A KEY TO THE

LATIN

LESSON S.

By JOHN R. BEARD, D.D.

(Continued from page 75, Vol. IV.)

Vol. III., p. 113.-LATIN-ENGLISH.

Vol III., p. 113.-ENGLISH-LATIN.

Vol. III., p. 130.-LATIN-ENGLISH.

Canem ve berant; filius patrem amat; epistolam scribis: Angl vincent hostes; hostes victi sunt ab Anglis; Carthago & Scipione deleta est; pax fortes decet; ducem Vellingtonum fecerunt Angli; Nap leonem nominârunt imperatorem Galli; vigen esimum ago annum; tricesimum annum ago [instead of age read ago]; frater multos menses caecus fuit; fossa de cem pedes est lata; exercitum transduxit flumen; somnium somniavit Josephus; aleâ ludunt; illud dubitas? illud mihi concedunt; regem adeo; boni veritatem How great your labour! alas! how wretched I am! O the nunquam egrediuntur; avaratia ca cos reddit homines; Socrates deceptive hope of men, and their frail fortune and our empty strifes; by the faith of gods and men! what great undertaking, Omusicam docent; Latinam docendi sunt pueri; eheu me miserum! sapiens es habitus; consul sententiam rogatus est; puellas sacred Jupiter, was ever accomplished not only in this city but in vae tibi, marite! all lands! alas! my labours have been undertaken in vain! O my fallacious hopes, and emp y thoughts! lo! here is the reason why the law was passed; aha! you have a talent of silver! I write a letter; I whip a dog; the son loves his father; the Romans conquered the Carthaginians; Scipio destroyed Carthage; the very swift foot-soldiers were able in running to keep up with the cavalry; serene pe ice befits men, fierce rage (befits) wild beasts; red hair is no discredit to a man among the Germas; let prudence never fail [in the note for infinitive read imperative] the orator; Themistocles did not escape from envy on the part of his fellow citizens; Ulysses wished to withdraw from warfare; fortune assists the brave; you think that I am a rival of Agamemnon; glory, like a shadow, follows valour; brave and wise men are not accustomed to seek so much the rewards of good deeds as good deeds themselves; Marius commanded in that part; he had formerly played a similar game; I dreamed a wonderful dream; I am of opinion that your fathers are alive; I enjoy that kind of life which alone deserves the name; I have sworn a very certain and very imposing oath; Siccius Dentatus had nine triumphs; I cannot make the same boast; that I doubt not; in that I agree with you; Pythagoras visited the magi of the Persians; the consuls entered on their consulship; Pythagoras went to many barbarous regions on foot; I met no one; all fates surround us on every side; soon the Roman legions besieged Carthage; Scipio did not refuse a conference; history ought not to depart from truth; the best plans are forming; this town is under siege; a very large inheritance comes into (your) possession; they declare that either by a letter or a messenger they are approaching him as if king; Caesar went to the colonies of his country; he wished to visit, and become acquainted with those nations also; with great hope I enter on the remainder of my speech; the mother called her son a brotherslayer; Ennius has well said that anger is the beginning of madness; he named Sicily the nurse of the Roman populace; the recollection of pleasures we have enjoyed makes life happy; cupidity and avarice make men blind; the Carthaginians appointed Hamilcar their commander-in-chief; the people created Ancus Martius king; Apollo judged Socrates to be the wisest of men; Socrates accounted himself an inhabitant and citizen of the whole world Ariovistus replied to Caesar that he should consider him not as a friend but as an enemy; what is more foolish than to account uncertain things certain, and false things true? Cato, by himself, is as good to me as a hundred thousand men; Artaxerxes asked the Athenians to let him have Iphicrates as a general; do you consider that nothing? the Achaeans sought aid from Philip; Verres (capital V) demanded from parents money to be allowed to bury their children; Caesar daily required corn from the Aedui; who taught Epaminondas music? I have not concealed the conversation from thee; know that my opinion has not been asked; Marius had learnt all military arts; am I even now to be taught to speak either Greek or Latin? in that you give me excellent advice; this one counsel I give my pupils; Apollo is asked to supply words; you must inquire your way; Epaminondas is taught music; Cato was asked his opinion; the legions were conveyed through Italy, Rhegium, and Sicily, and then from Sicily across into Africa; Miltiades reached the Chersonesus; all hurry together into the houses; Mithridates sent ambassadors as far as Spain to Cneius Pompey; Caesar's soldiers go up under the mountain; he sent his forces across the Hellespont; he commanded the army to pass over the Rhine; they pass the river on a bridge; we conversed from eight o'clock till evening; he will sleep till sunrise; he walked seventy miles; Ariovistus proceeded from his own boundaries three days' march; the plain of Marathon is distant from the town of the Athenians about ten miles; the towers stand eighty feet apart; the Arabians have their swords about four ells long; the soldiers raised a mound three hundred and thirty feet broad, and eighty feet high; Atticus for thirty years wanted no medicine; Appius was many years blind; Saguntum has now been three years in the power of the enemy; the name of Pythagoras flourished for many ages; Nestor had outlived two generations of men; I am in my eighty-fourth year; I sleep the winter through; like Mercury in all things, both voice and complexion

