thus, amicus, the accent being on the penult. There is another way of marking the same fact; it is by the use of a short straight line, as, and a curve, as . The former denotes a long or accented syllable-for instance, doctrina; the latter denotes a short or unaccented syllable-for instance, dominus. We thus see that doctrina and doctrína, dóminus and dominus point out the same thing-namely, that in pronouncing doctrína the stress of the voice must be laid on the i, and in pronouncing dóminus it must be laid on the o.

oase.

Another practice must be pointed out. In Latin, as will presently be learnt, the endings of words have a good deal to do with their meanings. It is, on that account, usual to pronounce them at least very distinctly. Indeed, we might say, that on every terminating syllable a sort of secondary accent is laid. Thus, dominus is pronounced dóminús. So in other forms of the word: thus, dóminí, dóminó, dóminúm. The object is to mark the distinction between, say, dominus and domino, a distinction of great consequence. Another form of this word is dominos. For the same reason a stress is laid on the termination os, which accordingly is pronounced as if it were written Words, too, which end in es have a secondary accent on the e; as vulpes, a fox, pronounced vulpees. In a few cases the vowel is what we call doubtful, that is, it is sometimes short and sometimes long. This peculiarity is marked thus, as in tenebrae, darkness, when the accent may be on the penult, as tenebrae, or on the antepenult, as tenebrae. Observe, also, that a vowel at the end of a word is always pronounced in Latin. Take, as an example, docéré, to teach, which is pronounced as it is marked, that is, with an accent on the last syllable no less than on the last syllable but one." Care must be taken to pronounce docéré as a word of three syllables, do-ce-re, and not do-cere, as if it were a word of two syllables only, remembering, as we have observed before, that the Latin language has no silent e, as we have: for instance, in wife. The reader may practise himself, according to these rules, in pronouncing thus the opening lines of that fine poem, Virgil's "Eneid." The translation made by the English poet Dryden gives a fair idea of the meaning of the original.

"Arma virúmque canó, Trójaé quí prímus ab óris
Italiám, fátó profugús, Lávinia vénit

Littora; múlt[um] ill[e] ét térrís jáctátus et álto,
Ví superúm, saévaé memorém Júnónis ob íram;
Múlta quoqu[e] ét bélló pássús dúm cónderet úrbem,
Inférrétque Deós Latió; genus únde Latínum,
Albáníque patrés, átqu[e] áltaé móenia Rómae."
"Arms and the man I sing, who, forced by fate,
And haughty Juno's unrelenting hate,
Expelled and exiled, left the Trojan shore.
Long labours, both by sea and land, he bore,
And in the doubtful war, before he won

The Latin realm, and built the destined town-
His banished gods restored to rites divine,
And settled sure succession in his line,
From whence the race of Alban fathers came,
And the long glories of majestic Rome."

In the above piece of Latin poetry will be noticed some letters enclosed by brackets. By certain rules which will be found in Latin prosody, these letters are dropped, or not sounded, under certain conditions of position in Latin poetry, although they are sounded distinctly in Latin prose. In pronouncing the third line, we must cut off the um in multum before the vowel i in ille; and the e in ille before the e in et. Also in the fifth line drop the e in quoque before the e in et. In the last line, too, the è in atque is dropped or elided before the vowel a in altae, and the two words are run into one, and pronounced as if written atqualtae. Accuracy of pronunciation, however, is not easily acquired from any written or printed directions. The living tongue is the only adequate teacher. And it will be well for the reader to get some grammar-schoolboy to read to him and hear him read the passage given above from Virgil, and the exercises, or some of them, which will be found in future lessons. Although the pronunciation of Latin is of secondary importance, yet it is well to be as correct as possible, if only from the consideration that what is worth doing at all, is worth doing well. But should any one, as he justifiably may, hope by these lessons to prepare himself for becoming even a teacher of Latin-say in a school-he would in that capacity find the pronunciation considered as a matter of consequence; indeed, a disproportionate value is, especially

in the old grammar schools, attached to the established methods of pronunciation. After all, we cannot pronounce the Latin as it was pronounced by the Latins themselves, nor can the best trained lips pronounce their poetry so as to reproduce its music.

