LESSONS IN BOTANY.-X. SECTION XX.-FURTHER CLASSIFICATION OF VEGETABLES. The names of his twenty-four classes, including cryptogamic plants as the twenty-fourth, are as follows: 7. 1. Monandria-one stamen. 2. Diandria-two stamens. 3. Triandria-three stamens. 4. Tetrandria-four stamens. 5. ALL the general principles we have discussed hitherto, and Pentandria-five stamens. 6. Hexandria-six stamens. taken advantage of, have merely furnished us with the means of Heptandria-seven stamens. 8. Octandria-eight stamens. dividing vegetable growths into three sections; the question, 9. Enneandria-nine stamens. 10. Decandria-ten stamens. therefore, presents itself, how we are to continue the division, 11. Dodecandria-eleven to nineteen stamens. 12. Icosandria how arrange the classification of the hundreds of thousands of-twenty or more on the calyx. 13. Polyandria-twenty or plants which exist? Various methods have been at different more on the receptacle. 14. Didynamia-four, two long, two times proposed for accomplishing this. We shall not mention short. 15. Tetradynamia-six, four long, two short. 16. them in the order of their organisation, nor shall we fully describe Monadelphia-stamens joined by their edges into one body. them, such not being the object with which these papers are 17. Diadelphia-stamens joined into two bodies. 18. Polywritten. We shall mention the general principles involved in adelphia-stamens joined into many bodies. 19. Syngenesiaeffecting some of these classifications, and shall point out in what respects certain classifications are better than others. Of all the different schemes of classification which have ever been proposed or carried into execution, that of the celebrated Swede, Linné or Linnæus, has undoubtedly attained to the greatest popularity. Indeed, so firm is the hold it has taken of popular appreciation, that no inconsiderable number of those who study Botany still fancy they have nothing better to learn than the number of pistils and stamens which are contained in different flowers, totally unconscious of all natural alliances. Suppose that some eccentric ethnologist should adopt the grotesque idea of classifying human faces according to the number of wives the individuals of each race were in the habit of marrying. Suppose that in reference to this master-idea the ethnologist should arrive at the conclusion, that inasmuch as Mussulman Turks, and Mussulman negroes, and Mussulman Kalmucs, and Malays, all marry a great many wives, that for this reason Turks, and negroes, and Kalmucs, and Malays, must all be similar races of men. Would not such a classification awaken a smile at its grotesque whimsicality? and would it not be considered an eminently false classification, not to say absurd ? Yet this is almost the parallel case to that of Linnæus, when he effected his celebrated artificial division of plants according to the number and portion of the male and female parts (stamens and pistils) of flowers. The cases are remarkably similar in all that relates to our argument, for although it is the manner of a Mussulman gentleman to have several wives, whereas it is the wont of a lady flower to have several husbands; yet this collateral discrepancy does not affect the general deduction. stamens joined by their anthers into a cylinder. 20. Gynandriastamens adherent to pistil. 21. Monacia-flowers bearing pistils exclusively, and flowers bearing stamens exclusively, on the same plant. 22. Dicacia-flowers bearing pistils exclusively, and flowers bearing stamens exclusively, on different plants. 23. Polygamia - flowers bearing stamens exclusively, or pistils exclusively, or either partially, on one or many plants. 24. Cryptogamia. In the annexed illustration, a representation is given of the fleshy rhizome, leaves and flower of the Iris Florentina, or White Iris, a beautiful variety of the family Iridaceae, and a native of Southern Europe. It flowers in May. According to the division adopted by Linnæus, this plant belongs to the first order Monogynia (having one pistil), of the third class Triandria (having three stamens). From an inspection of this arrangement, we observe that up to the eleventh class the number of stamens alone furnishes the distinctive sign, after which other circumstances are taken cognisance of. These circumstances are sufficiently indicated in the list of classes given above; but it is desirable to present the reader with the derivation of these terms. It will be remembered that the stamens are the male organs of the flower, and the names given to the first eleven classes are compounded of the Greek words for the numerals, one, two, three, four, five, six, seven, eight, nine, ten and twelve, and the Greek noun avnp (an'-ear), genitive avdpos (an'-dros), Nevertheless, the artificial classification of Linnæus has acquired a celebrity so great, and is so interwoven with popular botanical ideas, that it cannot be dismissed with the casual notice we have already afforded it. Let us, therefore, proceed to examine the general principles on which it is based. In the first place, Linnæus divided plants into cryptogamic and flowering, as we have done. The department of cryptogamic Botany