EAR AS AN ORGAN FOR SOUND SENSATIONS. 363 



by different musical instruments shows that they may be divided 

 into two great groups: (1) The simple or pendular form; (2) the 

 compound or non-pendular form. The simple or pendular form 

 of wave is given, for instance, by tuning forks. A graphic repre- 

 sentation of this wave form may be obtained by attaching a bristle 

 to the end of the fork and allowing it to write upon a piece of black- 

 ened paper moving with uniform velocity, the blackened surface, 

 for instance, of a kymographion. The form of the wave obtained 

 is represented in Fig. 163. The vibrating body swings symmetrically 

 to each side of the line of rest, and, inasmuch as this is also the form 

 of movement that would be traced by a swinging pendulum, this 

 form of wave is designated frequently as pendular. It is sometimes 

 called also the sinusoidal wave, since the distance of the vibrating 

 point to each side of the line of rest is equal to the sine of an arc 

 increasing proportionally for the time of the phase. A compound 

 (or non-pendular or non-sinusoidal) wave may have a very great 

 variety of forms. The different phases follow periodically, but the 

 movement of the vibrating body to each side of the line of rest is not 



Fig. 163. Form of wave made by tuning fork. 



perfectly symmetrical. Fourier has shown that any periodical vibra- 

 tory movement, whatever may be its form, may be considered as 

 being composed of a series of simple or pendular movements whose 

 periods of vibrations are 1, 2, 3, 4, etc., times as great as the vibra- 

 tion period of the given movement. That is, every so-called com- 

 pound wave form may be considered as being caused by the fusion 

 of a number of simple waves. Representing the wave movement 

 of the air graphically as water waves, this composition of simple 

 waves into compound ones is illustrated by the curves given in Fig. 

 164. In this figure A and B represent two simple vibrations such 

 as would be given by two tuning-forks, the vibrations in B being 

 double those of A. If these two waves are communicated to the air 

 at the same time the actual movement of the molecules will be a 

 resultant of the forces acting upon them at any given instant, and 

 the actual movement will be indicated, therefore, by the algebraical 

 sum of the ordinates above and below the lines of rest. If the 

 movements are so timed that e in curve B is synchronous with d in 

 curve A , then the resulting compound wave form is illustrated by C. 

 If, however, curve B is supposed to be in a different phase, so that e 

 is synchronous with d f , then a form of wave illustrated by D will be 



