...Harmonics. It is clear that if the value of V on the surface of a sphere whose centre is the origin can be expressed as a sum of terms each of which is a surface Spherical Harmonic, its value at any point not on the surface is the sum of the appropriate...

...sin k'x cos kx cos lycos I'y + B' I' cos k'xsml'ycosl'y) + . . . of which the terms in t — t0 can be expressed as a sum of terms, each of which is a product of sines or cosines, such as, s'm(k + k')xcos(l + l')y (1.24) The wavenumbers of this term...

...in, in this case And it follows that every rational integral concomitant of any number of m-ics can be expressed as a sum of terms each of which is a product of concomitants of types which give irreducible forms for то — 1 m-ics, and of types of...