Andrew Gray

“ Conduction of heat is the great agency by which energy is more and more dispersed in this unavailable form throughout the totality of material bodies. As has been seen, available motivity is continually wasted through its agency; and in the flow of heat in the earth and in the sun and other unequally heated bodies of our system the waste of energy is prodigious. Aided by convection currents in the air and in the ocean it continually equalises temperatures, but does so at an immense cost of useful energy. ”

“ To examine orally in a thorough way two students in each class-hour is about as much as can be done if there is to be any systematic exposition by lecture at all; and thus the conference between teacher and individual student can occur only twice a year at most. Nevertheless Lord Kelvin was undoubtedly right: oral examination and the training of individual students in the art of clear and ready expression are very desirable. The real difficulties of the subject are those which occur to the best students, and a discussion of them in the presence of others is good for all. ”

“ The mass or inertia of the body is only such a number that, for different bodies in the same circumstances as to the action of other bodies in giving them acceleration, the product of the mass and the acceleration is the same for all. It is, however, a very important property of the body, for it is one factor of the quantum of kinetic energy which the body contributes to the energy of the system, in consequence of its motion relatively to the chosen axes of reference, which are taken as at rest. ”

“ When the current was unit current and the temperature difference also unity,151 Thomson called the heat absorbed or evolved in a metal the specific heat of electricity in the metal, a name which is convenient in some ways, but misleading in others. The term rather conveys the notion that electricity has a material existence. A substance such as copper, lead, water, or mercury has a specific heat in a perfectly understood sense; electricity is not a substance, hence there cannot be in the same proper sense a specific heat of electricity. ”

“ An eminent physicist once remarked that Thomson was perhaps the only living man who made discoveries while lecturing. That was hardly true; in the glow of action and stress of expression the mind of every intense thinker often sees new relations, and finds new points of view, which amount to discoveries. But fecundity of mind has, of course, its disadvantages: the unexpected cannot happen without causing distractions to all concerned. ”

“ He has founded a school of thought in mathematical physics, of men in whose minds the symbol is always the servant of the ideas, whose motto is interpretation by dynamical processes and models as far as that is possible, who shirk no mathematical difficulties when they have to be encountered, but are never led away from the straight road to the goal which they seek to reach—the systematic and clear formulation of the course of physical action. ”

“ But then few politicians know anything of science; indeed some of those who guide, or aspire to guide, the destinies of the most scientific and industrial empire the world has ever seen are almost boastful of their ignorance. There are, of course, honourable exceptions.
It is convenient to refer here to the share which Stokes and Thomson took in the physical explanation of the dark lines of the solar spectrum, and to their prediction of the possibility of determining the constitution of the stars and of terrestrial substances by what is now known as spectrum analysis. ”

“ In hydrodynamics also Lord Kelvin never lost sight of practical applications, even while pursuing the most intensely theoretical researches into the action of vortices or the propagation of waves. In his later years he worked out the theory of ship-waves with a power which has made more than one skilful and successful cultivator of this branch of science say that he was no mere mathematician, but a man who, like the prophets of old, could divine what is hid from the eyes of ordinary mortals. ”

“ Thomson stated his views as to examinations and lectures in the Bangor address. "The object of a university is teaching, not testing, ... in respect to the teaching of a university the object of examination is to promote the teaching. The examination should be, in the first place, daily. No professor should meet his class without talking to them. He should talk to them and they to him. The French call a lecture a conférence, and I admire that idea. Every lecture should be a conference of teachers and students. It is the true ideal of a professorial lecture. ”

“ What is meant is that in a finite material system, which is isolated in the sense that it is not acted on by force from without, the total amount of energy—that is, energy of motion and energy of relative position (including energy of chemical affinity) of the parts—remains constant. The usual misstatement is that the energy of the universe is constant. This may be true if the universe is finite; if the universe is infinite in extent the statement has no meaning. In any case, we know nothing about the universe as a whole, and therefore make no statements regarding it. ”

