Mayer, Julius Robert
MAYER, JULIUS ROBERT
(b. Heilbronn, Württemberg [now Baden-Württemberg], Germany, 25 November 1814: d. Heilbronn, 20 March 1878)
physics, physiology.
Robert Mayer was one of the early formulators of the principle of the conservation of energy. His father, Christian Jakob Mayer, maintained a prosperous apothecary shop in Heilbronn and married Katharina Elisabeth Heermann, daughter of a Heilbronn bookbinder. The couple had three sons, of whom Robert was the youngest; both the older brothers followed their father’s profession.
Mayer attended the classical Gymnasium at Heilbronn until 1829, when he transferred to the evangelical theotogy seminary at Schöntal. Although he was a mediocre student, he passed the Abitur in 1832 and enrolled in the medical faculty at the University of Tübingen. In February 1837 he was arrested and expelled from the university for participation in a secret student society. The next year Mayer was allowed to take the doctorate of medicine, and in 1838 he also passed the state medical examinations with distinction. During the winter of 1839–1840 Mayer visited Paris and from February 1840 to February 1841 served as physician on a Dutch merchant ship on a voyage to the East Indies. While in Djakarta, Java, certain physiological observations convinced Mayer that motion and heat were interconvertible manifestations of a single, indestructible force in nature, and that this force was quantitatively conserved in any conversion. Mayer was inspired and occasionally obsessed by this insight. He elaborated his idea in various scientific papers which he published during the 1840’s after his return to Germany.
Mayer settled in his native Heilbronn, where he took up a prosperous medical practice and held various civic posts. In 1842 he married Wilhelmine Regine Caroline Ctoss; the marriage produced seven children, five of whom died in infancy. Mayer maintained a conservative position during the Revolution of 1848, and this position led to his brief arrest by the insurgents and to a lasting estrangement from his brother Fritz. Depressed by these events and by his failure to obtain recognition for his scientific work, Mayer attempted suicide in May 1850. During the early 1850’s he suffered recurrent fits of insanity, which necessitated several confinements in asylums at Göppingen, Kennenburg, and Winnenthal. Only after 1860 did Mayer gradually receive international recognition, He died in Heilbronn of tuberculosis in 1878.
Before his trip to Java, Mayer had shown much interest in science, but little creative ability. Flush with enthusiasm for his new idea about force, Mayer composed his “Ueber die quantitative und qualitative Bestimmung der Kräfte” immediately after his return to Heilbronn. In this paper Mayer groped toward a philosophical and mathematical expression of his new concept of force. Although he later altered the mathematical and the physical expressions of the ideas which he employed in this first paper, the philosophical and conceptual expressions remained virtually unchanged in his later work.
Mayer asserted that the task of science is to trace all phenomena back to their first causes. The laws of logic assure us that for every change there exists a first cause (Ursache), which is called a force (Kraft). In the world we observe “tension” or “difference” such as spatial separation or chemical difference existing between all matter. This tension is itself a force, and its effect is to prevent all bodies from quickly uniting themselves into a mathematical point. These tension-forces are indestructible, and their sum total in the universe is constant. Just as chemistry is the science of matter, so physics is the science of forces. Just as chemistry assumes that mass remains constant in every reaction, whatever qualitative changes the matter may undergo, so physics must also assume that forces are quantitatively conserved, no matter what conversions or qualitative changes of form they may undergo.
