hertz's researches ox electrical waves. ISy 



of a strong electric arc is never less than a few ohms we shall be justi- 

 fied in assuming- this as the minimum limit. From this it would follow 

 that the number of oscillations due to a single impulse must be reckoned 

 in tens, and not in hundreds or thousands, which is in accordance with 

 the character of the experimental results, and agrees with the results 

 observed in the case of the oscillatory Leydenjar discharge. In the 

 case of closed metallic circuits, on the other hand, theory indicates that 

 the number of oscillations before equilibrium is attained must be reck- 

 oned by thousands. 



Hertz compares lastly the order of the inductive actions of these 

 oscillations, according to theory, with that of the effects actually ob- 

 served. To do this it must be noted that the maximum electro motire 

 force induced by the oscillation in its own circuit is approximately 

 equal to the maximum potential difference at its extremities ; for if 

 there were no damping, these quanities Mould be identical, since at 

 any moment the potential difference at the extremities and the E. M. 

 F. of induction would be in equilibrium. In the exj)erimeuts under 

 consideration the potential diff"erence at the extremities was such as to 

 give a spark 7 to 8""". in length, which must therefore represent the 

 maximum inductive action excited in its own circuit by the oscillation. 

 Again, at any instant the induced e. 3I. f. in the micrometer circuit 

 must be to that in the exciting conductor in the same ratio as that of 

 the co-efficient of mutual induction ^> of the two circuits to the co-efli- 

 cient of self-induction P of the exciting circuit. The value of |> for the 

 case considered is easily calculated from the ordinary formuliP, and it is 

 found to lie between one-ninth and one twelfth of P. This would only 

 give sparks of from ^ to j""". in length, so that according to theory 

 visible sparks ought in any case to be obtained ; but, on the other hand, 

 sparks several millimeters in length, as were obtained in the experi- 

 ments previously described, can only be explained on the assumption 

 that the successive inductive actions produce an accumulative effect; 

 so that theory indicates the necessity of the existence of the resonant 

 effects actuallv observed. 



Dr. Hertz was at first inclined to suppose that as the micrometer cir- 

 cuit was only broken by the extremely short air space limited by the 

 maximum sparking distance under the conditions of the experiment, it 

 might therefore be treated as a closed circuit, and only the total induc- 

 tion considered. The ordinary methods of electro-dynamics give the 

 means of completely determining the total inductive effect of a current 

 element on a closed circuit, and would therefore in this case hav^e 

 sufficed for the investigation of the phenomena observed. He found 

 however that the treatment of the micrometer circuit as a closed circuit 

 led to incorrect results, so that it, as well as the primary, had to be 

 treated as an open circuit, and therefore a knowledge of the total iuduc- 