Conon for the most part lived at Cyprus, Iphicrates in Thrace, Timotheus at Lesbos; we were detained seven days at Corcyra; Miltiades tarried in the Chersonesus; the Gauls went to their homes; great things were carried on abroad in those times; M. Drusus was killed at his own house; I spoke those same things at my house; they carry gold and silver into the palace; they invite each other to their homes; I am not at my case in another person's house; at the house of Caesar there are no friends; many persons assemble at his house; the victory was announced at Corinth, at Athens, and at Lacedemon; he was brought over from Apollonia, a city of Pontus; the Romans came to the town Cirta; the strangers are in the town of Citium; Archias was born at Antioch, formerly a celebrated city; the soldiers stopped at Alba, a fortified city that was near; when I was directing my way to Mutina; there was a look-down from Gergovia into the camp (castra); I intended to go from Athens; ambassadors came from Ardea to Rome; a vessel is ready for us at Cajeta; Socrates introduced philosophy even into homes; Antony committed impure deeds even in a chaste family; discipline flourished in that house; Alcibiades was educated in the house of Pericles; he was said to celebrate mysterious rites in his own house; they went to their own rural properties; Pompey being conquered by Caesar hastened to Alexandria; the emperor Gallienus was slain at Milan; Caius Marius betook himself to Praeneste; many famous Romans are said to have gone to Rhodes; the Romans were brave at home and abroad; at Delphi there was a very famous temple of Apollo; wherefore both kings and peoples were accustomed to send ambassadors to Delphi, or to seek oracular responses from Delphi; the Romans sent ambassadors to Athens; Demaratus had fled from Corinth to Tarquinii in Etruria; we are punished by negligence in many things; they are in fault who desert their duties through weakness of mind; I beg you to think that I write to you more rarely than I was accustomed, not through forgetfulness of you, but through my bad health; anxiety had taken possession of the senators lest the people through fear and anger should appoint military tribunes; I almost lost my senses through excessive joy; the pilot's art is praised for its utility; one ought to grieve for a misdeed, and to rejoice at correction; I am wont to rejcice in nothing so much as in a consciousness of performing my duties; being glad at your lot you will live wisely; the Campanians were always proud of the excellence of their fields; Greece formerly flourished in opulence, dominion and glory; the Roman state laboured under two vices, avarice and luxury; oxen protect themselves by horns, boars by tusks, lions by jaws (bites); Lycurgus confirmed his laws by the authority of the Delphian Apollo; Atticus gratuitously supplied all the Athenians with corn; we are supplied and adorned with the gifts of the gods; it is the duty of the senate to assist the state by its counsel; many old men have found pleasure in cultivating the land; being oppressed with food and wine, we, in the hours of rest, see troubled and confused things; Varus (dele comma) is a man possessed of the highest religion and the highest authority; that belongs to each person which each enjoys and uses; the Helots among the Spartans performed the office of slaves; Caesar obtained the command of all Gaul; the Numidians for the most part lived on milk and the flesh of wild beasts; the crocodile is protected by his skin, which is very hard, against all blows; elephants breathe, drink, and smell by means of their trunk; some people eat locusts; the teeth are worn away by use, but are not burnt with fire; in silence he led his forces out of the camp; Miltiades restored order in Chersonesus with the greatest equity; let us always venerate the gods with a pure, sound and uncorrupt mind and voice; they went over the forests of the Alps not without loss; Dolabella (not Dolabellam) provided a fleet with the intention of going to Italy; allow me to say so; the stars accomplish their courses with the greatest speed; Iphicrates had a great soul; Caesar is reported to have been tall, light-complexioned, slender of limb, with a mouth somewhat large, black and brilliant eyes, and excellent health; all the Britons colour themselves with woad (blue), and on that account they have a more frightful appearance in battle, they also have

