P bread that will rid me of this trouble p" To Canterbury with 3. You must stop only as long as you can count one, two, their followers went four knights of Henry's court, and, acting three, four, entirely on their own responsibility, slew the archbishop on the 4. You must pronounce the word which is immediately before steps of the altar. a period, with the falling inflection of the voice. The outcry raised in England, where the archbishop was! 5. The falling inflection (or bending) of the voice is commonly looked upon with favour, not only on account of his bold marked by the grave accent, thus, '. conduct in standing up for his order, but also because he was Examples. supposed to be the champion of the Anglo-Saxon against the Charles has bought a new hàt. Norman Englishman, was loud and sincere. Abroad, the feeling I have lost my gloves. of grief was more than equalled by anger, and a sort of holy Exercise and temperance strengthen the constitution. horror was felt at the bare notion of slaying an archbishop. A wise son makes a glad fàther. King Henry, there is every reason to think, was genuinely sorry Tho fear of the Lord is the beginning of wisdom. for the violence that had been done. Though his "guido and II. THE NOTE OF INTERROGATION. 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, 1 6. The note or mark of Interrogation is a round dot with a hook on him was charged the whole guilt of the murder, Penance above it, which is always put at the end of a question. the most severe, disclaimers the most solemn, and ceremonies 7. In reading, when you come to a note of interrogation, you the most humiliating scarcely served to clear him. Purposely must stop as if you waited for an answer. the Papal Court, which saw in Henry the strongest opponent of 8. You must stop only as long as you do at the period. its pretensions, availed itself of the handle given to it, and l 9. You must in most cases pronounce the word which is strove to crush the king under a load of obloquy. To a very placed immediately before a note of interrogation, with the great extent it succeeded. Never again did Henry appear as rising inflection of the voice. the same strong champion of State rights as when he forced an 10. The rising inflection of the voice is commonly marked by assent to the Constitutions of Clarendon. The ghost of Thomas the acute accent, thus, '. à Becket, now St. Thomas of Canterbury, haunted him, and the · Examples. dead man's hand deprived the conqueror of his victory. Has Charles bought a new hát? The Constitutions of Clarendon were disregarded, the death Have you lost your gloves ? of Becket making it impossible for the king to fly in the face of Hast thou an arm like Gód ? Canst thou thunder with a voice like him? the papal veto upon them. Some little submission of the clerical If his son ask bread, will he give him a stúne ? to the kingly power was made, but the work marked out by If lio ask a fish, will he give him a sérpent ? Henry II., the entire subjection of the clergy to the head of the state, was left unaccomplished till the dawn of the Reformation 11. In general, read declaratory sentences or statements with in England, when it was renewed and carried out in the fullest the falling inflection, and interrogative sentences or questions possible manner by that “ stately lord who broke the bonds of with the rising inflection of the voice. Romne," and who mas saved by natural causes from committing, Examples. in the case of Cardinal Wolsey, the egregious blunder committed Interrogative. Has John arrived ? by the knights of Henry II. when they plunged their swords Declaratory. John has arrived. into the bosom of Thomas à Becket at Canterbury. Interrogative. Is your father well ? Declaratory. My father is well. Declaralary. Unto Cæsar shalt thou gò. Examples. Succession secured to Henry Dec. 30, 1170 What o'clock is it? by Stephen . . . . . 1153 England divided into Judges How do you do to-dày? Began to reign. . Dec. 19, 1154 Circuits. . . . . . . 1176 How much did he give for his book ? Becket made Archbishop of Subjugation of Ireland by Where is Abel thy brother? Canterbury . . . . 1163 Henry . . . . . . 