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LESSONS IN CHEMISTRY.-No. XXVI.

(Continued from page 381, Vol. IV.) ALTHOUGH refined methods of producing condensation of vaporised products will be mentioned presently, I must first state that a very large number of chemical distillatory operations may be conducted by driving the vapour to be condensed into a flask or receiver, and cooling the latter by means of a piece of filter paper, wetted by the dropping upon it of water from a receptacle placed above, as represented in the accompanying diagram, fig. 20,

Fig. 20.

Whenever the extemporaneous manner of procedure will not succeed, more elaborate methods of effecting condensation must be had recourse to. Amongst these the most elegant, the most advantageous, and in every respect the best for all cases in which the cooling power of mere water suffices, is the refrigeratory apparatus fist devised by Baron Liebig, and known by his name. It is represented in our diagram, fig. 21, attached to the beak of a retort heated by a gas flame; in other words, the whole apparatus is represented in action.

into the funnel-shaped tube, and thence to the lower end of the refrigerator. He will observe that water emerges from the other lateral bent tube and falls into a receiver. He will finally recognise the conditions and general arrangement of the apparatus to be such that a continuous stream of cold water is made to arrive in contact with the central glass tube, where, becoming heated, it rises to the upper portion of the metal tube, runs through the bent siphon-like pipe, and falls into a receiver.

This instrument is of great utility to the chemist. It possesses very many advantages over the worm and tub. In the first place, it admits of being made of glass, whereas the tubworm is almost necessarily made of metal. Occasionally I am aware it is made of earthenware, as, for example, when employed in the distillation of nitric and hydrochloric acids, either of which would act upon metal. In the second place, the central tube in Liebig's apparatus admits of being readily cleansed by friction, and the eye glancing along a straight orifice can satisfy itself as to the state of purity; whilst, on the contrary, the cleansing of a tub-worm can only be effected imperfectly by means of rinsing. Thirdly, the apparatus of Liebig furnishes a continuous stream of cold water, whereas the tub-worm is merely cooled by contact with a stationary mass of water continually growing hotter. Finally, it is cheap, whereas the tub-worm is expensive; so regard it from what point of view we will, the advantages are all in favour of the apparatus of Liebig.

Occasionally, however, water, although applied under the conditions most favourable to the exercise of its cooling properties, is not cold enough, in which case ice must be used, or a mixture of snow and ice, or, finally, some of those artificial cooling mixtures known to chemists. Many substances can only exist whilst exposed to excessive cold. Absolute pure prussic acid must be condensed by a mixture of ice and salt, and preserved surrounded by ice. Remove the icy protector, and the substance escapes in vapour.

These general remarks will suffice to demonstrate the fact that the degree of cold necessary to produce condensation altogether depends on the volubility of the substance under treatment. Generally speaking, the cooling agency of water well applied suffices; occasionally the greater cold of ice is Fig. 21.

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The refrigerator consists of a metal tube, tin plate, brass, or copper, about 2 inches in diameter, and not less than two feet long, through which passes a glass tube a little longer than itself, and retained in the middle of the metal tube by means of two perforated corks, one at either end, the punctures being rendered water-tight by means of white lead cement.

If the student now glances his eye at the metal tube he will discover that two bent tubes are attached to it externally and laterally, one towards either extremity. The student will also observe that water from the barrel or reservoir B trickles

required, and, still more rarely, artificial cooling mixtures. During some of his experiments on the condensation of gases, Professor Faraday applied cold of such intensity that it is represented by some 240 or 250 minus degrees of Fahrenheit, whereas the freezing point of water is 32° on the same scale! In addition to the modifications of the distillatory process already detailed, there are others dependent upon the nature of peculiar substances operated upon. Oil of vitriol, for example, is exceedingly difficult to be distilled in glass vessels. Its boiling point is high and its vapour is evolved in

explosive starts dangerous to the safety of the apparatus; yet oil of vitriol may be safely distilled from a glass retort into a glass receiver by heating it in contact with fragments of platinum foil, and applying the distillatory heat in such a manner that the surface rather than the inferior strata of the fluid shall be vaporised.

tion of which receives the sublimed solid, whilst the accompanying liquid sinks into the flask underneath.

