Vibration-Curves of String and Bridge. 449 



and find the consequent motion of this virtual image. Finally, 

 omit the mirror M 7 but regard the lens L^ as present, and 

 find the motion o£ the bright spot on the photographic plate 

 at R as due to the lens L x which focusses upon it the virtual 

 image of S. in the mirror Mi. A calculation on this prin- 

 ciple gave the linear magnification of the bridge's motion 

 lengthwise of the string to be 108 on the original negative. 



By inserting a piece of very thin blown glass under the 

 leg of the optical lever, see P : (fig. 2), and noting the con- 

 sequent movement of the bright spot on a card, the linear 

 magnification was estimated as 93 times. Thus we may say 

 that the magnification near enough for our purpose is of the 

 order 100. 



The exact action of the optical lever is best seen from 

 fig. 2, in which it is shown detached from its place at the 

 bridge, where when in use it is secured by indiarubber 

 bands so as to keep its three legs in contact with the hole, 

 slot, and plane shown by H and S on the bracket P Q R 

 and by 1 > 1 on the bridge B. The plane P x consisted of a 

 piece of glass cemented on to the head of a pin driven home 

 into the bridge. On the optical lever L is seen a little 

 tie-piece or strut from the mirror M to the plate L. Before 

 that piece was inserted the mirror yielded a little in the 

 middle of its rotation, and so displaced the spot horizontally 

 in the photographic plate. And though this yield was 

 of the order of only two minutes of arc, it produced a 

 horizontal motion of about 2 mm. on the plate and rendered it 

 worthless. 



In conjunction with the above special optical lever the 

 optical arrangements for recording the motion of the string, 

 now of 0*88 mm. diameter, are seen in fig. 1. In this M 2 

 represents a mirror of black glass which diverted part of the 

 beam from the lantern to the tin-foil screen having a vertical 

 slit at S 2 , whence the light passed to the lens L 2 which 

 focussed a bright image of the slit on the string at a point 

 about 5 cm. from its centre. Thence the light fell upon 

 the mirror M 3 , this reflected it to the lens L 3 which focussed 

 it upon the plate at R. The string's motion is accordingly 

 shown on the prints by a black line on a light ground due to 

 its shadow crossing the bright image of the slit. The motion 

 of the string at this point is hereby magnified 1J- on the 

 original plates. So on those and the reductions accompanying 

 this paper, the relative magnification of the bridge's motion 

 lengthwise of the string is 100/l|- = 67 nearly. 



In all the prints and their reproductions the left side 

 corresponds to the beginning of the time and the string's 



Phil. Mag. S. 6. Vol. 13. No. 76. April 1907. 2 I 



