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SCIENCE. 



[N. S. Vol. I. No. 5. 



mirror and -witli smaller resonators. The re- 

 sults improved with the increase of the di- 

 mensions of the mirror and the diminution 

 of the size of the exploring resonators. In a 

 subsequent series of experiments (C. R. 

 CXX., p. 688) carried out in a very large 

 hall with a mirror 8 meters high and 16 me- 

 ters mde and employiag circular resonators 

 of 50 and 75 centimeters in diameter these 

 investigators obtained completely satisfac- 

 tory results, proving beyond all reasonable 

 doubt that the velocity of propagation of 

 electromagnetic waves through dielectrics 

 is the same as along conducting wires and 

 equal to the velocity of light. The sources 

 of error in Hertz's experiments were clearly 

 demonstrated by these' experiments, for no 

 matter how large were the hall and the 

 mirror a sufficient increase in the dimen- 

 sions of the exploring resonators would al- 

 ways give misleading results, similar to 

 those obtained by Hertz. 



But among the many encouraging results 

 obtained by Sarasin and de la Rive there is 

 one result which causes much anxiety to 

 the mathematical physicist. It is the 

 serious disagreement between the theo- 

 retically calculated period of the resonator 

 and that determined experimentally by the 

 illustrious physicists of Geneva. In an ex- 

 ceedingly interesting mathematical discus- 

 sion of the functions of the resonator 

 Poincare shows that the wave length of the 

 fundamental vibration can differ but little 

 from twice the circumference of the re- 

 sonator, whereas Sarasin and de la Rive 

 found it to be equal to eight times the di- 

 ameter. The cause of this disagreement 

 must be explained by the theory, but how ? 

 Poiacare gives no definite answer to this 

 question. Many valuable suggestions are 

 thrown out, however, and the subject is 

 then dismissed after showing by a reference 

 to Blondlot's and Bjerkness' experiments 

 that the theorj' of the resonator just given 

 is correct in its main features. No other 



theory of the resonator has been given since 

 that given bj' Hertz, and Poincare's discus- 

 sion contains many valuable additions to 

 the rough outline of the subject sketched 

 out bjr Hertz. In this connection the re- 

 viewer ventures to refer to a paper by 

 Professor P. Drude (^Zum Studinni des Elee- 

 trischen Resonators, Wied. Ann. Nov. 1894). 

 Reflection and Absorption of Hertzian Waves. 

 — Resonator and mirror form the essential 

 instruments in every method of studying 

 electrical waves in the dielectric. The 

 phenomena of reflection and absorption of 

 these waves deserve, therefore, careful an- 

 alysis. To these Poincar6 devotes his at- 

 tention now. The case of orthogonal in- 

 cidence upon a plane metal mirror is first 

 discussed. It is shown that the penetration 

 of the wave into the metal is inverselj' pro- 

 portional to the square root of the product 

 of conductivity and permeability of the 

 metal and directly proportional to the square 

 root of the wave length. For instance, a 

 wave of a periodicity of 50 millions per 

 second, which is the ordinary Hertzian 

 frequency, will be reduced to nearly one- 

 third of its initial intensity at a distance of 

 gV mm. below the surface of a mirror of 

 copper. The relation, however, which 

 Poincare obtains between the penetrability 

 of the wave and the wave length, the con- 

 ductivity, permeability, and specific induct- 

 ive capacity of the metal does not hold good 

 for fi-equencies as high as those of light, 

 for on the one hand it gives by approxi- 

 mation a negative value for the specific in- 

 ductive capacity of all metals, and on the 

 other hand it gives a conductivity 300 to 

 400 times smaller than that obtained bj^ 

 ordinary resistance measurements. The 

 same relations hold good for oblique reflec- 

 tion. It is interesting to note that if, as 

 Cauchjr believes, the fundamental equations 

 of Fresnel (slightlj' modified) hold good for 

 metallic reflection then a retardation in 

 phase equal to half a period takes place at 