These general descriptions will suffice to give the reader a general notion of the nature and objects of distillation. The process, he will see, is one of remarkable simplicity, yet, strange enough to say, it appears to have been unknown to the ancient Greek and Romans, its origin being due to the Arabs.

And first as regards the platinum foil, let me illustrate the effect of this substance comparatively. The reader has probably observed a glass of champagne which had ceased to In stating that the Romans were unacquainted with distileffervesce, restored to its condition of primary effervescence bylation, I must be understood to limit the expression to distilladropping into it a crumb of bread, a bit of cork, or almost any tion in our sense of the term, understanding it to apply to the angular body. Now it is a general function of all solids, more compound operation of raising a liquid in vapour, and afterespecially pointed and angular solids, to promote the effer- wards condensing that vapour in a refrigeratory apparatus. vescence and ebullition of liquids into which they may be Nevertheless, a rude sort of distillation was occasionally folimmersed; and, in this respect, metals, beyond all other lowed by holding wool over the ascending fumes of a vapobodies, are pre-eminent. Platinum, however, is one of the rising body, and thus effecting their partial imbibition. very few metals on which oil of vitriol does not act, and for this reason it is employed. The rationale of the action of solids in promoting the ebullition of liquids is not yet fully understood, although the result is well known and taken advantage of in many important operations.

The peculiar method of applying heat so as to exercise its force on the upper rather than on the under layers of a liquid is represented by the annexed diagram, fig. 22, which repre

Fig. 22,

ON PHYSICS OR NATURAL PHILOSOPHY.
No. XXVII.

(Continued from page 379, Vol. IV.)
THEORY OF MUSIC.

Language of Music.-In arranging musical sounds in regular order, it has been already observed that, after having expressed a certain number of them according to an ascending or descending scale, all other sounds are only a reproduction of these, modified only by their passing from low to high, or from high to low; so that they are still recognised to be the same sounds. The smallest distance which separates two sounds of this kind is called an octave. In the interval from one octave to another, it is easy to distinguish twelve different sounds placed at equal distances from each other. This distance is called a semitone, and the series of these twelve semitones is called the Chromatic Scale, from the coloured mark used by the Greeks to point out that the music was to be softened by lowering the sounds half a tone. This series, sents a retort supported by a hollow truncated cone of sheet- however, was simplified by the reduction of the scale to the iron let into a charcoal furnace in such a manner as to fit it seven natural notes or sounds of the Diatonic Scale, so called almost exactly. This arrangement is such that glowing char- because they were produced by the transversal vibrations of coal being placed between the cone and the furnace, as repre- strings stretched across any hollow musical instrument. To sented in the diagram, will heat the surface layers of the oil these seven sounds was added an eighth, which was the reof vitriol almost exclusively. As regards the refrigeratory petition of the first sound, in order to complete the octave. In part of this apparatus, the reader will see that a simple flask this scale, instead of proceeding regularly by equal semitones, without any contrivance for wetting it is alone employed. a series of full sounds and of alternate semitones was adopted; In point of fact, the condensation of oil of vitriol does not and its name, Gamut, is evidently derived from the French require such artificial aid, which, instead of proving service-word gamme (which means the same thing), with the addition able, would, in all probability, crack the receiver. of ut, the name of the first or lowest note in the natural Occasionally a volatile solid is the subject of distillation, in scale. which case the term sublimation is applied. The reader has The sounds of the Gamut were originally indicated by more than once, whilst engaged in the investigation of arsenic, letters, of which the lowest was the Greek T, Gamma, corgone through the process of sublimation. Sometimes the responding to our C; hence, the French word gamme, as the result of distillation is partly a solid, partly a fluid, in which name of the scale of music. In the eleventh century, the case a compound receiver, as represented in the subjoined names from ut to la were used instead of the letters, namely, diagram, fig. 23, is occasionally employed, the globular por-ut, re, mi, fa, sol, la; and these names were taken from the first syllables of a religious hymn. Five centuries later, the note named si was added, and then ut repeated, which completed the series and the octave, as follows:

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Fig. 23.

