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About 75 B.C., Cicero the orator, stumbled upon an ancient monument. The lettering was illegible, but ‘on clearing away the brambles and thorns’ he discovered a curious design—a sphere with circumscribed cylinder.

In the Mathematics Section of the Science Museum, South Kensington, is a display cabinet that contains many specimens of Napier’s Rods, or Bones. In a corner of the same cabinet are some cardboard “rods” of very different design, expertly made by the Museum staff. Unfortunately they do not form a complete set, nor is their structure immediately obvious, which might account for the fact that they appear to have attracted very little attention. Be that as it may their appearance is certainly intriguing, as a glance at Figure 1 will confirm, and in operation they represent a distinct advance over Napier's rods, on which they are based.

In many textbooks on applied mathematics, mechanics, or applied mechanics, the impression is still given that the only absolute systems of units are either the CGS system, using the gramme and dyne, or the British system using the pound and poundal and also that the only alternative system is a gravitational one in which either the unit of force or both the unit of force and the unit of mass vary with position; a few bodies do include the MKS system.

Recent notes (1, 2) suggest the problem. Find necessary and sufficient conditions on a set of n(>3) real constants a1 …, anfor the inequality

The following definition of differential is not uncommon. It is to be found in Goursat’s and Hardy’s classical texts, as well as in a few more recent ones.

Gamesmanship is defined as being the art of winning games without actually cheating. I do not intend to define researchmanship similarly but rather as minimum energy research.

One can only start from what one knows and proceed to things unknown in the subject one likes best. For myself, I like the integers and can tolerate fractions but consider series anti-social. As for divergent series, they do not bear thinking about.

As a result of the present revolution in Mathematics teaching it is increasingly likely that the word Vector’ may fall into the hands of young people. This word has been used rather carelessly in the past, and I would propose that before it becomes generally available to children we should legislate a few safety regulations. (Polyvalency is one thing, but spreading confusion among the young is another.)

Now that formal Euclidean geometry is disappearing from the school syllabus the time is ripe for a reappraisal of the background to analytical geometry

Consider the following question. Find the coordinates of the fourth vertex of a parallelogram A BCD if the other vertices are A(2, 4), J5(l, 1) and (7(7, 2).

It is well known that the six rotations of an equilateral triangle form a group; that is to say that, if an equilateral triangle ABC occupies a certain triangular space, there are six operations and six only which when performed either singly or in succession will leave the triangle still occupying the same space, but with vertices in different positions. The set of six possible orientations of the movable triangle are drawn below and numbered.

In 1877, the English mathematician J J. Sylvester (1) announced the discovery of a rather complete formal analogy between the mathematical theory of the invariants and covariants of binary quantics and the chemical theory of valency as it then stood.

What is the effective rate of interest when a loan of £L is paid for by n equal payments of £P at equal intervals of time, as in hire purchase and other forms of time payment?