566 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF 
plete to the extent of accuracy of the observations.* The considerable discrepancy 
presented by Carnor’s result, deduced from experiments on air, is not to be 
wondered at when we consider the very uncertain nature of his data. 
45. The fact of the gradual decrease of y, through a very extensive range of 
temperature, being indicated both by ReGNAULT’s continuous series of experiments, 
and by the very varied experiments on different media, and in different branches 
of Physical Science, must be considered as a striking verification of the theory. 
II. On the Heat developed by the compression of Air, 
46. Let a mass of air, occupying initially a given volume V, under a pres- 
sure P, at a temperature ¢, be compressed to a less volume V, and allowed to 
part with heat until it sinks to its primitive temperature ¢. The quantity of heat 
which is evolved may be determined, according to Carnovt’s theory, when the 
particular value of u, corresponding to the temperature ¢, is known. For, by 
equation § 30, equation (6), we have 
dq Ep, », 
” ibn eae 
where d q is the quantity of heat absorbed, when the volume is allowed to in- 
crease from v to v + dv; or the quantity evolved by the reverse operation. 
Hence we deduce 
Ep,v, dv 
dg= 
Cc aamrentio 
(8), 
Ep 
oD ° . A 
Now, —~°—° is constant, since the temperature remains unchanged ; and 
fe 
therefore, we may at once integrate the second number. By taking it between 
the limits V’ and V, we thus find 

E p, % Vv 
where Q denotes the required amount of heat, evolved by the compression 
from V to V’. This expression may be modified by employing the equations 
PV=P’ V’=p, uv, (1+ E ¢); and we thus obtain 
EP V Vv EP’ V’ V 
* A still closer agreement must be expected, when more accurate experimental data are afforded 
with reference to the other media. Mons. Recnavir informs me that he is engaged in completing 
some researches, from which we may expect, possibly before the end of the present year, to be fur- 
nished with all the data for five or six different liquids which we possess at present for water. It 
is therefore to be hoped that, before long, a most important test of the validity of Carnor’s theory 
will be afforded. 
+ The Napierian logarithm of =. is here understood. 

