PART II. CONTRIBUTIONS TO SCIENCE. (continued 3)

We must, of course, be careful not to endeavour to learn from such a model lessons which it was not designed to teach, and we must remember that the behaviour of the mechanism does not represent the electrical action in all respects.

For many years Maxwell rendered valuable service to the British Association, especially in connection with electrical science. Some account of the meetings which he attended will be found in the letters printed in another part of this work, and though during the last few years of his life other engagements prevented his attendance at the annual gatherings, he always showed signs of keen enjoyment when discussing the “British Asses.” In 1862 he was appointed a member of “The Committee on Standards of Electrical Resistance.” In the report issued in 1863, the Appendix, “On the Elementary Relations between Electrical Measurements,” bears the name of Professor Maxwell in conjunction with that of Professor Fleeming Jenkin, while the general description of the method employed in the determination of the Ohm or B. A. unit of resistance, together with the mathematical theory and details of the experiments, are from Maxwell’s pen. In 1863-4 Maxwell was again at work on the same subject in the laboratory of King’s College, and most of the “spins”[259] were conducted under his own supervision. In 1869 the results of Maxwell’s experiments on the relation of the electromagnetic to the electrostatic unit of electricity, described above, were embodied in the Report to the British Association at the meeting at Dundee, and this forms the last of the Reports of the Committee.

In 1874 Professor Maxwell was elected a member of the committee appointed by the British Association for the purpose of investigating Ohm’s law. Most of the work executed by this committee was carried out by Professor Chrystal in the Cavendish Laboratory, under the supervision and at the suggestion of Professor Maxwell. An account of the investigations will be found in the report presented to the Association at the Glasgow meeting in 1876.

Before concluding our notice of Maxwell’s contributions to electrical science we must mention the preparation for the press of The Electrical Researches of the Honourable Henry Cavendish, published in 1879, only a few weeks before the death of its editor. The amount of labour which Professor Maxwell bestowed on this work during the last five years of his life can only be known to those who were constantly in his company. Nearly all the MS. he transcribed with his own hand, the greater part being copied after midnight, while he watched over Mrs. Maxwell during the long illness to which allusion has elsewhere been made. Every obscure passage or allusion was the subject of a long and searching investigation; and many were the letters written to the Librarian of the Royal Society and to scientific and literary friends in different parts of the country, to gain information respecting the meaning of obsolete words and symbols, or the history of individuals. But besides this, and a comparison of Cavendish’s results with those obtained by subsequent investigators, Maxwell repeated many of Cavendish’s experiments almost in their original form, only employing modern instruments for the purposes of measurement. The introduction and the appendices to the work evidence much labour, patient investigation, and very extensive acquaintance with the literature bearing on the subject. Maxwell was by no means one of the class of “thinkers” who only read their own writings; his acquaintance not only with scientific literature, but with nearly every other class of books was astonishing; and if any question of physics was brought before him, he could generally give an account of nearly all that had been done in the subject. In this respect he resembled the late Professor W. H. Miller, whom Cambridge men used to consult about everything.

It would be impossible here to give any adequate account of Maxwell’s work in connection with the Cavendish papers, but we may mention one experiment both on account of its intrinsic importance and of the interest which Maxwell took in it. Cavendish describes an experiment (see p. 104 of The Electrical Researches) in which a sphere of 12·1 inches in diameter was enclosed between two copper hemispheres 13·3 inches in diameter, and the copper hemispheres, which were supported in frames hinged together, and opened or closed by silk cords, were brought together so as to enclose the sphere, contact being made at the same time between it and the hemispheres. The outer sphere was then charged, and the connection between it and the inner sphere removed. On separating the hemispheres, the inner sphere was found to be discharged, or at least the charge, if any, left upon it was too small to affect Cavendish’s pith ball electrometer. Knowing what fraction of the original charge could not fail to be detected by the electrometer, Cavendish deduced from the results of the experiment that the law of variation of electrical action with the distance must lie between the inverse th and th power of the distance, and inferred that it is the inverse square.

