ter that may mer die serve. Am Abent, al die Kinder in das Sclaffämmerlein gingen, VOCABULARY. Am al'-bent, alss dee kin'-der in dass shlaht“-kem'-mer-line ging'-en, Pfirsiche, f. peach. Erziehen, to bring up, Weise, f. manner. frugte ber Bater: Nun wie Haben euch die schönen Aepfel Start, f. town, city. to educate. Raum, m. room. traho-tai dair fah'-ter: Noon vee hah'-ben oiy dee sho'-nen ep-fel Fünf, five. Brav, bravo, good. Sohn, m. son. grignedt? Herrlic, lieber Vater, fagte Aeltefte. Man, one ; French, Das heißt gesorgt für Aufklopfen, to open. son." gai-shmeckt ? Herr'-liġ, lee'-ber fah'-ter, zahch--tai dair eľ-tai-stai. (auf, preposition Frucht, f. fruit. be called, to take and prefix, open, G: ift cine chöne Frucht, so säuerlich und so sanft von Erst, first. care of up, upon, on.) Ese ist i-nai sho'-nai frdocht, zo zoi'-er-lių šont zo zanft fón Deshalb, therefore. (heißen, to be called, Kern, m. kernel. Erstmack. habe mir den Stein sorgsam bewahrt, Apfel, m. apple. command.) Nuß, f. nut. gai-shmack'. rý hah-bai meer dain shtine zory'-zahm bai-vahrt', Röthlich, reddish, Haushalterisch, econo- Berkaufen, to sell. mat will mit daraus einen Baum erziehen. Bade, f. cheek. mically. (Galten, Gelb, n. money. bënt vill meer dah-rouss' i-nen boum err-tsee'-hen. Zart, tender, delicate. to hold, to keep.) Nach, to, after. Pflaum, m. down. Zukunft, f. future. Schütteln, to shake. Bray! fagte der Vater, das heißt Haushalterisch auch Vertheilen, to distri- Geziemen, to behove. Kopi , m. head. Brahf! zaht'-tai dair fah'-ter, dass hi’st house'-hel-tai-rish ouch bute,divide. (Theil, Meinige, der, die, das, Natur f. nature. für die Zukunft gesorgt, wie es tem lantmanni geziemt. m. share, part.) mine. Himmel, m. heaven. fi'r dee tsooʻ-köönft gai-zöryt', vee ess dem lant-man gai-tseemt'. Vier, four. Sogleicy, immediately. Kaufmann, m. 3d babe Meinige sogleich aufgegessen, rief der Erhalten, to obtain, Jung, young. chant. Mann, m. hah'- bai dee mi-ny-gai zo-gli'y' out"-gai-ghess'-sen, reef dair to receive, to pre- Werfen, to throw; fort, man (Lat. vir.]). away. Befangen, embarZingste, und den Stein fortgeworfen, Mutter hat rassed. pink-stai, dūnt dain shtine fort"-gai-võr'-fen, dont dee moot'-ter hat Schmecken, to taste. Shrige, der, die, das, Offen, open, -ly. mir die alfte von der Shrigen gegeben. D! bad schmedte Herrlichy, glorious, -ly. hers, theirs, yours. Nachbar, m. neighneer dee hel-tai fon dair ee’-ri-ghen gai-ghey'-ben. Oh! dass shmeck-tai Ältest , eldest. (Alt, Süß, sweet. bour. for frig und zerschmilzt einem im Munde. old.) Somelzen, to melt; Fieber, n. fever. zo zu'ss cont tser-shmiltst i-nem im mõõn'-dai. Säuerlich, tart. (Sauer, zer, prefix, to pieces, Legen, to put, place. sour.) indicating separa- Hinweg, weg, away. fagte der Bater, tu þaft zwar nicht sehr flug, tion. Noon, zahch-tai dair fah'-ter, doo hast tsvahr nxýt zeyr klooch, Beidhmad, m. taste. Sanft, soft, mild. Gebraucy, m. use, cus Zwar, it is true, in tom. aber toch natürlich und nach kindlicher Weise gebandelt. Stein, m. stone. deed. Drei, three. ak-ber dóch na-tü'r'-*ý ošnt nahch kint'-By-yer vi-zai gai-han'-delt. Sorgsam, carefully. Klug, shrewd, clever. Bruter, m, brother. fir die Klugheit ist auch noch Raum genug im Leben. (-lam, affia, -some, -heit, affia, corresponds Schweigen, to be silent. It'r dee kloody-hite ist ouch noch roum gai-nooch' im ley'-ben. -ful.) with -ness, -head, Umarmen, to embrace. -hood. Da begann der zweite Sohn: Ich habe den Stein, den Baum, m. tree. (Arm, m. arm.) Dah bai-gan' dair tsvi'- tai zo'n: lý hah'-bai dain shtine, deyn ta Pleine Bruder fortwarf, gesammelt und aufgeflopft. LESSONS IN ARCHITECTURE.—XIV. dair kli-nai broo'-der fört-varf, gai-zam'-melt dönt ouf-gai-klopft. G# twar ein Kern darin, der schmeckte fo füg wie eine CHURCH ARCHITECTURE.