440 MR W. J. M. RANKINE ON THE CENTRIFUGAL THEORY OF ELASTICITY. 
If the body be a perfect gas, then 
Ka %e(Ps Ko) aK *) 
T) 
2) ea a Ba i712 
Leis kM kK <) 
Tea 
7 . 2 
K=K+(1-)-% BM oy =r) 
P vi 0 
T, T 1% 2p ao 

(32.) 
The fact that the specific heats of all simplé gases for unity of weight are in- 
versely proportional to their specific gravities, shews that on is the same for them 
all. 
(13.) Velocity of Sound in Fluids.—Let a denote the velocity of sound in a 
fluid, and d. P the total differential of the pressure. Then 
dicke\ we F DP o he dilrer OG Naa ’ 
a=u(9-" Olt Col Gerke cee ama 
‘Vv 
If it were possible to maintain the temperature of each particle of the fluid in- 
variable during the passage of sound, this velocity would be simply 
‘ (0-1) 
V 
But we have reason to believe, that there is not time, during the passage of 
sound, for an appreciable transfer of heat from atom to atom; so that for each 
particle 

dQ+dQ=0; or, K=O in equation (29). 
To fulfil this condition, we must have 


ire teks ap 
a Kk at 
Consequently, 
dP T—K dp | 
a= { 9X ( aw kK (5°) ds 
or, by equation (31 ) 
d 12 K, Q 
a=/ (975 -z) , (34) 
V 
That is to say, the action of heat increases the velocity of sound in a fluid, beyond 
what it would be, if heat did not act, in the ratio of the square root of the specific 
heat at constant pressure, to the square root of the specific heat at constant volume. 
This is Laptace’s law of the propagation of sound; which is here shewn to be 
applicable, not only to perfect gases, but to all fluids whatsoever. 
marg Danae 
