672 
Proceedings of the Royal Society 
which show that the acceleration of k , under the influence of K, 
follows simply the law of acceleration of a mass under the influence 
of a force. Again (for the motions of the solids), let 
£o = € - cue - o!k — &c., Y] 0 = 7] - /3k — (3'k — &C.,... (12); 
£ 1 Q 
and let , &c., denote variations of Q on the hypothesis of £ 0 , 
7] 0 , ... each constant. 
We have from (5), remembering that -P- Ac., denote variations 
of T, on the hypothesis of 77 , ... k, k', ... constant, 
tT_5Q dQf da \ dQ / dp M \ 
d%\ K dxlf + K d^ + "-J dnVdxU + h dxj, + t )- L + d$’ 
or, by (7) 
bT__gQ 
d\lr ddr 
&c. + 
dxjr" 
. (13). 
Hence by (1) 
. 93 
dt d\l/ 
+ &c. 
d& 
Now , remark that, according to the notation of (12), £ 0 , are 
the momentum-components of the solids due to their own motion 
alone, without cyclic motion of the liquid; and therefore eliminate 
£, by (12) from (14). Thus we find 
d £0 JQ 
dt + dxlr 
-f- &c. 
(15), 
which, with the corresponding equation for £ 0 , &c., and with (11) 
for k, k, &c., are the desired equations of motion. 
6 . The hypothetical mode of application of K, K',... (§ 1) is 
impossible, and every other (such as the influence of gravity on a 
real liquid at different temperatures in different parts) is impossible 
for our ideal “ liquid,” that is to say, a homogeneous incompres¬ 
sible perfect fluid. Hence we have K = 0, K = 0, and from (11) 
