372 
PRESTON. 
expression, similar to the above in general terms, and then 
integrating between limits which include the mass in all 
three of its dimensions. 
In Fig. 15, a represents an angular quantity, and r and z 
linear ones. If we take the elementary mass hounded by 
the lines r 2 a 2 — r v a 15 r 2 — r x , and 2 2 — z 1 (z being measured 
perpendicular to the plane of the paper) and if we take these 
differences small enough to be used as differentials, the mass 
of matter occupying the elementary space above considered 
is 
d r da dr dz, (3) 
where d is put for the density of the matter. The attraction 
exerted by this matter on the point J will be the mass di¬ 
vided by the square of the distance and multiplied by the 
constant k or 
k 8 r da dr dz ,., 
J J £j2 ' J 
This is the effect in a line joining 0 and J. To reduce it 
to a horizontal plane passing through J, it must be dimin- 
