EXPERIMENTAL DETERMINATION OF MOMENTS OF INERTIA. 53 



positions ; the corresponding times of oscillation T' and T" will then 

 give 



K'K + K" K'-K" 



2~ T'2 T" 2 "~ T'2 _ T" 2 ' 



If we merely propose to determine the torsion couple, we shall 

 have 



C = r, " ~~ ' ' 



it is sufficient therefore to know the difference K' - K" of the 

 moments of inertia of the movable system in the two positions. 



Suppose, for instance, that the movable system consists of the two 

 spheres of Gauss, or of two weights q of any given form, placed 

 successively at the distances d' and d", and symmetrically in respect 

 of the angle of rotation ; we shall have 



K'-K" = -(</ /2 -<T 2 ). 



We may also employ a rectangular rule of weight ^, arranged so 

 that two of its dimensions, a and , might be made alternately 

 perpendicular to the axis, by a simple rotation of 90 about a 

 parallel to the edge c. 



In this case the absolute values of the moments of inertia K' and 

 K" depend on the distance from the centre of gravity of the scale to 

 the axis of rotation, but their difference is 



705. Suppose, finally, that the moment of the directive couple is 

 in a known ratio to the weight of the system ; that, for instance, it is 

 proportional, as we shall see is the case with the bifilar suspension. 

 If P is the weight, and K the moment of inertia of the original 

 system, P' and K' are the same quantities relative to the additional 

 bodies, and h is a constant coefficient, we shall have 



