mm. Other observations have shown the movements at the stapes to have a

still smaller amplitude, varying from 0.001 to 0.032 mm. With tones of feeble intensity the movements must be almost infinitesimal. There may also be very minute transverse movements at the base of the stapes.

3. _Transmission in the Internal Ear._--The internal ear is composed of the labyrinth, formed of the vestibule or central part, the semicircular canals, and the cochlea, each of which consists of an osseous and a membranous portion. The osseous labyrinth may be regarded as an osseous mould in the petrous portion of the temporal bone, lined by tesselated endothelium, and containing a small quantity of fluid called the _perilymph_. In this mould, partially surrounded by, and to some extent floating in, this fluid, there is the membranous labyrinth, in certain parts of which we find the terminal apparatus in connexion with the auditory nerve, immersed in another fluid called the _endolymph_. The membranous labyrinth consists of a vestibular portion formed by two small sac-like dilatations, called the _saccule_ and the _utricle_, the latter of which communicates with the semicircular canals by five openings. Each canal consists of a tube, bulging out at each extremity so as to form the so-called _ampulla_, in which, on a projecting ridge, called the _crista acustica_, there are cells bearing long _auditory hairs_, which are the peripheral end-organs of the vestibular branches of the auditory nerve. The cochlear division of the membranous labyrinth consists of the _ductus cochlearis_, a tube of triangular form fitting in between the two cavities in the cochlea, called the _scala vestibuli_, because it commences in the vestibule, and the _scala tympani_, because it ends in the tympanum, at the round window. These two scalae communicate at the apex of the cochlea. The roof of the ductus cochlearis is formed by a thin membrane called the _membrane of Reissner_, while its floor consists of the _basilar membrane_, on which we find the remarkable _organ of Corti_, which constitutes the terminal organ of the cochlear division of the auditory nerve. It is sufficient to state here that this organ consists essentially of an arrangement of epithelial cells bearing hairs which are in communication with the terminal filaments of this portion of the auditory nerve, and that groups of these hairs pass through holes in a closely investing membrane, _membrana reticularis_, which may act as a damping apparatus, so as quickly to stop their movements. The ductus cochlearis and the two scalae are filled with fluid. Sonorous vibrations may reach the fluid in the labyrinth by three different ways--(1) by the osseous walls of the labyrinth, (2) by the air in the tympanum and the round window, and (3) by the base of the stapes inserted into the oval window.

When the head is plunged into water, or brought into direct contact with any vibrating body, vibrations must be transmitted directly. Vibrations of the air in the mouth and in the nasal passages are also communicated directly to the walls of the cranium, and thus pass to the labyrinth. In like manner, we may experience auditive sensations, such as blowing, rubbing and hissing sounds, due to muscular contraction or to the passage of blood in vessels close to the auditory organ. It is doubtful whether any vibrations are communicated to the fluid in the labyrinth by the round window. Vibrations which cause hearing are communicated by the chain of bones. When the base of the stirrup is pushed into the oval window, the pressure in the labyrinth increases, and, as the only mobile part of the wall of the labyrinth is the membrane covering the round window, this membrane is forced outwards; when the base of the stirrup moves outwards a reverse action takes place. Thus the fluid of the labyrinth receives a series of pulses isochronous with the movements of the base of the stirrup, and these pulses affect the terminal apparatus in connexion with the auditory nerve.

The sacs of the internal ear, known as the utricle and saccule, receive the impulses of the base of the stapes. They are organs connected with the perception of sounds as sounds, without reference to pitch or quality. For the _analysis_ of tone a cochlea is necessary. Even in mammals all the parts of the ear may be destroyed or affected by disease, except these sacs, without causing complete deafness.

It has been suggested by Lee (_Amer. Jour. of Physiol._ vol. i. No. 1, p. 128) that in fishes the sac has nothing to do with hearing, but serves for the perception of movements, such as those of rotation and translation through space, movements much coarser than those that form the physical basis of sound. He considers, also, that as fishes, with few exceptions, are dumb, they are also deaf. In the fish there are peculiar organs along the lateral line which are known to be connected with the perception of movements of the body as a whole, and Beard (_Zool. Anz. Leipzig_, 1884, Bd. vii. S. 140) has attempted to trace a phylogenetic connexion between the sacs of the internal ear and the organs in the lateral line. According to this view, when animals became air-breathers, a part of the ear (the _papilla acustica basilaris_) was gradually evolved for the perception of delicate vibrations of sound. (See EQUILIBRIUM.)

It is by means of the cochlea that we discriminate pitch, hear beats, and are affected by quality of tone.

Since the size of the membranous labyrinth is so small, measuring, in man, not more than 1/2 in. in length by 1/8 in. in diameter at its widest part, and since it is a chamber consisting partly of conduits of very irregular form, it is impossible to state accurately the course of vibrations transmitted to it by impulses communicated from the base of the stirrup. In the cochlea vibrations must pass from the saccule along the scala vestibuli to the apex, thus affecting the membrane of Reissner, which forms its roof; then, passing through the opening at the apex (the _helicotrema_), they must descend by the scala tympani to the round window, and affect in their passage the membrana basilaris, on which the organ of Corti is situated. From the round window impulses must be reflected backwards, but how they affect the advancing impulses is not known. But the problem is even more complex when we take into account the fact that impulses are transmitted simultaneously to the utricle and to the semicircular canals communicating with it by five openings. The mode of action of these vibrations or impulses upon the nervous terminations is still unknown; but to appreciate critically the hypothesis which has been advanced to explain it, it is necessary, in the first place, to refer to some of the general characters of auditory sensation.

4. _General Characters of Auditory Sensations._--Certain conditions are necessary for excitation of the auditory nerve sufficient to produce a sensation. In the first place, the vibrations must have a certain _amplitude_ and _energy_; if too feeble, no impression will be produced.

Various physicists have attempted to measure the sensitiveness of the ear by estimating the amplitude of the molecular movements necessary to call forth the feeblest audible sound. Thus A. Topler and L. Boltzmann, on data founded on experiments with organ pipes, state that the ear is affected by vibrations of molecules of the air not more in amplitude than .0004 mm. at the ear, or 0.1 of the wave-length of green light, and that the energy of such a vibration on the drum-head is not more than 1/543 billionth kilog., or 1/17th of that produced upon an equal surface of the retina by a single candle at the same distance (_Ann. d. Phys. u. Chem._, Leipzig. 1870, Bd. cxli. S. 321). Lord Rayleigh, by two other methods, arrived at the conclusion "that the streams of energy required to influence the eye and ear are of the same order of magnitude." He estimated the amplitude of the movement of the aerial particles, with a sound just audible, as less than the ten-millionth of a centimetre, and the energy emitted when the sound was first becoming audible, at 42.1 ergs per second. He also states that in considering the amplitude or condensation in progressive aerial waves, at a distance of 27.4 metres from a tuning-fork, the maximum condensation was = 6.0 X 10^-9 cm., a result showing "that the ear is able to recognize the addition or subtraction of densities far less than those to be found in our highest vacua" (_Proc. Roy. Soc._, 1877, vol. xxvi. p. 248; _Lond. Edin. and Dub. Phil. Mag._, 1894, vol. xxxviii. p. 366).

In the next place, vibrations must have a certain _duration_ to be perceived; and lastly, to excite a sensation of a continuous musical sound, a certain _number_ of impulses must occur in a given interval of time. The lower limit is about 30, and the upper about 30,000 vibrations per second. Below 30, the individual impulses may be observed, and above 30,000 few ears can detect any sound at all. The extreme upper limit is not more than 35,000 vibrations per second. Auditory sensations are of two kinds--noises and musical sounds. _Noises_ are caused by impulses which are not regular in intensity or duration, or are not periodic, or they may be caused by a series of musical sounds occurring instantaneously so as to produce discords, as when we place our hand at random on the keyboard of a piano. _Musical tones_ are produced by periodic and regular vibrations. In musical sounds three characters are prominent--intensity, pitch and quality. _Intensity_ depends on the amplitude of the vibration, and a greater or lesser amplitude of the vibration will cause a corresponding movement of the transmitting apparatus, and a corresponding intensity of excitation of the terminal apparatus. _Pitch_, as a sensation, depends on the length of time in which a single vibration is executed, or, in other words, the number of vibrations in a given interval of time. The ear is capable of appreciating the relative pitch or height of a sound as compared with another, although it may not ascertain precisely the absolute pitch of a sound. What we call an acute or high tone is produced by a large number of vibrations, while a grave or low tone is caused by few. The musical tones which can be used with advantage range between 40 and 4000 vibrations per second, extending thus from 6 to 7 octaves. According to E. H. Weber, practised musicians can perceive a difference of pitch amounting to only the 1/64th of a semitone, but this is far beyond average attainment. In a few individuals, and especially in early life, there may be an appreciation of absolute pitch. _Quality_ or _timbre_ (or _Klang_) is that peculiar characteristic of a musical sound by which we may identify it as proceeding from a particular instrument or from a particular human voice. It depends on the fact that many waves of sound that reach the ear are compound wave systems, built up of constituent waves, each of which is capable of exciting a sensation of a simple tone if it be singled out and reinforced by a resonator (see SOUND), and which may sometimes be heard without a resonator, after special practice and tuition. Thus it appears that the ear must have some arrangement by which it resolves every wave system, however complex, into simple pendular vibrations. When we listen to a sound of any quality we recognize that it is of a certain pitch. This depends on the number of vibrations of one tone, predominant in intensity over the others, called the fundamental or ground tone, or first partial tone. The quality, or timbre, depends on the number and intensity of other tones added to it. These are termed _harmonic_ or _partial tones_, and they are related to the first partial or fundamental tone in a very simple manner, being multiples of the fundamental tone: thus--

Fundamental Upper Partials or Harmonics. Tone Notes do^1 do^2 sol^2 do^3 mi^3 sol^3 si[flat]^3 do^4 re^4 mi^4 Partial tones 1 2 3 4 5 6 7 8 9 10 Number of vibrations 33 66 99 132 165 198 231 264 297 330

When a simple tone, or one free from partials, is heard, it gives rise to a simple, soft, somewhat insipid sensation, as may be obtained by blowing across the mouth of an open bottle or by a tuning-fork. The lower partials added to the fundamental tone give softness combined with richness; while the higher, especially if they be very high, produce a brilliant and thrilling effect, as is caused by the brass instruments of an orchestra. Such being the facts, how may they be explained physiologically?

Little is yet known regarding the mode of action of the vibrations of the fluid in the labyrinth upon the terminal apparatus connected with the auditory nerve. There can be no doubt that it is a mechanical action, a communication of impulses to delicate hair-like processes, by the movements of which the nervous filaments are irritated. In the human ear it has been estimated that there are about 3000 small arches formed by the _rods of Corti._ Each arch rests on the basilar membrane, and supports rows of cells having minute hair-like processes. It would appear also that the filaments of the auditory nerve terminate in the basilar membrane, and possibly they may be connected with the hair-cells. At one time it was supposed by Helmholtz that these fibres of Corti were elastic and that they were tuned for particular sounds, so as to form a regular series corresponding to all the tones audible to the human ear. Thus 2800 fibres distributed over the tones of seven octaves would give 400 fibres for each octave, or nearly 33 for a semitone. Helmholtz put forward the hypothesis that, when a pendular vibration reaches the ear, it excites by sympathetic vibration the fibre of Corti which is tuned for its proper number of vibrations. If, then, different fibres are tuned to tones of different pitch, it is evident that we have here a mechanism which, by exciting different nerve fibres, will give rise to sensations of pitch. When the vibration is not simple but compound, in consequence of the blending of vibrations corresponding to various harmonics or partial tones, the ear has the power of resolving this compound vibration into its elements. It can only do so by different fibres responding to the constituent vibrations of the sound--one for the fundamental tone being stronger, and giving the sensation of a particular pitch to the sound, and the others, corresponding to the upper partial tones, being weaker, and causing undefined sensations, which are so blended together in consciousness as to terminate in a complex sensation of a tone of a certain quality or timbre. It would appear at first sight that 33 fibres of Corti for a semitone are not sufficient to enable us to detect all the gradations of pitch in that interval, since, as has been stated above, trained musicians may distinguish a difference of 1/64th of a semitone. To meet this difficulty, Helmholtz stated that if a sound is produced, the pitch of which may be supposed to come between two adjacent fibres of Corti, both of these will be set into sympathetic vibration, but the one which comes nearest to the pitch of the sound will vibrate with greater intensity than the other, and that consequently the pitch of that sound would be thus appreciated. These theoretical views of Helmholtz have derived much support from experiments of V. Hensen, who observed that certain hairs on the antennae of _Mysis_, a Crustacean, when seen with a low microscopic power, vibrated with certain tones produced by a keyed horn. It was seen that certain tones of the horn set some hairs into strong vibration, and other tones other hairs. Each hair responded also to several tones of the horn. Thus one hair responded strongly to d[sharp] and d'[sharp], more weakly to g, and very weakly to G. It was probably tuned to some pitch between d" and d"[sharp]. (_Studien uber das Gehororgan der Decapoden_, Leipzig, 1863.)

Histological researches have led to a modification of this hypothesis. It has been found that the rods or arches of Corti are stiff structures, not adapted for vibrating, but apparently constituting a support for the hair-cells. It is also known that there are no rods of Corti in the cochlea of birds, which are capable nevertheless of appreciating pitch. Hensen and Helmholtz suggested the view that not only may the segments of the membrana basilaris be stretched more in the radial than in the longitudinal direction, but different segments may be stretched radially with different degrees of tension so as to resemble a series of tense strings of gradually increasing length. Each string would then respond to a vibration of a particular pitch communicated to it by the hair-cells. The exact mechanism of the hair-cells and of the membrana reticularis, which looks like a damping apparatus, is unknown.

5. _Physiological Characters of Auditory Sensation._--Under ordinary circumstances auditory sensations are referred to the outer world. When we hear a sound, we associate it with some external cause, and it appears to originate in a particular place or to come in a particular direction. This feeling of _exteriority_ of sound seems to require transmission through the membrana tympani. Sounds which are sent through the walls of the cranium, as when the head is immersed in, and the external auditory canals are filled with, water, appear to originate in the body itself.

An auditory sensation lasts a short time after the cessation of the exciting cause, so that a number of separate vibrations, each capable of exciting a distinct sensation if heard alone, may succeed each other so rapidly that they are fused into a single sensation. If we listen to the puffs of a syren, or to vibrating tongues of low pitch, the single sensation is usually produced by about 30 or 35 vibrations per second; but when we listen to beats of considerable intensity, produced by two adjacent tones of sufficiently high pitch, the ear may follow as many as 132 intermissions per second.

The sensibility of the ear for sounds of different pitch is not the same. It is more sensitive for acute than for grave sounds, and it is probable that the maximum degree of acuteness is for sounds produced by about 3000 vibrations per second, that is near fa^5[sharp]. Sensibility as to pitch varies much with the individual. Thus some musicians may detect a difference of 1/1000th of the total number of vibrations, while other persons may have difficulty in appreciating a semitone.

