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The leg3 then come to the surface, and you may afterwards think it necessary to notice here. We believe the instructions bring the arms round to the side, and float in the position now given will be found sufficient for all purposes of general shown in Fig. 6. But in floating you must remember to let the utility, and that practice in the modes described will suffice to chest play its proper part, as a bladder inflated to the fullest make not only a good but a dexterous swimmer. Variations possible extent; and in order to this you must inhale as much I upon them will come easy when the groundwork has been well zir as you can into the lungs, and when

laid, and there is perfect familiarity with you expel the air in respiration, you must

the water. draw a deep breath again immediately.

We must say a few words respecting Having assumed the position shown in

cramp, and on this point we cannot da Fig. 6, you are ready for swimming on

better than repeat Walker's instructions the back, which is usually performed in

on the subject :-"Those chiefly are the following manner :-Placing the

liable to it who plunge into the water hands on the hips, you draw up the knees,

when they are heated, who remain in it but at the same time depress the toes,

till they are benumbed with cold, or 80 as to raise the knees out of the water.

who exhaust themselves with violent You then strike out the legs, as in ordi

exercise. Persons subject to this af. nary swimming, and you find yourself

fection must be careful with regard progressing with the head foremost.

to the selection of the place where But it is possible to swim on the back

they bathe, if they are not sufficiently without using the legs, and in the case

skilful in swimming to vary their attiof fatigue or cramp it may become neces

tudes, and dispense instantly with the sary to do so. You then bring the hands

use of the limb attacked by cramp. towards the chest, and press back the

Even when this does occur, the skil. water in the direction of the feet with a

ful swimmer knows how to reach sweeping motion. By reversing this

the shore by the aid of the limbs movement of the hands, and sweeping the

Fig. 4.-THE DIVE.

which are unaffected, while the unin. wator gently towards the chest instead

structed one is liable to be drowned. of away from it, you are enabled to progress in the opposite | If attacked in this way in the leg, the swimmer must strike direction-i.e., feet foremost. The elbows in these movements out the limb with all his strength, thrusting the heel downward, should be kept near to the sides, only the fore-arm being used and drawing the toes upward, notwithstanding the momentary to give the hands their necessary action.

pain it may occasion; or he may immediately turn flat on his Swimming on the side is sometimes practised as a change back, and jerk out the affected limb

from the ordinary mode of progression. in the air, taking care not to elevate
Turning on either side, you throw out it so high as greatly to disturb the
the undermost arm along the water, balance of the body. If this does not
and, with the palm of your hand hol. succeed, he must paddle ashore with
lowed out for the purpose, you scoop his hands, or keep himself afloat by
or drag the water towards you. The their aid until assistance reach him.
action of the legs is much the same Should he even be unable to float on
as in ordinary swimming, and the upper his back, he must put himself in the
most hand is used at the same time as upright position, and keep his head
the legs in pressing back the water. The above the surface by merely striking
stroke of the legs must exactly alternate the water downward with his hands at
with that of the foremost arm.

the hips, without any assistance from
The hand-over-hand style of swimming the legs." But besides this, it must
consists in swinging the hands, one after be remarked that, although cramp is a
the other, forward out of the water to as dangerous thing, it is not so dangerous
great a reach as possible, then dragging as the fear by which it is occasionally
the water backward to the hips, each leg accompanied, and which sometimes
striking out alternately, as soon as the leads to entire loss of self-possession,
arm on the same side has completed its with the worst results. If attacked
movement. The whole movement of the by cramp, therefore, act with calmness,
arm describes an oval figure, of which the recall to mind the foregoing instruc.

lower part is in and the other out of tions, and, by adopting that method Fig. 7.-TREADING THE Fig. 5.-THE HEADER. the water, while the shoulder forms the which is best suited to the nature of

