i^ 
 
 . -/^f 
 
GIFT OF 
 Prof. C. A. Kofold 
 
IDABOLL'S 
 
 SCHOOLMASTER'S ASSISTANT 
 
 IMPROVED.AND ENLARGED, 
 
 BKING \ VLAr:^ 
 
 PRACTICx\L SYSTEM 
 
 OF 
 
 A R I T M BI E T I C," 
 
 ADAPTED TO THE UJNJTED STATES. 
 
 BY NATHAN DAEOLL. 
 
 T%7T// TU^ ADDITION OP ^ 
 
 O - - J J 3 • " "^ " 
 
 , , ^ 'J • J o «. .- -^ • 
 
 PRACTICAL- A€eOUNT ANT ; 
 
 FARMERS' AND .MECHANICS' 
 
 BEST METHOD OF BOOK-KEEPING; 
 
 FOR THE EASY JNSTKUCTiON OF YOUTH 
 
 DESIGNED 
 
 AS A COMPANION' TO DABOLL 3 AaiTHxMETIC 
 BY SAMUEiT GREEN 
 
 STEREOTYPE PRINT, 
 
 NEIV'LONDC/N I 
 i'RlNTED A^^D PUBLISHED BY SAMUEL GREEN, 
 
 rroprUiorof the Copij-RigJif. 
 
BE IT KEMEMBERED, That on th« eleYEntb c^ a? 1^^ 
 ry, in the forty-ninth year of the ind^pendeace of thft Uni4 
 flISttes of America, Samuel Greek-, of said Distxict, b&th d^osi* 
 ted in t^U ofQce, tfee title of a book, the rig-ht where- 
 of he cla^im^ as pfpftVi^t^ro \^ the v/ords following, 
 to wit : " jBiibalrs.SchoijlmdStejr'?? Assistant ; improv- 
 ed and entarged. Being a plain practical System of 
 Arithmetic. ad*iRl«4't'0 tne Uni^t^d States. By Na» 
 thai? BafeoU.— Whh,thc addition of the: Practical Ac- 
 or yafi.n4r^'*aOijf Mechanics' bes* metljod of Book-keep- 
 ing ; for the easy instruction of youth. Desired as a Compajo* 
 ton t^Daboji's Arithmetic. By Samuel Green. Stereotype Pnnt." 
 In conformity to the act of Congress of the United States, enti- 
 tled, '* An act for the encouragement of learning, by securing th» 
 copies of maps, charts, and books to the authors and propnctora 
 ef them, during the time'^ th reia mentioned. 
 
 CHARLES A. INGERSOLL, 
 
 Clerk of the District of Connccti^ui, 
 A trttc QOpy o record. Examined and sealed by me. 
 CHARLES A. INGERSOLL, 
 
 Clerk of the Disti id of GonnecUe^g, 
 
 countant 
 
 ^ / 
 
^ 
 
 «ReOMMENT)ATI05;S, 
 
 - -^f*-- 
 
 YALE-COIXEGE, NOV, 27, 1799. 
 
 I HAVE read Daroll's Schoolmaster's Assistant. 
 The arrangement of tlie different branches of Arithmetic 
 i^ judicious and perspicuous. The author has well ex- 
 plained Decimal Arithmetic, and has applied it in a plain 
 and elegant manner in the solution of various questions, 
 and especially to those relative to the Federal Computa- 
 tion of monej. I think it will be a very useful book to 
 Schoolmasters and their pupils. 
 
 JOSIAH MEIGS, Professor of 
 Mathematics and JVdtural Philosophy^ 
 [Now Surveyor General of the United States.] 
 
 X HAVE given some attention to the work above men- 
 tioned, and concur with Mr. Professor Meigs in his opin? 
 ion of its merit. NOAH WEBSTER. 
 
 Ifew-Haven^ December 12, 1799. 
 
 RHODE-ISLAND COLLEGE, NOV. 30, 1799. 
 
 1 HAVE run through Mr. Daboll's Schoolmaster's 
 Assistant, and have formed of it a very favourable opin- 
 ion. According to its original design, I think it well 
 ^* calculated to iurnish Schools in general with a method- 
 ical, easy and comprehensive System of Practical AriUi- 
 mfitic.'* I therefore hope it may find a generous patron- 
 ^^y and have an extensive spread - 
 
 ASA MESSER, Professor of the 
 Le(irned Lan^ua^es^ and Teacher of Mathematics 
 'NRw President of that Institution.'] 
 
^ 
 
 ::0, 1802. I 
 
 ■SSTSTANT, I 
 
 -2- MAJ. -^SSTSTANT, 
 
 in teac: ^meac, :uid think it the best 
 
 calciilat ff any v/Jiich lias falleu vrithiu 
 
 my obstru-k:; JOHN AiUMS, Rector of 
 
 Fltiinfield Jlcad&my 
 rNo\v Frmcipal of Piiillips A.« :\ '■ udovet-j Mass."^ 
 
 231LLERICA ACADE^iY. ■ ' :.C. 10, ISOT. 
 
 Haying examined Mr. Da Aritli- 
 
 metic, i am pleased with the juG;^:neMt ;!i;5playe(l in his 
 method J and the perspicuitj of his explanations, and 
 thinking^ it as easy txvA comprehensive a sjsteiu as anjr 
 with which I am acquainted, can cheertiilij recommend 
 it to the natronage of Instiuclors. 
 
 SAMUEL WHITING, 
 Taacher cf Mathematics, 
 
 FR0M MR. K7-X\-r.r;Y, TF,AniJER OF MATHEMATICS. 
 
 1 BEC ■ : _ .-,. ^3 ScHooi.MAs- 
 
 TE.E.':: AssisTAN'? on examining it 
 
 attentively, gave ... . >.ce to any otlier 
 
 system extant, a i -/{A ed i t UiV^i e pupi ! s 
 
 under my chari^e ^ «*.>. .'.... ...,^^ ;L...ie havAiusW it exclu- 
 sively in elementary tuition, to tliegrcti'^ advantage and 
 improvement ol'l' '" ^^* '^ -nt, as well as the ease and as- 
 sistance of the I I also deem ^t equally well 
 calculated for the ^ . -d of individu:)' ^ in private in- 
 struction ; and think it my duty to give tlie labour and 
 ingenuity of the a.H lu r the tribute of my hearty approval 
 and recommendation. 
 
 ROGF!{ KENNEDY 
 
-i. lU'j design of tLIs work is to fun 
 tho United States with a methodical and comprehensive 
 system of Practical Jlrithmetic^ in '•* hich I have endea- 
 voure<l, through the whole, to have the rules as concise 
 and fiimiliar, as the nature of the subject will permit. 
 
 During the long period which I have devoted to the 
 instruction of youth in Aritlimetic, I have made use ot 
 various systems which have just claims to scientific mer- 
 it ; but the authors appear to have been deficient in an 
 important point — the practical teacher's experience. — 
 The J have been too sparing of examples, especially in 
 the first rudiments; in consequence of v/hich, the young 
 pupil is hurried through tiie ground rules too fast for his 
 capacity. This objection 1 have endeavoured t» obviate 
 in the following ti*eatise. 
 
 In teaching the first rules, I have found it best to en- 
 courage the attention of scholars by a variety of easy and 
 familiar questions, which might serve to strengthen their 
 minds as their studies grow more arduous. 
 
 The rules are arranged in such order as to introduce 
 the most simple and necessary narts, previous to thos* 
 which are more abstruse and diiiicult. 
 
 To enter into a detail of the whole work would be te- 
 dious ; I shall therefore notice only a few particulars, and 
 refer the reader to the contents. 
 
 Although the Federal Coin is purely decimal, it is 8% 
 nearly allied to whole numbers, and so absolutely neces- 
 sary to be understood by every one, that I have intro- 
 duced it immediately after addition ot whole numbers, 
 and also shown how to find the value of goods therein, 
 iimnedfetely after simple multiplication 5 which may be 
 of gi-eat adyanta<je to many, who perhaps will not iiavc 
 an opportunity of learning fractions. 
 
 In the arrangement of fractions, i have taken an entire 
 new method, the advantages and fi^cility of which will 
 iufficiently apologiaie far it$ not F einfc nw^rclfi^ to other 
 
sYr,if r.is. As tleciiaial fractions raay be leavneu i^.vacli easier 
 tiian vulgar, and are more simpiej useful, anil neces- 
 sary, and soonest v^anted in more useful brandies of ■ 
 Arithmetic, thej ought to bfe learned iirst, and Vulgar 
 Fractlon^j omicted, until further prop;ress in iha science 
 shall make tliem necessary. It may be well to obtain a 
 general idea of them, and to attend to two or three easy 
 prol)lems therein : after which, t!ie scholar may 'ieaia 
 decimals, which will be necessary in the reduction of cur- 
 rencies, computing interest rnd r«iany other biancliCs. 
 
 Besides, to obtain a thorouj^h knowledge of Vulgar 
 Fractions, is generally a task too hard for young scholars 
 who have made no further progress in Arithmelic tlusu 
 Reduction, and often discourages them. 
 
 I have therefore placed a few problems in Fractiom*, 
 according to tlic method above hinted ; and after going 
 t?irought1ie principal mercantile rules, have treated upon 
 Vulgar Fractions at large, the scholar being now capable 
 of going through them with advantage and ease. 
 
 Li vSimple Interest, in Federal Money, I have given 
 several new and concise rules ; some of which are par- 
 ticularly designed for the use of the compting-house. 
 
 The •Appendix contains a variety of rules for casting 
 Interest, Rebate, &c. together with a nuriiber of the most 
 easy and useful problems, for measuring superficies and 
 solids, examples of forms commnnly used in transacting 
 business, useful tables, &c. which are designed as aids iJi 
 the common business of life. ^ 
 
 Perfect accuracy, in a work of this nature, can hardly 
 be expected ; errors of the press, or perhaps of tlie au- 
 thor, may have escaped correction. If any such arc point 
 ed out, it will be conxsislered as a mark of frieiK.; ship and 
 favor, by 
 
 The public^ s most hnmhle 
 
 and obedient Servant^ 
 
 NATHAN DAIUJLL. 
 
TABLE Oy CONTE>i;TS, 
 
 Addition, simple 
 
 ^ of Federal Money . 
 
 . Compound 
 
 Alligation 
 
 Annuities or Pensions, at Compound Interest 
 
 Arithmetical progression 
 
 Barter ...-.♦ 
 
 Brokerage . . . . .► 
 
 Characters, Explanation of 
 
 Commission 
 
 Conjoined Proportion 
 
 Coins of the United States, Weights of 
 
 Division of "Whole Nunibei's 
 
 Contections in 
 
 Compound 
 
 Discount 
 
 Duodecimals • . . . 
 Equation of Payments 
 Evolution, or Extraction of Roots 
 Exchange . • . • 
 Federal Money 
 
 Fellowship 
 
 Subtraction o! 
 
 Compound 
 
 Fractions, Vulgar and Decimal 
 Insurance .... 
 fnterest. Simple 
 
 — by Decimals 
 
 Compound 
 
 bv Decimals 
 
 Inverse Proportion 
 Involution 
 Loss and Gain 
 Multiplication, 
 
 Simple . 
 
 Application and use 
 Supplimentto 
 Conipouiiii 
 
 Kurneratior 
 
 Practice 
 
 Position 
 
 Vf^vmutatlon of Quantities 
 
 Qf 
 
 17 
 
 57 
 
 135 
 
 £28 
 
 1S8 
 
 179 
 
 151 
 
 21 
 
 27 
 
 144 
 
 146 
 
 74, 155 
 
 126 
 
 129 
 
 169 
 
 154 
 
 177 
 
 167 
 
 178 
 
 HO 
 
 23 
 
 S3 
 
 SS 
 
 51 
 
 15 
 
 109 
 
 200 
 
 20 
 
Cy.l TABLE OF CONTENTS, 
 
 Questf .« 's lor exercise . . , * . 209 
 
 Ileduttion ...*.... 65 
 
 — — of Currencies, do. of Coin . 89, 95 
 
 Rule of Tliree Direct, do. Inverse . 100, 108 
 
 Double 148 
 
 Rules, for reducing thedificrent currencies of the 
 several United States, also Canada and No- 
 va-Scotia, eacli to the par of all others 96, 97 
 
 • — — Application of the preceding ... 98 
 
 Short Practical, for calculating Interest 126 
 
 for casting Interest at 6 per cent. . . 215 
 
 •- ^- for finding the contents oj Superfices & Solids 220 
 
 — — -to reduce the currencies of the different 
 
 States, to Federal Money . . . 218 
 Rebate, A sliort method of fm^ding tlie, of any giv- 
 en sum for months and days . . 217 
 Subtraction, Simifle . T - . • 25 
 
 , — Compound .... 45 
 
 Table, Numeration and Pence .... 9 
 
 •™ — Addition, Subtraction, and Multiplication 10 
 
 of Weight and Measure . . • 11 
 
 •— — oF I'ime and Motion .... 15 
 
 « - showing i\\Q^ number of days from any day 
 
 of one month, to the same'day in any other 
 
 monlii . 172 
 
 Fhowing the amount uf iLor 1 dolhir, at 5 & 
 
 G per cent Compound Interest, for 20 years 232 
 *-™- showing theamount of 1Z. annuity, foroome 
 for 51 jeiirs or under, at 5 and 6 per cent. 
 
 Compound Interest . . . ' • 233 
 -— - shov.-nig the present worth of IJ. annuity, for 
 
 SI yrs. at 5 &i 6 per c. Compound Interest ib. 
 .«-^ — ^ of cents, ansv/ering to the currencies of the 
 
 United States, with Sterling, he. . . 256 
 -— - — showing the value of Federal Money in 
 
 other currencies . . . . * . 237 
 
 Tai-e and Trett 1 14 
 
 Useful Fonns in transacting business . . 238 
 Weiglits of several pieces of English, Portuguese, 
 
 h French, gokl coins, in dollars, cts. & mtlhs 2S4 
 
 — --of English ^^ Portu«vuese gold, do. do. 2So 
 
 of French twA Spamsh iJ!;old, city, d^ ib. 
 
jdhu^ CMoA^llu. 
 
 
 
 X>,lIjp^L'b 
 
 SCHOOLMASTER'S ASSISTANT 
 
 M>4^^« 
 
 ARITHMETICAL TABLES. 
 
 
 
 lVumreai07i TdbU 
 
 
 
 Pence Tfl&Ze. 
 
 
 
 
 
 flO 
 
 
 
 
 
 
 £?. 
 
 5. 
 
 d. 
 
 d. 
 
 s. 
 
 «} 
 
 
 
 ■§ 
 
 
 
 
 
 
 20 
 
 Is 1 
 
 8 
 
 12 U 1 
 
 1 
 
 
 
 C3 
 
 tft 
 
 
 
 
 
 SO 
 
 2 
 
 C 
 
 24 
 
 2 
 
 
 , 
 
 
 3 
 O 
 
 •§ 
 
 
 
 
 
 40 
 
 3 
 
 4 
 
 S6 
 
 3 
 
 1 
 
 £ 
 
 
 ^ 
 
 g 
 
 
 
 
 
 50 
 
 4 
 
 2 
 
 48 
 
 4 
 
 «ib4 
 
 13J 
 
 
 Cm 
 
 g 
 
 
 
 
 
 60 
 
 5 
 
 
 
 60 
 
 5 
 
 o 
 
 CO 
 
 £ 
 
 § 
 
 52 
 
 o 
 en 
 
 § 
 
 o 
 
 1 
 
 O 
 Pi 
 
 o 
 
 3 
 
 "5 
 1 
 
 1 
 
 43 
 
 QO 
 
 H 
 
 
 TO 
 80 
 90 
 
 too 
 
 110 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 8 
 6 
 4 
 2 
 
 72 
 
 84 
 
 96 
 
 108 
 
 120 
 
 6 
 
 »r 
 
 8 
 
 9 
 
 10 
 
 i9 
 
 8 
 
 / 
 
 6 
 
 5 
 
 4 
 
 3 
 
 2 
 
 1 
 
 120 
 
 10 
 
 
 
 1S2 
 
 U 
 
 
 9 
 
 8 
 
 7 
 
 6 
 
 5 
 
 4 
 
 S 
 
 2 
 
 
 
 
 
 
 
 
 9 
 
 B 
 9 
 
 7 
 8 
 9 
 
 6 
 7 
 8 
 9 
 
 5 
 
 6 
 
 7 
 8 
 
 4 
 5 
 6 
 
 7 
 
 3 
 4 
 5 
 6 
 
 
 •ti 
 
 niGti 
 
 e 
 
 
 
 
 
 
 
 
 9 
 
 8 
 
 ^ 
 
 4 faj-tlungs 1 
 
 pctujV/ 
 
 f/ 
 
 
 
 
 
 
 
 
 9 
 
 8 
 
 V2 pence., 
 
 1 i 
 
 jhillingj 
 
 ^ 
 
 
 
 
 
 
 
 
 
 9 
 
 m bit 
 
 iliiii. 
 
 ^,1 
 
 nouiui,/. 
 
 /. 
 
APl^UTXW/'Ai?li SUS'I'RACTION TABLE. 
 
 T\\: dU:^y.4) 5lM.7f S^ 9^ 
 
 10 11 Y\^ 
 
 2 4 5 6 j 7| 8 9 j 10 11 
 
 12 13 
 
 14% 
 
 3 5 6 7 j 8 I 9 { 10 11 12 
 
 IS 14 
 
 15 i 
 
 4 6 7 1 8 1 9 j 10 11 12 13 
 
 14 15 
 
 16 
 
 '5 7 8 9 1 10 i 11 12 13 14 
 
 15 16 
 
 17"^ 
 
 ij ^{ 8 9. 10 1 11 ! 12 13 14 15 
 
 16 17 
 
 18^ 
 
 i 7 i 9 10 11 I 12 t 13 14 15 16 
 
 17 18 
 
 19f 
 
 '^ S 1 10 11 12 Ijji4|i5 16 17 18 1 19 
 
 201 
 
 |9jii 12 33 14 j i5 1 IG 17 18 19 } 20 
 
 21 J 
 
 '10 f 12 13 14 15 1 16 j 17 J 18 19 20 ( 21 
 
 22 
 
 Kl'-L Tl V I . J C A T ID N T ABLE* 
 
 "I'l 2 i S i 4 : 5 i 6 I 7 i 8 1 9 
 
 10| 11 Igi 
 
 .2! 4! 6i 
 
 8 i 10 i 12 i 14 1 16 i 18 
 
 20i 22 24 
 
 f S\ 6 i 9 1 
 
 12 1 15 I 18 I 21 ; 24 i 27 
 
 S0| 33 36 
 
 4 1 8 1 12 1 
 
 16 1 20 i 24 ; 28 1 S2 J S6 
 
 40| 44 48' 
 
 d i 10 ! 15 
 
 20 1 25 1 SO 1 35 1 40 i 45 
 
 50 55 60 
 
 i 6 j 124. 18 
 
 24 i SO I S6 \ 42 i 48 | 54 
 
 60 66 7^ 
 
 W\ 14) 21 
 
 28 i S5 i 42 5 49 i 56 \ 63 
 
 701 77 S\ 
 
 * 8 i 16 1 24 
 
 1 32 j 40 1 48 1 5d ] 64 j 72 5 SOj 8S| 96 
 
 9 i 18 I 27 
 
 36 1 45 1 54 i 63 t 72 | 81 t 90] 99|108 
 
 10 i 20 1 SO 
 
 40 i 50 1 60 i 70 i 80 5 90 J 100J1101126 
 
 U 1 22 i 33 
 
 44 1 55 i 66 1 77 1 88 i 99 1 110|i21|132 
 
 12 ( 24 1 36 ; 
 
 48 1 60 i 72 J 84 ; 96 ! 108 ! 1201132114^ 
 
 To learn tins Table : Eind yam* mijitipiier in the left 
 Irand column, and tlie mnltiplicaiul a-top, and in the 
 conunon angle of meeting, or against your multiplier, 
 aloag at the right hand, and under yoUr fnultipIicJOidj,^ 
 tt^j vill fiT^jJ the |irjT(IiUt^ or ans^ver.. 
 

 
 ounces, 1 pound; lb * 
 
 .^ ..:. >-s. .,/ .»U'ikb 1 ounce, c-^. 
 
 , 16 ounct5^, 1 pound, lb, 
 
 I ^8 poimdi?, i qifarf^r of a hundred ueigu^ r'n 
 
 I 4 quarttn-^j 1 liundred^velglitj cjz'L 
 
 1 20 hundiiid w^iglif • 1 ton, -^ jtX 
 
 \ By iWs weight arc vclghed all coarse and drcsSy gpod:/. 
 Igi-ocery wares, and all metals except gold and silver. 
 
 4, nSpofhecuHe^ Wei^d\ 
 
 20 giralrra (^\) m&!;fc 1 scp«|iTe) 3 
 
 5 scruples, 1 dramt, 5_^ 
 
 S dranis, 1 ounce^ 5 
 
 'TS oanceK, 1 pound, f^ 
 
 Apotliecavies use mis wei^lit In CDrnpOundl-ng thcTr 
 medirines. 
 
 5. 6?fcfi Measure, . 
 
 4 nails (7Z/r.) niak'c 1 quarter of a j:u-d, (p\ 
 
 4 quart eirs, ' 1 jan!, ii<}. 
 
 S -uartcr?^ 1 fell FlemuHi, KfL 
 
 ' ;cart6rs, 1 Ell En^5isl'., j^. )ih 
 
 C garters, 1 Ell French, . ii'J^Jf. 
 
 t" 
 
 ■jjf.) ina'.<re T qi^ro't, o 
 
 8 qjisr r'^ I peck; 
 
 4 pecks. I bushel, 
 
 'fhis meaiiurei:^ applied te,^r-»'^!:. lenn^" 
 ir.ts, OTSters. con'. ^:o 
 
 ?. 
 
/ 
 
 » 
 
 
 I -^ 
 
 ARiTHi^IETIGAL TABLES, 
 
 
 ^' . 
 
 JVim Measure, 
 
 4 gills {gi.) 
 
 make 
 
 1 pint. 
 
 2 pints. 
 
 
 1 quart, 
 
 4 quarts. 
 
 
 1 gallon, 
 
 5.1 i gallons, 
 
 
 1 barrel, 
 
 42 gallons, 
 
 
 1 tierce, 
 
 63 gallons, 
 
 
 I hogshead, 
 
 2 hogsheads. 
 
 
 1 pipe, 
 
 2 pipes, 
 
 
 1 tun, 
 
 12 
 
 qt. 
 
 t 
 
 tier, 
 hhd. 
 
 V' 
 1\ 
 
 All brandies, spirits, mead, vinegar, oil, S:c. are mea 
 sured bj wine measure. Jfote,-^9>^\ solid inches, mak 
 a gallon. 
 
 8. Long Measure. 
 
 5 barley coras (&. c.) make 1 inch, marked in, 
 
 J 2 inches, 1 foot, ft, 
 
 3 ftetj 1 yard, yd. 
 
 5 i yards, 1 rod, pole, or perch, ri^. 
 
 40 rods, 1 furlong, fiu\ 
 
 8 furlongs, 1 mile, ?n. 
 
 5 miles, 1 league, ha, 
 
 69^ statute miles, 1 dep-ee, on the earth. 
 
 360 degrees, the circumference of the earth. 
 
 The use of long measure is to measure the dlstonce o 
 places, or any other thing, where length is considered 
 without regai'd to breadth. 
 
 N. B. In measuring the heightof horses, 4 inches mak( 
 1 hand. In measuring depths, six feet make 1 fatliopi 
 or Fsench toise. Distances are measured by a chain 
 four rods long, containing one hundred links* 
 
 ^ 
 
AHITUMETIGIAL TABLES. iS 
 
 9. Land J or S^juare Measure. 
 
 144 square inches mak6 1 square foat. 
 
 9 square feet, 1 square yard. 
 
 SOi square yarde, or > i square red. 
 272i square teet^ 3 
 
 40 square rods, 1 square rood. 
 
 4 square roods, 1 square acre. 
 
 640 square acres, 1 square mile. 
 
 10. Solid or Cubic Measure, 
 
 irSS solid inches make 1 sclld toot 
 
 40 feet of round timber, or > . . ^ > 
 
 50 feet or hewn timber, 3 
 1-28 solid feet or 8 feet long, > j^,,,.^ ^j- ^^^^_ 
 4 wide, and 4 nigh, 5 
 
 All solids, or things that have len|^tb, br eadtli and deptii, 
 are measured by this measure. N. B. The wine gallon 
 contains 251 solid or cubic inches, and the beer gallon, 
 282. A bushel contains 2150,4£ solid inches. 
 
 60 seconds {S.) make 
 
 1 minuie, 
 
 mi 
 
 irked- 
 
 S.Mi 
 
 €0 minutcsj 
 
 
 1 hour, 
 
 
 
 h. 
 
 24 hours, 
 
 
 I day, 
 
 
 
 (L 
 
 7 days, 
 
 
 1 week, 
 
 
 
 u\ 
 
 4 weeks. 
 
 
 I month, 
 
 
 
 VIO 
 
 13 months, 1 day 
 
 and 6 
 
 liours, 1 Ji 
 
 Lilian ycarj 
 
 yr. 
 
 Thnty days hath September, April, Jane, and Novembei , 
 February twenty -Kiiglit alone, all the rest have ihirty-one. 
 N. B. In bissextile, or leap yeai*, February hath 29 
 ♦Jays. 
 
 12. circular Motion* 
 
 €0 seconds ('') make 1 minute, ^ 
 
 60 minutes, 1 degree, 
 
 SO degrees, ; sign, S. 
 
 *t 5?\;^iS; or 560 degicei?, ihe ^,vho!c great Circus cf thf 
 
Ex^amlion of Chwracters used in tkU S^ok 
 
 :^. Kqiial to, as l£i. = Is. sigQliies tFiat i£ pence a;c 
 equal to 1 shilling. 
 
 -T .*i^^ors, iho. sign of addition, 
 that 5 and 7 added toii-ethcr; 
 
 - - Mr^nus, or /^ss, tlie s';. 
 sigiiiiies Hiat 2 subtrac:.;,^. .. 
 
 X Multiply^ or Yc'ilu?^ tlic s:;^'-- ^- M^''n-;'iciition ; .^ 
 4x3=125 signifies that 4 :::!:. t':: . is ecual Uj 
 
 12. 
 
 -r- The sign of Division ; cs o^^~2-~^.. slgniiles i}v^i S 
 d^ded by 2; is equal to 4 : or thus, v~49 each ^^r 
 wliich signify the sarne thiDg*. 
 
 : : Four points set iu the muklieof loi;i niiuibers. uc...>.. 
 ilieni to be proportional to one another, by iwQ rule- 
 of threes as'2:4 : : 8 : 16; that is/ as B to" 4* se is o 
 to 16, 
 
 V* Freilxed to anjni:ij:bc:> -^upDCSCs t^^at lhcsqv:ar-^ 
 of thatiuumbcr is reotilreiL 
 
 ^' Prefixed to any ncHnbe:'- •.■.{u^. ^ir-j.--.. 
 
 number is reouireu. 
 
 v' Denotes the bi^uadraie root, (>r fourth poxvcj^. ''< 
 
ARITHMETIC. 
 
 . X-RITHMETIC is tlie art of coinputiKg by riumbws, 
 nnd has five principal rules for its operation, viz. Numc- 
 r.ilioi); Addition, Subtraction, Multiplication, and Divf.- 
 
 KUMERxVTIO?!. 
 
 "' ineriitioii is the art of numbering. It teaches to 
 
 ;s the value of any proposed number by the follow- 
 
 iiractcrs, or figures : 
 
 1, 2, 5, 4, 5, G5 r, S. 9, 0— or cypher. 
 
 ■".••-ides tiic simple value of figures, each has a local 
 
 due, whicli depends upon the place it stands in, viz. 
 
 ^y r?.i!;ure in the place of units, represents only its sim- 
 
 3 value, or so many ones, but in the second place, oi' 
 
 Note. — Although a cypher standing alone signifies notli'- 
 jjig ; yet when it is placed on the right hand of figures, it in- ■'. 
 crertscs their vaUie in a tenfold proporti'>n, by throwing them ^ 
 •::tt> higher places. Thus 2 with a cypher annexed to il^ 
 
 como«5 20, twenty, and with two cyj^hcrs, thus, 200, two 
 
 . :!!K:rcd, 
 
 fi. When numbers consisting of many figures, are given to 
 ' i rcadj it will be found convenient to divide them into as 
 any periods as we can, of six figures each, reckoning from 
 right hand towards the left, calling the first the period of 
 it:;, (lie second that of million?, the third billions, the fouith 
 iHti^s, &CC. as iii the followin;!; nnm])er : 
 4i0 7i3C£5 46 27 G 90 12 5 792 
 Fcj-lod of \ S. Period of | £. Period of J . Penod {f 
 
 '^\!Ulons, i Billio'iis. Millions 
 
 Units. 
 506792 
 
 v.C7:> I 625182 } 739012 
 
 Till; foregoing number is read thus— Eight thousand and 
 v' •ty-tlivee trillions ; six hundred and twenty-five thou- 
 ' >iTr liitodred and sixty-iwo billions ; seven hundred and 
 •ine tho'4r>r.nd and twelve millions: five hundred and 
 r-ar.d, seven hundrt^d and njnety-two. 
 :. Billions h substitute 1 for millions of miilions. 
 ' iiions for millions of mr-Iions ef milliens. 
 Quatrillions for miilionfj of milUi ns of millions of mnHonsv 
 
phicQ ol tens, it becomes so many tens, or ten times its 
 simple value, aiul in t!ie third place, or place of hundreds, 
 it becomes an liii rKhed limes its simple value, and so on, 
 
 as in the rblio^vi!: ; 
 
 n y, g p X ^ ^^ js' C 
 
 C o ^' c c o 5 J3 g: 
 
 ^ hTI I Jj £i ^ ^ 
 
 TABLE : 
 
 Lc o: 
 
 1 .(h!(-. 
 ' 2 i - Twenty-one. 
 . • • ' " S 2 1 - Three hundred twentj-one. 
 ' , , '4321.- Four thousand 321. 
 
 5 4 3 2 1 -Fifty -four thousand 321. 
 i , ' 6 5 4 3 2 1 - 654'thousand 321. 
 , 7 6 5 4 3 2 1 - 7 miiiion 654 thousand 521. 
 
 87654321 -87 million 654 thousand 321. 
 987654321 -987 million 654 thousand 321. 
 123 4 56789 -123 million 456 thousand 789 
 9 8 7 6 5 4 3 4 8 - 987 million 654 thousand 348. 
 
 To knovr tiie value of any number of figures. 
 
 RULE. 
 
 1. Numerate from the right to the left hand; c .ch Sg- 
 tire in its proper place, by saying, units, tens, hundreds, ^ 
 ike, as in tlje Numeration Table. 
 
 2. To the simple value of each figure, join tlie name of 
 its place, beginning at the left hand, and reading to the 
 right. 
 
 EXAMPLES. 
 
 Head the. ftdlowiiig numbers, 
 
 365, Three liunilred and sixty-live. 
 5461, ¥ive thousand four hundred and sixty -one. 
 1234, One thousand tw^o hundred and thirty -four» 
 540^56, Fifty-foirv thousand nnd twenty-six. 
 
....... Une liiintlred and twentj .,..:. liousind four 
 
 liundrcd and sixly-one. 
 
 'if'G.':^40, Four millions, six hundred and six<y-si\' (hou- 
 - -nd two hundred and forty. , 
 
 I 
 
 i.. — i.\n convenience hi reading lar^e numbers, 
 lay be divided into periods of three figures each, 
 
 OVv\S J 
 
 OSr, Nine hundred and eighty-seven. 
 VST OOO5 Nine hundred and ei;^;hty-seven thousand. 
 r 000 000, Nine huudred and eighty-seven miHion. 
 " r, ! f.'!*!. Nine luinch'ed ;ind eigtity -seven million, 
 six hundred and iifty-four thousand, 
 
 Begin on tl.c ri^j.l: I'.aiid, write units in the uni^ts place, 
 
 ' n.s in the tens place, hundreds hi the hundreds ]?lace, 
 
 d so on, towards the left hand, vm ting each figure ac- 
 
 ./iling to its proper value in numeration; taking care 
 
 r:.upp]y those places of the natural erder with cyphers 
 
 ■tich are omitted in the question. 
 
 Yv'rite down in ]^roner ilscures the following numbers 
 Thirty-six. " 
 
 Two hundred tMid s?eventy-nine. 
 Thirty -seven thousaiid, five Imndred and fourteen, 
 -'sine millions, seventy -two thousand and two hundred. 
 lit hundredMn*;"* " ly-ibur thousand and nftv- 
 
 ':,-i^- 
 
 SIMPLE AUDITION, 
 
 'ilng tor^ctlier scveiiil smaller n?j!nber??, of iht^ 
 !''tominatioti, into one larger, equal to the whole. 
 '. ti;tal ; as 4(h>Ilarsniul six dollars in one sum is 10 
 
13 SIMPr.K AJlDVrtON^ 
 
 UULE. 
 
 Having placed units under units, tens under tens, &c. 
 draw a line underneath, and begin with the units ; after 
 adding up every figure in that column, consider how ma- 
 ny tens are contained in their sum ; set down the remain- 
 der under the units, an^^ carry so many as you have tens, 
 to the next column of tens ; proceed in the same manner 
 tTiroug]] every column, or row, and set down tlie whole 
 amount of tlie last row. 
 
 JiiXAMPLKS. 
 
 (!.) (2.) ,S.) (4.) 
 
 
 
 Hundreds. 
 
 Tens. 
 
 Units. 
 
 Tliousands. 
 Hundreds- 
 Tens. 
 Units. 
 
 C. of Thous: 
 
 X. of Thoiisj 
 
 Thousands. 
 
 Hundreds. 
 
 Tens. 
 
 Units. 
 
 4 2 
 
 
 4 1 4 
 
 17 5 6 
 
 5 5 
 
 2 6 2 1 
 
 5 3 
 
 
 2 9 1 
 
 4 3 2 
 
 3 4 6 9 7 7 
 
 5 2 
 
 
 8 5 1 
 
 9 4 7 8 
 
 4 1 
 
 3 3 3 9 
 
 1 3 
 
 
 i 5 2 
 
 16 6 6 
 
 3 2 
 
 10 12 
 
 8 9 
 
 
 6 9 8 
 
 7 4 2 2 
 
 8 7 
 
 6 5 4 5 
 
 
 
 
 
 
 (5.) 
 5 14 8 5 
 
 
 (6.) 
 64 179 
 
 
 S 7 1 4 5 
 
 6 7 2 3 
 
 7 
 
 
 2 5 7 12 
 
 
 5 17 14 
 
 4 2 7 1 
 
 9 
 
 
 8 4 19 4 
 
 
 6 8 4 5 
 
 9 7 14 
 
 5 
 
 
 S 2 5 1 6 
 
 
 5 7 3 5 7 
 
 S 2 8 5 
 
 1 
 
 
 7 1 4 S 2 
 
 
 6 17 8 4 
 
 14 5 7 
 
 2 
 
 
 S 27 1 9 
 
 
 5 2 10 1 
 
 * 
 
 
 
r> 1 
 
 siMj*:. 
 
 F. a;) in J 101 
 
 
 19 
 
 ...,; 
 
 
 (9.) 
 
 
 
 (to.) 
 
 
 8 4 rs 
 
 8 
 
 
 5 2 6 3 7 
 
 C-. 'V O 
 
 9 
 
 3 7 I 
 
 4 
 
 
 2 7 19 6 
 
 2 5 i) 
 
 •3714 
 
 " 
 
 
 3 8 4 19 
 
 4 1 7 
 
 1 
 
 8 3 2 
 
 1 
 
 
 5 3 19 2 
 
 7 2 r> 
 
 t 
 
 1 4 3 
 
 / 
 
 
 6 10 8 4 
 
 
 5 
 
 I r 2 
 
 6 
 
 
 3 7 19 5 
 
 
 /^ 
 
 2 5 1 
 
 b 
 
 
 2 9 14 7 
 
 
 
 
 
 • 
 
 
 
 
 
 • 
 
 
 
 
 
 
 (12.) 
 
 V' 4 yt 3 : r 8 
 
 5! 9 
 
 
 3 r 
 
 1 
 
 8 4 5 6 8 7 
 
 r 4 2 T 6 1 
 
 f) a 
 
 
 5 1 
 
 1 
 
 7 4 2 2 9 
 
 r 1 4 r. r 
 
 9 6 
 
 
 I 
 
 9 4 6 3 7 2 
 
 r G 2 3> 1 4 5 
 
 "r c*» 
 
 
 
 8 
 
 3 4 7 5 4 
 
 (^ (• 4 1 B 
 
 S 4 
 
 
 
 
 2 7 15 5 
 
 7 4 13 6 
 
 5 3 
 
 
 
 
 3 6 2 3 
 
 ;■ 6 r 8 9 S 
 
 p ^ 
 
 
 ,__. 
 
 _ 
 
 19 5 
 
 (15.) ' 
 
 
 
 
 
 (14.) 
 
 :^ 4 3 6 4 G 
 
 
 
 
 
 2 5 9 
 
 f) B 8 14 5 1 
 
 
 
 
 
 3 4 4 5 
 
 •116 4 5 2 
 
 
 
 
 
 5 4 4 4 3 3 
 
 7 6 10 4 2 5 
 
 
 
 
 
 3 7 5 5 3 2 6 
 
 3 4 G 2 1 4 
 
 
 
 
 
 4 5 2 17 4 
 
 4 3 9 
 
 
 
 
 4 
 
 06476269 
 
 9 8 2 r 
 
 
 
 
 
 2 6 8 5 9 1 
 
 
 
 
 
 
 
 j^To prove Addition^ ue^pii at the fep of the sum, 
 
 reckon the figures dovvnwardsin the same manner as 
 
 ' were added upwards, and if it be right, this sum total 
 
 . bo equal to the Hrst: Or cut off the upper line of 
 
 :^ ! ■'«, and find t\\Q amount of the rest; then if tlie amount 
 
 j^;w'? lipper line, when added.. be ef«^i>al to the total. {\^^ 
 
 I ^\iKvk U sf?Tino?.ad to be rid it. 
 
 r> 
 

 2. There is ruu^Lhirr ;ueL:io(l. oT prooi^ as ibiiows : — ■ 
 
 Reject or cast out l:;e nines in each example, 
 vow or ^v.i^u of Tigures. ajid set down thQ S 7 8 2 
 '^n.K i ideis, eacii directly even with the 5 7 6 6 
 ligurcs In itsniv/: find the suin of these 8 7 5 5 
 
 reniraiiders ; then if the excess of nines » 
 
 in t\ui sum found as before, is equal to the 18 vS 3 
 
 evcess of nines in the sum total^ the work 
 
 is siioposed to be rii^ht. 
 
 •*15* Add 86S5, ^194^ 7421, 5063, 2196, and 1245 
 f together *Rns, 26754. 
 
 16. Find the sum of S4S.% 783645, 318, 7530, and 
 9078045. ' ^ns, ir)473020. 
 
 IT, Find the ':uni total of 604, 4680, 98, 64, and 54. 
 *ins, Fi rt V -fiYO UHndred. 
 
 13. VHiat is the sum total of 24674, 16742, 34678, 
 10467, and 1 3459 ? ^Ins. One liiin<lred tliousand. 
 
 19. Add 1021, 24S9, 28763, 289, a!id64S8 together. 
 
 dns. Forty diousand. 
 
 ^0. 
 
 \\ na.1: 
 
 :Ni lie 1^)11 
 
 ::in total of the following numbers, viyrj 
 id 4005 ? Jm, UUi. 
 
 i;m total of the following numbers, vi?:. 
 
 and forty-seven, 
 
 1 six Ihundred and EvCj 
 
 sand si" hTnidrec!. 
 
 ^Hc ana ^ 
 s. and t 
 
 Hions, a 
 
 ne liiou^anU , 
 
 c^;i^;;ctr, 61374177 
 
 g2. Rcq : sum of the following numbers, vi*?:. 
 
 Five 'imuuvi'ii and sixty-eight. 
 Eight thousand eight hiidd red and five, 
 Fkiventj-nlne thousand six hundred, 
 Nine hundred and eleven thousand, 
 Kine milhons and tv/cmtv-bi^v 
 
 Ansmr^ 9999D')^ 
 
qUESTIONS. 
 
 t Wnai number oi dollars are in sii: bagSj containing 
 
 ench. 37542 dollars ? ^^ns. 2So252, • 
 
 ". If one quarter of a ship's cargo be worth eleven 
 
 ;sand and ninctj-nino dollars, how many doUai-s Is the 
 
 Ic cargo worth ? 
 
 Ans. 44S96dols. 
 ; . Money was first made of gold and silver at Argos, 
 o'-}\i hundred and ninety-four years before Christ; how 
 :; has money been in nse at this date^ 1814 ? 
 
 Jhis, 2708 years. 
 
 . Tlie distance from Portland in the Province of 
 
 •lie. to Boston, is 125 miles; from Boston to Isev/- 
 
 eu, 162 miles; from lUence to New-York, 88 ; from 
 
 ICO to j^liilatleiphia, 95; from thence to Baltimore, 
 
 iw.l; from thence to Charleston, South-Carolina, 716; 
 
 rv.d fro^a thence to Savannah, 119 miles — What is fliQ 
 
 V. !-<ie distance from Portland to vSavannah ? 
 
 diis, 1407 miles. 
 5. John, Thomas, and Harry, after counting their 
 pnxe money, John had one thousand three hundred and 
 fiCventy-five dollars : Thomas had just three times as ma* 
 ny as Jolm ; and Harry had just as many as John and 
 '1 iiomas both — Pray how many dollars had Harry ? 
 
 Jns, 5500 dollars. 
 
 FEDERAL MONEY. 
 
 -^ EXT in point of simplicity, and the nearest allied to 
 :1c numbers, is the coin of the United States, or 
 
 FEDERAL MONEY, 
 
 .'his is the most simple and easy of all money — itln- 
 
 ; cs in a tenfold proportion, lilie whole numbers. 
 
 10 mills, (7«.) make, 1 cent, marked c. 
 
 iO cents, 1 dime, d, 
 
 JO dimes, 1 dollar, S. 
 
 10 dollars, 1 Eagle, ^ E, 
 
 )olIar is the money unit; all otlier denominations b05 
 
 revalued according to their place from the dollar's 
 
 place. A point or comma, called a separairix^ iT\oy be 
 
 r.*>-T^T»i' nfrr^r;. ;>>^ f>rt!rMrs to separate fh^in from ftQlli&apir 
 
ci^noiDUiations ; thjeu the first figure at the ilght of this 
 separatr]x :s dimes, the second figure cents, and the third 
 mills.* 
 
 ^^.^ /'^ 
 
 ADDITION OF FEDERAL MONEY. "'^'' 
 RULE. 
 
 2. Place the numbers accoi-diiiff to their value ; that is, 
 '3lkrs under dollars, dimes under dimes, cents under 
 .-its, &c. and proceed exactly as in whole numbers; 
 
 ^n place the separatrix in the sum total, directhMindc!? 
 .e separating points above. 
 
 
 
 KXAMPLKS. 
 
 
 
 s. 
 
 d. c. w. 
 
 S. d. cm. 
 
 S. 
 
 d, c. m\ 
 
 sas. 
 
 5 4 1 
 
 439, 5 4 
 
 136, 
 
 5 14 
 
 487', 
 
 6 
 
 416, 3 9 
 
 125, 
 
 9 
 
 94, 
 
 6 7 
 
 168, 9 3 4 
 
 200, 
 
 9 9 
 
 439, 
 
 8 9 
 
 539, 6 
 
 304, 
 
 6 
 
 74-2, 
 
 5 
 
 143, 5 
 
 111, 
 
 19 1 
 
 2128, 8 6 
 
 2. When accounts are kept in dollars and cents, and 
 no othei dienominations are mentioned, which is the usu- 
 al mode in common reckoning, Uien the two first figure^ 
 at the right of the separatrix or point, maj be called so 
 many cents instead of dimes and cents ; for the place of 
 dimes is only the ten's place in cents ; because ten cents 
 make a dime ; for example, 48, 75^ forty-eight dollai'S, 
 seven dimes five cents, may be read forty-eight dollars 
 and seventy -five cents. 
 
 ^ It may be observed that ail the figures at the left hand 
 of the separatrix are dollars ; or you may call the first figure 
 dollars, and the other eagles, he. Thus any sum of tliis 
 money may be read differently, either wholly in the lowest 
 denomination, or partly in the higher, and partly in the low- 
 est ; for example, S7 54, may be either read S754 cents, oT 
 S75 dimes and 4 cents, or 37 dollars 5 d/mes and 4 ccnt^, oV 
 S eagles, 7 dollars ^' dimes and 4 centa# 
 
 A 
 
Ifiiie cents are less than ten, place a cypher in flie 
 ffen's place, or place of dimes. — Example. Write do^v^l 
 four dollars and T cents. Thus, 84, 07 cts, 
 
 EXAMPLES, 
 
 1. Find tlie sum of 504dollai*s, 39 cents; 291 dollars, 
 
 9 cents; 136 dollars, 99 cents; 12 dollars and lOcfrnts^ 
 
 r304, 59 
 
 ,p, J 291, 09 
 
 ^^^^' • 156; 99 
 
 I \% 10 
 
 Sum, 744^ 57 Sevon hundred forty-four dol' 
 — lars and fiftrj^-scvcn cents* 
 
 (2.) 
 
 (S.) 
 
 W 
 
 S. c/5.- 
 
 S. c's> 
 
 g. cts^ 
 
 0, 99 
 
 364, 00 
 
 3287, 80 
 
 0- 50 
 
 21, 50 
 
 1729, 19 
 
 0, 25 
 
 8, 09 
 
 4249, 99 
 
 0- 75 
 
 0, 99 
 
 140, 01 
 
 [0.) 
 
 (6.) 
 
 (7.) 
 
 ». 
 
 S. €ik?. 
 
 g. cf^. 
 
 £468 
 
 124, 50 
 
 , 165 
 
 1900 
 
 9, 07 
 
 , 99 
 
 24G 
 
 0, 60 
 
 , 861 
 
 H5 
 
 £31, 01 
 
 ' 'L 
 
 167 
 
 0, 75 
 
 ^ Q7ti 
 
 46 
 
 24, 00 
 
 , 72 
 
 •] \i 
 
 9, 44 
 
 , 99 
 
 o 
 
 0, 95 
 
 , 09 
 
 .. Wi.at IS tnesiuu total of 127 dols. 19 cents, 278 
 doli 19 cents, 5.4 dols. 7 ceuts^ 5 dols. 10 cents, and J 
 
9. Wliirt is ibeBuiii (U S7"'8 dois. 1 cl, ..:., .iC,.... _ . 
 S44 dolso 8 cts. and S63 ('"oi.^. ? ./??z<-. gl^-^- 
 
 10. Wliat is the sum Oi 4G cents. i;C cciiis, G;2 c:.; 
 and 10 cents ? ' J??i;, S^- 
 
 ■ i I . What is tue bUm of 9 dlaies^ S dimes, ViVaI SO •; :■ : : 
 
 '1^. I received «>!' A E and C a su:.i c<:' ;uu:- ^ 
 paid me 95 dols. 43 ci^. B paid me juso three ■■: : 
 much as A, :uid G "paid mc jii^-t as much as .'. r: •.. 
 
 bnth 5 ciiiiy^:i ;:.d! me lunvm' • , . .. - . ^ . ; ^ •. 
 
 838 cents; and o;:- • -..:■ '' her c^i^) iBv^o^h: > 
 
 dok. 65 csnt^js '-';,. y whilst m the valiie of* the wi>ele i,:..> 
 and curgor " ,/ijti.s'. 81137^2, 4dcts. ' 
 
 A TAILORS BILL. 
 
 Jlfr. Janies Taifwcll^ 
 
 To Timolhy Taijlui'^ ]J/, 
 
 April 15. To 2^ yds. uf Cloth, at 6, 50 p^r yd. 16 ;: > 
 
 To 4 yds. Shalloon, 75 " S ■:.:> 
 
 To making your Coat^ 2. J 
 
 To 1 silk Vest Piittern, f 4 IJ 
 
 To making your Vest, 1 50 
 
 To Silk, iButtonSj &c. for Veiit, 4J 
 
 Slim, S ^i^ -^^^ 
 
 li*^ By au act ot Congress, all tlie accaiints of t'^ij 
 United States^ the salaries of all officers, the reveiii: .^ 
 &c. ai^e to be reckoned in federal money : which made *; c 
 reckoning is so simple, easy and c^^ v*^.^!/ v,;. :% ,. . v. ; 
 fcc on ct}mc in :d common practice ir 
 
SIMPLE SUBTllACTiON. i':? 
 
 SIMPLE SUBTRACTION. 
 
 Subtraction of whole J^'^umba^) 
 
 1 EACHETH to take a less number from a gi-eiiter, qI 
 the same denomination, and therebj shows the difference^ 
 or remainder : as 4 dollars subtracted from 6 dollars, th« 
 remainder is two dollars. 
 
 RULE. 
 
 Place the least nuiixbcr under the ;:^reatcsr. so thai units 
 may stand under units, tens under tens, &c. and draw a 
 line under tliem. 
 
 S. Begin at the right hand, and take each figui'e in the 
 Imver lipe fitnn the iigure above it, and set down fhe re* 
 mainder. 
 
 S. If the Ixiwer figure is greater flian fliat obova it, 
 add ten to the upper iigure ; from whicli number so in- 
 creased, take the lower and set down the remain/iei*, car- 
 rjing one to the next lower number, with \yliich proceed 
 e§ before, and so on till tlie v/hole is finished. 
 
 mooF. Add the remainder to the least numbt^r, and 
 if tlie sum be cqtial to the greatest, the work is r]ght 
 
 QreaUsimmher,Q^4 6 8 G 2.\ '5 T 
 Leastmmber^ 1346 12148 
 
 8 7 9^6 4 7 5 
 16 4 3 4 8 9 
 
 Difterenccj 
 
 
 i^root, ■ 
 
 (4.) f5.) 
 From 416^8839 9187'64ofK) 
 Take S1542999 9124'S8a6 
 
 (5.) 
 65432167890' 
 1 23456?; 098 
 
 Rra 
 
S6 
 
 ^;lMrL>: Sl/BIRAOIIOX. 
 
 Take 
 
 '"'17144045605 
 40600832184 
 
 5562176255002 
 1235271082165 
 
 Him. 
 
 (9.) 
 From i 00000 
 Take 65321 
 
 Bift: 
 
 2521665 
 2000000 
 
 (11.) 
 200000 
 99999 
 
 (12.) 
 10000 
 
 Ms. 66666. 
 dnn. 730865. 
 ..3/Z.s. 142444. 
 
 Ms. 90037. 
 ..^?2S. 250822. 
 
 13. From 560418, take 293752. 
 l^. From 765410, take 34747. 
 
 15. From 341209, take 1987G5. 
 
 16. From 100046, take 10009. 
 
 17. From 2657804, take 2376982. 
 IS. From ninety thousand, fivo hundred and forty-^iX^ 
 
 take forty-two thousand, oae hundred and nine. 
 
 JhTS. 4843r. 
 r9. From fifty-l^irr Qiousand and tuiinty-six, talce itSflo 
 tiiousand two hundred and fifty -four. /nis. 44772. 
 
 20. From one million, take nine hundred and ninety- 
 nine thousand. Ans. One thousand. 
 
 21. From nine hundred and eighty-seven millions) 
 talce nino hundred aiid eighty-seven thousand. 
 
 Jxns. 986013000. 
 
 22. Subtract o^e from a million, and shew the remaih- 
 ocr. ' Ms. 999999. 
 
 qUESTIOSS. 
 
 ! . Hcv; inudi is six hundred and sixiy-seven, greater 
 J;an three hundred and ninety -live ? * Arts. 272. 
 
 2w What is the dilTsrencebetvveen tvv'ice tv/cnty-seven, 
 a ad €iree times forty -five ? Ms. 81. 
 
 S. How nmich is 1200 greater than 565 ami 721 added 
 togetlier? ^ Ms, 114. 
 
 4. From Kew-London to Pluladelphia is 240 miles. 
 Now it' a man should travel five days from New-London 
 towards rhiladelphia J at the rate of 39 mil23 each dav, 
 'GW far wuXil^ he tbei: be from Philadelphia. 
 
 M^, AS rxii\\iF' 
 
SIJBTIl ACTION OF JFi-OEUAI^ MQSlZY, U7 
 
 5i What other number with these four, viz. Gl, 32, Viy 
 and 12, ^vill niake 100 r .pis, 19. 
 
 6. A wine merchant bought 721 pipes of wine for 
 908-16 dollars, and sold 543 pipes thereof for 85049 dol- 
 lars ; how many pipes has he remaining or unsold, and 
 what do they stand him in ? 
 
 JJtis, 178 pipes unsold, and they stand him in 31797. 
 
 SDBTR ACTION OF FEDEKAT. ]VIO>fEY. 
 
 liULE. 
 Place ihe numbers according to their value; ihat :?, 
 iTolIai© under dollars, dimes under dimes, cents under 
 cents, &c. and subtract as in whole numbers. 
 
 EXATVIPLKS 
 
 g. d,c. in. 
 From 45, * 4 7 5* 
 Talce 43j 4 8 5 
 
 K(5m. SI, 9 9 one dollar, nine dimes, and nke centSf 
 or one dollar and ninety-nine cents. 
 g. d, c, g. d,c,vi, g. d, c.vf, 
 
 from 45, 7 4 46, S 4 6 £il, 1 1 
 
 Take 13, 8 9 36, l 6 4 ill, 114 
 
 Rem. ' " 
 
 g. g. cts. 
 
 From 4 2 8 4 411, 24 
 
 Take 19 9 3 16, 09 
 
 Rem. " 
 
 
 g. 
 
 960, 
 13G, 
 
 cts, 
 GO 
 41 
 
 g. cis, g. cts. g. cis. 
 
 From 4106,' 71 1901,08 S 65, GO 
 
 Take 221, 69 864, 09 109, 01 
 
 11. From l^doHarsj take 9 dollars 9 cents. 
 
 Jlmi, gllj, 91 cf^. 
 
 12. ^ifim 127 dollars 1 ccr.t take 41 dollars 10 cents. 
 
 Ms, 885, 91 cts 
 
^•B SXMPLK MUl.Tj.PI.XaAXXON. 
 
 15. From 355 dollars 90 cents, take 168 dols. 99 cents, 
 
 Ans. ^196, 91 cts. 
 
 34. From 249 dollars 45 cents, take 180 dollars. 
 
 dns, S69, 45 cts. 
 
 15. From 100 dollars, take 45 cts. .^ws. !g99, 55 cts. 
 
 16. From ninety dollars and ten cents, take forty dol- 
 lars and nineteen cents. Ans, ^49, 91 cts. 
 
 17. From fortj-one dollars eight cents, take one dollar 
 nine cents. Ms, ^39, 99 cts. 
 
 18. From 3 dols. take 7 cts. Ais, !g2, 93 cts. 
 
 19. From ninetj-nine dollars, take ninety -nine cents. 
 
 .^ns, S98, 1 ct. 
 SO From twenty dols. take twenty cents and one mill 
 .^ns. S19, 79 cts. 9 mills. 
 
 21. From three dollars, take one hundred and ninetj- 
 nine cents. ' Ans. ^1^ 1 ct 
 
 22. From 20 dols. take 1 dime, dns, S19, 90 cts. 
 
 ^ 23. From, nine dollars and nioety cents, take ninety- 
 nine dimes. Ans. remains. 
 
 24. Jack's prize money was 219 dollars, and Thomas 
 received just twice as much, lacking 45 cents. How 
 much money did ThomaiJ receive ? Am, g437, 55 cts. 
 
 25. Joe Careless received prize money to the amount of 
 1000 dollars; after which he lays out 411 dols. 41 cents 
 for a span of fine horses; and 12-3 dollars 40 cents for a 
 gold watch and a suit of new clothes 5 besides 359 dol^ 
 and 50 cents he lost in gambling. Hoy/ much will !-ft 
 nave left after paying his landlord's bill, which amounts 
 to 85 dols. and 11 cents ? Ans, S20, 53 els. 
 
 SIMPLE MULTIPLICATION, : 
 
 X EACIIETH to increase, or repeat the greater of two 
 numbers given, as often as there are units in the less, or 
 multiplying number; hence it performs the work of ma- 
 ny additions in tha most compendious manner. 
 *^The number to be multiplied is called the multiplicand. 
 
 The number you multiply by, is called themultipliei*. 
 
 The number found from the opemion, is called tha 
 
 p!OfllfCt> 
 
NoTK. Botli multiplier and multiplicand ai «: .a ^vnc- 
 ral called factors, or terms. 
 
 CASE L 
 When themuItlpliGr is not mere than Iv/clve. 
 RUI.E. 
 Multiply each figure in tlie nuiitiplicand bv tlie multi- 
 plier; carry one for every ten, (as in addition of whole 
 numbers) and you will have the product or answer. 
 PIIOOF.* 
 Multiply the multiplier by the multiplicand, 
 
 EXAMPLES. 
 
 "Whatmumber is equal to 3 tiincs S65 ? 
 
 Thus, Z'j5 multiplicand, 
 3 inidiinlier 
 
 Ans, 1095 jiroiliicL 
 
 90r5 
 
 (i 
 
 Midtiplicand 
 Midtipller 
 
 746 
 
 )35 
 
 i34 
 
 a 
 
 5432 
 4 
 
 S12GI 
 9 
 
 2345 
 6 
 
 Product 
 
 
 
 
 4r0[)4 
 
 4 
 
 )46 
 
 no 
 
 4S£0 
 10 
 
 
 
 143£( 
 
 
 2£406iS 
 1:2 
 
 4681114 
 
 CASE 11. 
 
 When tlie muUipiier consists of several iigiUTH. 
 
 ' ilUI.E. 
 
 The multiplier being placed under th(^ niulliiJicand 
 
 units under units, tens under tens, ^<c. multiply by each 
 
 significant figure in the multiplier separately, phicing ihi: 
 
 first figure in each product exactly under its multij>iier ; 
 
 * Multiplication may also ht* proved ity ca^tin-g out iho V/a 
 in Che two factors, and settin.:^ down the r^'iiiainders ; then 
 multiplying the two remaindLTS togetlier ; vi' the e.vcoss u( 
 9'3 in their product is equal to the excess of \i'^ h\ the tctal 
 piDduct, the work h supposed to he np.K> 
 
50 
 
 fllMPLB UVLTlVLXSiATlOiK* 
 
 then add the several products togBther ia the same ordej 
 as they stand, and their sum will be the total product. 
 
 EXAMPLES. 
 
 What number is efual to 47 times 365 ? 
 
 Multiplicand 3 6 5 
 Mvltiplier 4 7 
 
 
 1 
 
 Ms. 1 
 
 34293 
 74 
 
 9^5 5 
 4 6 
 
 
 7 15 5 product 
 
 MSiltlpllcitmh 5rS64 
 Midttfi'kY, 209 
 
 4704^ 
 91 
 
 540776 
 
 75728 
 
 
 
 VvoducL. 7915576 
 
 25S7682 
 
 4280822 
 
 8253 25203 
 826 4025 
 
 2193 9876 
 4072 9405 
 
 6816978 101442075 
 
 8929896 92883780 
 
 2G9181 
 4629 
 
 261986 
 7638 
 
 40634 
 42068 
 
 1246038849 2001049068 
 
 1709391112 
 
 154092 
 87562 
 
 
 918273645 
 1003245 
 
 11714545304 
 
 921253442978025 
 
 14. Multinly 760483 by 9152. .^is. 695994041G. 
 
 15. What is the total product of 7608 times 365432 ? 
 
 ^ns. 2780206656. 
 
 16. What number is equal to 40003 times 4897685 ? 
 
 Ms. 195922093055. 
 
SIMPLE MUiLTirHCATlO.N. 
 
 QASE III. 
 ^Vhcn there are cyphers on tlie right band of eitlier or 
 bnth oF tlic factors, nedect those cjimers ; then place the 
 significant figures under one another, and multiply by 
 tliem only, and to the light hand of the product, place as 
 many cyphers as were omitted in both the factors. 
 examplp:s. 
 21200 31800 84600 
 
 70 36 34000 
 
 (484000 
 
 1144800 
 
 55926000 
 S040 
 
 109215040000 
 
 2876400000 
 
 82530 
 98260000 
 
 U09397'800000 
 
 7065000x8700=61465500000 
 
 749643000 X 695000 ==»52100 1 885000000 
 
 360000x1200000:^^432000000000 
 
 CASE IV. 
 
 Wlmi the multiplier is a composite number, xli at s, 
 
 when it is produced by multiplying any two nunioers m 
 
 the table together ; multiply fn-st by one of those figur-es 
 
 and that product by the otlier; and the last prodiict w^l 
 
 be the total required. 
 
 EXAMPLES. 
 
 Multiply 41364 by 35. 
 
 289548 Product of 
 
 1447740 Product of 5J 
 
 SL Multiply 764131 by 48. 
 
 3. Multiply 342516 by 56, 
 
 4. Multiply 209402 by 72. 
 
 5. Multiply 91738 by 81. 
 
 6. Multiply 54462 by 108. 
 7 Mirltiply 615245 by 144. 
 
 £ns. 36073288. 
 .^iis. 19180896. 
 aiis. 15076944. 
 
 dns. 7430778. 
 
 Jins. 3721896. 
 .ins. Si§59i99Sl. 
 
»» .SIMPLE MULTIPLICATION. 
 
 CASE \\ 
 (To multipl J by lo, 100, 1000, &c. annex to the riniL 
 %licji;id all the cyphers in the multiplier, and it will 
 OJiake the product required. 
 
 EXAMPLES. 
 
 1. Multiply SS5 by 10. Ms, 3650 
 
 2. Multiply 4657 by 100. Ans. 465700 
 
 3. Multiply 5224 by 1000. Ms, 5224000 
 4 iVluitiply 26460 by 10000. *i$?2S. 264600000 
 
 EXAMPLES FOIi EXERCISE. 
 
 1. M^AirMj 1 £03450 by 9004. Ms. 10835865800 
 
 Go Multi;! - 90870G1 by 56708. Ms, 51530905518S 
 
 S. Bfuitiply 8706544 by 67089. Ms, 5841133S0416 
 
 4. Multiply 4321209 by 123409. Ms, 533276081481 
 
 5. iMultiply 3456789 by 567090. Ms, 1960310474010 
 a Multiply 8496427 by 874359. Ms, 7428927415293 
 
 98763542x98763542=9754237228385764 
 
 Application and Use of Multijilication* 
 In making out bills of parcels, and in finding the value 
 of goods ; wrien the price of one yard, pound, ike, is sp»v- 
 en (in Federal Money) to find the value of tlie whole 
 quantity. 
 
 RULE. 
 Multiply the given price and quantity together, as in 
 whole numbers, and the separatrix will be as many figures 
 fcrom the right hand in the product, as in the given price* 
 
 EXAMPLES. 
 
 1. What will 35 yards of broad- > g. d, c. w. 
 doth come to, at " 3 3, 4 9 6 per yard ? 
 
 3 5 
 
 17 4 8 
 104 8 8 
 
 Ms. S122, 3 6 0=122 dol 
 [lars, S6 cents. 
 ^4 What cost 35 lb. cheese at 8 cents per lb. ? 
 >08 
 
 4to^. ^^ 80—2 dollars, 80 cctits. 
 
SJMELE MULTirLlCATION. 53 
 
 3. WTiat is the value of 29 pairs of men'« shoes, at 1 
 dollar 51 cents per pair? ^ns, g43, 79 cent*. 
 
 4. What cost 131 yards of Irish linen, at 3& ^ents pc» 
 yard r Jns, g49, 78 c^nts. 
 
 5. What cost 140 reams of paper, at 2 dollars 3c« tent:* 
 per ream ? Ms, g,'»9. 
 
 6. What cost 144 lb. of hyson tea, at 3 dollars o I cenU 
 per lb. .^ •Ans. S505, 44 cents. 
 
 7. Wliatcost 94 bushels of eats, at 33 cents per bush 
 el ^ Jins. g31, 2 cents. 
 
 8. What do 50 firkins of butter come to, at 7 dollars 
 14 cents per firkin ? * Jins. g357. 
 
 9. What cost 12 cv/t. of Malaga raisins, at 7 dollaib 
 SI cents per cwt. ? Jlns, g87, 72 cents. 
 
 10. Bought 37 horses for shipping, at 52 dollars pei 
 head ; ^vhat do they come to } /ins. gl924. 
 
 11. Wliat is the amount of 500 lbs. of hog's -lard, at 15 
 cents per lb. ? •Sns. g75. 
 
 12. What is the value of 75 yards of i^atin, at 3 dollarn 
 75 cents j3er yard? ^ins, S281, 25 cents. 
 
 13. What cost 367 acres of land, at 14 doh. 67 cents 
 per acre ? Jlns, g5583, 89 cents. 
 
 14. What does 857 bis. pork come to, at 18 dols. 93 
 cents per bl. ? Ms, gl6223, 1 cent 
 
 15. What does 15 tons of Hay come to, at 20 dols. 78 
 Cts* per ton ? Ms. g311, 70 cents. 
 
 16. Find the amount of the following 
 
 BILL OF PARCELS. 
 
 New-London, Marcii 9, 1814. 
 Mr, James Faywell^ Bought of William Merchant* 
 
 S^. cts, 
 28 lb. of Green Tea, at 2, 15 'p^v lb. 
 
 41 lb. of Coffee, at 0, 21 
 
 34 lb. of Loaf Sugai-, at 0, 19 
 
 13 cwt. of jMalaga Raisins, at 7, 31 per cwt. 
 S5 firkins of Butter, vX 7, 14 perjir. 
 
 27 pairs of worsted Hose, at 1, 04 per pair. 
 ^ buslicis of Oats, at 0, 33 per hush. 
 
