102 GRAVITATIONAL METHODS [Chap. 7 



tion from the isochronous condition may be expressed by an equation of 

 the form T = Ti + AT, with 



/.2r 



AT = "^V^^ / ^.cos (^2 - <p), (7-18c) 



Zco2 Jo a 



where az and a are the ampHtudes of the second and of the fictitious 

 pendulum, and v'2 and (p, respectively, their phases. Since, in practice, 



/rp rp \2 



the difference T2 — Ti is usually small compared with T, — — may 



be neglected. Letting C02/W1 = 1, C02 — wi = — tt (T'2 — Ti)IT , and con- 

 sidering a2, oc, and cos {<p2 — (p) as constant, we have from eq. (7-18c) 



AT = -{T2- Ti) -.cos (v52 - <p). {7-18d) 



a 



The Vening Meinesz pendulum apparatus is designed to record the move- 

 ments of the fictitious pendulum by reflecting a light beam from one pen- 

 dulum to the other. In addition, one pendulum is photographed sepa- 

 rately to obtain T2 for the above correction. 



Vertical deceleration of a pendulum is equivalent to a change in the 

 value of gravity and produces little change in period, provided the ampli- 

 tude is kept reasonably constant during the observation. Relative move- 

 ments of knife edge or slippage on bearings are neghgible, provided the 

 amplitude remains sufficiently constant. Rotation about a vertical axis 

 does not affect the period. Rotation about a horizontal axis (inclination 

 of the plane of oscillation) changes the gravity from g to g cos /3 if jS is the 

 angle of inclination. The resulting change in period is 



AT = ^ (^eonst. + ^«<,), (7-18e) 



where /Scons t. is the constant tilt and ag is the amplitude of oscillation of 

 the gimbal frame about this position. Acceleration imparted to the 

 pendulum in the plane of oscillation by rotation about both horizontal and 

 vertical axes produces a change in period, 



AT=-^,al, (7-18/) 



so that by combination with eq. (7-1 8e) 



AT = ITiip^net. + Cal), 

 where 



-K'-'f 



(7-18^) 



