Popular Science Monthly/Volume 58/March 1901/The Law of Substance


By Professor R. H. THURSTON,


IN Haeckel's new and remarkable monistic book, 'The Riddle of the Universe at the Close of the Nineteenth Century/ which has just been translated by Joseph McCabe and published by the Harpers, the accepted laws of the persistence of matter and the persistence of energy are enunciated and their unity insisted upon; the union constituting what is denominated 'The Law of Substance/ Substance, 'Stoff' in other words, being in fact what we are familiar with as matter, including all its physical attributes, as essential parts of it, as a person's character and his material parts are one and, failing either of those attributes, is no longer the same. It is only by these characteristics that we can recognize or define either the person or the molecule; without them, so far as we can see, there would be neither person nor matter.

The principle and the law of substance are unquestionably now incorporated into the scientific code permanently and positively; but the time of recognition and the dates of discovery of the two elements of that law are not, in the opinion of the writer, precisely as stated by Haeckel; the discoverers are not given credit by this author in correct proportion. He accords to Lavoisier the discovery of the persistence of matter and the proof of that principle, undoubtedly, as generally believed, correctly. He gives Robert Mayer (1842) credit for the discovery of the principle of the persistence of energy and assigns to Helmholtz (1847) its more general application.

It was, in fact, Benjamin Thompson (Count Rumford), the American philosopher, who, in 1796-97, experimentally proved the equivalence of the two forms of energy, thermal and dynamic. He read the paper describing his work in 1798, before the Royal Society of Great Britain; while Sir Humphry Davy confirmed it and added further proof immediately afterward.

It must be carefully noted that there are at least three quantities to be observed, studied and quantitatively measured: (1) substance or matter; (2) the forces which affect matter; (3) energy. Matter can perhaps be conceived of as destitute of any designated force and possibly even of any known attributes, such as the physical forces; forces can possibly be conceived apart from any specific matter; energy involves both matter and motion, and infers the action of forces in its production or variation. Nevertheless, our only method of acquiring a knowledge of matter is through the action of its attribute forces upon our senses; it is indeed possible that matter only exists through that quality which makes it the residence of the physical forces; it is extremely probable that all natural forces affect all matter and originate in matter.

There are just three corollaries to the general 'Law of Substance' the Law of Persistence of all Existences; these are:

1. The Law of the Persistence of Matter per se.
2. The Law of Persistence of Force as an Attribute of Matter.
3. The Law of Persistence of Energy, whether as affecting a mass of matter or in process of transfer or of transformation; affecting varying quantities and kinds of matter; passing from one quantity of matter to another; changing, in inverse direction, the quantity of matter affected and the velocity-component of the energy; the product of mass and mean velocity-square remaining constant for the whole universe.

The distinction between force and energy was not, in earlier times, very exactly observed; but it is easy to perceive in the context to the enunciation of either corollary to the fundamental law the fact that writers usually well understood the principle which they sought to state. It had, by Faraday's time, come to be well understood by many scientific men that matter is persistent, that its characteristic forces cling to it persistently and that energy is the product of forces and motion, and is consequent upon inertia.

The writer took occasion, in a paper read before the American Society of Civil Engineers (December 9, 1873), criticizing Professor Tait's 'Sketch of Thermodynamics/ his assignment to Sir Humphry Davy of a prior place and his depreciation of the work of Mayer, to show that Rumford is entitled to a larger credit than is ordinarily assigned him even by those who admit his first appearance in this line of investigation at the close of the eighteenth century. It is easy to show that, not only was Rumford the first to exhibit by experimental research the fact of the equivalence of thermal and dynamic energy, but that he was the first to establish with some degree of approximation their quantivalence. In fact, he secured data giving a much closer determination of the 'mechanical equivalent of heat' than did Joule, or any other investigator of later years up to the middle of the century; at which date, while an approximate value had been hit upon, so great was the variety of constants published that the real value was still exceedingly uncertain. Professor Tait, however, was the first to call attention to the fact that Rumford actually gave data sufficient to afford a basis for computation of the equivalent, but he made the resultant figure 940 foot-pounds, assuming the horse-power at 33,000 foot-pounds per minute, and failing to note the fact that the engineer's 'horse-power' is considerably larger than the power of the average horse.

