IN MEMORIAM FLOR1AN CAJORI STANiFORD'S PRACTICAL ARITHMETIC, IN WHICH THE RULES ARE RENDERED SIMPLE IN THE OPERATION, AND ILLUSTRATED BY A VARIETY OF USEFUL QUESTIONS, CALCULATED TO GIVE THE PUPIL A FULL KNOWLEDGE OF FIGURES, IN THEIR APPLICATION TO TRADE AND BUSINESS ; ADAPTED PRINCIPALLY TO DESIGNED AS AN ASSISTANT TO THE PRECEPTOR IN COMMUXt CATING, AND TO THE PUPIL IN ACQUIRING THE SCIENCE OF ARITHMETIC ; TO WHICH IS ADDED, V NEW AND CONCISE SYSTEM OF BOOK-KEEPING, BOTH BY SINGLE AND DOUBLE ENTRY ; v THE FORMER CALCULATED FOR THE USE OF TRADERS IN RETAIL. BUSINE5S l FARMERS AND MECHANICS ; 4^ AND THE LATTER '* FOR WHOLESALE DOMESTIC AND FOREIGN TRADE,*AS CON- DUCTED IN THE UNITED STATES. BY DANIEL STAMFORD, A* M. Author of the Art of Reading Jnd the Elements of English Grammar. =, ^ Tantum scimus, quantum memoria tenemus. BOSTON: PRINTED BY J. H. A. FROST, FOR WEST, RICHARDSON & LORD, No. 75, CornhilJ, 1818. DISTRICT OF MASSACHUSETTSTO WIT : BE it remembered, that on the seventeenth day of November, in tht year of our Lord one thousand eight hundred and eighteen, and in the forty-second year of the Independence of the United States of America, DANIEL STANIFORD, of the said district, has deposited in this office, the title of a book, the right whereof he claims as author, in the words following, to wit : u Staniford's Practical Arithmetic, in 44 which the rules are rendered simple in the operation, and illustrat- 44 ed by a variety of useful questions, calculated to give the pupil a i4 full knowledge of figures, in their application to trade and business ; 44 adapted principally to Federal Currency ; designed as an Assistant 44 to the Preceptor in communicating, and to the pupil in acquiring 44 the science of Arithmetic ; to which is added, a new and concise 41 system of Book-Keeping, both by single and double entry ; the 44 former calculated for the use of Traders in retail business, Farm- 44 ers and Mechanics ; and the latter for wholesale, domestic and * 4 foreign trade, as conducted in the United States. The whole de- 44 signed for the use of Schools and Academies, By DANIEL, STANI- 44 FORD, A. M. Author of the Art of Reading, and Elements of Eng- * 4 lish Grammar." 44 Tantum scimus quantum, memoria tenemus.'^ In conformity to an act of the Congress of the United States, en- titled, 4t An act for the encouragement of learning, by securing the copies of Maps, Charts/and Books, to the authors and proprietors of such copies, during the times therein mentioned ;" and also to an act, entitled, u An act, supplementary to an act, entitled an act, for the encouragement of learning, by securing the Copies of Maps, Charts, and Books, to the authors and proprietors of such Copies, during the times therein mentioned ; and extending the benefits thereof to the arts of designing, engraving, and etching historical and other prints." J. W. DAVIS, Clerk of the District of Massachusetts. A true copy Attest, J. VV. DAVIS, Clerk. PREFACE. TO the question commonly asked, on the appearance of a new book, " Is there any thing new in it ?" the author replies, that al- though the subject of arithmetic can admit but little novelty, yet in this treatise there is something new, which may be easily discovered by an examination of its contents. rhe_^eneral_rules_ in jnoti)JLljie_Arithmetics used in our schools are too synthetical for the y_pung^Arithmelician. They contain too many principles blended together, unaccompanied with sufficient elucidations. The scholar therefore is in danger of passing over many essential parts, without fully comprehending them. One design therefore of this treatise is to give an Analysis of these general rules, resolving them into their simple constituent parts, illustrating them by easy practical questions. As the work, also, is principally designed to furnish a system of practical Arithmetic, adapted to the currency of the United States, all mathematical demonstrations ate-piirposely omitted v to give place " to clear illustrations of the rules by easy examples, and such as tend j to prepare the scholar for business ; referring those, who wish to ac- quire a knowledge of the higher branches of the Mathematics in those elaborate, though useful parts of the science, to authors par- i ticularly designed for the purpose. This omission will leave for the ; instructor enough for the exercise of his skill in explaining the nature of each rule to the pupil, as he advances in his pursuit, and becomes capable of comprehending those abstruse parts of the science. The instructor is left, also, to supply at his discretion various additional questions for exercise in the application of the several rules. This will prevent the fatal practice, too much indulged among scholars, of copying from each other's manuscripts. The same question should never be proposed by the instructor a second time. Although the currency of the United States is generally adopted through the work, yet, as the accounts and invoices of goods of American and English merchants trading together are kept in Sterling money, so much only of that money is applied as was thought neces- sary to give the scholar a competent knowledge to transact that part of commercial business. The whole arrangement of the work is founded on the natural de- pendence of the several parts on each other for their respective ope- rations. A few remarks are offered in support of the present ar- rangement, iv PREFACE. 1. REDUCTION. As by this rule compound addition, multiplication and division are performed, its place naturally precedes them. In reducing time 365 days is commonly called a year, omitting the fractional parts. 2. VULGAR FRACTIONS. These, having their origin from simple division, seem to require a place immediately subsequent to that rule ; yet as their operation depends on other rules, a place is assigned them, following those on which they are dependent, and preceding others which depend on them for an accurate solution. Vulgar Frac- tions being indispensably necessary for the solution of many impor- tant questions in common arithmetic as well as in the higher branches of Mathematics, they have received particular attention in this treatise. 3. DECIMAL FRACTIONS. These being similar in their operation with whole numbers, seem to claim a place. jn.jclojE connexion with themj yet as the changing of them from one form into another is performed by other rules, their order should succeed them. 4. CIRCULATING DECIMALS. These are subjoined for the benefit of those who would wish to have a comprehensive view of the whole nature and doctrine of Decimals ; particularly for^ those who wish to extend their mathematical enquiries. The finite decimals are con- tained in the first cases, and are all that is necessary for common bu- siness ; the circulates may, therefore., be omitted as circumstances may justify. 5. FEDERAL MONET. Some, perhaps, may have thought it more prop er to arrange this currency immediately following the simple rules of Arithmetic, because of their simplicity; yet as Federal jMQJftgyJs fouttdedon, the nature and principles of Decimals, and per- formed by the same rules in its operation, its natural order is cer- tainly subsequent to decimals. Particular attention has been given to it in connexion with decimals, as the foundation and only guide for the American Accountant. 6. The operations of Practice, Tare and Tret, with Duodecimals, being dependent on Compound Multiplication and Division, are placed after them. 7. RULE or THREE. The importance and extensive utility of this rule in the ordinary concerns of life, has given it the distinguishing title of " The golden Rule." As most of the subsequent rules in Arithmetic are performed by the Rule of Three, great care has been, taken to render it intelligible by a minute investigation of its nature, with an analysis of the general rule in simplifying it in all its varieties. 8. Position, Allegation and Permutation are inseited at the close t>f the Practical Arithmetic, more for the purpose of gratifying curi- osity, than for their utility in business. PREFACE. v In executing the work nothing superfluous has been added, and nothing omitted that would contribute to perfect its design, and ren- der it serviceable to youth. Those, however, who are in the habit of teaching superficially, with a view of flattering the pupil and the parent with the mistaken idea of extraordinary progress, may proba- bly raise objections against the work, as_c^ntainingjtQfi.jnany. things _ to be_committed to memory. They will burden, fatigue and confuse the mind of the scholar! Such persons have yet to learn both the susceptibility and capacity of the young mind, and that although a single complex idea in its undigested form, crowded into the mind of a child, may confuse and embarrass it ; yet, in direct proportion to the number of simple ones, impressed, will it become more invigo- rated, more enlightened, more improved. Similar objections would as readily be started against an abridgement of the smallest size, by those only who have neither the ability nor inclination to lay the whole nature of the subject open to the understanding, and lead the pupil, gradually, into that train of logical reasoning, peculiar to the mathematics. I 9. BOOK-KEEPING. This useful branch of learning has been almost i L totally neglected in our schools and academies. The neglect of a / study so essential to the best literary interest of youth proves a nia-^j/ terlal defect in the present system of education. It may, perhaps, be attributable, in a great degree, to the want of a concise treatise on the subject, divested of those numerous difficulties which envelope in mystery even the best system extant. So intricate and tedious are they, for the most part, that even instructors themselves have been deterred from giving instruction by them. The short system in this publication has been used by the author with considerable success. It is now offered as an attempt to simplify the Art of Book-keeping, and to adapt it to the capacity of youth. Jt furnishes such rules and explanatory remarks in discriminating the titles of Dr. and Cr. in journalizing and posting the several mercan- tile transactions, as were thought best calculated to render easy and clear a subject of so much importance. Of such immense benefit is this part of science to a young man of any respectable standing in society, that no scholar should be per- mitted to leave school, to become an apprentice either to a merchant, a mechanic, or even to a farmer, without a thorough knowledge of the principles and forms of Book-keeping ; as on his knowledge of 1/1 jhis_at essentially depends the security of all the fruits pOiis iTUJus__ jf I try through life. Many mechanics and farmers have lost half their ^/ earnings by neglecting to make a regular entry of their daily trans- actions peculiar to their employment ; and even wealthy merchant? vi PREFACE. have become the melancholy objects of penury and distress through the same neglect. The best interest of youth would be essentially promoted, were this important branch of science introduced into our schools, and to constitute a prominent part of their education. The work, with its trifling errors, is now presented to the public in full confidence that it will meet the acceptance it deserves. It claims no preference to the numerous publications on this subject. The author asks that patronage only, to which it is entitled by its real merits. And if, kind reader, you can find a better treatise, freely adopt it ; u At si non rectius invenire potes, hoc utere mecum ;'* And in either case it will be perfectly satisfactory to THE AUTHOR. Roston, September 30, 1818, The following typographical errors have escaped timely attention, which the reader is respectfully requested to correct on the margin of the page referred to in th* table of ERRATA. Page 16 Exam. 7, multiplicand, for 84 read 48. 20 Exam. 9, dividend, for 467 read 464. 26 Dry measure, for 4 gals, read 2 gals. 29 Question 18, insert 2 yds. 30 Exam. 30, after 37-^-, insert 1S=. 33 Question 13, insert cwt. after 9 1-2, also, Ib. after 31920. 33 15, Ans. for drs. read oz. 40 Exam. 11, Long measure, subtrahend, for 2 yds. read 4 yds. 43 Exam. 12, Time, in Ans. for 3 weeks read 0. G3 Note first, for numerator read denominator, and for denom. read numerator, 64 Question 6, for divided read multiplied. 67 Case II, line 4, for left read right. 67 Exam. 4, dele the second 2. 80 Exam. 12, in quotient, for 75 read 25. 109 Exam. 26, for 14<. read 4d. 114 Question 5, in Ans. for 6,6 2-3 read 85,5 5-9. 117 Exam. 13, Ans. for 59 urals. read 62 gals. 156 Line 7th from top, for 00 read 700. 172 Line 9th from bottom, dele in dividend. 181 and 182, for proportion read proposition. 256 Personal accounts, first line, for Dr. read Cr. also in lecond line, for Cr, read DJ , 290 Dr. Sugar, for 589 read 549, 4 Preface, remark S, for timpHcity read tlmilarity. ~* 40 Exam. 10, for tcru. grt. read dn, tcru. 48 Exam. 4, Ans. for 1-2 read 1-4. 58 Case IX. for denominator read numerator, 78 -Exam. 2, dele in dividend, also 7 in quotient. 96 Second method, top line, in dollars insert 8. 