->.- 1c University of California • Berkeley The Theodore P. Hill Collection 0/ Early American Mathematics Books 9r^ 'X9' 4 f, - f//y. ■^f i4^>^,.V. 9 -r'^^'^'^^m^.mm A KEW SYSTEM J' MERC A N T I L E A R I T II M E T I C ; ADAPTI'lD TO THE Commerce of tJje ®nitetJ &tztt^, IS ITS DOMESTIC AND FOREIGN RELATIONS; W ITH FORMS OF ACCOUNTS, AND OTHER V>RiTIXGS U3l^\LLY OCCURRING IN TRADE. 7ir .yrCHJEL WALSH, A. ]A. Iter est br*:i€ per cranphh ^?;^M ri^YVorcr, (M^^s.^r^t^ "KtOY.y JanuariL 1806. ^^^.:-.imS>. 4 RECOADIENDATIONS. Kexi:hiin/port, May 1, ISOO. AYR the subscribers having seen Mr. Walsh's New System of MKUCANTILE ARITHMETIC, and being satisfied, that it is better calcuUited than any yet published, to fit a youth for the business of the Compting-llouse, cannot but wish it an extensive circukition. The happy elucidation and extended application of the common rules, together with the many ori- ginal improvements, while they accommplish the student for commerce, are also extremely well adapted to assist and inform the merchant, the niaihier, tiud the trader in their various oc- cupations. Dudley A, Tj/iigy FMnczcr Stochcr, jnilia?}? Bartlcr, Sarnnel A. Otls,jiin, 'Dint ram Co/Jin^ 11 Hi lam IFjjer, J:'}} , ilichard Barf let, juu, WiUiam W. Proul, MicJiad Li i lie. Boston, May \6tJi, ISOO. ^VE the subscribers, having; examined INIr. ^VALSlI*s New System of MERCANTILE ARirilMETIC, and being per- suaded that it is better calculated than any we have met with, to cpialify young men for admission into Compting- Houses, we \\\A\ tlrat it may have an extensive circulation. Ihc clear ex- .■ini'lilioation and pertinent ap])]ication of .the common rules, logciher with the many useful additions and improvements Mhich it contains, will render it extremely useful for the mer- chant, the mariner, and all the other trading classes of society. Marsfon } I at son, I Jo/u? l.owcll^jxtn, John C Jones, J^pk Jlussell, John Codman, .^Kbld Welles, jun, Stephen lli^ginson, \ '^^^han Jackson, V ) Sakni, October 7 tlh ISOO. V'W t' c rnl'f-.crihor?, Merchants cf Salem, convinced of the y\vvv \'\^v\\vi^ the terms of bii-iiiess, the value of coins, ?A\\ ■-' of commerce, more familiar to the United St;;trs is a commercial people, do approve of the MERCAN- TiLI-: MUTIlMlCriC of Mr. Walsh, and recommend it as calculi;- ' I ) ouh^orvc in the bcbt manner the instruction of our youih, ami tl.c purposes of a well-informed merchant. U'ni. Gray, ji/n. luiij. Iiocigey, Jacob Ashton^ Wm. Prescot, Jacob C rownin shield y Elias Hasket Derhy, ^xtiut t^ tlje tijixh €Utmx. X HE merit of Walsh's INIkrca^tile Arithmetic having been submitted to the public, and Cbtablihlicd by tlic most liberal and unequivocal encouragement, the Editor feels a confidence in ofiering a third Edition of twenty thousand copies. It. is unnecessary now to urge tlic superiority of this, over every similar production extant. 1 Le disceriiment of men of letters, and the generous spirit of a commcrcitil public havr rendered panegyric useless by an unprecedented patronage. In the ver^r short period of its exi>ten:'e two extcnsivo imprcsi-ions liave been circulated through the country, and orders are al- ready received for a very large p:-oportion of the third. The value of any work must be decided by those to v.Iiom it is more immediately useful ; and if such persons pc:-sess tl;c« means of discrimination the decision will undoubtedly be cor- rect. The present publication is adapted as well to assist the researches of PJathematicians, as to facilitate the negrci- ations of Merchants. Such characters have supported it by their written approbati')n, and recoiiimended it by an intrc^uc- lion into their own Sturlies and Cumrting rooms. ^ chools ar. A2 PREFACE. Academics have made it the basis of a mercantile education, and it has become an indispensable assistant to every trading class of the community. This impression has received several valuable additions under the general head of Exchange, including the existing exchange v.ith Antwerp, Trieste, Genoa, Venice, Barcelona, and Pal- ermo in Sicily, and many useful rules under each of these par- ticular heads. A new subject is likewise added, entitled *^ Arbitration of Exchange,'' the importance of which v:i\\ easily be iseen by Merchants whose remittances may travel through several countries, and be liable to the rates of Exchange in each. The errors of the last edition were few and unimportant. "Hut to render the work perfect, they have been minutely con- sidered and corrected. The Editor is confident that the present edition will be taken up with the same avidity as the two former, and he assures the public that the work shall not suffer, cither in accuracy of beauty, by the liberality of its patrons. EDMUND M. BLUNT. January, 1806. 1^ CONTENTS, Numeration 13 Simple Addilion "^^i Subtraction 15 Multiplication 15 Division . , . . i6 Miscellaneous Questions 19 Table of Money, Weights, Measure?, Sec 19 Compound Addition . . . . , 23 Subtraction ... - 26 Practical Questions in Compound Addition and Subtraction ... 28 Reduction 21> To find the contents of Grindstones* 33 Reduction of American Monies . . . • CA Compound ]Muliiplicaticn ... * Martinico, Tobago and St. Chrli>to[>!icr's .... 20q French- West- Indies 207 , CONTENTS. ^ . Page Exchange with Si>anlsh West-ladies 210 Calcutta ^^^ Bombay ^^^ Madras ^^^ Batavia ' ^14 China 2^^ Manilla ^^^ Ceylon . . . ' 218 T 219 Japan Tonnage of Goods from the East-Indies to Europe 220 Arbdratioii of Exchange Mode of calculating American Duties S^-i Hates at which all foreign coins are estimated at the Custom-Houses of the United States ^^^ nog Arithmetical Progression ..." '^'11 Geometrical ProgTession JV^rmutation * ' E.vtracilon of the Square Ftoot ^"'^ of the Cube Root ^10 of the Biqnadvate Hoot ^' ' '' General TvulcfoF Extracting the Roots of all Powers ^'-i-^ Buodocimals contents of Bales, Cases, &c. in order to ascertain the freight ^^-^ To fuid ships' tonnage by Carpenter's measure --^^ the Government tonnage of ships ---^ CONTENTS. XI Pag6 Tables of Cordage 255 for receiving and pacing Gold Coins of France and Spain . 257 for receiving and pacing Gold Coins of G. Britain and Portugal 258 Mercantile Precedents 259 Bill of Exchange 259 Bill of Goods at an advance on the sterling cost 259 Promissory Note ... v j*. 260 Beceipt for an endorsement on a Note ........ 260 for money received on account 260 Promissory Note by two persons 260 General Receipt 260 Bill of Parcels 261 Invoices . , . . 262 Accounts of Sales * 264 Accounts Current . 267 Bill of Sale 271 Interest Account ,..,. 272 Charter Party ••.•.••...•• 27^h Bill of Lading ..•.•••,.•.,.,,.. 274 EXPLANATION OF THE CHARACrERS USED IN THIS WORK. :z: SIGNIFIES equality, or equal to : as, 20 sliillingsizonc pound : that is, 20 shillings are equal to 1 pound. -I Signifies more, or Addition: as ()-f6zzl2, that is 6 ad- ded to 6' is equal to 12. — Signifies less, or Subtraction : as, 6 — 2zz4, that is, 6 less 2 IS eqiuil to •!■. Sigindcs Multiplication ; as, 6x2z=12 ; that is, 6 multi- plied I) J 2 is equal to 12. Si - •ifies Division ; as 6-^2zz:o ; that is 6 divided b}' 2 is equal to 3. Division is sometimes expressed byplacii-^; i' ^ niiml^ors fraction, the upper figure being ti. > 1, and «cr tlic divisor ; thus, ^^y^=:9 ; tl;. divided b^, v^ .6 equal to 9• ; : : : Proportion ; as, 3 : 6 : : 9 : IS ; that is, as three is to 6 60 is 9 to 18. -v/ rr-:i\::,i to any number signiiios tii^t the square root of i;, re(;uired, MERCANTILE ARITHMETia JniRITHMETIC is the art of compiuing by numbers, ^r\(\ has five principal rules tor this purpose, viz. Numeration^ Addition, Subtraction, Multiplication^ and Diiision, KUMEllATION Tcachcth to express any proposed mimbor by these ten clia- ractcrs, O. 1. 2. 3. 4. 5. 6\ 7. 8. f).— O is called a cypher, and •the rest figures or digits. The relative value of which depends upon the place they stand in, when joined together, beginning at the right hatid as in tlK^. following TABLE, (j 14753 S9i4. 17C9OO 29684 675 574 5769"^ 29 9 171095 171095 SLMPLP. SUBTRACTION. i^ G.iHons. Y'dYih. RusIr'Is. 1/573 1 SOU 4- 1 r.^ooia -iGS 405).) 31R9t 57 83 :), J 9 73'2t; 7^^'^W As tlK,' lucrnintile mctFiud of provlnir" ad-iitloiv In to reckon downwards a Wi'Il ai upwdrd^s the sums uf wUi;h wiii be ciiual, whi'U l.htt addilioi> ib j\u»i two spaces are icit f«r the work. SIMPLE SUBTRACTION Tcachcth to take a less number from a greater of the .same deaouiination; and thereby to shew the ditfcrence. Examples. Yards. Gallons. From 5T46S532 From 2p68914l 'Jake 265S7491 Take I7i^3S76^ Rem. 30881041 Rem. 1175037S Proof 574()8532 Proof i;^^6'8C)141 3 fr^m 924357 take 565383 Rem. 35S974 4 517684 Q^S72 2*25812 5 510090 191939 318151 6 191191 ^9^7 188234 7 291619 ^W !?90790 8 500910 15723 485187 SIMPLE MULTIPLICATIOI^f Is a compendious way of adding numbers of the same name» 'ihe aumbei' to be multiplied is called the multiplicand. 'i he number which multiplies is called ti>e multiplier. The. number arising from the operation is called the produc: -OiPLK iMULTIPLlCATiCxN. MUiriPLICATION TABLB. 1 r '^ '5l 4 5 Bj 7| y . i> 10 11 12 -\ 4 6 1 8 10 12 1 14- 1 16 la 20 22 24 .kj 6 '9.\ 12 15 18 21 1 24 27 30 33 .'6 4f ^ 1 j.^ j IQ 20 f- 24 [ 28 32 - o(> 40 44 4b ;'. ; 1.'' !n 1 20 26 oO Ao I 40 45 50 0.') 60 , 24 30 36 ^42 48 o4 { 60 66 72 : 2«'j ."5 4T Ta I 6d 63 1 70- 77 84 21-.|32 40 48 56 1 d4 72 -j 80 88 V6 ) t'7 \ b6 1 45 54 63 1 72 81 1 90 99 lOti i SO 40 ^1 60 70 80- 90 j 100 110 120 i :-.;i 44 55 66 7? 88 yp 1 10 121 13 J ;;^{>f 4B 16U TiJ •84 yd 108 120 132 144 Examples. .ofiGOTd 5965468 47652:9-3 6281947 -ih/'T 2 3 4 11.930936 14295879 25127788 ■ :u]t, 26587 58 by 5 product 132Q37PO C) 67 437 2 6 58046232 7689657 7 53827599 2074876 9 24073884 4198543 10 41985430 7491685 11 82408535 26S94H9 12 3227386<^ 1768735 20 35374700 2vS914Q6 ^400 115659840a 5749857 7-8 44S4S8S46. 2653294 ~ 872 2313672368 7.SU(i5987 ^893 465346561391 56-2916859 49< 3070 ?75868665090lo(> SIMPLE DiriSIOK. i -i "o !h to lind how often one number h contained :u.i.ii)Lii<'r ot the same luime. The number Given to be divided, is called the dhideal Tlie numbei bv which to divide, is talked the dhisv> MMPLE DIVISION. 17 live numboT of tiiucs tlic dkhor is coiit;iined in tbo cli-lh nJ called the quotient. The remainder, if there be iiny, will be less than thv; u'.tto'^,. . PuooF. Multiply tlic quotient by the divisor ; to the product add tiie remainder, and the bum will be equal to the dividend, i' the work be right. Examples, V »- Dividend'. Divisor i;?)6<)45 68946* 3)27<3S954:- Quotrcnt 3472SU73 9229S4861 Vl ' Proof 6c}4j68946" . 276S9j-] Dividend. Quotient". Divisor 52)645;o436(124912 52 52 129 104 249824 624360 12 Kern; ^'^A *208 6495436 Prooi 474 468 t)3 b'2 12 2 2' .^4 IS SIMPLE DIVISION. Quotient. Rem. 4 : Divide 8965462 by 6 Ans ;. 1494243 and 4 5 3728675 8 466084 3 6 4054682 9 517 186 8 7 2768967 10 ^276896 7 8 19^9952 11 17726s 4 9 2968967 12 247413 11 10 5268794- 20 263439 14 11 29619145 40 740478 25 12 419825367 5G0 839650 367 13 296876234 64 4638691 10 14 47989536925 735 65201886 ,715 15 26574983184 8962 2965Q96 432 16 53479689236 7684 6959S7G 2052 17 491796S967 "^SMJ 2084768 1255 IS 325S675689 67^35 48323 14184 When the divisor is a compound number, that is, if any two figures, being^ ukiplit'd together, wiii m.al\e tliat number, then divide the dividend by one ;' figureb, and tJie first quotient by the other figure, and it will then give ticnt required. — But as it sometimes happens that there is a remainder c.-.ch of the quotients, and neither of them the true one, it may be found bj. .is Rule. Multiply the first divisor by the last remainder, and the product add the first remainder^ which will give the trtie Examples, BJvide 296876234 by 64 8)296576234 • 8)37109529—2 Quotient • divide 875763S by 28 Quotient 312772 and 19rem. Divide 1571196 by 72 'J;autient ■ 21822 and 12 rcin^ 4638691 aiid 1 X 84-2 = 10 remaining. Divide 18957492 by 42 451368 and 06 rem. Divide 3751749 bv 96 39080aud60reiT:. MONEY, NVEIGflTS^MEASURES, ^c. 15 MISCELLANEOUS QUESTIONS. 1. Add 5621G3, 219^)4, 56321, 18536, 4340, 279, and S3 together. Ans. 6Y)36'86. 2. What number is it, which being added to 9709 will make 110901 ? Ans. 101 192. 3. General \yASiiiNGTON was born in the year 1732 ; liow old was he in 1799 ^ A^^s. t^J years. 4. Add up twice 397, three times 79^, four times 3176^ five times 15880, six times 95280, and once 333040. Ans. One Million. 5. A cashier received^ viz. Four hundred and nine dollars^ Twenty thousand and thirteen dollars. Eight thousand live hun- dred and ten dollars. Nine hundred and twenty-eight dollars ; of which he paid away Filteen thousand fifteen hundred and fifteen dollars : What was the whole sum he received, and liov/ much remains after deducting the payment ? Ans. He received 298()0 dolls, and there remains 13345 dolls^ 6. What is the product of 15927 multiplied by 4009 ?. Ans. 6'3851343. 7. 128 men have one half of a prize, wortli 34560 dolliirs, to be equally divided between them : What is each man's part ? Ans. 135 dollars. Prove this answer to be right. 8. Three merchants. A, B, and C, have a stock ot J4S76 dollars, of which A put in 4963 dolls. B518S dolls, and € the remainder : How muih did C put in ? Ans. 4715 doikr&. .. TABLE OF MONEY, WEIGHTS, MEASURES, 4 c. Federal Money. 10 Mills ..make 1 Cent. 10 Cents 1 Dime, 10 Dimes, or 100 Ceiits • '1 J 10 Dollars. ..i 1_^_ Ex G LIS II Money. 4 I'arthings make. • • • . 1 Fenny. ji 2. Pence 1 Shillinc, '^0 Shillings r.»^,» ,,tf •»•»»•». .^«».« I IVuudf iO MONEY, \VL:iGnTS, ^MEASUilCS, ac rEi.'Cii Tahi.e. Shillings TAnir, d. s. d. s. £, 6\ 20 are- .1 8 20. . • -are. . . •! 30 2 6 SO 110 40 3 4 40 . -* 2 50 4 ^ 50 2 10' 60 5 60 5 70 5 10 70 3 10 80 6 8 80 c 4 ?0 7 6 90 4 10 100 8 4 100 5 Q 110 9 2 110 5 10 120 10 . 120 6 130 10 10 130 6 10 140 11 8 140 7 150 12 6 150- 7 10 200 16 a 200 10 0' Troy Weight. i24 Grains make • • • • • 1 Pennyweight,. QO Pennyweights • • * • • 1 Ounce. 12 Ounces. ..•.»..........* 1 Pound. Xori:. By this weight are weighed jewels, gold, silver and liq\iors. Avoirdupois Weight. 1 6 Drams make • • • 1 Ounce. 1 () Ounces • • • • 1 Pound. 28 Pounds » 1 Quarter.. 4 Quarters ....*.... 1 Hundred weight.. 20 Hundred weight I Ton. Noi'K. By this weighs arc weighed such commodities as are coarse ancf ii'.lycct to wasle, and all metals, except gold and silver. One pound Avoir- iu^joij is equal to 14 oz. 1 1 p vt. and I5f grs. Tio;y. Apothecaries Weight. 20 G rains • • • • • • make - • • • 1 Seruple.- 3 Scruples • ...••, . * l Drain, 8 Drams* .•... •• i Ounce. 1 2 Otmces 1 Pound. Kots. Apothecaries use this weigh' in coinpoimding their medicine^ j K^t t^cy buj and sell their drugs by Avoirdupois weight. Cloth Measure. 4 Nails - • make • 1 Quarter. 4 Quarters » - • • • — 1 Yard. ? Quaiters 1 Kll l-ieiyii^^\. 5 Quarters 1 Kll Kn-li.vh tj Qua: ;. io .. c r ..... » 1 Lil Prciicii. .MONEY, WEIGHTS, MEASURES, &c. 2t Long Measure. 3 Bailey Con>s make ••••••! Inclu 12 Inches •.... I Yoot, 3 Feet 1 Yard. 5^ Yards, or l6\J Feet 1 Pole, Rod, or Perclu 40 Poles • • • • • 1 Furlong.. 8 Furloiigs - 1 INiiie. 3 Miles • • 1 League. ()0 Geographical, or 7 , ^ 6yi Statute MUes J 1 Degree. Note. Li this measure, le-ngth only i& cuiisiJcrcd. Land oit Square Measuhe. 144 Square Inches • • • • make • • • • 1 Square Foot. 9 Feet 1 Yard. 30i Yards, or 7 -, r» 7 n i t> v .->-ni T- ^ c 1 Pole. Rody or Perch, 2/24 reet j ^ ^ 40 Poles or Perches 1 Rood. 4 Roods 1 Acre. Note. This measure respects length and breadth* Wine Measure. 2 Pints make 1 Quart. 4 Quarts • ••• * 1 Gallon. 42 Gallons 1 Tierce. ()3 Gallons • • • 1 Hogshead. 84 Gallons 1 Puncheon. 2 Hogsheads 1 Pip# or Butfe, 2 l^lpes or 4 Hogsheads •••••• 1 Tun, Kon:. I'he wine gallon contains 231 cubic inches. j I 11S^^« LE AND Beer Measure, 2 Pints • --^ • • • make • • • • 1 Quart. 4 Quar^«Bt*-« • » 1 Gallon. 8 CiiillonsW. . • 1 Firkin of Alo. " ^ ■ Ions • • • • 1 Firkin of Bet. r. ins • • • • ••.... 1 Kilderkin. '^ iviuierkins •••••• •....! Barrel ■>4 Ihillons 1 Hhd. of Beer. 3 Barrels . . . . f^. • • • 1 Butt. Noir. The^le gallon contaiiis ^82 cubic inches, 22 MONEY, WEIGHTS, ^MEASURES, &c. Cubic ok Solid Measure. 1728 Inches make 1 Foot. ^V Ecct V 1 Yard. 40 Eoet of round Timber or 7 _ „, . , 50 Feet of hewn Trml>cr \ 1 1 on or LoacL l!28 Solid Feet 1 Cord of Wood. KoTE. 8 feet in length, i in breadth, and 4 in height, making 128 solid ket,. contain a cord of wood. Ihis measure respects Icuglh, breadth and thicknc&s. Dry Measure, ^ Pints make 1 Quart. i2 Quarts • • • • • • 1 Pottle.. '2 Pottles ' 1 Gallon. ^ i2 Gallons 1 Peck. * Pecks 1 Bushel. ^ Bushels . • • . 1 Strike. 4 Bushels 1 Coom. 8 Bushels 1 Quarter. 36' Bushels 1 Chaldron. 5 QjLiarters • • •' i% . 1 Wey. tl Weys ; •"■- 1 Last. Note. The gallon dry measure contains 268 J cubic inches. Time. f)0 Seconds make • • • 1 Minute* (}0 Minutes* ..................... i Hour. 24 Hours 1 Day. 3(v5 Days 1 Vcar. NoTF. S65 chys -^ hours 48 minutes 57 seconds make a solar }ear, ac- cording to the uwst exact observation. The iJdmher of days in oaek month is thus found : Thirty dai/s hath September ^ Jpi'ily JunCy and Norcwher ; ycbniarii hath twenty-eight aloney and all the red have ihirty-one. When the year can be divided by 4 without a remainder, it £bssextiJc or Leep-Ycav, in which February hath 2'9 days. COMPOUND ADDITION, US COMPOUND ADDITION Teacheth to collect numbers of different dcRominations into ne total. Federal M( i}NF>Y. D. C. M. D. C. M, i74 74 3 396 J4 4 198 ^9 3 147 19 5 157 1^ 4 149 57 9 1^6' 7(i 9 157 83 8 English Money. £. ^. d. 149 14 6-4 387 19 8-^ *2.'>9 1() 7i 874 17 4* 678 15 (^^2 Trc Ih. oz. dui. 5''*- 48 7 14 19 9.> 4 17 '22 i27 5 14 15 6ly 6' 19 1() Id 7 13 15 £. ^. d. If 14 '^376 \6 18 6h 8| 14 9.'> 2^6' 16' 7-^ 174 17 10^ Troy Weight, lb. oz. dxLt. ^'•^ 83 11 15 O'.? 15 6 16 i:v 21 8 19 '^."'> 33 9 15 14 46 4 13 - 17 Avoirdupois Weight. \)n. CrtY. ^r. lb. t>z. dr. Cxif, qr. !h. 18 17 1 14 13 13 59s 1 ^9 36 15 3 16 13 15 187 3 19 -:) 15 2 19 12 13 159 2 25 1-V 16 3 27 14 12 283 3 1 > K) •19 25 13 10 146 IS 57 17 1 14 15 9 259 1 22 24 CO^rrOL^ND ADDITION, Apothecaries' Weight. Ih, oz. dr. sc. 5:^- lb. 0^. (/r. , ^r. .C^. 3 7 5 1 17 o 5 3 2 1! 1 3 o 2 13 1 2 2 1 14 2 5 3 o U 3 3 5 o 13 3 4 2 1 15 5 5 4 1 12 5 o 2 2 17 2 9 3 o 15 2 3 1 2 18 1 6' 4 2 17 Clcth Measure. 5/^. q7\ Til, E.FL qr, nl, E,Ir, qr, nh E,E, qr, nf. 571 1 3 873 2 3 i81 2 2 56 1 2 184 2 2 396' 2 2 19<3 3 3 li) 2 3 190" 2 3 158 1 1 157 4 14 3 2 283 3 2 147 2 3 168 3 3 26* 4 3 u6* 2 3 326 2 2 193 5 2 S3 2 2 375 3 2 XP4 2 1 214 2 3 57 3 3 Win ■E M: EASURE. • ~ .Vv.;*.*'-- Tz/;?. ///zc/, , gal qt. pt. TurJM, ^^^- 5^^!iiil^ 187 1 17 3 1 176 3 16 2*^ T 56* 3 15 2 1 59 2 57 3 I <) 1 29 3 1 S 3 14 2 1 36' 2 18 2 1 17 2 19 1 1 217 3 57 1 1 16'8 1 38 2 1 56 1 46 2 1 25 2 52 3 i Ale and Beer Measure. hhd, gaL qt. pf. hhd. gaL qt, pt. 49 38 2 78 17 3 38 45 ^ _ • 39 16 57 48 2 15 51 3 49 37 1 76 43 2 57 26 2 23 26* 3 28 18 3 52 33 2 _.— , COMPOUND ADDITION. ^r. Oi(S/i. yjcA-. qt. 57 4 <) 1 19 5 3 1 3S () o »> '.7 7 3 7 o 3 1 4 9 o o o 72 5 c Dry JNlEAsuin-.. iihaJ. hush, pcic, nf, 57 () 31 1 ■ y} () 1 G U 1.3 2 S 32 eO 3 '.! Long IMeasuuk. t/i'.^. 7viL Un\ po. ft. //?. bar. wil. /.r. ;;.9. 7/f/. ft. 217 17 7 19 14 9 1 87() 7 13 4 2 / 33 17 4 id 13 3 2 129 6* 2() 2 1 283 53 5 19 12 2 o l()7 4 5 9 3 2 346* 20' 6* 23 13 4 1 157 3 l':^ <; 2 189 32 3 27 14 5 o 28() 2 2? 1 •^ 17 () 14 2 15 15 6 «-■) 191- ^) •V") o *< > 921 15 4 18 IG 7 I 17 (; 4 18 5 2 Land IMeasure. (icr. ro'). 7;n\ (lev. TOO. T^fr. 7-n 1 19 870 3 19 6"9 3 29 19 o 16' ]5 2 16' 54 3 S7 37 3 14 129 o 26' 16- 2 13 187 3 14 29 3 27 i:;(; <> 1!) Time. f/r.9. J(7//s\ //r.y. 2;?/^?, sec. vrs, iJa'/s. /ws. nn,i. 5* . , i87 149 14 13 )2 14(> 126 16 16 16 .39: 180' 19 '^9 lf> ;e8 140 21 46 35 •? 119 22 IS 26 146' . 146 19 57 19 . 3f)0 1 6() 14 16 n 19 186 17 16 16 4 6 147 15 ^9 19 87 196' 23 46 4-7 157 219 14 .'2:^ 16 46 138 15 42 1 ,3 2o co:\irouND subtraction. CGJIPOUXD S UBTRACTION Tcndictb to find the invcjuahty between niiinbcrs of divers tleiioniinaljuiis. Federal JMoxev. doL ct. w. f?0/. ct. m. ^/(v/. ct. m. ''■!- 5;5 i 433 CO 1 17 30 3 ■ !/7 o .9 1.5 5) [) 50 2 ]■ roni 1 1 1 I 'lake lU 1() 21 Ex G LIS II iMoXLY. . d. ,. ^-C. ^. f/. 304 19 «i From 389 18 0| 'I'di 19 4 100 11 11 TncY Weight. IA. or. did. gr. I!k oz. dirt, gr. From 87 H 11 K Tcl.e 19 11 14 22 27 10 15 2'2 15 9 16" 23 AvoiuDurois Weight. ton. cut, qr. lb. oz. dr. From 100 10 1 11 11- 13 ^^ake 15 13 1 18 12 15 cut. qr. Ih. 59 1 1 1 19 3 27 AroTHECArviEs' Weight. Ih. oz. dr. sc. rry, //). OZ. dr. sc. gr. ! Ill 2 ikc 1 3 7 4 5 1 o J 3 10 2 1 1 4 3 o 1 o 15 17 _, . .. COMPOUND SUIVrilACTlON. Cloth ^^Ieasiih:. yd. From ^251 Take 1::/ qr. 1 :3 ?.'/. 3 1-0 ^ \> -11:) ^ '• 1 '{ -t .J '^ w. , , . tun, • '"•/■'• 800 . 'J i 149 2 61 3 I ^«;7. 7///^. g^/. qt, pt. From 591 1 13 1 1 Take VlG i2 56' 3 1 Ale and Beer ]Measur:-. hd, gal. gt.pt. ' /id. From 571 19 3 1 lOO ^b '2 1 Take 198 53 2 1 9 C7 3 I Dry jNIeasukk. qf\ hu, gal. qf, c/iul. ha. gaL qt. From 38 4 5 3 6'9 21 " 3 ^2 Take 17 5 1 2 49 S3 5 '^ Long ^Jeasure. jft d(g. m. fur. p. f. ill. b, j-^orn 8 19 13 1 19 1 1 3 1 'lake 159 4-9 2 27 10 8 2 ♦ 2< ^- fn: : 19 :'^ I 59 7 l.> 12 — - Land IMeasure. acr. ro'). J r)-. acr.rco.pcr. From 5CU l 'u r,Ol 3 13 'lake l':9 3 15 1< 2 21 acr. )00. pry, 21'- '^ ' ■; 1 1 .. . ■ 'i'll'.IE. ?//>. da. hr. w. Acr, urs. da. /'/. //'. l^;om I7i 143 11 ]4- 19 is i I 111 1.) CJ 'lake 12s 1/i- \[) 51 1 i 3^.<) 1<;0 21 -1 o C8 PRACTICAL Ql;ES•['K)N^. PRACTIC.il questions ly COMPOUNiy addi. TION AND SUBTRACTION. 1. Cast up tlie followino- sums, viz. twenty-tliree sliilling^ -■ ■! !'vo prnco, one pound ancl nino pen.co, se\'en shillings aiut ':^--..i jrnco three larthings, twenty pounds thirteen shtilin^s 'i.'.J, nii.o pence, lifteen pence three farthing-^. £. s. cL 1 3 5 1 9 7 H^ QO 1:3 .9 1 3* 7 24 Pi'ool' ^'. <^3 7 2i 2. Tvvcnty dollars and four cents, five c?onars and thre« JDilis, eighty-two cents, fcix dollars and five mills. Ans. 31 dols. 8() cts. 8 m, 3. Seventy dollars, tlirec dollars and three cents, thirty^ four cents and four mills, eighty dollars and a half, six dollar* 1 r.,; a (pciarter. Am, lO'O dols. r2cts, 4 mills. 'i'en pounds and threepence, forty-five shillings and ''"■'- half penny, thirty-seven shiljings and four-penc« liings, nine pounds and three fart'hings, one shilling 411. 1 M.\ pence farthing, eighty- two shillings and four-pence ^.ali-penny. Ans. £.27 7 5|. 5. Thirty dollars six cents and a half, fifty-three cents and hue quarters, eleNcn cents and a quarter, nine dollars eleven coi2ts and a half, fifty-four cents. Ans. 40 dols. 37 cts. (j. Take three shillings and four pence from one pound tw© j^Jjidings and a penny. Ans. ISs. gc/. 7. From c€.5 2.;?. Id. take nine shillings and six-pence half poM;y. Ans. £A 12 6*|. [•'."^ Take twenty shillings and three forthinjis from £,S, Ans. k\ 6' \9 111, , '). From IS dollars take eight mills. Ans. ]7 dols. 99 cts. 2 n . 10. Take 53 dimes from 53 eagles. Ans. 524- dols. 7 dimes or 70 ct^. 11. A merchant bought 112 bars of iron, weiiihii^o n()c\\{. 1 qr. 1 1 lb. of which he sold 59 bars, weighing 2|; c , RCDUCTIOX. '."^i !?r ffr. ,~ how many bars has he remaining, and what is ia,: wc'i^lit ? Ans. 53 bars, weighing 26 cwt. 1 qr. 18 lb. 12. Required the total weight of 4 hogsheads of sugar, weighing as. follows, viz. No. 1. p cwt. 2 qrs. 21 lb. No. 2. 10 cwt. 5 qrs. 23 lb. No. 3. 8 cwt. 2 qrs. ?5 lb. No. 4. 9 cwt. 3 qrs. 17 lb. ' Ans. 39-Cwt. 1 qr. 2 lb. 13. A ropemaker received 3 tons 15 cwt. 3 qrs. 14- lb. of hemp to be wrought, of which he delivered in cordage 34 cwt. 1 qr. 22 lb. ; how much remains ? Ans. 2 tons 1 cwt. 1 qr. 20 lb.. 14.1^ Received 57953 niills,. 4953 cents, 1913 dimes, and 45» eagles ; required the total sum ? " • Ans.. 748 dols. 78 cts. 3 mills. J 5. A cashier received, viz. one hundred pounds and nine- nee half-pennv, three thousand seven hundred and four *>uunds ten shillings,, twenty thousand and ninety pounds two- sliillings and eleven pence three farthings, of which he paid away sixteen thousand sixteen hundred and sixteen pounds ; how raucli has he on hand ^ Aiis. <£.()278 13 9,^. 1(). A farmer bought three pieces of land^ measuring, viz^ riie lirst piece 21 acres 3 roods 19 poles ; the second, 37 acres 2 roods 29 poles ; the third, 27 acres 2 roods 25 poles ; of which he sells 15 acres 2 roods 39 poles ;. how much has, he remaining .? Ans.. 71 acres 1 rood 34 poles. 17. A- has paid B £.9 15 6^, £A9 11 5l|, .€.14 I9.7hr and 54>9. S^d. on account of a debt of .€.50; how much ij* llu-ie still unpaid ? Ans. €.2 18 9^. REDUCTION-^ Reduction teacheth to change numbers from, one dettcHtl^ nj.tion to another, without losing their value. liUL£. \Vhen. the lleduclion is descendijii^, multijdy tiie- higliO-.t denomination by as many Qf the next less as inake one- <>f '.be greftter, lulding to the product tlic j^arts of t-h<^ sanie :;e; u^id SO on to tiie last. '•'vhen the Reduction is ascending., divide the give?i. mim^ber ajy rAa-ny of tfuit denominatioa as irudsc oue of the no"?^K LhqVr and so on to the denominatioa required^ and thtt h»-"t: tient with, the .- laiuder^ (it aii^) w-iil l^ \Lii: -..^wer- S^bm yrouf isj.-y revor^ing the qti^btioa*. ) REDUCTION. FeI>E11AL iNIONEY. I, In 53 dollars how many mills ? 63 dolls. 10 ) Or decimally, by adding a cypher for each inferior deuomination, ihus, 530 dimes. 10 5300 cents. 10 (lol.d.cjii. Ans. 53000 mills. 53,000 '2. In 14000 mills how many dollars ? 10)14000 yOr decimally, by s^^paratincj the f]i^nre?> 10)1400< coiin;ini^ from the riglit to the nam® J rec^aired, thus, 10) 140 (^ doJ.d.c.m, Alls. 14 dolls. 14,000 J. in 57i}35 mills how many dollars? Ans. 57 dollars, 93 ce-nts, and 5 mills-. 4. How many eagles in 1933 dimes ? Ans. 19 eagles, 3 dollars, 3 dimes.. 5. In 1290 mills how many dimes ? Ans. 12 dimes and 9 cents. ^. How many cents in 45 dollars ? Ans. 4(i00. 7. In 19OCO4 mills how many doilars ? A\\<, 190 dollars and 4 mills.. E X G L 1 S II ViO X io Y . \. Ill £jn 1 y 3h how manv farthings ? Proof.. '20 11 3 ^ 1; >31 i J shiil ing^ •- 1? ■ ' 4 pen< "C, 4; ^7 en > !:o ) 10.31 - .r^i 11 :^' Ans. 8/ 902 farthings. 'J. How many povmcis hi 3175 larlhing.^ ; Au>:, REDUCTION". 31 3. In l[).s. S|r/. how man}^ f«rthings ? Ans. ()\7 fluthings. 4. . How many pouiuis in i)7o2 pence ? Ans. £A0 12 S 5. In £a6 lio'.v many crowns oi 6s, JcL each ? x\ns. 13.9 crowns and 4- shillings and 1 1 pence. 6\ Mow many pounds in 493 dolLiis ? Ans. £AA7 l.S 7. In 14-3 pence, ' • r—iy shillings ? Ans. ils. lid. 8. Reduce 3S.V. 1 ii'pciije. Ans. i)2 1 half pence* Prove tlic above ii!isv.c'i.^ lo be right. TiioY Weight. 1. In 151b. troy how many grains ? Ar.s. S()400 gr;?. 2. How many ounces in ^749 dwt. ? Ans. 287 oz. 9 ti'"^^' 3. In 1 1 oz. 13 dwt, 13 grs. how many grains ? An«. oCOj p;r-^. • 4. IIow many grains in 15 spoons, cac'i !g 6 dwt. 15 grs. I ■ ^'385 grs. Avoirdupois V/eigiit. 1. In 19 tons 14cwt. 2 i\v<, 19 lb. lie :• ny d rams f Au>. i i.ji v i.j/ . ; , 5 . "^ 2. How msny cwt. in ^5^63 lb. ? Ans. S5 cwt. 1 ([Y. 15 lb., 3. In 13 cwt. 3 qrs. 21 ib. how many pounds ? Ans. 156i:lb 4. How mnr.y mc^s-pieccs of 4;Ub. and 3h lb. of each ai. equal nuniLc!, va 3 I cwt. 1 (jr. 12ib. of beef ? Ans. 439 pieces of each* Wine ^Ieasure. 1. In 25 tuns of wine how many pint-. ? An.s. 50400 pints. 2. How many hogsheads in 4935 ([uurls ? An?. 19h. 3()g. 3f[t. 3. In 3 hlids. 13 gals. 2 qts. Uow many half piutb ? Ans. 3240 half pints.. CtOTu Measue?., vards how manv nails ? Ans. 252S nailn 2. iiow niany ells Engii •.. 5 Ans. C9(i'-'l!s 3 q;- '-'9 pieces of .h.ollandj each containing 3() eiN Th'}:, - -— ■-• - ? An-, " ^ ' ■■ •' 52 nEDUCTior^. LoxG oMkasure. 1. In 29 miles how many inches ? Ans. lS3r-i4<0 rnciiea*. 2. How many furlongs in 19753 yards ? Ans. 89 fur. 173 yds,, 3. h\ 590057 inches how many leagues. ? Ans. 3 leag. 2 fur. 110 yds. If. 5 in. Time. 1. How many hours in 57 years, allowing each year to be "6j days 6* hours ? Ans. 499662 hours. 2. In 57953 hours how many weeks } Ans. 344 w. 6 da. 17 hr. 3. IIov> -ys from J 9th of INlarch to the 23d Sep- tember toM Ans. 188 days. 4. How > lys fiom 24th May, 1797, to 15th De- cember, 179'^ ^ Ans. 570 daysv Land Measure. 7. In, 41 acres 2 roods 14 perches, how many rods ? Ans.. 6654 rods or perches., 2. How many square rods in 7752 square feet ? Ans. 28 rods 129 f^et.. 3.. In 5972 perches^ how many acres ? Ans. 37 ac 1 rood 12 per^ Solid Measure^ 1 Til -1 i^i^e of wood 96 feet long^,, 5 feet high, anri 4 fcot \^ ; .-:;:ny cords ? Ans. 15 Coi'ds. ... .,2 toiis of round timber kow ma,ny inches ? Ans. 56'()7840 inches. 3. \^'!!nt r.ri^ tn? contents of a load of wood, 6 i'eet hjng, 4' i.Vi h:L':u iiLu J' i\vt wide ? Ans. 3j leet. .I'S are y.o]<] by the cubic foot,, co! ■ ' '' ;^ cu]ii.( iils c.;e ihi's found ; ' ■•- .■;--!. u:- add half of rh- rr:.^:-,.h.,- y- rhc same half, . v'ubic foot, -dnd liic quu'.iout is the uv ,ii.ed^ REDUCTION. 3a Examples. 4. I low many cubic feet in a grindstone, 24? inches diam- eter, and •!• inches thick ? 24 diameter. 12 half diameter. 36 12 432 4 tliickuess* 172H)J72S Alls. 1 foot. 5. What are the contents of a grindstone, 36 inches cHam^ etcr, and 4 inches tliick ? 36 18 54 18 54 972 4 1728)3888(2^ 3456 432 4 1728)1728(1 1728 Ans. 2l cubic feet* 3i REDUCTION. AMEIUCAX MONIES. To change New-England nud Mrginia currency to Federal niunev, the dollar bein^ !> -^^'im.^^. lluLE. As llic valu; 'iris equal to three tenths of a pi^und, when jxnuid^ i..v^.,wi tu be changed, annex three cv} iiers lo the M,ni, and divide the whole by 3; the quotient ib the answer in eents. Examples. "* 1. Change £.523 to Federal money. 3)523000 3 74333^^ cts. Ans. 1743 dols. 33jctS Change the following sums, viz. £, 5. 1 84 Ajis. 3. 29 4. 57 ' 5. 219 6. 81 7. 127 When pounds and shillings are given, to the pounds annex half the number of shillings and two C3'phers, if the number of shillings in the given sum be even ; but if the number be odd, annex half the number, and then 5 and one cypher, and divide by 3 ; the quotient is the answer in cents» Examples. 1. Change £.59 185. to Federal money. 3)59900 dols. cfs. 613 33\ 96 66f 190 730 270 423 33J 19961);^ cts. Ans. 199 dols. 66^ cts. Change £.93 13.v. to Federal money. 3)936'50 Ans. 312 dols. I65 cts. dols. cfs. Ans. 432 l6f 212 50 93 609 83^ 192 66i 40t 50 3121(51 cts, Chani^e the following sunis^ viz. £. s. 3. 129 13 4, 63 15 5. 27 IS 6. 182 19 7 , 57- 16 ^-. 121 7 11 EDUCTION. 35 Wlicn Iborc arc slnllings, pence, c\'C. in tlio given ^nm,pr.n<'x for the shillings us befoir directed, and to these add the lar- things in the given pence and ftirthinf:^. observing to increase their number by one when they exv ; i 1 J- .uui by two when lliey exceed 37? J^nd divide as before. Ex>\MPL£S. 1. Chanizo -^.Cl Ss. 4jt'/. to Federal money. i>)'Ji I];j 4 is aniicxed to the p.ounds for half ' the shilbngs, and J 9 ft>i' the fiir- 7 139! ^"^s* things in -ij^/. and excess of 12. Ans. 71 dols. :;; '] ci5, 2. Change cf. 117 1^^- ^<^^. to Federal money. 3)117808 392(>9i cts. Ans. 392 dols. 69] cts. 3. Change .£.721 9s. ll^r/. to Fet-leral money. 3)7214-97 In this example 4 is awncxcd to the pounds for half the even shillings, and 47 for the far- 240499 cts. things in 1 1^^^. and excess of 37? and then 5 is added to the figure next to half the shillings, making it 9 i'^^ place of 4 for the odd shilling, Ans. 2404 dols. 99 cts. 4. Change £.29 1 Fv. 2^/. to Federal men.-/. 3; 29.^.^9 Cii; 9^^153 cts. Ans. 9S dols. 53 ct3. (Jols. cts. 'D 9 Ans. 8() ()2;^ 6". 24 11 7|- 81 94 7. 1 238 10 94 4128 40' f 8. 2001 1 31 6070 21 1 9. lo3 17 G 512 91J SG REDUCTION. A TABLE lOR CIlANGIlsG SHILLINGS AND PEXCE INTO C£NT?5 AND MILLS. 6/ liL d/i//^. ^hiU. i7;ii/. ahUl. 1 2 3 4. 5 pence.' cts. in. r/5. ?•». cL«. 7n. rfs, 7?i, cts. in. cts. m. 16 7 33 3 50 66 7 83 3 1 ' 1 4 13 1 34 7 51 4 68 1 84 7 1> 2 8 19 5 36 1 52 8 69 5 86 1 •J 4 i> 20 9 37 5 54 2 70 9 87 5 4 5 6 2 '2 3 38 9 55 72 3 88 9 > 7 2. J 7 40 3 57 73 7 90 3 (5 8 :> 1;'5 41 7 58 3 75 91 7 r y 7 £>-J 4 43 59 7 76 4 93 8 11 1 ^7 8 44 4 61 1 77 8 94 4 9 i'i> 5 29 2 45 8 62 5 7 9 2 95 8 10 1 ;^> 9 30 6 47 2 63 9 80 6 97 2 11 1/> •■> 32 48 6 65 3 82 98 6 To cJiauge Federal Money to Ne^jc-Eii gland and Virginia Curreney, Rule. When tlic sum is dollars only, multiply it by 3 and tlouble th€ first iigurc oi" the proclucl lor shillings, and the rest of the product will be pounds. When there are cents in the given sum, multip''y th.e wliole Jjy 3, and cut olF three figures cf the product to the right hand tis a remainder, ]Midti])ly this remainder by CO and cut ofT as before. Proceed in this manner through the several parts of a pound, and the numbers standing on the left hand, make the answer, in the several denominations. Note, if there be mills, cut off fouriigurcs and [.roceed as abo\'e. Example. 1. Change 872 dollars to New-England txirrcncy. 872 3 ■ £, ^. 2(Jl 12 Ans. 2(U \Z KEDUCTIOX. 57 12. Civino;e 1971 dols. 96'^ cts. 3. Reaace 1259 c^t^j"^. ^"^.9 cts. lo MabSiicluibClts currency. and 7 anils, to IMas^. cnnvncy. 1971 9^>! ' ^ 3 ^ (/. 9,6'0() 4 t\-.J r,9'^9t '^'0 V ] cents c/. S. f/.!S. f/ S. (/. s.' d. <. -. (/. s. ' f/. 7-'.;l '2- i 0} 2. 4-1 3 t L>^;5 4- 1 4 8 it :-;*■ L 10^ ^ ^l 3 (Hi i « li 4 10|o 5| 2 H i ol 1 11 4 6\ 5>li3 H 4 3^ 4 11 5 6i 3 n n I 4^- 1 iH 2 7" 5 ^3 9i 4 4-^ 1 11|5 7 .5 0|i5 7^: > U^ 8| 4 5 3 10 10^ L b\ 1 6 2 0| 2 IV % 7-1 2 81 3 213 10 3 3|t3 10-!- 4 5^ 4 (5 6 4 'J nPi (>i 2 2 2 9 3 4i.i -^ ) 2 5 9 7 5 i o|^:! 