354 
MR. J. P. JOULE AND PROFESSOR THOMSON ON THE 
Let also e be the “ mechanical energy* * * § ” of the fluid, reckoned from some assumed 
standard or zero state, that is, the sum of the mechanical value of the heat commu- 
nicated to it, and of the work spent on it, to raise it from that zero state to the 
condition defined by (v, t ) ; and let N and K be its specific heats with constant 
volume, and with constant pressure, respectively. Then denoting, as before, the 
mechanical equivalent of the thermal unit by J, and the value of Carnot’s function 
for the temperature t by we have-f 
de 
dv' 
dp 
dt 
-P 
N— - * 
J it 
1 de 1 f de 
K = J Jt + 3\Iv +P 
dp 
dt 
dp 
dv 
(1) 
(2) 
( 3 ) 
From these we deduce, by eliminating e, 
(d£ 
K 
•N=~ 
ju. dp 
dv 
( 4 ) 
and 
(3) 
equations which express two general theorems regarding the specific heats of any 
fluid whatever, first published;}; in the Transactions of the Royal Society of Edinburgh, 
March 1851. The former (4) is the extension of a theorem on the specific heats of 
gases originally given by Carnot§, while the latter (5) is inconsistent with one of his 
fundamental assumptions, and expresses in fact the opposed axiom of the Dynamical 
Theory. The use of the absolute thermo-dynamic system of thermometry proposed 
in Section IV., according to which the definition of temperature is 
simplifies these equations, and they become 
JK— - JN=£ 
(7) 
rf(JN) _ dpp 
dv dt* 
( 8 ) 
* Dynamical Theory of Heat, Part V. — On the Quantities of Mechanical Energy contained in a Fluid in 
different States as to Temperature and Density, § 82. Trans. Roy. Soc. Edin., Dec. 15, 1851. 
t Ibid. §§ 89, 91. J Ibid. §§ 47, 48. 
§ See “ Account of Carnot’s Theory,” Appendix III. Trans. Roy. Soc. Edin., April 30, 1849, p. 565. 
