wrists and arms, and among the most suitable exercises for this the purpose of an imaginary wand for the guidance of the purpose are the following:gymnast in the position. 1. The dumb bells are held close before the chest, the arms from the shoulder to the elbow resting by the side. The body must be erect, the heels touching, and the feet at right angles. Now raise the dumb bells slowly, first with one hand and then with the other, as high above the head as you can reach; bringing them back to the position in front of you. Then exercise both arms together in the same way. 2. Hold the bells down by the sides, and raise the arms until they are extended at full length in a horizontal position from the shoulders; raise and depress each arm alternately, then lower them both down to the sides, and reI eat the former movement. 3. From the original position stretch the arms out before you, then bring them gradually back as far as you can without bending the elbows, and keeping the dumb bells grasped in the hands with the thumbs uppermost. Move the arms forward again, making the dumb bells meet in front, and then backward, trying to cause them to touch beFig. 5 hind, which you will be able to accomplish with practice. As the learner gains strength, the speed with which these movements are made may be increased. Some of the other exercises usually practised without apparatus, which we have described in our first paper on Gymnastics, may also be performed with the heavier dumb bells. 1. The light dumb-bell exercises are commenced by holding the arms straight down, with the bells in an exactly horizontal position from the hips, the thumbs outward. Now turn the thumb ends of the bells to the hips, and back again, ten times. Be careful at each turn to keep the bells perfectly straight, so that a line run through one dumb bell would also pass through the other. 2. Now, with the arm from the shoulder to the elbow close by the side, hold the bells before you with the thumbs outward. Then turn the bells until their ends are reversed, as before, making them come in line at each movement, and repeat this ten times in succession. These exercises will do much to strengthen the wrists. 3. Hold the bells straight in front, the arms being extended, and the knuckles pointing downward; then twist the arms until the position of the dumb bells is reversed, the knuckles being upward. Fig. 7. 7. Hold one dumb bell high above the head with the right hand, the arm being quite straight; let the other bell rest on the neck-the arm, of course, being bent; change the position of each arm alternately. Now, with the bells still in these positions, stretch the left leg backward as far as possible, and, when Fig. 6. it has reached its limit, sink the body towards the ground. Rise to the perpendicular again, and then stretch back the other leg in the same way. Repeat these movements five times. 8. Standing erect, arms down, carry them to the horizontal position in front; then above the head as seen in Fig. 8. Now down to the horizontal again, and then to the floor, as seen in the dotted lines in the figure. Repeat these movements ten times, and without bending the knees or the elbows. Here we must leave the dumb bells; but, as in the case of the other exercises, the examples which we have now given will be sufficient to suggest numerous variations and additions to the learner. We pass on now to another kind of exercise, which will give the learner more severe work than any of those to which we have yet alluded. INDIAN CLUBS. The clubs are made of wood; they should be about eighteen inches long, somewhat tapering in form, from three to four inches Fig. 8. in diameter at the thickest end, and the other forming a convenient handle for the grasp. The weight of the clubs should be just such as will allow the learner to use them with tolerable freedom; for anything like a violent or undue strain upon the muscles is to be avoided in our gymnastic training. We need not give a detailed list of Indian club exercises. Many of those performed with the dumb bells, etc., can be practised to equal advantage with the clubs, and the learner who has studied the rules and movements we have already given, will know how to proceed with these implements. It will assist him, however, to have before him the two illustrations given on this page. Fig. 7 indicates the proper position of the body from which all the exercises should be commenced, the clubs being used either in perpendicular or horizontal positions, or sometimes in both simultaneously, as in the cut. Fig. 6 shows the kind of movement which may be practised in order to obtain entire freedom with the clubs, the dotted lines describing their direction. Having reached the back, bring the arms to the side, with the clubs hanging downward; then sweep them the reverse way to that shown in the illustration, holding them above the head, and arching the body as much as possible. Remember in the club exercises, as in all others, the invariable rule, never to bend the knees or the elbows unless the character of the movement contemplated renders it absolutely necessary to do so. LESSONS IN BOTANY.-III. SECTION IV.-STRUCTURE OF THE STEM OF VEGETABLES. THIS is a very important point, and helps to furnish us with a means of dividing plants, at least flowering plants, into two primary groups or divisions. Let us consider that which takes place during the growth of an oak from the acorn. The acorn, on being planted in the ground, sends down its root, and sends up its stem. At first this stem is a tiny thing of very inconsiderable diameter; year by year, however, it grows, until a gigantic tree results. If we now cut this tree across and examine the structure of its section, we shall recognise the following appearances. In the first place, commencing our examination from without, we shall find the bark, or cortex (Latin, cortex, bark), separable into two distinct layers, the outer of which is termed the cuticle (Latin, cutis, skin), or epidermis, (Greek ridepuis, pronounced ep-i-der-mis, the outer skin), and the inner one the liber, so called because the ancients occasionally employed this portion of the bark as a substitute for paper in the making of books-liber being the Latin for book. Passing onwards, we observe the woody fibre and its central pith. The woody fibre itself is evidently of two kinds, or at least is 80 put together that wood of two degrees of hardness results. The external portion of wood is the softer and lighter in colour, and termed by botanists alburnum, from the Latin word albus, white; the internal is the harder, and termed by botanists duramen, from the Latin durus, hard, although carpenters denominate it heart-wood. Lastly, in the centre comes the pith or medulla, from the Latin, medulla, the marrow, which traces its origin to another Latin word, medius, the middle, the marrow being in the middle of the bone. Regarding this section a little more attentively, we shall 10. 18. gress, the winter to which they are exposed being so short, that their course of growth is scarcely interfered with by any impediment. Under these circumstances, there is scarcely any winter pause sufficient to create a line of demarcation between ring and ring; the progress of deposition goes on continuously. However, the manner of deposition is not the less external because we cannot see the rings. 11. 12. observe passing from the 10. HORIZONTAL SECTION OF AN EXOGEN. Very different from this method of increase is that by which another grand division of plants augments in size. For an example we must no longer have recourse to a section of a plant of our temperate zone, but must appeal to the larger tropical productions of this kind. If we cut a piece of bamboo, or cane (with which most of us are familiar), horizontally, we shall find a very different kind of structure to that which we recognised in the oak. There will be no longer seen any real bark, nor any pith, and the concentric rays will be also absent, but the tissue of which the stem is made up may be compared to long strings 14 18. 11. HORIZONTAL SECTION OF AN ENDOGEN. pith to the bark, and 12. DOTTED VESSELS OF THE CLEMATIS. Fig. 10 represents the internal structure of an exogenous stem. of woody fibre tightly packed together. These concentric rings, in point of fact, could not have existed; inasmuch as a cane does not grow by deposition of woody matter externally, but internally, or, more properly speaking, upwards. A young cane is just as big round as an old cane, the only difference between them consisting in the matters of hardness and of length. Hence, bamboos, and all vegetables which grow by this kind of increment, are termed endogenous, from two Greek words evdov (en'-don), within, and yevváw (gen-ná-o), I generate. The largest specimen of endogenous growth is furnished by palm trees-those magnificent denizens of tropical forests to which we are so much indebted for dates, cocoa-nuts, palmoil, vegetable wax, and numerous other useful products. Fig. 11 is a representation of the section of a palm tree, in which the peculiarities of endogenous structure are very well developed. All the endogenous productions of temperate climes are small, though very important. In proof of the latter assertion it may suffice to mention the grasses; not only those dwarf species which carpet our lawns and our fields with verdure, but wheat, barley, oats, rice, maize, all of which are grasses, botanically considered, notwithstanding their dimensions. Indeed, size has little to do with the definition of a grass; for if we proceed to tropical climes, we shall there find grasses of still more gigantic dimensions. Thus the sugar cane, which grows to the elevation of fifteen or sixteen feet, is a grass, as in like manner is the still taller cane, out of the stem of which, when split, we make chairbottoms, baskets, window-blinds, etc., and which, when simply cut into convenient lengths, is also useful for other purposes; one of which will, perhaps, occur to some of our younger readers. The reader will not fail to remember that we, a few pages back, divided vegetables into phænogamous and cryptogamic (we are sure we need not repeat the meaning of these terms). We may now carry our natural classification still further, and say that phænogamous plants admit of division into exogenous and endogenous ones. This division is quite natural, even if we SECTION V.