When I had the honour of being made President of the Mathematical Association, I did not foresee the unusual responsibility which it entailed. It was my intention to take as the theme of a presidential address the consideration of some aspect of those special subjects to which my own researches have principally been directed. Events have forced me to abandon that intention. It is useless to discuss abstract questions in the midst of dominant practical preoccupation. We callnot disregard the present crisis in European civilization. It affects every function of life. In the harder struggle for existence which lies before the nation, all departments of national effort will be reviewed for judgment. The mere nccessity for economy in resources will provoke this reformation.

During the past two years the Public Schools Special Committee has been considering a report on the teaching of Arithmetic. One of the chief principles underlying the report may be put shortly as follows. The Arithmetic course in the past has contained a good deal that a very large nurnber of teachers regard as unprofitable, or at any rate as less profitable than other subjects that might be substituted for it. It is proposed that such parts of the Arithmetic course should not be set in the compulsory Arithmetic paper in Pass Examinations, so that those people who do not wish to teach them are not compelled to do so.

My special object is to consider how extensive the tables should be for school use, and how far pupils who have used fairly complete sets of tables at school are likely to be handicapped in examinations for which scantier tables are provided, or tables less conveniently arranged, and to what extent steps could be taken to minimise this handicap. It is to be hoped that most of the important examining bodies will before long adopt one or other of the completer sets, as it seems a pity to give the candidates needless difficulty over mere computation. I confine my remarks to 4-figure tables. And, first, as to the tables which are the most essential.

We meet to-day to inaugurate a London Branch of the Mathematical Association. This is a step in a process of evolution.

The Mathematical Association is a continuation of the Association for the Improvement of Geometrical Teaching, commonly known as the A.I.G.T., founded in 1870.

I did not join the Association till 1883, but some of its earliest reports are in my possession; to thrse I shall refer

It owed its existence to a profound wide-spread dissatisfaction with the lack of geometrical knowledge, and still more the absence of geometrical power, displayed by students who had passcd through the ordinary school course of Euclid.

The list of suggestions issued by the London Mathematical Society is open to several amendments and possibly improvements.

1. The use of small fractions in the midst of letterpress is often open to the objection that such fractions are difficult to read, and, moreover, very often do not come out clearly in printing. It is especially difficult to distinguish 1/3 from 1/8, and the latter sometimes prints exactly like the former if the type does not ink properly or is slightly uneven. For this reason it would be better to confine the use of these fractions to such common forms as ¼, ½, ¾, 1/3 and to use the notation 18/22 for other fractions ; at any rate small fractions should not be used for both thirds and eighths, and as thirds are usually commoner, it would be well to restrict their use to these.