C: 



52 Dr. H. J. S. Sand on the Concentration 



and in order that equation 2 may be fulfilled, viz. that 



F "r 00 (mr \ 



c - K ^=2%cosy- r ^J, 



between ,v = and «r=Z, 

 we must, according to Fourier, make 



which is equal to or 



_2/ 2 ^ 



according as n is even or odd. 



Substituting these values in equation (4), we obtain 



or 



F 4/F A 2 a? _^ 1 , ^ _ 9 yB \ 



c== _# + c gxrls 73 " C0S7r T e — y-cos37T|^ « 2 """•) 



and remembering that : 



tt 2 _ 1 1 1 



8 " i 2 + a 2 + 5 2+ 



we find 



The infinite series in the above expressions for c converge 

 so slowly for large values of /, as to make them useless for 

 numerical application. For/=co all the single members of 

 the series in the last equation become infinitely small, and 

 the series assumes the nature of a definite integral. We 



* This equation also fulfils the condition F=K -~£ for x=l. It can 



therefore be taken accurately to represent the concentration in a cylinder 

 of length /, rilled e.g. with CuS0 4 into which F g.-equivalents are 

 introduced per unit of surface and time at the anode and the same amount 

 is being taken away at the cathode, a fact which is utilized hj Weber. 



