^^;-' :S«/^-r,.^.^-'s^ ^w^# "O^^ University of California • Berkeley A NEW SYSTEM OF JtSERCANTIlS ARZTHMETZq, ADAPTED TO THE eommetce of ttie aJniteir States, IN ITS DOMESTIC AND FOREIGN RELATIONS : WITH FORMS OF ACCOUNTS, AND OTHER WRITINGS USUALLY OCCURRING IN TRADE. BIT IMIICHABZi "V^AZiSH; A. M. ITER EST BREVE PER EXEMPLA. SENECA. FOURTH EDITION. TO WHICH IS ANNEXED A SYSTEM OF SOOXE-KBEPIIVG. SALExM : P'UBLISHED BY JAMES R. BUFFUM, (PROPRIETOR.) PRINTED UY JOHN D. CUSIimG, 1825. DISTRICT OF MASSACHUSETTS, to wit : District Clerk's Office. BE IT REMEMBERED, That on the twenty first day of July, A. D. I8i4, and in the thirty ninth year of the Independence of the United States of America. Edward Little & Co. of the said district, have depos- ited in this office the title of a book, the right whereof they claim as pro- prietors, in the Avords followino^, to wit: " A New Sysiem of Mercantile Arithmetic : adapted to the Commerce of the United States, in its Domestic and Foreign Relations : wiih Forms of Accounts, and other Writings usually occurring in Trade. By Mi- chael Walsh, A. M. Iter est breve per exempla — Seneca. Fourth Edition" In confonnity to the act of the Congress of the United States, entitled, '« An Act for the encouragement of learning, by securing the copies of maps, charts, & books, to the autliors and proprietors of such copies, during the times therein mentioued;" and al^o to au act, entitled *'An Act, supple- mentary to an act, entilled ' An Act for the encouragement of learning by securing the copies of maps, charts and books, 'oihe authors and proprie- tors of such copies during the times therein mentioaed, and extending the benehts thereof to the arts of designing, engraving and etching historical and other prints " WM. S. SHAW. Clerk of the District of Massachusetts Q/MOI RECOMMENDATIONS. A^ewburypnrt^ May 1 , 1 800. We the subscribers having seen Mr. Walsh's New Systein of MER- CANTILE ARITHMEnO, ami being satisfied that it is better calciilat- ed, than any yet publishecl, to fit a youth for the business of the Compt- inii^-Ho'ise, canno*^^ but wish it an extensive circulation. The happ elu- cidadon and extended appiicatioii of the common rules, together wish the many original improvements, while they accomplish the student for com- merce, are also extremely well adapted to' assist and inform the merchanjk, the mariner and the trader, in their variois occupations. nudley A. Tyns,, Mo^es Brown, Ebenezer Stoeker, William Wyer,jun. William Bartlett, Richard Bartlett,jun. Samuel A. Otis,jun. William W. Prout, Tristram Coffin, Michael Little, Boston, May 16, ISOO. We the subscribers having examined Mr. Walsh's New Sv-stem of MEROA.VTILE ARiniMEriC, and being persuaded that it is better calculated than any we have met with, to qualify young men for admis- sion into (.'omptii^g.Hou«es, we wish that it may have an extensive circu- lation. The clear exemplification and pertinent application of the com- mon rules, together wiih the many useful additions and improvements which it contains, will render it extremely useful for the merchant, the mariner, and all the other trading classes of society. Marston Watson, John Lowell, jun. Joseph Rii'^sell, Arnold Welles, jun Jonathan Jackson: John C. Jones, John Codman, St(*phen Higginson, 1 Vi^'^Hl*^ ^it.:^ X 1- iv RECOMMENDATIONS. Salem, October 7, 180«. We the subscribers, merchants of Salem, convinced of the necessity of renderi:ig the forms of business, the value of coins, and the nature of com- merce, more familiar lo the United States as a commercial people, do ap- prove of the MER JANTILE ARITHMEriCof Mr. Walsh, and recommend it as calculated to subserve in ihe best manner the instruction of our youth, and the purposes of a well informed merchant. William Grayyjun. JBenj. Hodges, Benj. Pickf?ian, JYaih. Bow ditch J Jacob Ashton, TVm. Prescott, Jacob Crowninshield, Elias Basket Derby» PREFACE TO THE THIRD EDITION. The merit of Walsh's Mercantile Arithmetic having been submitted to the public, and estab- lished by the most liberal and unequivocal en- couragement, the Editor feels a confidence in offering a third edition of ten thousand copies. It is unnecessary now to urge the superiority of this over every similar production extant. The discernment of men of letters, and the gen- erous spirit of a commercial public, have render- ed panegyric useless by an unprecedented pat- ronage. In the very short period of its exis- tence two extensive impressions have been cir- culated through the country, and orders are al- ready received for a very large proportion of the third. Tlie value of any work must be decided by those to whom it is more immediately useful : and if such persons possess the means of dis- crimination, the decision will undoubtedly be correct. The present publication is adapted as well to assist the researches of Mathematicians, as to facilitate the negociations of Merchants^ A 2 ti PREFACE. Such characters have supported it by their writ- ten approbation, and recommended it by an in- troduction into their own Studies and Compting- Rooms. Schools and Academies have made it the basis of a mercantile education, and it has become an indispensable assistant to every trad- ing class of the community. This impression has received several valuable additions under the general head of Exchange, including the existing exchange w^ith Antwerp, Trieste, Genoa, Venice, Barcelona, and Palermo in Sicily, and many useful rules under each of these particular heads. A new subject is like- wise added, entitled " Arbitration of Exchange," the importance of which will easily be seen 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. But to render the work perfect, they have been minutely considered and cor- rected. The Editor is confident that the present edi- tion will be taken up with the same avidity as the two former, and he assures the public that the work shall not sulfer either in accuracy or beauty, by the liberality of its patrons. EDMUx\D M, BLUNT. Septemhcr^ 1804. PREFACE TO THIS EDITION. There is subjoined to this edition an Intro- duction to Book-Keepiufr^ on the plan of R. Turner, LL.D. with a Waste Book, as an exam- ple for practice, corrected and improved, and calculated for the merchants and traders in the United States. Great simplicity has been used, in order that the learner may attain to a clear view of the principles of this science^ in which being once well grounded, he may apply them to the diversified objects and transactions of complicated and extensive commerce. This treatise has received the approbation of our most intelligent merchants. It having been suggested that an elucidation of the most approved mode of Eook-Keeping by single entry would be useful, a Set of Books has been subjoined, in which the utmost plainness and simplicity have been used. CONTENTS. PAGE Numeration r - - - - - - 1 Simple Addition ..---•. 2 « Subtraction " - - - - - S Multiplication . - - - - 3 Division _ - - - » - 4 Miscellaneous Questions . - - - - 7 Table of Moaey, Weights, Measures, &c. - - - 7 Compound Addition - - - - - l^ Compound Subtraction - - - - - l-^ Practical Questions in Compound Addition and Subtraction - l6 Reduction - - - - - --i8 To find the Contents of Grindstones {To find the value seepage 57)21 Reduction of American Moneys ... - - 22 Compound Multiplication . - - - . 30 Bills of Parcels ... _ - - 30^ Compound Division - - - - - - 37 Decimal FracUons - - - - - - 40 Decimal Tables of Coins, Weights and Measures - - 49 The Single Rule of Three Direct - - - 52 Inverse Proportion - - - - - - 60 Compound Proportion - - - - - 61 Vulgar Fractions -.-..- 64 Practice --..--. 75 Tare and Tret -«.--. 83 Single Fellowship - - - - - - 87 Dotible Fellowship - - - - - - 88 Simple Interest - _ - . - 89 Rule established by the Courts of Law in Massachusetts for mak- ing up judi^ents on securities for money, which r.reupoo in- terest and on which partial payments have been endorsed 104 A Table shewing the number of days, from any day in any month, to "he same day in any other month through the year - J 05 Compound Interest - - - - - - 106 Table shewing the amount of one pound or one dollar for ahy number of years under 33 at the rates of 5 and 6 per cent, per ■annum, compound interest - - - - - 107 Commission and Brokerage - - - - - 109 Jiisurance - - - - - --111 <*rcneial Averajre - - - - - - 112 X CONTENTS. 4 ' 5 PASE. Buying and Selling Stock* - - - - - 114 Dipcount - - - - -^ - - 115 Bank Discount - - - -*- - 117 Equation of Paj-ments - - - - - 120 Barter - 121 L.O s and Gain - - - - - - 123 Alligation Medial - - - - . - -126 Alligation Alternate - - - - - 127 Single Po i ion ... - - - 130 Doable Position - - - - - -131 Exchange with Great Britain . . . . . 131 Ireland . . . . . 133^ Hamburgh . . . . . \iil Holland . . . . .147 Denmark . . . . . 151 Bremen . . , . .153 Antwerp , , , . ,154 Rusja .... 156 Fraiice . . . . 158 Tables for chan|?;ing Livres Sols & Deniers, to Francs & Cen'imes 164- Table for reducing Francs & Centimes to Livres, Sols & Deniers 165 Exchange with Spiin ..... 166 Cadiz ..... 167 BilLoa . . . . . 172 Barcelona . . . , .174 Portu-al . . . , , . 1T# Leghorn . . . . . 178 Naples . . . . . 181 Triesie ..... 1S2 Genoa ..... 184 Venice . . . . 185 Smyrna ..... 1^6 Palermo (in Sicily) . . . ,100 Jamaica and Bermudas . , . 192 Barbidoes 194 Maninico, Tobago and St Christopher's . 19^ French West-Indies . . . .194 Spani-h West Indies .... 198 Calcutta ., ... 200 Bombay . . . . . 201 Madras . . . , . 201 Batavia . . ... 202 China . . . ^ . 204 Manilla ..... 206 Ceylon ..... 206 Japan ..... 207 Tonnage of Goods from the East Indies to Europe . 208 Arbitral ion 4^f Exchange . . , . .210 Mode of Calculating American Duties . . . 212' CONTENTS. * - PAGE. Rates at which all Foreign Coins are estimated at the Custom- Houses of the Unit fd States . . . . 215 Aritiiine icitl Progresfcion . . . - .216 Geometrical Progression . . . . . 2 ' 9 Permutatiofi .. . . . . . . 222 Extraction of the Square Root . . . . 223 Exirac'ionof the tube Hoot ..... 228 Extraction of the Biquadrate Root . . . 233 Ceueral Rule for extracting the Roots of all Powers . 233 Ouodecimals ..... 235 To find the (Contents of Bales, Cases, &c in order to ascertain the freight ^ . - . . . . 237 To fiiid Ships' Tonnage by (^arpenters' Measure . . 238 To find the Government Tonnage of Slips . . . 241 Tables of Cordage . . .... 244 Tablev for receiving and paying the Gold Coins of G. Britain, &c. 246 Tables for receiving and paying the Gold ( oins of France . 247 Tables for receiving and paying the Gold Coins of Spain, &c. 248 Mercantile Precedents . ... . . 249 Bill of Exchange . . . . . . 249 Bill of Goods at an Advance on the Sterling Cost , . 249 Promi'sory Note . . . . . . 2.30 Receipt for an Endorsement on a No! e . , . 250 Receipt for Money received on Account , . . 250 Promissory Note by Two Persons . , . . 250 General Receipt .... . . 250 Bill of Parcels ...... 251 Invoices . . • . . . . 262 Account of Sales ... ... 254 Accounts C urrent • . . . . . 257 Interest Account ...... 260 Bill of Sale ....... 262 Charter Party . . , . . . .263 Bill of Lading - * - . , 264 EXPLANATION OF THE CHARACTERS USED IN THIS WORK. = SIGNIFIES equality, or equal to: as, 20 shillings m one pound: that is, 20 shilling's are equal to 1 pound. + S.fgnifies more, or Addition : as, 6 + G = 12: that is, 6 ad- ded to 6 is equal to 1 2. — Signifies less, or Subtraction : as, 6 — 2=4: that is, 6 less 2 is equal to 4. X Signifii'S Multiplication: as, 6X2 = 12: that is, 6 multi- plied by 2 iS equal to I 2. -7- Signifies Division: as, 6-i-2=3: that is, 6 divided by 2 is equal to 3. Division is sometimes expressed by placing the numbers like a traction, the upper figure being the dividend, and the lower the divisor : thus, ^=9 : that is, 54 divided by 6 is equal to 9 : :: : Proportion: as 3 : 6 : : 9: 18; that is, as 3 is to 6, so is 9 to 18. ^ Prefixed to any numler, signifies that the square root of that number is required. Aline or vinculum, drawn over several numbers, signified, that the number^; under it are to be considered Join% as 8-^+T=:l ; but without the line, 8— 3-f 4=9. MERCANTILE ARITHMETIC. Arithmetic is the art of computing by numbers, and has five principal rules for this purpose, viz. Numeration, Addition, Subtraction, Multiplication, and Division. NUMERATION Teacheth to express any proposed number by these ten characters, 0. 1.2. 3. 4. 5. 6. 7. 8. 9. — is called a cipher, 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 hand, as in the following TABLE. 3 . i -§ o ^3 Though the table consists only of nine places, yet it may be extended to more places at pleasure ; as, after hundreds of millions, read thousands of millions, ten thousantJs of mil- lions, hundred thousands of millions, then millions of mil- lions, &c. TO WRITE NUMBERS. Rule Write down the figures as their values are express- €^5 and supply any deficiency in the order with ciphers. B SIMPLE ADDITION. EXAMPLES. Write down in proper figures the following numbers^ Twenty-nine, Two hundred and forty-seven, Seven thousand nine hundred and one, Eighty-four thousand three hundred and twenty nine, Nine hundred and two thousand six hundred and fifteen, Eighty-nine millions and ninety, Four millions four hundred thousand and forty. Nine hundred and nine millions nine hundred and ninety. Seventy millions seventy thousand and seventy. Eleven thousand eleven hun- dred and eleven, eleven thousand 11000 eleven hundred 1100 eleven 11 Fourteen thousand fourteen hundred and fourteen. fourteen thousand 14000 fourteen hundred 1400 fourteen 14 Total 12111 15414 To express in words any number proposed in figures. Rule. To the simple value of each figure, join the name of its place, beginnmg at the left hand, and reading towards the right. EXAMPLES. 46, Write down in words the following numbers. 199, 2267, 86693, 289'732, 51911911, 1169990,. 9919, 4320, 55000510. SIMPLE ADDITION Teacheth to collect numbers of the same denomination into one sum. EXAMPLES. galls. yds. bushels. 68965 59473 875496 14753 8914 170900 29684 675 574 57693 29 9 171095 171095 SIMPLE SUBTRACTION. 17573 18U041 750010 468 4095 31994 57 83 573 9 7326 74837 As the mercantile method of proving addition is to reckon downwards, as well as upwards, the sums of which will be equal^ if the addition is just, two spaces are left for the work. SIMPLE SUBTRACTION Teacheth to take a less number from a greater of the same denomination, and thereby to show the difference. EXAMPI^S. From Take Rem. Proof yards. 57468532 26587491 30881041 57468532 gallons. From 29689141 Take 17938762 Rem. 11750379 Proof 29689141 3. from 924357 take 565383 Rem. 358974 4. 5. 6. 7. 8. 517684 510090 191191 291619 500910 291872 191939 2957 829 15723 225812 318151 188234 290790 485187 SIMPLE MULTIPLICATION Is a compendious way of adding numbers of the same name. Th^^ number to be multiplied is called the multiplicand. The II (mber which multipliers is called the midtiplier. The number arismg from the operation is called the product SIMPLE DIVISION. MULTIPLICATION TABLE. } 2 3 4 5 6 1 7 8 9 1 10 1 11 12 1 i 4 ^ 8 10 12 |14 16 18 1 2(^ 22 24 j 3| ^^ ^ 12 15 18 21 1 24 27 1 30 j 33 36 4 •^1 8 12 1.6 20 24 1 28 32 36 1 40 44 48 ^5 20 25 30 35 40 45 50 1 55 60 ?1 .2 14 18 24 30 36 142 48 54 .^0| 66 72 21 28 35 42 49 56 63 1 70 1 77 84 , 8 IG 24 32 40 48 1 56 64 72 80 88 96 w 18 27 36 45 54 t63 72 81 1 90 99 108 10 20 30 40 50 1 60 po 80 1 90 100 110 120 1 1 22 33 44 55 66 1 77 88 99 110 1 121 132 12 24 36 48 60 _72_ (84 96 108 120 132 144 EXAMPLES. Multiplicand 5965468 Multiplier ' 2 Product 11930936 4765293 3 14295879 6281947 4 25127788 4. Mult. 2658758 by 5 product 1329379© 5. 9674372 6 58046232 6. 7689657 7 53827599 7. 2674876 9 24073r84 8. 4198543 10 41985430 9. 7491685 11 82408535 10. 2689489 12 32273868 11. 1768735 20 35374700 12. 2*891496 400 1156598400 13. 5749857 78 448488B46 14. 2653294 872 2313672368 15. 78965987 5893 465346561391 16. 562916859 490070 275868665090130 SIMPLE DIVISION Teacheth to tind how often one number is contained in another of the same name. SIMPLE DIVISION. S The number given to be divilfed, is called the dividend. The niiinber by which to divide, is called the divisor. T he number of times the divisor is contained in the divi- dend is called the quotient. The remainder^ if there be any, will be less than the divisor. PROOF. Multiply the quotient by the divisor ; to the product add the remainder, and the sum will be equal to the dividend, iif the work be right. EXAMPLES. Dividend. Divisor 2)694568946 Quotient 347284473 3)2768954584 922984861 — 1 rem. 3 Proof 694568946 2768954584 dividend, quotient. Divisor 52)6495436( 1 249 1 2 52 52 129 249824 104 624560 12 rem. 255 208 6495436 proof. 474 468 63 52 116 104 12 B2? ■m... SIMPLE DIVISION. 4. Divide 8965462 by 6 quotient, Ans. 1494243 rem and 4 6. 3728675 8 466084 3 6. 4654682 9 517186 8 7. 2768967 10 276896 7 o 1949952 11 177268 4 9. 2968967 12 217413 11 10. 5268794 20 263439 14 n. 29619145 40 740478 25 12. 419825367 500 839650 367 13. 296876234 64 4638691 10 14. 47989536925 735 65291886 715 15. 26574983184 8962 2965296 432 16. 53479689236 7684 6959876 2052 17. 4917968967 2359 2084768 1255 18. 3258675689 67435 48323 14184 When the divisor is a compound number, that is, if any two figures, being multiplied together, will make that number, then divide the dividend by one of those figures, and the first quotient by the other figure, and it will give the quotient re- quired. But as it sometimes happens that there is a remain- der to each of the quotients, and neither of them the true one, it may be found by this Rule. Multiply the first divisor by the last remainder, and to the product add the first remainder, which will give the true one, EXAMPLES. Divide 296876234 by 64 8)296876234 8)37109529—2 Quotient 4638691 and 1 X 8 + 2 = 10 remaining. Divide 8757635 by 28 Divide 18957492 by 42 Quot. 312772 and 19 rem. 451368 and 36 rem. Divide 1571196 by 72 Divide 3751749 by 96 Quot. 21822 aQdl2 rem. 39080 and 69 rem. MONEY, WEIGHTS, MEASURES, &c. nr MISCELLANEOUS QUESTIONS. 1. Add 562163, 21964, 66321, 18536, 4340, 279 and 83 together. Ans. t3(:c>686. 2. What number is it, which being added to 'J7vk) will make 110901 ? Ans. lOiiOvf. 3. General Washington was born in the year 1732; how old was hii in 17^9? Ans. 67 years. 4. Add up twice 397, three times 79 1, four times 3176, five times 15880, six times 95280, and once 333040. Ans. 1000000. 5. A cashier received, viz. four hundred and nine dollars, twenty thousand and thirteen dollars, eight thousand five hundred and ten dollars, nine hundred and twenty-eight dol- lars; of which he paid away fifteen thousand fifteen hundred and fifteen dollars : what was the whole sum he received, and how much remains after deducting the paymtmt? Ans. He received ^29860 and there remains ^13345. 6. What is the product of 15927 multiplied by 4009 ? Ans 63851343. 7. 128 men have one half of a prize, worth 34560 dollars, 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 of 14876 dollars, of which A put in 4963 dollars, B 5188 dollars, md C the remainder: how much did C put in? Ans. 4725 dolls. TABLE OF MONEY, WEIGHTS, MEASURES, kc. Federal Money. 10 Mills . - make - - 1 Cent. 10 Cents 1 Dime. 10 Dimes, or 100 Cents - . - l Dollar. 10 Dollars - . „ . 1 Eagle. MONEY, WEIGHTS, MEASURES, &c, English Money. 4 Farthings - - make - - 1 Penny. 12 Pence - « - 1 Shilling^. 20 Shillings - * - - 1 Pound. Pence Table. Shillings Table. d. s. d. s. £. s. 20 are 1 8 20 are 1 30 - - 2 6 30 - - 1 10 40 . . 3 4 40 - - 2 50 - - 4 2 50 - - 2 10 60 -.50 60 - - 3 70 . - 5 10 70 - - 3 10 80 . - 6 8 80 - - 4 90 - - 7 6 90 - - 4 10 100 - - 8 4 100 - - 5 110 - - 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 8 200 - - 10 Troy Weight. 24 Grains make - 1 Pen nyweiffht. 20 Pennyweights - - 1 Ounce. 12 Ounces - - - 1 Pound. Note. By this weight are weighed jewels, gold, silver, and liquors. Avoirdupois Weight. make 16 Drams - 16 Ounces 1 28 Pounds 1 4 Quarters - . - - i 20 Hundred weight - - - - 1 NoTR. By this weight are weighed such commodities as are coarse and subject to waste, and all metals, except golcj and Sliver. Oie pound Avoirdupois i§ equal to 14 «z. 1^' dwt. and 15^ gr». Troy, Ounce. Pound. Quarter. Hundred. Ton. MONEY, WEIGHTS, MEASURES, &c. 9 Apothecaries VVkight. 20 Grains - - make - - 1 Scruple. 3 Scruples ----- 1 Dram. 8 Drams - - - - - - 1 Ounce. 12 Ounces - - - - - i Pound. Note. Apothecaries use this weight in compounding their medicines; but they buy and sell their drugs by Avoirdupois Weight. Cloth Mf.asurk. 4 Nails ma [ke - 1 Quarter. 4 Quarters - 1 Yard. 3 Quarters - - 1 Ell Flemish. 5 Quarters - 1 Ell English. 6 Quarters - - - 1 Ell French. Long Measure. 3 Barley Corns make 1 Inch. 12 Inches - 1 Foot. 3 Feet - 1 Yard. 51 Yards, or 161 Feet - 1 Pole, Rod or Perch. 40 Poles, or 220 Yards - 1 Furlong. 8 Furlongs - 1 Mile. 3 Miles - 1 League. 60 Geographical, or > 691 Statute Miles S - 1 Degree. Note. In this measure, length only is considered. Land or Square Measure. 144 Square Inches make 1 Square Foot. 9 Feet - - - - 1 Yard. 301 Yards, or > i d i i> i t^ , 272I Feet \ ' - ' ^ ^^^^' ^^^"^ ^^ P^^^^' 40 Poles or Perches - - 1 Rood. 4 Hoods - - - 1 Acre. Note. This measure respects length and breadth. Wink Measure. 2 Pints - - make - 1 Quart. 4 Quarts 1 Gallon. 42 Gallons 1 Tierce. 63 Gallons 1 Hogshead. 84 Gallons 1 Puncheon. 2 Hogsheads 1 . - - 1 Pipe or Butt. 2 Pipes or i Hogsheads - - 1 Tun Note. The wme gallon eontams 231 cubic mcke§. 19 MONEY, WEIGHTS, MEASURES, &c. Alr and Befr Measure. 2 Pints 4 Quarts 8 Gallons - 9 Gaiions 2 Firkins - 2 Kilderkins 54 Gallons - 3 Barrels make 1 Quart. 1 Gallon, 1 Firkin of Ale. 1 Firkin of Beer. 1 Kilderkin. 1 Barrel, 1 Hhd. of Beer. 1 Butt. Note. The ale gallon contains 28^ cubic inches. Cubic or Solid Measure* make 1 Foot. 1 Yi^rd. 1728 Inches 27 Feet - 40 Feet of Round Timber, or j 50 Feet of Hewn Timber 128 Solid Feet - Note. 8 feet in length, 4 in breadth, and 4 in height, making 128 solid feet, contain a cord of wood. This mea- sure respects length, breadth and thickness. 1 Ton or Load. I Cord of Wood. Dry Measure. 2 Pints make 1 Quart. 2 Quarts - 1 Pottle. 2 Pottles - - 1 Gallon. 2 Gallons - - - _ 1 Peck. •4 Pecks - - - - 1 Bushel. 2 Bushels - » - - 1 Strike. 4 Bushels . . 1 Coom. 8 Bushels - - - - - 1 Quarter. 36 Bushels - - - - 1 Chaldron. 5 Quarters - - 1 Wey. 2 VVeys - . 1 Last. Note. The gallon, dry measure, contains 268J cubic inchei- Time. 60 Seconds - - make - - 1 Minute. 60 Minutes - - - - - 1 Hour. 24 hours - - - - - 1 Day. 365 Pays 1 Year. Note. 365 days, 5 hours, 48 minutes, 57 seconds, make a solar year, according to the most exact observation. COMPOUND ADDITION. 11 The number of days in eacL tnuuih Ls thus found: Thirty dixys hath September, April, June. an»l Nou!mI>er; February hath menty-eight alone, And all the rest have thirty one. When the year can be divided by 4 w thout a remainder, it is Bissextile or Leap Year, in which February hath 29 days. COMPOUND ADDITION Teacheth to collect numbers of different denominations into one total. Federal Money. dlb. ctS' m. dlls. cts. m. r/4 71 3 396 14 4 198 19 3 147 19 5 157 14 4 149 57 9 196 76 9 157 83 8 English Money. JE. s. d. £. s. d. 149 14 H 814 16 6^ 387 19 Bi 198 18 H 259 - 16 H 376 14 9^ 874 17 H 226 16 7f 678 15 H 174 17 lOi Troy Weight. lb. oz. dwt. gr- lb. oz. dwt. gr- 48 7 14 id 83 11 15 22 95 4 17 22 15 6 16 19 27 5 14 15 21 8 19 23 65 19 16 33 9 15 14 19 6 13 15 46 4 13 17 12 COMPOUND ADDITION. AvoiHDUPOis Weight. ton. cwt. qr. lb. oz. dr. cwt. qr. lb. 18 17 1 4 13 13 36 15 3 16 13 15 29 15 2 19 12 13 14 16 3 27 14 12 16 19 2 25 13 10 57 17. 1 14 15 9 593 1 19 187 3 19 159 2 25 283 3 13 146 2 18 259 1 22 Apothf;caf\ies Weight. lb. oz. dr. sc. gr. lb. oz. 6^r. sc. ^r. 3 7 5 1 17 2 5 3 2 11 1 3 2 2 13 1 2 2 1 14 2 5 3 2 14 3 3 5 2 13 5 4 2 1 15 5 5 4 1 12 5 2 2 2 17 2 9 3 2 15^ 2 3 1 2 18 I 4 2 17 Cloth Measure. yd. 571 qr.^nl 1 3 e.Jl. qr nl. 873 2 3 181 qr. 2 2 e.e. 56 qr. 1 2 184 2 2 196 2 2 196 3 3 19 2 3 196 2 3 158 1 1 157 4 2 14 3 2 283 3 2 147 2 3 168 3 3 26 4 3 146 2 3 326 2 2 193 5 2 83 2 2 375 3 2 194 2 1 214 2 3 57 3 3 "" Wine Measure. *""""■ ""*" " 187 hhd, 1 . gall. qt. pt. 17 3 1 ton. 176 3 .^a// qt. pt. 16 2 1 56 3 15 2 1 59 2 57 3 9 1 29 3 1 8 3 14 2 36 2 18 2 1 17 2 19 J 217 3 57 1 1 168 1 38 2 56 1 46 2 1 25 2 52 3 COMPOUND ADDITION 13i Ale and Beer Measure. hhd. gall qU pU hhd. gall, qt pt 49 38 2 1 78 17 3 1 38 45 3 1 19 16 2 1 57 48 2 1 15 51 3 1 49 -37 1 1 76 43 2 1 57 26 2 1 23 26 3 1 28 18 3 1 ' Measure. 52 38 2 1 Dry qr, bush,^ 57 4 ph. qt 2 1 chal. bush. pk. qt 576 31 1 3 19 5 3 1 19 2/ 2 2 38 6 2 3 56 15 3 5 27 7 3 7 26 8 2 4 5 3 1 4 9 9 16 9 2 2 3 14 15 2 S 72 5 3 2 iNG MeASUR' 32 26 3 2 Lo E. deg. mil. fur I 217 17 7 f.po. /t. 19 14 in. 9 be. 1 mil. furl po. yd. ft 876 7 13 4 2 733 17 4 16 13 3 2 129 6 26 2 I 283 53 5 19 12 2 2 167 4 19 3 2 346 26 6 23 13 4 1 157 3 15 2 2 189 32 3 27 14 5 2 280 2 27 I 1 176 14 2 15 15 6 2 194 5 32 2 2 921 15 4 18 16 7 1 176 4 18 5 2 Land Measure. acr. roo 741 1 . per. 19 acr. roo. per. 870 3 19 69 3 29 19 2 16 15 2 16 54 3 37 37 3 14 129 2 26 16 2 13 187 3 14 29 3 27 136 2 19 14 COMPOUND SUBTRACTION. Time. yrs. days. hrs. min. sec. 187 149 14 13 12 146 126 16 ^6 16 69 186 19 39 19 28 140 21 46 35 7 119 22 18 26 146 146 19 57 19 yrs. days. hrs. min. se€. 300 169 14 16 17 19 186 17 16 16 46 147 15 19 19 87 196 23 46 47 157 219 14 23 16 46 138 15 42 13 COMPOUND SUBTRACTION Teacheth to find the inequality between numbers of di- vers denominations. Federal Money. dolls, cts, ms. dolls, cts. ms. From 1901 95 1 435 00 1 Take 992 97 2 9 15 9 English Money. £ s. d. From 191 11 3^ Take 114 16 2i dolls, cts. tn*, 170 10 3 9 50 2 s. 304 1 9 81 From 389 18 Oi Take 9 19 4 126 16 H 100 n 11 5 2f Troy Weight. Ihs. oz. dwt. grs. From 87 11 11 13 Take 19 11 14 22 lbs. oz. dwt. grs, 27 10 \h 22 15 9 16 23 COMPOUND SUBTRACTION Avoirdupois Weight. ton. cwt. qr. lb. oz. dr. From 100 10 1 11 14 13 Take 16 13 1 18 12 15 16 ewt. qr. lb. 69 1 11 19 3 27 lb. 02. dr. sc. gr. From 2 3 4 1 13 Take 1 7 6 2 10 Apothecaries Weight. lb. oz. dr. sc. gr. 2 1 3 1 15 1 4 2 2 17 yd. qr. n. From 251 1 2 Take 127 3 3 Cloth Measure. elljl. qr. n. ell eng. qr. n. ellfr. qr. n. 189 2 1 419 13 389 2 2 120 2 2 174 3 2 189 5 3 Wine Measure. tun. hhd. gall. qt. pt. From 591 1 13 1 1 Take 126 2 56 3 1 tun. hhd. gall. qt. pt. 800 1 50 2 1 149 2 61 3 1 Ale and Beer Measure. hhd. gall. qt. pt. hhd. gall. qt. pt. From 571 19 3 1 100 36 2 1 Take 198 53 2 1 9 27 3 1 Dry Measure. qr. bu. gall. qt. chald. bu. gall. qt. From 38 4 5 3 69 21 3 2 Take 17 5 1 2 49 33 5 3 Long Measure. deg. m. furl. p. f. in. b. From 819 13 1 19 11 3 1 Take lo;i i'j 2 27 16 8 2 m. furl. p. f. 219 3 14 11 209 7 15 12 COMPOUND SUBTRACTION. Land Measure. acr. TOO. per. From 591 1 U Take 129 3 15 50 i 3 13 190 2 21 Time. yrs, da. hr. m. sec. From 171 143 11 14 19 Take 128 174 19 51 14 acr. TOO. per. 219 2 21 156 1 36 yrs. da. hr,. min. sec. Six ill 15 23 52 389 190 21 48 54 PRACTICAL qUESTfOJYS IM COMPOUND ADDI^ tiojY and subtraction. 1. Cast up the following sums, viz. twenty-three shillings and Ave pence, one pound and nine pence, seven shillings and eleven pence three iarlhings, twenty pounds thirteen shillings and nine pence, fifteen pence three farthings. £ s. d. 1 3 5 1 9 7 ^»? 10 13 9 1 3? Ans. £23 7 U Proof £23 7 ^ 2. Twenty dollars and four cents, ^we dollars and three mills, eighty-two cents, six dollars and ^\q mills. Ans. 31 dolls, m cts. 8 m. 3. Seventy dollars, three dollars and three cents, thirty- four cents and four mills, eighty dollars and a half, six dol- lars and a quarter. Ans. ! 60 dolls. 1 2 cts. 4 m. 4. Ten pounds and three pence, forty-five shillings and ten pence halfpenny, thirty-seven shillings and four pence three farthings, nine pound^ and three farthings, one shilling and six pence farthing, eighty-two shillings and four pence half penny. Ans. £ 27 7 5f PRACTICAL QUESTIONS. 1'^- 5. Thirty dollars six cents and a half, Miy three cents and three quarters, eleven cents and a quarter, nine dollars elev- en cents and a half, fifty four cents. Ans. 40 dolls. 37 cts. 6. Take three shillings and four pence from one pound two shillings and a penny. Ans. \Ss. 9d. 7. From £5 2*. id. take nine shillings and six-pence half- penny. Ans. £4 1^2 6i 8. Take twenty shillings and three farthings from £8. Ans. £6 19 11^ 9. From 18 dollars take eight mills Ans. 17 dolls. 99 cts. 2 m. 10. Take 53 dimes from 53 eagles. Ans. 524 dolls. 7 dimes or 70 cts. 1 1 . A merchant bought 1 1 2 bars of iron, weighing 56 cwt. 1 qr. 11 lb. of which he sold 59 bars, weighing 29 cwt 3 qrs. 21 lb: how many bai-s has he remaining, and what is the weight? Ans. 53 bars, weighing 26 cwt. 1 qr. 18 lb. 12. Kequired the total weight of 4 hogsheads of sugar, weighing as follows, viz. No. 1, 9 cwt. 2 qrs. 21 lb. No. 2, 10 cwt. 3 qrs. 23 lb. No. 3, 3 cwt, 2 qrs. 25 lb. No. 4, 9 cwt. 3 qrs. 17 lb. Ans 39 cwt. 1 qr 12 lb. 13. A ropemaker received 3 tons 15 cwt. 3 qrs. 14 lb of henip to be wrought, of which he delivered in cordage 34 cwt. I qr. 22 lb : how much remains? Ans. 2 tons 1 cwt. 1 qr. 20 lb. 14. Received 57955 mills, 4953 cents, 1913 dimes, and 45 eagles: required the total sum? Ans. 748 dolls. 78 cts. 3 mills. 15. A cashier received, viz. one hundred pounds and nine pence half-penny, three thousand seven hundred and lour pounds ten shillings, twenty thousand and ninety pounds two shillings and eleven pence- three farthings, of which he paid away sixteen thousand sixteen hundred and sixteen pounds : how much has he on hand? Ans £6278 13 9:|^ 113. A farmer bought three pieces of land, measuring, viz. the first piece 21 acres 3 roods 19 poles; the second, 37 acres 2 roods 29 poles; the th^rd, 27 acres 2 roods 25 poles; of which he sells 15 acres. 2 roods 39 poles : how much has he remaining? Ans. 7- acres 1 rood 34 poles. 17. A has paid B £9 15 6i, £19 11 9?, £l4 19 7^, and 51.9 5''/ on account of a debt ol' £50: how much is there still unpaid? Ans. £2 18 9^ C2 18 REDUCTION. REDUCTION Teacheth to change numbers from one denomination to another, without losing their value. Rule. When the Reduction is descending, multiply the highest denomination by as many of the next less as make one of the greater, adding to the product the parts of the same name, and so on to the last. When the Reduction is ascending, divide the given num- ber by as many of that denommation as make one of the next higher, and so on to the denomination required, and the last quotient with the several remainders (if any) will be the answer. The proof is by reversing the question. Federal Money. 1. hi 53 dollars how many mills? 63 dolls. 10 i Or decimally, by adding a cipher for 630 dimes. each inferior denominatiouj thus : 5300 cents. 10 dll.d.c.m. Ans. 53000 mills. 53,000 2. In 14000 mills how many dollars? 10)14000 ( Or decimally, by separating the hg- 10)1400 ^ures — counting from the right to the ( name required, thus, 10)140 dll.d.c.m. Ans. 14 dolls. 14,000 3. In 57935 mills how many dollars ? Ans. 57 dolls. 93 cents 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 9 cents. 6. How many cents in 46 dollars ? Ans. 4600. 7. In 19U004 mills how many dollars ? Aqs. 190 dollars 4 milla. REDUCTION. 19 English Mowey. 1. In £91 11 3-J how many farthings? 20 1831 shillings. 12 Proof 4)87902 12)21975—2 21975 pence. 4 20)1831—3 £91 11 3i Ans. 87902 farthings. 2. How many pounds in 3175 farthings? Ans. £3 6 If 3. In 195. 8Jd how many farthings? Ans. 947 farth. 4. How many pounds in 9752 pence? Ans. £40 12 & 5. In £40 how many crowns of 6*. Id. each ? Ans. 139 crowns and 4 shillings and 1 1 pence. 6. How many pounds in 493 dollars? Ans. £l47 iSs. 7. In 143 pence, how many shillings ? Ans. l]s. i\d» 8. Reduce 38^. 4^-c^. to halfpence ? Ans. 921 halfpence. Prove the above'answers to be right. Troy Weight. 1. In 15lb. Troy how many grains? Ans. 86400 grs. 2. How many ounces in 5749 dwt. Ans. 287 oz. 9 dwt. 3. In 11 oz. 13 dwt. 13 grs. how many grains? Ans. 5605 grs. 4. How many grains in 15 spoons, each weighing 6 dwt. 15 grains? Ans. 2385 grains. Avoirdupois Weight. 1. In 19 tons 14cwt. 2 qrs. 19 lb. 11 oz. 13drs. how many drams? Ans. 11316157 drs. 2. How many cwt. in 9563 lb ? Ans. 85 cwt. 1 qr. 15 lb. 3. In 13 cwt. 3 qrs. 21 lb. how many pounds ? Ans. 1561 lb. 4. How many mess-pieces of 4J lb. and SJ- lb. of each an equal number, in 31 cwt. 1 qr. 12 lb. of beef? Ans. 439 pieces of each. Wine Measure. 1. In 25 tuns of wine how many pints ? Ans. 50400 pints«. 20 REDUCTION. 2. How many hogsheads in 4935 quarts ? Ans. 19 hhds. 36 galls. 3 qts* 3. In 3 hhds. 13 galls. 2 qts. how many hail' pints? Ans. 3240 half pints. Cloth Measure. 1. In 158 yards how many nails? Ans. 2528 nails. 2. How many ells English in 5932 nails? Ans. 296 ells 3 qrs. 3. In 29 pieces of holland, each containing 36 ells Flem- ish, how many yards ? Ans. 783 yards. Long Measure. 1. In 29 miles how many inches ? Ans. 1837440 inches. 2. How many furlongs in 19753 yards? Ans. 89 fur. 1 73 yards. 3. In 590057 inches how many leagues ? Ans. 3 ieag. 2 fur. 110 yds. 1 ft. 5 in. Time. 1. How many hours in 57 years, allowing each year to be 365 days 6 hours ? Ans. 499662 hours. 2. In 57953 hours how many weeks ? Ans. 344 weeks, 6 days, 17 hours. 3. How many days from the 19th of March to the 23d of September followmg ? Ans. 188 days. 4. How many days from the 24th of May, 1797, to the 15th of December, 1798? Ans. 570 days. Land Measure. 1. In 41 acres 2 roods 14 perches, how many rods? Ans. h654 rods or perches. 2. How many square rods in 7752 square feet ? Ans. 28 rods 129 feet. 3. In 5972 perches, how many acres ? Ans. 37 acres 1 rood 12 perches. Solid Measure. 1. In a pile of wood 96 feet long, 5 feet high, and 4 feet wide, how many cords ? Ans. 1 5 cords. . 2. In 82 tons of round timber how many incbes? Ans. 5667840 incbes. 3. What are the contents of a load of wood, 6 feet long, 4 feet high, and 2^ feet wide ? Ans. 3J feet. REDUCTION. 21 Grindstones are sold by the cable foot, commonly called a stone, and the contents are thus found : Rule. To the whole diameter add half of the diameter, and mnltiply the sum of these by the same half, and this pro- duct by the thickness; divide this last number by 17!^8, the inches in a cubic foot, and the quotient is the contents or answer required. EXAMPLES. 4. How many cubic feet in a grindstone, 24 inches dia- meter, and 4 inches thick ? 24 diameter. 12 half diameter. •36 12 432 4 thickness. 1728)1728 Ans. I foot. 5. What are the contents of a grindstone, 36 inched dia- meter, and 4 inches thick ? 36 18 54 18 432 54 972 4 1728)3888(21 3456 432 4 1728)1728(1 1728 Ans. 2^ cubic feet. 22 REDUCTION. AMERICAJV MONEYS. To change New-England and Virginia currency to Federal monoy, the dollar being 6 shillings. Rule. As the value of a dollar is equal to three tenths of a pound, when pounds are given to be changed, annex three ciphers to the sum, and divide the whole by 3 j the quotient is the answer in cents. EXAMPLES. 1. Change £523 to Federal money. 3)523000 2. 184 3. 29 4. 57 5. 219 6. 81 7. 127 1743331 cents. Ans. 1743 dolls. 33^ cts. Change the following sums, viz. j£ dolls, cts. Ans. 613 35^ 96 66f 190 730 270 423 33i When pounds and shillings are given, to the pounds annex half f he number of shillings and two cipher-*, if the number of shillings In the given sum be even ; bat if the number be odd, anriex naif the number, and then 5 and one cipher, and divide by 3 ; the quotient is the answer in cents. PXAMPIES. 1. Change £69 18^. to FedcriU money. 3)59900 ! i* n>C>|- cts. Ans. 1 99 dolls. 66| cts. 2. Change £93 )ps. to Federal money. 3;V':^«'50 1 — m — 3121.61 cts. Ans. 312 dolls. 16| cts. Chaftg'e the followmg sums, viz. £ s flolls. cts. 3. 129 13 - - Ans. 432 16| 4. 63 15 - - - 212 50 5. 27 18 - - - 93 6. IP/^ 19 - - - 609 83i. 7. 57 16 - - - nn: 6>j| 8. 121 7 - - - 404 50 REDUCTION. ' 23 When there are shillings, pence, &c. in the given sum, annex ibr the shillings as belbre directe(?, t^tk! to these add the farthings in the given pence and farlh.rigs, observing to increaBs their number by one when they exceed 12, and bj two when they exceed 37, and divide as before. EXAMPLES. 1. Change £21 8s. 4^(1. to Federal money. 3)21419 4 is armexed to the pounds for half the shillings, and 19 for the farthmgs in 7139| cts. ^d. and excess of 12. Ans. 71 dolls. 39| cts. 2. Change £117 16^. 2d. to Federal money. 3)117808 392691 cts. Ans. 392 dolls. 69^ cts. 3. Change £721 9*. I X^d. to Federal money. 3)721497 In this example 4 is annexed to the pounds for half the even shillings, and 47 for the 240499 cts. farthings in W^d. and excess of 37, and then 5 is added to the figure next to half the shillings, making it 9 in place of 4 for the odd shilling. Ans. 2404 dolls. 99 cts. 4. Change £ 29 11 2i to Federal money. 3)29559 9853 cts. ' Ans. 98 dolls. 53 cts. Ghange the following sums, viz. , dolls, cts. - Ans. 86 62*. 81 94 4128 46f 8. 2001 1 3^: - - - 6670 2if 9. 153 17 6"* - . - 512 91| £ 's. d. 5. 25 19 9 6. 24 11 7f 7. 