Photographs of Vibration Curves. G17 



vertical slit cut in it. The images of the horizontal and 

 vertical slits fell, one immediately above the other, on the 

 slit in the plate. Only a very small length of the former, 

 i. e., practically only a point of light, was allowed to fall 

 upon the photographic plate. The dark slide which held 

 this was moved quickly by hand in horizontal grooves behind 

 the slit in the focal plane of the camera. No arrangements 

 were made to obtain a strictly uniform velocity of the plate, 

 as the main point of interest in the photographs was not 

 interfered with by want of it. 



Figs. 3 to 9 all show that the motion of the sounding- 

 board had a frequency strictly double that of the vibration 

 of the wire. From the vibration-curves of the wire in those 

 figures, it will be seen that the string was excited (by 

 plucking with the fingers) in various ways. In fact, subject 

 to the remarks made below, it may be stated that it was a 

 matter of indifference how the wire was excitea : the fre- 

 quency of the sounding-board was always twice that of the 

 vibration of the wire. 



Fig. 1, however, distinctly shows the presence of an oscil- 

 lation of the same frequency as the wire, supei posed upon an 

 oscillation of the double frequency. This is also perceptible 

 in fig. 2. The cause of the appearance of the " fundamental " 

 in these cases was successfully investigated. It will be seen 

 that the oscillation of the wire recorded on the plate is quite 

 large in fig. 1, and fairly large in fig. 2. This does not 

 mean that the oscillation of the wire had a smaller amplitude 

 in the other cnses, but only that the vertical oscillation of 

 the wire (which alone was recorded upon the plate) was 

 comparatively larger when figs. 1 and 2 were photographed. 

 As a matter of fact, the wire was plucked almost horizontally 

 when all the photographs except figs. 1 and 2 were taken. 

 In photographing fig. 2 it was the intention to pluck horizon- 

 tally, but it appears to have been carelessly done. In the 

 case of fig. 1 the wire was plucked vertically. Now it was 

 found that there was an important difference between the 

 oscillation of the wire in a horizontal and in a vertical plane. 

 The equilibrium position of the wire is not quite a straight 

 line, but a catenary of small curvature. The oscillation of 

 the sounding-board depends upon the second-order difference's 

 in the length of the displaced and equilibrium positions of 

 the wire. When the oscillation is in a vertical plane, the 

 fact that the equilibrium position is a catenary becomes ot 

 importance. The changes in length about the equilibrium 

 position become unsymmetrical, and this introduces a com- 

 ponent of the " fundamental " frequency into the oscillation 



Phil. May. S. 6. Vol. 21. No. 125. May 1911. 2 S 