6. _Analytical Power of the Ear._--When we listen to a compound tone, we have the power of picking out these partials from the general mass of sound. It is known that the frequencies of the partials as compared with that of the fundamental tone are simple multiples of the frequency of the fundamental, and also that physically the waves of the partials so blend with each other as to produce waves of very complicated forms. Yet the ear, or the ear and the brain together, can resolve this complicated wave-form into its constituents, and this is done more easily if we listen to the sound with resonators, the pitch of which corresponds, or nearly corresponds, to the frequencies of the partials. Much discussion has taken place as to how the ear accomplishes this analysis. All are agreed that there is a complicated apparatus in the cochlea which may serve this purpose; but while some are of opinion that this structure is sufficient, others hold that the analysis takes place in the brain. When a complicated wave falls on the drum-head, it must move out and in in a way corresponding to the variations of pressure, and these variations will, in a single vibration, depend on the greater or less degree of complexity of the wave. Thus a single tone will cause a movement like that of a pendulum, a simple pendular vibration, while a complex tone, although occurring in the same duration of time, will cause the drum-head to move out and in in a much more complicated manner. The complex movement will be conveyed to the base of the stapes, thence to the vestibule, and thence to the cochlea, in which we find the ductus cochlearis containing the organ of Corti. It is to be noted also that the parts in the cochlea are so small as to constitute only a fraction of the wave-length of most tones audible to the human ear. Now it is evident that the cochlea must act either as a whole, all the nerve fibres being affected by any variations of pressure, or the nerve fibres may have a selective action, each fibre being excited by a wave of a definite period, or there may exist small vibratile bodies between the nerve filaments and the pressures sent into the organ. The last hypothesis gives the most rational explanation of the phenomena, and on it is founded a theory generally accepted and associated with the names of Thomas Young and Hermann Helmholtz. It may be shortly stated as follows:--

"(1) In the cochlea there are vibrators, tuned to frequencies within the limits of hearing, say from 30 to 40,000 or 50,000 vibs. per second. (2) Each vibrator is capable of exciting its appropriate nerve filament or filaments, so that a nervous impulse, corresponding to the frequency of the vibrator, is transmitted to the brain--not corresponding necessarily, as regards the number of nervous impulses, but in such a way that when the impulses along a particular nerve filament reach the brain, a state of consciousness is aroused which does correspond with the number of the physical stimuli and with the period of the auditory vibrator. (3) The mass of each vibrator is such that it will be easily set in motion, and after the stimulus has ceased it will readily come to rest. (4) Damping arrangements exist in the ear, so as quickly to extinguish movements of the vibrators. (5) If a simple tone falls on the ear, there is a pendular movement of the base of the stapes, which will affect all the parts, causing them to move; but any part whose natural period is nearly the same as that of the sound will respond on the principle of sympathetic resonance, a particular nerve filament or nerve filaments will be affected, and a sensation of a tone of definite pitch will be experienced, thus accounting for discrimination in pitch. (6) Intensity or loudness will depend on the amplitude of movement of the vibrating body, and consequently on the intensity of nerve stimulation. (7) If a compound wave of pressure be communicated by the base of the stapes, it will be resolved into its constituents by the vibrators corresponding to tones existing in it, each picking out its appropriate portion of the wave, and thus irritating corresponding nerve filaments, so that nervous impulses are transmitted to the brain, where they are fused in such a way as to give rise to a sensation of a particular quality or character, but still so imperfectly fused that each constituent, by a strong effort of attention, may be specially recognized" (article "Ear," by M'Kendrick, Schafer's _Text-Book_, _loc. cit._).

The structure of the ductus cochlearis meets the demands of this theory, it is highly differentiated, and it can be shown that in it there are a sufficient number of elements to account for the delicate appreciation of pitch possessed by the human ear, and on the basis that the highly trained ear of a violinist can detect a difference of 1/64th of a semitone (M'Kendrick, _Trans. Roy. Soc. Ed._, 1896, vol. xxxviii. p. 780; also Schafer's _Text-Book_, loc. cit.). Measurements of the cochlea have also shown such differentiation as to make it difficult to imagine that it can act as a whole. A much less complex organ might have served this purpose (M'Kendrick, _op. cit._). The following table, given by Retzius (_Das Gehororgan der Wirbelthiere_, Bd. ii. S. 356), shows differentiations in the cochlea of man, the cat and the rabbit, all of which no doubt hear tones, although in all probability they have very different powers of discrimination:--

Man. Cat. Rabbit.

Ear-teeth 2,490 2,430 1,550 Holes in habenula for nerves 3,985 2,780 1,650 Inner rods of Corti's organ 5,590 4,700 2,800 Outer rods of Corti's organ 3,848 3,300 1,900 Inner hair-cells (one row) 3,487 2,600 1,600 Outer hair-cells (several rows) 11,750 9,900 6,100 Fibres in basilar membrane 23,750 15,700 10,500

7. _Dissonance._--The theory can also be used to explain dissonance. When two tones sufficiently near in pitch are simultaneously sounded, beats are produced. If the beats are few in number they can be counted, because they give rise to separate and distinct sensations; but if they are numerous they blend so as to give roughness or dissonance to the interval. The roughness or dissonance is most disagreeable with about 33 beats falling on the ear per second. When two compound tones are sounded, say a minor third on a harmonium in the lower part of the keyboard, then we have beats not only between the primaries, but also between the upper partials of each of the primaries. The beating distance may, for tones of medium pitch, be fixed at about a minor third, but this interval will expand for intervals on low tones and contract for intervals on high ones. This explains why the same interval in the lower part of the scale may give slow beats that are not disagreeable, while in the higher part it may cause harsh and unpleasant dissonance. The partials up to the seventh are beyond beating distance, but above this they come close together. Consequently instruments (such as tongues, or reeds) that abound in upper partials cause an intolerable dissonance if one of the primaries is slightly out of tune. Some intervals are pleasant and satisfying when produced on instruments having few partials in their tones. These are concords. Others are less so, and they may give rise to an uncomfortable sensation. These are discords. In this way unison, 1/1, minor third 6/5, major third 5/4, fourth 4/3, fifth 3/2, minor sixth 8/5, major sixth 5/3 and octave 2/1, are all concords; while a second 9/8, minor seventh 16/9 and major seventh 15/8, are discords. Helmholtz compares the sensation of dissonance to that of a flickering light on the eye. "Something similar I have found to be produced by simultaneously stimulating the skin, or margin of the lips, by bristles attached to tuning-forks giving forth beats. If the frequency of the forks is great, the sensation is that of a most disagreeable tickling. It may be that the instinctive effort at analysis of tones close in pitch causes the disagreeable sensation" (Schafer's _Text-Book_, _op. cit._ p. 1187).

8. _Other Theories._--In 1865 Rennie objected to the analysis theory, and urged that the cochlea acted as a whole (_Ztschr. f. rat. Med._, Dritte Reihe, Bd. xxiv. Heft 1, S. 12-64). This view was revived by Voltolini (Virchow's _Archiv_, Bd. c. S. 27) some years later, and in 1886 it was urged by E. Rutherford (_Rep. Brit. Assoc. Ad. Sc._, 1886), who compared the action of the cochlea to that of a telephone plate. According to this theory, all the hairs of the auditory cells vibrate to every note, and the hair-cells transform sound vibrations into nerve vibrations or impulses, similar in frequency, amplitude and character to the sound vibrations. There is no analysis in the peripheral organ. A. D. Waller, in 1891 (_Proc. Physiol. Soc._, Jan. 20, 1891) suggested that the basilar membrane as a whole vibrates to every note, thus repeating the vibrations of the membrana tympani; and since the hair-cells move with the basilar membrane, they produce what may be called pressure patterns against the tectorial membranes, and filaments of the auditory nerve are stimulated by these pressures. Waller admits a certain degree of peripheral analysis, but he relegates ultimate analysis to the brain. These theories, dispensing with peripheral analysis, leave out of account the highly complex structure of the cochlea, or, in other words, they assign to that structure a comparatively simple function which could be performed by a simple membrane capable of vibrating. We find that the cochlea becomes more elaborate as we ascend the scale of animals, until in man, who possesses greater powers of analysis than any other being, the number of hair-cells, fibres of the basilar membrane and arches of Corti are all much increased in number (see Retzius's table, _supra_). The principle of sympathetic resonance appears, therefore, to offer the most likely solution of the problem. Hurst's view is that with each movement of the stapes a wave is generated which travels up the scala vestibuli, through the helicotrema into the scala tympani and down the latter to the fenestra rotunda. The wave, however, is not merely a movement of the basilar membrane, but an actual movement of fluid or a transmission of pressure. As the one wave ascends while the other descends, a pressure of the basilar membrane occurs at the point where they meet; this causes the basilar membrane to move towards the tectorial membrane, forcing this membrane suddenly against the apices of the hair-cells, thus irritating the nerves. The point at which the waves meet will depend on the time interval between the waves (Hurst, "A New Theory of Hearing," _Trans. Biol. Soc. Liverpool_, 1895, vol. ix. p. 321). More recently Max Mayer has advanced a theory somewhat similar. He supposes that with each movement of the stapes corresponding to a vibration, a wave travels up the scala vestibuli, pressing the basilar membrane downwards. As it meets with resistance in passing upwards, its amplitude therefore diminishes, and in this way the distance up the scala through which the wave progresses will be determined by its amplitude. The wave in its progress irritates a certain number of nerve terminations, consequently feeble tones will irritate only those nerve fibres that are near the fenestra ovalis, while stronger tones will pass farther up and irritate a larger number of nerve fibres the same number of times per unit of time. Pitch, according to this view, depends on the number of stimuli per second, while loudness depends on the number of nerve fibres irritated. Mayer also applies the theory to the explanation of the powers of the cochlea as an analyser, by supposing that with a compound tone these are at maxima and minima of stimulation. As the compound wave travels up the scala, portions of the wave corresponding to maxima and minima die away in consecutive series, until only a maximum and minimum are left; and, finally, as the wave travels farther, these also disappear. With each maximum and minimum different parts of the basilar membrane are affected, and affected a different number of times per second, according to the frequencies of the partials existing in the compound tone. Thus with a fifth, 2 : 3, there are three maxima and three minima; but the compound tone is resolved into three tones having vibration frequencies in the ratio of 3 : 2 : 1. According to Mayer, we actually hear when a fifth is sounded tones of the relationship of 3 : 2 : 1, the last (1) being the differential tone. He holds, also, that combinational tones are entirely subjective (Max Mayer, _Ztschr. f. Psych. und Phys. d. Sinnesorgane_, Leipzig, Bd. xvi. and xvii.; also _Verhandl. d. physiolog. Gesellsch. zu Berlin_, Feb. 18, 1898, S. 49). Two fatal objections can be urged to these theories, namely, first, it is impossible to conceive of minute waves following each other in rapid succession in the minute tubes forming the scalae--the length of the scala being only a very small part of the wave-length of the sound; and, secondly, neither theory takes into account the differentiation of structure found in the epithelium of the organ of Corti. Each push in and out of the base of the stapes must cause a movement of the fluid, or a pressure, in the scalae as a whole.

There are difficulties in the way of applying the resonance theory to the perception of noises. Noises have pitch, and also each noise has a special character; if so, if the noise is analysed into its constituents, why is it that it seems impossible to analyse a noise, or to perceive any musical element in it? Helmholtz assumed that a sound is noisy when the wave is irregular in rhythm, and he suggested that the crista and macula acustica, structures that exist not in the cochlea but in the vestibule, have to do with the perception of noise. These structures, however, are concerned rather in the sense of the perception of equilibrium than of sound (see EQUILIBRIUM).

9. Hitherto we have considered only the audition of a single sound, but it is possible also to have simultaneous auditive sensations, as in musical harmony. It is difficult to ascertain what is the limit beyond which distinct auditory sensations may be perceived. We have in listening to an orchestra a multiplicity of sensations which produces a total effect, while, at the same time, we can with ease single out and notice attentively the tones of one or two special instruments. Thus the pleasure of music may arise partly from listening to simultaneous, and partly from the effect of contrast or suggestion in passing through successive, auditory sensations.

The principles of harmony belong to the subject of music (see HARMONY), but it is necessary here briefly to refer to these from the physiological point of view. If two musical sounds reach the ear at the same moment, an agreeable or disagreeable sensation is experienced, which may be termed a _concord_ or a _discord_, and it can be shown by experiment with the syren that this depends upon the vibrational numbers of the two tones. The octave (1 : 2), the twelfth (1 : 3) and double octave (1 : 4) are absolutely consonant sounds; the fifth (2 : 3) is said to be perfectly consonant; then follow, in the direction of dissonance, the fourth (3 : 4), major sixth (3 : 5), major third (4 : 5), minor sixth (5 : 8) and the minor third (5 : 6). Helmholtz has attempted to account for this by the application of his theory of _beats_.

Beats are observed when two sounds of nearly the same pitch are produced together, and the number of beats per second is equal to the difference of the number of vibrations of the two sounds. Beats give rise to a peculiarly disagreeable intermittent sensation. The maximum roughness of beats is attained by 33 per second; beyond 132 per second, the individual impulses are blended into one uniform auditory sensation. When two notes are sounded, say on a piano, not only may the first, fundamental or prime tones beat, but partial tones of each of the primaries may beat also, and as the difference of pitch of two simultaneous sounds augments, the number of beats, both of prime tones and of harmonics, augments also. The physiological effect of beats, though these may not be individually distinguishable, is to give roughness to the ear. If harmonics or partial tones of prime tones coincide, there are no beats; if they do not coincide, the beats produced will give a character of roughness to the interval. Thus in the octave and twelfth, all the partial tones of the acute sound coincide with the partial tones of the grave sound; in the fourth, major sixth and major third, only two pairs of the partial tones coincide, while in the minor sixth, minor third and minor seventh only one pair of the harmonics coincide.

It is possible by means of beats to measure the sensitiveness of the ear by determining the smallest difference in pitch that may give rise to a beat. In no part of the scale can a difference smaller than 0.2 vibration per second be distinguished. The sensitiveness varies with pitch. Thus at 120 vibs. per second 0.4 vib. per second, at 500 about 0.3 vib. per second, and at 1000, 0.5 vib. per second can be distinguished. This is a remarkable illustration of the sensitiveness of the ear. When tones of low pitch are produced that do not rapidly die away, as by sounding heavy tuning-forks, not only may the beats be perceived corresponding to the difference between the frequencies of the forks, but also other sets of beats. Thus, if the two tones have frequencies of 40 and 74, a two-order beat may be heard, one having a frequency of 34 and the other of 6, as 74 / 40 = 1 + a positive remainder of 34, and 74 / 40 = 2 - 6, or 80 - 74, a negative remainder of 6. The lower beat is heard most distinctly when the number is less than half the frequency of the lower primary, and the upper when the number is greater. The beats we have been considering are produced when two notes are sounded slightly differing in frequency, or at all events their frequencies are not so great as those of two notes separated by a musical interval, such as an octave or a fifth. But Lord Kelvin has shown that beats may also be produced on slightly inharmonious musical intervals (_Proc. Roy. Soc. Ed._ 1878, vol. ix. p. 602). Thus, take two tuning-forks, ut2 = 256 and ut3 = 512; slightly flatten ut3 so as to make its frequency 510, and we hear, not a roughness corresponding to 254 beats, but a slow beat of 2 per second. The sensation also passes through a cycle, the beats now sounding loudly and fading away in intensity, again sounding loudly, and so on. One might suppose that the beat occurred between 510 (the frequency of ut3 flattened) and 512, the first partial of ut2, namely ut3, but this is not so, as the beat is most audible when ut2 is sounded feebly. In a similar way, beats may be produced on the approximate harmonies 2 : 3, 3 : 4, 4 : 5, 5 : 6, 6 : 7, 7 : 8, 1 : 3, 3 : 5, and beats may even be produced on the major chord 4 : 5 : 6 by sounding ut3, mi3, sol3, with sol3 or mi3 slightly flattened, "when a peculiar beat will be heard as if a wheel were being turned against a surface, one small part of which was rougher than the rest." These beats on imperfect harmonies appear to indicate that the ear does distinguish between an increase of pressure on the drum-head and a diminution, or between a push and a pull, or, in other words, that it is affected by phase. This was denied by Helmholtz.

