STRINGS 77 



time diagram of the point of the string 

 under examination has the simple form 

 shewn in Fig. 30. The nature of the 

 modification in the Lissajous figures may 

 be illustrated in the case of unison 

 between fork and string. If the portion 

 of the broken line in Fig. 30 which lies 

 between A and B be wrapped round a 

 cylinder whose circumference is equal to 

 A B y its projections on planes through 

 the axis will include such forms as are 

 here shewn (Fig. 31)*. 



The period of vibration of the point 

 examined is made up of two intervals, 

 usually of unequal duration, during 

 which the point moves backwards and 

 forwards, respectively, with constant but 

 (in general) unequal velocities. The 

 ratio of the two intervals is further 

 ascertained to be equal to that of the 

 two segments into which the string is 

 divided by the point. These results have 

 been confirmed by subsequent observers 

 who have obtained the space-time dia- 

 gram in a more direct mannerf. In 

 order that they may come out clearly 

 some precautions are necessary. Some- 

 thing depends on the skill with which 

 the bow is used, and apparently on the 

 quality of the instrument. In order, also, 

 that the diagram should be free from 

 minor irregularities the bow should be 



* In the actual experiments of Helmholtz the 

 frequency of the string was four times that of the 

 fork. The circumference of the cylinder in the 

 above mode of representation then includes four 

 periods of the zig-zag line in Fig. 30. 



t Erigar-Menzel and Raps, Wied. Ann., vol. 

 XLIV. (1891). 



