122 



Jr 



GRAVITATIONAL METHODS 

 (ATi), = FrTl + (^);Cos (^2 - ^x)?\ 

 {ATdt = FrN + (^Vcos (v?2 - <pi)t] 

 (Ani)t = fJ 1 + (— j -cos (v?2 - s^i)t 



[Chap. 7 



} (7-286) 



(Ans)* = F„ 



1 + 



\0i2/t 



COS ((p2 — v^l) 



.] 



in which Fy and F„, respectively, are approximate values of the flexure 

 corrections obtained from equation (7-28a). The values of these cor- 

 rections for the entire observation period are found by integration between 

 the limits h and ti, reckoned from the time ^ when the phase difference is 

 exactly 180° and the amplitude ratio is (a:2/«i)o and (Q;i/a2)o: 



A3', = -f|i - (^)^ + ^[(^^cos (.p, - ^O)^ - (^cos (f, - ,,0)J 



+ %iT, 





(T2 - T,) + F 1 



-3(~ 



"o: 



r.2 



i^ — 

 1% — 



6(^2 



-m 



(7-28c) 



7^2 has the same equivalent as eq. (7-28c) with a^lai instead of aijax. 

 The correction for the coincidence interval, with n^ = (ni + ^2)2, is 



An 



1 = F„ < 1 + - ( — cos (9?2 - ¥>!) j + ( ^ cos (^2 - ip\)\ 



+ I, it. - Min., - n. J [(n., - n.J (^)^ + F„ (s (^;); - l)] 



(7-28d) 



The n2 has the same equivalent as eq. (7-28c?) with 0:1/0:2 instead of 

 02/0:1 and (n^a — Wmi) instead of (n„, — Um.^. 



The elimination of flexure by the simultaneous oscillation of two pen- 

 dulums is so perfect that, although the flexure itself may be 20-50 X 10~ 

 seconds, the corrections seldom exceed — 1 X 10~' seconds, provided the 

 phase differences do not deviate more than 30° from 180°. 



6. Exainples of pendulum observations have been published by various 

 authors for different instruments and procedures. A complete set of 

 U.S. Coast and Geodetic Survey observations has been reproduced by 



