272 PROFESSOR TAIT ON THE 



are both positive. In this case, infinite terminal vessels being supposed, (10) 

 gives for the steady state 



A = 



jA h i c i ( n * i ^i \ 1 dn i . n <n 



imjh 



whose integral, between limits as in (11) above, is 



.,_ P j Sn /it Cjnf 1 1 2^' Sj _ 2s 2 2 sA 1 



irnjh I 4s 2 V 2 + 3 V* 2 -^ 2 s i 2 -* 2 (% 2 -s 2 ) 2 s + (s 2 -s 2 2 ) 2 S s)] " 



Here A is the rate of passage of the first gas, in mass per second per unit area 

 of the section of the tube. 

 If now we put 



then, -when o- is small compared with s, the multiplier of C-^z/3 is 



(l + o- 2 /3s 2 )/s 2 , near i y< 



When a- is nearly equal to s, i.e. one of the sets of particles exceedingly small 

 compared with the other, it is nearly 



1-283/s 2 . 



Thus it appears that a difference in size, the mean of the diameters being 

 unchanged, favours diffusion. 

 Suppose, for instance, 



s 1 : s : s 2 : : 3 : 2 : 1 , 



and we have 



P (3 Ar 2C, / 4 , 36 . 3,4, 1\ ) 



^{3 /» + o ll . 086 ) p_ 1<24 



UV 2+3 1UyD j ~ tt^X ' 



A=- 



7r/s 2 ^/A 



= — /* 1-83. 



Compare this with the result for equal particles (§ 51), remembering that X 

 now stands for the mean free path of a particle of either gas in a space filled 

 with the other : — and we see that (so long at least as the masses are equal) 

 diffusion depends mainly upon the mean of the diameters, being but little 

 affected by even a considerable disparity in size between the particles of the 

 two gases. Thus it appears that the viscosity and (if the experimental part of 

 the inquiry could be properly carried out) conductivity give us much more 

 definite information as to the relative sizes of particles of different gases than 

 we can obtain from the results of diffusion. 



