extremity of the bird's wing (hand) merely serves the purpose hundred and thousand; it must not be rendered in French We of a support for feathers. The legs vary considerably in say: length, according to habits. Each foot has three or four toes, Mille hommes, one thousand men. terminated by claws; in aquatic birds connected together by an Cent francs, one hundred francs. intervening web--this is principally confined to the three (4.) When the words cent and mille are used substantively anterior toes. The feet and legs are generally covered with before the name of objects generally reckoned or sold by the horny, scale-like plates, and destitute of feathers. The power hundred or thousand, in number or in weight, the word un may of flight which many birds possess is indeed wonderful. The be placed before them; the name of the object being preceded muscles in connection with the upper extremity may be said to by the preposition de :consist of two classes : one by which great power is obtained ; Un cent, un mille (millier) de briques, one hundred, one thousand (0) bricks. and the other, speed at the expense of power. Un cent (un quintal) de sucre, one hundred (weight) of sugar. Generative System.-In their reproduction birds are strictly (5.) The words septante, seventy, octante, eighty, and nonante, oviparous. The generative organs exhibit for the most part a ninety, are now nearly obsolete. They are, as may be seen in close analogy to those of the higher reptilia. The ovary is the preceding table, replaced by awkward expressions : soixanteracemose and single, the right with its oviduot being perma- dix, sixty-ten; quatre-vingts, four-twenties (four score) ; quatrenently atrophied, a singular violation of symmetry which is con-vingt-dix, four-score-ten, eto. fined to birds. In this class of Vertebrata, incubation attains (6.) Before the words onze, eleven, and onzième, eleventh, the its highest perfection. It appears to arise from the concurrence article is not elided. We say le onze, le onzième, la onzième. In of these three exigencies—the necessary life and early maturity pronunciation, the s of the plural article les is silent when this of the young, the necessity of warmth to their development, article precedes onze or onzième. and the incompatibility of utero-gestation with flight.* Classification.-Birds are divided by Professor Huxley into § 25.- OBSERVATIONS ON THE ORDINAL NUMBERS. three orders. (1.) It will be seen that the ordinal numbers, with the er1, Saurure.- Distinguished by having a long tail like a ception of premier and second, are formed from the cardinal :lizard. This order contains only the extinct bird, archæopteryx. 1. By the change of f into vième in neuf; 2. Ratitæ.- From their raft-like keelless sterna. This order 2. By the change of e into ième in those ending with that comprises ostriches, rheas, emeus, cassowaries, and the apteryx. vowel; 3. Carinatæ.-Having the sternum raised into a median 3. By the addition of ième in those ending with a consonant. ridge or keel. All ordinary birds belong to this order. 4. Cinq requires wième to make cinquième, fifth. (3.) Premier and second alone vary for the feminine, and LESSONS IN FRENCH.-LV. make première, seconde, etc. $ 23.–VARIATIONS OF THE CARDINAL NUMBERS. (4.) Unième (first) is only used in composition with ringt, trente, etc. (1.) The following cardinal numbers vary : (5.) Second, deuxième (second).—Deuxième supposes a series, 2 (2.) Un, one, a or an, takes the gender of the noun to which continuation ; second merely indicates the order : it is prefixed :Un livre, a book; une feuille, a leaf. 1st. We may say of a work which has four or more volumes : When used substantively, un takes, at times, the form of the volume de cet ouvrage. J'ai le deuxième (or le second) I have the second volume of that work. plural :Masc. Les uns et les autres, these and those. 