s88 Mr . Knight on the Attraction of such Solids 
The magnitude of the element of the prism is dTrT, and the 
mass of this element is rd x f ( a,T ) TT ; whence the mass of 
the whole prism is rdf f ( a,T ) TT. 
The mass of a prism whose height is d and base a regular 
polygon of n sides, formed of triangles having this law of 
density, is ztiraf f ( a,T ) TT and its fluxionai coefficient, with 
respect to T, is a;zrf ( a,T ) T x d. 
Prop. 33. 
Let the last proposition be again proposed, but with this 
difference, that the solid, instead of being homogeneous, is to 
be formed of polygonal prismatic elements, having such a law 
of density as in the preceding lemmas. 
By proceeding as before, we shall have for the equation of 
the curve pr, fig. 13, 
2 nxr f (x, y)y 
(•£*4 -y*) v' x + 
+ C2»rf (x,y)y = 0, 
or . v, - n -/ tt 4 - C = 0 ; which is exactly the same equa - 
tion as when the solid was supposed to be homogeneous. 
When r== 0, we have, as before, a*x*= (x 1 -f-y 1 ) 3 ; which 
shews that the result of Mr. Playfair extends to an infinity of 
cases besides that of homogeneity . 
When, as in our last supposition, r = o, and the mass is a 
solid of revolution, the function f (a,T) expressing the density, 
is a function of the perpendicular let fall from any particle on 
the axis of the solid, and of the distance between the foot of 
that perpendicular and the attracted point. 