-CONCERNING LEAVES AND THEIR USES. THERE are two methods of teaching the nature of a thing; one is by definition, the other by example. Of these the latter is usually the more easy, but the former is the more precise. Accordingly, then, we shall commence by stating that in botanical language a leaf admits of definition as "a thin flattened expansion of epidermis, containing between its two layers vascular and cellular tissue, nerves, and veins, and per forming the functions of exhalation and respiration." Such is the botanical definition of a leaf. Probably the learner may not understand this definition just yet, but a little contemplation will enable him to do so. With the object of enabling him to understand the definition, suppose we go through its clauses one by one. Firstly, then, a thin flattened expansion of epidermis, we assume to be a self-evident expression. The epidermis means, as we have already stated, the outside bark-at least, this is its botanical acceptation. Literally, the Greek word emidepuls means skin, as we have said above, and is also applied to indicate that portion of the animal skin which readily peels off, which rises under the action of a blister, and which, when thickened and hardened, constitutes those troublesome pests on the feet which we call corns. As regards the epidermis of vegetables, it may readily be seen in the birch tree, from which it peels off in long strips. Well, a leaf, then, consists of two layers of this epidermis, one above and the other below, enclosing vascular and cellular tissue, the meaning of which terms we have now to explain to the reader. The word vascular means "consisting of, or containing vessels," and is derived from the Latin vasculum, a little vessel, while cellular, which is derived from the Latin cella, a hollow place or cavity, means, "consisting of cells." By vascular tissue is meant those little pipes or tubes which run through vegetables, just like arteries and veins through animal bodies, and which serve the purpose of conveying juices from one part of a plant to another. In plants, these pipes or tubes are so exceedingly small that their tubular character is only recognisable by the aid of a microscope or powerful lens, but their presence may be recognised by the naked eye. Thus, for example, we have little doubt that most readers of this work have noticed that, on breaking across a portion of succulent vegetable stem, such, for instance, as a piece of the long stalk of the rhubarb leaf, which is used for making pies and puddings, that the two portions do not always break clean off, but one part remains attached to the other by certain little fibrils. Now, these fibrils are vascular, that is to say, they are tubes, and tubes of various kinds, admitting of distinction amongst themselves. These distinctions we shall not enter upor here further than stating in general terms that, while some of the tubes are straight, others are twisted or spiral, like the perforator of a corkscrew; whence arises the term spiral vessels, which botanists have applied to them. Figs. 12, 13, 14, and 15, are magnified representations of the most remarkable kinds of vessels contained in vegetables; the spiral vessels of which we have been treating will easily be recognised by their peculiar appearance. Cellular tissue is, as its name indicates, an assemblage of little cells, the natural form of which is spheroidal or oval (fig. 10), but more frequently this form is modified from various causes, usually the mutual pressure of cells against each other. Thus the pith of trees, a portion of which is made up of cellular tissue, if examined under the microscope, will be found to be composed of cells having the form of honeycomb cells, that is to say, hexagonal (fig. 18). This last drawing represents the appearance of a thin segment of elder pith when submitted to microscopic examination. Occasionally the cells of cellular tissue assume a star-like or stellate (Latin stella, a star) form, as, for example, is the case in a common bean, of which our diagram (fig. 17) represents a section as seen when examined under the field of a microscope. Usually these vegetable cells are so very small that a microscope, or, at least, a powerful lens, is necessary for observing them. In certain vegetables, however, they assume such dimensions as to admit of being readily seen by the naked eye. For an example the reader may refer to an orange, especially an orange somewhat late in the season. If the fruit be cut, or, still better, pulled asunder, the cells will be readily apparent. Still more readily do they admit of being observed in that large species of the orange tribe to which the name shaddock, or forbidden fruit, is ordinarily given. We must now inform the reader that not only do the cells of this cellular tissue admit of being altered in form, but occa sionally they give rise to parts in the vegetable organisation which would not be suspected to consist of cells. The cuticle of which we have spoken is nothing more than a layer of cells firmly adherent; and the medullary rays, or silver grain, of exogenous stems, the appearance of which has been already described, is nothing more nor less than closely compressed cellular tissue. We commenced by describing a leaf, but observations have been so often directed to matters collateral to the subject that the description appears somewhat rambling. Nevertheless, it cannot be helped. In Botany, above all other sciences, there occur many curious names. They must be learnt, and the best way to teach them is to describe them as they occur. A leaf, then, we repeat, is an extension of two flat surfaces of cuticle enclosing nerves and veins, vascular and cellular tissue. All these terms have been pretty well explained. We may add, however, that when cellular tissue exists confusedly thrown together, as it does in the substance of a leaf, or as it appears in the orange, then such cellular tissue is denominated parenchyma, from the Greek word