[London: Harrison and Sons], 1910.
Presentation offprint, inscribed in Bohr’s hand to the chemist Einar Biilmann, of the ‘Second Royal Society Paper’ – what Bohr “learned by working in this field may have been a help to him when, more than a quarter of a century later, he showed that some of the properties of atomic nuclei can be understood by comparing them to liquid drops [i.e., Bohr’s liquid-drop model].” (J. Rud Nielsen).
In February 1905 the Royal Danish Academy of Sciences and Letters announced a prize concerning Lord Rayleigh’s 1879 theory that the surface tension of liquids could be determined from the surface vibrations of liquid jets. The problem proposed by the Academy was to perform quantitative experiments to implement Rayleigh’s method. Bohr faced formidable difficulties, not least the fact that, since the university had no physics laboratory, Bohr had to perform the experiments at night (to avoid perturbations due to passing traffic) in his father’s physiology laboratory. Bohr’s paper was submitted on the deadline of 30 October 1906, and on 23 February 1907 the Academy notified Bohr that he had won its 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 deviates from the latter at a number of points…
“In 1910, while Bohr was working on his doctor’s dissertation, a paper was published by P. Lenard, in which he claimed that a recently formed water surface has a high surface tension which rapidly decreases. Lenard stated that this was in agreement with Bohr’s results. This led Bohr to re-examine the matter and, in particular, to test by new calculations the claim made by Lenard that a variation of the velocity over the different concentric parts of a jet will prolong the periods of vibration and increase the wavelengths of surface waves on the jet. He made a direct calculation of the wavelength when the velocity in the jet varies with the distance from the axis and concluded that his experiments do not support the claims made by Lenard. In August, 1910, he submitted to the Royal Society a paper entitled ‘On the Determination of the Tension in a recently formed Water-Surface [i.e, the offered paper], which was published in its Proceedings. This was Bohr’s last work on surface tension. The results of this paper, and the merit of the experimental method described, have apparently been appreciated by most later workers in the field. Thus, N. K. Adam writes in his book The physics and chemistry of surfaces… ‘Bohr’s work on oscillating jets is probably the best of any dynamic methods.’
“What he learned by working in this field may have been a help to him when, more than a quarter of a century later, he showed that some of the properties of atomic nuclei can be understood by comparing them to liquid drops [i.e., Bohr’s liquid-drop model].” (J. Rud Nielsen, Collected Works, pp. 8-12).
Large 8vo (254 x 176 mm), offprint from the Proceedings of the Royal Society, A, Vol. 84, 1910, pp.  396-403 [404:blank], original light brown printed wrappers, inscribed in Bohr's hand to the upper right corner of front wrapper: 'Hr Professor E. Biilmann / ærbødisgst fra Forf.' (i.e., Mr. Professor E. Biilmann / respectfully from the author), Prof. Einar Biilmann (1873-1946) was a Danish chemist and early friend of Bohr, number in blue pencil to upper right corner of front wrapper (probably a library numbering from Biilmann).