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A little consideration will show the truth of this method.

OUR HOLIDAY.—IV.

An analogous method can be applied to multiplication by WE leave for the present the subject of gymnastics, which has

more than two figures, but it is liable to cause confusion.

EXERCISE 16.

1. Work the following examples in multiplication by the above method :

1. 3251 × 29.

4. 38256 × 86.

2. 25039 x 62.

7. 7504 × 78.
8. 70267 x 89.

3. 4275 x 93.

5. 4028 x 37.
6. 50389 × 59.

14. Multiplication in two lines by a number of four figures.
A multiplication by four figures can often conveniently be

effected in two lines as follows:

Multiply in one line by the figures in the units' and tens' places, as in Art. 13, and then again in one line by those in the Lundreds' and thousands' places, placing the second line under the first two places to the left.

EXAMPLE.-Multiply 3456 by 2342.

3456

2342

145152 (

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3456 × 42)

79188 ( = 3456 × 23, or by 2300, if the
ciphers were included.)

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EXERCISE 17.

been the topic of our last two papers, and turn for our recreation to a highly popular game at this season of the year, viz.,

FOOTBALL.

Football is one of the oldest of our English sports, having been played all over the country for some hundreds of years. The rough methods in vogue of playing the game brought it under the censure of one of our monarchs, King James I., but it survived his displeasure, and its popularity, if possible, increased. Towns and villages were pitted against each other -not, as in the case of cricket, through the medium of a few individuals chosen to represent them, but by the aid of nearly all their able-bodied representatives. For football is a game in which a large number of persons can join, and, where space was unlimited, an unlimited number could play. One or two vestiges of the ancient game still linger in Old England, where, on a certain day of the year, the more active members of the population turn out in a body, and play at football in the olden style. But this custom is now considered "more honoured in the breach than the observance," and football occupies a similar position to other games as a holiday recreation.

Many modes of playing football are in use, especially in our chief public schools, each of which has its own cherished rules and practices differing from the rest. The Eton game differs

1. Work the following examples in multiplication by the from that played at Harrow, and both from the famous game of

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Rugby. Winchester, Marlborough, and Shrewsbury, too, have their peculiar styles, and what is allowed in some is strictly forbidden in others. This variation in practice has been a disadvantage to the game, and several attempts have been made to bring about uniformity. In the case of the chief schools we have mentioned, little progress towards it has yet been effected; but something has been done by an association of football clubs in various parts of the kingdom, which have adopted a set of rules for their guidance. These rules are a digest of all other codes in use, and to these we shall presently refer.

In all football play, whatever the difference of the practice in particular points of the game, the object sought to be gained by the rival players is the same, namely, to drive the ball to the base or goal of their opponents. This will be best understood by a diagram of the ground, which in length should be from 50 yards upwards:

Touch.

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Here the lines drawn on each side represent the boundary within which the game is played. These lines are usually marked out by flags, and the space beyond them is technically known as touch. The two dots towards either end show the position of two posts, which constitute the goal of one of the two parties, say A or B, into which the players are divided. The play begins in the centre of the ground, and the object of each party is to kick the ball through the goal posts of their opponents. On attaining this, the game is won for the side that accomplishes it. It may be renewed again, the parties then changing goals, in order that each in turn may have any advantage arising from fall of ground, direction of wind, etc.; and at the termination of the play each side counts so many games as goals may have been secured by its players. Each side usually has its captain, and its goal-keeper, whose especial duty it is to guard the goal, as far as may lie in his power, when the ball is driven towards it.

