Chap. 7] 



GRAVITATIONAL METHODS 



205 



Table 26 



CALCULATION OF FOUR-POSITION TORSION-BALANCE RECORD 



(FROM LARGE DEFLECTIONS) 



U^, = Ai' + Ao 7.3m = -22.5 or = 



Uy, = A2 + As = +2. 2m = +6.8 or = 



-(As + Ai) = -7.2m = -22.2 

 -(Ai + Ai) = +2. 3m = +7.1 



t/„ = -(Ai" + AO = -7.7m' 23.5 or 



C/yz (A? + As") = +2. 4m' = +7.3 or 



= A," + At = -7.5m' = -22.9 

 = AC + At = +2. 6m' = +7.9 



II 



For five positions, calculations from deflections A with respect to the 

 torsionless position, and from the readings n are possible. Both calcula- 

 tions are given in Tables 27 to 30. The following formulas were used for 

 the calculations from deflections: 



Balance I: 



Balance II: 



U„ = -1.03 (aI - A3) - 1.66 (A5 - A2) 



Uy, = +3.16 (aI + A3) + 1.21 (A2 + Ae) 



C/a = +4.73 (A4 - A3) - 2.93 (Ag - A2) 



2U^ = -3.44 (a; + aS - 9.02 (A^ + A^) 



t/« = +1.01 (A^ - a;') + 1.64 (a;' - a;') 



Uy. = -3.12 (A'/ + a'/) - 1.19 (A^' + a;') 



C/a = +4.69 (a'/ - A^') - 2.90 (a;' - A^') 



2U^ = -3.40 (a'/ + a'/) - 8.93 (Aj' + A^') 



