# Popular Science Monthly/Volume 73/August 1908/The History of the Conservation of Energy: The Age of the Earth and Sun

THE

POPULAR SCIENCE

MONTHLY

AUGUST, 1908

 THE HISTORY OF THE CONSERVATION OF ENERGY; THE AGE OF THE EARTH AND SUN
By Professor FLORIAN CAJORI

IN the small town of Heilbronn, in Würtemberg, stands a monument erected to the memory of. the physician, Robert Mayer. It was unveiled in 1892, just fifty years after the publication of Robert Mayer's first essay on the conservation of energy. His career as a scientific discoverer is marked by many pathetic incidents. After the study of medicine he was made sanitary officer on a Dutch vessel, bent for the East Indies. During the long ocean voyage on the slow sailing vessel he was left much to himself. He gave his leisure hours to the contemplation of scientific subjects. He had occasion to observe that, in tropical countries, blood taken from the veins of patients looks almost like arterial blood. He concluded that in the tropics less oxidation is necessary than in a cold climate, in order to maintain a uniform bodily temperature. There must be a quantitative relation between the amount of heat generated and the temperature in which we live. In cold, northern climates "more heat must be developed for the maintenance of uniform bodily temperature. During the 219 days between February and September, 1840, spent on the water, Mayer dwelt in close intellectual communion with nature, and she gradually revealed to him one of her most precious secrets. Upon his return to Heilbronn he kept on thinking. A moving body is brought to rest by friction; heat appears. Has the motion disappeared into nothing? Has heat sprung out of nothing? If not, then there must be an equivalence between the heat generated and the motion destroyed. Causa æquat affectum, "Cause is equal to effect" became his favorite axiom. At first he thought that kinetic energy varied as the velocity. Later he recognized his error and perceived its variance with the square of the velocity.

On June 16, 1841, he sent an essay embodying his new ideas for publication in Poggendorff's Annalen, but the manuscript was not published nor was it returned to the author.[1] Thirty-six years later it was found among the papers of Poggendorff. In 1842 Mayer prepared a second short paper of seven pages and had the satisfaction of seeing it printed in Liebig's Annalen der Chemie. This was a happy time in his life, for at the very hour when he learned of the acceptance of his manuscript, he was bringing home his bride and presenting her to his aged parents.[2] But it is one thing to secure the publication of a manuscript and quite another thing to get scientific men to read and study it. A new discovery necessitates a new language. A new language is not generally understood. The curse of Babel fell upon Mayer's paper: "Confound their language, that they may not understand one another's speech." Other papers were printed by Mayer as pamphlets in 1845 and 1848.

Something of the personality of Mayer may be gained from the following stories.[3] During a hurried meeting with Mayer in Heidelberg once, Jolly remarked, with a rather dubious implication, that if Mayer's theory were correct water could be warmed by shaking. Mayer went away without a word of reply. Several weeks later. . . he rushed into the latter's presence, exclaiming, "Es ischt so!" (It is so, it is so). It was only after considerable explanation that Jolly found out what Mayer wanted to say. Of metaphysics Mayer had no appreciation. Rümelin narrates that in 1841 Mayer borrowed from him a copy of Hegel's "Logik" and Hegel's "Naturphilosophie," but returned the books a few days later with the remark that he did not understand a word, and that he could not understand any part of it, were he to study it a hundred years.[4]

For years Mayer was unable to bring his great discovery to the serious attention of scientific men. Later there followed controversies on his rights of priority. A gloom fell upon him through the death of two of his children. His mind became seriously affected, and on May 26, 1850, he unsuccessfully attempted suicide by jumping from a second-story window. In 1851 he was placed in an insane asylum, where he was cruelly treated. Two years later he was set free, but he never again regained complete mental equilibrium. Such is the pathetic story of the first discoverer of the conservation of energy.[5]

