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turn.

mistaken.

perdu de nouveau. 19. Ce boulanger vous fournissait-il de

EXERCISE 105, bon pain? 20. Il nous en fournissait d'excellent. 21.

Autrement, otherwise. Oubli-er, 1. to forget. Teind-re, 4. ir to dlje. Punissiez-vous souvent vos écoliers ? 22. Je les punissais Cass-er, 1. to break. Pêche, f. fishing. Teinturier, m. duer. quand ils le méritaient. , 23. Où étiez-vous ce matin quand je Chasse, f. hunting. Peind-re, 4. ir. to paint. Toile, f linen cloth. vous cherchais ? 24. J'étais dans ma chambre. 25. Je tinissais Dire, 4 ir. to say. Reven-ir, 2. ir. to re• Rencontr-er, 1 to meet. mon thême,

Montre, f. watch.

Val.oir, 3 ir. to be worth. Exercise 104.

Moins (au), at least. Sav-oir, 3 ir. to know. Ven-ir, 2. ir. to come, to 1. Who was at your house this morning? 2. My friend G.

Mort, e, dead.

Se tromp-er, 1. to be have juest.

Offens-er, to offend. was there, and was looking for you. 3. Did you speak to my

Vite, quickly. father yesterday? 4. I was speaking to him when they Parceque j'avais peur de me tromper. 3. Ne craizviez-vous

1. Pourquoi n'écriviez-vous pas plus vite ce matin ? 2. brought me your letter. 5. Did your father used to wear a white hat when he lived in London? 6. He use to wear a

pas d'offenser cette dime? 4. Je craignais de l'offenser, mais black hat, and my brother wore a black coat. ? Were you main 6. Je peignais un tableau d'histoire. 7. Votre tein

je ne pouvais faire autrements 5. Que peiglez-vous ce singing when my father came? 8. No, Sir, I was finishing my turier que teignait-il? 8. Il teignait du drap, de la soie et de exercise. 9. Had you lost your pencil this morning? 10. Í had lost it, and was looking for it when you spoke to me.

11.

la tvile. 9. De quelle couleur les teignait-il? 10. Il teignait You used to like reading (la lecture), did your sister (use to) le rap en noir, et 14 poie et la tvile en vert. 11. Conduisiez. like it also ? 12. She liked it also. 13. What song were you 12. Je conduisais mon fils ainé à l'église. 13. Que lisiez

vous le jeune Polonais à l'école lor:qiie je vous ai rencontre? singing this morning? 14. I was singing an Italian song. '15. Have you been afraid to speak to me: 16. I have never been vous ? 14. Je tisais des livres que je venais d'acheter 15. afraid to speak to you. 17. Have you brought my book? 18. Ne saviez-vous pas que ce monsieur est mort? 16. Je l'avais I have not brought it.

oublié. 17. Combien la montre que vous avez casséu valait

elle? 18. Elle valait au moins deux cents francs. Sectiox LIII.

19. Ne valait-il pas mieux rester ici que d'aller à la chasse? 20. Il THE IMPERFECT (continued).

valait beaucoup mieux aller à l'école. 21. Votre ami que 1. The imperfect of the indicative of every French verb, vous disait-il ? 22. Il me disait que son frère est revenu regular or irregular, ends in ais, ais, ait, ions, iez, arent, d'Espagne. 23. N'alliez-vons pas à la chasse tous le jours

2. No verb of the first conjugation, Er, is irregular in this lorsqne vous demeuriez à la campagne? 24. J'allais souvent tense.

à la pêche. 25. Mon frère allait tous les jours à l'école quand 3. The only irregularity found in the irregular verbs of the il était ici. second conjugation, ik, is that, to form the imperfect, the stem

EXERCISE 106. of these verbs takes ais, &c., instead of issais : as, ven-ir, je ven-ais; cour-ir, je cour-ais; cueill-ir, je cueill-ais. Exception: house? 2. I was afraid. 3. Of what were you afraid ? 4. I

1. Were you afraid this morning when you came to our Fuir, to flee-je fuyais.

was afraid of the horse. 5. Was not your friend afraid of 4. The irregular verbs of the third conjugation, orr, change falling? (de tomber. See Sect. 20, R. 2. 4.) 6. He was not that termination (oir) into ais, &c., like the regular verbs of afraid ot talling, but he was afraid of making a mistake (de ce the same ; as, sav-oir, je sav-ais ; av-oir, j'av-ais. Exceptions : tromper. See 2. in Exercise above). 7. Were you taking your se-oir, to become ; voir, to see; and their compounds, and son to school ? 8. I was conducting hiin to school.