WATER, centre. After being thrown forward, the the seizure, you may maintain yourself hand, as it reaches the surface of the water, is turned edgewise, safely in the water until the pain has gone, or assistance can so that it encounters little resistance on entering the water, but reach you. it is immediately afterwards turned with the knuckles upward One more word of advice, as to attempting to save a drown. and the palm hollowed out, as in side-swimming.

ing person. Never approach him from the front, but take him Treading the water is accomplished by allowing the feet from behind by the hair; and never allow him to grasp any to fall from the floating or swimming

part of your body if you can possibly position, and performing with the legs

prevent it. But if you should find the same motion that is made in going

yourself so seized, sink at once to the up a flight of stairs. The feat is more

bottom, when the hold upon you will easily achieved when the arms are em.

probably be relaxed, and you will be ployed to assist the legs by press

released from your perilous position. ing the water with a downward mo.

It is only a good swimmer who should tion, as shown in the illustration

make such an attempt in deep water, (Fig. 7).

as for a novice to try to rescue a drownMuch the same position as this is

Fig. 6.-FLOATING.

ing man by his own unaided efforts, ia maintained when standing in the water

greatly to imperil a second life with-or, as it is termed by some, perpendicular floating only that out reasonable chance of saving the first. Better hasten to the head is thrown back, with the nostrils elevated in the air, secure a rope or pole, which, thrown quickly to the person in while the arms are either folded across the chest, which is arched danger, may assist him in regaining shallow water or the well forward, or kept down close by the hips.

shore. Young swimmers should never go out bathing together There are other styles of fancy swimming, such as the “ dog. without having such a means of assistance at hand in case of like style," swimming under the water, etc., which we do not emergency.

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GEOMETRICAL PERSPECTIVE.-II. is perpendicularly over the plan e a. It will be observed that

ea cuts the base of the picture, pl pl, in c, from which a perIn this course upon Geometrical Perspective we propose to pendicular is drawn to meet the line E A in B, therefore B is place before our pupils several methods of construction, and the perspective projection on the picture-plane of the point or show where they are applicable to special cases. The ground- object, A. We give a similar representation of two points plan method is the most simple and general. The lineal method, (Fig. 6), which are the extremities of the line A B. A is on although it is equally useful, involves the necessity; in some the ground, B is above the ground; consequently the line instances, of a greater number of lines ; but as this system A B is inclined to the horizon. We need not enter into an dispenses with the use of a ground-plan, it may to some extent explanation of this after that of Fig. 5, as it will be seen curtail the amount of labour. Some of the problems will be by the working lines that cd is the perspective representation worked by both systems; and with regard to the ground-plan of A B.

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method, we shall introduce some modifications which we hope ! We shall have to consider objects under various positions. will enable our pupils to understand it thoroughly.

Case 1. When they are parallel with the picture-plane, and The station-point is sometimes determined by placing it at a also with the ground. given distance from the picture-plane, sometimes from the object Case 2. When they are perpendicular to the picture-plane, represented by its ground-plan, the picture-plane intervening. and parallel with the ground. In either case we must bear in mind that the visual rays from the Case 3. When they are perpendicular to the ground, and two extremities of the object must not form an angle greater than parallel with the picture-plane. 60°, meaning that the whole of the object must be included in Case 4. When they form an angle with the picture-plane, that angle, because the full extent of vision each way, right and and parallel with the ground. left, without moving the head, is not greater than 600. But Case 5. When they form an angle with the ground, and even if we include the object within 60° only, we should be too parallel with the picture-plane. near it to make a satisfactory and effective drawing; therefore Case 6. When they form an angle both with the picturean angle of about 25°

plane and the ground. or 30° at the outside

To illustrate the first is sufficiently large,

position, place a rectas in Fig. 4, where the

angular table before eye at E embraces tho

you, so that both ends PP

VP line A B within an

may be equally disangle of 60°, while at

tant from the eye : F the same line is in.

