bread that will rid me of this trouble ?" 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 outery 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 håt. 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 father. 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, 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 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 L.camples. 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 glóves ? of Becket making it impossible for the king to fly in the face of Hast thou an arm like God ? the papal veto upon them. Some little submission of the clerical Canst thou thunder with a voice like him ? to the kingly power was made, but the work marked out by If his son ask bread, will he give him a stúne ? If lso 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. Rome," and who fas saved by natural causes from committing, Ecamples. 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 & Becket at Canterbury. Interrogative. Is your father well ? Declaratory. My father is well. Declaralery. Unto Cæsar shalt thou gò. 12. Sometimes the sentence which ends with a note of interafter the Conquest, and the first of the Plantagenet dynasty. rogation should be read with the falling inflection of the voice. Born at Mans, Normandy 1133, Murder of Thomas à Becket 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, 1134 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 WITH HENRY II. be read with the rising inflection of the voice, and the last part Denmark, Kings of. Noricay, Kings of. Scotland, Kings of with tho falling inflection. These parts are generally separated Canute V. 1147 Sigurd III. 1131 by a Conma, thus, , Malcolm IV.. 1153 Waldemar the Gt. 1157 Maguus V. 1161 William 14. At the comma, the rising inflection is used, and at the 1165 Cannte VI. 1182 Sverre . 1184 note of interrogation the falling inflection. Eastern Empire. Portugal, Kings of. Spain, Kings of. Manuel I.. 1143 Alfonso I. Escamples. 1139 Alexius II. 1180 Sancho I.. Alfonso VIII. 1126 1185 Shall I give you a péach, or an apple ? Sancho III. 1157 Are you going hóme, or to school? Last Sabbath, did you go to church, or did you stay at home? France, Kings of Adrian IV. Whether is it easier to say, Thy sins are forgiven, or to say, Arise 1154 Louis VII. 1137 Sweden, Kings of. and walk ? Why did the heathen ráge, and the people imagine vain things ? 1129 Germany, Emperor of. | Urban III. Eric I.. 1155 Is your father well, the old man of whom ye spake ? 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 fáther? Is not the life more than meat ? and the body than ríment ? 1. THE Period is a round dot or mark which is always put at the What went yo out to see ? A man clothed in soft raiment ? end of a sentence. What went ge 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. Uutil seren times ? . 1183 1185 . . 1185 . . I. THE PERIOD, 16. In the following exercises some of the sentences are in this room? How vegūgest some of our fellow-pepils are! Ah! questions requiring the rising, and some the fandang babartina I en airsad zanny w regret that they have not improved their time! 0 th voice. A few sentences also ending with a pensà are way, beze oomas Churdes: Dad you that that be would return useried. No directions are given to the pavil with regard $swaI suspect that be has not been pleased with his visit. that manner of reading them, it being desirable that ... - is csasa Jade to be married washe make ssa rist before she is Fare gas, Charles? And were your friends chai to se poa? When understanding, under the guidance of nature Lima, sboris Szers married Or will she wait until she has changed ber me? lumBut it may be observed that questa is what can be My dear Edward, bow hope I sm to see toe! I beard of your answered by yes or no, generally require the man 22.12.0 of agroaching happiness with the herbest pleasure How does Rose the voice ; and that questions wird man he eiwwred IT pas d? And bor is or whimsical cà inena sihe Barce? You must or no, generally require the visione in.fisctazas. de pateat sad sasve ) ** yaestosas I have many inquiries to EILL.IS 1. be Erst dawa dising fund Terries the esplanade in John, where have son been this MALLINE bei atbeil Gottác gated the castle. Bas be paced it long before Have you seen my father tit! the Srsuinage es lovered He geodaced his case to the sergeant What excuse have rea far caming late this warning saat *the guard and was added the place of his friend's confinement know that it is past the schoai hot W2S a gloceny apartment in the centre part of the castle If you are su inattentve 10 pour lessons, as you tult thut you Do you expect to be ss högh in yoe els as your brother? Did will make much impiamai! ron recite pour lessons ss weiss he 50! Sa Lazy boy! CareWill yon ga, or star! Will you mar, a walk? less cha: Ton bure been playing these two hours. You have paid Shall you go to dr, or 12-mar! 29 attention to your lessons. To enot say a word of them. How Did ho resemble has father, or his moth isoasih you have been: What s tiste tipa sai toleats you bare Is this book yours, or mine! Hus, or hets! made LESSONS IN GEOMETRY.