-II. Esa Fahr ine kerrn da-rin', deyr schmeck-tai zo zu'ss vee i-nai In our previous paper we have traced the rise of church archiRus, aber meine Pfirsich habe ich verkauft, und so viel tecture from its earliest commencement, in the style of the miss; ah'-ber mi-nai pfirr-zly hah-bai įý ferr-kouft, dont zo feel civil architecture of the Romans, to its elaborate development in the various forms of the Gothic. The illustrations already Gelb dafür erhalten, daß ich, wenn ich nad; der Stadt komme, given will have afforded our readers an idea of the general gelt da-fu'r' err-har-ten, dass Yý, ven lý nahch dair shtat kèm'-mai, features of the chief styles in use in this country in earlier meil zwölf dafür faufen fann. times. We have now to mention some of the details which role tsvol da-fü'r kou'-fen kan. characterise the architecture of the several periods, and to Der Bater schüttelte ben Supf und glance at the internal arrangements of our church buildings sagte : Klug ist das when church architecture had reached its highest stages. Dair fah'-ter shüt-tel-tai dain kopf dönt zahch'-tai: klooch ist dass First, as to the materials used. There is no doubt that in mobil, aber fintlich und natürlich ist es nicht. Bewahre bich our earliest churches, as in those of the Continent, fragments Fole, ah-ber kint'-Ivý sont na- tu’r'-ty ist ess niyt. Bai-vah'-rai drý of Roman masonry were turned largely to account. This der Himmel, daß du fein Kaufmann werdest. masonry generally consisted of stone or flint embedded in dair him'-mel, dass doo kine kouf-man veyr'-dest. mortar, and bound at frequent intervals with layers of red Ilm tu, Gtmund ? Fragte tiles. Walls of this character, the remains of old Roman work, ter Bater. Unbefangen Gint doo, ed'-močnt? frahdi'-tai dair fah’-ter. 8ðn'-bai-fang'-en 8šnt oldest of our churches materials identical in their nature are are found in various parts of Britain. In some of the very ofen antwortete Gtmund: Ich habe meine Pfirsich bem discovered, but without the regular courses of tiles observed in X-fen ant-vor-tai-tai ed'-moont : lý hah'-bai mi’-nai pfirr'ziy daim the Roman masonry. An instance of this is found in the reSohn unsers Nachbars, tem tranfen Georg, der das Fieber cently-restored church within the walls of Dover Castle, believed zo'n &#n'-zeres nady'-bahrss, daim kran'-ken gai-ory', deyr dass feel-ber to have been built about the year 650. Close by it stand the hat, gebracht Er wollte sie nicht nehmen. Da hab ich fie remains of a tower undoubtedly Roman, in which the characbat, gai-brudt. Eyr võll'-tai zee niýt ney'-men. Dah hahb Yý zee teristic tile-courses are distinctly visible. Many of the ancient churches of Kent and elsewhere in bh auf das Bett gelegt und bin hinweggegangen. bem ouf dass bet gai-leyyť ošnt bin hin-vey"-gai-gang'-en. England are built of flint embedded in concrete, forming par ticularly solid and durable walls, which have stood and are Nun, fagte der Vater, wer hat denn wohl den besten Ge likely to stand for ages. One of the oldest of these churches Foon, zahch--tai dair fah’-ter, veyr hat den vole dain best'-en gai- is St. Martin's, at Canterbury, which is believed to have been brauch von seiner Pfirsich gemacht? rebuilt in the twelfth or thirteenth century with the materials brout fon zi-ner pfirr-zlý gai-macht' ? of a more ancient structure-perhaps the very earliest erected in Britain. Da riefen sie alle trei: Das hat Bruder Otmund gethan! Dah ree'fen zee al-lai dry: dass hat brooʻ-der ed'-moont gai.tahn! bound together at the angles with hewn stone, as in the case Some of the Anglo-Saxon churches were built of rubble, aber ich wieg still, und die Mutter umarmte ihn of the tower at Earl's Barton. The Normans largely used EX-tånt ah-ber shveey shtill, õõnt dee mådt-ter čom-arm-tai een the same materials, but also employed small stones cemented mit einer Thräne im Auge. together by mortar, which was poured in hot, and used larger mit -ner trey'-nai im ou’-gai. blocks of stone for more important buildings. Sometimes Grmund narrow stones were placed in regular courses, at an angle of marks of the various periods of Gothic architecture. In the about 45 degrees, the stone in each layer sloping in a different Norman buildings they were small and deeply recessed, while direction; and to this mode of building the name of "herring. they presented the characteristic form of the semi-circular or bone work" has been applied. segmental arch. The pointed or lancet-shaped window came In the reign of Henry I. more attention began to be paid to in with the Gothic style—being, in fact, an adaptation of the the external appearance of the Gothic