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Letters. C, D, E, F, G, A, B, C, Names ut, re, mi, fa, sol, la, si, ut. Notation.-There are two kinds of signs employed in musical notation; viz., those which express intonation, and those which indicate time or duration. The former are the notes; each note represents a distinct sound, and its value, that is, the time during which this sound is emitted. Five parallel straight lines at equal distances, with marks for the notes placed alternately on the lines and the spaces between them, constitute what is called the staff or stave, as in fig. 140, where the first octave is represented with the treble clef; the first note C being put upon a portion of a line called a ledger line. To this note, which is called ut, English musicians give the name

of do.

The place which a note occupies on the staff determines its intonation. The lower it is placed, the lower is its sound; and the higher it is placed, the higher is its sound. By a note being

placed higher or lower here is meant, placed nearer to or further from the bottom of the page of a book, or of the face of a board placed vertically, on which the lines of the staff are drawn horizontally. It has been observed in our last lesson, that the terms low and high, with respect to sounds, are arbitrary and conventional; and that the real difference by which they are distinguished consists in this, that the sonorous body which yields a low sound makes, in a given time, a less number of vibrations than that which emits a high sound. The notes placed on the lower part of the staff represent, therefore, Fig. 140.

Letters Names

.

F, G, A, B, C, fa, sol, la, si, do.

C, D, E, do, re, mi, sounds which are relatively lower than those do which are placed above them. The system of the gamut thus indicates that the notes rise to a greater height, as they are placed successively and alternately ascending from the lowest or first line of the staff;.then, on the space between the first line and the second; then, on the second line; next, on the second space; again, on the third line; next, on the third space; and so on. Yet, the distance which separates the sounds thus expressed is not regular; sometimes it represents a full sound, sometimes a semitone, as we have said, when speaking of the gamut. Sometimes the intervals between these successive sounds are called degrees. Two notes placed on the same line are said to be in unison; the interval from one degree to that which immediately follows it is called a second; the interval from the first degree to the third is called a third; and so on to the interval from the first degree to the eighth, which is called an octave; as explained in our last lesson. So much for intonation.

A measure, in music, is a space of time, at the end of which the ear feels the want of rest; this rest forms the starting point of the following measure. The smallest portion of melody is always divisible by the ear into a certain number of measures, and each measure is divided into three or four times. The times are also divided into parts which may be either irregular or symmetrical, and this is what constitutes rhythm. In the

divided into two Quavers; the Quaver into two Semiquavers; and the Semiquaver into two Demisemiquavers; and so on. The general rule for the relation subsisting between the length of these notes is, that each of the longer is double that of the shorter which follows it. The following table, fig. 141, exhibits the equivalent values and relative lengths of each note, with their corresponding times, and parts of a time.

The Breve is a note seldom used, but of course it would contain eight times; it was denoted by the same character as a semibreve with two bars on each side of it, as shown in p. 183, vol. iv. col. 1, line 19. The measure containing four times may be conceived as divisible into two equal parts; but there are also pieces written in the measure containing two times. For this purpose no change is made in the system of signs just explained, except that the full measure, instead of being represented by a semibreve, is represented by a minim or its equivalents. As to the measure of three times, it is represented by a minim and a point alongside of it, as shown in the page and column above referred to, line 26, the point being employed to denote the prolongation of the duration during a third time. The point is used to lengthen all the other values of the notes; so that, when placed alongside a crotchet, a quaver, etc., it adds to their duration one-half of its original value.

The Gamut.We have said that the diatonic scale proceeds by tones and semitones. By a full tone is understood the distance which separates any degree from that which immediately follows it, when this distance can be easily divided by the ear into two distinct sounds. In the contrary case, the interval is only a semitone. The diatonic scale is divided into five full tones and two semitones. In order to understand the position of both, we must consider the octave as composed of two equal parts, containing each four notes or degrees. Each of these parts, considered by itself, comprises two full tones and one semitone, to which must be added a full tone which separates the one from the other. Thus, in the first part, which extends from do or ut to fa, we find from ut to re a full tone, from re to mi a full tone, and from mi to fa a semitone. In the second, from sol to ut, we find between sol and la a full tone, from la to si a full tone, and from si to ut a semitone; lastly, if we join the two series, we find between fa and sol a full tone; which completes the construction of the octave. Whether this series of sounds be a consequence of the organisation of our auditory apparatus, or be the result of convention or of custom, it is no less true that the notes thus regulated are generally adopted

