of Energy in a System of Material Points. 307 



■path of the system, each separate condition of motion a phase 

 of this path. All the functions of coordinates and momenta 

 which remain constant during the whole path he calls the 

 parameter characteristic of the nature of the path, whilst all 

 other functions of coordinates and momenta depend also on 

 the phase. In order that the distribution of the systems shall 

 be a stationary one, it is necessary and sufficient that/ shall 



be equal to — , multiplied by an arbitrary function of the para- 

 meters characteristic of the nature of the paths. 



Maxwell considers the simplest case when this function is a 



Q 



constant, and therefore /= — ; then 



1$Cdq l ...dq n d p 2 . . . d p n ,^ 



Si- 

 is always the number of systems for which coordinates and 

 momenta lie between the limits (9), whilst p x is determined 

 by the equation of energy. 



This is, then, the simplest possible stationary distribution. 

 If the g's denote the rectangular coordinates of material 

 points, then the products of the component velocities into the 

 corresponding masses m^Ui, m 1 v 1 . . . are the corresponding 

 momenta ; then the kinetic energy 



t=k^+«i«!+.. : )=4; + ^+-» 



2 



where evidently - x 1 is the kinetic energy resulting from the 



motion of the first atom in the direction of the axis of x, and 

 so on. In like manner, generalized coordinates can always 

 be so transformed that 



J.--jp+... 2 i 



where the 7's contain simply the coordinates. Maxwell calls 



~^ the "kinetic energy resulting from the rth momentum," 



or simply the "kinetic energy of the rth momentum" The 

 mean kinetic energy of any one of the momenta, say of the rth 

 momentum, is therefore expressed by 



^...y r pldq 1 ...dp n _^ JJ- . .dg x . . ,dp n ^ 



X2 



