Another very common method of representing the operation | we read this line of the table in connexion with the top line. of division, is that of omitting the horizontal line, and using thus: 14 and 1 make 15, 14 and 2 make 16, 14 and 3 make 17, only the dots: thus, 12:4=3, which also means 12 divided and so on, till we come to 14 and 9 make 23. The same may by 4 is equal to 3. This method is very generally used in the be done with any other number as far as 19; so that the last theory and practice of proportion. Hence, when the ratio of sum obtained in this way will be that of 19 and 9, which make two numbers is equal to that of other two numbers, the equality 28. This plan may be extended to all numbers from 20 to 30, of the ratios is represented thus, 12: 4-15:5, and is read thus, from 30 to 40, &c., by making the corresponding changes on the ratio of 12 to 4 is equal to the ratio of 15 to 5. Such an the sums in the table: thus, to find the sum of 27 and 9; we expression as this constitutes what is called an analogy or pro- have in the table 7 and 9 make 16; now increasing the latter portion in arithmetic, the equality of the quotients or ratios by 20-that is, putting the figure 3 in the place of the figure being the test of the proportionality of the four numbers. A 1, we have 27 and 9 make 36, and so on. proportion, however, is more frequently written thus, 12:4::15:5; where the four points in the middle signify nothing more than equality, being a substitute for the sign called by us equation. Indeed, the four points may be considered as the four extremities of the two parallel lines which form the sign of equality. This expression is commonly read thus: as 12 is to 4, so is 15 to 5; or thus, 12 is to 4, as 15 is to 5. In performing the process of addition of numbers, it is plain that until we have gained some experience by practice, we must be content to use pebbles, stroke-marks, or our fingers, if we wish to know the sum of two or more numbers. Nor is this method to be despised, although school-boys have been foolishly punished for it. Every one is not born to be a genius or a calculating boy; and yet every one requires to count; every one has occasion to use the process of simple addition. In order to render pebbles, marks, or fingers unnecessary, we request our young readers to learn the following table by heart : This table is to be read and learned thus: keeping the top or upper horizontal line (which begins with 1 and ends with 9) constantly before the eye, take any figure in the left hand vertical or upright column (which also begins with 1 and ends with 9), say 3, and adding it in succession to the figures in the top line, you will find the sum in the same horizontal line with 3, immediately under the figure to which it is added: thus, 3 and 1 make 4, 3 and 2 make 5, 3 and 3 make 6, 3 and 4 make 7, &c. In like manner, if you take 9, and add it in succession, you will have 9 and 1 make 10, 9 and 2 make 11, 9 and 3 make 12, and so on, till you come to 9 and 9 make 18, which is the last sum in the table To render this table useful in the addition of higner numoers than it contains, certain considerations will be necessary. If we suppose each of the figures in the left hand upright column to be increased by 10-that is, to have the figure 1 placed on its left, as the place of tens-then the sum of each number so increased, when added to the figures in the top line, will be found in the same manner as before,-provided every figure denoting only units in the table of sums be increased by 10, or have the figure 1 placed to the left of it, and every number with 1 placed to the left of it, have the figure 2 placed to the left of it instead of the figure 1, and be read accordingly. For example if the figure 4, in the left hand vertical column, is supposed to be 14, then the numbers in the same line with it will become 15, 16, 17, 18, 19, 20, 21, 22, and 23; and, accordingly, The addition table may also be employed as a subtraction table, in the following way. Suppose we wish to know the difference between a given digit and any number greater than itself, but less than the sum of itself and the number 10. Look for the given digit in the left hand vertical column, and in the same horizontal line with it for the proposed number; then, immediately above this number in the same vertical column with it, at the top, you will find the required difference. Thus, the difference between 7 and 13 is found to be 6; for 13 is in the same horizontal line with 7, and above 13 stands 6 in the same vertical column at the top. For finding the differences between any digit and numbers greater than the sum of that digit and the number 10, an arrangement might