# Lectures on Ten British Physicists of the Nineteenth Century/Lecture 4

SIR WILLIAM THOMSON, FIRST LORD KELVIN
(1824-1907)
William Thomson, now Lord Kelvin, was born in Belfast, Ireland, on the 26th of June, 1824. He is of Scottish-Irish descent. His father was James Thomson, then professor of mathematics in the Royal Belfast Academical Institution, who had a remarkable career; he was descended from a family of Thomsons, who had for several generations occupied a farm near Ballynahinch, County Down, in the north of Ireland. When a boy he endeavored all alone to understand the principles of drilling and in this way was led to study mathematics. As a result he was sent to a small grammar school in his native place, where he rose to be an assistant teacher. Soon he became able to attend the University of Glasgow during the winter session, by teaching in the local school during the summer.
After studying in this manner for five years he was appointed to a position in the Belfast Institution mentioned, where he was promoted to the professorship of mathematics. He was the author of an algebra, which was popular with teachers for many years, and his reputation was such that in 1832 he was appointed professor of mathematics in the University of Glasgow.
William Thomson was then six years old, and his brother James Thomson nearly two years older. They were educated together at home by their father, and in 1834 they became students together at the University of Glasgow. At the Scottish Universities the conditions for entrance, were then, and still are, rather loose—no inferior limit to the age, and no entrance examinations to pass. William Thomson, when he entered, was but little over ten years of age. He studied for six years. ​but did not take a regular course leading to a degree. He had the genius of a mathematician, and his father was not slow to discover it. Accordingly he was sent when seventeen years of age to the University of Cambridge, where he became a student of St. Peter's College, the oldest foundation of that University (600 years). His undergraduate career at Cambridge extended over four years. In his first year he contributed a paper signed P. Q. R., to the Cambridge Mathematical Journal, in which he defended Fourier's Treatise on Heat from some criticisms made by Prof. Kelland of Edinburgh University. This paper was followed in the same journal by two others of still greater importance: "The uniform motion of heat in homogeneous solid bodies and its connection with the mathematical theory of Electricity" and "The linear motion of heat." In the former paper he points out the analogy between the theory of the conduction of heat in solid bodies and the theory of electric and magnetic attraction; and pursuing this analogy he makes use of known theorems about the conduction of heat to establish some of the most important theorems in the mathematical theory of electricity. The latter paper contains the foundations of the method which he afterwards applied to find limits to the age of the Earth. In his undergraduate career Thomson was well-known for his skill in boating; he was also president of the musical society. Probably he did not, as much as his rivals, concentrate his attention on the subjects which would pay in the final examinations; anyhow, he came out second wrangler. Although he was unsuccessful in the struggle for supremacy as determined by the blind adding of marks, one of the examiners declared that the senior wrangler was not fit to cut pencils for Thomson. In the subsequent more scientific test—the competition for the Smith prizes—he obtained the first place. He was immediately elected a Fellow of his college.
At this time (1845) the Analytical Society founded by Peacock, Herschel, and Babbage had accomplished its reform. But in Newton's University experimental investigation in physics had died out, the greatest mathematical physicists of the ​day were in Paris—Fourier, Fresnel, Ampére, Biot, Regnault. So William Thomson went to Paris, and worked for a year in Regnault's laboratory, where classical determinations of physical constants were being made. Partly as a consequence of this step, Thomson has always been very popular with the scientists of France. When resident in Paris he published in Lionville's Journal a paper on the "Elementary Laws of Statical Electricity," in which he examined the experiments and deductions of Sir. W. Snow-Harris. This investigator had made an experimental examination of the fundamental laws of electric attraction and repulsion, and his results were supposed to disprove the well-known simple laws of Coulomb. Thomson showed by pointing out the defects of Harris' electrometers that the results, instead of disproving these laws, actually confirmed them, so far as they went. From this examination dates Thomson's interest in electrometers, which led to the invention of the quadrant electrometer, the portable electrometer, and the absolute electrometer.