J. What déchoir (see § 621. 5. The changes which the stem of the irregular verbs of the colour was the dyer dyeing the silk? 10. He was dyeing

some red and some green, il. Was he dyeing his linen cloth fourth conjugation undergoes, in this tense, are too various to black or green ? 12. He was neither dyeing it black nor admit of a complete classification. We, however, offer the

green, he was dyeing it pink (rose). 13. What was the gentlefollowing :

man reading ? 14. IIe was reading a let'er which he had just PRENDRE, to take. ECRIRE, to write. CRAINDRE, to fear. received. 15. Were you cold when you came here? 16. I Je pren -ais, etc. écriv -ais, ete. craign ais, etc. was cold, hungry, and thirsty. 17. Were you not ashamed of CONNAÎTRE, to know.

CONDUIRE, to conduct.

your conduct (conduite) ? 18. I was ashamed of it. 19. Connaiss -ais, etc.

Conduis -ais, elo.

Whither were you going when I met you? 20, I was going 6. Like prendre and écrire are conjugated, in this tense, to your house. 21. Were you driving your brother's carriage? those verbs in which prendre and crire appear in composition : 22. I was driving my own (la mienne). 23. Were you writing as, comprendre, je comprenais ; souscrire, je souscrirais.-Like to me or to my father? 2 ì. I was writing to your friend's craindre and connaître, those ending in indre and aitre : teindre, cousin, je teignais ; paraître, je paraissais.- Like conduire, those ending in ire: as, lire, je lisais ; faire, je faisais ; luire, je luisais ; dire, je disais, &c.—Exceptions : rire, traire, écrire, and their com

LESSONS IN GEOLOGY. --No. XIV. pounds. 7. Mettre and its compounds, and être are regular in this

By THOMAS W. JESKYN, D.D., F.G.S., &c. tenee.

CHAPTER I. 8. The participle present, from which the French gram-ON THE ACTION OF VOLCANOES ON THE EARTH's crust. marians derive the imperfect, presents of course the same irregu

SECTION IX. larities : as, venant, valant, prenant, écrivant, craignant, connaissant, conduisant. Exceptions : avoir, ayant; savoir, sachant,

The subterranean fires that lie deep in the earth's crust, and RÉSUMÉ OF EXAMPLES.

cause the elevation of land described in the last lesson, act, not De quoi notre ami avait-il peur ? of rohat was our friend afraid :

only on the rocks which are in the open air, but also on : he Il n'avait peur de rien. He wous afraid of nothing.

beds which form the bottom of the sea. When the vents, which N'aviez-vous pas besoin de mon Did you not want my brother ? are formed by these interior fires, act beneath the waters of the frère ?

ocean, they are called submarine volcanoes. Nous avions besoin de lui.

It had been long suspected that such volcanic phenomena Le marchand n'avait-il pas besoin Did not the merchant want money? were occasionally taking place in the bed of the sea. Othvers d'argent?

and crews of vessels had frequently reported that, on their Il en avait grand besoin. He had great need of it.

voyages, they had seen in different places sulphureous smoke, Quelle voiture conduisiez-vous ? What carriage were ymi driving!

j-ts of Hame, and spouts of water, rising up from the sea. In Pour qui me preniez-vous ?

For whom were you trking mer Je venais vous trouver quand je I was coming to you when I met yri. coloured, and appeared in violent agitation, as if boiling. At

other places the waters of the ocean were found greatly disvous rencontrai. A qui écriviez-vous ce matin ? To whom were you writing this morn

some points, shoals and reefs of rocks were observed as having ing!

just emerged, where, on a previous voyage, the water was J'écrivals à ma sæur et à mon I was writing to my sister and to my known to have been many fathoms deep. These reports led frère.

scientific men to inser, that a power from below must be pro

brother,

ON SUBMARINE VOLCAXOES.

