EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 37 

 Furthermore, 



fie} Tf I I I 



v*5^ i = 2in\ ~ -, -IT mr 



\ gh<p i V/M 

 whence, since 6 = &N/2R 



, M 4ir 3 i 2 ^ M 



all of which quantities are easily determined with accuracy. To find the 

 radius of gyration i, for instance, a body of known moment of inertia may be 

 suspended at the end of the horizontal pendulum and the periods T of the 

 pendulum before and after suspension determined, with or without the float. 

 Finally the change of vertical inclination a becomes 



(17) a = =e<f> (nearly) = -~> r 



If the pendulum is damped, which will usually be the case, it may be neces- 

 sary to observe the logarithmic decrement, in order to compute the free period 

 in the usual way. 



If the buoyant force due to the float does not pass through the center of 

 gravity of the solid parts of the pendulum, but at a distance h' from the ver- 

 tical or pivotal axis, the new distance of the center of gravity h" when the 

 pendulum is partially floating will be 



. Mh-Vh' 



M-V 



Hence, if h' = h, then h" = h, resulting in the equations just deduced. But if 

 h' = o, i.e., if the buoyant force passes through the point of the lower pivot, 



,_ _M, 



= W^v h 



Thus the equations deduced become identical with the original equations (2) 

 et seq. The float therefore adds nothing to the sensitiveness except in so far 

 as it removes friction at the pivots and supplies a reliable damper for the pen- 

 dulum. It is in this form that the float will be applied below. Since the 

 torque equation is now again 



where all references are to solid parts of the pendulum, h may be accurately 

 found by placing weight m at a distance / from the plane of the pendulum, or 

 better, by placing weights alternately before and behind this plane, at a dis- 

 tance / apart. The torque applied is then T = mgl, whence 



(I9) h= We 



This method will be used effectively in several experiments below. It is an 

 excellent test on the reliability of the damper, since h can also be determined 

 directly by the suspension of the solid beam of the pendulum. In the adjust- 

 ment adopted, at a scale distance of 900 cm., m/ = gramXcm. on the scale- 

 pan, produced a deflection of about i mm. 



