ATOMIC THEORY AND RADIOACTIVITY 201 



sound, the ratio of the elasticities is found experimentally to be 

 5/3 for argon, helium, and other inert gases ; therefore they are 

 monatomic. 



If the argument does not appeal to Prof. Armstrong, 

 physicists are not to blame ; but the circumstance that it does 

 not so appeal is evidently largely responsible for the attitude 

 which he has consistently taken up in connection with those 

 unwelcome, or let us rather say indigestible, chemical dis- 

 coveries which have been made by purely physical processes. 



THE ARGUMENT 



It may possibly be helpful to indicate here the whole argument, so far as it can 

 be done with great brevity : 



Fundamental kinetic-theory-of-gas considerations, as old as Waterston, give for 

 the molecular velocity, u, of a perfect gas, at absolute temperature T, and with 

 absolute specific heats c 1 and c, 



u 2 = 3 P = 3RT = 3(c" - c)T (1) 



Equipartition of energy among the degrees of freedom available in molecular 

 encounters, combined with the fact that 3 of these degrees of freedom are necessarily 

 translational, causes 3/nths of the total heat imparted by any operation to go 

 towards increase of translational velocity ; where n is the whole number of 

 effective degrees of freedom possessed by each molecule. To express this 

 sufficiently well we may write : 



^(mcT) = -mu 2 . . (2) 



rr ' 2 



From these two equations we immediately deduce : 



Therefore - = 1 + - (3) 



c n 



which justifies the statements in the text ; for a rigid body under the circumstances 

 of molecular collisions has 6 effective degrees of freedom or modes of motion, 

 unless it is like a rod, when it has 5, or like a sphere, when it has only 3. 



The only additional equation needed is the one required to interpret the 

 acoustic experiment, viz. the Laplacean expression for the velocity of sound, 



Tj2 = e 1 P = c_> RT = i_ d_ u2 (j 



e p c 3 c 