We wanted hin.

pelling the bottom of the sea upwards towards the surface. In 1831, at a spot about thirty miles to the south-west of This philosophical conjecture or inference has been established Sicily, a submarine volcano rose out of the sea, and formed an by a copious variety of facts, in the formation of new islands island. Before its appearance, it was well known that the above the waters of the ocean.

depth of the sea at that place was 600 feet. The process The first well-ascertained instance of an island being elevated of its rise was this. First, there were violent spoutings of by a submarine volcano, was that near St. Michael in the steam and water from the bed of the sea, jetting sixty feet Azores. In the same neighbourhood, various eruptions had high. Then a small island of dry ground appeared with a been known in the years 1638, 1691, and 1719;. but in the burning crater in the centre of it. This crater ejected ashes, year 1811, a most terrific earthquake was felt at St. Michael. scoriæ, and thick volumes of smoke ; and the whole sea around For more than half a year previously several shocks had been became covered with Aloating cinders and with shoals of dead felt, but on January 31st, the convulsions were at the height fishes. of violence. On February 1st, at a spot about two miles out This volcanic island rose gradually till it reached the elevaat sea, from the village of Genites, volumes of sulphureous tion of nearly 200 feet, with a circumference of about three vapours were seen to rise out of the sea, which spread them. miles at the base. In its centre was the crater, which was no

ow selves in all directions. These were accompanied with jets of a basin, six hundred feet in diameter, full of dingy red water fire. At the same time, the wind carried volcanic ashes from in a boiling state, and continued so for three weeks. the sea as far as the town of Ponta del Gada, 18 miles off, This volcanic island continued above the sea for nearly three where they fell and covered the houses and the adjacent fields. months, and then it sank gradually again into the sea. Before

The columns of ashes and erupted materials, as they were it began to sink, its circumference became much diminished by rising from the sea, could be seen for many miles round, and the continued action of the waves on all its sides. It appeared appeared by night like pillars of fire. While these were rising, July 18, 1831. Towards the close of October, the whole was the sea boiled in terrible agitation.

nearly on a level with the surface of the sea. After it disapIn about eight days

peared, it left behind it these eruptions ended,

Tig. 30.

å dangerous reef of and the bottom of the

hard volcanic rock just sea was raised nearly

eleven feet under water, to a level with the

encompassed by shoals water. This was in a

consisting of scoriæ and part of the sea which

sand. Fig. 31 is a rewas known to be from

presentation of its 300 to 500 feet deep.

general appearance On June 13th another

when at its highest eleearthquake announced

vation. the approach of another

This little island reeruption, which broke

ceived seven different out at the distance of

names. It was well two miles and a half

known by the name of from the other spot,

Ferdinandea; but the a little to the west of

name "Graham Island" Cape Pico das Cama

has been fixed upon by rinhas, and on the 17th

both the Royal and the it was at its greatest

Geographical Societies. violence. Columns

I want you now to upon columns of ashes

apply, your geological and smoke rose at in

knowledge to the inves. tervals with fearfulagi

tigation of this phenotations, to the height

menon. Here was a sea of many hundred feet

600 feet deep, and here above the sea, and

is an island raised, in a spread themselves out

few weeks, 200 feet in thick clouds, which

high. Here is, therewere rendered more terrible by frequent Submarine Eruption, near St. Michael, in the Azores, 1811.

fore, a quantity of land

three miles in circumHashes of lightning.

ference, raised up to & At the close of this eruption, an island became visible, and total elevation of 800 feet in a very brief period. The shoals of rose gradually to the height of three hundred feet. It had, at dead fish, which were found in the volcanic sands around it, one end, a summit, in the form of a cone, and at the other, a will explain similar facts which have been discovered in strata deep crater, out of which violent flames of fire were gushing, connected with volcanic districts. When the crater of this though it was under water at full tide.

little island was ejecting mineral masses, it is probable that Captain Tillard, who was in the neighbourhood, visited the they would envelop some of the dead fish at the sea bottom, island, and called it, after the name of his ship, “Sabrina.” and that, when the erupted ashes fell again, both they and the Ile found its mass of ashes and cinders too hot for walking on fish which they contained were ingulfed in the bottom of the it. He could see that when the tide returned, the sea flowed ocean. You can imagine that if ever this sea bottom will bewith tremendous violence into the burning crater, where the come elevated above the waters of the sea, and be explored by water was boiling as in a hot caldron. Through the continued some future geologist or ichthyologist, the fossil fish of the eruptions of burning stones, sands, and ashes, from the crater, Mediterranean, imbedded in volcanic tufa, will prove an impor• the conical hill already mentioned, on one side of the island, tant study. rose eventually six hundred feet above the sea. After all, in Graham Island presents to you the advantage of having been the last days of February, 1812, the entire island'sank into the carefully examined by scientific men. On this account, the sea and completely disappeared. The annexed engraving study of its structure will much aid your inquiries into the (fig. 30) will assist you in imagining the appearance of these volcanic formation of rocks. As much of the island as was phenomena at sea.

