LESSONS IN ARITHMETIC.-I.

THE term Arithmetic, which is derived from the Greek verb pipe (pronounced a-rith'-me-o), to count, is properly applied to the science of Numbers, and the art of performing calculations by them, and investigating their relations. To a certain extent, this science must have been coeval with the history of man. As an art, arithmetic is indispensable in daily business; and the man who is best acquainted with its practical details has always the preference in every mercantile establishment. Our object in these lessons shall be twofold-to develop its principles as a science, and to show the application of its rules as an art. For this purpose, it will be necessary to begin with the first principles of Numeration and Notation, and to give such rules as will enable any one to read and write a given number correctly.

NOTATION AND NUMERATION.

1. Any single thing-as for instance, a pen, a sheep, a house -is called a unit: we say there is one such thing. If another single thing of the same kind be put with it, there are said to be two such things; if another, three; if another, four; if another, five; and so on.

Each of these collections of things of which we have spoken is a number of things; and the terms one, two, three, four, five, etc., by which we express how many single things or units are under consideration, are the names of numbers. A number therefore is a collection of units. This is also sometimes called an integer, or whole number.

It will be seen that the idea of number is quite independent of the particular kind of units, a collection of which is counted. Thus, if there are four pigs, the number of pigs is the same as if there were four pens. We can thus abstract a number from any particular unit or thing, and talk of the number four, the number five, etc. Numbers thus abstracted from their reference to any particular unit or thing are called abstract numbers. When a collection of things or objects is indicated, it is called a concrete number.

We shall treat first of abstract numbers.

2. The art of expressing numbers by symbols, or figures, is called Notation.

In the system of notation which we are about to explain, all numbers can be expressed by means of ten symbols (figures, or digits, as they are called), representing respectively the first nine numbers, and nothing, i.e., the absence of number., These

O called a nought, a cipher, or zero. N.B.-Ten times ten is called one hundred; ten times a hundred, a thousand.

3. Numbers are represented by giving to the figures employed what is called a local value-i.e., a value depending upon the positions in which they are placed.

Let a number of columns be drawn as below, that being called

Thus 794|3| would denote seven thousands, nine hundreds, four tens, and three ones; or, as it would be expressed, seven thousand, nine hundred, and forty-three.

Similarly, 8|3|0|5|4|7|would denote eight times a hundred thousand, three times ten thousand, no thousands, five hundreds, four tens, and seven ones; or, as it would be more briefly expressed, eight hundred and thirty thousand, five hundred and forty-seven.

We need not, however, draw the columns: it will be the same thing if we imagine them, and, instead of columns, talk of figures being in the first, second, third, fourth places, etc. The symbol 0 put in any place, as already indicated in the previous example, denotes that the number corresponding to the particular column or place in which it stands is not to be taken at all: the 0 only fills up the place-thus, however, answering the important purpose of increasing the figure after which it stands tenfold.

Thus, 10 means that once ten and no units are taken-i.e., it denotes the number ten; 100 means that once a hundred but no tens and no units are taken-i.e., it denotes the number a and one unit, are taken, or, as it would be more briefly exhundred; 5001 means that five thousands, no hundreds, no tens, pressed, five thousand and one.

4. Before proceeding further, we will give the names of the successive numbers :

The numbers between twenty and thirty are expressed thus. twenty-one, twenty-two, twenty-three, etc., up to twenty-nine, to which succeeds thirty; and similarly between any other two of the names above given, from twenty up to a hundred: thus, 95 is called ninety-five.

After one hundred, numbers are denoted in words, by mentioning the separate numbers of units, tens, hundreds, thousands, etc., of which they are made up. For example, 134 is one hundred and thirty-four; 5,342 is five thousand three hundred and forty-two; 92,547 is ninety-two thousand five hundred and forty-seven; 84,319,652 is eighty-four millions, three hundred and nineteen thousand, six hundred and fifty-two.

5. It is useful, in reading off into words a number expressed in figures, to divide the figures into periods of three, commencing on the right, as the following example will indicate:

Billions. Thousands of Millions. Millions. Thousands. Units. 561 234 826 479

365

Hundreds of Thousands.

If a figure-5, for instance-be placed in the first column, it denotes five units, or the number five; if it be placed in the second column, it denotes five tens; if in the third, five hundreds; if in the fourth, five thousands; if in the fifth, five times ten thousand; and so on, each column corresponding to a number ten times as great as the one immediately on its right.

Digita. So called from digitus, a "finger." This decimal notation clearly took its origin from these natural counting instruments.

and sixty-one billions, two hundred and thirty-four thousand eight hundred and twenty-six millions, four hundred and seventynine thousand, three hundred and sixty-five.

We have then the following

Rule for reading numbers which are expressed in figures :Divide them into periods of three figures each, beginning at the right hand; then, commencing at the left hand, read the figures of each period in the same manner as those of the right. hand period are read, and at the end of each period pronounce its name.

The art of indicating by words numbers expressed by figures is called Numeration.

EXERCISE 1.

Write down in figures the numbers named in the following exercises :

In the foreign system of numeration a thousand millions is called a billion, a thousand billions a trillion, and so on.

1. Thirty-four.

2. Four hundred and seven. 3. Two thousand one hundred and nine.

4. Twenty thousand and fifty

seven.

5. Fifty-five thousand and three. 6. One hundred and five thousand and ten. 7. Seven hundred and ten thousand three hundred and one.

8. Two

millions, sixty-three thousand and eight. 9. Eleven thousand eleven hun

dred and eleven.

