EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 51 



In the first place, therefore, 



m/M 

 mR 



so that the lightest available pendulum and the heaviest admissible disk is 

 to be selected, although the increase of sensitiveness is not quite proportional 

 to m/M, but diminishes as (i+mR/Mh)- 2 . This procedure, even when the 

 float is used, is relatively inefficient and the value of AN can probably not be 

 increased more than twice the above value (a difference of AAf= 2X0.00 12 

 for the two extreme positions of the disk) by this means. 



28. Equations for the vertical pendulum. A final word may be added with 

 regard to the inclination a. This can be 

 detected with such precision that a method 

 based upon it deserves consideration. 

 The apparatus in this case would take 

 the form of fig. 30, where ABCD is the iron 

 framework of the heavy, long, vertical 

 pendulum, with the massive bob at D and 

 knife-edges and tablets at e, so that the 

 pendulum is capable of swinging normally 

 to the plane of the diagram. The hori- 

 zontal pendulum is attached by two pivots, 

 a and b, to the central rod CD of the ver- 

 tical pendulum. It is to swing clear of it FlG< 3 - 



and to be in equilibrium in a parallel plane. The deflection of the horizontal 

 pendulum is also normal to the plane of the diagram, and it measures the 

 change of a of CD, as above, G being the grating, h the center of gravity. 



When gravitational attraction is to be observed, the bob D is one of the 

 attracting bodies and of mass m f , whereas the attracting mass m, with its 

 center on the same level, is placed in front of or behind the plane of the diagram. 



If the mass m' at the end of the vertical pendulum is at the distance L from 

 the horizontal axis, and the mass M' of the remainder of the pendulum 

 virtually at a distance H (center of gravity) from the axis, 



where d is the mean distance apart of m and m'. Hence 



(6) AW = ym 2 R/<pd 2 g(i +M'H/m'L) 



If m' is massive, so that M'H/m'L = i may be assumed ; if the bodies m and 



m' are equal spheres of radius r all but in contact, 



d= 2r and AN' = yirpRd/6(pg 



Thus if d=io cm., p=io, with the other magnitudes as in the above inter- 

 ferometer, AN' =10-^X7 -5 cm-, which increases but as the first power of the 

 diameter of the spheres. Hence, in spite of the precision of a measurement, 

 the method would not be available for the determination of 7. 



