The terminations Oev, 0, and de form adverbs by being added to nouns, pronouns, and verbs, to signify relations of place; thus Oev denotes, from a place (whence), Oi, at a place (where), and dɛ, to a place (whither): e.g. ovpavolev, from heaven; ovpavoðɩ, in heaven; ovpavovde, to heaven. With

EXERCISE 21. Develop by diagrams four other "flat keys" pronouns de becomes σe, thus alloge, to some other place; so

Adverbs of manner have commonly no peculiar adverbial termination, but employ, in the comparative, the neuter singular, and, in the superlative, the neuter plural of the corresponding adjectives. The same fact may be stated thus, namely, that the neuter singular of comparatives may be used adverbially, that, with an adverbial signification; and that the neuter plural of superlatives may be used with an adverbial "signification; e.g.

These "flats" or "sharps "at the beginning of the staff are Their only use to the called the "signature" of the tune. singer is to point out the key note. TO FIND THE KEY NOTE, therefore, remember that the last sharp towards the right hand stands upon TE (TE, the "piercing note,' will easily associate in the memory with sharps), and that DOH is consequently the next above. Remember also that the last "flat" flat towards the right hand stands upon FAI (associate " with "desolate note") and that DOH is the fourth below. EXERCISE 22. Put the proper key signatures to all the preced-rows ing exercises.

EXERCISE 23. Write from memory the signatures of the keys xapierws G, D, A, E, F, a fat, and r fat. These are the keys most used. Το ευδαιμόνως remember these signatures, notice the place of the first sharp acoxows and of the first flat. Then the sharps descend a fourth, ascend news a fifth, and so on; while the flat signatures ascend a fourth, descend a fifth, and so on. Thus they necessarily fall into Taxes parallel rows. Verify these remarks, and they will greatly help your memory.

The note Tu is expressed in the old notation by a sharp before the note which would otherwise have been FAH, except in tunes with flat signatures, when a "natural" is used instead.

186

The comparative and superlative of most other adverbs of gods; περιπαθης, ες, suffering greatly, acutely sensible to sufer place end in w, as

πως,

how?

όπως

τως, 80

ότε, when ού, where

ώς, as

Of these forms οἱ, τῇ, τοθεν, and τως, are found only in the poets, and consequently are not to be ordinarily used in prose composition.

EXERCISES FROM THE CLASSICS.-GREEK-ENGLISH.

1. Παν το σκληρον χαλεπως μαλαττεται. 2. Ο ουρανος χαλκους εστι τα εξω. 3. Ελεγεν ὁ Βιας, ατυχη ειναι τον ατυχιαν | μη φέροντα. 4. Η φιλοσοφια διδασκει, ότι δει μητ' εν ταις ευπραγίαις περιχαρεῖς ὑπαρχειν, μητ' εν ταις οργαις περιπαθεις και θηριώδεις. 6. Πῶς η αχαριστοι, η αμελεις, η πλεονεκται, η απιστοι, η ακρατεις ανθρωποι δυνανται φιλοι γιγνεσθαι ; 6. Ο πλουτος και τα εκτος αγαθα χωρις αρετης 7. Τίς ορνις ευφωνότερα εστιν ανωφελη εισι τοις εχουσι. αηδονος ; 8. Αἱ δευτεραι πως φροντίδες σοφωτέραι. 9. Δαρείου και Παρυσάτιδος γιγνονται παιδες δυο· πρεσβυτερος μεν Αρταξερξης, νεωτερος δε Κυρος. 10. Γυναικες ανδρων φιλοπενθέστεροι 12. Ὁ 11. Το αδικειν κακιον εστι του αδικεισθαι. Τί γαρ εμου Αγησιλαος περι του μεγάλου βασιλεως ειπεν. μείζων εκείνος, ει μη και δικαιότερος; 13. Ζηνων όρων του Θεοφραστον επι τῳ πολλους ἔχειν μαθητας θαυμαζόμενον, ὁ εκείνου μεν χορος, εφη, μείζων, ὁ εμος δε συμφωνότερος. 14. Σοφος Σοφοκλης, Ευριπίδης σοφώτερος, ανδρων δε παντων Σωκράτης σοφωτατος.

εισι.

18.

15. 'H μελιττα φυσικώς εν τοις ανθεσι εξανευρισκει το λειότατον μελι και χρηστικωτατον. 16. Παντες, ἃ επιστανται, ῥᾷστα τε και τάχιστα και καλλιστα και ήδιστα εργάζονται. 17. Καλως και ανδρείως έκαστα ποιει. Ο Αστυάγης, καλως, εφη, εποίησας, προειπων. 19. Τους ἁλισκομένους, ὡς κακως κλεπτοντας τιμωρούνται. 20. Αδηλον εστι 21. Πῶς καλλίον η ευσεβεστερον ειτε βέλτιον ειτε κακιον εσται, τιμψη θεους; 22. Σωκρατης ιδων μειρακιον πλουσιον και απαιδευτον, ιδου, εφη, χρυσουν ανδραπαδον.