“ In 1899, at the age of seventy-five, Lord Kelvin resigned the Chair of Natural Philosophy, and retired, not to rest, but to investigate more vigorously than ever the properties of matter. One remarkable fruit of his leisure we have in his great book, the Baltimore Lectures, in which theories of light are discussed with a power which excites the reverence of all engaged in the new researches and which recent discoveries have called into existence. ”

“ CHAPTER IX HYDRODYNAMICS—DYNAMICAL THEOREM OF MINIMUM ENERGY—VORTEX MOTION
Thomson devoted great attention from time to time to the science of hydrodynamics. This is perhaps the most abstruse subject in the domain of applied mathematics, and when viscosity (the frictional resistance to the relative motion of particles of the fluid) is taken into account, passes beyond the resources of mathematical science in its present state of development. But leaving viscosity entirely aside, and dealing only with so-called perfect fluids, the difficulties are often overwhelming. ”

“ It is visible even in the design of the apparatus. Microscopes, for example, have a perfection and a power undreamed of by our great-grandfathers, and they are supported on stands which lack the ornamentation of that bygone time, but possess stability and convenience. Everything and everybody—even the professor, if that be possible—must be business-like; and each moment of time must be utilised in experiments for demonstration, not for applause, and in brief and cogent statements of theory and fact. To waste time in talk that is not to the point is criminal. ”

“ When the plates are connected by the coil, this state of strain breaks down and motion in the medium ensues, not merely between the plates, but also in the surrounding space—in fact, in the whole field. This motion—which is not to be confused with bodily displacement of finite parts of the medium—is opposed by something akin to inertia of the medium (the property that confers energy on matter when in motion) , so that when the motion is started it persists, until it is finally wiped out by resistance of the nature of friction. ”

“ He points out, for example, that the friction which accompanies the relative motion of the waters of the earth and the land is attended by the production of heat, and that, by the doctrine of the conservation of energy, heat cannot be produced without a disappearance of an equivalent quantity of energy, either of motion or of position. The chief source of this energy is the earth's rotation. ”

“ Irrotationality of a fluid is secured, as stated above, when the velocity of each element in any direction is the rate of variation per unit distance in that direction of a certain function of the coordinates, the distances, taken parallel to three lines perpendicular to one another and drawn from a point, which specify the position of the particle. In fact, what is called a velocity-potential exists, similar to the potential described in Chapter IV above, for an electric field. This condition, together with the specified motion of the surface, suffices to determine the motion of the fluid. ”

“ There is always friction, always heat conduction and convection, so that as our stores of motional or positional energy, whether of chemical substances uncombined, the earth's motion, or what not, are drawn upon, the inevitable fraction, too often a large proportion, is shed off and the general temperature raised. After a large part of the whole existent energy has gone thus to raise the dead level of things, no difference of temperature adequate for heat engines to work between will be possible, and the inevitable death of all things will approach with headlong rapidity. ”

“ Thus his life had seen the growth of modern electrical science from its real infancy to its now vigorous youth. The discoveries of Faraday in electrical induction were given to the world when Lord Kelvin was a boy, and one of the great tasks which he accomplished was to weave these discoveries together in a uniform web of mathematical theory. This theory suggested, as we have seen, new problems to be solved by experiment, which he attacked with the aid of his students in the small and meagrely equipped laboratory established sixty years ago in the Old College in the High Street. ”

“ Sometimes Thomson would read the remarkable passage in Hegel's Logik, in which he refers to the Newtonian theory of gravitation and says, "The planets are not pulled this way and that, they move along in their orbits like the blessed gods," and remark upon it. On one occasion his remark was, "Well, gentlemen, if these be his physics, what must his metaphysics be?" And certainly that a philosopher should deny, as Hegel seemed to do, all merit to the philosophical setting in which Newton placed the empirical results of Kepler, is a very remarkable phenomenon. ”

