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Wenn,

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as soon,

as. as. SO. so.

f. So, after such conjunctions as, weil, ale, ba, wenn, nachdem, § 153. RULE.

obgleich obschon, obwohl, wenngleich and wiewohl, introduces the sub. The Prepositions aus, nußer, bei, &c. (See List § 111.) are consequent clause. This is chiefly the case, when the antecedent strued with the dative. (See Obs. § 112.)

clause is long, or consists of several members : Ex. Weil dich

Gott dies Alles gewahr werben ließ, so ist Niemand so weise als bu, since § 164. RULE.

God hath given thee to know all this, so (therefore) is no one The Prepositions durch, für, gegen, &c. (See List § 113.) are

so wise as thou. So commonly, however, denotes comparison:

as, der Knabe ist so gut, als das Mächen, the boy is 80 (as) good as construed with the accusative. (See Obs. § 114.)

the girl. So in the phrases, sowohl als aucy, or sowohl ald, so (as) § 155. RULE.

well as : sobald als, so (as) soon as, &c. With auch (io-aud) fol.

lowing, it signifies however : as, so groß die Schreden des Krieges auch, The Prepositions an, auf. þinter, &c. (See List § 115.) govern a , however great the terrors of war, &c.; so reicht er auch ist, ic. 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.

g. The following are the more common correlatives · as, (See Obs. § 116.)

Entweder, either, oder,

or.

Weber,
S 156. THE CONJUNCTIONS.

neither, nod),

nor.
if,
To,

so, or then. Rule.

Da,
when
so,

then,

the, Conjunctions connects words and sentences in construction,

ie,

the. and show their mutual relation and dependence; as,

the,
desto,

the.
Sobalt,

als, Johann und Wilhelm gehen zur Schule, John and William are

Sowohl,
as well,

als, going to school.

Wie,
as,

ro, 30 sah e$; daher weiß id es, I saw it; therefore I know it.

So,
30,

so, Er ist alter als ich, he is older than I.

Nicht,
not,
sondern,

but.

Nicht allein,
OBSERVATIONS.

not only, fonbern,

but. Nicht nur,

not only, sondern auch, but also. (1) Under the general name of Conjunctions in this Rule, must be included all words performing the office of Conjunc

$ 157. THE INTERJECTIONS. tions, whether properly such or not. Of these connective

RULE. 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 Interjections have no dependent construction. (§ 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

OBSERVATIONS. not remove the copula to the end, according as they stand be.

(1) Interjections stand generally before the nominative or the fore or after the subject ($ 160. 8.).

vocative; as, O! 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. D, 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 in- FRENCH READINGS.-No. V.
troduces what is contrary to what might be inferred from
what precedes : as, er ist sehr fleißig, allein er lernt sehr wenig, he is

MLLE DE LAJOLAIS.
very industrious, but he learns very little. Sondern serves to in.
troduce what is contradictory. It is used only when a negative

SECTION II. precedes; nicht edel, sondern fleinmüthig, not noble, but pusillani. A ces cris, à cette action imprévue, l'Empereur s'arrête mous; cf ist weder schwarz, noch braun, sondern grün, it is neither black nor brown, but green.

en fronçant les sourcils.' 6. Daß, also auf daß, introduces a clause expressing the end,

-Encore! .. .. s'écrie-t-il d’un ton d'impatience, j'avais object or result; as, ich weiß, daß er fommt, I know that he is pourtant dit que je ne voulais plus de ces scènes-là ! 2 coming. This form of expression is more common in German

Et croisant ses bras sur sa poitrine, il voulut passer than in English. When baß is left out, the copula comes im

outre.a mediately 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 ceeding from the antecedent: as, er ist sehr reich, und hat voch wenig conjure, écoutez-moi !?..