1<2>38 10 91 24- REDUCTION. A TABLE For changing Shillings and Pence into Cents and Mills* MIL skill. shiil. 6kilL shilL skdl. 1 2 3 4 5 pence. cts. m cts m. cts, m. cr;y. wi. cts, m. cts, m. 16 7 33 3 oO 66 7 83 3 1 1 4 la 1 34 7 51 4 68 1 84 7 o 2 8 19 5 36 1 52 8 69 5 86 1 3 4 2 20 9 37 5 54 2 70 9 87 5 4 5 6 22 3 38 9 55 6 72 3 88 9 5 7 23 7 40 3 57 73 7 90 3 6 8 3 25 41 7 58 3 75 91 7 7 9 7 26 4 43 59 7 76 4 93 8 11 1 27 8 44 4 61 I 77 8 94 4 9 12 5 29 2 45 8 62 5 79 2 95 8 iO 13 9 30 6 47 2 63 9 80 6 97 2 Jl 15 3 32 48 6 65 3 82 98 6 To change Federal Money to JV. England ^ Virginia Currency, RvLE. When the sum is dollars only, multiply it by 3, and double the first figure of the product for shillmgs, and the rest of the product will be pounds. When there are cents in the given sum, multiply the whole by 3, and cut off' 3 figures of the product to the right hand as a remamder. Multiply this remainder by 20, and cut off 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* four figures, and proceed as above. EXAMPLES. 1. Change 872 dollars to New-England currency. 872 3 £ s, 261 12 Ans. 261 12 REDUCTION. 25 2. Change 1971 dls. 96| cts. 3. Reduce 1259 dls. 89 cts. to Massachusetts currencj. and 7 ms. to' Mass. currency. 1971 96i 1259 89 7 £ 3 3 ;591,590 £377,9691 20 20 ^.11,800 5.19,3820 12 12 c?.9,600 eZ.4,5840 4 4 /•.2,400 /.2,3360 Ans. £591 11 9l Ans. £377 19 4^ A TABLE For changing Cents into Shillings^ Pence and Farthings, cts. Cts. CIS. cts. cts. cts. cts. cts. cts. 10 ^0 rJO 40 50 60 70 80 90 cts. d. ,. d. s. d. .. d. ^ d. ^. d. 5. rf. s. d. 5. c^. *. (i. 7J < n I ^ 2 4? 3 3 71 4 2^ 4 91 5 4| 1 3 4 8 i 3 1 10] 2 5^ 3 Of 3 8 4 3 4 101 5 51 2 'i 8-? 1 S^ I n 2 6i 3 4 3 8| 4 3f 4 11 5 61 .3 2} 9i I 4:- 1 'i| -2 7 3 2-i 3 91 4 4| 4 Uf 5 7 4 n 10 1 ^i 2 0.^ 2 7| 3 2f 3 10 4 51 5 01 5 7f 5 ■H lOf 1 6 i l| 2 8J: 3 31 3 lOf 4 6 5 11 5 81 e; ^ 11} 1 6| 2 S ^ 9 3 4 3 lU 4 6f 5 2 5 9 7 h 1 OJ 1 l-l .. 2| 2 9f 3 5 4 Oi 4 71 5 2| 5 9f o '>-i 1 1 ! 2 3} 2 lOf 3 5f 4 1 4 8 5 31 5 101 '^ t'l 1 1 If ' ^>i 4 4 2 1 H 3 61 4 If 4 8f 5 4 hi>l To change JSliw- York and North-Carol ina currency to Federal mrmey^ the dollar being eight shillings. Rule. Prop ae the eiveii sum by the rule for New- England money, and divide by 4 : the quotient is the answer in c ent S. m EXAMPLES. 1. Change £461 to Federal money. 4)461000 115250 cts. Ans. 1152 dolls. 50 cts. D 26 REDUCTION. 2. Change £419 10*. S^d. to Federal mOney. 4)419535 1048831 cts. x\ns. 1048 dolls. 83f cts. To change Federal money to JVew-York and North Carolina currency. Rule. As for Massachusetts currency, using 4 as a multi- plier instead of 3 ; the value of a dollar being equal to four tenths of a pound. EXAMPLES. 1. Change 1684 dollars to New- York and North-Carolina currency. 1684 4 Ans. £673 12 2. Change 1048 dolls. 83f cents to New-York currency. 1048,831 4 419,535 ^0 10,700 12 8,400 4 1,600 Ans. £419 10^. ^\d. To change New-Jersey^ Pennsylvania^ Delaware and Maryland currency to Federal money ^ the dollar being Is. 6d. Rule. As the value of a dollar is equal to f of a pound, multiply the given sum, when it is pounds only, by 8, and di- vide by 3, for dollars. If there be shillings, kc. increase the sum in pence by ^ of the whole sum for cents. EXAMPLES. 1. Change £471 to Federal money. 471 8 3)3768 Ans. 125G dollars. REDUCTION. 27 2. Change £480 19s. 9d. to Federal money. 480 19 9 20 9619 12 S) 11 5437 1282631 cents. Ans. 1282 dolls. 63^ cts. To change Federal money to JYew-Jersey^ Pennsylvania^ Dela- ware and Maryland currency. RuLK. Multiply the sum, when in dollars, by 3, and di- vide by 8, for pounds. If there be dollars and cents, multi- ply the given sum by 90, and the product (rejecting two figures on the right) is pence ; or deducting yV of the sum gives the pence likewise. EXAMPLES. 1. Change 1256 itollars to Pennsylvania currency. 1256 3 8)3768 Ans. £.471 2. Change 1282 dolls. 63^ cts. to Pennsylvania currency- 128263^ Or yV)< 282631 90 12826J- 12)115437,00 12)115437 20)9619—9 20)9619—9 Ans. £480 19 9 £480 19 9 as before. To change South-Carolina and Georgia currency to Federal money^ the dollar kcing 4s. Sd. Rule. As the value of a dollar is equal to ^\ of a pound, if the sum be pounds only, multiply it by 30, and divide by 7, for dollars. If there be shillings, &c. annex two ciphers to the pence in the given sum, and divide by 56, the pence in a dollar, the quotient is the answer in cents. 23 REDUCTION. EXAMPLES. 1 . Change j£28 to Federal money. 28 30 7)840 120 Ans. 120 dolls. 2. Change £11 4 8 to Federal money. 11 4 8 20 224 12 8X7=56 8)269600 7)33700 4814f cts. Ans. 48 dolls. 14fcts. To cJiange Federal money to South-Carolina and Georgia currency. Rule. Multiply the dollars by 7, and divide by 30, for pounds. If there be dollars and cents, multiply by 56, and the product (rejecting two figures on the right) is the an- swer in pence. examples. 1. Change 540 dolls, to S, Carolina and Georgia currency. 540 7 3|0)378|0 Ans. £126 2. Change 48 dolls. 14f cts. to South Carolina currency. 4814f 56 56 2 28884 7)112 24070 16 16 12)2696,00 20)224—8 114 8 Ans. £11 4 8 REDtfCTJON. 1^1; To change Canada and JVova-Scotia currency to Federal moncy.^ the dollar being 5 Shillings. Rule. As the value of a dollar is equal to one fourth of a pound, multiply the sum, when in pounds, by 1, for dollars. When there .are shillings, &c. reduce the given sum to pence, annex 2 ciphers, and divide by 60, for cents. EXAMPLES. 1. Change £36 Canada currency to Federal money. 36 Ans. 144 dolls. 2. Change £528 12 6, Canada currency, to Federal money. 20 Or thus, 528 10572 4 12 2112 lOshill. == 2 6|0)1268700|0 2^. 6^^. = 50 211450 cts. 2114 50 Ans. 2114 dolls. 50 cts. To change Federal money to Canada and JVova-Scotia currency,- Rule. Divide the sum in dollars by 4 for pounds. If there be dollars and cents, multiply the given sum by 60, and the product (rejecting two figures on the right) is the answer in pence. examples. 1. Change 144 dollars to Canada currency. 4)144 Ans. £36 2. Change 2114 dolls. 50 cts. to Canada or Nova-Scotia currency. 211 450 60 12)126870(00 • 2!0)1057|2— 6 528 12 6 Ans, £528 12 30 COMPOUND MULTIPLICATION. COMPOUND MULTIPLICATION Is the multiplying of numbers of different denominationg by a simple figure or figures, whose product shall be equal to a proposed number. I. When the quantity does not exceed 1 2, multiply the price by the quantity, and the product will be the answer. EXAMPLES. Multiply £19I 17 8^ £913 11 9f by 2 5 Ans. £383 15 5 £4567 19 05 Itiply £980 19 llf by 12 £209 18 4^ 9 1. What will 7 yards of shalloon come to at 3s. bd, per yard? s. d, 3 5 7 £1 3 11 s. d. £ .. d. 2. 4 lb. tea - ■ 6 8 - - 16 8 3. 5 bushels rye - 5 9 - - 18 9 4. 6 gallons wine 7 5 - - 2 4 6 6. 7 quintals fish - 19 6 - - 6 16 6 6. 9 cwt. iron ■ 29 10 . - 13 8 6 7. 1 1 gallons brandy 8 5- - 4 12 7 8. 1 2 quintals fish 22 10 - - 13 14 11. If the number or quantity exceeds 12, and is to be found in the table, multiply by its component parts. EXAMPLES. s. d. 1. 14 yards durant at 2 5 2 4 10 Ans. £1 7 13 10 COMPOUND MULTIPLICATION. 31 s- cZ. 2. 16 yards silk, at 4 9 3. 20 lb cotfee 1 9i 4. 2o g-ailons rum 6 5,^ 5. 45 cwt- iron 29 6 6. 56 yards broadcloth 28 7 7. 6S pair shoe!* 9 3 8. 84 qui 11 ta is tish 18 6 9. lUO gallons molasses 3 ^ 10. 121 bushels corn 4 3 11. 144 gallons brandy 5 •f £ #. d. 3 16 1 15 10 9 1 5 66 7 6 80 8 29 2 9 77 14 17 5 10 25 14 3 40 13 To multiply by fractional pa rts^ as |, }, J, ^c. Rule. Multiply the price by the upper figure of the frac- tion, and divide the product by the lower, the quotient will be the answer ; but when the upper figure is not more than one, dividing the price or sum by the lower figure gives the answer. EXAMPLES. 1. What is f of a yard of cambrick worth, at 12^. 6d, per yard? 12 6 3 8)37 6 Ans. 4s. Q^d. 2. What is f of a yard of broadcloth worth, at Sbs. per yard ? 35 Or thus, 2)35 3 4)105 Ans. 26^. Sd, 2)17 6 price of half a yard* 8 9 price of a quarter. 26 8 3. One quarter of a yard of fine linen, at 7^. 6d. per yard. 4)7 6 1 10J Ans. 1^. lO^df. 4. Multiply £4 5 3 by i, or take i of it. 3)4 5 3 Ans. £18 6 32 COMPOUND MULTIPLICATION. 5. Multiply £9 6^. Sd. by |, or tak^ f of it 9 6 8 7 8)65 6 8 Ans. £8 3 4 III. When the number does not exceed the table, and it^ cannot be found in it, find the nearest to it, either less or greater; then, after having found the price of this number, add or subtract the value of so many, as it is less or greater than the given number. EXAMPLES. 1. 37 bushels corn, at 4*. l\d. per bushel. 4 11 G 1 9 6 6 8 17 price of 36 bushels. 4 11 price of 1 bushel. 2. 3. 4. b. 6. 7. Ans. £9 111 price of 37 bushels. s. d. ^ £ s, 171 yards of shalloon, at 2 8 Ans. 2 6 23| lb. coffee, 1 10^ 2 4 bl\ gallons rum, 4 2} 12 1 87J yards baize, 2 1 9 2 109 quintals fish, 14 6 79 1371 gallons molasses, 3 8i 25 6 d. 6 1^- fV". When the number is above the table, find the price of each figure, as in the following : COMPOUND MULTIPLICATION. 33 EXAMPLES. 178 yards of muslin at 4^. bd. per yard. 4 5 10 2 4 2 10 22 1 8 price of 100 yards. 15 9 2 price of 70 115 4 price of 8 Ans. £39 6 2 price of 178 yards. 2. 284 J gallons of molasses, at 3s. 9^d. per gallon. 3 9^ 10 1 17 11 10 18 19 2 2 37 18 4 price of 200 gallons. 15 3 4 price of 80 15 2 price of 4 1 lOJ price of ± Ans. £53 18 8| price of 284 ^ gallons. s. d. £ s. d, 3. 183 gallons gin, at 7 5 Ans. 67 17 3 4. 346 quintals fish, - 23 9 - 409 13 9 5. 769| lb. coffee - 1 10 - 70 11 2^ 6. 809^ yards baize - 2 1^ - 86 2i 7. 2375^ galls, of molasses 3 5J - 410 15 3J 8. Three barrels of N. E. rum, containing 31, 32|, and 33i gallons, at 45. l\d. per gallon. Ans. £22 7 5^. 9. Four hogsheads of molasses, containing 97^, 99 j, 105^ and 111 J gallons, at 3^. 8|fl^. per gallon, are delivered by A to B, to whom he owed 258 dollars. It is required to know the balance, and in whose favour it is ? Ans. 4^. 1 ^ci. in favour of B. 34 COMPOUND MULTIPLICATION. When the amount of a cvvt is required at a certain rate per lb. Rule. Find the price of one or two quarters, and multi- ply the product by the component parts of a cwt. EXAMPLES. 1. 1 cwt. of flour, at 3c?. per lb. 3 7 1 9 14 price of two quarters. 2 Ans. £l 8 price of one cwt. Or by inverting the question thus, 9 4 the price of 112 lb. at Id. per lb. £\ 8 the price of 112 lb. at 3c^. per lb 2. 2 cwt. flour - 2id. per lb. - £2 6 s 3. 3 cwtr rice 2f - - 3 17 4. 4 cwt. iron 31 - - 6 1 4 5. 5 cwt. indigo 8*. 11| 250 le 8 1. What will 40U0 feet of boards come to at 38^. 4d. per thousand? 1 18 4 4 m Ans. £l 13 4 2. 3596 feet of boards at 365. per thousand. 3596 In this example three figures are pointed off 36 as a remainder, and the fourth figure of the product of this remainder, multiplied by 12, 21576 is set down for pence. The fourth figure 10788 of the product of the last remainder multi- plied by 4 gives the farthings. 12M,4 ^i'. Ans. £6 9 51 COMPOUNn MULTIPLTCATION. 35 853 feet of boards at 305. per thousand. 853 30 25,5905. Ans. £15 7 4. 3231 feet of 3 inch. W. 0. plank 225^. 5. 8637 2i - - IdO;?. 6. 960 2 - - 1005. 7. 888 ^ pine, IOO5. £36 6 11^ 64 15 6i 4 16 4 8 9^ Plank are sold per thousand of 2^ inches, th^ usual thick- ness for planking vessels ; and as there are generall}' other dimensions, as 2 and 3 inches, the price of each is regulated hy the price of the i?|, adding to it. or subtracting from it, in such proportion as may be agreed on wheu purchasing. In the above example, taken from an actual sale, I of 1 5O5. was added to it, for the. three inch, and i deducted from it, for the two inch, making the three inch 2255. and the two inch IOO5. per thousand. WEIGHTS AND MEASURES, lb, oz. dwt. grs. lb. oz. dwt. grs. Multiply 14 9 14 17 825 8 19 2§ by 5 8 Product 74 13 13 6605 11 19 8 ton. cwt. qrs. lb, cwt. qr. lb. oz. drs. 19 17 3 25 17 1 14 11 14 9 7 tun. hhd. gal. 87 1 57 5 tun. P- hfid. gal. 28 1 1 62 7 What is the weight of 47 casks of rice, each weighing 2 cwt. 1 qr. 23 lb. ? Ans. 115 cwt. 1 qr. 17 lb. 36 COMPOUND MULTIPLICATlOlSr. BILLS OF F Mr, George Rowk bought of Wii s. 8 pair worsted hose at 4 5 do. thread do - 3 3 yards kerseymere - 14 6 do muslin - - 4 2 do. tammy - - 1 4 shawls - - - 7 'ARCELS. Boston^ .LIAM RUSSEI d. 6 - . 2 - - - . 2 - - 8 - - 6 - - June 28, £\ 2 1 1 1804. 16 15 10 2 5 3 4 10 2 £7 12 2 25 dolls . 36 cts. Portsmouth., \ 9th May ^ IS04, Mr. Thomas Barrington bought of Simon Wilson, If lb. tea, 4^ bushels corn 6 quarts brandy 6 do. rum 7A yards chintz 4 6 5 4 8 4 per ga 7 6 do 2 5 SaU LeMUKL KlNG^ No. 1, at 4 2, 5 3, 5 9, 10 10, 11 11, 12 K 12, 14 - £0 T lOi illon £3 11 0| r. Amos Giles bought of ] 10 boys' coloured hats, 12 do. 4 do. 4 do. 4 do. 6 do, • 6 men's plain black do 1 1 dolls. 84i cts. ^, 23d May ^ 1804. 6 - £2 5 - 6 - - - - - £18 7 Trunk 1 4 £19 11 65 dolls. 16| cts. COMPOUND DIVISION. 3 Boston^ I Oih Au^ust^ 1 803. Mr. Nathan Perkins bought o/ George Allen, 641- yards striped nankins, at 2^. " £6 9 32 ells mode, - - 3^. 28JL yards calico, - -25. 4d. 2" gross gilt coat buttons, \us. 6c/. 3 pieces russel, - 34s. £21 10 6 71 dolls. 75 cts. JVezvburyport^ Sept. 10, 1803. Mr. William Sands bought of Stephen Nowland, 2 pieces muslin, at 30^. £3 25 yards Irish linen, 28-J do, stormont calico, 28^ do. red do. 1 pi?ce durant do. 2 pieces blue shalloon, 501. yards dimity, 3 pieces persian, it 305. 2s. ., 2.9. ed. 2s. 2d. 565. 575. 6d. 25. 6d 845. £39 12 3 152 dolls. 4 cts. Received payment by bis note of tlie above date, at three months, for Stephen Nowland^ Abraham Trusts. COMPOUND division Teacheth to find how often one nuruber is contained In another, of different denominations. examples. 1. Divide £19 145. 9^0?. by 2. 2)19 \\ 9^- An^'. £9 17 4-J 2. Divif^e £900 1 1 9] by ;^. Ans. £/.00 n 1 \\ Prove this answer to be right. E 38 COMPOUND DIVISION. 3. Divide £121 7^. 9Jc/. by 5. Ans. £24 55. e^d, 4. Divide £248 95. \^d. by 9. Ans. £27 12s. l^d, 5. Divide £1057 Is. 3d. hy 12. Ans £88 I5. 9}d. II. If the divisor exceeds 12, and it be found in the table, divide by its component parts. EXAMPLES. 1. Divide £278 C5. 9d. between 15 men equally. ^)278 8 9 "i^y^s 13 9 Ans. £6 3 9" each. 2. If 20 lb. of indigo cost £7 55. lOd. what is it per lb.? Ans. 75. o^d, 3. If 24 yards of durant cost 625. 6d. what it per yard ? Ans. 25. l}d. 4. If 72 bushels of corn cost £20 95. 6d. what is it per bushel? Ans. 55. H^d. 5. If 108 lb. of tea cost £45 135. 6d. what is 1 lb worth? Ans. 85. b^d. 6. When £166 135. 4d. is paid for 500 gallons of "rum, what is it per gallon ? Ans. 65. Sd. 7. If 1000 gallons of molasses cost £209 75. 6t/. what is it per gallon ? Ans. 45. 2|c?. III. If the divisor cannot be found by the multiplication of small numbers, as in the preceding examples, divide by ft as i;^ the following EXAMPLES. 1. Divide £46 I5. lid by 37. £ 5. d. 37)46 1 11(1 4 11 An?. 37 9 20 37)181(4 J 43 33 12 37)407(11 87 37 37. COMPOUND DIVISION. 39 2. Divide £33 13^. S\d, by 23. Ans. £l 9^. 3|c?. 3. If 345 quintals offish cost £409 135. 9d. how much is it per quintal ? Ans. 23*. 9c?. Dividing by fractional parts, as J , |, f , &c. is the same as multiplying^ by them. See the Kule under Case 11, in Com- pound Multiplication. J. How much is J of £91 11 5. 3d.l 91 11 3 Or thus 2)91 11 3 3 2)45 15 7 1 one half the Slim. 22 17 9 J one quarter. 4)274 13 9 Ans. £60 13 5i £t)8 13 5] 2. Divide £126 195. Sfc?. by f . Ans. £101 11 7. 3. If the whole of a ship is worth £960, what is f worth? Ans. £6U0. 4. Iff of a ship was sold for £1056 2s. Id. what was lh% whole valued at? Ans. £1689 15 4. IV. Having the price of a hundred weight, to know ho^ much it is per pound : Rule. Find the price of 1 or 2 quarters, and then divide by the component parts. 1. If 1 cwt. of steel cost £4 6*. 4t/. what is it per lb.? 4)4 6 4 Or thus 2)4 6 4 4)1 1 7 price of 1 qr. 7)2 3 2 price of 2 quarters. 7)0 5 43 8)0 6 2 Ans. 91 per lb. 9i per lb. 2. If 1 cwt. of flour cost 235. 4d. what is it per lb.? Ans ^d. o. When 2 cwt. of sugar cost £8 175. 4c?. what is it per !b.? Ans. d^d. 4. If 5 cwt. of iron cost £8 155. Od. how much is it per lb.? Ans. 33c/. I. \ mate and 3 seamen have to receive 600 dollars, for recapturino- their vessel, of which the mate is to have two share;^, and each seaman one share ; how much is the part of each? Ans.— The matp's part is 240 dolls. and each seaman"*? 120. 4t) DECIMAL FRACTIONS. 2. Capt. M. of the Jason, meets at sea with the wreck of the Hawk, of Boston, from which he takes sundry articles, which sell for 521 dollars 64 cents; two thirds of this snm are awarded to the owners of the Hawk ; of the other third, the owners of the Jason are to have one half; and the re- mainder is to be divided between the captain, mate, and nine seamen, allowing the captain three shares, the mate tivo^ and the seamen one share each; what are the respective parts of those concerned? dolls, cts. Ans. The owners of the Hawk, 347 76 owners of the Jason, 86 94 captain, - - 18 f'\^ mnte, - - - 12 12 each seaman, * 6 21 DECIMAL FRACTIONS. A Decimal Fraction is that, whose denominator is an unit, with as many ciphers annexed to it as the numerator has places, and is usually expressed by writing the numerator only, with a point before it called the separatrix ; thus, y^^, r o\) tWo? ^re decimal fractions, and are expressed hy ,5 ,25 ,125 respectively. The figures at 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. Ciphers placed at the right hand of decimals make no al- teration in their value ; for ,5 ,50 ,500, &c. are decimals of the same value, being each equal to ^ ; but when placed at th^ left hand, the value of the fraction is decreased in a ten- fold proportion; thus ,5 ,05 ,005, Sac. are 5 tenth parts, 5 hundredth parts, 5 thousandth parts, respectively. DECIMAL FRACTIONS. 41 The different value ot figures will appear plainer by the- following TABLE. INTEGERS. DECIMALS. 2, 2 ,2 2 ,© 2 2 ,0 2 20000, 002 200000, 0002 2000000, 0000 f\ n f\ n n (\ f\ n A rk A A From this table it appears, that as whole numbers increase in a tenfold proponion, from units to the left hand, so decimals decrease in the same proportion, to the right ; and that in decimals, as in whole numbers, the place of a figure determines its relative value. ADDITION OF DECIMALS. Rule. Place the given numbers so that the decimal points may stand directly under each other, then add as in whole numbers, and point off so many places for decimals to the right as are equal to the greatest number of the decimal places in any of the given numbers. EXAMPLES. 263,51 42,23 2,4 149,28 18,47 ,5 29.3,53 9,3 26,17 181,59 52,384 ,7 129,4 2,1 5, 1020,31 124,484 31,47 E2 42 DECIMAL FRACTIOIS-S. Required the sum of twenty-nine and three tenths, tTn*e^ hundred and seventy- four and nine millionths, ninety-severr and two hundred and fifthy-three thousandths, three hundred and fifteen and four hundredths, twenty-seven, one hundred and four tenths. Ans. 942,993009. Required the sum of ten dollars and twenty-nine cents, ninety-three cents and three mills, nine cents and 6 mills, and two dollars and eight mills. Ans. 13 dolls. 32 cts. 7 ms. SUBTRACTIOJy OF DECIMALS. Rule. Place the given numbers so that the decimal points' mny stand directly under each other, and then point ofi' the decimal places as in addition. EXAMPLES. From 219,42 87,26 67 311 Take 184,38 19,4 9,375 11,11 35,04 67,86 47,625 299,89 From two thousand and sixteen hundredths, take one thou- sand and four and four millionths. Ans. 990,159996. From twenty-four thousand nine hundred and nine and one tenth, take fourteen thousand and twenty-nine thousandths. Ans. 10909,071. Take eighty-five and seven hundred and thirty-seven thousandths 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 dolls. 98 cts. 6 ms. MULTIPLICATION OF DECIMALS. Multiply exactly as in whole numbers, and from the pro- duct cut off as many figures for decimals at the right hand as there decimals in both the factors ; but if the product should not have so manvy supply the defect by prefixing ci^ phers. Decimal fractions; EXAMPLES. 4^ Multiply 36,5 by 7,27 29,831 ,952 ,29 ,029 3,92 196 2555 730 2555 59662 149155 268479 2235 3528 392 Product 265,355 28,399112 768,32 Multiply ,285 by ,8 ,285 ,003 124 ,06 Prorluct ,2280 ,000855 7,44 Note. To multiply defcimal fractions by 10, 100, 1000, &c. is only to remove the separatrix so many places towards the right as there are ciphers : Thus, 7,362937 ("10 \ (73,62937 TV.T !*-^i u ) 100 f . 1736,2937 Multiply by ^,^^^ \ IS l^.^^^.^ (iOOOo) (73629,37 Multiply twenty-nine and three tenths by seventeen. Ans. 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 qUESTIOJVS. 1. How much will 93 yards of shalloon come to at 53 ctV. p,er vard ? 93 ,53 279 465 49,29 Ans. 49 dolls. 29 cts. 2. At 21 cents 9 mills per lb. what will 187 lb. of coffee come to ? Ans. 40 dolls. 95 cts. 3 mills. 44 DECIMAL FRACTIONS. 3. What will 27 cwl. ot iron come to at 4 dollars 56 cents per cwt.? Ans. 123 doiis. 12 cts. 4. How much will 281 yards of tape come to at 9 mills per yard? Ans. 2 dolls. 32 cts. 9 mills 5. What will 371 yards of broadcloth come to at 5 dollars 79 cents per yard? Ans. 2148 dolls. 9 cents. 6. How much will 29 J yards of mode come to at 75 cents^ per yard? Ans. 22 liolis. 12 cents 5 mills. 7. What will 23,625 feet of boards come to at 8 dollars 2& cBnts per m.? 23,625 8,25 118125 47250 189000 194,90625 Ans. 194dlls. 90cts. 6ms. I 8. How much will 712 feet of boards come to at 14 dol- lars per thousand ? Ans. 9 dolls. 96 cts. 8 ms. 9. What will 25,650 feet of clear boards come to at 17 dolls. 50 cts. per thousand ? Ans. 448 dolls. 87 cts. 5 ms. (Ills, cts* dlls. els. m. 10. 15,859 feet clear boards 11. 812 do. 12. 376 do. 13. 31,496 merch'ble do. 14* 269 . do. 15. 4, 1 14 refuse do. 16. 393 maple do. 17. 57 mahogany 18. 195 gallons molasses 19. 181) do. rum 20. 243 yards baize 21. 197 feet clear boards divisiojY of decimals. Rule. Divide as in whole numbers, and from the right hand of the quotient point off as many places for decimals as the decimal plac;^,s in the dividend exceed those of the divi- sor* If the places of the quotient are not so many as the 17 50 per m. 277 53 2 14 11 36 8 12 75 4 79 4 8 251 96 8 6 75 1 81 5 3 37 13 86 4 8 per foot 31 44 32 18 24 57 per gall. 111 15 93 175 77 23 per yard 55 89 2 per foot 3 94 DECIMAL FRACTIONS. 45 i:i>Ie requires, supply the defect hy prefixing ciphers. If at auY time there be a remainder, or the decJmal places in the divisor are more than those in the dividend, cipi.ors may he annexed to the dividend, and the quotient carried to any de- gree of exactness. ),863972(, 828 009391 EXAMPLES. ,853)89,000(104,337, 853 kc 359 276 837 828 3700 3412 2880 2559 92 92 3210 2559 6510 5971 539 The vario^is kinds that ever occur in division are inclu- ded in the following cases, viz. Divide ,803 by ,22 Ans. 3,65 ,803 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 + 222 3,65 60,821 + 222 365 ,60821 + As multiplying by 10, 100, 1000, &;c. is only removing the separating point of the multiplicand so many places to the right hand as there are ciphers in the multiplier, so to di- vide hy the s;ime is only removing the separatnx in the same manner to the left. 4$ DECIMAL FRACTIONS. PRACTICAL qUESTlONS, 1. When butter is sold at 12 cents 8 mills per lb. hoW m^ny lb. ma)' be bought for 224 dollars ? ,128)224,000(1750 128 960 89G 640 640 ^ns. 1750 ib. Here the ciphers annexed to the dividend being equal t© the decimal places in the divisor, the quotient is a whole number. 2. If 673 bushels of wheat cost 786 dolls. 73 cents 7 miyjs, \yhat b it per bushel ? 673)786,737(1,16^ 673 1137 678 4G43 4038 6057 6057 Ans. 1 doll. 16 cts. 9 miUs. in this example, as the divisor is a whole number, three places are pointed off in the quotient to equal those in the -dividend. 3. If 493 yards cost 4 dolls. 43 cents 7 mills, what is it per yard? Ans. mills. 4. if 125 gallons of molasses cost 95 dollars, what is 1 gallon worth ? Ans. 76 cents. 5. If '^05 yards of durant cost 107 dollars 62^ cents, what i^ It per yard ? hp%. 52^ centfe. DECIMAL FRACTIONS. 47 REDUCTIO.Y OF DECIMALS, Case I. To reduce a vulgar fraction to its equivalent decimal. Rule. Divide the numerator by the denominator, and iJ^e quotient will be the decimal required. EXAMPLES. 1. Reduce J to a decimal. 4)3,00 ,75 2. What is the decimal of | ? Ans. ,5 3. What is the decimal of } ? ,25 4. What is the decimal of -j\ ? ,1S 5. What is the decimal of ^J ? ,63 6. Express J decimally. ^876 Case H. To reduce numbers of different denominations to their equivalent^ decimal values. Rule I. Write the Sfiven numbers perpendicularly under one another for dividends, proceeding orderly from the least to the greatest. II. Opposite to each dividend, on the left hand, place such a number for a divisor as will bring it to the next su- perior name, and draw a line between them. III. Bei^in with the highest, and vvriie the quotient of each divisioi^, as decimal parts, on the right hand of the dividend next below it, and the last quotient will be the decimal sought. EXAMPLFS. 1. Reduce 145. Hd, to the decimal of a pound. 4 2 1 2 5,5 20 14,4583 Ans ,7239 2. Reduce 15 shillings to the decimal of a pound. Ans. ,75 3. Reduce 3 qrs. lo ibs. to the decimal of a cwt. Ans. .9107] 14- 4. Reduce 2 qrs 2 nails to the 'i^cimnl of a yard. Ans ,GiiJ5 Sft Reduce 14 galls. 3 qts. to the dcciniai of a hog>:. exceed 37. EXAMPLES. •1. Find the decimal of \3s. 9^d. by inspection. 36 half of 125. 5 for the odd shilling. 39 farthings in 9|cf. 2 for excess of 37. ,691 2. Find by inspection the decimal of 155. OJc^., 9s. 3^d. 195. C>-pi,, 3s.^Qd. k 2s. uy. Ans ,784 ,465 ,978 ,175 ,148. Cask IV. To find the value of any given deci?nal in the tenns of the integer. Rule 1. Multiply the decimal by the number of parts in vhe next less dcDomination, and cut off as many places for the remainder so the .right hand as there are places in the given decimal. II. Multiply the remairider by the parts in the next inferior denomi- nation, and cut off a remainder as before. III. Proceed in this manner through all the parts of the in*e^er, and tlie several denominations standing on the left hand make the answer. EXAMPLES. 1. Find the value of ,691 of a pound. ,691 20 13,820 12 9,840 4 3,360 Ans. 13s. 9jci. 2. What is the value of ,9 of a shilling? Ans. lU^rf. 3. What is the value of ,592 of a cwt. ? Ans. 2 qrs. 10 Ih. 4 oz. ir^-fdrams. 4. What is the value of ,258 of a tun of v/ine ? Ans. I hhd. 2-f galls. 5. What is the value of ,1278,^ o^ n yo.wl Ans. 4G days 15 hours 57 min. 574-ser. 49 Decimal Tables of Coin, Wp.tGHT and MEA!?rRe. TABLE 1. IvvciLisH Goi?r. £, 1 th^ Integer. 19 18 IF IG ir, -4 13 12 n 10 ptnrc 4 3 2 1__ farth. 3 1 dec. •y/i. 1 1 ,95 9 ,9 8 .85 7 .3 6 75 5 .7 4 ,65 3 ,6 o 55 I .5 dec .45 ,4 ,35 .3 ."25 .15 1 0, TABLE IIL Troy Weight, 1 lb. (he Integer decimals. .020833 ,0!0'6r;6 ,0125 ,0083:13 ,004166 dtcimul ,00311' ,00'^:0fU3|> OOiOlUi ^TABLE li. .'V.XG. Coin. I shidl ^OMG \IicAg. l/oo/ 1 he ftilpo^er. ence ar d ichcs 6 5 4 3 2 1 farth. 3 2 1 decimals, .5 .416666 ,333333 ,25 .166666 ,083333 Ounces the Fenct in Table, same as, tht last] penny ■ ei((ht 10 9 8 7 6 . 5 4 3 2 1 i^rains. \2 11 10 9 decimal'. ,041666 ,0375 .033333 .0-29166 :o-5 020833 016666 0125 .008333 _ .004166_ decimals. ,002083 001910 ,001736 ,201562 .0;.1389 ,0U! >15 ,001042 .00(i^(»3 ,0006«>4 ,00052 1 ,000347 ,000173 decimals. ,0625 ,041666 ,020833 1 oz. the Inte^^ir. PenuT/ wt. the. tame an Shil/in;rg {j^ ^/^ first Table. grains. decimals. 12 ,025 11 022916 iO .020833 9 ,01875 8 ,01fi666 7 ,014583 grains 6 5 4 3 2 1 decimals. ,0125 .010416 ,008333 .00625 ,054166 ,202033 TABLE IV. Avoirdupois VVt. 112 lb. the Irifrger., qrs 3 2 1 ibTT 14 13 12 11 10 9 8 7 6 5 4 3 2 I ouncf 8 7 6 5 4 3 2 1 3 2 1 dtcimuls .75 __,25 decimal 9. ... 25 ,116071 ,107143 ,098214 ,089-28f> ,08^^07 ,07!42;J ,0625 ,053571 ,044643 .0:^5714 .0267o'3 ,017857 ,008928 derrmaf*. ,0- 4164 ,003306 ,003348 ,00.7S0 ,00223^ .001674 .0011:6 ,000558 decimals ,000418 ,000270 ,000139 50 Decimal Tables of Coin, Weight and Measure. TABLE V. Avoirdupois Wt. 1 lb. the Integer. dtcimals. ,4375 ,375 ,3125 ,25 ,1875 ,115 ,0625 drms. 8 7 6 5 4 O 2 1 decimals. ,03125 ,027343 .023457 ,019531 ,015625 ,011718 ,007812 ,003906 TABLE VL LiaTJiD Measure. 1 iim the Integer. 1 tals> 100 90 80 70 60 50 40 30 20 10 9 8 7 G decimals, ,396825 ,357141 ,317460 27 *238005 JPf:412 ,150730 ,119047 ,079365 ,039682 ,035714 ,031746 ,027 ,023809 l^als. decimals- ,010841 ,015873 ,011904 ,007936 ,003968 ftnts. 4 3 2 1 decimals. ,001984 ,001488 ,000992 ,000496 A Hhd. the Integer. gals decimals 30 ,476190 20 ,317460 10 ,158730 9 142857 8 ,128694 7 ,111111 6 ,095238 5 ,079365 4 ,063492 3 ,047619 2 ,031746 1 ,015873 pints. 3 2 1 decim,als, ,005952 ,003968 ,001684 TABLE VIL Measure, Liquid, Dry. 1 Gallon. 1 Quarter. fn(cger. pf. I dcctm. I bu. 4 I ,5 14 3 I ,375 I 3 decim. ,25 ,125 bu. 1 qpt. 1 decim. I pk. 3 I ,09375 I 3 2 I ,0625 I 2 1 I ,03125 I 1 decim.als. ,0234375 ,015625 .0078125 decimals, ,005859 ,003906 ,001953 I q.pks. I ^ I 2 Ipfs. 3 12 1 TABLE VIIL Long Measure. 1 Mile the Intej^er yards. decimals 1000 ,568182 900 ,511364 800 ,454545 700 ,397727 600 ,340909 500 ,284091 400 ,T2n72 300 ,170454 200 ,113636 100 ,0568.18 90 ,051136 80 ,045454 70 .039773 60 ,034091 50 ,028409 40 ,022727 30 ,017045 20 .011364 10 ,005682 9 ,005114 51 Dfximal Tables of Coin, Weight and Measure. \f^ yards. dtcimals 8 ,004545 7 ,003977 6 ,003409 5 ,002841 4 ,002273 3 ,001704 2 ,001139 1 ,000568 feet. 2 1 decimals. ,0003787 ,0001894 inch. decimals. 6 ,0000947 5 ,000079 4 ,0000631 3 ,0U0^.'474 2 ,0000319 1 ,0000158 TABLE IX. Time. 1 Year the Integer. Monlha flit same a? Pence in the second Tabie. day* 365 300 ^•00 100 90 80 70 60 50 40 30 20 10 9 decimals. UOOOOOO .821913 ,547945 ;2r3973 ,246575 ,219178 ,19^781 ,164383 ,136986 ,109589 .082192 ,054794 027397 ,024657 lays. 8 7 6 5 4 3 o 1 dtcimals ,021918 ,019178 ,016438 ,013698 ,010959 ,008219 ,005479 ,002739 1 Day the Integer. hoars. 12 11 10 9 8 7 6 5 4 3 2 1 min. 30 20 10 9 8 7 6 5 4 3 2 1 decimals. ,5 .458333 ,416666 ,375 ,333333 ,291666 ,25 ,208333 .166666 ,125 083333 041666 decimals. .020833 013888 ,006944 ,00625 ,00555 ,004861 ,004166 003472 ,002777 ,002^)83 ,001388 ,000694 TABLE X. Cloth Measure 1 YarJ the lateger Quarters the same as Table IF. nails. decvmals. ,125 ,0625 TABLE XI. L£AD Weight. 1 Father the Integer. hund 10 9 8 7 6 5 4 3 2 1 qis 2 1_ ' IbT 14 13 12 11 10 9 decimals. ,512820 .461538 ,4102J6 ,358974 ,307692 ,256410 .205128 ,153846 .1025 4 ■0512 82 dtcimals 025641 ,012820 . dtcimals. ,0064102 ,0059523 .0054945 005- 366 ,0045787 ,0041208 ,0036630 0032051 ,0027472 ,0022893 ,0018315 ,0013736 ,0009157 ,0004578 SINGLE RULE OF THREE DIRECT. SINGLE RULE OF THREE DIRECT. The Single Rule of Three Direct teaches, from three Tiumhers given, to find a fourth, that shall he in the same proportion to the third as the second is to the first. \C more requires jnore^ or less requires less^ the proportion 1? direct. Rule 1. Make the number that is the demand of the ques- tion the third term, the number that is of the same name or quality the first term, and the remaining number will be the middie term. Reduce the first and third numbers into the same, and the irccond into the lowest denomination mentioned. 2. Multiply the second and third numbers together, and divide the product by the first, and the quotient (if there be no remamder) is the answer, or fourth number required. If after division there be a remainder, reduce it to the next denomination below that to which the second number was reduced, and divide by the same divisor as before, and the quotient will be of this last denomination. Proceed thus with all the remainders till you have reduced tliem to the lowest denomination, which the second number admits of, and the several quotients taken together will be the an- swer required. The method of proof is by reversing the question. EXAMPLES. 3 . If 2 yards of cloth cost 4^. what will 1 25 yards come to ? yds. s. yds. yds. £, s- yds. li' 2:4:: 125 Proof. If 125 : 1 2 10 : : 2 4 20 2)500 250 .2 20)250 Ans. .£12 1© 500 125)500(4 sliilling^. SINGLE RULE OF THRtE DIRECI*. 5*5 2. come If 1 bushel of itO? bush. If 1 : corn cts. 75 L cost 75 cents, bush. :: 257 75 1285 1799 what will 257 bushels 192,75 Ans. 192 dolls. 75 cts. 3. What will 931 yards of shalloon come to at 55 cts. 4 ms. per yard? - Ans. 515 dolls. 77 cts. 4 ms. 4. How many bushels of wheat at 1 doll. 12 cts. per bush- el, can I have for 81 dolls. 76 cts. Ans. 73 bushels. 5. What will 94 cwt. of iron come to at 4 dolls. 97 cts. 2 mills per cwt. ? Ans. 467 dolls. 36 cts. 8 mills.. 6. What will 349 Ifc^. of beef come to at 2d. per lb. ? Ans. £2 18 2 7. At 3s. per vard what will 59 yards of cloth come to? Ans. £8 17 Prove this answer to be right- 8. How many lbs. of beef at 5 cts. per lb. may be bought for 29 dolls. 85 cts. ? cts. lb. dUs.cts. If 5 : 1 :: 29,85 1 ,05)29,85 597 Ans. 597 lbs. 9. How many hhds. of salt at 4 dolls. 90 cts. per hhd. cau I have for 392 dolls. ? Ans. 80 hhds. 10. How manv lbs. of cofiec, at Is. Id. per lb. mav be bought for £8 12 7 ? Ans. 109 lbs. F2 U . SINGLE RULE OF '1 HREE DIRECT. 1 1 . When 25 yds. of cloth cost £2 12 U what is it per yrl.? yds. £ s. d. yd. If 25 : 2 12 1 :: I 20 52 12 '» 625 ^ 1 25)625(12125 50 — 2s. Id. 125 125 Ans. 2s. Id. 12. If 56 bushels of corn cost 42 dolls. 56 cts. what is it per bu«hcl ? bush. dlls.cts. bush. If 56 : 42,56 :: 1 1 56)42,56(, 392 76 336 336 Ans. 76 cts. 13. If 1 Albs, of beef cost \2s. Sd what is it per lb. ? Ans. 2 pence. 14. If G73 bushels of rye cost 769 dolls. 23 cts. 9 ms. what h I bushel worth ? Ans. 1 doll. 1 4 cts. 3 ms. 15. What is 1 yard of baize worth when 97 yards cost £l0 12^. 2icZ. Ans. 2^. 2id. ]C, When iron is sold at 5 dolls. 4 cts. per cwt. what is it per ib.? Ans. 4 cts. 5 mills. 17. If 891 gallons of molasses cost £l76 Gs. lO^d. what is it per gallon? Ans. 35. llJrA Prove this answer to be ri^ht. 18. What w^iil 253 quintal? offish come to at 17^. Gd. per fjulntcil? Ans. £221 Is. (jd< SINGLE RULE OF THREE DIRECT. 5 19. At 5 doils. 60 cts. per tbout-anci, wljat will 37 thonsanti of boards come to ? Ans. 203 dolls. 50 cis. 20 What will 4 hhds. of rum come to, containinp: v«z. 79 J-, 84, 104, and 1 12 galls, at G^. 9s. 3d. 24. B ow6s £2119 lis. Gd. and he is worth but£l324 18^. b^d.; if he delivers this tO his creditors, how much do they receive on the pound ? Ans. 12^. Gd. 25. A owes B £569 6s. 8 32 the diameter. cubic measure. S 16=haif the diameter, 48 ' IG 288 48 6 inch. s. s. d. " ' If 1728 : 5 :: 4608 : 13 4 Ans. i:^s. 4d. 44. What will a grindstone, 28 inches diameter, and Sc- inches thick, come to, at 1 dolls 90 cts. per cubic foot ? Ans. 2 dolls. 26 cts. 2 ms. 45. When a man's yearly income is 9 19 dolls, how much 8 it per day? Ans. 2 doils. 6U cts. 46. At 4^ percent, what is the commission on 1525 doiis? Ans. 08 doll?. 62 cts. 5 ms. 47. What is the interest of 456 dolls, for 1 year, at 6 per lent ? Ans. 27 dolls. 36 cts. 48. At 5 dolls. 50 cts. per M. what will 21,186 feet of boards come to ? Ans. 1 16 dolls 52 cts. 3 ms. 49. When boards are sold at 18 dolls, per M. \vh;^t is it per foot? Ans. I cent 8 mills. 50. What will 98 feet of boards come to at 4 cts. p-sr foot? Ans. 3 dolls. 9 J cts. 51 . What will 49 thotisand 3 hundred and ^5 casts O] staves come to at 17 dolls, per tliousand ? No J F.. Staves are counted by casting 3 at a time : 40 casts make I hundred, and 10 hundred 1 thousand. M. dolls. jM h. c. If 1 : 17 : : 49 3 25 10 10 493 iO 40 40 dlh. cts. ms. Casts 400 . 19715 Ans. 839 I'j 2 52. Wh.u will 1 M. 8 and 1 5 casts of white-onk hhd. staves come to, at 31 doiis. per M. ? Ans. 6J4 dolls. 96 cts. 2 ms. 58 SINGLE RULE OF THREE DIRECT. 53. What will 22 M. 9 and 37 casts of red-oak hhd. staves come to at 13 dolls, per M. ? Ans. 298 dolls. 90 cts. 2 ms. 54. What will 56 bundles of hoops come to at 25 dolls, per M. of 30 bundles ? Note. Hoops are sometimes bound in bundles of 30 hoops each, and four such bundles are 1 hundred, and ten hundred, or 40 bundles, 1 thousand. But they are generally bound in bundles of 40 each, 3 bundles making 1 hundred, and iea hundred, or thirty bundles, 1 thousand. 3)56 hund. dolls. Or bund. dlls. bund. If 10 : 25 : : 18| hundreds 30 : 2h : : 56 25 23 90 280 36 112 I6| li0)46|6| 310)U0|0 46,66| 46,6| Ans. 46 dolls. 6| dimes, or 66| cts. 55. How many bushels of salt, at 4 dolls. 75 cts. per hhd. can I have for 326 dollars? dlls.cts bush, dolls. If 4 75 : 8 : : 326 Ans. 549 bushels, when measured on board the vessel. If 4 75 : 71 : : 326 Ans. 514 bushels three pecks, nearly, when measured ashore. 5^>. What is the tax on lands, &c. valued at 2957 dollars in the direct tax, at 28 cents and three mills on the 100 dol- lars ? Ans. 8 dolls 3iS cents 8 mills. 57. What is the tax on a house, valued at 900 dollars, in the direct tax, at j\ per cent ? dolls. dolls. dolls. If 100 : ,3 : : 900 2^ 100 )^^70,0 Ans. 2 dolls. 70 cts. Or, as j\ per cent, is equal to 3 mills on the dollar, mul- tiplying the sum in dollars by 3, gives the answer m mills. SINGLE RULE OF THREE DIRECT. 59 58. What is the tax on 753 dollars at j\ per cent.? 753 dollars 3 mills 2"259 Ans. 2 dolls. 