Permeability 
139 
and u is the concentration at a point in the cylinder distant x from 
the initial surface of contact between water and the solution, and 
after a time t has elapsed from the commencement of diffusion, u 0 is 
the concentration of the original solution at the mouth of the 
cylinder and D is the coefficient of diffusion. The value of 
for different values of q is given in tables of the probability integral 
(see, for example, Peirce, 1910). 
It follows from this equation that if u is constant, that is, if we 
consider the march forward into the column of water of a particular 
concentration of diffusing substance, that q must also be constant. 
Hence 
—= = constant, 
2 VDt 
or, stated in words, the distance any particular concentration of salt 
has reached is proportional to the square root of the time of action 
and to the square root of the coefficient of diffusion. This relation 
has been repeatedly verified (Coleman, 1887, 1888; Chabry, 1888; 
Voigtlander, 1889). 
Various methods have been devised for the measurement of 
coefficients of diffusion. These may be classified as follows: 
(1) Those depending on the estimation after a certain time by 
chemical analysis of the concentration of the solution occupying 
different layers in the vessel in which diffusion is proceeding. 
(2) Methods in” which the concentration of different layers of 
solution is determined from estimations of the density of the solution. 
(3) Methods based on the estimation of the rate at which 
substances go into solution. 
(4) Indicator methods in which the presence of an indicator in 
the liquid shows when a certain concentration of the diffusing 
substance is reached at any particular place. 
(5) Electrical, and (6) optical methods. 
For a description of these various methods reference may be 
made to the article on Diffusion by Waitz (1908) in Winkelmann’s 
Handbuch der Physik. An electrical conductivity method is described 
by Haskell (1908). 
In Table IV are given the coefficients of diffusion of a number of 
substances in water. These values are taken from the results of 
Thovert (1901, 1902), Scheffer (1888), Schuhmeister (1879) and 
Heimbrodt (1903, 1904), and the calculations made by Stefan (1879) 
from the data of T. Graham. 
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