hertz's researches, on electrical waves. 157 



where contact could take place without effect ou the sparkinjj was be- 

 tween a and e. These results show that it is possible to excite at will 

 in the same conductor either the fundamental vibration or its first over- 

 tone, to use the language of acoustics. 



Hertz appears to consider it very doubtful whether it will be i)0ssible 

 to get higher overtonesof electrical vibration, the difficulty of obtaining 

 such lying not only in the method of observation, but also in the nature 

 of the oscillations themselves. The intensity of these is found to vary 

 considerably during a series of discharges from the coil even when all 

 the circumstances are maintained as constant as possible, and the com- 

 parative feebleness of the resonant effects shows that there must be a 

 considerable amount of damping. There are moreover many second- 

 ary phenomena which seem to indicate that irregular vibrations are 

 superposed upon the regular ones, as would be expected in complex 

 systems of conductors. If therefore we wish to compare electrical os- 

 cillations (from a mathematical point of view) with those of acoustics, 

 we must seek our analogy in the high notes intermixed with irregular 

 vibrations, obtained, say, by striking a wooden rod with a hammer, 

 rather than in the comparatively slow harmonic vibration of tuning- 

 forks or strings ; and in the case of vibrations of the former class we 

 have to be contented, even in the study of acoustics, with little more 

 than indications of such phenomena as resonance and nodal points. 



Keferring to the conditions to be fulfilled in order to obtain the best 

 results, shoidd other physicists desire to repeat the experiments, Dr. 

 Hertz notes a fact of very considerable interest and novelty, namely, 

 that the spark from the discharger should always be visible from the 

 micrometer, as when this was not the case, though the phenomena ob- 

 served were of the same character, the sparking distance was invaribly 

 diminished. 



Theory of the experiments. — The theories of electrical oscillations 

 which have been developed by Sir William Thomson, von Helmholtz, 

 and Kirchhoft", have been shown* to hold good for the open-circuit oscil- 

 lations of induction apparatus, as well as for the oscillatory Leyden-jar 

 discharge; and although Dr. Hertz has not succeeded in obtaining defi- 

 nite quantitative results to compare Avith theory, it is of interest to 

 inquire whether the observed results arc of the same order as those in- 

 dicated by theory. 



Hertz considers, in the first place, the vibration jieriod. Let T be the 

 period of a single or half vibration i)roper to the conductor exciting the 

 micrometer circuit; P its co-efficient of self-induction in absolute elec- 

 tro-magnetic measure expressed therefore in centimeters; G the capac- 

 ity of one of its terminals in electro-static measure, aiul therefore also 

 expressed in centimeters; and v the velocity of light in centimeter- 

 seconds. 



' Lorentz, Wiedemann's Annalen, 1879, vol. vii, p. 16L 



