RECREATIVE NATURAL HISTORY. "a smoky substance" noted by him on glass, and which he thought aided the fly's “bristles” in clinging to so smooth a THE HOUSE-FLY. surface. Was this “ smoky substance" the fluid observed by As the family of insects to which the house-fly belongs Power, or was it simply the corroded face of the glass ? Thero (Huscides) contains above one hundred species, we must limit is no doubt that glass does undergo a decomposition, which our attention, in this paper, to that buzzing and teasing creature working opticians call “the sweating.” The worn and irregular which so often worries us during the sultry days of summer. surface thus produced would aid an insect in clinging. Leuwen The common house-fly (Musca domestica) may seem too well hoek, the patient and profound Dutch naturalist, employed known to require any description. But there are many who will his improved microscopes in examining the “bristles" detected find, on examination, something to wonder at in this dipterous* by Dr. Hooke. Leuwenhoek saw them clearly, and thought insect. The wings and power of flight claim our consideration that the end of each resembled a hook. This conjecture has first. Those who closely watch will often be surprised at the been verified; the extremity of each “ bristle" is curved, and manner in which the fly moves through the air with its back so presents a hooked form. Dr. Derham, the friend of Hooke, dermwards. Of annan hon the insect and editor of Ray's works, Some may here ask whether the “buzz" "smoky substance" of Hooke, of the fly is produced by the rapid vibration while he himself may have in. HOUSE-FLY (MAGNI. of the wings against the air. This may, in distinctly noted what are now FIED). some cases, be the cause of so peculiar a called " the flaps” on the foot. sound, but no decisive answer can, with By combining all these, Der. our present knowledge, be given to the question. The fly ham might have got his notion is rightly called a two-winged insect, but the apparent rudi. of an adhesive cr "skinny ments of a second pair can be easily seen, just behind the true palm.” Gilbert White, though wings. These singular organs are called poisers, from a sup an acute observer of Nature, THE TRUNK OF THE HOUSE-FLI position that they enable the fly to balance itself during its was not likely to go deeply (MAGNIFIED). rapid somersaults in the air. These little thread-like filaments, into microscopic investigations. with the knob on the top of each, may remind some of the He therefore adopted the “ sharp hooked nails” of Dr. Hooke, halancing-poles used by dancers on the tight-rope. If the com the "skinny palms" of Derham, and the sucker theory as non notion respecting the use of the poisers be correct, we shall explanatory of the whole matter. White, however, clearly readily adınit that the fly is well fitted for its evolutions, pos admitted the action of two powers in the fly's foot, one for sussessing both a moving and balancing apparatus. pension, the other for producing a vacuum. Have we advanced The feet of the fly have long presented a puzzling problem to beyond this in certainty of knowledge ? Mr. John Blackwall, in naturalists, and some persons may even now doubt whether the 1830, described three conclusions to which he had been led. He action of these organs is yet clearly understood. The problem detected an expansion at the end of each hair or “tenter,” reis to explain how the fly can suspend itself from a ceiling or sembling a little pad or cushion, but denied the existence of any walk up a smooth pane of glass. The “sucker” theory was vacuum-producer or air-pump structure. Some persons reminded long popular, and we believed, with little questioning, that the him that each hair, with its expanded tip, might really be a Ay's feet were supplied with a kind of air-pump, by which a separate sucker. This conclusion he refused to admit, alleging vacanm was produced under the feet, enabling them to cling to i it to be unsupported by proofs. Here, then, was a distinct glass much in the same manner that a boy's denial, by an acute microscopic observer, of toy sacker adheres to a stone. Let no reader the sucker theory, accompanied, however, by prepare himself to listen to a new theory on a clear statement that the end of each hair the subject; we must content ourselves with on the fly's foot possesses a peculiar expansion, describing the successive views which have looking as if it must have some special work been advocated, and then stating that now to perform. Mr. Blackwall also arrived at a held by those who have most closely studied third conclusion—that a fly in walking along a these fine and complex structures. Our pane of glass leaves behind certain marks, as readers will bear in mind that very high and if a fluid