7^ 2 l»t I 9-1 3 5 4 5 2|5 9| 5 Sl\.^ lof 8 ■H L I'il 8' 2 :>J: -i 10.^ 3^ 514 1 i y 9 61 1 l^il 81 ;i 4 ^ Hi 3 6} 4 Jl4 8^ .5 4 !5 Ilk. 'ncy fo Federal To cka. :.~York and Novth-C. nwncijy the dollar bi ing S d/,ilLfigo. , Rule. Prepare the G^iven buni b^Mhe rule Tor New-Kn '^'^'^cl Bioiiey, and divide by 4 ; the quotient is the answer in c.iilo, 1. Cliange .£.4()1 to Federal money. 4)451000* ^ 115:250 ct.^, Ans. 1132 doli D e? REDUCTION. ' ,; n^c cf.419 IQs. S^d, to Federal mcnry, 104-883J cts. Ans. 1048 dolls. So.^ ^'^' To change Tcdtral ^aoncy to Neu-York and Norl/i-CaroIinn currcnciu KuLK, As for MMSsacluiH'tts currency, Tising 4 as a iiuilti- plier inbtead of 3 ; the vidue of a dollar bciiig Cvjuai to four- icnthb of a pound. Example!^. 1. Change l6S4 dollars to N^w-York and North-Carolina €urri-ncv, 1684- 4 Ans. £X)7o 12 Q, Change 1048 dolls. S3f cents to Nc^v-York currency. 1048, 83j 4 41 9,535 '10 8,400 4 1,GgO Ans. £.41.9 I0.s\ 8] J. To change Ncxi-Jcrsey^ Peinisyhaiua, Dclauare and Marylaml currency to Federal money, the dollar being Js- 6rA Rule. As the value of a dullar is equal to g o^ ^ pound, nivdtipiy the given bum, when it is pounds oidy, by 8, and di- vide by 3 for dollars, U there be shillings, &c. increabc tlw §uni in pence by ^ of the whole sum for cents. Examples. 1. Chan^je £A7l to Fedjeral money, 471 8 3)376'8 Ans. l^aO^doliai-s. ItnDUCTION. 39 ft Cluvngc .£.480 I.9.9. (>/. to Federal money . 20 KH^(ia| cents, Ai\^. 1':H'2 aoiln, (;:j^ ct^, To' change Ffdcral monnj foNew-Jerscij^Fennsj/hmuaj Dilaxi\n't; and MaryUmd currency. RutP.. Multiply the sum, when fn dollars, by 3, ami divide by 8 for pounds. If there be dollars and ccntj<, multiply the given mm by 90, and the product (rejecting two rigarcs on the right) is pence, or deducting ^^ of the sum •>iveb the pence like- wise. Examples. 1. Change 125& dollars to PennJ>ylvania currencv. 1255 3 S)37()iS Ans. £a71 ,2. Chan:z;e \'2^2 dolls. G3}> cts. to Pennsylvania cvirreu^^v., ^' 128203.i \)v ,'o)12826'3.^ 90 12S26^^ 3 2)11.5437,00 12)115437 20)9619—91 20)9619— i> Ans. cf .480 19 9 ^.480 \C) 9 as before. To c/aingc Saiffh-Carolina and Georgia a/rrcncu to Fediral mo- ncii^ the d/dliir being 4a\ S(/. RuLF>. As tlie value of a dollar is equal to .■J^^ of a pound, . ;!io "s, 0, and ihf product (rejecting two figures on the right) is tiic a.ri- »wcr in pence. Examples. 1. Change 144 dollars to Canada eurrenc}'. 4)144 Ans. £.30* r. ^ liai^gf^ 2114 (Iris. 50 ct^-. to Canada or Nova-Scotia c?»r- ti^Mcy. 21 14.50 ()0- 1»^ 12)l2()S7C!0O C!0)1057t2— ft 528 >2 S An3. £,oTi 112^. ^d-.. 42 COMPOUND MULTIPLICATIONS', COMPOUND MULTIPLICATION Is the multiplying of niiiirjcrs oi'diiToient denoi viivition?, by a sis)V)!e i-'j^awt cm- ligurcs wiio^e proiluct shall be c(|iiul to a pro- posed iraiiibc']-. I. \Vheii the ((uantity docs not exceed 1'?, multiply the price by the (pj-mtity, and the product will be the answer. JMultiply £aQI 17 8i 'bv 2^ Ans. £.333 15 5 £Ad67 1^ O;^ £.980 J9 11^ £.'209 18 4i 32 9^ I. What will 7 yards of shalloon come to at 3s. 5(L per yard ?• s, (I. 3 5 7 £.1 3 11 s. d. £. s J: x>. 4 lb. tea •• 6" 8 I () 8 3. o busbels rye 5 9 1 8 .9 4. () gallons wine •.•• 7 5 2 4 ()" 5. 7 quintals fish . . . . I9 6 6 \6 6 i\ 9 cwt. iron 29 10 13 8 G 7. 1 1 gallons brandy » • • • 8 5 > 12 7 - — ^ 8. 12 quintals lish 22 10 • .- 13 14 II. If the number or quantity exceeds 12, and is to- ber found in the table, multiply by its component part::. Examples. 5. (J. i. 14 vards durant at 2 5 4 10 . 7 Ans. £.1 13 10 COMPOUND MULTIPLICATION. 4*1 5. (I r. 5. l() vnrcls silk* ^at* • • '4 9 3. 20 lb. coffee...- 1 9j 4'. 28 gallons rum () .^) ,: • . • • .5. 4.5 cwt. iron 2,9 ^) • » • • 6. jOi yards broadcloth 2vi 7 . • • • 7. 0"3 pair shoes 9 :) • • • • 8. 84 quintals Ijbh ..•• is (> .... 9. 100 oalls. mclasscs • • 3 5.^ 10. 121 bushels cm 4 3' 11. 14 1 gallon- » . 5 I'l i 1 ,> .' u 9 1 3 (•() 7 (.; 80 8 29 o 9 77 14 17 5 lo 25 14 40 13 7'j inuliii^Jif l)!/ fracfionaf f !;■{■, ;/? .;, ^;, ~, .:^ :•. Rule. Multiply the price by the upper ligarc ot" tlie frac- tion, and divide the product by the lower, the quotient will Le the answer ; but when the upper figure is not more than one, dividing the price or sum by the lower iigure gives the answ.cr, •EXAMP.LES. 1 . What is 3 CI a yard of. cambric worth, aj: i2s, 6d. per vard ? \2 G Ans. 4/;. 8|(/. 2. What is Y -fa }aid of broadcloth wo^ih, at 35s. p-r ya: 3 ■) Or thus, 2)33 ' 2)17 6 p ri ce o f liu ! ( a }:! id , 4-) 103 8 9 a quarur. 3. One quiirter of a yard of fmc linen, at Js, 6c!, per yard, '4)7 0' An-. IsAOld, 4.. Multiply £A 5s, 3(L hy \, or take h ij( it. 3)4 3 3 Ans, £.1 8 5 4-t COMPOUN^D MULTrPLlCATION; 5-. Multiply £,9 6s. 8iT. by |, or take i of it^ 9 6 8 7 8)6\> () 8 Alls. £.8 3 4^ JIT. When the number does not exceed the tabfe, and it can- aot be found in it, find the nearest to it, either less or greater ; then, after having found the price of this number, add or sub- tract the value of so nuinyy as it is less or greater than the giv- en number. i'.XA-.MPLES. 1. 27 bushels- of corn, at 4?. lU/. per bushel.. 4 11 ♦ 9 6 6 8 17 price of 36 bu>hel?.. 4 1 1 price of I buhhcl. An*. <£'.S^ 1 11 price of o? bushels. 9, ITI yards siialloon' 'at- S. ^3-1 li).coilee 4. o7o galls, ruin 5. ^1 } yds, baiz^' • •• 6. IOC) oidntals fish 7. 137.1 gallons of molasses • s^ J, • 2 8 ' 1 lO.'j • 2 r ■ 1 4 () • 3 Si £. s, (L Ans. C! () 2 4 Oi VI 1 llf 9 ^3 94 () ' () 1^ ^' 9 .1 A "U the number is above the taMe, fh^.l the i^iicn ♦^t as ill fhe fullowina— COMPOUND .^lULTirLICATION. 43 Examples. I. 17s yanls of iwuslin at 4-.v. 5(7. per yarJ, 4 .5 10 2 4 2 10 ?2 1 8 price of rOO yards.. 15 p 2 price of 70 1 15 4 price of S AiiS. .t..3i; (j 2 price <;f 178 yarik, 2. *284^ gallons of molasses, at Ss. 9^(1 per gallon- 10 1 17 11 10 18 19 2 2 37 18 4 price of 200 gallcns. 15 3 4 price of 80 15 2 price of 4 1 10 1 price of J ' Ans £ .53 18 8 j price of 28:^^ gallons, s. . 801}^ yards baize., 2 ih" - ^() 21: 7. 23754 galls, of molasses. • 3 5| 410 15 3.^ 8. Tliroc barr(f{f^f N. E. rum, conty-iniug. 31, 32i 33.^ gallon*, at 4*'. 7i^A per gallon. Ans. ct'.22 7 ^| 9. Four hogsiicads of molasj-es, containing [)? rj, 99ij 105|j and 1 I;i:l gallons, at 3-s. 8.-^fA per gallon, arc delivered by A ro B, U) \sboyi he owed 258 dolij?. It is required to know the ba'-. i'Awv. an;] 'rv\\'l\Qse favour it is r Ane^. 4?. ihd, in favour of B.. » I ^ina 4(5 Cl>^\lPv)UNi) JvIlLl iPLICAiK v./.> Whorj the innoiinl ofa cwt. >s requiFcd at a certain ratepv^rnj. lluLi:. Find the ])rico of one or two quarters, and multipljf \lie product by the component parts of a cwt» 1. 1 cvvt. of Flour, at .^..7. per lln 3 7 14 price Qf Iwa qtmvft^fi* Am. £A ^ price of om cwt. Or by inverting the question thu^, ^ 4 ihc price of 112 Vm, at Id, per Ibr 3 £a B the price of 112 lb. at Sd per lb. 5, Two cwt. Flour ':h per lb, 2 0' 8 3, Three • . Rice '2^i --...... .3 17 4, Four • • Iron • • • • S\ » » • 6 \ 4 5f Five • f Imligo 8.v. i 1 4 .....*,.•.,,.. 250 16' 8 1. What will 4000 feet of boards coiue cO at 38^. Ad, pej thousand }■ 1 18 4 4 M. Aps. £.7 13 4 5, 3,5£/5 feet of boards at 305. per tliousand. 3b In ill!" cxamn-e Ihiro fiL'nres ^re m.,. p. irited off as a rciiniindcr, and thff 21576' lomlh ii'duri' of »bo prod\icl of this re- 107S8 rruiider, nniltiplitHl bv I'i; ;>; ^///v. 1'2!),456 Ans. X.6' Q a COMPOUN D ]>IULTIPLICATION, 47 853 feet of boarc^s at SOy. per thousuud. 853 30 chilh, 25,590 -€.36 6 11 64 15 6 4 16 4 8 9 A-,^. Sa 5 7 4. 5,C?31 feet of 3 inch W. O. piank, !2'255. 5, 8,()37 ^i •' •• '•• ' ^5t]6\ 6*. ,1)00 ^^ ]()0y. 7. ,888 2?> pine, .. •• ICOa'. Plank are sold per tlious.'u/J of 'J J iachfs, tlie usual thickHcss for planking '.-.•hscIs, mid ii'i there are geiieraUy other dimenskms as 2 and 3 inches, lh« price of each ii regulated by the price of the '2-\, adding to it, or subtracting l\oin it, in such pro])()rtion as may be agreed on uhcn purchasing. lii the above example, taken from an aciaal '^ak^ -I- of I50s, was added to it, for th« three inchj and J Uedvtcted from It for llie two inch, niuking the three iiirM ^^'■25s. and the two inch 100s. per thoi-jand. 11 EIGHTS AND PLEASURES. fb. oz. diift. grs. Ih. oz. dv.f, o-?-,^. Ihiltiply 14 9 14 17 825 8 1^ 22 by 5 8 Troduct t 74 13 13 ^605 11 10 8 T, CKt. qm. lb. 19 17 3 25 9 Cn't. qr. 17 1 lb. 14 oz. drs. 11 u 7 T. hhJ. gat. 87 I 57 5 T. 28 p. 1 I hhd. gal. 1 62 7 What is. the weight of 47 casks of rice, each weigliinir 2C. If/-. 23/i. ? Ans. 1 J5 cvvt. 1 qr.^ 17 lU 48 COMrOUNI) iMULTin X. BILLS or PAKCELS. )\\L boi'g/-f of WiLiAA-Td 11ussj:ll, .- iit 4 o £a 16' -3 2 ] 5 ] 14- ..2 2 4 '2 1 .5 1 S 3 4 7 6' 1 10 ^.7 12 2 TorisnwutJi, \£,ih 1. B oug/i I of S m o i^ ^V J t s t) N , i I 4*.() ^'.0 7 ] 0^ >: cc;in 5.^.4 .....e» /) (iiuiiis braiidy • 8^.4 per i!;• 12 4 •• -do. • A. '.V . £.2 5 G .1'. I.S 7 ']'ru:d. . . . . 1 ^ O ,t2 i :) H 65 d'jlU, 10-- eta. COMPOUND DIVISION. f9 Natiiax Perkins Boston, \Otli August, 1803. Bought of G K 11 G E A E L E X , 6^\ yds. striped iiLinkins. .at. • !25. ct'.6 9 v)'2 ells mode '>v. 28:^ yds. calico • -'•■^ 2 grocc gilt coat buttons .... 1 86.6 3 pieces russel ••••••• 3 i^. £.21 10 () 71 dols. 7-3 cUi. Af/-. William Sands NcxdncnjpQvt, Sept. 10, 1803. i>07/g^ ^ o/' St e p h e y N o w l a x , 2 pieces muslin 30a\ X.3 25 yards Irish linen « 2^. • 28 J do. stormount calico 'Is. 6 28^ do. . • red • • • • do. • • • • 2 v. 2 1 piece duraut 5()6-. 2 pieces blue shalloon • * 67-^.6' • • • 50| yards dimity '• • 2s.6 • 3 pieces persiasi • S4i. • £.y.O 12 3 132 dols. 4 cts. Received paymcr.t by liis note, of the above date, at tlwce months. For ''''■■ ucn Noiilun, ABRAHArj Trusty, COMFOUND DIVISION Teacheth to find how often ©ne number is contained iu another of difl'crent denomination^^. Examples. 1. Divide £.19 U.v. 9.W. by 2. e)19'l4' 9h Ans. £S 17 ^l 5. Divide £.900 11 9l> ^y 3. Ans. -£.300 5 llj Prove this answer to be right. E COMPOUND DIVISION. • 3. Divide .€.1 '21 7s. 9¥' ^n^ 5. Ans. £.'2-1' !y\s. 6|rf, 4. Divide £.'24-8 5)^. U^. by c). Ans. ^.27 12.>. 3^^ r^. Divide £.1037 1.^. 3^7. by 12. Ans. £.88 1.9. 9|d II. If the divisor exceeds 12, and it be found in the table, divide by its component parts. Examples. 1. Divide £.278 S^. ^d. between 45 men equally. 5)27 8 8 9 S)oo 13 9 Ans. £.6 3 9 each. ^. If 20 lb. of indigo cost £.7 5^. 10c/. what is it per lb. ? Ans. 7'^. o\(L 3. If 21 yards of durant cost 62s. Gd, what is it per yard : Ans. 2s. 7 id. 4. If 72 bushels of corn cost £.20 9a\ 6(/. what is it p rl tiie Jasoa are to have ^-, and the remainder i>< tr» be di^ vide J between the captain, mate^and nine seamen, aihjwing the captain 3 shares, the mate 2, and the seamen 1 share each ; what is the respective part of those concerned ? dols. c(i>. Ans. — The owners of the Hawk 347 76 owneis of the Jasoa 86 94f captain ............ 18 ()3 mate* • 12 42 each seaman ........ 6 2i DECIMAL FRACTIONS. A DECIMAL FRACTION is that, whose denominator is an unit, with as many cyphers annexed to it, as the numerator has phtCes, and is usually expressed by writing the numerator oniA, \\i;li a point before it, called the separatrix ; thus, j-^q, lou^ iVtAi? ^^'^ decimal fractions, and are expressed by ,5 ,'^5 ,125 respectively. The fissures to the left hand of the separatrix are whole numbers ; thus 4^5 yards is 4 yards and 5 tenths, or one half of another yard. Cypliers placed to the right hand of decimals make no al- tei.tl: 11 in their value; for ,5 ,50,500 m-- loa iVom units to the left hand, so dechnals decrease in th,e same j>roiior- t.ou U) the right — and that in decimals, as in whole numfccivs tli: . frgure d-iterraines its relative vahre. ADDITION OF DECIMALS, IluLE. Place the given numbers so that the decimal points* m::;/ stand directly uudoi' each other, then add as in whole liunibers, and point off so many places for decimals to x\\&..- rii^ict a. wvc equal to the izreatest number of lli€ decii-n:d plaCOft-. iL . .:■ given nunr-ors. ': -..'>r 4?,':3 2,1 11,^:8 ^%,A7 ,5 3S-k39 5::, 384. .? 1^9,^^ 2,1 .>■ ijO:^0, E2 l^i,-iS4»- 'd^iW ^^ DECIMAL FRACTIONS. RGqiiired the sum of fep^enfy-nine and three tenths, three liundred and seventy-four and nine miilionths, ninety-seven and TWO hundre«l and iifty-three thousandths, three hundred and litteen and four hundredths, twenty-seven, one hundred and iuur tenths. Ans. 942,9^3009. Required the sum often dollars and twenty-nine cents, nine- ty three cents and three mills, nine cents and six mills, and two duilargand eight mills. Ans. 13 dols. 32 cts. 7 mills. SUBTRJCTIOJSr OF DECIMALS, Rule. Place the given numbers so that the decimal points may sta'ul directly uncier each otjier, and then point off the de- cimal places as in addition. Examples. From 219,4-2 87,26 57 311 'Jake 184,38 19,4 9,375 11,11 35,04 , 67, 8() 47,625 299,89 From two thousand and sixteen hundredths take one thou- banii and four, and four miilionths. Ans. 996,15^)996. From twenty-four thousand nine hundred and nine and one teiitli take fourteen thousand and twenty-nine thousandths. Ans. 10909,071. Tnkc oiiihty-five and seven hundred and thirty-seven thou- saiuiths from one hundred. Ans. 14,263. From five hundred and thirty-one dollars two cents take one hundred and seventeen dollars three cents and four mills. Ans. 413 dois. 98 cts. 6m. MULTIPLICATION OF DECIMALS, Multiply exactly as in wiiole numbers, and from tli(^ product rut off as many figures for decimals to the right hand as tlicre - -o ?i(M'imals in both t!ie factors, Ijut if the product should liol .; nvany, supply the defect by prefixing cyphers. DFXIMAL FRACTIONS. 55 ^Multiply 36,5 by 7,27 Examples. 29,831 ,952 3,92 19^' 2555 730 2555 59662 149155 26'8479 2352 3528 392 oduct 265,355 28,399112 ,285 ,003 768,32 Multiply ,2S5 ,29 124 ,1 ,06 Product ,2280 ,000855 ,029 7,44 Note. To multiply dccim-il fractions by, 10, 100, 1000, &c. is only (• reaiove the separatrix so many places tovrards the right as there are cypheri»» Thus; 7,3G2937 rio -) r 73,62937 , . V , , 1 IOC) f . 1736,2937 n^ultipnedby J^^^ ^ ^^ S 7362,937 (10000 3 (73629,37 Multiply twenty-nine and three tenths by scvent^n. An?. 498,1 Multiply twenty-seven thousandths by four hundredths. Ans. ,00108. Multiply two thousand and four and two tenths by twenty- seven. Ans. 54113,4 PRACTICAL QUESTIONS. 1. How much will 93 yards of shalloon come to at 53 cents per yard r ' *^^^^^ / 9^ ,53 L 279 465 49,29 Ans. 49 dolls. 29 cents. 2. At 21 cents 9 mills per lb. what will 1S7 lb. of cofice come Vj ? Aiis. 40 duls. 9^ cents 3 mills. bG DECIMAL FRACTIONS. 3. ^Vliat will 27 cwt. of iron come to at 4 dollars 56 cent:* per cvvt. ? Ans. 123 dols. 12 centL>. 4. How much will 281 yards of tape come to at 9 mills per yard ? Ans.. 2 dols. 52 cents 9 njills. 5. What will 371 yards of broadcloth come to at 5 dols-. 79 cents per }ard ? Ans. 2148 doh. f) cents. 6. How much will 29i yards of mode come to at 75 centii- per yard ? Ans. 22 dols. 12 cents 5 mills. 7. Wliat will 23,()25 feet of boards come to at 8 dollar?, ^j cents per M, ? 23,()25 118125 47250 IS^OOO 104,^0625 Ans. Ipi dols. C)0 cents ^min«^. 8. How much will 712 leet of boarcis come to at 14^ dollar: per the usand ? Ans. p dois. £i6 cents 8 n)iHs. f). What will 25,6'50 fc^ot of clear boards come to at 17 dols. 50 cents per thousand ? Ans. 44S dois. 87 cents 5 mills. Lois. Cts. Do'.s. Cts- M. 10. 15,859 feet clear boards * ' » - 17 50 per I\I. 277 53 2 11. 812 •- do. •. 14- -.. 11 36 H 12. 37 ^' • do. . . 12 75 » • • 4 75) 4 13. 3 1,49() merchantable do. •- 8 251 9^ 8 14. 269 do.-' (;75 1 M :- 15. 4,114 reliisc do... 3 37 13 80 4 16. 393 maple d;>. -. 8 per i\ot 31 44 17. 57 nnihogany •• ^ 32 (!>-. •• 18 14- 18. 195 ;:allons nu)lasscs .... 57 pc :•;.:.■! . Ml 15 19. 1 6:) do. vuin ....... 9'3 175 77 20. 2'i3 yards laize 23 | er yard 55 89 21. 197 feet clear boards ... . 2 j.er foot 3 94- DIVISION OF DECIMALS. TrTK. Dixile as in whd^' rii;.;^--r-, nnd fiMn -.■1. .^;neiit pc' ihc >U\- ; J. luces in th Ijt' the places of the (pi quires, siippsy tire deie<. i .-. ; .: ,., tkere be a rcuiaiixdcr. or the dccihud • DECIMAL FRACTIONS. . 57 more than those in the dividend, cyphers may be annexed to the dividend, and the quotient earned to any degree of exact- ness. 9^),S53972(,009391 8^8 E: 'CAMPLES. ,853)89,000 (104,337, ^c. 853 3^9 270 3700 3412 837 828 92 2380 2559 3210 2559 6510 5971 539 The various kinds that ever occur in division are included in the following cases, viz. Divide ,803 by ,22 Ans. 3,65 ,806 2,2 ,365 ,803 22 ,0365 80,3 ,22 365 80,3 2,2 36,5 80,3 22 3,65 222 ,365 608,21 -f 222 3,65 60,821 -fn 222 3^5 ,6082 1 4- As mulrip'ying by 10, 100, 1000, &c. is only removing the separating pojrH of the muliiniicand so many places to the right hand as there are cj* phers ill the mnltiplior, so to divide by the same, is only removing thesc|)a- Irdtjrix, h\ vUq same manner to tUe left. 5a' DECIMAL FIIACTIONS. PRACTICAL QUESTIONS. 1. When butter is sultl ar 12 cents 8 mills per lb. how lua* X^y lb. mi!} be bought for 224' dollars ? ,12S)221<,000(1730 12'8 640 640 Ans. 17501b. Here the cypTiers annexed, to the dividend bemg equal to the decimal places in the divisor, the quotient is a whole number. 2. If 673 bushels of wheat cost 786 dols. 73 cents 7 mills* what is it per bushel ? 67 3)7 S6,7 37 {1,169 673 1137 673 4643 4038 6057 6057 Alls. 1 dol. 16 cts. mills* In this example, as the divisor is a whole number, three places are pointed. 4)iF in the quotient, to equal those in tfie dividend. 3. If 493 yards Cost 4 dols, 43 cents 7 mills, what is it per yard ? Ans. 9 mills. 4. If 125 gallons of molasses cost 9-5 dollars, what is 1 gal- lon worth ? Ans. 76 cents. 5. If 205 yards of^durant cost 107 dollars 62^ cents, what is it per yard ? « ' Ans. 52| cents., • "DECIMAL FRACriONS, 5^ REDUCTION OF DECIMALS. Case I. To reduce a tuIgHr fraction to its cquixakiit decimal. KuLE. Divide the numerator by the denominator, and the quotient will be the decimal required. Examples, 1. Reduce £ to a decimal. 4)3,00 Ans. ,75 What is the decimal of h ? Ans. ,5 What is the decimal of \ ? Ans. /^5 What is the decimal of f^ ? Ans. ,15 ^Vhat is the decimal oi \\ ? Ans. ,68 Express | decimally. Ans. ,^7^ Case II. To reduce numhers of different dcnorninations to their equivaknt decimal values. Rule. 1. Write the given numbers perpendicularly under one ancither for dividends, proceeding orderly from the least to tlie greatest. 2. Opposite to each dividend, on the left hand, place such a number tor a divisor as will bring it to the next superior name, and draw a line between them. 3. Begin with the highest, and write the quotient of each division, as decimal parts, on the right hand of the dividend next below it, and the last quotient will be the decimal sought. Examples. 1. Reduce 14^. 5ld. to the decimal of a pound. 4 2 12 5,5 2X) 14,4583 Ans. JQ^g 2. Reduce 15 shillings to the decimal of a pound, Ans. ,75 3. Reduce 3 qrs. 18 lb, to the decimal of a cwt. Ans. ,910714 + 4. Reduce 2 qrs. 2 nails to the decimal of a yard. Ans. ,()25 5. Reduce 14 gals. 3 quarts to the decimal of a hdgshoad. Aus. ,2341 + <)0 DECIMAL FRACTIONS. Case IIL Tojind the decimal of any number of ii hillings, 'pence and farthings^ iij ini,p€ciion. Rule. Write liaif the greates; c\cn number of shillings for (lie first de- ciniai iiLTiire, aiifi h:X {!'t> lar!l!ii.i;s, ii rhe ^iven pence aivl iarihiiiiis., yx^'^'^ess the >ecoiiv! and liiird j>Ii:ces ; "' sorvin^ \o increa;?e the second ])lace by :y, if the !s!iii:ings be odd, and tlie lin;d piace by 1, when ilie farthhigs exceed 12, 691 2. Find by inspection the decimal of 15^. Sid. ()s. 3ld. ]Qs^ 6^d, 3s. 6d. and 2s. ll^d, Ans. ,784 ,465 ,978 ,\75 ,148. Case IV. Tojind file xaluc of any given decimal in the terms of the integer, Kui.i;. 1. Miihijily (he decimal by the niimber of parts in tlie next less deiioininaioii, and cut off as many places for the remainder to the right liand as there are places in the given decimal. '2. JMultiply the remainder by the parts in the next inferior denomination, «.nd cut, oil a remainder as beloie. 3. Proceed hi this manner througli all the parts of the integer, and the -several denominations, standmg on the left hand make the answer. Examples. , 1. Find the value of ,691 of a pound. ,()91 20 13,820 12 9,840 4 3,360 Ans. \3s. 9jd H. Vv i;at i^^ the value of ,9 of a sbillini^ .? Ans. 10|r/. 3. \V]::.t is the value oi ,592 of a cvvt. ? Ans. 2 qis. 10 lb. 4 oz. 13 4-drs. 4. V, !.al i: t' :• value of ,258 of a tun of wine ? An?.. 1 hhd. 2 -|- galls. 5. v...... . -aliie of ,12785 of a year? Ans. 46 days 15 hours b7 n)inutes 57 -f see. j Di ciMAL Tabits oi COIN, WEIGirr AND MEASURE. Giiiinr,. j LfliitnniS. TABLE r. TABLE II L 6 * 5 1 ,ot:'5 ;()';o4i6 English Coin. TllOY \Vl K.H r. 4 3 1 ,(K'0333 ,0'06v5 1/. the Integer. 1 U). llie liite-er. 2 1 ,004 1 66 Sh. itr. ^/Y. r/-. C-. 19 ,9,5 9 ,45 Ounces the sa:nc as 'i ;:i '. ;,.. iv. 1[) ,9 8 ,4 Potee in the Lst V ,05 7 ,35 'Jabio. Avoiiujrrois Vv^t. | If. lo ,8 ,75 6 5 ,3 ,25 ilQlb. I he Iiitegcr. Penny Vt'cbiiuLs. 1^ l.S ,7 4 3 o ,15 irti^l.'t. 10 ,011666 ll >G 2 ,1 9 ,037 5 Q.s. Drchaah. 11 ,55 1 ,05 8 ,033333 3 ,7 5 K; ,5 7 ,029166 2 ,5 i't'»CC. 6 ,025 1 ,25# 6 5 ' 5 ,0,0833 r; /)i()iJ./3 4 ,0-i C666 4 ,016666 :] ,0125 Pi-':: 3 ,0r-^5 2 ,008333 14 ,11.3:»:i \ ,107 113 '• ,0:"l,->i4 t^ ,O0B3.13 ,004166 1 ,004166 13 12 U 1 3 2 Lee una Is. ,002083 i'.:o6 i as ShiUin2;s in the 6 ,0(.3343 ■ ,0i;2?90 : ,00t.'2:>2: ,0. "^11674 1 ,416666 ,o.>.j,j33 6 5 4 first Tab|e. 5 4 3 3 /:5 GraiiiS. Decimals. 2 ,001116 : 2 ,U)66^":6 12 ,0'j5 1 ,(.'C0558 1 ,()8').:,3J 11 1) ,022916 ,020833 Fartii. 7J('cv;ra?;,s. .1. , 3 ,0625 9 ,01875 3 ,^--.Mj s„:,:K' (:. '^■. J 'M /;,,•, '/s. t t. i A (•','/. /V/. ' iW y^.i: \. .") ,01 '.'ail o . w ') 2 '1 ,oi;,87-3 i ,1-5 1 A>, . \Vt. '2 ,011904 ,007936 1 ll>. I ■c iii-.ogcr. 1 ,003968 Q.pt. 3 2 Dcci:ti. ,0937 5 ;0(iV5 Ph. 2 Cz. Jhr^ymds. r/)r,'.s. ]Jccin>uh. 1 ,031i^5 1 1 8 7 4 ,0019C4 ,001488 6 ^''■75 2 ,0-00992 j;a^vH//5. Q.vhs. 5 4 1 ,00r:4pf^ ,0234;;75 3 2 o ,i;;7 "i A bnns!)cai ibe Integer. ,0078125 1 2 1 Ooo. V.'cinKils. 30 ^0 ,476190 Dccinnih. , I. )859 Pis. .3 ■ VrrnT Decimals. 10 ,1.^8730 ,(,03906 2 8 ,0:31;?;5 9 ,1 J 2857 ,001953 1 7 ,o^i'^::'l:] 8 ,126984 6 5 ,019^^'31 7 6 ,111111 ,0952>"8 4 ,0156-^5 5 ,07 9365 TABLE VIII. S ,01 i7J8 4 ,06;>J92 o ,007 ai 2 3 ,04 7619 Long Mf.asure. 1 ,003906 2 ,031 7 '16 1 ,015873 1 MUe iLe Integer. TAl LE VI. P///rs. Dccinui's. Yarrs. Decimals. LroL-iD TJeasure. 3 ,005952 1000 ,56818'^-, 2 ,003968 900 ,511364 1 7^.^ TABLE YIL -iro ,227:j7v ?■) ,:.:)7] J I 300 ,1704 54 of) AlrAfURr:. 100 J 13636 7.) (^ ■ : ) /,^7 1!0 90 ,056818 ,«. 151136 o) ,\4:) ,0i>191» 7 ,0;)oy77 ,0i'.n78 1 6 ,0!):vl09 () ,r "6 i.io ( 1 5 ,00:811 5 ,()lS(:9d i '] /■rJ-,7.> 1 ,oiu<=;)9 1 ;■.,, 2 o /)')vr:9 (■ 1 /yjO.nVo 1 ,()■-):/ J9 l\-i't. j_,-;,,; /j. 1 ;.'.;. .,, :.itb. 2 ,0i-0;j?8? o , 1 :•> 1 ,0001894 Hours. Dccim:ds. 1 ,06 i J 12 11 ,5 ,'{.)8333 /jifVi". Decimals. 10 ,416666 TABLE XI. I 6 ,{H).K)947 9 ,37.> 5 /»00i)79 8 ,,'> )o33') L I . A D A Vi'.icriT. 4 ,000)6 51 7 /291G66 r, ,000:)474 6 /^o 1 I\>tJ^a- t ic liilcgcr- ii ,0000319 5 ,908333 1 ,00001.53 4 ,166666 IlunU. D'.rJmab. o 1 ,1 :5 ,041666 10 9 8 ,.')128-'0 ,4 6 i. -138 ,410-256 TABLJ^^IX. % ■V 7 6 ,358974 ,307692 Time. Mi)!Htcs. Dccimiils. 5 ,'25'HlQ. 1 r.",/)- thn Integer. o) ,0j()L],;3 4 ,^05: 28 iiO ,013838 ,15384() f-i^uc as 10 ,o;;-6':m4 o ,102561 tUi s.co/r! 9 8 7 6 5 ! ,o;)6j5 ,005:>o5 ,004861 ,004166 ,003472 ,002777 1 ,05r28'i I,; s. IjLCinuils. ,025641 1 .012020 ])r,:s. Decimals. L'ouu,.^. i.t'ciiuals. oiii 1,00000;) ,00i'083 ' 11. ,C064iO'-2 ;• •() ,8lM91iS ,0013 {JO 13 . ,005952:; V '.) ,51794;) i ,000694 1! ,r:05;9l5 1 ■() ,'.'7r>9;:> ,VJ() )75 11 1 ) ,('0503(:6 ,00^157 87 i\:) /,' 19178 i) ,O04r20h' 7') ,l9i781 • 8 ,003663i» C ) ,|{M;)H.> 7 ,00.;'3v)51 .^0 ,i.;6'.>::(; () ,0O'27 47i' 4 ) o ) ,');jji--> 1 ,0022893 ,0018315 1.:) ,0:)179l 3 ,00K)736 ] > ,o'j-.s;7 ,0009 ! 57 o .O.Mo .7 1 . .0 -n-iV/!' €l' SINGLE RULK OF THREE DIRECT. lyic Single Rule of Three Direct, 'inclo Rulo of Three Direct teaches, froiii three num- i to lind a fourth, that shall t)e in the siiir.c pr(ipor- th)\\ io ;!>e liiird as tlie second is to the first. \i r:;orc requires 7narCy or less requires less, the proportion i%. direct. Rui.K 1. I\Take the number that is the demand of tiie ques- tion, the third term, the number that is of the snmc name or (raality, the first term, and the remaining number will be the Ir^L and third numbers into tlie same, fund the > 1 vi^vt. dciioraination mcniioned. lid and third numbers toireilier, and di- vide' the piuiUict by the tirLu, and the quctient (if there be no remainder) is the answer, or fourth number required. If, after division there be a remainder, jcduce it to the next denomination below that to which the seccnd number was re- duced, and divide by the same divisor as before, and the quo- tient will be of this last denomination. Proceed thus with all the remainclers till you have reduced them to the lowest denom- ination, which the second number admits of, and the several quotients taken together will be the answer required. The method of proof is by reversing the question. Examples. 1. If 2 yards of cloth cost 4-5. what will 12.> yards come to? yd.s. s. yds. yds. £. s. yd'^. If 2:4:: ^125 Proof if "l25 : 12 10 : :^ 2 4 20 2)5CO 250 , ^ 2 20)250 125)500(1 An-. £A2 10 500 SINGLE RULK OF THREE DIRECT. 65 y. If 1 bushel of corn cost 7-3 cents, what will '257 biislivl^ iuo to ? bifs/t, r/S\ biLs//, If 1 : 75 :: 257 75 1^85 . 1799 192,75 Ans. 19'2 (ids. 75 cts. 3. Wlint will 931 yards cf shalloon conii? to at 55 cts. 4 ms. per yard ? Ans. 515 dols. 77 els. 4 nis. 4. How many bushels of wheat at 1 do!. 12 cts. per bushel can I have for 81 dols. 76' cts. ? Ans. 7o bushcjs. 5. What will 94 cwt. of iron come at 4 dols. 97 cts. *2 rns. per cvvt ? Ans. 467 diois. SG cts. 8 ms. o. What will 349 lbs. of beef come to at 2,/. per lb. ? . An:^. .C.2 18 2-^ 7, .\t Cv. per \ard wb.at will 59 yards of cloth come to ? Ans. <£.S- 17 I'rovc this answer to be right. . "^ ■ ! '^'.' many lb-<. of beef at 5 cts. p^^^* ^' - .: \^. 85 cts. ? cAv. lb. (his. cis\ . K 5 : 1 : : 29,85 I 0^ How many hhds. of salt at 4 .cols. ^0 cl:f. per hlid. ^c;-)) kfi\(* ior 392 dols. ? ., Aus. hO hln'i: ' . How many lbs. of ccil\^c, at 1^. 7^/. rev lb. m:iy ht- \ F-2 66 SINGLE RULE OF TlJREt: DIRECT. U. Wlien 25 yds. of cloth cost £.2 V2 1, what is it per yd. ? ifL £. s. (1. ?/.7. If 25 : 2 12 1 :: 1 20 52 12 625 1 ,e5)()25(12 I 25 • 50 -^ 2s, hi, ] 25 125 Air,. 2.?. Id 1?. If 5o bu?hels of corn cost 42 dols. 56 cts. what is it per luihol? bush.dolsA'tsbmh, If 5() : 42,5ri :: L 1 5a)42,56"(,7(> 336' 336^ Ans. 7(^ ct«?. Kn If 112 lbs. o^ beef cost iS.5. 8 J. wlmt is it ])rr ib. h. } Ans. 2 pence. '73 l)iishcls of rye cost 7o9 dols, 23 cts. 9 nis. what ^''-rtb ? Am. 1 (h)l. 14- cts. 3 ids. 1 vard of baize wortli, when '^l yards cost ..,,/. ' Ans. -^. 2^/. n iioi) is sold at 5 dols. 4 cts. per cv.t. wh-u i> it pv>r '^^ , \ rl: . 5 :n-. 'Ijns of mola;- ^- . '• '^^1:;': ^^^ Prove t];is :' SINGLE RULE OF THREE DIRECT. €7 ig. At 5 dols. 50 cts. per thousand, what will 37 tliousand of b*)ards come to ? Aiis. '203 dols. 50 cts, 20. What will 4 hhds. of rum come to, containing viz. 79j> 81, lOU, and 112 gals, at 6s. 9(L per gal. ? Ans. £A'I7 4- 9 :!. Vv-hat will 327 hhds. of salt come to, at 5 d(ds. 25 cts. per iihd. ? Ans. 17l6' dols. 75 cts. C2. If 3 and 4 make 9, how many will 6 and 8 make ? Ans. 18. 23. If a chest of Hyson tea, weighing 7^ lb. neat, cost £.32 I U\ 9^/. what is it per lb. ? Ans. Ss, 3d, 24. B owes £.21 19 17s. 6(1. and he is worth but £'.1324 185. old.; if he delivers this to his creditors, how much do tliey receive on the pound ? Ans. 12.s, 6V. 2). A owes B £.069 6s. 8d. but failing in trade, he is able to pay but 15^. 6d. on the pound ; how much is B to receive, and what is his loss ? Ans. — He is to receive £.441 4 8 ITis loss is ...... 12s 2 2o. A merchant failing in trade, owes in all 29475 dols. and delivers up his wdiole propert}', worth 2189-1' dols. 3 cts. ; liow much per cent, does he pay, and what is B*^s loss, to whcMii he owed 325 dols. ? Ans. — He pays 74 dols. 28 cts. per cent. And B lo-es S3 dols. 59 cts. 27. How much will 4 cwt. 1 qr. 19lb. of butler come' to, v,% lb..? lb. 400 n: 4 hundred. 48 zz excess, 12 per cent: Ih ^ 28—1 quarter. 19 [f 1 : 9 : : 495 12)4455 20)371 5 Au-:. £.18 \\s. 3d. SCib. of bice; cobt 13 dols. 20 cts. what is it Aiis. 12 cerits. 63 SINGLE RULE OF THREE DIRECT; 29. If \6 cwt. 3qrs. of steel cost 157 dols. 45 cts. vvliat i> ■ 1 qr. worth ? Ans. 2 dols. 35 cts. Prove this answer to be right. 30. A captain of a ship is provided with 1 8000 lb. of bread for 150 seamen, of winch each man eats 4 lb. per week, hffw long will it last them ? Ans. 30' wef^ks. 31. How long would 2295 lb. of beef last for 45 seamen, if they get 1 lb. cach^ and that three times a week ? Ans. 17 weeks. 32. Suppose 120- seamen are provided with 7200 gallons of water for a cruise of 4 months, each montli 30 days; how much is each man^s share per day ? Ans. 2 quarts. o3. A ship's company of I6 men is on an aliowance of o ounces of bread per day, when meeting with a vessel from winch they are supplied with 2 cwt. of bread, what addition will this make to their daily allowance, if they suppose their voyage to . last2S days ? " ' Ans. 8 ounces. 34. If 17 tuns 2 hlids. of wine cost 54()3 dols. 40 cts. h-'^v much is one pint worth ? Ans. 15 cts. 5 ms. 35. IkrvV much will 4 pieces of linen, containing, viz. ooly . 36, 37 h, and 3S yards come to, at 79 cts. per yarci ? Ans. 110" (hds. 13 ct?, 36. How many crov/ns of 110 cts. each will pay a debt of . £. 82 I6.S. 7(1 ? " An^. 251 vvo^^rv,^, 37. IfCOJ tonspcwt. 3 qrs. 3lb. oftallow cost £.433^^ 3.0;/. what does 1 ton cost ? An?. i;.22 8 i\ 38. I low many cwt. of rice may be bought for 48/ dols. 50 cis. when 7 lb. cost 25 cents ? Ans. 121 cwt. 3 (jr?. 14 lb. 39. \V!ieii 9 dols. 36 cts. is paid for 2 ([rs. 22 ib. of sugar, . wiiat is 7 i-^. w^orth ? Ans. 84 cts. 40. "When 47 cwt. 3qr5. of sugar cost ^£.182 Is. llf/. what *. is I ([V. worth ? Ans. 19-^. I''/- -i 1 Ii" n t!). 6 oz.. xVvoirdupois cost 5 dols. JO cts. ^vi. -r i. it -. ;\rs. . ... ..-;i..,;it 40 tubs of butter wei-.v '" " ' ' '^ ' ' ^ nC'ir, i'oi' -!v2 dols. 2 els. ; paid coope; .t and labc-ur 4 d . 1 .would know wdial it stands- me in per ;.>. ? /v..;;. ; i SIXGLE RULE OF THREE DIRECT. 69- 4:3. How much will a grindstone, 32 inches iliiiinetcr, luul 6 inches thick, come to, at 5s, per cubictbot ? Sec iiedudwiiy \ 32 the diameter. 1 6 iz liii i 1' til c d i iiinc tc r. 48 If l/i^S : 5 :: 46'03 : 13 4 Ans. 13.?. 4?/.. 4i. Vv'hat will a grindstone, 28 inches diarnctfer, and 3^ in-, chcs thick, come to, at 1 dol. gOcts. per cubic foot ? • Ans. 2 dels. 26 cts. 45. When a man's yearly income is 2^9 dollars, Tfcw much is it per day ? Ans. 2 dols. 60 cts. 46". At '^l per cent, what is the commission en 1525 duls. ? Ans. 6S dols. 62 cts. 5 ms, 47. What is the interest of 456 dollars for 1 year, at 6 per cent. ? Ans. 27 dols. 36 cts. 48. At 5 dols. 50 cts. per Isl, what will 21,186 feet boards come to ? Ans. 1 16 dols. 52 cts. 3 uis. 4p. When boards arc sold at IS dols. per M. what is it per foot ? Ans. 1 cent 8 mills.' 50. What will 93 feet of boards come to, at 4 cts. per foot ? Ans. 3 dols. 92 c-ts. 5 1 . What will 45) thousand 3 hundred and 25 ca^ts of sIum s come to at 17 dols. per thousand ? NoTK. Stares nre cyuntcd by casUng three at a time ; 40 ca^-ts uvt*.ke 1' huiiUrtd, iii\d 10 hundred 1 lhou;and. '^l. (^•. 's. 3r. //. r. 1 : 17 ;; 49 3 26 ro 10 i^. 493 40 40 dirJs- Cts. m, Ans. 8J9. 16 2 400 19745 >0, V/nat will 19 M. 8 and 15 casts of white oak hhd, staves iic to, at 31 dols. per M. ? Ans. 6l4 d^ols. Q6 cts. 2 mk. ?0 SINULK l^ULK or UiRLK l^U[V.C 53. What will Q2 M. 9 aiul 3? ca'^t^ (;(" wd o-ik lilid. f-.iA!ve5 como to, at 1:) dois. ]:cr M. r An-. 'JfyN; (!ol>. (]0(:{<. QpAi. .5-k \Mi:it \\iil .50" bu:-uiiciot' iioops come to, at Qj doli^.pcr M. ot 30 bundles ? NoTi-:. ll:){)jis ai\: som^'/iriirs K..nr.fl iii Ir.u'.dlcs of 50 hoop- p:k-]), ai;;! 1 '^••'■^' '■ -'''"- ■■■■ ' 1 hinir}:ed, and 10 liui;d:-d i-v 40 bund'e^, 1 ihuii-aiu!. ]>i:t -\ b,ur,d li! l;ni;d'vv* ol'di/ eaclij o b'.indics iiiakinj; 1 liiUidrcd/, Ui.vj I'^ iiu.i.li^.i ei' hud, can I ba\c ior o'^ii dollars r 1(4 73: & :: o'26 An?. 5-1-9 biislieiN, \\lieii nioa^urcJ on, board tbo vi^^-d. If 4 75 : 7^:: 32u An-. 5U bu '--'■■— ^ -'•, —-'y, 5^?. W];at i< rlK (a- o-^ bo.d^, ^ (-. ^• ihc d.;\vt tax, at '2Sca a: - .a .; . ' ^ < . 57. \V;;;'t i~ {].' 1 - ' • ■ . N '■. the dliS'Ct t.ix, at /', lb too : ,a :: fy' lbO)C7i',0 nr \-. ^ n:i- r>^i:I is rq';:d to 3 nu'.h on u . > 1;.' u-i? ^iiin lu 8 SINGLE RULE OF TIirvEE DIRECT. 71 Examples. ■58. What is the tax on 7 bo ctoil.iis at ,\ per cent. ? 7.'^J dollars 3 mills 'J',"*.">f) ir.'.lis. Ans. 2 rlols, '25 cts. 9 ii'^"^* 59. Find ll:c t:ix on ihe following sums- • <■/()>. r/.;/.>. r/,?. ■vif'.. 1 .);)(.) at ;',) prr cent. An^. () "^0 4o00 1^ 2^: ^O 7S50 ;^ 4 7 JO \'2(h^0 /, 8S 7() i()9.5() ;■', ij.'> Co 2 ! M'20 ^'-'^ •••••• V 0^1 5 1; :).' S 10 1 3.38 40 60. W iiat will a pierce t^.f land. nucK-Lirinir 48 Ice: i.':s length and 4-0 kv\ \\\ widili at each end, amount to at 20 dolkub per square rod.? fr^f^* 48 40 /;,^ r/.,'.s. If \17-ll : 20 : : L920 Piy decimals. ^ Ans. Ill dols. 4 ct?. If 272,2.3 : 20 :: 1^20 61. A charter-party for a ve?Hel of 1 Si'T tnns commenced on 2$th of Ma^', and ended on tr.e lOih -f (October f'/ilowinL': : AVlifit does the hire amoiuit to for that tiiiie, Jit 2 < ois. per ton per niouili of 30 days ? dcn^.s, I^T;=y 4 J'iiui 3.) .1:.!