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= i — clk - o!k — &c., 7) 0 = 7] - /3k - /3'k - &c.,... (12); 
and let &c., denote variations of Q on the hypothesis of £ 01 
y 0 i ... each constant. 
hT 
We have from (5), remembering that &c., denote variations 
of T, on the hypothesis of £, rj, ... k, k ', ... constant, 
bT_$Q dQ/ da ,da! \ dQ/ dp dp \ 
d\\r d\f/ dg\d\Jr dxjr drj\ K dx!/ K d\f/ c ‘/ C ’ + dxfs y 
or, by (7) 
bT IBQ (da. da \ .(dp dp . \ i 
* \ K dxf} +K M + &C - ) " K K d$ + K chj, + &c - ) ' ' &c * + , 
Hence by (1) 
d 
( 13 ). 
dt dx!/ 
+m + 4? + &o -) - + «&+ & °)~ &c - + ^=’ f - < u >- 
TSow, remark that, according to the notation of (12), £ 0 ,r ] 0 ,... are 
the momentum-components of the solids due to their own motion 
alone, without cyclic motion of the liquid; and therefore eliminate 
ij by (12) from (14). Thus we find 
d&.m , dK 
dt + dxfs + a di + “ dt + 
+ &c - 
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 u liquid,” that is to say, a homogeneous incompres- 
sible perfect fluid. Hence we have K = 0, K' = 0, and from (11) 
