AND OF THE SECOND LAW 



51 



most of the molecules differ but little. The development shows 

 that this self-same distribution exists for every straight line that 

 can be drawn in the volume under consideration. 



Velocities. 



BOLTZMANN, in his Gas Theorie, has shown that for such a 

 state the " number of complexions " is a maximum, that is, the 

 entropy is then a maximum. 



From the preceeding expression (5) follows that the kinetic 

 energy U of the system is 



U = 



(6) 



where [w 2 ] is the mean square of the velocity. Integration gives 



fc 2 ........ (7) 



It is known that the measure of temperature is the mean kinetic 

 energy of the individual molecule and not simply the mean square 

 of its velocity, and we possess here therefore a perfectly precise 