In 1846 the chair of Natural Philosophy in the University of Glasgow became vacant, and William Thomson was appointed at the early age of 22. I have heard it said that in the matter of appointments at Glasgow the principle of nepotism was powerful; in this case it was fortunate. Thomson's father was still the professor of mathematics, and remained so for three years longer; his brother, James Thomson, a few years later, became professor of engineering. At the same time Thomson was made editor of the Cambridge and Dublin Mathematical Journal (hitherto the Cambridge Journal). Among the contributors who supported him in this enterprise were Stokes, Cayley, Sylvester, De Morgan, Boole, Salmon, Hamilton, of whom only two now survive—Sir George Stokes, and Rev. George Salmon, Provost of Trinity College, Dublin.
While Thomson was a student at Cambridge, Joule made his investigations which determined the dynamical equivalent of heat. Thomson had made a special study of Fourier's Treatise on Heat, and had begun to apply his methods; consequently, on his return to Glasgow it was not long before he took up the ​dynamical theory of heat. His first contribution, read before the Royal Society of Edinburgh in 1849, was a critical account of Carnot's memoir "Réflexions sur la puissance motive du feu." Joule's measurements were at first almost ridiculed, and had few hearty supporters; but one of these was Thomson. Carnot's theory of the heat-engine assumed that heat is a species of matter; Thomson set to himself the task to modify the theory to suit the doctrine that heat consists in the motion of the small particles of a body. His great stumbling block in the way of accepting the dynamical theory of heat was the difficulty of accurately defining temperature. Founding on Carnot's work Prof. Thomson put this matter upon a perfectly satisfactory scientific basis. Before he propounded his absolute scale of temperature, purely empirical scales founded on the behavior of various gases, liquids, and solids, had each its advocate, and there seemed to be no satisfactory reason for preferring one to another. Once he propounded the absolute scale, no question has ever since been raised but that it is the only rational scale to adopt as the absolute one. To carry out this idea he made experimental investigations in conjunction with Joule on the thermodynamic properties of air and other gases, and as a result showed how to define a thermodynamic scale temperature having the convenient property that air thermometers and other gas thermometers agree with it as closely as they agree with one another.
His thermodynamic investigations led to the doctrine of the dissipation of energy announced by him in 1852. "During any transformation of energy of one form into energy of another form there is always a certain amount of energy rendered unavailable for further useful application. No known process in nature is exactly reversible, that is to say, there is no known process by which we can connect a given amount of energy of one form into energy of another form, and then, reversing the process, reconvert the energy of the second form thus obtained into the original quantity of energy of the first form. In fact, during any transformation of energy from one form into another, there is always a certain portion of the energy changed into ​heat in the process of conversion, and the heat thus produced becomes dissipated and diffused by radiation and conduction. Consequently, there is a tendency in nature for all the energy in the universe of whatever kind, gradually to assume the form of heat, and having done so, to become equally diffused. Now, were all the energy of the universe converted into uniformly diffused heat, it would cease to be available for producing mechanical effect, since for that purpose we must have a hot source and a cooler condenser. This gradual degradation of energy is perpetually going on; and, sooner or later, unless there be some restorative power, of which we at present have no knowledge whatever, the present state of things must come to an end." Maxwell imagined a restorative process which might be applied by intelligent demons. Suppose a portion of gas to be confined in a closed space, it will have a uniformly diffused temperature. Suppose a partition stretched across with a little door guarded by an intelligent demon. The molecules by their impacts and collisions really have different velocities; what is uniform is the mean velocity. If the demon in charge opens the door so as to let the swift molecules in B go into A, and the slow molecules in A go into B, the degradation of the temperature will be gradually restored.