167 Exchange, France, for 4 6rf. sterl. exchange at par. read 2 6d, sterliim- 193 ABS. 4, decimal, dele second 3. RECOMMENDATIONS. Boston, October Qth, 1818. AT the Annual Meeting of the u ASSOCIATED INSTRUCTERS OF YOUTH IN THE TOWN OF BOSTON AND ELSEWHERE," the following Report of a Committee was made and accepted, viz : u The Committee appointed by the Association to examine a Treatise, entitled, ' Practical Arithmetic, and a short System of Book-keeping,' by DANIEL STANIFORD, A. M. have attended to that service, and after a careful examination, are of opinion, that it is a work, better calculated to facilitate the progress of youth, in these useful and important sciences, than any treatise of the kind, of which we have any knowledge. Signed, JONA. SNELLING, ) J. R. COTTING, > Committee. BENJAMIN HOLT, $ A true copy from the records and files of the Association. Attest, THOS. PAYSON, Sec. A. I. Y. THE undersigned having attentively examined a treatise on u Book- keeping, 11 By Daniel Staniford, A. M. are of opinion that it is better calculated to give pupils a knowledge of the rudiments of this impor- tant science, then any one of the kind we have hitherto seen. The introduction contains a large number of valuable rules for journalizing and posting, which are too often omitted in treatises of this kind ; and the several accounts in the Waste-book are so judi- ciously arranged as examples to each rule, that they may be readily comprehended by the learner. We sincerely hope that it will have a general circulation in our schools and academies, J. COTTING, EDWARD JEWETT. Explanation of the Characters used in the following Work. = Equal. The sign of equality ; as 4 qrs. =1 cwt. -{- Plus, or more. The sign of Addition ; as 8-f-4=12. Minus, or less. The sign of Subtraction ; as 6 4=2. X Multiplied by. The sign of Multiplication ; 4X3=12. Letters joined like a word express the continual multiplicatio* of them as, apr=aXpX r - -r- Divided by. The sign of Division ; as, 12-f-4=3. Division is likewise expressed by numbers placed in the form of a fraction ; as 2 _ 7 =9. Letters also placed in the form of a frac- tion signify that the upper letters are to be divided by the lower. : : : : The sign of Proportion ; as 4 : 8 : : 12 : 24, that is, as 4 is to 8, so is 12 to 24. ") 2 , or 32 , Signifies the second power, o* square. H 3, or 4 3 , Signifies the third power, or cube. ^/ Signifies the square root. %*/ Signifies the cube root. JVote. The number belonging to the above ligas of powers, and roots, is called the index or exponent. A line or vinculum, drawn over several numbers, signifies, that the numbers under it are to be considered jointly ; as 8 3-j-4=l ; but without the line, 8 3-{-4=9. CONTENTS. Page Numeration, 10 Simple Addition, .... 12 Subtraction, , 13 Multiplication, 14 Division, 17 ables of coins, weights and measures, 22 Reduction, 26 Compound Addition, 36 Subtraction, 39 Multiplication, 41 Division, 46 -"Vulgar Fractions, . 51 Decimals, finite and circulating, 64 Federal Money, 87 Practice, . . , 104 Tare and Tret, 109 Duodecimals, or Cross Multiplication, 113 Single Rule of Three, 121 Double Rule of Three, 131 Fellowship Single, 133 Double, 135 Simple Interest in Federal Money, 136 Sterling Money, 145 Commission, 147 Buying and Selling Stocks, 147 Ensurance, 148 Compound Interest, 150 Discount, . 152 Bank Discount, 153 Equation of Payments, 154 Barter, 154 Loss and Gain, 157 Exchange, 159 Conjoined Proportion, 172 Arbitration of Exchanges, 173 Ivolution, 174 Evolution, 175 Square Root, 176 Cube Root, 178 Biquadrate Root, 179 Arithmetical Progression, 181 Geometrical Progression, . . . 183 Permutation, . . . 189 Simple Interest by decimals, 191 Compound Interest by decimals, 194 Book-Keeping by Single Entry, 198 Double Entry, 236 Appendix, 318 Mercantile Forms, 320 PRACTICAL ARITHMETIC. ARITHMETIC is the art of computing by numbers. Number is that which answers directly to the question, " How many ?" and is either an unit, a multitude of units, part or parts of an unit, or a mixt expression. The whole art of Arithmetic is comprehended in the Tarious operations of the five following rules, viz. 1. Numeration, or Notation. 2. Addition. 3. Subtraction. 4. Multiplication. 5. Division. Practical Arithmetic is the application of the preceding fundamental rules, so as to be most useful in business. NUMERATION. NUMERATION teaches to read, or write, any number. All numbers are expressed by ten characters, called fig- ures, or digits, viz. 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. The nine first are called significant figures 5 the last, a cipher, or nought. The cipher is of no value when it stands alone, or at the left hand of a whole number ; .but, when annexed to any significant figure, it increases its value ten-fold. NUMERATION. The simple value of any figure may be known by inspec- tion, and the following table plainly shows the local value of any figure from the place of units towards the left hand, as far as may answer every purpose of calculation. NUMERATION TABLE CO &* i-< 9 8 7 . 6 5 4 . 3 2 1 9 . . 8 . . 7 . . o 6 . 5 . 4 . 3 2 1 RULE. There are three periods ; the first on the right hand, Units; the second Thousands; and the third Mil- lions, each of which consists of three places or figures. Reckon the third figure of each period, from ihe left hand, so many Hundreds, the next Tens, and the other, so many Units, of what is written over them; as the first period on the left hand, read thus, Nine hundred eighty-seven mil- lions } the second period, Six hundred fifty-four thousands; and the other period, Three hundred and twenty one units. It is obvious, that numbers increase in a ten-fold propor- tion from the right hand towards the left: that is, any NUMERATION. ^ figure, in the place of teas, is ten times the value of the same figure in the place of units ; and any figure in the place of hundreds, is ten times the value of the same figure io the place of tens, &c. CASE I. To read any number. RULE. Find out the place of each figure by the Table, and to the simple value of each figure join the name of its place, beginning at the left hand, and reading towards the right. EXAMPLES. Read the following numbers. 21 321 4321 54321 654321 7B54321 87654321 . 987654321 CASE II. To write, any number in figures. RULE. AVrite down ciphers to as many periods, qr places, as are named in the given number ; then, beginning at the left hand, observe, at each place, what significant figure is named, and, taking away the cipher, write tlie significant figure in its place. EXAMPLES. Write in figures the following : Five hundred and twenty-four. Nine thousand, seven hundred and ten. One hundred millions, one hundred thousand, and ten. One hundred millions and one. SIMPLE ADDITION. II.* . . . . Two. III. . . . . Three. iv.t . . . . Four. V. ... . Five. VI* . . . . Six. VII. . . . . Seven. VIII. . . . . Eight. IX. ... x Ten. XL Eleven, JVtymeration by Roman Letters. XXX Thirty. XL Forty. L Fifty. LX Sixty. LXX. . . . Seventy. LXXX. . . . Eighty. XC Ninety. C, . Hundred. XII Twelve. XIII. . . . Thirteen. XIV Fourteen. XV Fifteen. XVI Sixteen. XVII. . . . Seventeen. XVIIL . . . Eighteen. XIX. . . . Nineteen. XX Twenty. CC. . ccc. cccc. . D. . . . DC. . DCC. . DCCC. DCCCC. M MDCCCXVIII. Eighteen hundred eighteen. Two Hundred. Three Hundred. Four Hundred. Five Hundred. Six Hundred. Seven Hundred. Eight Hundred. Nine Hundred. . . Thousand. and SIMPLE ADDITION. ADDITION is the collecting of several numbers of the same denomination into one sum. RULE. Place the numbers under each other according to the value of their places, by putting units under units, tens Under tens, &c. ; then, beginning at the right hand column, add the figures in it, and set down the units, and carry the tens to the next left hand column, continuing so to do to the last column, under which set down its whole amount. The total amount in addition is called the sum. PROOF. Add the figures downwards in the same manner as they were added upwards, and the sum will be the same. * As often as any character is repeated, so many times its value is repeated. t A less character before a greater diminishes its value, i A less character after a greater increases its value. SIMPLE SUBTRACTION. 13 EXAMPLES. 4874835 8433487 7367485 4783438 4363567 4365687 8934874 8749863 25540761 26332475 SIMPLE SUBTRACTION. SUBTRACTION leaches to find the difference between two numbers of the same denomination. It has three parts, viz. 1. The greater number, or the minuend. 2. The less number, or the subtrahend. 3. The difference, or remainder. RULE. 1. Place the less number under the greater, ac- cording to their value, as in addition. 2. Beginning at the right hand, subtract each under figure, from that which stands above it, setting the remainder un- der them, and the several remainders together will express the difference required. 3. If the under figure is greater than that above it, ber- row ten and add it to the upper figure, from which sum take the under figure, setting down the remainder as be- fore; remembering, that every time ten is borrowed, to earry one to the next under figure, before it is subtracted. PROOF. Add the difference to the less number, and their sam will be equal to the greater. _ EXAMPLES. 8734874 Minuend. 83010014 834874 4837841 Subtrahend. 378749 18700 * 3897033 Difference. 82631265 816174 8734874 Proof. QUESTIONS. 1. If I lend my friend $9480 and receive in part pay- ment 81987; how much remains due ? Ans- S7493. 2. The revolutionary war in America commenced with Great Britain, in the year 1775, (April 19); how many years since, the present year being 1818 ? Ans. 43 yearsr. 8* 14, SIMPLE MULTIPLICATION. 3. Peace between the United States and Great Britain took place in 1733, and war again declared in 1812; how long did the peace continue ? ^ Ans. 29 years. SIMPLE MULTIPLICATION. SIMPLE MULTIPLICATION is a short method of performing many additions. It has three parts, v'iz. 1. The Multiplicand, or sum multiplied. 2. The Multiplier, or sum multiplied by. 3. The Product, or number found by the operation. NOTE. The Multiplicand and Multiplier are called the factors. MULTIPLICATION J1ND DIVISION TABLE. 2 Times 2|are 4 4 Times 4 are 16 7 Times 7 are 49 3 6 5 20 8 56 4 8 6 24 9 63 5 10 7 20 10 70 6 12 1- 8 32 11 77 1 14 9 36 12| 84 8 16; 10 40 8 Times ~8;aTe* 64 9 18 ; 11 44 9 72 10 20 1 12 48 10 80 11 22 5 Times 5 are 25 11 88 12 24 6 30 12 96 3 Times 3 are 9 7 8 35 40 9 Times 9 10 are 81 90 f 4 12 9 J45 11 99 5 15 10 50 12 108 6 18 11 55 7 21 12 60 lOTimes 10 are 100 8 24 6 Times 6 are 36 11 110 9 27 7 42 12 120 10 30 3 Aft 11 33 9 rO 54 1 1 Times 11 are 121 1* 36 10 60 12 132 11 66 _ | 12 72 12 Times 12 are 144 NOTE. The pupil should be instructed to change the multiplier in the preceding table. Example 6 tiies 8, or 8 times 6, are 48, and so for the rest. SIMPLE MULTIPLICATION. 15 GENERAL RULE. 1. Place the multiplier under the multiplicand according to the value of the figures, as in addition. 2. Beginning at the right hand, multiply each figure in the multiplicand by each in the multiplier, placing the first figure of every line directly under its respective multiplier, and to the product of the next figure carry one for every ten, as in addition. 3. Add the several products together, and their sum will be the total product required. PROOF. Make the multiplicand the multiplier and the multiplier the multiplicand, and proceed as before in the operation, if the product is like the former the work is right. CASE I. When the multiplier is not more than 12. RULE. Multiply the given number by the whole multi- plier. 1. 87487487 8 699899896 3. 7009748 11 77107228 EXAMPLES. Multiplicand. Multiplier. Product. 4387936 9 39491424 521984952 CASE II. AVhen the multiplier is more than 12, and such as two or more numbers in the table, when multiplied together, will make it. RULE. Multiply the given number by one of these fig- ures, and the product by the other: the last product will be the answer. SIMPLE MULTIPLICATION. EXAMPLES. 5. 6. Multiply 389074 by 24. 3350746 by 48. 4X6=24. 4 6 6X8=4*. 1556296 50104476 6 8 9337776 400835808 CASE III. When the multiplier consists of several figures. RULE. Multiply each figure in the multiplicand as di- rected in the general rule. EXAMPLES. 7. 8. 847483567 749084 768 759 3899868536 6741756 2924901402 3745420 3412384969 5243588 374387379456 568554756 CASE IV. When there are ciphers either in the multiplicand or mul- tiplier, or in both. RULE. Omit the ciphers and multiply by the significant figures, as before directed 5 and to the product annex as many ciphers as are given in both the factors. EXAMPLES. 9. 10. 11. 87487487 8740084500 98736509 120 11 900 10498498440 96140929500 88862850000 SIMPLE DIVISION. ^ CASE V. When there are ciphers between the significant figures of the multiplier. RULE. Omit them in the operation, and multiply by the significant figures, placing the first figure of each product tinder its respective multiplier. EXAMPLES. 12. 13. 48748043 48748744 40007 9003 341236301 146246232 194992172 438738696 1950262S56301 438884942232 CASE VI. To multiply by 10, 100, 1000, &c. RULE. To the given number annex as many ciphers as there are iu the multiplier. EXAMPLES. Multiply 78 by 10, 100, and 1000. CTo multiply by parts, Product. 780 .... 7800 . . 78000. \ see Division Case VII. SIMPLE DIVISION. SIMPLE DIVISION shows how often one number is contain- ed in another, of the same denomination. It has four parts ; viz. 1. The Dividend, or sum divided. 2. The Divisor, or sum divided by. 3. The Quotient, or answer. 