During the year 1929, 73 new members of the Association have been admitted. The number of members now on the Roll is 1223 : of these, 7 are Honorary Members, 61 are Life Members by composition, 17 are Life Members under the old rule, and 1138 are ordinary members.

AT the outset I desire to express my deep appreciation of the honour of being invited to lay before your Association some of the investigations into educational practice which I have undertaken during the past few years. I ask only that they be regarded aa any scientific experiment, as a search for some true principles, and that at any stage of that quest failure was to be welcomed as warmly as success, as affording suggestions for further enquiries. That the experiment has been attended with a measure of success does not make me ready to proclaim it as the ne plus ultra : I submit the facts to your judgment in the hope that they may afford material for a profitable discussion and stimulate some abler investigators to pursue the matter further.

In putting forward a plea for the inclusion of “Arithmetic of Citizenship” in the regular arithmetic course in secondary schools, there are two points which I want to make clear : (i) the purpose of such a course, and (ii) suggestions as to how it may be carried out in practice.

I received this morning a pamphlet in which the master of Stowe School, describing the Acropolis, says: “The physical beauty of the place alone would have moved even a mathematician’s heart,” and that appears to be what the world thinks of us, or, at any rate, a different part of the scholastic world. I am, of course, speaking to mathematicians and not to teachers, and I suppose we have all at one time or another suffered from the misguided hostess who introduces one as a mathematician. When that terrible word is mentioned the other person instantly curls up and says to the so-called mathematician, “How terribly clever you must be,” or else, “I never could do maths, at school.” Neither is a good opening in conversation, and it takes some time to beat down that barrier and get back to ordinary friendly terms. A mathematical reputation is rather like a clerical collar; it is a hindrance to intercourse and condemns one to a very great deal of loneliness. This may, of course, be partly due to jealousy of those who are academically superior on one particular point, although they are inferior on a great many other points, because there is a certain amount of truth in the gibe that a specialist is a person who has failed in every subject except one, having had neither time nor energy to succeed in the others.

I have read with interest Mr. E. T. Dixon’s criticism of my paper on a “Partial Failure of Euclid (I. 4) in Time-Space Theory.” Mr. Dixon takes objection to this title, although, in his own words, he admits that: “Time-Space Theory may, in a limiting instance, be incompatible with Euclid’s (I. 4).”

1. The course of Plane Trigonometry “up to and including the solution of triangles and the properties of the circles associated with a triangle” offers little difficulty to the teacher and no serious difficulty to the pupil. But in the further development of the subject, when the circular functions sin x, cos x, … are regarded as functions of the real variable x, the position is different.

A ball is placed anywhere on a billiard table made in the form of an acuteangled triangle. It is required to find a point in a cushion such that if the ball is driven from its initial position to that point and then rebounds once each from the two other cushions it shall return to the point in which it hit the first cushion. It is understood that optical laws of reflection are obeyed and that the balls are points.