VIBRATING TELEPHONE DIAPHRAGMS. 417 



axis. The reflected arc-light beam then fell upon the mirror M, 

 of a Duddell bifilar vibration galvanometer,^ in the same circuit as 

 the telephone receiver coils C, and so arranged as to vibrate about 

 a vertical axis, under the action of the current which actuated the 

 telephone. The beam finally produced a spot of light on the trans- 

 parent screen, S. Owing to the two independent mirror vibrations 

 being of the same frequency, but about mutually perpendicular axes, 

 this spot of light traced Lissajous figures on the screen, and the 

 observed shape of these figures enabled calculations to be made as 

 to the phase differences between the movements of the two mirrors 

 in and M. It was therefore necessary to make an initial examination 

 into the phase relations of the Duddell galvanometer mirror M, 

 with respect to the alternating current operating it. 



Observations on the phase relations of vibration galvanometer 

 mirrors have already been published.*' It was found, however, in 

 the research here reported, that as might be expected from the 

 differential equation of motion of such an instrument as an oscillo- 

 graph or vibration galvanometer, it inherently possesses a motional- 

 impedance circle, like a telephone receiver. The motional-imped- 

 ance circle of a vibration galvanometer, or an oscillograph, differs 

 from that of the ordinary telephone receiver, in having its diameter 

 coincident with the resistance axis, or very nearly so; so that I3i°=^ 

 jSg^^o. This means that the vibrational angular velocity at reso- 

 nance is in phase with the vibromotive force, which in this case is 

 also in phase with the actuating alternating current. From an ob- 

 servation of the instrument's motional-impedance circle and deflec- 

 tions, the essential mechanical and electrical constants of the instru- 

 ment, for its particular state of adjustment, can be readily deter- 

 mined. This theory and technique for vibration instruments, which 

 are only side issues of the main research here reported, are dis- 

 cussed in Appendix I. It suffices here to note that provided the 

 Duddell galvanometer is out of tune, even only a few per cent, with 

 respect to the actuating currents, its mirror displacements will be 

 substantially either in phase with, or in opposite phase to, the ac- 



5 Bibliography, 5. 



6 Bibliography, 6. 