/ .U A:-. II i ... 31 2 do!s>. ■[)er mo. Octf,»1)cr' • • • JO -II JO : ;■" J : : 1 -i in/3 37 -i 3,0)5059/ J '16BG40 An<'. 1636 (i'.)!s. 40c'J. Tn c;;)ru^itino- the linu', tli:^ d'lys of rcc-iving and tliicharnlj:^ the vcssvl :u« it>t;V included. T'2 INVliPiSE PROPORTION. INVERSE FROPO RTION. "Whereas m the Rule of Three Direct, more requires more, and less requires iess, in this rule more requires less and less requires more. Rule. After stating the terms as in the Rule of Three Di- rect, multiply the iirit and second terms together, and divide the product by the third, and the quotient is the answer. Examples. * 1. If 100 workmen complete apiece of work in 12 days, how many are suilicient to do it in 3 days ? d. m. il. 12 : 100 :: 3 1'2 3)1200 400 Ans, 400 men. 2. If 8 boarders drink a barrel of cyder in 12 days how long woitld it last if 4 more came among them? Ans. 8 days. 3. A ship's company of 15 persons is supposed to have biead to last their voyage, allowing each 8 ounces per day — when tlicy p;!ck up a C]-cvv' of 5 persons in distress, to whom they are wiliiTig to con.miinicate, what will the daily allowance of each person then be ? Ans. 6 ounces. 4 V.'hen wlieat is sold at p3 cts. per bushel, the penny loaf ^veighs 12 ounces — what must it weigh when the v. heat is 1 dol, 24 cts. per bushel ? Ans. 9 ounces. .5. Ifov7 many yards of baize, 3 qrs. wide, will line a cloak, whirh has in it 12 yds. ofcamblet, half yard v»ide? Ans. 8 3^ds. ('k '■■• no:^e 400 )^:cn in a garri. on rre ]^r»:vidcd witl^ i.r(;\!- : days, hew iiiany iv.en must \v -rnt Cit, ii ihcy \. \e th(- provisioi^s last 60 .Irys ? Awv,. iCO n^cn. 7. AVI. at sum should be put to iidi'ic^st to p;;n ns much in 1 nionlh, as 127doHarji would gain in 12 uh i ;!;■•? A..>. !,:- Idols. COMPOUND PROPORTION. 73 COMPOUND PROPORTIOX, Compound Propohtion teaches to resolve such ({ucstions, ns require two or more stalings by simple proportion. , ' Rule. State the question, by placing the three conditional terms in this order: that which is the principal caus6", and 6003 for per cent, pet auiumi ^omc'in!'^-? u.^cU in culculatijig interest. COMPOUND PROPORTION. 75 6. What is tlic interest of 65-^ dollars for iG-i days, at 6 per cent, per annum ? 100 654 dollars^ 365 l6'-t 6)36500 2616 392'\ 6083 the fixed divisor, 654 fcund as above directed. 0083) 107-256(17,632 6083 46426 42581 38450 30498 19520 18249 12710 12166 544 Am, I7d. 63c. $m. ^, What ia the iatcrcst cf 947 dollars^ for 294 days, at 5 per cent, [^i annum ? 947 dolls, 294 3788 8523 1-894 yixed Divisor 7300)278418(^30,13^^ 21-900 59418 58400 10180 7300 28800 21900 69000 65700 3.300 A»s. oBduIs. 13 Q. ^ la. 76 VULGAll FRACTIONS. VULGAK TRACTIONS. Fii ACTIONS, or broken nuriilcrs, are expressions for any as- sij,nable parts of an unit; and arc represented by two numbers, phited one above the other, with a line drawn between them. The number above the line is called the numerator., and that below the line the denominator. The denominator shews how many parts the integer is divid- ed into, and the numerator shews how many of those parts arc meant by the fraction. Tractions are either proper, impropei, compound, or mixed. 1st. A proper fraetion is when the numerator is less than the denominator, as J, |, f,^, {J^, &c. 2d. An improper j'raetion is when tlie numerator is either equal to or greater than the denominator, as f, V^il'lu? ^^» 3(1. A eo?)? pound fraction is a fraction of fractions, and knov.n by the word qf\ as h of §, y of /*q, |§ ^^ ih ^^' 4th. A 7nixcd ninnler or fraction is composed of a whole number and fraction, as 8f, izj, 29|, &c. I. To reduce a simple fraction to its lowest terms. Rule. Find a common measure by dividing the lower term by the upper, and that divisor by the remainder, continuing till nothing remains ; the last divisor is the common measure; then divide both parts of the fraction by the common measure, th'' quotients express the fraction required. NoTe. If the common measure happens to be i? tjie frac- tion is already in its lowest term; and whcii a fraction hath cyphers at the right hand, it may be abbreviated by cutting; them off, as f |2. Examples. 1 . Reduce /,\ to its lowest term. 91)117(1 91 26)9l# Common measure 13)2()(2 2() 1 ^)^^i (9 the answer. TULGAR FRACTIONS. 77 Or, divide the terms of the fraction by any number that will divide them without a remainder; divide the quotients in the same manner, and s6 on, till no number will divide them both, and the last quotients express the fraction in its lowest terras- Examples. 2. Reduce Hf to its lowest terms, W W C^) 192 24 3 1 zz — =z— n— the answer. 576 72 9 3 3. Reduce ^ t^ to its lowest terms. Ans. f, 4. Reduce ^^f to its lowest terms, Ans. |. 5. Reduce |f ^f to its lowest terms. Ans. |-ij. II. To reduce a mixt niDnber to an improper fraction. Rule. Multiply the whole numbers by the denominator of the fraction, and to the product add the numerator for a new numerat^l^and place it over the denominator. Note. To express a whole uumbcr fractiba-wise, set i, fur a denominator to the given number. ' "^'^ Examples. 1. Reduce^5g to an improper fraction. "*S>< a4-3=z^iji the answer. 2. Reduce 183 /j to An improper fraction. Ans. ^ff^. 3. Reduce 27f to an iitiproper fraction. Ans. ^|^. 4. Reduce 514 /^ to an improper fraction. Ans. ^f|". ^ III. To reduce an improper fraction to its proper terms. Rule. Divide the upper term by the low^r, and the quo- lent will be the whole number; the remainder, if any, will be ■■'^ numerator to the fractional part.^j^ Examples. . Reduce ^J- to its proper terms, o) 1 7 (3 g the answer. 15 2. Reduce ' J^.to its proper term*'. Ans. 275. 3. Reduce ^f P to its proper terms, Aus. 514/^- G2 the ?8 VULGAR FRACTIONS. IV. Tofind the hast common multiple or denominator. RuLF.. Divide the given denominators by any number that uill divide two or more of them without a remainder^ and set llie quotients and the undivided numbers underneath. Divide these quotients and undivided numbers by any number that will cli\ide two or more of them as before, and thus continue, till no two numbers are left capable of being lessened. Multiply the last quotients and the divisor or divisors to- gether, and the product will be the least common denominator required.. Examples. 1. What is the least common measure of |,^, ^^, & ^(^ ? 8)9 8 ]5 16' 3)9 1 15 2 3 1 5 2 3x5x2=z30x3x8=z720 ans. 2. What is the least number that can be divided by the nine digits without a remainder? Ans. 2520. V. To reduce vulgar fractions to a common denominator. Rule. Find a common denominator by the last case, in wliich divide each particular denominator, and multiply the quotient by its own numerator, for a new numerator, and the new numerators, being placed over the common denominator, express the fractions required in tlicir lowest terms. Examples. 1. Reduce i, |, and /^ to a common denominator. 36 the com. deuom. 4 9x^-n 9 4x5 — ^20 12 3x7=iV!l The fractions will l^e IJ, |g, fj. 2. Reduce I, f>.|, and I to a common denominator. /ins. 04, 04, 04, ex ^^. 3^. Reduce I, t, ? and A to a common denominator,. -*, Reduce K I, A and J to a common denominator. " ^ ^' A,.S J5 27 12 K, 25 VULGAR FRACTIONS. 79 VI. To reduce a compound JYaction to a single one. Rule. Multiply all the numerators for a new numerator, • and all the denominators for a new denominator, then reduoe the new fraction to its lowest term by Case I, Examples. 1. Reduce £ of ^ of ^.^ to a single fraction. 3x5x9—135 9, zz ■ .' the answer. 4x6x10 = 240 \6 2. Reduce f of f of I J to a single fraction. Ans. //g. 3. Reduce f of | of j to a single fraction. Ans.t^Aj. VII. To reduce a fraction of one denomination to the fraction of another, but greater, retaining the same ialue» Rule. Reduce the given fraction to a compound one, by multiplying it with all the denominations between it and that denomination, to which you would reduce it ; then reduce that compound fraction to a single one. Examples. 1. Reduce g of a penny to the fraction of a pound, d. 7x1x1 7 — — zn— • the answer. 8X12X20 1920 2. Reduce f of a pennyweight to the fraction of a pound Troy. Ans. jJo- 3. Reduce f- of a pound Avoirdupois to the fraction of a- cwt. x\ns. ^Iq, VIII. To reduce (he fraction of one denomination to the fraction of another, but less, retaining the same value. Rule. Multiply the numerator by the parts contained in the several denominations between k and that denomination to which you would reduce k for a new numerator, and place it ©ver the denominator of the given fraction. Examples. I. Reduce 9^0 of a pound to the fraction of a penny. 1X20X12 = 240 =+ the answer, 9(yo so VULGAR FRACTIONS. 2. Reduce s^q of a lb. troy to the fraction of a dwt. Ans.f 3. Reduce ^-Jg of a cwt. to the fraction of a lb. Ans. | IX. Tofnd the value of the fraction in the hioxcn parts of the integer. Rule. INIultiply the numerator by the known parts of the integer and divide by the denominator. Examples. 1. What is the value of f of a £. ? 2 20 shillings, 3)40 Ans. 13.?. 4 and cfo together. Ans. 1J|. 4] AJa i\^ II, and jf together. Ans. 2^^. II. To ac^(/ W2f.rec? numbers 'whose fractions hate a common de- nominator, RuLi:. Add the fractions by the last case^ and the integer as in whole numbers. Examples. . 1 . Add 2 A ? 3 /i , 4 ,\ , and 7 A together. ^1 1 79 '11 37 A answer. 2. Add 13A» 9i* » ^^^^ 3/5 together. Ans. 25j. 3. Add 1 ,\» 2 A* 3 A, and 4ji together. Ans. 12. 4. Add 9 J I, 7/4, 5 A, and 8 {{ together. Ans. 31?. III. To add fractions hating diffcj^nt denonwiafors. Rule. Find the least common denominator by Case III. • n Reductiun, in which divide each denominator, and multiply 82 VULGAR FRACTIONS. the quotient by its numerator ; the sum of the products is « new numerator to the common denominator, and the fraction required. Examples. 1. Add f, I, I, 2, and \i together. 24 com, denom. 3 8X 2 = 1^ 4 6x 3 = 18 6 4X 5 — 20 8 3X 7=21 12 2x11=22 I J =4-2-4 ^^^^ answer. 5. Aa^ |, 1 I, 1, and i together. Ans. l.^^^o' 3. Add f , I, t, L -nd ^5 together. 3^^. IV. To add mixt numbers whose jru^A^rins hate different denom'* inators» Rule. Add the fractions as in the last «ase, and c^^ x\\* tegers as in whole numbers. Examples, 1. Add 5f , 61, and 4J together. 24 com. denomv H 16 H 21 H 12 ns. 17/4 45—9 1 24 — -^24 2. Add If, J of J, and 9/0 together. Ans. llg-o- 3. Add li^o» 6i» I of J, and 7^ together.. Ans.lC'//^- V. JF/ie/i the fractions are af several denominations. Rule. Reduce them to their proper quantities by Case IXm, in Reduction, and add as before. VULGAR FRACTIONS. Examples. S3 i. Acia I of a £, to ^% of a shilling. s. d. I of a j^.~15 6f /o of a *. zz 85 15 common measure. 10 9 Ans. IT) 10r^3 tI = iA 2. Add f of a yard, | of a foot, and I of a mile together. Ans. J 540yds. 2ft. 9 inches. 3. Add J of a week, J of a day, and ^ of an hour together. SUBTRACTION OF lULGAR FRACTIONS. J. Tojind the difference hetucen s'mple fractions that hate a com* man denomiiiator^ Rule. Subtract the less numerator from the greater, and under the remainder put the denominator. From Take Rem. f f T Examples. 21 i4. i Z It) 13 10 1 i IT 35 J 3. 3S 4 33 m 5 209 II. To subtract a fraction or mixt nitmher from a tjohole m'mhcr* Rule. Subtract the numerator from the denominator, and under the remainder put the denominator, and carry one to be deducted from the integer. E "iAMPI.ES. From 3 6 10 9 100 ^ Take 0,\ .0/0 99 ?.^ B Ucm. '2\l o.i. 84, VULGAR FRACTIONS, III. To suhtrad simple fractions that have no common clcnomi- nator. Rule. By Case IV. in Reduction, find a common denom- inator, in which divide each denominator, and multiply the quotient by its numerator; the difference between the products thus found is a numerator to the common denominator, and the answer required. From -J-} take /^. Examples. 42 com. dcnom. 21 2X17: = 34 14 .3X 9- =27 Rem. 7 4il — ■■l> tlie: answer* From Take i 5 . HI Rem. 1. i A 1 1^1 In ord»r to distinguish the greater of two fractions, let them be reduced to a common denominator, as in case V. in reduction ; and that fraction, whose numerator is greater, is th.e greater i'r;iction; the ditlerejice lictv/een ihe new numerators, benig set over the common dcnonnnator, will slicw tljc excess or inequality. Example. Which of the two is the greater fraction, J J oi'IJ •'* 48 com. denom. 12 4X11=44 16' 3xl5rz45 Ans. -J I is greater by ^q» iV. To subtract a fraction or mixt mmihcr from a mixt nimilcr,, xvhcn the fractional part to he subtracted is greater than that from which it is to he subtracted. Rule. Find a common dcnomlnriior and a now numerator. Gs in the last case, and then subtract the numerator oi' tl gj-cutcr fraction from the common denominator, and to tiie \\ VULGAR FRACTIONS. 85 m^inder add the less numerator, and set the sum of botTi for a new numerator over the common denominator, and carry one lo the integral part, and proceed as in whole numbers. EXAIMPLES. 27 common denominator. From Take From 6} Take 0?^ li ^^2 7 3X1=3 IX Uzz:i-i Rem. 10^ lA ^60 12^ 6"^ ^9^ 0/. 1 o 1 6 ••? V. JFhcn the fractions arc of different denominations. Rule. Reduce them to their proper quantities and sub* tract as before. Examples. 1. From \j of a£. take j\ of a shilling. 15 common denominator^ .?. d. — 7) of a£.nl5 ^ lO ,^0 of a 5.1= 3J 9 Rem. 15 3,^5 2. From '^ of a £, take 2 o^ a shilling. Ans. 14.s. 3(f, 3. From 5 of a lb. troy take J of an ounce. Ans. 80Z. l6dwt. l6grs. 4. From 7 weeks take Pi^^o days. Ans. 5w. 4d. 7h. 12m. 5. From ^ of a yard take j of an inch. Ans. 5 inch. Ibc. MULTIPLICATION GF VULGAR FRACTIONS, li : LE. Reduce compound fractions to simple ones, and mixt nuni! :ts to improper fractions; then multiply the numerators top^ethL^r for a new numerator, aud the denoniiuatori for a nesv denominator. H S6 VrLGAR FRACTIONS. Examples. 3. ^Mutlip]}^ 4^ by J. 4i 9X1 2X8 /^, tlic answer. '2. Multiply ^ by ^. Ans. i^,. :]. Multiply ■ !)y ^. Ans. ^|. 4. I\lnlti])]y 4-:^| by ]3f. Ans. 67-2 f^. 5, Mu!tij)ly ^ off/ by ^. Ans. 5=L (). Multiply /;, by ~ oi g of f . Ans. ^. DIVISION OF VULGAR FRACTIONS. PlULE. Prejiaro the fractions if necessary; then invert the divio^)r, and proceed as in niuUiplicnlion. EXAMTLES. 1. Divide^ by §: 4X3 zz I ; rz ^' the answer, 7X2 2. Divide 3j by 9J. 6 2 19x2 J/ -\^ Then /r!i =: J the answer. 6X19 3. Divide 5 bv Z^,. Ans. 7-. 4. Divide ,^ by 4^. Ans. !'. 5. • Divide (]l by J of 7. Ans. i?'^ 6. Divide 5::Oj5 ly ^ ofOI. Ans. 7^^ MfS^'ELLANEOUS QUESTIONS IN THE rUECE])IXG RULES. 1. What pprt is 28]?. of 33,\ ? 2. ^Vhat will remain if 13 3 v. and 7i^d, be t;; .1 ? Ah.. JO. IK'^V. VULGAR FRACTIONS. 87 3. Wliich is tiie greater fraction, ^^ or /^ ? Ans. ^-^5 is greater by /% . 4. or what number is IjG the H part ? Ans. o68. 5. By how much must you multiply 13f that the product nui be 4^91 ? A«^s. 3?. (). Find two numbers so that .i| of the one will be as much as J^ of the other ? Ans. 1'26 & 208 or 63 ,. 4. If the penny whitc-h->af weigh 7 oz. when a l)ushel of W;5cat cost 5s. 6d. what is the bushel w-orth when the penny while-loaf weighs but 2 J oz. ^ Ans. 15^. 4^g?. FUACTICE I? a contraction of the Rule of Three direct, when the first term happens to be an unit, or one, and has its name from its frequent use in business. THE Ji ABLE. Parts of a jt. ,9. d, 10 is I 6 -8 A •^ I 4' I 3 4 1 2 6' 4 2 A 1 8 ^, I .^o Tarts ot a shiliing. d. G is i 4 i r. 1 O , .1 11 A 1 A i-'ailfc ot i Cxvt, Qr. 10 5 4 2 2 2 1 1 1 Parts of a Cwt. Qrs. lb. IG 14 8 7 4 2 "5 Parts ol ^ Cwt. lb. 28 is i 14 1 8 i 7 i ^ /. H A 2 A Parts of I Cwt. 14 is h 7 1 4 1 Si 1 9 1 ^ 3 4 1 ,J« PRACTTCE^ 83' Case I. U7ien the price Is an aliquot, or eicn part of a s/nlli?ig. Rule. Divide the given number by the part, and the quo-- tient is the answer in shillings; what remains is to be reduced^ as in Compound Division. Examples. 1. What will 4'596 yards cos,t at 6d» per yard? 6V. 2 2|0 4596' lU li Yards. d. Q, 3746 at 4 per yard. 3. 1095 3 4. 7596.. 5. 3747 •• 6\ 3.03.. Ans. £.114 18-?,- £. s. (]. Ans. 62 8 8 13 13 9 6*3 6 ■ 1 15 12 'U 20 4.V Case II. JVhcn the price is pence, or pence and fartliingSf and no even pari^ of a shilling. Rule. Find the even parts for the price, and proceed as in^ Case I, and the sum of the quotients is the answer. E>tAMl>LES. 1. What will 4937 yards come to, at 9c/. per var J ? ^ ' 4937 h i 2IO 246'8 6 1234 3 370I29 Ans. £aS^ 2 9. II 2 0^ PRACTICE. Yards, fl. 2. e76\5 at iSpcrvard. Ans. a. ^G2 7 ..- 4. 3159 7^-- 5. 1496^ 11 0\ 1895 10^ 7. 4-()89| 5^ 8. 36'89 84 *). 1871 2^ 10. 8914 8| 11. a^ji^oh 9h . 12. 9H loj.-- ... 13. 201i .... 9 £, 5.. (T, 92 3 4 109 14 6' 9cS 14 4.1 ()'8 11 4 82 IS 1^7 97 13 lU 126 15 2^ 19 9 9i 306 8 41 101 9 5| 4 3 91 7 10 Hi Case III. JF/icn the price is shillings, or shillings a?2d pence, and an €Te» p^rt (if a pound. Rule. Divide the given quantity by the even part, and tlie- quotient is the ansv;er m pounds. If there be a remainder^ leduce it as in Compound Division. Examples. 1. At Cy. Sc/. per yard, what will 473 yards come to? Gs. 8c/. I i I 473 Ans.^.i 57 135. 4f/. yards, s, d, 2. 387 at 10 An.?. 3. 478 5 4. ?A)7 3 4 5. 797^ 2 6' 6. 1594- 1 8 c£. s. d. ^9o 10 119 10 66 3 4 99 13 9 13 5 5 Case IV. lllicn the price is shillings or shillings and pence, tchich males n* even part of' a pound, ntTLE. Find the even parts for the price, and divide ns in \ise JU. or multiply the given cfuantity by the shillings, and 'ke the even parts of shillings for the penccj as in Case JL PRACTICE. 91 Examples. 1. What cost 287 yards at I?*. 6d. per yard. First method. Second method. 287 287 17 6 10 5 '2 6 ^- 143 10 71 15 .S5 17 6 Ans. 251/. 2s. 6d. 2009 287 e I i I 143 6 2 1 0)502 1 ^ 6 Abs. 251/. 2s. 6d. d. 4. 5. 6. 7. 8. 9. 10. XI. f/ards. s. "8172 at 15 .S69i 19 47G5 11 8 .. 3718 18 4 .. 709} 1 2 6 . . Sfl3 14 10 .. 961 2 H " 158 5 Si •' 4705i 3 9 •- 127 7 5| .. .£. S. Ans. 6129 .... 3506 9 2779 11 ..•• 3408 3 .... 443 5 .... 157 19 .... 13 9 . ..*. 45 5 882 6 d^. 8 4 6 41: 47 9 lOi Case V. 7f7zc;^ the price is an even number of shillings. Rule. Multiply the quantity by half the shillings, doub- ling the first (or right hand) figure of the product for shillings^ the rest are pounds. Examples. 1. What will 788 yards come to, at 2 shillings per yard ? 788 Izrhalf the shillings, Ans. £.78 \6 yards. 2. 347 ,n. 638 4. 589J 5, 246 6. su\ 7. 523 8. 745 o. 373^ 10. 270 11. 1721 33. 89;- 5. 4 6 8 10 12 14 16 18 20 22 «4 Ans. 69 8 ' ... 191 8 235 14 1 ^^3 .... 194 17 .... 366 S ..^. .596 3:^6 3 'i70 J 89 15 ...•. 1«7 2 s^ PRACTICE. Case VI. JF/ien the price is pounds^ slnllijigs, Src. Rule. INIultiply the integers of the given quantity by the pounds, and work tor the shillinus, &c. by such ot" the preced- ing rules as you think best, and work likewise for the fraction- al parts of the integer ; the sum of these will give the answer. Examples. 1. What will 1/3 cwt. 1 qr. 14 lb. of sugar come to, at £.3 155. 6c/. per?is. cwt. q-r. Ih. (lols. cis. doh. cts, 2. 24 18 3 18 of hemp at 289 50 per ton. Am. 7921 73 3. 31 iO ' 268 75 8546 25 4. 19 14 2 12 iron 110 2170 33 8 5. 17 3 24 cordage •••• 14 per cwt. •••. 251 50 J. R.per. diyls. cts. doh. cts, 6. 25 2 25 of land at 29 per acre. Ans. 744 3 7. 87 137 33 2886 88 8. 229 3 18 18 50 4252 45| 9. 3 26 » • • 25 22 81 1. How much will. 4-9 M. 3 hund. 25 casts of staves come to, at 17 dols. per M. .? 49 17 343 49 2 Ijund. I .'3,4 1 i 1,7 "20 casts i ,85 5 i ,212 839,162 Ans. 859 dols. 16 cts. 2m. 94. PRACTICE. M. hun. caf^ts. chls. - dnh. cfs. 2. 19 8 15 W.O. hhtl. staves :>] per BL Ans. 614 96 3. 22 9 o7 II. O. do. do. 13 298 90 4. 28 1, 8 W.O. barrel do. 16 449 92 5. 4 2 11 15.. 63 41 1. What will 8,7^7 feet of merchantable boards come to^ at 3Sa'. 6W. per M. ? 8,767 38 6 70135 . 26*301 6iL I 4383 20)337,529 shillings* Ans, £.16 17 6 The fourth figure of the product of the remainder, multipli- ed by 12, is set down for pence. s, d, £, s. d. 2. IS, 370 (t, mcr. boards 39 8 per M. Ans. 36 8 8 3. 2,819 do. do. -do. 37 4* 5 5 2 4. ,327 do. do., do. 410 13 5 5. ,lh:>do.reiusedo. 20 6 ...» 3 9 What is the amount of a seaman's wages from the loth of !March to the 6th ot December following, being 8 months and 20 tlays, at l6 dollars per month ? 16 8 128 for 8 months. 15 davs 8 5 2,66| 138,66f Ans. 138 dols^. 66-, cts. Note. Iu calculating the time of seaman's service, cither of the dajs of en^aning or beiiiL; disclsargcd is taken, but not both. What is the amount of a seaman's wages from 15th of JiuJ| to the 28th of May tbllovving, at 15 dols. per month .? ^ Ans. 171 dols. PRACTICE. 9^ At £A 11 3 per cwt. what will 3 qrs. 25 J lb. come to? £.4 113 # oqrs. h ^ ^ 7h 1 qr. i 1 2 ^1 3 4^ lb. J 11 45 7 ^05 8^6 3^. h 2 lOy^. r I 9ni2 Ans. £.4 9 2-Jil AVhat will 19 tons, 19cwt. 3qrs. 27^lb. come to, at £.19 ,)95\ ii5u. per ion ? "* Aks. £.399 19^. HHU- TARE AND TRET. Taue and Thet are allowances made in selling goods by weight. Tare is an allowance made to thcbu\^cr for thcwei^br of rhe hogshead, bavrcd, or bag, containing the c;)nii:;odiry. Tret is an allowance for waste, dust, is.c. generally at 4- lb. per 1041b. Cloff'ia an allowance for the turn of the scale, at 2 lb. per 3 cwt. Gross weiulit is tlie >ibt o( the goods, togctlier with the hogshead, l-arrel, oi' luls <^^c. that contains them. Sutt/e is wlicn part of the allowance is lieducted from tlic gross. Neai weight is what remains after all allowances arc made. S6 TARE AND TllET. Citstom 'house alloxcanccs Tare on whole chests of lb. bohea tea ........ 70 • •• •on every half chestdo. S6 • • • • on quarter do, 20 • • • • on every chest of h}-^ son, or other green teas, the gross wt. of which is 70lb. or up- wards 20 • • • • on every box of other tea, not less than 50 lb. or more than 70 lb. gross 18 If 801b. gross 20 And from SO lb. gross and upwards • • • 22 on tea, coffee, and svgar. Which tare shall include rope, canvas, and other cover* ings. Tare for all other boxes of tea, according to invoice, or act- ual weight thereof. Tare for coffee in bags 2 per 100 . • . . •...•. in bales S do. in casks 12 do. Oh sugar, other than loaf — ■ • • •in casks 12 ^o. in boxes] 5 do. .... ...... in bags or mats 5 do. There is an allowance of two per cent, for leakage on the quantity which shall appear to be contained in anj cask of lirfuor subject to duty by the gal- lon ; and ten per cent, on all beer^ ale, arid porter in boUles, and 5 per cent, on all other liquors in bottles in lieu of breakage, or the duties may be com- puted on the actual quantity, at the option of the im])ortcr, to be made at the time of cntnj. Examples. 1. Sold ten casks of allum, weighing gross 33 cw^t. 2 qrs. 15 lb. tare 15 lb. peroask ; what is the amount at 23^. 4c/. per cwt. .? cxvt, qr. //;. gross 33 2 15 10 casks, tare 1 1 10 15 lb. per cask. neat 32 1 112)150 C.l 1 10 tare. Ans. £.37 13 6^ 2. At 1 dol. 25 cts. per lb. what will 3 chests of hyson tea come to, weighing gr;.Sb 96 lb. 97l'o. and 101 ib. ; tare CC- lb. per chest > ^ ^ Ans. 2^2 dois. 50 cts. TARE AND THET. f)r 3. At 9 dols. 49 cts. per cwt. what will 3 lihds. of tobacco come to, weighing gross, viz. cwt. qrs. lb. lb. No. 1. 9 3 '25^ tare 149 2. 10 2 12 ioO 3. 11 1 25 158 Ans. 265 dols. 46J- cents. 4. At 79'^. 9^^* pr barrel. Ans* 82 dols. 47 cts. 7 iti, I [^ TARE AND TRET. 11. At 15 dols. 40cts. per cwt. what will 4 hhds. of sugar CODie to, weighing gross, viz. cwt. qrs. lb. Ko. 1. 7 S lo 2. 8 1 10 3. 7 2 12 4. 8 1 21 Tare 12 ]b. per cwt. Ans. 443-doIs. 45 cts. 7 ms. 1^2. A has in his possession a hluh of sugar, weighing gross 9 cwt. 3 qrs. owned equally between him and B. It is required to know how much sugar he should weigh out to B, allowing tare 12 lb. per cwt. ? Ans. 4 cwt. 1 qr. 1 U lb. 13. At 191 cents per lb. what will 2 hhds. of coffee come to, weighing gross 1 5 cwt. 3 qrs. 11 lb. allowing cuslom-htuse tare or"l2 lb. per 100 ? ^ 15 3 11 1500 zn filleen Inmrlrcd. 180 zz 15x 5 2 for excess in each cwt. 81 zz three quarters. 11 1775 Tare 1 2 per 100. Gross Tare Neat 1775 213 1562 19X 11058 1562 781 S0159 cts. 213,00. Ans. 301 dols. 59 ds. 14. B buys of C a hogshead of Coffee, weighing gross 9 cwt. 2 qrs. tare 12 lb. per cwt. what will it amount to at 23 cents per lb. ? Ans. 218 dols. 50 cents. 15. If custom-house tare, or 12 lb. per 100, were allowed on the above coffee, what would it amount to, and what differ- ence would it make to th.e buyer ? Aiis. It amounts lo ^15 dols. 51 cts. being 2 dols. 99 ct3. hi his favour. 16. What is the gross weight of a hogshead of tobacco, weighing neat 11 cwt. 1 qr. tare 14 lb. per c^vt. ? Ans. 12 cwt. 3qr.-. 12 lb. SINGLE FELLOWSHIP. 99 FELLOJVSHIP Is wlien two or more join their stocks and trade together, dividin*.'; their g;iin or loss, in proportion to each perbon's bliaie in the joint stock, SINGLE FELLOWSHIP. m Single Fellowship is when different stocks are employed for a certain equal time. Rule. As the whole stock is to the whole gain or loss, so is each man's particular stock to ixis particular share of the «jain or loss. Examples. 1.* A and B buy certain merchandizes, amounting to £.120, of which A pays £.80 and B £.4-0, and they gain by them £.32 — what part of it belongs to each ? A £.80 B 40 As7^-32-- I ^^ Ans.£.21 6 8 A. 2. A ship worth 8400 dollars being lost at sea, of which J belonged to A, J to B, and the remainder to C, what loss will each sustain, supposing they have OOOO dollars insured ? Ans. A's loss 6'00, B's 800, and C's TOOO dols. 3. A and B have gained 1260 dollars, whereof A is to hav« 10 per cent, more than B, what is the share of each ? Ans. A's 66Q), B*s Goo dols. 4. A bankrupt is indebted to A 500 dols. 37 cts, to B 228 dols. to C 1291 dols. 23 cts. to D 709 dols. 4-0 cts. and his es- tate is worth but 2046 dols. 75 cts. how much does he pay per vent, and what is each creditor to receive ? Ans. He pays 75 per cent, and A's part is 375 dols. 27^1 cts. B's 171 dols. C's 968 dols. 42^ cts. and D's 532 dols. 5 cts. 5. Three boys, John, James and William, buy a tottery ticket for 3 dols. of which John pays tjO cts. James 1 dol. and William the remainder. This ticket is entitled to a prize of 2000 dollars, subject to a deduction of 123 percent, how much is each to receive } Ans. John o25 dols. James 5^3 dols. 333 cts. William 64.1^ do Is. 661 cts.. ICO DOUBLE FELLOWSHIP. 6. Tlirce merchants made a joint stock — A put in £.565 6 8, B .£.478 5 4, and G a certain sum, and they :gaincd £.373 9 11, of which C took for his part £.112 11 11 — re- quired A and B's part of the gain, and how much C put in? Ans. A's gain £.141 6 8, B's£.119 11 4, and C put in £A50 7 8. 7. Three men have to share a legacy of 1500dols. of which B is to have |, C | and D the remainder, but C relinquishes his part to B and D, leaving it to be divided between them, ac- cording to their shares in the whole. It is required to know bow much of the legacy B and D receive respectively ? Ans. B's part u 1000, D's 500 dols. DOUBLE FELLOWSHIF. Double Fellowship is when the stocks are emplo^'ed for dif- ferent times. Rule. Multiply each man's stock by its time, and add them together, then say, As the sum of the products is to the whole gain or loss, so is the product of each man's stock and time to his share of the gain or loss. Examples. 1. Band C trade in company, B put in .£.950 for 5 months, and C £.785 for 6 months, and by trading they gain £.275 18 4 ; wdiat is each man's part of the profit ? B's fctock 930x5=:4750 C's 7o5x6=r47lO A TTHT. o'y-^o A ^ 4750 : M38 10 10 B's. As 9400 : 27o 18 4 : : I ^..^ ^..-, r, r f*> ( 4/10 ; lo7 7 Ls. 2. Two merchants enter into partncrshF}> for l6 months. A put into stock at first 1200 dols. and at the end of 9 months *200 dols. more, B put in at first 1500 dols. and at the expira- tion of 6 months took out 500 dols. — w ith this stock they gain- ed 7/2 dols, 20 els. what is each man's part of it } Ans. A's 401 dols. 70 cts. — B's ^370 dols. 50 cts. 3. Two pcrsoris hired a coach in Boston, to go 40 miles, for 20 dols. with liberty to take in 2 more when they pleased. Now when they had gone 15 miles, they admit C, who wished to go the same route, and on their return, within 25 miles of Jloston, they admit D fur the remainder of the journey. Now j»s each pers-on is to pay in proportion to the distance he rode, it is required to settle the coach-hire between them. Ans. A and B 6 dols. 40 cts. each, C 5 dols. 20 cts. and D $ dois. SmrLE INTEREST. lOi SIMPLE INTEREST h a compensation made by Hie borrower of any sum of mo- nc}^ to the lender, according to a certain rate per cent, agreed on for the principal only. The legal rate of interest in Massachusetts is 6 per cent. Principaly is the money lent. Bate, is the sum per cent, agreed on. Amount, is the principal and interest added together. General Rule. ' Multiply the principal by the rate per cent, and divide the product by 100, and the quotient is the' answer for one year. Examples. I. What is the interest of ^,496 for one year at 6 per cent* ?' 496 d 29|76 20 lo|20 i>|40 4 1|60 Ans. 29/. 15s. ^d: 2. What is the interest of £.383 15 9 for 2 years', at Sj per cent. ? 383 15 9: 3070- 6 191 17 lOf 32|62 3 lOi. ao 12|43 b\$6 4 sn. 125. 5^. for ono 1|06 yea?;-' S{ I 2 Ans. 66 4 lO-Jfor 2 ye^rv- 3 02 SIMPLE INTEREST. 3. What will ^.826 13 9 amount to in 1 year at 5 per cent. ? 3zi:./y)826 ]3 9 principal. 41 6 8i interest. Ans. <£.868 5l amount. 4. "What is the interest of ^.103 114, for 4 years, at 7 J percent, per annum ? Ans. ^£.31 1 4r;. 5. What will £36 14 9 amount to, in 3 years, at 5 per cent, per annum? Ans. ^€.42 4 ll|. 6. What is the amount of .£19 15 8, for 5 years, at 6'| per cent, per annum ? Ans. £,26 9 U- 7. How much is the interest of £.72 12 6, for 6' months, at C per cent, per annum ? 72 12 6 6 4 1 35 15 20 7jl5 12 1180 /. s. d. 4 t)m,|;)4 7 J J for one year. 3|20 ; Ans. 2 3 6^ for 6 inontlis. Note. Wlien tlie time is monllis, mulliplying by the rate for tlie time gwes the answer. This rate is found by multiplexing the time b}? the given- rate per cent, for a year, and dividing the product by 12. The quotient is the rate required, and is always equal to half the months when the yearly late is 6 per cent. 8. What is the interest of £.25 19 3 for 8 months, at 6 per cent. j>er annum ? 8 monthsi 25 19 3 6 4 12)48 1,03 17 — 20 4 rate ~ half the months. 0,77 12 9,24 Aas. £. i £>. SIMPLE INTEREST. 103 9. IIow much will £,5S 9 4 amount to, in 20 months, at G per cent, per annum ? Ans. £5S 16 3.. 10. How much is the interest on a bond of £.2g5 IJ 10- for 18 months, at 8 per cent, per annum ? j8 295 17 10 g 1 2 the rate for the time*. 12)144 35,50 14 20 12 10,14 * 12 1,68 4 2,72 AOS.-35/. 10s. Ifd. 11- How much is the interest of ,£80 12 9, for 23 months^ at 6 per cent, per annum ? Ans. £,9 5 5j. 12. How much is the interest of £.36 14" 9 froni I9th May to 25th October, at 6 percent. ? '^ 36 14 9 4ni.— 1)2 4 1 fgr 1 year. 14 8i 1 m.rzi 3 8 6 d.—i 8|; 2,20 8 6 20 4,08 Ans. 19 1 12 1,02 13. What will £.187 14 9 amount to, from 11th June, 1797, to 26ih October, 1798, at 6* per cent, per annum ? ' Ans. £.203 4 5j. 14. How much is the interest of £.19 13 7 from 3d. Janua- ry, 1797, to 18th May, 1798, at 6' per cent, per annum ? Ans. £.1 12 54. Tojind the interest of any sum for months, at 6 per cent, per an^ num, by contraction, lluLE. INIultiply the pounds by the number of months ; the first or units figure of the product is pence, and the rest are shillings, observing to increase the pence in the prod^uct by 1 ' «^ii they exceed 4. 104 SIMPLE inteuest: Examples. 15. What is the interest o^ £.56 for 1, 5, 7? and 12 monthsr 56 56 56 56 mo. 1 5 7 12 All's. 5s. 76 ,r ,8 ,9 decimals. Ans. 51. 4s. 2d. 21. How much is the interest of £.195 15 lOj for 10 months? 195,8 10 ,80 12 shillings 195,80 Ans. 9/. Ids. 9id. 4 2,40 The value of the remainder is thus shewn to be 9ld. SIMPLE INTEREST. 105 22. What is the interest of £.590 19 9£ for 3 years, 7 months and 19 days ? £.591 nearly. 43 1773 2364 15 days i 295 3 i 59 1 i 19 2578,6 -f 1 because it exceeds 4— see the Ruk. £.128 18 7 23. How much is the interest of £.476 9 8 for 9 montks and 13 innths, at 6* per cent, per annum ? 187,25 Cents 1498)00 Ans. 14 dols. 98 cts. 1 1. What is the interest of 95 dollars, for 2 months, at 6 |)er cent, per annum ? 1 ,95 Ans. Q5 cents. 12. How much is the interest of 126 dollars, 46 cents, for 9 months, at 6 per cent. ? 126,46 H 505,84 63,23 Cents 569,07 Ans. 5 dols. 69 cts. 13. How much is the interest of 124 dollars, for 1 month, ■Jit 6 per cent. ? ^)124 Or 124 " — ,5 ,6^ ,62,0 Ans. 62 cts. 14. What is the interest of 69^ dols. 84 cts. fer 9 months*, tit 10 per cent, per annum ? 694,84 Or 694,84 10 7|=rate for the time. Cents 6948,40 for 2 6 1 3474,2 a 1 1737,1 I year 4863,88 347,42 dols» a cts. 3 Cents 52,11,30 Ans. 52 52,11,3 K in. J! 10 SIMPL]-: INTEREST. ^■>. ■ How n'>.iir]j h the amount of 985 dollars, for 5 ycirs ■'i 8 moijths; iit 0' per cent, per annum ? r>4 half the months. 2^}35 334,90 infcrosf, f/85, principal. 1310j5)0 amount. Ans. 1319 dols. C/0 cts. Vv'hen tlic time Is months arui day«, and llie annual rate 6 per cent. — rjul- ti])h ijy Iialf liie nioiitlis and one sixth of the days, which is equal to tlie rate, tor \\i: <,;ivcn time, and separate one figure to the right" ibrihe decanal in the iL', and proceed as usual. Should there be a remainder in taking a sixth of .:• days, reduce it to a vulgar fraction ; this, and not the dccimai^ will always _.. ve the exact rate. • • • • ^ Examples. l6. V/hat is the interest of 194 dols. for 4 months and 12 days, at 6 ])ei- cent. ? (lol.s. 9?K V?, 1:,2 — tothe rate, found by the rule, 12 : 6 :: 4,4 or the annexed calculation. 