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ganglion, really consists of several fibres coming from different and pn very distant parts. In other words, I am led to suppose that a single dakbordered fibre, or rather its axis-cylinder, is the common channel forth* passage of many different nerve-currents having different destinations. It i common to a portion of a great many different circuits. The fibres which result from the subdivision of the large fibre which leaves the cell becont* exceedingly fine (the 100'000th of an inch in diameter or less), and pursue very long course before they run parallel with other fibres. As the fibre* which have the same destination increase in number, the compound trunk becomes gradually thicker aud more distinct. The several individual fibre* cualesce and form one trunk, or axis-cylinder, around which the protecnre white substance of Schwann collects. At the periphery the subdivision o* the dark-bordered fibre again occurs, until peripheral fibres as fine as the central component fibres result*.

[graphic]

Diagram to show the course of the fibres which leave the caudate nerve-cells «, » are parts of two nerve-cells, and two entire cells are also represented. Fibre* from several different cells unite to form single nerve-libres, 4, 4, 4. In parsing toward* the periphery these fibres divide and subdivide; the resulting subdivisions pass to deferent destinations. The fine fibres resulting from the subdivision of one of the caudal? processes of a nerve-cell may help to form a vast number of dark-bordered nerves, bin it is most certain that no single process ererforms on* entire axis-cylinder.

Although it may be premature to devise diagrams of the actual arrangement, if I permit myself to attempt this, I shall be able to express the inferences to which I have been led up to the present time in a far mori' intelligible manner than I could by description. But I only offer these schemes as rough suggestions, and feel sure that further observation wili

* "General Observations upon the Peripheral Distribution of Nerves," my 'Archives,' iii. p. 234. '* Distribution of Nerves to the Bladder of the Frog," p. 243. "Distribution of Nerves to the Mucous Membrane of the Epiglottis of the Human subject.," p. 249.

table me to modify them and render them more exact. The fibres would nature be infinitely longer than represented in the diagrams. The cell ;low c (fig. 5) may be one of the caudate nerve-cells in the anterior root 7 a. spinal nerve, that above b one of the cells of the ganglion upon the asterior root, and a the periphery. I will not attempt to describe the jurse of these fibres until many different observations upon which I am ow engaged are further advanced, but I have already demonstrated the assage of the fibres from the ganglion-cell into the dark-bordered fibres s represented in the diagram.

Fig. 5.

[graphic]

Diagram to show possible relation of fibres from caudate uerve-cells, and fibres from cells in ganglia, as, for example, the ganglia on the posterior roots, a is supposed to be the periphery; the cell above b one of those in the ganglion. The three caudate cells resemble those in the grey matter of the cord, medulla oblongata, and brain.

The peculiar appearance I have demonstrated in the large caudate cells, taken in connexion with the fact urged by me in several papers, that no true termination or commencement has yet been demonstrated in the case of any nerve, seems to me to favour the conclusion that the action of a nervous apparatus results from varying intensities of continuous currents which are constantly passing along the nerves during life, rather than from the sudden interruption or completion of nerve-currents. So far from any arrangement having been demonstrated in connexion with any nervous structure which would permit the sudden interruption and completion of a current, anatomical observation demonstrates the structural continuity of all nerve-fibres with nerve-cells, and, indirectly through these cells, with one another.

I venture to conclude that the typical anatomical arrangement of a 1 vous mechanism is not a cord with tico endsa point of origin ami < \ terminal extremity, but a cord without an enda continuous circuit.

The peculiar structure of the caudate nerve-cells, which I have described, ) renders it, I think, very improbable that these cells are sources of nervoas { power, while, on the other hand, the structure, mode of growth, and iu dee. the whole life-history of the rounded ganglion-cells render it very probable that they perform such an office. These two distinct classes at" nerve-cells, in connexion with the nervous system, which are very closely related, and probably, through nerve-fibres, structurally continuous, seen: to perform very different functions,—the one originating curreuts, while the other is concerned more particularly with the distribution of these, and of secondary currents induced by them, in very many different directions. A current originating in a ganglion-cell would probably give rise to mam induced currents as it traversed a caudate nerve-cell. It seems probable that nerve-currents emanating from the rounded ganglion-cells may be constantly traversing the innumerable circuits in every part of the nervous system, and that nervous actions are due to a disturbance, perhaps a variation in the intensity of the currents, which must immediately result bom J the slightest change occurring in any part of the nerve-fibre, as weJI as | from any physical or chemical alteration taking place in the nerve-centres, | or in peripheral nervous organs.

XXIII. "On the Physical Constitution and Relations of Musical Chords." By Alexander J. Ellis, F.R.S., F.C.P.S.* Received June 8, 1864.

When the motion of the particles of air follows the law of oscillation of a simple pendulum, the resulting sound may be called a simple tone. The pitch of a simple tone is taken to be the number of double -vibrations which the particles of air perform in one second. The greatest elongation of a particle from its position of rest may be termed the extent of the tone. The intensity or loudness is assumed to vary as the square of the extent. The tone heard when a tuning-fork is held before a proper resonance-box is simple. The tone of wide covered organ-pipes and of flutes is nearly simple.

Professor G. S. Ohm has shown mathematically that all musical tones whatever may be considered as the algebraical sum of a number of simple tones of different intensities, having their pitches in the proportion of the numerical series 1, 2, 3, 4, 5, 6, 7, 8, &c. Professor Helmholtz has established that this mathematical composition corresponds to a fact in nature, that the ear can be taught to hear each one of these simple tones separately, and that the character or quality of the tone depends on the law of the intensity of the constituent simple tones.

