of a homogeneous fluid mass that revolves upon an axis. 87 
symbol denoting a function of r, and the angles which that 
line makes with the axes of the co-ordinates. 
The distinguishing property of the expression V (r) is 
this : if we take its fluxions with respect to the variable 
quantities a, b, c, the differential coefficients — , 
— ( d 'Ib ^ ) > — ( d I )> respectively equal to the 
accumulated attractions of all the molecules of the body on 
the attracted point in the directions of a, b, c, and tending to 
shorten these lines. 
dimensions, and likewise having the parts similarly situated 
of the same density. If, therefore, this second body be di- 
vided into the same number of similar molecules as the first 
body ; every two molecules, dm and dm ' , situated alike, will 
be of equal density, and their volumes will be proportional to 
the volumes of the two whole bodies. Suppose, also, that 
z!, y , z! , are three rectangular co-ordinates of the molecule 
dm ! , drawn to planes situated in the second body, similarly 
to the like planes in the first ; and farther, let a!, b f , c be the 
co-ordinates of an attracted point, placed in the same relative 
situation in the second body, as the former attracted point in 
the first ; then. 
It is manifest from what has been said, that r and r',/ and 
ft are homologous lines of the two bodies ; and hence, 
Suppose now another body similar to the first in its lineal 
r'-=i/a'* + b' a +c' % 
f=V(a'— x'y+ ( 6 # — yy+ (c'—z'y 
