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RECREATIVE NATURAL HISTORY.

THE HOUSE-FLY.

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As the family of insects to which the house-fly belongs (Muscides) contains above one hundred species, we must limit our attention, in this paper, to that buzzing and teasing creature which so often worries us during the sultry days of summer. The common house-fly (Musca domestica) may seem too well known to require any description. But there are many who will find, on examination, something to wonder at in this dipterous* insect. The wings and power of flight claim our consideration first. Those who closely watch will often be surprised at the manner in which the fly moves through the air with its back Awards. Of ^^^^ -h the insect darts from a table to the ceiling it must perform a kind of somersault in the air. The feet, which were downwards on the table, must be turned uppermost to grasp the ceiling. The motion is so rapid and so unexpected that not one case in a thousand may attract our notice. A keen watchfulness will also enable us to observe that this insect can fly forwards or backwards with, apparently, equal ease. The rate of its motion is about twenty miles an hour, so that a fly can compete, for some time at least, with an ordinary railway train. Some may here ask whether the "buzz" of the fly is produced by the rapid vibration THE FOOT OF THE of the wings against the air. This may, in HOUSE-FLY (MAGNIsome cases, be the cause of so peculiar a FIED). sound, but no decisive answer can, with our present knowledge, be given to the question. The fly is rightly called a two-winged insect, but the apparent rudiments of a second pair can be easily seen, just behind the true wings. These singular organs are called poisers, from a supposition that they enable the fly to balance itself during its rapid somersaults in the air. These little thread-like filaments, with the knob on the top of each, may remind some of the halancing-poles used by dancers on the tight-rope. If the common notion respecting the use of the poisers be correct, we shall readily admit that the fly is well fitted for its evolutions, possessing both a moving and balancing apparatus.

The feet of the fly have long presented a puzzling problem to naturalists, and some persons may even now doubt whether the action of these organs is yet clearly understood. The problem is to explain how the fly can suspend itself from a ceiling or walk up a smooth pane of glass. The "sucker" theory was long popular, and we believed, with little questioning, that the fy's feet were supplied with a kind of air-pump, by which a vacuum was produced under the feet, enabling them to cling to glass much in the same manner that a boy's toy sucker adheres to a stone. Let no reader prepare himself to listen to a new theory on the subject; we must content ourselves with describing the successive views which have been advocated, and then stating that now held by those who have most closely studied these fine and complex structures.

Our

readers will bear in mind that very high and clear microscopic powers, great patience, and numerous observations are necessary for a satisfactory examination of such minute organs.

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a smoky substance' noted by him on glass, and which he thought aided the fly's "bristles" in clinging to so smooth a surface. Was this "smoky substance" the fluid observed by Power, or was it simply the corroded face of the glass? is no doubt that glass does undergo a decomposition, which working opticians call "the sweating." The worn and irregular surface thus produced would aid an insect in clinging. Leuwenhoek, the patient and profound Dutch naturalist, employed his improved microscopes in examining the "bristles" detected by Dr. Hooke. Leuwenhoek saw them clearly, and thought that the end of each resembled a hook. This conjecture has been verified; the extremity of each "bristle" is curved, and so presents a hooked form. Dr. Derham, the friend of Hooke, and editor of Ray's works, turned, for me, from experiments on pendulums and observations on une solar us, to investigate the structure of a fly's foot. His researches led him to adopt a notion resembling the sucker theory. He suggested that flies clung to smooth surfaces by what he vaguely calls their "skinny palms." Derham may have had in his mind the adhesive fluid of Mr. Power and the "smoky substance" of Hooke, while he himself may have indistinctly noted what are now called "the flaps on the foot. By combining all these, Derham might have got his notion of an adhesive cr skinny palm." Gilbert White, though an acute observer of Nature, was not likely to go deeply into microscopic investigations. He therefore adopted the "sharp hooked nails" of Dr. Hooke, the "skinny palms" of Derham, and the sucker theory as explanatory of the whole matter. White, however, clearly admitted the action of two powers in the fly's foot, one for suspension, the other for producing a vacuum. Have we advanced beyond this in certainty of knowledge? Mr. John Blackwall, in 1830, described three conclusions to which he had been led. He detected an expansion at the end of each hair or "tenter," resembling a little pad or cushion, but denied the existence of any vacuum-producer or air-pump structure. Some persons reminded him that each hair, with its expanded tip, might really be a separate sucker. This conclusion he refused to admit, alleging it to be unsupported by proofs. Here, then, was a distinct

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THE EYE OF THE HOUSE-FLY (MAGNIFIED).