In 1858 a few voices were heard in Germany in praise of Mayer, but the one who did most to bring him historical justice was John Tyndall, who in 1862 lectured before the Royal Institution on Robert Mayer.[6] I shall remain silent on the extremely bitter controversy, between Tyndall and Tait, regarding Mayer's researches.[7] Tait and William Thomson placed a low estimate on Mayer's work and brought the charge that Tyndall, by praising Mayer, was belittling the work of Joule. One would suppose that gross historical errors would have been eliminated by this time from a subject like the conservation of energy, about which so much has been written. Such is not the case. Professor E. T. Glazebrook, writing in the great "Dictionary of National Biography" (article, "Joule"), said in 1892, just before the publication of Mayer's correspondence, that Mayer in 1842 endeavored to measure the heat produced in the compression of air, but committed the very serious mistake of assuming without experimental evidence that "all the mechanical energy spent in compressing the air was used in producing change of temperature." This same criticism was passed upon Mayer by Joule, Tait and Helmholtz. A fundamental question is here involved, but the charge is not true. As early as September 12, 1841, in a. letter to his friend Professor Baur, Mayer explained Gay-Lussac's experiment of 1807 on the flow of gas into a vacuum, and drew upon it to complete his argument on the equivalence of the work of compression and the heat generated by the compression. Gay-Lussac had found that when a gas expands into a vacuum it undergoes no change in temperature large enough to be detected by his thermometers. Hence, during compression practically all the work done upon the gas goes to produce change of temperature, and Mayer's argument is sound. That the criticism of Mayer's reasoning is invalid is not generally known to recent writers on the subject, but can now be verified by any one who will examine Mayer's collected works and letters, edited by Weyrauch in 1893.[8] It should be added, however, that Mayer himself is partly to blame for the strictures passed upon his paper of 1812. Gay-Lussac is not mentioned and the whole matter is disposed of in a single sentence, though that sentence, we admit, is somewhat Germanic in its structure and linear dimensions.

Mayer's failure to secure recognition from the scientific public found its counterpart on a smaller scale with Joule and Helmholtz.

Joule was the son of a wealthy brewer. In 1830 he saw the first trains which traveled between Liverpool and Manchester. One of the happy circumstances of his boyhood life was his connection with John Dalton and Dalton's laboratory containing effective home apparatus. His association with Dalton gave direction to his constructive genius. Joule's father fixed up a room for a chemical laboratory. Before the boy was of age he began experimentation in chemistry and electricity.

After laborious tests he succeeded in showing that the heat developed by the union of two chemical elements effected in a battery is the same as that developed by combustion, and that the heat has a definite equivalent in the electromotive force between these elements.[9]0 He studied the relations between electrical, chemical and mechanical effects and was led to the great discovery of the mechanical equivalent of heat. In a paper read before the British Association in 1843 he gave the number as 460 kilogrammeters. This was only one year after Mayer had published his first paper. Friends who recognized the physicist in the young brewer persuaded him to become a candidate for the professorship of natural philosophy at St. Andrews, Scotland, but his slight personal deformity was an objection in the eyes of one of the electors and he did not receive the appointment.

The early papers of Joule attracted little attention. His facts were so novel, so apparently heterodox, and the language in which they were conveyed so unfamiliar, that the older physicists permitted them to remain without due consideration. Faraday was then busy with his experimental researches. Graham was studying the diffusion of gases. Wheatstone, Whewell, Herschel, Forbes, Airy were engrossed with problems of their own. Those who were first to applaud Joule a few years later were still pupils. William Thomson and Gabriel Stokes were at Cambridge; Bankine, a youth of 22, was studying engineering; Tait was a boy at school; Clerk Maxwell had just acquired the nickname of "Dafty" at Edinburgh Academy. In 1844 a paper of Joule, "On the Changes of Temperature produced by the Rarefaction and Condensation of Air," was rejected for publication by the Royal Society, but was printed in the Philosophical Magazine the year following.[10]

In April, 1847, Joule gave a popular lecture in Manchester, delivering the first full and clear exposition in England of the universal conservation of that principle now called energy.[11]

The local press would at first have nothing to do with it. One paper refused to give even a notice of it. The Manchester Courier, after long debate, published the address in full. In June, 1847, the subject was presented before the British Association meeting at Oxford. The chairman suggested that the author be brief. No discussion was invited. In a moment the section would have passed on to other matters without giving the new ideas any consideration, if a young man had not risen from his seat and by his intelligent observations created a lively interest in the new theory. The young man was William Thomson, now better known as Lord Kelvin. The result was that the paper caused a great sensation. Joule had attracted the attention of scientific men. After the meeting Joule and Thomson discussed the subject further and the latter obtained ideas he had never had before.

