Vibration Curves of Violin Bridge and Strings. 459 



for clearness sake. The clamp 00 is fixed at a corner 

 of the violin which is specially free from vibrations, and 

 carries the adjustable bracket BBBBB, at the end of which 

 is the table T. This table has the hole H and the slot S for 

 carrying the two upper conical feet of the optical lever, thus 

 forming its horizontal axis. The lower foot F of the lever, 

 when held in position by an elastic band, presses on the 

 plane P of the bridge, P being a piece of microscope-cover 

 glass fastened on with shellac. 



Magnification of Bridge's Longitudinal Motion. — As the 

 optical lever is now used in an oblique position, the magnifi- 

 cation requires special examination. Referring again to 

 fig. 1, we see that as the bridge moves lengthwise of the 

 string the lever is made to rotate about the axis mA through 

 a small angle d<j> say. Thus the normal mN to the mirror 

 changes to the position mN' where N' is above N and not 

 shown in the diagram. But since the incident beam IHm is 

 at rest when N rises to N', the reflected image R will rise 

 to R/ say where IN'R' is a straight line. Now it was 

 previously shown (Phil. Mag. April 1907, p. 448) that 



RR'/AR 2 tan * 



(1) 



NN'/AN tan a - tan 6' ' ' ' ' 



where u is the angle AmN and 6 is the angle N??iR. 

 But the angle 



NN'/AN = # = — (2) 



where h is the displacement of the foot F of the optical lever 

 and I is its distance from a line through the two upper feet 

 which fit in the hole and slot and so form its axis. 



For the case shown where the E-string corner of the 

 bridge is under test, the dimensions were as follows : — 



AR = 14 cms., a = 16° 3', 6 = 12° 33', I = 0'G8 cm. 



Thus the linear magnification, on the negative, of the 

 bridge's motion is given by 



RR' AR 2 tan a 14 Q .... 



—f- = r • I T ~a ~ 777^ x 8 " 84 b = 182\l. 



Ii I tana — tan 0*bO 



For the same arrangement the string's motion was mag- 

 nified 2*1 times. Hence the relative magnification which is 

 the same in any reproduction is 86*7. 



For the G-string corner of the bridge, all the arrangements 

 were similar but reversed laterally and a new optical lever 



