418 Error in Experiments on Torsional Vibrations, 



Determinations of Torsional Electricity. 



It is evident, from what has gone before, that when the 

 cylinders are suspended from the bar by threads, the torsional 

 elasticity, as inferred from the vibration-period, may be seriously 

 affected should the torsional vibration-period of the wire 

 approach to synchronism with the vibration-period of the 

 cylinders about their axes ; and to such an extent did I find 

 this to be the case, that the values of the torsional couple for 

 the same wire, as calculated from the previously given formula, 

 differed from each other by 10 per cent, or more when the 

 moment of inertia was varied. 



The effect of synchronism between the torsional vibrations 

 of the wire and the pendulous vibrations is not likely, if proper 

 care be taken in the construction and disposition of the bar 

 and its appendages, to be great ; but it may nevertheless be 

 very sensible, 



Synchronism between the torsional and transverse vibra- 

 tion-periods is not likely to occur except in extreme cases ; 

 but it must be remembered that the torsional vibration -periods 

 may be affected by synchronism between them and multiples 

 of the transverse vibration-period, though of course not to 

 the same extent as when the fundamental transverse vibration- 

 period equals the torsional vibration-period. A similar remark 

 to the above would also apply to the other two cases of 

 synchronism. 



Determinations of Magnetic Moments. 

 It is evident that determinations of magnetic moments by 

 the method of oscillations may be similarly affected by the 

 same causes as we have seen would affect determinations of 

 the torsional elasticity. 



Damping of Magnets. 

 Still greater error may be introduced from the above causes 

 in experiments on the damping of vibrating magnets ; for 

 the logarithmic decrement is much more seriously affected 

 than the vibration-period. 



Determinations of Moments of Inertia. 



When it is impossible to determine the moment of inertia 

 of a body by measurement of its dimensions and mass, it is 

 usual to find the time of oscillation, and afterwards to redeter- 

 mine this time when the moment of inertia has been altered 

 to a known extent. 



If t and t' be the two times of oscillation, K the required 



