## Über die Gültigkeitsgrenze des Satzes von thermodynamischen Gleichgewicht und über die Möglichkeit einer neuen Bestimmung der Elementarquanta. Offprint from Annalen der Physik, 4. Folge, 22. Bd., 1907.

Leipzig: Barth, 1907.

First edition, rare author’s presentation offprint with “Überreicht vom Verfasser” printed on front wrapper, of “Einstein’s third stage in his investigation of Brownian motion. In the first stage (1905) he obtained the explanation of the observed zigzag motion of suspended particles. In the second stage (1906) he looked at this phenomenon from a more general angle. In this investigation he extends the results to all macroscopic parameters by giving a general principle for the calculation of their fluctuations” (Lanczos, p. 148). In this paper, Einstein investigates “‘a phenomenon in the domain of electricity which is akin to Brownian motion’: the (temperature-dependent) mean-square fluctuations in the potential between condenser plates” (Pais, p. 98). “The [condenser] may be constructed as a double system of 30 plates pushed together. These plates can be separated, thus reducing the capacitance to 10. This gives a magnification factor of 500; thus, the fluctuation of the electric potential due to heat motion of the molecules becomes of the order of magnitude of half a thousandth of a volt, which is not immeasurably small” (Lanczos, p. 148). “Einstein used the thermodynamic approach to fluctuations in Brownian motion to predict voltage fluctuations in condensers. To test his theory, he needed a new, highly sensitive instrument – more sensitive than the available electrometers, which could measure to a few thousandths of a volt. Einstein designed it, had it built, and famously called it his Maschinchen (Little Machine). He toyed with the idea of patenting it but then dismissed the notion when manufacturers showed little interest” (Calaprice). Einstein’s “Little Machine” is held with great affection in the physics community as an example of the experimental, practical side of the man who was the ultimate theorist. Three known versions of this machine are known to exist, at least one of which was used in an experiment conducted by Walter Gerlach.

“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” (*Papers*, p. 206).

“Einstein further developed the thermodynamical approach in a paper on voltage fluctuations in a condenser [in the offered paper]. He gave a simple derivation of a formula for mean square fluctuations, a derivation that does not depend on dynamical premises, but is directly based on Boltzmann’s principle relating probability and entropy, both conceived by Einstein as thermodynamical quantities. Consequently, he stated that his treatment of fluctuations does not require any ‘definite stipulations concerning the molecular model to be applied’. The new element in Einstein's argument is his definition of probability in Boltzmann’s principle as the ‘statistical probability of a state’ …

“In the same paper, Einstein also elaborated the stochastic approach. He calculated pressure fluctuations in black-body radiation from the condition that the momentum they impart to a small mirror moving through the radiation just compensates for the momentum lost due to the average radiation pressure on the mirror. In his lectures on statistical physics, Einstein applied a similar technique to the derivation of his general formula for Brownian motion … Einstein continued to apply the stochastic and the thermodynamical approaches to fluctuation phenomena in his further research, in particular to problems of radiation” (*ibid*., pp. 214-5).

Einstein concludes the present paper by pointing out that to test his results experimentally would require a device capable of measuring very small voltages:

“Thus, if the condenser is short-circuited when the plate systems are pushed together, and the plates are pulled apart after the connection has been broken, potential differences of the order of magnitude of one-half millivolt will result between the plate systems.

“It does not seem to me out of the question that these potential differences may be accessible to measurement. For if metal parts can be electrically connected and separated without the occurrence of other irregular potential differences of the same order of magnitude as those calculated above, then it must be possible to achieve the goal by combining the above plate condenser with a multiplier. We would then have a phenomenon akin to Brownian motion in the domain of electricity that could be used for the determination of [Avogadro’s number].”

Already in 1907 Einstein discussed his ideas for building a machine to measure very small potential differences with the brothers Conrad (1876-1958) and Paul Habicht (1884-1948) who only after a few weeks built a first, however still deficient prototype together with their mechanic. In April 1908 Einstein published his invention in *Physikalische Zeitschrift* (Bd. 7, pp. 216-217) in an article with the title ‘A new electrostatic method for the measurement of smallest amounts of electricity’, which also contained first basic depictions of the Maschinchen.

Weil 16. Calaprice, *The Einstein Almanac*, 14. *The Collected Papers of Albert Einstein**, Vol. 2: The Swiss Years: Writings 1900-1909*. Lanczos, *The Einstein Decade* (*1905-1915*), 1974. Pais, *Subtle is the Lord,* 1982.

8vo (224 x 145 mm), pp. 569-572. Original printed wrappers. A fine copy.

Item #5069

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Price:
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