visible was formed of loose incoherent materials, such as sand, In a former lesson it was mentioned that some of the cavi- scoriæ, pumice, &c., ejected from the crater. These loose maties of subterranean fires must be of immense areas. This is terials, after having been hurled to a considerable height, fell proved by the fact that the reservoir of volcanic fires, which again on each side of the central basin, and settled down in lies under the southern part of Italy, extends far and wide be- regular strata, as represented by the dark lines on the left and neath the bed of the Mediterranean, and sometimes occasions the right of fig. 31, and parallel to the deep inward slopes of the rise of fresh shoals and new islands in that sea.

the crater. But at some distance from the rims around the crater, these fallen materials formed strata inclining outwards, conical hills upon it, rose from the sea a little to the east of as represented in fig. 32.

[graphic]

Kamtschatka. This island still remains. The section in fig. 32 represents an imaginary restoration of Islands of this description are not always raised to their full the island as represented in fig. 31. The dotted lines denote elevation by a single paroxysm of volcanic power, but are the upper parts of the cone, which surrounded the crater in raised by a succession of efforts which are repeated for months the centre. All those parts, which were once visible, have and years. Though the surfaces of these islands are formed been washed away by the denuding action of the sea. The much by the volcanic materials which are thrown up and fall strong lines represent the parts of the island, which are still again, there are instances in which they consist mainly of the under water. In the centre is a dyke of solid lava, one rocks which had formed the bottom of the sea, the beds of

which have been upheaved by the power from below. This is Fig. 31.

the case with an island called New Kameni, near Santorin, in the Grecian Archipelago, which was raised up in 1707, and is composed in great measure of limestone covered with, shells.

[graphic]

LESSONS IN GERMAN-No. XV

SECTION XXVIII. Wo refers to the place where anything may be supposed to exist or transpire. Ex.: Wo ist mein Messer? Where is my kvife! Wo laufen die Kinder ? Where (in what place) are the children running?

Da is used in answer to wo; that is, to designate some par. ticular place; as, Da ist es; da laufen sie.

Hin denotes direction, or motion from the speaker; as, Warum Isufen die Kinder hin? Why are the children running thither?

Her is the opposite, in signification, to hin; denoting motion

or direction toward the speaker; as, Warum laufen die Kinder her ? Graham Island, near Sciaccia, in 1831.

Why are the children running hither? hundred feet in diameter, which has cooled in the vent of the Why do the children remain here?

Hier signifies “in this place;" as, Warum bleiben die Sinder hier ? crater, where it was once in a fused state. It is this solid lava that now forms the reef already mentioned as being eleven thus, from wo and hin; we have the compound wohin; from wo

These words are frequently compounded, one with the other ; feet under water. This has withstood the action of the waves, and her, woher ; from da and hin, tahin; from ta and her, tahet, while all the loose materials around it, represented by the from hier and hin, hierhin; and from hier and her, hierher (sometimes dotted lines, have been washed away to a lower level. The beds which have settled on it are formed some of sand,

contracted to hi. her). S 103. 3. and some of stones and volcanic fragments. The stones which were ejected never exceeded a foot in diameter, and consisted Examples of the use of wo, da, hin, her and hier compounded. of dolomitic limestone. At no time did the island present the Wo reisen unsere Freunde hin? Where do our friends travel appearance of any overflowing of lava from the crater. It is, ster,

to? or, nevertheless, possible that melted matter may have flowed out Wohin reisen unsere Freunte? Whither do our friends travel?

Sie reisen dabin, wo ihre Ver. They travel thither, where their Fiz 32.

wandten wohnen.

relatives reside. Wo kommen diese Zugvögel her? Where do these birds of pas. oder,

sage come from? or, Woher kommen diese Zugvögel ? Whence do these birds of pas.

sage come ? Sie fommen daher, wo co jest zu They come from (there) where falt für sie ist.

it is now too cold for them.

SC

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EXERCISE 29.
Pad'stube, f. bake- liegen, to lie; Sciler, m. rope-maker;
house;
Müße, f. cap;

Sißen, to sit ;
Balt, soon;

Nirgents, no-where; Svringen, to spring,
Bil'dergallerie

, f. pic. Obgleich', although, leap;

ture-gallery ; notwithstanding; Stehen, to stand; Supposed section of Graham Island, 1831.