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THE TRUNK OF THE HOUSE-FLY (MAGNIFIED).

denial, by an acute microscopic observer, of the sucker theory, accompanied, however, by a clear statement that the end of each hair on the fly's foot possesses a peculiar expansion, looking as if it must have some special work to perform. Mr. Blackwall also arrived at a third conclusion-that a fly in walking along a pane of glass leaves behind certain marks, as if a fluid had been poured out at particular points. He thus agrees with the observations of Power, Hooke, Derham, and White. The examination was still carried on by naturalists, with the aid of the best microscopes. In 1841, Mr. E. Newman called attention to the almost inconceivable number of the "bristles." Hooke had estimated the whole number of the "tenters on the six feet at sixty; Mr. Newman declares they are "almost infinite."

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In 1664, Mr. Power, after long scrutiny of the fly's feet, suggested that the insect clung to surfaces by its hooked claws, and also by the aid of a fluid poured from tubes on the feet. He saw two powers at work; a gripping 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, mathematician, and naturalist, Dr. Robert Hooke, described in his "Micrographia" the "small bristles" on the "soles" of the fly's feet. He called them "tenters" (holders), and counted ten on each foot, thus giving to this small insect sixty holding instruments. But Hooke goes on to describe what he terms

· Diptera, a Greek word signifying "two wings."

VOL. III.

part of the complex structure. This fluid has been subjected to chemical analysis, but no remarkable element has been discovered. Water and oils appear to be the constituents, so that it is similar to the ordinary matter given off by the pores of the human skin.

Mr. Hepworth, in 1854, observed that "the flaps " of the fly's feet were trumpet-shaped, or resembling the form of a boy's sucker when supporting a heavy stone. This gentleman also 58

noticed the marks left on glass by "the flaps," but denied the existence of an adhesive fluid in sufficient quantity to support the weight of a fly. He advocated the sucker theory, giving no less than 12,000 suction tubes on one foot of a common fly. If this statement should stand the test of examinations, we shall then have in one small insect 72,000 suction machines. It may give some readers a clearer view of the minute scrutinies now made into insect structure when we state that the expanded edge of a fly's foot, called "the flap," has been found to be only 50th of an inch in thickness.

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of the fly. This can, however, only rank at present as a clever
supposition, which subsequent discoveries may prove to be true.
The proboscis or trunk of the fly consists of many suction
tubes, admirably fitted for pumping up the fluids on which the
insect feeds. This trunk would admit of a much longer
description than our space allows; we must, however, remind
the reader that a fly's proboscis really contains tongue, jaws,
and lips, all modified and combined in one organ.
The tongue
is a net-work of fine tubes; two fine hooks are visible near the
tip, one on each side, and the extremity is furnished with a
series of most delicate vessels, through which the food passes
up to the more fleshy parts of the tongue. An elaborate system
of exceedingly minute muscles draws out and retracts the tongue,
and aids in rolling un the whole trunk when the insect has
unished its meal. As nothing but a nuid can ascend the fine
vuves, it might be supposed that no fly could dine off a solid
lump of sugar. But the insect is able to dissolve such a sub-
stance by a liquid poured from the trunk, and thus the liquefied
sugar is easily drawn up the suction vessels.

