bread that will rid me of this trouble ?" To Canterbury with their followers went four knights of Henry's court, and, acting entirely on their own responsibility, slew the archbishop on the steps of the altar. The outcry raised in England, where the archbishop was looked upon with favour, not only on account of his bold conduct in standing up for his order, but also because he was supposed to be the champion of the Anglo-Saxon against the Norman Englishman, was loud and sincere. Abroad, the feeling of grief was more than equalled by anger, and a sort of holy horror was felt at the bare notion of slaying an archbishop. King Henry, there is every reason to think, was genuinely sorry for the violence that had been done. Though his "guide and his companion, and his own familiar friend" had proved to be the sharpest thorn in his side, he remembered too well the former days to wish him any personal harm. Notwithstanding, on him was charged the whole guilt of the murder. Penance the most severe, disclaimers the most solemn, and ceremonies the most humiliating scarcely served to clear him. Purposely the Papal Court, which saw in Henry the strongest opponent of its pretensions, availed itself of the handle given to it, and strove to crush the king under a load of obloquy. To a very great extent it succeeded. Never again did Henry appear as the same strong champion of State rights as when he forced an assent to the Constitutions of Clarendon. The ghost of Thomas à Becket, now St. Thomas of Canterbury, haunted him, and the dead man's hand deprived the conqueror of his victory. The Constitutions of Clarendon were disregarded, the death of Becket making it impossible for the king to fly in the face of the papal veto upon them. Some little submission of the clerical to the kingly power was made, but the work marked out by Henry II., the entire subjection of the clergy to the head of the state, was left unaccomplished till the dawn of the Reformation in England, when it was renewed and carried out in the fullest possible manner by that "stately lord who broke the bonds of Rome," and who was saved by natural causes from committing, in the case of Cardinal Wolsey, the egregious blunder committed by the knights of Henry II. when they plunged their swords into the bosom of Thomas à Becket at Canterbury. 3. You must stop only as long as you can count one, two, three, four. 4. You must pronounce the word which is immediately before a period, with the falling inflection of the voice. 5. The falling inflection (or bending) of the voice is commonly marked by the grave accent, thus, `. Examples. Charles has bought a new hat. I have lost my gloves. Exercise and temperance strengthen the constitution. The fear of the Lord is the beginning of wisdom. ? 6. The note or mark of Interrogation is a round dot with a hook above it, which is always put at the end of a question. 7. In reading, when you come to a note of interrogation, you must stop as if you waited for an answer. 8. You must stop only as long as you do at the period. 9. You must in most cases pronounce the word which is placed immediately before a note of interrogation, with the rising inflection of the voice. 10. The rising inflection of the voice is commonly marked by the acute accent, thus, ́. Examples. Has Charles bought a new hát? Canst thou thunder with a voice like hím ? If his son ask bread, will he give him a stone? 11. In general, read declaratory sentences or statements with the falling inflection, and interrogative sentences or questions with the rising inflection of the voice. Examples. Interrogative. Has John arrived? Declaratory. John has arrived. Interrogative. Is your father well? My father is well. Hast thou appealed unto Caesar? 12. Sometimes the sentence which ends with a note of interrogation should be read with the falling inflection of the voice. Examples. What o'clock is it? How do you do to-dày? How much did he give for his book? How long, ye simple ones, will ye love simplicity ? Where wast thou, when I laid the foundations of the earth? Sometimes the first part of an interrogative sentence should be read with the rising inflection of the voice, and the last part with the falling inflection. These parts are generally separated by a Comma, thus,, 14. At the comma, the rising inflection is used, and at the note of interrogation the falling inflection. Examples. Shall I give you a péach, or an apple? Are you going home, or to school? Last Sabbath, did you go to chúrch, or did you stay at home? Whether is it easier to say, Thy sins are forgiven, or to say, Arise and walk ? Why did the heathen ráge, and the people imagine vain things? Is your father well, the old man of whom ye spȧke? 