NATURE 



97 



THURSDAY, JUNE 4, 1896. 



TWO BOOKS ON ELECTRICITY AND 

 MAGNETISM. 



Elements of the Matltematiail Theory of Electricity and 

 Magnetism. By J. J. Thomson, M.A., F.R.S., Fellow 

 of Trinity College, Cambridge, and Cavendish Pro- 

 fessor of Experimental Physics in the University of 

 Cambridge. Pp. vi + 510. (The Cambridge Univer- 

 sity Press, 1895.) 



Elementary Treatise on Electricity and Magnetism, 

 founded on Jouberfs " Traite Eldmentaire d'Elec- 

 tricite." By G. C. Foster, F.R.S., Quain Professor 

 of Physics in University College, London ; and E. 

 Atkinson, Ph.D., formerly Professor of E.xperimental 

 Science in the Staff College. Pp. xix +552. (London : 

 Longmans, Green, and Co., 1896.) 



PROF. THO^LSON'S book will do good in many 

 ways. Even its title will correct a wrong impres- 

 sion which very generally prevails, to the effect that just 

 so much of the fundamentals and facts of the subject as 

 can be discussed with the aid of a smattering of geometry 

 and algebra, constitutes the truly elementary theory of 

 electricity. On the contrary', students will find that the 

 phrase Elements of Electricity and Magnetism really 

 means that satisfactory grounding in essential ideas and 

 their relations which is only possible to a student whose 

 mathematical education has been or is being made 

 adequate to the study of the higher parts of electricity. 

 No important part of the subject is omitted, and of 

 course this brings into play here and there mathematical 

 processes more recondite than some which many practical 

 men seem to shrink from. But there is no obtrusion of 

 purely mathematical discussion ; the analysis arises just 

 where it is wanted, to the extent to which it is wanted, 

 and goes no further. 



.A feature of the book which strikes the reader at once 

 is the use made of the idea of Faraday tubes of force, or 

 rather of electric induction in a dielectric. The dis- 

 tribution of these in the field in different cases of electri- 

 fication is very fully described and illustrated graphically. 

 This is a matter of very great importance. The exam- 

 ination of students supposed to have received a sound 

 training in elementary electricity has convinced us that 

 very few' have a really clear notion of the actual nature 

 of the electrification of a conductor in presence of external 

 and internal charges. Of the dependence on the mternal 

 system of charges of the amount and distribution of the 

 charge on the interior surface, and of the nature of the 

 effect of the external system on the distribution on the 

 exterior surface, they seem frequently to have no notion 

 whatever, though they talk glibly about Faraday's ice- 

 pail experiment and his "living" within the large tin- 

 foil covered cube he made and electrified. 



Avery good elementary account is given of the subject 

 of electric images, and several important particular cases 

 are discussed; for example, that of two unequal spheres 

 intersecting at right angles. This is then converted into 

 the useful problem of the effect of a small hemispherical 

 boss on the capacity of a large sphere. 

 NO. 1388, VOL. 54] 



The effect of dielectrics in the field is then considered 

 the method of electrical inversion introduced, and the 

 usual problems of mutually influencing spherical surfaces 

 solved. An excellent characteristic of this part of the 

 book, as indeed of the work as a whole, is the working 

 out of clearly formulated expressions which, on insertion 

 of the proper numerical data, give at once the absolute 

 values of important electrical quantities. 



What we have said as to the clearness of the dis- 

 cussion of electrostatic theory applies also to the treat- 

 ment of magnetism and the steady flow of electric 

 currents. The treatment of electrolysis strikes one as 

 rather meagre, but all the statements made are concise 

 and to the point. The table of electrochemical equiva- 

 lents on p. 282 stands in need of revision, the decimal 

 point seems misplaced in one or two of the numbers. 



In the discussion of the magnetic action of currents. 

 Prof. Thomson applies elementary methods successfully 

 to the determination of the magnetic fields of simple 

 systems of currents, and might possibly have gone further 

 in the same direction. But this chapter, the long one which 

 follows on electromagnetic induction, and the thirteenth, 

 which treats of dielectric currents and the electromagnetic 

 theory of light, are the most interesting and important in 

 the book. The first two of these deal with the pheno- 

 mena and their quantitative expression, the last discusses 

 the production of a magnetic field by the motion of 

 Faraday tubes. Maxwell's theory of the propagation of 

 electromagnetic disturbances, and the verification of this 

 theory by experiment. To show the extent and thorough- 

 ness of the discussion, we may mention that the concen- 

 tration of a rapidly alternating current near the surface 

 of a conductor is explained by general considerations 

 derived from the flow of heat, and, what is still better, 

 is illustrated quantitatively by the case, which is fully 

 worked out, of alternating currents induced in an infinite 

 mass of conducting material bounded by a single plane 

 face, beyond which in the insulating medium the inducing 

 system is situated. This leads to a comparison of the 

 distances to which currents sensibly penetrate in different 

 metals, such as copper and iron, which lie widely apart as 

 regards magnetic permeability. 



An account, necessarily of course very short, but good 

 so far it goes, is also given in the chapter on the 

 " Dimensions of Electrical Quantities," of the absolute 

 determination of resistance and the comparison of units. 

 The method of the revolving coil and that of Lorenz are 

 all that are described in the former case, and Maxwell's 

 bridge method (employed so successfully by Prof. 

 Thomson himself in conjunction with Mr. Searle) of 

 finding in electromagnetic units the capacity of a con- 

 denser, and thus finding a number for comparison with 

 the electrostatic value, is alone given in the latter case. 



Here as elsewhere the author does not shrink from the 

 introduction of a differential equation and its solution. 

 The only alternative is the insertion of the result without 

 proof. The inclusion of the necessary analysis, if it can 

 be done without undue prolixity, is not, as it frequently 

 seems to be regarded, an introduction of " useless mathe- 

 matics.'' The justification of the result ought always to 

 be indicated. If the reader cannot understand the proof, 

 he can pass it over ; its presence may serve to remind 

 him that besides the mere results there is something 



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