44 Prof. Barton and Miss Browning on Coupled 



distinctly marked especially about 6 per cent. In this case 

 the heavy bob gives up nearly all its energy to the light bob, 

 which then attains an amplitude more than three times that 

 with which the heavy bob started. For very small or very 

 large couplings there is very little fluctuation of amplitude 

 in the vibration of the heavy bob. This is seen in figs. 14, 

 15, and 20-22. This is in accord with the theory. For the 

 ratio between E and F, the amplitudes of the driver's super- 

 posed vibrations have been calculated for the initial con- 

 ditions in use. The results are given in Table III., which 

 shows that E/F has values near unity for couplings about 

 six per cent. Whereas for very small couplings much ex- 

 ceeding six per cent. E/F is very small. And either a large 

 or small value of E/F means inappreciable fluctuation of the 

 driver's resultant amplitude. 



Let us now consider the question of the ratio (p/q) of 

 frequencies of the superposed vibrations and the variation 

 of this ratio with coupling. When the coupling is zero this 

 ratio naturally has that value which applies to the pendulums 

 when separate. When the bobs were equal and lengths 

 unequal, the value of this ratio increased with the. coupling 

 until p/q almost merged into the value for equal pendulum 

 lengths (see fig. 2, p 75, Phil. Mag. January 1918). When 

 the bobs were unequal as well as the lengths but the heavy 

 bob was on the long pendulum, the same behaviour was 

 noticeable in the ratio p/q and its dependence on coupling 

 (see Tables I. and II.). 



On the other hand, when bobs are unequal as well as 

 lengths but the heavy bob is on the short pendulum, a quite 

 new feature is theoretically predicted (see Table III.). Thus 

 when the coupling is gradually increased from zero, the 

 value of p/q at first diminishes, reaches a minimum and 

 then increases. These striking features are to a first 

 approximation upheld by the experiments. For, as seen 

 in passing along figs. 14-20, the number of vibrations in 

 the beat cycle at first increases and then decreases. The 

 maximum number of vibrations in the cycle is about 13 

 and occurs in fig. 17 for a coupling of 6"3 per cent. 

 Accordingly this coupling should correspond to a minimum 

 value of about 108 of the ratio p/q. From Table III., 

 however, it is seen that the minimum value of p/q is about 

 1*054 and occurs for a coupling of about 5 per cent. These 

 slight discrepancies are easily accounted for by the presence 

 of the sand in the funnels and a possible error in estimating 

 the lengths of the simple pendulums equivalent to those 

 in use. Thus, if with the average amounts of sand in the 



