DAVIS. LONGITUDINAL VIBRATIONS OF A RUBBED STRING. 697 



made all parts of a vibrating segment accessible, and furthermore kept 

 the point which was being observed almost entirely free from the lateral 

 motion which imperfections in the shape of the rubbing wheel would 

 otherwise have caused. 



The excitor or "bow" of these experiments was a chamois-covered 

 wheel dusted with powdered rosin. In order to give an unbroken rub- 

 bing surface the chamois was cut from a skin in the form of a ring and 

 stretched over the edge of the wheel, a method which gave very satisfac- 

 tory results. During the first part of the work a wooden wheel 15.1 cms. 

 in diameter was driven by a 1/12 H. P., A. C. motor through a system of 

 wooden pulleys and belts which could be so adjusted as to give the pe- 

 ripheral velocity any one of eleven values from 5 to 91 cms. per second. 

 A more satisfactory wheel 4.9 cms. in diameter was subsequently made of 

 brass, to avoid warping, and was driven by the same motor through fric- 

 tion gears of brass and rubber so adjustable as to give a continuous varia- 

 tion in its peripheral velocity from about 3 cms. per second up ; it was 

 mounted on the slide rest of a small lathe bed, the two feed screws 

 giving slow motions along and perpendicular to the wire. 



These experimental conditions are unusually favorable, as compared 

 with those of previous observers, in three respects. In the first place, 

 as has already been noted, the use of a wheel instead of a bow enables a 

 given state of vibration to be kept up indefinitely and to be reproduced 

 at will, so that comparable observations can be made at different parts 

 of the wire, and the corresponding " velocity of the bow " measured. 

 In the second place, the vibrating segments are much longer than would 

 have been possible for transverse vibrations, so that given points can be 

 more accurately located and the effective width of the " bow " is more 

 nearly negligible. And finally, the system is very nearly " perfectly 

 flexible " because the sharp corners of a transversely vibrating string are 

 replaced by points whose only peculiarity is a change in the law of dis- 

 tribution of density. It is very true that sudden jumps in this law 

 necessarily imply instantaneous changes of finite magnitude in the veloc- 

 ities of the elements of the wire, but, other things being equal, " corners" 

 would not be rounded off so much for longitudinal as for transverse 

 vibrations. On the other hand, the amplitudes obtainable in this way, 

 even with long strings, are much smaller than those of transverse vibra- 

 tions, and furthermore it is always difficult to perform mechanically so 

 delicate an operation as that of bowing a string, so that the more compli- 

 cated vibration forms have sometimes been very hard to set up. 