Tapévxvμa (pronounced par-enku'-ma) “anything poured out." Before we quite finish with our remarks relative to the substances which enter into leaves, it is necessary to observe that the green colouring matter of leaves is termed by botanists and by chemists chlorophyl, from the two Greek words xλwpós (pronounced klō-ros), yellowish green, and púλλov (pronounced ful'-lon), a leaf. This chlorophyl is subject to become siennared in autumn, as we all know, but the cause of this alteration has not yet been explained. ་ 22. THE mark used for a comma is a round dot with a small curve appended to it, turning from right to left. 23. When you come to a comma in reading, you must, in general, make a short pause or stop, so long as would enable you to count one. 24. The last word before a comma is most frequently read with the falling inflection of the voice. 25. In reading, when you come to a comma, you must keep your voice suspended as if some one had stopped you before you had read all that you intended to read. 26. In the following examples keep your breath suspended when you come to the comma; but let the short pause or stop which you make, be a total cessation of the voice. Examples. Diligence, industry, and proper improvement of time, are material duties of the young. He is religious, generous, just, charitable and humane. By wisdom, by art, by the united strength of a civil community, men have been enabled to subdue the whole race of lions, bears, and serpents. The genuine glory, the proper distinction of the rational species, arises from the perfection of the mental powers. Courage is apt to be fierce, and strength is often exerted in acts of oppression. Wisdom is the associate of justice. It assists her to form equal laws, to pursue right measures, to correct power, to protect weakness, and to unite individuals in a common interest and general Examples. Did you read as correctly, speak as properly, or behave as well as James? Art thou the Thracian robber, of whose exploits I have heard so much? Who shall separate us from the love of Christ? shall tribulation, or distress, or persecution, or famine, or peril, or sword? How are the dead raised up, and with what body do they come ? Have you not misemployed your time, wasted your talents, and passed your life in idleness and vice? Have you been taught anything of the nature, structure, and laws of the body which you inhabit? Were you ever made to understand the operation of diet, air, exercise, and modes of dress, upon the human frame ? 28. Sometimes the word preceding a comma is to be read like that preceding a period, with the falling inflection of the voice. Examples. It is said by unbelievers that religion is dull, unsociable, uncharitable, enthusiastic, a damper of human joy, a morose intruder upon human pleasure. Nothing is more erroneous, unjust, or untrue, than the statement in the preceding sentence. Perhaps you have mistaken sobriety for dulness, equanimity for moroseness, disinclination to bad company for aversion to society, abhorrence of vice for uncharitableness, and piety for enthusiasm. Henry was careless, thoughtless, heedless, and inattentive. This is partial, unjust, uncharitable, and iniquitous. The history of religion is ransacked by its enemies, for instances of persecution, of austerities, and of enthusiastic irregularities. Religion is often supposed to be something which must be practised apart from everything else, a distinct profession, a peculiar occupation. 29. Sometimes the word preceding a comma is to be read like that preceding an exclamation. Examples. How can you destroy those beautiful things which your father procured for you! that beautiful top, those polished marbles, that excellent ball, and that beautifully painted kite, oh how can you destroy them, and expect that he will buy you new ones! How canst thou renounce the boundless store of charms that Nature to her votary yields the warbling woodland, the resounding shore, the pomp of groves, the garniture of fields, all that the genial ray of morning gilds, and all that echoes to the song of even, all that the mountain's sheltering bosom shields, and all the dread magnificence of heaven, how canst thou renounce them and hope to be forgiven! 0 Winter! ruler of the inverted year! thy scattered hair with sleetlike ashes filled, thy breath congealed upon thy lips, thy cheeks fringed with a beard made white with other snows than those of age, thy forehead wrapped in clouds, a leafless branch thy sceptre, and thy throne a sliding car, indebted to no wheels, but urged by storms along ita slippery way, I love thee, all unlovely as thou seemest, and dreaded as thou art! Lovely art thou, O Peace! and lovely are thy children, and lovely are the prints of thy footsteps in the green valleys. 