1172-5 How long, ye simple ones, will ye love simplicity ? Conference at Clarendon, Died at Chinon, Normandy Where wast thou, when I laid the foundations of the earth ? Wiltshire ... Jan. 25, 1164 July 6, 1189 Sometimes the first part of an interrogative sentence should SOVEREIGNS CONTEMPORARY WITI HENRY II. be read with the rising inflection of the voice, and the last part Denmark, Kings of Norcay, Kings of. ! Scotland, Kings of. with tho falling inflection. These parts are generally separated Canuto v. .. 1147 Sigurd III. . . 1136 4. Malcolm IV.. . 1153 by a Convma, thus, , Waldemar the Gt. 1157 Maguus V. . . 1164 14. At the comma, the rising inflection is used, and at the Cannte VI. . . 1182 Sverre . . . . 1184 "1181 Williain note of interrogation the falling inflection. E.camples. Shall I give you a péach, or an åpple ? Sancho III. . 1157 Are you going home, or to school? Alfonso IX. . . 1158 Last Sabbath, did you go to church, or did you stay at home ? Whether is it easier to say, Thy sins are forgiven, or to say, Arise Louis VII. . . 1137 Alexander III. , 1159 Sweden, Kings of. and walk ? Why did the heathen rage, and the people imagine vain things ? Germany, Emperor of. | Urban III. . . 1185 Eric I. . . . . 1155 Is your father well, the old man of whom ye spake ? Prederick Bar Gregory VII. . 1187 Charles VII. . . 1161 15. Sometimes the first part of an interrogative sentence barossa . . 1152 Clement III.. . 1188 Canute. . . . 1167 must be read with the falling inflection of the voice, and the last part with the rising inflection. READING AND ELOCUTION.-II. 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 bérd ? Is not the life more than meat ? and the body than míment ? 1. THE Period is a round dot or mark which is always put at the What went yo out to słe PA man clothed in soft raiment ? end of a sentence. What went ye out to see ? A próphet ? 2. In reading, when you come to a period, you must stop as How often shall my brother sin against me and I forgive him ? if you had nothing more to read. Until seren times ? 10. In the following exercises some of the sentences we in this room? How Degligent some of our fellow-pepals are! Ah! questions requiring the rising, and some the foulant Bartha I am airaad many wil regret that they have not improved their time! of the voice. A few sentences also ending with a pead are W , bare oomes Churches: Lod you that that be would return seried. No directions are given to the pail with regarà 52 saa? I suspect that be has not been dessed with his visit. Fare roc, Charles ? And were your friends ghad to see you? When tiat manner of reading them, it being desirable that is ou i casa Jade to be married! She make us a visit before she is uuerstanding, under the guidance of nature Diama, suti šest miT Or v.] she wait until she has cincapai ber se? tuin. But it may be observed that questions wat in de gent Edward, bow hope I am to see you! I heard of your aliswered by yes or no, generalls require the man aucz:n of croaching happiness with the bagbest plasser How does Rose the voice; and that questions which can be SISWwe do! And bow is ons whimsical cid imeni tihe Baron? You must or no, generally require the videiini n. fiacta... be getacat sed sasve gaestas I have many inquiries to EXIT 1. The Erst daw of g fand sterler ce the esplanade in John, where have yon been this DILI: Pret of the cel Gotte gate of the castle. Bet be paced it long before Have you seen my father t it! the Srau image was lowered He jedince bois orier to the sergeant What excuse hare rau far caming late this morning 2 st at the gaird, and was aimet The place of bs friends confinement know that it is past the schoai dom is a glocery spartment is the centre part of the castle If you are su inattintva 10 or lessons, ad rou the Eu Son Do you expect to be as high you iluss as your brother? Did will make much impreremar! For recite pour lessons as well as be 50? Sa Lazy boy! Care. Will yon ga, or star! I Youndt ovat: less chai! You have been usap these two hours. You have paid Shall you go to aur, or 12mTTO! 29 attention to your lessons. To esat say a word of them. How Did he nxmde his father, of luis mothes Sachsh you have been: his was a time i taleats you have LESSONS IS GEOVETRY.