arch- although at first, walls, which were now often built like the Norman windows, it was of stones squared or smoothed extremely narrow. The defect in on the outer surface, and finely the admission of an imperfect jointed together. light was remedied by placing With the introduction and de two or three of such windows velopment of Gothic architecture, side by side, thus forming one the softer stone called freestone more useful in character and came to be more and more em imposing in appearance. The ployed to supplement the brick glazing of church windows apor hard stone used as the chief pears to have been introduced in material of the fabric. The use the seventh century. The use of of freestone was rendered both painted or stained glass came in necessary and advantageous by with Gothic architecture, its porthe more regular and refined or pose being to subdue and mellow namentation which the Gothic the greater light admitted by the style introduced; and by degrees Gothic windows. The lancetthe Middle-age builders moulded shaped windows of the “Early it to the freest expression of English" style are illustrated in their ideas, whether those ideas the first cut below. But these were purely beautiful or simply plain windows were often acgrotesque and fantastic. companied, in large buildings, The solid masonry of the Anglo by others of a circular shape, Saxon and Norman walls required known as “Catherine Wheel little or no external support, but windows, which were highly ornathe lighter character of the walls mented. in Gothic buildings led to the de The general plainness and velopment of the buttress. The simplicity of the Early English early Norman buttresses were flat period gave place, in the “Decoprojections from the outer wall. NORMAN BUTTRESS. GOTHIC AND FLYING BUTTRESSES. rated " style, to a refined and As Gothic structures came in elegant manner of ornamentation, vogue, these projections were carried farther out, and sometimes Among other peculiarities, the window was widened, and its rose tier above tier, until the highest and narrowest range termi- upper portion was filled with geometrical tracery, varied in nated in a pinnacle. Moreover, when the upper storey of the character, and often of great beauty. A good example of the building was much narrower than the base, it was supported windows of the “Decorated Gothic” period is included in our by a buttress of its own, which rose from the buttress of the engravings. lower storey in the form of the segment of an arch. To these The “ Perpendicular" style shows less purity of taste, but is “DECORATED GOTHIC” WINDOW. “PERPENDICULAR GOTHIC" WINDOW. offshoots of the lower buttress the name of “flying" buttresses frequently productive of very rich effect. Our cut represents is applied, and they may be observed in many of our principal one of the most elegant of the windows of this period. The church edifices, such as Westminster Abbey. The earlier and mullions, or divisions between the window-lights, here run the later forms of the buttress are shown in the illustrations on up in perpendicular sections, instead of, as in the preceding style, branching off into geometrical figures; and this is one The windows are the most striking and distinguishing external of the distinguishing features which have caused the name this page. VVVV of "Perpendicular” to be given to the architecture of this | larger church buildings, such as that of Wimborne Minster, are period. termed the aisles. Westward of the nave is usually placed the An additional characteristic of the different styles will be principal entrance, frequently surmounted by a tower. (See plan, found in the nature of the smaller details A.) Other entrances are situated on the uf ornamentation, such as the figures in. south or the north side, according to controduced in mouldings, etc. We give venience of access, as in B. examples of the "tooth ornament” of the The form of the cross is given by the Early English Period, the four-leaved arms thrown out from the nave, usually flower of the Decorated style, and the at a distance of about two-thirds of the “Tudor flower" of that known as the Per length of the edifice. These arms, runpendicular. In the latter we see a dege