1901.] on Some Becent Work on Diffusion. 553 



colour of the air column would uniformly diminish from top to 

 bottom. 



Tins cau be illustrated by the diffusion of a coloured copper salt 

 down a gelatine column. If this column were cut off just where the 

 colour ceases to be perceptible, and the cut end were immersed in 

 water to carry off the diffusing salt as fast as it came tbrough the 

 column, then if the upper end of the column remained in contact 

 with the coloured copper solution, we should ultimately get a constant 

 steady flow of the salt down the column. 



Under these conditions it can be readily shown both experimen- 

 tally and theoretically, that the actual amount of substance diffusing 

 down the column in a given time will, in the first place, be directly 

 proportional to the difference in the concentration of the diffusing 

 substance at the two ends of the column ; it will also be directly 

 proportional to the area of cross-section of the column ; but inversely 

 proportional to its length. 



The fact which for the moment I wish you to bear in mind is that, 

 all other things being the same, the amount of diffusion down a 

 column of this kind varies directly as the area of the cross-section of 

 the column. 



This is roughly illustrated by these two cylindrical columns of 

 gelatine, of different diameters, down which a coloured solution has 

 been diffusing for equal times. 



The salt has penetrated both columns to the same depth, and 

 the gradation of colour is also the same — a proof that the rates of 

 diffusion down the columns must be proportional to their areas of 

 cross-section. 



But now let us consider what will happen if, instead of varying 

 the width of the column throughout its entire length, we only 

 partially obstruct the cylinder somewhere in the line of flow, say by 

 means of a thin diaphragm pierced with a single circular hole of less 

 diameter than the bore of the tube. 



We must resort to experiment to answer this question. 



Suppose we take a series of exactly similar flasks, such as I have 

 here, and produce a steady flow of atmospheric carbonic acid down 

 their necks by partially filling each flask with a solution of caustic 

 soda, the amount of carbonic acid entering the flasks being determined 

 by subsequent titration of the soda solution. We can then study the 

 effect produced by partially obstructing the mouths of the flasks with 

 thin discs of metal or celluloid pierced with a single hole of definite 

 size. 



The results of a series of experiments of this kind are given in 

 Table I., and you will see that under these conditions the amounts 

 of carbonic acid diffusing down the cylindrical neck in a given time, 

 are not proportional to the areas of the apertures, as might reason- 

 ably have been expected, but are directly proportional to their 

 diameters. 



