Vol. 6, 1920 
PHYSICS: A. G. WEBSTER 
605 
polar atoms, and not of ions, and to use the term ions only in its his- 
torical sense, that is to designate particles which migrate in the electrical 
field. 
1 Noyes and Maclnnes, these Proceedings, 5, 1919; /. Amer. Chem. Soc, 42, 1920 
(239). 
2 London, Phil. Mag., Ser. 6, 14, 1907 (3). 
3 m'J., 35, 1918 (214, 354). 
4 /. Chem. Soc, 113, 1918 (449, 627). 
5 Bjerrum, Zs. Elektrochem., 24, 1918 (321). 
6 J. Amer. Chem. Soc, 33, 1911 (1807, 1827, 1836). 
7 Ibid., 41, 1919 (1951); 34, 1912 (1631). 
8 Ibid., 33, 1911 (1864). 
ON A CONDITION FOR HELMHOLTZ'S EQUATION SIMILAR TO 
LAME'S 
By Arthur Gordon Wkbster 
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 sub- 
ject, the pessimistic view of Lord Rayleigh, and the amount of experi- 
mental 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 Set., December, 1911), an improvement on which has 
been recently made. The following paper is taken from a drawer, en- 
dorsed 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 oc- 
curred to me to examine the condition that there may be a function V 
satisfying the differential equation investigated by von Helmholtz, 
Ay -f kw = 0, (1) 
which comes from the wave equation 
g-r - (2) 
when we assume that (p contains a simple harmonic function of the time, 
the function V depending upon a single parameter q. If this is the case 
we have 
