Whereas the works on Trigonometry, Geometry and Determinants were published over the name of Charles L. Dodgson, Student and Mathematical Lecturer of Christ Church, Oxford, the two small works on Logic—The Game of Logic and Symbolic Logic, Part I — and the two interesting logical notes in Mind appeared over the signature of the creator of Alice. Thus on the theory of double personality which the Rev C. L. Dodgson tried so hard to establish (and so unsuccessfully, since his was a completely integrated though singular personality), the formal works on logic are to be classed with those informal ones which are the delight of the civilised world.

This article does not advocate dispensing with the calculus in the least; it suggests ways in which some of the traditional problems of calculus may be studied by other methods much earlier in the school. This makes a range of very interesting problems available to a much wider audience, and also shows how some of the problems of the sixth form science course can be treated with pupils who have the misfortune to be studying science without the calculus to help them.

The object of this paper is to discuss some properties of the Isosceles Tetrahedron, in which each edge is equal to its opposite. The last three theorems are possibly new, the remainder are included for their own interest or for completeness in listing elementary results; in the latter case, proofs are not given.

1. You all remember that in that well-known play, Waiting for Godot, the eponymous hero never actually appears. In the same way my talk should perhaps have been entitled Waiting for transcendental numbers—for while transcendental numbers are at the back of everything that follows, they will not become, for reasons of technical difficulty, proper part of the action.

In a recent paper (1) P. Holgate obtains the following equations for pk(t) [k = 1,2,…, n], the probability that, at time t, the n animals in a given area are grouped into k herds.

The number π (as all—or very nearly all—the world doth know) signifies the ratio of the circumference of a circle to its diameter and is also equal to the ratio of the area to the square of the radius. This suggests two generalisations of π which apply to plane figures of any shape: