Mr. D.K. Picken has done well to direct attention to the unsatisfactory nature of the elementary discussion of the Simple Pendulum, current in the text-books.

What is usually passed off as a proof is a downright wicked deceit, and deserves the serious attention of the advocate of rigour, when he can spare time to look elsewhere, beyond a fundamental axiom or a convergency test.

It is sometimes very difficult to recognise prime numbers at sight, or to discover them without laborious opertions, and mathematicians from the remotest times have endeavoured with varying success to discover suitable methods for the purpose.

In the present note I will assume that the junior student is familiar with the Sieve of Eratosthenes, and that he is required to make a complete list of primes and composite numbers between two limits such as 1601 to 1639.

Now that there is a tendency to cut out a good deal of useless matter in arithmetic and algebra, and to spend less time over formal geometry, it is possible, and I think profitable, to introduce boys quite early to a course of numerical trigonometry. For the last fifteen years, I have seen some such course as is here described taught successfully to boys of thirteen and fourteen years of age. The inclusion of certain types of question in arithmetic and algebra courses—such, for instance, as those wonderful creations that you will find in chapters on vulgar fractions—is, I suppose, justified on the ground that they call for patience, orderly arrangement of work, and accuracy. But scope can be found for the exercise of all these qualities in numerical problems which arise in connection with other branches of their work—geometry, mechanics, physics, etc.—and the range of such problems is greatly increased if the boy has an elementary knowledge of trigonometry Moreover, the work involved in solving triangles is often fairly complicated and must be done carefully and arranged in an orderly manner, otherwise it is liable to end in disaster. There is a certain amount of drudgery involved, but it is drudgery with some interest attached to it.

Few subjects deserve attention better than the problem of teaching higher mathematics to the average student.

Any man who does work in the world will some day, even though he may be a classical scholar investigating variants in manuscripts, be the worse for not knowing more mathematics ; and if he is not too closely limited by his environment he may even realise this fact. A goodly proportion of the work of the world must be done by quite ordinary folk. Something will be gained if the average student is helped even a little by being enabled to use the calculus and to think of its machinery as an engineer thinks of a drill, and not as a West Coast native thinks of a Ju-ju.

An illustration may be taken from the Astronomer Royal's recent text-book. A star of the third magnitude is very much brighter than a star of the fourth magnitude. But the fourth-magnitude stars are more numerous than the third-magnitude stars, so that in fact we receive more light from the fourth-magnitude than from the third-magnitude stars. To raise all fourth-magnitude stars to the third magnitude would increase our light more than to raise all third-magnitude stars to the second magnitude.

The majority of the boys who enter the Technical Day School of the Borough Polytechnic Institute come from elementary schools, a few only come from secondary schools. The general age of entry is about 13 years, and the boys are about up to the level of the VIIth standard of a good Council School.

As far as we are able, we select for admission boys who have a mechanical or constructive bias. All the boys who enter are expected to take the full three-years' course of work. At the end of that time they go into engineering workshops.