where E_t is the modulus of elasticity for torsion, and I the polar
moment of inertia of the section of the rod. If the rod is of circular
section, I = ½[pi]r^4. Let R be the radius of the disk, and b its
leverage, or the distance of its centre from the axis of the torsion
rod. The moment of the pressure of the water on the disk is
Fb = kb(G/2g)[pi]R²v²,
where G is the heaviness of water and k an experimental coefficient.
Then
E_t I[alpha]/l = kb(G/2g)[pi]R²v².
For any given instrument,
v = c [root][alpha],
where c is a constant coefficient for the instrument.
The instrument as constructed had three disks which could be used at
will. Their radii and leverages were in feet