128 GRAVITATIONAL METHODS [Chap. 7 



"period" or "pull-back" spring through the axis of rotation (Truman, 

 Mott-Smith), In vertical and horizontal seismo-gravimeters, the restoring 

 and labilizing forces act in the vertical plane with rotation about a hori- 

 zontal axis. It is also possible to produce a labilizing gravity moment 

 with action in a horizontal plane and rotation about a vertical axis (bifilar 

 suspension). The tendency of such a system to come to rest in the lowest 

 position of the mass, produces a horizontal torque. Bifilar systems may 

 be astatized by "twisting" the bifilar suspension 180° (Fig. 7-30), or by 

 addition of a helical spring ("trifilar" gravimeter, Fig. 7-31). 



By astatization the sensitivity to gravity variations is greatly increased. 

 If t; is the (positive) restoring force and k the (negative) labilizing force, 

 then the resulting restoring force, A^, is 



N = 7} - K. (7-30a) 



If the system is to be stable, tj must be greater than k. The degree of 

 astatization, A, may be defined*^ as the ratio of the labilizing force, k, and 

 the resultant force, N: 



A = k/N. (7-306) 



The degree of astatization. A, increases, therefore, with the labilizing force 

 and the difference between the restoring and the labilizing forces. Small 

 differences in either may be observed with great accuracy. In some 

 astatic systems differences in stabilizing force are the object of observation; 

 in others it is differences in the labilizing force (inverted gravity pen- 

 dulums). If the labilizing forces are held constant arid changes in the 

 stabilizing forces are observed, the resultant restoring force and the 

 degree of astatization change in accordance with 



f = (4 + 1)1' 



N r] 



A 7} 



(7-30c) 



On the other hand, if changes in the labilizing forces are observed, the cor- 

 responding relations are 



dN _ _ dK 

 N ~ ^'^ 



^ = (A 4- 1) ^^ 



A K 



(7-30d) 



" G. Ising, A.I.M.E. Tech. Publ., 828 (August, 1937). 