Maxwell placed a copper sphere about 10 inches in diameter within a hollow copper sphere, made of two hemispheres, about 12 inches in diameter, supporting it upon a ring of ebonite, so that the spheres might be concentric. The outer sphere was carefully insulated, and a hole cut in its surface, which could be accurately filled by a little trap door. To this trap door was attached a wire which rested on the inner sphere when the door was shut down. The door was carried on a metal arm which turned about a hinge attached to the outer sphere, and could be raised or lowered by a silk thread which passed over a pulley and hung in front of the operator. When the trap door was raised a wire connection could be allowed to fall by relaxing a second silk cord, so as to make contact with the inner sphere through the hole in the outer. The trap door was first closed and the outer sphere charged by means of a Leyden jar which was immediately removed (the electric machine being placed in a distant apartment). The trap door was then raised, the outer sphere discharged by connecting it to earth, and the inner sphere then put in communication with a quadrant electrometer by means of the wire above mentioned. Not a trace of electricity could be detected on the sphere. To test the accuracy of the method, a small brass sphere was insulated, and supported at a distance of about 60 centimetres from the outer sphere, and the experiment was repeated. When the copper sphere was charged the brass sphere was connected to earth, and thus a small negative charge was induced upon it by the positive electricity on the copper sphere, and the ratio of this charge to that on the copper could be easily calculated. The brass sphere was then insulated, the outer copper sphere discharged as before, and the inner sphere examined with the same result as previously. The brass ball was then discharged, the outer sphere being insulated, when it was found that there was sufficient positive electricity on the outer sphere to deflect the electrometer through more than 300 times the largest deflection which could escape notice. Now when the brass hall was insulated, the negative charge upon it was about th of the charge originally on the copper sphere, and this induced a positive charge on the sphere when in connection with the earth, which was about of its original charge. Hence of the original charge is more than 300 times the largest charge which could escape observation. From these figures it follows that, in the expression of the law of electrical action, the true index of the inverse power of the distance must be either 2 or differ from it by less than . These experiments were carried out in the Cavendish Laboratory by Mr. MacAlister of St. John’s College. In note 19 appended to the Cavendish papers, Maxwell describes the experiment, and gives its complete mathematical theory.

The idea that electricity flowing in conductors behaves like an incompressible fluid is at least as old as Cavendish; but before he had the opportunity of reading Cavendish’s papers, Maxwell taught that all electric discharges involve a displacement of electricity in a closed circuit, the electricity behaving both in conductors and in dielectrics like a perfectly incompressible fluid. Thus, when a Leyden jar is discharged, a certain quantity of electricity flows from the inner coating through the knob of the jar, and hence to the outer coating, but an equal quantity also passes across any surface which we may imagine drawn within the glass, so as to include the inner coating and exclude the outer. The glass, therefore, may be regarded as completing a circuit across every section of which the same quantity of electricity flows. Again, if positive electricity be communicated to a conductor by means of a wire which serves as an electrode, an equal quantity passes out from the surface of the conductor and is squeezed into the surrounding dielectric, causing a similar transfer of electricity across every surface drawn in the dielectric so as to surround the conductor, the extent of the displacement of course diminishing as we recede from the conductor on account of the increased area of the surface, but the displacement continuing until some external conductor is reached through which the circuit is completed. Thus, when we say that the charge of a body is increased, we mean that positive electricity is communicated to it through an electrode, but we know that an equal amount passes out of the body through its external surface and is squeezed into the dielectric, and it is this dielectric which is the only portion of the system really affected by the charge, and in which the whole energy of the charged body resides. This view has very recently been put forth under the title of The Conservation of Electricity. According to Maxwell’s view of the constitution of dielectrics, the squeezing of a quantity of electricity into a dielectric does not imply a condensation of the electricity, but a strain in the dielectric on account of the displacement of the electricity, which cannot move without distorting the “cells” of which the dielectric is supposed to be made up.

7. Ever since men began to think about Nature, philosophers have differed in their views respecting the primary constitution of bodies. When, with all the freshness of a first impulse, though unprovided with the barest means of verification, the human mind first went forth in search of physical truth, two paths at once appeared, leading to opposite poles, and both were trodden by pilgrims full of hope. Some found their satisfaction in contemplating the continuous fulness of the universe. They could imagine no gap in Nature, whose endless variety they were contented to refer to a principle of infinite divisibility and to the inter-play of contiguous elements whose changes were ordered by the mind that was interfused with all. To others, of a more analytical turn, it appeared impossible to account for the most obvious phenomena, except by the hypothesis of atoms moving in a void.

