the physical properties of aqueous SOLUTIONS. 117 
By direct determination of the quantities of each kind of ion which pass in opposite 
directions a given section of a solution in a certain time under the influence of a 
given current, Hittorf and others have obtained various series of values known as 
“ migration numbers.” These are tabulated for the anions, and are often represented 
by the letter n, so that 
so-called ‘‘ mobility of anion 
n = 
sum of so-called “ mobilities” of anion and kation’ 
o 
In order to make this fit in with the present nomenclature, it will be convenient t 
designate the Hittorf number by n 2 and the corresponding number for the kation by 
n v Then we have 
n, 
a u 
(AO 
, n 2 — -—, n x -\-n 2 = 1, 
and for the values of n u n 2 at infinite dilution 
N, = /,/A, N 3 = 4/A. 
Then, from equations (5), (6), and (7), we get 
n . = ' l ( 1 + < M n _ 4(1+ </>a) 
A (!+<£)’ 2 A (1 + <E») ’ 
or 
7 j±_ _ 1 + 4>i n 2 _ 1 + (f> 2 
N, ~ I+cp ’ N., — 1 + $ 
( 10 ). 
In the case of KC1 and NaCl, equation (8) may be written in the form 
B = B,N, + BoN 2 . (if)) 
which is the relation between the hydration numbers and the migration numbers, and 
equation (10) gives us 
n 2 = N 2 +N 2 (B 2 —B)(B + /U 3 )- 1 .(12). 
There arises thus from our theory a simple linear relation between the series of 
Hittorf numbers n 2 for an electrolyte and the corresponding series of values of 
(b + A ) . We shall see that this in fact Holds, and that equation (12) gives us a 
iead\ means for obtaining N 2 , the value of the Hittorf numbers at infinite dilution, a 
quantity of great importance in the theory of electrolytes. 
(b) Deduction oj Constant for NaCl.—In the former paper it was shown that in 
the case of KOI the function U was of the form U = BA -2 3 , and that the value of B 
was 3'33. This function was evaluated for KC1 upon the hypothesis that the 
modified Van t Hoff equation, 
A h . 
.(13), 
log lo g-—- = C 
1 —a 
would hold accurately if the coefficient of ionisation were corrected for viscosity and 
