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5. Ganz wie, with a verb, signifies “precisely," or "just as," 11. Der Staat Pennsylvanien liefert eben so viel Rohlen, als ganz England. or "like," as :-&r ist ganz wie ich, he is just as I (am), he is just 12. Arbeitet Gustav nicht eben so viel, wie sein Bruder Hermann? 13. Die like me.

Sie denkt ganz wie er, she thinks precisely as he fleine Elise gab ihrer Schwester Pauline eben so viel Pflaumen, wie ihrer (thinks), she thinks precisely like him.

Freundin Emma. 14. Haben unsere Nachbarn noch feinen Garten? 15. 6. Noch, besides meaning "nor," when used in conjunction Nein, sie haben noch feinen. 16. Bleiben Sie noch lange auf dem Lande? with weter, "neither," is variously rendered by “still some, or 17. Ich bleibe noch eine kurze Zeit da, und meine Freunde auch. 18. Gehen yet more, another, besides,” etc., as :- -Er schläft noch, he sleeps Sie heute noch spazieren ? (Sect. LXIV. 1.) 19. Nein, denn ich muß still. Gieb dem Kinde noch Brod, give the child some more bread. noch arbeiten. 20. Die Freudenthränen der lang getrennten Freunde rührten Wann þat er noch ein Pferd gekauft? when did he buy another die Herzen aller Zuschauer. 21. Sönnen Sie die Waaren nicht billiger vers horse ? Ginen Apfel hat das Kind gegessen, aber es pat noch einen, kaufen? 22. Es ist rein unmöglich. 23. Sie müssen dieses anders machen. the child has eaten one apple, but it has one besides (or 24. Was fann ich anders thun ? 25. Du kannst anders reden und another).

handeln. 26. Ich werde Sie besuchen, wenn Sie es erlauben. 27. Er 7. Mehr, connected with a negative word, is used like its erzählte die Sache ganz anders. 28. Es ist etwas anderes, ob ich schreibe : equivalent “more," as :-Ich habe teins mehr, I have no more. er ist , gelehrt,“ oder „geleert.“ 3o habe nicht viel mehr, I have not much more. Used with

EXERCISE 59. a noun, the adverb follows, while in English it precedes the

1. Has the teacher taken away the paper or the book? 2. He 8. Ander signifies other, in the sense of different; it must not has taken away both; for both belong to him. 3. Both towns be used in phrases like, “ I saw him the other day,” which is in are situated on navigable rivers. 4. Thoy may take either way, German, Ich sah ihn neulich (literally, recently); or, Ich sah ihn vor as they have proceeded so far. 5. A great part of the land in cinigen Tagen (literally, a few days ago).

America is still uncultivated. 6. He who wants the purpose, 9. The neuter anderes, preceded by etwas (in conversation must will the means. 7. The Rhine steamboat has just started usually contracted to was), is rendered by the phrase "another for Holland. 8. You err altogether when you say that you have thing," as :-Das ist etwas anderes, or, das ist was Anderes, that is quite surmounted every difficulty, otherwise all that you have another thing.

stated would be correct. 9. Which of us is right, I or he ? 10. 10. The adverb anders is readily distinguished by its form, You are both wrong. 11. It is quite another thing to say that and is rendered by “otherwise, differently,” etc., as :-Er spricht he was not well, and could not come in consequence of it. 12. anbers, als er denkt, he speaks otherwise than he thinks.

I shall speak no more about it; because I have found upon

closer investigation, that he is neither covetous nor prodigal. VOCABULARY.

13. They do not think themselves better than others. #fahren, to depart, Gustav, m. Gustavus., Spazie'rengehen, to Emma is just as intelligent as Eliza. 15. The sailor sets sail start.

Handeln, to act, deal. take a walk. for America to-morrow. 16. Do you drink wine or beer? 17. Anber, other (R. 8). Insgesammt', alto- Staat, m. state. I drink neither wine nor beer, I always drink water. 18. An'teres (R. 9).


Thaler, m. thaler (a Gustavus gave the boy thaler to buy some coals for his Inters, otherwise, Jeren, to err.

German coin, mother. 19. Pennsylvania is a rich and flourishing state in the differently. Kohle, f. coal.

worth about 3s.) United States of America. 20. She is just like her sister. 21. Uus bleiben, to remain Liefern, to furnish. Trennen, to separate. Give the boy some more plums. 22. I have no more. 23. The ont.