Taking the generally accepted and fair mean value for the power of the animal, and accepting Rumford's statement that the work was that which could be readily performed 'by a single horse' the writer showed that the quantity of heat developed in Rumford's experiments, compared with the accepted datum, 25,920 foot-pounds per minute as the power of the horse, as given by Rankine, for the average case, or better, say 25,000 for the average Bavarian horse of the last century, we obtain as the 'mechanical equivalent' 783.8 foot-pounds, differing from 778, the accepted figure of Rowland and later authorities, by but six units, less than 1 per cent, of its own value and vastly nearer than any figures obtained up to our own time.

Thus, as the writer claimed in 1873, we may state the achievement of that great philosopher and engineer in the following terms:

1. Rumford was the first to prove experimentally the immateriality of heat.
2. He was the first to indicate and directly to prove it to be a form of energy; publishing his proof a year before Davy.
3. Rumford first, a half-century before Joule, determined by experimental research the quantivalence of thermal and dynamic energies, and secured data giving the value of the factor of equivalence with almost perfect accuracy.
4. He is entitled to the sole credit of the experimental discovery of the true nature of heat, of its equivalence with mechanical energy and its measure of quantivalence.

The work of Sir Humphry Davy was of great importance; but it was in confirmation of the deductions previously announced to the Royal Society by his contemporary and colleague, Rumford.

"Benjamin Thompson, of Concord, New Hampshire, commonly known as Count Rumford, the Bavarian, should be accorded a higher position and a nobler distinction than has yet been given him by writers on thermodynamics."[1]

Rumford, above all others, ancient or modern, is entitled to the credit of not only laying down an experimental foundation for the 'Law of Substance' and the principle of persistence of energy, but also for actually making it a physical, rather than as previously a metaphysical, topic; for proving the falsity of the older views of the nature and origin of heat in thermodynamic systems, for proving by direct test and experimental investigation the immateriality of heat and its real character as a 'mode of motion' as Tyndall called it, as a form of energy more properly. He furnished a method and means of estimating the 'mechanical equivalent of heat'; he originated by actual work of research a true statement of the principle of the quantivalence of the two forms of energy and, inferentially, of the quantivalent relations of all energies. He originated the now usual method of determining the quantivalence of heat and thermal and dynamical forms of energy by the storage of the heat of friction in a mass of water, and, by the churning of liquids, of similarly storing the heat of fluid-friction. He adopted the view that the energy developed in the animal system is the measure of a certain proportion of the stored energy of the food thus utilized. Thus he extended the principle of persistence to the organic world and to living creatures, opening the way to the final generalizations and conclusions of the enunciator of the so-called 'Law of Substance.'

Thus Rumford was the first to prove by experimental investigation the transformability of the energies, to exhibit the principle in its most important example and to derive, by physical research, the principle of the thermodynamic equivalence of energies and the fact of heat being simply a form of energy and a mode of motion of substance.

Mayer seems to have been the first to recognize a now well-understood fact: that, if we are to gain a more effective development of the energies, potential in our fuels, which are practically our only sources of commercially useful energy, we must find a way to transform the potential energy of chemical union directly into some other form than the thermal and by some other than the thermodynamic process. He says[2] that 'the evident wastes of the thermodynamic process as illustrated in our best steam engines justify us in seeking other methods of energytransformation,' more particularly by the transformation into motion of electricity obtained by chemical means.

Mayer was probably the first to write under the definite title 'The Mechanical Equivalent of Heat.'[3] He was the first to declare, in so many words: 'the vis viva of the universe is a constant quantity.'[4] He stated that 'the heat produced mechanically by the organism must bear an invariable quantitative relation to the work expended in producing it.'

