296 



NATURE 



[July 30, 1891 



the right-hand side of the second landing of the public 

 staircase leading from the lower waiting hall up to the 

 Commons Committee Rooms, a brass plate having been 

 fixed upon the wall bearing the following inscription in 

 Elizabethan or church text :— Within this wall are de- 

 posited standards of the British Yard Measure and the 

 British Pound Weight, 1853." The certificate is signed 

 by G. B. Airy (Astronomer-Royal), John George Shaw 

 Lefevre (Clerk of the Parliaments), W. H. Miller, C. P. 

 Fortescue (President of the Board of Trade), H. W. 

 Chisholm, and H. J. Chaney ; and is dated March 7, 

 1872. 



It hardly appears, therefore, that the old standards 

 of 1758, which appear to have remained unnoticed for 

 the past fifty years, are now of any importance for the 

 purposes of measurement. 



MAXWELLS ELECTRO-MAGNETIC 

 THEORIES} 



A N account of Maxwell's electric theories from the pen 

 -^*- of Prof. Poincard could not but be full of interest. 

 The volume before us is the first of two on the views and 

 conclusions set forth in the " Electricity and Magnetism " 

 regarding electro- static and electro -magnetic action, and 

 their verification by Hertz and others ; and we must of 

 course wait for the completion of the work before we 

 can form any adequate idea of its scope and character, 

 and fully understand the results of the critical analysis 

 which it contains. But in spite of the fact that the treatise 

 is in the somewhat disadvantageous form of an edited 

 course of lectures, it is a contribution of great value to 

 the literature of the subject. Whether or not it is pos- 

 sible always to agree with the physical views expressed 

 regarding matters which are not yet outside the region 

 of speculation, it is impossible not to admire its style 

 and methods. Here are to be found exemplified that 

 order and harmony which render the work of the best 

 French mathematical writers so exquisitely clear, and 

 that artistic charm which is so seldom seen in the writings 

 of scientific men of other nationalities. It has been re- 

 marked by competent critics that Maxwell's work, though 

 essentially that of an artist and man of genius, is obscured 

 here and there by a certain vagueness and want of logical 

 coherence and completeness, which has tried the patience 

 and strength of many a devoted disciple. This was of 

 course to a great extent inevitable. He sought out new 

 fields of speculation for himself, and his greatest and 

 most successful generalizations were, one cannot help 

 feeling, the results rather of unerring intuition than of any 

 completely systematic process of reasoning. Those who 

 follow in his footsteps therefore are glad of the help of 

 any friendly guide who is able by his experience and 

 strength to point out the dangers and diminish the diffi- 

 culties which attend their progress. 



In his introduction Prof. Poincard gives a critical 

 estimate of Maxwell's theories which strikes one at first 

 sight as somewhat inappreciative. Thus he says : — • 



" La premiere fois qu'un lecteur frangais ouvre le livre 

 de Maxwell, un sentiment de malaise, et souvent meme 

 de defiance se mele d'abord k son admiration. Ce n'est 

 qu'apres un commerce prolong^ et au prix de beaucoup 

 d'efforts, que ce sentiment se dissipe. Quelques esprits 

 eminents le conservent meme toujours. . . . Ainsi en 

 ouvrant Maxwell un Frangais s' attend a y trouver un 

 ensemble theorique aussi logique et aussi precis que 

 I'optique physique fondde sur I'hypoth^se de I'^ther ; il se 

 prepare ainsi une deception que je voudrais dviter au 

 lecteur en Tavertissant tout de suite de ce qu'il doit 

 chercher dans Maxwell et de ce qu'il n'y saurait trouver. 



,* "Electricitd et Optique." I. Les Theories de Maxwell et la Theorie 

 Electromagnetique de la Lumiere. Par H. Poincar^, Membre de I'lnstitut. 

 (Paris : Georges Carre, 1890.) 



NO. II 35, VOL. 44] 



" Maxwell ne donne pas une explication mecanique 

 de r^lectricit^ et du magndtisme ; il se borne k ddmontrer 

 que cette explication est possible. 



" II montre dgalement que les ph^nom6nes optiques ne 

 sont qu'un cas particulier des phenomenes dlectromag- 

 ndtiques. De toute thdorie de I'dlectricite' on pourra done 

 ddduire immddiatement une theorie de la lumiere. 



" La rdciproque n'est malheureusement pas vraie \. 

 d'une explication complete de la lumic^re, il n'est pas tou- 

 jours aisd de tirer une explication complete d es pheno- 

 menes dlectriques." 



The author, however, shows throughout his exposition 

 that he is not only impressed with the extraordinary im- 

 portance of Maxwell's work, but also thoroughly ap- 

 preciates and admires, if occasionally under protest and 

 with longing after the more ancient classic models, its 

 somewhat wild and native beauty. 



An important part of the introduction is an exposition 

 of the theoretical basis of what Prof Poincare rightly 

 regards as the fundamental idea of Maxwell's treatment 

 of electro-magnetism — that is, the application of the 

 general processes of dynamics to any system of current- 

 carrying conductors. No doubt almost all the work 

 which had been done previously had been more or less 

 of this nature, but we refer here to the attempt which 

 Maxwell made with very considerable success to correlate 

 electro-magnetic phenomena by means of Lagrange's^ 

 general dynamical equations. 



In the Lagrangian method the physical state of a 

 system is defined by means of certain parameters ^j, ^.,,. 

 . . . qni n in number ; and a dynamical explanation is 

 obtained, or proved to be possible, when the values of 

 these parameters are found in terms of, or proved to be 

 related to the positions and motions of a system of con- 

 nected particles, either of ordinary matter, or of some 

 hypothetical fluid. 



If ;/2i, /«2, . . . mp be the masses of these particles, 

 Xi^ jfi, Zi the Cartesian co-ordinates of the particle of mass 

 nii, and if the system have potential energy V, a function 

 of the 3^ co-ordinates of type Xi, y^ Si, there are 3/ equa- 

 tions of motion of the form 



iHi Xi -\- dYjdxi 

 &c. &c. 



°} 



(I) 



The kinetic energy T is 



i2;«(i■^-f-j/2^-i2), 



and the principle of conservation of energy gives- 

 T -}- V = constant. 



Now we know V, and can express the co-ordinates of 

 each particle or molecule in terms of the « parameters 

 q■^, ^2, . . . q„. The celebrated Lagrangian equations in 

 terms of the parameters can then be obtained by direct 

 transformation of (i), and are of the type 



dt dqji 



8V 



Here T and V are homogeneous quadratic functionsir 

 the first of the quantities of type q, with coefficients which 

 are functions of the parameters themselves, the latter of 

 the parameters only. 



If we have reason to believe that the system we are 

 dealing with is a dynamical system, for which the values 

 of T and V (or, more properly, those parts of the total 

 kinetic and potential energies which are concerned in 

 the special phenomenon treated), can be obtained by 

 observation of parameters of type q, we can use thes© 

 equations in our discussions of results, whether or not w^ 

 can actually express the parameters in terms of co- 

 ordinates of particles of the system. The justification! 

 of this process is the agreement of the results with, 

 experiment. 



If now we imagine a system of particles (whethtr Pt 



