Mr. Ivory on the Attractions 
2. Let a, b, c, be three co-ordinates, that determine the po- 
sition of a point attracted by a solid : and let dM denote a 
molecule, or element of the mass of the solid, whose position 
is fixed by the co-ordinates x, y, z ? respectively parallel to 
a, b, c: then, supposing the invariable density to be denoted 
by unity, if we put/= [ (a — x) z + (b — y) 1 -f (c — !-§- 
the distance of the molecule from the attracted point, the di- 
rect attraction of the molecule on the point will be = —• 
This force of attraction is next to be decomposed into other 
forces, having fixed directions independent on the position of 
the attracting molecule ; and the directions most naturally sug- 
gested for this purpose, are the three axes respectively paral- 
lel to the co-ordinates. When the direct attraction is thus 
decomposed, the resulting forces, acting parallel to the axes, 
and directed to the planes from which the co-ordinates are 
reckoned, will be respectively, 
~/3~~^ J parallel to the axis of x, 
dM { yp - y — , parallel to the axis of y, 
parallel to the axis of z. 
Let A denote the accumulated amount of all the attractions, 
parallel to the axis of x ; and, in like manner, let B and C 
denote the same things for the attractions parallel to the axes 
of y and 2 : then, by restoring the value of/, and writing dx . 
dy , dz for its equivalent dM, there will be obtained. 
