DEPARTMENT OF TERRESTRIAL MAGNETISM. 341 



and the range of the corpuscles increases with the altitude, the variation of the 

 conduction current-density with altitude becomes more complex, and it 

 becomes possible in a natural way to explain on these lines the general features 

 of the variation of the conduction current with altitude in so far as this variation 

 is known. The argument in this connection is too involved to be made clear 

 in an abstract, and a similar remark applies to a consideration of the question 

 of annual and diurnal variation; it may be remarked, however, that the more 

 prominent features of these variations fall into natural line with the conclu- 

 sions resulting from the development of the hypothesis. 



In conclusion, it is to be remarked that there is considerable latitude in the 

 exact nature of the hypothesis which may be formulated in order to account 

 for the general features of atmospheric-electric phenomena along the above 

 lines. 



Equipartition of energy and radiation theory. W. F. G. Swann. Read at the meeting of 

 the American Physical Society in New York, October 30, 1915. 



The paper commences with a general discussion of the basis of the theorem 

 of equipartition of energy, after which an examination is made of the validity of 

 certain conclusions usually considered to be necessarily associated with the 

 theorem. The state of equipartition is one which is infinitely probable on a 

 dynamical scheme when we adopt a certain mathematical concept of prob- 

 ability. It is argued that the infinite mathematical probability of this state, 

 however, is by no means a criterion for the likelihood of its existence. The 

 reasonableness of the view is borne out when we observe, for example, that the 

 infinite value of the probabihty may very conceivably arise because the mathe- 

 matics in the process of counting the configurations takes account of all those 

 configurations which might be realized by the generalized coordinates of the 

 system when all the matter, as we know it, has broken down into its ultimate 

 constituents. In fact, the mathematics, in estimating the probability, takes 

 account of all the universes which might have been made in addition to the 

 one with which we are concerned, and, more particularly, it takes account of 

 all the arrangements which would be possible in a universe in which there is 

 no definite structure in matter. Several points for consideration in the above 

 connection are discussed in the paper, but are too involved for presentation 

 in an abstract. 



The second portion of the paper considers the bearing of the theorem of 

 equipartition of energy on the theory of radiation, and in particular it is 

 argued that in an analysis which attempts to apply the laws of equipartition 

 to radiation, the average energy of the fundamental degree of freedom should 



TiT 

 not be written as -^, where R is the gas-constant as ordinarily measured. 



Indeed, the very mechanism by which two gases come into temperature 

 equilibrium when separated from each other, so that only radiation has play, 

 is one which involves the internal coordinates of the molecules, and the con- 

 ditions are not such that the average energy of the center of gravity of a 

 molecule can in this case be equated to the average energy of one of the funda- 

 mental degrees of freedom. It is maintained that a subatomic analysis which 

 attempts to include radiation should not be one in which the centers of gravity 

 of gas-molecules figure at all as coordinates of the system. A difficulty pre- 

 sents itself, however, from the fact that the R which occurs in Rayleigh's 

 formula Ex = SirRT/\* is experimentally found to be the same number as that 

 derived from other considerations involving measurements on gases direct, 

 and from the fact that there is equipartition of energy among the energies of 

 the centers of gravity of the molecules themselves. Many of the difficulties 



