On tlxe Law of Distribution of Energy. 143 



of field, the magnetic-twist curve for nickel is exactly similar 

 to the same for iron. The reason is simply that with nickel 

 there is a field of maximum twist for each value of current 

 passing along the wire, although there is no field of maximum 

 elongation. The explanation of this is given in my paper of 

 1888 (Trans. R. S. E. vol. xxxv.). It is sufficient to note that 

 the twist, under a given combination of circular and longi- 

 tudinal magnetizing forces, depends not only upon the elonga- 

 tions but also upon some function of these forces which changes 

 sign with each, and to which the existence of the maximum 

 twist is largely or altogether due. For even in the case of 

 iron, which has a maximum elongation, the maximum twist 

 occurs in quite a different field. Indeed the field of maximum 

 twist varies with the value of the current along the wire. 



Meanwhile the broad character of the hysteresis in the 

 magnetic-elongation cycle, as established by Mr. Nagaoka's 

 delicate experiments, agrees perfectly with what might be 

 inferred from the character of the hysteresis in the magnetic- 

 twist cycle — a phenomenon whose experimental study is one 

 of the simplest in the whole subject of magnetic strains. 



Edinburgh University, 

 October 28, 1893. 



X. On the Law of Distribution of Energy. 

 By fS. H. Burbury, F.R.S* 



IF there be in any space a great number of mutually acting- 

 molecules, Boltzmann's law of distribution of energy 

 requires that the number per unit of volume of molecules 

 whose coordinates and momenta lie between assigned limits 

 varies as e -A(x+T) in the known notation. The proofs of that 

 law given by Boltzmann and Watson are based on the hypo- 

 thesis that, from the instant when mutual action commences 

 between two molecules to the instant when it ceases, no 

 action takes place between either of them and any third 

 molecule, or, as it is called, the encounters are binary. I 

 propose to consider the more general case when, for instance, 

 no group of molecules is ever free from the action of other 

 parts of the system. 



Part I. 



(1) The following is a known proposition in the theory of 

 Least Squares. 



Let the chance of a certain magnitude lying between x 

 and x + dx be f(x)dx, f(x) being a function which vanishes 



* Communicated by the Author. 



