Determination of Moments of Inertia. 453 



by means of the well-known relation between the oscillation- 

 period t, the bifilar directive force, and the moment of inertia 



K= — j ; then the body to be investigated is laid in the carrier, 



and the moment of inertia of both is determined in the same 

 way. 



I must refer to my former paper* for the method of deter- 

 mining the directive force I) from the distance apart, the 

 length, weight, and elasticity of the suspension-threads, and 

 the weight of the body, as well as for details of instrumental 

 adjustment and observation. 



If the body is magnetic, we have to eliminate from the 

 bifilar direction- force that arising from the earth's magnetism 

 with the relatively small magnitude of the latter. This is 

 easily done by arranging that during the oscillations the 

 magnet shall lie east and west. Or we may bring the sus- 

 pension with the magnet into the meridian, and observe the 

 oscillation-period t ± in the normal position and t 2 in the reversed 

 position of the magnet. Then the oscillation-period of the 

 unmagnetized body would be 



V2 



tfa 



Vt] + tt 



Lastly, the measurement of moment of inertia may be made 

 before the body is magnetized. 



It is a matter of course that the requisite care should be 

 bestowed upon the adjustment of the centre of gravity j\ 



The oscillations are performed generally very rapidly, much 

 more so than one is accustomed to with swinging magnets. 

 The observations, however, may be made with the same accu- 

 racy. We simply note the times of reversal on each side, in 

 doing which we may, if necessary, omit one or more. 



The accuracy which may be attained is not inferior to that 

 which may be obtained with slower vibrations. I found the 

 results of separate observations, when the oscillation-period 

 amounted to about 1 second, to agree to within a few ten- 

 thousandths of a second. 



The moments of inertia of the magnetic bar mentioned 

 before (16 centim. long, 216 gr. weight) agreed very well 

 with each other, as well as with that calculated from its 

 dimensions. 



The following may be mentioned as advantages of the bifilar 

 mode of determination: — 



* F. Kohlrausch, Wied. Ann. xvii. pp. 744 & 745 (1882). 

 t F. Kohlrausch, he. cit. p. 754. 



