Checking Level Changes of the Flats


An essential check we needed to run upon our Panama paraconical pendulum setup was to evaluate, to what extent solar illumination of the building over the day might cause the flats to tilt to and fro, due to thermal expansion/contraction of the walls and the ground etc.. For example, this type of objection was raised against the anomalous gravimetric results by Wang (see the prior art section of this website).

We operated with two high-sensitivity bull's eye levels, specified as having 2 mm bubble movement for 5 arc minutes of tilt. Since it was easily possible to verify the position of the bubble to closer than 1 mm, we think it is fair to claim that our observations were accurate within 2' of arc. (The diameter of the reference circle surrounding the bubble was 8 mm.)

The procedure was very simple. Early in the morning on a day which promised to be sunny, we parked the pendulums off the flats, and placed one bull's eye level on each flat. We made no particular effort to get the flat absolutely horizontal, so as to position the bubbles in the centers of the reference circles, since the objective was to measure variations. Then we took photographs of the levels at intervals during the day, to see if the bubbles moved.


Pendulum P1


This pendulum is located at the south-east corner of the building, so one wall and the pillar directly supporting the pendulum were directly exposed to irradiation from the rising sun from about 6:40 am until about 10 am, when a projecting roof started to be effective in providing shade. The general setup looked like this, with the bull's eye level on the flat:



By 8 AM the sun, which indeed that day did prove to be very strong, had been shining on the wall and pillar for a little over an hour, but actually they weren't particularly warm to the touch.

And at 8 AM, when we first put the level in place, the bubble was positioned like this, angled slightly towards 7 o'clock:



The following photos show the bubble at intervals during the day. Obviously the lighting conditions and the position of the camera were a bit different for each shot, and the effect of the camera flash varied, but the general trend of movement of the bubble (nil) is obvious.

9 AM:



10 AM:



11 AM:



12 noon:



1 PM:



3 PM:



4 PM:



5:30 PM:



7 PM:



8 PM:



9:30 PM:



Long before 9:30 PM the whole area including the building had cooled off from the heat of the day to night-time temperatures. Clearly, in the case of this pendulum #1, there was no perceptible movement over this entire period of solar heating and cooling, and tilting of the flat during the whole day due to thermal effects was certainly less than 2 arc minutes.


Pendulum P2


This pendulum is located along the south wall of the building, which (in April) is never directly illuminated by sunlight, so one would basically expect tilting due to thermal expansion to be less, than in the case of pendulum #1. The general setup looked like this:



At the start, at 8 AM, the bubble level was angled slightly towards 4 o'clock, or maybe 4:30:



9 AM:



10 AM:



11 AM:



12 noon:



1 PM..... At this point, just before we went to lunch, a certain culprit (who shall be nameless) picked up the bubble level on this pendulum #2 and immediately replaced it, obviously not quite in the same position - thus spoiling the observations to a certain extent. You can see a certain difference in the position of the bubble here; it has shifted a bit towards 5 o'clock. Anyway, we carried on....



3 PM:



4 PM:



5:30 PM:



7 PM:



8 PM:



9:30 PM:



Anyway, apart from the regrettable lunchtime episode, again there was no perceptible movement of the bubble over the whole day, so that we can be morally assured that, in the case of this pendulum #2, again, the thermal tilting of the flat over the day was less than 2 arc minutes.


These observations should be considered in the light of Prof. Allais's memoir, "Experimental Determination of the Influence of Inclination of the Bearing Surface upon the Movement of the Paraconical Pendulum...", which is available in English translation from our Notes download page here. Basically, Allais found that even much larger inclinations of the flat than 2 arc minutes exerted very little influence upon the precession of the pendulum (as one might intuitively expect). Therefore I think we can be confident that thermal tilting effects due to expansion and contraction of the structure of the building, did not cause the variations in precession that we have observed.



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