be made similar to that which is done for finding the sums of numbers beyond the limits of the table; but in the practice of arithmetic this arrangement is not required, and therefore we do not recommend its adoption. In performing the process of multiplication of numbers, it is evident that unless we have some method of shortening the process, it will be necessary to put down the multiplicand as many times as the multiplier denotes, and find the product by addition. Thus, if you wish to know what is the product of 6 and 7; by making 6 the multiplicand, and 7 the multiplier, repeating the former as many times as the latter denotes, and performing the addition indicated by the following expression, 6 +6 +6 +6 +6 +6 +6 = 42, you will obtain the product; for 6 and 6, make 12; 12 and 6, make 18; 18 and 6, make 24; and so on, until 36 and 6, make 42. Or, by making 7 the multiplicand, and 6 the multiplier, repeating the former as often as there are units in the latter, and performing the addition indicated by the following expression, 7+7+7+7 +7+7 = 42, you will obtain the product. But this process, even in small numbers, were it performed every time a product was required, would be too laborious and irksome. In order, therefore, to render this process unnecessary, the following multiplication table has been invented; and we most earnestly request our readers who are not acquainted with it, to commit it to memory. On a knowledge and complete command of this table, depends all future progress in arithmetic and mathematics, and to some, perhaps, in the business of life. MULTIPLICATION TABLE. say 3, and multiplying it in succession by the figures in the top line, you will find the product in the same horizontal line with 3, immediately under the figure by which it is multiplied; thus, 3 times 1, make 3; 3 times 2, make 6; 3 times 3, make 9; 3 times 4, make 12, &c. In like manner, if you take 9, and multiply it in succession, you will have 9 times 1, make 9; 9 times 2, make 18; 9 times 3, make 27; and so on, till you come to 9 times 9, make 81, which is the last product in the table. To render this table useful in the multiplication of higher numbers than it contains, the rules of multiplication must be learned; but we may extend its power to the multiplication of digits by tens, digits by hundreds, &c. If we suppose each of the figures in the left hand vertical column to be tens, that is, to have a cipher placed on its right, then the product of each number so increased in value, when multiplied by the figures in the top line, will be found in the same manner as beforeprovided every number in the table of products be increased ten times, or have one cipher placed to the right of it, and be read accordingly. For example, if the figure 4, in the left hand vertical column, is supposed to be 40, then the numbers in the same line with it will become 40, 80, 120, 160, 200, 240, 280, 320, and 360; and accordingly, we read this line of the table in connexion with the top line, thus: 40 times 1, make 40; 40 times 2, make 80; 40 times 3, make 120; and so on, till we come to 40 times 9, make 360. The same may be done with any other number as far as 90; so that the last product obtained in this way will be that of 90 times 9, which makes 810. This plan may be extended to all numbers from 100 to 1000; from 1000 to 10,000, &c., by making the corresponding changes on the products in the table; thus, to find the product of 700 and 9; we have in the table 7 times 9, make 63; now, multiplying the latter by 100, that is annexing two ciphers, we have 700 times 9, make 6300, and so on. The Multiplication Table may be also employed as a Division Table in the following way. Suppose we wish to know the quotient of any number divided by a given digit, the number being a multiple of that digit, and less than its product by the number 10. Look for the given digit in the left hand upright column, and in the same horizontal line with it, for the proposed number; then, immediately above this number in the same vertical column with it, at the top, you will find the required quotient. Thus, the quotient of 42 divided by 7 is found to be 6; for 42 is in the same horizontal line with 7, and above 42 stands 6, in the same vertical column at the top. To render this table useful in the division of higher numbers than it contains, the rules of Division must be learned; but we may extend its power to the division of decimal multiples of the digits. If we suppose each of the numbers or products in the table, to have one or more ciphers placed on its right hand, then the quotient of each number so increased in value, when divided by the digits in the left hand column, will still be found