History (cont.)

A 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 Onnes

The effect

Leonard Euler

It 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