PROFESSOR W. C. ROBERTS-AUSTEN ON THE DIFFUSION OF METALS. 
391 
to the diffusion of one metal in another. Fick’s law states that “ the quantity of 
salt, which diffuses through a given area, is proportional to the difference between the 
concentrations of two areas infinitely near each other.” 
Fourier’s theory of thermal conduction was applied by Fick to the phenomena of 
material diffusion generally. The law of diffusion is thus stated by Lord Kelvin 
The rate of augmentation of the “ quality per unit of time, is equal to the diffusivity 
multiplied into the rate of augmentation per unit of space of the rate of augmentation 
per unit of space of the “ quality.” In the case of diffusion of salts or metals, the 
“ quality ” is concentration of the matter diffused, or deviation of concentration from 
some mean or standard considered. 
The movement in linear diffusion may therefore be expressed by the differential 
equation 
dv , d~v 
~dt ~ k lb?' 
In this equation, x represents the distance in the direction in which the diffusion 
takes place; v is the degree of concentration of the diffusing metal, and t the time ; 
k is the diffusion constant, that is, the number which expresses the quantity of the 
metal, in grammes, diffusing through unit area (1 sq. centim.) in unit time (one day) 
when unit difference of concentration (in grammes, per cubic centim.) is maintained 
between the two sides of a layer one centim. thick. The unit of diffusivity has the 
dimensions [L 2 T -1 ] ; so that diffusion constants may be expressed in square centimetres 
per day. The constant has a definite value for each pair of metals (that is for the 
diffusing metal and its solvent) at a particular temperature, and the object of the 
experiments on diffusion is to determine this value. 
In the equation, clv/clt denotes the increase in the degree of concentration which 
takes place at any point during unit time, dv/dx represents the difference between 
the degrees of concentration at the two sides of a layer of unit thickness, and 
dh'/dx 2 in the equation represents the change which takes place in dv/dx as the 
position of the point under consideration is moved unit distance along the tube. 
In Plate 8, and in the figures in the text, x is represented by abscissae, v by 
ordinates, dv/dx is the tangent of the inclination of the curve to the horizontal, and 
d 2 v/dx z is the change in this value occurring for unit change in x ; that is, the 
curvature of the diffusion curve. 
It was not, however, until the experiments and calculations of the results were 
far advanced that evidence was obtained as to the applicability to the present 
method of investigation of the tables calculated by Stefan t for the diffusion of salts. 
By the help of these tables the diffusion constant can be determined, in the case of 
the single-tube experiments, if the distribution of the dissolved diffusing metal is 
known. 
* ‘ Mathematical and Physical PapeT's,’ vol. 3, 1890, p. 428. 
t Stefan, ‘Wien. Akad. Ber.,’ vol. 79, 1879, p. 161. 