The penetrating intellect of Democritus had early given consistency to an atomic theory, which became the foundation of the system of Epicurus. Yet, widely as this philosophy prevailed at certain periods, the doctrine of a plenum was on the whole the more prevalent in the ancient world.

The controversy has been handed on to modern science, or rather it has inevitably reappeared; some, with Descartes and Spinoza, resolving matter into continuous extension; while others, as Bacon would say, cut deeper into Nature, and would divide her if possible into her ultimate constituent parts. Experimental investigations, especially those through which chemistry became an exact science, have greatly favoured atomistic views, yet the tendency to maintain the continuity and plasticity of matter is still apparent, and the bold hypothesis of the vortex atom, due to Sir William Thomson, affords us perhaps the nearest approach to a reconciliation between these two contradictory theories. According to this hypothesis the whole of space is filled with a uniform and perfect fluid, and material atoms are vortices of one form or another which have been created within this fluid.

In order to reach the starting-point of Maxwell’s investigations in molecular physics we must go back to Daniel Bernoulli who, in his hydrodynamics, published in 1738, explained the pressure of the air on the hypothesis that air consists of a number of particles moving about in all directions and impinging on any surface exposed to its action. Le Sage of Geneva in 1818 explained the pressure of a gas in strict accordance with the modern Dynamical Theory. The theory of Le Sage was based upon his doctrine of “ultra-mundane corpuscles,” a doctrine borrowed from the older atomists, and employed by Le Sage to explain gravitation. For a concise account of this and of the older atomic theories the reader is referred to Maxwell’s article “Atom” in the ninth edition of the Encyclopœdia Britannica. In 1847 John Herapath published his Mathematical Physics, in which he supposed gases to consist of perfectly hard molecules impinging against one another, and against any surface exposed to their action; and he points out the relation of the motion to the temperature and pressure of a gas and explains gaseous diffusion.

But we are indebted for all the modern developments of the molecular theory of gases, as well as for its establishment on a sound dynamical basis, mainly to the researches of three men—Professor R. Clausius, Dr. Ludwig Boltzmann of Vienna, and James Clerk Maxwell. Maxwell’s principal contributions to the literature of this subject are his papers on “Illustrations of the Dynamical Theory of Gases,” presented to the British Association at the meeting in Aberdeen in 1859; “On the Viscosity or Internal Friction of Air and other Gases,” which constituted the Bakerian lecture read before the Royal Society on February 8th, 1866, and published in the Phil. Trans. for that year; “On the Dynamical Theory of Gases,” a paper read before the Royal Society on May 31st, 1866, and also published in the Phil. Trans.; the lecture “On Molecules” delivered before the British Association at Bradford in 1873, and which has been referred to in Part I.; a paper “On the Dynamical Evidence of the Molecular Constitution of Bodies” which was read before the Chemical Society in the Spring of 1875, and published in the June number of its Journal; and the article “Atom,” in the ninth edition of the Encyclopœdia Britannica.

According to the molecular theory all bodies are made up of molecules which are more or less free to move relatively to one another. In solids, each molecule can only move through a small distance from its normal position, so that all its movements are essentially of the nature of vibrations. In liquids the molecules are free to move through any distances within the substance of the liquid, but their motion is constantly impeded by neighbouring molecules, from whose interference they are never altogether free, each molecule in its movements resembling an individual endeavouring to work his way through a dense crowd. In a gas each molecule is perfectly free—except on the occasions, comparatively rare, unless the gas be very dense—when it comes into collision with other molecules of gas, or of some other body in contact with the gas. According to this theory, a gas consists of molecules moving in all directions in straight lines, except when they strike one another or some foreign body, when their motion is changed in accordance with the laws of impact of perfectly elastic bodies.

It is probable that the investigations connected with Saturn’s rings, which led Maxwell to contemplate the condition of the air in the midst of “a flight of brickbats,” first led him to take up the subject of the kinetic theory of gases. At any rate, these investigations led him to the adoption of what he aptly termed “the statistical method,” which in his hands became so fruitful in its applications to molecular science. This method consists in the separation of all the things considered into classes, which fulfil certain conditions, and the determination of the number of individuals which at any instant are to be found in each class, without reference to the behaviour of any particular individual. In “the historical method,” on the other hand, the life history of each individual is traced, and if classes are considered at all it is only in their relation to the particular individual we are contemplating. The first method deals with the interests of the community at large and disregards the fate of the individual, except as affecting the average condition of the community; the second deals with the interests of the individual alone. It is obvious that when the individuals are to be counted by millions the only way in which they can be successfully treated by a finite mind is by the statistical method, and this was the method which Maxwell adopted.

