FRENCH READINGS.

§ 153. RULE.

f. So, after such conjunctions as, weil, als, va, wenn, nachdem, obgleich obschon, obwohl, wenngleich and wiewohl, introduces the sub

The Prepositions aus, außer, bei, &c. (See List § 111.) are con- sequent clause. This is chiefly the case, when the antecedent strued with the dative. (See Obs. § 112.)

§ 154. RULE.

gegen, &c. (See List § 113.) are
(See Obs. § 114.)

The Prepositions durch, für, construed with the accusative. § 155.

RULE.

clause is long, or consists of several members: Ex. Weil dich Gott dies Alles gewahr werden ließ, so ist Niemand so weise als du, since God hath given thee to know all this, so (therefore) is no one so wise as thou. So commonly, however, denotes comparison: as, der Knabe ist so gut, als das Mächen, the boy is so (as) good as the girl. So in the phrases, sowohl als auch, or sowohl als, so (as) well as: sobald als, so (as) soon as, &c. With auch (so—auch) following, it signifies however: as, so groß die Schrecken des Krieges auch, The Prepositions an, auf, hinter, &c. (See List § 115) govern, however great the terrors of war, &c.; so reich er auch ist, tc. the dative or accusative: the accusative, when motion or ten- however rich he is, &c. dency towards is signified, but in the other situations the dative. (See Obs. § 116.)

$ 156. THE CONJUNCTIONS.

RULE.

Conjunctions connects words and sentences in construction, and show their mutual relation and dependence; as,

Johann und Wilhelm gehen zur Schule, John and William are
going to school.

Ich sah es; daher weiß ich es, I saw it; therefore I know it.
Er ist älter als ich, he is older than I.

OBSERVATIONS.

(1) Under the general name of Conjunctions in this Rule, must be included all words performing the office of ConjuncOf these connective tions, whether properly such or not. words three classes are to be distinguished: 1. those that do not affect the order of the words of a sentence in which they occur (§ 160. 8.); 2. those that always remove the copula to the end of the sentence (§ 160. 7.); 3. and finally, those that do or do not remove the copula to the end, according as they stand before or after the subject (§ 160. 8.).

g. The following are the more common correlatives as,

Entweder,

either,

Weder,

so, or then.

then,

Je,

the,

je,

the.

*Je,

the.

Sowohl,

as well,

Nicht allein,

not only,

sondern,

but.

Nicht nur,

not only,

sondern auch,

but also.

S 157. THE INTERJECTIONS.

RULE.

Interjections have no dependent construction.

OBSERVATIONS.

(1) Interjections stand generally before the nominative or the vocative; as, D! theuerster Vater! But sometimes the genitive, (2) The true force and use of the Conjunctions is best learned and sometimes the dative, is preceded by an Interjection: as, from examples; of which see a large collection in Section C., der Freude! O the joy! Weh mir! Woe to me! We subjoin, however, a few remarks in explanation of the following:

a. Aber, allein, sondern. Aber is less adversative than either of the others. It is often merely continuative. Allein always introduces what is contrary to what might be inferred from what precedes: as, er ist sehr fleißig, allein er lernt sehr wenig, he is very industrious, but he learns very little. Sonbern serves to introduce what is contradictory. It is used only when a negative precedes; nicht edel, sondern kleinmüthig, not noble, but pusillanimous; es ist weder schwarz, noch braun, sondern grün, it is neither black nor brown, but green.

b. Daß, also auf daß, introduces a clause expressing the end, object or result; as, ich weiß, daß er kommt, I know that he is coming. This form of expression is more common in German than in English. When tap is left out, the copula comes immediately after the subject.