was, however, very imperfectly known to Linnaus; it was to the classification of flowering plants that his chief efforts were directed, and it is on his mode of effecting this that his botanical fame depends. Linnæus arranged all flowering plants under twenty-three classes, founded on the number and arrangement of the male parts (stamens) of the flower. VOL. I. Icosandria is formed of the same Greek noun, and ELKOOL (i'-ko-si), the Greek for twenty; polyandria from the same Greek noun avmp and the adjective Toλus (pol-use), much or many. The term didynamia means two-powered, from the Greek duo (du'-o), two, and Suvauis (du-na-mis), power; the reason why the term is applied will be seen by referring to the explanation given above. Monadelphia means one brotherhood, from the Greek povos (mon'-os), one, and adeλpos (a-del-fos), brother, because all the stamens are connected together. Syngenesia is another term signifying a growing together, from the Greek ovv (sune), together, and yeivoua (gi-no-mi, the g hard), I grow. Gynandria signifies woman-man, from the Greek yuvn (gu'-ne, g hard), woman, and avnp, genitive avopos, a man, because the pistils and stamens are attached. Monacia signifies one-housed, from the Greek povos, one, and oikos (oi'-kos), house, for a reason which will be evident. Polygamia signifies many-married, from the Greek Toλus, many, yauos (gam'-os), marriage; the meaning of which term will also be 20 Example of "Slow" Movement. 2. Before and after an intervening phrase : Thou, who didst put to flight Primeval silence, when the morning stars O Thou, whose word from solid darkness struck "Moderate." There is something nobly simple and pure in a taste for the cultivation of forest trees. It argues, I think, a sweet and generous nature, to have a strong relish for the beauties of vegetation, and a friendship for the hardy and glorious sons of the forest. There is a grandeur of thought connected with this part of rural economy. It is worthy of liberal, and freeborn, and aspiring men. He who plants an oak looks forward to future ages, and plants for posterity. Nothing can be less selish than this. He cannot expect to sit in its shade, and enjoy its -helter; but he exults in the idea that the acorn which he has buried in the earth shall grow up into a lofty tree, and shall keep on flourishag, and increasing, and benefiting mankind, long after he shall have ceased to tread his paternal fields. The grammatical punctuation of sentences, by which they are divided into clauses by commas, although sufficiently distinct for the purpose of separating the syntactical portions of the structure, are not adequate to the object of marking all the andible pauses, which sense and feeling require, in reading aloud. Hence we find, that intelligible and impressive reading depends on introducing many short pauses, not indicated by commas or other points, but essential to the meaning of phrases and sentences. These shorter pauses are, for the sake of distinction, termed rhetorical." Some place the bliss in action, some in ease; The habitual tendency of young readers being to hurry, in reading, their pauses are liable to become too short for distinctness, or to be entirely omitted. In most of the above examples, the precision, beauty, and force of the sentiment, depend much on the careful observance of the rhetorical pauses. The student may obtain an idea of their effect, by reading each sentence first, without the rhetorical pauses-secondly, with the pausing as marked. Rule on the "Oratorical" Pause. The "oratorical" pause is introduced into those passages which express the deepest and most solemn emotions, such as naturally arrest and overpower, rather than inspire utter ance. 1 Examples. The sentence was-DEATH! There is one sure refuge for the oppressed, one sure resting-place for the weary—THE GRAVE. It was the design of Providence, that the infant mind | should possess the germ of every science. If it were not so, the sciences the field | a place wherein it may grow, regale the sense with its could hardly be learnt. 1 The care of God | provides for the flower of fragrance, and delight the soul | with its beauty. Is his providence less active | over those, to whom this flower offers its incense?—No. The soil which produces the vine | in its most healthy luxuriance, is not better adapted to that end, than the world we inhabit, to draw forth the latent energies of the soul, and fill them with life and Powerful emotion not unfrequently suggests another species cf pause, adapted to the utterance of deep feeling. This pause ometimes takes place where there is no grammatical point d, and sometimes is added to give length to a grammatical se. This pause may be termed the " oratorical," or the panse of "effect." The length of the rhetorical pause depends on the length of vigour. As well might the eye | see without light, or the ear hear the clause, or the significance of the word which follows it. The ful "rhetorical pause" is marked thus, the "half-rhetorical panse" thus |, and the short "rhetorical pause" thus '. Rules for "Rhetorical" Pauses. The "rhetorical" pause takes place, as follows:— without sound, as the human mind | be