Variably Coupled Vibrations, 341 



lath. One side wire is connected to the brass cap o£ the 

 lath, and hence to the central contact of the lamp-holder, 

 while the upper end or! the other wire is free. The current 

 enters by the wire GH (which is bent into a rectangular 

 form at N to avoid the lead weights — see fig. 3) and passes 

 through the lamp U and down the side wire Q to the point 

 P, where it passes to the lamp in M via a clip on the lath, 

 and special leads to the base of M. The spiral leads to and 

 from the lamp to the insulator F are not shown in fig. 3 for 

 clearness. To avoid interfering with the swinging of M, 

 the leads from the clips to F are bent into a circular form 

 near the knife edge. The current returns through a second 

 clip and down the side wire K to the battery at E. 



The masses of the lead weights which can be attached to 

 N are such that each is approximately equal to half that 

 of M. Thus the ratio of the masses, and with it the ratio of 

 the periods of M and N, can be altered within certain 

 limits. 



Figs. 1-24 (PI. X.) are reproductions of the traces 

 obtained with the apparatus under various conditions. It 

 should be noted that while the trace of the lower bob 

 gives the actual amplitude of the vibrations of this pen- 

 dulum, the trace of the upper bob is proportional but not 

 equal to the actual amplitude of its vibrations, owing to the 

 occurrence of a proportionality factor due to the reflexion of 

 the light at the mirrors D and its passage through the 

 lens L. The proportionality factor is the same in any pair 

 of photos, but is not in general the same for any two photos 

 selected at random. 



The reproductions are arranged in pairs, one for the upper 

 bob displaced, and the other for the lower bob displaced as 

 initial conditions, and each with the same coupling. The 

 dependence of the details of the traces on the initial con- 

 ditions is thus strikingly illustrated in certain cases. 



Figs. 1-8 (PL X.) are traces obtained for the case in 

 which the ratio of the masses p was 3 : 2, and that of the 

 frequencies rj 7 : 12. Except in figs. 4 and 8, the traces of 

 the lower bob are seen to be very nearly simple sine curves, 

 the amplitude of the second component vibration being so 

 small as not to affect the curve appreciably, while the traces 

 of the motion of the upper bob are throughout complex, 

 showing distinctly the existence of the two superposed 

 vibrations. 



Figs. 4 and 8 show component vibrations, the frequencies 

 of which are very nearly as 2:1, the characteristic kink of 

 the 2 : 1 curve showing plainly. Comparison with Table I. 