in the same vertical column at the top as before-provided this quotient has the same number of ciphers placed on its right hand, as are found in the proposed number. For example, if the number 1500 is to be divided by 5; then, looking for 15 in the same horizontal line with 5, we find 3 in the same vertical column at the top; hence, annexing two ciphers to the number 3, we have 300 for the quotient of 1500 divided by 5; and so on. What is QUESTIONS ON THE PRECEDING LESSON. What are called the four common rules in arithmetic? addition? What is the sign of addition, and its name? example of its application? What is the sign of equality, and its name? Give an example of its application? What is the result of addition called? What is subtraction? What is the sign of subtraction, and its name? What is the result of subtraction called? Give an example of the application of the sign. What is multiplication? What is the sign of multiplication, and its name? What are the numbers to be multiplied together called, individually and conjointly? What is the result of multiplication called? What is the meaning of multiple? Give an example of the application of the sign? What is division? What is the sign of division, and its name? How is the sign varied in its application? Give examples of each application? What is the meaning of ratio? of quotient? What is the test of proportionality? What is the use of the addition table? What is the use of the multiplication table? What is 80 times 7? what 700 times 6? What is the quotient of 450 by 9 of 3600 by 6? LESSONS IN BOTANY.-No. I. THE term Botany is derived from the Greek word Botane, which literally signifies pasture or grass; hence it may properly be defined as the science of plants. Plants appear to have been profusely scattered over the globe, like the stars in the firmament, to invite us by the united attraction of curiosity and pleasure to their contemplation. But the radiant orbs of heaven are placed at an immense distance from us; to study them aright requires much and varied knowledge; and optical instruments of great power and value are needed to bring them within our scope. Plants, on the contrary, grow under our feet; they are easily gathered by the hand, and a needle, a magnifyingglass, or at most a pocket-microscope, is all the apparatus required for their ordinary examination. Hill and dale, the broad expanse of waters, luxuriant verdure, and the variety of seasons with their successive productions, form a diversified drama, a continually shifting scene, which never cloys, and always delights the intelligent observer. The botanist, in his walks, pleasantly glides from object to object; every flower he observes excites in him curiosity and interest; and as soon as he comprehends the manner of its structure and the rank it holds in the system of nature, he enjoys an unalloyed pleasure, not less vivid because it costs him neither expense nor trouble. For the botanist, indeed, there is no solitude; wherever he wanders he finds plants which will amply reward his most attentive examination. Often will he be charmed with beauty and regaled by fragrance; but even where these are not, gratification and knowledge await his researches. Not a tree, A plant, a leaf, a blossom, but contains In short, every part of the vegetable kingdom may exalt his Fig.. In plants we discover, on attentive examination, a beautiful arrangement of tissues. If, for instance, we take a thin transverse slice of the then put it in a drop of stem of any plant, and water, and place it under a microscope, we shall see it chiefly consists of cells, more or less regular, resembling those of a honey-comb, or, to suggest the idea of a still more delicate fabric, a network of cobweb (see fig. 1). Their size varies in different plants, and in different parts of the same Cellular system, with some magnified cells: plant; and they are sometimes so minute as to require a million of cells to cover a single square inch of surface. This singular and beautiful structure, besides containing water, fluid, and air, is the store-house of the plant's various secretions; by its means the sap is diffused, and by it many changes occur in the juices it holds. If a branch be cut transversely, early in the spring, the sap The vascular system consists of another set of small vessels. will ooze out from numerous points over the whole of the cut surface, except that part which the pith and the bark occupy (see fig. 2). And if a twig, on which the leaves are already unfolded, be cut from the tree, and placed with its cut end in a watery solution of Brazil wood, the colouring matter will ascend into the leaves and to the top of the twig. 1 touch it, is to break