120

long hair, being shaved in every part of the body except the head and upper lip; Cato in all things possessed singular foresight and industry; Dionysius ordered boys of rare beauty to stand at his table; Caesar sent to Ariovistus Valerius Procillus, a youth of very high virtue and humanity; there was between Labienus and the enemy a river difficult to be passed and with broken banks; Chrysogonus purchased a Corinthian vase at a great price; Caesar shows the soldiers how much a victory must cost; the conquered purchased peace at a great cost; peace of mind is purchasable for neither gold nor gems; of old, boys were immolated to the gods at Carthage; Alexander died at Babylon; Pindar flourished at Thebes, Theocritus at Syracuse; in winter boars sleep in caves; no mortal is wise on all occasions; Iphigenia, the daughter of Agamemnon, was slain at Aulis; Dione was put to death (interfecta est.) at Syracuse; Dionysius got possession of Syracuse again; pleasure having dominion (dominante) all virtues of necessity lie low (are necessarily depressed), if all things were lost, yet virtue could uphold itself; calling God to witness, he promised many things; in the civil war nothing happened which I did not foretell; it is not advantageous to quit the banks of the Rhine, when now hostile nations are about to make irruptions.

LET A EFD be a section of the globe, wAL the wall, and c
the place of the lighted taper. Let ca be drawn through the
centre o, and cw and CL tangents to the section AEFD at D
Then
and E.
Join DE and Do, and let DE meet CA in G.
WL is the diameter of the shadow of the globe on the wall,
and DFE is a central section of the segment of the globe
whose surface is enlightened, and GF is its height.
the radius AO or Foa, and the distance CA; then
Now, by the similar triangles, CoD and
DOG, we have co: oc:: OD: 0 G, or x — a: a: :a: 0 G;
a2
and
whence o G equals
OF — OG equals
x-a

2 x

a2

x-a

ax- -2a2
x-a

F G

Let

But the area of the surface of the

enlightened segment, whose arc is EFD, is by mensuration,
that is, the product of its height by the
circumference of the globe, π being 3.141592, &c. Again, we
have, by the 47th Prop. of Euclid, Book I., CD=√(x2 — 2ax);
and by the similar triangles CDO and CA W, CD: DO:: CA;
Aw; or √(x2 - 2ax): a: x: ▲ w; whence Aw=.
√(x2-
x2-2ax)

and the area of the shadow on the wall

a2x

2 π

ax

(

√(x2 — 2ax)

-

2

This question was also solved by T. F., Ayrshire; and X PLUS Y. plane

Answer to D. F. F. C. H.'s query, to bisect a cone by
parallel to its base.

If a cone be divided by a plane parallel to its base, the upper part will be a cone similar to the whole; and similar solids are to each other as the cubes of their like dimensions. Hence, in the case proposed, we have this rule.

Cube any given dimension (either slant height, perpendicular height, or base) of the whole cone; divide this cube by 2, and the quotient will be the cube of the like dimension X PLUS Y. of the upper cone, or half. This question was solved also by Peter Simple, Fleet-street, and others.

CORRESPONDENCE.

THE GIFT OF ORATORY.

"Though I speak with the tongues of men and of angels !!'-1 Cor. xiii. 1. DEAR SIR,-As one of your pupils, allow me to ask your advice, through the medium of the P.E., viz.: What course of study must I pursue in order to become an orator, beginning at the very first rudiments of the art?

