when the latitude of B was taken as belonging to a 
fphere whofe degrees contained 60859.1 fathoms Rand the 
fame arc as now determined, viz. if 19A9, agrees very nearly 
* It is evident, that as the latitude of B increaf^s, the ftar’s azimuth, or the 
angle SfBP, and confequently the angle PBG, increafe likewife. But at G the 
angle PGB is diminiflied by the increafe of the angle GP, or the azimuth ; and 
therefore if the difference of the latitudes of B and G remains the fame, or 
nearly the fame, the fum of the angles PBG, PGB, will alfo be nearly the fame ; 
wherefore no fenfible difference in the angle BPG, or difference of longitude, will 
be found on this account. 
Vol. LXXX. 
Ee 
with 
