Kamerlingh OnnesA question that arises naturally after observing a Foucault pendulum
in operation is whether the pendulum support wire, because it is attached
to the rotating earth,
will affect the precession of the plane of oscillation. Now Foucault
could make his statement about the "fixity of the plane of oscillation"
because he had observed
that a long rod clamped into the chuck of a lathe and set to vibrate
did not change its plane of vibration as he rotated the chuck by hand.
However, that same year
G. B. Airy, Astronomer Royal in England, pointed out that if the pendulum
motion was not strictly back and forth but traced a narrow oval, there
would be an extra
precession of importance for short pendulums. It was understood that
a faulty support might generate such oval motion but a detailed theory
was not developed until
years later by H. Kamerlingh Onnes (famous now as the discoverer of
superconductivity). At that time Kamerlingh Onnes also introduced a mechanical
modification
that would compensate for a faulty support and built a short pendulum
of 1.2 m that he ran in a vacuum to verify the theory --- all this for
his dissertation in 1879.
This mechanical compensation is not incorporated into our pendulum
and instead two other devices are used. One is a variant of the Charron
ring introduced in 1931 and the other is a simple magnetic device invented
by H. R. Crane in 1981. The late Tom Riddolls of the Guelph physics department
machine shop constructed our pendulum essentially as described by Crane
in the American Journal of Physics, vol 63, p33 (l995).
Kamerlingh OnnesThe effect
Leonard EulerIt was quickly recognized that the analysis of Foucault's historic experiment
is simplified if one uses the theory of rotations developed by Euler a
century earlier. Thus
at our latitude y = 43º32', we should consider the rotation
frequency of the earth we = 360º/23hr56min
about its axis relative to the fixed stars as compounded from a vertical
component of magnitude we' = we
sine(y) = 10.36º/hr and a northward-pointing horizontal component
of magnitude we" = wecosine(y)
= 10.90º/hr (see Fig. 1).
Fig. 1