SECTION XXIL-STEMS AND TERMINATIONS OF THE REGULAR VERBS.-PRESENT INDICATIVE, N'aimez-vous pas les enfans atten- Do you not like attentive children? 1. If the ending or distinguishing characteristic of the conju. Ne recevez-vous pas beaucoup de Do you not receive many letters? gation of a verb, in the present of the infinitive, be removed, the part remaining will be the stem of the verb: Chant-er Fin-ir Rec-evoir Rend-re. lettres ? Nous en recevons beaucoup. Vendez-vous beaucoup de marchan dises ? Nous en vendons beaucoup. We receive many letters. Do you sell many goods? We sell many. Votre frère aime le boeuf et le Your brother likes beef and mutton. mouton. VOCABULARY. OBS.-We shall hereafter put a hyphen between the stem and the termination of the verbs placed in the vocabularies. The number indicates the conjugation. Aim-er, 1, to love, to like, to be fond of. Autre, other. Assez, enough. Donn-er, 1, to give. Compagnon, m., com- Maison, f., house. Non seulement, not wear. Rec-evoir, 3, to receive. Souvent, often. -e fourn-it perç -oit tend panion. Marchand, m., mer furnishes gathers tends. Dame, f., lady. PLURAL. De bonne heure, carly. De-voir, 3, to owe. chant. Marchandises, f. pl., Neveu, m., nephew. EXERCISE 39. [goods. entend-ons. hear. perd .ez. lose. mord -ent. bite. 6. The present of the indicative has but one form in French, therefore je chante may be rendered in English by I sing, I do sing, or I am singing. 7. The plural of the present of the indicative may be formed from the participle present by changing ant into ons, ez, ons. Ex.: Chantant, nous chantons; finissant, nous finissons; recerant, nous recevons; rendant, nous rendons. 8. This rule holds good not only in all the regular, but in almost all the irregular verbs. 9. Verbs may be conjugated interrogatively in French (except in the first person singular of the present of the indicative) [§ 98 (4) (5)], by placing the pronoun after the verb in all the simple tenses, and between the auxiliary and the participle in the compound tenses. 1. Votre mère aime-t-elle la lecture ? (Sect. XXII. 11.) 2. Oui, Mademoiselle, elle l'aime beaucoup plus que sa sœur. 3. Quel chapeau votre neveu porte-t-il? 4. Il porte un chapeau de soie, et je porte un chapeau de paille. 5. Cette dame aime-telle ses enfants? 6. Oui, Monsieur, elle les chérit. 7. Fournissez-vous des marchandises à ces marchands? 8. Je fournis des marchandises à ces marchands, et ils me donnent de l'argent. 9. Vos compagnons aiment-ils les beaux habits ? (Sect. XXII. 11.) 10. Nos compagnons aiment les beaux habits et les bons livres. 11. Cherchez-vous mon frère ? 12. Oui, Monsieur, je le cherche, mais je ne le trouve pas. 13. Votre frère perd-il son temps. 14. Il perd son temps et son argent. 15. Perdons-nous toujours notre temps? 16. Nous le perdons très souvent. Devez-vous beaucoup d'argent? 18. J'en dois assez, mais je n'en dois pas beaucoup. 19. Vendez-vous vos deux maisons à notre médecin ? 20. Je n'en vends qu'une, je garde l'autre pour ma belle-sœur. 21. Recevez-vous de l'argent aujourd'hui ? 22. Nous n'en recevons guère. 23. Votre menuisier finit-il son travail de bonne heure? 24. Il le finit tard. 25. A quelle heure le finit-il ? 26. Il le finit à midi et demi. 27. Nous finissons le nôtre à dix heures moins vingt minutes. EXERCISE 40. 17. 9. Do you 1. Does your companion like reading? 2. My companion does not like reading. 3. Does your father like good books? (Sect. XXII. 11.) 4. He likes good books and good clothes.* but my brother owes more than fifteen. 7. Are you wrong to 5. Do you owe more than twenty dollars? 6. I only owe ten, finish your work early? 8. I am right to finish mine early, and you are wrong not to (de ne pas) finish yours. receive much money to-day? 10. I receive but little. 11. Do we give our best books to that little child? 12. We do not give them, we keep them because (parceque) we want them. 13. Do you sell your two horses ? 14. We do not sell our two horses, we keep one of them. 15. Do you finish your work this morning (matin)? 16. Yes, Sir, I finish it this morning early. 17. Does your brother-in-law like fine clothes? 18. Yes, Madam, he likes fine clothes. 19. Do you seek my nephew? 20. Yes, Sir, we seek him. 21. Does he lose his time? 22. He loses not only his time, but he loses his money. 23. How much money has he lost to-day? 24. He has lost more than ten dollars. 25. Does your joiner finish your house? 26. He finishes my house and my brother's. 27. Do you sell good hats? 28. We sell silk hats, and silk hats are good. (Sect. XXII. 11.) 29. How old is your companion? 30. He is twelve years old, and his sister is fifteen. 31. Does your brother like meat? 32. He likes meat and bread. 33. Do you receive your goods at two o'clock? 