2nd. In speaking of a work which has only two volumes, we Fem. Les unes et les autres (the ones and the others). should say: (3.) Vingt and cent, when multiplied by a number, take an s J'ai le second (not le deuxième) I have the second volume of Bese volume du dictionnaire de Bes- cherelle's dictionary. in the plural : cherelle. Quatre-vingts, eighty; six cents, six hundred. (4.) Vingt and cent, although multiplied by a number, do not words, which are often used substantively : 3rd. Under the ordinal numbers may be placed the following take an s if they are followed by another number, or if they are used to indicate a particular epoch Trentenaire, thirty, of thirty years' duration, Quarantenaire, forty, of forty Cinquantenaire, fifty years old, of fifty Sexagénaire, sexagenarian, of sixty Nonagénaire, nonagenarian, of ninety (5.) Mille—(thousand). For the date of the year, reckoned Centenaire, contenarian, of one hundred from the commencement of the Christian era to the year 2,000 4th. Trentenaire and quarantenaire are law terms: of the same, we use the abbreviated form, mil : Possession trentenaire, quar Thirty, forty years' possession. L'an mil huit cent cinquante, the year 1850. antenaire, (6.) With regard to the years which have preceded our era, 5th. Of the others, sexagénaire, septuagénaire, and octogénaire and those which will follow our present thousand, we write the only, are in frequent use : full form, mille. Un octogénaire plantait. A man eighty years old was plantLa première irruption des Gaul The first irruption of the Gauls ing trees. ois, eut lieu sous le règne de Tare took place under the reign of Tarquin, $ 26.--RULES. quin, environ l'an du monde trois about the year of the world 3416. millo quatre cent seize. (1.) In speaking of the days of the month, the French use the (7.) Million, billion, take the plural form. cardinal, not the ordinal number : Le deux mars, the second of March, $ 24.-MISCELLANEOUS OBSERVATIONS ON THE Lo dix-sept avril, the seventeenth of April. (2.) We must, however, say :1.) In French, in computing from twenty to thirty, thirty to Le premior (not l'un) juin, the first of June. forty, etc., the larger number must always precede the smaller. (3.) The cardinal numbers are also employed in speaking of We may not say, as often in English, one and twenty, but always sovereigns and princes :vingt-et-un, vingt-deux, etc. Charles dix, Charles the Tenth. (2.) The conjunction et, after vingt, trente, etc., is only used Louis dix-huit, Louis the Eighteenth. before un: thus, we say vingt-et-un, twenty (and) one, and simply vingt-deux, twenty-two, etc. (4.) We must say, however :(3.) The word one frequently precedes in English the words Henri premier, Henry the First, (5.) Deux and second are, in this case, used indifferently Todd and Bowman. Charles deux, Charles second, Charles the Second. (6.) In speaking of Charles the Fifth of Gormany, and of Aucun and nul should be put in the plural only before such the Pope Sixtus the Fifth, the obsolete word quint (fifth) is words as are not used in the singular, or have in the singular a used :Charles-quint, Charles the Fifth, different acceptation. Sixte-quint, Sixtus the Fifth. (4.) CHAQUE is of both genders, and is used only in the singular. It always precedes the noun, and cannot be separated $ 27.- NUMERAL NOUNS, from it by an adjective or by a preposition. It should never bo We shall, in order to render reference easier, place here some used without a noun :observations on nouns and adverbs of number. Chaque âge a ses plaisirs, chaque Every age has its pleasures, every (1.) The numeral nouns in use with the French are: état a ses charmes situation its charms. Unité, unit. Quarantaine, two score. (5.) MÊME, placed before the noun, has the sense of same in Couple, paire, couple, pair. Cinquantaine, fifty. English. Placed after the noun it means, generally, hinself, Trio, trio, three. Soixantaine, sixty. herself, itself, or themselves. It may often be rendered by the Demi-douzaine, half-dozen. Quatre-vingtaine, oighty. word even. When même is an adjective it may take the form of Huitaine, cight days. Une centaine, a hundred. the plural, but does not vary on account of gender :- C'est la même vertu, it is the same virtue, C'est la vertu méme, it is virtue itself. Le peuple et les grands n'ont ni The people and the great have Vingtaine, score, twenty. Un million, a million. les mêmes vertus, ni les mêmes neither the same virtues nor the same Trentaine, thirty vices. vices. (2.) The termination aine signifies nearly, and when added to (6.) It is at times difficult to distinguish même an adjective words of number is equivalent to the English some, in cases from même an adverb, which is invariable. [See $ 97 (2.) (3.)] like the following: I have some twenty books, i.e., about twenty (7.) Nul is a stronger negative than aucun. It agrees in books. J'ai une vingtaine de livres, gender and number with the noun which it qualifies. Like aucun, when relating to the subject of the sentence, it requires § 28.