I have considered elsewhere the modelling of the pricing policies of Electricity Boards, Gas Boards and British Telecom [1]. In this article the combined effect of the standing charge rebate and estimate accounts are considered and two results contrary to popular belief are shown.

As A. M. Cohen’s paper has reminded me, Euler’s transformation for summation of the slowly convergent alternating series

is commonly derived by the following method, without enquiring into its validity which is distinctly dubious.

1. The applications of spherical harmonic functions in mathematical physics are closely connected with the various potentials—gravitational, electrostatic, magnetic, or the velocity potential in hydrodynamics. It is of interest to recall, briefly, the development of the potential theory. The actual name “potential function” or potential was first introduced by Green in the memoir of 1828 in which he published his famous theorem on the transformation of surface and volume integrals. But the use of the potential function goes back to Euler (1707–1783), who formulated the fundamental differential equations of hydrodynamics, and integrated them in the case where a velocity potential exists, which he recognized to be a special case.

Before reading this article, you may like to turn to page 297, where you will find a quiz on ‘famous-name’ mathematics. In each of the questions it seems reasonable to suppose that the mathematician indicated in the title of the result is the discoverer or inventor of the result. But a careful look at mathematical history shows, in each case, that there is a ‘story behind the story’. As you read on, keep in mind that even the answers given below are subject to revision as new historical data is found and interpreted.