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Mr. Tyrrell and Mr. West have devoted much time to the examination of these "flaps," and the following are the principal results:-Two distinct sets of hairs are found on the foot of a fly; one, called "tenents," rise from the inner side of the flap, and are employed to grip smooth on-f~~~~ rs," their office being to protect the finn hanked tips of the "tenents" from injury by friction. We must observe here that house-flies are not the only insects furnished with such a double system of hairs-most beetles are similarly supplied. 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 sixpressed 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; a 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 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 atmospheric pressure; let him also imagine the tip of his thumb to be armed with a number of fine hooks. He will be able to lift the edges of the little finger sucker by these thumb hooks, and thus the air will be admitted under the sucker. Somewhat after this fashion does the fly loosen its foot from a surface of glass.

vacuum.

The insect requires all its force thus to move the feet nimbly. When benumbed by cold or weakened by other causes, the fly remains fixed to one place, unable to lift its feet from the surface. Feeble or diseased flies may sometimes be seen violently struggling to extricate themselves. This was observed by White, who describes the insects as "labouring along and lugging their feet in windows, as if they stuck fast to the glass." Mr. West has endeavoured to estimate the exact amount of the forces which enable a fly to adhere to glass. He found that one-half the insect's weight is supported by the atmospheric pressure on the feet when the vacuum has been produced. Onefourth of the weight is upheld by the grip of the "tenent' hairs, and the remaining fourth part by the fluid emitted from the flaps. As a common house-fly weighs about half a grain, the supporting force exerted by each of the six feet will amount to one-twelfth of a grain only, and this force is distributed among three powers-the atmospheric pressure, the "tenent hairs, and the sustaining fluid. Each of these forces would have to support the 4th of a grain only, assuming the weight to be equally distributed throughout.

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We have devoted thus much of this paper to the investigations of eminent men into the structure of a fly's foot, with two objects in view-to induce some readers to make a more constant use of the microscope in their studies, and to deepen the conviction that there is nothing really little in the works of an infinite mind.

The antenna of the fly, or feelers, as some call them, must not detain us long, but we cannot pass over some peculiarities of structure in these organs. The third point in the antennæ of the blue-bottle fly (Musca vomitoria) is pierced with exceed ingly fine apertures, the diameter of each being onlyth of n inch. So numerous are these openings that both antennæ are estimated to contain 17,000. The mouth of each tube is protected by a fine curtain-like membrane, behind which a minute sac full of fluid can be seen. Some naturalists regard this singular system of apertures and sacs as forming the car

Many persons may ask, what special service do flies perform in the system of Nature? Their particular office appears to be the rapid consumption of those dead and minute animals whose decaying myriads would, otherwise, soon poison the air. It was a remark of Linnæus, that three flies would consume a dead horse sooner than a lion could. He, doubtless, included the families of the three flies, then he was certainly right. A single fly will sometimes produce 20,000 larvæ, each of which in a few days may be the parent of another 20,000, and thus the descendants of three flies would soon devour an animal much larger than a horse.

Our readers will see, in the preceding remarks, that even a common house-fly can offer to a student of Nature many marvels of structure, and numerous proofs of an infinite intelligence in the almost invisible organs of the meanest creatures.

READINGS IN FRENCH.-II.
LE SAPEUR DE DIX ANS.
SECTION V.

À PARTIR de ce jour, on ne se moqua (a) plus autant du petit
Bilboquet, mais il n'en devint (b) pas pour cela plus commu-
nicatif; au contraire, il semblait rouler dans sa tête quelque
fameux projet, et, au lieu de (c) dépenser son argent avec ses
camarades, comme ceux-ci s'y attendaient, il le serra soigneuse-
ment.2

Quelque temps après, les troupes françaises entrèrent à Smolensk, victorieuses et pleines d'ardeur; Bilboquet en était, et le jour même de l'arrivée, il alla se promener (d) dans la ville, paraissant très-content de presque tous les visages qu'il rencontrait; il les considérait d'un air riant et semblait les examiner comme un amateur qui choisit des marchandises. Il faut (e) vous dire cependant, qu'il ne regardait ainsi que les paysans qui portaient (ƒ) de grandes barbes.7 Elles étaient sans doute très-longues et très-fournies (g), mais d'un roux si laid, qu'après un moment d'examen Bilboquet tournait la tête et allait plus loin. Enfin, en allant ainsi, notre tambour arriva au quartier des Juifs. Les Juifs à Smolensk, comme dans toute la Pologne et la Russie, vendent toutes sortes d'objets et ont un quartier particulier.10 Dès que Bilboquet y (h) fut entré, ce fut pour lui un véritable ravissement: 11 imaginez-vous les plus belles barbes du monde, noires comme de l'ébène; 22 car la nation juive toute dispersée qu'elle est, parmi les autres