These constituent simple tones will here be termed indifferently partial 'The Tables beloupinp to this Paper will bo found after p. 422.

lira or harmonies, and the result of their combination a compound tone. \y the pitch of a compound tone will be mennt the pitch of the lowest tartial tone or primary.

When two simple tones which are not of the same pitch are sounded ogether, they will alternately reinforce and enfeeble each other's effect, producing a libration of sound, termed a beat. The number of these beats in one second will necessarily be the difference of the pitches of the two simple tones, which may be termed the beat number. As for some time the two sets of vibrations concur, and for some time they are nearly opposite, the compound extent will be for some time nearly the sum, and for some time nearly the difference of the two simple extents, and the intensity of the beat may be measured by the ratio of the greater intensity to the less. But the beat will not be audible unless the ratio of the greater to the smaller pitch is less than 6 : 5, according to Professor Helmholtz. This is a convenient limit to fix, but it is probably not quite exact. To try the experiment, I have had two sliding pipes, each stopped at the end, and having each a continuous range of an octave, connected to one mouthpiece. The tones are nearly simple; and when the ratio approaches to 6:5, or the interval of a minor third, the beats become faint, finally vanish, and do not reappear. But the exact moment of their disappearance is difficult to fix, and indeed seems to vary, probably with the condition of the ear. The ear appears to be most sensitive to the bents when the ratio is about 16 : 15. After this the beats again diminish in sharpness; and when the ratio is very near to unity, the ear is apt to overlook them altogether. The

effect is almost that of a broken line of sound, as ,

the spaces representing the silences.

Slow beats are not disagreeable; for example, when they do not exceed 3 or 4 in a second. At 8 or 10 they become harsh; from 15 to 40 they thoroughly destroy the continuity of tone, and are discordant. After 40 they become less annoying. Professor Helmholtz thinks 33 the beat number of maximum disagreeableness. As the beats become very rapid, from 60 to 80 or 100 in a second, they become almost insensible. Professor Helmholtz considers 132 as the limiting number of beats which can be heard. They are certainly still to be distinguished even at that rate, but become more and more like a scream. Though/8J and g* should give 198 beats in a second if e=264, and the interval is that for which the ear is most sensitive, I can detect no beats when these tones are played on two flageolet-fifes. Hence beats from 10 to 70 may be considered as discordant, and as the source of all discord in music. Beyond these limits they produce a certain amount of harshness, but are not properly discordant.

When the extent of the tones is not infinitesimal, Professor Helmholtz has proved that on two simple tones being sounded together, many other tones will be generated. The pitch of the principal and only one of these combinational tones necessary to be considered, is the difference of the pitch of its generating tones. It will therefore be termed the differential 394 Mr. A. J. Kllis on Musical Chords. [June 16, |

tone. Its intensity is geneially very small, but it becomes distinctly audible in beats. The differential tone is frequently acuter than the lower ■ generator, and hence the ordinary name "grave harmonic" is inapplicable. As its pitch is the beat number of the combination, Dr. T. Young attributed its generation to the beats having become too rapid to be distinguished. This theory is disproved, first, by the existence of differential tones for intervals which do not beat, and secondly, by the simultaneous presence of distinct beats and differential tones, as I have frequently heard on sounding/4, /*£, or even f*, f*$ together on the concertina, when the beats form a distinct rattle, and the differential tone is a peculiar penetrating but very deep hum.

The object of this paper is to apply these laws, partly physical and partly physiological, to explain the constitution and relations of musical chords. It is a continuation of my former paper on a Perfect Musical Scale*, and the Tables are numbered accordingly.

Two simple tones which make a greater interval than 6:5, and therefore never beat, will be termed disjunct. Simple tones making i smaller interval, and therefore generally beating, will be termed puhatittThe unreduced ratio of the pitch of the lower pulsative tone for which thf beat number is 70 to that for which it is only 10, will be termed the range of the beat. The fraction by which the pitch of the lower pulsative tone must be multiplied to produce the beat number, will be termed the be*' factor. The ratio of the pitches of the pulsative tones, on which the sharpness of the dissonance depends, will be termed the beat internal.

A compound tone will be represented by the absolute pitch of its primary

and the relative pitches of its partial tones, as C (1, 2, 3, 4 ). As

generally only the relative pitch of two compound tones has to be considered, the pitches will be all reduced accordingly. Thus, if the two primaries are as 2: 3, the two compound tones will be represented bv 2, 4,

6, 8, 10, ...., and 3, 6, 9, 12, 15 The intensity of the various

partial tones differs so much in different cases, that any assumption which can be made respecting them is only approximative. In a well-bowed violin we may assume the extent of the harmonics to vary inversely as the number of their order. Hence, putting the extent and intensity of the primary each equal to 100, we shall have, with sufficient accuracy—

Harmonics... 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

Extent... 100, 50, 33, 25, 20, 17, 14, 12, 11, 10.

Intensity... 100, 25, 11, 6, 4, 3, 2, 1, 1, 1.

It will be assumed that this law holds for all combining compound

• Proceedings of the Royal Society, vol. xiii. p. 93. The following misprints require correction:—P. 97, line 7 from bottom, for c2 read 6. Table Ip. 105, diminished 5th, example, read I: B; minor (Sth, logarithm, read 20412: Pythagorean Major 6th, read 27 : 16, 3r<: 2'; Table V., col. VI., lost line, nW t«$ tri} t*fr

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