SECT. 1] GRAVITY AT SEA 137 



includes a system for measuring and correcting for the horizontal accelerations 

 and may be used without a stabilized platform. It could also be used on a stable 

 platform. The theory of operation of meters in these two cases has been dis- 

 cussed elsewhere (Harrison, 1960) and this reference should be consulted for 

 the derivation of the results quoted below. 



A meter used on land need be leveled with an accuracy of only 5' in order 

 to attain an accuracy of 1 mgal. However, a meter used at sea on a stabilized 

 platform is very sensitive to stabilization errors that have the same period as 

 the wave accelerations, because, in this case, a part of the horizontal accelera- 

 tion is added to the vertical component. The error introduced depends on the 

 phase angle between the tilt of the platform and the horizontal acceleration. 

 For the most unfavorable phase angle, an error of 1 mgal is caused by a tilting 

 of 4" amplitude when the amplitude of the horizontal accelerations is 100,000 

 mgal, and by a tilting of 44" when their amplitude is 10,000 mgal. Stable 

 platforms can be made to satisfy the necessary requirements. 



LaCoste has pointed out a further source of error in gravity measurements 

 made with a beam gravity meter on a stable platform, and that is the cross- 

 coupling effect. The beam is deflected by the vertical accelerations, and the 

 horizontal accelerations, acting on the deflected beam, produce a couple which 

 depends on the product of the horizontal and vertical accelerations and the 

 phase angle between the beam deflection and the horizontal accelerations. This 

 effect is at a maximum for circular motion when the movement of the meter 

 beam lags 7r/2 radians on the vertical acceleration, as in a heavily damped 

 system whose free period is not very different from the wave period. The error 

 introduced by this effect can easily exceed 500 mgal for horizontal and vertical 

 accelerations of 100,000 mgal amplitude. It can largely be eliminated if the 

 meter is slowly rotated about a vertical axis, which has the effect of altering 

 the phase relation between the horizontal and vertical accelerations, and it is, 

 in any case, only important where there is a persistent phase relationship 

 between the vertical and horizontal accelerations. 



A meter suspended in gimbals swings in response to the horizontal accelera- 

 tions. It tends to hang in the direction of the total resultant acceleration 

 formed by the vectorial addition of the horizontal acceleration with the sum of 

 the vertical acceleration and the acceleration due to gravity. This sum is always 

 greater than the vertical component alone, no matter what the direction of the 

 horizontal acceleration, so that a correction must be subtracted from the 

 measured acceleration to compensate for the effect of the horizontal accelera- 

 tions. This eff"ect was first jDointed out by Browne (1937) in connection with 

 the correction of measurements taken with the Vening Meinesz pendulum 

 apparatus for horizontal accelerations of the submarine. The theory has been 

 extended by LaCoste (see Harrison, 1960) for gravity meters on surface ships. 

 LaCoste treats the gravity-meter unit in gimbals as a compound pendulum 

 performing oscillations forced by the wave accelerations in addition to swinging 

 with its own free period. The problem is simplified greatly if the sensing element 

 of the meter is positioned a distance below the gimbal support equal to the 