 £9 pairs of men's Shoes, at 1, 12 per pair. 
 
 Jlmount^ S5Jll> 78« 
 I^cciyed pavincnt in full, W^jlliam Mei?ojia;;t 
 
ClVI}5l6ji or WHOLE KUMHEKS. 
 
 A SHORT RULE. 
 
 ¥oTE. The -auieof 100 lbs, of any article will be jus! 
 
 as man J doiiars as de article is cents a pound. 
 For 1001b. at 1 ceiUper 1 b. = 100 cents =rl dollar. 
 1001b. of beef at 4 :ents a lb, comes to 400 centS5=4l 
 
 dollars, §cc. 
 
 DIVISION OF WHOLE NUMBERS. 
 Simple division teaches to find how many limes 
 one whole number is contained in another; antl also 
 what remains ; and is a concise way of performing seve- 
 ral subtractions. 
 
 Four principal parts are to be noticed in Division : 
 
 i. The Dividend^ or number given to be divided. 
 
 9.. The Divisor^ or number given to divide by. 
 
 S. The Quotient^ or answer to the question, which 
 shows how many times tlic divisor is contained in ih^ 
 dividend. 
 
 4. The Remainder^ which is always less than ih^ di- 
 visor, and of the same name with the Dividend. 
 RULE. 
 
 First, seek how many times the divisor is contained in 
 as many of the left hand figures of the dividend as are 
 just necessary, (that is, find the greatest figure that the 
 divisor can be multiplied by, so as to produce a product 
 that shall not exceed the part of the dividend used) Vvhen 
 found, place the figure in the quotient ; multiply the di- 
 ffisorby this quotient figure; place t'he product under 
 Aat part of the dividend used ; then subtract it there- 
 from, and bring down the next figure of the dividend to 
 the right hand of tiie remainder ; after which, you must 
 seek, multiply #nd subtract, till you have brought ihnvn 
 every figure of inn dividend. 
 
 Proof. Multiply the divisor and quotient togedier 
 and add the remainder if there be any to the producl: ; '\l 
 the work be right, the sum will be equal to tlie dividciid.* 
 
 "^ Another method Tvbich some make ima of to prove divi 
 sion is as follows : viz. Add th^ remainder and all the pro- 
 cIUQts of the 56^ era? quotient %ares multiplied b.y the dlvisc^r 
 
DIVISION OF WHOLE NUMBERS. 
 
 3? 
 
 I. Ho^v many timeii is 4 tZ. Divide 3b5G doUuri 
 
 contained in 9391 ? equally among 8 mea. 
 
 Divisor,Div,^uotient Vivisor^Div. Quotient, 
 
 4)9391( 2347 8)3656(457 
 
 8 4 S2 
 
 13 
 12 
 
 19 
 16 
 
 9388 
 -f 3 jRe?n. 
 
 9391 Proof. 
 
 45 
 40 
 
 56 
 56 
 
 SI 
 
 3656 Proof t^ 
 additionr 
 
 5 Eeniahider. 
 Di4}isDr,Div. Quotient. 
 a9) 15359(529 
 145 
 
 Proof by 
 careers of 9's 
 5 
 
 •x^ 
 
 85 
 
 58 
 
 fi79 
 
 261 
 
 565)^9640(136 
 S6t^ 
 
 1514 
 
 1095 
 
 2190 
 2190 
 
 Bemains 18 llem, 
 
 togedier, according to the order in which they stand in the 
 work 5 and this sum, when the work is right will be equal to 
 the dividend. 
 
 A third method of proof by excess of nines is as follows, Tie. 
 
 1 . Cast the nines out of the divisor and place th« mlcom 
 on the left hand. 
 
 £. Do the same with the quotient aad place it on the right 
 band. 
 
 3. Multiply these two figures together, and add their pro- 
 duct to the remainder, and reject the lunes and place the ex- 
 cess Ht top. 
 
 4. Cast the nines out of the dividend and plact; the esoesi 
 
 at bottom. 
 NoTs. S"Uic sum U ilgliT, (bo Ttv) fOid boKdm ti^wes trfll 
 
so DIVISION- OF "V^'UOLE NUMBKRSi. 
 
 DivisQr.Div.quotient. 95)85595(901 
 
 61 )28609(469 736)86S25S(1 17^ 
 
 47^2)25 1 1 04(532 there remains 664 
 
 9. Divide 1895312 by 912. Jlns, 2076. 
 
 0. U]v\(\e '893312 by 2076. Ans. 912» 
 
 U. iiivide 47254149 by 4674. ^ns. lOllO^Vr- 
 12. What is the quotient of 330098048 divided 6jr 
 4207 ^ Jlns. 78464. 
 
 IS. What is the quotient of 761858465 divided hj 
 8465 ? Jlns. 90001. 
 
 14. How often does 761858465 contain 90001 ? 
 
 Jlns. 8465. 
 
 15. How many times 38473 can you have in 119184693 ? 
 
 ^ns. 3097111^, 
 
 16. Divide 2B0208122081 by 912314. 
 
 quotient 307140^^3^-^ 
 
 MORE EXAMPLES FOIl EXBRC13E, 
 
 Divisor. Dividend. Remainder* 
 
 234063)590624922((itfoiien^)8S973 
 47614)327879186( } 9182 
 
 987654)988641654( ) •..0 
 
 CASE II. ^ ^ 
 When there are cyphers at the right IiailJ of the tlkl- 
 •or ; cut off the cyphers in the divisor, and the sanro 
 number of figures from the right hand of the dividend, 
 tlien divide the remaining ones as usual, and to the re 
 maindei^ (if any) annex those figures cut oS'from Ijlre dlvl* 
 ffend, and you will have the true remrander. 
 
 EXAMPLES. 
 
 1. Divide 4673625 bv 21400. 
 214{00)46736)25(2185\W^true quatient by Kestitutiott. 
 428.. 
 
 S4^5 true rem. 
 
COSTilAOTXONS IN* DIVISION. O/ 
 
 0. Diade Sr943*375 bj 6500 J^r.s. .^8374'^' 
 
 5. Divide 4£1400J00 ' 49000 ^^ds. 
 
 4. IVividc 1160911^. !>y 89000 .. i;2S. ;31a ' 
 
 5. Divide 9187642 b- 91700'J:;. '^i^. S-^ ,, 
 
 MOHE v. SAMPLES. 
 
 JDlvif' \ Di^'dend, - 
 
 \25000)4$(^^^'0i'^ql^otien 
 
 1 20000) I4959647t( i/t-ir?. 
 
 901000)6 4S47250( )2r:?30 
 
 720GOO)987654000( ^.5S40^ 
 
 CASE ill. 
 
 Short Division is whea the divisor does Kot exceed 12. 
 
 RULE. 
 
 Consider how many times the divisor is contained in 
 
 the firsi: iT;;;i)re oriiguresof the dividend, put the result 
 
 under, and carry as manj tens to the nesrt ii^ire as there 
 
 are cHies over. 
 
 Dmde evxry figure 'n the saHie manner till tlie wliole 
 is finished. 
 
 EXAMPLES. 
 
 Divhm\ Dividend, 
 
 £) 113415 3)85494 4)39407 5)94379 
 
 ^nothiit 56707 — 1 
 
 6)120616 7)152715 8)95872 9)118724 
 
 n)6986ig7 12)14814096 12)570196382 
 
 Contractions in Division. 
 
 When the divisor is such a mimber, t3ia.tany twofig* 
 ur£S in the Table, beingaiultipiied together will produce 
 it, divide the given dividend by one of those figures ; the 
 <]Uotient thence arising by the" other ; and *&e last qua- 
 Uentwill be the answer. 
 
 NoTK. The total rcRiaindci' is found b^ ccTi.trpnng 
 tiTctiist j*(5.inriin'.!cr by the fir.^ divisor, and t^ang m the 
 
SHrrLEMENT TO MULTIPLICATIOX. 
 
 Divide 16£641 by 72. 
 'i) 162641 or 
 
 EXAMPLfiS. 
 
 8)18071—2 
 
 J2258— 7 
 
 8)162641 last rem. 7 
 
 9)20530—1 x9 
 
 2258—8 63 
 frstrem. -|-2 
 
 True ((uotient 2258f| 
 
 by 16. 
 by 24. 
 by 35. 
 by m. 
 by 48. 
 by 54. 
 by 84. 
 by 108. 
 10. Divide 1575360 by 144> 
 
 2. Divide 178464 
 
 3. Divide 467412 
 
 4. Divide 942341 
 
 5. Divide 796S8 
 
 6. Divide 144872 
 
 7. Divide 937387 
 
 8. Divide 93975 
 
 9. Divide 145260 
 
 Time rem, 65 
 
 Jlns. 11154 
 
 dns. 19475-J-l 
 
 Ans. 269244^ 
 
 Ms. 2212j%. 
 
 J171S. 3018;^ 
 
 Ans. 17S59X 
 
 Ms. ln^i 
 
 Ms. 1345 
 
 Ms. 10946 
 
 2. To divide by 10, 100, 1000, Sgc* 
 
 RULE. 
 
 Cut off as many figures from the right hand oF i\ic divi- 
 dend as there are cypners in the divisor, and these figures 
 •0 cut of!' are the remainder; and the otiier figures of the 
 •Kvidend are the quotient. 
 
 Divide ''yGS 
 
 EXAMPLES, 
 
 by 10. Ans. 
 
 50 and 5 remains. 
 
 :>:'*ide 5762 by 100. Ans. 57 —62 rem. 
 Oi^ide '^65753 by 1000. Ms. 753 —753 rem. 
 
 vSUPFLEMSNT TO MULTIPLICATION. 
 
 T? multiply by a mixt number rthat is a whole num- 
 er Joined with a fraction, as Si, S^^Qiy occ. 
 
 RULE. 
 
 M*o ilaph by the whole number, and take i, f , ^. &c. of 
 fes M^i^caiiC; imi add it tothcnrcdact. 
 
^¥EPL^MBNT TO MULTJLPLIOATION. 89 
 
 EXAMPLES. 
 
 Multiply 37 bySSJ. Multiply 48 by H 
 
 2)37 48 
 
 23i ^ 
 
 I83 
 111 
 74 
 
 £4*J 
 
 12= 
 
 =i 
 
 96 
 
 
 1S2 Ms. 
 
 Ms. 
 
 106551 
 
 •ins. 
 
 205334 
 
 Ms. 
 
 6594 
 
 Ms. 
 
 334134 
 
 869i Mswer. 
 h Multiply 211 by 50i. 
 
 4. Multiply 2464 by 8^. 
 
 5. Multiply 345 by 19|. 
 
 6. Multiply 6497 by 5|. 
 
 ({iiesiions to Exercise Multiplication and Division. 
 
 1. Wliat will 9j tons of hay come to, at 14 dollars a 
 ton? Ms. S136i. 
 
 2. If it takes 320 rods to make a mile, and every rod 
 contains 5i yards ; how many yards are there in a mile ? 
 
 Ms. 1760. 
 
 3. Sold a ship for 11516 dollars, and I owned | of her 5 
 what was my part of the money ? Ms. S8637. 
 
 4. In 276 barrels of raisinsj eaeh 3} cwt. how many 
 hundred weight ? Ans. 966 cwt. 
 
 5. In 36 pieces of cloth, each mece containing 24i 
 yards ; how many yards infhe whole ? Ms. 873 yds. 
 
 6. What is the product of 161 multiplied by itself? 
 
 Ms. 25921. 
 
 7. If a man spends 492 dollars a year, what is that per 
 calendar month ? Ms. g41. 
 
 8. A privateer of 65 men took a prize, which being 
 equally divided amon^ them, amounted to 119/. per man ; 
 what is the value of me prize ? Ans. £77S5. 
 
 9. What number multiplied by 9, will make 225? 
 
 Ans. 25. 
 
 10. The quotient of a certain number is 457, and the 
 divisor 8 ; what is the dividend ? dns. 3G56. 
 
 1 1 What cost 9 yds. of cloth, at 35. per yard ? 
 
 Ans. 27s. 
 1 2. Wliat cost 45 oxen, at Si per head ? Ans. £360. 
 
40 cor.i)?oT;>'D ADinTiON 
 
 IS. What cost s -r • V'h of tn:ligo. at 2 dols. SO'ctR. nr : 
 250 cents per lb. ' dns, S360. | 
 
 14. Writedown four thou^sand-A i ; v- r.'l an^l ^even- 
 teenj multiply it by twclvej divide the product by nine, 
 and add 365 to the quotient, then from that sum subtract 
 live thousand five hundred and twenty-one, and the re^- 
 mainder will be just 1000. Try it and see. 
 
 it nua^j n j i Mwtn. -gt 
 
 COMPOUND ADDITION, 
 
 j-S the adding- of several nuin!)ers together, having dif- 
 terent denominations, but of i\v^ same generic kind, io 
 
 pounds, shiirin<5S and pence, ivr. ''\"-: ' —.dreds, rpaar- 
 tcrs, &c. 
 
 i. Place the iiunibers ^o that lliose of the stiinc dcnam- 
 1 nation may stand directly under eacli other. 
 
 2. Add the first coluiiip. or denomination together, a3 
 in. whole nu.vibers; then divide the sum by as many of 
 the same denomination as maiie one of iA\Q next greater t 
 setting dovrn the remainder under the column added, and 
 •: rv tlie quotient to i\\e r.ext superior denomination, 
 . » v^iaii.g tiiC eamc to tiie lust, uiucli add, as in simplo 
 .u' i'iion. 
 
 1. STERLING ]\IONEY, 
 
 '.:, tlie money of account in Great-Britain, and is reck- 
 .:-din Poun'fls, Shillings, Pence and Farthings, ^o 
 the Pence Tables. 
 
 * The reason of this rule is evidenff*: For, addition of ihls 
 money, as 1 in the pence is equal to 4 in flie farthings ; 1 in 
 the shillings, to K^hi the, peacii ; and I in the pounds, to SO 
 in the shillings ; .cvthre carrying as directed, is the ar- 
 ranging; the mon; , arising from each coliimn, nroperly in 
 the scale of denon/iiiations; and this reasoning will hold goMl 
 in the addition of compound nnnd>er3 of any dni(yminatitp 
 whatever. 
 
0OM?OUND ADDtTIOX. 41 
 
 
 
 EXAMPLES. 
 
 
 £. s d. 
 
 VViiat is 
 
 1 the sum total of 47/. 135. 
 
 
 "47 li> 6 
 
 6^?.~19Z. : 
 
 25. 9id 
 
 .-^14Z. lOs. md. 
 
 
 19 2 94 
 
 and 12^ 9s. Ud. ? 
 
 
 Thus^ 
 
 14 10 lU 
 
 
 
 
 
 J2 9 H 
 
 
 >! 
 
 %Slnswerf£. 
 
 93 16 4i 
 
 ..♦f 
 
 £. s. d. qr. 
 
 £' ^ 
 
 
 17 13 
 
 11 
 
 84 17 5 3 
 
 30 1 
 
 11 4 2 
 
 M 10 
 
 2 
 
 75 13 4 2 
 
 15 : 
 
 10 9 1 
 
 , 10 ir 
 
 5 
 
 50 17 8 2 
 
 1 
 
 12 
 
 I 8 8 
 
 / 
 
 20 10 10 1 
 
 3 
 
 9 8 3 
 
 3 5 
 
 4 
 
 16 5 
 
 4 
 
 6 3 1 
 
 
 
 
 
 
 (5) 
 
 
 (6)^ 
 
 
 ^^> . 
 
 i i^- ^'* 
 
 d. qi\ 
 
 £. s. d. qr. 
 
 £• 
 
 s. d, qr 
 
 ,' 4r 17 
 
 6 2 
 
 7 17 10 S 
 
 541 
 
 
 
 S 9 
 
 10 S 
 
 60 6 8 
 
 711 
 
 9 8 1 
 
 . 59 17 
 
 11 2 
 
 7 14 11 2 
 
 918 
 
 16 9 3 
 
 \ S17 16 
 
 9 3 
 
 18 19 9 3 
 
 14C 
 
 > 15 10 1 
 
 762 19 10 1 
 
 91 15 8 2 
 
 300 
 
 1 19 11 3 
 
 407 17 
 
 6 2 
 
 18 17 10 3 
 
 46 
 
 I 10 7 3 
 
 1 19 
 
 9 
 
 5 12 
 
 fl 
 
 1 14 9 3 
 
 
 
 
 
 (8) . 
 
 (9) 
 
 (10) 
 
 £' 
 
 s, d. 
 
 £. s. d. 
 
 £^ 
 
 s. d. 
 
 105 
 
 17 6 
 
 940 10 7 
 
 97 
 
 11 6i 
 
 193 
 
 10 11 
 
 36 9 11 
 
 20 
 
 4 
 
 901 
 
 13 
 
 11 4 10 
 
 144 
 
 1 10 
 
 319 
 
 19 7 
 
 141 10 6 
 
 17 
 
 11 9 
 
 48 
 
 17 4 
 
 126 14 
 
 9 
 
 le loi 
 
 104 
 
 11 9 
 
 104 19 7 
 
 
 
 15 9h 
 
 90 
 
 16 7 
 
 160 10 6 
 
 19 
 
 9 4 
 
 111 
 
 9 9 
 
 100 
 
 234 
 
 11 lOi 
 
 976 
 
 10 
 
 9 9 
 
 180 
 
 14 € 
 
 449 
 
 12 6 
 
 1*9 6 
 
 421 
 
 10 S| 
 
 ^0 
 
 10 4 
 
 12# 8 
 
 841 
 
 16 4 
 
 M 
 
 >^^ 
 
II. Find tlie amoinit of the foIlowing"^ f^, 
 aums, viz. 42/. 13s. 5af.— Hi. 10s. — 4/. t 
 irs. 8<^.— is;. Os. 7(^.— .19s. 4ifZ.— sr/.f 
 and 15L 6s, J 
 
 1 
 
 -5?2S. £. IM 7 0-h 
 
 1£. Add 504Z. 5s. and Oic?.-— 34Z. 19^\ TJ.— r/. TsM^i. 
 •^247/. Os. llrf.— 19s. 6d. lcp\ and 45/. togetlier. 
 
 Jlns. r640 5s. 5-^i/, 
 
 15. Find the sum total of 14Z. 19s. 6^/.— llZ.4s. ^d.-^ 
 ^51 10s. — iL Os. 6i/.— 3/. 5s. 8«f.^l9s. 6^. and 0.5. Bil, 
 
 Jus. £60 Os. 5n, 
 
 14. Find the amount of the following snuns, viy'. 
 Forty pounds, nine shillingSj . . - - £. .^, a. 
 Sixtj-tour pounds and nine pence, - - 
 Ninety -live pounds, nineteen shillings, - 
 Seventeen snillinsis and 4^fK - - - - 
 
 o 
 
 .fc« /:. 201 6 l\ 
 
 15. How much is the sum of 
 
 Thirty -seven shillings and six pence, - 
 
 Thirty-nine shillings^and 4M\. - - - - 
 
 Forty -four shillings and nine pence, - - 
 
 Twenty -nine shillings and fliree pence, - 
 Fifty-sinllings, - - - - - 
 
 ^ns, £. 10 Os. 10^/i- 
 
 16. Bought a quantity of goods for 125L 10s. paid iW 
 truckage forty -five sliiliings, for freight seventy-nine siril- 
 lings and six pence, for duties tliirty-five shillings and ten 
 pence, and my expenses were fifty -three shillings and 
 nine pence 5 what did t]\e goods stand me in ? 
 
 Ans. jT. 136 4s. iV, 
 
 W. Six men took a prize, and having divided it equafry 
 amongst them, each man shared two nund red and farty 
 pounds, thirteen sldllings and seven pence 5 how much 
 money did the wliole prize amount to ? 
 
 ^ . JUis. £. 1444 Is. erf. 
 

 „^ 
 
 lb, 
 
 oz. 
 
 V7Vt, 
 
 p-. 
 
 /A. 
 
 oz. 
 
 /}w5- 
 
 frr 
 
 16 
 
 11 
 
 19 
 
 25 
 
 8 
 
 n 
 
 19 
 
 ^i 
 
 4 
 
 4 
 
 16 
 
 SI 
 
 6 
 
 10 
 
 IG 
 
 8 
 
 8 
 
 8 
 
 19 
 
 14 
 
 7 
 
 8 
 
 17 
 
 21 
 
 6 
 
 9 
 
 14 
 
 17 
 
 4 
 
 6 
 
 8 
 
 ir, 
 
 4 
 
 fr 
 
 10 
 
 •^ 
 
 9 
 
 7 
 
 14 
 
 17 
 
 
 
 r 
 
 11 
 
 12 
 
 •4 
 
 9 
 
 15 
 
 10 
 
 S. AVOIJlinJPOIS WEIGHT, 
 
 f 
 
 .Z5. 
 
 lb. 
 
 (TX. 
 
 c^r. 
 
 T. 
 
 civi. 
 
 qr. 
 
 //;. 
 
 QZ, 
 
 ^. 
 
 27 
 
 24 
 
 15 
 
 14 
 
 9T 
 
 17 
 
 2 
 
 24 
 
 15 
 
 14 
 
 1 
 
 17 
 
 17 
 
 12 
 
 11 
 
 19 
 
 9 
 
 
 
 17 
 
 10 
 
 12 
 
 o 
 
 26 
 
 28 
 
 12 
 
 15 
 
 14 
 
 15 
 
 2 
 
 04 
 
 9 
 
 n 
 
 1 
 
 13 
 
 16 
 
 8 
 
 »r 
 
 47 
 
 H 
 
 5 
 
 19 
 
 14 
 
 5 
 
 5 
 
 15 
 
 24 
 
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 12 
 
 (^ 
 
 00 
 
 t 
 
 00 
 
 00 
 
 12 
 
 -2 
 
 16 
 
 U 
 
 12 
 
 12 
 
 T7 
 
 19 
 
 5 
 
 27 
 
 15 
 
 H 
 
 4. APOTHECARIES \S' EIGHT. 
 
 5 9 sr. 
 
 .a 
 
 ? 3 ^»*- 
 
 
 fe 
 
 S 
 
 f> 9 ^r. 
 
 9 1 17 
 
 7 2 19 
 
 
 V^ 
 
 11 
 
 G I 15 
 
 S 2 9 
 
 6 
 
 5 i:'. 
 
 
 4 
 
 9 
 
 7 12 
 
 6 1 17 
 
 i 
 
 ii 1 7 
 
 
 9 
 
 10 
 
 1 9, 16 
 
 4 16 
 
 9 
 
 3 2 12 
 
 
 4 
 
 8 
 
 1 2 13 
 
 5 2 12 
 
 6 
 
 1 If) 
 
 
 9 
 
 
 
 1 10 
 
 e 1 10 
 
 
 
 6 2 19 
 
 
 4 
 
 9 
 
 2 1 G 
 
 
 5. 
 
 CLOTH JfEAS 
 
 URD. 
 
 
 I . Hi 
 
 ji. qy,7i(L. 
 
 
 J». JB. 5ri\ 
 
 m. 
 
 
 JEJ.F. qr.tja. 
 
 n 3 
 
 
 44 5 
 
 o 
 
 
 
 84 e 1 
 
 Is 2 1 
 
 
 45 4 
 
 5 
 
 
 
 07 1 5 
 
 10 1 
 
 
 06 2 
 
 o 
 
 
 
 76 2 
 
 42 3 5 
 
 
 S4 4 
 
 1 
 
 
 
 ,52 2 3 
 
 57 2 2 
 
 
 07 
 
 
 
 
 
 55 2 2 
 
 49 2 2 
 
 
 61 2 
 
 I 
 
 
 
 09 2 5 
 
6. DRY MEASURE. 
 
 ^Icqt.pL 
 
 ?;?*. pk\ qt. 
 
 iiU.lpk.qLp, 
 
 1 T 1 
 
 17 ^ 5 
 
 9,5 ^ 7 X 
 
 £ 6 
 
 Q4 9. 7 
 
 64 2 6 1 
 
 15 
 
 13 3 6 
 
 43 4 
 
 2 4 1 
 
 16 5 4 
 
 52 3 5 1 
 
 2 G 1 
 
 sr 2 6 
 
 94- 2 3 
 
 S 6 T.r 
 
 56 7 
 
 54 3 r 
 
 f 
 
 yds.fL in. 
 
 //.'• 
 
 4 2 11 
 
 f; 
 
 5 1 S 
 
 1 
 
 1 2 9 
 
 o 
 
 G 2 10 
 
 1 
 
 1 G 
 
 8 
 
 3 17 
 
 
 
 f . WINE MP^ASURE. 
 
 /r^i. 
 
 ,0f. 2-'"-^' 
 
 hh^. 
 
 ■C"?. f/f. ^f. 
 
 iun»hhd,gaLqt. 
 
 :>9 
 
 3 I S 
 
 
 3 1 
 
 34 2 34 2 
 
 1 r 
 
 2 1 2 
 
 
 2 
 
 19 1 59 1 
 
 £4 
 
 3 1 
 
 9 
 
 14 i 
 
 28 2 2 1 
 
 1^^ 
 
 i '' ' * 
 
 
 
 C 1 
 
 19 a 3-2 2 
 
 8 
 
 
 
 16 
 
 
 3r 3 n 1 
 
 40 
 
 ': 
 
 "t 
 
 
 1 G 
 
 8. LONG MKASUREi 
 
 m. jOir. 
 
 ■??o. 
 
 46 4 
 
 16 
 
 58 5 
 
 23 
 
 9 6 
 
 34 
 
 ir 4 
 
 18 
 
 r 3 
 
 15 
 
 5 2 
 
 24 
 
 U. 
 
 m.fur. 
 
 pc. 
 
 86 
 
 2 6 
 
 32 
 
 52 
 
 1 7 
 
 16 
 
 64 
 
 2 5 
 
 19 
 
 * -.7 
 
 1 4 
 
 15 
 
 '•r 
 
 2 3 
 
 25 
 
 28 
 
 2 4 
 
 17 
 
 9, LAT;D or SqUARE MEAStrilE. 
 
 acregtrco: 
 
 Is. rods. 
 
 acTPS^-i 
 
 roods»rods. 
 
 ^rv./>. 
 
 5?,W. 
 
 478 3 
 
 s: 
 
 odS 
 
 2 
 
 IS 
 
 5 
 
 136 
 
 816 2 
 
 J / 
 
 U) 
 
 3 
 
 00 
 
 6 
 
 129 
 
 49 1 
 
 27 
 
 9 
 
 1 
 
 39 
 
 8 
 
 134 
 
 (?5 S 
 
 34 
 
 1 
 
 3 
 
 00 
 
 
 
 146 
 
 9 3 
 
 S7 
 
 
 
 2 
 
 27 
 
 4 
 
 54 
 
10. Si>LII> MPASIiRli:. 
 
 41 
 
 {t 
 
 
 3 
 
 ^ 
 
 15 
 
 1446 
 
 19 
 
 43 
 
 
 
 4. 
 
 114 
 
 
 le 
 
 172Qf 
 
 49 
 
 6 
 
 
 
 7 
 
 as 
 
 
 3 
 
 868 
 
 4 
 
 2r 
 
 
 
 10 
 
 127 
 
 
 14 
 
 £34 
 
 
 
 
 
 
 . 
 
 
 
 n. 
 
 TIME, 
 
 
 
 r. 
 
 «p. 
 
 w. 
 
 (ffl. 
 
 
 Vr. 
 
 ^ 
 
 A, 
 
 m. &at. 
 
 5r 
 
 11 
 
 S 
 
 6 
 
 
 24 
 
 536 
 
 23 
 
 54 34 
 
 5 
 
 
 
 e 
 
 3 
 
 
 2J 
 
 40 
 
 12 
 
 40 CA 
 
 ^ 
 
 8 
 
 e 
 
 5^ 
 
 
 13 
 
 119 
 
 14 
 
 09 17 
 
 40 
 
 10 
 
 2 
 
 4 
 
 
 14 
 
 9 
 
 11 
 
 18 14 
 
 10 
 
 7 
 
 1 
 
 S 
 
 
 8 
 
 24 
 
 8 
 
 16 15 
 
 IS. CIUOULAn MOTIOI/. 
 
 S.^fti S. ^ ' "^ 
 
 5 29 17 14 11 29 59 59 
 I 6 10 17 00 4D 10 
 4 18 17 11 4 10 49 
 
 6 14 18 10 4 11 6 10 
 
 COMPOUND SUBTRACTIOK, 
 
 X EACHES to find flie diftcrejicc> ^j^equalityor crces^j 
 betwetiTi any two sums of diverse dtfaominatiojiB.. 
 
 RULE. 
 
 Place those numbci^ under eacli other, \i hich ars cl 
 the same denomination, the less l>eing below the greater ; 
 ^egin with the least denomination, and if it exceed fiie 
 figure over it, borrow as many units as make one of the 
 liext ereater ; subtract if tlicrefrom ; and to fbc diftArcnrx 
 add tne upper fi;5ure, remembering always to add one to tko" 
 Ocxtsypcrinr defimnlmition f(ir Ihjrt wni^rhyfTU b(Trc<nvc>J. 
 
Note. Tne method of proof is the samea* insimple 
 fiubtraction. 
 
 From 
 'I'ake 
 
 KXAMPLE* 
 
 1. Steiibi"; Momu, 
 
 £, s, d.qr, £. s. (Lqr. 
 346 16 5 3 14 14 6 2 
 123 17 4 2 10 19 6 3 
 
 94 11 6 
 36 14 8 
 
 r:eH>. 
 
 £•7 19 1 1 
 ved 44 10 2 
 
 36 11 a 
 
 RS 
 
 lid 
 
 r. 5. d. 
 
 '^5 
 
 4 19 11 
 
 
 
 Borrov 
 Paid 
 
 Lent 
 Received 
 
 Due to m( 
 
 7 1112 
 4 17 3 1 
 
 £, s, d. gr 
 36 8 2 
 18 10 7 3 
 
 Kemal 
 unpj 
 
 % 
 
 Tate 
 
 £. s, d, qr. 
 476 10 9 1 
 277 17 7 1 
 
 I^ein. 
 
 
 
 From 
 
 Take 
 
 141 14 9 2 
 19 13 10 2 
 
 (10) 
 
 £. s. d. 
 
 125 01 8 
 
 124 19 8 
 
 (11) 
 
 C s. d.qr 
 
 10 15 7 1 
 
 9 6 3 
 
 Kcm. 
 
 
 
 
 12. i5onowed 27Z. Ms. and paid 19?^. 175. ^d. how 
 ;iu.c?5 remains due ? Jim. £7 ISs. 6rf. 
 
 VZ. llow jniich does 3I7Z. 6.^-. exceed Vi^l. 18^. 5^^. ? 
 
 ^/2-s. £138 75. 6^a. 
 11, Frcm eleven pounds take eleven pence. 
 
 Ms. £10 19s. \d. 
 15. From seven tliousand two liundred pounds, take 
 >y^ Us. GyL Ms. £7n\ 9.S. 5id. 
 
COMPOUND SUiri'KACYXOK. •^T 
 
 16. How much docs seven hundred and eight pounds, 
 exceed tldrty-nine pounds, fifteen shillings and ten pence 
 halfpenny? ^ns. ^668 4s. Ud. 
 
 17. From one hundred pounds, take four pence half- 
 penny. Ans. £99 I9s. 7 id, 
 
 18. Received of four men, the following sums of money, 
 viz. The first paid me 57^. lli\ 4rf. the second 25Z. 16s. 
 7d. the third 19Z. 14s. GJ. and tlie fourth as mucli as all 
 the other three, lacking i9s. 6d, I demand the whole 
 sum i^gipived ? Ans. y^ 165 5s. 4d, 
 
 Frmn 
 Take 
 
 lb, 
 6 
 
 oz. 
 
 11 
 
 3 
 
 O 
 
 pXvL 
 14 
 16 
 
 IROY WEIGHT. 
 
 oz.pwtgr. lb. ox. imit.gr. 
 4 19 21 44 9 6 19 
 2 14 23 17 5 16 IS 
 
 Rem. 
 
 
 
 
 
 
 Ih. 
 
 684 
 683 
 
 ox 
 2 
 
 i 
 
 pwt. 
 
 10 
 
 9 
 
 c:;* ih, ox. plot, p\ 
 
 14 ^ 942 2 
 
 15 892 9 2 
 
 
 
 
 
 • 
 
 Ih, oz. 
 7 9 
 3 12 
 
 dt\ 
 
 12 
 9 
 
 
 A V vO I K D U r 1 S E W B I G H T 
 
 5 i 15 n 12 i 1^0 9 
 
 
 
 
 P ' 
 
 T. cii'i*. qr, lb. oz. di\ T. ctvi, qr. lh.%z. dr. 
 
 810 11 .20 10 11 Sir 12 1 12 19 12 
 
 193 17 1 20 12 14 180 12 1 14 |o 14 
 
 AV0TKEC?IK1ES^ WEIGJlT. 
 
 19 8 7 4 1 37 iS5 7 5 I 14 
 
 9 11 6 1 £ 15 17 10 6 1 IB 
 
48 
 
 CQ.MiV)u':^l> SVBTKAfl^J.O>J(? 
 
 5*. OLO'fH MEASURE. 
 
 13. qr.n^ 
 55 1 £ 
 l| 1 3 
 
 E.E. m\ 
 
 467 S 
 291 5 
 
 1 
 
 C 
 
 76S 1 5 
 X49 £ t 
 
 
 
 
 
 y2, (7r».4i2i?!, 
 
 513 5 1 
 
 ir4 i 
 
 E.E. qi'. 
 615 
 
 £26 2 
 
 7ia. 
 
 1 
 
 
 
 E.FL qr,m. 
 
 
 
 
 
 &l. ^1\ q^ 
 14 3 4 
 
 6. DRY MT.ASUKiiN^- 
 
 8 15 -^ 17 fi 5 
 
 3 16 e 2 e i 
 
 0l ^. ^. ^. 
 £10 1 
 
 :4 2 1 
 
 r. VINE M:^.iSXJHE. 
 
 /iftt?, gal. qi. fit. T.hhd.gcd. qtph 
 13 3 £ 3 20 3 1 
 
 10 6051 ie£roo 
 
 hhd. gtll. qt. pt. 
 
 G12 £3 1 
 
 7:5 37 1 1 
 
 4 £ 11 
 
 e £ 11 1 
 
 2,7 1 '6 67 
 19 £ 4 SD 
 
 
 
 
 
 JJuL 
 5£1 
 256 
 
 14 
 £5 
 
 5#. ,;/. 
 £ 1 
 3 
 
 
 8. LONG MEASURE. 
 
 in. fuT.pc. 
 41 6 £2 
 
 10 
 
 6 
 
 £5 
 
 
 
 
 
 
 le, 
 16 
 10 
 
 1 
 
 fur. 
 3 
 
 3 
 
 5 
 
 .J 
 
 
 
 
 U:, m. far. pa. 
 86 2 6 S£ 
 24 1 7 31 
 
 
 15. 
 
 VI. 
 
 fdr. 
 
 ITO. 
 
 9 
 
 £ 
 
 
 
 r 
 
 1 
 
 1 
 
 1 
 
 J 
 
9. LAND OR SqUARB AQCAStJlOi:. 
 
 JK roods, rods. 
 ^9 1 10 
 
 CA 1 25 
 
 Jl. r. po. 
 
 s^fi.sg.iu. 
 
 29 e 17 
 
 599 181 
 
 17 1 56 
 
 19 1S3 
 
 •tf, ^r. r^d^. ^. qr. rods, sg.fi. sq.ixu 
 
 --^ 25 ISO 1 10 gfiO 84 
 
 rg 
 
 119 1 37 49 ^1 11 143 la 
 
 ID. SOLID MCASXJRJET^ 
 
 tans, jfif . 
 116 24 
 109 59 
 
 canf 5. /if. 
 
 tm^ S^ 
 
 vt. 
 
 72 114 
 
 45 18 
 
 140 
 
 61 120 
 
 16 14 
 
 145 
 
 11. Tj5ifr> 
 4B 11 S 5 14 356 20 49 19 
 
 yr9. mo, w. (tit, yr$. dcnjs, li. wi^ seSi 
 
 f^ 11 S 1 24 352 20 41 2p 
 
 
 
 
 WUJ2. 
 
 
 w. 
 
 d. 
 
 h. 
 
 set. 
 
 472 
 
 2 
 
 15 
 
 18 
 
 4Q 
 
 218 
 
 4 
 
 16 
 
 29 
 
 54 
 
 
 w. d. h. rtdru szc* 
 781 1 8 j^ 21 
 
 197 S*t|2fp 53 
 
 l2. OlBCLaAR JIOIIOJ^. 
 
 •;sr. • ' • iSr. • ' • 
 
 9 23 45 54 9 29 34 54 
 
 3 7 40 55 r 29 40 36 
 
 ■• "I •" llif-« ■■! ■ i^»M II I ■ I II 
 
 /y 
 
QUESTIONS, 
 
 S'howing the use of Compound Mdiiimi and Suhtraclii^ 
 
 NEvV-YORK, MARCH 22, IS 14. 
 
 3. Bought of George Grocer, 
 
 12 C. Sqrs. of Sugar, at 52s. per cwt. £ S3 13 
 
 2 8 lbs. of Rice, at 3c?. per lb. '^0 7 
 
 5 loaves of Sugar, Art. 35lb. at Is. Id. per lb. 1 1/11 
 
 S C. 2 qrs. 14lb. of E^iisins, at 36s. per CAvt, o I^ 6 
 
 £41 5 S 
 
 2. Wiiat sum added to 17 Z. lis. S^d. will make lOOL? 
 
 ^^KS. 8£Z. 8s. 3(^. 3r/?-* 
 
 S. Borrowed 501. 10s. paid again at one time 17^." i !«. 
 6i. and at another time, 9^. 4s. Sd. at another time 7L - 
 9s. 6^. and at another time 19s. did. how much remains 
 unpaid ? Ms. £ 15 4s. 9i(/. 
 
 4. Borrowed lOOZ. and paid in part as ibllov/s, viz. at 
 otte time 9.11. lis. 6d. at another time 19Z. 17s. 4kL at 
 another time lOdpUars at 6s. each, vrad at another time 
 two English guineas at 28s. each and two pi star eens^ at 
 I4irf. eacii ; how much remains due, or uiipaid ? 
 
 Ans. £52 12s. S^J. < 
 
 5. A, B, and C, drev/ tlicir prize money as foilov.s, viz. 
 A had f5l. 15s. 4.d. B iiad "^threc times as much as A, 
 lacking 15s. 6d. and C, had just as much as A and B bcih} 
 pr^y how ranch had C ? Jlns. £S02 5s. lOd, 
 
 6. I leHt Peter Trusty 1000 dols. and afterwards lent 
 him 26 dols. 45 cts. more. He has paid me at one tiaic 
 361 dols. 40 cts. and at another time 416 dels. 09 cts. be- 
 sides a note which he gave me upon James Paywcll, for 
 145 dols. -90 cts. : hov/ stands the balance between us ? 
 
 Jns. The bcdance is ^105 06 cis. due to me, 
 r. Paid A B in full for E F's bill on me, for 10 JL lOff. 
 v;z. Ij^ave him Richard Drawer's note for loL, 14.?. 9i» 
 l\'ter tfohn son's do. for SOL Os/^Cid. an order on llobert 
 j)oaler for S9L lis. the rest I mahC up in cash. I wai\| 
 c'j know ^^liat sum will make up fhe denclencj ? 
 
 dns. £^ s:.. ^iCt 
 
'^- 
 
 ULl'lPLlOATlON 
 
 r. \ nicrcuaut iind six debtors, M'ho togct:ier, owed him 
 9,91; l. 105. 6rf. A,B, C, D, and E, owed him 1675/. ISs 
 Qd. (S it; what was F's debt? Ans. £1241 16s-. 9iL 
 
 9. A merchant bou|[^ht 17('. 5-qrs. 14lb. of sugar, of 
 vhidi he sells 9C. oqrri. 25lb. how much of it remains 
 unsold ? y*- " .^ws. 7C. ^qrs. \7lh. 
 
 \{), From a fasliionable piece of cloth vvhich contained 
 52j(is. 2nn., a taylor was ordered to take three suits, eacli 
 6j('s. 5:(|vs. how mucli remains of the piece ? 
 
 Jins, S2yds, 2qrs. 2na. 
 
 1 . The war between England and America commen- 
 ced a^-i^ril 19, ,1775, and a freneral peace took place Jan 
 uarj -wOlh, 17S;1: Low 'oiiji; did the^ war continue? • 
 
 JiiiSs Tyrs, 9 mo. Id, 
 
 COMJPOUND MULTIPLICATION. 
 
 Co:!iIPOUND Multiplication is when the Multiplicand 
 consists of several denominations, &c. 
 
 T. To Midti/ply Federal Money. 
 
 RULE. 
 
 iSIultiplj as in whole numbers, and place the separa- 
 trix as many figures from the right hand in the product, 
 as it is in the multiplicand, or given sum. 
 
 -^ ' EXAMPLES. 
 
 •^ S cts. g f7. cm. 
 
 1. Multiply S5 09 bv25. 2 Multiply 49 5 by 9r, 
 
 25 " .97 
 
 1754b 54S0S5 
 
 7018 ^ ^ 441045 
 
 Frod. S87?, 4^ • S4753, 4 8 5 
 
 ^..Multi'}^^' 1 doi. 4 cts. by 505 Ms. 317, 20 
 
 4. iMuitiply 41 cts. 5 mills by 150 Ms. 62, 25 
 
 5. Multiply 9 dollars by 50 Ms. 450, 00 
 €. ?.lultiply 9 cdlmhy 50 Jtns. 4, 5a 
 r. Multiply 9 miflTby 50 Ms. 0,, 45 
 
3. There were forty-ane men concerned in tke paj 
 incnt of a sum of money, and each paid 3 dollars ana 9 
 mills ; how much was paid in all ? 
 
 Jlns. gl23 SGcfs. 9mills 
 
 9. The number of inhabitants in the United States i5 
 ilvf) millions ; now suppose each should pay the trifling 
 sum of 5 cents a year, for the term of 12 years, towards a 
 continental tax ; how many dollars would be raised 
 tftcreby ? "^ 
 
 Atts, three millions Dollar f, 
 
 £» 'H JTultijph tlie Denominations cf Sterling Monevj 
 Weights f Measures^ Sjz* 
 
 RULE.* 
 
 Write down the Multiplicand, and place the quantity 
 Gnderneath the least denomination, for the Multiplieip^ 
 and in multiplying by it, observe the same rules for carry- 
 ins from one denomination to another, as'nn Compouxdl ' 
 Audition. 
 
 INTBODUCTORY EXAMPLES 
 
 
 
 /:. 
 
 s. d, q. 
 
 
 
 
 
 s.d. 
 
 Ml!} 
 
 tjply 1 
 
 11 6 2 
 
 hj3. 
 
 
 How much is 
 
 S times 11 8 
 
 
 
 
 5 
 
 /;. 
 
 s. 
 
 a. 
 
 
 s 
 
 Vr 
 
 £^ 
 
 17 8 £ 
 
 1 15 5 
 
 
 d. 
 
 , 
 
 s. d. 
 
 '\5 
 
 10 
 
 8 
 
 2 
 
 
 9A 
 
 12 
 
 G 
 5 
 
 n 
 
 15 S 
 4 
 
 15 n 10 10 16 4 SI 10 9J 
 
 5 7 
 
 ® When accounts are kept in pounds, shillings and penCCj^ 
 (his kind of mdtiplication is a concis^mid elegant method of 
 irnding tlie value of goods, at so muflper yard, ib. &c. the 
 g^Tn^S v\i^ biytrf; to mitltipi^ fbe glveffprico by the qxiantity 
 

 
 flOMrOUA'D MULTlI'UiBATifN.. 
 
 
 6. 
 
 SI 
 
 IG 
 
 8 
 
 1:3 17 10 
 
 14 10 
 
 ri 
 
 
 
 S 
 
 9 
 
 
 10 
 
 
 32 
 
 12 
 
 10 
 
 G 19 1 
 
 26 8 
 
 4J 
 
 
 
 u 
 
 12 
 
 
 12 
 
 
 Fr act leal Questions. 
 
 W!:at cost nine yards of cloth at 5s. 6d. per yard ? 
 £0 5 6 price of one yard. ' 
 Tvluliiply by ' 9 yards. 
 
 Jiiis, £ 2 9 6 pric(? of nine yards. 
 
 r. «^. d. £. s. d. 
 
 4 Gallons oi v/inc, at 8 7 per gallon. 1 14 4 
 
 5 C. Maiaj;a Raisins, at 1 2 t^ per c^vt. 5 11 5 
 
 7 re:i:n.i of paper, at 17 9^ per ream. 6 4 GJ 
 
 8 yds. of broadcloth, at 1 7 9^ per yard, li 2 4 
 
 9 lb. of cinnamon, at 11 4i^perlb. 5 2 2| 
 
 11 tons of hay, at 2 110 per ton. 23 2 
 
 12 bwshels ofapples, at 1 9 per bush. 1 10 
 12 bushels of v/heat, at 9 10 per bush. 5 18 
 
 2. Wlicn the multiplier, that is, the quantity, is a com- 
 posite number, and greater than 12, take any two such 
 numbers as when muitiplicd together, will exactly pro- 
 duce the given quantity, and multiply first by one of those 
 figures, and that product by the other 5 and the last pro^ 
 duct ^viU be tlie answer. 
 
 EXAMPLES. 
 
 ■\Vliat cost 28 yards of cloth, at 6s. lOd. per ysrd ? 
 
 6 10 price of one yard. 
 
 '^' ' ''^ly by 7 
 
 2 7 10 price of 7 yards. 
 
 *^ 
 
 Mver, £ 9 11 4 jj^ice of 28 jaidSr 
 
 5* 
 
cq:^: i^Ou m :> Min,rjivi;,]cxTiOK . 
 
 
 
 
 <•* 
 
 il. 
 
 gr5. 
 
 
 ^ 
 
 yards 
 
 at 
 
 7 
 
 4 
 
 3 per yard, = 
 
 27 
 
 — 
 
 at 
 
 9 
 
 10 
 
 
 
 — , ~: 
 
 44 
 
 — 
 
 at 
 
 12 
 
 4 
 
 2 
 
 -— 
 
 5a 
 
 — . 
 
 r>A 
 
 8 
 
 S 
 
 1 
 
 s= 
 
 7^ 
 
 — 
 
 ^f 
 
 19 
 
 A 1 
 
 
 
 — «• =2 
 
 £D 
 
 ^_ 
 
 ^^ 
 
 3 
 
 6 
 
 55 
 
 -— = 
 
 &4 
 
 ._ 
 
 at 
 
 LS 
 
 4 
 
 2 
 
 <— = 
 
 fi3 
 
 . — , 
 
 at 
 
 11 
 
 9 
 
 
 
 *— =:= 
 
 G3 
 
 -^ at 
 
 £-i 
 
 17 
 
 6 
 
 
 
 — — ra 
 
 H4 
 
 --- at 
 
 1 
 
 4 
 
 o 
 
 
 
 •— rr: 
 
 AKswjs;:;^. 
 
 £• 
 
 .^. tf. 
 
 8 
 
 17 6 
 
 33 
 
 5 6 
 
 £7 
 
 4 6 
 
 22 
 
 14 lOj 
 
 71 
 
 14 
 
 3 
 
 10 10 
 
 77 
 
 3 6 
 
 56 
 
 8 
 
 118 
 
 2 G 
 
 174 
 
 
 
 3. ""."/hen no two numbers muUiplied together will ex- 
 actly make the nvaltipriGr, you must multiply by any two 
 ^rliose protluct will come the nearest ; then multiply ijhe 
 Upper line by what rcm?Jned ; vrliich added to the last 
 product gives the answer. 
 
 EXAMPLES. 
 
 ^'^Imt will 'u yds. of clotli come to at \7^?M, per yd. ? . 
 
 \7 9 price of 1 yai'd, 
 
 Multiply !>y 5 
 
 Produces 4 3 9 price of 5 yards, 
 J^IuUId'v bv 9 
 
 PrwliJccs 39 18 9 price of 45 yards* 
 1 15 6 price of 2 yard^* 
 
 *5;:t5s:-c:% /: 41 14 S price of 47 yards. 
 
 CttrES'no:rs. an'^WSRS* 
 
 25 ells of linen, at 3 0^ per ell. 
 
 !7 ells of dov/liicj at 1 6^ per ell. 
 
 \ d9 cwt. of siigar, at 3 10 6 per cwt 
 
 * 52 yds. of cloth, at 5 9 per yd. 
 
 ' X9 ibs. of indi«o, at 11 6 per lb. 
 
 ^ £9 yds. of caviibric. at IS 7 per yd. 
 
 ^tll vd^. broad dojh, at 1 S 6 « per yd. 
 
 gS^ U^ve h>'?L'^j set 1 9 4 a|^ccB> 
 
 4 
 
 1 
 
 5\ 
 
 1 
 
 6 
 
 ^i 
 
 137 
 
 9 
 
 6 
 
 14 
 
 19 
 
 
 
 10 
 
 18 
 
 6 
 
 19 
 
 IG 
 
 11 
 
 124 
 
 17 
 
 6 
 
 m 
 
 t? 
 
 a 
 
4^ To find ific value oi' a inniCH c^i wc^^i*,!", hy Viaviifv 
 
 [ fhc price of one I'O'mci. 
 
 I If the pice bo farthings, muitiplv 2*. 4t]. by the far- 
 {hin*;? in the j>rlce of one lb. — Or, if the j.'nccl>e nence, 
 mnltiplj 9.S. 4d. Ijy tiic pence in the price of one li). and 
 in either case tlie 'product will be the cms'.ver. 
 
 What will 1 cv;t. of rice cometOja.! 2^d. per Ih. ? 
 
 112 fi!rthings«=2 4 price 1 cwt. at ^<1. per lb. 
 
 9 faithings in tlic price of 1 ib, 
 
 ^nfi.£l 1 price of 1 cwt. at 9 v per Ib. 
 What will 1 cwt. o( lead coine to at Td. ner iV? 
 
 ^n^, £3 5 4 
 
 (liiestions, Jlnswers, 
 
 1 cwt. at 2^ per lb. = £1 S 4 
 
 1 ditto, at 2|d -« = i 5 8 
 
 1 ditto, at Sd —=180 
 
 1 ditto, at-2d --. = 18 8 
 
 1 ditto, at 5 id -» c= 1 12 8 
 
 Examf.es of Weights, Measures^ i^'t^ 
 1 KcTVTnuchfs 5 times Tcwt. 3q?^. 15 Ib. r" 
 Cwt. ijrs. lb. 
 r 5 Id 
 5 
 
 
 4ff»s. Cwt 
 
 . S9 
 
 .1 
 
 19 
 
 
 
 
 
 
 
 lb oz. 
 
 7?u*#. 
 
 i^r. 
 
 
 ( 
 
 :7^'f. 
 
 qr. 
 
 ?&. 
 
 oz. 
 
 S.A1 
 
 uttSj)!j 2D 2 
 
 7 
 
 isb 
 
 4 
 
 7 4. 
 
 P) 
 
 o-^ 
 
 I 
 
 13 
 
 12 
 
 p.r.; 
 
 »r! Pa 80 9 10 . 
 
 c4 
 
 
 I^. 
 
 1G4 
 
 
 
 £6 
 
 a 
 
 /r*' 
 
COMrOTJKD MULTlVMCA ( ION, 
 
 pr™', 
 
 ANSWERS* 
 
 yds. (jr. na. 
 
 7/is. qi\ na^ 
 
 4. Miiiti])l/i4 3 2 bv 11 
 
 163 2 2 
 
 hhd. -. qt. pt. 
 
 hhd. g. qt. ft. 
 
 5. ]\fiiltlply 21 i J C 1 by 32 
 
 254 61 2 
 
 le. r.i.jiw. fo. 
 
 le. m.fiir. jt>*. 
 
 6. Multiply 81 2 G 21 by S 
 
 6j5 1 4 8 
 
 ^i. r. p. 
 
 «. r. |7. 
 
 7. Multiply 41 2 U by 13 
 yr, vu IV. fi. 
 
 748 38 
 
 ?/r. 721. ic\ d. 
 
 8. Multiply 20 5 3 6 by 14 
 
 23G 5 2 
 
 S. "^ ' '/ " 
 
 fS', ^ ' " 
 
 5. Multiply 1 15 48 24 hv 5 
 
 r 19 2 
 
 cds.fL 
 
 cds. ft. 
 29 5^ 
 
 10. Multiply S 87 by 8 
 
 Fraciical ^^iicstions in 
 WEIGHTS & MEASURES. 
 
 1. What is the weight of rhlids. of sugar, each weigh- 
 ing 9 cwt. 3 (ps. 12 lb. ? Ms. 69civL 
 
 2. What is the weight of 6 chests of tea, each weigh- 
 ing 3 cwt. 2 qrs. 9 lb, ^ Ans. Qlcwt. Iqr. 26Z6. 
 
 3. How much brandy in 9 casks, each containing 41 
 gals. 3 qts. 1 pt. ? Arts, i^76gals. Qqts. Ipt. 
 
 4. In 35 pieces of cloth, each measuring 27^ yards, 
 how many yards ? Ans. 971yds, Iqr, 
 
 5. In 9 fields, each containing 14 acres, 1 rood, and 
 25 poles, how many acres .^ Jlns, 129a. Qqrs. QSrcds. 
 
 6. In 6 parcels of wood, each containieg 5 cords and 
 96 feetf how many cords ? *^ns. S4icords, 
 
 7. A gentleman is possessed of H dozen of silver 
 spoons, each weighing 2oz. 15 pwt. 11 grs. 2 dozen of 
 tea-spoons, each weighing 10 pwt. 14 grs. and 2 siivtar 
 tankards, each 21 oz. 15 pwt. Pray what is the weight 
 of i\\Q whole ? M9, Bib, IQq». ^wt ^^. 
 
GOMPOmrND DIVISION; 
 
 X EACHES to find how often one number is conUincd 
 in another of different denominations. 
 
 DIVISION OF FEDERAL MONEY. 
 
 ptr*Any sum in Federal Money may be divided aS ^ 
 whole number ; for, if dollars and cents be written down 
 a» a simple number, the wliole will be cents ; and if tin; 
 sum consists of dollars only, annex two cyphers to tlic 
 dollars, and the whole will be cents ; hejice the follo^/^ 
 
 GENERAL IIUI.E. 
 
 Writedown the given sum in cents, and divide as In 
 vh^l^umbers ; tao quotient will be the answer in cents* 
 
 Note. If the cents in the given sum are less than 1(^ 
 you must always place a cypher on their left, or in tll^ 
 (en's place of the cents, before you write them down. 
 
 EXAMPLES. 
 
 > 1. Divide 55 dollars 68 cents, by 41. 
 
 41)3568(87 the quotient in cents | and when fiiere 
 
 S28 13 any considerable remainder, you 
 
 ~— ^nav annex a cypher to it, if you pleasfij 
 
 288 , and divide it again, and you v/itl hiTve 
 
 2£r ^he mills, &c. 
 
 R»!m. I 
 
 S. Divide Gt dollars, 5 cents, by 14. 
 
 14)2105(150 cents=l dol. 50 cts. but to bring cents 
 14 into dollars, you need only poiiit off two 
 
 figures to the right hand for cents, arlfl 
 
 70 the rest will be dollars, &c. . 
 
 5 
 n. Divide 4 dols. 9 cts. or 409 cts. by G. ^ns. 68 ctT,^, 
 4 DiYide. 9 d^s; 9A cts.. by 1 P^ 4^S;. 7Z cts^' 
 
$. Divide 97 dols. 43 cts. by 85. J?/is. gl 14cfs. 6?fi, . 
 
 6. Divide 248 dols. 54 cts. by 125. >^ 
 
 ^ns. 198cis. 8m.=:Sl 98cfs. 8m. ; 
 
 7. Divide 24 dols. 65 cts. by 248. Am, 9cts. 9w. 
 
 8. Divide 10 dols. or 1000 cts. by 25. Ans. 4Qcts. 
 
 9. Divide 125 dols. by 500. Ms. 25cts. 
 10. Divide 1 dollar into 33 equal parts. Ms. Gcts,+ 
 
 PRACTICAI. QUESTIONS. 
 
 1. Boiiglit 25lb. cf cCiTce for 5 dollars 5 whatis tliat a 
 pound? Ans ^Ocfs. 
 
 2. if 151 yards of Iribh linen co3t 49 dob. ' ' "^t 
 is that per yard ? A, 
 
 3. If an cwt. (f sugar cost 8 dols. 96 cts. %v 
 
 per pound ? Jlnt ^f0t$. 
 
 4. If 140 reams of paper cost 329 dols. ^vliat is tnat 
 per ream ? Ms, S2 Socts, 
 
 5. If a reckoning of 25 dols. 41 cts. be paid equally 
 amon^ 14 persons, what do they pay a piece ? 
 
 Ms. ^\ Sleets, 
 
 6. If a man's wages are 235 dols. 80 cts. a year, v/hat 
 is that a calendar month r Ms. Sl9 65cis. * 
 
 7. The salary of tlie President of tlie United States, is 
 tvr<intv-five thousand dollars a vear : what is that a day ? 
 
 Ms. S68 49cfs. 
 
 2. Tf> divide the denominations of Sterling Moneij^ 
 Weights^ Measures y S[c. 
 
 RULE. 
 
 Begin Vv'itli the highest denomination as in simple di- 
 vision 5 and if any thing remains, find hmv many of the 
 next lower denomination this remainder is equal to; 
 which add to the next denomination ; then divide again;, 
 carrying the remainder, if any, as before; and so on^ till 
 the whole is finished. 
 
 Frohf — The s:fmc as ia Simple Division. 
 
COMPOUND DIVISXON.v 
 
 59 
 
 Divide 
 
 97 
 
 £XAMFL£5. 
 
 12 2 by 5. 
 
 Quo't. £19 8 9 2 
 
 3. 
 
 4. 
 
 5, 
 
 6. 
 
 7. 
 
 8. 
 
 9, 
 10. 
 11. 
 12. 
 13. 
 14. 
 15, 
 
 £• 
 
 Divide 31 
 
 Divide 22 
 
 Divide 70 
 
 Divide 56 
 
 fitvide 61 
 
 Divide 24 
 
 Divide 185 
 
 Divide 182 
 
 Divide 16 
 
 Divide 1 
 
 Divide 6 
 
 Divide 1 
 
 Divide 943 
 
 11 6 by 
 
 3 9 by 
 
 10 4 by 
 
 11 5i by 
 
 14 8 by 
 
 15 6^ by 
 17 6 by 8 
 
 16 8 by 9 
 
 1 11 by 10 
 19 8 by 11 
 
 6 6 by 12 
 
 2 6 by 9 
 11 6 by 12 
 
 £• ^' ^* 
 
 8)27 18 6 
 
 £3 9 9} 
 
 JiViS. 15 15 9 
 
 7 7 11 
 
 17 12 7 
 
 11 6 Si 
 
 10 5 9} 
 
 3 10 9i 
 
 23 4 81 
 
 20 6 Si 
 
 1 12 2J 
 
 3 7i 
 
 10 6^ 
 
 2 6 
 
 79 llj 
 
 2. When tlie divisor exceeds 12, and is the productof two 
 or more niiinbcrs in the table multiplied together. 
 
 Divide by one of those numbers first, and the quotient 
 by the other, and the last quotient will be the answer. 
 
 4. 
 
 Divide 29 
 Divitle 27 
 Divide 67 
 Divule 24 
 Divide 128 
 G. Divide 269 
 7 Divide 248 
 R. Divide 65 
 ■\ Divide 5 
 
 EXAMPLES. 
 
 ^5 by 21 
 16 by 52 
 
 9 4 by 44 
 16 6 br 36 
 
 9 l)y 42 
 12 4 by 56 
 10 8 by 64 
 14 by 72 
 10 3 by 81 
 
 £• 
 
 . s,d. 
 
 Ms. 1 
 
 8 4 
 
 
 
 17 45 
 
 1 
 
 10 S 
 
 
 
 IS Oi 
 
 5 
 
 ] 2 
 
 4 16 3i 
 
 3 
 
 17 8 
 
 
 
 18 3 
 
 
 
 14J 
 
d. 
 
 £*• 
 
 sr. 
 
 ({. 
 
 by SO. 
 
 1 
 
 6 
 
 g 
 
 6 by lOS. 
 
 1 
 
 5 
 
 4 
 
 6 by 121. 
 
 1 
 
 13 
 
 6 
 
 by 144. 
 
 
 
 4 
 
 9 
 
 60 rcp»(pot3S^o Dtv;sigj^^ 
 
 £. s. 
 <I0. Bivide 115 10 
 
 11. Divide 136 16 
 
 12. Divide 202 IS 
 
 13. Divide 34 4 
 
 3. When tlie divisor is large, and not a composlto 
 tfUiaber, you may divide by the whole di\isor at (Jnce> 
 afj;^ raanner of long division, as follows, viz. 
 
 EXAMPLES* 
 
 Divide 128Z. Us. ^d. by 47. 
 r. s. d £. 5. d. 
 4!r)lS8 13 3(2 ]4 9 quotient 
 94 
 
 54 pounds remaining. 
 fftUUiply by 20 and add in the 13s« 
 
 t producreB 693 Siiilllngs, ^vliicu divided by 4/", givqsi 
 ^ 47 [14s. ill the quotient. 
 
 223 
 183 
 
 35 shillings remainiugt 
 Multiply by 12 and add in the Sd. 
 
 ptoduees 4S3 pence, ivliich divided as above^ gives 
 '23 [9d. in the quotient. 
 
 .1^^ 
 
 £. Divide 115 
 5. Divide 85 
 4. Divide 315 
 IT. Divide 132 
 e; Divitle 740 
 7. jDivHe S^o 
 
 5. .'/. 
 
 £• 
 
 5. 
 
 <;; 
 
 13 4 by 31. 
 
 Ms, 3 
 
 13 
 
 4 
 
 6 S by 75. 
 
 1 
 
 
 
 9 
 
 3 10^ by 355. 
 
 
 
 ir 
 
 SJ 
 
 8 Uv G8. 
 
 1 
 
 IS 
 
 9J 
 
 16 8 l>y IDO. 
 
 >?• 
 
 s 
 
 <J 
 
 IS to hv 95: 
 
 ti 
 
 ■'^ 
 
 
v.* 
 
 EXAMPLES OF 
 
 WEIGHTS, MEASURES, &c. 
 1% Divide 14 cwt. 1 qr. 8 lb. t)f sugar equally ainQBg 
 8 m^. 
 
 0. gr. lb. oz. 
 8)14 18 
 
 1 S 4 8 Quotient* 
 8 
 
 14 1 8 Proof. 
 
 5a Divide 6 T. 11 cwt. 5 qi's. 191b. by 4 
 
 JIns. IT. I2cwt Sqr$. 2,5lh. l^ox. 
 G. Divide 14 avt. 1 qr. 1£ lb. by 5 
 
 Ms. SLcwt. S^. 13/6. 9(7r. 9ir-*-f. 
 4. Divide 16 lb. IS oz. 10 dr. by 6 
 
 *5ns. 2Z&. 12or. 15Jr. 
 ff. DivJdfe 56 lb. 6 oz. 17 pwt. of silver into 9 equd 
 
 6. Divide £5 lb. 1 oz. 5 pv.i:. by 24 
 
 */?ks. 1Z&. loz. ^pwt. l^y, 
 r. Divide 9 hhds. £8 gals. 2 qts. by 12 
 
 Jji.'?. Ohhds, 49gals. 2qls. Ipt^ 
 
 8. Divide 165 bu. 1 pk. 6 qts. by So 
 
 Jins. 4ku Spin's. 2iiU. 
 
 9. Divide 17 lea. 1 in. 4 fur. 21 po. by Gi 
 
 10. Divide 43. yds. 1 qr. 1 na. by li 
 
 JIns. 2vds. Cqrs, Snn, 
 
 11. Divide 9rE.E. 4 qrs. 1 nii. by o 
 
 12. Divide 44 galldns of brandy aqua! ly aiaoni^ 144 
 ffDldiers. • dns. i£ill a-plecc. 
 
 15. I#ougiit a <lozen of silver spoons, wluch togctl.er 
 weighed 3lb. £ oz. 13 ])v:t 12 '^rs.how much sliver did 
 eath sgoou contain ? Jlns, Soz. Anivt. 1 1,p'. 
 
 14. Bou^jht 17 cwt. 8 qrs. 19 B). of sit;;:ir, and sold cut 
 oireth?i-dof it} how much iiJinains nnsold ? 
 
 6 
 
<»2 •oMi'OUMD liivisiby, 
 
 15. From a piece of cloth containing 64 yards 2 ita, 
 a taylor was ordered to make 9 soldiers' coafts, which 
 took one -third of tlie whole piece ; how many yards didi 
 each coat contain ? Jlns. 2,7jds, Iqr, 2na. 
 
 PRACTICAL QUESTIONS. 
 
 I. If yards of cloth cost 4L Ss, 7 id. what is that per 
 yard ? 
 
 9)4 ^ 7 2 
 
 9 3 2 Answer 
 
 9., If U tons erf hay costSSZ. Cs. 2(f. what is th&tper 
 ton? *^ns. £2 Is. lOi. 
 
 3. IF 12 gallon:^ of brandy cost AU 15s. 6c?, wliat is thtf 
 
 per gallon .^ Jins, 7s, lid, ^qrs. 
 
