1 November 1866


by Fitz Hugh Ludlow

NOT wishing to deter from the perusal of this article any fastidions person whom Fourth of July orations may have tired of spread-eagleism, nor by the patriotic sound of its title to beguile any enthusiastic fellow-countryman into attacking a treatise for whose matter he has no real predilection, I hasten to say that my heading signifies the vital and essential unity, not of all the States, but of all the physical forces which operate in nature. My title invites the reader to a brief popular talk upon the subject which is now universally interesting scientific minds throughout Europe and America under the name of "Correlation;" a subject which, indeed, possesses so many elements of interest for any active intellect, whether trained or not in the abstruser studies technically known as science, that, unless I do it great injustice by my treatment, every reader whose education enables him to enjoy the other portions of this periodical will finish the article with the feeling of having had opened to him a new field for his thought as limitless and as noble as those trodden by the feet of Milton and of Dante.

For the elaboration of the idea of the Correlation, or what is equivalent, the basal unity of all the forces of nature, all the sciences were necessary; nevertheless, we who are not great specialists or great mathematicians may stand outside the developed structure which has been laid well nigh to the topmost stone by the combined labors of such scholars, and admire its sublime proportions, from the earth beneath our feet to the highest range of vision -- its still sublimer suggestions where the line grows vaguer and the pinnacles begin climbing into infinity. "Other men have labored," and we "enter into the fruits of their labors;" and, in this case, it is no arrogance to say that we shall enjoy the completed fabric, despite our inferiority in the erudite technicalities of abstract science, even more than any one of the builders, unless to his erudition he shall have added the spirit of the poet, the artist and the seer. Many a man from whose face the ever young stars win back no thankful radiance of delight feels a savage pleasure, as he sits by his study-lamp, in grubbing out, like a detective of the universe, the trail of all their movements; and in bragging, like Cicero to Catiline, that he knows where they were last night, where the night previous -- in baleful prophecies of the exact time when their "glim will be doused" by an eclipse. Many a philosopher, insensible to the exquisite grace of swallow flights and the majestic plunge of cataracts, took the first prize in his junior year for the best discussion of their parabolas. And the sole delight which ever reaches the beauty-proof soul of many a savant from the clouds of gold-fringed crimson floating above the kingly death-bed of the sun, is the grim satisfaction he finds in knowing that, gather or attennate as they may, they cannot elude the pneumatic formula for wind-driven bodies or refuse obedience to Marriotte's law. The true man of science begins with formulas, but he does not end there. The full possession of science demands a heart not less than brains. Never was the love of beauty a more vital supplement to the love of truth than in the appreciation of this particular subject of science -- the oneness in essence of all nature's energies and their capacity for endless mutual transformation.

Man is born into a tangle of forces. The threads of the skein are innumerable, and he perceives no continuity between them. Long after he has emerged from the fetish-worshipping period of his development, he perseveres in isolating every new phenomenon of the universe, ascribes to it a separate nature and gives it a distinct name. Though he no longer personalizes the forces, he continues to specialize them. No longer is there a soul in his amber, but on the behavior of the amber he bestows a title of its own, and electricity is conceived of as an utterly independent existence. His planet no longer has a Daimon for its charioteer, but the substituted conception of a resultant of forces by which he explains, is more complicated than the Daimon, without having attained any higher degree of universality. The heat that warms him and the cold that freezes; the light which illuminates and the lightning which appalls; the impetus by which his grain grows and that which in the swinging cradle cuts it down; every natural force working change of state or change of position has an essential difference in his eyes and a separate name in his vocabulary.

At a subsequent stage of his development, he attains the notion of a continuity between the surrounding forces, and leaps at once to the conclusion that it follows an ascending series. Then ensues one of those desperate periods in the history of intellectual progress, characterized by investigation for a Frst Cause. The Sages turn the tangled skein of physical forces, peering eagerly to find the ravelling end -- if but once they can get that upon their reel, think they, the matter resolves itself into a mere job of logical winding, and at the other end they shall find their Creator. But the report of the ages is that no such clue can be discovered; that though cause be tracked into cause forever, no tracking can reach the All-Causing and the Causeless; that no addition of finites can ever sum up into the Infinite; that God, like his kingdom, "cometh not with observation, but is within" us; that their tower of causes is a Babel which will not reach unto the heavens; to return to the original figure, that after all their turning and twisting, natural science can find no break in nature's skein. Why does the animal live? Because he contains an oxidizing apparatus. Why does the plant live? Because it contains a deoxidizing one. The waste of the one flows over into the want of the other, and the sequence of their vital processes leads us to the origination of neither, but to the reciprocal maintenance of both.