VOCABULARY.

The article is fre1. σκληρος, α, ov, dry, hard; παν το quently used in Greek when it must be omitted in English, as in general propositions; μαλαττομαι, I am softened.

|

ing ; θηριώδης, ες, like the animals, low, downcast.

5. αχαριστος, η, ον, ungrateful; αμελης, ες, neglectful; πλεονεκτης, ανaricious ; απιστος, unfaithful.

6. εκτος, adv. without; τα εκτ. αγ. external goods, advantages ; ανωφελής, ες, useless ; χωρις, apart from, τοις εχουσι, to those who have (them), that is, their possessors.

8. πως, how, somehow, some way, in a measure; the adverb restricts or qualifies the statement.

9. Δαρείου και Παρυς. These genitives depend on παιδες ; we should say, D. and P., have two sons.

10. φιλοπενθης, ες, fond of mourning ; πενθος, ους, το, grief, lamentation.

11. το αδ. The infinitive mood with the article is often equivalent to a noun in English, to injure another is worse than to suffer an injury.

12. ὁ μεγ. βασιλ. the great king, that is, the king of Persia, who was the great king to the Greeks; εκείνος, he, that one.

.13. δρων, seeing, pres. part. from οράω; επι τῳ, &c., in consequence of having many disciples; χορος, our chorus, here class, audience ; συμφωνος, ον, agreeing, harmonious ; ὁ εμος, mine ; literally, the mine.

14. ανδρ. παντ, σοφωτ. &c. The superlative governs a genitive; thus we say in English " the fairest of women.

15. φυσικώς, naturally, by natural impulse; λειος, α, ον, soft, mild, sucet ; χρηστικος, η, ον, useful.

18. εποιησας (from ποιειν) thou hast done; προειπων, in foretelling (that).

19. τους άλισκ. the captives ; άλισκειν, to take, capture ; κλεπτειν, to rob; τιμωρεομαι, I punish.

20. εσται, it will be, future of ειναι.

21. τιμψη, could he honour ? τιμαω, I honour.

α

22. μειρακιον, a young man, ανδραποδον, ου, το, a slave.

ENGLISH-GREEK.

Wise men seek not external advantages. Women suffer very much in adversity. An intemperate man cannot become a faithful friend. The nightingale is the sweetest (in voice) The of birds. Girls are more given to sorrow than women. wisest (man) is greatest. I am admired for having much wealth. How can men admire me for having much wealth? My brother is wise, my father is wiser, the philosopher is wisest. Children naturally. love their parents. Fight, Ο citizens, well and bravely for (περι) your (the) city.

Certes, j'ai eu souvent dépit de voir des juges attirer, par fraude et fausses espérances de faveur ou pardon, le criminel à découvrir son fait, et y employer la piperie et fimpudence. Il servirait bien à la justice, et à Platon même qui favorise cet usage, de me fournir d'autres moyens plus selon moi: c'est une justice malicieuse; et ne l'estime pas moins blessée par soi-même que par autrui. Montaigne,

On est quelquefois un sot avec de l'esprit, on ne l'est jamais avec du jugement.-La Rochefoucauld.

D'où vient qu'un boiteux ne nous irrite pas, et qu'un esprit boiteux nous irrite ? C'est à cause qu'un boiteux reconnaît que nous allons droit, et qu'un esprit boiteux dit que c'est nous qui boitons; sans cela nous en aurions plus de pitié que de colère.

Pascal.

Ceux qui jugent d'un ouvrage par règle, sont, à l'égard des autres, comme ceux qui ont une montre, à l'égard de ceux qui n'en ont point. L'un dit: il ya deux heures que nous sommes ici.

2. τα έξω, in regard to the things without, that is, on its L'autre dit: il n'y a que trois quarts d'heure. Je regards ma

adverbs and prepositions), which are combined with other words to vary or modify their signification. They are, also, often called Particles. The simple words with which they are united, are generally verbs; but often nouns and adjectives are, by prefixes, converted into verbs. Most of the prefixes are separable, that is, may stand apart from the radicals; some, however, are found to be inseparable; some are either separable or inseparable, according to circumstances.

to which they lead are only more or less approximate in accor dance with the results of experiment.

liquids: viz., the efflux of a liquid-1st, from an orifice in the There are several cases to be considered in the motion of thin wall of a reservoir, the thickness of which is less than half the smallest dimension of the orifice; 2nd, from an orifice of the same kind furnished with an adjutage; 3rd, through 5th, over a channel, as the beds of rivers. We shall particutubes of large diameter; 4th, through capillary tubes; and larly consider four of these cases.

