Determination of the Surface-Tension of Water by the Method of Jet Vibration.

London: The Royal Society, 1909.

First edition, offprint issue, author’s inscribed presentation copy, of Bohr’s first published scientific paper. “His first research project, a precision measurement of the surface tension of water by the observation of a regularly vibrating jet, was completed in 1906, when he was still a student, and it won him the gold medal from the Academy of Sciences. It is a mature piece of work, remarkable for the care and thoroughness with which both the experimental and theoretical parts of the problem were handled” (DSB). In 1879 Lord Rayleigh had proposed a method for determining the surface tension of liquids. “His idea was this. When a liquid jet with a non-circular cross-section emerges from a cylindrical tube, its surface vibrates. Rayleigh showed that from the velocity and cross-section of the jet and the wavelengths of its surface vibrations one can determine the surface tension of the liquid. He had not, however, performed quantitative experiments to implement this method. The problem posed by the Academy was to do just that. The question was purely experimental. Bohr, however, included in his work essential improvements on Rayleigh’s theory by taking into account the influence of the liquid’s viscosity and of the ambient air, and by extending the earlier theory from infinitesimal to arbitrarily large vibration amplitudes … The prize problem had been announced in February 1905. The deadline for submission was 30 October 1906. Bohr spent most of the intervening time working intensely on the problem, doing the experimental part in his father’s laboratory … He was his own glass blower, preparing long tubes with elliptical cross-section so as to produce an elliptical jet with mean radius less than a millimeter. He examined every tube under a microscope and accepted only those with uniform elliptical cross-section. The jet had to be maintained under stable conditions over long periods (it should not rapidly break up into drops) and at constant temperature. The jet velocity was accurately determined by cutting the jet at a given position at two different times, measuring the time interval and, photographically, the length of the segment cut out. Bohr analyzed the vibration amplitudes of the liquid used, tap-water, by photographic observation in nearly monochromatic light. In order to avoid perturbing vibrations due to passing traffic, many observations he made were at night” (Pais, Niels Bohr’s Times, pp. 101-2). ABPC/RBH list only two copies of this offprint: Bruun Rasmussen, 2014, inscribed to Einar Biilmann, €2625; and the Plotnick copy, Christie’s, 2002, inscribed to S. Weber, $7170, previously sold by Swann, 1995, $375.

Provenance: Carl Wilhelm Oseen (1879-1944) (inscription in Danish on upper wrapper in Bohr’s hand). Oseen was a theoretical physicist in Uppsala and Director of the Nobel Institute for Theoretical Physics in Stockholm. “The Bohr brothers had first met Oseen in the summer of 1911 at a congress of Scandinavian mathematicians in Copenhagen. The Swedish physicist, who had read Niels Bohr’s dissertation [offered here] with interest (as a Swede he had no difficulties with the Danish language), was among the first to recognize the genius of his colleague in Copenhagen” (Kragh, Niels Bohr and the Quantum Atom, p. 45). Nevertheless, Oseen could be critical. “In a letter to Bohr of 11 November 1913 in which he congratulated Bohr on his second paper in the trilogy [‘On the constitution of atoms and molecules’], [Oseen wrote that] Bohr had developed his theory ‘beyond the region of hypotheses and theories and into that of truth itself’. Praise apart, Oseen was curious to know ‘how the Maxwell – Lorentz theory should be modified to allow for the existence of an atom of your type’. Oseen (in contrast to Bohr) continued to worry about the problem, and in a detailed analysis in Physikalische Zeitschrift he reached the following, unequivocal conclusion: ‘Bohr’s atom model can in no way be reconciled with the fundamental assumptions of Lorentz's electron theory. We have to make our choice between these two theories. One of them may be correct, but not both of them’” (ibid., p. 125). Nevertheless, Oseen was full of admiration for Bohr’s theory. In his presentation speech at the award of the 1925 Nobel Prize to James Franck and Gustav Hertz, Oseen “emphasized that although the experiments of Franck and Hertz, were valuable by themselves, ‘even more important at the present time is the general finding that Bohr’s hypotheses concerning the different states of the atom and the connexion between these states and radiation, have been shown to agree completely with reality’” (ibid., p. 146). As a full professor of a Swedish university, Oseen had the right to nominate Nobel Prize winners, and it was Oseen who nominated Albert Einstein for the Nobel Prize in 1921, for Einstein's work on the photoelectric effect. Einstein was finally awarded the prize for 1921 when Oseen repeated the nomination in 1922.

“Niels Bohr (1885-1962) entered the University of Copenhagen in the autumn of 1903 and immediately began the study of physics, with mathematics, astronomy and chemistry as secondary subjects … With few lectures to attend, he began already as a young student to carry out original research in physics. The field of his earliest work, surface tension and surface waves on liquids, was determined more by the interest of his teachers than by his own choice …

“In those days the Royal Danish Academy of Sciences and Letters awarded each year gold or silver medals for monographs on topics specified by the Academy two years previously. Among the prize problems announced in February 1905 was one for physics which read as follows: ‘In the Proceedings of the Royal Society XXIX, 1879, Lord Rayleigh has developed the theory of the vibrations which a liquid jet carries out about the cylindric shape when it is somehow made to take another cross-section. From the theory, as well as from the experiments, which Lord Rayleigh has performed on these vibrations, it appears that they could serve to determine the surface tension of a liquid. The Academy, therefore, offers its gold medal for a more detailed investigation of the vibrations of liquid jets with special reference to the application mentioned. It is desired that the investigation be extended to a fairly large number of liquids. The results are to be compared with those previously found in other ways.’