-FRACTIONAL NUMERALS. ne before the verb:Un quart, one quarter. Un cinquième, one fifth. Nul homme n'est heureux ; nulle No man is happy; nothing can Deux quarts, two quarters. Deux cinquièmes, two fifths. chose ne peut le rendre tel. render him so. (8.) Nul is sometimes used alone, in the sense of no one :Deux tiers, two thirds. Un centième, one hundredth. Nul n'est content de sa fortune, No one is pleased with his fortune, La moitié, the half. Un millième, thousandth, ni mécontent de son esprit. nor displeased with his own wit. (1.) It will be seen that, with the exception of tiers, quart, and (9.) PLUSIEURS is, of course, always in the plural. It does moitié, these numbers take the form of the ordinal numerals. not vary its form :They may, therefore, take the form of the plural when neces Il faut bien qu'il y ait plusieurs There must necessarily be several sary. (2.) The word demi, when used adjectively and preceding the monde est d'accord pour bâiller. raisons d'ennui, quand tout le reasons for ennui, when all agree in yawning. noun, is invariable ; but it is joined to the noun by a hyphen : (10.) QUEL takes the gender and number of the noun to Une demi-heure, f., half an hour, Une demi-aune, f., half an ell. which it relates. It is sometimes immediately followed by its (3.) When coming after the noun to denote an additional half, noun, from which it may be separated by one or several words :it agrees in gender with the noun :Une heure et demie, one hour and a half. Quel tableau ravissant présentent What a delightful picture the les campagnes ! country offers ! Une aune et demie, one ell and a halj. (4.) When used substantively, demi may take the form of the (11.) QUELCONQUE is always placed after the noun, and plural : varies only for the plural:Cette horloge sonne les heures This clock strikes the hours and Toutes les jouissances sont pré All enjoyments are preceded by et les demies. the half-hours. cédées d'un travail quelconque, some sort of exertion. $ 29.-ORDINAL ADVERBS. (12.) QUELQUE in the sense of some (a certain number), or whatever, agrees in number with the noun :(1.) Premièrement, first; in the Quartrièmement, fourthly. first place. There is merit without elevation, Il y a du mérite sans élévation, mais il n'y a point d'élévation sans but there is no elevation without Secondement, Septièmement, seventhly. some merit. Troisièmement, thirdly, Dixièmement, tenthly. (13.) Quelque having the sense of about or some or however, is (2.) These, like adverbs of manner, are formed by the addition invariable :of ment to the feminine form of the adjective. Quel âge avez-vous ? Vous avez How old are you? You look well. bon visage! Eh! quelque soixante Oh! some sixty years, § 30.-INDEFINITE ADJECTIVES. (1.) The indefinite adjectives are used when anything is to be hommes, ils n'oseraient paraitre do not dare to appear enemies of Quelque méchants que soient les However wrieked men may be, they represented or referred to in a general or indefinite manner. ennemis de la vertu. virtue. They are (14.) TEL makes in the feminine telle ; in the plural mascuAucun, not any, not one. Quel, what. Chaque, every, each. Quelconque, whatever. line, tels; in the plural feminine, telles. It agrees with the noun Même, same. Quelque, some. which it qualifies :- Telles lettres, such letters. Plusieurs, several. Tout, all. (2.) Aucun is generally followed by a noun, with which it lar, but varies for the feminine : (15.) Tour, meaning every, is of course always in the singumust agree. It is followed by ne when it comes before a Tout citoyen doit servir son Every citizen should serve his Aucun homme, no man. Aucune femme, no roman. pays; le soldat de son sang, le country; the soldier with his blood, Aucun chemin de fleurs ne con prêtre de son zèle. the priest with his seal. No flowery path leads to glory. (16.) Tout, in the sense of all, agrees in gender and number (3.) Aucun is by the French authors sometimes used in the with the noun to which it relates :plural : Il était au-dessus de tous ces He was above all those vain objects Ils ne peuvent souffrir aucun em. They can bear no legitimate do vains objets qui forment tous les which form all the desires and all pire légitime, ne mettent aucunes minion, set no bounds to their crimes. aésirs et toutes les espérances des the hopes of men, bornes à leurs attentats. hommes, Deuxièmement, secondly. ans. verb: duit à la gloire. $31.