15. Sometimes the first part of an interrogative sentence must be read with the falling inflection of the voice, and the last part with the rising inflection. Examples. Where have you been to-day? At home? Who told you to return? Your father? What is that on the top of the house? A bird? What did you pay for that book ? Three shillings? Is not the life more than meat ? and the body than raiment ? What went ye out to see? A man clothed in soft raiment ? What went ye out to see? A prophet? How often shall my brother sin against me and I forgive him? Until seven times ? if. In the following exercises some of the sentences are Castions requiring the rising, and some the jaling mfection Of the VOICE. A few sentences also ending with a period are No directions are given to the pay with regard to La manner of reading them, it being desirable that is enz understanding, under the guidance of nature alone, shotää Lizert But it may be observed that questaans WIDDL C13T answered by yes or no, generally require the mang mberton of the voice; and that questions which cannot be answered by yrs or no, generally require the failing indecidah. EXELST 1 John, where have you been this morning Have you seen my father tondig & What excuse have you for coming has this sarung Zul you t know that it is past the school hom! If you are so inatteliv 12 your lessons, do you that that you will make much in prevement Will you go, or stay! WZ POL TIL or vult? Shall you go to dig, or to Did he resemble his father or las mother" Is this book yours or mine Eas, or hers Do you hold the watch toangit* Did you say that he was arme«! He was armeČ Art thon he that should come, or de we look for another? He wham hail the arm of the in this room? How neghrent some of our fellow-pupils are! Ah! I am afraid many will regret that they have not improved their time! Why, Lire comes Charles Ind you think that be would return en soca? I suspect that be has not bein plessed with his visit. Have you, Charles ? And were your fren is glad to see you? When 1 CUST2 June to be married? Wil she make us a visit before she is Or will she wait until she has changed her time? My dear Elward, bow happy I am to see you! I heard of your approaching happiness with the highest piessure How does Rose do? And how is our whimsien sûd friend the Baron? You must be patiat and answer my question. I have many inquiries to The first dawn of meing found Waverley on the esplanade in front of the old Gothar gate of the castle. But be paced it long before the invinige was lowered. He produced his crier to the sergeant of the guard, and was Limited The place of his friend's confinement was a gloomy apartment in the central part of the castle. Do you expect to be as hirt in your ches as your brother? Did you recite your lessons as well as he 513 Xo Lary boy! Carejess chod". You have been paying these two hours. You have paid Do attention to your lessons. You cannot say a word of them. How foolish you have been! What a waste of time and talents you have 9. As made is the intimation of two straight lines to each other, which meet in a poszt, and are not in the same direction. The point in which they meet is mũad the nema of the angle, and each of the two straight lines is called a prie or leg of the angle. The angle iseid is generally called a pirun rectilineal magle, because it necessarily bes in a puram, and is formed of straught MR. Curra, Latih zapirs are such as are formed on the suface of a sphere or globe: but the consideration of such angles belongs to the higher geometry. The magnitudes of angies de mot depend on the lengths of their legs or sides, but on the degree or amount of apertire between ★bem, taken at the shane distance from the TERSEL Az angie is generally represented by three letters, one of which is theng pabond at the perrea, we ästarush it particularly from every other angle in a pren frame, and the other two are placed somewhere ex the jars of the ancie, but generally at thver extremities and a redag er in speaking of the angle, the jetter at the vertex is always pinned between the other two, and atmered or women welacy Tras in Fig. 4, which ZUECOSERTS AZ angie de zame of the angle is either B A C or the Poczta is moed is verer, and the straight lines BACA subes de bees, 15 Angles are Aimbed onto twe kais, nýjir sad vrlique, and Surat angles are à mind az te spades, acute asi së ruse. When one strachi le mets antar at any point between ITS PITZVOLINs and mies the aqucnt de entrarns angies at mu to each other envà để them is met a run cape, and the Das a Fry 3 the start the AB meets the and makes the sijacent angles obtuse; and the angle D A B, which is less than a right angle, is called acute. 11. A plane figure, in geometry, is a portion of a plane surface, inclosed by one or more lines or boundaries. The sum of all the boundaries is called the perimeter of the figure, and the portion of surface contained within the perimeter is called its area. 12. A circle is a plane figure contained or bounded by a curved line, called the circumference or periphery, which is such that all straight lines drawn from a certain point within the figure to the circumference arc equal to each other. This point B æquus, equal, and latus, a side); isosceles (Greek, isos, equal, and skelos, a leg); and scalene (Greek, skalēnos, unequal), right-angled, obtuse-angled, and acute-angled. 19. An equilateral (equal-sided) triangle is that which has three equal sides (Fig. 8). 20. An isosceles (equal-legged) triangle is that which has only two equal sides (Fig. 9). 21. A scalene (unequal) triangle is that which has all its sides unequal (Fig. 10). 