One of the most agreeable fruits of the renaissance which has followed the achievement of national independence in Ireland has been the decision to make accessible, in a form worthy of their importance, the writings of the greatest Irish mathematician and natural philosopher. The responsibility for the work was undertaken by the Royal Irish Academy, with the cooperation of the University of Dublin and the National University of Ireland, and with assistance from the Royal Society and the editorship was entrusted to Professor A. W Conway, F.R.S., of University College, Dublin, and Professor J L. Synge of Trinity College, Dublin. The first volume, devoted to Hamilton’s writings on Geometrical Optics, was published in 1931, and we have now to congratulate the editors (Professor Synge having meanwhile been succeeded by Professor A. J McConnell) on the appearance of the second volume which contains the papers and manuscripts on Dynamics.

Thales of Miletus (640-546 B.C.) was the first cosmologist. Despite the naïvety of his particular theory, that “everything is water”, he was the first to formulate the hypothesis that, in all the multiplicity and diversity of its aspects, the World is One. Although the Babylonians are believed to have conceived the idea of an “Immutable Necessity” dominating all things, as far as we know they had no clear idea of the unity of the universe.

1. The stimulus that provoked this article was the following proof of the fact that the middle points of the diagonals of a complete quadrilateral are collinear.

Mr. Gibbins’ paper on the “Feuerbach Quadrilateral” (Math. Gazette, No. 249) deals with a delightful topic. The device employed is certainly ingenious. May I, however, be permitted to discuss the topic from an entirely different point of view, but with the same object in mind, namely of stimulating our pupils’ interest in Analytical Geometry I shall also bring out some interesting properties of the diagonal triangles and the diagonal-point triangles of certain quadrilaterals associated with a triangle, employing general rather than special methods to arrive at the results.

In many School Certificate courses of Algebra inequalities are scarcely mentioned, and yet in Higher School Certificate work it is often assumed that the pupil can, without any further teaching, carry out easy manipulations of inequalities. It is true that the gap is a small one, but even the most intelligent pupils may fail to bridge it satisfactorily for themselves, and difficulties will then arise. One example of such a difficulty is noted in the Report of the Mathematical Association on the Teaching of Mechanics in the section on friction. The Report reads “There is a tendency among some pupils to proceed at once to the limiting case when equilibrium is about to be broken, to write down the equations for this case, manipulate them, and finally change the resulting equality into an inequality, using > or <, according to the answer required.”

Mr. A. Blackwell’s doubts, published in the February Gazette, make sad reading for one who has spent his life teaching mathematics.

Mr. Blackwell and similar pessimists attack the basis of our ordinary curriculum, but he differs from some gloomy writers by including certain constructive suggestions which need consideration.

There is a healthy attempt to break down the barriers that have hitherto existed between the subjects that are taught in schools. At the same time it must, I think, be taken as an axiom that the several major subjects of the curriculum, especially in secondary schools, should be organised without reference to each other if each is to make use of its own distinctive discipline. A complicated articulation would be unworkable.