had been poured out at particular clear microscopic powers, great patience, and points. He thus agrees with the observations namerous observations are necessary for a of Power, Hooke, Derham, and White. The satisfactory examination of such minute examination was still carried on by naturalists, organs. with the aid of the best microscopes. In 1841, In 1664, Mr. Power, after long scrutiny of Mr. E. Newman called attention to the almost the Ay's feet, suggested that the insect clung inconceivable number of the “bristles." to surfaces by its hooked claws, and also by Hooke had estimated the whole number of the the aid of a fluid poured from tubes on the THE EYE OF THE HOUSE-FLY "tenters” on the six feet at sixty; Mr. leet. He saw two powers at work; a grip (MAGNIFIED). Newman declares they are “almost infinite." ping machine in the claws, and an adhesive action in the gummy | This observer also saw that a liquid was poured out from some Liquid. Three years later, in 1667, the Gresham professor, part of the complex structure. This fluid has been subjected mathematician, and naturalist, Dr. Robert Hooke, described in to chemical analysis, but no remarkable element has been diskis - Micrographia” the "small bristles” on the " soles" of covered. Water and oils appear to be the constituents, so that the fly's feet. He called them “ tenters” (holders), and counted it is similar to the ordinary matter given off by the pores of ten on each foot, thus giving to this small insect sixty holding the human skin. instruments. But Hooke goes on to describe what he terms Mr. Hepworth, in 1854, observed that "the flaps" of thə Aly's feet were trumpet-shaped, or resembling the form of a boy's • Diptera, 2 Greek word signifying "two wings." sucker when supporting a heavy stone. This gentleman also 58 VOL. III. noticed the marks left on glass by "the flaps,” but denied the of the fly. This can, however, only rank at present as a clever existence of an adhesive fluid in sufficient quantity to support supposition, which subsequent discoveries may prove to be true. the weight of a fly. He advocated the sucker theory, giving no The proboscis or trunk of the fly consists of many suction less than 12,000 suction tubes on one foot of a common fly. If tubes, admirably fitted for pumping up the fluids on which the this statement should stand the test of examinations, we shall insect feeds. This trunk would admit of a much longer then have in one small insect 72,000 suction machines. It may description than our space allows; we must, however, remind give some readers a clearer view of the minute scrutinies now the reader that a fly's proboscis really contains tongue, jaws, made into insect structure when we state that the expanded and lips, all modified and combined in one organ. The tongue edge of a fly's foot, called "the flap," has been found to be only is a net-work of fine tubes; two fine books are visible near the south of an inch in thickness. tip, one on each side, and the extremity is furnished with a Mr. Tyrrell and Mr. West have devoted much time to the series of most delicate vessels, through which the food passes examination of these " flaps," and the following are the principal up to the more fleshy parts of the tongue. An elaborate system results :-Two distinct sets of hairs are found on the foot of a of exceedingly minute muscles draws out and retracts the tongue, ily; one, called " tenents,” rise from the inner side of the flap, and aids in rolling in the whole trunk when the insect has and are employed to grip smooth --nollan “onard has vusavus; we ovner series are inished its meal. "As nothing, vui a noid can ascend the fine -- vl's,” their office being to protect, tha finn hankaa vuvus, it might be supposed that no fly could dine off a solid tips of the "tenents” from injury by Friction. We must observe lump of sugar. But the insect is able to dissolve such a subhere that house-flies are not the only insects furnished with such stance by a liquid poured from the trunk, and thus the liquefied a double system of hairs-most beetles are similarly supplied. sugar is easily drawn up the suction vessels. The fly's apparatus for walking and holding on may be thus The eyes of a fly are very large when compared with the size summed up :-On a rough surface the insect appears to use its of the head. If one of these compound eyes be examined under claws only; on glass, or on a ceiling, three processes are brought a glass with a linear magnifying power of 100, the organ will into action-first, the “almost infinite" number of hairs are be found to consist of many thousand tubes, each fixed in a sirpressed down on the smooth surface; a peculiar movement of sided case. Every one of these eyelets appears to be a perfect the bristles then expels all the air