....au nom de votre mère, sire, 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, sagen Sie mir doch, tell me, pray.

séduit; pardonnez-lui!.... Oh! sire, vous tenez la vie de d. Je, like the definite article in English, is put before com. mon père, la mienne dans vous mains. . . . . Ayez pitié paratives to denote proportion. It, then, has resto for its cor. d'unc malheureuse enfant qui vous demande la vie de son relative: thus, ie fleißiger « ift, testo gelehrter wird er, the more dili- père. . .. . Sire! sire! grâce .... pitié .... pardon. 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 vollfommener esant asseze rudement. ift, a work of art is the more beautiful, the more perfect it is. Sometimes je is employed before both comparatives : thus

, ir tence trop chère), Mlle de Lajolais, se traînant sur les

Mais, sans se laisser intimider, (il y allait d'une exismihr, je besser, the more, the better. Sometimes desto stands be dalles de marbre de la galerie, criait avec angoisse : fore a comparative without je answering to it: as, ich erwartete nicht meinen Freund zu finden, befto größer aber war meine freute, als ich Oh! jetez au moins un regard sur moi, sire!

-Oh! pitié, pitié, sire!... grâce!. pour mon père ! ihn sah, I did not expect to find my friend, but the greater was my joy when I saw him.

Il y avait' quelque chose de si déchirants dans cette voix e. Obgleich, obschon, obwohl, indicate concession. The parts are d'enfant demandant la vie de son père, que l'Empereur often separated, especially by monosyllables : such as, idy, bu, er

, s'arrêta malgré lui, et regarda celle qui l'implorait avec €8, wer, ihr, sie. Often two or three such little words come be tant hi d'instance.? tween : as, ob er gleich alt ift, a., although he is old, &c.; ob ich Mule de Lajolais était fort bien, mais, dans ce moment, sa mich gleich freue, a., although I rejoice, &c

beauté tenait de l'ange. Blanche comme un cygne, la

b

:

15

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 i 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 park 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 from the hidden treasures she would willingly conceal; but in visage baigné de larmes, levant ses grands yeux bleus vers mental giant,

with amazing alacrity, performing his incredible celui duquel elle semblait attendre la vie ou la mort,'° elle feats of intellectual gymnastics over the rugged play-ground ne pouvait plus ni parler, ni pleurer, ni respirer.

of mathematical calculation. -N’êtes-vous pas Mlle de Lajolais ? ii lui demanda l'Em

Zarah Colburn, the subject of the present short memoir, was pereur.

an American boy belonging to the state of Vermont; according Sans répondre, Maria pressa la main de l'Empereur avec to our authority he was born in 1807. When only six years plus de force, 12

of age, his knowledge of arithmetic began to be discovered, his Il reprit? avec sévérité : Savez-vous que c'est la seconde father having, to his astonishment, accidentally heard him tell fois que votre père se rend coupable d'un crime envers the product of two numbers ; and on asking him the multil'Etat, Mademoiselle ? 13

plication table, and a series of similar questions in the rule of -Je le sais m répondit Mlle de Lajolais, avec la plus multiplication, he found that the little prodigy answered them grande ingénuité; mais la première fois il était innocent,

all with the greatest possible ease. sire.

In November, 1813, this astonishing youth, accompanied by - Mais, cette fois, il ne l'est pas, répliqua Bonaparte.!

his father, happened to be in Newry for a few hours, on his

way from Dublin to Belfast, whence he intended to proceed to -Aussi c'est sa grâce que je vous demande, sire, reprit Glasgow College. During his short stay in Newry, he had Maria, grâce .... ou je mourraio devant vous.

scarcely time to take his hurried refreshment; for the people L'Empereur, ne pouvant plus maîtriser 16 son émotion, se of that intelligent town were too eager to see and to hear the baissa vers elle en lui disant :

young philosopher, of whom they had previously heard so -Eh! bien, oui, Mademoiselle, oui je vous l'accorde. much. Here, many intricate questions were proposed to him, Mais, relevez-vous.17

and, as if by instinct, he solved them all with the greatest Et, lui jetant un sourire d'encouragement et de bonté, il rapidity and accuracy; and "all by the mere operation of the dégagea p ses mains tenues toujours avec force 18 et s'éloigna mind, without the assistance of any visible symbol or convivement.

