The centenary of the birth of Oliver Heaviside last year has been the occasion of celebration by electrical engineers and physicists in this and other countries. In the discussions of his work much has been said about the Operational Calculus ; and as the versions of its history which have been given both in these commemorative celebrations and in most of the textbooks of the subject are seriously incorrect, this may serve as an occasion to recount that history more correctly. The story in widest circulation is that the Operational Calculus was discovered by Heaviside (Boole being sometimes—and incorrectly—named as the discoverer of its applications to ordinary differential equations) and rejected by British mathematicians because of Heaviside’s lack of rigour. The facts, as I shall show, are that the Calculus was well known in Britain and France before Heaviside’s birth, and that the rejection of his paper had nothing to do with his use of symbolic methods.

Consider a rigid body having one point O fixed, which is acted upon by a set of forces Fs (s = 1, 2, ..., n). Then the equation of motion of the body is given by

where H is the angular momentum of the body with respect to the point O and rs = OPs, Ps being the point of application of Fs. A similar equation holds in the general motion of a rigid body if H denotes the angular momentum with respect to G, its centre of gravity.

In this note I discuss the general bilinear transformation

where a, b, c, d are any given complex numbers (with c, d not both zero), and where w, z are complex variables, whose planes are regarded as coincident.

In recent years the people concerned with admission of students to undergraduate courses reported that a good deal of difficulty and confusion had arisen from the multiplicity of applications and from students accepting places in several Universities without notifying the Departments concerned, or withdrawing at the last minute from a place already accepted. In this way places were often kept for applicants who did not turn up in the end and vacancies were left for which suitable candidates would have been available earlier.

In the discussion of this problem various remedies had been suggested, including a deposit to be paid either at the time of application or at the time when a place was offered, but it was felt that this would not be a complete remedy and in addition might, in some cases, cause hardship.