618 Triple Pendulums with Mutual Interaction. 



For F, G, and H (PL XII.), the coupling between pen- 

 dulums P and R was decreased by moving the connector DD' 

 nearer to E. The curves are very similar, F was obtained with 

 Q pushed aside, and G with It pushed aside. From the 

 photographs it is seen that the couplings are small between 

 P and each of: the other pendulums, but that between Q and 

 JR is very much larger. The interaction between the pen- 

 dulums Q and R does not seem to be communicated to P at 

 all, although the reaction of the slow waxing and waning of 

 the amplitude of P is clearly seen in the traces of both the 

 other pendulums. 



Photograph H was obtained with an arrangement of pen- 

 dulums like those used for F and G. R was started and 

 after three complete cycles of change was held stationary; 

 the pendulum I hen settled quickly to a state showing two 

 superposed simple harmonic vibrations, as in coupled 

 pendulums. 



At this point it was thought probable that the two con- 

 nectors B and would be sufficient. D was removed. 

 Everything else was kept the same. The photograph I 

 (PL XIII.) shows traces with the couplings between P and 

 each of the other pendulums considerably reduced, but other 

 things much the same. 



The connectors were then lowered considerably, and curve J 

 was obtained by drawing aside P. This was found to be 

 almost identical with G, which shows that connector D was 

 superfluous. 



Photographs K and L were obtained with the two con- 

 nectors at the same position on the cords. The photographs 

 show which bobs were drawn aside, and the resultant effect 

 was that of a light bob driving one heavy bob which is com- 

 posed of the other two. There is little to indicate more than 

 two harmonic vibrations in the curves. 



M and N were obtained with the connectors together on 

 the cords, but with the coupling increased. Studying the 

 four last photographs carefully, it is seen that the two 

 pendulums which are the driven ones to begin with do not 

 give exactly identical curves, the distance between the nodes is 

 gradually increasing. This points to the fact that there are 

 more than two simple harmonic vibrations involved. 



Other experiments have already been carried out with a 

 simpler arrangement of three interconnected pendulums, but 

 these are reserved for a separate paper. 



Nottingham, July 14, 1920. 