4. The Remainder, or what is left after division. The remainder is of the same name with tfie dividend and quotient, and must always be less than the divisor. g SIMPLE DIVISION. PROOF. Multiply the quotient by the divisor, add the remainder, if any, to the product, and the sum wiH he equal to the dividend. CASE I. When the divisor is not more than 12, it is called Short Division 5 then the quotient is placed under the dividend. RULE. 1. Find how often the divisor is contained in the first figure, or figures of the dividend, setting it under the dividend, and carrying the remainder, if any, to the next figure, as so many tens. 2. Find how often the divisor is contained in this divi- dend, and set it down as before, continuing so to do, till all the figures in the dividend are used. NOTE. The work in Short Division is done mentally, that is, divided in the mind, and the result only written down; whereas in Long Di- vision the operation is written at large. EXAMPLES. 1. 9. Divisor. 8)38748747 9)876874854 -Rem. Quotient. 4843593 3 97430539--.3 8 -* , Proof. 38748747 NOTE. When there is no remainder, the quotient is the perfect an- swer to the question ; but if there is a remainder, set it at the end of the quotient, above a small line with the divisor under it, which is part of another unit. Hence the origin of Vulgar Fractions, the remainder being the numerator, and the divisor the denominator, which will Ire particularly explained in their proper place. 3. 4. 11)7387487487 12)87487487 671589771-6 rem. 7290623-11 rem. CASE II. Long Division is when the divisor exceeds 12, then the quotient must be placed at the right hand of the dividend. RULE. 1. Having written the divisor at the left hand of the dividend, find how many times the divisor is contained SIMPLE DIVISION. 19 in the first figure of the dividend, or if not in the j?rs, how many times it is contained in the two first figures, and place the number at the right hand of the dividend for the quo- tient figure. 2. Multiply the divisor by the quotient figure, and place the product under the dividend. 3. Subtract this product from the dividend, and to the remainder bring down the next figure in the dividend, and write in the quotient the number of times the divisor is con- tained in this new dividend. 4. Multiply the divuor by the last quotient figure and proceed as before directed ; thus continue to do till all the figures in the dividend are brought down. If the remainder, after having bro flown a figure, is still less than the divisor, a cipher in : be carried to the quotient, and another figure brought dovni, and wrought as before directed. EXAMPLES. 5. 6. Divisor. Dividend. Quotient. 24)34748748(1447864^ 48)74848748(1 559348 j| 24 48 J07 288 96 240 .114 284 96 240 188 418 163 432 207 167 192 144 154 234 144 192 108 428 96 301 12 Remainder. 44 Remainder. NOTE. The fraction must always be reduced to its lowest terms before it i* annexed to the quotient, as in the two last Examples. SIMPLE DIVISION, CASE III. When the divisor is a composite number, that is, such an two or more figures in the table, when multiplied together,; will make it. RULE. Divide the dividend by one of these figures, and the quotient by the other ; the last quotient will be the an- swer. EXAMPLES. 7. 8. Divide 84874 by 48. Divide 487488 by 84. 6X8=48. 7X12=84. 6)84874 7)487488 8)14145-4 1st rem. 12) 69641-1 1st re. 1768-1 2d rem. 5803-5 2drem. NOTE. To find the true remainder, when there is a remainder to each of the quotients. RULE. Multiply the first divisor into the last remainder, to the product add the first remainder, the sum will be the true remainder. Thus in example 7. The first divisor 6x1 the last re- mainder is 6, to which add 4 the first remainder, the sum is 10 equal to the true remainder. CASE IV. When there are ciphers in the divisor. R\JLE. Cut them off, and as many places from the right liand of the dividend ; but they must be annexed to the remainder. EXAMPLES. 9. 10. 42,000)467567,000 11,00)435678,34 3871311000 Rem. 39607134 Rem. CASE V. To divide by 10, 100, 1000, &c. RULE. Cut off as many places from the right hand of the dividend, as there are ciphers in the divisor, the left Land figures will be the quotient, and the right hand figures cut off will be the remainder. SIMPLE DIVISION. 21 EXAMPLES. 11. Divide 787484 by 10. . . Answer, 78748 T % 12. ... 787104 by 100. . . Answer, 7874^ 13. ... 787484 by 1000. . Answer, 787 T Wo CASE VI. To divide by fractions, or parts of an unit. RULE. If the numerator, or upper figure, is an unit, multiply the given number by the denominator, or un- der figure, and the product will be the answer: but if the numerator is more than an unit, multiply the given num- her by the denominator, and divide the product by the nu- merator. EXAMPLES. 14. Divide 848 by j. 16. Divide 484 by i. 4=denominator. 2=deuomina. 3392 Answer. 968 Answer. 15. Divide 483 by f . 17. Divide 496 by f. 4=denominator. 8=denomina. > T umer. 3)1932 Numer. 3)3968 644 Answer. 1322f Answer. CASE VII. To multiply by fractions, or parts of an unit. RULE. If the numerator is an unit, divide the given number by the denominator, and the quotient will be the answer; but if the numerator exceeds an unit, multiply the given number by the numerator, and divide the product by the denominator, the quotient will be the answer. EXAMPLES. 18. Multiply 843 by 1. 19. Multiply 874 hy |. Deaomin. 4)843 Denomin. 2)874 210| Ans. 437 Ans. 3 COINS, WEIGHTS, AND MEASURES. 20. Multiply 8740 by f . 21. Multiply 840 by f . 3=Numerat. Denom. 4)26220 6555 Ans. 5=Numerat. Denom. 3;4200 525 Ans. TABLES OF COINS, WEIGHTS, AND MEASURES. 1. ENGLISH MONEY. 4 Farthings, marked qis. make 1 Penny, marked d. 12 Pence 1 Shilling, . . s. 20 Shillings ....... 1 Pound, . . . . NOTE. 4d=l groat. PENCE TABLE. to Pence. s. d. Shillings. 20 equal to 1 8 2 equal 30 ... 2 6 3 . . 40 ... 3 4 4 . . 60 ... 4 2 5 . . 60 ... 5 6 . . 70 . . . 5 10 7 . . 80 ... 6 8 8 . . 90 ... 7 6 9 . . 100 ... 8 4 10 . . 110 ... 9 2 11 . . 120 . . . 10 12 . . d. 24 36 Shillings. . s. 20 equal to 1 30 ... 1 10 48 40 ... 2 60 50 . . . 2 10 72 60 ... 3 84 70 ... 3 10 96 80 ... 4 108 90 ... 4 10 120 100 ... 5 132 HO ... 5 10 . 141 120 ... 6 COMPARATIVE VALUE OF COINS. Lawful. Sterl. Fed. Mon. A Guinea =1 8=l 1=$4 66 2-3 Doubloon = 4 8= 3 6=14662-3 Johanna = 2 8= 1 16= 8 Dou.Joh.= 416= 312=16 Moidore = 1 16= 1 7= 6 Pistole = 1 2= 16.6=3 77 1-3 Crown = 6.8=0 5= 1 10 Spanish doll. 6= 4.6=1 Engl. shil.= 1.4= 1= 222-9 French Frank 1.1$ 181-2 Pagoda of China=$l 94 Tale of China = 1 40 Milrea of Portu.= 1 25 Livre Tournois = 18 \- : l Rixdol. of Den.= 1 Guilder or Florin= 40 Ruble of Russia= 66 Rupee of Bengal= 55 1-2 Marco Banco of Hamburgh == 331-3 Real Plate of Spain. = 10 P'd. ster 'g. in Ireland=l 0.0=4 10 Pound sterling ... =1 0.0=4 44 1-2 COINS, WEIGHTS, AND MEASURES. gg 2. TROY WEIGHT. 24 Grains, marked grs. make 1 Pennyweight, marked pwt. 20 Pennyweights ... 1 Ounce, oz. 12 Ounces 1 Pound, lb. NOTE. By Troy Weight, all jewels, gold, silver, electuaries, and liquor?, are weighed. 3. AVOIRDUPOIS WEIGHT. 16 Drains, marked drs. make 1 Ounce, .... marked . . . 055. 16 Ounces 1 Pound, . . . . lb. 28 Pounds 1 Quarter of a cwt. . qr. 4 Quarters 1 hundred cwt.or 11 2lbs. cwt. 20 Hundred Weight . . 1 Ton, .... . T. NOTE 1. By this weight all coarse and drossy goods are sold, and all metals, except gold and silver. 2. In Avoirdupois Weight several other denominations are used in particular goods : viz. A bbl. of Pot Ashes, =200 Ibs. { 144 dozen, . ' =1 great gross. A bbl. of Pork, . =220 Ibs. $ 20 particular things, =1 score. A bbl. of Beef, . =220 Ibs. $ 5 do. do. =1 tally. A quintal of Fish, =112 Ibs. } 24 sheets of Paper, =1 quire. 12 particular things, =1 dozen. S 20 quires, . ... =1 ream'. 12 dozen, . . . =1 gross. $ 4. APOTHECARIES' WEIGHT. 20 Grains, marked grs. . make 1 Scruple, . marked 9- 3 Scruples 1 Dram, .... 5 8 Drams 1 Ounce, .... 12 Ounces 1 Pound, . lb NOTE. Apothecaries mix their medicines by this Aveight, but buy and sell their commodities by Avoirdupois. It is the same as Troy Weight, except its having some different divisions. 4 COINS, WEIGHTS, AND MEASURES. 5. LONG MEASURE. 3 Barley-corns, marked bar. make 1 Inch, marked . in. 12 Inches ...... 1 Foot, ..... ft. 3 Feet ....... 1 Yard, ..... yd. Yards, or 16-|- Feet . . 1 Rod, Perch, or Pole, pol. 8 Furlongs ..... 1 Mile, .... mile. 60 Miles on the equator . 1 Degree, ..... 360 Degrees ..... 1 Great Circle of the Earth. NOTE 1. This measure is used to ascertain the distances of places, or any thing which has length only. 2. Distances are measured with a chain 4 rods long, containing 100 links. 3. 4 inches, = a hand. $ 5 feet, = a geometrical pace. 6 feet, = a fathom. $ 66 feet, =a gunter's chain. 3 miles, = a league. "TVVo" mcn ? = a link. 6. CLOTH MEASURE. 2 Inches, marked in. make 1 Nail, marked n. 4 Nails ....... 1 Quarter, . . . . qr. 4 Quarters ..... 1 Yard, ..... yd. 3 Quarters ..... 1 Flemish EH, . Fl.E. 5 Quarters ..... 1 English Ell, . . E.E. 6 Quarters ..... 1 French Ell, . . Fr.E. 4 Quarters ..... 1 Scotch Ei!, . . S.E. 7. TIME. 60 Seconds, marked sec. make 1 Minute, marked m. 60 Minutes ...... 1 Hour, . . . h. 24 Hours ....... 1 Day, . . . d. 7 Days ........ 1 Week, . . . w. 4 Weeks ....... 1 Month, . . . mo. 13 Months, 1 Day, 6 Hours . 1 Year, . . . yr. 365]- Days ........ 1 Year, . . . yr. 52 Weeks ....... 1 Year, . . . yr. 100 Years ....... 1 Century, . . C. NOTE. When the year of the Christian Era, can be divided by 4, without a remainder, it is then Bissextile, or Leap Year; the remain- der, if any, shows what year it is after Leap Year. COINS, WEIGHTS, AND MEASURES. 2 8. CIRCULAR MOTION. 60 Seconds, marked " make 1 Prime or Minute, marked ' 60 Minutes 1 Degree, 30 Degrees 1 Sign, S 12 Signs, or 360 . . . 1 Circle of the Zodiac. NOTE. The Zodiac is a space of 16 degrees wide, within which the motions of all the planets are performed, except the newly dis- covered Asteroids. 9. LAND, OR SQUARE MEASURE. 144 Inches, marked in. make 1 Square Foot, marked ft. 9 Feet 1 Square Yard, . . yd. 30i Yards, or 272 Feet . 1 Rod, rod. 40 Poles, or Rods ... 1 Rood, . ... rood. 4 Roods, or 160 Rods . 1 Acre, .... acre. 620 Acres 1 Mile, .... mile. NOTE. Land is measured by the chain. 10. SOLID MEASURE. 1728 Inches, marked in. make 1 Solid, or Cubic Foot. 27 Feet 1 Yard. 40 Feet round timber ... 1 Ton, or Load. 50 Feet hewn timber ... 1 Ton, or Load. 128 Solid Feet, that is, 8 feet in") length, 4 in breadth, and t 1 Cord of Wood. 4 in height, . . . . J NOTE. All things which have length, breadth, and depth, are measured by Solid or Cubic Measure. 11. WINE MEASURE. 2 Pints, marked pts, make 1 Quart, marked qrt. 4 Quarts 1 Gallon, . . . gal. 42 Gallons 1 Tierce, . . . tier. 63 Gallons 1 Hogshead, . . hhd. 84 Gallons 1 Puncheon, . . pun. 2 Hogsheads .... 1 Pipe, or Butt, . pi. b. 2 Pipes 1 Tun, . . . . T. 31i Gallons 1 Barrel, . . . bar. NOTE. By this measure all brandies, spirits, perry, cider, mead, Tinegar, and oil, are measured, 3* g@ REDUCTION. 12. ALE, OR BEER MEASURE. 2 Pints, marked pts. make 1 Quart, marked qrt. 4 Quarts 1 Gallon, . . . gal. 54 Gallons ...... 1 Hogshead of beer, hhd. 2 Barrels 1 Puncheon, . . pun. 3 Barrels, or 2 Hogshead . 1 Butt, . . . butt. 13. DRY MEASURE. 2 Pints, marked pts. make 1 Quart, marked qrt. 4 Gallons 1 Peck, .... pc. 4 Pecks, or 5 Pecks water? . ^ , , measure ... 5 l Bushel > ' ' bus * 32 Bushels 1 Chaldron, . . ch. 36 Bushels 1 Chaldron in London, ch. NOTE. Salt, coal, sand, fruits, oysters, roots, corn, and dry goods, are measured by Dry Measure. REDUCTION. REDUCTION teaches to exchange numbers of one denomi- nation to another, retaining the same value. It consists of two sorts; viz. Descending and Ascending, CASE I. Reduction Descending is bringing a greater denomina- tion into a less. GENERAL RULE. Multiply the highest denomination given by so many of the next less, as make one of that greater, and thus con- tinue to do till the number is brought into the denomination o.required. REDUCTION. gv EXAMPLES. 1. In 945, how many pence ? 945 20=shilliugs in a pound. 18900=shi1Hngs. 12=pence in a shilling. 228800=pence. Ans. 226800. PROOF As Reduction Descending is performed by mul- tiplication, t is proved by division ; that is. by changing the order of (be question, and dividing the last product by the last multiplier. In the preceding question the order will be. In 226800 pence, how many pounds ? Last mult. 12)226800=last product. 2.0)1890,0 945 Ans. as above. Ans. 945. CASE II. To reduce a mixt number to a less denomination. RULE. Multiply the highest denomination as before di- rected, adding the less units, which stand in the given number to the products, which are of the same name. EXAMPLES. 2. In 344 18 4| how many farthings ? 20 6898-{-18 shillings. 12 5780-{-4 pence. 4 331122+2 farthings. Ans. 331122 qrf. 1. MONEY. 3. In 35, how many shillings ? Ans. 700 s. 4. In 35 guineas, how many pence ? Ans. 11760 d. 5. lu 348 12 ' 84- how many farthings ? Ans. 334690 o/s. g REDUCTION. 2. TROY WEIGHT. 6. Reduce 149 Ib. to grains. 149 12 1788=ounces. 35760=penayweigh(s. 24 143040 71520 858240=grs. * Ans. 858240 grs. 7. In 39 11 12 14 grs. how many grains ? Ans. 230222 grs. 8. How many grains are in a silver tankard, weighing 11 Ibs. ? Ans. 63360 grs, 3. AVOIRDUPOIS WEIGHT. 9. Reduce 49 cwt. to ounces. 49 '?& 4 196= q rs. 28 1568 392 5488=lb, 16 32928 5488 87808=oz. Ans. 87808 oz. 10. In 39 2 14 8 4 drs. how many drams P Ans. 11 36260 drs. 11. In 12 14 3 qrs. how many pounds ? Ans. 28532 Ib. 12. Reduce 8 tons to ounces. Ans. 286720 ozr, REDUCTION. 