CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL 

 LABORATORY, HARVARD UNIVERSITY. 



THE LONGITUDINAL VIBRATIONS OF A RUBBED 



STRING. 



By Harvey N. Davis. 



Presented by Wallace C. Sabine, October 11, 1905. Received January 25, 1906. 



§ 1. Introductory. 



§2. Aliquot Cases — Experimental Work. 



§3. Aliquot Cases — Theory. 



§4. Rational Cases — Kkigar-Menzel's Law. 



§ 5. Integral Surfaces. 



§ 1. Introductory. 



This work was originally undertaken as the first step in an investiga- 

 tion of the effect of vibration on magnetic quality. In the previous 

 study of this subject, although many exact measurements of the mag- 

 netic phenomena had been made by a number of writers, in no case 

 had the conditions been such as to admit of an equally exact description 

 of the mechanical phenomena involved. It seemed desirable, there- 

 fore, to renew the attack upon the subject, using as the mechanical dis- 

 turbance a steady state of vibration whose character was known, and 

 whose intensity could be accurately measured and easily controlled. It 

 was found that longitudinal vibrations suitable for this purpose could be 

 maintained in a steel wire by means of a mechanically operated rubbing 

 wheel, and a study of their nature has shown them to be identical in all 

 respects with the familiar transverse vibrations of a violin string, so that 

 the parallelism between longitudinal and transverse vibrations which the 

 mathematics of the subject predicts, finds here a unique and exceedingly 

 detailed experimental verification. This purely mechanical discussion 

 has thus acquired a considerable interest in itself, and has, therefore, 

 been carried far beyond the requirements of the original problem. It is 

 now presented as a separate paper ; the magnetic problem will be con- 

 sidered at another time. 



