614 



Prof. Barton and Miss Browning 



Then using equations (4) and (11), equation (8) may be 

 written 

 pS(l-^-/3 2 -ry 2 -2*l3y)-p i [lXl-* 2 ) + m 2 (l-/3 2 ) 



+ n 2(i _ y)] +p*(p m * + m 2 n 2 + n 2 l 2 ) - l 2 m?n? = 0.. (12) 



Thus it is seen that in general the vibrations after coupling 

 the circuits differ from the free vibrations of the separate 

 systems. 



The less the coupling the more nearly do the superposed 

 vibrations approximate to those of the systems when free. 



III. Arrangement of Three Connected Pendulums. 



The apparatus shown in fig. 13, Plate V. " Coupled Vibra- 

 tions " (Phil. Mag. July 1918) was adapted for the tripled 

 pendulums. Figs. 1 and 2 give the side and end elevations 



Fig-. 1. — Side elevation. 



3o\ 



E~ 



o£ the actual arrangement used. The masses are confined as 

 far as possible to the bobs P, Q, and R, which are heavy 

 carriers with funnels containing sand. 



