CHAPTER V. 



THE LAW OF DISTRIBUTION '(CONTINUED). 

 EXTENSION TO MOLECULES OF THE MOST GENERAL CONSERVATIVE TYPE. 



71. IN the present chapter we abandon the supposition that the mole- 

 cules are hard and smooth elastic spheres, and try to develop a theory for a 

 gas of which the molecules are conservative systems of the most general type. 

 The assumption that the molecules form conservative systems finds no justifi- 

 cation in nature, but the analysis of this chapter is a necessary preliminary to 

 the discussion of the more general case, in which the dissipation of energy is 

 taken into account. 



We shall no longer suppose the molecules of the gas to be all exactly 

 similar, but shall suppose that the gas consists of a mixture of a finite 

 number of definite types of molecules. Also we shall no longer suppose that 

 forces only come into play between two molecules when they are in actual 

 contact, but shall suppose that the forces may act between the molecules at 

 all distances. These forces may be of the most general type consistent with 

 the conservation of energy, subject only to an assumption which is justified 

 by experiment, and which will be explained later. We may still find it con- 

 venient to speak of a "collision" between a pair of molecules, but a "collision" 

 is not, as before, a clearly defined occurrence. When the forces between a 

 pair of molecules become very great, as they necessarily will when the 

 centres of the molecules approach sufficiently near to one another, we may, if 

 we please, say that the molecules are in collision with one another, but this 

 statement rests upon the assumption of a purely arbitrary standard for the 

 magnitude to which the forces must attain before we regard their action as 

 constituting a collision. If- we assign a high value to this quantity, a collision 

 may, in general, be expected to change somewhat abruptly the paths described 

 by both molecules, but we shall not be justified in assuming that the path 

 between collisions is rectilinear. If on the other hand we assign to it a low 

 value, the average change in the paths of the molecules will be much less, 

 but then possibly it will not be legitimate to assume, even as a first approxi- 

 mation, that a molecule is not engaged in more than one collision at once. 



