3rd , Audit, he hears 3rd , Auditur, he is heard Plural. Plural. 1st per. Audimus, we hear 1st per. Audimur, we are heard 2nd a Auditis, you hear 2nd ,, Audimini, you are heard 3rd in Audiumt, they hear 3rd , Audountur, they are heard vocabul.ARY. . Custodio, 4 I guard Fulcio, 4 I sup Venio, 4 I come Dormio, 4 I sleep Nutrio, 4 I not Westio, 4 I clothe Erudio, 4 I instruct Punio, 4, I punish Vincio, 4 I conquer Ferio, 4 I strike Reperio, 4 I find Cur, means Why? ExERCISEs.-LATIN-ENGLISH. Custódis; fulcitur; venit; cur dormis bene dormit; eruditur ; pungis; occidit; valde fallis; auditur ; sivalde dormis puníris; repérit; si bene erudis laudāris; vincitur; cur taces 2 tacet et unitur; reperiuntury vestiris; bene vestiuntury, sibene vestimini electamini; male erudiuntur; si vinceris vinciris. ENGLISH-LATIN. Why do you slay? he is o they guard; if you are guarded ou are conquered; he blames and punishes; he hears and is nstructed; you are well educated; thou sleepest much; they read; if you dance you are delighted; he is supported; why are they punished they are heard; I am clothed ill; they are struck and reminded. RECAPITULATION-TERMINATIONS or PERSoN-ENDINGS OF The Fourt Conjugatrons. INDICATIVE Mood, PRESENT TENSE. ACTIVE Worce. PASSIVE VoICE. ENGLISH-LATIN. They yield; if you yield you are conquered; if you are conquered you are bound; I am supported; they sleep; why do they punish why are they punished? you are clothed ill; thou conuerest; thou art conquered; thou bindest; thou art bound; they prick; they are pricked; why dost thou move 2 for my purpose. Singular, Plural. 1st per. Sum, I am lst per. Sumus, we are 2nd , Es, thou art 2nd , Estis, you are 3rd , Est, he is 3rd ... Sunt, they are jugation? of the third * of the second of the fourth *"memory a table of the four conjugations, with the oaning appended to each. What is the English sign of ow mood? when are pronouns prefixed to verbs in Latino yount usually prefixed as in English what is the perof the second person, present tense, indicative mood of jugation? the same in the passive voice? how do the ough what language have some words of Latin e English language? what is denoted by these what is accent? what good may be exdying Latino write down in your own words the which may accrue from studying Latin, not mentioned tructions. What is the of: of inversion f what -ins express by inversion ? what is the meaning of esser -torm the plural of bonus? from the plural docts form *hat is the meaning of salvus? of caecus? of lifference between salvi sunt and sunt salvio --
LeSSONS IN ARITHMETIC.—No. III. DeriNitions AND SIGNS. IN arithmetic, there are four different methods of perfo calculations with numbers, and these are usually called the fewr wea rules, namely, Addition, Subtraction, Multipliestion, and Division. Addition is the process by which we collect several numbers into one, which is called their sum. In order to shorten the language of arithmetic, a character has been invented which is o the sign of addition; it is in the form of an upright cross, thus +; and its name is plus or were, signifying added to. It is placed between two or more numbers to denote that their sum is to be found: thus, 6 + 7 make 13; 4 + 6 + 10 make 20; and so on. In these examples, the number 13 is the sum of the numbers 6 and 7; and the number 20 the sum of the numbers 4, 6, and 10. Another character has been invented, which is called the sign of equality; it is in the form of two small parallel strokes, thus - ; and its name is equation, signifying that which is, or is made, equal to. It is placed between numbers, or combinations of numbers, to denote that the expressions or numbers on each side of it are equal: thus, 6 +7=13, means 6 added to 7 is equal to 13; and 4 + 6-H 10=20, means 4 added to 6 added to 10 is equal to 20; and so on. Subtraction is the process by which we find the difference between any two numbers; the difference signifies the number which must be added to the smaller of two numbers to make the sum equal to the other number. A character has also been invented, which is called the sign of subtraction; it is in the form of a small horizontal line, thus —; and its name is minus or less, signifying made less by. It is placed between two numbers, of which the greaterstands on the left, to denote that their difference is to be found: thus, 14–6=8, means 14 made less by 6 is equal to 8. In this example, the number 8 is the difference between the numbers 14 and 6. Multiplication is the process by which we find the sum of one number repeated as many times as there are units in another number; the two numbers are called factors, the former being called the multiplicand, and the latter the multiplier; and the sum thus obtained is called the product of both numbers, or the multiple of either. A character has been invented, which is called the sign of multiplication; it is in the form of an oblique cross, thus x: and its name is into, or times, signifying multiplied by. It is inced between two or more numberstoodenote that their prouct is to be found: thus, 6x7=42, means that 6 times” is equal to 42; and 4 × 6 x 10=240, means that 4 times 6 times 10 is equal to 240; and so on. In these examples, the number 42 is the product of the factors 6 and 7, or a multiple of 6 or 7; and thenumber 240, the product of the factors 4, 6, and 10, or a multiple of 4, 6, or 10. In the former example, the number 6 may be the multiplicand, and the number 7 the multiplier; or, conversely, the number 7 the multiplicand, and the number 6 the multiplier. Division is the process by which we find how many times one number is contained in another; the former number being called the divisor, the latter the dividend, and the number of times the quotient. A character has been invented, which is called the sign of division; it is like the sign of subtraction, with this difference, that when the dividend stands on the left, and the divisor on the right of it, the horizontal line has a dot above it and a dot below it, thus +; and its name is upon or by, signifying divided by. It is placed between two numbers to denote that their quotient is to be found ; thus, 12+ 4 =3, means that 12 