healthy and athletic without descending into the natural world, and breathing the.mountain air. Is there aught in Eloquence | which warms the heart ? She draws her fire from natural imagery. Is there aught in Poetry | to enliven the imagination ? There is the secret of all her power. Is the aught in Science | to add strength and dignity to the human 1. Before a verb when the nominative is long, or when it is The natural world || is only the body, of which she is the so emphatic : Life is short, and art is long. books, Science is presented to the eye of the pupil, as it w structor will take him by the hand, and lead him by the running streams, and teach him all the principles of Science, as she comes from her Maker; as he would smell the fragrance of the rose, without gathering it. 1 This love of nature; this adaptation of man to the place assigned him by his heavenly Father; this fulness of the mind as it descends into the works of God, is something, which has been felt by every one, though to an imperfect degree, and therefore needs no explanation. It is the part of science, that this | be no longer a blind, affection; but that the mind be opened to a just perception of what it is, which it loves. The affection, which the lover first feels for his future wife, may be attended only by a general sense of her external beauty; but his mind gradually opens to a perception of the peculiar features of the soul, of which the external appearance | is only an image. So it is with nature. Do we love to gaze on the sun, the moon, the stars, and the planets? This affection in its bosom | the whole science of astronomy, as the seed the future tree. It is the office of the instructor to give it an existence and a name, by making known the laws which govern the motions of the heavenly bodies, the relation of these bodies to each other, and their uses. contains contains Have we felt delight in beholding the animal creation,-in watching their pastimes and their labours? It is the office of the instructor to give birth to this affection, by describing the different classes of animals, with their peculiar characteristics, which inhabit the earth, the air, and the sea. Have we known the inexpressible pleasure of beholding the beauties of the vegetable world? This affection can only expand in the science of botany. Thus it is, that the love of nature in the mass may become the love of all the sciences, and the mind will grow and bring forth fruit || from its own inherent power of development. LESSONS IN GEOMETRY.—X. IN our last lesson we considered the various series of data necessary for the construction of an isosceles triangle: we will now do the same for any kind of scalene triangle, or triangle of which all three sides are unequal. A scalene triangle, as it has been stated, may be an acuteangled triangle, an obtuse-angled triangle, or a right-angled triangle. To determine any scalene triangle, it is plain that we must have one of the following series of data. I. With regard to the sides without the angles : 1. The length of each of the three unequal sides. 2. The length of two sides and the altitude of the triangle. III. With regard to the sides and angles combined : : 4. The length of any two of the sides of the triangle and one of its angles. 5. The length of one side of the triangle and two of its angles. 6. The length of one side of the triangle, its altitude, and one of its angles adjacent to the given side. As in the construction of the isosceles triangle, the first case is met by Problem VIII. (page 191), but the second brings us to PROBLEM XXIV.-To draw a triangle of which the length of two of its sides and the altitude are given. Let A and B (Fig. 32) represent the length of two of the sides of the triangle required, and c its altitude. In any straight line, D E, of indefinite length, set off F G equal to B, and by Problem X. (page 192), draw the indefinite straight line, H K, parallel to DE, at a distance from it equal to c, the altitude of the required triangle. Then from F as centre, with a radius equal to A, draw an arc cutting H K in the point L. Join L F, LG; the triangle LFG is a triangle answering the requirements of the data, for its sides, LF, F G, are equal to A and B respectively, and its altitude shown by the dotted line L N is equal to the given straight line c. The triangle M F G, drawn in the same way, is also a triangle which meets the requirements of the data, for its sides, MG, G F. are equal to A and B respectively, and its altitude, shown by the dotted line м O, is equal to c. 1 The triangles LFG, MFG, are equal to each other in every respect, namely, the length of their sides, their altitude, and their superficial area. They are upon the same base, FG, and yeen the same parallels, D E, H K, and they are what we may mmetrical triangles. From this we learn that symmeingles on the same base and between the same parallels to one another; and this is true, not for symmetrical, triangles only, but for any triangles, whether symmetrical or not, that are upon the same base and between the same parallels. Thus, the triangles L F G, MFG are each of them equal to the triangle P F G, which is on the same base, F