34. We receive them at half after twelve. 35. We receive them ten minutes before one. *Repeat the article. VI. LESSONS IN BOTANY. SECTION IX.-ORGANS WHICH LOOK LIKE LEAVES, BUT WHICH ARE NOT LEAVES. WE already discovered, at a very early period in our investigations, that Nature plays some strange tricks in the construction of plants, causing one thing to look like another, as though for the express purpose of deceiving us. We discovered that neither pine-apples, nor strawberries, nor figs were merely fruits. We shall now discover that certain things which appear like leaves are not leaves. What would the reader think as regards many of the cactus tribe? Would he not think these curious plants were all leaves ? Botanists denominate an enlarged and flattened organ of this kind by the term phyllodium, a word derived from the Greek puλov (pronounced ful-lon), a leaf, and eidos (i-dos), form, and which therefore means having the form or semblance of a leaf. One example more of a portion of a plant resembling a leaf, but which is not a leaf, and we have done. It might have been mentioned whilst we were treating of the cactus, to the condition of which the phenomenon about to be mentioned is similar. Perhaps the student has occasionally seen growing in the hedges the shrub called the butcher's-broom, Ruscus aculeatus. Like the cactus, this plant seems to present the curious appearance of flowers springing from the surface of a leaf. Flowers, however, never grow in that position. The part resembling a leaf 52. STIPULATE LEAF-LEAF OF PANSY. 53. BRANCH OF THE BUTCHER'S-BROOM. 54. LEAVES OF THE AUSTRALIAN ACACIA. 55. LATHYRUS АРНАСА. 56. VINE TENDRIL. 57. PITCHER PLANTS. The fact is, they are totally without leaves, the leaf-like portions being merely flattened stems which fulfil the functions of leaves. What would he think, again, of those two little leaf-like expansions recognisable in the pansy, of which we give a drawing (Fig. 52)? These are not separate leaves, but leaf appendages which botanists denominate stipules. Hence the leaf of the pansy is said to be stipulate; and the reason why we did not represent the pansy leaf amongst the other leaves a short time back was, because the term stipulate had not been explained. The word stipule is derived from the Latin stipula, the husk round straw, because the stipules stand out from the stem of the real leaf in much the same manner as the leaves of wheat or barley spring from the stalk at intervals. Occasionally the petiole, or leaf-stalk, itself becomes expanded into a leaf-like form, and the real leaves are stunted. This peculiarity characterises many of the acacias which grow in Australia. The appended diagram (Fig. 54) will render the peculiar condition more evident. is no leaf at all, but only a flattened branch. The accompanying diagram (Fig. 53) represents a sprig of butcher's-broom, in which this peculiar conformation is very evident. SECTION X.-METAMORPHOSES OR CHANGES TO WHICH LEAVES ARE SUBJECT. Just as certain parts of vegetables not leaves may assume the general appearance of leaves, so, on the other hand, leaves occasionally lose their own specific appearance, and look like things they are not. For example, who at first glance would think that the prickles on common furze were leaves? Nevertheless, they are; the ordinary flat leaf-like appearance being lost. Again, many of those tendrils which shoot from slender plants enabling them to lay hold of neighbouring objects and derive support, are nothing more than modified leaves. This is the case with the plant Lathyrus Aphaca, a representation of which we give above (Fig. 55). The student is not, however, to imagine that all tendrils are modified leaves. In certain plants-for example, the cucumberstipules undergo this metamorphosis, in others it is the petioles or the branches themselves which change; such, for example, are the tendrils of the vine (Fig. 56). But the most curious modification of the leaf is seen in the pitcher-plants, some of which are represented in the diagram (Fig. 57). In one of these the leaf tapers into a stalk, at the extremity of which the pitcher is situated, the arrangement being such that the pitcher shall always retain its upright position. The pitcher is covered by a well-fitting lid. In another kind, also figured in our plate, the pitcher is made up of the whole leaf, and there is no lid, so that the orifice is constantly wide open; and there are also other varieties. and finding that it sprang from a small root which ran horizontally (about as large as two fingers or a little more), I soon detached it and removed it to our hut. To tell you the truth, had I been alone and had there been no witnesses, I should, I