In the earliest papers of Clausius he treated all the molecules of a particular gas at the same temperature as moving with the same velocity. Maxwell showed that this could not be the case, and that, even if all the molecules were started with the same velocities, their mutual collisions would increase the velocity of some and diminish that of others, until at length the velocities would be distributed “according to the law of errors.” This law will be best understood from Maxwell’s own illustration. He prepared a diagram illustrating the distribution of bullet marks on a target on the hypothesis that all the shots are aimed at the centre of “the bull” by the same marksman, while the probability of an error of any given magnitude occurring is less the greater the error: diminishing very rapidly as the error increases, according to the ordinary hypothesis respecting “errors of observation” developed by Laplace. If on such a diagram a series of concentric circles be drawn, say an inch apart, about the centre of the target, and the number of shots between each consecutive pair of circles counted, the number will be found to be greatest for a particular pair, but there is nothing to prevent some shots from hitting the target at any distance from the centre. If the length of the line joining the centre of the target with any bullet mark be taken to represent the velocity of a molecule, the diagram will represent the law of distribution of velocities among the molecules of a gas when they have acted on one another for an indefinite time. They will congregate about a particular value, but there is nothing to prevent some individuals possessing a velocity as great or as small as we please.

The momentum of a particle depends on the product of its mass and its velocity; its kinetic energy on the product of its mass and the square of its velocity. One of the first and most important properties of gases which Maxwell showed to be a consequence of the kinetic theory was, that when two groups of molecules are in equilibrium, being separated only by a diaphragm which can transmit the impacts of the particles, the average kinetic energy of the molecules must be the same in each group. Identifying the kinetic energy of the molecules with the heat of the gas, since we know that for equilibrium the gases must be at the same temperature, it follows that the specific heat varies inversely as the mass of a molecule, which is the dynamical expression of the law of Dulong and Petit, a law which states that the products of the specific heat and combining weight is the same for each element. The pressure of a gas is proportional to the kinetic energy of unit volume of a gas, and, since the average kinetic energy of the molecules is the same for each gas at the same temperature, it follows that equal volumes of two gases at the same pressure and temperature contain the same number of molecules, and hence the density of a gas at standard temperature and pressure is proportional to the mass of a molecule, i.e. to its combining weight, which is Gay Lussac’s law of equivalent volumes.

If two gases be in communication with one another, the particles of each are found to penetrate the other until the gases become uniformly mixed, unless some external force act to prevent the uniformity of the mixture. This phenomenon, known as gaseous diffusion, has been studied by Graham, Loschmidt, and others, and is a direct consequence of the dynamical theory. It is plain that the rate of diffusion of one gas into another will be proportional to the average velocity of the particles in the case of two gases being separated by a diaphragm perforated by very fine holes, so that each mixture may be considered homogeneous up to the diaphragm. Maxwell showed that in this case, when the pressures on the two sides of the diaphragm are equal, “the volumes diffused will be as the square roots of the specific gravities inversely, which is the law of diffusion established by Graham.”

The slowness of gaseous diffusion was for some time regarded as an objection to the kinetic theory of gases. Clausius overcame this difficulty by the introduction of the conception of the mean free path of a molecule, and by showing how short this path is. The mean free path is the average distance through which a particle passes between two successive collisions with other particles. The first estimate of the mean free path in air at ordinary pressure and temperature was made by Maxwell from determinations of viscosity or rate of diffusion of momentum in air. Depending on the length of the mean free path are (1) the diffusion of matter; (2) the diffusion of momentum or viscosity; and (3) the diffusion of energy, or the thermal conductivity of the gas. From determinations of the rate at which these three kinds of diffusion proceed, independent determinations of the mean free path in different gases have been made. For hydrogen, at standard pressure and temperature, it is about of an inch. For other gases and air it is somewhat less. The length of the mean path in air given by Maxwell in 1859 was of an inch.

