Temperature Compensated Pendulum

The Trinity Clock has a temperature-compensated pendulum, and it would be great to take it apart to see how it works. We think we know, but to be sure we need to take a look. But our clock runs continuously and is not stopped for more than an hour in March and October for the time change. As it happens, we have access to a clock by the same maker and of the same vintage (Smith of Derby, 1903 - the Trinity clock is 1910). We've carefully dismantled the pendulum and photographed the insides - we've found a bi-metal compensation system using steel and zinc. The science is elegant and simple, as is the engineering. Really very nice.
Temperature compensation has long been perfected since the time of Harrison and his gridiron pendulum (1726). The principle is to take advantage of two materials with different coefficients of thermal expansion. Here, for instance, we have steel and zinc. It is easy to see that the dimensions in the photograph are about right:
(1) Zinc (30ppm/oC) expands roughly 2.5 times as much as steel (12ppm/oC).
(2) The pendulum has two steel elements going 'down' total length 2L and one zinc element going 'up' of length Z
(3) For zero net expansion then 2L * 12 = Z * 30 so Z = 0.8 L

So the zinc tube needs to be about 80% of the length of the steel tube. I say "about" because the actual coefficients of expansion will depend on the exact alloys used. Clock makers will have made small adjustments from one clock to the next, eventually settling down on a set of dimensions that give perfect compensation.

The Trinity 1.5-sec pendulum has L = 2.25m, so the zinc element would be Z = 1.8m (we've not measured it yet - can't do that without stopping the clock)

Compensation on the Trinity clock looks to be pretty good, but we have two particular problems:
(1) You might notice that there are holes in the steel and zinc tubes. These allow air to flow freely around the three elements which helps to allow temperature equilibrium to be reached quickly. This works fine for changes in air temperature, but we have a window that allows sun to shine directly on the pendulum at certain times of day, particularly in the summer months around noon to 4pm. This causes the outer steel tube to warm up without the inner zinc compensating tube (kept in the shade) changing temperature.
You can see in summer 2009 for instance that there is a large variation of "going" with daily temperature changes, perhaps 100ms/day per oC, almost as bad as for an uncompensated pendulum. Yet the variation over the full 9 days where temperature in the clock case rises by 8oC shows no obvious change in "going", and certainly not the 800ms/day that the daily oscillations suggest we should be seeing. Just as well!
(2) Another complication for us is that the pendulum swings in a case that extends to the room below. This means that differential temperature between the two rooms causes air flow past the pendulum (warm air rises) which can influence pendulum amplitude.

What are we doing about these two problems? Well, we've put reflective film on the glass but this hasn't made a lot of difference. Plans now include:
* slats to shade the sun while not impeding the view;
* plugging holes in the case to prevent drafts;
* installing air conditioning (only kidding).