part being larger than the opening in the vessel, the flow will slightly exceed the calculated amount. These differences are partly accounted for by currents which are formed in the water, and which by collision with the issuing stream destroy a portion of its velocity.

B

T

Fig. 23.

When liquids have to be conveyed in pipes care should be taken to make the bends even and gradual, and in this way to prevent the formation of eddies and currents. It should also be remembered that there is a considerable amount of friction between the liquid and the sides of the pipe, so that the portion in the centre of the pipe flows more rapidly than that against the sides. In the same way the velocity of a canal or river is greater in the centre than at the sides. This friction increases with the velocity at which the liquid moves, and also with the area of the surfaces in contact. From all these causes the flow of liquids through pipes is much less than theoretically it should be, and hence in laying down pipes considerable allowance has to be made for this loss. In former times the flow of water was used as a means of measuring time, the apparatus constructed for this purpose being called a clepsydra, or water-clock. The water is allowed to flow from a jet into a reservoir below, in which is a float rising with the water and carrying at the top a pointer. The reservoir is made of the same size throughout, so that the addition of equal quantities of water causes equal rises in its surface. The water is allowed to flow in for a given time-say, half an hour-and the rise noted; marks are then made at this distance apart, and by these the time may be told. As, however, the rate of flow depends upon the pressure, it is necessary in such an apparatus to maintain the same head of water in the upper cistern, and this may be accomplished in the way mentioned above, by letting the water constantly overflow the vessel.

There are, however, better ways of accomplishing this, which are frequently used. In the boiler of a steam-engine, and other machines, it is frequently very important thus to maintain a constant level, and this is attained by means of a ball-cock or float. A block of wood, or hollow ball of metal, floats on the liquid; this block is either fixed on to a lever or fastened to a cord, so that when the level of the water becomes lower, and the float descends, it opens a valve or turns a tap, and allows the water to enter till the level is restored.

We will now look at the most common hydraulic machines, and examine their construction, and the principles on which they act. The simplest division is into three classes, the first embracing those whose object is to employ the force of falling water as a prime mover; the second, those which are intended to raise water to any required elevation; while the third contains those which are used to propel vessels through the water, and other machines not included in the previous classes.

In many districts, especially mountainous ones, there exist many waterfalls and rapid streams. In these there is a large amount of motive power, which is frequently utilised in giving motion to the machinery employed in mining and other operations. This power would be much more employed than it is, were it not that sometimes, from long-continued droughts, the body of water is much diminished. If we take any two points in a stream, we shall find that the one higher up the stream has a greater elevation than the other, and the power capable of being exerted by the stream between these points is equal to the power of the body of water there is in the stream falling vertically through this distance. If the stream discharge 1,000 gallons per minute, and the difference in height between the two points be four feet, the power stored up in the water is 1,000 x 10 x 4, or 40,000 foot pounds per minute, but even in the best machines a large portion of this is lost.

This is fixed to a pole, and held in some part of the stream for a given time; the velocity at this point is thus noted, and in a similar way it may be found at other points and a mean taken. A simpler way, however, is to observe the velocity at the surface. A substance of nearly the same specific gravity as the water is thrown in, and the time occupied in passing between two points noted; from this we easily find its speed per second. Now the mean velocity is found to vary from about to of that at the surface, and tables have been constructed showing the mean velocity corresponding to each surface velocity. If we multiply this mean velocity by the area, we ascertain the amount of water passing per second.

Having thus seen the power there is in a stream, we must notice the different machines employed to utilise it.

The simplest and most common of these is the water-wheel. This consists essentially of a wheel turning on an horizontal axis, and carrying on its circumference a number of floats or boards. The water strikes against these, and thus causes the wheel to turn with considerable force, and the motion is by means of cog-wheels transmitted from it to the machinery which has to be driven.

Water-wheels are divided into three classes, according to the way in which the water acts on them, or rather the point of their circumference at which it is applied.

Sometimes the wheel is placed so that its lower floats just dip into the stream, and it is then called an undershot wheel (Fig. 24). When the water is confined by an embankment, and allowed to flow against the wheel a little below its middle, it is called a breast wheel; and when the water is received on the upper part, it is an overshot wheel. The first of these three is the simplest in construction, no embankment or artificial channel for the water being absolutely necessary, though a much greater power is gained when the wheel is made to fit into a properly shaped watercourse, so that no water can pass without turning it. Less power is, however, derived from this than from the other kind of wheel, as the water strikes violently against the floats, and thus expends much of its force uselessly in straining the wheel. It is always found that there is the greatest advantage gained when the water strikes the wheel with as little velocity as possible, but "acts merely by its weight and pressure.

