Law of Partition of Energy. 585 



or the mean kinetic energy is the same for each degree of 

 freedom. 



In this paper I propose to deal with the theory only as it 

 relates to velocities of translation. If the system consist of 

 molecules having masses M and m, and if U, u are their 

 respective velocities, then the law of equal partition assumes 

 the form 



mtf = MO* = &c. 



2. A necessary qualification. — The energy of translation 

 which is to be the subject of equal partition will be under- 

 stood not to include that of any common velocity which the 

 molecules may have — for instance the earth's motion in 

 space — or of any sensible stream motion. I maintain further 

 that in addition to sensible streams there exists generally 

 what may be called a molecular stream — that is, that 

 molecules very near each other in space have on average 

 a certain velocity in common. But that this applies only 

 to distances comparable with the dimensions, or with the 

 radius of action, of a molecule. It cannot therefore, any 

 more than individual molecules themselves, be the subject 

 of observation. The existence of such molecular streams is, 

 as I maintain, when intermolecular forces exist or the 

 molecules have finite dimensions, an analytical condition of 

 stationary motion. If that be true, we may perhaps find 

 that the energy which is to be the subject of partition 

 should be exclusive of the energy of the molecular stream 

 as well as of the energy of all sensible streams. 



The necessary Condition. 



3. It is a necessary condition for our law that the motion 

 be stationary. But -that is not a sufficient condition, lor it is 

 possible to construct systems which are in stationary motion 

 without satisfying the law. As, I think, Lord Kelvin has 

 done in his " decisive test case.' 7 Some other condition 

 must then be satisfied besides that of stationary motion. 

 What is that other condition ? Before we can either prove 

 or disprove the law, we require an enunciation of it. 



So far as I know we have only to choose between Max- 

 well's condition (Cambridge Phil. Soc. Trans, xii., p. GAS) 

 and Boltzmann's, as given in his Vorlesunyen uber Gas 

 Theorie. Let us first consider Max a ell's, as expounded by 

 Lord Rayleigh in Phil. Mag. January 1900. 



Maxwell's Condition. 



4. Maxwell and Payleigh maintain that the only assump- 

 tion necessary for the truth of the law is that the system, if 



Phil. May. S. 5. Vol. 50. No. 307. Dec. 1900. 2 T 



