THE ARITHMETICAL PRIMER. NEW TABLE-BOOK; OR, TABLES OF ARITHMETIC MADE EASIER, BY D. O. UNDERHILL, FORMERLY TEACHER IN FRIENDS' SCHOOL, NEW YORK.;iA N A N RW EDITION, REVIRFaD, ENLARGED, AND IMPRO'VD. NEW YORK: CHAREL21ES COLLINS, Publisher, THE BAKER & TAYLOR CO., 740 BROADWAY. PREFACE. UNDZEHILL's Nxw TABLE-BOOK, which, under one name or another, has for so many years enjoyed popular favor, is now presented to tho public in an enlarged and improved form, and in a more worthy style of typography. Alphabetical primers are no novelty; the present book, in its various editions, has been as yet the first and only attempt to produce an aritaical primer fitted to initiate the young into the mysteries of figures, and to render the subject of numbers, in their uses and application, attractive rather than repulsive to children. A number of new pictorial illustrations will be foand in the present edition. The Tables of Money, Weight, Measure, &c., have also beer Inserted in verse as well as in the standard form, in order to fix the facts permanently in the mind of the learner, so that they, either from memory or association, may be as promptly reproduced, when needed, as that universal onie which recalls the number of days in each month. It is only necessary to add that this little book is suited to the capacity of every child who is able to read, that it is designed to meet the wants of schools in every section of the country, and is equally well-adapted for home or parental instruction ZaSend, asrJdin4 to A et of CosCress, in the yew 1544, by Usins ADAM$, aod rS eated in the year 1154, by W. P. CooLsos, in the Clrk'0 05e Of oshe Dstret Ce srt for th^ Soutborn Dl)aiet of New Taok 0. C. *I,.vs, S*sa.sYwrSa, 18 Chesmbtra a., New Y]r Notation. —Table of Figures. iI~~~~A t A I I C. 1 2 3 4 5 6 7 S 9 10 ROM A N. I LL III. IV V VI. VI VIII IX, X. W RI T TE N. 2~3. 5 6 7 9 /0 O.NE Steanmship to cross the sea, I TWO Hives of honey-naking bees, E1 THRER Steamers stemming swift the tide, [II 4 FOUR [Horses saddled for a ride; IV FIVE Cows that give us milk and cream, V SIX Boys who in a hurry seem; VI SEVEI lie w ch ring a merry peal, VII EIUHT Little girls all standing still; vmI NINE Trees that in the orchard grow, IX TEN House standing in a row X __~~~~~~~~~.AVA1 6ALA6J NUMERATION o0 Roman and Arabic Figures. Roman. A-rabic. Roman. Arabic. l. One - - - 1 XXX. Thirty - - 30 II. Two. - 2 XXXI. Thirty-one- - 31 III. Three.... 3 XL. Forty - - 40 IV. Four.... 4 XLI. Forty-one. - 41 V. Five. 5 L. Fifty -.50 VI. Six -. -. 6 L. Fifty-one. - 51 VII. Seven -.. 7 LX. Sixty - - 60 VIII. Eight-.. 8 LXI. Sixty-one. 61 IX. Nine - - -. 9 LXX. Seventy - - - 70 X. Ten -. - 10 LXXI. Seventy-one - 71 XI. Eleven - - - - 11 LXXX. Eighty - - - 80 XII. Twelve - - 12 LXXXI. Eighty-one - 81 XIII. Thirteen - -13 XC. Ninety - - - 90 XIV. Fourteen - - 14 XCI. Ninety-one - 91 XV. Fifteen- - - - 15 XCV. Ninety-five - - 95 XVI. Sixteen - - - 16 XCIX. Ninety-nine - 99 XVII. Seventeen - 17 C. I hundred - - 100 XVIII. Eighteen- - - 18 CC. 2 hundred - 200 XIX. Nineteen - - - 19 CCC. 3 hundred - - 300 XX. Twenty - - 20 CCCC. 4 hundred - 400 XXI. Twenty-one - - 21 D. 5 hundred - - 500 XXII. Twenty-two - 22 DC. 6 hundred 600 XXII1. Twenty-three - 23 DCC. 7 hundred - 700 XXIV. Twenty-four- - 24 DCCC. 8 hundred 800 XXV. Twenty-five - - 25 DCCC-C. 9 hundred - - 900 XXVI. Twenty-six - - 26 M. 1 thousand - 1000 XXVI1. Twenty-seven - 27 M,DCCC,LIV. Onethousand XXVIII. Twenty-eight - 28 eight hundred and XXIX. Twenty-nine- - 29 fifty-f~ur, 1854. NoTr. —The Roman characters are seven in number —I. V. X. L. C. D. I. —nd any number may be formed by combinations of them. The repetitiou of a letter repeats its value In the number. X being ten, XX make twenty, XXX thirty, &c. A letter of less value, placed at the right-hand of one of a greater value, increases the number; placed at the left-hand, it diminishes the number. Thus, V being five, and I one, V1 Is six, and IV four; XI eleven, and IX nine, &e, The Roman mode ef numbering is now but little need 1 * Arabo being preferred for business and other purpose 47 Numeration. 1 2 3 4 5 6 7 8 9 10 How many balls are there * * ~ * ~ O * O * * in each line, counting three &* * * * * * * ways? Begin at 1, and count all around on the oult ~ S O ~ ~ * 1 aide back to 1 again, and * * * *4 * see if there are not twentyseven Then count the e w hole, and ee if there are W 0 not 55 *. Read the following numbers.:45, 78, 67, 13, 46, 79, 35, 68. 14, 80, 36, 69, 15, 48, 81, 37. 70, 49, 82, 43, 76, 17, 50, 83. 38, 18, 51, 84, 39, 72, 19, 52. 85, 20, 53, 41, 74, 87, 42, 75. 22, 55, 88, 23, 56, 24, 57, 90. 11, 44, 25, 91, 77, 26, 59, 33. 92, 66, 27, 60, 93, 32, 65, 94. NUMEBRATION TABLE. The amount expressed by figures increases from right to left, but in reading or numerating them, commence at the left hand. a 888,8 777, 66,S 5/,44,83,23,111 a s sv;-a3 t Englih mthod point off sx figures to a perod......... ___ i`.TT'4 rtiab o giAt41dition.e - _,......... 4 and I ar e 2 i and 1 are 3 i and 2 are 3 2 and 2 are 4: I and 3 are 4 2 and 3 are 5 2 I and 4 are 5 2 and 4 are 6 I and 5 are 6 2 and 5 are 7 i and 6 are 7 2 and 6 are S I and 7 are 8 2 and 7 are 9 1 and 8 are 9 2 and 8 are 10 I and 9 are 10 2 and 9 are 11 I and 10 are 11 < and 10 are 12 I and 11 are 12 1 and I I are 13 i and 12 are 13 2 and 12 are 1.4 3 and i are 4 and 1 are 5. 3 and 2 ar e 5 1-.id 2 are 6 3 and 3 are 6. a nd 3 are 7 3 and 4 are 7 4 and 4 are 8 3 anud 5 are 8 4 and 5 are 9 3 and 6 are 9 4 apd 6 are 10 3 and 7 are 10 4 and 7 are 11 3 and 8 are 11 4 and 8 are 12 3 and 9 are 12 4 and 9 are 13 a 3 and 10 are 13 4 and 10 are 14 3 and 11 are 14 4 and 11 are'15 3 atnd 12 are 15 4 and 12 are 186 3 and 1 are 6 6 and 1 are 7; and 2 are 7 6 and 2 are 8 Z i ed 3 are 8 6 and 3 are 9 5 and 4 are 9 6 and 4 are 10 5 and 5 are 10 6 and 5 are 11 5 and 6 are 11 6 and 6 are 12.5 and 7 are 12 6 and 76 are I3 5 and 8 are 13 6 and 8 are 14 S5 and 9 are 1 4 6 and 9 are 1:, 5 and 10 are 15 6 and 10 are 1: 5 and 11 are 6 6 and 11 are 17 5 and 12 are.. 6 and 12 are 18 Ta le of Addltion.