Although Mayer’s mathematical-physical exposition of his ideas was highly original, it was also quite obscure and revealed his lack of acquaintance with the principles of mechanics. Mayer first considered a moving particle and argued that the measure of its “quantity of motion” is its mass times its speed. He then considered the special case of two particles, each having mass m and speed c and approaching each other on a straight line. The “quantitative determination” of the force of movement present is 2mc. The “qualitative determination,” however, is formally zero, since the motions are equal and opposite; this Mayer expressed by the symbolism 02mc. Unless the particles are totally elastic, the “quantitative determination” of the force of motion present will be less after the collision than before the collision; for totally inelastic panicles it will be zero after collision. The force present as motion is never lost, Mayer insisted; rather a part of it is “neutralized” in the collision and appears as heat. From this assertion Mayer generalized obscurely that all heat can be thought of as equal and opposite motions which neutralize each other, and that 02mc is somehow a universal mathematical expression for the force of heat. Finally Mayer showed how, in the more general case in which the colliding particles do not lie in a straight line, the paralletogram of forces may be employed to determine how much force of motion would be “neutralized” in the collision.
Upon completing “Ueber die … Bestimmung der Kräfte,” Mayer submitted it to the Annalen der Physik und Chemie for publication. The editor Poggendorff ignored the paper and it was not printed. Although he was angry and disappointed, Mayer quickly became aware of the limitations of the treatise and immediately set himself to studying physics and mathematics. Between August 1841 and March 1842 Mayer discovered that mν2, not mν is the proper measure of the quantity of motion and that this form of force is identical to the vis viva of mechanics. He incorporated that discovery into his second paper, “Bemerkungen uberdie Kräfte der unbelebten Natur,” which he had published in Liebig’s Annalen der Chemie in May 1842.
In this second paper Mayer elaborated the conceptual basis of his theory, examining, he said, the precise meaning of the term “force,” As in the previous paper, Mayer concluded that forces are first causes; hence the law causa aequat effectum assures us that force is quantitatively indestructible. Like matter, forces are objects which are able to assume different forms and which are indestructible. Forces differ from matter only because they are imponderable.
Elaborating an idea mentioned in his previous paper, Mayer asserted that the spatial separation of two bodies is itself a force. This force he called “fallforce” (Fallkraft). Where one object is the earth and the second object is near the earth’s surface, the fall-force can be written md, m being the weight of the object and d its elevation. In actual fall, fall-force is converted into force of motion. Mayer expressed this conversion as md = mc2, where c is the vetocityattained by an object of weight m in falling the distance d to the earth’s surface.
On the basis of this concept of fall-force. Mayer concluded that gravity is not a force at all but a “characteristic of matter.” Gravity cannot be a force, Mayer argued, because it is not the sufficient cause of motion; in addition to gravity, spatial separation is prerequisite to fall. If gravity were a force, then it would be a force which constantly produces an effect without itself being consumed; this, however, would violate the principle of the conservation of force. Throughout all his later papers and letters Mayer clung staunchly to this position. He continually argued that the entity “force” in its Newtonian sense is illogically and misleadingly named and that hence a different term should be introduced for it. The word “force” should be reserved for the substantial, quantitative entity conserved in conversions. Even after physics later adopted the term “energy” to describe Mayer’s concept of force, Mayer continued to feet that the idea of force as a conserved entity was conceptually prior to the Newtonian entity and that hence the traditional name “force” should have been reserved for his own concept of force.
After discussing the interconvertibility of fall-force and force of motion in his 1842 paper, Mayer noted that motion is often observed to disappear without producing an equivalent amount of other motion or fall-force. In these cases motion is converted into a different form of force, namely heat, Fall-force, motion, and heat are different manifestations of one indestructible force, and hence they maintain definite quantitative relationships among themselves. This means, Mayer concluded, that there must exist in nature a constant numerical value which expresses the mechanical equivalent of heat. He stated that this value is 365 kilogram-meters per kilocalorie; that is, the fall-force in a mass of one kilogram raised 365 meters is equal to the heat-force required to raise one kilogram of water one degree centigrade.
