NATURE 



409. 



'THURSDAY, MARCH 2, 1905. 



.1 TEXT-BOOK OF ELECTROMAGNETISM. 

 Elements of Electromagnetic Theory. By S. J. 



Barnett, Ph.D. Pp. 480. (New York : The Mac- 



millan Company; London: Macmillan and Co., 



Ltd., 1903.) Price 12s. 6d. net. 

 IV/rODERN electromagnetic theory is so full of 

 ■*■ interest, and yet at the same time so full of 

 difficulties, that every fresh attempt to present an 

 elementary account of it in a. systematic and con- 

 nected form is sure to attract the attention of 

 students who are endeavouring to gain a grasp of 

 the fundamental principles of the subject. Such 

 students are always looking out for a " good text- 

 book," hoping that this book, when found, will be 

 better adapted to their needs than those they already 

 possess. Their desire for something better probably 

 arises, in part, from the difficulty of the subject, and 

 the large number of new ideas which it presents to 

 their minds. It is perhaps too much to expect that 

 a student should be able to gain from any single 

 book really vivid physical conceptions of electric and 

 magnetic phenomena and principles, for perhaps, 

 after all, these can only gradually grow in the mind. 

 Tlie author of the treatise under review has, it is 

 clear, made a serious attempt to supply the student's 

 want, so far, at least, as the more formal theory is 

 concerned. 



The book is meant to give an introduction to the 

 subject, and thus the author does well to keep the 

 analytical processes within the limits which are 

 suitable for students whose mathematical attainments 

 do not go beyond some knowledge of the differential 

 and integral calculus and of simple differential equa- 

 tions. 



In the first part of the book, general electrostatic 

 theory is treated in a fairly complete way, many 

 problems being solved. The chapters on the con- 

 duction current, on electrolysis and on thermal and 

 voltaic E.M.F. 's, which then follow, will be found 

 useful. The author next introduces magnetism, the 

 magnetic action of currents, electromagnetic induc- 

 tion and the magnetic effects of moving charges, and 

 concludes with a chapter on the transference of 

 electromagnetic energy and on electromagnetic 

 waves. 



Throughout the book the system of rational units 

 originated by Mr. Oliver Heaviside is employed. On 

 this system, if two unit charges are placed at unit 

 distance apart in a vacuum, each exerts a force of 

 I /4ir dynes upon the other. The adoption of this 

 system banishes the great 4^ from many important 

 formulae ; for instance, on the rational system, the 

 magnetomotive force in any circuit is numerically 

 equal to the total current linked with the circuit, and 

 the energy per unit volume in an electrostatic field 

 i^ icE-, where E is the electric force and c the 

 specific inductive capacity. But though the 4Jr is 

 driven from some formulae it finds a refuge in others, 

 with the result that every one of the rational units 

 corresponding to the practical units, i.e. to the 

 NO. 1844, V<^L. 7 I 



Coulomb, Volt, Farad, Ampere, Ohm, Gauss, Max- 

 well and Henry, differs from the practical unit by 

 some power of 4^. Yet the rational system is doubt- 

 less an advantage from the point of view of pure 

 theory, and would probably have been adopted in 

 practice if only there had been someone to suggest 

 it in the early days of the science. The student must 

 remember that he is using the rational system when 

 he compares the formulae in this treatise with those 

 in most other text-books. 



The magnetic properties of currents are deduced 

 from Ampere's result that the mechanical action 

 experienced by a circuit carrying a current I is the 

 same as it would experience if each element of length 

 dL were acted on by a force IB sin d.dh, where B 

 is the magnetic induction and B is the angle between 

 (iL and B ; the direction of the force is at right 

 angles to both dL and B. In this way the idea of 

 the equivalent magnetic shell is avoided, and, in fact, 

 we have found no mention of a magnetic shell in the 

 bcx>k. Yet the ideas which group themselves round 

 a magnetic shell and the solid angle subtended by it 

 are of real assistance, and are not easily replaced. 



The book, for the most part, goes over well worn 

 ground, and thus the reviewer's attention is naturally 

 directed more to the treatment of the various proposi- 

 tions than to the propositions themselves. The 

 treatment is generally fresh and vigorous, but in a 

 few instances is hardly satisfactory. Taking the 

 electrostatic field due to a point-charge, the author 

 considers the equilibrium of a portion of the field 

 bounded by an elementary circular cone and two con- 

 centric spheres, and shows that the tension along the 

 lines of force requires a pressure of equal amount 

 at right angles to them. The result is extended to 

 the general case by the remark that " since the field 

 within the element of volume is uniform when the 

 element is made indefinitely small, and since this is 

 true of any electric field, the result just obtained for 

 a radial field holds universally." 



The attempt to establish a general result by the 

 consideration of a single special case is seldom satis- 

 factory. In the present instance the student would 

 not fail to notice that the method which succeeds for 

 the non-uniform field within the conical element will 

 not apply if the tube of force is a circular cylinder 

 so that the field within the element is really uniform. 



In chapter xiii. " the coefficient of self induction 

 (L) of a coil or circuit is defined to be the quotient 

 of the coil flux, N, due to the coil's own magnetic 

 field divided by the current I in the coil." This is 

 the way in which the coefficient is usually defined, 

 but it is an exceedingly unsatisfactory way, for unless 

 the conductivity of the wire be infinite, lines of 

 magnetic induction penetrate the wire, and then it 

 becomes difficult to understand what is meant by the 

 " coil flux." It is impossible to escape from the 

 difficulty by supposing the wire to become infinitely 

 thin, for the only result of this is to make L become 

 infinite. 



Later in the chapter the coefficient of self induction 

 is defined by means of the expression (JLI-) for the 

 energy of the system. It would be preferable to follow 



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