OUR HOLIDAY.

As the possession of a healthful frame and strength of muscle and sinew is absolutely necessary to all who desire to make the most of their mental powers, we have thought it desirable to devote a portion of the POPULAR EDUCATOR to a series of papers on what is generally termed Physical Education, or, in other words, the culture of the powers of the body.

We intend, therefore, to take "Our Holiday" at regular intervals, and invite our readers on these occasions to dismiss all thoughts of graver studies for a while, and enter heartily into the consideration of the art of developing the strength, endurance, and agility of the human form by properly regulated gymnastic exercises and athletic sports and games. We will take first a game which has during the last few years attracted special attention in this country

Across

LA CROSSE, THE NATIONAL GAME OF CANADA, a game lately introduced into this country from the "New Dominion," where it occupies a position like that so long held by cricket in England. It is of Indian origin, and has been played here by Canadians and Indians brought over for the purpose. It is a ball game, and derives its name from the implement used in striking the ball, which is a long hickory stick bent at one end like a crosse, or bishop's crosier. this curve of the stick stout network is stretched, and extends nearly half-way down its length. The "crosse" has, therefore, something of the appearance of a racket-bat, but is much longer. To the spectator the game presents the appearance of a combination of football and hockey, with some striking variations from both. It is a very animated game, interesting to the looker-on, and highly exciting to those engaged in the contest. It requires a large space of ground, not less, as a rule, than about 400 yards square, and tolerably level. Towards the two ends of this ground goal-posts are fixed, as at football, and the players are divided into two parties, each having its own goal. Each goal consists of two poles about six feet high and seven feet apart, ornamented with flags of the colour-say red or blue-chosen by the party who may take that side in the game. The distance between the two goals is optional, depending upon the space of ground in which the game may be played, and other conditions either accidental or the subject of agreement between the contending parties. The number of persons who may play is optional also, but they are usually equally divided, as in other field amusements.

The object which is pursued by either party throughout the game is to drive the ball through the opponents' goal-that is, between their goal-posts. When this is done the game is over, having been won by that side which has succeeded in the attempt. The ball used is made of hollow india-rubber, and must not be more than nine nor less than eight inches in circumference. It must, as a rule, be touched only with the "crosse," and it may either be struck with this implement or carried upon it. The crosse is about four feet long, and the network with which it is provided is nearly tight, but just sufficiently loose to hold the ball when resting on it. It is not allowed to assume the shape of a bag. Thus fashioned the ball may be readily picked up from the ground and carried upon the crosse, or flung from it towards the opponents' goal.

The principal players engaged on either side occupy the following stations:-d. Goal-keeper, who places himself near the goal, it being his duty to defend it when in imminent danger. 2. Point, some twenty or thirty yards in front of the goal-keeper. 3. Cover-point, about the same distance in advance of point. 4. Centre, who faces the centre of the field; and, 5. Home, who is stationed nearest the opponents' goal. The remaining players are called the fielders, and have no fixed position.

The game is commenced midway between the two goals, the ball being struck off by the captain of one side, as may have been decided by lot. The struggle at once ensues, one party endeavouring, by striking and following up the ball, to carry it

onward until their opponents' goal is reached, and the other striving by every means in their power to beat back the ball, and force it in turn into the opponents' ground. Great agility and dexterity are required to play an efficient part in the game. Fleetness of foot and quickness of eye are the essential qualifications of a good player. When one has caught and is carrying the ball upon his crosse, it is allowed to any of the opposite side to strike the ball from his crosse with their own weapon. Thus, at the moment when, after a long contest, he may be on the point of winning the game by a dextrous fling of the ball, which he has obtained with much difficulty, it may be jerked or beaten out of his crosse in a contrary direction, and the struggle may have to be renewed as from the beginning.

