ܪ ; and this fraction is read fire-twentieth parts, or simply fire. noted by the denominator. We have said that the denominator of twentieths, of a loaf. If we wish to express in figures the whole of the fraction is neither multiplied not divided, but we might have tho parts into which any whole thing or unit has been divided, we said also that it is neither added nor subtracted, but remains simply as must write this number of parts above the line as well as below the name of the fraction in such operations ; for to multiply by 4 it. Thus, if we wish to express in figures the whole of the parts is the same as to add ļ to itself by repeating it as often as the num. of a loaf divided into 20 equal parts, we must put 20 above the ber 4 denotes ; thus, 8 +++. Here the sum of repeated line and 20 under it thus å8 ; and this fractional expression is read 4 times is **, which is the same as multiplying by 4. Again, to twenty-twentieth parts, or simply twenty-twentieths, of the loaf. divide by 5 is the same as to find the number of fifths which We have called this only a fractional expression, and not a fraction, must be subtracted 5 times from 2h in order to leave no remainder. because although it is written in the form of a fraction it is not Now, as we know that the number 5 is contained in the number 20 really a fraction, but a whole or unit, seeing that it expresses all four times it is plain that must be substracted from five times the parts into which the unit or loaf is supposed to be divided; for in order to leave no remainder; that is, . --*-*-*-=0, or it is an axiom that the whole is equal to all its parts. If we suppose 4 is contained in * five times; hence 22 divided by 5 gives for two equal sized loaves to be divided each into 20 equal parts, and the quotient. We wish to express in figures a number of parts greater than 20 of 6. By extending our view of the nature of fractions exhibited in these parts, say 25 parts, we must write this number above the line the preceding paragraph, we may say that every expression in. and the number of parts into which each loaf is divided below the volving a dividend and a divisor is a fractional expression ; and linie thus 26; and this fractional expression is read troenty-five further, that the quotient, whether whole or mixed, is that fraction twentieth parts, or simply twenty-five twentieths, of a loaf. Now, or part of the dividend which the divisor denotes. Thus, it is a though this expression is written in the form of a fraction, it is plain fractional expression, in which 31 is the dividend, and 17 is the that it expresses more than a fraction, that it expresses first 30, divisor; in its present form, it is called an improper fraction, actwenty-twentieths, of a loaf, that is, a whole loaf; and then 2, cording to our definitions given above ; but if we take the quotient, fire-tuentieths, of a loaf, that is, an additional fraction of a loaf. which is 2 (for 1=2), we find that the whole number, 2, is that 3. DEFINITION 1.-In every fraction or fractional expression, part of the dividend 34, which the divisor 17 denotes ; that is, 2 such as those above considered, the number written above the line is is the seventeenth part of 34; or, in a fractional form, 2 is '; of called the numerator, because it expresses or shows the number of 34. Again, 4. is another fractional expression, where the quotient parts of which this fraction or fractional expression consists; and of 49 divided by 8; that is, the mixed number 6) is that part of the number written below the line is called the denominator, because the dividend 49 which the divisor 8 denotes; in other words, 6) is it expresses or shows the number of parts into which the whole the eighth part of 49 ; or 6} is of 49. By a mixed number, in thing or unit is divided, of which the fraction or fractional expression contradiction to a whole number, we mean an expression consisting is given, and also because it gives name or denomination to these of a whole number and a fraction, as 6% ; now as 6) is the quotient parts. Thus, in the fraction, the number 5 is called the numerator, of 4, it is plain, that these two expressions are equivalent to each . the number 20 che denominator ; also, in the fractional expressions other, or that 6)="". Therefore, every mixed number is re29 and 36, the upper numbers 20 and 25 are called the numerators, ducible to an improper fraction. We have, in this case, only to and the lower number, 20 in each, the denominator. The numerator reverse the process in order to obtain the expression required; that and denominator of a fraction are called the terms of the fraction. is, to multiply the whole number 6 by the divisor 8, add to the 4. DEFINITION 2.