trivance." Zarah Colburn, be it remembered, never made

use of pen or pencil in solving the most difficult problems, no COLLOQUIAL EXERCISE.

matter how long or how abstruse the process might be that 1. Que fit l'Empereur en enten- 9. Où étaient les mains de was required. I have been often told that an humble house dant ces cris ?

l'enfant ?'

in Water-street, Newry, was for many years afterwards 2. Quo dit-il d’un ton d'impa- 10. Que faisait-elle aux pieds de pointed out to the inquisitive tourist as the place where "the

Napoléon ?

calculating boyonce stopped.

In his progress on his journey, before Zarah Colburn reached 3. Quelles paroles énergiques la 11. Que lui demanda-t-il alors? Belfast, his extraordinary intellectual capacity was a favourite jeune fille adressa-t-elle à Bo- 12 Quelle réponse lui naparte?

Maria ?

topic; and many a juvenile arithmetician was ransacking his

own brains in order that he might find "a few puzzlers," as 4. Que dit l'Empereur et que 13. Que lui dit Napoléon, rela- questions, to propose to the much talked-of youth. fit-il ? tivement à son père ?

Zarah, shortly after his arrival in Belfast, was, on the 16th 5. Pourquoi Mlle de Lajolais ne 14. Que répondit-elle ? se laissa-t-elle pas intimider ? 15. Que repliqua Bonaparte ?

of November, 1813, introduced to a meeting of the members

of the Royal Academical Institution; and the young readers 6. Qu'ajouta-t-elle en se traî- 16. L'Empereur semblait - il of the POPULAR EDUCATOR may rest assured that his capanant sur les dalles de marbre ? ému ?

bilities were sufficiently tested under a high standard by those 7. Que fit alors l'Empereur ? 17. Que dit-il ?

literary gentlemen, and that to a degree that raised wonder 8. Quel caractère la douleur 18. Que fit-il avant de s'eloi- and delight to their very climax. donnait-elle aux traits de

Here the amazing calculating boy," of only nine years of Maria ?

age, stood to be questioned ; and here it was that he called NOTES AND REFERENCES.-a, passer outre, to go on, to pro- forth such a strength of intellectual energy as to be almost ceed.-6. aura, has without doubt, probably; the future tense, in without a parallel in history. He was first

asked the product French, is often used to express probability.-c. assez rudement, of 365 and 13, and his answer, on the moment, was simply with some abruptness.-d. il y allait

, etc.

, 80 precious a life was in 4,745. But it was soon seen that such questions as this were danger, at stake.e. dalles, floor; literally, flat stones.-J. L. too easy for such a pet of Nature's choosing. He was next told part ii., § 61–2.-. déchirant, heart-rending-h. avec tant d'in: to extract the cube root of 307,546,875, and with the greatest stance, so earnestly.-i. tenait, resembled that.-. L. part ii., $ nature were proposed, and their solutions were effected by

readiness he answered 675. Other questions of a similar 49. R. (4).—k. fini par, mechanically, unconsciously; literally, at him with the same readiness and accuracy. A writer in one last.-I. from reprendre; L. part ii., p. 100.-m. from savoir ; of the journals of the day says, “in short, there appeared to L. part ii., p. 104,

:--. l', 80.--. from mourir ; L. part ii., p. 96. be no limits to the powers of his mind in calculation. -P. L. part ii., $ 49, R. (1).--. tenues, held; from tenir; L.

After exhibiting such rare proficiency at the Institution, and part ii., p. 108.