ning north and south, are called the tranneration into fanciful and extravagant septs, and the chief tower or steeple of forans, which, extending to all features the building usually surmounts this interalike, by degrees vitiated the Gothic style, section of its two principal lines. and did much to bring it into disrepute at The continuation of the building paa later date. rallel with the nave, and eastward of the We now come to the internal arrange tranzepts, is chiefly occupied by the chanment of churches, which was not affected “EARLY ENGLISH" ORNAMENT. cel, wherein the altar occupies the most promaterially by the introduction of the ninent place. The chancel in the plan has Gothic style. We its aisles, like the have alluded in our nave; and its cen. first paper to the tral portion westearly adoption of ward is occupied the form of the by the choir. This cross, and its gene space, as the name ral prevalence in implies, is devoted the ground-plan of in part to the cho. church buildings; risters, but is often and this necessarily ORNAMENT OF THE large enough to be “ PERPENDICULAR GOTHIC" ORNAMENT. used as a chapel, gave a certain de DECORATED GOTHIC." gree of uniformity in which the worin general design. We may take, as an example of general | shippers are assembled when not sufficiently numerous to ground-plan, one of our oldest religious edifices of importance, occupy the main body of the edifice—i.e., the nave and its the collegiate church of Wimborne Minster, in Dorset, believed aisles. to have been founded in the eighth century, and which bears in The chancel is the most richly-decorated portion of the interior + A + W TOWER + + P + PULPIT + + B + NTH PORCH + L + LECTERN. + C + VESTRY its architectaral features a combination of the Saxon, the of the edifice. The altar, which occupies its extreme end, is often. Norman, and the Gothic, as different portions were erected at lavishly embellished, and in Continental churches and cathedifferent times. drals the masterpieces of the greatest painters frequently adorn The body of the church throughout the greater portion of its this portion of the building. The flooring of that part of the length is called the nave, and the side passages found in the chancel which contains and adjoins the altar is usually raised and railed off, while sometimes this part is separated from the 97. If there are numeral co-efficients prefixed to the letters, the rest of the building by a handsome carved screen. In parish co-efficients of the dividend must be divided by the co-efficients of churches the chancel, consisting only of the central portion the divisor. here marked in the ground-plan, often terminates in a semi EXAMPLES.-(1.) Divide bab by 26. Ans. 3a. circular recess called the apse, which is occupied by the altar. (2.) Divide 16dxy by 4da. Ans. 4y. The lectern (L in the plan), situated almost in the centre of (3.) Divide 25dhr by dh. Ans. 25r. the transept in this instance, as in some others, is the place (4.) Divide 12xy by 3. Ans. 4xy. from which the lessons are read; and the letter P marks the (5.) Divide 34 dra by 34. Ans. dr. position of the pulpit. It must, however, be noticed that in (6.) Divide 20hm by m. Ans. 20h. cathedrals, where the service is almost invariably performed in the chapel (the position of which is marked in our present the former enters into every term of the latter. [Art. 76.] Thus 98. When a simple factor is multiplied into a compound one, ground-plan by the “ choir "), the pulpit and lectern are often a into b + d, is ab + ad. Such a product is easily resolved again placed in the chancel, near the spot marked thus +. The division marked C, which to a certain extent mars the into its original factors. Thus ab + ad = a x (6 + d). symmetrical arrangement of the ground-plan, is for convenience' EXAMPLES.-(1.) Resolve ab + ac + ah into its factors. sake commonly occupied either, as in this case, by the vestry, Here ab + ac + ah= ax (b+c+h). Ans. or by a chapter-house. Here, also, are frequently found the (2.) Resolve c'n + code + cya into its factors. Ans, X cloisters, or covered ways which in olden times were used for (n + dx + y) or c(n + dx + y). the purpose of exercise by the persons engaged in the service of (3.) Resolve bd + b cd? + bcod into its several factors. Ans. the church. bd (1 + bcd + c). (4.) What are the factors of amh + amx + amy? Ans. am LESSONS IN ALGEBRA.