264 Prof. F. Y. Edgeworth on the Application of 



P 2 in the direction y. Then, by reasoning of parity with 

 that employed in the simpler cases, the required function is 

 of the form 



Const, exp-h (T + /^i + ZP 2 ). . . . (28) 



Each genus being thus distributed normally, the universe 

 which comprises all the genera must be so distributed, whence 

 (27) can be deduced. 



III. The assumptions involved by the third argument may 

 be illustrated by a simple example. Let the molecules of 

 one set be shaped each like a flat ruler with one side AIB in 

 fig. 2 A rectilinear, but the other side not*. And let another 



Ffr. 2. 



B' 



a 



\ 



\ 

 % 



* \ 

 \ \ 



* \ 



\ I 



set of molecules consist of disks, both sets moving in the 

 same plane. Fig. 2 A represents a collision between two 

 such bodies. Say U.Vare the velocity components for 

 the centre of gravity of the ruler ; XI is the velocity of 

 rotation about the centre of gravity ; cj) is the angle 

 made by the straight line A.B with the vertical ; u and v 

 are the (translational) velocities of the disk. If T is the 

 point on the ruler which comes into contact with the disk, 

 let the velocity of I just before impact resolved in the 

 direction normal to the colliding surfaces be W, and that of 



* To secure that the velocities of the bar after a collision of type A 

 might not he replenished by an impact from behind, as in the case of 

 a symmetrical disk (ahove, p. 261). Impact from behind, say at J, is 

 to be distinguished from the " back-hand " collision at I'. 