In 1852 he was married to Miss Margaret Crum, daughter of Walter Crum, Esq. of Thomliebank; a devout lady much attached to the Presbyterian Church. As a consequence, he resigned his fellowship in St. Peter's College; but he was afterwards made an honorary fellow. About this time he organized the first physical laboratory in Great Britain. He had an abundance of experimental problems for his students to tackle particularly on the properties of metals. About four years after Thomson located at Glasgow, submarine telegraphy became an object of practical science. In the working of a submarine cable between England and Holland, it was observed that the signals were more difficult to receive than those from the end of an aerial line. Faraday was the first to investigate the cause of this overlapping of the signals. At first there was a great deal of confusion; speed of signaling was mixed up with velocity ​of transmission; the duration of the signal was not distinguished from the time required to traverse the cables. Thomson investigated the phenomenon, and found that it was due to the capacity of the cable; and he deduced the practical result that with cables of equal lateral dimensions the retardations are proportional to the squares of the lengths. This law became known generally as the "law of squares." A Mr. Whitehouse, experimenting with a cable 1125 miles in length, found that the maximum effect of a signal communicated instantaneously at one end was received at the farther end in one second and a half. Applied to these data the "law of squares" said that as the distance from Ireland to Newfoundland is twice the length of the experimental cable, the time in which a signal communicated instantaneously would be received at the further end is 2.5$^2$.seconds: that is, six seconds. It became evident that if only five signals could be sent in a minute, the financial success of an Atlantic cable was very doubtful, so Whitehouse fought manfully against the "law of squares." He said, "I can only regard it as a fiction of the schools, a forced and violent adaptation of a principle in physics, good and true under other circumstances but misapplied here." He also made experiments and published results which seemed entirely opposed to the law. To this Prof. Thomson replied in the Atheneum newspaper (Nov. 1, 1856), reiterating the application of the "law of squares" to submarine telegraphy, and showing that the experiments cited really confirmed the law they were supposed to disprove. He further maintained that, notwithstanding the law of squares, Atlantic telegraphy was possible, and stated his conviction that increase of the electric pressure was a development in the wrong direction. Prof. Thomson showed that the condition for rapid signaling consisted in being able to observe the first beginning of the electric current at the far end, and to stop the signal as soon as it had risen to this observable value. To realize these conditions he invented the delicate reflecting galvanometer in which the minute turning of the magnet is magnified by the motion of a spot of light. Maxwell wrote a parody on ​Tennyson's "Blow, bugle, blow," and called it "A Lecture to a Lady on Thomson's Reflecting Galvanometer":
In the above verses Maxwell describes the process of taking a quantitative reading for the amount of a steady electric current; for signaling, all that is necessary is to observe the direction towards which the spot of light is going to move. It was by the reflecting galvanometer that the historic message through the first Atlantic cable was received: "Europe and America are united by telegraphic communication. Glory to God in the highest, on earth peace and goodwill towards men."
Prof. Thomson was personally engaged in the laying of the first cable. It transmitted several messages, then stopped. It served to prove the feasibility of the project which many engineers up to that time regarded as chimerical. By the labors of Thomson, Varley, Jenkin and others the construction of the cable was improved, as well as the mechanical means for laying it, and in 1866 a new cable was successfully laid, and the old one of the previous year raised from the depths and ​repaired. On his return from this labor in 1866, Prof. Thomson along with others of his distinguished coadjutors, received the honor of knighthood. Subsequently he invented a recording receiver for long cables, called the siphon recorder. We have seen that in 1860 Thomson and Tait entered upon the preparation of their treatise on natural philosophy, which was planned to extend to four volumes, but of which the first and last appeared in 1867. In this interval of years Thomson was likewise engaged on the Atlantic Cable, and in writing several cosmological papers, which have ever since been famous subjects for discussion: they were on the age of the Sun, the physical state of the interior of the Earth, and the age of the Earth as an abode for life.
The last mentioned subject was treated of in a paper "On the secular cooling of the Earth," read before the Royal Society of Edinburgh in 1862. He introduced the subject as follows: "For eighteen years it has pressed on my mind, that essential principles of thermodynamics have been overlooked by those geologists who uncompromisingly oppose all paroxysmal hypotheses, and maintain not only that we have examples now before us on the Earth, of all the different actions by which its crust has been modified in geological history, but that these actions have never, or have not on the whole, been more violent in past time than they are at present. It is quite certain the solar system cannot have gone on, even as at present, for a few hundred thousand, or a few million years, without the irrevocable loss (by dissipation, not by annihilation) of a very considerable proportion of the entire energy initially in store for Sun heat, and for Plutonic action. It is quite certain that the whole store of energy in the solar system has been greater in all past time than at present; but it is conceivable that the rate at which it has been drawn upon and dissipated, whether by solar radiation, or by volcanic in the Earth or other dark bodies of the system, may have been nearly equable, or may even have been less rapid, in certain periods of the past. But it is far more probable that the secular rate of dissipation has been in some direct proportion to the total amount of energy ​in store at any time after the commencement of the present order of things, and has been therefore very slowly diminishing from age to age. I have endeavored to prove this for the Sun's heat, in an article recently published in Macmillan's Magazine (March, 1862), where I have shown that most probably the Sun was sensibly hotter a million years ago than he is now. Hence, geological speculation, assuming somewhat greater extremes of heat, more violent storms and floods, more luxuriant vegetation, and harder and coarser grained plants and animals, in remote antiquity, are more probable than those of the extreme quietist, or "uniformitarian" school. A middle path, not generally safest in scientific speculation, seems to be so in this case. It is probable that hypotheses of grand catastrophes destroying all life from the Earth, and ruining its whole surface at once, are greatly in error; it is impossible that hypotheses assuming an equability of sun and storms for 1,000,000 years can be wholly true."
