I. "On certain Dimensional Properties of Matter in the Gaseous State. Part I. Experimental Researches on Thermal Transpiration of Gases through Porous Plates, and on the Laws of Transpiration and Impulsion, including an Experimental Proof that Gas is not a Continuous Plenum. Part II. On an Extension of the Dynamical Theory of Gas which includes the Stresses, Tangential and Normal, caused by a Varying Condition of the Gas, and affords an explanation of the Phenomena of Transpiration and Impulsion." By OSBORNE REYNOLDS, F.R.S., Professor of Engineering at Owens College. Received January 17, 1879.

Abstract of Part I (Experimental).

Section I (Introduction).

1. The motion of gases through minute channels such as capillary tubes, porous plugs, and apertures in thin plates has been the subject of much attention during the last fifty years. The experimental study of these motions, principally by Graham, resulted in the discovery of important properties of gases, and it is largely, if not mainly, as affording an explanation of these properties, that the molecular theory has obtained such general credence.

It does not appear, however, that either the experimental investigations of these motions, or the theoretical explanations of the properties revealed, have hitherto been in any sense complete. There exists a whole class of very marked phenomena which have escaped the notice of Graham and other observers, while several of the most marked and important facts discovered by Graham have hitherto remained unconnected by any theory.

2. Amongst the best known of the phenomena is the difference in the rates at which different gases transpire through minute channels, and the consequent difference in the pressure which ensues when two different gases, initially at the same pressure, are separated by a porous plate. But it does not appear that hitherto any attempt has been made to ascertain the existence of what may be considered a closely analogous phenomenon-that a difference of temperature on the two sides of the plate might cause gas, without any initial difference of pressure or any difference in chemical constitution, to pass through the plate-nor am I aware that such a result from a difference of temperature has been in any way surmised.

I have now ascertained by experiments, which will be described at length, that a difference of temperature may be a very potent cause of transpiration through porous plates. So much so, that

with hydrogen on both sides of a porous plate, the pressure on the one side being that of the atmosphere, a difference of 160° F. (from 52° to 212°) in the temperature on the two sides of the plate secured a permanent difference in the pressure on the two sides equal to an inch of mercury; the higher pressure being on the hotter side. With different gases and different plates various results were obtained, which, however, as will be seen, are connected by definite laws.

3. Again, although Graham found that he obtained not only very different results, but also very different laws of motion with plates of different coarseness, or with plates and capillary tubes, neither he nor any subsequent observer appears to have followed up this lead. As regards Graham, this appears to me to be somewhat surprising. For although he may have considered the mere difference in the results to have been analogous to the difference found by Poiseuille for liquids, it would seem as though the difference in the laws of motion should have excited his curiosity; and then, as he was avowedly of opinion that gas is molecular, he could hardly have failed to observe that so long as the mean distance separating the molecules in the gas bore a fixed relation to the breadth of the openings in his plates, he should have had the same laws of motion. This view, however, appears to have escaped him as well as all subsequent observers, otherwise it would have been seen that with a simple gas such as hydrogen, similar results must be obtained so long as the density of the gas is inversely proportional to the lateral dimensions of the passages through the plates.

By experiments to be described I have now fully established this law. I find that with different plates similar results are obtained when the densities of the gas with the different plates bear certain fixed ratios, and that this is the case whatever may be the cause of transpiration, i.e., a difference of temperature or a difference of pressure; a difference of gas I have not investigated, as it was obviously unnecessary to do so. Thus, with two plates, one of stucco and the other of meerschaum, similar results of transpiration caused by pressure were obtained when the densities with the two plates were respectively as 1 to 5'6 both with hydrogen and air, and at pressures ranging from 30 to 2 inches of mercury; also with the same two plates similar results of thermal transpiration were obtained when the densities were respectively as 1 to 6.5 both for hydrogen and air, and through a range of densities from 30 inches to 25 of an inch of mercury, the discrepancy between 5.6 and 6.5 being in all probability owing to a slightly altered condition of the plates.

This correspondence of the results at corresponding densities holds although the law of motion changes. Thus, with air at 30 inches through the stucco plate, the law of motion was the same as that found by Graham for a stucco plate, while at the smallest pressure

(25 inch) it was nearly the same as he found for graphite plates, or for apertures in thin plates.

Having established this law of corresponding results at corresponding densities, it became apparent that the results obtained with plates of different coarseness, and with the same plates, but with different densities of gas, followed a definite law. This law, which admits of symbolical expression, shows that there exists a definite relation between the results obtained, the lateral dimensions of the passages, and the density of the gas.

This law is important in reconciling results which have hitherto appeared to be discordant and as tending to complete the experimental investigation, but it has another and a more general importance.

It may not appear at first sight, but on consideration it will be seen that this law amounts to nothing less than an absolute experimental demonstration that gas possesses a heterogeneous structure-that it is not a continuous plenum of which each part into which it may be divided has the same properties as the whole.

It would appear that Graham must have had this proof, so to speak, under his eyes, and it is strange that both he and other observers have overlooked it. It seems possible, however, that they were not alive to the importance of such a demonstration. It is now so generally assumed that gas is molecular, that the weakness of the evidence on which the assumption is based and the importance of further proof are points which are apt to escape notice.