--Every real fraction has its numerator less than product 48, the numerator 1, and under the dividend 49 thus obits denominator ; and is, therefore, called a proper fraction. Thus tained, put the divisor 8, which gives you for the fractional expression u is a proper fraction, because its numerator is less than its deno. originally proposed. minator. A fractional expression, on the contrary, which has its 7. In the case where the dividend is less than the divisor, as in numerator equal to, or greater than its denominator, is called an the fraction }, no other quotient can be obtained than $, and this improper fraction. Thus , and are improper fractions, because expression considered as a quotient, indicates that $ is that part of the numerator of the one is equal to its denominator, and the numer. the dividend 4 which the divisor 5 denotes; that is, $ is the fifth ator of the other is greater than its denominator. It is plain from part of 4. Hence, we justly infer that the fifth part of 4, is the what has been said above that every fractional expression whose nu- same as four-fifth parts of 1 ; or } of 4 is equal to 1 of 1. Thus, merator is equal to its denominator, as s', or %, or, is just exactly we see by reverting to article 5. (i. e., the paragraph marked 5 equal to unity or l; and every fractional expression whose numera- abore) that four-fifths of one quartern loaf is the same as one-fifth tor is greater than its denominator is greater than unity or l; and of four quartern loaves ; or, that in order to divide 4 quartern it is greater in proportion as the numerator exceeds the denomina- loaves among 5 people, we may either divide cach loaf into 5 equal parts, and give away 4 of each to 4 persons, when there will be 4 5. There is another method of viewing the nature of fractions left for the 5th person; or, we may divide the 4 loaves into 20 equal which must not be omitted, and which, indeed, we have already men- parts, and give 4 parts to each person, until the whole 20 parts are tioned in our Lessons in Arithmetic, No. IX., p. 141, vol. I.' This exhausted, and the 5 persons have each had their share. method consists in considering every expression denoting the quo- 8. DefinitioX 3.-A compound fraction is a part or fraction tient of any given number by a larger number as a fraction. The rea- of another fraction. Thus, we have in the preceding examples, shoan son of this is very plain from the following example: Suppose that we how to divide 4 loaves among 5 persons, and we have found that each have to divide four quartern loaves among five persons, and that person's share is of a loaf. Now if one person who had received each person is to receive an equal share of the bread, it is evident % of a loaf were to divide bis share among 3 boys, it might very that we cannot give each person one loaf, but something less than a naturally and properly be asked what part or fraction of a loaf did loaf. How then shall we proceed? We must divide each of the each boy get ?' The answer of course would be one-third of 4 of a four loaves into as many parts as will enable us to give an equal loaf, or} of . Now this is a compound fraction, and the ques. share to each person, and therefore all the parts of these loaves tion is to reduce it to a single or simple fraction of a loaf. It is to taken together must be such as to be exactly divisible by the num- be considered here, first, that each of the $ of a loaf is } of a loaf, ber of persons, namely, five. This can be most easily accomplished and that if this ! of a loaf were divided into 3 equal parts, one of by dividing each loaf into five equal parts, and consequently the these parts would be its of a loaf; for if all the 5 equal parts of a whole four loaves into turniy equal parts of the same kind ; thus loaf were each divided into 3 equal parts, there would be 15 such cacha loaf is represented by the fractional expression, five-fifths, equal parts in a loaf, and of course, each part would then be 1's of of a loaf; aud the whole four loaves are represented by the fraco a loaf, according to article 1. Hence } of } of a loaf, is 15 of a tional expression , tuenty-fifths, of a loaf; for x 1= If loaf; and as there would be four of these parts in 9 of a loaf, so these 2.o, tuenty-fifths, be divided by 5, the number of persons, there is 7 of a loaf in of of a loaf; and thus, the compound the quotient will be 5 of a loaf to each person; for .=-5=s. It fraction of = 15, a single or simple fraction; thus also we see will be observed in these operations of multiplying and dividing any that the two denominators, 3 and 5 of the single fractions } and 3, number of fifths by a whole number, such as 4 or 5, that the de- which form the compound fraction, must be multiplied together in nominator of the fraction is neither multiplied nor divided, because order to find the denominator of the single fraction composed of it is only the name of the fraction ; but that these operations are them; and that the two numerators, 1 and 4, must be multiplied performed only on the numerator, because it is the numerator only together, in order to find the numerator of the same. In like ibat expresses the value of the fraction as so many of the parts de manner it may be shown that the compound fractions of f is tor. THE POPULAR EDUCATOR. equivalent to the simple fraction * But fractions may be still mains the same, to multiply the dividend by any number is in effect more compounded ; for we may divide each of the preceding com- multiplying the quotient by that number; and, if the dividend repound fractions into smaller parts, siy each balf of the former ; mains the same, dividing the divisor by any number, is in effect and then the expressions will be of of $, or of g of ; which multiplying the quotient by that number. Here we have only, as are respectively equivalent to al; and 55, as may be found on the before, to substitute the words denominator, numerator, and value, same principles as those above developed. for the words divisor, dividend, and quotient respectively, and the 9. Definition 4.