GRAVITATIONAL METHODS 



251 



A deflection <^ of the bar produces a corresponding angle of reflection 

 (2(f>) of the light from the mirror. Prior to placing the two large masses 

 Ml and Mz in position, the undeflected position of the torsion balance was 

 Ho. After placing Mi and Mg in position, the deflection <^ of the bar corre- 

 sponds to a scale reading of Ui — Hq. The deflecting torque due to the 

 attraction (since two sets of masses are acting) will be approximately equal 

 to 2FI. The resisting torque of the wire for a deflection <}> is equal to — t</), 



TELESCOPE 





y 



PLAN VIEW 



POSITION 2 



Fig. 183. — Sketch of general equipment used by Cavendish for 

 determining the gravitational constant G. 



the minus sign denoting that the direction of the torque is opposite to the 

 deflection </>. At equilibrium, —T(f> = 2FI. Attracting force 



F = -G 



Mm 



Hence, 



2Fl = -G 



2Mml 



T <p 



(3) 



The scale reading for the undeflected position of the beam is tio, for a deflection ^ in 

 position 1, ni, and for a deflection ^ in position 2, ni. Let iii — no = i^s/2. 



Then tan 2 <j) = — — — = — — , and for small angles 2(j> = — — - 



For the total deflection or 2(j> \ 



T A.y _ G 4 M ml 

 2D ~ r" 