Frosch, m. frog; D'pernhaus, n, opera. Teich, m. pond;
Gans, f. goose;

house;

Werkstatt, f. work. from the flames of the cone, at some depth under water, as is Hin'gehen, to go away; Ritter, m. knight; shop;

whither? often the case on land, and this flowing of lava may have Hirte, m. shepherd; Schau'spieler, m.actor; Wohin' ? spread in a broad sheet over the bed of the ocean, and en- Irgendwo, some. Schon, already;

what way? veloped some Mediterranean fish.

where;

Schwager, m. brother. Zud'erbäder, m. This reef furnishes an instance of what has been regarded Jeßt, now;

in-law ;

fectioner. by some as a geological paradox, in which the lava, which was Kopf, m. head; Schwimmen, to swim; the lowest part of the island while rising, and a part which scarcely rose to the level of the sea, is now become the highest Wo ist das größte Glüc, an dem Where is the greatest happipoint of the land.

Hofe eines tyran'nischen Könige, ness, at the court of a tyranThese two islands, Sabrina, in the Azores, and Graham, in

oder in der Hütte eines zufrie'de. nical king, or in the cottage the Mediterranean, as being the most modern and the best nen Tag'lobners ?

of a contented day-laborer? examined, are instances sufficient to explain to you the pheno- Wo gehen Sie hin? an den Hof oder Whither do you go? to the mena of submarine volcanoes. I would, otherwise, have re- in die Hütte?

court or into the cottage ? ferred you to the rise of an island called Nyöe, on the coast of Der Feldherr sist auf dem Pferde The commander-in-chief upon Iceland, during the tremendous eruption of Skaptar Jokul, which und reitet ruhig längst den Ncihen the horse rides tranquilly occurred in 1783; an island which afterwards disappeared : ber Solda'ten hin und her.

along the ranks of the sol. and to another which, in the form of a peak, with some low

diers to and fro

PMorgen reitet er mit seinen Sdaaren To-morrow he rides with his antern bleiben in New York. 18. Die Ginwanderer in Amerila find auf tas Schlachtielt

troops to the battle-field.

Auswanterer aux Ouropa und aus antern Theilen ter alten Welt. 19. 311 ter borinung fintsn tie Un glück. The unfortunate find consola. Wann wollen Sie auf tag Feld gehen? 20. 34 bin schon auf dem Felte lichen Troji.

lion in hope. Trr Vater ist da, aber der Bruter The father is here, but the gewesen, und fann nicht wieder dahin gehen, aber ich muß icpt bald in ten ift in ter Statt.

brother is in the city.

Garten gehen, denn nein febrer ist ba und will mich seben. 21. Warum 3d gebe veute rabin, worin ich don I go to-day (thither) where I will tiefer 3taliener nicht englisơ sprechen? 22. Er wollte es wohl gestern geben wollte.

wished (already) to go yester. (Sect. 44. IV.) (rechen, aber er tann es noch nicht; er spricht nur ita. day.

lienisch und spanisch. 23. Wie vi.1 Sprachen können Sie sprechen? 24. 1. Wo ist ter Schwager? 2. Er ist an dem (am) Tiiche. 3. Wo geht Id spreche nur zwei

, aber ich will nocty andere lernen. ter Zuderbader hin? 4. Gr geht in die Badstube. 5. Wo ist sein Freund, ter Staufrieler? 6. Er ist in dem Crernhause. 7. Wo geht sein Freund,

1. When did he live? 2. He lived in the fourteenth century, ter Seiler, hin? 8. Er geht in seine Werkstatt. 9. Wu ift ter Hirte? 3. My friend told me he would never go there again? 4. Do

you go to Spain? 5. No, I shall not go thither. 6. The com. 10. Er ist auf dem Verge. 11. Wo geht ter Hirte hin? 12. Er geht mander-in-chief has sent his troops where the danger was most". auf ten Berg. 13. Wo geht un er alter Nachbar hin? or, Wohin geht 7. Is this ship from Spain or from Havre ? 8. No, it is neither: unser alter Nachbar? (S 89. I.) 14. Er ist iept in tem fleinen Garten, from Spain nors from Havre ; it comes from Hamburg. 9. aber er geht bald in den großen Garten. 15. Seine Frau ist in diesem These immigrants are going to Milwaukee, and are emigrants Hause, aber sein Vetter geht in jene Viltergallerie