The balls are usually made of ox-bladders covered with leather, but india-rubber is sometimes employed for the lining. A good ball for the game may be obtained at from 8s. to 12s. The rules which we subjoin will be sufficient explanation of the precise mode of commencing and continuing the play. But

1. Work the following examples in multiplication by the we may remark with regard to all rules, that the more nearly

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the practice of the players is confined to the impelling of the ball by kicks alone, and the more closely the kicks are confined to the ball, and not distributed among the players, the more perfect is the game itself, and the more likely to retain and increase its popularity. It is the barbarous custom (we can use no other term), in some celebrated modes of play, to allow the practice of hacking, or kicking freely at the shins or legs of an opponent, in certain positions of the game, in order to disable him from carrying on the ball. From this custom serious consequences have occasionally resulted. Accidents will occasionally happen, from the nature of the game, under any circumstances; and that it requires courage to make an efficient player, and a disregard of the chance of a little danger, will not be considered a drawback by high-spirited youths who engage in it. But there is no occasion to add to the probability of personal injury by rules and practices which seem to invite it. The following are the laws of the game, as determined in February, 1867, by a general meeting of representatives of clubs forming the Football Association. These laws, however, it is understood, are subject to such modifications as future experience may suggest :

1. The maximum length of ground shall be 200 yards, the maximum breadth shall be 100 yards; the length and breadth shall be marked off with flags; and the goals shall be upright posts, eight yards apart, with a tape across them eight feet from the ground.

2. The winners of the toss shall have the choice of goals. The game shall be commenced by a place kick from the centre of the ground by the side losing the toss. The other side shall not approach within ten yards of the ball until it is kicked off. 3. After a goal is won, the losing side shall kick off, and goals shall be changed.

4. A goal shall be won when the ball passes between the goal posts, under the tape, not being thrown, knocked on, or carried.

5. When the ball is in touch, the first player who touches it shall throw it from the point on the boundary line where it left

the ground, in a direction at right angles with the boundary line, and it shall not be in play until it has touched the ground; and the player throwing it shall not play it until it has been played by another player.

6. When a player has kicked the ball, any one of the same side who is nearer to the opponent's goal line is out of play, and may not touch the ball himself, nor in any way whatever prevent any other player from doing so until the ball has been played, unless there are at least three of his opponents between him and their own goal; but no player is out of play when the ball is kicked from behind the goal line.

7. When the ball is kicked behind the goal line, it must bo kicked off by the side behind whose goal it went, within six yards from the limit of their goal. The side who thus kick the ball are entitled to a fair kick off in whatever way they please, without any obstruction, the opposite side not being able to approach within six yards of the ball.

8. No player shall carry or knock on the ball.

9. Neither tripping nor hacking shall be allowed, and no player shall use his hands to hold or push his adversary. 10. A player shall not throw the ball, or pass it to another. 11. No player shall take the ball from the ground with his hands while it is in play, under any pretence whatever. 12. No player shall wear projecting nails, iron plates, or gutta percha on the soles or heels of his boots.

The following is a definition of the terms used in the above rules:

A place kick is a kick at the ball while it is on the ground, in any position in which the kicker may choose to place it. Hacking is kicking an adversary intentionally. Tripping is throwing an adversary by the use of the legs. Knocking on is when a player strikes or propels the ball with his hands or arms.

Holding includes the obstruction of a player by the hand or any part of the arm below the elbow.

Touch is that part of the field, on either side of the ground, which is beyond the line of flags.

LESSONS IN GEOMETRY.-IV. INSTRUMENTS USED IN PRACTICAL GEOMETRY (continued). In addition to the mathematical instruments described in our last lesson, there is also an instrument called a Protractor, for measuring angles upon paper, which is represented in Fig. 14, and consists of a semicircle divided into degrees, from 0° to 180° each way, the 90th degree being right above the centre, o. The straight line, A B, in the figure is the diameter of the semicircle, and is called the fiducial (or true) edge of the protractor to be applied to one of the legs of the angle to be measured;

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the arch, A M B, being the fiducial edge to be applied to the other leg. Thus, in order to measure the angle x o Y, the centre of the instrument is placed on the vertex, o, of the angle, and the edge o A on the leg o Y, so as to coincide with it exactly; then the angle A O M, on the arch A M в, determined by the point м, through which the other leg, o x, passes, is the measure of the angle x o Y. In this case, the measure appears to be nearly 45 degrees, as the figure represents divisions on the arch or limb of the protractor at every five degrees.

This apparatus for measuring angles is sometimes engraven on the upper side of a pair of parallel rulers, and sometimes on the obverse side of a plane scale. The protractor is more commonly made so that the centre of the semicircle, and the fiducial edge containing it, shall be on the outside of the instrument rather than on the inside, as above.