25 cts. 9 ms. 59. Find the tax on the following sums, viz. 1 550 dolls, at y*^ per cent. 4580 j\ ... 7850 j% ... 12680 j\ ... 16950 j\ ... 240^20 j\ ... 35840 1 ... 60. What will a piece of land, measuring 48 feet in length and 40 in width at each end, amount to at 20 dollars per square rod? feet. 48 40 feet. dolls. If 272i : 20 :: 1920 By decimals. Ans. 141 dolls. 4 cts. If 272,25 : 20 :: 1920 61. A charter-party for a vessel of 186 tons commenced on the 28th of May, and ended on the tenth of October fol- lowing : What does the hire amount to for that time, at S dolls, per ton per month of 30 days ? dlls.cts. Ans 6 20 - 22 80 47 10 - 88 76 135 60 221 58 358 40 days. 186 tons May 4 2 dolls. per month. June 30 days. July - 31 30 : 372 August 31 136 September - October - 30 10 2232 1116 136 372 3,0)5059,2 1686,40 Ans. 1686 doll?. 40 cts. In calculating the time, the days of receiving and discharg- ing the vessel are both included. S9 INVERSE PROPORTION. INVERSE PROPORTION. Whereas in the Rule of Three Direct, more requires more and less requires less, in this rule more requires less and less requires more. Rule. Alter stnting the'terms as in the Rule of Three Di- rect, mulfiply the tirst arid second terins together, and divide the product by the third, and the quotient is the answer. EXAMPIES. 1. If ?00 workmen complete a piece of work in 12 davs, how many are sufficient to do it in three days ? d. m. d. 12 : 100 :: 3 12 3)1200 400 Ans. 400 men. 2. If 8 boarders drink a barrel of cider in 12 days, how long wouhi it last if 4 more came among them? Ans. t) days. 3. A ship's comp:inv of 15 persons is supposed to have bread to last their voyage, allowing each 8 ounces per day; when they pick up a crew of 5 persons in distress, to whom thoy rjre wdimg to communicate: what will the daily allow- ance of each person then be? Ans. 6 ounces. 4. When wheal is sold at 93 cents per bushel, the penny loaf weighs 12 ounce? ; what must it weigh when the wheat is I dollar 24 cts. per bushel? Ans. 9 ounces. 5. How many yards of baize, 3 qrs. wide, will line a cloak which has in it 12 yards of camblet, half yard wide ? Ans. 8 yards. 6. Suppose 400 men in a garrison are provided with pro- visions for thirty days ; how many men must be sent out, if they would have the provisions last 50 days ? Ans. 160 men. 7. What sum should be put to interest to gain as much in 1 month, as 127 dollars would gain in 12 months? Ans. 1 524 dolls. COMPOUND PROPORTION. 61 COMPOUND PROPORTION Teaches to resolve such questions, as require two or more statings by simple proportion. Rule. State the question, by placing the three condi* tional terms in this order : that which is the principal cause of gam, loss, or action, possesses the first place ; that which denotes space of time, or distance of place, the second ; and that which is the gain, loss, or action, the third : then place the other two terms, which move the question, under those of the same name, and if the blank place fall under the third, multiply the three last terms for a dividend, and the two fir^t for a divisor ; but if the blank fall under the first or se- cond place, multiply the first, second and last terms together for a dividend, and the other two for a divisor; and the quotient will be the answer. EXAMPLES. 1. If £100 in 12 months gain £5, how much will £400 gain m 3 months ? £. mo. £. 100 : 12 : : 5 400 : 3 3 100 1200 12 5 12|00)60jOO £5 Ans. £5 2. If 8 men make 24 rods of wall in 6 days, how many men will build 1 8 rods in 3 days ? m. d. r. 8 : 6 : : 24 3 18 6 M 108 3 8 72 ) 864(12 . , 72 '^■ 144 ^ H4 Ans. I 2 men. 62 COMPOUND PROPORTION. 3. If a family of 9 persons spend 450 dollars in 5 months, how much would be sufficient to maintain them 8 months, if five more were added to the family ? Ans. 1120 dolls. 4. What is the interest of £240 for 50 days, at 5 per cent, per annum ? £. days. £. 100 : 365 : : 5 240 : 50 50 100 12000 365 5 365100 )600|00(1 12 10^ 365 235 20 365)4700(12 4380 320 12 365)3840(10 365 190 4 365)760(2 730 30 Ans. £1 12 10|- N. B. By omitting to multiply by the rate per cent, and dividing 36500 by it, are found the fixed divisors of 7300 for 5, and 6083 for 6 per cent, per annum, sometimes used in calculating interest. COMPOUND PROPORTION. 63 b. What is the interest of 654 dollars for 1G4 days, at 6 per cent, per annum ? 100 654 dollars. 365 164 6) 36500 2G16 6083 the fixed divisor, 3924 found as above directed. 6^4 6083)107256(17,632 6083 46426 42581 38450 36498 19520 18249 12710 12166 544 Ans. 17 dolls. 63 cts. 2 ms. 6. What is the interest of 947 dollars, for 294 days, at 5 per cent, per annum ? 947 dolls. 294 3788 8523 1894 Fixed divisor 7300)278418(38,139 21900 59418 58400 10180 7300 28800 21900 69000 65700 3300 Ans. 38 dolls. 13 cts. 9 ms. 64 VULGAR FRACTIONS. VULGAR FRACTIONS. Fractions, or broken numbers, are expressions for anj assignable parts of an unit; and are represented by two numbers, placed 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 denommator shows how many parts the integer is divided into, and the numerator shows how many of those parts are meant by the fraction. Fractions are either proper, improper, compound, or mixed. 1st. A proper fraction is when the numerator is less than fhe denominator, as ^, §, ^\, f|, &,c. 2d. An improper fraction is when the numerator is either equal to or greater than the denominator, as |, y , jf, |f , &c. 3d. A compound fraction is a fraction of tractions, and known by the word of as a of f, f of /^, || of |J, &c. 4lh. A mixed number or fraction is composed of a whole number and a fraction, as 8f , 17^, 293, &c. I. To redute 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, con- tinuing till nothing remains ; the last divisor is the common measure ; then divide both parts of the fraction by the com- mon measure ; the quotients express the fraction required. Note. If the common measure happens to be I, the frac- tion is already in its lowest term ; and when a fraction hath ciphers at the right hand, it may be abbreviated by cutting ihem off, as m. EXAMPLE. }. Deduce jYt ^^ ^^^ lowest term. 91)117(1 91 26)91(3 78 (Common measure 13)26(2 26 i''^)h\{i *^^^ answer. VULGAR FRACTIONS. 65 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 so on, till no number will divide them both, and the last quotients express the fraction in its lowest terms. EXAMPLES. 2. Reduce j-Sf to its lowest terms. (8) (8) (3) 192 24 3 1 = — = — =- the answer. 576 72 9 3 3. Reduce l^ to its lowest terms. - Ans. | 4. Reduce |^f to its lowest terms. - - Ans. f 5. Reduce ||^J- to its lowest terms. - Ans. |i II. To reduce a mixed number to an improper fractian. Rule. Multiply the whole numbers by the denominator of the fraction, and to the product add the numerator for a new numerator, and place it over the denominator. Note. To express a whole number fraction-wise, set one for a denominator to the given number. examples. 1. Reduce 5f to an improper fraction. 5x8-f 3=V the answer. 2. Reduce ISS/y to an improper fraction. Ans. 3|i8 3. Reduce 27^ to an improper fraction. Ans. 2^5 4. Reduce 514/g to an improper fraction. Ans, 82,|y III. To reduce an improper fraction to its proper terms. RuLF. Divide the upper term by the lower, and the quo- tient will be the whole number; the remainder, if any, will be the numerator to the fractional part. 1. Reduce y to its proper terms. 5)17(3| the answer. 15 2 2. Reduce 215 to its proper terms. Ans. 27f 3. Reduce «ff ^ to its proper terms. Ans. biij\ G2 66 VULGAR FRACTIONS. IV, To find the least common multiple 07' denominator. Rule. Divide the given denominators by any number that will divide two or more of them, without a remainder, and set the quotients and the undivided numbers underneath. Divide these quotients and undivided numbers by any numr ber that will divide two or more of them as before, and thus continue, till no two numbers are left capable of being less- ened. Multiply the last quotient and the divisor or divisors to- gether, and the product will be the least common denomina- tor required. EXAMPLES. L What is the least common measure off, f, /-, and f^g ? 8)9 8 15 16 3)9 1 15 3 15 2 3X5X2=30X3X8=720, Ans. fi. What is the least number that can be divided by the aine 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 which 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 denomina- tor, express the fractions required in their lowest terms. examples. 1. Reduce J, f and y^ to a common denominator. 36 the common denominator. 4 9X3=27 9 4X5=20 12 3X7=21 The fractions will be |J, |f , |i. % Reduce f , |, | and J to a common denominator. Ans. If, if, iJ, andfi. 3. Reduce |, f , f and /j- to a common denominator. Ans. ||,f|,HandJ.|. Af Reduce J') I, x*j aud f to a common denominator. Ans. ih Ih if and f f . VULGAR FRACTIONS. 67 VI. To reduce a compound fraction to a single one. RuLpfl Multiply aU the numerators for a new numerator, and all the denominators for a new denominator, then reduce the new fraction to its lowest term by Case I. EXAMPLES. 1. Reduce f of f of ^^ to a single fraction. 3X5X 9=135 9, = — the answer. 4X6X10=240 16 2. Reduce f of ^ of |^ to a single fraction. Ans. //^ 3. Reduce f of f of f to a single fraction. Ans. /j VII. To reduce a fraction of one denomination to the fraction of another^ but greater^ retaining the same value. Rule. Reduce the given fraction to a compoimd one, hy 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 ^ of a. penny to the fraction of a pound. d 7X1X1 7 = the answer. 8X12X20 1920 2. Reduce a of a pennyweight to the fraction of a pound Troy. Ans. ^^^ 3. Reduce ^ of a pound Avoirdupois to the fraction of a cwt. Ans. j}^ VIII. To reduce the fraction of one denomination to the frac- tion of another.^ hut less^ retaining the same value. Rule. Multiply the numerator by the parts contained in the several denominations between it and that denomination to which you would reduce it for a new numerator, and place it over the denominator of the given fraction. EXAMPLES. 1 . Reduce ^^^ of a pound to the fraction of a peany. 1X20X12=240 — =1 the answer. 960 68 VULGAR FRACTIONS. 2. Reduce 3^^^ of a lb. Troy to the fraction of a dwt. Ans. f 3. Reduce yig; of a cwt. to the fraction of alb. Ans. ^ IX. To find the value of the fraction in the known parts of the integer. Rule. Multiply the numerator by the known parts of the integer, and divide by the denominator. EXAMPLES. L AVhat is the value of | of a lb. ? 2 20 shillings. 3)40 Ans. 13^. 4^^. 2. What is the value of | of a shilling? Ans. 4d. 3| qrs. 3. Reduce | of a lb. Troy to its proper quantity. Ans. 7 oz- 4 dvvt. 4. Reduce | of a mile to its proper quantity. Ans. 6 fur. 16 poles, X. To reduce any given quantity to the fraction of a greater denomination of the same kind. Rule. Reduce the given quantity to the lowest denomina- tion mentioned for a new numerator, under which set the intregal part (reduced to the same name) for a denominator, and it will express the fraction required. 1. Reduce 16j. Zd. to the fraction of a pound. 16 8 1^ 2©0 5 =-the answer. 240 6 2. Reduce 2 quarters 3^ nails to the fraction of an ell En- glish. Ans. f 3. Reduce 4*. 6-J-ci. to the fractioa of a pound. Ans. f Jf VULGAR FRACTIONS. 6» ADDITION OF VULGAR FRACTIONS, I. To add fractions that have a common denominator. Rule. Add their numerators together, and place the suta over one of the given denominators. EXAMPLES. 1. Add ^, J, f, ^ and | together. 1 2 4 5 7 19 -Q=2^ the answer. 2. Add /^, |i and if together. Ans. 12^. 3. Add ig^ \l and /^ together. Ans. l|^. 4. Add j\, }| and || together. Ans. 2yV- II. To ac2 and 3/^, together. Ans. 25|. 3. Add It>5, 2fV, 3y\ and 4ii together. Ans. 12. 4. Add 9jf , 7yV, 5t*4 and 8H together. Ans. 314. III. To add fractions^ having different denominators. Rule. Find the least common denominator by Case IV, in Reduction, in which divide each denominator, and multiply 70 VULGAR FRACTIONS. the quotient by its numerator ; the sum of the products is a new numerator to the common denominator, and the fraction required. EXAMPLES. 1. Add I, 1, 1, f and H together. 24 com. denominator. 3 8x 2 = 16 4 6X 3=18 6 4X 5 = 20 8 3X 7=21 12 2X11=22 |J=4^\^ the answer. 2. Add I, i, i, 4 and | together. Ans. l^Vj^. 3. Add f , I, f , f and fy together. Ans. 3j\\, IV. To add mixt numbers whose fractions have different de- nominators. Rule. Add the fractions as in the last case, and the inte- gers as in whole numbers. Add 5|, 6f and 4^ together. 24 com. denominator. 5| Ans. 17^V 16 21 12 2. Add If, ^ of JL and 9 i^* together. Ans. 11^^^. 3. Add \\%'^ 6|, I of i and 7^ together. Ans. le^Vo- V. When the fractions are of several denominations. Rule. Reduce them to iheir proper quantities by Case IX in Reduction, and add as before. VULGAR FRACTIONS. 71 1. Add J of a £ to j\ of a shilling. 15 common measure. s. d. J of a £=15 6§ /^ofa5.=0 3| Ans. 15 10y4_ 10 9 1 5 — * IS 2. x\dd I of a yard, | of a foot, and | of a mile together. Ans. 1540 yds. 2 ft. 9 inches. 3. Add ^ oi a week, ^ of a day, and j of an hour, together. Ans. 2 days 14^ hours. SUBTRACTION OF VULGAR FRACTIONS, I. To find the difference between simple fractions that have a common denominator. Rule. Subtract the less numerator from the greater, and under the remainder put the denominator. EXAMPLES. From Take 4 13 If m Rem. ? \ 3 4 5V jfir II. To subtract a fraction or mixt number from a whole number. Rule. Subtract the numerator from the denominator, and under the remainder put the denominator, and carry one to be deducted from the integer. EXAMPLES. From 3 G 10 9 100 Take Oy'e Of OtV H 9Wir Rem. m ^ 9tV Sf OriT 72 VULGAR FRACTIONS. III. To subtract simple fractions that have no common deno minator. Rule. By case IV in Reduction, find a common denomi nator, in which divide each denominator, and multiply the quotient by its numerator; the difference between the pro- ducts thus found is a numerator to the common denominator, and the answer required. Iexamples. From ^^ take ^-^ 42 com denom. 21 2x17—34 14 3x 9=27 Rem 4\=^ the answer. From f ff I ^% ^^ Take ^ f^ £ ^ ^ In order to distinfifuish the greater of two fractions, let them be reduced to -a conjmon denominator, as in case V in Reduction ; and that fraction, whose numerator is greater, is the er^ater fraction ; the difierence between the new numerators, being set over the common denominator, will shew the excess or inequality. Which of the two is the greater fraclion, \l or }| ? 48 com denom. 12 4X11=44 16 3X15=45 Ans. if is greater by Jj^. IV. To subtract a fraclion or mixt number from a mixt num- ber^ when the fractional part to be subtracted is greater than that from which it is to be subtracted. Rule. Find a common denominator and a new numerator, as in the last case, and then subtract the numerator of the greater fraction from the common denominator, and to the VULGAR FRACTIONS. 73 remainder add the less numerator, and set the sum of hoth for a new numerator over tlie common denommator, and carrv one to the integral part, and proceed as in whole num- bers. EXAMPLES. 27 common deuominalor. From ^H r'Xl = 3 Take m 4H 1X14=14 1 6 5T From 6f 10,-^ »2/5 19fV Take Of h\ H Vk Rem. 5f m Hi ma V. When the fractions are of d'iff:'rent denominations. Rule, Reduce them to their proper quantities, and suh- iract as before. rxAMPLrs. ]. From 5 of a ;£ take -^^^ of a sluliinpf. 15 common denominator. S. d — jr of a £- 15 62- 10 1 y of a 5.= ^ 9 Rem. 15 3^'. 2. From J of a £ take ^- of a shillinsr. Ans. 14^ 3J. 3. From £ of a lb. troy tako ^ of ;ui ounce. Ans 8 oz. 16 dwt. IG f^rs. 4. From 7 weeks take 9/^ days. Ans. 5w. 4d. 7h. l^m. 5. From J- of a yard take 2. of an inch. Ans. 5 inch. 1 be. MULTIPLICJITIOJV OF FULGJIR FRACTIOXS. Rule. Reduce compound fractions to simple onrs, and mixt nuTihers to irn;)ro()er fractions; y| 4X3 ■ lE — o 1 4 — 7 the answer. 7X2 o Divide 6 31 by 9 2 h 19X 2 y> y Then — — TV4=i ^^^ answer. 6X19 3. Divide 5 by y*^^ Ans. 7^ 4. Divide ^% by 4^ Ans. ^- 5. Divide 9^ by i of 7 Ans. ^2^^ 6. Divide 52051 by |- of 91 Ans. 7U mSCELLANEOUS QUESTIONS m TUK rRECET'IKG BULES. 1. What part is 28j| of 33^V • Ans. | 2». What will remain if I3^s. and I'^d. be taken from £1? An?. b$. 6# VULGAR FRACTIONS, 75 3". Which is the greater fraction, j\ or -^^ ? Ans. y8_ i§ greater by j\ * 4. Ot what number is 176 the \^ part? Ans. 368 5. By how Tiuch mast you multiply I3| that the product may be 49^ ? Ans. 3f 6 Find two numbers so that f J of the one will be as much as j\ of the other ? Ans. 126 & 208, or 63 Sl 104, &c. 7. Which is greater, } of 6*. or l^. 2Jc^. ? Ans. 1*. 2ic^. is greater by j\d, 8. A has I of I of a ship, and B f of |, which is the great- est share, and by how much ? . Ans. A's share is greater byj 9. \ farmer, being asked how many sheep he had. an- swere 1, that he had them in 5 fields; in the first he had i ot his tlock, in the second }, in the third |, in the fourth J^, and in the fifth 450 ; how many had he ? Ans. 1200. RULE OF THREE DIRECT IJV VULGAR FRACTIOA'S, Rule. Having stated the question, make the necessary preparations, as in Reduction of Fractions, and invert the lirst term } then proceed as in Multiplication of Fractions. EXAMPLES. 1. If 1 of a yard of cloth cost | of a shilling, what will f of a yard come to? yd. s. yd, Ifx : ^ :: 1 inverted. 4X2X7 s. =11=2^. 4d. the answer. lX3i^8 2. If j\ of a ship cost £273 2*. 6d. what are /^ of her worth? Ans. £227 12^ Id. 3. If I of a yard cost | of a pound, what will f of an ell English come to, at the same rate ? Ans. £2. 4. \ person, having | of a coal mine, sells f of his share for £i71 ; what is the whole mine valued at? Ans. £380: PRACTICE. SIJVGLE RULE OF THREE LYVERSE FRACTIONS. LY VULGAR EXAMrm:s. 1. If 25f5. will pay for the carriage of an cwt. 145} miles, how far mi\y 6i cwt. be carried for the same money? Ads. 22/^ miles. 2. If 3:{- 3'(ls. ofcloth that is I^ yard wide be sufficient to make a cioak, how much must I have of that sort which is I yard wide, to make another of the same bigness ? Ans. 4 J y. 3. If 3 men can do a piece of work in 4^ hou^s, in how many hours will 10 men do the same work? Ans. 1/^ 4. {f the penny white loaf weigh 7 oz. when a bushel of wheat costs 5*. 6d. what is the bushel worth when the penny while loaf weighs but 2^ oz.? Ans. 15^. 4|c?. PRACTICE Is 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 TABLE. P^artsofa£. Parts of a Ton. Parts ofi Cwt. s. d. cwt. qr. ii. 10 is ^ 10 is i 28 is -J- 6 8 - 1 5 - i 14 - i 5 - 1 ^ - i 8 - 4- 4 . 1 Q O . 1 7 - ^- 3 4 - i 2 4 - 2 6- I 2 - > 1 3^^ - tV 2 - -'- ^^ Parts of a Cwt. (jrs. lb. 1 8 - -V 1 - -J Parts of a J- Cwt. / 2 Parts of a Shilling. 2 is i 1 i lb. U is 1 is Jt. 4 - I 3 . 1 2 - i 1 - r'. 7 - 1 4 - 1 8 -X 7 tV 4 h 2 .V 3^ - i 2 - tV 1 - ^V PRACTICE. 77 Case I. When the price is an aliquot or even part of a shilling. Rule. Divide the given number by the part, and the quotient is the answer in shillings ; what remains is to be re- duced as in Compound Division. EXAMPLES. 1. What will 4596 yards cost at 6c?. per yard ? 6(/. i 4596 2|0 22918 114 18 2. yds, 3746 at d. 4 per yard. 3. 1095 3 4. 7596 2 5. 3747 1 6. 3203 H - Ans. £114 ISs, £ s. d. Ans .62 8 8 - 13 13 9 - 63 .6 - 15 12 3 - 20 n Case II. When the price is pence^ or pence and farthings^ and no even part 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. EXAMPLES. 1. What will 4937 yards come to at 9d. per yard? 4937 210 2168 6 1234 3 370|2 9 Ans. £185 2 9 H2 8 PRACTICE. yds. d £ s. il 2. 2765 at 8 pe r yard, Ans. 92 3 4 3. 3762 7 - - 109 14 6 4. 3159 ^i - . 98 14 H 5. 1496 11 - - G8 11 4 6. 1895 »0i - - 82 18 H 7, 46891 5 - - 97 13 Hi 8. 3689 H - - 126 16 2i 9. 1871 H - - 19 9 n 10 8914 H - - 306 8 H 11. 25631 9i - - 101 9 5; 12. 95| m - 4 3 H 13. 201J- 9 - 7 10 iH Case III. When the price is shillings^ or shillings and pence^ and an even part of a pound. Rule. Divide the given quantity by the even part, and the quotient is the answer in pounds. If there be a remain- der, reduce it as in Compound Division. EXAMPLES. 1. At 6s. Bd. per yard, what will 473 yards come to? Qs. Sd. I i- I 473 yds. s. d. 2. 387 at 10 3. 478 5 4. 397 3 4 5. 797^ 2 6 6. 1591- 1 8 Ans. £157 13.^. 4d. - - - Ans. £ s. d. 193 10 119 10 66 3 4 99 13 9 13 5 5 Case IV. When the price is shillings., or shillings and pence^ which make no even part of a pound. Rule. Find the even parts for the price, and divide as in Oase HI, or multiply the given quantity by the shillings, and tilie the even parts of shillings for the pence, as in Case If. PRACTICE. 79 EXAMPLES. [. What co<;t ?87 yards at 17*. 6cl per yard? First method. Second methoU. 287 287 17 6 s. d. 10 i h 143 10 5 k 71 16 2 6 k 35 17 6 Ans. 251/. 2s. 6d yards. s. d. 2. 8i72 at 15 3. 3691 19 4. 4765 11 8 6. 3718 18 4 6. 709i 12 6 7. 2i3 14 10 8. 96i 2 H 9. 158 6 81 10. 47051 3 9 , 11. 127 7 51 2009 287 6 1 i 1 143 6 210)5022 Ans. 251 I. 2s. ed. £. s. d. Ans. 6129 3506 9 2779 11 B 3408 3 4 443 6 7i 157 ;9 6 13 9 4| 45 5 2i 882 6 61 47 9 lOi Case V, Whe?i the price is an even number of shillings. Rule. Multiply the quantity by half the shillings, dou- bling the first (or right hand) figure of the product for shil- lings ) the rest are pounds. EXAMPLES. I. What will 788 yards come to at 2^. per yard? 788 l=half the shillings. yards. 2. '347 3. 638 4. 5894 6. 246 6. 3241 7. 523 8. 745 9. 373i 10. 270 1. 1724 2t S94 at Ans. £78 16 s. £ i: 4 - • - - . ^ Ans. 69 8 6 191 B 8 235 J 4 10 123 12 194 17 14 S66 2 16 - . 696 18 386 3. 20 * 270 22 - ... w - 189 15 24 ----- - 307 2 80 PRACTICE. Case VI. JVhen the price is pounds^ shillings^ 4*c. Rule. Multiply the integers of the given quantity by the pounds, and work ibr the shillings, &c. by such of the pre- ceding rules as you think best, and work likewise for the fractional parts of the integer; the sum of these will give the answer. EXAMPLES. 1. What will 173 cwt. 1 qr. 14 lb. of sugar come to at £3 155. (yd. per cwt.t 173 1 14 3 15 6 s. d. 519 10 J. 86 10 5 ± 43 5 6 tV 4 6 G 1 qr. 1 ■ 4 18 lOi 14 lb. 9 5^ Ans. £654 9 9| cwt. qrs. 2i9 2 310 3 lb. 19 22 at 69 53 d. 11 8 Ans. £ s. d. 7G7 18 61 834 7 5^ In w^orking questions of this kind, when the quantity is not above the multiplication table, the following method is used. 1. What will 45 cwt. 2 qrs. 14 lb. of sugar come to at £3 7 9 per cwt.? 3 7 9 5 16 18 9 9 2 qrs. } 14 1b. \ Ans. 152 8 9 price of 45 cwt 1 13 UU price of 2 qrs. - 8 .hi price of 14 lb. £154 11 I PRACTICE. tonsxwi. qr. lb, £ s. d. 2. 67 2 8- - 3 17 9 8. 19 3 13 - 2 5 10 4. 75 3 25 - - 48 5 6. 2 1 18 - - 59 8 6. 1 1 11 - - 63 9 7. 3 19 - - 54 8. 37 14 2 14 hemp 89 6 8 9. 27 56 3 18 - - SO iO 10. 15 2 - ^2 5 - 11. 17 10 2 - - i I 10 81 £ s. d. 223 {6 2 - 45 iO 6 183 18 .44 7 3^0 4 5 1ii 2 9 7| per ton 3370 IS 2 2520 5 71 9 10^ 1603 10 9 1. What will .37 cwt. 3 qrs. 7 lb. of sugar come to, at 14 dolls. 40 cts. p TARE AND TRFT. 83 At £4 11 3 per cwt. what vvlii 6 qrs. 25^^ lb. come to? £4 11 3 2 qrs. 1 qr. 14 lb. 7 1 Ans. £4 9 ^^ Whit will 19 tons, 19 cwt. 3 qr? 27 j lbs. come to at £19 195. n^c/. perton? Ans. "^oiiS ly^. b\m^ 1 2 2 f) n 1 2 1 2 9J i li H 1 2 5 8/j 1 2 2 J03\ 4 CI y,v. TARE AND TRET Are allowances made in selling goods by weight. Tare i« an allowance made to the buyer for th^ weight of the hogshead, barrel, or bag, containing the commodity. Tret is an allowance for waste, dust, ^c. generally at 4 lb. per 104 lb, Cloff IS an allowance for the turn of the scale, at 2 lb. per 3 cwt. Gross weight is the whoFe weight of the goods, together with the hogshead, barrel, or bag, &c. that contains them. Suttle is when part of the allowance is deducted from the groRH. Neat weight is what remains after all allowances are made. 84 TARE AND TRET. Custom-house allozcances on iea^ coffee and sugar. Tare on whole chests of //;. bohea tea - - - 70 on every ~ chest do. 36 on quarter do. - 20 on every chest of hyson, or otlier gre'^^n teas, the gross wt. of which is 70 ih or ur- wards 20 on every box of other tea, not less than oO lb. or more than 70 lb. gross 18 IfSO lb. gross 20 And from 80 lb. gross and upwards - - - 22 There is an allowance of two per cent, for leakage on the quantity which shall .;ppear to be cpixlained in aav cafck of liquor subject to duty by -he gallon; and .0 per cent, on a,ll fcer, ale. and porter in Lo.tJeg, and 5 per cent, on all Ovher liquors in boliies in lieu of breakage; or the duties may be computed on ihe actual quantity, at the option of the im- porter, to be made at the ^jme o/r/z/?-?/. Which tare shall include rope, canvass, and other coverings. Tare for ail other boxes of tea, according to invoice, or actual weight thereof. Tare for colfee in bags 2 per lUO in bales 3 do. in casks {^ do. On sugar, other than loaf- in casks 12 do. in boxes 15 do. - - in bags or mats 5 do. EXAMPLES. 1. Sold ten casks of alum, weighing gross 33 cwt. 2 qrs. 15 lb. tare 15 lb. per cask : what is the amount at 25s. 4«. per cwt. ? ' / civf. qr. lb. gross 33 2 15 10 casks, tare 1 1 10 15 lb. per cask. neat 32 1 5 112)150 C.l 1 to tare. /ns. £37 13 G^- 2. At 1 doll. 25 cts. per lb. what will 3 chests of hyson tea come to, wpi^4iing Toc;s, viz. CtJ'f. qrs. lb. No. I. 7 \ 14 2. 8 2 21 .3. 7 1 21 4. 6 3 25 5. 7 23 6. 8 1 12 41 3 neat. Ans. Z\^Q, 9 ^ B. At 625. per cwt. what will a hhd. of susfar come to., rt^ighing gross 7 cwt. 1 qr.; tare 12 lb. per cwt.? Ans. t:2() 1 4 6. At 21 cts. per lb. what will 6 hhds. of coffee come t©^ lb. tare 96 98 91 90 89 100 Ans. 904 dolls. 32 cents. 7. "What wonld the a])Ove coffee amount t(i. all(nvin<>' 12 lb. percivl. .\^ tare on the gross weight? Ans. 9{U> <)oiIs. 7 5 cts. W. Ai 72.. 6^A per cwt. how much will 8 hhds. of sugar come to, weighing gros^ each 8 cwt. 3 qrs. 7 lb.; tare 12 lb. per cut? ^ Ans. t'^^'^B 3 7} 9. \t 2.3 cpnts j)er lb what will 4 bags of coffee come to, weighing gross 450 lb. tare 2 per cent or 2 lb [)er U)0 lb.? Ans. lul dolls. 43 cts. 10. At 12 lolh. 50 ct<». per cwt. what will 3 barrels of ItJgar come to, vveig'i nar Tross, viz. cwt. qrs. lb. V No. 1. 2 2 10 2. 2 I 21 t. 2 15 tare 2nb. perbftrrel. An8.82doll8. 47cti. Tmi. I 86 TARE AND TRET. 11. At 15 (lolls. 40 cts. per cwt. what will 4 hhds. sugar come to, weighing gross, viz. cx&)t. qrs. lb. No. I. 7 3 13 2. 8 1 10 3. 7 2 12 4. 8 1 21 tare 12 lb. per cwt. Ans. 443 dolls. 43 cts. 7 ms». 12. A has in his possession ahhd. of sugar, weighing gros» 9 cwt 3 qis. owned equall}^ between him and B. It is re- quired to know how much sugar he should weigh out to B, allowing tare 12 lb- per cwt? Ans. 4 cwt I'qr. 11 J lb. 13. At 19i cts per lb. what will 2 hhds. of coffee come to, weighing gross 1 5 cwt- 3 qrs. 1 1 lb. allowing custom-house tare, or 12 lb. per 100? 15 3 11 15U0 3«= fifteen hundred. 1 80:= 15x 12 for excess in each cwt. 8 l=three quarters. 11 Gross 1775 1775 Tare 213 Tare 12 per 100 Neat 1562 213.00 14058 1562 731 30459 cts. An?. 301 dolls. 59 ct«. 14. B buys of C a hogshead of coffee, we ghing gross ^ cwt. 2 qrs.; tare 12 lb. per cwt. what will it amount to iA 23 cts. per lb? Ans. 218 do!ls 50 cU. 15. If custom-house tare, or 12 lb. per 100, \\vre aL wed on the above coffee, what would it amount to, oik! ubal clif- fercnce would it niake to the buyer? Ans. It amounts to 215 dolls. 35 cts. 3 ms, being 3 dolls. 11 cts. 7 ms. in his favour. IG. What is the gross weight of a hog^ilL•ad of tobacco, HveighiHg neat 1 1 cwt. 1 qr ; tare 14 lb. per cwt.? Ans. 12 cwt. 3 qrs. 12 lb. SINGLE FELLOWSHlf. 87 FELLOWSHIP Is when two or more join their stocks, and trade together, dividing their gain or loss, in proportion to each person^ share in the joint stock. SLVGLE FELLOWSHIP Is when different stocks are employed for a certain equal time. UuLF. R^ the whole stock is to the whole gain or loss, so is each m:m-s particular stock to his particular share of the gain or loss. EXAMPLES. I K A and B hny certain merchandises, amounting to £120, of which A pays'£80, and B £40, and they gain by them £32 ; what part of it belongs to each ? A £^;o B 40 As 1^0 • 32 .• V^^^ Ans. £21 6 8 A. 2. A ship worth G400 dollars being lost at sea, of which { belonged to A, i to B, and the remainder to C ; what loss will each sustain, supposing they have GOOO dollars ensured ? Ans. A's loss is 600, B's 300, and C's lOOu dolls. 3. A and B have gained 1260 dollars, whereof A is to have 10 per cent, more than B ; what is the share of each ? Ans. A's 060, B's 600 dolls. 4. A bankrupt is indebted to A 500 dolls. 37 cts. ; to B 228 dolls. ; to C 1291 dolls. 23 cts. ; to I) 709 dolls. 40 cts. and his estate is worth but 2046 dolls. 75 els. ; how much does he pay per cent, and what is each creditor to receive ? Ans. He pays 75 per cent, and A's part is 375 dolls. 27| cts.; B's 171 dolls.; C's 968 dolls. 42} cts. j and D's 532 dolls. 5 cents. 5. Three boys, John, James and William, buy a lottery ticket for 3 dolls, of which John pays 90 cts. James 1 doll, and William the remainder. This ticket is entitled to a prize of 2000 dollars, subject to a deduction of 12j per cent, how much is each to receive ? Ans. John 525 dolls. James 583 dolls. 33^ cts. William 641 dolls. 66| cts. 88 DOUBLE FELLOWSHIP. 6. Three merchaiUs made a joint stock — A put in £56^ Qs. 8d. B £478 5 4, and C a certain sum, and they gained £373 9 II, of which C took toi his part £lI2 11 11; required A and B's (>art of the gain, and how much C put in? Ans. A'sgain £141 6 8, B's£ll9 11 4, and C put in £450 7 8. 7. Three men have to share a legacy of 1500 dolls, of which B is to have 4, C |, and D the remainder; hut C re- linquishes his part to B and D, leaving it to be divided be- tween them, according to their shares in the whole. It i« 3pequ.red to know how much of the legacy B and D receive respectively? Ans. B's part is lUOO, D's 5UU doiis. DOUBLE FELLOWSHIP Is when the stocks are employed for different 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 lo his share of the gain or loss. EXAMPLES. 1. B and C trade in company ; B put in £950 for 5 months, and C £785 for 6 months, and by trading they gain £^tl% 18*. 4'/., what is each man's part of the profit? B's stock 950X5=1750 C'« do. 785X6 = 4710 2. Two merchants enter into partnership for 16 months. A put into stock at tirst 1200 dolls, and at the end of 9 months 200 dolls, more ; B put in at tirst 1500 dolls, and at the ex- piration of 6 months took out 500 dolls. ; with this stock thej gained 772 dolls. 20 cts.: what is each man's part of it ? Ans. A's 401 dolls. 70 cts.; B's 370 dolls. 50 cts. 3. Two persons hired a coach in Boston, to go 40 miles, for ^0 dolls. With liberty to take in "i more when they pleas- ed. Now when they had gone 15 miles, they admit C, who wished to go the same route, and on their return, with n 25 miles of Boston, they admit 1) for the remainder of the jour- ney. Now as each person is to pay in |)ro|>ortion to the distance he rode, it is required to settle the coach-hire be- tween them. Ans. A & B 6 dolls. 40 cts, each, C 5 dolls. 20 cts. D 2 dolls. SIMPLE INTEREST. 89 SIMPLE INTEREST Is a compensation made by the borrower of any sum of money to tiie lender, according to a certain rate per cent, agret^d on for the principal only. I'he leg-al rate of interest in Massachusetts is 6 per cent. Principal is the money lent. ^ Rate is the sum per cent, agreed on. Amount IS the principal and interest added together. General Ritle. Multiply the principal by the rate per «ent. and divide the product by 100, and the quotient is the answer for one year. KXAMPLE3. 1 . What is the interest of £496 for one year, at 6 per cent. 496 G_ 29|76 20 151^20 12_ 2|40" 4 l|oO Ans. £29 155. ftid. 5. What is the interest of £383 15 9 for 2 years, at U percent? 383 15 9 H 3070 6 191 17 loi 20 sTol 32|i2^ 1243 12 6|26 4 1)06 £32 125. Bid. for 1 year. Ans. 65 4 10 J- for 2 years. 12 90 SIMPLE INTEREST. 3. What will £826 13 9 amount to in one year at 5 per cent? 5=:2'^)826 13 9 principal. 41 G 8i interest. Ans. £868 r^i amount, 4. What is the interest of £103 11 4, for 4 years, at 7^ per cent per annum ? Ans. £31 1 4f 5. VYliat will £36 14 9 amount to, in three years, at 5 per cent, per annum ? Ans. £42 4 IH 6. What is the amount of £l 9 15 8, for 6 years, at^Gf per cent per annum ? Ans. £26 9 2J- 7. How much is the interest of £72 12 6, for 6 months, at 6 per cent, per annum ? 72 12 6 6 4135 15 20 7115 12 1180 £ s. d. 4 6 m. 1)4 7 If for 1 year. 3|20 Ans. 2 3 6| for 6 months. Note. When the time is months, multiplying by the rate for the t-ime gives the answer. This rate is found by multiplying the time by 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 rate is 6 per cent. 8. What is the interest of £25 19 3 for 8 months, at 6 per cent, per annum ? 8 months. 25 19 3 4 12)48 1,03 17 ^ '20 4 rate=half the months. 0,77 12 9,S4 Ans. £10 0. SIMPLE INTEREST. 91 9. How much will £o3 9 4 amount to, in 20 months, at 6 per cent, per annum ? Ans. £58 16 3. 10. How much is the interest on a bond of £295 17 10, for 1 8 months, at 8 per cent, per annum ? 295 17 10 18 1 2 the rate for the time. u 35 50 14 12)144 20 12 10,14 12 1,68 4 2,72 Ans. £35 10 1 11. How much is the interest of £80 12 9, for 23 months, at G per cent, per annum? . Ans. £9 '5 5^ 12. iToiv much is the interest of £36 14 9, from 19th May to 25lh October, at 6 per cent. ? 36 14 9 4 m.=i)2 4 1 for 1 year. 6 *if,20 8 20 14 H 1 m.=i 3 8 6 d.=:l ,8| 4,03 Ans 19 1 12 1,02 13. What will £l87 14 9 amount to, from 11th June, 1797, to 26th October, 1798, ut 6 per cent, per annum? Ans. £203 4 5J 11. How much is the interest of £l9 13 7 from 3d Ja- nuary, 1797, to 18th May, 1798, at 6 per cent, per annum ? Ans. £1 12 51 To find the interest of any sum for months^ at 6 per cent, per anniun^ by contraction. TiiJLK. Multiply the pounds by the number of months; he first or units figure of the product is pence, and the rest 92 SIMPLE INTEREST. are shillings, obscrvini;:: to increase tiie pence in the product hy i when they exceed 4. EXAMPLES. 15. What is the interest oi'£b& for 1, 5, 7 and 12 months? 56 56 56 56 mo. 1 5 7 i2 .ns. ba. Id. 2.-i Od, 395. 2^. 675. 2d. 16. £45 for 6 months. . Ans. £1 7 17. 32 4 5 - 8 2 18. 19 7 - - 13 3 19. 11 1 - . . 1 1 // there are shillings^ ^c. To the pounds add the decimal of the nearest even num- ber of shillings (this will be suoicientiy exact for business) and multiply by the month* as before, separate two figures of the product to the right, and the left haml figures are the shillings, then multiply the figures pointed off by 12, and the product, rejecting two figures to the right, is the pence ♦f the answer. 2 4 6 8 10 12 14 16 18 shillings. ,1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 decimals. 20. How much is the interest of £347 6 9 for 3 months? 347,3 3 shillings 104,19 Ans. £5 As. 2d. 21 How much is the int. of £195 15 10;^ for 10 monthe T 195,8 ,80 10 12 shillings 195,80 Ans. £9 155. d^J. 2,40 The Talue of the remainder is thus shewn to be 9~d, SLMPTE INTEREST. 95 J?. Whnt is the interest ol i:590 Id 9f for 3 years, 7 monthij and 19 days? £69 1 nearly. 43 1773 23G4 13 days } 295 3 j 59 1 i 19 2578, 6-f 1 because it exceeds 4. (See Rule.) £128 IB 7 23. How much is the interest of £476 9 8 for 9 months aEfli 13 days? £476,5 9 10 days ^ 3 do. yV 4288,6 158,8 47,6 449,4t Ans. £tt 9 6| 24. Whnt is the interest of £40 for 7 years, 5 months, and 2^ days? 40 89 montbf. 3560 IB day •i 20 10 do. ^ IS I do. tV 1 £17 369,4 A»s. 19 h n SIMPLE INTEREST. 25. What is the interest of £240 for 50 flays, at 6 perct.? Or by Conjpound ProportiOK* 240 240 6 50 14,40 6083) J 2000(1 20 6083 8,00 i9I7 20 d. dQ5 : £U Ss, : : 50 : £1 195. 5id. 6083)118340(19 6083 57510 54747 2763 12 6083)33156(5 30415 2741 4 60S3)10964(i 6083 4881 Ans. £1 19 51 SIMPLE INTEREST IN FEDERAL MONEY. The principal given in English money, and the interest required in federal. Rule. Rod 'ice the given sum to shillings, the product gives the answer in cents, and the pence are mills nearly — the reason is, that at 6 per cent, per annum, one fifth of a dol- lar is the annual interest of a i)ound — that is, 20 cents for 20 shillings, or 1 cent, for every shilling in any given sum. EXAMPLES. 1. Required the interest of £194 15 3 for 1 year in fede- ral money. 194 15 3 20 3895 ccuts. Ans. 2^ dolls. 95 cts. 3 ms. SIMPLE INTEREST. 96 2. What is the interest of Jt:i29 13 2 for 2 years in fede- ral money ? 129 13 2 26y3,2 for 1 year. 2 5186,1 Ans. 51 dolls. 86 cts. 4 ms. 3. What i» the interest of £91 12 1 for 5 years, in fede- ral money ? 91 12 1 20 1832,1 for 1 year. 91,605 for 5 years. Ans. 91 dolls. 60| el«. 4. What is the interest of £139 17 2 for 4 months? 139 17 2 20 4 mo. 1 2797,2 9,32,4 Ans. 9 dolls. 51 cts. 4 ms. Principal in Federal Money^ and Interest required in the same, RuLF,. Multi|)ly the principal by the r:ite per ct^nt. and as you siinposf^ 100 for a divisor, point oil the (pjolient as in divisioii of decimal*. The following rule answers^the same purpose. When the principal is dollars only, multijMy by the rnte, and from the product ponit otf two tig-ures to the rjght, the fiofures to the M\ hand of the point j^ive the answer in dol- l.us, and the rest are d' cimal parts or cents. If there are ceutn. <^h\ in the p^ • -- • s^ multiply by the rat'% and po-nt off a^ ausve. i': to the ieff of tiiC po lU r ' ^' th • uuw^r .1) the same nuiiiLi with the lowest de- nommailjii .n tue principal. 