Appendix VI
Moment of Inertia
The Method of Double Suspension
In certain cases, as for example when determining the moment of inertia of the body of a bird, it is not convenient to employ the method of § 172 owing to the difficulty of accurately locating the centre of gravity. In such cases the method of double suspension may be employed, the value of λ2 being deduced from two determinations of the time period, made with two different points of suspension a known distance apart.
When a single determination of the time period is made, the length of the pendulum (i.e., the l of § 172) being unknown, a curve may be plotted for a series of assumed values of l, the ordinates representing the values of λ2 corresponding to values of l as abscissae. The resulting curve is a parabola passing through the origin and through a point distant from the origin by an amount equal to the length of a simple pendulum corresponding to the observed period.
By plotting two curves from origins O1 and O2, Fig. 167, separated by the distance apart of the two points of suspension, the value of λ2 is given by the point of intersection; this is the only value of λ2 consistent with both observations.
In Fig. 167, the line O1 O2 represents the distance between the two alternative points of suspension, and the two curves representing possible values of λ2 are found to intersect in the manner shown, giving the required value of λ2. The plotting of these two curves may be effected over just the necessary portion
