The ear and its diseases

Front matter

r;

THE EAR AND ITS DISEASES

Open Knowledge Commons and Harvard Medical School

Preface

In the preparation of this work I have endeavoured to keep in view the interests of the student, the practitioner, and the aurist. In order to achieve this end satisfactorily, it seemed essential to begin with the first principles, and I have therefore devoted a chapter to the acoustical aspect of the subject. In this portion it was important to bear in mind the requirements of the medical man. Hence my aim has been to discuss the laws of harmonic motion and the transmission of sonorous vibrations, rather than those of harmony which appeal more particularly to the musician.

The anatomy of the subject has been described in considerable detail. With the exception of the brain, there is probably no part of human anatomy more difficult for the student to grasp than that of the temporal bone and the structures which it contains. By means of stereoscopic illustrations and special methods of preparation, I have endeavoured to overcome these difficulties as far as possible.

I have kept in view throughout the book the importance of associating the -clinical phenomena with the pathological conditions present.

The cases and anatomical and pathological preparations from which the illustrations were made, with very few exceptions, are my own. The illustrations also have, in the majority of cases, been made by myself. I am, however, indebted to Dr. Leslie Buchanan for the care which he exercised in obtaining the photomicrographs, and to Dr. D. Otto McGregor for the illustration in Fig. 56.

The drawings of the tympanic membrane were made from vi PREFACE

my own cases by Mr. A. Kirkpatrick Maxwell, and I take this opportunity of thanking him for the trouble which he took in their execution.

The illustrations of instruments are from blocks kindly lent by Messrs. Mayer and Meltzer. A few of the illustrations are from Quain's 'Anatomy/ Politzer's 'Diseases of the Ear/ and from Everett's ' Sound and Vibratory Motion/ I am indebted to the publishers for permission to reproduce these illustrations.

The stereograms have all been made by myself from my own preparations. On examining them with the stereoscope, the great majority of readers will at once obtain the stereoscopic image. Some, however, may require a few minutes' practice to enable them to do this, and there may be a few in whom some visual abnormality prevents the appearance of the solid image. In these the correction of the ocular defect will enable them to obtain the stereoscopic picture.

The stereoscopes (which will be found inserted into the cover) have been made by the firm of R. and J. Beck, and I am much indebted to them for the trouble they have taken in making them optically accurate and at the same time exactly suited for the purpose in view.

I must take this opportunity of thanking Robert F. Muirhead, D.Sc, and my nephew, Dr. Arnold H. Gray, for the great trouble which they took in correcting the manuscript and proofs.

Finally, I must express my indebtedness to the publishers

for their valuable advice and the care they have taken in

the work of publication.

ALBERT A. GRAY.

14, Newton Terrace, Glasgow,

Contents

CHAPTER

I. ACOUSTICS --------

II. ANATOMY AND PHYSIOLOGY OF THE OUTER AND MIDDLE EAR -------

Chapter I Acoustics A

If a rod of wood or other elastic material of suitable length be fixed at one end, it takes up a certain position ; this is termed the position of equilibrium (Fig. i, A). If now the free end be displaced laterally to B and then released, the elasticity of the rod will cause it to spring back to the position of equilibrium, and, having acquired a certain amount of kinetic energy, it will pass through this position and ultimately reach a position C, almost as remote on one side from the position of equilibrium as the original displacement was on the other side. The motion will then be reversed, and so on ; the extent of the movement, however, becomes gradually less, until finally the rod assumes permanently the position of equilibrium. This is an example of harmonic motion, and the movement from B to C and back to B is termed a vibration. If the vibrations are of sufficient magnitude and are performed with sufficient frequency, sound is produced.1

1 Some writers use the term ' vibration ' to indicate the movement from B to C alone. In order to distinguish the two conventions, the term ' single vibration ' should be applied to the latter, while the terms ' complete vibration ' or ' double vibration ' may be used to indicate

Fig. i.

The distance travelled by any particle of the rod from the position of equilibrium to that of extreme displacement is termed the amplitude. The time occupied by a complete vibration from B to C and back to B is termed the period, and the number of periods per second is termed the frequency. Phase in simple harmonic motion is that fraction of the whole period which has elapsed since the particle was last in its position of maximum displacement. Thus, the particle has a different phase at each point of its path, and returns to the same phase after one or any exact number of periods.

