Decembek 9, 1898.] 



SCIENCE. 



807 



all these researches upon current-flow, in- 

 teresting questions regarding partial diifer- 

 ential equations were treated, but much is 

 still left for the mathematician to do. In 

 fact, it was in this same j'ear, 1888, that a 

 striking sensation was produced in the 

 scientific world by the publication of the 

 experimental researches of a new genius, 

 Heinrich Hertz, who produced in the labora- 

 tory the electrical waves conceived by Max- 

 well, and for the first time confirmed the 

 theory by demonstrating the finite veloc- 

 ity of propagation. Experimental papers 

 now succeeded each other with astonishing 

 rapidity, confirming one point after another 

 of the theory, and the experiments of Hertz 

 immediately obtained a vogue which has 

 not yet subsided. The energies of mathe- 

 maticians were now taxed anew, for the 

 question of the nature and period of the 

 electrical motions in the curiously shaped 

 ' oscillators ' used by Hertz and his follow- 

 ers to produce the waves became very im- 

 portant. The previous investigations al- 

 ready described did not cover the case even 

 for spheres and ellipsoids, for, in the case of 

 vibrations of the rapidity now experimen- 

 tally realized, the eifect of the displacement 

 currents could no longer be neglected nor 

 could the velocity of propagation be con- 

 sidered infinite, while the phenomenon of 

 radiation of energy from the conductor 

 into space demanded mathematical recog- 

 nition and treatment. This it failed to get, 

 except in an approximate manner, for any- 

 thing except the simplest case, that of the 

 sphere. This was treated by J. J. Thom- 

 son and Poincare. Nevertheless, the theory 

 has not been experimentally verified for the 

 sphere, because the sphere is a badly-shaped 

 conductor for experimental purposes. In 

 order to retain energy enough to maintain 

 the vibrations for a number of oscillations, 

 the conductor should be long or even dumb- 

 bell-shaped, and not at all like a sphere. 

 The long spheroid is then next to be 



attacked, and then other surfaces, perhaps 

 those obtained by the revolution of the 

 curves known as cyclides. The introduction 

 of suitable curvilinear coordinates into the 

 partial differential equation concerned. 



will lead, even in the case of the spheroid, 

 to new linear differential equations analo- 

 gous to but more complicated than Lame's, 

 and will necessitate the investigation of 

 new functions and developments in series. 

 The remarkable experimental skill shown 

 by Hertz is not his only title to our admira- 

 tion. His inaugural dissertation had been 

 a treatment of the flow of electricity in 

 spheres, and his electrical researches re- 

 ceived a fitting completion in two mathe- 

 matical articles in which Maxwell's theory 

 was systematized and stated in an extremely 

 clear and symmetrical manner. The equa- 

 tions of Maxwell, stated above, are unfortu- 

 nately lacking in symmetry, and certain 

 questions that have since arisen were not 

 contemplated by him. These improvements 

 were made in a very satisfactory manner 

 by Hertz, as we shall describe later. We 

 can not, however, award to Hertz the credit 

 of priority in this matter, for the work had 

 already been done by another writer, of 

 whom I must now speak at length — I mean 

 that extraordinary Englishman, Mr. Oliver 

 Heaviside. Of this undoubted genius I feel 

 that it is no exaggeration to say that he 

 understands the theory of electricity prob- 

 ably better than anyone else now living. 

 Of a decidedly eccentric personality and 

 mode of expression, unknown to and unseen 

 by most of his scientific countrymen, this 

 self-taught luminary appeared on the hori- 

 zon over twenty years ago, and slowly but 

 surely approached the brilliancy of a star 

 of the first magnitude. Unnoticed at first, 

 he forced himself upon the attention of 

 physicists by the sheer quantity of his pro- 