-CoNrTUrT-0-D. 7 anda AZ re 8 1 8 and I are 91 7 and'2 are 9 8 and 2 are 1O 7 and 3.are 10 8 and 3 are 11 7 and 4 are 11 8 and 4' are 12 7 and 5 are 12 8 and 5 are 13 7 and 6 are 13 8 and 6 are 14 7 and 7 are 14 8 and 7 are 15 7 and 8 are 15 8 and 8 are 16 O 7 and 9 are 16 8 and 9 are 17 7 and 10 are 17 8 and 10 are 18 7 and 11 are 18 8 and 11 are 19 7 and 12 are 19 8 and 12 are 20 9 and 1 are 10 10 and I arle 11 9 (;nd 2 are 11 10 and 2 are 12 9 and 3 are 12 10 and 3 are 13 9 and 4 arel3 13 0 and 4 are 14 9 and 5 are 14 10 and 5 are 15 9 and 6 are 15 10 and 6 are i 9 and 6 are 16 10 and 7 are ef 9 and 8 are 17 1 0 and 8 are.S8 9 and 9 are 18 10 and 9 are -1 9 and 10 are 19 10 and M10 are 20 9 and 11 are 20 10 and 11 a:roe 2, 9 and 12 are 21 10 and 12 are 2 11 and 1.are 12 12 and I a-re 1t 11 and 2 are 13 12 and 2 are 14 11;and 3 are 14 12 and 3 are 15 11 and 4 are 15 12 and 4 are 1 t 11 and 5 are 16 12 and 5 are 17 11 and 6 are 17 12 and 6 are 18 11- and 7 are 18 12 and 7 are 19 11 and 8 are 19 12 and 8 are 20'i1 and 9 are 20 12 and 9 are 21 t and 10 are 21 12 and 10 are 22 an 1.1 are 22 12 and 11 are 23..,nd. 12 are 23 12 and 12 are 24 -is.,@K< M -r —- o < _ _ _ a~~~~~~~~~~~~~~~~ Addition in lRhyme. Two pennies had John, His sister had 1, t They gave them to me, And then I had 3, Thus you may see, That 2 and 1 make 3. Two apples had Jane, And Mary 2 more, They gave themi to Sarah, And then she had 4; Thus, 2 and 2 are 4, we know, Th ie apples -.2,ke it plainly so. James hate 2 pears we see, Then auppose I give him 3,.......... ow many will tnere be I 2 and 3 are 5 we know, ~ ii 8So 3 and 2 fot 5 must g,4, Look in the tablo and find it so. ii Margaret had a pincushon, | I'/'/ Presented by her mother, i It had 5 pins upon ohoe die, And 4 pins on the otherOn the little velvet ball, -How many pins were there i r}t t'! 5 and 4, as 9 we view,'"j ~:'~'~?:'"'" And 4 and 5 are 9, as true,,' 2._ -- The table will say the sarne to you. I.=_a__ sk~" 98~' Subtraction Table. 1 from 1 leaves 0 4 from 4 leaves 0 1 from 2 leaves 1 4 from 5 leaves 1 1 from 3 leaves 2 4 from 6 leaves 2 1 from 4 leaves 3 4 from " leaves 3 1 from 5 leaves 4 4 from 8 leaves 4 1 from 6 leaves 5 4 from 9 leaves 5 I from 7 leaves 6 4 from 10 leaves 6 1 from 8 leavAs 7 4 from 11 leaves 7 1 from 9 leaves 8 4 from 12 leaves 8 I from 10 leaves 9 4 from 13 leaves 9 1 from 11 leaves 10 4 from 14 leaves 10 1 from 12 leaves 11 4 from 15 laves 1, 2 from 2 leaves 0 5 from 5' leaves "0 2 from 3 leaves 1 5 from.6 leaves' I 2 from 4 leaves 2 5 from'7 leaves 2 2 from 5 leaves 3 5 from 8 leaves 3 2 from 6 leaves 4 5 from 9 leaves 4 2 from 7 leaves 5 5 from 10 leaves 5 2 from 8 leaves 6 5 from 11 leaves 6 2 from 9 leaves 7 5 from 12 leaves 7 2 from 10 leaves 8 5 from 13 leaves 8 2 from 9i leaves 9 5 from 14 leaves 9 2 from 12 leaves 10 5 from 15 leaves 10 2 from 13 leaves 11 5 from 16 leaves 11 3 from 3 leaves 0 6 from 6 leaves 10 3 from 4 leaves 1 6 from 7 leaves 1 3 from 5 leaves 2 6 from 8 leaves 2 3 from 6 leaves 3 6 from 9 leaves 3 3 from 7 leaves 4 6 from 10 leaves 4 3 from 8 leaves 5: 6 from 11 leaves 5 3 from 9 leaves 6 6 from 12 leaves 6 3 from 10 leaves 7 6 from 13 leaves 4 3 from 11 leaves 8 6 from 14 leaves 8 3 from 12 leaves 9 6 from 15 leaves 9 3 from 13 leaves 10 6 from 16 leaves 10 3 from 14 leaves 11 6 from 17 leaves 11 Subtraction Table.-CoNT UnmED. 7 from 7 leaves 0 10 from 10 leaves 0 7 from 8 leaves 1 10 from 11 leaves i 7 from 9 leaves 2 10 from 12 leaves 2 7 from 10 leaves 3 10 from 13 Cleaves 3 7 from 11 leaves 4 10 from 14 leaves 4 7 from 12 leaves 5 10 from 15 leaves 5 7 from 13 leaves 6 10 from 16 leaves 6 7 from 14 leaves 7 10 from 17 leaves 7 7 from 15 leaves 8 10 from 18 leaves S 7 from 16 leaves 9 10 from 19 leaves 9 7 from 17 leaves 10 10 from 20 leaves 10 7 from 18 leaves 11 10 from 21 leaves 11 8 from 8 leaves 0 11 from 11 leaves 0 8 from 9 leaves 1 11 from 12 leaves I 8 from 10 leaves 2 11 from 13 leaves 2 8 from 11 leaves 3 11 from 14 leaves 3 8 firom 12 leaves 4 11 from 15 leaves 4 8 from 13 leaves 5 11 from 16 leaves 5 8 from 14 leaves 6 11 from 17 leaves 6 8 from 15 leaves 7 11 from 18 -leaves 7 8 from 16 leaves 8 11 from 19 leaves 8 8 from 17 leaves 9 11 from 20 leaves 9'8 from 18 leaves 10 11 from 21 leaves 10 8 from 19 leaves 11 11 from 22 leaves 11 9 from 9 leaves 0 12 from.12 leaves 0 9 from ]O leaves 1 12 from 13 leaves 1 9 from 11 leaves 2 12 from 14 leaves 2 9 from 12 leaves 3 12 from 15 leaves 3 9 from 13 leaves 4 12 from 16 leaves 4 9 from 14 leaves 5 12 from 17 leaves 5 9 from 15 leaves 6 12 from 18 leaves 6 9 from 16 leaves 7 12 frdon 19 leaves 7 9 from 17 leaves 8 12 from 20 leaves 8 9 from 18 leaves 9 12 from 21 leaves 9 9 from 19 leaves 10 12 from 22 leaves!0 9 from,20 leaves 11 12 firom 23 leaves 11 -,)i William had 3 peaches fair,.....: - George and Thomas each his share, One 8, the other 7; Now search the table, and yos will see, That peaches 8 and peaches 3, Make peaches just 11; Add 7 peaches to 11, as the table shows, And you'll have just 18, so the story' goes. Subtraction in Rhyme. Three apples on a table li1e, i And Jane takes one in passing by; How many does she leave I I from 3 leaves 2, So says the table true; And 2 from 3 leaves 1, When the work is rightly done And so must all believe. [ _'-e.jiii!' "j~;lJ' Charlotte had 11 pins, And gave Eliza 4; Then all she had remaining Were 7 and no more. 4 and 7 make 11, Then 4 from 11 leaves 7, And 7 from 11, four. Peter has just 18 plums, And gives his sister 10,,r~~~ * ~As gaily in the room he conmes; Hlow many has he then' The table makes it cleai and straight, That 10 from 18 leaves just 8; <-1?~~ i;And 8 from 18, ten8 plums are left,'tie plain as day. From 18 plums take 10 away, Table of Multiplication. 