-VII. (h+3+4). (5.) What are the factors of 4ad + sah + 12am + 4ay? Ans. DIVISION 4a (d + 2h + 3m + y). Art. 91. (1.) A man divided 480 apples among 6 boys. How In these examples, if the whole quantity be divided by one of the many did each receive ? factors, according to Art. 96, the quotient will be the other factor. Here, if 6 boys receive 48x apples, it is manifest that 1 boy Divido (ab + ad) by a. will receive 1 of 48x apples; but of 48x = 8c apples; for Here ab + ad ; a=b+d. Ans. 48.6 - 6 = 8x. Whence 8x apples is the answer. Divide ab + ad by b + d. (2.) If 8 hats cost 24a shillings, what will 1 hat cost ? Here (ab + ad) = (b +d) = 0. Ans. Here, reasoning as before, 1 hat will cost of 24a shillings, Hence, if the divisor is contained in every term of a compound but 24a - 8 = 3a; therefore 3a shillings is the answer. dividend, it must be cancelled in each. The process followed in these examples is called DIVISION. It (6.) Divide ab + ac by a. Ans. b + c. consists in finding how many times one quantity contains another, (7.) Divide bdh + bdy by b. Ans. dh + dy. and is the reverse of multiplication. The quantity to be divided (8.) Divide aah + ay by a. Ans. ah + y. is called the dividend; the given factor, the divisor ; and that (9.) Divide drx + dhx + day by dr. Ans. r +h+y. which is required, the quotient. (10.) Divide 6ab + 12ac by 3a. Ans. 25 + 4c. 92. DIVISION, therefore, is finding a quotient, which multiplied (11.) Divide 10dry + 160 by 2d. Ans. 5ry + 8. into the divisor will produce the dividend. As the product of (12.) Divide 12hx + 8 by 4. Ans. 3h + 2. the divisor and quotient is equal to the dividend, the quotient (13.) Divid3 35dm + 14dc by 7d. Ans. 5m + 20. may be found by resolving the dividend into two such factors, 99. On the other hand, if a compound expression, containing any that one of them shall be the divisor. The other will, of course, factor in every term, be divided by the other quantities connected be the quotient. by their signs, the quotient will be that factor. [See Art. 98.] Suppose, for instance, that abd is to be divided by a. The EXAMPLES.-(1.) Divide ab to ac + ah by b +c+h. Ans. d. factors a and bd will produce the dividend. The first of the (2.) Divide amh + ana + amy by h +*+y. Ans. am. bring a divinor, may be set aside as the one factor. The other (3.) Divide 4ab + Say by b + 2y. Ans. 4a. Ivor is the quotient. (4.) Divide ahm + ahy by m + y. Ans. ah. 33. When the divisor therefore is found as a factor in the 100. In division, as well as in multiplication, the caution must eller udend, the dirision is performed by cancelling this factor. be observed, not to confound terms with factors. (See Art. 76. EXAMPLER--(1.) Divide ex by c. Ans. x. EXAMPLES.-(1.) Divide (ab + ac) by a. (2.) Divido dh by d. Ans. h. Here (ab + ac) = a=b+c by Art. 98. (3.) Divide drx by dr. Ans. «. (2.) Divide (ab X ac) by a. (4.) Divide hmy by hm. Ans. y. Here (ab x ac) - a= aabe → a= abc by Art. 95. (5.) Divide dhøy by dy. Ans. hx. (3.) What is the quotient of (ab + ac) = (b + c)? Ans. a. 94. Proor.--Multiply the divisor and the quotient together, (4.) What is the quotient of ab X ac = (b X c)? Ans. ac. and the product will be equal to the dividend, if the work is right. RULE FOR SIGNS IN THE QUOTIENT. Thus ax + a gives the quotient x. Proof. Here x x a gives the dividend ax. 101. In division, the same rule is to be observed respec.ng 95. If a letter is repeated in the dividend, care must be taken dividend are both positive, or both negative, the quotient mast the signs as in multiplication; that is, if the divisor and that the factor which is rejected be only equal to the divisor. EXAMPLES.-(1.) Divide aab by a. Ans. ab. be positive: if one is positive and the other negative, the (2.) Divide bbx by b. Ans. bac. quotient must be negative. [Art. 82.] This is manifest from the consideration that the product of (3.) Divide aadddo by ad. Ans. adda. the divisor and quotient must be the same as the dividend. (4.) Divide aammyy by amy. Ans. amy. For if + ax +b= + ab, then + ab +b=+a; (5.) Divide aaaxxxh by aaxx. Ans. axh. If – ax+b=-- ab, then - ab +b=-a; (6.) Divide yyy by yy. Ans. y. If + ax-b=-ab, then - ab = -b=ta; In such instances as the preceding, it is obvious that we are And if-ax-b= + ab, then + ab -not to reject every letter in the dividend which is the same with EXAMPLES.