1901.] on Some Recent Work on Diffusion. 557 



uniform diminution in the density of the diffusing suhstance from 

 one end of the columu to the other, evidenced in the case of a 

 coloured suhstance by a gradual and uniform thinning out of the 

 colour in the direction of the axis of the column. But in any 

 horizontal cross-section of the column, the colour is of the same 

 intensity in all parts of the section, which means of course that the 

 diffusing substance is of equal density along these planes. 



In a diagrammatic section of such a column we should therefore 

 represent the surfaces of equal density by straight lines drawn at 

 right angles to the axis of the cylinder, and the stream lines of the 

 diffusing substance by straight lines drawn parallel to the axis. 



I am able to show you the horizontal lines of equal density in a 

 cylinder, produced by a process of intermittent diffusion presently 

 to be described. 



When diffusion goes on into a flat absorbent disc, or aperture, 

 instead of into a cylinder, it is clear that the stream lines of the 

 diffusing substance must strongly converge towards the disc, instead 

 of moving vertically downwards as they do in the cylinder, and it is 

 also clear that the lines or surfaces of equal density in the diffusing 

 substance, must form curved surfaces of some kind over the disc. 

 We must now consider the exact form which these lines and surfaces 

 will take. 



It so happens that there is a problem in electrostatics which is 

 analogous to the one before us, and it is one which has been fully 

 worked out by mathematical physicists. 



When an insulated conductor receives an electric charge, the form 

 taken by the surfaces of equi-potential around the conductor depends 

 on its shape, and on the nature and distribution of other charges in 

 its neighbourhood. 



If we suppose the absorbing disc or perforation used in our dif- 

 fusion experiments to be replaced by an electrified disc of similar 

 dimensions, embedded flush in a wide non-conducting rim, then the 

 surfaces of equal electric potential in the air above the disc will take 

 the form represented in Fig. 1. The surfaces will form a series of 

 hemi-spheroids which in any vertical section passing through the 

 centre of the disc will give a series of ellipses, having their common 

 foci in the edges of the disc. Faraday's lines or tubes of force on 

 the other hand will, in this case, be represented by a series of 

 hyperbolas, also having their foci in the edges of the disc. 



Now we have every reason to believe that in a diffusion experi- 

 ment with an absorbent disc the surfaces of equal density of the 

 diffusing substance over the disc are the exact analogues of the 

 surfaces of equal potential over the similar electrified disc, and that 

 the stream lines of the diffusing substance are the analogues of the 

 lines or tubes of force. If this be so, the diagram will equally well 

 represent an experiment in which, for instance, the carbonic acid of 

 perfectly still air is being absorbed by a disc of soda solution, sur- 

 rounded by a wide rim. 