I am confident that I might be the means of doing much public good in this manner, for I possess (I am not writing under any egotistical disposition, but simply telling the truth) many rare talents, being about the middle stature, of commanding and pleasing features, a fine yet powerful voice, with perfect command over it, having studied singing for the last six years with that object in view; and from what little experience I have had, I have discovered that I possess that great secret of success in oratorypower to sway the multitude. Yet with all these talents I lack knowledge; you will, therefore, confer a great boon upon one of your earnest pupils by giving the advice he earnestly seeks. Yours, &c. RESPICE FINEM.

[The author of the preceding letter having sent us his real name and address, we cannot but insert it as a specimen of many which we receive, and to give our subscribers an idea of the labour which we have to undergo as the Editor of the POPULAR EDUCATOR. How truly does the letter show, as he confesses himself, that the author lacks knowledge, the best of all knowledge, namely,-self knowledge! We would strongly recommend to his perusal Mason's "Treatise on Self-Knowledge," and to his reflections the celebrated adage of antiquity, uttered by Solon, yvwlı σɛavrov, nosce teipsum, know thyself. We would also recommend the perusal of the book once printed separately from the Bible, and used as a class66 The Proverbs book in the parochial schools of Scotland, namely, of Solomon," who was even wiser than Solon. Lastly, we would recommend him to begin at the first volume of the P.E., and study every word of it, in order to gain that knowledge which he himself seems to feel the want of. We give him a year to make himself master of it. After that the second volume awaits him; then the Having thus got something into his third and the fourth. cranium, he may try to spout or make an oration to the public, with advantage to himself and instruction to his hearers.]

ANSWERS TO CORRESPONDENTS.

W. FOLLETT (Bognor) should study well all Mr. Cassell's publications, especially the Popular Educator, vols. 1, 2 and 3; and 4 as far as published. -J. LOVETT (Ashfordby) and A WELL-WISHER (Grahamston) are right.— T. HILL (Manchester): Lessons on Elocution are almost ready.-BENE: Wrong on the wolf question, and right on the taper question.-F. GOLDING (Abingdon): Received, and under consideration.-A STUDENT OF KING'S: The omission has been noticed.-SUBSCRIBER (Wigtonshire): If a ball be thrown at an angle of 45° it will have the greatest range. The stature of an individual has nothing to do with the angle of elevation. W. TAYLOR (Cowbridge): We must defer the subject of annuities for some time. Lingua in Latin means both the instrument of speech, the tongue, and that which is spoken by it, language. In French, this word becomes La Langue, and means the same two things; but the French have a word, Le Langage, derived from this, which signifies only that which is spoken. language.

(2). Consequently, we have, by the question, The English word tongue, like the Latin Lingua and the French La Langue,

means both the instrument of speech, and that which is spoken by it, language. The English word language, borrowed from the French, has the same Sa2 meaning, namely, that which is spoken by the tongue. Hence, it appears that tongue and language are synonymous when applied to that which is spoken, but that the latter cannot be applied to the instrument of speech. -J. W. TAPPER (Kilkenny); Covers for the P. E. may be had at this office, 18. common, 1s. 6d. fine edition. The cheapest cases of Mathematical Instruments are said to be sold at the "Society of Arts," Adelphi, London, -INDOCTUS (Lubenham): Spirit-lamps may be had at all prices, from 18.9d. and upwards according to their uses; see Knight and Son's Catalogue (Foster-lane. London), where you will also get Manganese, and a vast variety of other chemicals. Here also you will get chemical apparatus of every description.-WARIN (East Dereham). Received,

(7±√17). Now, since a=

1 inch, we have, by taking the upper sign, x=5·56155, &c. inches, the distance of the taper from the wall. We hope some of our correspondents will give us an explanation of the case when the under sign is taken, that is, when x 1.4384. &c.

ON PHYSICS OR NATURAL PHILOSOPHY.

No. IX.

ON THE EQUILIBRIUM OF LIQUIDS.