Suppose two trains to be moving in opposite directions, side by side on parallel lines, and suppose that as they pass each other a number of passengers from each train jump into the other. It is clear that each passenger will carry with him the momentum he possesses into the other train which is moving in the opposite direction, and will consequently diminish the momentum and therefore the velocity of that train. If a continuous interchange of passengers, backwards and forwards, between the trains were to take place, the trains would ultimately be brought to rest relatively to one another. This is an illustration of the diffusion of momentum, and was originally given by Balfour Stewart. How, suppose two streams of gas to be passing each other tangentially. There will be a continuous interchange of molecules by diffusion between the two streams, and the molecules carrying with them the momentum they possess, the effect of the diffusion will be to tend to bring the two streams to relative rest. Diffusion of momentum consequently introduces a tangential action between layers of gas which are moving relatively to one another, and therefore causes a resistance to any “continuous change of form, depending on the rate at which that change is effected,” that is, it confers upon the gas the property of viscosity. Thus, the so-called viscosity of gases received from Maxwell its complete explanation in accordance with the kinetic theory.

The viscosity of a gas depending on the rate of diffusion of momentum, and therefore on the rate of diffusion of matter, is proportional, like the latter, to the average velocity of the molecules. If the gas be very rare, each particle will meet with fewer collisions, and consequently its course will be less interrupted than when the gas is denser, so that Maxwell found that between two strata of gas at a given distance apart the rate of diffusion was the same whatever the density. He thus “arrived at the startling result that the coefficient of internal friction is independent of the density of any particular kind of gas.” The experimental verification of this result occupied a considerable portion of Maxwell’s leisure time in 1865. The description of the experiments and the statement of the result arrived at form the subject of the Bakerian lecture of 1866. There plates of glass were suspended by a steel piano wire, and caused to oscillate in their own planes between four fixed plates, which were placed at equal distances apart, and so that the moving plates were suspended half way between each pair of fixed plates (see Part I. p. 341). The distance between the plates was varied in different experiments, and the whole system was enclosed in a receiver which could be filled with different gases and the pressure regulated at will. The oscillations of the discs were observed by means of a mirror and scale, and the experiment consisted in determining the rate at which the oscillations died away, from which the viscosity of the gas was calculated. For experiments at high temperatures the receiver was surrounded by a steam jacket. The results arrived at showed that dry air is more viscous than damp air, and that the viscosity of air is greater than that of hydrogen or carbonic acid, nearly in the same ratio as was determined by Graham in his experiments on the transpiration of gases through capillary tubes. But the most remarkable results were (1), that the viscosity of any particular gas is independent of the pressure; and (2) that it is directly proportional to the temperature measured from the absolute zero of the air thermometer.[260] From the last result, Maxwell deduced “that the force between two molecules is proportional inversely to the fifth power of the distance between them.” If the molecules only acted by impact, it would follow that the viscosity must be proportional to the square root of the absolute temperature.

In the paper “On the Dynamical Theory of Gases,” read before the Royal Society on May 31, 1866, the molecules are dealt with in the most general manner, no hypothesis being made respecting their constitution. The paper discusses (1) the phenomena of diffusion, depending on the average value of the velocities; (2) the phenomena depending on the average square of the velocities, which determines pressure and viscosity; and (3) the phenomena depending on the average value of the cubes of the velocities, on which depends the diffusion of energy or the conduction of heat in the gas. In this paper Maxwell showed that if a number of gases be enclosed in any space under the action of any external forces, each gas will arrange itself as if the others were absent, and this result is independent of the law of action of the particles on each other. This is the arrangement which Dalton suggested would probably exist in the atmosphere if the effect of winds could be annulled. He also showed that in a vertical column of air in equilibrium under the action of gravity the temperature must be the same throughout. This was contrary to the then current opinion that the temperature must diminish as we ascend, but Maxwell showed independently that it is a consequence of the principle of the dissipation of energy. Boltzmann was, however, the first to show how, in dealing with a collection of molecules, to take account of external forces acting upon them. In discussing the diffusion of energy Maxwell showed that the thermal conductivity of iron at , as determined by Principal Forbes, is 3525 times that of air at .

