228 Prof. A. McAulay on the 



were so defined, it would eo ipso facto cease to be " molecular 

 ungeordnet." But the working assumption which he actually 

 makes use of in the special case, as a deduction from his 

 general assumption, is the same as that used by Dr. Watson 

 and other writers, namely that, regarding / and F as the 

 chances that a molecule shall have velocities between the 

 limits (1) or (2), these chances are independent of the relative 

 position of the molecules — at least that this is the case for 

 molecules approaching collision. Hence / and F being inde- 

 pendent, the number per unit of volume and time of collisions 

 between members of the class /and members of the class F is 

 proportional to F/. And from this, by a well-known method, 

 it is proved that 



Y = Q e -*M(U2+ V2+W2) . 



and therefore mit?=MJJ~ &c, which is the law. 



But the question arises whether the state of things 

 assumed by Boltzmann to exist, from which the theorem of 

 equal partition of energy follows as a mathematical deduction, 

 can exist, and continue to exist, in fact in a finite system of 

 molecules left to their own mutual actions for infinite time 

 undisturbed from without. 



I think Lord Rayleigh's argument, p. 109 et se<p, requires 

 some assumptions : — 



(1) Systems on the same path move independently of one 

 another. 



(2) Systems cannot exchange paths ; or if they can we 

 must assume a law of interchange. 



I think there may be other constants besides E, e. g. if two 

 elastic spheres with velocities w 1? u 2 , &c. collide, u x u 2 + v x v z -f w x w % 

 is constant as well as E. 



Does not the method prove too much ? namely that not 

 merely the law of equal partition (p. 115), but in effect the 

 distribution e~ m must hold for all states of matter. 



XVIII. Notes on tlte Electromagnetic Theory of Light. — I. Geo- 

 metrical Properties of the Wave-Surface fyc. II. Reflexion 

 and Refraction at the Boundary of Crystals, treated by a 

 TJieorem of Sir William Howan Hamilton. By Prof. A. 

 McAulay, University of Tasmania *. 



1. Geometrical Properties of the Wave-Surface 8fc. 



MR. OLIVER HEAVISIDE (< Electrical Papers,' vol. ii. 

 p. 1 ; Phil. Mag. xix. June 1885, p. 397) first, I 

 believe, investigated the properties of the general electro- 

 * Communicated by the Author. To be read at the Meeting of the 

 Australasian Association for the Advancement of Science, January 1900. 



