217] A MEMOIR ON THE PROBLEM OF THE ROTATION OF A SOLID BODY. 477 
then attending to the equation dn = — f - da, we have 
dh = n 2 ada, 
na 2 e 
dk = ^ na Vl — e 2 da — na 6 
and thence 
n 2 a dil 
Vl -7 2 dk ’ 
and the formuise are very easily transformed into 
dh = 2 n ~P dt, 
dg 
dk = 
dm = 
cot 0 do. cosec <f) dil n 
7 7 7 /"1 CIjuy 
cosec (f> dil , 
~T~ d$ dt ’ 
dd = ^ 
where il = O (/¿, g, k, m, (/>, a, 6). 
This is the system of formulae which will be obtained in the sequel for the 
variation of the elements in the problem of rotation, the new meanings of the 
symbols being explained post, Art. IV. 
And if in either of the two problems, instead of the angles a, 6, which 
refer to a fixed plane of reference and origin of angles therein, we have the angles 
d>, X, ©, referring to a variable plane of reference and departure-point as an origin 
of angles in such plane, the position of these in respect to the fixed plane of 
reference and origin of angles therein being determined by 
6', the longitude of node, 
a, the departure of node, 
cf7, the inclination,