Folgerung aus den Capillaritätserscheinungen. Offprint from Annalen der Physik, 4. Folge, 4. Bd., 1901.

Leipzig: Barth, 1901.

First edition, rare author’s presentation offprint with “Überreicht vom Verfasser” printed on front wrapper, of Einstein’s first published paper, on the thermodynamics of liquid surfaces, which Einstein completed in December 1900. In both this and his second published paper (1902), “Einstein was looking for experimental support for a hypothesis concerning molecular forces. Making an analogy with gravitation, he conjectured that the potential between two molecules of species i and j is of the form cicjφ(r), where the c’s are characteristic for the species and φ(r) is a universal function of distance … He was able to relate the c’s to the specific volume and to the surface tension and its temperature derivative. Using known data, he could check his hypothesis, which, he found, actually worked fairly well for a limited range of carbon compounds (with molecular weights mainly of the order of 100) but not for lighter molecules, such as water” (Pais, p. 56). Einstein’s hypothesis was incorrect, but “it shows how from the start he was groping for universal principles, in the present case for a relation between molecular forces and gravitation. ‘It should be noted,’ he remarked, ‘that the constants c increase in general but not always with increasing weight; however, this increase is not linear. Therefore the question if and how our forces are related to gravitational forces must for the time being be kept completely open’” (ibid.). Einstein later condemned this paper as “worthless”; however, Pais (p. 18) characterized this and Einstein’s other pre-1905 papers as “important warming-up exercises in Einstein’s own development”.

“Einstein’s first two papers have a common theme: an investigation of the nature of molecular forces by means of the effect of such forces on various observable phenomena in liquids … Popular-scientific books and school texts no doubt familiarized Einstein at an early age with the general ideas of the atomic-molecular theory and the concept of cohesive forces between molecules. Violle’s textbook of physics, which Einstein studied in 1895, argues strongly for the molecular outlook, and contains a lengthy chapter on capillarity, based on Laplace’s theory of short-range forces between the molecules of a fluid (see below). Mach’s Mechanik, which Einstein read about 1897, also introduces such forces to explain the shape of fluid bodies. A record of his nascent interest in studying the nature of these forces dates from Einstein’s ETH years. His notes on Weber’s physics lectures contain the marginal comment ‘Investigate! Holidays’ next to his summary of Weber’s comment on the unknown function of the distance between two identical molecules that characterizes the cohesive force between them.

“In his first published paper, Einstein chose the phenomenon of capillarity to study the nature of intermolecular forces. Before him, many physicists had sought to explain capillarity on the basis of cohesive forces acting between the constituent particles of matter. Laplace had proposed an ambitious program for unifying physics by postulating the existence of various central forces between molecules in order to explain a number of physical phenomena. The most detailed and successful example of this approach is his theory of capillarity, based on the hypothesis of an attractive intermolecular force with a range so short that the force vanishes at microscopic distances. On the basis of this assumption, Laplace was able to explain the existence of surface tension and several other capillary phenomena. His theory of capillarity was elaborated by Poisson and Gauss, among others. Such static molecular models could not be used for the investigation of the thermal aspects of capillary phenomena. In the latter part of the nineteenth century a strictly thermodynamical approach to capillarity was developed, which relates various capillary phenomena without any assumptions about the underlying cause of the assumed surface tension. The concurrent successes of the kinetic theory of gases led to attempts to develop a kinetic theory of liquids, and thus to a revival of interest in the molecular theory of capillarity. Van der Waals, in particular, used the study of capillarity as a way of investigating molecular cohesive forces. His work was the first to combine the methods of the Laplacian theory with those of kinetic theory. Maxwell, Rayleigh, William Thomson, and Boltzmann are other leading physicists who worked on the theory of capillarity during the last quarter of the nineteenth century. However, no substantial progress toward a kinetic theory of liquids was made.

“A fellow ETH student later reported that Einstein was very impressed by a lecture on capillarity given by Minkowski during Einstein's last term at the ETH (April-July 1900). In September 1900 he finished reading Boltzmann’s Gastheorie, which contains a discussion of capillarity, based on Van der Waals’s approach that may have further stimulated Einstein’s interest. The first evidence that he was actually at work on a theory of molecular forces dates from the following month. In a letter to Mileva Marić he refers to results on capillarity that he had recently found. He believes the results to be completely new, and suggests that they look for empirical data to test them. ‘If a law of nature results’, he wrote, a paper would be submitted to the Annalen der Physik. Two months later, on 16 December 1900, the manuscript of [the offered paper] was received by the Annalen.

