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only necessary to place the balloon near a gasometer, and fill the excess of the weight of the air displaced above the whole it by means of a connecting-pipe.

weight of the apparatus, be about ten pounds. It is to be In fig. 90 is represented the mode of filling a balloon with observed that this force remains constant so long as the pure hydrogen. On the right of the figure is shown a series balloon is not completely

inflated by the expansion of the

interior gas. For, if the atmospheric pressure be reduced to Fig. 91.

one-half, the gas in the balloon, according to Mariotte's law, is increased to double its volume. Whence it follows, that the volume of air displaced is itself doubled, and its density is reduced to one-half; therefore its weight, and consequently its upward pressure or buoyancy are still the same. But as soon as the balloon is completely inflated, if it continue to rise, the force of ascent diminishes; for the volume of air displaced remaining the same, the density diminishes. Accordingly, the balloon will ere long reach a point where the upward pressure is zero. Consequently, the balloon can only take then a horizontal direction, being carried by the currents of air which exist in the atmosphere.

The indications of the barometer are the most certain means by which the æronaut knows when he is ascending and when he is descending. In the former case, the column of mercury falls ; in the latter, it rises. By the assistance of the same instrument, he is enabled to ascertain the height which he has reached. A long streamer fixed to the car, fig. 91, also indicates, by the position which it takes above or below the car, whether he is ascending or descending. When the æronaut wishes to descend, he draws the cord which opens the valve placed at the upper part of the balloon; the hydrogen mixes with the exterior air, and the balloon descends. On the contrary, in order to slacken his descent when it is too rapid, or to re-ascend if placed in a perilous situation, the æronaut empties bags full of sand, a sufficient quantity of which had been placed in the car for this purpose. Thus lightened, the balloon rises again, in order to descend in a more suitable place. The descent is facilitated by suspending an anchor to the car by means of a long cord. When this anchor has taken hold of a proper obstacle on the ground, the ear and balloon are lowered by gently drawing the cord.

Balloons have not as yet received any important applications. At the battle of Fleurus, in 1794, a balloon, retained by a cord, was employed to discover the movements of the enemy, which were made known to the army by signals made by an observer seated in the car. Several ascents have also been undertaken with the view of making meteorological observations in the higher regions of the atmosphere. But balloons will only become of real utility when the power of directing them has been attained. The trials hitherto made for this purpose have completely failed. At present, we can only rise in the atmosphere until we meet a current of air which will carry us in

the direction answerable to the end we have in view, of casks, which contain iron filings, water, and sulphuric acid, The Parachute.-The object of the parachute (from the French, substances necessary for the preparation of the hydrogen. a guard from falling) is to enable the aeronaut to leave his balFrom each cask, the gas is conveyed to a central cask, open at loon, by giving him the means of slackening the velocity of his bottom, and immersed in a butt full of water. The gas, after descent. This apparatus is composed of a large circular sail, passing through this water, is conveyed into the balloon by a fig. 92, of about five or six yards in diameter, which, by the long canvas pipe, fixed at one end to the central cask, and at effect of the resistance of the air, expands and forms a huge the other to the bottom.

umbrella which slowly descends to the ground. On its edges In order to facilitate the filling of the balloon, two masts are fastened cords, which support a car, in which the wronaut are erected, having at their top pulleys traversed by a rope, is seated. In the centre of the parachute, there is an opening which passes through a ring fixed at the top of the valve. By for the escape of the air which is compressed by the effect of this means, the balloon being at first raised about a yard above the descent; without this, the air would produce oscillations the ground, the gas is admitted; then, in proportion as the on the parachute, which would be communicated to the car balloon is filled, it is raised a little higher, and it is allowed to and render the position of the æronaut perilous. In fig. 91 is expand more and more, until it frees itself from this apparatus. shown, on the side of the balloon, a parachute folued and It is now necessary to oppose the force with which it hegins to attached to the netting, by means of a cord passing over a ascend. For this purpose, a number of men are employed to pulley and fixed to the car. By loosening this cord, the hold it down by means of cords fixed to the netting. When parachute is placed in the power of the æronaut. M. J. the balloon is completely filled, it is then necessary to remove Garneri vas the first who descended in a parachute; but the pipe which conveyed the gas, and to attach the car to the M, Blanchard appears to have been the inventor: net-work. These different preparatory operations require at Weight required to raise a Balloon.-In order to calculate the least two hours. The seronaut is then seated in the car, and weight required to raise a balloon of given dimensions, when at a given signal, the cords are loosed, and the balloon ascends it is supposed to be perfectly spherical, the following formula with a velocity in proportion to its lightness as compared with is employed : v= **0%, which represents geometrically the the air which it displaces.