Neither origination nor annihilation of force having ever come within the field of human experience, the best thinkers of to-day have wisely accepted the conclusion to leave to the heart and the religion of mankind all considerations of a First Cause, as necessarily beyond the province of a philosophy which deals with an endless chain of causes running into each other. Instead of limiting or degrading science, this conclusion really presents her with a freer field and more unhampered arms. Knowing what she can do, and acknowledging what she cannot, she does the former all the better for having entrusted to religion all functions connected with the latter. To Job's question, "Who by searching can find out God?" she has frankly answered, "Not I;" and in this honest reply has deserved of all the good full privilege of research, free thought and plain enunciation upon the subjects of her special realm. To her now belongs the field of proof; to religion, the knowledge higher than any physical experiment or logical deduction of realities, grander than all things provable, together with their application as stimulus and solace in the vital exigencies of man's immortal career.

Out of the vast mess of experiments made by science with the newly received convictions of her true purpose have come two well-established and inter-depending doctrines, known severally as the Persistence of Force and the Correlation of the Forces. Together they amount to the statement that experience reveals no break in the continuity of force, but a perpetual translation of special forces into each other. As a deduction from the continuity of forces, there is rapidly gaining ground among scientific men a conviction of the unity of all force, heat, affinity, molecular and massive motions of all kinds being but the phenomena, of this single existence as manifested in varying relations to space and time. We might be allowed to carry deduction one step further, and assert that because our only cognitions of matter are cognitions of force, matter in the scientific sense is force. I believe this probable, but it is not in the path of the present article.

Leaving to the reviewer of Herbert Spencer the delightful task of considering the persistence of force in the light of the proofs and illustrations by that clear thinker, let us devote our attention to the Correlation of Forces, and the investigations whereby it has been elucidated. This subject is put in its dearest light and to its most exhaustive analysis by the little volume into which Professor Youmans has gathered the prominent treatises upon Correlation, written in Europe during the last quarter of a century by six of the most eminent investigators in this scientific field, with an introduction from the editor's own pen, which is one of the most valuable portions of the work.*

Science is cosmopolitan, but there are several reasons why an American must take a special pride in this book.

Primarily, because it is the first collection which has been made of the treatises composing it, and the only one likely to be made in the English language. Each treatise was originally published as an independent monograph. The difficulty of persuading the several British publishers to act in concert has thus far proved an insuperable obstacle to the collection of the pamphlets in a single volume on the other side of the water. No such obstacle existing in this country, we may congratulate ourselves on possessing the only portable edition of the most valuable researches made in modern physics.

In the second place, it clearly establishes the fact that the grand impetus in the direction whither all modern research is most profitably tending, was originally given by an American.

Monopoly can rarely be claimed in the discoveries of science. As with the Calculus, so with Correlation -- the idea was simultaneously conceived by several minds. But Prof. Youmans has conclusively shown Benjamin Thompson, Count Rumford, our own countryman, to be the first philosopher who expressed absolute convictions upon the subject of correlated or translated forces, and established them upon a basis of experiments at all approaching our modern requisitions in delicacy, magnitude or rigor of interpretation. We may almost assert that Rumford did for the doctrine of force in general an equivalent service to that which the understanding of chemical forces owes Dalton, Lavoisier, and their compeers. He cleared experiment of all avoidable mysteries; corrected all unnecessary aberrations, and stopped all discoverable leakages. His Munich experiments upon the nature of heat did away with slovenliness in all such researches forever. The time had come when chemists could no longer account for every loss of weight in their combustions by the convenient excuse that something had been "burned up," and when dynamists in all departments must give strict account for every equivalent of force passing through their tests. Count Rumford was the first and most conspicuous champion of the doctrine that heat is a mode of motion; and his bold disavowal, both on à priori and inductive grounds, of the old theory of a caloric fluid, may be regarded as the opening protest in our modern era of scientific conscientiousness. It is in the highest degree creditable to Professor Tyndall, whose pen Professor Youmans justly calls "chivalric," that in his late work on "Heat Considered as a Mode of Motion," he has paid due honors to our compatriot as the chief original investigator of that subject.

