plates, i. e. the maximum distance fallen, was 4.7 cms.; the rate of fall when negative ions alone came into action thus did not exceed 1.6 cm. per second. Treating these data in the manner described by Professor Thomson*, we find that the number of negative ions present, in the absence of an electric field, is less than 1000 per c.c.: this is in agreement with the value calculated above from the data afforded by leakage experiments.

LXXVI. Escape of Gases from Atmospheres. To the Editors of the Philosophical Magazine. GENTLEMEN,

A LETTER under the

LETTER under the above heading, by Mr. S. R. Cook in Nature' of the 24th of March, puts forward views which ought not to remain on record without reply; and as between 30 and 40 years ago I carried on the investigation into the rate at which gases can escape from atmospheres in the same way as Mr. Cook has done, and arrived from the premisses employed by him at substantially the same conclusions, perhaps the best answer will be to state the considerations which led me to distrust that line of argument, and finally to abandon it. To do this, however, requires more to be said than can be brought within the compass of a letter to a weekly journal; and on this account, and because the discussion is a physical discussion and concerns one of nature's greater operations, I venture to request for the following pages the hospitality of the Philosophical Magazine.

A study of the phenomena attending the escape of gases from atmospheres has been approached in two ways— inductively, by arguing upwards from events which are found to have occurred or to be in process of occurring in nature; and deductively ‡, by drawing inferences from the supposition that it is legitimate to attribute to the real gases of nature, behaviour which it has been ascertained would prevail in certain models of gas, so much simpler in their *Electrical Properties of Gases,' p. 121.

+"Of Atmospheres upon Planets and Satellites." By G. Johnstone Stoney, F.R.S. See Scientific Transactions of the Royal Dublin Society, vol. vi. p. 305 (October 1897); or Astrophysical Journal, vol. vii. p. 25 (January 1898).

"On the Escape of Gases from Planetary Atmospheres according to the Kinetic Theory." By S. R. Cook. See Astrophysical Journal, vol. xi. No. 1 (January 1900).

"The Kinetic Theory of Planetary Atmospheres." By Professor G. H. Pryan, F.R.S. See Philosophical Transactions, A. vol. excvi. p. 1 (March 1900).

constitution than real gases that the progress of events within them is susceptible of mathematical treatment.

The two methods, as hitherto employed, have led to contradictory results, of which one at least must be erroneous. Mr. Cook, who has of recent years employed the deductive. method, expresses the opinion in his letter that the numerical results which have been arrived at by this method "will have to stand" until they can be disproved "by other a priori reasoning." Serious students of nature must, I think, hold that man, in his dealings with nature, is not in a position to limit in this way the kind of proof he will accept; and that it is sufficient if in any way Mr. Cook's inferences from Maxwell's researches can be disproved, whether by valid a priori or by valid a posteriori reasoning. And, moreover, that when once they are disproved we are brought face to face with the fact that there has been a mistake somewhere in the data which have led those who trusted in them to a false conclusion.

What convinced me several decades ago that the conclusion at which I arrived, and at which Mr. Cook has arrived, is false, is that it represents the moon as incompetent to get rid of the atmosphere which it originally shared with the earth, and of the gases which it has since evolved in abundance from its own interior. We knew 35 years ago, as we know now, that any reasoning which makes out that the moon has retained its atmosphere, must have a flaw in it somewhere. Furthermore, since that time, other facts not then known have come to light, and in a marked degree confirm the judgment which was then formed. Our confidence that we are on the right track is justifiably strengthened when, as in this case, further discoveries as they emerge confirm the view to which we had been led when our materials were more scanty. The presence of helium on the earth was not then known: and the argument which has been based on what is now known of its behaviour may be summarised as follows:-Helium is supplied to the earth's atmosphere through certain hot springs, and under circumstances which indicate that it also oozes up through the soil. It is, however, what is carried up by the water of these springs that can be subjected to experimental examination. The other gases of our atmosphere, such as nitrogen, oxygen, and argon, are found to accompany the

* The argument here summarised is based on the marvellous determinations made by Sir William Ramsay, K.C.B., F.R.S., or in his laboratory, and will be found with the necessary details in a paper "On the Behaviour of Helium in the Earth's Atmosphere," by G. Johnstone Stoney. See Astrophysical Journal, vol. xi. p. 369 (1900).

helium in those springs: but with this marked difference, that whereas the other gases are present in such proportions as are consistent with their merely being portions of those gases which are being returned to the atmosphere after having been washed down into the earth from the atmosphere by rain, the case is entirely different when we come to helium. The quantity of helium passed into the atmosphere through those springs, is found to be from 3000 to 6000 times more than can be accounted for as a return to the atmosphere of helium which had been washed down out of it. Accordingly we are justified in regarding this great surplus of helium as being an addition which is being uninterruptedly made to the atmosphere. Notwithstanding this, the quantity of helium in the atmosphere has not gone on increasing. The earth at the present rate of supply furnishes in a small number of years a quantity of helium equal to the quantity which the atmosphere can at present retain,-i. e. in a number of years which is exceedingly small from a geological standpoint, which is the point of view that is here appropriate. The inference from these facts is the obvious one, that helium is by some agency being eliminated from our atmosphere as fast as it is being introduced into the atmosphere from the earth. Two possible agencies for the elimination of the helium suggest themselves-chemical reactions; and an escape of helium from the upper part of the atmosphere. Of these, chemical agency is excluded by the extreme chemical inertness of helium. What remains then is that there is an outflow of helium from the top of the atmosphere equal to the inflow at the bottom, and that the trace of helium which is at any one time present in the atmosphere is helium part of which is slowly making its way upwards to the situation from which some of its molecules can escape, and so produce that outflow which balances the net influx at the bottom of the atmosphere.

