268 Prof. Barton and Miss Browning on Coupled 



Cord and Lath Pendulum. — In the present work this 

 arrangement was used with the lengths, r and s, of the pen- 

 dulums equal and the masses, P and Q, of the bobs equal. 

 Accordingly the equations (58)-(60) apply and also those 

 based upon them. Calculating from these we derive the 

 values given in Table II. The length of the simple pen- 

 dulum equivalent to one of the lath pendulums used alone 

 was 112 cm. The lengths SR ( = 112 a) were accordingly 

 calculated and are shown in the Table. The positions of R 

 for the various desired couplings were then marked on the 

 lath to facilitate setting. For completeness' sake several 

 values of coupling are included in the table, though they 

 have not been used with the present model. For example, it 

 is difficult to set the coupling for values less than 15 per 

 cent, or greater than 55 per cent. 



Table II. — Cord and Lath Pendulums. 



Coupling 



Ratio RS : QS 



Length SR 



7- 



= «. 



=«Xll2 cm. 



Per cent. 





cm. 



5 



0-051331 



5-75 



10 



0-105680 



11-84 



15 



0-163660 



18-33 



20 



0226020 



25-31 



25 



0-293675 



32-89 



30 



0-367800 



41-19 



35 



0-449612 



50-36 



40 



0-541945 



60-70 



45 



0-646610 



72-42 



50 



0767591 



85-97 



55 



0-910181 



101-94 



57-7 



1 



112 



Plate VI. presents fourteen sets of traces obtained with 

 various couplings or under different initial conditions. Of 

 these the first ten, figs. 17 to 26, show single traces from the 

 lower bob when the upper bob was struck; the couplings 

 vary from 15 to 55 per cent. In fig. 24 the coupling was 

 about 48 per cent., the adjustment was made by trial to give 

 2 : 1 as the ratio of frequencies. To show that the exact 

 ratio was practically attained two lines of traces were taken, 

 12 waves occurring between them. It is seen that the kink 

 shifts its position but slightly on the main wave after the 

 lapse of 26 of the long periods. To trace the slow shift of 

 the kink because the 2 : 1 relation is not fulfilled the figures 

 for the 50 and 55 per cent, are taken in duplicate or 



