of Energy in a System of Material Points. 309 



Z 2 = NC C r (*)] V71 72 • • • y M (2E -2V) 2 dq x . . . dq n * 

 ^ (B-Y-*)T3*r(*) 



( B-v) - •*r(»r(- r -) 



This number, and consequently the law of distribution of kinetic 

 energy, has the same value for all momenta. For large values 



of n, 



& 



Zi 6 «^ . 



p tt 



where K = is the mean value of the kinetic energy of a 



n bJ 



momentum corresponding to these values of coordinates, and 

 the same for all momenta. 



In order to apply these equations to the theory of Heat, 

 Maxwell imagines amongst the systems S precisely similarly 

 constituted warm bodies enclosed in absolutely rigid envelopes 

 impermeable to heat, which are completely independent of 

 each other, and all possess the same energy E. The systems 

 S therefore now represent to us very many similarly consti- 

 tuted real bodies of equal temperature and under equal external 

 conditions. The condition of motion of each of these bodies 

 is to be determined by the coordinates and momenta q x ...p n 

 formerly employed. The different bodies are to have started 

 from very different initial conditions; and the number of 

 systems for which, at the commencement of the time, coordi- 

 nates and momenta lay between the limits (9), is to be given 

 by the formula (15). We know that then the distribution is 

 a stationary one. The systems which had the phase {pq) at 

 the commencement of the time, it is true, soon pass out of this 

 phase; but exactly as many systems enter on this phase to 

 replace them, and thus it continues for all times. The equa- 

 tions obtained above hold, therefore, for all bodies. The mean 

 kinetic energy must have the same value for each of the 

 momenta, viz. the value calculated above. The case might, of 

 course, occur that the equations should not hold good for each 



11—2 

 * When V is small with reference to E, and n is large, (E-V) 2 



u— 2 _ nV 



approaches to the limit E 2 e 2E > and the hydrostatic differential equa- 

 tion for polyatomic gases follows from the equation in the text. 