volume of a sphere, whose diameter is , # being the ratio or It is important to observe that a balloon should not be com- the circumference to the diameter, or 3.1416 nearly. Thus, pletely inflated; for the atmospheric pressure diminishing in if a balloon of thirty-six feet in diameter were completely proportion to the height of the

ascent, the interior gas expands filled with hydrogen, its volume would be about 24,430 cubic in consequence of its elastic force, and tends to make the val- feet. But in general, the balloon, when it begins to aseend, is loon burst. It is suficient that the force of ascent; that is, only about half filed, whence its volume may be assumed at

12,215 cubic feet; and such is the volume of displaced air at may be readily accomplished in a Florence flask, -all the more the first moment of its ascent. According to calculations rapidly under the influence of a gentle heat. The solution will formerly shown, this quantity of air weighs about 991 lbs. or be perfectly colourless and transparent ; not the slightest amount oj nearly nine cwt., and this is the upward pressure which tends milkiness will be perceptible. I can fancy many a reader poring

over his solution at this moment, and imagining the writer of these Fig. 92.

lessons to have erred. Some, in looking at a milky opalescent solution, will be ready to think that the assurance of perfect clearness" is altogether untrue. If the water be quite pure, the solution will be absolutely transparent; but inasmuch as nitrate of silver is a most delicate test for certain classes of impurities, it is more than probable that many students may get a turbid solution.

Should this be the case in the present instance, heed it not. The occurrence will serve to mark a fact, without interfering with the current of our experiments. You have only to wait awhile, and the turbidity will settle, leaving a clear solution above, well adapted for our purposes. Having followed out the preceding directions, it is evideni that a solution of nitrate of silver in water will have been obtained. We will proceed to investigate its chemical characters presently; meantime, let it be well impressed upon the mind that the solution is colourless : hence it follows that any, solution which is not colourless, must contain some other substance besides nitrate of silver. We may generalise still more, and say that all silver solutions are colourless, Strictly true this assertion is not, I am aware; but it is, nevertheless, so nearly true, as to warrant its being considered by the student as a universal fact. Accepting the proposition as absolute, we may then make the further assertion, that, though a metallic coloured solution may contain silver, it must contain some metal in addition to silver.

The appreciation of these broad qualities—these general characteristics, are of the highest importance in chemistry: several metals being recognisable at once, by noticing the colour of their solution. That the reader may at once see the force of this remark, let him dissolve a small silver coin in some pure aquafortis, diluted with about an equal volume of water, for the purpose of

moderating the violence of the action which ensues. The experito raise the balloon. But in order to calculate the real force ment is best conducted in a Florence flask, which may be placed of the ascent, we must subtract from this pressure the weight in hot sand on a grate hob, in order that the injurious fumes of the hydrogen in the balloon, and of the globe of which it is which escape may be carried up the chimney. made, with its appendages. Now, the weight of hydrogen is When the operation of solution has been effected, remark well about t part of the weight of air'; whence, the weight of the the tint of the resulting fluid. The experimenter has employed gas in the balloon is about 9914;14371 lbs., nearly. Adding a silver coin, I have assumed, dissolved it in an acid, i. e. aqueous to this weight that of the globe and its appendages, formerly nitric acid or aquafortis. Having regard to the substances used, reckoned at about three cwt., we have upwards of 34 cwt., therefore, it would seem that a solution of nitrate of silver should Bay four cwt., for the weight to be subtracted from the nine result. Nevertheless the solution is no longer colourless but blue, ewt. just mentioned ; this leaves a remainder of about five and if the student evaporates it, blue crystals will appear. It cwt. for the force of the ascent. But we have seen that it is follows, therefore, that if there be any truth in what I have sufficient for the force of ascent to be about 10 lbs.; whence, stated, the silver coin must have contained something in addition there is a little less than the weight of five cwt. remaining to silver. Now supposing the colouring agent to be metallic, and for the additional weight which à balloon may safely carry it must be so— by "construction," as geometers say-in other words, into the atmosphere.