10. _Beat Tones._--Considerable difference of opinion exists as to whether beats can blend so as to give a sensation of tone; but R. Konig, by using pure tones of high pitch, has settled the question. These tones were produced by large tuning-forks. Thus ut6 = 2048 and re6 = 2304. Then the beat tone is ut3 = 256 (2304-2048). If we strike the two forks, ut3 sounds as a grave or lower beat tone. Again, ut6 = 2048 and si6 = 3840. Then (2048)2 - 3840 = 256, a negative remainder, ut3, as before, and when both forks are sounded ut3 will be heard. Again, ut6 = 2048 and sol6 = 3072, and 3072 - 2048 = 1024, or ut6, which will be distinctly heard when ut6 and sol6 are sounded (Konig, _Quelques experiences d'acoustique_, Paris, 1882, p. 87).

11. _Combination Tones._--Frequently, when two tones are sounded, not only do we hear the compound sound, from which we can pick out the constituent tones, but we may hear other tones, one of which is lower in pitch than the lowest primary, and the other is higher in pitch than the higher primary. These, known as combination tones, are of two classes: _differential_ tones, in which the frequency is the difference of the frequencies of the generating tones, and _summational_ tones, having a frequency which is the sum of the frequencies of the tones producing them. Differential tones, first noticed by Sorge about 1740, are easily heard. Thus an interval of a fifth, 2 : 3, gives a differential tone 1, that is, an octave below 2; a fourth, 3 : 4, gives 1, a twelfth below 3; a major third, 4 : 5, gives 1, two octaves below 4; a minor third, 5 : 6, gives 1, two octaves and a major third below 5; a major sixth, 3 : 5, gives 2, that is, a fifth below 3; and a minor sixth, 5 : 8, gives 3, that is, a major sixth below 5. Summational tones, first noticed by Helmholtz, are so difficult to hear that much controversy has taken place as to their very existence. Some have contended that they are produced by beats. It appears to be proved physically that they may exist in the air outside of the ear. Further differential tones may be generated in the middle ear. Helmholtz also demonstrated their independent existence, and he states that "whenever the vibrations of the air or of other elastic bodies, which are set in motion at the same time by two generating simple tones, are so powerful that they can no longer be considered infinitely small, mathematical theory shows that vibrations of the air must arise which have the same vibrational numbers as the combination tones" (Helmholtz, _Sensations of Tone_, p. 235). The importance of these combinational tones in the theory of hearing is obvious. If the ear can only analyse compound waves into simple pendular vibrations of a certain order (simple multiples of the prime tone), how can it detect combinational tones, which do not belong to that order? Again, if such tones are purely subjective and only exist in the mind of the listener, the fact would be fatal to the resonance theory. There can be no doubt, however, that the ear, in dealing with them, vibrates in some part of its mechanism with each generator, while it also is affected by the combinational tone itself, according to its frequency.

12. Hearing with two ears does not appear materially to influence auditive sensation, but probably the two organs are enabled, not only to correct each other's errors, but also to aid us in determining the locality in which a sound originates. It is asserted by G. T. Fechner that one ear may perceive the same tone at a slightly higher pitch than the other, but this may probably be due to some slight pathological condition in one ear. If two tones, produced by two tuning-forks, of equal pitch, are produced one near each ear, there is a uniform single sensation; if one of the tuning-forks be made to revolve round its axis in such a way that its tone increases and diminishes in intensity, neither fork is heard continuously, but both sound alternately, the fixed one being only audible when the revolving one is not. It is difficult to decide whether excitations of corresponding elements in the two ears can be distinguished from each other. It is probable that the resulting sensations may be distinguished, provided one of the generating tones differs from the other in intensity or quality, although it may be the same in pitch. Our judgment as to the direction of sounds is formed mainly from the different degrees of intensity with which they are heard by two ears. Lord Rayleigh states that diffraction of the sound-waves will occur as they pass round the head to the ear farthest from the source of sound; thus partial tones will reach the two ears with different intensities, and thus quality of tone may be affected (_Trans. Music. Soc._, London, 1876). Silvanus P. Thompson advocates a similar view, and he shows that the direction of a complex tone can be more accurately determined than the direction of a simple tone, especially if it be of low pitch (_Phil. Mag._, 1882). (J. G. M.)

HEARN, LAFCADIO (1850-1904), author of books about Japan, was born on the 27th of June 1850 in Leucadia (pronounced Lefcadia, whence his name, which was one adopted by himself), one of the Greek Ionian Islands. He was the son of Surgeon-major Charles Hearn, of King's County, Ireland, who, during the English occupation of the Ionian Islands, was stationed there, and who married a Greek wife. Artistic and rather bohemian tastes were in Lafcadio Hearn's blood. His father's brother Richard was at one time a well-known member of the Barbizon set of artists, though he made no mark as a painter through his lack of energy. Young Hearn had rather a casual education, but was for a time (1865) at Ushaw Roman Catholic College, Durham. The religious faith in which he was brought up was, however, soon lost; and at nineteen, being thrown on his own resources, he went to America and at first picked up a living in the lower grades of newspaper work. The details are obscure, but he continued to occupy himself with journalism and with out-of-the-way observation and reading, and meanwhile his erratic, romantic and rather morbid idiosyncrasies developed. He was for some time in New Orleans, writing for the _Times Democrat_, and was sent by that paper for two years as correspondent to the West Indies, where he gathered material for his _Two Years in the French West Indies_ (1890). At last, in 1891, he went to Japan with a commission as a newspaper correspondent, which was quickly broken off. But here he found his true sphere. The list of his books on Japanese subjects tells its own tale: _Glimpses of Unfamiliar Japan_ (1894); _Out of the East_ (1895); _Kokoro_ (1896); _Gleanings in Buddha Fields_ (1897); _Exotics and Retrospections_ (1898); _In Ghostly Japan_ (1899); _Shadowings_ (1900); _A Japanese Miscellany_ (1901); _Kotto_ (1902); _Japanese Fairy Tales_ and _Kwaidan_ (1903), and (published just after his death) _Japan, an Attempt at Interpretation_ (1904), a study full of knowledge and insight. He became a teacher of English at the University of Tokyo, and soon fell completely under the spell of Japanese ideas. He married a Japanese wife, became a naturalized Japanese under the name of Yakumo Koizumi, and adopted the Buddhist religion. For the last two years of his life (he died on the 26th of September 1904) his health was failing, and he was deprived of his lecturersbip at the University. But he had gradually become known to the world at large by the originality, power and literary charm of his writings. This wayward bohemian genius, who had seen life in so many climes, and turned from Roman Catholic to atheist and then to Buddhist, was curiously qualified, among all those who were "interpreting" the new and the old Japan to the Western world, to see it with unfettered understanding, and to express its life and thought with most intimate and most artistic sincerity. Lafcadio Hearn's books were indeed unique for their day in the literature about Japan, in their combination of real knowledge with a literary art which is often exquisite.

See Elizabeth Bisland, _The Life and Letters of Lafcadio Hearn_ (2 vols., 1906); G. M. Gould, _Concerning Lafcadio Hearn_ (1908).

HEARNE, SAMUEL (1745-1792), English explorer, was born in London. In 1756 he entered the navy, and was some time with Lord Hood; at the end of the Seven Years' War (1763) he took service with the Hudson's Bay Company. In 1768 he examined portions of the Hudson's Bay coasts with a view to improving the cod fishery, and in 1769-1772 he was employed in north-western discovery, searching especially for certain copper mines described by Indians. His first attempt (from the 6th of November 1769) failed through the desertion of his Indians; his second (from the 23rd of February 1770) through the breaking of his quadrant; but in his third (December 1770 to June 1772) he was successful, not only discovering the copper of the Coppermine river basin, but tracing this river to the Arctic Ocean. He reappeared at Fort Prince of Wales on the 30th of June 1772. Becoming governor of this fort in 1775, he was taken prisoner by the French under La Perouse in 1782. He returned to England in 1787 and died there in 1792.

See his posthumous _Journey from Prince of Wales Fort in Hudson's Bay to the Northern Ocean_ (London, 1795).

HEARNE, THOMAS (1678-1735), English antiquary, was born in July 1678 at Littlefield Green in the parish of White Waltham, Berkshire. Having received his early education from his father, George Hearne, the parish clerk, he showed such taste for study that a wealthy neighbour, Francis Cherry of Shottesbrooke (c. 1665-1713), a celebrated nonjuror, interested himself in the boy, and sent him to the school at Bray "on purpose to learn the Latin tongue." Soon Cherry took him into his own house, and his education was continued at Bray until Easter 1696, when he matriculated at St Edmund Hall, Oxford. At the university he attracted the attention of Dr John Mill (1645-1707), the principal of St Edmund Hall, who employed him to compare manuscripts and in other ways. Having taken the degree of B.A. in 1699 he was made assistant keeper of the Bodleian Library, where he worked on the catalogue of books, and in 1712 he was appointed second keeper. In 1715 Hearne was elected architypographus and esquire bedell in civil law in the university, but objection having been made to his holding this office together with that of second librarian, he resigned it in the same year. As a nonjuror he refused to take the oaths of allegiance to King George I., and early in 1716 he was deprived of his librarianship. However he continued to reside in Oxford, and occupied himself in editing the English chroniclers. Having refused several important academical positions, including the librarianship of the Bodleian and the Camden professorship of ancient history, rather than take the oaths, he died on the 10th of June 1735.

Hearne's most important work was done as editor of many of the English chroniclers, and until the appearance of the "Rolls" series his editions were in many cases the only ones extant. Very carefully prepared, they were, and indeed are still, of the greatest value to historical students. Perhaps the most important of a long list are: Benedict of Peterborough's (Benedictus Abbas) _De vita et gestis Henrici II. et Ricardi I._ (1735); John of Fordun's _Scotichronicon_ (1722); the monk of Evesham's _Historia vitae et regni Ricardi II._ (1729); Robert Mannyng's translation of Peter Langtoft's _Chronicle_ (1725); the work of Thomas Otterbourne and John Whethamstede as _Duo rerum Anglicarum scriptores veteres_ (1732); Robert of Gloucester's _Chronicle_ (1724); J. Sprott's _Chronica_ (1719); the _Vita et gesta Henrici V._, wrongly attributed to Thomas Elmham (1727); Titus Livy's _Vita Henrici V._ (1716); Walter of Hemingburgh's _Chronicon_ (1731); and William of Newburgh's _Historia rerum Anglicarum_ (1719). He also edited John Leland's _Itinerary_ (1710-1712) and the same author's _Collectanea_ (1715); W. Camden's _Annales rerum Anglicarum et Hibernicarum regnante Elizabetha_ (1717); Sir John Spelman's _Life of Alfred_ (1709); and W. Roper's _Life of Sir Thomas More_ (1716). He brought out an edition of Livy (1708); one of Pliny's _Epistolae et panegyricus_ (1703); and one of the Acts of the Apostles (1715). Among his other compilations may be mentioned: _Ductor historicus, a Short System of Universal History_ (1704, 1705, 1714, 1724); _A Collection of Curious Discourses by Eminent Antiquaries_ (1720); and _Reliquiae Bodleianae_ (1703).

Hearne left his manuscripts to William Bedford, who sold them to Dr Richard Rawlinson, who in his turn bequeathed them to the Bodleian. Two volumes of extracts from his voluminous diary were published by Philip Bliss (Oxford, 1857), and afterwards an enlarged edition in three volumes appeared (London, 1869). A large part of his diary entitled _Remarks and Collections, 1705-1714_, edited by C. E. Doble and D. W. Rannie, has been published by the Oxford Historical Society (1885-1898). _Bibliotheca Hearniana_, excerpts from the catalogue of Hearne's library, has been edited by B. Botfield (1848).

See _Impartial Memorials of the Life and Writings of Thomas Hearne by several hands_ (1736); and W. D. Macray, _Annals of the Bodleian Library_ (1890). Hearne's autobiography is published in W. Huddesford's _Lives of Leland, Hearne and Wood_ (Oxford, 1772). T. Ouvry's _Letters addressed to Thomas Hearne_ has been privately printed (London, 1874).

HEARSE (an adaptation of Fr. _herse_, a harrow, from Lat. _hirpex_, _hirpicem_, rake or harrow, Greek [Greek: arpae], a vehicle for the conveyance of a dead body at a funeral. The most usual shape is a four-wheeled car, with a roofed and enclosed body, sometimes with glass panels, which contains the coffin. This is the only current use of the word. In its earlier forms it is usually found as "herse," and meant, as the French word did, a harrow (q.v.). It was then applied to other objects resembling a harrow, following the French. It was then used of a portcullis, and thus becomes a heraldic term, the "herse" being frequently borne as a "charge," as in the arms of the City of Westminster. The chief application of the word is, however, to various objects used in funeral ceremonies. A "herse" or "hearse" seems first to have been a barrow-shaped framework of wood, to hold lighted tapers and decorations placed on a bier or coffin; this later developed into an elaborate pagoda-shaped erection of woodwork or metal for the funerals of royal or other distinguished persons. This held banners, candles, armorial bearings and other heraldic devices. Complimentary verses or epitaphs were often attached to the "hearse." An elaborate "hearse" was designed by Inigo Jones for the funeral of James I. The "hearse" is also found as a permanent erection over tombs. It is generally made of iron or other metal, and was used, not only to carry lighted candles, but also for the support of a pall during the funeral ceremony. There is a brass "hearse" in the Beauchamp Chapel at Warwick Castle, and one over the tomb of Robert Marmion and his wife at Tanfield Church near Ripon.

HEART, in anatomy.--The heart[1] is a four-chambered muscular bag, which lies in the cavity of the thorax between the two lungs. It is surrounded by another bag, the pericardium, for protective and lubricating purposes (see COELOM AND SEROUS MEMBRANES). Externally the heart is somewhat conical, its base being directed upward, backward and to the right, its apex downward, forward and to the left. In transverse section the cone is flattened, so that there is an anterior and a posterior surface and a superior and inferior border. The superior border, running obliquely downward and to the left, is very thick, and so gains the name of _margo obtusus_, while the inferior border is horizontal and sharp and is called _margo acutus_ (see fig. 1). The divisions between the four chambers of the heart (namely, the two auricles and two ventricles) are indicated on the surface by grooves, and when these are followed it will be seen that the right auricle and ventricle lie on the front and right side, while the left auricle and ventricle are behind and on the left.

