Chap. 7] 



GRAVITATIONAL METHODS 



196 



The ratio Kjr follows di- 

 rectly from the (undamped) 

 period T = 2-^ s/kJt, which 

 may be determined to a high 

 degree of accuracy (1/100 of a 

 second) bj'^ using a coincidence 

 method. Since in most base- 

 ment laboratories the gravity 

 field is disturbed by adjacent 

 walls and excavations, it is 

 necessary to make period ob- 

 servations in two directions at 

 right angles to each other 

 (ai, and 0:2 = «i + 90") to 

 eliminate such efifects. Then 

 the equations for two periods 

 are 



Prism of the 

 suspended — 

 beam s(/sfem 



suspended +-€T3 



>m lJ±L 



■^^ /5.0 cm. 



Bi -filar 

 suspension 



American Aakania Corp. 



Fig. 7-68. Balance beam of tilt-beam balance. 



(1) 



(2) 



n 



47r^K 

 Tl 



= T - {Kij\ cos 2ai - 2KUxy sin 2ai) 



{-KUi, cos 2a2 + 2KU^y sin 2a2). 



(7--59a) 



\ Addition of the two equations gives 



K 



T\Tl 



2t\TI + Tl) 



(7-596) 



By observing the deflection of the beam due to a known mass at a 

 known distance, t can be determined independently from the equation 



T<p = 



mMk 



CI, 



(7-59c) 



where <p is the deflection angle; C is a constant (C = 



1/1 + fc' 



with 



Im = length of cylindrical mass m)] p = the distance between center of 

 gravity of m and M ; and k = gravitational constant. Since p is difficult 

 to measure^ the mass M is used on a swivel and rotated from one side of 

 the weight to the other. For equal deflections on both sides, the radius 

 of the swivel arm is equal to p and 



mMkl 



/^- 



2f 



n — no 



H-bM) 