from between or beneath the simple eye, resembling in all essentials that of man. Dr. Hooke hair-like cushion ; lastly, a fluid is poured out round the base of gave the number of eyelets in each eye at 7,000, and Dr. Carthe entire hair-pad, and the expelled air is thus prevented from penter estimates them at 4,000. Thus, at the lowest compuentering. A vacuum is in this manner secured and maintained tation, a house-fly possesses 8,000 separate organs of vision. so long as may be necessary. When the fly wishes to move, the Few insects seem to lead a happier life than this nimble little flap, firmly pressed down on the glass, must be first raised, and creature. But its days are not always free from trouble ; 2 this is accomplished by the hooked claws which lift up the thin disease of a peculiar character attacks the fly, producing a edges of the hair-pad, and thus let in the air and destroy the white eruption on the body, suggesting the idea of insect vacuum. The movement of the claws in this process is very leprosy. The fly is also infested by little parasitic animals, peculiar. Some notion of it may thus be gained :-Let a which some enthusiastic naturalists have carefully figured and reader suppose that a sucker is fixed to the tip of his little described. finger, and that this sucker becomes fastened to a table by Many persons may ask, what special service do flies perform atmospheric pressure ; let him also imagine the tip of his in the system of Nature ? Their particular office appears to be thumb to be armed with a number of fine hooks. He will be the rapid consumption of those dead and minute animals whose able to lift the edges of the little finger sucker by these thumb decaying myriads would, otherwise, soon poison the air. It was hooks, and thus the air will be admitted under the sucker. Some- a remark of Linnæus, that three flies would consume a dead what after this fashion does the fly loosen its foot from a surface horse sooner than a lion could. He, doubtless, included the of glass. families of the three flies, then he was certainly right. A single The insect requires all its force thus to move the feet nimbly. fly will sometimes produce 20,000 larvæ, each of which in a few When benumbed by cold or weakened by other causes, the fly days may be the parent of another 20,000, and thus the remains fixed to one place, unable to lift its feet from the descendants of three flies would soon devour an animal much surface. Feeble or diseased flies may sometimes be seen vio- larger than a horse. lently struggling to extricate themselves. This was observed Our readers will see, in the preceding remarks, that even a by White, who describes the insects as “labouring along and common house-fly can offer to a student of Nature many marvels lugging their feet in windows, as if they stuck fast to the glass." of structure, and numerous proofs of an infinite intelligence in Mr. West has endeavoured to estimate the exact amount of the the almost invisible organs of the mçanest creatures. forces which enable a fly to adhere to glass. He found that one-half the insect's weight is supported by the atmospheric READINGS IN FRENCH.-II. pressure on the feet when the vacuum has been produced. Onefourth of the weight is upheld by the grip of the "tenent" LE SAPEUR DE DIX ANS. hairs, and the remaining fourth part by the fluid emitted from SECTION V. the flaps. As a common house-fly weighs about half a grain, À PARTIR de ce jour, on ne se moqua (a) plus autant du petit the supporting force exerted by each of the six feet will amount Bilboquet, mais il n'en devint (b) pas pour cela plus commuto one-twelfth of a grain only, and this force is distributed nicatif ; au contraire, il semblait rouler dans sa tête quelque among three powers—the atmospheric pressure, the "tenent” fameux projet, et, au lieu de (c) dépenser son argent avec ses hairs, and the sustaining fluid. Each of these forces would have camarades, comme ceux-ci s'y attendaient, il le serra soigneuseto support the sth of a grain only, assuming the weight to be ment.? equally distributed throughout. Quelque temps après, les troupes françaises entrèrent à We have devoted thus much of this paper to the investi. Smolensk, victorieuses et pleines d'ardeur; Bilboquet en était , gations of eminent men into the structure of a fly's foot, with et le jour même de l'arrivée, il alla se promener (d) dans la two objects in view—to induce some readers to make a more ville, paraissant très-content de presque tous les visages qu'il constant use of the microscope in their studies, and to deepen rencontrait ;5 il les considérait d'un air riante et semblait les the conviction that there is nothing really little in the works of examiner comme un amateur qui choisit des marchandises. 