Discontinuous Wave-Motion. 355 



hand, if one of the points is fixed earlier than the other by 

 an interval of less than half a period, the discontinuities 

 cross at some point on the line A B other than the centre of 

 the string, the position of such point being capable of ad- 

 justment by a suitable alteration of the interval of time 

 between the fixing of the string at the points A and B. 



The experiment here indicated may be successfully per- 

 formed with a steel " string " stretched on a light frame 

 capable of motion round a horizontal axis at right angles 

 to it. The necessary tension is secured and maintained by a 

 spring-balance fixed to one end of the frame, which keeps the 

 string taut. A small load fixed to the frame on one side 

 causes it to swing into a horizontal position with the angular 

 velocity desired. At this position the string comes up 

 against two stops, one on either side of it, situated at equal 

 distances from the horizontal axis about which the frame 

 and string move. If the two stops A and B are exactly in 

 line with the string at this instant, the impacts take place 

 simultaneously. By putting one of the stops out of line, any 

 desired interval between the impacts may, however, be secured. 

 It is found (with the arrangements adopted by us) that a 

 vertical displacement of one of the stops by a millimetre is 

 equivalent to about half a period in the interval between 

 the impacts, smaller displacements securing proportionately 

 smaller intervals. Just before the impacts take place, the 

 dark slide containing the photographic paper is released 

 automatically, and moves in a direction parallel to the string, 

 recording the initial motion and the vibration of the string 

 at any point desired. The optical arrangements are similar 

 to those described in the first paper of the series. 



Fig. 1 (Plate VIII.) shows eight records secured by these 

 arrangements for various points on the string, and exhibits a 

 complete agreement with the indications of theory. Two of 

 the records (for 3Z/8 and 52/8) show a close approach to the 

 simple two-step zigzag form for the point at which the discon- 

 tinuities cross. The ratio of the two velocities of this point 

 or of any other point lying outside the limits 1/2 + b is equal 

 to the ratio of the distances of such point from the centre 

 and the nearer end of the string. The photographs furnish 

 a confirmation of this kinematical law. Numerous records 

 (not published) have also been secured of the vibration-forms 

 obtained for values of b ranging from zero to 1/2. When 

 6 = Z/4, the two sides of the two-step zigzag for the points 

 1/2 -±b are equally steep, and a vibration of the type con- 

 sidered here cannot therefore be elicited by the bow with a 

 two-step zigzag motion at the bowed point if 6>//4. As b 



