November 5, 1914] 



NATURE 



25' 



complex quantity, but are scarcely sufficiently 



difficult to bringf out any advantages for it, as the 



ctual working- is exactly the same as would be 



clone by an intelligent student who had never 



heard of the Steinmetz methods. In a later 



hapter on polyphase circuits, other examples 



'ccur in which algebraic processes have to be 



carried out befor6 substituting numerical values. 



In these the advantages become more obvious. 



The authors do not quite attain to the standard 

 set in their preface of " avoiding the error of pre- 

 senting unnecessary formulas." On the contrary, 

 we feel that a formula has been inserted wherever 

 the slightest excuse for it can be found, even when 

 the same formula has been given several times 

 Iready. 



The facts of nature xlo not depend on a particular 

 'noice of units, or, indeed, upon the existence of 

 ny vmits at all. It is therefore quite superfluous 

 > introduce units into the mathematical treatment 

 t these facts. Why will all authors not let their 

 symbols stand for the thing itself, instead of for 

 the number of times it contains some particular 

 unit? The length of a foot-rule remains the same 

 whether we call it "one foot," "12 inches," 

 ;;o"48 . . . centimetres, or 3048 . . . millimetres. 

 The symbol L can just as well represent the 

 length itself as any of these numbers, and in this 

 way we are freed from the necessity of continually 

 -topping to name the units to be employed, and 

 .cm the irritating repetition of numbers such as 

 10^, 47r-^ 10, 60, -46, 33,000, and so forth, which 

 have nothing whatever to do with the laws, but 

 arise from some particular (and unfortunate, 

 ahhough customary) choice of units, and thus 

 distract attention from the real point under dis- 

 cussion. In the book under review, pages and 

 pages might have been saved in this way. 



Taking the book as a whole, the explanations 

 are not as clear and concise as they might be ; 

 indeed, we found it exceedingly difficult to follow 

 '>me, of them. Several hydraulic analogies are 

 J iven, but we are very doubtful whether these are 

 ally helpful, because the laws of hydro-dynamics 

 have to be strained to make them fit the electrical 

 case, and not infrequently the student's know- 

 ledge of that subject is less than of electricity. 



(2) Except that part v. goes rather more fully 

 into the technical side than is customary in books 

 with its title, this book covers the well-worn 

 ij^round of elementary magnetism and electricity. 

 It contains little that is original in matter or in 

 method, and its mathematics is uneven. 



Many of the statements given ought to have 

 attached to them the qualifying conditions under 

 which alone they are true. Parts of the book are 

 NO. 2349, VOL.. 94] 



painfully laboured over some small point, while 

 others are extremely superficial and betray a lack 

 of insight into the true inwardness of the matter 

 discussed. 



In our science we have many traditions and 

 dogmas from which we must ultimately break 

 loose, and the sooner this is recognised by the 

 writers of elementary text-books the better it will 

 be for our students. What was best half a cen- 

 tury or more ago is not necessarily even good now. 

 Consider the electrostatic and electromagnetic 

 systems of definitions. In chapter 39 the 

 absurdity of the dimensional relations which arise 

 from these definitions is pointed out; but in the 

 other chapters which form the real book, we still 

 have the old Gauss system omitting jtc and k. 

 Why not omit the electrostatic system altogether? 

 The sum total of our loss would be a fund of 

 examination questions and a source of confusion 

 as to what is intended when one of our most 

 prominent physicists tells us that the charge of an 

 electron is so many "units." Tlie dielectric con- 

 stant (we object to our author's "dielectric 

 capacity ") of air or other material would then 

 appear to" be what it really is — a thing the value 

 of which has to be determined by experiment like 

 its density, elasticity, or any other property. 



Ohm's law, electromotive-force, and potential 

 difference are always stumbling blocks. We 

 should not deliberately blind our students to more 

 than one-half of the phenomena by telling them 

 that the current must flow from high potential to 

 low potential ; that a current must be flowing if 

 two parts of a conductor are at different poten- 

 tials ; that a current cannot flow, unless there is a 

 potential difference; and that the P.D. is equal 

 to the product of the resistance and current. 

 When restricted to the proper cases, all these 

 statements are quite true ; but not a single one of 

 them is always true, and the first and last are 

 not even true in the majority of instances. We 

 have only to consider what takes place in the 

 battery branch of a circuit; in a homopolar 

 dynamo ; in a copper ring while a magnet is being 

 thrust symmetrically into it, or in an ordinary 

 electric motor, to see how badly we treat our 

 students when we saturate them with these ideas, 

 which they must later unlearn if they continue 

 the subject. 



In this book we have "resistance" in chapter 

 24, "Ohm's law" in chapter 25, and "Joule's 

 law " in chapter 35. Surely the essential thing 

 about resistance is that it causes a generation of 

 heat when a current flows, and these two laws are 

 merely different ways of looking at the same phy- 

 sical fact. A true understanding of electromotiv** 