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 BIOGRAPHY.-No. XIII.

electric agency; so that crowds of the literati thronged to the

coffee-room of the inn where he resided for the time, in order ZARAH COLBURN.

to prove by their own experience what the most Aexible cre

dulity could scarcely believe. When Nature, as if to show her own dignity, bestows on a Of the complex nature of the numerous questions proposed mere child, extraordinary mental powers, exceeding in magni- to Zarah at this exhibition, our readers may form some remote tude what experience and the most wonderful development idea from the few following examples. He was requested to can scarcely approach, our pride is so completely humbled, extract the cube 100t of 51,230,158,344 ; his answer, immedithat the pleasure we feel in contemplating the sublime pheno- ately given, was 3,714. menon is almost lost in the disappointment we meet in being He, in an instant, multiplied 349,621 by 5, and gave the corunable to reach its superlative grandeur.

rect 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 indefatigable application, calling forth | 652,183. Here, it is to be expected that the astonishment and

gner ?

pleasure of his auditors were great indeed; and it may be obtained by this means he should be enabled to get a college safely inferred that the problems proposed were still becoming education. An eminent literary gentleman even undertook to more and more abstruse.

write his life; but whether the laudable proposal was ever Now, it was proposed to him, given the sum and difference executed or not, I cannot tell, or whether the “calculating of two numbers, 728, and 16, to find the numbers themselves; boy" ever got to college I never was able to ascertain. he answered 372 and 356. On being asked what factors would Perhaps, indeed, the vigorous flame of his intellect, so early produce 765,621, his answer was 85,069, multiplied by 9. kindled by “nature's touch," and so often called on to act Again, 877 was given as one of the factors of the same number mechanically, was neglected, suffered to run to waste, flicker, to find the other; and he instantaneously gave 873 as the and die, without ever knowing the blessings of a proper answer.

development! For the sake of humanity and science, I hope Again, he was required tell the fourth root of 3,701,506; but not-but I cannot banish my doubts on the subject, as I never he immediately said there was no root, which was indeed true, heard of him figuring in the mathematical world after he left the proposer having intentionally read the number wrong, for

Belfast. the purpose, if possible, of " flooring" the young genius. In disposition, Zarah was modest and playful, and in

But the active powers of his mind seemed by far too great appearance presented nothing singular beyond other children to be taken by surprise on the broad arena of cuiculation. of his age, not even in the formation of his forehead, that

Shortly after the proposal of the preceding question, he was portion of the human fabric to which critics so eagerly direct asked the fourth root of 37,015,056 (the right number), and attention. Yet there is no doubt that, in after years, the gradual the modest little arithmetician, with his usual expertness, ease, development of such a mind would have acted on the counteof the whole auditory. Thus

it was that the “: American Cal which I have been a constant reader from the first) expressed and accuracy, answered 78, to the great surprise and delight nance of such an extraordinary person.

As some of the correspondents of the POPULAR EDUCATOR (of culating Boy,” Zarah Colburn, spent some time in Belfast, experiencing kindness wherever he went, and exciting the a desire to know something of this wonderful boy, I have admiration of all by his truly wonderful facililty of managing endeavoured thus hurriedly to place before them this rather numbers, through the unassisted instrumentality of mental scanty memoir, collected from what I had heard of him, and operation.

from my old papers of the year 1813. Like those of many an eminent genius in humble life, his

My féllow-readers, keep good heart; my promise concernparents were poor, his father was struggling to send him to ing the memoir of our celebrated Dr. Thomson will be fulfilled. ihe University, but he had no money, it was therefore sug. The POPULAR EDUCATOR shall have it when finished, before gested that a memoir of his life should be published, that it the ink is quite dry; but some time must yet elapse. should cost a guinea and a half, and that with the money Katesbridge, February 20th, 1854.

H. H, ULIDIA.

are contained 10 of such equal parts, or 18 of an inch ; from 2 INSTRUMENTAL ARITHMETIC.-No. IV. to the same point, are contained 20 of such equal parts or SCALES OF VARIOUS EQUAL PARTS TO AN INCH.

if of an inch; from 3 to the same point, 30 equal parts, or is

of an inch; and so on. A unit of this line, the first one adjaIN Lesson No. III. on Instrumental Arithmetic, we gave acent to the number 10, which should have been marked with drawing and description of an instrument called a Piane Scale zero or 0, at its extremity on the right hand, is subdivided into and Protractor; we then omitted the drawing of the other side 10 equal parts at the bottom of the space which it occupies, and of the instrument for want of room; but we now insert it below, into 12 equal parts at the top of this space. Of the former sub. fig. 1, with a short description of its nature and use.

