662 Prof. Taylor Jones and Mr. Roberts on Musical 



The apparatus used in the present experiments was the 

 same as that previously described ; the mutual inductance 

 of the coils was varied by moving the primary along the 

 axis of the secondary, and for each position of the primary 

 coil the secondary capacity (a variable condenser with oil 

 dielectric) was adjusted so that the two notes were equally 

 stable. In a certain position of the primary coil the interval 

 between the notes, as judged by ear, was a fourth, and if 

 then the lower note is sounding, and the arc-length is gradually 

 reduced, at a certain point the note suddenly falls by an 

 interval which can be recognized as a twelfth, although the 

 deep note thus produced generally dies away rapidly. 



The terminals of the secondary condenser were connected 

 to the electrostatic oscillograph, and after a considerable 

 number of attempts a photograph was obtained showing the 

 wave of potential* in the secondary circuit when this 

 difference tone was sounding. The curve in the photograph 

 (PL XIII. fig. 1) shows the grouping of the waves characteristic 

 of simultaneous oscillations of different frequencies. The 

 damping is strong in this case, but it was often mucn less 

 than is shown in the photograph. The curve somewhat 

 resembles those which may be produced by simply breaking 

 a current in the primary circuit |. 



The frequency of the groups determined from the photo- 

 graph, by comparison with the curve given by the 768 

 tuning-fork, was 200' 6. 



The constants of the circuits were determined by methods 

 which have been fully described by one of us in previous 

 papers. In the paper above referred to it was shown that 

 in order to calculate correctly the frequencies of singing-arc 

 oscillations, it is necessary to assume that the arc possesses 

 self-inductance which must be added to that of the primary 

 circuit, the value of the apparent self-inductance of the arc 

 depending upon the distance between the carbons. 



In the present case it w T as found that there was no value 

 of Lj which made rig/n^ 4/3, if the resistances of the circuits 

 were neglected. After a number of trials the following results 

 were calculated. Assuming the value *0005 henry for the 

 self -inductance of the arc, then Ni 2 = P693.10 7 , N 2 2 = T823.10 7 

 c.G.s.,P = '086o6. Hence, neglecting the resistances,?! 2 = 7 94* 7, 

 m = 585-7, n 2 — n! = 209, n 2 /n 1 -P357. 



Taking the resistances into account, however, and assuming 

 about 4 ohms for the arc, then Pi = 5 ohms, P 2 = 14000 ohms; 



* As explained in previous papers the ordinate of the curve is pro- 

 portional to the square of the difference of potential at the terminals of 

 the instrument. 



t Cf t E. T. Jones, Phil. Mag. January 1909, Plate, figs. 5, 6, 7, 8. 