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system of notation, every measure is indicated by a bar perpendicular to the straight lines of the staff; consequently the assemblage of values comprised between two bars of this kind ought always to represent one equal period or duration divisible into equal times. The longest measure is that containing four times. The note which represents it in its whole duration is called a Semibrere. If this measure be divided into two notes of equal length or duration, these are call Minims; consequently, two Minims are equal to one Semibrere. When the same measure (that of the semibreve) is divided into four notes, each of them is called a Crotchet, The Crotchet is

and satisfy all ears. On this point, therefore, viz, the construction of the scale, all the combinations and thrilling effects of modern music depend.

Our remarks on the structure of the scale are especially applicable to that which begins at the note do or ut, and which is considered as the normal scale. Bat if we begin with any other note, with re' for example, it is plain that, in order to preserve the same ratios between the tones and semitones, it must be made to undergo a modification according to the intervals established in the scale of ut. These ratios are such that the semitones are found between mi and fa, and between si and ut,

that is, between the third and fourth degree, and between the third is minor, that is, composed only of a tone and a semitone, seventh and eighth degree. as may be seen in the following example: fig. 142.

Now, in the scale commencing with re' we should have a full tone between re' and mi, but between mi and fa only a semitone. It will be necessary to raise fa by a semitone, and between this elevated fa and sol, that is, from the third to the fourth degree, the semitone is necessarily found re-established in its proper position. The same thing will take place between si and t, which are separated by a semitone in the normal scale; but in raising ut by a semitone, the order from the sixth to the seventh degree, and from the seventh to the eighth degree, would be equally re-established. These modifications are effected by the aid of two signs, the sharp, # and the flat, b. The sharp raises by a semitone, the note before which it is placed; the fiat, on the contrary, lowers it by a semitone. When the note sharpened or flattened is required to return to its normal or natural intonation, we prefix to it another sign, called the natural, viz. . In this manner, the necessary order of tones and semitones in any scale can be fixed, and consequently as many scales as there are ones in the whole extent of the octave can be obtained. In order not to unnecessarily load the notation with signs, we place as the beginning of any piece of music, the accidents (that is, the sharps, the flats and the naturals), which ought to affect the modified notes throughout, and we give to each scale thus fixed the name of the note with which it commences. For example, when we say that a piece of music is in re', we mean that is the first low note, of the scale in which it is

or the fundamental note written.

Modes. Our preceding observations relating to the structure of the scale have reference to the scale of ut as the model; we shall add here, of ut major, and we employ this phrase of transition in order to explain what is meant by mode. The word mode is applied to two different arrangements of the me scale-modifications which are very slight at bottom, but which communicate to it a character and properties entirely different. The language of music possesses two modes: the major and the minor. The former is especially applied to the expression of joy, happiness and expanded sentiments; the other expresses sadness, grief, and dark, close, and contracted scutiThese two modes, which are so different in their effects, differ from each other only by a slight alteration in the ystem of the scale. We have said that in the mode major, the semitones are situated between the third and the fourth, and between the seventh and the eighth degrees; in the mode minor, they are situated between the second and third, and between the seventh and eighth. Consequently, the difference consists simply in this, that in the mode minor, the first semitone is situated between the second and third degree, instead of between the third and fourth.

ments.

The normal scale of the mode minor is that of la. In commencing with this note, we find a semitone between si and ut, that is, between the second and third degree. In following the ascending scale, we meet a semitone between mi and fa, and a full tone between sol and la final. This has been the source of many disputes among musicians. Some have raised the fa as well as the sul by means of a sharp; others have preserved the fa in its natural state, and only raised the sol; a third set have made no alteration, so that the semi: cne remained in its natural place between the sixth and seventh degree. Thus, there are three ways of terminating the ascending scale minor, and three ways of employing them at pleasure, but with very different effects; but it is to be especially observed that the principal character of this scale consists in the interval from the second to the third degree, which is always a semitone. All this proves, however, that the termination of the ascending scale minor is not an essential characteristic; but in descending this scale we can alter it as well as in ascending; and what is more remarkable is, that the interval between the seventh and eighth degree, which is called the sensible note, and which is almost forced to be a semitone in ascending, is more grateful to the ear in the descending scale when it is a full tone.

