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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 dumbbells are held close before the chest, the arms 7. Hold one dumb bell high above the head with the right from the shoulder to the elbow resting by the side. The body hand, the arm being quite straight; let the other bell rest on must be erect, the heels touching, and the feet at right angles. the neck—the arm, of course, being bent; change the position Now raise the dumb bells slowly, first with one hand and then of each arm alternately. Now, with the bells still in these posiwith the other, as high above the head as you can reach ; bringing tions, stretch the left leg backward as far as possible, and, when them back to the position in front

it has reached its limit, sink of you. Then exercise both arms

the body towards the ground. together in the same way.

Rise to the perpendicular again, 2. Hold the bells down by the

and then stretch back the other sides, and raise the arms until

leg in the same way. Repeat they are extended at full length

these movements five times. in a horizontal position from the

8. Standing erect, arms down, shoulders; raise and depress each

carry them to the horizontal arm alternately, then lower them

position in front; then above both down to the sides, and re

the head as seen in Fig. 8. Now feat the former movement.

down to the horizontal again, 3. From the original position

and then to the floor, as seen in stretch the arms out before you,

the dotted lines in the figure. then bring them gradually back

Repeat these movements ten as far as you can without bend.

times, and without bending the ing the elbows, and keeping the

knees or the elbows. dumb bells grasped in the hands

Here we must leave the dumb with the thumbs uppermost.

bells; but, as in the case of the Move the arms forward again,

other exercises, the examples making the dumbbells meet

which we have now given will in front, and then backward, try

be sufficient to suggest numeing to cause them to touch be

Fig. 5

Fig. 6.

rous variations and additions to hind, which you will be able to

the learner. accomplish with practice. As the learner gains strength, the We pass on now to another kind of exercise, which will give speed with which these movements are made may be increased. the learner more severe work than any of those to which we

Some of the other exercises usually practised without appa- have yet alluded. ratus, which we have described in our first paper Gymnastics may also be performed with the heavier dumb bells.

The clubs are made of wood; they should be about eighteen i. The light dumb-bell exercises are commenced by holding the inches long, somewhat tapering in form, from three to four inches arms straight down, with the

in diameter at the thickest end, bells in an exactly horizontal

and the other forming a con. position from the hips, the

venient handle for the grasp. thumbs outward. Now turn

The weight of the clubs should the thumb ends of the bells

be just such as will allow the to the hips, and back again,

learner to use them with tolerten times. Be careful at each

able freedom; for anything turn to keep the bells per

like a violent or undue strain fectly straight, so that a line

upon the muscles is to be run through one dumb bell

avoided in our gymnastic would also pass through the

training. other.

We need not give a de2. Now, with the arm from

tailed list of Indian club exerthe shoulder to the elbow

cises. Many of those perclose by the side, hold the

formed with the dumb bells, bells before you with the

etc., can be practised to equal thumbs outward. Then turn

advantage with the clubs, and the bells until their ends are

the learner who has studied reversed, as before, making

the rules and movements wo them come in line at each

have already given, will know movement, and repeat this ten

how to proceed with these im. times in succession. These

plements. It will assist him, exercises will do much to

however, to have before him strengthen the wrists.

the two illustrations given on 3. Hold the bells straight

Fig. 7 indicates in front, the arms being ex

the proper position of the tended, and the knuckles

body from which all the exerpointing downward; then

cises should be commenced, twist the arms until the po

the clubs being used either sition of the dumbbells is

in perpendicular or horizontal reversed, the knuckles being Fig. 7.

Fig. 8.

positions, or sometimes in both upward.

simultaneously, as in the cut. 4. Thrust the bells downward, upward, forward, and Fig. 6 shows the kind of movement which may be practised sideways, bringing them back to the chest after each move- in order to obtain entire freedom with the clubs, the dotted ment, and repeating the series five times. Take great care that lines describing their direction. Having reached the back, bring at each movement the arms and the bells be exactly parallel to the arms to the side, with the clubs hanging downward; then each other.

sweep them the reverse way to that shown in the illustration, 5. Swing the bells energetically backward and forvard, holding them above the head, and arching the body as much making them meet both in front of the chest and behind the as possible. Remember in the club exercises, as in all others, back.

the invariable rule, never to bend the knees or the elbows unless 6. Go through the “charging " exercises already described the character of the movement contemplated renders it absoamong the wand movements, each dumb bell in turn serving lutely necessary to do so.

