Vibrations : Both Masses and Periods Unequal. 47 



where 7 is the coupling and u. is the ratio in which the 

 second suspension divides the lath. 



So that here also with increasing positive values of ol, 

 7 only approaches but never reaches unity except for a = oc . 

 But for negative values of a. we see that 7 may reach unity 

 for «== - 1. 



This suggested plotting a graph giving 7 as ordinates, 

 a being the abscissae. This is shown in fig. 23 (PL V.). The 

 graph has a maximum and a minimum at <z= — 2 and points 

 of inflexion at a= — 0*344 and —2*906 nearly, and it also 

 asymptotes to 7= + 1. 



VI. Possible Further Work. 



The vibrations of two coupled pendulums have hitherto 

 been developed for their own sake and as an analogue to 

 -electrical vibrations in coupled circuits. It appears, how- 

 ever, that by modification of the pendulums the analogue 

 may be usefully extended so as to illustrate phenomena in 

 various other branches of physics. 



The following have occurred to us as worthy of investi- 

 gation and plans of attack of several have already been 

 matured : — 



1. Kater Pendulum for " g " and the possible disturbance 

 of period due to vibration of bracket. Theory and experi- 

 ment will enable us to evaluate the possible error and 

 eliminate it. 



2. Large vibrations with restoring forces not simply 

 proportional to the displacement but involving its squares 

 or cubes. 



3. Such a system under double forcing. 



4. Optical Dispersion. 



5. Dynamical Analogies to Colour Vision and Hearing. 



6. Any of the above but further specialized by damping 

 -where necessary. 



Nottingham, 

 March 16, 1918. 