-THE PRONOUN. n'ai pas de couteau sur moi. 15. Portez-vous un couteau sur vous ? (1.) The pronoun, in French, as in other languages, is a word 16. Je ne porte jamais de couteau. 17. M. votre frère n'a-t-il pas 19. Voulez-vous used to represent the noun, in order to prevent its too frequent d'argent sur lui? 18. Il n'a pas d'argent sur lui. mettre ces crayons sur la table ou dessous ? 20. Je les mettrai dana repetition. le tiroir. 21. Combien avez-vous donné pour ce blé ? 22. Je l'ai (2.) The pronoun serves also to designate the parts which acheté à raison de vingt-cinq francs l'hectolitre. 23. La maison de each person or thing takes in speech. This part is called cette dame est-elle hors de la ville ? 24. Elle n'est pas hors de la person. ville, elle est dedans. 25. Votre sæur n'a-t-elle pas mis les assiettes (3.) There are three persons: the first, or that which speaks ; sur la table ? 26. Elle a mis les assiettes sur la table et les cuillères the second, or that spoken to; the third, or that spoken of. dessous. 27. Avez-vous fait réparer votre maison ? 28. J'ai fait réparer (4.) There are five sorts of pronouns : le dedans, mais pas le dehors. 29. Combien vous coûte cette soie ? The personal; The demonstrative; 30. Je l'ai achetée à raison de cinq francs le mètre. 31. Vous êtesThe possessive; The relative; vous marié à l'insu de votre père ? 32. Je me suis marié à son insu. The indefinite. 33. Avez-vous vendu mes livres à mon insu? 34. Je les ai vendus à votre insu. 35. Je les ai vendus à l'insu de ma sæır. KEY TO EXERCISES IN LESSONS IN FRENCH. LESSONS IN MUSIC.-XXV. 1. Avez-vous acheté cette maison à l'insu de votre père ? 2. Je l'ai THE DEAD MARCH IN “SAUL"-BOYCE'S CHANT. achetée à son insu. 3. Avez-vous oublié de fermer la porte de devant? The strikingly effective piece which follows, adapted from 4. J'ai fermé la porte de devant et la porte de derrière. 5. J'ai apporté Handel's “ Dead March " in his oratorio of "Saul," and tous mes livres, excepté deux ou trois. 6. Votre frère occupe-t-il le devant de votre maison ? 7. Il occupe le derrière. 8. Qui avez-vous reprinted from Mr. Curwen's " People's Service of Song,” will rencontré derrière cette maison ? 9. Je n'ai rencontré personne derrière exhibit to the pupil the effects of transition in a still more la maison ? 10. Ce monsieur demeure-t-il derrière votre maison ? striking manner. [The key-note r is in the lowest space, except 11. Personne ne demeure derrière notre maison. 12. Il n'y a pas de in the bass. There it is in the fourth line from the bottom.} maison derrière la vôtre. 13. Avez-vous un couteau sur vous ? 14. Je Boyce's Chant illustrates both transitions. M. 50. EXERCISE 45.-DEAD MARCH IN SAUL (IN THE NEW NOTATION). KEY F MAJOR. [MUSIC FROM HANDEL. BY KELLY.] WORDS EXERCISE 46.-BOYCE'S CHANT. KEY E MAJOR. M. 66. To the following music may be chanted—Psalms li., cxxxix. ; Isaiah Ixiii. 1—7, 9–16; Romans xi. 33–36; 1 Corinthians w. 51-58; 1 Thessalonians iv. 13-18. D P G EXERCISES IN EUCLID.-IV. to on. Therefore in the two triangles O AL, O AM, since 0 L, L A are equal to om, MA, each to each, and on is common, PROPOSITION XXI.—Given two straight lines A B, AC (Fig. therefore the triangles are equal (Euc. I. 8); therefore angle 20) meeting in A, and another line D Е, of limited length. Required OAL= angle O AM. Q. E. D. to describe an isosceles triangle A LM, such that a I may coincide Note.-It will be observed in the figure that on coincides with A B, and AM with a C, and L M may be equal to D E. with o a, but this is not assumed in the proof. This proposition Take two points P, Q in AB, AC, such that AP=AQ. Join will be proved in a future article for any triangle not isosceles. c PQ, and produce po to R, so that PROPOSITION XXV.- In the figure of Euc. I. 1, if the circles PR may be equal to D E. At the cut again in F (Fig. 24) and c A produced cut the circle in 1, Rm cut Ac in m; then if A L be radii of equal circles. Hence taken in A B equal to AM, ALM ABC, ABP are equilateral triFig. 