to be the exact opposite of what Henry had looked for in him. The case which induced the king to try conclusions with Becket and the clerical party was an exceedingly gross one. A priest in Worcestershire had violated a gentleman's daughter, and afterwards murdered her father. When the scoundrel was about to be brought to trial before the king's justices, Becket claimed him as a clerk, and getting possession of him, degraded him from his priest's office, and then insisted that he could not be tried again in the king's court for the same offence. These were the circumstances under which King Henry summoned the bishops to Westminster; and the meaning of the words "saving our own order" is sufficiently clear. Henry left the hall in a rage, but it was not an impotent one. By promises, If a by threats, by various means, he detached most of the prelates from their primate, and he won over the Archbishop of York by significant hints about the next incumbent of the see of Canterbury. Last to give in was Becket, who yielded only to the universal pressure brought to bear upon him, and repented as soon as he had assented. But repentance or no repentance, he did assent, and with the rest of the prelates professed his willingness to observe "the ancient customs of the kingdom"which did not recognise the clerical claims-and to withdraw the saving clause. which, if once allowed, would not only have made the clergy This monstrous immunity, with its yet more monstrous abuses, was like the last straw that broke the camel's back. So flagrantly unjust was it, both in principle and practice, that all honest men were indignant, and cried aloud for some check upon it. The king, who was by means of it and the other pretended rights of the clergy gradually ceasing to be master in his own dominions, resolved to apply a curb, and to wipe away the scandal. From the time when he mounted the throne in 1154 he had striven to restrain the power of the clergy, and, aided by the clear head and bold hand of his bosom friend Thomas à Becket, had striven not unsuccessfully. Great had been the wrath poured on Becket's head when, as Lord Chancellor of England, he had made havoc altogether of many a pet clerical abuse. Under the idea that he would continue the same policy in a sphere where that policy would have the largest possible scope, Henry offered Becket the archbishopric of Canterbury when that see was vacant in 1161. Becket, it must in fairness be admitted, was very averse to accept the offer, and for thirteen months held out a persistent refusal. Finally, however, he yielded to the earnest solicitations and orders of the king, and was duly installed as Primate at Canterbury. To the surprise of all men, and to the infinite disgust of the king, Becket from the day of his consecration pursued a totally new course to that he had formerly taken. Nowhere was there so bold an asserter of clerical rights, nowhere a more untiring worker on behalf of the power of the Church. He claimed lands which had once belonged to the see of Canterbury, but which had long been independent and in laymen's hands; he excommunicated the owner of an advowson for ejecting a priest who had been presented by himself; he asserted the right of the spiritual courts to inquire into questions of contract confirmed by oath; and in every respect he proved himself Henry knew with whom he had to deal. He knew that a confession of this sort was quite useless unless it could be embodied in some visible instrument. Taking advantage of his success, of the schism in the Papacy (there were at this time two Popes, one at Rome, the other in France, and Henry played off one against the other), and of the resolute support of the barons, who were only too glad to give the spiritual lords a kick down, Henry summoned the primate and all the bishops to meet him at Clarendon, a village in Wiltshire, and there, being backed, like Stephen de Langton on a later occasion, by "the whole nobility of England," he required their sworn assent to what have been called the Constitutions of Clarendon, The "Constitutions" were dreadfully hard eating for the bishops, divesting them as they did of nearly all their invidious privileges, some of which it must be confessed were sanctioned by those "ancient customs" which the king had sworn the bishops to observe. Suits concerning advowsons and rights of presentation were to be decided in the civil courts; no clerk, no matter of what rank, was to quit the kingdom without the royal permission; the pretended right to try questions of contracts made on oath was to be renounced; excommunicated persons were not to be made to find security for their residence in any appointed place; laymen were not to be tried in spiritual courts except by approved good witnesses; no chief tenant of the crown to be excommunicated without the king's assent; the final appeal in all spiritual causes to be in the king; prelates to be regarded as barons of the realm, and to be taxed accordingly; bishops not to be elected without the royal assent; the privilege of sanctuary to be curtailed; and clerks accused of any crime to be tried in the king's courts, like other men. The Great Council of the barons unanimously approved the Constitutions, and, sour as the food was, all the prelates, except the primate, swore to accept it "legally, with good faith, and without fraud or reserve." Becket was resolute, though alone; friends as well as foes besieged his constancy, still he held out; and it was not till Richard de Hastings, Grand Prior of the Templars, a man who seldom bent his knee, even in prayer, went down on his knees and besought him, that he gave in. Unwillingly, and in hope of getting the Pope to annul his oath, he swore like the rest to accept the Constitutions "with good faith, and without fraud or reserve." Pope Alexander refused to ratify the treaty; he released all who had sworn from their oaths, and threatened to excommunicate everybody who should try to support the king's demands. A long trial of strength ensued. Becket got over to France, and plotted there against his former friend; Henry took the revenues of the hostile bishops into his own hands, and by dint of perseverance managed to keep the clergy in check; and it is Excommunication was the expulsion of a man, by the highest probable he would have done