This he deduced from his 'physiological theory of combustion.' He anticipates the idea of the permanence of the universe in its present general aspect by the suggestion that this redistribution of energy, 'degraded' by other phenomena, may be effected 'by the falling together of previously invisible double stars' or equivalent phenomena.[5] He finds by computation that the energy transformed through such collisions 'would considerably exceed that which an equal weight of matter could furnish by the most intense process of chemical action'—in other words: it would resolve the solid mass into its elementary atoms; which is precisely the idea now held by Haeckel and other contemporary men of science.

Mayer accepted the principle and, basing his computations on the then accepted values of the specific heat of air, determined an equally approximate mechanical equivalent. Joule followed, in 1845-49, and later, determining this equivalent by admirable direct experiment. English writers have sometimes insisted upon assigning all credit to the latter for this determination; but Tyndall is less insular in his attitude and frankly and cordially gives Mayer the credit to which he is undoubtedly entitled. Both are certainly to be credited with important original work, and the method of Mayer gives a more accurate and certain measure of the constant sought than did any of the earlier experiments of the English physicist, the more exact measures of specific heats as now known being employed. Had Mayer known of Regnault's work, or had that work been completed before Mayer attempted his computations, the latter would have obtained more accurate figures than Joule secured years afterward. It was only when Prof. Henry A. Rowland took up the task and performed his marvelously fine work that an acceptable valuation was secured.

Meantime, Helmholtz had accepted and applied the law of equivalence of the energies broadly, as holding in all physical phenomena; but he was distinctly anticipated by Grove, the English physicist, who in January, 1842, in a lecture before the London Institution, asserted that 'Heat, light, electricity, magnetism, motion and chemical affinity are all convertible material affections' and that 'all these affections are resolvable into one, namely motion.'[6] This thesis he enforced then and thenceforward continuously. In 1862, he summarized his work in a published study of 'The Correlation of the Physical Forces,' later reprinted by Youmans in his famous collection of similar papers of 1864. His paper concludes with an excellent bibliography, in which he shows the origin of the now unquestioned view of authority in the minds of the old Greeks, and its gradual establishment by observation, experience and, finally, by experiment in the nineteenth century.

Helmholtz's lecture 'On the Interaction of the Natural Forces' was delivered at Königsburg, in 1854; he at the time holding the professorship of physiology at that university. In this lecture he states his first ideas to have been published in a pamphlet, in 1847, 'On the Conservation of Force,'[7] in which he 'endeavored to ascertain all the relations between the different natural processes.' In his lecture of 1854, he credits earlier writers on the subject, in the following order: Carnot (1824), Mayer (1842), Colding (1843), Joule (1843), and states that he was awakened to this work by the last-named.

To the Carnot law, Helmholtz gives the following expression: 'Heat only when passing from a warmer to a colder body, and then only partially, can be converted into mechanical work.'

This is obviously no other than the essence of the principle as not only asserted, but actually proved, a quarter of a century before Carnot by Benjamin Thompson and Humphry Davy, by direct experiment, so far as it is an assertion of the convertibility of the two energies. Helmholtz acknowledges the indebtedness of the scientific world to Mayer, whose paper 'On the Forces of Inorganic Nature' had been printed in 1842, that 'On Organic Motion and Nutrition' in 1845, and that 'On Celestial Dynamics' in 1848; while his paper 'On the Mechanical Equivalent of Heat' was not published until 1851.[8]

Helmholtz concludes: 'Thus the thread which was spun in darkness by those who sought a perpetual motion has conducted us to a universal law of nature which radiates light into the distant nights of the beginning and to the end of the history of the universe.'