Fig. 24.

At first the floats were arranged to stand out perpendicularly from the wheel, but experience shows that it is better to let them have an inclination towards the stream of twenty or thirty degrees, as thus they break the violence of the current, and allow it to act more advantageously. Another matter to be considered is the proportion which should exist between the speed of the wheel and that of the stream. It is evident that there are two extreme cases which may occur. If the circumference of the wheel move at exactly the same velocity as the stream, no power can be derived from its motion; and if the motion be reduced to a minimum, nearly all the power would be lost. The greatest amount of work is accomplished when the motion is about midway between these two extremes, that is, when the wheel moves at about half the rate of the stream.

ANSWERS TO EXAMPLES IN LESSON IV.

1. The specific gravity of the silver is 10'359. 2. 1.694.

3. The elm weighs 69 896 oz.; the limestone 276 042; and the lead 1182-292.

4. The specific gravity of the oil is 0.916.

5. The stone weighs in air 26 grains, and it loses 10 grains in water. Its specific gravity is there or 2.476.

26 10.5'

6. The two together displace 6'84 oz. of water; of this 1.92 oz. is due to the metal; the wood therefore displaces 4'92 oz., and its weight is 3.3. Its specific gravity is therefore 0.670.

7. The volume of any body is represented by its weight divided by while that

of the zinc is

48 8.9'

75 sp. gr.

its specific gravity. Hence the volume of the copper is 27 The volume of the compound is therefore 7.191' and this gives the specific gravity of the

Hence

Act, action.

Cast, throw.

Rent. Cooked.

All, quite.

Pedagogia

pai-dah-go-jée-ah

Education and government of children.

III-THE SEMI-VOWELS.

There are six semi-vowels in the Italian language, so called because in their utterance a vowel must be placed before the consonant. They are not pronounced in one syllable only, as in the case of the mutes, but require the utterance of two syllables, which syllables are substantially the same, though in an inverse order. The semi-vowels are

1. Ff, named in the alphabet effe (pronounced in the following manner-éf-fai).

2. Ll, named in the alphabet elle (pronounced êl-lai). It has two sounds-one like the English consonant ; the second is a peculiar sound, of which I shall have occasion to speak in the pronouncing tables.

3. Mm, named in the alphabet emme (pronounced ém-mai). To ensure perfect accuracy in the pronunciation, I may remark that when m is preceded by a vowel with which it forms one syllable, and a consonant being the next, it must be very softly sounded, and the voice must glide quickly to the next consonant, almost as if it formed part of the same syllable: for example, ambizione, ahm-bee-tzee-ó-nai, ambition; empio, ém-peeo, impious; ombra, óm-brah, a shadow.

4. Nn, named in the alphabet enne (pronounced en-nai). Generally speaking, this letter is pronounced just as in English; but the observation made on the m is equally applicable to n. In similar circumstances, the voice must glide quickly from the n to the succeeding consonant: for example, andare, ahn-dáhrai, to go; entrare, en-tráh-rai, to enter; onda, ón-dah, a wave. After g, n has a peculiar sound, which I skall have occasion to explain in the pronouncing tables. Often n is pronounced like m before words commencing with the consonants b, m, and p; as, gran bestia, pronounced grahm bê-steeah, a boorish, insolent

fellow, great blockhead, etc.; scolpire in marmo, pronounced skol-pée-rai im mahrr-mo, to chisel in marble; con poca fatica, pronounced kom pô-kah fah-tée-kah, with little fatigue. This is certainly the finest pronunciation, because it is the genius of the Italian language, as in the classical tongues, particularly Greek, to soften the transition, or passing over, from one word to another, and often from one syllable to the other, by changes

of consonants.

5. Rr, named in the alphabet erre (pronounced ér-ra). R, when it is followed by a consonant, must be vibrated with a stronger emphasis than in English; and it is on the other hand very soft before a vowel; as, carta, pronounced kahrr-ta, paper, and soft in cara, pronounced káh-rah, dear.

6. Ss, named in the alphabet esse (pronounced ês-sai). This consonant has considerable variations, and is one of the most difficult to pronounce throughout correctly, for even in Italy there are variations.