-II. DEFINI73053 and 9. As w e is the fac astate of two straight lines to each the arm the Lord heen revonded: that, it meet is post. and are not in the same direction. The post we they set is call the more of the angle, m, THE NATIF AGAXARCO desch of the two straight es is t s sadece ley of the sarie. The sagie itself 3 gema a d s plein rectilineal 1: Thu Watsoma a nia it is a 2 : ne 12. becs.ase it seessay ba s pia, sai is formed of 7p dash arst a r a es la meus ni ci het niin ruupia inne. Curabi onas se soci as are formed on the asrniruit rayuan suma, asmesim . mmber, or sims-3. serísde of schere o ciode: tes the consideration of such to in or rider stemy op: saras beings to the phe gecemetry. The agnitades of is in mains win recome a m e sclamatie s es do not depand ca tine dangtis the lags og sides, but Tive must seep the same man is were i Date of the degree amount aperte between tees, taken at the I must sang emas dan s TE : at a period 12 ampie is gemaran Negesented by three letters, one of 2. Tomas para evade sihr ward wa Bomas S ous isand at the Trato distinguish is particularly mmodis su ausimai. 2.2 i 16. aastaste ocher smie 2. greu frune uni the other two are g rad somewhere on tihe japs ei inn upla, bat generally at Booms top extres: amd niaga saking the angle, the a na simu sede st the Terties is as pissed between the other two, Vlag . Jei nese sai ziured or w hen sariasis. Thas in Fig. 4, which ay h min shes geents star the same tine sugie is either BA Cor CA 30 W i s w so u miru u SS Re Inne" :43: tibe pati Terta: mł the straight lines wum a maury mlen, mm. Veps of war sihat VUL N L Leiru Lisum, n sun, my Laras are te me nis rogut and o ne, and L: வாழd a risia Ippai arai iotire Is itali sme su inn de We ao striscia e mets suiz. si point between Da im niss u viisang i mries Let wer them se na sple, and the i r yr 2211232004 mi . ut ay sinisimm, mit spezie A s a shase anns se saat s be perpendier to one amir Duster 2 gen rulers ID.D. 120 2 F i sine steungita Sme A B meets the mr marks me 7cuI. le stazuat was t be pesmi mes tis sscent angles 230 V Nm 3 rui. Imst stop. Is he u SADA : euch of these sagles is there Nun mur dui. In ami tarpi. Vàuve U SR : DE UN ses he is said to be TER F Flur mit der Iseni. unger pas surii de primir e sursacht im A SDI al consequently natie han se 22 m 2 röm sentence. The need of 1:2 ID DE ! Sua lone mus suther, at may point between D un mas tint set angis menal to each I may he de m ani, na mort a burs is muito un vehe. . S URE » mismo septie: that which is SES imut vitatum de ne unge wa JULISH. te DL k sitam & ut sagie met u DCIS maple; and that the house is the three me disais me dis die wat W 2 angle smile an ATAY angle. Thus, the Gracia Um m is site sugas line c d in i que en se ajung sagus megal to each e nek v Westris ssr miled u odam engle; 20 Sagne who is a s a yosh onak duk ma w swtve neve whan s regras angie, is calle! obtuse ; and the anzle D A B, which is less than a right angle, aquus, equal, and latus, & side); isosceles (Greek, isos, equal, is called acute. and skelos, a leg); and scalene (Greek, skalēnos, unequal), 11. A plane figure, in geometry, is a portion of a plane surface, right-angled, obtuse-angled, and acute-angled. inclosed by one or more lines or boundaries. The sum of all 19. An equilateral (equal-sided) triangle is that which has the boundaries is called the perimeter of the figure, and the por- three equal sides (Fig. 8). tion of surface contained within the perimeter is called its area. 20. An isosceles (equal-legged) triangle is that which has only 12. A circle is a plane figure contained or bounded by a two equal sides (Fig. 9). curved line, called the circumference or periphery, which is such 21. A scalene (unequal) triangle is that which has all its that all straight lines drawn from a certcin point within the sides unequal (Fig. 10). figure to the circumference are equal to each other. This point 22. A right-angled triangle is that which has one of its angles & right angle (Fig. 11), in which the anglo at A is the right c Fig. 14, Fig. 15. Fig. 16. Fig. 6. Fig. 7. angle. The side opposite to the right angle is called the is called the centre of the circle, and each of the straight lines is hypotenuse (the subtense, or line stretched under the right called a radius of the circle. The straight line drawn through angle), and the other two sides are called the base and the perthe centre and terminated at both ends in the circumference, is pendicular ; the two latter being interchangeable according to called the diameter of the circle. the position of the triangle. It is plain, from the definition, that all the radii must be 23. An obtuse-angled triangle is that which has one of its equal to each other, that all the diameters must be equal to | angles an obtuse angle (Fig. 10). each other, and that the diameter is always double the radius. 