Joule experimented on the mechanical equivalent of heat for about forty years. By magneto-electric currents he got in 1843 the value of 460 kilogrammeters as the equivalent of the large French calorie. By the friction of water in tubes he obtained 424.9; by the compression of air, in 1845, 443.8; by the friction of water he obtained, in 1845, 488.3; 'in 1847, 428.9; in 1850, 423; in 1878, 423.

Comparing Joule with Mayer, it will probably be admitted nowadays that Joule stands first as an experimentalist, while Mayer towers above Joule as a generalizer, as a physical philosopher.

The same year, 1847, in which Joule announced his views on energy before the British Association, Helmholtz, a youth of 26, read before the Physical Society in Berlin a *paper on the same subject, entitled, "Die Erhaltung der Kraft." It was at first pronounced a fantastic speculation. The editor of Poggendorff's Annalen, who in 1841 declined Mayer's paper, rejected Helmholtz's also. As Joule was supported by William Thomson, so-Helmholtz was defended by his fellow student Du Bois-Beymond, and by the mathematician C. G. J. Jacobi. Helmholtz's paper was published in pamphlet form in 1847. For a time it attracted little notice, but in 1853 some parts in it were vigorously attacked by Clausius in Poggendorff's Annalen. Later it subjected its author to bitter attacks from Eugen Karl Dühring[12] and others, who accused him of being a dishonest borrower from his forerunner, Robert Mayer. In a publication of 1898, issued in Berlin, Dr. Thomas Gross does not quite accuse Helmholtz of plagiarism, but claims that Helmholtz did all he could to discredit Mayer. In my judgment both Dühring and Gross failed to establish their contentions. In the absence of clear evidence to the contrary we prefer to accept Helmholtz's own statement, as given in one of his lectures. Helmholtz says in one place, "The first who saw truly the general law here referred to and expressed it correctly was a German physician, J. E. Mayer, of Heilbronn, in the year 1842." Then he says, "I myself, without being acquainted with Mayer or Colding, and having first made the acquaintance of Joule's experiments at the end of my investigations, followed the same path."[13]

We have now briefly sketched the birth of the principle of the conservation of energy in the minds of Mayer, Joule and Helmholtz. After examining the facts we are convinced that these great physicists were independent discoverers. Lack of time prevents us from making reference to forerunners like Count Rumford,[14] Sadi Carnot,[15] Seguin,[16] Mohr[17] and to the Dane, named Colding,[18] who in 1843 gave utterance to the law before the Academy in Copenhagen. We pass by the researches of Rankine, to whom we owe the expression, "conservation of energy," as well as William Thomson's doctrine of the "dissipation of energy."

We come now to the second part of this paper—the application of the conservation of energy and other principles of physics to the examination of the age of the sun and of the earth. The two problems are closely interrelated; the earth-age is measurable by the sun-age.

Before the time of the Scotch geologist, James Hutton, some 6,000 years was believed to indicate the age of the earth, and, indeed, of the entire universe. The advent of the uniformitarian school of geologists marks a radical departure from the old estimates. The pendulum swings from one extreme to the other. Boundless distances of time were now drawn upon. So great an antiquity of the earth seemed to reveal itself to geologists, as to defy all attempts at measurement. In the further pursuit of Hutton's line of investigation, Play fair and Lyell were unable to discover among the records of the earth and in planetary motion either a beginning or an end of the present order of things. They found no indication of infancy or decaying old age.[19]

This convenient doctrine of infinite durability came to be rudely attacked by the physicists. Here, as in the history of the conservation of energy, the earliest investigator is Robert Mayer. To be sure, he did not attempt an estimate of the age of the solar system, but he discussed the preliminary question as to the source of solar heat. As soon as Mayer had convinced himself that energy can not be destroyed, and that the energy of the earth comes mainly from the sun, he began to study what Sir William Herschel had called "the great secret" of the maintenance of solar heat. In 18-11, before the publication of his first paper, he asked questions relating to solar heat, in a letter to Baur, "Is it the glowing of the sun? Why does he not cool off? Is it a burning depending upon willing meteoric stones?"[20]

In 1816 he had a paper ready on this subject. Being reminded by a friend that no one can be a prophet in his own country, he sent the paper to the Academy of Sciences in Paris. A committee of the academy was directed to report on this paper, but it failed to do so and the paper was ignored. It could be published only at his own expense. It appeared in 1818 under the title, "Celestial Dynamics." Mayer concludes that the sun can not be a glowing mass, sending out radiation without compensation; solar heat can not be due entirely to chemical changes; solar heat can not be due to solar rotation. He finally embraces the theory that solar heat is due to the energy of meteors falling into the sun. He did not overlook the fact that the resulting increase of mass of the sun would increase its attraction for the planets, and would shorten the sidereal year. He knew that observation does not disclose any variation in the length of the year. An easy explanation would be offered by Newton's corpuscular theory of light, according to which the sun sends out matter into space. But this theory was then known to be untenable. In this dilemma Mayer takes refuge in an idea which rests on a misconception of the unclulatory theory of light, and he offers an explanation which is now easily recognized as invalid.