-II. DEFINITIONS Blund Why are yoon so sim:! HE TOE Dothing to say: Who hath believed om 21: En büz bull the urn the Assume is the iscöstice ce ** strséght lines to each Lord been rouled! that, we meet in a post. sad se ast in the same direction. The post in wise they meet is iad tibe rota o the angle, m. THE NITI OF CAXASOK ad esch of the two straight lines is as de ce leg of the sagie. The angle itself is generat ad s pisin rectilineal 17. Thu nais na mesto E-zienti it is a 2 at ni el 22. because it seessa bes sa panza, sad is formed of 7ggi dash or stoly aun Thai Es Camous qui ei that their drengia Cursinabi onpas sre speil ss are formed on the a sonarni vayrun suyu, ameshuman water, or simanze serisce é a zbere ce globe: bus tibe consideration of such How or olup stem. sag'as beisags to the ghz gecimetry. The magnitades of as in malang, wbun Tua cama * a * erromatas segles de sex depand ca tine dengths in the legs sides, but Tova must süzr the same manner 13 war 1 Date de ce the degree ce smont apertere between thes, taken at the Heagatst. same distance from the verta To mnt stay at using as toe 3: si a period Az angle is gems regeesented by three letters, one of 2. VE TN par exaDe tih wzi wa cime siis rous pisons at the price to estimesh is particularly munduan na namin. -12 76 bugaderia stery other ange is gren fra, ai the other two are 1... zhe von and somewhere a tibe japs de sine sapla bat generally at Booms s extremis: 2 raiag e usoaking the angle, the E non iu* setter st the Tertzi is siis pued between the other two, Wag kantu hrse u sni ztered ce vrsten szeragis. Tas i Fig. 4, which pich min sms cesents se us the JE sine magie is either B a C or w so mir un o musa I e huone" :43: tibe patisserta: # the strsight lines swim u mary Islom, ml. zu VEDUS Jf wensiert" VRUL N:14 Uusi Lisium, 25 sun, ay sa !! Las are z o estis rapsai bbque, and . : : sul ms Jums. Ir guru cine swiss aze izini z two specs, arte sei otese. I sirrali sme si inng de co: storia a mess sutüdz. si say point between . isep ustantam positie musa 3 Stremtas i mates the rent ce ceangeoes sngles Is ann II hiss u vinne i mres Et meat the entire s ml a mai napis, and the Ives r 21, 2729 mig um2 by swisiem, mi vozi shae sapies se sunt u be perpendicular to one ma tay Luistes a hugsa vlers D.Dr. Tus 2 Fisite stranit Ene A B meets the nur maris m peruni. iu stanient was this 22 si maias tiks siiscent angles *2*6 m Nm D 3 prui, le nust stap. ss i ze :15:12. RTL 2 aste: such of these sngles is there waling mura y vuis au mi se paskaapit, vāutāne view wit: Mit stort ke 4 3 is said to be Nu r au mur mes de ser unger pats savez il bei wemaja biarow the streapta imt ACDI à consequently male n. 36 29 mi si sa röm entence. The antes :D Timise necen ami tenisimaun romeruly sure panses ef sku W momime mos suthar, at may point between enta via te pan. Du an tas tint set antas nequal to each I may luma de sune ni, na ni saalis svars miles de vie. wakit um si sa map sacle : test which is PULARES vitant de se engait visit us. ww grze uke staz a suit syis a malet an DIGIS maglit; and that mis w si mag ry mase vis mes son bure obtuse ; and the anzle D A B, which is less than a right angle, aquus, equal, and latus, a 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 certain 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 D B 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 nes 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 CB, 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 (that is, extended beyond either of its extremities in straight lines 0 A, O B, O C, O E, is a radius, and the 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. 14. A segment of a circle is the surface inclosed by an arc and its chord. Fig. 17. 15. A sector of a circle is the surface inclosed by an arc, and Fig. 18. Fig. 19. the two radii drawn from its extremities. 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 A c is the chord of either of these arcs. The sur- angles; as parallelograms, including the rectangle, the square, face included between the arc AMC and its chord A c, is the the rhombus, and the rhomboid ; and trapeziums, including the gegment AMC; there is also the segment A B C. 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 c O B; 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, C D, 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, A C B 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). E F н D 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 sides. No figure can be formed of two straight lines ; hence, of its sides parallel (Fig. 19). 