The Importance of an Experimental Demonstration that Gas Possesses Molecular Structure.

5. The idea of molecular gas does not appear to have originated from the recognition of properties in gas which were inconsistent with the idea of a continuous plenum, but from a wish to reconcile the properties of gas with the properties of other substances, or, more strictly, with some general property of matter. And the general conviction which may be said to prevail at the present time is owing to the simplicity of the assumptions on which the molecular hypothesis is based, and the completeness with which many of the properties of gas have been shown to result from this hypothesis. But it will be readily seen that however simple may be the assumptions of the kinetic theory, and however completely the properties of gases may be shown to follow from these assumptions, this is no disproof of the possibility that gas may be a continuous substance, each elementary portion of which is endowed with all the properties of the whole, and unless this is disproved there may exist doubts as to the necessity for the kinetic theory.

Any direct proof, therefore, that gas is not ultimately continuous altogether alters the position of the molecular hypothesis.

The Sufficiency of the Demonstration that Gas is not Structureless.

6. In order to prove that gas is not structureless, it is not necessary that we should be able to perceive the actual structure; we have only to find some property of a certain quantity of gas which can be shown not to be possessed by all the parts, some property which is altered by a rearrangement of the parts.

Hitherto I believe that no such property has been recognised, or, at all events, the conclusions to be drawn from such a property have not been recognised. The phenomena of transpiration, as well as those of the radiometer, depend on such properties, but these properties have not been sufficiently understood to bring out the conclusion. This conclusion, however, follows directly from the law indicated in Article 4, viz., that the results of transpiration depend on the relation between the size of the passages and the density of the gas.

The Results Deduced from Theory.

7. Although the existence of the phenomena of thermal transpiration, and the existence of the law of corresponding results at corresponding densities, have been verified by experiment, they were not so discovered; they followed from what appeared to be a successful attempt to complete the explanation which I had previously offered of the forces which result when heat is communicated from a surface to a gas, and the phenomena of the radiometer.

Having found, what I had not at first perceived, that according to the kinetic theory the excess of pressure resulting from the communication of heat to a gas must depend on the fact of the surface from which the heat flows being of limited extent, and must follow a law depending on some relation between the mean path of a molecule and the size of the surface, it appeared that by using vanes of comparatively small size the force should be perceived at correspondingly greater pressures of gas.

On considering how this might be experimentally tested, it appeared that to obtain any result at measurable pressures the vanes would have to be very small indeed; too small almost to admit of experiment. And it was while searching for some means to obviate this difficulty that I came to perceive that if the vanes were fixed, then instead of the movement of the vanes we should have the gas moving past the vanes—a sort of inverse phenomenon; and then instead of small vanes small spaces might be allowed for the gas to pass. Whence it was at once obvious that in the porous plugs I should have the means of verifying these conclusions. I followed up the idea, and by a method which I devised of extending the dynamical theory of gases, so as to take into account the forces (tangential and normal) arising from a

"Proc. Roy. Soc.," vol. xxii, p. 402, and "Phil. Trans.," vol. clxvi, p. 726.

varying condition of molecular gas, I was able to deduce what to me to be a complete theory of transpiration.

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This theory appears to include all the results established by Graham, as well as the known phenomena of the radiometer, which, for the sake of shortness, I shall call the phenomena of Impulsion. I was also able definitely to deduce the results to be expected as regards both thermal transpiration and the law of corresponding densities for transpiration and impulsion.

Having made these deductions I commenced the experiments on transpiration, which so completely verified my theoretical deductions that I have been able to produce the theory in its original form, with some additions but without any important modification.

Moreover, having succeeded (not without some trouble) in rendering apparent the effect of differences of temperature in causing gas to inove through fine apertures, I recurred to the original problem, and by suspending fibres of silk and spider lines to act as vanes, I have now succeeded in directly verifying the conclusion that the pressure of gas at which the force in the radiometer becomes apparent varies inversely as the size of the vanes. With the fibre of silk I obtained repulsion at pressures of half an atmosphere.

The Arrangement of the Paper.

8. My object in this paper is to describe the reasoning by which I was led to undertake the experiments, as well as the experiments themselves; but as the theory will be better understood after an acquaintance with the facts, I have inverted the natural order and given the experiments first. I include here, however, a somewhat full account of the results to be expected as deduced from the theory.

Then follows a statement of the laws of transpiration and impulsion as deduced from theory: :-

Section II is devoted to the description of the experiments on thermal transpiration; Section III to the experiments on transpiration under pressure, and Section IV to the experiments on impulsion.

In this abstract it will not be possible to give more than a sketch of the matter contained in these sections. The numerous precautions and tests will have to be left unnoticed, and only a few of the experimental results can be given. The investigation occupied from February, 1878, till the beginning of August, every result being verified by repeated experiments.

The Apparatus for Thermal Transpiration.

This consisted principally of an instrument called a thermo-diffusiometer, of which the essential feature is two chambers, separated by a plate of porous material, means being provided for keeping the chambers at constant, but different, temperatures for many hours at a