CONSTITUTED OF SPHERICALLY SYMMETRICAL MOLECULES. 479 



The special forms of the coefficient of diffusion, corresponding to the three molecular 



hypotheses considered in Part II., are as follows : 







, /i _ i / 1 4. i Y" i * " id elasticN 



V T <,+</' U + ^/ 



37r I/2 _ 1 _ f / 1 . 1 \ 2p e \w A, e \_ /centres\ 



= ~ K'x'/^rH *1 \(w+ w'l p.9.1 P 'e - , I of fiW' 



JV n 



n ,J A/2__i_ /I + lV*/fi.ri&/ir_L. /attractin 

 -A V 



_. 

 , j> TT \ spheres ; 



where after substitution from equations (45), (48), and (52) we have put the formulae 

 into a more convenient form as above ; iv and it/ are, as before, the specific gravities 

 relative to a standard gas whose density at pressure p a and temperature 8 a is p^ ; v is 

 AVOGADRO'S constant, at the same pressure and temperature. It may be noticed 

 that MAXWELL,* by applying the methods of his fifth-power-law theory to the case 

 of a gas whose molecules were elastic spheres, obtained an expression J times as great 

 as (but in other respects identical with) the first of the equations just given ; as he 

 did not give any details, it is impossible to say how his error arose probably by a 

 numerical slip. 



The following equations simply express the law of variation of D u with temperature, 

 as shown by the above three equations : 



Du/(Dw)o = (0/0 ) Va (rigid elastic spheres), 



"^ (point-centres of force), 



{ 1 + C/0}/{ 1 + C >^} (attracting spheres). 



So far as I am aware, the variation of the coefficient of diffusion with the 

 temperature has never been properly examined experimentally ; the values of D u are 

 generally found only at one temperature, or two at most, and this is insufficient to 

 decide between the second and third of the laws just given. From the analogous 

 behaviour of viscosity, as affected by temperature, however, the third law is probably 

 most nearly true, and the values of C 18 have been worked out by SUTHERLAND on this 

 hypothesis.! In view of the importance of the constant C, it is desirable that 

 further experiments be made on the variation of the coefficient of diffusion with 

 temperature. 



* ' Nature,' vol. viii. ; ' Scientific Papers,' vol. ii., p. 343. 



t The present theory shows that C r >, the temperature constant for diffusion, is a different multiple of 

 the mutual potential of two molecules in contact from that in the case of C n , the temperature constant for 

 viscosity. This fact was not indicated in SUTHERLAND'S investigation; see ' Phil. Mag.' (5), 38, p. 1, 1894. 



