According to the standard-text-books, an asymptote is a line which meets a curve at two points at infinity, but is not wholly at infinity. Regarded as a flash of mathematical wit the definition is clever and illuminating, but it is far too subtle for a raw student. He may have learnt that to call parallel lines “lines that meet in a point at infinity” is merely a Pickwickian way of saying that they do not meet at all, but, being in a plane, had (so to speak) their chance of meeting and just failed to take it; but even if he understands that, he may still be mystified here. For the asymptote and the curve meet, he is told, at two points at infinity, and who could guess what complicated tragedy of failure that euphemism conceals?

The following solution is suggested of Mr. J. Katz’s problem, “How is e to be introduced into our teaching?” published in the December number of the Gazette.

In teaching beginners the elements of the calculus, the teacher’s first real difficulty arises when he has to present the differentiation of the logarithmic and exponential functions; these being a natural outcome of an attempt to complete the rule for xn for all values of n, including the case when n=−1. He either has to make the approach as in texts on “practical mathematics,” by differentiating the series for ex, with all the tacit assumptions that have to be made; or he is dependent on non-rigorous treatment of limits, necessary to show that (ax−1)/x tends to the limiting value logea; or to find solutions of dy/dx=y by some such process as is given in Lamb’s treatise on the Calculus, without the necessary proofs of convergence and differentiability of the series assumed; or he is bound to discuss convergence and continuity fairly fully, and give such proofs as Lamb gives, or the equally severe method of Hardy’s text.

In the Memorandum from the Girls’ Schools’ Committee of the Mathematical Association, published on pages 13-15 of the Mathematical Gazette for January, 1926, we are told that the Committee deprecates the use of the term “inferiority” as applied to girls’ mathematical work by the Report on the Differentiation of Curricula between the Sexes. Further, the Girls’ School Committee says: “Where boys and girls are given equal opportunities, as in some mixed schools, the consensus of opinion is that very little difference in capacity between boys and girls is shown in work up to Matriculation standard….” It seems desirable that the question should be put on a sound basis, and with this in mind the writer has endeavoured to draw on material available to him for a statistical inquiry into the points involved. For the last two years he has been engaged in teaching in a mixed school where the boys and girls are taught mathematics together by the same teacher in the lowest two forms, and the forms are chosen on a basis of general standard in school work. The marks are given below. In each case the marks are those obtained by equating the quartiles (by a modification of a method due to Prof. Nunn and given by the writer in the Forum of Education in papers in 1924 and 1925) to 40 and 60, in homework, weekly tests, and terminal exams. The two marks given are those obtained at the ends of the Christmas and Midsummer terms.