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gress, the winter to which they are exposed being so short, that

their course of growth is scarcely interfered with by any im. SECTION IV.STRUCTURE OF THE STEM OF VEGETABLES. pediment. Under these circumstances, there is scarcely any This is a very important point, and helps to furnish us with a winter pause sufficient to create a line of demarcation between means of dividing plants, at least flowering plants, into two ring and ring; the progress of deposition goes on continuously. primary groups or divisions. Let us consider that which takes However, the manner of deposition is not the less external beplace during the growth of an oak from the acorn.

The acorn,

cause we cannot see the rings. on being planted in the ground, sends down its root, and sends Very different from this method of increase is that by which up its stem. At first this stem is a tiny thing of very incon. another grand division of plants augments in size. For an exsiderable diameter; year by year, however, it grows, until a ample we must no longer have recourse to a section of a plant gigantic tree results. If we now cut this tree across and examine of our temperate zone, but must appeal to the larger tropical the structure of its section, we shall recognise the following ap- productions of this kind. If we cut a piece of bamboo, or cane pearances. In the first place, commencing our examination from (with which most of us are familiar), horizontally, we shall find withont, we shall find the bark, or cortex (Latin, cortex, bark), a very different kind of structure to that which we recognised separable into two distinct layers, the outer of which is termed in the oak. There will be no longer seen any real bark, nor any the cuticle (Latin, cutis, skin), or epidermis, (Greek éridepuis, pith, and the concentric rays will be also absent, but the tissue pronounced ep-i-der-mis, the outer skin), and the inner one the of which the stem is made up may be compared to long strings liber, 80 called because

of woody fibre tightly the ancients occasionally

packed together. These employed this portion of

concentric rings, in point the bark as a substitute

of fact, could not have for paper in the making

existed ; inasmuch as a of booksliber being the

cane does not grow by Latin for book. Passing

deposition of woody matonwards, wo observe the

ter externally, but interwoody fibre and its cen.

nally, or, more properly tral pith. The woody

speaking, upwards. A fibre itself is evidently of

young cane is just as big two kinds, or at least is

round as an old cane, 80 put together that wood

the only difference be.

15 of two degrees of hard


tween them consisting in ness results. The exter.

the matters of hardness 18. nal portion of wood is the

and of length. Hence, softer and lighter in col.

bamboos, and all vegeour, and termed by bota

tables which grow bg nists alburnum, from the

this kind of increment, Latin word albus, white;

are termed endogenous, the internal is the harder,

from two Greek words and termed by botanists

{vdov (en'-don), within, duramen, from the Latin

and yevrów (gen-na-o), I dures, hard, although car.

generate. The largest penters denominate it


specimen of endogenous heart-wood. Lastly, in 12

growth is furnished by the centre comes the pith

palm trees—those magni. of medulla, from the

18. ficent denizens of tropical Latin, medulla, the mar

forests to which we are Fox, which traces its ori.


so much indebted for gin to another Latin word,

dates, cocoa-nuts, palmmedius, the middle, the

oil, vegetable wax, and marrow being in the mid.

numerous other useful dle of the bone. Regard. 16.

products. Fig. 11 is a reing this section a little

presentation of the secmore attentively, we shall

tion of a palm tree, in observe passing from the 10. HORIZONTAL SECTION OF AN EXOGEN. 11. HORIZONTAL SECTION OF AN ENDOGEN, which the peculiarities of pith to the bark, and


very well developed. 16. OVOID CELI, 17. STELLIFORM CELLS. 18. ANGULAR CELLS, between the two, a series