12

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Le pauvre marchand voulut faire entendre (a) raison1 au petit Bilboquet, mais il était entêté comme un cheval aveugle," et il s'engagea (b) une dispute qui attira bientôt quelques soldats. Ils entrèrent pour s'informer du motif de la querelle, et ils trouvèrent l'idée du tambour si drôle,3 qu'ils obligèrent le pauvre Juif à lui céder sa barbe, et l'un d'eux, Gascon et perruquier du régiment, tira des rasoirs de sa poche, se mit (c) à raser le malheureux marchand et remit (d) solennellement le tout à Bilboquet qui l'emporta (e) en triomphe. En arrivant au régiment, il la fit (f) coudre par le tailleur sur un morceau de peau d'un tambour crevé, et sans rien dire de son dessein, la mit au fond de son sac.8 On en causa (g) pendant quelques jours, mais il fallut (h) bientôt penser à autre chose. On se remit en (1) marche, et on ne pensait plus au petit Bilboquet, quand on arriva à Moscou.

Alors il arriva d'affreux malheurs, le froid et la dévastation privèrent l'armée française de toutes ses ressources, 10 la famine atteignit (j), et bientôt il fallut se retirer à travers un pays sert et des neiges sans fin. Je ne veux pas vous faire un tableau de cet horrible désastre; c'est une chose trop vaste et top épouvantable à la fois, pour que je vous en parle dans cette histoire; qu'il (k) vous suffise (1) de savoir que chacun en retournait comme il pouvait,13 et que c'est à peine s'il (m) restait quelques régiments réunis en corps d'armée et obéissant (n) I généraux. Celui de Bilboquet était de ce nombre. Il était de l'arrière-garde, qui empêchait des milliers de Cosaques, qui vaient la retraite de l'armée, 15 de massacrer les malheureux soldats isolés.

Un jour, ils venaient de (o) franchir une petite rivière, et, Pour retarder la poursuite des ennemis, on avait essayé de faire Panter (p) deux arches d'un pont de bois qu'on venait de traTerser; mais les tonneaux de poudre avaient été posés si prepitamment, 17 que l'explosion ne produisit (q) que peu d'effet: arches furent cependant démantibulées, mais toute la charate appuyait encore sur une grosse poutre qui la (r) retenait, 18 et qui, si les ennemis fussent arrivés, eût bientôt permis de construire le pont.19

KEY TO EXERCISES IN LESSONS IN FRENCH.

EXERCISE 79 (Vol. I., page 371).

1. At what hour did your sister come? 2. She came at a quarter before eight. 3. Were those young ladies born in Rouen or in Caen? 4. They were born neither in Rouen nor in Caen, they were born in 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, 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 him. 13. Has your hatter gone out to-day? 14. He has not been out, he is sick. 15. Is the mason at home? 16. No, Madam, he is gone out. 17. When did he go out? 18. He went out an hour ago. 19. Did your hatter arrive to-day or yesterday? 20. He arrived yes21. Has our tailor been to terday at four o'clock in the morning. see his father to-day? 22. He has left for Lyons. 23. Has not my cousin's goldsmith left for Spain? 24. No, Sir, he has returned to Germany. 25. My sister has been at church this morning, and is gone to school half an hour ago.

EXERCISE 80 (Vol. I., page 371).

11.