In the paper “On the Dynamical Evidence of the Molecular Constitution of Bodies,” published in the Journal of the Chemical Society, June 1875, Maxwell introduces Clausius’s conception of the “virial” of a system, a quantity of which great use has been made in the discussion of molecular theories since a name has been given to it by Clausius. This quantity is the sum of the products of the attractions between each pair of molecules into the distance between them. Maxwell commences by explaining Clausius’s equation, which states that the energy of a quantity of gas is the sum of two quantities, one of which is the virial, and the other is proportional to the product of the pressure and the volume. Now Joule showed that when a gas expands into a vacuum its temperature remains sensibly unaffected, though no energy is communicated to or taken from it, and since the gas obeys Boyle’s law the product of its pressure and volume is constant. Hence the energy being unchanged, and the product of pressure and volume remaining the same, it follows that the virial must he unaffected by expansion. But the virial must depend on the density if there he any sensible forces between the molecules when at sensible distances, unless the force between two molecules varies inversely as the distance between them, a law which Newton showed to be inadmissible in the case of molecular forces. We must therefore conclude that the force between two molecules is sensibly zero, unless the distance between them be very small compared with the average distance between molecules, and that the virial is therefore sensibly zero in a gas, so that the energy and pressure of a gas depend on the motion of the molecules and not on the forces between them.

The experiments of Regnault indicated that in most gases as the density increases the pressure falls below that indicated by Boyle’s law, which shows that when the particles approach very near together the virial is positive, or there is attraction between the molecules. When the pressure is made still greater the gas reaches a condition in which a small increase of density is accompanied by an enormous increase of pressure, so that the virial is negative, and the forces between the particles repulsive. This is the case in the liquid state. Maxwell infers that as the particles of a gas approach each other the forces between them become attractive, attain a maximum, then diminish, and when they are within a certain distance become repulsive, the repulsion increasing so rapidly “that no attainable force can reduce the distance of the particles to zero.” The same conclusion as far as the attraction between the particles at small distances is concerned, was indicated by the experiments which Joule conducted, in company with Sir William Thomson, on the expansion of air into a vacuum, when very careful measurements indicated that a slight cooling effect took place.

The greatest difficulty which the kinetic theory of gases has to face is the observed relation between the specific heats of gases at constant pressure and at constant volume. Boltzmann showed that if each molecule possess “degrees of freedom” the ratio of the kinetic energy of translation to the whole kinetic energy of the system must be equal to the ratio of 3 to . Now in a rigid body capable of rotating in any manner n is equal to 6, and this makes the total energy equal to twice the energy of translation. This requires that the ratio of the two specific heats should be 1·33 instead of 1·408, and the observed ratio therefore disproves the hypothesis of hard bodies. If we suppose the molecules to be material points, incapable of rotation or vibration n is equal to 3, and the energy of translation is the whole of the kinetic energy possessed by the molecules. This would make the ratio of the specific heats to be 1·66, which is too great for any real gas except mercury vapour, for which the ratio has been shown by Kundt and Warbourg to be nearly 1·66.

The spectroscope shows that the molecules of a gas are capable of executing vibrations in various periods. They must therefore be material systems, and cannot have less than six degrees of freedom. The ratio of the specific heats cannot therefore be greater than 1·33, and this is too small for most gases. Every additional degree of freedom possessed by the molecules makes the ratio less, and requires that the specific heat of the gas should be greater than is observed to be the case.

In a paper “On Boltzmann’s Theorem on the Average Distribution of Energy in a System of Material Points,” read before the Cambridge Philosophical Society on May 6, 1878, Maxwell showed that whatever be the forces acting upon or between the molecules, provided they be subject to the principle of conservation of energy, the average kinetic energy of any two given portions must be proportional to the number of degrees of freedom of these portions, and hence the total kinetic energy corresponding to an increment of temperature of is shown to be proportional to the product of the number of degrees of freedom into the absolute temperature.

The actual dimensions of molecules were first estimated by Loschmidt in 1865, then by Stoney in 1868, and by Thomson in 1870. At his lecture “On Molecules,” before the British Association at Bradford, Maxwell gave the following

TABLE OF MOLECULAR DATA,

Divided into three ranks, according to the degree of accuracy with which the Quantities are known.

Hydrogen. Oxygen. Carbonic Oxide. Carbonic Acid.

Mass of Molecule (Hydrogen=1) 1 16 14 22

Rank I. Velocity (of mean square) metres per second at } 1859 465 497 396

Mean path, tenth-metres 965 560 482 379

Rank II. Collisions in a second (millions) 17,750 7646 9489 9720

Rank III. Diameter, tenth-metres.

Mass, twenty-fifth-grammes 46 736 644 1012

30th June 1877.

