354 Prof. C. V. Raman and Mr. Ashutosh Dey on 



the ratio (I — 2b) /I, according as b is smaller or greater 

 than Z/4. 



The form of the vibration-curve at other points on the 

 string in the case considered above may also be found by 

 tracing the successive changes of velocity. It is obvious 

 that the curves for points lying outside the limits 1/2 ±.b are 

 different in character from those for points lying between 

 these limits. For, the discontinuities pass any point lying 

 outside the limits 1/2 ±b alternately in opposite directions, so 

 that the velocity of such point alternates between two, and 

 only two,' constant values. But within those limits the dis- 

 continuities pass any given point, first successively in the 

 same direction, and then successively in the opposite direction. 

 The vibration-curves of points lying outside the limits lj2±b 

 are four-step zigzags, in which alternate lines are parallel to 

 each other. The vibration-curves of points within the limits 

 1/2 + b are also four-step zigzags, in which two of the lines 

 are parallel to each other, but the other two are not. The 

 most characteristic vibration-curve is that for the centre of 

 the string. This point remains at rest for a considerable 

 interval, twice in each period of vibration, the two positions 

 of rest lying one on either side of the undisturbed position of 

 the string. The smaller the distance b is, the more closely 

 are the two positions of the centre of the string situated. The 

 vibration-curve of the middle point of the string thus consists 

 of two long horizontal lines which take up a considerable 

 fraction of the period of vibration, and are separated by short 

 steep lines representing the motion from one position of rest 

 to the other, and vice versa. 



Experimental Method. 



It is evident that the modes of vibration described above 

 would be perfectly reproduced if a string has initially a 

 uniform angular velocity about one point, and if in the 

 course of this motion two other points on it situated at equal 

 distances on either side of the first are suddenly fixed with 

 the result of isolating the string between them. If A and B 

 are the points thus fixed and C is the point about which 

 the string has initially a uniform angular velocity, so that 

 AC = CB, the mode of vibration elicited would evidently 

 depend upon the simultaneity, or otherwise, of the fixation 

 of the string at A and B. If the two points are fixed at the 

 same instant, the discontinuous changes of velocity travelling 

 inwards from A and B meet at the centre, and the string would, 

 as already explained, vibrate in two segments. On the other 