11 an infinite mind. faut (e) vous dire cependant, qu'il ne regardait ainsi que les The antennæ of the fly, or feelers, as some call them, must paysans qui portaient (1) de grandes barbes.? Elles étaient not detain us long, but we cannot pass over some peculiarities sans doute très-longues et très-fournies (9), mais d'un rour si of structure in these organs. The third point in the antennæ of laid, qu'après un moment d'examen Bilboquet tournait la tête the blue-bottle fly (Musca vomitoria) is pierced with exceed- et allait plus loin. Enfin, en allant ainsi, notre tambour arriva ingly fine apertures, the diameter of each being only towth of au quartier des Juifs. Les Juifs à Smolensk, comme dans yn inch. So numerous are these openings that both antennæ toute la Pologne et la Russie, vendent toutes sortes d'objets are estimated to contain 17,000. The mouth of each tube is et ont un quartier particulier. 10 Dès que Bilboquet y (h) fut protected by a fine curtain-like membrane, behind which a entré, ce fut pour lui un véritable ravissement : 11 imaginez-vous minute sac full of fluid can be seen. Some naturalists regard les plus belles barbes du monde, noires comme de l'ébène;" this singular system of apertures and sacs as forming the car car la nation juive toute dispersée qu'elle est, parmi les autres rire " 18 NOTES. nations, a gardé la teinte brune de sa peau et le noir éclat de ses COLLOQUIAL EXERCISE. cheveux.13 Voilà donc notre Bilboquet enchanté. Enfin il se 1. Le marchand chercha-t-il à 11. Que fut-elle bientôt obligée de décide, et entre dans une petite boutiques où se trouvait un le dissuader? faire ? barchand magnifiquement barbu.15 Le marchand s'approche 2. Pourquoi ne put-il lui faire 12. Pourquoi l'auteur ne veut-il de notre ami et lui demande humblement en mauvais français- entendre raison ? point faire le tableau de cet hor"Que voulez-vous, mon petit Monsieur ?" 16 3. Comment les soldats trou rible désastre ? * Je veux (i) ta barbe,” répondit cavalièrement Bilboquet.17 vèrent-ils l'idée du tambour ? 13. Que suffit-il de savoir ? " Ma barbe !” dit le marchand stupéfait; " vous voulez (j) 4. Quo firent-ils? 14. Où se trouvait le régiment de 5. Que fit le perruquier du régi Bilboquet ? ment? "Je te dis, vaincu, que je veux ta barbe,” reprend le vain 15. Que faisnient les Cosaques ? 6. Le tambour parut-il content de 16. Qu'avait-on essayé de faire çceur superbe en posant la main sur son sabre; "mais no crois si prise ? après avoir passé la rivière ? pas que je veuillo (k) te la voler :19 tiens, (l) voilà un nepoléon, 17. Pourquoi l'explosion n'avaittu me rendras mon romani im). arrivant ? elle pas eu beaucoup d'effet ? 8. Où la plaça-t-il ensuito ? 18. Pourquoi la charpente da pont COLLOQUIAL EXERCISE. 9. Parla-t-on longtemps de cetto ne tombait-elle pas ? 1. A partir de ce jour, comment| 11. Dès que Bilboquet y fut entre, aventure ? 19. Qu'est-ce que les ennemis traita-t-on notre héros ? qu'éprouva-t-il ? 10. Qu'arriva-t-il à l'armée fran-1 auraient pu faire, s'ils étaicnt 2. Que fit-il de son argent ? 12. Quelle était la couleur de leurs çaise après son entrée à arrivés ? Que firent les troupes françaises barbes ? Moscou ? quelque temps après ? 13. Quelle est la teinte qu'a gardée Que fit le petit tambour le jour la nation juive ? de son arrifée ? 14. Quand il eut décidé, que fit. (a) Faire entendre raison au (1) On se remit en marche, the 5. De quoi parnissait-il content ? il ? petit B., induce little B. to march was resumed. 6. De quelle manière considérait- 15. Qui s'y trouvait-il ? listen to reason. (1) From atteindre. ul le visage des habitants ? 16. Que lui dit le marchand ? (6) Il s'engagea une dispute, (le) Qu'il, let it. 7. Quelles personnes regardait-il 17. Que lui répondit le petit tam an altercation comnienced. (1) From suffire. particulièrement? bour? (c) From se mettre. (m) S'il restait, if there remained. Enfin où arriva-t-il ? 18. Que lui répondit le mar. (d) Remit, delivered. (n) Obéissant, obeying, 9. Que Tendent les Juifs à Smo chand? () Carried it. (o) Ils venaient de, they had just. lensk? 19. Quelle fut la réponse du petit (f) Fit coudre, had it sowed. (P) Faire sauter, blow up. 11. Y'ont-ils pas un quartier par. tambour ? (9) Causa, talked, spoke. () From produire. siculier ? (h) From falloir. (1) La retenait, supported it. NOTES. (a) They did not laugh any more. (9) Thick, bushy. 1. From devenir. (1) Y, there. KEY TO EXERCISES IN LESSONS I FRENCH. 14 Au lieu de, instead of. (0) I want. EXERCISE 79 (Vol. I., page 371). (d! I alla se promener, he went 6) Vous voulez rire, you are to take a walk. 1. At what hour did your sister come? 2. She came at a quarter joking. (1) Il faut vous dire, I must tell (1) Je veuille, subj., from vouloir. 4. They were born neither in Ronen nor in Caen, they were born in before eight. 