The _right auricle_ is situated at the base of the heart, and its outline is seen on looking at the organ from in front. Into the posterior part of it open the two venae cavae (see fig. 2), the superior (a) above and the inferior (b) below. In front and to the left of the superior vena cava is the right auricular appendage (e) which overlaps the front of the root of the aorta, while running obliquely from the front of one vena cava to the other is a shallow groove called the _sulcus terminalis_, which indicates the original separation between the true auricle in front and the sinus venosus behind. When the auricle is opened by turning the front wall to the right as a flap the following structures are exposed:

1. A muscular ridge, called the _crista terminalis_, corresponding to the sulcus terminalis on the exterior.

2. A series of ridges on the anterior wall and in the appendage, running downward from the last and at right angles to it, like the teeth of a comb; these are known as _Musculi pectinati_.

3. The orifice of the superior vena cava (fig. 2, a) at the upper and back part of the chamber.

4. The orifice of the inferior vena cava (fig. 2, b) at the lower and back part.

5. Attached to the right and lower margins of this opening are the remains of the _Eustachian valve_ (fig. 2, h), which in the foetus directs the blood from the inferior vena cava, through the _foramen ovale_, into the left auricle.

6. Below and to the left of this is the opening of the _coronary sinus_ (fig. 2, k), which collects most of the veins returning blood from the substance of the heart.

7. Guarding this opening is the _coronary valve_ or _valve of Thebesius_.

8. On the posterior or septal wall, between the two auricles, is an oval depression, called the _fossa ovalis_ (fig. 2, g), the remains of the original communication between the two auricles. In about a quarter of all normal hearts there is a small valvular communication between the two auricles in the left margin of this depression (see "7th Report of the Committee of Collective Investigation," _J. Anat. and Phys._ vol. xxxii. p. 164).

9. The _annulus ovalis_ is the raised margin surrounding this depression.

10. On the left side, opening into the right ventricle, is the _right auriculo-ventricular opening_.

11. On the right wall, between the two caval openings, may occasionally be seen a slight eminence, the _tubercle of Lower_, which is supposed to separate the two streams of blood in the embryo.

12. Scattered all over the auricular wall are minute depressions, the _foramina Thebesii_, some of which receive small veins from the substance of the heart.

The _right ventricle_ is a triangular cavity (see fig. 2) the base of which is largely formed by the auriculo-ventricular orifice. To the left of this it is continued up into the root of the pulmonary artery, and this part is known as the _infundibulum_. Its anterior wall forms part of the anterior surface of the heart, while its posterior wall is chiefly formed by the septum ventriculorum, between it and the left ventricle. Its lower border is the margo acutus already mentioned. In transverse section it is crescentic, since the septal wall bulges into its cavity. In its interior the following structures are seen:

1. The _tricuspid valve_ (fig. 2, l, m, n) guarding against reflux of blood into the right auricle. This consists of a short cylindrical curtain of fibrous tissue, which projects into the ventricle from the margin of the auriculo-ventricular aperture, while from its free edge three triangular flaps hang down, the bases of which touch one another. These cusps are spoken of as septal, marginal and infundibular, from their position.

2. The _chordae tendineae_ are fine fibrous cords which fasten the cusps to the musculi papillares and ventricular wall, and prevent the valve being turned inside out when the ventricle contracts.

3. The _columnae carneae_ are fleshy columns, and are of three kinds. The first are attached to the wall of the ventricle in their whole length and are merely sculptured in relief, as it were; the second are attached by both ends and are free in the middle; while the third are known as the _musculi papillares_ and are attached by one end to the ventricular wall, the other end giving attachment to the chordae tendineae. These musculi papillares are grouped into three bundles (fig. 2, o).

4. The _moderator band_ is really one of the second kind of columnae carneae which stretches from the septal to the anterior wall of the ventricle.

5. The _pulmonary valve_ (fig. 2, p) at the opening of the pulmonary artery has three crescentic, pocket-like cusps, which, when the ventricle is filling, completely close the aperture, but during the contraction of the ventricle fit into three small niches known as the _sinuses of Valsalva_, and so are quite out of the way of the escaping blood. In the middle of the free margin of each is a small knob called the _corpus Arantii_ (fig. 2, q), and on each side of this a thin crescent-shaped flap, the _lunula_ (fig. 2, r), which is only made of two layers of endocardium, whereas in the rest of the cusp there is a fibrous backing between these two layers.

The _left auricle_ is situated at the back of the base of the heart, behind and to the left of the right auricle. Running down behind it are the oesophagus and the thoracic aorta. When it is opened it is seen to have a much lighter colour than the other cavities, owing to the greater thickness of its endocardium obscuring the red muscle beneath. There are no musculi pectinati except in the auricular appendage. The openings of the four pulmonary veins are placed two on each side of the posterior wall, but sometimes there may be three on the right side, and only one on the left. On the septal wall is a small depression like the mark of a finger-nail, which corresponds to the anterior part of the fossa ovalis and often forms a valvular communication with the right auricle. The auriculo-ventricular orifice is large and oval, and is directed downward and to the left. Foramina Thebesii and venae minimae cordis are found in this auricle, as in the right, although the chamber is one for arterial or oxidized blood.

At the lower part of the posterior surface of the unopened auricle, lying in the left auriculo-ventricular furrow, is the coronary sinus, which receives most of the veins returning the blood from the heart substance; these are the right and left coronary veins at each extremity and the posterior and left cardiac veins from below. One small vein, called the oblique vein of Marshall, runs down into it across the posterior surface of the auricle, from below the left lower pulmonary vein, and is of morphological interest.

The _left ventricle_ is conical, the base being above, behind and to the right, while the apex corresponds to the apex of the heart and lies opposite the fifth intercostal space, 3(1/2) in. from the mid line. The following structures are seen inside it:--

1. The _mitral valve_ guarding the auriculo-ventricular opening has the same arrangement as the tricuspid, already described, save that there are only two cusps, named marginal and aortic, the latter of which is the larger.

2. The chordae tendineae and columnae carneae resemble those of the right ventricle, though there are only two bundles of musculi papillares instead of three. These are very large. A moderator band has been found as an abnormality (see _J. Anat. and Phys._ vol. xxx. p. 568).

3. The _aortic valve_ has the same structure as the pulmonary, though the cusps are more massive. From the anterior and left posterior sinuses of Valsalva the coronary arteries arise. That part of the ventricle just below the aortic valve, corresponding to the infundibulum on the right, is known as the aortic vestibule.

The walls of the left ventricle are three times as thick as those of the right, except at the apex, where they are thinner. The septum ventriculorum is concave towards the left ventricle, so that a transverse section of that cavity is nearly circular. The greater part of it has nearly the same thickness as the rest of the left ventricular wall and is muscular, but a small portion of the upper part is membranous and thin, and is called the _pars membranacea septi_; it lies between the aortic and pulmonary orifices.

_Structure of the Heart._--The arrangement of the muscular fibres of the heart is very complicated and only imperfectly known. For details one of the larger manuals, such as Cunningham's _Anatomy_ (London, 1910), or Gray's _Anatomy_ (London, 1909), should be consulted. The general scheme is that there are superficial fibres common to the two auricles and two ventricles and deeper fibres for each cavity. Until recently no fibres had been traced from the auricles to the ventricles, though Gaskell predicted that these would be found, and the credit for first demonstrating them is due to Stanley Kent, their details having subsequently been worked out by W. His, Junr., and S. Tawara. The fibres of this _auriculo-ventricular bundle_ begin, in the right auricle, below the opening of the coronary sinus, and run forward on the right side of the auricular septum, below the fossa ovalis, and close to the auriculo-ventricular septum. Above the septal flap of the tricuspid valve they thicken and divide into two main branches, one on either side of the ventricular septum, which run down to the bases of the anterior and posterior papillary muscles, and so reach the walls of the ventricle, where their secondary branches form the _fibres of Purkinje_. The bundle is best seen in the hearts of young Ruminants, and it is presumably through it that the wave of contraction passes from the auricles to the ventricles (see article by A. Keith and M. Flack, _Lancet_, 11th of August 1906, p. 359).

The _central fibrous body_ is a triangular mass of fibro-cartilage, situated between the two auriculo-ventricular and the aortic orifices. The upper part of the septum ventriculorum blends with it. The _endocardium_ is a delicate layer of endothelial cells backed by a very thin layer of fibro-elastic tissue; it is continuous with the endothelium of the great vessels and lines the whole of the cavities of the heart.

The heart is roughly about the size of the closed fist and weighs from 8 to 12 oz.; it continues to increase in size up to about fifty years of age, but the increase is more marked in the male than in the female. Each ventricle holds about 4 f. oz. of blood, and each auricle rather less. The nerves of the heart are derived from the vagus, spinal accessory and sympathetic, through the superficial and deep cardiac plexuses.

_Embryology._

In the article on the arteries (q.v.) the formation and coalescence of the two _primitive ventral aortae_ to form the heart are noticed, so that we may here start with a straight median tube lying ventral to the pharynx and being prolonged cephalad into the ventral aortae and caudad into the vitelline veins. This soon shows four dilatations, which, from the tail towards the head end, are called the sinus venosus, the auricle, the ventricle and the truncus[2] arteriosus. As the tubular heart grows more rapidly than the pericardium which contains it, it becomes bent into the form of an S laid on its side ([rotated S]), the ventral convexity being the ventricle and the dorsal the auricle. The passage from the auricle to the ventricle is known as the _auricular canal_, and in the dorsal and ventral parts of this appear two thickenings known as _endocardial cushions_, which approach one another and leave a transverse slit between them (fig. 3, E.C.). Eventually these two cushions fuse in the middle line, obliterating the central part of the slit, while the lateral parts remain as the two auriculo-ventricular orifices; this fusion is known as the _septum intermedium_. From the bottom (ventral convexity) of the ventricle an antero-posterior median septum grows up, which is the _septum inferius_ or _septum ventriculorum_ (fig. 3, V). Posteriorly (caudally) this septum fuses with the septum intermedium, but anteriorly it is free at the lower part of the truncus arteriosus. On referring to the development of the arteries (see ARTERIES) it will be seen that another septum starts between the last two pairs of aortic arches and grows downward (caudad) until it reaches and joins with the septum inferius just mentioned. This _septum aorticum_ (formed by two ingrowths from the wall of the vessel which fuse later) becomes twisted in such a way that the right ventricle is continuous with the last pair of aortic arches (pulmonary artery), while the left ventricle communicates with the other arches (the permanent ventral aorta and its branches); it joins the septum ventriculorum in the upper part of the ventricular cavity and so forms the _pars membranacea septi_ (fig. 3, T. Ar).

The fate of the sinus venosus and auricle must now be followed. Into the former, at first, only the two vitelline veins open, but later, as they develop, the _ducts of Cuvier_ and the _umbilical veins_ join in (see VEINS). As the ducts of Cuvier come from each side the sinus spreads out to meet them and becomes transversely elongated. The slight constriction, which at first is the only separation between the sinus and the auricle, becomes more marked, and later the opening is into the right part of the auricle, and is guarded by two valvular folds of endocardium (the _venous valves_) which project into that cavity, and are continuous above with a temporary downgrowth from the roof, known as the _septum spurium_. Later the right side of the sinus enlarges, and so does the right part of the aperture, until the back part of the right side of the auricle and the right part of the sinus venosus are thrown into one, and the only remnants of the partition are the crista terminalis and the Eustachian and Thebesian Valves. The left part of the sinus venosus, which does not enlarge at the same rate as the right part, remains as the coronary sinus. It will now be seen why, in the adult heart, all the veins which open into the right auricle open into its posterior part, behind the crista terminalis. The septum spurium has been referred to as a temporary structure; the real division between the two auricles occurs at a later date than that between the ventricles and to the left of the septum spurium. It is formed by two partitions, the first of which, called the _septum primum_, grows down from the auricular roof. At first it does not quite reach the endocardial cushions in the auricular canal, already mentioned, but leaves a gap, called the _ostium primum_, between. This has nothing to do with the _foramen ovale_, which occurs as an independent perforation higher up, and at first is known as the _ostium secundum_. When it is established the septum primum grows down and meets the endocardial cushions, and so the ostium primum is obliterated. The _septum secundum_ grows down on the right of the septum primum and is never complete; it grows round and largely overlaps the foramen ovale and its edges form the annulus ovalis, so that, in the later months of foetal life, the foramen ovale is a valvular opening, the floor of which is formed by the septum primum and the margins by the septum secundum. The closure of the foramen is brought about by adhesion of the two septa.

The pulmonary veins of the two sides at first join one another, dorsal to the left auricle, and open into that cavity by a single median trunk, but, as the auricle grows, this trunk and part of the right and left veins are absorbed into its cavity.

The mitral and tricuspid valves are formed by the shortening of the auricular canal which becomes telescoped into the ventricle, and the cusps are the remnants of this telescoping process.

The columnae carneae and chordae tendineae are the remains of a spongy network which originally filled the cavity of the primary ventricle.

The aortic and pulmonary valves are laid down in the ventral aorta, before it is divided into aorta and pulmonary artery, as four endocardial cushions; anterior, posterior and two lateral. The septum aorticum cuts the latter two into two, so that each artery has the rudiments of three cusps.

Abnormalities of the heart are very numerous, and can usually be explained by a knowledge of its development. They often cause grave clinical symptoms. A clear and well-illustrated review of the most important of them will be found in the chapter on congenital disease of the heart in _Clinical Applied Anatomy_, by C. R. Box and W. McAdam Eccles, London, 1906.

For further details of the embryology of the heart see Oscar Hertwig's _Entwicklungslehre der Wirbeltiere_ (Jena, 1902); G. Born, "Entwicklung des Saugetierherzens," _Archiv f. mik. Anat._ Bd. 33 (1889); W. His, _Anatomie menschlicher Embryonen_ (Leipzig, 1881-1885); Quain's _Anatomy_, vol. i. (1908); C. S. Minot, _Human Embryology_ (New York, 1892); and A. Keith, _Human Embryology and Morphology_ (London, 1905).

_Comparative Anatomy._

In the Acrania (e.g. lancelet) there is no heart, though the vessels are specially contractile in the ventral part of the pharynx.