Mit'nehmen, to take un'angebaut, unculti- girl shed tears of joy when she saw her mother. 24. That Beide, both.


ware is cheap, and the pattern of it is beautiful.

25. My Beibed (R. 1).

Mittel, n. means. Unmögʻlich, impossible friend has purchased a new winter coat. 26. This merchant Besu'hen, to visit. Muster, n. pattern. Unrecht, wrong.

sends his goods to the town in a wagon. 27. Will you take a Da'bleiben, to remain Pennsylva'nien, Verstän'dig, intelli- walk to-morrow? 28. It is impossible. (there).

Pennsylvania. gent, sensible. Dampfidiff, n. steam- Pflaume, f. plum. Waare, f.ware, goods. ship.

Recht, n. right. Weg'nebmen, to take

Gben so, jast as (R.4). Reben, to speak, talk. away.
Gi'nige, some, several. Rühren, to move, af- Win'terroc, n. winter



Erlau'ben, to allow. Sache, f. thing, af- Wohlfeil, cheap. OF Levers there are commonly reckoned three kinds, of which
Freudenthräne, f. tear fair.

Zu'schauer, m. specta- Figs. 45, 47, and 49 furnish illustrations, in which the bar Som'merrod, m. sum- tor.

extends to equal distances on either side of the fulcrum, F; Geleert', empty.

mer coat.

Zwed, m.aim,purpose. in order that, the centre of gravity being supported at F, it RÉSUMÉ OF EXAMPLES.

may not by its weight interfere with the action of the Weight

and Power, In that case Gr hat zwei Söhne, aber beite sind He has two sons, but both are

12T UN we must consider the true taubftumm. deaf and dumb.

lever only as so much of the Der Riese faßte die Reule mit bei- The giant seized the club with

bar as is between P and w, ten Händen. both hands.

Fig. 45.

or p or w and F, the points Fat ter Kaufmann ein Pferd over Has this merchant a horse or a

of application and the ful. einen Wagen ? wagon ?

These levers are said to be of three orders.
Gr bat Beves.
He has both.

First Order.—When the fulcrum is between the Power and Die Wahrheit und die Rose find The truth and the rose are Resisting Weight. sehr schön, aber Beide haben Dors very beautiful, but both have Second Order.— When the fulcrum is at one end, and the


Weight nearer to it than the Power. Ein aufrichtiger Mann verab'icheut An upright man abhors a lie. Third Order.- When the fulcrum is again at one end, but

the Power nearer to it than the fait jeter Mensch hat eben so viel Nearly every human being has Weight. kummer als Freude.

quite as much sorrow as joy. First Order.-The Condition of EXERCISE 58.

Equilibrium in this we have

already determined in connec1. Wollen Sie ein Muster von diesem oder jenem Tuche haben? 2. tion with the balls in Lesson Ben feinen von beiten.

Fig. 46. 3. Wir geben ihm einen Thaler für jeden der VI. (Fig. 44). The Resisting beiden Männer.

4. Trinken Sie Wein oder Bier ? 5. Ich trinke Weight (Fig. 45) is to the Power inversely as w F to P F, or meter Wein noch Bier (or, ich trinfe feines von beiden). 6. Sie haben the weight multiplied by the arm, w F, is equal to the power Recht, taß Sie das getyan haben. 7. 3st ef recht, daß Iohann so lange multiplied by the arm P F. Of this kind of lever the examples azábleibt? 8. Nein, es ift unrecht von ihm, da er seine Aufgaben zu lernen are very numerous. In Fig. 46 the crowbar is used as a lever, bat. 9. Wie viel Tuch braucht tér fleine Friedrich zu (Sect. LXXIII. 1) by means of the fulcrum in the middle, to lift the chest, the ette Sommerrede? 10. Gr braucht eben so viel, wie zu einem Winterrođe. push of the hand and the weight of the chest, both parallel


of joy.




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LESSONS IN GERM SECTION XXXI.-INSEPAR BESIDES the separable particles (Se class (be, emp, ent, er, miß, ver, etc., are never used apart from the ra prefixed, and hence are called inse union of these particles be, emp, fehlen, etc., we have the compou erholen, mißfallen, verhören, germalm tion to the English compound take, etc. With few exception German, unlike most English r. as in combination with prefi to demolish.

Many particles in German verbs, have their exact equi interpret; mißteuten, mi befall, etc. (97. 1, 2, et

In German, as in Englis the primary accent.