20. will be the triangle required. angles, and therefore also equi. For because the angles at the angular (Euc. I. 5, Cor.); but, base of an isosceles triangle are equal (Enc. I. 5), and that AQP by Euc. I. 32, the angles of a =RQM (Euc. I. 15), and that APQ=QRM by construction, triangle are together equal to therefore angle MRQ=mQR; therefore, by Euc. I. 6, Mr = two right angles; therefore MQ. But since AM = A L, and A Q = A P, therefore, by Axiom each angle of an equiangular III., MQ=PL; therefore also RM=PL (Euc. I. 28). Also, since triangle is equal to one-third Fig. 24. angle A P Q = QRM, therefore A L is parallel to rm (Euc. I. of two right angles--i.e., each of the angles CA B BA F is equal 27); therefore r M is equal and parallel to PL. Join pm, then to one-third of two right angles. Therefore angle C A F equals the angle R MP = angle MPL (Euc. I. 29); also side e m= two-thirds of two right angles; hence, by Euclid I. 13, angle side PL, and side m pis common, therefore base R P = base ML-FAH is equal to one-third of two right angles; therefore angles i.e., ML = D E (Euc. I. 8), and a m=AL; therefore A M L is A H F, AFH are together equal to two-thirds of two right angles the triangle required. E. F. (Euc. I. 3), but they are equal, since AH=AF; therefore PROPOSITION XXII.-If A BC (Fig. 21) be an isosoceles triangle each of them is equal to one-third of a right angle, hence the of vertex A, with Bc the base pro triangle AHF is equiangular, and therefore also eqnilateral duced to D, and if from centrec, at (Euc. I. 6, Cor.); therefore I F is equal to 1 , or equal to distance c A, a circle be described AB. Q. E. D. cutting BA produced in E, then PROPOSITION XXVI. ---If in a triangle A B C (Fig. 25), B C be exterior angle ECD shall be equal bisected in G, and AG joined, and the angle BAG be equal to the to three times angle A B C or A C B. angle C AG, then B A shall be equal to CA. For if AB be not equal For since CA, CE are radii of the to A c, one of them must be greater. Let A B be the greater; from same circle, angle CAE = angle Fig. 21. A B cut off A H equal to AC. Join CH, GH; then because AH= CEA (Euc. I.5); but exterior angle AC, and ag is common, also included angle GAH= included angle CA E equals two interior and opposite angles A B C and ACB= GAC, therefore base Gu=GC (Euc. twice angle ACB (Euc. I. 32); therefore angle CEA equals twice I.' 4). But GCEG B, therefore G H = angle A B C or ACB. But exterior angle E CD equals two interior GB, and angle GHB=angle GBH(Eac. and opposite angles ABC and AEC (Euc. I. 32) equals three I. 5). Also since GH=G C, angle GCH times angle A B C or ACB. Q. E. D. = angle guc (Euc. I. 5). Therefore PROPOSITION XXIII.-In the figure of Euc. I. 5, draw cl angles Gic and GHB are together (Fig. 22) at right angles to CB, meeting BA equal to GBH and och together- Fig. 25. ALC; therefore, taking away ACB, we have Note.—This kind of proof is called “Reductio ad absurdum." Fig. 2. remainder A CL= remainder A LC; therefore PROPOSITION XXVII.-Given two straight lines, A B, A C (Fig. AC=AL (Euc. I. 6). Q. E. D. 26), meeting in A, and another straight line, D, of limited length. PROPOSITION XXIV.—If in the figure of Euclid I. 5 the Required to form a right-angled triangle, of which the base shall angles F BC, BCG (Fig. 23) be bisected by lines CO, B 0, meet coincide with Ac; one side shall ing in o, then 0 A shall bisect the angle BAC. Draw OL, OM, coincide with A B, and the other side on perpendicular to GC, CB, B F, then in the two triangles be equal to D. OLC, Onc, because the right angle oc=right angle ONC, From A draw A E at right angles and angle ico=angle noo, each being by construction half to AB (Euc. I. 11), and from a E cut the angle Lcn, also side off A F, equal to D (Euc. I. 3); from oc is common, therefore F draw FG at right angles to A E, triangle o LC= triangle cutting Ac in G (Euc. I. 11); from ONC (Euc. I. 26); there G draw G H perpendicular to AB (Euo. A fore cl=CN, and OL= I. 12); then will A H G be the triangle Fig. 26. ON. Similarly, BMS BN, required. For since G H A, H AF, A F G are right angles, A IGS and om=ON; but since is a rectangular parallelogram ; hence in the two triangles FAG, ON B, ONC are right angles, A GH, because the angle FAG is equal to alternate angle A GH and angles OC N, O BN are Fig. 23. (Euc. I. 29), and right angle AFG equal to right angle ANG equal, being halves of the also side AG is common, therefore the triangles are equal in equal angles LCN, M B N, and side on is common (Eac. I. 5), every respect (Euc. I. 26). Therefore side AF=G H, but ar therefore the triangles ON B, O N Care equal; therefore cn=NB. =D; therefore Gu=D, and Au coincides with a B, and a But Lo=CN, and mB=BN; therefore L'C=BM. But Aca with’ac, and A IG is a right angle; hence A 1 G is the triangle A B; therefore AL=AM, and o L, O M are equal, each being equal required. Q. E. F. н D B M |