Interferometer to the Horizontal Pendulum. 509 



F R ' = 2 X 10" /31 = 6 X 10" dynes, roughly. 



This would be equivalent to the attraction of two 30 gram 

 weights at 1 centimeter of distance. 

 Furthermore, 



T = 2*i \/-\- \=r nr = (15) 



y gficf> 1 — V/M 



whence, since 6 = AJV/2R 



F*=% -^ ^ ( 16 ) 



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 hori- 

 zontal pendulum and the periods T of the pendulum before and 

 after the suspension determined, with or without the float. 



Finally the change of vertical inclination a becomes, <£ being 

 given by (15), 



hd 

 a = -J. — 8(fi (nearly) (17) 



If the pendulum is damped, which will usually be the case, 

 it may be necessary to observe the logarithmic decrement, in 

 order to compute the free period in the usual way. 



If the end of the horizontal pendulum is loaded with the 

 weight m of a disc at a mean distance R from the axis for the 

 measurement of gravitational attraction, since 



(M + m) fi = Mh + mH 



the new force at R is 



F B ' = F B ll + 



Mh) 



When the end of the pendulum is similarly loaded for the 

 determination of its radius of gyration, since 



i n = i* + mR'/M 

 the new period is 



/ m E 2 



T' = T ! M IF 



y m a 



1 + M X 



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. 



