impossible to convey any adequate idea without going fully into the subject. Some idea of the scope of the investigation may be gathered from the last section in the paper, which is accordingly introduced here. Section XIII.-Summary and Conclusion. Article 125. The several steps of the investigation which have been described may be enumerated as follows: (1.) The primary step from which all the rest may be said to follow is the method of obtaining the equations of motion so as to take into account not only the normal stresses which result from the mean motion of the molecules at a point, but also the normal and tangential stresses which result from a variation in the condition of the gas (assumed to be molecular). This method is given in Sections VI, VII, and VIII. (2.) The method of adapting these equations to the case of transpiration through tubes and porous plates is given in Section IX. The equations of steady motion are reduced to a general equation expressing the relation between the rate of transpiration, the variation of pressure, the variation of temperature, the condition of the gas, and the lateral dimensions of the tube. In Section X is shown the manner in which were revealed the probable existence (1) of the phenomena of thermal transposition, and (2) the law of correspondence between all the results of transpiration with different plates, so long as the density of the gas is inversely proportional to the linear lateral dimensions of the passages through the plates; from which revelations originated the idea of making the experiment on thermal transpiration and transpiration under pressure. (3.) It is also shown in Section X that the phenomena of transpiration resulting from a variation in the molecular constitution of the gas (investigated by Graham) are also to be deduced from the equation of transpiration. (4.) The method of adapting the equations of motion to the case of impulsion is given in Section XI. In Section XII is shown how it first became apparent that the extremely low pressures at which alone the phenomena of the radiometer had been obtained were consequent on the comparatively large size of the vanes, and that by diminishing the size of the vanes similar results might be obtained at higher pressures, whence followed the idea of using the fibre of silk and the spider-line in place of the plate vanes. (5.) In Section XII it is also shown that while the phenomena of the radiometer result from the communication of heat from a surface to a gas, as explained in my former paper, these phenomena also depend on the divergence of the lines of flow, whence it is shown that all the peculiar facts that have been observed may be explained. VOL. XXVIII. 2 A (6.) Section II, Part I, contains a description of the experiments undertaken to verify the revelations of Section X respecting thermal transpiration, which experiments establish not only the existence of the phenomena, but also an exact correspondence between the results for the different plates at corresponding densities of the gas. (7.) Section III contains a description of the experiments on transpiration under pressure undertaken to verify the revelations of Section X with respect to the correspondence between the results to be obtained with plates of different coarseness at certain corresponding densities of gas, which experiments proved not only the existence of this correspondence, but also that the ratio of the corresponding densities in these experiments is the same as the ratio of the corresponding densities with the same plates in the case of thermal transpiration a fact which proves that the ratio depends entirely on the plates. (8.) Section IV contains a description of the experiments with the fibre of silk, and with the spider-line undertaken to verify the revelations of Section XII, from which experiments it appears that, with these small surfaces, phenomena of impulsion, similar to those of the radiometer, occur at pressure but little less than that of the atmosphere. Conclusion. Article 126. As regards transpiration and impulsion, the investigation appears to be complete; most, if not all, the phenomena previously known have been shown to be such as must result from the tangential and normal stresses consequent on a varying condition of a molecularly constituted gas; while the previously unsuspected phenomena to which it was found that a variation in the condition of gas must give rise, have been found to exist. The results of the investigation lead to certain general conclusions which lie outside the immediate object for which it was undertaken; the most important of these, namely, that gas is not a continuous plenum, has already been noticed in Article 5, Part I. The Dimensional Properties of Gas. Article 127. The experimental results considered by themselves bring to light the dependence of a class of phenomena on the relations between the density of the gas and the dimensions of the objects owing to the presence of which the phenomena occur. As long as the density of the gas is inversely proportional to the coarseness of the plates the transpiration results correspond; and in the same way, although not so fully investigated, corresponding phenomena of impulsion are obtained as long as the density of the gas in inversely proportional to the linear size of the objects exposed to its action; in fact, the same correspondence is found with all the phenomena investigated. We may examine this result in various ways, but in whichever way we look at it, it can have but one meaning. If in a gas we had to do with a continuous plenum, such that any portion must possess the same properties as the whole, we should only find the same properties, however small might be the quantity of gas operated upon. Hence, in the fact that we find properties of a gas depending on the size of the space in which it is enclosed, and on the quantity of gas enclosed in this space, we have proof that gas is not continuous, or, in other words, that gas possesses a dimensional structure. In virtue of their depending on this dimensional structure, and having afforded a proof thereof, I propose to call the general properties of a gas on