All the endogenous proof white rays, termed by

ductions of temperate the botanist medullary rays, and by the carpenter silver climes are small, though very important. In proof of the latter Train. We shall also observe that the section displays a series assertion it may suffice to mention the grasses ; not only those of ring-like forms concentric one within the other. These are dwarf species which carpet our lawns and our fields with verdure, a very important characteristic. They not only prove that but wheat, barley, oats, rice, maize, all of which are grasses, the trunk in question was generated by continued depositions botanically considered, notwithstanding their dimensions. In. of woody matter around a central line, or, in other words, by an deed, size has little to do with the definition of a grass ; for if we outside deposition, but they enable us in many cases actually to proceed to tropical climes, we shall there find grasses of still more read off the age of any particular tree-the thickness cor- gigantic dimensions. Thus the sugar cane, which grows to the responding with

one ring being indicative of one year's growth. elevation of fifteen or sixteen feet, is a grass, as in like manner Inasmuch as the formation of an oak tree is thus demonstrated is the still taller cane, out of the stem of which, when split, we to be the consequence of a deposition of successive layers of make chairbottoms, baskets, window-blinds, etc., and which, Woody fibres externally or withont—it is said to be like all when simply cut into convenient lengths, is also useful for other others snbjected to the same kind of growth, an exogenous plant purposes; one of which will, perhaps, occur to some of our from two Greek words, rtw (ex-o), without, and yerda (gen-younger readers. rid, g hard, as in gun), I generate.

The reader will not fail to remember that we, a few pages Fig . 10 represents the internal structure of an exogenous back, divided vegetables into phænogamous and cryptogamic

(we are sure we need not repeat the meaning of these terms). It is true that the peculiar disposition of rings thus spoken We may now carry our natural classification still further, and of cannot always be recognised. For example, as a rule,

trees say that phænogamous plants admit of division into exogenous which grow in hot climates are checked so little in their pro- and endogenous ones. This division is quite natural, even if we

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have regard merely to the structure of the stem; but the an example the reader may refer to an orange, especially an ugreement is much wider than this, and recognisable by other orange somewhat late in the season. If the fruit be cut, or, still analogies, as we shall see presently, when we come to consider better, pulled asunder, the cells will be readily apparent. Still the nature and peculiarities of leaves and seeds.

more readily do they admit of being observed in that large

species of the orange tribe to which the name shaddock, or SECTION V.-CONCERNING LEAVES AND THEIR USES.

forbidden fruit, is ordinarily given.

We must now inform the reader that not only do the cells of THERE are two methods of teaching the nature a thing; one this cellular tissue admit of being altered in form, but occar is by definition, the other by example. Of these the latter is sionally they give rise to parts in the vegetable organisation usually the more easy, but the former is the more precise. which would not be suspected to consist of cells. The cuticle of Accordingly, then, we shall commence by stating that in which we have spoken is nothing more than a layer of cells botanical language a leaf admits of definition as "a thin firmly adherent; and the medullary rays, or silver grain, of flattened expansion of epidermis, containing between its two exogenous stems, the appearance of which has been already layers vascular and cellular tissue, nerves, and veins, and per described, is nothing more nor less than closely compressed forming the exhalation and respiration."

cellular tissue.

frembo kamiliceafu definition for a better pero bulbopithin corner chuais celwer commenced by describing a leaf, but observations have

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not understand this definition just yet, but a little contemplation been so often directed to matters collateral to the subject that will enable him to do so. With the object of enabling him to the description appears somewhat rambling. Nevertheless, it understand the definition, suppose we go through its clauses one cannot be helped. In Botany, above all other sciences, there by one. Firstly, then, a thin flattened expansion of epidermis, occur many curious names. They must be learnt, and the best we assume to be a self-evident expression. The epidermis way to teach them is to describe them as they occur. means, as we have already stated, the outside bark—at least, A leaf, then, we repeat, is an extension of two flat surfaces of this is its botanical acceptation. Literally, the Greek word cuticle enclosing nerves and veins, vascular and cellular tissue. étridepuis means skin, as we have said above, and is also applied All these terms have been pretty well explained. We may add, to indicate that portion of the animal skin which readily peels however, that when cellular tissue exists confusedly thrown off, which rises under the action of a blister, and which, when together, as it does in the substance of a leaf, or as it appears thickened and hardened, constitutes those troublesome pests on in the orange, then such cellular tissue is denominated parenthe feet which we call corns. As regards the epidermis of chyma, from the Greek word rapevxvua (pronounced par-envegetables, it may readily be seen in the birch tree, from which ku-ma) "anything poured out." it peels off in long strips. Well, a leaf, then, consists of two Before we quite finish with our remarks relative to the sublayers of this epidermis, one above and the other below, enclosing stances which enter into leaves, it is necessary to observe that vascular and cellular tissue, the meaning of which terms we have the green colouring matter of leaves is termed by botanists and now to explain to the reader. The word vascular means “con- by chemists chlorophyl, from the two Greek words xawpós (prosisting of, or containing vessels,” and is derived from the Latin nounced klõ-ros), yellowish green, and parov (pronounced vasculum, a little vessel, while cellular, which is derived from ful'.lon), a leaf. This chlorophyl is subject to become siennathe Latin cella, a hollow place or cavity, means, “consisting of red in autumn, as we all know, but the cause of this alteration cells.” By vascular tissue is meant those little pipes or tubes has not yet been explained. which run through vegetables, just like arteries and veins through animal bodies, and which serve the purpose of couveying juices from one part of a plant to another. In plants, these pipes or tubes are so exceedingly small that their tubular READING AND ELOCUTION.-III. character is only recognisable by the aid of a microscope or