6 388 388 12)26,4 4,2G,8 2,2 Ans. 4 dols. 2() cts. 8 m-s, 17. How much is the interest of 263 dollars, 48 cents, for 2 months and 21 days, at 6 per cent. ? dols. cts. 263,48 i,3i 7904 1 2u3-i-8 13174 Ccnt^ S5 ,(-^8 Ans. 3 uoh. 55 cV^. 6 n\s. SI MTLE INTEREST. 1 1 1 IS. How much is the interest oi'olS dols. for 10 moiulis mid i'S days, at 6 per cent. ? . 318 6:}6 t ]0{) \ IOj dols. 10,7-1,8 Ans. iG dols. 7-i' cts. 8 m. 10. What is the inlerest of -ili^ doL;. for 1 ^ccir, 7 months, and ]/ days, at 6* per cciit. ? 4:8 418 dols. 4 0,S<);V A:is. 40 doh,. 83 cts. 4 m. i20. How imich is the iiUcrcst of '208 dois. 44 cti. for 3 ytViTS; J ijionihb, aud 2o days, at 6' per ceut, r 208,44 V!;\!0 bl&7. ^^0 1 =r34S (AMits 6()1:;,;34,4 Ans. 5o doU. l!}cts. 5m. • 1. What is the interest of I dollar, for 18 days, at 6* ];cr c-ent. ? 1 ,3 ,00, J mills. Ans. 3 mills. One niiirre i^ j-or;ir:i(ocl for the decimal 'wi th'Mnultiplicr, and tv.'C) cyp.hvr^ w: 1 and pointed, uccoitlini;, to the ^eneial rul e. i 12 SIMPLE INTEREST. 22. What is the interest of 910 dols. 50 cts. for 3 years, ^ Kionths, and 2() days, at 7 per cent, per annum ? 910,50 7 63,73,50 3 Or thus, 910,50 22,9J 8 19450 182100 182100 *s. 30350 191,20,5 for 3 years. 6' mo. I 31,86,7 3 mo. I 15,93,3 ■J)208,80;S010at5per cent. 15davs i 2,65,5 34,80,1 lOdnys -J 1,77,0 . 1 day /o ?17?7 tlols. 243,60,9 at 7 per cent. dv/is. 243,60,7 Ans. 2-13 dols. 60 cts. 8 nis. 23. How mucli will 1.85 dols. 26 cts. amount to, in 2 years, 3 months, and 1 1 days, at 7k P^'^ cent, per annum ? Ans. 216 dols. 94 cts. 4 ms. 24. What is the interest of 57 dols. 78 cts. for 1 year, 4 months, and 17 tl ays, at 4 per cent, per annum ? Ans. 3 dols. I9 cts. 25. How much is the amount of 298 dols. 5Q cts. from 19th May, 1797, to the 1 ith of August, 1798, at 8 per cent, per an- num ? Ans. 327 dols. 98 cts. 4 ms. 26. How much is the amount of I96 dollars, from June 14, 17.9s? to April 2[)j 1799? ^t 5:| per cent, per annum ? Ans. 205 dols. 86 cts. 27. Vvhat is the interest of 658 dollars, from January 9 to Qctober 9 following, at h per cent, per month .? Ans. 29 dols. 61 cts. Ja the calculation of inlcrcst in federal money, thus far, the year is siippov p(l to be It> months of SO days each, making it only 360 days. Most persons- Tise this method of computing the time, but as it is 5 days less in a year than the tr-iie number, some merchants calculate by days, without any regard t» vuQiiUis, as being more accurjilc. SMMPLE INTEREST'. US Examples. 2^; What is the interest ot 7 0S6' dollars, for 39 days, at per' c^nt. per aniiuui ? By Compound Proportion. 7086 39 63774 21258 dols. cts. 6083)276.154(^45 43 2-J 332 J^ *'' "* 33034 30415 26190 24332 185^0 18249 331 Ans. 45 dol.s. 43 ctd, i20. Wliat is the interest of 87 dols. oGcts. for 72 days, at^ 6 per cent, per ^.nniHn ? 07,56 72 17512 61292 cts. m. €083)6304,32(103 6^ 6083 22132 18249 38830 36498 2342 Ans. Idol. 3clff. 6ni. fids. cts. daiiK dots, cts, m»' 30. 2962 li^ for 2.S4 at 6 per cent, per ami. " Ans. 123 68 8 o J . S5 256 147 2 32. 1733 97 102 29 7 5' 33. 455 52 47 3 51 9 ' 34. 215 80 125 4 43 4^ 35. 517 90 84 7 15 I 56. 73 63 92 1 H . 5 > K2 tli SIMPLE INTEREST. The following method of calculating the interest upon ac- counts, when there arc partial payments, is sometimes used. 1798. dols. days. Prod.princ.i^'tinw, Janaanj 2, Lent -100 on interest for 13 » loOO ^13, Lent 110 "^ . ' "^0 * '5. -lOoa 20, Received l62 * 48 14 672 Febn/an/ 3, hcnt 95 143 ••.- 7 to5r*^ 10, Received .90 53 6*0 318 iGjLeni- ISG 239 1©........2390 ' 26, Received 70 169 3 507 March 1, Lent 250 419 2..,. .. .. S3% 3;, Received 2/0 1.49 10.... «... 1490 13, Received 143 20, Time of adjustment 6 ............ 7 ....... . 42 96O8 d. cfs. Then (J083)9608( 1,57 interest at 6 per cent. 60S3 6, the principal due. 35250 7,57 the amount due March 20th. 30415 48350 425^1 ^76'9 SIMPLE INTEREST, . Ilj By this method interest may be calcuhited on accounts, mul- tiplying each sum by the days it is at interest, and taking the (quotient of 36500, divided by the rate per cent, as a fixed di- visor to the sum of the products. Thus, the rate in the hist example being 6 per cent, the divisor is (j083 ; for 5 per cent, it would be 7300 ; for 7 per cent. 5214, &c. If the time '\^ months^ multiply each sum by the months it is at interest, and take the quotient of 1200, divided by the rate as a divisor. Thus, for6 per cent, the divisor is 200 ; for 5 per cent. 240 ; for 8 per cent. 150, &c. — {See Compound Propor-- iio?iy page 73') m COMPUTING INTEREST ON NOTES, S^c. It has generally been the custom to find the amount of the principal from the time the interest commenced to the time of settlement, and likewise the amount of each payment, and then deduct the amount of the several payments from the amount of the principal. Example. A, by his note dated April 25th, 179^, promises to pay to B 774 dolji. 7^ cts. on demand, with interest to commence 4 months after the date. On this note are the following endorsements : Received, Ocf. 12th, 1798, 260do\s, igcis.—Oct, 13th, 1798, 60 dols. — Nov, 2, 1 79S, 200 dols. And the settlement is made Dec. 15 th, 1798. Calculation. doh. ctx. The principal carrying interest from 25th Aug. 1798 • • • •. 774 76 Interest to Dec. 15, 1798 (3 ni. 20 days) 14 20 Amount of the principal • 788 96 dols. cts. First payment, Oct 12t]i, 1798 260 19 Imerest to Dec. 15tli, 1798 (2 ms. 3 days) . . Secowd payment, Oct. 13th, 1798 ■ Interest to Dec. 15th, 1798 (2 m». 2 days) • . Third payinenl, Nov. 2, 1798 ■ iQterest to Dec. 15, 1798 (1 m. 13 days). Amount of the payments • 524 97 SeUlement is made for D|:i-7r|.>06|276 ^.M5 215J181 1.5o|12o 92 62 ^vJht 1 .0^1 L'8j.:i65|a:;4|o04 ■^4312 r2jl8l| 151 12(? 90 Apr. j 90 1 .59| 31 1. -565 i.->>5! :^04 '274|24:i 21i? 18y 151 121 ^ ;v»a^V r^uj 89 01 1 :yj ,io5 SoO ;i04 27.5 -X4'-J 212 18; 1->1 Jun- 151|1^^0 n\ 61 .Sl( S6o o35 304127.5 243 212 182 .fuiv 1 181 |l.5(»i 1^221 91 61| tiCi S65I334|.N0.5 273 '>42 ^212 AUL'. |-21/(18l|l5^:|lt^'^| 9t^ bl 3l|o6.)|^c*4io0'l 27.> 2-13 ^vpX. l-:i4;.|2l'L'|184jl5.S lii.S 9-^ 6v 31(3651335 .31 ;4 -'?4 Uil. |-V:)i-r4^^|i^l4il85 15o, 1-- 92 61 1 30|:»65 :rM >{)4 Nov. \r>{H\^^7S\<245 2l4|l8]i 15.1 123} 92 1 61 1 :^)\ 365 .S35 Dec. |;3:]4|:io:iii^75 V4i|ji4| ]8:,i 153:1221 91 1 61 30 36.0 IIS SIMPLE INTEREST. THE USE OF THE TABLE. Suppose the number of days between the Gci of .May and 3d of November was required ; look in the coliinjn under M for November, and against that month you will iind 184. If the given days be different, it is only adding or subtracting tlieir inequality' to or from the tabular number. Thus, from May 3d to Nov. 37th is 184--f Urz I98 days, and from Nov. J 7th to May 3d is 181 — 14- — 167 days. If the time exceed a year, 305 days must be added ; thus from the 4th of February, 17i)8, to the 4th of Sept. 1799, is 212-f 5()5=:577 days. IV'OTK. Ill leap years, if ilie end of tiie month of Febraarj be in the lime ©ftj day niu^t be added on ihat account. COMPOUND INTER EST Is that which arises both from the principal and interest^ that is, when the interest on money bccoines due, and not paici, it is added to the principal, and interest is calculated on this amount as on the principal before. Kltli:. Find the simple intere^-t of the glv<*n sum for one-yenr, and add it to the principal, and then find liic interest lor tlitit amoiitit ior ijjo next year, and so on for ihe number of years recji^uired. Subtract the priacipal from the lii first year's intere^it. 4 j ?46' 14 12 6 '2 9 261 1 b h a mount o f t h e i\ rs t \- ea r . 13 1 6[] , , • .\ IJ7 4 4-4 amount of the sec 13 17 2', 7 2 15 5ii third year's intcrc:: 293 17 amount of the third year. 24(i 14 6 iirst piineipal. 0" comiponnd interest for 3 years. Ans. .t'.47 2..V. CfL CO^IPOUND INTEREST. 119 . Wluil is the compound interest of £.760 10^. ror4ycars, t Ju per cent, per annum ? Ans. £,\99 12*- 2(/. ^^3. How much is the amount of £.1^8 17 s, 6d. for 0' years, ?it per cent, per annum, compound interest ? Ans. £.182 \6 2|. 4. How m.uch is the amount of 500 dolhirs, for 3 years, at ^ per cent, per annum, compound interest ? ' ^ 500, 1 1 i 1 3 'ih'-' interest. 530, " ''^^ > second interest. 5,.:.0 3 5 1 Q 561,80 1 1 5 28,09 5,6"1| ) third interest. 595, 50j the amount required. Ans. 595 d. 50| c. 5. What is the amount of 629 dols. ior 7 years, at 6'4)er cent, per annum, compound interest ? Ans. 94-5 dols. 78 cts. 3m. 6, How much, is the compound interest of 1256 dols. for 15 years, at 6 per cent, per annum ? Ans. 1754- dols. 6 cts. 6 m. A TA RLE shewin<:^ the amount of ^it pound or one dollar for any moi'her of Ijcays under :>.:3, at the rates nf 5 find 6 per cent, per ami. compound interest. Veins. 5 Rates. 6 Years 5 Rates. 6 j 1 1,05000 1,06000 17 2,29201 2,69277 2 1,10J50 1,1 '2:360 18 2,40662 2,85434 3 1,15762 1,19101 19 2,52695 3.02.559 4 1,'>15.")0 1,26'247' 20 2,65329 3,20713 5 1,'276 28 l,3o8i?2 21 2,78:V96 3,39956 6 1,. J 1009 1 ,4 1 852 ! 22 2,92526 \ 3,60353 7 1,40710 1,50.-163 23 3,07152 3,81975 8 1,4774) ],;39584 24 25 3,V2510 4,04893 9 l,55i:i^i 1,63948 3,38635 4,29187 10 1,62089 1,79084 i 26 S,h5b67 4,.54938 11 l,710o'4 1,898'<>9 1 27 3,73345 4,82234 n 1,79^85 2,01219 i 28 3.92013 5,11168 13 1,B8')65 2,13292 29 4,11613 .5,41838 li l,9799r» 2,26090 30 4,32194 .5,74349 15 2,07 89^i ^,fi^655 31 4,53804 6,08810 \6 *?.18'J87 2,510.')5 32 4,76494 6.45338 The use of this Table is pl«ia aud easy, for multiplying t!ie f^mires standing against tjie number of years, by the given piiacipal, the-jproducl is (he amuunt required. 120 COMPOUND INTEREST. 1 Examples. 7. AVhat is the amojint of 500 dollars, for 3 years, at 6 per €cnt. compound interest ? 1,19101 the tabular number for the time. 500 the principal, 595,50500 Ans. 695 doh. 50 cts. 8. A merchant, on inspecting some old accounts in March, 1799) fi"fis a settlement dated March 1771, by which it ap- pears there is due from him to A. B. £.2 8a. this sum be pays with compound interest at 6 per cent, per annum. The amount of it is required ? 5,111(38 the tabular number for 28 3^ears. 2,4 the principal with the shillings inserted decimally. 2044672 1022336 £.12,268032 20 ■ % s, 5,360640 12 (L 4,327680 4 ^rs. 1,310720 Ahs. £.12 5s.4ld. or 40 dols. 89 cts. Shis, Calculated in Federal Money. 5,11168 8 dollars. Ms. 40,89344 Ans, 40 dols. ^9 cts. 3 mills, as above. COMMISSION AND BROKERAGE. Kl COMMISSION A^jy BROKERAGE. Commission and Brokerage are compensations to Fac- tors and Brokers for their respective services. The method of operation is the same as in Simple Interest. Examples. 1. What is the commission on £.59^ 18 4, at 6 per cent. ? 59(3" 18 4- Or thus, £.5 35181 10 20 16Y30 12 3|6'0 4 A 596 18 4. i 29 16 5 19 II 4i £.35 16 ^2. 214-0 Ans. £.55 16 3^ 2. What is the commission on 1974 dollars at 5 per cent. ? 197^ 9S,70 Ans. 98 dols. 70 cfs. 3. Wluit : ; the commission on £.525 11 5 at oh per cent. ) Ans. £.18 8 7 4. What is the commission on £.1258 17 3 at 7% per cent.? Ans. £.93 3 14. 5. What is the commission on 2176 dols. 50 cents, at 2| per cent. } Ans. 54 dols. 41 cts. 2 m. 6. The sales of certain (];oods amount to 1873 dols. 40 cts, what sum is to be recciv(vl ibr them, allowing 2| per cent, for commission, and \ per cent, for prompt payment of the neat proceeds ? Ans. 1821 dols. 99 ct5. 9 m. V22 COMMISSION AND BROKERAGE. 7. Required the iicat proceeds of certain j^oods amoimtiii^ to .€.456 118, allowing a commission of 2| per cent. £,5 A i 456 11 8 I j 22 16" 7 commission at 5 per cent. 11 S 3j commission at 2h per cent. Ans. ^\445 3 4| neat proceeds. S, Vvhat is the commission on .£.1371 9 5 at 5 per cent, f kns. £f)S 11 5J 9. What is the commission on £.1958 at 5 J per cent. ? Ans. £.107 13 9h iO. What is the commission on £.1859 7 6 at | per cent.? Ans. £.16 5 4^ 11. W^hat is the brokerage on 1853 dols. at | per cent, f Ans. 13 dols. 89 cts. 7 ms. 12. What is the brokerage on £.874 15 3 at J percent.? Ans. £.2 3 8| 13. What is the brokerage on 129S dels* 53 cts, at | per cent. ? 1298,53 3 8)3895,59 Doh, 4,86,94 Ans. 4 dols. 86 cts. 9 m. 14. What is the brokerage on £.1321 11 4 at ij per cent.? Ans. £.14 17 4 15. A factor receives 988 dollars to lay out, after having deducted his commission of 4 per cent, how much will remain to be laid oufc ? d. 100 4 d. d. A If 104: 100 : : 988 : 950 dols. the ans wer*| 16. A factor has in his hands 369O dollars, which he is di- rected to lay out in iron, reserving fn^^m it his commission of 2 J percent, on the purchase ; tlie iren being 9^ dols. per ton: liow much did he purchase ? Ans. 37 tons 17 cwt. 3 qrs. 161^9 lb. INSURANCE. t^o INSURANCE. Insurance is an exemption from liazard, by paying, or ©tbciwise securing a certain sum, on condition of being indem- liified for loss or damage. Policy is the name given to the instrument, by which tie eontract ot indemnity is efixicted between the insurer and insured* Average loss is 5 per cent. ; that is, if the insured suffer any loss or damage not exceednig 5 per cent, he bears it himicli",. and the insurers are free. Rule. The method of operation as in interest. Examples. 1. What is the premium of insuring c€.924 at 7 per cent, t Ans. ^'.64 13 7 2. What is the premium- on i650 dollars, at 12 per cent. ? Ans. 198 dols. 3. What is the premium of insuring 1250 dollars, at 7 5 per cent. ? Ans. 93 dols. 75 cts. 4. What is the premium of insuring 4500 dollars, at 25 per cent.? Ans. 1125 dols. 5. What is the premium of insuring l650 dollars, at 15 J per cent. ? Ans. 255 dols. 75 cts. 6. What is the premium of insuring 1873 dollars, at -J per cent. ? Ans. 2 dols. 34- cts. 1 m. 7. What sum is to be received for apolicy of l658 dols. de* ducting the premium of 23 per cent. ? Ans. 1276 dols. 66 cts, 8. What sum must a policy be taken out for to cover 1800^ dollars, when the premium is 10 per cent. ? 100 policy. 10 premium. r?. d. d. 90 sum covered. If 90 : 100 : : 1800 Ans. 2000 dots.. Troof, 2000 dollars at 10 per cent. 10 200,00 the policy 2000 the premium 200 sum covered 1800 dols. 9. What sum must a policy be taken out for to cover 39^6 dola. 7 cts. when the premium is 6 per cent. ? Ans. 4176 dols. 67 cts. iJl GENERAL AVERAGE. GENERAL AVERAGE. Whatever the master of a ship in distress, with the ad- vice of his officers and sailors, deliberately resolves to do, for tlic preservation of the whole, in cutting away masts or cables, or in throwing goods overboard to lighten his vessel, which is ivhat is meant by jettison or jetson, is in all places permitted to be brought into a general average, in which all, who are concerned in ship, freight and cargo, are to bear a:i ecjual or proportionable part of the loss of what was so sacrihced for the common w elfare ; and it must be made good by the insurers in such proportions as they have -underwritten. EXAMPLES OF ADJUSTED AVERAGES. 1. A loaded ship met with such bad weather, that the raaster and mariners found it impossible to save her without throwing part of her cargo overboard, which they are authori- i:ed to do \oi' preservation. Being thus necessitated ^ they threw .such goods as lay nearest at hand, and lightened the ship of 10 casks of hardware, and 40 pipes of Madeira wine, which they judged suflicient to keep her from sinking. Soon after that the ship arrived at her destined port, and then an average bill was immediately made in order to adjust the loss, and to pay the proprietors of those goods, which were thrown over- board, for the good of the whole. Average accrued to ship , for goods t/wcnvn oierboard for presertatio/i of ship, freight and cargo. Dnh. Ship valued at 12000 Freight (wages and victuals deducted) SOOO Thomas Kugeiit's vahie of goods 4000 Thomas Morgan's vahie of goods ^rA)0 James Simpson's value of goods • 8500 Andrew Wilson for 40 pipes of wine 4000 Laurence Ward for 10 casks of hard ware 600O 40000 Dch. JsFr. AinJrew Wilson's goods thrown overboard were valued at 400l> Mr. Laurence Ward- do. • • 6000 10000 1140000 give 10000 loss, what loss will 100 give ? Ans. 25 per cent. GENERAL AVERAGE. 12S The ship must pay to A. W. and L. W. for 12000 dollars, at 25 per cent. • 3000 ^ The freight 3000 dollars, at the same rate 750 Thomas Nugent, for 4000 dollars, at the same rate 1000 Thomas iMorgan, for 2500 dollars, at the same rate 6'25 James Simpson, for 8500 dollars, at the same rate 2125 A. W. and L. W. receive of the owners of the goods saved, and the ship's owners 7-'''00 Their property being insured, the underwriters pay them 2500 loooa- 2. The Sea Horse, capt. Dix, laden with h^mp^, cordage, . and iron, bound from Riga to Boston, ran on shore, coming through the grounds at Elsineur. The captain Ivired a great number of men, and several lighters, to lighten the ship, and to get her afloat again, which was done ; but he was obliged to pay 409 dols. 23 cts. for their assistance. This expense be- - ing incuircd to preserve both ship and cargo, the average must. coiise(juently be general. When the ship arrived at Boston, the captain immediately made a protest and an. Average bill,, which was thus stated : Average accrmng to the ship Sea-IIorse from Riga to Boston^ in • ^^ 99yfof cisai^tance in. getting oj/' the strand of ELineur. dels, cts, . For sundry charges paid at t?he Sound for lighters and assistance in getting ofl' the ship • •• 409 ^^ ' Protest and postage .•..*..•...•. /^ »...,*• 35 37 444 b'O. Tlic ship's freight money 34()0 Wages for all the people, (4 ms. and 20 d.) 5()0 7 ^ Victuals for ditto .....,*....... 300 | ^"® 2()00 The ship Sea-Horse valued at • • • . . . ...... .... ICOOO Freight valued at o^'co W liham Jenkins for value. of hemp 1SO('0-. Daniel Jones fur value of cordage 400O iiEOch Fiinn lor value of iron • ..... 2400 L2- 3<;oao-» V26 gkni:ral average. Jf 3900,0 dols. lose 44-ldolb. 60 cts. what will 100 dols. lose ? Ans. 1 dol. 14 cts. dots. cis. Theship must bear 12000dols. at 114 cts. per lOOdols. 136 Sa The freight 2600 dols. at the same rate 29 64» j William Jenkins for 1 8000 • 205 20 J Daniel Jones for 4000 45 6Q Hjlmch Flinn for 2400 27 36' 444 60 BUYING AND SELLING STOCKS, Stock, in the sense in which it is here used, is a fund es- tablished by government or individuals in a corporate capacity, tte value of which is variable. Examples. 1. What is the amount of 1565 dollars national bank stocl?^^ at 134 per cent. ? 1565 134 "6260 4695 1565 2097,10 Ans. 2097 dols. 10 cfs. 2. What is the anaount of 2958 dols. bank stock, at 25 per cent, advance ? 2958 25 J 739.50 3697,50 Ans. 3697 dols. 50 cts. dols-, dols. els, 3. 6959 of 8 per cent, stock, at 1 10 percent. Ans. 7654,90 4. 1796 6 91 1 1643,34. 5. 1 284 3 54| 696,57 6. 3172 deferred 89 2823,08 7. 1518 state notes 83^ 1271, 32j. «. 1086 UnioaBank 128 215S;0a DISCOUNT. 127 DISCOUNT Is the abating of so much money to be received before it k due, as that money, if put at interest, would gain in the same lime and at the same rate. Thus 100 dollars would discharge a debt of 106 dollars pay- able in 12 months, discount at G per cent, per annum, because the 100 dollars received would, if put to interest, regain the 6 dollars discount. Rule. As 100 dollars, with the interest for the given time, is to 100, so is the given sum to the present worth, and the difference between the present worth and the given sum is the discount. Examples. 1 . What is the present worth of 450 dols. due in 6 months^ discount at 6 per cent, per annum ? 6w. I 6 3 100 103 : 100 : : 450 Ans. 435 dols. 89 cts.. 2. How much is the discount of £.308 1 3s. due in 18 months,^ at 8 per cent, per annum ? Ans. £.33 1 7f 3. What is the present worth of 5 150 dols. due in 4.J months, discounting^ at the rate of 8 per cent, per annum,, and allowing 1 per cent, for prompt payment ? Ans. 4^50 dols. 4. A is to pay 5927 dols. on the 19th of April, 1799, and 59^9 dols. the 19th of July following — It is required to know hyw much money will discharge both sums on the 19th of Jan- uary, 1799? discounting at 8 per cent, per annum ? Ans. II5G9 dols. 43 cts. Though the discount found by the precedmg method is thought to be the simi that should be deducted for present payment in justice to both purlie*^, j.et in. business the iuiercst for the time is taiigu for the discouut.. 12M DISCOUNT. Examples. 5. What ready money will discharge a note of 150 dollars,, due in 60 days, allowing legal interest, or 6* per cent, per an* num as discount ? 150 1 zzhalf the months. 1,50 150 the debt. 1,50 the interest. 14-8,50 Ans. 148 dols. 50 cts. 6. Bought goods to the amount of 95^ dollai*s, at .90 days eredit, what ready money will discharge it, allowing the inter- est for the time at 6 per cent, per annum as discount ? Ans. 9^5 dols. 75 cts. if calculated for 3 months. 935 dols. 95 cts. if calculated for 90 days. When the interest fi)r the time is allowed as discoiwif, it is presumed that neither party suffers any loss, but the following statement evinces the contrary. A owes B 100 dollars payable in 12 months, for present pay- ment of which B allows 6 dollars or the interest for the time, . and receives 9^ dollars ; this sum he immediately lends to C for the same space of time, and then receives the amount, be- ing 99 doUars 6'4 cents, which is 36 cents less than he would have to receive from A, had he left the money in his hands — but if he had allowed A the discount, and not the interest, for the time, he would have received from him 94 dols.^ 34 cents, and this sum being put to interest, would amount to 100 dolso . in one year, which shews that the discount and not the interuiit, is the just deduction for prompt payment. Bat wlicn discouHt is to be made for present payment, without any regard to tiiucj tke uitcrest ot the suia, as calculated for a year, i.', liie discoujnt, . DISCOUNT. 123 Examples. 7. How much is the discount of 853 dols. at 2 percent. ? 853 dols, 17,00 Ans> l7dol.. 6cts. 8. How much money is to be received lor 98.5 dols. 76 cts. discounting 4 per cent. ? Ans. i)-i6 dols. 32 ct*. BANK DISCOUNT. The method used among hankers, in discounting notes, &c. is, to iind the interest of the sum, iVom the date of the note to the time when it becomes due, including the days of grace ; the interest thus found is reckoned the discount. Thus, if a note for IGO dollars, dated the 2d September, be discounted at a bank for 30 days, the interest of that sum for 33 days being 55 cents, is deducted for discount. It may be asked, why in- terest for 33 days is calculated on a note for 30, the answer is, that as custom has allowed the borrower three days of grace — ■ that is, though the time of the note expires on the first of Octo- ber (the day of the date being included in the 30 days) he may withhold the payment till the 4th — it is therefore reasonable that he should pay interest for it. If a note of 100 dollars were discounted at a bank for ^0 days, the interest of that sum for 63 days, being 105 cents, would be deducted for the same reason. In case payment of a note be not convenient at the proper time a new note must be presented on the day of discount, im- mediately preceding the expiration of the time, paying the same discount or interest for the time, as before stated. Thus, a note of 100 dollars, dated October 7th, 1800, for 30 days, though it is not payable till November 8th, yet must be re- placed by a new note on Tuesday, November 4th, paying at the same time 55 cents. A note of the same date, for 100 dols. for ()0 days, though not payable till Monday, December 8th, (including in this time the days of grace) must be replaced by a new note on Tuesday, December 2d, paying likewise 105 cents. In the former case the borrower sustains a loss of 5 rja DISCOUNT. days in 30, and in the latter 7 days in CO by re n (•win i^. Al^ Banks have their stated times of discount, generally once in a week. In the preceding cases, the Bank is supposed to dis- count on Tuesday. Some Banks discount twice a week — others- oftener. The discount of any sum, discounted for 30 or 60 days, is found by multiplying it by one sixth of the days. [See iiUeresty page 110.] Examples. 1. How much is the interest 5. What is the interest of of 2oS dols. discounted for 30 564: dols. dibcouuted for 6"0^ days ? days ? 238 56'4 ,5 J iz^ of 33 days. l,0| = J-of63days. 1190 564^0 119 282 1,30,9- 5,92,2 Ans. 1 dol. 30 cts. 9 m.. Ans. 5 dols. 92 cts. 2 ms.. What is the discount of the following sums, viz. doh. doh.cts.msi. 5. 159 discounted for 30 days. Ans. 87 4- 4. 273 '-* do. 1 50 1 5. ()S3 do. 3 75 6 6. 7^9 do. 4 33 9 7. 2194 do, 12 06 7 8. 219 discounted for 60 days. Ans. 2 29 9 9. 187 do. 1 96 3 10. 319 do. 3 34 9 n. 6.58 do. () 90 9 12, 216*9 do. 22 77 4 tS. How DISCOUNT. 131 1:3. How much is the discount of a debenture of 319 dols. payable in 210 days, di'jcounting for 30 days. Note. 28 days are allowed for a month, interest being calculated as if the note were renewable. 28)210( 196 [7 mo. 319 ,5| — J of 33 days. 1^ days. 159 5 15 9 14 d. 1 1,75,4 for 1 mmitlu 7 12,27,8 for 7 months. mo. 877 13,15,5 Ans. r3'dols. 15cts. 5 m. 14. What is the discount of the above sum, discounting for 60 days ? Note. As notes are renewable in 56 days, the interest of all securitie* is calculated accordingly. 56)210(3 disc 168 42 days. :ount 1 28 d. 14 nor i iths. mo. 319 1,0J=:1 of 63 days. 3190 159 3,34,9 for 1 discount mo, 3 10,04,7 for 3 ditto. 1,67,4 83,7 12,55,8 Ans. 12 dols. 55 cts. 8 m. The preceding examples shew the difference between dis* counting for 30 and 60 days. 132 DISCOUNT. What is the discount of the followin;^ sums, discounting for 30 days ? *" dols. days. dols. cts. m$. 15. ]87 for 79 Ans. 2 i)0 16\ 219 115 4 C;4. 5 17. 658.-.. 47 6 74 18. 2169. ...128 54 53 2 What is the discount of the following- sums, discounting for 60 days ? dnls. days. dols. cts. ms. 19. 187 for 79 Ans. 2 7^ 8 20. 219.... 115 4 72 2 21. 658.... 47 5 79 8 22. 2169 128 52 54. When a note is offered at a bank for discount, two endorsers are generally required^ to the first of whom it is said to be payable : Thus — A having occa- sion for a sum of money, procures B and C as endorsers to liis note, and of- fers it for discount in the following form. 1 00 Dollars. , Tor Taliie received, I promise to pay B, or order, of the Bank, on demand , one hundred dollars, xvith interest ajter ^ays. A, When state notes, bank shares> &c. are lodged in a bank as security for mo- nies a note is presented in this form . For value received, I promise to pay the President, Directors and Company of the Bank, or their order, at said Bank, on demand, dollars, with interest aJter days, C. D. EQUATION OF PAYMENTS. The design of this Rule is to find a mean time for the pa}'- tlionT of several sums due at different limes. Rule. INIidtiply each sum by itb time, and divide tlie sum of the products by the whole debt; the quotient is accounted the mean time. i::quation op payments. 153 Examples. 1. A owes B 200 dols. whereof 40 dols. is to be pmd in 3 months, 6'0 dols. in 5 months, and the remainder in 10 monthli «,t what time may the whole be paid without any injubtice to either ? dois, mo, 40 X 3~ 120 60 X 5r= 300 100 XlOiirlOOO 200 500)1420 Ans. 7 months and 3 da}^, 2. A is indebted to B .£.120, whereof one half is to be paid 'in 3 laonlhs, one quarter in 6 months, and the remainder in 9 months, what is the equated time for the payment of th-evvhoiet Ans. 5 months and 7| days. 3. C owes D 1400 dols. to be pa4d in 3 months, but I) being in want of money, C pays hini, at the expiration of 2 months:, 1000 dols. how much longer than 3 months ought C, in equity, to defer the payment of the rest ? Ans. 2| months. Tliose who are exact in these calcul-dtions, find the present wt)rlh of each particular sura, then find on what time these preseirt worths will be increased to the total of tlic particular sums payable at the particular times to come; and that is the true equated time for the payment of the wli^jle. BARTER Is the exchtingingof one commodity for another on such terras as may be agreed on. l!lxAMPLr.S. 1. How many quintals of fish, at 2 dols.^7cr quintal, will pay iov 140 hhds. of aalt, at 4 dols. 70 cts. per \\ki\, ? 140 4,70 <:soo :/6o d»h. qtl. If 2 : 1 : : (;5S,00 the ^.mount of the salt. An«. 329 quinteJ-i, U 234 BARTER. . Q. A biws of B 4- libels, of" rum containing 410 gallons, at 1 (lol. JJ cts. jier gallon ; and 253 lb. of coffee, r.t 21 cts. per 3b. in part of which he pays 21 dollars in cash, and the balance in boards, at 4 dols. per thousand ; how many feet of boards ut in barter he will have 8.9. ; I) has tobacco worth 9d. per lb. ; 1k)v» much must he rate it per lb. that his profit may be ecjual to C's ? Ans. Old. 8. A has tea which he barters with B at lOd. per lb. more than it cost him, against cam.brick which stands B in 10-5. })er yard, but he puts it at 125. 6d. ; I would know the first cost of* llie {c'd ? Ans. 3.9. 4f/. per lb. "- A h:'^- 240 buslicls of rye, which cost him 90 cts. per i.c bartei-s with B at 95 cts. for wheat that stands ^ or buelicl ; iiow many buchels of v;hcat is he t« LOSS AND GAIN. 135 Tfccive in barter, find at what price is it to bo rated, that their gains may be equal ? Ans. 21S ro^c> bushels, at 104 J cts. per bushel. 10. A and B barter some goods — A put his at 30.^, shil- linnrs, and gains 8 per cent. B puts his at 24- ^-^^j shillings, and gains at the same rate ; what was the first cost of the goods ? Ans. 28c«f. and 2'^?. 6V. ' 11. A and B barter ; A has cloth that cost 28r/. B's cost liini 22^. and he puts it at Q5cl. ; how high must A put liis to gain 10 per cent, more than B ? Ans. 3o(J. 12. C and D barter — C makes of 7s. 6s, S(L D makes of 7^. 6c/. Ja. 3c!»; who has lost most, ajul by how mucli per cent, f Ans. C loses if- per cent, more than D. LOSS AND GAIN Is a rule that discovers what is gained or lost in buying or selling goods, and instructs merchants and traders to raise or iall the price of their goods so as to gain or lose so much per cent. &c. EXA^VIPLES. 1. Bought a piece of broadcloth containing 53 yards, at 4 dols. Go cts. per yard, and sold at 5 dots, per yard ; what is tkc profit on the whole ? 5 4,65 yd, yd'^^ If 1 : ^35 :: 53 35 26\5 159 18,55 Ans. 18 dob. 55 cts 2. If 1 lb. of coffee cost 28 cts. and is sold for 31 cts. what is the profit on 3 bags, weighing 293 lbs. neat ^ Ans. 8 dols. 79 cts. >3^ LOSS AND GAIN.. o. Bought Ji piece of baize of 42 yards, for £A 14 6\ anA sold it at 2*, 6d. per yard; wiiat is the gain or loss on the whole pit'ce ? Ans. 10^. 6c?. gain. 4. A merchant bought 59 cwt. 3 qr. 14 lb. of iron, at \l% dols. per ton, paid freight and charges, 24 dols. what is the £Liin or loss, if he sells the whole at 37s, ^d, per cwt. ? Ans. 13 dols. 26" cts. gain. 5. If a gallon of wine cost 6s. 8d, and is sold for 7s. Qd^ yvh'dt is tile gain per cent. ? 7 2 6 8 s. d. £, li' 6 8 : 6 : : 100 Ans. 7 J per cent, gain* 6. When 20 per cent, loss is made on coflee, sold at 20 cts^ per lb. what was the first cost ? Ans. 25 cts. 7. At 13^ cts. profit on the dollar, how much is it per cent. ^ Ans. 13j per cent, or 13 dols. 50 cts. per 100 dols. 8.. A trader sells his goods at 2jrf.. profit on the shilling, iow much is it per cent. ? Ans. 20f , or ^.20 l6 8 9. Which is the better bargain, iri purchasing fis?i^ 1'7 shil- lings per quintal, and 4 months credit, or Kis. Sd, cash ? Ans. TJu^ are alike. Pkoof. The present worth of 175. found by disGonnt, is equal to 163. 8d. and 1G.>;. '6(L \%i:h 4 months interest, will amount to 17.5. iO. A bought a piece of shalloon, containing 34 yards, at' 3.V. 4f/. per yard, and sold it at 12^ per cent, loss, iiow muck •iid he sell it per yard ? Ans. 2s, lid. 11. Bought rum at f)^ cts. per gallon, at what rate must it. l?e sold to gain 20 per cent. ? Ans. lOS cents. 12. A trader bought 1 hhd. of rum, of a certain proof, con- taining 115 gallons, at 1 dol. 10 cts. per galhm, how many i^allons of water n^ust l\c put into it togain5 dollars, by selling it at 1 dollar per gallon ? Ans. 16.^ gallons. 13. Bought 4 hhds. of rum, containing 450 gallons, at 1 dol. per gallon, and sold it at 1 dol. 20 cts. per gallon, and gave 3 months credit ; now allowing the leakage of the rum while in n^.y possession to be 10 gallons, I would know the gain or loss, er annum ? Ans, 70 doh, IJ) Cts. gain. LOSS AND GAIN. 137 14. A vintner buys '595 gallons of wine, at Gs, 3(1 pergallon, in ready money, and sells it immediately at Gs. ^d. per gallon, payable in 3 months, how much is his gain or loss, supposing he allows the interest for the time, at 6' per cent, per annum, as discount for present payment ? Ans. £.11 17 8 gained, 15. What would be the gain or loss on the aforesaid wine, supposing the discount for present payment to be made at 2per cent, without any regard to time ? Ans. .£.10 1/ 6^ gain. l6'. A merchant bought a parcel of cloth at the rate of 1 doU fur every 2 yds; of which he sold a certain quantity at the rate of 3 dols. for every 5 yds. and then found he had gained asmucji as 18 yards cost, how many yards did he sell t Ai^.s. ^0 yds. 17. Bought rum at 1 dol. 25 cts. per gallon, which not prov- ing so good as I expected, I am content to lose 18 per cent, by it, how must I sell it per gallon ? Ans. 1 dol. 2-2 cts. 1 8. II sells a quantity of corn at T dollar a bushel, and gains 20 per cent, some time after he sold of the same, to the amount of 37 dois. jO cts. and gained 50 per ceiU. how many bubhels >^ere there in the last parcel, and at what rate did he sell it per bushel ? An>^. 