32. A trapezoid is a plane quadrilateral figure, which has two 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 Ess wie Deet is a sides and angles equal to each other; and the latter having any sopare containing 24, which is therefore the prodact of 4 uus. variation whatever in these respects. The sum of all the sides pbed by 6. of a polygon is called its perimeter, and when viewed in position It may be cheerred that 6 in the top Ene sod 4 in the left. its contour. Irregular polygons are also divided into consez and hasi zde tine stand in lines which meet in a square also connon-convex ; or, those whose angles are all salient, and those taining 24. The reason of this is that when the product of to of which one or more are re-entrant. The irregular polygon sombes is required, it is indifferent which we consider to be the (Fig. 20) has its angles at B, C, and D, salient; and its sagles Ezlepber and which the multiplicand. Thas, 4 added to itself 6 at A and E, re-entrant. tises, is the same 83 6 added to itself 4 times. The truth of 34. Polygons are also divided into classes, according to the this may be seen, parhaps, more clearly as follows:number of their sides ; as, the pentagon (Fig. 21), having fire If we aske foar vertical rows containing sir dots each, as sides; the hexagon (Fig. 22), having six sides; the buztagoa represented in the figure, it is quite evident that the having seven sides; the octagon having eight sides : and so on. whole number of dots is equal ether to the number According to this nomenclature, the triangle is called a ton, of dots in a vertical row 151 repeated 4 times, or to and the quadrangle a tetragon. the number of dots in an horizontal rou (4) repeated sis times. And the same is clearly trae of any other two numbers. LESSONS IN ARITHMETIC.-IV. Hence we talk of to numbers being multiplied MULTIPLICATION. tapier, it being indifferent which we consider to be the multi plier and which the multiplicand. 1. The repeated addition of a number or quanity to itse is 4. If several numbers be multiplied together, the result is called multiplication. Thus, the result of the reber 5, for ear the cine product of the anciers. Thus, 30 is the instance, added to itself 6 times, is said to be 5 81 21293j ty 6. Corel prolact of 2, 3, and 5. becacze 2 X 3 X 5 = 30. 5 + 5 + 5 + 5 + 5 + 5 = 30, or 5 multiplied by 6 is 30. X.B. On learning the multiplication table, let the following facts be noticed :When the numbers to be multiplied are large, it is evident that the process of addition would be very laborioss. The process addisg a cipher to the number. The product of any number multiplied by 10 is obtained by of multiplication which we are going to expain is therefore, is reality, a short way of performing a series of ad St. Let it The Erst nige results of multiplying by 11 are found by merely The results of multiplying by 5 terminste alternately in 5 and 0. then, be borne in mind, that multiphcasion is in fact, os repating the figure to be multiplied. Thns, 11 times 7 are 77. addition. 2. Definitions.—The number to be repeated or mais figure regularly decreases, and the left hand figure increases by I the frst ten results of multiplying by 9 the right hand called the multiplicand. The number by which we stiply is i; also, the sum of the digits is 9. Thus, 9 times 2 are 18, called the multiplier: it, in fact, indicaies how many times the 9 times 3 are 27. multiplicand is to be repeated, or added to itselt. Tie sauber produced by the operation is called the future. The mover 6 X 5 = 3.9 in multiplying any number, 5, for instance, by 5. It is erident that as 2 X 3 X 5 = 30, and 2 X 3 = 6, and and multiplicand are also called the factors of which the prodact another, 6. for instance, it will be the same thing if we multiply is composed, because they make the prodact. 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 it successively by the factors of which the second is composed. factors of the number 30. by multiplying it first by 7, and then multiplying the result The sign placed between two cambers means that they by are to be multipbed together. 3. Before proceeding farther, the learnar 13-1 uke himself andering a cipher to the number. The product of any number, The product of any number multiplied by 10 is obtained by familiar with the following tabs, which gives secasia of therefore, multiplied by 100 will be obtained by adding two two numbers up to 12 : ciphers, because 10 x 10 = 100; first mnltiplying 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 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. 12 6. The process of multiplication which we now proceed to 4 | 8 i 12 '16 explain, depends upon the self-evident fact that if the separate numbers of which a number is made up be multiplied by any 5 10 15 20 25 35 35 ) factor, and the separate products added together, the result is the same as that obtained by multiplying the number itself by 6 12 18 25 30 35 42 53 that factor. Thus 5 + 4 + 2 = 11 14 21 28 35 40 40.5563 77 7 * 5 = 35, 7 * 4 = 29,7 x 2 = 14. 