From Mayer we pass to William Thomson, the late Lord Kelvin, who, six years later, took up the very same problem and arrived independently at almost identically the same conclusions. That solar heat may be due to falling meteors was first suggested in England by Waterston. Unlike Mayer, Thomson sees no objection to the increase in the sun's mass resulting from meteoric showers, for, "according to the form of the gravitation theory" which he proposed, "the added matter is drawn from a space where it acts on the planets with very nearly the same forces as when incorporated in the sun." In an appendix to the paper, Thomson ventures an estimate of the age of the sun. This is the first attempt, made by a physicist, to compute the age of our great luminary and to prepare a mortuary estimate of it. He goes on the supposition that the solar energy of rotation is derived from the energy of falling meteors. He calculates that, allowing for the constant loss of solar energy by radiation, the sun could acquire its present energy of rotation in thirty-two thousand years. From an estimate of the limited amount of meteoric matter available near the sun, he concludes that "sunlight can not last as at present for three hundred thousand years." This calculation of the year 1854 attracted no attention at the time. Later, the theory was abandoned by its author, as at variance with known facts.

Evidently the theory of solar heat was still in a very crude form. But important new ideas were brought into view in the same year, 1854, by Helmholtz, in a popular lecture at Königsberg, delivered on the occasion of the Kant commemoration.[21] Unlike Mayer and Thomson, he starts out with the nebular hypothesis of Kant and Laplace, and derives solar heat from nebular contraction. During the contraction of the nebula from which sun and planets were formed, and also during the contraction of the sun, now assumed to be in progress, the kinetic energy obtained thereby is converted into heat and compensates for the loss of solar heat by radiation. He concludes that if the sun contracts the ten-thousandth part of its radius enough heat is generated to supply radiation for 2,100 years.[22] His figures yield twentytwo million years as the probable age of the sun, on the assumption of uniform radiation and homogeneous density. Experimental data on the intensity of solar radiation, found later by Langley, reduced this age to eighteen million or less.

Helmholtz's theory was a tremendous advance on that of falling meteors, assumed by Mayer and Thomson. No doubt meteors fall into the sun, as assumed by Mayer and Thomson, but the Mayer-Thomson theory made demands upon these meteors that bordered on extravagance. We are certain that a part of the solar heat is due to falling meteors, but its amount is as nothing, compared with the heat resulting from the gravitational energy of shrinkage. Until recently these were the only important sources considered.

In the sixties fresh attacks were made on the problem of the age of the sun by William Thomson. In 1862 appeared in the Macmillan's Magazine an article, "On the Age of the Sun's Heat,"[23] in which he favors a meteoric theory like that of Helmholtz, by which there is no difficulty in accounting for 20,000,000 years' heat radiated by the sun. He concludes that we may accept "as a lowest estimate for the sun's initial heat, 10,000,000 times a year's supply at present rate, but 50,000,000 or 100,000,000 as possible, in consequence of the sun's greater density in his central parts."[24] "As for the future, . . . inhabitants of the earth can not continue to enjoy the light and heat essential to their life, for many million years longer, unless sources now unknown to us are prepared in the great store-house of creation." More detailed studies of the same subject were made in 1887, in a lecture "On the Sun's Heat," delivered before the Royal Institution of Great Britain.[25]

In this lecture Sir William Thomson refers to a very able paper, "On the Theoretical Temperature of the Sun," by J. Homer Lane,[26] of Washington, which establishes the apparently paradoxical statement that, within certain limitations, the more heat a gaseous body loses by radiation, the hotter it will become. This theorem was discussed in connection with the solar heat by Benjamin Peirce,[27] Simon Newcomb[28] and Sir Robert Ball.[29] Results similar to Lane's were reached in the years 1878-83 in a series of very exhaustive papers by A. Bitter.[30] A rival to the Helmholtz-Thomson theory of solar heat was advanced about 1882 by William Siemens,[31] who imagined the rotating sun to hurl, by centrifugal action at his equator, enormous quantities of gas into space, which returned to him again at the poles.

