Triple Pendulums ivith Mutual Interaction. 33 



in that the bob P shows a resultant compounded of only two 

 simple vibrations, whereas Q* and P for any considerable 

 coupling show a resultant compounded of three simple 

 vibrations. The cycles are, of coarse, distinctly shorter for 

 the tighter couplings. 



Plate I. fig. 3 gives six sets of triple traces, the corre- 

 sponding pendulum lengths being given in Table III. In all 

 these cases the bob R was started, and, as might be expected, 

 the traces obtained for the same couplings are very similar to 

 those in Plate I. fig. 2. 



Table III. 



a = 138 cms. 



Trace. b. c. 



E 134 cms. 130 cms. 



. W 134 „ 124 „ 



n 130 „ 124 „ 



I 130 „ 116 „ 



g 130 „ 105 „ 



q 124 „ 116 „ 



Plate I. fig. 4 gives six sets of triple traces with two bobs 

 started simultaneously, the corresponding lengths being 

 shown in Table IV. In the trace S the starting was by 

 hand with slightly different amplitudes for the bobs Q 

 and P. Consequently, as seen on the photograph, the 

 bob P is set in motion. In the photographs T and y, 

 the bobs Q and P were tied together in a displaced position, 

 the starting being effected by burning the thread. Thus the 

 bob P is scarcely moved. 



Table IV. 



a — 138 cms. 



Trace. , — * N 



b. c. 



S 134 cms. 130 cms. 



T 134 „ 130 „ 



h 105 „ 105 „ 



w 116 „ 111 „ 



y 116 „ 111 „ 



x 116 „ 111 „ 



Plate I. fig. 5 gives six triple traces with lengths as in 

 Table V. In five of these cases (viz. : Z, b, a, d, and e) two 

 pendulums were locked together so as to form a single pendu- 

 lum of doable mass. This afforded an additional test of the 



Phil. Mag. S. 6. Vol. 42. No. 247. July 192]. 1) 