A strictly correct and irreproachable pronunciation of this consonant can only be acquired by closely marking its utterance in all its shades by Italians who speak purely. Speaking generally, there are two leading sounds. One is a sharp, hissing sound, as in the English words sing, sieve; the other is a much milder sound, as in the English words cheese, ease, please, etc. The following general rules will be sufficient for the guidance of the learner at present: the different exceptions to them will be stated more fully hereafter :

First, the sharp sound of this consonant may be said to be the ruling sound, because it is heard in the greater number of syllables and words. I shall invariably mark it by the single letter s; and wherever this is used, the reader will remember that it represents the sharp, hissing sound of the letter, thus avoiding multiplicity of signs, which would be caused by using ss. It has always the sharp, hissing sound in the beginning of a word before a vowel; as, for example, sale, pronounced sáhlai, salt; sole, só-lai, the sun; sempre, sêm-prai, always; subito, sóo-bee-to, suddenly. It has also the sharp, hissing sound before the consonants c, f, p, q, and t; as, for example, in scaltro, skáhl-tro, shrewd; sforzo, sfôr-tzo, compulsion; crespo, krái-spo, crisp; pasqua, páh-skwah, Easter; pasto, páh-sto, a meal. It has also the sharp and hissing sound after the consonants 1, n, and r, and I may say a pre-eminently hard and hissing sound in this case; as, for example, falso, fáhl-so, false; corso, kórr-so, course; arso, áhrr-so, burnt; forse, fórrsai, perhaps; pianse, peeahn'-sai, he wept; vinse, vín-sai, he vanquished. In Rome, the sharpness of the s after 1, n, and r is generally so very audible, that it almost amounts to the utterance of a ts, as if the examples just given were written with the hard pronounced with the English sound in the word Switzer; which, however, with all respect for the Eternal City and the "bocca Romana," I must pronounce to be a provincialism.

Secondly, the milder sound of the s occurs generally when it is placed between two vowels. As the nearest possible approach to it, I shall follow the practice of Mr. Walker in his English pronouncing dictionary, and mark it with a 2: for example, avviso, ahv-vée-zo, opinion; guisa, gwée-za, guise, manner; tesoro, tai-zô-ro, treasure; usura, oo-zó-rah, usury; sposa, spo-za, bride; accusa, ahk-kóo-zah, accusation; miseria, mee-zé-reeah, misery; misura, mee-zóo-rah, measure; and many other words, which might be cited as examples.

This rule is subject to several exceptions, the most important of which I must state here.

Many Italian adjectives end in oso and osa, and whenever before these terminations there is a vowel, the terminational s has the sharp, hissing sound; as, for example, glorioso, pronounced glo-reeó-so, glorious; virtuoso, virr-tooó-so, virtuous; to. tuoso, torr-tooó-so, tortuous.

There are many compound words in Italian having the particles dis and mis, and before consonants the final s of these particles must have the sharp, hissing sound; as, for example, disposizione, pronounced dis-po-zee-tseeó-nai, disposition; disAsura, dis-mee-zóo-rah, excess (the reader will note in the two foregoing words, that the s of the particle dis has the hissing sound, while the next s, placed between two vowels, follows the general rule, and has the mild sound); dispiacenza, dis-peeah-tchen-tsah, displeasure; discreditare, dis-krai-deetih-rai, to discredit.

In the greatest part of compound words, where s begins the syllable, it has the sharp, hissing sound; as, for example, proseguire, pro-sai-gwée-rai, continue; risolvere, ree-sôl-vai-rai, to dissolve; presumere, prái-sóo-mai-rai, to presume; risorgere, ree-sórr-jai-rai, to rise again; trasustanziato, trah-soo-stahntseeá-to, transubstantiated.

There are other exceptions which I shall take occasion to point out as examples occur.