3. Were those young ladies born in Rouen or in Caen? (1) Tiens, tako, here. From porter. (m) Mon reste, my change. Strasburg. 5. Is the watchmaker at home? 6. No, Sir, he is gone to his warehouse. 7. Has he been in Paris this year? 8. Yes, Madam, SECTION VI. he has been there. 9. Has he bought goods there? 10. He has bought jewellery there. 11. Did you go to my father? . 12. I went to Le pauvre marchand voulut faire entendre (a) raison au him. 13. Has your hatter gone out to-day? 14. He has not been petit Bilboquet, mais il était entêté comme un cheval aveugle, out, he is sick. 15. Is the mason at home? 16. No, Madam, he is et il s'engagea (6) une dispute qui attira bientôt quelques gone out. 17. When did he go out? 18. He went out an hour ago. soldats. Ils entrèrent pour s'informer du motif de la querelle, 19. Did your hatter arrive to-day or yesterday! 20. He arrived yeset ils trouvèrent l'idée du tambour si drôle, qu'ils obligèrent terday at four o'clock in the morning. 21. Has our tailor been to le pauvre Juif à lui céder sa barbe, * et l'un d'eux, Gascon et see his father to-day? 22. He has left for Lyons. 23. Has not my perruquier du régiment, tira des rasoirs de sa poche, se mit () Germany. 25. My sister has been at church this morning, and is cousin's goldsmith left for Spain? 24. No, Sir, he has returned to i maser le malheureux marchand et remit (d) solennellement le gone to school half an hour ago. tout à Bilboquet qui l'emporta (e) en triomphe. En arrivant au régiment, il la fit (1) coudre par le tailleur sur un morceau EXERCISE 80 (Vol. I., page 371). de peau d'un tambour crevé, et sans rien dire de son dessein, 1. Le médecin est-il à la maison? 2. Non, Monsieur, il n'est pas à il la mit au fond de son sac. On en causa (9) pendant quelques la maison, il est sorti. 3. Etes-vous sorti ce matin? 4. Non, Monsieur, jours, mais il fallut (h) bientôt penser à autre chose. On se je ne suis pas sorti , je suis malade. 5. La petite fille de votre sour estremit en (1) marche, et on ne pensait plus au petit Bilboquet, elle sortie ? 6. Oui, Monsieur, elle est sortie, elle est chez mon frère. quand on arriva à Moscou. 7. À quelle heure le chapelier est-il arrivé? 8. Il est arrivé hier au Alors il arriva d'affreux malheurs, le froid et la dévastation soir à neuf heures. 9. Le bijoutier a-t-il été à Paris ou à Lyon cette privèrent l'armée française de toutes ses ressources,lo la famine Avez-vous été trouver mon frère ou ma sæur? 12. Je n'ai pas eu le année? 10. Il a été a Paris il y a six mois, mais il est de retour. 11. atteignit (), et bientôt il fallut se retirer à travers un pays temps d'aller les trouver. 13. Où ce monsieur est-il né? 14. Il est désert et des neiges sans fin." Je ne veux pas vous faire un né en Angleterre, à Exeter ou à Portsmouth. 15. Votre soeur n'esttrhleau de cet horrible désastre ; c'est une chose trop vaste et elle pas née à Paris? 16. Non, Monsieur, elle est née à Madrid, en trop épouvantable 12 à la fois, pour que je vous en parle dans Espagne. 17. M'avez-vous dit que M. votre frère a acheté une bonne cette histoire; qu'il (k) vous suffise (1) de savoir que chacun maison? 18. Il a acheté une très bonne maison à Londres. 19. Savezl'on retournait comme il pouvait, 13 et que c'est à peine s'il (m) vous à quelle heure l'horloger est arrivé? 20. Il est arrivé ce matin à restait quelques régiments réunis en corps d'armée et obéissant (n) cinq heures moins un quart. 21. A-t-il apporté beaucoup de bijouterie ? 13 généraux. Celui de Bilboquet était de ce nombre. Il était de montres. 23. A-t-il été en France ou en Allemagne ? 24. Il a été 22. Il n'a pas apporté beaucoup de bijouterie, mais il a apporté beaucoup de l'arrière-garde, 14 qui empêchait des milliers de Cosaques, qui en France, en Allemagne et en Suisse. 25. Malle, votre seur est-elle souvaient la retraite de l'armée, 15 de massacrer les malheureux à la maison, Monsieur? 26. Non, Monsieur, elle est sortie, elle est allée à l'église. 27. A-t-elle été à l'école, hier? 28. Elle a été à l'école Cn jour, ils venaient de (o) franchir une petite rivière, et, et à l'église. 29. Y est-elle à présent? 30. Non, Monsieur, elle en rotz retarder la poursuite des ennemis , on avait essayé de faire est revenue. 31. Le chapelier ect-il arrivé? 32. Oui, Monsieur, il est sauter (p) deux arches d'un pont de bois qu'on venait de tra- arrivé. 33. Quand est-il arrivé ? 34. Il est arrivé hier, à neuf heures Tamer ; mais les tonneaux de poudre avaient été posés si pre du matin, capitamment,17 que l'explosion ne produisit (a) que peu d'effet: EXERCISE 81 (Vol. I., page 372). szches furent cependant démantibulées, mais toute la char 1. Is the young man gone far! 2. He is not gone very far, he is only I ate appuyait encore sur une grosse poutre qui la (9) retenait, 18 gone as far as Paris. 