acted on by small Forces. 207 
(7.) The sum of the products of each particle into the 
reciprocal of its distance, for one of the pyramids into which 
‘ Ase A, : 
the mass is divided, has been found to be ae or ultimately 
2 
&. sin, 0.50.39. For one of the wedges, then, this. will be 
soft sin. 6. And it is plain, that one of the lines, which deter- 
mine the limits of integration for the wedge, is in the direction 
of the ordinate c; and the other is the tangent of the curve, formed 
by the intersection of one of its planes with the surface, at the 
attracted point; the direction of which is determined by making p = 0. 
2 
be taken between the lmits 6=0, 6=90. This must then be 
integrated with respect to ¢~ through a whole circumference; 
and thus the value of that part of V which arises from the 
Let © be the value of 6 which makes p=0: then af - sin. @ must 
attraction of the particles, is if St e sin. 6, taken between the 
limits above-mentioned. 
(8.) To determine © we observe that p=2 (c cos. 6+4 cos. ¢ sin. 6) 
— x’ (c).p cos. 0+ XC) cos.’ 0— &e. 
Jee Ls 
+ 
P 
a 
= 2(ccos. 6+ a@cos. ¢ sin. 0)— x’ (c) cos. 0 + x19) cos.’ 6—&e. 
where x‘(c), x’ (c), &c. are the differential coefficients of x‘ (c) taken 
with respect to c. In this expression make p=0, 9=0; 
then 0=2 (c cos. 9 +4 cos. ¢ sin. 8),— x’ (c) . cos. 8; 
sea (6) ;.sin. 9 
acos.d 
c—ty’ (c) —acos.? 
SST COS. O= aa 
Via cos. pl’ + ¢— 3x’ (c)I'} V {a cos. g\'+e~7Xx (D3 
which gives tan. © = — 