think, have been fearful of mentioning the dimensions of this flower, so much does it exceed every flower I have ever seen or heard of; but I had Sir Stamford and Lady Raffles with me, and Mr. Palsgrave, a respectable man resident at Manna, who, though all of them are equally astonished with myself, yet are able to testify to the truth. "The whole flower was of a very thick substance, the petals and nectary being in but few places less than a quarter of an inch thick, and in some places three-quarters of an inch; the substance of it was very succulent. When I first saw it a swarm of flies was hovering over the mouth of the nectary, and apparently laying their eggs in the substance of it. It had precisely the smell of tainted beef. The calyx consisted of several roundish, dark-brown, concave leaves, which seemed to be indefinite in number, and were unequal in size. There were five petals attached to the nectary, which were thick, and covered with protuberances of a yellowish-white, varying in size, the interstices being of a brick-red colour. The nectarium was cyathiform (cup-shaped), becoming narrower towards the top. The centre of the nectarium gave rise to a large pistil, We must not quit the subject of leaves without devoting a passing word to the gigantic leaf of the Victoria regia, one of the tribe of Nymphæacea, or water-lilies, and a native of Central America. A specimen of this truly wonderful plant is now flourishing in great vigour at Kew Gardens. Its leaves are from fifteen to eighteen feet in diameter, and its flowers and capsule, or seed-case, proportionately large. Fig. 58 is an engraving of this wonderful plant. A child is represented standing on one of its floating leaves, which, on account of its size, acts the part of a boat, and supports the child on the surface of the water. 58. THE VICTORIA REGIA WATER-LILY IN THE CONSERVATORY AT CHATSWORTH, While we are calling attention to the enor mous leaves and beautiful flowers of the Victoria regia, we may direct the student to another giant flower, the largest indeed known, Rafflesia Arnoldi (Fig. 58b), which was discovered by a botanist of repute, Dr. Arnold, in 1818, when on an excursion into the interior of Sumatra with Sir Thomas Stamford Raffles and some other friends. The following is Dr. Arnold's account of the discovery of this monster plant and the general appearance of its blossoms. The plant was found on the banks of the Manna river, not far from Pulo Lebban: Fig. 58b. RAFFLESIA ARNOLDI. "Here," says Dr. Arnold in a letter to a friend, "I rejoice to tell you I happened to meet with what I consider as the greatest prodigy of the vegetable world. I had ventured some way from the party, when one of the Malay servants came running to me with wonder in his eyes, and said, 'Come with me, sir, come! a flower, very large, beautiful, wonderful!' I immediately went with the man about a hundred yards into the jungle, and he pointed to a flower growing close to the ground, under the bushes, which was truly astonishing. My first impulse was to cut it up and carry it to the hut. I therefore seized the Malay's parang (a sort of instrument like a woodman's chopping-hook), which I can hardly describe, at the top of which were about twenty processes, somewhat curved, and sharp at the end, resembling a cow's horn; there were as many smaller, very short processes. A little more than half-way down, a brown cord, about the size of common whipcord, but quite smooth, surrounded what perhaps is the germen, and a little below it was another cord, somewhat moniliform (shaped like a necklace). "Now for the dimensions, which are the most astonishing part of the flower. It measures a full yard across; the petals, which were subrotund, being twelve inches from the base to the apex, and it being about a foot from the insertion of the one petal to the opposite one. The nectarium, in the opinion of all of us, would hold twelve pints; and the weight of this prodigy we calculated to be fifteen pounds." This curious plant forms one of a distinct order, called RafflesLike our iaceo, which will be noticed in a future lesson. mistletoe it is a parasite, and grows on the prostrate stems and roots of plants; but unlike the mistletoe, the plant is peculiar in having no leaves, or any organ like the phyllodium, or enlarged petiole of the Australian acacia, that resembles a leaf. LESSONS IN ARITHMETIC.-XII. FRACTIONS (continued). 