30. Sometimes the word preceding a comma and other marks, is to be read without any pause or inflection of the voice. Examples. You see, my son, this wide and large firmament over our heads, where the sun and moon, and all the stars appear in their turns. Therefore, my child, fear and worship, and love God. He that can read as well as you can, James, need not be ashamed to read aloud. I consider it my duty, at this time, to tell you that you have done something of which you ought to be ashamed. The Spaniards, while thus employed, were surrounded by many of the natives, who gazed, in silent admiration, upon actions which they could not comprehend, and of which they did not foresee the consequences. The dress of the Spaniards, the whiteness of their skins, their beards, their arms, appeared strange and surprising. Yet, fair as thou art, thou shunnest to glide, beautiful stream! by the village side, but windest away from the haunts of men, to silent valley and shaded glen. made. But it is not for man, either solely or principally, that night is We imagine, that, in a world of our own creation, there would always be a blessing in the air, and flowers and fruits on the earth. Share with you! said his father-so the industrious must lose his labour to feed the idle. 31. Sometimes the pause of a comma must be made where 32. The pupil may read the following sentences; but before reading them, he should point out after what word the pause should be made. The pause is not printed in the sentences, but it must be made when reading them. And here it may be observed, that the comma is more frequently used to point out the grammatical divisions of a sentence, than to indicate a rest or cessation of the voice. Good reading depends much upon skill and judgment in making those pauses which the meaning of the sentence dictates, but which are not noted in the book; and the sooner the pupil is taught to make them, with proper discrimination, the surer and more rapid will be his progress in the art of reading. Examples. The golden head that was wont to rise at that part of the table was now wanting. For even though absent from school I shall prepare the lesson. For even though dead I will control the trophies of the capitol. It is now two hundred years since attempts have been made to civilise the North American savage. Doing well has something more in it than the fulfilling of a duty. You will expect me to say something of the lonely records of the former races that inhabited this country. There is no virtue without a characteristic beauty to make it particularly loved by the good, and to make the bad ashamed of their neglect of it. A sacrifice was never yet offered to a principle, that was not made up to us by self-approval, and the consideration of what our degrada. tion would have been had we done otherwise. The succession and contrast of the seasons give scope to that care and foresight, vigilance and industry, which are essential to the dignity and enjoyment of human beings, whose happiness is connected with the exertion of their faculties. A lion of the largest size measures from eight to nine feet from the muzzle to the origin of the tail, which last is of itself about four feet long. The height of the larger specimens is four or five feet. A benison upon thee, gentle huntsman! Whose towers are these that overlook the wood ? The incidents of the last few days have been such as will probably never again be witnessed by the people of America, and such as were never before witnessed by any nation under heaven. To the memory of André his country has erected the most magnificent monument, and bestowed on his family the highest honours and most liberal rewards. To the memory of Hale not a stone has been erected, and the traveller asks in vain for the place of his long sleep. MECHANICS.-III. FORCES APPLIED TO A SINGLE POINT-PARALLELOGRAM OF FORCES, ETC. In this lesson we have to consider how the resultant of two, and thence of any number of forces, applied to a single point may be found. You will keep in mind that by a "single point," I mear a point "in a body;" and that will save me always adding the latter words when I use the former. Of course, forces applied to a material point" are included in the description, and these you will find, in due time, to be of very great importance. As the joint effect of two or more forces so applied is termed their "resultant," so we name the separate forces of which it is the effect its components. There are thus two operations, the Composition of Forces, and the Resolution of Forces, with which we may be concerned in Mechanics; by the former of which we denote the putting together, compounding, or finding the resultant of any number of forces, and by the latter the separating, or resolving, of any given force into the two or more to which it may be considered equivalent. The composition we first consider; but this requires a short digression on THE PARALLELOGRAM. The resultant of two forces is found by the aid of the "parallelogram of forces;" and, as some of you may not know what a parallelogram precisely is, I shall explain the term, and tell you a few things about it which, in Mechanics, it is desirable you should know. D Fig. 1. B с A parallelogram is a four-sided figure whose pairs of opposite sides and opposite angles are equal. In the adjoining figure, ABCD is a parallelogram, if the side A B is equal to D C, and also B C to A D. The two cross lines, A C and B D, are called the "diagonals of the parallelogram." Now, if you examine the two triangles, A B C, A D C, which are on opposite sides of the diagonal, A c, you will see reason for believing that they must be equal to each other. They are, in fact, the same triangle on opposite sides of that line; for they have A c for a common side, and the two other pairs of sides are equal, namely, A B equal to D C, and AD to BC; and you cannot out of three straight lines make two different triangles. This you can satisfy yourselves of by experiment, by putting three rods of different lengths together so as to form a closed figure. Now, the point to which I am trying to lead you, and which you will soon find