July i8, 1901] 



NA TURE 



275 



magnetic subdivision of spectral lines. Outside such 

 properties our power of tracing relations is very limited 

 and imperfect, in the absence of control over the individual 

 molecules, there being little to go upon except the two 

 principles of thermodynamics, those of energy and 

 entropy. The difference between the two points of 

 view, the definite but partial and limited mathematical 

 illustration and the wider but largely undetermined 

 model, crops up, for example, in M. Poincar^'s discussion 

 of conducting media (§417), in which the combination of 

 polarisation with conduction arising from wandering ions 

 does not appear to suggest itself; "remarquons d'abord 

 qu' ayant affaire a des conducteurs on n'a plus de polari- 

 sation," so that he has only to deal with electric current 

 and electric density, doubtless in some degree with a 

 view to save complication in a didactic exposition ; 

 whereas from the other more physical representation of 

 a material medium one does not readily conceive a state 

 of affairs in which only conduction and convection of free 

 charges are present, but would proceed rather to examine 

 under what circumstances polarisation can be practically 

 neglected in comparison with conduction. This, of course, 

 can be done in ordinary electrodynamics, as was doubt- 

 less in the writer's mind. But in the optical phenomena 

 of metals it was recognised by Maxwell himself from the 

 earliest stages — thanks mainly to the physical models on 

 which he cultivated his ideas — that both agencies were 

 essential ; while recent closer examination has shown 

 (cf. Phil. Trans. ^ 1895 ^1 P- 7") a"d in detail in recent 

 papers by Drude) how naturally their combination repre- 

 sents the general features of metallic reflection as revealed 

 by the most valuable and extensive measurements of 

 Drude and other experimenters. 



In working out the analysis, our author fellows Lorentz 

 in calculating directly the electrodynamic effects propa- 

 gated from the moving electric charges which are the 

 source of all the disturbance. He expresses this in terms 

 of the " retarded vector potential '' of the true current, a 

 vector whose components are the potentials of the three 

 components of its distribution, considered, however, as 

 travelling out from them and becoming established 

 around them with the velocity of radiation. A procedure 

 which concentrates attention on the simply extended 

 though molecularly constituted medium, to the exclusion, 

 as far as possible, of the individual moving electrons, can 

 get on more simply in Maxwell's manner by using the 

 fictitious total current, which includes aethereal displace- 

 •ment as well as translation of charges ; then the retard- 

 ation of the vector potential is dispensed with, and all 

 the functions are referred to the same instant of time, so 

 that attention can be concentrated on the processes of 

 averaging, undisturbed by mathematical complexities. 



The distinction above sketched between the crystal- 

 lised mathematical and the fluent physical point of view 

 is at the root of what is a prominent characteristic of the 

 writer's criticism. The development of electrodynamics 

 appears as split up into so many mdependent and largely 

 irreconcilable theories; there are headings, " theorie de 

 Weber, de Maxwell, de Helmholtz, de Hertz, de Lorentz, 

 de Larmor." Whereas on the view which works by 

 models and general ideas rather than by formulas there 

 is but one theory of electrodynamics— at any rate only 

 one ;cther-theory— which has put on various modifica- 

 NO. 1655, VOL. 64] 



tions and has adopted various forms of expression, in the 

 course of gradual improvement so as to become a closer 

 and closer mental picture of the orderly course of phe- 

 nomena ; the subject presents itself rather as a continuous 

 historical development, into which somewhat different 

 paths all converge, than as a series of competing modes 

 of explanation. 



There is one feature in M. Poincard's exposition for 

 which the English reader will be grateful. A consider- 

 able trouble in the assimilation of mathematical inves- 

 tigations on this subject is the diversity of the notations 

 (not to speak of systems of units) that are in use. All 

 the available letters of most available alphabets have 

 been pressed into service to represent the numerous types 

 of quantities that occur ; and if there is not a consistent 

 basis of usage it must follow that the same symbol will 

 be made to represent different things by different writers. 

 M. Poincare has kept as close as circumstances allowed 

 to Maxwell's own notation, thereby acting up to the 

 appeal of Boltzmann (" Vorlesungen uber Maxwell's 

 Theorie," 1S91, preface), who found it necessary to 

 actually construct a key for his own use to connect the 

 notations of the principal German writers. Although the 

 simplifications introduced by Heaviside, and subsequently 

 in more formal guise by Hertz, did much to clear aw^ay 

 the unessential accumulations that had overlaid Max- 

 well's theory, they did not in any sense transform it ; 

 and recent developments may be held to have justified 

 the superiority, as a working basis for further advance, of 

 the original elastic framework in which Maxwell set the 

 theory, over the condensed precis of established results 

 by which Hertz temporarily replaced it. It seems, there- 

 fore, unfortunate that the condensation of notation which 

 was a part of Hertz's modification should have reacted 

 to introduce some confusion in the notation of the more 

 complete theory. 



The development of electrodynamics, which was firmly 

 established as the proximate foundation of all physical 

 science, certainly of all that has relation to the ajther, by 

 Maxwell about forty years ago, has been going on with 

 rapidly accelerated progress, both on the experimenta 

 and on the theoretical side, during the last ten years. 

 New points of view have rapidly come up, have some- 

 times been as rapidly transcended. It is not surprising, 

 therefore, that the discussion in the last chapter, which 

 mainly relates to the mechanical and ^?^(j.f/-mechanica 

 models of the British school, is somewhat out of date , 

 indeed, it is largely constructed on the basis of an abstract, 

 published in advance, of an imperfect first draft of theory 

 contained in a memoir of date 1894, much as a paleon- 

 tologist reconstructs a fossil organism from some of 

 its bones. In the recent Lorentz-memorial volume M. 

 Poincare has himself revised some of his positions. 



It is by this sort of discussion that crude theories are 

 sifted and worn down into symmetry and order. And it is 

 matter of congratulation that an analyst of M. Poincare's 

 vast command of all the resources of modern mathe- 

 matics finds time not only to apply his genius to a 

 thorough revision of the methods of mathematical 

 astronomy, but also to survey the field of general physics 

 as he has done in this interesting volume. In these days 

 of extreme specialisation such surveys promise a special 

 harvest, but few have sufficient breadth of learning to 



