The average Coriolis force *F*c = 2 *m* w_{e}*V
*exerted on the pendulum bob is of the order of 10^{-6} times
the gravitational force *F*_{g }= *m g*. Yet we would
like not only

to detect it but to measure its effect, namely measure w_{e}'
to an accuracy of say 0.5% or better. That is, we want w_{e}
to be larger than any spurious precession rate

caused by the gravitational force by a factor of more than 102. How
this remarkable enhancement of 108 to 109 is achieved is outlined below.

The numerical value of the ratio of Coriolis to gravitational effects is given on the left. Begin with

10^{-6} = average Coriolis force / gravitational force.

But note that the pendulum bob is supported
by a wire and most of the gravitational force is cancelled by the tension
force in the wire. The remaining

gravitational force is less by a factor of
the maximum displacement b = 4º (= 0.07
rad) of the pendulum. That is 10^{-6}/0.07 or

1.4 x 10^{-5} = w_{e}'/w,
The ratio of the direct effect of the Coriolis force to the
gravitational force.

The pendulum is approximately an harmonic oscillator.
Only the residual anharmonic forces can give rise to a precession competing
with the Coriolis

precession. The ratio anharmonic / harmonic
force is = ½b^{2 }so that

5x10^{-3} = w_{e}'/w,
Maximum possible precession rate from the anharmonic gravitational force.

The anharmonic force produces no precession
if the pendulum motion is strictly planar. The maximum possible precession
is reduced to the actual

precession by the ratio *b/a*, the measure
of the ellipticity of the motion. For our support anisotropy and Charron
ring the maximum *b/a* = 1/50. The

result is

0.25 = w_{e}'/w,
Spurious precession rate. This, being of the order unity, shows that the
earth's rotation is now just barely observable.

The precession caused by the anharmonic residual
of the gravitational force is reduced by a compensating anharmonic magnetic
force. The cancellation

cannot be made perfect because of uncontrollable
fluctuations in various drive and damping mechanisms. There are also corrections
of order (*b/a*)^{2} in

the preceding ratio that are not affected
by the magnetic force. With reduction by another factor of 50 there remains

10 = w_{e}'/w,
Compensated
spurious precession rate.

The spurious contributions to the precession
are still mostly of an oscillatory or random nature. The mean of these
spurious contributions is more than

an order of magnitude smaller so that by measuring
over the period of a week, say, we get

2 x 10^{2} = w_{e}'/w,
Mean compensated spurious precession rate.

An accuracy of 5 x 10^{-3} or 0.5%
on w_{e}' means we can determine the
latitude of our Foucault pendulum with an uncertainty of about 30 km.