THE INTERNAL CONSTITUTION OF BODIES. 4.57 
By making the substitutions in the equation (4) we shall be able to 
exhibit the result in the following form: 
x { LleeMG@vigM]_2 @Q;) G1) agQi™ 
~ 4% | ars 
dr? r2 r2 dr 
as a} |- aah gi? _4Auf 4Qi 
7 i i dr 
The foregoing equation is satisfied by taking 
d?Q; Pas Me (1) 
Cae = anf Q; 
This equation is of the same form with that proposed (4), except 
only that 7 is replaced by i—1. If therefore again, in the latter, we put 
1 9, 1 4a 
(2) 
we shall deduce from it another in terms of Q,, in which 2 — 1 will be 
replaced by i — 2; and by continuing these substitutions we shall finally 
obtain the equation 
which is integrable by the known methods, and gives 
B / ae ae fe 
(é) 
Q; = T,e + V;e 
where 7’, and V; may be considered as two arbitrary functions of @ and 
of the order 7 which satisfy the equation (3). 
(3) 
By adopting this value Q;, and by afterwards taking 
(%) 
(FA) ys ine ag shi) dQ; 
Q; iF er Q; el dr 
(i=1) 
(@—-2)y (j—-1) 1 dQ; 
2; ep es “~ "2 dr 
(i-3) eB en 
ti— 1 t— 1 i 
Ohne ar? ae 