29 13. How many pounds are in 30 hogsheads of sugar, each weighing 9| cwt. ? Ans, 31920 lb. 4. APOTHECARIES' WEIGHT. 14. In 27 11 7 1 18 grs. how many grains ? 12 335=ounces. 2687=drams. 3 8062=scrupleg. 20 161258=grains. Ans. 161258 grs. 15. Reduce 34 Jb. 10 %. to drams. Ans. 3344 drs. 5. LONG MEASURE. 16. In 100 miles, how many feet ? 100 8 800=furlongs. 40 32000=rods, 160000 16000 176000=yards. 3 528000 Ans. 528000 ft. 17. In 84 miles, how many inches ? Ans. 5322240 in. 18. In 15 7 30 2 feet, how many inches? Ans. 1011876 in. 19. How many rods in a mile ? Ans. 320 rods. 20. In 100 leagues, how many yards ? Ans. 528000 yds. 21. How many yards from Boston to Salem, the dis- tance being 18 miles ? Ans. 31680 yds. 30 REDUCTION. 22. How many barley-corns will reach round the world ? Ans. 410572800C bar. 23. How many inches from Boston to London, allowing the distance 3000 miles ? Ans. 190080000 in. 6. CLOTH MEASURE. 24. In 84 yards, how many nails? Ans. 1344 n. 25. Reduce 124 3 3 nails to nails. Ans. 1999 n. 26. In 25 pieces of cloth, each piece") f 500yds. 20 yards, how many yards, quar VAns. -s 2000 qrs. ters" and nails ? 'J t 8000 n.. 7. TIME. 27. How many hours in 40 years ? Ans. 350400 h. 28. In 29 11 36 23 hours, how many seconds ? Ans. 870908400 sec. 29. How many minutes since the birth of our Saviour, the present year being 1818 ? Ans. 955540800 m. TV". B. . To reduce Longitude into Time. RULE. Multiply the Longitude by 4, observing that miles produce seconds, and degrees minutes ; or divide the longitude by 15, the degrees equal to an hour. EXAMPLES. 30. The Longitude of Boston is 70 37' ; difference of time between it and London ? 70 37 4 4 42 28 seconds, Ans. Or, 70 37-M 42 28 se. 2. To change Time into Longitude. RULE. Multiply the time by 10, adding one half of the product to itself. EXAMPLES. 31. In 4 42 28 seconds, how many degrees of Longi- tude ? 4 42 28 10 |)47 04 40 23 32 20 70 37 00 Ans. 70 37'. REDUCTION. 8. LAND, OR SQUARE MEASURE. 32. In 44 acres, hovv many pi rein-* ? Ans. 7040 per. 33. la 49 2 18 pules, hovv many poles? Ai.s. 7958 pol. 34. In 34 acres, how iaan> roods and > A $ 136 roods. *' $5440 rods. 9. SOLID MEASURE. 35. In 12 tons of round timber, how many cubic inches? Ans, 8294 10 in. 30. Hovv many solid or cubic inches in 12 ions of hewn timber? An*. 1036800 in, 37. Hovv many solid inches in a cor $ 1260 gal. Inns of wine ? S *' ? 10080 pts. 39. Reduce 5 pipes to pints. Ans. 5040 pts. 11. DRY MEASURE. 40. In 30 chaldrons of coal, hovv many bushels ? Ans. 960 bush. 41. Reduce 24 bushels to pints. Ans. 1536 pts. 42. In 20 chaldrons, hovv many bushels. London mea- sure ? Ans. 720 bush. REDUCTION ASCENDING. REDUCTION ASCENDING teaches to bring a less denomi- nation into a greater. RULE. Divide the lowest denomination given by so many of that ua.iie as make one of the next higher; and thus continue to do till the number is brought into the denomi- nation required. PROOF As Reduction Ascending is performed by divi- sion, it is proved by multiplication ; that is, by changing the order of the question, and multiplying the last quotient by the last divisor, adding the remainders, if any. g REDUCTION. EXAMPLES. 1. MONEY. 1. In 752640 farthings, h\v urxny pounds ? 4)752ri40:=farthings. Prooi ,34-=last quotient. - - 20=lAt divisor. 12)188100 pence. 15680=shiiliugs. 12 784=pounds. 752640=farthings as alicve. NOTE. When there are remainders after" dividing-, they are of the same name with their respective dividends, and mast be placed after the last quotient, according to the order of their names, the highest denomination first; the several mixt numbers, thus formed, will be the answer. 2. lu 331122 farthings, how many pounds? 4)331122 12)82780 i qrs. rem. 2,0)689,8 4 d. rem. 344 18 4i Ans. 344 18 4. 3. In 700 shillings, how many pounds ? Ans. 35. 4. In 11760 pence, how many guineas ? Ans. 35 guin. 5. Bring 334690 farthings into pound*-. Aus. 348 12 8i. 2. TROY WEIGHT. 6. In 858240 grains, how many pounds ? 2,0 24)858240(3576,0 72 r 12)1788 138 120 149 Ib. Ans. 149 Ib. 182 168 144 144 REDUCTION. 33 7. In 230222 grains, how many pounds ? Ans. 39 11 12 14 grs.~ 8. How many pounds will a tankard weigh, which con- -ains 63360 grains ? Ans. 1 1 Jb. *. AVOIRDUPOIS WEIGHT. ?. Reduce 159488 ounces to cwt. (28) (4) 16)159488(9968(356 144 84 89 cwt 154 156 144 140 108 168 96 168 128 128 Ans. 89 cwt." .dO. In 1136260 drams, how many cwt. ? Ans. 39 2 14 8 4 drs. 11. How many tons in 28532 pounds ? Ans. 12 14 3 qrs. 12. Bring 286720 ounces to tons. Ans. 8 tons. 13. How many hogsheads, weighing 9^ each, are in 31920? "Ans. SOhhdw 4. APOTHECARIES' WEIGHT. 14. Reduce 161253 grains to pounds. 2,0)16125,8 3)8062 18 8)2687 1 12)335 7 27 11 7 1 18 grs. Ans. 27 11 7 1 18 grs. 1ft. Reduce 3344 drams to pounds ? Aiis. 34 10 dm 34 REDUCTION. 5. LONG MEASURE. 16. In 528000 feet, how many miles ? 3)528000=feet. 5^)17GOOO=yards. 4,0)3200,0=rods. 8)800=furlongs, 100=miles. Ans. 100 DL 17. In 5322240 inches, how many miles ? Aus. 84 m. 18. I 1011876 inches, how many miles ? Ans. 15 7 30 2 2 ft. 19. How many miles in 320 rods ? Ans. 1 m* 20. In 528000 yards, how many leagues? Ans. 100 Jeag. 21. If 31 680 yards will reach from Salem to Boston, how many miles? Ans. 18 in. 22. If 4105728000 barley-corns will reach round the globe, how many degrees ? Ans. 360. 23. Suppose that 190080000 inches would reach from Boston to London, how many miles ? Ans. 3000 m. 6. CLOTH MEASURE, 24. In 1344 nails, how many yards ? Ans. 84 yds. 25. Reduce 1999 nails to yards ? Ans. 124 3 3 n. 26. Reduce 8000 nails to quarters > . f2000qrs. -and yards. $ I 500 yds. 7. TIME. 27. How many years in 350400 hours ? Ans. 40 yrs. 28. In 870908400 seconds, how many years ? Ans. 29 11 3 6 23 h. 29. In 955540800 minutes, how many years ? Ans. 1818 yrs, 8. LAND, OR SQUARE MEASURE. 30. Reduce 7040 rods to acres ? Ans. 44 acres. 31. In 7938 poles, how many acres? Ans. 49 2 18 pol. 32. How many acres in 136 roods? Ans. 34 acres. 33. How many acres in 5140 rods ? Ans, 34 acres. REDUCTION. 35 9. SOLID MEASURE. 34. How many tons of round timber in 829440 solid, or cubic inches ? Ans. 12 tons. 35. In 221 1G4 solid inches, bow many cords ? Alls. 1 cord. 10. WINE MEASURE. 36. Reduce 1260 gallons to tuns. Ans. 5 tuns. 37. How many pipes in 5040 pints ? Ans. 5 pipes. 11. DRY MEASURE. 38. In 960 bushels, how many chaldrons ? Ans. 30 eh. 39. Reduce 1536 pints to bushels. Ans. 24 bush. 40. In 720 bushels, how many London chaldrons ? Ans. 20 ch. REDUCTION ASCENDING AND DESCENDING Is exchanging numbers from a greater to a less, and from a less to a greater denomination, as the nature of the ques- tion may be, and is performed by multiplication and divi- sion. EXAMPLES. 1. MONEY. 1. How many shillings, crowns "1 f2240 shillings. and pounds are in 80 t- Ans. < 336 crowns. j (_ 112 pounds. 2. In 84, how many pence, ^ i * three pencea." groats V Ans. ] * three pences, andmoulores? $ ^0 groats. ' ^ 46 j moidores. 3. A person had 20 purse?, in each purse 18 guineas, 8 pounds, a crown, and a moidore; how many pounds ster- ling had he ? Ans. 530. 2. TROY WEIGHT. 4. In 29 o 12 19 grains Troy, how many pounds Avoir- dupois ? Ans 24 7 mil 5. How many rings, each weighing 6 8 grs. may be made of 4 6 13 pwt. of gold? Ans. 172 rings, and 3, 1G grs. over. 36 COMPOUND ADDITION. 6. A gentleman sent a tankard to lis goldsmith, which weighed 84 12 pwts directing him to make it into spoons of 3 6 pwts. each ? how manj had he ? Ans. 25 spoons and 2, 2 pwt over. 7. A gentleman sent his goldsmith 11 5 6 Drains of silver, and directed him to make it into tankards of 1 5 15 10 grains each ; spoons of 1 9 11 13 grains perdnz. salts of 3 10 pwt. each; and forks of 1 11 13 grains per doz ; and for every tankard to have one salt, a dozen of spoons, and a dozen of forks ; what number of each must Le have ? Ans. 2 of each sort, and 899 grs. over. 3. AVOIRDUPOIS WEIGHT. 8. In 34 pounds Avoirdupois,* how many pounds Troy? Ans. 41 3 16 16 grs. 9. How many parcels of sugar, of 14 pounds each, are in a hogshead which weighs 18 1 14 pounds ? Ans. 147 of 14 Ib. each. 4. LONG MEASURE. 10. How many times the length of a ship's keel will reach from Boston to the Land's End, in England, a direct course being about 2500 miles, and the ship's keel 110 feet in length? Ans. 119187f 11. How many times will the wheel of a chaise turn la running from Boston to Salem, the distance being 18 miles, and tlie circumference of the wheel 15 feet? Ans. 6131if. 12. How many steps, of 2 6 inches each, must a person take in walking* from Boston to Cambridge Common, the distance being 3 miles ? Ans. 6864. COMPOUND ADDITION. COMPOUND ADDITION is the collecting of several num- bers of different denominations into one sum 5 as pounds, shillings ; hundreds, quarters, &c. RULE. 1. Place the numbers of the same denomination under each other. * 7000 grs.=l Jb. Avoirdupois, and 5760 grs.= lib. Troy. COMPOUND ADDITION. 37 rJ. Add the figures in the lowest denomination, as in Sim- ple Addition. 3. Divide this sum by as many of the same name as make one of the next higher denomination, as in Reduction Ascending. 4. Set the remainder under the denomination added, and carry the quotient to the next higher denomination ; continue so to do to the highest denomination, which add, as in Simple Addition. NOTE. This rule is applicable to all sums in Compound Addition of money, weights and i^easures. PKOOF. Cut off the upper line of numbers by drawing .a line below it ; add the rest of the numbers, and set them down as in the operation ; then add the last 1'ound number and upper line together, their sum will be the same as the first addition. . 387 14 11 87 8 134 3 EXAMPLES. 1. MONEY. . s. 487 12 9 f 8 4- 1484 5 4 Sum. d. qrs. 8 i 389 18 10 i 78 19 11 | 874 13 8 f 609 7 5 f 1484 5 41 Proof. NOTE. 4=1 farthing, or a quarter of any thing. 5=2 farthings, or half of any thing. 3=3 farthings or three quarters of any thing. Ib. of. pwt. grs. 437 11 18 23 707 8 14 19 487 9 16 14 736 10 18 12 2. TROY WEIGHT. lb. oz. pwt. grs. 983 8 14 13 487 7 15 12 787 10 18 15 148 9 17 13 lb. os. pu-t. 874 11 14 987 8 13 787 10 12 187 10 16 2500 8 20 2408 1 2838 5 15 38 COMPOUND ADDITION. 3. AVOIRDUPOIS WEIGHT. cwt. qrs. Ib. oz. drs. cwt. qrs. Ib. oz, dr.- 345 2 19 13 13 487 1 18 12 12 749 3 17 14 12 373 2 17 13 14 300 1 8 14 14 748 3 14 14 !> 748 2 14 11 12 874 2 18 13 11 2144 2573 2484 2 14 4. APOTHECARIES' WEIGHT. Ib. own. drs. sent. Ib. oun. drs. scri{. grs. 487 11 6 2 874 10 6 2 18 787 8 6 1 987 9 4 1 19 900 732 387 7 3 2 17 709 11 7 2 487 3 2 1 14 2886 3 7 1 2737 7208 5. LONG MEASURE. . fur. pol. yds. miles, fur. poL yds. feet. in. bar. 874 6 36 41 874 4 28 3-1- 2 11 2 973 4 26 3| 389 5 18 1* 1 81 187 6 14 li 187 3 17 4f 272 874 7 18 3 874 1 14 li 1 10 1 2911 1 16 2^ 2325 6 39 3i 20 6. CLOTH MEASURE. yds. qrs. n. E.E. qrs. n. F/.E. . n. Fr.E. qrs. n. 48*7 3 2 834 4 2 824 2 2 879 5 2 878 1 2 739 3 1 347 2 1 654 4 2 983 2 1 487 2 2 678 1 2 783 1 1 756 3 2 578 3 1 487 2 1 874 3 2 3106 2 3 2640 3 2 2338 2 2 3192 2 3 COMPOUND SUBTRACTION. 7. TIME. mo. ic. d. K. years, mo. U'. d. h. m. 874 11 3 6 23 837 8 3 5 18 33 784 8 1 5 19 478 9 2 6 22 39 130 7 1 4 12 748 11 3 5 13 24 898 6 2 1 15 874 o 1 6 14 13 2688 10 1 4 21 2940 3 3 20 54 8. MOTION. Signs, deg. m. sec. deg. TO. sec. dcg. m. sec. 9 22 35 44 18 34 14 14 25 18 10 13 19 18 17 36 38 18 48 13 8 13 23 38 18 14 17 12 13 18 11 28 44 46 24 39 48 11 16 15 40 18 3 26 79 4 57 56 43 COMPOUND SUBTRACTION. COMPOUND SUBTRACTION teaches to find the difference between two numbers of different denominations. RULE. 1. Subtract the under number* from the upper, and set tbeir difference under their respective denomina- tions. 2. If the under number of any of the denominations is greater than the upper, take it from as many as make one of the next higher denomination ; add the difference to rhe upper number, and set down their sum, remembering to carry one to the next higher denomination, before subtract- ing it. EXAMPLES. 1. MONEY. 1. 2. . s. d. qrs. . s. d. qry. 8745 10 11 i Minuend. 483 13 10 1 189 8 3 I Subtrahend. 90 17 11 8556 2 8 i 392 15 10 40 COMPOUND SUBTRACTION. 2. TROY WEIGHT. 3. 4. 5. ib. os. pwt. grs. Ib. oz. pwl. Ib. or. pwl. grs, 387 10 13 13 784 8 15 898 7 14 14 187 11 18 19' 387 11 14 187 10 15 18 199 10 14 18 396 91 710 8 18 20 3. AVOIRDUPOIS WEIGHT. 6. 7. cu-t. qrs. Ib. oz. drs. civt. qrs. Ib. os. drs. 437 2 19 13 12 874 2 14 13 13 C9 3 24 13 14 87 3 27 14 15 347 2 22 15 14 786 2 14 14 14 4. APOTHECARIES' WEIGHT. 8. 9. 10. Ib. oun. drs. scru. grs. Ib. oun. drs. Ib. oun. scru. grs. 348 10 3 2 12 874 8 4 434 10 3 2 89 11. 5 2 15 99 10 7 379 11 6 2 i58 10 5 2 17 774 95 54 10 5 5. LONG MEASURE. 11. 12. miles, fur. poL yds. ft. miles, fur. pol. yds. ft. in. 387 5 27 2i 1 834 3 25 4 1 10 93 6 36 4| 2 87 4 29 3| 2 11 293 6 30 3 2 746 6 35 5 1 11 6. CLOTH MEASURE. 13. 14. 15. 16. yds. grs. n. E.Eng.qrs.n. E.Fl. qrs. n. E.Fr. qrs. n. 431 21 834 4 2 874 21 874 5 1 139 3 3 89 4 3 89 2 3 87 5 2 291 22 744 4 3 784 22 786 5 3 COMPOUND MULTIPLICATION. 4JI 7. TIME. 17. 18. yrs. mo. w. d. h. m. sec. yrs. mo. u\ d. k. wf.. 987 11 2 4 14 13 18 8743 8 1 2 22 14 374 11 3 5 16 46 55 87 11 3 4 23 56 612 U 5 21 26 23 8660 8 1 4 22 18 21. tun. hhd. gal. 834 1 18 89 2 28 hhd. 834 87 19, gal. 1 1 25 qrt. 2 3 8. pt. 1 1 WINE MEASURE. 0. tier. gal. qrt. 38 11 1 18 24 2 746 48 3 19 28 3 QUESTIONS. 