132 MR. .7. S. TOWNSKXJ) ON THE DIFFUSION OF IONS INTO CASKS 



'IB less than the acceleration of a body falling under gravity, and consequently is 

 of a much smaller order than dpjdx. 



When each of the n, molecules of the first gas carries an atomic charge (0 X 10~' 

 electrostatic unit), forces come into play which may be of any order compared with 



f 1 . In an electric field having a potential gradient of 1 volt per centini., the fortv 



H '' 



on n'| ions would l)e 3^7 X 6 X 10~ 10 X n\, which is large compared with the above 



, ,/,, rio^v.i 



value of T e 1.^15- J 



In general six equations of the form given by MAXWELL are required, but when, 

 as in the present case, one of the gases is present in very small quantities, the 

 system of equations reduces to three, and the process of diffusion of the ions miiy be 

 considered as having no effect on the mean velocities of the gas through which they 

 diffuse. The second gas, B, has practically no motion in passing along a tube, except 

 along the axis, which we take as coinciding with the axis of coordinates z. The 

 notation can therefore be simplified, and in what follows we shall let n be the number 

 of ions per cub. centim. ; p, their partial pressure ; e, the charge on each ion ; X, Y, 

 and Z, the electric forces at any point ; u, v, and w, the velocities of the ions ; W, 

 the velocity of the gas, B, through the tube ; (a) the radius of the tube ; and K, the 

 coefficient of diffusion of A into B. 



The differential equations giving the motion are : 



dp 

 '^ 



1 dp 



-p, - - 



~pw=- & 



When the steady state is reached, p is constant at any point in the tube with 

 respect to the time, and the equation of continuity becomes 



dp/dz can be omitted from the third equation, as it is small compared with the 

 other terms, thus, in practice, - ^ is of the order - 2 L -, W 100, and K = '03 ; so 

 that dp/dz is only about one ten-thousandth of -= pW. 



In the case with which we are dealing, W = - - (a 2 r 2 ), where V is the mean 



ft 



velocity defined by the condition, ira?Vt = total volume of the gas B, crossing any 

 section in a time t. Confining the investigation to the case where the numbers of 



