On Discontinuous Wave- Motion. Ail 



Columns 4 and 5 of Table IX. show the agreement between 

 the values of b calculated from (xiii.) and those given directly 

 from the surface-tension observations. It is very probable 

 that with more extended data the form of this relation 

 between 6 and b will be altered, but the fact remains that 

 there is a definite relation between the absolute boiling- 

 point of an unassociated liquid and the temperature co- 

 efficient of its surface-tension, so that this temperature 

 coefficient may be calculated from observations of the 

 boiling-point alone. 



It may be remarked in conclusion that associated liquids 

 so far as I have tested them do not agree with equation (iii.) 

 — in fact, agreement with (iii.) may form a very convenient 

 test of non-association. I hope to return to this point 

 later. 



University College of North Wales, 

 Bangor. 



July 1915. 



IV. On Discontinuous Wave-Motion. 

 By C. V. Raman, M.A., and S. Appaswamaiyar *. 



[Plate I.] 



AN analytical discussion of the principal mode of vibration 

 of a bowed string as ascertained from the form of its 

 vibration-curves, leads to the result that at two epochs in 

 each period of vibration the string should pass as a whole 

 through its position of statical equilibrium, alternately in 

 opposite directions. At the first epoch, according to the 

 analysis, the velocity at every point on the string is propor- 

 tional to its distance from one end, there being a discontinuous 

 fall of the velocity to zero at the other end. At the second 

 epoch the state of matters is reversed, the motion being 

 such that the velocities are proportional to the distances 

 from the farther end, the discontinuous fall being at the 

 nearer. These results are of importance as defining the 

 essentially discontinuous nature of the motion involved, but 

 it is noticed from the literature of the subject f that they are 

 obtained by an elaborate and indirect analytical process from 

 the observed form of the vibration -curves, and have not so 

 far received direct experimental confirmation. Some time 

 ago it occurred to one of us that an experimental test was 



* Communicated by the Authors. 



+ See Riemann and Weber's ' The Partial Differential Equations of 

 Mathematical Physics,' pp. 216-223. 