G, and between the same parallels, D E, H K, and each of them would be equal to any triangle that may be formed by drawing lines from the points F and G to any point in the straight line H K, produced both ways indefinitely. Triangles also which stand upon equal bases and between the same parallels are equal to one another. H D GO. Thus, the triangles LNG, MOF, which stand on equal bases, N G, Fo, and between the same parallels, DE, H K, are equal to one another, as are also the triangles LN F, MOG, which are E between the same parallels and stand on equal bases N F, And this is also as true of unsymmetrical triangles as of symmetrical triangles, for if we join the dotted line N P, the triangles LN F, PN F, are equal to one another, because they are on the same base, N F, and between the same parallels; and since the triangle M G O is equal to the triangle L N F, it must also be equal to the triangle P N F. In Case 3, when two of the angles of the required triangle are given, it is manifestly necessary only to make at two points in the same straight line, and on the same side of it, two angles equal to the given angles, each having its opening turned towards the apex of the other, and then, if necessary in order to inclined to the side that is common to both. The student must complete the triangle, to produce the sides of the angles that are notice that when two angles of a required triangle are given without any special requirement as to their relative position, an endless number of pairs of symmetrical triangles may be drawn, similar in form but of different superficial areas, all satisfying the general requirements set forth in the data. Thus, in Fig. 33, if A and B represent the given angles of the triangle required, it is plain that to make a triangle having two angles equal to the given angles A and B, we have only to make at any point, c, in a straight line, x Y, of indefinite length, the angle Y CE equal to A, and at another point, D, in the same straight line, the angle X D E equal to B, each angle having its opening opposite or turned towards the apex of the other, as, in this figure, the opening of the angle at c is opposite the apex D of the angle at D, and vice versû; and to complete the triangle produce the sides, C E, DE, of the angles at C and D that are inclined to the common side, CD, until they meet. If we reverse the position of the angles, making the angle at c equal to the angle at B, and the angle at D equal to the angle at A, the triangle assumes the form shown by the triangle FCD in the figure. The triangles ECD, X A F C D, are symmetrical and equal` in every respect. The triangles KG H, LG H, shown by dotted lines, are also equal and symmetrical in every respect, and satisfy the general conditions of the data, although their superficial area is greater than the area of the triangles E C D, F C D, because the points G and H, at which the angles necessary for the construction of the triangle required are made equal to A and B, are taken on the indefinite straight line, x Y, at a greater distance apart than c and D. Fig. 33. PROBLEM XXV.-To draw a triangle of which two sides and one of the angles are given. First, let the given angle be included between the given sides, and let the straight lines B, C represent the length of the given. sides of the triangle required, and A the given angle included between them (Fig. 34). Draw any straight line, X Y, of inde finite length, and at any point, D, in x Y, make the angle Y DE equal to the given angle A. Along D Y set off D F, equal to c and along D E set off D G, equal to B. Join GF; the triangle G D F answers the requirements set forth in the data, as does also the triangle KD н, obtained by setting off D H along D Y equal to B, and D K along D E equal to c. The triangles G D F, K D H are symmetrical and equal in every respect; but if the position of the given angle had been required to be opposite to one of the given sides, instead of being included between them, a very different result would have been obtained. B C We will suppose, firstly, that it is required to place the angle opposite the shorter of the two given sides. At the point L in the straight line of indefinite length, x Y, make the angle X L M equal to the given angle A, and as this angle is to be opposite to the shorter side, set off along L X the straight line L N, equal to c; and from N as a centre, with a radius equal to B, describe the arc o P, cutting the straight line L M in the points 0, P. Join o N and P N. Either of the triangles oN L, PNL, will satisfy the requirements of the data, for in the triangle ONL the sides ON, NL are equal to в and c respectively, while the angle OL N is opposite to the shorter side ON; and in the triangle PNL, the sides PN, NL are equal to в and c respectively, while the angle P L N is opposite to the shorter side PN. H F N Fig. 34. If it be required to place the angle opposite to the longer of the two given sides, it is manifest that we must set off LQ along LX equal to B; and from Q as centre, with a radius equal to c, describe an arc cutting the straight line L M in R. By joining EQ. we get a triangle, RQL, that satisfies the requirements of the data, the sides L Q, QR being equal to в and c respectively, and the angle QL R, which is equal to the angle A, opposite to the longer side R Q. The learner may make an endless variety of practical exercises on this problem, by varying the length of the given sides and the opening of the given angle. Practice of this kind will be found to ensure neatness and accuracy in geometrical or mechanical drawing, and will tend to render the draughtsman skilful in the use of his compasses and parallel ruler. PROBLEM XXVI.