Equilibrium of a Liquid in a single Vessel.-In order that a liquid should remain in equilibrium in a vessel of any shape, the two following conditions are necessary:

1st. Its surface at every point must be perpendicular to the direction of the force which attracts the particles of the liquid. 2nd. Every particle of the mass must in all directions be under the aetion of equal and contrary forces

The first condition has already been considered, when treating of the influence of gravity on the direction of the free surface of a liquid. The second condition is self-evident; for, if the pressures which urged a particle in two opposite directions were not equal and contrary, it would be urged in the direction of the greater presBure, and the equilibrium would be destroyed, seeing that motion would ensue. This condition is, besides, a consequence of the principle of the equality of the pressure and reaction which every force produces when applied to a liquid.

The Equilibrium of a Liquid in Vessels which communicate with one another.-When several vessels of different forms contain the same liquid and communicate with one another, equilibrium can only take place in each vessel when the preceding conditions are satisfied, and when the free surfaces of this liquid in all the vessels are situated in the same horizontal plane. Thus, let the different vessels in fig. 27, communicate with each other, and be Fig. 23

potassa, alcohol coloured red, and oil of naphtha. When the via is shaken, the four liquids are mixed together; but when it is at rest, the mercury, which is the densest, sinks to the bottom; then above the mercury, the water will place itself; above the water, the alcohol; and above the alcohol, the oil of naphtha. Such is the order of these bodies according to their decreasing der sities. The water in this experiment is saturated with carbonate of potassa, in order that it may not be mixed with the alcohol, in

which this salt is not soluble.

The separation of the liquids in the preceding experiment, is referable to the same cause which makes solid bodies immersed in a liquid more dense than they are, rise and float on its surface.

In consequence of this principle of hydrostatics, we find that the fresh waters at the mouths of rivers float to a considerable distance above the salt water of the ocean into which they fall. For the same reason, cream, which is lighter than milk, separates from the latter by degrees and is found floating on its surface.

Equilibrium of two Heterogeneous Liquids, in two Vessels which communicate with each other. When two liquids of different densities, and incapable of chemical action on each other, are contained in two communicating vessels, to the conditions of equilibrium already stated, must be added the following: that the heights of the columns of the liquids which are in equilibrium, are in the inverse ratio of their densities.

In order to prove this principle by experiment, we take a bent tube, fix it on a board placed vertically, fig. 28, and pour mercury

filled to a certain height with water; and suppose that a vertical layer of the liquid in the tube of communication is under our consideration. This layer cannot remain in equilibrium unless the pressures which act upon it in the directions from M towards N, and from N towards M, are equal and contrary. But we have seen in our last lesson, that these pressures are equivalent to the weight of a column of water which has for its base the layer under consideration, and for height the vertical distance of its centre of gravity from the surface of the liquid. Now if we suppose a horizontal plane м N drawn through this centre of gravity, it is plain that the equilibrium cannot take place unless the height of the liquid above this plane is the same in each vessel; therefore, the surface of the water in the different vessels must be in the same horizontal plane.

into it; we then pour water into one of the branches of the tube. Now, the column of water A B pressing on the mercury at B, the level of the mercury in the tube is lowered in the branch A B, and raised in the other branch by a quantity CD; when the equilibrium takes place, if we suppose a horizontal plane BC to pass through the point в, then the column of water AB balances the column of mercury c D. Measuring the altitudes CD and AB, by means of two equally graduated scales fixed to each vertical branch of the tube, we find that the ratio of AB to CD is 13 to 1. Hence, we infer that the density of mercury is 13 times that of water; consequently the altitudes of the columns of mercury and water, above the horizontal plane, are to one another in the inverse ratio of their densities. The reason of this is plain; for as the pressures on the same horizontal plane B c are the same, the equilibrium can only be established by any column gaining in altitude what is lost in density.

