June 20, 1901] 



NATURE 



193 



SOME RECENT WORK ON DIFFUSION} 



W^ 



II. 



TE have seen that when steady diffusion is going on down a 

 cylindrical column which is absorbent at the bottom there is 

 a uniform diminution in the density of the diffusing substance from 

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

 coloured substance 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 there- 

 fore 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 fiat 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 cylin- 

 der, 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 

 diffusion 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. i. 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 ex- 

 periment with an absorbent disc the surfaces of equal density of 

 the diffusing substance over that disc are the exact analogues of 

 the surfaces of equi-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 is so the dia- 

 gram 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, surrounded by a wide rim. 



Fig. 2 represents what we might expect to be the state of 

 things when diffusion takes place through a circular aperture in a 

 diaphragm. Here the stream lines of the substance, which are 

 convergent as they approach the aperture, diverge again when 

 the opening is past, and we should expect to get a double 

 system of the ellipsoidal zones of equal density on either side of 

 the aperture. 



Did time permit I could show you that this hypothesis is not 



1 Discourse delivered at the Royal Institution, Friday, March 22, by Dr. 

 Horace T. Brown, F.R.S. (Continued from p. 174.) 



NO. 1 65 I, VOL. 64] 



only capable of giving reasonable and consistent explanations of 

 all the phenomena of diffusion into and through apertures, but 

 completely explains the "diameter law," and also enables us to 

 predict the amount of gas, vapour, or solute which will pass under 

 given conditions, and the results can be verified by experiment. 



I have only time to glance at one or two readily verifiable 

 deductions from this hypothesis. In the first place, it fully 

 accounts for what I have called the " diameter law," that is to say, 

 that diffusion through circular apertures in a diaphragm is 

 proportional to their diameters, not to their areas. 



In two diagrams on the wall we have represented the arrange- 

 ment of the equi-density curves and istream lines over two ab- 

 sorbent discs, one double the diameter of the other. We may 

 take these discs to represent an alkaline solution absorbing car- 

 bonic acid from the air. 



The two systems are on the same relative scale, but one is 

 magnified by two diameters. 



It will be seen that a curved line corresponding to any given 

 actual density of the diffusing substance must be twice as far 

 from the surface of the larger disc as it is from the surface of the 

 smaller ; that is to say, the ^raii'/eH/ of density on which the flow 

 depends is twice as steep over the small disc as it is over the 

 large one. From this it follows that for equal areas the flow 

 into the smaller disc is twice that into the larger and that the 

 total flow must be proportional to the diameters, which is just 

 what is found to be the case- 

 Wherever we get conditions favourable for the formation of a 



system of equi-density zones on one or both sides of a perforated 

 diaphragm, diffusion will go on in accordance with this 

 "diameter law." But one system of zones is quite sufficient 

 for the purpose, so that in a case like that of Fig. 2, which 

 represents the course of diffusion of atmospheric COoin perfectly 

 still air into an absorbent chamber, we might allow the outer 

 system of equi-density shells over the aperture to be completely 

 swept away by air currents, and still the " diameter law " would 

 hold good on account of the inner series of zones, which, from 

 their position, are protected from the air currents. This explains 

 in a very satisfactory manner why it is much more easy to 

 demonstrate the diameter law with apertures in a diaphragm 

 than simply with absorbing discs, where only one external 

 system of equi-density shells can exist, which is, of course, 

 extremely liable to be influenced by disturbing currents. 



Satisfactory, however, as this hypothesis is in explaining 

 everything connected with these curious facts of diffusion, it 

 must be borne in mind that the reasoning on which it is based 

 is ill part deductive and in part dependent on an analogy. 



Nearly 30x3 years ago it was said by Sir Thomas Roe that 

 " many things hold well in discourse, and in the theorique, 

 satisfie curious imaginations, but in practice and execution are 

 found difficult and ayrie. " 



Fortunately this does not apply to the present case, and I am 

 able to bring before you this evening for the first time an experi- 

 mental demonstration of the existence of zones of equal density 

 in the neighbourhood of an aperture through which diffusion is 