2 times 1 are 2 5 times 1 are 5 2 times 2 are 4 5 times 2 are 10 2 times 3 are 6 5 times 3 are 15 2 times 4 are 8 5 times 4 are 20 2 times 5 are 10 5 times 5 are 25 2 times 6 are 12 5 times 6 are 30 2 times 7 are 14 5 times 7 are 35 2 times 8 are 16 5 times 8 are 40 2 times 9 are 18 5 times 9 are 45 2 tirues 10 are 20 5 times 10 are 50 2 times I1 are 22 5 times 11 are 55 2 times 12 are 24 5 times 12 are 60 3 times 1 are 3 6I times I are 6 3 times 2 are 6 6 times 2 are. 12 3 timles 3 are.) 6 times 3 are 18 3 times 4 are I ti mes 4 tire 4; 3 times 5 are I 6 times 5 atre 0 3 times 6 are.. 6 timines 6. 36 3 times 7 are tines 7 are 4 3 times S are 1. times 8 are 48 3 times 9 are 2 6, 6; tinrle 9 ure 4 3 times 107 are'3 i4 tinmes 10- are 60 3 times 11 aie q | t8 times I] a re 66 3 times 1 2 are 36 6 times 12 are 72 4 times I are 4 7 times I are 7 4 times 2 are 8 7 times 2 are 14 4 times 3 are 12 7 times 3 are 21 4 times 4 are 16 7 tiriles 4 are 2t 4 times 5 are' (` 7 timles i5 are 35 4 times 6 are 24 7 times 6 are 42 4 ti es 7 are 28 7 times 7 are 4 i 4 t;imes 8 are 32'7 times 8 are 1 4 ti imes 9 are 36 7 times 9 are 24. 4 timres 10 are 40 7 times 10 are 70 4 t imes 1 are t 7 times 6I. are 477 4 times 12 are 48 7 timnes 12 a12 ri: 12 Table of HItURiplicationD. —Co NThrUED. 8 times 1 are 8 11 tilmee 1 are 11I 8 times 2 are 16 i 1i times 2 are a22 8 times 3 are 24 I1 times 3 are 33 8 times 4 are 32 11 times 4 are 44 i!8 times 5 are 40 1 1 times 5 are 55 8 times 6 are 48 11 times 6 are 66 8 tim3es 7 are 56 l1 times 7 are 77 0 8 times 8 are 64 11 tinles 8 are 88 i i 8 times are 72 1 times 9 are 72 11 tins a 8 times 10 are 80 11 times 10 are 110 8 times 11 are — S8 11 times 11 are 121 8 times 12 are 96 11 tines 12 are 132;, 9 times I ar 9 12 times I are 12; 9 times 2 are 18 1 12 times'2 are 24 5 times 3 aL-e 27 12 tiines 3 are 36 ] 9 times 4 are 36 12 timles 4 are 48 9 tim;es 5 avrc 45 12 times 5 are 60 9 t,inles 6 art, 54 i2 times 6 are 72 i! -9 times 7 ar', 63 12 timer;, 7 are St i9'im~les 8.tare 7I:712'timles 8 are 96 tim~es 59 are 81 12 times 19 ~are zi, 9 time's l0 are 80 12 times.. i zl I 20 g 9 times 11 are 99 12 times 1. are 13'1 9 tines 12 are 99 12 times,2 are 132 10 times 1 are 10 1]3 time~s.r. e 13 F 10 tkiaes 2 are 20 1. times 2 are I,. re 10 times 3 are 30 13 tim es are:39 10 times 4 are 40 13 timec& 4 are 52 F 110 times 5 are.50 13 times 6 are 65 10 times C are 60 13 ti-mr. are 78 10 times 7 are 70 13 timnes 7 are 91 10 times, 8 are 80 13 timern 8 ir, - iO0 10 times 9 are 90 13 ti'mes 4e ar e 11 10 times 10 are 100 13 ti-mes 1 are 1 3 10 times 11 are 110 13 times 1i are. i 1 times 12 are 120 13 times 12 are I 91;i 0gte M.lultiplication in Rhymne. Samuel has 2 knives, And Moses twice the same;.... " How many then for Moses, "s'~ t,[t W Ought we to name Twice means as many more, Then Moses must have 4; Twice 1 are 2, Says the table to you: And twice 2 are 4, It says furthermore. "~:'..... Amelia has 2 r-'ses, And Frances has 2 more, Miss Helen has another 2, To add unto the 4 — And 4 and 2 are 6 we call, The number which tt;ey lad in all s So 3 times 2 are 6 we soe, And 6 we say for 2 tnimes 3. Four boys at marbles play, - A And each has 5 t';ey eay; 6' ]'; How many marbbios I'amvo they all' +';t' Can any one tile number call? Yes, 5 and 5 we know are 10, Two other fives the, same again; And then 2 tens are 20; So 4 times 5 do 20 make, _ ___- -';And here are marbles plenty Division in Rhyme. —: Since 2 ones make 2 we know, Then 2 but once in 2 will go I'5 - Thus the father doth divide 2 apples, one to either side, Which 2 good children share As you can see them there. 14 Division Table. I in 2 goes 2 times 4 in 8 goes 2 times 1 in 3 goes 3 times 4 in 12 goes 3 times I in 4 goes 4 times 4 in 16 goes 4 times 1 in 5 goes 5 times 4 in 20 goes 5 times 1 in 6 goes 6 times 4 in 24 goes 6 times I in 7 goes 7 times 4 in 28 goes 7 times 1 ii; 8 goes 8 times 4 in 32 goes 8 times 1 in 9 goes 9 times 4 in 36 goes 9 times I in 10 goes 10 times 4 in 40 goes 10 times 1 in 11 goes 11 times 4 in 44 goes 11 times 1 in 12 goes 12 times 4 in 48 goes 12 times 1 in 13 goes 13 times 4 in 52 goes 13 times 2 in 4 goes 2 times 5 in 10 goes 2 times 2 in 6 goes 3 times 5 in 15 goes 3 times 2 in 8 goes 4 times 5 in 20 goes 4 times 2 in 10 goes 5 times 5 in 25 goes 5 times 2 in 12 goes 6 times 5 in 30 goes 6 times 2 in 14 goes 7 times 5 in 35 goes 7 times 2 in 16 goes 8 times 5 in 40 goes 8 times 2 in 18 goes 9 times 5 in 45 goes 9 times 2 in 20 goes 10 times 5 in 50 goes 10 times 2 in 22 goes 11 times 5 in 55 goes 11 times 2 in 24 goes 12 times 5 in 60 goes 12 times 2 in 26 goes 13 times 5 in 65 goes 13 times 3 in 6 goes 2 times 6 in 12 goes 2 times 3 in 9 goes 3 times 6 in 18 goes 3 tirmes 3 in 12 goes 4 times 6 in 24 goes 4 times 3 in 15 goes 5 times 6 in 30 goes 5 times 3 in 18 goes 6 times 6 in 36 goes 6 times 3 in 21 goes 7 times 6 in 42 goes 7 times 3 in 24 goes 8 times 6 in 48 goes 8 times 3 in 27 goes 9 times 6 in 54 goes 9 times 3 in 30 goes 10 times 6 in 60 goes 10 times 3 in 33 goes 11 times 6 in 66 goes 11 times 3 in 36 goes 12 times 6 in 72 goes 12 times 3 in 39 goes 13 times 6 in 78 goes 13 times Division Table.-CoNTtuMvD. 