He proceeded in the paper cited, to apply Fourier's results to deduce a limit to the age of the Earth. Suppose a solid slab of uniform thickness and of great lateral dimensions to be originally heated to a temperature $V^{\circ }$, one side to be kept exposed to a temperature $O^{\circ }$, and the other to be kept exposed to a temperature $V$. Let $k$ denote the conductivity of the solid, when measured in terms of the thermal capacity of the unit of volume; and let $v$ denote the temperature at any distance $x$ from the surface at any time $t$ from the beginning of the cooling. Fourier showed that under these conditions,
${\frac {\;dv}{\;dx}}={\frac {V}{\sqrt {\pi kt}}}e^{-x^{2}/4kt}$
Here ${\frac {\;dv}{\;dx}}$ means the gradient of temperature, along a line normal to the face; it is the rate of change of the temperature as you go along the direction of $x$. This formula does not apply to any time prior to the beginning of the cooling, for then $t$ will be negative and the formula involves the square root of $t$.
But what application has this result to the case of the Earth? ​No doubt there still are people who think that the Earth is an infinite slab; but if the investigation has any application, it is to a solid globe, originally at one uniform temperature, exposed to a cooling agent at the surface. But the case of the Earth is reduced to the simple case of the slab by the following considerations. It had been ascertained by the observations of Forbes on underground temperature that change of temperature due to day and night, or summer and winter, disappears at about 24 feet below the surface; and observations in coalpits and borings show that the temperature thereafter increases at the rate of about one degree Fahrenheit per 50 feet of descent; but Fourier's results show that this rate will practically vanish at a small depth compared with the distance to the Earth's centre. Hence a spherical plate of the Earth if such thickness may be treated as a plate of the kind specified. The best value of $k$ then known was 400; hence for the case of the Earth,
${\frac {\;dv}{\;dx}}={\frac {V}{35.4{\sqrt {t}}}}e^{-x^{2}/1600kt}$
When $t$ is very large and $x$ small, the exponential factor is negligible; and we know that then is; hence and
${\frac {1}{50}}=V{\frac {1}{35.4{\sqrt {t}}}}$,
${\sqrt {t}}=V{\frac {50}{35.4}}$
Suppose V, the original temperature of the Earth, when it had just solidified, to be 7000° F., the temperature of melting rock, then $t$ = 98,000,000 years.
Prof. Thomson concluded that the age of the Earth as a possible abode for life must lie between 400,000,000 years and 20,000,000 years. These results came like a bolt from the blue sky on the geologists and biologists of the day. The former supposed that ​physical changes went on in the past at the slow rate at which they take place now; and by a simple application of the rule of three, to the sedimentary rocks, demanded as much time as the above for a small portion of the secondary period. In the Earth they discovered no trace of a beginning, no indication of an end; and some of them, leaving the solid crust of the Earth, and looking out into the Universe could see no signs of age or decay in the solar system. The biologists too were explaining the evolution of forms by unlimited amounts of time. The great Darwin spoke of the proposed limitation of geological time as one of his "sorest troubles." It was indeed inevitable that a clash should come.