16. Ich stebe an tom froun Bohemia and Venedig. 10 Can you leap over that gate?

11. I could when I was young. 12. He hade me to go thither (am) Fenster, und fie femmen anß ($ 4. 2) genster. 17. Der Ritter fibt that he might speak to me about it. jden auf seinem guten Piete, und ter Kuedt springt auch so eben auf sein

lim vierzehnten Jahrhuntert. ?wieter. Sie meiste Gefahr.wter. gutes Pjerd. 18. Der Viann siýt am ($ 4. 2) Tifcie, und das Buch liegt

bnoch. Thor. bat. auf dem Tische. 19. 3ch habe feinen Hut auf tem Repse. 20. Wo geht ter Setrat hin? 21. Die Soltaten gehen aufs (8 4. 2) Feld; sie sind schon auf tem Felte. 22. Ter Fresch írringt in den Fluß und schwimmt

LESSONS IN GEOME IRY.-No, XI. 1:1 tem Flusse, und tie Gans Atwimmt in tem Teiche. 23. Ich habe diese

LECTURES ON EUCLID, Werte irgendwo gelesen. 24. 3ch fann meine Müße nirgents finden, ob

DEFINITIONS. Book I. From XIII. To XVIII. INCLUSIVE. gleich sie irgentwo in diesem Ziminer sein muß.

XIII. 1. Where is the picture.ga'lery of this town? 2. Where was

(A term or boundary is the extremity of any thing.) This definition is that gentleman born? 3. He was born in Bohemia. 4. Where unnecessary, being merely verbal. does your friend, the actor, reside? 5. He resides in the city.

XIV. 6. Whither do these emigrants go? 7. Whence do these im. A figure is that which is enclosed by one or more boundaries. This defi migrants come? 8. They come from France. 9. Where much nition is applicable to solid figures, as well as to plane figures. is given, much is required. 10. llere the revenge and whetted

XV. sword • of a traitor enter not?;-beneath the shade of this tree A circle is a plane figure contained for, bounded) comes no king 11. He threw down the book before me. 12. by one line, which is called the circumference, and is Whither art thou going? 13. I am going to my brother in-law. such that all strught lines drawn from a certain point 14. Will these emigrants go to America. 15. No, they will stop within the figure to the circumference, are equal 10 here, 16. There is water in the pond. 17. Where does she

The circumference of a circle is

its boundary. The space contained within the come from? 18. She comes from Germany.

boundary, is called the circle. 'geboren. ?trirgt nicht. 3Rache. “gewette Delch. Sunter.

XVI,
EXERCISE 30.

And this point is called the centre of the circle. The straight line drawa

from the centre to the circumference, is called the radius. Yus'wanterer, m. emi. Dahin zichen, to pro. Italic'ier, m. Italian ;

• XVII. grant ;

ceed thither; Italie'nilo, Italian Dition'te, m. servant; Gin'wanterer, m iin. (adj.);

A diameter of a circle is a straight line drawn through the centre, and Botannte, m.acquaio- migrant;

Mie, never ;

terminated both ways by the circumference. tance; Englisch, English; Sra'nien, n. Spain;

XVIII Böhmen, n. Bohemia; Guro'pa, n. Europe; Spanish, Spanish ; A semicircle is the figure contained by a diameter and the part of the cir Wwmen, n. Bremen; felrherr, m. cominan. Theil, m. part; cumference cut off by the diameter. abin'gejen,

to

go der-in-chief; Vencrig, n. Venice; thither; Franzönity, French; Wie viel? how much?

From the 14th definition it will appear that the diagrams of Dabin'reisen, to travel fremte, m. stranger; how many ?

the preceding definitions, as well as those of a few subsequent thither; Havre, n. Ilavre; Wohl, well.

definitions, and of many propositions in Euclid, are not to be Dahin'idican, to send hierher'lommen,

considered as figures in the geometrical sense of the word.

to thither; come hither;

The common meaning of the term figure is, according to John.