PUNCTUATION (continued). powerful lens, but their presence may be recognised by the naked eye. Thus, for example, we have little doubt that most

IV. THE COMMA. readers of this work have noticed that, on breaking across a portion of succulent vegetable stem, such, for instance, as a 22. THE mark used for a comma is a round dot with a small piece of the long stalk of the rhubarb leaf, which is used curve appended to it, turning from right to left. for making pies and puddings, that the two portions do not 23. When you come to a comma in reading, you must, in always break clean off, but one part remains attached to the general, make a short pause or stop, so long as would enable other by certain little fibrils. Now, these fibrils are vascular, you to count one. that is to say, they are tubes, and tubes of various kinds, 24. The last word before a comma is most frequently read admitting of distinction amongst themselves. These distinctions with the falling inflection of the voice. we shall not enter upor here further than stating in general 25. In reading, when you come to a comma, you must keep terms that, while some of the tubes are straight, others are your voice suspended as if some one had stopped you before you twisted or spiral, like the perforator of a corkscrew; whence had read all that you intended to read. arises the term spiral vessels, which botanists have applied to 26. In the following examples keep your breath suspended them. Figs. 12, 13, 14, and 15, are magnified representations when you come to the comma; but let the short pause or stop of the most remarkable kinds of vessels contained in vegetables; which you make, be a total cessation of the voice. the spiral vessels of which we have been treating will easily be recognised by their peculiar appearance.

Examples. Cellular tissue is, as its name indicates, an assemblage of little cells, the natural form of which is spheroidal or oval duties of the young.

Diligence, industry, and proper improvement of time, are material (fig. 10), but more frequently this form is modified from various He is religious, generous, just, charitable and humane. causes, usually the mutual pressure of cells against each other. By wisdom, by art, by the united strength of a civil community, Thus the pith of trees, a portion of which is made up of cellular men have been enabled to subdue the whole race of lions, bears, and tissue, if examined under the microscope, will be found to be serpents. composed of cells having the form of honeycomb cells, that is to

The genuine glory, the proper distinction of the rational species, say, hexagonal (fig. 18).

arises from the perfection of the mental powers. This last dratning represents the appearance of a thin segment

Courage is apt to be fierce, and strength is often exerted in acts of

oppression. of elder pith when submitted to microscopic examination. Wisdom is the associate of justice. It assists her to form equal Occasionally the cells of cellular tissue assume a star-like or laws, to pursue right mensures, to correct power, to protect weak; stellate (Latin stella, a star) form, as, for example, is the case in ness, and to unite individuals in a common interest and general e common bean, of which our diagram (fig. 17) represents a welfare. section as seen when examined under the field of a microscope. Heroes may kill tyrants, but it is wisdom and laws that prevent Usually these vegetable cells are so very small that a micro- tyranny and oppression. scope, or, at least, a powerful lens, is necessary for observing 27. When a rote of interrogation occurs at the end of a sen, them. In certain vegetables, however, they assume such dimen- tence, the parts, and even the words, of the sentence separated sions as to admit of being readily seen by the naked eye. For | by commas, should each be read like a question.



there is no pause in the book. Spaces are left in the following Did you read as correctly, speak as properly, or behave as well as

sentences where the pause is proper to be made. James ?