As played by the Indians, who adopt a light and picturesque costume for the purpose, the game, as we have said, is highly interesting to the spectator. Their skill in the finer points of the game is admirable. A player, running at full speed, will frequently catch up the ball on the end of his crosse, drop it to the ground to baffle a pursuer, dextrously catch it again, and repeat this until he has either passed it on to one of his own side who is nearer the adversary's goal, or carried it well forward himself. For, contrary to the rule in football, in this game the player is allowed to do all he can to pass the ball on to another competitor on the same side who may place himself in a more favourable position.

The following are the rules to be observed in playing the

game:

The ball must not be caught, thrown, or picked up with the hand, except to take it out of a hole in the grass, to keep it out of goal, or to protect the face.

The players are not allowed to hold each other, nor to grasp an opponent's crosse, neither may they deliberately trip or strike each other.

If the ball be accidentally put through a goal by one of the players defending it, the game is won by the side attacking that goal.

If the ball be put through a goal by one not actually a player, it does not count for or against either side. A match is decided by winning three games out of five, unless otherwise specially agreed upon.

We give an illustration of the play, and believe the instructions herein contained will be sufficient to enable any party of players who may not have seen the game to commence it for themselves. It has all the elements of popularity, especially as a winter amusement, and possesses many of the advantages of other games, without that element of danger which is found, for instance, in football and hockey. An accidental blow from the light stick with which the crosse is fashioned could cause no serious hurt, and beyond this, or the chance of an occasional fall, there is nothing to cause incidental injury to the players.

We conclude our notice of the game with an anecdote, from which it will be seen that it once was on the point of endangering the English rule in Canada. About the middle of the last century, after the conquest by Wolfe, the Indian chief Pontiac planned an attack on some of the principal forts, which was to be carried out by stratagem through the medium of "la crosse." The known skill of the Indians in the game frequently induced the officers of the garrison to invite them to play when they were in the locality, and occasionally some hundreds were engaged. Pontiac designed, on one of these occasions, that the ball should be struck, as if accidentally, into the forts, and that a few of the Indian party should enter after it. This was to be repeated two or three times, until suspicion was lulled, when they were to strike it over again, and rush in large numbers in pursuit. They were then to fall upon the garrison with concealed weapons. This ruse was carried into effect, and partially succeeded; but the Indians failed to enter the strongest of the fortifications, and were beaten back with much slaughter. Pontiac afterwards made friends with the English, but he was a treacherous ally, and it was a subject of congratulation when he was at last killed by one of his own race.

MECHANICS.-I.

FORCE: ITS DIRECTION, MAGNITUDE, AND APPLICATION. THE aim of these Lessons is to make evident to ordinary intelligent persons, who will take a little trouble, the principles of Mechanics-to treat that subject in a popular way, yet so that the reader may form accurate notions about it, and be enabled to apply it to practice in solving common problems by calculation. We have much to do, but all depends on the way of doing it. The reader I desire to have is the intelligent mechanic or artisan, the country schoolmaster or pupil-teacher, the young student who wants to learn the science through a book without a master, the college B.A. or M.A. whose mechanics was made a mess of in his young days, and would be glad, without again going to a "coach," even late in life to learn it. I should not despair of finding even ladies among my scholars. More faith should be placed in the average human intellect than commonly is. It ought to be possible to teach the sciences of form, and number, and force to more persons than usually learn them. These are the "common things" of life, and a knowledge of the laws which regulate them ought to be within the reach of most people, if only the first principles be properly laid down and explained, consequences deduced from them in a simple and natural order, and language used which they can understand. I ask you, then, to approach the subject without fear. Study simultaneously with these lessons those upon Arithmetic; for, as we proceed, a knowledge of the four Common Rules of Arithmetic and of Proportion will be found essential. Any other mathematics you may require, I shall teach you as we go along, but the amount will be small. Observe: accurate mechanical conceptions, and the power of solving mechanical problems by construction by rule and compass or calculation, are the objects we aim at. First, then, let us ascertain what our science treats of. I believe it may accurately be described as follows:MECHANICS is the science of force applied to a material body or bodies.

