Disks to the Optical Analysis of Vibrating Bodies. 25 



finally appears at rest, if the disk of the vibroscope, regarded as 

 a siren, gives the tone of the bar. It is easy to see that theore- 

 tically the result must be the same if the rotating disk gives the 

 next deeper, or indeed any n times deeper octave of the tone of 

 the bar. For in this case, at each passage of a hole in front of 

 the eye, the point of light would always be seen in one and the 

 same position of its path, even if in the time between the passage 

 of two holes n complete oscillations of the point have been ef- 

 fected. This is in fact the case; but, instead of a spot, a band 

 of light is seen, which is longer the deeper the octave of the vi- 

 broscope below the tone of the bar. The explanation is simple. 

 During the stay of a hole in front of the eye, the point describes 

 a greater portion of its entire path the slower the vibroscope-disk 

 rotates. This of course is the case with all other vibrating 

 bodies ; the lower octaves indeed resolve the vibrations, but the 

 more indistinctly the greater the interval of the note. The case 

 is quite different if the vibroscope is one or many octaves higher 

 than the vibrating body. Let the elliptic curve, fig. 3, repre- 

 sent the path of the vibrating point of light a, which for the 

 same height of octave of the vibroscope slowly advances in the 

 direction of the arrow; it is clear that if the vibroscope is an 

 octave higher, the point of light is seen twice during, each vibra- 

 tion, and on opposite points of its path. Hence two points of 

 light are then seen which slowly advance in the same direction. 

 In short, if the vibroscope is n octaves higher, n points of light 

 are seen as a rotating string of pearls. If the velocity were the 

 same in all points of the ellipse, the points of light would have 

 the same distance. Yet at the ends of the major axis the points 

 of light appear closer packed, and, as is readily seen, the mutual 

 distance of two points of light gives a measurement of the abso- 

 lute velocity on the curve. 



From the above explanation the following phenomenon is at once 

 explicable. Using the disk with from twenty-four to thirty-six 

 holes, if the clockwork is wound up and allowed to run out without 

 adjustment, at first a great number of points of light are seen 

 rotating, which at certain moments stand still and change their 

 direction. From now the apparent movement is more rapid until 

 the image becomes confused. It then becomes clear again, but has 

 one point less; at length it stands still, changing finally the direc- 

 tion of its motion. This process is repeated, a point of light 

 disappearing each time, until finally only a single one describes 

 the path. It is moreover clear that the complicated luminous 

 figures of the 'kaleidophone present analogous phenomena. 



The multiplication of images may be observed under the above 

 circumstances also in other vibrating objects — for instance, vibra- 

 There is the advantage in this case, if only one 



