I 



Kinetic Theory of Gas. 373 



Another important matter to be referred to is that in the 

 cases in which the theorem holds good, y, the ratio of the two 

 specific heats (at constant pressure and at constant volume) 

 has the following value — 



7=1+-, 

 m 



where m is the number of terms— each the square of a mo- 

 mentoid multiplied by a selected coefficient — in the expression 

 for the energy. Now observation gives 7 in many cases, and 

 we thus arrive, by the foregoing equation, at m, the number 

 of the terms in the expression of T, which is the same as the 

 number of degrees of freedom in the molecule of those events 

 with which the theorem is concerned, if the constitution of the 

 gas be such that the theorem approximately applies to it. To 

 what motions these degrees of freedom are to be supposed to 

 correspond will depend on what experiment has been made 

 use of in determining 7. If the experiment is one that laets 

 a long time — for instance a whole second or more — then the 

 B& motions as well as the A and the Ba motions will usually 

 have had abundant time to operate ; but if it depends on 

 rapidly changing events, as where the velocity of sound in the 

 gas is the fact that is ascertained, then we may expect that 

 some of the Bb events will be unable to influence the result. 

 It is very convenient to distinguish the internal events into 

 Ba motions and B5 motions ; but it must be remembered that 

 this distinction is one of degree, and that, although in most 

 gases they appear as different as is the chin from the cheek, 

 it wxmld nevertheless be quite as impossible to indicate pre- 

 cisely where the one ends and the other begins. 



The following table of the best determinations of 7 is given 

 by Mr. Capstick in ' Science Progress ' for June 1895. I 

 have added the last two columns in which are given the values 

 of m which the determinations would suggest, if the Boltz- 

 mann-Maxwell theorem could be regarded as holding good 

 for the gas. 



In this table, 7 is the ratio of the two Specific Heats, as 

 given by observation ; m is the number of degrees of freedom 

 of each molecule ; and m— 3 is the number of degrees of 

 freedom of its B, or internal, motions : according to the 

 Boltzmann-Maxwell theorem. 



may "be in its way instructive if we use it to enable us to picture modes 

 of action that occur in gases, and if we are careful not to be misled into 

 fancying that any of our models can be accepted as even in a remote 

 degree resembling the state of things that does prevail within the mole- 

 cules of matter. 



