Walter Stiles 
138 
of salt diffusing through unit area of the solvent depended on the 
concentration of the salt, on the nature of the salt, and on the 
temperature. The greater the difference of concentration, the more 
salt diffused in unit time, and the higher the temperature the faster 
the rate of diffusion. 
The subject was later investigated by Fick (1855) who, by 
comparison of the problem with that of the conduction of heat 
worked out by Fourier, propounded the well-known equation which 
has come to be known as Fick’s law. This equation is 
dC = -D d ^dt, 
dx 
where C is the quantity of salt passing through unit area in a time 
dt at a point x where the concentration gradient (i.e. the rate of 
3 c 
change of concentration with distance) is The value of D is 
constant for any particular substance in any definite concentration 
and at a definite temperature and is called the coefficient of diffusion 
for the substance, or the diffusivit}^. It is thus the quantity of salt 
diffusing across unit area in unit time when the concentration 
gradient is unity (that is, when two cross-sections of the liquid at 
unit distance apart differ by unity in their concentrations). 
Tick’s law states therefore tfyat the quantity of salt diffusing 
across unit area is proportional to the coefficient of diffusion, to the 
concentration gradient and to the time of action. This law has been 
abundantly verified since the time of Fick. For the solution of the 
differential equation reference may be made to the work of Fourier 
(1822, 1878) or to the various more modern works dealing with 
Fourier’s equations (for example, Carslaw, 1906; Weber and Rie- 
mann, 1910-1912). Reference may also be made to a paper by 
Kelvin (1889, 1890) in v(hich are given the curves showing the 
relation between concentration of solution at a point distance x from 
the initial surface of contact between water and a saturated solution, 
the position of the point x, and the time of action. 
It will be sufficient here to consider only the simplest case, that 
of a salt diffusing into a cylindrical column of water. If we regard 
the column of water as infinitely long, the solution of Fourier’s 
equation for this case is 
u — 
X 
q 2 VDt ’ 
where 