-Sire! cria la jeune fille, à laquelle la position de son c. Doch introduces something unexpected or not properly pro-pere donnait une énergie au-dessus de son âge, je vous en .... au nom de votre mère, sire, ceeding from the antecedent: as, er ist sehr reich, und hat doch wenig conjure, écoutez-moi! 3 gearbeitet, he is very rich, yet has he worked little. It is some- écoutez-moi! au nom de votre père, accordez-moi la grâce times elliptically employed to indicate certainty, entreaty, and du mien! . . . . C'est mon père, sire; il aura été entraîné, the like: as, fagen Sie mir doch, tell me, pray. séduit; pardonnez-lui!.... Oh! sire, vous tenez la vie de Ayez pitié d. Je, like the definite article in English, is put before com- mon père, la mienne dans vous mains. . paratives to denote proportion. It, then, has testo for its cor- d'une malheureuse enfant qui vous demande la vie de son · pitié . . . . pardon. relative: thus, je fleißiger er ist, desto gelehrter wird er, the more dili-père. . ... Sire! sire! grâce. gent he is, the more learned he becomes. Defto sometimes -Laissez-moi, Mademoiselle, dit l'Empereur, la repouscomes before je: as, ein Kunstwerk ist desto schöner, je vollkommener es sant assez rudement.1 ift, a work of art is the more beautiful, the more perfect it is. Sometimes je is employed before both comparatives: thus, ie mihr, je besser, the more, the better. Sometimes befto stands before a comparative without je answering to it: as, ich erwartete nicht meinen Freund zu finden, desto größer aber war meine Freute, als ich ihn fah, I did not expect to find my friend, but the greater was my joy when I saw him.

e. Obgleich, obschon, obwohl, indicate concession. The parts are often separated, especially by monosyllables: such as, ich, du, er, es, wer, ihr, sie. Often two or three such little words come between: as, ob er gleich alt ist, 2., although he is old, &c.; eb ich mich gleich freue, sc., although I rejoice, &c

....

....

Mais, sans se laisser intimider, (il y allait d'une existence trop chère), Mlle de Lajolais, se traînant sur les dalles de marbre de la galerie, criait avec angoisse : -Oh! pitié, pitié, sire!. grâce!.... pour mon père! Oh! jetez au moins un regard sur moi, sire!

Il y avait quelque chose de si déchirants dans cette voix d'enfant demandant la vie de son père, que l'Empereur s'arrêta malgré lui, et regarda celle qui l'implorait avec tant d'instance."

Mlle de Lajolais était fort bien, mais, dans ce moment, sa beauté tenait de l'ange. Blanche comme un cygne, la

k

douleur donnait à ses traits un caractère énergique et pas- innumerable scientific truths for the benefit and to the astosionné; ses beaux cheveux blonds ruisselaient sur ses nishment of man; and in the midst of our wonder, we are épaules; ses petites mains, crispées par la fièvre, avaient forced to acknowledge and admire the omnipotence of study fini par saisir une des mains de l'Empereur, et lui com-in exploring the secret bosom of Nature, and snatching theremuniquaient leur chaleur brûlante..... Agenouillée, le visage baigné de larmes, levant ses grands yeux bleus vers celui duquel elle semblait attendre la vie ou la mort, elle ne pouvait plus ni parler, ni pleurer, ni respirer. -N'êtes-vous pas Mule de Lajolais ? lui demanda l'Em

pereur.

10

Sans répondre, Maria pressa la main de l'Empereur avec plus de force.12

Il reprit' avec sévérité: Savez-vous que c'est la seconde fois que votre père se rend coupable d'un crime envers l'Etat, Mademoiselle ?13

-Je le sais répondit Mlle de Lajolais, avec la plus grande ingénuité; mais la première fois il était innocent, sire.14

-Mais, cette fois, il ne l'est" pas, répliqua Bonaparte.15 -Aussi c'est sa grâce que je vous demande, sire, reprit Maria, grâce. . . . ou je mourrai devant vous.

L'Empereur, ne pouvant plus maîtriser 16 son émotion, se baissa vers elle en lui disant:

-Eh bien, oui, Mademoiselle, oui je vous l'accorde. Mais, relevez-vous.17

Et, lui jetant un sourire d'encouragement et de bonté, il dégagea ses mains tenues toujours avec forces et s'éloigna

vivement.

COLLOQUIAL EXERCISE.

9. Où étaient les mains de

l'enfant ?'

10. Que faisait-elle aux pieds de
Napoléon?

11. Que lui demanda-t-il alors?
12 Quelle réponse lui
Maria ?

13. Que lui dit Napoléon, rela-
tivement à son père ?

14. Que répondit-elle ?
15. Que repliqua Bonaparte?
16. L'Empereur semblait il
ému ?

from the hidden treasures she would willingly conceal; but in the child, Zarah Colburn, we find the young and powerful mental giant, with amazing alacrity, performing his incredible feats of intellectual gymnastics over the rugged play-ground

of mathematical calculation.

