;76 



NATURE 



\Aiarch ii, 1875 



the help of this medium, we shall only increase the calculated 

 specific heat, which is already too great. 



The theorem of Boltzmann may be applied not only to deter- 

 mine the distribution of velocity among the molecules, but to 

 determine the distribution of the molecules themselves in a region 

 in which they are acted on by external forces. It tells us that 

 the density of distribution of the molecules at a point where 



_ + 

 the potential energy of a molecule is i//, is proportional io e 

 where fl is the absolute temperature, and k is a constant for uU 

 gases. It follows from this, that if several gases in the same 

 vessel are subject to an external force like that of gravity, the 

 distribution of each gas is the same as if no other gas were 

 present. This result agrees with the law assumed by Dalton, 

 according to which the atmosphere may be regarded as con- 

 sisting of two independent atmospheres, one of oxygen, and the 

 other of nitrogen ; the density of the oxygen diminishing faster 

 than that of the nitrogen, as we ascend. 



This would be the case if the atmosphere were never dis- 

 turbed, but the effect of winds is to mix up the atmosphere and 

 to render its composition more uniform than it would be if left at 

 rest. 



Another consequence of Boltzmann's theorem is, that the tem- 

 perature tends to become equal throughout a vertica) column of 

 gas at rest. 



In the case of the atmosphere, the effect of wind is to cause 

 the temperature to vaiy as that of a mass of a'r would do if it 

 were carried vertically upwards, expanding and cooling as it 

 ascends. 



But besides these results, which I had already obtainel by a less 

 elegant method and published in iS66, B jltzmxnn's theoremseems 

 to open up a path into a region more purely chemical. For if the 

 gas consists of a number of similar systems, each of which may 

 assume different states having different amounts of energy, the 

 theorem tells us that the number in each state is proportional to 



e "" where ij/ is the energy, 9 the absolute temperature, and k a 

 constrnt. 



It is easy to see that this result ought to be applied to the 

 theory of ttie states of combination which occur in a mixture of 

 different substances. But as it is only during the present week 

 that I have made any attempt to do S3, I shall not trouble you 

 with my crude calculations. 



I have confined my remarks to a very small part of the field 

 of molecular investigation. I have said nothing about the mole- 

 cular llieory of the diffusion of matter, motion, and energy, for 

 thougli the re3ult>!, especially in the diffusion of matter and the 

 transpiration of fluids are of great interest to many chemists, 

 and though from tiiem we deduce important molecular data, they 

 belong to a part of fur study the data of which, depending on 

 the conditions of the encounter of two molecules, are neces- 

 sarily very hypothetical. I have thought it bstler to exhibit ihe 

 evidence that the pans of fluids are in motion, and to describe 

 the manner in which that motion is distributed among molecules 

 of different masses. 



To show that all the molecules of the same substance are 

 equal in mass, we may refer to the methods of dialysis intro- 

 duced by Graham, by which two gases of diflerent densities may 

 be separated by percolation through a porous plug. 



If in a single gas there were molecules of different masses, the 

 same process of dialysis, repeated a sufficient number of times, 

 would furnish us with two portions of the gas, in one of which 

 the average mass ol the molecules would be greater than in the 

 other. The density and the combining weight of these two 

 portions would be different. Now, it may be said that no one 

 has cairieJ out this experiment in a sufficiently elaborate manner 

 for every chemical substance. But the processes of nature are 

 continually cairying out experiments of the same kind ; and if 

 there were molecules of the same substance nearly alike, but 

 differing slightly in mass, the greater molecules would be selected 

 in preference to form one compound, and the smaller to form 

 another. But hydrogen is of the same density, whether we 

 obtain it from water or from a hydrocarbon, so that neither 

 oxygen nor carbon can find in hydrogen molecules greater or 

 smaller than ilie average. 



The estimates which have been made of the actual size of 

 molecules are founded on a comparison of the volumes of bodies 

 in the liquid or solid state, with their volumes in the gaseous 

 state. In the study of molecular volumes we meet with many 

 difificulties, but at the same time there are a sufficient number of 

 consistent results to make the study a hopeful one. 