The Plane Scale is a flat ruler with several lines of equal parts, on one side divided according to certain proportional parts of an inch; and having, on the other side, the diagonal scale, decimally divided so as to measure units, tens, and hundreds of equal parts, with a very considerable degree of exactness. The construction of this scale, so useful in graphical (ie., drawing) operations, such as the construction of plans, maps, and charts, architectural designs, plans and sections of machinery, etc., is founded on the properties of similar triangles, as treated in the sixth book of Euclid. We shall endeavour to give our readers a practical idea of its construction.

On a straight line, A E (Fig. 15), divided into any convenient Ag87054321

Fig. 15. number of equal parts, A B, B C, C D, D E, etc., one, A B, is assumed as the standard unit of measure. From the different points, A, B, C, D, E, etc., perpendiculars of a convenient length, as A A, BB, CC, DD, E E, etc., are drawn to the straight line A E, and terminated in the straight line A' E' parallel to A E. The unit A B is divided into 10 equal parts; then the opposite part, AB, is similarly divided; next the perpendicular B B' is divided into 10 equal parts, and through each division straight lines parallel to A E or A' E' are drawn. The divisions of the straight line A E are now marked with the numbers 1, 2, 3, etc.,

VOL. I.

from c to E, to denote units. The divisions of the standard unit A B are marked 1, 2, 3, 4, 5, 6, 7, 8, 9, from B to A, to denote tenth parts of a unit; and the divisions of the perpendicular B B' are marked 1, 2, 3, 4, 5, 6, 7, 8, 9, from в to B', to denote hundredth parts of a unit. Or, if the divisions of the straight line A E denote hundreds, those between B and A denote tens, and those between B and B' denote units. The scale is rendered complete by drawing straight lines from в on в A, to 1 on B' A'; from 1 on в A, to 2 on B'A'; from 2 on в A, to 3 on B' A'; and so on, till one be drawn from 9 on в A, to A' on B' A'.

By the nature of similar triangles, hereafter to be explained, the small part of the parallel to the base 1 B', within the triangle B 1 B', at the division marked 1, is one-tenth part of the base 1 B', and consequently one-hundredth part of the line A B; the small parts of the other parallels are in succession, twohundredths, three-hundredths, etc. Hence, if a straight line is to be measured, take its length in the compasses, and apply it to the scale from B towards E. If it measures an exact number of units, say from в to E, then the straight line may be said to measure 3, 30, or 300 equal parts, according as A B is made to stand for 1 unit, 1 ten, or 1 hundred. If it does not measure from E to B exactly, but extends from E exactly to one of the division marks between B and A, say 4, then the straight line may be said to measure 34, 34, or 340 equal parts, according to the standard unit, as before. If it does not extend from E to the division marked 4 between B and A exactly, but falls somewhere between 4 and 5, then move the compasses downwards, preserving one point always in the line E E', and both points parallel to A E, till the other point fall on the intersection of the diagonal marked 4, 4, with one of the parallel straight lines marked on B B', say 6; then the straight line may be said to

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Fig. 17.

A

Fig. 16. measure 3.46, 34.6, or 346 equal parts, according to the standard unit, as before.

For the purposes of navigation, dialling, etc., the plane scale has frequently on the side obverse to the diagonal scale just described, a set of lines, besides those of equal parts, containing divisions for the measurement of leagues, rhumbs, chords, sines, tangents, semi-tangents, secants, lines of longitude, etc. Such scales are considered the best, as they are generally executed with great care. The scale called Gunter's scale has the same divisions on one side of it, as are to be found on the plane scale, but of a larger size, and when well constructed, admitting of greater accuracy; but being usually made of boxwood, this is seldom the case. The obverse side of Gunter's scale has a set of lines representing the logarithms of the numbers which denote these divisions; by means of the logarithmic lines, arithmetical calculations can be performed instrumentally, that is, without the operation of the ordinary rules. A modification of this instrument, called the sliding Gunter, is still more ingenious in its construction, and still more useful as an instrument of calculation. The explanation of these instruments, however, belongs to a more advanced state of knowledge among the generality of our readers. This we hope to reach by their perseverance.

