On A Condition For Helmholtzs Equation Similar To Lames (1902)(en)(3s)

VOiL. 6, I1920 PHYSICS: A. G. WEBSTER 605 polar atoms, and not of ions, and to use the term ions only in its historical sense, that is to designate particles which migrate in the electrical field. 1 Noyes and MacInnes, these PROCZIDINGS, 5, 1919; J. Amer. Chem. Soc., 42, 1920 (239). London, Phil. Mag., Ser. 6, 14, 1907 (3). 1918 (214, 354). Soc., 113, 1918 (449, 627). Zs. Elektrochem., 24, 1918 (321). Chem. Soc., 33, 1911 (1807, 1827, 1836). 1919 (1951); 34, 1912 (1631). 8 Ibid., 33, 1911 (1864). 2 3 Ibid., 35, 4 J. Chem. 5 Bjerrum, 6 J. Amer. 7 Ibid., 41, ON A CONDITION FOR HELMHOLTZ'S EQUATION SIMILAR TO LAME'S By ARTHUR GORDON WUBSThR CLARK UNIVERSITY Communicated July 14, 1902 During the last thirty years the writer has been very much interested in the diffraction of sound, a -subject suggested to him for theoretical treatment in 1888 by his teacher, the great von Helmholtz. Considering the great amount of paper spoiled in futile attempts to further the subject, the pessimistic view of Lord Rayleigh, and the amount of experimental results obtained by the writer, but not published, it seems proper, in accordance with a policy recently announced by the writer, to publish whatever he has in storage, however modest. A small attempt was made in a paper "On the Wave Potential of a Circular Line of Sources (Proc. Amer. Acad. Arts Sci., December, 1911), an improvement on which has been recently made. The following paper is taken from a drawer, endorsed February 20, 1908, and like the other was written in the attempt to advance the theory of the megaphone. The condition obtained by Lame that a singly infinite family of surfaces shall be the equipotentials for some distribution is well known. It occurred to me to examine the condition that there may be a function V satisfying the differential equation inve