82 DISPLACEMENT INTERFEROMETRY BY 



determine the attractions in terms of the mere acceleration of balls resulting. 

 With an ocular micrometer this would not be difficult, as the fringes move 

 slowly enough so that the position can be sharply specified; but with a needle 

 of long period in vacuum, the screw micrometer would also be available. If 

 there is no damping we may write 



yMm/R 2 ax = zma 



where a is the acceleration, x the displacement of m, and a the torsion coeffi- 

 cient, referred to the displacement of m, t the time, supposing the needle 

 starts from rest, and the gravitational force is applied at t = o. If at the out- 

 set we may put x vt/2 = at z /2 



an equation whose interesting feature is that if t is kept very small (which 

 should be possible with an ocular micrometer and the achromatic fringes, 

 a fine quartz fiber presupposed), the term involving t may be neglected 

 and the experiment interpreted as a case of uniformly varied motion, in 

 which 



For instance, if R = 5 cm., M =io 3 grams, and 7 = 6.7 Xio~ 8 , and if* = 

 sec. is admissible, a=i.3Xio~ 7 cm./sec. 2 and the distance traversed in 100 

 sec. would be 0.0065 cm - we U measurable on the interferometer, quite so if 

 the work is done reciprocally and the interference fringes are used individually. 

 The theoretical error will be a minimum if m is as large as the fiber can 

 safely carry and t as small as possible. On the other hand, x is independent of 

 m, and if t is to be kept small, the result may be compensated in a large M/R 2 . 

 The measurement is thus to consist in keeping the fringes at zero by moving 

 the micrometer screw for the small interval t during which the weight M 

 acts. The constant would then follow from the micrometer reading M and 

 R only, all other quantities entering secondarily as corrections. The ex- 

 periment seems well worth while. 