The fundamental difference between the mode major and the mode minor is expressed by saying that, in the former the third (the interval between the first and third degree) is major, that is, composed of two full tones; and that in the latter, the

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These two modes are connected with each other by very natural reciprocal relations, which exist either between the tones which bear on the clef the same accidents, or between the Thus the tone of ut major has for its relative minor that of la scale major and the scale minor of the same fundamental note. minor, because neither bears any accident on the clef. The tone of re' major (with two sharps) has for its relative si minor; the tone of re' minor (with a flat), is the relative of the tone of fa major, etc. Every scale can pass from the mode major to the mode minor, and reciprocally, without changing the fandamental note. For this purpose, it is sufficient to modify the signs of the clef so as to re-establish the required intervals by and the flats as negative signs, we pass from the mode minor to either mode. The sharps being considered as positive signs the mode major, by adding to the clef three positive signs; and in order to convert the mode major into that of minor, we that effacing the flats is equivalent to adding the sharps, add to the clef three negative signs. Moreover, it is evident and effacing the sharps is equivalent to adding the fiats. Examples: fig. 143.

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From this arises an important point in the reading of music, namely, the determination of the tone of the fundamental note of the scale in which the piece is written. By the inere inspection of the signs placed on the clef, every musician must know what is the scale which is used as the foundation of the piece which he is about to perform. These signs are subject in their arrangement to rules so symmetrical that they are easily fixed in the memory as soon as they are studied with attention. The following is a summary of the preceding details in a few words :

The first sharp placed on a clef is always a fa. The following sharps are placed from fifth to fifth in the ascending scale: fa, ut, sol, re, la, mi, si.

clef.

In the sharpened tones the fundamental note or tonic major is always a semitone below the last sharp placed on the In the flattened tones the first flat is placed on the si. The following flats are placed from fifth to fifk on the descending scale; si, mi, la, ré, sol, ut, fa.

In the flattened tones the fundamental note is always five degrees below the last flat; if there be several flats, the funda

mental note rests on the last but one.

The fundamental note of a relative minor is always two degrees above the fundamental note major, and inversely.

Transition is made from a fundamental note major to the same fundamental note minor, by adding to the clef three negative signs, or their equivalent.

Transition is made from a fundamental note minor to the same fundamental note major, by adding to the clef three positive signs, or their equivalent.

One point often embarrasses the student, respecting the determination of the tone; and this is the choice between the mode major or the mode minor represented by the same signs on the clef. One simple method of determining it is this: when the fundamental note is not clearly fixed by the first or the last concords of the piece, we search for what would be the sensible note (the 7th degree) of the tune if it be minor. In this case, the sensible note would be necessarily affected with an accident (positive or negative) in the course of the first

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Points may be added to the rest-signs, and they serve also to increase them by half their value. It is plain, as this table shows, that the values of the notes and the values of the rests are the same in point of duration, and are employed to complete the measure in the same proportions. Their difference consists in their expression being negative instead of being positive.

