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potential T = W- U, which is determined from the solution of the
boundary problems of mathematical physics. At the earth’s surface, T
satisfies the boundary condition

where H is the height over the ellipsoid, γ is the force of gravity in the
field U, H is the normal height derived from the condition that the
Q
increase ∫gdh of the potential W from the start of the gravity head
count be measured in the field U, and dh is the incremental excess of
the geometric level determination. Several methods involving the

solution of the corresponding integral equations were developed for
thederivation of T.
Gravity is usually measured in units of acceleration. In the SI

system of units, the standard unit of acceleration is 1 metre per second
2
squared (abbreviated as m/s ). Other units include the gal (sometimes
known as a galileo, in either case with symbol Gal), which equals 1
2
centimetre per second squared, and the g (g ), equal to 9.80665 m/s .
n
The value of the g approximately equals the acceleration due to
n
gravity at the Earth's surface (although the actual acceleration g varies
fractionally from place to place).

An instrument used to measure gravity is known as a gravimeter,
or gravitometer (Figure 13.1.).
Besides precision, stability is also an important property of a

gravimeter, as it allows the monitoring of gravity changes. These
changes can be the result of mass displacements inside the Earth, or of
vertical movements of the Earth's crust on which measurements are
being made: remember that gravity decreases 0.3 mGal for every

metre of height. The study of gravity changes belongs to
geodynamics.
The majority of modern gravimeters use specially-designed metal

or quartz zero-length springs to support the test mass. Zero-length
springs do not follow Hooke's Law, instead they have a force
proportional to their length. The special property of these springs is

that the natural resonant period of oscillation of the spring-mass
system can be made very long - approaching a thousand seconds. This
detunes the test mass from most local vibration and mechanical noise,

increasing the sensitivity and utility of the gravimeter. Quartz and
metal springs are chosen for different reasons; quartz springs are less

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