Examples. Art thou the Thracian robber, of whose exploits I have heard so

The Europeans were hardly less amazed at the scene now set much ?

before them. Who shall separate us from the love of Christ ? shall tribulation,

Their black hair long and curled floated upon their or distress, or persecution, or famine, or peril, or sword ?

shoulders or was bound in tresses around their head. How are the dead raised up, and with what body do they come ?

Persons of reflection and sensibility contemplate with interest For what is our hope, our joy, or crown of rejoicing ?

the scenes of nature. Have you not misemployed your time, wasted your talents, and

The succession and contrasts of the seasons give scope to care passed your life in idleness and vice ?

and foresight diligence and industry which are essential to the Have you been taught anything of the nature, structure, and laws

dignity and enjoyment of human beings. of the body which you inhabit ?

The eye is sweetly rested on every object to which it turns. Were you ever made to understand the operation of diet, air,

It is grateful to perceive how widely yet chastely Nature hath erercise, and modes of dress, upon the human frame ?

mixed her colours and painted her robe. 28. Sometimes the word preceding a comma is to be read Winter compensates for the want of attractions abroad by fire. like that preceding a period, with the falling inflection of the side delights and homefelt joys. In all this interchange and voice.

variety we find reason to acknowledge the wise and benevolent Examples.

care of the God of seasons. It is said by unbelievers that religion is dull, unsociable, uncharitable, 32. The pupil may read the following sentences; but before enthusiastic, a damper of human joy, a morose intruder upon human reading them, he should point out after what word the pause pleasure.

should be made. The pause is not printed in the sentences, but Nothing is more erroneous, unjust, or untrue, than the statement it must be made when reading them. And here it may be in the preceding sentence.

observed, that the comma is more frequently used to point out Perhaps you have mistaken sobriety for dulness, equanimity for the grammatical divisions of a sentence, than to indicato a rest moroseness, disinclination to bad company for aversion to society,

or cessation of the voice. Good reading depends much upon abhorrence of vice for uncharitableness, and piety for enthusiasm. Henry was careless, thoughtless, heedless, and inattentive.

skill and judgment in making those pauses which the meaning This is partial, unjust, uncharitable, and iniquitous.

of the sentence dictates, but which are not noted in the book ; The history of religion is ransacked by its enemies, for instances of and the sooner the pupil is taught to make them, with proper persecution, of austerities, and of enthusiastic irregularities.

discrimination, the surer and more rapid will be his progress in Religion is often supposed to be something which must be prac- the art of reading. tised apart from everything else, a distinct profession, a peculiar

Examples. occupation.

The golden head that was wont to rise at that part of the table was 29. Sometimes the word preceding a comma is to be read

now wanting, like that preceding an exclamation.

For even though absent from school I shall prepare the lesson. Examples.

For even though dead I will control the trophies of the capitol.

It is now two hundred years since attempts have been made to How can you destroy those beautiful things which your father civilise the North American savage. procured for you! that beautiful top, those polished marbles, that Doing well has something more in it than the fulfilling of a duty. €Icellent ball, and that beautifully painted kite, oh how can you de

You will expect me to say something of the lonely records of the stroy them, and expect that he will buy you new ones!

former races that inhabited this country. How canst thou renounce the boundless store of charms that

There is no virtue without a characteristic beauty to make it partiNature to her votary yields ! the warbling woodland, the resounding cularly loved by the good, and to make the bad ashamed of their sbore, the pomp of groves, the garniture of fields, all that the genial neglect of it. ray of morning gilds, and all that echoes to the song of even, all A sacrifice was never yet offered to a principle, that was not made that the mountain's sheltering bosom shields, and all the dread

up to us by self-approval, and the consideration of what our degrada, magnificence of heaven, how canst thou renounce them and hope to

tion would have been had we done otherwise. be forgiven!

