762 



greater influence of the (ay^/^nfré'Tz^) molecule diminution in consequence 

 of the decreasing influence of the field of force at higher temperatures. 

 But we shall see (in the sequel) that also Boi.tzmann's function 

 of the distribution cannot be maintained, so that we shall have to 

 draw up an entirely neio theory for the calculation of a and b. 



VII. The virial of collision on compression of the 

 molecules. 



Though the influence in consequence of the compression of the 

 molecule during collisions in the case of hydrogen considered bj us 

 may consequently be assumed to be very slight, it may yet be 

 desirable to examine this case briefly, with a view to other sub- 

 stances where this influence might make itself felt to an appreciable 

 extent. 



Put the distance of equilibrium of the charges of the two atoms 

 in the molecule =: ?-o, the quasi-elastic force for a small displacement 

 (f = ;• — /-J can be represented by : 



F^e{r — r,) , (10) 



in which e = — , when v represents the valency of the atoms (or 



atom groups) and e the elementary charge. If ?'^;'„, there arises 

 an attractive force between the two atoms; if /' <C To, then there 

 arises a repulsive force. Now the distance r„, to which the atoms will 

 most closely approach each other, can evidently be calculated from 



V, ^(F,)'„ 3= ƒ26 (r - rj dr = 6 (r„ - r„)' = f (r. - r.V , 



when n is the mass of a molecule and ( Vr)n the relative normally 



directed velocity, with which one molecule collides against another. 



In this we of course assume that at very high temperatures Va can 



never become = 0, because this would be prevented by the very 



great repulsion then appearing, which is no longer represented by 



the above equation (10), this holding only for comparatively small 



values of 6=r — ?',. (The factor 2 has been introduced, because at 



the impact the force action is exerted by the two molecules together). 



3 RT 

 Now the mean value of ^LiiV* is equal to , when ^ denotes 



the total number of molecules present, so that the mean value of 

 V,f*(^/)«' ^vill be the V, part of this^), hence =RT.N. For the 

 determination of ra we have therefore the equation 



1) This is namely the mean relative, normal velocity. Now Vr= V 1^2, hence 



