NA TURE 



537 



THURSDAY, OCTOBER i, 190S. 



MXTHEMATICAL ASPECTS OF ELECTRICITY 

 AND MAGNETISM. 



The Mathematical Theory of Electricity and Mag- 

 netism. By Prof. J. H. Jeans, F.R.S. Pp. viii + 

 536. (Cambridge : University PresSj 1908.) Price 

 15s. net. 



ELECTRICITY and magnetism now form so vast 

 a subject that their mathematical aspects 

 cannot be all dealt with in a single volume even of 

 the present size. Thus a choice has to be made by 

 the author, and one's estimate of his success naturally 

 depends to some extent on what one believes most 

 appropriate for the type of reader whose wants he 

 professes to supply. In his preface the author tells 

 us that whilst his work covers much the same range 

 as Maxwell's treatise, it is in many respects more 

 elementary; that it is not, like Maxwell's great work, 

 fo«- the fully equipped mathematician, but more 

 especially for the student and for the physicist of 

 limited mathematical attainments. 



The difficulties experienced by a good mathe- 

 matician in Maxwell's treatise arise more from what 

 it omits than from what it contains. The difficulty 

 lies in following Maxwell's train of thought, and in 

 seeing what exactly it is he is trying to prove. There 

 is a substantial substratum of truth in the remark 

 once made to the writer that it w-ould have been an 

 immense improvement to Maxwell's " Electricity " to 

 have been written by Routh. Maxwell's treatise is a 

 work of genius, but it never was a good text-book 

 for students. The distinguished editors of the second 

 and third editions have very naturally treated the 

 treatise as a species of sacred writing, not to be 

 lightly modified even in details, and though Prof. J. J. 

 Thomson's " Recent Researches " appeared as a 

 supplementary volume to the electrical part, it is not 

 a complete treatise in itself. Thus there does appear 

 room for a complete mathematical treatise in English, 

 such as might be written by an accomplished 

 mathematician who had the time, the knowledge, and 

 the natural gifts necessary for clear exposition. The 

 production of such a book, it may be added, need not 

 be regarded as showing any lack of reverence for 

 Maxwell's memory. 



Now it seems to the present writer that while Prof. 

 Jeans's eye when he started writing may have been 

 focussed on the reader of " limited mathematical at- 

 tainments," it gradually extended its range of vision 

 until it view-ed in the distance, though but dimly, the 

 complete treatise hinted at above. The result is that 

 the book seems not unlikely to reduce the self-esteem 

 of any conscientious reader of limited mathematical 

 attainments who has no one at hand to advise him 

 what to omit, at least for a first reading. 



Chapters i. to viii., pp. 5-294, i.e. more than half 

 the book, are devoted to electrostatics. This apparent 

 disproportion the author ascribes to space being given 

 in chapter viii. to the explanation of the mathematics 

 of spherical and ellipsoidal harmonics, conjugate 

 functions, Schwarz's transformation, and similar 

 matters. This chapter is a very long one, dealing 

 NO. 2031, VOL. 78] 



also with inversion and the theory of images, and 

 containing the solution of problems which illustrate 

 the various methods. Chapters ix. and x. deal with 

 currents, mostly steady currents ; chapters xi. and xii. 

 treat of " permanent " and " induced " magnetism, 

 including a few pages on terrestrial magnetism. 

 Chapter xiii. deals with the magnetic field produced 

 bv steady currents, chapter xiv. with the induction of 

 currents in linear circuits, make and break currents 

 and oscillatory discharges, and chapter xv. with the 

 induction of currents in continuous media and current 

 sheets. The three last chapters, xvi., xvii. and xviii.. 

 treat of Hamilton's principle, Lagrange's equations, 

 the general electromagnetic equations, and the 

 electroxnagnetic theory of light. 



An important feature of the book is the insertion of 

 examples for the student at the end of most of the 

 chapters. In all, there are some 250 of these, varying 

 much in difficulty, but mostly of the type characteristic 

 of Cambridge college and university examinations. 

 Another feature is the insertion of numerical results 

 in the text illustrating the size of practical electrical 

 units; these should reduce the risk of mistakes in 

 applications of general formulae. There are not infre- 

 quent references in the text to physical results 

 calcul,ated to warn the student against improper appli- 

 cations of the mathematical theory, but they do not 

 always seem quite adequate. The statement, for 

 instance, p. 400, that magnetic permeability in iron 

 continually increases as temperature is raised up to 

 the point of recalescence is too general. At the end 

 of each chapter is a list of authorities. These lists 

 are, however, mainly devoted to stating which precise 

 part of a few English books (especially Maxwell's 

 treatise and J. J. Thomson's " Elements ") deals with 

 the subject of the chapter. A single really good name- 

 index would probably be more generally useful. In 

 the absence of a name-index, the general index, pp. 

 532-6, seems hardly adequate. It does not contain, 

 for instance, the names of Kelvin, Larmor, Lodge, 

 Rayleigh or Thomson. Amongst the subjects to 

 which little space is devoted are methods of measure- 

 ment and comparison, the theory of instruments, 

 problems relating to dynamos, electric lighting _ or 

 traction, and electrical engineering generally, rapidly 

 alternating currents, detailed theories of electrons or 

 moving charges, atmospheric electricity and conduc- 

 tion in gases. 



The printing and general appearance are what one 

 expects of the Cambridge University Press. _ Even 

 Cambridge proof-readers, however, must occasionally 



miss something, e.g. o=V/5.v. p. 59, and j j j ^^' 



P- 372- 



The signs attached to the Gaussian constants 

 B„, B^o and B^^ (Neumayer's values) in art. 456 

 appear to be wrong; but B,, is given the correct 

 sign in art. 457. It seems curious, by the way, that, 

 notwithstanding the great prominence given to Cam- 

 bridge sources of information, there is no reference 

 to J. C. Adams's great work on the Gaussian con- 

 stants, or to Shelford Bidwell's article on magnetism 

 in the last edition of the " Encyclopaedia Britannica " 

 (Prof. Jeans's references seem all to the ninth edition). 