744 2 53 1. From 1 take '- qrs. Ans. 19 11 qrs. 2. From 1 Ib. Troy, take 1 grain. Ans. 11 19 23 grs. 3. From 1 cwf. take 1 oz. Ans 3 27 15 oz. 4. From a mile lake an inch. Ans. 7 39 4^ 2 11 in. 5. From a year take a second. Ans. 364 23 59 59 sec. 5. T;ike one second from the Christian era, allowing even years, and 365 days for a year. Ans. 1817 364 23 59 59. COMPOUND MULTIPLICATION. COMPOUND MULTIPLICATION is the multiplying of sums of different denominations. RULE. Multiply the lowest denomination by the given multiplier, and divide the product by as many as make one of the next higher denomination ; set down the remainder, and add the quotient to the next higher denomination, after it is multiplied. PROOF, By Division. 4# COMPOUND MULTIPLICATION. EXAMPLES. J. MONEY. 1. 2. . $ d. qrs. . s. d, qrs, Multiply 874 10 6 i 8343 18 11 by 8 12 C996 4 4 Product. 100187 7 9 2. TROY WEIGHT. 2. 4. Z6. o. jpu7. grs. Ib. os. j?w/. gr^, Multiply 874 10 12 11 343 8 8 3 by 24. by 9 4X6 7873 11 12 3 8248 9 15 3. AVOIRDUPOIS WEIGHT. 5. 6. civt. qrs. Ib. os. cwt. qrs. Ib. oz. Multiply 28 2 14 12 37 3 18 2 by 16. by 11 4X4 314 3 22 4 606 2 10 4. APOTHECARIES' WEIGHT. 7. 8. Ib. oun.drs. scru. Ib. oun.drs, scru. Multiply 18 11 5 2 804 8 3 2 by 3G. by 8 6X6 151 951 28969 440 5. LONG MEASURE. 9. 10. milts, fur. pol. yds. miles, fur. pol. yds. Multiply 34 3 10 4 80 7 34 3 by 7 10 240 6 35 4 809 6 25 2 COMPOUND MULTIPLICATION. 43 6. TIME. 11. 12. Multiply 34 11 2 3 12 87 10 3 2 12 10 18 by 12 12 419 7200 1054 10 2 2 3 36 Compound Multiplication is an useful and concise rule for finding the value of goods. It is a contraction of the Rule of Three, when the first number is an unit. GENERAL RULE. Multiply the price by the quantity. CASE. I. When the quantity is not more than 12. Multiply the price 1 the product will be the answer. EXAMPLES. RULE. Multiply the price by the whole quantity, and "I be 1. What will 8 yards of cloth cost at 3 12 6 per yard ? 3 12 6i 8 29 4 AIJS. 29 4. 2. What will 12 Ib. of tea cost at 13 84- per pound ? Ans. 8 4 6. CASE II. When the quantity is more than 12, and a composite number, that is, such that two figures will make it when, multiplied together. RULE. Find two figures which will make the quantify when multiplied together, arid multiply the price by these figures, the last product will be the answer. 44 COMPOUND MULTIPLICATION, EXAMPLES. 3. What will 24 yards cost at 4 10 8|- per yard ? i=price. J 4 yards. 18 2 10=value of 4 yards. 6 yards. 108 17 = value of 24 yards. Ans. 108 17. 4. What will 132 yards cost at 3 8{ per yard ? Ans. 400 10 9, CASE III. When the quantity is such that no figures in the table will make it. RULE. Multiply hy two such figures that will come the nearest to it, and add the price of the odd quantity, if less, but subtract it. if greater. EXAMPLES. 5. What will 29 Ib. cost, at 2 8 4 per Ib. ? 4x7=28 nearest. 2 8 4=price. 1 odd. 4 Ibs. 29 Ib. 9 13 6 =value of 4 Ibs. 7 67 14 6 =value of 28 Ibs. Q o 4i _ Rvalue of 1 Ib. add- 2 ed, because less. 70 2 10i=value 29 Ibs. Ans. 70 2 101. 6. What will 127 yards cost at 8 Of. Ans. 1016 7 11|, CASE IV. To find the value of a hundred weight. RULE. Multiply the price by 7, its product by 8, and this product by 2, the last will be the answer. COMPOUND MULTIPLICATION. EXAMPLES. T. What will 1 cwt. cost at 3 10 4! per lb.? 3 10 4i 7 24 12 7i=value of 7 lb. 197 10 =valueof 56 lb. 394 2 =value of 1 cwt. or 112 lb. Ans. 394 5. 5. What costs 1 cwt. at 3 8f per lb. ? Ans. 340 1 8. CASE V. To find the value of two or more hundreds. RULE. First find the value of one hundred weight, (by Case IV.) then multiply the price of one hundred weight by the given number of hundreds. EXAMPLES. 9. What will 12 cwt. cost at 3 8 41 per lb. f 3 8 41 7 23 18 7i=value of 7 lb. 8" 191 9 0=value 56 lb. 382 18 0=value 1 cwt. 12=given hundreds. 4594 16 0=12 cwt. Ans. 4594 16. 10. What will 87 cwt. cost at l 13 44- per'lb ? Ans, 16260 6. 5 6 COMPOUND DIVISION. CASE VI. When there is a fractional part in the quantity. RULE. 1. Find the value of the whole numbers by the preceding rules, according to the question. 2. Multiply the price by the numerator, and divide the product by the denominator; the quotient will be the value of the fraction, which, added together, will be the value of the whole quantity. (See Case VII. in Simple Division.) EXAMPLES. 11. What will 8i yards cost at 3 2 GI per yard ? i)3 2 6i 8 25 4 =value of 8 yards. 1 11 3i=value 1 yard. 26 11 7=value Bk yards. Ans. 26 11 7j. 12. AVhat will 144f yards cost at 2 18 3| per yard ? Ans. 420 15 COMPOUND DIVISION. COMPOUND DIVISION is the dividing of sums of different denominations. RULE. Divide the highest denomination by the given number, and if any thing remains, reduce it to the next lower denomination, by multiplying it by as many of the next less as make one of that name, adding to the product, the number, if any, in the next lower denomination, and divide as before, selling each quotient under its respective denomination. PROOF. By Multiplication. EXAMPLES. 1. MONEY. 1. 2. Divide 384 18 4 by 8. 387 13 4Jbyl2. 8)384 18 4 ' 12)387 13 4A " 48 2 3^ Ans. 32 6 1^ Ans. COMPOUND DIVISION. 47 2. TROY WEIGHT. 3. 4. lb. oz. put. grs. lb. os. pwt. grs. Divide 9 11 13 14 by 8. 18 8 12 13byl2. 8)9 11 13 14 12)18 8 12 13 1 2 19 4+6 1 6 14 9+1 3. AVOIRDUPOIS WEIGHT. 5. 6. cwt. qrs. lb. cwt. qrs. lb. os. drs. Divide8)84 2 18by8. 11)874 3 27 13 13byll. 10 2 9 4 79 2 5 1 4+1 4. APOTHECARIES' WEIGHT. 7. 8. lb. ou.drs.scr. lb. ou. drs.scr.grs. Divide 7)134 9 3 2 by 7. 8)874 10 5 2 14byC. 19 3 1 11+3 109 422 4+2 5. LONG MEASURE. 9. 10. miles. fur.pol:yds.ft. miles, fur.pol.yds.ft. Divide 12)384 6 24 3 2 by 12. 9)874 7 34 3 2 by 9. 32 22 11 in. 97 1 30 2 2 6 2 6. TIME. 11. 12. yrs. mo. w. d. h. m. sec. yrs. mo. w. d. h. Divide 11)874 11 2 3 18 43 24 9)874 11 1 4 22 79 620 8 14 51+3 97 2 2 2 21 6 40 COMPOUND DIVISION is useful in finding the value of 1 lb. 1 yard, &c. having the value and the quantity given. 4g COMPOUND DIVISION. It is a contraction of the Rule of Three, when the third term is an unit. GENERAL RULE. Divide the price by the quantity, and the quotient will be the answer. CASE I. When the quantity does not exceed 12. RULE. Divide the price by the whole quantity. EXAMPLES. 1. If 8 yards cost 29 4, what will 1 yard cost ? 8)29 4 3 12 6| Ans. 3 12 6. 2. If 12 Ib. cost 8 4 6, what will 1 Ib. cost? Aus. 13 8i. CASE II. When the quantity is more than 12, and such a number that two or more figures will make it, when multiplied to- gether. RULE. Divide the price by these figures, and the last quotient will be the answer. EXAMPLES. 3. If 24 yards cost 108 17, what will 1 yard cost ? 4X6=24. 4)108 17 6)27 4 3 4 10 8 Ans. 4 10 8^ 4. If 132 Ib. cost 400 10 9, what will 1 Ib. cost? Ans. 3 8| COMPOUND DIVISION. 49 CASE III. When the quantity is such that no two figures in the Table will make it. RULE. Divide the whole price by the whole quantity, as in Long Division. EXAMPLES. 5. If 29 yards cost 70 2 10, what will 1 yard cost? 29)70 2 10| (2 8 4| Ans. 58 12 20 29)242 232 10 12 29)130 116 14 4 29)58 58 Ans. 2 8 4|. 6. If 127 yards cost 1016 7 11^, what will 1 yard cost? Ans. 8 Q Of. CASE IV. When the quantity is one hundred weight, to find the value of 1 Ib. RULE. Divide the price by 8, its quotient by 7, and this quotient by 2, the last quotient will be the answer. 5* 0Q COMPOUND DIVISION. EXAMPLES. 7. If one hundred weight cost 394 2 what will one pound cost ? 8)394 2 7)49 5 -3 2)7 9 3 10 4$ Ans. 3 10 4$. 8. If one hundred weight cost 340 1 8, what will one pound cost ? Ans. 3 8|. CASE V. When the quantity is two or more hundreds to find the price of one pound. ' RULE. Divide the -given price hy the given number of hundreds, the quotient will be the price of one hundred weight, then divide by 8, 7 and 2, the last quotient will be the price of one pound. EXAMPLES. 9. If 12 cwt. cost 4594 16, what will 1 Ib. cost? 12)4594 16 8)382 18 7)47 18 3 2)6 16 9 3 8 4| Ans. 3 8 4i. 10. If 87 cwt. cost 16260 6, what will 1 Ib. cost ? Ans. 1 13 4i. CASE VI. When there is a fractional part in the quantify. RULE. Multiply the integer of the given quantity by the denominator of the fraction, and to the product add the numerator, for a divisor; multiply the given price by the denominator, and divide by the new divisor, the quotient will be the answer. (See Case YI. iu Simple Division.) VULGAR FRACTIONS. 5^ EXAMPLES. 11. If 8i yards cost 26 11 7i, what will 1 yard cost? 8i 26 11 7i 2~ 2 17=y. 17)53 3 2^(3 2 GI 51 2 20 17)43 34 9 12 17)110 102 8 4 17)34 34 Ans. 3 2 6. 12. If 144f yards cost 420 15 10i-f 1, what will 1 yard cost? Ans. 2 18 3i. VULGAR FRACTIONS. 1. A FRACTION is a part, or parts, of an unit. 2. A fraction is written with two numbers, placed one above the other, with a line drawn between them ; as f . 3. The number above the line is called the na-\^ merator. r 4. The number below the line is called the denomi-f ~ nator. 5. The denominator shows into how many parts the unit is divided, and the numerator how many of these parts are expressed, or meant by the fraction* 5J VULGAR FRACTIONS. 6. A fraction Las its origin from Division, the numera- tor being the remainder, and the denominator the divisor. (See Note in Simple Division, jmge 18.) 7. The numerator of a fraction is to he considered as a dividend, and the denominator as a divisor, and the frac- tion as an expression of the quotient, arising from the divi- sion of the nu/nerator by the denominator. Hence, 8. A fraction is less, equal, or greater than an unit, as the numerator is less, equal, or greater than the denomi- nator. 9. The nature of a fraction may be illustrated by the following example. Let 11 be divided by 3. 3)11 The quotient is three whole units, the remainder signifies that the 2 is divided by 3, and that the quotient is f of an unit. 10. A vulgar fraction is that which can have any denom- inator, and may be either proper, improper, compound, or mixt. 11. A proper, single, or simple fraction is that whose numerator is less than its denominator; as f. 12. An improper fraction is that whose numerator is greater than its denominator ; as f . 13. A compound fraction is a fraction of a fraction, and is connected by the word o/; as | of % of f . 14. A mixt number, or fraction, is composed of a whole number and a fraction; as 5J. 15. The value of a fraction depends on the proportion which the numerator has to the denominator ; therefore the same fraction may be expressed by many different num- hers ; as T Yo> ?f If > If T 6 2 f j are alt e q ual fractions, each being equal to one half of an unit. 16. When the numerator and denominator are alike, the fraction is equal to 1. 17. A fraction whose numerator is greater than its de- nominator, is equal to some whole, or rnixt number; as 3=*f 18. A whole number may be expressed fractionally by placing 1 under it ; as ^=to 4. NOTE. As fractions can neither be added, subtracted, multiplied, nor divided, before they change their forms by Reduction, it is neces- sary that this rule should be explained before Addition. VULGAR FRACTIONS. 53 REDUCTION OF VULGAR FRACTIONS. Reduction of fractions teaches to bring them from one form into another, to prepare them for the operations of Addition, Subtraction, Multiplication and Division. PROBLEM I. To find the greatest common measure of any two numbers. RULE. Divide the greater number by the less, and the last divisor by the remainder, till nothing remains ; the last divisor will be the greatest common measure. NOTE. A number which can divide several numbers exactly, is called their common measure. EXAMPLES. 1. To find the greatest common measure of 48 and 256. 48)256(5 240 16)48(3 48 16 being the last divisor, is the greatest common measure. Ans. 16. 2. Find the greatest common measure of 216 and 768. Ans. 24. PROBLEM II. To find the greatest common measure of three or more numbers. RULE. Find the greatest common measure of the two least given numbers ; then find the common measure of this measure, and the next greater of the given numbers, and again of this last measure, and the next greater, and so on till all the given numbers are used. EXAMPLES. 3. Find the greatest common measure of 48, 80, and 136. 80-:-48=16 and 136-r-16=8=greatest common measure. Ans. 8. 4. What is the greatest common measure of 216, 270, and 405. Ans. 27. PROBLEM III. To find the least common multiple of several numbers. 04 VULGAR FRACTIONS. RULE. Set the numbers in a line, and divide them by any number which will divide two or more of them \vithout a remainder ; place the quotients and the undivided numbers in a line under them; divide them continually as before, until it appears that no two can be divided ; the continual product of all the undivided numbers, and the several divi- sors, will be the least common multiple required. NOTE. A common multiple is a number which can be divided by two or more numbers. EXAMPLES. 5. What is the least common multiple of 2, 3, 6, 9, 12, and 15 ? 332 3 6 9 12 15 2)2 1 2 3 4 5 11132 5X2X3X2X3=180. Ans. 180. 6. What is the least common multiple of the nine digits ? Ans, 2520. CASE I. To reduce fractions to their lowest terms. RULE. Divide the numerator and denominator of the given fraction by any number which will divide them with- out a remainder, and so on till there is no number greater than an unit, which will divide them. Or divide the nu- merator arid denominator by their greatest common mea- sure, and the quotients will form the fraction in its lowest terms. NOTE. If the common measure happens to be 1, the fraction is in its lowest terms. EXAMPLES. 