372 POPULAR LECTURES AND ADDRESSES. 



tion. Figure 2 represents the second or quicker 

 fundamental mode ; the vibration of the upper 

 pendulum being in this instance excessively small 

 in comparison with that of the lower, and forced by 

 the influence of the latter to a period much smaller 

 than its own would be if undisturbed. 



CASE II. 



Figure 3 represents the graver mode. The 

 vibration of the upper pendulum through but a 

 very small arc in comparison with the lower, has its 

 period augmented by the influence of the lower, 

 which, in the course of the vibrations, exerts a 

 force upon it always from its middle position. 

 Figure 4 represents the quicker mode ; the vibra- 

 tions of the upper pendulum being made somewhat 

 faster by the influence of the lower, and the lower 

 being influenced so as to vibrate as if it were 

 shortened to the length OA, which is somewhat 

 less than the length CP'. If ?' consisted of the 

 frame and work of a spring clock, and V P were its 

 pendulum, then, in Case I., the vibrations which 

 \\-ould be maintained by the action of the escape 



