340 
MR. J. P. JOULE AND PROFESSOR THOMSON ON THE 
that would exactly compensate the cold of expansion, or which amounts to the same, 
the quantity of heat that would be evolved by compressing a pound of the gas from 
the volume V' to the volume V, when kept at a constant temperature, we have 
i{w-(PV-PV)}=H-Kj^, 
whence H= J+(-I(P'V'-PV)+Kmt?}. 
Now, from the results derived by Regnault from his experiments on the compressi- 
bility of air, of carbonic acid, and of hydrogen, at three or four degrees above the 
freezing-point, we find, approximately, 
P'V'— PV _ / .P-P' 
PY •' 11 ’ 
where f= ‘00082 for air, 
f = '0064 for carbonic acid, 
and f— — ‘00043 for hydrogen. 
No doubt the deviations from Boyle’s law will be somewhat different at the higher 
temperature (about 15° or 16° Cent.) of the bath in our experiments, probably a little 
smaller for air and carbonic acid, and possibly greater for hydrogen ; but the pre- 
ceding formula may express them accurately enough for the rough estimate which 
we are now attempting. 
We have, therefore, for air or carbonic acid, 
PVAP-P' w PV/JK m ,\ 
yj-n-=J+T (."PV f ) 
P-P' 
n 
The values of JK and PV for the three gases in the circumstances of the experiments 
are as follow : — 
For atmospheric air JK= 1390 X '238 =331 
For carbonic acid JK=1390x ‘217 =301 
For hydrogen . . JK= 1390 X 3*4046 = 4732 
and for atmospheric air, at 15° Cent. PV=26224(1 + 15 X '00366) =27663 
for carbonic acid, at 10° Cent. PV= 17154(1 -J- 10 X ‘00366) = 17782 
for hydrogen . . at 10° Cent. PV=378960(1 + 10 X ‘00367) =393000. 
Hence we have, for air and carbonic acid, 
T , w . PV ,P-P' 
H -j + r l T’ 
where X denotes ‘0024 for air, and ‘013 for carbonic acid ; showing (since these 
values of X are positive) that in the case of each of these gases, more heat is evolved 
in compressing it than the equivalent of the work spent (a conclusion that would hold 
for hydrogen even if no cooling effect, or a heating effect less than a certain limit, 
were observed for it in our form of experiment). To find the proportion which this 
excess bears to the whole heat evolved, or to the thermal equivalent of the work spent 