7 in 14 goes 2 times 10 in 20 goes 2 times 7 in 21 goes 3 times 10 in 30 goes 3 times 7 in 28 goes 4 times 10 in 40 goes 4 times 7 in 35 goes 5 times 10 in 50 goes 5 times 7 in 42 goes 6 times 10 in 60 goes 6 times 7 in 49 goes 7 times 10 in 70 goes 7 times 7 in 56 goes 8 times 10 in 80 goes 8 times 7 in 63 goes 9 times 10 in 90 goes 9 times 7 in 70 goes 10 times 10 in 100 goes 10 times 7 in 77 goes 11 times 10 in 110 goes 11 times 7 in 84 goes 12 times 10 in 120 goes 12 times 7 in 91 goes 13 times 10 in 130 goes 13 times 8 in 16 goes 2 times 11 in 22 goes 2 times 8 in 24 goes 3 times 11 in 33 goes. 3 times 8 in 32 goes 4 times11 in 44 goes 4 times 8 in 40 goes 5 times 11 in 55 goes 5 times 8 in 48 goes 6 times llin 66 goes 6 times 8 in 56 goes 7 times 11 in 77 goes 7 times 8 in 64 goes 8 times 11 in 88 goes 8 times 8 in 72 goes 9 times 11 in 99 goes 9 times 8 in 80 goes 10 times 11 in 110 goes 10 times 8 in 88 goes I1 times I in 121 goes 11 times 8 in 96 goes 12 times 11 in 132 goes 12 times 8 in 104 goes 13 times 11 in 143 goes 13 times 9 in 18 goes 2 times 12 in 24 goes 2 times 9 in 27 goes 3 times 12 in 36 goes 3 times 9 in 36 goes 4 times 12 in 48 goes 4 times 9 in 45 goes 5 times 12 in 60 goes 5 times 9 in 54 goes 6 times 12 in 72 goes 6 times 9 in 63 goes 7 times 12 in 84 goes 7 times 9 in 72 goes 8 times 12 in 96 goes 8 times 9 in 81 goes 9 times 12 in 108 goes 9 times 9 in 90 goes 10 times 12 in 120 goes 10 times 9 in 99 goes 11 times 12 in 132 goes 11 times 9 In 108 goes 12 times 12 in 144 goes 12 times 9 in 117 goes 13 times 12 in 156 goes 13 times 16 Harriet has 4 oranges, For little Jane and Mary, In equal share, each has a pair, The numbers do not vary. And thus we see Division true; Both have the 4, and each has 2; 2 twos are then in four we know, And 2 in 4 will 2 titnoq go. Six large apples Henry had, To, give to Silas, John, and I Thomas, And 2 he gave each little lad, According to his promise; And as he dealt them round, 3 twos in 6 were found; 80 2 in 6 will 3 times go, Then 3 in 6 goes twice we know. A teacher had just 20 toys, 1- F -- sI~tI 71To give to 4 good little boys, l He would the fives in 20 teach, e And so he gave 5 toys to each, 4 fives in 20 thus he shows, And then 5 fours, as each boy knows; So 5 into 20 will go 4 times, And 4 into 20 go 5, correctly chimes; The table will show you the truth of the rhymes. The Uses of the Tables. Notation writes the figures down, Adds much with little labor, And VNtineration reads them- And with two numbers makes a Addition makes two numbers one, third, And more so, when it needs A far superior neighbor. them. Dwiision with two numbers shows Sabtraotiou of two numbers makes How many times attaining, A third-as you have seen them- The less one in the larger goes, The smaller from the larger takes, And what there is remaining. And shows the odds between them, The large squarn table at a view, Multipicstions, in a word, Will show what each and allcan do TABLES OF MONEY, WEIGHTS, MEASURES, ETC. 1. MIONEY. Money has various names, or rates: FEDERAL, or that of the United States, Has Eagles, Dollars, Dimes, and Cets. STERLINO, or English, which one sees In England and her colonies, Has Guineas, Pounds, Shillings, and Pence. FRENca, used in France through all her ranks, Has simDle Centimes, DCcimes, Francs 10 Cent 3 Conts so Cents t60 Cents. sO Cents. 26 Cents. FFDERAL OR UNITED STATES MONEY.-The value of this money increeses by tenis, which inakes it very sitmple and easy to reckon, and hence accounts are mostly kept in Dollars and Cents, in this country. TABLE. 10 mills m. make. -. I cent, c. 10 cents - 1 dime, d. 10 dimes -. - 1 dollar, $. 10 dollars - - eagle, E. Observe the denominations-Eagle, Z.; dollar, $; dime, da. ent,. mill, m. __=cents -, 1 dime, co The mill is not a coin, and is only used in counting. Beside money made of silver, gold, ind copper, there ale also pieces of ornamented paper representing money, upon which are printed sums from one dollar to one thousand; these pass readily for what is stamped upon them for all the purposes of business. We count 10 mills to every cent, 10 cents to every dinme; 10 dimes are in the dollar spent, 10 dollars in the eagle chime, 6 _ONE pi SHRILLIN G6 Pence i Shilling. I Ssnsrsl ENGLISH OR STERLIN(G MONEY.-This currency is used in England and the British colonies. TABLE. 4 farthings, qr., make - - 1 penny, d. 12 pence - - - 1 shilling, a. 20 shillings - - - 1 pound, ~. 5 shillings - - - 1 crown, c. 20 shillings - - 1 soveeign, sot 21 shillings - - - 1 guinea, 0. Observe the denominations-Pound, ~; shilling, a. penec, d.; farth Ing, qr.; from the Latin words, ibra, a pound; solidu, a shilling; denarius, a penny; 1usdrana, a farthing. Farthings are marked in fractions thus: —, one farthing, i, two farthings, or half-penny; f, three farthings. The sovereign, which is made of gold, is of the same value.s he pound. Whatever costs a pound, therefore, a sovereign wil, pay for. There is no coin called a pound. 4 farthings make one English penny; 12 pence are in one shilling found: While 21 shillings make one gusnei, And 20 shillings form one pound. 5 shillings make a silver erowtn, & o wereign is a golden pound. 1 9 3 5 Ceantimes I Franc. 5 France. FRIENCH MONEY.-This money is need in France, and also in the French colonial possessions to some extent. TABLE. 10 centimes,* c., make - 1 d6cime, d. 10 d/cimes,t. - 1 franc,t fr. Observe the donominations-Franc, fr.; deimrne, d.: centime, e. The five-franc piece is frequently met with in this country, and passes currently at 94 cents. Coins of a less number of h-ancs, pass also at the rate of 19 cents to the franc. 10 centimes in one dlcime meet, 10 decimes make one frane complete. FEDERAL and F- efNCH are decimal, They count by te, alone: Of coins it alwav take 10 small To make the next larger one. The ENGLISH currency,'tis thought, To the same standard will be brought. The guinea then no more we'll see, The Found 1000 mills will be; And all the lower coins will range, In just accordance with this change. TaoT WEIGHT of silver and gold disposesAPOTHECARIES' WEIGHT is for doctors' doses t Whatever else your trade employs, Comes under the rule of AvolRDUPoro. ~ Pronounced Aonim. t Pronounced daeasse. I Pronounced frauag, or frank.'9616i~~~~~~~~~ TROY WEIGHT-Is used to weigh Gold, Silver, Jewels, and Liquors. TABLE. 24 grains, Ar,, mako 1 pennyweight, dwt. 20 pennyweights. ~ 1 ounce, oz. 12 ounces -. 