870 



§ 2. Tlie second virial coefficient for a gas the raoleciiles of vvhicli 

 fiillil (lie coiidilious (A) can be deduced bj the method given in 

 Suppl. N°. 24, for which method Boltzmann's entropy principle 

 serves as basis. This deduction follows more particularly the lines 

 of the treatment in § § 4 and G of that paper; it differs, however, 

 from that treatment in the following points-. 



I*''. The three principal moments of inerlia are now supposed to 

 be unequal. In this case also iu delerininiug micro-elements of equal 

 probability the expression d / dêd-idi/ dOily^. y, and '/. being the 

 angles which determine the position of the principal axes of inertia 

 relative to a fixed system of coordinates, and rf, and x being the 

 corresponding moments of momentum, may be replaced by dod-/jdp^dq^di\, 

 where do represents a surface element of the sphere of unit radius, 

 which serves for marking the position of one of the principal axes 

 of inertia, and /^,, g, and )\ represent the velocities of rotation 

 about the principal axes of inertia. 



2'"'. For determining the relative position of the two members of 

 a pair of molecules, we now need, besides the coordinates r, i^,, (V^, y, 

 which as iu Suppl. N". 24A § and receinly N°. 39rt fix the distance 

 of the centres and the relative orientation of a definite arbitrarily chosen 

 principal axis of inertia of one molecule relative to the correspond- 

 ing axis of inertia of the other molecule, two more angles, which 

 for each molecule specify the azimuth of the plane going through 

 the principal axis of inertia mentioned above and a second principal 

 axis of inerlia. As such we may choose the angle y, between that 

 plane and the plane which contains the first principal axis of 

 inertia and the line joining the centres . -^ , and similarly x^. ^or 

 the second molecule, are counted from to 2.t. 



Quite analagously to Suppl. N". 24/; § 6 the following result 

 is obtained : 



B = ln(^.To' - P') (4) 



where now '): 



P = ^JJj jJJ{e'''m-l) r'- sin 0, sin 4rdO ,dO Jy^dyJ,f . (.5) 



c U U 11 



In this formula Ub\ is again the potential energy of a pair of mole- 

 cules in the position indicated by definite values of r . . . (f, the 



1) As in P' the manner in which the density is distributed over the spherical 

 molecule does not occur, it appears that the limitation to molecules of spherical 

 symmetry observed in Suppl. N". .2-ii § 6, can be omitted (of Suppl. N"*. 39« 

 § 2 note). 



