NATURE 



26= 



THURSDAY, JULY 22, 1897. 



THE ELEMENTS OF PHYSICS. 

 The Elements of Physics. By Edward L. Nichols and 

 William S. Franklin. Vol. i. Mechanics and Heat. 

 Pp. X + 228. Vol. ii. Electricity and Magnetism. 

 Pp. ix + 272. Vol. iii. Light and Sound. Pp. vii. + 

 201. (New York: The Macmillan Company. London: 

 Macmillan and Co., Ltd., 1896.) 



THE title and contents of such a work as that before 

 us open up many questions regarding physical 

 theory and its presentment, on which every teacher must 

 hold more or less strong views resulting from his training 

 and experience. Hence, in reviewing it, the temptation 

 to discuss particular points rather at length is almost 

 too powerful to be resisted, and perhaps need not always 

 be overcome. If then, in what follows, there is any 

 noticeable tendency of this kind, it is not to be supposed 

 that the pronouncement of the authors is necessarily 

 objected to ; but that some passage or other has 

 suggested what may appear to be rather a digression. 



The authors have endeavoured to give a short and 

 clear account of the various quantities in the subjects of 

 Mechanics, Heat, Electricity, Optics, and Acoustics, which 

 are capable of exact measurement. Of course, within the 

 limits of space assigned, a full theoretical discussion is 

 impossible ; but each concept is carefully explained, and 

 an indication is given of how its numerical magnitude 

 can be determined. The work is in our opinion a tho- 

 roughly sound and satisfactory introduction to the 

 science of physical measurements. 



Volume i. begins with a chapter on Length, Time, 

 and Mass. It includes an account of such length- 

 measuring instruments as the scale and vernier, cathe- 

 tometer, dividing engine, and spherometer, and of 

 instruments for weighing and the measurement of time. 

 These discussions are merely in skeleton, and must be 

 supplemented as regards both the theory and the use of 

 the instruments by reference to more exhaustive special 

 treatises. 



VV'^ith regard to the measurement of time, variation 

 in the amplitude of vibration of a clock-pendulum ought, 

 as the authors say, to be avoided as far as possible by 

 making the gear and escapement of fine workmanship, 

 and no sensible alteration of the rate of a clock ought to 

 be allowed to arise from such a cause. Since, however, 

 the word " pendulum," as used by the authors, appears to 

 include the balance of a pocket chronometer or watch, it 

 would have been well to point out here that, in such a 

 case, large variations of amplitude with changes of position 

 of the chronometer cannot be avoided, and to mention 

 the interesting fact that practical equality of period is, in 

 such circumstances, secured by carefully adjusting the 

 balance-spring to the exact length for which the long 

 and short vibrations are most nearly isochronous. We 

 may refer, in connection with this very important subject, 

 to a valuable, though apparently little known, memoir by 

 M. Phillips in Liouville's Journal, Ser. ii., Tome v. 

 (i860), in which the Breguet form of balance-spring, with 

 NO. 1447, VOL. 56] 



its peculiarly curved over-coil, now generally adopted in 

 compensated chronometers, is arrived at as a result of 

 mathematical calculation. 



The chapter on Physical Quantity contains a very 

 short account of the Dimensions of Derived Units. The 

 exact meaning and force of a dimensional equation are 

 6f great importance, and a page or two of additional 

 space might with advantage have been devoted to this 

 subject, at the expense, if need were, of the explanation 

 of vector-products which comes immediately after, and 

 which, so far as we have observed, is not called into 

 active service subsequently in the book. 



The authors rightly devote a little space to making 

 clear exactly what is meant by the equality of action and 

 reaction asserted in the third law of motion. It is 

 curious that the most essential point is not more em- 

 phasised in elementary text-books of dynamics, namely, 

 that the action and reaction, which are equal and opposite, 

 and which act across the same cross-section of a wire or 

 rod, or across the surface of contact of two links of a 

 chain, and which the ordinary learner often thinks ought 

 to cancel one another, are opposite forces acting on 

 different portions of matter, and therefore do not annul 

 one another, unless the rate of change of momentum of 

 a system including both portions of matter is under 

 consideration. 



It is remarkable that the paradoxer who insists on 

 making the mistake here indicated, and supports his 

 views with so much nonsensical rigmarole, mixed up with 

 wild talk about conspiracies of mathematicians to defend 

 the views of Newton, never commits a similar error in 

 financial matters ! He does not consider the handing 

 over of a sum of money by one person — himself, for 

 example — as cancelled by its receipt by another person. 

 Yet the two aspects of this transaction (like the forces 

 which are the two aspects of a stress) are equal and 

 opposite ; but they affect different persons, and he sees 

 clearly enough that one cannot be regarded as annulling 

 the other, unless the question is as to the total sum of 

 money possessed by the two persons concerned. 



We may remark that it does not seem clearly brought 

 out in connection with the experiments of Galilei, 

 mentioned on p. 36, that what was proved by his 

 famous experiments on bodies let fall from the top of the 

 leaning tower of Pisa to the pavement beneath, and also 

 by Newton's pendulum experiments, was the proportion- 

 ality of the gravities of different bodies to their inertias. 

 Hence the experiments show that when the masses of 

 bodies are measured by their inertias, the results are 

 equivalent to those obtained by the process of weighing. 

 In this chapter the authors call a velocity of one centi- 

 metre per second a " kin." There is undoubtedly an 

 advantage in having names for the units of quantities 

 which are apt to be confounded ; but velocity and 

 acceleration are both so fundamental conceptions as to 

 make it imperative on the student to completely master 

 their meaning and the manner in which they involve 

 the fundamental units, if he wishes to make any progress 

 at all ; and we question if there is any real want of 

 names for their units. 



Equation (48) on p. 50, expresses a result in simple 

 harmonic motion which is one of the few formulae in 



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