December 26, 1913] 



SCIENCE 



907 



of his great work he does not commit him- 

 self as to its conclusions, but states that 

 Clausius has shown that the hypothesis that 

 the potential is propagated like light does 

 not lead to the known laws of electrody- 

 namics. Curiously enough, to-day this is 

 exactly what we do believe, and it is inter- 

 esting to know that such a result was vainly 

 sought for by Gauss. 



It is easy to conceive, the equations of 

 electrical propagation being so similar to 

 those of the propagation of sound waves, 

 how the question of fundamental functions 

 arises in connection with electrical oscilla- 

 tions emitted by a conductor of given form. 

 The only case of anything except a linear 

 conductor that has been completely treated 

 is that of a sphere and of this a treatment 

 was given in the same lectures in 1893 by 

 Poincare. One of the most important ques- 

 tions in wireless telegraphy has been dur- 

 ing the last ten years and still is the expla- 

 nation of the possibility of sending Hert- 

 zian waves across the Atlantic, a distance 

 of perhaps one tenth of the way around the 

 earth. The question of diffraction has al- 

 ways been an attractive one and in the case 

 of electric waves makes great demands 

 upon the powers of the mathematician. 

 After a number of articles on the subject 

 Poincare in 1909 applies to it the method 

 of integral equations, which he continues 

 in a lecture on the Wolfskehl foundation at 

 Gottingen, and later in a tremendous paper 

 in the Palermo Bendiconti. 



The development of Maxwell's electro- 

 magnetic theory that has taken place in the 

 last twenty-five years has led to a theory 

 that has attracted the greatest interest 

 among mathematical physicists and has, in 

 fact, become in certain parts of the world 

 no less than a mania. I refer to the so- 

 called principle of relativity, a name which 

 was given to it first, if I am not mistaken, 

 by Poincare. This principle is no less than 



a fundamental relation between time and 

 space, intended to explain the impossibility 

 of determining experimentally whether a 

 system, say the earth, is in motion or not. 

 In an elaborate paper published in 1905 in 

 the Palermo Bendiconti entitled, "Sur la 

 dynamique de I'electron," he defines the 

 principle of relativity by means of what he 

 calls the Lorentz transformation. If the 

 coordinates and the time receive the follow- 

 ing linear transformation, 



x' = kl{x + €t), t' = kl{t + &), y' = ly, 

 z' = lz, h = ^- , 



the function x- -|- y- -^-z^ — t.^ and the 

 equations of electric propagation will re- 

 main invariant. Prom this follows the 

 impossibility of determining absolute mo- 

 tion. Poincare then submits the Lorentz 

 transformation, which he shows belongs to 

 a group, to an examination with regard to 

 the principle of least action, which he shows 

 holds for the principle of relativity. He 

 further shows that by the aid of certain 

 hypotheses gravitation can be accounted 

 for and shown to be propagated with the 

 velocity of light. This is a subject which is 

 now very much in the air, but it must be 

 said that various writers arrive at conflict- 

 ing results. 



From what I have said, it will have been 

 seen that Poincare was exceedingly up-to- 

 date and at once made the newest specula- 

 tions and theories his own. As the final ex- 

 ample of this may be named a theory which 

 has created nearly as great a shock as that 

 of relativity. I mean the theory of light 

 quanta introduced by Planck to account for 

 the laws of radiation from a hot body. In 

 order to apply the laws of probability to 

 electric resonators Planck had felt obliged 

 to introduce the hypothesis that energy is 

 emitted by resonators not in continuous 

 amounts but in amounts depending upon 

 certain multiples of a definite quantity 



