NATURE 



505 



THURSDAY, MARCH 30, 1893. 



ELECTROMAGNETIC WAVES. 



Electrical Papers. Two vols. By Oliver Heaviside. 

 (London: Macmillan and Co., 1892,) 



IN these two volumes the author has collected the 

 papers on electrical subjects which he has rom time 

 to time contributed to the Philosophical Magazine, the 

 Philosophical Transactions, the Electrician, and other 

 technical journals. The result is a work of some eleven 

 hundred closely printed octavo pages ; that is to say, on 

 a rough estimate, it contains in printed matter about half 

 as much again as Maxwell's two volumes on Electricity 

 and Magnetism, and considerably more than the two 

 volumes of Thomson and Tait. When we add that the 

 author brings into action freely (though with perfect 

 mastery) some of the most elaborate weapons of mathe- 

 matical physics, and that considerable passages are more- 

 over written in a special condensed notation, it will be 

 evident that the task of the reviewer is no easy one. All 

 that we shall here attempt is to give a general idea of 

 the nature of the book, with some reference to its more 

 original features. 



The first few articles are devoted to practical questions, 

 such as duplex telegraphy, signalling with condensers, 

 the best arrangement of Wheatstone's bridge, and so on. 

 These are thoroughly readable, and, apart from their 

 technical value, may be commended to mathematical 

 students as containing interesting concrete applications 

 of electrical theory. The rest of the book is partly a 

 commentary on, and partly a development of, the latter 

 part of Maxwell's treatise, and deals mainly with the 

 propagation of electromagnetic effects in space and 

 time. It is therefore closely connected with the theo- 

 retical work of Poynting and J. J. Thomson on the one 

 hand, and with the practical investigations of Hertz and 

 his followers on the other. At the present time there is 

 no great difficulty in following in imagination the propa- 

 gation of inductive effects from one conductor to another 

 across the intervening space ; and that this should be 

 the case is due in no small degree to the labours of 

 our author, for although probably few readers have been 

 found to follow him step by step, yet many have 

 admired the tenacity with which he attacks problem 

 after problem bearing on his subject, and have gathered 

 valuable ideas and suggestions from his exuberant pages. 



One of the most noteworthy features in the author's 

 theoretical work is the elimination of the " vector-poten- 

 tial " from Maxwell's equations of the electromagnetic 

 field, with the result that the equations in question are 

 obtained in a "duplex form" in which there is perfect 

 symmetry as regards the parts played by the electric 

 and the magnetic variables respectively, so that the 

 equations are unaltered in form when a reciprocal substi- 

 tution between the two sets of variables is made. The 

 same simplification has been made independently by 

 Hertz. It is of importance for this reason, that the 

 vector-potential is to a certain extent indeterminate. 

 This was indeed insisted upon by Maxwell himself, but, 

 strange to say, he did not always remember his own 

 warning, with the result that more than one most impor- 

 NO. 122 2. VOL. 47] 



tant passage of his great work is rendered needlessly 

 obscure. Another function which the author seeks (we 

 think rightly) to relegate to the position of a mere mathe- 

 matical implement, without physical significance beyond 

 the domain of electrostatics, is the electric potential. 

 There is nothing paradoxical in this, for the original 

 definition of this function postulates a state of equili- 

 brium. 



The last paper (but one) in the book forms a 

 sort of crown to the whole. It is entitled " On the 

 Forces, Stresses, and Fluxes of Energy in the 

 Electromagnetic Field," and is reprinted from the 

 Philosophical Transactions for 1892 (A). Unfor- 

 tunately this paper is by far the hardest to read. Free use 

 is made of the scalar and vector products of Hamilton, 

 but the author is careful to give us his emphatic opinion 

 that quaternions proper are unsuited to the purposes of 

 mathematical physics. This courageous declaration will, 

 we fear, cause a wicked joy in the hearts of many who 

 have struggled in vain with these refractory symbols. For 

 the special system of mathematical shorthand affected by 

 Mr. Heaviside there is much to be said, but for our own 

 part we should prefer to have papers which profess to 

 give new and important results written in the more 

 homely language of " Mr. Cartesian." Another pro- 

 minent feature in this memoir is the frequent appeal to 

 the principle of " continuity of energy," but this imposing 

 phrase seems to mean nothing more nor less than Max- 

 well's negation of action at a distance. The author, in- 

 deed, takes care to explain that he does not countenance 

 the notion of " identity of energy " which one prominent 

 physicist has attempted to base on a well-known paper 

 by Poynting. It is now generally recognised that the 

 flux of energy in the electromagnetic field is 

 indeterminate. In his treatment of induction in 

 moving media, a very important but most difficult 

 subject, the author is led to at least one definite 

 conclusion of great interest, viz. the existence of a 

 magnetic force acting on a body moved across the 

 lines of electric induction, just as there is an electric 

 force on a body moved across the lines of mag- 

 netic induction. This is in conformity with the duplex 

 character of the fundamental equations already referred 

 to. Finally, we must not omit to notice a somewhat 

 startling proposal for a radical change in the system of 

 electric and magnetic units. In the "rational" system 

 advocated by our author, one line of force would emanate 

 from a unit magnetic pole, instead of 47r such lines, so that 

 the force between two poles w,w' at a distance r apart 

 would be w/«747rr2 instead of mm'jr'^ as at present. The 

 existing system is denounced as containing an absurdity 

 of the same nature as if we were to define the unit area 

 to be the area of a circle of unit diameter. 



It remains to say a word or two about the style in 

 which the book is written. It is exceedingly fluent, 

 often discursive, and occasionally boisterous, as when 

 the author, introducing the functions called zonal 

 harmonics, remarks that "these are Murphy's /"s ; not 

 praties, but the functions invented by Murphy " ; or 

 again, when in his impatience of vector and other poten- 

 tial functions he gives utterance to the wish to " murder 

 the whole lot." A more serious matter is that the papers 

 in these volumes often overlap, whilst the frequent cross- 



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