-The value of a fractiou, or a fractional principles are one and the same, as before. To exemplify the expression of any kind, is the simplest form in which it can be former, let us take the fraction it, and let its numerator we multiexpressed. Thus, the value of the fraction is , because if a plied by the number 4, its denominator remaining the saine ; the unit be divided into 10 equal parts, and 5 of these parts be taken result is 18. Now, taking any unit of which the value of the fracin order to constitute a fraction, it is plain that its value must be tion can be easily found, say a pound Avoirdupois; it is plain of the unit, seeing that the number of parts taken is just one that as i'd of a pound is 1 ounce, so i'd of a pound is 3 ounces, and half of the whole number of parts. Again, the value of the frac- lê of a pound is 12 ounces; but 12 ounces are 4 times 3 ounces; tion 4, being simply of a unit, it is already in the simplest form therefore, multiplying the numerator of the fraction * by any num. which it will admit of; for to say that its value is } of 4 units, is to ber, 4 increases its value, viz., 3 ounces, as many times as that number render the expression more complex than before. But if the nature denotes, viz., to 4 times 3 ounces or 12 ounces. Aguin, let the of the unit of which the fraction is a part be stated, it is then denominator of the fraction is be divided by the number 4, its possible to arrive at a simpler expression for the value of the frac- numerator remaining the same; the result is 1. Now, taking the tion ; thus, if the fraction be of a pound sterling, we can now, by same units as before, we find that is of a pound is 3 ounces, and 1 a few considerations, arrive at a simpler form of its value; for we of a pound is 12 ounces (1 of a pound being 4 ounces); but, as be. know that } of a pound is 4 shillings, consequently of a pound is fore, 12 ounces are 4 times 3 ounces; therefore, dividing the 4 times 4 shillings, or 16 shillings, which is the value required; and denominator of the fraction by any number 4, increases its value every one will admit that 16 shillings is a simpler form of expres- 3 ounces, as many times as that number denotes, viz., to four times sion than of a pound. Next, as to fractional expressions : such 3 ounces, or 12 ounces. Besides, we know that i=1; for if both as 12, 13, 1979, &c. It is plain that the value of is the number the numerator and denominator of the fraction à be divided by 5, an expression much more simple than the fractional expression any number, say 4, its value will not be altered. Whence, multiitself ; also the value of ** is 5 g; or 5 }; either of which expres- plying the numerator only of a fraction, or dividing its denominator sions is more simple and easy to be understood than the original only, by the same number, multiplies the fraction by that number, one; and in like manner, the value of 1979 is 59 17; a value of 12. PrincipLE 3.-If the numerator only of a fraction be which every one understands the integral part 59, if they do not divided by any number, the denominator remaining the same, quite understand 17; but of the original fractional expression the ralue of the fraction is diminished as many times as tbat 1444, thousands would have no conception; yet with regard to number denotes; or, if the denominator only of a fraction be this very expression, there is no mystery in it at all, for it simply multiplied by any number, the numerator remaining the same, means the seventcenth part of 1010, or is of 1010; and its meaning the value of the fraction is diminished as many times as that is clearly understood, when we say that the screnteenth part of number denotes. This principle combines the two general 1010, is 59 and a fraction; or, 59 and 17;or, 59, and a seventeenth principles of Division laid down in Vol. I., p. 380, col. 1, Nos. part of 7. We come now to three important principles, which must 11, and III., viz. If the divisor remains the same, dividing the be perpetually kept in mind in the whole of our operations relating dividend by any number, is in effect dividing the quotient by that to Vulgar Fractions. number, and if the dividend remains the same, multiplying the 10. PRINCIPLE 1.-If the numerator and denominator of a divisor by any number is in effect dividing the quotient by that fraction be both multiplied by the same number, the value of the number. Here, again, if we substitute the words denominator, fraction is not altered, that is, the valuu of the fraction remains the numerator, and value for the words divisor, dividend, and quotient same as before ; and if the numerator and denominator be both respectively, the principles will be found to be identical. To divided by the same number, the value is not altered, that is, the exemplify the fornier, let us take fraction lë, and let its numevalue remains the same as before. This principle is the same in rator be divided by the number 4, its denominator remaining the effect as that general principle in division laid down in vol, I., p. 380, same; the result is 15. Now, if we guppose the unit to be a pound col. 1, No. V., viz., that if the divisor and dividend are both mul- Avoirdupois as before, then