Having satisfied myself that the deductive method as I applied it (and as Mr. Cook has applied it) lands us in erroneous results, I set to work to scrutinize the data of the deductive argument with a view to ascertaining how far they may be depended upon, and at what points they are doubtful. All branches of physics require us to be more or less on our guard against trusting without sufficient scrutiny to inferences from that mixture of theory and hypothesis of which we are obliged to make use in order to be able to employ mathematics in physical research. The demand for this caution becomes a pressing one when, as in gases, we are obliged to deal with immense numbers of events, each of which has its own dynamical history with incidents peculiar to itself, and where

what chances on some of these occasions differs enormously from that which occurs in most of them. Of this kind are the interactions between the molecules of a gas and the interfused æther, and especially those complicated struggles between molecules which we call their encounters-events each of which, when viewed, as it ought to be viewed, from the molecular standpoint, is a battle lasting a long time as time has to be measured in molecular physics, and with an immense number and variety of incidents. These-the interactions between the molecules and the æther, and the interactions between molecule and molecule-are the primary events, the real determining events, which occur within a gas while the movements of the molecules as they dart about between one encounter and the next; the spectrum radiated by the gas; the ions which present themselves after some of the encounters; the compounds which result from chemical reactions during some of the encounters (if what we are dealing with happens to be a mixture of suitable gases); and finally that remarkable partition of energy between the events going on within the molecules and the translational motions of the molecules, which is effected during some of the encounters-all of these are subordinate events depending upon those which are above spoken of as the primary events. When dealing with such almost immeasurably intricate and obscure operations of nature, it behoves us with the very utmost caution to distinguish between what is theory and what hypothesis in the data we employ, in order to be able to ascertain how far any conclusions we draw follow from the one, and how far they involve the other with the risks inseparable from it.

Theories are suppositions we hope to be true; hypotheses are suppositions we expect to be useful. As to theories, they are either correct or erroneous. They may be, they usually are, but they by no means need be, of use to man. The virtue of a theory is simply to be true. On the other hand, hypotheses usually make use of machinery which we can see to be simpler than that operating in nature; and especially is this the case with those hypotheses to which we are obliged to have recourse in mathematical investigations, which, in order to be of use, must be so great a simplification of the complex intricacies of nature that human mathematics shall be able to cope with them.

The theory of gas universally put forward in scientific books when the present writer was young, was the erroneous statical theory that the molecules of a gas may be stationary, that they have a capacity for expanding and contracting, and that each molecule presses against its neighbours. An illustration

66

frequently made use of in those days was that of a froth of bubbles pressing against one another. This erroneous theory held the field in Avogadro's time and for more than thirty years afterwards; but in the fifties of the nineteenth century it was gradually, though not without protest, displaced (chiefly through a masterly series of papers by Clausius) by the Kinetic Theory, which is now the prevalent theory. The Kinetic Theory of Gas, as formulated by Clausius, regards the molecules of a gas as missiles of equal mass, darting about in space and not acting sensibly on one another except when encounters" chance to take place, i. e., not until the centres of mass of two molecules get within an interval of one another which is less-usually much less-than the average length of the free paths which the molecules describe between the encounters; which free paths are accordingly approximately straight and pursued with unvarying speed except so far as they may be slightly influenced by gravity or other external cause, or by some excessively minute part of the interactions between molecules, if any such survives when the interval between molecules gets beyond what we may call their encountering distance.

This is the Kinetic Theory of Gas as put forward by its founder, and any system of bodies which conforms to this definition may be called a Kinetic System. Thus, there are in nature as many kinetic systems as there are distinct gases; and moreover, all those models of gas in which the progress of events has been studied by mathematicians are each of them a kinetic system. So also are the cosmic bodies of celestial space, if we eliminate from the definition the condition that the masses must be equal; and, in fact, some modification of this clause of the definition is essential even as regards gases, inasmuch as in all the gases of nature there are found some of the missiles differing in mass from others—thus, in diatomic gases ions present themselves with masses that seem to be half the mass of average molecules. We may add further details without trespassing beyond the domain of theory, i. e., while still endeavouring to describe events as they occur in nature. Thus we may that elaborate internal events are going on within all these missiles, which internal events absorb about one-third of the

add

*Clausius's papers were preceded by a paper by Waterston which was presented to the Royal Society in 1845, but which was not then published. This paper when it long afterwards came to be printed was found to contain a most valuable anticipation of the kinetic theory as developed by Clausius. If Waterston's paper had been printed in due course, the Kinetic Theory would probably have been adequately dealt

with some years sconer.