35 + 33 + 14 = 77 = 7 x 11. 8 16 24 32 40 48 56 7. We shall take two cases: first, that in which the multiplier 9 | 18 27 | 36 | 45 54 63 72 81 consists only of one figure; and, secondly, when it is composed of any number of figures. 70 80 Case 1.- Requir.d to multiply 2341 by 6. 11 23 53 54 | 55 | 66 77 88 99 110 121 132 2341 = 2 thousands + 3 hundreds + 4 tens + 1 unit. 12 27 30 13 GO | 72 85 90 103_120 122 141 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, areTo determine the product of any two numbers by the above table, find one of the numbers in the top lino reading across the pago, and then find the other in the line on the left hand which runs down the page. Follow the column down tho page in 19000 which the first number tonda, and the column across the pago in whle econd number stands. The number standing in Giving as the result 14046 thong two columna moot 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 4 multiplied by 0; 4 in 1110 top from tho preceding explanation : 6 9 15 4 45 53 54 6) 66 (2.) 2221 1234 4321 2221 4442 8884 8884 9. 99999 X 999 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. 341 multiplicand the 4 or right-hand figure under the figure 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 14046 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 lino ono figure to the right of the preceding line. to make himself familiar with the process of multiplying any Thus, in multiplying 2221 (1.) 2221 number by one figure, by means of the following by 1234, we may proceed as 2221000 (1.) Multiply 83 by 7; 549 by 5; 6879 by 9 ; 7891011 by 8; figure of the multiplier ; or beginning with the left-hand 444200 567893459 by 3; 9057832917 by 11, and the result by 7. 6663 66630 (2.) Find the continued product of 1, 2, 3, 4, 5, 6, 7, 8, 9. we might, to avoid confusion, (3.) Find the products of the number 142857 by the nine digits. operation (2), and proceed in reverse the multiplier, as in (4.) Find the products of the number 98998, the smallest num. 2740714 2740714 ber contained in the second square in Ex. 4, page 23, by the nine which we omit in practice are added in the last operation, to the same way. The ciphers digite, and you will find these products in the same table. (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. 5875 4. 900195 7. 1967311 10. 20907683 1. 463 X 45 18. 1534693 x 4762 2. 63294 5, 354764 8. 4192093 19. 142857 X 70000 3. 82563 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 X 20202 1. 42937 4. 323599 7. 9988776 10. 19977991 5. 75 x 42 x 56 22. 98548050 X 97280 2. 34012 5. 765102 8. 4039007 11, 832159-16 6. 84 X 37 X 69 23. 53600000 X 75300 3. 896-15 6. S58455 9. 2595139 12. 18671868 7. 7198 x 256 25. 99999999 X 90009 (8.) Multiply the following numbers first by 6 and then by 7: 8. 93186 X 445 25. 6785631090 X 1000000 26. 9959925683 X 7060301 1. 51785 4. 839769 7. 9611437 10. 73689202 10. 7422153 X 468 27. 7684329009 X 100007 2. 49333 5. 467458 8. 3902914 11. 12345678 11. 76854 X 800 28. 1428573893 X 987654 3. 36523 6. 370223 9. 7856374 12. 9122334 12. 90763 x 700 29. 9698596985 X 2168103 (9.) Multiply the following numbers first by 8 and then by 9 :- 13. 3854 X 3854 X 3854 30. 14285714257 X 7965841 1. 73925 4. 995323 7. 6778899 10. 79911997 14, 9264397 X 9584 31. 10101001000 X 100101000 2. 21045 5. 201567 8. 7129305 32. 7070808090 x 90908070 3. 31698 6. 551853 9. 9315925 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? | the multiplier. (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 by 30, and by 300 successively, we shall obtain the required product. Arrange the work as in operation (1): LESSONS IN BOTANY.-II. (1.) 675 (2.) 675 SECTION II.-ON THE SCIENTIFIC CLASSIFICATION OF 337 337 VEGETABLES. 4725 = 675 X 4725 The observer who takes a survey of the various members of 20250 - 675 X 2025 the vegetable world becomes cognisant of at least one promi. 20-2500 = 675 * 300 2025 nent distinction between them. He soon perceives, that whilst certain vogetables lave flowers others have not; or perhaps, Hence 227475 = 675 x 337 227475 moro correctly speaking, if the second division really possess In working by this method it is unnecessary to write down flowers, they 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 classi. noughts 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 fox Multiplication. naturalist termed the evident flowering vegetables phænogamous, (1.) When the multiplier consists of one figure, write it down from the Greek word favouai (phai-no-mai), I appear ; or, under 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 kpuntós (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 wal by each figure of the multiplier separately, beginning with study with advantage just yet. Hereafter we shall proceed to tes units, and write the products so obtained in separate lines, explain the principles on which it was based; but in ther" |