THE INTERNAL EAR. 1165 



to the membranous sacs which contain the endolymph, and in which we 

 find the nerve-endings. 



It is also of importance to observe that, as already pointed out (p. 1159), 

 the dimensions of the internal ear are so small as to form only a small part of 

 the wave-lengths even of tones of high pitch. The whole of the membranous 

 labyrinth may be regarded as part of any wave acting on the ear, and the 

 waves are not arrested by the labyrinth as waves of light are arrested by the 

 retina, but they sweep onwards through the bones of the head. The fact of 

 the labyrinth being so small relatively to the size of the wave, makes no 

 difference to the result, so that the labyrinth is acted on in the same way 

 whether a wave of 30 feet in length, such as is produced by the longest pipe 

 in a modern organ, or a wave of two-thirds of an inch, produced by the 

 highest note of a piccolo flute, falls upon the ear. The nerve-endings are still 

 smaller, but they also act as minute portions of any wave, and any reasoning 

 as to the effect of such waves is quite irrespective of the small dimensions of 

 the receiving organs in the internal ear. 



If, now, we consider a wave of sound as a series of states of condensation 

 and states of rarefaction, travelling on continually in one direction ; and, further, 

 if we remember that the motion of each individual particle forming the wave 

 is very small, and is alternately backwards and forwards, in the same line as 

 that in which the wave travels, — we see that the movements, inwards and out- 

 wards, of the base of the stapes correspond to these oscillations, or, in other 

 words, to increase and diminution of pressure with each wave. Further, the 

 length of time occupied by each excursion inwards and outwards of the base 

 of the stapes will correspond to the frequency of the waves, the amplitude of 

 the movement of the stapes to the amplitude of the wave, while the way in 

 which the base of the stapes moves out and in will correspond to the form or 

 character of the wave communicated to it. We also know, from physical 

 experiments, that the frequency of the movements determines pitch, the 

 amplitude intensity or loudness, and the form quality of tone. No doubt it 

 is difficult to appreciate what is termed form of wave when applied to waves 

 of sound, because our ideas of form of wave are derived from our knowledge 

 of waves in which particles move in a direction more or less at right angles 

 to the direction in which the wave travels, as in waves on the surface of 

 water ; and it is difficult to conceive of vibrations of particles in the same 

 direction as that in which the wave progresses, as in a wave of sound. 1 

 Consequently all writers assist the mind in forming ideas of waves by the use 

 of curves representing waves in which the particles vibrate transversely ; but it 

 must never be forgotten that the movements so represented are totally unlike 

 those occurring in waves of sound. 



Suppose the base of the stapes to be at rest, and that any movement 

 inward is called a positive movement, and any movement outward a negative 

 movement, the positive movement would correspond to a positive pressure 

 or condensation, and the negative movement to a negative pressure or 

 rarefaction. Suppose the bone is now moved inwards and outwards through a 

 certain distance, at the same rate, from the two extreme points of its excursion, 

 positive and negative. This is what we may term a simple pendular move- 

 ment or vibration. But it is easy to conceive that, in moving inwards from 

 its position of rest, it might not move to the extreme point of its positive 

 excursion, but only a short distance, say half the distance, when it might 

 move, for an instant, in the opposite direction ; then again reverse its move- 

 ment, and proceed to the limit of its positive excursion ; then swing back to 

 the position of rest ; then move in the negative direction to the extreme point 

 of excursion ; and then, finally, return to the position of rest. This would 



1 Sir G. B. Airy, "On Sound," 2nd edition, London, 1871, p. 22; also plate i. figs. 



6, 7, and 8. 