divisions, each one is a tenth part of an inch; hence this line

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In this scale there are fourteen lines of equal parts, all of with the bottom subdivisions is a decimal scale of inches, and which contain a certain number of equal parts to an inch. from it we can take off or measure any number of irches and The numbers placed at the left-hand side of the scale show tenths of an inch as far as the scale will permit, as, 107, 2-5, how many equal parts of the line on which it stands, one inch 3.8, etc. inches. Of the top subdivisions, each one is a twelfth contains, each unit of the line containing ten of these equal part of an inch; hence this line with the top subdivisions is a parts. Thus, the first line on the scale at the bottom has 10 duodecimal scale of inches, and from it we can take off or meamarked at the left-hand side, and the units 1, 2, 3, and 4, sure any number of inches and primes or twelfths of an inch as inarked along the line from left to right; this means that an far as the scale will allow, as lin.7', 2 in.5', 3 in. 8', etc. inch contains ten equal parts or subdivisions of this line, each Again, the second line on the scale, reckoning from the unit on this line containing 18 of an inch; hence, from 1 to bottom upwards, has 11 marked at the left-hand side, and the the beginning of the smaller divisions on the line on the right, I units 1, 2, 3, 4, and 5, marked along the line from left to right: this means that an inch contains 11 equal parts or subdivisions and the other half or ten on the other side.

The range of of this line, each unit on this line containing H of an inch; these scales is as follows:-. hence, from 1 to the beginning of the subdivisions on the On the one side, the numbers of the subdivisions to an inch right, are contained 10 of such equal parts, or li of an inch; arefrom 2 to the same point, are contained 20 of such equal parts,

10, 11, 12, 13, 15, 161, 18, 20, 22, 25; or if of an inch; and so on. A unit of this line, the first one and on the other side, the numbers of the subdivisions to an adjacent to the number 11, is subdivided into 10 equal parts at | inch arethe bottom of the space it occupies, and into 12 equal parts at

28, 32, 36, 40, 45, 50, 60, 70, 85, 100. the top of this space. Of the former subdivisions, each one is the left-hand primary division or unit of the lines on these a tenth part of a unit of this line, or a tenth part of ten-elevenths scales is sometimes subdivided into 10, 12, and 8 equal parts ; of an inch, that is, one-eleventh of an inch; hence any number as these subdivisions are of great use in drawing the parts of a of elevenths of an inch may be obtained from this line as far as fortress, a piece of cannon, an engine, or of the different orders the scale will permit, as 5, 12, 25, etc. elevenths of an inch, of architecture. 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 on the Engineer's Rule and on Gunter's Scale.

In our next Lesson we shall explain the Logarithmic Lines as a line of equal parts, and prefer the duodecimal to the decimal 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,

ANSWERS TO CORRESPONDENTS. marked along the line from left to right; this means that an YORICK : The only fluids adapted for burning in lamps without wicks inch contains 12 equal parts or subdivisions of this line, each are some of the highly volatile hydrocarbons, of which those are best which unit on the line containing ts of an inch; hence, from 1 to the this purpose, must be constructed on peculiar principles;

ordinary lamp: beginning of the subdivisions on the right, are contained 10 will not do. Is our correspondent aware that a patent has been taken out of such equal parts, or 1% of an inch; from 2 to the same point, for this description of lamp by Mr. Holloway? He has a depot in Holborn are contained 20 of such equal parts or if of an inch; and so inconvenience, and have given rise to numerous accidents, some of them on. A unit of this line, the first adjacent to the number 12, is fatal. subdivided into 10 equal parts at the bottom of the space it laco: The employment of the words “either""or" certainly are am. occupies, and into 12 equal parts at the top of this space. Of biguous, let our correspondent supply the words“ both " " and " in their the former subdivisions, each is a tenth part of a unit of this placeWhat we meant to state was, that iron, manganese, cobalt, and

nickel, are not precipitated from their solutions by hydroeulphuric acid line, or a tenth part of ten-twelfths of an inch, that is, one- alone, but are precipitated from their solutions by hydrosulphate of twelfth of an inch; hence any number of twelfths of an inch ammonia.--R. G. SMITH: The precipitate furnished by sulphuretted may be obtained from this line as far as the scale will permit, hydrogen in a pure solution of silver, is black.

