Vibrations elucidated by Simjjle Experiments. 269 



triplicate, the board being again passed under while the 

 pendulum was still swinging unchecked. 



Figs. 27-30 on the bottom row of Plate VI. show double 

 traces obtained simultaneously from the upper and lower 

 bobs, the two boards being placed together in right relation 

 for photography. The coupling is the same in each, viz., 

 of the order 48 per cent, as to give approximately 2 : 1 as 

 the ratio of frequencies. Figs. 27 and 28 show very plainly 

 that the bob which is not struck executes the compound 

 harmonic motion whether it is lower or upper, but that the 

 bob which is struck has a very different motion according as 

 it is upper or lower. See equations (77) to (84). 



Figs. 29 and 30 show the results of pulling one bob aside, 

 the other being at rest in its equilibrium position as dealt 

 with in the theory. See equations (85)-(94). The pulling 

 aside was effected by a horizontal thread which was burnt 

 when all was steady. 



IX. Summary. 



1. The paper describes two types of coupled pendulums 

 which are considered useful both for lecture demonstration 

 and for quantitative work in the laboratory, especially as 

 they illustrate many important points in the phenomena of 

 inductively-coupled electrical circuits. 



2. One of these, called the double-cord pendulum, is like a 

 pair of Blackburn's pendulums in parallel planes connected 

 by a stiff tube at the droop of the bridles. Its vibrations 

 occur perpendicularly to these parallel planes. It may be 

 used with couplings gradually varied from very loose to very 

 tight, say from 1 to 60 per cent. It exhibits, by double sand- 

 traces simultaneously formed on a moving board, the gradual 

 change of the vibrations from the phenomena of slow beats 

 to those of compound harmonic motion. Most of the curves, 

 however, show the superposition of two simple vibrations of 

 incommensurable frequencies. 



The pendulum shows also the effects of different initial 

 conditions. 



This form is specially suitable for laboratory work, as it 

 may be set up from the simplest materials and yet give 

 results of distinct and quantitative value. 



If the lengths are equal and the masses also, then the 

 vibrations of this pendulum are quite interchangeable. 



Photographic reproductions are given of sixteen double 

 traces obtained with this pendulum. 



3. The other form of apparatus, or cord and lath pen- 

 dulum, is yet easier to use for simple lecture illustration, but 



Phil. Mag. S. 6. Vol. 34. No. 202. Oct. 1917. U 