 4. If 84 llis. of cheese cost i^. l6s. 9cf. what is that per 
 p<fund ? Ans. 5 la, 
 
 5. Bought 48 pairs of stockings for 11/, 2s, how mu(ih 
 1 pair do tlicy stimd me in ? Jtns, 4s. 7hd, 
 
 6. U a recKoning id' 5L 8s\ lOjid, be paid equally among 
 13 persons, ',vliat do they i'i:ij a-picce ^ Jins. 8y. 4^^.^. 
 
 7. A niece of clolli containing 24 yards, cost IS/, 6/. 
 U'l^at did it cost per yard ? Snis, 15.«. 3^. 
 
 8. If a hogshead ol" wijie cos^t 53^. 12s. what is it a 
 gallon ? ^ Jfns, 10s. Si, 
 
 9. If i ewt. of sugar cost 3Z. 10.?. wiiat is it per pound? 
 
 Jilts. 7ld. 
 
 10. If a man spends 7ll. 14s. 6d, a year, v/liat is that 
 ptr calendar month? .^^ns. /J5 19s. G^d, 
 
 11. The IVincc of ^\'alcs' saJaiy is 150,000/. ayearf 
 wiiat is that a day ? Jns. £ 4 1 1 9s. 24. 
 
 12. A privateer tako3 a prize worth 12,465 dollars, of 
 which ihQ owner takci enc-half, xhQ oficcrs one-fourth 
 and ilie remainder is equally divided among ihi sailors 
 who are 125 in number • hew much is each sai lor-a part ? 
 
 ^nir g24 9Sa/§. 
 
ir/,Dv 
 
 13. ']'liro<>, marciKims, A, II, and ('. lave a sliip ^.li 
 company. A hath -J, B |, and C J. and lliey receive far 
 ft-eight '22o!, IGs. oJ. it is required to divide it among 
 tlieowncr^ accord in£^ to tl;eir respective shares. 
 
 Jhi^.JVs Hhare £N3 Os. 5cL IPs share £57 4s. 2a. 
 C's share £28 12s. Id. 
 
 14. A jirivaieer haviu'; taken a pnzc v.-nrth S6S50, it 
 is divided into one hundred shares; of which the cap- 
 tain is to have 11: 2 lieutenants, each 5; 12 midship- 
 men, each 2 1 and the remainder is to be divided equally 
 among tiic snilors, wlin twd 105 in. number. 
 
 J:is, CapUiurs' share S75:: fAkts, Lkid^^. Sn342 :A^cfs. 
 amidsJiijrmans S^37, and a sailor's ^ooS^cts. 
 
 REDUCTION, 
 
 X EACUES to brino- or change numbers from one name 
 to another, without altering their value. 
 
 Reduction is either Descending or Ascending. 
 
 Descending is when great names are brought into 
 small, as pounds into sliillings, days into hours, &c.-- 
 This is done by Multiplication. 
 
 Ascending is when small names are brought into creat, 
 as shillings into pounds, hours into davs, &c. Tills ii 
 performed by Division. 
 
 REDUCTION DESCENDING, 
 
 RULE. 
 
 Multiply the liigliest <]enomJ nation given, by so many 
 cf the next less as make one of tliRt greater, and thus 
 continue till you !iave brought it down as low as your 
 question requires. 
 
 Proof, Change the order of the question, and divide 
 your last prciiuct by tl;e last multiplier, and so on. 
 
 EXAMPLES. 
 
 t , I\\ &3L ioL 9d. Sqm, haw many faithings ? 
 
u4 REDUCTION. 
 
 £r s. d. qrSs 
 
 S5 15 9 £ Proof. 
 
 20 4)24753 Ms. 24758 
 
 515 sliillings* 12)6189 2qrs. 
 
 12 
 
 2|0)51j5 9d. 
 
 6189 pence. 
 
 4 £25 15 93 
 
 £4758 fari;hiug&. 
 
 y^TY.. Jn mi?)Jp]yh:- by 50, 1 aildcd in the I5s,^t>y 
 X^ tlic P<L— auii I;v - •■; > ^lors, wliich iiuist always b^ 
 done in like cases. 
 
 ^. In 31^. lis. lOi. Iqr. how many farthings ? 
 
 .i/i^^ 30329 
 
 5. In 46/. 5s. lief. S^rs. how many farthings ? 
 
 Ans. 44447 
 
 4. In til, 125. how many shillings, pence and far* 
 (hings ? *5ks. 1232s. U7S4d. 59lS6qrs. 
 
 6. In 84/. how many shillings and pence ? 
 
 ^ws. 1680s. 20160 J, 
 C In 18s. 9d. how many pence and farthings ? 
 
 Ans. 9.9.5a. ^QOqrs. 
 
 7. In 512Z. 8s. 5d, hov/ many half-pence ? 
 
 Ans. 149962 
 
 5. In 846 dollars at ^s, each, how many farmings ? 
 
 1^.^25. 243^48 
 i9. In 41 guineas at 28s. cacli, how many ncnce.^ 
 
 Ans. TSr76 
 
 10. In 59 pistoles, at 22s. how many shillings, penc^^ 
 dnd fartliings ^ 
 
 Jlns. 1298.9, IjjTGd. 62S04gr5. 
 
 11. In 87 half-johaniies, cil -?.<^. h(n7 many shilling 
 SiX-penccs, and three-pence?^ P 
 
 Ans. 1776s. $^552 six-pemca: 7'iOA three-pences. 
 
 12. In 121 French ciT.wriS, at Gs. ScL each, how many 
 (fence and fartliings ? .-^ .'Z?:-^. [)mod. Sgrr^Ogrs- 
 
HEDlUCTION ASC£NDJ«G, 
 HULE. 
 
 Divide tlic lowest denomination given, by so many of 
 that name as make one of the next higher, and so on 
 tlirough all llie dentminations, as far as your question 
 npmiires. 
 
 rRoov. Multiply inversely by the several divisors. 
 
 KXAMPLES. 
 
 1. In ^24765 fai*things, how many pence, shillings ani 
 pounds ? 
 Fa rtl lings in a penny = 4)224rC5 
 
 Per^e in a shilling = 12)56191 1 
 
 Shillings in a pound = 2!0)468|2 Td, 
 
 '/:234 2s. rd. Iqr. 
 Ans. 5619U7. 4682s. 2S4t. 
 NoTi:. Tlie remainder is always of the same name as 
 ^tlie dividend. « 
 
 r. Bring 50329 farthings into pounds ? 
 
 Jlris. £Sl lis. lOd, Iqr. 
 S. In 4444r fartiiiugs, how many pounds ? 
 
 .6ff?s. £46 5s. lid. Sqrs 
 
 4. In 59136 farthings, how many pence, shillings, and 
 pounds ? Ans. UTS4d. 1232s. £61 12s. 
 
 5. In 20160 pence^liow m^any shillings and pounds ? 
 
 .^ns. i680s. or £84. 
 G. In 900 fartliings, how many pounds ? 
 
 Ms. £0 ISs. 9d. 
 7. Bring 74981 half-pence into pounds r 
 
 Ms. £156 4s. 9,hL 
 3. lu 243648 farthings, how many dollars at 6s. Ciicii.^ 
 
 Sms. B846. 
 9. Reduce 15776 pence to guineaSj^at 283. per guinea* 
 
 Jlns. 41 --. , 
 ID. In' 6^^04 ftr^.hings, how many pistoles, at 22s. 
 
U. Ja ri04 tiu:Q^e-pejices,ho\7manjhaIirjohatit[e$^5^t 
 
 12. la SSrso ftrtliings, how many French crowns, at 
 69. 8d. ? ^Ks. 121. 
 
 Reduction Ascending and Descendhig 
 1. MONEY. 
 
 1. Tn ISl?. Os. 9^d. how many half-pence ? 
 
 e^ns. 58099 
 
 2. In 58099 lialf-pencG^ how many pounds ? 
 
 Am. iSlL 05. 9^^. 
 S. Bring SSrGO half'pence into pounds. *^ws. £49 105, 
 
 4. In £14L Is. Sd. how many shillings, six-pences^ 
 tTireepences, and farthings? " Ans, 4f281.s. 856a|sf or- 
 
 pences, in 25 ihree-pences^ and ^05500 farthings. 
 
 5. In isn. how many pence, and English, ^r French 
 browns at 6s. 8d. each ? Ans, S2880rf. 41 1 crowns, 
 
 G. In 249 English half-crowns, how many pence and 
 gounus ? Jns. 996{)d,and£4:l 10s. 
 
 7. In 545 guinCi^j at 21 s. each, how many shilling?, 
 goats and pence ? Ans, 7266^?. 21798 grHs and 87192ff* 
 
 8. In 48 guineas, at 28s. each, how mai5v 4^d. pieces ? 
 
 " Ans, 3584 
 
 9. In 81 guineas, at 278. Ad. each how many pounds ? 
 
 Ans. £110 145. 
 
 10. In 24596 pence, how many shillings, pounds and 
 Jjistoles ? Ans, 20S5s. £10\ 135. and 92 pistoles. 
 
 1)5. over, 
 
 11. In 252 moldores, at T^Gs. each, how many guineas 
 at28s. each.^ ' Ans, 524. 
 
 12. in J 680 Dutch guilders, at £s.4d. each, how many 
 pistoles at 22s. each ? Ans. 178 j>?*,se;o6V5, 4s. ^ 
 
 15. Borrowed 1248 English crowns, at 6s. 8d. eachjj 
 how many pistarcens, at 14 ^d. each will pay tlie debt ? 
 Ans. 6885 pistarcens a:id 7^. 
 14. In 50?. how many shillings, ninc-pcuces, six-peri« 
 cpSjfQur-pfinccs, and pence, and of each ancqua number r 
 \9.d.Ar^d.^M*'r^d.-\'ld. =C2fZ. and £50 r^ 
 XSJ000(^rfy52==^'S7.T A)\}i 
 
ili:,DUCTiON OF. FEDERAL MOXI^Y. 
 t. Reduce Cr45 dollars into cents. 
 
 2745 dolhi-s "^ 
 100 
 
 ^ins. 274500 
 
 Here I multiply by 100, the 
 cents in a dollar ; but dollars are 
 >readily brought into cents bj an- 
 nexing two cyphers, and into 
 mills by annexing three cyphers. 
 Also, any sum in Federal money may be wi-itten down 
 as a wliole number and expressed in its lowest denomina- 
 tion ; for, when dolliirsand cents are joined together as 
 a whole number, without a scparatrix, they will sliew 
 Iiow many ecu Is tlic frivcn sum contains; and when dol- 
 lars, cents, i^nd mills are so joined together, i]\(^y will 
 p'vew tlie whole number of niills in the given sum. — 
 Ilj'uce, properly speakiiig, tiiere is no reduction of this 
 moii'^y : for ccntr> are readily turned into dollars by cut- 
 ting olV tl^iC two riglit hand figures, and nVills by pointing 
 aft' tliree fjgiircs with adot : tlie figures to the left hand 
 of the dot, aiiMlolIars; and tlie figures cut ofl* are cents, 
 orcenU and mills. 
 2. In 345 dollars, how many cents and mills ? 
 
 J71S. S4500cts. 345000 mills, 
 5. Reduce 43 dols. 78 cts. into cents. ^Ins, 4878 
 
 4. Reduce 25 do!s. 8 cts. into cents. Jinsi, 2503 
 
 5. Re^luce 54 dols. 56 cts. 5m. into mills, w^ns, 54365 
 
 6. Reduce 9 dols. 9 cts. 9m. into mills. Ans, 9090 
 
 . S cf^. 
 
 r. "R^iduce 419£!5 cents into dollars. Ans, 419 £5 
 
 ^. Change 4896 cents into dollars. 48 96 
 
 9. Change 45009 cents into dollars. 450 09 
 
 V>. Bring 4625 mills into dollars. 4 63 5 
 
 2. TKOY V/EIGHT. 
 
 K How many grams m asHvcr tankard j t^f *.«^nf 
 Ub. no.-, 15 pwt? 
 
 4 d ■ - 
 
• / lb. 9%, j>wt 
 
 ^ 1 11 15 
 
 REDVQTfOlC. 
 
 X 11 15 
 
 IS ounces in a pound. 
 
 23 ounces. 
 
 20 pennyweights in one oun^c. 
 
 h . — 
 
 475 pennyweights. 
 £4 grains in one penwjweigJit. 
 
 1900 
 950 
 
 Eroof. 24)11400 grains. .Ins. 
 2,0)47.5 
 (12)23 15 pwt. 
 
 1 lb. 11 oz, 15 pwt, 
 
 ^. In 246 Qz. Iiow many pwts. and grains ? 
 
 Ms. 49^0pivt llSOaO^TVv 
 5. Bring 46080 grs. into pounds. Jlns. 8 
 
 4 . In 97397 grains of gold how many pounds ? 
 
 Ms. 16lh. IOdz. ISpivt. 5grs. 
 
 5. In 15 ingets of g©ld, each weigliing 9 oz. 5 pwt. 
 how many grains ? JIns. 66600 
 
 6. In 4 lb. 1 oz. 1 pwt. of silver, liow many table 
 spoons, weighing 23 pwt each, and tea-spoi?ns, 4 pwt. 
 6 grs. each, can be made, and an equal number of each 
 sort ? 
 
 ^Spwt.+^pict. 6^rs.=:654gTS. the diviser and 4lh. 
 loz. lpwt.^25544grs. the dividend. Therefore 25544 
 ^654=36 Jlnsiver. 
 
 S, AVOIRDUrOlS WEIGHT. 
 
 in 89 Qwt. S ^rg. 14 lb. 12 qz. hsw man^r ounces ? 
 4 
 
 ^9 q*art6rs. £S|ftriIed Uf .] 
 
S59cp&>tei'3* Proof. 
 
 S8^- 16)161068 
 
 ^876 28)10066 \Qox* 
 
 ^19 
 
 4)359 14Z&. 
 
 10066 poumls. — 
 16 BOcwt Sgrs. 14C&. 12qx. 
 
 60398 
 10067 
 
 161068 ounces. Answer. 
 
 B. Ih 19 lb. 14 oz. 11 dr. how many drams ? 
 
 Ms. 5099. 
 5. In 1 ton how many drams ? Ans. 573440. 
 
 4. In 24 tons, 17 cwt. 3 qrs. 17 lb. 5 oz. how many 
 «Ilices? Ans. 892245. 
 
 5. Bring 5099 drams into pounds. 
 
 Ans. 19lb. Uoz. lUr. 
 6i Bring 573440 drams into tons. Ans. 1. 
 
 7. Bring 892245 ounces into tons, 
 
 Ans. 24 tonsy ITcwt. Sqrs. I7lb. 5oz. 
 
 8. In 12 hhds. of sugar, each 11 cwt. 25lb. how many 
 pounds? Ans. 15084. 
 
 9. In 42 pigs of lead, each weigiiing 4cwt. 3qrs. how 
 (Oany fother, at 19cvvt. 2qrs. ? Ans. W father ^ A^cwt. 
 
 lOyA gentleman has20hhds. of tobacc.^ each 8cwt. 
 3qrs. 14lb. and mshes to put it into bo: 35 contai-iing 
 TjQtb. each, I demand the number t -,0 <*« muat get ? 
 
 Ans. 384. 
 
 4. AVOTHECAtiiEs' Av;:i.j; : 
 
 t^ la 9f5 B§ 15 23 lOgrs. how many grains. 
 
 Ans. 5579^. 
 £.Mn5- 55799 graitfS, how many pounds ^ 
 
 •^rs. 9ft 85 15 29 19^r. . 
 
5, CI.OTII MKASUnE> 
 
 1. In 95 yards, howinanv<»uiirters and nails? 
 
 2. In S41 yards, Sqrs. Ina. how many nails ? 
 
 Jna. 54G9. 
 S. In 3783 nails, how many yards r 
 
 JJjzs. 23Giffh. l<7r. 3 ??/■/. 
 
 4. In 61 Ktis English, how many quarters and nails ? 
 
 5. In 56 Ells Flenilsli, hov,' niany quarters tLJid nails? 
 
 6. In 148 Eiis English, how many Ells Flemish? 
 
 Anfi.9.4CjE,F. 2qrs. 
 
 7. In i9£0 nails, \io\y many yards, Elis Flemish, an(J 
 EllsEneilish? 
 
 Ans, im;ds. 16QE. R andSSE.E. 
 
 8. How many coats can be made out oP 36| yards dF 
 I'-oadcloth, allowing If yards to a coat r Jlns. 21 
 
 6. DS.Y MEASUriE. 
 
 1. In 136 bushels, how many pecks, quarts and pints ? 
 
 Ans. 544pks. 4S52qis. STMpts. 
 S. In 49 biisli. 3pks. 5qts. how many quarts ? 
 
 Ms. 1597. 
 
 3. In 8704 pints, how many bushels ? dns, 136. 
 
 4. In 1597 quarts, how many bushels ? 
 
 driii, 49bus, Spks, 5qts. 
 
 5. A man wouhl sldp 720 bushels of corn in barrels, 
 which Vvriilhold S bushels, 3 pecks each, how many bar- 
 rels must he get ? Ms, 192. 
 
 r. V;iNE MEASURE. 
 
 1. In 9 tuiis cf wine, how many hogslicads, gallom 
 and quarts ? 
 
 Ans, ^6hhds, 22(jSgal D072gf5. 
 
 2. In24hhds. 18 gals. 2qts.how many pints ? 
 
 Jh:s. 12244. 
 5. In 9072 quarts, hew many tuns ? ' Ans, 9* 
 
 4. In 1905 pints of wine, how many hogsheads ? 
 
 Ans. Shhds, 49sah. fr/f. 
 
J: In 17S9 quarts of cider, how many barrels ? 
 
 Ans. Ubls. QoqtS. 
 
 6. What number of bottles, containing a pint and a 
 hftlf each, can be filled with abarrcl of cider ? dns. 168. 
 
 7. How many pints, quarts, and two quarts, each an 
 caual numbers may be filled from a pipe of wine ? 
 
 * Ms. 144. 
 
 8. LONG MEASURE. 
 
 1. Ill 51 miles, how many furlongs and poles ? 
 
 Ms. 40Sfur. l6S20poles. 
 
 2. In 49 yards, how manv feet, inches, and barley 
 corns ? Ms. i47ft. \764inch. 59,92b.c. 
 
 3. How matiy inches from Boston to New-York, it 
 b^iqg.£48 mile? ? Ms. 157lS2SQinch. 
 
 4. Ift 4352 inches, how many yards r 
 
 Ms, mOyds. 9ft . Sm 
 
 5. Xn 682 yards, how many rods ? 
 
 Ans, 682x2-j-ll=124ro/f5. 
 
 0. Ih 15840 yards, how many miles and leagues ? 
 
 Ms. 9ra, Slea. 
 ?. How many limes will a carriage wheel, 16 faet and 
 Scinches in circumference, turn round in going from 
 New-York to riuladelphia ; it being 96 miles ? 
 
 Ms. 30261 tiines^ and Si feet over. 
 
 8. How many barley-corns will re«ich round the glob^ 
 itbeing560 degrees r^ Jns. 4755801600. 
 
 9. LAND Oil SqUv^-lUi MEASURE. 
 
 1. In 241 acres, 3 roods and 25 poles, bow many square 
 rods or perches ? Ms. SSTOSperdies, 
 
 2. In 20692 square polps, Iww maiiy acres ? 
 
 Jhis. 129(/. if. !%•. 
 5. Ifa piece of land contain 2 i iicres, anii an inclosuft 
 Cf 17 acres, 3 roods, and 20 ro^^s be taken out of it, how 
 mSDy perches are there in the i e.aainder ? 
 
 Ms. 980 jierche-p. 
 4. Three nekls coiitsiii, the iri/^t 7 acres, the second 10 
 acres, the third 12 acres, 1 rood ; how many shares caa 
 tlievbe dividcu inti?, eacli sliare Lo contain 76 rods ? 
 
 MX 61 shaye^ciiid4i jWs^Jrer^ 
 
 ^S 
 
10. SOLID MEASURE. 
 
 1. In 14 tons of hewn timber, how muny solid ittchea? 
 
 Ms. 14x50x1728=1209600. 
 .*i. In 19 tons of round timber, how many inches ? 
 
 Ms. 1313280. 
 ~. !ii 21 cord3 of wood, how many solid {e^t ? 
 Ms. 21x128=2688. 
 
 4. In 12 cords of wood, how many solid fe^t and inches ? 
 
 ^ns. 15S6ft. and 2654208fnc7^ 
 
 5. in 4608 solid feQt of wood, how many cords ? 
 
 11. TlAfK. 
 
 !. In 41 weeks, how many days, hours, minute?, ahii 
 seconds ? 
 
 Jiis. QSrd. 6888/;. 413280mi?. aiid £4796^,^^:. 
 
 2. In 2l4d, 15h. 31m.. 25s^. how many 9et>ondii ^ 
 
 A)iS, 185454SjS«i% 
 
 3. In 24796800 seconds, how many v/eeks ? 
 
 Ms. 41 Tfeelcx 
 
 4. In 184009 minutes, how many days ? 
 
 Ms. lQ7d. ISli. 49min. 
 
 5. How many days from the birlhof Cliilsf, to Chvist- 
 uras, 1797, allowing i\iQ year to contain 365 (Lap, 6 hours. 
 
 Ms. 656S5^id. 6h. 
 
 6. Suppose your age to be 16 years and £0 (lays, how 
 ruiny seconds old are you, allowing 365 days and 6 hours 
 •?> tlie yaar ? •3tis. 5u6649600sec. ^ 
 
 7. !«Vom March viJ,, to November 19th followiiig, in- 
 clusive; how many days? Ms. 262. 
 
 12. ClUCULAR MOTION. 
 
 1. In 7 signs, 15^ 24' 40" how many di*^recs, miniiles* 
 and seconds ? Ms. 225*» 1S524' cutd 811480" 
 
 2. .Bring 1020300 seconds into signs. 
 
 Ms. Q-slgns^ 13^ 25' 
 
 qUKSTIONS TO EXERCISK REDUCTION'. 
 
 1. In 1259 groats, how many farthings, pence, fclilirO":! 
 am! gifjntas a;: 2Ss. .5725;r£0X4i5rs, d030i< 
 
 • ^ "^. ^ J. ffKfiJ U^uirieass 27s. S^ 
 
2. i^orrowed 10 English guineas at £Ss. each, and 24 
 English crowns at 6s. and 8d. each ; how.many pistoles 
 at 22s, each will pay tlie debt ? ^ns. 20. ^ 
 
 3. Four men brought each 17L 10s. sterling value in 
 gold into the mint, how many guineas at 21s. each must 
 they receive in return ? Ans, 66 giiin. 14s. 
 
 4. A silversmith received three ingots of silver, each 
 weighing 27 ounces, with directions to make ti em into 
 spoons of 2 oz. cups of 5 oz. salts of 1 oz. and snuiT boxes 
 01 2 oz. and deliver an equal number of each 5 what was 
 the number ? Jim. 8 of eachy and 1 oz, over, 
 
 5. Admit a ship's cargo from Bordeaux to be 250 
 pipes, 130 hhds. and 150 quarter casks [i lihcis.] how 
 many gallons in all ; allowing every pint to be a pound, 
 what burden was the ship of? Ȥks. 44415 ^c^s. tmd 
 
 the skip^s burden vms 158 tons, 12cirf. 9>qTS, 
 
 6. In 15 pieces of cloth, each piece 20 yds. how many 
 French Ells .^ Jins. 200, 
 
 7. In 10 bales of cloth, c:ich bale 12 pieces, and each 
 piece 25 Flemish Ells, how many yards -^ •Ans, 2250. ^ 
 
 8. The forward wheels of a waggon are 14^ feet 11^ 
 circumference, and the hind wheels 15 feet 9 inclies, how 
 many more times will the forward wheels turn round than 
 the hind wlieels, in running from Boston to New-York, 
 it being 24S miles ? Ms, 71^7. 
 
 9. How many times will a ship 97 feet 6 inches long, 
 sail her length in the distance 01 12800 leagues and ten 
 yards ? Ans. 2079508. 
 
 10. The sun is 95,000,000 of miles from the earj'x, 
 ami a cannon bail at its first discharge fiieS about a nuie 
 in 7^ seconds ; how long would a cannon ball be, ,'».t i:i*it 
 raie in flying from h^re to the siui ? 
 
 Am, 2%r. 2l6t?. Vlh, ^"Jhn. 
 
 1 1 . Tlie Sun travels through H signs of the Zodiac in 
 half a year ; how many degrees, minutes and seconds ? 
 
 dns, liiQdeg. i0S00mi?i. 648000s«c. 
 
 12. Ilow many strokes tlo^s a. • ^^gular clock strike in 
 565 days, or a year ? ms, 56940. 
 
 13. ilow lon^j will it take to '^ruul a miliioii at fiierate 
 of 5^; amintite ^ .to.5.33^. ;;^t cr XSd 'ZMi.'lOnu 
 
14. Tk« national debt of England amounts to about SI9 
 
 Bijlli'^V"'? >f pounds r^terling ; now long would it take to 
 >l,t in dollars (4s» 6d. sterling) reckoning 
 i-iv^sioii twelve hours a day at the rate of 50 
 r\tty und So5 days Iq tlie jear ? 
 Ans, 94 yearsM 1S4 dai^s^ 5 hours, 20 min. 
 
 FRACTIONS. 
 
 Jf RACT1ONS5 or broken nambers, are expressions fo? 
 any assignable part el an unit or whole number, and (in 
 general) are oi two kinds, \iz. 
 
 VULGAR AND DECIMAL. 
 
 A Vidgar Fraction^ is represented by two numbers pla- 
 ced one above another, with a line drawn between thenij 
 thut, J, |,&c. Signifies three-fourths, five-eights, &c. 
 
 The figure abcrve the line, is called the numerator, and 
 jlSthat below it, the denominator, 
 Thus $ 5^ Numerator. 
 ' ^ 8 Denominator. 
 
 The denominator (which is the divisor in division) 
 show,s hovv iTiSLh Y parts the integer is divided into ; and the 
 nur?.ei*ator (whkh j>^ ! erernaiiider after <livision) shows 
 how many of t jose |>ai^s are i»ieantby therfraction. 
 
 A traction u said to be in its least or lowest terms, 
 when it is expressed by the least numbers possible, as | 
 when reduced to its lowest terms will be i, and ^ i% 
 equal tv» l-, ^c. 
 
 PROBLEM I. 
 
 T© abbreviate or reduce fractions to their lowest teana 
 RULE. 
 
 Divide th^ terms of the given fraction by any numbei 
 which will divide thein without a remainder, and the quo- 
 tients again in the same manner ; and so on, till it apnear^ 
 ^lat there is no number greater than 1, which mil diTiJe 
 
 ^^5 and tht fraction will be in its least t^ns\ 
 
JPEAOTIOKS. ^^ 
 
 EXAMPLES. 
 
 1* R^uce 444 to its lowest terms. 
 (5) (2) 
 6)|44=7#=^=T the Answer. 
 2. Reduce f|| to its lowest terms. dnstvers h 
 
 5. Reduge f ^| to its lowest terms. i 
 
 4. Reduce ^Yt *^ ^^^ lowest terms. -^ 
 
 5. Abbreviate f f as much as possible. |4 
 
 6. Reduce |f f to its lowest terms. f| 
 
 7. Reduce |4t *^ ^^^ lowest terms. § 
 
 8. Reduce ^^^ to its lowest terms. | 
 
 9. Reduce \^l to its lowest terms. ^ 
 10. Reduce li^ to its lowest terms. | 
 
 PROBLEM II. 
 To find the value of a fraction in the known parts of 
 #he integer, as to coin, weight, measure, &c. 
 RULE. 
 Multiply the numerator by the c-ommon parts of the 
 jXteger, and divide by tlie denominator, &c. 
 
 EXAMPLES. 
 
 What is the value of f of a pound sterling ? 
 
 Numer. 2 • 
 
 20 shillings in a pound. 
 
 5enom, 5)40(155. 4rf. Ans. 
 
 10 
 9 
 
 1 
 12 
 
 — • 
 
 5)12(4 
 12 
 2. What is the value of -J| of a pound sterling ? 
 
 ^lins. Ifes. 5d» 2^yr5. 
 5. Reduce | of a shilling to its proper quantity. 
 
 •-ins. 4id. 
 4.. What is the value of | of a shilling ? *>iiis. Md 
 5, AVhat is the value cf H of a powid troy ? An?. 9oa. 
 
6 How inucli is .^ oi an hundred '.veiglit .^ 
 
 Jlns. Sqrs.Tlb, lO-f^QSS* 
 r. What is the value of f of a mile ? 
 
 Ms. Gfur. QGpo, 1 \ft. 
 
 8. How much is J of an cwfc. ? 
 
 .Urn, Sqrs, Sib, loz, l.'2^^r. 
 
 9. Reduce | of an Ell Englisii to its proper quantity. 
 
 Ans. '^.qrs. S-lnn, 
 
 10. How much is f of a hlui. of wine ? Jns, 54gaL 
 
 11. What is the value of ^- of a day ? 
 
 Jus. ]Gh. SGmin. 55 ,^-^ sec, 
 ^ PROBLEM III. ^ ^ ' 
 To reduce any given quantity to the fraction of any 
 greater denomination of the same kind. 
 RULE. 
 Reduce the given quantity to the lowest term mention^ 
 ed for a numerator: then reduce the integral part to the 
 samef term, for a deoominatori which will be the frac- 
 tion required. 
 
 EXAMPLES. 
 
 1. Reduce 13s. 6d, 2qrs. to the fraction of a poutjd. 
 
 20 Integral part 15 6 2 given sum, 
 
 12 19. 
 
 240 162 
 
 4 4 
 
 960 Denominator- 650 Num. Jns. f f §~if/;. 
 £. Wliat nartof an liMudred weidit is Sqrs. 14lb. .^ 
 Sqrs. \4lb.=mb. dns. -^,%=:^i 
 
 3. What part of a yard is Sqrs. Sna. ^ Jlns, \ 5- 
 
 4. What part of a pound sterling is 13s. 4d.? An^, -|. 
 dH What part (; ^^ 3 weeks. 4 days r 
 
 6. What*part oi a mile is tlur. ^2r 
 fur. 2>o* yd, ft. fed^ 
 
 6 £6 3 2r=:4400 Num. 
 
 a mile =5280 Denora. Ms. f||S-=|' 
 
 r. Reduce 7oz. 4pwt. to tne fraction of a pound tror. 
 
 8» What part of an acre is 2 roods, 20 poles ? Jln^* g 
 
% Reduce 54 gallons to tlic fraction of a hogshead of 
 
 wine. • •^'^^- ^ 
 
 *. What part ©f a hogshead is 9 gallons ? Jins. \ 
 Ih What part of a pound troyislOoz. lOpwt. l^'S;/ 
 
 BECIM AlT fractions. 
 
 A Decimal Fraction is that whose denominator is an 
 unit, with a cypher, or cyphers annexed to it, Thus, ^, 
 
 The integer is always divided either into 10, 100, 1000, 
 &c. equal parts ; consequently the denominator of the 
 fraction will always, be either 10, 100, 1000, or 10000, &c. 
 nvhich being understood, need not be expressed 5 for the 
 true value of the fraction may be expressed by writing 
 the numerator only with a point before it on the left hand 
 thus, ^,%, is written ,5 ; ^^^ ,45 ; y^V 5^^^^ &^- 
 
 But if tlie numerator has not so many places as the 
 denominator has cyphers, put so many cyphers before it, 
 viz. at the left hand, as wilPmake up the defect 5 so write 
 y|^ thus, ,05 ; and ^^^^ '^'^^^'^9 5^^^? ^c. 
 
 Note. The point prefixed is called the separatrix. 
 
 Decimals arc counted from the left towards the right 
 hand, and each figure takes its value by its distance from 
 the unit's place ; if it be in the first place after units, (or 
 separating point) it signifies tenths 5 if in the second, 
 hundredths, &c. decreasing in each place in a tenfold pro- 
 poj'tiou, as in the following 
 
 NUMERATION TABLE. 
 
 
 Ui (A 
 
 7654521 S$456r 
 
 jr/4oJc JS'^iimhers. Dccimai-s 
 
(> jpluu-s placed at the right hand of a decimal fracumi 
 do not alter its. value, since every si-giuficant figure con- 
 fv:.» -i". : 1 ::r...^ the same place: so ,5 ,50 and ,500 are 
 4/ % and equal to ^^ or ^. 
 
 ^ j^'iaced at the left hand of decimals, de- 
 crease t eir value in a tenfold proportion, bj removing 
 them Irirtoer from the decimal point. Thus, ,5 ,05 ,005, 
 ikf. are five tenth parts, five hundredth parts, live thou- 
 san^t^ parts, &c. respcctiveij. It is tiicrefore evident 
 that the magnitude of a decimal fiaction, compared Vvith 
 anofeer, does not depend upon the number of its fi<jurej?, 
 but upe» tlio value of its first left hand figure : tor in- 
 staMte, a fraction beginning with any figure less tlian ,9 
 su«ii as ,899229, &c. if extended to an infinite number 
 of figures, will not equal ,9. 
 
 ADDITION OF DECIMALS. 
 RULE. 
 
 1. Place the mumliers, whether mixed or pure decimal 
 under each other, according to tlie value of their places 
 
 2. Find their sum as in v/hoic numbers, and point oiv 
 so many places for the decimals, as are equal to the great- 
 est number of decimal parts in any of the given numbers. 
 
 EXAMPLES. 
 
 1. Find the sum of 41,653+56505+24,009 + 1,6. 
 
 "41,653 . 
 
 Thus J2^'05 
 1,6 
 
 iSum^ 103,312 v»hich is 105 integers, and -^-^^^ parts of 
 in unit. Or, it is 103 units, and 3 tenth parts, 1 hun- 
 dredth, part, and 2 thousandth parts of an unit, or 1. 
 
 Hence we may observe, fnat Decimals, and Federai^ 
 Money, aze sulkct to one, and the same law of notation^ 
 $ij^ conse.ffiently of operation. 
 
,)%QlM.\;j I'll ACTIONS. 
 
 (2) 
 
 Yards, 
 
 (3) 
 
 Ounces, 
 
 46,23456 
 
 H,3456 
 
 24,90400 
 
 7,891 
 
 17,00411 
 
 2,34 
 
 3,01111 
 
 5.6 
 
 
 
 For since dollar is the money unit; and a dime being 
 tlie tenth, a cent the hundredth, and a mill the thousandta 
 part of a dollar, or unit, it is evident that any number of 
 dollars, dimes, cents and mills, is simply the expression 
 of dollars, and decimal parts of a dollar : Thus, 11 dollars^ 
 6 dimes, 5 cents, =11,G5 or ll-jV^ doL &c. 
 
 B, Add tlie ft Uowiag mixed numbers together. 
 
 (4) 
 
 Dollars, 
 
 48,9103 
 
 1,8191 
 
 3,1030 
 
 ,7012 
 
 3?. x\dd the following sums of Dollars together, vix» 
 gl2,S4565-f7,891+2,S4+14,i-,0011 
 
 Ans. SS6,57775, or g36, 5di, Tcts, T-^-^-^mills. 
 G. Add the following parts of an acre together, viz. 
 ,75694-,25+,654+5l99 
 
 Ans, l,8599acrej. 
 r. Add 72,5-1-32,071 +2,1574+371,44-2,75 
 
 Ms. 480,8784 
 S. Add 30,07+2130,71+59,4+3207,1 
 
 Ms, 3497,28 
 9. Add 71,467+27,94+16,084+98,009+86,5 
 
 Ms, 300 
 IQ. Add 57509+,0074+,69+,8408+,6109 
 
 Ms, 2,9 
 
 11. Add ,6 + ,099+,37+,905+,026 Ms. 2 
 
 12. To 9,999999 add one millionth part of an uni^ 
 and the sum will be 10. 
 
 13. Find the sum of 
 
 Twentv-five hundredths, - - - - - 
 Tkree hundred and sixty -five tlio«isandtlvs^ 
 Sixtenilu; and ninemiliionths, - - - . 
 
 Mswer^ 1,215009 
 
80 r^zcjy :-.':. yxACTioj^s. 
 
 SUBTRx\CTION OF DECIMALS. 
 
 RULE. 
 
 Place the numbers according to their value; then sub- 
 tract as in ^vhole numbers, and pokit oft' the decimals as 
 Ih Addition. 
 
 EXAMPLE'5^ 
 
 Bollai'S, Inches. 
 
 1. From 125.64 2. From 14,674 
 
 Take 95,58756 Take 5,91 
 
 $. From 761,8109 719,10009 27.15 
 
 Take 18^9113 7,1 CI i;51 679 
 
 6. From 480 take 245,0075 ./?«.s. 234,9925 
 
 7. From 2S6 dols. take ,549 dols. Jlns. 8235,451 
 
 8. Fnmi ,145 tske. ,09684 Jm. ,04816 
 
 9. From ,2754 take ,9.S71 .^«.«. ,0385 
 iO. From 271 take 215,7 Jlrn^. 55S 
 
 11. From 270,2 tr>ke 75,4075 .^tf.s. 194,7925 
 
 12. From 107 takfi ,0007 .ins, 106,9993 
 
 13. From an unit, or 1, s/abiract the millionth part ol 
 itself. ' ' .itis. ,99l>999 
 
 >IULTI PLICATION OF DECDJALS. 
 
 1. Whether tliey he ir.ixed numbers^ or pure Jcclmals, 
 jJace ihefactorvS raiil nmitiply themas iji whole numbers. 
 
 2, Vu\i\t oW so WAUiy fjgui-es from iho. prodTirt as tJioro 
 aredecin.ai ph-^ees in both the Tactorj; ; and if there be 
 not so many places in the product, supply the defect by 
 prefixing (cyphers to iliQ. left hand. 
 
DECIMAL FRAOTIONS, 
 
 ^ 
 
 EXAMPLES. 
 
 1. Multiply 5,236 2. Multiply 3,024 
 
 by ,008 hj 2,23 
 
 Product ,041888 6,74352 
 
 5. Multiply 25,238 by 12,17 307,14646 
 
 4. Multiply 2461 bj :j29 130,1869 
 
 5. Multiply 7853 by S,5 27485,5 
 
 6. Multiply ,007853 by ,035 ,000274855 
 
 7. Multiply ,004 by ,004 ,000016 
 
 8. What cost 6,21 yards of clotli, at 2 dola. 32 cents, 5 
 mills, per yard ? Jns, 814, 4^. Sc. Bj\%-vu 
 
 9. Multiply 7,02 dollars, by 5,27 dollars. 
 
 Ans. 36,9954^0^5. or g56 99cfs. 5j%vu 
 
 10. Multiply 41 dels. 25 cts. by 120 dollars. 
 
 Ms. 84950 
 
 11. Multiply 3 dels. 45 cts. by 16 cts. 
 
 •5ws\ jg0,5520i=55ct9. 9>mills. 
 
 12. Multiply 65 cents, by ,09 or 9 cents. 
 
 Ms. 80,0585 ==5ces. Shmills. 
 
 13. Multiply 10 dols. by 10 cts. Ms. gl 
 
 14. Multiply 341,45 dols. by ,007 or 7 mills. 
 
 Ms. 82,39+ 
 
 ^ To multiply by 10, 100, 1000, &c. remove the separa^ 
 ting point so many places to tlie right hand, as the mul- 
 tipfier ha« cyphers. 
 
 r Multiplied by 10, makes 4,25 
 
 So ,425 < by 100, makes 42,5 
 
 I by 1000, is 425, 
 
 For ,425X10 is 4,250, &c. 
 
 Ill ^ mum 
 
 DIVISION OF decimals: 
 
 UUT.E. 
 
 t. TliC [L;lac<\s of the decimal parts of the divisor an4 
 Cjijotifnt c<>^(nted tc»;ctlHT. nv1s^ nlv^r^vs be equal to those 
 
1^ 
 
 l^SiOlMAI. FRACTIONS^ 
 
 m tlie dividend, therefore dfvide as in "whole numbegs, 
 and from the right hand of the quotient, point off so ma- 
 ny places for decimals, as the decimal places in the divi- 
 dend exceed those in the divisor. 
 
 2. If the places in the quotient are not so many as the 
 rule requires, supply the defect by prefixing cyphers to 
 tiie left hand of said quotient. 
 
 Note. If the decimal places in the divisor be mare 
 than those in tlie dividend, annex as many cyphers to the 
 dividend as you please, so as to make it equal, (at least) 
 to the divisor. Or, if there be a remainder, you may 
 annex cyphers to it, and carry on the quotient to any de- 
 gree of exactness. 
 
 EXAMl'LES. 
 
 ^351)77,41 14(8,14 
 
 rem 
 
 1,331 
 951 
 
 3804 
 3804 
 
 5,8),S1318(,05&1 
 190 
 
 00 
 
 00 
 
 ♦ffnszrers. 
 
 $. Divide 780,517 by 24,5 
 
 4. Divide 4,18 by ,i8TS 
 
 5. Divide 7.25406 by 957 
 
 6. Divide ,00078759 by y5'^l5 
 
 7. Divide 14 by ^65 
 
 8. Divide S!246,1476 by ^604,25 
 
 9. Divide §186513,239 bv S304,81 
 10. Divide 81,^-8 hy »8,3i 
 M. Divide 5Gci&. by 1 del. 12ets. 
 IS. Divide 1 drtllar by 1.^ cents. 
 15. y iJlj or 21,75 yards of c!o»th cost 34^317 dollars^ 
 
 what will one yard cost ? 21,577 
 
 Note. When decimate, or whole numbers, are to be 
 Sivideil bv 10, ICO, 1000, &c« (vlr.. unit v with cyphers) 
 
 S2,l£ 
 
 ,25068+ 
 
 ,00758 
 
 .00150+ 
 
 ,058356+ 
 
 ,40736+ 
 
 611,9+ 
 
 ,154+ 
 
 8,533+ 
 
DEeiMAL f RAOTXOKS. o^ 
 
 a isperfottned by removing the separatrix in the divi- 
 dend, so many places towards the left hand as there a5C 
 cjphers in the divisor. 
 
 .1 
 
 '11 
 
 EXAMPLES. 
 
 ' 10, the quotient, is ^7^9. 
 
 57SL divided hj{ 100, - ^ - 5,72 
 
 1000, - - ,572 
 
 REDUCTION OF DECIMALS. 
 
 CASE I. 
 
 To reduce a Vulgar Fraction to its equivalent Decimal 
 RULE. 
 
 Annex cyphers to the numerator, and divide by the 
 denominator ; and the quotient will be the decimal re» 
 quired. 
 
 Note. So many cypher^ as you annex to the given 
 jitmerator, so many places must be pointed in Hh^ quo- 
 tient; and if there be not so many places of figures ia 
 the quotient, make up the deficiency by placing cyphers 
 to the left hand of the said quotient^ 
 
 EXAMri.ES. 
 
 1. Reduce -f to a decimal. 8)1,000 
 
 JUns, ,125 
 
 2. "What decimal is equal to i ? Answers. ,5 
 S. What decimal is equal to i? - - ^ - ,75 
 
 4. Reduce 4- to a decimal. - ,2 
 
 5. Reduce -54 toadccima], - - - - „ ,6875 
 
 6. Reduce |^J to a decimal. ^ - - - .. - ^85 
 
 7. Bring //to a decimaL ------ ,09375 
 
 8. What decimal is equal to -^^ ? . . ,0S7037-r 
 
 9. Reduce ^ to a de<;imal. '*- - ^ - ,333i5C>3-f 
 1!K R«duce ^^j^i to its equivalent decimal. - ^OOS 
 
 * Itr Reduce-^ to « decimal. - - - j- 523075^ 
 
84 
 
 DECIMAL FRACTION':. 
 
 CASE 11. 1 
 
 Vo reduce quantities of several denominations to a 
 Decimal, 
 
 RULE. 
 
 Bring the given denominations first to a vulgar fraction 
 bj Froblem HI. page 76 ; and reduce said vulgar frac- 
 tion to its equivalent decimal ; or 
 
 Rule 2. Place the several denominations above each 
 other, letting the highest denomination stand at the hot 
 torn ; then divide each denomination (beginning at tht 
 top) by its value in the next denomination, the last qUD* 
 tlent will give the decimal required. 
 
 EXAMPLES. 
 
 1. Reduce 12s. 6d. Sqrs. to the decimal of a poun^* 
 12 
 
 150 
 4 
 
 
 
 
 9G0)6O5,00O000(, 
 
 5760 
 
 628125 
 
 Jlnswer. 
 
 sroo 
 
 1920 
 
 \ 
 
 Rule 2. 
 
 7800 
 7680 
 
 
 12 
 20 
 
 6^75 
 
 12,5625 
 
 1200 
 
 9G0 
 
 £400 
 1920 
 
 
 ,628125 
 6 
 
 4800 
 4800 
 
 
 
 
DECIMAL MACTION?^ 88^ > 
 
 5. Ileducfe 15s. 9(1. Sqrs. to the decimal of a pound* 
 
 Ans. ,790625 
 
 5. Reduce 9d. Sqrs. to the decimal of a shilling. , 
 
 Jlns. ,8125 ^ 
 4. Reduce 3 farthings to the decimal of a shilling. 
 
 Ms. ,0625 
 ^ 5. Reduce 3s. 4d. New-England Currency, to the de 
 cimal of a dollar. Ms, ^555555+ 
 
 6. Reduce 12s. to the decimal of a pound, dns. ,6 
 
 Note. When the shillings are even, half the number 
 ivith a point prefixed, is their decimal expression ; but 
 if the number be odd, annex a cypher to the shillings, and 
 then by halving them, you will have their decimal ex- 
 pression. 
 
 7. Reduce 1, 2, 4, 9, 16 and 19 shillings to decnnals 
 Shillings 1 2 4 9 16 19 
 
 Mswers. ,05 ,1 ,2 ,45 ,8 ,95 
 
 8. What is tl\e decimal expression of 4L 19s. 6^d.? 
 
 Ms, £4,97708+ 
 
 9. Bring 34^. iGs. 73d. into a decimal expression. 
 
 Ms. £34,8322916+ 
 10* Reduce 25Z. 19s. ojd. to a decima-iT 
 
 Ms. £25,972916+ 
 
 11. Reduce Sqrs. 2na. to tlie decimal of a yard. 
 
 Ms. ,875 
 
 12. Reduce 1 gallonjo the decimal of a hogshead. 
 
 Ms. ,015873+ 
 
 13. Reduce 7oz. 19pwt. to the decimai-cf a lb. troy. 
 
 Ms. ,6625 
 
 14. Reduce Sqrs. 211b. Avoirti^pois, to the decimal of 
 an cwt. . Ms. ,9375 
 
 15. Reduce 2 ruodiS, 16 perciKis to the decimal of an 
 acre. ^ * Ms. ,6 
 
 16. IL'duce 2 fccjt 6 inches to the decimal of a yard. 
 
 Ms. ,833333+ 
 
 17. Reduce 5fiir, -iGpo. to the decimal of a mile. 
 
 *J?ts..,675 
 
 18. Reduce 4i calendai' mo*ntlig to ilie decimal oi' 
 
O 3£G1MAL hhaotiqki 
 
 CASE in. 
 
 Ti^find the value of a tfecimal in tHe known parts of thi 
 
 integer. 
 
 R¥LE. 
 
 1. Multiply the decimal by the number of parts in tim 
 Wxt less denomination, and cut off so many places for a 
 remainder, to the right hand, as there are places in the 
 given decimal. 
 
 2. Multiply the remainder by the next inferior denom* 
 illation, and cut off a remainder as before 5 and so on 
 tlnough all the parts of the integer, and the several de- 
 nominations standing on the left hand, make tlie ai>sweif. 
 
 EXAMPLES. 
 
 1. What is the vake of ,5724 of a pound Sterling? 
 £. ,57»k 
 20 
 
 11,4480 
 12 
 
 5,.sr6o 
 
 4 
 
 1,5040 Jlns. Uss. 5d. t,5^. 
 
 2. What is the value of ,75 of a pound ? Ans. 155. 
 S. What is the valie of ,85251 of a pound ? 
 
 Ms. 17s. Od. 2,4grs. 
 
 4. What is the value of ,040625 of a pound ? 
 
 Ms. 9ii. 
 
 5. Find the value of ,8125 of a shilling. Ans. O^d. 
 
 6. What is the value of ,617 of an cwt. 
 
 Jns. ^qrs, ISlb. loz. lOfidr. 
 T. Find the value of ,76442 of a pound troy. 
 
 ^^tm. 9d». Sipiet. ll^r. 
 S. Whatis tlic value of .875 of a yd. ? Ms. Sqrs. ^l 
 9. Wktt i# the value of ,875 of a hhd. of \^ne ? 
 
 M% £5>^(d. 0(yt Iff,. 
 
1! 
 
 DEC J MAT. FRACTIONS. 
 
 iT 
 
 10. Find tlie proper quantity of ,089 QJ||Ji:ule, 
 
 Ans. kSpo. P.ijds^t. llj04i}K 
 
 11. Find the proper quantity of ,9075 of an acre. 
 
 Ana, Sr.^25,2po. 
 
 12. What is the value of ,569 of a year of S65 dajs ? 
 
 Ans, 20rrf.^l6/i. 267/1. 24sec. 
 15. What is the prefer quantity of ,002084 of a pound 
 ^roy? Ans. 12,003S4^r, 
 
 14. What is the value of ,046875 of a pound avoirdu- 
 a\s ? Ans. 12rfr. 
 
 15. What is the value of ,712 of a furlong? 
 
 Jns, mvo.Qyd, Iff. 11.04f?!. 
 
 16. What is the proper quantity of ,142465 of a year ? 
 
 \:hi^, 51,999r25ifff2/s- 
 
 CONTRACTIONS IN DECIMALS. 
 
 PROBLEISI I. 
 
 A CONCISE and easy method to find the decimal 6f 
 any number of shillings, pence and farthings, (to three 
 pinces) by Ixspkction. 
 
 RULE 
 
 1. Write half the greatest even number of shillings for 
 the first decimal figure. 
 
 2. Let the farthings in the given pence and fartliings 
 possess the second and third places ; observing to increase 
 the second place or place of hundredths, by 5 if the shilr 
 lings be odd 5 and the third place by i \vhen the far- 
 '.hings exceed 12, and by 2 when they excmi^^il 36, 
 
 EXAMPLES. 
 
 I. Find the detimal of Ts. 9 Jd. by inspection. 
 
 ,3 ==:i 6s. 
 5 for tlie odd shillings. 
 39=the farthings in 9|d. 
 2 for the cxce^ii of Sti. 
 
 £. ,391— dtxima) required 
 
r 
 
 dg DECIMAL FRACTIONS* 
 
 5. Find tlie decimal expression of 16s. 4 id. and 17 £ 
 *^^' .A .fws.£. ,819, flntfjQ. ,885 I 
 
 S. WritePPown £47 18 10^ in a decimal expression* 
 
 \ . Jns, £47,943 
 
 4. Red^ice £ 1 8s. 2d. to an equivalent decimal. 
 
 Ans. £1,408 
 
 PROBLEM II. 
 
 A short and easy method to find the value of any deci- 
 mal of a pound by inspection. 
 
 RULE. 
 
 Double the first figure, or place of tenths, for shillings^ 
 and if the secoud figure be 5, or more than 5, reckon 
 another shilling ; then, after t]\\s 5 is deducted, call the 
 figures in the second and third places so many farthings, 
 abating 1 when they are above 12, and 2 when above 36^ 
 and the result will be the answer, 
 
 Note. When the decimal lias but 2 figures, if any 
 filing remains after the shillings are taken ou^ a cypher 
 must be annexed to the left hand, or suppose i . u a ; r. 
 
 EXAMPLES. 
 
 1. Find the value of £. ,679, by inspection. 
 12s.=doubleof 6 
 1 for t!.c 5 in the second place which is to 
 [be deducted out of T. 
 ^d rid.=29 farthings remain to be added. 
 
 Deduct id. for the excess of 12. 
 
 1 
 
 j3ns. i3s. rd, 
 
 % Find the value of £. ,876 by inspection. 
 
 Jins. 17s. 6id, 
 S, Find the value of £. ,842 by inspection. 
 
 Ans. 16s. lOd. 
 4« Find the value of £. ,097 by inspection. 
 
 dn$. is. IIK 
 
JS^ii'-York, and ') 
 JS^orth' Carolina. 5 
 
 REDUCTION OF CURRKNCIES. 
 
 RULES, 
 
 1^ OH reducing the Currencies of the several United 
 States* int'j Feilcral ."^toiej. 
 
 CA.8E I. 
 To reduce the currencies of the different states, where 
 & dollar is an even number of shillings, to Federal Money. 
 They are 
 (A"e ic 'Engla nd^ 
 J Virginia^ 
 ^\ KentkckVy and 
 
 L'" •■■- 
 
 !. Vv'hcii liic sum consists of pounds only, annex a cy 
 |;her to the p'vjnds, vjmI divide by i\alf the number of 
 5;ijiHiiigs in a dollar 5 tiie quotient will be dollars.t 
 
 '2, But if Hie sura consists of pounds, shiliings, pence, 
 f'X. bring ciie given sum into shillings- and reduce the 
 pence and farthing:s to a decimal of a shilling ; annex said 
 decimal to theshilfin^s, Avith a decimal pointbetvveen, tlieu 
 divide the v.h.de by the number of shillings contained in 
 :i dollar, and tiie quotient will be dollars, cents, mills, ^c. 
 
 •^'Formerly the pound was of the same ster!i>-<; vakie in all 
 the colonics as in Groat-Britain, and i Spanish Dollar worth 
 4sf>— but the l^^gisiatures of the different colonies emitted bills 
 of credit, v/hich afterwards depreciated in their value, ki 
 s,ome states more, in others less, he. 
 
 Tlius a dollar is reckoned in 
 
 Js^W' Engl and r\ 
 Virginia y \n 
 
 Kentucky, and f 
 
 .VeW'Fork, ^' " 
 «V*. Carolina. 
 
 8s 
 
 JVew-rkrseij^ 
 Pennsylvania^ 
 Bdaware* and 
 
 Mary land . 
 
 >7s6 
 
 South' "^ 
 Carolina, \.^ 
 and p^^ 
 Georgia. J 
 
 f Adding a cypher to the pounds, multipues the whole by 
 •O, bringing them into tenths of a pound ; then because a 
 iQi'-r is just three^tenlhs of a pound N. E. currency, divi- 
 s!),; tbos^f tenths hy S, brings them into dollars, fcc. See 
 
 a* & 
 

 I . n *M i I c« - 1 ' i\9,l and and Virginia Cii rrency . 
 
 ;o '¥<<':■-. -, 5)730 
 
 2. Reduce 45/. I5s. 7hd, New-England currencj, to 
 20 [federal money. 
 
 AdoI]ar=6)915,e25 .^s-^ -.. 
 
 Note. 1 farthing is .23 "1 which aniicx to tac pence, 
 
 2 — - .T^ ,50 1. and divide bj 12, you wftl 
 
 3 __ —^ .75 J luwcllr^. declnial required. 
 5. Reduce S45^. 10^. 1 U J. Ncw-IIainpshirit, &c. cur 
 
 rencj, to Spanisli ndlled dollai-s, oj* federajl monev. 
 £545 10 111 .' ^ 
 
 20 .- cl - 
 
 12)1152500 ■ 
 
 6)691059375 
 
 ^92 7 '^ clecimu. 
 
 81151,8229+ ^fis, 
 4. Reduce 105^ lis. S|(i. New-York and Nd-th-Cai'd* 
 Ihia currency, to federal money. 
 
 /:i05 14 SJ " d. 
 
 ^)3,.: 
 
 20 12)3,7500 
 
 A dollar=B)21 14,3125 ,3125 decimat 
 
 ^264,289 05 Ans. 
 Or S dcm. ^^^ 
 5. Reduce 43 IL New- York currency to federal raoneyt 
 This being pounds only.*—. 4)4310*^ 
 
 Ans. 81077^=1077550 
 
 *j2 aollar is Ss. in tkts currency — ^4=^\ of a pound $ 
 Hin'('ff}r:^ ■ '.■<' /.»^ hij 10, and divide % 4, brivgs tlm 
 pounds ■ /F, §-c. 
 
^ REDUGTIOK OF CURKEKCIES. 0^ 
 
 6. Reduce 28^ lis. 6d. New -England and Virgiiii^ 
 C-iiTCucy, to federal money. Ans, g95j 25cts. 
 
 r. Change 46SL 10s. Sd. New-England, &c. currency, 
 fi) federal moTiey. Jlns. S1545, lids. Im.-J-' 
 
 o. Reduce 3f5L 193. Virginia, &c. currency, to federal 
 
 ney. Jlns. ^119, 8Scfs. S?u.+ 
 
 9. Reduce 214/. 10s. 7 id. New-York, &c. currency, 
 to icderal money. Ms. g536, Z2cis. 8m.-i- 
 
 10. Reduce 304^ lis. 5d. North-Carolina, &c. cur- 
 cy, to federal money. Arts. grGl, 42cf5. Tm.-^- 
 
 :f. Change 219/. lis. Tjd. New-England and Vir- 
 ginia currency, to federal money. Ans. g7Sl, 94c^s.-i- 
 
 12. Change 24iZ. Ncv/-En^land. occ. currency, int© 
 federal money. Jjis. S803, SScts.-f 
 
 1?. Erin:: 20!. 13b. v-England currency, iuto^^ 
 
 dollars'. Jhis. ,§69, 74cts, 6^m.4- 
 
 14. Redi _re-A-york currencvjto federal mo- 
 l^-^y: " Jins. Sliro 
 
 15. Reduce ITs. G^d. New-York, ike. currency, to 
 «;l!-\rs, £xc. *^/:s. £2, .2-acfi?. 6j5m>-{- 
 
 15. Borrowed 10 English crowns, at 6s. Sd. each, how 
 ?:^y doilr.rs at Gs. eacli, will pay the debt ; 
 
 Ms. Sll, 
 Note. — Tliere are several short practical methods of 
 lucing New-England and New -York cun^encics to 
 Federal Monev, fof wIii(Bfcee the Appendix. 
 
 To rcd'jce the currency of New-Jersey, Pennsylraul^i^ 
 IKdawareand Ivlarvland, to Federal Money. 
 RULE. 
 '^"''I'inly the given sum by 8, and divide iSid. product 
 :'l t!ie quotient will be dollars, &c.* 
 
 JiXAMPLES. 
 
 :. Reduce 24dZ, New-Jersey, Sec. currency, to federal 
 
 <8==::1960, ttjz^Z 1960-4-5 =:S65?4 =S653, 53Jrf^. 
 «:v i ff.. — .When there are shillings, pence, &c. in the 
 
 /! ('-''aris 7s.6d.=^90d.in this cur renctj^zT^^^j^^:^ of 
 %'^:r' ? ; therefore, r.mltipljiug by 8, and dividing hy 3> 
 
^^ n. nUGTIOX OF CJsURRENCIES. 
 
 « 
 
 given sum, reduce them to the decimal of a pound, tlien 
 multiply and divide as above, &c. 
 
 2. Reduce 36/. lis. S^d. New-Jersej, &c. currencj, 
 to federal money. £36,5854 decimal vahie. 
 
 8 
 
 g 
 
 3)292,6852(97,50106 Ans, answef.s, 
 £. s. (L g c^s. 711. 
 
 5. Reduce 240 to federal money 640 GO 
 
 4. Reduce 1-25 8 ' — S34 40 
 
 5. Reduce 99 7 6:^ ^^-- 265 00 5 -f 
 
 6. Reduce 100 -~^. 266 66 6 -f 
 
 7. Reduce 25 3 7 67 14 4 
 
 S. Reduce 17 9 2 56 6,6 
 
 C^SE ill. 
 
 To reduce the currency of South-Carolina and Georgia, 
 to federal money. 
 
 RULE. _ ^ . •■ 
 
 Multiply the given sum by 30;? and divide the product 
 by 7, the quotient ^^i\\ be the dollars, cents, &c.* 
 
 EXAMPLES. 
 
 1. Reduce lOOZ. South-Carolina and Georgia currency, 
 to federal money. 
 
 100/.x50=S000 5 5000-v-7=g428.5714 Ms. 
 
 2. Reduce 54/< 1 6s. 9 jd. Georgia currency, to federal 
 money, 54,8406 deciwdl Expression * 
 
 30 
 
 7)1645,2180 
 
 dnS. 255,0311 ANSWERS. 
 
 £. s, d. S cts, m. 
 
 S: Reduce 94 14 8 to federal money, 405 99 S-f 
 
 4. Reduce 19 17 G^ 85 18 7-^ 
 
 5. Reduce 417 14 6 1790 25 
 
 6. Reduce 140 10 602 14 2+ 
 
 7. Reduce 160 685 71 4 
 
 — k -^-, ■ — - 
 
 *4s. Sd. or 56d. to the efo/tar=^2^V=/7 ^/ * ]?omd; 
 tfiex^ore x30-r-7. 
 
REDUCKION ©F COIN. 
 
 to- 
 
 s. 
 
 d. 
 
 lled lice 
 
 11. 
 
 G 
 
 Ileduce 41 
 
 ir 
 
 9 
 
 ^ 1 
 
 55 ct^' m. ' 
 2 46 4«h 
 179 51 4f^ 
 
 CASE IV. 
 
 I'l; reduce the currency of Canada and Nova-Scotia^ to- 
 Federal Money. 
 RULE. 
 Multiply tlie given sum by 4, the product will be dollars.. 
 i>oTE. Five shillings of this currency are equal to a 
 dollar ; consequently 4 doilais make one pound 
 
 EXATviPLES. 
 
 1. Heduce 125?. Canada and Nova -Scotia cUrrenc}', ID* 
 ^C'lciT,! innnoy. 1C.5 
 
 Ms. B500 
 
 2. Reduce 551. 10: . 6d. Nova-Scotia cuirency, toCSlr 
 lArs. 55,59.5 decimal value. 
 
 ^' 4 
 
 S cis. 
 
 Ms. 82225 100=222 10 AKSWERST^ 
 
 5. Reduce 241 18 9 to federal money* 96r 75 
 
 4. Reduce 58 13 6i 234 70 
 
 5. Reduce 528 17 8 « 2115 5S 
 
 6. Reduce 12 6 4 50 
 
 7. Reduce 224 19 - 899 80 
 
 8. Reduce 13 lU 2 79 
 
 REDUCTION OF COIN. 
 
 RULES 
 
 For reducing the Federal Money io the currencies of thft 
 
 several United States. 
 
 To i?educe Federal Money to the currency of i^^. 
 
 „ ^^S^'"'^^ ^rM«ltiplythegivensumby,5 
 1 < AT.„fc.;'i-,;. nr,Ac-i\ ar4t!.eproductmllbepoui\a* 
 
 1 
 
 /v-en^'cfc^ nnd\i\ and the product mil be pouiid* 
 Tenwssit j « Und decimals ot a pound.. 
 
^,Gj ik-c* 
 
 ULES) f6r redyi^n^ tlio: currencies of tlie 
 
 aUt' 
 
 to the par of a^pbe others. See tl 
 
 ji'jglit hand, till jou coir*e under the required cuiTencj: 
 
 e\M5fal {jnU 
 vcn curiiency 
 
 Virgirda, 
 Kentucky^ 
 
 and 
 Tennessee, 
 
 ^\ England. 
 
 Virginia^ 
 
 Kentucky ^^ 
 
 and 
 *Fe.nnessep.. 
 
 ^'iw-Jersey, 
 (Pennsylvania^ 
 j Delaware^ 
 \ and 
 j Maryland, 
 
 WeW'Forkf 
 
 \^orih'CarO' 
 
 ► linn, X 
 
 IS'Quth'Ccfroli- 
 
 na^ and 
 Genr2:'a, 
 
 JSI'eW'Je^^sey^ 
 Fennsylvafiia^ 
 
 Delaware^ 
 and 
 
 Maryland, 
 
 Deduct one, 
 liiVii from the 
 jxiven sum. 
 
 V 
 
 Deduct one 
 4th from the 
 New-York, 
 
 &c. 
 
 ^ew-Yorkj 
 
 ' and 
 JVl Cnralimz. 
 
 Add pne 4th 
 to the given 
 
 sum. 
 
 Add one Sc 
 to the give: 
 
 iiUUl. 
 
 Deduct one 
 ifith trom the 
 
 New-York. 
 
 u;iven sum Ov 
 9, and divide 
 ^]i(^ product 
 
 I Multiply the. 
 given sum by 
 45, and divide 
 the product 
 
 IVy 28. 
 
 Add one 5th 
 I to the Cana- 
 
 Add one half 
 G the Canada 
 
 Add one fif- 
 teenth to the 
 'i:iven sum. 
 
 IMuitipiy the 
 ffiven sum bv 
 12, and di- 
 vide the pro^ 
 
 duct by T. 
 
 Multiply the 
 given sum bj 
 8, and divid 
 tlie product 
 by 5. ^ 
 
 iultiply the Multiply tht 
 
 ;iish ^um said 
 
 ;oue thiri 
 
 .^D^l'hnior^ 
 ^y^^>j and m- 
 j'vide thii pro- 
 iduct by 3 
 
 suns 
 
 English 
 
 b>'' "l6,anti r.'j-. 
 
 ih- 
 
 t;ie ., 
 
llULf^il FOIl HEDUfiXJiiS, &.C^ 
 
 .1\ 
 
 ted States, also Canada, Nova -Scotia, and Sterling, eatli 
 in the left hand column, and then cast your eye to the 
 and you will have the rule. 
 
 South-Carolina^ 
 
 and 
 
 Gior^lrt, 
 
 ' Canada^ 
 
 and 
 JVova-Scotia^ 
 
 Sterling* 
 
 Multiply the giv- 
 en sum by 7, and 
 divide the product 
 Dy 9. 
 
 rSJultlpIy iii\Q div- 
 ert sum by 28, ^xn^l 
 divide the product 
 
 Multiply the giv- 
 
 II Sum by 7, and 
 ivide the product 
 by 12. 
 
 Multiply t^'i^fi giv 
 en sum by 5, and 
 divide the product 
 bv6. 
 
 Deduct one third 
 rom the given 
 sum. 
 
 Multiply the giv- 
 en sum \ij> 5. and 
 divide tlic pre duct 
 by 8. ' 
 
 Deduct 
 fourth from 
 jdven sum. 
 
 one 
 the 
 
 Multiply the giv- 
 en sum by 3, and 
 divide the produQ^ 
 by 5. 
 
