The desirability of affording facilities, to mathematical teachers and others, for post-graduate studies in mathematics during the summer vacation, was commented on by the writer in an article in the March, issue of this Gazette. It was there proposed that a “Summer School” should be organized for this purpose by teachers themselves, acting through the Mathematical Association, and after the publication of the article the suggestion was more formally communicated to the Association through the Manchester branch. It proved to be unlikely, however, that the matter could be taken up by the representative body, whose members met rather infrequently, and who were already fully occupied in other business of the Association, in sufficient time to make arrangements for such a School during the present year. The proposal was therefore brought before the Extra-Mural Committee of the University of Manchester, who agreed to the experiment being made under their auspices, and voted a grant for organizing and advertising the project. The Board of Education were next approached, and they agreed to recognize the School and to make a limited grant to cover a possible deficit on the cost of working it. Provisional arrangements were proceeded with meanwhile, and in April and the early part of May circulars announcing the School and inviting students to register were distributed to the heads of the mathematical departments of nearly every secondary, grammar and high school, and many technical schools and colleges, throughout England and Wales. The School was also advertised in various educational journals. The response was satisfactory, thirty-two students being registered, whereas twenty was the number decided upon as the minimum required if the School was to be held.

A striking article under this title appeared in Nature of 10th May, 1924. The anonymous writer deplored the present position of mathematical physics in England, and suggested that the mathematical course at Cambridge was now much inferior to what it was in the days of Kelvin, Stokes and Maxwell, in that the physical aspect had been almost crowded out, leaving pure mathematics predominant. As a result, it was declared, there was only one man out of all those who had taken the Mathematical Tripos in the last forty years who had any claim to be recognised for his researches in mathematical physics apart from astronomy and relativity, in which it was admitted that excellent work had been done. The remainder of the article was a strong plea for the inclusion of physics in every mathematical course.

Some teachers may not have noticed that there is a real connection between the parallel postulate and another and more fundamental property of space which it is also more natural to assume, viz. that stated by John Wallis in the seventeenth century:

The recent discussion of this subject * cannot fail to have important effects. It must certainly have aroused in many a new conception of the part Similarity should play in Elementary Geometry.

In this article—which embodies an integral part of work on elementary geometry, most of which has recently been published —a presentation of the ideas of Parallelism is given, which is designed to bring the conviction on this subject that has too commonly been lacking, and to show how central its place is in Euclidean Geometry. Together with the discussion of the Plane theory, an indication is given (in 5) of a sufficient elementary treatment of Similarity: “sufficient,” in no disparaging sense, but in the sense of sufficing for every reasonable need at the stage in question.