24. An acute-angled triangle is that which has all its angles In speaking or writing, the circle is usually denoted by three acute; Figs. 8 and 9 are examples as to the angles, but there letters, placed at any distance from each other, around the is no restriction as to the sides. circumference; thus, in Fig. 7, the circle is denoted by the In any triangle, a straight line drawn from the vertex of one letters A C B, or A E B; or by any three of the other letters on of its angles perpendicular to the opposite side, or to that side the circumference. The point o is the centre ; each of the produced produced (that is, extended beyond either of its extremities in straight lines o A, O B, O C, O E, is a radius, and the straight straight a continued straight line), is called the perpendicular of the line A B is a diameter. triangle; as in Fig. 12, where the dotted line A D is the perpen13. An arc of a circle is any part of its circumference; the dicular of the triangle A B C; and in Fig. 13, where the dotted chord of an arc is the straight line which joins its extremities. line g h drawn from the point G 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 Fig. 8. Fig. 9. Fig. 10. Fig. 11, Fig. 17. Fig. 19. figure contained by four straight lines, called its sides. The Thus, in Fig. 7, the portion of the circumference A MC, straight line which joins the vertices of any two of its opposite • whose extremities are A and c, is an arc; and the remaining angles, is called its diagonal. Quadrangles are divided into portion A B C, having the same extremities, is also an arc; the various kinds, according to the relation of their sides and straight line Ac is the chord of either of these arcs. The sur-angles ; as parallelograms, including the rectangle, the square, face included between the arc A M C and its chord A c, is the the rhombus, and the rhomboid ; and trapeziums, including the segment AMC; there is also the segment ABC. The surface | trapezoid. included between the radii o C, O B, and the arc c B, is called 26. A parallelogram is a plane quadrilateral figure, whose the sector COB; the remaining portion of the circle is also a opposite sides are parallel ; thus, Fig. 14, A C B D, is a parallelosector. gram, and A B, CD, are its diagonals. 16. A semicircle is the segment whose chord is a diameter. 27. A rectangle is a parallelogram, whose angles are right Thus, in Fig. 7, ACB or A E B is a semicircle. The term angles (Fig. 15). semicircle, which literally means half a circle, is restricted in 28. A square is a rectangle, whose sides are all equal (Fig. 16). BDO F 1 Fig. 20. Fig. 21. Fig. 22. Fig. 12. Fig. 13. 29. A rhomboid is a parallelogram, whose angles are oblique. geometry to the segment thus described; but there are many The opposite angles of a rhomboid are equal to one another other ways of obtaining half a circle. (Fig. 14). 17. Plane rectilineal figures are described under various 30. A rhombus, or lozenge, is a rhomboid, whose sides are all heads; as trilateral or triangular; quadrilateral or quadrangular; equal (Fig. 17). and multilateral or polygonal. 31. A trapezium is a plane quadrilateral figure, whose oppo18. A triangle (Figs. 8, 9, 10, and 11) is a plane rectilineal site sides are not parallel (Fig. 18). figure contained by three straight lines, which are called its 32. A trapezoid is a plane quadrilateral figure, which has two sides. No figure can be formed of two straight lines ; hence, of its sides parallel (Fig. 19). an angle is not a figure, its legs being unlimited as to length. 33. A multilateral figure, or polygon, is a plane rectilineal Triangles are divided into various kinds, according to the figure, of any number of sides. The term is generally applier relation of their sides or of their angles : as equilateral (Latin, to any figure whose sides exceed four in number. Polygon divided into regular and irregular; the former having all their line and 6 in the left-hand Ene stand in Eses the Deet in a sides and angles equal to each other; and the latter having any sopare containing 24, which is therefore the prodact of 4 db. variation whatever in these respects. The sum of all the sides pbed to 6. of a polygon is called its perimeter, and when viewed in position It