it must be so, because we have only used a metallic coin, then it follows, firstly, that the coin was not of pure silver, but an alloy, Secondly, that the alloying substance was a metal yielding a blue

nitric acid solution. Now I am only aware of two metals which LESSONS IN CHEMISTRY.-No. XIX.

are capable of yielding such a blue solution. These metals are

copper and nickel; and most people know, I presume, that copper THB subject of our present lesson shall be the metal silver ; is the metal used for alloying our silver coins. Pure silver not only so interesting for its commercial value, but as regards would be altogether too soft for the purpose, as the reader will its striking chemical qualities.

not fail to see when he shall have developed a little of that metal There are not many metals which admit of being traced through from its liquid combination. a long list of combinations, and again obtained in the metallic Put away this cupreous silver solution, duly labelled. To form, so easily as silver. Its chemical physiognomy is, in point of expatiate on it here would be so far out of order, that we are fact, exceedingly well marked, as we shall presently see. It is discussing the properties of silver, not copper. It will, neverthealways well to begin the chemical examination of a substance, by less, come under our notice when we treat of the latter metal ; choosing the same in a pure condition, unmixed with any access indeed even before, for I shall put the student in possession of an sory that might veil its properties or obscure the result. I easy moans by which all the silver may be separated, and the therefore recommend, as the source for obtaining a silver specimen, copper left behind. & few grains, say eighteen or twenty, of the salt called: nitrate of Returning now to our solution of nitrate of silver, let the silver. This substance occurs in commerce under two forms: student question it thus : either as sticks something like slate-pencil, only whiter, or as (1) What is its nature ? crystals. The latter will be somewhat the purer of the two; but To arrive at an answer to this question, drop a little of your the former, known popularly as “ lunar caustic," will answer very strong solution, say twenty or thirty drops, into a wine-glass ; vell.

fill up the wine-glass with distilled water, and test with hydroLet the student then take about eighteen or twenty grains sulphuric acid solution. We get a well-pronounced black preciof lunar caustic, or rather more of crystallised nitrate of silver, pitate, on observing which we immediately deduce the following and effoct a solution of the substance in about half a pint of dis- truths. (1) The solution contains as its base, a metal. (2) A calfilled water. The solution takes place with great facility, and cigenous metal (vide Lesson p. 39). (3) Neither zinc, arsenic,

&

с

10

antimony, cadmium, nor tin, in the state of persalt; because the precipitate would either have been white or yellow. (4) Nor

FRENCH READING S.--No. II. iron, manganese, nickel, cobalt, or uranium, because hydrosul. phuric acid without ammonia does not precipitate them. Con.

LE SAPEUR DE DIX ANS. sider, then, the nature of these deductions, and see into what a corner we are driving metal, even by the evidence of one single

SECTION III. witness.

Let us now try another witness, namely, ferrocyanide of potassium; Cependant il entrait a encore quelque hésitation dans la and once for all let the student remember that hydrosulphuric compagnie, et déjà deux fois le capitaine qui commandait acid, hydrosulphate of ammonia, and ferrocyanide of potassium, avait donné l'ordre au tambour-maître de prendre deux are the three witnesses always first cited in a court of chemical tambours, de se mettre en avant, et de battre la charge. inquiry, supposing the substance ander question to be in Celui-ci restait appuyé sur sa grande canne, hochant la the state of liquidity and totally unknown. Whatever evidence tête et peu disposé à obéir. Pendant ce temps Bilboquet, à is to follow, theirs comes first ; all three, if we want them, or cheval sur son tambour* et les yeux levés sur son chef, two or one as the evidence may require. As regards the case sifflait un air de fifre et battait le pas accéléré avec ses now under consideration, the reader will not fail to see that doigts