“Solutions were to be submitted anonymously by October 30, 1906. Although most winners of these prizes had been mature scholars, the 19-year-old Niels Bohr decided to try his hand on the problem. He carried out the experimental work in the physiological laboratory of the University of Copenhagen, of which his father, Professor Christian Bohr, was the director. His father had to put pressure on him to terminate the experiments and cease making new and time-consuming corrections to the theory. The paper was written at his grandmother’s estate, Naerumgaard, a few miles north of Copenhagen. The fair copy was handwritten by Niels Bohr’s two years younger brother, Harald. Consisting of 114 pages and 19 figures, it was submitted on the very day of the deadline …

“On November 2, 1906, Bohr submitted an eleven-page addendum with the following note: ‘It is respectfully requested that the enclosed addendum, which, owing to an accident in the copying, was not submitted with the main essay, may be appended to the paper with the motto βγδ which was submitted as physics prize essay.’ That there was difficulty in meeting the deadline is indicated by the fact that this addendum was handwritten in part by Harald, in part by Niels himself, and in part by their mother …

“The physics prize essays were judged by Professors C. Christiansen and K. Prytz. Their report to the Royal Academy reads: ‘In answer to the Physics Prize Problem set by the Society for 1905, in which a detailed investigation of the vibrations of liquid jets was requested, two essays have been submitted … The author of the other essay, who designated himself by the mark βγδ [i.e., Bohr], has only managed to investigate the surface tension of water, on account of the experimental arrangement used. On the other hand, he has carried out a very extensive investigation of the conditions in the water jet. To produce a sufficiently long, regular, undivided and untwisted jet, the author let the water flow out through a long narrow glass tube whose orifice was made elliptic to bring about the vibratory motion. The jet was examined at a distance of about 25cm from the orifice to permit the viscosity to smooth out regularities in the motion. By selecting from a large number of prepared tubes, a few were found which gave the jet a symmetrical shape with respect to two mutually perpendicular planes through the axis. This symmetry was tested by an optical method which was also used to measure the wavelength. The amplitude of the vibration was found by measurement on an enlarged photograph of the jet.

“To determine the constant of capillarity, the author measured the amount of water flowing out in a given time, the velocity of the jet, and the wavelength. The velocity was found by a clever method which consists in cutting through the jet at a given place at two instants separated by a short time interval and measuring the length of the segment cut out and the corresponding time (ca. 1/50 s). The length of the segment cut out was found by photographing the cut jet by instantaneous illumination. The method gave very good results which could be checked by varying the time interval.

“To measure the wavelength, the aforementioned optical method was applied. It consists in reflecting a light source at the surface of the jet and finding the positions on the jet where the tangent planes are parallel to the axis.

“The performance of a single determination by the author’s method requires continued work through many hours. Hence, the jet must be maintained for a long time and under very constant conditions. This long time limits the applicability of the method in the case of liquids which change under exposure to air, and requires a comparatively large amount of liquid.

“When the problem was formulated, it was thought that the theory given by Lord Rayleigh should form the basis for the investigation. However, this theory gives only the first approximation. The author of this essay has remedied this by extending the theory so as to take into account viscosity and amplitudes that are not infinitely small. It is obvious that these investigations are of great interest for judging the value of the method and finding under what conditions it may be expected to yield the best results.

“This work does not solve the problem as completely as the former, in that it has studied only a single liquid, water. On the other hand, its author has earned so great merit by carrying the solution further at other points that we feel we must recommend that also this essay be awarded the Society’s gold medal …

“After receiving the gold medal, Bohr carried out additional measurements of the surface tension of water. At the same time he was occupied with the considerable task of preparing his work for publication. In the latter part of 1908 he submitted a paper entitled ‘Determination of the Surface-Tension of Water by the Method of Jet Vibration’ to the Royal Society of London. This paper is not a simple translation of the prize essay but deviated from the latter at a number of points …

“On June 9, 1909 he sent a reprint of the paper to his brother Harald, then in G ttingen. The paper appeared in the Philosophical Transactions of the Royal Society. Of all the papers published by Bohr, this is unique, not only in being his earliest publication, but also in being the only paper in which he reports experimental work carried out by himself.

“The addendum submitted three days after the main part of the prize essay was an investigation of the influence of the finite amplitude upon waves on the surface of deep water, progressing without change in shape under the influence of gravity and surface tension” (Collected Works, Vol. 1, pp. 3-11). It was first published in Bohr’s Collected Works (in English translation).

The other entry for the prize, which also won the gold medal, was by Pio Pedersen.



Offprint from: Philosophical Transactions of the Royal Society of London, Series A, Vol. 209. 4to (305 x 231 mm), pp. 281-317, [1]. Original printed wrappers (wrappers detached, spine slightly damaged).

Item #4432

Price: $5,500.00