( 635 ) 



pression that Di\ Pannekoek considers as tlie distinctive feature which 

 renders the original motion "iingeordnet" its dissipating influence, and 

 that which makes us call the reversed motion "geordnet" its bringing 

 the velocity points nearer together. When in consequence of the col- 

 lisions the "poi]its of velocity" get dissipated the state would be "unge- 

 ordnet"', when they draw nearer to each other, it is "geordnet". But 

 this holds only in this special case, and it might just as well be just 

 the reverse. 



For what does "molecular-ungeordnet" mean. This appears when we 

 examine the place where Boi.tzmann introduces this idea. We lind it 

 p. 20 in the formula (17): Z$ = * i'^, rfw,. Here represents the 

 sum of the contents of all the oblique cylindres, into which a mole- 

 cule of the 2""^ kind must get in order to collide with one of the 

 1" kind. The formula now expresses that the molecules of the 2'"i 

 are, in proportion to the volume, as numerous in all these cylindres 

 together as in the whole gas mass, or that these cylindres constitute 

 a quantity taken at random from the gas mass with regard to the 

 molecules of the 2"^* kind. 



Now in my opinion an "ungeordnete" distribution might very well 

 be imagined, in which the points of velocity are more dissipated 

 than in the stationary state. And of a gas in such a state the points 

 of velocity would be brought nearer together by the collisions till 

 Maxwell's distribution of velocity is reached. 



^ 3. With reference to the foregoing Prof. Lorentz was so kind 

 as to dii-ect my attention to the work of Jeans on the kinetic 

 theory '). In this work a derivation of Maxwell's distribution of 

 velocities occurs, which is called a new one by the author, but which 

 essentially agrees with the reasoning of Boltzmann in the above 

 mentioned § 6 on the "Mathematische Bedeutung der Grosse H", 

 though the outward form is quite different. It is true that an impor- 

 tant improvement has been made, Avhich for the first time renders 

 it in reality a derivation of the law ; it is viz. not onl}' demonstrated 

 there, that the most probable state of a gas is that, for which the 

 distribution of velocities in question occurs, but also that the chance 

 is very great that a state will make its appearance, differing but 

 very little from the most probable : for w^hen it is onl^- known that 

 a state is the most probable, its probability may yet be so very small, 

 that it does not say anything as to whether that state will occur or not. 



Accordingly Jeans calls this most probable state the "normal state", 

 in W'hich he is now perfectly justified. 



1) "The dynamical Theory of Gases" by J. H. Jeans; Cambridge, 1904, 