. Enfin l'ordre venait d'être e donné une troisièmo hydrosulphate of ammonia could only afford positive testimony, fois au tambour-maître, et il ne paraissait' pas disposé à given already negatively by hydrosulphuric acid. Now, in many chemical examinations, negative testimony is as valuable as posi- ; obéir, lorsque tout à coup, Bilboquet se relève, accroche tive. It is so in the present instance. Let us now proceed to son tambour à son côté, prend ses baguettes, et passant use the third test, ferrocyanide of potassium ( yellow prussiate of sous le neze du tambour-maitre, il le toise avec orgueil, lui potash), in solution of course. For this purpose, add a few drops rend d'un seul mot toutes les injures qu'il avait sur le of the strong nitric acid solution to a little distilled water, and cæur, et luit dit:-Viens' donc, grand poltron !8. test with prussiate of potash. We now get a whitish sort of Le tambour-maître veuts lever sa canne, mais déjà Bil. precipitate.

boquet était à la tête des deux compagnies,1° battant la Omitting to repeat such of the evidence yielded by this test as charge comme un enragé. Les soldats, à cet aspect, we happen to know already, what novelty does it communicate ? s'avancent après lui et courent vers la terrible batterie.si What has it to say of its own specific knowledge? Why it tells Elle décharge d'un seul coup ses six pièces de canon, et des us that, in addition to all the metals amongst which 'ours is not, it furthermore is not

rangs de nos braves voltigeurs s'abattent et ne se relèvent

plus.12 La fumée, poussées par le vent, les enveloppe, le Copper

fracas du canon les étourdit; mais la fumée passe, le bruit Uranium

cesse, un instant, et ils voient debout, à vingt pas devant Molybdenum

eux, l'intrépide Bilboquet battant la charge, 13 et ils en. Titanium ;

tendent son tambour, 17 dont le bruit, tout faible qu'il soit,'

semble narguer tous ces gros canons qui viennentm de tirer. because either of these, similarly treated, would have yielded a Les voltigeurs courent toujours, et toujours, 15 devant eux le mahogany brown colour. This fact I have not brought before the tambour et son terrible rlan rlan les appelle ;• enfin une student hitherto ; let it therefore be committed to memory at once, second décharge de la batterie éclate et perce d'une and never forgotten. It follows, then, that our unknown metal is grèle de mitraille les débris acharnés des deux belles comat length hunted into an exceedingly narrow corner. If the student pagnies.16 A ce moment, Bilboquet se retourne et voit qu'il will only refer to a list of metals, and see the names of those of which reste à peine cinquante hommes des deux cents qui étaient the present is not, he will arrive at the conclusion that it must be one of a very few. At this point I will assume the operator to partis, 2. et aussitôt, comme transporté d'une fureur de venappeal to the evidence of another test, either bydrochloric acid geance, il redouble de fracas : 18 on eût dito vingt tambours (spirit of salt), or else common salt dissolved in water; practi- battant à la fois ; jamais le tambour-maître n'avait si hardically, so far as relates to the present investigation, these tests are ment frappé une caisse. Les soldats s'élancent de nouveau the same, and the student may use whichsoever he pleases. et entrent dans la batterie,'' Bilboquet le premier, criant à

Treated with either of these substances, our solution (assumed to tue-tête P aux Russes : be unknown) will throw down a dense white precipitate ; hence -Les morceaux en sont bons, les voici ; 20 attendez, we know at once that the metal we are hunting for is either silver attendez ! or mercury; no other metals being capable of producing a similar

COLLOQUIAL EXERCISE. effect.

Finally, the addition of a little hartshorn (liquor ammoniæ) 1. Que remarquait-on néan- | 11. Que firent les soldats en causes the precipitate to dissolve and the whiteness totally to

moins dans la compagnie? voyant son intrépidité ? disappear; which characteristic result demonstrates the metal to 2. Quelordre le capitaineavait- 12. Quel effect produisit le débe silver, nothing but silver.

il donné au tambour-maître ? charge des six pièces decanon? 3. Que fit celui-ci après avoir 13. Que virent les soldats quand reçu cet ordre ?

la fumée fut dissipée ? CURIOSITY.

4. Où était Bilboquet pendant 14. Qu'entendaient-ils malgré ce temps là ?

le bruit du canon ? Its aim oft idle, lovely in its end,

5. Que faisait-il ?

15. Que firent alors nos volti. We turn to look, then linger to befriend;

6. Le tambour-maître paraisThe maid of Egypt thus was made to save

sait-il disposé à obéir au troi. 16. Quel fut l'effet d'une seA nation's future leader from the wave;

sième ordre ?

conde décharge ?
New things to hear, when erst the Gentiles ran,
Truth closed what Curiosity began.

