the Trigonometrical Operation , 215 
the meridian of Botley Hill, paffing through GoudhurfL 
We fhall then have PB, the co-latitude of Botley Hill, 
“3 8° 43' iS^.46, and PR, the co-latitude of R, = 38° 53' 
7 y/ .i4. Now, if the latitudes of B and R are nearly true, it 
follows, that the point G mujl be fomewbere in the great circle 
RG, whatever may be its longitude. Therefore the angle BPG, or 
the difference of longitude between B and G, will be found iri . 
the following manner. 
Augment the obferved angle PBG= 119 0 2 T i3 /7 .2, and dimi- 
ni/h the obferved angle PGB = 6o° 1 f 1 by the fame quantity of 
a degree , until PR determined from the triangle BPG becomes zz 
38° 53 ' nearly % which will be when that quantity is f 
2i // . Thus the angles for computation will be ii9°2i / 2 f'.z- 
+ 9 / 2i // =ii9° 30 / 34G2, and 6o° if 1 2i // == 
6o° f 5 4". 7 9 whence the angle RPG, or difference of lon- 
gitude between B and G, will be found = 2 f 36" 75, and the 
arc RG — 1 f 2c/ 7 . 06 nearly = 1 7695 fathoms. And hence the 
degree of a great circle , perpendicular to the meridian , of this 
new fpheroid , will \ m the latitude of R, contain 61248 fathoms 
nearly . 
This follows as a corollary from what hath been already faid ' 
concerning fpheroidical triangles . 
But fince the difference of longitude between B and G was 
formerly determined to be nearly the fame, viz, zf when 
the obferved angles at thefe two Rations, and alfo the latitude 
of B, were fuppofed to be on a figure different from this new” 
ipheroid ; it therefore follows, that the difference of longitude 
between any twofations B and G, difant in the prefent cafe from 
each other twenty-three miles (and they fliould never be much 
ids remote) may be found with fujfcient exadlnefs 7 by having the 
horizontal 
