266 Prof. Barton and Miss Browning on Coupled 



from rest. A small circle against the other trace indicates 

 that it was held in the zero position and both bobs let go 

 together. Arrows along the traces show the sense in which 

 they were described. In some experiments the board was 

 drawn along before the bob was let go. These traces 

 accordingly show their own initial conditions. 



Looking at figs. 1-9 of Plate V. we may trace the gradual 

 change from a 5 per cent, coupling to one of 60 per cent. 

 The contrast between the first and last is very striking, and 

 at first glance it would seem impossible to bridge the gulf. 

 The first figure with loose (or moderate) coupling exhibits 

 the phenomena of beats and the slow surging of the energy 

 to and fro between the bobs. The vibrations appear to 

 be practically simple harmonic throughout but of slowly- 

 changing amplitude. This is the natural consequence of the 

 superposition of vibrations of only slightly different periods. 

 (See Table I.) Moreover, while these beats are recognizable 

 the numbers of vibrations from node to node are in accord- 

 ance with the theory. Thus, for fig. 1 the first line of 

 Table I. gives the ratio of frequencies as 1*05 or 21 : 20, and 

 the traces show the correct number of vibrations between 

 the nodes. So with the others. It is perhaps worth men- 

 tioning that some early traces for the 5 per cent, coupling 

 w T ere found to give about 27 waves from node to node. This 

 was disconcerting, as the following couplings were right. It 

 was thought that the connector CC between the two cords 

 might allow a little lost motion or back lash. It was examined 

 and found not to fit quite tightly, though possibly friction 

 might prevent any shake. Of course, if there were lost 

 motion, a theoretical 5 per cent, might be reduced to an 

 actual 4 per cent, (or less), and the number of waves in- 

 creased to 25 (or more). The connector was accordingly 

 made quite tight and traces again taken. They still showed 

 about 27 waves from node to node. But it was soon dis- 

 covered that an electric lead crossing the room for another 

 research had sagged and touched the bridle cords, and thus 

 very slightly vitiated their motion. This disturbance was 

 removed and the trace taken which appears as fig. 1, showing 

 the correct 20 waves. 



Turning now to fig. 9 we see that it shows nearly, but not 

 quite, the compound harmonic curve characteristic of a tone 

 and its octave. If the 2 : 1 relation were exact the kink 

 would not wander on the main curve, but would reappear 

 each time in the same position. Now this case corresponds 

 with the ninth line of Table I., and was calculated to give 

 a frequency ratio of 2:1, but on the supposition that the 



