NA TURE 



97 



THURSDAY, MAY 30, igor. 



A NEW TREATISE ON PHYSICS. 

 A Treatise on Physics. By Prof. Andrew Gray, F.R.S. 



\'ol. i. Pp. xxiii + 688. (London : J. and A. Churchill, 



1901.) Price i~,s. 

 A BRIEF abstract of the contents of this book will 

 suffice to show at once the enormous amount of 

 information it contains and the labour which has been 

 expended on its production. Its aim is "to provide a 

 treatise on physics which may serve for those who, 

 beginning at the elements of the subject, wish to have in 

 one book an account of theoretical and experimental 

 physics which may be sufficient for most practical pur- 

 poses of scientific and technical education." Accordingly, 

 the first volume contains nearly 700 pages devoted to 

 dynamics and the properties of matter. 



The book commences with an account of the funda- 

 mental units ■ of measurement. Then comes a long 

 chapter of nearly 100 pages given to kinematics ; this 

 is followed by chapters on dynamics, work and energy ; 

 after this we have statics of solids and fluids, gravitational 

 attraction, astronomical dynamics, and the tides. The 

 theory of elasticity fills some 70 pages, to be followed 

 by 30 pages on capillarity, while the book closes with a 

 very short section on measurements and instruments. 

 As a book of reference, a kind of encyclop;udia of physics, 

 the work will be most useful ; whether a student who is 

 really beginning the subject would profit by the attempt 

 to peruse it is perhaps open to doubt. For such a student 

 the whole is too condensed ; the range of subjects 

 enumerated above is ordinarily dealt with in some six or 

 eight different books, and though there is much force in 

 Prof. Gray's protest against " the division of a great 

 subject like physics into isolated compartments," yet most 

 beginners will find that the subjects dealt with need a 

 fuller treatment than Prof Gray can give them, at least 

 so far as their elementary parts are concerned. 



It should be noted that the book contains no examples 

 for the student to work out. Now while at Cambridge 

 the practice of setting problems may be carried too far, 

 most teachers will agree that it is only by practice in 

 working e.xamples that the fundamental laws of a subject 

 such as dynamics can be driven home to an ordinary 

 student. An engineer has to apply his mathematics to 

 the questions which are brought before him for solution 

 in his practice. The problems of the examination room 

 differ, no doubt, in a marked degree from those which 

 occur in real life, but a man who has been trained to 

 their solution has a better chance of success when he is 

 faced by some practical difficulty to which he must apply 

 his mathematics than one whose training has consisted 

 solely in studying the book work of his subject. How- 

 ever considerations such as these deal with the general 

 scheme of the work, they do not touch the question, how 

 the scheme has been carried out. 



In looking at a new book on dynamics the reader turns 

 naturally to the sections dealing with the laws of motion, 

 and here the treatment might, we think, be clearer. 



The ideas of inertia, mass, momentum, force, are not 

 easily grasped by a beginner. Prof. .Gray commences 

 NO. 1648, VOL. 64] 



by the consideration of stress, the mutual action between 

 two bodies whose relative motions are undergoing change ; 

 he then goes on to Newton's first law, in which the word 

 "force" is introduced; it would be well to explain that 

 the " impressed forces " of the law constitute one aspect 

 of the stress which has been discussed just previously, 

 indeed it may perhaps be questioned whether it is 

 desirable to introduce the term stress at all in this con- 

 nection. Strictly, a stress is measured by the force 

 applied per unit of area ; it has the dimensions of force 

 divided by the square of a length, and we might more 

 strictly call the mutual action between a falling body and 

 the earth a force rather than a stress. 



We then have a section on inertia or mass, and here 

 Prof. Gray does not seem quite happy in his treatment. 

 We are told that we get the idea of inertia from the 

 observation " that different bodies have, when placed in 

 what we are justified by experience in regarding as the 

 same circiunstances, different accelerations." Then we 

 are to take the inertia of a body " as a measure of the 

 quantity of matter in the body or, as it is called, the 

 body's mass, and we shall see (§ 144) that the comparison 

 of masses thus obtained must agree with that carried out 

 by weighing." Again, the inertias of two bodies are com- 

 pared by comparing the accelerations produced by 

 applying to each in turn for one second a spring with a 

 given stretch ; the inertias are said to be inversely as 

 the accelerations. Thus inertia is used throughout as 

 equivalent to mass or quantity of matter, and practically 

 the second law of motion, which, however, is not intro- 

 duced until a later stage, is assumed ; the spring with a 

 given stretch exerts a definite force, and this force is 

 equal to the product of the inertia and acceleration. 



Such a treatment is open to criticism ; for one thing 

 the experiment suggested is an almost impossible one to 

 perform ; it is better either to start from some such state- 

 ment as that whenever two bodies are moving under 

 conditions in which each is free from all action, except 

 that which arises from the second body, all the circum- 

 stances of the motion are consistent with the supposition 

 that the ratio of the two accelerations is a constant, and 

 to define this constant as the reciprocal of the ratio of the 

 masses. 



If it be objected, as perhaps it fairly may be, that the 

 conditions assumed are never realised, we may have 

 recourse to experiments with an apparatus such as Prof 

 Hicks's ballistic balance, in which two bodies swinging as 

 pendulums are allowed to impinge directly in such a way 

 that they are both brought to rest ; experiments with this 

 show at once that the ratio of the two velocities with 

 which the bodies are moving at the moment of impact is 

 a constant so long as the bodies remain unchanged. We 

 define the ratio of the masses of the bodies as the 

 reciprocal of this constant, and thus we obtain a means of 

 comparing masses without the introduction of the idea of 

 force ; moreover, it is easy to pass naturally from this 

 to the idea of mass defined as measuring the quantity of 

 matter in the body. 



Thus, having obtained aknowledgeof mass and velocity, 

 we can introduce the idea of force as the time rate of 

 change of momentum, using Newton's second law to 

 define and measure force. 



Prof. Gray is careful to explain that he does not look 



F 