A refinement of the theory as presented by Helmholtz was introduced in 1899 by T. J. J. See,[32] wherein he abandoned the Helmholtzian hypothesis of a sun of homogeneous density and, using Lane's law, investigated minutely the more complex case of central condensation. Thereby the probable solar age was extended from about 18 to about 32 million years.

Returning to the problem of the age of the earth, considered independently of the sun, we find William Thomson the great moving spirit. He approached the subject from more than one point of view. One argument for limitation of the earth's age was based on the consideration of underground heat.[33] "The heat which we know by observation to be now conducted out of the earth yearly is so great that if this action had been going on with any apparent uniformity, the history of life on the earth could not exceed a few thousand million years." Another consideration leading to similar conclusions was based on the shape and rigidity of the earth. With Sir William Thomson, the age of the earth continued to be a question studied with great predilection. His aim was not so much to determine the exact age as to fix an upper age limit. As the years passed by, investigation supplied much of the knowledge which was at first wanting regarding the thermal properties of rocks, and Sir William Thomson was able greatly to reduce this upper limit.

"The Physical Condition of the Earth" was the topic of Sir William Thomson's presidential address in 1876, before Section A of the British Association. He took the gradual increase of temperature downwards to be on an average 1° C. for 30 meters of descent and gave reasons for his belief that for great depths the rate of increase does not diminish. He concludes that if at great depths the temperature does not exceed 4,000° C., then the geological age of the earth does not exceed 90 million years. This argument involves some very uncertain factors. Sir William Thomson has shown quite conclusively that the earth's interior is solid, but at what temperature the substance of the earth would begin to melt under the high internal pressures was a matter of pure conjecture.

About 1885 Carl Barus, of the United States Geological Survey, made a series of very important experimental researches on the physical properties of rocks at high temperatures, for the purpose of supplying trustworthy data for geological theory.[34] Mr. Clarence King, in an article published in the American Journal of Science,[35] used the data on specific heats, thermal conductivities and temperatures of fusion of rocks, which had been supplied by Barus, for a more accurate determination of the age of the earth. King concludes from these experimental data on diabase, "that we have no warrant for extending the earth's age beyond 24,000,000 years." A computation made by Lord Kelvin led to about the same figure.[36] These results were embodied by him in his address of 1897 before the Victoria Institute.

What was the attitude of geologists toward these researches? In England, geologists did not pretend to be able to find any flaw in the argument of Lord Kelvin, but they were in a position described in the well-known couplet,

"A man convinced against his will
Is of the same opinion still."

To the geologist, yonder snow-capped peaks symbolized eternity; to the physicist, the mountains were as transient as the clouds.

A calm statement of the geologists' attitude was made before the British Association in 1892 by Sir Archibald Geikie.[37] In one place he expresses himself as follows:

Lord Kelvin is willing, I believe, to grant us some twenty millions of years, but Professor Tait would have us content with less than ten millions. . . . I frankly confess that the demands of the early geologists for an unlimited series of ages were extravagant. . . and that the physicist did good service in reducing them. . . . That there must be some flaw in the physical argument I can, for my own part, hardly doubt, though I do not pretend to be able to say where it is to be found. Some assumption, it seems to me, has been made, or some consideration has been left out of sight, which will eventually be seen to vitiate the conclusions, and which when duly taken into account will allow time enough for any reasonable interpretation of the geological record.

Five years later an American geologist, Professor T. C. Chamberlin, invaded the domain of physics and made a vigorous attack on Lord Kelvin's argument, challenging the correctness of some of his assumptions.[38] This criticism did not secure the attention it deserved, for scientific events soon took a different turn.

Lord Kelvin's address of 1897 is permeated, as Professor Chamberlin puts it, "with an air of retrospective triumph and a tone of prophetic assurance." "It is only by sheer force of reason," says Kelvin, "that geologists have been compelled to think otherwise, and to see that there was a definite beginning and to look forward to a definite end of this world as an abode fitted for life." Nor was this feeling of retrospective triumph confined to Lord Kelvin or to the students of the problem of the age of the sun and earth. At the close of the century physicists and chemists gloried in the triumphs of their predecessors, in such achievements as are indicated by the words "conservation of energy," "conservation of mass," and "atomic theory." In physical research the nineteenth century was a golden age. It produced Faraday, Helmholtz, Mayer, Joule, Kelvin, Rayleigh, Rowland and many other great men. With the close of the century timid souls doubtless feared that the golden age had come to a close, and they perhaps experienced strange emotions like those attributed to Adam in the Garden of Eden, on seeing the sun go down, not knowing that it would ever rise again.