which the phenomena of transpiration and impulsion depend, the Dimensional Properties of Gas. This name is also indicative of the nature of these properties as deduced from the molecular theory; for by this it appears that these properties depend on the mean range, a linear quantity which, cæteris paribus, depends on the distance between the molecules. In forming a conception of a molecular constitution of gas, there is no difficulty in realizing that there must exist such dimensional properties; there is, perhaps, greater difficulty in conceiving molecules so minute and so numerous that in the resulting phenomena all evidence of the individual action is lost; but the real difficulty is to conceive such a range of observational power as shall embrace, on the one hand, a sufficient number of molecules for their individualities to be entirely lost, while, on the other hand, it can be so far localized as regards time and space, that, if not the action of individuals, the action of certain groups of individuals, becomes distinguishable from the action of the entire mass. Yet this is what we have in the phenomena of transpiration and impulsion. Although the results of the dimensional properties of gas are so minute that it has required our utmost powers to detect them, it does not follow that the actions which they reveal are of philosophical importance only; the actions only become considerable within extremely small spaces, but then the work of construction in the animal and vegetable worlds, and the work of destruction in the mineral world, are carried on within such spaces. The varying action of the sun must be to cause alternate inspiration and expiration, promoting continual change of air within the interstices of the soil as well as within the tissue of plants. What may be the effect of such changes we do not know, but the changes go on; and we may fairly assume that, in the processes of nature, the dimensional properties of gases play no unimportant part. II." Absorption of Gases by Charcoal. Part II. On a new Series of Equivalents or Molecules." By R. ANGUS SMITH, Ph.D., F.R.S. Received January 30, 1879. (Abstract.) In the "Transactions of the British Association," 1868, Norwich, on page 64 of the "Abstracts," there is a preliminary notice of an investigation into the amount of certain gases absorbed by charcoal. I made the inquiry from a belief previously expressed in a paper of which an abstract is in the "Proceedings of the Royal Society," page 425, for 1863. I said in that paper that the action of the gas and charcoal was on the border line between physics and chemistry, and that chemical phenomena were an extension of the physical; also that the gases were absorbed by charcoal in whole volumes, the exceptions in the numbers being supposed to be mistakes. results given were :— The It was remarked that the number for nitrogen was probably too low; I had some belief that the charcoal retained a certain amount which I had not been able to estimate. For common air, the number 40.065 crept into the paper or abstract instead of the quotient 7.06. I considered the numbers very remarkable, but was afraid that they would be of little interest unless they could be brought more easily under the eyes of others; my experiments were somewhat laborious; the exact numbers were seldom approached by the single analysis, but were wholly the result of a series of irregular averages and apparently irregular experiments. The cause of this was clear, as I believed, namely, the irregular character of the charcoal with which I had to deal. The experiments which I had published were forgotten, I suppose, by most men, but the late Professor Graham told me that he had repeated them with the same results which I had given. I might have considered this sufficient, but waited for time to make a still more elaborate investigation of the subject, and to take special care with oxygen, in the belief that, the rule being found, the rest of the inquiry would be easy; this was extended to nitrogen, but not by so many experiments as with oxygen. I am now assured of a sound foundation for inquiries, which must take their beginning from the results here given. It is found that charcoal absorbs gases in definite volumes, the physical action resembling the chemical. Calling the volume of hydrogen absorbed 1, the volume of oxygen absorbed is 8. That is, whilst hydrogen unites with eight times its weight of oxygen to constitute water, charcoal absorbs eight times more oxygen by volume than it absorbs hydrogen. No relation by volume has been hitherto found the same as the relation by weight. The specific gravity of oxygen being 16 times greater than hydrogen, charcoal absorbs 8 times 16, or 128 times more oxygen by weight than it does hydrogen. This is equal to the specific gravity of oxygen squared and divided by two or it is the atomic weight and specific gravity multiplied into each other, 16 x 16, and divided by two =128. 256 2 162 Nitrogen was expected to act in a similar way, but it refused. The average number of the latest inquiry is 4.52, but the difficulty of removing all the nitrogen from charcoal is great, and I suppose the correct number to be 466. Taking this one as the weight absorbed, 14 × 4.66=65·3, or it is 142 Oxygen is a dyad; nitrogen a triad. We have then carbonic acid not divided, but simply 22 squared =484. Time is required for full speculation, but the chemist must be surprised at the following: These four results belong to the early group not corroborated lately, but so remarkably carrying out the principle of volume in this union giving numbers the same as those of weight in chemical union, that they scarcely require to be delayed. I am not willing to theorize much on the results; it is here sufficient to make a good beginning. We appear to have the formation of a new series of molecules made by squaring our present chemical atoms, and by certain other divisions peculiar to the gases themselves. Or it may be that the larger molecule exists in the free gas, and chemical combination breaks it up. These new and larger molecules may lead rs to the understanding of chemical combinations in organic chemistry, |