the ’Trigonometrical Operation . 21 g 
Art. VII. Application of the refults of the pole-far obfervations 
to computations on M. Bouguer’s fpkeroid, for the difance of 
the parallels of Greenwich and M. 
Hitherto the refults obtained by the geodetical meafurement 
and pole-ftar obfervations have been applied to fpherical com^ 
putations on two fpheres fuited to the different lengths of de- 
grees found in two oppofite directions, at right angles to each 
other, the meridian and its perpendicular ; and from thefe 
computations it has been clearly proved, that the earth cannot 
be either of the affumed fpheres. 
Let us therefore, in the next place, fuppofe the earth to 
have the figure, and the dimenfions of M. Bouguer’s fpheroid, 
and by way of comparifon apply the fame refults to computa- 
tions on that figure. Thus the latitude of the point r will be 
found 51 0 f 12T09, and the arcrMzr T 27' 49 // .03„ Hence,, 
as rad. : cofine rP :: cofine rM : fine 51° T 48 // .85 the lati- 
tude of M nearly. Now, let the points r and M be repre° 
fen ted by B and v (Plate X. fig. 2.) then will A reprefent the 
point whofe latitude is 51 0 T 48T85 ; and by proceeding in 
the manner formerly directed for a fpheroid, we get GW~ 
15.12 fathoms = to the diflance in the axis between the points 
where the verticals from the latitudes 51° f iT'.oy and 51 0 i< 
48T85 meet the faid axis. Hence, as rad. : 15.12 (GW) :: cofine 
51° i' 48". 8 5 (angle SWG) : 9.509 fathoms =: GS, or the arc Av 
extremely near. Now the value of Av, as an arc of the meridian, 
is o / 7 .5 6, which being added to 38° 58' n^.15 (AP), gives 
38 58' 1 1T71 mP'u, the co-latitude of v ; and hence the true 
latitude of v 9 or M (fig. 7.), is 51 0 1' 48". 29, which being 
fubtradled from 51° 28' 40", the latitude of Greenwich, there 
remains 26' 5 1 1 for the arc between them, or diflance of 
their 
