Place of greatejl Attraction. 9 
9. Having now obtained a general formula for the 
meafure of the attraction in any fort of triangle, if the 
particular values of the letters be fubftituted which any 
practical cafe may require, and the fluxion of this at- 
traction be put - o, the root of the refulting equation 
will be the required height from the bottom of the hill. 
10. But for a more particular folution in Ampler 
terms, let us fuppofe the triangle abc to be ifofceles, in 
which cafe we fhall have d — e, and g-ib- 2 c, and 
then the above general formula will become 
2 J±AJA±b + x x h. 1. ~ +Jiz±L 
dd b + d . X 
+ CZC . 2^3 x h. 1 . + ** -*•* 
2V' . a — x 
for the value of the attraction in the cafe of the ifof- 
celes triangle, where cf is = ^adb 2 - /\.aPx + d 2 x 2 . 
And the fluxion of this expreflion being equated to o, 
the equation will give the relation between a and x for 
any values of b and d, by a procefs not very trouble- 
fome. 
11. Now it is probable that the relation between a 
and x, when the attraction is greateft, will vary with 
the various relations between b and d, or between b and 
a. Let us therefore find the limits of that relation, 
between which it may always be taken, by ufing two 
particular extreme cafes, the one in which the hill is 
Vol. LXX. C very 
