of Energy in a System of Material Points. 311 



where r is the distance of the atoms m x and m 2 , r— — ; a is 



the double of the projection of the triangle m x m 2 m 3 on the 

 yz-plane. If we have again an infinitely great number of 

 similarly constituted systems S' given for which the magni- 

 tudes E, U, V, W, F, Gr, H have equal values throughout, we 

 find, exactly as before, that the distribution of these systems is 

 stationary when the number of those for which x x . . . z n , v 3 . . . w n 

 lie between the limits x x and w-i + cLi\. ,.w n and iv n + dw n , is 



equal to — ' 1 " '. — . Maxwell calculates, exactly as in the 



former case, the number of systems for which, with any velo- 

 cities, the coordinates of the atoms lie between infinitely close 

 limits, and, further, the number of those for which the 

 velocity-components of an atom also lie between infinitely 

 close limits, the mean kinetic energy of an atom, &c. I quote 

 two only of the results. 



1. If I,?;, £ be the velocity-components = of an atom of mass m 

 referred to new axes of coordinates, of which, at the instant in 

 question, the e-axis passes through the atom, but the two 

 others are axes of the section of the m omental ellipsoid by their 

 plane, whose origin at each instant is the centre of gravity of 

 the system, and which revolve with the angular velocities 

 which the system acquired in suddenly becoming solid through 

 the operation of internal forces, then the mean values of the 



Wit" 11XY) 



magnitudes m^ 2 , z. — - — ,j , — ~ are the same for all atoms. 

 s * ' 1— ayz 2 1 — byz 2 



In particular, the law according to which these magnitudes are 



distributed amongst the atoms is the same as that according 



to which mu 2 , mv\ mio 2 were distributed in the former case. 



At the same time 7= -^ ; if M is the total mass of the 



M— m 



system, z is the distance of the centre of gravity of the system 

 from a straight line passing through the atoms whose direc- 

 tion-cosine, with reference to the new axes of coordinates, are 



« 1 + t i> t +i BC-L 2 , AO-M* 

 proportional to £, n, and £. Lastly, a— — y\ — > b= ^ 



if A, B, C are the moments of inertia of the system with refer- 

 ence to the new axes of coordinates, L, M, N the sums Zmyz, 

 %msez i %mxy with reference to the system of coordinates, and 

 A, -N, -M 

 D= -N, B, -L 

 -M, -L, 



If the number of atoms is very large, then still — — — —> 