it is evident that is of a pound is 12 tiplied or both divided by the same number, the quotient will not ounces, and is of a pound is 3 ounces; but 12 ounces divided by be altered. Here we have only to substitute the words denominator, 4 gives 3 ounces; therefore, dividing the numerator of the fraction to numerator, and value for the words divisor, dividend, and quotiević by any number 4, diminishes its value, viz., 12 ounces, as many times respectively, and the principles are one and the same. But in order as that number denotes ; for 12 ounces - 4 = 3 ounces. Again, to illustrate the former, let us take the fraction 15; if we multiply let the denominator of the fraction 13 be multiplied by the number both numerator and denominator of this fraction by 10 its value 4, its numerator remaining the same; the result is 1, which by will not be altered, for it then becomes . Now, whether a unit principle 1, Art. 10, is it; for i= my by dividing both numer. be divided into 10 equal parts, and 5 of them be taken, or into ator and denominator by 4. Hence, multiplying the denominator 100 equal parts and 50 of them be taken, it is plain that half the only of the fraction 13 by any number 4, diminishes its value as number of parts is taken in either case, and that the value of these many times as that number denotes, for, 12 – 1= 3, and = parts is of the whole in both fractions, so that the value of the is as before. Whence, dividing the numerator only of a fraction, fraction remains unaltered ; that is, 1:500. Again, let us take or multiplying its denominator only, by the same number, divides the fraction 15; if we divide both numerator and denominator of the fraction by that number. this fraction by 25, its value will not be altered, for it then becomes 1. Now whether a unit be divided into 100 equal parts and 75 of them be taken, or into 4 equal parts and 3 of them be taken, it is evident LESSONS IN GERMAN.-No. XXIV. that three-fourths of the number of parts is taken in either case, and that the value of these parts is of the whole in both fractions ; Section XLIV. for 25 parts is of 100 parts, and as 75 is 3 times 25, thererore 75 I Mern, gladly, freely, fain, &c., (comparative fiber, ratlst, parts is 1 of 100 parts; also, 1 part is of 4 parts, and 3 parts is See $ 106. 1.) with an appropriate verb, forms the equivalent of 4 parts; so that the value of the fraction remains unaltered; of our phrase, "to be fond of, to like," &c. Ex.: ininti that is 76=; gern Wein; he is fond of (drinking) wine. Gr raudt gern; 11. Principle 2.-If the numerator only of a fraction be multi- he is fond of smoking; or, he likes to smoke. Gr trige gern plied by any number, the denominator remaining the same, the schone Kleiter ; he likes (to wear) finc clothes. Id mitte ger tt value of the fraction is increased as many times as tbat number de wissen, rb mein freund nu lebt; I would fain know whether my notes ; or, if the denominator only of a fraction be divided by any friend is still living. ?d) midte licöer geben, als bleiben. I number, the nuinerator remaining the same, the value of the fraction is increased as many times as that number denotes. This principle For conjugation of dürfen, fönnen, mögen, &c., in the subjunctive combines two of the general principles in Division, laid down in Sce s 83, 2, &c. See also remarks connected with these convol I. p. 380, col. 1, Nos, I. and IV., viz. :-If the divisor re- jugations. would rather go than stay. With haben, it may often be Wohl bes're Männer thun's tem Better men do it not after the rendered by "dear." Ex. : Idh habe meine Freunde gern; I hold Tell nicht nad. (Schiller). manner of Tell (as Tell did). (have) my friends “dear." Es war ein gutes Jahr, der Bauer It has been a good year; the II. Nöthig haben, signifies, to need, to have need of. Ex.: fann schon wieder geben. (Schil. peasant can even (now) give Haben Sie bicies Buch nöthig; Do you need (have you need of) ler.) again. this book? Er hat Geld nöthig; he needs money; or, has need Den Mörder wird die gerech'te The righteous punishment will of money. Strafe schon erei'len. certainly overtake the mur Ill. Im Stante sein, signifies, to be able; literally, to be in derer. the position or situation. Ex.: Sind Sie im Stande zu schreiben? 1. Sehen Sie meinen Schwager gern? 2. Ja, ich sehe ihn geri. Are you able to write ? In this construction the verb de. pendent upon im Stunde sein“ is often omitted and the pro. 3. Der Oheim möchte gern eure Zeichnungen sehen. 4. Ich habe gern noun es, is introduced. (Sect. 36. VI.) Ex.: IM bin es nicht Freunde in meiner Nähe. 5. In meiner Jugend studirte ich sehr gern, im Stante; I am not able. aber nun thue ich es 1!ngern. 6. Gr spridit gern von seinen Reisen und IV. Several words, as toch, in, ichon, vielleicht, wohl and zwar seinen Erfahrungen. 7. Wenn sie die Bücher nöthig haben, so leisje ichy &c. are often used with a signification different from their primary one, or where no corresponding one is employed in Ihnen dieselben von Herzen gern. 8. Er trennt sich ungern von seiner English. Ex. : Sind Sie vielleidst frant? Are you (perhaps) Familie. 9. Itty habe gern ein warmes Zimmer. 10. Könnt ißr uns sick? Werten Sie wohl morgen abreisen? Shall you (probably) idyer über diesen Strom fahren? 