18 



Prof. Barton and Miss Browning on 



a vibration which is the resultant of three simple harmonic 

 components of undetermined amplitude and phase. The 

 frequencies of these components are identical for the three 

 pendulums. On examining the general relations between 

 the amplitudes of these nine components, it is found, that for 

 one pendulum, one of the possible components fails and 

 for the other eight still remaining three constants are suffi- 

 cient to express them. Further, for a component of a given 

 frequency the phase was found to be the same for each 

 pendulum. 



This left in the solution six arbitrary constants to be 

 determined by initial conditions. These are then worked 

 out for several typical cases. The theoretical results are 

 found to be in satisfactory agreement with the experiments. 



Thirty-six photographic records of the tripled traces are 

 reproduced in the paper. 



II. Experimental Arrangements. 

 The general disposition of the pendulum is shown in the 



Fig. l. 

 General Perspective View. 



a" e-" 



perspective sketch of fig. 1. Side and end elevations are 

 given in figs. 2 and 3 respectively, while fig. 4 shows in an 



