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



assigned genus (defined by the values of the Q's and ^'s) — 

 will be restored by a back-hand collision of type B : granted 

 postulates analogous to (16) and (30). 



The new axiom may be stated thus (31) : — For any assigned 

 values of the co-ordinates pertaining to a set of molecules, the 

 class defined by particular values * of the velocities of the 

 centre of gravity (or the corresponding momenta), and of 

 the other components of velocity (or momentum), occurs 

 with the same frequency as the class defined by the reverse 

 of the components for the centre of gravity, together with 

 the same values as before for the other components. Which 

 frequency is the same as that of the class defined by retaining 

 the components of velocity or momentum for the centre of 

 gravity and reversing all the other components ; as follows 

 from the received axiom that (32) the frequency of a class 

 is not altered by changing the signs of all the components of 

 velocity or momentum f. 



To combine this datum with the leading equations analogous 

 to (13) and (29), transform the co-ordinates so that one of 

 them may be the abscissa of the centre of gravity of the 

 molecules of mass M measured on an axis parallel to the 

 normal with corresponding velocity U at the point of impact 

 and another the ordinate thereto with corresponding 

 velocity V, and likewise for the molecules of mass m. 

 Considering any species defined by the proximity of two 

 molecules of assigned classes J, say (U, V, Q,, Q 2 ...) and 

 (u, v, q u g 2 . . .), suppose the points of impact on the 

 contour of the two molecules to be moving just before 

 the collision with respective normal velocities W and to 

 (say, W>w). Let these be changed by the collision to 

 W and w\ the velocities of the points in a tangential 

 direction remaining unchanged. 13y (32) the frequency 

 of the species with the dashed components which results 

 from the collision will be the same as the frequency of the 

 species formed by reversing all those components. To 

 secure that the loss to the original class (U, V, -f Q) through 



* I. e., values between limits separated by small finite differences, 

 e. g. Q, and Q + aQ. 



t Op. Burbury, 'Kinetic Theory of Gases,' ed. 2. p. 21; Bryan, 

 " Report on Thermodynamics," Brit. Assoc. Report, 1891, p. 92. The 

 generally admitted (32) is to be distinguished from the now proposed 



(31). 



J Classes defined by velocities (or momenta) and species constituted 

 by members of two classes within a certain proximity. (Ci). above, 

 pp. 256, 260.) 