Zarah Colburn, the subject of the present short memoir, was an American boy belonging to the state of Vermont; according to our authority he was born in 1807. When only six years of age, his knowledge of arithmetic began to be discovered, his father having, to his astonishment, accidentally heard him tell the product of two numbers; and on asking him the multiplication table, and a series of similar questions in the rule of multiplication, he found that the little prodigy answered them all with the greatest possible ease.

In November, 1813, this astonishing youth, accompanied by his father, happened to be in Newry for a few hours, on his way from Dublin to Belfast, whence he intended to proceed to Glasgow College. During his short stay in Newry, he had scarcely time to take his hurried refreshment; for the people of that intelligent town were too eager to see and to hear the young philosopher, of whom they had previously heard so much. Here, many intricate questions were proposed to him, and, as if by instinct, he solved them all with the greatest rapidity and accuracy; and "all by the mere operation of the mind, without the assistance of any visible symbol or contrivance." Zarah Colburn, be it remembered, never made use of pen or pencil in solving the most difficult problems, no matter how long or how abstruse the process might be that was required. I have been often told that an humble house in Water-street, Newry, was for many years afterwards pointed out to the inquisitive tourist as the place where "the calculating boy" once stopped.

In his progress on his journey, before Zarah Colburn reached Belfast, his extraordinary intellectual capacity was a favourite topic; and many a juvenile arithmetician was ransacking his own brains in order that he might find "a few puzzlers," as questions, to propose to the much talked-of youth.

Zarah, shortly after his arrival in Belfast, was, on the 16th of November, 1813, introduced to a meeting of the members of the Royal Academical Institution; and the young readers of the POPULAR EDUCATOR may rest assured that his capabilities were sufficiently tested under a high standard by those 17. Que dit-il ? literary gentlemen, and that to a degree that raised wonder 18. Que fit-il avant de s'eloi- and delight to their very climax. gner?

pro

NOTES AND REFERENCES.-a. passer outre, to go on, to ceed.--b. aure, has without doubt, probably; the future tense, in French, is often used to express probability.-c. assez rudement, with some abruptness.-d. il y allait, etc., so precious a life was in danger, at stake.-e. dalles, floor; literally, flat stones.-f. L. part ii., § 61-2.—g. déchirant, heart-rending-h. avec tant d'instance, so earnestly.-i. tenait, resembled that.j. L. part ii., § 49. R. (4).-k. fini par, mechanically, unconsciously; literally, at last-1. from reprendre; L. part ii., p. 100.-m. from savoir; L. part ii, p. 104.n. 1', so.-o. from mourir; L. part ii, p. 96. -P. L. part ii, § 49, R. (1).—g. tenues, held; from tenir; L. part ii., p. 108.

BIOGRAPHY.-No. XIII.

ZARAH COLBURN.

WHEN Nature, as if to show her own dignity, bestows on a mere child, extraordinary mental powers, exceeding in magnitude what experience and the most wonderful development can scarcely approach, our pride is so completely humbled, that the pleasure we feel in contemplating the sublime phenomenon is almost lost in the disappointment we meet in being unable to reach its superlative grandeur.

Here the amazing "calculating boy," of only nine years of age, stood to be questioned; and here it was that he called forth such a strength of intellectual energy as to be aimost without a parallel in history. He was first asked the product of 365 and 13, and his answer, on the moment, was simply 4,745. But it was soon seen that such questions as this were too easy for such a pet of Nature's choosing. He was next told to extract the cube root of 307,546,875, and with the greatest readiness he answered 675. Other questions of a similar nature were proposed, and their solutions were effected by him with the same readiness and accuracy. A writer in one of the journals of the day says, "in short, there appeared to be no limits to the powers of his mind in calculation.

After exhibiting such rare proficiency at the Institution, and before such a learned body, the result of his examination naturally spread through all parts of the town, to garret, cellar, and drawing-room alike, as if carried on the wings of electric agency; so that crowds of the literati thronged to the coffee-room of the inn where he resided for the time, in order to prove by their own experience what the most flexible credulity could scarcely believe.

