STRINGS 



67 



these, account being taken of sign. The line of this middle 

 portion moves parallel to itself, with constant velocity, back- 

 wards and forwards between the two corners of the parallelogram 

 of which the initial form constitutes two adjacent sides. 



Fig. 27. 



In the annexed Fig. 27, which corresponds with Fig. 26, the 

 plucking is supposed to take place at a distance of one-fourth 

 the length from one end, and the phases shewn follow one 

 another at intervals of one-sixteenth of a complete period, the 

 successive forms being APB, AQ&B, AQ^B, AQ 3 R 3 B, AQ 4 R 4 B, 

 and so on. It is evident on inspection of the figure that any 

 point of a plucked string moves backwards and forwards with 

 constant velocity between two extreme positions, in which it 

 rests alternately during (in general) unequal intervals. The 

 space-time diagrams of the middle point, and of the point 

 plucked, under the conditions of Fig. 27, are given in Fig. 28. 



Fig. 28. 



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