June 13, 1901] 



NATURE 



171 



SOME RECENT WORK ON DIFFUSION} 



'T'HE subject of my lecture is one which, though essentially of 



a physical nature, had its origin in what may be regarded 



as a no man's land, a strip of neutral territory which can be 



claimed exclusively neither by the physicists nor the biologists. 



An attempt to reconcile some apparently contradictory facts 

 connected with the nutrition of plants has led, somewhat un- 

 expectedly, to an extension of the laws of gaseous diffusion, so 

 that we shall have to deal with one of those comparatively rare 

 cases in which biology has been able to react to some extent on 

 physics. 



It has long been known that the primary source of the carbon 

 of all plants is the carbonic acid existing in small quantities in 

 ordinary atmospheric air, and that their green parts, more 

 especially the leaves, are able to utilise the energy of sunlight in 

 decomposing the carbonic acid and water and building up trom 

 their elements a whole series of substances, such as sugars and 

 starch, which contribute directly to the nutrition of the plant. 



The immediate seat of this synthetic and assimilatory process 

 is found in the minute green chlorophyll granules which occur 

 in great numbers within the cells of the leaf tissue, and one of 

 the first problems to be dealt with in the study of the process is 

 to show in what manner the highly dilute carbonic acid of the 

 air can gain entry into the leaf with sufficient rapidity to supply 

 these assimilating centres with material for the needs of the 

 plant. 



In a typical leaf, such as is represented in section in the 

 diagram, both sides are covered with a cuticle and epidermis 

 pierced at regular intervals on one or both sides with extremely 

 minute openings, whose size is capable of being regulated accord- 

 ing to the requirements of the plant. These are the stomales 

 which open out into a relatively large cavity within the leaf, 

 and this cavity in turn communicates with the numerous and 

 roomy air-spaces between the cells containing the green chloro- 

 phyll granules. 



One of the most important functions of the stomates is un- 

 doubtedly to regulate the transpiration of water from the plant, 

 but the question of how far these minute openings play a part in 

 the interchanges of gases between the interior of the leaf and the 

 outer air has been a subject of very lively controversy. 



It is now about thirty years since the eminent French chemist, 

 Boussingault, came to the conclusion that the carbonic acid of 

 the air gains access to the leaf, not through the stoviales, but 

 through the continuous substance of the cuticle and epidermis, 

 by a process of osmosis similar to that by which carbonic acid 

 had been shown by Graham to pass through a thin film of 

 india-rubber. 



So convincing did Boussingault's experiments and arguments 

 appear to his contemporaries that this view became an article of 

 faith for something like a quarter of a century, until, in fact, some 

 five or six years ago, when Mr. F. Frost Blackman took up the 

 subject and proceeded most inconsiderately to shatter all the 

 most cherished statements of our text-books on this question. 



I regret that time will not allow me to do more than state the 

 general conclusions at which Mr. Blackman arrived and which 

 may be briefly summarised as follows : 



In the first place there is no appreciable passage of atmospheric 

 carbonic acid through the surface of a leaf which is naturally 

 devoid of stomates, such, for instance, as the upper surface of a 

 normal leaf, which is quite imperforate ; neither is any entry of 

 carbonic acid possible when the stomates have been artificially 

 blocked or made to close spontaneously. 



In additition to this, if a leaf has stomates on both surfaces the 

 relative in-take of carbonic acid by those surfaces bears a 

 distinct relation to the distribution of the stomates. 



We can, in fact, no longer doubt that when a leaf is resp"iring 

 or assimilating mere osmosis of carbonic acid through the sub- 

 stance of the cuticle and epidermis plays little or no part in the 

 gaseous exchanges, and that whatever the exact nature of the 

 process may be it must be carried on exclusively by the minute 

 openings of the stomates. 



Since anything like a mass movement of the air through these 

 openings is out of the question, we must look to the phenomena 

 of diffusion for the true explanation, and especially to that form 

 of it which was first described by Graham as free diffusion, that 

 is to say the natural tendency possessed by gases or liquids to 

 form a perfect mixture when they are in contact with each other 

 and there is no partition of any kind between them. 



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

 Horace T. Brown, F.R.S. 