22. A right-angled triangle is that which has one of its angles a right angle (Fig. 11), in which the angle at A is the right is called the centre of the circle, and each of the straight lines is called a radius of the circle. The straight line drawn through the centre and terminated at both ends in the circumference, is called the diameter of the circle. It is plain, from the definition, that all the radii must be equal to each other, that all the diameters must be equal to each other, and that the diameter is always double the radius. In speaking or writing, the circle is usually denoted by three letters, placed at any distance from each other, around the circumference; thus, in Fig. 7, the circle is denoted by the letters A C B, or A E B; or by any three of the other letters on the circumference. The point o is the centre; each of the straight lines o A, O B, O C, O E, is a radius, and the straight line A B is a diameter. 13. An arc of a circle is any part of its circumference; the chord of an arc is the straight line which joins its extremities. 23. An obtuse-angled triangle is that which has one of its angles an obtuse angle (Fig. 10). 24. An acute-angled triangle is that which has all its angles acute; Figs. 8 and 9 are examples as to the angles, but there is no restriction as to the sides. In any triangle, a straight line drawn from the vertex of one of its angles perpendicular to the opposite side, or to that side produced (that is, extended beyond either of its extremities in a continued straight line), is called the perpendicular of the triangle; as in Fig. 12, where the dotted line A D is the perpendicular of the triangle A B C; and in Fig. 13, where the dotted line G H drawn from the point a to the dotted part of the base produced is the perpendicular of the triangle E F G. 25. A quadrilateral figure, or quadrangle, is a plane rectilineal 14. A segment of a circle is the surface inclosed by an arc and its chord. 15. A sector of a circle is the surface inclosed by an arc, and the two radii drawn from its extremities. Thus, in Fig. 7, the portion of the circumference A M C, ⚫ whose extremities are A and c, is an arc; and the remaining portion A B C, having the same extremities, is also an arc; the straight line A c is the chord of either of these arcs. The surface included between the arc A M C and its chord A C, is the segment A M C; there is also the segment A B C. The surface included between the radii o C, O B, and the arc C B, is called the sector C O B; the remaining portion of the circle is also a sector. 16. A semicircle is the segment whose chord is a diameter. Thus, in Fig. 7, A C B or A E B is a semicircle. The term semicircle, which literally means half a circle, is restricted in Fig. 17. Fig. 18. Fig. 19. figure contained by four straight lines, called its sides. The straight line which joins the vertices of any two of its opposite angles, is called its diagonal. Quadrangles are divided into various kinds, according to the relation of their sides and angles; as parallelograms, including the rectangle, the square, the rhombus, and the rhomboid; and trapeziums, including the trapezoid. 26. A parallelogram is a plane quadrilateral figure, whose opposite sides are parallel; thus, Fig. 14, A C B D, is a parallelogram, and A B, C D, are its diagonals. 27. A rectangle is a parallelogram, whose angles are right angles (Fig. 15). 28. A square is a rectangle, whose sides are all equal (Fig. 16). Fig. 13. Fig. 12, geometry to the segment thus described; but there are many other ways of obtaining half a circle. 17. Plane rectilineal figures are described under various heads; as trilateral or triangular; quadrilateral or quadrangular; and multilateral or polygonal. 18. A triangle (Figs. 8, 9, 10, and 11) is a plane rectilineal figure contained by three straight lines, which are called its sides. No figure can be formed of two straight lines; hence, an angle is not a figure, its legs being unlimited as to length. Triangles are divided into various kinds, according to the relation of their sides or of their angles: as equilateral (Latin, Fig. 20, 29. A rhomboid is a parallelogram, whose angles are oblique. The opposite angles of a rhomboid are equal to one another (Fig. 14). 30. A rhombus, or lozenge, is a rhomboid, whose sides are all equal (Fig. 17). 31. A trapezium is a plane quadrilateral figure, whose opposite sides are not parallel (Fig. 18). 32. A trapezoid is a plane quadrilateral figure, which has two of its sides parallel (Fig. 19). 33. A multilateral figure, or polygon, is a plane rectilineal figure, of any number of sides. The term is generally appli to any figure whose sides exceed four in number. Polygon divided into regular and irregular; the former having all their sides and angles equal to each other; and the latter having any variation whatever in these respects. The sum of all the sides of a polygon is called its perimeter, and when viewed in position its contour. Irregular polygons are also divided into conrer and non-convex; or, those whose angles are all salient, and those of which one or more are re-entrant. The irregular polygon (Fig. 20) has its angles at B, C, and D, salient; and its angles at A and E, re-entrant. 34. Polygons are also divided into classes, according to the number of their sides; as, the pentagon (Fig. 21), having fire sides; the hexagon (Fig. 22), having six sides; the heptagon having seven sides; the octagon having eight sides: and so on. According to this nomenclature, the triangle is called a trigon, and the quadrangle a tetragon. LESSONS IN ARITHMETIC.