136 MR, J. S. TOWNSEND ON THE DIFITSIOX OK IOXS IXTO GASES. 



M*> (u - r) r Jr =0 .......... (7o). 



From these three equations the coefficients c,, c.,, &c., can be determined. 

 Since p p > when 2 = 0, we have 



Po = c,M, + c 2 M, + , &c. 



Multiply this identity by M,, (cr - - r~) r dr, and integrating from r = to r = a, 



we obtain 



ap, 



*. 



Hence 



and 



M, 'JgL M t 



P=~Po 



8 



(8). 



On entering the tube the quantity of the gas A, per cub. centim., is proportional 

 to jp , so that p 7ra 2 V is proportional to the quantity of A entering the tube per 

 second (which is found by the conductivity when A consists of ions). The quantity 

 of A which crosses a section at a distance z from the origin per second is proportional 



(a 2V 



p X -v ( 2 r 2 ) 2irr eZr, where p has the value given in Equation (8). The 

 & 



ratio R of the quantity of A which passes a section at a distance z to that which 



enters the tube is 



4 f 



p (- r~) r dr. 

 Fo'J<> 



Substituting for p its value and using Equation 7 (c), we get 



The values of which are admissible are roots of the equation M r = = regarded 

 as an equation in 6. 



[We may here point out that, if the gas, A, on entering the tube w;is distributed 

 across the section according to the law p = \(v), where x denotes any function, the 





