200 SCIENCE PROGRESS 



physical facts, the bearing of which he fails to understand. Let 

 me therefore explain. 



The monatomic character of certain gases is physically 

 proved by arguments deduced from an experimental deter- 

 mination of the velocity of sound through them. It is done by 

 a curiously simple, and apparently to Prof. Armstrong 

 despicable, experiment of stroking a glass tube containing the 

 gas and a powder. Physicists thus ascertain the appropriate 

 velocity of sound. This velocity, combined with a knowledge of 

 pressure and density, gives the ratio of the two elasticities — the 

 adiabatic to the isothermal ; which ratio is well known to be the 

 same as the ratio of the two specific heats. The value of the 

 elasticity-ratio shows how the heat generated by sudden com- 

 pression is disposed of, and therefore exhibits the number of 

 effective degrees of freedom of the molecules. For all the 

 translatory motions go to increase the velocity of sound, while 

 none of the rotatory motions have any effect upon it. 



(This is one of the few cases where vulgar fractions, i.e. com- 

 mensurable numbers, enter into physics : all such cases are 

 necessarily important.) Assuming a perfect gas : if the ratio of 

 its elasticities is 7/5, the significance of that number is that each 

 molecule possesses 5 degrees of freedom altogether, 2 of rotatory 

 and 3 of translatory freedom ; so the molecule must be diatomic, 

 having some analogy with a rigid dumb-bell. 



If the ratio were 4/3, there would be 3 degrees of rotatory 

 freedom, and the molecule must be tri- or polyatomic. 



But if the ratio is 5/3, then all the heat goes to increase the 

 translatory molecular motions, no rotation at all being excited 

 by the collisions. For that to be possible the molecules must be 

 monatomic, and must act on each other during collision to all 

 intents and purposes like smooth spheres. 



More can be said about complications introduced by incipient 

 cohesion among the molecules— the so-called " imperfection " of a 

 gas; but this is sufficient. The argument is clear and only 

 assailable either by suspecting the law of partition of energy or 

 by insisting that ordinary molecular collisions must excite 

 atomic vibrations. Some physicists feel a difficulty on this 

 latter head in the case of di- and tri-atomic molecules, though I 

 think it rather a needless difficulty, but I never heard one raised 

 about the monatomic case. 



Now for the application. On determining the velocity of 



