Eine neue Bestimmung der Moleküldimensionen. Offprint from Annalen der Physik, 4. Folge, 19., 1906.

Leipzig: Barth, 1906.

First edition, rare author’s presentation offprint with “Überricht von dem Verfasser” printed on the front wrapper, of the expanded version of Einstein’s doctoral thesis, ranked by his biographer Abraham Pais as being on the same level as his 1905 papers on relativity, the light quanta and Brownian motion. In his thesis, Einstein presented a new theoretical method for determining molecular radii and Avogadro’s number (the number of atoms or molecules needed to make up a mass equal to a substance’s atomic or molecular weight, in grams). The original version of the thesis was first published as a pamphlet in the spring of 1905. In the version he submitted to the Annlen der Physik, published at the beginning of 1906, Einstein added a brief appendix containing an improved value of Avogadro’s number. “It is not sufficiently realized that Einstein’s thesis is one of his most fundamental papers. Histories and biographies invariably refer to 1905 as the miraculous year because of his articles on relativity, the light-quantum, and Brownian motion. In my opinion, the thesis is on a par with the Brownian motion article. In fact, in some—not all—respects, his results on Brownian motion are by-products of his thesis work. This goes a long way toward explaining why the paper on Brownian motion was received by the Annalen der Physik on May 11, 1905, only eleven days after the thesis had been completed. Three weeks after the thesis was accepted, this same journal received a copy [of the thesis] for publication. It was published only after Einstein supplied a brief addendum in January 1906 … As a result of these various delays, the thesis appeared as a paper in the Annalen der Physik only after the Brownian motion article had come out in the same journal. This may have helped create the impression in some quarters that the relation between diffusion and viscosity – a very important equation due to Einstein and Sutherland – was first obtained in Einstein’s paper on Brownian motion. Actually, it first appeared in his thesis … Quite apart from the fundamental nature of some results obtained in the thesis, there is another reason why this paper is of uncommon interest: it has had more widespread practical applications than any other paper Einstein ever wrote … [T]he thesis, dealing with bulk rheological properties of particle suspensions, contains results which have an extraordinarily wide range of applications. They are relevant to the construction industry (the motion of sand particles in cement mixes), to the dairy industry (the motion of casein micelles in cow’s milk), and to ecology (the motion of aerosol particles in clouds), to mention but a few scattered examples. Einstein might have enjoyed hearing this, since he was quite fond of applying physics to practical situations” (Pais, pp. 89-90). Pais notes that during the period 1970-1974, the 1906 journal version of Einstein’s thesis was cited four times more often than his 1916 paper on general relativity, and eight times more often than his 1905 paper on light quanta.

“Einstein submitted a dissertation to the University of Zürich in 1901, about a year after graduation from the ETH, but withdrew it early in 1902. In a successful second attempt three years later, he combined the techniques of classical hydrodynamics with those of the theory of diffusion to create a new method for the determination of molecular sizes and of Avogadro’s number, a method he applied to solute sugar molecules. The dissertation was completed on 30 April 1905 and submitted to the University of Zürich on 20 July. On 19 August 1905, shortly after the thesis was accepted, the Annalen der Physik received a slightly different version for publication [offered here] …

“By 1905 several methods for the experimental determination of molecular dimensions were available. Although estimates of upper bounds for the sizes of microscopic constituents of matter had been discussed for a long time, the first reliable methods for determining molecular sizes were developed in the second half of the nineteenth century, based on the kinetic theory of gases. The study of phenomena as diverse as contact electricity in metals, the dispersion of light, and black-body radiation yielded new approaches to the problem of molecular dimensions. Most of the methods available by the turn of the century gave values for the size of molecules and for Avogadro’s number that are in more or less satisfactory agreement with each other.

“Although Einstein claimed that the method in his dissertation is the first to use phenomena in fluids in the determination of molecular dimensions, the behavior of liquids plays a role in various earlier methods. For example, the comparison of densities in the liquid and gaseous states is an important part of Loschmidt’s method, based on the kinetic theory of gases. A method that depends entirely on the physics of liquids was known as early as 1816. Young’s study of surface tension in liquids led to an estimate of the range of molecular forces, and capillary phenomena were used later in several different ways to determine molecular sizes.

“A kinetic theory of liquids, comparable to the kinetic theory of gases, was not available, and the methods for deriving molecular volumes exclusively from the properties of liquids did not give very precise results. Einstein’s method, on the other hand, yields values comparable in precision to those provided by the kinetic theory of gases. While methods based on capillarity presuppose the existence of molecular forces, Einstein’s central assumption is the validity of using classical hydrodynamics to calculate the effect of solute molecules, treated as rigid spheres, on the viscosity of the solvent in a dilute solution.

“Einstein’s method is well suited to determine the size of solute molecules that are large compared to those of the solvent. In 1905 William Sutherland published a new method for determining the masses of large molecules that shares important elements with Einstein’s. Both methods make use of the molecular theory of diffusion that Nernst developed on the basis of Van’t Hoff’s analogy between solutions and gases, and of Stokes’s law of hydrodynamical friction … In developing a new method for the determination of molecular dimensions, Einstein was concerned with several other problems on different levels of generality. An outstanding current problem of the theory of solutions was whether molecules of the solvent are attached to the molecules or ions of the solute. Einstein’s dissertation contributed to the solution of this problem. He recalled in 1909:

‘At the time I used the viscosity of the solution to determine the volume of sugar dissolved in water because in this way I hoped to take into account the volume of any attached water molecules.’

“The results obtained in his dissertation indicate that such an attachment does occur.

