170 Prof. Barton and Miss Browning on the Resonance 



paper cones and weighted with a ring of copper wire (like those 

 used in Mechanical " Resonators/' Phil. Mag. April 1919) . 

 These hang by suspensions of black thread from the stout 

 cord HJI, to which is attached the driving pendulum JK 

 whose true length must be reckoned from J'. It is adjustable 

 to various required lengths by a tightener as shown. A second 

 cord is shown by HML, from which is suspended a second 

 driving pendulum MN (of virtual length M'N) and whose 

 bob N is equal in mass to the bob K. These two cords are 

 connected by the wooden bridge T, thus the two driving- 

 pendulums are only loosely coupled to each other but each 

 acts quite distinctly upon the set of respond ers. 



The camera lens is along the line HJ produced so that in 

 the photographs all the responding pendulums will seem to 

 hang from the same point. Further, the responding bobs all 

 lie along a straight line QH in order that each respond er 

 shall experience the same driving influence (see " Forced 

 Vibrations," p. 176, Phil. Mag. Aug. 1918). 



Results and their Significance. — Plate II. gives six repro- 

 ductions of time exposures of the responders actuated by two 

 drivers of widely differing periods, the slower of the two 

 being gradually increased in length from figure to figure 

 throughout the series. In fig. 1 it is obvious that the length 

 of the driver is about midway between those of the responders 

 whose bobs are third and fourth from the bottom. Or, in 

 musical terms, we might say that the pitch of the driver 

 was about midway between E|? and D, the E[> being 

 slightly favoured. In the second figure we may, in like 

 manner, refer to the pitch of the driver as being slightly 

 nearer D than E|}, since the bob third from the bottom 

 responds better than the fourth. In the third figure, the 

 third bob from the bottom responds much better than any 

 other, but the fourth shows a distinctly better response than 

 the second. Hence the pitch of the driver is recognized as 

 distinctly sharper than D. In the fourth figure the driver is 

 still slightly sharper than D, whereas in the fifth it is slightly 

 flatter than D. In the sixth figure the driver is distinctly 

 flatter than D. Hence, in five steps we have passed over 

 about a quarter of a tone, giving an average interval of a 

 twentieth of a tone, or ten logarithmic cents. 



It is evident by inspection of these figures that pitches 

 midway between the adjacent ones given would be discernible 

 as differing one from the other. Thus between figures 1 

 and 2 with fourth bob favoured and third bob favoured we 

 might have had another case with neither favoured. Hence,, 

 with nervous discrimination of relative amplitudes equivalent 