30 bushels^ at I doL 25 cts. per bushel. 19. A distiller is about pu releasing 10000 gallons of molasses, which he can have at 48 cents per gallon, in ready money, or 50 cen1s with two months credit, it is required to know which is more advantageous to him, cither to buy it on. credit, or to borrow the cioney at 8 per cent, per anoum to pay the ca^li price ^ Ans. He will gain 13G dols. by paying thciCash, 20. A tobacroTiisi'^t)ti^-s 4-^hocrchea'ds of' to^f.^'^co ucigM 38 cwt. 2 qrs. 8 lb. gj^osij tai'e '^4^ Ib/'per hhd: 'at * ^5)' lI 61 •?por cwt. ready money, ail ({ J>dl^ it at 11 Jr/. per fb. allo<\'}ti^g' tare at 1 4- lb. per cwt. to rc^ccive two-thirds in cash, and for the rc~ n^iiindcr a note at ^0 days credit ; his gain or loss js required, suppe>sing the note is discounted at a bank where discouiit is made for 60 days. Ans. 283 dois. 43 cts. caiu,. M2 138 ALLIGxXTION MEDIAL. A LLIGATION MEDIAL Is when iao^ quantities and prices of several things are given^ to find the mean price of the rnixture compounded of those things. RuLK. As the sum of the quantities or whole composition is to their total value,, so is any part of the composition to its mean price. Examples, 1. A grocer would mix 25 lb. of raisins, at 8 cents per lb. «ncl 35 11). at 10 c^nts per lb. with 40 lb. at 1.2 cents ^3er lb. — ■ >vhat is 1 lb. of this mixture worth ? //.'. cts, cts. 2.3 at 8 200- 35 10 350 40 12 .... 480 100 103a Ih. cts. lb. If 100 : 1030 : : 1 1 llG0)10i3O els, 10,3 Ans. 10 cents,. 3 mills. 2. A goldsmith mixes 8 lb. og oz. of gold, of 14 carats fine^ with 121b. S^oz. of 18 carats fine ; what is the fineness of this^ mixture ? Ans. lO^W carats. 3. A grocer would mix 12 cwt. of sugar, at 10 dols. percwt. with 3 (w.t. .at 8f dols. per cwt. and a cwt. at 7 J dols. per cwt. what will 5 cwt. of this mixture be worth } Ans. 44 dob. 78 cts. 2 ms. 4. A refiner melts 2g lb. of gold^ of 20 carats fine, with 4 lb. of 18 carats fine; how much alloy m.ust he put to it to make' it 22 carats fine ? Ans. It is not fine enough by 3 c:, carats, M) that no alloy must be })ut to it, but more gold. !). A nialster mingles 30 quarters of brown mult, at 28,?. per cjuartcr, with 4() quarters oi' pale, at 30a\ per quarter, and Vi' (uiartcrs of high dried ditto, at 25^. per quarter; \Aliat is i!:o .;iiuc oi' tj bushels of thiii mixture ? Ans. ^'.1 86. 2it^.| ALLIGATION MEDIAL. 13^ 6. If I mix 27 bushch of wheat, at 5s, 6d. the bushel, with the same quantity of rye, at 4-5. per bushel, and 14 bushels of barley, at 2s. 8d. per bushel, what is the worth of a busliel of this mixture ? Ans. 4^. 3|(i.f § 7. A grocer mingled 3 cwt. of sugar, at 56s. per cwt, 6 cwt. at c£. 1 17 4- per cwt. and 3 cwt. at £,3 14 8 per cwt, what is 1 cwt. of this mixture worth ? Ans. £.2 114 8. A mealman has flour of several sorts, and would mix 3 bushels at 3^. 5d. per bushel, 4 bushels at 5s..6d. per bushel, and 5 bushels at 4a\ Sd. per bushel,, what is the worth of a bushel of this mixture ? ^ Ans. 4 9. A vintner mixes 20 gallons of Port, at 5s. 4:d. per gal- Ion, with 12 gallons of White wine, at 5s. per gallon, 30 gallons of Lisbon, at 6s, per gallon, and 20- gallons of Mountain, at 4-^. 6d. per gallon, what is a gallon of this mixture worth ? Ans. 5*. 33^. If 10. A farmer mingled 20 bushels of wheat, at 5s. per bush* fl, and 36 bushels of rye, at 3^, per bushel, with 40 bushels of barley, at 2s. per bushel, I desire to know the worth of a buslw el of this mixture ? Ans. 3 shillings. 11. A person mixing a quantity of oats, at 25. 6f/. per bushel, with the like quantity of beans, at 'is. 6d, per bushel,. "Would be glad to know thq value of 1 bushel of that mixture ? Ans. 3s. 6d, 12. A refmer having 12 lb. of silver bullion o£ 6 oz. fine,, would melt it with 8 lb. of 7 oz. fine, and 10 lb. of 8 oz. fine,, required the fineness of 1 lb. of that mixture ? Ans. O'oz. ISdwt; l()grs, 13. If with 40 bushels of corn, at 4a'. per bushel, there are mixed' 10 bushels, at 6s. per bushel, 30 bushels, at 5s. per bushel, and 20 bushels, at 3^. per bushel, what will 10 bushels of that mixture be worth } Ans. £.2 3s.. ' ALLIGATION ALTERNATE Is the method of finding what quantity of any number of simples, whose rates are given, will compose a mixture of a givrn rate ; so that it is the reverse of Aiiigiition Medial, aiid ftuiy be proved by it. U0 ALLIGATION ALTERNATE. Rule. L Write the rates of the simples in a column tin- der each other. 2. Connect or link with a continued line the rate of each simple which is less than that of the compound, with one, or any number, of those that are greater than the compound, and each greater rate with one or any number of the less. 3. Write the difierence between the mixture rate and that of each of the simples, opposite the rates with which they are linked. 4. Then if only one ditfcrcncc stand against any rate, it will be the quantity belonging to that rate ; but if there be several their sum will be the quantity.. Examples. 1. A merchant would mix wines at 14.9. ipv. t5s. and S'?^?. per gallon, so that the mixture may be worth 185. the gallon j ivhat quantity of each must be taken ? '"l ip- 22- 4 at 14.9. 1 at ] ,3.9. 3 at ] ri.v. . 4 at '22.S, Or thus l-f4 5 at M.9.. I 1 at 1 5.V. 44-3 7 at 1Q9.. 4 4 at 226.. NoTF. Questions in this rale adnnt of a great variety of answers^ accord- irig to the manner of hnking tlieni. 2. How much wine, at 6s. per gaRon, .and at 4^. per gallon, must be mixed together, that the composition may be worth 06'. per gallon ? Ans. 1 qt. or 1 gal, of each, &c. .3. How much corn, at Qs. 6cL 3v. Sd. 4^. and 4.9. 8(A ]^or hushel, mu'^i be mixed together, that the compound riuiy be woilh 3*. lOd. per bushel ? Ans. 12 at 2s. 6d. 19 at '^s. Sd. 10 at 4s. and IC at 4s. M. 4. A goldsmith lias gold (,f 17, IS, 22 and ?4 carats fine- ]row much must be tale of each lo m;ike it 21 carats fine ^ AiUi 3 of 17, 1 of 18, 3 of 22, aari i of '^4& ALLIGATION ALTERNATC. Ul 5. It is required to mix brandy at 8.9. wine at 7^» cidor afc l5. and water together, so that the mixture may be worth 5} gallons of wine, and l6f of water. 7. A grocer has currants at 4^. 6cL 9(L and ild. per Ib^ and he would make a mixture of 240 lb. so that it might bo atlbrded at 8^. per lb. how much of each sort must he take? Am. 72 lb. at 4tf. 24 at 6d. 48 at 9d. and 9d at 11(/. 8. IIow much gold of 15, of 17, of 18, and of 22 carats, fme, must be mixed together, to form a composition of 40 oz^ of 20 carets fine ? \ni. 5 oz^ of 15, of 17, and of 18, and 25 oz. cf 2!^,> 14^ ALLIGATION ALTERNATE. JJlien one of the wgrecUents is limited to a certain quantify. Rule. Take the clifTcrence between each price and the mean rate, as before ; theii. As the difference of that simple, whose quantity is given, is to the rest of the differences severally, so is the quantity given, to the several quantities required. Examples. 9. How much wine, at Ss. at 5.9. ()c/. and at (7,5. the gallon, must be mixed with three galhms, at 4s9. per gallon, so that the mixture may be worth 5^. ^d. per gallon ? 64. 48— 60- — -^ 66- ) 70 1 4, JO : 10 JO : 20 10 : 20 8-f 2=1:10 8-f2==10 164-4=20 16-f 4—20 : 3 : 3 ; 3 : 6 : 3 : 6 Ans. 3 gallons at 5^. ', 6 at Ss, 6d, and 6 at 6s, 10. A ^irocer would mix teas at 12^. 10^. and 6s. with 20 lb. at 4.9. per lb. ; how much of each sort must he take to make the composition worth 8^. per lb. ? Ans. 201b. al 4s. ; 10 ib. at 65. ; 10 lb. at lOs. ; and 20 lb. at 125. 11. How much gold of 15, of 17? iin<-l cf 22 carats fine, must be mixed with 5 oz. of 1 8 carats fine, so that the com- position may be 20 carats fine .? Ans. 5 oz. of 15 carats fine, 5 oz. of 17? and 25 of 22». position: Position is a rule, which, by false or supposed numbers, taken at pleasure, discovers the true one required. It is divi- ded into two parts, Single and Double. SINGLE POSITION Is, by using one supposed number, and working with it as the true one, you find tiic real number required by the following- POSITION. 14^ "Rule: As the total of the errors is to the given sum, so is the supposed number to the true one required. l^iiooF. A(!d the several parts of the result together, and if •it agrees with the given sum, it is right. Examples. 1, A school-master, being asked how many scholars he had, said, If I had as many, half as many, and one quarter as many more, I should hMve'26'4 ; how many had ho Suppose he had 72 As maiiy 72 J as many ...... 36 ^ as many • • • •• 18 As 19s : 9.64^ : : 72 72 ? Proof. 528 9() J 848 5)6 48 198) 19008(96 Answer. 24 ' 1782 ■ 264 ^. A person, after spending J and J of his money, had 6& (dollars lett ; what had he at first ? Ans. 144 dols. 3. A certain sum of money is to be divided between 4 per- sons, in such a manner, that the first shall have J of it, the second {, the third J-, and the fourth the len^.ainder, which is 28 dollars ; what was the sum ? An.';. 112 dols. 4. A person lent his friend a sum of money unknown, to receive interest for the s^me, at 6 {>er cent, per annum, simple interest, and at the end of 5 years he received for principal and interest 044 dollars SO cents ; what vyas the sum lent ? Ans. 496 dols. DOUBLE POSITION Is, by making use of two supposed nu!iibers, v.hich, if both prove iiilse, are, with tlieir errors, to be thgti disposed : iluLE. 1. Place each error {ig'iii..st its lO'.nective position. t. I>IuUinlv them cross vviie. 444 • POSITION. 3. If the errors are alike, that is, both greater of both less than tlie given number, divide the difierence of the products by the difference of the errors, and the quotient is the ansyver : But if the errors be unlike, divide the sum of the products by the sum of the errors, and the quotient will be the answer. Examples. 1. B asked C how much his horse cost ; C answered, that if he cost him thn t- limes as much as he did, and 15 dollars moie, he would stand him in 300 dollars ; what was the price of the horse ? doh, dols, Suppose he cost 90 Suppose he cost 96 S ' 3 270 2S8 15 15 QS5 too lit. by 15 dls. 303 too much by 3 dls, 90 15-- X 96 3 + 15 1440 270 3 270 Sum of the errors 1«) 1710 (95 answer 95 162 3 90 15 300 proof. 2. Two p'crsons, A and B, have both, the same income ; A saves one-lifth of his yearly : but R, by spending 150 dollars per annum, moi^ than A, at tlie Qwd of 8 years tinds himself 4-00 dollars in debt ; what is their iiicome, and what does each spend per annum ? Ans. Their income is 500 dollars per annum ; also A spends 400, and B 5 '30 dollars per annum* 3. There is a fish whose head is 9 inclies long^ and his tail is as long as his head ar.d half his body, and his body is as long as the head and tail } what is the whole length of the fisli ? Ans. 6 feet. POSITION. 1 15 4. Divide 15intohvo such parts, so tliat ^vhcn tlic greater is multiplied by 4, and the less by \6, the products will be e- flual. Ans. 12 and 3. 6. A man had two silver cups of unequal weight, having one cover to both, 5oz, ; now if the cover is put on the less cup it will be double the weight of the greater cup, and put on the greater cup it will be three times as heavyas the less cup : what is the weight of each cup ? Ans. 3 oz. less — 4 oz. greater. 6, A person being aj^ked, in the afternoon, what o'clock it was, answered that the time past trom noon was equal to ^-3 of the time to midnight : required the time ? Aus. 30 minutes past one. EXCHANGE. Exchange is the paying of money in one place or country, for the like value to be received in another place or country. There are two kinds of money, viz. Real, and Imaginary, Real movetj is a piece of metal coined by the authority of the State, tind current at a certain price, by virtue of the said au- thority, or of its own iatrinsic value. Imaginary money is a denomination used to express a sum of mofiey of which there is no real species, as a/ivrc in France, a pound in America, because there is no species current, in this or that country, precisely the value of either of the sums. Tar of Exchange is the intrinsic value of the money of one country compared with that of another country, as one pound ' sterling is equal to thirty-five shillings Flemish. Course of exchange is the current or running price of ex- change, which is sometimes above, and sometimes below par, varying according to the occurrences of trade, or demand for mone)'. Of this course, there are tables published daily in commercial cities : thus by Lloyd's List, of 2i^\. December, "^799^ tlie course of exchange between Hamburgh and London, was 32-v. G}id, Flemish, per pound bterling, being i'5. b^d, under par, or loss to London. ^ U6 EXCHANGE. GREAT-BRITAIN. The money of account is pounds, shillings, pence and far- things. The English Guinea is 21 shillings, Sterling. Weights and measures generaljy as in the United States, The United States dollar is equal to 4*. 6d, Sterling. To Change Sterling to Federal money. Rule. Annex three cyphers to the sum (if pounds only) and multiply itby 4 ; this product divide by 9> andyou have the answer in cents. 11 there be shillings, &c. the usual method is to reduce it to Massachusetts money, by adding one third to it, and then reduce this sum to Federal. Examples. 1. Change .£.48 Sterling to Federal. 48000 4 9)192000 21333J cents. Ans. 213 dols. 33§ cts. 2. Change £.389 17 4J;SterlingtoFederal,exchangeat33j per cent, that is, £.133j INIassachusetts for £.100 Sterling. J)389 17 4J Sterling 129 19 1| Exchange 519 16* 6 Massachusetts ,3)519,825 Cts. 173275 Federal. Ans. 1732 dols. 75cts» Note. Sterlini:: is cbanscd to Massaclmsclls money by adding one-third to the suiW; and MassachubcUs lo Sterling by deducting ouc-lbi5rtli Irom it. To change Federal Cnrrenci/ to Sterling, PvULB. Work bv either of the following method?. EXCHANGE. 147- Examples. Chatige 1732 dollars 75 cents to sterluig. First Method. 1732 4.. i 6d. i 50 cents 25 cents 346 8 43 6 2 1 3 1.^ Ans. £.389 17 H Second Method. 1752,75 ,3 5191825 20 16(500 12 6|000 1)519 l6 6 Massachusetts 129 19 U Exchange Ans. £.389 17 4j Sterling. 1, What is the- Federal amount of an invoice of goods, charged at £.196 14 6 Sterling advancing on it 25 per cent. ? 25 J) 196 14 6 Sterling 49 3 7J Advance 245 18 ll Exchange at33j per cent. 81 19 4^ £.327 17 6 Massachasctts 3)327S75 cts. 109291^ Ans. 1092 dols. 9lf cts. 2. The Sterling cost of certain goods being c£.6'0 12 6, what does it amount to in Massachusetts money, advancing on it 50 per cent. ? 60 12 6 50 per cent, advance 30 6 3 90 18 9 Exchange at 33 J per cent. 30 6 S Ans. £.121 5 JMaisachusotts money. The mercantile method, with 50 per cent, advance, is to double the Sterling for Massachusetts money ; thus, 60 12 6 Sterling. 2 £.121 5 jMassachuietts, as above. lis EXCHANGE. 3, An invoice of goods, charged at £.6'2 19 7 stciTingj h Srold at 75- per cent. ad\ance on tlie sterling cost, how much is it in ^Jassachusetts money ? 52 19 7 Advance at 50 26 9 9 -J 25 13 4 10| 92 U Si Exchange at Sol percent. 30 18 1 Ans. .£.123 12 4| JMassachiisetts money. The mercantile method, with 73 per cent, advance, is to multiply' the ste?- ?hig by 2| for MHSsichusetts money. Thus, 52 19 7 105 19 3 17 13 2i £.123 12 4| Massachusetts money,as above. 4. The sterling cost of certain goods being £.214- 11 6, tow much is it in Federal money, advancing thereon 60 per cent. ^ 214 11 6 343 6 4| Exchange J 114 8 9 J 457 ^o 24 Massachusetts Or thus, 214 11 6 Sterling Exchange J 71 10 6 286 2 50 J 143 1 10 j 28 12 2J 457 15 2l Massachusetts ,3)457,759 Dollars 1525,861 Ans. 1525 dols. 86^ cts. EXCHANGE. 149 5. What is the amount of a bill of exchange of £.115 14 9 sterling, sold in Boston at 1 J per cent, advance ? J) 115 14 9 Sterling 38 11 7 Exchange Or thus. 154 6 4 INIai ,3)] 154,317 514,39 n Federal 51439' 25719 Cents Value at Advance 771 par par pr. c do. 158 dch. cl3: 514 39 7 7li Amount 522 lOj Value at 514 cts. 39 Adv. at 1 t. 5 2 14 3 57 1 7- 71 4 ; Amount 5-22 10 4. 6. A merchant in Boston receives a parcel of goods from London, charged in the invoice at the following prices, and marks them for sale at()0 percent, advance on the sterling cost ; required the selling price of each in Massachusetts money ; 5. d. s. d. doh. ct'f. m, 8 sterling, adv. 60 per ct. 29 d A Massa. raonev, or 4 85 3 12 51 • 2 7 .'» 7 jl 1 18 3 13 Oi-v.... o 17 6 36 3 6 4 70 61 11 75 (7 2 5| 41 18 10 40 2 6 69 4 11 23 5i .. 3 91 2 4 4 Hi 82 3 32 3 68 9^- 11 46 G 27 9 50 n • • . • 9 86 3'^ K 2 """■ ' 13 8: 6 10 3 4 6 1^ 17 S3 1 1 2 130 EXCHANGE. 7. A watcli that cost 15 guineas in London, was sold in Boston at 50 per cent, advance on the sterling cost, \vha.t was the price ? 15 guineaszi:£.I5 15 Sterling 2 31 10 Massachusetts ,3)31,5 Ans. 105 dollars. S. How much is the premium of insuring c€.294? at 8 guin* eas per cent. ? Ans, £.24: 13 11 Sterling, Mercantile methods of calculating^ tiz» At 25perct. disc, from the sterling co>t, multiply it by 1 for the answer ia Massachusetts money. 10 li pai- H 12| per ct. adv. on the sterling cost, multiply it by ll 2o 1| SIJ l| 60 2 m H 65 2l 75 4 m 4 100 c 2| 125 . 3 140 • 3i 150 si 162| 3f 175 3| 200 4 IRELAND. The money of account as in England, but different in value. The par between Plngland and Ireland is 83 per cent, that is, i^MOO sterling money is ^.108 6" 8 in Ireland. Mercantile weights and measures, the same as in England. The United States dollaris equal to 4a\ lO^^i. Irish. The English guinea is equal to 22s. ^d. Irish. To reduce Irish money to Federal, IluLF,. Reduce the given sum to halfpence, annex two cy- phers to it, and then divide by 117, (the half pence in a dollar) EXCHANGE. 151 and the quotient is the answer in cents. Or reduce the Irisb to Sterling, by deducting ^^ trom it, and then work as for Sterling. ExAMPLEr Change £.Q7S 15 9 'rish money to Federal. First method. Serond method'. 578 15 9 1-3)278 U 9 Irish. 20 21 8 II Kxchange 557i> ^57 10 Sterling 12 85 15 7i 66909 345 2 5i Mass. 2 9)13381800 ^3)343,122 5X13 = 117 1143,74 cents 13)1486866 1 14374 cents. Ans. 1 143 dols. 74 cts. To chancre Federal money to Irish, m Rule. Multiply the given sum by 117, reject two figures from the product to the right hand, and the remaining figures lire the halfpence in the given sum. 1. Change 1143 dols. 74 cts. to Irish. 114374 117 8OO6I8 114374 114374 2)133817158 12)66908| 2l0)557|3 8 Ans. £.278 15 8£ If the sum is dollars only, work by cither of the following methods, , 152 EXCHANGE. 2. "Change 1537 dollars to Tfish. met] )37 .3 First method. Second method. 1537 at 45. lOld, 1537 45. J 307 8 Sd. i 51 4 2 J 12 \6 h- i 3 4 01. 8d ^ 51 4 8 461 2 Massachusetts 2 J 12 l6 2 J 115 5 6 Exchange at 25 per ct.. 1 Q /i nl 345 16 6 SterlincT Ans.£.374 12 10^ ^\ 28 1() 4iEx.8ipr.Gt.orlJ.onl^. £.374 12 lOi In changing Sterling to Irish money at par, ^\ is added to the sum for Irish ; and in chaHging Irish to Sterling, ~^^ is de- ducted for Sterling because 12 pence English are equal to 13 pence Irish, making the Exchange Id, in a shilling, 1^. Sd. in a pound; and £,S 6 8 per cent. Examples* 1. Change £.394 17 5 Sterling to Irish, at par, or £.8| per cent. ,\)394^ 17 6 32 18 U Ans. £.427 15 71 Irish* 2. Change £.427 15 7| Irish money to Sterling, at 83 per cent, in favor of England. ^3)427 15 n 32 18 U Ans. £,394 17 6 Sterling. 3. Change £.370 Sterling to Irish, at 9 per cent; £. £. £. . 100 : 109 : : 370 Ans. £.403 6 4. Ptcduce £.403 6 Irish money to Sterling, at 9 per cent. 9 100 £. s. 109. : 100 : : 403 6 Ans. £.370 EXCHANGE. ir>3 HAMBURG H. Accounts are kept in Hamburgh in Marks, Shillings Lubs or Stivers, and Deniers. 12 deniers, or 2 grotes, make* • • • 1 shilling lubs, or stiver. 1() shillings lubs, stivers, or 7 ^ , oo . r 1 mark. 32 grotes ••••••#••••••• j ALSO, * 12 grotes or pence Flemish make 1 shilling Flemish 20 shillings Flemish • • • 1 pound. Note. 3 marks •...••.. make 1 rix dollar. 7 5 do. • • 1 pound Flemish. A shippound in Hamburgh • • • • 280 lb. A ring of staves • • do. 240 100 lb. in Hamburgh 107^ lb. in U. States* 100 ells. . • do. •• 62i yards. The currency of Hamburgh is inferior to the bank money ; the agio, or rate, is variable ; May 14th, 179S, it was 20 per cent, in favor of the bank. The mark banco is 33^ cents ; (See Laxvs of the U. States.) Examples. 1. Change 12843 marks to Federal, at 33} cts. per mark, 33j=:J)12843 Ans, 4281 dollars. 2. In 4967 marks 8 stivers banco, how many dollars, ex* t-hange as above ? 331-^)4967, 8 stivers ,l6^- Dols. 16'55,83 Ans. 1655 dols. 83 cts. To change Ilamhirgh 7noncy to Sterling, Rule. As the given rate is to one pound, so is the Ham- haxgii sum to the Sterling required. 154 EXCHANGE. Examples. 1. Change 2443 marks 9| stivers to Sterling, exchange at 32^. 6d, Flemish per pound Sterling. *. d, £. m, St. 32 6 : 1 : : 2443 9i 12 grotes. 32 2 350 48 S6 19 grotes 7329 19 78195 1 390)78 195 (200;^, 780 195 20 Ans. £,200 10 390)3900(10^* 3900 2. In 12093 marks 12 stivers, how many pbunds sterling, exchange at 32^. 3d, Flemish per pound SterJmg ? Ans. £.1000 3. In 4178 marks 2 stivers, how many pounds Sterling, exchange at 31^. lOd, Flemish per pound Sterling ? Ans. £.350 4. Change 1971 marks 13 stivers to Sterling, exchange at 35^. 6d, Flemish per pound Sterling. Ans. £.148 2 4 To change Sterling to Hamburgh nw?iei/. Rule. As 1 pound Sterling is to the given rate, so is thft Sterling sum to the Hamburgh required. EXCHANGE. 155 Example. Change £.350 Sterling to Hamburgh money, exchange at 3U\ lOd, Flemish per pound Sterling. £, s, d, £, 1 : 31 10 : : 350 12 382 grotes 350 1()100 1146 2)133700 grotes 1 6) 66850 stivers 4178 2 Ans. 4178 marks 2 stii^ers. Proving the answers in the preceding case will further exemplif]y this. To reduce Current to Bank money. Rule, As 100 marks with the agio added, is to 100 bank, fco is the current money to the bank required. Examples. 1. Change 560 mfeks 8 stivers current to banco, agio at 18 per cent. 18 100 . 118 : 100 :: 560 8. Ans. 475marks* 2. Change 2366 marks current to banco, agio at 20 per cent. Ans. 1^71 marke, 10| stivers. 3. Change 7^56 current marks to banco, agio at 22 per cent, Ans. 6lll marks, 7 stivers* 156' EXCHANGE. To change Bank to current money. Rule. As 100 marks is to 100 with the agio added, so is the bank given to the current required. Examples. 3. Change 4/5 marks banco to current, agio at 18 per ct. 18 100 m. m. 100 : 118 :: 475 Ans. 560 marks, 8 stivers. Or thus, 475 18 .3800 475 560 8 as above. 851 50 16 8|00 2. Change 1971 marks, lOf stivers banco to current, agi® ^t 20 per cent. m. s. 20 J) 1971 lOf banco 39^ 5I agio Ans. 2366 current. PRACTICAL QUESTIONS. 1. How much will 634521b. of cotton ccnie to, at 8 grotes per lb. ? lb. gr. lb. 1:8:: 63452 8 2) 507616 grotes 16)253808 stivers Ans, 15803 marks* exchange:. 157 H. What will 35 lib. of cotton come to at 5Qd. per lb. ? Note. d. is the mark for pence Flemisli, ec^ual in valae to half stivers O'r ^alt'shiJliu^s lubs. lb. d. Ih. 1 : : 50 : : 351 50 2)17550 grotcs or pence flemisli. l6')S775 stivers. 5^\^8 7 Alls. 54S marks 7 stivers. 3, What will 33.9 bars Ptussian iron come to, \vt. 1S062 lb, *t 35 J marks per shippound ? lb. n. Ih. 280 : 35| :: I9662 Ans. Q^O'^ m, U 6tiv. 4. 2801b. of cotton 5. 4002i- lb. coffee « S. 2438 pipe staves • 7. 3510 hlid. ditto - 8. 529 barrel ditto -^ • • « 9. 1790 lb. stignr 10. 4892 lb. rice 11. 4 pieces 10-4 bcdiick . • • • 1 2. 140 half pint tumblers 13. 1)0 boxes windo-.v rlass • • • • 14. lDi6\ lb. coll'ee 15. 245 hi ; iron, vrt. G4:i4 lb. • • 16. 10 ' -s he.T.p, ■• t. 14108 lb. at 21 grotes perlb. • 183 12 8| stivers -..-.... 2063 10 16 marks per ring of 240 • • 162 9 8| ditto ditto 1^5 -6 5^ ditto ditto 11 9 • 21^ pence per lb. 1188 it) lo^ marks per 100 • 892 12 24 ditto 96 ditto per 100 11 3 23 ditto ])er box 2^00 • 16^- stivers per lb. 1574 3 41 marks per shippound ••• • li?35 74 ditto ditto 3723 17. V iiat is I. J commission on 18270 marks, at 2r> per cent.? Ans. 45^ m. 12 st. 18. What is the interest of 6370 marks, for 3 months, at 5 . ^ ^j^g jf^ j^^^ ^^ ^^ per cent, per annum ? O ioS EXCHANGE. 19. Change 5955 marks 71 stivers to Dutch fioriiis,at 38| grotes per liorin. mar. st. 5955 7k grotes in a markzz 32 2 orrotes a stiver. ] 1910 15 grotes in 7h stivers 17S65 15 grotes 38| 190575 grotes. 2 2 77 ) 381150 ( 4950 gilders. 308 Til 693 .,^ 385 385 Ans. 4950 gild, or flot. 20, An American merchant orders his correspondent in Amsterdam to remit 49S0 florins l6g stivers to Hanrtburgh 5 this being done, when the exchange is 39i stivers for 2 marks, what sum is he credited for in Hamburgh? St. M. F. St. S9l : 2 :: 4980 1(3| 4 20 '^ 157 996l6i 2 199-233 4 157)796"932(507^ marks 785 1193 1099 942 942 ' " Ans. 5076 marks* EXCHANGE. 159 HOLLAND. Accounts arc kept in Florins ov Gilders, Stivers, Deniers or Pcnnings. 8 pcnnings make • • • 1 grotc. 2 grotes, or 1() pennings • • • • 1 stiver. 20 stivers, or 40 grotes " • 1 gilder or florin. ALSO, 12 grotes, or 6 stivers l shilling. 20 shillings, or 6' gilders • . - . • 1 pound Flemish. 2h florins • • 1 rix dollar. The florin or gilder of the United Netherlands is estimated in the United States at 40 cents, or 2 cents per stiver. 100 lb. in Amsterdam make 109| lb. in the U. States. 100 ells» • • •do.* • • • 75 yards do. Ill liquid measufe,X6' mingles make 1 stcckan,8 stcckaus 1 aum. 1. Change 1954; florins to Federal money, at 40cts.perflorin. 1954 40 dols. 781,00 Ans. 781 dels. 60 ct% i 2. Change 2653 gilders 17 stivers tO Federal money, at 40- cents per gilder. 2653 17 Or thus, 2(V.''i.3 17 40 2 20 1061 .^0 34 . 5^077 stivers. 34 2 els. per stiver. 1O01j4 cts. 1001,34 ■ Ans. 1061 dols. 54 cts. 3. Change lO^I dols. 54 cts. to gilders, at 40 cts. per gilder. 2) 1 06' 154 cents. 2|0)53O7l7 stivers. ^53 17 Ans. 2()53oild. I7 5tiv. I 169. EXCHANGE. 3. What must be paid in Boston for an invoice sfgoods charg- ed at ,5.91 florins 17 stivers ; allowing the exchange at 40 cents per florin, or 2 cts. per stiver, and advancing on it 60 per cent.? 591 17 20 <^. 11837 stivers. Am, of invoice, 23G 74 2 Advance, 142 04 •lols. 23(),74 Ans. 378 7S 60 per cent. 142,0440 To change Sterling to Flemish, KuLE. As 1 })oimd sterling is to the given rate, so is t|i« sterling given to the Flemish required. Examples. 1. In i^.lOO \Qs. sterling, how many gilders, exchange at 035. 9d, Flemish per pound sterling ? £. 6. d. £. s. 1 : 33 9 :: 300 IQ 20 12 20 20 405 grts. 2010 405 10050 80100 210)81405,0 2)40702.^ grotes. 2lO)2035|l| stivers. 1017 11| Ans. 10 17 gild. Hi st. % To change Flemish to Sterling. Rule. As the given rate is to £.1 sterling, so is the Flem* isk given to the sterling required. IIXCIIAKGE. I'ST Example. Change 1017 gilders llj stivers to sterling, exchange at 536-. 9^/^ Flemish per £, sterling. s, d, £, fl. St. 33 9 : J :: 1017 Hi 12 40 2 405 grotes. 40(580 22j 22i 4.03)407 02K 100' 405 202i 20 405)4050(10 4050 Ans. £.100 10> ^' To change Current Money to Bank. Rule. As 100 gilders with the agio added, is to 100 bank^ «o is the current money given to the bank required. Example. ^^ Change 823 gilders pj stivers- current mone}^. into bai^, ag!«» at 4^ per cent. g' g' g' -y- 104 J : 100 :: 823 pi 20" 2.0 .2090 164691 100 2O9O)l046'C)2O(78S gilders. To change Bank Money into Current, Rule. As 100 gilders bank is to 100 with the agio addedp. so is the bank money given to the current required. Example. Change 7^^ gilders bank money to current*, agio at 4| percent^- g, g, g, ZOO : 1041 :: 7SS Ans. 823 gilderS; 9j stiv. l62 - EXCHANGE. PRACTICAL QUESTIONS. I. Wliatwill 1867 lb. ot cofiee come to at IQ stivers pcrllo 3 867 19 16803 1867 2|0)3.>47 \3 stivers. 1773 13 Ans. 1773 gilders, 13 stivers. 2. What will 9- hhds. of sugar come to, wcighino; 104'242 lb, gross, deducting 2 per cent, tor good weight, tare iH ^er c^^l,. at 21 grotes per ib. ? 104^42 ' deduct 2 per cent. 2085 102157 •are 18 per cent, 183B8 83769 nt. wt. 21 8>769 167538 2)1759149 grptcs. ^^ ■ $|0)87957|4i stivers. 43978 14| Ans. 43978 gilders, 14 J stivers. 5. What will 251 brirs of iron come to, weighing gross 10364' ib. ^t 9j gilders per 100 ib. deducting 2 per cent. ? 10364 H 931^76 g. s. p. ^l^ 2pr.ct.=:5^o)i^iO y U '^0 4 3 2591 1010,49 9,80 16 12,80 EXCHANGE. l63> 4. What will 143 stcckauh 2 mingles of brandy como to at- 42 gildeiii per auai ? 8)14.3 17 7 2- S4 48tPClvans J 21 2 I 10 10 1 i 5 5 2 miugles | 13 2 751 8 2 Ans. 751 gild. 8stlv. ^ppnnmgSr- 5. ?1315 lb of sugar 23 grotes per lb. 1^:2'56 2 6. 56560 25 35.i50 7. v7()9J 25^ 17'>71 15 8. 8 1 H9 ib. coIFee ^o{ st.vers !:>622 1 9. 4650 23^ 5405 1 2 10. U)7 ) 19J 1945 7 11. 39285 2i;- 417^0 6 12. 212 f lis liiien, 208 pasabk 30 312 l.J. 4l«0lb buuei- 13 aiki pcr4()ib,..-. 1.61 1.5 14. 6i76 lU 1861 17 15. 2012 ib. lend l.S^ do per 100 lb... 271 12 lb, 2l4&lcck. 11 ming. biHiui^V 42 do. per aum •••• 1127 2 D E N M A R K. •^ Accounts art? kept in Danish current dollars and skillingsy . rcckonmi; yObKillinvJs to the dollar. The Course ot exchange on London in September, 1799, was- 5 rix or Danish dollars tor 1 pounct stcrhno;. % The rwc dollar ot Dennuirk is ebluii.acd at 100 cents. — CSce Laws of the UnitcH Sfnfcs.) i;ti pounds ot Denmark make ICO pounds in the U. States, Ul.eir weights arc shippounds, lispounos and pounds — 10 p(iunds make 1 lispiaind. 20 II- pounds, or 3*20 pounds 1 shippuund. 1. How much will 8 pieces of platillas come to, at 9 doh, 5(xbkiLs, per piece? 9 56 8 76 64 Aos. 76 doU 64 skills. 164 EXCHANGE. 2. How miicli will 1418 bars of iron come to, weighing 2^3 shippoijnds 9 lispoundsand 4 pounds, at 15 dols. pcrshippound? lb. d, s. lis. lb. Or, ship, 320 : 15 :: 26'3 9 4 263 20 15 5769 Us, 3945 }6 5 ;^ 3 72 4 J 3 00 31^18 4/6.1^6 18 5269 Ans. 3951 90 84308 15 3210)12646210(3951 304 2.88 "166 160 ~2 32 30 9^ 32)2880(9© ♦ 2880 . Ans. 3951 dols. 90 sk. 3.. What is the commission on 21545 Danish dols. 13 skiH^ At 2 per cent. ? 21545 13 2 430,90 26 810 «6,66 Ans. 430 dols, 86 sk^lki EXCHANGE. 165 4. What will 4 hhds. of sugar come to, weighing gross 4314> lb. tare 17 per cent, at 22 skillings per lb. ? . Ans. 820 dols. 62 skills. dfs. s\s. dls. shs- 5. 4 pieces table cloth S 80 15 32 6. 50 9 56 479 16 7. 13 17 64 229 64 8. 24 12 288 00 9. 50 15 • 750 00 10. 100 coils cord, wt. 62sh. i6L 'lib. .30 pershippound 1884 18 11. 85 bun. cl. hemp, 250 36 •• 9000 00 rz. 1951 bars Rus. iron, 362 8 10 14 5074 3 13. How many Danish dollars will be received in Copenha>* gen, for a bill of £.2300 on London, exchange at 5 rix dollar* por pound sterling .? Ans. 1 1500 dols. 14. A bill is drawn inCopenhagen for 18574 marks, 7 stivers, Hamburgh money, v;hen the exchange is 128 Danish dollars for 3 00 rix dollars in Hamburgh, how many Danish dollars does it amount to ? ^^oTE, Three marks are equal to 1 rix dolla»» m, r.d. m, st, r.d, sk. If 3 : 1 :: 18374 7 : ^Ipl 46* • r.d, D.d, r.d, sic. If 100 : 128 :: Cngi 46 Ans. 7925 Dan. dols. 6sk. Or thus, 3)18574 7 Hamburgh money. 6191 46 28 per cent. 1733 56 79^5 6 Dan. money, as above. B R E M E N. Accounts are kept in rix dollars and grotes, reckoning 72 grotes to the rix dollar, which is equal to2i marks. On the 29th Nov. 1795, the exchange on London was 551 rix dollars lor .£.100 sterling. In 1802, the course of exchange on the United States was 75 cents per rix dollar. The Bremen last is equal to 80 bushels in the U. States. 100 lb. in Bremen ^re equal to 110 lb. in the U. States, l66 EXCHANGE. 1. Wliatuiil 11041b. of coffee come to at 32^ grotes pcrlb. ? 1104. 32| 2208 3312 552 276' ■ r.d. s;rote&f 72)36156(502 12 360 156 144 12 Ans. 502 rix doTs. 12 grofe** 2. What is the commission on 7621 rix dols. 6 gr. at S^pesfr cent. ? ^ Ans. 266 rix dols 53 grotes. r. dots. gr. 3. 3071 lb. coffee •• 32i grotes per lb. •• 135/6 63 4. 400 32| ••- 181 18 5. 706 .# 33^ 328 35. 6. 31407 lb. sugar ... 15^ ••• ••••• 6870 2P A N T W E R P. Accounts arc kept in Antwerp in gilders, shillings, and grotes, 12 iirotes • • • • «• make 1 shilling. 3^ shillings, or 40 grotes 1 gilder. The Braband or Antwerp grotes are of the value of the cents of the UnigEd Stato'^, a gihier being reckoned at 40 cents. In the current money ot Antwerp t! ey have slivers of the value of the stiver of Anisterdam, or 2 cents United States currency. 100 pots Braband rz 36;^j gallons U. States. <)6 ib. Antwerp ■=: 100 lb. do. 100 Bral)and ells, about 74 yds. American. . The new quintal of Antwerp consists of JO myriagrammesor^ 204 lb. 14 oz. Avoirdupois weight. , The loss on sugar exported from America to Antwerp is 22 J per cent. viz. tare 14 lb. per 100 ib.-^good weight 2 lb.- -loss - of weight 5 lb. — discount Ij lb. equal to 22^> ib. per lOO lb. Loss gn cotton i2| per cciit.— -on cofici^ ia bags 1 1^ per cent* , Exchange. isr Examples. 1. A cargo consisting of 48 hhds. sugar, weighing 37^ cwt. 1 qr. 14 lb. valued per invoice at 12 dols. per cwt. and 63 bags cofiee weighing 7345 lb. at 32 cents per lb. is sold in Antwerp; what sum wa-. received for it, in gilders and grotes, at 40 cents per gilder, allowing the customary deductions for tare, ike. at an advance of 33 3 pe^ cent, from the invoice ? cwt. qr. lb. Ih. 376 1 14 . 7345 Tare,&c.22^perct. 84 2 20| Tare,&c.lljpcrct. 844|- Neat 291 2 22 J Neat 6jOOJ • 32 Ms. cfs. 1300Q 12 00 19500 10 16 120 00 ^ols. 2080,16 10 . 1200 00 ^ 2 2400 00 val. of 200 cwt. 1080 00 90 12 00 1 6 00 2 qrs. 1 50 14 lb* 75 7 10 7 1 5 3 .... i Value of sugar 3500 41 291 2 22| do. coft'ee 2080 16 . 5580 57 4|0)74407!5 centsi^ Adr. 331 = 3 ^^(^0 19 IS601 36 Dols. 7440 76 — ' — Ans. I8COI gild. 36 gr. it)8 EXCHANGE. 2. What sum must be paid in Boston for an invoice oF goo^s imported from Antwerp, amounting to73J3 gilders, exchange 40 cents per gilder, at an advanse of 40 per cent ? 