In the Cyclostomata (lamprey and hag), and Fishes, the heart has the same arrangement which has been noticed in the human embryo. There is a smooth, thin-walled sinus venosus, a thin reticulate-walled auricle, produced laterally into two appendages, a thick-walled ventricle, and a _conus arteriosus_ containing valves. In addition to these the beginning of the ventral aorta is often thickened and expanded to form a _bulbus arteriosus_, which is non-contractile, and, strictly speaking, should rather be described with the arteries than with the heart. In relation to human embryology the smooth sinus venosus and reticulated auricle are interesting. Between the auricle and ventricle is the auriculo-ventricular valve, which primarily consists of two cusps, comparable to the two endocardial cushions of the human embryo, though in some forms they may be subdivided. In the interior of the ventricle is a network of muscular trabeculae. The conus arteriosus in the Elasmobranchs (sharks and rays) and Ganoids (sturgeon) is large and provided with several rows of semilunar valves, but in the Cyclostomes (lamprey) and Teleosts (bony fishes) the conus is reduced and only the anterior (cephalic) row of valves retained. With the reduction of the conus the bulbus arteriosus is enlarged. So far the heart is a single tubular organ expanded into various cavities and having the characteristic [rotated S]-shaped form seen in the human embryo; it contains only venous blood which is forced through the gills to be oxidized on its way to the tissues. In the Dipnoi (mud fish), in which rudimentary lungs, as well as gills, are developed, the auricle is divided into two, and the sinus venosus opens into the right auricle. The conus arteriosus too begins to be divided into two chambers, and in Protopterus this division is complete. This division of the heart is one instance in which mammalian ontogeny does not repeat the processes of phylogeny, because, in the human embryo, it has been shown that the ventricular septum appears before the auricular. This want of harmony is sometimes spoken of as the "falsification of the embryological record."

In the Amphibia there are also two auricles and one ventricle, though in the Urodela (tailed amphibians) the auricular septum is often fenestrated. The sinus venosus is still a separate chamber, and the conus arteriosus, which may contain many or few valves, is usually divided into two by a spiral fold. Structurally the amphibian heart closely resembles the dipnoan, though the increased size of the left auricle is an advance. In the Anura (frogs and toads) the whole ventricle is filled with a spongy network which prevents the arterial and venous blood from the two auricles mixing to any great extent. (For the anatomy and physiology of the frog's heart, see _The Frog_, by Milnes Marshall.)

In the Reptiles the ventricular septum begins to appear; this in the lizards is quite incomplete, but in the crocodiles, which are usually regarded as the highest order of living reptiles, the partition has nearly reached the top of the ventricle, and the condition resembles that of the human embryo before the pars membranacea septi is formed. The conus arteriosus becomes included in the ventricular cavity, but the sinus venosus still remains distinct, and its opening into the right ventricle is guarded by two valves which closely resemble the two venous valves in the auricle of the human embryo already referred to.

In the Birds the auricular and ventricular septa are complete; the right ventricle is thin-walled and crescentic in section, as in Man, and the musculi papillares are developed. The left auriculo-ventricular valve has three membranous cusps with chordae tendineae attached to them, but the right auriculo-ventricular valve has a large fleshy cusp without chordae tendineae. The sinus venosus is largely included in the right auricle, but remains of the two venous valves are seen on each side of the orifice of the inferior vena cava.

In the Mammals the structure of the heart corresponds closely with the description of that of Man already given. In the Ornithorynchus, among the Monotremes, the right auriculo-ventricular valve has two fleshy and two membranous cusps, thus showing a resemblance to that of the bird. In the Echidna, the other member of the order, however, both auriculo-ventricular valves are membranous. In the Edentates the remains of the venous valves at the opening of the inferior vena cava are better marked than in other orders. In the Ungulates the moderator band in the right ventricle is especially well developed, and the central fibrous body at the base of the heart is often ossified, forming the os cordis so well known in the heart of the ox.

The position of the heart in the lower mammals is not so oblique as it is in Man.

For further details, see C. Rose, _Beitr. z. vergl. Anal. des Herzens der Wirbelthiere Morph. Jahrb._, Bd. xvi. (1890); R. Wiedersheim, _Vergleichende Anatomie der Wirbelthiere_ (Jena, 1902) (for literature); also Parker and Haswell's _Zoology_ (London, 1897). (F. G. P.)

HEART DISEASE.--In the early ages of medicine, the absence of correct anatomical, physiological and pathological knowledge prevented diseases of the heart from being recognized with any certainty during life, and almost entirely precluded them from becoming the object of medical treatment. But no sooner did Harvey (1628) publish his discovery of the circulation of the blood, and its dependence on the heart as its central organ, than derangements of the circulation began to be recognized as signs of disease of that central organ. (See also under VASCULAR SYSTEM.)

Among the earliest to profit by this discovery and to make important contributions to the literature of diseases of the heart and circulation were, R. Lower (1631-1691), R. Vieussens (1641-1716). H. Boerhave (1668-1738) and the great pathologists at the beginning of the 18th century, G. M. Lancisi (1654-1720), G. B. Morgagni (1682-1771) and J. B. Senac (1693-1770). The works of these writers form very interesting reading, and it is remarkable how careful were the observations made, and how sound the conclusions drawn, by these pioneers of scientific medicine. J. N. Corvisart (1755-1821) was one of the earliest to make practical use of R. T. Auenbrugger's (1722-1809) invention of percussion to determine the size of the heart. R. T. H. Laennec (1781-1826) was the first to make a scientific application of mediate auscultation to the diagnosis of disease of the chest, by the invention of the stethoscope. J. Bouillaud (1796-1881) extended its use to the diagnosis of disease of the heart. To James Hope (1801-1841) we owe much of the precision we have now attained in diagnosis of valvular disease from abnormalities in the sounds produced during cardiac movements. This short list by no means exhausts the earlier literature on the subject, but each of these names marks an era in the progress of the diagnosis of cardiac disease. In later years the literature on this subject has become very copious.

The heart and great vessels occupy a position immediately to the left of the centre of the thoracic cavity. The anterior surface of the heart is projected against the chest wall and is surrounded on either side by the lungs, which are resonant organs, so that any increase in the size of the heart, "dilatation," can be detected by percussion. By placing the hand on the chest, palpation, the impulse of the left ventricle, or apex beat, can normally be felt just below and internal to the nipple. Deviations from the normal in the position or force of the apex beat will afford important information as to the nature of the pathological changes in the heart. Thus, displacement downwards and outwards of the apex beat, with a forcible thrusting impulse, will indicate hypertrophy, or increase of the muscular wall and increased driving power of the left ventricle, whereas a similar displacement with a feeble diffuse impulse will indicate dilatation, or over-distension of its cavity from stretching of the walls.

By auscultation, or listening with a suitable instrument named a stethoscope over appropriate areas, we can detect any abnormality in the sounds of the heart, and the presence of murmurs indicative of disease of one or other of the valves of the heart.

The pericardium is a fibro-serous sac which loosely envelops the heart and the origin of the great vessels. Inflammation of this sac, or _pericarditis_, is apt to occur as a result of rheumatism, more especially in children. It may also occur as a complication of pneumonia. It is a serious affection associated with pain over the heart, fever, shortness of breath, rapid pulse and dilatation of the heart. As a result of the inflammation, fluid may accumulate in the pericardial sac, or the walls of the sac may become adherent to the heart and tend to embarrass its action. In favourable cases, however, recovery may take place without any untoward sequelae.

Diseases of the heart may be classified in two main groups, (1) Disease of the valves, and (2) Disease of the walls of the heart.

1. _Valvular Disease._--Inflammation of the valves of the heart, or _endocarditis_, is one of the most common complications of rheumatism in children and young adults. More severe types, which are apt to prove fatal from a form of blood poisoning, may result when the valves of the heart are attacked by certain micro-organisms, such as the pneumococcus, which is responsible for pneumonia, the streptococcus and the staphylococcus pyogenes, the gonococcus and the influenza bacillus.

As a result of endocarditis, one or more of the valves may be seriously damaged, so that it leaks or becomes incompetent. The valves of the left side of the heart, the aortic and mitral valves, are affected far more commonly than those of the right side. It is indeed comparatively rarely that the latter are attacked. In the process of healing of a damaged valve, scar tissue is formed which has a tendency to contract, so that in some cases the orifice of the valve becomes narrowed, and the resulting stenosis or narrowing gives rise to obstruction of the blood stream. We may thus have incompetence or stenosis of a valve or both combined.

Valvular lesions are detected on auscultation over appropriate areas by the blowing sounds or murmurs to which they give rise, which modify or replace the normal heart sounds. Thus, lesions of the mitral valve give rise to murmurs which are heard at the apex beat of the heart, and lesions of the aortic valves to murmurs which are heard over the aortic area, in the second right intercostal space. Accurate timing of the murmurs in relation to the heart sounds enables us to judge whether the murmur is due to stenosis or incompetence of the valve affected.

If the valvular lesion is severe, it is essential for the proper maintenance of the circulation that certain changes should take place in the heart to compensate for or neutralize the effects of the regurgitation or obstruction, as the case may be. In affections of the aortic valve, the extra work falls on the left ventricle, which enlarges proportionately and undergoes hypertrophy. In affections of the mitral valve the effect is felt primarily by the left auricle, which is a thin walled structure incapable of undergoing the requisite increase in power to resist the backward flow through the mitral orifice in case of leakage, or to overcome the effects of obstruction in case of stenosis. The back pressure is therefore transmitted to the pulmonary circulation, and as the right ventricle is responsible for maintaining the flow of blood through the lungs, the strain and extra work fall on the right ventricle, which in turn enlarges and undergoes hypertrophy. The degree of hypertrophy of the left or right ventricle is thus, up to a certain point, a measure of the extent of the lesion of the aortic or mitral valve respectively. When the effects of the valvular lesion are so neutralized by these structural changes in the heart that the circulation is equably maintained, "compensation" is said to be efficient.

When the heart gives way under the strain, compensation is said to break down, and dropsy, shortness of breath, cough and cyanosis, are among the distressing symptoms which may set in. The mere existence of a valvular lesion does not call for any special treatment so long as compensation is efficient, and a large number of people with slight valvular lesions are living lives indistinguishable from those of their neighbours. It will, however, be readily understood that in the case of the more serious lesions certain precautions should be observed in regard to over-exertion, excitement, over-indulgence in tobacco or alcohol, &c., as the balance is more readily upset and any undue strain on the heart may cause a breakdown of compensation. When this occurs treatment is required. A period of rest in bed is often sufficient to enable the heart to recover, and this may be supplemented as required by the administration of mercurial and saline purgatives to relieve the embarrassed circulation, and of suitable cardiac tonics, such as digitalis and strychnin, to reinforce and strengthen the heart's action.

2. _Affections of the Muscular Wall of the Heart._--Dilatation of the heart, or stretching of the walls of the heart, is an incident, as has already been stated, in pericarditis and in the earlier stages of valvular disease antecedent to hypertrophy. Temporary over-distension or dilatation of the cavities of the heart occurs in violent and protracted exertion, but rapidly subsides and is in no wise harmful to the sound and vigorous heart of the young. It is otherwise if the heart is weak and flabby from a too sedentary life or degenerative changes in its walls or during convalescence from a severe illness, when the same circumstances which will not injure a healthy heart, may give rise to serious dilatation from which recovery may be very protracted.

Influenza is a common cause of cardiac dilatation, and is liable to be a source of trouble after the acute illness has subsided, if the patient goes about and resumes his ordinary avocations too soon.

Fatty or fibroid degeneration of the heart wall may occur in later life from impaired nutrition of the muscle, due to partial obstruction of the blood-vessels supplying it, when they are the seat of the degenerative changes known as arteriosclerosis or atheroma. The affection known as _angina pectoris_ (q.v.) may be a further consequence of this defective blood-supply.

The treatment will vary according to the nature of the case. In serious cases of dilatation, rest in bed, purgatives and cardiac tonics may be required.

In commencing degenerative change the Oertel treatment, consisting of graduated exercise up a gentle slope, limitation of fluids and a special diet, may be indicated.

In cases of slight dilatation after influenza or recent illness, the Schott treatment by baths and exercises as carried out at Nauheim may be sometimes beneficial. The change of air and scene, the enforced rest, the placid life, together with freedom from excitement and worry, are among the most important factors which contribute to success in this class of case.

_Disorders of Rhythm of the Heart's Action._--Under this heading may be grouped a number of conditions to which the name "functional affections of the heart" has sometimes been applied, inasmuch as the disturbances in question cannot usually be attributed to definite organic disease of the heart. We must, of course, exclude from this category the irregularity in the force and frequency of the pulse, which is commonly associated with incompetence of the mitral valve.

The heart is a muscular organ possessing certain properties, rhythmicity, excitability, contractility, conductivity and tonicity, as pointed out by Gaskell, in virtue of which it is able to maintain a regular automatic beat independently of nerve stimulation. It is, however, intimately connected with the brain, blood-vessels and the abdominal and thoracic viscera, by innumerable nerves, through which impulses or messages are being constantly sent to and received from these various portions of the body. Such messages may give rise to disturbances of rhythm with which we are all familiar. For instance, sudden fright or emotion may cause a momentary arrest of the heart's action, and excitement or apprehension may set up a rapid action of the heart or _palpitation_. Palpitation, again, is often the result of digestive disorders, the message in this case being received from the stomach, instead of the brain as in emotional disturbances. It may also result from over-indulgence in tobacco and alcohol.

_Tachycardia_ is the name applied to a more or less permanent increase in the rate of the heart-beat. It is usually a prominent feature in the affection known as Graves' disease or exophthalmic goitre. It may also result from chronic alcoholism. In the condition known as paroxysmal tachycardia there appears to be no adequate explanation for its onset.

_Bradycardia_ or abnormal slowness of the heart-beat, is the converse of tachycardia. An abnormally slow pulse is met with in melancholia, cerebral tumour, jaundice and certain toxic conditions, or may follow an attack of influenza. There is, however, a peculiar affection characterized by abnormal slowness of pulse (often ranging as low as 30), and the onset, from time to time, of epileptiform or syncopal attacks. To this the name "Stokes-Adams disease" has been applied, as it was first called attention to by Adams in 1827, and subsequently fully described by Stokes in 1836. It is usually associated with senile degenerative change of the heart and vascular system, and is held to be due to impairment of conductivity in the muscular fibres (bundle of His) which transmit the wave of contraction from the auricle to the ventricle. It is of serious significance in view of the symptoms associated with it.

_Intermittency of the Pulse._--By this is understood a pulse in which a beat is dropped from time to time. The dropping of a beat may occur at regular intervals every two, four or six beats, &c., or occasionally at irregular intervals after a series of normal beats. On examining the heart, it is found, as a rule, that the cause of the intermission at the wrist is not actual omission of a heart-beat, but the occurrence of a hurried imperfect cardiac contraction which does not transmit a pulse-wave to the wrist. It is not characteristic of any special form of heart affection, and is rarely of serious import. It may be due to reflex digestive disturbances, or be associated with conditions of nervous breakdown and irritability, or with an atonic and relaxed condition of the heart muscle. The treatment of these disorders of rhythm of the heart will vary greatly according to the cause and is often a matter of considerable difficulty. (J. F. H. B.)

