On the determination of the tension of a recently formed water-surface. Offprint from: Philosophical Transactions of the Royal Society of London, Series A, Vol. 84, No. 572, 15 December 1910.

[London: Harrison and Sons], 1910.

First edition, author’s presentation offprint, inscribed in Bohr’s hand to his student friend and later brother-in-law PoulNørlund, of the ‘Second Royal Society Paper’ on the surface tension of liquids. 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]” (Collected Works, p. 12). 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’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. 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. The present paper describes Bohr’s subsequent work on surface tension, prompted by a paper by Philipp Lenard, winner of the Nobel Prize for Physics in 1905 for his work on cathode rays, in which he claimed that a recently formed water surface has a high surface tension which rapidly decreases. Bohr’s measurements and calculations did not support Lenard’s conclusions. ABPC/RBH lists only one copy. OCLC lists Smithsonian only in US.

Provenance: Inscribed in upper corner of front wrapper by Bohr, ‘Til Poul fra Niels’, to PoulNørlund (1888-1951), historian and later director (1938-1951) of the Danish National Museum, and the brother of Bohr’s future wife Margrethe. Bohr enrolled at the University of Copenhagen in 1903 where he was taught physics by Christian Christiansen and philosophy by Harald Høffding, a friend of his father. A group of 12 students began to meet after Høffding’s lectures to continue the discussion of various topics in philosophy. This group, which called itself ‘Ekliptika’, included Bohr and PoulNørlund, as well as their brothers Harald and Erik, both mathematicians. Bohr met Poul’s sister Margrethe in 1910 and they were married two years later.

As early as 1877 Quincke had observed that the effective surface tension of certain solutions continued to decrease for hours. Ten years later, Lenard gave reasons for believing that the tension of a newly formed water surface is higher than that of an old surface; and in 1890, Lord Rayleigh observed that if the surface was less than 0.01 sec. old, the effective surface tension of a certain soap solution was only a little less than that of pure water, although its equilibrium value was about a third of that of water. He states that, as early as 1869, Dupré had observed that the tension of a recently formed surface of a soap solution is abnormally great. Lenard returned to this question in 1910.

“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(Clarendon Press, Oxford 1930, p. 324): “The various dynamic methods give the surface tension of more or less recently formed surfaces, and may yield results different from the static methods, if adsorption occurs, and is incomplete at the moment when the tension is actually measured. One factor in dynamic measurements which cannot be satisfactorily measured at present, is the time which has elapsed between the formation of the surface from the homogeneous interior liquid, and the actual measurement of the surface tension. If this could be varied, and measured with an accuracy of say 10-4 second, a valuable new weapon would be available for investigating the progress of adsorption. Bohr’s work on oscillating jets is probably the best of any dynamic methods” (Collected Works I, pp. 11-12).



Large 8vo (254 x 176 mm), pp. [395], 396-403, [404, blank], original light brown printed wrappers.

Item #5043

Price: $2,800.00