very much more than he did had ecclesiastical authority, from the communion of Christian men. The rights and comforts of the Church were refused to the excommunicated; the sacraments were not allowed to be administered to him; it not been for the brutal murder of Thomas à Becket, which was a blunder as well as a crime. In the autumn of 1170 Becket had returned to Canterbury, he was reckoned accursed; and, in times of superstition, he was sup nominally reconciled to the king; but the old question-which posed to be eternally lost if he died without absolution. Excommunieation was the great weapon of ecclesiastics, and it was a powerful one in the age of ignorance and moral darkness. should be the greater-being revived, Henry is reported to have said in a hasty moment, "Is there not one of those who eat my 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 outery 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, '. How do you do to-day? 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. Gregory VIII. Clement III.. 1188 16. In the following exercises some of the sentences are questions requiring the rising, and some the falling inflection of the voice. A few sentences also ending with a period are inserted. No directions are given to the pupil with regard to the manner of reading them, it being desirable that his own understanding, under the guidance of nature alone, should direct him. But it may be observed that questions which can be answered by yes or no, generally require the rising inflection of the voice; and that questions which cannot be answered by yes or no, generally require the falling inflection. EXERCISE 1. John, where have you been this morning? What excuse have you for coming late this morning? Did you not know that it is past the school hour? If you are so inattentive to your lessons, do you think that you will make much improvement? Will you go, or stay? Will you ride, or walk ? Did he resemble his father, or his mother? Is this book yours, or mine? His, or hers? Art thou he that should come, or do we look for another? Why are you so silent ? Have you nothing to say? Who hath believed our report? Lord been revealed? III. THE NOTE OF EXCLAMATION. ! in this room? How negligent some of our fellow-pupils are! Ah! I am afraid many will regret that they have not improved their time! Why, here comes Charles! Did you think that he would return so soon? I suspect that he has not been pleased with his visit. Have you, Charles ? And were your friends glad to see you? When is cousin Jane to be married? Will she make us a visit before she is married? Or will she wait until she has changed her name? My dear Edward, how happy I am to see you! I heard of your approaching happiness with the highest pleasure. How does Rose do? And how is our whimsical old friend the Baron? You must be patient and answer all my questions. I have many inquiries to make. The first dawn of morning found Waverley on the esplanade in front of the old Gothic gate of the castle. But he paced it long before the drawbridge was lowered. He produced his order to the sergeant of the guard, and was admitted. The place of his friend's confinement was a gloomy apartment in the central part of the castle. Do you expect to be as high in your class as your brother? Did you recite your lessons as well as he did? No. Lazy boy! Careless child! You have been playing these two hours. You have paid no 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 made! LESSONS IN GEOMETRY.—II. DEFINITIONS (continued). To whom hath the arm of the 9. AN angle is the inclination of two straight lines to each other, which meet in a point, and are not in the same direction. The point in which they meet is called the vertex of the angle, and each of the two straight lines is called a side or leg of the angle. The angle itself is generally called a plain rectilineal angle, because it necessarily lies in a plain, and is formed of straight lines. Curvilineal angles are such as are formed on the surface of a sphere or globe; but the consideration of such angles belongs to the higher geometry. The magnitudes of angles do not depend on the lengths of their legs or sides, but on the degree or amount of aperture between them, taken at the same distance from the vertex. 17. The note or mark of Exclamation is a round dot with an upright dash or stroke above it, which is always put at the end of a sentence expressing surprise, astonishment, wonder, or admiration, or other strong feelings. 18. In reading, when you come to a note of exclamation, you must stop in the same manner as if it were a note of interrogation. 19. You must stop only as long as you do at a period. 20. You must generally pronounce the word which comes immediately before a note of exclamation with the falling inflection of the voice. What a beautiful house that is! How brightly the sun shines! How mysterious are the ways of God! How are the mighty fallen in the midst of the battle! How are the mighty fallen, and the weapons of war pèrished! It is a dread and awful thing to die! 21. In our remarks on the period, the student was taught that when he comes to a period, he must stop, as if he had nothing more to read. At the end of a paragraph, whether the period or any other mark be used, a longer pause should be made than at the end of an ordinary sentence. The notes of interrogation and exclamation generally require pauses of the Eame length with the period. It may here be remarked, that good readers always make their pauses long; but whatever be the length of the pause, the pupil must be careful that every pause which he makes shall be a total cessation of the voice. EXERCISE 2. The sentences to be read as if marked. George is a good boy. He learns his lesson well. He is attentive to the instructions of his teacher. He is orderly and quiet at home. A good scholar is known by his obedience to the rules of the school. He obeys the directions of his teacher. His attendance at the proper time of school is always punctual. He is remarkable for his diligence and attention. He reads no other book than that which he is desired to read by his master. He studies no lessons but those which are appointed for the day. He takes no toys from his pocket to amuse himself or others. He pays no regard to those who attempt to divert his attention from