Chap. 7] 



GRAVITATIONAL METHODS 



103 



Tg (the period of oscillation of the frame in the gimbal suspension) and 

 j8 (the tilt angle) are recorded separately by a highly damped pendulum in 

 marine gravity apparatuses. Lastly, the customary reductions for ampli- 

 tude, chronometer rate, temperature, and air pressure are applied. 



B. Observation and Recording Methods; Pendulum Apparatus 



The high accuracy required in pendulum observations is attained by 

 using the "coincidence" or "beat" method. This method may be likened 

 to a vernier. Two nearly equal periods are compared by observing which 

 time "divisions" coincide. The gravity pendulum is compared with a 

 chronometer (or an astronomic clock or reference pendulum) of very nearly 

 the same (or double) period, and the number of chronometer seconds are 

 measured which elapse between two subsequent coincidences, that is, 



T^'TR-'Z 



T.'^'T, 



' Pentf. f'T^) 



Coincidence 

 Interval 



Fig. 7-11. Coincidence method. 



between two successive instants when pendulum and chronometer are "in 

 phase." The pendulum may lag behind (Fig. 7-1 la) or be ahead (Fig. 

 7-116) of the chronometer. In case a, the pendulum makes (n — 1) 

 oscillations for n oscillations of the chronometer; in case 6, (n 4- 1) oscil- 



lations. The pendulum period is Ty = 



n — 1 



• To in the first case and 



Tp = — ; — - • To in the second case. When the periods of the two time 



n + 1 ^ 



pieces are a small integer multiple of each other, that is, if the ratio Tp/To = 

 q, the coincidence method is applicable if 5 is slightly less or greater than 

 1, or slightly less or greater than 2, and so on. Letting To (the period of 

 the chronometer) ^qual one second, the following relations apply in the 

 general coincidence case: 



r„ = 



qn 

 n ±.q' 



(7-19a) 