The preceding principle may be deduced from a very simple calculation. Let d and d be the densities of water and mercury respectively; and let h and h' be the altitudes of the columns of these liquids respectively, when they are in a state of equilibrium; and let g denote the intensity of gravity. The pressure at B, being proportional to the density of the liquid above it, to Equilibrium of Supernatant Liquids.-When several hetero- its height, and to the intensity of gravity, has for its measure the geneous liquids float above one another in the same vessel, stable product dhg. For the same reason, the pressure at o has for its equilibrium cannot take place, unless each satisfies the conditions measure the product d'h'g. But in a state of equilibrium these already stated regarding a single liquid; and, in addition to this, pressures are equal; therefore, we have dhg=d'h'g; whence, unless the liquids are arranged above each other in the order of suppressing the common factor g. we have dh-dhd their densities, that is, diminishing in their densities upwards.::h: h; which is the algebraic expression of the principle to be This condition is clearly proved by the experiment with the vial proved.

of the four elements. This name is given to a long and narrow This hydrostatic principle may be employed in determining vial containing mercury, water saturated with carbonate of the density of a liquid. Thus, supposing that one of the branches

VOL. IV.

87

Fig. 30.

ing the instrument to the practice of levelling. We have seen that the differences in the vertical distances on the staff show the differences of the levels; now by the addition of these consec :tive distances when the ground is ascending, and by their sub rac tion when it is descending, we ascertain the respective position. of any number of points on the ground with reference to any assumed horizontal plane. The level found by this instrument is only the apparent level, that is, the level which corresponds to the points contained in a plane touching the surface of the globe, supposing it perfectly spherical. The true level is that which corresponds to points equally distant from the centre of the earth. In the case of short distances, the apparen level may be taken for the true level; at the distance of one mile the difference between them is only 8 inches; the geners approximate rule for finding the difference of level between tw points on the earth's surface being to square their distance in miles, and take two-thirds of this square for their difference of level in feet.

ends with two short tubes of glass at D and E, fig. 30. In using this apparatus it is placed horizontally on a three-legged stand or support, with the bent ends turned upwards, and coloured water is poured into the tube till it rises to a certain height in both ends in the glass tubes. As soon as the water is at rest, its level, that is, the surface of the water in these tubes, is the same; or in other words, a horizontal plane will pass through the two surfaces of the water at D and E. This instrument is employed in taking levels in surveying, that is, in determining how much one point on the ground is more elevated than another. Thus, if it were required to find how much the point в on the ground is above another point A, we place a graduated levelling staff at the point A. In the present instance, this staff is formed of two vertical wooden rods, sliding on each other in a groove, and terminated at the top by a piece of tin M, which has a mark in the middle of it. This staff being adjusted vertically at A, an observer at the level at D, directs his sight along the surface of the water at D and E, to the staff, and makes signs to his assistant who holds it, to lengthen or shorten it, until the central mark м be found in the continuation of the horizontal line D E. By measuring then the height ▲ M, and subtracting from it the height of the level above than the water-level. It consists of a tube of glass, fig. 31, very the ground, the observer ascertains at once the difference of level between A and B, that is, how much the point в is above the point A. The following enlarged view of the water-level and levelling staff, with their adjusting apparatus, will give our students a better idea of these instruments. The figures F and G

F.

Air-Level. The air-level is more sensible and more accurate

Fig. 31.

M

slightly curved, filled with water, hermetically sealed at both ends, and containing a small bubble of air which tends always to occupy the most elevated part of it. This tube is enclosed in a metal case c D, and fixed lengthwise on a stand, which is so carefully adjusted, that when at rest on a horizontal plane, the air-bubble M is always found in the middle between two points marked on the case; and part of the case is left open, so that the oscillations of the air-bubble may be observed until it finally settles in the true horizontal position. In taking levels with this instrument, a telescope is fixed on it for the more accurate determination of the horizontal positions. The following figure L shows the

L:

mode of adjusting the telescope to the level, and the mode of bringing the air-bubble to the centre of the level, and under the middle of the telescope, by means of adjusting screws.

The Slope-Level, N, invented by M. Chézy, is adjusted in a similar manner. But on the right of the figure there is placed a small hole intended for the eye-piece; and on the left, a moveable sight with diaphragm, for the more accurate determination of the slopeline. To this sight there is attached a graduated vertical scale, for ascertaining the degree of the slope or inclination of any line