366 



NATURE 



\August 14, 1879 



We are informed that at Sir Thomas Maclear's funeral, 

 on July 16, all the principal residents in the colony were 

 present. The Cape Parliament has passed a resolution 

 or memorandum acknowledging the work he did for the 

 colony. 



A POINT AFFECTING THE DIFFUSION OF 

 THE GASES OF THE ATMOSPHERE IN 

 RELATION TO HEALTH 



THE great importance in relation to health of the part 

 played by the internal motion of gases, as indicated 

 by the now established and admirably simple kinetic 

 theory, would seem scarcely to receive adequate appre- 

 -ciation. The old and vaguely developed statical idea of 

 a stagnant atmosphere with molecules at rest, has given 

 place to the opposite view of a high activity of motion, 

 even when the atmosphere appears to the senses to be 

 stilL By this motion noxious vapours or gases, instead of 

 remaining stagnant, are rapidly scattered by diffusion, and 

 thereby rendered harmless. The part apparently played 

 here by inequality of molecular velocity (dependent on in- 

 equality of molecidar mass) in contributing to this end, 

 would seem scarcely to have received the attention it ap- 

 pears to deserve. In Prof. Tait's work, " Lectures on 

 some Recent Advances in Physical Science " (p. 237, 

 second edition), reference is made to the diffusion of 

 the gases of the atmosphere under the kinetic theory, and 

 here it would seem as if the influence of the inequality of 

 the normal velocity of the molecules of the different 

 gases of the atmosphere (dependent on inequality of mole- 

 cular mass) had not been taken into account, and hence 

 it would appear as if the gases in their mutual diffusion 

 were regarded as subject to the pure contingencies of 

 chance, as they would be if the velocities of the molecules 

 were equal (or their masses equal) ; this necessarily lead- 

 ing to some rather startling conclusions, which make the 

 continuance of life and health (as dependent on the equable 

 mixture of the constituents of the atmosphere) a matter 

 more or less dependent on contingency or accident. The 

 passage in question runs as follows : — 



" There is another extremely important point of this 

 statistical question as to the particles of gases which I 

 must carefully explain ; and it is this, how it happens 

 that in the enormous bulk of the whole atmosphere of the 

 earth these particles of oxygen and nitrogen, moving about 

 amongst one another, should not by chance, at some place 

 or other, operate on one another in such a way that in 

 some particular cubic inch the particles of nitrogen might 

 for a moment expel from it all the particles of oxygen, so 

 that in virtue of the great extent of the earth's atmosphere, 

 compared with the size of a particle of gas, there might 

 be at some definite instant a region filled mainly with 

 nitrogen, and other regions filled mainly with oxygen. 

 Now the beauty of this statistical method is that it ex- 

 plains to us how such an event, though perfectly possible, 

 can never occur. It is a thing which is itself absolutely 

 possible, but it never can occur in practice, because the 

 probability of its occurrence is so exceedingly small. 

 There is a probability (numerically measurable) for every- 

 thing which is possible, but if that probability (reckoned 

 in numbers) is as small as the probability of the accident 

 we are considering, we never expect to find it occur. And 

 not only do we never expect to find it at any time, but we 

 can say boldly from experience that it is never met with 

 at all, however long our observations are conducted, or 

 through however great an extent of space we conduct them. 

 If you had originally in a box divided into two equal parts, 

 nitrogen in the one part and oxygen in the other, and then 

 allowed them to mix with one another, the probability that 

 in any assigned time you could find all the nitrogen back 

 again in the space where it was originally, and all the 

 oxygen back again in the space where it was originally, is 

 certainly one which can be measured, but it is one which 



is so infinitesimally small that we know perfectly by ex- 

 perience that it can never be realised." 



The above appears a somewhat unsatisfactory concln- 

 sion to contemplate, and there would seem to be some- 

 thing scarcely consistent in the inference that an event 

 which is itself absolutely possible never can occur in prac- 

 tice, "because the probability of its occurrence is so 

 exceedingly small." For we know from the doctrine of 

 probabilities that an event of chance (if possible at all) 

 must occur, if the range of time be not restricted, or at 

 least its probability approaches with indefinite closeness 

 to absolute certainty in that case. That the probability, 

 for example, of suffocation in a room [taking the above 

 illustration of a box on a large scale] within a given range 

 of time, by the oxygen separating itself sufficiently from the 

 nitrogen,couldbe rigidly calculated, seems scarcelypleasant 

 to contemplate, however remote the contingency might be, 

 and it is hardly satisfactory to think that the contingency 

 of such an event approaches with indefinite nearness to 

 absolute certainty if an adequate time be conceded. The 

 very fact that considering the vast extent ,of the atmo- 

 sphere and the range of historic time, no record whatever 

 exists of any irregularity having been detected in the con- 

 stitution of the atmosphere, would surely be strong argu- 

 ment for the existence of some physical cause tending to 

 prevent such irregularity from occurring, and removing it 

 from the pure contingencies of chance. The above quota- 

 tion that — " we can boldly say from experience that it \i.e. 

 the irregularity] is never met with at all, however long our 

 observations are conducted"- — would surely tend to prove 

 that some preventive means existed. 



If the molecules of nitrogen and oxygen of a mass of 

 air confined in a room were supposed subject to the pure 

 contingencies of chance in their mutual actions in diffu- 

 sion, they would be comparable to a number of equal per- 

 fectly elastic black and white balls imagined to be moving 

 and colliding freely among themselves, or left to their own 

 dynamics in an analogous manner. In this case there 

 would evidently be practically an infinite number of 

 chances against the molecules of the two gases (repre- 

 sented by the two differently coloured sets of balls) from 

 becoming uniformly diffused through the room ; indeed 

 the probability of this event would be exactly the same as 

 the probability of the oxygen being all separated in one 

 part of the room and the nitrogen in the other (or in 

 analogy all the black balls separated from the white) ; for 

 we know that, according to the doctrine of probabilities, 

 every assigned arrangement for all the balls is equally 

 probable. 



1 venture to suggest that the inequality in the mean 

 velocity of the molecules of the two gases (dependent on 

 the inequality of the masses of the molecules) plays an 

 important part here. If this particular point has been 

 considered elsewhere (without my knowledge), I may still 

 perhaps give an elementary analysis of the problem, as it 

 has occurred to me. It may be remarked that on account 

 of the simplicity of the kinetic theory, its problems fre- 

 quently admit of elementary treatment, and it will at least 

 be admitted that wherever this is practicable, perspicuity 

 does not lose thereby. We will imagine for illustration a 

 portion (say spherical shaped) of pure oxygen gas to be at 

 a given instant of time surrounded by an atmosphere of 

 hydrogen. [We may neglect the existence of gravity, for 

 simplicity, as it does not affect the point with which we 

 have to deal.] Then diffusion at once commences. The 

 molecules of hydrogen which have one-sixteenth less mass^ 

 are known to possess a normal velocity four times that of 

 the molecules of oxygen. The molecules of hydrogen by 

 their own normal motion will therefore rush into this 

 spherical space occupied by the oxygen, four times as fast 

 as the molecules of oxygen can move out by their natural 

 motion. Owing to this inequality in the rate of exchange 

 of places of the two gases, the mass of gas occupying the 

 spherical space will begin to increase in density, and (for 