3. Your children make too much noise ; why do et qui, si les ennemis fussent arrivés, eût bientôt permis de you not take them away ? 4. They are sick, they cannot walk. 5. construire le pont.19 How have you brought them here? 6. I brought them in a carriage. soldats isolés. 2xy 13@y are ax 7. At what hour do you bring the physician? 8. I bring him every alike, as + 4b + 56, or — 4y— 3y, etc. Find the sum of the co. day at twelve. 9. How many times a day do you take your pupils to efficients, annex the common letter or letters, and prefix the com. church? 10. I take them to church twice a day. 11. How many mon sign. times have you been there? 12. I have been there several times. 13. EXAMPLES.-(1.) What is the sum of 3a, 4a, and 6a ? Which way did those travellers come ? 14. They came through Amiens and Rouen. = 13a. Ans. 15. Whence do you bring this news? 16. I Here, 3a + 4a + 6a bring it from Cologne. 17. Whence have you brought those superb (2.) 3xy (3). 76 + y (4.) ry + 3abh (5.) cdwy + 3mg horses? 18. I have brought them from England. 19. If you leave 7xy 8b + 3xy 2cdxy + ng France, do you intend to take away your son? 20. I intend to tako ay 5cdxy + 7mg him away. 21. What have you brought from France? 22. We have 6b + 5xy 7cdzy + 8mg brought magnificent silk goods, fine cloths, and Lyons hats. 23. Have you brought your daughter on foot or on horseback? 24. I 23b + 1lcy 15cdæy + 19mg brought her in a carriage. 25. Your brothers have brought us books. 50. The mode of proceeding is the same, when all the signs EXERCISE RA (VAI T - học: . 1. Combien de temps M. votre fils a-t-il demeuré à Londres ? 2. EXAMPLES.-(1.) What is the sum of - Buc, Il y a demeuré dix ans. 3. Jusqu'où le médecin est-il allé ? 4. Lo Here — 3c - bc - 5bc = -9bc. médecin est allé jusqu'à Cologne. 5. A-t-il emmené son fils avec lui? (2.) (3.) – 2ab my (4.) Засh. 8bdy 6. Il ne l'a pas emmené. 7. Comment avez-vous amené vos deux petites ach - bdy filles ? B. J'ai amené l'une en voiture, et ma femme a porté l'autre. 9. Зах 2ax - 5ach — 7bdy Est-elle trop petite pour marcher? 10. Elle n'est pas trop petite pour marcher, mais elle est malade. 11. Avez-vous amené votre cheval? 12. баа - 10ab - 12my Sach 16bdy Nous avons amené deux chevaux. 13. Avez-vous apporté les livres 51. Case 2.-When the quantities are alike, but the signs que vous m'avez promis ? 14. J'a oublié de les apporter. 15. Cette unlike, that is, only one of each, as + 9b and — 6b; dame a-t-elle amené son fils aîné ? 16. Elle a amené tous ses enfants. 17. Comment sont-ils venus ? 18. Ils sont venus en voiture. 19. Take the less co-efficient from the greater ; to the difference, Par où M. votre frère est-il venu d'Allemagne ? 20. Il est venu par annex the common letter or letters, and prefix the sign of the Aix-la-Chapelle et par Bruxelles. 21. Avez-vous l'intention de mener greater co-efficient. votre fils à l'école, cette après-midi? 22. Je n'ai pas l'intention de l'y Suppose a man's loss is £500, and his gain £2,000. The mener, il fait trop froid. 23. Cet enfant est-il trop malade pour algebraic notation is - 500 + 2000, i.e., £500 is to be subtracted marcher ? 24. Il est trop malade pour marcher, et j'ai l'intention de from his stock, and £2,000 added to it. But it will be the same le porter. 25. Pourquoi ne l'y menez-vous pas en voiture? 20. Mon in effect, and the expression will be greatly abridged, if we add frère a emmené mon cheval. 27. Avez-vous amené le médecin ? 28. the difference between £500 and £2,000, viz., £1,500 to his Je ne l'ai pas amené, il n'y a personne de malade chez vous. 29. stock. Voulez-vous porter ce livre à l'église ? 30. J'en ai un autre, je n'en ai pas besoin. 31. Avez-vous porté ma lettre à la poste ? 32. Je l'ai EXAMPLES.-(1.) What is the sum of 16 ab and — 7ab? oubliée. 33. Jusqu'à quelle heure avez-vous écrit ? 34. J'ai écrit Ans. 9ab. jusqu'à minuit. 35. D'où Mlles. vos seurs viennent-elles ? 36. Elles (2.) (3.) (4.) (5.) (6.) viennent de Paris. To + 4b 5bc 2hm dy + 6m 3hAdd -- 66 7bc Ohm 4dy - 5h + 4de LESSONS IN ALGEBRA.-III. -26 — 25c -7hm 3dy + 5m 8h + 3ds 52. If several positive and several negative quantities are to ADDITION. be reduced to one term, first reduce those which are positive, EXAMPLES.-(1.) John has a marbles and gains 6 marbles more. and next those which are negative, to one term, and then proHow many marbles has he in all ? ceed as in Art. 51. In this example we wish to add a marbles to b marbles. But EXAMPLES.