 Multiply the giv^ 
 en sum by 9, and 
 divide the producJ 
 Ibv 16. 
 
 1 Multiply the giv- 
 Jen sum by 15, and 
 [divide the product 
 joy 14. 
 
 I 
 
 From the glvenj 
 sum, deduct cnri 
 
 L\,en-y-cip;]ua. ! 
 
 I Deduct one flF-JI 
 jUenth irom the.; 
 jgiv'Bn sum. 
 
 I J ' 
 
 \ T(i tiie EngUsii 
 
 Fiiey add 
 eitty'Seventli. 
 
 Add one nintu 
 onclto tiio givwi Slim. 
 
 ' lieuuci 
 
 tenth from 
 i^iven iTwim, 
 
 thfil 
 
 vr, 
 
98 HEDUCTIOX OF CQIN. 
 
 APPLICATION 
 
 Of the Rules contained in the foregoing TahU. 
 
 EXAMPLES. 
 
 I. Reduce 46L 10s. 6 J. of the currency of New-Haiflj» 
 sliire^int© that of New- Jersey, Pennsylvania, &c. 
 
 See i\\Q, Rule 
 in the Table. 
 
 Jlns. £58 3 1^ 
 £. Reduce 25/. 13s. Ot^. Connecticut currency, to 
 N«w-York currency. 
 
 £. s. d. 
 
 $)25 13 9 
 
 By the Table,+} &c. -f 8 H S 
 
 4)f6 
 +11 
 
 10 6 
 
 12 7J 
 
 \ 
 
 ^^ ^ns. £34 5 
 
 3. Reduce 125/. 10^. Ad. New-York, &c. turrcncy, 
 South-Carolina currency. 
 
 £. 5. d. 
 
 Rule by the Table, 125 10 4 
 
 xr,-f-by 12, &8, 7 
 
 12)8r8 12 4 
 
 Jins. £73 4 4i 
 
 4. Reduce 46f. lis. 8i. New-York and North«Car<K 
 jVia currency, to sterling or English Money. 
 
 £. 5. iZ. 
 
 AG n 8 
 9 
 
 See the Table. ) 16=4x4Ml9 5 
 Xgiven sum by v 4)104 16 3 
 
 9n-16,&c. J 
 
 4ks. ^26 4 Oj 
 
RE'DUCTiON or COIN. ^iL 
 
 To rexluce any of thf diflerent currencies of thc^scrW 
 ral States into each other, at par ; yoii may consult the 
 preceding Table, which will pve you the fiules. 
 
 MORE EXAMPLES FOP*. EXERCISE* 
 
 5. Reduce 84^ 10s. M. New-TTa/r»r.<^iiIre, &.c. curren-^ 
 cy, intoNew-Jeisev curreiicy. 
 
 , . J- £105 ISs. 4iL 
 
 6. Reduce 120/. 8>\ ScL Connecticut currency, into 
 New-Y«rk currency. Jns, £160 lU. (>/. 
 
 7. Reduce 120L lOs. ^?assachasetis currency, into 
 South-Carolina and Georgia currency. 
 
 Jns, £93 Kfr 5iiL 
 
 8. Reduce 410L I8s. Ih'/. Rhode-Island currency, in- 
 to Canada and Nova-Scotia currency. 
 
 Jns, £542 9s. id 
 
 9. Reduce 524^. 8s. 4d. Virginia, 5tc. currency, into^ 
 Sterling money. * . Jus, £39o Gsi Sd, ^ 
 
 10. Reduce 214/. 9s. 2f?. New-Jersey, &c. currency, T 
 fauto New-Hampshire, Massachusettji, ^c, currency. ' ^ 
 
 .ins, £171 lis. 4d. |J 
 
 11. Reduce lOOL New-Jersey, ^cc. currency, into N.^' 
 York and North-Carolina currency. * 
 
 'M^. £105 ISs. 4 J. • 
 i2. Reduce 100/. Delaware an4 ^lajylar.d currency^ 
 in,to Sterling monev, »J^>5. ;(J60. 
 
 13. "Reduce 116?. -York curreii(?y, into Con* 
 n€cticut currency. .Ins. £3V. 7s. Cd, M 
 
 14. Reduce i l£/. Ts. Sd, S. Cnrolhia a!id Georgia 
 currency, into Connecticut, &c. currency. w^ 
 
 M$/£IU 93. $id. 
 
 15. Reduce 100/. Canada and Nova-Scotia currency, 
 into Connecticut currency. *dns, £ I-^^IO, 
 
 16. Reduce 116/. 14-^, 9d, Sterling money, into Con- 
 necticut currency. Jins, £155 ISs, 
 
 17. Reduce 104/. IGs. Canada and Nova-Scotia cur- 
 rency, into New- York cirrency. ^ns, £167 4s. 
 
 18. Reduce 100/. Nova-Scotia ciinency, into Nejv- 
 Je;;3ey, &c. currency. ' Jhis, £150 
 
^f .. Ky.LK OF XHRE.^ DIRECT. 
 
 RULE OF THREE DIRECT. 
 
 , X HE Rule of Tiiree Direct Teaches, by having Hwe.% 
 Tuimbers given to find a fourth, which shall have the same 
 
 ^proportion to the third, as tlie second has to the first. 
 1. Observe that two of the given liimbers in your 
 jl^question are always of tlie sair^e name, or kind ; one of 
 Oxvhich must be the*^ first number in stating, and the other 
 , the third number ; consequently, the first and third num- 
 f^ bers must always be of the same name, or kind ; and the 
 ^ other numbBr, which is of the same kind with the answer, 
 r or tiling For..!>;]it, will always possess the second or middle 
 
 \ 2. lh%tly''(l term is a demand ; and may be known by 
 these or the like v/ords before it, viz. What will 5 What 
 co^ ? How many ? } Jo w far ? Kow long ? or, Ho w 
 much ? &c. 
 
 RULE. 
 
 1. State i]iQ question ; that is, place the numbers s« 
 tiiatthe first and third terms may be of the same kind; 
 and the second term of the same kind with the answer, or 
 thing sought. 
 
 2. Bring tlie first and tiiird terms to the same denom- 
 sjination, and reduce the second term to the lowest name 
 sT mentioned in it. 
 
 \ S. Multiply the second and third terms togetlier, and 
 \flivide their product by the first term 5 the quotient will 
 J be the answer to the question, in the same denomination 
 ^you left the second term in, wliich may be brought into 
 y any other denomination required. 
 \ The metliod of proof is by inverting the question. 
 
 NOTE.- -The following methods of operation, when they 
 can bo used, perform the work in a much shorter manner 
 than the general rule. 
 
 1. Divide the second term bj^ the first; multiply the quo- 
 tient into the third, and the product will be the answer. Or 
 
 2. Divide tlic third term by the first ; multiply the quotient 
 i;ifo tlie second, and the product will be the answer. Or 
 
 3. Divide the first term by the second, and the third oy 
 that quotieiit, and the last quotient will be the answer. Or 
 
 4. Divide tJie first term by tae third, and the second hj 
 tRr,t ffUCtiRnt, and th^ Irtst q\tdti6nt will b<; the answer.^ 
 
rt:t.k or TH^I^ upiRxc '.'. 
 
 U):. 
 
 >Ev^MPL^s, 
 
 t. If 6 yards of cloth coSfQVlollarsiHvliat ivlU iS^ yards 
 
 cost at the same rate ? 
 
 
 Fds. S Yds. 
 
 Here 20 yards, whiclx moves 
 
 6 : 9 : : 20 
 
 the question, is tlie third term 5 
 
 9 
 
 6 yds. the same kind, is 
 
 the first. 
 
 
 and 9 dollars tlie second. 
 
 6)180 
 
 
 
 Ms. gSO 
 
 2. If 20 yards cost 5 
 
 dels. 5. 
 
 If 9 dollars will buy 6 
 
 what cost 6 yards ? 
 
 yards 
 
 ;, how many yards will 
 
 rds. S Yds 
 
 30 dollars buy ? 
 
 20 : so : : 6 
 
 
 S yds. g 
 
 6 
 
 
 9 : 6 : : so 
 6 
 
 2,0)18,0 
 
 
 9)180 
 
 Ms. »9 
 
 
 Ans. myds. 
 
 4. If Scwt. ofsu»ar 
 
 cost Si. 8s. w 
 
 hat will 11 cwt. 1 qr. 
 
 §4 lb. cost ? 
 
 
 
 S cwt. SI. 85. C. qr. 
 
 lb. lb. 
 
 s. 
 
 112 20 11 1 
 
 24 As 336p : 168 : : 1284^^, 
 
 -^ 4 
 
 
 168 
 
 S^6Z&. 168s, — 
 
 
 \ 
 
 4^ 
 
 
 10272 
 
 28 
 
 r^' 
 
 7704 
 
 ...^ 
 
 / 
 
 1284 
 
 564 
 
 
 — ■(2,0) 
 
 92 
 
 
 536)215712(64,2 
 
 
 
 2016 
 
 1284 » 
 
 
 32Z.2S, 
 
 1411 Ms. 
 1344 
 
 672 
 
 672 
 
 
 ft* 
 
 ^ 
 
 
 * 
 
 
;\ n cac ;;.aii: ^>lv sc^^fLiUngs ccfi^ 4s. Ga. wluii will 19 
 
 6,-1. " ' I pair oT & ■ -vtZ. 6s. what will one 
 
 piiir Civ ^ns. 4s. 6(f. 
 
 r. Ai iOk.. per pound, what is the value of a firkin of 
 t>utter, weight 56 pounds ? ^?is. £^ 95. 
 
 8. Kuw iiiuch sugar caiuyou buy for 23Z. Ss. at98. a 
 pound ? Jins. 5C. ^rs. 
 
 9. Bought S chests of sugsir, each 9 cwt. 2 qrs. what 
 do they come to at 2^. 5s. j^ercwt. ^ Ans. £17i. 
 
 10. if a man's wages arc 751. 10s. a year, what is that 
 a calendar month ? Ji'iis, £6 5s, lOd. 
 
 1 1. If 4^ tons of hay will keep 5 cattle over the v/inter : 
 Iiow many tons will it take to keep 25 cattle the same 
 time ? " ^Ins. 37^ tons. 
 
 12. If a man's yearly income he 20SL Is. wl^.at is that 
 a day ." Jlus. lis. 4d. S-^/^qrs, 
 
 IS. If a man sp^inds Ss. 4d. per day, how muchi? that 
 a year? t,^ns. £G0 ICs. Sd. 
 
 14. ilCidlngat 12s. Cd. per week, how long will o£L 
 IB.?, last me .^ .•^?2.s.' 1 ?/^/?r, 
 
 15. A owes B C>475l. Dut I> compounds with him iht 
 73s. 4d. on the pound ; pray what must he receive for 
 his debt r ^ Ms. £2S\6 ISs. 4d. 
 
 16. A j^klsmith sohl a tankard for SL 12s. at 5s. 44* 
 gpr r?r;i:c:;, what was the weight of the tankard ? 
 
 » ^^ns. 9.11). ?>oz. 5pivh 
 
 17. i;2cvf. S qrs. 21 Io\ of Sugar cost 6L Is. 8d. w^hat 
 cDst 35:^ cut r ,lns. £7o. 
 
 18. Bought 10 piecei^ of cl;)thj each pj ecc cnntainin^ . 
 9^ }Tu-ds^ at Its. 4i ponce jVCr yard 5 what did thc.M'hole, 
 
 
 FIH)ERAL MONEY. 
 
 KOTE 1. You must state the question, as taught in 
 the Rules foregoing, and after reducing the first and third 
 fi!rms to the same name, &:c. you may multiply and di- 
 vide according to ^i\^ rales in decimals ; or by tl:e rule^ 
 ^or multiplying and divMiug Federal MojiQ". \ 
 
..(]:- 
 
 :s3 
 
 19, If r yds, of cloth cost 15 dollars 47 cents, what 
 willl3yds/cost? Vds. Scis. yds, 
 
 7 : 15,47 : : 12 
 12 
 
 7)185,S4 
 
 •3m5, 26,53=8-<3. 52n\^. 
 •But any sum in dollars and cents may be written down 
 CS a whole number, and expressed in its lowest denomi- 
 nation, as in the following example : {See Reditctipn of 
 Federal Moiiey^ page 67.) 
 
 £0. What will 1 qr. 9 lb. sugar come to. at 6 dollars 
 45 Cts. per cwt. ? 
 
 gr. Ih, Ih, cts, lb. 
 
 19 M 112 : 645 : : 37 
 
 as 
 
 r.r 
 
 lb. 4515 
 
 1935 
 
 -^ cts. 
 
 112)23865(213+ .-3ws.=g2, IS. 
 224 
 
 345 
 
 \ 
 
 9 
 
 NOTE 2. When ihe first and third numbers are fede- 
 ral money, you may annex cyphers, (if necessary) un^l 
 j!t)U malie tfieir decimal plrxcs or figures at the right 
 hand of the separatrix, equal: which will reduce them to 
 a Hke denonr?inatioa. Then you may multiply and di- 
 vide, as in whole numbers, and the quotient will expreis 
 the answer in the least denomination mentioned in _tli« 
 f^cmd, or mi^id'e ter)^. 
 
IQi 
 
 nULE of THUEE PIRECT. 
 EXAMPLES. 
 
 SI. If 3 dolidfs will buy T yards of cloth, how many 
 Jjfcrds can I buy for ISO dollars, 75 cents ? 
 cts. ijds, cts. 
 
 As SO0 s 7 f : nor 5 
 7 
 
 yds. 
 
 500)84525(2811 *^m: 
 22. If 1 ■^. lb. of Tea cost 6 dols. 600 
 
 rS cts. and 9 mills, what ^yill 5 lb. 
 
 cost at the same rata } 2452 
 ib. mills. Uh 2400 
 As 12 : 6739 : : 5 
 
 525 
 500 
 
 12)35945 
 
 Zct^'in. 225 
 
 ^Ins 2828-F-mi/I^j=2582,S. 4 
 
 900(a2i*5* 
 900 
 S cfs. — 
 
 23. ir a ma/i lays out ]2I. 25 in merchandize, and 
 thereby gains 39 dolhirs, 51 cts. iiovv much will he gain 
 by laying out 12 dollars at the same rate t 
 
 Cents, cents. cenis. v 
 
 As 12123 : 3951 : : 1200 
 1200 
 
 cts, S cts. 
 
 121£3)4741200(391 =55,91 .in$. 
 36369 
 
 110450 
 109107 
 
 15250 
 1S123 
 
 nor 
 
^ 
 
 wi 
 
 •latTIK 0? THREE ©IREOT- 105 
 
 54. If the wages of 15 weeks come to 64 do!-.. lO rts. 
 ©at is a year's wages at that rate ? 
 
 Jlns. 8222, 5.:...... ..... 
 
 55. A man bought sheep at 1 dol. 11 cts. per head, to 
 the amount of 51 dols. 6 cts. j liow many sheep did he 
 buy ? , .4«s. 46. 
 
 26. Bought 4 pieces of cloth, each piece containing 31 
 yards, at l6s. 6d. per yard, (^New-England uxnency) 
 what does the whole amount to in federal money ? 
 
 Ans. 8341. 
 Sr. When a tun of wine cost 140 dollars, what cost a 
 quart ? dns. IScts, S^-^m. 
 
 23. A merchant agreed with his debtor, that if he 
 would pay liim down 65 cents on a dollar, he would give 
 him up a note of hand of 249 dollars, 88 cts. I demand 
 Ti'hat the debtor must pay for his note ? 
 
 Ans. 8162, 42ci<J. 2m. 
 29. If 12 horses eat up SO bushels of oats in a week, 
 tow many bushels will serve 45 horses the same time ? 
 
 Ans» 112^ bushels. 
 
 50. Bouglit a piece of cloth for 848 27 cts. at 1 dollar 
 19 cents per yard ; how many yards did it contain ? 
 
 Ans. 40yds. 2qrs. y\^^. 
 
 51. Bought 3 hhds.of sugar, each weighing 8 cwt. 1 qr. 
 IS lb, at 7 dollars, 26 cents per cwt. what come they to ? 
 
 Ms. 8182 let. 8m. 
 ^ ^. What IS the price of 4 pieces of cloth, tlie first 
 piece containing 21, the second 23, the third 24, and tlie 
 liwrth sr yards at 1 dollar 43 cents a yard f 
 
 Ms. 8135 '66cfs. 21+25+244-2r=0%!/>-. 
 ^. Bought Shhds. of brandy, contaiiiing 6}.. 'H, f^:Li 
 gallons, at 1 dollar, 38 cents per gallon, I demand .'.ow 
 much tiiey amount to ? Ms. S255, Vj/is. 
 
 34. Suppose a gentleman's income is 1836 dollars a 
 year, and lie spends 3 dollars 49 cents a day, one dav 
 with another, now much will he have saved at the yea^-'s 
 end ? Ms. 8562, ] 5cU. 
 
 35. If m^ horse stands me in 20 cents per day kcep- 
 tng, v/hat Avill be the churgc of 11 horses for the yeai-, at 
 Inatratef? ^ Ms. g803. 
 
So. A merchant boijiglit 14 pipes of wine, and Is allo^vH 
 ed 6 months credit, but for ready money gets it 8 cents a 
 gallon cheaper ; how much did lie save by payirsg ready 
 
 EX^MPLES^i 
 
 Cr. Sf^L: 
 
 at 
 
 was my pi^ri ^;i t.io niouey r .iVh. £-^Ji 
 
 33. if -^5- of a vshlp cost TSl dolhirs 25 cents, M'hat is 
 
 t^ie whole wortli ? S 
 
 As 5 : r8l.*:^5 : : i6 : 2500 .2;zi?. 
 59. If I buy 54 yards of cluih fi-^T S\L 10s. what did 
 
 '^, cost per Eli Englisli ? dn<i, 14s, 7d. 
 
 40. Bought of Mr. Grocer, 11 cwL 3 qrs. of sugar, at 8 
 dollars 12 cents per cwt. and gave idiii James Payweirs 
 note for 19^. Ts. (Ncw-Englau<l currency) the rest I pay 
 in cash; tell nie how inaiiy uidiars vvill make up W\q 
 balance t ^ .Qns, S50, 91 cis. 
 
 41. If a stair 5 feet long casts a shade on level groumi 
 8 feet, wluit is the lieight of that steeple whose shade at 
 the same time measures 1 81 feet .^ Ans. llS}ft, 
 
 42. If a gentleman has an income of 300 Englisii guin- 
 eas a year, how mrich may he spend, one day with anoth- 
 er, to lay up 500 dollars at tiie yearns end ? 
 
 dns. S2, 4Gch, 5m. .^ 
 
 43. Bought 50 pieces of kerseys, each 34 Klis-Flemish, *' 
 at 8s. 4d.per Ell-Ei^lish; wliat da) tiic whole coi;t.^ 
 
 Jhis. £4^25. 
 
 44. Bought 200 yaitls of canitjiick for 00/, but being 
 damaged, i am willing to lose 71, 10s. by tl\e sale of it ; 
 what must I demand per Ell -English ? Ans, lOs, Sfr/. 
 
 4.5. Hov/ many jneces oi ii<.liaad, each 20 Ellg-FIem- 
 ish, may I have fxM* 25/. 8s, at 6s. 6d. per Ell-English ? 
 
 An^, 6 lueces, 
 46. A merchant bought a bale of ch^th containing £-10 
 yards, at the rate of 7^ dollars for 5 yards, and soiii it 
 again at the rate of 1 H doHajs for 7 yard^jj did he gaia 
 or loae by the bargain, and how much ? 
 
 .fi:t$, lie gained S25, 71 .^/.«:. Ad:. -^ 
 
RULE OF THREE DiREfJT. 1^? 
 
 47. Bougjit a pipe of wine for 84 dollars, and fonad it 
 had leaked out 12 gallons ; I sold the remainder at 12 J 
 cents a pint 5 what cfid 1 gain or lose ? 
 
 Ms, I gained S'30. 
 
 48. A gentleman bought 18 pij}Gs of wine at 12s. 6d. 
 (New -Jersey c\irrencj) per gallon 5 how many dollars 
 will pay the purchase ? •^ns. g3780. 
 
 49. Bought a quantity of plate, weighing 15 lb. 11 oz. 
 ISpwt. 17 gr. how many dollars will pay foritj at the 
 rale of 12s. 7d. New -York currency, per ounce ? 
 
 Jins, |g;301, 5Uct^ 2j%w. 
 
 50. A factor bought a certain qiiautity of br(jadc*oth 
 and dru^et, which together cost 81/. the quantity ot 
 broadcloth was 50 yards, at 1 8s. per yard, and for every 5 
 yards of broadcloth 1^ iiad 9 } ards of chugget ; I demand 
 how many yard« of drugget he iiad, and wha^ it cost him 
 per yai-d r 3ns. 90 yards at Ss, per yard, 
 
 51. If I give 1 etigl 65*2 dollars 8 dimes, 2 cents and 5 
 tnills, for 675 tops, now many tops will 19 mills buy ? 
 
 •fins, I top 
 53w Whereas an eagle and a cent jr.st tliree score yards 
 did buy, 
 H6w many yards of that same cloth for 15 cliin^.3 had I P 
 
 •^ns. Si/ds, Sqrs, Sna.+ 
 55. If the Legislature of a State grant v ta?: of 8 milU 
 Qfi the dollar, how much must that man pa - • 9 d 0! - 
 
 lars, 75 cents on the list? 
 
 dns. S2, 55cts, 8r»i, 
 
 54. If 100 dollars gain 6 <lollars interest in a yeai, 
 how much will 49 dollars gahi la the same time .^ 
 
 55, If 60 gallons of watftr, in one hotti-. 6^1 iuu: & c;^ 
 tern containing SOOgallofis, ano by a »>ipe in t-m eMmi^ 
 S5 gallons run out in an liour : in what tiiae will n b?. 
 fdl»*d ? ^ns, in l^houTH, 
 
 ol), A and B depart Iron t{>e sanie piace ana trard 
 the game wad; but A ipoji 5 (ir'r? befai-e I J. at ll-e mh- 
 of 15 miles a day ; 1^ follows vit trie »"itfi cf siO mils* ^ 
 day 'f what dis*tanr.e must, he travel to ov«M'take A r 
 
 Jns. 500 mlUB* 
 
11 
 
 KULE OF THREE iiJVKRSE. 
 
 JLE OF THREE INVERSE., 
 
 ^ ,ip iff Three Inverse, teaches by liavJng ihxi^ 
 r •*-'■'' 4 ''Jiirth, which shall have the same 
 . u?i> as the iirsthas to the third. 
 ) >re equires more, ov less requires less, the quesT* 
 iio ' -'iHigs to the Rule of Three Direct : 
 
 fiut it more requires less or less requires morcy the 
 question belongs to the Rule of Three Inverse ; \thicli 
 may always be known from the nature and tenor of tlie 
 question. ' For Example ; 
 
 If 2 men can niowa field in 4 days, how many days 
 will It require 4 men to mow it ? 
 
 771 en days meyt 
 
 1. If 2 require 4 how much time will 4 re* 
 quire ? Anstver, £ days. Here more requires Ifis?, Vii^ 
 the more men the less time is xi^qyii'e^ 
 
 men days ^ii^tt 
 
 2. If 4 require 2 how much time ^vill £i f^* 
 quire ? Answer;, 4 days. Here less requires more, vi«. 
 the less the number of men are, the more days are requir- 
 ed — therefore the question belongs to Inverse Proportion* 
 
 RULE. ^ 
 
 1. State and reduce lint terms as in the Rule ofThrefc 
 Direct. 
 
 2. Slultiply the first and second terms together, and 
 divide the product by the third ; the quotient will be thJfe 
 answer in th^ same denomination as the middle term 
 was reduced into. 
 
 EXAMPLES. 
 
 1. If V2 m£n can build a wall in 20 day^, How iriaj^y 
 men ra:i do the same in 8 days ? *flns. SO ttien, 
 
 2. If a manpcsforms a jounic j in 5 days, when iFie 
 tlav 1 UUioia's long, in how many days v;iil he perform 
 it {vLen the dav is In- 1 10 hours long ? dns.G iUijiB. 
 
 "> What h^nj^ : : vd 7i iilcHes tvido* will maice Si 
 
raACTXOE. l(i^ 
 
 4. If live dollars will paj for tlic carriage of 2 cwt. 150 
 miles, how far may 15 cv;t. be carried for the same mo- 
 ney ? •''his, 20 miles, 
 
 5. If when wheat is 7s, 6d. the bushel, the penny loat 
 will weigh 9oz. what ought it to weigh when wheat is 6s. 
 pep bushel ? Ms, Uoz, 5pivt. 
 
 6. If 30 hushels of grain, at 50 cts. per bushel, will 
 pay a debt, how maiw bushels at 75 cents per bushel, will 
 pay the same ? " •^na, 20 bushels. ^ 
 
 7. If lOOl, in 12 months gain 61, interest, what princi- 
 pal will gain the same in 8 months ? Jins. £150. 
 
 8. If 11 men can build a house in 5 months, by work- 
 ing 12 tours per day — in what time will the bame num- 
 ber of men do it, when they work only 8 liours per day ? 
 
 Jiizs, 7h intriUihS, 
 
 9. Wkai nuiuber of men must be employed to fiidsh in 
 5 days, what 15 men would be £0 days about ? 
 
 w2?i5. 60 mtn. 
 
 10. Suppose 650 men are in a garrison, and their pro- 
 visions calculated to last but two months ; how many men 
 must lea\ e the garrison tliat the same provisioiis may be 
 gufficient fur those who renuiin live months ? 
 
 Jlns. ^90 men, 
 
 11. A regiment of soldiers consisting of 850 men are 
 to be clothed, each suit to contain 3^ yds. of cloth, which 
 is li yards Wide, and lined witli shalloun | yard wide^ 
 liow many yards of sliaiicon will comolete ^wo. liriing? 
 
 Jim, e94iyds, ^qrs, ^na. ' 
 
 FKACTICE. ^-s 
 
 Practice is a contraction of t:ie Rule of 'ilirce 
 I'iirect, v/hen the first term happens toi.e an unit or owe, 
 and is a concise method of resolving ir;ost questions that 
 occur in trade or business where monev is reckoned in 
 pounds, shillings and jXiuce ; but reck^'jji'ng in federal 
 Money will render this rule almost v.sr.lis's : for vhirl; 
 reason I shall net enlar^^e so much o-. Oir ;in])ject as ma-r 
 Dv ether wiiters We done. 
 
no 
 
 WiACTICE. 
 
 Parts of a Shiihne;, 
 is !j 
 
 Tables vf Jiliquot, or Even Farts. 
 
 6 
 4 
 
 S 
 
 2 
 
 1 
 1 
 
 Parts of 2 Shillings. 
 Is. is i 
 
 8d. 
 6d. 
 4d. 
 3d. 
 2d. 
 
 
 Parts of a PouTid.l Parts of a cwt. 
 
 d, 
 10 
 6 8 
 5 
 4 
 3 4 
 2 G 
 1 8 
 
 £• 1 
 
 i&. 
 
 cwU 
 
 i 
 
 56 
 
 ii h 
 
 ^ 1 
 
 28 
 
 = i 
 
 i 
 
 16 
 
 4 
 
 i 
 
 14 
 
 i 
 
 1 
 
 ir 
 
 1 
 
 •B 
 
 i 
 
 15- 
 
 I 
 
 
 
 ¥ 
 
 
 
 tV 
 
 
 
 The aliquot part of any number, 
 is sucli a pai't of it, as being taken a 
 certain number of times, exactly 
 makes that number. 
 
 CASE I. 
 
 When the price of one yard, pound, &c. is an even part 
 of one shilling. — Find the value of the given quantity at 
 Is. a yard, pound. Sec. and divide it by that even part 
 and the quotient will be the answer in shillings, &c. 
 
 Or find the value of the given quartity at 2s. per yard, 
 &c. and divide said value by the even part whicli the 
 given price is of 2s. and the quotient will be the answer 
 in shillings, &:c. whicli reduce to pounds. 
 
 N. B. To find the value of any quantity at 2s. you need 
 only double^ the unit figure for shillings; the other fig- 
 ures will be pounds. 
 
 EXAMPIUilS. 
 
 1. "What will 46U yards of tape come to, at 1 id per yd, r* 
 s. d, 
 Ud. ( ^ I 461 6 value of 461 6 yds. at Is. per yd. 
 
 5,7 V>i 
 
 £2 ITS, 8icZ. value at l^id. 
 What cost 25Glb. of cheese at 8<i. per 
 
 noujid ? 
 
 Sd. 
 
 j /:2j 12s. value of 2561b. at 2s. per lb. 
 
 xC^^ 
 
 8f?. va!u<it of 8d. per pound 
 
PRAOTICE. 
 
 Yarck, per yar'dy 
 
 486i at Id. Answer}$. 
 
 862 at 2il. 
 
 911 at 3d. 
 
 749 at 4d 
 
 113 at 6d 2 16 
 
 899 at 8d. 29 19 4 
 
 CASE \L 
 
 When the price is an even part of a pound — Find the 
 value of the given quantity at one pound per yard, &c. 
 and divide it by that even part, and the quotient will be 
 the answer ki pounds. 
 
 EXAMPLES. 
 
 WTiat will 129^ yards cost at 2s. 6d. per yard ? 
 s,d. £. s, £. 
 
 2 6 I I I 129 10 value at 1 per yard. 
 
 dns, £ 16 3s. 9i. value at 2s. 6d. pw yard. 
 
 Yds. #. rf. r. s. d. 
 
 123 at 10 per yard Jimwerf 61 10 ^ 
 
 687^ at 5 — 171 17 6 W 
 
 21U at 4 ■— 42 5 
 
 543 at 6 8 — 181 
 
 127 at 3 4 — . 21 3 4 
 
 461 at 1 8 —. 38 8 4 
 
 Note. Wiien the price is pountls only, the given quan- 
 tity multiplied thereby, will be the answer. 
 
 Example. — U tons of hay at Al. per ton. Thus li 
 
 4 
 
 Ans* £44 
 
 CASE III. 
 
 When tlie given price is any number of shillings ua 
 der; 20. 
 
 1. When the shillings are an even number, nnlltiply 
 
no 
 
 IVIiACTlCE. 
 
 Parts of a Shiilmg. 
 d. s. 
 
 is !j 
 
 Tablet, *iff Aliquot^ or Even Farls, 
 
 6 
 4 
 
 S 
 
 2 
 
 u 
 
 1 
 
 "iS" 
 
 Parts of 2 Shillings. 
 Is. is 
 8d. = 
 6(1. 
 
 4d. 
 3d. 
 2d, 
 
 \ 
 
 1 
 
 Parts of a Pouiid.l Parts of a cwt. 
 
 5. d, 
 
 10 
 
 6 8 
 
 5 
 
 4 
 
 3 4 
 
 2 G 
 
 1 8 
 
 £• 
 i 
 
 
 Ih, 
 
 5(S 
 
 liB 
 
 * 
 
 %» 
 
 i 
 
 16 
 
 1 
 
 "5 
 
 14 
 
 ^' 
 
 r 
 
 1 
 
 
 IT 
 
 
 tV 
 
 
 cwU 
 
 The aliquot part of any number^ 
 is such a part of it, as being taken a 
 certain number of times, exactly 
 ^2^ makes that number. 
 
 CASE I. 
 
 When the price of one yard, pound, &c. is an even part 
 of one shilling. — Find the value of the given quantity at 
 Is. a yard, poiinJ, Sec. and divide it by that even part 
 and the quotient will be the answer in shillings, &c. 
 
 Or find the value of the given quartity at2s. per yard, 
 &c. and divide said value by the even part whicli the 
 f^iven price is of 2s. and the quotient will be the answer 
 in shillings, &c. which reduce to pounds. 
 
 N. B. To find the value of any quantity at 2s. you need 
 only double^ the unit figure for shillings; the other fig- 
 ures will be pounds. 
 
 EXAMPUiS. 
 
 1. What will 46U yards of tape come to, at 1 id per \s^. .^ 
 s. d.'^ , 
 lid. [ ^ I 461 6 w'u"',}:.^ of 461 h yds. at Is. per yd. 
 
 5,7 ?>\ 
 
 £2 I7s, 8 i^. value at Ud. 
 , What cost S56lb. of cheese at 8d. per pou^id ? 
 Sd. [ ^^ I /:2j 12s. value of 2561b. at2s. per lb. 
 
 f^2 4 of 8d. per pound 
 
PRAOTICE. 
 
 r' 
 
 Yards, fZTyar'dy £* s, d. ^ 
 
 486i at Id. Jinswer^. 2 6J 
 
 862 at 'M. '758 
 
 911 at 3d. 11 7 9^^ 
 
 749 at 4d 12 9 Wff 
 
 113 at 6d 2 16 6 
 
 S99 at 8d. 29 19 4 
 
 CASE 11. 
 
 When the price is an even part of a pound — Find the 
 value of the given quantity at one pound per yard, &c. 
 and divide it bj tfiat even part, and the quotient will be 
 the answer ki pounds. 
 
 EXAMPLES. 
 
 WTiatwiii 129i yards cost at 2s. 6d. per yard ? 
 s.d, £. s, £. 
 
 2 6 I j I 129 10 value at 1 per yard. 
 
 ^ns, £16 3s. 9^^. value at 2s. 6d. pwyard. 
 
 Yds. #. rf. r. s. d. 
 
 123 at 10 per yard Jlmiverf 61 10 4l 
 
 687^ at 5 — 171 17 6 v*' 
 
 211i at 4 — 42 5 
 
 543 at 6 8 ■— 181 
 
 127 at 3 4 — > 21 3 4 
 
 461 at 1 8 --. 38 8 4 
 
 NoTE.^ Wlien the price is pounds only, the given quan- 
 tity multiplied thereby, will be the answer. 
 
 Example. — U tons of hav at 4L per ton. Thus li 
 
 4 
 
 Ms. £44 
 
 CASE III. 
 
 When tlie given price is any number of shillings un 
 dei; 20. 
 
 1. Whe.n the shillings arc an even number. muUipIy 
 
$ 
 
 vn A or I OF., 
 
 <Tie qu|nf;ltjl>y]:airi]ie nm-ibrvf^F ^Mn^:-gs. and double 
 the firsi ilgure of the product ' \^\s ; and the rest 
 
 of the product will be pounds. 
 
 2. "^^c shillings be odd; niulliply the <]uaTititj by Iho 
 wiioleQpimber of .shillings, and the' product wilf be tlie 
 answer in shillings, which reduce to poiimL-. 
 
 1st. 124 Yds. at 8p. 
 
 £49 12.-?. Ms. 
 
 2,0)92.4 
 
 
 Yds. £. f. 
 
 562 at 4s. Jus. 112 & 
 378 at 2s. 57 IG 
 915 at 14s. 059 2 
 
 rAM Ms. 
 
 fcU. ' 
 ^,7^2 at lis. 
 264 at 9s. 
 2oO at I6s. 
 
 SiwT., 5^4 12 
 200 00 
 
 CASl 
 
 3 IV. 
 
 
 Wlien tiic given price is pence, o?- pence andTarthin^s, 
 and not an even part of a shilling — Find tne value of flie 
 given quantity as Is. per yard, &c. which divide by the 
 greatest even part of a snilling contained in the given 
 price, and take parts of i\\^ quotieni for the reriiaincier of 
 tlie price, and the siun of these several quotients vrili be 
 tTie answer in shillings. &c. which reduce to pomnds. 
 
 KXAMPI/ES. 
 
 What will 245 lb. of raisins codk i> . u^ . ^v;. ,.vrlb. ? 
 s. d. 
 
 6d. 
 Sd. 
 
 ^ 
 
 15 value of 245 lb. at Is. per pound. 
 
 122 G valweof do. at (kl. per !b. 
 Gl S valucof do. at 5d, perlb. 
 i 5 5 J value of do. at i'd. ];or lb. 
 
 2,a)19,9 OJ 
 
 M^, £9 19 0;' value cf tlic v. h(j!e at 9id. per lb 
 
rilACTICE. 
 
 Sr£ at 1} .in^. '^ 14 3 
 
 325 at 2i .< S 1 U 
 
 "^^7 at 42 ' 15 10 U 
 
 576 at 7i Ms 
 541 at 9^ 
 672 at Hi 
 
 11 
 
 1300 
 
 32 18 
 
 C\SK V. 
 
 Wken the price is fyhilliiigs, pence and farthings, and 
 not the aliquot part of a pound — Multiply tiie given quan- 
 tity by the shillings, and take parts for the pence and far- 
 mings, as in the foregoing- cases, and add them togetlier; 
 tlie sum will be the answer in shillings. 
 
 EXAMPLES. 
 
 1. What AviU 246 yds. of velvet come to, at 7s. Sd.per 
 yard? s, \L 
 
 Sd. [ d {246 value of 246. yards at 1«. per yd. 
 
 1722 value of do. at 7s. per yard. 
 61 6 value of do. at Sd.per yard. 
 
 2,0)178, 3 6 
 
 ^iis, £89 3 6 value of do. at 7s. per yard. 
 
 ANSVVKRS. 
 
 5. cL £. s. d. 
 
 2 What cost 159 yds. at 9 10 per yd. } 68 6 10 
 
 S. What cost 146 yds. at 14 9 per yd. ^ 107 13 6 
 
 4. Wliat cost 120 cwt. at 1 1 3 per cwt. } (S7 10 
 
 5. What cost 127 yds. at 9 8^ per yd. ^ 61 12 11 ^ 
 
 6. What c«st 49^ ib« at 3 lU perU. ? 9 15 lU 
 
 CASE VI. 
 
 When th** price aiid qur^ntity given are of several de- 
 noiiiinations-^^Multiply the price by the integers in the 
 gtven quantity, and take part? for mt rest from the price 
 of an integer ; whicli added together will be ihe '^«*r«' 
 This is applirnble ^c FedcraJ ^lonev 
 
n4 
 
 TAKE AND TRV/IT. 
 
 i:XAMPL3<:S. 
 
 1. What cost 5cwt. Sqrs. 
 I4lb. of raisins, at 2L lis. 
 fid. per cwt. ? 
 
 -' ~ \£, s. d. 
 
 Sqrs ^2 11 S 
 
 i 5 
 
 iqr. 
 14 1b. 
 
 2. What cost 9cwt. Iqr. 
 8lb. of sugar, at 8 dollars, 
 65 cts. per cvvt. ? 
 
 S cts. 
 1 qr. -i 8,65 
 9 
 
 7 ]]>. 
 1 lb. 
 
 ?.,16^5 
 ,5405 
 
 Ms. £15 5 ' 6,v| Ms, g80,6S'03 
 
 €. grs. lb. answers. 
 
 7 5 16 at S9, 58cts-.-^>ei-e'^rt.-"-.- ^75, 6lcts. Sm. 
 
 5 10 at 2/. irs. percwt. ; /•14 19s. Sd. 
 
 14 S 7 atOZ. ISs. 8d. pcrcvrt. £\Q 2^, 5R 
 
 32 r at S6, r>4cts. per cwt ^76. 4rcif5. 6:?u 
 
 24 at Sll, 91cts. per p\vt. S2, 55cis. 2-j^m. 
 
 TARE AND TRKTT. 
 
 ,1 ARE and Trc it are practical Rules for dcductinj; 
 certain allowances ^v]lich are made bj niercbants. in 
 ))uyingand selling goods, Sec. by weight : in VvliicL are 
 noticed the following particulars : 
 
 1. Gross JVeightj wiiich is the whole weight Oi any 
 sort cf goods, together with the box, cask, or bag, &c. 
 which contains them. ^99^ 
 
 2. Tarc^ whicli is an allowance made to tT^e buyer 
 for the weight of the box, cask, or bag, &c. whicli can- 
 tains the goads bmightjand is cither at soniuch per box 
 &c — or at so much per cwt. crat so much in the whole 
 gross weight. 
 
 S. Trett, whicli is au allowance cf 4 lb. on every 104 lb 
 
•3 AKK ANI» TKKl I. > 13 
 
 4. CTofl^, v/liicli is rh allowance made of ;I ib. upon. 
 GV4?ry 3 cwc. 
 
 5. Suttte, is ^vhat remains after one or tv/o allowances 
 have been deducted. 
 
 CASE I. 
 
 When the question is an Invoice. — Add the gross 
 >veig;hts into one sum and the tares into another : then 
 subtractthc total tare from the whole gross, and the re- 
 liiaiiider will he tlie neat weight. 
 
 KXAMPLKS. 
 
 1 . V/hat is tlie neat vreiglit of 4 hcgslicads of Tobacco 
 
 marked with the gross \^'eight as follov/s : 
 
 C. cp\ lb, Ih, 
 
 No. l-~9 13 Tare 100 
 
 o_^ 3 4 — 95 
 
 S -^ 7 X ^ 83 
 
 4--G 3 £5 -— 81 
 
 Vv'hole gross 52 13 559 total tare. 
 
 Tai-e 359 ]b.=5 23 
 
 Ms. £8 3 18 Kcat. 
 2. What is tlie neat weight of 4 barrels of Indigo, No. 
 and weight as foliov/s : 
 
 C. qr. lb, Ih 
 
 ^^o. 1 — 4 1 10 Tare 56"^ 
 
 i2 — 5 5 iVZ — £9 ( 
 
 5 — . 4 19 — 52 f cwL qr. U 
 
 4 — 400 — S5J Ms. 15 11 
 
 CASE II. 
 
 When the tare is at so much per box, caskj bag, &c.— 
 Multiply the tare cf 1 by the number of bags, bales, &;c. 
 the product is the v/hele tare, which subtract from the 
 gvoas, and the remainder will be the neat weight. 
 
 KXAMrLHa. 
 
 1. In 4 hhfls. of sugar, each weighing lOcwt. l({r. 15lb* 
 gmas ; ti:Lr2 T5\b. per iihd. ho\7 much rscat ? 
 
J T5 1AK14 AND TRETT. 
 
 ^Toss weight of one hhd. 
 
 10 
 
 qrs. 
 I 
 
 15 
 
 4 
 
 41 
 
 75X4=2 
 
 2 
 
 4 
 £0 
 
 4 gross weight of the whole. 
 £0 whole tire. 
 
 \flns. 58 3 12 neat. 
 2. What is the neat v.eight of 7 tierces of rice, each 
 weighing 4cwt. Iqr- 9Ib. ^^ross, tare T>er iTerce 34lb. ? 
 
 .iiw,^9.Sa Oqr. 2llh. 
 5. In 9 firkins of butter, each weighing 2([rs. 12lb. 
 gross, tare lilb. per firkin ; how much neat ? 
 
 .^ns, 40. Qqrs, 9lb, 
 
 4. In 241 bis. of ligSj each Sqrg. 191b. gnrss, tare lOlb 
 per barrel; how many p(*untls neat .^ *'^Ins. 22413. 
 
 5. In 16 bags of pepper, each 85lb. 4oz> gross, tare per 
 bag, Sib. 5o7>, ; hov/ manyponnds neat.^ •Bus, 1311. 
 
 6. In 75 l)arreis of figs, eacli 2([is. 52rlb. gross, tare in 
 the whole, 507\h. ; how much neat weigh.t ? 
 
 .ins, 50 C. \qv. 
 
 7. What is the neat v/eidit of 15 hlwls. of Tobacco, 
 each weighini*; Tcwt. \p^v. ISlb, tare lOOib. per hhd. ? 
 
 Am, or a Oqr, \)lh, 
 
 CASE ilf. 
 
 When the tare is at so much per cwt. — Divide the 
 gi'033 weight by Hii^ aliquot part of a cwt. for the tare, 
 which subtract' from the gross and tha remainder will be 
 neat weight. 
 
 ii::A:.i?Lr.s. 
 
 1, What is the ne.it weight of 44cwt. Sqrs. iSlb 
 gross, tare 14Ib. ptr cv/t. ? 
 
 C. //r.>. lb. 
 
 ! 14lb. [ } I 44 '3 IG gross. 
 
 -5 2 122 tare. 
 
 ^jHf. Sf9 1 Sk neat. 
 
TAiiv . ... . ;;■ 
 
 ;:. What is the neat 'weight of 9 hhds. of tobacco, each 
 weighing gross 8cwt. Gqrs. 141b. tare I6lb. per cwt. ? 
 
 ./?r?s. eScivt. U;r. 24/6. 
 5. What is the neat weight of 7 bbls. of potash, each 
 weighing £91 lb. gross, tare lOfb. per cwt. ? 
 
 Ms. "1281/6. Ooz. 
 . In £5 barrels of %s, oacli Scwt. Iqr. gross, tare 
 pi:r cv»t. I61b. , how iiiucu neat wcichtr 
 
 "./?'«.«?. ABcwt. Mia. 
 5. In SScwt. Sc^rs. gross, tare 201b. per cwt. what 
 neat weight? 
 
 G.'Iii 45c\yt. Cqn;. CIIj. ^^rus^^ iiuo bib. pur cwt, how- 
 much neat weigjit r 
 
 jJns. 4^cwt, %r<;. IT^lb. 
 
 r. Vrhat istiic value of ilie neat weight of B hhds. of 
 S.ugar, at ;S^, 54cts. per c^\t. each weighing ICcwt. Ic^^. 
 I4lb. gross, tare 14lb. per cwt. r 
 
 Vv hen Trclt is allowed witli the Tare. 
 
 I. Find the tare, whicli subtract from the gi'oss, and 
 aHl the rcraainder s'attie. 
 
 S. Divide the suttic by 26, and the quotient will bo ihe 
 trett, which subti-act froin the ?iufile, and t'ne remainder 
 wil'l be tha neat wciglit. 
 
 T. In a i:o^^^hc:i:l orsu;;ar, weighing iOcVv-t. Iqr. 12ib. 
 gross, tare I4lb. ]«Cr cwL treU'4lb.' per 1 041b.*. how 
 much neat weight ? 
 
 *Tkis is th^ iveit ailcwcd in London, TUe'^reahtm of 
 dividing hu £6 U Im'iuL^r. Alh. U t,^^ of 104lb, hit if Vt9 
 Irett is at anij other rate, other "pavtry must bz falcon^ aC" 
 O'cdin^ to iha veil p: fro ;w$pdx S'c. 
 
♦L'/lRB ANP THRTT. 
 
 cwt. qr. lb. 
 10 1 12 
 4 
 
 Or thus 
 
 cwt. 
 
 14lbo4)10 
 
 1 
 
 qr. 
 I 
 
 1 
 
 lb. 
 
 12 gl'0S9. 
 
 5 tare. 
 
 41 
 
 28 
 
 26)9 
 
 
 1 
 
 7 suttle, 
 11 trett. 
 
 sso 
 
 8S 
 
 An$. 8 
 
 2 
 
 24 neat 
 
 4 =1)11 GO gros^'.. 
 ^45 t:ir-. 
 
 26)1015 suttle. 
 39 trelt. 
 
 
 
 
 Mtis, 9761b, neuL 
 
 
 
 
 2. In 9 cwt. 2 qrs. 17 lb. gross, tare 41 lb. trett 4 lb. 
 per 104 lb. how irmch neat^^ Ans. Scwt. Sqi^s. QOlb. 
 
 S. In 15 chests of sugar, weighing 1 1/ cwt. 21 lb. gross, 
 tare 173 lb. trett 4 lb. per 104, how many cwt. neat ? 
 
 Ms. lllcivt. 22^6. 
 4* What is the neat weight of S tierces of rice, each 
 weighing 4 cwt. 3 qrs. 14 lb. gross, tare 16 lb. per cwt. 
 and allowing trett as usual .^ 
 
 .dns. 12ewt. Oqrs. 6lb. 
 
 5. In 25 barrels of figs, eacli 84 ib. gross, tare 12 lb. 
 per cwt. trett 4 lb. per 104 Ib.^ how many pounds neftt? 
 
 \^ns. 18034- 
 
 6. What is the value of t}>e neat weight of 4 barrels 
 of Spanish Tobacco ; nunibers, weights, and allowanfres 
 as follows, at 9 id. per pound ? 
 
 cwt, qrs. lb. 
 No 1 Gross 1 2 irr^ 
 
 1 25 1 Tare 16 lb. per cwt. 
 1 09 f Trett 4 lb. per 104 lb. 
 
 S 2!^ 
 
 */lns..£]7 I6». .^ef. 
 
TARE iND TRETT ilD 
 
 CASE V. 
 
 When Tare, Tr^tt, aiid Cloft' aie allowed : 
 Deduct the tare and trett as before, and divide the sut- 
 Hq by 168 (because 2 lb. is the -j}^ of 3 cwt.) the quo- 
 tient will be the clolT, w hich subtract from the suttle, and 
 the remainder will be the neat weight. 
 
 2:XAMPLES. 
 
 1. Jn 5 hogsheads of Tobacco, each weighing 13 cwt. 
 S qr§. 23 lb. gross, tare 107 lb. per hogshead, trett 4 lb. 
 per 104 lb. and clofT 2 lb. per 3 cwt. as usual 5 how much 
 neat. 
 
 cwt, qrs. lb. 
 
 00 
 
 28 
 
 443 
 
 112 
 
 1563 Ib.p-rossof 1 hiid. 
 
 4689 whole gross. 
 
 10rx5« 321 tare. 
 
 26)4368 suttle. 
 168 tvQit 
 
 168)4200 suttle. 
 25 cloli: 
 
 Jins. 4173 neat weight. 
 
 S^ What IS tlie neat v/elght of 26 cwt. S qrs. 20^). gross 
 tar9 52]b. the allowance ofti'^Ut and cIorTasusu.-il f 
 
 dns. neat^Z^cwt, lqr::5lb. loz, iiearli/ ; qtMUh^ 
 
 further fractions^ 
 
INTEREST. 
 
 InIIiIUEST is of two kinds ; Simple and CompOttad* 
 SIMPLE INTEREST. 
 
 Simple Interest is i}\Q sum paid by the borrower ta the 
 lender for the use of money lent ; and is generally at A 
 certain rate per cent, per annum, which in several of the 
 United States is fixed by law at 6 per cent, per annum ; 
 tliat is, 6/. for the use of lOOL Or 6 dollars for the use of 
 100 dollars for one year, &c. 
 
 Princina!, is the b'um lent. 
 
 Rate, IS t]\Q sum jifcr cent, agreed o*n. 
 
 Amoant, is flie principal and interest added together. 
 
 CASE I. 
 
 •n> Slid the interest Of any given sUm for one year. 
 
 RtJLE. 
 
 Multiply the principal by the rate pet cent, and divide 
 the product by 100 5 the quotient will be the answer. 
 
 EXAMPLES. 
 
 1. What is tlie interest of 39Z. lis. S^d. for one year. 
 
 at 6/. per cent, per annum ? 
 
 £. 5. d. 
 S9 11 8^ 
 6 
 
 21S7 10 S 
 
 7\5() 
 
 6|03 
 4 
 
 0|I2 JIiis, r;i Th eri^ii, 
 
 2. What is thciiiUrcsl of 536^ 10s. 4.^- lor ajraf, ai 
 rje^cfiJit^ *vti3\ £U IBs. Qd. 
 
SIMPLE INTERJiSn l£l 
 
 5: VVI/at is tlic interest of 571?. 13s. 9d. for one year, 
 at 6/. per cent. ? dns, £34 6s. O^d. 
 
 4. What is the interest of 2?. 12s. 9^d. for a year, at 
 6?. per cent. ? dns. £0 5s. Qd. 
 
 FEDERAL MONEY. 
 
 o. Wliat is the interest of 468 dols. 4,5 cts. for one year 
 at 6 per cent. P S cts, 
 
 468, 45 
 6 
 
 \ S&jlO, rO==S28, Wcls. 7m, Ans. 
 
 Here I cut oil' the two right hand integers, which di- 
 vide by 100 : but to divide federal money by 109, yon 
 need only call the dollars so many cents, and the inferior 
 dsnominations decimals of a cent, and it is done. 
 
 Therefore you may multiply the principal by the rate, 
 and place the separatiix in the proauct, as in multiplica 
 ^on of federal money, and all the figures at tlie left ol 
 tiie separatrix, will be the interest in cents, and the first 
 figure on the right will lie mills, and the others decimals 
 ofamiil, as in the follow! m^5 
 
 EKAMPLES. 
 
 6. Required the interest of 135 dols. £5 cts. for ayeat 
 at 6 per cent. B els 
 
 year at 5 per cent 
 
 or, 5n=^9rcts. 5hm. Ms. 
 ^\ "What is i'^e liitcrcst of 436 doi.ui^s for one year, at 
 
 135, 
 
 G 
 
 lie 
 hrs 
 
 5 i cen 
 
 Jlns. 
 ts for 
 
 
 811, 
 
 Ucrest 
 
 50=.SS, 
 cf ID da 
 $^ ct:<. 
 19. 51 
 
 one 
 
 
 6 
 
 
 
 
 
pi SiMi'LIi iKlERES,!'. 
 
 ANOTHER METHOD. 
 
 Write down the ^Iven principal in cents, whicli imiUI- 
 ply by t.ic rate, and divide bj 100 as before, and you will 
 have the interest for a year, in cents, and decimals of a 
 cent, as follows : 
 
 9. What is ihe Lilerestof §73, o5 cents ibr a year, at 
 6 per cent. ? 
 
 Priucinal 7365 cents. 
 6 
 
 .Ins, 44\,90cts,=r=:44i-^^c{s. or S4,41cf5. 9m. 
 10. Required the interest of ^85, 45cts. for a year, at 
 7 per cent. ^ Cents. 
 
 Principal 8545 
 
 Jlns. 598, 13 cenfs^r=^^5fiocts.ihm. 
 CASE ir. 
 
 'io find the simple interest of any sum of money, for any 
 number of years, and parts of a year. 
 
 GENERAL RULE. 
 
 1st.' Find tiie interest of the jj;iven sum for one year. 
 
 2d. Multiply the interest of one year by the g»-e!i 
 number of years, and the product v, ill be tl ic answer for 
 til at time. 
 
 3d. IF tiiere be parts of a yea", as iiU)ritlLS and day.^, 
 work for the months by tlie alicjuot parts of a fenvn and 
 for the days by tiie Rrde of Tluee Direct, or by allowin;!; 
 30 days to Uu^ ;.:;:!,. and taking arfquot parts of the 
 
 ^' By ri[l(;\ving tlie ni. ..:'.. U) wc CO days, and taking aliquot 
 jKirtsthrreof, you will l:.avc the intercut jif any ordiniv.'y sum 
 sulficirnliy. exact for common use; hut if the surn be! very 
 jnrj^e, yon rrmv ^vo-v. 
 
 As :a>:/ (iay.'i : \^ to the intcrefst of onf y^ :-" : : so is ti:;. 
 ^ivci! i-umbc." s!i' :::iv3 • to the iotcr:- ' 
 
• IMTLF TKTEnKST. 
 
 '\ri 
 
 :. What is tlic interest of To/. F.s. 4u. lor 5 years and 
 £ months, at G/. per cent per aiiiuim ? 
 
 75 8 4 
 
 4;5s 10 
 
 G I tlnw.^-VA 10 IiiiCroL.t Tor] vear. 
 
 20 
 
 UJ|50 
 ()iOO 
 
 9.^1 le G (ia. ibr 5 years. 
 OUT do. for 2 raonths. 
 
 2. What is the iiiierrst of 64 lioiian:, 53 cents, for 2 
 ycai'S, 5 months, and 10 chr:, ;it 5 per cent. .^ 
 
 522,90 l!itcre*t for 1 vcr.r in cental, per 
 S " rCare L 
 
 4 mo. ^ 
 X mo. i 
 
 OCS,rO tlo. lur 3 years. 
 107,63 do. fur 4 mourns. 
 2G'90 (h>. (Vm- 1 ?nonth. 
 
 lOdavs,^ 8.9G do. for 10 days. 
 
 .te. 1112,ir):=ll!^:cf<?. o:- Sn, 1::<\ ^^Jf. 
 
 o. Vriiat is iiie interest of TS9 dollar::- tor 2 years, at 6 
 pt-rcent. ? Jlns. S94, GScis, 
 
 4. Of 37 dollars 50 cents Uiv 1 years at G percent. per 
 annum .^ * jLis, OOOr/'y. or S9 
 
 5. Ur 525 dollars 41 ccnt^, i'ov 3 years and 4 monthsj 
 at 5 percent.? *6f?2s. ;['>'54, HP.cts, 5m, 
 
 G. Of S^:i5/. 1,^2. 3d. fx' 5 years, at 6 per cent. ? 
 
 J^ns, £97 33.?. 8^. 
 r. Of 174^ ICs. 6*1. for 3 and a half vears at 6 per 
 cent.? Ans, £3G 13.s. 
 
 8. Of 150/' I6s. ud. for ^ vears and 7 months, at 6 per 
 
 nt. ? " .^ns, fAi a<?. rd 
 
9. Of i dollar for 12 years at 5 per cent. ? 
 
 Ans, 60cts, 
 ID. Of 215 dollars 34 cts. for 4 and a half years, at 5 
 and a brnf per cent. ? Jn$, ^33, 9lcts> 6m. 
 
 11. What is tne amount of 3^4 dollars, 61 cents? for5 
 jcars aiid 5 months, at 6 p^^r cent. ? 
 
 ..2;2S. S450, lOc/5. 3-^W^i. 
 
 12. What will SCOO'. amount to in 12 years and 10 
 months, at 6 per cent. ? ^Ins. £5310. 
 
 13. Wliat is die interest <?f 257^. 5s. Id. for 1 year and 
 5 quarters, at 4 per cent. ? ^flns. £18 Os. Id, Sqrs. 
 
 14. What is tiic interest of 279 dollars, 87 cents for 2 
 jGiirij and a half, at 7 per cent. ]>i}v annnr.i ? 
 
 ^^ » A (.-.''. |j»4S, "cfTcts, T^ui 
 
 15. Wiiat will £r9/. K-.', od. amoiuit t(>4n 3 years and 
 a half at 5-|per cent. !)er aiui'uii ? x 
 
 J?.ris, £331 Is. 6d. 
 
 16. What is the amount orG41 dol^. 60 cts, for 5 years 
 and o (|uai'ters, at 7 and a lialf per cent, per annum ? 
 
 17. What v/ill TSCi dols. amount to at 6 per cent, in § 
 years, 7 months and 12 days, or -gVj of a year if 
 
 'dns. '^975, 99cts. 
 
 18. Wlait is the interest of 1S25L at 5 per cent, per 
 annum, from March 4th, 1796. to March 29th, 1799, (al- 
 lowing the year to contain 365 days ?) Ans, £280. 
 
 Note, — The Rules ibr Simple Interest serve also to 
 calculate Commission, Brokerage, Insurance, or any thing 
 
 else cstijnatcd at urafiiyar ceuh 
 
 COr.I?viISSION, 
 
 IS an allowance of so niucli per cent, to a factor or cor- 
 respondent abroad, for buying and scl!!ng goods for Ids 
 ejnployer 
 
 EXAMPLES. 
 
 1. What will tlvc commissiou of 843.^ tOs. come to at 
 5 per c^nt» ? 
 
£, s. Or thus, 
 
 8& 10 £. s. 
 
 42j 17 10 v^w.9. £42 5 6 
 
 - 20 
 
 SjSO 
 12 
 
 6|00 £42 3s. ed, 
 
 2. Required tlie commission on 964 dols. 90 cts. at 2i 
 percent.? .^«5. S21, 71ct9.^ 
 
 3. What may a fiictor tlemantl on 1 ^ per cent, commls- 
 sion, for lavinp; out S568 dollars ? .:i/i>'. ^^2. 44c{s, 
 
 lUlOKEIlAGE, 
 
 IS an allowance of so much per cent, to persons assist- 
 ing merchants, or factors, in purciiasHng or s*d ling goods. 
 
 EXAMTLES. 
 
 1. What is tlie brokerage of 750!. 8s. 4d. vd 6s. Sd. 
 per cent. ? 
 
 s. (L 
 
 Here I first find the brokerage at 1 
 pound per cent, imd then for the 
 given rate, v/hich is ^| of a pouniV. 
 
 £. s. 
 
 750 8 
 
 d 
 4 
 1 
 
 7,50 8 
 20 
 
 4 
 
 10,08 
 12 
 
 
 .9. fZ. £. S, (?. fiTS. 
 
 G S=zl)7 10 I 
 
 .i?2S. £2 10 H 
 
 -1,00 
 
 2. What is iAc. brokerage upon 4125 dols. at i or vo 
 <^ints per cent. ? .fiua. gSO, 93c^v. 7Ai». 
 
 3. if a broker sells goods to tiie amount of 5000 dwls. 
 what is h's demand nt Go cts. per ccui. ? 
 
 > *'2,^s. g32, 50ciS 
 
 it is tAc brokerage ui: 
 
4. Wfiat niiiY abrolcer dcniandj when hos«^Ilsgooas i:»> 
 the. value of oO'iL i 7*. iOd. and I allow him 1 ^ per cent. ? 
 
 INSURANCE, 
 
 IS a premium ai so luiich per cent, allowed to persons 
 and oiTices, for rnakiiig good tlie loss of ships, houses, mar- 
 chandr/.e, &c. whicli miiy iiapperi from storms, lire, &c 
 
 ICXAM?LES. 
 
 1. What IS the iusiirance of T'25L 8s. I'Od, at 12^ per 
 c&rit, ? */2n.*^. rOu 13s. 7i^. 
 
 2. Whni h the insurance of an East-fmna ship and 
 cargo, valued at 12o4£5 dollars, at 15}^ ?)er cent. ? 
 
 5. A maifs house estiinated at 3500 dollars, was insu- 
 red against fire, for i| per cent, a year : v.hat insurance 
 did lie annually pay ^ ^flns. S6l, ^5ots: 
 
 SHORT PRACTICAL RULES, . 
 
 Jun^ calczilfiliv^' iHlerest citQjier cent, either for monthsif 
 or montlis and days, 
 
 L FOR STERLING MONEY- 
 
 RULl!:. 
 
 1. If the principal coni^lsts of pounds only, cut oiTtk* 
 nnit figure, and as it then stands it will be the interest for 
 one month '^ in shillings and decimal parts. 
 
 2. If the principal consists of pounds, shillings, &c. re 
 d nee it to its dcci»^-ml value; then remove the decimal 
 point one |)iace, or figure, furtker towards the left hand, 
 and as tl^e decimal tmn stands, it will shew the interest 
 for one month, iu shillings, and decimals of a shilling. 
 
 KXAMPLILS. 
 
 t. Requue<! tUe interest of 541 for seven montlis and i 
 
 ten o'ays, at; G i>er cent 
 
10 ihjs=};5,4 Interest for oneHfiontlv 
 
 57,8 ditto i\)Y 7 months. 
 1,8 ditto lor 10 days. 
 
 Ms. 39,6 shi!Iings=£l 195. TfitL 
 12 
 
 2, What IS the interest ol' 42f. 10s. for 11 month?, at 6 
 j;;D? cent. ? 
 
 /;. .^. £. 
 
 4'2 10 «=: 4£^ deciuuil value.' 
 Thcrorof e 4^25 sbiin!';?;s interest for 1 n^oiith. 
 'll 
 
 - *^is. 46,75 Interest for 11 mo. p=- ,"3 6 9 
 
 Q, llequiriBfl the interest of 94L 7s. Gxl. for one yer.r, 
 d'/e mon^s and a half,, at % per cent, per ;ui;.i;m. 
 
 Ans, £8 5s. Id, ry,r>qvs. 
 
 4. Whiit \s the interest of 121. 18s. for one third of a 
 KCSith, at 6 per cent. .^ . J^ns. 5;l6d, 
 
 II. FOK FEDERAL MONEY 
 
 RULE. 
 
 i. Divide the principal by £, placing the soparatn:: a% 
 usAial, and the quotient will be the interest for one month 
 in cents, and decimals cf a cent 5 that I^, the figui*es at 
 the left of the separatrix v/ili be cents, and those on the 
 rj-rht, tiecimalsoi a cent. I 
 
 9. -VHuItiplythe inler^'st of one nuM?t'» by the given nunv 
 ?>.;- >f tnontJui, or month j*,iir»(l decini;'! parts tiiercof, or for 
 V e dr^ys Uikc the even v.:v:l6 of a month, <fcc. 
 
EXAHPLES. 
 
 1. What is the^tercst of 341 dols. 52 cts. for 7h montha i 
 £)S41,52 
 
 Or tlius, 170,76 Int. for 1 monihi 
 
 170,76 Int. for 1 month. x7,5 months 
 
 r^ 
 
 85580 
 
 1195,32 do. for 7 mo. 119532 
 
 B5,SS do. for ^ mo. g cfs.?7i. 
 
 1280,700c^s. =12,80 7 
 
 1^80/0 ^ns. 1280,rcf.s.=S12, SOc^s. 7«i. 
 2. Required'tKe interest of 10 dols. 44 cts. for S v&AXS^ 
 5 months and 10 daj|, 
 
 2)10,44 
 
 10 (lays~I) 5,22 Interest for 1 month. 
 41 months. 
 
 5,23 f 
 208,8 
 
 214,02 ditto for 41 months. 
 1,74 ditto for 10 days. 
 
 rZ15,76cts. Jlns,==^9., IScts. Tw.-f* 
 5. Wliat Is the interest of 542 dollars for 11 months ? 
 
 The i is 171 Interest for one monfc 
 11 
 
 Jns, ldSlci5.==St8, Slcts. 
 
 NoTB.^ — To fuid the interest of any sum for 2 months 
 at 6 per cent, yon need only call the dollars so many cents, 
 .ind the inferior denominations decimals of a cent, and it 
 is done : Thus, the interest of 100 dollars for two mouths, 
 IS 100 cents, or I dollar; and S25, 40 cts. is 25 cts. 4 m, 
 &c. which gives the following 
 
 RULE II. 
 
