6 
MR. J. W. CAPSTICK 0^^ THE RATIO OF THE SPECIFIC HEATS 
Then 
C^8^ = ST + /8ST4-pc^T, 
= S(STj + 2:>I dv), 
dv being tlie same tor each component. 
But 
for unit mass of a gas. 
Therefore 
Therefore 
'p^v — |Tj, 
/hSv = IST^. 
8^ — 5^ (i -p STj. 
But, since the average kinetic energy of a molecule is the same for each of the 
constituents, and the pressure is proportional to the number of molecules, 
or. 
Therefore 
Similarly 
Therefore 
= 'Up, =... = T/p, 
ST, = (^^18T)/ P, 8T3 = (p, 8T)/P, &c. 
CV8() = 2(1 + /3,2VP + I) ST. 
C.S« = 2(1 +fti)i/P)8T. 
C,/C, = r = I + i/2 (1 + ft .|>i/P). 
and since, for a single gas, 
H-/3=2/{3(y-l)}, 
the above reduces to 
P/(r-i) = 2iV(r ,-0 ■ • 
(3). 
This equation is equivalent to 
P (1 + /3) = Spi (1 + /3i), 
and merely expresses the fact that -tlie total increment of energy per degree rise of 
temperature is equal to the sum of the increments for each of the components. 
Analyses of the marsh gas and ethane used showed that there was alwaj^s a little 
air present. The correction for this, calculated from (3) was only one or two parts 
in a thousand, which is within the errors of observation, so that for the other gases, 
where nothing was known as to the nature or amount of the possible impurities, no 
appi'eciable error is likely to have resulted from omitting it. 
