206 On Discontinuous Wave-Motion. 



intervals for which they subsist are thus known, and 

 the vibration-curve which represents the resulting dis- 

 placements may be plotted from these values without 

 difficulty. The records shown in the Plate are found to 

 be completely in agreement with the results thus obtained. 

 The special feature of interest is that the vibration-curves 

 are seen to be intermediate in form between the two-step 

 zigzags of a bowed string and those characteristic of a 

 plucked string *. The reason for this is not far to seek. 

 When one of the discontinuities is zero, we have, as already 

 seen, the case of the bowed string. When d=— C 2 , the 

 motion reduces exactly to that of a string plucked at the 

 point at which the discontinuities cross. The cases actually 

 recorded in these experiments are those in which (\ and C 2 

 are unequal but of opposite signs, and are thus intermediate 

 between the two extreme types referred to above. 



The cases in which Ci and 2 are of the same sign are 

 also of interest in connexion with the theory of the special 

 forms of vibration of a bowed string obtained at the " wolf- 

 note " pitch, and also under other conditions when the 

 vibration-curves assume the form of four-step zigzags. 

 Experiments are being undertaken to reproduce these 

 special forms of vibration by the method indicated in this 

 paper. 



Summary and Conclusion. 



In these experiments, the characteristic vibration-forms 

 produced by the motion of two unequal discontinuous 

 changes of velocity of opposite sign have been observed 

 and recorded photographically. Some are of the sym- 

 metrical type and the others are asymmetrical. The results 

 are in full agreement with the mathematical theory first 

 given bv Harnack. The vibration-curves are found to be 

 intermediate in form between those characteristic of bowed 

 and of plucked strings. The cases in which the discontinuities 

 are of the same sign are also of special acoustical interest 

 and will be studied separately. 



The Indian Association for the 

 Cultivation of Science, Calcutta, 

 29th September, 1916. 



* Krigar-Menzel and Raps, Sitzungberichte of the Berlin Academy, 

 1898, p. 509. 