_Surgery of Heart and Pericardium._--As the result of acute or chronic inflammation of the lining membrane of the fibrous sac which surrounds the heart and the neighbouring parts of the large blood-vessels, a dropsical or a purulent collection may form in it, or the sac may be quietly distended by a thin watery fluid. In either case, but especially in the latter, the heart may be so embarrassed in its work that death seems imminent. The condition is generally due to the cultivation in the pericardium of the germs of rheumatism, influenza or gonorrhoea, or of those of ordinary suppuration. Respiration as well as circulation is embarrassed, and there is a marked fulness and dulness of the front wall of the chest to the left of the breast-bone. In that region also pain and tenderness are complained of. By using the slender, hollow needle of an aspirator great relief may be afforded, but the tapping may have to be repeated from time to time. If the fluid drawn off is found to be purulent, it may be necessary to make a trap-door opening into the chest by cutting across the 4th and 5th ribs, incising and evacuating the pericardium and providing for drainage. In short, an abscess in the pericardium must be treated like an abscess in the pleura.

Wounds of the heart are apt to be quickly fatal. If the probability is that the enfeebled action of the heart is due to pressure from blood which is leaking into, and is locked up in the pericardium, the proper treatment will be to open the pericardium, as described above, and, if possible, to close the opening in the auricle, ventricle or large vessel, by sutures. (E. O.*)

FOOTNOTES:

[1] In O. Eng. _heorte_; this is a common Teut. word, cf. Dut. _hart_, Ger. _Herz_, Goth. _hairto_; related by root are Lat. _cor_ and Gr. [Greek: kardia]: the ultimate root is _kard_-, to quiver, shake.

[2] This is often called bulbus arteriosus, but it will be seen that the term is used rather differently in comparative anatomy.

HEART-BURIAL, the burial of the heart apart from the body. This is a very ancient practice, the special reverence shown towards the heart being doubtless due to its early association with the soul of man, his affections, courage and conscience. In medieval Europe heart-burial was fairly common. Some of the more notable cases are those of Richard I., whose heart, preserved in a casket, was placed in Rouen cathedral; Henry III., buried in Normandy; Eleanor, queen of Edward I., at Lincoln; Edward I., at Jerusalem; Louis IX., Philip III., Louis XIII. and Louis XIV., in Paris. Since the 17th century the hearts of deceased members of the house of Habsburg have been buried apart from the body in the Loretto chapel in the Augustiner Kirche, Vienna. The most romantic story of heart-burial is that of Robert Bruce. He wished his heart to rest at Jerusalem in the church of the Holy Sepulchre, and on his deathbed entrusted the fulfilment of his wish to Douglas. The latter broke his journey to join the Spaniards in their war with the Moorish king of Granada, and was killed in battle, the heart of Bruce enclosed in a silver casket hanging round his neck. Subsequently the heart was buried at Melrose Abbey. The heart of James, marquess of Montrose, executed by the Scottish Covenanters in 1650, was recovered from his body, which had been buried by the roadside outside Edinburgh, and, enclosed in a steel box, was sent to the duke of Montrose, then in exile. It was lost on its journey, and years afterwards was discovered in a curiosity shop in Flanders. Taken by a member of the Montrose family to India, it was stolen as an amulet by a native chief, was once more regained, and finally lost in France during the Revolution. Of notable 17th-century cases there is that of James II., whose heart was buried in the church of the convent of the Visitation at Chaillot near Paris, and that of Sir William Temple, at Moor Park, Farnham. The last ceremonial burial of a heart in England was that of Paul Whitehead, secretary to the Monks of Medmenham club, in 1775, the interment taking place in the Le Despenser mausoleum at High Wycombe, Bucks. Of later cases the most notable are those of Daniel O'Connell, whose heart is at Rome, Shelley at Bournemouth, Louis XVII. at Venice, Kosciusko at the Polish museum at Rapperschwyll, Lake Zurich, and the marquess of Bute, taken by his widow to Jerusalem for burial in 1900. Sometimes other parts of the body, removed in the process of embalming, are given separate and solemn burial. Thus the viscera of the popes from Sixtus V. (1590) onward have been preserved in the parish church of the Quirinal. The custom of heart-burial was forbidden by Pope Boniface VIII. (1294-1303), but Benedict XI. withdrew the prohibition.

See Pettigrew, _Chronicles of the Tombs_ (1857).

HEARTH (a word which appears in various forms in several Teutonic languages, cf. Dutch _haard_, German _Herd_, in the sense of "floor"), the part of a room where a fire is made, usually constructed of stone, bricks, tiles or earth, beaten hard and having a chimney above; the fire being lighted either on the hearth itself, or in a receptacle placed there for the purpose. Like the Latin _focus_, especially in the phrase for "hearth and home" answering to _pro aris et focis_, the word is used as equivalent to the home or household. The word is also applied to the fire and cooking apparatus on board ship; the floor of a smith's forge; the floor of a reverberatory furnace on which the ore is exposed to the flame; the lower part of a blast furnace through which the metal goes down into the crucible; in soldering, a portable brazier or chafing dish, and an iron box sunk in the middle of a flat iron plate or table. An "open-hearth furnace" is a regenerative furnace of the reverberatory type used in making steel, hence "open-hearth steel" (see IRON AND STEEL).

Hearth-money, hearth tax or chimney-money, was a tax imposed in England on all houses except cottages at a rate of two shillings for every hearth. It was first levied in 1662, but owing to its unpopularity, chiefly caused by the domiciliary visits of the collectors, it was repealed in 1689, although it was producing L170,000 a year. The principle of the tax was not new in the history of taxation, for in Anglo-Saxon times the king derived a part of his revenue from a _fumage_ or tax of smoke farthings levied on all hearths except those of the poor. It appears also in the hearth-penny or tax of a penny on every hearth, which as early as the 10th century was paid annually to the pope (see PETER'S PENCE).

HEARTS, a game of cards of recent origin, though founded upon the same principle as many old games, such as _Slobberhannes_, _Four Jacks_ and _Enfle_, namely, that of losing instead of winning as many tricks as possible. Hearts is played with a full pack, ace counting highest and deuce lowest. In the four-handed game, which is usually played, the entire pack is dealt out as at whist (but without turning up the last card, since there are no trumps), and the player at the dealer's left begins by leading any card he chooses, the trick being taken by the highest card of the suit led. Each player must follow suit if he can; if he has no cards of the suit led he is privileged to throw away any card he likes, thus having an opportunity of getting rid of his hearts, which is the object of the game. When all thirteen tricks have been played each player counts the hearts he has taken in and pays into the pool a certain number of counters for them, according to an arrangement made before beginning play. In the four-handed, or sweepstake, game the method of settling called "Howell's," from the name of the inventor, has been generally adopted, according to which each player begins with an equal number of chips, say 100, and, after the hand has been played, pays into the pool as many chips for each heart he had taken as there are players besides himself. Then each player takes out of the pool one chip for every heart he did not win. The pool is thus exhausted with every deal. Hearts may be played by two, three, four or even more players, each playing for himself.

_Spot Hearts._--In this variation the hearts count according to the number of spots on the cards, excepting that the ace counts 14, the king 13, queen 12 and knave 11, the combined score of the thirteen hearts being thus 104.

_Auction Hearts._--In this the eldest hand examines his hand and bids a certain number of counters for the privilege of naming the suit to be got rid of, but without naming the suit. The other players in succession have the privilege of outbidding him, and whoever bids most declares the suit and pays the amount of his bid into the pool, the winner taking it.

_Joker Hearts._--Here the deuce of hearts is discarded, and an extra card, called the joker, takes its place, ranking in value between ten and knave. It cannot be thrown away, excepting when hearts are led and an ace or court card is played, though if an opponent discards the ace or a court card of hearts, then the holder of the joker may discard it. The joker is usually considered worth five chips, which are either paid into the pool or to the player who succeeds in discarding the joker.

_Heartsette._--In this variation the deuce of spades is deleted and the three cards left after dealing twelve cards to each player are called the _widow_ (or _kitty_), and are left face downward on the table. The winner of the first trick must take the widow without showing it to his opponents.

_Slobberhannes._--The object of this older form of Hearts is to avoid taking either the first or last trick or a trick containing the queen of clubs. A euchre pack (thirty two-cards, lacking all below the 7) is used, and each player is given 10 counters, one being forfeited to the pool if a player takes the first or last trick, or that containing the club queen. If he takes all three he forfeits four points.

_Four Jacks (Polignac or Quatre-Valets)_ is usually played with a piquet pack, the cards ranking in France as at ecarte, but in Great Britain and America as at piquet. There is no trump suit. Counters are used, and the object of the game is to avoid taking any trick containing a knave, especially the knave of spades, called _Polignac_. The player taking such a trick forfeits one counter to the pool.

_Enfle_ (or _Schwellen_) is usually played by four persons with a piquet pack and for a pool. The cards rank as at Hearts, and there is no trump suit. A player must follow suit if he can, but if he cannot he may not discard, but must take up all tricks already won and add them to his hand. Play is continued until one player gets rid of all his cards and thus wins.

HEAT (O. E. _haetu_, which like "hot," Old Eng. _hat_, is from the Teutonic type _haita, hit_, to be hot; cf. Ger. _hitze, heiss_; Dutch, _hitte, heet_, &c.), a general term applied to that branch of physical science which deals with the effects produced by heat on material bodies, with the laws of transference of heat, and with the transformations of heat into other kinds of energy. The object of the present article is to give a brief sketch of the historical development of the science of heat, and to indicate the relation of the different branches of the subject, which are discussed in greater detail with reference to the latest progress in separate articles.

1. _Meanings of the Term Heat._--The term heat is employed in ordinary language in a number of different senses. This makes it a convenient term to employ for the general title of the science, but the different meanings must be carefully distinguished in scientific reasoning. For the present purpose, omitting metaphorical significations, we may distinguish four principal uses of the term: (a) Sensation of heat; (b) Temperature, or degree of hotness; (c) Quantity of thermal energy; (d) Radiant heat, or energy of radiation.

(a) From the sense of heat, aided in the case of very hot bodies by the sense of sight, we obtain our first rough notions of heat as a physical entity, which alters the state of a body and its condition in respect of warmth, and is capable of passing from one body to another. By touching a body we can tell whether it is warmer or colder than the hand, and, by touching two similar bodies in succession, we can form a rough estimate, by the acuteness of the sensation experienced, of their difference in hotness or coldness over a limited range. If a hot iron is placed on a cold iron plate, we may observe that the plate is heated and the iron cooled until both attain appreciably the same degree of warmth; and we infer from similar cases that something which we call "heat" tends to pass from hot to cold bodies, and to attain finally a state of equable diffusion when all the bodies concerned are equally warm or cold. Ideas such as these derived entirely from the sense of heat, are, so to speak, embedded in the language of every nation from the earliest times.

(b) From the sense of heat, again, we naturally derive the idea of a continuous scale or order, expressed by such terms as summer heat, blood heat, fever heat, red heat, white heat, in which all bodies may be placed with regard to their degrees of hotness, and we speak of the _temperature_ of a body as denoting its place in the scale, in contradistinction to the quantity of heat it may contain.

(c) The quantity of heat contained in a body obviously depends on the size of the body considered. Thus a large kettleful of boiling water will evidently contain more heat than a teacupful, though both may be at the same temperature. The temperature does not depend on the size of the body, but on the degree of concentration of the heat in it, i.e. on the quantity of heat per unit mass, other things being equal. We may regard it as axiomatic that a given body (say a pound of water) in a given state (say boiling under a given pressure) must always contain the same quantity of heat, and conversely that, if it contains a given quantity of heat, and if it is under conditions in other respects, it must be at a definite temperature, which will always be the same for the same given conditions.

(d) It is a matter of common observation that rays of the sun or of a fire falling on a body warm it, and it was in the first instance natural to suppose that heat itself somehow travelled across the intervening space from the sun or fire to the body warmed, in much the same way as heat may be carried by a current of hot air or water. But we now know that energy of radiation is not the same thing as heat, though it is converted into heat when the rays strike an absorbing substance. The term "radiant heat," however, is generally retained, because radiation is commonly measured in terms of the heat it produces, and because the transference of energy by radiation and absorption is the most important agency in the diffusion of heat.

2. _Evolution of the Thermometer._--The first step in the development of the science of heat was necessarily the invention of a thermometer, an instrument for indicating temperature and measuring its changes. The first requisite in the case of such an instrument is that it should always give, at least approximately the same indication at the same temperature. The air-thermoscope of Galileo, illustrated in fig. 1, which consisted of a glass bulb containing air, connected to a glass tube of small bore dipping into a coloured liquid, though very sensitive to variations of temperature, was not satisfactory as a measuring instrument, because it was also affected by variations of atmospheric pressure. The invention of the type of thermometer familiar at the present day, containing a liquid hermetically sealed in a glass bulb with a fine tube attached, is also generally attributed to Galileo at a slightly later date, about 1612. Alcohol was the liquid first employed, and the degrees, intended to represent thousandths of the volume of the bulb, were marked with small beads of enamel fused on the stem, as shown in fig. 2. In order to render the readings of such instruments comparable with each other, it was necessary to select a fixed point or standard temperature as the zero or starting-point of the graduations. Instead of making each degree a given fraction of the volume of the bulb, which would be difficult in practice, and would give different values for the degree with different liquids, it was soon found to be preferable to take _two fixed points_, and to divide the interval between them into the same number of degrees. It was natural in the first instance to take the temperature of the human body as one of the fixed points. In 1701 Sir Isaac Newton proposed a scale in which the freezing-point of water was taken as zero, and the temperature of the human body as 12 deg. About the same date (1714) Gabriel Daniel Fahrenheit proposed to take as zero the lowest temperature obtainable with a freezing mixture of ice and salt, and to divide the interval between this temperature and that of the human body into 12 deg. To obtain finer graduations the number was subsequently increased to 96 deg. The freezing-point of water was at that time supposed to be somewhat variable, because as a matter of fact it is possible to cool water several degrees below its freezing-point in the absence of ice. Fahrenheit showed, however, that as soon as ice began to form the temperature always rose to the same point, and that a mixture of ice or snow with pure water always gave the same temperature. At a later period he also showed that the temperature of boiling water varied with the barometric pressure, but that it was always the same at the same pressure, and might therefore be used as the second fixed point (as Edmund Halley and others had suggested) provided that a definite pressure, such as the average atmospheric pressure, were specified. The freezing and boiling-points on one of his thermometers, graduated as already explained, with the temperature of the body as 96 deg., came out in the neighbourhood of 32 deg. and 212 deg. respectively, giving an interval of 180 deg. between these points. Shortly after Fahrenheit's death (1736) the freezing and boiling-points of water were generally recognized as the most convenient fixed points to adopt, but different systems of subdivision were employed. Fahrenheit's scale, with its small degrees and its zero below the freezing-point, possesses undoubted advantages for meteorological work, and is still retained in most English-speaking countries. But for general scientific purposes, the centigrade system, in which the freezing-point is marked 0 deg. and the boiling-point 100 deg., is now almost universally employed, on account of its greater simplicity from an arithmetical point of view. For work of precision the fixed points have been more exactly defined (see THERMOMETRY), but no change has been made in the fundamental principle of graduation.

