Although the timing of a freely falling body was the first method of measuring, the accuracy was poor because of the difficulty in measuring small time intervals.
The method has been revived as a result of instrumentation improvements and elaborate free-fall installations are now located at several national laboratories.
It is necessary to measure time to about 10-s and distance to < 1 um to obtain an accuracy of 1 mGal with a fall of 1 or 2 m.
Until recently, the standard method for measuring employed a modified form of the reversible Kater pendulum.
The value of g was obtained by timing a large number of oscillations.
Relative Measurement of Gravity
(a) Portable pendulum.
used for both The pendulum has been geodetic and prospecting purposes.
Since g varies inversely as the square of the period, we have T’g – constant Differentiating,
we get 4g – -28 AT/T28(T2- 7)/T(2.32)
Thus, if we can measure the periods at two stations to about 1 us, the gravity difference is accurate to 1 mGal.
This is not difficult with precise clocks such as quartz crystal, cesium, or rubidium.
The pendulum has been used extensively for geodetic work, both on land and at sea in sub-marines.
Portable pendulums used in oil exploration during the early 1930s had a sensitivity of about 0.25 mGal.
Pendulum apparatus was complex and bulky.
Two pendulums, swinging in opposite phase, were used to reduce sway of the mounting; they were enclosed in an evacuated, thermostatically controlled chamber to eliminate pressure and temperature effects.
To get the required accuracy, readings took about hr.
(b) Torsion balance.
A fairly complete account of the salient features of the torsion balance can be found in Nettleton (1976).
Figure 2.9 is a schematic of the torsion balance. Two equal masses m are separated both horizontally and vertically by rigid bars,
the assembly being supported by a torsion fiber with an attached mirror to measure rotation by the deflection of a light beam.
Two complete beam assemblies were used to reduce the effects of support sway. Readings were taken at three azimuth positions of the beam assemblies, normally 120° apart, to get sufficient data to calculate the required results.
Elaborate precautions were required to minimize extraneous effects such as temperature and air convection.
Each station had to be occupied for approximately one hour so that daily production was only 8 to 10 stations.
The deflection of the torsion balance beam is due to horizontal and vertical changes in the gravity field resulting from curvature of the equipotential surfaces.
Torsion-balance measurements permitted calculation of Uy, Ueじゃ and V,,l
The plotted values are usually the horizontal gradient [the vector (U,i + Val) and the differential curvature la vector with magnitude given by Equation and direction relative to (1/2) tan'(20,,AU,y the axis of usually in Eötvös – *D! Measurements were units (EU) equal 10-6 mGal/cm.
(c) Stable-type gravimeters.
The first gravimeters dating from the early 1930s were of the stable type but these have now been superceded by more sensitive unstable meters.
Nettleton (1976) describes a number of different gravimeters. All gravimeters are essentially extremely sensitive mechanical balances in which a mass is supported by a spring.
Small changes in gravity move the restoring force of the spring weight against the basic elements of a stable gravimeter. Whereas the displacement of the spring is small, Hooke’s law applies, that is, the change in force is proportional to the change in length; hence, AF – M8g=k&s or 8g – k8s/M