the front edge of the cluded within an angle

Fig. 7. table will be parallel of 25o. The latter

with the picture-plane, point, F, is a better

HL

and the top will be pa. distance for viewing

rallel with the ground; the object, A B. An

and at the same time explanation of the

the retiring edges of practical operations

the ends will be per. of perspective and

pendicular to the pictheir results may be

ture-plane and parallel limited to that which BP

with the ground. This relates to a point, or

PC2
BASE OF PICTURE, OR PLANE OF PICTURE, BROUGHT DOWN.

answers to the second in the same way to

case. The front of the a series of points ;

table, from the top to for as points are the extremities of straight lines, no matter the ground, will explain the third case, because it is perpendicular their positions, it must be evident that if we can determine the to the ground, and parallel with the picture-plane. Now push position of one point upon the plane of projection, which we call one end of the table away from you, so as to cause the distance the picture-plane, we can do so of more, and thus determine between the two ends from the eye to be different, then the the extremities of lines. Let A (Fig. 5) be a point in space front edge will be at an angle with the picture-plane, but the top that is, somewhere in the air above the ground, and away from will remain parallel with the ground. This illustrates the the picture-plane, PP, p'pl. The horizontal projection of this fourth case. Bring the table back to its first position, and let point-in other words, its plan-will be a. Let E be the posi- one end be raised, then the top will form an angle with the tion of the eye, e will be the horizontal projection of the eye- ground, and the front edge will be parallel with the picture-plane. that is, over where the eye is placed, otherwise called the This answers to the fifth case. The sixth case will be explained station-point, sp. Now if e and a are joined by a straight line, if you push the raised end of the table away from you, as was the line ea will be the horizontal projection or plan of the done in Case 4, then the front edge will be at an angle with the visual ray from the object, A, to the eye, E; because A a and picture-plane, and the top will be at an angle with the ground. Ee are perpendicular lines, therefore every part of the line EA These positions might have been illustrated by a line only, but

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SP

probably they will be better understood from the table, as the

LESSONS IN ENGLISH.—XXI. positions of the several parts will be easily recognised. We

WORDS THAT ARE BOTH PREFIXES AND SUFFIXES. rooommend our pupils to go through this experiment with a table, it will help them better to understand the positions of Some of the words which we treated of in the last Lesson 23 objeots in the problems that will be given in the course of these uncombined suffixes, may also be regarded as uncombined prelessons,

fixes. The same word stands before and after its stem. You In ground-plan perspective the rule for finding the vanishing- may take, as an instance, to cast-down, and down-cast. In this point is:

instance the meaning varies, but does not greatly vary; to Draw a line from the station-point, SP, parallel with the cast-down is used physically, and down-cast signifies dejected, ground-plan, as jar as the plane of the picture, PP, from which sorrowful. Besides this difference, there is a difference also as draw a perpendicular line to the horizontal line, hl; this will to the function of the two words, for the former is a verb, the give the vanishing point, vp.

latter is an adjective. Rarely, perhaps, does the import remain In order to assist the pupil in comprehending this, we request the same, if the position of the adverb is altered. Make a prefir him to turn to Fig. 7 in the preceding page, and he will a postfix (or suffix), and in general you produce a greater or less notice first the ground-plan, of a line only, A B, at an anglo with modification of meaning. Indeed, some of the most delicate the PP. It must be remembered that this line, PP, is the plan shades and hues of thought expressed in the English language or projection of the whole surface of the picture, supposed to be are connected with, if not dependent on, the varied use of these in an upright position, and as we cannot draw upon a piece of movable particles. It may, therefore, be proper to go into paper so placed, it is necessary to rabat it—that is, turn it down some little detail on the point. and lay it flat upon the table. This is done by bringing down It is not all the prefixes and suffixes that usage permits to the picture-plane, and all the points of intersection of visual rays take their stand before or after their principal word. Out enjoys and points of contact (anywhere, so that there may be sufficier the privilege, and makes free use thereof. Look at these space to make the drawing), towards the station-point, $P- examples :we have marked it BP, “ base of picture, or plane of picture, cast-out, out-cast.

