as are terminated by Planes , &c. 
289 
Scholium. 
If the preceding lemmas had been treated on the supposi- 
tion that the density was variable along the line ks, fig. 1, 
(which is the same as making the density f ( t ), or more ge- 
nerally f [a, T,t) a function of a,T, and t) their application 
to the problem we have been considering, would give an inde- 
finite number of different equations, for the curve pr, fig. 15, 
according to the nature of the assumed function f (a, T, t ) ; 
every one of which equations will, however, have this pecu- 
liarity, that if we make r~o, it will become a\ t l = 
For when r — 0, t = 0, and f [a, T, t) becomes a function of 
a and T only, and the case enters into Prop. 33 just now con- 
sidered. 
It may be worth while to see an example of this ; we should 
have had, in general, for the action of the polygonal prismatic 
element of the solid, by Prop. 1, 
and the mass of the same element would have been 
2nafff(a,T,t) ft. 
These must be integrated, with respect to t, from l ™ 0 to 
t = rT: which cannot be done till we assign a form for the 
function f (a, T, t). Let this be a 2 - 1 - T 2 -j- f, that is to say, 
let the density at any point q, in the triangle vrm, be as the 
square of its distance pq from the attracted point p. This will 
give 
L ( r ^ 4“ ( 1 + r*) T 2 } 
L V a 2 4 - T 2 1 T ; and for the mass 