Further, s has the mild sound when it immediately precedes the consonants b, d, g, l, m, n, r, v; as, for example, sbarra, pronounced zbáhrr-rah, bar, barrier; disdire, dis-dee-rai, to retract; sguardo, zgwáhrr-do, look; slontanare, zlon-tah-náh-rai, to remove; smania, zmáh-neeah, madness; snervare, znerr-váhrai, to unnerve; sradicare, zrah-dee-káh-rai, to eradicate; svolto, zvél-to, lively, clever, nimble, easy. I have stated that the particles dis and mis before consonants have the sharp, hissing sound. There is no deviation from this rule, and these particles retain the sharp, hissing sound even before the last-mentioned consonants: for example, disbandire, pronounced dis-bahndée-rai, to banish; disdire, dis-dec-rai, to retract; disgombrare, dis-gom-bráh-rai, to empty; disleale, dis-laiáh-lai, disloyal; dismettere, dis-mét-tai-rai, to dislocate an arm, to dismiss (an affair); disnervare, dis-nerr-váh-rai, to unnerve; disradicare, dis-rah-dee-káh-rai, to eradicate; disvenire, dis-vai-née-rai, to swoon; misgradito, mis-grah-dée-to, disagreeable; misleale, mislaiáh-lai, disloyal; misvenire, mis-vai-née-rai, to swoon.

When ss is between two vowels, it does not follow the rule of the single s, but must be sounded with a sharp, hissing sound; as, for example, fosso, pronounced fos-so, a ditch, a canal; rosso, rós-so, red; posso, pós-so, I can.

1. It will contribute to the confidence of our pupils, and to their hopes of some day singing at sight, to remember that every tune, with the exception of "minor" tunes to be mentioned hereafter, and some few others, begins on DOH, ME, or SOH; so that having taken the key-note from your tuningfork, and struck the chord, you are sure to be in possession of the right note to begin with. You will also find that the accompanying "parts" of a tune (adapted to lower voices) commence always on some note of this "common chord."

2. For the sake of the thorough workers, those who are so diligently following the course in which we are guiding them, it will be well to remind our pupils of the process through which they must pass in connection with each exercise, and of the reasons for each step of that process. Every exercise should first be

a. LEARNT BY PATTERN from the MODULATOR. This will cultivate the ear and voice generally. It will teach the particular tune along with a pictorial representation of its intervals, and will accustom the mind more and more to that beautiful language of interval, which, by giving a distinct and uniform syllabic name to each interval of the scale, enables us, by the ever renewed association of the syllable with the sound, to sing with increasing ease and confidence. The "second part should be learnt in the same manner as though it were a separate exercise-before it is sung with the "air." The exercise should next be

b. SOL-FAED from the book. This will give scope for a more accurate observance of measure, as indicated by the accent marks, and allow the "parts" of a tune to be sung together. It also strengthens the association between the syllables and their proper intervals. But lest the syllables of a tune should come to be sung by mere "rote"-the pupil having no mental picture of their relative position on the modulator-it will be found advisable to require each exercise to be

c. POINTED on the MODULATOR from memory. This will complete the knowledge of the tune, and greatly increase its beaching power. Every pupil should do this in his private

practice, and should be ready to do it at the teacher's call, before the class. But the sol-fa syllables, though invaluable as the mnemonics and interpreters of interval, and likely to be always useful in learning new tunes, and in studying the difficulties or beauties of particular passages, are only instruments for accomplishing the higher purposes of music. The learner must acquire the power of perceiving the musical "property" of a note, and of producing it, in connection with any syllable. With this view, the pupil should not shrink from the mental effort of pointing each exercise. This will make the perception of the characters and intervals of notes more perfectly mental, and independent of syllabic associations. It will also introduce the use of slurs each utterance corresponding with a syllable of the verse, and not, as before, with every note of the music. But the highest attainment is reached when, the tune itself being perfectly mastered, it is

d. SUNG TO SUITABLE WORDS. This exercise should not commence until the words themselves are thoroughly under

stood, enjoyed, and loved; and then it should be performed with careful regard to EXPRESSION. Thus the pupil is introduced to a new study, most elevating and ennobling to the mind, which he will pursue in sympathetic converse with his teacher.

It is not necessary that the pupil should thus make the fullest use of one exercise before he passes to the next. It would be better that, at every season of practice, each of the above employments should have place-some new exercise being taught by pattern, a previous one sol-faed from books and pointed on the modulator, and an earlier one still "numbered" and sung to words. The pupil should keep a record of progress, both on the book and separately, showing to what extent each exercise has been used. On the book each exercise would be marked with the letters above used in connection with each employment -a indicating that the exercise had only been learnt by pattern -a, b, that it had also been sol-faed from the book, etc. A separate entry might be made in this wise: "May 6, Ex. 20, a; 19, b, c; 18, d; 13, 14, 15, d."