may be cheered that 6 in the top Ene sod 4 is the left. its contour. Irregular polygons are also divided into one and hapi sie lene stand in lines -hich meet in & square also connon-convex ; or, those whose angles are all salient, and those taining 14. The reason of this is that when the prodact of 150 of which one or more are re-entrant. The irregular polygon. sambes is required, it is indifferent which we consider to be the (Fig. 20) has its angles at B, C, and D, salient; and its angles altiple and which the multiplicand Thus, 4 sided to itself 6 at A and E, re-entrant. tise, is toe same as 6 added to itself 4 times. The truth of 34. Polygons are also divided into classes, according to the this may be sxn, perhaps, more clearly as follows:number of their sides ; as, the pentagon (Fig. 21), having fire If we rske foor vertical rots containing si dots each, as sides; the hexagon (Fig. 22), having six sides; the buytagon represented in the figure, it is quite evident that the having seven sides; the octagon having eight sides : and so on o pight sides and so on . .... shole number of dots is equal ether to the number According to this nomenclature, the triangle is called at ... . of dots in a vertical row 161 repeated 4 times, or to and the quadrangle a tetragon. ... the number of dots in an horizontal row (4) repeated sir times. And the same is clearly true of any other . . . . tro ambers. LESSONS IN ARITHMETIC.-IV. .. Hence we talk of two numbers being multiplied MULTIPLICATION. topotier, it being indifferent which we consider to be the multi plier and which the multiplicand. 1. The repeated addition of a number or quantity to itsas 4. If several numbers be multiplied together, the result is called multiplication. Thus, the result of the I ber 5, for cald the ind product of the nucles. Thas. 30 is the instance, added to itself 6 times, is said to be 5 si 1296j ty 6. corrigei prodact of 2, 3, and 5. beescse 2 X 3 X 5 = 30. 5 + 5 + 5 + 5 + 5 + 5 = 30, or 5 multiplied by 6 is 30. N.B. On learning the multiplication table, let the following facts be noticed :When the numbers to be multiplied are large, it is endent that The product of any number multiplied by 10 is obtained by the process of addition would be very laborioss. The process addig a cipher to the number. of multiplication which we are going to erpain is tbezefore, is The results of multiplying by 5 terminate alternately in 5 and 0. reality, a short way of performing a series of a stras Let it The Erst nine results of multiplying by 11 are found by merely then, be borne in mind, that maitphcation is in fact, os. - repaing the figure to be multiplied. Thns, 11 times 7 are 77. addition. 2. Definitions.—The namber to be repeated or maitinis L the Erst ten results of multiplying by 9 the right hand Egure regularly decreases, and the left hand figure increases by called the multiplicand. The number by which we echiply is P l ; also, the sum of the digits is 9. Thus, 9 times 2 are 18, called the multiplier: it, in fact, indicates how many times the on te 9 times 3 are 27. multiplicand is to be repeated, or added to itself. Tie sauber 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 pict. The meter 6 X 5 = 30 in multiplying any number, 5, for instance, by and multiplicand are also called the fact TS of wbuch the product another. 6. for instance, it will be the same thing if we mnltip! is composed, because they make the prodact. it successively by the factors of which the second is composed. Thus, since 5 multiplied by 6 is 30, 5 and 6 are called are called Thus, the product of any number multiplied by 28 might be got factors of the number 30. by multiplying it first by 7, and then multiplying the result The sign X placed between two cumbers means that they are to be multipbed together. ! The product of any number multiplied by 10 is obtained by 3. Before proceeding farther, the learner 331 uke self annering a cipher to the number. The product of any number, familiar with the following tatue, which gives a casta of the therefore, multiplied by 100 will be obtained by adding two two numbers up to 12 : ciphers, because 10 x 10 = 100; first multiplying by 10 adds MULTIPLICATION TABLE one cipher, and then multiplying the result by 10 adds another cipher. Similarly a number is multiplied by any multiplier in: 2:3 4 5 6 7 B 15 11 12 which consists of figures followed by any number of ciphers, by first multiplying by the number which is expressed by the figures 4 6 8 15 22 16 36 is : 26 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 i 12 16 39 24 23 44. explain, depends upon the self-evident fact that if the separate numbers of which a number is made up be multiplied by any 29 25 35 35 45 5) 55 GO factor, and the separate products added together, the result is the same as that obtained by multiplying the number itself by 6 12 18 30 36 42 that factor. Thus 5 + 4 + 2 = 11 | 35 | 42 49 53 7 * 5 = 35, 7 X 4 = 9,7 x 2 = 14. 