[ 123 ] 
landing upon the fphere in an angle, which is equal 
to part of the angle fubtended by the arc EM. 
And in higher latitudes thefe quantities will be ftill 
lefs. Let us now return to Fig. VII. and fuppofing 
the point E to be fituated in latitude 45 0 , let the arc 
EM cutting PE at right angles, confift of 2 0 (near 
140 Eat ute miles) then will the fide PM, of the tri- 
angle P M E, confift of 45 0 2' 5 // i r , and confequently, 
if LM in Fig. 7. be fuppofed to correfpond to EM 
in Fig. 8. the diftance of thefe two points E and M, 
in the latter Fig. will be only 2' 5" 4 , the t * o part 
of the verfed fine of which is a little more than 4 of 
an inch, to the radius of the earth, which will there- 
fore be the diftance of the point M upon the earth’s 
furface, and the point of the imaginary fphere, defcri- 
bed by IK, immediately over it. Hence alfo, the 
inclination of the real perpendicular at M, and the 
imaginary one (landing upon the arc IK, at the fame 
place, to each other, will be lomething lefs than a 
lecond, a quantity in itfelf almofl too fmall to be 
regarded, unlefs the inflruments made ufeof are both 
very large and very excellent in their kinds, and 
which, being wholly in the plane of the meridian, 
will produce an error, that mud be perfedtly infen- 
fible, with any inflruments whatfoever, in an obfer- 
vation of the angle PME, Fig. 7. which will there- 
fore, to all intents and purpofes, be the fame, as if the 
curvature of the earth in the direction of the meridian, 
and in the dire&ion of ME orLE were accurately 
the fame. 
I have fuppofed the arc ME, to (land at right 
angles to the meridian PE, which paffes through one 
of the extream ftations ; the method here propoled is, 
R 2 however^ 