Although Mayer’s 1842 paper merely stated the mechanical equivalent of heat without giving its derivation, later papers also gave his method. Let x be the amount of heat in calories required to raise one cubic centimeter of air from 0° C. to 1° at constant volume. To raise the same cubic centimeter of air one degree centigrade at constant pressure will require a larger amount of heat, say x + y, since, in the volume expansion, work must be done against the force which maintains constant pressure. If this latter expansion is carried out under a mercury column, then the extra heat y will go into raising that mercury column. Hence if P is the weight of the mercury column and h is the distance that it is raised in the expansion, we can write y = ph; the problem is to find y. From published data Mayer knew that 3.47 × 10−4 calories are required in order to raise one cubic centimeter of air one degree centigrade under a constant pressure of 1,033 gm./cm.2 (that is, 76 cm. of mercury); hence x + y = 3.47 × 10−4 calories. He also knew from data of Dulong that the ratio of the specific heats of air at constant volume and at constant pressure is 1/1.421; hence x/(x + y) = 1/1.421. Knowing the value of x + y, Mayer then easily found y 1.03 × 10−4 calories. Since the expansion was known to raise the mercury column 1/274 centimeters, Mayer then had for the equation y = ph.
1.03 × 10−4cal. = 1,033 gm. × 1/274 cm.
The reduction of these figures yielded the equation 1 kilocalorie = 365 kilogram-meters.
Mayer’s derivation of the mechanical equivalent of heat was as accurate as the value chosen for the ratio of specific heats would permit. Mayer’s derivation rests upon the assumption that his cubic centimeter of air does no internal work during free expansion; that is, that all of the heat y goes to raise the mercury column. Although in 1842 Mayer already knew of an experimental result by Gay-Lussac which would substantiate this assumption, he did not invoke it publicly until three years later (1845).
The paper of 1842 set out Mayer’s definitive view on the conservation of force and established his claim to priority; historically the paper also provides insight into the processes through which Mayer arrived at his theory. During the 1840’s various European scientists and engineers were formulating ideas which were suggestive of the conservation of energy. Several different interests influenced these formulations. Among these interests was the growing concern with the efficiency of steam engines and with the many new conversion processes which were being discovered in electricity, magnetism, and chemistry. Mayer’s early papers show little interest in these problems but instead suggest that philosophical and conceptual considerations largely guided Mayer’s theorizing. One of these considerations was his constant identification of force and cause; another was his intuitive understanding of force as a substantial, quantitative entity. The source of these ideas of Mayer’s and their relationship to the larger context of German science and philosophy remain unsolved historical problems. Both concepts seem to have been unique to German science and to have led Mayer to interpret familiar phenomena in a radically new way. An example of this interpretation can be seen in the events which apparently led Mayer to his initial speculations about force conservation.
Like several other formulators of the conservation principle, Mayer was led to his theory through physiological, not physical, considerations. While letting the blood of European sailors who had recently arrived in Java in July 1840, Mayer had been impressed by the surprising redness of their venous blood. Mayer attributed this redness to the unaccustomed heat of the tropics. Since a lower rate of metabolic combustion would suffice to maintain the body heat, the body extracted less oxygen from the red arterial blood. This observation struck Mayer as a remarkable confirmation of the chemical theory of animal heat, and he quickly generalized that the oxidation of foodstuff is the only possible source of animal heat. Conceiving of the animal economy as a force-conversion process—the input and outgo of which must always balance—Mayer realized that chemical force which is latent in food is the only input and that this input could be expressed quantitatively as the heat obtained from the oxidation of the food. To this point Mayer’s reasoning differed little from contemporary physiological theory, but once it was reached Mayer proceeded to a conceptual leap which was well beyond any facts at his disposal. He decided that not only the heat produced by the animal directly as body heat, but also that heat produced indirectly through friction resulting ultimately from the animal’s muscular exertion must be balanced against this input of chemical force. Muscle force and also body heat must be derived from the chemical force latent in food. If the animal’s intake and expenditure of force are to balance, then all these manifestations of force must be quantitatively conserved in all the force conversions which occur within the animal body. This inference, however fruitful, seemed to rest largely upon Mayer’s preconceived notion of force and conversion rather than upon any empirical observations.