7. Que fit alors le petit tam- 17. Combien d'hommes restait-
bour.

il ?
How many a noble art, now widely known,
Owes its young impulse to this power alone;

8. Comment apostropha-t-il le 18. Que fit Bilboquet à la vue E'en in its slightest working, we may trace

tambour-maître ?

du carnage ? A deed that changed the fortunes of a race :

9. Que voulut faire le tambour | 19. Que firent alors les soldats? Bruce, banned and hunted on his native soil,

maître ?

20. Que cria alors le petit tamWith curious eye surveyed a spider's toil;

10. Où était alors notre héros ? bour?
Six times the little spider strove and failed;
Six times the chief before his foes bad quailed;

NOTES AND REFERENCES.—a. Il entrait, there was ; the verb "Once more," he cried, " in thine, my doom I read, is unipersonal in French ; L. part ii., § 43, R. (7).—5 à cheval, Once more I dare the fight, if thou succeed ; ”

seated across.-C. venait d'être, had just been ; L. S. 25, R. 2.'Twas done : the insect's fate he made his own :

d. from paraître ; L. part ii., p. 98.-e. sous le nez, close to the Once more the battle waged, and gained a throne. face; literally, under the nose.-f. from venir ; L. part ii., p.

19

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geurs ?

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108.-9. from vouloir ; L. part. ii., p. 110.-h. enragé, madman. 13. Que dit le général, quand il 18. Les voltigeurs se moquniant

- . 8. 4, R. 1.-3. 8. 98, R. 1.-k. from voir ; L. part ii., p. 110. eut remarqué que Bilboquet ils de lui ? - h. subjunctive of être.-m. from venir ; L. S. 25, R. 2.-n. L. n'était qu'un enfant ? 19. Qu'allait-on faire en sa fapart ii., § 49, R. (4).-0. on cut dit, one would have thought 14. Que lui donna-t-il ?

veur ? that ; literally, said.p. à tue-tête, with all his might.

15. Bilboquet prit-il la pièce ? 20. Que dit-il enfin au géné

16. Regardait-on le petit tam. ral. SECTION IV.

bour ?

21. Que fit-il après avoir mis 17. Que faisait-il alors ?

l'argent dans sa poche ? Pendant ce temps, Napoléon monté sur un tertre, regardait exécuter cette prise héroique. A chaque décharge,

NOTES AND REFERENCES.-4. L. S. 20, R. 2.-6. from dire, il tressaillait sur son cheval isabelle ; puis,

quand les soldats L. part ü, p. 88.-c. se mirent, commenced ; L. 8. 68, R. 3.-4. entrèrent dans la batterie, il baissa sa lorgnette en disant ils s'y connaissaient, they were good judges of such things ; L. S.

86, R. 6.tout bas: Braves gens!?

:-e. from courir ; L. part ii., p. 84. f. from revenir ; Et dix mille hoinmes de la garde, qui étaient derrière lui, mit, presented; from remettre ; L. part ü, p. 102.-—_. fit en

L. part ii., 104.-9. from prendre ; L. part ii., p. 100.-h. rá se mirent à battre des mains et à applaudir: en criant:

tendre, uttered; from faire ; L. part ü., p. 92.. accent, tone.---Bravo, les voltigeurs!! Et ils s'y connaissaient,d je 16. L. p. ii, $ 38, R. (8).-6. planté, standing ; literally, planted,

posted.-m. j'en étais, I was one of them, of the number.---. L. Aussitöt, sur l'ordre de Napoléon, un aide-de-camp cou- part ü., $ 33, R. (9).- :-0. from baitre ; L. part ii., p. 80.- p. L. rut. jusqu'à la batterie et revint' au galop.

