20 g Gen. Roy’s Account of 
PG*, the ftar’s azimuth = 2° 54' 20". 8, which being fub- 
traded from the angle BG* obferved at Goudhurft between 
the lamp on Botley Hill and the ftar, there remains the angle 
BGP = 6o° if 15". 7 comprehended at Goudhurfr, between 
Botley Hill and the meridian. 
Now with thefe data let us fuppofe, in the fir ft place, the 
earth to be a fphere, whofe diameter is a mean between the 
longeft and Ihorteft of M. Bouguer’s fpheroids, the latitude of 
B, and of courfe its co-latitude BP, given ; alfo the angles 
PBG and PGB refpedively 119 0 2t / i3' / .2 and 6o° if if'.J, 
we fhall then have PG the co-latitude of G, and the angle 
BPG or difference of longitude of B and G. And becaufe the 
degree of fuch a fphere contains 60859.x fathoms, the latitude 
of* Botley Hill will then be 51 0 16 41 '.45, and BP its co- 
latitude = 38° 43' 1 8 / -55- This laft fide, with the former 
angles PBG and PGB refpedively 1 1 9° 21' 13". 2 and 60^ if 
if'.j, give PG= 38° 53' 6A72 the co-latitude of G ; and alfo 
the angle BPG, the difference of longitude of the points B 
and G equal to 2j' 36".']. Again, in the right-angled 
fpherical triangle PRG, rad. : tang. GP :: coline of the angle 
RPG : tang. 38° 53' 3 ,/ .47 = RP. But the point R is 22094 
fathoms fouth from Greenwich, and nearly on its meridian, 
therefore its latitude will be 51 0 6' 52G8 ; and hence PR the 
co-latitude will be 38“ 53' 7". 2, which exceeds PR formerly 
found by fpherical computation to be 38^ 53' 3A47 ^y 3 //# 73’ 
an arc equal to 63 fathoms. Alfo EG, the diftance of Goud- 
liurft from the meridian of Botley Hill, on a perpendicular to 
that meridian, is equal nearly to 1 7695 fathoms, which, allow- 
ing 60859.1 fathoms for a degree, correfponds to an arc of 
if 2b". 7. But fpherical computation formerly gave RG = 
if 20", the difference confequently is 6".y = 1 13I fathoms; 
therefore the earth cannot be this mean fphere, which was 
afl'umed 