15. Multiplication of Fractions. To multiply by t. This means to take four-fifths of the fraction; that is, it is the same thing as finding the value of the complex fraction of 3. Now, if be divided into five equal parts, i.e., if be divided by 5, we get; because, to divide a fraction by a whole number, we multiply the denominator by that number (Art. 5); and taking four of these fifth parts of 3-viz., four times we get as the required result. This result is plainly got by multiplying the numerators together and the denominators together of and, to form a numerator and denominator respectively. The same method would evidently apply to any other two or more fractions. Hence the following Rule for the Multiplication of Fractions. Multiply together all the numerators for a numerator, and all the denominators for a denominator. Obs. In multiplying fractions we can often simplify the operation by striking out or cancelling factors (as we are at liberty to do, Art. 6) which are common to the numerator and denominator of the fraction formed by multiplying the numerators and denominators together. EXAMPLE.—Multiply together,,,. Their product is equal to Dividing by a whole number is finding how many times the divisor is contained in the dividend. Now, a seventh is contained in unity 7 times, and therefore a seventh is contained in X 7 times; 5 sevenths will be contained therefore in onefifth of this number of times, and therefore the quotient of by is, that is, , and the same method will be true for any other two fractions. Hence the following Rule for the Division of Fractions. Invert the divisor, and then proceed as in multiplication, i.e., multiply the numerators together for a numerator, and the denominators for a denominator. Obs. In performing the process, the Obs. of Art. 15, with reference to cancelling factors which are common to both numerator and denominator, must be attended to. 17. By this and the foregoing rules we are able to simplify complex fractions. add and multiply the result the indicated expressions : 1.÷ 2. 11 ÷ 13. : (120 being the L.C.M. of 24 and 40). Such fractions are represented by a method of notation which is an extension of that employed for whole numbers. In whole numbers the figures increase in a tenfold ratio from right to left; or, what is the same thing, decrease in a tenfold ratio from left to right. If we extend this method of representation towards the right beyond the units' place, any figure one place to the right of the units' place will be one-tenth of what it would be if it were in the units' place, and will thus really denote a decimal fraction; any figure two places to the right of the units' place will be one-hundredth of what its value would be if it were in the units' place; and so on for any number of figures and places. Hence, if we choose some means of indicating the point in any row of figures at which the units' place occurs, we can write down any decimal fraction without the trouble of expressing the decimal denominators. This is done by putting a dot, or decimal point, as it is generally called, between the figure in the units' place and the figure in the place to the right of it, which we may call the tenths' place. Thus, 14 would mean 1+; 3 would mean; 3.14159 would mean 3+1+180 + 1000 + 10000 + 100000. 2. We generally speak of any figure in a decimal as being in rich a place of decimals. Thus, in the last example we should say that the 5 is in the fourth place of decimals, the 9 in the fifth place, and so on, reckoning from left to right. Observe that the denominator of the fraction corresponding to the figure in any decimal place is unity followed by the same number of ciphers as the decimal place; or, what is the same thing, that the power of 10, which is the denominator, is the same as the number of the decimal place. 3. The figures 1, 2, 3, 4, 5, 6, 7, 8, 9 in a decimal are sometimes called significant figures, or digits. Thus in such a decimal as 0002356, we should say that 2 is the first significant digit, because it is the first figure which indicates a number, the ciphers only serving to fix the place in which the 2 occurs. 4. To express a Decimal as a Vulgar Fraction. Rule for expressing a Decimal as a Vulgar Fraction. Write down the figures which compose the decimal (both integral and decimal part, if there is an integral part) for the numerator, omitting the decimal point; and for the denominator put 1, followed by as many ciphers as there are decimal places in the given decimal. Thus 5. Conversely, if we have a fraction with any power of 10 for its denominator, we can express it as a decimal by placing a decimal point before as many right-hand figures in the numerator as there are ciphers in the denominator. 