96 SIMPLE INTEREST. EXAMPLES. ft. What is the interest of 4 1 9 dolls, for 1 year at C per tP. 4i9 6 25,14 Ar\9. 25 dolls. 14 cts. C. What is the interest of 173 dolls. 50 cts. ibr 1 jear, at 6 percent.? 173,50 6 cents 1041,00 Ans. 10 dolls. 4t cts. 7. What is the interest of 327 dolls. 82 cts. 5 mills for 1 year, al 8 per cent. ? 327,82,5 8 mills 2'')226,00 Ans. 56 dolls. 22 cts. 6 ms. 8. How much is the interest of 325 dolls, for 3 years, at per cent, per annum? 325 Or thus, 325 6 18 rate for the time. 19,50 for 1 year. 265)0 3 325 58,50 for 3 years. 58,50 Ans. 58 dolls. 50 ctl. When the time is months, RuLK. Multiply hy b^jlf the number ; this, as wa.a before ohserved, is always equal to the n^te, for the lane-, vviien the annual rate is 6 per cent, per annum. EXA>5PfJ.S. 9. What is the interest ot 284 dollars, for 8 months at S i^erceot.? 284 4 11, oS Ans. 11 dolls. 36 cts. SIMPLE INTEREST. 97 It. How much is the interest of 187 dolls. 25 cts. for 16 mouths, at 6 per cent, per annum? 187,25 8 cents 1498,00 Ans. 14 dolls. 98 cts. 11. What is the interest of 95 dollars, for 2 months, at 6 per cent, per annum ? 95 1 ,95 Ans. 95 cents. 12. How much is the interest of 126 dolls. 46 cents, for 9 months, at 6 per cent. ? 126,46 44 5t»5;84 63,^3 cents 5n9,07 Ans. 5 dolls. 69 cts. 13. How much is the interest of 124 dolls, for 1 montk at 6 per cent. ? i)124 Or 124 ,5 62, ,6 -,0 Ans. 62 cts. 14. What is the inter^«»t o^*6 '4 dolls 8 4 cts. for if months at 10 per I'snt. per annum? 694,84 Or 694,84 10 7rJ=rate for the time. cents 694y,i'^ for a year. 4863,S8 347,42 e i 3474,2 5 1 1737,1 cents 52,1 1,30 ^2,11,3 Ans. 52 dolls. 1 1 ctsv 3 me. K 98 SIMPLE INTEREST. 15. How much h the ftmonnt of PrSo dollars, for 5 years and 8 months, at G per cent, per annum? dolls. 985 34 half the months. 3940 2955 3>4,00 interest. 9v;5, principal. 1319,90 amount. Ans. ISIH dolK 90 ctt. When the time is mon-hs nnd dayj*, nnd tl f^ nr.riiol rate 6 per cenh muUiply by k-lf ^be r, • ;; -i-: ' ol' Ikl v. tr^i-] to the r.*i.e, for the irivei. = ■ ■•■: - ( ., \:t nO\ lor .i.e decimal in the r:< o, - ^ i .1 ere Lea rer-iriider in lakirg a sivt]: of > *^ 1590 ^ J 06 i 1U6 dolls: 16,74,8 Ans. 16 dolls. 74 cts. 8 ms. 19. What is the interest of 413 dolls, for 1 year, 7 months and 17 days, at 6 per cent. ? 418 418 9,7f 5 2926 6)^090 3762 fori 2^^»^=348J. ^^^* ^ 2o9> _„, 139^ =348^ dolls. 40,89,4 Ans. 40 dolls. 89 cts. 4 m»r 20. How much is the interest of 268 dolls. 44 cts. for 3 years, 5 months and 26 days, at 6 per cent. ? 268,44 20,9^ 241596 536880 8948 cents 5619,34,4 Ans. 56 dolls. \9 cts. 3 ms. 21. What is the interest of 1 dollar, for 18 days, at 6 per «ent.? 1 ,0ii,3 mills. Ans. 3 mills. One fior,ire is sopnratoH for the decimal in the multiplier? anrl two Ciphers are supplied and pointed, according to the general rule. 100 SIMPLE INTEREST. 22. What is the interest of 910 dolls. 50 cts. for 5 years, 5 months and 26 days, at 7 per cent, per annum ? 910,50 Or thus, 910,50 7 22,9i- 63,73,50 819450 3 182100 182100 1 9 1 ,20,5 for 3 years. 30350 6 mo. I 31,86,7 3 mo. i .15,93,3 J)208,80,80iO at 6per ct. 15 days } 2,65,5 34,80,1 10 days | 1,77,0 1 day j\ ,17,7 dolls. 243,60,9 dolls. 243,60,7 Ans. 243 dolls. 60 cts. 8 ms. 53. How much will 185 dolls. 26 cts. amount to, in 2 years, 3 months, and 11 days, at 7^ per cent, per annum? Ans. 216 dolls. 94 cts. 7 ms. 24. What is the interest of 57 dolls. 78 cts. tor 1 year, 4 Rionths and 17 days, at 4 per cent, per annum? Ans. 3 dolls. 19 cents. 25. How much is the «mount of 2i>8 dnli?. ^9 cts. froa 19th May, 1797, to the 11th of August, 1798, at 8 per cent, per annum ? Ans. 3'ii7 dolls. 98 cts. 4 ms. 26. How much is the amount of 196 dollars, from June 14, 1798, to April 29, 1799, at 5| per cent, per annum? Ans. 205 dolls. 86 cts. 27. What is the interest of 658 dollars, from January 9 i% October 9 following-, at ^ per cent, per month ? Ans. 29 dolls. 61 cts. In the calculation of interest in federal money; thus far, the year is .supposed to be 12 months of 30 dayb each, making il only 360 days. Most persons use this rnelhod of computing the lime, but as it is 6 dayf less in a year than the ^rue number, f oinc merclianis calcul^-iite by dayt without any regard to monihs, a» being more accurate* SIMPLE INTEREST. 101 EXAMPLES. J8. What is the interest oi 7086 dollars for 39 da)^s, at 6 per cent, per annum ? By Compound Proportion. 7086 39 ' 63774 21258 dis. cts. ««83) 276354(45 4« 24332 33034 30415 26190 24332 185S0 18249 331 Ans. 45 dolls. 48 cfs. 29, What is the interest of 87 dolls. 5(5 cts. for 72 days 5 at 6 per cent, per annum ;' 87,56 72 17512 61292 cts. «*. «0S3)6304,32(103 6 6083 22 32 18249 38830 36498 2332 Ans. 1 doll. 3 cts. 6 ms. dlls, cts, days* dils.cts.m. 80. 2962 19 for 254 at 6 per cent, per ann. Ans. 123 68 8 31. 35 250 - - - 1 47 2 32. 1733 97 102 - - - 29 / 5 83 45 J 52 47 - - - 3 5 9 84. 215 SO 125 - - - 4 43 4 S5 5.7 90 84 - - - 7 15 1 3«. 73 63 92 - . . 1 11 3 K2 1©2 SIMPLE INTEREST. The following method cf ralculat-ng the interest upon a<> oiQunts, when there are partial payments, is sometimes uscd- 1798. dolls. days. prod.princ.'!^-tmie. "^January 2, Lent 100 on 15, Lent 110 int. for 13 - . 1300 210 20, Received 162 - 5 1050 48 February 3, Lent, 95 - - 14 - - 672 143 10, Received 90 • 7 - - 1001 53 16, Lent 186 - - 6 - .318 239 26, Received 70 - - 10 - 2390. 169 March 1, Lent 250 • - 3 507 419 3, Received 270 - . 2 838 149 13. Received 143 - ► 10 149© 20, time of adjustment, 6 - - 7 - - 42 d.cts. 9608 Then 6083)9608( 1,57 interest at 6 per cent. 6083 6 th" p.irjcipal due. 35250 7,57 tiie amount due March 20th. 30415 48350 42581 67*9 SIMPLE INTEREST. lOS T5y this method interest mav b<* C'llciilated on account?, multiulyitii^ eacU sum i)V the Anys it is at interest, and tak- ing" the quotient of 36500, divided by the rat« per cent, as a fixed vlivisor to the sum ot'the product?. Thus, the rate in the last example being- G per c#^nt. the divisor is 6083 ; l"Or 6 per cent, it woiiid be 73oO ; for 7 per cent 5214, kc. It' the time is months, multiply each sum by the months it is at interest, and take the quotient o\ 1 iOO, divided by the rate as a divi^sor. Thus, tor 6 per cent, the divisor is ^2<>0 ; for 5 per cent. 240 ; for 8 per cent. 150, fcc. — [*See Compound Proportion.^ m COMPUTING lATEREST OJV AOTES, ^^c. It has 2:<^nerany been the custom to (ind the amount of the principal from the time the interest commenced to the time of settlemeni, and likewise the amount of each payment, and then deduct the amount of the several payments from the amount of the principal. A, by his note dated April 25th, 1798, promises to pay B 774 doils. 76 cts on demand, with interest t© commence 4 months after the date. On this note are the following en- dorsements : Received, Oct. \2th, \19S, 260 dolls. 19 cts.— Ocf. 13/^, 1793, 60 doll3.~A*ov. 2, 1798, 200 dolls. And the settlement is made Dec. Ibth^ 1798. CALCni.ATTON^. The principal carrying interest from 25th Aug. 1798 - 774 76 Interest to Dec. 15, 1798 - 3 m. 20 days. • 14 2* Amount of the principal - - - * * 788 9€ dlls. cts. First payment, Oct. 12, 1798 - - - 260 19 Interest to Dec. 15th, i 798 - 2 m. 3 days. - 2 73 Second payment, Oct. 13, 1798 - - - 60 00 Interest to Dec. }5ih, 1793 - 2 m. 2 days. - 62 Third payment, Nov. 2, ; 798 - - - 200 00 Ihlerestto Dec. 15, 1798, - 1 m. 13 days. - 1 43 Amount of the paymen.s 624 97 etLlement is made for . . • , ggiu, 2«8 99 104 3IMPLK INTEREST, RULE established by the Courts of Lazv in Massachusetts for tnakiriir up j'l'Igments on sii^.URi'iiKS for monkv, ivh/ch are upon vnicrest^ and on waick partial paynients have btea en- dorsed. Compute the interest on the principal sum, from the time wh.»:i the interest commenc-Ml, vo ih2 nrt-t tiaj<^ wlv^n a [^^ly- ment was mnie, which exc<' ' n. :^,e r- <^n. with the preceding- puvm. ;.>; i!;e . at time due;' add thai iuleft-si to liie jMin; j>aU aii.i from the sura .Subtract the payment m-i je u ili.jt tiru ., together with the preceding payments (ifai)}; aiid ihe rema luier torn;s a new princip.il ; on which compute and sp.btract tlie interest, as upon the tiist principal : an.i f>roc-?ed in this maaner to the time of the jii i;^ment. iiy Jh:s rule, ihe payments are first applied to keep dovvo the in-yrest ; and no part of the interetjt ever ibrms a part oi a praicipal carrying interest. The following example wdl illustrate the rule, in whick the interest is computed at the rate of 6 per cent, by the year, ihat being the legal rate of interest in jMassachusetts. A, by his note dated Jan. I, 17 HO, promises to pay to B lOUO dolls, in 6 ^nonths from the date, Avith interest from the date. On this note are the following endorsements : Received, Jipril 1, 178Q, 24 dolls. — flugust I, 1780,4 dolls. Dec. 1, 1780, 6 doJJs. — Fe6. I, 1781, 60 dolls.— J«/i/ 1, 1781, 40 dolls.— /imc I, 1781, 300 dolls.— 5e/>/. 1, 1784, 12 dolls. — 7rni. K 1785, J 5 dolls.— Oc^ 1, 1785, 50 dolls. And the judgment is to be entered Dec. 1, lldQ. CALCULATION. dlls. ct» The principal sum carrying interest from January 1, 17S#, 1000 GO Interest to Apnl 1, 1780, '6 months . _ - - 15 00 Amount 1015 00 Paid, April 1, 17S0, a sura exceeding the interest - - 24 00 Remainder for a new principal 991 0§ Interest on99i dlb. from April 1, 178©, to Feb. 1, 1781, 10 mo. 49 55 Amount 1040 5I» Paid Aug. 1, 1780, a sum less than the interest then due ^'4 00 Paid Dec. 1, 17S0, do. do. 6 00 Pfiid Feb. 1, 17«i, do. greater ihaa the interest then due 60 00 79 Of SIMPLE INTEREST. Ids dlh. cts. Remainder fbr a new principal - - - _ . 97O 55 Inte.est 0.1 070 dolls. 55 cts. from Feb. 1, 1781, to July 1, 1781, 5 months - - - - * - - 24 2fi Paid .July 1, 1781, a sum exceeding the interetrt Amount 994 81 40 Of Remainder for a new principal - - - . • 954 31 Interest on 954 doHs. 81 cts. from July 1, 1781, to June 1, 1784, 2 years 11 months. - - - • - - - 167 Of Paid June 1, 1784, a sum exceeding the interest Amount 1121 90 300 0« Remainder for a new princip.il ----- 821 9t Inierest on 82 dolN. 90 cts. from June 1, 1784, to Oct. 1, 1785, 1 year 4 months - - - - - - --65 75 Amo'jnt 887 %h Paid Sep. 1, 1784, a sum less than the interest then due $; : 2 00 Paid Jan. J, 1785, do. 16 00 Paid Oct. 1, '785, do. greater with two last payments than interest then due - - * - - 50 00 77 60 Remainder for a new principal - - • • - 810 65 Inicrert on SO dalU £>5 cti-. from Oct. T, 1785, to Dec. 1, 1790, the time when judgment is to be entered, 6 years 2 months 251 3t Judgment rendered for the amount 1061 9S A TABhE^ sheiioing the number of days ^ from any day in any months 10 the same day in any other mnath through the year. From Tan. Feb, M. Ap.Ma.Jun. Jul. Au.Sep. Oc. No.De. t'o~j"an.l365|334|3b6J2>5|245 214|184|753iT22r92| 61|Tl ~FV^| 3'iJ865lir37i¥06|276g '^^M^|"~^Ts|;}65|334:a(M^ 90 April.f90| 59| 3 ? J365 ;335!304|274:24i^272| » 82| i 5 1 1 ! 2 1 ^^Ma^72bT]8^ 2| i sTjTsT June.fi 5 l]T20! 92j_6 1 1 " 3Jl|365L^^!30 iT273!243]2T 2|"^2 ~Ji7I7r;'l8]|150| r22j~9if61|" 30j365[384 jOOir 273Vl2J2 12 " Au^-|2 1 2iT8 I|"r53r<22} 92|'6 1| 3i]3.;246j2Hlp^ \b^]2^^ 92ij6_''| 3"M3G5;3:^| "l ^ec.|334 S 03;275|244|2 i4|l83h53|{ 22"|T:|'"6"r| ~30J365 | 106 COMPOUND INTEREST. THK USK OF THE TABLE. Suppose the number of d.iy« between the 3(1 of M?iy ani the 5(1 of November vras required ; look in the coiiiTnn nnder May tor November, and ag-am^t that month you will lind 184. It'ihe sfiven dnvs be different, it is only adding or snb- traciinq; rhpir inequality to or from the tabular nnmbi^r. — Th.is, from May 3d lo Nov. 17th h 184 + 14=198 days, and from Nov. nth to May rkl is i d I — 14—16 7 days. If the time exceed a year, 365 day? must be added ; thus Ir-.-.a i:;e Uh cl February, 1798, to the 4tb of ^ept. 1799, ii 2; ;-f 3^5-:'i77 d^vs. Np.te. la leip - enr-, if the end of the month of February be in th« time, Oiie day ma^i oe adde first year's interest. 64 amount of the first year. 9 of / second year's interest. 10 6 277 4 l-{- amount of the second year. 13 17 2^ " 2 15 51 third year's interest. 2V)3 17 V amount of the third year. 216 H 6 first principal. 47 2 6 compound interest for 3 years. Ans.*£47 2 6 S. What is the compound interest of i^76o lO for 4 y^ars, at 6 percent, per aauum? Aas. j^lC^ 12 3i €OMPOUND INTEREST. 107 3. How much is tho Mmonnt of £ 1 28 17 j. 6^/. for years, at 8 p(^r ct. fxM- annum, eo.'n?)0'inv1 inttresl? Aiis. 182 i6 2f 4. How mnch is th*^- -^monn* of 500 uolh»rs, for 3 jeai^, at 6 per cent, per annum, i ifiierest? ?0 X 500, iir^t interest. 5 I 1 3 530, •iife^SO 5,00 56 1 ,80 2 second interest. s,09 > 5,(51,8 ^ third interest. I 595,50,8 um't req. An-. §^5^5 50 cts. R ra. B. What 13 the amount of 62tj dolls, ior 7 years, al i> per tent, per annum, compound mLerest? Ans. 945 dolls. 78 c!s. 3 ms. 6. How mnch is the compound inierc^t ot 1^56 doiis. for 15 year?, at 6 per cent, per aonvmi ? An-'. 1 754 dolls. ^ ct^. f^ ms. A TABLE shewing; ^T-" amo^int of one potirid or one dollar for any number of years under S3, at the rates of 6 and b per centy per aniiuiny compound interest. |Fears.| ~' 6 Rates. 6 Years. \ 1 l,or>000 2 I,i0:r50 3 1,^5 (2 4 1,2. 5u0 5 1,27028 6 l,^i 009 7 J,M)7 ^ ■,1.7 M 5 *'. ,v 1.^2 . v) ;,<>:ssf) i i (,/ O.il • 2 S;;^.>^t) ^3 i,>^>=:r)65 14 l,s:9<>3 J 5 2,0/^92 6 2,.82S7 1,00000 ],'2;:60 ],:5) 01 l,.2o2i7 1,33 -^^2 1, 4; 852 l,c0.363 7,5'jaS4 !,7:)0:^4 KSJ>'-2<) 2,0 2 .9 2, 3202 2,2f0.90 2,^i96j5 2,51035 17 18 19 20 2i 22 23 24_ "25 2G 27 2S 29 GO 3i 32 2,29201 2,-J0c62 2,b2(;96 2,65329 2,78696 2,92i;:^« 3,0 Ir'-' _ 3,38^o5 3,?'5i>67 3,7bM5 3,920 3 4, 6:3 4,12 94 4,53804 4,76494 Rate>i. 6 ~2,6P277~ 2,«5434 3,02559 3,20753 3,3Jiy56 3.f,0353 4,29 !S7 4,: 4938 4,S22S4 5,- * .68 6,4:838 6,74349 *6,088 6,45r>.^S i'he une of Jiis faWe i plain Aiid easy: for, iiiultip! i Tg tiio figure* itandisj rtr:vi;nr, tj.»» number of years, by the given priiiCipai, the product if the ^inoaul required. 1#8 (TOMPOUND INTEREST. 7. What is the amoiint of 50o doihu's, ior 3 years, at 6 per cent, compound interest ? 1,19101 the tabn'c^r r;imib<^r for ihe time. 50U the jjiinc pui 5lj5,5U500 Ans. 595 dnJls. 50 cts. 5 ms. 8. A merchant, on in?pectfng- sonie -^id acccujJs in March, 1799. fih.ie a ^^etilemi^nt dated i-Vlaich, J 77 I, i*; v. >; ri* »i ap- pears liicre is dne ironi h:m lo A B £,2 Bs. ; ll.i ^ \:iu he pays w.ih compound inter. -si at 6 per com. per annum. Ihe amount of it is reqniret- ? 5,11 Mo .'.t tabular number for 2^1 yetirs. ';i,i the principal with tbv shiiiings inserted * decimaiiy. 2044672 10i!i:33U 20 5. fevJ^o:- 10 12 4 ^r. 1,3)0720 ln». XI 2 5^. ^^J. or 40 dolls. 09 cU. 3 ms. Calculated in Fe/hral Money. 5,11168 § dollars. /rfo//*. -10,^9. '44 Ans. 40 dolls. €9 cts, 3 mills, as above. COMMISSION AND BROKERAGE. 109 COMMISSION AND BROKERAGE Are compensations to Factors and Brokers for their res- pective services. The method of operation is the same as in Simple Interest. ■^^-' EXAMPLES. 1. What is the commission on £596 18 4, at 6 percent.? 596 18 4 Or thus, £5 | ^\ \ 596 18 4 6 Mi! 29 16 11 35|81 10 6 19 ^ £35 16 U 20 16|30 12 3|60 4 2|10 Ans. £35 16 3 J 2. What is the commission on 1974 dollars at 5 percent.? 1974 5 98,70 Ans. 98 dolls. 70 cts. 3. What is the commission on £526 11 5 at 3i per cent. ? Ans. £18 8 7 4. What is the commission on £l25b 17 3 at 7§- per cent.? Ans. £93 3 \\ 5. What is the commission on 2176 dolls. 50 cents, at 2^ percent.? Ans. 54 dolls. 41 cts 2 ms. 6. The sales of certain goods amount to 1873 dolls. 40 cts. what sum is to be i-^ceived for them, allowing 2-^ per cent, for commission, and \ per cent, for prompt payment of the neat proceeds? Ans. 1821 dolls. 99 cts. 9 ms. no COMMISSION AND BROKERAGE. 7.^ Required the neat proceeds of certain goods amounting to £456 1 1 8, allowing a commission of 2^ per cent. £5 5V I 456 11 8 2J i I 22 16 7 commission at 5 per cent. 11 8 3i commission at 2j per cent. Ans. £445 3 4j neat proceeds. What is the commission on £1371 9 5 at 5 per cent? Ans. £t^8 jl 5J 9. What is the commission on £1958 at bj per cent. ? Ans. £U>7 13 9} 10. What is the commission on £1859 7 6 at | per cent. ? Ans. £16 5 4^- 11. W'hat is the brokerage on 1853 dolls, at | per cent. ? Ans. 13 dolls. 89 cts. 7 ms. 12. What is the brokerage on £874 15 3 at { per cent.? Ans. £2 3 8| 13. What is the brokerage on 1298 dolls. 53 cts. at | per cent. ? 1298,53 3 8)3895,69 dolls. 4,86,94 Ans. 4 dolls. 86 cts. 9 ms. 14. What is the brokerage on £l321 U 4 at IJ- per cent.? Ans. £14 17 4 15. A factor receives 988 dollars to la\ out, fifter having deducted his commission of 4 per cent, how much will re- mam to be laid out ? d. 100 4 If 104 : 100 : : 988 : 950 dolls, the answer. 16. A factor has in }\'\< hrinds 3G90 dollars, which he is di- rected to lay out in i»^< >. r-^^nvinir fp'un li his commission of 2* percent, on the pLi h;ise ; the iron bcvin^: 95 dolls, per ton: how much did he [:nr< h^^'^e ? Ans. 37 tons. 17 ewt 3 qrs, I6j\ lb. INSURANCE. Ill INSURANCE Is an exemption from hazard, by paying or otherwise se- curing a Cf^rtain sum, on condition of being indemnified for loss or damage. Policy is the name given to the instrument, by which the contract of indemnity is effected between the insurer and in- sured. Average loss is 5 per cent.; that is, if the insured suffer any loss or damage not exceeding 5 per cent, he bears it himself, and the insurers are free. Rule. The method of operation as in interest. EXAMPLES. 1. What is the premium of insuring £924 at 7 per cent. ? Ans. £64 13 7 2. What is the premium on 1650 dollars at 12 per cent. ? Ans. 198 dolls. 3. What is the premium of insuring 1250 dollars, at 1^ per cent. ? Ans. 93 dolls. 75 cts. 4. What is the premium of insuring 4500 dollars, at 25 per cent. ? Ans. 1125 dolls. 5. What is tlie premium of insuring 1650 dollars, at 15J per cent. ? Ans. 255 dolls. 75 cts. 6. What is the premium of insuring 1873 dollars, at | per cent ? Ans 2 dolls. 34 cts. 1 m. 7. What sum is to be received for a policy of 1658 dolls, jdeducting the premium of 23 per cent.? Ans. 1276 dolls. 6Q 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. d. d, d. 90 sumcovered. If 90 : 100 :: 1800 Ans. 2000 dolls. Proof 20U0 dollars at 10 per cent. 10 200,00 the policy 2000 the premium 200 sum covered 1800 dolls. 9. What sum must a policy be taken out for, to cover 392^ ddls. 7 cts. whon the prcm^um is 6 per cent. ? Ans. 4176 dolls. 67 ct?; 112 GENERAL AVERAGE. GENERAL AVERAGE. Whatever the master of a ship in distress, with the advice of his officers and sailors, deliberately resolves to do, for the preservation of the whole, in cutting away masts or cables, or in throwing goods overboard to lighten his vessel, which is what is meant by jettison or jetson, is in all places per- mitted to be brought into a general average, in which all, who are concerned in ship, freight and cargo, are to bear an equal or proportionable part of the loss of what was so sacri- ficed for the common welfare ; and it must be made good by the insurers in such proportions as they have under written. EXAMPLES Of Adjusted Averages, 1. A loaded ship met with such bad weather, that the master and mariners found it impossible to save her without throwing part of her cargo overboard, which they are au- thorized to do for 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 sufficient 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 W ad- just the loss, and to pay the proprietors of those goods which were thrown overboard for the good of the whole. Average accruing to ship ''^for goods thrown overboard for preservation of ship^ freight and cargo. Ship valued at - - - doUs. 12,000 Freight (wages and victuals deducted) 3,000 Thomas Nugent's value of goods - - 4,000 Thomas Morgan's value of goods - - 2,500 .fames Simpson's value of goods - - 8,500 Andrew Wilson for 40 pipes of wine - " 4,000 Laurence Ward for 10 casks of hardware - 6,000 40,000 Mr. Andrew Wilson's goods thrown overboard valued at 4,000 .!\Ir. Laurence Ward's do. - - 6,000 ^ 10,000 If 40,000 give 10,000 loss, what loss will 100 give? Ans. 25 per cent. GENERAL AVERAGE. Hi The ship must pay to A. W. and L. W. for 12000 dollars, at 25 per cent. . - - - 3000 The I'reight 3000 dollars, at the same rate - 760 Thomas Nuj;ent, (or 4000 dollars, at the same rate 1000 Thomas Morgan, for !^oOO dollars, at the same rate 625 James ISimpson, 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 - - 7500 Their property being insured, the underwriters pay them 2500 10,000 2. The Sea Horse, Capt. Dix, laden with hemp, cordage and iron, bound from Riga to Boston, ran on shore, comuig through the grounds at Elsineur. I'he captain hired 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 dolls. 23 cts. for their assistance. This expense being incurred to preserve both ship and cargo, the average must consequently be general. When the ship ar- rived at Boston, the captain immediately made a protest and an average bill, which was thus stated : Average accruing to the ship Sea Horse^ from Riga to Boston^ in nij9, fur assistance in getting off the strand of Elsineur. For sundry charges paid at the sound for lighters and assistance in getting oif the ship dolls. 409 23 Protest and postage ---;.. 35 37 The ship's freight money Wages for all the people, 4 ms. and 20 d. 560 > Victuals for do. - - - - The ship Sea Horse valued at Fre ght valued at William Jenkins for value of hemp Daniel Jones for value of cordage Enoch Flinu for value ol iron L2 444 60 - 3460 bO j[ Dot; 860 2600 . 12000 - 2600 - 18000 . 4000 2400 dolk. 3C»U00 114 BUYING AND SELLING STOCKS. If 39000 dolls, lose 444 dolls. 60 cts. what will 100 dolk lose? Ans. 1 d^I. 14 cts. The ship must bear 1 2000 dls. at 1 1 4 cts. per 1 00 dls. 1 36 80 The freight 2600 dolls, at the same rate 29 64 William Jenkins for 18000 205 20 Daniel Jones for 4000 45 60 Enoch Flinn for 2400 27 36 dolls, 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 ca- pacity, the value of which is variable. EXAMPLES. 1. What is the amount of 1565 dollars national bank stock, at 134 per cent. ? 1565 134 6260 4695 1565 2097,10 Ans. 2097 dolls. 10 cts. 2. What is the amount of 2958 dolls, bank stock, at 25 per cent, advance ? 2958 25 i 739,50 3697,50 Ans. 3697 dolls. 50 cts. dolls. dolls, cts. 3. 6959 of 8 per cent, stock at 1 10 per ct. Ans. 7654,90 4. 1796 6 - - 9U - - 1643,34 5. 1284 3 - . . 54^ - - . 696,57 6. 3172 deferred - 89 - • 2823.08 7. 1518 slate notes - 83f - - - 1271,32| 8. 16d6 Union Bank •128 - - 2158,08 DISCOUNT. lift DISCOUNT Is the abating of so much money to be received before it is due, as that money, if put to interest, would gain in the same time and at the same rate. Thus 100 dollars would discharge a debt of 106 dollars payable in l!iJ months, discount at 6 per cent, per annum, be- cause the 100 dollars received would, if put to interest, re- gam 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 dolls, due in 6 months, discount at 6 per cent, per annum ? 6 w. I 6 3 100 103 : 100 :: 450 Ans. 436 dolls. 89 cts. 3 m. ^. How much is the discount of £308 15^. due in 16 months, at 8 per ct. per annum? Ans. j£33 1 7f 3. What is the present worth of 5150 dolls, due in 4i months, discounting at the rate of 8 per cent, per annum, nnd allowing 1 per cent, for prompt payment? Ans. 4950 dolls. 4. A is to pay 5927 dolls, on the 19th of April, 17^)9, and 5389 dolis on the 19th of July following: it is required to know how much money willdi.scharge both sums on the 1 9th of January, 1799, discounting at 8 per cent, per annum ? Ans. 11569 dolls. 43 cts. 7 m». Though the discount found by the preceding method is thought to be the sum that should be deducted lor the pres- ent payment, in justice to both parties, yet in businese the interest for the time is taken for the discount. 116 DISCOUNT. EXAMPLES. 5. What ready money will discharge a note of 150 dollars^ due in 60 days, ailowing legal interest, or 6 per cent, per annum as discount? 150 Irshalf the months. 150 150 the debt. 1,50 the interest. 148,50 Ans. 148 dolls. 50 cts. 6. Bought goods to the amount of 950 dollars^^at 9^ days credit, what ready money will discharge it, allowing the m- terest for the time at 6 per cent, per annum as discount? Ans. 9J5 dolls. 75 cts. if calculated for 3 months. 935 dolls 95 cts. if calculated for 90 da^'s. When the interest for the time is allowed as discount, it is presumed that neither party suffers any loss, but the fol- lowing statement evinces the contrary. A owes B 100 dollars payable in 12 months, for present payment of which B allows 6 dollars or the mterest for the time, and receives 94 dollars ; this sum he immediately lends to C for the same space, of time, and then receives the amount, being 99 dollars 64 cts, 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 dollars J4 cents, and this sum being put to interest, would amount to 100 being in want of money, C pays him, at the expiration of 2 months, 1000 dolls.: how much longer than 3 months ought C, in equity, to defer the payment of the rest ? Ans. 2J months. Those who are exact in these calculations find the pre- sent worth of each particular sum, then find on what time these present worths will be increased to the total of the particular sums payable at the particular times to come ; and Jthat is the true equated time for the payment of the whole BARTER Is the exchanging of one commodity for another on such terms as may be agreed on. EXAMPLES. 1. How many quintals of fish, at 2 dolls, per quintal, will pay for 140 hhds. of salt, at 4 dolls. 70 cts. per hhd. ? 140 4,70 9800 560 dlls. qtl If 2 : 1 :: 658,00 the amount of the salt* Ans. 329 quintals. M 122 BARTER. 2. A buys of B 4 hhds. of rum containing 410 gallons, at 1 doll. 17 cts. per gallon ; and 253 lb. of coffee, at 21 cts. per lb., in part of which he pays 21 dolls, in cash, and the balance in boards, at 4 dolls, per thousand : how many feet of boards did the balance require? Ans. 127957i feet. 3. B has C's note for 250 dolls, with 6 months interest due on it, and to redeem it C delivers him 60 bushels of wheat at Is. (?d, per bushel, 50 bushels of corn at bs. M, per bushel, and the balance in staves at 30 dolls, per thousand : what number of staves did B receive ? Ans. 5550 staves, or 4 m. 6 bun and 10 casts, 4. B bought of D the hull of a schooner of 70 tons, at 16 dolls, per ton, and paid him in cash 500 dolls. 3 hhds. of mo- lasses containing 350 gallons, at 64 cts. and is to pay the ba- lance in New-England rum at 74 cts. per gallon : how many gallons is D to receive? Ans. 535-5- galls. 5. A buys of B 250 quintals offish, at 25*. per quintal ; in payment B takes 100 dolls, in cash, 2 hhds. of molasses con- taining 87 and 92 galls, at 3s Sd. per gallon, 1 pipe of bran- dy containing 120 galls, at Is. 6d, per gallon, and gives 3 months credit for the remainder : required the balance due, and what cash would pay it, allowing the interest of it for the time at 6 per cent, per annum, as discount for prompt payment ? Ans. Balance is 682 dolls 27 cts. 6 ms.==672,04,2 in cash. 6. C sells to D 28,674 feet of boards at 8 dolls. 50 cts. per . thousand, and takes in payment i cash, 4 barrels N. E. rum containing 128 gallons at 78 cts. per gallon, 1 barrel of sugar weighing neat 2 cwt. 2 qrs. 4 lb. at 10 dollars per cwt. and the balance in coffee at 25 cts. per lb. : how much money and coffee is C to receive ? Ans. 81 dolls. 24 cts. 3 ms. and 149//„- lb. of coffee. 7. C has nutmegs worth Is. 6c/. per lb. in ready money, but in barter he will have 8*. ; D has tobacco worth 9d. per lb. : how much must he rate it per lb. that his profit may be equal to C's? Ans 9|J. 8. A has tea which he barters with B at \0d. per lb. more than it cost him, against cambrick which stands B in \0s. per yard, but he puts it at 12s. 6d. : 1 would know the first cost of the tea? Ans. 35. 4c/. per lb. 9. A has 240 bushels of rye, which cost him 90 cts. per bushel ; this he barters with B at 05 cts. f c r wheal that stands B in 99 cts. per bushel : how many bushels of wheat LOSS AND GAIN. irs is he to receive in barter, and at what price is it to be rated, that their gains may be equal ? Ans. 218/oV bushels, at lO'U cts. per bushel. 10. A and B barter some goods; A puts his at SO^e^ shil* lings, and gains 8 per cent. B puts his at 24^^ shillings, and gains at the same rate : what was the first cost of the goods? Ans. 28^. and 22s. (jd. 11. A and B barter; A has cloth that cost 2Sd. B's cost him 22d. and he puts it at 2bd, : how high must A put his to obtain 10 per cent, more than B? Ans. 35c?. ^ 12. C and D barter; C of Is. makes 65. Qd. D of 7^. 6d. makes Is. Sd. : who has lost most, and by how much per cent. ? Ans. C loses 1| per cent, more than D. LOSS AND GAIN is a rule that discovers what is gained, or lost in buying pr selling goods, and instructs merchants and traders to raise or fall the price of their goods so as to gain or lose so much per cent. &c. EXAMPLES. 1. Bought a piece of broadcloth, containing 53 yards, at 4 dolls. 65 cts. per yard, and sold at 5 dolls, per yard: what is the profit on the whole ? dls. cts. 5 4,65 yd^ yds. If I : ,35 : : 53 35 266 159 1«,55 Ans. 18 dolls 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? Ana Q rlrklla »70 r-fc lU LOSS AND GAIN. 3. Bought a piece of baize of 42 yds. for £4 14 6, anS sold it at 2s. 6d. per yard : what is the gain or loss on the whole piece? Ans. \0s, 6d. gain. 4. A merchant bought 59 cwt. 3 qrs. 14 lbs. of iron, at 112 dolls, per ton, paid freight and charges, 24 dolls. : what is the gain or loss, if he sells the whole at 37^. 4d. per cwt. ? Ans. 13 dolls. 26 cts. gain. 5. If a gallon of wine cost 6^. Sd, and is sold for 7*. 2d> what is the gain per cent. ? 7 2 6 8 s.d, £ If 6 8 : 6 : : 100 Ans. 7^ per cent. gain. 6. When 20 per cent, loss is made on coffee, sold at 20 cts. per lb. what was the first cost ? Ans, 25 cts. 7. At l^ cts. profit on the dollar, how much is it per cent. ? Ans. 13| per cent, or 13 dolls. 50 cts. per 100 dolls. 8. A trader sells his goods at 2^d. profit on the shilling, how much is it per cent. ? Ans. 20f or £ 20 16 8. 9. Which is the better bargain, in purchasing fish, 17 shil- lings per quintal, and 4 months credit, or 16*. 8d, cash? Ans. They are alike. Proof. The present worth of 1 75. found by discount, is equal to I65. 8c^. ; and I65. 8c?. with 4 months interest will amount to 17^. 10. A bought a piece of shalloon, containing 34 yards, at 35. 4d. per yard, and sold it at 12^ percent, loss : how much did he sell it per yard ? Ans. 2^. 1 Id. 11. Bought rum at 90 cts. per gallon : at what rate must it be sold to gain 20 per cent ? Ans. 108 cents. 12. A trader bought 1 hhd. of rum, of a certain proof, containing 115 gallons, at 1 doll. 10 cts. per gallon: how many gallons of water must he put into it to gain 5 dollars, by selling it at 1 dollar per gallon ? Ans. 16^ galls. 13. Bought 4 hhds. of rum, containing 450 gallons, at 1 doll, per gallon, and sold it at 1 doll. 20 cts. per gallon, and gave 3 months credit : now allowing the leakage of the rum while in my possession to be 10 gallons, 1 would know the gain or loss, discounting for the present worth ot the debt at 6 per cent, per annum ? Ans. 70 dolls. 19 cts. gain. LOSS AND GAIN. 125 14. A vintner buys 59G gallons of wine, at 65. 3d. per gal- lon, in ready money, and sells it immediately at Qs. 9a. 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 2 per cent, without any regard to time i Ans. jtJlO 17 6 J gain. 16. A merchant bought a parcel of cloth at the rate of 1 dollar for every 2 yds. of which he sold a certain quantity at the rate of 3 dolls, for every 5 yds. and then found he had gained as much as 18 yds. cost; how many yards did he sell? Ans. 90 yards. 17. Bought rum at 1 doll. 25 cts. per gallon, which not proving so good as I expected, I am content to lose 18 per cent, by it; how must 1 sell itpergallon? Ans. 1 doll. 2^ cts. 18. H sells a quantity of corn at 1 dollar a bushel, and gains 20 per cent. ; some time after he sold of the same, to the amount of 37 dolls 50 cts., and gained 50 per cent. : how many bushels were there in the last parcel, and at what rate did he sell it per bushel ? Ans. 30 bushels at 1 doll. 25 cts. per bushel ? 19. A distiller is about purchasing 10,000 gallons of mo- lasses, which he can have at 48 cts. per gallon in ready money, or 50 cents with 2 months credit : it is required t© know which is more advantageous to him, either to buy it on credit, or to borrow the money at 8 per cent, per annum to pay the cash price ? Ans. He will gain 136 dolls, by paying the cash. 20. A tobacconist buys 4 hogsheads of tobacco, weighing 38 cwt. 2 qrs. 8 lb. gross, tare 94 lb. per hhd. at 9 dolls, per cwt. ready money, and sells it at I \^iL per lb. allowing tare at 14 lb. per cwt. to receive two thirds in cash, and for the remainder a note at 90 days credit: his gain or loss is re- quired, supposing the note is discounted at a bank where dis- «count is made for 60 days. Ans. 283 dolls. 42 cts. 6 ms. gain. M2 126 ALLIGATION MEDIAL. ALLIGATION MEDIAL Is, when the quantities and prices of several things are given, to find the mean price of the mixture compounded ot those things. Rule. 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 ^5 lb. of raisins, at 8 cts. per lb., and 35 lb. at 10 els. per lb., with 40 ib. at 12 cts. per lb.; w^hat is 1 lb. of this mixture worth? lb. cts. cts. 25 at 8 - 200 35 - 10 - 350 40 - 12 - 480 100 1030 lb. cts. lb. 100 : 1030 : 1 : 1 If 1|00)10|30 cts. 10^3 Ans. 10 cents 3 mills. 8. A goldsmith mixes 8 lb. 5i oz. of gold, of 14 carats line, with 12 lb. 8^ oz. of 18 carats fine ; what is the fine- ness of this mixture? Ans. J6y\V carats. 3. A grocer would mix 12 cwt. of sugar, at 10 dollfe per cwt. with 3 cwt. at 8| dolls, per cwt. and 8 cwt. at 7^ dolls, per cwt. ; what will 5 cwt. of this mixture be worth ? Ans. 44 dolls. 78 cts. 2 ms. 4. A refiner melts 2j lb. of gold, of 20 carats fine with 4 lb. of 18 carats fine ;"'how much alloy must be put to it to make it 22 carats fine ? Ans. It is not fine enough by 3^^ carats, so that no alloy must be put to it, but more gold. 5. A maltster mingles 30 quarters of brown malt, at 28*. per quarter, with 46 quarters of pale, at 30*. per quarter, and 24 quarters of high-dried do. at 255. per quarter: what is the value of 8 bushels of this mixture ? Ans. £i ds. 2^c/.|. ALLIGATION ALTERNATE. 127 6. If I mix 27 bushels of wheat, at 5^. 6d. the bushel, with the same quantity of rye, at 45. per bushel, and 14 bushels of barley, at ^s. 8d. per bushel ; what is the worth of a bushel of this mixture ? Ans. 4^. 3|(/.ff. 7. A grocer mingled 3 cwt. of sugar, at 565. per cwt. G cwt. at £l 17 4 per cwt. and 3 cwt. at £3 14 8 per cwt. ? what is 1 cwt. of this mixture worth? Ans. £2 11 4. 8. A mealman has flour of several sorts, and would mix 3 bushels at 3* bd. per bushel, 4 bushels at 5*. i)d. per bushel, and 5 bushels at 4^. Sd. per bushel; what is the worth of a bushel of this mixture? Ans. 4s\ Ijd.r^^. 9. A vintner mixes 20 gallons of Port, at 5^. 4d. per gal- lon, with 12 gallons of White wine, at 55. per gallon, 30 gal- lons of Lisbon, at Qs. per gallon, and 20 gallons of Mountain, at 45. iod, per gallon ; what is a gallon of this mixture worth ? Ans. 55. 3Jdf|. 10. A farmer mingled 20 bushels of wheat, at 55. per bushel, and 3i^ bushels of rye, at 35. per bushel, with 40 bushels of barley, at 25. per bushel ? 1 desire to know the worth of a bushel of this mixture ? Ans. 35. 11. A person mixing a quantity of oats, at 25. Qd. per bushel, with the like quantity of beans, at 45. Qd. per bushel, would be glad to know the value of 1 bushel of that mixture ? Ans. 35. 6d. 12. A refiner, having 12 lb. of silver bullion of 6 oz. tine, 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. 6 oz. 18 dwt. 16 grs. 13. If with 40 bushels of corn, at 45. per bushel, there are mixed 10 bushels, at Qs. per bushel, 30 bushels at 55. per bushel, and 20 bushels, at 3s. per bushel, what will 10 bushels of that mixture be worth? Ans. £2 3> ALLIGATION ALTERNATE Is the method of finding what quantity of any number of simples, whose rates are given, will compose a mixture oi a given rate: so that it is the reverse of Alligation Medial, and may be proved by it. 128 ALLIGATION ALTERNATE. Rule. 1. Write the rates of the simples in a column un- 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 difference between the mixture rate and that of each of the simples, opposite the rates with which they are linked. 4. Then if only one difference 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^. 19^. 1 bs. and 225. per gallon, so that the mixture may be worth 185. the gallon: what quantity of each must be taken? at 145. at 165. at 195. at 225. 6 at 145. 1 at 165. 7 at 195. 4 at 225. Note. Questions in this rule admit of a great variety of answers, according to the manner of linking them. t. How much wine at 65. per gallon, and at 45. per gal- lon, must be mixed together, that the composition may be worth 55. per gallon? Ans. 1 qt. or I gall, of each, &c. .3. How much corn, at 25. Gc?., 35. 8c?., 45. and 4^. Sd. per bushel, must be mixed together that the compound may be worth 35. lOd. per bushel? Ans. 12 at 25. 