Dr. W. B. Carpenter, in a lecture before the Royal Society, published later in their Transactions for 1851, summarized the work in this field, to his date, under the title 'The Correlation of the Vital and Physical Forces,' and showed, probably for the first time in this field, the unity of the principle of equivalence of energies in organic and vital, as well as in inorganic and lifeless nature. He attributes to Dr. Mayer, of Heilbronn, the first annunciation of the great principle of 'Conservation of Force,' in its then broadest form, in his paper of 1845, already mentioned; while Carpenter considers his own paper of 1850 'On the Mutual Relations of the Vital Physical Forces, as the first announcement of the extension of the law beyond the latter class of phenomena into the range of vital energies. It is in his lecture on this subject that Carpenter states the fact, since recognized perhaps most explicitly, among contemporary writers, by Haeckel, that 'what the germ supplies is not the force but the directive agency.' 'The actual constructive force is supplied by heat.' Even 'the life of man, of any of the higher animals, consists in the manifestation of forces of various kinds, of which the organism is the instrument,' and, further: 'during the whole life of the animal, the organism is restoring to the world around it both the materials and the forces which it draws from it.'

"But there is this marked contrast between the two kingdoms of organic nature in their material and dynamic relations to the inorganic world: that while the vegetable is constantly engaged in raising its component materials from a lower plane to the higher, the animal, whilst raising one portion of these to a still higher level by the descent of another portion to a lower, ultimately lets down the whole of what the plant had raised; in so doing, however, giving back to the universe, in the form of heat and motion, the equivalent of the light and heat which the plant had taken from it."

Thus, as Tyndall later wrote: "As experimental contributors, Rumford, Davy, Faraday and Joule stand prominently forward; as theoretic writers (placing them alphabetically) we have Clausius, Helmholtz, Kirchoff, Mayer, Rankine, Thomson," and he distinguishes sharply between the two classes, as the world of science always must, without denying to either credit for that practical genius which makes the work of the one party useful or for that genius of foresight and insight which often leads the other far in advance of the investigator, giving quantitative values to relations thus earlier recognized.

Thus, also, the ideas now taking expression as scientific statements of nature's laws originated in a distant age, grew into form with experience and observation and restricted experimental research, until, with the opening of the XIXth century, and with the enormous development of scientific method and of experimental systems, and with the production in marvelous exactness and perfection of every form of instrument of research, quantities came to be exactly measured and the law of persistence of energy could be stated positively and quantitatively.

When the idea of equivalence of thermal and dynamic energies and of the formation of a thermodynamic science had come to be familiar to the leaders of scientific thought, the extension of the idea to embrace all the physical forces and energies was a simple and inevitable matter. The comprehension of all physical energies within the stated law naturally and promptly, and just as inevitably, led to the suggestion of the extension of the law to the so-called vital energies and forces and to its enunciation in that general form which permitted its application by Carpenter to the vital forces and its introduction by the biologists into their department of life and work. It was in the extension of such apparently obvious deductions to the seeming limit, and without a thought of the fact having originality at the time, that the writer, in the Vice-President's address before the American Association for the Advancement of Science, at St. Louis, in 1878, made that extension in an enunciation of the principle now called by Haeckel the 'Law of Substance.'[9] The deduction from all previous experience, and the inference from all experimental work to that date, seemed entirely obvious. But, so far as the writer is aware, this expression of the 'Law of Substance,' thus enunciated in August, 1878, is unanticipated. It was then stated as follows:[10]

"The facts revealed by the researches of Rumford, Davy and Joule have been grouped and systematically united by Rankine, Thomson, Clausius and other scarcely less eminent men and the science of thermodynamics, which has been thus created, has been applied and put to the proof by Hirn and other distinguished engineers of our own time. Finally, it has now become evident that this last is but another branch of the universal science of energetics, which governs all effective forces in all departments of science. The man is still to be found who is to combine all the facts of this latest and most comprehensive of all sciences into one consistent and symmetrical whole and to illustrate its applications in all methods of exhibition of kinetic energy.