Among the earlier experimenters in the field of Correlation should be mentioned with honor the names of Joule, Tyndall, the brothers Thompson, Clausius, Colding, Rankine, Holtzmann, Seguin. To Professor Grove, however, we must concede the honor of occupying the relation of organizer to the ideas which all of these had in common with him. Each contributed special researches to the establishment of a law which Grove was the first to systematize in all its phenomenal applications.

Helmholtz and Mayer follow Grove in Professor Youmans' book; the former with a treetise of thirty-five pages on the "Interaction of Natural Forces;" and the latter with three treatises severally devoted to "The Forces of Inorganic Nature," "Celestial Dynamics," and "The Mechanical Equivalent of Heat."

Grove takes a brave step toward the doctrine of the unity of force when he dismisses the hypothesis of an all-pervading ether, and explains the action of light on the plain principle of a universal diffusion of matter throughout space -- generically identical with that at the earth's surface but in a state of indefinite rarefaction. His abundant excuse for the abandonment of ether is that there is no occasion for it. Why make distinctions where none exist? If we call the perceptible nebula ponderable matter, what is to prevent the existence throughout the universe of ponderable matter so comminuted as to be imperceptible? Grove still further fortifies his view by setting forth the reactions which must ensue during the passage of a ray of light through a porous body, and the inconceivability of propagating such an impulse at all in an ether whose continuity was everywhere broken by particles of ponderable matter. His illustration of this view by the interference which wave-motion would encounter in a thickly studded archipelago is very happy indeed.

Grove further simplifies physics by denying a separate place to the force of gravitation, and is further inclined to agree with Mosotti in the opinion that whatever it be, cohesive attraction is one with it. He advances another step by identifying both of these with mechanical force, through the similarity of their behavior in passing from the dynamic to the static condition.

Perhaps the largest and noblest idea which has lately been expressed in science, is the hypothesis which Grove enunciates and evidently favors, to the effect that no solution of continuity anywhere exists in the atmospheres of the universe; that a chemical combination in Uranus may eventually effect transformations in matter at Philadelpbia; that the electrosphere of a fixed star is incapable of boundary, and that a positive current sweeping down from Alpha Lyrae may affect the position of the terrestrial poles and modify the variations of the compass over every foot of our globe's surface. That the heat of the solar system is not isolated, and that the perpetual compensatory motions of universal matter preserve the total amount of heat eternally the same throughout entire space. This bold creed comes just in time for the consolation of those who have adopted despondent views of the universe through Mr. W. Thompson's mathematical (and by the limited theory irrefutable) proof that it is tending to an eternal stoic period of absolute cold, rest, silence and darkness. It would be a pleasing task, which I wish we had time for, to trace the poetic suggestions arising from this view of Grove's. It means a universal stellar brotherhood, each feeling every best of the pulse of all -- all interacting with each by a stupendous nervous system of allotropic forces. It is the science corresponding to Mrs. Browning's poetry, where she says:

Each creature holds an insular point in space;
Yet what man stirs a finger, breathes a sound,
But all the multitudinous beings round
In all the countless world, with time and place
For their conditions, down to the central base,
Thrill, haply, in vibration and rebound,
Life answering life across the vast profound,
In full antiphony, by a common grace?
I think this sudden joyaunce which illumes
A child's mouth sleeping, unawares may run
From some soul newly loosened from earth's tombs.
I think this passionate sigh, which half begun,
I stifle back, may reach and stir the plumes
Of God's calm angel standing in the sun."

The wonderful woman who wrote this mighty sonnet was one of the greatest among original correlators, though unconscious of the fact. Had she written the lines as a text to "Grove's Treatise," she could have embodied its whole spirit, and the spirit of all correlatiou, no better than she has done under mere inspiration of her genius.

