June 13, 1901] 



NA TURE 



17: 



The salt has penetrated both columns to the same dep-.h, 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 w^hat will happen if instead of varymg 

 the width of the column throughout its entire length we only 

 partially obstruct the cylinder somewhere in the line of How, 

 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 solu- 

 tion 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 necks 

 in a given time are not proportional to the areas of the aper- 

 tures, as might reasonably have been expected, but are directly 

 proportional to their diameters. 



Table I. 



Diffusion of Atmospheric CO2 through single apertures of varying 5 



This, of course, implies that as we make the aperture smaller 

 the flow through a given unit of its area is proportionately 

 increased ; in other words, the acceleration of flow is inversely 

 proportional to the diameters of the apertures. 



This unexpected fact, which lies at the root of the whole 

 question we are considering to-night, may be experimentally 

 illustrated in a variety of ways. 



We may, for instance, cause the aqueous vapour of the air to 

 dift'use into a similar series of flasks, using in this case strong 

 sulphuric acid as the absorbent, and determining the amount of 

 diffusion of the water vapour by weighing the flasks from time 

 to time. You will see from the results of such an experiment 

 that the diffusion rates again follow pretty closely the ratios of 

 the diameters of the apertures, and are widely divergent from 

 the ratios of areas. (See Table II. ) 



This " diameter law " is also applicable to circular liquid 

 surfaces, the amount of absorption or evaporation from such 

 surfaces varying, under certain conditions, not in accordance 

 with the area of the surfaces, as might have been expected, but 

 with their diameters. 



I have here a short burette-like tube with a wide rim of metal 

 round the top. When this tube is completely filled by letting 

 in a solution of caustic soda we have a circular surface of the 

 solution lying in the same plane as the rim. When this has 



NO. 1650, VOL. 64] 



been exposed to the air for a given time the carbonic acid 

 absorbed by the disc of liquid can be determined by drawing off 

 and titrating. 



If such absorptive discs of different dimensions are exposed 

 to air which is in slight movement, we shall find that the car- 

 bonic acid absorbed is proportional to the area of the surface. 

 The smaller, however, we make the discs, and the greater pre- 

 cautions we take to keep the air over them perfectly still, the 

 nearer do the absorptions become proportional to the diameters. 

 (See Table III.) 



There is always, however, more difficulty in obtaining these 

 results with plane absorbing surfaces than by diffusion through 

 a perforated diaphragm. The reason for this will be apparent 

 later. 



Table III. 



."Absorption of Atmospheric CO2 by Circular Surfaces of Solutions of 

 Caustic Alkali. 



Before entering on an explanation of these facts I wish you to 

 note a very important conclusion to be drawn from them, and 

 one which readily admits of experimental verification. 



We have seen that when we partially obstruct the diffusive 

 flow of a gas or liquid by a thin septum with a single circular 

 perforation, the velocity of the flow through each unit area of 

 aperture increases as the diameter of the aperture decreases. 



One might, therefore, expect that if a number of fine holes 

 were suitably arranged in such a septum, the acceleration of flow 

 through the individual holes might assume such proportions 

 that a perforated septum of this kind would exercise little or no 

 obstruction on the diffusive flow, although in such a case the 

 aggregate area of the holes might only represent a small fraction 

 of the total area of the obstructing septum. 



Strange and paradoxical as such a conclusion may at first 

 sight appear, it will bear the test of experiment. 



I have here a thin film of celluloid ; in fact, a piece of the 

 ordinary Kodak roller-film. This has been perforated with holes 

 about '4 millimetre in diameter, arranged at a little more than 

 25 diameters apart, so that there are just one hundred of such 

 perforations on a square centimetre of area. The clear holes 

 represent about i/ioth of the area of the film, 9/ioth of the sieve 

 being blocked up with impervious celluloid. 



Here are two columns of gelatine, down which a blue solution 

 of copper-ammonium sulphate has been diffusing for equal 

 times. One of these columns is unobstructed in any way, being 

 in direct contact with the coloured liquid. In the other case a 

 finely perforated celluloid film has been interposed, which has 

 the effect of blocking out 9/ioths of the cross-section of the 

 column. You see that, notwithstanding this, there is no appre- 

 ciable difference in the amounts of coloured salt which have 

 diffused in the two cases ; the salt has, in fact, gonethrough the 

 finely-pierced septum as readily as if no obstruction were 

 present.' 



We find that exactly the same holds good with gaseous 

 diffusion. 



If finely perforated septa of this kind are luted on to short 

 tubes containing caustic soda and are exposed to still air, the 

 amount of carbonic acid diffu'-ing through the holes in the 

 diaphragm can be compared with the amount which we know 

 would diffuse down the open tube under like conditions. 



Some results of this kind are given in Table IV. 

 1 The celluloid film is itself not permeable. 