($ 1. Vor, which is often the latter, always prece! as :-Er war vor zwei (literally, he was here

Seit (since), when answers to "for" or he has been (literall Ich habe ihn seit einem during a whole year

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Antworten, to answ

(intransitive). Beantworten, to

swer (transitiu Begrün'ren, to co

tute. Beschreiben, to

scribe. Betra'gen, to be Grfin'den, to in Grhalten, to r Erniedriger, ti

Diesen schöne

mir mein

gegeben. Die Freunde

ten bege'be Die feintlid

ben. Der Lehret


3. ಬದTata
jer sam time this onts i

dar the numbers in the
2 fit the spread. I to in the

FACZNIC. ** support st w It is at ** CV a szmatkuszug about maitspiring

fare pag bor the prmeiple of monessa, + : mund at Ps equal to 4 times the s prarad ie the sound ifter st P,; that: ER)!! pound. But this forme fat SIL "Izplied at r, in the proportion of !

; of of pound, and this ere, *** at w of off of that unit, 2. Luation, the 1 pound balances 13 pounds

Marne, what is true of these numbers is to - soi the rule you arrive at is this

Eus-Multiply together the fractions obert natzox of the Power arms to the Resistances obtained is the number of pounds of the Resistan pound of the Power balances. When she Powe 1 pound, multiply this number into that of the fractions of a pound in it. | And this leads us to another resalt, which express tion between the power and resistance wathos Trata in the above example, we had the resistanse edas 4 of! of the power, it is evident that the stare den. multiplied into the resistance must be anal to the te rators into the power, and thas, extending the pres

may say that Fr. sa

The Power multiplied by tie seen in the arms is equal to the Resistenze suisbez la ceea

ance arms.
the mechanical adrantage is against the And you thus have a result st miksi
ving sexrer the fulcrum must be greater for a single lever. And there is the

The best eramples are found in the limbs only for a combination of mass
be can make into one or use separately as or all of the third, æ m as is

1. WID er hat Knabe getrag



ne for each kind, and therefore i arms are horizontal. The desired position is then one of stable » reason I have above avoided, equilibrium (see Lesson VII.), to which the beam will revert principle, the terms “long arm when displaced from it, and in which the line F G is perpendi. cead "power arm" and "resist- cular to the line A B, joining the points of suspension of the the arms that work with the scales. For a good pair of scales, therefore, there must be

stability as well as accuracy. n of levers which is most likely But a balance should also be sensitive-should indicate a non weighing machine, used for slight difference of weights in the scales. How is this secured ? s, or luggage at railway stations. Suppose the scales equally loaded, and that a slight additional In Fig. 52 is a ground-plan of weight (call it P), is thrown into the scale a in Fig. 53, this piece of mechanism, where causing it to decline through some angle agreed upon as suffiat A, B, C, D, the four corners cient to indicate a difference of weights to the eye. As a deof the bottom of a shallow box, scends, the centre of gravity, g, of the beam ascends at the other are the fulcrums of four levers side, until its weight (call it w), acting at g, balances P. We of the second order, which meet, have thus a new lever, AD, the fulcrum of which also is F, and two and two, on either side at at whose ends the forces P and w act. And since in that case, F, and are joined across by a as proved in the last lesson, P multiplied by A F must be equal to stout steel pin, by which they w multiplied by FD, the length A B, and the weight w, of the are also connected with the lever beam being the same in any number of balances in a manufacof the second order, E G, which tory, that one which moves through the angle agreed on, with has its fulcrum at E. The end, the smaller additional weight P, must also have F D smaller; or, G, of this lever is connected by which comes to the same thing, since the angles of the triangle

a rod which ascends perpendi. FGD are given, that at F being a right angle, it must have F G d, and is attached above to the short smaller. Everything else, therefore, being the same, that balance one of the first order, generally a steel- has the greater sensibility, the centre of gravity of whose beam escribed—to the longer arm of which the is as little as possible below the fulcrum. Summing up, then, we is attached. We thus have a triple com have for the requisites of a good balance the following first four at the bottom, by being united 1. For Accuracy.—That the arms be equal. ne lever. On these four at a, b, c, d, are 2. For Stability and Horizontality.—That the centre of d steel, presented upwards, on which rests gravity of the unloaded beam be below the fulcrum, on a line atform, on which the cart or luggage to be through its supporting point, perpendicular to that which joins The weight pressing at a, b, c, d, tends to the points of suspension of the scales.

end, F, of the four levers, and with it also 3. For Sensibility.—That the centre of gravity of the beam be er E F G. The latter tries to pull down the as little as possible below the fulcrum. 10 short arm of the steelyard above, which You will observe that the second and third conditions oppose

the counterpoise on the longer arm of the each other. The lower the centre of gravity is below the g equilibrium, and making known the weight fulcrum, the greater is its stability, but the less its sensibility. age.

