674 
Proceedings of the Royal Society 
efficients ; and by &c., variations of Q depending on 
variations of p, p, &c. ; we have [compare Thomson and Tait, 
§ 329 (13) and (15)] 
fo = 
and 
dQ ^ 
dp 
Vo = 
(IQ 
dxj, 9 
JQ = _ dQ ^ gQ 
dp dp dp 
and the equations of motion become 
dQ 
dQ 
dp’ 
( 21 ); 
d dQ 
dt dp dp 
d dQ dQ 
dt dp ~~ dp 
+ {?, P}fi + {0, P}0 + 
- {<P> P}P + <P}6 + 
dp 
Ttfd-70-M + 
<£ - 
dQ 
( 22 ). 
The first members here are of Lagrange’s form, with the remark- 
able addition of the terms involving the velocities simply (in 
multiplication with the cyclic constants) depending on the cyclic 
fluid motion. The last terms of the second members contain traces 
of their Hamiltonian origin in the symbols^ , , ... . 
8. As a first application of these equations, let p = 0, p = 0, 
0 = 0, ... . This makes £ 0 =0, Vo = 0..., and therefore also 
Q = 0; and the equations of motion (16), (now equations of equi- 
librium of the solids under the influence of applied forces <1>, 
■&c., balancing the fluid pressure due to the polycyclic motion 
k, k,...), become 
(b - 
dp J 
dp 
&c., 
( 23 ); 
a result which a direct application of the principle of energy 
renders obvious (the augmentation of the whole energy produced 
by an infinitesimal displacement, Sp, is ^%P, and ^ Sp is the 
work done by the applied forces). It is proved in §§ 724 ... 730 of a 
volume of collected papers on electricity and magnetism soon to be 