(2) The prefixes are themselves, also, either simple or compound; as, herkommen, to come here or hither; herüberkommen, to come over here, or hither. In most instances, the prefixes may be translated severally as above; but often they are found Let us first consider the flow of water from the orifice of a 1. Efflux through orifices in a thin wall; and Liquid Vein.to be merely intensive or euphonic. This is likewise often vessel having thin walls or sides. If at any point in such a the case in English: thus, ex (which literally signifies wall we make a small opening, the liquid will issue from it out or out of) has, in some words the signification very, ex-under the action of two forces: 1st, gravity, which acts upon ceedingly or the like; as, exasperate, to make very angry; so a, it in the vertical direction; and 2nd, the pressure of the liquid, in the word ameliorate is merely euphonic, the derivative form which acts perpendicularly to the wall, and proportionally to (ameliorate) meaning nothing more than the simple one, the depth of the orifice.

meliorate.

$ 90. SIMPLE PREFIXES SEPARABLE. from, off, down;

to, at, in, on, towards;

up, upward, on high;
onward, away, forward;

A6,

An,

Auf,

on, upon, up;

Aus,

out, out of, from;

Empor

Fort,

Gegen,

towards, against;

Abseßen, to set or put down;
to depose.

Anfangen, to catch at, i.e. to
begin.

Aufgehen, to go up; to rise.
Ausnehmen, to take out; to

choose.

The jet of the liquid which thus issues from the reservoir is denominated the vein. If the orifice is made in the bottom of the reservoir, the action of gravity being in the same direction as the interior pressure of the liquid, these two forces are added together, and the vein is vertical and rectilinear. But if the orifice is made in a wall vertical or inclined, the two forces which act upon the liquid are such that the one is vertical, and the other horizontal or oblique in its direction. In this case, the liquid vein following the direction of the resultant, takes a curvilinear form, which, abstracting the resistance of the air, would be exactly that of the curve which projectiles describe in a vacuum, and known under the name of the parabola.

Structure of the Liquid Vein.-To the investigations of M. Savart we owe the following particulars relating to the nature Einkaufen, to buy in; to pur- of the liquid vein. It is composed of two distinct parts: the first, which is in contact with the orifice, is completely calm and transparent, and presents the appearance of the most limped crystal cylinder; the second, on the contrary, is troubled and agitated, and presents elongated swells, which are regularly arranged at intervals, as shown in fig. 41, and which may be termed protuberances.

Emporheben, to lift up.
Fortfahren, to drive or bear
on; to continue.
Gegenhalten, to hold against;
to resist; to compare.
Inwohnen, to dwell in.
Heimkehren, to turn home-
wards; to return.

Herbringen, to bring hither,
or along.

Hingehen, to go thither, or

away.

Mitnehmen, to take with, or
along.

Nachfolgen, to follow after; to
succeed.

Nicberreißen, to pull down.

on, over, on account of; Obliegen, to lie on, i.e. to ap

ply one's self to; to be in-
cumbent on.

Vorgehen, to go before; to

surpass.

Wegbleiben, to stay away.
Zugeben, to give to; to grant.

ON PHYSICS OR NATURAL PHILOSOPHY.

No. XIII.

HYDRODYNAMICS.

Object of the Science.-It has been already stated that hydrodynamics is that part of Rational Mechanics which treats of the motion of liquids; and that the part of this science which particularly treats of the art of conducting and raising water, is called hydraulics; that is, hydraulics is the practical department of hydrodynamics.

In hydrodynamics as well as in hydrostatics, liquids are considered to be incompressible, perfectly fluid, and consequently free from all viscosity. But liquids possess these properties only imperfectly; hence the theoretical consequences

see

This second part of the vein is not continuous; for when an opaque liquid, such as mercury, is made to flow through the orifice, we through the vein. Savart has observed that the protuberances are formed of discontinuous globules, elongated in a direction transverse to that of the vein; and that the contractions or nodes are formed, on the contrary, of globules elongated in the direction of the vein itself, as shown in fig. 42. He has also observed, by looking at the vein in a strong light, that the limped part is formed of annular swells which originate near the orifice, and are propagated at equal intervals until they reach the troubled part of the vein where they are separated. These swells proceed from periodic pulsations which take place near the orifice. Their number is in the direct ratio of the velocity of efflux, and in the inverse ratio of the diameter of the orifice.

