THE EAR AND HEARING. 567 



which is repeated exactly on the other side of the abscissa, 

 are known as pendular vibrations. 



The Composition of Vibrations. The vibrations of a 

 seconds pendulum set the air-particles in contact with it in 

 similar movement, but the aerial waves succeed one another 

 too slowly to produce in us the sensation of a musical note. 

 If, for the pendulum, we substitute a tuning-fork (the prongs 

 of which move in a like way), and the fork vibrates 132 times 

 per 1", then 132 aerial waves will fall on the tympanic mem- 

 brane in that time, and we will hear the note c of the unac- 

 cented octave. If the larger continuous curve in Fig. 169 

 represent the aerial vibrations in this case, the distance to 

 1 on the abscissa will represent T ^ of a second. Let, simul- 

 taneously, the air be set in movement by a fork of the next 

 higher octave, c', making 264 vibrations per 1"; under the 

 influence of this second fork alone, the aerial particles would 

 move as represented by the line 0, b 1 , b 3 , and so on, the 

 waves being half as long and cutting the abscissa twice as 

 often. But when both forks act together the aerial move- 

 ment will be the algebraic sum of tjhe movements due to 

 each fork; when both drive the air one way they will rein- 

 force one another, and vice versa; the result will be the 

 movement represented by the dotted line, which is still 

 periodic, repeating itself at equal intervals of time, but no 

 longer pendular, since it is not alike on the ascending and 

 descending limbs of the curves. We thus get at the fact 

 that non-pendular vibrations may be produced by the fu- 

 sion of pendular, or, in technical phrase, by their compo- 

 sition. 



Suppose several musical instruments, as those of an or- 

 chestra, to be sounded together. Each produces its own 

 effect- on the air-particles, whose movements, being the alge- 

 braical sum of those due to all, must at any given instant be 

 very complex; yet the ear can pick out at will arid follow the 

 tones of any one instrument. From the complex aerial 

 movement it can select that fraction of it which one vibrat- 

 ing body produces. The air in the external auditory meatus 

 at any given moment can only be in one state of rarefaction 

 or condensation and at one rate and in one direction of move- 

 ment, this being the resultant of all the forces acting upon 

 it; all clashing, and some pushing one way and others an- 

 other. If the resultant movement be not periodic it will be 