Immediately after his return from Java Mayer had planned a paper on physiology which would set out these ideas, but he purposely postponed the paper in order first to lay a proper physical basis for the theory. Having done so in the treatise of 1842, he published privately at Heilbronn in 1845 Die organische Bewegung in ihrem Zusammenhang mit dem Stoffwechsel, his most original and comprehensive paper. In this work Mayer again set out the physical basis of his theory, this time extending the ideal of force conservation to magnetic, electrical, and chemical forces. In Die organische Bewegung he described the basic force conversions of the organic world. Plants convert the sun’s heat and light into latent chemical force; animals consume this chemical force as food; animals then convert that force to body heat and mechanical muscle force in their life processes.
Mayer intended Die organische Bewegung not only to establish the conservation of force as the basis of physiology, but also to refute views held by the organic chemist Liebig. In 1842 Liebig had published his influential and controversial book Die Thierchemie oder die organische Chemie in ihrer Anwendung auf Physiologie und Pathologie. In that work Liebig had come out as a champion of the chemical theory of animal heat, which Lavoisier and Laplace had first proposed in 1777. Reasoning much as Mayer had done, Liebig had concluded that animal heat produced from any source other than the oxidation of food was tantamount to the production of force from nothing. Hence he concluded that the oxidation of food is the sole source of animal heat. Liebig also believed that muscle force was derived ultimately from chemical force through an intermediary vital force localized in the protein substances of muscle tissue. Well aware of Liebig’s acquaintance with his 1842 paper, Mayer regarded Die organische Chemie as possible plagiarism and as a definite threat to his priority. In his Die organische Bewegung Mayer joined Liebig in championing the chemical theory of animal heat, but he then proceeded to refute Liebig’s other views wherever possible.
Mayer opened his attack on Liebig by criticizing Liebig’s frequent recourse to vitalism. The vital force served various functions in Liebig’s theory, the chief function being to prevent the living body from spontaneously beginning to putrefy, its tissues being constantly in the presence of oxygen and moisture. Mayer denied that putrefaction would occur in the tissues as spontaneously as Liebig had assumed. Mayer argued that if putrefaction did occur the putrefying parts would nevertheless be carried off in the blood as rapidly as they began to decay. Hence postulating a vital force was not merely unscientific, it was unnecessary.
Liebig had argued further that while starch and sugar are oxidized in the blood to produce heat, only the protein-bearing muscle tissue can undergo the chemical change necessary to produce mechanical muscle force. Hence those changes occur in the muscle, not in the blood; the muscle literally consumes itself in exertion. Against this argument Mayer employed his mechanical equivalent of heat to compute the amount of muscle tissue which must be consumed daily in order to support the exertions of a working animal. The high rate of assimilation necessary continuously to replace that loss, Mayer argued, made Liebig’s theory improbable at best. He concluded that it seemed most reasonable to assume all oxidation to occur within the blood, whatever the form and locus of the force released. At the end of his 1845 paper Mayer finally reconciled the main observations of classical irritability theory with his own hypothesis and argued the dependence of the contractile force upon the blood supply.
Die organische Bewegung exercised little influence on German physiology, although Mayer’s attack on Liebig’s vital force found enthusiastic response, and the work received several favorable reviews. After 1845 Liebig’s younger disciples quietly dropped his speculations about the vital force, much as Mayer had suggested. The issue of muscle decomposition remained controversial among physiologists, although by 1870 it was agreed that the oxidation of carbohydrates in addition to proteins contributed to the production of muscle energy. Mayer’s writings had little direct influence on either of these developments.
