﻿Vibrational Responders under Compound Forcing. 575 



frequency as before, but showed also by higher maxima the 

 quicker vibrations which are the harmonic components of 

 the compound motions now executed by D. Three cases 

 of such harmonic analysis were carried out with this 

 apparatus and the vibrations and results are shown in figs. 1, 

 2, and 3 of PI. III. The curves shown below each indicate 

 the motions given to the bob by hand, and the photographic 

 reproductions above give time-exposures of the responders. 

 In fig. 1 (PI, III.) the motion is compounded of vibrations of 

 relative frequencies one and two, or tone and octave, to adopt 

 musical language. In fig. 2 the motion of the bob was com- 

 pounded of vibrations of frequencies one and three, and the 

 result of analysis is seen to be that of a tone and its twelfth. 

 In fig. 3 the motion of the bob, as shown below, is com- 

 pounded of frequencies one, two, and three, and the responders 

 give maxima at the corresponding places, which the musician 

 would call tone, octave, and twelfth. 



Coupled Vibrations. — The arrangement now adopted is 

 shown by the reproduction in fig. 4, PL III. There it may be 

 seen that the two pendulums of nearly equal mass (each 

 suspended by a bridle and vertical cord) are coupled by the 

 bridge across the near part of the bridle. On the far part 

 of the bridle of one pendulum a set of thirteen responders 

 are in use. These are of precisely the same type and 

 arrangement as the twenty-five used for the harmonic 

 vibrations, but here only one octave of the chromatic scale 

 is provided instead of two octaves. (The white cones which 

 constitute the bobs are clearly visible, but the black suspension 

 threads do not show.) For convenience, the responders may 

 be named according to the chromatic scale of C. It was 

 recently found to be far more convenient to have the bridge 

 adjustable along the bridle instead of fixed at the junction of 

 the bridle and vertical suspension for the heavy bob. If a 

 line is drawn from the bridge across either of the coupled 

 pendulums with heavy bobs to the distant end of the bridle, 

 and the suspension cord imagined to stretch vertically upwards 

 to meet this line, then the completed length of the suspension 

 gives the vibrating length of the coupled pendulum when the 

 bridge is held at rest, and therefore this length defines 

 the quick period peculiar to the coupled system with the 

 coupling in question. 



Fig. 5 shows the effect of starting the vibration by burning 

 a thread which held the bobs near together. In this case the 

 bridge (as shown in the photograph) remains at rest, and 

 the bobs execute the quick vibration alone. This is exhibited 

 by the responders, which show a maximum amplitude at a 



