242 
ON THE ROTATION OF A SOLID BODY ROUND A FIXED POINT. 
[37 
then the values of p, q, r are respectively 
where 
and then 
dt 
n 
q<?~ i (A -C)<t> [, 
, dd> 2dv dv , dé 
= i—=-rr> or v7 = i—; 
r 0 - Q (B - A) <f) (•, 
pqr 
4 tan -1 -y- = 2S + k 
L 
pqr 
(h + ap + bq + cr) d<b 
k J 0 (№ + Apa, + Bqb + Crc)pqr ’ 
in which form it is exactly analogous to the equation there obtained, p. 230, [6, p. 34] 
(h + kr) def) 
4 tan -1 v 0 = 
(k + Gr) pqr ' 
On the Variation of the Constants, when the body is acted upon by Forces. 
The dynamical equations of a problem being expressed in the form 
ddT_dT = dV 
dt d\ r cl\ d\ ’ 
ddT_dT = dV 
dt df dp clp ’ 
ddT_dT = dV 
dt dv dv dv 
suppose the equations obtained from these by neglecting the function V, are integrated; 
each of the six integrals may be expressed in the form 
a =/ (A, p, v, V, p, v, t), 
where a denotes any one of the arbitrary constants. Assume 
dT dT dT 
d\'~ u ’ dp ~~ V ’ dv w ’ 
then A/, p, v may be expressed in terms of X, p, v, u, v, w, and the integrals may be 
reduced to the form 
a — F(X, p, v, u, v, w, t). 
These equations may be considered as the integrals of the proposed system, taking 
into account the terms involving V, provided the constants [say a, b, c, d, e, f ] be sup-