Of the complex nature of the numerous questions proposed to Zarah at this exhibition, our readers may form some remote idea from the few following examples. He was requested to extract the cube root of 51,230,158,344; his answer, immediately given, was 3,714.

He, in an instant, multiplied 349,621 by 5, and gave the correct product, 1,748,105.

In men such as Newton and La Place, we find genius, by Again, he divided 2,608,732 by 4, and gave for answer the force of culture and defatigable application, calling forth | 652, 183. Here, it is to be expected that the astonishment and

376

this means that an inch contains 11 equal parts or subdivisions of this line, each unit on this line containing of an inch; hence, from 1 to the beginning of the subdivisions on the right, are contained 10 of such equal parts, or of an inch; from 2 to the same point, are contained 20 of such equal parts, or of an inch; and so on. A unit of this line, the first one adjacent to the number 11, is subdivided into 10 equal parts at the bottom of the space it occupies, and into 12 equal parts at the top of this space. Of the former subdivisions, each one is a tenth part of a unit of this line, or a tenth part of ten-elevenths of an inch, that is, one-eleventh of an inch; hence any number of elevenths of an inch may be obtained from this line as far as the scale will permit, as 7, 12, 25, etc. elevenths of an inch. Of the top subdivisions, each one is a twelfth part of a unit of the scale; this is intended for those who use this line merely as a line of equal parts, and prefer the duodecimal to the deci

mal subdivision of the unit.

Again, the third line on the scale, reckoning upwards, has 12 marked at the left-hand side, and the units 1, 2, 3, 4, 5, marked along the line from left to right; this means that an inch contains 12 equal parts or subdivisions of this line, each unit on the line containing 19 of an inch; hence, from 1 to the beginning of the subdivisions on the right, are contained 10 of such equal parts, or 1 of an inch; from 2 to the same point, are contained 20 of such equal parts or if of an inch; and so on. A unit of this line, the first adjacent to the number 12, is subdivided into 10 equal parts at the bottom of the space it occupies, and into 12 equal parts at the top of this space. Of the former subdivisions, each is a tenth part of a unit of this line, or a tenth part of ten-twelfths of an inch, that is, onetwelfth of an inch; hence any number of twelfths of an inch may be obtained from this line as far as the scale will permit, as 7, 14, 27, etc. twelfths of an inch. Of the top subdivisions, each one is a twelfth part of a unit of the scale.

Next, the fourth line on the scale, reckoning upwards, has 13 marked at the left-hand side, and the units 1, 2, 3, 4, 5, 6, marked along the line from left to right; this means that an inch contains 13 equal parts or subdivisions of this line, each unit on the line containing 10 of an inch, or 20 of an inch; 13 27 hence, from 1 to the beginning of the subdivisions on the right, are contained 10 of such equal parts, or of an inch; from 2 to the same point, are contained 20 of such equal parts, or of an inch; and so on. A unit of this line, the first adjacent to the number 13, is subdivided into 10 equal parts at the bottom of the space it occupies, and into 12 equal parts at the top of this space. Of the former subdivisions, each one is a tenth part of a unit of this line, or a tenth part of 10 of an inch, or

13 a tenth part of twenty twenty-sevenths of an inch, that is, two twenty-sevenths of an inch; hence any number of parts of which 13 make an inch may be obtained from this line as before, only as far as the scale will permit. each one is a twelfth part of a unit of the scale. In the latter Of the top subdivisions, case, the part of an inch thus obtained is a compound and complex fraction denoted by 1 10 of

5

of an inch.

81

12

1

or

13

12

of 20

27

that is,

In the same way we might proceed to explain the remaining lines of this scale; but we presume that we have sufficiently explained the first four lines on the scale, to render the remaining ten lines equally easy of comprehension. Besides, we must leave a little to the ingenuity of our students, otherwise there would be no excitement for them to study. Moreover, all these different lines may be used as scales of equal parts differing from one another in the magnitude of the unit by very small and gradual differences, so that a student from amongst them may get almost any scale that will answer his drawings. The relation of the units of these scales to an inch is a matter in general of small importance to a vast variety of mechanical drawings; still, if such relation be wanted, it can be fully obtained on the principles which we have already explained. Some plane scales of the kind which we have described may be had with twenty lines on them adapted to different scales of measurement, namely, the one half or ten on the one side,