3. _Comparison of Scales based on Expansion._--Thermometers constructed in the manner already described will give strictly comparable readings, provided that the tubes be of uniform bore, and that the same liquid and glass be employed in their construction. But they possess one obvious defect from a theoretical point of view, namely, that the subdivision of the temperature scale depends on the expansion of the particular liquid selected as the standard. A liquid such as water, which, when continuously heated at a uniform rate from its freezing-point, first contracts and then expands, at a rapidly increasing rate, would obviously be unsuitable. But there is no a priori reason why other liquids should not behave to some extent in a similar way. As a matter of fact, it was soon observed that thermometers carefully constructed with different liquids, such as alcohol, oil and mercury, did not agree precisely in their indications at points of the scale intermediate between the fixed points, and diverged even more widely outside these limits. Another possible method, proposed in 1694 by Carlo Renaldeni (1615-1698), professor of mathematics and philosophy at Pisa, would be to determine the intermediate points of the scale by observing the temperatures of mixtures of ice-cold and boiling water in varying proportions. On this method, the temperature of 50 deg. C. would be defined as that obtained by mixing equal weights of water at 0 deg. C. and 100 deg. C.; 20 deg. C., that obtained by mixing 80 parts of water at 0 deg. C. with 20 parts of water at 100 deg. C. and so on. Each degree rise of temperature in a mass of water would then represent the addition of the same quantity of heat. The scale thus obtained would, as a matter of fact, agree very closely with that of a mercury thermometer, but the method would be very difficult to put in practice, and would still have the disadvantage of depending on the properties of a particular liquid, namely, water, which is known to behave in an anomalous manner in other respects. At a later date, the researches of Gay-Lussac (1802) and Regnault (1847) showed that the laws of the expansion of gases are much simpler than those of liquids. Whereas the expansion of alcohol between 0 deg. C. and 100 deg. C. is nearly seven times as great as that of mercury, all gases (excluding easily condensible vapours) expand equally, or so nearly equally that the differences between them cannot be detected without the most refined observations. This equality of expansion affords a strong a priori argument for selecting the scale given by the expansion of a gas as the standard scale of temperature, but there are still stronger theoretical grounds for this choice, which will be indicated in discussing the absolute scale (S 21). Among liquids mercury is found to agree most nearly with the gas scale, and is generally employed in thermometers for scientific purposes on account of its high boiling-point and for other reasons. The differences of the mercurial scale from the gas scale having been carefully determined, the mercury thermometer can be used as a secondary standard to replace the gas thermometer within certain limits, as the gas thermometer would be very troublesome to employ directly in ordinary investigations. For certain purposes, and especially at temperatures beyond the range of mercury thermometers, electrical thermometers, also standardized by reference to the gas thermometer, have been very generally employed in recent years, while for still higher temperatures beyond the range of the gas thermometer, thermometers based on the recently established laws of radiation are the only instruments available. For a further discussion of the theory and practice of the measurement of temperature, the reader is referred to the article THERMOMETRY.

_4. Change of State._--Among the most important effects of heat is that of changing the state of a substance from solid to liquid, or from liquid to vapour. With very few exceptions, all substances, whether simple or compound, are known to be capable of existing in each of the three states under suitable conditions of temperature and pressure. The transition of any substance, from the state of liquid to that of solid or vapour under the ordinary atmospheric pressure, takes place at fixed temperatures, the freezing and boiling-points, which are very sharply defined for pure crystalline substances, and serve in fact as fixed points of the thermometric scale. A change of state cannot, however, be effected in any case without the addition or subtraction of a certain definite quantity of heat. If a piece of ice below the freezing-point is gradually heated at a uniform rate, its temperature may be observed to rise regularly till the freezing-point is reached. At this point it begins to melt, and its temperature ceases to rise. The melting takes a considerable time, during the whole of which heat is being continuously supplied without producing any rise of temperature, although if the same quantity of heat were supplied to an equal mass of water, the temperature of the water would be raised nearly 80 deg. C. Heat thus absorbed in producing a change of state without rise of temperature is called "Latent Heat," a term introduced by Joseph Black, who was one of the first to study the subject of change of state from the point of view of heat absorbed, and who in many cases actually adopted the comparatively rough method described above of estimating quantities of heat by observing the time required to produce a given change when the substance was receiving heat at a steady rate from its surroundings. For every change of state a definite quantity of heat is required, without which the change cannot take place. Heat must be added to melt a solid, or to vaporize a solid or a liquid, and conversely, heat must be subtracted to reverse the change, i.e. to condense a vapour or freeze a liquid. The quantity required for any given change depends on the nature of the substance and the change considered, and varies to some extent with the conditions (as to pressure, &c.) under which the change is made, but is always the same for the same change under the same conditions. A rough measurement of the latent heat of steam was made as early as 1764 by James Watt, who found that steam at 212 deg. F., when passed from a kettle into a jar of cold water, was capable of raising nearly six times its weight of water to the boiling point. He gives the volume of the steam as about 1800 times that of an equal weight of water.

The phenomena which accompany change of state, and the physical laws by which such changes are governed, are discussed in a series of special articles dealing with particular cases. The articles on FUSION and ALLOYS deal with the change from the solid to the liquid state, and the analogous case of solution is discussed in the article on SOLUTION. The articles on CONDENSATION OF GASES, LIQUID GASES and VAPORIZATION deal with the theory of the change of state from liquid to vapour, and with the important applications of liquid gases to other researches. The methods of measuring the latent heat of fusion or vaporization are described in the article CALORIMETRY, and need not be further discussed here except as an introduction to the history of the evolution of knowledge with regard to the nature of heat.

5. _Calorimetry by Latent Heat._--In principle, the simplest and most direct method of measuring quantities of heat consists in observing the effects produced in melting a solid or vaporizing a liquid. It was, in fact, by the fusion of ice that quantities of heat were first measured. If a hot body is placed in a cavity in a block of ice at 0 deg. C., and is covered by a closely fitting slab of ice, the quantity of ice melted will be directly proportional to the quantity of heat lost by the body in cooling to 0 deg. C. None of the heat can possibly escape through the ice, and conversely no heat can possibly get in from outside. The body must cool exactly to 0 deg. C., and every fraction of the heat it loses must melt an equivalent quantity of ice. Apart from heat lost in transferring the heated body to the ice block, the method is theoretically perfect. The only difficulty consists in the practical measurement of the quantity of ice melted. Black estimated this quantity by mopping out the cavity with a sponge before and after the operation. But there is a variable film of water adhering to the walls of the cavity, which gives trouble in accurate work. In 1780 Laplace and Lavoisier used a double-walled metallic vessel containing broken ice, which was in many respects more convenient than the block, but aggravated the difficulty of the film of water adhering to the ice. In spite of this practical difficulty, the quantity of heat required to melt unit weight of ice was for a long time taken as the unit of heat. This unit possesses the great advantage that it is independent of the scale of temperature adopted. At a much later date R. Bunsen (_Phil. Mag._, 1871), adopting a suggestion of Sir John Herschel's, devised an ice-calorimeter suitable for measuring small quantities of heat, in which the difficulty of the water film was overcome by measuring the change in volume due to the melting of the ice. The volume of unit mass of ice is approximately 1.0920 times that of unit mass of water, so that the diminution of volume is 0.092 a cubic centimetre for each gramme of ice melted. The method requires careful attention to details of manipulation, which are more fully discussed in the article on CALORIMETRY.

For measuring large quantities of heat, such as those produced by the combustion of fuel in a boiler, the most convenient method is the evaporation of water, which is commonly employed by engineers for the purpose. The natural unit in this case is the quantity of heat required to evaporate unit mass of water at the boiling point under atmospheric pressure. In boilers working at a higher pressure, or supplied with water at a lower temperature, appropriate corrections are applied to deduce the quantity evaporated in terms of this unit.

For laboratory work on a small scale the converse method of condensation has been successfully applied by John Joly, in whose steam-calorimeter the quantity of heat required to raise the temperature of a body from the atmospheric temperature to that of steam condensing at atmospheric pressure is observed by weighing the mass of steam condensed on it. (See CALORIMETRY.)

6. _Thermometric Calorimetry._--For the majority of purposes the most convenient and the most readily applicable method of measuring quantities of heat, is to observe the rise of temperature produced in a known mass of water contained in a suitable vessel or calorimeter. This method was employed from a very early date by Count Rumford and other investigators, and was brought to a high pitch of perfection by Regnault in his extensive calorimetric researches (_Memoires de l'Institut de Paris_, 1847); but it is only within comparatively recent years that it has really been placed on a satisfactory basis by the accurate definition of the units involved. The theoretical objections to the method, as compared with latent heat calorimetry, are that some heat is necessarily lost by the calorimeter when its temperature is raised above that of the surroundings, and that some heat is used in heating the vessel containing the water. These are small corrections, which can be estimated with considerable accuracy in practice. A more serious difficulty, which has impaired the value of much careful work by this method, is that the quantity of heat required to raise the temperature of a given mass of water 1 deg. C. depends on the temperature at which the water is taken, and also on the scale of the thermometer employed. It is for this reason, in many cases, impossible to say, at the present time, what was the precise value, within 1/2 or even 1% of the heat unit, in terms of which many of the older results, such as those of Regnault, were expressed. For many purposes this would not be a serious matter, but for work of scientific precision such a limitation of accuracy would constitute a very serious bar to progress. The unit generally adopted for scientific purposes is the quantity of heat required to raise 1 gram (or kilogram) of water 1 deg. C., and is called the calorie (or kilo-calorie). English engineers usually state results in terms of the British Thermal Unit (B.Th.U.), which is the quantity of heat required to raise 1 lb. of water 1 deg. F.

7. _Watt's Indicator Diagram; Work of Expansion._--The rapid development of the steam-engine (q.v.) in England during the latter part of the 18th century had a marked effect on the progress of the science of heat. In the first steam-engines the working cylinder served both as boiler and condenser, a very wasteful method, as most of the heat was transferred directly from the fire to the condensing water without useful effect. The first improvement (about 1700) was to use a separate boiler, but the greater part of the steam supplied was still wasted in reheating the cylinder, which had been cooled by the injection of cold water to condense the steam after the previous stroke. In 1769 James Watt showed how to avoid this waste by using a separate condenser and keeping the cylinder as hot as possible. In his earlier engines the steam at full boiler pressure was allowed to raise the piston through nearly the whole of its stroke. Connexion with the boiler was then cut off, and the steam at full pressure was discharged into the condenser. Here again there was unnecessary waste, as the steam was still capable of doing useful work. He subsequently introduced "expansive working," which effected still further economy. The connexion with the boiler was cut off when a fraction only, say 1/4, of the stroke had been completed, the remainder of the stroke being effected by the expansion of the steam already in the cylinder with continually diminishing pressure. By the end of the stroke, when connexion was made to the condenser, the pressure was so reduced that there was comparatively little waste from this cause. Watt also devised an instrument called an _indicator_ (see STEAM ENGINE), in which a pencil, moved up and down vertically by the steam pressure, recorded the pressure in the cylinder at every point of the stroke on a sheet of paper moving horizontally in time with the stroke of the piston. The diagram thus obtained made it possible to study what was happening inside the cylinder, and to deduce the work done by the steam in each stroke. The method of the indicator diagram has since proved of great utility in physics in studying the properties of gases and vapours. The work done, or the useful effect obtained from an engine or any kind of machine, is measured by the product of the resistance overcome and the distance through which it is overcome. The result is generally expressed in terms of the equivalent weight raised through a certain height against the force of gravity.[1] If, for instance, the pressure on a piston is 50 lb. per sq. in., and the area of the piston is 100 sq. in., the force on the piston is 5000 lb. weight. If the stroke of the piston is 1 ft., the work done per stroke is capable of raising a weight of 5000 lb. through a height of 1 ft., or 50 lb. through a height of 100 ft. and so on.

Fig. 3 represents an imaginary indicator diagram for a steam-engine, taken from one of Watt's patents. Steam is admitted to the cylinder when the piston is at the beginning of its stroke, at S. ST represents the length of the stroke or the limit of horizontal movement of the paper on which the diagram is drawn. The indicating pencil rises to the point A, representing the absolute pressure of 60 lb. per sq. in. As the piston moves outwards the pencil traces the horizontal line AB, the pressure remaining constant till the point B is reached, at which connexion to the boiler is cut off. The work done so far is represented by the area of the rectangle ABSF, namely AS X SF, multiplied by the area of the piston in sq. in. The result is in foot-pounds if the fraction of the stroke SF is taken in feet. After cut-off at B the steam expands under diminishing pressure, and the pencil falls gradually from B to C, following the steam pressure until the exhaust valve opens at the end of the stroke. The pressure then falls rapidly to that of the condenser, which for an ideal case may be taken as zero, following Watt. The work done during expansion is found by dividing the remainder of the stroke FT into a number of equal parts (say 8, Watt takes 20) and measuring the pressure at the points 1, 2, 3, 4, &c., corresponding to the middle of each. We thus obtain a number of small rectangles, the sum of which is evidently very nearly equal to the whole area BCTF under the expansion curve, or to the remainder of the stroke FT multiplied by the average or mean value of the pressure. The whole work done in the forward stroke is represented by the area ABCTSA, or by the average value of the pressure P over the whole stroke multiplied by the stroke L. This area must be multiplied by the area of the piston A in sq. in. as before, to get the work done per stroke in foot-pounds, which is PLA. If the engine repeats this cycle N times per minute, the work done per minute is PLAN foot-pounds, which is reduced to horse-power by dividing by 33,000. If the steam is ejected by the piston at atmospheric pressure (15 lb. per sq. in.) instead of being condensed at zero pressure, the area CDST under the atmospheric line CD, representing work done against back-pressure on the return stroke must be subtracted. If the engine repeats the same cycle or series of operations continuously, the indicator diagram will be a closed curve, and the nett work done per cycle will be represented by the included area, whatever the form of the curve.

8. _Thermal Efficiency._--The thermal efficiency of an engine is the ratio of the work done by the engine to the heat supplied to it. According to Watt's observations, confirmed later by Clement and Desormes, the total heat required to produce 1 lb. of saturated steam at any temperature from water at 0 deg. C. was approximately 650 times the quantity of heat required to raise 1 lb. of water 1 deg. C. Since 1 lb. of steam represented on this assumption a certain quantity of heat, the efficiency could be measured naturally in foot-pounds of work obtainable per lb. of steam, or conversely in pounds of steam consumed per horse-power-hour.

In his patent of 1782 Watt gives the following example of the improvement in thermal efficiency obtained by expansive working. Taking the diagram already given, if the quantity of steam represented by AB, or 300 cub. in. at 60 lb. pressure, were employed without expansion, the work realized, represented by the area ABSF, would be 6000/4 = 1500 foot-pounds. With expansion to 4 times its original volume, as shown in the diagram by the whole area ABCTSA, the mean pressure (as calculated by Watt, assuming Boyle's law) would be 0.58 of the original pressure, and the work done would be 6000 X 0.58 = 3480 foot-pounds for the same quantity of steam, or the thermal efficiency would be 2.32 times greater. The advantage actually obtained would not be so great as this, on account of losses by condensation, back-pressure, &c., which are neglected in Watt's calculation, but the margin would still be very considerable. Three hundred cub. in. of steam at 60 lb. pressure would represent about .0245 of 1 lb. of steam, or 28.7 B.Th.U., so that, neglecting all losses, the possible thermal efficiency attainable with steam at this pressure and four expansions (1/4 cut-off) would be 3480/28.7, or 121 foot-pounds per B.Th.U. At a later date, about 1820, it was usual to include the efficiency of the boiler with that of the engine, and to reckon the efficiency or "duty" in foot-pounds per bushel or cwt. of coal. The best Cornish pumping-engines of that date achieved about 70 million foot-pounds per cwt., or consumed about 3.2 lb. per horse-power-hour, which is roughly equivalent to 43 foot-pounds per B.Th.U. The efficiency gradually increased as higher pressures were used, with more complete expansion, but the conditions upon which the efficiency depended were not fully worked out till a much later date. Much additional knowledge with regard to the nature of heat, and the properties of gases and vapours, was required before the problem could be attacked theoretically.