S. 80, R. 2.-9. que veux-tu, how can I help it ; literally, what do Combien sont-ils arrivés ?5 dit l'Empereur.

you wish.- r. L. 8. 61, R. 6.-s. en attendant, meanwhile.-t. from -Quarante, répondit l'aide-de-camp.

dire ; L. part ii., p. 88.-U. il s'était fait, there was.-. from -Quarante croix demain, dit l’Empereur en se retour- paraître ; L: part ü, p. 98.-10. L. S. 26, R. 2.-3. toujours, nant vers son major-général.

notwithstanding ; literally, always. Véritablement, le lendemain, tout le régiment forma un grand cercle autour des restes des deux compagnies de vol

SBOTION V. tigeurs, et on appela successivement le nom des quarante A partir de ce jour, on ne se moqua * plus autant du braves qui avaient pris la batterie, et l'on remith à chacun petit Bilboquet, mais il n'endevint pas pour cela plus d'eux la croix de la Légion-d'Honneur. La cérémonie communicatif ; au contraire, il semblait rouler dans ma tête était finie, et tout le monde allait se retirer, lorsqu'une quelque fameux projet, et, au lieu de dépenser son argent voix sortit du rang et fit entendre ces mots,'' prononcés avec ses camarades, comme ceux-ci s'y attendaient, il le avec un singulier accent de surprise :

serra soigneusement.? -Et moi ? moi !" je n'ai donc rien ?

Quelque temps après, les troupes françaises' entrèrent - Le général qui distribuait los croix, se retourna et vit à Smolensk, victorieuses et pleines d'ardeur ; Bilboquet en plantei odevant lui notre camarade Bilboquet, les joues était, et le j. ur même de l'arrivée, il alla se promener dans rouges et l'ail presque en larmes."

la ville," paraissant très content de presque tous les vi-Toi ? lui dit-il, que demandos-tu ? - Mais, mon général, j'en étais m dit Bilboquet presque et semblait les examiner comme un amateur qui choisit

sages qu'il rencontrait :& il les considérait d'un air riant en colère ; 12 c'est moi" qui battaiso la charge en avant, c'est des marchandises. Il faut' vous dire cependant, qu'il ne moi qui suis p entré le premior. -Que veux-tu,9 mon garçon ? on t'a oublié, répondit le barbes.

regardait ainsi que les paysans qui portaienti des grandes

Elles étaient sans doute très longues et très général; d'ailleurs, ajouta-t-il en considérant que c'était un fournies, mais d'un roux si laid, qu'après un moment enfant, tu es encore bien jeune, on te la donnera quand tu d'examen Bilboquet tournait la tête et allait plus loin. aurası' de la barbe au menton ;13 en attendant, voilà de Enfin, en allant ainsi, notre tambour arriva au quartier des quoi te consoler.

Juifs. Les Juifs à Smulensk, comme dans toute la Pologne En disant ces paroles, le général tendit une pièce de et la Russie, vendent toutes sortes d'objets et ont an vingt francslé au pauvre Bilboquet, qui la regarda sans quartier particulier. Dès que Bilboquet yl fut entré, ce penser à la pendre. Il s'était fait un grand silence fut pour lui un véritable ravissement: 11 imaginez-vous les autour de lui, et chacun le considérait attentivement ; lui, plus belles barbes du monde, noires comme de l'ébène;"> demeurait immobile devant le général et de grosses larines car la nation juive toute dispersée qu'elle est, parmi les raulaient dans ses yeux." Ceux qui s'étaient le plus autres nations, a gardé la teinte brune de sa peau et le moqués de lui paraissaient' attendris,1s et peut-être allait- noir éclat de ses cheveux.13 Voilà donc notre Bilboquet on élever une réclamation '' en sa faveur, lorsqu'il releva enchanté. Enfin il se décide, et entre dans une petite vivement la tête, comme s'il venait" de prendre une grande boutique où se trouvait un marchand magnifiquement résolution, et il dit au général :

barbu.16 Le marchand s'approche de notre ami et lui de -C'est bon, donnez toujours, ce sera pour une autre mande humblement en mauvais français :

-Que voulez-vous mon petit Monsieur p16 Et sans plus de façons, il mit la pièce dans sa poche et

-Je veux" ta barbe répondit cavalièrement Bilboquet. ?7 s'en retourna dans son rang en sifflant d'un air délibéré et

- Ma barbe ! dit le marchand stupéfait ; vous voulezo satisfait.2

rire ? 18 COLLOQUIAL EXERCISE.

