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 opera. tions 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 first 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.

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

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, however, was simplified by the reduction of the scale to the seven natural notes or sounds of the Diatonic Scale, so called because they were produced by the transversal vibrations of strings stretched across any hollow musical instrument. To these seven sounds was added an eighth, which was the repetition of the first sound, in order to complete the octave. In this scale, instead of proceeding regularly by equal semitones, a series of full sounds and of alternate semitones was adopted; and its name, Gamut; is evidently derived from the French word gamme (which means the same thing), with the addition of ut, the name of the first or lowest note in the natural scale.

The sounds of the Gamut were originally indicated by letters, of which the lowest was the Greek T, Gamma, corresponding to our C; hence, the French word gamme, as the name of the scale of music. In the eleventh century, the names from ut to la were used instead of the letters, namely, ut, ré, 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:

ut, ré, 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

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 Semibreve. If this measure be divided into two notes of equal length or duration, these are call Minims; consequently, two Minims are equal to one Semibreve. When the same measure (that of the semibreve) is divided into four notes, each of them is called a Crotchet. The Crotchet is

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 fe 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 ut, 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. 4. 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 the accidents (that is, the sharps, the flats and the naturais), with signs, we place at the beginning of any piece of music, 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 re is the or the fundamental note of the scale in which it is

written.

first low note,

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 The transition in order to explain what is meant by mode. word mode is applied to two different arrangements of the same 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 exprcssion of joy, happiness and expanded sentiments; the other expresses sadness, grief, and dark, close, and contracted scutiments. These two modes, which are so different in their <ffects, 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 sinor, 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 semirone is situated between the second and third degree, instead of between the third and fourth.

Fig. 112.

Mode major. Mode minor. Mode major.

Mode minor.

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 relatice 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 fanFor this purpose, it is sufficient to modify the and the flats as negative signs, we pass from the mode minor to signs of the clef so as to re-establish the required intervals by 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 add to the clef three negative signs. Moreover, it is evident that effacing the flats is equivalent to adding the sharps, and effacing the sharps is equivalent to adding the fiats. Examples: fig. 143.

damental note.

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 mere 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, ré, la, mi, si. In the sharpened tones the fundamental note or tonic major 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 fifck on the descending scale; si, mi, la, ré, sol, ut, fa.

clef.

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 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 is 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 sol by means of a sharp; others have preserved the fa in its natural state, and only raised the sol; a third set have inade no alteration, so that the semitone 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

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

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 Semibreve. If this measure be divided into two notes of equal length or duration, these are call Minims; consequently, two Minims are equal to one Semibreve. When the same measure (that of the semibreve) is divided into four notes, each of them is called a Crotchet. The Crotchet is