198 



GRAVITATIONAL METHODS 



{Chap. 7 



W 20 JO 40 50 Pap 

 Fio. 7-69. Change of rest position 

 of torsion wires with treatment (after 

 Shaw and Lancaster-Jones). 



new coefficients are: 



t/« = 



since beam deflections ard^produced by 

 convection currents in the narrow in- 

 terior compartment. It has been 

 found that this effect can be nearly 

 eliminated by deternuning an optimum 

 transverse position of the beam in the 

 interior compartment. 



When a wire breaks in the field and 

 a new wire is inserted, the coefficients 

 o, p, q, and r, as well as s and t, are 

 changed (see formula [7-52/]). If t( 

 is the torsion coefficient of a broken 

 wire in balance I, t'I the t.c. of a 

 broken wire in balance II, t2 the t.c. 

 of a new wire in balance I, and t2 the 

 t.c. of a new wire in balance II, the 



t/„. = 



t/A = 



' r ' " 1 "^ 



■''2 / i ' . /\ T1T2 / . // i"\\ 



-, (A2 - As) - S --f-j, (A2 - A3 ) 



Ti L T2T1 J 



p iTcA^ + A^) 



Tl L 



s44!(a;' + a;')1 



-q'iir(A^-A^) + t44!(A;' 



Tl L T2T1 



w. 



— r 



1 L T2T1 J 



(7-61) 



and similarly for other beam positions. The replacement of a torsion 

 wire must be done with great care to avoid kinking or overstraining the 

 wire. Directions given by the manufacturers should be closely followed.*^ 

 3. The sensitivity of a torsion balance is a function of its geometric dimen- 

 sions, of the torsional coefficient of the suspension wire, and of the optical 

 magnification. According to eq. (7-51 a), the angular deflection increases 

 in the proportion K/t for curvatures and in the proportion mhl/r for 

 gradients. The optical magnification is given by 2f/i' for single and 

 4f/v for double reflection, where f is focal length and v scale interval. 

 Since the latter is generally so chosen that 1/10 division may still be 



*' C. A. Heiland, Directions for the Askania Torsion Balance, American Askania 

 Corporation (Houston and Chicago, 1933). H. Imhof and A. Graf, loc. cit. A. 

 Schleusener, Zeit. Geophys., 9(6/8), 30L 



'• For a description of steps necessary to readjust the beam after insertion of a 

 new wire, see Directions for the Askania Torsion Balance, op. dt. 