It is a general truth that, unless the displacement of any elastic body from its position of equilibrium is very considerable, its frequency remains constant. That is to say, no matter how great or how small the amplitude of the vibration may be, the time occupied by the vibration remains the same. This fact depends upon Hooke's law, the force is proportional to the displacement. Thus, if the rod be displaced i inch by a certain force, then it will require twice that force to displace it 2 inches.

Now, in the case of sound the pitch is dependent entirely on the frequency, and not on the amplitude, and it follows therefore that the pitch will remain constant whatever the amplitude may be. Thus, a tuning-fork, which is simply a rod bent double, will give a note of constant pitch, whether its vibrations be extensive or not. On the other hand, the loudness of a sound, provided the pitch remains constant, depends on the amplitude of the vibrations. If, however, the pitch be altered, this law is subject to limitations of a physiological nature, which will be referred to later.

The sensation of sound, then, is produced by vibrations, which are an example of harmonic motion ; and from what has been said above we may arrive at the following definition of harmonic motion : When a particle is vibrating in a straight line under the influence of a force which urges it towards the middle point of its path, and which varies directly as the distance of the particle from this point, that particle is in simple

the complete movement described above in the text. The contractions v.s. and v.d. are employed to represent the two expressions respectively. In this work it will always be understood that a vibration means a complete or double vibration.

harmonic motion. This is one of the fundamental laws of acoustics.

Suppose a particle to be vibrating along the line AA± (Fig. 2), then its position of equilibrium will be at C. Now describe a circle with AAX as diameter, and let the particle be at a point X in the diameter. Then, according to the definition, the particle is urged towards C by a force represented by XC. From X draw XD at right angles to AAly and join DC. Now, if a particle be moving with uniform / velocity in the circle DBA1B1, we know that it is acted on by a constant force directed towards C. This force is represented by the line DC.

From D draw D Y \\AA1 to meet BB1

at Y. The force DC may be resolved into the two forces DY and DX — that is, into CX and CY respectively. But we have already seen that CX represents the force acting on the particle X when it is undergoing harmonic motion along the line AAV Therefore we may say that, if the path of a particle which is in harmonic motion be taken as the diameter of a circle, and a line be drawn from the particle perpendicular to the path, the point at which the perpendicular meets the circle will travel round the circle with uniform velocity. This circle is called the ' auxiliary circle.1

Since the circle ADBAX represents the path of a particle travelling with uniform velocity, it may be allowed to represent time, and the time of a complete revolution of the particle is represented by the whole circumference. In harmonic motion, however, the particle vibrates along the line AAV and its displacement from the position of equilibrium C at

1 — 2

Fig. 2.

any given moment may be determined by means of the auxiliary circle. Thus, suppose the particle D to be revolving with uniform velocity in the direction AB, and that it has moved from the position A to Z), then the arc AD represents the time it has taken. But if the particle, instead of travelling with uniform velocity round the circle, were oscillating, with the same periodic time, in harmonic motion along the line AAV it would have passed from A to X, and the displacement of the particle from the position of equilibrium will be represented by the line XC. AC is the amplitude of movement of the particle oscillating along AAV Let AC=a, and let XC=x. The angle DCA varies as the arc AD, and therefore represents the time. Let the angle DCA = 9 ; then

This gives us the displacement at a given time of the particle oscillating in harmonic motion between the points AAV

By means of the auxiliary circle it is easy to find the velocity at any given moment of the particle oscillating between A and Av As the particle D moves with uniform velocity towards B, the particle X moves towards C with increasing velocity, and the angle 9 increases with the time. The rate of increase of this velocity is obtained by differentiating equation (i) with respect to 9 :

Hence the velocity of the particle oscillating in harmonic motion along the line AAX varies with the sine of the angle representing the time elapsed since the particle was at A .

A further — and, from the point of view of the aurist, a more important — relationship can now be obtained in respect to the energy of the particle undergoing harmonic motion.

The kinetic energy of any particle in motion is found by

multiplying the mass into half the square of the velocity :

mv E = — , where E = kinetic energy, m = the mass, and v = velocity. But v = a sin 9, and is greatest when sin 9 = ± i (that is, when the particle is passing through the position of equilibrium; C), and is least (that is, zero) when the partide is at the points of extreme displacement, A and A19 for at these points sin 6 = o.

TT 4. • x 77 m(a Sm ^)2 rr

Hence at any given moment E= — — — — ; or, modify-

ing the equation, E = — ' — — , where e represents

the angle measured from any given radius to the line AAV

If, therefore, any particle be undergoing harmonic motion, its capacity for overcoming frictional resistance is greatest when it is passing through the central point of its course — that is, the position of equilibrium ; and, conversely, this capacity is least at the points of extreme displacement.