The theory of the possible vibrations of a molecule has not 

 yet been studied as it ought, with the help of a continual com- 

 parison between the dynamical theory and the evidence of the 

 spectroscope. An intelligent student, armed with the calculus 

 and the spectroscope, can hardly fail to discover some important 

 fact about the internal constitution of a molecule. 



The observed transparency of gases may seem hardly consis- 

 tent with the results of molecular investigations. 



A model of the molecules of a gas consisting of marbles scat- 

 tered at distances bearing the proper proportion to their diame- 

 ters, would allow very little light to penetrate through a hundred 

 feet. 



But if we remember the small size of the molecules compared 

 with the length of a wave of light, we may apply certain theo- 

 retical investigations of Lord Rayleigh's about the mutual action 

 between waves and small spheres, which show that the trans- 

 parency of the atmosphere, if affected only by the presence of 

 molecules, would be far greater than we have any reason to 

 believe it to be. 



A much more difficult investigation, which has hardly yet been 

 attempted, relates to the electric ])roperties of gases No one 

 has yet explained why dense gases are such good insulators, and 

 why, when rarefied or heated, they permit the discharge of 

 electricity, whereas a perfect vacuum is the best of all insulators. 



It is true that the diflTusion of molecules goes on faster in a 

 rarefied gas, because the mean path of a molecule is inversely as 

 the density. But the electrical difference between dense and 

 rare gas appears to be too great to be accounted for in this way. 



But while I think it right to point out the hitherto uncon- 

 quered difificulties of this molecular theory, I must not forget to 

 remind you of the numerous facts which it satisfactorily e.xplains. 

 We have already mentioned the gaseous laws, as they are called, 

 which express the relations between volume, pressure, and tem- 

 perature, and Gay Lussac's very important law of equivalent 

 volumes. The explanation of these may be regarded as com- 

 plete. The law of molecular specific heats is less accurately 

 verified by experiment, and its full explanation depends on a 

 more perfect knowledge of the internal structure of a molecule 

 than we as yet possess. 



But the most important result of these inquiries is a more dis- 

 tinct conception of thermal phenomena. In the first place, the 

 temperature of the medium is measured by the average kinetic 

 energy of translation of a single molecule of the medium. In 

 two media placed in thermal cominunication, the temperature as 

 thus measured tends to become equal. 



In the next place, we learn how to distinguish that kind of 

 motion which we call heat from other kinds of motion. The 

 peculiarity of the motion called heat is that it is perlectly irre- 

 gular ; that is to say, that the direction and magnitude of the 

 velocity of a molecule at a given time cannot be expressed as 

 depending on the present position of the molecule and the time. 



In the visible motion of a body, on the other hand, the velo- 

 city of the centre of mass of all the molecules in any visible 

 portion of the body is the observed velocity of that portion, 

 though the molecules may have also an irregular agitation on 

 account of the body being hot. 



In the transmission of sound, too, the different portions of 

 the body have a motion which is generally too minute and too 

 rapidly alternating to be directly observed. But in the motion 

 which constitutes the physical phenomenon of sound, the velo- 

 city of each portion of the medium at any time can be expressed 

 as depending on the position and the time elapsed ; so that 

 the motion of a medium during the passage of a sound-wave 

 is regular, and must be distinguished from that which we call 

 heat. 



If, however, the sound-wave, instead of travelling onwards in 

 an orderly manner and leaving the medium behind it at rest, 

 meets with resistances which fritter away its motion into irre- 

 gular agitation.*, this irregular molecular motion becomes no 

 longer capable of being propagated swiftly in one direction as 

 sound, but lingers in the medium in the form of heat till it is' 

 communicated to colder parts of the medium by the slow pro- 

 cess of conduction. 



The motion which we call light, though still more minute 

 and rapidly alternating than that of sound, is, like that of sound, 

 perfectly regular, and therefore is not heat. What was formerly 

 called Radiant Heat is a phenomenon physically identical with 

 light. 



When the radiation arrives at a certain portion of the medium, 

 it enters it and passes through it, emerging at Ihe other side. 

 As long as the medium is engaged in transmitting the radiation 