9. _Of the Nature of Heat._--In the early days of the science it was natural to ascribe the manifestations of heat to the action of a subtle imponderable fluid called "caloric," with the power of penetrating, expanding and dissolving bodies, or dissipating them in vapour. The fluid was imponderable, because the most careful experiments failed to show that heat produced any increase in weight. The opposite property of levitation was often ascribed to heat, but it was shown by more cautious investigators that the apparent loss of weight due to heating was to be attributed to evaporation or to upward air currents. The fundamental idea of an imaginary fluid to represent heat was useful as helping the mind to a conception of something remaining invariable in quantity through many transformations, but in some respects the analogy was misleading, and tended greatly to retard the progress of science. The caloric theory was very simple in its application to the majority of calorimetric experiments, and gave a fair account of the elementary phenomena of change of state, but it encountered serious difficulties in explaining the production of heat by friction, or the changes of temperature accompanying the compression or expansion of a gas. The explanation which the calorists offered of the production of heat by friction or compression was that some of the latent caloric was squeezed or ground out of the bodies concerned and became "sensible." In the case of heat developed by friction, they supposed that the abraded portions of the material were capable of holding a smaller quantity of heat, or had less "capacity for heat," than the original material. From a logical point of view, this was a perfectly tenable hypothesis, and one difficult to refute. It was easy to account in this way for the heat produced in boring cannon and similar operations, where the amount of abraded material was large. To refute this explanation, Rumford (_Phil. Trans._, 1798) made his celebrated experiments with a blunt borer, in one of which he succeeded in boiling by friction 26.5 lb. of cold water in 2(1/2) hours, with the production of only 4145 grains of metallic powder. He then showed by experiment that the metallic powder required the same amount of heat to raise its temperature 1 deg., as an equal weight of the original metal, or that its "capacity for heat" (in this sense) was unaltered by reducing it to powder; and he argued that "in any case so small a quantity of powder could not possibly account for all the heat generated, that the supply of heat appeared to be inexhaustible, and that heat could not be a material substance, but must be something of the nature of motion." Unfortunately Rumford's argument was not quite conclusive. The supporters of the caloric theory appear, whether consciously or unconsciously, to have used the phrase "capacity for heat" in two entirely distinct senses without any clear definition of the difference. The phrase "capacity for heat" might very naturally denote the total quantity of heat contained in a body, which we have no means of measuring, but it was generally used to signify the quantity of heat required to raise the temperature of a body one degree, which is quite a different thing, and has no necessary relation to the total heat. In proving that the powder and the solid metal required the same quantity of heat to raise the temperature of equal masses of either one degree, Rumford did not prove that they contained equal quantities of heat, which was the real point at issue in this instance. The metal tin actually changes into powder below a certain temperature, and in so doing evolves a measurable quantity of heat. A mixture of the gases oxygen and hydrogen, in the proportions in which they combine to form water, evolves when burnt sufficient heat to raise more than thirty times its weight of water from the freezing to the boiling point; and the mixture of gases may, in this sense, be said to contain so much more heat than the water, although its capacity for heat in the ordinary sense is only about half that of the water produced. To complete the refutation of the calorists' explanation of the heat produced by friction, it would have been necessary for Rumford to show that the powder when reconverted into the same state as the solid metal did not absorb a quantity of heat equivalent to that evolved in the grinding; in other words that the heat produced by friction was not simply that due to the change of state of the metal from solid to powder.

Shortly afterwards, in 1799, Davy[2] described an experiment in which he melted ice by rubbing two blocks together. This experiment afforded a very direct refutation of the calorists' view, because it was a well-known fact that ice required to have a quantity of heat added to it to convert it into water, so that the water produced by the friction contained more heat than the ice. In stating as the conclusion to be drawn from this experiment that "friction consequently does not diminish the capacity of bodies for heat," Davy apparently uses the phrase capacity for heat in the sense of total heat contained in a body, because in a later section of the same essay he definitely gives the phrase this meaning, and uses the term "capability of temperature" to denote what we now term capacity for heat.

The delay in the overthrow of the caloric theory, and in the acceptance of the view that heat is a mode of motion, was no doubt partly due to some fundamental confusion of ideas in the use of the term "capacity for heat" and similar phrases. A still greater obstacle lay in the comparative vagueness of the motion or vibration theory. Davy speaks of heat as being "repulsive motion," and distinguishes it from light, which is "projective motion"; though heat is certainly not a substance--according to Davy in the essay under discussion--and may not even be treated as an imponderable fluid, light as certainly is a material substance, and is capable of forming chemical compounds with ordinary matter, such as oxygen gas, which is not a simple substance, but a compound, termed phosoxygen, of light and oxygen. Accepting the conclusions of Davy and Rumford that heat is not a material substance but a mode of motion, there still remains the question, what definite conception is to be attached to a quantity of heat? What do we mean by a quantity of vibratory motion, how is the quantity of motion to be estimated, and why should it remain invariable in many transformations? The idea that heat was a "mode of motion" was applicable as a qualitative explanation of many of the effects of heat, but it lacked the quantitative precision of a scientific statement, and could not be applied to the calculation and prediction of definite results. The state of science at the time of Rumford's and Davy's experiments did not admit of a more exact generalization. The way was paved in the first instance by a more complete study of the laws of gases, to which Laplace, Dalton, Gay-Lussac, Dulong and many others contributed both on the experimental and theoretical side. Although the development proceeded simultaneously along many parallel lines, it is interesting and instructive to take the investigation of the properties of gases, and to endeavour to trace the steps by which the true theory was finally attained.

10. _Thermal Properties of Gases._--The most characteristic property of a gaseous or elastic fluid, namely, the elasticity, or resistance to compression, was first investigated scientifically by Robert Boyle (1662), who showed that the pressure p of a given mass of gas varied inversely as the volume v, provided that the temperature remained constant. This is generally expressed by the formula pv = C, where C is a constant for any given temperature, and v is taken to represent the specific volume, or the volume of unit mass, of the gas at the given pressure and temperature. Boyle was well aware of the effect of heat in expanding a gas, but he was unable to investigate this properly as no thermometric scale had been defined at that date. According to Boyle's law, when a mass of gas is compressed by a small amount at constant temperature, the percentage increase of pressure is equal to the percentage diminution of volume (if the compression is v/100, the increase of pressure is very nearly p/100). Adopting this law, Newton showed, by a most ingenious piece of reasoning (_Principia_, ii., sect. 8), that the velocity of sound in air should be equal to the velocity acquired by a body falling under gravity through a distance equal to half the height of the atmosphere, considered as being of uniform density equal to that at the surface of the earth. This gave the result 918 ft. per sec. (280 metres per sec.) for the velocity at the freezing point. Newton was aware that the actual velocity of sound was somewhat greater than this, but supposed that the difference might be due in some way to the size of the air particles, of which no account could be taken in the calculation. The first accurate measurement of the velocity of sound by the French Academie des Sciences in 1738 gave the value 332 metres per sec. as the velocity at 0 deg. C. The true explanation of the discrepancy was not discovered till nearly 100 years later.

The law of expansion of gases with change of temperature was investigated by Dalton and Gay-Lussac (1802), who found that the volume of a gas under constant pressure increased by 1/267th part of its volume at 0 deg. C. for each 1 deg. C. rise in temperature. This value was generally assumed in all calculations for nearly 50 years. More exact researches, especially those of Regnault, at a later date, showed that the law was very nearly correct for all permanent gases, but that the value of the coefficient should be 1/273rd. According to this law the volume of a gas at any temperature t deg. C. should be proportional to 273 + t, i.e. to the temperature reckoned from a zero 273 deg. below that of the Centigrade scale, which was called the absolute zero of the gas thermometer. If T = 273 + t, denotes the temperature measured from this zero, the law of expansion of a gas may be combined with Boyle's law in the simple formula

pv = RT (1)

which is generally taken as the expression of the gaseous laws. If equal volumes of different gases are taken at the same temperature and pressure, it follows that the constant R is the same for all gases. If equal masses are taken, the value of the constant R for different gases varies inversely as the molecular weight or as the density relative to hydrogen.

Dalton also investigated the laws of vapours, and of mixtures of gases and vapours. He found that condensible vapours approximately followed Boyle's law when compressed, until the condensation pressure was reached, at which the vapour liquefied without further increase of pressure. He found that when a liquid was introduced into a closed space, and allowed to evaporate until the space was saturated with the vapour and evaporation ceased, the increase of pressure in the space was equal to the condensation pressure of the vapour, and did not depend on the volume of the space or the presence of any other gas or vapour provided that there was no solution or chemical action. He showed that the condensation or saturation-pressure of a vapour depended only on the temperature, and increased by nearly the same fraction of itself per degree rise of temperature, and that the pressures of different vapours were nearly the same at equal distances from their boiling points. The increase of pressure per degree C. at the boiling point was about 1/28th of 760 mm. or 27.2 mm., but increased in geometrical progression with rise of temperature. These results of Dalton's were confirmed, and in part corrected, as regards increase of vapour-pressure, by Gay-Lussac, Dulong, Regnault and other investigators, but were found to be as close an approximation to the truth as could be obtained with such simple expressions. More accurate empirical expressions for the increase of vapour-pressure of a liquid with temperature were soon obtained by Thomas Young, J. P. L. A. Roche and others, but the explanation of the relation was not arrived at until a much later date (see VAPORIZATION).

11. _Specific Heats of Gases._--In order to estimate the quantities of heat concerned in experiments with gases, it was necessary in the first instance to measure their specific heats, which presented formidable difficulties. The earlier attempts by Lavoisier and others, employing the ordinary methods of calorimetry, gave very uncertain and discordant results, which were not regarded with any confidence even by the experimentalists themselves. Gay-Lussac (_Memoires d'Arcueil_, 1807) devised an ingenious experiment, which, though misinterpreted at the time, is very interesting and instructive. With the object of comparing the specific heats of different gases, he took two equal globes A and B connected by a tube with a stop-cock. The globe B was exhausted, the other A being filled with gas. On opening the tap between the vessels, the gas flowed from A to B and the pressure was rapidly equalized. He observed that the fall of temperature in A was nearly equal to the rise of temperature in B, and that for the same initial pressure the change of temperature was very nearly the same for all the gases he tried, except hydrogen, which showed greater changes of temperature than other gases. He concluded from this experiment that equal volumes of gases had the same capacity for heat, except hydrogen, which he supposed to have a larger capacity, because it showed a greater effect. The method does not in reality afford any direct information with regard to the specific heats, and the conclusion with regard to hydrogen is evidently wrong. At a later date (_Ann. de Chim._, 1812, 81, p. 98) Gay-Lussac adopted A. Crawford's method of mixture, allowing two equal streams of different gases, one heated and the other cooled about 20 deg. C., to mix in a tube containing a thermometer. The resulting temperature was in all cases nearly the mean of the two, from which he concluded that equal volumes of all the gases tried, namely, hydrogen, carbon dioxide, air, oxygen and nitrogen, had the same thermal capacity. This was correct, except as regards carbon dioxide, but did not give any information as to the actual specific heats referred to water or any known substance. About the same time, F. Delaroche and J. E. Berard (_Ann. de chim._, 1813, 85, p. 72) made direct determinations of the specific heats of air, oxygen, hydrogen, carbon monoxide, carbon dioxide, nitrous oxide and ethylene, by passing a stream of gas heated to nearly 100 deg. C. through a spiral tube in a calorimeter containing water. Their work was a great advance on previous attempts, and gave the first trustworthy results. With the exception of hydrogen, which presents peculiar difficulties, they found that equal volumes of the permanent gases, air, oxygen and carbon monoxide, had nearly the same thermal capacity, but that the compound condensible gases, carbon dioxide, nitrous oxide and ethylene, had larger thermal capacities in the order given. They were unable to state whether the specific heats of the gases increased or diminished with temperature, but from experiments on air at pressures of 740 mm. and 1000 mm., they found the specific heats to be .269 and .245 respectively, and concluded that the specific heat diminished with increase of pressure. The difference they observed was really due to errors of experiment, but they regarded it as proving beyond doubt the truth of the calorists' contention that the heat disengaged on the compression of a gas was due to the diminution of its thermal capacity.

Dalton and others had endeavoured to measure directly the rise of temperature produced by the compression of a gas. Dalton had observed a rise of 50 deg. F. in a gas when suddenly compressed to half its volume, but no thermometers at that time were sufficiently sensitive to indicate more than a fraction of the change of temperature. Laplace was the first to see in this phenomenon the probable explanation of the discrepancy between Newton's calculation of the velocity of sound and the observed value. The increase of pressure due to a sudden compression, in which no heat was allowed to escape, or as we now call it an "adiabatic" compression, would necessarily be greater than the increase of pressure in a slow isothermal compression, on account of the rise of temperature. As the rapid compressions and rarefactions occurring in the propagation of a sound wave were perfectly adiabatic, it was necessary to take account of the rise of temperature due to compression in calculating the velocity. To reconcile the observed and calculated values of the velocity, the increase of pressure in adiabatic compression must be 1.410 times greater than in isothermal compression. This is the ratio of the adiabatic elasticity of air to the isothermal elasticity. It was a long time, however, before Laplace saw his way to any direct experimental verification of the value of this ratio. At a later date (_Ann. de chim._, 1816, 3, p. 238) he stated that he had succeeded in proving that the ratio in question must be the same as the ratio of the specific heat of air at constant pressure to the specific heat at constant volume.

In the method of measuring the specific heat adopted by Delaroche and Berard, the gas under experiment, while passing through a tube at practically constant pressure, contracts in cooling, as it gives up its heat to the calorimeter. Part of the heat surrendered to the calorimeter is due to the contraction of volume. If a gramme of gas at pressure p, volume v and temperature T abs. is heated 1 deg. C. at constant pressure p, it absorbs a quantity of heat S = .238 calorie (according to Regnault) the specific heat at constant pressure. At the same time the gas expands by a fraction 1/T of v, which is the same as 1/273 of its volume at 0 deg. C. If now the air is suddenly compressed by an amount v/T, it will be restored to its original volume, and its temperature will be raised by the liberation of a quantity of heat R', the latent heat of expansion for an increase of volume v/T. If no heat has been allowed to escape, the air will now be in the same state as if a quantity of heat S had been communicated to it at its original