it; yet, so carefully is it protected In both cases, a close examination with a powerful micro- that seeds are often rudely handled, thrown on the ground, scope, will show that the sap perspires from the divided tossed into sacks, and shovelled into heaps, without the germ portion of the stem, and that the colouring matter rises suffering the slightest injury. to the top of the twig through real tubes. These are the sap, or conducting vessels of the plant. But if we examine a transverse section of the vine, or of any other tree at a later period of the season, we find that the wood is comparatively dry, whilst the bark, particularly that part next the wood, is swollen with fluid. This is contained in vessels of a different description from those in which the sap rises; they are found only in the bark, in trees, and may be called returning vessels, from their carrying the sap downwards, after its preparation in the leaf. The passage of the sap has been thought to take place, like that of the blood in the human frame, from the regular expansion and contraction of the vessels; but their extreme minuteness seems to render certainty impossible. Their diameter seldom exceeds a 290th part of a line, or a 3000th part of an inch. Leuwenhoeck reckoned 20,000 vessels in a particle of an oak about one-nineteenth of an inch square. Other vessels of a plant are called trachea; they are formed of membraneous tubes, tapering at each end, and either having a fibre coiled up spirally in their interior, or having the membrane marked with rings, bars, or dots, arranged in a more or less spiral form (see fig. 3). The fibre is generally single, but sometimes numerous fibres, varying from two to more than twenty, are united together, assuming the appearance of a broad riband. The fibre is elastic, and can be unrolled. If, for example, a leaf of a pelargonium be taken, and after a superficial cut is made round the stalk, the parts be pulled gently asunder, the fibres will appear like the threads of a cobweb. Spiral vessels occur principally in the higher classes of plants, and are well seen in annual shoots, as in asparagus; in the stems of bananas and plantains, where the fibres may be pulled out in handfuls, and used as tinder; and in many aquatic plants (see fig. 4). In hard woody stems, they are principally found in the sheath surrounding the pith, and they are traced from it into the leaves. They are rarely found in the wood, bark, or pith. Spiral vessels occasionally have a branched appearance. Every perfect plant, whether an annual, a biennial, or a perennial, whether an herb, a shrub, or a trec, is raised from seed. A seed is composed of several parts, of which ene | is the germ of the future plant (see fig. 5). As folded up in the seed the germ is exceedingly delicate and brittle; to If a garden-bean be selected for examination, and the Fig. 6. covering be removed, the substance of the seed may be easily divided into the two seed-lobes (see fig. 6). These lobes are united by a small point, like the tongue of a buckle: this is the germ. And then, it should be particularly remarked, that it is placed in a soft or fleshy substance, to yield it nutriment, before support can be derived from the surrounding soil. Of this, the cocoa-nut, the seed of the future tree-rising to the height of seventy or eighty feet, while from its summit shoot forth from twenty to thirty vast leaves, some of which are six or seven yards in length, hang ing in a graceful tuft all round the trunk-may be taken as an example The milk it contains is the nutriment of the young piant, just as the yolk of the egg is the early food of the chicken till it is fully developed, and provision can be readily picked up by its mother and itself. The Garden Bean. The germ consists of two parts; the plume, which rises and forms the future stem: and the radicle which descends, and becomes the root. Astonishing, indeed, is the ascent of the one and the descent of the other. It is, in fact, an effort of the plume to get into the air, and of the radicle to enter the earth. These results would even occur were the germ placed on the roof of a cave, or in an inverted flower-pot (see fig. 7). Fig. 7. A The root is not only designed to fix the plant in the soil, but to become a channel for the conveyance of nourishment. It is therefore provided with pores or spongioles as they are called, from their resemblance to a small sponge, that they may suck up whatever comes within their reach, just as a lump of sugar absorbs the liquid in which it is placed. Roots are various in their form, and consequently adapted to a great variety of soils and circumstances. curious fact is observable in the history of the orchis. One