7315 40 per cent, ( 7315 idv. 2926 adv. 2926,00 10241 40 cents per gild f.-. 4096,40 Ans. 4096dols. 40ct R U S S 1 J. Accounts are kept in Petersburgh, in Rubles and CopccSj beckoning 100 Copccs to 1 ruble. The course of exchange on London, in July, 17^6, was S4.f J, sterling per ruble. Ditto •••• on Amsterdam ••*• 30 stivers banco per ruble. . Ditto .... on Hamburgh, Aug. 1798, 22j st. banco do. Ditto •... on U. States, Sept. 1802, 55 cents do. 100 lb. Petersburgh weight are equal to SS| lb. in theU. States, Their weights are Barquits, Poods, Pounds, and Zollotnicks--r 96 zoilotnicks ........ make 1 pound. 40 pounds •.•.........•. 1 pood. 10 poods 1 barquit. Their long measure is the Arsheen, of 2S American inches : ^ aroheens are at 200 ^siopecs per pood ? 2846 200 .569200 5 lb. I 8'i^72 92 5<>26 91 3580 90 12^5 88 8nb9 87 CJ'VS EXCIIANGi:. 177 Livres. Fr. Cent. 12 11 85 1.5 14 81 20 19 75 24 2o 70 30 20 63 40 39 ;) I 50 49 38 60 59 ^6 70 69 14 72 71 11 80 79 01 90 ...... 88 89 96 94 81 100 98 77 200 197 5.1 300 296 30 400 395 06 500 493 83 1000 98? 65 6000 • . 4938 27 10000 9876 54 Fr. Cent. . 11 85 . 14 81 • 19 75 . 23 70 . 29 62 • 39 50 . 49 38 . 59 25 . 69 1$ . 71 11 . 79 01 . 83 88 . 94 81 . 98 76 . 197 53 . 296 Q9 . 3':\^ 06 . 493 82 . 987 65 4938 27 . 9876 54 iOyOOOths of a centime, 1852 4815 .3086 3704 96:30 6173 2716 9259 5803 1111 2346 8889 4815 ^ 5432 ^i 08f)4 ^ ^ 6^297 1729 7161 4322 1608 3217 For reducing FraN' Cent. sol. den, 1 ' 2 • 3 . 4 . 5 . 10 . 15 • 20 . 25 . SO . 35 40 . 45 - 50 • 5.^ . 60 . 65 • 70 . 75 . IK) . 8.> - 90 . 95 . Francs. 1 . 2 4 7 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 2 15 2 16 2 17 2 18 2 19 2 A CS AND CeN tooths of den. 43 86 2 TABLE TIMES TO Livres, Sols an© Denie^i^ 15 30 45 60 75 90 05 20 35 50 65 80 95 10 25 40 55 70 85 liv. sol:, den, 10 3 Francs. liv. sol. den. 4 4 5 5 6 6 7 7 8 8 9 9 10 10 15 15 20 20 30 SO 40 40 50 50 60 60 70 70 80 81 90 91 100 101 200 202 300 303 400 405 500 506 1000 10 J 2 5i)00 5062 10000 10125 1 1 1 1 2 2 2 3 5 7 10 12 15 O 17 6 2 6 5 10 15 5 W 10 a 178 EXCHANGE. SPAIN, Spanish reckonings are of two sorts — Money of plate, distinguished hard or plate dollars, &c. INIoney of vellon, distinguished by current dollars. The former is 88 ^^ per cent, above the latter. 100 reals plate being equal to 188^-7 reals vellon. 100 reals vellon 53 J do. phite. 17 reals plate • • • 32 do. vellon. 17 piasters or current dollars 256 do. do. 4 maravadiesmake 1 quarto, 8| quartos or 34 inaravadies 1 real. The peso, piaster, or current dollar of 8 reals plate, passes €^yl5 reals vellon in trade, but in exchange it is estimated at xS reals vellon 2 maravadies. The ducat of exchange is 375 maravadies. The real plate, is estimated 10 cents, and the real vellon at 5 cents, in the United States. The Spanish arobe, is 25 lb. 100 lb. of Spain is 97 lb. English. To change reals vellon to reals plate. Rule. I^Iultiply the given sum by 17> and divide by 32 f©5 reals plate. Example. Change 800 reals vellon to reals plate, 800 17 32)13600(4-25 128 80 6'4 160 160 Ans. 425 reals plate. To change reals plate to reals lellon. Rule. ]\luliij)ly the given sum by 32, and divide by 17 for reals vellon. EXCHANGE. 17D Example. In 4,25 reals plate, how many reals vellon ? 455 32 850 1275 17)13600(800 130' 00 Ans. 800 reals vellon. To change reah jJate and reals t'cllon, to Federal money, TlULE. Multiply ihe retds plate by 10, and the reals vellon )>y 5, tor the ccntb ni the given sum. Examples. 1. Change 14958 reals plate, to Federal money. 14t)58 10 145^5, .^0 Ans. 145)5 dels. SO cts. 2. Change \15^Z reals vellon, to Federal money. 17593 5 879,6'5 Ans. ^7^ dols. 65 cts. CADIZ, Accounts are kept by some ia hard or plate dollars, reals Tcllon, and quartos. 8 J quartos make 1 real vel'on. 20 reals vcUun • • I (.iiiinr ot plate. Others kooj' ilieir accounts in reals phne and maravadics, reckoning 34 maravadies to 1 real plate. To bring reals plate to dollars. Rule. Multiply the ^iven sum b} 39, and divide by l7 ^or reals vellon, and uividt^ the leais vellon hy 'rd dollars ? 320 32 640 96'0 17)10240.(602 reals velloB 102 40 34 6 8J 2]0)60|2 reals velloB 17)31(3 quartos, dol. 36 2 3 51 Ans, 30 dol. 2 r. v. 3 q. To change hard dollars to reals plate, , UtTLE. Multiply the dollars by 20 for reals vellon, and the reals vellon being multiplied by 17 and divided by 32 give the real^ plate required. — Or, multiply the dollars by lOf lor reals plate. Example. In l6 hard dollars how many renls plate ? 16* Or thus, \6 20 lOf 16 . 5 320 l6t) — 17 10 8)80 ,2 240 170 il. P» 10 320 32)o4-l0(170 32 224 224 Aus. IfO reals platt»i EXCHANGE. 181 Practical Questions, The answers to xchich arc in doUarSy reals tellon, and qvartos, 1. "What "Nvill 4594^0 pipe staves come to at 80 piastres or current dollars per M. or 1200? 45940 80 12100)36752100 3062f current dollars. S reals. 24501 J reals plate. 32 49002 73503 10| 17)7840421 (461 2e 68 104 102 20 17 2,0)46X2,0 34 ^ols. 2o06 1 34 I7)22i(l 17 5| Ans. 2306 h.dols. r. 1 n. fi(i6t. D. R. Q. ^. 21800 barrel staves at 30| per 1200 •••• 417 3 7 3. 1200 hhd. do. 40" do. .... 30 2 3 4. 2 casks sherry wine 30 per cask • « t • 45 3 4? Q 18C EXCHANGE. The result of the following is in reals plate, and maravadies^ 5, In 610 hard dollars, how niany reals plate? ; 20 reals vellon zz. 1 hard dollar. 12200 17 85400 12200 32)207400(6481 192 154 ' 128 2oO 256 40 32 8 Ans. 6481 r.p, 8 nlaf* 6, What will 2632 barrels of flour come to^ at 1 1 current dollars per barrel ? 2632 It 28^52 piastres or current dollars. 8 reals plate ir: 1 piastre or current doh Ans. 231616 reals plate. 7. 88 lasts of white dry salt, at 6 piastres per last, 88 6 528 8 4224 Ans. 4224 reals plate^ EXCHANGE. 183 8. Change £,600 sterling to reals plate, exciiange at 36'|(/. sterling per piastre. 600 20 12000 12 261 M40G0 4 4 145 ) 576000 ( 397'^ current dnllars, 435 8 1410 3 305 31770 3 10 1050 1015 31779 10 350 200 GO 8 145)480(5 435 1 reah» 45 34 ISO. 135 145)1530( 145 10 maravadios. 80 Ans. 31779 r. p. 10 mar. 9- In ^.3200 sterling^ how many reals plate, exchange at 3()]r/. steriingvpcf piastre*? Ans. 1(;9489 r. p. 22 mar. N. B. In S\. LucAR accounts arc kept in Reals plate and Qiraitos, 16 (^uaitoi lo 1 Ileal plate. lU EXCHANGE. B I L B A. Accounts are kept in Reals vellon and Maravadies, 34 mara- >adies making 1 real. The pound in Bilboa consists of 17 oz. except in iron whick is but l6* oz. 32 vclts are equal to 66 gallons in the U. States. 1 00 fanagues • \5'2 bushels do. 100 varas* •••••• • 108 yards do. To change piastres or cvrrcnt dollars to reals plate. KuLE. As 1 current dollar is to 15 reals 2 maravadics, so is the given sum to the reals required ', or, multiply the sum by 1 5 reals 2 maravadies, for reals. Example. In 5000 current dollars, how many reals vellon ? 2= ,^7 )«000 Or Uius, 5000 15 2z=l c, dol, 2 525000 5000 2^4 4 75294^ 4. 54)10000 Ans. 75294 r. vel. 4 mar. To change current dollars to sterling, RulTe. As 1 dollar is to the rate of exchange, so is the gir- •n sum to the sterling required. Example. In 5000 piastres or current dollars, how many pounds ste'i^ ling, exchange at 3d^d, per dollar ? p. d. p. As 1 : 361 : 5000 o6i 180000 1875 12)181875 210)151516 3 Aus. £,767 16 3 5000 S) 15000 1875 EX CI I A KG E. IS^ To change sterling to current dollars, Rule. As the rate of exchange is to 1 dollar, so is the given sum to the dollars required. Example. In £J7^7 \6s, 3(1. sterling, how many current dollars, ex- change at 36^(1. sterling per dollar ? (L doL £. s, d. As o6|- : 1 :: 7.37 16 3 Aiis. 5000 cur. dols. or piast. To change sterling to reals rello??. Rule. As the rate of exchange is to 15 reals 2 maravadics^ so is the given sum to the reals required. Example. In £A36^ 10s. sterling, how many reals vellon, exchange at 36jj sterling per current dollar ? r/. As o6| ; 8 r. 7n, £. s. • lo 2 : : 436 10 20 291 ' • 8730 12 104760 8 2 mar .Z=j\ 838080 lo 2 4190-1-00 i 838080 49298 29 t) 12620498(43369 V1164 980 873 lf)7i ^73 2010 1746 27;8 2619 119 34 mar.~l riuJ. Or, 838080 34)167 6160 mar. ^- 49298 reals* 291)4046(13 A;i% ^i3:C9 rculs 13 man Q 2 186 EXCHANGE- Practical Questions. 1. What will 122 quintals of iish come to, at 13^ reals per quintal ? 122 136' Ans. 16592 reals. 2. What is the cranage of 1137 quintals offish, at 10 ma*- ravadies per quintal ? ^ ^ - Ans. 334 R, U M. BARCELONA. The monies of account in Barcelona and throughout the Province of Catalonia are Livres, Sols and Deniers. 1 2 deniers make 1 sol. 20 sols > .1 livre. 27 s sols, or l| livre 1 hard dollar. 28 sols . . • 1 cur. dol. the piast. of exchange,^ To change litres to hard dollars. Rule. Divide the livres bv 3 and then by 5 and add thf two quotients together for hard dollars. Examples. 1, How many hard dollars in 360 livres ? 3 360 120 72 192 Ans. 192 hard dols. 2. How many hard dollars must be paid for an invoice (;if |pods amounting to 7134- livres ? 3 7334. 2378 1426$ S804f Ans. SS04 h. d. SO soU. EXCHANGE. IS7 To change hard dollars to livres. Rule. Add to the given sum, the half, quarter, and eighth. Bf it, and the sum will be the livres required. Examples. 1. In 192 hard dollars, how many livres ? 192- 9G 4S 24 360 Ans. 360 livreg. 2. IIovT many livres in 3804f hard dollars ? 3804,8 1902,4 951,2 ^75,6 7134,0 Ans. 7134 livres. To change livres to current dollars. Rule. Multiply the livres by 5 and divide that product" by 7 for current dollars. Example.. Change 271^ livres to current dollars. 2716 5 7)13580 1940 Ans. 1940 cur. dok. To change current dollars to livres. Rule. Multiply the current dollars by 7 and divide the product by 5 for livres. Example. Change ]940 current dollars to livres. 1940 7 5)13580 271^ Ar9, 27iaiivrMi 188 EXCHANGE. P R T U G J L, Accounts are kept in Millrcasand Rcas, reckoning 1000 reas to 1 millrea oi 5s. 72<^. sterling, or 1 dol. 25 cts, in the U. States. A vinten is 20 reas, and 5 \ inlens is a festoon of 100 reas. 1. Change 579 millreas 740 reas to Federal, at 1 dol. 25 cts,. per millrea. M, R. 579,740 Or tlms, 579,740 1,25 I added 144,935 2898 700 Dollars 724,6/5 69568 80 Cents 72467,500 Ans. 724 dols. 67 J cts. 2. Change 724 dols. 6712 cts. to millreas, at 1 dol. 25 cts^ per millrea. 1,25)724,675(579 mill. 740 reas. Or, deducting J from the sum in Federal money gives the^^ millreas, &c. Example. |) 724,67 5 144,935 5 79?7 40 as before. 3. Change 579 millreas 750 rcas to sterling, at 5s. 7ld. per miire a. 579J50 67h 4058,250 34785,00 289,875 12)39133,125 2iO)326|l 1 Ans. ^M63 1 Ij 4. In ^.163 1 Ij sterling, how many millreas, at 5<.v. 7h(h jlcr millrea ? s. iL 7'cas. £. s. (I. 5 7! : 1000 : : I63 1 ih Am, 579 mill. 750 reas"^ EXCHANGE. 189 5. What is the commission on 6245 mill. 46 reas, at 2^ per teat, ? 6245,046 I 2| per 1,00 12490092 3122523 156,12615 Ans. 156 mill. 126 rcag. 6. Suppose a cargo is sold for 6245 mill reas, at 2 monthi credit, for prompt payment of which J per cent, per month is allowed ; how much is the discount ? ^)6245 Or thus, I per cent, for 2 monthsnl per cen(. 31,225 for 1 month. 6245 2 1 Ans. 62,450 for 2 months. 62,45 7. Suppose you import 596O hhd. staves and 5060 barrel staves on which there is a duty of 23 per cent, which is taken ki kind, how many of each remain for sale ? Ans. 4590 hhd. and 3897 bbl. M, R. M. R. 8. 702 barrels of flour at 8,600 per bbl. • . • • 6037,20© 9. 4590 hhd. staves ,030 per stave. ... 137,700 10. 3897 bbl. do. ,020 per do. 77,940 XI.. 71 alquiers of beans. • ,480 per alquiqr • • 34,080 Measures of Portugal. Cloth Measvre, A vara is 43 § inches English. A covedo is 26f ditto. Wine Measure. 1 almude is 12 canados. 1 canado is 4 quarteels. An almude is 4^ gallons English wine measure. A canado is 3 pints Enjlisl^ ^90 EXCHANGE. Corn Measure, 1 moy is 15 fangas. 1 faiiga is lour alquiers. 1 moy of Go alquuTS is 3 English quartevs, or 24 bushels AVin- chester measure. 1 quarter is 20 alquiers. 1 English bushel is 2^ alquiers in Lisbon, 2 alquiers in Oporto, and 2 J alquiers in Figuiras. A moy of salt is the same measure as corn. A pipe of coals is l6' fangas. 1 fanga is S alquiers. A pipe of coals is 128 alquiers, which at 2j- alquiers per bush- el, is 5l| bu-jheis English. Weights of Portugal. 1 quintal is 4- arches. 1 arobe is 32 pounds, so that a quintal is 128 lb. Portugal wt. which is equal to about 132 lb. English, avoirdupois wci.lit. A pound is about l6J ounces English, Loss ^j/ exchanging English money inPortuguL An English guinea passes at Lisbon for 3 m. ()00 r. which is 134 reas, or 9 pence less than the value. An English crown passes for 800 reas, which is 89 reas, or G pence less than the value. An English shilling passes for \G0 reas, which is 18 reas, or a- bout 1.^ penny less than- the value. L E G II R X. Accounts arc kept in Piastres, Soldi, and Dennri, reckoning 12 deniers to 1 soldi, and 20 soldi Jtp 1 piastre or dollar of 48'A sterling at par. 1 J paul, or 2 sols, are equal to I livre. 6" livres 1 piastre or dollar. 5|- livres (effective money) • • 1 do. 1 ducat 1 J do. EXCHANGE. ISl Weis^lits — A pound is only 12 ounces in all commodities. 145 lb. is said to be cqi.uil to the English quintal of 112 lb. but fish generally renders about 156' to 138 lb. per quintal. 145 lb. in Leghorn make 112 lb. in the U. States. 4 brasses 1 cane. 100 brasses 6'4 yards, U. States. 1 palm • • • 9j inched", do. 4 sacks are 2 per cent, less than an Lnglish quarter, of 8 bushels. 1. How much will 5630 lb. of ginger -come to at 9 piastres per 100 ? 5630 9 506170 20 14 |0d Ans. 506 piast. 14 sol. 2. What will 9760 lb. of pepper come to^ at 271 tlucat* per 100? 5760 27i 68320 I90QO 2440 J)20o^6a 44326'f piast. 310;<:|86f 20 soldi 17i33^ J 2 ^cn. 4100 Aqs. 3102 piast I7s0l. 4 deft< 192 EXCHANGE. 3. Wliat will 143700 lb. of pitch come to, at 26 paiils per 100 ? NoTi;. 1 paul is equal to | of a livrc. 14370G 26 852200 287400 37362,00 pauls. 2 3)74724 j6) 24908 livres. 4151 6 8 Ans. 4151 piast. 6 sol. 8 dei, 4. How much will 4200 sacks of wheat come to, at .26li>TOfi^ . of Vienna are equal to 123 lb. Enghsh. A barrel of wine is equal to 18 gallons. A brace of Trieste is equal to J of a yard English. A staro of wheat is 2|- bushels nearly — 3-| siaros is equal to an Engli' li quar- iicr of 8 bushels. The tares on articles of Colonial produce, are Sugars in Brazil large cases 271 lbs. of Vienna middle sized do. 244 per Case small do. 217 do. llavannah boxes .50 do. hogsheads 14 per cent. Coffee, Cocoa, pepper, ^:c. arc enij)tied, and ihc package welgl.ed. ICo (ares or allowances are made on d\ewood3. Sales arc made for bilk on Vienna at 3 nioulhs date, and remittances genet- ally made thiou^h the baaLcrs of that place, EXCHANGE. ^9^ 1. ^Vhat Is the amount of 263 lb. Vienna \veiglit of soap, at 22 kreutzcrs per lb. ? 263 22 5 26 526 610)57 8K^ 96 26 Ans. 96 dor. 26 kreutzers-. 2. 758 gallons wine, at 21 florins 30 krcutzcrs per barrel ? 758 21 758 1516 30 kr. J 379 18)16297(905 162 "^ 90' 7 60 18)420(23 36 "~6o 54 6 Ans. 905 fl. 23j kr. " Jl. hr. fi- kr. 3: 120 stares of wheat at 4 20 per staro. Ans. 520 00 4. 715 braces of silk • • • • 3 50 per brace. • • • • 2740 50 .5. 1730 lb. coffee 58 per lb. l672 20 i^^ EXCHANGE. PJLEiaiO IN SICILY. Accounts arc kept in Onzcs, Tarins and Grains. 50 Grains make 1 Tai in. 30 Taiins • ...*# 1 Onze or Once. i'eb. 3, IS03, the value of the money of Palermo in United States cuiiency was as follows : 1 Grain equal to 4 Mills. '20 do. HZ 1 Tarin =z 8 Cents. 210 do. =r 12 do.nl Sc. dollar. • in. • 90 do. 600 do. — 30 do. — 2l do. — 1 Onze = 240 do. The Spanish dollar is current at 25'2 grains. The value of the onze at par is 11^. 3(1. sterling, 'i he exchange on London Feb. 3, \'j>03, was 56 tarina for the £, bterliiig, or 10is\ 3|c/» sterling per onze. The Cantar of Sicily rr 176 lb. Avoirdupois. The llottoli zz l|lb. do. 100 llottoli make a Cantar. A Cantar of Oil is 25 gallons English measure. The Sici- lian barrel contains 9 gallons. Mahogany is sold by weight ; one foot board measure will 1^'eigh about 2 rottoli. The measure called Caffis is 3| gallons. The lb. in Sicily is 12 oz. avoirdupois. The Saiin is 485 lb. avoirdupois.' Examples. 1. What cost 264 Cantars 25 rottoli of Mahogany at 8 oii- ^C5 15 tarins per cantar ? 2(S4 • 8 2112 15 tar. J =: 132 25 rot. I zz: 2 3 15 52246* 3 15 Als. 2246 onz. 3 tar. 15 z^* EXCHANGE. 197 2. A cargo consisting of 356'4 quintals of Fish invoiced at 5 dels. 50 cts. per quintal, is sold in Palermo at 75 per cent, ad- vance ; what sum must be received for it at 252 grains pep^ dollar ? 3564^ 5 17820 50 cts. J zz 1782 19602 50 perct. | =: 5)801 25 I z= 4000 50 dols. 34303 50 252 6S<)06 171515 6S605 2|0)86'444S|2 grains. - 3lO)43222|4 2 14407 14 2 Ans. 14407 onx. 14 tar. 2 gr^- 3. What is the Brokerage on 13 Ul onz. 12 tar. at 1 J per eent. ? 13131 12 1 13131 12 I = 1641 12 15 147172 24 15 30 21184 20 R2 16'|<}5 x\ns. 147 0112. 21 tar. l6 gi\ l^S EXCHANGE. • GENU A. Accounts are kept in Denarii, Soldi, and Pczzos or Lire?. 12 denarii nuike 1 soldi.. 20 soldi . . • . 1 pezzo or lire. 1 pezzo of exchange 5 1 iires. The course of exchange is various — from 47<:/. to 58c/. ster- ling per pezzo or lire. in Milan, 1 crown rz 80 soldi of Genoa. • •Naples, 1 ducat zn 85 do. • • Leghorn, 1 piastre n: 20 do. • • Sicily, 1 crown zz 127 3 ^^• To reduce Exchange money to Lire money. Rule. ^Multiply the exchar'ge money by 5| for lire mo- Ex.l^iJ^LE. In 384* pezzos of exchange how many Iires ? 384 1C)'20 \ 192 \ })6- 220S Ans. 2:CS Iires. To reduce Lire money to Exchange, Rule. i\Iultiply the lire money by 4 and divide the pr«- • .',( i i^y. 23 for exchange. Example. In. 2208 Iires how many pezzos of exchange ? 2208 4 23)883:. ■ 1.93 184 — Ans. 384 pezzos of exchange. ^ EXCHANGE. 199 To reduce Lives to Sterling. Rule. Asl lire is to the rate of exchange so is the lircs to the sterling required. Example.. In 3()0 lires how much sterling, exchange at 54c?. sterling per lire ? /. d. L 1 : 54 :: 3(50 54» 1440 1800 12)19440 2,0)16'2|0 £.81 Ans..€.81 sterl. V E N I C E. Venice has three kinds of money, viz. Banco money, Banco current money, and Picoli money. Banco nmney is 20 per ct. better than banco current, and banco current 20 per ct, bettey than picoli. The different denominations of money are Denari, Soldi^ Grosi. and Ducats. 12 rienari, or deniers d'or, make 1 Soldi, or sol d'or. 5 J soldi ••• 1 gros, or grosi. 24 gros, or grosi 1 ducat. 100 ducats banco of Venice in Leghorn rz ^3 pezzos. Home zz. 6'8i crowns, Lucca zz 77 do. • • ' • Frankfort zz 1 39| florins. The par of exchange in 1793 was oO^r/. stciling per ducat Ijaiicu. eoO EXCHANGE. Example. IIow much sterling is equal to '2712 ducats banco, exchange- at 50^(1, steilmg per ducat banco ? due. d. due. 1 : 50i :: 2712' 4. 201 201 2712 54240 4)545112 farth. 12)13b"278pence. 2lO)lIS5|6 6 shills. Ans. £.567 l6 6 sterling. S M Y R N J. Accounts are kept in piastres and hundredths, except the Knglish accounts, which from ancient custom are kept in pias- tres and eightieths or half paras. The fractional parts are sometimes called aspers, 100 aspers to 1 piastre. The foiiowing calculations are made in piastres and hun- dredths. A piastre is equal to 40 paras, and a Spanish dollar to 136 paras. 340 piastres are equal to 100 Spanish dollars. The exchange on London was 13 piastres for 1 pound ster- ling, J\iay ]4th, 1800. Their -weights are the Rotola, Oke, Cheque and Tiffee — A rotola u;arked Ho. is 180 drams. An oke Y^ is 400 do. A cheque of opium • • • • is 250 do. do of goal's wool is 800 do. or 2 okes. A tiiiee of silk • is 6*10 do. 100 rotolas, or 1800 drams, or 45 okes are a quintal of this country. 112 lb. Lnglish should render here 40:| okes, or 5)0^ rotolas, 43 okes of this country render l2o^ lb. Lnglish. A pike is 27 incUcsi nearly. EXCHANGE. 201 To change piastres to dollars, Ru Li:. Mulnply the piastres by 5, and divide the product by 17, tor cents. Example. Change 1277 Mq piastres to dollars. 1277,53 17)G387,75(375;75 51 123 iiy 85 127 119 85 85 Ang. 575 dols, 7o cts, 7'o change dollars to piastres, Rule. Multiply the dollars by3f tor piastres. Example. Change 375 dollars 75 cents to piastres. S75J5 H 1127,25 Ans. 1277,55 piastres. Practical Questions. 1. Plow much will 10 serons of cochineal come to, ^veigh• in^ neat 724- okes 73 rotolas, at $0 piastres per oke ? 724,73 80 Ans. 57978,40 piastres. 205 EXCHANGE. 2. 299 l^ags of sugar, weighing 506 quintals q6 rotolas, tare 14 rotolas per bag, at 110 piastres per quintal, gross 506 96 239 tare 41 «5 14 neat 465 10 1196 110 299 Ans. 511(31 OOpiast. 100)4186 41 S6 3. 4 cases of opium, weighing gross 1026 rotolas, tare 84 •kes 75 rotolas, at 10^ piastres per cheque. Kofc, 1 rotola is equal to /^3 of an oke, and I oke to if chequO* rot. 1026 9 20)9234 rot. gross okes 46l 70 tare 84 75 okes 376 95 If S76 95 3 S76 95 226 17 5)1130 85 226 17 cheques 603 12 10| 6031 20 301 56 150 78 Ans, piast, 6483 54 4. 893 pieces of copper, neat okes 19743,85, at |o ^^ 70 paras per oke. 0. R, 19743,85 70 4J0) 1382069510 Ans. piast. 34551,73 EXCHANGE. 203 5. What is the custom -house duty on 1 974-0 okes of copper at H amo 2^ per cent. ? Note. The chargejs are all established by a tariff of the Levant Companj. 15>740 ^ 39480 9870 4|0)4935iO agio 2j =1 4-0) 1233,75 amount of duty at 2| paras. 30,84 agio at 2^ per cent. Ans. piast. 1264,59 6. English consulage on 430 quintals, at 51 piast. agio 7 per cent, 430 H 2150 215 2365 7 An?, piast. 165,55 7. Custom-house duties on 88 quintals 9O rotolas, at J^% .iigio 2| per cent. 88,90 20 n|o)i7780io ,40 Ans. piast. l6,5^' IB* EXCHANGE. ^ ^ 8. What will the follow! nij; charges amount to, \]2, porterac^e 4*0* hoube porters ^%, weighing /(^, chan duty /y, visiting and marketing /^ per quintal on 438 quintals r porterage-... 8 433 house porters 4 _ -^ weighing o ' chan duty. ..'1 4|G) 74416 17 Ans. piast. 1SG,15 ENG LISH WEST-INDIES. Accounts are kept in Pounds, Shillings, and Pence. JAMAICA A N D BERMUDAS, The Spanish dollar passes at 6s. ScL ; 3 dollars are equal to 20 shillings, or J pound, Jamaica currency. To change Jamaica currency to Federal. Rule. Multiply the pounds by 3 tor dollars. If there be shillings, &c, increase the pence in the given sum by \ for cents. Examples. 1. When lumber is sold in Jamaica at ^.15 per M. how much is it in Federal money ? 15 3 Ans. 4-5 dols. Ht, Change ^.54 125. lid, Jamaica currency to Federal, 54 20 12 cts-, 11 1692 12 i)131l5 327 8 J; AiiSc iQo dols. SH ^^- EXCHANGK. 505 What wilH02,896feet of boaids come to, at £.15 per M.i 102,896 15 514480 102896 £.1543,440 20 s. 8,800 12 d. 9,600 Ans.£.1543 8 9 4. What will 5 hhds. of sugar come to, weighing 8519 l^* neat, at 70 shillings per 100 lb. ? 8519 70 . 2lO)596|3,30 Ans. £.298 3 3 5. How much will 5 hhds. of sugar come to, weighing 910^ lb. neat, at 75 shillings per 100 lb. f 9103 75 i ■ ,»»;f» fh?»''^ ■ 45515 63721 2lO)682|7,25 1 Ans. £.341 7 3 BA READ OES, The Spanish dollar is 6s, 3d, Barbadoes currciicv-, S 20a EXCHANGE. y'o change Barhadoes ciirrcncij to Federal, iPwULE. Increase the pcnc-e in the given sum by J for ccnt^ Example. Change <£.49 l^s^ 10c/. Barbadoes money to Federal. Proof I) 1586.9 J cents. £.49 11 10 3967I 20 12) 11902 pence 991 12 2;0)99ll 10 101b902 ^.49 11 If) 3967} 158, 69 J Ans. 158 dols. 6^1 ccn4». Other calculations.asin Jamaica^ 31 ARTIXICO, TOBAGO, a^d ^7\ CHRISTOPBERS. These islands being inhabited by French and English, the former keep their accounts in I..ivres,8oIs, and Deniers, and the latter in Pounds, Shillings, and Pence. A current dollar is 8^. 3d, \ A round dollar passes for ^s. When payment of freight or goods is mentioned in Spjinish dollars, di5a- greement respecting their vahic has frequently arisen ; and to [)reveni it, some persons distinguish them by round and cinrait dolhirs ; others ni.ention the bitsio each. But the most certain \vay is to specify the number of sliiilings or livres, instead of dollars ; tlius, A sells to 13 a barrel of flour, a( SI' sliiilings or livres ; in pnynjent Bmay allow him 11 dollars at 9 shillings each, cr 12 , dollars at 86. 3c/. each, cillicr being equal to S'9 shillings or livres, the turn \ i-pccilied by ihch' a^ieemcnt^ 'exchange. mr FRENCH WEST-INDIES. Accounts are kept in Livres, Sols, and Deniers. 12 deniers make 1 sol, and 20 sols 1 livre. The Spanish dollar passes in some places for 8 livr<)S 5 sols, and in othci-s for 9 livres. 1 cwt. or 112 lb. in the U. Staties is equal to 104- lb. French. 100 lb. French are equal to 108 lb. nearly, in the U. States, When any commodity is to be marked in French weight 4 per cent, is added to the neat hundreds ; thus a hogshead of fisli wcighingneat 10 cwt. is marked 10401b. Fish shipped from the United States will answer to the weight thus marked, provided it comes out in good order, and the cask weighs exactly the customary tare, which is 10 per cent. 100 lb. of coftee or cotton, bought in the French islands, vill, or ought to weigh 108 lb. (it will often weigh 110 lb.) in the United States ; and as these articles are sold here per lb. there is a gain of 8 to 10 per cent, in the weight. But on su- gar, which is bought for lOOlb. and sold here per 112, there is a loss of 6 per cent, because there is 4 per cent, between the American cwt. and 100 lb. French, and 2 per cent, difference in the tare. The tare on brown sugar in the P^rench islands being 10 per cent, and the American tare 12 per cwt. Th« loss on cla3^ed sugar is greater, occasionediJjy the customary tare, which is but 7 per cent, in the French islands, whereas it is here 12 per cent, the same as on brown sugar. Note. The tare allowed on sugar among niercliants is 1? per 112 ; that allowed by the custom-house is 12 per 100. [.SVe Tare and Tret, page 9o.] 1- Change 10^92 livres to dollars, at 8| livres per dollar. Si 10692 4 4 'J^3 ) 427()8(129ff 33 97 66 3\6 198 li)8 Ara.lQ^dijm ^08 EXCHANGE. x\ Chano^e 7713 livres to dollars, at g livres per dollar. 9)7713 Ans. S57 dollars. 5. In IQgS dollars, at S| livres each, how many livres ? H 10368 Ans. 10(H)2 livres* 4. S57 dollars, at 9 livres each, how many livres ? Ans. 7/ io iivn«. 5. What will l642 lb. of coife© come .to at'lcl sols per ll^.'l 15 8210 I()42 .!!?|0)240'310 sols. livres 1231 10 Ans. 1231 Jiv. 10 sols. 6, 17 SO ib. cotton at 157 livres 10 sols per ICO lb. 1780 157 12460 8(,'00 1780 10 sols. J 8<]0 liv. 2803150 20 sols lOlOO Ans. 2S03 liv. 10 sols. EXCIIANCE. ^ y. 24 barrels of beef at 101 liv. I sol 3 den. per barrel. Uv. s, d. 101 1 3 6 Go6 7 6 4 2425 10 0' Ans. 2425 liv. 10 sols. S. How many dollars, at 8 livres 5 sols |x?r dol. will }3^for l^hhds.of brownsugar/wdghing 133^5 Ib.at 40 liv. per 100 lb;? 1336^5 40 8J 534(),00 4 4 33)21384(648 doK- J 98 in 158 152 "264 2^4^ Ans. C48dols. 9. A cargo, amounting to 12536 dels, in the United States ir. Sold at 12^ per cent, advance on the invoice ; how many livrea will it amount to, estimating the dollar at 8| livres each ? 12|~^) 12536 invoice. 1567 advance. 14103 amount. 8 112824 livres at 8 per dollar. « sols J 3525| Ans. Il6349:| livres at S^ per dollar. Si? eiO EXCHANGE. safe. d. 10. 6 hlids. coflTee, weighing 4471 lb. at 14 6 per lb. • . 11. 14 do. siigas do. 16477 58 liv. per 100 12. 1 bale ol" cotton, do. •• ^^i'7« • • • 150 . . . • do. .. 13. 94 hhds. fish, . . do. 101313 33 ...do... 14. 16 cajbks of rice, do. .. 6575- ••• 40 lO.-do. -. 15. 1390 hoops 480 per M. 16. 1.5059 feetof boar Js ^ 100- .. do.-... 17. 48 shaken hhds. wilh heads- • ' 7 15 per Iihd. 1 3. 29 barrelsof beef 90 15 j)cr bbJ. 1 9. 6759 veits ef molasses 2fr per veit %0. 32070 gills, do. at 7 31 7«.9d. per tierce of 60 gals. .... SPANISH W£ST-INDIES.- Accounts are kept in Havanna, La<:;uiia, Vera Cruz, he, in^ dulhirs and reals,' reckoning 8 reals to a dollar. The^'Spanisharobe is 26 ib. 1. vWiiat will 123 pieces Bretagnes come to^ at 26' reals per- piece ? f3?. .1. d,^ 3241 9 6 61261 5 2 340 10 33433 5 9 266^2 17 6 6G7 4 1505 18 37'-2 2631 15 87^6 1<* 399.) t) 9 ;o 8)3iy8 3^9 ^ Ans.'spp dols. G led^ 5. 2178-i feet boards, at 45 dollars per thousandv 21784 45 per M, 108920 87136' - ' " '■ '■>■■■ 9S0J'.28O 8 ?|^40 Ans. 080 clois. 2 reals. EXGHANGX. ^l 5, 153 cases of gu^ At §§ dpllq^rs per. case. 1224 2 dp. .38 2 Ip3j8^.^ Aus.;1338,dols, ^Teafe. - •-. , ,' ,»^ 4., \Yihat is-^, ppmmi^io.n ;pfi •14^^9)^^dftUa]|? 3 rieals, ,^t 4j percent.? .-i-,- ^ ^ ; v i ■• «!i :;■■<■>» • • .,• v, ..i. , . . . '. .- .. 14792 5 mhvnm X •' . i : ''^iLi 59H70 4'" 8 5l(},4, Ans, 591 dbls. 5rcals. ^ 5. What\vill42 bbls. of white sugar come to, weighinggross 415 arobes 18 lb. tare and* tret on the whole 858 ib, at 26' reals per arobe ? a/\ ,Z/>. '/ 415 18 858 lb. make 34 8 381 10 26' 2286 762 - ■ IGlb.nJarube 10 8)9916 reals. '■ • .-^ ^ — — -^Ot 9ffi0} 'tl. * 1239 4. Ai\s. 1239 dols. 4 reals/ duh. rcal.f. (j, 125 pieces bretagncs at 26 reals • .• • 406 2 7. 500 do. •• do..... 24| do. ••.. ...... 1^31 2 S. SO umbrellas .••••• (j A dollars ...... ^20 0- 9. 1 47 arobes of butter .. 2^^ (\o. per 100 lb. ^918 6 10. 2405 arobes I9lb. sug:ii 2^ reals pei^^^Aroby ^ ^^518 11. I66O do.. .12. .do. .^ 21, do,..^-do. -V^ 3-358 7 :2. lW9^,fe]e^:Jj9a|Hh? .... 4P,:d(^.^.^er M. .. 667 ^ iit EXCHANGE. . 1 EAST-INDIES. C A L C U T T J. Accounts are kept in Rupees, Annas, and Vice* 12 pice make 1 anna, 16 annas 1 rupee. By the bazar, or market exchange, for June, 1797, the efC-p. ghan^e was, viz. — 106 English guineas were equal to 956 rupees 4 annas,- 100 Spanish tioliars were equal to 212 rupees. In weights — 16 chittacks make 1 seer, 40 seers 1 maud. The factory maud is 7^ lb, English. The bazar maud is 84 ditto. The imports are sold by the factory maud and current rupees. The exports are bouglit by the bazar maud and sicca rupees* 100 sicca rupees are equal to ll6 current rupees. Bednah, tin-plates, and hides, are sold percorge, 20toacorge. The cavid is half a yard English. l..Wliat will 3905 dry hides amount to, at 12 rupees percorge? h. r. h. 20 ; 12 :: 3905 12 2|0)4680lO 2343 Ans. 2343 rupees. 2. How much will 189 bazar mauds oi seers 8 chittacks- ©i sugar come to, at 6 rupees per maud ? 189 31 8 6 ■w 11 34 20 seers h 3 10 h 1 8 1 A 2 4 S^chit. 4 m 1 n 11 38 11 6 Ans, nSSr. lU. ft^.- EXCHANGE. ' -h^ BOM B A Y. Accounts are kept in Rupees, Quarters, and Rees. 100 rees make 1 quarter ; 4 (]uarters I rupee. ?>ii; 2 ISrCupees were equal to lOOSpAnisli dollars, iji April, 1800. ' The current money is ift Mohurs, Rupees, and Pice. 50 pice nurke 1 rupee ; 15 rupees 1 mohur. The.wG^ghtfe are pounds, mauds, ajid candies ; the pound t^ same as English. A Bombay maud is 28 lb. A Surat maud is o7 }^ lb. 21 Surat mauds or 78-1 lb. make 1 Surat candy. Cotton 14 -sold by the Surat candy. {'iiinphirc and M©cha cotlee are sold by the Surat maud. Malabar pepper is feold by the Bombay *caiidy of a88 ib» In 274 bales of cotton, weigliing neat 996 cwt. 2 qrs. 23 lb. how many Surat candies ? 784lb.ii:7cwt. 7)99^ 2 23 142 200 two hundreds. 24 excess 12 per cent. 56 twa quarters, 23 303 Ans. 142 can. 3031b. MA D R A S. Accounts are kept in Pagodas, Ei^nams, and Cash. 80 cash make 1 fanam ; SG fanams 1 pagoda. The Spanish dollars were in 1793 and \Qf), at l6'j dollars for 100 star pagodas ; making the paga4* worth 16'5 cents. I'he revenue laws of the United States reckon them at 184 cents. The Bengal, or Sicca (new) rupee is worth 46 to 47 cents. The revenue laws of the-United "&nit<:s vaKie ttiem at 50 cents. 214 EXCHANGE. The current exchange is 340 Sicca rupee?!, for 100 Star pa- godas. A Lack of rupees is 100,000. Cowries are sea shells used as small money in India, and on . the coast of Africa, to make change among the natives in the bazar, or market, and in payment to the coolies or labourers. In May, 179-?-^ rupeewas worth 5120 cowries. The common cowries are generally at 5 t© 7 rupees per Bazar maud, the bet- ter sort from 10 to 14 rupees per maud, the price varying ac- cording to the kind. The piculis 133 J lb. English. 100 cattas make a picul. A maud is 25 lb. Troy, 20 mauds make 1 candy. The excellence of their cloth is defined by the t/ireada in the warp. The duty payable at the cu&tom-house is 2 J per cent, out- - wards and inwards. This is taken on imports according toth#- invoice, and on exports at the actual co&tat the bazar or market. B A T A V I A. Accounts arc kept in Rix Dollars and Stivers. The.rix dollar is 48 stivers. The ducatoon is 80 do. The Spanish dollar is 6*4 ditto; sometimes it passes at 60 stiv*. 125 lb. Dutch are equal t© 133 J lb. English. 3 25 do. make 1 picul. 100 cattas 1 ditto. In 1333 rix dols. \6 stiversjhow many ducatoonsr 1333 l6 48 10670 5333 >|0)6400|0 Ans. 800 Jucatooni.. EXCHANGE. ^li 2. Wliat will 127477 cattas of bar iron c6mc to, at 9 t«S dollars per picul ? cat. r.d. cat. As 100 : 9 '•' 1^7^77 9 11472,93 48 744 372 44,64 Alls. 11472 r. dols. 44 st, 3. What will 3894 bottles of wine come to, at 36 stiver* 'per bottle f 3894 Or thus, 36 stiv.ziS rix dol. 3894 24 s 12 tiv. i 19-^7 973 24 *) 3 1 ^f^9,^ 2520 24 I 1 wo -* 2920 24 Ans . 2920 rix (lols. 24 stivcrf* L In 3 1478 lb 12 . ofsucjar, how 5)31478(251 250 many \ )icul s? 647 625 228 125 103 Ans. 251 piculs 103 lb, pic. Pfs 5. In 50632 lb. how many piculs ? Ans 405 7 6, 1264s •••... 101 23 ^5=1- 1953 139 24 1 24 2094 00 :.T. . Wliat \vilf279 piculb 25 lb. of siigar come t6y'ii^7|'nx dollars per picul ? ;' • 279 71 Ans. 2094 rix dols. CHINA, ^ Calculations are made in Tales, Mace, Candareens, and Cash. 1 cash •••••. make 1 candarcen, 10 candareens • • • • • 1 macje. 