1. Le médecin est-il à la maison? 2. Non, Monsieur, il n'est pas à la maison, il est sorti, 3. Êtes-vous sorti ce matin? 4. Non, Monsieur, je ne suis pas sorti, je suis malade. 5. La petite fille de votre sœur estelle sortie ? 6. Oui, Monsieur, elle est sortie, elle est chez mon frère. 7. À quelle heure le chapelier est-il arrivé? 8. Il est arrivé hier au soir à neuf heures. 9. Le bijoutier a-t-il été à Paris ou à Lyon cette année? 10. Il a été a Paris il y a six mois, mais il est de retour. Avez-vous été trouver mon frère ou ma sœur? 12. Je n'ai pas eu le temps d'aller les trouver. 13. Où ce monsieur est-il né? 14. Il est né en Angleterre, à Exeter ou à Portsmouth. 15. Votre sœur n'estelle pas née à Paris? 16. Non, Monsieur, elle est née à Madrid, en Espagne. 17. M'avez-vous dit que M. votre frère a acheté une bonne maison? 18. Il a acheté une très bonne maison à Londres. 19. Savezvous à quelle heure l'horloger est arrivé? 20. Il est arrivé ce matin à cinq heures moins un quart. 21. A-t-il apporté beaucoup de bijouterie?

22. Il n'a pas apporté beaucoup de bijouterie, mais il a apporté beaucoup de montres. 23. A-t-il été en France ou en Allemagne? 21. Il a été en France, en Allemagne et en Suisse. 25. Mdlle. votre sœur est-elle 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 et à l'église. 29. Y est-elle à présent? 30. Non, Monsieur, elle en est revenue. 31. Le chapelier est-il arrivé? 32. Oui, Monsieur, il est arrivé. 33. Quand est-il arrivé? 31. Il est arrivé hier, à neuf heures du matin.

EXERCISE 81 (Vol. I., page 372).

1. Is the young man gone far? 2. He is not gone very far, he is only gone as far as Paris. 3. Your children make too much noise; why do you not take them away? 4. They are sick, they cannot walk. How have you brought them here? 6. I brought them in a carriage.

5.

7. At what hour do you bring the physician? 8. I bring him every day at twelve. 9. How many times a day do you take your pupils to church? 10. I take them to church twice a day. 11. How many times have you been there? 12. I have been there several times. 13. Which way did those travellers come? 14. They came through Amiens and Rouen. 15. Whence do you bring this news? 16. I bring it from Cologne. 17. Whence have you brought those superb horses? 18. I have brought them from England. 19. If you leave France, do you intend to take away your son? 20. I intend to take him away. 21. What have you brought from France? 22. We have brought magnificent silk goods, fine cloths, and Lyons hats. 23. Have you brought your daughter on foot or on horseback? 24. I brought her in a carriage. 25. Your brothers have brought us books. EXERCISE 82 (Vol T

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1. Combien de temps M. votre fils a-t-il demeuré à Londres? 2. Il y a demeuré dix ans. 3. Jusqu'où le médecin est-il allé ? 4. Lo médecin est allé jusqu'à Cologne. 5. A-t-il emmené son fils avec lui? 6. Il ne l'a pas emmené. 7. Comment avez-vous amené vos deux petites filles? 8. J'ai amené l'une en voiture, et ma femme a porté l'autre. 9. 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. Nous avons amené deux chevaux. 13. Avez-vous apporté les livres que vous m'avez promis ? 14. J'a oublié de les apporter. 15. Cette 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. Par où M. votre frère est-il venu d'Allemagne ? 20. Il est venu par Aix-la-Chapelle et par Bruxelles. 21. Avez-vous l'intention de mener votre fils à l'école, cette après-midi? 22. Je n'ai pas l'intention de l'y mener, il fait trop froid. 23. Cet enfant est-il trop malade pour marcher? 24. Il est trop malade pour marcher, et j'ai l'intention de le porter. 25. Pourquoi ne l'y menez-vous pas en voiture ? 26. Mon frère a emmené mon cheval. 27. Avez-vous amené le médecin? 28.

29.

Je ne l'ai pas amené, il n'y a personne de malade chez nous. 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 oubliée. 33. Jusqu'à quelle heure avez-vous écrit ? 34. J'ai écrit jusqu'à minuit. 35. D'où Mlles. vos sœurs viennent-elles ? 36. Elles viennent de Paris.

