. The Earth beneath the sea : History . ->- Dial reading spring -diH Rest position l\^ognet Fig. 3. Diagram of the Graf Sea Gravimeter delineating quantities used in the equations. 0 = 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 + 2

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. The Earth beneath the sea : History . ->- Dial reading spring -diH Rest position l\^ognet Fig. 3. Diagram of the Graf Sea Gravimeter delineating quantities used in the equations. 0 = 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

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Keywords: ., bookcentury1900, bookcollectionbiodivers, booksubjectoceanbottom