-(1.) Reduce 136 + 66 +6 - 46 - 55 — 7b, to addition in algebra is denoted by the sign +. Hence +b is one term. the answer, i.e., John has the sum of a marbles added to b Here, 136 + 66 +b=20b; and — 46 — 5b - 76= - 16b; marbles. Whence 20b - 166 = 46. Ans. (2.) What is the sum of 36 pounds added to the sum of c (2.) Add 3xy - xy + 2xy — 7xy + 4xy – 9xy + 7y - 6xy. pounds and f pounds ? Here, 3xy + 2xy + 4xy + 7xy = 16xy. By algebraic notation, 36 +c+f pounds is the answer. And, - xy - 7xy - Ivy - 6xy = -:- 23xy; 44. The learner may be curious to know how many marbles Whence, 16ay - 23xy = - 7xy. Ans. there are in a + b marbles; and how many pounds in 3b + ctf (3.) Add 3ad had + ad + 7ad - 2ad + 9ad-Bad - dad. pounds. This depends upon the number each letter stands for. Here, 3ad + ad + 7ad + 9ad=20ad; But the questions do not decide what this number is. It is not And, -bad-2ad-sad-4ad = 20ad; the object, in adding them, to ascertain the specific value of a Whence 20ad -- 20ad = 0. Ans. .and b, or 3b, c, and f; but we find an algebraic expression, which (4.) Add 2abm- abm + 7abm - 3abm + 7abm. will represent their sum or amount. This process is called Here, 2abm + 7abm + 7abm = 16abm; addition. Hence And, abm -- 3abm= -4abm; 45. ADDITION in algebra may be defined, the connecting of Whence, 16abm 4abm = 12abın. Ans. several quantities with their signs into one expression. (5.) Add axy — 7axy + Boxy — axy — Saxy + 9axy. 46. Quantities may be added, by writing them one after another, Here, axy + Saxy + 9asy = 18axy ; without altering their signs. And, - 7axy- awy — Saxy = - 16awy; N.B.-A quantity to which no sign is prefixed is always to Whence, 18axy -- 16axy = 2axy. Ans. be considered positive, that is, the sign + is understood (Art. 53. If two equal quantities have contrary signs, they destroy 12]. each other, that is, the results of their addition is 0, and they EXAMPLE.—What is the sum of a + m, 6 - 8, and 2h – 3m may be cancelled. Thus + 66 - 6b = 0. And (3 X 6) --- 18 + d? a + m +b - 8+2h — 3m + d. Ans. 0, so 7bc -- 760 = 0. 47. It is immaterial in what order the terms or letters are 54. If the letters, or quantities in the several terms to be added, arranged. If you add 6 and 3 and 9, the amount is the same, are UNLIKE, they can only be placed after each other, with their whether you put the 6, the 3, or the 9 first-namely, 18. But it proper signs (Art. 46). is frequently more convenient, and therefore customary, to arrange EXAMPLES.-(1.) If 46, — 6y, 3x, 17h, — 5d, and 6, be added, the letters in alphabetical order. their sum will be 46 - 6y + 3x + 17h - 5d + 6. 48. It often happens that the expression denoting the sum or (2.) Add ad, aad, to cr, arx, and exxx. amount may be simplified by reducing several terms to one. Different letters, and different powers of the same letter, can Thus, the expression 2a + 7a+ 4a may be abridged by uniting no more be united in the same term, than pounds and guiness the three terms into one. Thus, 2a added to 7a makes 9a, and can be added, so as to make a single sum. Six guineas and four 4a added to 9a makes 13a, that is, 2a + 7a + 4a = 13a. pounds are neither ten guineas nor ten pounds; therefore the There are two cases in which reductions can be made. sum of the above = aa + aaa + ax + xxx + xxxx. 49. Case 1.-When the quantities are alike, and the signs 55. From the foregoing principles we derive the following b 6 abc 6 GENERAL ROLE FOR ADDITION, 23. az", a*x, y, xy, and 3bya. 6ab2 Write down the quantities to be aaded without altering their + 13, and 503 – 4a*b - ab? + 363. signs, placing those that are álike_under each other; and unite 30. 2 - 5,3- 3.c + 1, 22-3 + 6x2 + 5x + 3, 3x3 22:2 — *-1, and 4x3 such terms as are similar. 22 + 2x - 5. Otherwise.-Write the quantities to be added one after another, 31. - @ +b+c+d, a-b+c+d, a + b -c+d, and a +b +o- d. putting the sign + between them, and then simplify the expression 32. a - 26, 2b - 3c, 3c - 4d, 4d - 5e, and 56 - 6f. by incorporating like quantities. 33. 33 + 2yz - 3yz", 2y3 + 2yaz + 5yz, and 343 – 4yaz – 2y22. Nate 1.-If any of the quantities be in brackets and the sign S4. ax3 + bx, bas – cx, and can + dx*. + be before the brackets, the brackets may be removed without 35. mai – nz, nza - pz, and 2z - . altering the result. By brackets is meant the vinculum or parenthesis, already KEY TO EXERCISES IN LESSONS IN ALGEBRA. EXERCISE 1. be included in any manner between brackets or parentheses, 1. (a - b) (b + c + a) 37m + h + 6 they must be treated as a single quantity, that is, the result of the operation of the signs within the brackets is to be used 2. a + b : :: ac : 19h, instead of the quantities themselves, as a general rule. If the a + b + c signs of the quan ties within the brackets be either plus or 3. 