NA TURE 



145 



THURSDAY, DECEMBER 14, 1893. 



A BOOK OF PRACTICAL EXAMPLES LV 



ELECTRICITY. 



Problt-ines et Calculs Pratiques d^EIectricitc. Par M. 



Aime Witz. (Paris : Gauthier-Villars et Fils, 1893.) 

 ' I ""HIS is, in the main, a book of fully worked-out 

 -L exercises in electricity and magnetism, designed 

 for the help of practical students. Its idea and arrange- 

 ment are good, and the examples seem to have been 

 chosen with much care, and, as far as possible, from 

 actual cases which have occurred in laboratory and 

 practical work. The aim of the author has not been to 

 furnish a set of examples, like the collection of Walton, 

 in theoretical mechanics, or that of Hall Turner, in heat 

 and electricity. These works illustrate general mathe- 

 matical theories by examples, the solutions of which are 

 in many cases important or interesting particular 

 theorems ; but their interest is, to a great extent, mathe- 

 matical. M. Witz has had in view the wants of students 

 endeavouring to obtain a sound elementary knowledge 

 of electricity, who are not afraid of a piece of calculation 

 involving, when necessary, a little differentiation or 

 integration, when it comes. in its proper place as the 

 simplest and most direct means of attaining the required 

 result. » 



The work is divided into three parts : (i) containing 

 definitions and formulas, (2) numerical constants, and 

 (3) the greater portion of the book — a collection of illus 

 trative examples. Part i deals first with magnetism, and 

 gives the ordinary relation between magnetic intensity 

 and magnetic induction, introduces the notions of mag- 

 neto-motive force and magnetic resistance, and shortly 

 states the main facts of lamellar and solenoidal magnet- 

 isation. In like manner the next chapter states, merely, 

 some of the principal theorems of electrostatics ; the 

 third deals with phenomena of steady currents ; and the 

 last two with electro-magnetism and induction of currents. 



In connection with electro-magnetism a paragraph is 

 devoted to the researches of Ewing and " M. Hopkins " 

 on the magnetization of iron. All the latter experimenter 

 (the distinguished inventor of characteristic curves of 

 dynamos appears to be meant !) is credited with is a 

 demonstration that the " travail" (consumed in putting a 

 sample of iron through a magnetic cycle) " exprime en 

 ergs et rapport^ a I'unite de volume, est dgal au produit 

 de la force coercitive de I'echantillon par I'induction 

 maximum, divise par ir." The measure of coercive force 

 assigned by Hopkinson does not seem to be explained 

 in the book, and so a really important idea, rendering 

 definite what was before a perfectly vague expression, is 

 passed over. As to the demonstration referred to, we 

 must confess to never having heard of it. Dr. Hopkinson, 

 we had supposed, simply used the rule stated in the 

 quotation as a rough and ready method of rapidly find- 

 ing the approximate dissipation of energy in a closed 

 magnetic cycle. 



Ampere's law (" formule classique, connue de tous 

 nos lecteurs") of the action between two current 

 elements is explained, but no hint is given that any 

 number of other laws can be obtained which give for the 

 only cases with which we can without ambiguity deal, 



NO. 1259, VOL. 49] 



those of closed circuits, precisely the same result as is 

 given by Ampere's formula, although the latter may have 

 certain advantages in point of simplicity. 



The word " law " is a good deal misused in electrical 

 science ; we have Kirchhoff's laws, Ohm's law. Joule's 

 law, Lenz's law, and many others ; but we have here a 

 law that we do not remember to have come across before, 

 namely " Pouillet s law, ' which asserts that the quantity 

 of electricity conveyed by a current I in time /is 1/ ! 

 No doubt if the electro-magnetic definition and measure 

 of a current are adopted, it is a proper subject of inves- 

 tigation to settle whether it is simply proportional to 

 the current defined electrostatically as the time rate of 

 flow of electricity ; but the real proof that this is the 

 case, is the consistency with the results of experiment of 

 the great mass of results deduced from this propor- 

 tionality. 



The chapter on induction is brief, but contains a great 

 deal of information very accurately expressed. The 

 function of the current which multiplied into the speed 

 gives the electromotive force of a dynamo, is referred to 

 as the " fonction caracteristique ' of M. Marcel Depres ; 

 but Hopkinson's extremely important dynamo character- 

 istic curves are merely referred to, without any mention 

 of their author. 



The so-called law of Jacobi, namely, that " Le travail 

 utile d'un moteur est maximum lorsque sa force contre- 

 electromotrice est egale a la moitie de la force electro- 

 motrice de la generatrice," is no doubt correctly stated^ 

 since by " le travail utile " is meant the electrical work done 

 on the motor in a given time, otherwise than in heating its 

 conductors. But it would be better to say that the elec- 

 trical activity as specified in the motor is a maximum 

 when the condition stated is fulfilled. The phrase " useful 

 work," here used, has caused this result, simple as it is, to 

 be completely misunderstood by many practical electri- 

 cians of high standing. In the present case the tendency 

 to error is obviated by the statement immediately follow- 

 ing, that " Le rendement electrique d'une transformation 

 d'energie, est egal au rapport de la force contre-electro- 

 motrice e de la rdceptrice a la force electromotrice E de 

 la generatrice. Ce rendement peut devenir egal k I'unitd 

 lorsque e devient egal a E ; mais alors le travail produit 

 tombe a zero. C'est la lot de Siemens.''' 



The late Sir William Siemens objected in 18S3 to the 

 erroneous interpretation put upon Jacobi's result by 

 Verdet and others, and likewise stated the true principle 

 of efficiency ; but the law of maximum efficiency of a 

 circuit containing a motor was given in Lord Kelvin's 

 very important paper on the " Mechanical Theory of 

 Electrolysis," published in 1851 in the Philosophical 

 Magazine. As not only this result, but others, forming 

 practically the whole r,{ the simple but immensely im- 

 portant elementary theory of the electrical efficiency of a 

 generator and motor, are there incidentally given by 

 Lord Kelvin, and are usually stated in practical treatises 

 and lectures as theorems of much later date, we may be 

 allowed to give here a short abridgement of the passage. 



Denoting by w the angular velocity with which a 

 Faraday disk magneto-electric machine is driven, by .1 

 the velocity with which the machine would have to be 

 driven to give a back electromotive force equal to that 

 of the generator (a battery in this case), Lord Kelvin 



H 