—IV. MULTIPLICATION. 1. THE repeated addition of a number or quantity to itself is called multiplication. Thus, the result of the number 5, for instance, added to itself 6 times, is said to be 5 mafisted by 6. 5 +5 +5 +5 +5 + 5 = 30, or 5 multiplied by 6 is 50. When the numbers to be multiplied are large, it is evident that the process of addition would be very laborions. The process of multiplication which we are going to explain is therefore, in reality, a short way of performing a series of stitions Letih then, be borne in mind, that multiplication is in fact ca addition. line and 6 in the left-hand Ene stand in lines which meet in a senare containing 24, which is therefore the product of 4 multiphed by 6. It may be observed that 6 in the top line and 4 in the lefthandle line stand in lines which meet in a square also containing 24. The reason of this is that when the product of two numbers is required, it is indifferent which we consider to be the per and which the multiplicand. Thus, 4 added to itself 6 times, is the same as 6 added to itself 4 times. The truth of this may be son, perhaps, more clearly as follows:If we make four vertical rows containing six dots each, as represented in the figure, it is quite evident that the whole number of dots is equal either to the number of dots in a vertical row 16. repeated 4 times, or to the number of dots in an horizontal row (4) repeated six times. And the same is clearly true of any other two numbers. Hence we talk of two numbers being multiplied together, it being indifferent which we consider to be the multiper and which the multiplicand. 4. If several numbers be multiplied together, the result is called the contined product of the numbers. Thus, 30 is the ccntioned product of 2, 3, and 5, because 2 x 3 x 5 = 30. N.B. On learning the multiplication table, let the following facts be noticed :— The product of any number multiplied by 10 is obtained by adding a cipher to the number. The first nine results of multiplying by 11 are found by merely The results of multiplying by 5 terminate alternately in 5 and 0. repeating the figure to be multiplied. Thus, 11 times 7 are 77. In the first ten results of multiplying by 9 the right hand figure regularly decreases, and the left hand figure increases by 1; also, the sum of the digits is 9. Thus, 9 times 2 are 18, 9 times 3 are 27. 2. Definitions.-The number to be repeat or mulighed is called the multiplicead. The number by which we multiply is called the multiplier: it, in fact, indicates how many times the multiplicand is to be repeated, or tiled to itself. The number 5. It is evident that (as 2 x 3 x 5 = 30, and 2 x 3 = 6, and produced by the operation is called the product. The 6 x 5 = 30 in multiplying any number, 5, for instance, by and multiplicand are also called the fort is of which the product another, 6, for instance, it will be the same thing if we multiply is composed, because they sicke the product. it successively by the factors of which the second is composed. Thus, since 5 multiplied by 6 is 30, 5 and 6 are called Thus, the product of any number multiplied by 28 might be got by multiplying it first by 7, and then multiplying the result by 4. factors of the number 50. The sign X placed between two numbers means that they are to be multipled together. 3. Before proceeding farther, the learner mot make himself familiar with the following tatue, which gives all products of two numbers up to 12 The product of any number multiplied by 10 is obtained by annexing a cipher to the number. The product of any number, therefore, multiplied by 100 will be obtained by adding two ciphers, because 10 x 10 = 100; first multiplying by 10 adds one cipher, and then multiplying the result by 10 adds another cipher. Similarly a number is multiplied by any multiplier which consists of figures followed by any number of ciphers, by first multiplying by the number which is expressed by the figures without the ciphers, and then annexing the ciphers to the result. Thus, 5 times 45 being 225, we know that 500 times 45 is 22500. 6. The process of multiplication which we now proceed to explain, depends upon the self-evident fact that if the separate numbers of which a number is made up be multiplied by any factor, and the separate products added together, the result is the same as that obtained by multiplying the number itself by that factor. Thus 5+4+2 11 7 x 5 = 35, 7 x 4 = 2,7 x 2 = 14. 7. We shall take two cases: first, that in which the multiplier consists only of one figure; and, secondly, when it is composed of any number of figures. Case 1.-Required to multiply 2341 by 6. 23112 thousands + 3 hundreds + 4 tens + 1 unit. Multiplying these parts separately by 6, we get 6 units, 24 tens, 18 hundreds, and 12 thousands, which, written in figures and placed in lines for addition, are 6 200 1800 19000 Giving as the result 14046 The process may be effected more shortly, as follows, in one line; the reason for the method will be sufficiently apparent from the preceding explanation: 14046 Writing the numbers as in the margin, proceed thus: 6 imes 1 unit are 6 units; write the 6 units under the figure multiplied. 6 times 4 tens are 24 tens; set 2341 multiplicand the 4 or right-hand figure under the figure 6 multiplier multiplied, and carry the 2 or left-hand figure to the next product, as in addition. 