W. B. HODSON (Harby): It is not necessary to study Logic before as 7, 14, 27, etc. twelfths of an inch. Of the top subdivisions, Euclid; the geometry of Euclid is the finest specimen of Logic the world each one is a twelfth part of a unit of the scale.

ever saw. Whateley's Logic is reckoned among our best modern treatises.-Next, the fourth line on the scale, reckoning upwards, has M. K. W. (Brixton): Won't do; must try again ; but before doing so, read 13} marked at the left-hand side, and the units 1, 2, 3, 4, 5, 6, Moody is quite correct as far as Latin is concerned. The English has no marked along the line from left to right; this means that an ablative. inch contains 13} equal parts or subdivisions of this line, each Geometry in their corder, that is, Arithmetic first; then Algebra and

E. H. B. (Birkenhead) should study Cassell's Arithmetic, Algebra, and 10

20 unit on the line containing of an inch, or of an inch ; I will do as well. The French Dictionary will soon be finished, is not so

13

27

already. The suggestions made will be kept in view.-H. GEORGE (Bristol): hence, from 1 to the beginning of the subdivisions on the right, It is most likely that the Lessons in Geology will assume a separate form. are contained 10 of such equal parts, or jy of an inch ; from z Any book on navigation is a guide to the compass. to the same point, are contained 20 of such equal parts, or ti of Lessons in English are published at 35.-J.

CHADWICK (Royton) should

WILTON (Bebbington): The Geography will be issued with an Atlas; the an inch; and so on. A unit of this line, the first adjacent to make the experiment referred to; we have never seen the statement. It is the number 133, is subdivided into 10 equal parts at the bot- generally considered that the best glass for an electrical machine is the tom of the space it occupies, and into 12 equal parts at the top that which contains a large proportion of silex; and it should not be too of this space. Of the former subdivisions, each one is a tenth thick.

10 part of a unit of this line, or a tenth part of of an inch, or Vol. iv. page 2, col. 2, line 23 from bottom, for 400th. read 40,000th.

131

page 126, col. 2, line 15 from top, for £170 read £180. a tenth part of twenty twenty-sevenths of an inch, that is, two

page 126, col. 2, Une 10 from botlom, for Liveryool read Manchester, 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. Of the top subdivisions,

LITERARY NOTICES. each one is a twelfth part of a unit of the scale. In the latter

CASSELL'S LATIN DICTIONARY, BY J. R. BRARD, D.D.-The publicacase, the part of an inch thus obtained is a compound and tion of this Dictionary has commenced, and will be completed in about 1 10 1 20

Twenty-six Numbers, THREEPENCB each, or in Monthly Parts, One of

of that is, Shilling each.. Part the First is now ready; Part the Second will be ready 131 12 27'

with the Magazines for April. 5 of an inch,

CASSELL'S FRENCII AND ENGLISH DICTIONARY.-The FRENCH and 81

ENGLISH portion of this important Dictionary is now completed, and may be

had, price 4s., or strongly bound, 5s. The ENGLISH and FRENCH portion In the same way we might proceed to explain the remaining is in the course of publication, and will be completed in about Twelve lines of this scale; but we presume that we have sufficiently volume, will be ready with the Magazines for a pril, price 9s6d. explained the first four lines on the scale, to render the remain

DICTIONARY.-The GERMANing ten lines equally easy of comprehension. Besides, we English Portion of this Dictionary is now ready, price 58. iu stiff covers, must leave a little to the ingenuity of our students, otherwise or 5s.6d, strong cloth:- The English-German Portion will be completed there would be no excitement for them to study. Moreover, all | Volume, strongly bound,

at Is., will shortly be issued.

as quickly as possible, in Numbers, THREEPENCB each; and the entire these different lines may be used as scales of equal parts differ- CASSELL'S SHILLING EDITION OF First LESSONS IN LATIN. By Pro ing from one another in the magnitude of the unit by very feasors E. A. ANDREws and S. Stoddard. Revised and Corrected." Prico small and gradual differences, so that a student from amongst is. paper covers, or 1s.6d, neat cloth.

