Zur Theorie der Brownschen Bewegung. Offprint from Annalen der Physik, 4. Folge, 19. Bd., 1906.

Leipzig: Barth, 1906.

First edition, rare author’s presentation offprint with “Überreicht vom Verfasser” printed on front wrapper, of Einstein’s second paper on Brownian motion, but the first to acknowledge the relationship of his theory to Brownian motion. “In 1905, Einstein was blissfully unaware of the detailed history of Brownian motion. At that time, he knew neither Poincaré’s work on relativity nor the latter’s dicta ‘On the Motion Required by the Molecular Kinetic Theory of Heat of Particles Suspended in Fluids at Rest,’ as Einstein entitled his first paper on Brownian motion. In referring to fluids at rest, he clearly had in mind the fluids in motion dealt with in his previous paper, finished eleven days earlier. The absence of the term Brownian motion in this title is explained in the second sentence of the paper: ‘It is possible that the motions discussed here are identical with the so-called Brownian molecular motion; the references accessible to me on the latter subject are so imprecise, however, that I could not form an opinion about this.' This paper, received by the Annalen der Physik on May 11, 1905, marks the third occasion in less than two months on which Einstein makes a fundamental discovery bearing on the determination of Avogadro’s number” (Pais, p. 94). “Having been informed by colleagues that the considerations of the preceding paper indeed fit, as to order of magnitude, with the experimental knowledge on Brownian motion, Einstein entitles his new paper ‘On the Theory of Brownian Motion.’ He gives two new applications of his earlier ideas: the vertical distribution of a suspension under the influence of gravitation and the Brownian rotational motion for the case of a rotating solid sphere. Correspondingly, he finds two new equations from which [Avogadro’s number] can be determined” (ibid., p. 98).

“The irregular movement of microscopic particles suspended in a liquid had been noted long before the botanist Robert Brown published his careful observations in 1828, but he was the first to emphasize its ubiquity, and to exclude its explanation as a vital phenomenon. Advances in observational technique and in theory served to eliminate a number of unsatisfactory explanations of Brownian motion by the end of the nineteenth century, if not to verify the correct one …

“Einstein’s study of Brownian motion constitutes one of the high points in the long tradition of research on the kinetic theory of heat and of his own contributions to this field. Some of the consequences of his work were of great significance for the development of physics in the twentieth century. Einstein’s derivation of the laws governing Brownian motion, and their subsequent experimental verification by Perrin and others, contributed significantly to the acknowledgment of the physical reality of atoms by the then still numerous skeptics. His papers on Brownian motion helped to establish the study of fluctuation phenomena as a new branch of physics. The methods he created in the course of his research prepared the way for statistical thermodynamics, later developed by Szilard and others, and for a general theory of stochastic processes …

“In his first paper on Brownian motion, Einstein proved:

‘that, on the assumption of the molecular theory of heat, bodies of the order of magnitude of 1/1000 mm suspended in liquids must already carry out an observable random movement, which is generated by thermal motion.’

“Einstein wrote this paper ‘without knowing that observations concerning Brownian motion were already long familiar.’ He did not mention Brownian motion in the title of [his first paper], although in the text he conjectured that the motion he predicted might be identical to Brownian motion. Boltzmann’s Gastheorie, which Einstein carefully studied during his student years, explicitly denies that the thermal motion of molecules in a gas leads to observable motions of suspended bodies …

“Three elements of Einstein’s approach are characteristic of his decisive progress [in the first paper]:

(1) he based his analysis on the osmotic pressure rather than on the equipartition theorem;

(2) he identified the mean square displacements of suspended particles rather than their velocities as suitable observable quantities; and

(3) he simultaneously applied the molecular theory of heat and the macroscopic theory of dissipation to the same phenomenon, rather than restricting each of these conceptual tools to a single scale, molecular or macroscopic.

“His second paper on Brownian motion, shows ‘how Brownian motion is related to the foundations of the molecular theory of heat’. It includes two new fluctuation formulas, both of which are derived from the probability distribution for a canonical ensemble given in Einstein’s papers on statistical physics. The first formula (eq. [I] on his p. 373), which is closely related to the formula for energy fluctuations he had derived in 1904, gives the probability of deviations from the equilibrium value, due to irregular molecular motions, of a suitable observable parameter α of a system subject to an external force with potential Φ(α) … Einstein applied eq. (I) to a harmonic oscillator in equilibrium with a gas to derive the black-body radiation law in the limit of large wavelengths and high temperatures. An investigation of how small a particle must be in order to remain in suspension in a gravitational field provides another application.

“Eq. (I) does not, however, allow the treatment of Brownian motion, a time-dependent process involving the interplay of fluctuations and dissipation. In order to derive a fluctuation formula that generalizes eq. (1), Einstein related a general dissipation mechanism, analogous to Stokes’s law, to the condition for stability of the distribution, eq. (I), now interpreted as giving the number of systems in a certain state, rather than the probability of that state. The potential I refers to a fictitious force. The resulting formula for the time dependence of the mean square fluctuation (eq. [II] on his p. 378) enabled Einstein to treat rotational as well as translational motions of suspended particles” (Papers, pp. 208-213)

Weil *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. 371-381. Original printed wrappers (wrapper split along spine, restored, a little chipped along spine).

Item #5067

Price: $24,000.00