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SCIENCE. 



[N. S. Vol. I. No. 4. 



whose oscillations are due to a sudden re- 

 lease of a uniform electrostatic field. The 

 solution of this case is complete. The actual 

 values of both the period and the decrement 

 are expressed in terms of the radius of the 

 sphere. The smallness of the period and 

 the exceedingly rapid rate of decay of the 

 wave are striking. 



This theorj^ throws much light upon 

 Hertz's method of calculating the period of 

 an oscillator. Poincare applies it also to 

 the explanation of the Hertzian method of 

 calculating the decrement due to electrical 

 radiation and the force of Poynting's 

 theorem is exhibited in a masterly manner, 

 although, of course, the calculation for more 

 general cases is not as complete as that for 

 Lodge's oscillator. More experimental 

 guidance is necessary and will not be sought 

 in vain in siibsequent chapters. 



Phenomena of Electrical Resonance. — Wave 

 Propagation along a Wire. — Having described 

 Hertz's method of calculating the period 

 and the decrement, Poincare discusses next 

 some of the more important experimental 

 researches dealing with these two principal 

 characteristics of an oscillating system. 

 The earliest method employed in researches 

 of this class is that devised by Hertz. A 

 secondai'y circuit, the resonator, consisting 

 of a turn of wu-e Avith an adjustable spark 

 gap is brought into the inductive action of 

 the oscillator. The length and intensity of 

 the induced sj)ark measures the inductive 

 effect between the two. When the peiiods 

 of the two are equal the effect is a maxi- 

 mum; they are then in resonance. But 

 experiment reveals the fact that the reson- 

 ance effect is not as pronounced as in the 

 case of acoustical resonance. Sarasin and 

 de la Eive (Arch, des sciences phys. 23, p. 

 113; 23, p. 557, Geneve, 1890) mferred fi-om 

 this that the oscillator sends forth a com- 

 plex wave which, if analyzed in the manner 

 of a ray of sunlight, would give a contin- 

 uous spectrum. Poincare, guided by a 



carefully worked general theory of reson- 

 ance, ascribes the absence of a strong reson- 

 ance effect to the large decrement of the 

 oscillator. An appeal is then made to ex- 

 periments bearing on this point and the 

 subject of stationary waves in long wires is 

 taken up. Such waves are produced in 

 the same way as in the case of sound waves. 

 When a train of electrical waves travels 

 along a wire and the leading wave reaches 

 the end of the wire it is reflected there and 

 by the interference between the direct and 

 the reflected waves stationary waves are 

 formed. Hertz's theorj^ of propagation of 

 these waves is given, showing that their 

 velocity is the same all along the wire and 

 equal to that of light for all wave lengths. 

 If the view of Sarasin and de la Eive be 

 correct then stationary electrical waves 

 should have no pronounced nodes and ven- 

 tral segments and, therefore, a resonator 

 which, unlike the oscillator, gives a simple 

 wave of definite j)eriodicity will pick out of 

 the stationary waves that component only 

 which is in resonance with it. In other 

 words, every resonator, within large limits, 

 Avill respond to stationary waves and if mov- 

 ed along a wire which is the seat of such 

 waves its spark will rise and fall in intensity 

 everj' time the resonator passes bj^ a node or 

 a ventral segment of that component con- 

 tained in the complex stationarj' wave with 

 which it is in resonance. It measures, 

 therefore, the wave length corresponding to 

 its own period and not that corresponding 

 to the period of the oscillator. This wave 

 length divided by the calculated period of 

 the vibrator will give, therefore, a wrong 

 velocity of j)ropagation. A mistake of this 

 kind was suspected in Hertz's earliest ex- 

 periments by which he obtained a different 

 A'elocity of propagation along a wire from 

 that in the dielectric. Sarazin and de la 

 Eive called this phenomenon, first observed 

 by them, the phenomenon of multiple reson- 

 ance. It is undoubtedly one of the most 