One of the most useful instruments in a mathematical case, is the sector; a mere sketch of its appearance is given in Fig. 16. It is composed of two flat rulers, movable on an axis, or jointed at one end like a pair of compasses; hence it is called by the French, compas de proportion-the compasses of proportion. From the centre of the axis or joint, several scales are drawn on the faces of the rulers, so as to correspond exactly with each other. The two rulers are called the legs of the sector, a represent the radii of a circle; and the middle point of joint, its centre. It contains a scale of inches, lines of eq

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Moyen should be pronounced as if printed thus, namely, moiien; divided thus, namely, moi-i-en, but pronounced in two syllables, Assing namely, moi-ien.

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A give one

rastration. A and O B

e divisions of d straight lines ortion. Suppose, raght line whose ne as 3 to 10. Open uts marked 10 on its en line, which may be

common compasses or

two points marked 3 on its ght line required.

sight lines are given, and it o each other in numbers. Open of the two points marked 10 on its .. of the greater of the two given the length of the smaller of the pair of compasses, apply this distance to any number less than 10 marked on its legs, that it coincides exactly with that of two says the same number, say 3; then the two given are to one another in the ratio of 10 to 3; or, in y words, the smaller is three-tenths of the greater. 410 Proportional Compasses, called by the French compas de the compasses of reduction are represented in Fig. 17, and consist of two legs A N, C M, intersecting (i.e., crossing) each other at any point within certain limits, according to the position of the button and screw, B, round which they are made These legs are graduated in such a manner that, by to turn. Borowing the button at the proper place, the distance from A to e may be at pleasure one-half, one-third, one-fourth, etc., of the distance from M to N. By this instrument, a straight line may be easily divided into any number of equal parts, or into any other proportional parts required.

The invention of this instrument is claimed, by a recent writer, for James Besson, a French mechanician, who published an account of it in his "Théâtre des Machines," a work of which the plates were engraved before 1569. He says it is usually attributed to Justus Byrgius, who published his description of it in 1603. John Robertson, librarian to the Royal Society, in his "Treatise on Mathematical Instruments," London, 1775, ascribes the invention of a similar instrument to Fabricius Mordente in 1554, according to a statement made by his brother, Gaspar Mordente, in his book on the Compasses, published at Antwerp in 1584.

LESSONS IN FRENCH.—VIII.
SECTION I.-FRENCH PRONUNCIATION (continued).

III. NAME AND SOUND OF THE VOWELS.

46. Y, y.-Name, EE, ee; sound, like the letters ee in the English word bee.

This letter is also a word; that is, it is one of the parts of speech in the French language. It is usually an adverb, meaning there. It is also used as a noun, and a pronoun.

When y stands alone, and thus becomes a word, its pronunciation is invariably like that of the letters ee in the English word bee, viz. :-Il y a, pronounced eel ee a. This last a must be sounded like a in the English word fat.

Y is also pronounced like the letters ce in the English word bee, when it begins or ends a word; and also when it occurs in the body of a word, after a consonant, namely:

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Joyeux should be pronounced as if printed thus, namely, joiieu; divided thus, namely, joi-i-eu, but pronounced in two syllables, namely, joi-ieu.

Royaume should be pronounced as if printed thus, namely, roiiaume; divided thus, namely, roi-i-aume, but pronounced in two syllables, namely, roi-iaume.

The pupil need not attempt to pronounce these three French words used as examples, because the combination of vowels and other letters occurring in them has not yet been illustrated.

The pronunciation of y with these and other combinations of letters will be explained in future lessons.

In the two following words the y, though not placed between two vowels, is under the same rule, namely:

:

Pays, meaning a country, should be pronounced as if printed paiis; divided thus, namely, pai-is, and pronounced pa-ee.

Paysage, meaning a landscape, should be pronounced as if printed paiisage; divided thus, namely, pai-i-sage, and pronounced pa-ee-zazh.

IV. NAME AND SOUND OF THE CONSONANTS.

distinct and independent sound, unless immediately followed by As a general rule, none of the consonants, when final, have a a word commencing with a vowel or h mute; in which case the consonant is joined with the following word in pronunciation. 47. B, b.-In any position within a word, this letter has the sound of the English letter b.