Dear Garnett—... I have been considering diffusion of gases, and the method of separating heavy gases from light ones, and I find it hopeless to do it by gravity, but if a tube 10 cm. long with two bulbs, and the straight part stuffed with cotton-wool, were filled with equal volumes of H and , and spun 100 times round per second for about half an hour, then the ratio of to H by volume would be greater in A than in B by about , which is measurable. I have got a new light about equilibrium of temperature in two different gases. Let forces having potentials act on the molecules of two gases, but differently on each. Let the potential of forces acting on the gas be zero in the region A and very large in B, diminishing continuously in the stratum C. Let the potential for gas be zero in B and very great in A, diminishing continuously in C. Then the region A will contain the gas A nearly pure, and B the gas B nearly pure, and in the stratum C there will be encounters between the two kinds of molecules. By Boltzmann and Watson the average kinetic energy of a single molecule is the same throughout the whole vessel. Hence the condition of thermal equilibrium between two gases (not mixed, but kept pure though in contact) is that the mean kinetic energy is the same in each. And it is difficult to see where this method breaks down when applied to solids.

I find the electric conductivity of air supposed of conducting spheres to be .

Where = distance of centres at striking.

Number in cubic centimetre.

Mean velocity.

Now for air, and .

But this is in electrostatic measure. In electromagnetic measure the resistance is so that per cubic centimetre, or about greater than that of copper; but this is far smaller than that of gutta-percha. Hence the insulating power of air is not consistent with its molecules being conducting spheres.

But why should the molecules be conductors?—Yours very truly,

J. Clerk Maxwell.

Maxwell’s investigations in the Kinetic Theory of Gases led him to a conclusion which is of great value in the theory of energy. The principle of the dissipation of energy, sometimes called the second law of Thermodynamics, states that it is impossible by means of inanimate material agency to obtain work at the expense of heat by cooling a body below the temperature of the coldest body in the neighbourhood. This principle was first distinctly given by Sir William Thomson. Maxwell showed that it obtains only in consequence of the coarseness of our faculties not allowing us to grapple with individual molecules. If we could seize upon individual molecules, and bring them to rest in the same way as we can lay hold of a fly-wheel, and compel it to do useful work until it has been deprived of all its motion of rotation, we could convert the whole of the heat of a body into work, and bring it to the absolute zero of temperature. As it is, we are at the mercy of the molecules, and capable of obtaining from them only so much work as they are willing to give in the most favourable circumstances in which we are able to place them. Maxwell imagined a quantity of gas, all initially at the same pressure and temperature, to be divided into two portions, A and B, by a partition full of little trap doors which might be opened or closed without the expenditure of energy. Each trap door he supposed placed in charge of a “demon” that is a creature whose eyes are sharp enough to see the molecules and estimate their velocities, and hands agile enough to open and close the trap doors in time to allow or prevent the passage of any particular molecule which is approaching the partition. The operation depends on the difference of the velocities of the particles in the same mass of gas, and the office of the demon is purely selective, so that any mechanism which could be devised to sort the molecules in the same way would be equally effective. Suppose each demon to open his trap door when a molecule is approaching the partition from A with a velocity above the average, but to keep it closed when the velocity of the molecule approaching from A is below the average; while in the case of a molecule approaching the partition from B the door is opened if the velocity be small, and closed if it be great. In this way all the slowly moving molecules will gradually be sorted into the compartment A, while the rapidly moving particles will be accumulated in B. Thus the temperature of the gas in B will be raised, and that in A lowered without any loss of energy or any work being done by an external agent. A heat engine may now be employed, using B as the source and A as the condenser, and doing work at the expense of part of the heat of A until equilibrium of temperature between B and A has been produced, when the services of the demons may be again utilised, and the process repeated until the whole of the heat of the gas has been converted into work. This is contrary to the principle of dissipation of energy, which has thus been circumvented by intelligence. No corresponding method of overcoming the principle of conservation of energy can be devised, and this principle is thus shown to rest on an entirely different kind of footing from that of the second law of Thermodynamics.

The following extract from Maxwell’s article “Atom” in the ninth edition of the Encyclopœdia Britannica is characteristic. Speaking of the teaching of molecular science respecting the size of atoms, he says:—

It forbids the physiologist from imagining that structural details of infinitely small dimensions can furnish an explanation of the infinite variety which exists in the properties and functions of the most minute organisms.