6 times 3 hundreds are 18 hundreds, and 2 to carry make 20 hundreds; set the 0 under the figure multiplied, and carry the 2 to the next product, as above. 6 times 2 thousands are 12 thousands, and 2 to carry make 14 thousands. There being no more figures to be multiplied, set down the 14 in full, as in addition. The required product is 14046. Before proceeding to the second case, the learner is requested to make himself familiar with the process of multiplying any number by one figure, by means of the following EXERCISE 6. (1.) Multiply 83 by 7; 549 by 5; 6879 by 9; 7891011 by 8; 567893459 by 3; 9057832917 by 11, and the result by 7. (2.) Find the continued product of 1, 2, 3, 4, 5, 6, 7, 8, 9. (3.) Find the products of the number 142857 by the nine digits. (4.) Find the products of the number 98998, the smallest number contained in the second square in Ex. 4, page 23, by the nine digits, and you will find these products in the same table. (5.) Multiply 857142 by 9; 76876898 by 2; 1010400600 by 7; 79806090 by 8; and 999999999999 by 5. (6.) Multiply the following numbers first by 2 and then by 3: (10.) I have a box divided into two parts; in each part there are three parcels; in each parcel there are four bags; in each bag there are five marbles. How many marbles are there in the box? (11.) There are six farmers, each of whom has a grazing farm of seven fields; each field has eight corners, and in each corner there are nine sheep. How many sheep do the farmers own, and how many are feeding on their farms? Case 2.-To multiply 675 by 337 : Since 337 is 300+30 +7, if we multiply 675 by 7, by 30, and by 300 successively, we shall obtain the required product. Arrange the work as in operation (1): placing the first figure of each line directly under the figure by which you multiply. Finally, adding these lines together, their sum will be the whole product of the two given numbers. 8. Method of testing the Correctness of the result.-Multiply the multiplier by the multiplicand, and if the product thus obtained be the same as the other product, the work may be presumed to be correct. (1.) 2221 (2.) 2221 9. Multiplication by reversing the Multiplier. It may be remarked that multiplication may be performed by commencing with the last figure (that is, the extreme left-hand figure) of the multiplier, instead of with that in the unit's place. In this case, however, as will be seen from an example, we must set down each line one figure to the right of the preceding line. Thus, in multiplying 2221 by 1234, we may proceed as follows, as in operation (1), figure of the multiplier; or beginning with the left-hand we might, to avoid confusion, operation (2), and proceed in reverse the multiplier, as in the same way. The ciphers which we omit in practice are added in the last operation, to explain the truth of the process. 1234 4321 2221 2221000 4442 444200 6663 66630 8884 8884 2740714 2740714 EXERCISE 7. (1.) Find the products of the following numbers : (2.) Multiply 2354 by 6789, and 23789 by 365, by reversing the multiplier. (3.) Multiply 857142 by 19, by 23, by 48, by 97, by 103, by 987, and by 4567. (4.) Find the products of the number 98998 by all the numbers from 11 to 49 inclusive. The answers will be found in the second square given in Ex. 4, page 23, on Addition. LESSONS IN BOTANY.-II. SECTION II.-ON THE SCIENTIFIC CLASSIFICATION OF THE observer who takes a survey of the various members of the vegetable world becomes cognisant of at least one prominent distinction between them. He soon perceives, that whilst certain vegetables have flowers others have not; or perhaps, more correctly speaking, if the second division really possess flowers, they are imperceptible. This distinction was first laid hold of as a basis of classification by the celebrated Linnæus, and to this extent the classification adopted by that great philosopher was strictly natural; beyond this, however, it was altogether artificial, as we shall find hereafter. Now, taking advantage of this distinction, the great Swedish naturalist termed the evident flowering vegetables phænogamous, from the Greek word fairóμai (phai'-no-mai), I appear; or, phanerogamous, from the Greek word pavepós (phan'-er-os), (1.) When the multiplier consists of one figure, write it down under the unit's place of the multiplicand. Begin at the right hand, and multiply each figure of the multiplicand by the multi-evident; and he designated the non-flowering, or more correctly plier, setting down the result and carrying as in addition. (2.) When the multiplier consists of more than one figure, write down the multiplier under the multiplicand, units under units, tens under tens, etc. Multiply each figure of the multiplicaal by each figure of the multiplier separately, beginning with the units, and write the products so obtained in separate lines, speaking, the non-evident flowering plants, by the word cryptogamic, from the Greek word кρUTτós (kroop'-tos), concealed. The further classification of Linnæus was artificial, as we have already stated. The nature of this classification we cannot study with advantage just yet. Hereafter we shall proceed to explain the principles on which it was based; but in the |