268 Prof. F. Y. Edge worth on the Application of 



a third co-ordinate which does not figure in the expression 

 for the energy, viz. the angle made with a fixed axis by an 

 arbitrary line through the centre of gravity ; and for the 

 remaining co-ordinates such as do not relate to points or 

 lines fixed in space (but only to parts of the complex 

 molecule) *. 



The characteristic defect of the third argument, that 

 it does not prove the necessity of the normal distribution, 

 may, as before, be remedied by the first argument. 



The analogues in three dimensions f of the preceding 

 problems, and other generalizations not involving other 

 principles of Probabilities, are here passed over. 



D. So far we have supposed two molecules colliding with 

 each other and separating with velocities determined by the 

 laws of impact for perfectly elastic bodies. We are now to 

 entertain the more general conception of an encounter % 

 between two molecules supposed to come within each other's 

 sphere of influence and to be deflected from their previous 

 path according to some unknown law of repulsion (perhaps 

 preceded by attraction). Considering first the simple case 

 of equal disks moving in a plane, we suppose the circles of 

 influence to be so small and rare that the path of a molecule 

 after leaving- one of these circles, and likewise before entering 

 it, is rectilinear, and that throughout a considerable space 

 (in a large unit of area) there occur only molecules moving 

 in free straight paths. The remainder of the unit area — a 

 constant proportion — consists of regions within which the 

 movements of the couples are correlated as Dr. Burbury 



* The energy will then "be of the form 



MU 2 +wzw 2 4- M/W+T'i, 



where 12 is the velocity of the molecule about its centre of gravity. 

 k 2 involves co-ordinates other than that of which Q, is the differential 

 coefficient. Ti, the remainder of the energy, is a quadratic function of 

 the remaining- velocities (or momenta) with coefficients involving- the 

 corresponding co-ordinates. The signs of the P"s for the back-hand 

 collision are obtained by observing- the signs of the L's and Vs in 

 equations (23) and (24). 



t Analogous to the view of the molecular system from above (16) is 

 now the view in any direction. The configuration at a " back-hand" 

 collision will now depend not only on the configuration, but also on the 

 velocities of rotation about each centre of gravity, at the direct collision 

 between two molecules. 



\ Cp. Watson, p. 36, Jeans, etc. A good representation of encounter 

 is given by Clerk Maxwell in his ' Dynamical Theory of Gases : Collected 

 Papers,' vol. ii; p. 42. 