-Je te dis, vaincu, que je veux ta barbe, reprend le vain

queur superbe en posant la main sur son sabre ; mais ne 1. Que faisait Napoléon pen 7. Que fit le régiment le len crois pas que je veuillep te la voler:!' tiens, voila un nadant ce temps-là ?:

demain ?

poléon, tu me rendras mon reste." 2. Que fit-il quand les soldats 8. Qu'appela-t-on successive

entrèrent dans la batterio ? ment? 3. Que firent les soldats de sa

COLLOQUIAL EXERCISE. 9. Que donna-t-on à ces braves garde ?

1. A partir de ce jour, comment 5. De quoi paraissait-il con4. Quel ordre Napoléon donna. 10 Qu'arriva-t-il lorsque la cé- traita-t-on notre héros ?

tent? t-il à un aide-de-camp ?

rémonie fut finie ?

2. Que fit-il de son argent ? 6. De, quelle manière consi. 5. Que dit-il à l'aide-de-camp 11. Que vit alors le général ? 3. Que firent les troupes fran. dérait-il le visage des babià son retour ? 12. Que répondit le petit tam. çaises quelque temps après

s ? tants ? 6. Quel ordre donna-t-il au bour à la question du géné- 4. Que fit le petit tambour le 7. Quelles personnes regardaita général ? ral ? jour de son arrivée ?

il particulièrement ?

16

13

17

fois, 20

21

gens ?

Icere

8. Oà arriva-t-il enfin ? 14. Où Bilboquet entra-t-il en. Let them be produced and meet towards B and D, in the point G; 9. Que font les Juifs en Rus- fin ?

then G E F is a triangle. sie?

15. Qui trouva-t-il dans la bou. Now, in the triangle G E F the exterior angle A BP is greater 10. Où demeurent-ils?

tique ?

(I. 16) than its interior and opposite angle e PG; but the angle 11. Quel sentiment éprouva 16. Que dit le marchand au A Er is equal (Hyp.) to the angle erg; therefore the angle A E F Bilboquet, quand il fut entré petit tambour?

is both greater than, and equal to, the angle BYG; which is imposdans ce quartier ?

17. Que lui demanda celui-ci ? sible. Wherefore the straight lines A B and CB, if produced, do 12. Pourquoi était-il si content? 18. Quelle fut la réponse du not meet towards B and D. In the same manner it may be proved, 13. Quelle remarque l'auteur marchand ?

that they do not meet if produced towards A and c. But those fait-il à propos de la nation 19. Qu'ajouta Bilboquet en met-straight lines in the same plane, which do not meet when juive ?

tant la main sur son sabre? produced ever so far either way, are parallel (Def. 33). There

fore A B is parallel to od. Wherefore, if a straight line falling NOTES AND REFERENCES.—a. From se moquer ; to laugh at. upon two other straight lines, &c. Q. E. D. -6. en, on that account.-c. from devenir; L. part ii., p.

88.-

Scholium 1. The angles A B P and E F D are called alternate angles, d. L. S. 34, R. 4.-. ils s'y attendaient, they expected.-S. L. or more properly interior alternate angles, because they are on oppopart ii., $ 145.-9. L. S. 35, R. 5.--h. from paraitre; L. part ii., site sides of the straight ține E F, and the one has its vertex at e p. 98.-. il faut, I must; from falloir ; L. S. 47; also L. part ü., the one extremity of the portion between the parallels, while the p. 92.j. portaient, wore.-k fournies, thick.--. L. part ii., $ other has its vertex at F the other extremity of the same. 39, R (18).-m. voilà donc, behold then.-». from vouloir ; L. Scholium 2. In the diagram the crooked lines E B G and YDG part ii., p. 110.-0. vous voulez rire, you are joking, you are not must be considered straight lines, and the figure EPDG B a triangle, in earnest.-P. from vouloir.-9. tiens, here; literally, hold ; for the sake of the argument. Otherwise, the figure might have from tenir, L. part ii., p. 108.-. reste, change.

been constructed so that the straight lines AB and CD should
actually converge and meet in a point.

EXERCISE I. TO PROPOSITION XXVII.
SKELETON MAP S.-No. V.

