602 Mr. J. H. Jeans on the 



Any point in the space which remains will represent a 

 single possible configuration of the molecules of the gas. 

 This configuration will, in the course of the natural motion of 

 the gas, give place to other configurations, and these will be 

 represented by new points in the generalized space. The 

 natural motion of the gas may accordingly be represented by 

 the motion of a representative point in the generalized space. 

 Any single point will describe a "path" or "trajectory" in 

 this space, and in this way the whole of the generalized space 

 may be mapped out into trajectories. Since the motion of 

 the gas is completely determined when all the coordinates (1) 

 are given, it follows that through any point there is one and 

 only one trajectory : two trajectories can never intersect. 

 Since the motion of the gas is dynamically reversible, it can 

 be seen that there will be a symmetry in the arrangement of 

 these trajectories. Each trajectory will have an "image" 

 which can be obtained from it by changing the signs of the 

 velocity-coordinates u, v, w. So also each point has an image 

 obtained in a similar way. If P is any point and P' its image, 

 P' represents the system which is obtained by reversing the 

 motion of the system represented by P*. 



§ 8. We are now going to start an infinite number of our 

 dynamical systems, so as to have systems starting from every 

 conceivable configuration, and try what we can discover 

 about their subsequent motion. Or, what comes to the same 

 thing, we are going to imagine the generalized space filled 

 with a continuous fluid, allow this fluid to move along stream- 

 lines which coincide with the trajectories already found, and 

 examine the motion of this fluid. 



It is obvious that the initial distribution of density in this 

 fluid may be chosen in a perfectly arbitrary way : all that is 

 necessary is that every point of the generalized space shall 

 be occupied. 



We shall find it convenient to choose that the initial distri- 

 bution of fluid shall be homogeneous. The special advantage 



* If we revert to the orthodox standpoint for a moment we see that of 

 all the systems represented in our generalized space, some will he 

 ungeordnet and some not. "We can imagine our generalized space 

 divided into ungeordnet and geordnet regions and points. If P is an 

 ungeordnet point, its image P' will, according to Boltzmann ( Vorlesungen, 

 i. p. 48) he geordnet, although the converse is not necessarily true. Thus 

 fully half of our g-eneralized space must be geordnet. The conventional 

 treatment of the kinetic theory compels us to assume, that if a trajectory 

 starts from an ungeordnet point, it must pass only through ungeordnet 

 points throughout its whole length. In view of the fact that less than 

 half of the space is ungeordnet, this assumption would seem to be anything 

 but axiomatic. 