35 + 33 + 14 = 72 = 7 * 11. | 32 40 48 56, 6+ 72 89 83 93 7. We shall take two cases : first, that in which the multiplier 45 | 54 63 81 90 99 consists only of one figure ; and, secondly, when it is composed of any nnmber of figuras. Case 1.- Requir.d 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 | 19 24 36 430072 896 203 120 132 144 tens, 18 hundreds, and 12 thousands, which, written in figures and placed in lines for addition, are To determine the product of any two numbers by the above table, find one of the numbers in the top line reading across the page, and then find the other in the line on the left hand which 1800 runs down the pare. Follow the column down tho page in 19000 which the first number standa, and the column across the pago in whi econd number stands. The number standing in Giving as the result 14046 thong two columns moet is tho product of the The process may be effected more shortly, as follows, in one line : the reason for the method will be sufficiently apparent product of multiplied by 6; 4 in the top' from tho preceding explanation : 14 21 182 12 121 132 2221 Writing the numbers as in the margin, proceed thus : 6 placing the first figure of each line directly under the figure by mes 1 unit are 6 units ; write the 6 units under the figuro which you multiply. Finally, adding these lines together, their , multiplied. 6 times 4 tens are 24 tens ; set sum will be the whole product of the two given numbers. 2341 multiplicand the 4 or right-hand figure under the figuro 1 8. Method of testing the Correctness of the result.--Multiply the 6 multiplier multiplied, and carry the 2 or left-hand figure multiplier by the multiplicand, and if the product thus obtained 140465 to the next product, as in addition. 6 times be the same as the other product, the work may be presumed to 3 hundreds are 18 hundreds, and 2 to carry be correct. make 20 hundreds; set the 0 under the figure multiplied, and 9. Multiplication by reversing the Multiplier. - It may be carry the 2 to the next product, as above. 6 times 2 thousands remarked that multiplication may be performed by commencing are 12 thousands, and 2 to carry make 14 thousands. There with the last figure (that is, the extreme left-hand figure) of the being no more figures to be multiplied, set down the 14 in full, multiplier, instead of with that in the unit's place. In this case, as in addition. The required product is 14046. however, as will be seen from an example, we must set down Before proceeding to the second case, the learner is requested each line ono figure to the right of the preceding line. to make himself familiar with the process of multiplying any Thus, in multiplying 2221 (2.) 2221 number by one figure, by means of the following by 1234, we may proceed as 1234 4321 EXERCISE 6. follows, as in operation (1), 2221 beginning with the left-hand (1.) Multiply 83 by 7; 549 by 5; 6879 by 9; 7891011 by 8; 2221000 444200 567893459 by 3; 9057832917 by 11, and the result by 7. figure of the multiplier ; or 6663 66630 we might, to avoid confusion, (2.) Find the continued product of 1, 2, 3, 4, 5, 6, 7, 8, 9. 8884 8884 (3.) Find the products of the number 142857 by the nine digits. reverse the multiplier, as in (4.) Find the prodncts of the number 98998, the smallest num. operation (2), and proceed in 2740714 2740714 ber contained in the second square in Ex. 4, page 23, by the nine the same way. The ciphers digits, and you will find these products in the same table. which we omit in practice are added in the last operation, to (5.) Multiply 857142 by 9; 76876898 by 2; 1010400600 by 7; explain the truth of the process. 79806090 by 8; and 999999999999 by 5. EXERCISE 7. (6.) Multiply the following numbers first by 2 and then by 3: (1.) Find the products of the following numbers :1. 58745 4. 900195 i 7. 1967311 i 10. 