196 GRAVITATIONAL METHODS [Chap. 7 



The more common practice is now to determine both K and r before the 

 instrument is assembled. K is obtained by oscillating the beam on a 

 calibrated wire with known t. For this purpose an oscillation box is 

 made, usually of wood, provided with extensions for the lower (and upper) 

 parts of the beam and of sufficient capacity to keep air damping down. 

 Observations are corrected for (wire) temperatures and amplitude of 

 oscillations. Where large gravity anomalies exist, observations are made 

 in two positions of the box. Wires are very thoroughly tested. The 

 following characteristics are of practical importance: (1) torsional coeffi- 

 cient, (2) carrying capacity, (3) temperature coefficient, and (4) elastic 

 hysteresis. The carrying capacity of a wire varies with the square of the 

 diameter, while the torsional coefficient varies as the fourth power of the 

 radius and inversely as the length: 



4 



|47rr 

 r = 



^, (7-60a) 



where r = radius, Z = length, and y = modulus of rigidity. For other 

 wire sections (ribbons, and the like) the torsional coefficient is given by 

 the relation 



r = ^, (7-606) 



where S = section, C a constant, and Jp the polar moment of inertia. 



For a rectangular section, Jp = {ah^ + ha)/ 12, where a and 6 are the 

 sides of the rectangle. For ratios of a/h = 1, 2, 3, 4, and so on, the con- 

 stant C takes the values 234 X 10"" (for a/b = 1), 238, 249, and 

 260 X 10~*. For thin ribbons in which the one dimension is less than 

 one-third the other, the torsional coefficient is closely enough 



- ^ a6= 



" = 3Z 



(l - 0.63. -Y (7-60c) 



in which the last term may be generally neglected. Ribbons have the 

 advantage that for a given carrying capacity the torsional coefficient is 

 less, but they are more difficult to obtain. In practice torsional coeffi- 

 cients of torsion balance wires are determined from oscillation observations 

 with calibrated weights. For this purpose a specially built instrument is 

 used, consisting essentially of an upright tube with torsion head above and 

 observation window below, and provided with a heating coil and ther- 

 mometer. 



After a wire has been cut to length, provided with its clamps, and heat- 

 treated, it is placed in the instrument with a mass of calibrated moment of 