“Einstein studied the dependence of capillary phenomena, and hence of molecular forces, on the chemical composition of neutral liquids. Like many contemporary treatments of capillarity, Einstein’s paper combines the use of both thermodynamic and molecular-theoretical methods. The paper starts with an ingenious thermodynamical argument, based on the experimentally observed, approximately linear decrease in surface tension with increasing temperature, to prove that the surface energy of a fluid consists almost exclusively of potential energy. Einstein then calculated this surface potential energy on the basis of an assumption about the nature of molecular forces. Guided by a presumed analogy with gravitational forces, he postulated a similar form for the potential between two molecules:

P = P* – c1c2p(r),

where p(r) is a universal function of the distance r between the molecules. At the time, such an expression for the intermolecular potential was not uncommon; the masses of the interacting molecules were usually chosen as the constants c. In Einstein’s paper, however, the constants c1 and c2 are assumed to depend on the chemical nature of the molecules. The atoms of a chemical element are characterized by a certain value of c; the c of a molecule is assumed to be the sum of the c’s of its constituent atoms. Einstein did not discuss the range of the intermolecular force in the paper, but his assumptions about the form of the potential imply that the range is the same for all molecules. Einstein derived relations between the constants c for the molecules of a neutral liquid and several measurable properties of the liquid. Comparison with experimental values of these properties for various liquids allowed him to establish (relative) values of c for a number of elements. From these, he calculated the values for a number of compounds, which he then compared with the experimentally established values for the latter. On the whole, he found the agreement between observed and calculated values to be satisfactory. Einstein continued to work on the topic of liquid surfaces during 1901, apparently without any further success. He also derived a consequence from his theory that appeared to be in contradiction with the Van der Waals theory of liquids.

“After the paper was published on 1 March 1901, offprints were sent to several prominent physicists, notably Wilhelm Ostwald (who is cited in the paper), as part of Einstein’s unsuccessful attempt during that spring to find a position as Assistent at some university. In a letter to Ostwald accompanying the offprint, Einstein expressed his indebtedness to Ostwald’s work. If Ostwald read the paper, he was presumably not sympathetic to Einstein’s molecular approach. Ostwald had been an ardent energeticist for some time, and was quite hostile to atomistic explanations. In 1891 he already wrote somewhat disparagingly about Laplace’s work. Two years later, he stated that atomistic explanations of capillarity depend on so many arbitrary assumptions that the topic is ‘not so much clarified as obscured’ by such explanations. In spite of a second note by Einstein, and a letter from his father appealing for a word of encouragement, Ostwald apparently did not respond.

“A review of Einstein’s paper comments on the ‘not altogether clear and unobjectionable derivations’ and notes that Einstein overlooked a thermodynamical relation between two equations he derived. [Einstein’s paper] is cited with more favorable comments several times in the literature on capillarity, and one of its thermodynamical results was later called Einstein’s equation.

“Einstein evidently was highly gratified by the ability of his theory of molecular forces to explain several apparently unrelated phenomena. A letter to Marcel Grossmann enthuses: ‘It is a glorious feeling to recognize the unity of a complex of phenomena, which appear to direct sense perception as quite distinct things.’ Even more ambitious hopes for the theory are suggested by Einstein’s allusions to gravitation in connection with it. Although he acknowledged that his results leave the question of whether molecular forces are related to gravitation completely open, he continued to hope. In the letter to Grossmann just quoted, Einstein asserted that a generalization of his theory to gases would enable him to evaluate c for almost all the elements, which would take him a large step closer to settling this question. The next day he wrote to Marić expressing similar hopes. However, there is no further mention of the question in his letters, nor in his second paper on molecular forces.

“Toward the end of 1901, Einstein hoped to obtain a doctorate with a dissertation based on all of his work on molecular forces. He failed to obtain the doctorate at this time, but continued his study of molecular forces …

“Although he published nothing further on his theory of molecular forces for the remainder of the decade, Einstein remained actively interested in the subject until at least 1903. In January of that year he wrote: ‘In the near future I will occupy myself with molecular forces in gases’. In March he wrote: ‘I am having great difficulty collecting the material for my work on molecular forces.’ A few years later, Einstein wrote deprecatingly about his two papers on molecular forces. He sent Stark a collection of his offprints, omitting ‘my two worthless beginners’ works’” (Papers, pp. 3-8).

Weil 1. Shields, “Writings of Albert Einstein” (in Albert Einstein: Philosopher-Scientist [1948], pp. 689-758), no. 1. The Collected Papers of Albert Einstein, Vol. 2: The Swiss Years: Writings 1900-1909. Pais, Subtle is the Lord, 1982.

8vo (222 x 146 mm), pp. 513-523. Original printed wrappers (a little chipped and stained, front hinge tender, tab extension with punched holes pasted to spine).

Item #5068

Price: $28,500.00