NO. 1650, VOL. 64] 



This spontaneous mixing is quite independent of any currents 

 or mass movements of any kind, and is brought about by the 

 gradual interpenetration of the molecules of the one gas or liquid 

 by the molecules of the other. 



.\s an example of this kind of diffusion I have here a cylinder 

 which a few weeks ago was partly filled with 5 per cent, gelatine 

 solution. After the gelatine haci set, the cylinder was filled up 

 with a highly-coloured solution of a copper salt, which you 

 now see has permeated the jelly to a certain depth. There 

 has been no mixing of the solutions in the ordinary sense of 

 the word, for the gelatine is virtually a solid. The effect 

 has been produced by the molecules of the coloured copper 

 salt, by reason of their rapid movement in all directions, gradu- 

 ally penetrating into the spaces between the molecules of the 

 gelatine layer. Given a sufficient length of time and there would 

 be an equal partition of the coloured substance between the two 

 layers. 



Difl'usion takes place, as is well known, much more rapidly 

 with gases than with liquids. Had our cylinder contained, for 

 instance, carbonic acid in the lower half and air in the upper, a 

 complete mixing would have taken place in a comparatively short 

 time, even if all convection currents had been prevented. 



The classical researches of Graham on the diffusion of gases 

 through thin porous septa established the general law that the 

 rate of diffusion of the different gases, under identicil conditions, 

 varies inversely as the square roots of their respective densities. 

 Graham's results, however, only acquaint us with the relative 

 velocities of diffusion, whereas for the particular problem which 

 we have before us we must know the absolute velocities of 

 diffusion under strictly defined conditions. 



It is mainly to the Viennese school of physicists, and especially 

 to Prof. Loschmidt, that we owe our present knowledge of the 

 actual rate of penetration of one gas by another in free diffusion. 

 By observing the speed with which different pairs of gases 

 spontaneously mix in a tube, Loschmidt was able to deduce 

 certain absolute values expressing the velocity of their inter- 

 penetration. 



Some of these results for different pairs of gases are given in 

 the diagram, the last column representing the " constant of 

 diffusivity" expressed in centimetre-gram-second units. 



Let us consider the constant for carbonic acid and air, which 

 at o" C. is '142. This means that when air and carbonic acid gas 

 are freely diffusing into each other, an amount of either gas 

 corresponding to '142 cubic centimetre will pass in one second 

 of time across an area of one square centimetre when the partial 

 pressure of the gas varies by one atmosphere in one centimetre 

 of length. 



Now when we come to apply these absolute values of diffusivity 

 to the passage of the extremely dilute CO.i of the air into the leaf 

 stomates (whose dimensions can of course be determined), we find 

 that free diffusion through these openings is apparently able 

 to account for only a portion of the gas which we know must 

 enter the leaf, unless we make some extremely improbable 

 assumptions as to the very low point at which the partial pressure 

 of the carbonic acid is maintained immediately under the 

 apertures. 



I shall not, however, trouble you with the calculations on 

 which this statement is based, since I prefer to put the matter 

 in a more concrete form, which has also the advantage of 

 emphasising the extraordinary power which an assimilating leaf 

 possesses of extracting carbonic acid from its surrounding air. 

 There are two methods by which we can determine the actual 

 amount of atmospheric carbonic acid used up by an assitriilating 

 leaf, one a direct the other an indirect method. 



Part of the apparatus used in the direct method is shown on 

 the table. 



The leaf, which may be still attached to the plant, is enclosed 

 in a glazed case, through which a measured current of air is 

 drawn of 'which the carbonic acid content is accurately known. 

 When the air emerges from the case it passes through an ab- 

 sorption apparatus, which retains the whole of the COo left in 

 the air after passing over the leaf. This absorbed carbonic 

 acid is determined at the close of the experiment, and we then 

 have all the data for estimating the carbonic acid abstracted 

 from the air by the leaf. The area of the leaf being known, 

 the COj absorbed can be referred to a unit area of leaf and a 

 unit time. 



By the indirect method, which is due to Sachs, the actual 

 increase in dry weight of a given area of an assimilating leaf 

 is determined, and since this increase in weight is due to 