6(i., 12 at 35. 8d,^ 18 at 45., and 18 at 45. 8c?. 4. A goldsmith has gold of 17, 18, 22 and 24 carats fine^ how much must he take of each to make it 21 carats line ? Ans. 3 of 17, a of 18, 3 of 22^ and 4 of 24. ALLIGATJON ALTERNATE. 129 5. It is required to mix brandy at 8*., wine at 7*., cider at 1^ , and water, together, so that the mixture may be worth Iss. per gallon? Ans. 9 galls, brandy, 9 of wine, 6 of cider, and 5 of water. When the xvhole composition is limited to a certain quantity. Rule. Find an answer as before by linking ; then say, As the sum of the quantities, or differences, thus determined, is to the given quantity, so is each ingredient found by link- ing to the required quantity of each. EXAMPLES. 6. How many gallons of water must be mixed with wine worth 3s. per gallon, so as to fill a vessel of 100 gallons, and that a gallon may be afforded at 2*. ^d. ? -Iso 30 (36 36 : 100 :: 6 36 3G : 100 :: 30 6 30 36)600(16 36)3000(83 36 288 240 120 216 108 24 12 Ans. 83i gallons of wine, and 16| of water. 7. A grocer has currants at 4c?., 6fl?., 9d. and \]d. per lb. and he would make a mixture of 240 lb. so that it might be afforded at 8c^. per lb. : how much of each sort must he take ? Ans. 72 lb. at 4d.^ 24 at 6c?., 48 at 9^., and 96 at 1 Id, 8. How much gold of 15, of 17, of 18 and of 22 carats fine, must be mixed together to form a composition of 40 oz. of 20 carats line ? Ans. 5 oz. of 15, of 17 and of 18, and 25 oz. of 22. 1^0 POSITION. When one of the ingredients is limited to a certain quaiitity. Rule. Take the difference between each price and the mean rate, as before ; then, 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 55., at 5*. 6cf., and at 6^., the gallon, must be mixed with 3 gallons, at 45. per gallon, so that the mixture may be worth 55. 4d. the gallon ? ] , 8 + 2=10 )— [— U I 8 + 2=10 ;_L.U I 16+4=20 >-_|-.^ / 16 + 4=20 ) : 10 : : 3 : 3 10 : 20 ': : 3 : 6 10 : 20 : : 3 : 6 Ans. 3 gallons at 55., 6 at 55. 6d.^ and 6 at 65. 10. A grocer would mix teas at 125., IO5., and 65., with 20 lb. at 45. per lb. : how much of each sort must he take to make the composition worth 85. per lb. ? Ans. 20 lb. at 45., 10 lb. at 65., 10 lb. at IO5., and 20 lb. at 125. 11. How much gold of 15, of 17, and of 22 carats fine, must be mixed with S oz. of 18 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 Is a rule which, by false or supposed numbers, taken at pleasure, discovers the true one required. It is divided into two parts ; Single, and Double. sijYgle position Is by using one supposed number, and by working with it as the true one, you find the real number required, by the follow mg Rule. As the total of the errors is to the given sum, so is the supposed number to the true one required. POSITION. 131 Proof. Add the sereral parts of the result together, and if it agrees with the given sum it is right. EXAMPLES. 1. A schoolmaster, being asked how many scholars he had, said, If I had as many, half as many, and one quarter as ma- ny more, 1 should have 264 : how many had he ? Suppose he had 72 As many - - 72 I- as many - - 36 } as many - - 18 As 198 : 264 :: 72 72 Proof. 528 96 1848 96 48 24 264 198)19008(96 answer. 24 1782 1188 1188 2. A person, after spending i and J of his money, had 60 <]ollars left; what had he at tirst? Ans. 144 dolls. 3. A certain sum of monf^y is to be divided between 4 per- sons, in such a manner, that the first have i ot it, the second J, the third i, and the fourth the remainder, which is 28 dol- lars ; what was the sum ? Ans. 1 1 2 doll?. 4. A person lent his friend a sum of money unknown, to receive interest for the same, at 6 per cent, per annum, sim- ple inttM-est, and at the end of .^ years he received for prin- cipal and interest 644 dollars 80 cents; what was the sum lent? Ans. 496 dolls. DOUBLE position- Is by making use of two supposed numbers, which, if both prov^ false, are, with their errors, U' he thus disposed : Kli.e. 1. Place each error against its respective position. 2. Multiply them crosswise. 3. If the errors are alike, that is, bctiL 4r>:ater or i^oili less ilian the given number, divide the diiierence ol the products J52 POSITION. by the difference of the errors, and the quotient is the an- swer ; but if the errors be unlike, divide the sum of the pro- ducts 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 three times as much as he did, and 15 dollars more, he would stand him in 300 dollars : what was the priqe of the horse ? dolls. dolls. Suppose he cost 90 Suppose he cost 96 3 3 220 288 15 15 285 too little by 15 dlls. 303 too much by 3- 90 15— X 96 3+ 15 1440 270 3 270 3rs 18) 1710(95 answer. 95 162 3 90 285 90 15 300 proof. 2. Two persons, A and B, have both the same mcome ; A saves one-fifth of his yearly ; but B. by spending 150 dol- lars per annum more than A, at the end of 8 years finds himself 400 dollars in debt ; what is their income, and what does each spend per annum ? Ans. Their income is 500 dollars per annum ; also A spends 400, and B 550 dollars per annum. 3. There is a fis^h whose head is 9 inches long, and his tail is as long as his head and half his body, and his body is as long as the head and tail : what is the hole length of the fish? Ans. 6 feet. EXCHANGE. 135 4. Divide 15 into two such parts, so that when the greater is multiplied by 4, and the less by 16, the products will be equal. Ans. 12 and 3. 5. A man had two silver cups of unequal weight, having one cover to both, 5 oz. ; now if the cover is put on the less cup, it wiU be double the weight of the greater cup, and put on the greater cup it will be three times as heavy as the less cup : what is the weight of each cup ? Ans. 3 oz. less, 4 oz. greater. 6. A person, being asked in the afternoon what o'clock it was, answered, that the time past from noon was equal to j\ of the time to midnight; required the time. Ans. 36 miautes pas^t one. EXCHANGE Is the paying of money in one place or country, for the like vahie to be received in another place or country. There are two kinds of money, viz. Real and Imaginary. Real Money is a piece of metal coined by the authority of the state, and current at a certain price, by virtue of the said authority, or of its own intrinsic value. Imaginary Aiuiiey is a denomination used to express a sum of money of which there is no real species, as vi livre in France, a pound in America, because there is no specie cur- rent, in this or that country, precisely the value of either of the sums. Par 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-tive shillings flemish. Course of Exchange is the current or running price of ex- change, which is sometimes above and sometimes belov* par, varying according to the occurrences of trade, or demand for money. Of this course, there are tables pnblii^hed daily in commercial cities: thus by Lloyd's List, of 3d December, 1791.), the course of exchange between Hamburgh and Lon- don wari 32*. 6W Flemish, per pound sterling, being 25. 5|^. under par, or loss to London. N 134 EXCHANGE. GREAT BRIT Am. The money of account is Pounds^ Shillings^ Pence and Farthings. The English Guinea is 21 shillings sterling. Weights and meiuures generally as in the United States. The United States Dollar is equal to 4^. 6d. sterling. To change Sterling to Federal AJoney. Rule. Annex three ciphers to the sum (if pounds only) and multiply it by 4; this product di\ide by 9, and you have the answer in cents. If there be shillings, kc. the usual me- thod is to reduce it to Massachusetts money, by adding one third to it, and then reduce this sum to Federal. EXAMPLES. 1. Chanje £48 Sterling to Federal. 48000 4 9)192000 21333^ cents. Ans. 213 dolls. 33i- cts. 2. Change £389 17 4^ Sterling to Federal, exch.mge at 331 per cent, that is, £133^ Massachusetts for £100 Ster- ling. 1)389 17 4^ Sterling. 129 19 U Exchange. 519 16 6 Massachusetts. ,3)519,825 cts. 173275 Federal. Anc. ^732 <^o]h 75 ctJ«. Note. Sterling is changed to Massachusetts nioj.ej by uddinp, one third lo the sum, and Massachusetts to Sterling by deducting one fourth from it. To change I eileral Currency to Sterling. Rule. Work by either of the following methods. EXCHANGE. ISb EXAMPLKS. Change 1732 dollars 75 cts. to sterling. First method. Second method. n32 1732,75 ,3 4*. J 346 6/y. 1 43 50 cents 25 cents 8 6 2 1 3 H Ans. 389 17 ^ 5i9|825 20 lelooo 12 6|000 1)519 16 6 Massachusetts. 129 19 li Exchange. Ans. £389 17 4^ Sterling. 2. What is the Federal amount of an invoice of goods, charged at £196 14 6 Sterling, advancing on it 25 per ct? 25 i) 196 14 6 Sterling. 49 3 7| Advance. 245 18 11 Exchange at 33i per ct. 81 19 4^ £327 17 6 Massachusetts. "3)327875 cts.~T09291| Ans. 1092 dls. 91| cts. 3. The Sterling cost of certain goods being £60 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^ per cent, 30 6 3 Ans. 121 5 Mnss. money. The mercantile method, with 50 per cent, advance, is to double the Sterling for Massachusetts money, thus : 60 12 2 £121 5 Massachusetts, as abore. 136 EXCHANGE. 4. An invoice of good?, charged at £52 19 7 sterling is sold at 75 per cent, advance on the sterling cost ; how much is it in Massachusetts money ? 62 19 7 Advance at 50 26 9 9^ 25 13 4 10| 92 14 31 Exchange at 33i per cent. 30 1 8 1 Ans. £123 12 4} Mass. money. The mercantile method with 75 per cent, advance is, to multiply the sltrling by 2l for Massachusetts money. '' Thus, 52 19 7 ^t 105 17 19 2 13 2 Ans. £123 12 4j Mass. money ,^ as above. 6. The sterling cost of certain goods b^ing £214 11 6^ how much is it in Federal money, advancing thereon 65 per cent.? 214 11 6 50 A 107 5 9 > , 10 } 21 9 1|^" advance. Exchange i. 343 6 4| 114 8 91 457 15 21 Massachusetts^. Or thus, 214 11 6 Sterling. Exchansre -i- 71 10 6 286 2 50 i 143 1 10 I 28 12 2i 457 15 2j- Massachusetts. ,3)457,759 ilollars 15?5,86i Ans. 15 dolls. 86 J cts^ EXCHANGE. 137 6. What is the amount of a bill of exchange of £ll5 14 9 sterling, sold in Boston at 1| per cent, advance ? 1)115 14 9 Sterhng. 38 11 7 Exchange. Massachusetts money. 154 6 4 Mas ^3)154,317 514,39 n Federal 51439 25719 cents 771|53 dolls, els. Value at par 514 39 Advance 7 71^ Amount 522 10^ dolls, cts. Or thus, Value at par 514 39 Advance at 1 per ct. 5 14 3 '- do. 2 57 1 7 71 4 Adv. at li per cent. Amount 522 10 4 7. 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 60 per ct. advance on the sterling cost; required the selling price of each in Massachusetts money. s. d. s. d. dlls. c. m 13 8 ster. adv. 60 per ct. 29 U Mass. money, or 4 85 3 6 10 - - - 12 5i - - - 2 7 3 S4.-- 7U -- 183 6 li - - - 13 04 - - - 2 17 6 17 . - - 36 3i • - - 6 4 6 S3 1 - . . 70 6i - - - 11 75 6 1 2 - - - 2 5i ... 41 18 10 - - - 40 2 - - - 6 69 4 11 - - - 23 5i - . - 3 91 2 4... 4 lU ... 82 3 32 3 - - - 63 9i - - - 11 46 6 27 9 . - - 59 2i - - . 9 86 3 >i 2 138 exchange:. 8. A watch, that cost 1 5 guineas in London, was sold }» Boston at 50 per cent, advance on the sterling cost; what was the price ? 15 guineas=£l5 15 sterling. 31 10 Massachusetts. ,3)31,5 Ans. 105 dollars. 9. How much is the premium of insuring j£294 at 8 gui- neas per cent.? Ans. j£24 13 11 sterling. MERCANTILE METHODS OF CALCULATING, vIz. *^i 2b per cent, discount from the sterling cost^ multiply it by I for the answer in Massachusetts money. 10 li par ----_. li 12| per ct. adv. on the sterl. cost, multiply it by l^. 25 ----- 1| 31i .... - 1-1 50 - - ... 2 62^ - - - - - Sli 65 - - - - - 2| 75 - - . . . 2i 87i - - • - - 2i 100 2| 125 .... - 3 "' 140 - - - - - 31 450 ..... 31 1621 31 175 . - - - - 3| 200; - - - - -4 IRELAND. if The money of account as in England, but different in va- lue. The par between England and Ireland is 8i per cent, that is, iilOO sterling money is £j08 6 8 in Ireland. Mercantile weights and measures the same as in England The United States dollar is equal to 4^^ \0\-d. Irish. The English guinea is equal to 22.^ 9(/. Irish. EXCHVNGE. 139^ pence in a Or reduce t, and Iheu work To r€(]tice Irish money to Federal. Rule. Reduce the given sum to half pence, annex two ciphers to it, ami then divide by 1 17 (the hall dollar) and the quotient is the answer in cents, the Irish to Sterling, by deducting Jg from as for sterling. EXAMPLE. Change j£278 15 9 Irish money to Federal. First method* Second method. i^78 i5 9 y'gj 27b 15 9 Irish. 20 21 8 1 1 Lxchrtnge. 5575 12 257 6 10 sterling. 85 15 71 66909 2 343 2 b\ Mass. ,3)343,122 1143,74 cents. 9)13381800 X 13= 117 13)1486866 114371 cents. Ans. 1143 dolls. 74 cts. To change Federal money to Irish, Rule. Multiply the given sum by 117, reject two figure* from the product to the right hand, and the remaining figure* are the halfpence in the given sum. 1. Change 1143 dolls. 74 cts to Irish. 114374 117 80061 a 114374 114374 2)l3^8l7|5a 12)66908 J 2|';)557|5 8 Ans. £278 15 8f 140 EXC|TANGK. If the Slim is dollars only, work bj' either of the foUomo^ methofls. -^v 2. Change 1537 dollars to Irish. "h"; .. First method. Second method* 1537 at 4*. lOirf. 1537 3 4.. \ 307 8 Sd. i 51 4 8 2 1 12 16 2 i i 3 4 ^ 461 2 Massachusetts, i 115 5 6 Exchange at 25 per ct. 345 16 6 sterling. Ans. £374 12 10^ ^3 28 16 4^ exc. 8J p.ct. or Ic^. on l^. £374 12 \0X In changing Sterling to Irish nioney at par, ^^ is added to the sum for Irish : and in changing Irish to sterJmg, ^l is deducted for sterling, because 12 pence English are equal to 13 pence Irish, making the exchange Id. in a shilling, 1*. '6d. m a pound, and £8 6 8 per cent. EXAMPLES. 1. Change £394 17 6 sterling to Irish, at par, or £8^- per cent. 3?2)394 17 6 32 18 U Ans. £427 1.^ 7J Irish. 2. Change £427 15 7j- Irish money, to sterling, at gj per cent, in favour of England. yV)427/15 li 32 18 1^ Ans. £394 17 6 sterling. 6 Change £370 sterling to Iriih at d per cent. £ £ £ 100 : 109 :: 370 Ans. £403 6 4. Reduce £403 6 Irish money to Sterling, at 9 per ct. 9 100 -- £ s. 109 : 100 :: 403 6 Ans. £370 fe EXCHANGE. 141 HAMBURGH. Accounts are kept in Hamburgh in Marks^ Shillings Lubs^ or Stivers^ and Dtniers. 12 deniers, or 2 grotes, make 1 shilling lubs, or gtiver. 16 shillings lubs^ stivers, o''' ^ i u 32 grotes " - - j Jilso^ 12 grotes or pence Flemish make 1 shilling Flemish, SO shillings Flemish - - 1 pound. Note, 3 marks - make - 1 rix dollar. Ik do. - - - - • ] pound Flemish- A shippound in Hamburgh - 2S0 lb. A ring of slaves do. - 240 100 lb, in Hamburgh - - 1074 in U. States. 100 ells do. - - 62i yards. The currency of Hamburgh is inferior to the bank money ; the agio.^ or rate, is variable; Maj 14th, 1798, it was 20 per cent, in favour of the bank. The mark banco is 33^ cents. (See laws of the U. States.) EXAMPLES. 1. Change 12843 marks to Federal, at 33^ cents per mark. 33^=1)12843 Ans. 4281 dollars. 2. In 4967 marks 8 stivers banco, how many dollars, ex- change as above ? 331=1)4967, 1655,66| 8 stivers ,16| dolls. 1665,831 Ans. 1655 dolls. 83i ets. To change Hamburs^h money to Sterling, Rule. As the oiven rat^ is to one pound, so is the Havtt* burgh sum to the sieriiog required. 142 EXCHANGE. EXAMPLES. 1. Chang-e 9443 marks 9 J stivers to Sterling, exchange at 325. 6d. Flemish per pound Sterimg. s. d. £, m. St. 32 6 : 1 :: 2443 9^ 12 grotes. 32 2 390 4886 19 grotes. 7329 19 78195 390)78 195(200£ 780 195 20 390)3900(105. 3900 Ans. £200 10 2. In 12093 marks 12 stivers, how many pounds sterling, exchange at 32^. 3rf. Flemish per pound sterling ? Ans. £1000 3. In 4178 marks 2 stivers, hov^r many pounds sterling, exchange at 3U. 10^. Flemish per pound sterling? Ans. £350 4. Change 1971 marks 13 stivers to sterling, exchange at 355. 6d. Flemish per pound sterling. Ans. £148 2 4 To change Sterling to Hamburgh money, KuLE. As 1 pound sterling is to the given rate, so is the «tening sum to the Hamburgh required. EXCHANGE. 143 EXAMPLE. Change £350 Sterling to Hamburgh money, exchange at 31*. lOd. Flemish per pound Sterling. £ s. d. £ I : 31 10 :: 350 12 382 grotes. 350 19100 1146 2)133700 grotes. 16)6t)859 Slivers. 4178 2 Ans. 4178 marks, 2 stivers. Proving the answers in the preceding case will further exemplify this. To reduce Current to Bank money. Rule. As 100 marks with the agio added is to 100 hank, 30 is the current money to the bank required. EXAMPLES. 1. Change 560 marks 8 stivers current to banco, agio at 18 per cent. 18 100 118 : 100 :: 560 8. Ans. 475 marks. 2. Change 2366 marks current to banco, agio at tO per cent. Ans. 1971 mark;-, !0| stivers. 3. Change 7456 current marks to banco, agio at -'Z'-Z per cent. Ans. 6111 marks, 7 slivers. 144 ^ EXCHANGE. To change Bank to Current Money, Rule. As 100 marks i« to 100 with the agio added, so is the bank given to the current reuuired. EXAMPLES. 1. Change 475 marks banco to current, agio at 18 per ct, 18 m. m. 100 : 118 :: 475 Ans. 560 marks, 8 stivers. Or thus, 475 18 475 bank. 85 8 agio. 3800 .— . — 475 560 8 as above. 85150 16 8100 2. Change 1971 marks, 10| stivers banco to current, agio at 'iO per cent. m. 9, 20 J) 1971 10| banco. 3^J4 51- agio. Ans. 23{j6 current. PRACTICAL qUESTIOjYS, 1. How much will 63452 lb. of cotton come to at 8 grote« per lb. ? ib. gr. lb. 1:8:; 63452 8 2)507610 grotes. 16)253808 stivers. Ans. 15b 6 3 marks. EXCHANGE. 145 g. What will 361 lb. of cotton come to at bOd. per lb. ? Note. cL is the mark for pence Flemish, equal in value to half sti- vers or half shillings lubs. lb, d, lb, 1 : 50 : : 351 50 2)17550 grotes, or pence Flemish. 16)8775 stivers. 548 7 Ans. 548 marks 7 stivers. S. What will 339 bars Russian iron come to, wt. 19662 lb. at 35^ marks per shippound ? lb. m. lb. 280 : 351 : : 19662 Ans. 2492 m. I4stiv m. St. 4. 280 lb. of conon - at 21 grotes per lb. - 183 12 6. 40024 lb. coffee Si stivers - 2063 10 €. 2438 pipe staves 16 marks per ring of 240 162 9 7. 3540 hhd. do. 8h do. do. - 125 6 8. 529 barrel do. 54 do. do. . 11 9 9 1 790 ib. sugar 214 pence per lb. - IISS 10 10. 4892 lb. rice 184 m:irks per 100 - 892 12 11. 4 pieces ;0-4 bedtick 24 do. do. - 96 12. 140 half pint tumblers 8 do. per 100 . 11 3 13. 100 boxes window glass 23 do. per box . ^300 14. 1526i lb. coffee IQh stivers per lb. - 1574 S 15. 245 bars iro-i, wt. 8434 lb. 4 1 nKirks per shippound 1235 16. 10 bales hemp, wt. 14' OS lb. 74 do. do. 3728 17. What is the commis^iun on 18270 marks, at 2^ per || cent.? Ans. 456 m. I2"st, 18. VVhat is the interest of 6370 marks, for 3 months, at 5 per ct. per annum? Ans. Id m. 10 st, O 146 EXCHANGE. 19. Change 5955 marks 7^ stivers to Dutch Florins, at 38i grotes per florin. m. St. 5955 71 grotes in a niark=32 2 grotes a stiver. 1 1 910 15 grotes in 7 J stivers. 17865 15^ grotes 381 190575 grotes. .2 2 77" ) 381750 ( 4950 gilders. 308 731 693 385 385 — ^- Ans. 4950 gild, or flop. 20. An American merchant orders his correspondent in Amsterdam to remit 4980 florins 16^, stivers to Hamburgh; this heing done when the exchange is r^9i stivers lor 2 marks, vsrhat sum is he credited for in Hamburgh ? St. m. Jl. St. 391 : 2 :: 4980 lUj 4 20 157 99616^ 199233 4 157)79^932(5076 marks. 785 1193 1099 942 942 Ans. 5076 marks. EXCHANGE. 147 HOLLAND, Accounts are kept in Florins or Gilders^ Stivers^ Dcniers or Pennings, 8 penning"? - make - 1 grote. 2 grotet, or 16 pennings - - - 1 sliver. 20 stivers, or 40 grotes - - - 1 gilder or florin. Also, 12 grotes or 6 stivers - - - i shilling. 20 shillings, or 6 gilders - - - 1 pound Flemish^ 2k dorms - - - - - 1 rix dollar. The florin or gilder of the United Netherlands is estima- ted m the United States at 40 cents, or 2 cents per stiver. 100 Ih. in Amsterdam make 109| in the United States. 100 ells do. 75 yards do. la liquid measure, 16 mingles make 1 steckan. 8 steckans - 1 aum. EXAMPLES. 1. Change 1954 florins to Federal money at 40 cts. per floria. 1954 40 dolls. 78 1,(50 Ans. 781 dolls. 60 cts. £. Change 2653 gilders 17 stivers to Federal money, at 40 cents per gilder. 2653 17 Or thus: 2653 17 40 2 20 106120 34 53077 stivers. 34 2 cents per stiver. 106154 cents. 1061,54 Ans. 1061 dolls. 54 cent j», 3. Change 1061 dolls. 54 cts. to gilders, at 40 cts. per gilder. 2)106154 cents. 2|0)5'^0717 stivers. 2653 17 Ans. 2653 gild. 17 stiv. 148 EXCHANGE. 3. What must be paid in Boston for an invoice of goods charged at 691 florins 17 stivers ; allowing the exchange at 40 cents per florin, or 2 cents per stiver, and advancing or it 60 per cent.? 591 17 20 dolls. cts. 1 IQdl stivers. am. of invoke 236 74 2 advance 142 04 dolls. 236,74 Ans. 378 7» 60 per cent. 142,0440 To change Sterling to Flemish. Rule. As 1 pound sterling is to the given rate, so is the sterling given to the Flemish required. EXAMPLE. 1. In £100 10^. sterling, how many gilders, exchange ai 33*. Od. Flemish per pound sterling? £, 9. d. £, s. 1 ! 33 9 :: 100 10 20 12 20 20 405 grts. 2010 403 10050 80400 f|0)8 1405,0 2)40702| grotei. ^j0)2035|li stivers. 1017 11 J Ans. 1017 gild, llj stir. To change Flemish to Sterling. Rule. As the given rate is to £l sterling, so is the Flent- i$h given to the sterling required. EXCHANGE. 149 EXAMPLE. Ghani^f* 1017 gildors 11 J- stivers to sterling, exchange at 335. 9ii. Flemish per pound sterling. s. d, £ fl. St. 33 9 : 1 :: 1017 111 12 40 2 405 grotes. 4U680 221 221 405)40702^(100 405 2U2J 20 405)1050(10 4050 Ans. £100 1# To change Current money to Bank. Rule. As 100 gilders with the agio added is to 100 bank, so is the current money given to the bank required. EXAMPLE. Change 023 gilders 9i stivers current money into bank, agio at 4^ per cent. S' g' g' ^• I04i : 100 : : 823 9J 20 20 2090 164691 100 2090)164^920(788 gilders. To change Bank money into Current. Rule. As 100 gilders bank is to loo with the agio added^ tso IS the bank mouey given to the current required. example. Change 788 gilders bank money to current, agio at 4^ per cent. g. g. g. 100 : lu4i :: liS3 Ans. 023 gilders, 9] stir. 2 I5(i EXCHANGE. PRACTICAL qUESTIOJVS, I. What will 18f'.7 lb. oi coffee come to at 19 stivers per lb.? 1867 19 16803 1867 210)3547|3 stivers. 1773 13 Ans. 1773 gilders 13 stivers; 2. What will 9*2 hhds. of sugfar come to, wcig-hmg UM242 lb. gross, deducting 2 per cent, for good weight, tare 18 pei* cent, at 21 grotes per Ih. ? 104242 deduct 2 per cent. 2085 102157 rare 18 per cent. 18388 83769 neat wt. 21 83769 167638 8)1769149 grotes* 2|0)87957|4i stivers. 43978 14i Ans. 4397S gilders, 14^ stiven> 3. What will 251 bars of iron come to, weighing groSi^ 10364 lb. at 9f gilders per lb. deducting 2 percent.? 10364 91 93276 6182 2691 g- 2percent.=:J^)10iO 8 9 4 12 8 1010,49 20 Ans. 990 6 -0 9,80 16 i2,8d EXCHANGE. 151 4. What will 4 43 steckans 2 miogles of brandy come to at 42 giidei*s per ap.ni ? 8)M3 17 7 a 42 34 68 4 steckans h 21 2 do. k 10 10 1 do. h 5 5 2 mingles X 13 2 d. 2^315 1b. of sugar 6. 5650 18 Ans. 3951 9d 84308 15 32l0)126462lu(3951 96 304 166 160 62 32 ' 30 96 32)2880(90 2880 Ann. 3951 dolls. 90 skills. 3. Whnt is the commission on 21545 Danish dolis. 13 skil- lin^y, at 2 per cent. ? 21545 13 2 43o,9n 26 96 566 810 r^C^,6^ Ans. 450 dolls. 86 skills. dls. sks. dls. sks. 3 80 - 15 32 9 5t> - 4713 16 17 G4 . 229 64 12 - 288 08 15 - 750 00 SOpVshi W 'dl884 18 3G 9000 00 11 5074 3 EXCHANGE. 158 4. What will 4 hhds. of snp^ar come to, weighing gross 4314 lbs. tare 17 per cent, at 22 skilling^s per lb. ? An8. 820 dolls. 62 skills. 8. 4 pieces table cloth 6. 50 do. - - - 7 13 do. ... 8. 24 do. - - - 9. 50 do. 10. 100 coils cord, wt. 62sk. 16/. 2/6. 11. 85 bund. cl. hemp, 250 12. 1951 bars Kus. iron, 362 8 10 13. How many Danish dollars will be received in Copen- hagen for a bill of £2300 on London, exchange at 5 rix dol- lars per pound sterling t Ans. 1 1500 dolls. 14. A bill is drawn in Copenhagen for 18574 marks 7 stivers, Hamburgh money, when the exchange is 128 Danish dollars for 100 rix dollars in Hamburgh: how many Danish dollaus does it amount to ? Note. Three marks are equal to I rix dollar. m, r.d. m. st. r.d. sk. If3 : 1 :: 18574 7 : 6191 46 r.d, D.d. r.d. sk. If 100 : 128 :: 6191 46 Ans. 7925 D.dolls. 6 sjc. Or thus, 3)18574 7 Hamburgh mone^'. 6191 46 t8 per cent. 1733 56 7925 6 Danish money, as above. BREMEK Accounts art kept in Rix Dollars and Gr'otes^ reckoning 72 grotes to the rix dollar^ which is equal to 2-\ marks. On the 29th November, 1795, the exchange on LondoQ was 551 rix dollars for £iOO sterling. In 1^02, the course of exchange on the United States was 75 cents per nx dollar. '1 he BremiMi last is equal to 80 bushels in the U. States. lUO ib. m Bremen are ecjual to 110 lb. m the U. States. 154 EXCHANGE. EXAMPLES. \. What will 1104 lb. of coffee come to, at 32 J grotes per lb. ? 1104 S2| 2208 33 2 552 276 r.d. groteSi 72)36156(602 12 360 156 144 12 Ans. 602 rix dollars 12 grotes; 2. What is the commission on 7621 nx doils. 6 gr at 3J per cent. ? Ans. 26fci nx doils. 53 grotes. r. dUs. gr, 3. 3071 lb. coffee at 32 J grotes per lb. - 1396 63 4 400 - 3^f - - . 181 18 5. 706 - 33^ . . - 328 35 6. 31407 lb. sugar 15| * - - 6870 20 AKTWERP. Accounts are kepi in Antwerp in Gilders^ Shillings and Grotis. 12 grotes - make - - 1 shilling. 3^ shiHm<2:s, or 40 grotes, - - 1 gilder. The Braband or Antwerp grotes are of the value of the cents of the Unifed States, a j^ilder being reckoned al 40 cents. In the current mo- ney of Aniweip they have stivers of the value of the stiver of Amster- dam, or 2 cents Uniied States currency. 100 pots binband = 36^ gallons United States. 96 lb. AnUverp = 100 lb. do. 100 Brabiuid ells, about 74 yards American. The new quintal of Antwerp consists of 10 mjriagramme* dr 204 lb. 14 oz. ^voirdupois weight. The loss on Sugar ex(>orted from America to Antwerp if 22| per cent, viz tare 14 lb. per 100 lb. — good weight 2 lb. —loss of weight 5 lb. — discount 1| lb. equal to 221 lb. per lOu lb. Loss on Cotton 12J- per ct, — on coffee in bags ll-J- per ct. EXCHANGE. 155 EXAMPLES. 1. A cargo consisting of 48 hhds. sugar, weighing 376 cwt. 1 qr, 14 lb. valued per invoice al 12 dolls, per cvvt. and 6b bags coffee weighing 7.345 lb. at 32 cents per lb. is sold in Antwerp; what sum wat?^ received for it in gilderg and grote^, at 40 cents per gdder, allowing the customary deductions for tare, ^c. at an advance of 33^ per cent, from the Invoice ? cwt. qrs. lb. lb, 37t) 1 14 7345 Tare, &c. 22J per ct. 84 2 20^ Tare SiC. Ill p. ct. 844 1 NeatSyi 2 21^ Neat 65004^ 32 dolls, cts. 13000 12 00 19500 10 16 120 00 10 1200 00 2 dolls. 2080,16 2400 00 value of 200 cwt. 80 00 . 90 12 00 • 1 6 09 - 2 qr<5. 1 50 . 14 lb. 75 «. 7 5 3 ^ ^ Value of suirar 3500 40 3 291 2 2!^ do. coffee 2080 H". ■ Adv. 331=1- ineo 18 7 5530 56 3 4|0)74107j5 cent« 18601 35 dolla. 7440 75 Ans. 18601 gilders 35 grains. J 66 EXCHANGE. 2. What sum mupt be paid in Boston for an invoice of goods imported from Antwerp, amonntins^ to 7315 gilders, exchange 40 cents per gilder, at an advance of 40 percent.? 7315 731F, 40 per ct. advance. 2926 advance. 2926,00 10241 40 cts per gilder. Ans. 409e dolls. 40 cts. RUSSM. Jiccowits are kept in Petersburgh in Rubles and Copets^ reckon- ing 100 copecs to 1 ruble. The course of exchange on London, in July, 1796, was 34|c/. sterling per ru'tle. Ditto on Amsterdam, 30 stivers banco per ruble. Ditto on Hamburgh, Aug. 1798, 2^'! «5tivers banco do. Ditto on United States, Sept. 1802,^55 cents do. 100 lb. Petersburgh weight are equal to 883 lb. in the United States. Their weights are Barquits, Poods, Pounds, & Zollotnicke. 96 zollotnicks - make - 1 pound. 40 pounds ----- 1 pood. 10 poods 1 barquit. Their long measure is the arsheen, of 28 American inch- es: 9 arbheens are equal to 7 ^'anls. EXAMPLES. 1. What will 7500 arsheens of ravens duck come to at 14i rubles for 50 arsheens? arsh, rvb. ar^h. 50 : 14V :: 7500 Ans. 2175 rubles. EXCHANGE. 157 2. What will 813 poods 5 lb. of clean hemp come to at 30^ rubles per barqait? ib. rub. p. lb. 400 : 30^ : : 813 5 40 32525 30| 975750 16262 4|00)9920il2 2480,03 Ans, 2486 rubles 8 copecs,* 3. What Will 284S poods 5 lb. ot bar iron co^ie to at 200 copecs per pood ? 2846 200 569200 5 lb. I 25 copecs 569225 Ans. 5692 rubles 25 copecs. 4. What is the commission on bzbo rubies dd copecs, at 3 per cent.'/ 5266,33 3 157,68,99 Ans. 157 rubles 68 copocs. rub. cop. 5. 4997i arsheens flems 24 rubles per 50 arsheens 2393 SO 6. 1700 do. drillings 34 copecs per arsheen 578 7 355 do. ticking 100 do. do. 355 8. U8| do. do. 110 do. do. 180 62 9. 200 pieces of sail cloth 21 rubles per piece 4200 10. 2 1. i poods 25 lb. hemp 31 do. per barquit 65.5 04 11. ;;0.v ill iiiy rubles uiust be r- ceiveJ iii Petersinirgh, for a bill orio*)OU fi^ilders on Amsterdam, when the exchange is 30 slivers per ruble? St. cop. gild. gild. A«30 : 100 :: 15500 Or thus, i)l"6500 20 5166,6G| 310000 stiyers. 10333,331^ 100 -. 3l'>)3l0u(>o(;|0 10333,331 Ans. 10333 rub. 33^ cop. P 158 EXCHANGE. 12. A bill of £3000 sterling is drawn on London, ex- change al 31|c/. sterling per ruble: what is its value in Fe- te rsburgh ? d, rub, £. As 31J : 1 : : 3000 4 20 127 60000 12 720000 4 127)28auOOO(22677 rubles. 254 340 254 860 762 980 889 910 889 127)2100(16 copecs. 127 830 762 68 Ans. 22677 rub. 16 cop^ Two cipbor«« are annexed to the remainder instead of (ftiultiplying by 100 copecs. FRAACE, 12 deniers = 1 sol, 20 sols = 1 lirre. The crown of exchange is 3 livres tournois. A livre tournois of France is estimated at 18 J cents in the IJnit^d States. NOTE, The word tournois, is applied to the money of France, as sterling i» to the money of Engkad. EXrHANGE. 15§ 1. Chani^e £1220 sterling to French money, exchange at 17|857 Hv. 18*. Id. EXCHANGE. IGl G. What is the freight of 3302^ veils, at 9 livres per ton^ of 1«0 veits ? Ans. 241liv. 13^ 9d. 7. VVhat is the commission on 36591 liv. 2 sols, 4 den. at 2^ percent.? Ans. 914 liv lbs. 6 den. '8. What is the interest of 66476 liv. \0s. 9 den, for one month and 10 days, at \ per cent, per month? A)b6476 10 9 332|38 5 4 20 7165 12 7|84 332 7 7 10 days i 110 15 10 Ans. liv. 443 3 5 9. What is the interest of 3255 livres. for 28 days, at l> per cent, per month ? ^)3255 16|27 10 20 5l50 12 16 6100 5 6 for 1 month, 15 daysl 10 ^^ i 8 5 2 9 8 '6 3 " i 1 12 6 Ans. liv. 15 3 9 The present money of account in France is in francs ani centimes or hundredths. in iNov. 180U, an Eni^lish cruinea was worth 25 fr 75 cts, A Spanish dollar - 5 do. 65 do* P2 162 EXCHANGE. To change Francs to Livres Tournois. Rule. Multiply the francs by 81, and divide by 80 fov livres. EXAMPLE. Change 3756 francs to livnss. 3756 81 3756 30048 850)3U4l>3,6 38U2 76 20 8,0)152,0 19 Ans. 3802 liv. 19 sols. To change Livres Tournois to Francs. Rule. Multiply the livres by 80, and divide the product by 81 for francs. example. Change 5469 livres to francs. ^ 5469 80 81)4:^7520(5401,48 405 325 324 120 81 390 324 660 648 12 Ans, 5401 fr. 48 cch» EXCHANGE. 163 To change Sols and IJeniers to Centimes, Hvi.K T:ike one half of the ^oh and deniers, as if they were iulegei*s ; this half is the number of centimes required. EXAMPLES. sol. den. sol. den. sol. den. sol. den. Chansre 4 6 12 2 6 8 10 6 to centimes. Ans. 23 61 34 83 centmes. When there i« a remainder in dividing the sols, it is to he carried to the demers, and reckoned 10 and not 12; add this )() to the deniers, and take one halt of the sum for the remaining centime. sol. den. 5 8 EXAMPLES. sol. den. 15 4 sol. 19 den. 6 to centimes. •i9 77 98 centimes. Reduce Ans. If thie number of deniers be 10 or 1 1, thoy are to be re* jecled, and m place of them you are to add i to the number of sols preceding, and then annex a cipher to it; oae half of this is the centimes required. sol. den. Change 1 lu EXAAtPLES. sol. den. sol. den. 7 1 1 and 15 1 to centimes. 2)20 Ans. 10 2)80 2)! 60 40 80 centimes. Sols and deniers are reduced to centimes hy the preced- ing rule ; and though the result is not accurate, yet from ite simplicity and conciseness it is generally used. 164 EXCHANGE. TABLES For chan^insr TAvrrs^ Sols and Dea'ers to Francs and Centimes. {^N. B. The first i» suJBciently exact for business ; in the seco..d the answer is calculated .o the ten-thoudandth part of a cen!inie.) rAbi.K i Tabl K V i 10,000th8 Deniers. Fr. Cent. Fr . Cent, . of a I ent 1 - '- 4 5 2 - 1 8230 3 - 1 1 2:.46 4 - 2 1 6461 5 / 2 2 0576 6 - 2 2 4*;9l 7 3 2 8807 8 3 3 2922 9 4 3 7037 10 4 4 1:52 11 5 4 5267 Sols. 1 5 4 9383 2 10 9 8765 3 15 14 8 4S 4 20 19 7531 5 25 24 69:4 6 30 29 6296 7 35 31 5(>79 8 40 39 5062 9 44 44 4444 10 49 49 3827 11 54 54 32 12 59 69 2593 13 64 64 1975 14 69 69 1358 15 74 74 0741 16 79 79 23 17 84 83 9506 18 89 88 8889 19 91 93 S272 Livres. 1 99 98 7654 2 1 98 1 97 5309 S 2 m 2 96 2963 4 3 95 3 95 06 7 6 4 94 4 93 8272 6 5 93 5 92 6926 7 6 91 6 91 3580 8 7 90 7 90 1235 9 8 89 8 88 8889 10 9 88 9 87 6543 12 11 85 11 85 1852 15 14 81 14 81 48 --5 26 19 76 19 75 80S€ EXCHANGE. ^ 16^ 10,000th» Li^Tci. Fr. Cent. Fr. Cert. O' H . eat 24 23 70 23 70 s: [)4 SO 29 63 29 62 9(. >0 40 39 51 39 50 6 73 60 49 38 49 38 27 6 60 59 26 59 25 92 59 70 69 14 69 13 6803 72 71 11 71 11 11 11 SO 79 01 79 01 2344 JO 88 89 88 ,88 8889 96 94 81 94 > ' 81 48 5 100 98 77 ''. 98 76 64 32 200 197 53 197 53 OS 64 SCO 296 30 296 29 62.97 400 395 06 395 06 1729 600 493 83 493 82 7i 61 1000 987 65 987 65 4322 5000 - 49 3S 27 - 4938 27 1608 10000 . 9S76 64 - 9876 54 3217 A 1 'ABLE For reducing Francs and Cent imes to Livres^ Sols and Dcnkr 100[hs Cent. Sol. Den. of Uen. Francs. Liv. Sol Dea 1 - 2 43 2 2 6 2 . 4 S^ 3 3 9 3 7 29 4 4 1 4 - 9 72 5 5 1 3 5 1 ]5 6 6 1 6 10 - 2 30 7 7 1 9 15 3 45 8 8 2 20 - 4 60 9 9 2 3 25 - 5 75 10 10 2 6 30 7 90 15 15 3 9 35 - 6 05 20 20 5 40 - 8 20 30 80 7 6 45 - 9 35 40 40 iO SO 10 50 50 50 12 6 55 - U 65 60 60 15 60 - 12 80 70 70 17 6 65 - 13 95 80 81 70 - 14 2 10 90 91 2 6 75 - 15 2 25 100 101 5 80 - 16 2 40 200 202 10 85 . 17 2 55 300 303 15 90 - 18 2 70 400 405 95 - 19 2 85 500 1000 606 10 2 5 10 Prunes. Liv Sol. Den. 5000 5062 10 1 1 % 8 lOtfOO lOil^i t f lU EXr MANGE SPJIJV. Spanish reckonings are of two sort* : Money of Plate, d siing-nisheti by hani or > (are f\n]hr^^ &C. Money of Vellon, d^shng-uished by cifrrenf dollars. The former is c>li-j\ por cent, above ttie letter. 100 reals plato being equal to 188y\ reals vellon. 100 reals vellon - - 55} reah piale. 17 reals plate - - 32 reals vellon. 17 piastres or current dollars 256 reals vellon. 4 maravadies - make - I quarto. 8;\ quartos, or 34 maravadies, - 1 real. The peso, piastre, or current dollar of 8 reals plate, pass- es at 15 reals vellon in trad«, but m exchange it is estimated at 15 reals vellon 2 maravadies. The ducat of exchange is 375 maravadies. The real plate is estimated at 10 cents, and the real vel- lon 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. Multiply the giren sum by 17, and divide by 3S for reals plate. EXAMPLE. Change 800 reals vellon to reals plat«. 800 17 32)13f300(425 128 80 64 160 160 Ans. 425 reals plate. To change Reals Plafe to Reals Fellon. RuLF.. MuH.piy the given sum by 32, and divide by l?^ for reals vellon. EXCHANGE. 167 EXAMPLE. f In 426 reals plate, how many reals vellon ? 32 850 1275 17)13600(800 136 00 Ans. 800 reals vellon. To change Reals Plate and Reals Vellon to Federal Money. JRuLE. Multiply the reals plate by 10, and the reals vel- lon by 5, for the cents in the given sum. EXAMPLES. 1. Change 14938 reals plate to Feileral money. 14958 10 1495,80 Ans. 1 495 dolls. 80 cts. 2. Change 17593 reals vellon to Federal money. J 7593 5 879,65 Ans. 879 dolls. 65 cts. CADIZ. Accounts are kept by some in hard or plate dollars^ reals vellon^ and quartos. 8^ quartos - make - 1 real vfllon. 2U reals vellon - - - 1 dollar of plate. Others keep their accounts in reals plate and maravadieS| reckoning 34 maravadies to 1 real plate. To bring Reals Plate to Dollars, Rule. Multiply the given sum by 32, and divide by 17, for reals vellon, and divide the reals vellon by 20 for dollars. 168 EXCIIVNGE. EXAMFLK. In 320 reals plate, howmau^ hard dollars? 32 640 960 17)10240(602 reals velloi>. 102 40 34 8|- 2;0)60|2 reals vellon. 17)51(3 quartos. dolls. 30 2 3 15 Ans. 30 dolls. 2 r. v. 3 q. To change hard Dollars to Reals Plate. "Rule. Multiply the dollars by 20 for reals vellon, and the reals vellon bf ni^ mnitipl;ed by 17 and divided by 32 ^^e the reals plate required. — Or, multiply the dollars by iOf for rtals piate. ''example. In 16 hard dollars how uiany reals plate ? 16 Or thus, 16 20 lOf 16 3:,^^ 160 — 17 10 8)80 2210 17U -R. P. 10 320 J2)5440(170 32 S:21 224 Ans. no reals plate. EXCHANGE. 160 PRACTICAL qUESTIOA'S. The'answers io xMch are in Dollars^ Reals Fellon and Quartos. 1. Whnt will 45940 pipe staves come to at 8 piastres or current dollars per M. or UOO? 45940 80 12|00)36752tOO 3062| current dollars, 8 reuls. 24501 1 reals plate, 3S 49002 73503 lOf 17)78404^1(46130 68 104 lOi 17 8,0)46 It^O u Mih nm 1 34 ii n)§^l(i \i 5| Am. 9306 Ufi M\9. r.. 1 q. jpml, ^. r, Q- %^ 81800 ha?fel atw^l at 30J p^p IgOO 411 3 7 a, 1200 hh'i do, 40 c|q, so 2 3 4t I ^si^s §h§?ry wir\§ 30 pev e'^^k 45 3 4 H 170 EXCHANGE. The result of the following is in Reals Plate^ and Moravadies. 5. In 610 hard dollars, how many reals plate ? 010 20 reals vellon=:l hard dollar. 12200 85400 12200 32)207400(6481 192 154 128 260 256 40 32 8 Ans. 6481 reals plate 8 mar. 6. What will 2632 barrels of flour come to at 1 1 current dollars per barrel ? 2632 11 28952 piastres or current dollars. 