CON'STITUTEI) OF SPHERICALLY SYMMETRICAL MOLECULES. 



453 



\\linv E, F, F,, G are given by the following equations, in which the quantities 

 / , /,,. /., have the values assigned to them in equations (27) and (37) : 



E M*-&(l-*.)-8(*,-*b)-' 



' 



(41) 



W 



G = %k-S(l-k l )-$(k l -k 3 ) + 



w w 



This completes the first part of the paper. We proceed now to the evaluation of 

 the quantities P' 12) R',.,, k, k t , and k t in some special cases. 



PART II. ON CERTAIN SPECIAL FORMS OF MOLECULAR INTERACTION. 



12. The general expressions which we have obtained in 7-11 contain four 

 integrals, P', 2 , R' 12) R" 12 , S', 2 , given by the equations 



(42) 



' F u = f V () <Q' 12 ( V.) 



Jo 



',, = r V O SQ ' ( v ) 



Jp 



R" 12 = 



" U (V.) 



vv 



dV , 



The remaining integrals, P' n and R" u can be obtained at once from P' 13 and R",., 

 by changing m to m', and i2 12 to Q n . 



We recall the values of i2', 3 (V ) and i2" 12 ( V,,) from the latter part of 3. They are 



(43) & ( V ) = 4^V r sin" x . p dp, Q" u ( V ) = xV f * sin j 2 x .pdp 



Jo Jo 



\\lu-re 2x is the angle through which the direction of the relative velocity V is 

 turned by the mutual action of the two molecules m and m', while p is the distance 

 between the asymptotes of their orbits relative to their mass centre ( 1 ). 



As the above expressions cannot, however, be integrated except in certain special 

 cases (which fortunately include the most interesting cases) we consider these in 

 order. 



13. Rigid Elastic Spheres. 



The simplest case is that of molecules which are rigid aiid perfectly elastic spheres, 

 of radii a- and a-'. Clearly if p exceeds o-+<r' the spheres will not affect one another's 

 motion, so that x = 0. \Vhen_p is less than or+o-', it is evident that 



sin x = 