Signs of Measure.-The measure of a piece of music is indicated on the clef by the following signs. The measure of two times, that is the binary measure, is expressed by a C, or by the figures that of four times, by a C crossed vertically by a bar, thus ; the measure of three times, that is the ternary measure, is expressed by, or only 3, which signifies that it is composed of the value of three crotchets. An important variety of the measure of two times, or binary, is that which is marked, and of which each time is divided into three quavers. In the measure of four times, or quarternary, marked 12, each time is divided into three quavers, which is called a triplet. The measure is one of three times, each being represented by a quaver. General rule:-In every measure expressed by two figures of which one is placed above the other, the upper figure indicates how many times this measure must contain the division of the measure of four times expressed by the lower figure considered as unity. Thus indicates that the measure contains three times the fourth part of the measure of four times, or three crotchets; indicates that it contains nine times the eighth part of the same measure, that is, nine quavers; and so on. We must now determine the proper duration of this division of the measure taken as unity. There are two methods, the one approximate the other very exact. The former, which is the most common, consists in placing at the commencement of a piece of music a word generally taken from the Italian language, which indicates the movement of the composition. The words of this kind, although many, can be reduced to some standards which are modified by augmentative or diminutive expressions. Thus, a very slow movement is indicated by the words lento, largo, larghetto; when it is somewhat less slow, it is indicated by the terms grave, adagio, cantabile, moderato; a more firm and animated movement is indicated by the words andante and andantino; a gay and lively movement, by the terms allegro and allegretto; lastly, a quick and rapid movement, by the words presto, prestissimo, vivace, etc. All these words, of which the value is well known to musicians, have been long employed to express the movement of a musical piece. Nevertheless, it is evident that in order to express these different rates of movement exactly, mechanical means must be employed. After a great number of trials, the metronome of M.

Maëlzel has generally been adopted. This instrument is composed of a pendulum which is put in notion by a clock, and which divides a unit of time, the minute, for instance, into a greater or less number of parts, accor ding to the length given to the rod. This length has a certain ratio to the duration which the division of the measure taken as unity must represent, and it is regulated by means of a bob which is made to rise or fall on the rod, which is graduated accordingly.

Signs of Expression-The signs of musical expression have for their object the indication of those varied shades of feelings, such as the sweetness, force, etc., of the notes, which give to music, so to speak, its physiognomy, and enable it to represent all the different emotions of the soul. The following signs are employed in the regulation of such expressions; some are applied to the intensity of the sounds; others to the association of the notes; others to the modification of the general movement. The first set vary between the limits of pianissimo (the softest or sweetest), expressed by PP., and fortissimo (the strongest or loudest), expressed by FF. A single Pindicates piano (soft or sweet), as forte, denoted by a single F, indicates strong or loud. P and F themselves are also modified by the signs sf or rf (that is, sforzando or rinforzando), or by dim. (diminuendo), cres. (crescendo), cal. (calendo), etc. The signs or express the increase or decrease of the force of a single note or of a member of a passage in music. The lozenge <> indicates a crescendo of small extent, or a note merely strengthened. Two signs are sufficient to denote whether the notes are connected or detached. The curve indicates that the notes which they unite must be run together or connected in their utterance, and the points placed above each note signifies that these notes must be detached. When the points thus separated are surmounted by a curve, the notes besides being connected must be articulated in a sensible manner. Lastly, the momentary acceleration of the general movement is indicated by the letters accel. (accelerando); or they are moderated by these, ritard. (ritardando). When a rest greater than its normal value is to be made on a note, it is surmounted with the sign which is called a point of

rest.

Clefs.-The clefs or keys are chiefly required in order to supply the want of extent in the staff. Every voice and every instrument has its diapason, that is, its own proper extent or compass of sound. The limits of each must be marked accordingly. The clef is employed to show the extent of the staff, to determine its position in the long series of sounds appreciable by the ear, and to represent in short compass the range of the pianoforte. By help of this artifice, a piece writ ten for a given voice or instrument can be performed by a different voice or an instrument of a different diapason. The whole of a piece may be thus transposed into the medium staff which better suits every instrument or every voice.

There are three principal clefs: the clef of sol, which is that of the tenor voice, of violins, flutes, clarinettes, hautboys, horns, and the right hand of pianists; the clef of fa, which is commonly used for the bass; it determines the place of fa on the fourth line; when applied to the voice, its position may be varied. As to the clef of ut or do, it gives its name to the note on which it is placed. The alto of the clef of ut is written on the third line; its place can also be changed when applied to the voice. These three clefs seem placed at the ascending fifth from each other; yet the medium ut of the clef of fa is at the lower octave of that of the clef of ut, and at the double octave of the medium ut of the clef of sol. The following table shows the form, the relative position of the clefs in use, and the place of the medium ut on their respective staves. Fig. 145,

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