Again, supposing the mass, m, and the amplitude of movement, a, to remain constant, the velocity, v, will vary according to the ! frequency/ When, for example, the particle performs 200 vibrations per second, it is obvious that the mean velocity must be greater than when the particle performs only 100 vibrations per second. And as the velocity varies, so also does the energy in still greater degree.

On the other hand, the velocity, and therefore the energy, may remain the same when the particle is performing vibrations of different frequencies, provided the amplitude of movement is made to undergo corresponding variations.

Applying these laws to the case of sonorous vibrations, it will be seen that in the case of a note of high pitch — that is, one of great frequency — the same energy may be obtained with movements of small amplitude as may be obtained with movements of great amplitude from notes of low pitch. (It is assumed, of course, that the mass remains constant.) Consequently, if a restriction be placed upon the amplitude of movement, the energy will be restricted to a much greater extent in the case of the low than in the case of the high notes. Now, this has an important practical bearing from the point of view of the aurist, for it enables us to understand why, in the case of middle-ear disease, where the movements of the tympanic membrane or of the ossicles are interfered with, the hearing-power for the low notes is much more seriously affected than that for the high notes. Upon these principles depends one of the most valuable tests for hearing in the deaf (see p. 83).

A graphic representation of simple harmonic motion may be obtained by attaching to the free end of a prong of a deep-toned tuning-fork a piece of spun glass or other light style about \ centimetre in length. A piece of smoked paper is then passed along with uniform velocity parallel with the prong, the style being in contact with the paper. The curve thus traced out represents the movement of the prong, which is an example of simple harmonic motion. The curve itself is called the harmonic curve or the ' curve of sines ' (Fig. 3). Hitherto we have spoken of the motion of the individual particles which are concerned in the generation or transmission of sound. But when sound travels through any medium it travels in the form of waves. The waves of sound, however, are not similar to those produced in a pond of still water by dropping a stone into it. In the latter case the waves are travelling in the plane of the surface of the pond,

Fig. 3.

while the particles of water are moving in circles or ellipses in a plane perpendicular to this and to the wave-front. But when sound is travelling through any medium, the particles oscillate in the plane in which the waves are travelling. In fact, their motions are identical in character with the horizontal components of the motions of the particles of water referred to above. Hence in the case of sound-waves we get alternate condensations and rarefactions of the medium instead of elevations and depressions of the surface. When the transmitting medium is undergoing condensation, the sound-wave is said to be in its ' positive phase,' and, conversely, when the medium is undergoing rarefaction the wave is in its ' negative phase.' This may be expressed in other words by saying that when the particles are moving away from the source of sound they are in the positive phase, and when moving towards the source of sound they are in the negative phase.

It must be remembered therefore that, though for the sake of convenience we represent sound-waves graphically by a curved outline like those of water in a pond, such movement never actually occurs. The particles move in a straight line parallel with the force that produces the sound-waves.

When sound-waves spread out unhindered from the generating instrument, they are subject, like other forces, to the law of inverse squares. Thus, if a tuning-fork be sounded in an open space, the particles of air at a distance of I inch are possessed of a certain amount of energy, those at 2 inches distance are possessed of a quarter of that energy, and those at 3 inches distance of a ninth of the energy, and so on. This lawr has important practical bearings from the point of view of the aurist in respect to the testing of the hearing-power of the deaf. For example, if a patient hears a given sound at half the normal hearing distance, then his hearing-power for that sound has diminished to one-fourth of the normal, not to one-half, as is usually stated. Conversely, if a patient's hearing distance has, as the result of treatment or in the course of nature, been doubled, then his hearing-power has been quadrupled.

Waves vary in length inversely according to their frequency. Thus, a note of the frequency 512 is composed of waves of a length of one-half that of the waves composing a note of a frequency of 256. The normal human ear is capable of hearing all sounds of a certain intensity produced by vibrations of between 16 v.d. and 20,000 to 30,000 v.d. approximately. The lengths of these waves are about 70 feet and § to \ inch respectively, but it must be pointed out that, particularly in regard to the upper limit, considerable individual differences occur without indicating any pathological condition. There is very good reason for supposing that some animals can hear sounds of a higher pitch than man is capable of perceiving.

Pitch is entirely dependent upon the frequency of the vibrations, and notes of small frequency are said to be of low pitch, while those of great frequency are said to be of high pitch.