of its two lobes perishes annually, and the other shoots up on the opposite side; as therefore, the stem rises every spring from between the two, th plant moves a little onward every year. From the ground, the root draws forth the necessary aliment of the plant, namely, carbonic acid, ammonia, and alkaline salt contained in water. The elements of carbonic acid (oxygen and carbon), of ammonia (hydrogen and azote), of water (oxygen and hydrogen), uniting with the atmospheric influence, produce the plant. Carbonic acid and water form the cellular system, the wood, the sacchariue matter, the gum, &c. An excess of oxygen produces all acid vegetables; an excess of hydrogen the oily and resinous plants. The azote of ammonia, together with water and carbonic acid, give birth to the alkaline vegetables. The Root. One large class of the vegetable kingdom is formed of those products where the growth of the plant takes place by additions from without; or by external increase, and they are termed Exogenous, from two Greek words which describe their so doing. A stem of this kind characterises the trees of this country. It consists of a cellular and vascular system; the former including the bark, medullary rays, and pith; the latter, the inner bark, woody layers, and medullary sheath, In the early stage of growth the young stem of this kind is entirely cellular; but before long, tubes appear, forming bundles having the appearance of wedges, arranged in a circle round a central cellular mass of pith, which is connected with the bark by means of the medullary rays. Fig. 8. To explain this more fully, if we cut horizontally the branch of a tree, the pith will be observed in the centre (see fig. 8). This part of trees and plants during their early development, is circular; so also are cotton and rice paper. The pith is developed in an upward direction, the cells diminishing in size towards the circumference, and being often hexagonal. In the young plant it occupies a larger portion of the stem, and sends cellular processes outwards at regular intervals to join the medullary rays. The pith has at first a greenish hue, and is full of fluid, but in course of time it becomes pale-coloured, dry, and full of air. The extent of pith varies in different plants, and in different parts of the same plant. Immediately surrounding the pith is a layer of a greenish hue, the medullary sheath, from which the medullary rays proceed towards the circumference, dividing the vascular circle into numerous compact segments, which consist of woody vessels, and of others which are porous. These are surrounded by a moist layer of greenish cellular tissue, called the cambium layer, which is covered by three layers of bark, the whole being inclosed by the epidermis. Section of a Branch. Another large primary class into which the vegetable kingdom is divided, is called Endogenous, in consequence of its new woody matter being constantly developed in the first instance towards the interior of the trunk, only curving outwards in its subsequent course downwards. To this class belong palms, grasses, rushes, and liliaceous plants. In such instances the vascular bundles are scattered through the cellular tissue, and there is no distinction of pith, wood, bark, and medullary rays. In the young state, the centre of the stem is occupied entirely by cells, which may be said to represent pith, and around this the vessels are seen increasing in number towards the circumference (see fig. 9). The central cellular mass has no medullary sheath. In some instances its cells are ruptured, and dis Externally, roots have a cellular covering of a delicate texture. Internally, they consist partly of cells, and partly of vascular bunches, in which there are no vessels with fibres which can be unrolled. axis of the root gives off branches which divide into radicles or fibrils, the extremities of which are called spongioles, or spongelets. When the central axis goes deep into the ground in a tapering manner, without dividing, a tap root is produced, of which there is an engraving, and of which the carrrot will afford a familiar example (see fig. 10). When the descending axis is very short, and at once divides into thin, nearly equal, fibres, the root is called fibrous, as in many grasses. When the fibrils become short and succulent, the root, as in fig. 11, is said to be fasciculated and when some of the fibrils are developed in the form of tubercles, containing starchy matter, as in the orchis, it is described as tubercular (see fig. 12). Fig. 13. The term cotyledon, from a Greek word meaning a hollow or cavity, is applied to the perishable lobe of the seed of plants, which encloses and nourishes the embryo. Some