424 M. I. Pwpin — Electrical Oscillations oj 



-!« 



where T = natural period of the circuit 



2tt 



' LC 4L" 



When — 2 is small in comparison to — - then 



that is the natural period of the circuit is independent of the 

 ohmic resistance. 



To show that it is only under very exceptional circumstances 

 that this condition is not fulfilled, I shall consider a circuit 

 consisting of a large Bell telephone connected in series with 

 a condenser of 1 microfarad capacity. The resistance of the 

 telephone is 100 ohms, very large indeed, considering that its 

 coefficient of self-induction is only about 0*5 henrys. Making 

 this circuit a part of the secondary circuit of the small trans- 

 former excited by the electro-dynamic interrupter described 

 in part 1 of this paper* it is found that the sound of the 

 telephone is loudest when the frequency of the vibrator is 

 about 225. The pitch of the sound is not sensibly altered by 

 changing the resistance within very large limits ; a result re- 

 quired by theory. For the period calculated from formula 



T=27rv / LC gives 224,4 vibrations per second. 



Adding the correction given by formula (5) we get for the 

 corrected period T x = 224,9 a difference of only about J of one 



per cent. Since the dissipation ratio r=- — we get for the 



2,25 



1 it 



damping factor e ' , that is to say the electrical oscilla- 

 tions would disappear almost completely after only 10 complete 

 oscillations, which shows that the ohmic resistance produces a 

 very strong damping and yet the period is practically inde- 

 pendent of it. 



In circuits consisting of well made coils with finely divided 

 but split iron cores the dissipation ratio r is very small even 

 for frequencies as low as 100 periods per second. The period, 

 therefore, will be independent of the dissipation losses even if 



* This Journal, April, 1893. 