-(1.) Divide abx by Ans. one in the divisor. (2.) Divide 8a - 10ay by — 20. Ans. 5y-4. 96. If the dividend consists of any factors whatever, expunging (3.) Divide 3ax -- 6ay by 3a. Ans. * - 2y. one of them is dividing by that factor. (4.) Divide 6am X dh by -- 2a. Ans. — 3mdh. Divide a (b + d) by a. Ans. b + d. 102. If the letters of the divisor are not to be found in { by b + d. Ans. 0. dividend, the division is expressed by writing the divisor under ut c+d) by 5 +. Ans. c + d. dividend in the form of a vulgar fraction. ((d - h)x by d - h. Ans.(b + y)ą. NOTE.—This is a method of denoting division, rather than ba. + bc - bc bt a a actaal performing of the operation. But the purposes of division ESSAYS ON LIFE AND DUTY.-XV. may frequently be answered by these fractional expressions; SINCERITY. for as they are of the same nature with other vulgar fractions, they may be added, subtracted, multiplied, or divided. SINCERITY is one of the most beautiful words in the English EXAMPLES.--(1.) Divide vy by a. language, and, like many other words, it has a history. It comes ty from two Latin words, sine and cerd, without cement, and its origin Here, xy = a= was in this wise. In the golden days of Roman prosperity, (2.) Divide (2-x) by - h. when her merchants were very affluent, and dwelt in their d—* -d marble palaces on the banks of the Tiber, there was a very Here, (d-x) =-= natural sort of emulation in the grandeur and artistic adorn h And here it may be observed that if the signs of all the of the gems of Grecian art the possessions of the Roman people. ments of their dwellings. Their successful wars had made many terms of a fraction be changed both in the numerator and de A taste for sculpture had been awakened, and the sons of Rome - bc nominator, its value will not be altered ; for +c= set to work themselves in the schools of design. Good sculptures b were quickly bought up. bc and But dodges sometimes took place then, as now: for instance, if the sculptor came upon a flaw in b the marble, or if his chisel missed its aim, he had a carefully 103. If some of the letters in the divisor are in each term of constructed cement with which he filled in the chink, and so the dividend, the fractional expression may be rendered more cleverly fixed it as to be imperceptible. In time, however, and simple, by rejecting equal factors from the numerator and after the purchase had been long completed, heat or damp, or denominator. 6 accident would affect the cement, and it would reveal its preEXAMPLE.-Divide ab by ac. Ans. c sence there. The consequence was that when new contracts came to be signed for commissioned works of art, there was a These reductions are made upon tho principle that a given clause put in that they were to be sine cerâ, or without cement. divisor is contained in a given dividend, just as many times as What a picture story in a word! What a moral meaning in it! double the divisor is contained in double the dividend ; triple the viz., that true characters should be sincere, or without cement. divisor in triple the dividend, and so on. In the formation of character sincerity occupies a very essential 104. If the divisor is in some of the terms of the dividend, place. Cement of all sorts drops out in time, and reveals the but not in all, those which contain the divisor may be divided fractured character. We should, therefore, be on our guard w in Art. 93, and the others set down in the form of a against all false appearances; the very risk of detection makes fraction. the deceiver restless and uneasy; and when the disclosure comes EXAMPLE.