242 



NA TURE 



[April 28, 1910 



tickets from London to Cardiff and Cardiff to 

 Glasgow, could get to their destinations simul- 

 taneously by the 2 p.m. London to Glasgow. It 

 would be far better to omit all these old-fangled mis- 

 statements, including the one that "if a particle has 

 simultaneously three velocities represented by the sides 

 of a triangle it remains at rest," and merelv to give 

 the definition of component velocities in § 5, and some 

 discussions on relative velocity. 



Atwood's machine seems too fashionable to be 

 omitted nowadays, but it would be better to bring 

 friction up to the front before discussing the motion 

 of a 10 lb. weight on a table, pulled opposite ways 

 by weights of i^ lb. and 2 lb. hanging over the edge, or 

 a 4 lb. mass on an inclined plane. In the figure of the 

 condensing pump the arrow seems to suggest that 

 air enters the barrel when the piston is moving the 

 opposite way. "Whole pressure," which is meaning- 

 less except for plane areas, again crops "up on 

 p. 217. When shall we see the last of it? The oar 

 once more figures as a lever of the second class. It 

 is to be wished that every person who placed it 

 there would try pulling a boat out in shallow water 

 with the ends of his oars touching the bottom and a 

 boy on the bank holding the boat back with a string. 

 Under " machines " the so-called " first and third 

 systems of pulleys " crop up with their usual per- 

 tinacity. It would be interesting if those who take 

 so much interest in these particular machines and 

 ignore the crab were asked to arrange for lifting 

 building materials to the top of a high scaffolding, 

 and to watch the result when their instructions were 

 carried out. 



Our general conclusion is that if boj's have to 

 learn what is contained in this book they will be 

 efficiently and well trained on these Hnes by follow- 

 ing Messrs. Jones and Blomfield ; but there are a 

 good many things they had far better leave unlearned, 

 and a good many other things they ought to learn 

 Instead. It should be mentioned that calculus is not 

 used, and moments of inertia are not included 

 in the scope of the book. 



(2) Controversial questions regarding the teaching of 

 mechanics do not enter so prominently in connection 

 with Prof. Loney's book, for by the time its standard 

 has been reached dynamics has practically become a 

 branch of pure mathematics, while, on the other 

 hand, the student has had a good laboratory course 

 in physics or engineering. The book, in fact, pretty 

 exactly fits the requirements of B.Sc. candidates in 

 a modern university college in the third year of their 

 curriculum. It deals with rectilinear motion (includ- 

 ing resisting media), central orbits, motion about 

 a fixed axis, uniplanar rigid dynamics, energy and 

 momentum, a little three-dimensional rigid, 

 Lagrange's equations, &c. There is always a diffi- 

 culty with these students, because this ground 

 assumes a knowledge of pure mathematics that they 

 cannot acquire before their third year. The appendix 

 on differential equations is useful in this connection. 

 A few points will have to be attended to in a future 

 edition. The equation of motion for varying mass 

 (p. 130) does not generally hold when a body is 

 NO. 21 13, VOL. 83] 



parting with matter. D'Alembert's principle re- 

 quires more explanation than is contained in the 

 statement, " Now the internal forces of the body 

 are in equilibrium among themselves, for by New- 

 ton's third law there is to every action an equal and 

 opposite reaction." This explanation the lecturer 

 can, however, give. But a most amazing and 

 doubtless unintentional mistake is made on p. 

 302, where the equations of motion in three dimen- 

 sions are given as Ad^WxJdt'^ = L instead of Euler's 

 equations. We should like to have seen a few more 

 examples in which the answer leads to a definite- 

 conclusion in the form of a numerical result instead 

 of so many algebraic formulae connecting masses ni, 

 lengths 2a, and angles 6. But such questions are, 

 we admit, rather hard to collect, and the teacher and 

 student should, therefore, be grateful for the flywheel 

 questions on pp. 217-9. u 



Up till the present no one book has sufficed for 

 students taking this course, and, indeed, there has 

 been great difficulty in advising them as to what to 

 get. Prof. Loney has done useful work in providing 

 students with a suitable work, and when he states 

 that he has verified every question, the task cannot 

 have been an easy or profitable one. 



In this revision, the paradoxical rough board on 

 a smooth plane seems to have escaped notice in 

 p. 210, ex. 2, while on p. 217 we have "A uniform 

 rod AB is freely movable on a rough inclined plane 

 whose inclination to the horizon is i and whose co- 

 efficient of friction is /* about a smooth pin fixed 

 through the end A." "Coefficient of friction of a 

 rough plane about a smooth pin " reminds us 

 of the newspaper English so often quoted in 

 Punch. 



The treatment of centrodes is very useful. 



(3) M. Guillaume's " Initiation '" is stated to be one 

 of a series intended to be used for teaching children. 

 In this connection, the question arises. What is the 

 age of the children contemplated by the author? In 

 the editorial preface by M. C. A. Laisant four to 

 twelve years is suggested. But, even after allowing 

 for the differences between English and French 

 children, the author's treatment of the subject seems , 

 too philosophical for such young pupils. As a pre- { 

 liminary preparation to the study of mechanics we t 

 have a chapter on " How Nature is Studied," the 

 headings of the paragraphs being " Observation and 

 Experiment," "Approximation and Simplification," 

 "Need of Simplicity," "The Limits of Experiment," I 

 "Illusion," "Education of the Senses ; Measurement," | 

 "Induction and Deduction." Illustrations are taken j 

 from the photographs of moving bullets, photometry, 5 

 and so forth. In the next chapter, which deals with | 

 kinematics, we have a discussion of space, velocity,, 

 and acceleration graphs. The author in the prefac*^ 

 considers that dynamics should be treated before,' 

 statics. His argument might, however, very well 

 be used the other way. He asks why the majority of 

 bodies on the earth appear to be at rest, and points 

 out that this is due to the existence of resistances 

 such as friction, and remarks inter alia that if these 

 forces are unknown at the time when statics is begun 