10. Fourteen millions and fifty11. Four hundred and forty mil.

six.

lions and seventy-two. 12. Six billions, six millions, six

thousand and six. 13. Ninety-six trillions, seven hundred billions and one.

EXERCISE 2.

exercises :

15. 400031256 16. 967058713

17. 20830720000 18. 8503467039

19. 450670412468

20. 58967324104325

LESSONS IN LATIN.-I.

INTRODUCTION.

IN giving to the readers of the POPULAR EDUCATOR lessons which may enable them to learn the Latin language, with no other resources than such as may be supplied by their own care and diligence, we take it for granted that they are desirous of acquiring the necessary skill, and willing to bestow the necessary labour. If the study were not recommended as a good mental discipline; if it were not recommended as giving a key to some of the finest treasures of literature; if it were not recommended as a means of leading us into communion with such minds as those of Cicero, Virgil, Horace, Livy, and Tacitus, it would have a sufficient claim on our attention, as greatly conducing to a full and accurate acquaintance with our mother-tongue-the English. The English language is, for the most part, made up of two elements-the Saxon element and the Latin element. Without a knowledge of both these elements, we cannot be said to know English. If we are familiar with both these elements, we possess means of knowing and writing English, superior to the means which are possessed by many who have received what is called a classical education, and have spent years in learned universities. In order to be in possession of both these elements, we should, for the Saxon element, study German; for the Latin element, the lessons which ensue will suffice.

In the instructions which we are to give, we shall suppose ourselves addressing a reader who, besides some general acquaintance with his mother tongue, has acquired from the English lessons in the POPULAR EDUCATOR, or from some other source, a knowledge of the ordinary terms of English grammar, such as singular, plural, noun, adjective, verb, adverb, etc. The meaning of such words we shall not explain. But everything peculiar as between the English and the Latin shall be explained, as well as any grammatical term which, though used sometimes in English grammar, the reader possibly may not understand. In these explanations we think it safer to err on the side of superfluity rather than on the side of deficiency. We have said that we shall suppose the reader to possess a general acquaintance with the English language. But it is well to suspect oneself as being probably acquainted with it but in an imperfect manner. And this advice is given in the hope that it may lead to the constant use of a good English dictionary. In every case in which there is the least doubt whether or not the exact meaning of any word used is known, the word should be looked out in a dictionary, and put down in a note-book to be kept for the purpose, with the meaning added. When there are, say, a score of words thus entered in the note-book, they must be looked at again and again until their signification is impressed on the memory. If the reader listens to this sugges. tion, and continues to make progress, he will soon find numerous exemplifications of the assertion above made-namely, that a large proportion of the words of the English language are of Latin origin. Take, for instance, the last sentence. In that sentence alone the following words are derived from the

PRONUNCIATION OF LATIN.

We may practically regard the Latin alphabet as the same as the English; and in the pronunciation, too, we may in the main follow the best English usage, remembering always that every vowel is pronounced in Latin, and that some words which in English would be words of one syllable, are words of two syllables in Latin, owing to the distinct pronunciation of every vowel. Thus the word mare in English, the feminine of horse, is pronounced ma-re in Latin, just as we pronounce the English name Mary, and means the sea. The Latin language, in short, has no silent e as we have in English.

Every modern nation pronounces the Latin as it pronounces its own tongue. Thus there are divers methods of pronunciation. This diversity would be inconvenient if the Latin were, like the French, a general medium of verbal intercourse. At one time it was so, and then there prevailed one recognised manner of pronunciation. Now, however, for the most part, Latin is read, not spoken. Consequently the pronunciation is not a matter of consequence. Even in our own country there are diversities, but such diversities are secondary matters. To one or two remarks, however, we should carefully attend. In Latin the vowels are what is called long or short. In other words, on some the accent or stress of the voice is thrown, on others it is not thrown. The vowel a, for instance, is mostly long; the vowel i is mostly short. A long vowel is said to be equal to two short vowels. We English people, however, have no other way of marking a long vowel, except by throwing on it the accent or stress of the voice. It is also a fact that in Latin the same vowel is sometimes short and sometimes long-in other words, the same vowel sometimes has, and sometimes has not, the accent on it: thus the i in dominus, a lord, is without the accent, while the i in doctrina, learning, has the accent: the former, therefore, is pronounced thus, dóm-i-nus; the latter thus, doc-trí-na. Now observe that these words are trisyllables, or words of three syllables. Of these three syllables the lastnamely, us-is called the ultimate; the second, in, is called the penult; the first, or dom, is called the antepenult. And the general rule for pronouncing Latin words is, that the accent is thrown on the penult, or if not on the penult, then on the antepenult. In doctrína the accent is on the penult, or last syllable but one. In dóminus, the accent is on the antepenult, or last syllable but two. In order to indicate where to lay the stress of the voice, we shall mark, as in dóminus and doctrína, on which syllable the accent lies. It will then be understood that when we put a mark thus over a vowel, we mean thereby that the voice should rest, as it were, on that vowel. For example, in the word incur, the accent falls on the last syllable, for the stress of the voice is thrown on the syllable cur. This is indicated thus, incúr. So in the Latin amicus, a friend, the accent is on the i, and the word is to be pronounced

thus, amícus, 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 deetrína, 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.

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 oase, 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" Æneid." 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 townHis 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. În 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 e 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 on its introduction into this country a few years ago attracted special attention

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 a party of 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. Across 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:-1. 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 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, it is the game for 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 crosse, 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

VOL. I.

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 equilibrio, 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:

:

STATICS is the branch of Mechanics in which forces aro 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

2