140 WORZEL AND HARRISON [CHAP. 9 



as changes of the axial position of the trace on the record. When the trace 

 approaches the margin of the record, as gravity changes, a change of the dial 

 reading will return the axis of the trace to an appropriate place on the record. 



->- Dial reading spring 

 -diH Rest position 



l\^ognet 



Fig. 3. Diagram of the Graf Sea Gravimeter delineating quantities used in the equations. 

 = angular deflection of main springs when beam is horizontal, if = main spring 

 constant (torque/unit angle), »S = damping coefficient, p{h — hQ) = force produced by 

 reading spring, A cos cot = horizontal acceleration of waves, and A sin cot = vertical 

 acceleration of waves. 



From Fig. 3, one may see that the differential equation of motion of the beam, 

 where 6 is small (less than 1° in this instrument), is 



d + 2nd+pW = X, (1) 



where 



2/x = SdjI, 

 „ K mAl sin cot sin a niAl cos cot cos a mql sin a 



^ K p{h —ho)i mAl sin cot cos a mAl cos cot sin a mgl cos a 

 X^j (d-a) + + 



The solution of (1) is 



d = — + e-'^HBe'i + De-'t), (2) 



p^ 



where c = {(x^ —p^)^^. 



In this meter fi >p so that the solution is that of a forced oscillation super- 

 imi)osed on an exponential ajjproach to {X/p^). 



Since a is very small ( < 11"), 



X _ K{d —a) —p{h —ho)i + mAl sin cot —mql 

 p^ K —mAl cos cot 



