'Place of great ejl AttraPIion. 13 
hill; the formula gives \sa x 2 + h. 1. 3 —sa x *7746531 
for the attraction at the bottom of the hill ; which is 
between j and | of the greater! attraction, being fome- 
thing greater than j but lefs than | of it. 
25. The annexed table exhibits a fummary of the 
calculations made in the preceding 
articles; where the firft column 
fhews at what part of the altitude 
of the hill the obfervation is made; 
the fecond column contains the 
correfponding numbers which are 
proportional to the attraction ; and 
the third column fhews what part 
of the greateft attraction is loll at each refpeCtive pi ace of 
obfervation, or how much each is lefs than the greateft. 
26. Having now fo fully illuftrated the cafe of the 
firft extreme, or limit, let us fearch what is the limit for 
the other extreme, that is, when the hill is very low or 
flat. In this cafe b is nearly equal to d , and they are 
both very great in refpeCt of a ; confequently the for- 
mula for the attraction in Art. 10, will become barely 
s x : x x h. 1. — + 2 . a - x x h. 1. Anl ; the fluxion 
X a — X 
6 
To 
8109843 
I 
4 
5 
1 0 
9340963 
2 
TT 
4 
To 
IO224232 
I 
5 o' 
3 
Tc 
IO7O25I 2 
1 
no 
252 
Too 0 
IO7637OO 
O 
I 
4 
10763589 
1 
'STsTT 
2 
To 
IO684622 
X 
TT 4 
TT 
9986188 
T 4 
O 
7746531 
I 
2 
T 
of which being put = o, we obtain o = h. 1. 
= h. 1, 
ah.l. 
- h. 1. 
= h. 1. 
2 a — x 
■tit 
Ct — X 
x . 2a — x 
hence therefore a - x < 2 = x . 2a - x, and x ~ a x \ -V\- 
"2g2ga„ 