7. Reduce /$ to its lowest terms. Or 96)544(5 480 com. meas. 32) I V ? = T 3 T as before. 64)96(1 64 = T 3 T Ans. 32(64(2 64 Ans. VULGAR FRACTIONS. 3. Reduce f f -ff . to its lowest terms. Ans. . 9. jVyW to its lowest terms. Ans. |-. CASE II. To reduce a mixt number to its equivalent improper fraction. RULE. Multiply the whole number by the denominator of the given fraction, add the numerator to the product for a new numerator, which written over the denominator will form the fraction required. EXAMPLES. 10. Reduce 12f to an improper fraction. 12 8 denominator. 96 3 numerator added. And 99 new num. 99 new numerator. 8 denom. Ans. -/ t 11. Reduce 120 ji to an improper fraction. Ans. ^f 1 . CASE III. To reduce an improper fraction to its equivalent whole or mixt number. RULE. Divide the numerator by the denominator, the quotient will be the whole number, and the remainder, ii* any, placed over the given denominator will form the frac- tional part. EXAMPLES. 12. Reduce 9 9 to a whole or mixt number. 8)99 12f. Ans. 12f. 13. Reduce 1 ff 1 to a whole or mixt number. Ans. 120ft. CASE IV. To reduce a whole number to a vulgar fraction, whose denominator shall be given. RULE. Multiply the whole number by the given denom- inator for the numerator, which, placed over the given de- nominator, will form the fraction required, 06 VULGAR FRACTIONS. , EXAMPLES. 14* Reduce 3 to a fraction whose denominator shall be 4. 3X4=12. And V 2 =Ans. 15. Reduce 12 to a fraction whose denominator is 11. Ans. V- CASE V. To reduce a compound fraction to a simple one. RULE. Multiply all the numerators continually to- gether for a new numerator, and all the denominators for a new denominator of the simple fraction. EXAMPLES. 16. Reduce \ of of f to a simple fraction. 1X3X5=15 new numerator. . , i s _A n( 15 2X4X8=64 new denominator. J d ?- Ans - * * 17. Reduce f of f of 8 to a simple fraction. Ans. 2f. CASE VI. To reduce fractions of different denominators to fractions having a common denominator. RULE. Multiply each numerator, taken separately, in- to all the denominators, except its own, for new numera- tors ; then multiply all the denominators continually to- gether for the common denominator. NOTE. When there are integers, mixt numbers, or compound frac- tions, given in the question, they must first be reduced to their sim- ple forms by their proper rules. EXAMPLES. 18. Reduce f , f , and f to fractions having a common de- nominator. 3X8X7=1681 5x4x7=140 I new numerators. 6X8X4=192 J And fff iff |4|=Ans. 4x8x7=224 common denominator. 19. Reduce f, f- off, and f to fractions having a com- mon denominator. Ans. ff|, |f |, |||. 2CU, Reduce f , f and 7| to a common denominator. Ans, Iff, Ao, VVV- VULGAR FRACTIONS. $y 21. Reduce , f, -2 of T 3 T , and ~ of 14f to a common de- nominator. Ans. -.' CASE VII. To reduce any fractions to others, which shall have the least common denominator. RULE. Find the least common multiple (by prob. 3d) of all the denominators of the given fractions, and it will be the common denominator required ; divide the common de- nominator by. the denominator of each fraction, and multi- ply the quotient by the numerator, the product will be the numerator of the fraction required. EXAMPLES. 22. Reduce , f , and -f- to fractions having the least com- mon denominator. 2)4 8 7=denominators. 2)2 4 7 1 2 7x2x2x2=56 least com. multiple.=to the least common denominator. Then 56-^-4x3=42 first numerator. 56-^-8x5=35 second do. 56-^-7x6=48 third do. Whence, |f, |f, I-*. Au. 23. Reduce |, f , and to fractions with the least com- mon denominator. Ans. , CASE VIII. To reduce a given fraction to another equal to it, that shall have a given denominator. RULE. Multiply the numerator by the given denomina- tor, and divide the product by the former denominator 5 the quotient, written over the given denominator, will form the fraction required. EXAMPLES. 24. Reduce f to a fraction of the same value, whose de nominator shall be 12. 2xl2=24-f-3=8, And -,-% Aus. 6 58 VULGAR FRACTIONS. 25. Reduce f to a fraction of equal value, whose denom- inator is 9. Aus. 7 9 =rf ' CASE IX. To reduce a given fraction to another equal to if, that shall have a given denominator. RULE. Multiply the denominator by the given numera- tor, and divide the product by the former numerator, the quotient, written under the given numerator, will form the fraction required. EXAMPLES. 26. Reduce f to a fraction of the same value whose nu- merator shall be 12. 12x3-^-2=18. And ||. Ans. 27. Reduce" f to a' fraction of the same value whose nu- merator shall be 15. Ans.J^f. CASE X. To reduce fractions from a less denomination to a greater / retaining the same value. RULE. Make the given fraction a compound one by comparing it between the denomination given and that to which it is to be reduced ; then reduce this compound frac- tion to a simple one. EXAMPLES. 28. Reduce of a farthing to the fraction of a pound. 4 of i of T V of A; then /^^fe } *** = > > - Ans * 29. Reduce f of a penny to the fraction of a pound. 30. Reduce f of a pennyweight to the fraction of a pound Troy. Ans. ^Ib. 31. Reduce f of an ounce to the fraction of a cwt. Ans. ^ T cwt. 32. Reduce | of an inch to the fraction of a mile. Ans. T^g-jo- ^* 33. Reduce J of a nail to the fraction of a yard. Ans. G \ yd. 34. Reduce J of a minute to the fraction of a year. Aug. ^ ear, VULGAR FRACTIONS. 59 CASE XI. To reduce fractions from a greater denomination to a less, retaining the same value. RULE. Multiply the numerator of the given fraction by the parts contained in all the denominations between if, and that, to which it is to be reduced, for a new numerator, which, placed over the denominator of the given fraction, will form the fraction required. EXAMPLES. 35. Reduce TSTT ^ a pound to the fraction of a farthing. 36. Reduce 3^ of a pound to the fraction of a penny. Ans. |d. 37. Reduce ^| of a pound Troy to the fraction of a pen- nyweight. Ans. f pwt. 38. Reduce ^| 7T of a cwt. to the fraction of an ounce. Ans. oz. 39. Reduce TTT^TO" f a m ^ e to the fraction of an inch. Ans. f in. 40. Reduce 6 - 4 of a yard to the fraction of a nail. Ans. f nail. 41. Reduce asr!?^ f a vear to the fraction of a minute. Ans. min. CASE XII. To reduce a mia^t fraction to a simple one. RULE. 1. When the numerator is a mixt number, re- duce it to an improper fraction ; then multiply the denom- inator of the fraction by the denominator of the fractional part for a new denominator. EXAMPLES. 42. Reduce to a single fraction. 48 36x3+2=110 numerator. 48x3= 144 new denominator. And }^=f4 An*. 2. When the denominator is a mixt number, reduce it as before, then multiply the numerator of the fraction bv 60 VULGAR FRACTIONS. the denominator of the fractional part for a new numera- tor. 47 43. Reduce to a simple fraction. 65! 65x5-1-4=329 denominator. A . o~r_r A 47X5= 235 new numerator. Ar CASE XIII. To reduce any mixt quantity of coins, weights or meas- ure to the simple fraction of an integer. RULE. Reduce the given number to the lowest denom- ination in it for the numerator, and the integer to the same denomination for the denominator of the fraction required. s. d. 41. Reduce 18 4^ to the fraction of a pound. #. d. 18 41 20 12 12 220 240 4 4 Andfff={-HAns, 882 numerator. 960 denom. 45. Reduce 8 7 p\vt. to the fraction of a Ib. Troy. Ans. if I Ib. 16. Reduce 3 14 12 7 drs. to the fraction of a cwt Ans. Iff if cwt. 17. Reduce 7 34 1 2 11 inches (o the fraction of a mile. Ans. |||p mile. -13. Reduce 145 18 40 13f seconds to the fraction of a vear. Ans. fVYsVeWc y ear * CASE XIV. To find the value of a fraction. RULE. Multiply the numerator of the given fraction by the parts contained in the next less denomination, and di- vide the product by the denominator, and thus continue to do till the fraction is reduced to the lowest denomina- VULGAR FRACTIONS. (>1 EXAMPLES. 49. What is the value of 4 of a pound r 4 20 7)80(11 51d. 77 3 12 36 35 ~T Ans. 11 5i d. questions. Answers. 50. What is the value of 4 of a guinea ? 12 5i-fi qrs. 51 ^ofacwl? 3181010|drs. 52 2 - f a mile ? 68428 in. 53 I of a yard ? 3 2 n. 54 fhhd.ofale? 21 2| qrs. 55 of a year ? 9 1 2 8 h. 56 | of a month? 3 3 12 li. ADDITION OF VULGAR FRACTIONS. RULE. 1. Reduce compound fractions to simple ones; mixt numbers to improper fractions ; fractions of different denominations to the same, and all of them to a common denominator. 2. Add all the numerators together, and place their sum over the common denominator. PROOF. Find the value 1 of the given fractions severally and add them together ; then find the value of the fraction making the an- swer ; if they agree, the work is right. EXAMPLES. 57. Add f and f together. 3X5=15 4X4=16 31=sum numerators. And fiHJ. AHS, 4X5=20 denominator. 6* 62 VULGAR FRACTIONS. 58. What is the sum off, 3|, and i off ? Ans. 4f. 59. Add -i- of a . T \ of a s. and of a d. together. Ans. fH- GO. What is the sum of -J- of a foot, yd rod, J fur. mile ; ? Ans. -f|i=7 8119 2i barley-corns. 61. Add } of a week. day. h. ] m. and f sec. together. Ans. jfffii=2 6 45 12f seconds. SUBTRACTION OF VULGAR FRACTIONS. RULE. Prepare the fractions as in Addition, and the difference of the numerators, written over the common de- nominator, will form the fraction required. NOTE 1. To subtract a fraction from a whole number, take the numerator from the denominator, and 1 from the Avhole number. Ob- serve the same rule in mixt numbers, when they have a common de- nominator. 2. When the lower fraction is greater than the upper, sub- tract the numerator of the lower fraction from the denominator, and fo the difference add the upper numerator, carrying 1 to the whole number. EXAMPLES. 62. What is the difference between f and f ? 5X8=40 3X6=18 22=diff. of the numerators. 7 T . nsii A 6x8=48=comniou denominator. J 63. What is the difference between 9| and f of 6 ? Ans. 7 T V. 64. What is the difference between f of 6i . and | of a shilling ? Ans. 2f. 65. From f of a cwt. take f of an oz. An. 66. What is the difference between ^yd. and f of a mile? Ans. f|3. 67. From a year take f of an hour. Ans. -f f; 68. From 99 take T V Ans. 69. From 11| Uke5f. An- 70. From 98 f& take 45 |f . Ans, VULGAR FRACTIONS, MULTIPLICATION OF VULGAR FRACTIONS. RULE. Reduce whole or mixt numbers to improper fractions, compound fractions to simple ones, then multiply the numerators into each other for the numerator of the product, their denominators into each other for the denom- inator of the product. NOTE. A fraction is best multiplied by an integer by dividing the numerator by it, if it can be, otherwise, multiply the denominator by it. Proof by Division. EXAMPLE;?. 71. Multiply 4 by |. =f - An8 -*- 72. Multiply 12-& by 6 7 T 7 . An*. 80 T f. 73. What is the product off and 14 ? Ans. 10|. 74. What is the product of 8 and 4 of 9 ? Ans. 57| DIVISION OF VULGAR FRACTIONS. RULE. Prepare the fractions as in multiplication ; then invert the divisor, and proceed as in multiplication. PROOF. By multiplication. EXAMPLES. 75. Divide f by . 5 S X X 4 3=!=- 76. What is the quotient of 4 by 7 r Ans. ^. 77. Divide 8 by 4, of 9. Ans. 1. 78. Divide 84 by 7-f. Ans. l T y . 79. Dividef of | by A of 6 A. Ans. ^j. 80. Divide 8 by 12. Ans. f . NOTE. Multiplication and division of vulgar fraction?, as in ivhole nv.rnber.-, muuia-'ly prove each other. That the rules give a true re- sult Vv''l] appeal evident by putting <'ny two whole numbers into the form of fractions, ai ;iii them as these rules direct, and '1:6 rcvajt oft v.'iti: lliiit of the -:mc kind ia whole numb* Qk DECIMAL FRACTIONS. PRACTICAL QUESTIONS IN VULGAR FRACTIONS. J. AVhat is the sum, difference, product and quotient of -li and i? ? Ans. sum, iy-. diff. ^. product, |f|. quotient l^f 2. The difference of two numbers is 1 |f , the less number 2*- ; what is the greater number ? Ans. 3f . 3. What number is that, which, if added to 3f , will give the sum 8|f ? Ans. 4 T 7 T . 4. What is f of 130f ? Ans. 81|. 5. What number is that, which, if multiplied by a. will produce 25| P Aus. 42J. 6. What number is that, which, if divided by % will be 10-| ? Ans. 14. DECIMAL FRACTIONS. ~3. A DECIMAL is the tenth part of an unit. 2. If 1 lb. or yd. was divided into ten equal parts, and each of these parts into ten other equal pans, and each of these again into ten others, and so on in a ten-fold propor- tion, without end, then would an expression of any num- ber of these parts be called a decimal fraction. 3. The denominator of a decimal fraction is always 1, with as many ciphers annexed as the decimal has places. The denominator therefore, being known, is never written, the parts being distinguished by a dot prefixed, called the separatrijc, or decimal point ; thus .5= T %. 4. The numerators of infinite decimals consist of the same figure, or figures, repeated ; and their denominators consist of as many nines as there are figures in the repe- tend; thus G -, and 5. A pure decimal is when the fraction is proper ; as >5=A- 6. A mixt decimal is when the fraction is improper; as 19,45=^M, or 19 T W 7. When the denominator is an even part of the nume- rator, increased by affixing ciphers to it, the decimal equal in value to such a fraction will be/wite aud complete : as. DECIMAL FRACTIONS. Qj 8. But if the denominator is no even part of the nume- rator thus increased, the decimal equal in value to such a fraction will be infinite ; that is, it will constantly repeat either one figure only, as -f = ,666, Sec. ; or else it \vi!i re- peat a certain number of figures perpetually, as 4 = 5714285 & c . ; and T 3 f =,181 81 8 &c. forever. 