LESSONS IN ALGEBRA.—III.

ADDITION.

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52. If several positive and several negative quantities are to be reduced to one term, first reduce those which are positive, EXAMPLES.—(1.) John has a marbles and gains b marbles more. and next those which are negative, to one term, and then proHow many marbles has he in all?

In this example we wish to add a marbles to b marbles. But addition in algebra is denoted by the sign +. Hence +b is the answer, i.e., John has the sum of a marbles added to b marbles.

(2.) What is the sum of 36 pounds added to the sum of c pounds and ƒ pounds?

By algebraic notation, 3b+c+f pounds is the answer. 44. The learner may be curious to know how many marbles there are in a + b marbles; and how many pounds in 3b+c+f pounds. This depends upon the number each letter stands for. But the questions do not decide what this number is. It is not the object, in adding them, to ascertain the specific value of and b, or 3b, c, and f; but we find an algebraic expression, which will represent their sum or amount. This process is called addition. Hence

45. ADDITION in algebra may be defined, the connecting of several quantities with their signs into one expression.

46. Quantities may be added, by writing them one after another, without altering their signs.

N.B.-A quantity to which no sign is prefixed is always to be considered positive, that is, the sign is understood [Art. 12].

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EXAMPLE.-What is the sum of a + m, b— 8, and 2h-3m a+m+b 8+2h- 3md. Ans. 47. It is immaterial in what order the terms or letters are arranged, If you add 6 and 3 and 9, the amount is the same, whether you put the 6, the 3, or the 9 first-namely, 18. But it is frequently more convenient, and therefore customary, to arrange the letters in alphabetical order.

48. It often happens that the expression denoting the sum or amount may be simplified by reducing several terms to one. Thus, the expression 2a + 7a + 4a may be abridged by uniting the three terms into one. Thus, 2a added to 7a makes 9a, and 4a added to 9a makes 13a, that is, 2a + 7a + 4a = 13a. There are two cases in which reductions can be made. 49. Case 1.-When the quantities are alike, and the signs

ceed as in Art. 51. EXAMPLES. (1.) Reduce 13b + 6b + b − 4b — 5b — 7b, to one term.

Here, 136 +66 +b=20b; and -4b - 56 - 7b = — 16b; Whence 206 — 16b4b. Ans.

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EXAMPLES.-(1.) If 4b, 6y, 3x, 17h, -5d, and 6, be added, their sum will be 46-6y+ 3x + 17h5d+ 6. (2.) Add aa, aaa, to xx, xxx, and xxxx. Different letters, and different powers of the same letter, can no more be united in the same term, than pounds and guiness can be added, so as to make a single sum. Six guineas and four pounds are neither ten guineas nor ten pounds; therefore the sum of the above = aa + aaa + xx + xxx + xxxx.

55. From the foregoing principles we derive the following

GENERAL RULE FOR ADDITION.

Write down the quantities to be aaded without altering their signs, placing those that are alike_under each other; and unite such terms as are similar.

Otherwise. Write the quantities to be added one after another, putting the sign + between them, and then simplify the expression by incorporating like quantities.

Note 1.-If any of the quantities be in brackets and the sign +be before the brackets, the brackets may be removed without altering the result.

By brackets is meant the vinculum or parenthesis, already explained [Art. 21]. This is one of the most important things in the study of Algebra; its use is unlimited. If quantities be included in any manner between brackets or parentheses, 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 instead of the quantities themselves, as a general rule. If the signs of the quan ties within the brackets be either plus or minus, or a combination of both, and if a factor be outside the bracket, each of the quantities within may be multiplied by that factor, preserving their signs, and the product will be the same as if the result were multiplied by that factor. Thus, z (a+b−c) = ax + bx - ex; or, if a + b − c = e ; then (a + b −c) = ex. Conversely, if the result of the quantities within the brackets be multiplied by any factor, the result will be the same as if each of the quantities were multiplied by that factor. Thus, if a + b -ce; then, ex = (a + b c) x = a+br -xx. If several factors be employed, the same results will take place. Thus, axy + bxy. cxy = xy (a + b c) (a+be) xy; and mbed- nbcd+pbcd= bcd (m · n + p) = (mn+p) bed; and pryz+qxyz rxyz = xyz (p + q − r) = (p+q―r) xyz. Expressions of this kind may be varied indefinitely.