 Multiply the principal by half the number of moijthf, 
 and tiic product will shew the intere^for the given time, 
 in ccr.ts and dcoinials of a cent; as above. 
 
■.:m?:.e ixterkst. 
 
 EXAMPLIi^S. -^i 
 
 Mtquiredtueiaterestof 316 dollars for 1 year and 
 nionttis. 1 1 =half the number of ino. 
 
 Ans, S4r6cis. =S34, 76cts. 
 \ What is the interest of 564 dols. $25cts. for 4 months? 
 S cts. 
 
 2 half the months. 
 
 'IL IVhcn Iho pijncipai Is given in feilen'vi monev, at 
 rr'^ercent. tofiiiu iiuw niuchthc^ iiiontlvv interest m'iU be 
 lit New-England^ CSX. cui-:-eiicj. 
 
 RULE. 
 
 ?.Inltiply the given principal liy ,03 and tlie product 
 v.iW be the interest for one inoniii, in sliillings and deci- 
 mal parts of a shilling. 
 
 EIIAMPLES. 
 
 : . What IS tlie interest of 325 dols. for 11 months ? 
 
 ,03 
 
 9,73 shil. int. Cor 1 month. 
 
 XH montlis. 
 
 .5ii.s\ 107S5s.~£5 7s. Sd, 
 - Vvhat is tlie iiiterest in New-Kngland currency, of 
 
 . 7^'s. 68 ct?^ for 5 montiis? 
 
 r-rincipal GI.GS doh, 
 
 .950*4. Intercut for one month. 
 
 5 
 
 UIZ^O 
 
180 ,IM-LE l^rrKRK**'". 
 
 IV. When the ];rincipru is given in pounds, shiiiings, 
 &:c. New-England currency, nt G per cent, to find how 
 muck iYiQ man tidy interest will be hi federal money. 
 
 RULE. 
 
 Multiply the pounds, &c. by 5, and divide that pro- 
 duct by 3, the quotient will be the interest for one months 
 in cents, and decimals of a cent, &c. 
 
 EXAMFLES. 
 
 1. A note for £411 Nev/ -England currency has been 
 on interest one nioiitli ; how much is the intea^Bt thereof 
 in fedend nionev ^ f\. 
 
 sm55 
 
 2, Required tlie interest of 59^. 18s. N. E currency 
 for 7 months t £, 
 
 S9p9 decnnal value 
 5 
 
 3)199,5 
 
 Interest for 1 nio. GG^5 cents. 
 
 r.-^ 
 
 V. When tlie principal is given ia !Nf^;v -England anil 
 Vir2:inia currency, at G per ceutt to find the mterest for 
 a 
 
 V. Vvhen the principal is given la iNf^;v-r^ngiand 
 irginia currency, at G per ceutt to find the mteres 
 yeai*, in doH arrtHiiills, by inspec^LOin__ 
 
 koi.^: 
 
 Since the inlerer^t of a year will he ju^t so many cents 
 as the given principal contains shillirtj^s, tiierefore, write 
 down the shillings and calltliem cents. Vend the pence ifl 
 tlie principal made less by 1 if they exceed 3, or by ^ 
 whan tlwy exceed 9, will *be the mills, very nearly. , 
 
SIMPLE INTEREST* 131 
 
 EXAMPLES. 
 
 1 . What is iht interest of 2/. 5s. for a year at 6 per ct.? 
 
 £2 5 s,=z45s. Interest 45cts. the Jiii&tter, 
 
 2. llequireilthe interest of IQOL for a'year at 6 per ct? 
 
 £100»=2000h\ Interest 2Q0Qcts.==^20 Ans. 
 S. Of Srs. 6d. for a year .^ 
 
 dns, 27s. is SlTcts. and 6d, is 5 mills. 
 4. Required the interest of 51. 10s. lid. for a year ? 
 
 £5 10s.=UOs. Interest IWcts.^^i, lOcts. Qnu 
 1 1 pence — 2 ;}cr rn le ha ves 9 = 9 
 
 Jlns. SI, 10 9 
 
 VI. 'i'o compute tiie interest on any iicte or obligatioV, 
 when there are payments in part, or indorsements. 
 RULE. 
 
 1. ^ift^ tl^e amount of the whole principal for the whole 
 time/jK 
 
 2. C^t the interest on the several payments, from the 
 time tiiey were paid, to the time of settlement, and find 
 their amount; and lastly deduct the amount of the seve- 
 ral payments, from the amount of the principal. 
 
 EXAMPLES. 
 
 Suppose a bond or note dated April 17, 1793, was given 
 for 675 dollars, interest at 6 per cent, and there were 
 payments indorsed upon it as follows, viz. 
 
 First payment, 148 doHars, May 7, 1794. 
 
 Second payment, 341 dols. August 17, 1796. 
 
 Third payiiient, 99 dols. Jan. 2, 1798. I demand how 
 much remains due en said note, the 17th of June, 1798 ? 
 
 118, 00 first payment, May 7, 1794. Yr. mo. 
 o6, 50 interest up to—June 17, 179S.=4 H 
 
 184, 50 Umount. 
 
 341, CO second payment, Aug. 17, 1796. Yr.mo. 
 57, 51 Interest t\) June" 17, 1798. =1 10 
 
 5/8, 61 amount ^ 
 -. — ' Carried ovei^ 
 
99, 00 tJiud pavinent, January 2, 179S. 
 2, 72 Intere.st" to—June 17, 1798.«5ifito. 
 
 lOi. r£ aiuount. 
 
 1K»>. 
 
 184, 501 
 
 578, 51 I several amounts. 
 101, r2j 
 
 664, rs total amount of payments. 
 
 €75, 00 notci, (lat^d AiirU IT, irH:-, 
 ^09, 25 Inbvest to— June IT, iTNo. 
 
 884, 25 anion lit of tiie note. 
 664, 73 amount cf pnyirsents. 
 
 8219, 52 HMiialns i\\\<t. on the nolo, JuiKi 17Jf_ 
 St, On the i6th of JiDiunry, 1795. 1 lent James faywell 
 ^00 dollars, on interest at 6 per cent, ^vliicli I received 
 bads in the follovvini;- partial payniei;!?., us iiTidcr, v;/.. 
 Istof April, 179G - '- ~ - S ^'JO 
 16th of July, 17?u - - - - 40O 
 
 1st of Sept." 1798 - - - - CO 
 
 How stands ih^ balance bctv.ecn i:s, on the 16th Nu» 
 YCmbcr, 1800 ? Ans, due to me S63, IBcls. 
 
 3, A IllOMISSOllY NOTE. VIZ. 
 
 £Cr2 105, J.'*ew-Lo}}xluiU .fjpnt 4, 1797. 
 
 Oa demand I proiuise to pay Timothy Cureiul, bixly- 
 two pounds, t^n shillings, and i'licrest at 6 |:er cent, per 
 annum, till paid; value i(:celved. 
 John Staxijv, I'KTKR PAYWELL. 
 
 RiCIIAUD Tf-stis. 
 
 Tiidonri^ient^* £* ■§» 
 
 1st. Heccivcd iu piirt of liie above note, Sep* 
 
 tembcr 4, 1799, 50 
 
 And payment June 4, ISOO, 12 10 
 
 IIow«u;ch rcrnuiiUi due oa .-jaid note, i.lu> {<Ktydi day ft 
 Oeccmber, 1800 ? 1*. .*^-. f*^ 
 
SIMILE INlEHESr. 135 
 
 KOTK. jtV/5 preceding Bide^ by customh rendered so 
 popular, and so much jiractised and esteemed hj many on 
 account of its being simple and concise^^ thati have given 
 it a place : it may answer for short periods of time^ but in 
 a lo9^ coursa oj years it will be found to be very erro- 
 neouff, 
 
 Mhoiigh this method seems at first vieiv to leuponihe 
 ground of simple intevcf^t* yet upon a little attention the 
 jollowing objection ivill be found most clearly to lie against 
 it^vi::^, that the interest will^ in a course (f yvars, covti- 
 ptsldy expunge, or as it r,iay be said eat up tfi£ debt. For 
 an explanation of Ihis^ take the following 
 
 A lends B 100 doHars, at 6 per ccirt. iiitcrest, and 
 takes his note of hand ; B docs no more tluin puj A at 
 every year's cad 6 dollars, (which is then justlv due to 
 Bfortao use of his money) u:ad has it endorsed on his 
 gjote. At tliO end of 10 years 13 takes up his note, aii'J 
 tlie sUm };e has to pay is reckoned thus : The principal 
 lOOdallarSj on interest 10 years amounts to 160 dolhu-s ; 
 there are nine endorsements of G jh')![ars each, upon 
 "which tlic debtor claims iiiierest^ one for 9 ye?: rs, the 
 §ccond for 8 years, the third lor 7 years, and so do\vn to 
 the time of settlement: tno \YiioIe a!nount of ih-c several 
 cndorscmcnis and their intei'cst, (as any one can see by 
 casting n) is S^O, 20 cts. this subtracted from 1(30 dol.-^. 
 the amount of the debt leaves in iiivour of ilio creditor, 
 389, 40 els. or iglO, 20 cts. less tl^an the original princl- 
 ]3al, of which he has nat rctcived a cent, but only its an- 
 nual interest. 
 
 If the same note should He '20 years in the same v/ny, 
 3 M'onid owe but 27 dols. CO cts. without paying xhi:^ 
 least fraction of die 100 dollars borrowed. 
 
 Extend it to 28 years; and A tlic creditor v.-rndd fa!I 
 in debt to 15 withoi'.t leceivin^ a cent of llie 100 dollars 
 which he lent him. Sco a better Rule in Bhinna hittr- 
 cat by ^Decimals, pag& I*!"?. 
 
io4 trj'j^VQtjsD INTEREST, 
 
 eOMPOUND INTEREST, 
 
 is when the interest is added to the pnncipal, at tlie end 
 of t}^ jear^ and on i^. amount the interest cast for anotli- 
 er year, and added again, and soon : this is called Inter- 
 e»it upon Interest. 
 
 RULE. 
 
 Find tliQ interest for a year, and add it to the principal, 
 \\ luch call the amount for tlic first year ; find tlie interest 
 of tins amount, vAnch add as before, for the amount of the 
 second, and so on ibr any number of years required. 
 Subtract the original principal from the last amonnt, and 
 the remainder will be the Compound Interest foi* tli^ 
 whole time. 
 
 1. Requircd tlic amount of 100 dollars fbr 5 jelrs at 6 
 per cent, per annum, compound interest ? 
 
 Q\'h. S cts. 
 
 ist Principal 100,00 Amount IU65OO for I year. 
 2d Principal 106,00 Amount 112,36 for 2 year:-;. 
 Sd Principal 112,36 Amount 119,10l6for Syps. .^/is. 
 
 2. What is the amount of 425 dollars, for 4 years, at 5 
 ?ier cent, per annum, compound interest P 
 
 dns. S516, odds. 
 S. Wiiat will 400^'. amoinit to, in 4 yeais, at 6 per cent* 
 per annum, compound interest .^ ^Ins, £504 \9s, 9 id, 
 
 4. What is the compound interest oi 150/. 10s. for 3 
 years, at 6 per ct. per annum ? dns. ^j28 145. llld,-]" 
 
 5. What Ts the compound interest ol 5C0 dollars for 4 
 yearo, at Gper cent, per annum ? Jlns. gl31,238-f 
 
 6. Vv'hat will 1000 dollars amount 10 in 4 years, at T 
 per cent per annum, compound interest ? 
 
 .']ns, S1310, 79c[s. Gnu-h 
 
 7. What is i\\(^ amount of 750 dollars lor 4 years, at 6 
 per cent, per annum, compound interest ? 
 
 Jins, S046, Sods. r,7272i. 
 
 3. What is tiic corapound interest of 876 doIs.OO cts. 
 for 3*A ynuh ^^^ C p,cr cent, pef^aapum ? 
 
 dns, S198, S3ef5.-l| 
 
DISCOUNT, 
 
 iS an allowaucc made for llic payir.cnl of aiiv sum of 
 money before it becomes due : or upon adva-ncing ready 
 moi>€y for notes, bilis^ &c. whicb-are ])ayab]o at a future 
 day. NVhat remains after the discount is deducted, is the 
 present >vorth, or such a sum as, if put to interest, would 
 at the given rate and lime, rDnount to the given si;m or 
 tiebt. 
 
 RULE. 
 
 As the aiTiount of 100/. or 100 dollars, at the given rate 
 and time : is to the inlcrcfit of 100, at iho. same rate and 
 time : : bolfj tl*.e v:ive'n sn:=i : to t!i^^ d.iscount. 
 
 Subtract the di^V^ount fro?n the given sum, and the re- 
 mainder is the present worth. 
 
 Or — as tbe amount of K)0 : h to ICO : : so is the 
 giv^^ sum or debt : to the present worth. 
 
 Puoor. — Find the amount of t'ao. present worth, at the 
 given rate and time, and if the work is ri^hU that will be 
 eyual to the given sum. 
 
 KXAMTLr.S. 
 
 1, What must be discounted fm- tha ready payment of 
 100 dollars, due a vcar lience at G per centi a year ? 
 
 'S S B S cts. 
 As lOG : 6 : : 100 : o 66 ih^ answer. 
 IOO5UO given sum. 
 5,66 discount. 
 
 S5-^S34 tricp'-escnt worth. 
 
 2. What sum in ready money v/iil discliarge a debt of 
 925?. due 1 year and 8 montiis hence, at G per cent, r 
 
 10 Interest for £0 montiis. 
 
 110 Am-t. £, £. £. £. s. d. 
 
 As 110 : lUO : : 9^5 : 840 18 2+^tis. 
 C. What is the preser.t worth of GOO dollai'S, duQ 4 
 years hence, at 5 per cent, t Jna* S5C0 
 
 4. What is tl;c tliscouiit of ^T5L 10s. for 10 months, 
 at € Dcr cent, per.atinum ? diis, £\S Qs, 4^4 
 
i ":» o ,-, :> M \ 
 
 5. Bought gO(,uls ainounniig to 615 clol:?. T^> ccutSj r-^ 
 tuonths credit; how muck ready moPiej jn.nst 1 pay, dis- 
 count at 4A per cent, per anninii? "^ .'Lis, gGOG. 
 
 G. Wliat sum of ready money must be received (or a 
 hill of 900 doIIarSydue TS days hence, discount at 6 per 
 cent, per annum ? " dns. gBSS), S'Zcts. Sm, 
 
 Norn. — When sundry sums are to be paid at different 
 tiine-^, find the Rebate or present vrorth of each particular 
 [laymeat separately, and when so found, add thcra intot 
 ciiesum. 
 
 It of 7oS/. ih^ one half payable 
 
 :. -. . ... .. . :!icr hall in six months after that, 
 
 o. ii a iegacy is iei'tine of 2000 dollars, of which 500 
 tlols. arc payable in 6 niontiis, 800 dols. payable in 1 year, 
 and i'ae re^t at the end of 5 years : how much ready moncj 
 ought 1 1;; recch e lor i:?mi legacy, allowing 6 per cent. 
 discounts 'Jin?. B1833, Sfcfs. 4m. 
 
 ANNIliTiES.c/ 
 
 /\N Annuity h a sum of jnouey, payable. every year, oi: 
 for a certain nuuiber of rears, or forever. 
 
 V/hen the debtos* kecp.^. ike annuity in Ids o^vn lumds?, 
 beyond the time of nayin^nt, it is said to'De in arrears. 
 
 The sum of all the annuities for the tiine th.ey have been 
 favborne, together wiui the intei'-snlue on caclu i.> called 
 liie amount. 
 
 If an annuity is bongr.i vii. <m' paid all at once at the 
 bcginnfng of the lirst ye.ir. (.i.vi price which is paid fi>r it 
 h called the present wonh. 
 
 To find the amount of an aniiuii v at siuinle interest. 
 ■RULE. ^ 
 
 1 Find iitm interest of tiie given riunuivy (or 1 year. 
 
 2. Aud tlien for 5, 3. kc. yc:irs, up io the given time, 
 less 1. 
 
 o. MultiJily th(i annuity by t'.'i number of years given 
 and iv^d ili'j "product to the u'lu'^ ' ' aiul tl^e sum 
 
 ♦, 
 
:. liau annuity ofTOLhe forbornseO' ycais, what will 
 b« due fur the prindpal ami iiHeiest at fn^end of said 
 term, simple interest being completed at 5 pei* cent, per 
 annum? « IV. £. s. 
 
 • let Interest of 7QL at S.^^cent. for 1— 3 10 
 
 W^ 2— r 
 
 3—10 10 
 
 4—14 
 
 ^2u, Anr ;»' yi'S. ;ninuiij,at TOt. per yr. Is 350 
 
 .fins. £385 o 
 
 ?L, A IiouaC being let upon a lease of 7 years, at 400 
 
 dollai-s per annnn;. and the rciit Imh^ in arrear for the 
 
 \\\w\q term, I demand tlic sum du<» at th€ end of i\\Q term, 
 
 simple interest being allowed at 61. percent, per annum ? 
 
 dns. S5304. 
 
 To find the present worth of an annuity at simple interest. 
 
 RULE. 
 
 Find t]\G present v.-orth of eacl; year by itself, discouril- 
 ing from tlic time it falls duo, and the sum of nil these 
 present worllis will be the preiiciit worth rcqrjred. 
 
 EXAMPLES. 
 
 I. Wjiat is the present ^vorth of 400 dols, pci' annum, 
 to continue 4 years, at 6 per cent, peri* annum P 
 106"^ 3rr.35849 = Pres. worth ot 1st vr. 
 
 ^^ L . inn . . Am . 357.1428.5 == 2d yr. 
 
 118 r 3385983O0 — Sd vr. 
 
 I24J 522,58064 = -~- 4th yr. 
 
 JJiis, S1396,C6503~=S1396, Gct<i. 5m, 
 2. How mucli ^ircsent money is oquivalvint to an an- 
 nuity ot 100 dollars, to continue 3 yeju-s ; rebate bein;» 
 iiade at 6 per cent. ? Jlns," S268, STcts, Im. * 
 
 S. What IS SOL yearly rent, to continue 5 years, worth 
 bi reajy mon^. at 6L per cent. ? .fins, /;S40 155. -h 
 
 12^ 
 
KOUATION OF PAYMENTS, 
 
 is nulling- tiie equated time to paj at once, several 
 debts due at difiTerciit periods of timcj so that no loss shall 
 be sustained hj either party. 
 
 RULE. 
 Multiply each payment by its time, and divide the sum 
 of the several products by the whole debt, and the quotient 
 will be the equated time for the payment of thev/hole. 
 
 EXAMPLES. 
 
 1. A owes B 580 dollars, to be paid as follov^s — viz. 
 100 dollars in 6 months, 120 dollars in 7 months, and 160 
 dollars in 10 months : What is tlie equated time for the 
 payment of the whole debt ? I 
 
 100 X 6 ^ 600 
 
 1^0 X r ^^ 840 
 
 160 X 10 ^ 1600 
 
 7 
 
 SSO ;3040(8 monlhs. An.. 
 
 ^. Anierchantliath owing himSOOL io be paid as fol* 
 iOws : 50Z. at 2 months, 100/. at 5 months, and the rest at 
 8 months ; and it is agieed to make one payment of the 
 ^vhole ; I demand i\\^ equated time ? Ans, 6 mont7is, 
 
 o. F owes 11 1000 dollars, whereof 200 dollars is to be 
 paid present, 400 dollars at o months, and the rest at 15 
 months, but they agree to make one payment of the whole ; 
 1 demand vrhen that time must be ? Jlns. 8 months. 
 
 4. A merchajit has due to him a certain sum of money, 
 to be paid one sixth at 2 months, one third at 3 months, 
 and the rest at 6 months ; what is the equated time for 
 the payment of the whole ? dns. 4| months. 
 
 BARTER, 
 
 Is the exchanging of one commodity for anothei-, and di- 
 rectB merchants and tradeis how to make the exchangei 
 \>ithout loss to either party. 
 
 RULE. 
 Eind the value of the commodity whose quantity is 
 gij.eii : then linji wliat quantity of t!ic other at the pro- 
 
n A JIT K.r.. ^ 
 
 fOp^*i rale can be bouglit Tor the same money, and it gives 
 (he answer. 
 
 EXAMPLES. 
 
 1. What, quantity of flax at 9 cts. pei* lb. must be given 
 in barter for 12lb. of indigo, at 2 dols. 19 cts. per lb. ^ 
 
 12lb. of indigo at 2 dols. 19 cts. per lb. comes t().?6 
 dols. 28 cts.— therefore, As 9 cts. ; lib. : : 2tv28cts. : 
 292 the ansrver. 
 
 2. How much Vueat at 1 dol. 25 cts. a bushel, must be 
 given in barter for 50 busliels of rye, at 70 cts. a basliel ? 
 
 ^^ns, 28 bushels, 
 5. How much rice at 28s. per cwt. must be bartered 
 fi)r 3icwt. of raisins, at 5d, per lb. ? 
 
 Ms. 5civt. oqrs. 9^f|^y. 
 
 4. How much tea at 4s. 9d. per lb. must be given in 
 barter for 78 gallons of brandy, at 12s. Sid. per gallon ? 
 
 Jhi3. Q.inlb, 13-1^-0::;. 
 
 5. A and 15 bartered : A had 8dcwt. of sugar at 12 cts 
 per lb. for which B gave him IScv.t. of flour; what was 
 the lh)ur rated at pcV lb. ? Jus, diets, 
 
 6. B delivered S hhds. of brandy, at Gs. 8d, per gallon, 
 to C, for 12G yds. of clolli, what wa?» the cloth pe ' yar;l ^ 
 
 7. F) ^ivesE 250 yards of il •.!•/' 
 fop 5191b. of pepper; what :;::::. 
 
 iutcr lb. ? . ;" 
 
 8. A and B bartereu : A had ^ixwi- 
 per cwt. for w'nich B gave WiTi 20/. in 
 
 rest in sugar, at 8d. \x^v ib. : l demand .iOv • 
 Bgavc A besides the 20/. .^ Jina tdvt- Qqy. 
 
 9. Two farmers bartered ; A had iCO bus-ieJ« o: ,. .: 
 at n dols. per bushel, for which B gave him 100 busrie:- 
 of barley, worth fi5 cts. per bushel, and the balance in (rat- 
 al 40 cts. per bushel ; v.hat quantitv of oats did A roct r"- 
 
 10. A hath linen clotli worth 20d. an ell ready m -.u-, ; 
 bul in barter he v;iU have 2s, B liatli broadcloth v/ot th 
 14s. 6d. per yard vendj money, at v/hat price ougiit 33 to 
 ratejtis bix)adcloth in barter, so as to be eqiiivnlent to 
 A^ bartering pnr.c ? Jh:$, \rs. irJ, Sf^cr:?, 
 
A and B barter: A nath 145 gallons of brand j &t 
 
 jL £0 cts. per gallon ready money, but in barter lie 
 
 .ill have 1 del. 35 cts, per gallon ; B has linen at 58 cts.' 
 
 per yard ready money ; hov/ must B sell liis linen per 
 
 yard in proportion to A's bartering price, and how many 
 
 yards are equal to A's brandy ? 
 
 Jlns, Bai'ter price of B's Jinen is 65cts. S^wi. and he 
 must give A 500 yds, for his brandy. 
 
 12. A has £25 yds. of shalloon, at £5. ready money, per 
 yard, which he bralcrs v/ith B at £s, 5d. per yard, takir 
 mdi^oat l£s. Gd, per lb. which is worth kit lOs, how 
 much indigo >vill pay for tlie shalloon ; and vrho gets the 
 best bargain ? 
 
 *^ws. 4Si?&. at barter price will pay for the shalhjon, 
 and B has the advantage in barter. 
 
 Value of A's cloth at cash price, is /:££ 10 
 
 Value o(4Silk of indigo, at lOs. per lb. '^£i 15 
 
 B gets tlie best bargain by £ 15 
 
 Is a rule by which merchants and ti-aders discover their 
 profit or loss in buying and selling their '^oods : it also in- 
 structs them how to rise or fall in the price of their good^, 
 so as to gain or lose so much per cent, or otherwise. 
 Questions in this mle are answered by the Rule of Thr(?e. 
 
 EXAMPLES. 
 
 1. Bought a piece of cloth containing 05 yards, ibr 
 191 dols. £5 cts. and sold the same at 2 tlols. 81 cts. per 
 yard; wliatis the profit upon the whole piece ? 
 
 Ms, S4r, eocts. 
 
 2. Bought 12^ cv;t. of rice, at 3 dols. 45 cts. a cwt. 
 and sold it again at 4 cts. a pound ; what was i]\e whole 
 gain ? ^iis. S12, STcts. 5m 
 
 3- Bought 1 1 cwt. of sugar, at 64d. per lb. but could 
 not sell it again for any more than 2l. iGs. per cv.t. ; did 
 1 gain or lose by my bargain r .Ins, Lost, £2. lis. Ad, 
 
 4. Bou^lit 44 lb. of tea for 6/. It-s. and sokl it again for 
 S?. lOs. 6d. ; vvliat v/us the profit on each pound r 
 
 Ms, to id. 
 
iOSS AND GAIN l^; 
 
 o* Kougkt a had. of molasses containing 119 gallons, 
 f.t 52 cts. per gallon; paid jfor carting the same 1 dollar 
 25 cents, and by accident 9 gallons leaked out ; at what 
 Fate must I sell the remainder per gallon, to gain 13 dol 
 lare in the whole ? Ms. 69cts. 2m.-|- 
 
 II. To know what is gained or lost per cent. 
 RULE. 
 
 First see what the gain or loss is by subtiiaction ; then 
 As the price it cost : is to the gain or loss i : so is 1 00^ 
 or SI 00, to the gain or loss per cent. ^ 
 
 EXAMPLES. 
 
 1 . If I buy Irish linen at 2s. per yard, and sell it again 
 at 2s. 8(1. per vard ; what do 1 gain per cent, or in laying 
 out lOOt.r As : 2.«?. 8^. : : lOOL : £35 6s. 8c?. Ans, 
 
 2. If I buy broad«loth at S dols. 44 cts. per yard, and 
 sell it again at 4 dols. 80 cts. per yard 5 what do I gain 
 per cent, or in laying out 100 dollars ? % 
 
 S ctsr] 
 Soldfai-4, SOI S cfs. cts. g g 
 
 Cost 3, 44 ^ As 3, 44 ; 8S : : 100 : ^^ 
 
 I Jins. 25 per cent. 
 
 Gained per yd. 86J 
 
 S. If I buy a cwt. of cotton for 34 dols. 86 cts. and sell 
 it again at 41 i cts. per lb. what do I gain or lose, and 
 what per cent. ? S cts. 
 
 1 cwt. at 41 ids* per lb. comes to 46,48 
 Prime cost 34.86 
 
 Gained in tlie gross, Sn,62 
 xis 54,86 : 11,62 : : 100 : SS^ ^Ans. 53-]- j^er cent. 
 
 4. Bought sugar at S^d. pQ4' lb. and sold it again at 4Z. 
 ITs. per cwt. wliat did 1 gam per cent. ? 
 
 Jus. £25 195. did. 
 
 5, If i buy 12 hhds. of wine for 204'. and sell the same 
 again at 14^ 17s. Cd. perhhd. do I gain or lose, and. what 
 \yex cent. ?. Jlns. I lose 12^^ per cent. 
 
 (). At ^l{\. profit in a shilling;, how much percent ? 
 
 Ms. r\9. 105. 
 
5 i^w LOSS AN'S) GArV. 
 
 r. At 25 cts. prolU in a d-]!iir, how iuuv^h por ccnf, ? 
 
 .^•?-?.<>'. £5 ;;??• cent. 
 
 Note. — When goods are l>ou<^!it or gold on credit, you 
 must calculate (by" discount) tlie present worth of tlieir 
 price, in order to ibid your tiue guia or loss, k^cc. 
 
 k:lamplks. 
 1 Bouglit iC4 yards of broadcloth, at 148. 61], per yd. 
 ready money, and sold the same again for 154/. lOs.'on 
 
 6 months credit; what did I «;;;tin by the whole; allow- 
 ing discount at 6 per cent, a vear ? 
 
 As 1j3 : 100 : : 1j4 10 : Iju present worth. 
 
 I iS IB prime cost. 
 
 Gained /jSl 2 Answer, 
 2. If I buy ciotli at 4 doLs. lt> cts. per yard, on eigi»t 
 montlis credit, and ^ell it ai^ain at 3 dols. 90 cts. per yd. 
 ready money, what do I lose per cent, allowing 6 per cent. 
 discount on the purchase price ? Jliis, 2^ per cent. 
 
 III. To kg^w how a commodity must be sold, to gain 
 m* kkse so much per cent. 
 
 RL'LE. 
 As 100 : is to the purchase price : : so it» lOOi^. or 
 TOO dols* with the profit add^d,* or loss subtracted : to, 
 the selling price. 
 
 EXAM?Lr.?>. 
 
 1. If I buylnsh linen at 2s. 3d. per yard ; now r^*i 
 I sell it per yard to g-ihi £5 p^r cent, v 
 
 As lOOZ. : 2s. SJ. : : 125/. to 2f. 9d, Sfjrs. Jins> 
 
 2. If I buy Rum at 1 del. 5 cts. per gallon; how must 
 I sell itpergalk'jn to gain SO per cent. ? 
 
 As SlOO : Bl,05 : : B130 : Sl,SG.3cis. j]}is. 
 S. If tea cost 54 cents per lb. ; how must it be sold p^r 
 
 lb. to lose ^Q.l per cent, r 
 
 As SlOO : 54 cts. : : ^Sr, 50 cts. : 4rcfs. Stlm.Jns, 
 4, Bouglit Cioth ITs. Ch\, per yard, which not provin** 
 
 so ^od as I expected, 1 am obliged to lose 15 per cent. 
 
 hf^ij how must I sell it per vard .^ ^^ns. \A^. IQ-'ii', • 
 
5. If 11 c\vt. 1 qri£.5 lb. of sugar cost 126 dols. 50 cts. 
 kow must it be sold per lb. to gain SO per cent. ? 
 
 dns, IScf.s. Siru 
 
 6. Bouglit 90 gallons of wine at 1 dol. 20 cts, oei oali. 
 but by accident 10 gallons leaked out, at what rate i^cvit i 
 sell the remainder per gallon to gain upon i'ne whole prime 
 cost,attlie rate of 12^ per cent. ? Jins, gl, 6icts, ^'fjfn. 
 
 IV. When there is gained or lost per cent, to knoy. 
 » what the commodity cost. 
 
 RULE. 
 As 100^. or 100 dols. with the gain |>er cent, added, \}t 
 loss per cent, subtracted, is to the price 5 so is 100 to the 
 prime cost. 
 
 EXAMPLES. 
 
 1. If a yard of cloth be sold at 14s. Td. and thei-eis 
 gained 16/. ISs. 4d. per cent. 5 what did the j&xd coat? 
 
 £. s. d. s. d. £. 
 As 116 15 4 : 14 7 : : 100 to 12^. 6d. Jns, 
 
 2. By selling broadcloth at 3 dols. 25 cts. per yard, 1 
 lose at the rate of 20 j^er cent. ; whut is t! -^ prime cjat oi 
 said cloth per yard ? Jns. g4, Qticis. ^.h'm, 
 
 S. If40 lb. of chocolate be sold at 25 cts. psr lb. arxd I 
 gain 9 per cent. 5 what did tiie whole cost me ? 
 
 Jus. S9, I7cts. 4m.-i- 
 4. Bought 5 cwt. of sugar, and sold it again at 12ceftt3 
 per lb. by which I gained at tlie rate of 25^ per cent ^ 
 what did the sugar cost me per cwt. 
 
 Jhis, SiO, 70c4s,9m.-t 
 
 V. If by wares sold at a ^ivcn ral» tSwe U ^ ?ai«jh 
 gained or lost per cent. t« km>w what would be ^iWf^ w 
 lost per cent, if sold at another rat*. 
 
 RULE. 
 
 As the first price : is to lOOZ. or 100 dols. wdth the f refit 
 per ccjit. added, or loss per cent, subtracted : : so is tb€ 
 other price : to the gain or loss per cout. attJ^e other rate. 
 
 N. B. If ycur answer exceed ICO/, or 00 dols. the 
 •xccss is you:* jjaln per cent. ; but if It N ^ss than 100, 
 ftit deficiency 13 flic Io*s percent 
 
144 FELLOWSUir. 
 
 EXAMPLES. 
 
 1. If I sell cloth at 5s. per yd. and thereby gain 15 per 
 cent what shall i gain per cent, if I sell it at 6s. per yard ? 
 
 6-. £, s, £. 
 
 As 5 ." llo : ; 6 : 138 Jns, gaimd SS per cent 
 
 £. Li' I retail ruiii at 1 dollar 50 cents per gallon and 
 thereby gain £5 per cent, what sliall i gain or lose per 
 cent, if 1 sell it at 1 dol. Sets, per gallon ? 
 
 S cts. S S cts, S 
 
 1,50 : 125 : : 1,08 : 90 Ans. I shall lose 10 per cent. 
 
 5, If 1 sell a cwt. of sugar fbr S dollars, and thereby 
 lose IS per cent, what shall I gain or lose per cent. HI 
 sell 4 cwt. of the same sugar for 36 dollars ? 
 
 dnt^. Hose vnly I per cenK 
 
 4. I sold a watch lor i7"L Is, 5d. and by so hieing bst 
 15 per cent, whereas 1 ojglit in trading to jiave cleared 
 20 per cent: j how much was it sold under its real \a!ae ? 
 
 £ • £ • £• ^' ^^* 
 
 As 85 : : ido : 20 1 8 the pi'ime cxyst 
 
 100 : ^20 13:: 120 ; 24 2 the real rulut. 
 Bold ibr IT 1 5 
 
 £T 7 diisiver. 
 
 FELLOWSHIP, 
 
 Ife a rule by whicli the accorapfs of several uiercliants or 
 other persons, trading in partnership, are so adjusted, 
 that each may have Ids sliare oi' the gain, or sustain his 
 aliare of the loss, in proportion to his share of the joint 
 itock. — Also by this Rule a bankrupt'*s estate maybe di- 
 vifled among liis creditoi-s, &c. 
 
 SINGLE FELLOWSHIP, 
 
 Is when the several shares of stock are continued in 
 trade an equal term of tirae. 
 
 RULE. 
 
 As tne v.'hplc stock is to tlie whole giun or less : sal% 
 each man's particrJir stuck, tohi»partiCiililr sh.**"*^ 'vVlV^ 
 
TKLLOWSUIF. 145 
 
 Proof.— Add all the particular shares of tlie gain or 
 loss together, and if it be right, the sum will be equal to 
 the whole gain or loss. 
 
 EXAMBLES. 
 
 1. Two partners, A and B, join their stock and buy a 
 quantity of merchandize, to the amount of 820 dollars ; 
 in the purchase of which A laid out S50 dollars, and B 
 470 dolLars 5 tlie commodity being sold, they find their 
 clear gain amounts to 250 dols. AVhat is each person's 
 share of the gain r 
 
 A put in 550 
 B 470 
 
 A^ 800 . 2.0 . . S^^O : 106,7073+A's share. 
 AS b^u . ^ju . . ^^^Q , 145,2926+B's share. 
 
 Proof 249,9999+ =S250 
 
 2. Three merchants make a joint stock of 1200/. of 
 which A put in 240/. B S60/. and C 600/.— and by trading 
 they gain 325/. what is each one's part of the gain ? 
 
 Ms.A'spart£65, B's £97 10s. C's£l62 10s. 
 5. Three partners, A, B, and C, shipped 108 mules for 
 the West-Indies 5 of which A owned 48, BS6,andC 24. 
 But in stress of weather tlie mariners were obliged to 
 throw 45 of them overboard ; 1 demand how much of the 
 loss each owner must sustain ? 
 
 JIns. Jl 20, i? 15, and 10. 
 
 4. Four men traded with a stock of 800 dollars, bj 
 which they gained 307 dols, A's stock was 140 dols. B^ 
 £60 dols. C's SOO dols. I demand D's stock and what 
 each man gained by trading ? 
 
 dns. JJ^s stock was glOO, and A gained g53, 72c/s. 5m. 
 B g99, 77icts, CS115, 12^cis. and I) gS8, S7jicts, 
 
 5. A bankrupt is indebted to A 21 1/, to B 300/. and to 
 C 391/. and hitt whole estate amounts only to 675L 10s. 
 which he gives up to these creditors ; liow mucn must 
 each have in proportion to his debt ? 
 
 ^ns. Jl must kaverioQ C:>'. 3 Ja'. B £^£4 15s. 4-.<* ana 
 G £2Q2 IG3 Sii 
 
140 COMPOUND f i:LLO,WSi£li». 
 
 6. A captain, mate ana 20 seamen, took a prize worth 
 5501 dols. of which the captain takes 11 shares, and the 
 mate 5 shares ; tho. remainder of the prize is equally di- 
 vided among the sail^irs ; h©w much did each man re- 
 ceive ? §5 cts, 
 
 Ans. Tiie captain received 1069, 75 
 1-^ie uiaic 486, 25 
 
 Each sailoi- 97, 25 
 
 7. Divide the number of 360 into 3 parts, which shall 
 be to each other as 2, 5, and 4. Arts, 80, 120. and 160. 
 
 8. Two mei chants iiave gained 450/. of v/hich A is t^ 
 (.ave 3 tijues as much as 15 : hov»' much is each to have ? 
 
 Ais. J £537 105. and B £ il2 105.--^1+S=:4 : 
 450 : : 3 : £337 iO-s. A's shci::e. 
 
 9. Three persons are to siiare 600/. A is to have a cer- 
 tain sum, B as much again as A, and C tliroe limes as 
 mucli as 15. I demand' each man's part .^ 
 
 Ans. A £66|, B £153f, and G £400 
 
 10. A and B traded together and gained 100 (U)is. A 
 put in 640 dols. B put in so much that he must receive GO 
 dols. of ihe. gain ; I demand B's stock ? Am. S960 
 
 11. A, E, and C, traded in company : A put in 140 dols. 
 B 250 dols. and C put in 120 yds. of cloth, at cash price-; • 
 tliey gained 230 dols. of which C t<5ok 100 dols. for hii 
 share of the gain ; hovv did C value his cloth per yard in ■ 
 I ommon stock, and wiiat was A and B's part of the gain ? 
 
 Ans, C jmi In the cloth at S2^ per ijard, Agaiiicui 
 S46, 67c/.'^'. 6;jt.4- and B B83, oZcts. 5?n,-r 
 
 ■ ■ ■ !! ■ ■ ! I ll■ m^T^^l» 1l m« l<■ ^«r^^» ^ ¥T^ lTa "^^-^ •^^^^-»'-^»''^■~^' «n'^^""^»«^^^ i ■ ■ iiiiii i ii mm n i M 
 
 COMPOUND FELLOWSHIP, 
 
 Or Fellowship with time, is occasioned by scvoial 
 shares of partners being continued in trade an une(|uai 
 term of time. 
 
 RULE. 
 Multiply each man's stock or share by the time it v^aa 
 continued in trade : th.en. 
 
 As the sum of the several products, 
 
 Is to the whole gain or loss : 
 
 So is each man's particular product, 
 
 To his particular share of tho gain or loss. 
 
)i:ni) i^KLLO'.vsnrp. I i- 
 
 KXAMPIKS. 
 
 £• ^'?. 
 
 d. 
 
 ; 3 3 
 
 4 A'spt. 
 
 ; 6 6 
 
 8 B-s — 
 
 : 9 10 
 
 C's — 
 
 1. A, C and C hold a pasture m common, for wliich 
 Lliej pay 19/. per annum. A ])ut in 8 oxen for 6 weeks ; 
 B liZoxen for 8 weeks; and C 12(|^cn for 12 weeks ; 
 
 what must each pay of the rent ? ^'^'''■ 
 
 sx 6= 48") r h 
 
 12x 8= 96 I 96 : 
 
 ' \vlo=^l44 Las 288 : 19/. : :<; 144 
 
 Sum 288J tProofl9 
 
 'Z, Two merchants traded in company ; A put in 215 
 dols. for 6 months, and B 390 dols. for 9 months, but by 
 misfortune they lose 200 dols. ; how must they share the 
 loss? Am\ d's loss S5S, 75cts. B's S146, 25cts. 
 
 3. Threft, ]X'rsoR3 had received 665 dols. interest : A 
 had put in 4000 dols. for 12 months, B SGOO dols. for 15 
 months, and C 5000 dx)ls.4br 8 months : how much is each 
 man's part of the interevt } 
 
 Ms, A S240, B SS.25 and C S200 ^ 
 
 4. Two partners gained by trading llOL 12s. r A's 
 stock was 120/. lOs. for 4 months, and B's 200/. for 6i 
 months; "what is each man's part of tlie gain ? 
 
 Ms. A's part £29 18s. S^^.^^Af. B's £80 lSs,Sid.,^^^^. 
 
 5. Two merchants enter into partnership for 1 8 months. 
 A at first put into stock 500 dollars, and at the end of 8 
 months he put in 100 dollars more ; B at first put in 800 
 dollars, and at 4 month's end took out 200 dols. At the 
 expiration of tlie time they find they iiave gained 700 dol- 
 lars ; what is each man's share of the gain ? 
 
 .^ ^ ^^24, 07 4-J-.TS share, 
 ''^^' • I SSr5, 92 5-tB's. do 
 
 6. A an<l B companied ; A put in the first of January, 
 1000 dols.; but B could not put in any till the first of 
 May ; what did he tlien put in to have an equal share 
 with A at the year's end ? 
 
 Mo, g Jib. S 
 
 As 12 : 1000 : : 8 : 1000x12=1500 Jlns. 
 
 .0 
 
The 
 
 I4§ BOUBLii Rur,r. of thref,, 
 
 DOUBLE RUI;E of THREE. 
 
 Double Rule of Tlircc tcaclics to resolve at 
 
 once such questions as require two or ::"fiore statings ia 
 simple proportion, -wlietber direct or inverse. 
 
 In this rule tliere are alv/iiys five terms given to find a 
 sixtlij the three firit terms of which arc a supposition, 
 the two last a demaucL 
 
 RULE. 
 
 In stating the question, place tlie terms of the supposi- 
 tion so that the principal cause of loss, gain or action pos- 
 sess the first place; that which signifies time, distance of 
 place, Ike. in the second place 5 and i}\Q remaining tenii 
 m the third place. Plac*5 the terms of demand, under 
 those of the same kind in the supposition, if the blank 
 place or term bought, tall under the third tcrift, tl^e pro- 
 portion is direct; then multiply the first and second 
 terms together for a divisor, and the other iAivaa for tt 
 dividend : but if the blank fall under the first or second 
 term, the proportion is inverse ; then multiply the third 
 and fourth terms toother for a divisor, and the other 
 three for a dividend," and the quotient will be the answer, 
 
 EXA MPLES. 
 
 L If 7 men can build S6 rods of wall in S days; liow 
 many rods can 20 men build in 14 days ? 
 
 7 : S : : 36 Terms of supposition. 
 £0 : 14 Terms of deuuind. 
 
 S6 
 
 84 
 
 42 
 
 504 
 20 
 
 7x3==2il) 10080(480 rods Ms. 
 2. If lOO/.principal will gain 6^. interest in 12 months, 
 what will 400u gain in 7 m^ntlis ? 
 
 Principal iOOl. : 12mo. ; : 61. Int. 
 
 400 : 7 Jlns. ML 
 
•J^Oi.'JOlKED PROPORTION. 343 
 
 5. ir lOOL ulll gain 6/. a year; in ^vhat tiii-iC %vil! 
 400Lgain H/. /;. mo. £. 
 100 : la : : 6 
 400 : : : 14 dns, 7 iivontlSe, 
 
 4. If 400Z. gain 14^ in 7 mouths ; wha|; is the rate per 
 cent, per annum ? £. mo. Lit,' 
 
 400 : r : : 14 
 
 100 : 12 Ms. £6.^ 
 
 5. What Principal at 6/. per cent, per annum, will gain 
 3 4f. in 7 mouths r £, mo. . Int. 
 
 100 : 12 : ": 6 
 
 7 : : 14 ^ Ms. £400. 
 
 6. An usurer put out S6l. to receive interest for the 
 ^ame ; and when it had continued 8 months, he received 
 urincipul and interest, 88/. 17s. 4d. 5 1 demand at wliat 
 rate per cent, per ann. he received interest r Ans. 5 per ct. 
 
 7. if 20 bushels cf wheat arc sulHcient for a ikmilj of 
 8 persons 5 months, how much will be sufficient for 4 per- 
 sons 12 months ? Ms. 24 bushels. 
 
 8. If 30 men perfwrn a piece of work in 20 days : how 
 many men v.ili accomplish another piece cf vvork 4 times 
 a3 large in a iifth part of tUa (hue r 
 
 no : 20 : : I 
 
 4 : ; 4 Ms. 600. 
 
 9. If the carriage of 5 cwi;. 3 qrs. 150 miles, cost 24 
 dollars 58 cents ; what must be paid for the carriage of 
 7 cvvt. 2 qrs. 25 lb. 64miles at the same rate ? 
 
 Jlns. S14, OBcis. 6?n.-|- 
 
 10. If S men can build a wall 20 [eei long, G i^et high 
 and 4 feet thick, in 12 days ; in what time will 24 men 
 butld one 200 icet long, 8 tect high, and 6 feet tiiick ? 
 
 8 : 12 : : 20x6x4 
 
 200x8x6 80 da^s^ Ms. 
 
 CONJOINED PROPORTION, 
 
 Is wher. the coins, weiglits or measures of several coun- 
 tries are compare^^ intlie^me qyest»on . <jr it i;i Joiaiii 
 
l5Q C5.0NJ0I^'ED mOPOKTlw- 
 
 several antecedents have to their consequents, the pro. 
 portion between the first antecedent ano the last conse- 
 quent is discovered, as well as the proportion between 
 the others in their several respects. 
 
 Note. —This rule may generally be abridged by can- 
 celling equal quantities, or terms that happen to be the 
 same m both columns : and it may be proved by as many 
 statings in tlie Single Rule of Three, as the nature of the 
 question may require. 
 
 CASE 1. 
 
 When it is required to llnd how many of tlic ilvst sort 
 of coin, w^eight or measure, mentioned in the ([ucstion, 
 are equal to a given quantity of llie last. 
 RULE. 
 
 Place the numbers alternately, beginning at tlie left 
 hand, and let the last number stand on the left hand col 
 umn; then multiply the left hand column cor.tinually for 
 a dividend, and tlie right hand for a divisor, and the*<juo- 
 tient will be the answer. 
 
 EXAMPLES. 
 
 1. If 1001b. English make 95lb. Flemisli, and 191b. 
 Flemish 25lb. at Bologna; how^ many pounds Engllijh 
 are equal to oOlb. at Bologna ? 
 
 lb, lb, 
 
 100 Eng.=^5 Flemish. 
 19 Fie. =25 Eolo-na. 
 50 Bologna. ' Tlien 95x25=2375 the divisor. 
 
 95000 dividend, and 2375)95000(40 JIns. 
 
 2. If 401b. at New-York, make 48lb. at Antwerp, and 
 SOlb. at Antwerp, make 36lb. at Leghorn ; how many 
 lb. at New-York are equal to 1441b. at Lcgliorn ? . 
 
 Ms. lOOlh. 
 S. If 70 braces at Venice be equal to 75 braces at Leg- 
 horn, and 7 braces at Leghorn be equal to 4 American 
 yards ; how many braces at Venice are equal to 64 Ame- 
 rican yards ? " . Jhis. 104^-^ 
 CASE IL 
 When it is required to find how many of the last sort 
 of coin, w'elght or meiisure, mentioned in the question 
 ai'C equal to a given quantity of the first. 
 
rule: 
 
 Place the numbers aUeniately, beginning at the lefl 
 hand, and let the last number stand on the right hand ; 
 then multiply tlic first row Tor a divisor, and tlie second 
 for a dividend. 
 
 K:;AMrLEs. 
 
 1. If 24lb. at New-I^ond(m make COlb. at Amsterdam, 
 and 50lb. at Amsterdam 60ib. at Paris : liow many at 
 Paris are efjual to 40 at New-London ? 
 
 Left, Might. 
 24 = 20 20 X 60 X 40 = 48000 
 
 50 = GO --= 40 .Ins. 
 
 40 24 X 50 tr=: 1)300 
 
 2. Jf 501b. at New-York make 45 at Amsterdam, and 
 BOlb. at Amsterdam make 103 at Dantzic ; iiow many lb. 
 at Dantzic are ctiual to 240 at N. York r .^us, 278-1^ 
 
 3. if 20 braces at Lcj:;liorn be equal io 11 vares at 
 Lisbon, and 40 vares at Lisbon to 80 braces at Lucca ; 
 how many bract^s at Lucca are equal tw 100 braces at 
 Leghorn? *'2ns. 110 
 
 jJ Y this rule merchants know wliat sran of money ought 
 to be received in one country, for any sum of different 
 specie paid in another, according to tlie given course cf 
 exchange. 
 
 To reduce the monies of foreign nations to that of the 
 United States, vou mav consult the followiu'^ 
 
 \ "FABLE: 
 
 Showing the value of tlie monies of account, of foreign 
 nations, estimated in Federal Money.* S cts. 
 
 Pound Sterling of Great -15ri tain. 
 
 Pound Sterling of Ireland, 
 
 Livre of France, 
 
 Guilder or Florin of theU. Netljcrlands, 
 
 Mark Banco of Hamburgh, 
 
 Rix DoUai- of Denmark, 
 
 ""haws U. S. j! 
 
 4 44 
 
 4 
 
 10 
 
 0. 
 
 ,185 
 
 
 
 59 
 
 
 
 S3I. 
 
 1 
 
 
 
152 *ixcrkA^:GB, 
 
 Rial Plate of Spain, 10 
 
 IVlilrea of Portugal, 1 24 
 
 Tale of China, 1 48 
 
 Pagoda of India, 1 94 
 
 Rupee of Bengal, 55i 
 
 L OF GREAT BRITAIN. 
 
 EXAMPLES. 
 
 1. In 45^. 10s. sterling, how many dollars and cents ? 
 
 A pound sterling being3=444 cents, 
 Therefore—As IL : 444cts. ; : 45,5/. : 20202cfs. dns. 
 
 2. In 500 dollars how many pounds sterling ? 
 A»444cts\ : IL : : 50000cfs. : 112^. I2s. 3rf.-h .9n.^. 
 
 II. OF IRELAND. 
 
 EXAMPLES. 
 
 1. In 901, TOs. 6d. Irish money, how many cents ^ 
 IL Irish =r410ci5. 
 £. cts. £. cts. S cts, 
 
 Therefcft-e— As 1 : 410 : : 90,525 : S7115^=3f 1, 15i 
 £• In 168 dols. 10 cts. how many pounds Irish ? 
 As410cf5. : 1/. : : iCSlOcfs. : £41 Irish. Jns. 
 
 III. OF FRAiSCE. 
 
 Accounts are kept in livres, sols and deniers. 
 512 deniers, or pence, make 1 sol, or shiliiug, 
 1 20 sols, or shillings, — 1 livre, or pound. 
 
 EXAMPLES. 
 
 1. In 250 livres, 8 sols, how many dollars and cclits ? 
 
 1 livre of France=18T^- cts. or 185 mills. 
 £• '^'^' £' '^"- S» (^ts. 711. 
 
 As 1 : 185 : : 250,4 : 46524=46, 32 4 Ans, 
 
 2, Reduce 87 dols. 45 cts. 7 m. into livres of France^ 
 mills, liv, mills, liv. so. den. 
 
 As 185 : 1 : : 8745r : 472 14 94- Jlns. 
 
 IV. OF THE U. NETHERLANDS. 
 
 Accounts are kept here in guilders, stivers, groats and 
 pfennings. 
 
 r 8 phennings make 1 groat. 
 < 2 groats — 1 stiver. 
 
 (^20 stivers — 1 guijder, or florin 
 A guL'der is =^9 cent§. or 390 mills. 
 
F.XAMri.F.^. 
 
 iicJucc 19A ;*iiiki'r;.s, 14 stivers, into federal money. 
 Guil, cts. GuiL S d- c. m. 
 As 1 : S9 : : 124,7 : 48, G 3 3 ^?«.<?. 
 milh, G. vdJls. G, 
 As S90 : i : : 48633 : 124,7' Froof. 
 
 V. OF IIAMUUllGH, IN GERMANY 
 
 Accounts cire kept in Hamburgh in marks, sous antl 
 (leniers-lubs, and by some ia rix dollars. 
 
 fl2 denicr's-lubs r.iakc 1 sous-lubs. 
 
 ■i \i) so;?s-!i;h^. — 1 niark-lubs. 
 
 (^ 3 ?\tark-hi'..s. — I rix-doliar. 
 NoTK.. — A ii.wirk Is -- 33-V ct..^^. oi* just -? of a dollar. 
 
 RULE. 
 Divide Ihc luaiksby 3, the quotient will be dollars. 
 
 KXAMl'LKS. w. 
 
 Reduce G41 n:arks, 8 sous, to federal raoney. A> 
 
 S)641,j ;,.V 
 
 S213,83r. ^/7.c:. 
 But to reduce Federal Money into Marks, multiply 
 the given sum by 3, &c. 
 
 lleduce 121 dollars. 90 els. into marks banco. 
 i2l,90 
 
 565,r0=365 ir.nrks II sous, £,4 den. Jiri^. / 
 
 VI. OF SPAIN. 
 
 Accounts are kept in Spai n i rij^iastres, rials and maiTadie«. 
 ^34 marva(ii?.\s of rihJj^ make 1 njal of plate. 
 ?. Serials of plafe — 1 piastre oi piece of 8. 
 
 To reduce rials of plate to^Federal Money. 
 Since a rial of plate is = 10 centsj or 1 dirae,yoiJ need 
 only call the rials so many dimes, and it is done. 
 
 KXAMrLP.S. 
 
 485 ria:snr:r485 i!iir.rs,^-48 do^s. 50 ci«;. 5&c. 
 
Sul to reduce cents into rials of plate^ divide 1>>' 10-— 
 llras, 345 cents-f-l 0=84,5 =84 rials, 17 maiTadieSj fcc4' 
 
 YII. OF PORTUGAL. 
 
 Ax:counts arc kept tliroughoiit this kingdom in milreas^ 
 and reas, reckoning 1000 re;is to a miirea. 
 
 Note. — A miirea is = 124 cents ; therefore, tQ reduce 
 milreas into Fe<leral Money, multiply by 124, and the 
 product will be cents, and decimals of a cent. 
 
 EXAMPLES. 
 
 1. In r;:'; ^..\]]rc:i^ hnw m:\nr cents? 
 
 C. Ill Q! j iinire'i^. .... ..... liow many cents ? 
 
 Kci.:. — WliMi the reas are less than IGO, place a cy- 
 pher before them.— Thus, 21 1,048 x 124 «=£6 169,952 cts, 
 or 261 dols. G9cenL->. 9 mills. + Ms, 
 
 Bu^ to re(iuce cents into milreas, divide them by 1£4'; 
 and if decimals arise, you must carry on the quotient as 
 far as lluee decimal places ; then the whole numbers 
 thereof will he the milreas, and the decimals will betlic 
 reas. 
 
 EXAMPLES. 
 
 1. In 4195 cents, how many mili-eas ? 
 
 4 1 95 -i- 1 24 =33,850 -f or ^Smilr. ^^Qreas. Jins. 
 
 2. In 24 dols. 92 cts. how many milreas of Portugal ? 
 
 Ans. 20 milreas^ 096 reas. 
 
 YIIT. EAST minx ]\IOjir&Y. 
 
 To reduce india^iwine^^ to Federal, viz. 
 
 ["Tales of Ciiiaa, m;^ltiply v/ith 148 
 -^, Pagodas of India," 194 
 
 (^ Rupee of Bengal^ 55^ 
 
 l<:XiOi?i'LES. 
 
 1. In 641 Tale s/m'Chjiia,'hcw many cents? 
 
 ' £ ^ . *'?»'^« 94863 
 
 2. In 50 Pagodas ^^India, how many cents? 
 
 7. ' ' Am. 9r00 
 
 5. In 98 liunces of Bengal, lw)w mauv cents? 
 
 ^ Jim. 5439 
 
VULGAii FRACTIONS. 
 
 Having briefly introduced Vulgar Fractions imme* 
 diatcly after reduction of whole numbers, and given some 
 general definitions, and a few such problems therein as 
 were nocessary to prepare and lead the scholar immedi- 
 ately to decimals ; the learner is therefore requested to 
 read those general definitions in page 74. 
 
 Vulgar Fractions are either proper, improper, single, 
 compound, or mixed. 
 
 1. A single, simple, or proper fraction, is when the nu- 
 merator is leas than the denominator, as ^ :| | ||, &c. 
 
 C. An Improper Fraction^ is when the numerator ex- 
 ceeds the denominator- as 4 -J V^, &c. 
 
 3. A Compound Fraciion^ is the Traction of a fraction, 
 coupled by tlie word of, thus, | of -jI^j ^ ^^ I o^ l^ ^^' 
 
 4. A Mured A\miher^ is composed of a whole number 
 ^id a fraction, thus, 8 J, 14|^, oic 
 
 5. Any whole number may be expressed like a fraction 
 bv drawing a line under it, and putting 1 for denoniana- 
 tor, thus, 8=f, and IGthuj-:, \S &c. 
 
 6. The comm(;n measure of two or mere numbers, is 
 that number v/liich v»'iil divide cacli of thcin without a 
 remainder; thus, 3 is the common measure of 12, 24 and 
 SO; and the greatest number which will do this, is called 
 the greatest common measure. 
 
 7. A number, winch can be measured by two or more 
 rmmbers, is called their common midilple : and if it be the 
 least number that can be so measured, it is called the least 
 common multiple: thus, 24 is the common multiple of 2, 
 S and 4 ; but tlicir least common multiple is 12. 
 
 To find iho least common multiple of two or more 
 r limbers. 
 
 RULK. 
 .. D'.vi'Ie by any number that wllldiviue ^v/o or more 
 CMC given numbers without a remainder, and set tli« 
 «>tient::, togetl;er with tLeui»'Jivided rii;iiiber;>. in aline 
 ^: nealh. 
 
 2. liividc the second ll:t-e« as bc^fmv, p.vaI so on tiH 
 il^^re are nwtwo nuTiibei^hat can be divided} ^hen the 
 
/ 
 
 io6 JIEBUOTION OF VULGAR FKAOTiONS. 
 
 IHi continued product of the divisors and quotients, 'wiligive 
 ^^ tlic multiple required. 
 
 EXAMPLES. 
 
 I. *V\Tiat is tlic least common multiple of 4, 5, 6 and 10 ? 
 Operation, x5)4 5 6 10 
 
 \ X2)4 16 2 
 
 X2 1X3 I 
 
 5x2x2X3=60 Jns. 
 S. What is the least common multiple of 6 and S ? 
 
 Jns, 24 
 5. What is the least uumbci? that 3, 5> 8 and 12 will 
 measure? ^fJns, 120 
 
 4. What is the least number that can be divided by the 
 9 digits separately, v/ithout a remainder ? Aiis, 2/^20 
 
 REDUCTION OF VUl.GAIi LRAGTIONS, 
 
 IS the bringing them out of one form iato anothci', in 
 order to prepare them for the operation of Addition, Sub- 
 traction, &c. 
 
 CASE I. 
 
 To abbreviate or reduce fractions to their lowest terms. 
 RULE. 
 
 1. Find a common measure, by dividing the greater 
 tcvmby the less, and this divisor by i:he remainder, and 
 so on, aUvays dividing the last divisorjby tlie last remain- 
 der, till nothing remains^ tlie last divisor is the common 
 measure.* 
 
 2. l>i vide both of the terms of the fraction by the com- 
 mon measure, and the quotients vvill make the fraction 
 required. 
 
 *']Sojind the greatest common measure of viore than 
 two numbers, you must find the greatest common measure 
 of two of them as par rule ahovs.^ then, of that common 
 measure and one of the other numhevs^ and so on through 
 ell the numbers to the lasts then wUHhe greSf^^t co^n^ion 
 
1 
 
 REJDUCTION OF VULGAR TRAOTIONS. 157 
 
 OR-^If you choose, you may take that easy method in 
 Problem I. (page 74.) 
 
 EXAMPLES. ^^ 
 
 1. Reduce ^f to its lowest tenns. 
 48)||(i Operation. 
 
 ^l|4fl/6 common mea. 8)f|=f Ms. 
 
 2. Reduce ^ to its lowest terms. Ms. 
 
 ^8 
 
 Reduce |f| to its lowest terms. •fins. ^ 
 
 4. Reduce f pfl to its lowest terms. Ms. i 
 
 CASE II. 
 
 To reduce a mixed number to its equivalent improper 
 fraction. 
 
 RULE. 
 
 Multiply the whole number by the denominator of the 
 given fraction, and to t]\e product add the numerator, 
 this sum v/ritten above the denominator will form the 
 fraction required, 
 
 EXAMPLES. 
 
 1. Reduce 45} to its equivalent improper fraction. 
 
 45x8+r==3|7 Ms. 
 
 2. Reduce 19^ f to its equivalent improper fraction. 
 
 Ms. V/ 
 
 3. Reduce 16^^^ to an improper fraction. 
 
 Ms. x^^ 
 
 4. Reduce 6l-Jg J- to its equivalent impropei fraction. 
 
 Ms. 2|«^5 
 
 CASE lU. 
 
 To faul the value of an improper fraction. 
 
 Divide ihQ numerator by the denominator, and the 
 quotient wiH be the value sought, 
 
 EXAMPLES. 
 
 1. Find the value of V 5)48(9| Jn$. 
 
 2. Find the v.ihie of W^ Ms. IQif 
 •^lEbjl the value of ^t *^«5- 84^ 
 
 i^gfS^^m] tiie value of %%^ * ^ns. 6^^ 
 
 \ '^ Find the value of V •to^- S 
 
..jS reduction of vulgar fhactions. 
 
 CASE IV. 
 
 To rciluce a wliole number to an equivalent frd.ci'.gfly 
 ing a given denomiiiator. * 
 
 RULE. 
 
 Multiply tlie whole number bv tlie given den 
 place the product over tlie said denominator, i 
 form the traction required. ff 
 
 fc:XA:iPLES. 
 
 1. Reduce 7 to a fraction wliose deiuKiiinri' o 
 9. Thu- '^ -^^-r63, and ^^ in- 
 
 2. Reduce IS to a vhose denomi: 
 be 12. 
 
 3. Reduce 100 to Its equivalent fraction, Ik >/ ; ^3 
 (or a denominaJ:or. ' Jln^. ^ o.o o ^ 9 o o ^, v 
 
 C 'VhE V. 
 
 To reduce a compound fraction to a simple one r ' 
 vr.hie. 
 KJ -LE, 
 
 1. Reduce all whole aiul mixed nuinbers.to i~ " 
 valent fractions. 
 
 2. Multiply all (lie numeiators to^jether (or 
 merator, vmd ail the den<f,nJLiat'.MS for a nev/ 
 tor; and they ^vill form the fraction recjiiircd. 
 
 EXAM PL FS. 
 
 1. Reduce -J of 4 ^'^ ^ ^^ r?^ to a ^>iIT5<,'o cnii- 
 
 1x2x3x4 
 
 ■ ^^o^Tu «^^5- 
 
 2. Reduce 4 of | cf ^ Je ^ctioa. .' 
 
 3. Reduce | of |^ (fi ,3 .. . a single fractir. 
 
 v^ ; I 
 
 4. Reduce ioi'" . - ' , ■ ^- ^--^ion. 
 
 5. Reduce ^ (- v.i a^:;. iVaction. 
 
 ■) 2 6 G . 
 t. u 0" ' 
 
 Note. — If i\\e denon.inator u( ai 
 br)UGd fractic!! be equal to tlu- ^" 
 
ilJF. D \: U r ! '.) N O F V I. \. I . A !<. F \\ A < "i J.(. 
 
 I^fl ':• thereof, tliej may both be expuRgc.:, www tue 
 
 r ..embers continually' multiplied (as by i}\t rule) 
 
 duce t!ie fraction required in lower t-erms. 
 
 <m!ucc %- of Of 4 to a simple fraction. 
 
 Tiius, 2x5 
 
 4x7 
 * Malice I of J of I of |4^ to a simple fraction. 
 
 CASK VI. : 
 
 ^'? fractions of diifercnt denominations to cr 
 fiactiqi^s having a ccinmondenominatoi. 
 
 1. lu'duce alifraction.'^ to simple terms. 
 •>. Multiplj each numerator into all the denominators 
 o}:t its ov.n, for a nev/ numerator ; and all the denom- 
 ,;oi.'^ into each other continually for a common denom- 
 . U>i ; this Avritten^'tuidei- tlie :' iiew Btuuerators, 
 
 : 1 ^^ive the fractions recpiired. 
 
 EXAMPI 
 
 ^:duce \\\ to c; 
 I denominator. 
 
 iractions, having a 
 'e nominator. 
 
 16 IS nev/ muncnitors 
 
 24 lw4 
 Reduce ^ 
 
 
 r-. Reduce i 2 
 
 dem/nduat «*s. 
 and W to a comnuiJi dfMiorninator. 
 
 J?'iO ■ »'-*<l ^i^* /IW// 8 80 
 *^...'. j,.^ 5^0 '''^" 9^ 
 
 f andT^ioa coiniDon denominator. 
 <» .J'..?. js|^ -^^-j -j^-g- ana -5;,^^ 
 
M REDUCTION OF VULGAR FRACTIONS. 
 
