Vibration- Curves of String and Bridge. 151 



Group IV. consists of figs. 27-39 contained in column 3 

 of Plate XI. These all show the vibrations of the bridge 

 parallel to the length of the string, which is throughout 

 bowed at 90 cm. from the bridge as in the previous group. 

 Thus columns 2 and 3 of Plate XI. allow comparison of the 

 two motions of the bridge under given conditions of pitch 

 and excitation. They also allow of comparison with the 

 corresponding columns in the previous papers*, where the 

 motions of belly and air were shown. 



Group V. comprises figs. 40-47 on Plate XII. Here the 

 string is loaded in the middle by having a wire coiled round 

 it and cemented where necessary to preclude all jarring. In 

 the first column of this plate the photographic plates were 

 shot fast ; in the second slow, to obtain more vibrations on a 

 plate and reveal the progressive changes in type due to the 

 inharmonic relation between their partials. In all these figs, 

 the white curves show the bridge's motion lengthwise of the 

 string. The loads used had masses which were respectively 

 0-002, 0*004, and 0'008 of the mass of the string between the 

 bridges. After fig. 12 the attempt to bow the string was 

 abandoned. A moment's reflection will show its difficulty. 

 When the string carries a load at the middle each partial 

 having a node there is unaffected in pitch, i. e. all the 

 evenly-numbered partials. Whereas all the other partials 

 having an anti-node at the middle are flattened by the presence 

 of that load. Hence, when the string is tightened to restore 

 the fundamental tone to its original pitch, all the even 

 partials are sharpened. But the compound vibration excited 

 by the forcing action of the bow must be strictly periodic, 

 and hence by Fourier's theorem all its partials commensurate. 

 Thus when the departure from this state of things is slight 

 the bow can force the partials into tune, but when the de- 

 parture is great the bow refuses to "bite" audit becomes 

 difficult to coax the string to speak with any tolerable quality 

 of tone. 



Accordingly for the figs. 41-17 constituting the second 

 column of Plate XII., plucking only was adopted. And this 

 had the advantage of leaving each partial free to vibrate at 

 its own natural period although inharmonic with the others. 

 The inharmonic character of the partials, of course, causes a 

 slight change in the resultant vibration as their relative 

 phases vary. And this progressive change of type is well 

 shown in these four figures, where the plates were shot 

 slow so as to obtain a number of complete vibrations on each. 

 These curves give a graphic representation of the disturbance 

 * Phil. Mag. July 1905 and Dec. 1906. 

 212 



