[From Nature, Vol. vm.] 



LX. On the Final State of a System of Molecules in motion subject to forces 



of any kind. 



LET perfectly elastic molecules of different kinds be in motion within a 

 vessel with perfectly elastic sides, and let each kind of molecules be acted on 

 by forces which have a potential, the form of which may be different for 

 different kinds of molecules. 



Let x, y, z be the co-ordinates of a molecule, M, and f, 17, the com- 

 ponents of its velocity, and let it be required to determine the number of 

 molecules of a given kind which, on an average, have their co-ordinates between 

 x and x + dx, y and y + dy, z and z + dz, and also their component velocities 

 between and +cZ 17 and -rj + d-rj, and and + d. This number must 

 depend on the co-ordinates and the components of velocities and on the limits 

 of these quantities. We may therefore write it 



dN=f(x, y, z, TTJ, ) dxdydzdgdr)dt, (1). 



We shall begin by investigating the manner in which this quantity depends 

 on the components of velocity, before we proceed to determine in what way it 

 depends on the co-ordinates. 



If we distinguish by suffixes the quantities corresponding to different kinds 

 of molecules, the whole number of molecules of the first and second kind within 

 a given space which have velocities within given limits may be written 



/, (, i?,, .) dfi dr,,. d^ = n, (2), 



and / s (, 77,, 3 ) d^. d-r) 3 . d^ = n, (3). 



The number of pairs which can be formed by taking one molecule of each 

 kind is n v n v 