The pulsations just mentioned may be so rapid as to give rise to a sound, which is increased by receiving the vein on any tightened membrane. By producing a sound in unison with that of the vein, by means of a musical instrument, Savart has modified the Figs. 41. 42. vein in such a manner, that the protuberances and nodes have taken a more regular form, and the transparent part of the vein has entirely disappeared. He has also found that the resistance of the air hes no effect on the

form and dimensions of the vein, or on the number of pulsations. He has likewise observed that the structure of the horizontal or oblique veins does not essentially differ from that of veins which fall vertically.

Vena Contracta, or the Contraction of the Vein.-When efflux takes place through a circular orifice made in a thin wall orside of a vessel full of water, the liquid vein preserves the circular form in its transverse sections, but the diameter is variable. This diameter is at first equal to that of the orifice, it then rapidly diminishes, and at a distance from the orifice nearly equal to its diameter, the section of the vein is no more than of that of the orifice. If the direction of the vein is vertical as in fig. 41, the section decreases slowly till it reaches the troubled part. If the direction of the vein is horizontal, the section decreases insensibly. If the angle of inclination of the vein varies from 25° to 45°, the vein preserves nearly the same diameter; but if it exceeds 45°, the section increases from the part contracted to the part troubled. The part where the diameter of the section reaches its minimum, is called the contracted section.

The contraction of the vein originates in the converging directions which the liquid particles assume in the interior of the vessel, when they proceed towards the orifice. This phenomenon is rendered visible by putting the water in a transparent vessel, and mixing small light substances with it which are kept in suspension in it, the orifice being made in a thin wall or side of the vessel. If the orifice be half an inch in diameter, we see at twice or thrice that distance from it within the vessel, the substances suspended in the water drawn from all parts of the vessel towards the orifice, and describing curve lines, as if they were attracted towards a centre, as shown in fig. 43. The convergence of the particles which Fig. 43.

took place in the interior of the vessel is continued exteriorly, and the liquid vein is gradually contracted till it reaches the point where the particles, by the effect of their mutual action, take a parallel or diverging direction. The vein thus forms a species of truncated cone or frustrum, of which the greater base is the orifice, and the smaller base the contracted section. In the preceding remarks we have supposed that the orifice is of the circular form. If it be polygonal, or of any form different from that of a circle, the vein no longer preserves a section of the same form as the orifice. Its form changes as the vein recedes from the orifice, and continually gives rise to protuberances and nodes.

Theorem of Torricelli.-When a liquid issues from a reservoir by an orifice in a thin wall or plate, the velocity of the discharge is determined by the following theorem: The liquid particles as they issue from the orifice have the same velocity as if they fell freely in a vacuum, from a height equal to the vertical distance from the centre to the upper surface of the liquid in the reservoir. This theorem was discovered by Torricelli in 1643, and was by him considered as a corollary to the laws of falling bodies established by his master, Galileo. This law can be experimentally proved to be a result of the principle demonstrated in mechanics, viz., that when a body is projected upwards with a given velocity, it will rise to the same height from which it would have fallen in order to acquire that velocity. Thus, when the discharge is made to take place vertically upwards, as represented in fig. 44, the liquid vein reaches very nearly the height of the level of the liquid in the vessel from which it is discharged, and the reason why it does not reach it entirely, is the resistance of the air, and the action of the liquid particles in falling, which oppose the ascent of the jet. Hence, at its issue from the orifice n, the liquid spouts upwards with

The following important corollaries are deduced from the Theorem of Torricelli: 1st. All bodies in a vacuum falling with equal velocity, it follows that the velocity of discharge is independent of the density of the liquid. For example, water and mercury issue with the same velocity, if the height of the level above the orifice be the same for both liquids. Experiment, indeed, proves that in the case of equal heights and orifices of the same diameter, equal volumes of these liquids are discharged in the same time. 2nd. The velocity of discharge at the issue of a liquid from the orifice, is proportional to the square root of the height of the level in the reservoir above the centre of the orifice. This is, in fact, a consequence of the laws of gravity, for we have seen, in a former lesson, that representing the velocity acquired by a moveable which falls in a vacuum by v, and the height of the fall by h, we have v=V2gh. The velocity calculated by this formula is called the theoretical velocity.

Theoretical and Effective Discharges.-The volume of a liquid which is actually discharged from an orifice in one second, is called its effective discharge; and the volume of a liquid equal to that of a cylinder or prism which has the orifice for its base, and the theoretical velocity above mentioned for its height, is called the theoretical discharge.

The effective discharge is always less than the theoretical discharge. The effective discharge is in reality the product of the contracted section of the vein, and the mean velocity of the liquid particles at the instant that they pass this section.