Chap. 7] 



GRAVITATIONAL METHODS 



131 



trifilar gravimeters which are capable of the greatest sensitivity yet at- 

 tained in such instruments. The trifilar gravimeter consists of a disk 

 supported by a hehcal spring at its center and by three equally spaced 

 wires at its circumference. It was first described by A. Schmidt.^^ Fig. 

 7-31 is a schematic showing only one of the suspension wires, fastened at 

 the ceiling at C and attached to the disk at A. The vertical distance of C 

 above the disk is CB = d, and its horizontal distance from the center is 

 OB = o. The radius of the disk is OA = r and the horizontal distance 

 AB = e. When a disk deflection, <p, has been brought about by a torsion- 

 head rotation, a, the suspension wire is deflected by the angle, /8, from the 

 vertical. The total weight, W, is so dis- 

 tributed that the coil spring bears a weight 

 W — w and the suspension wires each 

 w/2 or w/3, depending upon whether two 

 or three wires are used. If w/2 is re- 

 solved into its components, Q and H (see 

 Fig. 7-31), it is seen that Q is ineffective 

 and H = w/2 tan /3 = we/2d. Its tan- 

 gential component, H cos ^, produces the 

 couple 2Hr cos \p. In the triangle OAB, 

 e-sin (90 -f ^) = a sin (p. With cos ^ = 

 a sin (p/e, the couple D2 = wra sin <p/d. 

 It is opposed by the moment of torsion 

 of the main coil, Di = T{a — (p). Thus 

 in the equilibrium position. 



ria — (p) 



vfra 



sin <p = 0. (7-33a) 



,19 cm. 



Small changes in the weight of the disk c-x^i^^..*-^ 



and hence in gravity will produce large Fig.7-30. Isingbifilar gravimeter. 

 deflections, since 



ar . 

 sm (p 



. (7-336) 



d<p 

 dw 



war 

 ~d 



cos (p •{■ T 



It is seen that maximum sensitivity occurs when the denominator is 

 zero or when cos ^ = — rd/war. As t is small, the position of maximum 

 sensitivity is very close to 90° from the position of zero deflection. With 

 a trifilar gravimeter, Tomaschek and Schaffemicht*'^ have recorded the 



" Beitr. Geophys., 4, 109-116 (1900). 

 " Zeit. Geophys., 9(8), 126-136 (1933). 