Both qualities are essential, and are therefore secured only by a king the four platform-levers as one, suppose compromise; the centre for sensibility may approach the fulis in the combination are each one-fifth of the crum, but not too close ; for stability it keeps off, but not too evidently, as proved above, the resistance is far.

times into the power—that is to say, 1 pound Further, observe the consequence of making the line joining teelyard balances 125 pounds, or 1 cwt. and 13 the points, A B, of suspension pass through the fulcrum. Howlatform. If the proportion were one-eighth, it ever the pans are loaded,

cwt. 8 pounds, which strikingly illustrates the it is only the difference (P)
"antage gained in these machines. We will now of the weights in them that
ummon balance, and, in the next lesson, examine affects the sensibility. The

of other weighing instruments, bent levers, and resultant of the lesser one
axle, and their combinations.

in B, and of as much of that

in A as is equal to it, passes THE COMMON BALANCE.

through and is resisted by ng instruments, the scale, or common balance, F, and affects neither stabi. first attention. It is a lever of the first order, in lity nor sensibility. If A B

WW sounterpoise, or power, is equal to the resistance, or were not to pass through

weighed. There is first the beam, A B, at the ends of F, then these weights would .:3 553) are the hooks, from which hang the chains or have influence as regards

= 3 ch support the pans or scales below. Since the these qualities, but that -90 n the scales are required to be equal, the fulcrum, F, kind of balance we are not

in the middle of the beam, equally distant from the here considering. 72877b4 suspension of the chains, else the balance is fraudu- A most important ques.

Fig. 53. the purchaser who has his tea or sugar served to him tion is, how to detect fraud

He end of the longer arm is getting less than his money's in a pair of common scales. The arms in that case not being smisi I shall direct your attention to the case in which the equal, all the purchaser has to do, if he doubts the honesty of

ining the points, A B, of suspension passes through the his tradesman, is, after the first weighing, to make the shop ting point of the fulcrum, as it is the simplest ; and weight and the substance weighed change pans. If the two

ses of this kind, as you will see, have a peculiar advantage balance each other equally as before, the scales are honest, their sensibility.

the arms are equal; but if not, fraud is proved. w, it is evident, since A B is bisected at F, and the scales, But how, in that case, may the purchaser still get his true 1, and weights on either side are equal forces, that what- pound of tea, or sugar, or other commodity? The shop weight be the position in which I place the beam, the resultant of being supposed true, the imperial stamped weight, let the

forces must pass through F, and, being there resisted, deficient tea be weighed as before from the longer dishonest ra the whole apparatus at rest. Moreover, if the centre of arm. Leaving it then in the scale, let him require the shopman svity of the beam is at F, so far as its weight is concerned, to remove the weight from the other scale, and fill it with tea

De will be equilibrium in every position. But such a pair until that in the first ne is balanced. He now has a true scales would be utterly useless, since, for equal weights, the pound of tea balancing the deficient pound, as the imperial was should rest only in an horizontal position.

weight first did. Let him carry off this pound, and he has his How, then, is this latter object accomplished ? By having money's worth. centre of gravity of the beam below the fulcrum, when the But there is another way by which the purchaser may not only get his due quantity, but turn the tables on the vendor, happiness of kindred, and parents, and children. We welcome you to and by the very fraudulent balance itself get more than his the immeasurable blessings of rational existence, the immortal hope of money's worth. Suppose he is buying two pounds; then let Christianity, and the light of everlasting truth! him have one pound weighed in one scale and the other pound


ImpassionedForce. in the other scale ; it so happens that invariably the two to

Shame! shame! that in such a proud moment of life, gether are more than two pounds. The reason you will under

Worth ages of history,-when, had you but hurled stand by an example. Suppose one arm is 14 inches long, One bolt at your bloody invader, that strife and the other 15 inches. Then, weighed at the latter arm, the Between freemen and tyrants had spread through the world, purchaser gets only liths, which is less, but at the former 1 ths, which is more than one pound. But by the latter he gains

That then,-oh! disgrace upon manhood !--c'en then

You should falter,--should cling to your pitiful breath,a gth of a pound more than he is entitled to, while at the for

Cower down into beasts, when you might have stood men, mer he loses only itth. So on the whole, since a t;th is greater And prefer a slave's life to a glorious death! than a ith, he is a gainer ; he has caught the vendor in his own trap. Or, you may add up the two fractions ths and

It is strange !-it is dreadful !-Shout, Tyranny, shout, uths, and the sum you will find to be greater than 2 by the

Through your dungeons and palaces, “Freedom is o'er !"

