Chap. 7] GRAVITATIONAL METHODS 119 



where pb is the manometer or barometer reading in millimeters, pv the 

 saturation pressure of water vapor, h the relative humidity in per cent. 

 Then the period as reduced for air pressure is 



Tred.air = T - C p(5 - 5„), (7-256) 



where 8o is the mean density of the air (constant) and Cp is the pressure 

 coefficient to be determined by experiment.^^ The coincidence interval 

 reduced for air pressure is 



Wred.air = n + Cp(8 — 80), (7-25c) 



where the relation of Cj, and Cp is given by 



Cp = (2nred. - l)^Cp, or c'p = ^^^ — --Cp. (7-25d) 



(^i red.)'' 



5. The flexure correction is due to the fact that the vibrating pendulum 

 produces oscillations of the receiver case, of the pillar, and of the surface 

 soil. Rather complex coupled vibration phenomena arise and the period 

 of the pendulum itself changes. Numerous methods have been suggested 

 to correct for this influence or to eliminate it. Since the correction is of the 

 order of 10 to 40-10"^ on solid rock or cement and may increase to as much 

 as 500-10" sec. on marshj'' ground (Berroth), it must be determined 

 accurately. 



The displacement of the point of suspension of the pendulum is 



y = ^, (7-26a) 



where Y is the horizontal tension produced by the pendulum and t the 

 elasticity of the support. The tension, Y, may be assumed to be equal 

 to the restoring force. Hence, from equation (7-16a), Y = Mgs sin 6/1 

 and ty = Mgs sin 6/1. Then the differential equation of motion, 



is identical with the equation given for the Vening Meinesz pendulum 

 (7-18a) and the "disturbed" pendulum length and the change in period 

 are given by 



Mgs 



2tP' 



" Ibid. 



(7-266) 



