394 PROFESSOR W. C. ROBERTS-AUSTEN' OX THE DIFFUSION OF METALS. 
Column 6 gives the theoretical concentration in each section in cases where the 
factor 2 ^ 7/1 has ^ ie values 0*11 and 0’12, because the actual results of this experiment 
(on the diffusion of gold in lead) were seen by inspection to lie between these values. 
Stefan* applied the formal analogy between diffusion-movements and wave- 
motions, to the calculation of Graham’s results ; both motions are expressed by the 
differential equation already quoted, ^ = k ^. Stefan calculated his results 
for the case of a cylinder of infinite length. In order to apply his results to a 
cylinder of limited length, which is the case in these lead-gold experiments, use is 
made of the principle of reflection and superposition, in accordance with which the 
quantity of a substance that would have passed beyond the end of this limited 
cylinder is considered to be totally reflected, distributed by diffusion, and retained in 
the several sections of the tube. 
The figures in column 6 have been adjusted in this manner to suit the diffusion 
tube, which was divided (as column 1 of Table A shows) into fourteen sections. 
The final column, 7, gives for each section the value of equivalent to the con¬ 
centration actually observed, calculating by interpolation the figures which lie 
between those actually given in the double column G. If the diffusion were in 
accordance with Fick’s law and the experiments free from error, all the numbers in 
column 7 should be identical. It will be seen that they do agree closely, and that 
the differences which occur may be attributed to experimental errors. It will be 
evident that the value to be attached to an experiment may be gathered from the 
degree of uniformity exhibited by the numbers in column 7. 
* Stefan, loc. cit., and Ostwald, ‘ Solutions,’ p. 130. 