 4 Reduce 4 -^^ and j\ to a coinmon denominator. 
 800 SCO 400 ^^ 
 
 — ^'^'^ ;% ro ^^^^ A ==^tV •^W^- 
 
 1000 1000 1000 
 
 5. Reduce J ^j and 12-| to a common denominator. 
 
 jiim 5 4 6 8 8 8 
 
 . fj<t.>. Y2; Ti T'i 
 
 6» Reduce | -| and | of || to a ccniino:i denominator. 
 
 i]po 768 259219R0 
 
 ..^/..S. -s-^jrsg- ^--tTIT T4T^ 
 
 The foregoing 13 a general Rule for reducing fractions 
 to a common denominator; but as it will save much la- 
 bour to keep the fractions in the lov/est terms possible, 
 tlie following Ride is much preferable. 
 
 For reducing fractions to t -on denominator. 
 
 (By Rule, page 155) find tlie least common multiple of 
 all the denominators of the given fractions, and it will be 
 the common denominator required, in which divide each 
 particular denominator, and multiply the quotient by its 
 own numerator for a new numerator, and the new nume- 
 rators being placed over the common denominator, will 
 express the fractions required in their lowest terms. 
 
 EXAMPLES. 
 
 1. Reduce 1 4 and I to tl\eir least common denomina- 
 
 4)2 
 
 £)r2 1 £ 
 
 111 4x£=8 the least com. denominator. 
 
 8-7-£xl=4 the 1st. numerator. 
 
 8-r-4x3=6 the Sd. numerator. 
 
 ^ 8-~8x5=5 the 3d. numerator. 
 
 These numbers placed over the denominator, give the 
 answerlff equal in value, and in much lower terms 
 tlian the general Rule, whicli would produce H |^ |^ 
 2. Reduce | % and -^^ to their least commoa tienomi-* 
 
 X' 
 
UEDUOTION OF VULOAR FRACTIONS. 
 
 5^ ^ -J anu -fj 
 nomiuator. *^ns. ^ ,\ ^| ^f 
 
 4. Reduce^ f f and ^^^ to their least common denom 
 inator. Jlns. ^\ fi ^ ^-V 
 
 ^ASE VII. 
 
 To reduce the fraction of one denomination to tlie fractio 
 of another, retaining tlie same value. 
 
 RULE. 
 
 Keduce the given fraction to such a compDund one, as 
 !i express the value of tiie given fraction, bj comparing 
 vith all the denominations between it and that denomi- 
 ien vou would reduce it to; lastly, reduce this com- 
 ind iVaction to a single one, ' Y. 
 
 EXAMPLi..-. 
 
 ^ . Reduce J of a penny to the fiaction of a pound. 
 By comparing it, it becomes |- of ^\ of r;\ of a pound. 
 
 5 X 1 >f 1 "5 ^ 
 
 i-.,4M^ = ,^«,?, 
 
 6 X- 1^^ 20 1440 
 
 2. Keduce j^tj of a pound to the fraction of a penny. 
 
 Compared" thus, T-^ of \o of Y'd. 
 Then 5 x 20 x Is 
 
 440 1 I '^"\y 
 
 5. Reduce ^ ©fa fartiiiii,^ to th^ iraci; on of a shilling. 
 
 *. Ans. ^,*;. 
 
 4. Reduce | of a shilling to tlie fraction of a pound. 
 
 5. Reduce f of a pwt, to the fraction of a pound troy. 
 
 6. Reduce f of a pound r^irdupois to the fraction ol 
 
 7. What part of a pound avoirdupois is -j^i^ oF a cvrt. ? 
 Compounded t\\v^. r^,. of t f >t ^^ =-}-|-| = « ^/J/j^?. 
 
 S. Wiiatpartof ar ' iM'k? 
 
iOB REDUCTION 05 VULGAR rRA0TiONS# 
 
 9. Reduce i of a pint to the fraotioii of a hbd. 
 
 10. Reduce ^ of a pound to the fraction of a guinea 
 
 Compounded thus, | of ^ of tj^^^t •^^^• 
 
 11. Express 5^ furlongs in the fi^Gtion of a mile. 
 
 Thus, 5^^^^ of 1=11- Ans. 
 
 12. Reduce | of an English crown, at 6s, 8d. to the 
 fraction of a guinea at 28s. dns. A of a p^idma. 
 
 CASE Yill. 
 
 To find the value of a fraction in the known parts of the 
 integer, as of coin, weight, mcHsuie, 6cc. 
 
 RULE. 
 
 Multiply the numerator by the parts in the next inferi- 
 or denomination, and divide the product by the denomina- 
 tor ; a^d if any thing remains, multiply it by the next in- 
 ferior denomination, and divide by the denominator/ ai 
 before, and so on as far as necessary, and the quotfcnt 
 will be the answer. 
 
 Note. — This and the following Case are the same 
 vrith Problems II. and III. pages 75 and 7^ ; but for 
 the scholar's exercise, I shall give a few more examp^ s 
 in each. 
 
 EXAMPLES. 
 
 1* What is the value of |}^ of a poimd ? 
 
 Jns. 85. 9id. 
 % Find the value of J of a cwt, 
 
 II 
 
 4. How much is ^Vt ^^ ^ pound avoirdupois ? 
 
 Ans. 7oz. lOJr. 
 
 5. How much is ^ of a hhd. of wine ? Ms^ 45gals. 
 6* What is the value of |f of a dollar ? 
 
 jflfws. 55. 7id, 
 7. What is the value of j^ of a guinea ? Jlns. 18s. 
 
 Ms. Sqrs. Sib. loz, l^dr 
 S. Find the value of | of 6s. 6(1. Ms. 5s. Oid. 
 
..iiDlTXOn or VULGAH FIlACTIO^b, . 153 
 
 8. Required the value of ^J^ of a pound apotliecaries. 
 
 ^ns, ^oz, Sgrs. 
 
 9. How much is ^ of 5L 9s. ? Ms. £4 ISs. 5\d. 
 10. How much is ^ of § of J of a hogshead of wine ? 
 
 dris. ISgals. Sqt&, 
 
 CASE IX. 
 
 To reduce any given quantity to tlie fraction of any grea^ 
 
 er denomination of the same kind. 
 
 [See the Rule in Problem III. page 75.'] 
 
 EXAMPLES FOR EXERCISE. 
 
 1 Reduce 12lb. 3oz. to the fraction of a cwt. 
 
 2. Reduce IScwt. Sqrs. £Oib. to tlie fraction of a ton. 
 
 Jlns. 11 
 
 3. Reduce 16s. to the fraction of a guinea, •^ns. ^ 
 
 4. Reduce 1 hhd. 49 gals, of wine to the fraction of a 
 fun. Jlns, ^- 
 
 5. What part of 4cwt. Iqr. 24Ib. is 3cwt. Sqrs. 17lb. 
 8oz. Jlns. I 
 
 ADDITION OF VULGAR FRACTIONS. 
 
 RULE 
 
 REDUCE compound fractions to singl^||es ; mixed 
 numbers to improper fractions ; and all oI|^^^ to their 
 least common denominator (by Case YI. KITle II.) then 
 the sum of the numerators written over the common de- 
 nominator, will be the stjm of the fractions required. 
 
 EXAMPLES. 
 
 1. Add 5^ I and f of J together. 
 
 •^i-V and f of I .=-41 
 
 Then y | \^ reduced to theii- l^^ast coiunion denominator 
 
 by Case VI. Rule \\ \Jf! bef:oiiie Vr il i'^ 
 
 Then ir>!2+18+14«:i^y=6ff or (3|. Jinswer. 
 
..ii ADDITIOK OF VULGAR FiiACTIONS; 
 
 2, Add 4 1- and | togetlier. Ms. 1| 
 
 5. Add i I- and f together. Ms. 1| 
 
 4. Add 1^ 3§ and 41 together. Ans. '20\^ 
 
 5. Add 1 of 95 and ■} of 14i together. ^^ns. 44^ 
 
 Note 1. — In adding mixed nuinbers that are not com- 
 pounded with other fractions, you may first find the. sum 
 of the fractions, to which add the whole numbers of the 
 given mixed numbers. 
 
 6. Find the sum of 5| 7| and Id] 
 
 I find the sum of | and | to be |^=UJ- 
 
 Then I|^-f5-r^+15rnr28|j Anf^. 
 
 7. Ajdd I and ir| together. Ai:3. 17-^\ 
 
 8. Add 25, 8i and | off of -f^ Jlns. SS-/^- 
 
 NoTE 2.— To add fractions of moneys weight, &c. re- 
 duce fractions of different integers to those of the same. 
 
 Or, if you please you may find the value of each frac- ^ 
 lion by Case VHI. ii\ reduction, and then add them in 
 their proper terms. 
 
 9. Add ^ of a shilling to |- of a pound. 
 
 2d Method. 
 |.£.=7s. 6d. Oqrs. 
 |s. =0 6 ^ 
 
 Ms. 8 ^ 
 
 By Case VIIL Reduction. 
 
 1st Method. 
 
 ^of^V==TlF:C- 
 
 Then^|^+|.=:,'^//o£- 
 
 Whole value by Case VIIL 
 
 is 8s. Od, Sfqrs. Ms. 
 
 ID. Add IBr Troy, to | of a pwt. 
 
 ; Ms. 7qz. 4pwi. IS^-gr 
 
 11. Add ^ of a ten, to -Z^- of a cwt. 
 
 Ms. ISlcwt \qr. Uh. VZ^^oz. 
 
 12. Add A of a mile to ^^^ of a furlong. 
 
 .61ns. Gfur. ^Spo. 
 
 IS. Add " of a ynrd, | of a foot, and J of a mrle to- 
 gether. '' ^ Ms. 1540yds. ^ft 9in. 
 
 14. Ad«l I of a week, ^ of a/day, | of an hour, and -J- of 
 » minmte together. Am^^a. 2ho. SOmin. iSsec 
 
sun: OF VULGAR FRACTIONS. 
 
 SUBTRACTION OF VULGAR FRACTIONS. 
 
 RULE.* ^ 
 
 PllEPARK the fractions as in Addition, and the dif- 
 ference of the numerators written above tlie common de- 
 i^ouiiuatorj will give tht^difterenceof the fraction requii-ed. 
 
 EXAMPLES. 
 
 I. JVom i take I of I 
 
 I of |-=H=i^ ^^^^«n ' and J^^:^!^ ^ 
 
 Therefore 9— r=-j%=-|- ^^^^ *^^^' 
 
 \ From IJ take ^ Answers, \\ 
 
 :. From 11- take y, ^^ 
 
 . From 14 take \} 13^% 
 
 . Whatift the diifcrei-ee of -,^^ arul ]I r ^fy 
 
 .. AVhatditTers -j>^ fioui ^ ? ' -^V^ 
 
 r. From 14i take f of 19 1^ 
 
 8. From || take -||^ remains, 
 
 'j. From 14 of ammnd, take ^ of a shilling. 
 
 5 of ^V=Tlo^^• Then from f|£. take^-J^£. Arts. |}£. 
 
 Note. — In tractions of money, weight, occ. you may, if 
 you please, find tiie value of tlie given fractions (by Case 
 VIIL in Reduction) and then subtract them in their pro- 
 per terms. 
 
 10. From -jV£- take ^ sliilling. Jlns. 5s. 6d, 2^qrs. 
 
 II. From -f of an oz. take J of a pwt. 
 
 *'9ns. llpivt 3gr. 
 
 12, From } of a c>vt. ta^ie y^ of a lb. 
 
 Jins. Iqr. mb. 6oz, 10^%dr. 
 
 13. Froju ^ weekis, take f of a day, and ^ of f of ^ of 
 an hour. •dns. Sick 4da. l2ho, 19 hum. IT^sec, 
 
 *In subtracting mixed numbers, when the lower fraction is 
 greater than the upper one, you may, without reducing them 
 to improper fractions, subtract the numerator of the lower 
 fraction from the common denominator, and tQ that difference 
 add th« upjjer numerator, carrying one to the unit's place of 
 t]<i lowfcr whole number. 
 
 llso, a fraction may be snbtracted from a wholo number 
 bj taking the numerator of the fraction from its denomina- 
 tor, and placing the remainder over tlie denominator, then 
 thkinpf one from thfc whoJe number. 
 
 \ 
 
) MUI/n PLICATION 07 > . ! FRACTION^,. 
 
 REDUCE vr Moers to the improper 
 
 fractions, mixc .}le ones, and timseof 
 
 dilTerent integers to the same ; tly^n multiply all the au- 
 meratots together for a Fiew numerator, and all the de- 
 nominators together foi- anew denorainator. 
 
 Mr:[liply f b^ 4 
 
 £. Muitlpij |. by ? 
 S, .^liiltipiy 5i by i- 
 
 4. Multiply I of 7 bv '* 
 
 5. Multiply 1^1 bv >. ■■ 
 
 6. Multiply I'of ' :'^ 
 r. Multiply f!2 by 
 
 Multiply I Gf^| by | of SI 
 
 --'If 
 
 23 
 Y4 
 
 9. Wluitis thQ continued product of J of !• 7, 5t^ and 
 
 DIVISION OF VULGAR FRACTIONS. 
 
 RULE. 
 
 PREPARE iLe fractions as before ; then, invert iiie 
 divisor and proceed exactly as in multiplication : — ^The 
 products will be the quotijent required. 
 
 r,X A TRIPLES. 
 
 4X5 
 
 1. Divi^^.' I by J Thus, =|^ diis. 
 
 S X 7 
 
 2. Divide .]^ oy v dnsivers. 1-^^ 
 
 5. Divide I of I by i $ 
 4. What is the quotient of 17 in- f ? * 59^ 
 D. Divide 5 by fy ' ' 7-J- 
 
 6. Divide i o'f f of -J by } of i 3 J 
 
 7. Divide 4|- by f of 4 ^ 
 
 8. Divide 71 by 127 ^V 
 ^ Divide d205^ bv -f of 91 714 
 
KIJLE OF THUEF DlilEC I", IKVEXlSE, &C. 16T 
 
 RULE OF THREE DIRECT IN VULGAR 
 FRACTIONS. 
 
 RULE. 
 
 i'REPAIU''. tlie iVaclions as before, then state your 
 question agreeable to the Rules already laid down in the 
 Rule of Three in whole numbers, and invert the first term 
 in the proportion ; then multiply all the three terms con- 
 tinually together, and the product will be the answer, in 
 the same name with the second or middle term. 
 
 EXAMI'LES. 
 
 1. If f of a yard cost J of a pound, what will r^^ of an 
 Ell English cost? 
 
 |yd.=A of ^ of i^U or i Ell English. 
 Ell. £. Ell. s, d. qrs. 
 
 \ 2. If 4 of a yard cost J^ ot a pound^what will 4C^J- yds. 
 come to? .Tns. £59 Ss. 6^d. 
 
 3. If 50 bushels of wheat cost 17 f I. wliat is it per bush- 
 el ? Jtns. 7s. Gd. Hfqrs. 
 
 4. If a pistarcen be worth 14| pence, what are 100 pis- 
 "tareens worth ? ^ns. £6 
 
 5. A merchant sold 5^ pieces of cloth, each containing 
 244 yds. at 9s. -^d. per yard ; what did the whole amount 
 to.^ ' Jlfii. £60 lOs. Od. 3|</rs. 
 
 6. A person having |. of a vesical, sells f of his share for 
 : :S12?. ; wliat is the whole vei-sel worth ? dns. £780 
 >. 7. if I of a sidp be worth f of her cargo, valued at 
 ! 'I^OO^L ^vhat is the whole ship and cai-go worth ? 
 
 Arts. £10031 14s. lU\-fZ. 
 
 iN VERSE PROPORTION. 
 
 RULE. 
 
 PREPARE tlie fractions and state the question as be- 
 fore, then invert t!ie tliird term, and multiply all the thre^ 
 . ns togetlicr, the product will }Mi the answer^ 
 
.Lii Oif 
 
 1. How nuich h) " h J van! vih \ 
 
 yards ot cloth whi( ; ^ j.wd wide ? 
 
 l'{/s. ?/r/s. yds. ids. 
 
 As 1|:'ai:;| AndJxVx!-vW^l^A'^«^• 
 2. If a man perform a journey in S-} days, v/hen t'^e 
 day is t2-| hours long ; in how many days will lie do \t 
 ^vhen the day is but 9ihoiirs. ' Ans»^^ rrs- daijs. 
 
 S. If IS men in 11 |daj3, rnow ?:1 ,; acres, m how many 
 days will 8 men do i\\^. sarnie. ./^.s. 18|| day^. 
 
 4. How much in leiigth that i^ '' ^ -■ <:s b-oad, wii! 
 make a square foot ? r. 9.^1 wches, 
 
 5. If 25|.s. ^-iU ^^-^^ n>- ^';e Cu..:,,^., ... un cwt. \A5\ 
 miles; how f.:. be carried for the saine mo- 
 ney ? • •. "^'l^^ miles, 
 
 6. How many yards of baize v ! yards wide, 
 will line 18J yVnas of cainbU^^ -^ 
 
 liVLl^ Oi^ THREE DlRKv, TALS 
 
 RULE. 
 
 REDUCE your fractions to decimals, and state yciir 
 question as in wh./le numbers s iKiultipiv the second and 
 third to;;ether; divide by the iirsc, aiid liie quotiont ^vill 
 be the answer, &c» 
 
 t. If I of a vil. 
 come to ? 
 
 Gosfc -j'^2 ^^3 pound ; what will 15^ yds* 
 i^,S75 y7^=,58S+and ^-=5fj 
 Yds. £ 14/5. /;. £. s. iL ^r.5. 
 
 As ,875 : ,583 : ,: 15,75 : i0,494==10 9 10 2,e4Au3 
 2. If 1 pint of wine cost S,2s. ^^'*'■■^ -"=r 13.5 hlids. ? 
 
 ?. If4ijyd3. <:osii3s.4jd. what ;;.L -^^ ' -^* ' 
 
5 
 SIMPLE INTEREST BY DECIMALS. li 
 
 4. If 1,4 cwt. of sugar cost lOdols. 9 cts.what wUl 9 
 cwt. S qrs. cost at the same rate ? 
 
 civt, S cwt, 8 
 
 As 1,4 : : 10,09 ; : 9,75 : 70,£69=g70, 9.6cts. 9?n.-f 
 
 5. If 19 yards cost 25,75 dols. what will 435^ yards 
 come to ? diis. |g590, Qlcts. T-^^m. 
 
 G. If 345 yards of tape cost 5 dols. 17 cents, 5m. what 
 %vill 1 yard cost? Ans, ,015n=licfs. 
 
 7. Ka man lays out 121 dols. 23 cts. in merchandize, 
 and thereby gmns 59,51 dols. how much will he gam in 
 living out \ 2 dollars at the same rate ? 
 
 ..3?fS. 3,91 c/o/s.=S3, 91cfs. ^ 
 
 8. How many yards of ribbon can I buy for 25^ dols. 
 if )Z^l yds. cost 4^ dollai-s } .Ins, ITSh yards, 
 
 9. li 17Sh yds. cost 25i dollars, what cost 5-9| yards ? 
 
 Jlns, mi 
 
 10. If 1,6 cwt. of sugar cost 12 do^s. 12 cts. what cost 
 S hhds. each 11 cwt. 5 qrs. 10,12 lb. .= 
 
 Jus. 269,0:2 t/o/s.:^S269, 7cis. 2m.+ 
 
 SIMPLE INTEREST 
 A TABLE OF 
 
 BY DECIMALS. 
 
 RATIOS. 
 
 Hate per cent. | 
 
 Ratio, 1 Rale 
 
 percent. \ 
 
 Ratio, 
 
 I i 
 
 f 5 ^ 
 
 .03 
 
 ,045 j 
 
 ,05 i 
 
 
 ? 1 
 
 .055 
 
 ,06 
 
 ,065 
 
 ,07 
 
 Ratio is the simple interest of 1/. for one year; or in 
 fg^eral money, of SI for one year, at tht rate per cent. 
 
 agreed on 
 
 RULE. 
 
 Multiply the Principal, Ratio and iimo continually to- 
 gethcr, and the lasi product will be the interest required. 
 
 ESASIPLHS. 
 
 i. Required the intcresiof 21 1 dob. 45 eta, foi' 5 ywr* 
 ^ 5 Ml cent mi &nnmn ? 
 

 SIMPLE INTEREST BY pECtMAJLS. 
 
 S cts, 
 211 ,45 Principal. 
 5O5 Ratio. 
 
 lOjorSo Interest ior (me year, 
 5 Multiply by the time. 
 
 52.8625 £ns.r=.^5Q, SGcts. ^m. 
 
 2. What is the interest of 645/. iOs. for 3 years, at 6 
 per cent, per annum ? 
 
 /;64555x06x5=ll6,l90r:=/;ilG Ss. QtZ. 2,4(/rs. .to. 
 
 S. What is the interest of 1.21/. 8s. 6d. for 4^ years, at 
 J per cent, per annum .^ ^^jis, £32 ids. 8d. lS6qr&. 
 
 4. What is the amount of 536 dollars 39 cents, for IJ 
 yearSj at 6 per cent, per annum ? Ans, S5 84,6651 
 
 5. Required the amount of 648 dols. 50 cts. for ISJyrgi 
 at 5^ per cent, per annum ? Ans, §1103, 26cfs,+ 
 
 CASE II. 
 
 The amount, time and ratio given, to find tlie principal, 
 
 RULE. 
 
 Multiply the ratio by the time, add unity to tlie product 
 
 for a divisor, by which sum divide the amount, and the 
 
 quotient will be the principal. 
 
 EXAMFLES. 
 
 1. What principal will amount to 12S5j9r5 dollars, in 
 5 vears, at 6 per cent, per annum .^ S S 
 
 ,06x5-1-1=1,30)1235,575(950,75 Jns. 
 
 2. What principal will amount to 873/. 19s. inQyeai'S, 
 at 6 per cent, per annum ? Arts^ £567 10?. 
 
 3. W^hat principal will amoiiiitto 626 doi*6 cts. in 12 
 years, at 7 per cent. ? Ans. S340,25=S340, 25ci5. 
 
 4. "Wliat principal will amount to 956/. 10s. 4,1 2od. 
 in 8| years, at 5^ per cent. ? Jhis. £645 15s. *^ 
 
 , » CASE HI. 
 The amount, principal ami liuie given, tcfind the ratio. 
 RULE. — Subtract tlie principal from vhe amount, di« 
 Tide the remainder by tlic product of the time and princi*' 
 T^-^l, and the quotient will be the ratio. 
 
 EXAMPLES. 
 
 -. At what rate per cent, will 950^75 doljf-aQiLOiinf id 
 
 ■■ :^75 doI& m 5 j'ears ? 
 
Fi-om the amount = l!:35,9r5 ^ ^ "^ 
 Take the principal = 950,75 
 
 950,75x5=47'55575)28552250f506=6perccnt 
 .eS5,S250 Ans. 
 
 2. At what rate per cent, will 567/. 10s. amount to 
 875/. 19s. in 9 years ? dns, 6 per cent. 
 
 3. At what r«ite per cent, will 340 dols. 25 cts. amount 
 to 6;J6 dols. 6 cts. in i:'2 years } Jns, 7 per cent. 
 
 4. At what rate per cent, will 645/. 15s. amount to 
 D561. 10s. 4A9.5d, in 8^^ years t Jlns. 5-^ 2Je\' cent. 
 
 CASE IV. 
 
 Tiie amoiuit, f>iiiu:;pal5 and rate per cj;iL r:*'- cn to find 
 
 the time. 
 
 RULE. 
 
 Subtract the principal from the amount; divide the 
 
 remainder bj the protiuct of the ratio and principal : and 
 
 the quotient will be the time. 
 
 EXAMPLES. 
 
 1. In wiiat time will 950 dols. 75 cts. amount to 1235 
 'vollarsj 97,5 cents, at G per cent, per annum ? 
 From the amount SI 235,975 
 Take the principal 950,75 
 
 « ■ .,., , ■ 
 
 950,75x06=:57.0450';285,2250(5 years, M?, 
 
 ' 235,2250 
 
 2. In what time will 567/. lOs. amount to 875/. 19s. 
 at 6 per cent, per annum ^ Jinn, 9 years. 
 
 3. In what time will 340 dols. 25 cts. amount to 6^ 
 dols. 6 cents at 7 per cent, per annum ? Ans. \9^ years. 
 
 4. In what time will 645/. 15s. amount to 956/. 10s, 
 4.125d. at oh per ct. per annum .^ ./^ - 'V*".- v^"" - -•— . 
 
 • -- — ^-^ — 
 
 TO CALCULATE INTERE>ST FOR DAYS. 
 
 ;> Multiply tlie principal by the given number of days, 
 ' and that product by the ratio 5 divide tlie last product W 
 \ 365 (the number of days in a year) and it will give the 
 \ injtere^trefiiiirc^ 
 
fl* 
 
 SlMi-i^K INTEREST BY DECTMALS. ^ 
 j EXAMPLES. 
 
 . {What is the interest of S60Z. 10s. for 146 days^ at 6 
 cent ? 
 S60,5xi46x,06 £, £. s. d. qrs, 
 
 =8653= 
 
 SG5 
 
 565Sr=:8 13 1,9 Ms, 
 
 2. 
 
 at 6 
 
 S. 
 
 5pci 
 
 4. 
 days 
 
 What is the interest of 640 dels. 60 cts. for 100 dayi 
 fer cent, per annum ^ Jlnfi. 310,530^5.+ 
 
 Required the interest of 250?-. iTs. for 120 days at 
 - cent, per annum ? Ms. £4,1235=4L 2s. S^d.-i- ^ 
 
 Required the interest of 481 dollars 75 cents, for 25 
 
 n' '" ' "r annum ? Ms. S-? SOcfs. 9m,+ 
 
 Is. 
 
 
 
 
 
 
 ^ '^ 
 
 ?2 
 
 g< 
 
 p. 
 
 ^?^ 
 
 O 
 
 > 
 
 o 
 
 r 
 1 
 
 •2. 
 
 o 
 
 F 
 
 1 
 
 
 c 
 
 
 
 
 
 
 rD 
 
 'b 
 
 O 
 
 
 5 ~" 
 
 CO 
 
 0- 
 
 cO 
 
 CO 
 
 ^* 
 
 -• 
 
 
 00 
 
 OO 
 
 en 
 
 C7? 
 
 00 r:^-' 
 
 
 
 io 
 
 
 
 
 '." o 
 
 GO 
 
 00 
 
 en 
 
 Cj» 
 
 00 
 OO 
 •^7 
 
 
 1* 
 
 to 
 
 4^ 
 
 ID 
 
 •-- 
 
 H-4 
 CO 
 
 0{ 
 CO 
 
 10 
 
 CD 
 
 a» 00 
 
 CO 
 0( 
 
 00 
 00 
 
 00 
 
 o 
 crj 
 
 
 
 
 Ox 
 
 i 
 
 '-JD 
 
 n 
 
 O 
 
 
 00 
 CO 
 
 00 
 
 o 
 
 
 CJ»*-«i 
 
 1 
 
 CO 
 
 CM 
 
 
 to 
 
 r^ 
 
 C5 
 
 GO 
 
 O 
 
 00 Go 
 CJi 00 
 
 00 
 
 o 
 
 
 
 10^ 
 
 1 
 
 2" 
 
 C>3 
 
 8 
 
 
 
 o 
 
 GO 
 
 CO CO 
 CO O 
 
 07 ,'ii 
 
 ^■1 
 
 00 
 
 
 l# 
 
 
 
 2 
 
 Co 
 
 Cp 
 
 CO 
 
 00 ^o 
 
 ?o 
 
 ^0' 
 
 CO 
 
 4i> 
 
 si" 
 
 CD 
 
 O 
 
 r"t 
 
 CO 
 
 CO 
 
 C'i 
 
 
 - 
 
 oe 
 
 00 
 
 g| 
 
 1 
 
 CT) 
 
 
 
 
 
 
 
 ■- 
 
 0( 
 
 to 
 
 OO 
 
 
 
 0'> 
 
 o 
 
 C'- 
 
 i) 
 
 f^ 
 
 
 
 r.; 
 
 r>: 
 
 io 
 
 o 
 
 t^ 
 
 
 
 0-) 
 
 
 
 
 
 
 
 K> 
 
 
 a 
 
siMr:/i: .xTr.iiF.sr ry decimals. 
 
 5 
 
 W^'hcn interest is to be calculated on casU accounts, &-c. 
 ^v]1ele partial pavments are made : maltiplj ihfi several 
 balar.ccs into tiie days they are at interest, tlicn multiply 
 the Sinn of these products by the rate on the dollar, and 
 divide the ia^t product by 365, and you will have the 
 whole interest due on the account, &c. 
 
 EXAMPLES. 
 
 Lent Peter Trusty, per bill on demand, dated 1st ot 
 Tunc, 1800, ^000 dollars, of which I received back the 
 
 ^ih oC August, 400 dollars: on the 15th of October, 600 
 liars :' on the 11th of December, 400 dollars ; on the 
 
 . rh of February, 1801, 200 dollars; and on the 1st of 
 -. i! 0, ^00 doHars: howniUi:h,interest is due on the bill, 
 
 rccK<inni^ at b i^.^v cer 
 i BOO, 
 
 June 1, Principal per bill, 
 August 19, Keccived in lart, 
 
 dniis, da^js. products. 
 
 October 15. 
 
 Balance, 
 Ueceiveil ia part, 
 
 2000 
 400 
 
 1600 
 600 
 
 Dec^i 
 
 inbcr 1 1 
 
 T^alance, 10 
 
 57 
 
 158000 
 
 91200 
 
 57000 
 
 1801, 
 F.cbruarv 1 
 
 lune J, Rec'<i 
 
 •e-l 
 
 m j)^ 
 
 200 
 
 Balance, 400 
 
 68 ! 40800 
 
 104 41600 
 
 -.88600 
 
 Then G8S600 
 
 ,06 Ratio. 
 
 S cfs. m. 
 
 S65V:^S3l6,00(o3,8r9 ^?z.s. == 05 87 9 -f- 
 
 27ie fallowing liule for computing interest on any nrde^ 
 
 OT ohllgation^ when there are payments inpartn orend(/rse» 
 
 ments^ teas established by the Superior CGiirt of the State 
 
 of Connecticut, in 17S-1. 
 
 RULE. 
 *•' CQinpute tlie interest to the time of the first pay- 
 
174 SIMPLE liVTKHEST BY DECI>rAt.^. « 
 
 ment; if that be one year or more from the time the in- 
 terest commenced, add it to the principal, and deduct the 
 payment frotn the sum total. If there be after payments 
 made, compute i\ie interest on the balance due to the 
 next payment, and then deduct the payment as above; 
 ap.d in like man-ier froia wae payinent to another, till all 
 the payments ai'^ absorbed ? provided the time between 
 one payment and anotiier be one year or more. But if 
 any payment be made before j)nt; year's intei-est liath ac 
 crued, then compufe th^ interest on the principal sum 
 due on the r»' :' ar, add it to the principal, 
 
 and compiitv - sam paid, from the time 
 
 it^vaspaid, up to Uia .nd ;.ttlie year; add it to the sum 
 paid, and deduct tiiatsui!! IVointhe principal and interest 
 added as above, "^ 
 
 " If any pajuienis he rnadc of a less sum than thein^ 
 terest arisen at (he tinie of such payment, no interest is 
 to be computed but only on the* principal sum for anj 
 period . ' ' " Klrbij's liiyaris^ page 49. 
 
 E::A:.irLi:s. 
 A bond, or note, dated January 4th, 1797, was given 
 for 1000 dollar.-, iiit'orest at 6 per cent, and tliere were 
 payments endorsed up<;n it as tollows, viz. §S 
 
 1st payment FeUruarv 19, i798. ' 200 
 
 2d payment Jr, ne 29," 1 799. 500 
 
 Sd payment November 14, 1799. 260 
 
 I demand 1k3w much remains due on said note the 24th 
 of D^.cember, 1 800 ? 
 
 1000,00 dated .lanuary -1, 1797. 
 67,50 interest to February 19, 1798~13i mo7?f/js. 
 
 1067,50 amount. [Carried up 
 
 *If a year does not extend beyond the time of final settle- 
 ment ; but if it does, tiien find th'o amount of the principal sura 
 due on the obligation, up to the tsni^ of settlement, aud bkewiee 
 find the amount of the sum paid, from tbe time it was paid, up 
 to the time of final i^ettlement, and deduct this amount from 
 the amount of the principal. But if tbere he several payments 
 made witbjn tbe said tinje, find tlie amount of the several pay- 
 ments, from the time they were paid, to the time of settlemenj^ 
 wad deduct their amount from the amount of the principal. 
 
SIMPLE INTEREST BY DECIMALS. 175 
 
 1067,50 amount. [Brought up, 
 
 200,00 first payment deducted. 
 
 867,50 balance due, February 19, 1798. 
 70,845 Interest to June 29, 1799=16^ months. 
 
 938,345 amount. 
 
 ^►00,000 second payment deducted. 
 
 438,345 balance due, June 29, 1799. 
 26-jj^^ Interest for one year. 
 
 464,645 amount for one year. 
 
 269-750 amount of third payment for 7^ months,* 
 
 194,895 balance due June 29, 1800. wo. da, 
 5,687 Interest to December 24, 1800, 5 25 
 
 200,579 balance due on the Note, Dec. 24, 1800. 
 RULE II. 
 Established by the Courts of Law in Massachusetts for 
 computing interest on notes^ c^'c. on which partial pay" 
 merits have been endorsed, 
 
 " Compute the interest on the principal sum, from the 
 time when the interest commenced to the first time when 
 a payment was made, which exceeds either alone or in 
 conjunction witii the preceding payment (itany) the in- 
 terest at that time due : add that interest to the princi- 
 pal, and from the sum subtract the payment made at that 
 time, together with the precedin;^ payment (if any) and 
 the remainder forms a nesv principal ; on which compute 
 and subtract the payments as upon the lirst piincipal, 
 and proceed in this manner to the time of final settle- 
 ment." 
 
 8 cts. 
 *260,00 third payment with its interest from the time it 
 9j75 ivas paid^ np to the end of the year^ or fror 
 ' ■■ ■• JV or. I i- ;^99, to June 29, 1800, which i$ ' / 
 £69,75 amount. '^wi^ki ! 
 
»r6 SIMPLE INTEREST BY SECI^IALS. 
 
 Let the foregoing example be solved by tiiis Rule. 
 
 A note for 1000 dols. dated Jan. 4, 1797, at 6 per cent* 
 1st payment February 19, 1798. g200 
 
 2d payment June 29, 1799. 500 
 
 3d payment November 14, 1799. 260 
 
 How much remains due on said note the 24t]i of De 
 
 cember, 1 800 ? g cts. 
 
 Principal, January 4, 1797, 1000,00 
 
 Interest to Feb. 19, 1798, (15^ Vdo.) 67,50 
 
 Amount, 1067,50 
 Paid February 19, 1798, 200,00 
 
 Remainder for a new principal, 867,50 
 
 Interest to June 29, 1799, (16^- mo,) 70,84 
 
 Amount, 938,34 
 
 Paid June 29, 1799, 500,00 
 
 Remains for anew principal, 438,34 
 
 Interest to November 14, 1799, (4i mo,) 9,86 
 
 Amount, 448,20 
 
 November 14, 1799, paid 260,00 
 
 Remains a new principal, - 188,20 
 
 Interest to December 24, 1800, (15i vio ) 12,70 
 
 Balance due on said note, Dec. 24, 1800, 200,90 
 
 S cts. 
 
 The balance by Rule T. 200,579 
 
 EyRule 11. 200,990 
 
 Difterence, 0,4 U 
 
 Another Example in Rule II. 
 
 A bond or note, dated February 1, 1800, was given fo" 
 
 500 dollars, interest at 6 per cent, and there were pay 
 
 ments endorsed upon it as follows, viz. S cts, 
 
 1st payment May l, 1800, 40,00 
 
 2d payment November 14, 1800, 8,00 
 
COMrOUND INTEREST BY DEOIMA1.S. 177 
 
 Sd payment April 1, 1801. 12,00 
 
 4th payment May 1, 1801. v^0,00 
 
 How much remains due on sa'*! »j«»m» tJ^e i-r.. o' »«0(> 
 
 tember, 1801 ? 6 •*». 
 
 Principal dated February 1, 180U, d'JO,00 
 
 Interest to May 1, 1800, (3 wo.) 7,50 
 
 Amount, 507,50 
 Paid May 1, 1800, a sum exceeding the interest, 40,00 
 
 467,50 
 year.) _ 28,05 
 
 New principal, May 1, 1800, 
 Interest to May 1, 1801, (1 ; 
 
 Amount, 495,55 
 Paid Nov. 4, 1800, a sura less than the 
 
 interest then due, 8,00 
 
 Paid April 1, 1801, do. do. 12,00 
 Paid Mav 1, 1801, a sum greater, 30,00 
 
 50,00 
 
 New principal May 1, 1801, 445,55 
 
 Interest to Sep. 16, 1801, (4i mo,) 10,02 
 
 Balance due on the note, Sept. 16, 1801. ^455,57 
 ICJ* The payments beirtg applied according to thh Rule, 
 Jceep down the interest^ and no part of the interest ever 
 forms a part of the principal carrying interest, 
 
 COMPOUND INTEREST BY DECIMALS. 
 RULE 
 
 MULTIPLY the given prinvipal continually by the 
 amount of one poosid, uron*: diJUi, for one yeai^at the 
 rate per cent, given, until the number of multiplications 
 are equal to the given number oC years, and the product 
 will be the amount recjuired. 
 
 Or, In Table 1. Appendix, find tiie amount of one dol- 
 lar, or one pound, for the given number of years, which 
 multiply by the given principal, and it will give the 
 tmount as before. 
 
17S rN VOLUTION. 
 
 ■VPLES. 
 
 1. Wh-; to in 4 ye^ii-u at G per cent. 
 
 per:: 
 
 ^:504,99-f or 
 
 : /;oo-'i ivs. '^a. ^ -- .^?25. 
 
 ';'.:c :::Mne bv Table 1. 
 
 V amount - 
 
 £. Required t!ie aincunt cf 425 dols. . 3 years, 
 
 at 6 per cent, coiripound iriterest. .1. .7^cfs.-f 
 
 5. What is the compound interest o^ 5Ji' dels, for 14 
 years, at 5 per cent. ? Bj Table L Ans, go-lo^secf^.-f 
 
 4. What will 50 dollars amount to ia 20 years, at 6 per 
 cent, compound interest ? t^ns, gl60'35cts'. &lm. 
 
 ^ INVOLUTION. 
 
 Is the multiplying^ any nimber with itself, and that pro* 
 duct by the former multiplier ; and so on 5 and ^^(i several 
 products which aris€ are called powers. 
 
 Tlie au)iiber denoting the height of the power, Is called 
 the index, or e:?ponent of that pov/er. 
 
 EXAMPLES 
 
 What is the 5th power of 8 ? 
 8 the rooter ist po^.vcr. 
 8 
 
 64 = 2d po^ver, or square, 
 8 
 
 519. = ZiX power, orxube. 
 
 4096 = 4th power, or biquadrate. 
 8 
 
 52768 =» 5th power, or surselld. Jim. 
 
-iwvOLUHON, OR EXTRACTION OF UOOTS. 179 
 
 What is the sqiiajc ol 17,1 ? .'his, :02,4l 
 
 What is the square of ,085 ? J./ . ,«.:;: 25 
 
 What is tlic cube of 25,4 ? * .;.-.-. ' 
 What is tlie biquadrate of 12 ? 
 
 What is the square of 7^ ? ^Li ■ ,. 
 
 EVOLUTION, OR EXTRAC'»(fN OF ROOTS. 
 
 W HEN the root of any powei is required, the busi- 
 ness of finding it is called the Extraction of the Root. 
 
 The root is that number, whicli bv a continual multipli- 
 cation into itself, produces the given power. 
 
 Although there is no number but what will produce a 
 perfect power by involution, jet there are manj numbers 
 of "xhiQii precise roots can never be determined. But, by 
 the li^eip of decimals, we can approsimrite towards the 
 root to any assigned degree of exactiiej^s. 
 
 The roots which approximate, are called surd roots, 
 and those wliich are perfectly accutate are called rational 
 roots. 
 
 A Table of the Squares and Cubes of the rdri£ digits. 
 
 Roots. 
 
 |1 
 
 2 
 
 s 
 
 ^ 
 
 5 
 
 6! 
 
 T 
 
 8| 
 
 9 
 
 Sq'iiares. 
 
 11 
 
 4| 
 
 9 
 
 IG 
 
 25, 
 
 S6| 
 
 49 
 
 64 1 
 
 81 
 
 Cubes. 
 
 M 
 
 i«! 
 
 il7 
 
 64 
 
 i i^irf 
 
 -3 J 6 
 
 343 
 
 512 1 
 
 729 
 
 EXTRACTION OF THE SQl^VKS ROOT. 
 
 Any number multiplied into itself produces a square. 
 
 To extract the square root, i- nlv to lind a {lumber, 
 which being multiplied into itself. duce the giveo 
 
 number. ' ^ 
 
 RULE. 
 
 1, Distinguish the given number into periods of two 
 figures each, by putting a point over the place of units, 
 another over the place of hundreds, and Sv) on ; and if 
 tliere are decimals, poiut them in tlie same manner, from 
 units towards the right band ; whicl« noJn^^ siiow tke 
 Uttmber of figures ti^e r^ot will ro^lsif »!'. 
 
 S. Fiud tii« gi-eatest «(n:are uunibcT lu the tirst^ or teft 
 
 / 
 
J 80 EVOLUTION, OR fiXTKACTiOM OF ROOTS. 
 
 hand period, place tlie root ot it at the riglit hand of the 
 given number, (after the iganner of a quotient in division) 
 for the first figure of the root, and the square number 
 under the period, and subtract it therefrom, and to the 
 remaindei briiig down the iiexi period for a ^dividend. 
 
 S. Place the double of the root, already found, on the 
 left hand of the divklaad for a divisor. 
 
 4. Place such a figure at the riglit hand of the divisor, 
 and also the same figure in the root, as when multiplied . 
 into the whole (increased divisor) the product shall be 
 equal to, or the next less tiian the dividend, and it will be 
 the second figure in the root. 
 
 5. Subtract the product from the dividend, and to the 
 remainder joio the next period for a new dividend. 
 
 6. Double the figures already found in the root, for a 
 new divisor, and from these find the next figure in the 
 root as last directed, avid continue the operation ift the- 
 same manner, till you nave brought down all the periods. 
 
 Or, to facilitate' the foregoing Rule, when you have 
 brought down a period, and formed a dividend, in order 
 to find a new figure in the root, you may divide said divi- 
 dend, (omitting the right hand figure thereof,) by double 
 the root already found, and the quotient will commonlv 
 be the figures sought, or being made less one, or two,v^iri 
 generally give the next figure in the quotient. 
 
 EXAMPLES. 
 
 1. Hequircd the square root of 141225,64. 
 141225,64(375,8 the root Exactly without a remaindcF ; 
 9 but when the periods belonging to any 
 
 — given number are exhausteu, and still 
 
 67,512 leave a remainder, the operation may 
 
 469 be continued at pleasure, by alnn^xiflg 
 
 . periods of cyphers, &c. ] 
 
 745)4325 
 5725 
 
 7508)60064 
 G0064 
 
 '} tCtoamvc 
 
EVOLUTION, •R EXtllA«TION OF ROOTS^ kl i 
 
 2. What is the 
 
 square 
 
 root of 1296 ? 
 
 *Mswers^ 
 36 
 
 5. Of 
 
 
 56644 r 
 
 
 4. Of 
 
 
 0499025 » 
 
 5. Of 
 
 
 36372961 P 
 
 -;" 6(1 >^ 
 
 6. Of 
 
 
 !84,4P 
 
 < • K^,5? + 
 
 r. Of 
 
 
 9712,693809? 
 
 9^,5 ^S 
 
 8. Of 
 
 
 0,45569 ? 
 
 56/3+ 
 
 9. Of 
 
 
 ,002916 ? 
 
 ,054 • 
 
 10. Of 
 
 
 45? 
 
 6,708-f 
 
 TO EXTRACT THE SQUARE ROOT OF 
 
 VUL«IAR FRACTIONS. 
 
 RULE. 
 
 Btduce ihe fraction to its lowest terms ibr this and all 
 other roots ; then 
 
 1. Extract the root of th« nuinerator for a new nume- 
 rator, and the root of the denominatt4> for a new denomi- 
 nator. 
 
 2. If -the frtctioa be a surd, reduce it to a decimal, and 
 extract its root. 
 
 EXAMPLES. 
 
 1. What is the square root of -^f^^- ? ^ns. -| 
 
 2. What i# the square yoot of -^%\^ ? Jlns. ^| 
 5. What is the square root of ||| ? .^ns. ^ 
 
 4. What A the square root of 20^ ? ^^s. 4i 
 
 5. WhatT the square root of 243^^ ? ^^ns. 15 i 
 
 SURDS. 
 
 6. What is the squart root of |^-? Mb. 9I3«-f 
 
 7. What is the square root of 4^| ? Ans, ,7745 -f 
 
 8. Required the square poot of 56:t ? ^ns. 6,0207+ 
 
 APPLICATION AND USE- OF THE SQUARE 
 ROOT. 
 
 P'roulem I, .A certain Gonefa] r^s ansinnjor SlU'i 
 men ; how many must he place m rank am Uq* to faun 
 V h (» !n into a giiua re ? ., 
 
tTOo 
 
 A KVOLUTIOK, OB. EXlWoTION OJf ROOTS. 
 
 .^ ^ RULE. 
 
 ^ Extract the square root of the given number. 
 
 ^/5184=r2 Ans. 
 
 i. :l A certaifi square pavement contains 20rSe 
 ' ; ' • c:.^ ^ul't CI tJie sariiC si/.e : I demaiid how many 
 
 . .v-: .u M.i,. .:X A:: side: ? v/2073G==:i44 dns^ 
 
 K)H, iix, io liiida mean proportional between two 
 lumbers. 
 
 RULE. 
 Multiply the given numbers together, and extract the 
 square root of the product. 
 
 EXAMPLES. 
 
 What is the mean pjoportional between 18 and 72 ? 
 72x18^1296, and v/1296=36 dns. 
 
 pROB. IV. To form any body of soldiers so tliat thcj 
 may be double, triDle, vkc.*^ as many in rank as in file- 
 RULE. 
 Extract tiie square root of 1-2, 1-3, &c. of the given 
 . imniutjf of iueiiu and that will be the number pf men in 
 ^I" r. i! double, triple, 5cc. and theproduc?t will be the 
 .■Ilk. * 
 
 EXAMPLES. 
 
 I be so farmed, as tiiat the mimber in 
 : ■;:'e the number in file. 
 .-:.r^u. i. and v^656l=81 in fUe, and 81x2 
 U: rank, 
 -'"OB-r^V. Admit 10 hhds. of water are^ischarged 
 ;:^ii. a leaden pipe of 2^ inches in diamelW, in a cer- 
 • iij.'ie; 1 demand what the diameter of another pipe 
 >:»- be, to discharge four times as much water in the 
 ^ Hme. 
 
 RULE, 
 ijuare the given drameter, and multiply said square 
 i>y the given proportion, and the square root of the pro- 
 duct is the answer. 
 
 S^««2,5, and 2^x2,5=6,25 square. 
 
 4 given proportion. 
 
 y^'y.OOrrsS iJKh. dlam. Ans. 
 
EVOLUTION, OR EXTli ACTION ,0F aoOTS. 183 
 
 PiioB. VI. The sum of any two numbers, and ihev 
 products being given, to find each number. 
 RULE. 
 
 From the square of their sum, subtract 4 lir • 
 product, and extract the square root of t^e i.^ 
 which will be the difference of tlie tuo r,- „ j 
 
 half the said difterence added to half tie ^n/^fV p^^ tSf 
 greater cf tl^e two numbers, and the said \w'f mflli^* ^ 
 subtracted from the half sum, gives the lessei ^ix^iU<i^i. 
 
 EXAMPLES. 
 
 The sum of two numbers is 43, and their product r 
 
 442 ; what are those two numbers ? 
 
 The sum of the numb. 43x43=1849 square of do 
 The product of do. 442x 4 = 1768 4 times the ^r- 
 
 Then to the ^ sum of 21 ,5 rnruii/. 
 
 -fand— 4,5 v'81=9 diff. ofthf 
 
 Greatest numb. 26,0 ^ 4^ the h diff, 
 
 ^Answers. 
 
 Least numb. 17,0 J 
 
 EXTACTION OF THE CUBE HOOT. 
 
 A Cube is anj number multiplied by its square. 
 
 To extract the cube root, is to find a number, which, 
 being multiplied into its square, shall produce the given 
 number. 
 
 RULE. 
 
 \. Separate the pven number into periods of iluee fig- 
 ures each, by putting a point over the unit figure, and 
 every third figure from the place of units to the left.; and 
 if tliere be decimals^ to the right. 
 
 2. Find the greatest cube in the left liand period, and 
 place its root in the quotient. 
 
 S. Subtract the cube thus found, from the said period, 
 and to the remainder bring down tlie next period, calling 
 this tlie dividend. 
 
 4, Multiply the suqare of the qiiotient by SOO, cM\jit 
 it the divisor. 
 
184 EVOLUTION, OR KXTIIACTION OF KOOra. 
 
 5. Seek how often tlie tUvisoi^mav be had in the divi- 
 dend, and place the vamlt in the quotient : then multiplj 
 the divisor by this hist quotieiit tigure, placing tlie pro- 
 duct under the dividend. 
 
 6. Multiply the foniier quotient figure, or %ures bj 
 the square of the last quoiiejit figure, and that product bv . 
 SO, and place the product unikr tho last ; then under these 
 t^vo products place the cube 5;f !■ o !a,s( r« i^oli en t figure, and 
 
 ^fi*iH|i]-f together, cal»L ■ trahend. 
 
 ^ '7:mMrm the subtra . . ^ idend, and to ' 
 
 the remainder bring down the next period for a new divi- 
 dend : with which proceed in tii same manner, till the 
 whole be finished. • 
 
 Note. — If the subtrahend (found bj the forego? ng rule) 
 happens to be greater than the dividend, and consequent- 
 ly cannot be subtracted f ' . vou must make the 
 last quotient figure oi^e ( which find a uew sub- 
 
 trahend, fby the rule forc-;j, ;. i^^;) dud so on until you can 
 subtract me subtrahend froia tlka dividend. 
 
 EXAMPLES. 
 
 1. Required the cube root\f 18399,744. 
 
 18399,744(^26.4 Root, dns, 
 8 
 
 2X2=4X500 = 1200)10399 first dividend. 
 
 7200 
 
 6x6=S6x2=r£x50=rr2i60 
 
 6x6x6= 216 
 
 9576 1st subtrahend. 
 26x26==676x300=«202800)82Sr44 2d dividend. 
 
 811200 
 
 4x4=l6x26=:416x50==: 12480 
 
 4X4X4=== 64 
 
 825744 Sd subtrahend. 
 
JBiyOtUTIOXj on EXTRACTION OF ROOTS. 18;:; 
 
 Note. — The foregoing example gives a perfect root; 
 and if, when all the periods are exhausted, there happens 
 to be a remainder, you may annex periods of cyphers, and 
 continue the operation as far as you think it necessary. 
 
 2. What is the cube root of 205379 ? 59 
 
 614125? &"> 
 
 41421736 .> 546 - 
 
 146363,183.^ 5%r 
 
 ' 2S,5036£9.J^ 3,09 -f 
 
 ' 80,763 ? 4,3£ V 
 
 ,162771336.? ,!A6 
 
 JjQuQS^ i 34 r- *"■ '"' ^ - 
 122615527232"^ 
 
 1. Find by trial, a oil he near to .'• 
 call it the supposed cube. 
 
 2. Then as twice the supposed cube, addci} tothegiv 
 en number, is to twice the given number added to the 
 supposed cube, so is th» ioot of the supposed cube, to 
 the true root, or an approximation to it. 
 
 3. By taking tlie cube of the root thus found, for the 
 supposed cube, and repeating the operation, the root wili 
 be liad to a greater degree of exactness. 
 
 EXAMPLES. 
 
 Let it be requii-ed to extract the cube root of 2. 
 
 Assume 1,3 as' the root of the nearest cube; then— 
 l,Sx.l,3xl,3==2,197=supposed cube. 
 ' 'fhen, 2,197 2,000 given number. 
 
 4.394 4,000 
 
 2,000 2,197 
 
 As 6,394 : G,197 : : K3 : 1,2599 root, 
 which is true to the last place of decimals ; but might by^ 
 repeating the operation, be brought to greatei exactness, 1 
 2. What is the cube -oot of 584^277056 
 
IS6 EVOLUTION, OR EXyilACTICK OF ROOTS. 
 
 5. Required the cube root cf 729001101 ? 
 
 Ms, ^0050094 
 
 QUESTIONS, 
 
 Showing the use of the Cube Root, 
 
 1. The statute bushel contains 2150,425 cubic or solid 
 fhclies. I demand th5 fide of a cubic box, which shall 
 contain that qufmtitj ? 
 
 f/21 50,425=12,907 inck. dns. 
 Note. — TliD Solid contents of si»rmlar figures are in 
 proportion to each othm*, as the cubes of their similar 
 sides or diameters. 
 
 2. If a bullet 3 inchef diameter, weigh 4lb. what will 
 a bullet of the Sftme metal weigh, w^hose diameter is 6 
 inches? ^^^ 
 
 SxSx3=»t27 6x6x6=216 As 27 : 4lb. t : 216: 
 52lb. Ms. 
 
 S. If a solid globe of silver, of 3 inche?s diameter, be 
 wortli 1 50 diOUars ; what is the value of anotlicr globe of 
 silver, whose diameter is six inched r S 
 
 3x3x3=27 6x6x6=216 As 27 : 150 : : 216 •: 
 gl200. Ms. 
 
 The side of a cube being given, to faid the side of that 
 cube wich shall be double, triple, &c. in (]fuantitj to the 
 given cube. 
 
 RULE. 
 
 Cube your ^/vcn side, and multiply by the given pro- 
 portion betwi?;en the given and required cube, and tlic 
 ciube rof>t of the product will be the side sought. 
 
 4. If a cube of silver, whose'side is two inches, be worth 
 20 dollars; I demand the side of a cube of like silvei;;, 
 whtSe value shall be 8 limes as much ? 
 
 2x2x2=8 and 8x8=64^64=4 inches. Ms, 
 
 5. There is a cubi«cal vessel, whose side is 4 feet: I 
 demand the side of another cubical vessel, w'nich shall 
 contain 4 times as much ? 
 
 4x4x4=64 and 64x4=256^256«=6,549-j;A. .^'^?. 
 €i A cooper Imving a cask 40 incl^? lon'r, ;:'''♦ f;;' •''- 
 
, ^ riOX OF ROOTS. > ";, 
 
 c:h;^ ai u>»^ liung diainelei', is ojdered ft) make anotlier 
 cask of the same shape, but to hold just twice as much ; 
 \vhat will be the bung diameter and length of the new 
 cask ? 
 
 40x40x40x2=128000 then ^3/ 128000 =50,3+ length. 
 32x52x32x2=65o3(i and -^>'G55S6==40.3+&u?z^ dtam. 
 
 J General Rule for Exivactin^ the Roots of all Powers, 
 RULE. 
 
 1. Prepare iJat given iiiin!]>er for extraction, by point 
 ing off* from tlie unit's place, as the required root directs 
 
 2. Find the first figure of the root by triiil, and subtract 
 its power from tlie left hand period of t'le given number. 
 
 5. Totlie remainder bring down tlie first fignre in the 
 next period, and call it the dividend. .J** 
 
 4. Involve the root to the next inferior power to t'hat 
 which is given, and multiply it bj the number denoting 
 the given power, for a di^sor. 
 
 5. Find how many times the divisor may be had in 
 W\^ dividend, and ^^ c^uotient will be another figure of 
 the root. 
 
 6. Involve the whole root ioih^ given power, and sub- 
 tract it (always) from as many i^cj'iods of the given num 
 ber as you have found figures in the root. ^^^ 
 
 r. Bring dovrn the first figure of the nQ::{i period tt) the 
 remainder for a new dividend, to wliich find a new divi- 
 sor, as before, and in like manr^cr proceed till the whole 
 be finished. 
 
 Note. — Wlicn the number to be subtracted is greater 
 than those^periods from which it is to be ^ >.^:' v ^'^^ l-^-^t 
 quotient figure must be taken less, &c. 
 
 EXAMPLES. 
 
 1. Required the cube root of 135790,744 by the above 
 I^Qiicral melihod. 
 
^Sb # ?iYOX*uTmN, on ExyRACTioN- v^ir aoots. 
 
 155796744(51,4 the root. 
 125=t=lst subtrahend 
 
 75) lOr dividend. 
 
 132651 =2d subtrahend, 
 rSOS) S1457=2d dividend. 
 
 155r96r44=3d subtraltend. 
 
 5x5x3=75 iirst divisor. 
 51x51x51=132651 second subtranend. 
 51x51x3=7803 second divisor. 
 514x514x514=135796744 third subtrahend. 
 
 S. Required the sursolidj or fifth root of 6436345. 
 6436348'J23 root 
 
 2X2X2X2X5=80)323 dividend. 
 23X23X23X23X23=6436343 subtrahend. 
 
 Note..— The roots of most powers may be found by the 
 square and cube roots only 5 therefore, when any even 
 power is given, the easiest method will be (especially in 
 a very high power) to extract the square root of it, which 
 reduces it to half tiie given pov* er, then the square root of 
 that power reduces it to half the same pov/er ^^and so on^ 
 till you come to a square or a cube. 
 
 For example: suppose a 12th power be given; the 
 square root of that reduces it to a sixth power : and the 
 square rapt of a sixth power to a cube, 
 
 EXAMPLES. 
 
 3. What is llie biquadrate, or 41h root of 19957173576 i 
 
 Jns. 37G. 
 
 4. Extract tlie square, cubed, or 6feh root of 1223059( 
 464. ' *^)is. 48. 
 
 5. Extract the square, biquadrate. or Stli root of 72131 
 95789358SS6. Jlns. 96 
 
ALLIGATION, 
 
 Is the mciliocl of mixing several siin|^!e3 of liifterent qual- 
 ities, 90 that the composition may be of a mean or middle 
 quality ; It insists of two kinds, viz. Alligation Medial, 
 and Alligation Alternate. 
 
 ALLIGATION MEDIAL, 
 
 Is wlien the quantities and prices of several things are 
 given, to find the mean price of the mixture composed of 
 'those materials. , 
 
 RULE. 
 
 As the -vvliole composition : is to the whole value : : so 
 }s any part of tliji composition : to its mean price. 
 
 EXAMTLES. 
 
 1. A farmer mixed lo busliels of rye, at 64 cents a 
 bushel, 18 bushels oF Indian corn, at 55 cts. a bushel, and 
 21 bushels of oats, at 28 cts. a bushel 5 I demand '^vhat a 
 bushel of this mixture. is v/orth.^ 
 
 hu. cts. ^cts. . hu, g cts. III. 
 15 at 64=9,60 As 54 : 25,38 : : 1 
 18 55=^-9,90 1 
 
 21 Ii8=5,8S cii^. 
 
 — , 54)25.58(,4r Answer. 
 
 54 25,3S 
 
 2. If 20 bushels of wheat at 1 dol. S5 cts. per bushel, 
 be mixeil with 10 busliels of rye at 90 cents per bushel, 
 what will a bushel of tjiis mixi'jve be wcrlli r 
 
 Jns. St, 9.0cis. 
 
 3. A Tobacconist mixed 36 lb. of Tobacco, at Is. 6d. 
 r lb. 12 lb. at 2s. a pound, v/ilh 12 lb, at Is. lOd. per 
 
 :b.5 what is the price of :. ' this nuxture ? 
 
 Alls. is. Sd. 
 
 4. A Grocer mixed 2 C. of t-u<^ar, at 56s. per C. and 1 
 C. at 433. per C, and 2 C. at 50s. per C. together 5 I de- 
 mand tlic price of 3 cwt. of this mixture ? Ans. £7 ISs. 
 
 5. A Witie merchant mixes 15 gallons of wine at 4s. 
 2d. per gallon, with 24 gall or* s at 6s. £d, and 20 gallons, 
 at 6s. Su. ; what is a i>;ai!ou of tliis composition worth P 
 
 Ans. 5s. IQd. 2f|grs. 
 
 r,. 
 
6. A grocer hith several sorts of sugar, v'iz. one sort? 
 p.t 8 ilols. percwi. an other sort at 9 dols. per cwt. a third 
 sortxit lOtiols. percvvt. and a Iburth sort at 12 dols. per 
 cwt. and he v.ould mix an equal quantityl)f each togeth- 
 er; I demand the price of 3\ cwt. of this mixture ? 
 
 \^ns, S34 IQcts. 5m. 
 
 7. A Goldsmith melted together 5 lb. of silver bullion, m 
 of 8 oz. fine, 10 It^. of 7 oz. fine, and 15 lb. of 6 oz. fine ; • 
 pray what is the quality, or fineness of this composition i* 
 
 Jlns. 6oz. ISpwt, ^gi\jini>r 
 
 8. Suppose 5 lb. of gold of 22 carats fine, 2 lb. of 2! | 
 c;iratB fine, and I lb. of alloy be melted together ; what is 1 
 the quality* or ilneness of this n^.ass ? \ 
 
 Jins. 19 carats f.na 
 
 ALLIGATION ALTERNATE, 
 
 IS the method of finding what quantity of each of the 
 ingredients, whose rates are given, will compose a mix- 
 ture of a given rate ; so that it is the reverse of alligation 
 medial, and may be proved by it. 
 
 CASE. I. 
 
 When the mean rate ot the whole mixture, and ihe 
 rates of ail the ingredients are given without any }in\ited 
 
 quantity. 
 
 "^ RULE. 
 
 ^ 1. Place tliC several i-ates, or prices of the simples, be- 
 ing reduced to one denomination, in a column under each 
 other, and the meaa price in the like name, at the left 
 hand. 
 
 2. Connect, or link, the pnce of each sim.ple or ingre- 
 dient, v/hich is less than that of the mean rate, with one 
 f)r any number of those, whicii are greater than the mcaa 
 rdt^^ and each greater rate, or price with one, or any 
 number of the less. 
 
 S. Place the difference, betv/een the mean price (or 
 mixtui^c rate) and that of each of the simples, opposite 
 to tno rntcs with which thev are connected. 
 
ALLIGATION ALA iill.S A IE. l9i 
 
 4. Then, if only one difference stands against an^ r;ite, 
 it will be the quantity belonging to that rate, but it there 
 be itieveral. their sum will be the quantity. 
 
 J^ EXAMPLES. 
 
 1. A merclflnt has spices, some at 9d. per lb. some at 
 ^s. some at S and some at 2s. 6d. per lb. how much of 
 ^. ch sort must lie mix, tliat he may sell tlie mixture at Is 
 8d. per pound ? 
 
 d. d. lb. d lb, 
 
 f 9 ,10 at 9^. . r"9^ 4*^ .^• 
 
 d.JliTi 4 12 [^Glvesthe d,\ 12-f-^ 10 [ g 
 
 20 ] 24 J I 8 24 r-'hisirer, or 20 ] 24 J j H f g 
 
 ^ 
 
 24J j 11 j^l 
 50 — ^ 8j '^S 
 
 (^30_^ll 30 J {J 
 
 2. A gi*acer would mix the ibilov/ing quantities of su- 
 gar 5 viz. at 10 cents, 13 cents, and 16 cts. per lb. : what 
 quantity of each sort must be taken to make a mixture 
 worth 12 cents ner pound ? 
 '^na. Sib. at lOcis. ^Ib. at \Scts. and 9lb. at 16 cts. per lb. 
 
 5. A grocer has two sorts of tea, viz. at 9s. and at 155. 
 per lb. how must he mix them so as to afford the compo- 
 sition for 12s. per lb. .^ 
 
 Ans. He must mix an equal quantity of each sort. 
 
 4. A goldsmith would mix gold of 17 carats fine, with 
 some of 19, 21, and 24 carats line, so that the compound 
 may be 22 carats tine j what quantity of eacli niubt h^ 
 take. 
 
 ^ns. 2 of each of the first three sorts^ and 9 of the last. 
 
 5. It is required to mix several sorts oi rum, viz. at 5s. 
 . and 9s. per gallon, with water at per gallon to- 
 
 !Z:cthcr, so that the mixture may be worth 6s. per s:allon ; 
 [low much of each sort must the mixture consist of .^ 
 *ins. 1 gal. of Rum at 5s. 1 do. at 7s. 6 do at 9s. and 3 
 
 fals. water. Or^ 3 gals, mm at 5s. 6 do. at 7s. 1 
 o. at 9s. and 1 gal. water. 
 
 6. A grocer hath several sorts of suf^ar, vi/.. one sort 
 at 12 cts. per ib. another at 11 cts. a tiiird at 9 Cts. and a 
 fourth at 8 cts. per lb. ; 1 demand how much of each sort 
 ;i»ust he mix together, that tlie whole <Ji;-u;(ily may bi> 
 ifitfrdrd at 10 &wU ;;cr noinni - 
 
W^ ALTEIINATIOK IPARTIAIii. 
 
 ^. cts, lb. cts. lb. cts. 
 
 f £ at 12 ri at 12 fs at 12 
 
 Ist Anq ^ 1 at 11 , . J 2 at 11 ^ , ^^ J 2 at 11 
 
 Uat 8 Llat 8 IB tsat 8 
 
 4th Ans. Slh, of each sort.'* w 
 
 CASE 11. 
 
 ALTERNATION PARTIAL. 
 
 Or, when one of the ingredients is limited to a certain 
 quantity, tlience to find the several quantities of therest> 
 in proportion to the quantity given. 
 
 RULE. 
 
 Take the difterenee between each price, and the mean 
 rate, and place them alternately as in Case L Then, as 
 the difference standing j^ainst that simple whose quantity 
 IS given, is to that quantity : so h each of the other dif- 
 ferences, severally, to the several quantities required. 
 
 EXAMPLES. 
 