Eon, as used by Addison, "something formed in reseinblance of 1. Die Sultaten find bier, und ter Feltherr fomit auch hierher. 2. somewhat else.” This definition applies to the use of the term Der feint ist siten ta, und unsere tapfern Brüter müssen dahin ziehen. 3. figure as denoting diagrams, representations, or drawings of Wann gehen sie nachy Sranien? 4 Ich will gar (Sect. 15. III.) nicht mind of what are called geometrical figures, which are entirely

every kind ; but it does not apply to the ideas formed in the tahin gehen, aber mein Vater will in nådster Woche dahin reiýn. 5. Sind creatures of the understanding. Sie idon ta goresen? 6. Nein, aber einer meiner Wefannten war da und With regard to the definition of a circle this has already been will nie wicier tahin geben 7. Wir gehen auf ten Berg, wellen Sie mit explained at some length in Lesson VIII. p. 277, and, thereund gelca? 8. Wili ter Ruissc seinen Vetieuten in die Start itiden? ticulars of importance relating to the circle. We find that

fore, it will only be necessary to advert to some additional par. 9. Er hat ihn jehen tahin geschickt. 10. Werten tie Truppen hierher iom- geometers in general are not sufficiently precise in speaking of men? 11. Sie werden nicht hierher fommen. 12. Wo tommen diese the circle ; very often when they use this term they mean only ôremten Her? 13. Sie sind Einwanderer und fummen aus Böhmen. 14. the circumference of the circle, i.e., the outward boundary ex. Sítticfee Schiff von Premen eter Gavre? 15. Gs ist weter von Vremen. defined in the 15th definition, is meant the space contained

clusive of the space contained within it. Now by the circle, as ned ron Kavce, co ist ren Benerig. 16. Gehen riese franzöjjhen Eins within the boundary, and the boundary too; for we cannot winterer nach Milwaukee 3 17. Gin Theil von ihnen geht bahin, tieconceive of space of a certain forin without including its out,

one another.

line or contour in the idea. But we can conceive of the proportion in question, what more do you want? it must be boundary of a circle, without the space contained within it, right, for we have measured. But, my good friends, measure just as we can conceive of a ring without the finger which fills as often as you like, and take more exact things than the crown up the space within the ring. It is better, therefore, when of the hat, if you will ; still this ratio is erroneous to the ex. the space is included in the idea of a circle, to use the term tent that we have said. And mind, that a small error in the circle only; but when the outline or circumference only is meant circumference, leads to a greater error in the surface or area of to say the circumference of the circle. Here it may be added, the circle ; and to still greater error in the cubic content of the that any part of the circumference of a circle is called an arc, sphere; for errors are increased by multiplication. a term evidently borrowed from its likeness to a bow, which in Seeing the necessity of being more accurate in regard to the Latin is called arcus. In like manner, carrying out the analogy, ratio of the diameter to the circumference, Metius, a Dutch the straight line which joins the extremities of an arc is called mathematician of the 17th century, discovered the proportion a chord, from the Latin chordı, a string ; while the space in- 113: 355; that is, the diameter of a circle is to its circumference, clled within the arc and its chord is called a segment, i. e., a very nearly as 113 is to 355. Besides its close approximation cal'ing, from the Latin secare, to cut. As to the term radius, it to the truth, this ratio is also easily remembered; for we have is ulso taken from the Latin, in which it first signified a rod or only to write the first three odd numbers in pairs, thus : 113355 staff, and then the spoke of a wheel, whence it came to be and then divide them into triplets, thus, 113 : 355, and we have applied to the straight line drawn from the centre to the circum- the ratio in question. The Hindoos, however, appear to have ference. Then, as to the term diameter, this comes from the been early acquainted with a convenient approximation much Greek, and signifies a measuring off or through, that is, the used by us in the present day. In the Ayeen Akberry, or greatest measure of the circle, being right across the centre, Institutes of Akbar, the diameter is said to be to the circumwhich gives the fullest or truest measure of the circle; it is ference as 1250 is to 3927; now if we multiply both terms of also applied to the straight line which joins the extreme points this ratio by 8, which does not alter its value or meaning, we of any figure: and hence, metaphorically, to points or questions have that of 10000 to 31416, or decimally that of 1 to 3.1416,in metaphysics, which are exactly opposite to each other. a very commonly used proportion. The meaning of this proHence, the meaning of the emphatic expression, diametrically portion is that the circumference is equal to 3 times the diaopposite to each other. From their definition it is plain that meter and a part of the diameter, additional to this three times, the diameter of a circle is double of its radius.

