Henley's electrometer

I found this electrometer in the Whipple Museum in Cambridge. In terms of analysis I normally use two balls with identical charge on threads - a symmetrical problem.

So how do we model the Henley electroscope? Will the ball and the the central pole have the same charge? It looks like a rod not a string. Does that make a difference? Anyway, here's my first sketch:

I don't know whether the electroscope was to show relative charge or actual charge using Coulomb's Law but the latter looks possible once the angle is known.