104 GRAVITATIONAL METHODS [Chap. 7 



By substituting Xlq s v: 



where n is the coincidence interval. In these formulas the - sign 



lower 



applies if q — and v — - (or ^ any other integer). Tliey may also be 



written 



and, by substituthig the reciprocal of g, 



V v(vn ±1) 



Hence, for a half-second pendulum, compared with a full-second chronom- 

 eter, V = 2 and therefore 



'^ 2n± 1 

 and 



If the pendulum swings slower than the chronometer, 



dT = !— .dw, and dg=^.dT. (7-19/) 



Vn— 1 V rp V ^/ 



If the pendulum is so made" that 



^i = ^ (Vs^n + 1), (7-19^) 



dg = dn and o?ie inillisecond change in coincidence interval corresponds to 

 07ie milligal change in gravity. 



Coincidence intervals may be observed visually (stroboscopic method) 

 or be recorded photographically. In the fiist method the gravity pendu- 

 lum is observed only during a short interval when the Reference pendulum 

 or chronometer passes through its zero position. Therefore, the image of 

 the gravity pendulum appears in the telescope every second with a dif- 



" H. Schmehl, Zeit. Geophys., 5(1), 1-15 (1929). 