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Note 2.-If the sign be before the brackets, they cannot be removed without vitiating the result, until the signs of all the terms within the brackets be changed, viz., + into and conversely.

EXAMPLE. TO 3bc6d + 2b3y, add bg, and 2d + y +3x+b.

These may be arranged thus: 3bc6d2b-3y

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1. The product of a and b increased by the quotient of 3 times h

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 h divided by the sum of 6 and 6.

2. If a be added to 7 times the sum of h and x, and from this sum, the quotient of c less 6 times d, divided by the sum of twice a and 4, be subtracted, the remainder will be equal to the sum of a and h, multiplied by the difference of b and c.

3. The difference of a and b, is to the product of a and c, as the difference of d and 4, divided by m, is to 3 multiplied by the sum of h, d, and y.

4. If the quotient of the difference between a and h, divided by the sum of 3, and b less c, be added to the quotient of the sum of d and the product of a and b, divided by twice m, the whole will be equal to the quotient of b times a multiplied by the sum of and h, divided by a times m, lessened by the quotient of c times d divided by h increased by d times m.

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3bc+x

за

3 x 6

1.

2

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2 x 6

3.

4+ (3 × 6)

+ (4 × 2 × 8)

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EXERCISE 4.

22

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Add together the following quantities—

-

1. ab + 8, to cd 3, and 5ab 4m + 2. 2x+3yde, to 7-x- 8+ hm.

3. abu

3 + bm, to y-x+7, and 5x 4. 31m+67xy 8, to 10xy 9+ 5am.

5. 6ahy7d1+mxy, to 3ahy

6. 7adh + 8ry

7. 2by

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ad, to 5ad + h − 7xy.

3ax + 2a, to 3bx

xy, to

9. 41cdf - 10xy

by + 2xy + 5ar.

18b, to 7xy+21b+3cdf.

10. 3b-17xy + 18a, to 4ax - 5bx+63cx.

11. 8abfibe + 4cd

7xy, to 17mn + 18fg - 2ax.

12. 42abe + 10abd, to 50abc + 15abd + 5xyz.

13. 4-y

6df44, to 4df 20+ 3ax + 75y.

14 45a 106 + 4cdf, to 82b

4cdf + 10a 46.

10 (a + b).

15. 12 (a + b) + 3 (a + b), to 2 (a + b) 16. zy (a + b) + 3xy (a + b), to 2xy (a + b) 4xy (a + b). 17. az + ua, x + xxx, 4aa + 2x + ax, and 2xxx.

18. yyy + xy, 2rx + 10yy, to 4xy+6y8xx.

19 aaa+ 4aaa, to 10aaa 14aaa +8aaa.

20. 12yyyy-10xr, to 20xx

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26. 5abe - 6xy + mn, a + 6abc + 14xy 11a + 6mn, to 15xy 17abc 151-abc zy-3mn + abc.

27. a (x + y) · 36 (x + y) −4a (x + y) − 4 (x + y) − (x + y), to 4b (x + y) +7a (x + y) + 5 (x + y) + 6b (x + y). Note.-As the expressions a2 (square x), y3 (cube y), etc., are used for the first time in the following exercises, the learner is referred to Art. 28:

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WE are about to lay before the student a large portion of the roots of the Latin language. In the study of them, he may become acquainted with the treasures of the Roman literature, and the tone and strength of the Roman mind. These lessons do not indeed, lie on the surface. Nevertheless, they are to be learnt by care and diligence. For this purpose, the learner should impress on his mind the preceding remarks, and remembering that a language is the mirror of a nation's mind, accustom himself to see and contemplate the Romans in their wordsthose unerring tokens of thought, those mental miniatures.

Of course it is only so much of the Latin vocabulary as exists in English that I shall set forth in these pages. The Latin

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