1 pound, lb. Observe the denominations-Pound, lb.; ounce, oz.: pennycoight, d. grain, gr. This rule for weighing gold, will state That 24 grain8 make one pennytweig/ht: And 20 pennyweights in an ounce are found, While 12 good ounces make a pound. APOT ARIES' WEIG}HT.-Is used in mixing doses of medicine, but drugs and medicines, like most other merchandise, are bought and sold by AvoIaDUPOIS WEIGHT. TABIL 20 grains, gr., make 1 scruple, 3 3 scruples - 1 drachm, 3. 8 drachms.. ounce, 12 ounces I. 1 pound, b. Observe the denominations-Pound,!b.; ounce, 3.; drachm, 3. scruple, 9., grain, gr. In mixing doses, Doctors say That 20 grainr one scruple weigh; 2 scruples make one drachm they held, 8 drachms are to the ounce enrolled, And ounces 12 for a pound are sold. AVOIRDUPOIS WEIOHT-Is used in weighing all coarse taid heavy good, groceries, &c.; and all metals except silver and gold. TABLE. 16 drachms, dr., make - I ounce, oz. 16 ounces 1 pound, lb. 25 pounds - 1 quarter, qr. 4 quartcr, -, 1 hundredweight, tw. 20 hundred weight - 1 tun, T f~~~~~~~~~~~~~~~~~~~~ll~~~~~~~~~~~~~~~~~~ Observe the denolnitntious-Tuln, T.; hundred weight, coa.; quarter, fr.; pound, lb.; ounce, oz.; drachm, dr. 2000 pounds make a tun in the table; when, as it sometimes is, it is 2240 lbs., 28 pounds make a quarter. Except in special cases, the tun is now regarded as 2000 pounds by the principal merchants of our cities. 16 drachms make one ounce, -16 ounces make one pound, 25 pounds one quarter counts, 4 quarters make a hundred round; And 20 hundred weight are run, To make a full and perfect tun.'Twas once absurdly held and said 112 pounds make a hundred weight; And then this table always read, That a quarter hundred was 28 By different measures, we obtain Due quantities of wood or grain, Of cloth, or land, or wine, and tell How much of each we buy or sell. CLOTH Ma.ASURE is for ribbor.s, tapes, And clotlih, and( silk, for coats or capes. LoN.O MASURFst serves to tell and trace The distarnces from place to place. 8PRVEYORS' M:EASURES, understand, Are only used in measuring land. DRaY MLEASURE tells how much we gain Of salt, coal, fruit, potatoes, grain; While LIQUID MEASURE justly classes Wine, spirits, beer, oil, milk, molasses. SqUARE MEASURE deals with surfaces, As walls, and floors, and fields, and seas; And CuBIc MEASURE ascertains What any solid shape containAs. TIMrE MEASURrE tells us, as they fly, How days, months, years, are rushing by; And CIRCULAR MEASURE shows the worth Of lines that circle round the earth, And of the bands which reason's eye Traces across the glittering sky. 22 1. MIASURZ OF L NoT H. CLOTH MIASURE-Is used to measure Cloths, Ribbons, Tapes,,o. TABL2. 2j inches, in., make - - 1 nail, n. 4 nails - - - 1 quarter of a yard, qr. 4 quarters - 1 yard, yd. FOREIGN CLOTH MEASURES. 2j quarters, make - - I ell Hamburgh, E. H. S quarters - - 1 ell Flemish, E. F. 5 quarters - 1 ell English, E. E. 6 quarters - 1 ell French, E. Fr. Observe the regular denominations- Yard, yd.; quarter, qr.; nail,. t inch, in. In measuring cloth for use or sale, 21 inches make one nail; 4 nails one qzarter we regard, And four full quarters make one yard. Nails now are seldoml used, we've heard, Eighths and sixteenths are much preferred. L0ONG MEASURE-la used to measure distances, and to ascertala the length of anything without regard to breadth. TABLX. 10 lines, 1., make. 1 inch, ts. 12 inches - -. 1 foot, ft. 3 feet.1 yard, yd. 54 yards. 1 rod or pole,p. 40 poles, or 220 yards I furlong, fur. 8 furlongs.. 1 mile, M. 3 miles - - - 1 league, L. 60 geographic, or 69J statute miles 1 degree, Deg. 360 degrees - the circumference of the earth. Obserre the denominlations-Dlgr, Dcg.; leasgut, L.; mile, M., furlong, fur.; rod, or pole, p.; yaird, y,. foot, ft.; inch, E. I lnao, L,' Twelve lines make an inch in France. In measuring the height of horses the hand, 4 inches, is used; and in measuring the depth of water, the fathoen, 6 feet, is used. In measuring distances or lengths, 10 lines are said to make one inck; 12 inches make a perfect foot, 3 feet into a yard are put; 5i yards make a rod or pole, And 40 rods a furlong whole; 8 furlongs make a msle quite big, And 3 full miles make up a league. In measuring round the earth, we see, That 60 miles make one degree; Degrees 360, then, The earth's circumference will span. STRVIEYOR'S KEASUREI.-This measure is used in aseortatnlng the alength and breadth of land, roads, &c. TABLU. 7 92-100 inches, in., make - 1 link, 1. 25 links -- - 1 pole, p. 4 poles, or 100 links 1 chain, e. 10 chains -.. 1 furlong,fur 8 furlongs - - - i mile, M. Observe the donominations-Link, i.; pole, p.; chain, c.; furlong, /fr.; mile, M. 7 inches and ninety-two hundredths, make One link in the chain surveyors take, 100 links his chain embraces, With 80 chains one mnile he traces. 2. MXASURtsz OF CAPACITY. LIQUID ]EASUR —Is nsed In measuring Wine, Spirits, heer, Oil, Vinegar. Milk, Molasses, &c. TABL.]" 4 gills, g., make - 1 pint, pt. 2 pints. 1 quart, qt. 4 quarts... 1 gallon, gal. 31k gallons.1 barrel, bbl. 2 barrels - - 1 hogshead, hid. 2 hogsheads - 1 pipe, p. 2 pipes - - 1 tun, t. Observe the regular denominations-Tun, t.; pipe, p.; hogshead, kAd. I barrel, bbl.; gallon, gal.; quart, Mq.; pint, pi.; gill, g. 24 MEASURES O CALPACITY SELDOM USED. TABL. 9 gallons, g., make - 1 firkin,f. 10 gallons - - - 1 anker, a. 2 firkins, or 18 gallons - 1 kilderkin, k. 2 kilderkins, or 36 gallons 1 barrel of beer, &e. bbl. 1 j barrels, or 54 gallons - 1 hogshead of beer, Ad. 42 gallons 1 tierce, t. 2 tierces, or 84 gallons - 1 puncheon, p. Most liquids are now sold by the gallon, quart, and pint, and not by the other denominations of liquid measure; in fazt, vessels are rarely made to hold the exact quantities stated in the table, and frequently retain the names though containing much more, the hogshead and barrel for instance. In measuring liquids, first we take 4 little gills one pint to make; 2 pints then make one quart, and still 4 quarts the gallon measure fill. Gallons one half and 31, Will fill a barrel to the bung. 2 barrels to the hogshead go, 2 hogsheads fill a pipe, and so 2 pipes will near a tun o'erflow. Though many good things aret measured still By gallon, quart, and pint, and gill, Yet Liquid Measure oft seems to me " The measure of human misery." For 0, what countless evils come From brandy, whiskey, gin, and rum, Which it were better ne'er to touch, For a single drop is " a drop too much." DRY M[EASURE —I used in measuring Grain, Potatoes, Fruit, Goal, 4 8slt, Seads, &c. TABLE. 