Simple and Compound Tones. — Hitherto we have only considered the conditions occurring when one series of waves, all of identical length, are passing through the air ; or, expressed in terms of the number of vibrations, when the sound has been produced by one set of vibrations occurring a certain number of times per second. A sound produced by such a series of vibrations is termed a simple tone or a pure tone. But we can easily imagine two or more sets of vibrations traversing the air at the same moment. Thus, one set may consist of 256, and another of 200 or 300 vibrations per second, and so on. The tones produced under such conditions are termed compound tones. Almost all notes used in music and all noises are of this description. Pure tones, such as those produced by a tuning-fork when not sounded too loudly, are certainly very sweet, but musicians would not find them rich enough in quality for the purposes of their art.

The production of a compound tone in music is most easily illustrated by the stringed instrument. Suppose a cord to be stretched between the points A and B (Fig. 4). If this be s

Fig. 4.

set into vibration, the cord from A to B will perform vibrations at a certain rate per second, and will give out a corresponding note. But besides this motion of the cord as a whole, certain portions of it will also vibrate on their own account. Thus, the two portions from A to C and from C to B will vibrate on their own account, and, according to the laws governing the vibrations of strings, they will vibrate twice as rapidly as the whole portion, and will therefore give out a note correspondingly higher in pitch. Similarly, the portions from A to D and D to C, and C to E and E to B, will vibrate independently. With these and other modes of vibration there will arise a series of notes, each of which has a frequency which is an exact multiple of the frequency of the cord vibrating as a whole. The note produced by the cord vibrating as a whole is called the fundamental, while those produced by the separate segments are called the partial tones, overtones, or harmonics. In practice the fundamental determines the name of the note. Thus, if the note G be referred to, that note is meant which has a fundamental tone of a certain frequency corresponding to the pure tone G.

Quality (German, Klangfarbe ; French, Timbre). — Since all notes used in music have partial tones, it will not be out of place to consider the effect these have upon the notes as perceived by the ear. If the note G be sounded upon different instruments, a different sensation will be produced in each case. It is this difference which determines the quality of the note, and which is due to the pitch and intensity of the partial tones present. Thus, in the case of the violin the partial tones present are high and of considerable intensity relative to the fundamental, whereas in the organ this feature is much less pronounced.

Interference. — When two independent sources of sound produce vibrations simultaneously in the same region, interference occurs. If the two notes have the same period, then there are some points at which, at a given instant, both sources are producing condensations, and some at which one source is producing condensations and the other rarefactions. At the points first mentioned the sound is reinforced, and this reinforcement is permanent. At the other points the sounds neutralize each other, more or less, and this condition is also permanent. If the ear moves through this region, it passes alternately points of both sorts, and perceives a periodic variation in the loudness of the sound passing from reinforcement to neutralization and back.

Beats. — This periodic change of loudness is also produced when two notes, whose frequencies differ by only a small number, are produced in the same region. At any given instant the sounds reinforce or neutralize one another, but the position of the points is no longer fixed, and the ear, if stationary, perceives the same periodic variations of loudness as it did in the previously described case when in motion. Take, for example, the case of two notes whose frequencies are respectively 256 and 257. If at any instant condensations (or rarefactions) arrive at the ear simultaneously from both sources, then this state of affairs will only last for a short time. At the end of half a second the condensation produced by one of the sources of sound will coincide with the rarefaction produced by the other source, which by this time will lag half a period behind. Half a second later, again, reinforcement will be re-established, to give place again to neutralization, and so on.

It is clear from this that the frequency of the periodic changes of loudness, which is called beating, will be exactly equal to the differences between the frequencies of the two notes ; e.g., notes of frequencies of 500 and 506 will give beats of 6 per second.

Beats are also produced by compound notes, provided any harmonic of one differs only slightly in frequency from any of the others or their harmonics. Since each harmonic is, except in frequency, physically identical in character with a pure fundamental note, the explanation in this case is the same. As an example, we might hear beats of a frequency of 2 from notes whose frequencies are 258 and 386 respectively, if the former contains the harmonic 3 x 258 and the latter the harmonic 2 X 386, because these frequencies differ by 2.

Beats when occurring slowly are not unpleasant to the ear, but when rapid they give a jerky effect which is disagreeable. If the beats occur still more rapidly, above about 20 per second or more, then they are no longer perceived as beats by the ear, but a new and interesting phenomenon occurs. The beats blend to form a new tone, whose frequency is still equal to the difference between the frequencies of the two generating tones. This new tone is therefore called the differential tone or beat tone. According to Helmholtz, another tone is also heard under such circumstances, this tone having a frequency equal to the sum of the frequencies of the two generating tones — i.e., in the particular case cited, a frequency equal to 258 + 386=644 vibrations per second. Helmholtz termed this the summational tone. Many observers cannot hear any such tone, and some doubt its existence altogether.