Four years later, 1866, Sir William Thomson read another paper to the Edinburgh Society, "The doctrine of uniformity in geology briefly refuted." It contained only a few sentences and was a formal indictment of the fundamental doctrine of the geologists. The geologists put up Prof. Huxley to defend them; which he did in an address to the Geological Society of London in 1869. We have seen in a previous lecture how much Huxley knew of the nature of mathematics; he was scared at a few italic letters, particularly if they were small, not to mention the more formidable ${\frac {\;dv}{\;dx}}$. He could not discuss Thomson's arguments scientifically, all he could do was to make fun of them, and encourage his colleagues in their indifference. He said, as an introduction, "I do not suppose that at the present day any geologist would be found to maintain absolute uniformitarianism, to deny that the rapidity of the rotation of the Earth may be diminishing, that the Sun may be waxing dim, or that the Earth itself may be cooling. Most of us, I suspect, are Gallios, 'who care for none of these things,' being of opinion that, true or fictitious they have made no practical difference to the Earth, during the period of which a record is preserved in stratified deposits." If researches which are the outcome of dynamical reasoning, combined with observational and experimental data, applied to determine the constancy of the length of the day, the intensity of sunshine in different ​ages, the age and temperature of the Earth are not geology, it is difficult to adduce anything which has a right to that title. Yet Huxley in the name of the geologists said that they were intellectual Gallios, caring for none of these things. It is certainly a very remarkable, fact that one who fought all his life against ecclesiastical Gallios as regards evolution should, in the matter of the application of physical science to a geological problem, borrow their precise attitude and maxims.
The controversy has gone on ever since, and has enlivened many a meeting of the British Association. The geologists say to Lord Kelvin "Look at our arguments." Lord Kelvin says to the geologists "Look at mine." The former call out "cosmogonist"; the latter replied "geological calculus." As a result of the controversy the uniformitarian doctrine has disappeared; but no agreement has been reached about the age of the Earth when it became an abode for life. Kelvin's reasoning can be attacked only by questioning the values which are assumed for the constants, or by denying the conditions which are assumed to be true in applying Fourier's problem to the case of the Earth. The former course was adopted a few years ago by Prof. Perry; by modifying the constant $k$ he increased the time about tenfold. It is the only course which presents any avenue of escape such as the geologists desire to see. Is the Earth a body which was once molten hot, and has been subsequently left to cool, without any further generation of heat in the interior by oxidation of its contents? If the geologists had more mathematical training, they might be able to make better use of their data. As it is their reasoning is too much of this character: the Mississippi now carries down so much mud in a year, how long will it take at this rate to reduce the whole valley to the level of the Gulf of Mexico? This is a specimen of "logical calculus." A very slight knowledge of mathematics suffices, however, to show that natural changes take place at a variable rate which depends at any time on the amount to be changed, and until one gets a clear idea of a logarithm and an exponential he will not be able ​to reason to much purpose on the time required for any of the works of Nature.
Sir William Thomson's labors in connection with the laying of the Atlantic cables called for his presence on board ship, and thus attracted his attention to the art of navigation, if indeed he could live in Glasgow without being in some measure drawn into it. He became a skillful yachtsman, and he used his yacht for testing improvements in the means of navigation. His achievements in this direction are numerous and important, but the principal ones are his improved mariner's compass, and his improved sounding line. The use of iron in the construction of ships introduces a serious interference with the compass needle; the needle may direct itself towards a point in the ship instead of a point in the Earth. The action of the ship's magnetism must be cancelled; and this is no easy matter in the case of the ordinary mariner's compass. The improved compass of Sir William Thomson had instead of one large needle, a number of very small needles placed parallel to one another; and instead of a heavy continuous card a light card with the centre wholly cut away. It is more steady, more free to move, and more easily protected from the ship's magnetism. His sounding-line consists of a sinker of 20 to 30 pounds, carried by a strong steel wire. The greatest vertical depth of the sinker beneath the surface is recorded by an instrument which measures the greatest water pressure; and it is read after the instrument has been brought back on board ship. In the old method of casting the lead the depth is determined from the length of rope run out. With the old method a ship must be brought to a standstill, if any trustworthy measure is desired in deep water; with the improved line, a steamer may be running at a speed of 20 knots.
Connected with navigation is his invention of a machine for calculating the heights of the tides at a given port. "It is essentially a mechanical contrivance by which the sum of ​a Fourier series is obtained by mechanical means. The tides for a given part for a whole year can be wound out of it in four hours, thus facilitating their prediction to an extraordinary degree. The form in which it gives the prediction being a continuous curve on paper, it enables the height of the water at any moment to be ascertained by inspection, while any arithmetical result that could possibly be worth the trouble of calculating, would only give the times of high and low water."