11. Nein, wir sind es nicht im Stande depart to morrow? Er wird 113 liten finden; he will already denn dieser Nachen ist zu flein. 12. Wenn Sie fähig sind, diese Zeitungen (doubtless) find us. Wenn er frant ist, To fann er nicht fommen; 1 zu überlegen, so thun sie es. 13. Da ist die englische Sprache vollfommen if he is sick, (then) he cannot come. Er liegt nicht und zwar, weil er fein Buch ljat; he does not read, (and indeed) because verstehe, so will ich gern Ihren Vorjihlag annetmen. 14. Wenn er fähig he has no book. Gehen Sie ja nicht ; do not go by any means. ist, die Arbeit gut zu machen, so soll er zu mir fommen; ist er es aber nid;t Es tirste (See note) wohl so femmen; it might indeed so happen im Stande, so wäre es unnüş. 15. Er glaubte nicht, taß ich im Stante (come). Wollen Sie schon gehen? Are you going already? Ja. Teir fönnte, all seine Befehle auszuführen. 16. Wenn du deine feiten. wohl; yes, (certainly) or, yes, indeed. Ich glaubte, er fönnte unsichaften ganz zu beherrschen weißt, fo bist du zu beneiten. 17. Mein iden hente besuchen ; I thought he could (already) visit us to-day. Freund Gruarð wir jo idwach , taß er nicýt im Stande war, allein zu Er glaubte, er fönne sich wohl jetzt an ihm richen; he thought he could now (indeed) avenge himself upon him. gehen, und er bat mich deßwegen, daß icy ihu führen möchte. 18. Er V. The causative adverbs, deshalb or teßwegen (therefore) dira glaubte, daß Niemand im Stante sein tonne, auf dieses rauße Papier zu turdy, (thereby) &c., are frequently introduced into a leading schreiben. 19. Er Hatte gestern Geld nöthig, teßhalb bat er mich, daß ich sentence where the corresponding English word is omitted. ihm einiges geben midte. 20. Er ist mir zwar schon einige Thaler Ex.: Er ist toibals unzufrieden, weil sein Freund nicht hier ist; he is itutrig, aber ta er das Geld nötlig ḥatte, so gab ich ihm welthcs. 21. G# (therefore) discontented because his friend is not here. VI. Schulrig with sein, signifies “to be indebted, to owe;" ist Niemand im Stante außzugehen, weil es zu start regnet. 22. Er wird the word denoting the amount being put in the accusative. bald im Stande sein, sein Werk zu vollenten. 23. Er faun sein Wort ($ 132. 3.) Ex.: Er ist mir nur einen Gulden schuldig; he owes nicht halten und zivir aus foigenden Grünten. me but one florin. Bertanken also signifies to owe, but only in the sense of “to be obliged for, to ascribe to.” Ex.: Id vero have undertaken it. 2. Will he be able to fulfil ' his promise ? 1. If he had not been able to perform the work, he would not cunfe meine Genesung ter reinen lust der Schweiß; I owe my recovery 3. Ile has not been able. 4. We ought not to promise more to the pure air of Switzerland. than we are able to perform. 5. Are you able to deliver a better EXERCISE 48. explanation upon this subject ? 6. I am indeed able, but I Alfgeben, to deliver; Führen, to conduct, Sicher, safe, safely; have no time now. 7. Does the boy go for my stick freely ? Aus'führen, to carry guide; Stand, m. position, 8. When he does, it is unwillingly; I would rather go myself. Ve genstand, m. sub (III.); 9. Do you like to see your relations ? 10. Yes, I do like to see Befehl', ject; Studi'ren, to study ; them. 11. When you have need of those books, then I wil mand; Gern, willingly, (I.); Ueberse'ben, to trans. lend you them freely. 12. He needed money yesterday, thereBehert'svjen, to go. Grund, m. ground; late; fore he desired me that I would give him some. 13. Therefore vern, rule; Heilen, to heal; Ungern, unwillingly; it is useless to ask for more, when you already owe so much. Eruart, m. Edward; lei’tenschaft , f. pas. linnug, useless, fruit. 14. Who would not freely heal the wounds of a wounded heart. Grfalʻrung, f experi. less; ence, knowledge; leihen, to lend ; Rollen'den, to finish, SECTION XLV. Erklärung, f. expla. Nachen, boat, complete ; nation; skiff; Vorschlag, m. proposal; The conditional mood is used where a condition is supposed Familie, f. family; Nun, now; Wunde, f. wound; which may or may not be possible. It is also sometimes used Folgen, to follow; Rauh, rough ; Zeidnung, f. drawing. in exclamation and interrogation. Ex. : Wenn sie noch lebte, wäre ich glücklich; if she were still living, I should be happy. Idy Er fommt nicht, und zwar weil er He does not come, (and indeed) tätte die Sache anters gemacyt ; I should have arranged the matter frant ist. because he is sick. differently. Ware er doch noch am beben! O, that he were still Mein Onfel fisicht und meine Neffe My uncle is fond of fishing, and alive! Wäre es möglidy, Bater? could it be possible, Father ? jagt gern. my nephew of hunting. (See $. 