"The grand principle which we are just beginning to indistinctly perceive, and to recognize as underlying every branch of knowledge and as forming the foundation of all positive science, seems, when stated, to be simply an axiom. The Scriptural declaration that the world shall endure until its Maker shall decree its destruction by Omnipotence is but a statement of a principle which is more and more generally admitted as a scientific truth, viz.:

"The two products of creation, matter and force, and the fruit of their union, energy, are indestructible.

"The grand underlying basis of all science is found in the principle:

"All that has been created by infinite power—matter and its attribute, force, and all energy—is indestructible by finite power and shall continue to exist, so long as the hand of the Creator is withheld from its destruction."

"This 'Law of Substance,' as Haeckel proposes to call it, the writer then stated, has "been admitted almost from the time of Lavoisier, so far as it affects matter; it has been admitted as applicable to physical energies since the doctrine of the correlation of forces and of the persistence of energy became accepted by men of science and we are gradually progressing toward the establishment of a Law of Persistence of all Existence, whether of matter, of force and energy, or of organic vitality, and perhaps even to its extension until it includes intellectual and soul-life."

"The truths of science are thus coming into evident accord with those doctrines of religious belief which are common to all creeds. We are, however, as far as ever from the determination of the question whether those higher forms of force and energy have quantivalent relations and intertransformability; although a belief that mind and matter have a certain identity, and that in matter can be discerned 'the promise and potency of all terrestrial life/ has been avowed, explicitly or implicitly, by more than one great thinker when wandering into the realms of speculation."

In this, Tyndall long anticipated our contemporary writers.[11] Lavoisier showed to the satisfaction of the scientific men of his time that matter is indestructible, whatever the apparent result of chemical action. Faraday, and probably many among his predecessors, recognized that the forces are indestructible, and that great investigator wrote:

"To admit that force may be destructible, or can altogether disappear, would be to admit that matter could be uncreated; for we know matter only by its forces."[12]

Liebig fully recognized the distinction between the proper use, of the term, force and energy, and usually called the latter 'power' as when he says:

"Man by food not only maintains the perfect structure of the body, but he daily inlays a store of power and heat, derived in the first instance from the sun. This power and heat, latent for a time, reappears and again becomes active when the living structures are resolved by the vital processes into their original elements."[13]

Carpenter clearly saw these distinctions and recognized the nature of energy, as distinguished from force, when, in his discussion of the action of the vital forces, he asserted:

"What the germ really supplies is not the force but the directive agency; thus rather resembling the control exercised by the superintendent builder, who is charged with working out the designs of the architect, than the bodily force of the workmen who labor under his guidance in the construction of the fabric."[14]

Carpenter says explicitly:

"Hence we seem justified in affirming that the correlation between heat and the organizing forces of plants is not less intimate than that which exists between heat and motion." He includes both animal and vegetable vitality in his generalization.

"The life of man, or of any of the higher animals, essentially consists in the manifestation of forces of various kinds, of which the organism is the instrument."

All organic life involves the direction of nature's forces and their utilization by direction of the energies; but this striking and important distinction is observed, as Carpenter first definitely asserted: The animal employs energy derived by the disintegration of vegetable growth to its will-directed, and to its internal automatic, work; while the vegetable directs the energy of the sun's rays and of chemical action to the building up of new organic matter into its life-forms. A cycle thus transfers and transforms energy radiated to the earth from the sun, building up the vegetable, sacrificing the structure in the building of the animal organism, breaking down the animal structure again, and setting free the circling energy to continue its progress along other paths into other organic matter, or elsewhere, as directing agencies may compel.

Thus, in all nature and in all manifestations of natural law and of motion, general experience has satisfied us that matter is persistent, that it is endowed with inalienable properties which include the so-called physical forces, similarly persistent in their character and methods of action and their intensities, and that energy, a property of matter in motion, is also persistent, but not also permanently affecting any given mass; its total quantity is invariable, but it may be distributed indefinitely, transferred in any manner and transformed to any extent, irrespective of other than quantitative measures of matter affected. Matter not only permanently retains its characteristic forces, but, reciprocally, the forces permanently require and maintain matter as their residence. No exception to this constancy of union of matter and forces is yet known, and the only question now remaining to be fully answered is: How far may such relations be traced into the more intangible realms of nature and life and consciousness.