If there lingers one spark of her fire, tread it out, fraction zio. And what is true of these numbers is true of

And return to your empire of darkness once more, all others, which represent the proportion of the arms—what you lose at the long arm is more than recompensed by what

III.—DISTINCT ARTICULATION. you gain at the short one.

Correct articulation is the most important exercise of the voice and of the organs of speech. A reader or speaker, pos

sessed of only a moderate voice, if he articulates correctly, will READING AND ELOCUTION.-IX.

be better understood, and heard with greater pleasure, than one ANALYSIS OF THE VOICE (continued).

who vociferates. The voice of the latter may, indeed, extend

to a considerable distance; but the sound is dissipated in con. II.-DUE QUANTITY, OR LOUDNESS.

fusion : of the voice of the former not the smallest vibration is THE second characteristic of good reading, is the use of that wasted-overy sound is perceived at the utmost distance to degree of loudness, force, “volume,” or “quantity,” of voice which it reaches; and hence it even penetrates farther than which enables those to whom we read or speak, to hear, without one which is loud, but badly articulated. effort, every sound of the voice ; and which, at the same time, In just articulation, the words are not hurried over, nor precigives that degree of force which is best adapted to the utter- pitated syllable over syllable; nor, as it were, melted together ance of the sentiments which are read or spoken.

into a mass of confusion; they are neither abridged nor proAll undue loudness is a great annoyance to the ear, and an longed ; nor swallowed, nor forced, and, if I may so express injury to the expression; while a feeble and imperfect utterance myself, shot from the mouth; they are not trailed nor drawled, fails of the main purposes of speech, by being partly or entirely nor let slip out carelessly, so as to drop unfinished. They inaudible, and consequently utterly unimpressive.

are delivered out from the lips, as beautiful coins newly issued The failure, as regards loudness, is usually made on passages from the mint, deeply and accurately impressed, perfectly of moderate force, which do not furnish an inspiring impulse of finished, neatly struck by the proper organs, distinct, sharp, in emotion, and which depend on the exercise of judgment and due succession, and of due weight. discrimination, rather than of feeling.

This department of correct reading belongs, properly, to the It is of great service, however, to progress in elocution, to stage of elementary lessons. But negligence in general habit, possess the power of discriminating the various degrees of force and remissness in early practice, are extensively the causes of which the utterance of sentiment requires. The extremes an imperfect articulation. of very " loud” and very "soft,” required by peculiar emotions, A paragraph or two of every reading lesson should, prehave been exemplified in the exercise on versatility” of vious to the regular exercise, be read backward, for the purpose voice.

of arresting the attention, and securing every sound in every There are three degrees of loudness, all of great importance word. to the appropriate utterance of thought and feeling, required The design of the present lesson does not admit of detail in in the usual forms of composition. These are the following : the department of elocution now under consideration. The “Moderate, forcible," and "impassioned.” The first, the importance, however, of a perfectly distinct enunciation can “moderate,” occurs in the reading of plain narrative, descrip- never be impressed too deeply on the mind of the student. An tive, or didactic composition, addressed to the understanding, exact articulation is more conducive than any degree of loudrather than to the feelings; the second, the “forcible,” is ness to facility of hearing and understanding. Young readers exemplified in energetic declamation ; the third, the "impas- should be accustomed to pronounce every word, every syllable, sioned,” occurs in the language of intense emotion, whether in and every letter, with accuracy, although without laboured the form of poetry or of prose.

effort. The faults of skipping, slighting, mumbling, swallowWatchful attention will be required, on the part of the ing, or drawling the sounds of vowels or of consonants, are student, in practising the following examples, so as to enable not only offensive to the ear, but subversive of meaning, as him to detect, and fix definitely in his ear, the exact degree of may be perceived in the practice of several of the following loudness appropriate to each passage. The exercises should be examples. repeated till they can be executed with perfect precision, so as