“Einstein’s concerns extended beyond this particular question to more general problems of the foundations of the theory of radiation and the existence of atoms. He later emphasized:

‘A precise determination of the size of molecules seems to me of the highest importance because Planck’s radiation formula can be tested more precisely through such a determination than through measurements on radiation.’

“The dissertation also marked the first major success in Einstein’s effort to find further evidence for the atomic hypothesis, an effort that culminated in his explanation of Brownian motion. By the end of 1905 Einstein had published three independent methods for determining molecular dimensions, and in the following years he found several more.Of all these methods, the one in his dissertation is most closely related to his earlier studies of physical phenomena in liquids.

“Einstein’s efforts to obtain a doctoral degree illuminate some of the institutional constraints on the development of his work on the problem of molecular dimensions. Einstein’s choice of a theoretical topic for a dissertation at the University of Zürich was quite unusual, both because it was theoretical and because a dissertation theme was customarily assigned by the supervising professor. By 1900, theoretical physics was slowly beginning to achieve recognition as an independent discipline in German-speaking countries, but it was not yet established at either the ETH or the University of Zürich. A beginning had been made at the ETH soon after its founding, with the appointment of the German mathematical physicist, Rudolf Clausius. His departure a decade later may have been hastened by lack of official sympathy for a too-theoretical approach to the training of engineers and secondary-school teachers, the primary task of the school.

“Clausius’s successor – after the position had been vacant for a number of years – was H. F. Weber, who occupied the chair for Mathematical and Technical Physics from 1875 until his death in 1912. During the last two decades of the nineteenth century, he did original research, mainly in experimental physics and electrotechnology, including work on a number of topics that were important for Einstein's later research, such as black-body radiation, the anomalous low-temperature behavior of specific heats, and the theory of diffusion; but his primary interests were never those of a theoretical physicist.

“The situation of theoretical physics at the University of Zürich at the turn of the century was hardly better. Four other major Swiss universities either had two full professorships in physics or one full and one non-tenured position, while Zürich had only one physics chair, held by the experimentalist Alfred Kleiner. Since the ETH was not authorized to grant doctoral degrees until 1909, a special arrangement enabled ETH students to obtain doctorates from the University of Zürich. Most dissertations in physics by ETH students were prepared under Weber’s supervision, with Kleiner as the second referee. As noted above, almost all physics dissertations prepared at the ETH and the University of Zürich between 1901 and 1905 were on experimental topics suggested to the students by their supervisor or at least closely related to the latter’s research interests. The range of topics was quite limited, and generally not at the forefront of experimental research. Thermal and electrical conductivity, and instruments for their measurement, were by far the most prominent subjects. General questions of theoretical physics, such as the properties of the ether or the kinetic theory of gases, occasionally found their way into examination papers, but they were hardly touched upon in dissertations.

“In the winter semester of 1900-1901, Einstein intended to work for a degree under Weber. The topic may have been related to thermoelectricity, a field in which Einstein had shown an interest and in which several of Weber’s doctoral students did experimental research. After a falling out with Weber, Einstein turned to Kleiner for advice and comments on his work. Although Kleiner’s research at this time focused on measuring instruments, he did have an interest in foundational questions of physics, and Einstein’s discussions with him covered a wide range of topics. Einstein showed his first dissertation to Kleiner before submitting it to the university in November 1901. This dissertation has not survived, and the evidence concerning its contents is somewhat ambiguous. In April 1901 Einstein wrote that he planned to summarize his work on molecular forces, up to that time mainly on liquids; at the end of the year, [Mileva] Marić stated that he had submitted a work on molecular forces in gases. Einstein himself wrote that it concerned ‘a topic in the kinetic theory of gases’. There are indications that the dissertation may have discussed Boltzmann’s work on gas theory, as well as Drude’s work on electron theory of metals.

‘By February 1902 Einstein had withdrawn the dissertation, possibly at Kleiner’s suggestion that he avoid a controversy with Boltzmann. In view of the predominantly experimental character of the physics dissertations submitted to the University of Zürich at the time, lack of experimental confirmation for his theoretical results may have played a role in the decision to withdraw the thesis. In January 1903 Einstein still expressed interest in molecular forces, but he stated that he was giving up his plan to obtain a doctorate, arguing that it would be of little help to him, and that ‘the whole comedy has become tiresome for me.’

‘Little is known about when Einstein started to work on the dissertation he completed in 1905. By March 1903 some of the central ideas of the 1905 dissertation had already occurred to him. Kleiner, one of the two faculty reviewers of his dissertation, acknowledged that Einstein had chosen the topic himself and pointed out that ‘the arguments and calculations to be carried out are among the most difficult in hydrodynamics.’ The other reviewer, Heinrich Burkhardt, Professor of Mathematics at the University of Zürich, added: ‘the mode of treatment demonstrates fundamental mastery of the relevant mathematical methods.’ Although Burkhardt checked Einstein’s calculations, he overlooked a significant error in them. The only reported criticism of Einstein’s dissertation was for being too short …

“Einstein’s dissertation was at first overshadowed by his more spectacular work on Brownian motion, and it required an initiative by Einstein to bring it to the attention of his fellow scientists. But the wide variety of applications of its results ultimately made the dissertation one of his most frequently cited papers” (Papers, pp. 170-182).

Weil 7a. Shields, “Writings of Albert Einstein” (in Albert Einstein: Philosopher-Scientist [1948], pp. 689-758), no. 11. The Collected Papers of Albert Einstein, Vol. 2: The Swiss Years: Writings 1900-1909. Pais, Subtle is the Lord, 1982.



8vo (224 x 145 mm), pp. 289-306. Original printed wrappers (a bit chipped and stained, small split in spine, extension tab punched with holes pasted to spine).

Item #5071

Price: $25,000.00