Herbert Spencer has stated the fundamental idea of science in this field most concisely, accurately and clearly. He says in 'First Principles': "We cannot go on merging derivative truths in these wider truths from which they are derived without reaching at last a wider truth which can be merged in no other or derived from no other. And whoever contemplates the relation in which it stands to the truths of science in general will see that this truth, transcending demonstration, is the Persistence of Force." Indeed, Faraday had already, years before, asserted this law to be the highest that our faculties can appreciate in physical science. In fact, as we may perhaps still more strongly put it: The Law of the Persistence of Substance, including its every attribute, must necessarily underlie every permanent existence and the universe itself.

The number of world-riddles, as Haeckel says, is diminishing rapidly, and our scientific knowledge has come to be so far-reaching that if we cannot resolve every minor problem of the universe, we have at least gone far toward the solution of the mightiest among the larger questions. One 'comprehensive question/ as he calls it, remains: What is the foundation of the 'Law of Substance,' the law of the persistence of matter and its attribute, force?

"What is the real character of this mighty world-wonder that the realistic scientist calls Nature or the Universe, that the idealist philosopher calls Substance or the Cosmos, what the pious believer calls God?"

"We must admit that we know as little of its essence, as did the ancients or the philosophers of the later centuries, up to our own. The mystery deepens as we probe it; there remains beneath all and behind all an apparently 'unknowable,' to-day, as in all earlier times." Haeckel throws no new light upon this eternal sphinx-life. He claims that the eternity of matter, with its inalienable eternity of unchanging attributes, its eternally persistent motion and energy, means eternal life of the universe, with never-ending renewal of such movements as we are now conscious of and in this probably all men of science are ready to agree with him. But he goes on to assert that the necessary conclusion is the destruction of 'the three central dogmas of the dualistic philosophy—the personality of God, the immortality of the soul and the freedom of the will.' He finds few philosophers willing to go with him to the end of his logic and thinks that 'consecutive thought is a rare phenomenon in nature.' The majority of philosophers are desirous of clinging to the old beliefs on the one hand, while taking hold of the monism of the newer time on the other, seeking to ride both the differently moving steeds and usually ending by dropping from the younger at the limit of their powers of holding on.

This has undoubtedly been true in the past and will probably remain true in the future and as long as man retains his apparently eternal and immortal convictions relating to a higher power; but, admitting Haeckel's accusation and going with him to the ultimate of his deduced facts and law, it seems extremely probable that, arrived at its end, they will all be found much in the position of Haeckel himself, confronting the deduction of Clausius and Lord Kelvin, and will still ask the unanswerable question:

What lies beyond? Who or What inaugurated this eternity? What or Who originated matter? What or Who marked the limits of the universe? If limitless: Who and What filled it with matter and motion and life?

There will still within the soul of every thinking human being remain the conviction, apparently implanted at the origin of things, of some real 'First Cause/ of some necessary beginning of our time, space and life, and a conviction that what we call eternity affords time and the universe space for all the evolution of higher life that imperfect human nature aspires to. It will be admitted that, as Goethe says:

'By eternal laws of Iron Rules,
Must all fulfil the cycle of their destiny'

All can see that

'The times are changed, old systems fall,
And new life o'er their ruins dawns;'

yet, as in all past times, new interpretations and adjustments of the beliefs and the creeds of the fathers will be found to reconcile fundamental principles in religion and in morals with the older inspirations and the newer readings of the Book of Nature, and we may unquestionably hope that, in the future as in the past, the newer readings will tend toward evolution of higher thought, nobler life, more perfectly ideal and spiritual philosophy. We may all go with Haeckel and the greatest interpreters of the laws of Nature, and yet may find it possible to look beyond the limits of things seen into 'The Unseen Universe' with no loss of the spiritual.