Others were perhaps haunted by another fear—a feeling that the great and fundamental truths of science were all revealed to the full sight of man, and it now remained only to work out the less important details. Some doubtless felt disheartened because of lack of opportunity, as did the Edinburgh anatomist, Dr. John Barclay a century ago. Dr. Barclay looked upon the great anatomists of earlier periods as "reapers who, entering upon untrodden ground, cut down great store of corn from all sides of them. . . . Then come the gleaners who gather up ears enough from the bare ridges to make a few loaves of bread. Last of all come the geese, who still continue to pick up a few grains scattered here and there among the stubble, and waddle home in the evening, poor things, cackling with joy because of their success." But the history of science shows that Dr. Barclay's reapers, gleaners and geese do not belong to separate epochs. They are contemporaneous. The reaping, gleaning and cackling go on as a rule in the same field, all at one time, in a grand comic medley of sounds. It is certain that anatomists had not so nearly exhausted their field one hundred years ago as Dr. Barclay believed that they had.

The principle of the conservation of energy has quite withstood all attacks. To be sure, Le Bon claims to have overthrown it, too,[41] but the validity of his argument is questionable. Even scientists sometimes play with logic. You have heard the story of the Assyriologist who argued: "The Assyrians understood electric telegraphy, because we have found wire in Assyria." "Oh," replied the Egyptologist, "we have not found a scrap of wire in Egypt, so we know the Egyptians understood wireless telegraphy."

In the presidential address before the British Association in 1907, Professor E. B. Lankester uttered the following weighty words: "The kind of conceptions to which these and like discoveries have led the modern physicist in regard to the character of that supposed unbreakable body—the chemical atom—the simple and unaffected friend of our youth—are truly astounding. But I would have you notice that they are not destructive of our previous conceptions, but rather elaborations and developments of the simpler views, introducing the notion of structure and mechanism, agitated and whirling with tremendous force, into what we formerly conceived of as homogeneous or simply built-up particles, the earlier conception being not so much a positive assertion of simplicity as a non-committal expectant formula awaiting the progress of knowledge and the revelations which are now in our hands."[42]

This same address touches questions of cosmical physics. It says:

Radium has been proved to give out enough heat to melt rather more than its own weight of ice every hour; enough heat in one hour to raise its own weight of water from the freezing point to the boiling-point. . . . Even a small quantity of radium diffused through the earth will suffice to keep up its temperature against all loss by radiation! If the sun consists of a fraction of one per cent, of radium, this will account for and make good the heat that is annually lost by it.

He continues to say:

This is a tremendous fact, upsetting the calculations of physicists as to the duration in past and future of the sun's heat and the temperature of the earth's surface. The physicists, notably Professor Tait and Lord Kelvin, . . . have assumed that its material is self-cooling. . . . It has now, within these last five years, become evident that the earth's material is not self-cooling, but on the contrary self-heating. And away go the restrictions imposed by physicists on geological time. They now are willing to give us not merely a thousand million years, but as many more as we may want.

Some of the views relating to radium, expressed in the summer of 1906 at the York meeting of the British Association, appeared to Lord Kelvin open to objection. It seemed to him that some of the younger men were carried away by the strangeness of the new phenomena and were ready to adopt the most extravagant theories when there was no logical necessity for abandoning old views and, in their intoxication, were embracing new hypotheses without exercising due circumspection. After the meeting Lord Kelvin boldly opened a controversy in the London Times. Almost single-handed the old warrior fought with great intellectual keenness against the transmutational and evolutionary doctrines, relating to the chemical elements, framed by the younger investigators, to account for the properties of radium.[43] Among his opponents were Sir Oliver Lodge, the Hon. Mr. Strutt, Mr. A. S. Eve and Mr. F. Soddy. It can not be said that Kelvin was victorious, but the controversy helped to define the points at issue. Among other things, Lord Kelvin said that there was no experimental foundation for the assertion that the heat of the sun was probably due to radium. He was still inclined to ascribe it to gravitation. Lord Kelvin also denied that it was proved that the heat of the earth is due to radium. It was possible, he claimed, that radium does not decompose under the conditions prevailing in the interior of the earth, and in that case it emits no heat.