 1. A farmer would mix 10 bushels of wheat, at 70 cts. 
 per bushel, with rye at 48 cts. corn at SQ cts. and barley 
 at 30 cts. per bushel, so that a bushel of the composition 
 ma J bci^old for 58 cents ; what quantity of each must 
 be taken. 
 
 rzo- — ^ 8 sptands against the given quan« 
 Moan .ate, SsJg | f, ftity 
 
 [so i 3-2 
 
 As S : 10 
 
 F 2 : 2^^ bushels of rye. 
 ; •< 10 : 12 i bushels of corn. 
 (^32 : 40 bushels of barley. 
 
 * Th^se four answers arise from as nmny various ivaij^ 
 of linking the rates of the ingredients together. 
 
 Questions in this rule adrdit cf an infinite variztif of an- 
 swers : for after the quantities are found from different 
 inetkods of Unking ; any other numbers hi the samevropor- 
 tion between themselmSyaSithemmioers which compose the 
 ^nswor^ imll Jifce;t%^5 saii0 the conditions ofih^i^u^tion 
 
ALiKRNATlON PARilAA- AiSh 
 
 2. How much water miist be mixed with lOO gallons 
 of rum, worth 7s. 6d. per gallon, to reduce it to 6s. Sd. 
 per gallon ? Jim, 20 gallons, 
 
 S, A farmer would mix 20 bushels of rye, at 65 cents 
 
 Eer bushel, witii barley at 51 cts. and oats at 30 cts. per 
 ushel ; how much barley a?ul oats must be mixed with 
 the £0 bushels of rye, that the provender may be worth 
 41 cents per bushel ? 
 
 ^ns. 20 bushels of bavhij^ and 61^ bushels of oats. 
 4, With 95 gallons of rum at 8s. per gallon, I mixed 
 other rum at 6s. 8(1. per gallon, and some water; then 1 
 found it stood me in 6s. 4d, per gallon 5 I demand how 
 much rum and how much water I took ? 
 
 ^^ns. 95 gals, rum at 6s, S(L and SO g^als, water. 
 
 CASE III. 
 
 When the whole composition is linl^ted to a given quantity. 
 
 RULE. 
 
 Place t:LC diflerence between tlie mean rate, and the 
 several prices alternately, as in Case I. ; then, As the 
 sum of the quantities, or diflerence thus determined, is to 
 the given quantity, or whole composition : so is tiie diife- 
 renceof each r^Ucjto the required (quantity of each rate. 
 
 EXAMI'LES. 
 
 1, A grocer had ("our sons of tea, air Is. 5s. 6s. and 10s. 
 per lb. tiie worst would not sell, and the best were too 
 dear; he tluuefore mixed UMilb. and so much of each 
 sort, as to sell it at 4s. per lb. 5 how nuich of each sort did 
 ne take ? 
 
 >V^T 
 
 s. 
 
 lb. 
 
 Vk 
 
 1 — ^ 
 
 6 
 
 "6 
 
 S^ 
 
 2 Ih. Ik 
 
 6J 
 
 I As 12 : 12Q ; 
 
 :^ 1 
 
 10-— J 
 
 3 
 
 ^3 
 
 60 
 
 at 
 
 1-^ 
 
 20 
 
 —. 
 
 S 
 
 10 
 
 «» 
 
 6 
 
 30 
 
 .^ 
 
 10 
 
 Sum, 12 120 
 
 i[7 
 
.■^.i AIUTHMETICAL rKOGKESSION. 
 
 2. Hcrvy much water at per galloiu must be mixed 
 with wine at 90 cents per gallon, so as to iill a vessel of 100 
 gallons, which may be ailbrded at 60 cents per gallon ? 
 ^n's. 334 gals, ivater^ and 6o-| gals, ivine. 
 S. A grocer having sugars at 8 cts. 16 cts. and 24 cts. 
 per pound, would make a comptisition of 240 lb. worth 
 £0 cts. per lb. without gain or loss ; what quantity of each 
 must be taken ? 
 
 ^ns. 40 lb. at 8 cts. 40 (d 16 cts. and I16O at 24 cts, 
 
 4. A goldsmith had two sorts of sliver^ bullion, one of 
 10 oz. and the other of 5 oz. line, and has a mind to mi:. 
 a pound of it so that it shall be 8 oz fine 5 how much oi' 
 each sort must he take s' 
 
 Jins. 4| of 5 oz.fne, and 7^ of \0 oz.fine. 
 
 5. Brandy at Ss. 6d. and 5s. 9d. per gallon, is to be 
 mixed, so that a lihd. of 63 gallons may be sold for If:;. 
 12s. 5 how many gallons must be taken of each ? 
 
 Jihs. 14 gals, at 5s. 9 J. and 49 gals, at Ss. 6d. 
 
 ARITHMETICAL PROGRESSION. 
 
 Any rank of numbers more than two, increasing by 
 common excess, or decreasing hv common difierence, is 
 said to be in Arithiii«itical Progression. 
 
 <;, C 2, 4, 6, 8, &c. is an ascending arithmetical series : . 
 I 8, 6, 4, 2, &:c. is a descending arithmetical series : 
 
 The numbers which form the series, are called the 
 \ erms of the progression ; the first and last terms of which 
 are called the extremes.* 
 
 PROBLEM I. 
 
 The first term, the last term, and the number of terms 
 being given, to find the sum cf ail tlie terms. 
 
 *A series in progression includes five vutcs^ viz. the 
 first term, last teriUj number of terms^ common difference^ 
 and sum of the series. 
 
 By having any three of these parts given, the other two 
 may be fourui', ivJiich adraitsof a ^^ -.'/-' * of rrohlems ; bu* 
 most of them are best inukvstou 'i!:€h'aic "pr-aces':^, 
 
 an^ arc ■^^^^" 'y'^itied* 
 
HULK. 
 
 Multiply tlie sum of tha extremes by the number of 
 terms, and half the [yroiluctwill be the answer. 
 
 KXAMTLES. 
 
 1. The first term ol" an arithmetical series h 3,tiie last 
 term ^3, and the number of terms 1 1 : recpjircd tlic sum 
 of the series 
 
 ^3+3=26 Slim of the extremes. 
 Then 26x11-^^^143 the Answer. 
 ^2, IIov/ many strokes clue^ tlie hammer of ;i c^ock 
 strike, in twelve hours ? *f}ns. 78 
 
 3. A merchant sold 100 y;!i<ls < viz. the first 
 yard for let. the second for 2 cts. me nwva for 5 cts. Sec* 
 1 demand \vliat t\\^ cloth came to at that rate ? 
 
 Ms. S50^. 
 
 4. A man bois^lit 19 yards ofjinen in arithmetical pro- 
 gression, for the iirst yard }\egave Is. and for the last yd. 
 IL irs. what did the vv!ir*le come to? *B.ns. £18 1^. 
 
 5. A draper sold 100 yds. of broadcloth, at 5 cts. for 
 the first yard, 10 cts. for the second, 15 ii)v the third, &c. 
 increasing 5 cents for ^\tvj y^viX : What did the whole 
 amount to, and wliat did it avera^^c per yard P 
 
 M^, Ji^T.Gurit^ S252i, and the average {irice is §2, 52cts. 
 5 mills per yard. 
 
 6. Suppose 144 oranges were hdd2yards distant from 
 each otlier, in a right line, and a basket placed two ynnls 
 from the first i>range, whatjength <>f «i;rotind will tliat boy 
 travcl over, v/ho gathers tltem nn Finclv, leturnin^'; witli 
 them one by one to the br^ske- ' 
 
 'Bus. 'IS m. , . . ^;:;, ISO lids. 
 
 PROBLEM 11. 
 
 The first term, ti»e last term, and the number of terms 
 given, to find the common tlifference. 
 
 RULE. 
 
 Divide the dill'erence ol ihe^ extremes by the number 
 of terms less 1, and tae quotient ^v?n i^o the cianmon dif- 
 ference. 
 
19^ ARlTHMETrCAJ. I'UQGHESSION. 
 
 1 
 
 EXAMPLES, 
 
 1. The extremes are 3 and S9) and tlie number ol 
 terms 14, what is the common diiibrence? 
 
 '"^ i Extremes. 
 
 Number of terms less 1=13)26(2 ^ns. 
 
 2. A man had 9 sons, whose several ages diffeiftd alike, 
 the youngest was 3 years old, and the oldest 55; what 
 was the common diilerence of their ages ? 
 
 Jifis. 4 years. 
 
 3. A man is to travel from Kew-London to a certain 
 place in 9 days, and to go but 3 miles the first day, in- 
 creasing every day by an equal excess, so that the last 
 day's journey m?.j be 43 miles : Required the daily in- 
 crease, and the length of the whole journey ? 
 
 ^ins. The daily increase is 5, and the whole jmvney 
 207 miles, 
 
 4. A debt is to be discharged at 16 difterent payments 
 (in arithmetical progression,) the first payment is to be 
 lAl. the last lOOZ. : What is the common difference, and 
 the sum of the whole debt ? 
 
 Ans, 5L I4s. St/, common dlference^ and 9121, thewhoh 
 debt, 
 
 PROBLEM III. 
 
 Uiven the first term, last term, and common difference,. to 
 ill 1 1 the number of terms. 
 
 l^ULE. 
 
 Divide tlie^ difference of tlie extremes by the common 
 diffei-ence, and the quotient increased by 1 is the number 
 of Icrms. 
 
 EXAMPL] 
 
 1. If tlie extremes be 3 and 45, and the common dif- 
 ference 2 ; what is the number of terms ? %dns> 22. 
 
 2. A man going a journey, travelled the first day five 
 miles, the last day 45 miles, and each day increased 
 his journey by 4 miles: how many days did he travel j 
 and how far ? 
 
 Jr.?. 11 days^ and thf*: 'wh-l ' travelled ^75 miles. 
 
JE^I 
 
 \ 
 
 geSKietrioal progressiov. 197 
 
 GEOMETRICAL PROGHESSION, 
 
 IS V, hen any rank or series of numbers incioased by one 
 common multiplier, or decreased by one common divisor , 
 as 1, 2, 4, 8, 16, &c. increase l)y the multiplier Sj and 
 £7, 9, 3, 1, decrease by the divisor 3. 
 
 PROBLEM I. 
 
 The first term, ih<i last term (or tlie extremes) and the 
 ratio given, to find the sum of the series* 
 
 RULE. 
 
 Multiply tlie last term by the ratio, and from the pro- 
 duct subtract tlie fust term ; then divide the remainder 
 by the ratio, less by ],aud tlie quotient will be tlie sum 
 of all the terms. 
 
 1. If the series be 2, 6, 18, 54, \G9.. 486. I^.-).^. nnd 
 the ratio S, what is its siiui total ? 
 
 SX145S-— 2 
 
 " =2186 thc.^nsiver. 
 
 2. The extremes of a geometrical seiics are 1 iind 
 65536, and the ratio 4 ; what is the sum of tlie sc-ics .^ 
 
 Jlns. srnbi. 
 
 PROBLEM IL / 
 
 Given the first term, and the rati(?, to find any /ther term 
 assigned.* "/ 
 
 CASE L 
 
 When the first term of tlie series and the ratio are equahf 
 
 *As the last term in a long serks of numbers is very fe- 
 dioiis to he found by continual inidtipliccilions^ it ivill he 
 necessary for the readier finding it ont^ to have a serie:^ 
 of numbers in arifhmetical vroportion^ called indices^ 
 U'hor.p cnminnnciijjvrence is I. 
 
 t 'r/ '.n the first term of the :ierie^nd the ratio are equals 
 Ihe i/i'lices must beginivith the unity and in this case^ t}i$ 
 
 n» 
 
4n- c 
 
 ?93 GEOMV.TRIOAL FROGIIESSION* 
 
 1. Write do^?n a few ot tlic leadiwg terms of the se- 
 ries, and place their indices over them, beginning the 
 indices with an unit or 1. 
 
 2. Add together sudi indices^ whose sum shall make 
 up the entire index to tlic sum required, 
 
 5. Multiply "Ai^ terms of the geometrical series belong, 
 ing to those indices together, and the product will be the 
 it^xa. sought. 
 
 EXAMPLES, 
 
 1. If the ilrstbe % and tlie ratio £; Vviiat is the 13tk 
 term. 
 
 1, 2, S, 4, 5, indices. Ih^*" '" - ' -™1S 
 
 2, 4, 8j 16j S2, leading terms. Z'-: 'I ^ns. 
 
 2. A draper sold 20 yards of .superfine cloii), the first 
 yard for Sd. the second for 9d. the tliird for ^7d, &c. in 
 triple proportion geometrical x what did the cloth come 
 to at that rate ? ■ • ' 
 
 The SOth, or L'lst term is 3486784401^. 
 Then 3+3486784401—3 
 
 ■ ==5230176600f/. the sum of all 
 
 the.terms (by Frob. I.) equal to £21792402 10s. Jns. 
 
 S. A ricli miser thought 20 guineas a price too much 
 for 12 fine horses^ but agreed to give 4 cents for the first, 
 16 cents for the second, and 64 cents for the third horse, 
 and so on in quadruple or four-fold proportion to thelasl^ 
 w^hat did "they come to at that rate, and how much did 
 tliey c©st per head, one with another ? 
 
 Sns, Tlie 12 horses came to g223696, 20ci,9. and the 
 average price uas gl8641, ^5ct$, per head, 
 
 product of avj^ fivo terms is equal to that teriiu signi^ 
 by the sum of\their indites, 
 
 rpj C123 4 5 S(c,I%dizes or arithmetical seriei 
 -itius, ;^£ 4 s 16 32 ^V. ^eomeirical' series. 
 JS'*(nvy 3+2 r^. 5 rrz^theindea'of tkffftktermj and 
 4x8 »« 32 « ike ffthterm , 
 
GEOiMETRlCAL PHOGHESSION . 199. 
 
 CASE II. 
 When the first term of the series and the 'ratio are diffe- 
 rent, that is, when the first term is either greater or 
 less than the ratio.* 
 
 1. Write down a few of the leading terms of the series, 
 and begin the indices with a cjpiier; Thus, 0, 1,2, S, &c. 
 
 2. Add together the most convenient indices to make 
 an index less by 1 than the niraiber expressing the place 
 ofthtf term sought. 
 
 S. Multiply tlie terms of the geometncal series to- 
 getli«r belonging to those indices, and make the product 
 a dividend. 
 
 4. Raise the first term to a power wliose index is one 
 less than the number oT the terms multiplied, and make 
 the result a divisor. 
 
 5. Divide, and the quotient is the term sougl^t. 
 
 F.XAMPI,I<:S. 
 
 4. If the first of a geometrical scries he 4, and the ratio . 
 S, what is th.«a 7th term ? 
 0, 1, 2, 3, Indice.i. 
 4, 12, S6, 108, leading terms. 
 
 5-f 2+1=6, e(\^. index of liie 7i\\ lers.*. 
 108X36X12=46656,, 
 
 r=291'6 the 7th term required. 
 
 16 
 Here the number of terms multiplied are three; there- 
 fore the first term raised to «t. povv-er less than three, is the 
 2d power or square of 4 = 16 the divisor. 
 
 * When the first term of the series and the ratio are dif' 
 ferent J the indices mustbe^in with a ojpher, and tM sum 
 of the indices made choice of virviilhe one less tJian the num- 
 ber of terms given in the 'question: because 1 in the indices 
 stands over the second te^rm^ and 2 in the indices over the 
 third term, ^"c. and in this case, the prodnct of any tivo 
 terms, divided bij the firsts is equal to thai term beyond the \ 
 Jirstj si;:^nifie'f hj- the siim of their indices^ 
 .„.^^. <;o,. r, 2, S, 4,' iyc. Indices. 
 
 '^" ■} T, 3, 9,2:', PI, ^'c. Geometrical series. 
 ; > . :- ^3 ^7 the index of the Wi term, 
 
 . < irvr^c'iar the Sik thmiy or tJie 7th beyond tJiA-lsL 
 
200 
 
 rosiTioN. 
 
 5. A GoklsiniCii sold 1 lb. of gold, at 2 cents for tlie 
 first ounce, 8 cents for the second, 32 cents for the third, 
 &CC. in a quadruple proportion geometrically ; what did 
 the whole come t(j ? ' /Ins. ^11184^, lOc/s. 
 
 3. Yv'iiat debt can be disc]5a!>';ed ni a year, by paying 
 
 1 farthing the first nr. * ' ' '' " rthings, (or 2^d.) the se- 
 en nd, and so ou. eiich '- old proportion ? 
 ."ills. ' ^40 U^..9d. Sqrs. 
 
 r. A tlircshcr worked :':.:: a fanner, and receiv- 
 ed for tlie tlrst day-s \v{)rk four i>ariey-corns, i\tr the second 
 12 barley-corns, for tne tiiird 36 barley-corns, and so ob 
 in triple proportion geometrical. I demand \vhat the 20 
 days' labor came to, supposing a^pint of barley to contain 
 7680 corns, andtlKi whole quantity to i}e sckl at 2s. 6d, 
 per bushel ? ^ns. £177 o 7s, 6d. rejecting remainders. 
 
 8. A man bought a horse, and by a,Q;reeu)ent was i& 
 give a farthing for the first nail, two fur iha second* four 
 tor the tiiird, ckc. There were four shoes, and eight nails 
 in each shoe ; what did the horse come to at that rate ? 
 
 Ans. /j 4473924 5s. S^d. 
 
 9. Suppose a certain body, put in motion, should move 
 the length of one barley-corn the first second of tlmv^^ one 
 inch the secon<i, and three inches the tliird second of 
 time, and so continue to increase its motion in triple pro- 
 portion geometrical ; how many yards would the said 
 body move in the term of half a minute ? 
 
 .^ns. 953199685623 j/t/s. Iff. lin. Ih.c. which is no 
 kss \hanfive hundred and fart i/ -one rrdllionsof miles. 
 
 POSITION. 
 
 1 OSITION is a rule wliich, by false or supposed num- 
 bers, taken at pleasure, discovers the true ones required. 
 It is divided into two parts, Single or Double. 
 
 SINGLE POSITION, 
 
 Is when one number is required^ the prOjpertios of 
 are given i^itb© question. 
 
<i IN O I.K POSIT low. CU » 
 
 [iULE. 
 
 1. Take any number and perform tiie same operation 
 with it, as is described to be performed in the question. 
 
 2. Tfeen say ; as tiie result of the operation : is to the 
 given sum in the question : : so is the supposed number : 
 to tlie true one required. 
 
 T^he method of proof is bj substituting the answer in 
 the question. Kj 
 
 EXAMPLES. ^^ 
 
 ■J. A schoolmaster being asked how many scholars h^^ 
 had, said, If I had as many more as I now have, half a|( 
 many, one-tliird and oncrloiJ rth as many, I sliould theifti 
 have 148 : How many scholars had he ? ^ • 
 
 Suppose he luid ^12 As S7 : 148 : : 12 : 48 ^«i* 
 
 24 r 
 
 16 •^ 
 
 Eesiilt, S7 Proof, 148 ^ 
 
 2. What number is that v;i]ic]\ being increased by 4, J,^ 
 and i of itself, the sum will be 125 ? ^^ns, 60, ' 
 
 S. Divide 93 dollars bct^v^en A, B and C, so that B^^s 
 share may be half as much as A^s, and C's share three i 
 ti jiies as much as B's. 
 
 Jliis, .r:> share 51, ^'s 152, and (Ps 461 dolls, 
 
 4. A, B and C, joined their stock and gained 360 dols, 
 of v.hich A took up a certain sum, B took 3| times as 
 much as A, ant! C took up as much as A and B both 5 
 M'liat share of ihi'^- gain had each ? 
 
 Jr.>^, .i S40, B S140, and C S18D. 
 
 5. Delivered to a banker a certain sum of money, to 
 receive interest for the same at G/, pei^ cent, per annum, 
 simple interest, and at tlie end of twelve years received 
 rsiZ. principal and interest together : What was the sum 
 delivered to him at first ? *8ns. £425. 
 
 6. A vessel has 3 cocks, A, B and C ; A can till it m 
 1 hour, B in 9 hours, and C in 4 hours 5 in what time^vili 
 they all fill it to»ether ? JIvs. SAmin, ITlsec, 
 
 
 as many 
 
 =2 
 
 12 
 
 i 
 
 as many 
 
 = 
 
 G 
 
 ^ 
 
 as many 
 
 = 
 
 4 
 
 i as many 
 
 = 
 
 
 
'1 ,. 
 
 sitions oT i,. 
 
 
 liUi/:. 
 
 ^ - two suppi)- ' 
 
 1^ Take any 1 
 
 wo (■ 
 
 .:,,-(->* • 
 
 3, and proceed ; 
 
 v/it\i eacii accord 
 , 2. Find iio^v 111 
 
 uch - 
 
 
 : :: 13. question. 
 ll.ent IVom the 
 
 ^ A'osults hi the queslluii. 
 
 fW^ 3. Multiply the first posltioi] ; . ^.-t error, and ilie 
 
 f -Ixist position by the first error. 
 ^ 4. If tliG errors are alike, divide the diirerence of the 
 ^)r(iuucis by the diuercnc of the errors, and the quGticnt 
 
 J ^willbe theliiisvrer. 
 
 ^ 0. If the erro]s ai-e iinlikcj divide the sum of the pro- 
 'ducts by tlie sum of tlie errors^ and ""dxt quotient "will be 
 <the answer. 
 ..,• Note. The errors arc said to b? ■'''-" -.hen they are 
 
 Y both too gi-eat, oi-botfi too small : ?, vvlien one ' 
 
 ^ ^ too great, and "^'^ ^ -'' '^:" ^ . 
 
 • 
 
 ^[ 1. A purse of 100 dollars is to be divideji among 4 
 
 r men, A, l^^C and 1). ^;> th.r ^* iimv I'^ive 4 dollars more 
 • than A, and C 8 d .id D twice as 
 
 the money? 
 
 Suppose A 8 
 B 12 
 C 20 
 I) 40 
 
 80 
 100 
 
 70 
 
 1 Of I 
 
 ist. error 50 9A. error 20 
 
 *Tkose qucaiions^ in ivhich the results are not propor- 
 tional to their positions^ belong to this rule ; such as those^ 
 in ivhich the nitmher sought is increased or diminished hij 
 som» given number^ ivhich is no known part rfthemmiber 
 required 
 
BOUBLE POSITION. 203 >^ 
 
 The errors being alike, arc both too small, ther'^fore, 
 
 Pos, Err, 
 6 SO 
 
 2Il 
 
 
 S 
 
 'A 
 B 
 
 12 
 
 16 
 
 24 
 
 ^D 
 
 48 
 
 Proof, 
 
 100 . 
 
 8 20 
 
 £40 120 
 
 120 
 
 10)120(12 A'spait 
 
 2. A, Baud C, built a house which cost 500 dollars, 
 of which A paid a certain sum ; B paid 10 dollars more 
 ihan A, and C paid as much as A and B both 5 how much 
 did each man pay ? 
 
 Jins, Jiimul 120, S lSO,awfZ C^50dols. 
 
 5. A man bequeathed lOOL to three of his friends, aftei 
 this manner : the first must have a certain portion ; the 
 second must have twice as mucli as the first, wanting 8^ 
 and the tliird must have three times as much as the first, 
 wantins; 15l.i 1 demand how much each man must liavc ? 
 
 dns.^The first £Q0 10s. second £S5, third £46 10s. 
 
 4. A laborer was hired for 60 days upon this condition ; 
 that for every day k« v. roiiglit he sliould receive 4s. and 
 for every day he was idle, should forfeit 23. : at the ex- 
 piration of the lime he received 7L 10s. ; how many days 
 did he work, and liow many v/as he idle ? 
 
 ^ns. He wrought 45 days^ and ivas idle \ 5 days. 
 
 5. What number is tliat which being increased by its 
 i, its i, and 18 more, will be doubled } Jins, 72. 
 
 6. A man gave to his three sons all his estate in money, 
 viz. to F half, wanting 50Z. to G one-third, and to H tile 
 rest, which was XOt'Jess than the share of G5 I demand 
 iho^ suuj given, and each mari'spart.^ 
 
 Ans, The sum giv.en was £S60. ivhereof F had £lSOf 
 
i04 PERMUTATION OF QUANTITIES. 
 
 7. Two men J A and B, lay out equal sums of money 
 Jji trade ; A gains 126/. and B looses S7L an'd A's money 
 is now double to B's : what did each lay out ? 
 
 Jns. £500. 
 
 8. A farmer having driven his cattle to market, reciv- 
 ed for them all ISOZ. being paid for every ox 7/. for every 
 cow SL and for every calf 1/. 10s. there were twice as 
 many c^wsasosen, and thn«e times as many calves as 
 cows 5 how many were there of eacli sort ? 
 
 Ans, 5 oxen^ 10 coivs^and SO calves, 
 
 9. A, B and C, playing at cards, staked S24 crowns ; 
 but disputing about tricks, each man took as many as he 
 could : A got a certain number; E as many as A and 15 
 more 5 C got a fifth part of both their sums added togeth- 
 er : how many did each get ? 
 
 Jns. .d isri, B 142^, C 54. 
 
 PERMUTATION OF QUANTITIES, 
 
 Is the showing hov/ many diiTerent ^vays any given 
 number of things may be changed. 
 
 To find the number of Permutations or chanc:es, that 
 can be made of any given number of tilings, all different 
 from each other. 
 
 liULi:. 
 
 Multiply all the terms of the natural series of numbers, 
 from one up to tlie ^ven number, confinually together, 
 and the last product will be the answer retjuired. 
 
 EXAMPLES. 
 
 1. How many changes can be f 1 
 
 made oi tlic three first letters of j ^3 
 
 the alphabet? Proof, <j 
 
 a b c 
 a c b 
 b a 
 
 4 b c a 
 
 5 c h a 
 1x2x3=^6 Jvifi, {6 cab 
 
 2. Ilovf ifi'iXny Atinr^^B iViay be iMng &n 9 bells ? 
 
AXKiriTIES OR PENSIONS. £05 
 
 S. Scvci\ gentlemen met at an mn, and were so well 
 pleased witli their host, and with each other, that thej 
 agreed to tarry so Inn*^ as t!ioy, together with their host, 
 could sit every day in a dilVerent position at dinner ; how 
 long must iUi^y have staitl at said inn to liave fuliilled 
 then- agreement ? JIns, liO^l-^^ years. 
 
 ANNUITIKS Ofl PKiXSlONS, 
 
 COMrUTED AT 
 
 CASE r. ^' -^^-^^^ 
 
 To find tlie amount of an annuity, or Pension, in an'cars, 
 at Compound Interesi:. 
 
 RULE. 
 
 ^l^<^ ^fj 
 
 1. Make 1 the firet term of a geometrical progression, 
 and the amount of ^l or £1 tor one year, at the given 
 rate per cent, the ratio. 
 
 2. Carry on the scries up to as many terfiis ai ^^ given 
 number of years, and tind its su.t 
 
 5. Multiply the sum thus found, by the given annuity, 
 and the product will be the auiount sought. 
 
 EXAMTLES. 
 
 1. If 125 dols. yearly v(t\\t. iw annuity, be forborne, (or 
 unpaid) 4 years 5 what Vvill it amount to, at 6 per cent, 
 per annum, compound interest? 
 
 1+1,06+1. 1^36fl,l9i(3i(5==:4,3746l6 sum of tl^c 
 icries.*— Then, 4,37'4()1.jx 125=^546,8^^7 the amount 
 sought. 
 
 OR EY TABLE I 
 
 Multiply the Tabular number under tlie rate and op» 
 posite to the time, by tlie annuity, and the product will be 
 the amount sought* 
 
 *Ttie sum of the series thus fmincUis the amount of 
 IL or 1 (loUar annuity . for the ^ivea iime^ ivhichvuuj le 
 foiindinl\tblc TL ready calculated. 
 
 Iience, either the amount criireseiit ivorth of (innuiH€$ 
 Wif be readUv fmmd by Tahkafor that mirj^iose, 
 :'8 
 
^i> ANi^UlTlES Oil i'EK5I0NS> 
 
 2. If a salary of 60 dollars per annum to be paid year- 
 ly, be forborne 20 years, at G per cent, compound In- 
 terest; what is the amount ? 
 
 Under 6 per cent, and opposite 20, in Table II, jou 
 will find, 
 
 Tabular number=36,78559 
 
 60 Annuity. 
 
 Ms, g2207,lS540=S2207, IScts. 5m.^ 
 
 4 v^ Suppose an Annuity of lOOL be 12 years in arrears, 
 U is required to find what is now due, compound interest 
 being allowed at ^L per cent, per annum ? 
 
 .Ans. £1591 14s.SfiMd. (by Table II.) 
 
 4. What will a pension of 120L per annum, payable 
 yearly, amount to m 3 years, at 51, per cent, compound 
 interest? dns, £STS 6s. 
 
 II. To find the present wortli of Annuities at Compound 
 Interest. 
 
 RULE. 
 
 Divide the annuity, &c. by that power of the ratio sig- 
 nified bj the number of years, ana subtiact the quotient 
 from the annuity: This remainder being divided by the 
 ratio less 1, the quotient will be the present value of tlie 
 Annuity sought. 
 
 EXA:.irLES. 
 
 I. What ready money will purcha se an Annuity of 50L 
 to continue 4 years, at 5L per cent, compound interest ? 
 
 "^^I^P^^^^^^^l ==1,215506)5 
 
 From . 50 
 
 Subti-act 41,13515 
 
 Divis. 1.05—15=05)8,86487 
 
1 
 
 TA' TAELE II 
 
 Under 5 poT cent, and even with 4 j'cnrs. 
 We have S554:j9cl —.present vvOith of \l. im* 4 years. 
 Multiply by :^U=:Anmnty. 
 
 Ans. £ irr529r;)0=present worth of the annuity. 
 
 G. What Is the present worth of an annuity of GO dels, 
 per annum, to continue 20 vears, at 6 per cent, compound 
 interest? " ^??2S. §688 19^ cts\-f. 
 
 0. What is oOZ. peraiiiuuo, to continue 7 years, %vorth 
 in rcaJv monev^ at 6 rjer cent, compound interest ? 
 
 Ans, £167 9s, 5d.+ 
 
 m. To liiid the present v.ortli of Annuities, Leases, 5cc» 
 taken in Reversion, at Compound Interest ? 
 
 1. Divide the Annuity by that power of tiie ratio deno- 
 tetl by the time of its continuance. 
 
 S. Subtract the quotient from the Annuity: Divide the 
 remainder f.>y the ratio less 1, and th& quotient will be the 
 present worth to commence immediately. 
 
 3. Divide this quotient by that power of the ratio deno- 
 ted by the time of Reversion, (or the time to come before 
 tJie Annuity commences) and the quotient will be the 
 present worth of the Annuity in Reversion. 
 
 EXAMPLES. 
 
 1 . Wiat ready money will purchase an Annuity of 50^. 
 pa*yable yearly, for 4 years : but not to commence till two 
 years, at 5 per cent. ? 
 
 4th power of 1,05=1,215506)50,00000(41,13513 
 Subtract the quotient =4 1,1 35 13 
 
 Divide bv l,05--l==:.t>5V^>.36487 
 £d. power 6r i,05=l,1025Vl77',29r(l60,8i36=£l60 
 I6s. Si. lay, present w'orth of tl^iC Annuity in Reversion. 
 
 OR BY TABLIi III. 
 
 Find the present value of IL at the liven rate for tire 
 sum of the time of continuance, and time in reversion 
 added togetl)er ? from vvliirh value subtract the present 
 worth of iL for the time in reversion, and multiply the re- 
 mainder bv the AnnTiity ; tlic product will be the answer. 
 
SOS AVNUiTlES OR PENSIONS. 
 
 T)iiis In Example I. 
 Time of continuance, 4 years. 
 Ditto of I eversloii; 2 * 
 
 The sum. =6 years, gives 5,075692 
 Tiniein reversion, =h2 years, 1,859410 
 
 Remaindar, 5,2 16282 x50 
 dns, £160,8141 
 S. \Vhat is tlie present worth of 75L yearly rent, which 
 is not to coir.iTienco urJi! 10 years lience, and then to con- 
 tinue r ve^; t 6 per cent. ? 
 
 Ms, £2S3 15s. Od. 
 5. Yf hat is tb.e present worth of the reversion of a 
 lease of GO dollars per annum, to continue 20 years, but 
 not to comnience till the end of 8 years, allowing 6 per 
 cent, to ihQ purchaser ? J?2S. S-^^l TScts. Q-^^m, 
 
 IV. To f.nd the present woi-th of a Freehold Estate, or 
 an Annuitv to continue forever, at Compound Interest. 
 
 rule: 
 
 As tlie rate per cent, is to 1C^(. : so is the yearly rent to 
 tlie value reqi-ired. exajniples. 
 
 1. Wiiat istiie worth of a l**reeho]d Estate of 40^. p^r 
 annum, allowing 5 per cei^t. to ihe purchaser ? 
 
 As £5 : £100 . : £40 : £800 Ms, 
 
 2. An estate brings in pearly 150/. what would it sell 
 for, allowing the pinxhaser 6 per cent, for his money? 
 
 ' £2500 
 
 »'ir&o». 
 
 V. To find the pi^esent worth of a Freehold Estate, ki 
 Reversion, at (\>mr««)und Interest. 
 
 1. Find tlie present va^ue of the estite (by thefore^o- 
 in<5 rule) as thoii> ■< it w\v^ to be entered on immediately, 
 and divide the fiald value f v i}\kit power of the ratio de- 
 noted by.th.e time of rcvcrMoii., and the quotient will be 
 the presCiU v: "^ : '' " ■ - ' te Lr Ueve'-^iun. 
 
 1. Suppo;^e a iiv^; :• A ; c:-*.ueor 40L per annum to com** 
 mence two years hence, be put on sale ; what is its value, 
 til owing the purchnr ' . "' • r cent, t 
 
As 5 : 100 : : 40 : 800=tprcsent worth if entered on 
 unmediatelj. 
 
 Then, 1,05"= 1,1 025) 800.00(725,62358=725/. 12s. 
 5icf.r=prcsent worth of £800 in two years reversion, •/iws. 
 
 OR RY TABLE III. 
 
 Find the present worth of the annuity, or rent, for the 
 time of reversion, whicli subtract from tlie value of the 
 immediate possession, and yon will have the value of the 
 estate in reversion. 
 
 Thus in the foregoing example, 
 l5859410=present worth of 1^. for 2 years. 
 40=annuity or rent. 
 
 74,376400 ^present worth of the annuity or rent, for 
 [the time of reversion. 
 From 800,0000 =va1ue of immediate possession. 
 Take 74,S764=i)resent worth of rent. 
 
 /; 725,623 6 =£725 12.<?. 5 Ad. .(?«<?. 
 
 2. Suppose an estate of 90 dollars per annum, to com- 
 mence 10 years hence, were to be sold, allowing the pur- 
 chaser 6 per cent. ; what is it worth ? 
 
 Jlns. S8S7, 59cts, 2m. 
 
 o. Which is the most advantageous, a term of 15 ;y^ears, 
 in an estate of 100/. per annum; or the reversion of sueh 
 an estate forever after the said 15 years, computing at the 
 rate of 5 per cent, per annum, compound interest ? 
 
 •^ns. The first term of 15 years is better than the re* 
 version forever afterv/ards, by £75 18.s. 7UL 
 
 A COLLECTION OF* QL^ESTIONS TO EXKRCISE 
 THE FOREGOING RULES. 
 
 1. I demand the sum of 1748^ added to itself? 
 
 Jns, 3497. 
 
 2. What is the difference between 41 eagles, and 4099 
 ^imes.^ Jns, lOcfs. 
 
 3. What number is that wliich being multiplied by 21^ 
 Uie product will be 1365 .^ Jtus, 65. 
 
210 
 
 qUESilONS rOU EXERCISE. 
 
 4. What number is that which being divided by 19, the 
 quotient will be 72 ? dns, 1368. 
 
 5. What number is that which being multiplied bj 15, 
 the product will be j ? Jins, ^^, 
 
 f». There are 7 chests cl drawers, in each of which 
 there are 18 drawers, and in each of tlicsc there are six 
 divisions, in each of wliich is 16L Cs. 8d.; how much 
 money is there in t]:c v " ' " 
 
 7. bought Z^- -^ 
 I sell it a pipe i 
 rest for v/liat i\\(^ 
 
 8. Just IG vii. 
 For 90 (In: 
 IIow manv ,,= 
 Will 14 el><j;icy 
 
 9. A certain quanf^ 
 weeks, how many mi: 
 remainder 9 weeks ? 
 
 10. A grocar beir^ht a\\ ei^ual q^i 
 tiwA coflee. kn- r4(; la^-- '■" * '■■^ '•'^'-- ' 
 the sugar, cu ct;. per 
 the coilee ; ic^jiureu Ihc ^iuct:,vi.. v in v.^vij,. 
 
 Jns. 89,9.1.0, r^oz. 8|fZr. 
 
 11. Bought cloth at SU a yard, and lost 25 per cent. 
 Low was it sold a yard ? .Qns, 93|cf5. 
 
 12. The third part of an ramy was killed, tlie fourth 
 part taken ]}risoners, anti 1000 lied ; how ?nany were in 
 this army, h::v - ' ^:'''--\ :-| how many captives ? 
 
 • army^ HOO killed^ and 
 
 Jins. £1£348. 
 18 for 4536 dollars 5 h»w must 
 uiv my own use, and sell the 
 Jns, St29/60cfs. 
 
 ?s. MSijds, Sqrs, ^na. 
 
 ■■r.'. >--» ]-tst 963 sheep 7 
 
 t it will last the 
 
 --■??s. 214. 
 
 sugar, tea, 
 
 per lb. for 
 
 . per lb. for 
 
 13. Thomas sold 1;"' 
 and received as much vnone 
 
 iits a piece, 
 ceived for a 
 
 certain number of w^atcr-niclloiis, v/l-jch lie sold at 2:> 
 cents a piece 5 how m^ic- 
 how many me] Ions luid I* 
 
 *^]ns. Each received ''^ " 
 
 1 4 . S ai d J ol 1 n 1 1 ; \ 
 9^. 2s. but the money is cvvc-ir*-:: 
 purse; I demand IlOvs' murh luorv 
 
 : .<*j anu 
 
 noney are wortli 
 l:-)uvs as u\uch as the 
 was in it ? 
 
 Jns, rS 15s 
 
qiJESTIONS FOR EXERCISE. 211 
 
 15. A jcmng man received 210/. whicli was § ©f liig 
 elder brotlier's portion ; now three times the elder broth- 
 er's portion was half the father's estate ; what was the 
 value of the estate ? Ms. £1890. 
 
 16. A hare starts 40 yards betore a greyhound, and is 
 not perceived by him till she has been up 40 seconds ; she 
 scids away at the rate of ten miles an hour, and the dog^ 
 on view, makes after her at the rate of 18 miles an hour : 
 How long will the ci>urse hold, and vvhat space will be ran 
 over, from tiic spot wlicre the^dog started ? 
 
 Ms, GOJjSec, and 5S0yds, space, 
 
 17. What number multiplied by 57 will produce just 
 what 1S4 multiplied by 71 will do ? Ms, l6Gff 
 
 18. Tlicreare two numbers, whose product is 1610, the 
 greater is given 46 ; I demand tlie sum of their squares, 
 viid the cube of tlieir difference ? 
 
 Ms. T}ie sum of their squares is 3341 . The cube of 
 their aiffirence is 1S31. 
 
 19. Suppose tiiere is a mast erected, so that -J- cf its 
 length stands in the ground, 1 2 feet of it in tlie water, and 
 f f« its lengtli in the air, or above v/ater: I demand the 
 whole length ? ' Vhis, 216 feet. 
 
 20. What difference is tliCre between the inteVest of 
 50Q.L ai 5 per cent, for 12 years, and tlie discount of the 
 same sum, at the same rate, and for lUe same time ? 
 
 y Ms. £112 10.?. 
 
 - 21. A stationer sold quills ai. \U. per thousand, by 
 which he cleared | of the money, but growing scarce, 
 raised them to IS*;, tid. per tliousaifd ; what miglit he clear 
 per cent, by the kitter price? 
 
 ^ ' .^^ns. £96 '7s, S^^d. 
 
 22. Three persons purchase a TVest-iladia sloop, to- 
 wards i]\Q payment of wliich A advanced -f, B l,and C 
 14DZ. How much paitl A and I], and what ];art. of the 
 vessel had C ? . 
 
 Ms. Jlim'ul £26r^3^, B £CG3-f., and C's pari of 
 the vessel ivas ^-J-. 
 
 23. What is the purchase of 1200/. bank stocl:, ;it I03| 
 percent. .^ Ms. £\9A:o iOf. 
 
 £4. Eough.t 27 pieces of Nankeeri- oujh II \ wri^. ni 
 
5i?v' QUESTIONS rOR EXERCISE. 
 
 14s. 4^d. a piece, which were sold at 18d. a vard^ rCt 
 quired the prime cost, what it sold for, and the gain. 
 
 £. s, d. 
 
 CFrimecosty 19 8 ii 
 JinsA Sold for^ 23 5 9 
 (^ Gain^ S IT ' 7J 
 
 9.5. Three partners. A, B and C, join their stock, and 
 buy goods to i\\Q amount of /j 1025,5 ; of which A put in 
 a certain sum; B put in....! know not how mudi, and C 
 the rest 5 they gained at tlic rate of 9AL per cent. : A's 
 part of th- gain is h, B^s \, and C's the rest. Required 
 Qach man^s particular stock. £, 
 
 CA^s stock teas 512,75 
 
 Jns. < B's ^ 205,1 
 
 iC's 307,65 
 
 S6. What is that iiunibcr which being divided by J, the 
 quotient will be 9A ? Ans. 15|. 
 
 S7 If to my age there addled be, 
 
 One-half, one-third, and three tiirics thiee, 
 Six score and ten the sura will be : 
 Wliat is mj age-- pray sitew it nie ? 
 
 Ans. 66, 
 
 28. A gentleman divided liis fortune among his three 
 sons, giving A 9/.- as often as B 5L and to C but SL as 
 often as B 7L and yet C's dividend was 25S4L ; what did 
 the wiiole estate aincunt to ? 
 
 £ns, £19466 2$, Sd. 
 
 29. xV gentleman left Ids son a fortune, ^ of which he 
 spent in three months 5 I of the remainder lasted him 10 
 months longer, when he had only 2524 dollars left; praj 
 '^^hat did his fatlier bequeath liim ? 
 
 .^ns. S58o9, HScts.-r 
 SO. In an orchard of fniit trees, § of them bear apples, 
 i pears, | plums, 40 of them peaches, and 10 cherries 5 
 how many trees does tlic orciiard contain ? ^^m. 600. 
 
 31. Hiere is a certain number, which being divided by 
 7, the quotient resulting multiplied by 3, that product 
 divided by 5, from iAm quotient 20 being subtracted, and 
 SO added to the remainder, the half sum shall make Or 
 c-^n vou tell mc the number ? ''?''=>. '•'-=.1. 
 
HUERTIONS FOR EXERCISE. ^3 
 
 3Z. What part of 25 is | of an unit ? 
 
 Ms. :^\. 
 SS. If A can do apwcc of work alone in 10 days, B in 
 SO dajs, C in 40 days, and D ^ct all four 
 
 about it together, in what tvno < it ? 
 
 Ju6, 5^ days. 
 
 34. A farmer being asked how many sliccp he had, an- 
 swered, that he had them in five fields, ia the first he had 
 f of his flock, in the second ^, in the third |, in the foiii-tli 
 j^, and in the fifth 450 ; how many had he ? 
 
 Ms. 1200. 
 
 S5. A and B together can build a boat in 18 days, and 
 witli tlie assistance of C they can do it in 11 days ; in 
 what time would C do it alone ? Jlns. 28^ days. 
 
 36. There are three numbers, 23, 25, and 42; what is 
 the difference between the sum of the squares of tlie first 
 and kst,and the cube of the middlemost ? 
 
 Ans. 13332. 
 
 S7. Part 1200 acres of land among A, B, and C, so 
 that B may have 100 more than A, and C 64 more than 
 B. Ms. Jl 312, B 412, C 476. 
 
 38. If 3 dozen pairs of gloves be equal in value to 2 pie 
 aC8 of hoUand, 3 pieces of holland to 7 yards of satin, 6 
 yards of satin to 2 pieces of Flanders lace, and 3 pieces of 
 rlanders lace to 81 shillings; how many dozen pairs of 
 gloves may be bought for 28s. ? 
 
 Ans. 2 dozen pairs, 
 
 39. A lets B have a liogshead of sugar of 18 cv/t. worth 
 5 dollars, for 7 dollars the cwt. ^ of which he is to pay in 
 cash. B iiath paper v/orth 2 dollars per ream, which he 
 gives A for the rest of his sugar, at 2 1 dollars per ream. — 
 Which gained most by the bargain ^ 
 
 Ms. A % S19, 20cf5. 
 
 40. A father left his two sons (the one 1 1 and the other 
 16 years old) 10000 dollars, to be divided so that each 
 share, being put to interest at 5 per cent, might amount 
 to equal sums when they would be respectively 21 years 
 ef age. Ueqjuired the shares } 
 
 Alls. 5454 j^j and 4545-^^ dollars. 
 
 41. Bought a certain quantitir of broadcloth for 5SS^ 
 
^14 quESTic:.,^ i-oR Exr.Ficjf,?:. 
 
 5s. and if tlic numl ings v.iiich It cost per yard 
 
 were added to the nui.ibei oi vanis bouglit, tlie sum would 
 be 386 1 1 demand the iiuir.bor of yards boii^^ht, and at 
 what price per yard ? 
 
 Jluf^. C>o5 yds. at SI 5. permriL 
 Solved by Problem Yi. page 183. 
 42. Two partners, Peter and John, bougiit^oods tothe 
 amount of 1000 dollars; in the purchase of \vhici«, Peter 
 paid more than John, and Joiin paid....! know not how 
 much : Thej tiien sold their goGiis for ready money, and 
 thereby gained at the rate of 200 per cent, on the prims 
 cost : they divided the gain between thcrri in proportion 
 to tlie purchase raoney that each paid in buying thQ goods ; 
 and Peter says to John, Mj part of the gain is really a i 
 handsome sum of money ; 1 wish I had as many such sums^ 
 as your part contains dolhirs, I should then have ^960000.: 
 I demand each man's particular stock in purchasing th$: 
 goods. 
 
 Arts. Feter paid 600 dullars, and John paid 400. 
 
 THE FOLLOWING QUESTIONS ARE PROFOSED TO 
 SURVi^YOKS. 
 
 1. "Required to lay out a lot of land in form of a Ion* 
 square, containing 3 acres, 2 roods, and £9 rods, that shall 
 take just 100 loih of wall to enclose, or fence it round 5 
 pray how many rods in lengtli, and how many wide, r.iust 
 said lot be? 
 
 *?72s. 31 rods in lengthy and 19 i7i breadth. 
 Solved by Problem Yl. page 183. 
 
 2. A tract of land is to belaid out in form of an equal 
 square, and to be enclosed with a post ami rail fence 5 
 rails high ; so that each rod of fence shall contain 10 rails. 
 How large must this noble square be to contain just as 
 many acres as there are rails in the fence that encloses it, 
 so that every rail shall fence an acre ^ 
 
 dns. the tract of land is 20 miles sqnarL\and 
 contains 256000 acres. 
 Thus,] mile=320 rods: then 320x320->-l60=640 
 acres : and 320x4x10=12800 rails. As 640 : 12800 : : 
 12800 : 256000 rails, which will enclose 256000 acres ==* 
 2{) miles square. 
 
:*15 
 
 AM 
 
 APPENDIX, 
 
 CONTAINING 
 
 SHORT RULES, 
 FOR CASTING INTEREST AND REBATE 5 
 
 TOGETHER WITH SOME 
 
 USEFUL RULES, 
 
 OJl eiHDIKG THE CONTENTS OF SUPERFICIES, SOLlDJS^ 
 
 SHORT RULES, 
 
 ?0R CASTING INTEREST AT SIX PER CENT 
 
 To find the interest of any sum of shillings for anj 
 number of days lesis thaaa month, at 6 per cent. 
 
 RULE. 
 
 1. Multiply the sluliings of the principal by the num- 
 r of days, and tliat product by 2, and cut off three 
 2;ures to the ri^ht hand, and all at)()ve three figures will 
 5 the interest in pence. 
 
 2. Multiply th^ figures cut oiT by 4, still striking off 
 ree figures to the right ijand, and you will have tHe 
 rthings, very nearly. 
 
 EXAMPLES. 
 
 1. Required the interest of oL Ss. for '25 days. 
 
 5,8=108X25X2=5,400, and 400x4=1,600 
 
 Ans. 5d, l,6^rs. 
 
 2. What IS ftie interest ot 21 L Ss. for 29 days? 
 
210 APPENDIX/ 
 
 FEDERAL MONEY. 
 
 II. To find the interest of any number of cents for any 
 number of days less than a month, at 6 per cent. 
 
 RULE. 
 
 Multiply the cents by the number of days, divide tlie 
 product by 6, and point oft* two figures to the ridit, and 
 ail the figures at the left hand of i\\Q dash, will be tho 
 Miterest in mills, nearly. 
 
 EXAMPLES. 
 
 Required the interest of 85 dollarSj for 20 days. 
 JS cts, mills. 
 
 85=8500x20-~63=283,33 .te. 283 whicli is 
 
 £8cis. 3 milb. 
 2. What is the interest of 73 dollars 41 cents, or 7341 
 cents, for 27 days, at 6 per cent. ? 
 
 Ans. 330 miilU^ or ^3cts, 
 
 III. \yhen the principal is^given in pounds, shillings, &c. 
 New-England currency, to find the interest wt any 
 number of clays, less than a month, in Federal Money, 
 
 RULE. 
 
 Multiply the Siullings in the principal by ihQ number 
 of days, and divide the ji-oduct by S6^ t\\e quotient witt 
 be the interest in mills, for the givei^ time, nearly 5 omit* 
 ting fractions. 
 
 EXA^IPLK. 
 
 Required the iatert^t, in Federal Money, of Q7L 15s- 
 for 27 days, at 6 per cent. 
 
 £ • ^' •'^• 
 Aiis, 27 15=555 x27-7-56=416hu7Zs.=41c^s. 6?n. 
 
 IV. When t:ic principal is given in Federal Money, and 
 you want the interest in shillin2;s5 pence, &c. Ncw-Engj 
 land currency, for any uum&er of days Idss than a 
 
APPENDIX. SIJJJ 
 
 IIULK. 
 
 Multiply the principal, in cents, by the number of days, 
 and point oflf live figures to tiic ri«;ht hand of the product, 
 whicn will give the interest for the given time, in shil- 
 lings and decin;a!s of a shilling, very nearly. 
 
 EXAMPLKS. 
 
 A note for 65 dollars, 31 cents, has been on interest 25 
 days; bow much is the interest thereof, in New-England 
 currency ? 
 
 S ct$, s. s. (Lgrs, 
 
 *5?2S. 65,Sl=65SJXi:5 = l,63Sr5— I T >» 
 
 Ret^iaukf. — In tli*e above," and likewise in tiic preced- 
 ing practical Rules, (page 127) the interest is confined at 
 six per cent, wliich admits of a variety of short methods 
 of casting ; and when the rate of interest is 7 per cent, av^ 
 established in New-Yorl:, &c. you may first cast t!\e in- 
 terest at 6 per cent* and add tlieieto one sixth of itself, 
 and the sura vv^ill be the interest at 7 per cent, wh.ich per- 
 haps, many times, will be found more convenient than t^ie 
 general rule of casting interest. 
 
 EXAMPLE. 
 
 Ucf[uired the interest of 75L hv 5 i-iontiis :it 7 |)et 
 cent. 5. 
 
 7.5 for 1 month. 
 '5 
 -^ £.s. a'. 
 37,5=1 17 fi lor 5 montiis at 6 per cent. 
 
 4.1:= 6 3 
 
 Jins £2 3 9 for ditto at 7 per cent. 
 
 fjnOKr METHOD FOR FINDING THE REBATE Oi" AN*-" 
 GIVEN SUM, FOP. MONTHS AND DAYS. 
 
 ^iULE. 
 
 Dmijiii^li tlie inte'-estof the given sum for the time by 
 ; own interest, and this gives the Rebate very nearly- 
 
 EXAMPLES. 
 
 • . What is the. vr.Ki'xe of 5Q d.oUar* for sir moiiU*^!. 'it 
 
S cts. 
 
 'he intci-c-i inonliiS^ is 1 50 
 
 rjM 
 
 cent ? 
 
 ."^jzs. Ilphaie. gJ 45 
 rebate of 150L for 7 montlis, at 5 per 
 
 /;• 
 
 <:. 
 
 fL 
 
 ** 
 
 ?■ 
 
 G 
 
 
 o 
 
 Gi 
 
 Interest oi 1501. ibr T ni:.)nllis, is 
 Interest of 4Z. 7-. C;L lurr i^ioiith 
 
 .^iis, £4 4 11^ nearlv. 
 Bj llic above Rule, those \\\\q use inte-est tables m 
 tiieir couutiiig-housesj have oulj to deduct the interest of 
 the intcrcs^t, and the remainder is ii\o discount. 
 
 A concise Rale to reduce the currencies of the different 
 States, where a dollar is an even number of shillings^ 
 to Federal Money, 
 
 RULE L 
 Brliv^ (IjC ^ivcn sum into a decimal expression by in 
 spectioii, (;is in Problem L pv^ge 87) then divide the ^ z :■ ^ 
 by ,S in New-England and by ,4 in Ncv/-York curr^ r , 
 and the quotient will be dollars, ceutB, &c. 
 
 EXAMPLES 
 
 L 8-3. 
 Federal iVIonev. 
 
 1. Reduce '6Al. Ss. oAd. New-England currency, to 
 
 ,3)54,415 decimally expressed. 
 
 Am. SlSl.SScf.^. 
 g. Reduce 7s. Hid. New-England currency, to Fedc- 
 i*al Money. 
 
 rs. n|d==.<:0,599 then. ,S),599 
 
 * Ms. SI ,33 
 S. Reduce 515L 16s. lOd. New-York, &c. currciicj^ 
 to Federal •Money. 
 
 j4) 5 135842 decimal 
 
 nn<: §1284,60* 
 
219 
 
 4. Reduce 19s. j^il. New-Ywk, Sec. currency, to Fede- 
 ral money. 
 
 ,4)0,974 decimal of 19s. 5Jd. 
 
 S2.43i Ans. 
 
 5. Reduce 64 ^ New-Kngland currency, to Fadevai 
 Money. 
 
 ,3)64000 decimal expression 
 
 S^l 5.35-1 Ans, 
 
 Note. — By the foregoing rule you may carry on the 
 decimal to any degree of exactness : but in ordinary prac- 
 tice, the followin,-?; Cordractlon uuiy be useful. 
 
 RULE II. 
 
 To the sisillings contained in the given sum, ann«x -q 
 times the given pence, increasing the product by 2 ; then 
 divide the whole by tlie number of shillings contained in 
 a dollar, and tlic qv.otient will be cents. 
 
 EXAMPLES. 
 
 1. Reduce 45s. 6d. New-England currency, to Feto 
 ral Money. 
 
 Gx8-f2 = 50 to be annexed. 
 6)45j50 or 6)4550 
 
 S7',58| Jlns. 75S cents, =7,58; 
 
 2. Reduce SZ. 10s. Od. New-York, Sec. currency, t 
 Federal Money. 
 
 9xS+2=r4 to be annexed. 
 Then 8)5074 Or thus, 8)50,74 
 
 S els. 
 
 Ans. 634 cents.=^6 54 86,34 dns» 
 
 N. B. When there are no pence in the given sum, you 
 must annex two cyphers to the shillings ; then divide as 
 before, &c. 
 
 S. Reduce Si. 5s. New-England currency, to Federal 
 Money 
 
 S^. 5s.=65s. Then 6)6501) 
 
 renfs^ insf^ ,^n» 
 
 /a 
 
SECTlOh 
 
 Tlic miperiicles or v.v\':i 1^5 anj pame suviace, is com- 
 posed or mader.p of H^KUires* either greater or less,» iic- 
 f>rdln^ to the dliien?!it uieasiues by wiacii the dh^jen- 
 ;.ans of tlie figure ;ire taken or ineaj-ii-red : — a,nd because 
 i^iiiches in i^^igth make 1 foot of long measure, there- 
 fore, 12xl2™144. u\Q square iiiches in a superticiai foot, 
 vkc. 
 
 Aht. I. To find tUe rrrca of a s^iuare 'lavin'^ equal 
 
 Midtiplj t]\Q side of 1:1-l2 square into it^^eii, and th2 pro- 
 duct will be the area, or content. 
 
 EXATvfPLKS. 
 
 1. How manj sqnnre feet of bu ined in 
 the floor of a rooia whicli is 20 iect square ? 
 
 S. Suppose a S(Mi- ' rods o^i 
 
 ^\adi side, how luati v 
 l^crE. — 160 squ:: 
 
 Thereio^-p> rC-xf' :^r;----lG0™4«. 
 
 . .^ircr. 
 Aa"\ i::. ... .square. 
 
 iMultiply tlic ieiigiii by the bread tii, and iae product 
 vnll batfiearea or superficial content. 
 
 KXAMPJ.Kn. 
 
 i. A certain garden, m unra oi a ion^| square, is 96 ft* 
 long, and 54 wide ; liow uiaiiy square teet of ground art* 
 contained in it ? Jlns. 9G x 54 ==5 1 ?, 4 square feet 
 
 2. A lot of land, in form of a lon'^; scnuirc, is 120 rod? 
 in length, and GO reds wide ; how v;ia:iv acres are in it ? 
 
 1^6x^0^7200 sq. rods, then, y^s^4o acreSy Jns. 
 5. If a board or plank be £1 feet long, and 18 inches 
 ^road 5 how many square f\ict are cgntained in it? 
 
 IS i}'ic^''St-=1^^ ■'^- ' -<^ -7, 121 XT, 5 — :^ 1,5 Jins* 
 
Or, in measuring boarilsj jz^z :Br.T multiply iiie length 
 iu feet by the breadth ,n iuclies/f.riil divicic by 12, the 
 quotient v.ill give the iinswer in square teet.&c. 
 
 Thus, iu the tbiTgoiug example, 21x18-7-12=31,5 as 
 before. 
 
 4. If a board be ft iiiclies v/idc, how much in lengtk 
 \\\\\ make a sciuure foot ? 
 
 Rule.— Divide 144 by the breadth, thus, 8)144 
 
 Ans. 18 in. 
 
 5. If a piece (f lar.d be 5 rods wide, how many rods in 
 length will wvdhi an aci-e ? 
 
 Rule. — Divide 1 GO by tlic breadth, and the quatiei^ 
 will be the length required, thus, j)lCO 
 
 Ans, S2 TOih in length* 
 
 Aht. 3. To measure a Triangle. 
 
 .Definition, — A Triangle is any three eernered figui^e 
 wliichis bounded by three right lines.* 
 
 RULE. 
 
 Multiply the base of tlic given triangle into half its 
 pci-pendicular height, or lialf the base into the v/hole per- 
 pendicular, and i\ie product will be the area. 
 
 EXAMPLES. 
 
 1. Required tlie area of a triangle whose base or long- 
 est side is S2 inches, and tlie perpendicular height 14 
 iiichcs. 3^2x7=224 square inches, the Jlnsiver. 
 
 '■2, There is a triangular or tliree cornered lot of land 
 whose base or longest side is 51i»rods ; tlie perpendicular 
 from the corner opposite tlie basi:;, measures 44 rods : how 
 many acres doth it contain ^ 
 
 51,5x22^=1133 square r()ds,=:x7 acres, 13 rods, 
 
 '^Jl Triangle Qiiaji be either right anzled or oblique; in 
 e'iher case the teacher can easily give the scholar a right 
 idea of th& base and jperpendiculai , byviarkm^ it down 
 '' '.• slate » vaper^ Sec 
 
^ »2ii AVPENDiX. 
 
 TO MEASURE A CIRCLE. 
 
 Art. 4, Tlie diameter of a Circle being given, to 
 find the Circu inference. 
 
 RULE. 
 As r : is to 22 : : so is tlie given diarr.ctcr : to the 
 circumference. Or, more exactly, Ab 113 : h to 355 * : 
 &ic. file diameter is found inversely. 
 ^ Note. — T)\e diameter is a right line dra^rn across the 
 circle throug'n its centre. 
 
 L Wliatis tlie circumference of a wheel Vvliose diam- 
 eter is 4 fleet?— As T : PS. : : 4 : 1^,57 t-:^ r^rciimfe 
 rence. 
 
 2. What is the circumference cf a circ' : -ame- 
 
 ter is S5?— -As 7 : £3 : : 55 ; liOJns\ : sely 
 
 as £2 : 7 :: no : S5, the dianr^^--- '" 
 
 Art. 5. To find the : 
 RULE. 
 Multiply half the diameter by half the circumference, 
 and the product is ilie area ; or if tlie diameter is givea 
 without the circumference, multiply the square of the 
 diametei' by 57854 and the product will be the iivea. 
 
 EXA.MPLKS. 
 
 1. Requirel the area of a circle v.hosc diameter is 12 
 inches, anil " rence 37,7 inches. 
 
 35 =half the circu inference. 
 G==half the diameter. 
 
 113,10 area in square inches. 
 2. Kequired the area of a circular garden whose diame- 
 ter i>s 11 rods ^ .7854 
 By t:ie second metliDd, 11x11 ^ l^i 
 
 Jns, 95,0334 rods, 
 
 SI^CTION 2. OF SOLIDS. 
 
 Solids are estimated by the solid inch, solid foot, ^r, 
 1728 of these inches, that is 12x12x12 make I c»b' 
 or golid foot. 
 
APJ'ENDIX. 2i^3 
 
 Art. G. To measure a Cube. 
 
 Definition, — A cube is a solid of sk equal sides, each 
 of which is an exact square. 
 
 RULE. 
 
 Multiply the side by itself, and that product by the 
 same side, and this last product will be the solid content 
 of the cube. 
 
 EXAMPLES. 
 
 1. The side of a cubic block being IS inches, or f foot 
 and 6 inches, how many solid inches doth it contain r 
 
 JL in. ft. 
 1 6=1,0 and 1,5x1.5x1,5=3,375 solid feet, JIns. 
 Orj 18xl8xlSr=5852 Sulid inches, and -ff|i =3,375. 
 
 2. Suppose a cellar to be dug that shall contain 12 fcQt 
 every way, in length, breadth and deptli ; how many solid 
 feet of earth mu&t be taken out to complete the same ? 
 
 12x12x12=1728 solid feet, the Jlnsiim\ 
 Aut. 7. To find trie content of any regular solid of three 
 dimensions, length, breadth and tliickncss, as a ])iece of 
 timber squared, whose length is mure tluin the breadth 
 and depth. 
 
 RULE. 
 
 Multiply the breadth by the depth or tliickncss and 
 tliat product by the length, which gives i\\Q^ sc)!5d co2itciit. 
 
 EXAMPLES. 
 
 1. A squaoe piece of timber, bein.*; 1 ^'Mt 6 inches, m 
 18 inches broad', 9 inches thick, and 9 fe^t ur 103 inches 
 long; how many solid feet doth it co:it:ibi r 
 
 1 h. 6 in. =1,5 foot. 
 
 9 inches = ,75 foot. 
 
 Prod. 1,125x9=10,125 s^^/a: :. ,. ;. 
 in, in. In. solid in. 
 Or, 18x9xl08-=17496-r-1723=10J25 feet. 
 But, in measuring timber, you may mul tiply the bread t!i 
 in inches, and tlie depth in inches, and that product by 
 the length in feet, and divide the last product by I-W, 
 / ' ..h v.' ill give tte solicfccontcnt in fcctp &c. 
 
 A^ 
 
'£24 
 
 Arr-F.NDii:. 
 
 2. A j>iect: of timber being 16 iaches broad, 11 iftchec 
 thick, and 20 feet long, to fiiit^ the cmiterut r 
 Breadth 16 inches. 
 Depth 11 
 
 Pi-od. ir6x£0=3520 then, 3:£0 -v- 144 =24,4 /eef, 
 
 the Answer, 
 r>. Apiece of timber 15 inclics broad, 8 inches thick, 
 and 25 [eat long; liow many solid ^i^ct doth it contain ? 
 
 fins. SlO.S-^feet. 
 
 Airr. S, V/iien tlic Isrciidth and thickness of a piece of 
 timber are given in inches, to find how miicli in length 
 will make a solid foot. 
 
 Divide ir£8 bj tlie product of the bretidih aiii! depth, 
 aiid tiie quotient will be tlie iengtli niuking a suli<l foot. 
 
 KXAMPLKS. 
 
 1. ir a piece of timber !}c 1 1 Inclics broad and 8 inches 
 deep, liow n:any incites in lengtli will make a solid foot? 
 Ilx8=:8S)ir28(19,6 inches, Jlns. 
 
 S. If apiece of timber be 18 inches broad and 14 in- 
 ches deep, how many inches in length will make a solid 
 foot ? 
 
 18xl4==.£5£ drjisor, then 252)1728(6,8 inches, Ans, 
 
 Art. 9. To measure a Cylinder. 
 iJ^/Ijzi^io/?.— A Cylinder is around body whose bases 
 arc circles, like a round column or stick of timber, of 
 
 equal bigness iioiu end to end. 
 
 RULE. 
 
 Multloly tj:e sciuare of the diameter of the. end by 
 ,7854 v/nich gives the area of the base ; then multiply 
 the area of ihn u;!se by the length, and the product v. ill 
 be the solid coritcnt. 
 
 EXAMPLE. 
 
 What is the solid content of a round stick oi timber cf 
 equal bigness from end to end, whose diameter is 18 ii.- 
 cbcs, and length 20 feet ? 
 
18 111. =1,5 Tt. 
 
 '.[uarc 2,25 X .ro54 ~ 1^7^,715 area of the base. 
 X20 lrjm-t.h. 
 
