ACOUSTICS AND GRAVITATION. 41 



The ratio of compression in case of the interferometer direct and the interfer- 

 ometer and pin-hole conjointly is thus 9.7Xio- 3 /i.6Xio- 4 = 6i,of the same 

 order of value as estimated for the same pipe. 



With 1,000 ohms in the telephone circuit, however, the waves were scarcely 

 perceptible on the interferometer, equivalent, therefore, to a double amplitude 

 of o.i fringe, whereas the pin-hole valve showed about 25 fringes (fig. 58). 



The bg" overtone with smooth, sinuous waves is not easily explained, for 

 in the normal diapason the nodes are respectively rare and dense and thus with- 

 out effect on the interferometer. It may be plausibly argued, therefore, that 

 in the telephone-blown pipe both nodes are together either dense or rare, an 

 abnormal condition impressed by the telephone. The central node in the a' 

 pipe is thus halved and the two halves symmetrically shifted outward, to be in 

 equilibrium with the impact of air from without . Hence bg" is the fundamental of 

 two identically sounding half -pipes and the above relations remain unchanged. 



The e" overtone was also strong, but the waves were no longer sinuous, 

 consisting rather of successive arches, meeting in cusps at their abutments, 

 and with the curves of the arches sharply serrated. The mean double ampli- 

 tude was again about one fringe. In proportion as the vibration telescope 

 dies down in amplitude, the fringes gradually assume the appearance of par- 

 allel strands of beads. 



Notes near a' (like g', 6') usually emit strongly beating wave-trains from the 

 two ends of the pipe, even when the halves are of equal length. The same is 

 true of notes near bg" (g" and a") . The interferometer record usually shows 

 waves of nearly the same amplitude as at the regular overtones ; but they are 

 highly compound successive serrated inclines, and the like. Waves are running 

 from end to end of the tube, without steadiness of motion. Only at c" and 

 f" was the fringe-band approximately straight. With the d" pipe (unstop- 

 pered) a', d", \>g" gave a sinusoidal record, while b' ', c", e" were strongly 

 beating trains, but the maximum double amplitude did not here much exceed 

 a half fringe, agreeing with the case of figure 58. 



Finally, the open pipe was tested with the small magneto actuating the 

 telephone. Scarcely any effect was discernible, even when all extra resistance 

 was removed from the circuit. This current is thus not strong enough to blow 

 the pipe appreciably. If the telephone, provided with a mirror for observation 

 on the interferometer, is examined the effect is throughout quite marked, as 

 will be instanced ( 56) below, Chapter VI. 



36. Helmholtz spherical resonator. It is interesting to compare with the 

 complicated results described the graphs for a telephone-blown Konig reso- 

 nator (c"}. These are given in figure 63 for probe depths of 2, 4, 8 cm. belowthe 

 mouth. Here the U-tube reservoir contributes no appreciable overtones. 

 It was necessary to withdraw the extra resistance from the telephone circuit 

 to obtain large fringe displacements, owing to the small entrance channel 

 (neck) for the telephone note and the relatively large diameter (7 cm.) and 

 mouth of the resonator. For this reason, also, no appreciable effect was 



