The Association will mourn the untimely death of its President, Professor Louis Napoleon George Filon, less than a week before the Annual Meeting to which he had looked forward with such keen anticipation and at which he had hoped to preside and to give his Presidential Address. It is easy for those who knew him and his work to understand how strongly the objects of the Association appealed to him and how deeply he appreciated his election as its President.

Alfred Lodge became a member of the A.I.G.T. in 1888, was Honorary Treasurer from 1891 to 1896, and first President of the Mathematical Association in 1897-1898. Until recently he was constant in his attendance at meetings of the Council; we shall not easily forget his keen interest in all the activities of the Association or the charm of his kindly manner. His first contribution to the Gazette appeared in No. 1; his last in No. 239.

The Annual Meeting of the Mathematical Association was held at the Institute of Education on 4th and 5th January, 1938. On Tuesday, 4th January, Professor E. H. Neville took the chair for the Business Meeting at 2.30 p.m. Professor Neville spoke of the loss suffered by the Association through the death of the President, Professor L. N. G. Filon, on 29th December.

During the year 1937, 153 new members have joined the Association, of whom 40 are junior members. The number of members now on the roll is 1648, of whom 9 are honorary members, 108 are life members, 1463 are ordinary members and 68 are junior members.

The Council reports with the deepest regret the untimely death of the President, Professor L. N. G. Filon, and wishes to record its appreciation of the services rendered by him to the Association.

The considerations which I propose to put before you to-day arose from an attempt, when teaching students, to build up the classical laws of Newtonian Mechanics inductively from laboratory experiments.

In this task we are immediately confronted with two fundamental notions, those of mass and force.

It will probably be admitted that no definition of a physical quantity can be accepted as adequate unless it implies a criterion leading to an unambiguous measure of the thing defined.

On connaît le problème classique ou le problème simple de Dirichlet. On donne une surface fermée S qui partage l’espace en deux domaines, l’un intérieur, l’autre extérieur. On suppose que la surface satisfait à certaines conditions de régularité, par exemple, être douée d’un plan tangent. On assigne une fonction continue U(M) d’un point M sur la surface S, et l’on demande de déterminer la fonction U(P), harmonique et bornée dans l’un des deux domaines précédents, qui tend vers U(M) quand le point P tend vers le point M de la frontière. Le problème est intérieur ou extérieur selon le domaine considéré.

The solution of the general case of a cable having constant resistance R, inductance L, capacitance C, and leakance G, all expressed per unit length, is usually obtained in the form of an expansion. Using his operational method, Heaviside was the first person to obtain a solution. F. W Carter points out that Heaviside’s result seems to be incorrect, and proceeds to find a solution in the form of a double summation. By aid of complex integration, the integrand being expanded in Bessel functions, H. Jeffreys gives another form of series solution. As this type of problem may arise in lectures on applied mathematics, it is proposed to show how a compact result can be got by contour integration, using a suitable transformation.

We propose to study in this paper the properties of a set of points on a proper rectangular hyperbola. We call this set an H-set, which is characterised as pure or mixed according as the points of the set belong to one branch or to both the branches of the hyperbola.

I. There are three ways of trisecting an angle bounded by OA and OB ( = 3αor 3α +2π or 3α +4π), namely:

(i) OX1 and OY1,

(ii) OX2 and OY2,

(iii) OX3 and OY3,

as shown in Fig. 1.

It is well known that if the Euclidean angles of a triangle ABC are trisected as in Fig. 2, then the triangle xyz (commonly quoted as Morley’s Triangle) is equilateral. But angles CAB, ABC, BCA may be trisected each in three ways, so that there are really 27 “Morley” triangles to be considered. The purpose of the present paper is to show that 18 of these 27 triangles are equilateral.

In this address I use the word Euclid not as the name of the man but as a short title for the XIII books of his Elements of Geometry. The “Euclid” of our schooldays was but a small part of the whole, just as the “Newton” of our Cambridge days was a mere fragment of the Principia. We learnt the whole of Books I-IV, about half of VI and about half of XI, of the rest we knew nothing.

If a series of points be pricked at random through a strip of paper, and the strip be held horizontally, certain of the points will appear as peaks, namely those which happen to be higher than either of their immediate neighbours. These we call maximal points. Similarly there are others, minimal points, which are lower than either of their immediate neighbours. Between each maximal point and an adjacent minimal point is a “run”, either a “run up” or a “run down”, the points in a run forming a steadily ascending (or descending) series. These runs will naturally be of various lengths, the length of a run being defined as the number of points in the run, including the first and the last. The shortest runs will thus be of length 2, others may be of length 3, 4, or some greater number, up to m, where m is the total number of points on the strip. Clearly where the points form a run of m there is only one run throughout the whole strip, the greatest possible number of runs is m-1, in which case each run is of length 2.

The circle will in future have 400 degrees in Germany, instead of 360, as at present, and the right angle 100, instead of 90. This is ordered in a new decree of the German Minister of the Interior.

Degrees will continue to be divided into minutes and seconds, but these will also be arranged on the decimal principle.

Several years will be allowed to elapse before the new geometry is made obligatory, especially for use at sea, but it will be taught in the schools next year.—Daily Telegraph and Morning Post, Nov 1, 1937.