Binal Fractions. The reciprocals (1/N) of any number (N) will be termed Binal Fractions, or shortly Binals, when expressed in the binary scale. The notation used is similar to that of ordinary decimals. Thus (see table at end):

1°. A point is used to mark the beginning of the fraction.

2°. The binal (1/N) consists of a certain sequence of ciphers and units (the only digits used) to the right of the point; partly non-recurrent and partly recurrent.

What is the use of mathematics?

There are many parents who would find it extremely difficult to answer this question, and if they attempted to give an answer, they would in many cases repeat what appears to be a widespread current belief, namely, that mathematics is of no use in itself, but that a school course in the subject affords valuable mental training and develops the brain.

If this were all that could be said in favour of mathematics, a strong case could be made out for the rival claims of philately to be included in the curricula of our schools and universities. The intelligent study of a collection of postage stamps may be made of greater educational value than the unintelligent manipulation of mere meaningless collections of algebraic symbols. The detection of watermarks and the measurement of perforations may be used to afford valuable mental training, and are well calculated to develop a child’s powers of observation and accurate measurement.

The current method of founding the teaching of Theoretical Statics on the experimental proof of the “Parallelogram of Forces” seems open to grave objection. The experiment is too remote from the facts of ordinary observation; and it is not so very easily performed. Moreover, the result, when accurately obtained, appears to the pupil to be so remarkable, that it is a pity not to reserve it for use as a verification of the soundness of pure reasoning.

Messrs. Godfrey and Siddons in the preface to their Geometry express both a hope and an expectation that a recognized sequence of propositions will ultimately be adopted not widely differing from that of Euclid. In the Athenœum of January 9th, 1904, the writer of a review on Messrs. Godfrey and Siddons’ book scouts the idea.