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.

The Report of the “Other Secondary Schools” Special Committee was published in the Mathematical Gazette of January, 1914, page 231. Since that time the re-constituted Committee, which fully endorses the Eeport, has held only two meetings. In view of the fact that the London University has not yet modified its Matriculation Syllabus in Mathematics, the Committee feels that a wider circulation of the Report is most desirable.

A Little more than three hundred years ago Napier announced to the world his discovery of Logarithms in the Mirifici Logarithmorum Canonis Description “ I have always endeavoured,” we read in one of his works, “ according to my strength and the measure of my ability to do away with the difficulty and tediousness of calculations, the irksomeness of which is wont to deter very many from the study of mathematics. With this aim before me, I undertook the publication of the Canon of Logarithms which I had worked at for a long time in former years; this canon rejected the natural numbers and the more difficult operations performed by them, substituting others which bring out the same results by easy additions, subtractions and divisions by two and by three.” Soon after the publication of the Canon, what he calls “another and better kind of logarithms “occurred to him, practically logarithms to the base 10, as we now know them, and a similar change in his system also suggested itself to Briggs, then Gresham Professor of Geometry in London, one of the first to recognise the immense value of Napier’s discovery In the interval between 1614 and Napier’s death in 1617, they had devised several methods for the construction of the new Tables; but owing to Napier’s failing health he had decided to leave the actual computation to Briggs. As early as 1617 Briggs was able to publish the logarithms of the numbers from 1 to 1000 to eight places. In 1624 he followed this with the numbers from 1 to 20,000 and 90,000 to 100,000 to fourteen places. In 1628 Vlacq, a Dutchman, published the logarithms of all numbers from 1 to 100,000 to ten places, along with a Table of the Logarithms of the Trigonometrical Ratios for every minute, to the same number of places. These Tables of Briggs and Vlacq have never been superseded—their work was done for all time. They contain errors which have gradually been discovered and corrected, but all the Tables that have been published since their time, with one single exception, have been copied, directly or indirectly, from their work.

I propose to give you in outline the short course on Indices and Logarithms taken at the present time by the Upper Fifth Form at the Holloway County School. Soon I hope it may be attempted by the Lower Fifth Forms, and, later on, perhaps by kind permission of the examining authority, it may be found possible to include it in the work of the Fourth Forms.

§ 1. Index Notation.—Let a denote any positive numerical quantity, and n any positive integer. Then “ x a” means “ multiplied n times in succession by a.” “an” alone means “1 x an”, i.e. “unity multiplied n times in succession by a.” The index n tells us the number of multiplications.

This Committee has met three times during the year, and the sub-committee appointed by it has met twice. It has elected as its Chairman, Miss Gwatkin, and as its Secretary, Miss Punnett. One member has been co-opted—Miss Waters of the Bromley County Secondary School.