9. Those decimals which constantly repeat or circulate, are called repetends or circulates. 10. Those decimals, in which one figure only repeats, are called a single repetend ; as ,333 Sec. 11. Those, in which several figures repeat, are called a compound repetend : as ,185185 oce. 12. A dot is placed over a single repetend, and over the first and last figure of a compound repetend, for the greater perspicuity in the operations of repeating decimals ; as ,318 185 &c. 13. In a compound repetend, any one of the circulating figures may be made the first of the repetend; thus in the repetend 6,8395395395 &c. it may be made 6,83953 ; or 6,839539. By which means any two or more repetends may be made to begin and end at the same place ; and ihen, they are said to be similar and conterminous. 14. If the numerator has not so many places as the de- nominator has ciphers, make them equal by prefixing ciphers ; thus, T H = ,05 ; 7 ^ =,007. 15. In all decimal numbers, if the decimal point be re- moved one place towards the right hand, every figure will be increased in a ten-fold proportion ; thus, 4,856 48.56 485,C 4856, each of which is ten times of greater value than the one preceding. Consequently, 16. By removing the decimal point one place towards the left hand, the value will be decreased in a ten-fold propor- tion ; thus, 4856, 485,648,56 4,856 ,4856. 17. Ciphers, placed at the left hand of decimals, de- crease their value in a ten-fold proportion, by removing them further from the decimal point; ,000005 = J-Q-O O - TTvith the facility. ADDITION OF DECIMALS. CASE I. To add finite 'decimals. RULE. Place the numbers under each other according to the value of their places ; add them as in whole mi in- DECIMAL FRACTIONS. Q^ berg, set the decimal point as many places from the right hand as are equal to tS'e greatest number of decimal places in any one of the given decimals. PROOF. As in \vhob numbers. EXAMPLES. 1. 2. 3. 83,845 38,45 1.074 ,80435 8,078 43'.8074 3,0085 43.34 ,8U 487,08 1,04 ,1007iU ,3874 38,7454 9,000 ,0007 18,003 1,3471 575,20595 Sums 147,6564 53,944-584 In example first, five being the greatest number of given decimals, therefore the decimal point is set five places from the right hand. C 4 ASE II. To add repeating decimals, when there is a single repetend. RULE. Make thorn conterminous, that is, end together, and then add them as in whole numbers, adding to the last or left hand place of decimals, as many units as there are nines in the sum 5 the last figure will be one of the repe- tends. EXAMPLES. 4. Add 123,23 63,516 0,3' 8.8 4,83 and 18.016 to- gether. 123,333 63,516 tf: 0,333 .1 3 8,800 4,833 18,016 218,833 08 DECIMAL FRACTIONS. n. Add 8,3428,83,1043 and 7,34 together. 8,3422 8,8888 | 3,1043 27,6798 NOTE. In the 4th example the sum of the repetend? is 21, AvhK u es two nines, therefore 2 i? added to the sum of the repetends. The sum of the repetends in example 5, being 17, give.*; one nine, Therefore 1 is added to the sum of the repetends. CASE III. To add decimals having compound repetends. RULE. From the place where all the repetends begin together, continue each decimal to a number of places equal to the least common multiple of all the number of figures in each repetend; then add as before directed, and to the last place add as many units as there are 10's in the place where all the repetends begin together, and the figures in these two places will be l\ie- first and last of the repetends. EXAMPLES. 6. Add 2,9543 1,04 3,7 4,065820 and 4,731 to- ther. Number of figures in each repetend. ' 4,3,2,6,4 2,954395433543 1,041041041041 3,737373737373 4,065826065820 gether. 1,1,1.1,1 4,731473147314 16,530109431099 ;;X2X2=12 least com. raultiple=to the number of places to be in the repetend. In the above example the number of 10's where the repetends be- gin i* 2, therefore 2 is added to the last place or right hand figure. DECIMAL FRACTIONS. gg SUBTRACTION OF DECIMALS. CASE I. \ To subtract finite decimals. RULE. Place the numbers according to their value ; subtract as in whole numbers, and point off for decimals, as in Addition. EXAMPLES. 1. 2. From 793,74 38,4567 Take 324,73564 8,2 469,00436 30,2567 491,9926 CASE II. To subtract repeating decimals with single repetends. RULE. Place and subtract them as usual, observing, when the subtrahend is the greater number, to increase the upper figure by 9 only, and in such case to carry 1 to the next place. EXAMPLES. 4. 5. 6. From 45,03333 34,5289 14,4516 Take 9,84136 7,583 3 9,3ooe 35,79196 26,9456 5,1516 CASE III. When the decimals are compound repetends. RULE. Prepare them as directed in Case II. in addi- tion ; then subtract, observing to add 1 to the right hand place of the subtrahend, if one is borrowed where the repe- tends begin together ; the remainder either whole or in part will show the repetend. EXAMPLES. 7. From 9,4i78 take 5,56. 3,2 3x2=6=multiple. 9,4178178 > similar and 5,56565653 conterminous. 3,8521612 yO DECIMAL FRACTIONS. MULTIPLICATION OF DECIMALS. GENERAL RULE. CASE I. Place the numbers under each other without any regard to their value ; multiply them as in whole numbers, and, for decimals, point off from the right hand as many places in the product as there are decimal places in both the factors. EXAMPLES. Multiply by i. 84,374 8,5 2. ,347 7,04 1388 24290 2,44288 421870 674992 717,1790 CASE II. 33736 59038 ,624116 When there are not so many places in the product as there are decimals in the two factors. RULE. Multiply as before, and make up the deficiency by prefixing ciphers* 4. 5. 6. 5,72 3,347 ,34567 ,006 ,0008 ,0003 9 03432 ,0026776 .,000103701 CASE III. To multiply any decimal by 10, 100, 1000, &e. RULE. Remove the decimal point in the multiplicand as many places towards the right hand as there are ciphers in the multiplier. 7. Multiply ,8744 by 10, 100, 1000, &c. Ans. 8,744 87,44874,4. NOTE. Any number multiplied by a pure decimal is diminished, ;jbut by a mixt, it is increased. DECIMAL FRACTIONS. CASE IV. 71 When the multiplicand has a single repetend and the multi- plier a single figure. RULE. Multiply as usual, ubserving to add to the last place in the product as many units as it contains nines, and that place will be a repetend. EXAMPLES. Multiply by 8. 8,7016 5 43,5083 9. 34,444 CASE V, When the multiplier consists of several figures. RULE. Multiply as before directed, making each partic- ular product conterminous, by continuing the single repe- tend of each towards the right hand. EXAMPLES. 10. Multiply 234,64 by ,634 93857 703933 14078666 148,76457 11. 84,36 ,425 42183 16873s 33746c G 35,85583 CASE VI. When the multiplier is a repetend. RULE. Multiply as usual; add a cipher to the product, or which is the same, cut off one decimal less than usual, and divide by 9, continuing the quotient till it becomes a single or compound repetend, which will be the answer. DECIMAL FRACTIONS, EXAMPLES. 12. 13. 14. Multiply 8,35 712,54 37,23 by ,04 . ,03 ,26 9)3,340 9)213,763 9)22,340 j37i=true product. 23,751*48 2482 7446 9,928 CASE VII, When the multiplicand is a compound repetend, and the multiplier a single figure only. RULE. Multiply as in whole numbers, observing to add to the right hand place of the product as many units as there are tens in the product of the left hand place of the repetend. The product will contain a repetend whost places are equal to those in the multiplicand. EXAMPLES. 15. 16. 17. Multiply 582,347 924,378 3749,23 by 8 ,03 ,007 4658,778 27,73135 26,24464 CASE VIII. When the multiplier consists of several figures. RULE. Multiply as before, making each particular pro- duct conterminous towards the right hand. DECIMAL FRACTIONS. 73 EXAMPLES. 18. 19. Multiply 873,2586 8427.3012 by 43,7 4370,2 61128106 168546025 26197759? 58991 1089n 349303^634 2528 i 9038i9o 3370920509205 38161,40338 36828992,02332 CASE IX. When the multiplier is a compound repetend. RULE. Multiply each figure in the repetend, as in whole numbers, and add the several products together; then add the result to itself by placing the first left hand figure so many places forward as exceeds the number of places in the repetend by one, and the rest of the figures in order after it; proceed thus till the result last added be carried beyond the first result ; add these several results together, heginning under the right hand place of the first, and from that place point off with a dot as many figures for a repe- tend as there are figures in the repetend of the multiplier, EXAMPLES. 20. 21. Multiply 1235,01 42710,36 by 3,26 ,20403 741006 12813108 247002 17084144 370503 8542072 First result. 4026.1326 8714,1947508 first result, '40261326 87141975 4026 &c. 871 &c. True product 4030,1627 8714,2818936 y-j, DECIMAL FRACTIONS. CASE X. When the multiplicand and multiplier both are compound repetends. RULE. The places of the repetend in the product will be uncertain as to their number, -and can only be determined by continuing and repeating the first product, which will contain a certain repetend., being equal in places to those of the multiplicand. NOTE. If the finite figures, (that is the figures preceding the repe- tend) are few, and the places of the repetend many, the work may he shortened by subtracting the finite figures from those of the repe- tend, whidh will give a new multiplier. EXAMPLES. 22. Multiply 3,145 4,297 by 4,297 4=finitepart. 4,293=new multiplier. 3.145 4,293 9436 28309o 6290 9 o 12581318 JFirst product 1350343636 3 6 &c. 13503436s &e. 135034 &e. 135 &c. True product 13,5169533 DIVISION OF DECIMALS. CASE I. RULE. Place the numbers and divide them as in whole Burnbers, and point off, at the right hand, for decimals, us many places as the decimal places in the dividend exceed those in the divisor. DECIMAL FRACTIONS, y^ OBSERVATION 1. If after dividing there should not be so many places in the quotient and divisor together as there are in the divi- dend, make them equal by prefixing ciphers to the quotient. 2. The quotient figure is always of the same value with that figure of the dividend, under which the unit's place of its product stand*. Or, 3. The decimals in the quotient and divisor added together must always be equal in number with those in the dividend. 4. When the decimal places in the divisor and dividend are equal in number, the quotient will be whole numbers. 5. When the decimals in the dividend exceed those in the divisor^ the decimals in the quotient must be equal to that excess. 6. If the decimals in the divisor exceed those in the dividend, they must be made equal by annexing ciphers to the dividend ; and then all the figures in the quotient will be whole numbers, till all the ciphers annexed are used. 7. When there is a remainder after division, ciphers may be an- nexed to the dividend, and the work prolonged at pleasure, and in such cases the quotient will be decimals. In division of decimals, there may occur nine varieties, with respect to the nature of the three sorts of numbers ; viz. 1. Integers, or whole numbers. 2. Mixt numbers, that is, integers and decimals. 3. Pure decimals, that is, without any whole numbers. *fhe dividend, therefore, being itself of three kinds, and capable of a divisor of three kinds, there may arise nine varieties, viz. Whole number. 1. A whole number may be divided by a 2, A mixt number may be divided by a 3. A pure decimal may be divided by a Mixt number. Decimal. Whole number. Mixt number. Decimal. Whole number. Mixt number. Decimal. The various cases more fully explained by the subse- quent operations at large, will, with attention to the prece- ing observations, render Division of Decimals sufficiently easy and plain. The whole 1 may be exemplified in this simple example ; Let looG be divided by 12. First variety. 12)1866,0 155,5 (By obs. 7 and 5.) DECIMAL FRACTIONS. In variety first the divisor and dividend are both whole numbers, and because there was a remainder of 6 a cipher is annexed to the dividend (obs. 7.) which gives one decimal figure in the quotient (obs. 5.) Variety 2d. Variety 3d. Variety 4th. Variety 5th. Variety 6th. 12)186,60 15,55 (By obs. 5.) 12),18660 ,01555 (By obs. 1.) 1,2)1866,0 1555 (By obs. 4 and 6.) 1,2)186,60 155,5 (By obs. 3 and 5.) 1,2),18660 ,1555 (By obs. 3.) Variety 7th. ,12)1866,00 15550 (By obs. 4 and 6.) Variety 8th. ,12)18,660 155,5 (By obs. 5.) Variety 9th. ,12),18660 1,555 (By obs. 5.) The following examples will further illustrate the gen- eral rule, and more clearly exemplify the preceding obser- vations. 10. Divide 295,75 by 8,45. 295*75-j-8,45=:35 Ans. 11. Divide ,4884 by ,0074. 4884-r-,0074==66 Ans. NOTE 1. In examples 10 and 11, the decimals in the divisor and dividend are equal, the quotients, therefore, in both instances are whole numbers. See obs. 4. 12. Divide 780.516 by 24,3. 780,51624,3=32,12 Ans. 13. Divide ,3953 by ,67. ? 3953-r- ? 67= ? 59 Aps, DECIMAL FRACTIONS. yy 2. In examples 12 and 13, the decimal places in the dividend ex- ceed those in the divisor by 2 figures ; therefore two figures are point- ed off for decimals in the quotient. See obs. 5. 14; Divide 192,1 by 7,684. 192,1-7,684=25 Ans. 15. Divide 441. by ,7875 ,7875)441.0000(560 Ans.. 39375 47250 47250 00 3. In examples 14 and 15. the decimal places in the dividend are not so many as those in the divisor by 3 and 4, therefore ciphers are annexed (See obs. 6.) to make them equal ; and the quotient is whole numbers. See observation 4. 