move towards the magnet, and stick to it, in the very same way that the stone moves to, and sticks to, the earth until some person pulls it away by a stronger force. And so likewise does the electrified ball draw towards itself the small pieces of cork or feather we place near it. In all these cases, you see, there is, first, a body, the ball, or bolt, or stone, or iron-filing, or cork; secondly, a force applied to it; and, thirdly, motion produced. But take now the lamp which hangs from the ceiling. It is at rest; but the earth, by its attraction, is trying to pull it down, and down it would come were we to cut the chain or rod by which it is suspended. Here, then, is force again, but it produces only tendency to motion. But observe further, that although the lamp does not move, the chain that holds it is strained by its weight. And not only is the chain strained, but so is the ceiling joist to which it is attached; and, as this joist rests its ends on the walls, this strain is transmitted to the walls in the form of pressures on them. There is thus tendency to motion, strain, and pressure produced as the effect of the force applied by the earth to the lamp, but no motion. And, if any of you feel a difficulty in believing in those strains, let him suppose, instead of the lamp, a ton weight of iron suspended from the ceiling: what will follow? The chain will snap, or the joist, or even ceiling, will give way, and down all will come on the floor. They snap or give way because they are strained beyond their strength. So, in like manner, when a train stands at rest on one of those great iron girder bridges that span our rivers, there is tendency to motion, with strains and pressures; the great Earth below pulls at the train to bring it into the water; but the bridge resists, bears the pressure of the weight on it,

and is strained throughout its length besides. A more familiar instance is the struggle of two wrestlers. No one will doubt that in the contest great force is put forth by each. For a moment they are motionless, like statues; the forces are balanced, but the strain on their muscles is terrific. There is in each tendency to motion, caused by the force put forth by the other, but as yet no motion. At last one of the combatants prevails; his force ends in producing motion, and his adversary falls to the ground.

This let me fully explain. Mechanics is concerned about force -that is its great subject. But it considers it only in the consequences which follow its application to a body or bodies which must be material. A force may push through an empty point of space; but, as it can make no impression on that point, Mechanics does not consider it under such circumstances. The body to which it is applied may be of any size, even an atom of matter, sometimes termed "a material point;" and Mechanics does inquire what effect forces have on such atoms. But, in the more common problems, it is concerned about bodies of visible and tangible magnitude, such as a block of stone, a beam of timber, a girder of iron, a cannon ball, the earth itself, the moon, or the sun.

This being clearly understood and agreed on, our next question is, What is force? I answer

FORCE is the power, or agent, whatever be its nature, by which motion is produced in a body, or a tendency to motion accompanied by strains or pressures in its parts.

For instance, a blow is given by the bat to the cricket ball, or a bolt is fired from a cannon: the blow in the one case, and the exploding gunpowder in the other, furnish forces, the effect of which is the motion of the ball or bolt. Steam enters the cylinder of an engine, and away to work goes the machinery connected with it, moving and printing this POPULAR EDUCATOR. Here again is force, the elasticity of the steam, and its effect is motion. A stone is let loose at the top of a tower, or from a balloon, and it falls to the ground: what makes it fall? The great Earth does, which, by its attraction, pulls the stone towards itself. This attraction is the force producing the stone's motion. And if any of you doubt, or feel any difficulty about this, let him take a magnet and put one of its ends near a few loose iron-filings, scattered over a piece of paper, and he will see how this is possible. The filings will

