64 The Law of Distribution [OH. v 



E a , the energy of the molecule A to which the coordinate q g belongs ; and 

 hence we have 



d^ = d_E_ a 

 dq s dq s ' 

 Equation (132) may now be written in the form 



and from this it follows that the coordinates we have specified form pairs of 

 true coordinates of position and momenta for the whole system of molecules 

 of which the energy is (. 



If, therefore, we construct a generalised space of 22jV a ?i a coordinates, to 

 represent all the coordinates of position and momenta of all the molecules, 

 and if we fill this space with fluid, initially homogeneous, the motion of 

 which is to represent the motion of the gas, then this fluid will, by the 

 theorem proved in the last section, remain homogeneous through all time. 



74. We now turn to the assumption which has to be made about the 

 intermolecular forces. 



If a gas is compressed into a vessel, and is then allowed to stream out 

 into a vacuum, the total energy of the gas, given by equation (133), must 

 remain unaltered by the process. 



Now as we shall see later, a measure of the quantity E a + E b + . . . , or 

 what is the same thing, of (5 <E> is supplied by the temperature of the gas. 

 Joule and Kelvin have found experimentally that the change in the 

 temperature of a gas, consequent on allowing it to stream into a vacuum, 

 is extremely small. The inference is that the change in the quantity <t> 

 is extremely small. When the gas is very rare, it is obvious that <I> must 

 be very small, and hence we conclude that for a gas 4> is in general very 

 small, at any rate within the limits covered by the experiments just quoted. 



The quantity <I> is of course the potential energy of the forces of cohesion 

 of the gas. Thus Joule and Kelvin's result may be stated by saying that 

 the cohesion in gases is extremely small. And from this we infer that equation 

 (133) may, without appreciable error, be written in the form 



= E a + E b + .............................. (135). 



Stated in words this equation expresses that the energy of a gas may be 

 assumed equal to the sum of the energies of its molecules. 



75. From this point the treatment is exactly similar to that of 

 Chapter III. 



Let a molecule of type a be specified by the 2rc a coordinates 



fe, &-"&n a .............................. (136), 