Mayer's researches upon the subject of heat have been depreciated by some English writers with the mistaken notion of adding importance to those of Dr. Joule. Both these philosophers pursued the same end, and when in certain places we correct Mayer's calculations by substituting for his formula an improved one, not attainable when he wrote, his results and Joule's are found practically identical. Mayer's mathematical perceptions are immensely vivid. They resemble intuitions. It would be interesting to stand inside the man's mind and see how he looks at a formula. It is no skeleton to him. The dry bones of Km, II and x2 stand up in his valley of vision; the sinews and flesh come upon them; he prophesies and they live. Grim Surds unbosom to him. The sphinx of calculus has whispered in his ear. The furthest fixed star entrusts to him the direction of its orbit, unaware that in that simple statement it is betraying its whole past history and its present climate. He is the loving detective of the heavens -- and the skill with which he "works up" a clue has no equal in the police force of the world.

It is impossible to condense Mayer's arguments for the purposes of a magazine article. They are already as compact as could be understood by any scientific amateur. But the results which follow upon his irresistible logic are happily presentable, and some of them we append.

He shows that the heat which the earth receives each hour from the sun would suffice to raise 300 cubic miles of ice-water to the boiling point. That this vast quantity of heat is only one twenty-three hundred millionth of the entire solar radiation; whence it follows that the sun hourly gives forth sufficient heat to raise to the boiling point seven hundred thousand million cubic miles of ice-water.

As a further aid to the realization of the sun's heat, we may appropriately call in the illustration used by Herschel in the last edition of his astronomy, to the following effect:

If we consider the sun's heat all gathered into a single spot upon its surface, and fire against this spot with the speed of light (200,000 miles per second) an indefinitely long cylinder of ice forty-five miles in diameter, it will be melted as fast as it strikes, yet the sun's temperature will not be lowered a single degree!

Assuming the sun's source of heat altogether internal and its capacity for heat equal to that of a mass of water of equal volume, the sun's temperature must annually decrease 1.8 degrees C., and its loss during the 5,000 historic pears of our planet mould have amounted to 9,000 degrees C.

No such secular decrease appears in history. All recorded observation from the earliest times reveals the solar heat received by the earth as a practically constant quantity. The sun's independent store of heat must be constantly reënforced by some force acting ab extra. Mayer asks whether the restoring agency be a chemical process, and answers that if, taking the most favorable assumption, the entire solar mass were one lump of coal, its combustion would be able to sustain the present expenditure of light and heat for but forty-six centuries. We have records of such expenditure for a longer period than that, and being neither in darkness nor ice, are ourselves a reductio ad absurdum for the chemical hypothesis.

But again: can the re-generation of solar heat be accounted for by the sun's axial rotation? The sun rotates only four times faster than the earth, yet at the least calculation is twenty-three hundred million times hotter; while neither light nor heat is perceptibly generated by the rotation of Jupiter, six times, and of the outer ring of Saturn, ten times faster than a point on the solar equator. Here appears that simple symbol from which Mayer extracts so much. From the relations of Km (the unit measure which in Meyer's discussions correspouds to Joule's foot-pound), he deduces the exact heat-effect of the sun's rotation, and finds that it would cover the sun's present expenditure for only 183 years.

Neither affinities nor friction accounting for the persistence of the sun's heat, Mayer proceeds to explain it by the perpetual fall into the sun of comets, asteroids, meteorites, and other wandering masses of cosmical matter. From the secular decrease in the diameter of the orbit described by such bodies, and by a series of simple erperiments which a child could understand, he shows that the inevitable fate of these bodies is sepulture in the sun. His calculations on the subject of the quantity of heat produced by this fall into the sun of cosmical masses have an absolute artistic beauty. They delight as a statue delights, or like a noble façade of marble. The steps without the processes of the reasoning are these.

The maximum velocity of bodies falling to the earth from any height within its sphere of attraction is 11,183 metres per second.