 .^i;:i^. 35jS-1300 solid content. 
 , IS inclios. 
 18 inches. 
 
 324 X ^rs ji =:--r.a J4.4G9G iuclies; area of the base. 
 CO Ien<rth in leet. 
 
 1 M)::0:^:.-,^!J20(S5,S43 ndld fc(^t. ^'his. 
 T. 10. To uiui iiov/ 111 any solid teet a round stick (>f 
 imber, equally thick from end to end, will contain 
 , hen hewn square. 
 
 RULK. 
 lultiply twice t':e square of its ftemi-dlameter in in- 
 s by the lenglU in feet, tii-en divide the product by 144, 
 i the quotient v/ill be the answer. 
 
 EXAMPLE. 
 
 r the diameter of a round stick of timber be 22 inches 
 
 . its length. 20 feet, '; — -r-.v solid feet will it contain 
 n hewn scpviare ? 
 
 ; i Xllx2x2G-- ' : f-t, the solidity when 
 
 . n square. 
 
 V. 11. Toiind no^v ujaijv u-ct oi' square edged bonrds 
 Ta given thickness, can be sav/n froja a log of a given 
 'iameter. 
 
 'ind the solid content (jf V.n^ lo^. when niade square, 
 the last article — Then r-^ay. As -vwq thicknefs of Uiq 
 ni including the s:i\r calf : is to the solid feet : : so is 
 Inches) to the number of feet of boards. 
 
 low many feet of square edged boards- 1^ inck thick, 
 lading the «avv c;tif, can be sawn from a log 20 fiet 
 5 and 24 inches diameter ? 
 
 12x12x2x20—144=40 /'f^ solid content. 
 
 As U : 40 : : 12 : 384 feet, the Jlns, 
 
Art. 1^2. Tiic length, breaiUh and deptli fiTany s^pare^ 
 box being given, to lind how many bushels it wilfcontain. 
 
 RULE. ^ 
 Multiply ihe. lengtli bj the breadth, and th.at product^ 
 by tlie deptli, divide the last product bj 2150,425 the 
 solid inciieft in a statute bushel, and the quotient will be 
 ike answer. 
 
 KX AMPLE. 
 
 There is a square box, the length of its bottom is 50 
 inches, breadth of ditto 40 inches, and its de])th is 60 
 inches ; how many bushels of corn v/ili it liold ? 
 
 50x40x60~^£150,425=:55,84+ or 55 bushels, ihres 
 pecks. Arts. 
 
 Art. \^, The dimensions of the walls of a brick build- 
 ing being given, to find how many bricks are neces- 
 sary to build it. 
 
 HULE. 
 From the whole circumference of i>;0 vvall measured 
 round on the outside, STibtract four ti::r m Its thickness, 
 then multiply the remainder by tlie he;^:;-:, and that pro- 
 duct by the thickness of tlic v/all, pve3 u^Q, solid content 
 of the whole Vv all ; which multiplied by the number of 
 bricks contained in a solid foot, ci'v es tlic ansvvcr. 
 
 How map.y l- 
 2i inches thick 
 40 io-^t wide, r 
 loot thick ? 
 
 8x4x^,5-=., : 
 =»21,6 bricks in 
 
 44+40-f^4-f-' 
 
 a so 
 
 id:- ' ^ "^ 
 
 1 C:- 
 
 Multiply 
 
 ^J 
 
 1 ;J4 rc:y.:ii :i 
 20 height. 
 
 ix^s wide, and 
 L' 44 feet long,. 
 .ills to be one 
 
 ilea 172»8-~80 
 
 of wall. 
 
 •■.kncss. 
 
 S280 solid i^^itt in fiie wha.e walk 
 Multiply by 21,6 bricks in a solid foot. 
 
 Fmdii ct, 70848 bricks. Ms. 
 
APPENDIX. 
 
 •a^y 
 
 1 
 
 Art. 14. To find t!io tonnage of a slirp. 
 UULK. 
 
 Multiplj trie -cngtii of the keel by tiie breadth of tne 
 beam, and that pro, uct by the depth of tisc hold, and di- 
 vide the last piodi.ict t>v 93, and the ciuoticrit is tlie ton- 
 nage. 
 
 iCXAMiv:.:-".. 
 Suppose a s]<ii> 72 feet by ttse kcul, aiid ^24 feet by tlie 
 beam, and 12 feet dcf^p ; v. Vat is the tonnage ? 
 
 n2x24xJ2-r-95=«218.S+ions. Jlns. 
 KULK 11. 
 Multiply iiie len^^ih of the keel by tlie breadth of the 
 beam, and that product by half the bieadth of the beam, 
 and divide by 95. 
 
 EXAMPLE. 
 
 Asliip 84 feet by the keel, 28 feet by the beam; Avhat 
 is tlie tonnage ? 
 
 84x28x14-^95=350,29 tons. Jris. 
 
 Art. 15. From the proof of any cable, to find the 
 strength of another. 
 
 RULE. 
 
 The strength of cables, and consequently the» weights 
 of tlieir anchors, are as tlm cube of their peripheries. 
 Therefore; As the cube of the periplicry of any cable, 
 
 Is to the welglit of its anchor : 
 
 So is tiic cube of tiie per'n)]iery of any other cabU, 
 
 To the v/eiglit of It? anc!)or. 
 
 KXAMPLKS. 
 
 !• If a cable G Inches about, re({Uire an anchor of 2| 
 cwt. of Avhat v/cight must an anclior be for a 12 inch cable ? 
 
 As 6x6x6 : 2icwL : : 12x12x12 : IScwt. Jlna. 
 
 2. If a 12 inch cable require an anchor of 18 cwt. what 
 wuist the circumference of a cable be, for an anchor of 
 2i cwt. ? 
 
 c:vt. cwL tn. 
 
 As 13 : 12x12x12 : : 2,25 : 216^216=6 dns. 
 
 Art. 16. Having the dimensions of two similar built 
 s!up=> of a diiTerent i opacity, with the burthen of onft 
 
 ;?': i:i%in^ to frnd thcburSien of lli€ oth*.ir , 
 
22ft APPENDIX. 
 
 RULE. 
 
 Tlie burtliens of similar built ships are to each oti: r, 
 as the cubes cl tl 2it like dimensions. 
 
 EXAMPLE. 
 
 If a ship of 500 tons burthen be T5 ieet long in the k* ■ ', 
 I demand the burthen of another ship, whose keel is '.' 'J 
 feet long r - ' T.cwt.qrsJi'. 
 
 As 75x75x75 : 300 : : 100x100x100 : 711 2 i ■ ' - 
 
 DUODECIMALS, 
 
 CROSS MULTIPLICATION, 
 i.S a rule m?Ae use of by \vorknien and artificers in c<:::*- 
 
 inguptkc contents of tlieir wcrk. 
 
 RULE. 
 
 1. Under the multiplicand write thQ corresponding dc ■ 
 uoininaticns of tiie multiplier. 
 
 2. i\ii'h"::]v each ten: ' " ^^ "-and^beginnh^ 
 
 (•.tthe los\^v-t5 by the h= :i in the m::: - 
 
 piicr. and .\ rite the ]--■ its respeci'^ ■ 
 
 term? ^^;- rvmg to c ;., v 12jfrom e^. . 
 
 lower denominatioii (o i 
 
 5. Ih (;13 sn.n"ie Tuni-; '• niulthilKT ' < 
 
 by the i;':'- ' • :isTi^iii:itL;>n. !-i the nmltiph-^ 
 
 ;:rid s'^:: ' rvvwjnenhice removed to i ■' 
 
 ri-hf-: 
 
 niidtii)li'^i\ - 
 
 ling the result of eaca te: 
 of those in tiU! mu!t:plicn 
 
 Multiply 7 
 By " 4 
 
 F, 
 
 L 
 
 F. 
 
 X 
 
 4 
 
 6 
 
 9 
 
 7 
 
 ■3 
 
 8 
 
 9 
 
 " 
 
 09 '' ..J 6 91 IC 
 
APPENDIX £29 
 
 F. I. F. L F. L 
 
 Multiply 4 7 3 8 9 7 
 
 Bv 5 10 7 6 S 6 
 
 ti 
 
 Product, 
 
 2G 8 10 
 
 MuUipiv 
 By 
 
 F, I. 
 
 S 11 
 9 J 
 
 Product. 
 
 36 10 7 
 
 27 G 32 6 6 
 
 F. 7. 
 
 6 5 
 
 7 6 
 
 48 1 G 
 
 TEET, INCHES AND SECONDS. 
 F. L " 
 
 Multiply ,9 8 6 
 By 7 9 3 
 
 F. L 
 
 7 10 
 
 8 U 
 
 M 
 
 C9 10 
 
 % 
 
 [tiplier. 
 
 67 11 6 '" =prod. by the feet inthemul- 
 7 3 4 6 ''"=ditto by the inches. 
 2 5 1 6=ditto by the seconds. 
 
 75 5 3 7 6 Ms. 
 
 F. L " F. L " 
 
 Multiply 7 19 5 6 7 
 
 By " 7 8 9 8 9 iO 
 
 Product, 55 2 9 3 9 48 11 2 8 10 
 
 How many sqnare ieet in a board 16 feet 9 inches' 
 lon^, and 2 feet 3 inches wide ? 
 Sy Duodecinuds. 
 
 F. L 
 
 \Q 9 
 
 4 2 
 
 Am. 57 
 
 Ih, 
 
 Decimals. 
 
 h\ 
 
 L 
 
 15 
 
 9^16,75 feet 
 
 2 
 
 3= 2,25 
 
 
 8375 
 
 
 3S50 
 
 
 3350 
 
 
 F. 
 
 20 
 
 Ms. 37,6875 «. 37 8 $ 
 
^0 APPr^NDIX. 
 
 TO mp:asure loads of wood. 
 
 i ^ RULE. 
 
 % Multiply the length by the bread tii, and tlie product by 
 
 t, th.e depth ©r height, which will give the content in soli(i 
 
 feet 5 of which 64 make half a cord, and 128 a cord. 
 
 EXAMPLE. 
 
 How many solid i^eet are contained in a load of wood, 
 7 feet 6 inches long, 4 feet 2 inches wide, and 2 feet 3 
 inches high .^ 
 
 7 ft. 6 in.— 7,5 ami 4 fL 2 2;i.=4,l6r and 2 ft 3 z?2=» 
 2,25; then,7,5x4,l6r='si52525x2,25==70,3181'S5so^if^ 
 feetj Jns, 
 
 But loads of wood are commonly estimated by the foot* 
 allowing the load to be 8 feet long, 4 feet wide, and then 
 £ feet high will make half a cord, which is called 4 feet of 
 wood ; but if the breadth of tiie load be less than 4 feet, 
 its height must be increased so as to make half a cord 5 
 which is still called 4 feet of wood. 
 
 By measuring the breadth and lieighthof the load, the 
 content may be found by the following 
 RULE. 
 
 ^lultiply the breadth by the height, and half the pro- 
 Aict will be the content in feet and inches. 
 
 EXAMPLE. 
 
 Required the content of a load of wood which is 3 l^et 
 9 inches wide and 2 feet 6 inches high. 
 By Duodecimals. By Deciv.ids. 
 F.hu F. 
 
 S 9 
 S 6 
 
 7 6 
 1 10 
 
 6 
 
 Vu73 
 
 1875 
 750 
 
 9 4 
 
 4 8 
 
 6 
 5 
 
 <),575 
 
 F, in. 
 
 4,6875=4 8i, 
 
 -^rtS.4 8 5 4,6875=4 8^, or half a cord and 
 
 S} inches over, 
 ^he foregoing method is concise and easy to those who are well 
 '-4quajnted w'lih Duodeciiiials, but the following Table will give th« 
 ©Oirtent of any lc^ad of wood, by inspection only, sufficieDtly exaiQf 
 Ibi' corasoD practice ; wbicb nui Iw fo^d very ccryeaieat. 
 
*'?! 
 
 .3 T.ii 
 
 V; 
 
 
 '(lulih^ 
 
 Ilei 
 
 -;«<, 
 
 and Content. 
 
 
 BreaAth.] 
 
 J'L in. 
 2 6 
 
 Kei'^AJ in/cf ?.| 
 
 
 7/ic//M, 
 
 
 1 
 15 
 
 i^" 
 
 I: 
 
 T 
 
 2 3| 
 
 4| 
 
 5 G|7|8|9|10l 
 
 11 
 
 30 
 
 s 
 
 T 
 
 IT 
 
 T 
 
 5 
 
 "cr 
 
 7 9 
 
 10 11112 
 
 14 
 
 T 
 
 16 
 
 31 
 
 4r 
 
 .e 
 
 I 
 
 5 
 
 4 
 
 5 
 
 G 
 
 8 9 
 
 10 
 
 12 13 
 
 14 
 
 8 
 
 |1G 
 
 32 
 
 48 
 
 6^ 
 
 1 
 
 3 
 
 4 
 
 5 
 
 7 
 
 8 9 
 
 11 
 
 12 13 
 
 15, 
 
 ! 9 
 
 17 
 
 33 
 
 49 
 
 66 
 
 1 
 
 3 
 
 4 
 
 G 
 
 -' 
 
 8 
 
 9 
 
 11 
 
 12 14 
 
 14 
 
 10 
 
 lir 
 
 34 
 
 ^>l 
 
 GS' 
 
 2 
 
 3 
 
 4 
 
 G 
 
 7 
 
 9 
 
 10 
 
 11 
 
 43 14 
 
 ir; 
 
 , 11 
 
 118 
 
 35 
 
 53 
 
 70 
 
 o 
 
 3 
 
 4 
 
 6 
 
 r 
 
 9 
 
 10 
 
 12 
 
 1SJ15|1GJ 
 
 IT 
 
 18 
 
 SG/J4 
 
 72 
 
 ¥ 
 
 3 J 
 
 ^ 1 
 
 O 
 
 9 11 
 
 12 14 15 17' 
 
 ! 1 
 
 19 
 
 371.56 
 
 74 
 
 o 
 
 3 5 
 
 G { 
 
 8 
 
 9 11 
 
 12 14 16 17 
 
 o 
 
 19 
 
 SS -57 
 
 76 
 
 o 
 
 3i5 
 
 '6 ! 
 
 8 lOJll 
 
 13 14 16 i:^ 
 
 1 3 
 
 jl9 
 
 39 59 
 
 78 
 
 2 
 
 3 
 
 5 
 
 « 1 
 
 8 10 111 
 
 13 15 16 18, 
 
 4 
 
 20 
 
 40 60 
 
 8C 
 
 2 
 
 3 
 
 5 
 
 
 8 10 
 
 12 
 
 13 15 17 18 
 
 5 
 
 21 
 2i 
 
 41 62 
 
 42 33 
 
 82 
 S-1 
 
 2 
 
 3 
 
 5 
 
 7 
 
 8 10 
 
 12 
 
 14 16 17 19 
 
 6 
 
 "o" 
 
 4 
 
 5 
 
 _,^_. 
 
 9 ill 
 
 12|14|16|1S 
 
 19 
 
 7 
 
 o:^ 
 
 43 G4 
 
 SCI 
 
 2!4 
 
 5 
 
 i 
 
 9 11 
 
 13 
 
 14 16 18 
 
 20 
 
 8 
 
 iS^ 
 
 44 oG 
 
 88 1 2 U 
 
 6 
 
 7 
 
 9 11 
 
 15 
 
 15 17 18 
 
 2Q 
 
 ) 9 
 
 !.>; 
 
 45^68 
 
 90 2,4 
 
 6 
 
 
 9 
 
 11 
 
 13 
 
 15 17 19 
 
 2f 
 
 10 
 
 ii-jS 
 
 46 69 
 
 92' 2 4 
 
 6 
 
 7 
 
 9 
 
 12 
 
 13 
 
 15 17 19i2l| 
 
 ! ^^ 
 
 1^23 
 
 4770 
 
 94i 2 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 18 20 
 
 22 
 
 4 i 
 
 [24 
 
 48 7.2 
 
 961 2 14 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 18 20 
 
 22 
 
 TO USE THE FOREGOING TABLE. 
 
 First measure the breadth and height of your load to the 
 nearest average inch ; then find the breadth in the left hand 
 column of the table ; thfn move to the right on the same line 
 til! you come under the height in (eM, and you will have the 
 content in inches, answerinf^ the fcetj to which add the cor.- 
 tent of the inches on the right and divide the sum by 12, and 
 you will have the tvue content of the load in feet and inches. 
 
 Note.— The contents answering the inches being always 
 small, may be added by inspection. 
 
 EXAMPLES. 
 
 1. Aduiit a loa4 of wood is 3 feet 4 inches Vvide, and 2 feet 
 10 inches high ; required the content. — 
 
 Thus, agaiiist 3 ft. 4 inches, and under 2 feet, stands 40 inch- 
 es ; and under 10 inches at top, stands 17 inches: then 40-f- 
 17=57 true content in inches, which divide by 12 gives 4 feet 
 9 inches, the answer. 
 
 2. The breadth being 3 feet, and height 2 feet 8 inches ; 
 required the content. — 
 
 Thu9, with bf2»4th S feet inches, and under 2 ft^Jt 
 
S.'i 
 
 Al'PKNDIX. 
 
 atop, stands S6 iiul.cs ; and uwdcr 8 inches^ sta&da 1%^ 
 inches : now 35 and 12, make 48, the answer in iacheai 
 arid 48-7-12=4 feet or just half a cord. 
 
 3. Admit the breadth to be 3 feet 11 inches, and height 
 3 feet 9 inches ; required the content. 
 
 Under 3 fee.t at top, stands 70 ; and under 9 inches, is 
 18 : 70 and 18, make 88-~-12~7 feet 4 inches, or 7 ft. 1 
 qr. 2 inches, the answer* 
 
 TASLE T. 
 
 Showing: the anumnf of £'i^ or %\,at 5 and 6 pcT cent. per 
 
 ammm^ Om^womid Interest^ for 20 years. 
 
 i'ra. 
 
 5 2)er ceut.\Gpii>r cent. 
 
 1 Vs. 15 per cent. 
 
 6 per cent. 
 
 1 
 
 1,05000 
 
 1,06000 
 
 11 
 
 1,71034 
 
 1,89829 
 
 2 
 
 1J0250 
 
 1,12360 
 
 12 
 
 1,79585 
 
 2,01219 
 
 S 
 
 1,15762 
 
 1,19101 
 
 13 
 
 1,88565 
 
 £,13292 
 
 4 
 
 1,21550 
 
 1,26247 
 
 14 
 
 1,97993 
 
 2,26090 
 
 5 
 
 1,27628 
 
 1.33822 
 
 15 
 
 2.07893 
 
 2,39555 
 
 6 
 
 1,54009 
 
 1,41851 
 
 16 
 
 2,18287 
 
 g.54727 
 
 4 
 
 1,40710 
 
 1,50565 
 
 17 
 
 2,29201 
 
 2,69277 
 
 t 8 
 
 1.47745 
 
 1.59S84 
 
 18 
 
 2,40661 
 
 ^ 2,85433 
 
 f 9 
 10 
 
 1,55132 
 
 1,68947 i 19 
 
 2,52695 
 
 3,02559 
 
 1,62889 
 
 1,7<)084 1 20 
 
 2,65329 
 
 3,20713 
 
 VII, The weights of the coins of tlie United States. 
 pwt. gr. 
 11 6 1 
 5 15 V 
 
 2 m ' 
 
 17 
 8 
 4 
 1 
 
 Ea^le^, 
 
 llalf-Ea^Ies, 
 
 Quarter-Eagles, 
 
 Ooilars, 
 
 llalf-Dollars, 
 
 Quarter-Dollars, 
 
 Dimes, 
 
 Half-Dimes, 
 
 Centr5, 
 
 Half-Cents, 
 
 16 
 
 8 
 
 Stuiidaid 
 Gold. 
 
 Standard 
 
 . f" Silver. 
 
 2ajJ 
 
 8 K^PP^'- 
 
 Tlie standard for gold coin is 11 parts piire gold, and one part al» 
 foy— the alloy to consist of silver and copper. The sianuord for 
 silver coin is U25 perts doe Uk 179 parU a!lov~^.V, alloy to be wtiolU 
 If copper. 
 
APPEjiDiX. 
 
 ANNUITIES 
 
 Table ii. 
 
 Showing the amoiint of 
 £ 1 annuity^ forborne 
 Jor 31 years or under, 
 at 5 and 6 jier cent, 
 comvound interest. 
 
 Frs. 
 
 / 
 
 8 
 
 9. 
 
 10 
 
 11 
 12 
 15 
 14 
 15 
 
 16 
 IT 
 IS 
 19 
 
 20 
 
 21 
 
 23 
 
 24 
 
 25 
 
 26" 
 
 27 
 
 28 
 
 29 
 
 SO 
 
 SI 
 
 l.OUOOOO 
 2,050000 
 3,152500 
 4,310125 
 5'525631 
 
 6,801913 
 
 8.142009 
 
 9^549109 
 
 11,026564 
 
 12.577892 
 
 ^4,206/87 
 15,917126 
 17,712982 
 19,598632 
 
 21,578564 
 
 23,657492 
 25,840366 
 28,132385 
 50,539004 
 33,065954 
 
 1. 000000 
 2,060000 
 3,183800 
 4,374616 
 5,637193 
 
 6,975319 
 
 8.393838 
 
 9,897468 
 
 11,491316 
 
 15,180770 
 
 I4,97i6*ic? 
 16,869942 
 18.882133 
 21,015066 
 
 23,275969 
 
 25,672528 
 28,212380 
 30,905653 
 33,759992 
 36,78559: 
 
 35,719252 
 38,505214 
 
 41,430475 
 
 44,501999 
 
 47. 727099 ) 
 
 5],Tr3'45^ll59,156382 
 
 54fiG0V2C>\QS,705T65 
 
 39,992727 
 43,392291 
 46,995828 
 50,815578 
 54,854512 
 
 58,402583 
 62,322712 
 66,438847 
 70,760790 
 
 68,528112 
 73^639798 
 79,058186 
 84, 801677 
 
 TABLE ill. 
 
 Showing the jiresent 
 ivorth of£ 1 annuity, 
 to continue for 51 
 years, at 5 and 6 per 
 cent, compound int. 
 
 0,952381 
 1,859410 
 2,723248 
 3,545950 
 4.329477 
 
 5.075692 
 
 5,786278 
 6,463213 
 7,107822 
 7,721735 
 
 8,306414 
 8^863252 
 9.393573 
 9,89864 f 
 10,579658 
 
 10,837769 
 11,274066 
 M ,639587 
 12,085321 
 12,462210 
 
 125821153 
 13,163003 
 13,488574 
 15,798642 
 14.093944 
 
 0,943396 
 1,853393 
 2,673012 
 3,465106 
 4,212364 
 
 4.9J7S24 
 5,582381 
 6,209794 
 6,801692 
 7.360087 
 
 7,886875 
 S,385844 
 8,852685 
 9,294984 i 
 9,712249 
 
 10,105895 
 10,477260 
 10,827603 
 11,158116 
 11,469921 
 
 11,764077 
 12,041532 
 12,305330, 
 12.550357 
 12,783356 
 
 14,375185 13,003160 
 
 14,643034 
 14,898127 
 
 15,14^073^15,5907 
 15,372451 """^ 
 15,592810 
 
 ^5,210534 
 15,406164 
 
 >1 
 '15,764851 
 15,929086 
 
^ €34 
 
 APPKNPXX. 
 
 TABLES.^ 
 
 X TIE three following Tables are calculated agreeable 
 to an Act of Congress passed in November, 1 792, making 
 foreign Gold and Silver Coins a legal tender for the pay- 
 ment of all debts and demands, at the several and respec* 
 tive rates following, viz. The Gold Coins of Great-Bri- 
 tain and Portugal, of their present standard, at the rate of 
 100 cents for i:^\ery 2.7 grains of the actual v/eight there- 
 of. — Tiiose of France and Spain 27| grains of the actual 
 weight thcieof. — Spanish milled Dollars v/eighing If 
 pwt. 7 gr. equal to 100 cents, and in proportion for the 
 parts of a dollar. — Crowns of France, weighing 18 pwt» 
 ITgr. equal to 1 10 cents, and in proportion f >r the parts 
 of a Crown. — Tliej have enacted, tliat every cent shall 
 contain 208 grains of copper, and every half-cent 104 
 grains. 
 
 TABLE lY. 
 
 ^Feighis of several pieces of English^ Portuguese, and 
 French Gold Coins, 
 
 Johannes 
 
 FwL 
 
 [ (Jr. 
 
 Dols. Cis. M. 
 
 18 
 9 
 5 
 2 
 5 
 2 
 
 16 
 8 
 4 
 6 
 
 6 
 15 
 
 6 
 15 
 12 
 
 G 
 
 S 
 
 16 
 8 
 
 4 6(>| 
 2 SS^ 
 
 4 59 8 
 
 £ 29 9 . 
 
 14 45 2 1 
 
 r 22 6 1 
 
 5 61 3 U 
 
 6 14 si 
 
 Single, ditto, 
 
 finglish Guinea, .... 
 
 Half, ditto, 
 
 French Giwnea, . . . . , 
 
 Half, ditto, 
 
 4 Pistoles, 
 
 C Pistoles, 
 
 I Pistole, 
 
 Moidore, 
 
APPJINPIX. 
 
 S55 
 
 
 Ip5 
 
 •0.7»i-«^- ^> - t- CO »:^ ^t- « CS 10 0«0 W- W«0»0 
 
 -n 
 
 
 3 
 
 
 •• 
 
 s 
 
 1 
 
 
 •^ CI CO -^ kC CO t- CO CV O ^ G) CO "«f «0 « r- CO {y> M -« ©» 60 
 
 1 
 
 I 
 
 CO CO CT> 
 
 xo CO tc 6< C5 o G* CO U-; -. M T* ^ <•£ T* o i^ eo 
 
 d 
 
 ooir- * CO — i?5 n -?■» T o CO t- — •* CO e-» «o crs «0 'X. o eo 
 
 -«'- — G^G^&<cocO'r'!^TJ•^r;lOi00t^cp^-t-ooco 
 
 
 — e^eOTfio-ci-ccc-.o — S'icorp«5or-Gooo»-'«^r> 
 
 
 I 
 
 t- to o -3* CO s-i — < r- to lo >»• CO G< -* 
 
 iC: -< G! CO •*i« '-O '-0 C-- CO C^3 ffi O • 
 
 ~ 
 
 SlCO-^iCtOt^OCOO 
 
 - 
 
 ei eo rj" o CO r^ CO o 
 
 
 - 
 
 s* 
 
 eo 
 
 t- -* — CO o e^ o to CO f T? P-. 00 «.o e< <a3 ri* — &< uo «» 
 
 ?»-ieic^"^»o®l*c90>0'-4e*co'-*ir>ot-o»oor-c?co 
 
216 
 
 APPENDIX. 
 
 YIII. TJiBLE of Cmts, answering to the Cufrmcks 
 of the United States, with Sterling , Sfc. 
 Note. — The figures on the right hand of the space, 
 show the parts of a cent, or mills, &c. 
 
 
 6s. to 
 
 8s. to 
 
 7s 6d. 
 
 4s.Sd. 
 
 5s. to 
 
 4s.6d. 
 
 4s. Und. 
 
 
 tlie 
 
 the 
 
 to the 
 
 to the 
 
 the 
 
 to thp 
 
 to the 
 
 
 Boll 
 
 Boll 
 
 Boll. 
 
 Boll. 
 
 Boll. 
 
 Boll. 
 
 Bollar, 
 
 P. 
 
 cents. 
 
 cents. 
 
 cents. 
 
 cents. 
 
 cents. 
 
 cents. 
 
 cents. 
 
 1 
 
 1 3 
 
 1 
 
 1 1 
 
 J 7 
 
 1 6 
 
 ■ 1 Sj 1 
 
 7 
 
 s 
 
 2 7 
 
 2 
 
 2 2 
 
 S 5 
 
 3 3 
 
 3 7 
 
 3 
 
 4 
 
 5 
 
 4 1 
 
 5 1 
 
 3 3 
 
 5 5 
 
 5 
 
 5 5 
 
 5 
 
 1 
 
 4 
 
 5 5 
 
 4 1 
 
 4 4 
 
 7 1 
 
 6 3 
 
 7 4 
 
 6 
 
 8 
 
 5 
 
 6 9 
 
 5 2 
 
 5 5 
 
 8 9 
 
 8 6 
 
 9 2 
 
 8 
 
 5 ' 
 
 6 
 
 8 S 
 
 6 2 
 
 6 6 
 
 10 7 
 
 10 
 
 ?* 1 
 
 10 
 
 2 f 
 
 7 
 
 9 7 
 
 7 2 
 
 7 7 
 
 12 5 
 
 11 6 
 
 1'19 
 
 11 
 
 9 
 
 8 
 
 11 1 
 
 8 3 
 
 8 8 
 
 14 2 
 
 13 3 
 
 .^B 
 
 13 
 
 6 
 
 9 
 
 12 5 
 
 9 3 
 
 10 
 
 16 ^ 
 
 15 
 
 16 6 
 
 15 
 
 3 
 
 10 
 
 13 8 
 
 10 4 
 
 ii 1 
 
 17 8 
 
 16 6 
 
 18 5 
 
 17 
 
 
 11 
 
 15 2 
 
 11 4 
 
 12 2 
 
 19 6 
 
 18 3 
 
 20 3 
 
 18 
 
 
 S. 
 
 
 
 
 
 
 
 
 
 1 
 
 16 6 
 
 12 5 
 
 13 3 
 
 21 4 
 
 20 
 
 £2 2 
 
 20 
 
 
 £ 
 
 S3 3 
 
 25 
 
 26 G 
 
 42 8 
 
 40 
 
 44 4 
 
 4) 
 
 •i 
 
 5 
 
 50 
 
 57 5 
 
 40 
 
 64 2 
 
 60 
 
 66 6 
 
 61 
 
 5 
 
 4 
 
 66 6 
 
 50 
 
 53 3 
 
 85 7 
 
 80 
 
 88 8 
 
 82 
 
 
 5 
 
 83 S 
 
 62 5 
 
 66 6 
 
 107 1 
 
 100 
 
 111 1 
 
 102 
 
 5 
 
 6 
 
 IGO 
 
 75 
 
 80 
 
 123 5 
 
 120 
 
 133 S 
 
 123 
 
 
 7 
 
 '116 6 
 
 87 5 
 
 93 3 
 
 150 
 
 140 
 
 155 5 
 
 143 
 
 5 
 
 8 
 
 133 3 
 
 100 
 
 106 6 171 4 
 
 160 
 
 177 7 
 
 164 
 
 1 
 
 9 
 
 150 
 
 112 5 
 
 120 
 
 192 8 
 
 480 
 
 200 
 
 184 
 
 5 
 
 10 
 
 166 6 
 
 125 
 
 133 3 
 
 214 2 
 
 200 
 
 222 2 
 
 205 
 
 1 
 
 11 
 
 183 5 
 
 137 5 
 
 146 6 
 
 235 7 
 
 220 
 
 244 4 
 
 225 
 
 6 ; 
 
 12 
 
 200 
 
 150 
 
 160 
 
 257 1 
 
 240 
 
 266 6 
 
 246 
 
 1 < 
 
 15 
 
 216 6 
 
 162 5 
 
 173 S|278 5 
 
 260 
 
 288 8 
 
 ^66 
 
 6 1 
 
 14 
 
 233 3 
 
 175 
 
 186 O'SOO 
 
 280 
 
 311 1 
 
 287 
 
 1 1 
 
 15 
 
 250 
 
 187 5 
 
 200 
 
 32 i 4 
 
 300 
 
 333 5 
 
 307 
 
 6 i 
 
 16 
 
 266 6 
 
 200 
 
 213 3 
 
 342 8 
 
 320 
 
 355 5 
 
 328 
 
 £" i 
 
 17 
 
 283 3 
 
 212 5 
 
 226 6 
 
 564 2 
 
 340 
 
 
 348 
 
 / 
 
 18 
 
 300 
 
 225 
 
 240 
 
 385 6 
 
 360 
 
 400 
 
 369 
 
 o 
 
 19 
 
 316 6 
 
 237 5 
 
 253 3 
 
 407 1 
 
 380 
 
 ^i^r ^ 
 
 '■ ' ^ '"•; 
 
 
 20 
 
 333 3 
 
 250 
 
 266 6 
 
 428 5 
 
 :n') 
 
 
 
 
APPENDIX. 
 
 isr 
 
 TABLE IX, 
 
 Showing the value of Federal Money in other Currencies, 
 
 Federal 
 Money, 
 
 J>rtW'En^ 
 
 land^ Vir- 
 
 ^iniaj ami 
 
 Kmtucky 
 
 currency. 
 
 *MeW'Fork 
 
 andJVorth- 
 
 Carolina 
 
 currency. 
 
 ^, Jersey y 
 Fennsylva- 
 nia^ i)ela- 
 ware, and 
 Maryland 
 currency. 
 
 South-Car- 
 
 olina 
 
 t, and 
 
 Georgia 
 
 currency. 
 
 s. 
 
 d. ■ 
 
 
 
 OJ 
 
 1 
 
 1 
 
 
 
 n 
 
 
 
 '2k - 
 
 
 
 ^li 
 
 r 
 
 H 
 
 
 
 4 
 
 
 
 44 
 
 
 
 5 
 
 
 
 5J 
 
 
 
 6i 
 
 
 
 6* 
 
 
 
 7i 
 
 
 
 n 
 
 
 
 8i 
 
 
 
 9 
 
 
 
 94 
 
 
 
 10 
 
 
 
 10S 
 
 ">" 
 
 !ia^•c 
 
 Cerits, 
 1 
 
 S 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 10 
 11 
 12 
 
 3 
 
 S4 
 
 4i 
 5 
 
 5J 
 64 
 
 rj 
 
 8 
 8j 
 9i 
 10 
 
 A L.. 
 
 1 
 
 S 
 
 S| 
 41 
 51 
 6J 
 7i 
 8J 
 94 
 104 
 114 
 04 
 14 
 24 
 Si 
 4i 
 5^ 
 
 s. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 I 
 1 
 1 
 
 1 
 1 
 
 1 
 
 1* 
 
 21 
 34 
 4^ 
 
 9 
 
 10 
 
 lOJ 
 
 113 
 
 04 
 
 14 
 
 24 
 
 H 
 
 4i 
 
 RNO Wail men bvl 
 in tor .111(1 
 
 received to my full satis^favini 5 J 
 tiiis (lay 01 in the year of oiir ^. 
 
 demised and to farm let, and "do by these presents, de- 
 mise and to farm letj inito t!iC said P. V. his heirs, execu- 
 tors, admiTiistrators and asssi<;ns,onu certain piece oFIand, 
 lying and being situated in said bounded, &g 
 
 fHere describe th.e boundaries"! with a dwellin*^ -house 
 tliereon standing, tor the term ot one year from this date. 
 To HAVE and to hold to him the ^aid I'. V. his \w\vs, 
 ^xeoutorS} administrators and assign* foi sail tern?, tor 
 
S3S 
 
 APPEKOIX. 
 
 A FEW USEFUL FORMS IX TRANSACTING IJUiilNKSS. 
 
 AN OBLIGATORY BOND. 
 
 KNOW all men by these presents, tluat I, C. D. of 
 in the couiitj of aiu held and iinnly bound to 
 
 H. W. of in the pen-il sum of to be paid 
 
 II. W. his certain atternej, executors and administrators; 
 to which payment, well and truly to be inade and done, 
 I bind myself, my heirs, execiiturs aiHl administrators, 
 firmly by these presents. Signed v. ith my hand, and 
 sealed with my seal. Dated at fms day 
 
 of A. D. 
 
 The condition of this obligailo, . That if the 
 
 above bounden C. D. &c. [Here iu^ert the condition,'] 
 Then this obligation to be void and of none eftect ; other- 
 wise to remain in full force and virtue. 
 Signed J sealed and delivered J 
 in the presence of ^ 
 
 A BILL OF SALE. 
 
 KNOW all men by these presents, tiiat I, B. A. of 
 for and in consideration of to me in hand paid by 
 
 D. C. of the receipt whereof I ' ' 
 
 knowledge, have bargained, sold and d^^'5 
 these presents, do bargain, sell and deJa 5 
 D. C. [Here specify tlie pruvertu sol {'^j " 
 HOLD the aforesaid bargained prer 
 C. his executoi's, admiriisi:rafi)(70 
 
 -.-'.^ the said II. /Hi 
 
 12 
 13 
 14 
 15 
 16 
 17 
 }8 
 19 
 20 
 
 200 
 216 6 
 235 3 
 250 
 9,6Q 6 
 283 S 
 
 00 
 316 
 
 162 
 175 
 
 187 5 
 
 200 
 
 212 
 j225 
 237 
 250 
 
 160 
 173 
 
 186 6 
 200 
 213 3 
 226 6 
 240 
 253 3 
 266 6 
 
 7 1 
 
 Sf278 5 
 
 SCO 
 
 321 4 
 
 342 8 
 
 ;64 
 
 >85 6 
 407 1 
 
 42B 5 
 
 220 
 240 
 
 260 
 280 
 300 
 320 
 340 
 
 ;6o 
 
 380 
 
 0') 
 
 200 
 
 222 g 
 244 4 
 
 288 8 
 311 1 
 
 n r^ r> r 
 
 355 5 
 377 7 
 400 
 
 422 ^ 
 
 143 
 
 5 
 
 164 
 
 1 
 
 184 
 
 6 
 
 205 
 
 1 
 
 225 
 
 6 
 
 246 
 
 1 
 
 266 
 
 6 
 
 287 
 
 1 
 
 307 
 
 6 
 
 328 
 
 2 
 
 348 
 
 / 
 
 369 
 
 
 
APPENDIX. S39 
 
 and bequeatli to mj dear brother, R. A. the sum of ten 
 pounds, to buy him mourning;. I give and bequeath to 
 my son, J. A. the sum of two hundred pounds. I give 
 and bequeath to my daughter, E. E. the sum of one hun- 
 dred pounds ; and to my daughter A. V. the like sum of 
 one hundred pounds. All the rest and residue of mj 
 estate, goods and chattels, I give and bequeatli to mj 
 dear beloved wife, E. R. whon* I nominate, constitute 
 and apptnnt sole executrix of this my last will and tes- 
 tament, hereby revoking all other ancl former ^ilis by me 
 at any time heretofore made. In witness whereof, I have 
 hereunto set my hand and seal, the day of 
 
 ill the year of our Lord 
 
 Signed, sealed, publislied and declared by the said 
 testator, B. A. as and for his last will and testament, in 
 the presence of us who have subscribed our names as wit- 
 /jesses tliereto, m the presence of the said testator. 
 
 R. A. 
 S. D. 
 L. T. 
 
 Note.— The testator aRer taking off his seal, must ia 
 presence of the witnesses pronounce these words, " I pub- 
 lish and declare this to l>e my last will and testament.'' 
 
 Where real estate is devised, three witnesses are abso- 
 lutely necessary, who must sign it in the presence of the 
 testator. 
 
 A LEASE OF A HOUSE. 
 
 KNOW all men by these presents, that I, A. E. of 
 in for and in consideration of the sum of 
 
 received to my full satisiaction of P. V. of 
 this day of in tlie year of our Lord, have 
 
 demised and to farm let, and do by these presents, de- 
 mise and to farm let, unto the said P. Y. his l.eirs, execu- 
 tors, admiTiistrators and asssigns, on.! certain piece of land, 
 lying and being situated in said bounded, &g 
 
 fHere describe the boundaricsl wiiii a dwelling-house 
 tliereon standing, tor the term of one year from this date. 
 To HAVE and to hold to him the -aid i'. V. his heirs, 
 meoutors, atimiui^trators and assigns foi sail tci nr, lor 
 
f40 APPENDIX. 
 
 bim the said P. V. to use and occupy, as to him shall seem meet 
 and proper. And the said A. B. doth further «ovenant with 
 the said P. that he hath good right to let and demise, the said 
 letten and demised premises in manner aforesaid, and that he 
 the said A. during- tlie said time will suffer the said P. quieUy 
 lo HAVE and to HOLr, use, occupy and enjoy said demised pre- 
 •nises, and that said P. shall have, hold, use, occupy, possess 
 and enjoy the same, free and clear of all incumbrances, claims, 
 rights and titles whatsoever. In witness whereof, I tlie said 
 A. B. have hereunto set my hand and seal this 
 day of 
 ISignedj sealed and delivered ) AT? 
 
 In presence (if ) . ' ' 
 
 A NOTE PAYABLE AT A BANK. 
 [g500, GO] Hartford, May 30, 1815. 
 
 FOR value received, I promise to pay to John Merchant, 
 or order, Five Hundred Dollars and Sixty Cents, at Hartford 
 Bank, in sixty davs from the date. 
 
 WILLIAM DISCOUNT. 
 
 AN INLAND BILL OF EXCHANGE. 
 
 [g83, 34] Boston, June 1, 1815. 
 
 TWENTY days after date, please to pay to Thomas 
 Goodwin or order, Eighty-Three Dollars anil Thirt}'"-Four 
 Cents, and place it to my account, as per advice from your 
 humble servant, SIMON PURSE. 
 
 Mr. T. W. Merchani, } 
 JVexV'York. J 
 
 A COMMON NOTE OF HAND. 
 
 [;J1303 New- York, March 8, 1821. 
 
 FOR value received, I promise to pay to John Murray, 
 One Hundred and Thirty Dollars, in four months from this date, 
 with interest until paid. JOHN LAWRENCE. 
 
 A COMMON ORDER. 
 
 NEw-Yor June 10» i822 
 
 JSlr. CJuirlcs Careful^ 
 
 P>Rase to deliver Mr. George Speedwell, the amount di 
 Twenty -Five Dollars, in goods, from your store; and charge 
 the same to the account of Your ObH. Servant, 
 
 E. WHITE. 
 FiNIB. 
 
THE 
 
 PRACTICAL ACCOUiTTANT, 
 
 OR, 
 
 BEST METHOD OP 
 
 FOa THE 
 
 EASY INSTRUCTION OP YOUTH. 
 
 DESIGNSD 
 
 AS A COMPANION TO DABOLL^S 
 
 ARITHMETIC. 
 
 BY SAMUEL GBEEN. 
 KfBUSHED BY SAMUEL GKEEN. 
 
 ICBVV',L0N2iDK 
 
INTRODUCTION. 
 
 Scholars, male and female, after they have acquired a 
 
 * rit kuowledg-e of Arithmetic, especially in the funda* 
 
 ! rules of Addition, Subtraction, Multiplication, and Di- 
 
 1., should be instructed in the practice of Book Keeping, 
 
 v this it is not meant to recommend that the son or daughter of 
 V very farmer, mechanic, or shop keeper, should enter deeply 
 into the science as practised by the merchant, engaged in exten- 
 sive business, for such study would eng-ross a great portion of 
 time which might be more usefully employed in acquiring a 
 proper knowledge of a trade, or other employment. 
 
 Persons employed in the comiton business of life, who do not 
 ^leep regpilar accounts, are subjected to many losses and incon- 
 veniences; to avoid which, the following simple and conreot 
 plan, is recommended for tlieir adoption. 
 
 Let a small book be made, or a iew sheets of paper sewed 
 together, and ruled after the examples given in this system. In 
 the book, termed the Day Book, are duly to be entered, daily, 
 all the transactions of ths master or mistress of the family, which 
 require a charge to be made, or a credit to be given to any per- 
 ion. No article thus subject to be entered, should on any con- 
 sideration, be deferred till another day. Great attention should 
 be given to write the transaction in a plain hand ; the entry 
 ■should mention all the particulars necessary to make it fully un- 
 derstood, with the time when they took place ; and if an article 
 ^e delivered, the name of tlie person to whom delivered is to be 
 mentioned. No scratching out may be suffered ; because it in 
 sometimes done for dishonest purposr j, and will weaken or de- 
 stroy the authority of your accounts. But if, through mistake, 
 any transaction should be wrongly entered, the error must be 
 rectified, by a new entry : and the wrong one may be cancelled 
 by writing the word Error ^ in the margin. 
 
 A book, thus fairly kept, will at all times show the exact state 
 of a person's affairs, and have great weight, should there at any 
 tine be a necessity of producing it in a court of Justice. 
 
FORM OF A DAY BOOk'. 
 
 * JEREMIAH GOODALE, Alhviu, January 1, 
 
 Entered. 
 
 1 
 
 Joseph Mii5tii>?vs, 
 By 3 montlis' wages, at ^o i 
 (late, . . 
 
 Entered. Samuel Stacy, 
 
 1 'To 2 weeks' wa^R «"' 
 spinning \^ri\, at 7^ 
 tiiisday, 
 
 Entered. 
 
 1 
 
 Entered. 
 1 
 
 Entered. 
 
 1 
 
 Entered. 
 
 1 
 
 Entered. 
 
 1 
 
 Anthony Biliinj^s, . . Cr. 
 
 By my order in favor of Joseph Hasting-s, 
 
 15 
 
 Joseph liastiii^;^, . . . Dr. 
 To my order for goods out of the store of 
 Anthony Billings, 
 
 Thomas Grosvenor, . . Dr. 
 To the frame of a house completed and raised 
 this day on his Glover Fann, so called, 
 4000 feet at 2.^ cents per foot, 
 
 1 8 _.! 
 
 Edward Jones, . . . Cr. 
 By his team at sundiy times, carrying ma- 
 nure on my farm, . . . . ii 
 
 25 • 
 
 Entered. 
 1 
 
 filtered. 
 1 
 
 Thomas GrosvenOr, . . Dr. 
 To 48 window sashes delivered at his Glover 
 Farm, so called, at g 1,00, . . ^48,00 
 Setting 500 panes of glass by my son 
 
 John, at 1 i cents, . . 7,50 
 
 10 days' work of myself finishing front 
 
 room, at ^1,25 a day, . . 12,50 
 7i do. of William, my hired man, ^ 
 
 laying tlif kitchen floor and hang- > 6,30 
 
 ing doors, at 84 cents a Jay, ) — 
 26-— 
 
 Anthony Billings, . . . Cr. 
 
 By 2 galls, molasses at 33 cts. pergail. 0-,72 
 
 *4 yds. of India Coljon, at 18|fcents, .0,74 
 
 2 flannel sMrts to Joseph Hastings 2J6 
 
 Joseph Hastings, 
 To 2 shirts of A. Billings, 
 
 Dr. 
 
 II T 
 
 « Thtrt pvt the name of the owur <f the iofJc. andjirsi date. 
 
"Entered. 
 1 
 
 Entered. 
 
 1 
 
 Entered. 
 1 
 
 Entered. 
 1 
 
 jBntered. 
 1 
 
 Entered. 
 1 
 
 Entered. 
 1 
 
 Entered. 
 1 
 
 FORM OF A DAY BOOK. 
 
 Albany, February V2, 18^2. 
 
 Joseph Hasling"s, 
 To my order, on T. Grosvenor, 
 
 16 
 
 Thomas Grosvenor, . . *T>v. 
 To 3 days' work of myself on yorrr fence 
 atgl,25perdaT, . " . . 3,75 
 3 days' do. my man Wm. on your stable 
 and finisliing off kitchen, at 84 cts. 2,52 
 2 pr. brown yam stocldngs, at 4*2 cts, 0,84 
 
 ^ . _1 
 
 Edward Jones, . . . Cr 
 By 4 months' hire of his son William at glO 
 a month, 
 
 Edward Jones, . . . Dr 
 To my draft on Thomas Grosvenor, 
 
 Lntered. 
 1 
 
 Thoinas Grosvejior, . . Cr. 
 By my order in frv'or of Joseph Hastings, 
 
 ©r. 
 
 "^4« 
 
 Thomas Grosrenor, 
 By my draft in fafor of E. Jones, 
 
 -.28 — ■' 
 
 Cr. 
 
 Tliomas Grosvenor 
 To t-ie frame cf h barn 
 
 Dr. 
 
 Anthony Billings, . . Cr. 
 
 For the following articles, 
 14 lbs. muscovado sugar at ^12 prc"*vt 1,50 
 
 1 larg-e dish, 
 
 6 plates, 
 
 4 cups and saucers, 
 
 1 pint French Bmudy, 
 
 1 quart Cherry Bounce, 
 Thread and ta]: e, . 
 
 2 Thimbles, 
 1 pair Scissors, . 
 1 quire p-Aper, 
 Wafers, 4 ; ink, 6 ; 1 bottle, 8 ; 
 
 0,23 
 0,30 
 0,20} 
 0,17, 
 0,33 
 0,1$ 
 0,04 
 0,17 
 0,25 
 0,18 
 
 Peter Dciboll, . . . Dr. ' 
 
 To a cotton Coverlet delivered Sai-ah Brad- 
 
 fortij bv vonr wf Kten order, dated 14, Jan. 
 
tO'RM OF A DAY BOGK. 
 
 1 
 
 Entered. 
 1 
 
 Entered. 
 
 1 
 
 Entered. 
 1 
 
 Entered. 
 1 
 
 Entered. 
 2 
 
 Albany, Marchl^l822. 
 
 Thomas Grosvenor, . . Cr. 
 By 1 b^el containing cider sold and deliv- 
 ered to Anthony Billings, . 
 10 
 
 Thomas Grosvenor, 
 B" cash paid me this date, 
 
 ' 4 
 
 Cr. 
 
 Anthony Billings, . . Dr. 
 
 To one Barrel of Cider, . . jl,17 
 
 1 baiTel containing the same (from 
 
 Thomas Grosvenor,) . . . 0,58 
 
 Anthony BiUings, . . . Dr. 
 To casii per his order to George Gilbert, 
 : — 1 5 ., 
 
 Cr. 
 
 Peter Dabo?!, 
 By amount of his shoe account, . §4,48 
 Yam received from him for the bal- 
 ance of his account, . . .1,03 
 
 Samuel Green, 
 
 Cr, 
 
 By amount dne for 12 months New- 
 London Gazette, . . . ^2,00 
 4 SpeUmg books at 20cts. for chil- 
 dren, . . . . . 0,80 
 
 1 Daboil's Arithmetic, for my son 
 Samuel, .... 0,42 
 
 2 Blank Writing books at 1 2^ cents, 0,25 
 1 quire of Letter Paper, . . 0,34 
 
 Eutcred. 
 
 2 
 
 Entered. 
 2 
 
 Cntered. 
 
 -24- 
 
 Notes pavable, . . Cr. 
 
 By my note ol this data trri,loi*sed by Ephraim 
 Dodge, ut 6 .i'o;%tlis, for a yoke of Oxen 
 bought of Daniel Mason, at Lebanon, 
 
 , 28 
 
 Jonathan Curtis, . . . Dr, i 
 To an old bay horse, . . ^23,Oo!i 
 a four vrheeled waggon, and lialf 
 
 worn harness, . . • 42,00 
 
 I Samuel Green, 
 To cash in full, 
 
 Dr. 
 
rORM OF A DAY BOQK. 
 
 ESered. 
 
 Albany, April 8, 1822. 
 
 Entered. 
 1 
 
 Entered 
 1 
 
 Entered. 
 
 2 
 
 Entered. 
 1 
 
 Anthony Bill ing-s, . . . Dr. 
 To 2 tons of Hay at gl 1,25, . . g22,50 
 
 Amount of order dated March 26 th, ) 
 1822, in favour of Fanny White, > 0,54 
 paid in 1 pair yam stocking, ) 
 
 Hire of my wag-g-on and horse to i 
 bring sundry articles from Provi- ^ 3,00 
 dence, 3d of this montii, . ) 
 
 12 ■ 
 
 Entered. 
 
 2 
 
 Entered. 
 1 
 
 fotered. 
 
 Thomas Grosvenor, . . . Cr. 
 By his order on Theodore Barreil, New- 
 London for 68 dollars, . 
 
 Anthony Billings, . . . . Dr. 
 
 To 1 hogshead Rum from Theodore Barrell, 
 
 100 galls, at 50 cents, . . g50,00 
 
 Cash received from said Ban-ell for 
 balance due on Thomas Grosve- 
 nor's order, . ♦ . . 1 8,00 
 
 — 18- 
 
 Jonathan Curtis, . . . Cr. 
 By a coat ^M,75, pantaloons ^5,00, 
 
 ■ .^ 22 
 
 Thomas Grosvenor, . . Dr. 
 To mending your cart by my man Wil- 
 liam, gl,00 
 
 Paid Hunt, for blacksmith's work on 
 your cart, . . . .0,5.8 
 
 Setting 6 panes of glass, and finding 
 fflass, . . . . . 0,66 
 
 -25- 
 
 John Rogers, . . . . Dr. 
 To a voke of oxen, at 60 days' Credit, 
 
 Anthony Billings, . . . Cr. 
 By gardeti seeds of various kinds, $0,56 
 
 1 pair of boots, myself, §4,00, and 1 
 pah- for John, §J3,50, . . 7,50 
 
 1 pair of thick shoes for Joseph Has- 
 tings, . . . . . 1,25 
 
 Tea, Sugar, and Lamp Oil, per bill, 0,68 
 
 Notes payable, 
 By my note to Isaac Thompr 
 
rORM OF -A r>AY KOOIC. 
 
 Albciiiy, May 3, 1(^22, 
 
 Thecxiorc JbcUToU, Nev/-London, Dr. 
 To 16 cheeiie, 308 ibs. at 5 cents, g 1 5,40 
 217 lbs. of butter, at 15 2-'3 cents, 34,00 
 24 lbs. of honey, at 12^ cents, 3,00; 
 
 Entered. 
 
 Entered. 
 1 
 
 Entered. 
 1 
 
 Entered. 
 1 
 
 Entered. 
 
 Batercd. 
 1 
 
 Entered. 
 
 Entered. 
 
 2 
 
 Joseph Hastings, . . • Dr. 
 To 1 pair shoes, 2yth April, f:..;m Antimony 
 
 Biliin?^, 
 
 12 — 
 
 Anthony Billing's, . . .Dr. 
 To 84 bushels of seed potatoes, at 33 1-3 
 
 cetiLs, . . . g28,G0 
 
 8 pair rnittcns at 20 cents, . .1,60 
 
 Cash, 14,00 
 
 •15- 
 
 Joseph Hastings, 
 By 4h months -vf o^-es at 7 dollars, 
 
 iO 
 
 Cr. 
 
 Theodore Bari-oil, 
 By cash in full of all demands, 
 
 Or. 
 
 Thomas Grosvenoi*, . . Cr. 
 By his acceptance of ray order in favor of 
 
 Anthony Billinj^s, 
 
 Anthony Biihngs, . . Dr. 
 
 iToamount of mv order on Thomas Grosrc- 
 
 -.Sept. 24- 
 
 ' Notes payable, . . . Dr. 
 To cash paid for my nolo, to D. r.Iason, 
 
 C. 
 
 52 
 
 3 
 62 
 
 40 
 
 25 
 
 60 
 
 
 40 
 
 54 00 
 
 54 00 
 
 48 loo 
 
 'ln& foregoiijg exaajplc of a Day Bckjk. r»iay suince to give a g<jod idea of 
 the way in which it i3 p'-oper to make the original entries of all debt and 
 credit articles. Anotber small book should next be prepared, according to 
 the foiiowmg form, termed the book of Accounts, or Leger. into this book 
 must be posted the whole contents of the iM^y Book ; care being taken that 
 every article be carried to its correspondiuix title; tlie debt amounts to be 
 entered iii the left, and the credit in the right hand page. Thus, should it 
 lit any time be required to know the ^late of an accouiit, it will only be ne- 
 cessary to sum up the two columns, and to subtract the smaller amount 
 from the greater, the remainder wili be the balance. 
 
 When an ar<icle is posted from the Day Book into the Leger. it will be 
 proper, opposite the article, to nole the «ame in the margin of the Day Book, 
 by writing the worrt Entered^ or making two parallel stiokes with the pen- 
 to which should be added the figure deaoting the page in the Leger, whera 
 the account is. 
 
 On a blank page at the beginning, or end of the Leger, an aiphahetcal 
 index shoulcl be written, containing th? muxfe^ ef every pereoa v^'ik ^^r^KKM 
 %aa have accounts, in the Leger, with t» B^aah^ eC IM ^«f* W9iik ^ 
 ;)Ccounts are. 
 
Dr. 
 
 FORIVf OF A LEGEKr 
 
 Joseph Hastings, 
 
 1822. 
 
 Fcb'y. 
 May 
 
 To my order on Anthony Billings for gooids, 
 2 shirts of Anthony Billings, 
 My order on Thomas Grosvenor, 
 1 pair shoes, 29th April, from A. Billing^s, 
 
 2|18 
 
 50 
 
 Djt. Samuel Stacy, 
 
 1022. J 1 g O 
 
 Jap.''y.j 6 To 2 weeks' wages of my daughtep at 75 ) - ^^ 
 
 1 cents a week, . . . , \ 
 
 Dr. Anthonj Billings, 
 
 1822. 
 March 
 
 April 
 
 May 
 
 4 To 1 barrel of cider and barrel, 
 10 Cash paid your order in favor of G. Gilbert 
 
 6 Sundries, ,...'.. 
 12 ditto. . . - . ' . 
 
 12 ditto 
 
 25] My order on Thomas Grosvenor, 
 
 75 
 
 32 
 04 
 
 68 00 
 
 60 
 00 
 
 Dr. 
 
 Thomas Grosvenor, 
 
 1822. 
 Jan'y. 
 
 Feb?y. 
 
 April 
 
 To the frame of a house, 
 Sundries, 
 Sundries, 
 
 The frame of a bam. 
 Sundries, 
 
 IlOOf 
 i 74^0 
 
 7,U 
 75.00 
 
 I 2m 
 
 Dr. 
 
 1822. I 
 Feb'y. 24 
 
 Edward Jones, 
 
 To my draft on Thomas Grosvenor, 
 
 i 38 oe 
 
 Dr. 
 
 Eater Daboil, 
 
 1822. I 
 
 F^b'j. 1 28(Tci suirtlrffes* 
 
 if' 
 
FQMI O? A LEGEK, 
 
 A \nre6 !af! 
 
 Farmer, 
 
 Cr. 
 
 1822, 
 JaaV. 
 May 
 
 1 
 15 
 
 By 3 iiiuiilhs' v/a;;'^'^ dii'j ihi^ tiL.y 2.1 ^^, 
 4i mciitlis' \Ysges at g7, 
 
 18 
 31 
 
 C. 
 
 00 
 50 
 
 Cr. 
 
 Merchuiit, 
 
 Cr 
 
 1822. I I 
 
 Jan'}% I 5 IB J my order in faror of Joseph Hastmgs, 
 
 2G Sundries, 
 Feb'y.NS ditto. 
 April 29 ditto 
 
 C. 
 
 50 
 
 62 
 55 
 00 
 
 Judge of County Court, 
 
 Cn 
 
 Fv. '22 
 
 12 
 
 By my order in favor of Joseph Hastings, 
 
 g3|50 
 
 ss'ao 
 
 
 24 
 
 My draft in favor of Edward Jones, 
 
 March 
 
 1 
 
 Cash paid me this day, 
 
 75 OO 
 
 
 
 1 en^pty cider bairel, . 
 
 5» 
 
 April 
 
 12 
 
 Amount of \ ourordcr on Theodore Barrell, 
 
 68 00 
 
 May 
 
 25 
 
 My order in favor of Anthony Billing-s, 
 
 54 00 
 
 Labourer, 
 
 Cr. 
 
 1822. I 
 
 Jan'y* |l<>ii^y team hire at sundry limes, 
 
 Feb'y. II 8 1 4 mon ths' lure of his son WiUiam at g 1 0, 
 
 5 64 
 4o!ort 
 
 Farmer, 
 
 Cr. 
 
 1822. I I 
 
 MarchUaJBy sundries in full> 
 
 ■. I 5161 
 
w 
 
 « 
 
 
 FOMT OF A LEGER. 
 
 
 
 Dr. Samuel Green, 
 
 Mar. 
 
 28 To cash in full of hh occount, 
 
 3 81 
 
 Dr. Notes Payable, 
 
 
 Sept. !'24'To cash psJd for mf note to D. Mascm, 
 
 May I 31 To 16 cheese, weight 308 lbs. at 5 cents, 
 \ I 217 lbs. butter at 15 2-3 cents, . . 
 \ j 24 lbs. honey at 12^ cents, 
 
 % 
 
 4f! 
 
 Dr. Jonatnan Curtis, 
 
 1822. j 
 
 Blarcb!28 To abay liorse, 
 
 i A wagg-on aud harness, . . • . 
 
 23 00 
 
 42 00 
 
 Dr. John Rogers, 
 
 1822. 1 
 
 ilpril 25 To 1 yoke of oxen at 60 days' credit, 
 1 
 
 i c. 
 
 60 0.0 
 
 Dr. Theodore Barrel!, 
 
 34 
 
 52 
 
 INDEX TO THE LEGER. 
 
 RarrcU Theodore, 
 
 PAGE. 
 
 . 2 
 . 1 
 
 H. 
 
 Hastings Joseph, . 
 
 PAG^i 
 
 . . 1 
 
 Billings Anthony, 
 
 J. 
 
 Jones Edward, , 
 
 
 C. 
 
 . 2 
 
 1 
 
 Curtis Jonathan, . 
 
 N. 
 Notes Payable, . 
 
 
 D. 
 
 . 1 
 
 • . ^ 
 
 DaboU Peter, 
 
 R. 
 
 Rogers John, 
 
 
 G. 
 
 . 1 
 . 2 
 
 . 
 
 Grosvenor Thomas, 
 Chrten Samuel, 
 
 B. 
 Stacy Samnol, . 
 
 . . t 
 
FORM Ot^ A l.EGfiR 
 
 New London, 
 
 Cr. 
 
 1822. 
 March 
 
 U 
 
 By sunJnes, . ... 
 
 3 81 
 
 Cr. 
 
 /822. 
 March 
 
 April 
 
 24[By »y note to Daniel IVIason, at 6 months, 
 
 endorsed by Ephraim Dodge, 
 29 Do. Isaac Thompson, at 6 months, 
 
 48 
 90 
 
 c. 
 
 00 
 00 
 
 Danbury, 
 
 Cr. 
 
 1822. 
 April 
 
 1 1 
 
 IBjByacoat, 
 
 1 A pair of pantaloons. 
 
 if 
 
 1473 
 
 5[oa 
 
 Hudson, 
 
 Cr. 
 
 1 i 
 
 1 I 
 
 i\o 
 
 New London, 
 
 Cr. 
 
 1822. 
 IM^y 
 
 20 
 
 By cash m full, 
 
 52 
 521 
 
 Cv 
 40 
 
 40 
 
 QUESTIONS TO EXERCISE THE STUDENT. 
 
 What is the stale of the following Accounts, 
 
 Joseph Hastings, 
 Samuel Stacy, 
 Anthony Billing, 
 Thomas Grosvenor, 
 Eflward Jones, 
 Notes Payable, 
 Jbnathrtu Curtis^ 
 
 Due Joseph Hastings, 
 
 ^Edward Jones, . 
 
 ^Notes Payable, . 
 
 Samuel Stacy owes, 
 I Anthony Billings owes, 
 Thomas Grosvenor owes, 
 (Jonathan Curtis owes, 
 
 g31,0» 
 
 7,64 
 
 90,00 
 
 1,50 
 
 189,05 
 19, 6*^ 
 
 45,25 
 
•& Farmer^s ThUj or Acxmml. 
 
 Auburn, Oct. 21, t8a«. 
 ^omas Yates, Esq. 
 
 To John Mominaton, Dr. 
 
 April 5. To 5 barrels Cider, af g2,00 . . g 10,00 
 
 20 bushels Potatoes, at 0,25 . • . 5,00 
 
 55 lbs. Butter, at 0,17 . . 9,35 
 
 June 6, ■ 1 ton of Hay, . . ... 10,00 
 
 Juljr 15. 40 lbs. Cheese, at 0,08 . » 3,20 
 
 2 cords of Wood, at 4,00 . . . 8,00 
 
 Received the amount. lS^"?j^5 
 
 JOHN MORNINGTON. 
 N. B.-5rTo prevent accidents, care should bs taken not to re* 
 ceipt an account until it is paid. 
 
 A negotiahle J^oie, 
 
 New-Haven, March 21, 1822. 
 Six monthjs after date, I promise to pay to William Walter, o? 
 order, (at my house,) One Hundred Dollars, value received in 
 imo yoke of oxen. JAMES HILI^IOUSE, 
 
 Qi^^It is best to mention where the note sliiall be paid, and for 
 what it is given. Without' the words, " or order^'' a note v. 
 
 not negotiable. ■ 
 
 A Receipt in full, 
 Received, Hartford, Mav 2^2, 1822, of Theodore Barrell, Esq. 
 Fifty-two DoUars in full of all demands. GEO. GOODWIN. 
 (t^If the payment be not hi full, write " on accounV^ 
 N. B. — For other useful foims see the Arithnretic. 
 
 .VOTE. 
 
 The affectionate Instructer, who alp/ajs feels a parental soli- 
 citude for the permanent welfare of his pupils, cannot m any way 
 8o much contribute to their success in life, witii so little trouble, 
 as to teach them to understand this abridged, complete and sim- 
 ple system of Book Keeping*. It contains all the important 
 principles of extended and expensive works on the science ; alt,^ 
 in fact, that is necessary to he loiov/n by the Farmer, Mechan- 
 ic, and Shopkeeper, relating" to accounts ; and yet with very 
 little explanation and repeated copying* and balancing tlie ac- 
 counts, will fee so fully understood and deeply impressed on ihd 
 memory of sckolars of common mind, as never to be forgotten; 
 wiiile tteir knowledge of common arithmetic and practical 
 S^empHMhip wiil tliwcby be greatly improved. 
 FINIS' 
 
1 
 

 VA- 03572 
 
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 I 
 
 Ivilll475 
 
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 THE UNIVERSITY OF CALIFORNIA LIBRARY 
 
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