-To draw a triangle of which one side and tro of the angles are given. Let A represent the length of the given side of the required triangle, and B and c the given angles, and first let both of the given angles be adjacent to the given side, or in other words, let them be at its opposite extremities, on the same side of it. A D E H K Fig. 35. Draw any straight line, x Y, of indefinite length, and in it take DE equal to A. At the point D make the angle E D F equal to the angle B, and at the point E make the angle D E F equal to C. Let the sides D F, EF meet in the point F; the triangle F D E satisfies the requirements of the data; as will also the triangle GDE, constructed by making the angle G DE equal to c, and the angle GED equal to B. Next, let one of the given angles be opposite to the given side, as, for example, when the angle equal to the larger angle B is required to be in this position. Take HK, in the straight line of indefinite length, XY, and at the point н make the angle KHL equal to the angle c. Through K draw K м parallel to HL, and at the point к in the straight line M K make the angle MKN equal to the angle B, and let the straight line K N meet the straight line HL in N. The triangle NHK has the angle EHN equal to C, and the angle H N K equal to B (for it is equal to its alternate angle N K M, which was made equal to B), and the larger angle HNK is opposite to the side H K, which is equal altitude, and one of its angles adjacent to the given side, are given. Let A represent the length of the given side of the required triangle, B its altitude, and c the given angle. Draw any straight line, X Y, of indefinite length, and, by Problem X. (page 192), draw the straight line D E, also of indefinite length, parallel to it, at a distance from it equal to B. Set off FG in XY equal to A, and at the point F in the straight line G F make the angle G F H equal to the given angle c. Let FH meet DE Join G H. in H. The triangle F G H answers the requirements of the data, for it has a side F G equal to A, an angle G F H equal to c, and it is of the altitude H K, which is equal to the given altitude B. A triangle equal to the triangle G F H in every respect, and symmetrical with it, may be obtained by making an angle at G, in the straight line F G, equal to c, and following the same process of construction. If the given angle be an obtuse angle, as c, the line which represents the altitude of the triangle required will fall on a point in x Y without the line which is set off upon it equal to the given side. If it be an acute angle, as the angle z, the line representing the altitude of the triangle may fall between the extremities of the line set off equal to the given side, as NO in the triangle N L M, which is drawn having the side L M equal to A, and the angle M L N equal to the given angle z; but whether this be the case or not depends entirely on the size of the angle and the relative proportions of the altitude and given side. In the construction of right-angled triangles, as one angle is always necessarily known, less data are required than in the construction of obtuse-angled and acute-angled triangles; thus any right-angled triangle may be constructed if we know 1. The length of either of the sides containing the right angle (as A B and AC in Fig. 37). 2. The length of either of the sides containing the right angle, and the side which subtends the right angle (as A B and B C, or A C and BC, in Fig. 37). 3. The side which subtends the right angle, and the perpendicular let fall on it from the right angle (as AD and B C in Fig. 37). Thus, if the sides that contain the right angle be equal to P and R, draw at right angles to each other A B and A C, and make A B equal to P, and AC equal to R, and join BC: ABC will be the triangle required. R S F Again, if one of the sides containing the right angle be given equal to P, and the side that subtends the right angle equal to s, draw BC equal to s; bisect it in E, and from E as centre, with the distance E B or EC, describe the semicircle BA C. Then from B as centre, with a radius equal to P, draw an arc cutting the semicircle BAC in A. Join AB, AC; the triangle ABC will be the triangle required. E Fig. 37. If the side which subtends the right angle be given equal to s, and the perpendicular let fall on it from the right angle equal to Q, draw B C equal to s, bisect it in E, and draw the semicircle B A C as before; through E draw E F perpendicular to в C, and along it set off EG equal to Q. Through a draw & A parallel to B c, cutting the circumference in A, and from A draw A B, AC, to the points B and C. The altitude, A D, of the triangle A B C is equal to Q. |