There is a well-known story about the late Archbishop Temple, that he once had to listen to a sermon by a youthful and inexperienced clergyman, and to dine with him afterwards, the young man, by way of making conversation during the meal, ventured to remark, “I think, my lord, that I chose a good text for my sermon” Instantly there came the grim reply, “There was nothing wrong with the text”. It may be that the consequence of my having selected a seductive title which does not possess a very close connection with the actual subject of my address will be that, when we adjourn presently, I may get the impression that my audience has consisted entirely of archbishops.

The remarks I have to offer are made with no little diffidence, but no great reluctance. I am diffident because I feel I can only offer a very humble contribution to your meeting, at the same time, recalling the aims of the Association and the purpose of this meeting, I am glad to bring up for discussion a subject which concerns our teaching in all branches of the subject and at all stages.

The following extension of Van der Mond’s Theorem enables us to express as an infinite series one of the solutions of the equation

xr+ axs+ b=0.

It is true that the results can all be obtained from Lagrange’s Theorem, but the process is interesting in that it enables us to obtain the series by an algebraical method.

Psychology has been described as the science which tells us what everyone knows, in language that no one can understand. It has a fatal attraction for those whose paucity of ideas is concealed by an exuberance of rocablilary The leading authorities not only ignore each others’ conclusions, but even refuse to use words in the same sense. “When I use a word”, said Humpty Dumpty, “it means just what I choose it to mean-neither more nor less.” The discussion of such a point as the nature of intelligence, sufficiently difficult in itself, becomes hopeless when everyone attaches a different meaning to that term. It is the object of this article to show how, by the application of mathematical methods, Professor C. Spearman has found a way of escape from this jungle of verbal entanglements. As a preliminary we shall require some account of the idea of correlation.

The interest of pure mathematicians is nowadays shifting from the study of special functions to general function theory. In fact the study of special functions might ultimately be forsaken, as for example in geometry the study of the triangle is now virtually a closed chapter, were it not for one important consideration. That is, that these functions must always be in constant use in mathematical physics. Hence their properties tend to become questions of practical application rather than of theoretical interest. It follows that there is a demand for some method, even if only a formal one, which will derive the required properties in an expeditious manner, without always calling for the services of the professional pure mathematician.

It does not seem to be generally known that a sundial, which has been correctly constructed and graduated for a particular latitude, can be used in any other latitude if it is set up at the proper angle. This appears from the very simple observation that if a sundial is moved in any way without rotation (of course within a range small compared with the sun’s distance), the shadow of the style will continue to fall upon the same figure of the dial, and if it remains on the same half-meridian of the Earth, where the local time is the same, the dial time will be still the same; when transported to another meridian, without change of latitude, it will give the correct local solar time for that meridian. (In transporting to another meridian, the dial will of course be rotated, so that its inclination and orientation relative to the earth’s surface shall be unaltered.) Thus a horizontal sundial constructed for north latitude ø will be accurate when erected as a prime-vertical sundial, facing north, in south latitude 90° – ø (Fig. 1).

The connection between the fact that 212 – 1 is a multiple of 45 and the angles of pedal triangles may not be obvious but it is there, as Euclid may have remarked when chaffed about his suggestion of a liaison between medial section and the angles of an isosceles triangle.