But "the solar radius is 112.05 times that of the earth, and the velocity produced by gravity upon the sun's surface is 28.36 times greater than the same velocity on the surface of our globe; the greatest velocity, therefore, which a body could obtain in conseqence of the solar attraction ... is equal to 630,400 metres, or 85 geographical miles, in one second." The minimum he afterward shows to be sixty such miles.

By expanding one of his simple formulas, which expresses in functions of the striking body's velocity the degree of best generated by its percussion, Mayer next shows that the caloric effect of an asteroid stopped by the sun's surface must amount to between 27 1/2 and 55 millions of centrigrade degrees of heat. "An asteroid, therefore, by its fall into the sun develops from 4,600 to 9,200 times as much heat as would be generated by the combustion of an equal mass of coal." Dulong's experiments give 3,850 degrees C. as the heat produced by the combustion of hydrogen, and "we find the heat developed by the asteroid to be from 7,000 to 15,000 times greater."

Mayer further pursues his idea in the following picturesque deductions: "The surface of the sun measures 115,000 millions of square miles or 6 1/3 trillions of square metres; the mass of matter which, in the shape of asteroids, falls into the sun every minute is from 94,000 to 188,000 billions of kilogrammes; one square metre of solar surface, therefore, receives on an average from 15 to 30 grammes of matter per minute.

"To compare this process with a terrestrial phenomenon, a gentle rain may be considered which sends down in one hour a layer of water one millimetre in thickness; this amounts on a square metre to 17 grammes per minute."

We have now to ask what becomes of all this matter. After compensating for the sun's loss by radiation, is there any surplus of it which goes to increase the sun's weight? Mayer's answer is so compact that we must be excused for quoting him once more:

"The weight of the sun is 2.1 quintillions, and the weight of the cosmical matter annually arriving at the sun stands to the above as 1 to from 21 to 42 millions. Such an augmentation of the weight of the sun ought to shorten the sidereal year from .... 3/8 to 3/4 of a second.

"The observations of astronomers do not agree with this conclusion; we must, therefore, fall back on the theory .... which assumes that the sun, like the ocean, is constantly losing and receiving equal quantities of matter. This harmonizes with the supposition that the VIS VIVA of the universe is a constant quantity."

The italics are our own. This assertion is the height of the great argument. Mayer has climbed to the centre where the correlation of all physical forces may most naturally be looked for. If we arrange all the forces under two categories -- one that of massive, the other that of molecular motion; the one operating at indefinitely great distances between aggregations of matter indefinitely large -- the other at indefinitely small distances between particles of matter indefinitely small; the former perceptible as motion in the popular sense; the latter never appearing as such, unless it undergoes translation by resistance to its original mode of action, we shall then have within the former list all the forces of mechanical momentum, including what Grove thinks to be the unnecessarily distinguished form of gravitation, while chemical affinity, light, heat, electricity, magnetism and every recondite force likely to be discovered hereafter (the massive forces being obvious to the rudest tests from the beginning), fall into the second division.

The first division evidently finds its most natural correlation at the centre of our system; the velocity and direction of its forces being constantly expressed in terms of their relation to the sun's weight. This division is correlated with the second in many ways to which we have already referred -- but especially by the direct equivalence between mechanical motion and the amount of interstitial expansion appearing as heat in bodies which have extinguished such motion on violent impact.

Thus, there is not a single dynamic mode or agent which we cannot express in solar terms, by availing ourselves of their correlative connections in ways more or less direct, and the sun becomes the grand correlator of our system. Indeed, with our present scientific illumination, we shall be much more correct in calling him that, than if we entitled him the source of cosmical energy. In such a series of perpetual exchanges between the centre and the periphery as is going on in the tremendous bombardment which the sun suffers from asteroids and his resulting radiation of heat into space, source may be assumed anywhere within the sphere of his attraction. The point between Jupiter and Saturn, where the secular shortening of its orbit's diameter begins to be perceptible in any asteroid on its gradual but accelerating way to sepulture in the sun, may be called the source of our heat as logically as that fiery grave itself.

The function of the sun is, therefore, to equilibrate the cosmical forces. It is, in this view, the fly-wheel which steadies the engine of our system. Or, it is the counter across which all the dynamic agencies effect their exchanges. Or, again, it may be compared to a heart, viewed according to the ingenious Hypothesis of Professor Draper, not as a pump (the osmotic action of the tissues in his opinion abundantly accounting for circulation), but an elastic reservoir in which all the propulsions of the blood are modified and equalized.