cry-out, out-cry. brought down." From this line we arrange the height of the bid-out, out-bid.

laugh-out, out-laugh. eye, or horizontal line. Now to find the vanishing point for grow-out, out-grow.

look-out, out-look. the line represented by its ground-plan :--Draw a line from SP do-out, out-do.

right-out, out-right. to vP, parallel to A B, and draw a perpendicular line from VP

live-out, out-live. to vpl. vpl will be the vanishing point for the given line An out-cast is one who undergoes the result and consequences represented by the plan A B. This must be learnt at once, as it of being cast-out. Corresponding with out-cast, is out-law. But will be wanted in almost every case of ground-plan perspective. though we may say to out-law, we cannot say to law-out. Out. It does not signify whether the given line is inclined or parallel post is again different from out-cast, for out-post does not make to the horizon; it is the plan only of the line we use for the idea of action so prominent as does out-cast. In this respect finding the yp, as will be seen when we come to problems out-cast is not unlike out-lay. Out-lay may be reversed ; thus

, relating to inclined lines and planes.

lay-out. But while the verb is lay-out, the noun is out-lay. To We advise the pupil to work the problems that we shall bid-out, is to bid with a clear, loud voice ; but to out-bid, is to bring under his notice in the course of these lessons to a bid more than another. To grow-out is very different from to scale of half an inch to the foot—that is, if we say he is to out-grow. A young brother, by becoming taller, out-grows a draw a line five feet long, he will make it five half inches; elder brother; and the elder brother, who is thus surpassed, and, to save a great deal of repetition, we will settle at once may be grown-out at the shoulders so as to be hump-backed. that the height of the eye, hl, from the ground is five feet, To do a person out of anything, is to cheat him; bat to out-do a and ten feet from the picture-plane. This scale may be competitor is to excel him. If my children live-out the century, employed until we propose another, when we come to other they will out-live me. By crying-out lustily, boys make a great problems.

out-cry. That shameless man, by laughing-out so loud and 80 PROBLEM I. (Fig. 7).— Draw the perspective view of a given long, out-laughed all the company. If you look-out at the line, A B, five feet long, lying on the ground, forming an angle window, you will have a pleasant out-look. with the picture-plane of 35°, and touching the picture-plane; the eye to be opposite the centre of the given line.

We have taken all the out-lying parts of the Spanish monarchy."

Temple. Draw a line, PP, to represent the picture-plane; from any

"But for public dormitories, how many a poor creature would have point, A, draw a line, A B, at an angle of 35° with PP (see Les- been obliged to lie-out of doors in the nights of the last severe winter ** sons in Geometry, Problem XX., Vol. I., page 256), and make it, -Anon. according to the given scale, five feet long; find the centre of

“Oh, my lord, A B in c, and from c draw a line perpendicularly to the picture

You said that idle weeds are fast in growth; plane to any length; mark the point d on PP. Anywhere

The prince, my brother, hath out-grown me far." - Shakespeare below, draw the base of the picture, BP, parallel to PP, and

"Albert has grown-out of his clothes." —Anon. draw the line il parallel to BP or PP. From d make d sp

" But breathe his faults so quaintly equal to ten feet. Now find the vanishing-point, vp', as we

That they may seem the taints of liberty; have already explained. Because the end of the given line A B

The flash and out-break of a fiery mind."-Shakespeare, touches the PP at A, therefore A is the point of contact of the "A fire breaking-out in the cellar, consumed the whole house." line A B; mark it PC. Bring it down perpendicularly to the Anon, line BP to pc?. Draw a line from pcl to vpl, and somewhere

" Nor they which use To out-drink the sea.'

