Here I yam, Builder!
xausa, I have been providing this measure for some 12 years now, although with a differing measuring device. I use a constant torque turntable with one revolution timed from start to completion. My current database is over 600 guns with gun description, weight, balance (teeter-totter point balance = CG, not some magical feel sort of thing), unmounted swing effort (MOI at CG), mounted swing effort (MOI at butt), and half weight radius (compactness). The turntable is kept calibrated via metal bars of calculated MOI; several differing MOI's are used to make a chart with a regression line (R squares are very high indicating a high degree of accuracy).
Thomas's device was based on a torsional pendulem. It is sufficiently accurate, but does not lend itself to "production" of data. My data fits well with Thomas's.
What more would you like to know?
DDA