CASSELL'S LATIN GRAMMAR. For the use of Schools and Colleges. By them may get almost any scale that will answer his drawings. Professors E. A. ANDREWS and S. STODDARD. Revised and Corrected. The relation of the units of these scales to an inch is a matter Price 3s.6d. in cloth boards. in general of small importance to a vast variety of mechanical unrivalled by thousands of students. Many who have studied Latin from

CASSELL'S LESSONS IN LATIN. These Lessons have been pronounced drawings; still, if such relation be wanted, it can be fully other grammars and on other systems, and have completely failed, hare obtained on the principles which we have already explained. acquired more real knowledge of the Latin Tongue from these Lessons in Some plane scales of the kind which we have described may six months,

than they have acquired in as many

years by the means hitherto be had with twenty lines on them adapted to different scales adopted. Price 2s.6d In paper covers, or 3s. In cloth. of measurement, namely, the one half or ten on the one side, I all

the Exercises. Price 19. in paper covers, or 18. 6d. cloth.

BRRATA.

complex fraction denoted by in

, or

CASSELL'S

GERMAN

PRONOUNCING

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{means of fragments of lines which indicate their relative ON PHYSICS, OR NATURAL PHILOSOPHY. position. The other consists in the use of keys or clefs, which

are signs employed to raise or lower the gamut by several No. XXVI.

tones, and even several octaves. The clefs are commonly at

the beginning of a piece of music, and the normal intonation (Continued from page 364.)

is determined by them. They are accompanied with a variety

of other signs which regulate the different conditions of the PHYSICAL THEORY OF MUSIC

performance; these will be afterwards explained. Quality of Musical Sound.—The result of continued, rapid, and isochronous vibrations, which produce on the organ of

Fig. 135. hearing a prolonged sensation, is called a musical sound. Such & sound can always be compared with others of the same kind as to their unison or discord; and in this respect it is to be wholly distinguished from mere noise. The ear can perceive

ut ré mi fa sol la si ut ré mi fa in musical sounds three particular qualities—height, intensity, and distinctness ; the last of which the French call timbre.

The impression made upon the organ of hearing by the greater or less number of vibrations made in a given time, is called the height of a musical sound. Sounds which are pro

bangi la ei us re mi fa sol la a duced by a small number of vibrations, are called low; and those which arise from a great number of vibrations, are called

The notes of the gamut can be represented by numbers. high. Those sounds, therefore, which are at the extremities of the scale of perceptible sounds, are properly called low For this purpose, we take for ut, the fundamental sound of the or high. All the intermediate sounds are called low or high sonometer explained in a former Lesson ; that is, the sound only in a relative manner. Yet we speak of a low sound or a produced by a cord vibrating throughout its whole length. high sound, as we speak of a low temperature or a high By varying the position of the moveable bridge B, fig. 129, No.1, temperature, by comparing the sound with those which most page 362, an experimenter, who has a practised ear, can easily commonly fall upon the ear. The relative depth or height of find the length which must be successively given to the two sounds is called tone; that is, this word expresses the vibrating part a B, in order to produce the six other notes. degree of the height of a given sound; and in a musical point which gives ut, we find that the lengths of the cords which

Thus, by representing by unity or 1, the length of the cord of view, it expresses the degree of the height of the scale to give the other notes will be represented by the following which it belongs.