The succession and contrast of the seasons give scope to that care O Winter! ruler of the inverted yearl thy scattered hair with sleet.

and foresight, vigilance and industry, which are essential to the dignity like ashes filled, thy breath congealed upon thy lips, thy cheeks fringed and enjoyment of human beings, whose happiness is connected with with a beard nade white with other snows than those of age, thy the exertion of their faculties. forebead wrapped in clouds, a leafless branch thy sceptre, and thy A lion of the largest size measures from eight to nine feet from throne a sliding car, indebted to do wheels, but urged by storms along

the muzzle to the origin of the tail, which last is of itself about four ita slippery way, I love thee, all unlovely as thou seemest, and dreaded

feet long. The height of the larger specimens is four or five feet. us thog art!

A benison upon thee, gentle huntsman! Whose towers are these Lorely art thon, O Peace! and lovely are thy children, and lovely that overlook the wood ? ere the prints of thy footsteps in the green valleys.

The incidents of the last few days have been such as will probably 30. Sometimes the word preceding a comma and other marks, never again be witnessed by the people of America, and such as were is to be read without any pause or inflection of the voice.

never before witnessed by any nation under heaven.

To the memory of André his country has erected the most magnifi. Examples.

cent monument, and bestowed on his family the highest honours You see, my son, this wide and large firmament over our heads, and most liberal rewards. To the memory of Hale not a stone has where the sun and moon, and all the stars appear in their turns. been erected, and the traveller asks in vain for the place of his long Therefore, my child, fear and worship, and love God.

sleep. He that can read as well as you can, James, need not be ashamed to I consider it my duty, at this time, to tell you that you have done

MECHANICS.—III. something of which you ought to be ashamed. The Spaniards, while thus employed, were surrounded by many of

FORCES APPLIED TO A SINGLE POINT-PARALLELOGRAM the natives, who gazed, in silent admiration, upon actions which they

OF FORCES, ETC. could not comprehend, and of which they did not foresee the conse. In this lesson we have to consider how the resultant of two, and grences. The dress of the Spaniards, the whiteness of their skins, thence of any number of forces, applied to a single point may be thoir beards, their arms, appeared strange and surprising.

found. Yet, fair as thou art, thou shunnest to glide, beautiful stream! by

You will keep in mind that by a single point," I mean the village side, but windest away from the haunts of men, to silent

a peint" in a body;” and that will save me always adding the valley and shaded glen.

latter words when I use the former. Of course, forces applied But it is not for man, either solely or principally, that night is

to a material point" are included in the description, and

these you will find, in due time, to be of very great importance. We imagine, that, in a world of our own creation, there would As the joint effect of two or more forces so applied is termed dways be a blessing in the air, and flowers and fruits on the earth. their “resultant," so we name the separate forces of which it is Share with you! said his father-so the industrious must lose his the effect its components. There are thus two operations, the

Composition of Forces, and the Resolution of Forces, with which 31. Sometimes the paase of a comma must be made where we may be concerned in Mechanics ; by the former of which we

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denote the putting together, compounding, or finding the resultached weights, be thrown over two pulleys, P Q, which move tant of any number of forces, and by the latter the separating, freely in the same plane round axles fastened into a wall or or resolving, of any given force into the two or more to which it upright board. Arrange, then, the weights and cords until may be considered equivalent. The composition we first equilibrium is produced. It is evident, from the principle stated consider ; but this requires a short digression on

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 The resultant of two forces is found by the aid of the “paral. the cord o P, a length 0 A, lelogram of forces ;” and, as some of you may not know what a equal in inches to the num. parallelogram precisely is, I shall explain the term, and tell you ber of pounds in U, and on a few things about it which, in Mechanics, it is desirable you o o another, o B, equal to should know.

the pounds in v, and then A parallelogram is a four-sided figure whose pairs of opposite draw the parallels, A R and sides and opposite angles are equal. In the adjoining figure, ABCD B R, to o P and o g, meeting

is a parallelogram, if the in R; O R will then be the
side A B is equal to DC, resultant of u and y, if the
and also B C to A D. The principle of the parallelogram
two cross lines, A c and of forces be true. It should,
BD, are called the “dia- therefore, be opposite in di.
gonals of the parallelo- rection to the force w, and
gram. Now, if you ex- the number of inches in it

amine the two triangles, should be equal to the num.
Fig. 1.
A B C, A DC, which are ber of pounds in w. Now,