4 (a + b + c)- d. minus, or a combination of both, and if a factor be outside the = 7a bracket, each of the quantities within may be multiplied by 36" that factor, preserving their signs, and the product will be the EXERCISE 2. same as if the result were multiplied by that factor. Thus, : (+ b - c) = ax + bx — c; or, if a + b c = e; then 1. The product of a and 6 increased by the quotient of 3 times hi 2(a + b - c) = er. Conversely, if the result of the quantities minus c, divided by the sum of a and y, is equal to the product of d by a increased by the sum of b and c, and diminished by the quotient of within the brackets be multiplied by any factor, the result will h divided by the sum of 6 and b. be the same as if each of the quantities were multiplied by that 2. If a be added to 7 times the sum of h and x, and from this sum, factor. Thus, if a + b c = e; then, ex = (a + b -- c) the quotient of c less 6 times d, divided by the sum of twice a and 4, et br - cz. If several factors be employed, the same results be subtracted, the remainder will be equal to the sum of a and hig, will tako place. Thus, axy + bæy - cxy = æy ( a + bc) multiplied by the difference of b and c. (a + b - c) zy; and mbed — nbcd + pbcd=bcd (m – n+p) = 3. The difference of a and b, is to the product of a and c, as the (mn -- + p) bed; and payz + qxyz rxyz = xyz (p+q--7)= difference of d and 4, divided by m, is to 3 multiplied by the sum of (P+9-9) rys. Expressions of this kind may be varied in-h, d, and y. definitely. 4. If the quotient of the difference between a and h, divided by the Note 2.-If the sign – be before the brackets, they cannot be the product of a and b, divided by twice m, the whole will be equal to sum of 3, and b less c, be added to the quotient of the sum of d and removed without vitiating the result, until the signs of all the the quotient of b times a multiplied by the sum of 2 and h, divided by terms within the brackets be changed, viz., + into and con a times m, lessened by the quotient of c times a divided by h increased versely. by d times m. EXAMPLE.—To 3bc -- 60 + 26 - 3y, add 3bc + 2 - 3d EXERCISE 3. + bg, and 20+ y +3x + b. 3 x 6 These may be arranged thus : 3bc — 6d + 26-3y 1. + 3 + 8 x 10 = 9 + 3 + S0 = 92. 2 -3bc - 3d +*+bg 4 + 80 (4 2) + 10 2. 7 + 1 = 8. 4 + (4 x 2 x 10) 4 + 18 - 72 +36 - 2y +4c +- bg And the sum will be 3. + 64 EXERCISE 4. + 6+ -7 = 68. Add together the following quantities (3 x 4) + (3 x 6) (3 x 4 x 10) - (6 x 2) 12 + 18 I eh + 8, to cd - 3, and 5ab 4m + 2. 4. 4 X8 + =32 + 2 2+ 3y - dz, to 7 - X-8 + hm. 12) - 12 108 32 + 5 – 3 = 34. 3. abu - 3+ bm, to y - x + 7, and 5x – 6y + 9. 36 36 4. 3am # 6 – 7xy - 8, to 10xy - 9 + 5am. 2 x 4 5. (3 x 4 x 8) + 5. 6ıky + 7d - 1 + wxy, to zahy - 78 + 17 + (2 * 10) = 96 + + 20 = 118. - may & 7ad - h + 8xy - ad, to 5ad + h - 7xy. 8-4 3 = 5 x 2 + 7. Pby - Jax + 2a, to 3bx 6. (3 + 2) * (10 - 8) + by + a. - 3= 9. ž &. ax + by - xy, to - by + 2xy + 5ar. 3 x (6 + 2) (2 + 4) (8 6) + 24 9. 4lodf - 10xy - 186, to 7xy + 25 + 3cdf. 10 - 6 10 (* x 2) 10.3 - 17xy + 18a, to fax 5x + 63cx, 6 x 2 12 = 6 + 24 - 24. 11. Bab - 6ibe + 4cd 7xy, to 17mn + 18fg – 2ax. 42abe + 10abd, to 50abc + 15abd + 5xyz. (9 x 2) + (5 x 8) 6 + 40 8. (4 x 6 - 4) * (3-2) + 8 - (2 x 4) + 13. -y; 6 - df + 44, to 4df – 20 + 3ax + 754. (2 x 10) + 3 10 20 + 3 46 (24 — 4) x 1 14 450 - 106 + 4cdj, to 826 - 4cdf + 100 – 20 + 0 + 10 15, 12 (Q + b) + 3 (a + b), to 2 (a + b) – 10 (a + b). 16. zy (a + b) + Sry (a + b), to 2xy (a + b) - day (a + b). 17. ax + ea, * + axr, 4aq + 2x + ax, and 2xrx. 18. y - m + , 2x + 10g, to 4xy + 6g Sex. 19 aad + taga, to 10aaa 14aaa + 8aaa. 8+ 18 + 4+ (3 x 6) + (4 * 2 * 8) 2 3 x 4, 12 3 x 2 x 6 6 30 6 =32 + 8 8 8 - 6 24 18 12. 23 LATIN STEMS. 29. 12yvyy - 10xx, to 20xx - Syyyy + 211 + 3yyyy. 21. 4 (2-y) - 13, to (a + b) - 16 (x - y) - 7(a + b). We are about to lay before the student a large portion of the 22. a (x + y) - 6y, to 40 (a - b) + 8a (x + y) - 36 (a - b). roots of the Latin language. In the study of them, he may 23. 10axy + 17bcd axy, to Gaxy 14bcd, become acquainted with the treasures of the Roman literature, 24. - 2+ y + 6* (a - b) - 7x, to 16y - 15x (a - b) + 25%. and the tone and strength of the Roman mind. These lessons dom 3. - 4(x + y) + 16 (x + y), to 15abc - 10 (x + y). not indeed, lie on the surface. Nevertheless, they are to be learnt B. Sabe - Bay + min, a + 6abc + 14cy - 11a + 6mn, to 15xy - 17abc by care and diligence. For this purpose, the learner should 156 -abc + xy - 3mn + abe. 27. a (x + y) – 36 (2 + y)-4a (x + y) – 4 (x + y) – (x + y), to 4b (x + y) that a language is the mirror of a nation's mind, accustom impress on his mind the preceding remarks, and remembering + 78 (2 + y) + 5(x + y) + 6b (x + y). himself to see and contemplate the Romans in their wordsNote. As the expressions (square a), y) (cube y), etc., are those unerring tokens of thought, those mental miniatures. used for the first time in the following exercises, the learner is Of course it is only so much of the Latin vocabulary as exists referred to Art. 28: in English that I shall set forth in these pages. The Latin LESSONS IN ENGLISH.—XXIX. |