I HAVE to thank several correspondents for assistance in this matter. Mr. G. J. Bennett finds that my case of n = 3 can really be solved by elliptic integrals, and, of course, Lord Rayleigh’s solution for n very large is most valuable, and may very probably suffice for the purposes I have immediately in view. I ought to have known it, but my reading of late years has drifted into other channels, and one does not expect to find the first stage in a biometric problem provided in a memoir on sound. From the purely mathematical standpoint, it would still be very interesting to have a solution for n comparatively small. The sections through the axis of Lord Rayleigh’s frequency surface for n large are simply the “cocked hat” or normal curve of errors type; for n = 2 or 3 they do not resemble this form at all. For n=2, for example, the sections are of the form of a double U, thus UU, the whole being symmetrical about the centre vertical corresponding to r = 0, but each U itself being asymmetrical. The system has three vertical asymptotes. It would be interesting to see how the multiplicity of types for n small passes over into the normal curve of errors when n is made large.