—Divide ab + d by a. the name for honesty is gone. It is possible to keep out of the ab + d ab d d Here (ab + d) = a= + Ans. clutches of the law, and to evade the risk even of any distinct charge of wrong-doing, and yet not to be sincere. We may 105. The quotient of any quantity divided by itself or its recommend an article in general terms with some secret reserva abc tion, or we may by our look and manner suggest that all is equal, is evidently unity or 1. Thus = 1, 1 = 1, 1, etc. perfectly secure and safe, when we know the concern we are abc 106. If the dividend is greater than the divisor, the quotient connected with is rotten at the core. Apart, however, from must be greater than a unit : but if the dividend is less than the trade and commerce, in common life a sincere friend is of inexdirizor, the quotient must be less than a unit. pressible value---one who will not flatter for the sake of giving us a passing thrill of pleasure, nor defame us when absent from EXERCISE 7. any begrudging envy. Like all other virtues, time alone can dePerform the following exercises in division. velop its excellency. We must, in all matters of character, 1. Ahz by dy. 10. 6a by 4a + 2a. wait for the test of experience; and although guile and craft 2. aka - 3ay by ab. 11, a + b - 3h by a - 3h + b. may secure certain ends, and for the time being seem to get on 16 bu by by. 12. a2 + a by x. well, yet, in the end, sincerity wins the day. Once deceived, we 4. Ben by Pry. 13. Sud 3d by 3d. are trustless for the future. We cannot will to have confidence 5. day + - hd by X. 14. 4axy - 4a + Sad by 4a. in any one-that must be the result of well-tested experience. 6. Pak + ad + by a. 15. 3ab + 3 - 6m by 3. An insincere character becomes very despicable in the eyes of 1. bei + 3y by -0. 16. 25a by 5a. all right-judging persons. You meet now and then with one lay + dh by 2m. 17. 4x by 20a. %. Bax by Saz. who has painted you before, and then proceeds to blacken you behind, as the old proverb has it, and your instincts of righteousness are not more outraged than your sense of dislike KEY TO EXERCISES IN LESSONS IN ALGEBRA. is aroused. It is not uncommon to hear in certain circles that EXERCISE 6. you must discount well all that Mr. A. says to you; if you find 1. 15aʼzy. 19. 16x* - y. that to be indeed the case, you in time not only discount, but 20. a3 + 3a+b + 3ab2 + 73. dishonour, Mr. A.'s accounts altogether; and his loud protesta21, 23 + x*y - xy - y". tions,“ Upon my word, now, my dear sir, I can swear to that!" 22. 216abx + 216aby. only makes you believe more surely that who his word does not 23. 3axyz + 3bxyz + 3cxyx + 3dxyz. hold, his oath will not bind. 24. W yyy. Sincerity is a sweet domestic virtue; it ought to shine forth 7. exty - 3y + 3ar y3. bbbbbb. . in the home relationship-any guile or deceit there is fatal to 1-2+2-23-47*. 26. aaa + axx. family peace and prosperity. To seem elsewhere is sad enough, 9.- 2a2 + a*. 27. yyyy - aaaa. 16. P-4 - 3ez + 6xz, but to seem there cuts at the root of all that is peaceful and 28. 45aa 80bbbb. 11 12 + fab 1899 + 8. 29. 12aRx + 12 a2y + 12abx + 12aby: when he knows he is on the very verge of bankruptcy; or for good. For the husband to pretend to be busy and getting on, 12. Hamry - Sabır + Sabha. 30. aaaa + 4aaab + baalb + 4abbb 19. ledledna - 240_lry. + bbbb. the wife to conceal accounts that are due, or calamities that 14. Stabd 14hd? + 140 + 48abdx 31, 4:6 - 3x® - 4x? + 27-18x9. have happened in the case of some favourite child ;-these work - Sdah + Sdx. 32. 35y® – 897% + 85y3 – 17y2 -8y. out terrible results in misery and distrust. Concealment is in15. Sedky + 2ahy + dh2 4ah 33. a – 20% + 2a* 4a3 + 6a* + 6a sincere ; and if we go to the very broadest interpretation of the + Sauny + 2hæy + hør - 4hx word we shall see that it includes within its meaning all deceit, + Sadya + dy2 - Idy + Saaya 34. ? have + 21a2y 3503y* fraud, and guile whatsoever. There may be insincerity of word, + y - 4xy. + 35a4ys 21a5y2 + 7av on + bdh + baba or look, or demeanour, because the eye and the manner speak - Ah + bd + 6ahx 4h 35. axt + a2y3 + 3a3,2 – 4atx as well as the voice, and an honest countenance is one of the + dk + Bar - 4h + d. + 4a". handsomest on earth. Children sometimes see sad instances of 17. 24. + 2a + 2093 – 34 36. ** -- 23.7 - 18+ + 40. insincerity. When the endearing epithets with which visitors 37. 1 + - 223 +* - -**. are addressed give place to sharpish criticisms upon them after 18. - - **+ 20** + 2y9z. the hall door is shut, we need not wonder that they learn an un 190. |