168 MR W. J. M. RANKINE ON THE 
Thus it appears, that for the simple substances, oxygen and hydrogen, the 
ratio N is the same, while for atmospheric air it is somewhat smaller.* 
(12.) The ordinary mode of expressing the specific heats of gases is to state 
their ratios to that of an equal volume of atmospheric air at the same pressure and 
temperature. 
When . is a very small fraction, specific heats of wnzty of volume of a perfect 
gas are given by the equations 
Die i 
(24. 
Left 
nMK=% (x +1) | 
That is to say, the specific heat of unity of volume at constant volume is 
inversely proportional to the fraction by which the ratio of the two specific heats 
exceeds unity ; a conclusion already deduced from experiment by Dutone. 
The following is a comparison of the ratios of the apparent specific heats 
under constant pressure, of unity of volume of oxygen and hydrogen respectively, 
to that of atmospheric air, as deduced from Equation (24.), with those determined 
experimentally by Dr 1a Rocue and BERARD. 
nM K, (Gas) 
SOR ee 
Gas. By Theory. By Experiment. 
Oxygen, : ; : ; 0-973 0:9765 
Hydrogen, . ; s 3 0:973 0:9033 
This comparison exhibits a much more close agreement between theory and expe- 
riment than has been hitherto supposed to exist, the errors in the constants 
employed having had the effect of making the ratio 1+N seem greater for atmo- 
spheric air than for oxygen and hydrogen, while in fact it is smaller. 
To treat the other substances on which both M. Dutone and MM. De La 
* The following are some additional determinations of the value of y for atmospheric air, 
founded upon experiments on the velocity of sound :— 
us a y 
Observers. Centigrade. Métres per second. 
Bravais and Martins: mean of several experiments 
at temperatures varying from 5° to 11° centigrade, 0° 332°37 1-40955 
reduced to 0° (Comptes Rendus, xix.) 
Moll and Van Beck: reduced to. ; : 0° 332°25 1:40853 
park Se and Myrbach : reduced to 0° (not corr ete } 0° 332-96 1:41456 
or moisture) 5 : : : 
Académie des BOT e 1738: (not corrected for } 6°1 337-10 1-418 
moisture) : : : 
A variation of one métre per second in the velocity of sound at 0° corresponds to a variation of 
0085 in the value of . 