Examples. to form a standard for all similar expression, in subsequent

1. That lasts till night : that last still night. reading.

2. He can debate on either side of the question : he can debate on Exercise in “ModerateForce.

neither side of the question. An author represents Adam as using the following language :-"I 3. The steadfast stranger in the forests strayed. remember the moment when my existence commenced : it was a 4. Who ever imagined such an ocean to exist ?-Who ever imagined moment replete with joy, amazement, and anxiety. I neither knew such a notion to exist ? what I was, where I was, nor whence I came. I opened my eyes : 5. His cry moved me: his crime moved me. what an increase of sensation ! The light, the celestial vault, the 6. He could pay nobody: he could pain nobody. verdure of the earth, the transparency of the waters, gave animation 7. Up the high hill he heaves a huge round stone, to my spirits, and conveyed pleasures which exceed the powers of 8. Tho' oft the ear the open vowels tire. utterance."

9. Heaven's first star alike ye see. “ DeclamatoryForce.

The following description of a whale chase, taken from Advance, then, ye future generations! We bid you welcome to this Goodsir's “ Arctic Voyage,” will furnish a useful exercise in pleasant land of the Fathers. We bid you welcome to the healthful

distinctness of articulation. Read it with animation and skies and the verdant fields of New England. We greet your accession to the great inheritance which we have enjoyed. We welcome “moderate force,” but not too fast. you to the blessings of good government and religious liberty. We We pulled in the direction in which the whale was "heading," where welcome you to the treasures of science and the delights of learning the rest of the boats already were ; before we got up to them, she had We welcome you to the transcendent sweets of domestic life, to the made her appearance at the surface; a second boat had got fast to her,

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and just in time, as she was seen to be “loose" from the first. She and according to the relation of their angles, as-
did not take out much line from this boat, but remained away a con-


ACUTE-ANGLED, siderably longer time than usual, greatly to our astonishment, until Having one rightangle, Having one obtuse Having three acute We found that she was “blowing" in some holes in the floe, a good

and, of necessity, two angle, and, of neces- angles, distance from the edge of it. One of the harpooners immediately

acute angles ;

sity, two acute angles. proceeded over the ice with a hand-harpoon, trailing the end of the line with him, assisted by part of his crew, and from the edge of the Now, as the three interior angles of a triangle are together hole drove his weapon into the body of the poor whale; whilst some equal to two right angles or 180 degrees, and as an obtuse of the others following plied the bleeding wretch with their long angle is any angle greater than a right angle or 90 degrees, lances, so that she was soon obliged to betake herself again to the while an acute angle is any angle less than a right angle or 90 open water outside the floe. Here more of her enemies were waiting, degrees, it is manifest that, for one boat was immediately upon her, and a gun-harpoon was at once

An equilateral triangle must necessarily be an acute-angled driven almost out of sight into her huge side, which was already bristling with weapons. Our boat was on her very back as she dived with triangle, since it has three equal angles,

each of which is less.

than 90 degrees, being one-third of 180 degrees ; while en unwieldy roll, which sent it surging gunwale under, taking the line whistling out for a score of fathoms, until the harpooner, knowing she

An isosceles, or a scalene triangle, may be a right-angled was pretty well exhausted, stopped her way, by taking three or four triangle, or an obtuse-angled triangle, or an acute-angled turns round the “boltard." But every few seconds she would make a triangle. start, drawing the boat almost head under, until the line was permitted To proceed still further into an analysis of the conditions to run out again, which, as it did so, made a grinding, burring noise, under which the different kinds of triangles will appear, it may eating deep into the hard lignum vitæ of the boltard, enveloping the be said thatharpooner in smoke, and causing the most distinct smell of burning,

I. An acute-angled triangle may have which was only prevented from actually taking place by the linemanager throwing water constantly on it.

1. Three sides equal, and three angles equal, when it is an equilateral Again she appeared at the surface, but far exhausted; still she made triangle. a strong fight for it, lashing about with her tail and fins in fury when- 2. Two sides equal, and two angles equal, when it is an acuteever she seemed to have regained breath. It was no very pleasant angled isosceles triangle. sight to see her tail quivering high up in the air, within but a short 3. All its sides unequal, and all its angles unequal, when it is an distance of us, and coming down on the water with a loud, sharp acute-angled scalene triangle. crack, like the report of a dozen rifles, and which, had it alighted on

II. An obtuse-angled triangle may haveany of our boats, had power sufficient to have converted their timbers into something very like lucifer matches. A few more lances soon

1. Two sides equal, and two angles equal, when it is an obtusesettled her; and ere long, she was rolling on her back. The usual angled isosceles triangle.