To Mayer's interesting use of the new views in the discussion of tidal motion -- to his almost axiomatic explanation by tidal resistance of the fact that the terrestrial day has not shortened during the historic period, although the vis viva of its rotation, independently considered, must be receiving constant increment as its diameter lessens by the devection of the earth's internal heat, and to the treatise upon the mechanical equivalent of heat, we cannot here do justice; and as little to Professor Faraday, who follows Mayer in a tract of twenty-three pages, entitled, with its author's habitual modesty, "Some Thoughts upon the Conservation of Force." To the other treatises in this volume: by Liebeg, on the "Connection and Equivalent of Forces," and by Dr. Carpenter, on the "Correlation of the Physical and Vital Forces," we can do no more than allude in connection with this subject. Though the monograph of Liebig is rather a sketch of the field in which general scientific thought is working than a collection of views original with himself, it is to be remembered that he was the earliest in that field to enunciate for organisms the doctrine "ex nihil, nihil fit," and to show that the loftiest phenomena of the brain no less than the elementary motions of inorganic matter demand a prior force with which they are in relations of equivalence.

We may also include among those whose researches have contributed in America to the study of Correlation, Profcssor Joseph Le Conte, Professor Henry, of the Smithsonian, and Professor W. A. Norton, of Yale. The paper read by Professor Le Conte before the American Association for the Advancement of Science, at its Springfield meeting, in 1859, may be regarded as the foremost step which has been taken toward a complete understanding of the relations between the organic and inorganic world. The profound researches and reasonings of Professor Henry are known to every expert in the higher mathematics of physical philosophy. Professor Norton has been for some time engaged in a work upon molecular physics, wherein he undertakes the gigantic task of systematizing and formulating all the laws and relations of ultimate particles -- equivalent to laying the base for a pyramid of knowledge coextensive with the whole material universe.

Here let us part from our subject as from the newly opened door of some vast temple, conceive that we have only looked, not entered in. Broken by massive mullions end stained by tinted panes, light enough still breaks through to show us that the fabric is continuous, block firmly keyed to block, rafter locking in with rafter. Nothing hangs suspended upon vacancy; every portion passes cleanly into every adjoining portion, and we say of the structure not "this is so many beams of oak; so many pieces of stone; so many pounds of paint; so many days' work of carving; so many leaves of gilding" -- but "this is a temple." In the light of the doctrine of the Correlation of Forces, the vast energies and protean forms of the universe for the first time attain intelligible organization, plan and unity.

Thus much we can pronounce, but grander knowledge and delights remain for those of us who may hereafter enter the temple and those who shall enter it after us. Of such it may be the privilege to correlate soul and body; the builder and the built; the creative genius and the matter which it shapes; the mind's world of perceplion and the physical world of touch. Though the highest mind in vain be sought along the ladder of logic, it may yet be given us to develop some conclusive law which shall explain the relations of all existence, for the thought of tho age tends toward a belief in the primal unity of being.


* The Correlation and Conservation of Forces; a series of Expositions by Professor Grove, Professor Helmholtz, Doctor Mayer, Doctor Faraday, Professor Liebig and Doctor Carpenter. With an Introduction, and brief Biographical Notices of the Chief Promoters of the New Views, by Edward L. Youmans, M. D. New York. D. Appleton & Co.


In Frank B. Carpenter's obituary of Fitz Hugh Ludlow (The New York Evening Mail, December 1870), he writes:
[W]ith all his wonderful versatility, his greatest delight was in works of scientific inquiry. He was stocked with the latest publications in this department, his sick bed being frequently loaded with them, and he would devour these with the zest which many persons give to what is called light literature. His whole heart seemed never more given to anything he wrote than to an article for the Galaxy in 1867 on the correlation of forces, which was published under the heading of "E Pluribus Unum." The article, as he wrote it, was too long for the purpose of the Galaxy, and it was cut down and changed somewhat in form in its publication, which annoyed him very much, as any interference with his manuscript always did.

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