20907683 18. 1534693 x 4762 2. 63294 5 1. 463 x 45 , 354764 8. 4192093 11. 42765401 2. 348 X 62 19. 142857 X 70000 3. 82563 1 6. 822073 9. 8765137 12. 22663973 3. 793 x 86 20. 7050860 X 70508 (7.) Multiply the following numbers first by 4 and then by 5: 4. 989 X 90 21. 10101010 ~ 20202 1. 42937 i 4. 3235931 7. 9988776 10. 19977991 5. 75 x 42 x 56 22. 98548050 X 97280 2. 54012 5 . 765102 8. 4039007 11. 83215916 6. 84 x 37 x 69 . 53600000 x 75300 3. 89645 1 6. S58455 I 9. 2595139 1 12. 18671868 7. 7198 X 256 26. 99999999 x 90009 (8.) Multiply the following numbers first by 6 and then by 7: 8. 93186 X 445 25. 6785634090 X 1000000 9. 99999 X 999 26. 9959925683 x 7060301 1. 51785 1 4. 839763 i 7. 9611437 10. 73689202 10. 7422153 * 468 27. 7684329009 X 100007 2. 49233 5. 467453 8. 3902914 11. 12345678 11. 76854 x 870 28. 1428573893 * 987654 3. 36523 6 . 370223 9. 7856374 12. 91223344 12. 90763 x 700 29. 9698596985 * 2168103 (9.) Multiply the following numbers first by 8 and then by 9: 13. 3854 X 3854 * 3854 30. 14285714257 x 7965841 1. 73924 4. 995323 7. 6778899 10. 79911997 14. 9261397 x 9584 31. 10101001000 X 100101000 2. 21045 5. 201567 8. 7129304 11. 64951238 15. 9507340 X 7071 32. 7070808090 x 90908070 3. 51693 1 6. 5548531 9. 9315925 1 12. 89012315 16. 999999 x 9999 33. 300010003000 x 400100020000 17. 6929867 x 8000 (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 (2.) Multiply 2354 by 6789, and 23789 by 365, by reversing there are five marbles. How many marbles are there in the box? (11.) There are six farmers, each of whom has a grazing farm | (3.) Multiply 857142 by 19, by 23, by 48, by 97, by 103, by of seven fields : each field has eight corners, and in each corner | 987, and by 4567. there are nine sheep. How many sheep do the farmers own, (4.) Find the products of the number 98998 by all the numbers and how many are feeding on their farms ? from 11 to 49 inclusive. The answers will be found in the second Case 2.---To multiply 675 by 337 : square given in Ex. 4, page 23, on Addition. 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): LESSONS IN BOTANY.-II. 675 675 SECTION II.-ON THE SCIENTIFIC CLASSIFICATION OF 337 337 VEGETABLES. 4735 = 675 X 7 4725 The observer who takes a survey of the various members of 20250 - 675 x 30 2025 the vegetable world becomes cognisant of at least one promi. 20300 = 675 * 300 2025 nent distinction between them. He soon perceives, that whilst Hence 227473 = 675 * 337 227475 certain vogetables lave flowers others have not; or perhaps, more correctly speaking, if the second division really possess In working by this method it is unnecessary to write down flowers, thoy are imperceptible. the one nought at the end of the second line, and the two. This distinction was first laid hold of as a basis of classinoughts at the end of the third line, etc., as in operation (1), if fication by the celebrated Linnæus, and to this extent the we only place each line one figure to the left of the one pre- classification adopted by that great philosopher was strictly ceding, so that the work appears as in operation (2):- natural ; beyond this, however, it was altogether artificial, as The above examples will be sufficient to explain the truth of we shall find hereafter. the following Now, taking advantage of this distinction, the great Swedish Rule for Multiplication. naturalist termed the evident flowering vegetables phænogamous, (1.) When the multiplier consists of one figure, write it down from the Greek word arróuar (phai'-no-mai), I appear; or, tinder the unit's place of the mult plicand. Begin at the right phanerogamous, from the Greek word pavepós (phan'-er-os), 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. speaking, the non-evident flowering plants, by the word crypto (2.) When the multiplier consists of more than one figure, gamic, from the Greek word kpumTÓS (kroop'-tos), concealed. The write down the multiplier under the multiplicand, units under further classification of Linnæus was artificial, as we have units, tens under tens, etc. Multiply each figure of the multipli. already stated. The nature of this classification we cannot al by each figure of the multiplier separately, beginning with study with advantago just yet. Hereafter we shall proceed to tou units, and write the products so obtained in separate lines, explain the principles on which it was based; but in ther" |