2 pints, pt., make - 1 quart, q. 8 quarts * 1 peck, p. 4 pecks 1 bushel, bush. 36 bushels 1I chaldron of coal, ciat. 8 bushels - - 1 quarter of corn, qr. Observe the regular denominatlons-Chaldron. chal i bushel, buad I peok, p.; quart, qt.; pint, pi. 25 2 pints DRY MLtIsuaz make one quart, 8 quarts one honest peck containis, 4 pecks are in a tuehel brought; 8 bushels, if you are measuring graitn Are to the quarter# counted out; But if bituminous coal,t you take Then 6 and 30 bushels make The chaldron, which in trade obtains. 3. Xxs URES oF CONT T. LAND OR SQUARE MEASURE —Is. used in reckoning th eons. tents of any surface by its length and breadth. TABLE. 144 square inches, a. in.,make 1 square foot, S. F. 9 square feet - - 1 square yard, S. Y. 30* square yards - 1 square rod, pole, or perch, S. P. 40 square poles-. 1 square rood, S. R. 4 square roods 1 square acre, S. A. 640 square acres - - square mile, S. M. Observe the denominatoans-Square mile, S. M.; square acrae, 3 A., square rood, S. It; square perch, S. P.; square yard, S. Y.; square foot, 8. F.; square Inch, S. I. Square inches one hundred and forty-four Make one square foot, and nothing more. 9 square feet make one square yard, 30 yards and a quarter are one pole aqiu-rtd; 40 square poles make one square rood, Yet 4 square roods make an acre good; And acres 640 the while, Are wanted to make up one square mils. SOLID OR CUBIC MEASTJRE-Is used to reakoa the contents of anything by its length, breadth, and depth. TABLE. 1728 solid inches, J. in., make 1 solid foot, S F 50 feet of hewnd, } timber 1tun, Tun. 27 solid feet - 1 solid yard, S. Yd. 16 solid feet of wood - 1 cord foot of wood, Ft. IF 8 cord feet of wood - 1 cord, C. Observe the denominations-Cord, C.; cord foot of wood, at. F., solid yard, S. I.; solid foot, S. F.; smlid inch, S. L * Wheat is measured in Great Britain by the quarter of 480 Ibs. i Bituminous, or soft coal, is sold by measure, and anthracite, or hard soal, by weight. One thousand seven hundred and twenty-,ight Inches one solid foot complete. In timber, 40 feet, if round, Or 50 hewn, a tun is found. In measuring ships the rule must run, Feet 2 and 40 make a tun. Feet 27 one solid yard we rate, A cord of wood one hundred twenty-eight. 4. M DURTION ND CIRCULAR DSTACE 4. IetSURES oF DURATION AND CIRCULAR DISTANCES. TIME MESU8RE-la used in computing the different periods in which any transactionl or event occurs. TAk.LI 60 seconds. sec., make 1 minute, m60 minutes. 1 hour, A. 24 hours - I day, d. 7 days... 1 week, to. 4 weeks. 1 month, mo. 12 months -... 1 year, yr. 100 years... 1 century, C. Observe the denominations - Century, 0.; year, y.; month, mno. week, so.; day, d.; hour, 4.; minute, s.; second, sea. 12 calendar months, or 13 lunar months, 1 day, ard 6 h6urs, or 365 days, 6 hours, 1 common, or Julian year. The year is divided by the calendar as follows: — 1st month, January, has 31 7th month, July, has 31 2d " February, 28 8th " August, 31 3d " March, 31 9th " September, 30 4th " April, 30 10th " October, 3 5th M May, 31 1 lth " November, 30 6th ~ June, 30 12th " Docembr, 31 181 365 February has 29 days every fourth year. which is called Bissextile, or Leap Year. Every Leap Year may be divided by 4 without a remainder; other years, divided by 4, leave one, which shows their number after Leap Year. Thus, 1854 divided by 4, leaves a remainder of 2: that is, it is the second after Leap Year, &c., &c. The number of days in each month, may easily be remembered by the following verse:Thirty days have September, April, June, and November; All the rest have thirty-one, Excepting February alone, Which hath twenty-eighlt, nay more, Hath twenty-nine one year in four. There are in every year four seasons, viz: SPRING, SBulMLa, AUTUMN, and ~WINTER. The Spring months are March, April, and May. The ummtner months are June, July, and August. The Autumn months are Septemberi October, and November. The Winter months are December, January, and February. The Spring is the season of flowers; the Summer of fruits; the Autumn of the decay of vegetation and the fall of the leaf and the Winter of frost and snow. 60 econdls make 1 minute, Time enough some good to do; 60 minutes mrake 1 hour, Who will dare to waste it? 7Who? 24 hours nmake up the day, Time for work, and sleep, and play; 7 days to the week are given. Six for toil and one for heaven. God gives me six for work and play, I will not steal tihe seventh away. 4 weeks in every month appear, 12 months make up1 the rolling year; 100 years —few live them to seeAre what are called a centurv. SGCULAR MEASUREr-:s used by Astronomners, Navigators &e i making their calculations. TABL]. 60 seconds, "make - - I mirute,' 60 minutes - - - 1 degree, o 30 degrees - sig4, S. 12 signs, or 360 degrees - 1 circle of the Zodiac, C. Observe the denominations-Circle, C. i sign, S.; degree, ~; minute,'; second, I". 28 60 seconds make one minute, 60 minutes one degree: 80 degrees one sign has in it, 12.. sk bcircle 2 sgns we __In the zodiac see.'Tis knowledge gained from this, that guides The ship, that o'er the ocean rides, And shows the pilot how to steer From place to place, remote or near. -!IV. BOOKS, PAPER, AND PARCHMENT. BOOKS, PAPER, PARCHMENT, all concern M en of a literary turn: As authors, printers, and booksellers — A race of genuine clever fellows — The paper manufacturer, too, With these, of course, has much to do The stationer and binder thenknown as industrious, thrifty menBear each an honorable part In the noble, intellectual art, Of furnishing the mind and heart. 