and the other half or ten on the other side. The range of
these scales is as follows:-
are--
On the one side, the numbers of the subdivisions to an inch

and on the other side, the numbers of the subdivisions to an
10, 11, 12, 13, 15, 16, 18, 20, 22, 25;
inch are-
The left-hand primary division or unit of the lines on these
28, 32, 36, 40, 45, 50, 60, 70, 85, 100.
scales is sometimes subdivided into 10, 12, and 8 equal parts;
as these subdivisions are of great use in drawing the parts of a
fortress, a piece of cannon, an engine, or of the different orders
of architecture.

In our next Lesson we shall explain the Logarithmic Lines on the Engineer's Rule and on Gunter's Scale.

ANSWERS TO CORRESPONDENTS.

are some of the highly volatile hydrocarbons, of which those are best which
YORICK: The only fluids adapted for burning in lamps without wicks
approach nearest to the composition of Benzole. The lamp, however, for
will not do. 1s our correspondent aware that a patent has been taken out
this purpose, must be constructed on peculiar principles; ordinary lamps
for this description of lamp by Mr. Holloway? He has a depot in Holborn
(No. 117, we believe).
fatal.
inconvenience, and have given rise to numerous accidents, some of them
Wickless lamps are attended with considerable
biguous; let our correspondent supply the words "both" "and" in their
IACO: The employment of the words "either" "or" certainly are am-
nickel, are not precipitated from their solutions by hydrosulphuric acid
place. What we meant to state was, that iron, manganese, cobalt, and
ammonia.-R. G. SMITH:
alone, but are precipitated from their solutions by hydrosulphate of
hydrogen in a pure solution of silver, is black.
The precipitate furnished by sulphuretted

Euclid; the geometry of Euclid is the finest specimen of Logic the world
W. B. HODSON (Harby): It is not necessary to study Logic before
H. K. W. (Brixton): Won't do; must try again; but before doing so, read
ever saw. Whateley's Logic is reckoned among our best modern treatises.-
Moody is quite correct as far as Latin is concerned. The English has no
much good poetry, as Milton, Cowper, etc.-DOUBTFUL (Bishop-Auckland):
ablative.

Geometry in their order, that is, Arithmetic first; then Algebra; and
E. H. B. (Birkenhead) should study Cassell's Arithmetic, Algebra, and
then Geometry; or if he prefers it, the lessons on these subjects in the P. E.
will do as well. The French Dictionary will soon be finished, if not so
It is most likely that the Lessons in Geology will assume a separate form.
already. The suggestions made will be kept in view.-H. GEORGE (Bristol):
Any book on navigation is a guide to the compass.
Lessons in English are published at 3s.-J. CHADWICK (Royton) should
WILTON (Bebbington): The Geography will be issued with an Atlas; the
make the experiment referred to; we have never seen the statement. It is
generally considered that the best glass for an electrical machine is the
that which contains a large proportion of silex; and it should not be too
thick.
whitest, the most transparent, the hardest, and freest from bubbles, and

ERRATA.

Vol. iv. page 2, col. 2, line 23 from bottom, for 400th. read 40,000th.
page 126, col. 2, line 15 from top, for £170 read £180.
page 126, col. 2, line 10 from bottom, for Liverpool read Manchester.

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The notes of the gamut can be represented by numbers. For this purpose, we take for ut, the fundamental sound of the sonometer explained in a former Lesson; that is, the sound produced by a cord vibrating throughout its whole length. By varying the position of the moveable bridge B, fig. 129, No. 1, page 362, an experimenter, who has a practised ear, can easily find the length which must be successively given to the vibrating part ▲ B, in order to produce the six other notes. Thus, by representing by unity or 1, the length of the cord which gives ut, we find that the lengths of the cords which give the other notes will be represented by the following scale of numbers containing fractions of unity

The notes of the Gamut are represented to the eye by placing them on what is called the staff, which consists of five parallel straight lines and four intervening spaces. The double staff used for the music of the pianoforte represents, within its extent, a series of three octaves, as exhibited in the, etc., of the preceding table, in order to find the exact following table, fig. 135.