DISPLACEMENT INTERFEROMETRY. 



117 



micrometer n', n" ', ri", virtually normal to the rays, was also tested, 

 achromatic fringes were used. 



The 



89. Needle in air. The two methods. To obtain some notion of the be- 

 havior to be expected, a number of experiments were made in series with the 

 needle air-damped. Its motion was then practically aperiodic. With the 

 quartz fiber used, the total deflections were so large that there are two methods 

 for measuring the displacement of the small masses m, m'. For one can 

 express the angle described by the needle either in terms of the displacement 

 of the slit-image in the telescope relative to a fixed ocular scale or to a fixed 

 collimator micrometer-scale; or again, with far greater accuracy, one can use 

 the achromatic fringes moving within the slit-image and register their displace- 

 ment either by the same ocular or collimator scale micrometer, or by the bodily 

 displacement of the mirror N', figure 117, along the micrometer- screw n. Both 

 methods give identical results, the former being coarse as compared with the 

 latter. I first used a collimator micrometer in preference. When put in place 



25 



f 



\o 



I 



+05,. 

 -05 



10 20 



40 50 60 



FIG. 114. 



of the slit of the collimator it may be adjusted laterally at pleasure and fixed 

 in any position. Different scales may be used. (Compare Chapter X, 85.) 



If x is the actual displacement of the mass m and 6 the corresponding angular 

 displacement of the needle of radius r (between centers of m and m'), x = rd. 

 If y is the observed displacement of the image of the collimator micrometer 

 in the telescope (since reflected rays are in question), 6 = y/zf, f being the 

 (large) focal length of the collimator, so that x = ry/2/. If f= 44.5 cm. and r = 

 12.6 cm., # = 0.142 y. 



Again, on the interferometer, if AN is the displacement of the mirror microm- 

 eter, b = 10 cm. the breadth of the ray parallelogram and 1 = 45 the angle of 

 incidence, A Accost = 60 so that 



x -r&N cos i/b = 12. 6XAA/"Xo. 707/10 = o.SpiAW 



Both methods give identical results. To test this, experiments in table 6 

 and figure 114 were made over a wide range, but without aiming at special 

 accuracy. The needle started from its position of equilibrium with the mass 

 M placed on the left 4.2 cm. from m at zero minutes. Observations were 

 thereafter taken at the end of each succeeding minute (t) for about an hour. 

 The displacement x was computed from y and %' from A*. In figure 114, x' 

 is laid off downward in centimeters. The two curves are manifestly identical 



