Feb. 26, 1 885 J 



NATURE 



385 



were robust, and showed considerable vitality, others 

 sickly and short-lived. But, bad or good, among them 

 they have practically exhausted the resources of the sub- 

 ject, so far as the theorems presentable to a beginner are 

 concerned. The only ringing of the changes has been in 

 arrangement, modes of presentation, and proofs. 



But from the books of the future, some of which, at 

 least, we may expect to see starting into existence in the 

 present, we naturally, though perhaps vainly, look for 

 something higher and better than this. We now have 

 elementary treatises on the various branches of mathe- 

 matics required in Dynamics (two, in fact, due to Prof. 

 Williamson himself) so much superior to any that existed 

 even twenty years ago, that we no longer require to have 

 intricate steps of ordinary differentiation or integration 

 introduced into a text-book of that subject. What we 

 require may be summed up in two words, Foundation 

 and Arrangement. To these must, of course, be added, 

 as a requirement in ever)' scientific treatise, Consistency. 



The foundations of the subject, in by far the best form 

 in which they have yet been presented, were given by 

 Newton. He expressly states, before proceeding to give 

 his second interpretation of the Third Law of Motion, 

 that (so far) he had been giving principles generally 

 accepted among mathematicians. But we can barely 

 imagine the effort which must have been made by that 

 transcendent genius in extracting such simple and yet all- 

 comprehending statements from the portentous verbiage 

 of even the most able of his precursors. Step by step, in 

 Britain, Newton's system was forsaken ; one of his Laws 

 was split up into fragments, another ignored and its place 

 supplied by gratuitous additional Axioms ; till at last the 

 monstrous process culminated in the adoption of Du- 

 chayla's so-called statical Proof of the Parallelogram of 

 Forces. Thus everything was ripe for Thomson and 

 Tait's reintroduction of the grandly simple system of 

 Newton. The results of this step have been alike re- 

 markable and important. These authors also introduced, 

 after the example of Ampere, 1 the notion of separating 

 the science of motion in the abstract {Kinematics) from 

 that of motion of matter : — thus lightening the student's 

 work, in Dynamics proper, to at least as great an extent 

 as it is lightened by his previous study of integration and 

 differential equations. 



Now, in the book before us, these improvements on the 

 text-books of twenty years ago are only partially adopted. 

 Kinematics is not made a strictly preliminary study, but 

 inserted in detached fragments. The exploded " statical 

 measure " of force haunts us all through the book, some- 

 times leading to extraordinary results. Thus, opening at 

 p. 30, we find the following passages, in which we have 

 italicised a few words : — 



" Acceleration varies as Pressure." 



" This equation enables us to determine the velocity- 

 generated ... by a constant force . . . whenever the 

 pressure which measures the force is known, and also the 

 weight of the body." 



" Thus a force which is capable of supporting a weight 

 of 1 12 lbs. is called a force of 1 12 lbs." 



"... the same effort which would project a small 

 stone to a considerable distance will move a large one 

 but slightly." 



1 Ampere has never, to our knowledge, received the credit due to him for 

 much of his best dynamical work : — e.g. the u, ff equation of central orbits. 



Here we see, at a glance, the effects of want of system 

 Pressure, Force, and Effort are used as completely 

 synonymous and interchangeable terms. Now the first 

 term has a perfectly definite meaning in science (intro- 

 duced without definition or warning by our authors in 

 § 290 of the book, to the utter bewilderment of the reader 

 fresh from p. 30), and it means something differing from 

 force in exactly the same way as a linear inch differs from 

 a cubic inch. As to the Effort exerted in throwing a 

 stone, we imagine that, if employed at all in scientific 

 language, it would signify properly the work done, not 

 the force applied ; the two things differing as a square 

 foot does from a linear foot. Of course our authors do 

 not require to be told this, but why muddle the student 

 by giving him slipshod information which he must unlearn, 

 if he is ever to make progress ? 



On the opposite page (31) we find : — 



" If a uniform pressure [force] of 3 lbs. [weight] produce 

 a velocity [speed] of 10 feet [per second] in the first 

 second, find the weight [mass] of the body acted on." 



The insertions are ours, made with the view of showing 

 how the question ought to be stated unless there is to be 

 complete confusion of nomenclature. 



Since Clerk-Maxwell published his admirable little 

 book on " Matter and Motion " there has been left no 

 excuse whatever for a misuse of the word Velocity. The 

 adoption of Hamilton's Vector ideas effected an immense 

 improvement in all these elementary matters. Yet we 

 not only find constantly, in the book before us, this con- 

 fusion of speed and velocity, but something even more 

 grave, of which one example appears in the above extract. 

 This is the use of the word " velocity " in the sense of so 

 many units of length. See, for instance, pp. 28, 29 : — 



" ' In what time will a falling body acquire a velocity of 

 400 feet ? ' 



"' If one minute be taken as the unit of time, what 

 should be taken as the value of gl ' 



' Ans. The velocity per minute acquiredjn one minute 

 by a falling body.' " 



Now, what on earth is a " velocity of 400 feet " or a 

 " velocity per minute " ? To make the first statement 

 intelligible we must add " per (specified unit of time) " ; 

 and for " velocity," in the second statement, we must read 

 " velocity in feet " ; or, preferably, " speed in feet." The 

 " per unit of time " is already present on this occasion. 



Under this category we must quote the truly sensational 

 heading of § 19 : — 



"Relation between Velocity and Space," 



for this is also obviously based upon the above erroneous 

 designation of " velocity " as so many units of length. 



In p. 124 we find : — 



"... time becomes a necessary element when we come 

 to compare the efficiency of different agents. For instance, 

 if one agent . . . performs an amount of work in one 

 hour which it requires another five hours to accomplish, 

 the former is said to be five times as efficient." [The 

 italics are in the text.] 



But, turn to p. 438, and we read :— a heat-engine being 

 now the " agent " : — 



"... the ratio of the heat converted into work to the 

 heat drawn from the source is called the efficiency of the 

 engine." [Again, the italics are in the text.] 



