130 GRAVITATIONAL METHODS [Chap. 7 



The N0rgaard gravimeter** has two inverted quartz pendulums leaning 

 toward one another, with an index rod between them. The distance 

 between the ends of the quartz rods is read with a microscope and is a 

 measure of gravity. The entire system is immersed in water of constant 

 temperature and is thus highly damped and insensitive to vibration. 

 The mean error is about 0.3 milligal. 



6. Vertical seismo-gravimeters fall into two groups: (1) instruments in 

 which gravity changes produce rotations about a vertical axis (bifilar or 

 trifilar suspensions) ; (2) gravimeters in which this rotation takes place in a 

 vertical plane and about a horizontal axis. In the hifilar gravimeters, 

 the restoring force is due to the torsion of the suspension wires (equivalent 

 torsional coefficient t) as well as to gravity, since the suspended mass is 

 raised upon rotation. If 2a is the distance of the suspension points above, 

 26 the distance below, and d their vertical distance, the effect of gravity is 

 given by the expression mg-ab/d and, therefore, the resulting restoring 

 force is 



AT = ^ + 2r, (7-32a) 



where d' is the vertical distance corrected for a reduction in length which 

 occurs because of the bending of the wires. With a moment of inertia 

 K, the period of oscillation of a mass on bifilar suspension is 



T = 2t yK / (^2r + ^y .mflf^ , (7-326) 



which, however, is much too short to give sufficient sensitivity to gravity 

 variations. A bifilar system can be readily astatized by changing the 

 sign of the second term in the denominator of eq. (7-326), that is, by 

 making gravity the labilizing force (reversing the suspension 180* as shown 

 in Fig. 7-30). Then 



T = 2^ ^k/(2t -prng\ (7-32c) 



With high astatizing factors this procedure increases the sensitivity to 

 gravity variations about 1000-fold, which is an improvement of similar 

 order as in the Lejay-Holweck pendulum, where gravity likewise acts as a 

 labilizing force. Bifilar gravimeters have been constructed by Berroth, 

 Ising,^ (Fig. 7-30), and Hart Brown. 



Bifilar instruments with crossed wires appear to be inferior to the 



*« G. N0rgaard, Dansk Geodaetisk Inst. Medd., No. 10 (Kpbenhavn, 1938). 

 *o Zeit. Geophys., 8(8), 366 (1932). 

 " Loc. cit. 