Immediately after publishing his treatise on physiology, Mayer applied his theory of force conservation to a second critical problem which he had treated unsatisfactorily in 1841: the source of the heat of the sun. In 1846 he advanced an explanation of solar heat which he incorporated into a memoir submitted to the Paris Academy, “Sur la production de la lumiére et de la chaleur du soleil,” and into the expanded Beiträge zur Dynamik des Himmels in populärer Darstellungen, which was published privately at Heilbronn in 1848. After demonstrating in these papers the insufficiency of any chemical combustion to sustain the sun’s enormous radiation, Mayer advanced what rapidly became known as the “meteoric hypothesis” of the sun’s heat. Mayer speculated that matter, mostly in the form of meteors, daily enters the solar system in immense quantities and begins to orbit the sun. Friction with the luminiferous ether causes this matter gradually to spiral into the sun at inordinate velocities. Upon striking the sun this matter yields up its kinetic energy as light and heat. Mayer employed his mechanical equivalent of heat to show that each unit of mass striking the sun would yield four thousand to eight thousand times as much heat as would be produced by the combustion of an equivalent mass of carbon. Hence if the quantity of matter falling into the sun is assumed to be sufficiently large, this process can sustain the sun’s total output of heat.
After 1850 the meteoric hypothesis received wide currency, largely on account of versions of the theory which were advanced independently of Mayer by Waterston and William Thomson. The explanation of solar heat that won general acceptance and that survived well into the twentieth century, however, was proposed by Helmholtz in a popular lecture of 1854, “Ueber die Wechselwirkung der Naturkräfte und die darauf bezüglichen Ermittlungen der Physik.” According to Helmholtz the sun’s heat is sustained by the gradual cooling and contraction of the sun’s mass. As the sun’s density increases the sun’s matter yields its potential energy directly as heat. Although this was not a true meteoric hypothesis, Helmholtz’ explanation of the sun’s heat resembled Mayer’s in many respects. Mayer’s hypothesis may have influenced Helmholtz in the formulation of his own hypothesis, for by 1854 Helmholtz knew of Mayer’s 1848 treatise and had discussed it in his 1854 lecture shortly before setting out his own views on the origin of solar energy.
Mayer’s astronomical papers also revived another hypothesis which was to become important after 1850. In the Dynamik des Himmels of 1848 and in his 1851 memoir, “De l’influence des marées sur la rotation de la terre,” Mayer showed that tidal friction deflects the major axis of the earth’s tidal spheroid some thirty-five degrees from the earth-moon line. Hence the moon’s gravitation exercises a constant retarding couple on the earth’s rotation, a couple which gradually dissipates the earth’s energy of rotation as heat.
Although minute, this quantity is perceptible. Citing Laplace, Mayer noted that on the basis of data from ancient eclipses, the length of the day, and hence the velocity of rotation of the earth, can be shown to have been constant to within .002 seconds over the last 2,500 years. This failure to observe the predicted retardation due to tidal friction indicated to Mayer the presence of a compensating phenomenon. He found this in geology. By 1848 many geologists believed that the earth had originally condensed as a molten mass and had since then been cooling at an undetermined rate. This theory faced a critical difficulty, for cooling should have produced a contraction of the earth, which in turn should have accelerated its rotation. No such acceleration could be observed, and Laplace had already used the apparent constancy of the day to prove that no contraction greater than fifteen centimeters could have occurred within the last 2,500 years. At this juncture Mayer boldly hypothesized that tidal retardation of the earth’s rotation is offset by the acceleration due to cooling and contraction. Mayer pointed out that this assumption rescued both hypotheses and reconciled both with the observed constancy of the day. The predicted retardation of .0625 seconds in 2,500 years, Mayer showed, would permit an offsetting contraction of the earth’s radius by 4.5 meters.
The influence of Mayer’s speculations is difficult to assess; the 1848 treatise was not widely read, while the memoirs to Paris had been reported upon but not printed. In 1858 Ferrel published a similar hypothesis, apparently independently of Mayer, and noted that tidal retardation and the earth’s contraction might produce compensating changes in the earth’s rotation. In 1865 Delaunay invoked tidal friction to explain a newly discovered inequality in the moon’s motion and noted that the hypothesis of tidal friction had already been formulated in several printed works.
