50 EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 



The method of attachment of the disk d to the horizontal pendulum is 

 shown on a smaller scale in fig. 29. Here G is the grating, secured by three 

 adjustment screws to the table T, the cylindrical shaft of which is grasped 

 on a clamp (open form) of the horizontal pendulum P. To the bottom of 

 the shaft in question, a cross-piece hgh is screwed and fastened with a lock-nut. 

 The two fibers//" which support the disk d are wound above around the pulley 

 screws hh and thus adequate vertical adjustment of disk d is available. 



The slide micrometer is attached to the pier by a firm horizontal rail capable 

 of adjustment forward and rearward. A strong clamp attaches the base of 

 the slide micrometer to this rail, so that the whole instrument may also be 

 adjusted to the right or left, roughly. The fine adjustment is completed on 

 the slide micrometer itself. 



Finally a case is provided covering the disks D and d and part of the micro- 

 meter, so that only the drumhead and scale projects. The apparatus was found 

 to work satisfactorily. It is quite possible to reject the water damper at the 

 end of the horizontal pendulum, above, and to rely solely on the effective air 

 damping produced, when the disk d is very close to D or D'. In fact, the tin 

 cover, in this case, was all but superfluous. D could be shifted from end to 

 end of the course, without materially interfering with the visibility of the 

 ellipses in the spectrum of the interferometer. The real interferences unfavor- 

 able to the gravitational measurement were incidental, due either to the change 

 in inclination of the pier, or to changes in the magnetic field (inasmuch as the 

 pendulum was preliminarily constructed of steel tubing), or to the causes 

 discussed in this chapter; for what was found was not an attraction at all, 

 but a repulsion, much larger in absolute value than the attraction anticipated. 



27. Equations. The chief equations to be used in the present work have 

 already been given above. It is merely necessary to add those which bear 

 upon the sensitiveness of the method. Since the disk of mass m is added, at 

 the mean distance R, to the mass of the pendulum M, the force at R from the 

 axis is now 



The gravitational attraction /' of the disks necessarily involves spherical 

 harmonics, but may be written temporarily as 



where m' is the mass of the stationary disk at a mean distance d from m. 

 Equating these forces and inserting the value of F R , the equation for AN, the 

 displacement at the micrometer, becomes 



t m 



^ 

 (3) 