1 mace 1 tale. The tale of Cliina is estimated at 1 dollar 48 cents in the United States. The Spanish dollar is current at 72 candareens. AVeights ar^iii Tales, Piculs, and Cattas — 16 talcs make 1 catta ; 100 cattas 1 picul. A picul is equal to ISSj lb. English. The cavid of China is 14i^o inches; it is divided into lOparts, To cJiovge pounds English to Cattas. Rule. Deduct 25 per cent, or one quarter, for cattas. Example. In 6266s lb. English, how many cattas ? J)62668 15667 Ans. 47001 cattas. To change cattas to pounds English, IUtlE. Add one ihird for pounds English. Example. In 47001 cattas, how many lb. English? 1)17001 15667 Ans. 62668 lb. English. EXCHANGE. Jtf Practical QuESTioiNS. 1. What is the amount of 308 chests of bohea ten, \vciohing ttcat 1019j6 lb. at 15 tales per picul ? 4)101956' lb. 25489 cat. tal. » 100 : 15 ;: 7^467 cattas. 15 382335 7()4G7 1 1470,05 Ans. 1 1470 tales 5 cand. 2. What will 7^ chests of souchong tea come t©, weighing »^at 4875 lb. at 44 tales per picul ? i)4S75 1218| o6j6\ cattas. 44 14624 14^24 11 1608,75 Ans. l608 tal. 7 ma. 5 cand. 5. How many dollars will pay for an invoice of tea, amount- ing to 6446 talcs 1 mace 6 candareens ? 72)6446 1 6(8953 576 648 381 360 I 2.l6 2l6 Ans. 8953 dois. 218 EXCHANGE. M A N I L L J. Accounts are kept in Dollars, Reals, and Quartos. 12 quartos make 1 real ; S reals 1 dollar. The arobe is 25 lb. 51 arobes make 1 picul. Their 100 lb. is equal to 104^ lb. English. 1. What will 1897 bags of sugar amount to, weighing neat 1:^61 piculs 1 arobe 17^ it), at 6' dollars per arobe ? 136T 1 17^ 6 8166' 1 ar. 12J lb. 5 i i X s 1 n li 8l6"8 Ans. 8l68 dollars. pic. ar. lb. dol.re. dol. re, 2. 118 bags of sugar, weighing 89 1 22| at 5 7 Ans. 524 G 3. 66'3 do.....do. 469 3 IS •• 6 ....2819 COLUMBO, ISLE OF CEYLON. The money is in paper, silver, and gold. Paper money is in the bills of the Company, and is of un- certain value. Silver is in the ru;)ees of different parts of India. The Sicca rupee is worth more than any other by 7 to 8 per cent. Gold is the Mohur pagoda. The exchange is various, as silver is rarely seen. 6 slivers * * • • make • * • • 1 bhiiliM:.': Flemibh. 8 shiPings 1 rix dollar. 30 >ti\ers 1 nipoi . 64 Mo. •••• f»»t... 1 Spanish dollar. EXCHANGE, JAPAN. 2l9 Accounts arc in Tales, Mace, and Candarecns. 10 candarecns make 1 mace. 10 mace • 1 talezz| of a dollar, or 75 cents. Ten mace arc equal to 1 rix dollar. Six tales make a corban, a gold coin not used in accounts. In weights — 10 tales make i mace ; l6 mace 1 catta. The ichan or hickey is 3^ feet. The balce is 65 quarts. Thirty-fke per cent, was the duty on privileged imports in 1799. It is on the exports (which are all free of duty) that the Dutch make their prolit upon their return to Batavia. A privilege is granted to ihe Captain of the Dutch shijjsto carry money, which oi'teii icils at au advaiico. How much is the neat proceeds of 4? silver watches, at 35 ta!ci tach, deducting the duty of 35 per cent. ? 35 tales, 4 140 ^5 per cent* 7 00 4C'0 Sales 140 Duty 49 49,00 Ans. neat proceeds 91 talts. rORM OF AN ACCOUNT OF SALFS. Dr III s. Neat. talcs. talcs. tuU's. 4 -silver watches, 1st kind o5 40 91 6 silver watches, '2i\ kind 23,1 48,5,1 90,0,9 The article is aiven in the first column, the price in the next column, the duties in the third, and ihc neat procccus in ihM fourih. 2^0 EXCHANGE. V A RTI C U L A RS 0/fhe To N^- AGE (/Goods, as calculated to maJte np the Ton- iwgefor the Freight of Goods, brought in East-India or China ships to Europe — viz. Port St. George. PIECE GOODS. Bengal. Pleca to Pieces tc the Ton. the Ton. ALLEIARS 800 Elatches . R.80(> Belellcs 400 Eiiirnerlies 600 Callawapores 800 Gurrahs 400 Chintz of all sorts • • . R,400 Ditto, Jong 2oa Cjinii])ams 800 Ginghams, coloured. 600 -Izzurees 800 Humhums 400 Longcioths 160 Habassies 600 Moorees 800 Ilumhiims, quilted • • 100 Salianjpores • 400 Jamdaunies 8oa fcastiacuiidk'S . .. 800 Jarawars 600 Laccowries 6Q0 Beng AL. Lungees Herba 800 Addaties 700 Mulmuls 400 AliibaUies 400 Ditto handkerchiefs 400 Aliachaws 1200 Mahamodietei . . • 400 Aiiibannies .. R.800 Mam'odies . R.40O Arras .. R400 Nillaes 800 Atcliabannles 800 Nainsooks 400 Baftaes . . R..400 Peniascoes 800 BandaiinoeSjOr Taffi deFoolas R.800 Photacs . R.800 Carridarrie^j 600 Percaulas • • 800 C.!iii}):Utifs 400 Putcahs . R.40O r'oojjces 600 Roma Is . R800 Cailicocs 400 Sannoes 400 Chillaes 600 Seerbetties 400 Cliowiars 600 Secrbands 60O (;hundcibannlcs 800 Seersuckers 600 Chiniiaclmres . .. R.800 Scerhaudconnaes • • 400 Cambrics . ■ R.400 Seershauds . R.'K)0 Chucklaes 400 Seerbafts 400 Ciishtaes 800 Shauibafts 400 Cossaes 400 Succatoons . R.800 Charconnacg 600 Soosevs 40O Cuttaiintics .. R.800 Sorts 400 I)i)()*iO'>rie'i . . R.400 I'afTcties of all sorts . R.800 iJiingariea . . R.4-;)0 Tanjetbs 400 Doroiis 400 Tcpoys . R.8(,'0 Dimities 600 Terrindams 400 Diapers, broad 400 Tains©*k» 4U# Jb^ilto, uarrovT tiUO RXCIIANGF.. ^^\ PIECE GOODS. BOMBAV. Anna?>atchc8 Bombay stiUli Byrainpauls •• Bcjutapauts Boralchawdcrs or brawJs Betellce* Chelloe-s Chiinz of nil sorts • • Doolies Guinea stuffs, large Ditto, small Longcloths, whole pieces Ditto, half ditto Leiiiances Musters Nurisarees Neganepauts Niccanees) large • • Ditto, small Salaiupores Stuffs, brown Tapseils, larje l>itt04 small ritcis to ila Ton. . II 400 . ]l.40() 400 . rv.4oo 1200. 400 . R400 . R.400 . R.400 600 1200 IGO 320 . R.800 400 . R.400 400 600 600" 400 . R.400 400 600 ClilNA. Pieces {'■)' the Ton. R.400- R.800 X-ankeen cloth Silks', of all sorts •• Chiiui ware, .30 cabical feet totlie ton, or about 4 cl.-ests of the Uiual di- mensions. Other measurable goods, 50 cubical feet to the ton. N. B. Where the letter R. is set asainsi pieces of 400 to the ton, it shews those goods nre to be reduced, or brought to a standard of %6 yard* loiiiz and 1 broad. Where again.4 pieces of 800 to t]:c toil, to 10 yards long and I broad. tXAMPI-F. 1000 pieces of 12 yards long and 1-J broad, at 400 to the ton, make 8 14 pieces, ©r 2 tons 44 pieces. 1000 pieces of lOf yards long and 1^ broad> at 800 to the ton, "is 1181^ pieces,- or 1 ton 381 pieces. WEIGHABLE GOODS. A'rrangocs Aloes • • Benjamin Borax Cardemons, fine goods Gakelack • • • Carraenia Wool Cambogium Cassia Lipnea- ....... Cassia Buds Camphire Cut. to the Ton. 'iO .... 16 20 12 16 10 20 8 12 1.5 Cotton Yarn/ Fine Goods •..••• 10 } Cowries* •••Gruff^di'to • Coffee* •••••Pine do. • Cinnabar Gloves , . . .^. Dragon's Blood Gum Arabic • ^^•Elerai •• • » .^^ . Amaiooiacuro T% 20 18 10 12 20 16 16 16 CiCU ^9 the Ton, Gum Opoponax 1 (1 • • • • Satjapenum • 18 . . . • Sarcocol ....-•.•• 18^ Indigo 12 Iron Kintlage 20 Musk .^ ..*..... 20 Myrrh 1 1^^ Pitto, packed ia Ch^ia ware • ' • • — Tutenague <2{j TAirai'.ric • j (t Xiucdl It) the Ton. Tea, Green - 8 ' • • • Bohea 10 Arrack. • • • Gauge gallons 251 Canes Tale oOO Wanghoes and Bar[ib(!es ■ 3000 Llattan^ equVl to 16 cut. 6000 ARBITRATION o^ exchange: Whex the rates of exchanfrc between several countries m succession are given, to find the rate ot exchange between the ^rst and last phice in the correspondence. Rule. Find by proportion (he value of the sum originally remitted in the different monies of the countries through which it passes according to tiie rates of the different exchanges and so proceed till the whole is finished. Or, i\Iultiply all the first terms of the difi'erent statings together for a divisor, and the second terms, together with the sum re- mitted, for a dividend, and the quotient is the amount received in the denomination of the last place in the correspondence : trom this result the rate of exchange is readily found by pro- portion. Examples. 1. A merchant in London has credit for 500 piastres in Lcgi' horn for which he can draw directly at 52d. sterling per {)ias- tre;'but chusing to have it remitted by a circular rout, they are sent, by his orcljej,. to Venice at <)5 piastre* for 100 ducats ban- co ; from thence" to Cadiz at 350 maravedies per ducat banco; from thence to Li^bon at 630 reas per piastre of ^72 marave- dies ; from thence to Amsterdam at 48(/. Flemish for. 400 reas; from thence to Paris at 54-^/. Flemish per crown ; ai^d f"oni thence to London at 30r/. sterling per crown : Whiit is the ar- bitrated price between London and Leghorn per piastre, and >vhat is gained or lost by this circular rQuiiUunce vnthout reck*- ^laing cxpcnccs ? AnBlTRATION OF EXCHANGE. 525 jtiaft. d. ban. piast. d. ban. 9^ 100 : 500 : 526^% in Venice. d.b. mor. fl.h. mar. 1 360 :: 520^ 184210jf in Cadiz. mar. re5SM4)60S.'56(4 558144 50112 £. s. d. Amount received l)y circular remittnnce 118 10 4^ 500 piastres at 52c/. • 108 6 8 C Gained by circular remittance • • • • ^.10 ^ C Arbitrated value oJ a piastre by do. t^-i ARBITRATION OF EXCHANGE.- 2. A merchant in Boston has £.225 sterling in LonsJvm 1^'hich he can draw for at 5-^d, sterling per dollar, but chusin^; to try a circuhir rout it is sent to Dublin at .£.100 sterling foi- i^. 109 Irish ; ihcnce to Hamburgh at 12^ marks banco per pound Irish ; thence to Amsterdam at 33 florins for 40 marks banco ; thence to Copenhag^en at 5 florins for 2 rix dollars of Denmark; thence to Bremen at 3 marks per rix dollar of Den- mark ; thence to Russia at 5 marks for 2 rubles ; thence to Bordeaux at 5 francs per ruble ; thence to Cadiz at 18 reals plate for 10 francs ; ihcnce to Lisbon at 1250 reals plate for 100 milreas ; thence to Leghorn at 750 soldi for 88 miircas ; thence to Smyrna at 2 soldi per piastre ; thence to Jamaica aS 24^7. Jamaica currency p^r piastre ; and thence to Boston at 80r/. Jamaica currency per dollar : What is gained or lost by this circular remittance ?. Ans. 117 dols. 42 cts. gained.. AMERICAN DUTIES ARE CALCULATED AS IN^ THE FOLLOWING EXAMPLES. 1. What is the duty on 2885 gallons of molasses, at 5 ctti*. per gallon ? 2885 5 1-4425 cents. Ans; 144 dols. 25 ct^,. 1^ 2. What is the duty on the above molasses, if imported in a- foreign vessel, the rate being 65 cents per gallon, or 10 per cent, more than an American vessel ? 2885 Or, 144,25 as above. 5.§ 10 per cent. 14,42. J 14425 dol*. }6S,67k 1442i- 4ol». 15 8^67 i An5. 158doi8. 67 J c«t»;. AMERICAN DUTIES. 2?5 3. How much is the duty on 3720 gallons of gin, at 31 ^^^ eents per gallon ? 3720 3720 31 1^0 9 3720 10)33480 11160 3348 3348 dols. 1186',6*8 Ans. 1186 dols. 68 cent*. ^ dols. ctt» 4. 1273 lb. chocolate at 3 cents • Ans. 38 ly 5. Q65 lb. do. in a foreign vessel at 3,^o do. • • • • 31 84 J 6*. 1 149 lb. cheese at 7 ditto • • • . 80 43 7. 1295 lb. do. in a foreign vessel at7i^ do. * * * ' 99 T'l J 8. 1879 gar^ 52a 12 V 3836 i23,0Ji ^2- 7672 1918 95,90 Anr^. 0^ t^^la. S'O ^'tf. 13. What is the duty on this sugar, in a foreign vessel, at. §f cents per lb. ? Ans,~10-5 dols. 49 cts. The mode of eslimating ad valorem rates of dufij. The ad valorem rates of duty, irpon goods, wares and mer- chandizes, at the place of importation, shall be estimated by adding 20 per cent, to the actual cost thereof, if imported from the Cape of Good Hope, or from any other place, bryond tlie same, and 10 per cent, on the actual cost thiMcof, if imported from any other place or country, includir.g all charges, com- misssions, outside packages and insurance excepted^ — f6Vc Laus^ of the United States.) -^ AMERICAN DUTIES. 227 Examples. 1. What is the duty on an invoice of silver and plated ware. Imported from London, the cost exclusive of commissions, &c, being £,359 IS 4, dt 15 per cent, ad valorem ? 1^ 359 ^ > ^^ * 444 cents per £. sterling. 143G 14SG 1436 10^. 1 222 5 ■ ^ 111 3 4rd.i 74 actual cost 139803 centi 10 per cent, added 139SO 175783 10 ,\ 1757S 5 I 8789 for 15 per cent. 2636*7 cents. Ans. 263 dols. €7 cents. 2. What will it amount to in a foreign vessel, at 16J per cent, ad valorem ? Ans. 290 dols. 4 cents. The rates at 'which all forrign coins and currencies are estimate j at the Custom- Houses of the United States, Dols. Cts. Each pound sterling of Grent Britain, at 4 44 Each pound sterling of Ireland ••• 4 10 Each livre touriiois of France • 18| Each rlorin or gilder oilhe Unit<-d Netherlands •• 40 Each mark hanco of J lamburgii . . •• 33 J Each rix dollar of Denmark 1 Each real oi' -late of Spain • 10 Each n-al of vcilon of Spain » . > 5 Each jiiilr-vie of Portugal 1 24 Each tale of China *^^^ ^ ^^ Each pagoda of i ndi'a • • ••d||y * i S4 Each rupee of Bengal • • .jJT. • #••... 50 (228 ) PR OG RE SSION Consists in two parts — Arithmetical and Geometrical. ARITHMETICAL PROGRESSION' Is when a rank of numbers increase or decrease regularly, by the continual adding or subtracting of some equal number: As 1, 2, 3, 4, 5 J 6, are in Arithmetical Progression by the continual increasing or adding of one, and 11, 9, 7, 5, 3, 1, by the continual decrease or subtraction of two. Note. When any even number of terms differ by Arith- metical Progression, the sum of the two extremes will be equal to the two middle numbers, or any two means equally distant from the extremes : As 2, 4, 6, 8, 10, 12, where 6-f 8, the two middle numbers, are zz 12 -f 2, the two extremes, and rz 10 + 4 the two means rz 14. When the number of terms are odd, the double of the middle term will be equal to the two extremes, or of any two means equally distant from the middle term : As 1, 2, 3, 4, 5, where the double of 3=5+ lrz2 + 4 = 6\ In Arithmetical Progression five things aret® be observed, viz, 1. The first term. 2. The last term. 3. The number of terms. 4. Tke equal difference. 5. The sum of all the terms. Any three of which being given, the other two may be found. Thejirst, second and third terms given to find the fifth. Rule. Multiply the sum of the two extremes by half the number of terms, or multiply half the sum of the two extremes by the whole number of terms, the product is the total of all the terms. Examples. 1. How many strokes docs the hammer of a clock strike ia 12. hours? 12-i-lr=i3 f/;cw I3x6lr=78 Ans. 2'. A man buys 17 yards of cloth, and gave for the first ;^';ird. 2.y. aiid for the last iO^. what did the 17 yards amount to? Ads. £%^ 2s, rnOGRRSSION. 2...,> -^t was 4 xears old, and the ekiest 32, and that he in- treated one in his iamily every 4 years 3 how many had he ? Ans. 8. T/ie sccmJ, flurd and fourth given fofijid the first. Rule. Multiply the fourth by the third, made less by \, the product subtracted from the second gives the first. Examples. 1. A man in 10 days went from Boston to a certain town in tlie country, every day's journey increasing the former by 4, ar.d the last day he went was 4-6 miles ; what was the first ? Alls. 10 miles. 4 X 10— 1 =3() then 46— 36 rr 10, the first da^-'s journey. 9, A man takes out of his pocket at 8 several times, so many dilTerenc numbers of shillings, every one exceeding the former by 6, the last 46' ; what was the first ? Ans. 4. The second y third and fifth given to find the first, T:tm r. IVivide the fifth by the third, and from the quotient b irthe product of the fourth, multiplied by the third ]•>: AMPLE. A m:in is to receive f ..j6o at \2 several payments, each to c:\ceed ti:e f(;rmer by £A-, and is willing to bestow the first payment on any one that can tell him what it is ; what will "that person have for his pains ? Ans. ^'.8. 4x17-^ S60— r2--30 then 30 =zS, the first paymei^^ The first, third and fourth given tofnd the second, Uvi !•. Subtract the huirth from the product of the third, PROGRESSION. 231 Example. What is the last number of an Arithmetical Progression, be- lining at 6', aucA continuing by the increase of 8 to '20 places? Ans. 1.3S. oQxS— Sr=15<2 then 1524-6iz:158, the last number. GEOMETIUCJL PROGRESSIOX Is the increasing or decreasing of any rank of numl-cis by some common ratio, that i^, by the continual multiplication or division of some ecjual number : As ^, 4, 8, l6, inc!\v>se by the multiplier 2, and Iv), 8, 4, 2, decrease by the divide .• .'. Note. When any number of terms is continued m Geo- metrical Progression, the product of the two extremes* will be equal to any two means, equally distant from the extremes : As 2, 4, 8, 16, 32, 64, where 04 X 2z=4 X32zr8 X l6i:zl28. When the number of terms are odd, the middle term multi- plied into itself will be equal to the two extremes, or any two means equally distant from the mean: As 2, 4, 8, l6, 32, where 2X32=:4X l6nSx8 — ()4. In Geometrical Progression the same five things arc to be ob- served as in Arithmetical, viz. 1. The first term. 2. The last term. 3. The number of terms. 4. The equal dilference or ratio. I 5. The sum of all the terms. Note. As (lie. last term .in a long series of numbers, is very tedious to C(>r»c at, by continual multiplication ; therelbre, for the readier finding it out, there is a series of numbers made use of in Arithmetical Proportion, called indices, beginning with an unit, whose coramin diifeience is one, whatever nriiuher of indices 3'ou make use of, set as many numbor.s ^in such G;'oii'?tncal IVopoi- tion as is given in the question^ under them : . 1, 2, 3, 4, 5, 6 indices. 2, 4, 8, 16, 32, 64 numbers in Geometrical Proportion. But if the first term in Geometrical Proportion be different from the ratio, the indices m^st begin with a cypher. ^^0, 1, 2, 3, 4, 5, 6 indices. 1, 2, 4, 8, 16, 32, 64 numbers in Geometrical Proportion. 53:2 PROGRESSION. V;iien tlic indices begin with acypiier, the sum of the indices made choice of must he always one less than the number of ternis aivcn in the question, for 1 in the indices is over the se- cuiiJ tfrin, a:i,l 2 over the third, kc. Add any two of the indices toii;cther, and that sum will agree with the product of tiuir respective terms. As in the lirst table ot indices 2-f- 5zz 7 Geometrical proportion .... 4 X 32zz 1^8 Then in the secoiul ^'^~ t.— ^. 4x ]6iz 64 In any Geometrical Progression proceeding from unity, the ratio L-eii.g known, to find any remote term, without producing all ihe iLtennediate terms. Rule. Find what figures of the indices added together would give the exponent of the term wanted, thcii multip'ly the num- bers standing under such exponent into each other, and it will give the term required. Koiz. Wlicji t!ic exponeiit 1 blands over the second terra, the number of €iponc:its m\ii>t be 1 le^s than the number of termi. Examples. 1. A man agrees for 12 peaches, to pay only the price of the last, reckoning a farthing for the first, a half-penny for the se- cond, 405 farthings. Ans. £.5SQ5 Ss, 5i(l. 2. A man bought a h.orse, and by agreement was to give a far tiling for the iir>t nsil, three lor the secon:], t the chan^iniz or varying of the order of things. "a V: c].E. Multiply fil the given terms one into another, and th.' labi |?roduct will be the number of changes required. KXAMPLES. 1. IT )w many clninges may be rung upon 12 bells, and how loni: vvould V\cy be ringing; but once over, supposing 10 changes i.r: :ht L(^ rang iri oiie minute, and the year to contain 36o days (' lioui-s r 1 X2x3X4xr)X6x7 XSX9X 10X11 X 12 = 479C*Ol6CO i^-;)g(^S whirii -^ 10r=47900l60 minutes, t\nd it reduced PER MUTATION. 235 2. A young scholar coming into a town for the conveniency of a good library, dcnmnds of a gentleman with whom he lodg- ed, what his diet would cost for a year, who told him ^*.10 ; hut the scholar, not being certain what time he should stay, asked him what he must give him for so long as he could place his famil)^ (consisting of 6' persons besides himself) in difi'erent positions, every day at dinner; the gentleman, thinking it could not be long, tells him £.5, to which the scholar agrees : what lime did the scholar stay with the gentleman ? Ans. 5040 days^ EXTRACTION ov th^ SQUARE ROOT: ExTRACTixG THE Square Root is to find out such a numher as being multiplied into itself, the product will be equal to the given number. PcULE. 1. Point the given number, beginning at the unit's j^lace, then to the hundred's, and so upon eveiy second figure throughout. 2. Seek the greatest square number in the first point, to- wards the left hand, placing the square number under the first j^oint, and the root thereof in the quotient; subtract the square number from t!ie first point, and to the remainder bring down the next point and call that the resolvendf 3. D<|nble the quotient, and place ItJ^c^S^drvisor on the left hand of the resoivend ; seek how often the divisor is con- tained in the resoivend (reserving always the unit's place) and put the answer in the quotient, and also on the right hand side (f the divisor ; then multiply by the figure last put in the quo- tient, and subtract the product from the resoivend; bringdown the next point to the remainder (if there be any more) aixd proceed as before. Roots. 1. f:. 3. 4. 5. (). 7. S. .9. ^bQUAUi^s. 1. 4. :), 16\ 25. ^0'. 4f). 64. SU * t3G EXTRACTION OF THE SQUARE ROOT. Examples. 1. What is the square root of 1 19025 ? 119025(31-5 9 64)290 25() 685)34.25 34:25 Ans. S'^S. 2; What is the square root of 10^929 ? Ans. 327 5. What is the square root of 22GS741 ? Ans. 1506*,23-f 4. What is the square root of 7596795' ? Ans. 2756,22S-{- 5. What is the square root of 3t)3729()l ? Ans. 603i • 6. Wlvdi is the square root of 22071204. ? Ans. 46'93 When the given number consists of a whole number and de- cimals togetuery make the number of decimals even, by adding cj^phers to tliem, so that there may be a point fall on the unit's place of the whole number. 7. What is the square root of 3271,4007 ? Ans. 57,19H- 8. What is the square root of 4795,25731 ? Ans. 60,247 + 9. What is the square root of 4,372594 ? Ans. 2,091 -f 10. What is the square root of 2,2710957 ? Ans. 1,50701-f- H. What is the square root of ,00032754 ? Ans. ,01809-f 12. Wi;at is the square root of 1,270054 ? Ans. 1,1209 + 1, To extract iJ^ square roof of a "c id gar fraction. Rule. Reduce the fraction to its lowest term'^, then extract the square root of the numerator for a new luimerator, and jhe square root of tlie d.onominator for a new (ieiK^minator. If tlio fraction be a surd, (i. e,) a number whose root can- ncvor bo exactly found, reduce it to a decimal, and extract the root from it. Examples'. \3, \Vhat is the square root of 5.20 +. } /^.m. |,- 14. What is the square root of vJH^ ? Ans. f. 15. What i» the square root of 1^5'/'. ? Ans. f'. EXTRACTION OF THE SQUARE ROOT. ^Z7 Surds* 16\ What is the square root of V^ ? Ans. ,89802 + ir. What is the square root of J f J ? Ans. ,86'602 + 18. What is the square root of \\%} Aus. ,93-OS-f To extract the square root of a mixed nimiher. Rule. 1. Reduce the fractional part of the mi.xed number to its lowest term, and then the mixed number to an improper fraction. '2. Extract the roots of the numerator and denominator for a new numerator and denominator. If the mixed number gi\en be a surd, reduce the fractional part to a decimal, annex it to the whole number, and extract the square root therefrom. Examples. 19. WHiat is the square root of 5l|{ ? 20. What is the square root of 27/^6 ^ 2L What is the square root of 9|^ ? Surds. 22. What is the sciuare root of S5lf ? 23. What is the square root of 8f ? 2-l!. What is the square root of 6'| ? The Application. 1. There is an army consisting of a certain number of men, who are placed rank and iile, that is, in the form of a square, each side having 576 men, I desire to know how many the whole square contains ? Ans. 331776. 2. A certain pavement is made exactly square, each side of ^vhich contains ^7 ^^^i^t, I demand how many scpiare feet are contained therein ? Ans. 9409. Ans. n- Ans. 6-i. Aus. 3f. An; 5. 9.*: 7-^- An: s. 2,9 -'3i9-f An: <. 2,5 ^^98-1:- Tojlnd a mean proportional between any two given numbers. Rule. The square root of the product of the given num- bers is the mean proportional sought. 238 EXTRACTION OF THE SQUARE ROOT, Examples. 1, What is the mean proportional between 3 and 12 ? Ans. 3 X 12—36 then v'SOzzO" the mean proportional. 5. What is the mean proportional between 427^ and 842 ? Ans. 1897,4 + Tofind the side of a square equal in area to any given super feces. Rule. The square root of the content of any given super* ices, is the square equal sought. Examples. - 3. If the content of a given circle be \60, ^vhat is the side •f the square equal ? Ans. 12,64911. 4. If the area of a circle is 7^0, what is the side of the square equal ? Ans. 27,386 12. The area of a circle given to find the diameter. Rule. As355 : 452,or asl : 1,273230 :: so is the area ; to the square of the diameter ; — or, multiply the square root of the area by 1,12837, and ttic product will be the diameter. Example. 5. What length of cord will tit to tie to a cow's tail, that other end iixed in the ground, to let her have liberty of eating nn acre of grass, and no more, supposing the cow an;! tail to be 5 yards and a half? Ans. 6,136 perches. T/ie area of a circle given to find the periphery, or circumference. Rule. As 113 : 1420, or as 1 : 12,56637 :: the area : to the square of the periphery, or multiply the square root of the area, by 3,3449, and the product is the circumference. SQUARE ROOT. 239 Examples. 6, When the area is IQ, what is the circumference ? Ans. 12,^798. 7. When the area is l60, what is the periphery ? Ans. 44,84. Ani/ tivo sides of a rigid angled triangle given to find the third side. 1. The base and perpendicular given to find the hypothec- lUlsC. Rule. The square root of the sum of the squares of the Jjase and. perpendicular is the length of the hypothenusc. Examples. 8. The top of a castle from the ground is 45 yards high^ ftnd is surrounded with a ditch 6'0 yards broad ; what length muit a ladder be to reach from the outside of the ditch to \\v^ top of the castle ? Ans. 7.5 yards. if; o Ditch. JZS Base 00 yards. p. The wall of a town is 2.5 feet high, which is surrounded by a moat of 30 feet in breadth, I desire to know the length of a ladder that \^ ill reach from the outside of the moat to the top of the wall. Ans. 3^,03 feet. The hypofhenuse and perpendicidar given to find the base. Rule. The square root of the difrerencc of the pquares of the hypothenusc and perpendicular is the length of th- base. no SQUARE ROOT. The base and /ivpofJtcnii.yc giren to find the 'perpendicular. Rule. The square root of the djffcreiu'e of the hypothenus© and base is the height of the perpendicuhir. N. P). The two last qucslions may be varied lor examples to (he two last pro])ositious. Any number of men being given to form them into a square bat'- tic, or to find the number of ranks and files. Rule. The square root of the number of men given, is the number of men either in rank or file. 10. An army consisting of 331 77() men, I desire to knovV how many in rank and file ? Ans. bl6. 11. A certain square pavement contains 48 841 s(juare stones, all of the same size, I demand how many are contained in one of the sides ? Ans. 221. EXTRACTION OF THE CUBE ROOT. To extract the Cube Root is to find out a number v»hich Ic- ing nuiltiplied into itself, and then into that product, produccth the given number. Rule 1. Point every third figure of the cube given, begin- ning at the unit's place, seek the greatest cu))e to the fist j^.oint and subtract it therefrom, ])ut the root in tlie quotient, and bring down the figures in the next point to the remainder for a resolvend. 2. Find a divisor by multiplying the square of the ({uoticnt by 3. See how often it is contained in the resolvend, rejecting tliC units and tens, and put the .answer in the quotient. 3. To find the subtrahend. 1. Cnbe the Inst figure in the q'jotient. 2. INIultiply all the figures in the (juotient by 3 ex- cept the last, andthatproductby thescjuare of the hist. 3. INIul- tiply the divisor by the last figure. Add t]u\-e products togeth- er, gives the subtrahend, which subtract from the resolvend; to the remainder bring dov.m the next point and proceed as before. Roots. ]. 2. 3. 4. 5. C). 7. S. p. Cubes. 1. 8. 27. 64. 125. Clu. 343. 512. 729. CUBE ROOT. ^^^ Example. What is the cube root of 99252S47 ? 99252847(463 G4zzCube of 4. Divisor. Squareof4x3zz4S)35252 Resolvend j^lGzzCube of G 432 iz:4 X 3 X by square of 6 288 —Divisor X by G 33336 Subtrahend Divisor. Sq. of 46 X 3=6348) 1916847 ResoKcnd 27=Ciibc of 3 1242 zn^'S Xo A b}' square of 3 19044 ^Divibor X by 3 1916847 Subtrahend. Anotlier nexD and more concise method of extracihig the Cube Root. Rule. 1. Point every third figure of the cube given be- ginning at the unit's phice, then find the nearest cube to the first point, and subtract it therefrom, put the root in the quo- tient, bring down the. figures in the next point to the remaind- er for a resolvend. 2. Square the quotient and triple the square for a divisor — ■ as, 4X4X3:ii4S. Find how often it is contained in the re- solvend, rejc^ctiiig I' nits and tens, and put the answer in the quotient. 3. Square I he his-t figure in the quotient, and put it en the right hand of the divisor: As 6x6=^36 put to the divisor 48 =r. 4836. 4. Triple the last figure in the quotient, and multiply by the former, put it under tiie other, units under the teiis, add them together, and multiply the sum by the last figure in the quotient, subtract that product from the resolvend; bring down the next point and proceed as before, X '3 ^ CUBE ROOT. Examples. \s\nit is the cube root of <}9252847 ? / Square of 4 x 3=48 divisor 59252847 (463 Square of 6 put to 48=4836 ()4. O'X 3X411: 72 35252 5556' X 6 = 33336 Square of 46=2116x3=6348 divisor . Square of 3=9 put to 6348=*634809 19l6S47 3X3X46= 414 6389^9 X 3= 1916847 2. What is the cube root of 389017 ? Ans. 73. 3. What is the cube root of 5735339 ? Ans. 179. 4. What is tlie cube root of 32461759 ? Ans. 319. 5. What is the cube root of 8 V601519 ? Ans, 439. 6. What is the cube root of 259694072 ? Ans. 638. 7. VVhat is the cul^e root of 48228544 ? Ans. 364. 8. What is the cube root of 27054036008 ? Ans. 3002. 9. V, hat is the cube root of 22069810125 ? Ans. 2805. 10. What is the cube root of 12261532/232 ? Ans. 4968. 11. What is the cube root of 2 19365327791 ? Ans. 6031. 12. What is the cube root of 673373097125 ? Ans. 8765. Wbien , irani])er consists of a whole number and de- cimal toiv , i.^ake tb.e number of decimals to consist of 3, 6, 9> ^C' ph:"(' ., by adein:: cypliers thereto, so that there may- be a point fall on the unit's place of the whole number. 13. What is the cube root of 12,977875 ? Ans. 2,35 14. What is the cube root of 361d5,0':7576 ? Ans. 33,C6-f 15. What is the cube root of ,001906624 ? Ans. ,124 16. What is the cube root of 33,2--0079637 ? Ans. 3,2l5-f 17. What is the cube root ( : 72504 ? Ans. 25,l6-f 18. What is the cube root 01 / _ . /279 ? Ans. ,376 + * When 1]^, quotient is j, 2, or 3, there m\i\\ Ic a (;yp],er put to suppij" the ])lace of tens. CUBE ROOT. 24S To extract the cube root of a 'vulgar fraction. Rule. Reduce the fraction to its lowest terms, then extract the cube root of the numerator and denominator for a new nu- merator and denominator; but if the fraction be a surd, reduce it to a decimal, and then extract the root from it. Examples. 19. What is the cube root of gt| ? Ans. |. 20. What is the cube root of {\\^q ? Ans. I. 21. What is the cube root of l{l% ? Ans. ■:. SuiiDS. 22. What is the cube root of t ? Ans. ,829 + 23. What is the cube root of ^3 ? Ans. ,822 + 24. What is the cube root of § ? Ans. ,873 + To extract the cube root of a mixed number. Rule, Reduce the fractional part to its lowest tenuis ninl then the mixed number to an improper fraction, cy" cube roots of the numerator and denonuiiJitor f.r li 1 rator and denominator ; but if the nii:. 1 Ll a surd, reduce t!ie fractional part to a c;.^ — , ,......:. u to U.y wliijle iiaUib'jr, and extract the root therefrom. Examples. 25. What is the cube root of 12^f ? Ans. 2\. 9ii What is the cube root of 3lX^.5 ? A;. 27. What is the cube root of 405 i^Aj ? A... Surds. 28. What is the cube root of 71 ? Ans. 1,93 + 29. What is the cube root of 9 J ? Ans. 2,002 + SO. M'hat is the cube root of 8f .? Ans. 2,057 + The Appltcatiois^. 1. If a cubical pi-oce of timber be 47 inclies lon?^, 47 inches broad, and 4:7 inches deep, how many cubical inches doth it contain ? Ans. 103823. 2. There is a cellar dug that is 12 feet every way, in length, breadth, and depth, how many solid feet of eaitli were taken out of it ? Ans. 172s. ^U CUBE ROOT. 3. ThcM'c is a stone of a cubic form, which contains 3S9017 solid (cot; what is the supcriicial content ofone of its sides ? Ans. 5329. Bctxeen fico 7iitmhcys ghen, to find tKo mean proporfio?2als. Rule. Divide the greater extreme by the lesser, and the cube root of the quotient multiplied by the lesser extreme gives tlie less'jr mean; multiply the said cube root by the lesser mean, and th^ product will be the greater mean proportional. Examples. 4. What are the two mean proportionals between 6 and 1(}2? Ans. 18 and 54. 5, V\'hat are the tvv^o mean proportionals betv.cen 4 and 108? Ans. \2 and 36. To find the side of a c III e that shall he equal in solidity to any gken solid, as a globe, cylinder, prism, cone, SfC, Rule. The cube root of the solid content of any solid body- given is the side of the cube of equal solidity. Example. 6. If the solid content of a globe is lOCiS, what is the side of a cube of equal solidity .? Ans. 22. The side of the cube being given, to find the side of that cube, that shall be double, treble, ^^c. in quantity to the given cube. Rule. Cube the side given, and multiply it by 2, 3, »Scc. the cube root of the product is the side sought. Example. 