The Dynamik des Himmels marked the end of Mayer’s creative career, for his numerous later articles were primarily popular or retrospective. At this point Mayer had received almost no recognition in important scientific circles, and to this disappointment was added the frustration of seeing other men independently advance ideas similar to his own. Liebig had anticipated many of Mayer’s views in 1842, and in 1845 Karl Holtzmann computed a mechanical equivalent of heat without reference to Mayer. In 1847 Helmholtz set out a complete mathematical treatment of force conservation in his treatise Ueber die Erhaltung der Kraft. Mayer’s main rival was Joule, and in 1848 Mayer became embroiled with him in a priority dispute carried out mainly through the Paris Academy. Although the dispute remained inconclusive, it later developed bitter nationalistic overtones when other scientists took up the quarrel.
After 1858 Mayer’s fortunes improved. Helmholtz apparently read Mayer’s early papers around 1852, and thereafter he argued Mayer’s priority in his own widely read works. Clausius, too, regarded Mayer deferentially as the founder of the conservation principle and began to correspond with him in 1862. Through Clausius, Mayer was put in touch with Tyndall, who quickly became Mayer’s English champion in the priority dispute with Joule, Thomson, and Tait. During the 1860’s many of Mayer’s early articles were translated into English, and in 1871 Mayer received the Royal Society’s Copley Medal. In 1870 he was voted a corresponding member of the Paris Academy of Sciences and was awarded the Prix Poncelet.
Although the scientific world lionized Mayer before his death in 1878, in reality he exercised little influence on European science. In every field in which he worked his principal ideas were later formulated independently by others and were well established in science before his own contributions were recognized. In an age in which German science was rapidly becoming professionalized, Mayer remained a thorough dilettante. He conducted almost no experiments, and although he had an exact, numerical turn of mind, he neither fully understood mathematical analysis nor ever employed it in his papers. His scientific style, his status as an outsider to the scientific community, and his lack of institutional affiliation were all factors that limited Mayer’s access to influential journals and publishers and hampered the acceptance of his ideas. Mayer was a conceptual thinker whose genius lay in the boldness of his hypotheses and in his ability to synthesize the work of others. Mayer actually possessed only one creative idea—his insight into the nature of force—but he tenaciously pursued that insight and lived to see it established in physics as the principle of the conservation of energy.
BIBLIOGRAPHY
Mayer’s major scientific works were collected in Jacob J. Weyrauch, ed., Die Mechanik der Wärme, 3rd ed. (Stuttgart, 1893). Mayer’s letters, short papers, and other documents related to his career were reprinted as Jacob J. Weyrauch, ed., Kleinere Schriften und Briefe von Robert Mayer (Stuttgart, 1893). In both works Weyrauch provides not only extensive nn. and commentary, but also a thorough biog. of Mayer. Other documents relating to Mayer’s career and family background are included in the commemorative vol., Helmut Schmolz and Hubert Weckbach, eds., J. Robert Mayer, Sein Leben und Werk in Dokumenten (Weissenhorn, 1964).
Existing biographies of Mayer tend to whiggishness; one of the better ones is S. Friedländer, Julius Robert Mayer (Leipzig, 1905). On Mayer’s place in the formulation of the principle of the conservation of energy and on the European context of his work, see Thomas S. Kuhn, “Energy Conservation as an Example of Simultaneous Discovery,” in Marshall Clagett, ed., Critical Problems in the History of Science (Madison, Wis., 1959), 321–356. Mayer’s concepts of force and causation are discussed by B. Hell in “Robert Mayer,” in Kantstudien, 19 (1914), 222–248. Although he does not mention Mayer, Frederic L. Holmes discusses the milieu of German physiology in the 1840’s in his intro. to Liebig’s Animal Chemistry, facs. ed. (New York, 1964). On Mayer’s role in astrophysical speculations see Agnes M. Clerke, A Popular History of Astronomy During the Nineteenth Century, 3rd ed. (London, 1893), esp. 332–334, 376–388.
R. Steven Turner