J. Cable [1] suggests that if the word “vector” is going to be introduced into secondary school mathematics then it should at least be done properly Probably nobody would explicitly disagree with this, although there is a fair amount of evidence that implicitly many have and still do. But why must “vector” be introduced properly? Why the special fuss about vectors? The basic mathematics necessary to introduce vectors properly is common to many other mathematical ideas. (We wish to make it clear at the outset that our remarks in this article only refer to the printed text of the paper mentioned above. We do not wish to imply, for instance, that Mr. Cable does make a special fuss about vectors, but that the implication of his article is that vectors deserve special attention.)

The purpose of this article is to show how elementary properties of the cubic curve can give rise to an abstract structure with interesting properties and to investigate some of the simpler of these.

The collection of papers and books of the late Dr. F. W. Lanchester, F.R.S., held in the library of the Lanchester College of Technology, Coventry, contains a paper cover booklet entitled Lanchester’s “Potted Logs”, Parts I and II, printed and published by Taylor and Francis Ltd., Red Lion Court, Fleet Street, E.C.4, in 1939, priced 2s. The booklet measures 4ξ × 7¼ and consists of 27 pages devoted to “a concise tabulation (slide rule auxiliary)” of common and natural logarithms for engineers. In Part I (14 pages) “a new system is disclosed by which the Logarithms of Numbers running to seven or eight figures may be evaluated to seven places of decimals and vice versa” Of these 14 pages, 5 only are required for the tables, the remainder being devoted to preface, introduction and worked examples. In Part II (8 pages, 4 of which are tables) the system is extended to cover natural logarithms. The remaining pages contain a note on the musical scale (“of interest to the musician, it is a table in antilog form to the base 1-059463 . . and is the foundation of the system of equal temperament”) and lists of papers, lectures, reprints, reports, memoranda and books by Lanchester.

George Boole gave (in his books, listed under [1] and [2] in the references at the end of this article) a method for solving any equation in his algebra. This part of his work is now largely ignored in the many modern books on boolean algebra which are making their appearance (I can think of several reasons why). Nevertheless, the method can be adapted to conform with our standards of rigour.

In certain computer applications to engineering problems such as the automatic control of machine tools the computing equipment derives its input in digital form, from, for example, an angle-indicating device on a rotating shaft. The indicating device may take the form of a multiple commutator or a coded disc read by photoelectric means. Since the shaft is rotating at mechanical speeds and the reading device is operating at electronic speeds a possibility of false readings exists when for example a change from 1999 to 2000 is taking place. In fact any of the readings 1999, 1990, 1900, 1000 or 2000 may occur in the same sort of way that a mileage recorder could be misread under similar circumstances.

The recent introduction of logic and group theory in the secondar; schools has inspired many young students to investigate these area of modern science. The purpose of this paper is to bind togethe propositional logic and the theory of symmetric groups in a elementary fashion so that new vistas may be revealed to those wh wish to explore.

(1) Definitions. In the system of n coplanar straight lines each line is produced indefinitely in both directions so that all possible points of intersection (vertices) are obtained. The plane of the system is thus divided into regions which may be closed (of finite extent) or open (of infinite extent).

We are concerned with the problem of constructing on a sphere maps whose faces (regions) all have the same number of edges.