In considering the perturbations produced by radium in the progress of our ideas, it is well to remember that, thus far, we have been able to experiment with radium in only small amounts. Professor Lankester remarks that the Curies never had enough of radium chloride to venture on any attempt to prepare pure metallic radium.

Altogether the Curies did not have more than some four or five grains of chloride of radium to experiment with, and the total amount prepared and now (1906) in the hands of scientific men in various parts of the world probably does not amount to more than 60 grains at most. When Professor Curie lectured on radium four years ago at the Royal Institution in London he made use of a small tube an inch long and of one-eighth inch bore, containing nearly the whole of his precious store, wrenched by such determined labour and consummate skill from tons of black shapeless pitch-blende. On his return to Paris he was one day demonstrating in his lecture room with this precious tube the properties of radium when it slipped from his hands, broke, and scattered far and wide the most precious and magical powder ever dreamed of by alchemist or artist of romance. Every scrap of dust was immediately and carefully collected, dissolved, and re-crystallised, and the disaster averted with a loss of but one minute fraction of the invaluable product.[44]

In a reinvestigation of the age of the earth it is extremely important to undertake extensive investigation of the amount of radium contained in the various rocks. Such researches have been begun by the Hon. E. J. Strutt. He has made determination of the amount of radium in rocks at the surface of the earth, and has found about ${\displaystyle 3\times 10^{-12}}$ grains of radium as the average amount present in 1 c.c. of soil.

From the rate of increase of temperature below the earth's surface and the heat conductibility of rocks, Mr. Strutt concludes that radium is confined to a comparatively thin crust of the earth. While these reasons are not conclusive, they are weighty. Our incomplete knowledge of the properties and the distribution of radium and other radioactive substances, makes it necessary to suspend judgment on the age of the earth. There is no necessity that the question be settled immediately.

The same remark applies to the antiquity of the sun. Much depends upon the presence or absence of radium there. As yet this substance has not been found in the sun, but the presence of helium, combined with the fact that helium may be obtained from radium, renders the presence of radium in the sun quite probable. That radium affects the problem of the solar age was pointed out by Mr. G. H. Darwin in the following words:[45]

Knowing, as we now do, that an atom of matter is capable of containing an enormous store of energy in itself, I think we have no right to assume that the sun is incapable of liberating atomic energy to a degree at least comparable with that which it would do if made of radium. Accordingly, I see no reason for doubting the possibility of augmenting the estimate of solar heat as derived from the theory of gravitation by some such factor as ten or twenty.

In conclusion, it is very evident that, however unpleasant it may be for the older men to revise their theories to meet the demands of new observations, we have in radio-activity the entrance into a region of new knowledge which will cast light upon many a dingy avenue of philosophy. Great are the trials and great the final triumphs of experimental science.

In Norse mythology there is a wonderful tree called Igdrasil, whose branches spread over the whole earth and reach up into the clouds. At the foot of the tree, away down at the deepest root, is a well from which the tree draws its sap. To us of the twentieth century that tree symbolizes science. The well which nourishes the tree is the fountain of eternal truth.