7. There is a cubical vessel, whose side is 12 inches, and it is required to iind the side of another vessel that is to contain liiree times as much? Ans. 17?30(}, BIQUADRATE ROOT. 545 EXTRACTION OF THE BIQUADRATE ROOT, To extract the Inquaclrate Root is to ila,! out a iuiiribci> \\hich being involve.! IjW): tii:;c. i.. > " '.": will prcduco the given number. Rule. First extract the square root of the given luimber, then extract the squaic root of that squaie root, and it v.iil give the l/iquadrate root required. Examples. 1. What is the biquadrate of 27 ? Ans. 53U4:K 2. What is the biquadrate of 76' ? 3336"2176. 3. What is the biquadrate of 273 ? 57191-^0625. 4-. What is the biquadrate root of 531441 ? 27. 5. What is the biquadrate root of 33302176 ? 7(>. 6". What is the biquadrate root of 57 1914-0625 ? 275. J GENERAL RULE rOR EXTRACTING THE ROOTS OF ALL POWERS. 1. Prepare the number given for extraction, b}^ pointing off from the unit's place, as the root rc(;iiiic.l direct:-;. 2. Find the first tipure in the root, by liie table of pov.er^, \vhich subtract from the given number. 3. Brin<: down the first fv-iwvQ 'u\ \\\q r::.t point to tlie re- mainder, and call it ihe dividend. 4. Involve the root into tlie next inferior [lower to that \vi;ich is given; multiply it by the given power, and call it the divisor. 5. Find a quotient figure by common division, and annex it to the root ; then involve the whole root into the given power, and call that the subtrahend. . (k Subtract that number from as many points of tjc given power as is brought down, beginning at the lowest place, and to the remainder bring down the first figure of the next point for a new dividen-l. 7. Find a new divi ->:()!•, and proceed in all repect- a.^ before. X 2 i>4^' RULE FOR EXTRACTING, &c. Examples. 1. What is the square root of 14137^ ? 141376(376 9 G')d1 dividead oX-ziG divisor . 37Xo7— 1369 subtrahend 1369 subtrahend 37X^^r=:74 divisor 376 X376zz 141376 subtrahend 74) 447 dividend 141376 subtrahend Ans. 376. 2. What is the cube root of 53157376 ? 53157376(376 27 S7)261 dividend oXoxS—^7 divisor 37X^7X37— 50653 subfraliend 50653 subtrahend 37X^'37x3i=:4107 divisor S76y,37 6y(,S7 6zi:ooi57 37 6 subtrahend 4107)25043 dividend 53157376 subtrahend Ans. 37^ S.. What is the biquadrate root of 1998717337(5 I 199871733?6(376 81 108)1188 dividend 1371161 subtrahend e026U') 1245.363 dividend 19987173576 subtrahend- 3 X " X •'^ X 4 zzlOS divisor ''7X -''"X '>*'X 37iz;18?416l subtraliciid :>7X '^^X ^^7X 4 =202612 divisur 5-.?6X376X376X376— 15987173376 subtrahend Ans. 376.. DUODECIMALS, ?47 DUODECIMALS. Duo DECIMALS, OF Cross Multiplication, is a rule made use of in measuring and computing the dimensions of the several parts of buildings ; it is likewise used to find ships* tonnage and the contents of t)ales, cases, &c. Dimensions are taken in feet, inches, and parts. Artificers* work is computed by different measures, viz. Glazing, and masons* fiat work, by the foot ; Painting, paving, plastering, &;c. by the yard. Partitioning, flooring, roofing, tiling, &c. by the square of 100 (t^ Brick-work, &c. by the rod of iG^j feet, whose square is 2/25. The contents of bales, cases, &c. by the ton of 40 cubic feet. The tonnage of ships, by the ton of ^S feet. rult: for multiplying duodecimally^. 1. Under the multiplicand write the corresponding denom- inations of the multiplier. 2. Multij^ly each terrain the multiplicand, (beginning at the lowest) by the feet in the multiplier ; write eacli result under each respective term, observing to carry an unit from each lower denomiiuition to its superior. 3. In the same manner, multiply the multiplicand by the inches in the multiplier, and write the result of each term, one place more to the right hand of them, in the multiplicand. 4. V/ork in the same manner with the other parts in the multiplier, setting the result of each term two places to the right hand of those in the multiplicand, and so on lor thirds, fourths, <^c. o. Pi-occcd in the like manner v>'ith all tlie rest of tlie dc nominatiuii^. and their sum will give the answer required*. U$ DUODECIMALS. Examples. 1. Multiply 4 feet 9 inches by 8 inches. V 8 Ans. 3 (eet 2 inches. Multiply 9 feet 6 inches by 4 feet 9 inches. ^ 9 6 4 9 /?. ?«. 9 6x4 feetzzSS 9 6x9 inc.3: 7 1-6 45 1 6 Ans. 45 feet 1 inch and 6 twelfths. 3. Wliat is the price of a marble slab, whose length is 5 ket 7 inches, and breadth 1 foot 10 inches, at 1 dolhir per foot ? Ans. lOdols. 23 cents. 4. There is a house with three tiers of windows, 3 in a tier, tiie height of the first tier is 7 feet 10 inches, of tlie second 6 feet 8 inches, and of the third 5 feet 4 inches, and the breadth of each is 3 feet 11 inches ; what will the gliizin:;^ corae to, at 14^/. per tbot ? Ans. £.13 lis. lOUL 5. If a house mea<^ures within the walls 52 feci 8 inches in lengtli, and 30 feet 6" inches in breadth, and-^tlie roof be oi' a true pitch or tlie rafters J of the breadth of the building, what will it come to roDliugat 10^. 6d, per square ? Ans. £.12 12^. ni. DUODECIMALS. 249 Application of Duodecimals. To find how many cubic or solid square feet (in order to ascer^ tain the freight) are contained in cases, baleSj 4^c. that is, hoi» tnani/ cubic feet they uill take up in a ship. Examples. 1. Suppose the dimensions of a bale- to be 7 feet 6 inches, 3 feet 3 inches, and 1 foot 10 inches ; what is the solid content? ft. in. 7 6 3 3 ft' in. 7" 6X3 ft.=:^'2 6 7 6X3 m.— 1 10 2'1 4 1 10 i\. in. tw. 21 4 6X1 ft.zz24 4 6 24 4 exiOin.— ^0 3 9 44 8 3 Ans. 44 feet 8 inches and 3 twelfth parts. 2. What is the freight of a bale containing 65 feet 9 inches^ at 15 dollars per ton of 4-0 feet ? tlccinially. 65,7 b 1.5 S'28r5 6575 (Joh. cts. 1 5,00 for 40 feet 20 ft. i 7,50 5 ft. I 4" 1,87,5 6 in. 1 1 ,18,7 3 i ,09,3 40)986,'25 24,65,5 24,65,6 Ans. 24 dols. 65\ cts. 3. A merchant imports from London 6 bales of the follow- ing dimensions, viz. Length. Ileiglit, Depth. ft. in. ft. in. ft. in. No. 1. 2 10 2 4 19 2. 2 10 2 6 13 3. 3 6 2 2 18 4. 2 10 2 8 19 5. 2 10 2 6 19 6. 2 U 2 8 13 25d DUODECIMALS. What are the solid contents, and how much will the freight amount to, at 20 dollars per ton ? "" Feet. 71,58 20dols.pcrton« The contents arc, viz. ft. in. No. 1. 11 7 2. 8 10 3. 12 7 4- 13 2 b. 12 5 6. 13 71 7 40)1431,60 o5,79 Ans. 35 dols. 79 ctf» To find SJti/s Tonnage hj Carpentcr^s Measure. Rule. For single decked vessels, multiply the lengthy breadth at the main beam, and depth of the hold together, and divide the product by 95. Example. What is the tonnage of a single decked vessel, whose length is 60 feet, breadth 20 feet, and depth 8 feet ? 60 length 20 breadth 1200 8 depth 95)9600(1019^5 100 95 5 Ans. 101/^ tons. Iliis is tlie usual method of tonnaging a single-decked vessel, liaving tlie deck bolted to the wale. 13ut if it be required that the deck be bolted at any lieight above the wale, the custom is to pay the carpenter for okg half of the additiooal height, to which- the deck may be thus raised ; tliat is, one half of the difference bein^ added to the former depth givoo the depth to be used ia calculating the tomiage. DUODECIMALS. 251 Example. A merchant, after having contracted with a carpenter to t>uild a single-decked vessel of 6'0 ieet keel, 20 feet beam, and 8 feet hold, desires that the deck be laid for 10 feet hold ', re- quired the tonnage to be paid for ? 6'0 length 20 breadth 1200 1=J diff. of depth + S zz 9 95) 10800(1 13ff 95 130 95 3.50 65 Ans. Ii3t)f tons. Rule. For a double-decked vessel, take half the breadth of the main beam for the depth of the hold, and work as for a" single decketl vessel. Examples. 1. What is the tonnage of a double-docked vessel, whose length is 6'j lect, and breadth 21 feet 6 inches ? 65 length i?l 6 breadth 65 ft. X 6 in. r: in. ft 1397 6xl0rt.rrl39r5 1397 6x 9 in-=T 1043 1 95)15023 1(43895- 475 "773 760 1^ Ans. ioSll tons, 25f!. DUODECIMALS. The preceding question may be wrought thus 65 21 6 65 130 6 i 1365 32 6 6 3 ■ 1397 6 10 9 13975 i 69s 9 i 349 4 95)15023 1 as before. 15SJ5 tons. 2. What will the above tonnage amount to, at I6 dols. per ton ? dols. 158 16 16 13 948 48 158 16 2,18 95)208(2,18 2530,18 190 180 850 76'0 Ans. 2530 dols. IS cents. 90 3. Required the tonntigc of a ship of 74 fcc-t keel, and 26 feet 6 inches beam ? Ans. 273 gy tons. DUODECIMALS. 555 To find the GoTcrrnnent Tonnage, *' If tlic vessel be double- decked, take the Icivo/Ji tliereof from the fore part of the main stem, to ; the stern post, above the upper deck ; the 1; : i!,. . : ..L-.the broadest part ^bove the main wales, half of which ])rca(lth shall be accounted the depth of such vesrel, and then deduct from the length, three-fifths of the breadth, multiply the re'ir.-iiiuler by the breadth, and the product by the depth, and divide tliis last product by 95> ^1^^ quotient wiiereof shall be deemed the true contents or tonnage of such ship or vessel ; and if such ship or vessel be single-decked, take the length and breadth, as above directed, deduct from the said length three-fifths of the breadth, and take the depth from the under side of the deck plank, to the ceiling in the h©ld, then multiply and divide as aforesaid, and the quotient shall be deemed the tonnage." Examples. 1. What is the government tonnage of a single-decked vessel, whose length is 69 feet 6 inches, breadth 22 feet 6 inches, and depth 8 feet 6 inches ? ft. in. 69 () length, 22 6 breadth deduct 13 G for | breadth. 3 56' 5)67 6 22 6 breadth. 13 6' 112 112 6 in. i 28 "0 1260 8 G deptk 10080 G in. J 630 9o}l0710 0(112j^ tons. 321 260 iS)0 70 _ Ans. 1121? tens. 25 4. DUODECIMALS, ^. Wluit is the government tonnage of a double-decked rcs- sel, oithe following dimensions; length 75 feet 6 inches, breadtk 2o feet 4 inches, and depth 3 1 feet 8 inches ? 75 6 ft. in. 14 for 4 breadth Or, 75 6 14 61 6 23 4 61 ^ 23 4 breadth 183 122 6 in. i 11 6 4 in. i 20 6 1435 1 1 8 depth 15785 6 in. J 717 6 2 in. A. 239 2 61ft, X SSft.; —1403 6 in. X' L\'>ft.: zz 11 6 61ft.6in x 4 ill. •r= 20 6 1435 11 8 15785 1435 ft. X 8 m.r : 956 8 16741 8asb«forc 95)16741 8(l70|i tons. 95 724 665 591 • 570 21 Ans. 17611 tons. 3. What is the government tonnage of a double-decked ves- sel, of the following dimensions ; length 82 kei 3 inches, breadth 24 feet 3 inches, and depth 12 feet Ih inches ? Ans. 209| f tons. TABLES OF CORDAGE. 255 TABLES OF CORDAGE. A Cordage Table, shewing how many fathoms^ fed, and inches of a rope, of any size, not more than 14 inches, male a hundred weight ; with the use of the teible. i ■ i ^ p^ ^ >C Fathoms. Feet. Inches. •^ 3 . 2 i~ 406 4J: t'6 3 7f ~8~;Tr T(;y" '""■l'"f o \\ 313 3 4| 24 8 3 6 11 4 3 \\ 216 3 H 21 3 8 7 3 6 11^ 3 5 7 i| l^'O 3 5 19 3 81 7 -. " ' ' ' 3 4 1 « l'i4 V*) 6| 17 4 U t; 3 3 3 51 96 S 51- 1h 1 8j (> 3 'J 3 77 3 9 65 4 (j 91- .» 3 54 <3.l 12 2 p! 5 ■: o ^ - !-" '2 ?- G 'V- 45 5 '2 61 11 3 C;l 5 6 2 5 3 .:jf 39 3 j Ql 10 4 vf 4 5 1.')^ 2 1 9 ^ 34 3 9 1 7 9 5 6 10} 4 4 1 1 ^• 2 1 4 30 1 6 7-- 9 16 lOi 4 2 e 1^ 2 3 6 2 2 1 USE OF THE TABLE. At the top of the table, marked incites, fathoms, fvcf, fnche?^, the (irst column is tlie thickness of the rope in inches and quar- ters, and the other three the falfioms, feet, and inches that make up a hundred weight of such a rope. One example will make it phiin : Suppose you dA?sire to know how much of a seven-inch i' o will make a hundred weight : Tiiul 7 in the third column un- der inches, or thickness ol rope, and against it in the fourth col- umn you find 9 5 6, which shews that there will be 9 fathoms 5 ieet 6 inches recj^uired to iiiake one hundred weight. 256 A T. TAELKS OF CORDAGE. ■Jag t'ic urig/it of any Cable or Rope of ICO fuilj- , ..:;ujur Licri/ halj inch, from 5 to 'Z\ inc/us hi i -~ 1 ^- . i ie Inches. G 6* t ^ -i ! ;- '^* "^ s Cq^ 3 \i i 7 12 1 11 30 i 15^ &.) 20 100 H S n- 14 11' S3 16 (M 2()I 105 4 4 8 Ui 1-2 oG 16^- 63 21 110 1 1 41 fj H 18 1^1 39 17 72 1 2U 115 £i 5 6 1 9 20 1 13 42 1 17^- 76 2 22 121 Gl -^^ 7 2 9i 22 '2 131 45 2 18 81 c;oi 1-26 2 1 6 9 10 '2b 14 49 18i 85 2 23 132 1 0} 10 2 lOi 27 i2 14X 52 2 19 90 1 231 138 15 56 1 191 95 24 141 USE OF THE TABLE. The first coiumn marked for inches, is the thickness or cir- cuniicrence of the cable to every half inch from 3 to 24 inch- es ; tho bccoii.!, rriarked cwt. qr.-. for the hundred weights and quarters that it \\\A Wvi:;i], it" 1*^0 fiUhoms in length. For in-tance : Su;-,;jsc it be a cable of 14^ inches ; look ligainst 14^ and you wiil find in the other column 52cvvt. 2 qrs. which shews that 120 fathoms of 14j inch cable wall Aveigh 52cwt. 2qrs. and so in others : and any quantity of a less length will weigh in proportion. A ship was brought to anchor in a gale of wind, but the gale increasing, it was thought safest to cut the cables, in conse- quence of which 75 fathoms of l6 inches, and 50 fathoms of 12 inches were lost; what must they be valued at in calculating the average ; new^ cordage being then 14 dollars per cwt ? CALCULUrOX 120f:il]i. 16in. cable— 64 cv.t. 120 fatli. 12 in.cab.=:i36c\vt. 60 do.... 15 do .. . •32 . 8 40 .do... 10 do... ...12 75 fath. weighing 50 do.... 50 luth. weighing • . 15 . 40 .15 — dols^ cts. 55 cwt. at I4 dols. pcrcwt..»«»770 00 OhC third deducted lor new. • . •2")6 GS"] Answer— :Zcjij. 513 33 J TABLES OF GOLD COIN. A TABLE ^For receiving and }>ai/in9 3S . 665 6i) 4 7 13 . • 47 61 3 . . 52 55 65 S9 - 683 21 23 14 . . 51 13 4 . . 70 7 41 40 • 700 72 136 15 . . 54 102 5 . • ^7 59 17 41 - 718 24 112 16 . • 58 54 6 . . 105 10 130 42 • 735 76 St) 17 . . 62 6 7 • . 122 62 106 43 • 753 28 64 18 . . 65 9o 8 . • 140 14 82 44 . 770 80 40 19 • • 69 47 9 • . 157 66 58 45 . 7S8 32 16 20 . . 72 136* 10 . . 175 18 34 46 - 805 83 120 21 . . 76 88 11 . . 192 70 10 47 . 823 35 105 22 . • 80 40 12 . . 210 21 123 48 . 840 87 81 23 . . 83 129 13 . . 227 73 99 49 . 858 39 57 24 . . 87 81 14 . . 245 25 75 50 . . 875 91 33 dut. 15 . . 262 77 51 51 • . 893 4'3 9 1. . . 87 81 16 . . 280 29 27 52 . • 910 9^ 122 2 . • 1 75 25 17 • • 297 81 3 53 . . 928 46 f}8 3 . . 2 6*2 106 18 . . 315 32 116 54 . . 9-^5 98 74 4 . • 3 50 50 19 • . 332 84 9*2 55 . . 963 50 50 5 . • 4 37 131 20 . • 350 36 68 56 . . 9S1 2 26 6 . • 5 25 75 21 . . 36'7 88 44 57 ' . 5A9S 54 2 7 •. • 6 13 19 22 • . 385 40 20 58 . .1016 5 115 8 . • 7 100 23 • . 402 91 131 59 • .1033 57 91 9 • • 7 SS 44 24 - . 420 43 109 60 . .1051 . 9 67 10 . • 8 75' 125 '25 . • 437 95 85 61 . .1068 61 43 11 . • 9 63 69^ 26 . . 455 47 Y2- 61 62 . .1086 13 19 t53 TABLES OF GOLD COIN. A TA BLE Tor rccching andp ayiug the Gold Coin ^'o/'Great-Britain andVor- tu gal, r/^ lOOcT/i/^i^or^ 7 grains J accordb (g to Act oj Congress. 277/:5. ( ^ihs 9th3 ^vs. dol.cts. of act. dwt. dol ct^. of a ct. OZ. (Jol. cts. of a ct. 1 •• 3 19 12 • • 10 66 6 28 • 497 77 7 «2 '• 7 ]1 13 • . 11 55 5 '2d • • 515 55 5 3 '• 11 3 14 . . 12 44 4 30 - 533 33 3 4 '. 14 22 \5 . • 13 S3 3 31 . 551 11 1 5 .. 18 14 l6 . • 14 22 o 32 .- 568 88 8 6 - 22 G 17 • • 15 11 1 33 . 586 66 6 7 • 25 2.5 18 . . i6 00 34 . 604 44 4 8 • 29 17 L9 • . 16 88 8 35 . 622 22 2 9 • 33 9 20 . • 17 17 7 36 . 640 00 10 • 37 1 ouncts 37 • 657 77 7 11 • 40 20 1 . • 17 77 7 38 . 675 55 5 12 . • 44 12 o , . 35 55 5 39 • . 693 33 3 IJ . • 48 4 3 . . 53 33 3 40 . 711 11 1 U • 51 53 4 . . 71 11 1 41 . 728 88 8 15 . 55 15 5 . . 88 88 8 42 . 746 66 6 \G • 59 7 6 . . 106 66 6 43 . 764 44. 4 17 . 62 26 7 • . I'-n 44 4 44 - 782 22 2 18 .. 66 IS 8 . . 142 22 2 45 . 800 GO 19 .. 70 iO 9 • . 160 00 46 - 817 77 7 *20 . 74 2 10 . . 177 77 7 47 • 835 55 5 '21 .. 17 21 11 . . }()5 55 5 48 . 853 33 3 :-2 . 81 \3 12 . . 213 33 3 49 • 871 11 1 ' ', . . 85 5 13 . . 231 11 .1 50 . 888 88 8 . . 88 24 jj, . . 248 88 8 51 . 906 66 6 9ihs 15 . . 266 66 6 52 . 924 44 4 *ii t. UiJ.rtS. 9i\icl. 16 . . 284 4i 4 53 . . 942 22 2 1 . . 88 8 17 • . 302 22 2 5\ . 96'0 00 o .. 1 17 7 18 . . 320 00 55 . 977 77 7 3 . . 2 66 6 19 • . S'-J 77 7 56 . 995 55 5 4 . . 3 55 5 20 . . 355 55 5 57 .1013 33 3 5 . . 4 44 4 21 . . 573 33 3 5% .1031 11 1 () • • 5 33 3 22 • ' 391 11 1 '^9 .1048 88 8 7 . . 6 22 2 ■4 -J • . 408 88 8 60 . 1066 66 6 8 ..7 11 1 21. . . 426 66 6 6\ .1084 44 4 9 . . 8 00 25 . . 4-44 44 4 62 . 1 102 22 2 10 . . 8 88 8 26 . . 462 22 9 63 .1120 00 ii - 9 77 7 27 • . 480 00 64 . .1137 77 7 ( 539 ) MERCANTILE PRECEDENTS; BILL OF EXCHANGE. Neubiin/port, Feb. 12, 1804. EXCHANGE for £.1000 sterling.. At twenty clays sight of this uiy first of exchange (second and third of the same tenor and date not paid) pay to John. Parker, or order, One Thousand Pounds Sterling, with ox without further advice from Your humble servant,. WILLIAM PRINCE. Messrs. Dutton & Green, Merchants, LoDdon. BILL OF GOODS,, At an advance on the sterling cos^, Boston, May 5, ISO-K Mr. William Poole,. Bovg/i t of Elmo's Si m m o n d s , 32 ells mode Is. 8fA sterl. £.2 13 4 6*4 yds. striped Nankins Is. 6d. • ' » • 4 l6' 28 . • striped calico 1 6-. C}.-/. • 2 9 4 pieces russel •••... 24 y. • . . . 4 i6 SterL 14 14 4 Exchange 33 J per cent. 4 18 l| £A9 12 5i Advance at 20 per cent. 3 18 53 ^^.23 10 II Dollars 78,48 Fveceivcd his note at 2 months, St 2^0 MERCANTILE PRECEDENTS. FROMISSORY NOTE. Boston, May 5. 1S04. For value received, I premise to pav to Simon Sirniiionds, or order, seventy-, iglit dollais forty-eight cents on demand, with interebt after tv/o months. Attest, William Poole. Saul James. A RECEIPT FOR JN ENDORSEMENT ON A NOTE. Boston, July 12, 1804. Received from Mr. William Poole, (by the hands of Mr. Benjamin I^iintO 1 hii ty-eight dollars seventy cents, which is endorsed on ' -te of May 5, 1804. ciMON Simmon Ds. 38 dols. 70 cts. RECEIPT FOR MONEY RECEIVED ON ACCOUNT. Boston, January 10, 1804. Received from i\Ir. D. Evans^ (by the hands ot Mr. Thomas Dunmore,) Four hundred and flirty dollars on account. 430 dols. G-EORGE Pace. PROMISSORY NOTE BY TWO PERSONS, Kevvluiryport, l'2tli July, 1804. For value received we jointly and sevenilJy promise to pay to Mr. Samuel Rich, or order. Five hundred dollars lifry-four cents, on demand Wftli- interest. Attest, Nathan Sayeotix. William Bolton, Stephen Needy. GENERAL RECEIPT. New- Bedford, March 27, 1804. Received from V.v. N. B. ten dollars Uventy-nine cents in full of all dcnmnds. 10 dols. 29 cts. E. D. MERCANTILE PRECEDENTS. 26l BILL OF PARCELS. A\':d'un/portj June 20, 1S04). Mv. William IIolman Bought o/' Daniel Greei^", 8 lib lis. sugar, \\t. viz, C. q. Ih. C. (f. Ih. No. 1. 5 2 7 5. b 3 UJ 2. 5 1 22 6\ ^ 1 17 3. 6" 13 7. 5 1 7 4. 5 2 13 8. 5 3 U 22 2 27 22 2 i 22 2 I 45 1 Tare 12percwt. 4311 ~ — dais, cti* Neat 40 1 17 at 12 duls. per c\vt, ...•*. 484 83 3 ijbls. sugar, v/r, C. q. lb. 2 2 25 1 3 17 4 2 14 Tare 21lb. per bbl. 1 14 Neat 4 1 at 10 dels. 42 50 3 hhds. molabscs, viz. gals. 101—9* lOS— 5 107—7 316—21 21 295 gallons at 50 cents 147 50 1 quarter cask Malaga wine 25 00 5 cases gin, at 4 dois. 25 cts. 21 25 Dols. 721 07 *l'he ullage is thus uoted. ^62 MERCANTILE PRECEDENTS. INVOICES. INVOICE of 20 hhds. clayed sugar and 10 lihds. coflfbe, shipped by .••... of Boston, in the United States of America, on his own account and risqae, on board the ship , A. B. master, bound for and a market, consigned to the said A. B. for sales and returns, viz, ■ 50 hhds. clayed sugar, viz. B.C. C. q. lb. C. q. lb. ^0. 1 a 20 Ko. 1.* 11 3 14 11. 12 14 2. . 10 3 21 12. 10 2 14 3. 110 13. 10 2 21 4. 12 1 14. 11 3 21 5. 11 1 14 15. 10 1 14 0. 10 3 7 v;. 10 2 7. 10 '2 17. It 2 21 8. 11 7 18. 10 1 14 9. 11 ^1 liJ. ^J 1 7 le. 10 7 20. 10 a u 111 110 2 7 110 2 a Tare 12 per cwt. 197 3 8 neat, at lOdoIs. 25cts. (loh. rt,h 2027 67 30 hhds . coffee, wt. viz. B.C. No. C. 7. /^. r^re. No. C. (/. Ih. Tare. No. 1 a : 10 1. 9 2 7 108 6. 6 1 14 79 2. 9 3 112 7. 6 16 61 3. 10 1 21 106 8. 8 2 4 84 4. 10 2 14 103 9. 9 1 8 91 5. 8 14 94 10.' 10 14 103 48 2 5'23 40 2 18 42;* 40 2 18 423 946 89 18 — 99861b. deduct tare 946 90401b. neat at §1 cts. 1898 40 3926 07 Premium of insuring 4176 dols. 67 cts. at 6 percent. "^ ^^.^ ^^ to corer the amouut' •••♦••• ••- ....• ) *' Bo}«.. 4176 ^7 Bo tom^ fl-c. MERCANTILE PRECEDENTS. INVOICE. 2G3 INVOICE of merchandize on board the brig Swan, A. B. master, shipped by A. M. on his own account and risque, for the West Indies, and consigned to said master for sales aiid rer turns, viz. 140 M.of boards and pbnk, dol. lOdols. 1400 20 M. of white-oak hhd. staves30 6^00 12M. of red'oak hhd. do. 12 144 130 M. shingles 3 390 B. No. 1—18. 1 8 hhds. of cod-fish, 173031b. 4pr.C. 692 12 B. No. 1— 52. 52 bbls. of beef 12 624 E. No. 1—30. 30 bbls. of salmon 10 300 F. No. 1 2. 2 bbls. pork 18 SG L. No. 1 7, 7 casks of rice, neat S9 C. 3 qrs. 21 lb. 4pr.cwt.159 7B 3 M. of hoops 25 75 1300 pair of shoes • • • 50 cts. 650 Dols. 5070 8f Portsmouth, Sept. 7, 1804. Errors excepted, A, M. Mr. Abraham Jones to Waller Brown Br. 1804. Jan. 5. 8. p. Feb. IMar. May 7. 15. '29. 5. For 1 4 9 7 3 o 5 2 barrel of flour Dols lb. coffee • • • 2s, lb. of sugar 1 IrZ. gallons of molasses • • • • os, 9d. quintalsoffish 15^. lb. hysmi tea 8.S. Gd. lb. chocolate 1^. Gd. bushels of corn ••.... 4^. 9d. EiTors excepted. 10 1 1 4 7 o 1 1 33 37 2>7 50 S3 25 5S Dols. 30 23 $(J4 MERCANTILE PRECEDENTS. ACCOUNTS OF SALES. SALES of^O hhds, 7 htls. and 31 hogs coffee, for and on risk of Mr, William Slillman, wenhant in Portland, 1804. — — . ^ Marcli 15 William Edcs, ^0 hhds. wt. 7 ^ , ^^^^ ^ 14376 lb. at 23 cts. per lb. | ^'^'' ^^^^ ^^ IG George Watts, 7 bbls. wt. 1493at23 cts. 343 SQ 17 Petci^ Bates, 31 bags, 5507 23 1266*61 Charges, 4916 48 Advertising* • Dol. 1 46 Storage • 3 50 ^ Commission on .491 6 dols. 48 cts. at 2 J per cent. 122 pi 127 87 Neat proceeds passed to his credit Do/5.478S 6I Errors excepted, &c. SALES of sundry merchandize received per the ship Juno, Capt. Dane, from Machins and disposed of for account and risk of Amos Goodivin, merchant there. Date, To whom sold c -i5 1 i5 tCii 11 C 1 X5 Price a < 1804. dis.cts. dols.cts. June 4 James Yates ^0 3 90 8 Wm. Howe 120 3 27 292 40 27 John Payson 6 12 72 July 4 James Nugent Cash .50 ^22 4 8 7.5 88 437 50 8 Sim. Sands S,'^\6 6 5 20 90 21 Stock 15 9 1:35 29 Paul SImson Vo 3 50 45 50 Aug. 6 Jona. Rose Taken to fiil up 1 1,259 6 7 55 1501 7 .50 1 1 13^22 4,476 15 11' 88 85 Jlemaining unsold, 40 barrels of herring. Charges, viz. -Storage of nsh • DoJs. 10 50 Commission on 1288 dols. 85 cts. at 2J per cent. 32 22 ]S'eat proceeds carried to the credit of his acQOUiit, Errors excepted, &:c» 42 7% Vols. 1246 13 MERCANTILE PRECEDENTS. 565 SALES of l^ hogsheads and 7 barrels of rum, received per the schooner l\ul>i/, Richard Butler, master from Fortsi/touth, for account and risk of Daniel Edwards, 7ner chant thcre» 5 a Date. To whom sold. -a ^ Contents. Amount. P-i 1804. 1 Cts. dols. cts. Maj24iBy Walter King 1 291 io6 29 50 June f By David Jonss 2 ne 100 110 and 106 216 20; [5y Jarne* Ray 4 438 96 108,110,111,109 420 48 24; Jiy Aaron Judson 3 81 95 26l,27| 27 76 95 July 23.ByTljo's Ropes 1 115 951 109 82 Aug. s'ByParsonsicElv 1 25 951 23 87 25 By 3imon Sands 2 222 98 109 113 ^]7 56 Sept. 4 By Miles Youna 1 1 138 96 110 28 132 48 10 By Moses Bliss .^ 1 342f 99 107,104,103,281 339 7 J^jByAiiiosDundas 6 — . 65^ 981 109,162,106 > 111,112, 92 5 622 52 19 7] 2239 2183 2.J Charges. dls. ets. dls. cts. Paid Capt. Butler freight of 19 hlids. rum, at 2 50 47 50 ditto .... 7 bbls. 66 4 62 Porterage 19 hhds. • 40 7 60 ditto 7bb!s. •• 10 70 Gauging 26 caiks 12| 3 25 Cooperage 3 dols. on hhds. 1 dol. 50 cts. on bbls. 4 .50 Advertiiing • • . — 1 25 Coaumisaioii on 2io8 dols. 25 cts. at 5 per cent. 109 41 178 83 Neat proceeds • . Dols. 2009 42 Outstanding in hands of dh. cts. >([oses BHss •..339 7 Amos Dundas ...>.» 622 52 Boston, 25th Sept^mhcr, 1804. Errors excepted, 5cc. Q66 mercantile PRECEDENTS. y nXS of the S hip Hi raw's Cargo, hi/ WiUiam Stiff on. ' ^- lb- lio. Hv. sol. den. lie. sol. deti' ..;, Jl.G^y ]\]\d.(i^-:,wt. nt. 7^^537at33 per 100, 23953 14 2 6 do. (Jo. 6515 3-2 2084 16 2 r\o. do. oiS6 31 662 3 2 .'^.4 do. d). 36658 30 10997 8 2 do. parii^ d:im.-2184soidatauctiuuror 22'6 — , 37924 1 4> 109 Vr. sol. den. 24 !yh]s. beef, at JOl 1 ,3perbbl. 2425 10 7 do. do. 99 8*5 695 18 11 29 do. do. 90 15 2631 15 4 do. do. 83 332 6085 3 11 64 Ih. sol. 13 bbls. pork 136 1768 25 do. porter • 80 20(!0 5 box. liii. con. 169 pice. 96 pr. piec. 16224 1] i:ik.bulter,wt.ll^^9lb, 2 5 pr. lb. 2540 5 5 tl^ousandhoops 240 pr. M. 1200 59 do. sbingles 16 do. 944 15949 feet boards 120 do. 1913 17 7 170 sliakeu hhds. 3} pr.hhd. 1402 10 27992 12 .7 liv. sol. den. 7 2001 17 10 Commission on 7 2001 17 10 at 5 per cent. • • • • 3600 1 10 Liv. 68401 16 Errors Excepted, &c. .1 )i^;hiir.s(-}f>ri.^fs, D/fU/s, Sc. ]y'id on Ship liiraw^ ffji IVm. Sutton, IS'.^'k liv. s. d. liv. s. d, i\i ■, '^ CO o o rr\ CO O cr-, ^ CO o o *r oi ci , -; > p , ^ ^ '^ .i2 O o ,c/ -^ ^ :« o .§ §:?, ^- "3 cr! -^ ^ ^ -^ 3-^1 ^ c/T r^ ' ^ CO rj' ^ '^ 9 CO C-» S3i c c '^'o g o ^ ''t^ -^ -tt ^ jo 5 3 ^ .2 "5 GC O ^ ^^ cri T*. ■[? 3 O .■'^ p cC «-• ^5. £ o CTi'O o ^ r-^ O^ ^ O O o o HH H 5h O 01 rH O pq o ^6$ MERCANTILE TRECEDENTS. O p:5 CO CO o ^6 O oc O ^c C^ O C> O ^ 'f^ •»!!^ r-i to <:o CO CV CO ^ •-^ P3 iS ? Tr, ^ '^ g S^ ;S H '^ '^ '^'^ ^- -- ' o c o Ch H H C-. *^ o MERCANTILE PRECEDEXTS' <^ • Xj H d CTi CTj ^ C/3 . ^ D r^ o b ■~ -■-1 i-^u. -4 1-H f ^ •2 *0 ^ ^j 'O 0/ ♦o vr> Cv Jj 'O C^. -^2 CO t^ iTi i>. »c c^ vC C^ cr. , ;^ <2 <>^ (^ ^ 9 c/ •^ 'T3 • • • » • • O ^ ! * j^ I C; 9 ' *. ^"^ * L^ 1 • • "■^ * t>* o o o ^^^ 0/ Q CO CO Of OD CO CV \^ CO '£ "^S CO ^i) • := f-v. • iO a o> c? I— ( .-i ,__, • ^ C( -»^ C" • -a s- • • c^-^ ^ • 'e Ert^ 3 O 2: C :i J J - 'o >- ^ -- ,^ c ,0 ^o S- ir> O OC ^- ^ «^» c/ --* =^ S ^ ^r ^ p .^^ '^. 5 ^ »r '^ :2^ ^ 5 ^ b ^ « ? £ = - C^ Si s 2^:- &, ;^ .2 s 1 -^^ ^ » "^ ^ in •^ W ^ ^^ ( 271 ) "* BILL OF SALE. TO all people to vvliom this present Bill of Sale shall come, I R, P. of Kewburyporl, in tlic Slate of JM;issachusetts, Merchant, send Greeting ; KNOW YE, That I the said R. P. for and in consideration of the sum of three thousandy two hundred and twriity-two dollars, to me in hand well and Irnl^' paid at or before the ensealing and delivery of these presents, bj S. T. oi the said Newburyport, Merchant, the receipt whereof I do hereby ac- knowledge and am there with fully and entirely satisfied and contented, have granted, burgained and sold, and by these presents do grant, bargain and sell, unto the said S. T. all the hull or body of the good brig Sally, together witU all and singular her masts, spars, sails, rigging, cables, anchors, boats and ap- purteaances, now lying at Newburyport, and registered at the port of New- buryport, the certificate of whose registry is as follows : IN pursuance of an Act of the Congress of the United States of America, en- titled, ** A i. ACT concerning the registering and recording of ships or vessels," 11. P. of Newburyport, in the State of Massachusetts, Merchant, having taken or suhscrihed tha oath required hi/ the said act, and havii.g sworn that he is the onlij owner of the ship or vessel called the Sully, of Neichuryporl, whereof Wit- ii'tm Smith is at present master, and is a citizen of' the United States, as he hath sworn, and that the said ship or vessel ivas built at Salisbury, in the said state, in the year seventeen hundred and ninety-nine, as also appears by a certi- ficate of enrolment, No. 129, issued in this district on the fourth day of August last, now surrendered — and N. S. Surveyor of this district, having certified that the said sltip or vessel has one deck and two masts, and that her length is slxtii- iiine feet five inche'?, her breadth twenty two feet and one half inch, her depth eight feet two inches, and that she measures one hundred and six tons and forty ninetyfifths, that she is a square sterned brig, has no galleries and no figure head, and the said R. P. having agreed to the description and admeasurement above specified, and sufficient secu) ity having been given according to the said act, the said brig has been duly registered at the port of Newburyport. Given under my hand and seal at the port of Newburyport, this first day of January, in the year one thousand eight hundred. To have and to hold the said granted and bargained brig Sally and prem- ises with the appurtenances, unto the said S. T. his heirs, executors, adminis- trators or assigns, to his only proper use, benefit and behoof forever. And T the said R. P. do avouch myself to be the true and lawful owner of the said brigand appurtenances, and have in myself full power, good right and lawful anthorily to dispose of the said brig as aforesaid, and licr appurtenances in manner as aforesaid, and furthermore, I the said R. P. do hereby covenant and agree to warrant and defend the said brig and premises, with the «ppur- tenances against the lawful claims and demands of all persons whaisoever un- to the said S. T. In witness whereuf, I the said R. P. have hereunto set my band and j^eal, ihii tcnlh day of June, iu the year of our Loid one tboiuand cii-ht hundred D; MERCANTILE PRECEDENTS. ]\I)\ Thomas Gibson in interest dols, cis. (laijs. (loLcfs, To Int on 35 00 fr. Jan. 31, '9Cr to Oct. 12/96, 256 1 47 To do. on 2962 19 ..Feb. 2 ...to.. do. ...... 254 123 68 To do. on 2500 42 .-May 31 • .7 427 81 • I", nf, d, 767 48 — 6 IS 25 32 Balance carried to account current » • 417 21 dols. 442 53 Salc;n, August iGth, \7^9. Errors Excepted, THOMAS MERCHANT, V 274- ) CHARTER-PJRTF. THIS Charter-party of afFreigbtment, indented, made and fully conrlude^f upon iliib niiiih day of June, in the year of our Lord, one thousand ci'4it hun- dred, between J. F. of Boston, in the county of Suifolk, and Cornniirnweahh of Massachusetts, merchant, owner of the good slnp Ileltn, of the burden of two liundred tons, or thereabouts, now iying in tlie harbour of Boston, whereof II. P. is at pre>eiit master, on the one part, and C. D, of said Boston, mer- chant, on liie other part, iVityicsscth, That the said J. P. for the consideration liereaiter mentioned, hath letlen to freight tlie aforesaid bhip, with the a|)pur- tenances to her belonging, tor a voyage to be made by the said ship to Lon- don, wliere sh.e is to be discharged (ihe danger of tlie seas excepted) and the said J. P. dalii by these presenis, covciiant and agree with tlie said C D. in manner foilowing. That is lo S'/y, Tlial the said ship in and during the voyage aforesaid, shall be tight, staunch and strong, and sufTiciently tackled and ap- paralled with all things necessary for such a vessel and voyage ; and that it shall and may be lawiul lor the said C. D. his agent« or factors, as well al London as at Boston, to load and put on board the said ship, loading of such goods and merchandize as they shall think pro])er, contraband goods excepted. IN consideration wliereof, the said C. D. doth by these presents agree with the said J. P. well and truly to pay, or cause to be paid, unto him, in full for the ireight or hire of said ship and appurtenances, the sum of three dollars per ton, per calendar month, and so in })r()portion ior a Icss time, as the said ship shall he co.itinued in !he aforesaid service, in sixty days after her return to B;jston And the said C. D. d :\h agree to pay llie charge of victualing and manning said ship and all port cliarges and pilotage during said voya:;e, and to deliver the said iliip on her rct-,'>r:) {^ B'.r'.cn, to (lie owner aforesaid ; r his order. And to the true and faiihlul of all and singular the covenants, |)ay- jnienls and a'^reemcn's afore-mentiontxl, eacli of the p;u-t'es arore-named binds and obliges hnnseil, his executors and mid admi. i,4rators, in the penal sum of two [[(ousaiid d'.;l!ari hi uily by these presents. In witness whereof, the par- ties afDresaid have hereunto interchangeably set their hands and seals the daj tiad year afore-writtcii." J. R. 1 a o 3 Casks Fot / 'hh. Inn cir!. 8 13 /. s. at 80s ;;;; 12 J^i iini!i>^€ 5 |>r. ct. i 15 BILL OF LADING. SHIPPED in good order and well conditioiied by John Roily, in and upon th.e giverj)oo!, to ^■dy,fj'tu-ihree casks of pot ash) cojitaiu' i».^' cii'-ht /;)■.•>• and e}g!itccn cu.t. being marked and num- be.d as in fl'.c niargii:, and are to be delivered in l! e like 7 go(.(l order iwA well coiiditioned, at the afore-itid ju rt of L;vc);;(».ji (the danger of the seas cxeepled ) I'nto ^Tr. J. .f . 37 7 7 ^!;.y or kj !iisa>:;rli!ev|)ay:ni2: fieig! 1 :'.i the K("d goods. Jour pounds Ihill^li sU'iling ptr iou^ \s\ui Uvv per cent. priuia,<:e. in witness yvliereoij the master or pers'T oi' ihe said ship ha'h afhrmed lo three bills oi lading all of thic, tenor and dale, the one of which being acc^uiplishc^i, the other two to stand void. Dated at Newport, Julv Til:^ IL^U. C. ELY. District of Massachusetts District : . . TO WIT : . . BE IT REMEMBERED, That on the seventeenth day of April, in the twenty-fourth year of the Independence of the United States of America, MICHAEL WALSH, of the said District^ hath deposited in this office, the title of a Book, the right whereof he claims as Author, in the words following, to wit: ^ A X£W SYSTEM OF MERCANTILE AllITHMETIC: ADAPTED TO THE COM.MERCE OF THE UNITED STATES, IN ITS DOMESTIC AND rOREIGN RELATIONS; WITH FORMS OF ACCOUNTS, AND OTII'eR WRITINGS, USUALLY OCCURRING IN TRADE BY MICHAEL WALSH.' In conformity to the Act of the Congr^^s of the United States, intituled " An Act for the encourage- ment of learning, by securing the copies of INIaps, Qiart^ and Books, to the Authors and Proprietors of such Copies, during the times therein mentioned." N. GOODALE, Clerk of the District of Massachusetts District A true copi/ of record, Attest^^-^r—N. GOODALE, Clerk. PRINTING^ LeTTER-PRESS <^^ COPPER.PLATE PRIISITING executed in a style of elegance and on reasonable terms at the Office of Edmund M. Blunt, State-Street, Newbnry- port. January, 1806. '» • n tf /c. % o -^ m 1^ N- \ h-^. M^t^