the mean Denfity of the Earth. 75 1 
Eaft-and-Weft line, bcde one of the little fpaces, and f 
its center or foot of the axis of the pillar whofe bafe is 
bcde; the figure awnea being a horizontal or level fec- 
tion through the point a. Join a, f, and with the center 
a defcribe the middle circle gfh. Let a denote the length 
of the axis on the point f, or the mean height of the pil- 
lar on the bafe bd ; and s - the fine of the angle of ele- 
vation of that pillar as obferved at a, to the radius 1, or 
s — -7=1== . Then will the magnitude of that column 
or its quantity of matter be exprefled by xbexa, 
which is fuppofed to be all collected into the axis: con- 
sequently, if the attraction of each particle of matter be. 
in the reciprocal duplicate ratio of its diftance, the attrac- 
tion of the matter in the pillar, fo placed on the plum- 
met at a, in the direction of the meridian an, will be. 
BC-f-ED S BC-j-ED GIT 
X BE x a x ~ x C — -- --- - x BE X SC - - — x BE x S 0 
2 AF a 2 AF AF 
nearly, fuppofing f to be equally diftant from bc and 
Eb, and c the cofine of the angle fan to the radius i. 
• -But — x £ is nearly equal to d the difference of the 
fines of the angles ban, can, as is thus demonftrated. 
Draw gk, fl, hm, perpendicular, and gp parallel to aw; 
and draw the chord gh. Then ak, am are the fines of 
the- angles gan,: Han, to the radius af, their difference 
i • . • f i n ■ being 