"-Donne. apon this line will be the perspective view of the given line, A B,

" You have drunk-out the cask. to be found thus:--As the line A B touches or is in contact with

Children cannot well drint out of

goblets."- Anon. the PP, therefore the perspective view will commence at pc!;

“He looked and saw what numbers numberless the other end , away from PP, is found by drawing a visual

The city gates out-poured."-Milton. ray, V R, from B towards the sp, stopping at the picture-plane, from which it is taken perpendicularly until it cuts the line

“Pour-out a glass of wine for the famished woman."-Anon. PC and vpl in b; a b is then the perspective representation

"The workmen, in standing-out for the wages, have ott-atood the

appointed time."-Anon. of the given line A B. Make the space between a and b some

"Sense and appetite out-vote reason."-South. what darker than the rest of the line.

“A large majority of the constituency voted the old member ent."We advise the pupil to repeat this problem until he knows Anon, the method of working by heart, then to turn the line or plan

“Better at home lie bed-rid, idle, the other way; and, again, increase or diminish the angle of

Inglorions, unemployed, with age out-worn."-Vilton. inclination with the picture-plane. Also change the height

" This reverent leecher, quite worn out of the eye, or horizontal line, and the distance of the eye from

With rheumatisms, and crippled with his gout."-Dryden the picture-plane; these various positions of the object will

“ By Shakespeare's, Johnson's, Fletcher's lines, very materially assist the pupil in understanding the method of

Our stage's lustre Rome's out-shines,"Denham. working the problem.

"Out of Zion, the perfection of beauty, God hath shined."-Psalm 1 2

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Over produces many combinations.

your report to a child, say a younger brother or sister ;

I menlook-over, over-look. flow-over, over-flow.

tion a child, because in speaking to a child you will speak readily reach-over, over-reach,

persuade-over, over persuade. and naturally. There is another advantage : in order to gain a run-over, over-run.

ride-over, over-ride, child's attention you must take a simple subject, and on simple You look-over your workmen and find faults that you cannot subjects you will not want words. Subjects such as I contemover-look. A bad tradesman reaches-over his counter and over plate are constantly occurring wherever there are human beings. reaches his customers. Cisterns over-run, and drivers run-over.

You may take as your theme some accident that has happened A river over-flows its banks, and the water flows-over the fields. in the house where you reside, in a neighbouring mine, on the You persuade an opponent over to your own party, and so over. high road; or you may describe a bird's nest; the peculiar form, persuade an associate that he relinquishes your company. If colour, and habits of the swallow, the dog tribe, the cat tribe, the yon persuade a person over you cannot over-persuade him. In daisy, the wild rose, the honey-bee, etc. attempting to over-ride a competitor, take care you do not ride

Well, having described the object to a child, take your pen and over him. The boy having run over his companion in the race, write down as well as you can the very things you said, and easily over-ran him.

having carefully corrected them according to the best of your Other particles are of less frequent use, but not less curious ability, copy out the

whole in your composition-book. are they. To back-stitch differs from to stitch-back. By reckoning

Many children would be far better as an auditory than one his income a man learns how much he has coming in. The out. child. And very desirable for your purpose is it that utility to goings of a family should be regulated by its income. If I with others should be immediately in your view. For these reasons I hold my opinions I may continue to hold with you. He talks so advise you to become a teacher in a Sunday-school, or if that is much of bearing with me that I can hardly forbear to reprove not possible or not convenient, then gather around you a number him. The poor man has been taken off as if he were the of- of children and form a class. By preparing to teach them you scouring of the streets. That young girl was taken off at the will give your mind useful discipline, and in communicating to early age of seventeen, being overtaken by disease. One them what you know you will take effectual lessons in the diffi. general made an onslaught on the cavalry, while the other fell cult art of correctly expressing your thoughts. By teaching on the infantry.

others you will best teach yourself. To diligence there is

nothing impossible. Report to a child or two the following Immediately the mountains huge appear

anecdote :-
Emergent, and their broad, bare backs up-heave

SOUTHEY'S SCHOOLING.
Into the clouds."

