6 
Doctor hutton’s Determination of the 
when x — c is / = ~ x g - d — j x hyp. log. 
— the force of a body at a in the direction ab. 
6. To find the attraction of the 
right-angled part bcd on the point 
a. — Ufing here again the fame 
notation as in the laft article, we have 
— . The correct fluent 
PQ- _ 
•SX X 
f — S SX - SX X , — 
J ACL VfV 2 - iCdx + (V 
of which, when x - c, is 
/ bcs 
= 77* S 
d * — .x hyp. log. 
e £ -\- eg — dc 
de — dc ' 
7. To apply now thefe premifes to the finding of the 
place where the attraction of a hill is greateft, it will 
be neceflary to fuppofe the hill to have fome certain fi- 
gure. That pofition is moft convenient for obferving 
the attraction, in which the hill is moft extended in the 
eaft and weft direction. Suppofing then fuch a pofition 
of a hill, and that it is alfo of a uniform height and 
meridional feCtion throughout ; the point of obferva- 
tion muft evidently be equally diftant from the two ends. 
But inftead of being only confiderably extended, I fhall 
fuppofe the hill to be indefinitely extended to the eaft 
and to the weft of the point of obfervation, in order 
that the inveftigation may be mathematically true, and 
yet at the fame time fnfficiently exaCt for the before- 
faid limited extent alfo. It will alfo come neareft to the 
1 practical 