13888 = 5·3459. If the figures in the numerator be fewer than the ciphers in the denominator, we must place before the left-hand figure of the numerator ciphers equal in number to the excess of the number of ciphers in the denominator over the number of figures in the numerator, and then prefix the decimal point. For example 235 Toboso 00235. Obs. It will be perceived from the foregoing remarks that placing ciphers on the right of a decimal does not alter its value, for this does not alter the place of any of the significant figures. Thus, 23, 230, 2300 are all equal in value, for, expressed as fractions, they are respectively, 230 2300 But prefixing ciphers between the decimal point and the first significant figure does alter the value of the decimal, because this alters the places of the significant digits. Thus 23, 023, 0023 have all different values, being respectively equal to 1800 18000. MECHANICS.-V. PARALLEL FORCES.-CENTRE OF GRAVITY. 23 BEFORE proceeding to the subject of the Centre of Gravity, I must direct your attention to two consequences which flow directly from the principles established in the last lesson, and furnish the basis on which the properties of that centre rest. You have seen there that the centre of a system of parallel forces is found by cutting in succession certain lines which join certain points in certain definite proportions, namely, inversely as the forces acting at their extremities. Now, such cutting can give for each line, and therefore for all, as final result, only one point. For example, the centre of two parallel forces of six and four pounds acting at two points, A B, of a body, as in the last lesson, is got by dividing A B into ten parts, and counting off four parts next to A, or six to B, and the result evidently can be only one point. If we now suppose a third parallel force of five pounds added, acting at some other point, c, of the body, and join the point last found with c, and divide the joining line into fifteen parts, taking ten next to c, here again only one point is the result. And so on for any number of forces it can be shown that there is but one centre. But, lest it should be thought possible that, on cutting these lines in a different order of the points, A B C, etc., a second centre should turn up, let us think that possible, and apply forces at these points parallel to each other, but not parallel to the line joining these two centres. Their resultant then passes through both of these points, and therefore must act in the line joining them, which is impossible; since, as I have proved, it must be parallel to its components. Furthermore, you will observe that all these lines are cut only in reference to the magnitudes of the forces; no account is taken of their direction. Whether they pull upwards or downwards, or obliquely to left or to right, so long as the magnitudes remain the same, or even keep the same proportion-say that of six, four, and five-the centre cannot change. Of course, the points are supposed not to change. Whatever be the number of points and forces this is true; as for three, so for any other number. And mark, moreover, that it makes no difference how this change of direction is produced, whether, leaving the body in one fixed position, you make the forces change directions as at a and b (Fig. 17), or, preserving the direction, you turn the body round, as from a to c in the same Fig. In neither case does the centre change. These results may be summed up in the two following propositions: с 1. A System of Parallel Forces acting at given points in a body, has ONE Centre of Parallel Forces, and only one. 2. The Centre of Parallel Forces does not change its position when the direction of the forces is changed in reference to the body. THE CENTRE OF GRAVITY. The centre of gravity is the particular case of the centre we have been last considering, in which the forces are those by which bodies on the earth's surface are drawn by attraction towards its centre. The smallest body, particle, or atom, is drawn in proportion to its mass, equally with the largest; and it is to the tendency of these bodies so to move downwards in obedience to this attraction, that we give the name of "weight." The term "gravity," carries a similar meaning, being derived from the Latin gravis, heavy. Now, since every particle of matter is thus drawn to the earth's centre, it is evident that the weight of all large masses, such as of a block of marble, beam of timber, or girder of iron, is the joint effect, or the resultant, of the attractions of the separate atoms. But these attractions are all so many parallel forces; for, pulling, as they do, towards the earth's centre, which is nearly 4,000 miles away down in the ground, they incline, even in the largest objects, so little towards one another that practically they may be considered not to meet, that is, to be parallel. Hence you see that all the principles we have proved about parallel forces hold good of the earth's attraction of these atoms, and that we may affirm that— |
