(395 ) 
unity of density acts therefore on the umity of mass in S with a 
force, of which the component in the direction | PQ is: 
r—c oo 
l 
1 fp (r) > dz = do' fs (vr) dr = do'C (r‚)), 
az 
where we assume that d.¢(r) = — p(r)dr and €(«)=0. 
Let us now imagine in the plane PQ a system of polar coordi- 
nates with A as origin and the line L to the paper as fixed axis. 
We take as surface element y dy dp. Let the density in A be g, 
then in an arbitrary point of the plane PQ the density is: 
dar," i ide Dye ae 
— Sin G — —— * SUN G whic. ic ze 
Oe On PLO cts ster at art 
: : dû, 7 
It is easy to see that if the terms g + zj Bae alone existed, 
ah 
the attraction which the substance right of PQ would exercise on 
the unity of mass in the direction L PQ, would be the same as 
in ease of a homogeneous density g and therefore : 
ew (u). 
We have still to add to this attraction: 
| | nh al ge ar Te 
wd 2 a med ey dy dp c(r) . 
{ sin? pdp=n 
0 
and so the expression becomes: 
y= 00 
1 d? ) pr 4 1 1 > . 
De | (r) wy? dy = ar iD | 20 f(r) (r2—u?) r dr 
0 Mik 
for r?= w+ y? and so rdr=ydy. 
For this latter expression we may also write: 
