During the year 115 new members, including Junior members, have joined the Association. The membership is at present 1784, of whom 9 are honorary members, 1691 are ordinary members and 84 junior members. Thirty libraries are also on the roll. There have been a few resignations, mainly in consequence of war-time difficulties the Council hopes that these members will be able to rejoin later The Council records with regret the deaths of the following members of the Association Mr C. J H. Barr (1902), Mr H. C. Beaven (1906), Mr F C. Boon (1910), Prof. S. L. Loney (1896), Rev J J Milne (1884), Mr A. R. Prestwich (1904), Mr J Leadbeater (1934).

In a lecture delivered to the London Branch on 19th October, 1935, and reported in the Gazette, Vol. XX, p. 233, Mr C. V Durell showed a large number of interesting loci suitable for boys and girls up to school certificate standard. It is proposed in this article to pursue the matter further for those of higher certificate standard.

Any plane KLPQN cuts the edges of a tetrahedron ABCD in six points forming a complete quadrilateral. If UVW is the triangle formed by the diagonals of this quadrilateral, then

1. (i) the triangular f aces BCD, ACD, . of the tetrahedron are each of them in perspective with the triangle UVW from points A1, B1, C1, D1 respectively

2. (ii) the tetrahedra ABCD, A1B1C1D1 are in perspective f rom U, V, W and from a fourth point Ω.

The algebra taught at present in schools and colleges and discussed in recent reports is essentially that of Euler and Chrystal as regards both content and method. Must this tradition continue? It is hoped that this short note will suggest the contrary and indicate the possibility of incorporating the ideas and methods of modern algebra in elementary teaching. To this end attention will be drawn to some of the simpler concepts of the subject.

We will consider first the second order partial differential equation

where α, β, γ, δ, ε, η are all functions of x or t only

Suppose the six coefficients are functions of x. Then since

we have

for none of the six coefficients contains t.

“Please Sir, what’s the use of learning this?”

I wonder how many times we have all—that is, if we are at all “approachable”—been asked this or similar questions? To-night I hope to show why the question is ever asked and, in my opinion, how to stop it arising in the minds of the pupils.

But first let me make clear this one fact. Although this is being presented to you in the month of February it was commissioned by your committee in December last, and though in the interim the Spens Report has been published it has not been used in any way in the preparation of this paper.

1. Heaviside’s operational method has for some time been in fairly general use among engineers for solving problems in circuit theory, and appears in most of their textbooks. The average man who has read these seems able to manipulate the “expansion theorem” and to solve problems in which E.M.F is applied to an initially “dead” circuit, but he is not at all clear about the foundations or correctness of the theory and apt to be worried by any slightly more complicated problem, such as cases in which the circuit is not initially dead or problems involving switching operations (which are usually dealt with in the textbooks by artifice). It is now pretty well recognised that the Laplace transformation provides a satisfactory approach to the operational methods, but it is not perhaps fully realised just how simple it is and how extremely easy to teach.