When doubled within a word, only one b is sounded, viz. :

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At the end of proper names, b is always sounded. In these two words, namely, a-plomb and plomb, the b is silent, and the next two preceding letters in each word, namely, om, take the nasal sound of on.

48. C, c.-This letter has two entirely distinct sounds, namely, hard and soft. Before the vowels a, o, u, and œ, and also before the consonants c, l, n, and r, it has the hard sound of the letter k in the English word kill, namely:FRENCH. PRONUN. ENGLISH, FRENCH PRONUN. ENGLISH, Calamité Ka-la-me-tay Calamity. Succès Suh-gai Success. Ko-me-tay Committee. Classe Klahss Class, Cube. Cnique Kneek Horse-thistle. Heart. Crédit Kray-de Credit.

Comité

Cube

Cour

Kube Kuh-rr

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In a few words, however, e final is not sounded, and these exceptions are best found out by consulting a French pronouncing dictionary. In a few words, c has the sound of the letter g in the English word go, namely, second, secondaire, secondairement, seconde, secondement, seconder, secondine.

In these words the c, which commences the second syllable, has the sound of the g, namely, second, as if printed segond; pronounced s'-gonh, etc. We do not illustrate all the sounds of these French words here, because of the nasal sounds contained

in them.

49. D, d.-This letter generally has the sound of the letter d in the English word deed. It is usually silent when final, except in proper names.

The principal exception to the above rule is, when d is final just before a vowel or an h mute. In such a case, the d has the sound of the letter t in the English word top; and in pronuncia

* See foot-note, page 19.

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Artère, f., artery.
Barbe, f., beard,

Bouche, f., mouth.

Bras, m., arm.

Cervelle, f., brain.

Chair, f., flesh.

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Lèvre, f., lip.

Membre, m., limb.

Menton, m., chin.
Moëlle, f., marrow.

Moustache, f., moustache.

Muscle, m., muscle,

Nerf, m., nerve,

Nez, m., nose.
Ongle, m., nail.
Orteil, m., toe.
Os, m., bone.

Palais, m., palace.
Paupière, f., eyelid.

Peau, f., skin.
Pouce, m., thumb.

Poumon, m., lungs.

Prunelle, f., pupil of the eye.

Rate, f., spleen.

Reins, m. pl., loins.

Sang, m., blood.

Sein, m., bosom.

Sourcils, m. pl., eyebrows.

Squelette, m., skeleton.
Talon, m., heel.

Teint, m., complexion.
Tempes, f. pl., temples.
Trait, m., feature.
Veine, f., vein.

Visage, m., face.

ETC.-MALADIES, INFIRMITIES, ETC.

Fièvre nerveuse, f., nervous fever.

Fièvre scarlatine, f., scarlet fever. Goutte, f., gout.

Guérison, f., cure.

Hydropisie, f., dropsy.

Indisposition, f., indisposition.
Louche, adj., squinting.
Malaise, m., indisposition.
Mutisme, m.,

dumbness.

Onguent, m., pommade, f., salve. Ordonnance, f., prescription. Petite-vérole, f., small-pox.

Pulmonie, f., consumption.

Remède, m., remedy.
Rhume, m., cold.
Rougeole, f., measles.

Surdité, f., deafness.

Toux, f., cough. Ulcère, m., ulcer.

Vertigo, m., dizziness.

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Diamant, m., diamond.
Dentelle, f., lace.
Doublure, f., lining.

Ecrin, m., casket, jewel-box.
Épée, f., sword.
Eperons, m. pl., spurs.
Epingle, f., pin.
Étui, m., needle-case.
Eventail, m., fan.

Fourrure, f., fur.
Frac, m., dress coat.
Frange, f., fringe.
Garniture, f., trimming.
Gilet, m., vest, waistcoat.
Grenat, m., garnet.
Guêtres, f. pl., gaiters.
Habit, m., coat.
Ivoire, f., ivory.

Flacon, m., smelling-bottle.

Linge, m.,

linen.

Lunettes, f. pl., spectacles.

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