32 M. J. Antolne on the Multiple Sounds 



two images of the rod are seen perfectly traced and as it were 

 immoveable in the positions AC, AD.' The rod passes very 

 rapidly each intermediate position, and reaches Fiw. 1. 

 the extreme positions AC, AD, with velocities 

 which are annulled and then increase again by 

 imperceptible degrees. The images produced 

 on the retina by the rod, when it is in the positions 

 near the minima of velocity, where it remains al- 

 most immoveable for a comparatively long time, 

 must be more vivid than in the other positions; 

 thence the appearance observed. The two clearly 

 visible images of the rod also approach by degrees, 

 in proportion as the magnitude of the vibrations 

 diminishes. 



If the rod possesses at last a vibratory movement and a 

 motion of translation, instead of two images, a very consider- 

 able number will be perceptible at regular distances over the 

 whole extent that the movement of translation causes the rod 

 to pass. Thus, if a knife be held in the middle, and one of 

 its ends be struck on a fixed obstacle, leaving the knife free 

 to rebound and vibrate, there will be perceived ten, twenty, 

 thirty knives regularly distributed in front of the obstacle. If 

 an object be struck with a bow, several images of the bow will 

 be seen, each presenting a perfect and very distinct design of 

 all the parts of the bow. 



These multiple images 

 are easily explained. Let 

 us suppose that a rod AB, 

 jBg.2,deviated towardsAC, 

 is left to itself, and that 

 at the same time it is im- 

 pressed by a movement of 

 translation which carries 

 the point A in the direction 

 of the line AM. Let us 

 take on AM the lengths A A', A' A", A" A'". . . ., traversed by 

 the point A in the time which each simple oscillation takes to 

 accomplish. When the point A is at A', the rod will be at 

 A'D' at the end of its first simple oscillation ; in the same way 

 the rod will terminate its second, third .... oscillation in the 

 positions A'C, A"'D' . . . These positions are very near those 

 which correspond to minima of velocity ; the other positions 

 are traversed very rapidly, and it is on this account that images 

 of the rod are distinctly seen nearly in the positions AC, A'D, 

 A"C', A"'D'. . . . They will be seen simultaneously if the move- 

 ment of translation is suitable. 