denoted by the fraction 1000 or 170; this fraction again, But the question may be asked – What is the ratio or pro- means that if the diameter were divided into 10000 parts, we portion of the circumference to the diameter? At first sight, must add 1416 of these parts to 3 times its length to get the this question seems quite absurd ; for what ratio can possibly length of the circumference; or if the diameter were divided into exist between two things that are perfectly unlike the dia- 1250 parts, we must add 177 of these parts to three times its meter of a circle is a straight line ; but the circumference of a length to get the length of the circumference. The proportion of circle is a curve line; therefore it does not appear that we can Metius, however, is really more accurate than the preceding; for compare two such unlike things together,-that is, they have it states that the circumference is 3 times the diameter, and a part no ratio to each other; and, taking them as they actually exist of the diameter denoted by 113 ; that is, if the diameter were in the circle, this is perfectly true. But if we say, supposing divided into 113 parts, we must add 16 of these parts to three that the circumference of a circle were stretched out in a times its length to get the circumference. The following list straight line to its full extent, just as we should do with a wire of proportions will show the most important and useful approxi. ring, by cutting it through in one part, and then stretching it mations to the truth, the last being true to the lowest figure of out into a straight piece of wire; what would then be the pro- the decimal, but capable of indefinite extension. portion of the circumference thus stretched out, to the dia

Authors, Original Ratios.

The Same in Decimals. merer of the circle? The question is easily put, but not so

7: 22

Archimedes Mechanics have, in all ages, fancied that Lambert easily answered.

!: 3:142857142857+ 106: 333

1: 3:141509433962+ they could reach the determination of this proportion by me- Hindoos

1250: 3927

1: 3.141600000000 chanical means; but from the days of Archimedes until now, Metius

113: 355

1: 3:141592920353+ they have signally failed ; and that failure is simply owing to

Lambert
33102: 103993

1: 3:141592653011+ the nature of the thing. We can never compare the physical

Lambert
33215; 104318

1: 3:141592653921+ with the ideal ; the mechanical operations of the finest aris, Lambert

66317 : 208341

1; 3:141592653467+ with the pure and simple abstractions of the mind. Even in the fine arts, there is an ideal beauty which no artist or connois. Wallis 1: 2

&c.) 1: 3:141592653589+ scur could ever reach ; so in the mathematical sciences, there

In the latter ratio, that of Wallis, the series continues to inis an accuracy of ratio or proportion, which the finest in. finity, the numerators of the fractions in the parenthesis being struments ever constructed, or ever to be constructed by the series of the squares of the even numbers, and the denoman, can never attain.

But ideas can reach it; mathe-minators being the series of odd numbers reduplicated as matical expression can reach it; and yet it surpasses the factors in the denominators in the manner shown. The fracsimply ariihmetical and practical. We can only approxi- tions in this series are continually approaching to the value 1, inate to this proportion by ordinary numbers; for, it is positively an intinite series of which the law cannot be ex mal values with the last, which is correct as far as it

or unity. By comparing these ratios as reduced to their deci.

the pressed in the ordinary terms of the decimal notation. It is amount of error in each can be duly appreciated. Thus, in the

goes, between 31% and 3}f as found by Archimedes ; that is, the circumference of a circle is less than 3% times the diameter case of that of Metius, it will be seen that his ratio makes the and greater than 31 times the diameter. As 3:8 is the same as the diameter is 4 millions. This is what we call “ being down

circumference too great by a little more than 1, or unity, when 3 or 22, it is usually said that theratio of the circumference to the diameter is that of 31 to 1, or of 22 10 7; in other words, that upon the eircle;" but we must delay the rest of our lesson on

this subject till our next opportunity. if the diameter of a circle be 1 foot, its circumference will be 34 feet; or if the diameter be 7 feet, the circumference will be 22 feet. This approximation is very well adapted for rough cal

LESSONS IN ENGLISH.-No. XVI. culations, but it is not sufficiently accurate for many important

By John R. BEARD, D.D. purposes. It gives the circumference too large by rather more ihan I part when the diameter is divided into 800 parts; that

PREFIXES (concluded). is, if the diameter of a circle were 800 feet, the circumference Quadr, quadra, of Latin origin (quatuor, four), is found in quadr. found from the Archimedean proportion, would be rather more angle, four-angled; quadruped (pes, Lat. a foot), four.footed; than I foot too much.

quadruple (plica, Lat. a fold), fourfold ; also quater, as in quaternica Many persons think that it is a very easy matter to determine (quaternio, the number four), &c. this ratio. For instance, suppose, say they, that we take the

* Aire and ye elements, the eldest birth crown of a hat, and measure it right across , well, perhaps this

Of Nature's womb, that in quaternion run, is 7 inches. Now take a string or tape and measure it round;

Perpetual circle, multiform; and mix well, perhaps this is found to be 22 inches. Here, then, is the

And nourish all things." Dhilton, " Paradise Lost."

22 1.3

3.6

5.7

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