68 DISPLACEMENT INTERFEROMETRY BY 



action of the bifilar and the load, stress or spurious torque about the vertical 

 (hence Aa) is introduced; but it is extremely difficult to state just how 

 when all loads are symmetrically vertical. To obviate this the permanent 

 parts of the apparatus should be cast in one piece. 



An interesting corroboration of these observations is given by the pendu- 

 lum oscillations of the loads. These produce (even for loads as small as i 

 kg.) marked vibration of fringes if the load vibrations are transverse to 

 the rays, while vibrations are ineffective if longitudinal (in direction of the 

 rays). Noticing the behavior of fringes for the first time, I supposed that 

 the centrifugal accelerations introduced by the vibration might be the cause. 

 In fact, if the length of the compound pendulum (load w, figs. 28 and 29) 

 treated as a simple pendulum is L and its mass M, the centrifugal force at 

 any displacement 5, corresponding to the displacement velocity v, is 



Mv z 



ly __ _ _ __ 



But if s = A sin ut, then v = Aucos o>/, and thus 



since co 2 = g/L. This force is a maximum at / = o sec., or F Q = Mg. A Z /L 2 . 

 If A = i cm. and L=is cm., F is but ^ of the weight of the load Mg, 

 say a maximum not exceeding 2 5 grams of weight. Since the whole displace- 

 ment is but a few fringes, this small fraction could not be discernible with a 

 body like the steel rod above. Thus the alternating transverse stress pro- 

 duced by transverse swinging alone can account for the observed effect. 



38. Ocular micrometer. Collimator micrometer. These methods of meas- 

 uring the displacement of fringes have been discussed in Chapter I, 4, 5. 

 It was of interest to test them here. The scale on the ocular plate inserted 

 divided the field width into 100 parts, the division being in o.i mm. The dis- 

 tance apart of the achromatic fringes was a little more than this (1.4 cm.) 

 The correspondence could be made exact by rotating the auxiliary plate 

 (bar F, fig. 28) about a vertical axis slightly, but the adjustment was not 

 necessary here. These excessive tenth millimeters thus correspond roughly 

 to an elongation zAl of both rods, equal to the mean wave-length of light, 

 or more accurately, _, 



2 A*=-X 



where zR is the distance apart of the interfering rays ab (fig. 27) and 2R' 

 the distance apart of the rods rr'. 



If the size of fringes is known on the ocular micrometer, they may be 

 counted by their displacement along it, since the central achromatic fringe 

 is always distinguishable and serves as an index. But the width of fringes, 

 if the laboratory is not quiet, is hard to measure, for they quiver or vibrate. 

 It is easier to express the displacement A# of fringes in the ocular in terms of 

 AN, the corresponding displacement of the micrometer of the interferometer. 



