Title: Spherical Harmonics: an Elementary Treatise on Harmonic Functions, with Applications
Abstract: THE object of this work is to provide a text-book on the elements of the theory of spherical harmonics with applications to mathematical physics so far as this can be done without employing contour integration. Within these limitations the author has certainly provided a useful book: The actual treatment of spherical harmonics occupies ten chapters with gravitational, electric, and magnetic applications. There is also a treatment of spheroids. No applications to hydrodynamics are mentioned. Chap. i. contains an account of Fourier expansions subject to Dirichlet's conditions, which should prove useful. Chap. ii. deals with the conduction of heat, and in Chap. iii. an interesting discussion of the vibrations of harp, violin, and piano strings is given, which offers a striking contrast in the effect of initial conditions. The last three chapters of the book give, a valuable account of Bessel functions and their applications to the vibrations of a circular membrane and the flow of heat. Spherical Harmonics: an Elementary Treatise on Harmonic Functions, with Applications. Prof. T. M. MacRobert By. Pp. xii + 302. (London: Methuen and Co., Ltd., 1927.) 15s. net.