Kater's Pendulum (shown in the adjacent picture) is supposed to work. There are two pivot points (a), one at each end. At one end there is a major weight (d) and at the other end a minor weight (b & c). The minor one is adjustable, and by moving it in or out, the period (the rate at which the pendulum swings) can be changed. So, what you do with this thing is hang it from one pivot and time the swing, then flip it over and time it again, moving the minor weight in and out until the two times are the same. Moving the minor weight counter-balances the major one and makes the whole thing effectively an 'ideal' pendulum.
Knowing the distance between the pivot points and the time of the swing, we can use this formula to get the value of gravity at that point. Of course Tom isn't going to be using a calculator over there, so all he's going to do is collect the numbers at various points and bring them back to Frank to do all the number crunching.
It turns out that Frank just happens to have a museum-quality piece that he's going to let Tom take through the Door to do some testing. It wasn't designed to be portable at all, so Frank has to make some modifications to the frame where Tom will be hanging the thing. Frank also has a set of hourglasses (though they really should be called minute-glasses) that Tom will be using as timers. I'm not certain if Tom (or ANYone for that matter) will have enough patience to do all this stuff. Those physicists must have been really dedicated to their field of study to invent stuff like this.
We'll see what we have to report next week. Until then, keep swinging!