NATUKE 737 



as derivatives of the parameters q, or as combinations of these para- 

 meters and their derivatives. 



Here then a question occurs : among all these quantities measured 

 experimentally which shall we choose to represent the parameters q? 

 and which shall we prefer to regard as the derivatives of these para- 

 meters? This choice remains arbitary to a large extent, but a me- 

 chanical explanation will be possible if it is done so as to satisfy the 

 principle of least action. 



Next, Maxwell apks: Can this choice and that of the two energies 

 T and U be made so that electric phenomena will satisfy this prin- 

 ciple? Experiment shows us that the energy of an electro-magnetic 

 field decomposes into electro-static and electro-dynamic energy. Max- 

 well recognized that if we regard the former as the potential energy 

 U, and the latter as the kinetic energy T, and that if on the other 

 hand we take the electro-static charges of the conductors as the para- 

 meters q, and the intensity of the currents as derivatives of other 

 parameters q under these conditions, Maxwell has recognized that 

 electric phenomena satisfies the principle of least action. He was 

 then certain of a mechanical explanation. If he had expounded this 

 theory at the beginning of his first volume, instead of relegating it to 

 a corner of the second, it would not have escaped the attention of 

 most readers. If therefore a phenomenon allows of a complete me- 

 chanical explanation, it allows of an unlimited number of others, 

 which will equally take into account all the particulars revealed by 

 experiment. And this is confirmed by the history of every branch of 

 physics. In Optics, for instance, Fresnel believed vibration to be 

 perpendicular to the plane of polarization; Neumann holds that it is 

 parallel to that plane. For a long time an experimentum crucis was 

 sought for, which would enable us to decide between these two theo- 

 ries, but in vain. In the same way, without going out of the domain 

 of electricity, we find that the theory of two fluids and the single fluid 

 theory equally account in a satisfactory manner for all the laws of 

 electro-statics. All these facts are easily explained, thanks to the 

 properties of the Lagrange equations. 



Jt is easy now to understand Maxwell's fundamental idea. To 

 demonstrate the possibility of a mechanical explanation of electricity 

 we need not trouble to find the explanation itself; we need only know 

 the expression of the two functions T and U, which are the two 

 parts of energy, and to form with these two functions Lagrange'ft 

 equations, and then to compare these equations with the experimental 

 laws. 



How shall we choose from all the possible explanations one in 

 which the help of experiment will be wanting? The day will per- 

 haps come when physicists will no longer concern themselves with 

 questions which are inaccessible to positive methods, and will leave 