divided by 4 is equal to 3. In this example, the number 12 is the dividend, the number 4 the divisor, and the number 3 the quotient. In the use of this sign, the greater number is always placed on its left. In the use of the sign of dirision, the dots may be dispensed with, if we place the dividend above and the dirisor below the horizontal line, thus: o -3. This mode of representing di 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 only the dots: thus, 12:4–3, which also means 12 divided by 4 is equal to 3. This method is very generally used in the 3. and practice of proportion. Hence, when the ratio of two numbers is equal to that of other two numbers, the equality of the ratios is represented thus, 12:4-15:5, and is read thus, the ratio of 12 to 4 is equal to the ratio of 15 to 5. Such an expression as this constitutes what is called an analogy or proportion in arithmetic, the equality of the quotients or ratios being the test of the proportionality of the four numbers. A 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 to or upper horizontal line (which begins with 1 and ends wit 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 numbers 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 sup1. to be 14, then the numbers in the same line with it will come 15, 16, 17, 18, 19, 20, 21, 22, and 23; and, accordingly, thus: 14 and 1 make 15, 14 and 2 make 16, 14 and 3 make 17, and so on, till we come to 14 and 9 make 23. The same may be done with any other number as far as 19; so that the last sum obtained in this way will be that of 19 and 9, which make 28. This plan may be extended to all numbers from 20 to 30, from 30 to 40, &c., by making the corresponding changes on the sums in the table: thus, to find the sum of 27 and 9; we have in the table 7 and 9 make 16; now increasing the latter by 20–that is, putting the figure 3 in the place of the figure 1, we have 27 and 9 make 36, and so on. The addition table may also be employed as a subtractiox 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, 8-|-6-H6+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-H 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 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 . 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 before— provided 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, . above 42 stands 6, in the same vertical column at the p. 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 roducts 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. QUESTIons on THE PRECEDING LEsson. What are called the four common rules in arithmetic * What is addition ? What is the sign of addition, and its name? Give an example of its application ? What is the sign of equality, and its name? Give an 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 2 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 oins of ratio of quotient? What is the test of proportionality hat is the use of the addition table What is the use of the multiplication table? What is 80 times 73 what?00 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 expanseof 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, In short, every part of the vegetable kingdom may exalt his conception of the Supreme Being, of whose wisdom, power, and goodness it presents most striking exemplifications. In plants we discover, on attentive examination, a beautiful arrangement of tissues. If, for instance, we take a thin transverse slice of the stem of any plant, and then put it in a drop of 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. The vascular system consists of another set of small vessels. If a branch be cut transversely, early in the spring, the sap 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 colouriug Fig. 1. matter will ascend into the leaves and to the top of the twig. In both cases, a close examination with a powerful microscope, will show that the sap perspires from the divided portion of the stem, and that the colouring matter rises to the top of the twig through real tubes. These are the “o or conducting vessels of the plant. ut 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 #. 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 tracheae; they are formed of membraneous tubes, tapering at each end, and either having a fibre coiled up spirally in their interior, or havi the membrane marked with rings, bars, or dots, arrange in a more or less spiral form (see fig. 3). The fibre is i. single, but sometimes numerous fibres, varying om two to more than twenty, are united together, assum:* 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 #.. 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. perfect plant, whether an annual, a biennial, or a perennial, whether an herb, a shrub, or a tree, is raised from seed. A seed is composed of several parts, of which one is the germ of the future plant (see tig. 5). As folded up in the seed the germ is exceedingly delicate and brittle; to touch it, is to break it; yet, so carefully is it protected that seeds are often rudely handled, thrown on the ground, tossed into sacks, and shovelled into heaps, without the germ suffering the slightest injury. If a garden-bean be selected for examination, and the Fig. 6. be removed, the substance of may be easily divided into the two seed-lobes (see fig. 6). These lobes are united by a sm oint, 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 germ consists of two parts; the * plume, which rises and forms the - future stem: and the radicle which The Garden Bean. descends, and becomes the root. Astonishing, indeed, is the ascent of the one and the descent of Fig. 7. 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}. 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. A 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, the plant moves a little onward every year. coverin the see The Root. 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 amulonia (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 saccharine 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. 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 Erogenous, 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 |