48 DISPLACEMENT INTERFEROMETRY APPLIED TO 



and n is the total fringe displacement. Hence, if I = 20 cm., w=i/io, X = 

 6Xio~ 5 cm., p = 0.0013, 



A = i. 03X10-* 



for the soft pipe-note. Rayleigh considers dp/p = 6 X 10 9 just audible, so that 

 my value is of a reasonable relation to it, holding about 2.4X io 5 times more 

 energy per average cm. 3 (pdp/'p = io 3 X 1.05 ergs/cm. 3 ) than Rayleigh 's limiting 

 note. For the shorter adjutages the mean energy would be correspondingly 

 larger. An open cylindrical resonator close to an equipitched open organ- 

 pipe can just be seen to respond. Blown at its edges by a lamella of air, how- 

 ever, strong waves antedate the first audible sibillation of pitch. 



43. Stroboscopic and other secondary phenomena. As the amplitude of the 

 objective of the vibration telescope diminishes (electro-magnetic apparatus 

 not being necessary), interrupted fringes, oblique, as shown in figure 70, are 

 frequent. To account for these, it suffices to observe that the wave-length is 

 continually diminishing. When the diminution is such that the distance apart 

 of the ends of two consecutive waves (direct and return) whose beginnings 

 coincide is the horizontal distance apart of two sinuous fringes, it is obvious 

 that in the middle of these waves the light and dark parts of the fringes will 

 overlap. Thus the fringes here vanish. This occurs periodically along the 

 horizontal. 



As the fringes die down in wave-length for the reason given, the waves 

 become more and more nearly zigzag in outline. Under these circumstances 

 diagonal patterns, as indicated in figure 71 (though not usually at 45), are 

 common. 



For photographic purposes a simple swing of the spring of the objective 

 would suffice, as there is great abundance of light when the arc lamp is used. 

 A very fine slit conduces to sharpness of fringes and wave- lines. 



In addition to the vibration telescope, I also tested the revolving telescope 

 described in 6 1 . In this case the fringes came out beautifully sharp and lumi- 

 nous, with the central achromatic fringe distinguishably white. It thus stands 

 out from the others. If the rotation is rapid, the horizontal fringe bands are 

 apparently stationary. Taps on the table displace them irregularly, but they 

 at once return to the stationary position. Within the limits of continuous 

 fringe bands, fast or slow rotations display the phe- 7 i 



nomenon equally well. Fringes may also be displaced / / / 

 by moving the micrometer during the rotation. Any y y y 

 lack of clearness can usually be compensated by / / / 

 focussing the eye-piece, so that adjustment at the ' 

 interferometer is not necessary. But the waves of 

 the organ-pipe are not well displayed in the case of this apparatus, not even 

 the overtones. The reason of this is the length of the waves ; they become mere 

 inclines. Continuous patterns are not liable to occur, as the waves seen are 



