BOLTMAXX'* THBOWai OK THB ATEBAOB DISTRIBUTION 



remembering that equation (92) shews that . is independent of v, and v 



The result it 



* ( 94 \ 



. for the three particles m,, TO,, TO,, 



l ............... (95), 



where r, r. and r n ore the distances between the particles, and a is the area 

 of the triangle ,'.'"> 



Also r B Xmi+ r,,'ro,i + n.X= famr* + M***f) ......... (96). 



We may now write equation (90) in the form 



^ l ^..*'. ........... (97). 



Continuing the integration by equation (87) we find 



*i-8 /r>l\w- , . Sn -8 



C /_ ( mi ...m n }-*M n -* I?.-*/."!- .......... (98), 



where /, is what we have defined as the energy of internal motion of the 

 system, or the work which the system would do, in virtue of its motion, 

 against the system of internal forces which would be called into play if the 

 distances between the parts of the material system were in an insensibly small 

 time to become invariable. 



In order to determine the number of systems in a given configuration for 

 which the velocity-components of the particle m n lie between the limits 

 *|C/H, vldv, w$dw, we must form the expression for N (b, V H , r n , ) 

 by stopping short before the last triple integration. 



We thus find N(b, u n , v n , w n ) 



r /^" 1 "" 7 "- -' 



r 