There has been much discussion as to the point of origin of these differential and summational tones. According to some authorities, they arise in the air, while others hold that they are purely subjective and are generated in the mind of the listener. The reader will find the matter discussed in the ' Textbook of Physiology/ vol. ii., p. 1187, chapter by McKendrick and Gray, edited by Schafer. Other references to the subject will also be found there.

ACOUSTICS ii

Analysis. — When two or more pure notes of different frequencies are sounded together, the ear can, by a certain degree of effort, analyze the compound tone thus produced. The faculty of being able to analyze compound notes in this way varies greatly in individuals, and the possession of it in a high degree underlies what is termed a ' good ear for music/ Thus, if a chord be sounded on the piano, an individual possessing a good musical ear will be able to hear as such the various pure tones of which it is composed. It must be understood that these must be present with a certain degree of intensity. This power of analysis of sounds composed of various pure tones is only present to a limited degree even in the finest musical ears. Thus, a noise as distinguished from a musical note can never be entirely analyzed into its constituents, yet there is no doubt that physically it also is composed ultimately of simple pure tones.

There is, however, a mechanical means by which the ear may be assisted in analyzing compound notes, and to a certain extent even noises. This will be referred to under the heading Sympathetic Resonance.

Before leaving the subject of analysis of compound tones, it is necessary to say a few words on the mathematical aspect of the question. Suppose a compound note be represented graphically by a curve. This curve will in general be irregular in proportion to the number and frequencies of the pure tones which go to produce the compound tone which it represents. Further, however complicated such a curve may be, it will ultimately come to repeat itself, provided the quality of the sound remains unaltered.

Now, Fourier, the mathematician, showed that such a curve, however complex, could be finally analyzed into a series of simple harmonic curves, whose periods are submultiples of the fundamental, each representing one of the pure tones of which the compound tone is composed. This is known as Fourier's theorem. It of course applies to other quantities than those representing sonorous vibrations, but with these we have nothing to do at present. The important point to remember is, that within certain limits the ear performs for us an analysis of compound tones, comparable with that which the mathematician can do with the abstract quantities which represent such notes.

Communication of Vibrations ; Sympathetic Resonance.

All vibrating bodies communicate their motion to surrounding media and to any other body that may be in proximity. Thus, a tuning-fork sets the air in vibration, and the air sets the tympanic membrane or any other object such as the walls of the room and various objects in it, in vibration. In this process some of the energy is transformed into heat, but if the structure be not too massive and be elastic in character, such as a stretched membrane or a thin board of wood, it will begin to vibrate with the same frequency as the instrument which generates the sound.

Such are termed forced vibrations, in contradistinction to what we now proceed to describe as free vibrations.

Suppose two tuning-forks of exactly the same pitch (that is, of the same frequency) be placed in proximity to each other, and one of these be set vibrating, it will be found that after a short interval the other fork begins to vibrate ; and if the first fork be stopped, the second one is still heard to be sounding loudly. Let us consider what has occurred in this case. The moment the first fork is set vibrating, the vibrations are transmitted by the air to the second fork, and this is displaced for a certain length of time, according to the pitch of the forks. At the end of this period the particles of air surrounding the second fork begin to move in the opposite direction, and tend to drag it back with them. There thus occurs an accumulation of energy in the second fork, and after a few vibrations have taken place the resulting movement is of such an amplitude as to produce a sound quite audible. Further, the amplitude of movement being so great, the inherent elasticity of the second fork keeps up the movement for some considerable time after the first fork has been stopped. Vibrations which continue after the exciting cause has ceased acting are called ' free vibrations,' and the whole phenomenon is known as sympathetic resonance. There is, of course, no necessity for the two instruments to be of the same kind ; all that is requisite is that the period of vibration of the generating instrument be the same as that of the sympathizing or resonating instrument. For scientific purposes the instrument generally used as a sympathizer, or resonator as it is called, is a hollow brass sphere which has two openings at opposite poles (Fig. 5). The larger opening, about 2 centimetres in diameter, is to allow the vibrations to gain entrance from the air ; while the smaller opening, of about 5 millimetres diameter, is placed at the end of a little cone-shaped pro- Sj