It has been already shows that tne intensity or the force of scale of numbers containing fractions of unity :the sound depends on the amplitude of the oscillations, and not Names of the Notes

(A)

ut, re, mi, fa, sol, la, si; on their number. The same sound may preserve the same Relative lengths of the Cords 1, 4, , 1, , %, f. degree of height or depth, and yet assume a greater or less

Thus, the length of the cord which gives the note ré, is only intensity, according to the amplitude of the oscillations which of the length of that which gives the note ut ; the length

of produce it. This is seen in a tense cord, as it is made to the cord which produces the note mi, is only of that which depart more or less from its position of equilibrium. Distinctness, or timbre, is observed in the case of two dif- which are employed to represent the notes of the gamut,

produces the note ut; and so on. Such are the numbers ferent instruments which yield each & sound of the same according to the relative length of the cords which produce height or intensity; and yet these two sounds can be per- them. By continuing to advance the place of the bridge on fectly distinguished from each other. Thus, the sound of the the sonometer, we find that the eighth sound produced by the hautboy is very different from that of the flute; or the sound half of the length of the cord is the same as the fundamental of the horn from that of the bassoon. In the same way, the sound. The same series of ratios already given recommences human voice varies much; that is, it presents a very different at this sound, and we obtain a new gamut, perfectly cortimbre, according to the individual, the age, or the sex. The

responding to the first; the length of the cord corresponding cause of this quality is unknown. It appears to depend not to each note of this second gamut, being the half of that only on the matter of which the instruments are composed, which answers to the note of the same name in the preceding but also on their form, and on the mode in which they are put gamut; and so on, for a third and a fourth gamut. in action. Thus, the sound of a brass trumpet is completely In order to ascertain the relative number of vibrations in changed by being strongly heated in an oven, and a straight the same time corresponding to each note, we have only to take trumpet has a louder sound than a curved one.

the reciprocals of the fractions in the preceding table ; for, Unison.-When two sounds are produced by the same according to the first law of the vibrations of cords, formerly number of vibrations per second, they are said to be in unison; stated, the number of the vibrations of a cord is in the inverse that is, they are equally, low or equally high. Thus, the ratio of its length. Representing, therefore, the number of wheel of Savart and the siren are in unison when their counters the vibrations of a cord which give the fundamental sound ut indicate the same number of vibrations in the same time. The by unity or 1, we have the following table (B) of the reciunison of a musical sound can always be determined; but not procals of the preceding table (A) :that of a noise. The number of vibrations of any sonorous body is, in fact, determined by putting it in unison with the (B) Relative Num. of Vibrations

Notes of the Gamut

ut, , mi, fa, sol, la, si; siren.

1, 4, 6, 1, 3, , 14 The Musical Scale, or Gamut.-We give the name of the The gamut, of which the ratios of the vibrations of the notes Musical Scale to a series of sounds separated from one another have now been given, is called the Diatonic Scale; the gamut by intervals, which appear to have their origin in the nature of which proceeds by semitones, and which contains thirteen our organization. In this series, the sounds are reproduced sounds, is called the Chromatic Scale. in the same order by periods of seven sounds, each period being Abrolute Number of Vibrations to each Note.--The siren affords denominated a Gamut, and the seven sounds, or notes of each a simple method of deducing from the preceding table the gamut, are known by the names, ut, ré, mi, fa, sol, la, si. real number of vibrations which are produced by each of the

The notes of the Gamut are represented to the eye by notes of the musical scale. Thus, if we put this apparatus in placing them on what is called the staff, which consists of five unison with the fundamental note ut, it will point out to us parallel straight lines and four intervening spaces. The the exact number of vibrations which correspond to this note. double staff used for the music of the pianoforte represents, We have then only to multiply this number by the ratios , within its extent, a series of three octaves, as exhibited in the 4, etc., of the preceding table, in order to find the exact following table, fig. 135.

number of the vibrations of the other notes. When it is necessary to go beyond the extent of this staff, Now, as the fundamental sound which is taken for the note two methods are used. The one consists in giving to the ut, varies with the length of the cord of the sonometer, with its notes which exceed the normal staff, a supplementary staff, by tension and with its nature, so the number of vibrations corVOL. IV.

104

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