of importance, is that, since these triangles are equal-in fact, one and the same triangle in two positionstheir angles must be equal to each other. Hence we arrive at the following important properties of a parallelogram: 1. That the opposite angles, A B C and A D C, are equal, also the opposite angles, B A D and B C D. 2. That either diagonal makes equal angles with the pairs of opposite sides, A B D equal to C D B, and A D B equal to C B D. It is on account of this latter property the figure is called "parallelogram." The opposite sides are not only equal, but parallel, on account of their making equal angles with either liagonal. However, keep in mind that these angles are equal, for this knowledge is necessary to your properly understanding what we next come to, namely THE PARALLELOGRAM OF FORCES. The forces in our cuts and diagrams being represented, as agreed on, by lines, and their directions by arrow-heads attached to their remote ends, this principle may be stated as follows:If two forces applied to a point are represented in magnitude and direction by two straight lines, their resultant is represented in magnitude and direction by the diagonal passing through that point of the parallelogram of which these lines are twe adjoining sides. P R In Fig. 2 let o P, o Q be the two forces, and draw from P and Q the two dotted lines parallel to them which meet in R, then the dotted diagonal, o R, of the parallelogram thus formed is the resultant, both in magnitude and direction, of o P and o Q. Now, I shall not here give you the strict mathematical proof of this proposition; it is too complicated, and involves so much close reasoning, that to force it on a student in the beginning of a treatise on mechanics would be tc throw an unnecessary difficulty in his way. The best course is to defer it until you have become more accustomed to mechanical reasoning, and then return to it. In the meantime you can satisfy yourselves that it is true by a reference to the two following experiments, one derived from equilibrium, the other from motion. Fig. 2. First Experiment.-Let three weights, u v w, be attached to three cords, as in Fig. 3, which are knotted together at o; and let two of the cards, longer than the third, with their at B tached weights, be thrown over two pulleys, P Q, which move freely in the same plane round axles fastened into a wall or upright board. Arrange, then, the weights and cords until equilibrium is produced. It is evident, from the principle stated at the close of the last lesson, that the force, w, must be equal and opposite to the resultant of U and v, acting over the pulleys at o. Now, take on P the cord o P, a length o A, equal in inches to the number of pounds in U, and on o q another, o B, equal to the pounds in v, and then draw the parallels, A R and B R, to o P and o Q, meeting in R; O R will then be the resultant of u and v, if the principle of the parallelogram of forces be true. It should, therefore, be opposite in direction to the force w, and the number of inches in it should be equal to the number of pounds in w. Now, on trial it is found that o R is opposite to w, that is to say, that it points vertically upwards in the plomb-line; and it is also found that the number of inches in its length is that of the pounds in w. W Fig. 3. Second Experiment.-Let us suppose that a parallelogram O AR B is described anyhow on a perfectly smooth horizontal table, and that at the point o, two springs are fitted so that one of them, on being let go, would make the unit ivory ball move over o A in the same time that the other would make it move over O B. It is evident that the lines o A and O B would then represent these forces. Furthermore, it should follow, if the principle of the parallelogram of forces be true, that, when both springs are let go together so as together to strike the ball, it should move over the diagonal o R of the parallelogram in the same time as the ball moved over o A and OB wherstruck separately. Now, this is what, on trial, exactly hap pens. The ball does move over the diagonal, and moves over it in the same time that it previously moved over the sides. This it could not do if the resultant of two forces was not represented in magnitude and direction by the diagonal. Instruments are fitted up for lecture-rooms by which the experiment can be made, and the result always is as I have stated. R Taking the principle, then, as established, let us observe its consequences. You are given two forces, acting at a point, and you want their resultant. Make, you will immediately say, a parallelogram of the two forces, and the diagonal is the required line. Not so fast; you need not describe the whole of that figure, a part will suffice. Now, if from the end A of o A, you draw A R parallel and equal to o B, it is clear you do not want to draw BR at all. A R gives you the far end of the resultant, and all you have to do then is to join R with o, and your object is o gained. Thus your parallelogram of forces suddenly becomes a triangle of forces; and you may lay this down as your rule in future for compounding two forces. Fig. 5. B Draw from the extremity of one of the forces a line equal, and parallel to, the other force; and the third side of the triangle so formed by joining the end of this line with the point of application is the resultant. There is great advantage in this substitution of the triangle for the parallelogram, for it saves the drawing of unnecessary |