If a straight line falling upon two other straight lines, make the
MAP OF SOUTH AMERICA.

exterior alternate angles equal to each other, these two straight

lines are parallel. Our Map of Russia in Europe (the approximate seat of war) not being ready, as intended, for this month, we insert in this

In fig. 28, let the straight line E F, which falls upon the two Number a Skeleton or Outline Map of the Continent of South straight lines A B and cd, make the two exterior alternate angles America, including the continental part of the West Indies A GE and fun equal to one another ; then a B is parallel to cn. called Guiana, and the small islands adjacent to the con

Because (I, 13) the two angles A G E and A G H are equal to two tinent all around it. This Map will be useful to emigrants, right angles; therefore (Ax. 1) the two angles age and AGU

right angles, and the two angles F H D and GH D are equal to two Bettlers, or colonists, who wish to transplant themselves to South America, where there is abundance of room for specu.

are equal to the two angles Fh D and G HD. But (Hyp.) the angle lations of all kinds. If such persons have sufficient time and A G E is equal to the angle run; therefore (Ax. 3) the angle A G H skill to fill up this Map for themselves, the process of doing fore (1. 27) the straight lines AB and C D are parallel. Q. E. D.*

is equal to the angle GHD; and they are alternate angles; where80 will make them better acquainted with the country in which they intend to settle, than many Lessons in Geography,

EXERCISE II. TO PROPOSITION XXVII. which consist of the mere descriptions of places, but give no if a straight line falling upon two other straight lines, inake the two idea of their relative position in regard to one another. An extensive list of the latitudes and longitudes of the chief

exterior angles on the same side of it equal to trvo right angles,

these two straight lines are parallel. or capital towns in the various countries and sub-divisions of the continent, and of the islands of South America, will be In fig. 28, let the straight line E F, which falls upon the straight found in Vol. iii., at page 250; and, as the continental part lines ab and op, make the two exterior angles on the same side of of the West Indies is included in this Map, the latitudes and it, B G B and Y AD, equal to two right angles; then A B is parallel longitudes for the chief towns of this part will be found at to co. page 118. On the marginal space of the Map, we have given Because (I. 13) the two angles Eo B and EQ $ are equal to two the latitudes and longitudes of the principal ic'ands, capes, right angles, and (Hyp.) the two angles B G B and pup equal to bays, rivers, and ports along the eastern and western coasts of two right angles; therefore (At. 1.) the two angles BG B and EGA the continent, from Cape Horn to the Isthmus of Panama, in are equal to the two angles B G B and vid; from these equals regular order, proceeding from south to north, and along the take away the common angle g , and (Ax. 3) the angle E Gis is coast of America situated on the Caribbean Sea. These we equal to the angle F Hp; but these are the trco exterior alternate have added to the latitudes and longitudes of the places in the angles; wherefore, by the preceding exercise, the straight lines A B interior of the continent above-mentioned, so as to enable and c d are parallel. Q. E. D. our students to make their Map as complete as possible.

PROPOSITIOX XXVIII.--THEOREM,
If a straight line falling upon two other straight lines, make the

exterior angle equal to the interior and opposite angle upon the LESSONS IN GEOMETRY.-No. XXVI.

same side of the straight line; or make the two interior angles LECTURES ON EUCLID,

upon the same side of it, together equal to two right angles; these

two straight lines are parallel to one another. (Continued from page 256.)

Let the straight line EP, falling upon the two straight lines A B PROPOSITION XXVII.-THEOREM.

and cp, make the exterior angle E G B equal to the interior and If a straight line falling upon two other straight lines, make the opposite angle aud upon the same side of alternate 'angles equal to one another ; these two straight lines BP;

or make the two interior angles

Fig. 28. are parallel.

BG. and GHD on the same side of it,

together equal to two right angles; then In fig. 27, let the straight line

Fig. 27.

A B is parallel to CD. E F which falls upon the two

Because the angle BG is equal (Hyp.) straight lines AB and CD, make

to the angle G HD, and the angle BOB is C the alternate angles A E F and EPD

equal (I. 15) to the angle AQH; therefore equal to one another : then A B is

the angle a @u is equal (Ax. 1) to the parallel to CD. Por if AB be not parallel to D,

• Solved by Q. Pringle, Glasgow; J. H. Eastwood, Middleton; and these two straight lines will

E. J. Bremner, Carlisle. meet, if produced either towards A and o, or towards B and D. + See new edition of Cassell's Euclid, 1854.

E

A

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