PROFESSOR THOMSON ON THE SPECIFIC HEATS OF AIR. 
81 
Hence, for such a fluid, 
/fN-N=- 
f4(l +E^)^ 
In the case of dry air these laws are fulfilled to a very high degree of approxima- 
tion, and, for it, according to Regnault’s observations, 
Y^^^=26215, E='00366 
(a British foot being the unit of length, and the weight of a British pound at Paris, 
the unit of force). 
We have consequently, for dry air, 
;iN-N= 
26215E^ 
f*(l+E/) 
( 1 ) 
Now it is demonstrated, without any other assumption than that of Carnot’s prin- 
ciple, in my “Account of Carnot’s Theory” (Appendix III.), that 
E H 
i«.(i+Ei;)""W’ 
if W denote the quantity of work that must be spent in compressing a fluid subject 
to the gaseous laws, to produce H units of heat when its temperature is kept at t. 
Hence 
^N-N=26215Ex -^=95-947 (2) 
If we adopt the values of ^ shown in Table I. of the “Account of Carnot’s Theory,” 
depending on no uncertain data except the densities of saturated steam at different 
temperatures, which, for want of accurate experimental data, were derived from the 
value for the density of saturated vapour at 100°, by the assumption of the 
“gaseous laws” of variation with temperature and pressure; we find 1357 and 1369 
E 
for the values of at the temperatures 0 and 10° respectively; and hence, for 
these temperatures, 
(^=0) ^N-N=^^=-0707l 
(^=10°) ;fN-N=?^ = '07008 
(«)• 
w. 
Or, if we adopt Mayer’s hypothesis, according to which is equal to the mechanical 
W 
equivalent of the thermal unit-f', we have ^ = 1390 ; and hence, for all temperatures, 
/fN-N=^^^ = '06903 {a'). 
* This equation expresses a proposition first demonstrated by Carnot. See " Account of Carnot’s Theory,” 
Appendix III. (Transactions Royal Society of Edinburgh, vol. xvi. part 5.) 
t The number 1390, derived from Mr. Joule’s experiments on the friction of fluids, cannot differ by 
and probably does not differ by of its own value, from the true value of the mechanical equivalent 
of the thermal unit. 
MDCCCLII. 
M 
