EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 35 



Hence the angle corresponding to a vanishing ring is, since A7V = 



8= 3 Xl0 " 8 = 13 X io- 8 radian = 0.028" 

 2X111 



Furthermore, if<p=i = o.oi75 radian 



F/M = 98iX.oi75Xi3Xio- 8 =2.3Xio- dyne 



per vanishing ring per gram-mass at the center of gravity of the pendulum. 

 The total pull of the center of gravity of the above pendulum is thus 



F= 2.3 Xio- 6 X 1 245 = 2.9X10-* dyne 



per vanishing ring, on one side. By lengthening the radius from h to R this 

 may be decreased to about 2Xio~ 3 or less. Hence in case of gravitational 

 attraction at one centimeter of distance it would require two equal masses m 

 (since 7 = 6. 7X10-8 roughly) of the value m = \/2oX io 4 /6. 7 = 1.8 Xio 2 grams, 

 or 1 80 grams per vanishing interference ring, at a distance of i cm. On the 

 other hand, the framework of the above pendulum is unnecessarily heavy, and 

 was constructed out of the material at hand. It could easily be reduced in 

 weight much below the above datum, or the greater part supported on a float, 

 so that the case may be stated many times more favorably. 



Resuming equation (3), if K is the moment of inertia, i the radius of gyra- 

 tion, and T the period and / the length of the horizontal pendulum, 



(6) 



V gh<p 



an equation from which <p may be found in terms of T, i, and h which must be 

 measured. 



Again, the indicated length H of pendulum (distance from the center of 

 gravity to the point of intersection of the axis and the plumb-line through 

 the center of gravity) is 



(7) H = h/sm<f> = h/<f>, nearly. 



The change of vertical inclination a of the axis of the pendulum correspond- 

 ing to the horizontal deviation 6 is, then, 



h.9 



(8) a =-H =e <f>> nearly, 



or if the period T be introduced from (6) and 6 from (5) 



47T 2 * 2 A7V 



(o) = ., 5- 



T*hg 2K 



It is in equation (8) that the condition of remarkable sensitiveness resides. 

 Thus, if the interferometer is used, a = <p&N/2R, and, if AA r = 3oXio- 9 and 

 <p= io~ 2 (somewhat less than i of arc), R = in cm., as above, 



a = 13 X i o- 10 radians = 00028" 

 per vanishing interference ring. 



