Connection with Experiments on Torsional Vibrations. 417 



have arrived at the solution of the problem ; but as it was 

 four weeks were spent in endeavouring to find the effect of 

 change of temperature, change of load, and change of mode 

 of attaching the cylinders, until I discovered that the pheno- 

 menon was simply caused by approach to synchronism between 

 the periods of torsional and pendulous vibrations of the wire. 

 Of course, if the axis of the wire passed accurately through 

 the centre of mass of the vibrator, the phenomenon would not 

 occur, but it is impossible quite to secure this ; and as a con- 

 sequence so-called centrifugal force on the one hand, and the 

 force of gravity on the other, set up pendulous vibrations 

 which may seriously interfere with the vibration-period due 

 to the torsional elasticity, and still more so with the loga- 

 rithmic decrement of arc. 



Having thus discovered two enemies in ambush, I thought 

 that the ground was now clear, at least as far as any danger 

 from synchronism was concerned ; but in this I was mistaken : 

 for happening to pursue my investigations still further with 

 comparatively light loads and small moments of inertia, I at 

 length became acquainted with a third source of error arising 

 from approach to synchronism between the torsional and 

 transverse vibrations of the wire. It is, I believe, quite im- 

 possible to excite torsional vibrations without at the same 

 time exciting transverse ones ; and should synchronism nearly 

 occur between the periods of these vibrations, we may have 

 beats quite as strongly marked as in the two cases before 

 mentioned. 



There is yet another source of error to which it is desirable 

 to draw attention. When a wire has been recently suspended, 

 the torsional vibration-period will always be found slightly 

 greater than when it has been suspended for some time and 

 frequently set in vibration. The length of time which must 

 elapse before a wire has reached its state of maximum torsional 

 elasticity depends upon the nature of the metal ; with copper, 

 for instance, a few hours will suffice, whilst iron may require at 

 least a couple of days. Now suppose that this state of maxi- 

 mum elasticity has been reached : if we wish to preserve 

 it, care must be taken not to jar the wire or to subject it to a 

 change of temperature of even two or three degrees Centi- 

 grade ; for in either case the elasticity will be slightly di- 

 minished, and a few hundred vibrations will be required to 

 restore it to its former condition. Since it is very difficult to 

 avoid such slight changes of temperature as those mentioned 

 above, it is always advisable after any rest to cause the 

 wire to vibrate a few hundred times before beginning fresh 

 observations. 