2. All its sides unequal, and all its angles unequal, when it is an cheers of triumph were given, and we had time to breathe and shake ourselves, for it may be believed we had not escaped the showers of obtuse-angled scalene trianglo. spray which the defuuct had sent about so liberally. The water far III. A right-angled triangle may havearound us was dyed with blood, and covered with a thick pellicle of

1. Two sides equal, and two angles equal, when it is a right-angled oil, upon which the Mollys were as busy as they could be, whilst the isosceles triangle. edges of the ice, as far as we could see, were deeply crimsoned; and a

2. All its sides unequal, and all its angles unequal, when it is a hummock, on the edge of the floe, beside which the final struggle had right-angled scalene triangle. taken place, was from the summit downward streaked with the black blood which the last few blasts of the dying monster had sent over it, We have already learnt, as it has been said above, how to

draw an equilateral triangle of any dimensions, the conditions IV.-CORRECT PRONUNCIATION.

necessary for its construction being given. Let us now see what That pronunciation is correct which is sanctioned by good data we require to enable us to draw any isosceles or scalene usage or custom, Good usage implies the habit of persons triangle characterised by having one right angle, one obtuse of good education, as regulated by the decisions of learning angle, or three acute angles. and taste, exemplified in standard dictionaries—a style which To determine any isosceles triangle, it is plain that we must is equally free from the errors of uneducated or negligent have one or the other of the following series of data. custom, and the caprices of pedantry-which falls in with

I. With regard to the sides without the angles :the current of cultivated mind, and does not deviate into peculiarities, on the mere authority of individuals. Good taste

1. The length of the two equal sides, and the length of the third.

side or base. in pronunciation, while it allows perfect freedom of choice

2. The length of the two equal sides, and the altitude of the triangle. as to the mode of pronouncing words liable to variation in sound

3. The length of the base, and the altitude of the triangle. Or accent, requires a compliance with every fixed point of

II. With regard to the sides and angles combined :The subject of pronunciation like the preceding one

4. The angle at the vertex of the triangle, and the length of the articulation-belongs properly to the department of elementary

two equal sides. instruction. But as this branch of elocution does not always

5. The angle at the vertex of the triangle, and the length of the

base. receive its due share of seasonable attention, many errors in 6. The angle at the vertex of the triangle, and the altitude. pronunciation are apt to occur in the exercise of reading, as 7. The equal angles at the base, and the length of the equal sides. performed by even the advanced classes in schools. To avoid 8. The equal angles at the base, and the length of the base itself, euch errors, it will be found useful to discuss, closely and 9. The equal angles at the base, and the altitude, minntely, the correct pronunciation of every word which in any In any case, when the length of the sides or altitude is given, lesson is liable to be mispronounced, the standard of reference either with or without the extent of the opening of all or any being any good dictionary of the English language.

of its angles, an isosceles triangle can be constructed, which is the only form of the isosceles triangle which will satisfy the parti

cular requirements laid down in the data ; but where the angles LESSONS IN GEOMETRY-IX.

only are given, an endless number of triangles similar in form, In the construction of triangles the student has learnt, by but of different superficial areas, may be drawn, all of which Problem XVI. (page 209), how to draw an equilateral triangle of shall satisfy the general requirements set forth in the data, for any dimensions, the only two data (or facts given from which it must be remembered that the size of an angle is determined other facts may be deduced) that are required in the formation by the extent of the opening between the lines that form its Op construction of an equilateral triangle being, the length of sides, and not by the length of its sides; and this leads us to one of its three equal sides on the one hand, or its altitude on the construction of an isosceles triangle under general conditions,

namely: It will be remembered that, in Definition 18 (page 53), it was

III. With regard to the angles without the sides :stated that triangles are classified according to the relation of 10. The angle at the vertex of the triangle.

11. The equal angles at the base of the triangle. EQUILATERAL, ISOSCELES,


The first case named above of the construction of the isosceles Having three equal

Having two equal Having three unequal triangle, when the length of the two equal sides, and that of sides; sides;


the third side is given, is met by Problem VIII. (page 191), in

Eanctioned usage.

the other.

their sides, as

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