1. PAPER AND PARCHMENT TABLE OF PAPER AND PARCHMENT. -This table Is used by I'sprlnmakers, Printers, and dealers in Stationery, d&c., &c. TABLE. 24 sheets of paper, make - - 1 quire, qr. 20 quires. - 1 ream, Rm. 2 reams - 1 bundle, Bd/. 10 reams. - 1 bale, BI. 29 12 skins of parchment - 1 dozen, doz. 5 dozen 1 roll, rl. Observe the denominattons-Qutre, gr.; ream, Rm.; bundle, Bdl.; bale, Bli.; dozen, doz.; roll, rk Two dozen sheets one quire will take, And 20 quires one ream composes; 2 reams we in a bundle make, 10 bundles a full bale encloses. By dozens parchment-skins are told; 12 to the dozen, as of old; 5 dozen for a roll are sold. The different sizes of paper are-Foolseap, post, demi, medium, royal, super-royal, imperial, and elephant. Larger papers are described by their length and breadth in inches; thus, cg0 by 32, 24 by 38, 26 by 40, 29 by 44, &o., &o. 2. SIZES or BooKs. TABLE OF BOOb. —This table is used by Authors, Printers, and Bookeidlers, in ascertaining and naming the sizes of books. TAZLE. 1 sheet of paper folded into 2 leaves is a folio, Fol. 1 sheet of paper folded into 4 leaves is a quarto, 4to. 1 sheet of paper folded into 8 leaves is an octavo, 8ro 1 sheet of paper folded into 12 leaves is a duodecimo, 12mo. 1 sheet of paper folded into 18 leaves is an octodecimo, 18mo. Observe the denominations-Folio, fol.; quarto, 4to.; octavo, 8eo.; duodacimo, 12No.; octodeoimo, 18mo. Whoever with a book engages, Well knows each leaf will count 2 page.; One folio sheet 2 leaves will rate, A quarto 4, octavo 8; A duodecimno' a dozen clean, An octodecimo eighteen; Vicceimo quarto makes up twenty-fou. Tricesrameo ecundo thirty-two, no more. The duodecimo. octodecimo, viceseine quarto, and trieoesime seoundo, which are Latin numerals, are generally called l2mo., lSmo., 4rmo., and 3imo. There are also 48mo., 64mo., and 72mo. 30 1. TABLE OF WEIGHTS. A barrel of flour weighs - - 196 lbs. A barrel of beef or pork 200 " A barrel of pot ashes - 200 " A firkin of butter - 56 " A bushel of salt - - 56 " A peck of salt.....14A gallon of train oil -. 7 A stone of wire weighs 10. " A stone of sheet iron, or horseman's weight 14 " A quintal of fish - - - 100 A faggot of steel.... 120 A fother of lead. 2184 " B. TABLX OF PAITICULARS, 12 things make - dozen, dox. 12 dozen, or 144 - - 1 gross, gro. 12 gross or 1728 - 1 great gross, g. gr. 20 things..... 1 score. 5 score - - 1 hundred,?. 8. VALUE OF SIL AD GOLD COINS. s.$. An English shilling 24 " " crown. 1 20 " sovereign. 4 84 a " pound. 484 " guinea 5 00 A franc of France -.... 19 A thaler of Germany.. 67 A Spanish doubloon... 16 00 A South A-merican doubloon.. - 15 60 Four shillings and two pence sterling * 1 00 4. OLD ENGLISH 0OILL &. A groat..... 4 A tester...... 6 A noble........6 8 An angel.. 10 0 A mark... 13 4 81 6. TABLES OF ALIQUOT, OR EVEN PARTS. Being fractions or broken parts of certain things and their value. Parts of a Dollar. Parts of a Shilling. Parts of a Pound. lcentis 1 3 cts. are 5 " it" 1a d. 10" " 1 1 penny is 1 8 are 25" " - 1~ pence are 8 20 " 50.. " 2 " ". 26 " 6,21" " 3 " " d 34 " 75 " " 3 4 " " 4 40 " 87 5 " " rl 5 0 " 6 6 " " 68," 8 I 8.4 Is (,, 2 12 0 ( 9 3( cc S 13 0 " Parts of a Penny. 15 0 " I farthing is 16 0 " 2 farth's are 17 0 s 3 " " 1 18 0 " Partb of a Cwt. Parts of a 2Tnh Parts of a Year Parts of a Cwt. of 112 lb, of 2240 lbs, o 12 months. of 100 lba 4 lbs. c.. lqr. 1 mo. is llb. isTh 7 " {1 1 0 is 21 2mos. are 5 " 8 " * 2 0 are T 3.... 10 " 14" 2 2" 4" "20 16 4 0" 5 " 25 4" 28" 5 " 6 " " 50 56 " ~ 10 0" 8 " 75 " 4 84 " 15 0 t 9 " " 3 80 " - Fractions in Arithmetic are so made, that if all the parts into which a number is divided are added together, they will just equal that number; as when an apple is cut into parts of various shapes, you can join them together and form the apple again. 32 6. TABLES OF STERLING CURRENCY. Table of Shillings and Pence. Table of Shillings and Pounda a d. d.. d. S. ~ *. S..~ o. 1 is 12 20 are 1 8 20 are 1 0 140 are 7 0 2 are 24 30 " 2 6 30 " 1 10 150" 7 10 3 " 36 40 " 3 4 40 " 2 0 160" 8 0 4 " 48 50" 4 2 50" 2 10 170" 8 10 5 " 60 60 " 5 0 60" 3 0 180 9 0 8 " 72 70" 5 10 70" 3 10 190 "9 10 7 84 80" 6 8 80 " 4 0 200 " 10 0 8 " 96 90 " 7 6 90 " 4 10 210 " 10 1 9 " 108 100 " 8 4 100 " 5 0 220 " 11 0 10 "120 110" 9 2 110" 5 10 230 " 11 10 11 " 132 120' 10 0 120 " 6 0 240 " 12 0 12 " 144 130 " 10 10 130 " 6 10 500 " 25 0 METRICAL SYSTEM OF WEIGHTS AND MEASURES. WEIGHTS. The Gram is equal to 1543 grains Avoirdupois. 1 Decigram is One-tenth Gram. 1 Centigram One-hundredth Gram. 1 Millogram One-thousandth Gram. 1 Dekagram - - Ten Grams. i Hectooram One Hundred Grams. 1 Kilogram One Thousand Grams. 1 Myriagram - - Ten Thousand Grams. 1 Quintal - One Hundred Thousand Grams. 1 Millier - One Million Grams. LONG MEASURE. The Metre is equal to 393-kJ70 inches. 1 Decimetre is - - One-tenth Metre. 1 Centimetre- - - - One-hundredth Metre. 1 Millimetre - - - - One-thousandth Metre. 1 Dekanmetre - - - Ten Metres. 1 Hectometre - - - One Hundred Metres. 1 Kilometre - - - One Thousand IMetres. 1 Myriametre - - - Ten Thousand Metres. CUBIC MEASURE. The Litre is equal to 1 Cubic Decimetre, that is ao5 Quart Dry Measure, or 1Ti50 Quarts Liquid Measure. 1 Decilitre is. - - One-tenth Litre. 1 Centilitre -One-hundredth Litre. 1 Millilitre - —. One-thousandth Litre. 1 Dekalitre-. Ten Litres. 1 Hectolitre - - - - One Hundred Litres. 1 ilolitre - One Thousand Litres. 33 METRICAL SYSTEM. SQUARE MEASURE. 1 Centare is - 1 Square Metre, equal to 1550 Square Inches. 1 Are - - - 100' " " 119f-f Square Yards. 