In its revised form the Report of the M.A. Committee on the Teaching of Elementary Mechanics strikes me as being on the whole an exceedingly good and helpful one, though of course open to criticism in some of its details. On two or three points relating to Kinetics, I offer these remarks:

The simple approximation for the rth root of a number which is nearly an exact rth power, given by Mr. Whipple last month, is found as a rule in Bonnycastle’s Arithmetic. Perhaps the most elegant form is this:

The Jahresbericht der Deutschen Mathematiker-Vereinigung has lately published an address given by Professor Harzer on “The Exact Sciences in Old Japan.” At first sight it seems difficult to see why the celebration of the birthday of the Emperor of the Germans should have been selected for the delivery of an oration on this topic. The Professor is himself an astronomer, so that it is interesting to note that he brushes aside as of little value anything that Japan has accomplished in the pursuit of his favourite science. Nor does he discover any ground for supposing that anything will be accomplished along this line by those whose sudden prominence in other realms has given the Western world so furiously to think. The history of the science of mathematics in the Island Empire is full of paradoxes. In the days of Pythagoras, it will be remembered, the secrets of the science were entrusted to what was to all intents and purposes a Masonic body, bound by oath not to divulge the mysteries in which they participated. And this body had a further curious and unexpected resemblance to the Masonic order as seen among the Latin races, inasmuch as its intrusion into politics led to more than one popular outbreak. In Japan the parallel almost holds good, save for the utilisation of the society for political purposes. The elementary parts of the science were open to all. He who ran might read. But before the student was permitted to penetrate into the arcana he was compelled to join a brotherhood and to take an oath of secrecy. Things have, of course, considerably changed since those days. The powers that be have become more and more convinced of the paramount necessity of improvement in the direction of mathematical training. And with the courage and directness which is such a marked characteristic of this astonishing race, they refuse to allow entrance to any of the higher courses at the University or higher technical institutions to those who have not the necessary preliminary mathematical equipment. We shall be very much mistaken if the results of these drastic measures do not make themselves very evident in the course of the next half-century.