Haeckel is one of the few, even among scientific men, who accept the necessary, or apparently necessary, conclusions coming of his logic to the very extremity and, in this case, he finds them carrying him to the deduction that there can be no immortal life of the individual soul. Whether this conclusion must follow or not, he is more far-reaching in his deductions relating to physical phenomena, as consequences of the 'Law of Substance,' than any among his predecessors; for he accepts the conclusion that there cannot be a dead eternity and that there must be some return from that swing of the pendulum which, with Sir William Thomson (now Lord Kelvin), left a cold and still universe to eternal death. This he finds absurd and admits the probability that the backward swing will come, during the eternities, through the occasional collision of suns, suns and planets, planet with planet, of binary systems and meteoric masses and star-dust, such as have been actually, not infrequently, seen during our own historic period, by the astronomer at his telescope, and by his ancestor, the astrologer, and even occasionally by the unobservant people of all times. Such a collision is sufficient in its development of thermal energy to reduce the colliding bodies into vapor and to disperse it throughout space in nebula and meteoric matter, and to renew the cycle.

As Haeckel says: The law of the persistence of force proves, also, that the idea of a 'perpetuum mobile' is just as applicable to, and as significant for, the cosmos as a whole, as it is impossible for the isolated action of any part of it. Hence the theory of 'entropy' is likewise untenable. It is not the fact that the 'end of the world' is to come as supposed in the theories of entropy and with the degradation of energy to a uniform and unchanging lifelessness. Sooner or later—and time is nothing, 'a thousand years are but as a day'—sooner or later, the collection of masses will return mass-energy to the form of molecular and atomic energy, now here, now there, throughout the universe, and the round of eternities will be unceasing. "The eternal drama begins afresh—the rotating mass, the condensation of its parts, the formation of new meteorites, their combination into larger bodies, and so on."[15]

  1. Transactions of the American Society of Civil Engineers, 1873. 'Note relating to Rumford's Determination of the Mechanical Equivalent of Heat.'—Thurston.
  2. Forces of Inorganic Nature; 'Liebig's Journal' 1842.
  3. 'The Mechanical Equivalent of Heat,' 1851.
  4. 'Celestial Dynamics,' 1848.
  5. 'The Mechanical Equivalent of Heat,' 1851.
  6. Perhaps the best presentation of the work of the earlier men of science, recognizing these great and fundamental truths, is that of Prof. Edward L. Youmans, the founder of the Popular Science Monthly and one of the most broad-minded and far-seeing men of his time, who, in his 'Correlation and Conservation of Forces,' published by the Appletons in 1865, brought together the records of the great pioneers in this evolution of the scientific basis of all natural science, including the papers of Grove, Helmholtz, Mayer, Faraday, Liebig and Carpenter.
  7. It will be noted that it was very usual among these earlier writers to employ 'force' synonymously with 'energy,' as we now define the latter.
  8. All these papers may be found in Youman's collection, already alluded to.
  9. At that time there were two Vice-Presidents in the organization of that Association, both of whom were expected, annually, to present addresses before the whole Association at special meetings held for that purpose.
  10. Proc. A. A. A. S., Twenty-seventh Meeting, at St. Louis, Mo., 1878; Sec. A, Mathematics, Physics and Chemistry; Address of the Vice-President, p. 43. Vide also Thurston's 'Manual of the Steam Engine,' Vol. L, 1st Ed., 1891, Chap. III., p. 241.
  11. See his 'Heat Considered as a Mode of Motion,' N. Y., D. Appleton & Co., 1864, for an admirable statement of this point and for his splendid championage of Mayer.
  12. 'The Conservation of Force.'
  13. 'The Connection and Equivalence of Force.'
  14. 'The Correlation of Vital and Physical Forces.'
  15. 'The Riddle of Existence'; pp. 239-248.