8 reals plate=l piastre or current dollar. Ans. 231616 reals plate. 7. 88 lasts of white dry salt, at 6 piastres per last? 88 , 6 528 8 4 2'M Ans. 4224 reals plate EXCHANGE. 171 8. Change £600 sterling to reals plate, exchange at 36i(i. sterling per piastre. 600 20 12000 12 561 144000 4 4 146 ) 576000 ( 3972 current dollars. 435 8 1410 31776 1305 3 10 1050 31779 10 1015 350 290 60 8 145)480(3 reals. 435 45 34 180 135 145)1530(10 maravadies. 145 80 Ans. 31779 reals plate, 10 mar. 9. In £3200 sterling how many reals plate, exchange ai 36ic/. sterling per piastre ? Ans. 169489 r. p. 22 mar. ' N. B. In St- Lucar, accounts are kept in reals plate and quartq^ 16 quartos to i real plate. 172 EXCHANGE. BILBOS. Accounts are kept in Reals Vellon and Maravadies^ 34 mar«- vadies making 1 real. The pound in Bilboa consists of 17 oz. except in iron, which is but 16 oz. 32 veltB are equal to 66 gallons in the U. States. 100 fanagues - 152 bushels do. 100 varas - lOB yards do. To change Piastres or Current Dollars to Reals Plate, Rule. As 1 current dollar is to 15 reals 2 maravadies, so is the given sum to the reals required : or multiply the sum by 15 reals 2 maravadies, for reals. EXAMPLE. In 6000 current dollars, how many reals vellon? 2=r J^)5000 Or tlius,. 5600 15 2=1 curr. doll. 2 25000 34)10000 5000 294 4 294 4 75294 4 Ans. 75294 reals vel. 4 mar. To change Current Dollars to Sterling, Rule. As 1 dollar is to the rate of exchange, so is the l^lven sum to the sterling required. example. In 5000 piastres or current dollars, how many pounds ster- ling, exchange at 36f per dollar ? p, d. p. Aa 1 : 36J :: 5000 36f 180000 5000 1875 ^ 3 12)181875 8)15000 210)1 5 1 5|6 3 1876 Ans. £.757 16 3 EXCHANGE. 178 To chancre Sterling to Current Dollars, !RtTLE. As the rate of exchange is to 1 dollar, so is the given suim to the dollars required. EXAMPLE. In £757 165. Sd, sterling, liow ma»y current dollars, exchange at S6jd. sterling per dollar I d. doll. £ s d. As 361 : 1 : ; 757 16 3 Ans 5000 cur. dolls, or piastres. To change Sterling to Reals Ft lion. Rule. As the rate of exchange is to 15 reals 2 maravadies, so is the given sum to the reals required. example. In £436 10s. sterling, how many reals vellon,, exchange at B6ld: sterling per current dollar 1 d. r. m. £ s. As 363 : 15 2 : : 436 10 8 20 291 873« 12 104760 8 2 mar.= 1 838080 '^ 152. Or, 83808a 2 4190400 8380S0 49298 34)1676160 mai%. 49298 reals' 291)12620498(43360 1164 980 873 1074 873 2019 1746 2- 38 20*9 119 34 mar.=l reil. 291)4046(13 Ans . 48369 reals 13 ai^ Q2 174 EXCHANGE. PRACTICAL qUESTIOJVS. 1. What will 122 quintals offish come to at 136 reals per quintal ? 136 732 366 122 An?. 16592 reals. S. What is the cranage of 1 137 quintals offish at 10 ma- ravadies per quintal ? Ans. 334 reals 14 mar. BARCELO.N-A. The moneys of account in Barcelona and throughout the pro- vince of Catalonia are Livres^ Sols and Deniers, 12 deniers - make - 1 sol. 20 sols - - - - - 1 hvre. 37 1 sols, or IJ lirre • - 1 hard dollar. 28 sols - . 1 curr. doll, the piast. of exchange. To change Ldvres to hard Dollars, Rule. Divide the livres by 3 and then by 5, and add the- two quotients together, for hard dollars. EXAMPLES. 1. How many hard dollars in 360 livres ? 3 360 120 72 192 An». 102 hard dollarn, 2. How many bard dollars mtist be paid for an invoice o/ foods amoootin^ to 7134 livres? 3 7134 Am^ 3S04 b, do]l«, 30 «ofc EXCHANGE. 17i To change Hard Dollars to Livres, Rule. Add to the given siim the half, quarter and eighth of it, and the sum will be the livres required. EXAMPLKS. 1. In 192 hard dollai-s, how mmy livres 192 48 I 24 360 Ans. 360 livres, 2. How many livres in 3804| hard dollars ? 3801,3 1 902,4 9j1,2 475,6 7134,0 Ans. 7134 livre». To change Livres to Current Dollars. Rule. Multiply the livres by 5, and divide that product by 7, for current dollars. EXAMPLE. Change 2716 livres to current dollars, 2716 5 7) 1358a 1940 Ans, 194a cur. dolls-. To change Current Dollars to Livres. HtJLE. Multiply the current dollars by 7, and divide the product by &, for iivres. EXAMPtK. Change 1040 current dollars to Uvref. Ji)40 T 6)U5f>cja 27ia An?. §716 ;iTr«^». 17S EXCHANGE. P0RTUG./1L, Accounts ore kept in Alilbeos i\n ( Hcus^ reckoning 1000 reas to 1 Tuiltrea ofbs. 7-^i/. strrling^ or I Joll. 25 cts. in the U. States. A vinten is 20 rt;as, and 5 vintens is a festoon of 100 reas. FXAMI'I.KS. 1. Changfe 579 millreas 740 reas to Federal, at 1 doll. 26 Cts. per mxilrea. m. r. 579,7 10 Or thus, 579,740 1,25 i added 144,935 2898,700 dolls. 724,675 69568,80 cents 7i>'167,5 Ans. 724 dolls. 674 cents. 2. Change 7:24 dolls. 67i cts. to millreas, at 1 doll. 25 cts. per millrea. 1,25)724,675(579 mill. 740 reas. Or dedurtinjg^ i from the sum in Federal money gives the millreas, 4«c. EXAMPLE. i)724,675 144,9.35 579,740 as before. 3. Change 579 millreas 750 reas to sterling, at 5^. 7J be eqnal to the English quintal of 112 lb. but tish geno.rally renders about Ii»6 (o 138 lb. per quintal. 145 lb. m Leghorn makes 112 lb, in the United States. 4 brasses - - - - i cane. ^ ^ 100 brasses - - - - 64 yardii U. States. 1 palm - - - ^5 incbes do. 4 sacks are 2 per cent, less than an English quarter, of 8 bushels. EXAMPI.KS. 1. Hovf much will 5630 lb. of ginger come to at 9 pias- tres per 100? 5f530 9 50ii|7O 20 14100 Ans. 596 piast. 14 sol. 2. What will 9764 lb, of pepper come to at 27] ducats per 100? 9750 271 G8320 19520 2440 ^)265960 4432GI piast. 3102|86| . 20 soldi 171^31 12 den. 4|00 Ans. 3102 piast. 17 sol. 4 den. 100 EXCHANGE. 3. What will 143700 lb. of pitch come to at 26 pauls per 100? Note. One paul is equal to |. of a livrc. 143700 26 862206 287400 37o62,00 pauls. 2 3)74724 6)24908 livres.. 4151 6 8 Ans. 41 5J pinst. 6 sol. 3 den. 4. TTnvv m^irb will 4200 saclis of wheat come to at 26 Uvres, tiliccuvM mgnt y, pt r Rnck ? 42n0 gfj^OO 8400 liv, piff^t, 5 3 J I \ \ lOB^OO livros. * Ang, 10U9) plnst. sol \ de«, 5. too barre^l^ pork 16 pinstrfs per barrel )BUQ 6. lOUO c]o/ flour 10| do, do, lU^OO 7. !^tim» lb, coifee ^tr do. per 100 691 12 0. 6570 lb. pimonte 18 dt.. do 1184 9. 0370 lb, rice 24 liv, eur mf>n pr.ieo 374 10 JO dl'Uli) lb, loj^wood U pJH^tres per lOOO 1^50 4 JU 4170 Uk Rua. wan 3q ducats p^r 100 11^9 15 6 n\ 104060 lb. mgnr tiO pjpgfreg per 151 lbjMG74 3 6 1:3. 33biMb lo»f*oprgO de, p^r lOO 1005 IJ, lOOOeHsUstur 4i do. per cnek 4500 15. lOOOUO lituves t)' uo. per 100 4000 EXCHANGE. 181 JVJPLES. Accounts are kept in Ducats and Grains^ reckoning 100 grains to 1 ducat. The current coins are grains, carlins, ducats, dollars, and ounces. 10 grains make I carlin ; 10 carlins 1 ducat; 3 ducats 1 ounce. The Naples dollar passes for 120 grains, and the Spanish dollar for 126 grains. 100 lbs. Naples weight are equal to 64f lb. English. Brandy is sold per cask of 12 barrels, or 132 gallons: 60 karafts make a barrel. Sewing Silks are sold per lb. of 12 ounces. Lustrings are sold per cane of 84 inches. Sugar, coffee, fish and tobacco are sold per cantar of 196 lb. in the United States. The cantar is subdivided into 100 rotolas of 33 ounces each. EXAMPLES. 1. What is the amount of 10 casks 6 barrels 29 karafts of brandy, at 92 ducats per cask ? 92 10 6bbl. 20 kar. 5 do. 4 do. 920 i 46 T^a 2 55 1 64 nearest. i 51 909 70 Ans. 969 ducats 70 grains. 2. What is the amount of 2 casks of clayed sugar, weigh- ing neat 10 cantars 51 rotolas, at 65 dollars per cantar? rot. dolls. rot. 100 : 65 :: 1051 Or thus, 65 65 10 5255 6 506 650 50 rot. i 32 50 1 do. I 57 65 due. 683 15 Ans. 683 ducats, 15 grains. 1£ EXCHANGE. 3. How much is the amount of 1 box of scented soap, containing 100 parcels of 16 ounces each, at 22 grains per rotola? 100 16 oz. gr. 33 : 22 : : 1600 oz. Ans. 10 ducats, 66 grains. 4. What is the commissson on 996 ducats, at 2 per cent. ? Ans. 19 ducats, 92 grains. ducats. 73 per cantar can. rot. 5. 3 73 of coffee - 6. 16 19| soap - - 21 7. 1 59 do. - - 21 " " 0. 7 97f do. - - 21 " " 9. 67L scented do. - 30 '' '^ 10. 52 white do. - 17 " '' 11. 7 64 raisins - - 12 " " 12. 2 casks 1 1 bbls. 4 kar. brandy 102 per cask 13. 10 do. 43 do. do. 92 " " 14. 9 do. 12 do. do. 92 '' " 15. 355 canes of silk 2 50 per cane due. gr. 272 29 340 14 33 39 167 52 20 25 8 84 . 91 68 298 06 82 16 70 53 887 50 TRIESTE. Accounts are kept in Florins and Kreutzers — 60 kreutzers make 1 Jlorin. The exchange on London (8th July, 1803) was 12 florins for the pound sterling. The other kinds of money are Soldi and Livres. make 1 1 livre. florin. 20 soldi o\ livres - 100 lb. Vienna weight=123 lb. Avoirdupois. A brace is 27 inches, or J of a yard English. A barrel of wine is 18 gallons. A staro of wheat is 2| bushels nearly — 3^ staros is equal to an English qtiarter of 8 bushels. Sales and purchases are usually made in bills on Vienna at 3 months date. EXCHANGE. 183 EXAMPLES. 1. What is the amount of 263 lb. Vienna weight, of soap, at 22 kreutzers per lb. ? 263 22 526 526^ 6|0)578|G 96 26 Ans. 96 flor. 26 kreutzers. 2. 758 gallons wine, at 21 florins 30 kreutzers per barrel? 758 21 758 1516 30 kr. i 379 18)16297(905 162 97 90 7 60 18)420(23 36 60 54 6 Ans. 905 flor. 23^ kp. Ji, kr. Ji. 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. 1672 20 184 EXCHANGE. GENOA. Accounts are kept in Denarii^ Soldi and Fezzos^ or Lires. 12 denarii - - make 1 soldi. 20 soldi - - - - 1 pezzo or lire. 1 pezzo of exchange ^ - 53 lires. The course of exchange is various — from 41d. to bSd. sterling per pezzo or lire. In Milan, 1 crown = 60 soldi of Genoa. Naples, 1 ducat = 86 do. Leghorn, 1 piastre= 20 do. Sicily, 1 crown = 127| do. To reduce Exchange Money to Lire Money. Rule. Multiply the exchange money by 5J for lire money. EXAMPLE. fn 384 pezzos of exchange, how many lires? 384 1920 192 96 2208 Ans. 2208 lires. To reduce Lire Money to Exchange. Rule. Multiply the lire money by 4, and divide the pj^o- duct by 23, for exchange. EXAMPLE. In 2203 lires, how many pezzos of exchange ? 2208 4 23)8832(384 69 193 184 92 92 — Ans. 384 pezzos of exchange. EXCHANGE. 18& To reduce hires to Sterling. Rule. As 1 lire is to the rate of exchange, so are the lires to the sterling required EXAMPLE. In 360 lires how much sterling, exchange at 54d. sterling per lire ? 1 : 64 :: 360 54 1440 1800 12)19440 2|0)I62|0 81 Ans. £81 sterlings. VEMCE. Venice has three kinds of money, viz. Banco money, Ban- co current money, and Picoli money. Banco money is 20 per cent, better than banco current, and banco current 20 per cent, better than picoli. The different denominations of money are Denarii, Soldi, Grosi, and Ducats. 12 denarii, or deniers d'or, make 1 soldi, or sol d'or. 5J- soldi ► - - - 1 gros, or grosi. 24 gros, or grosi - - - 1 ducat. 100 ducats banco of V^enice, in Leghorn = 93 pezzos. do. Rome = 68^ crowns, do. Lucca = 77 do. do. Frankfort = 139} florins. The par of exchange in 1798 was 54|c/. sterling per ducat banco. R2 186 EXCHANGE. How much sterling is equal to 2712 ducats banco, ex- change at bO^d, sterling per ducat banco ? due. d. due, 1 : 501 :: 2712 4 201 201 2712 54240 4)545112 farth. 2|0)1135|6 6 shillings. Ans. £567 16 6 sterling. SMYRJVA. Accounts are kept in Piastres and hundredths^ except the English accounts.^ which from ancient custom are kept in piastres and eightieths or half paras. The fractional parts are sometimes called aspers, 100 as^ pers to 1 piastre. The following 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 sterling, May 1 4th, 1800. Their weights are the Rotola, Oke, Checque and Tiffee. A rotola - - marked Ro. is IbQ drams. An oke - - - ^y^ 400 do. A cheque of opium - - 250 do. do. of goats wool - - 800 do. or 2 okes. Atiffeeofsilk - - - 610 do. 100 rotolas, or 11500 drams, or 45 okes, are a quintal of. this country. 112 lb. English should render here 40| oke?r, or 90f roto- las. 45 okes of this country render 123f lb. English. A pike is 27 inches nearly. EXCHANGE. 187 To change Piastres to Dollars. Rule. Multiply the piastres by 5, aad divide the product f 17, for cents. EXAMPLE,^ Change 1277/^, ] ; piastres to dollars. 1277,55 5 17)6387,75(375,75 51 12S 119 97 85 127 119 85 85 Ans. 375 dolls. 76 ct^ To change Dollars to Piastres. Rule. Multiply the dollars by 3| for piastres. EXAMPLE. Change 375 dollars 75 cents to piastree, 375,75 31 1127,25 75,15 > r • 76,16; ^"^f Ans. 1277,55 piastres. PRACTICAL qUESTIOJSrS. I. How much will lOserons of cochineal come to, weigh- ij3g neat 1^1 okes 73 rotolas, at 80 piastres per oke ? 724,73 80 Ans. 57978,40 piastres^. 188 EXCHANGE. 2. 299, bags of sugar, weighing 506 quintals 96 rotolas, tare J 4 rotolas per bag, at 1 10 piastres per quintal ? gross 50G 96 299 tare 41 86 14 neat 465 10 1196 110 299 Ans. 51161 00 piast. 100)4186 41 86 3. 4 cases of opium, weighing gross 1026 rotolas, tare 84 okes 75 rotolas, at 10| piastres per cheque. Note. 1 rotola is equal to /^ of an oke, and I oke to 1| cheque. rot. 1026 9 gross okes tare 20)9234 rot. 461 70 84 75 neat okes 37t3 95 If C76 95 3 376 95 226 17 5)1130 85 c)9R 17 cheques G03 12 lOf 6031 20 5lii o6 150 78 Ans. piast. 6483 54 # 4. 893 pieces of copper, neat okes 19743,85, at J| op ,76; paras per oke ? o. r. 19743,85 70 ' 4|0)l382O695l0 piast, 34^51,73 EXCHANGE. 189 5. What is the custom-house duty on 19740 okes of cop- per at 21, agio at 2^ per cent. ? To Note. The charges are all established by a tariff of the Levant Company. 19740 2^ 39480 9870 4|0)4935|0 agio 2i=jV)l 233,75 amount of duty at 2^ pars. piast. 16,56 190 EXCHANGE. 8. What will the following charges amount to, viz. porter- age /^jy, house porters 5*^, weighing /„ , chan duty Z^, visit- ing and marketing ^'^ per quintal on 438 quintals .? porterage house porters 8 4 438 17 weighing ehan duty visiting 2 2 1 4J0)744|6 — Ans. piast. 186,15 17 PALERMO LY SICILY. Accounts are kept i?i Onges^ Tarins and Grains. 20 Grains - make - 1 Tarin. 30 Tarins . - - - 1 Onge or Once. Feb. 6, 1 803, the value of the money of Palermo in U. S. currency was as follows : equal to - - 4 Mills. - - = - - 8 Cents. 1 Sc. doll. == - 96 do. 21 do. = 1 Onge = 240 do. The Spanish dollar is current at 252 grains. The value of the onge, at par, is II5. 3d. sterling. The exchange on London, Feb. 3, 1 803, was 56 tarins for the jt sterling, or lOs. S^d. sterling per onge. The Cantar of Sicily = 176 lb. Avoirdupois. The Hottoii - = If lb. do. 100 Rotloii make a Cantar. A Cantar of oil is 25 gallons English measure. The Sief- lian barrel contains 9 gallons. Mahogany is sold by weight ; one foot board measure will weigh about 2 rottoli. The measure called Caffis is 3^ gallons. The lb. in Sicily is J 2 oz. Avoirdupois. The Salm is 485 lb. Avoirdupois. 1 Grain 20 do. = 1 Tarin 240 do. = 12 do. = 600 do. = 30 do. = EXCHANGE. 191 EXAMPLES. 1. What cost 264 cantars 25 rottoli of mahogany, at 8 onges 15 tarins per cantar? 264 8 2112 15 tar. ^ = 132 25 rot. i = 2 3 15 2246 3 15 Ans. 2246 ong. 3 tar. 15 gr. 2. A cargo, consisting of 3564 quintals offish, invoiced at 5 dolls. 50 cts. per quintal, is sold in Palermo at 75 per cent, advance : what sum must be received for it at 252 strains per dollar ? 3564 5 17820 50 cts. 1 = 1782 19602 50 per ct. -J = 9801 25 - - i, = 4900 50 dolls. 34303 50 252 68606 171515 68606 50 cts. i = 126 210)864448|2 grains. 3|0)43222|4 2 14407 14 2 Ans. 14407 ong. 14 tar. 2gr. 192 EXCHANGE. 3. What is the brokerage on 13131 ong. 12 tar. at 1| per cent. ? 13131 12 1 13131 12 1641 12 16 147172 24 16 30 21|84 20 16|95 Ans. 147 oTig. 21 tar. 16 gr. ENGLISH WEST-INDIES. Accounts are kept in Pounds^ Shillings and Pence. JAMAICA AND BERMUDAS, The Spanish dollar passes at 6s, Sd. ; 3 dollars are equal to 20 shillings, or 1 pound, Jamaica currency. To change Jamaica Currency to Federal. Rule. Multiply the pounds by 3 for 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 £16 per M, how much is it in Federal money ? 15 3 Ans. 45 dollars. EXCHANGE. 193 ^. Change £54 I'l". 1 1./. Jam.iica currency to Federal. b\ 12 11 20 1092 12 1)13115 3..: 18 J 1»^3,933 Ans. 1^3 flollg. 9P.? cents. 3. What will 102,8 '6 feet of boards come to at £l5perM? 102,896 15 514480 102H96 £1543,140 20 «.8,8v)0 12 I rf.9,G00 Ans. £1543 8 9 r 4. Whnt will 5 Uh4s. of sno^ar come to, weighing ^519 lb. neat, at 70 shillings per llH) ib. ? 8519 70 2|0)59G|3,30 Ans. £298 3 3 5, How much will 5 hhdg. of su§far come to, weighing 9103 lb. neat, at 75 shillings per 100 lb.? 9103 75 45515 C3721 2!0)6ft2|7,25 Ans. £341^7 3 S 194 EXCHANGE. BARBADOES. The Spanish dollar is (^s. Sd. Barbadoes cnrrftncy. To change Barh&does Currency to Federal. Rule. Increase the pence in the given sum hy ^ for cents. EXAMPLE. (Ihan,^e £\9 lis. \0d. Barbadoes money to Federal. £19 11 10 Proof 1)151^691 cents. 20 39G7i 991 12)1191)2 pence. 12 2lO)99|l 10 011902 39671 £49 11 10 1bb.)iS9^ Ans. 158 dolk. 09 J- cents. Other calculations as in Jamaica. MARTLYICO^ TOBAGO A^''D ST. CHPISTOPHEE'S. These islands being inhabited hy French and English^ the /(.rrner keep their accounts 'in Livre'^y Svls arid DtJiitrs, and the latter in Fou7ids, Shillings atid Pence. I\ curieHf. dollar is Bs. 3d. A rounrf dollar pn««es for Or. When payment of freight or goods is r};eniioi ed in Ppr^rish dollars, disagreement reij]»eerir.g /} eir value has frequeiitlv i^r'iyer : : i v o }>,t^ fnt it some persons disiin^-ui-h tj em hy round and cwninl CoWcn ; o.l ers mention the hits to e.-cb. But ll e rro^^t certain wa\ i* \o .-],(( jfy the number of shillings or livret-, instead of dollars; thus A -til; (■ V i- \ ;,r- rel of flour, at 9$> shiiJhig- or livret ; in pa^n er.t B m.ay iij;(r>. 1 h. H dollars at 9 ^hi]lir;^=f- c; ch, or :2 dollars at S**. ?ri. each, tiihe. Leing^ equal to 99 shillings or livrcs, the sum tpeciiiedb^ their aj^reement. FRENCH WEST-INDIES. Accounts are kept in Livres^ Sols and Deniers. 1^^ (K-^niers - make - 1 ?oh 20 sols - - - - 1 in re. The Spanish dollar passes jn some places for 8 livres sols, and in olber< for 9 livres. EXCLIAi^GE. 195 ' 1 cwt. or 1 1 2 lb. in the U. States U equril to 104 lb. French. 100 lb. French are equ.il to 108 lb. nearly in the U. States. When any commodity is to be marked in French weifj^ht, 4 per cent, is added to the neat hundreds; thus a hoo-shcad of iish wei^hin^ neat 10 cwt. is marked 10 JO lb. Fish ship- ped from the United Siate«5 will answer to the weight thus marked, provided it comes out in g^ood order, and the casJz weighs exactly the cusiomary tare, which is 10 percent. 100 lb. of coifee or cottoa, bought in the French islands, will, or ou^ht to, weigh 108 lb. (it will often weig-h I 10 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 sugar, which is bought per 100 lb. and sold here per 1 12, there is a loss of tj 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 French islands being 10 per cent, and the American tare 12 per cwt. The loss on clayed sugar is greater, occasioned by the customary tare, which is but 7 per cent, in the French islands, whereas it is here 12 per cont. the same as on brown surar. Note. The tare allowed on «ugar among merchants is 12 per 112^; that allowed by the custom-house is j2 per 100. {See Tare and Tret, page 84.) EXAMPLES. 1. Change 10692 livres to dollars, at 8} livres per dolLfr. ^ 10692 4 4 33) 42768(1290 33 97 66 316 297 V 198 ^98 Ans. 1296 dolk 19^ 'EXCHANGE, 2. Change 7713 lirres to dollars, at 9 livres per dollar. 9)7713 Ans. 857 dollars. 3. In 1296 dollars, at Fi livres each, how many livres! 1296 10368 324 Ans. 10692 livres. 4^ 857 dollars, ati^ livres each, how many livres? 857 9 Ans. 7713 livres. 5. What will 1642 lb. of coffee came to at 15 sols per Ykt 1642 15 8^10 1642 2!0)2 463|0 sols. livres 1231 10 Ans. 1231 livres 10 sols. 6. 1780 lb. cotton at 157 Uvres 10 sols per iOO lb.? ^^ 1780 157 1246a 8900 nbo 10 fols J 890 liv. 28U3I50 ^^0 sols. lOi'JO Ads. 2803 liv. 10 sols. EXCHANGE 197 7. 24 barrels of beef at 101 liv. 1 sol, 3 den. per barrel? liv. s. d, lUl 1 3 6 606 7 6 4 " <2J42o 10 Ans. 2 125 liv. 10 sols.- 8. How many dollars, at 8 livres 5 sols per dollar, will pay ior 12 hhis. of brown sugar, weighing 1330 5 Vix at 4§ hvres per 100 lb. ? 13365 40 5346,00 4 33 ) 21384(648 198 158 132 264 264 Ans. 648 dolls. 9. A cargo, amounting to 12536 dolls, in the United Stales, is sold at 12^ per cent, advance on the invoice : how manyi livres will it amount to, estimating the dollar at Q^ livres each I 12^=1)12536 invoice. 1567 advance. 14103 amount. 8 1 12824 livres at 8 per dollar, sols 1 3525J Ans. 11 6349 J livres at 8^ per dollar. S2 198 EXCHANGE. 10. 6 hhds. coffee, wt. 4471 lb. at 14 6 per lb. 3^41 9 e 11. 14 do. mgr, do. 16477 - 38 iiv. per 100 6261 6 2 12. 1 bale CO on, do. 227 - 150 do. 340 10 13. 94 hhda. ii.h, do. i0:3i3 - 33 do. 33433 5 9 14. 16 casks, rice, do. 6575 . 40 10 do. 2662 17 6 15. 1390 Loops, .... 460 per M. 667 4 16. 15059 leet of boards, 100 do. 1505 18 17. 48 shaken iiiids. with heads, - 7 15 per hhd. 372 18. 29 barrels of beef, - 90 15 perbbl. 2631 15 19. 6759 velts of molasses. 26 per velt 8786 14 20. 32070 galls, do. at 73/. 7s. 9d. per t jerce of 60 galls. 39969 9 19 SPANISH WEST-INDIES. Accounts are kept in Havana^ Laguircu Fera Cruz^ ^c. in DoU Ian and ReaU^ reckoning b reala to a dollar. The Spanish arobe is 26 lbs. EXAMPLES. ^ 1. What will 123 pieces bretagnes come to at 2G reals per piece I 123 26 738 V 246 8)3198 399 6 Ans. 399 dolls. ^ reali?. f: 21784 feet boards, at 45 dollars per thousand? 21784 45 per M. 108920 87136 08U1280 8 3«.«40 Ans. 980 dollr. 2 real? EXCHANGE. l^B 3. 153 cases of gin, at 8| doUars per case. \h3 1221 4 rpals 16 4 2 do. 33 2 13.38 6 Ans. 1338 dolls. 6 reals. "i 4. What is the commission oa 14792 doijars 5 reals at 4 per cent. ? 14792 5 4 591|70 8 5l64 Ans. 591 dolls. 5 reals. 5. What will 42 bbls. of white susfar come to, we>j:hing gross 4io a robes 18 lb. ; tare and tret on the whole 850 lb? at 26 reals per arobe ? ar. lb, 415 18 858 lb. make 34 8 381 10 26 2286 !Q lb.=a arobe 10 8)9916 reals. 1239 4 Aiis. lC39dolls. 4 reals. dlh, rh^ 6. 125 pieces brctagnes at 2G reals - • - 4('6 2 7. 500 do. do. - - 241 do. - . - 1551 2 8. 80 umbrellas - - Qi dollars - - 520 9. 1 17 arobes of butter 25' do. per 100 lb. 918 10. 2405 arobes of l9ib.S!i;T;ar 25 renls pr. arobe 7'»18 llf Kveodo^. "1215. do. 21 do. i]o. 4358 7 12. 166D5 fe|>:iiU9b dollars were e i 1 8 1 tV 2 4 8 chit, i 1 2 UcJS 11 6 Ans. 1138 r. 11 a. C p. EXC RANGE. 201 BOMDJY. Accounts are kept in Rupees^ Quoriers and Ree&. 100 ree« mvtke I q'lirt r, \ qnartcr? ! rupee. 218 rupees were equal to loo Spariii!*h dolls, in April 1800. The current money is in Mohnrs, Rupees and Fice. 60 pice make 1 rupee, 15 rupees I mohur. The. weio^hts are pound:^, mauds and candies ,• the pound the same as in English. A Bombay maud is 23 lb. A yurat maud is 37^ lb. 21 Surat maad^s, of 784 lb. make 1 Surat candy. Cotton is sold by the Surat candy. Camphire and Mocha coffee are solcKby the Sur:it maud. Jlaiabar pepper is sold by the Bombay candy of 5t?8 lb. EXAMPLE. In 274 bales of cotton, weighing neat 996 cwt. 2 qrs. 23 lb. how many Surat candies? 764 lb.=7 €wt. 7;996 2 23 142 200 two hundreds. 2i excess i^ percent. 56 two quarters. 23 8U3 Ans. 142 can. 303 Ik MjWR^S. Jieeounis are kept in Pagodas^ Fanams and Cash. 50 cash make 1 fanam, 36 fanams J pagoda. The Spwuish dollars were in 1798 and '99, at 165 dollars for lOOstcir pHgodaf^ ; making the pagoda worifi 16.^ cenl6. The rt* venue laws of the United States roxkon them at 181 ceii^s. Vhr i-;' r: il. i)r <\(]C.\ ^rww) rupno is worlh 46 to 47 els. The rcveuae uuva oi iho U. ;:?tatei> value thtj;^ ai 50 cents. P 202 EXCHANGE. The current exchange is 34U sicca rupees for 100 star pf^gcdas. A lack of rr.poes is 1 00,000. Cowries -ive. sea shells us^ed as small money in India and on the coast of Africa, to make ch.tuge among* ihe natives in the bazur or m:^rket, and in payment to the cooties or la- bourers. In May, 17^2, a rupee vxa? north 5120 cowries. The common cowries are generally at 5 to 7 rupees \u\v bazar maud, the b-tter sori f n m 10 to 14 rupees per maud, the pr'ce vary ns; acconhng to the kind. I'he picul is 153^ lb. Ersglish. lOu c Utiis mi^ke a picul. A maud is 251 h. troy : 20 mauds make 1 candy. The excejUi'J34^^^i' their cloth is delined by the threads in the warp. The duty payable at the custom-house is 2^ per cent, outwards and inwards, '^rhis is taken on imports according to the invoice, and on exports at the actual cost at ihe bazar er market. BAT AVI A. Accounts are kept in Rix Dollars and Stivers. The rix dollar is 48 stivers. The ducatoon is 80 ditto. The Spanish dollar is 64 ditto ; fiometime? it passes at 60 st. 125 lb. Dutch are equal to K3 J^ lb. English. \'?b do. ^ make - 1 picul. 100 cattas - - 1 ditto. EXAMPLES. 1. In 1333 rix dollars 16 stivers, bow many ducatoons ? 1333 16 48 10670 5333 810)640010 Ans. 800 ducatooDS. EXCHANGE. 203 2. What dollars per jj will 127477 cattas of bar iicul ? ircn come to at 9 fix As cat. luO rd. : 9 : cat. 9 ^ U 472,93 48 744 372 29^0 24 44,t)i Ans. 11472 r. dolls. 44 st. 3 What will 3894 bottles of wine eome to at 36 stivers per bottle ? 3894 Or thut?, 3'5 Miv.=f rix doll. 3894 24 stiv. I- 1947 3 I 97;^ 24 4}i]c.a2 2^)2t) 24 An?. 2920 rix dolls. 24 stiv. 4. In 31478 lb. of sun^ar, how many piculs? 12o)31478(25l 20O 647 625 228 125 103 Ans. 251 picii^s, 103 lb. 5. In 50r)32 lb. how many plculs ? An.^. 405 7 6. in l^o48 101 rj 204 EXCHANGE. 7. AVhat will 279 piculs 26 il>. oi' feugar com^ to at 7-J rix doiiar^ per picul ? 279 H 1953 K39 n 25=1 1 '24: 2094 OO . An5. 2094 rix dolls. CIJLVA 9iilcukiiion9 arc made in 7(//e, Alace^ Canr^oreens and Cash* JO citsli - mnke * 1 cahdareen. 10 c.mflareens tw ^ _ j mace. 10 mace - '• - 1 tale. Th<» tn'.e oi" China is optima ed at 1 dollar 48 cents in the Up'ttd Stati-s. The Spanish dollar i* current a1 72 candareens Weights are in 'i'ale.s, Ficuls and Cattas 5 16 tales make I e^d'ia ; 100 catla? 1 picui. A picul i?* eipial to \:yd^ \h Ensrlis^h. The cav d o\ China is l4/|f inches: it is divided into 10 parts. To change English Ptmnds to dtitas. Rule. Ded»?ct lb per cef)t. or one quarter, lor cattas. F.XAMTME. In C2668 lb. English, he^v many cattas ? 15t67 Ans 47001 caftns. To change Cattas to Fo^/nds English. Ilrr.r. Add one third Ibr pounds English. FXAVri F.. Fn 47001 cattas how manj lb. English? ^)47()0} 156G7 Ans. G2GG3 lb. English. EXCHANGE. 205 PRACTICAL qUESTIO.JVS, 1. Wliat is the amount of 308 chests of bohea tea, weighing Tieat 101956 lb. at 15 tales per picul? 1)101956 lb. 25489 cat. tal. 100 : 15 :: 76467 cattas. 15 382335 7G467 1 1470,05 Ans. 1 1470 tales 5 can'd. 2. What will 75 chests of souchong tea come to, weighing neat 4875 lb. at 44 tales per picui? i)4875 1218| 36561 cattas. 44 14624 14624 11 1608,75 Ans. 1608 tal. 7 mar. 5 cand. 3. How many dollars will pay for an invoice of tea., amounting to 6446 tales 1 mace 6 candareens? 72)6446 1 6(8953 576 648 381 360 216 216 Ans. 8953 dollars. ^06 EXCHANGE. MAJVILLA. Accounts are kepi in Dollars^ Reals and Quarics. 12 qua (OS make 1 real, 8 reals 1 dollar. The arobe is ,:5 ib. 5J arobes make 1 picul. Their lOOlb. is equ.il to 104 lb. English. EXAMPLE. 1. What will 1^97 bags of sugar amount to^ weighing neat 1^61 piculs 1 arobe I74r lb. at 6 dollars per picul? 1361 1 171 6 1 ar. 121 lb. 8167 6 10 Ans. 8167 doll?. 6 r. 10 q. pic. ar. lb. dlls re. 2. 118 bags of sugar, weighing 89 1 22i at 5 7 Ans. 524 dolls. 7 reals. ^ pic. ar. lb. dlls. 3. 663 bags of sugar, weighing 469 3 18 at 6 Ans. 2819 dolls. 8166 fr 1 8J i 4 4J- i 1 9 * COLUMBO, ISLE OF CEYLOJV. The money is in Poper^ Silver and Gold, Paper money is in the bills of the Company, and is of un- certain value. Silver is in the rupees 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 Feen. 6 stivers make 1 shilling Flemish. shillings - - - 1 rix dollar. ::0 stivers - - - - 1 rupee. G U- do. - - - 1 Spanish dollar. EXCHANGE. 207 JAPAN. Accounts are kept in Tales^ Mace and Candareens. 10 candareens make I mace. 10 miice - 1 tale = f of a dollar, or 75 cents. lU mace are equal to 1 rix dollar. 6 taies make a corban, a gold coin not used in accounts. In weights — 10 tales m\ke I mace, 16 maces 1 catta. The ich m, or hickey, is 3i feet. The balee is 65 quarts. 35 per cent, was the duty on privileged imports in 1799. It ts on exports (which are all free of daty) that the Du'ch make their profit on their return to Batayia. A privilege is granted to the captains of the Dutch ships to carry money, which often sells at an advance. EXAMPLE. How much is the neat proceeds of 4 silver watches, at 35 tales each, deducting the duty of 35 per cent ? 35 tales 4 140 35 per cent. 700 420 Sale 140 Duty 49 4J,00 Ans. Neat proceeds 91 tales. FORM OF AN ACCOUNT OF SALES. 4 silver watches, 1st kind 6 «,lver watches, 2d kind tales. 35 23,1 Duties. tales. 49 48,5,1 iNeat. tales. 91 90,0,9 The article is given in the first column, the price in the next column, the duties in the third, and the neat proceeds in the fourth. .208 EXCHANGE. PARTICULARS Of the ToNxVAGE of Goods, as calculated to make up the Ton- nage for the Freight of Goods^ brought in East-India or China ships to Europe- — viz; PIECE GOODS. Fort St. George. Bengal. Pieces to Pieces to the ton- the ton. Allejars - 800 Elatches - R.SOO Betelles - - - 400 Emmertiea - 600 Callawapores ■- 800 Gurrahs 400 Chintz of all sorts - K;400 Ditto, long - 200 Ginghams . 800 Ginghams, coloured 600 Izzares - - 800 Humhums - 400 Longcloths - - 160 Habassies 600 Moorees - - - 800 Humhums, quilted - 100 Sallampores - - 400 Jamdannies 800 Sastracundies - - 800 Jamwars - 600 Bengal. Laccowries - 600 Addaties - 700 Lungees Herba - 800 Alliballies - - 400 Mulmuls 400 All a chaws . 1200 Ditto handkerchiefs - - 400 Allibannies . R.800 Mahamodietes 400 Arras - _ - R.400 Mamodies - R.400 Atchabannies - . - 800 Nillaes 800 Baftaes . - R400 Nainsooks - 400 Ba.idannoes, or Taffa de Peniasoces 800 Foolas - _ - R.800 Photaes R.SOO Carridanies - - 600 Pcrcaulas - 800 Callipatties . 400 Putcahs R.400 Coopees _ 600 Romans - R.800 Calicoes . 400 Sannoes 400 Chillaes » 600 Seerbetties 400. Chowtars . 600 Seerbands 600 Cimndeibannies _ 800 i Seersuckers 600 Chinitachures _ R.SOO 1 Seerhaudconnaes 400 CambMcs - R.400 Seershauds R.400 CTiucklaes - > 400 Seerbafts 400 Cushtaes _ 800 Shaulbafts 400 Cossaes - 400 Succalcons R.800 Charconnaes - . 600 Sooseys 400 Cuttannaes - R.SOO ; Sorts - 400 Doosoqties _ - R.400 \ Terridams 400 Dun^^aries - R.400 ' Taffeties of all sorts R.800 iloreas - . 400 1 Tanjeebs. 400 Dimities - 600 '; Tepoys - R.SOO Diapers, broad - 400 1 Tainsooks • 400 l^iUo, narrow - «00 1 EXCHANGE. PIECE 209 Bombay. Annabatches Bombay stuflfs Bvrampauts Bejuiapauts - Boralchawders, or brawls BefeHees (Jhelloes Chintz of all sorts Dooties - - - Guinea StufFw, large Ditto, small Loiigcloths, whole pieces Difto, half do. Lemanees PJusters - - - Nunsarees Nej^enepauts !Nicanees, large Diito, small S'llampores S-uiFh, brown Tapseils, large Diuo, small Pieces to tlie to?i. R400 - R400 400 - R.400 1200 400 R.400 1^400 R 400 600 - 1200 leo 320 R.800 400 R.400 400 . 600 600 - 400 R.,10f> - 4C0 6C0 W ' Arrangoes Aiocs •♦ Benjamin Borax Cardemons, fine good^ Cakelack Carmen i a \^'ool Cambo*(ium Ca«sia JJgnea Ca.-,i • buds Camphire Co Oil yarn, fine goods Co.vie^-, gruff do. ( olT» e, fine do. Ciz.jiaber Cloves Dra^Oii's Blood Gum Arabic Elcmi AmiTiO-iiacum EIGHABI Cwt to the ton, 20 16 20 20 12 16 10 20 - 8 12 - vl.3 10 20 18 10 - J2 20 - 3 6 16 16 T GOODS. China. i-W ,";'.'; it) the ton. Nankeen cloth - - R.100 Silks, of all roris - R.SOO China ware, 50 cubical feet ^o :hs ton, or about 4 chests of iLe usual dimensions. Other meae^urable good^, 50 cubi- cal feel to the 'on. N. B. Where the letter R is set against pieces of 400 .o the ton, it shows tho'.e goods are to . e reduced, or brought ;o a standard of • 6 yards long aid ; b' o.^d. Where against pieces 800 to the ton, to iO yards long ai-^d i Lroud. EXAJMPI.E. 1000 pieces, of 12 atd- long and 1 1-8 broad, at 4(}0 to 'he' lo., make 844 piece-, or 2 tons 44 pieces. 1000 piece- of 0^ Tard.s long and 1 1-S bro d, at 800 to .he ton, is J 181 pieces, or 1 ton SSI pieces. LE GOODS, Cidt. to the ton. Gum Opoponax Sagape.'iUm ♦ Saroocol IS Indigo lion Kintlage 12 20 Musk 20 Myrrh ^?OTher of Pearl Shells 16 20 Nux Vomica 15 Pepper Quicksilver 20 Rhubarb S Raw Silk 10 Ditto in chests s Dii»o in bales or bujidles 10 Redwood 20 Rice . 20 Shellac 16 Secdlac . , . 18 Siickbck le 210 ARDITR\TION OF EXCriANGE. WEIGH ABLE GOODS. Cwt. to the ton. Saltpetre . . 20 Cwt to the ton. Tea, Green . . S Seaaa . , . 8 ; Boiiea . . 10 Sa<;o . . . 16 i Arrack Gauge gallons 251 Diito, packed in china ware - - ! Canes . . Tale 300 Tu'eiia/;ue . . 20 . Wangliees and Bamboos 3000 Turmeric , . . IG Rattans equal to 16 cwt. 6000 Tiiical . . - 16 ARBITRATION OF EXCHANGE. When the rates of exchange between several cntrritries in succession are given, to find the rate of exchange between the first and last place in the correspondence, Rule. Find by proportion the value of the sum originally remitted in the different moneys of the coimlrios through which it -passes, according to the rates of the different ex- changes, and so proceed till the whole is finished. Or, Multiply all the first terms of the different statings toge- rber for a divisor, and the second terms, together with the S'lm remitted, for a dividend, and the quotient is the amount received in the denomination of the last place m the corre- spondence : from this result the rate of exchange is readily foupd by proportion. fxampi.es. 1. A merchant in London has credit for 500 piastres in Leghorn, tor which hti can draw directly at 52r/. sterling per piastre, but choosing to have it remittetl by a circular route, they are sent by his order to Venice, at 95 piastres for lUO ducats banco; from thence to Cadiz at 350 maravadies per (3k It banco; from thence to Lisbon at t)3() reas per piastre o. 2 2 maravadies ; from thence to Amsterdam at 4Sd. Flem- ish for 100 reas; from thence to Pans at5Uy. Flemish per crown ; and from thence to London at oOd. sterling per crown. What is the arbitr;}ted price between London and Leif'iorn lev p.astre, and whit is gained or lost by this circular remit- tal uce, without reckoning expeu'-jci ? AUBiTRATION OF EXCflANGE. 2lt yid.-^t. d. ban. piast. d 6a/j. 95 : 100 : : 500 : o'^i^i^ in Venice. d.b mar. d!. 6. war. 1 : 350 : : 52G.^, : 18i2I()' J in Cadiz. mar. rea.^. ??iar. reas. 270, : t3.V) : : 184i!0;-5 : 4^2o ;')4 in Lisbon. reas. d.fl. reas. ^./. 400 : I. J : : 4h>oo4 : 51 Hitl- in Amsterdam. d.JI. 51 cr. : 1 :: d.fl 5.1 '9 J er. : 945,^ in Par.s. cr. 1 d. St. .50 : : cr. £ s. : l.ij iO d. !• sterlinw". Or thus piast. d.b mar. reas d.fl. cr. :j.> X -I X i7i X 40U X >i X » = 55314400 piast. d. b. mar. reas. d.fl cr. d. st. 5j^ X 100 X JfoO X ^^^^) X 4<3 X I X 00=1587600000000 558 1 4 ]| JO) 1 587600000 j .>0(12)2844i| lllBi^BB 2iu;.^s7iO i\ 47l.3li0 jbn8 iO 4]- as above. 2nHG80 2232576 *i 1710 10 2232576 2:^84^i40 2232576 152064 4 piiut. £,, s. d, piast, d. 500 : 118 10 4| : : 1 : 56||JJ 553144)boa25b^ 5=)B14 4 1 f 50112 AmoTint received by circular remittance 600 piastres at b2d C Gained by circui r re • ittiince Ans. / ( Arb.lmteJ value of a p.actrc by do. £ s. d. 118 10 H 108 G 8 £10 3 ^} bmud.st. ^12 AMERICAN DUTIES. 2 A merchant in Bosion has £'ii'ib sterling in LonHoD, wh ch he can draw lor at ok/, sterling per dollar, but choos- ing to try a circular route, it is sent to Dublin at £lO() ster- ling for £l09 Irish ; thence to Hamburgh at 12-J marks bni> CO per pound Irish ; thence to Amsterdam at ;53 florins for 40 marks banco ; thence to Copenhagen at 5 florins for 2 rix dollars of Denmark; thence to Bremen at 3 marks per rix dollar of Denmark ; 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 ; thence to Lisbon at li'50 reals plate for 100 roillreas; thence to Leghorn at 760 soldi for 88 millreas ; thence to Smyrna at 2 soldi per pias- tre ; thence to Jamaica at 24^^. Jamaica currency per pias-v tre ; and thence to Boston at OOri. Jamaica currency per dollar : what is gained or lost by this circular remittance ? Ans. 117 dolls. 42 cts. gained. AMERICAN DUTIES ARE CALCULATED AS IN THE FOLLOWLN*- EXAMPLES. 1. What is the duty on 2885 gallons of molasses, at 5 ctSy per gallon ? 2885 5 14i25 cents. Ans. 144 dolls 25 ct^. ?. What is the duty on the above molasses, if imported in n ft'] ei^a vessel, the rate being 5] cts. per gallon, or 10 per c^iit, more than m an American vessel? ^^85 Or, 14 1,25 as above. 5,^ U) per cent. W^i'i'j llMb dolls. 158,G7J- 1 '.\'li ioUs, Ibl'fil^. An?. 158 dolls. 67J ct8K AMERICAN DUTIES. 213 3. How much is the duty on 3720 gallons of gin, at 3ij;\ cents per giiilon ? 3720 3720 31tV 9 3720 10)33480 11160 3348 3348 dolls. cts. ^ns. 33 19 34 84^ - 80 43 99 Hi 845 55 dolls. l;186,6a' Ans. 1186 dolls. 68 cents. 4. 1273 lb. chocolate at 3 cents 5. 965 lb. do. in a foreign vessel, at Sy'g do. 6. 1149 lb. cheese, at 7 do. 7. J 295 lb. do. in a foreign vessel, at 1-^^ do. 8. 1879 galls. Champaigne wine, at 45 do. 9. 2675 do. London particular Madeira, at 58 do. 1551 50 10. What is the duty on 53 cwt. 2 qrs. 21 lb. of untarred cordage, at 225 cts. per cwt. ? 225 5;i 675 1125 2 qrs. i 112J 14 lb. 1 23 7 do. i 14 120,79-J- Ans. 120 dolls. 