1. "Mechanik der Wärme," von R. Mayer (ed. J. J. Weyrauch), Stuttgart, 1893, p. 16; "Kleinere Schriften u. Briefe," von Robert Mayer (ed. J. J. Weyrauch), Stuttgart, 1893, V., p. 99.
2. "Kleinere Schriften," p. 379.
3. Mach in the Monist, Vol. 6, 1896, p. 171, copied in Cajori's "History of Physics," New York, 1899, p. 210. Several passages in this address are taken from this "History of Physics."
4. G. Rümelin, "Reden und Aufsätze," Freiburg i. B., 1881, p. 380.
5. For a statement, by Clausius, explaining the manner in which Mayer's publications became known, consult "Die Mechanische Warmetheorie," von R. Clausius, dritte umgearbeitete und vervollstandigte Auflage, Erster Band, Braunschweig, 1887, pp. 394-403.
6. Proceedings of the Royal Institution, June, 1862; Philosophical Magazine, Vol. 24, p. 57.
7. See Thomson and Tait's article in the Philosophical Magazine, April, 1863, and various articles by them and Tyndall in Vols. 25 and 26 of the Philosophical Magazine, as well as translations into English of Mayer's papers.
8. "Kleinere Schriften u. Briefe," p. 131; "Mechanik der Wärme," pp. 53, 130, 269.
9. "Memoir of James Prescott Joule," by Osborne Reynolds, 1892, p. 50.
10. Reynolds, op. cit., p. 78.
11. Reynolds, op. cit., pp. 104, 105.
12. Dr. E. K. Dühring, "Robert Mayer, der Galilei des Neunzehnten Jahrhunderts," Chemnitz, 1880; Zweiter Theil, Leipzig, 1895.
13. "Popular Lectures," by H. Helmholtz (transl. by E. Atkinson), New York, 1897, p. 167.
14. "The Complete Works of Count Rumford," published by the American Academy of Arts and Sciences, Boston, Vol. I., pp. 481-488.
15. "Réflexions sur la puissance motrice du feu," 1824, reprinted in Ostwalds Klassiker, No. 37; English translation by R. H. Thurston appeared in 1890.
16. "De L'influence des Chemins de Fer," Paris, 1839, pp. 378-397.
17. "Allgem. Theorie der Bewegung," Braunschweig, 1869, pp. 80-84.
18. A. Colding, Det. Kongel. dansk vidensk. selsk. naturv. ogmath. afh. (5), II., 1843, p. 121, 167.
19. Sir Archibald Geikie, presidential address before British Association, in Report, British Association for the Advancement of Science, 1892, Vol. 62, pp. 3-26; Smithsonian Report, 1892, p. 124.
20. "Mechanik der Wärme," p. 146.
21. H. Helmholtz, "Popular Lectures" (transl. by E. Atkinson), New York, 1897, pp. 153-193, "On the Interaction of Natural Forces."
22. Op. cit., p. 190.
23. Sir William Thomson's "Popular Lectures and Addresses," Vol. I., 1891, pp. 356-375.
24. Op. cit., p. 375.
25. Op. cit., pp. 376-429.
26. American Journal of Science, 2d S., Vol. 50, 1870, pp. 57-74.
27. Proceed. Am. Acad., XV., p. 201.
28. "Popular Astronomy," 1st ed., p. 508; "The Stars," New York, 1901, p. 210.
29. "Story of the Heavens," London, 1893, p. 497.
30. Wiedemann's Annalen, V., p. 405; X., p. 13; XI., p. 978; XII., p. 445; XIII, p. 360; XIV., p. 16; XVI., p. 166; XVII., p. 322; XVIII, p. 488; XX., pp. 137, 897. See Rosenberger, "Geschichte der Physik," Vol. III., 1887, pp. 689, 690.
31. "Ueber die Erhaltung der Sonnenenergie," Uebersetzt von C. E. Worms, Berlin, 1885; see Rosenberger, "Geschichte der Physik," Vol. III., p. 687.
32. Science, N. S., Vol. IX., 1899, pp. 737-740.
33. W. Thomson, "The Doctrine of Uniformity in Geology Briefly Refuted," read in 1865 before the Royal Society of Edinburgh. See Smithsonian Report, 1897, p. 343.
34. Am. Jour, of Science, 3d S., Vol. 42, p. 498; Vol. 43, p. 56.
35. "On the Age of the Earth," 3d S., Vol. 45, 1893, pp. 1-20. See also Smithsonian Report, 1897, p. 345.
36. Smithsonian Report, 1897, p. 346.
37. Smithsonian Report, 1892, p. 125.
38. Science, N. S., Vol. IX., pp. 889-901; Vol. X., pp. 11-18, 1899. Reprinted in Smithsonian Report, 1899, pp. 223-246.
39. See J. J. Thomson, "Conduction of Electricity through Gases," 1903, p. 534.
40. Dr. Gustave Le Bon, "The Evolution of Matter" (translated by F. Legge), 1907, Charles Scribner's Sons.
41. Le Bon, op. cit., pp. 17, 18, 53, 54.
42. E. Ray Lankester, inaugural address before British Association, Nature, Vol. 74, 1906, p. 325.
43. See Nature, Vol. 74, 1906, pp. 516-518.
44. Nature, Vol. 74, 1906, p. 323.
45. Nature, Vol. 68, 1903, p. 496.