Fig. 3. on opposite sides of the diagonal, A C, you will see reason foron trial it is found that o R believing that they must be equal to each other. They are, is opposite to w, that is to say, that it points vertically in fact, the same triangle on opposite sides of that line; for upwards in the plomb-line; and it is also found that the number they have a c for a common side, and the two other pairs of of inches in its length is that of the pounds in w. gides are equal, namely, A B equal to DC, and A D to BC; and you Second Experiment.—Let us suppose that a parallelogram cannot out of three straight lines make two different triangles. OA B B is described anyhow on a perfectly smooth horizontal This you can satisfy yourselves of by experiment, by putting three table, and that at the point o, two springs are fitted so that one rods of different lengths together so as to form a closed figure. of them, on being let go, would make the unit ivory ball move

Now, the point to which I am trying to lead you, and which over 0 A in the same time that the other would make it move over you will soon find of importance, is that, since these triangles O B. It is evident that the lines o A and 0 B would then represent are equal—in fact, one and the same triangle in two positions, these forces. Furthermore, it should follow, if the principle of their angles must be equal to each other. Hence we arrive at the parallelogram of forces be true, that, when both springs are the following important properties of a parallelogram :

let go together so as together to strike the ball, it should move 1. That the opposite angles, A B C and A DC, are equal, also over the diathe opposite angles, B A D and B C D.

gonal 0 k of 2. That either diagonal makes equal angles with the pairs of the paralleloopposite sides, A B D equal to C D B, and A D B equal to C B D.

gram in the It is on account of this latter property the figure is called same time as "parallelogram.” The opposite sides are not only equal, but the ball moved parallel, on account of their making equal angles with either over o A and liagonal. However, keep in mind that these angles are equal, OB wherstruck for this knowledge is necessary to your properly understanding separately. what we next come to, namely

Now, this is


exactly hap

Fig. 4. The forces in our cuts and diagrams being represented, as pens. The ball does move over the diagonal, and moves over agreed on, by lines, and their directions by arrow-heads attached it in the same time that it previously moved over the sides

. to their remote ends, this principle may be stated as follows:- This it could not do if the resultant of two forces was not repreIf two forces applied to a point are represented in magnitude sented in magritude and direction by the diagonal

. Instruments and direction by two straight lines,

their resultant is represented are fitted up for lecture-rooms by which the experiment can be in magnitude and direction by the diagonal passing through made, and the result always is as I have stated. that point of the parallelogram of which these lines are two Taking the principle, then, as established, let us observe its adjoining sides.

consequences. You are given two forces, acting at a point, and In Fig. 2 let O P, o be the two forces, and draw from P and a you want their resultant. Make, you will immediately say, the two dotted lines parallel to them which meet in r, then the parallelogram of the two forces, and the diagonal is the required dotted diagonal, o R, of the parallelogram thus formed is the line. Not so fast; you need not describe the whole of that resultant, both in magnitude and direction, of o P and o Q. figure, a part will suffice. Now, if from the end A of 0 A, you

Now, I shall not here draw A R parallel and
give you the strict ma- equal to o B, it is clear

thematical proof of this you do not want to draw
proposition ; it is too B R at all. A R gives you
complicated, and involves the far end of the result.
so much close reasoning, ant, and all you have to
that to force it on a do then is to join R with

student in Fig. 2.

the begin-and your object is o ning of a treatise on me- gained. Thus your paral.

Fig. 5. chanics would be to throw an unnecessary difficulty in his way. lelogram of forces suddenly becomes a triangle of forces ; and The best course is to defer it until you have become more you may lay this down as your rule in future for compounding accustomed to mechanical reasoning, and then return to it. In two forces. the meantime you can satisfy yourselves that it is true by a reference to the two following experiments, one derived from and parallel to, the other force; and the third side of the

Draw from the extremity of one of the forces a line equal, equilibrium, the other from motion.

triangle so formed by joining the end

of this line with the point First Experiment.—Let three weights, u v w, be attached to of application is the resultant. three corda, as in Fig. 3, which are knotted together at o; and There is great advantage in this substitution of the triangle Let two of the cards, longer than the third, with their at- for the parallelogram, for it saves the drawing of uncecessary

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