( 636 ) 



The "normal" state is now the same as the "stationary" state. 

 However, the same objection applies to this derivation as to tiiat 



of BOLTZMANN. 



Jeans calls his method "The method of General Dynamics" in 

 opposition to the usual one, Avith the aid of collisions, which he 

 calls "The statistical Method". This name, however, does not seem 

 very appropriate to me ; the considerations here are just as much 

 statistical as in the usual method. Dynamics do not play any part 

 in it but this, that the state of a gas witli aY molecules, so deter- 

 mined by 6 iV-coordi nates and components of velocity, is represented 

 by a point in a 6 ^-dimensional space, and that now the change 

 of state of the gas runs parallel with the motion of this point in the 

 generalized space. 



A great number of possible states gives therefore a great number 

 of points, and their changes a great number of orbits, the general 

 course of which is to be studied. Instead of with these mathematical 

 points we may also imagine the generalized space to be tilled with 

 an homogeneous liquid, the motion of which we must examine, 

 which then according to the author is a "steady-motion" in hydro- 

 dynamic sense, the stream-lines of which are determined by (he 

 property that their energy is constant. 



This, however, brings us about to the end of tlie dynamic conside- 

 rations. They form an illustration, but nothing is proved by them. 



The author now examines, what part of the generalized space is 

 taken up by points representing systems of a certain state. But this 

 is the same as what Boltzmann calls the probability ofa system of a 

 certain state. Both represent the proportion of the number of systems 

 of equal possibility possessing a certain property, to the total number 

 of systems. The objections to be made to the expression for the 

 )»robability iiold a,lso for tiiat of the part of the space. 



Jk.ans treats successively two problems : 



1. What part of the generalized space is occupied by the systems 

 Avith a certain distribution of the coordinates of the molecules (or 

 what chance is there of a certain distribution of density of the gas) 

 and in connection with this : how are the S3'stems distributed in 

 that space with regard to the distribution of the coordinates. 



2. What part of the generalized space is occupied by the systems 

 with a certain distribution of velocities of the molecules (or what 

 chance is there of such a distribution) and how are the systems 

 distributed in that space with regard to the distribution of velocities ? 



Only the first problem is fully treated by Jeans; lor the second, 

 the most important, we are I'eferred to the first. 