79^ cts. 11. What is the duty on the above cordage in a foreiga vessel, at 247^ cts. per cwt.? Ans. 13i dolls. 87i cts. 214 AMERICAN DUTIES. 12. How much is tho duty on 4 hhds. of brown su^far, wt. gross 30 cwt. 3 qrs. 19 lb., tare 12 lb. per 100, at 2^ cts. per lb.? 3800 456=excess 12 per cent. 84 19 gross tare 4359 523 3836 2J 4359 12 623,08 7672 1918 95,90 Ans. 95 dolls. 90 cts. 13. What is the duty on this sugar in a foreign vessel, at' ^ cents per lb. ? Ans. 105 dolls. 49 cts. The modes of estimating ad valorem rates of duty. The advalorem rates of duty upon goods, wares and mer- chandises, at the place of importation, shall be estimated by adiiing 20 per cent, to the actual cost thereof, if imported from the Cape of Good Hope, or from any other place be- yond the same, and 10 per cent, on ibe actual cost thereof, if imported from any other place or country, including all charge!* ; commiJisions, outside packages and insurance ex- cepted. — [See Laws oj iht United States.) AMERICAN DUTIES. 215 EXAMI^LES. 1. What is the duty on an invoice of silver and plated ware, imported from London, the cost, exclusive of commis- sions, kc. being £359 1(5 4, at 15 per cent, ad valorem? 359 444 cent5 per jj sterling. 105. 5*. 35. 4d. 1436 1436 1436 i ?22 i 111 i 74 actual cost 159H03 cents. 10 per cent, added 1590O 175783 lOJ-,. ,17578 6^ 8789 for 15 percent. 2G3G7 cts. Ans. eBf5 dolls. 67 cts. 2. What vv'll it amount to in a fore'*2:n v»>*i?oi, at 16^ per cent, ad valorem? Ans. 2\j\J duils. 4 cent*. TJie rates at which all foreign coins avd currencies are estima' ted at ike Custom-Houses oj^ the United Slates. dolls, cts. Each pound sterling of Great Britain, at - Each pound sterling ot Ireland - - - Each livre tournoisJ of France - - - - Each florin or guilder of the United Netherlands Each mark banco of Hamlnirgh - - - Each rix dollar of ])onm:irit - . . - Each real of plate of Sp.iin - - - - Each real of vellon of Spain - - - - larh miliree of Portugal - . - - Each tale of China Each pa4^oda of India - - . - . Each rupee of Bengal • - . - - 4 44 4 10 I8i 40 33 L 1 10 5 1 24 1 43 I 84 50 216 PROGRESSION. PROGRESSION Consists of two parts — Arithmetical and Geometrical. ARITHMETICAL PROGRESSIOJST Is when a rank of numbers increases or decreases regu- larly, by the continual adding or subtracting of some equal number: As 1, ^2, 3, 4, 5, 6, are in arithmetical progression by the continual increasing- or adding of one 5 and 1 1, 9, 7, 5, 3, I, by the continual decrease or subtraction of two. JVoTE. When any even number of terms dilTer by arith- metical prog-ression, the sura of the two extremes will be equal to tbe two middle numbers, or any two means equally distant from the extrt'mes : As 2, 4, G, 8, 10, 12, where C-l-8, the two middle numbers, are =:^ 12-f-2, the two ex- tremes, and =r)0-f 4, tbe two means, = 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 I, 2, 3, 4, 5, where the double of 3=54.1c=:2-f 4=6. In arithmetical progression five things are to be observ- ed, VIZ. J. The first term. 2. The last term. 3. The number of terms. 4. The equal difference. 5. The sum ot all the terms. Any three of which being given, the other two may be found. The firsts 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 tbe two ex- tremes by the whole number of terms, the product is thi3 tatal of all the terms. EXAMPLES. 1. How^ many strokes does the hammer of a clock strike in 12 hours? 12-fl = !3, then 13X6=78. Ans. 2. A man buys 17 yards of cloth, and gives for th'G first yd. 2s. and for the last 10s. what do the 17 yards amount to ? Ans. £5 2s. PROGRESSION. 217 3. If 100 eggs were placed in a right line, exactly a yard asunder from one another, and the first a yard from a bas- ket, Avhat length of ground does that man go who gathers up these 100 eggs singly, returning with every egg to the basket? Ans. 5 miles 1300 yards. The fir st^ second and third terms givcn^ to find the fourth. Rule. From the second subtract the first, the remainder divided by the third less one gives the I'ourth. EXAMPLES. 1 . A man had 8 sons ; the youngest was 4 years old, and the eldest 32 ; they increase in arithmetical progression : what was the common difference of their a«es? Ans 4. 32—4=28 then 28 — 8—1=4 the common difference. 2. A man is to travel from Boston to a certain place in 12 days, and to go but 3 miles the first day, increasing every day by an equal excess, so that the last day's journey may be 58 miles; what is the daily increase, and how many miles distant is that place from Boston ? Ans. 5 miles daily increase. Therefore as 3 miles is the first day's journey ; 3-f 5= 8 second ditto, 84-5=13 third ditto, &c. The whole distance is 366 miles. The firsts second and fourth' terms given., to find the third. Rule. From the second subtract the first, the remainder divide by the fourth, and to the quotient add 1, gives the third. EXAMPLES. 1. A person, trayelling into the country, went 3 miles the first day, and increased every day by 5 miles, till at last ho went 58 miles in one day ; how many days did he travel ? ro c , ^ Ans. 12. 58— 3 = 55 then 55-T-5x=li and 11 + 1=12 the number of days. U tl8 PROGRESSION. 2. A man, being asked how mnny son? he had, said that the youngest was 4 years old and the eldest 32, and that he increased one in his family every four years ; how many ^'^^^ lie? . Ans. 8. The second^ third and fourth giren^ to find the first. Rule, Multiply the fourth by the third, made less hy 1^ the product subtracted from the second gives the first. EXAiMI'I.ES. L A man in 10 days went from Boston to a certain town in the country, every day's journey increasing the former by 4, and the hist day he went was 46 miles : what was th« first? Ans. 10 miles. 4x10—1=36 then 46—30=10, the first day's journey. 2. A man takes out of his pocket, at 8 several times, so many different numbers of shillings, every one exceeding the former by 6 ; the last 46 ; what was the first ? Ans. 4. The second^ third and fifth given., to find the first. Rule. Divide the fifth by the third, and from the quo- tient subtract half the product of the fourth, multiplied by the third less 1, gives the first. EXAMPLE. A man is to rpceive £360 at 12 several payments, each to exceed the former by ,£4, 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 4X1?^ 3G0-T- 12=30 Ihen 30 =6, the first payment. The firsts third and fu'th given^ to find the second. Rule. Subtract the fourth from the product of the third, multiplied by the fourih, that remainder added to the first sives the second. PROGRESSION. 21» EXAMPLE. What is the last number of an arithmetical progression, beg^inning at 6, and continuing by the increase of 8 to 20 places? Ads. 158 20x^—8=152 then 152 + 6=158, the last number. GEOMETRICAL PROGRESSIOJ\' Is the increasing or decreasing of any rank of number? by some common ratio, that is, by the continual multiplication or division of some equnl number: as 2, 4, 3, IG, increase by the multiplier 2, and 16, 8, 4, 2, decrease by the divisor 2. Note. When any number of terms is continued in 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, 61, where 64x2=4X32=8x 10=128. When ihe number of terms are odd, the middle term mul- tiplied into itself will be equal to the two extremes, or any two means equally distant from the middle: as 2, 4, 8, 16, 32, where 2X32=4X l6=8Xc'=-64. In geometrical progression the same five things are to be •bserved as in arithmetical, viz. 1. The fir>t term. 2. The last term. 3. The number of terms. 4. The equal difference, or ratio. 5. The sum of all the terms. NoTK. As the last term in a l^ng series of numbers is very tedious to come at by continual multiplication ; there- fore, lor the readier tinding it out, there is a series of num- bers made use of in arithmetical j)roportion, called indices, beginning with an unit, whose common difference is one ; whatever number of indices yo^ make use of, set as many numbers (in such geometrical proportion as is given in the question) under them: . 1,2, 3, 4, 5, 6 indices. 2, 4, 8, 16, 32, 61 numbers in geometrical proportion. But if the first term in geometrical proportion be differ- ent from the ratio, the indices must begin with a cipher : ^g 0, 1, 2, 3, 4, 5, 6 indices. 1, 2, 4, 8, 16, 32, 64 numbers in geometrical proportion. £20 PROGRESSION. When the indices begin with a cipher, the sum of the in- dices made choice of must be always one less than the num- ber of terms given in the question ; for 1 in the indices is over the second term, and 2 over the third, (^-c. Add any two of the indices together, and that sum will agree with the product of their respective terms. ^ As in the first table of indices 2-f 5= 7 Geometrical Proportion 4X32=123 2+ 4=^ 6 Then in the second 4X it)= 64 In any geometrical progression proceeding from unity, the ratio being known, to find any remote term, without produ- cing all the intermediate terms. Rule. Find what figures of the indices added together would give the exponent of the term wanted, then multiply the numbers standing under such exponent into each other, and it will give the term required. Note. When the exponent one stands over the second term, the number of exponents must be one less than the number of terms. EXAMPLES. 1. A man agrees for 12 peaches, to pay only the price of the last, reckoning a farthing for the first, a halfpenny for the second, ^c. doubling the price to the last ; what must he give for them ? 0, 1, 2, 3, 4 exponents. 16=4 1, 2, 4, 8, IG number of terms. 16=4 b=3 4-f4+3=:ll, number of terms less 1,— r 4)2018=11 num. farth. 12)i:12 20)42 8 Ans. £2 2 8 2. A country gentleman, going to a fair to l>ny some oxen, nif^ets wnh a person who had 2.^ ; lie demand sno- the [)rxe •f them was answei:ed JjliS apiece ; Uie jjenileman bido him PROGRESSION. 221 £15 apiece, and he would buy all; the other tells him it would not be taken, but if he wonld give what the last ox would come to, at a farthing for the tirst, and doubling it to the la9t, he should have all. What was the price of the oxen ? Ans. £4369 U, 4rf. In aay Geometrical Progression, not proceeding from unity, the ratio being given, to lind any remote term, with- out producing all the intermediate terms. Rule, Proceed as in the last, only observe that every product must be divided by the first term. EXAMPLES. 1 . A «um of money is to be divided among eight persons^ the tirst to have £^20, the second £60, and so on in triple porportion : what will the last have ? 640x510 14580X60 0. 1. 2. 3. =14500 then =4374« 20. 60. 180. 540. 20 20 Ans. £443740. 3+3-f 1=7 one less than the number of terms. ?. A gentleman, dying, left 9 sons, to whom and to his «xecutor he bequeathed his estate in the manner following: To his executor £50 ; his youngest son was to h^ive as much more as the executor, and each son to exceed the next younger by as much more ; what was the eldest son's per* lion ? Ans. £25G00. The first tenn^ ratio andmunher of terms given ^ to find the sum of (ill the terms. Rule. Find the last lorm as bofore, then subtract the fir^t from it, and divide the remainder by the ratio le?-s oce, to the quotient of which add the greater, and it gives the sum required. EXAMPLES. 1. A servant skilled in nur!ibcrs agreed with a gentlcmaa to serve him 12 mouilis provided he would give him a farth- U 2 222 PERMUTATION, in^ for his first month^* service, a { e-.inv for the second, and 4iL for the third, mc. : what did his wages amoim' to? 256x26G=G55:i6, then 6i).;3 Xb4-- 4,9 1304 0. 1. 2. 3. 4. 4I943U4— 1 1. 4. 16. 64. 256. =1398101, then (4-f 4 + 3=11. No. of terms less 1.) 4—1. 1398101+4194304=5592405 farthings. Ans. £5825 8*. 5|J. 2. A man bought a horse, and by agreement was to give a farthiiig for the first nail, three for the second, &,c. ; there were 4 shoes, and in each shoe nails : what was the worth of the horse? Ans. £965114681693 13*. 4d. 3. A certain person married his daughter on new year's day, and gave her hushand one shilling towards her portion, promising to double it on the tirst day of every month for one year: what was her portion ? Ans. £^^04 155. 4. A laceman, well versed in numbers, agreed with a gen- tleman to sell him 22 yards of rich gold brocaded kce for 2 pins the first yards, 6 pins the second, &ic. in triple pro- portion. 1 desire to know what he sold the lace for, if the pins were valued at 100 for a iarthing: also, what the laceman got or lost by sale thereof, supposing the lace stood him in £7 per yard. Ans. The lace sold for £326886 06-. 2d. Gain £326732 0*. 9c/., PERMUTATION h the changing or varying of the order of thinji:s. Rule Multiply all the given terms one into another, and the last product will be the number of changes required. EXA.MI'LF.S. 1. How many chancres m »y be rung upon 12 belh, and how long would they he rini^uig but once over, supposing 10 changes might he rung m one minute, and the year to contain 365 days 6 hours ? 1X2X3X4X5X6X7X8X9X10X11X12=479001600 changes, -7- 10=47900160 m nutes, and if reduced is = 91 jears, 3 weeks, 5 days and 6 hours. 5Q[T\HE ROOT. 22S t. \ young- scholar, coming into a town for the conYenien- cv of a t^ooil library, dem in*e5 being multiplied into itself the product will be equal to th;- given numbor. KuLti:. 1. Point the given numher, beginning at the nnit-3 place, then lo the hundred's, and so upon every second fig- ure througliout. 2. Seek the greatest square number in the first point, to- wards the left hand, placing the squire number under tbe first point, and the root thereof m the quotient: subtract the square number from the first point, and to the remamder braig down the next po*nt, and call that the resolvend. 3. Double the quotient, and place it for a divisor on the l"!! hand of the resolvend ; seek bow ot'ten the divisor is con- tained in the resolvend, (reserving always the unit's place) and put the answer in the quotient, and also on the right hand side of the divisor; then multiply by the figure last put in the quotient, and subtract the product from the res(d- vend; 1)ring down the next point to the remainder, (if there be any more) and proceed as before. Roots. I. 2. 3. 4. 5. (3. 7. 8. 9. Squares. 1. 4. 9. Itj. 25. 3U. 49. 64. 81. Mi iJQUARE ROOT. EXAIMFLKS. 1. What is the square root of 119025 ? 119025)345 9 64)290 256 685)3425 3425 Ans. 345 2. What is the square roet of 106929 ? Ans. 327 3. What is the square root of 2268741 ? Ans. Ia06,23-f- 4. What is the square root of 7596796 ? Ans. 2756,228+ 5. What is the square root of 36372961 ? Ans. 6031 6. What is the square root of 22071204 ? Ans. 4(i98 When the given number consists of a whole number and elecimals together, make the number of decimals even, bj adding ciphers to them, so that there mdj be a point fall oa the unit's place of the whole numbe:. 7. What is the square root of 327 1 ,4007 ? Ans. 57, 1 9+ 8. What is the square root of 4795,25731 ? Ans. 69,2474- 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 + 1 1. What is the square root of ,00032754 ? Ans. ,01809+ 12. What is the square root of 1,270054 ? Ans. 1,1269+ To extract the Square Root of a Vulgar Fraction, RuLK. Reduce the fraction to its lowest terms, then ex- tract the square root of the numerator for a new numerator, and the square root of the denominator for a new denomi- nator. If the fraction hn a surd, (i. e. a number whose root can never be exactly found) reduce it to a decimal, and extract the root from it« KXAMPLES. 13. What is the square root of | J|| ? Ans. | 14. What is the square root of f^Jj ? Ans. |. 15. What is ihe square root of /-^-.'^s. ? ^jjg^ . SQUARE ROOT. Ce. f5 ^V^J^ e> ^ Surd's. 16. What is the square root of fff-? . Ans. ,89802+ 17. What is the square root of If ^? Ans. ,866t>24- 18. What is the square root of fj| ? ^ns. ,93308-f To extract the square root of a mixed number. Rule. 1. Reduce the fractional part of the mixed number to its lowest term, and then the mixed number to an impro- per fraction. 2. Extract the roots of the numerator and denominator for a new numerator and denominator. If the mixed number given be a ^^urd, reduce the frac- tional part to a decimal, annex it to the whole number, and extract the square root therefrom. EXAMPLES. 19. What is the square root of 51 If ? Ans. 7^ 20. What is the square root of 27,^^ ? Ans. 5^^ 21. What is the square root of 9|| ? Ans. ^ Surds. 22. What is the square root of 85f-|? Ans. 9,27 + 23. What is the square root of 8f ? Ans. 2,9519 + 24. What is the square root of 6| ? Ans. 2,5298 + Thp: Application. 1. There is an army consisting ot a certain nnm!)er of men, who are placed rank and hie, that is, in the form of a square, each Side hnviUg 576 men ; i desire to know how many the whole square contains? Ans. 351770 2. A certain |)avement is made exactly square, each side of which contains 97 feet; I demand how many squan^ feet are contained therein ? Ans. 9409 To find a mean proportirmol huxi^een any Uen q'lven numbers. KuLK. The «qu;«re ront of the product of the given num- ber is the mean proportional sou;;;ht. 22G SQUARE ROOT. 1. Whr^t is the mean proportional lietween 3 and 12 ? Ans. :>X 1^=36 then ^:^{)=zid the mean proportional. 2. What is the mean proportional between 4276 and 848 5 Ans. 1 897,4 -f To find the side of a square^ equal in area to any given tuperficiet. Rule. The square root of the content of anj giren u%- periicies is the square equal sought. EXAMPLES. 3. If the content of a given circle be 160, what is the side •f the square equal ? Ans. 12,6491 1 4. if the area of a circle is 750, what is the side of the square equal? An*. 27,38612 The area of a circle given^ to find the diameter. Rule. As 355 : 452, or as 1 : 1,273239 : : the area i% the square of the diameter ; or, multiply the square root of the area by 1,12837, and the product will be the diameter. 5. What length of cord will fit to tie to a cow's tail, the other end fixed in the ground, to let her have liberty of eat- ing an acre of grass, and no more, supposing the cow and tail to be 5 yards and a half? Ans. G,136 perches. The area of a circle given^ to find the periphery^ or circiimfc rente. RuLK. As 1 13 : 1420, or as I : 12,56637 :: the area : quare of tlie periphery; or multiply the square root of the irea by 3,5 149, and the product is the circumference. area SQUARE ROOT. 221 EXAMPLES. 6. When the area is 12, what is the circumference ? Ans. 12,2798 7. When the area is 160, what is the peripliery ? Ans. 44,84 Any two sides of a right angled triangle givcn^ to find the third side. 1. The base and perpendicular given, to find the hypo- thenuse. Rule. The square root of the «!um of the squares of the l»ase and perpendicular is the length of the hypothenuse. S. The top of a castle from the ground is 45 yards high, and is surrounded with a ditch 60 yards broad ; what length must a ladder be to reach from the outside of the ditch t© the top of the castle ? Ans. 75 yardf. Ditch. Base, 60 yards. 9. The wall of a town is 25 feet high, which is surround- ed by a moat of 30 feet in breadth ; I desire to know the length of a ladder that will reach from the outside of the moat to the top of the wall. Ans. 39,05 feet. ■^; Thchypothenuse and perpendicular given^ to find (he base. Rule. The square root of the difference of the squares of the hypothenuse and perpendicular is the length of the base. 223 CUBE ROOT. The hafit and hypothenuse given^ to find the perpendicular. Rule. The square root of the difference of the hypothe nuse and base is the height of the perpexuiicular. N. B. The two last questions miiy be varied for examples to the two last propositions. Any number of men being given^ to form them into a square battle^ 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 331776 men, I desire to know- how many in rank and liie. Ans. 576 11. A certain square pavement contains 48841 square stones, all of the sfime size ; 1 demand how many are con- tained in one of the sides? Ans. 221 EXTRACTION OF THE CUBE ROOT. To extract the Cube l^oot is to find out a number which, be^n?: multiplied into itself, and then into that product, pro- duceth the given number. lluLK. 1. Point a^jevy third figure of the cube given, be- 2:inning at the unit's place : seek the greatest cube to the first point, and subtract it therefrom ; put iho root in the quotient, and bring down the figures in the next point to the remrtinder for a resolvend. 2. Find a divi^^or by multiplying the square of the quo- tient by 3. See how often it is contained in the resolvend, rejectiHg the units and tens, and put the answer in the quo- tient. 3. To find the subtrahend. 1. Cube the last figure in the quotient. 2. Multiply all the figures in the quotient by 3, exeept the last, and that product by the square of the last. 3. Multiply the divisor by the last figure. Add these pro- ducts together gives the subtrahend, which subtract from the refiolvend ; to the remainder bring down the next point, and proceed as before. Roots. I. 2. 3. 4. 5. 6. 7. 8. 9 Cubes. 1. 8. 27. 64. 125. 216. 313. 512. 729 CUBE ROOT. ^^^^ "What is the eube root of 99252847 ? 99252847)403 64i=cufee of 4 Divisor. Square of 4X<3=48)35252 Resolvend. 216=:Cube ofG. 432 ==4x3Xby square of G. 288 =Divisor x by b. 33336 Subtrahend. Divisor. Sq. of 46X3=6348)1916847 Resolvend. 27=:Cube of 3. 1242 =46 x3xby square of 3. 19044 =DiYisor X by 3. 1916847 Subtrahend. Jinolher nea> and more concise method of extracting the Cube Root. Rule. I. Point every third llgure of the cube given, be- ginning* at the unit's place, then tind the nearest cube to the rst point, and subtract it therefrom, put the root in the quo- tient, brins: down the %ures in the next point to the re- mainder for a resolvend. 2. Square the quotient and triple the sq\iare for a divisor: -, 4X4X3=18. Find how often it is contained in the re- rioivend, rejectiiig units and tens, and put the answer in the quotient. 3. Square the last fi«fure in the quotient, and put it on the right hand of the divisor. As 6X6=36 put to the divisor 48=4836. 4. Triple the last figure in the quotient, and multiply by the former, put it under the other, units under the tens, add them together, and multiply the sum by the last figure in the quotient, su'^ti-arl that product from' the Resolvend, bring down the next point, and proceed as before. X 230 CUBE ROOT. EXAMPLCS. 1. What is the cube root of 99252847 ? Square of 4X3=48 divisor. 99252847(463 Sfjuare of 6 put to 48=4i]i56 64 6X3X4= 72 35252 5556 X 6 = 33oo6 Sqnare of 46—21 16x^=6348 divisor Square or3--=r9 put to 634P.==:*b348u9 193 6847 3X3X46= 414 6o89i9x3=1916847 2. What is the cube r-^ot of 38:^01 7? Aus. 73 3. What is the cube root ot 5"/ 35339? Ans. J 79 4. What is the cul.e root of 32461759 ? Ans. 319 5. What is the cube root of 84604519? Ans. 439 6. What is the cube root of 2 >9694U72 ? Ans. 638 7. What is the cube root ol 48228544? Ans. 364 8. What is the cube root of 27(i54('36()08 ? Ans. 3U02 9. What is the cube root of 22069^810125 ? Ans. 28U5 10. What is the cube root of 12^61532^232? Ans. 4i^68 11. What is the cube root of 2I9S65,5277!U ? Ans. 6031 12. What is the cube root of 673373097 125 ? Ans. 8765 When the given number consists of a whole number and decimal together, make the number of decimals to con5;ist of - 3, 6, 9, &:c places, by adding ciphers thereto, so that there may be a point fall on the unit's place of the whole number. 13. What is the cubo root of 12,977875? Ans. 2,35 14. W^hat ir« the cube root of 361 55,027576 ? Ars. 33.06 + 15. W^hat is the cul)e root of ,001906624 ? Ans. ,124 16. What i« the cube root ©f 33,230979637? Ans. 3,215 + 17. What is the cube root of 15926,972:04? Ans. 25,16+ 18. What is the cube root of ,053258279 ? Ans. ,376 + * When il)0 quotient is 1, 2 or S, there must be a cipher put to supply the place 6f tens. CUBE ROOT. 231 To extract the Cube Root of a Vulgar Fraction. Rule. Re.iuce the fniction to its lowest terms, then ex- tract the cube root ©f the numerator and denominator ibr a new numerator and denominator; but if the fraction be a surd, reduce it to a decimal, and then extract the root from it. s EXAMPLES. 19 AVhat is the cube root of f f|t ? Ans. f 2%. What is the cub3 root of //-^,y ? Ans. | 21. What is the cube root of If* a? Ans. 1 SURDS. 22. What is the cube root of 4 ? Ans. ,8204- 23. What is the cube root of a ? Ans. ,82^J-f 24. What is the cube root of J? Ans. ,873+ To extract the Cube Root of a Mixed Kumbcr. Rule. Reduce the fractional part to its lowest terms, and then the mixed number to an improper fraction ; extract the cube roots of the numerator and denominator for a new nu- merator and denominator : but if the mixed number given be a surd, reduce the fractional part to a decimnl, annex it to the whole nuoiber, and extract the root therefrom. EXAMI'LKS. 25. What rs the cube root of 12.]} ? Ans. 2} 26. What is the cube root of 3IJ^%? Ans. 3| 27. What is the cube root of 405//^? Ans. 7f Sunns. 28. What is the cube root of 7} ? Ans. 1,93 + 29. What is the cube root of 9J^^ ? Ans. 2,092+ 30. What is the cube root of 84? Ans. 2,057 + 252 CUBE ROOT. The ArpLicATiOx\. 1. If a cubical piece of timber be 47 inches long, 47 inches broad, and 47 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 earth were taken out of it? Ans. 1728 3. There is a stone of a -cubic form, which contains 389017 solid feet: what is the superficial content of one of its sides ? Ans. 6329 Betzveen two numbers givcn^ to find two mean proportionals. Rule. Divide the greater extreme hy the lesser, and the cube root of the quotient multiplied by the lesser extreme gives the lesser mean : multiply the said cube root by the lesser mean, and the product will be the greater mean pro- porticnaL EXAMPLES. 4. What are the two mean proportionals between 6 and jG2? Ans. 18 and 54. 5. What are the two mean proportionals between 4 an4 108? Ans. 12 and 36. To find the side of a cube that shall he equal in solidity to any given solid^ as a globe^ cylinder^ prism^ cone^ 4'C. 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 10648, what is the r^ide of a cale of equal solidity? Ans. 2^ BIQUADRATE ROOT. 233 T^ie side of a cube being given^ to find the side of that cube that shall be double^ treble^ uting the dimensions of the ?-eviM"al parts of buildiiii^s ; it is likewise used to iind ships' tonnage, and the contents of bales, cases, 4rc. Dimensions are taken in feet, inches and parts. Artifieers' work is computed by diiTt^-ent measures, viz. Glazing, and masons' flat work, by the foot. Painting, pavins^, plastering", &c. by the yard. Partitioning, flooring, roofing, tiling, &c. by (lie square of 100 feet. Brick-work, kc. by the rod of IG^ ft. who^e square is 2T2'- The contents of bales, cases, &c. by the ton of 40 cubic feet. The tonnage of ships, by the ton of 95 feet. 23k:^ duodecimals. lilTLE FOR MULTIPLYLXa DUODECIMALLY, 1. Under the multiplicand write the corresponding de- nominations of the multiplier. 2. Multiply each term in the multiplicand (beginninsf at the lowest) by the feet in the multiplier; write each result under each rej^pective term, observing to carry an unit from each lower denomination to its superior. ?j. In the same manner, multij)ly 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 multipli- cand. 4. Work 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 for thirds, fourths, t product by 95, the quotient whereof 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 Y .24S DUODEriMALS. three fifths of the breadth, and lake the depth from the un- der side of the deck plank, to the ceilins: m th«^ hold, then multiply and divide as aforesaid, and the quotient shall be fleemed the tonnage." EXAMPLES. 1. What is the government tonnage of a single decked Tes?el, whose length is 69 feet, 6 inches, breadth 22 feet 6 inches, and depth 8 feet 6 inches ? ft. in. 69 6 lensrth. 22 6 breadth, deduct 13 6 for> breadth. 3 56 5)67 6 22 6 breadth. 13 6 112 112 6 in. I 28 1260 8 6 depth. 10080 9 in. J 630 95)10710 0(il2J| tons. 95 121 95 260 190 70 Ans 11211 tons. DUODECIMALS. 248 2. What is the government tonnage of a double docked vessel, of the following dimensions ; length 75 feet G inches^ breadth 23 feet 4 inches, and depth 11 feet 8 inches? ft. in. 75 6 14 for I breadth. 61 23 4 breadth. 183 61 ft. X 23 ft.=:1403 122 6 in. X 23 ft.= 11 6 « in. I 116 61 ft 6 in. X 4 in.= 20 6 4 in. ^ 20 6 1435 1435 118 1 1 8 depth. lo785 15785 1435 ft. X 8 in.= 956 8 6 in. 1 717 6 t in. i 239 2 16741 8 as before. 95)16741 8(17614 tons. 95 724 665 591 570 21 Ans. I76Ji tons. 3. What is the government tonnage of a double deck; 3 Yessel, of the follovvingdimensions; length 82 feet 3 inches, kreadth 24 feet 3 inches, and depth 12 feet U inches? Ans. '209f I tons. *'»4 TABLES OF CORDAGE. TABLES OF CORDAGE. A Cordage Table, shewing how many fathoms^ feet and incheg of a Rope^ of any nze^ not more than 1 4 inches^ make a hun- dred weight; with the use of the table. ^ eo OS <;^ '0 6 m G lOi n 4tj6 313 216 159 124 96 77 65 54 45 39 34 30 3 3 3 3 2 3 4 5 2 3 3 9 1 6 n 5 5i O4 6 6i, 6f 7 ' 7i 26 5 24 21 19 17 16 14 13 12 n 10 9 9 103 n Hi ill 12 \n 12« 12J 13 131 13| 14 1 5 4 3 2 2 2 7 5 4 4 3 2 2 Z/6£ OF THE TABLE. At the top of the table, marked inches, fathoms, ^eei.^ inch- es, the first cohinnn is the thickness of the rope in inches and quarters, and the other three the fathoms, feet and inch- es, that make up a hundred weight of such a rope. One example will make it plain: Suppose you desire to know how much of a seven-inch rope will make a hundred weight ; find 7 in the third col- umn under inches, or thickness of rope, and aa^ainst it in the fourth column you find 9, 5, 6, which -shews that there will he 9 fathoms, 5 feet, 6 inches required to make up one hua- dred weigiit. TABLES OF CORDAGE, 246 A TxBf.F, shcxvhifr the weight of any Cable or Rope of 1^0 fatkoins m Uiitgtli^ ana for every ha finch, from 3 to iii 1 tncheSy in circunfertucc. ~3"" 2 J 1 1 7 12 I 'Si 3 7i 14 4 4 8 16 4i 5 84 18 5 6 1 9 20 1 5i 7 2 9i 22 2 6 ! 9 10 25 6i 10 2 m 27 2 30 I 33 36 39 42 1 45 2 49 11 Uh 12 13 I3i 14 , - 14^ 52 2 15 56 1 "l5i 16 I I6i| 17 17i 18 i 18^ 19 I 19^1 00 64 68 72 I 76 2 8i 85 2 90 1 95 20 , 20^ 2; I 2li- 22 j 22^, 23 , 23ii 24 I H iOO i05 IIO 1 lio 2 121 126 2 132 1 138 144 USE OF THE TABLE. The first column, markeil ior inches, is the thickness or circumference of the cable to every half inch from 6 to 24 inches; the second, marked cvvt. qrs. for the hundred weights and quarters that it will weigh if 120 iathoms in length. For instance: Suppose it be a cable of \A\ mches; look against 14A and you will find in the other column 52 cwt. 2 qrs. which shews that 120 tathoms of 14^ mch cable will weigh 52 cwt. 2 qrs. and so in others ; and any quantity of a less length will weigh in proportion. A ship was hrouglit to anchor in a gale of wind; but the gale increasing, it was thought safest to cut the cables, in consequence of which 75 fathoms of 16 inches, and 50 fa- thoms of 12 inches were losi ; what must they be v ilued at in calculating the average, new cordage being then 14 dol- lars per cvvt. ? CALCULATION. 120 fath. 16 in. cable=64 ewt. 120 fath. 12 in. cab =36 cwt* 60 15 do. do. 75 fath. weighing 50 do. 32 8 40 15 40 10 do. do. 12 3 60 fath. wei-;hing 15 65 cwt. at 14 dolls, per cwt. One third deducted lOr new dlls. cts. 770 00 256 662: ¥2 Ans doUs. 513 33^- 246 TABLES OF GOLD COIN. TABLES OF GOLD COIN. A TARLE For receiving and paying the Gold Coins of Greot-Bntain and Portngal^ of their present sWndard^ at 100 cts.for ^7 grains^ According to an Act of Congress, passed Ajfyil 29, \\}\Q. grs. ch. 1 dzi)t. dls. ctt. 1 (kvt. (ILs.cts 1 dz^'t. dls. cts. 1 - 4 7 - 6 22 39 - 34 67 70 - iJt ^2 o . 7 8 - 7 11 40 - 35 55 71 - 63 11 3 . 11 9 - 8 00 41 - 36 44 72 - iy\ 00 4 - 15 10 - 9 39 42 - 37 33 73 - 64 89 : 5 - 19 11 - 9 78 43 - ^8 22 74 - 65 78 6 - 22 12 - 10 67 44 - 39 1 1 75 - 66 67 7 . 26 13 - 11 55 45 - 40 00 76 - 67 55 8 - 30 14 - 12 44 46 40 8!^ 77 - 68 44 9 - 33 15 - 13 33 47 - 41 78 78 - 69 33 10 - 37 16 - 14 22 48 - 42 67 79 ^ 70 22 11-41 17 - 15 1 1 ' 49 - 43 55 80-71 11 12 - 44 18 - 16 00 50 - 44 44 81-72 00 ii 13-48 19 - 16 89 51-45 33 82 - 72 89 • 14 - 52 20 - 17 78 52 - 46 22 83 - 73 78 15-56 21 - 18 67 53-47 11 84 - 74 67 16-59 22-19 55 54 - 48 00 85 - 75 55 17-63 23 - 20 44 55 - 48 89 86 - 76 44 18 - 67 24 - 21 33 56 - 49 78 87 - 77 33 19-70 25 - 22 22 57 - 50 67 88 - 78 22 20 - 74 26-23 11 58 - 51 55 89 - 79 1 1 21 - 78 27 - 24 00 59 - 52 44 90 - 80 00 22 - 81 28 - 24 89 60 - 53 33 9 1 - 80 89 23 - 85 29 - 25 78 61 - 54 22 92- 81 78 24 - 89 30 - 26 67 62 - 55 1 1 93 - 82 67 31-27 55 63 - 56 00 94 - 83 55 dwt. dllsMs. 32 - 28 44 64 - 56 89 95 - 84 '44 I - 89 33 - 29 33 65 - 57 78 96 - 85 33 2 - 1 78 34 - 30 22 66 - 58 67 97 - 86 22 3 - 2 67 35-31 11 67 - 59 55 98- 87 11 4 - 3 55 36 - 32 00 68 - 60 44 99 - 88 00 5 - 4 44 37 - 32 89 69 - 61 33 100- 88 89 « . 6 33 38 - 33 78 TABLES OF GOLD COIN. A TABLE 24*r }or receiving and pacing the Gold Coins of France^ of (heir present .standard^ at 100 cents for 27 t grains. According to an act of Congress^ passed April 29, 1816. grs. cts. dwt. (Hi. CIS. dxvt. dls. cts. 1 (iz<:t. fii^. cts^ I - 1 7 - 6 1 1 39 - 34 U3 70-61 07 2- 7 8 - t> 98 40 - 31 90 71 ' 61 95 3 - n 1 9 - 7 R5 41 - 35 77 72 - 62 82 4-15 1 10 - 8 73 42 - 36 65 73 - G3 69 5- 18 1 11 - 9 i-.O 43 - 37 52 74 - 64 57 6 - 22 12 - 10 47 44 - 38 39 "5 - 65 44 7 - "zo 13 - I 1 34 45 - 39 26 76 - 66 31 8 - 29 14 - 12 21 46 - 40 13 77 - 67 18 9-33 15 - 13 09 47 - 41 01 78 - 68 05 10 - 36 16 - 13 96 48-41 88 79 - 68 93 11 - ^k) 17 - 14 83 49 - 42 75 80 - 691180 12 - 44 18 - 15 71 50 - 43 63 81 - 70 67 13- 47 19 - 16 58 51 - 44 50 82 - 7i 5a 1 i - 51 20 - 17 45 52 - 4£» 37 83 - 72 42 1 5 - 55 21 - 18 32 53 - 46 24 84 - 73 29 16-53 22 - 19 19 51 - 47 1 1 85 - 74 16 17 - 62 2.5 - 20 07 55 - 47 99 86 - 75 03 13- 65 24 - 20 94 5') - 4 8 86 87 - 75 91 19-89 25 - 21 81 57 - 49 73 88 - 76 78 . 50 - 73 26 - 22 69 58 - 50 61 89 - 77 6o 21-76 27 - 23 56 59 . 51 48 90 - 78 53 22 . 80 28 - 24 43 60 - 52 35 91-79 40 23 - 83 29 - 25 30 61 - 53 22 92 - 80 27 24 . 87 30 - 26 17 62 - 54 09 93-81 14 31 - 27 05 il^ . 54 97 64 - 55 84 91 - 82 01 95 - 82 89 dwl dla. cts. 32 - 27 92 1 - 87 33 - 28 79 65 - 56 71 96 - 83 78 2 - 1 75 34 - 29 67 GQ - 57 59 97 - 84 63 3 - 2 62 35 - 30 54 67 - 58 46 08 - 85 51 4 - 3 49 36 - 31 41 68 . 59 33 Vk) - 86 38 5 - 4 36 37 - 32 28 69 - 60 20 ' 100 - 87 25 6 - 5 23 38 - 33 15 i48 TABLES OF GOLD COLTST. A TABLE For receiving and paijini{ Om Gold Coins of Spahi^ and ike doininlous of Spain^ (f thc>r prcatnt dnwJard^ at iOO cents for 2^'>\ irrams. Accordmg to an act of Congress^ jjamed •. r.v cts. 1 ■r.t. aL. I - ic'(. dis. et.s. 1 d-ci^t. ://■.';. rts. J - 3 7 - 5 oo 3H - 32 7 6 70 - 58 80 2 - 7 8 - 6 7^ 40 - 33 6m 71 - 59 64 S - ) 1 9 - 7 56 41 - 34 44 72 - 60 48 4 - 14 10 . 8 40 4 2 - 35 28 73-61 32 5 - 17 1 1 - 9 21 45 - 36 12 64-62 16 6 - 21 12 - 10 08 44 - 36. 96 75 - 63 00 7 - 25 13 - 10 92 45 - 37 80 76 . 63 84 n - 23 U - i 1 76 46 3o 64 77 - 64 68 9 ' 31 15 - 12 60 47 - 39 48 78-65 52 m - So 16 - 13 44 4H - 40 32 79 . (jC) 36 11 - 39 17 - 14 28 49 - 41 16 80 - 67 20 12 - 4^ 18 - <5 12 50 - 42 00 81-08 04 13 - 45 19 - 15 \)6 5i - 42 84 82 - 68 88 14 - 49 20 - 16 80 52 - 43 68 83 - 69 72 3 5 - 53 21 - 17 64 53 - 44 52 84 - 70 56 16 - b6 22 - 18 48 54 . 45 36 85-71 40 17 - 59 ■ 23 - 19 32 55 - 46 20 86- 72 24 18 - 63 24 - 20 16 56 - 47 04 87 - 73 08 19 - 67 25 - 21 UO 57 . 47 88 88- 73 92 20 - 70 26 - 21 84 58 - 48 72 89 - 74 76 21 - 73 27 - i2 68 59 - 49 56 90 - 75 60 2^2 - 77 28 - 23 52 60 - 50 40 91 - 76 44 23 - 81 29 - 24 36 61 - 51 24 92 - 77 28 24 - 81 3J - ^25 20 62 - 52 08 93-73 12 M - 26 26 t'4 63 - 52 92 94 - 78 96 cf-^^. dls. cts. 32 - 88 64 - 53 76 95 - 79 80 1 - 84 33 - 27 no 65 - 54 60 96 - 80 64 2 - I 68 34 - 28 56 66 - 55 44 97 - 81 48 3 - 2 52 35 - ?9 40 67 - 56 28 93 - ;^2 32 4 - 3 36 36 - 30 24 68 - 57 12 99-83 16 5 - i 20 31 - 31 08 69 - 57 96 100-84 00 C - 5 04 i 38 . 31 92 ' Note. — The Act of Congress, on which the foregoing tables were onlculated, expired oa the iirst Nov. 1819, when all forei^a Gold Cain4 cca&ed Xq be a lawful tender. MERCANTILE PRECEDENTS. 249 MERCANTILE PllECEDEiNTS. BILL OF EXCHANGE, Sahnu September 12, 1822. EXCHANGE for £1000 sterling. At twenty days sight oi'this my first of exchange (second and third of the sanrie tenor and date not |)al(l) pay to John P-arker, or order, one thousand pounds sterling, with or witit* #ut further advice from Your humble servant, WILLIAM P£ABODY. Messrs. Button Si Green, Merchants, London. BILL OF GOODS, At an advance on the sterling cost. Boston^ Oct. 5, 1822. Mr. William Poole Bought of Simon Simmonds, 32 ells Mode - - Is. Sd. steri. £2 13 4 64 yds. striped Nankins \s. Od. - - 4 16 28 do. striped Calico - \s dd. - - 2 9 4 pieces K\issel . - 24*. - - 4 IG Sterling 14 14 4 Exchanf;e, 331- per cent. '^ ^^ U £19 12 bi Advance at 20 per cent. 3 18 5^ £23 10 11 Dollars 73,43 Received bis note at 2 months, Simon Sjmmonds. 250 MERrANTlLE PRECEDENTS. PROMISSORY JVOTE. Boston., Oct. 5, 1822. For value received I promise t« pay to Simon Simmoiuis, or order, seventy eight dollars for- ty eight cents, on demand, with mterest alter two months. Attest. William Foole. Saul Jamec. A RECEIPT FOR AjY ENDORSEMENT ON A NOTE. Boston, Dec. 12, 1822. Received from Mr. William Poole, (by the hands of Mr. Betijamin Flint) thirty eight dollars^ seventy cents, which is endorsed on his note of Oct. 5, 1822. Simon jjimmonds. 