Milton, « Thou hast made my curdled blood run back, my heart heave up, Here one year of my life was passed with little profit, and with a good my hair to rise in bristles."— Dryden.

deal of suffering. There could not be a worse school in all respects.

Thomas Flower, the master, was a remarkable man, worthy of a better Alongside the cutter we coasted along the shore. The under station in life, but utterly unfit for that in which he was placed. His takings of your father are under-paid. The understanding was whole delight was in mathematics and astronomy, and he had con that you stand under the spout. The undertaker receives funereal structed an orrery upon so large a scale that it filled a room.

What a arrangements under his care.

misery it must have been for such a man to teach a set of stupid boys, "An under-plot may bear such a near relation to the principal design year after year, the rudiments of arithmetic! And a misery he seened

to feel it. When he came to his desk, even there he was thinking of as to contribute towards the completion of it, and be concluded by the

the stars, and looked as if he were out of humour, not from ill-nature, same catastrophe."-Spectator.

but because his calculations were interrupted. But, for the most part, “ In under praising thy deserts

he left the school to the care of his son Charley, a person who was Here find the first deficience of our tongue."-Dryden. always called by that familiar diminutive, and whose consequence you “ Under two conditions the poet engaged to compose the eulogy."- may appreciate accordingly. Writing and arithmetic were all they Anon.

professed to teach; but twice in the week a Frenchman came from " For this assembling all the peers

Bristol to instruct in Latin the small number of boys who learnt it, of Whose counsels now must under-prop the throne.”Drayton.

whom I was one. That sort of ornamental penmanship, which I now He placed a line of props under the falling wall. An influx of

fear has wholly gone out of use, was taught there. The father, as well

as Charley, excelled in it. They could adorn the heading of a rule in gold causes bank-notes to flow out of circulation. The inlets arithmetic in a ciphering-book, or the bottom of a page, not merely are more numerous than the out-lets, consequently you will be with common flourishing, but with an angel, a serpent, a fish, or a pen, compelled to let out the water by artificial means.

formed with an ease and freedom of hand which was to me a great

object of admiration; but, unluckily, I was too young to acquire the EXERCISES FOR PARSING.

art. I have seen, in the course of my life, two historical pieces proOur abodes out-last our bodies. Curtail your outlays if you wish duced in this manner; worthy of remembrance they are, as notable for ease of condition. He laughed out-right. Let thine eyes look specimens of whimsical dexterity. One was David killing Goliath ; it right on. You shall be driven out right forth. This way, right down was in a broker's shop at Bristol, and I would have bought it if I could to Paradise, descend. An over-much use of salt, besides that it have afforded, at that time, to expend some ten shillings upon it. occasions thirst and over-much drinking, has other ill effects. You They taught the beautiful Italian, or lady's hand, used in the age of have yourself your kindness over-paid. He gained a large fortune our parents; engrossing (which, I suppose, was devised to ensure disover the counter. Parents too often overpraise their children. Come tinctness and legibility); and some varieties of German text, worthy, d'er the brook, Bessy, to me. With an over-running flood God will for their square, massy, antique forms, to have figured in an antimake an

end the place. Were it not for the incessant labours quarian's title-page. of this industrious animal, Egypt would be overrun with crocodiles. Milk while it boils, and wine while it works, run over the vessels they

EXERCISES IN COMPOSITION. are in. I shall not run over all the particulars that would show what

Historical Theme-The formation of the Hebrew Tabernacle. Perpains are used to corrupt children. Should a man run over the whole sonal Theme-What have been my thoughts during this day ? Poetical circle of earthly pleasures, he would be forced to complain that plea-Theme-The stillness of the country. sure was not satisfaction. The zeal of bigotry runs out into all manner of absurdities. The zeal of many outruns their discretion. Form each of the following words into a simple sentence :COMPOSITION.

