Lessons in Elementary Dynamics. Arranged by H. G. Madan, M.A., Assistant Master in Eton College. Pp. 180. (Edinburgh: W. and R. Chambers, 1886.)

     In this little book the author has provided teachers of elementary mechanics with a rich storehouse of materials for experimental demonstrations, although the work is not quite satisfactory in some other respects. His endeavour has been to explain some of the properties of matter, Newton's laws of motion, and the modern conceptions of energy and work, in such a manner as involves only the most elementary knowledge of mathematics. Thus symbolical reasoning and formulæ are dispensed with, and nothing assumed beyond a knowledge of arithmetic and a little easy geometry. There is a successful attempt made to arouse a real interest in the subject by continual reference to phenomena of every-day life, and especially by illustrations drawn from the sports and games of the pupils. In some cases detailed instructions are given for performing the experiments. These are valuable, and similar aid might with advantage be provided in many other instances.

     The author is of opinion that mechanics ought to have the first place in a boy's scientific education. This position would be strengthened, if some series of simple experiments, to be performed by the pupils themselves, were provided, and regarded as essential.

     Some expressions, such as "above," "below," "on the same level," which are usually left undefined, have their exact scientific meaning pointed out. On the other hand, there is occasionally looseness and confusion in the use of technical terms. For example, in Section 103 we read: "Momentum is the term used to express the force with which anything is moving." In Section 159 we have the accurate statement that, by finding the momentum of a body, we learn what impulse has been applied to it: here the accepted expression for the time-integral of a force is used, but we do not notice any definition of the word "impulse"; and the exposition of the second law of motion appears vague in consequence. Similarly, the force exerted in throwing a cricket-ball is spoken of in Section 156, where the time-integral of the force is in question.

     Section 302 is devoted to the "exact valuation of the energy in a moving body," and the usual expression-- energy = ½ (mass x velocity²) --is obtained, but by a process which is at least startling. Witness these statements:--"If the work could be done in an instant, the energy would be exactly expressed by the product of the mass x velocity²;" and again, "The whole amount of work which a moving body can do in the time during which its motion is being stopped will correspond to the average or mean amount of energy between that which it has at the beginning of the time and that which it has at the end of the time." Unde, quo veni?

     After the preceding, it is a small matter to refer to Section 311, where this statement occurs: "The motion of the pendulum is an accelerated motion, and, as in all other uniformly accelerated motions, the spaces described are as the squares of the times." Here, of course the reasoning is fallacious; and, although the proof intended is sound, it involves the doctrine of limits, and wants development. It is surely better at this stage of the pupil's progress to rely on the experiments in Section 312.

     There is an appendix on the metric system, and, in conclusion, a dozen pages of questions and exercises on the several chapters of the book.

A. R. W.