Sir William Thomson was for many years a member of the Committee of the British Association, which had in charge the development of an absolute system of units. He was the champion of the centimeter as opposed to the metre; and his argument was that it was important that the density of water should be unity, not 1,000,000. Electrical measurement was then in its infancy. Looking at the question in the light of recent development, we see that the adoption of the centimeter was a mistake for the desired system of C.G.S. electric units is too small for practical purposes, and the actual system which is used involves the fundamental units multiplied by some power of ten. Hence electrical computations now include the metric system proper, the C.G.S. system, and the practical electric system. Sir William Thomson designed many instruments for the purpose of electrical measurements, and for the manufacture of these instruments established a large workshop in Glasgow, under the management of James White. This has been a principal source of his fortune.
When I was at work in Tait's laboratory, Sir William Thomson was president of the Royal Society of Edinburgh; and I have often heard him read papers and make addresses. These meetings brought him to Edinburgh frequently, and it was his custom to visit the laboratory of his colleague Tait. He must originally have been about six feet high. But for many years his height has been diminished by a stiff leg which was brought about in the following way. He broke his leg when skating on the ice, and would not remain at rest until it had recovered properly. Otherwise his appearance was athletic. Compared with Tait, he was not so elegant a speaker, but his ​papers have more of the stamp of a genius. He has strong opinions on most subjects, and like most Irishmen, he is not afraid of a controversy. If Tait made a move and was not immediately successful, he was apt to retire resolved to have nothing further to do with it; not so Thomson; if baffled, he returns to the attack again and again. On social matters he has strong conservative opinions; at a club meeting after the regular meeting of the Royal Society of Edinburgh he was asked: "Sir William! what do you think? Should a man be allowed to marry his widow's sister." "No sir, the Bible forbids it, and I hope the law of the land will continue to forbid it."
Sir William Thomson visited America at the time of the Centennial Exposition at Philadelphia, 1876, and he brought back to Scotland a wonderful account of Graham Bell's telephones. In 1884 he made another visit, to deliver a course of lectures at the Johns Hopkins University. This course of lectures, twenty in all, treated of the wave-theory of light, principally with the outstanding difficulties of the theory, and they partook largely of the nature of conferences. "Discussion did not end in the lecture-room; and the three weeks over which the lectures extended, were like one long conference." He was also a member of the Commission which solved the problem of harnessing Niagara.
In 1892 he was created a member of the House of Lords, under the title of Baron Kelvin. He took his title from the stream which flows past the hill on which the University of Glasgow is built. In 1896 the jubilee of his professorship was celebrated with great éclat at Glasgow. The exercises lasted three days and there were present representatives from all the scientific institutions of Great Britain, and from many of the scientific institutions of other countries. After a further tenure of three years, he resigned his chair. He now spends his time mostly at his country seat at Largs on the coast of Ayrshire, and at his house in London. The degrees and honors conferred upon him are numbered by hundreds, and the enumeration of these honors might be most briefly made by mentioning the ​few not conferred; he is still open, I believe, to receive some distinguished mark of recognition from the geologists.
Lord Kelvin has been twice married, but there is no direct heir to inherit either his genius or title. Notwithstanding the fact that he has long been the acknowledged leader of science in Great Britain, and indeed in Europe, his disposition has remained simple and kindly. A multitude of honors, and great fame and power has not spoiled the grandson of the small Irish farmer. He is still active in the production of scientific papers, and although now nearly 78 years of age is making preparations to again cross that ocean which has been the scene of so many of his exploits, and which is now much more safely navigated through the instrumentality of his inventions.
* ↑ This Lecture was delivered on March 25, 1902.—Editors.
* ↑ One desiring to follow this celebrated controversy further should consult the article on Geology in the Eleventh Edition of the Encyclopædia Britannica.—Editors.
* ↑ Lord Kelvin died on December 17, 1907, in the 84th year of his age. His activity in scientific discussions did not diminish with age. He revised the lectures on the wave-theory of light which he had delivered at Johns Hopkins University and published them in 1904. In that year also he was elected Chancellor of the University of Glasgow. He continued to take an active part in the work of scientific societies; only a few months before his death he delivered at the meeting of the British Association a long and searching address on the electronic theory of matter. He was buried in Westminster Abbey a few feet south of the grave of Newton.—Editors.
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