his book. Do you know who is a good scholar? Can you point out many An angle is generally represented by three letters, one of which is always placed at the vertex, to distinguish it particularly from every other angle in a given figure, and the other two are placed somewhere on the legs of the angle, but generally at their extremities; and in reading or in speaking of the angle, the letter at the vertex is always placed between the other two, and uttered or written accordingly. Thus, in Fig. 4, which represents an angle, the name of the angle is either B A C or CAB: the point A is called its vertex; and the straight lines B A, C A, its sides or legs. 10. Angles are divided into two kinds, right and oblique, and oblique angles are divided into two species, acute and obtuse. When one straight line meets another, at any point between its extremities, and makes the adjacent or contiguous angles equal to each other, each of them is called a right angle, and the legs of each of these angles are said to be perpendicular to one another. Thus, in Fig. 5, the straight line A B meets the straight line C D in the point A, and makes the adjacent angles CA B, D A B, equal to each other; each of these angles is therefore called a right angle; and the straight line A B is said to be perpendicular to the straight line A C, or D A, and consequently A C or A D is perpendicular to A B. When one straight line meets another, at any point between its extremities, and makes the adjacent angles unequal to each other, each of them is called an oblique angle; that which is greater than a right angle is called an obtuse angle; and that 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 are equal to each other. This point 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 EB; or by any three of the other letters on the circumference. The point o is the centre; each of the straight lines o▲, O B, O C, O E, is a radius, and the straight line A B is a diameter. 13. An are of a circle is any part of its circumference; the chord of an are is the straight line which joins its extremities. angle. The side opposite to the right angle is called the hypotenuse (the subtense, or line stretched under the right angle), and the other two sides are called the base and the perpendicular; the two latter being interchangeable according to the position of the triangle. 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 ▲ 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 AMC, whose extremities are A and C, is an arc; and the remaining portion ▲ B C, having the same extremities, is also an arc; the straight line Ac 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 AMC; 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). с 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. Fig. 21. Fig. 22. 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 applied to any figure whose sides exceed four in number. Polygons are 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 convex 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 five 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 multiplied by 6. 5 +5 +5 +5 +5 +5 = 30, or 5 multiplied by 6 is 30. When the numbers to be multiplied are large, it is evident that the process of addition would be very laborious. The process of multiplication which we are going to explain is therefore, in reality, a short way of performing a series of additions. Let it, then, be borne in mind, that multiplication is, in fact, only addition. 2. Definitions.-The number to be repeated or multiplied is called the multiplicand. The number by which we multiply is called the multiplier: it, in fact, indicates how many times the multiplicand is to be repeated, or added to itself. The number produced by the operation is called the product. The multiplier and multiplicand are also called the factors of which the product is composed, because they make the product. Thus, since 5 multiplied by 6 is 30, 5 and 6 are called factors of the number 30. The sign placed between two numbers means that they are to be multiplied together. 3. Before proceeding farther, the learner must make himself familiar with the following table, which gives all products of two numbers up to 12: To determine the product of any two numbers by the above table, firone of the numbers in the top line reading across the page, and then find the other in the line on the left hand which runs down the page. Follow the column down the page in which the first number stands, and the column across the page in which the second number stands. The number standing in the square where these two columns meet is the product of the two numbers. Thus, to find the product of 4 multiplied by 6; 4 in the top line and 6 in the left-hand line stand in lines which meet in a square containing 24, which is therefore the product of 4 multiplied by 6. It may be observed that 6 in the top line and 4 in the lefthand side line stand in lines which meet in a square also con. taining 24. The reason of this is that when the product of two numbers is required, it is indifferent which we consider to be the multiplier 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 seen, 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 (6) 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 multiplier and which the multiplicand. 4. If several numbers be multiplied together, the result is called the continued product of the numbers. Thus, 30 is the continued 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 results of multiplying by 5 terminate alternately in 5 and 0. The first nine results of multiplying by 11 are found by merely 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. 5. It is evident that [as 2 x 3 x 5 = 30, and 2 x 3 = 6, and 6 x 5 = 30] in multiplying any number, 5, for instance, by another, 6, for instance, it will be the same thing if we multiply it successively by the factors of which the second is composed. 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. 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 × 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 = 28, 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. 2341 2 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 6 240 1800 12000 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 Irom the preceding explanation : |