370 POPULAR LECTURES AND ADDRESSES. 



same direction from the vertical ; the lower 

 through a greater angle than the upper. In the 

 quicker fundamental mode, the two deviate in 

 opposite directions. The period of the graver 

 fundamental mode is always longer than that of 

 a simple pendulum, of length equal to that of the 

 longer of the two cords ; the period of the quicker 

 fundamental mode is always shorter than that of 

 the simple pendulum, equal in length to the shorter 

 cord. If the upper mass is much greater than the 

 one hung from it, and if the two strings be not 

 approximately equal in length, the two funda- 

 mental periods differ but little from those of 

 simple pendulums equal in length to the two 

 cords respectively. The diagrams Figs. I to 4 

 illustrate the circumstances in the cases ; first, 

 when the upper cord is considerably longer than 

 the lower ; and second, when the lower cord is 

 considerably longer than the upper. In each case 

 OA is the length of the the simple pendulum 

 vibrating in the same period as that of the 

 .fundamental mode represented. 