144.) Ich mötte gern wijfen, wie viel Uhr I would like to know what EXERCISE 49. e8 ist. o'clock it is. orciheit , Gerechtigfeit und Wahr. Liberty, righteousness, and Nu'forterung, f. claim, Vrúce, f. bridge ; Heim'suchen, to visit; heit sollten alle Menschen gern truth, all men should love. demand ; Einlassen, to engage; Hier'bleiben, to remain haben. An gelegenheit, f. trans- Entspre'chen, to here; Wieviel' bin ich Ihnen cultig? How much do I owe you? action, aflair; answer ; Mit'theilen, to impart; Er vertunft' sein Leben ter Schuel's He owes his life to the fleetness An'yaltend, persever- Grípa'ren, to spare, Soweijen, be ligfeit seines Partes. of his horse. ing, continual; avoid ; silent; Es ist Niemand im Stinte, tie There is no one able to prede. An'licht, f. view, Ferne, f. distance; Schwerlidy, hardly; Dauer fcinco fcband voraus zu termine the duration of his opinion; fest, n. feast; Sowie'rigfeit, f. dif. bestim'men. life. Aus'treten, step Fort'reisien, to carry ficulty ; Wohl läßt der Pfeil jich aus den: The arrow may indeed be drawn Strand, strand, Herzen zichen, toch nie wirt ter out of the heart, yet the in- Velul'ten, to kerp, Ole'genwart, f pre shore; Verlep'te mehr gerin'ten. jured (one) will neyer recover. out; com sion; CONDITIONAL MOOD. to to forth, appear; (tear) away ; retain ; sence; 71. Un'annehmlichkeit, f.dis. Verpflich'ten, to oblige; Zöllner, m. toll- tator " was an old "standard periodical work." Complete copies of it may agreeableness; Verschwin'den, to gatherer now be ha: in any bookseller's shop, or at any book-stall. Verdruß', m. vexation; vanish; Thomas M'LAREN (Grandtully): We have already said Liddeli and Scott's Lexicon.-L. W.F.: Correct.-E. P. (Wigan) should study Dr. Beard's Verschönern, to em- Widerspre’iten, to con Lessons in English Arst, and then the French. Exercises must of course be bellish, improve ; tradict; written out, and we would advise the rules also to be written out in a book; for by carefully writing out anything, eren once, you thereby fix itin Ich würde tag Vuch noch haben I should still have the book, if the memory.-SINE PRECEPTORU (Fire) is right; there are some misprint wenn ich es nicht verlo’ren hätte. I had not lost it. and inaccuracies in the places to which he refers. We shall take an oppor tunity of rectifying them.-FENELON (Stockwell): Thanks for the follor. Du würdest jett freude haben, wenn Thou wouldst now have com- ing corrections : in vol. 1., p. 76, col. 2, line 20 from bottom, for mauvais read Du teine Schul'rigkeit getban' fort, if thou hadst done thy mauvaise; p. 78, col. 1, line 32 from top, for boiteaux read boiteux; col. 2 Vättest. duty. line 2, for amusunt read amusant ; p. 171, col. 1, line 25 from bottom, fur the first chantons read chansons; p. 261, col. 2, line 1, for barber read Gr' würde bei'iere Freunde haben, He would have better friends, barbar, in the German.-SIGMA (Dollar): Thanks for his observations and wenn er auf'richtiger wäre. if he were more upright. suggestions; they will be attended to.-CRSAR (Walworth): Thanks.-C. Wir wütten Geld haben, wenn wir We should have money, if we W. STYRING (Doncaster): Soon.-APPRENTICE (Edinburgh): Only two errors in 1 and 5.-R. H. HAMMOND: We can't exactly say.-P. (Milford spar'jamer wären. were more economical. Haven): Her verses are very creditable indeed.-J. J. NEWTON (Bridge. Ihr würtet Trauer statt Freude You would have sorrow, in water) : Right.-D. D. (Kincardinshire): Rue St. Honore.-J. W. (Wacer): haben, wenn tas Kind gestor'ben stead of joy, if the child had Thanks for his suggestions.-H. Wilson : On the different kinds of galvanic or hydro-electric batteries, see Peschell's Physics, vol. III., p. 75–91. wäre. died. AŃ ALGEBRAIC STUDENT has proposed two questions which, from their Sie warten mehr Klugheit haben, They would have more pru- manner of statement, are literal absurdities, thus : 1. "To find the side of a wenn sie mehr Verstand hätten. dence, if they had more un square whose area is equal to twice the sum of the sides; and 2. To find the side of a cube whose solid content is twice its surface.” An area or a derstanding. number of square inches can never be equal to a length or number of long Gr würte ein großes Glück gehabtle would have had a great inches ; and a solid, or a number of cubic inches, can never be equal to & haben, wenn er we’niger träge fortune, if he had been less surface or a number of square inches ! Yet the number which expresses an slothful. gewe'sen wäre. area may be equal to the number which expresses a length; and the nun ber which expresses a solid content may be equal to the number which 1. Iity hätte mir schon machen Verdruß (Syn.) ersparen können, wenn questions have any meaning; their solution is quite easy. 1. Put the expresses a surface. In these senses, and in these only, can the preceding ich, statt zu widersprechen, geschwiegen hätte. 2. Ich möchte wissen, was square of x (the side of the square', equal to twice four times 5, or twice Sie gethan hätten, wenn Sie an meiner Stelle gewesen wäre. 3. Wenn the cube of x (the side of the cube), equal to 6 times the square of r, or the the sum of the sides, and you find x is equal to 8, the first answer. 2. Put das Sdicíal mich nicht heimgesucht hätte, würde ich schwerlich zu riesen surface of the cube, and you find * = 6, the second answer.-QUADRANT : Really we cannot say.-GEORGE AMBROSE DAMERHAM: Riddle's Young Ansichten gefommen sein. 4. &r hätte glüdlich sein fönnen, wenn er die Scholar's English-Latin Dictionary 5s., and Latin-English Dictionary is. Gelegenheit zu benußen verstanden hätte. 5. Hätte das Wasser tie Brücke is by no means necessary to go back to pothooks and strokes ; many persons mit fortgerissen, so wäre der Zöllner verloren gewesen. 6. Hätte ich zu would admire her writing ; ve admire her desire for improvement; and reDir Pommen können, so würde ich gewiß nicht hier geblieben sein. 7. Es from A to Z; then two or three copy-books of the half text, or next size of würden nie große Männer aufgetreten sein, wenn sie sich durch Schwierig, writing, from A to 2; and lastly, two or three copy-books of the courl-harul from A to Z; and if she will attend to the method of holding the pen, and of feiten und Unannehmlichkeiten hatten aufhalten lassen. 