506 Mr. ]S . C. Krishnaiyar on Amplitude of Vibrations 



which any diminution of tension brings about a sudden 

 collapse of maintenance. 



(3) The amplitude graph though parabolic in parts is not 

 continually so ; the arc at one end produced parabolically 

 does not coincide with the arc at the other end but is nearly 

 parallel. 



(4) The maximum amplitude maintained increases if a. 

 increases in value. 



(5) There is a lower limit to the value of a for maintenance 

 to happen. 



(6) There is an upper limit to the value of the excess 

 tension, i. e. an upper limit to the magnitude of p 9 ' — n 2 

 when n>p if maintenance should happen. Beyond this, 

 there is no vibration of the wire at all. The projection of 

 the wire by a magic-lantern on a distant screen remains a 

 sharp image. 



(7) This upper limit to excess tension increases with 

 increase of a. In other words, when a is larger, main- 

 tenance starts with a larger excess tension. 



Most of the observations detailed above have been con- 

 firmed by R. N. Ghosh * by an entirely different method of 

 maintenance, viz. by means of an electric motor vibrator 

 originally designed by J. A. Fleming and subsequently 

 improved by C. V. Raman f . 



In the theory developed below, a term /3y 2 is introduced 

 in the part of the equation representing tension to denote 

 the variation proved J experimentally to occur in free oscil- 

 lations of sensible amplitude. This variation is due to the 

 second order differences in length between the equilibrium 

 position and the displaced position of the wire and is propor- 

 tional to the square of the displacement. The frictional force 

 is put down as the sum of two terms, one proportional to 

 the velocity and the other proportional to the square of the 

 velocity. Ordinarily, as Sir Gr. G. Stokes has shown, the 

 frictional force is proportional to the velocity when the velo- 

 city is small, and propoitional to the square of the velocity 

 when the velocity is relatively large. This apparent change 

 of the law of friction with increase of velocity can be ex- 

 plained by the assumption that the frictional force always 

 consists of two terms, the first term proportional to the 

 velocity and the second term proportional to the square of 

 the velocity, the coefficient of velocity being relatively larger 



* Proc. Indian Assoc. 1920, vol. vi. 

 f Physical .Review, November 1919. 



X C. V. Raman, " Photographs of vibration curves," Phil. Mag. May 

 1911 : Physical Review, December 1912. 



