Acting Secretary. INTUITIONISM AND FORMALISMS

established in his Munich dissertation,* "Ueber die Ausbreitung der Wellen der drahtlosen Télégraphie auf der Erdkugel," for the case where ƒ(0) is continuous in the interval (0, w) and is subject to certain other restrictions, is also capable of representing a function which has a finite number of finite discontinuities in this interval, and that at such a point of discontinuity the integral represents the mean of the two limiting values of the function. In the second part of the paper use is made of the method employed in establishing the integral representation to obtain the well-known development of an arbitrary function in a series of spherical harmonics. The method has the advantage of not requiring a proof of the possibility of the development, as this is made to depend upon the possibility of the development of an arbitrary function in a Fourier series of special form.