Girl; boy; dove; California; amendment; Adam; England; dis.

turbance. As minds are differently formed and capacity varies with every successive individual, I am desirous of making another Describe a butterfly; a robin; a lark; a salmon; a mackerel ; suggestion or two, which may possibly smooth the way to original a sheep; a rabbit. composition for some whom the instructions previously given Supply suitable adjectives in the ensuing sentences :may have left in difficulty. I advise you, then, to accustom

Wise men love

counsels,

men must die. The yourself to report as correctly as you can, to a child, something fruit of autumn is delicious. Small faults produce that has struck your attention, whether in what you have heard,

how - is hypocrisy ! what you have scen, or what you have read. I say report the substance by word of mouth. Endeavour to employ suitable Complete the following propositions :words, to pronounce them correctly, and to put them together

for having teen too exacting.

to respect the aged. Srammatically. At first you will commit errors ; but, in time, the prevention of evil.

for having soiled his book. perseverance will enable you to overcome all difficulties. Make the scholar's negligence.

ones.

DEFINITIONS-THE THREE LAWS OF MOTION.

MECHANICS. --XVI.

The motion of any body may be either uniform or variable.

It is uniform when equal spaces are always passed over in equal DYNAMICS.

times, and its velocity is then measured by the number of feet

actually passed over in a second. When this number is not We have now to pass on to the second and more difficult part constant, the motion is variable, and the velocity at any point of Mechanics; but as we have already acquired a knowledge of of time is measured by the space it would pass over in one some of the fundamental principles of the science, the difficulty second if it continued during the whole second to move at the will not be great, and by a little thought and application will same rate as at the given moment. A variable motion may be easily be overcome.

either accelerated or retarded, and if the gain or loss of velocity Hitherto we have had to deal with forces which acted on a in equal times be equal, it is said to be a uniformly accelerated body and produced equilibrium. If any of these forces be or retarded motion. now altered or modified in any way, so that one or more A railway train when first started affords an illustration of remain unbalanced, some motion will take place, and the nature accelerated motion. The power of the engine is more than of this motion will, of course, depend upon the forces. It is the sufficient to overcome friction and the resistance of the air, object of dynamics to inquire what these motions will be, and and therefore the speed increases ; but the resistance increases what are the laws that govern them; and though at first they in a greater ratio, till, after a time, exactly equals the power may appear comparatively unimportant, we shall find as we of the engine, and then equilibrium ensues, and the train conadvance that an acquaintance with them is of great practical tinues in a state of uniform motion. use for many purposes.

The actual measurement of the space passed over in a given The investigation of the action of the earth's attraction, of the time is often a difficult thing, especially as there are always motion of bodies projected with any given velocity, and of many counteracting forces which impede the motion in a greater or other common things, depends on the principles of dynamics, and less degree. There are, however, various ways in which this the laws we discover by examining these are found to apply on may be accomplished, some of which we shall see as we proceed. an infinitely more grand and glorious scale in nature, for by Now there are two modes in which we may regard force ; their action all the stars and planets are kept in their orbits one is, by considering merely the velocity imparted without any and made to perform their varied revolutions. By these laws reference to the quantity of matter moved; force considered astronomers can not only explain and account for their varying thus is called accelerating force. The other mode is by taking distances and motions, but can foretell with the utmost accuracy into account the quantity of matter moved as well as the eclipses and other phenomena of the heavenly bodies. Calcula- velocity, and this is called moving force. These are not two tions like these require, indeed, a far deeper acquaintance with different kinds of force, but merely two ways of regarding the the higher branches of mathematics than we can acquire from same force. It is clear that a different amount of force is these lessons; but still the principles we shall investigate are required to impart the same speed two bodies of different those on which all such calculations are based, and the subject weights. The impulse that would impart a very great velocity will, we hope, be pursued by many far beyond the point to to a pistol-bullet may scarcely be able to move a large cannonwhich we can advance here.

