[swilhelm73]

A finite amount of air (or steel, or water, or whatever) has a given mass, no matter what temperature it may be.

Density can be consider to be the measure of the amount of matter within a given area. The ambient temperature is the primary determinate of the density of air. Cold air is denser the warmer air. As such, there are more "air" molecules in the area around the pendulum if the air is cooled.

So, cold air does indeed generate a stronger gravitational pull then warmer air.

However, as I pointed out originally this effect would be very very small.

[steve in DC]

One might suggest that the differential in mass might place more air molecules in closer proximity to the pendulum, but overall, the mass of air in the atmosphere has to be considered static for these purposes.

Regarding a change in proximal mass, and its discernable impact in the speed of the pendulum, I would suggest that the near transit of a heavy truck would have more significant gravitational impact than a slight change in air temperature, no matter how swiftly that change in temperature might occur.

(But I am too poorly schooled and too lazy to perform the calculations to support my statement:-)