1 Hectare - -10000 " " " 24 —,a Square Acres. TABLE OF ARITHMETICAL SIGNS. + Plus, or more, meaning added to. This sign when placed between two numbers, shows that they are to be added together and considered as one number; thus, 24+36; that is, 24 added to 36, which is read 24 plus 36. [..equalitas, or equality, meaning equal to. This sign when placec between two or more numbers, shows that those which precede the sign are equal to those which follow it; thus, 24-r'-.660; that is, 24 added to 36 are equal to 60. - Minus, or less, meaning subtracted from. This sign, when placed between two numbers, shows that one is to be taken from the other; thus, 84 —42; that is, 42 is to be subtra.ted from 84, which is read 84 minus 42. X Multiplico, to multiply, meaning multiplied by. This sign placbd between two numbers signifies that one is to be multiplied by the other; thus, 24X36; that is, 24 is to be multiplied by 36, which is read 24 multiplied by 36. -+t Divido, to part, meaning divided by. This sign placed between two numbers shows that one is to be divided by the other; thus, 60+15; that is, 60 is to be divided by 15. When placed horizontally between two numbers, the one above and the other below, the dots are dispensed with; thus, i; that is, 1 divided by 2. EXAMPLES. Read the following: 72+47=119; 656+809=1465; 1400 +700-=2100; 76-38-38; 104-26=78; 290-145=145; 25 X 12=300; 99 X 9=891; 425 X 50-21250; 64-+ 8=8; 144 +12-12; 1728-+-12=144; 1728+ 144-576X12+-288 -54; 64+-8X16-128; 36X12=144X3; 600X101-30047X90+4701 4 —2X6-12. ---- Vitcwunum, or a bond of union, meaning that the numbers over whicl, it is placed, are to be considered as united or one, and to be subjected to the same operation' thus, 12+13X19. _~~~~~~~34 :::Proportio, or proportion. ThAse signs are placed between numbers to show their relation to each other, so that knowing the relation of two numbers, two others may be found that have the same relation; thus, 3: 6:: 9: 18, which is read as follows: As 3 is to 6 so is 9 to 18, because 3 is the half of 6 and 9 half of 18, theref ire the proportion of 3 to 6 is the same as 9 to 18. This sign is read thus: As, is to, so is, to. I Potentia, or power. Every number is a power, and to Increase its power you must multiply it by itself the number of times answering to the power to which you wish to mime it. The figure which expresses the power to which another is to be raised is called an exponent or index, which is a small figure placed against its right hand upper part; thus, 43; that is, 4 is to be multiplied three times by itself, or 4X4X4-64; therefore, 64 is the third power of 4, and is the same as 43. / Radix, or root, meaning that the root is to be extracted. The root of a number is such a one as multiplied by itself a given number of times will produce the number whose root is wanted. V/ means the square root, IV the cube root, 41/ the fourth root, /V the fifth root, &c.; therefore, 1/V64 shows that 8 is wanted, because 8X8-64. 5/V64 shows that 4 is wanted, because X4X4X464. 4V16 shows that 2 is wanted, because 2X2X2X2,16. sV243 shows that 3 is wanted, because 3X3X3X 3X3-=243. ILLUSTRATIVE EXAMPLES. ODD NUMBZES. Odd numbers begin with 1, and consist of every second following figure; thus, 1, 3, 5, 7, 9, 11, 13, 15, 17, 1t, sre odd numbers. Odd numbers X by odd numbers - odd numbers. Odd numbers X even numbers - even numbers. Bven numbers X even numbers - even numbers. Bven numbers +- even numbers - even numbers. Odd numbers + odd numbers even numbers. Odd canbers + even numbers odd numbers. Many of the odd numbers above 3 that can only be -,- 1, can o - 6 by subtracting I or adding 1. For instance, 13 can only be -+- 1 but 13-1 may be -s- 6, so with 17, 19, 25, &dc. WHAT IN A TRILLION? a thousand billions; written thue — 1,000,00,0009,000. But if you were to count 200 a minutes it would take you 9512 years 34 days 5 hours and 20 m;nutes to count it, which is nearly twice as long as the world has existed 35 THE NUMIER NINE. The powers of the figure 9 are more numerous and remark.. able than those of any other figure. The figures composing the product of every figure from I to 9 multiplied into 9, addod together, make xINz; thus-. * 9 9 1 4 7 9 9 36. 3+6-9 63. 6-+39 2 5 8 s18. 1+8-9 45. 4+5-9 72. 7+2-9 3 6 /9 27. 2+-7-9 54. 5+4-9 81. 8+1-9 The above multipliers ffom 1 to 9 added together=45 and 4 4-5-ixil. Their several products added together -405, which -e- 9-45 and 44-5-wNIEz. The amount of the first product (9) added to the remaining eight products (eight 9s)e81, and 8-+1,-9 and 81-9X9; 81 is therefore called the sqware of waNl. The 405 mentioned above + 81-486, and this +9=54, and 5+-4=N-INx. The number of changes that may be rung on 9 bells is 362,880, which figures added together make 27, and 7+2=-NINz. And 362,880-+9-40,320, and these figures added together make NINE. THE GAME OF CHESS. Se"ea, who invented the game of chess for an Bast Indian king, was promised in return any reward which he should ask. Understanding, better than his patron, the power of numbers, and wishing to rebuke his rashness, he asked simply for one grain of wheat for the first square on the chess-board, two for the second, four for the third, and so doubling to the sixtyfourth. The king was astonished tt the apparent smallness of the gift, but still more so, when told that the number of grains would be 18,446,744,073,709,551,615. There are in a bushel 589,824 grains of wheat, and 18,446,744,073,709,551,615 +589,824 gives 31,274,997,411,295 bushels; more than the whole surface of the earth could produce in many years, and more in value probably than the whole wealth of the globe The king, therefore, did not keep his promise' 0xoReG BIDDER. This wonderfhl boy, whose portrait is on the title-p.ts when very young and uneducated, could solve the most diffieul arithmetical questions entirely in his own mind without the use of pencil or slate, and mor quickly than any one could in the common way. A6