A microscopic germ is, we know, capable of development into a highly organised animal. Another germ, equally microscopic, becomes when developed an animal of a totally different kind. Do all the differences, infinite in number, which distinguish one animal from another arise each from some difference in the structure of the respective germs? Even if we admit this as possible we shall be called upon by the advocates of Pangenesis to admit still greater marvels. For the microscopic germ, according to this theory, is no mere individual, but a representative body, containing members collected from every rank of the long-drawn ramification of the ancestral tree, the number of these members being amply sufficient not only to furnish the hereditary characteristics of every organ of the body, and every habit of the animal from birth to death, but also to afford a stock of latent gemmules to be passed on in an inactive state from germ to germ, till at last the ancestral peculiarity which it represents is revived in some remote descendant.

Some of the exponents of this theory of heredity have attempted to elude the difficulty of placing a whole world of wonders within a body so small and so devoid of visible structure as a germ, by using the phrase structureless germs. Now, one material system can differ from another only in the configuration and motion which it has at a given instant. To explain differences of function and development of a germ without assuming differences of structure is therefore to admit that the properties of a germ are not those of a purely material system.

A paper “On Stresses in Rarefied Gases arising from Inequalities of Temperature,” by Professor Maxwell, was read before the Royal Society on April 11, 1878, and published in the Phil. Trans. for 1879. The notes and appendix added to the paper in May and June 1879 embodied the results of Maxwell’s last investigations in the kinetics of gases. In this paper Maxwell showed that when inequalities of temperature exist in a gas the pressure at a point is not generally the same in all directions, but the maximum and minimum pressures differ by an amount depending on the rate of change of the increase of temperature per unit length in the direction in which this rate is greatest. The stress thus arising from variation in rate of change of temperature varies inversely as the pressure of the gas, and is therefore most conspicuous in high vacuo. If two small bodies are warmer than the air, the line joining them will be a line of maximum pressure, and they will repel each other, while they will attract one another if they are colder than the air. If, however, a ring be placed so as to have the line joining the bodies for its axis and be sufficiently heated the repulsion may be changed into attraction. In the case of a cup, as noticed by Stokes, the variation of the rate of change of temperature is much greater on the convex side than on the concave, where it is nearly uniform, like the electric potential within a hollow vessel, and hence the normal pressure is greater on the convex surface than on the concave, which will account for the motion of the cup radiometer if tangential stresses are neglected. But when the tangential stresses on any portion of gas are considered, it appears, that they, with the normal forces, form a system which is in equilibrium, so that inequality of temperature has no tendency of itself (i.e. without the action of gravity, etc.), to produce currents in the gas. Maxwell therefore concludes that the above explanation is insufficient, and that the true cause of the motion is to be found in the character of the tangential action between the solid and the gas, allowing the gas to slide over the surface of the solid, and thus diminishing the tangential stresses without affecting the normal stresses. In the appendix, dated May 1879, Maxwell determined the character of the tangential action on certain hypotheses respecting the nature of the surface of the solid, and the character of the collisions, and concluded that the gas may slide over the surface of the solid with a finite velocity, and that inequalities of temperature at the surface “give rise to a force tending to make the gas slide along the surface from colder to hotter places.”

Most of the more elementary theorems respecting the kinetic theory of gases are given in a very concise form by Maxwell in his Theory of Heat, the more recent editions of which also give an account of Professor Willard Gibbs’ Thermodynamic Surface. This surface, in which the co-ordinates represent respectively the energy, entropy, and volume of the substance to which it corresponds, was modelled in clay by Maxwell’s own hands in the Cavendish Laboratory. From the clay model a number of plaster casts were taken. These casts Maxwell placed in the sunshine in particular positions, and drew upon them in water-colours the boundary-lines between the light and shadow, which correspond to constant pressure or constant temperature, on the part of the substance. An account of this surface, and many of the properties which it represents, will be found in the work referred to.

We have now presented to the reader a scanty selection from the results of Maxwell’s scientific work. The mere enumeration of his original papers would occupy several pages of this book, and those who are desirous of forming any approach to a true conception of his contributions to science should consult the memorial edition of Maxwell’s papers, edited by Mr. W. D. Niven, F.R.S., and about to be published by the Cambridge University press.

FOOTNOTES:

END OF PART II.