38 EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 



A few other equations of minor importance may be added. If the indicated 

 length is H and the horizontal pendulum be treated as a vertical pendulum 

 of length L, the point of suspension being the intersection of the plumb-line 

 through the center of gravity and the line determined by the points of the 

 two pivots, the observed period is 



(20) T = 2irVL/g and P = LH 



where / is the corresponding radius of gyration. 



If the end of the horizontal pendulum is loaded with the weight m of a 

 disk at a mean distance R from the axis for the measurement of gravitational 

 attraction, since (M+w) h' = Mh-}-mR, the new force at R is 



When the end of the pendulum is similarly loaded for the determination of 



its radius of gyration, since 



(22) i'* = 



the new period is 



Since T' and T are observed and m, M, R, h given, i may be computed. 

 The horizontal pendulum itself thus supplies the value of i. 



If the lower pivot is provided with a strong micrometer screw, by which it 

 may be moved over a small distance z to the front or rear of the plane of the 

 pendulum, the computed value of a may be tested independently. Thus let 

 y be the distance apart of the pivots and z the displacement of the lower, then 



(24) a = z/y = <f>0= : <f>x/4D 



when in the method of deflection x is the increase of the distance apart of the 

 two images of the slit, at a distance D from the further mirror. Hence 



where <p must agree with its corresponding datum from the pendulum meas- 

 urement in terms of period. Thus, since v and h may be obtained inde- 

 pendently, the torque T, etc., is given independently. This method will also 

 be applied below. 



21. Observations with a grating rotating on a fixed vertical axis. When 

 the opaque mirrors M and N are identically concave and are put on the ordi- 

 nary interferometer at a distance equal to their radius of curvature from the 

 stationary grating, the latter may be rotated (without translation) as far as 

 the breadth of the opaque mirror N permits, without readjustment. The 

 ellipses are not lost. Inasmuch, however, as different thicknesses of glass are 

 introduced into the rays when the grating is rotated, the ellipses travel hori- 

 zontally through the spectrum from the red to the violet end or the reverse. 



