A very similar piece of apparatus is in the 1928 Central Scientific Company of Chicago, and is sitting next to me as I write. The vertical shaft is pivoted, and the masses on the sliding cross-rod can be slid in and out to vary the moment of inertia of the oscillating system. The spiral spring provides both a zero point, and a linear restoring torque in both angular directions. 

   The torsion constant of the spring is determined by hanging various masses on one end of the string; the other end is wrapped around a pulley of known radius. The period of the system can be measured as a function of the moment of inertia of the system: the square of the period is proportional to the moment of inertia.