Arc Oscillations in Coupled Circuits. 663 



hence, by Drude's equations*, n 2 = 791*49, // 1 = 591'03, 

 n,,—,^ 200*46, »j 2 //ii= 1-339. 



Jt is therefore clear that if the arc be assumed to have a 

 self-inductance rather less than *0005 henry, and a resistance 

 slightly greater than 4 ohms, the ratio o£ the frequencies of 

 the two oscillations will be exactly 4/3, and their difference 

 will agree with the observed value ot the group-frequency. 



PL XIII. fig. 2 shows the curve obtained with the coils iu 

 the same relative position but with larger capacities in the 

 circuits. This photograph covers the period of change from 

 the lower primary note to the difference tone. In this case, 

 again assuming- -0005 henry for the self-inductance of the 

 arc, we find N, 2 = 1-3468. 10 7 , N 2 2 = 1-3329. 10 7 , F = *08636. 

 Hence ? neglecting the resistances, n 2 ~ 693*28, n 1 = 512*14, 

 7i 2 — ?z 1 = 181*14, n 2 jni= 1*3538. Again taking Rj = 5 ohms, 

 B 2 = 14000 ohms, we find by Drflde's equations n^ — 690*6, 

 n 1 = 517*4, n 2 — 7^ = 173*2, w 2 /w 1 = 1*3348. 



The frequency of the groups determined from the photo- 

 graph is 174*8. In this case also the effect of taking the 

 resistances into account is to diminish the ratio of the fre- 

 quencies, and possible values can be found for the self- 

 inductance and resistance of the arc which will make the 

 ratio of the frequencies exactly 4/3, and make their difference 

 agree with the observed frequency of the groups. 



By withdrawing the primary coil to greater distances 

 along the axis of the secondary, some of the smaller musical 

 intervals, the major third and minor third, may be obtained, 

 and deep difference tones sometimes heard ; these are, however, 

 very unstable and no photographs were obtained for these 

 cases. 



By increasing the coupling coefficient to a certain value, 

 the two notes maybe brought to an interval of an augmented 

 fourth, and with a certain value of the secondary capacity 

 the two notes may be produced simultaneously. The dif- 

 ference tone was not prominent in this case ; the impression 

 was rather that of the two primary notes sounding together. 

 The photograph was easily obtained and is shown in PL XIII. 

 fig. 3. This photograph was obtained with a new oscillograph 

 wdiich was at the time arranged for measuring much higher 

 potentials, the phosphor-bronze strip being replaced by one 

 of steel, and this being under very great tension. This 

 accounts for the smallness of the amplitude of the curve. 

 The curve was not measured, but it probably represents the 

 case rc 2 /ni=7/5. 

 Bangor, July 1910. 



* Drude, Ann. der Phydh. xiii. p. 531 (1904). 



