THERMAL EFFECTS OF FLUIDS IN MOTION. 
361 
rature and density are determined. Should they turn out to be inconsistent with 
facts, other equations of condition will have to be introduced and other constants of 
the empirical formula determined, to do away with the discrepancies; but probably 
no experiments have yet been made of sufficient accuracy to test them. 
The following expressions are derived from the general equations (7) and (8) for 
the mechanical values of the specific heats of a fluid, by substituting for p the parti- 
cular expressions for the case of air afforded by the empirical formula (39), and inte 
grating the second of the two results with reference to v : — - 
J(K - N ) = ®+?(“-f+?)v ( 4 °) 
jN=jfi+25(=4?r)? (4i) 
in the second of which, Jj0 denotes the value of JN when v=oo . Using a similar 
notation with reference to the specific heat of air at constant pressure, we have 
from these two equations, 
JU=J©+7 (42) 
‘0 
j k=j»+x(“-t+?)?; ( 43 > 
or with || j instead of — , 
JK=JK+^(a-f+ff)g (44) 
TC 
Lastly, denoting the ratio of the specific heats, — , by k, and the particular value, 
corresponding to the case of extreme dilatation, by k, we have, to the same degree of 
approximation as the other expressions, 
t 
(6— 3ft)y ~| <S> 
f J v 
(45) 
In the Notes to Mr. Joule’s paper on the Air-Engine*, it was shown that if Mayer’s 
hypothesis be true we must have approximately, 
K=-23/4 and N=*1684, 
because observations on the velocity of sound, with Laplace’s theory, demonstrate that 
Ar= 1*410 
within -jQQ °f its own value. Now the experiments at present communicated to the 
Royal Society prove a very remarkable approximation to the truth in that hypothesis 
(see above, Section I.), and we may therefore use these values as very close approxi- 
mations to the specific heats of air. The experiments on the friction of fluids and solids 
MDCCCLIV. 
* Philosophical Transactions, March 1852, p. 82. 
3 A 