“ In Professor Gregory's opinion, "Lord Kelvin in one respect showed a keener insight than Huxley, who, referring to possible changes in the rate of rotation of the earth, or in the heat given forth from the sun or in the cooling of the earth, declared that geologists are Gallios, 'who care for none of these things.' An ever-increasing school of geologists now cares greatly for these questions, and reveres Lord Kelvin as one of the founders of the geology of the inner earth." ”

“ Lord Kelvin's work in the theory of heat and in the science of energy generally would have given him a title to immortality even if it had stood alone; and there can be no doubt, even in the mind of the most determined practical contemner of the Carnot cycle, of the enormous importance of these achievements. ”

“ It is easy to calculate the exhaustion of potential energy caused by the coming together of the matter of the sun from universal dispersion through infinite space to a sphere of uniform density of the present size of the sun. The result is about as much energy as would be generated by burning seven million million million million million tons of coal. The amount radiated in each hour is about as much as would be generated by burning something like nine tons of coal every hour on every square yard of the sun's surface. ”

“ Thomson's demonstration that a reversible engine is the most efficient is well known, and need not here be repeated in detail. The reversible engine may be worked backwards, and the working substance will take in heat where in the direct action it gave it out, and vice versa: the substance will do work against external forces where in the direct action it had work done upon it, and vice versa: in short, all the physical and mechanical changes will be of the same amount, but merely reversed, at every stage of the backward process. ”

“ We find a little discussion of mechanics, hydrostatics and pneumatics, a little heat, and a very little optics. Electricity and magnetism, which in our day have a literature far exceeding that of the whole of physics only sixty years ago, could hardly be said to exist. The professor of the beginning of the nineteenth century, when Lord Kelvin's predecessor was appointed, apparently found himself quite free to devote a considerable part of each lecture to reflections on the beauties of nature, and to rhetorical flights fitter for the pulpit than for the physics lecture-table. ”

“ If the resisting force for finite motion is very great, as for example when the vibrating mass of the pendulum or spring is immersed in a very viscous fluid, like treacle, oscillation will not take place at all. After displacement the mass will move at first fairly quickly, then more and more slowly back to the position of equilibrium, which it will, strictly speaking, only exactly reach after an infinite time. ”

“ These were all deemed necessary for a liberal education at that time: in the scientific age in which we live it is more imperative than ever that neither should be excluded from the Arts curriculum of our Universities. The common distinction between Arts and Science is a false one, and the product of a narrow idea which is alien to the traditions of our northern Universities.
It is to be noted, however, that the laboratory thus founded was essentially a research laboratory; it was not designed for the systematic instruction of students in methods of experimenting. ”

“ The idea of the charge as a quantity of some kind of matter, brought up and placed on the insulated plate of the condenser, has only a correspondence to the fact, which is that the medium between the plates is the seat, when the condenser is charged, of a store of energy, which can only be made available by connecting the plates of the condenser by a wire or other conductor. The charge is only a surface aspect of the state of the medium, apparently a state of strain, to which the energy belongs. ”

“ If the air when raised in temperature, and at the same time increased in volume, contained less internal energy than when simply heated without alteration of volume, the energy evolved would be available to aid the performance of the work done against external forces, and less heat would be required, or, in the contrary case, more heat would be required, than would be necessary if the internal energy remained unaltered. ”

“ On the other hand, the mathematical theory of electricity and magnetism had led to quantitative measurement and absolute units at an earlier time, when the need for these was beginning to be felt clearly by scientific workers and dimly by those far-sighted practical men who dreamed—for a dream it was thought at the time—of linking the Old World with the New by a submarine cable. ”

“ If any diameter of the spherical portion be taken as the axis, and any plane through that axis be considered, the velocity of a particle at right angles to that plane can be at once expressed as the rate at which the velocity-potential varies per unit distance along the circle, symmetrical about the axis, on which the particle lies. The integral of the velocity-potential round this circle vanishes, and so the angular momentum for any thin uniform ring of particles about the axis also vanishes, and as the sphere is made up of such rings, the whole angular momentum is zero. ”