Kater's Pendulum: Why Discard l1-l2?

[avocadogirl]

Why is it that, when using a Kater's Pendulum where the pivot points are fixed and one weight is adjustable, it is acceptable to discard the factor of the difference between the two distances of the individual pivot points from the center of gravity (1/(l1-l2)) in the following formula?

T^2 = [(T1^2 + T2^2)/2] + [{(T1^2-T2^2)/2} * {(l1+l2)/(l1-l2)}] --where T^2 is the period of an equivalent ideal pendulum, squared, and, T1 and T2 are the respective periods of corresponding ends of this reversible pendulum, then, l1 and l2 are the lengths from the respective end of the pendulum to the center of gravity.

 

[kuruman]

Because the essence of the experiment is to adjust one of the masses, at fixed pivot separation, so that the periods $T_1$ when the pivot is "1" and $T_2$ when the pivot is "2" are as close as possible to being equal while the difference $I_1-I_2$ is as large as possible. Then the term involving $T_1^2-T_2^2$ is negligible relative to the first term.