8. Wenn ich tas sitting at the table, which we have recommended in Lesson 1. of Penmanship, kätte erreichen wollen, was ich wünschte, so hatte icy fleißiger und anļaltenter we feel quite certain that her next letter to us will both astonish ber and arbeiten müssen. 9. Wennn er gerufen hätte, würde ich ihn gehört haben. A SUBSCRIBER : There is an "express" almanack for the P. E, and it 10. Wir wollen nicht ausgehen, es möchte regnen. 11. Wenn Sie mit is not the same as the one for the . Illustrated Exhibitor, "-see Literary etwas Näheres über diese Angelegenheiten mittheilen (Syn) möchten, To try and give each an hour or two a-week, and not alternately.-UN SOLDAT wirten Sie mich sehr verpflichten 12. Es wäre meine größte Freude, mons, when applied to the indicatire mood; quani, when applied to the alle Menschen glüdlich zu sehen. 13. Id hätte ohne Verstand (Syn.) ein subjunctive, is a synonyme for si; your note is pretty correct.-J. A. F; müssen, wenn ich mich auf diese Sache hatte einlassen wollen. 14. Ver course his book on that subject.-Y. P. F. (llounslow): See p.288, vol. 1. , schwunden ist der Strand in der Ferne, o wie gerne, wär' ich noch im Vater, col.2, line 19.-S. G. (London): Terpsichore, pronounced terp-sick-o-re. land! 15. Wenn er wäre, wie ich ihn wünsche, und wenn er allen meinen be attended to.-J. T. (South Shields) need not expect to find corresponding Anforderungen entsrrochen hätte, würde ich ihn behalten þaben. (Wolverhampton): A scalene triangle inay also be a right angled triangle. 1. Had your friend not become ill, he would certainly have and 5 inchos in length; and it will be a scalene right angled triangle embellished the seast by his presence. 2. If you were more Juvenile CHEMIST, &c. (Notting-hill): We do not see the application of prudent, you would not have met with this inconvenience. his citation from Newton. Righi in the arithmetical question. But his 3. I would have settled your business, if you had mentioned it own must lie over at present. to me. 4. His brother would have been better received, if he had had letters of recommendation. 5. He would have better LITERARY NOTICES. friends, if he were more agreeable. 6. You would have had ALL NOW READY. more difficulties, if you had not followed the advice of your Price 1s., beautifully printed, super-royal 8rc., friends. 7. I should not have the least doubt, that you would THE UNCLE TOM'S CABIN ALMANACK; or, The À BOLITIONIST have succeeded, if you acted more prudently. 8. We should MEMENTO FOR 1853.- The most complete work on the question of slavery set sail for Holland, if we had a fair wind. 9. He would be that has hitherto been published. Everybody who has read " Unde Tom's the first among our merchants, if he were more sociable. Cabin” should possess themselves of a copy of this book, which more than 10. If I had had the power, I should have acted in another verifies all the statements in Mrs. Stowe's thrilling narrative. This work is manner, because I should not have had so much patience. splendidly Illustrated by George Cruikshank, Esq.; J. Gilbert, Esq.: 11. What would be the felicity of man, if he always sought Harvey, Esq.; 11. K. Browne, Esq. (“ Phiz”); and other eminent artists ; and his happiness in himself? 12. You would be richer, if you contains upwards of 70 pages super-roy al 8vo., replete with the most etienne were more enterprising. incidents-Lives of Escaped Negroes; the Workings of the Fugitive Slave Law; Anecdotes, Narratives, and Historical and Descriptive Accounts of ANSWERS TO CORRESPONDENTS. American Slavery. The sale already is very large, nearly 20,000 copies having been disposed of in a fortnight. JUVENIS DISCIPULUS (Wigton) should consult a variety of works on the ILLUSTRATED Exhibitor ALMANACK, Thirty splendid Engravings, 6l. ancient laws to which he refers. He will get information in some of the large Popular EDUCATOR ALMANACK, Notices and Essays on Education , 2. al Dictionaries recently published.- Cos: His solution is riglit. Il be glad to see his perpetual calendar.-J. W. D. (Lambeth): TEMPERANCE ALMANACK, Tale by the Authoiess of U'ncle Tom, &c., m. ince M. N. measures 215 equal parts, and the distance P. M. measures PROTESTANT DISSENTERS' ALMANACK, with new Historical Notices,&c. 6d. parts.-CHARLES HUGHES (London) has made a good selection of CASSELL's Elements or ARITHMETIC, 18. paper cover; Is. Gl, neats let him go on and prosper. Cassell's Arithmetic is intended for bound in cloth. o with that other.-B. P. (Islington): bee Bradshaw.. Continental Guide." Printed and Published by John CASSELL, La Belle Sauvage Sard, Ludgatealloch's " Commercial Dictionary."