ball. The quantity of matter or mass of a body is thus an There is one important difference between statics and important element in measuring the force required to produce dynamics, and that is, that the latter is one of the inductive motion in it. Now we cannot determine exactly what the sciences, though perhaps the simplest of them. Some sciences, mass of a body is, as we do not know the ultimate particles like arithmetic and geometry, are called deductive, their of which it consists ; but we can always measure it by the principles being deducible from abstract truths without re- weight of the body, for gravity may be considered to act ference to experiment, though that is sometimes resorted to equally on all particles, and therefore two substances on which as a corroborative evidence or a simpler mode of proving their it acts equally—that is, which have the same weight-may be truth. To this class statics belongs, for all its fundamental considered to contain the same quantity of matter. Hence, truths can be mathematically proved. Not so with dynamics, when we want to find the quantity of motion or momentum of many of the truths of which can only be ascertained by experi. any body—that is, the force which would be required to gene ment, and in order to ensure accuracy in these experiments they rate in it a motion equal to its own, or which it would exert must be repeated again and again, for slight errors are likely against any obstacle which obstructed it—we have to multiply to creep in, and it is only by taking the average of many its velocity by its weight. different experiments that we can arrive at accurate results. This is usually given as a definition : The momentum of any Many, however, of its principles can be ascertained by deduc. body is its mass multiplied by its velocity. If, for example, s tion, and it thus approaches much more nearly to the deductive body weighing 100 lbs. be moving with a velocity of 15 feet sciences than the other branches of natural philosophy, to which per second, its momentum is 1,500. we shall turn our attention shortly.

After thus much by way of definition, we pass on to the As previously stated, we have in dynamics to introduce a laws of motion; but we shall have to return to momentum. fresh idea, that of time. In statics force was considered only the most important principles of motion were drawn up by as producing pressure, and therefore this element did not enter Newton in the shape of three general laws. These have since into our calculations, but it is clear that, in treating of motion, been altered in their form, but assert nearly the same facts, the time occupied is an important thing to consider.

The first teaches that every body will continue in its state of It is needful at starting that we should have some mode of rest or uniform motion in a straight line unless acted upon by measuring the degree and intensity of motion, that is, the some external force or forces. This law merely asserts the velocity of any body, and, as we saw, two quantities are needed inertia of matter, that is, its inability of itself to alter or to determine this, the space passed over, and the time occupied modify in any way any motion which has been imparted to it in passing over it. We may know that a force applied to a We can easily understand that a body at rest will remain su body causes it to move over a certain space, but to form a unless some force be applied to it, as we see constant illustra correct idea of the force, we must also know how long it takes tions of the fact. It is, indeed, one of the earliest truths which to travel this distance. When we speak of a speed of 12 miles we acquire from observation, bnt the other part of the law an hour, we mean that if the motion continued uniform through seems more at variance with experience. In fact, almost every that space of time the body would have travelled 12 miles. It motion we observe seems at first sight to point out the inaccuracy does not, however, imply that the body actually passes over of the law; but it is only at first

sight, and a little examination 12 miles, but merely that it moves with that degree of speed. will show its truth. Let a stone be rolled along the ground Great inconvenience often results from thus requiring two with great speed, it comes to rest in a very short time ; so, too, numbers to represent a velocity, and hence it is usual to ex. a boat when rapidly rowed along soon stops if the man ceases press it by the number of feet passed over in one second. If to ply the oars. The true reason, however, why in these and a body moves a mile in 8 minutes, it passes over a furlong, or similar instances the motion ceases, is,' that other forces 660 feet, in one minute, and therefore over 11 feet in one second, neutralise that which has been acquired. In the first case, and it is said to have a velocity of 11. When, therefore, we these forces are friction along the ground and the resistaneu represent a velocity by a number, it is always to be understood of the air;

in the second, the resistance of the water, for the boat as the number of feet passed over by the body in one second. as it advances must displace some of the water, and all the

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