These examples will, I trust, be sufficient to make clear to you the account I have given you of force, namely-that it is the agency by which motion is produced in a material body, or a tendency to motion with pressures or strains. You will now understand the reason why Mechanics is divided into two branches, Statics and Dynamics. Statics is the branch which treats of forces which balance each other, and produce only tendencies to motion with pressures and strains, and is so called from the Latin word sto, which means "to stand," or "be at rest." Forces which thus balance one another are said to be in equili brio, a Latin expression which denotes the balancing of equal weights; and it is important that you should keep the expression in memory, as we shall have frequent occasion to use it. The other branch, Dynamics, treats of force or forces which do not balance.one another, but produce motion, and was so named from the Greek word duvauis (du'-na-mis), power, under the mistaken notion that there was more power in force when its effect is motion, than when it produces strain. This, we have seen, is not the case; but the term "Dynamics" may, notwithstanding, continue to be used without leading to error. The two branches we may therefore define or describe as follows:

:1

STATICS is the branch of Mechanics in which forces are considered which equilibrate, or balance one another, producing tendencies to motion, with strains and pressures.

DYNAMICS is the branch of Mechanics in which forces are considered which produce motion.

Now it so happens that, of these branches, Statics is the simpler and easier, and more natural for the student to commence with. Questions about forces which balance each other are not so complicated as those which involve motion. The reason is, that time enters into all problems of motion, but

not generally into those of equilibrium. The speed or velocity of a cannon-ball must be considered at every varying moment of its flight; but the strains and pressures among and on the beams of the roof of a railway station are the same at all moments. Time does not affect the latter unless by wear and tear. With statics, therefore, we commence, and, of course, with the simplest class of questions, those which relate to a force or forces acting on a single point. But here I must turn back to the notion of force, and endeavour to fix it with greater accuracy in your minds. I must show you how it is said to be applied and measured to the body it moves or strains; and this will best be done under the three following heads :1. The Direction of a Force.

2. The Point of Application of a Force. 3. The Magnitude of a Force.

1. The Direction of a Force.-In Mechanics, forces are assumed to act in right lines. The assumption is made for the best of reasons—namely, that of experience. All the simpler cases of motion confirm it, and all the more complicated can be accounted for by it. A ball falls to the ground in a right linethat which points to the centre of the earth, whence the force of attraction which moves it acts. The billiard-ball moves in a right line; and the calculations of the skilful player, which are based on the supposition that it so moves, are never found to be wrong. A ship, with her sails square set and wind aft, moves in a right line; and to make it leave that line the steersman must put the helm to port or starboard, and by turning the face of the rudder against the water, cause another force to be applied to the ship across the line of its course, and at her stern, turning her round. It is true that the stone thrown obliquely into the air moves in a curved path; but in this case we know that there are two forces-not one only-acting on it, namely, the original impulse, which makes it move in a right line, and the earth's attraction, which pulls it from that line into a curved course. Moreover, all the calculations on which are based the predictions of astronomers as to the places in which the sun, moon, and planets will be on a certain day, hour, and minute, are based on this assumption, that forces act in right lines; and the predictions invariably prove true. Our first mechanical axiom may, therefore, on the ground of experience be assumed to be true-namely, that the direction in which a force acts is that of a right line. Indeed, it is not easy to conceive how it could act otherwise.

2. The Point of Application of a Force.-The direction of a force being disposed of, we must fix our ideas as to its point of application. The rule is, that any point on the line of its direction may be considered such; but this you must understand with a limitation, or exception, which should not be forgotten. The point of application can only be on so much of the line of direction as lies within the body. For instance, suppose a person to push with an iron rod, which he holds in his hand, at the point A (as in the diagram), against a block of iron which lies on a table. Then, clearly a is the point of application of the force with which he pushes. Let now a hole be drilled through the block in the direction of the push from A to E, into which the rod may fit closely but freely; and also other holes, downwards, b B, c c, d D, to meet the passage, A E, into which thumbscrews, b, c, d, are fitted. Let the rod now be passed through the block so as to emerge at the other side, and clamp it down firmly by the thumb-screw, b. If it be now pushed against the block with the same force as before, it is clear that the force will be arrested by the thumb-screw, b, at B, and that B will become its point of application to the body. So, in like manner, may it be applied to C and D, by tightening in succession each screw, while the others are left loose. In all these cases the force is the same, and the direction the same; but the points of application are different. But will the effects in the several cases be different? No; for the portion of the rod within the block, and extending from A to any of the points of application, performs the same part in transmitting the force from A to the point within, as the iron which was removed did when the force was first applied directly at A. The removed iron has its place filled by an equivalent of that metal in rod, and the body is virtually in its original condition. The force of the hand may still be considered applied at A, thence to be transmitted to B, or C, or D, as we please, by the portion of rod within. The second case becomes identical with the first, and the effects, therefore, must be identical in every respect; and, nothing