seeds have two lobes; others one only, and others none. On this fact is founded the tripartite division of the vegetable kingdom into dicotyledonous (a), plants with seeds having two lobes; monocotyledonous (b), plants with seeds having one lobe; and acotyledonous, plants (c) with seeds without lobes (see fig. 13). If a leaf be examined by a powerful glass, in its early state, there will appear what all the art of man can never produce. Fig. 14. Springing from the inner bark are short and thick vessels to form the mid-rib of the leaves, while others of a delicate texture issue from either side. A juice flowing from the vessels of the bark appears on them in little bladders; these are covered by fibres and another row of bladders; and so the process goes on, till a fine cuticle or skin covers the whole. When the leaf is nearly complete, the edges, on being opened, show a double row of bright bubbles; these generally divide, and when no longer wanted, dry up, and leave horny points. A leaf, in general, consists of a flat, expanded portion, called the blade, of a narrower portion called the petiole, or stalk, and sometimes of a portion at its base, called the sheath (see fig. 14). Compound leaves are those in which the divisions extend to the mid-rib, or petiole, and receive the name of leaflets. The mid-rib or petiole has thus the appearance of a branch, with separate leaves attached to it; but it is considered properly as one leaf, because in its early stage it arises from the axis as a single piece, and its subsequent Section of a Leaf. LESSONS IN BOTANY. divisions, in the form of leaflets, are all in one plane. When | simple, and proceeds from the development of the flowerbuds of a single branch. a compound leaf dies, it usually separates as one piece. Leaf-buds contain the rudiments of branches, and are found in the axil of previously Fig. 15. formed leaves; that is, in the angle formed between the stem and the leaves (see fig. 15.) According to the nature of the stems, leaf-buds are either aerial or subterranean; the former occurring in plants which have the stems above ground, the latter in those in which the stems are covered. In the case of asparagus and other plants which have a perennial stem below ground, subterranean buds are annually produced, which appear above ground as shoots, or branches covered with scales at Leaf-bud. first, and ultimately with new leaves. A good example of a subterranean bud occurs in the bulb, as seen in the hyacinth, lily, and onion. Flower-buds, like leaf-buds, are produced in the axil of In other instances a raceme, or cluster (fig. 16) is produced, as in the hyacinth, currant, and barbery. If the secondary floral axis gives rise to tertiary ones, the raceme is branching, If the peduncles in the middle of a and forms a panicle. dense panicle are longer than those at the extremities, a thyrsus is produced, as in the lilac (see fig. 18). If in a raceme the lower flower-stalks are elongated, and come to nearly a level with the upper, a corymb is formed, which may be either simple or compound (see fig. 17). If the flowers thus disposed are sessile, or not stalked, they have an ear. The spike (see fig. 19), sometimes bears unisexual flowers, the whole falling off by an articulation, as in willow or hazel, and then it is called a catkin (see fig. 20). At other times spadix (see it becomes succulent, bearing numerous flowers, surrounded by a sheathing bract, and then it constitutes fig. 21), which may be simple, as in arum maculatum, or branching, as in palms. Fig. 16. Fig. 17. Fig. 21. Fig. 22. Fig. 20. Fig. 19. Thyrsus. this respect it differs from the leaf-bud. Sometimes the Capitulum. Calathium. middle in full bloom. In the figure this kind of inflorescence is shown on a shortened axis, the outer flowers expanding first, and those in the centre last. If there are numerous flowers on a flattened convex, or slightly concave receptacle, having either very short pedicels, or none, a capitulum or calathium (see figs. 23 and 24), is formed, as in dandelion, daisy, and other composite plants. QUESTIONS ON THE PRECEDING LESSON. What is the meaning of the term Botany? What is the nature of the cellular system? the vascular system? the trachea? the spiral vessels? the seed? What are the seed-lobes? the germ? the plume? the radicle? the root: What is the aliment of a plant? What is the difference between Exogenous and Endogenous growth? What between fasciculated and tuberculated roots? What between monocotyledonous and acotyledonous plants? Describe the nature of a leaf; a leaf-bud; and a flower-bud. What is a raceme? a panicle? a thyrsus? a corymb? a spike? a catkin? a spadix? an umbel? a capitulum? a calathium ? |