-J. A, (Leicester): The "Spec. hill, London, November 27, 1852. W. NUMEROUS applications having been made to us regarding the Describe and explain the Barometer, the Siphon, the ominor inquiry whether SELF-TAUGHT students are permitted to Matri- Pump and Forcing-Pump, and the Air-Pump. culate at the University of London-that is, to enroll their names Acoustics. in the list of UNDER-GRADUATES of the said University,---we have Describe the nature of Sound. made special inquiry into this matter, and we are enabled to Optics. announce to our students that it is quite competent for any of State the Laws of Reflection and Refraction. them, whether self-taught or not, to become a member of the Explain the formation of Images by Simple Lenses. University of London by passing the Examination for Matri CHEMISTRY. culation, and even to take honours at the said Examination. The The Atmosphere. Its general nature and condition ; its comfollowing are the REGULATIONS of the University on this head, ponent parts. Oxygen and Nitrogen; their properties. which we extract from the “ University Calendar for 1853." Water and Carbonic Acid. Proportions of these substances in the air. Chlorine and Iodine, as compared with Oxygen. Water. Its general relation to the atmosphere and earth; its The Matriculation Examination shall take place once a-year, natural states and relative purity. Sea-water, river-water, and commence on the first Monday in July. spring-water, rain-water. Pure water : effects of heat and No Candidate shall be admitted to the Matriculation Examina. cold on it ; its compound nature; its elements. tion unless he have produced a Certificate showing that he has Hydrogen. Its nature and proportion in water ; its presence in most ordinary fuels ; its product when burnt. completed his Sixteenth year. This Certificate shall be transmitted to the Registrar at least Sulphur, Phosphorus, and Carbon generally. Nitric Acid, Sulphuric Acid, Carbonic Acid; their elements. fourteen days before the Examination begins. A Fee of Two Pounds shall be paid at Matriculation. No Can. Hydrocholoric or Muriatic Acid. didate shall be admitted to the Examination unless he have Alkalies, Earths, Oxides generally. Salts. Their nature generally; Suiphates, Nitrates, Carpreviously paid this Fee to the Registrar. If a Candidate fail to bonates. pass the Examination, the Fee shall not be returned to him, but he shall be admissible to any subsequent Examination for Matricula Metals generally. Iron, Copper, Lead, Tin, Zinc, Gold, Silver, Platinum, Mercury. tion without the payment of any additional Fee. Powers of Matter, Aggregation, crystallization, chemical The Examination shall be conducted by means of Printed Papers ; affinity, definite equivalents. but the Examiners shall not be precluded from putting, for the Combustion. Flame; nature of ordinary fuel; chief results purpose of ascertaining the competence of the Candidates to pass, of combustion, i. e., the bodies produced. Heat. Natural and artificial sources; its effects. Expansion; viva voce questions to any Candidate in the subjects in which they solids, liquids, gases. Thermometer ; conduction; radiaare appointed to examine. tion; capacity; change of form; liquefaction; steam. Candidates for the Matriculation Examination shall be examined The chief elements of Vegetable bodies ; of Animal bodies. in the following subjects : CLASSICS. THE GREEK AND LATIN LANGUAGES. One Greek and one Latin subject, to be selected one year and ARITHMETIC AND ALGEBRA. a-half previously by the Senate from the works of the underThe ordinary rules of Arithmetic, mentioned authors:* Vulgar and Decimal Fractions. Homer ....One Book. Extraction of the Square Root. Xenophon.. One Buok. Addition, Subtraction, Multiplication, and Division of Alge Virgil ....One Book of the Georgics, or the Sixth Book of the Encid. braical Quantities. Horace ....One Book of the Odes. Proportion. Sullust ....The Conspiraey of Catiline, or the War with JuArithmetical and Geometrical Progression. gurtha. Simple Equations. Cæsar .... The Civil War, or the Fifth and Sixth Books of the Gallic War. GEOMETRY. Livy ......One Book. The First Book of Euclid. Cicero .... The Treatises De Senectute and De Amicitiâ ; or NATURAL PHILOSOPHY. two of the shorter, or one of the longer Orations. MECHANICS. THE ENGLISH LANGUAGE. Explain the Composition and Resolution of Statical Forces. The Grammatical Structure of the Language. Proficiency in Composition will be judged of by the style of Describe the Simple Machines (Mechanical Powers), and state answers generally. the Ratio of the Power to the Weight in each. THE FRENCH LANGUAGE OR THE GERMAN LANGUAGE, Define the Centre of Gravity. OUTLINES OP HISTORY AND GEOGRAPHY. Give the General Laws of Motion, and describe the chief ex History of England to the end of the Seventeenth century. periments by which they may be illustrated. The papers in Classics shall contain questions in History and State the Law of the Motion of Falling Bodies. Geography. HYDROSTATICS, HYDRAULICS, AND PNEUMATICS. Easy Grammatical questions shall be introduced in the Classical Papers. Explain the Pressure of Liquids and Gases, its equal diffusion, Simple and easy sentences to be translated from English into and variation with the depth. Latin, shall be introduced in the Latin Paper. Define Specific Gravity, and show how the specific gravity of It shall be indispensable for passing the Exantination that each bodies may be ascertained. Candidate answer the questions and translate the sentences in a manner generally satisfactory to the Examiners in Classics. A popular knowledge only of these subjects in Natural Philosophy will be required, such as may be attained by attending a Course of Experimentul • The Classical Subjects for 1853 are, Homer : Odyssey, Book XI., aud Lectures. Livy, Book III, VOL. II. 25 |