38 dolls. 70 cts. RECEIP T FOR MONE Y RECEIVED ON ACCOUNT. Boston.^ January 10, 1804. Received from Mr. D. Evan?, (by the hands of Mr. l homus Dunmore) four hundred ani thirty dollars on account. Geokgi!: Page. 43u dolls. PROMISSORY NOTE BY TWO PERSONS. Salem., July 12, 1822. For value received we jointly and {»everaily promise to pay to Mr. Samuel Rich, or order, five hundred dollars fifty four cents, on demand, with interest. Attest Nathan Say born, William Boltox. Stlfhen Needy. GENERAL RECEIPT. Nexi^- Bedford^ March 27, 1822. Received from Mr. N. B, I'he st,:n (.itrn ^l-l'ars twenty nine cts. iatuii of all demands. 10 doiis. 29 ct.«. E. D. MERCANTILE PRECEDENTS. 251 BILL OF PARCELS. Salem^ June 20^ 1804. Mr. William Holman Bought q/* Daniel Green, 1 hhds. sugar, wt viz. C. q. lb. C. 9. /^r. No. 1. 5 2 7 No. 5. 5 3 19 2. 5 1 22 6. 5 I 07 3. 6 13 7. 5 1 07 4. 5 2 13 8. 5 3 14 22 2 27 22 2 1 45 I Tare 1 2 per cwt. 4 3 IT 22 2 1 Neat 40 I 17 at 12 dolls, per cwt. 2 bbls. sugar, viz. dolls, cts. 484 82 a 2 I q, lb. 2 25 3 17 Tare 21 lb. per bbl 4 4 viz. 2 14 1 U Neat 3 hhds. molasses, 1 at 10 dolls. galls. 101-9* ion— 5 107—7 316-21 21 - 42 5© 295 ^allon5» at 50 cK - 147 5« 1 quarter cask Mahira wirio - 25 00 5 cases gin, at 4 dolls. 25 cts - 21 25 dolU. 721 07 * The ullage is thus noted. ^52 MERCANTILE PRECEDENTS, LYFOICES. Invoice of 20 hhds. clayed suoar and 10 hhds. coffee, shipped by of Boston, in the United SU\tos of America^ on his own account and risk, on board the ship A B master, bound for and a market, consigned to the said A B for sales and return:^, viz. 50 hhd? clayed sugar, viz. B. C. No. C. q. lb. No. C. q, lb. No. 1 a 20 I. 113 14 11. Vl !4 2. 10 3 "21 12. 10 ^Z U 3. 110 13. 10 2 21 4. 12 10 14. 113 21 5. 11 1 14 15. 10 I 14 6. 10 3 7 16. 10 2 7. 10 2 17. 11 2 21 8. 110 7 18. 10 I 14 9. II 21 ^ 19. 1117 10. 10 7 20. 10 3 14 111 no 7 2 221 23 2 7 2 27 110 2 Care 12 per cwt. dolU. cts. 197 3 8 neat, at 10 d. 25c. 2u2 7 67 10 hhds. coffee, \vt. viz. B. C. " No. C. q. lb. Ta-e. No. C. q. 'b. Tare. 1^0. I. a 40 I 9 2 7 i08 6. 6 I 14 79 2. 9 3 12 7. 6 1 6 CI 3. 10 I 21 '06 8. 8 2 4 84 4 10 2 14 i03 9. 9 I 8 91 ». 8 14 94 10. 10 14 108 48 2 523 40 2 18 428 40 2 18 423 946 8.0 lS=9986j^ deduct tare 946 9010 Ib.neat, at 21 cts. 1898 4f 3926 07 Premi'im of iiT^nring 4176 dolls. 67 cts. at 6 per7 250 69 cent, o at 23 cts. per lb. \ ^^^^^- 3S06 48 16. George Watts, 7 bbls. wt. 1943 lb. at 23 cts. 843 Z9 17. Peler Bates, 3i bags, '* 5507 23 cts. 1266 61 Charges. Ad/ertising . - - - dolls. 1 .^^0 Storage - . - - . 3 rg Commission on 4916 dolls. 48 cts. at 2i per cent. 491G 48 Neat proceeds passed to hi- credit. Errors excepted, &c. 122 91 127 91 dolls. 4788 67 SALES of sundry inerchani'ise received per ship Juno., Cant. Dane from A'lachias. and disposed of for account and risk of Amos Goodwin., mcrrJiant^ there. Date, j To whom sold. barrels oil bbls. salmon bbls. herring cords wood cords bark feet boards barrels beef PHce. o 1 1822 dls.cts. dh. cts. June 4 James Yates SO 3 90 8 1 Wm. Roc 120 3 27 292 40 27 ' John Pavson 6 12 72 July 4 James Nugent 22 4 88 - Cash 50 S 75 437 50 8 [ Simon Sai dri 3,216 6 50 20 90 21 Stock 16 9 135 29 Pnvil Sim-on 13 1 3 50 45 50 ^uo. S Jona. Ho e 1,259 6 7 55 Taken to fill '^p J — *~ 1 50 7 .50 13 22 4,475 .5 I28S 85 Remaining unsold, 40 barrels of herring. Charges i viz. Storage of fish dolls. 10 50 Commission on 1288 dolls. 85 cts. at 2| per cent. 32 22 ^eat procecdr, carried to the credit of liis account, dolls. 1248 IS Errors excepted, &c 42 72 MERCANTILE PRECEDENTS. 255 S.ILFIS of 19 fih.Js. an I 7 bhh. of ruin^ receiver! per brig Ruhy^ John, Butler master^ from Portland^ for account end risk of Daniel E'kvards^ merchant^ there. " . ) — ii § 1< a >> OD CO ^ GO — -f .^ CO G^ CO 'i: a c .g|2 vr: T-. CQ d6 -t GO CO 5^ CO CO .^j -g^ CO OG^i-g ^■| "I ^ o" -- ^ ;-i Sf o a; :-| fl — 6 d t^ T3 -a a> O) >g 0^ . ^ ^ c^ a .g 00. CN ^ kO -^ a CO £.660 Oh CO ^ &H — . ^ «3 CO -^ '^ CO CO CO "^ 00 00 CO "1 ^ ^ CO -* ** 2 ^ ^ <^ CO -a a CO 0) ^ a CO ^ CO S CO 5 rr CO "So d t^ • . . o CO S 2 a i 0^ r< •^ C5 CO H ^ G>l rt CO c f-4 EhH EHh Z 2 258 xAIERCANTILE PRECEDRNTS. *> o o o ^ ~3 ©^ re^vT bJDO •5! o C — rO 2 ii^ \ ^ ^ a -c^ fl^ ^ ^ = .B-^ ^-^^ 'Jo X^ £ --=: ^' ,o o c^ o ^'- O t-' no tt g4 CO G^ (N oo . r-4 ■4-' o O ^ 2i O o CD c^ C^ iO »0 o •^ C!i :a3 G^ W ^cc ^•9 0/ H o ^3 "^^ ^ >i *^ CO S: J '^ ^v^ c t- — » €0 c >- CN t- K* ^ ^ '"^ ^s»« —K ri-j -o "^ G^ CD in — ©3 CO Hn. c» ^ O O ©^ _2 ^ O-^ O o o If) c cc 1^ *' c § 2i £ ^ C a, o 2: be s o O " o o ^c o o o ©< oi in in -^ 1 1 c^^ 1 6 in CO ^. c ^ hn d. (^ 3 p 0) Sf-**-* •< M > a ^ o H 05 MERCANTILE PRECEDENTS. 25J o O) I- CO .5 "7: > r/j ^ 'Z ^ =: -c - o 56 ^ ^ . ^ i? ^ - I L = « g ^ 1^ £ £ a. o t- c ^ '-^ 2^ >^^ ^ -~ 1 C- \ o O O o w O 2) ^ o <§ §^ CM o o o o I- o o o ^ *i CO =3 0< G^ O OD CO GJ O w ?^ (>^ : CO p2 -^ . ^ ?^ =: » o 0) 1 o CO • G^ (N O • JWJ Q 1 CM n t? '^ S 1 s s^ei • = 3 » t- a . 6 SS'^gc • r-H ^ d . p. r/j — .i: ir _5 ^ TD "2 J5^ -C -G i« s ^ 5 ^-^ ^ ^ t« lO ^ O '^ o u o o o O C O C O HH EhH^=^^^ 0^ 5^ 3^ i6 ^ssisi CO 4) a ^ g3 H. D 7 5 « »-JL >-i <; CO 'S 5 ^, =o w ^ se 5 \3 IQO MERCANTILE PRECEDENTS. Dr. Mr. Thomas Gibson^ in Interest (lis. cts. days. dls. cts. 35 00 fr. Jan 31, '22, to Oct. 12,'2i!,256 1 47 on To Int To do. on 2962 00 Feb. 2, To do. on 2590 42 May 31, To do. on 1733 97 July 2, To do. on 73 63 July 12, To do. on 455 52 Aug. 25, To do. on 15871 Sept. 30, do. 254 123 68 do. 134 57 Oft do. 102 29 07 do. 92 1 11 do. 47 S 51 do. 12 31 dolls. 216 21 Dr, Mr. William Mace.^ in Interest 1321. dolls, cts. ?/• m. d. dls. cts. March 3. To Interest on 3869 20 for 1 5 11 338 97 April 26. do. on 273 6 ' 1 3 18 21 29 Aug. 18. do. on 400 ' 11 26 23 73 Dec. 28. do. on 414 6 ' 7 16 15 59 '22Ja.l5. do. on 200 ' 7 9 7 30 Feb. 19. do. on 300 ' 5 25 8 75 Mar. 2xj, do. on 1300 ^ 4 18 , dolls. 29 90 442 53 MERCANTILE PRECEDENTS. 261 Account with Thomas Merchant. Or. dolU. daifs. dlls. cts. By rut on 500 fr. Apr. 24, '22, to Oct. 1 2, '22, 171 14 5 liy do. 11.53 25 ' 25, i\o. !2, 170 .31 67 By do. 296 24 May J, do. 12, 1G2 7 88 By do. 215 ' 5, do. 12, 160 5 65 By do. 215 80 June 9, do. 12, 125 4 4,5 hy do. 109 74, ' 24, do. 12, 110 2 By do. 517 90 July 20, d.). 12, 84 7 15 Balance ; due oil this ac't carried to the debit of ac't. 1 43 43 doll?.21G 'Si Salem^ Sic. Aceount wich Thomas' McrcJiant. Cr. 1822. dolls, cts. dt^lls. cts. Jan. 16. By interest on 339 67 427 • 81 - y. m. d. 7(37- -48 _ e jo^ 05 30 Balance carried to account current - - 417 21 dolls. 442 53 Salem^ September 26, 1822 Erroi-s excepted, THOMAS MERCHANT. 262 MERCAXTILK PRECEDENTS. BILL OF SILE. To all people to whom t\.i< preseat Bill of Sale shall come, I. R. P. of Silem, 1.1 the Sla'e of vlassacha^etr-*, merchdiit, seijcl greeting. KNOW iK, That I, the f^aid il. P. for and in consideratioa of tl e sum of THRE^ THOUSAND TWO HUNDRED AND TWEN T Y-TVVO DOLLARS, to me in liand well and Tuly paid at or before the eiisealing and delivery of these presents, by S. T. of the said Salem, merchant, tl e receipt whereof I do hereby acknowledge, and am therewith f illy and entirely satisfied and conten ed, have granied, ban^ained and sold, and by these presents do grant, bargain and sell unto rhe said S. T all the hull or body of the good brig Sally, together with all and singular her masts, spars, sails, rigging, cables, anchors, boats and appurtenances, now ly- ing at Salem, and registered at the port of Salem, the certificate of whose registry is as follows : In p irsuance of an Act of the Congress of the United States of A- merica, endiled, " AN ACT concerning the registering and recording of ships or '. essels, " R. P. of Salem, in the State of Massachusetts, merch- ant, having taken or subscribed the oath reqired by the said act, and having sworn he is the o ily owner of the ship or vessel called the Sallv, of Salem, whereof William Knapp is at present master, and i.5a citizen of the Uni>ric^ having certified that the said ship or vessel has one deck and tw^o masis, and that her length is sixtynine feet five inche--, her breadth twenty-tvvo feet and one half inch, her depth eiglit feet two inches, and that she measures one hujidred and six tons and forty ninety-fifths, that she i, a square-s^erned brig, has no galleries and no fi'ure heid, and the said R. P. leaving agreed to the description a: d admeasarement above speciiied, and sufficient security having been i:iv en according to the said act, the said brig has been duly registered at the port of Salem. Given under my hand and seal at the jjort of Salem^ this sixth day of" September^ in the year eighteen hundred and twenty two. To have and to hold the said granted and bargained brig Sally and premises with the appurtenances unto the said S. T. his heirs, executors, administrators or as igns, to his only proper use, benefit and behoof for- ever. And I the said R. P. do avouch myself to be the true and lawful owner of the said brig and appurtenances, and have in myself fall power, good right and lawful authority to dispose of the said brig as afores-aid, and her appurteiiances in manner as aforesaid, and furthermore I the Kaid R. P. do hereby covenant and agree to warrant and defend-the said brig and premises, wdth the appurtenances against the lawful claims and de- mands of all per-ons whatsoever unto the said S. T. In witness where- of, I the 8?iid R. P. have hereunto set my hand and seal, thishrst day of September, in the year of our Lord one thousand eight hundred and tweu- t^-two. MERCANTfLE PRECEDENTS. $63 CHARTER-PARTY. THIS Charter-party of affieii^htment. indented, made and fally concluded upon this ninth ^^y of Sej)teniber, in the year of our Lord, one thousand eight hundred and twenty- two, hetween J. P. of Salem, in the county of Essex, and Commonwealth of Massachusetts, merchant, owner of the good shfp Ifelen, of the burden of two hundred tons, or thereabouts, now lying in the harbour of Salem, whereof 11. S. is at present master, on the one part, and C. D. ot said Salem, mercliant, on the other part, Wiinesseth^ ^\ hat the said J. P. for the consideration liereafter mentioned, huh lettento freight the aforesaid ship, with the appurten.uices to her belonging, lor a voyagf^ to be made by the said sliip to London, where sh«» is to be discharged (the danger of the seas excepted;) and the said J. P. doth by these {)resents covenant and agree with the said C. I), in manner following, That is ^'> 5rt//, that tiie said ship in and during the voyage aforesaid, shall be tight, staunch and strong, and sufhciently tackled and apparelled with all things necessary for such a vessel and voyage, and that it shall and may be lawful for the said C. D, his agents or frjctors, as well at London as at Salem, to load and put on board the said ship, loading of such goods and merchandise as they shall think proper, con- traband goods excepted. IN consideraion whereof, 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 freight or hire of said ship and appurtenances, the sun) of three dollars per ton, per calendar month, and so in prop rtion for a less time, as the said ship shall be continued in the aforesaid service, in sixty days after her return to Salem. And the said C. D. doth agree to pay the charge of victualling and manning said ship, and all port charges and pilotfige during said voy- age, and to deliver the said shi[), on her return to Salem, (o the owner aforesaid or his order. And to the true and faith ful of all and singular the covenants, paym^Mit^ and agree- ment^ aforementioned, each of the parties aforenamed binds and obliges himself, his executors and administrators, in the penal sum of two thousand dollars firmly by these presents. In witness whereof, the parties aforesaid have hereunto in- terchangeably set their hands and seals the day and year afore-written. 264 MERCANTILE PRECEDENTS. BILL OF LADLXG. SHIPPED in orood order and well con- J. R. ditioned by John Roily, in and upon the 1 a 53 good ship called the Iris, whereof is nias- Casks Potash^ tor for this present voyage Charles i'ly, ton. cwt. and now ridln?^ at anchor in the harbour of 8 18 £ 5. f^. Salem and found for EiverpooK to say, at HOs — 35 12 fifty three cash of potash.; contawins eight Primage I07is and eighteen czvt beinsr mark<^d and 5 per cent. 115 7 numbered as in the margin, and are to he delivered in the like good order ani of it to every particular circumstance that usually ii; I Jones (John) 5 K L M Morgan (James) ^ 25 N Page 4 - 7 o P Pay ton (Richard) Proiit and Loss, Q : R Richards (Thomas) - 3 Stock, Sugar, s - 1 8 T Taylor (Samuel) Tohacco, Thompson (Andrew) 3 - 5 -6 V^oyage V to New-York, - 8 w Wine, 2 X Cc 1819 26 Stock Dr. Jan. 1 1 To Sundry Accounts as per Journal, To John Forrest, on bond To Sannuel Taylor, on account - To Balance for the neat of my estate Jan Feb. 8 Cash Dr. To Stock, in ready money To Hops, received ior 4 bags To Wine, received in part for 2 pipes To Bills Receivable, received oi Thomas Richards To Jimies Morgan, borrowed of b'm To Profit and Loss, won at billiards To Profit and Loss ier a Icgac}^ ieit me by my urclc - . - Cr D. 50 10 1 9 1 5 1973 1000 63 50 40 20 1201 1] 1819 Jan. 1 27 Contra Cr. By Sundry Accounts, as per Journal, 3y Cash, in reaily money By Hopf?, 10 bags, at 10,U0 per bag By Wine, 4 pipes, at 65, 50 per pipe By Broadcloth, 6 pieces, at 90, 10 per piece ----- By Thomas Richards, due on de- mand - - - , ■■ By PrOiit and Loss, gained ^in trade Jan. 1 3 22 Feb. 5 9 10 lo 15 13 23 97 I Contra Cr. By Cheese', paid tor half a ton By Cider, paid in part for 4 hhds. By Andrew Thompson, lent him By Bills Payable, paid John Forrest By Profit and Loss, paid a quarter\s interest - - - - By Profit and Loss, given A B Esq's servants - - By Profit and Lo3s,'paid household expenses - - - - By Profit and Loss, paid my book- keeper a quarter's salary, and other expenses - - - ^y Voyage to N. York, p:\idfreight and custom - - - - By Sugar, paid do. - - , - By Profit and Loss, paid for sup- porting the poor - - - By Balance, rem^iins in my hand I Df D. 0. 1000 00 100 00 262 00 510 60 45 75 24 G8 1973 03 3^2 75 25 50 20 00 40 00 00 75 00 15 00 1009 120 ! 80 G7 r*«2'- 45 87,1. 9.-1 1 1819 Jan, 1 28 Hops Dr. To Stock, 10 bags, at 10,00 per bag To Profit and Loss gained 2] JatK. 1 Wine Dr. To Stock, 4 pipes, at 65,50 per pipe t To Profit and Loss, gained ^an. 1 D. c. 100 00 23 00 123 00 262 00 29 66 Broadcloth Dr. To Stock, 6 pi<-ce-^, at 90,10 per piece - - - - -j 1 To Profit and Loss, gamed , 7 291 66 640 7 M7 60 05 65 2T 1819. Jan. ' 29 Contra Cr. By Cash, received for 4 bags, al 1 5,7.j per bag - - - By Balance, reaiain 6 bigs, at 10,00 per bag - - . _ Contra Cr. Jan. 10 By Sundry Accounts, as. per Journal JBy Cash, received in part for 2 pipei I By Samuel Taylor, ren)ains due jBy Balance, remains 2 pipes Jan, 15 Contra Cr. By John Jones, to pay in 1 month flBy Balance, remain 5 pieces, al 90,10 per piece - - - Cc Ja D. G. G3 00 GO 00 123 00 50 75 109 91 131 00 291 66 97 15 450 50 547 65 30 1819 Jan. 1 Ian, 29 Thomas Richards Dr. To Stock due on demand John Forrest Dr. To Bills Payable, for Qne drawn on me, to pay at sight - To Balance, remains due to him Jan. 10 Samuel Taylor Dr. To Wine, due on demand Cr 45 45 C. 75 75 40 10 50 00 00 00 109 109 91 91 3] 1819 Jan. 26 Jan, 1 Jan. 1 31 Contra Cr. By Bills Receivable, for one drawn on him, to be paid at sig-ht By Balance, remains due on demand Contra Cr. By Stock, due on bond Contra Cr. By Stock, due on account By Tobacco, for 2 hhds. By Balance, due me- Dr D. 6 20 9 25 45 00 75 75 50 5(» 00 00 10 00 79 20 -^0 71 109 91 1819 Jan. 1 32 Cheese Dr. To Cash, paid for half a ton of Cheshire _ - - - To Cider, bartered 4 hos-sheads, at 10,00 per hhd. for half a ton of Gloucester _ - - To Profit and Loss, gained Dr Cider Dr. Jan. 3 To Cash, paid in part for 4 hhds. I To Richard Pay ton, remains due i Richard Payton Dr. Jan. 3jTo Balance, re mains due to him [4 D. 32 40 2 74 C. 00 20^ 954 25 50 17 50 43 00 50 4] 1819 Contra Cr. Feb, 16 'By Voyage to New-York, for 2 cvvt, orChe««hire _ - - By Balance, n^mains half a ton Gloucester By Balance, remains 8 cwt. of Cheshire . . - - feb. 19 fan. 3 Contra Cr. By Cheese, half a ton of Gloucester receiverl in barter for 4 hhus. at 10,()(> per hhrl. By Profit and Loss, lost Dr^ D. I 'W^' Contra Cr, By Cider remains due at one month 40 26 20 74 951. 40 3 00 00 13 I 00 4 17 50 1810 Jan. 5 34 Tobacco Dr. To Samuel Taylor, for 2 hhds. toj be paid in 3 months Jan. 15 John Jones Dr. To Broadcloth, for 1 piece, to pay in one month Note. The Debtor side of all accompts of goodSi shows wliat they cost ; the Creditor sidej what returns they have ^ipade. Note also, That the Debtor side of all accomps of nun., m the charge, or what they stand indebted to you ; and the CrcditQr is the discharge. # [5 Cr I D. C. Ibi9 35 Contra Cr. By Balance, remains 2 hhds. Dr D. Contra Cr. By Balance, remains due to me - 'Note. When the Debtor side of ac- compts belonging to men exceeds then the balance is due to me ; but if the Creditor side is most, the balance is due to him. C. 20 97 15 1S19 36 [6 Andrew Thompson Dr. ' ^'^ ^* ( ^' Jan. 22 To Cash, len,t to him Jan. 26 Bills Receivable Dr. To Thomas Richards, for one drawn on him, to be paid at sight Bills Payable Dr. Feb. 5 To Cash, paid John Forrest hi? bill drawn on me paj'able at sight - 20 20 00 00 10 00 1819 37 Contra Cr. By Balance, remains due to me Dri Contra Cr» Jan. 28 By Cash, received the bill Jan. 2 D. 20 C. 00 m Contra Cr. By John Forrest, for a bill drawn on me - . . - 20 00 40 00 Dd 3H [7 U119 j Profit and Loss Dr. Feb, 9 To Cash, paid John Forrest a quar- ter's interest . - - 10 To Ca«h, given A B Esq's serrants 13 To Cash, paid 1 month's household j expenses - - - iSjTo Cash, paid my hook-keeper one quarters salary, and other ex- penses . - - - To Cash, paid for supporting the poor To Cider, lost To Stock, gained by trade Cr D. James Morgan Dr. To Balance, remains due on demand 9 00 00 15 50 00 24 96 C. 75 80 G7 75 87i 00 68 40 OU n IS 19 Feb, n 20 39 Contra Cr. By Cash, won at billiarJs By William Cowley, gained by sell- ing; my goods at New- York By Cash, tor a legacy left me by my unele By Hops, gained By Wine, gained By Broadcloth, gaineel ^ - By Cheese, gained Dr D. 1 7 8 7 1 20 2 23 o 29 2 7 4 2 961 Feb. 8 Contra Cr. By Cash, borrowed 40 37^ 23J 00 00 66 05 20i- 52-1. 00 40 rs isid eh. n 20 Feh. 23 Voyage to New-York Dr. To Sundry Accounts, as per Journal, To Cheese, for 2 cvvt. of Cheshire To Cash, paid freight and custom William Cowley Dr. To Sundry Accounts, as per Journal, To Voyage to New-York To Profit and Loss, gained by sell- ing goods - . - , Sugar Dr. To Sundry Accounts, as per Journal, To William Cowley, for one chest, neat weight 3 cwt. 2 qrs. valued at To Cash, paid freight and custom Cr 4 1 D. 8 2 11 a 751 33i 09 8 7 8 1 11 7 18 09 231 321 15 2 18 871 45 321 • {q 41 1319 Contra Cr. Feb. 20 By William Cowley, who has re- ceived the 2:oods sent thither - Dr 1^ FehT23 ^ Contra Cr. By Sugar, received 1 chest, neat wt. 3 cwt 2 qrs. ji'alued at , - By Balance, remains due to me - Contra Cr. By Balance, remains 1 chest, neat wt. 3 cwt. 2 qrs. valued with charges at D. 11 09 15 2 18 45" 32;^ 18' 32-1- Dd 2 m ■"^S^ 42 1B19 i Balance Dr. To Cash, remaining in nvj hands - To Hops, 6 bags remain, at 10,00 per bag - - * _ To Wine, remain 2 pipes, at 65,50 per pipe To Broadcloth, remain 5 pieces, at 90,10 per piece To Thomas Richards, remains due on demand - - - - To Cheese, remains | a ton of Gloucester, at BO, 00 per ton 40,00 " "- 8 cwt. of Cheshire, at 05,50 per ton 26,20 To Tobacco, remains 2 bhds. at 39,60 per hhd. To John Jones, remains due to me To Andrew Thompson, remains due to me To William Cowley, remains due to me To Samuel Taylor, remains due to me - - To Sugar, remains in my hands - Cr'j D. These articles on the Debtor side are the several branches of my present estate 1009 60 131 450 25 66 79 97 20 2 20 18 1980 [9 c. 24|- 00 00 50 75 20 20 15 00 45 71 321 5^ 1819 4S Contra Cr. By John Forrest, remains due to him \]y Richard Payton, remains due to him By James Morgan, remains due to him r»v Stock for the neat of my estate Dr D. m These articles on thij Creditor side (except the last, which is the neat value of my estate) are the several debts I owe 10 17 7; 40 1^913 C. 00 50 00 03 1980 53 End of the Ledger. LIST OF AUXILIARY BOOKS, MORE OR LESS NECESSARY TO DIFFERENT KINDS BUSINESS, AND TO BE MODIFIED ACCCfeDlNGLY. Cash Book, (Ledger-wise) in which receipts of monej are entered on the left, and payments on the right hand page. Invoice Book, of all shipments out a»d home. Letter Book, containing copies of letters sent and received. Bill Book, of exchange and acceptances. House-Expense Book. Charges-on-Merchandise Book. Till Book^ in which Retailers enter their daily cash sales. WASTE-BOOK AS AN EXAMPLE FOR PRACTICE, 4B Boston, March 15M, 1819- Bought of Henry Gerry 10 pipes of brandy, at 120,00 per pipe Paid in cash , . . 150,00 Gave a bill on John Jones for . 97,15 Due at 3 months . - . 952,85 -20th.- Borrowed of John Jackson, for 3 months, at 5 percent. - - - - --24th~ Paid James Burrows in full for fish 21 th Bartered with James Dobson, 6 cwt of Gloucester cheese, at 5,00 per cwt. - - - 30,00 2 hhds. of tobacco, at 42,00 per hhd. 84,00 For 6 barrels of cider, at 3,00 per bj^rrel - - - 14 do. of strong beer, at 7,00 18,00 98,00 -30th- [Received in full for wine, of John Fenton I John Jones is deceased, and has left me a leeracy, payable by his executor, John Palmer - . . « D. O. 1200 400 00 00 10 00 114 116 70 200 00 00 00 00 19 JJoston, Jpril 3d, 1819. D. ! r iThomas Richards has faileil, and I havci i compounded my debt ol 25,76 with' him.i Composition received is - 14,50; j Discount is - - -: l\^b\ -6(h- Paid a quarter's house-rent, due April 1st 9th V Sold Edward Nelson 20 quintals of cod fish, at 3,50 per quintal. Received in cash - - 15,25 His bill on John Burrows - - 54,75 -15th- Bou2:ht for cash 20 pieces of nawkeen, at 1,00 per piece - - 20,6(' 5 pieces of moreen, at 7,00 - - 35,00 .■:d, i 7o 25 GO 70 Received from on hoard the Friendship* Isaac Watson masior, from Hamburgh. shipped, by my order, by Herman Vai Beck, merchant tlierp, GO pieces of Russia sheeting, at 14,00 per! piece - , - . ' 840,001 20 do platillas, at 7,00 per piece MO^OOJ 30 pair of silk hose, at 1,25 per pair 37,50i 1 Amount carried forward^ 1 1 7,50! E K 00 00 50 Boston, Jpril 20tk, 1819. Amount brought forivard^ 1 1 7 ,5o Charsfes at shipping:, per invoice - 10,00 Freight, custom, and other charges here - - - 100,50 ^.24th- R.cceive<] of John Burrows, in full for Ed- ;vard Nelson's bill - - --2eth- Sold for cash 10 pieces of nankeen, at 1,25 per piece - - - - ► -.26th- Bong;ht of John lliirrows 40 barrels of flour, at 10,00 per barrel. Paid in cash - - - 100,00 Gave a bill on John Palmer - 150,00 Due at 3 months - - 150,00 -2Sth- Scnt as an adventure to the Havana, per Recovery, Joseph Jiollin master, ., ;. ^ncd to said Rollin for sales and re- i turns, the goods following*, viz. [20 bhls. of tlour, at 10,00 per bbl. 200,00 ,30 pieces Russia sheeting, at 16,00 j per piece - - ' - 480,00 jlO do. nankeen, at 1,25 -. - 12,50 'Charges at shippii^g - - 45,50 %. 51 Boston, April ^0, 1819. D. C. Bought of James Knight 50 pieces of Irish linen, 25 yards each, at 8,50 per piece Paid in cash - - - 41,00 Due at 90 days - - 381,00 Sold for cash 5 barrels of flour, at 1 2,0; per barrel - . - -May 1st jCharges on my trade last month -ad- Received from on board the Pollj^, James Smith master, from Baltimore, shipped by John Flint on my account, 75 barrels oi flour, at 7,50 per barrel, as per mvoice - - 562,50 20 bu>h. of corn, at 50 cts. per bush. 10,00 Received in cash - - 105,30 Paid freight - - - 75.00 The above is the neat proceeds of my 3 bales of India cottons, as per John Flint- account of sales. Sold for cash 3 barrels of cider, at 5,50 pei barrel - _ . . 425 GO 40 00 00 OQ 832 80 IC 50 Boston, May Gth, 1819. Bought of William Lamsoii 4 bbls. of strong- beer, at 8,00 per bbl. Paid him in cash - - . ^._8th- S old for cash 10 barrels of flour, at 12,00 per barrel - . . -^9th- ; Gave in charity -10th- iccepted William Lamson'S bill on me, pay- able at 3 days' sight, for — lltb Paid John Burrows Abated me for cash 47,50 ^,50 — 13th- D. i C. 32 00 75, 00 120 00 CO 150, 00 Paid William Lamson in full for his bill on -14th- 50 150 00 00 Sold John Foot 50 barrels of flour, at 12,C0 per barrel Received in pnrt, cash I His promissory note, payable in 7 I davs _ . - 250.00 COO 600 00. 00 Boston, May ^Gth, 18 1^ D. Bought of William Gordon 40 pieces ofl baadannoes, at 5,01) per piece - 200,00 20 do. pulicat handkerchiefs, at G,00 per piece - - - 120,00] 30 do. India chintz, at 3,50 per piece 105,00| C. Paid in cash 50,00 425 1 10 bbls of ilonr, at 12,00 per bbl. 120,00; Due in 30 days - - - 255,00| ~17th. [ have drawn a bill on John Foo.t, payjible| at sight, ibr - « . - i 425 125 00 00 00 John Foot has paid the bill I drew on him 12c .»l| Sold for cash 15 pieces of India chintz, at 5,00 per piece _ - . -18ih- Sold for cash 30 pieces of bandannoes, af 7,00 per piece . - - -20ili- Bartered with Joseph Mann, 5 pieces of Russia sheeting, at 20,00 per piece . - . 100,00 3 do. moreens, at 10,00 - - 30,00 75' CO 210 00 130 00 Ee 2 54 Boston, May 20th, 1819. tor — 1 hogshead of sugar, 71 cvvt. at 8,00 per cwt. - . - - 60,00 200 lbs of coffee, at 0,25 per lb. - 50,00 20 pair of shoes, at 0,75 per pair - 15,00 -21st- Received of John Foot in full for flour 22d Shipped for Sumatra, in the ship Britain Gapt. Colby, consigned to him for sales and returns, 5 pipes of brandy, at 120,00 per pipe . * - > 26th- Paid premium for insurance on 600 dollars on voyage to Sumatra, premium at 12| per cent. - - - -27tli- (Paid James Morgan in full D. C. 125 125 00 00 600 -2Sth- Paid William Gordon 30th- 'iil'l for house expenses End of the Waste-Book. 75 40 255 00 00 00 00 50 A JOURNAL & LEDGER BY SINGLE ENTRY. 56 It having been sufi^g^estcd that an elucidation of the most approved mode of Book-Keenin2f by Singlr Entry wouhl he useful, the first fVaste Book is here journalized^ and posted into Ledger^ upon that system. The utmost simplicity and plainess areused_^in this, as in the former set of books. A Cash'f3o()k^ separately, may be used, or some pages in the Ledger may be appropriated for that purpose. In real business, som;? or all the other auxiliary hooks will be needed. Their use has been already explained. When an account is Debtor, the n ord '^ Dr." in the Jour- nal entry follows^ when it is Creditor, '•' Cr." goes before, the name of the account. This is an additional guard against posting on the wrong side. Sometimes a single transaction, or Waste Book entry, will require two Journal entries : for instance. Stock and Cash transactions, which accounts, if the hooks are properly kept ;md adjusted, must necessarily partake of the Double-Entry nature. This Ledger being paged like that of the Double- Entrij one, the same alphabet answers for both. Let the Waste>&ook be carefully examined before jour- nalising, and the Journal compared with the Waste-Book before posting into the Ledger ; and again, the Ledger com- pared with the Journal after posting. It may he well here to observe, that charges should be made as soon as possible, and in a plain and full manner. Also, that receij)ts should be taken for all payments on ac- count ; and a person making a payment on a note should sec the same properly endorsed. JOURNAL. (Single Entry.) 57 Boston^ January \st^ 1819. I ^- C. Cr. Stock, By Sundries, per Inventory in Waste Stock Dr. — iTo buntlries, per ditto, ditto. I ct 1 Cash Dr. To Stock, per ditto, ditto. Note. This is to be posted into the Cash-Book or the Cash Acct. m the Ledger ; and it partakes of the Double-Entry nature. 1918 CO 1000 Cr. Cash, By Cheese, \ ton Ciieshire 3d. Cr. Cash, By Cider, paid in part for 4 hhds. Cr. Richard Payton, By Balance Cider, due 1 mo. jtii. Cr. Samuel Taylor, By 2 hhds. Tobacco, 3 nios. ■7th.. Cash Dr. To 4 ba;-; \\o\)<. sold J. Willinnfis 10th. 35 GO 00 00 63 Casli Dr. To rcc'd of S. Taylor in part, 2 pipos Wine' 50 20 00 38 JOURNAL. (Single Entry.) Boston J Jamianj lOthj 1810. Samuel Taylor Dr. To Balance, ditto, ditto, demand - 1 5tlu-^ John Jones Dr. To 1 piece Broadcloth, 1 month [9th Note. The barter of cider for cheese, in Single Bart. Entry Book-Kceping, need not be Journalised, but Mem. Poitcd immediately into a Barter Book, or memoran- dum. .22d- Andrew Tliompson Dr. Vo Cash lent, demand Cr. Cash, By lent Andrew Thomnson, as ahove , ^>6'th Cr. Thomas Richards, By BiH drawn at si2;ht ._! J^ S th Bill Note. As Thomas Richards has before been Book ^^^^ ^''^' ^^^i^ amount post this pajinent into Bili Book or Memorandum. .^'.'tb. J* hn Forrest Dr. Fo Bill drawn at sight Fob. 5th-.- Bill Note. This entry need not be journalised ; post Book Idirectly into Bill Book or Memoraiidum, JOURNAL. (Single Entry.) dd 1 H.Ex Boston^ February Sth^ 1819. Cash Dr. f^^* nature of Double E7itnj\ To James Morgan, borrowed Cr. James Morgan, By Cash, borrowed Otb D. 40 C. 00 Cr. Cash, By Interest, paid J. Forrest 10th Cr. Cash, By given A. B's Servants - - - Note. Post this also into House Expense Book. 1 1 th \0 00 Ch. Mer Cash Dr. To won at Billiards 1 Sth. Cr. Cash, By Household Expenses, last month Note. This may be supposed to be taken from House-Expense Book. >th. Cr. Cash, By, paid Book keeper 1 quarter Note. Post this also into Charges-on-Merchan- dize Book. ,.-16th. 75 80 15 371 67 5(' 75 Wm. Cowley, N. York, Dr. for sale, 2 cwt Cheese - . . - - 7^>» 60 JOURNAL. (Single Entry.) Boston^ February 1 6/A, 1819. Cr. Cash, By paid freight, he. on the above -liJOth- William Cowley Dr. To amount Cheese sold - - 21,07| Deduct former debit - B,75i '-^ charges .- 2,75 11,501 23d Cr. William Cowley, By 1 chest Sugar . > - - Cr. Cash, By paid Freight and Custom on ditto 25th- Cash Dr. To Leiracy left by uncle __-! ! 27th-. Cr. Cash, By paid Poor Note. When you post into Ledger, if it is a Cr. entry, put into the marsrin of the Journal *he p-^.i e of the account in the Ledger, -wi'}; a snail ii' e over ii ; if it is a Dr entry, put the small line under it. End of the Journal. THE LEDGER. ^^ In the following Ledger the entriejs are posted verv ' concisely. In real transactions they may be as full as the room, convenience and particular business of the person may allow and require. F F G2 LEDGER. (Single Entry.) b 1819 Dr. Stock D. ./«n. 1 To Sundries, per Journal 60 Dr. Cash Jan. 1 7 10 28 Feb. 8 11 25 To Stock on hand To Hops - - - - To Wine - - - - To Bill, T. Richards To James Morgan - - - To Billiards .... To Legacy .... 1000 63 50 20 40 7 20 120! [Page 3] Dr. Thomas Richards /an. 1 To Stock, on demand 45 c. 00 0§ 00 75 00 90 37J 00 "^ 124 7g 11 [Page 3] Jan. 26 Feb. 27 LEDGER. (Single Entry) Contra Cr. &o Contra Cr. By Cheese .... By Cider, part By A. Thorn psoii By Bill, J. Forrest By Interest .... By Expenses . . . . By ditto .... By Charges, merchandise By Freight and Custom By ditto, Sugar By Poor By Balance on hand, for new acct. Contra Cr, By Bill, on sight By Balance, remains due me for new acct . . . D. 1948 32 25 20 40 15 50 2 1009 1201 20 25 45 'U 1819 Jan. 29 Feb. 27 Jan. 10 kf AGC 4] Feb. 27 Ta/i. 15 LEDGER. (Single Entry.) Dr. John Forrest To Bill, at sight To Balance, due him for new acct. [3 D. 40 10 50 OQ 00 00 ^Dr. Samuel Taylor To Wine^ on demand 109 91 Dr. Richard Pay ton To Balance., due him for new acct. 17 60 Dr. John Jones To Broadcloth, I mo. 97 15 3] 1819 Jan. 1 LEDGER. (Single Entry.) Contra Ci\ By Stock, secured by bond Jan. 1 5 Feb. 27 [Page 4] Jan. 3 (Page 5] Feb. 27 Contra Cr. By Stock, due him By Tobacco, 2 hhds. By Balance, due me for new acct. Contra Cr. By Cider, 1 mo. Contra Cr. By Balance, due me for new acct. Ff2 D. 60 50 10 GO 79 20 20 71 109 91 17 97 65 C. 00 00 5d 15 ►6 LEDGER. (Single Entry.) CJ 1819 Dr. Andrew Thompson D. c. Jan. 22 To Cashv lent 20 00 [Page 7] Dr. James Morgan Feb. 27 To Balance, due him for new acct. 40 00 • [Page 8] Dr. William Cowley Feb. 16 50 To Cheese, /or 5a/c To ditto, balance 8 ■ 9 751 571 f 18 33 S] 1819 Feb. 27 [Page 7] Feb. 8 [Page 8] Feb, 23 27 [Page 9] LEDGER. (Single Entry.) Contra Cr. By Balance, due me for new acct. 67 Contra Cr. By Cash, borrowed Contra Cr. By Sug-ar .... By Balance, due me for new acct. Balance acct. same as in Double Eedger, Both should be dated Feb. 27, 1819. D. 20 C. OQ 40 00 15 18 33 JAMES R. BUFFUM (Proprietor of Walsh's Mercantile Arithmeti«) i Keeps constantly for sale^ at his NAVIGATION AND COMMERCIAL BOOK:STORE, CEJSTTRAL BUILDLVG, ESSEX STREET, SALE^jj., A GENERAL ASSORTMENT OF CKikXtTSy ^or the navigation of every sea, parti- •ularly Lambkrt's late and improved Charts oi the American Coast, viz. Massaciiusetts Bay, on a scale of 12 inches to a degree ; Nantucket Shoals and George's Banks, 7 inches to a degree ; Coa«t of Connecticj^t, 4^c. extending from Mon- tock Point to Chincoteague Shoals, on the same scale ; the Coast from Nova-Scotia to the Chesapeake ; Chesapeake Bay; North and South Carolina? the Missisippi River; and the Bahama Banks, Islands, &;c. Also^ QXTADRAJNTTSp Telescopes, cases of Mathematical Instruments, Gunter's Scales, Protractors, steel-jointed and oommon Dividers, Parallel Rules, Thermometers, &,c. BO^CI7DITCK'S Practical Navigator, teaman's Daily Assistant, Searjien's Journals, Nautical Almanacks, Cargo Books, Shipmaster's Assistant, Abbot on Shipping. BLXriffT'S American Coast Pilot; the. Oriental Nav- igator, or Sailing Directions to and from thfe Eaet-lndies ; Sailing Directions for the Coast of Africa, North Sea, Baltic, West-Indies, and Ohio and Missisippi ; Treatise on the Navigation of St. Domingo, with sailing directions for the coasts, bays and harbours thereof. COMMISRCXAK DICTX09JA11Y, »i* tionary ot Merchandise, L reatise on the law relative to Principals, Agents, Factors, Auctioneers and Brokers, Oliver's Practical Convejancino;, Marshal on Insurance, Annerican Trader^s Compendium, Brice's Revenue Laws, Jackson's Commerce of the Mediterranean, Beaujour's Commerce of Greece, System of Exchange with all parts of the world, India Directory for purchasing Drugs and Spices, Merchant and Shipmaster's Ready Calculator, Cieavland's Exchange Tahles. TaARlTSBTL'S DICTIOSffAHY, Malham'e Naval Gazetteer, Worcester's Gazetteer, Brookes's do. Morse's, Oummings's, Adams's, Dwight's, Parish's, Pinker- ton's, Mann's, Goldsmith's, and other Geographies. Art of Mast-Making, with a book of plates, Art of Sail-making, Ship-builder's Assistant, Pakenham's Substitute Tor a Lost Rudder. SOOK-KEEFIMa. Merchant's System, inv proved upon Turner; Turner's and Shey's System; Perry's Man of Business. A SKTJS'^DSr SirST£2M[ of Mercantile Arithmetic, adapted to the Commerce of the United States^ in its Domes- tic and Foreign Relations; with Forms of Accounts, and oth- er VVritmgs usually occurring in trade. By Michael Walsh, A. M. This work is strongly recommended by the first Merchants in the Siaie^ " as better calculated than any yet published to fit youth for the Compting-house, and from the useful commercial information it contains, extremely well adapted to assist the merchant, the mariner and the trader, in their various occu[)ations." To which is annexed, a Sys- tem of Book-Keeping. Also^ Temple's, Adams's, VVelsh'Sj Daboll's, and other Arithmetics. Histories, Voyages, Travels^ Novels, and a great variety of Books of instruction and amusement, loaned on resonable terms. S!1B£!^S, I'lrge and small, Testaments, Psalm aB^ Hymn liooks, and all kinds of School Books. STATIONARY, &C. ^^riting-, Wrapping-, Cart- ridge, L«'g-iiook, iilu( , Mari ie, Wove, Hot Pressed, Gilt, Letter, Drawing and Ruled PAFLR, of every size and qual- ity, European and American. Qnilis, Ink, Inkpowder, Wa- fers, sealing Wax, Elastic Gum, Black Sand, Sponge, India Ink, Paint Boxes, Durable Ink tor marking linen with a pen ; Inkstands for tlie compting house, schools, portable writing desks, and the pocket, band Boxes, Penknives, Gutteaux, Pencils, Pencil Gases, Shaving Soap, Slates and Pencils, Purses, Folding Knives, Pocket Rules, Stationers' Tape, Scissors, Tooth, Head, and Glothes Brushes, Gourt Plaister, 4^c. Merchants' Account Books, and Blank Books •f various kinds, Giphermg and Writing Books, Ladies' and Gentlemen's Pocket Books, Memorandum Books, &c. Blanks. — Commercial, Nautical, Notarial, Jus- ticiary, Military, &z.c he. kc. Printed Note Books. Music^ Musical Instruments, Music Paper, and a g^eneral Stock for a Book and Stationary Store. ALL KINDS OF H^o^ $t S^%^ priif ting HANDSOMELY EXECUTED BY Jfohn D. Oushingj f>NE DOOR WEST OF SALEM HOTEL, ESSEX STREET, SALEM, ORDERS LEFT AT THE BOOK-STORE OF JAMES R. BUFFUM, WUX BE IMMEDIATELY ATTENDED TO, \y 1 A new syistem of mer- cunt lie ar ithmetio B2^ t, ■^'' 17283911 ^/^ lot THE UNIVERSITY OF CAUFORNIA UBRARY -1^ ^■■m.. r^