being changed, intensity, direction, nor effect of the force, it is clearly indifferent which point we make the point of application. Another instance is the raising of a weight by a rope. Weight and rope together make one body; and whether the lifting power be applied by engine, by horse, or by man, whether it acts over a pulley or not, every point of the strained rope may be considered a point of application. Or let the case be that of three strings attached to a ring, and pulled in different directions by three persons. It makes no difference, in this compound body of ring and strings, whether the hold taken of the latter be long or short-all their points are points of application of their respective forces.

We thus see that, in all cases, we may assume that the point of application of a force is any point on so much of its line of direction as lies within the body. To suppose it applied to a point outside would be absurd; for, as we have shown, though a force may act or push through a point of empty space, it can make no impression on that point, either in the way of strain or motion, and therefore cannot come under the consideration of Mechanics.

3. The Magnitude of a Force.-To find a suitable measure of the intensity or magnitude of a force, we must also look to experience. It would be very convenient to measure forces by comparing them with weights; but this is not always practicable, and, even if it were, it would not answer all the purposes of Mechanics. I may as well, therefore, explain to you the perfect method, as that is as simple as any other. Experi ence teaches that a double force produces a double velocity, a treble force a treble velocity, and so on, in any body to which it is applied. But then a difficulty occurs: the same force will produce different velocities in bodies of different sizes. If it make a ball of one pound weight move at a certain rate, it will give double that speed to a half-pound ball, and half to one of two pounds. As a general rule, the greater the mass of the body, the less the speed produced. Everybody is familiar with this fact. We see, then, that if we desire to measure forces by the velocities they produce, we must try them on bodies of some fixed weight or mass. Tried on this particular mass, experience teaches that that which produces the greater velocity is the greater force. Now, the mass of matter which mechanicians choose for this purpose is that of any substance which is equal in weight to a cubic inch of distilled water. That much matter is designated the Unit of Mass, and for a reason I shall hereafter more fully explain. Imagine, then, a round ball, say of ivory, whose weight is that of a cubic inch of pure water, and suppose that several forces are in succession applied to it; the velocities they produce will be accurate measures of their intensities, or of their magnitudes.

But, then, how are the velocities to be ascertained? Clearly by the spaces the ball would move over in any given time, say the unit of time-a second-on the force being applied to it. Suppose, then, the unit ivory ball, put on a perfectly smooth floor, and then suddenly struck by a blow equal to the force you want to measure. By some means-and there are many which may be devised-manage to ascertain the distance the ball moves over in one second. That space, or length of line, will be the measure of the force; and if any number of such forces be tried in the same way and on the same ball, that which causes it to move over the greater space is the greater force, over a double space a double force, and so on.

The final result, then, is that, in considering a force in Mechanics, we must first suppose drawn within the body a line representing its direction. Then, on that line, let any point be taken for its point of application. Thirdly, on the line of direction so fixed, let as many inches be measured from the point of application as, on any scale you agree to use, represents the space the force would cause the unit ivory ball to move over in one second. Then you have a line which also in magnitude represents the force. Or in fewer words—

A FORCE is represented, both in magnitude and in direction, by a finite right line passing through its point of appli cation.

If in the above explanations I have succeeded in giving you clear notions of the aim of Mechanics, and of the nature and effects of force, you are prepared for the consideration of a force, or forces, applied to a single point, which will be the subject of our next Lesson.