16. Divide 7,25406 by 957. 7,25406-r-957=,00758 Ans. 17. Divide ,0007475 by ,575. ,0007475-f-,575=,0013 Ans. 4. In examples 16 and 17, after the division was finished there were not so many places in the quotient and divisor added together, as there were in the dividend ; therefore, they are made equal by prefixing 2 ciphers to the quotient. See obs. 1. CASE II. To divide any whole, mixt, or decimal number by 10, 100, 1000, &c. RULE Remove the decimal point towards the left hand so many places, as there are ciphers in the divisor. EXAMPLES. 1. Divide 1866 by 10, 100. 1000, &e. Ans. 10)186,6 100)18,66 1000)1,866 &c. CASE 111. When the dividend has a single repetend and the divisor a single finite figure. RULE. Divide :.s usual, and when the repetend is brought down the quotient will begin to repeat. yg DECIMAL FRACTIONS, EXAMPLES. 2. Divide 734,02 by 8. 3. Divide 3184,6 by ,6. 8)734,02 ,6)3184,6 91,77 perpetual repeteud. 5306 perpetual repetend. CASE IV. When the divisor contains a number of finite figures. RULE. Divide as usual, and the quotient will repeat a single figure, but will not always begin when the repetend is brought down. EXAMPLES. 4. Divide 79,26 by,48. 5. Divide 1 06036,783 by 487,65. ,48)79,26(165,138 487,65)106036,783(217,4 48 97530 312 85067 288 48765 246 363028 240 341355 66 216733 C perpetual 48 195060 \ repetend. 186 21673 144 426 C perpetual 384 I repetend. 42 CASE V. When the divisor is a single repetend and the dividend a finite number. RULE. Multiply the dividend by 9, cut off from the right hand of the product one figure more than usual (this being the same as dividing by 10) for a new dividend; then divide the new dividend as usual, and the quotient will be the answer. Or place the given dividend under itself, but one place forward towards the right hand, and subtract 5 the remainder will be the new dividend. DECIMAL FRACTIONS. yg EXAMPLES, 6. Divide 572,4 by ,8. Or, 572,4 9 5724 a figure forward. ,8)515,16 = newdivid'd. ,8)515,16 as before. 643,95 Ans. 643,95 Ans. CASE VI. When the divisor consists of finite numbers joined to the repetend, and the dividend is finite. RULE. Subtract the finite numbers of the divisor from the divisor itself* and the .remainder will be a new diviser, then prepare the dividend as in Case V. for a new divi- dend which divide as usual. EXAMPLES. 7. Divide 8569,88 by 4,86*. From 4,86 From 8569,88 Take 48 =finite number. Take 856988 4.38=new divisor. 7712,892=new dividend. Then 7712,892-4-4,38 =1760,9 Ans. CASE VII. When there is a repetend both in the divisor and dividend. RULE. Prepare them as before directed in Cases V. and VI, then divide and the quotient will be either finite, a sin- gle, or a compound repetend. EXAMPLES. 8. Divide 234,6 by 7. 9. Divide 134,26 by ,6. From 234,6e From 134,26 6 Take 2346 13426 7)21 l,20=new dividend. ,6)120,84 =^new dividend, 30,1 714285= Ans. 201,4= Ans. CASE VIII. When the divisor or dividend, or both contain compound repetends. RULE. Set the divisor and dividend under themselves so many places forwards to the right hand, ;is there are places in the repetend of the divisor exclusively ; subtract them and the remainders will be respectively a new divisor and dividend. 80 DECIMAL FRACTIONS. EXAMPLES. 10. Divide 243,306 by 11 1,98. From 243,306 243 111,98 11 243,063=new dividend. lll,87=new divisor. 111,87)243,063(2,172 Am. NOTE 1. If there is no finite part in the divisor, no subtraction must be made from it. 11. Divide 395,273614 by ,317. 395,273614 395273 ,317)394,878341(1245,673 Ans. 2. If there is norepetend in the divisor, whatever the dividend may be, no subtraction is to be made either in the divisor, or divi- dend. 12. Divide 319,28007*112 by 764,5. 764,5)319,280071 12(,4176375 Ans. 30580 13480 7645 58350 53515 48357 45870 24871 22935 19361 15290 40712 38225 2487 J Perpetual repetend DECIMAL FRACTIONS. g[ Xo IP. . 1 . A series of nines, infinitely continued, is equal to unity* or one. in the next left hand place ; thus, 0,999 &c. is equal to 1 : and ,0999 &c.=,l ; and ,00999 c.=,01 ; and 54,999 &c.=55. DEMONSTRATION. It is obvious that ,9=yk wants only T V of unity, and ,99 wants only T 7 , ,999 wants only y oV 5 of unity ; so that if the series were continued to infinity, the difference between that series of nines and an unit, would be equal to unity divided by infinity, that is, nothing. 2. A single repetend multiplied by 10, and then subtracted from that product, the remainder will be the same number, made finite, in the next superior place ; thus ,6666 &c. multiplied by 10 will be equal to 6,666 Sec. ; from which subtract ,666 &c. there will re- main 6 a whole number ; as 6,666 &c. ; 666 &c. ; 6 *=whole number. 3. If, therefore, a compound repetend be multiplied by an unit with as many ciphers annexed as are equal to the number of places in the repetend, and then subtracted from that product, there will remain at the left hand the same numbers made finite Avhich made the repe- tend ; thus 325 multiplied by 1000=325,325 from which if ,325 be subtracted, there will remain 325 made finite. 4. If any repetend be multiplied by so many nines as it contains places, the result will be the repetend made finite, for any number multiplied by 10 and once subtracted is the same as multiplied by 9 ; thus ,666 &c. X9=5,999 &c.=6. by note 1. And 527X 999= 526,999=527. by note 1. REDUCTION OF DECIMALS. CASE I. fo reduce a vulgar fraction to its equivalent decimal. RULE. Divide the numerator with ciphers annexed, by the denominator, the quotient will be the decimal. EXAMPLES. 1. Reduce |, | and f to decimals. 4)1,00 2)1,0 4)3,00 ,25 Ans. ,5 Ans. ,75 Ans. 2. Reduce fi to a decimal, Ans. ,916. NOTE. A whole number may be expressed decimally by annexing ciphers and the decimal point ; thus, 874=874,000 &c. 8 $2 DECIMAL FRACTIONS. CASE II. To reduce coins, weights, measures and time to decimal fractions. RULE. Place the numbers perpendicularly under each other, beginning with the lowest denomination, and, after annexing ciphers, divide it by so many as make one of" the next higher denomination, as in Reduction Ascending ; continue thus to divide till it is reduced as high as the question requires ; the last quotient will be the decimal. EXAMPLES. 3. Reduce 12 8 qrs. to the decimal of a . 4)2,0 12)850 20)127083 ,635416. Ans. ,635416. 4. Reduce 4s. to the decimal of a guinea. Ans. ,142857. 5. Reduce 7 13 pwt. to the decimal of a pound Troy. Ans. ,6375. 6. Reduce 4213 Ib. to the decimal of a ton. Ans. ,230803571428. 7. Reduce 3 14 Ib. to the decimal of cwt. Ans. ,875. 8. Reduce 412 inches to the decimal of a mile. Ans. ,00249368. 9. Reduce 52 days to the decimal of a year. Ans. ,142465753. 10. Reduce 3 18 14 18 seconds to the decimal of a year. Ans. ,01030117960426. CASE III. r o reduce shillings, pence and farthings to decimals by inspection. RULE. To half the greatest even number of shillings, add the farthings contained in the given pence and far- things, increasing the second decimal place by 5, when the shillings are odd, and the third place by 1 when the far- thiiigs exceed 12, and by 2 when they are more than 35 : the three places will be the decimal. DECIMAL FRACTIONS. 33 EXAMPLE. 11. Reduce 12 8 qrs. to the decimal of a pound. 6 =half the greatest even number of shillings* 34=farthings in the given pence and farthings. l=excess of 12. ,635=deeimal of a . Ans. ,635 . NOTE. If the second and third places of the decimal are 25, 50, or 75, the decimal is finite and complete ; but if not, more figures may be found by the following, RULE. If the second and third figures are under 25, multiply them by 4, and for every 24 add 1 to the product, and the result will be more places which may be annexed to the former number. If the second and third places are more than 25, multiply the excess of 25, 50, or 75 by 4, adding 1 for every 24, and so on till the decimal be- comes finite or infinite. EXAMPLE. 12. Reduce 12 8 qrs. to the decimal of a . 6 =half even shillings. More figures than Hint?.- 34=farthings in 8. 10=excess of 25. l==excess of 12. 4 635=decimal of a . 40 l=24*s in 40. 63541 41=t\vo more figures. 16=excess of 25. 4 635416 64 2=24's in 64. 66=tvvo more figures. ,635416 Ans. NOTE. Half the even number of shillings, with the decimal point prefixed is their decimal, and when the shillings are odd, a ci- pher annexed arid divided by 2, the quotient will be the decimal. 13. Reduce 1, 2, 3, 4, 5, 6, 7, shillings to decimals, \nswers ,05-,l-,15-,2-,25-,3-,35. 4 DECIMAL FRACTIONS. CASE IV. To find the value of a decimal. RULE. Multiply the given decimal by so many of the next less denomination as make one of the same with the given decimal, as in Reduction Descending, and cut oft* from the right hand of the product, as many places for decimals, as there are decimals in the given fraction ; in this manner proceed till the decimal is reduced to the lowest denomina* tion, each time cutting off as before ; the several denomi- nations on the left hand will be the answer. EXAMPLES. 14. What is the value of ,635416 of a ? 20 12,70833 12 ,50000 4 2,0000 Ans. 12 8| qraf 1 . 15. What is the value of ,142857 of a guinea ? Ans. 4s. 16. What is the value of ,6375 of a Ib. Troy ? Ans. 7 13 pwt. 17. What is the value of ,230803571428 of a ton ? Aus 4 2 13 Ib. 18. What is the value of ,875 of a cwt ? Ans. 3 14 Ib. 19. What is the value of ,00249368 of a mile ? Ans. 4 1 2 in. 20. What is the value of ,142465753 of a year ? Ans. 52 days. 21. What is the value of ,01030117960426 of a year ? Ans. 3 18 14 18 seconds. CASE V. To find the value of any decimal of a pound by inspection. RULE. Double the first decimal figure for shillings, adding one when the second figure is more than 4 ; call DECIMAL FRACTIONS. 85 the figures in the second and third places, after deducting 5, 04545454 tiple of the sev- eral given repe- ,027 ,025 ,112857 tends. ,02777777 J- | g ,02500000 FEDERAL MONEY. 1. By an act of the government of the United States, accounts- must be kept in dollars, dimes, cents, and mills. These de- nominations perfectly correspond in their nature with decimal frac-r tions, increasing and decreasing in tenfold proportion. The method of operation, therefore, is the same as decimal fraction?, or whole numbers. 2. By an act of Congress it was resolved, that there should be Pure. Standard. Two Gold (1. The Eatfe . =$10 weighing 247,5 grs. coins ; viz. { 2. The half Eagle . =5 123,75 f 1. The Dollar . . =1 371,25 2. Half Dollar . . =,50 cents. 185,625 Six Silver j 3. Quarter Dollar =,25 92.8125 coins; \\zA 4. Double Dime . =,20 74,25 j 5. Dime . . . =,10 37,125 LG. Half Dime . . =,05 18,5625 2 Copper < 1. The Cent . . =,10 mills. 208 coins ; viz. ( 2. The half Cent . . =,5 mills. 104 270 grs. 135 416 208 104 83,2 41,6 20,8 208 104 Any sum in federal money may be read either in the lowest denom- ination, or partly in the higher, and partly in the lowest ; thus, $54,321 may be read 54321 mills, or 5432 cents 1 mill, or 543 dimes 2 cents 1 mill, or 5 eagles 4 dollars 3 dimes 2 cents 1 mill ; all which denominations may be easily distinguished by the decimal point, thus JE.:/. dot- di. cent mill, 5,4, 3,2 , 1. The method best adapted to practical purposes, and which has been sanctioned by a law of the United States, is the decimal form of expres- sion by a decimal point, making the dollar the money unit. Dollars, therefore, will occupy the place of units, and the less denominations will be decimal parts of a dollar and distinguished by the decimal point. Qg FEDERAL MONEY. The established custom is to read them in dollars cents and mills ; thus, $54,32,1. NOTE. Some accountants omit the decimal point, keeping the several denominations distinctly apart. REDUCTION OF FEDERAL MONEY. CASE I. To change, dollars into cents. RULE. Add two ciphers. EXAMPLE. 1. In 89 how many cents ? Ans. 8900 c. CASE II. To change dollars into mills. RULE. Add three ciphers. EXAMPLE. 2. In $79 how many mills ? Ans. 79000 m. CASE III. To change mills to dollars and cents. RULE. Cut oft' the three right hand figures, the left hand figures will be dollars, the two first figures on the right hand will be cents and the third mills. EXAMPLE. 3. In 8748 mills how many dollars and cents ? 88,748=g8,74,8 * Ans. $8,74,8. CASE IV. To reduce cents to dollars. RULE. Cut off t!e two right hand figures for cents, the left hand figures will be dollars. EXAMPLE. 4. Reduce 74874 cents to dollars. Ans. $748,74. CASE V. To change pounds to dollars, Add a cipher and divide by 3. FEDERAL MONEY. gg EXAMPLES. Reduce 36 to dollars. 3)360 $120 Ans. $120. $. la 225 how many dollars ? Ans. $750. CASE VI. To reduce pounds and shillings to dollars, cents and mills. RULE To the pounds annex half the greatest even number of shilling, to which annex three ciphers if the shillings are even ; but if the shillings are odd, to the pounds annex a 5 and two ciphers ; divide by 3, cut off three right hand figures for cents and mills, the left hand figures will be dollars. EXAMPLES. 7. In 44 16 how many dollars, cents and mills ? 44=pounds. 8=haif the greatest even number of shillings-, 000 3)448000 $149,33,3|. Ans. g!49,33,3i. 8. Reduce 74 15 to dollars, cents and mills. 3)747500 $249,16,6-| Ans. $249, 16,6|. CASE VIL To reduce pounds, shillings, pence and farthings to dollars, cents and mills. RULE. For the shillings proceed as in Case VI. to which add the farthings contained in the given pence and farthings, increasing their number by 1 when they exceed 12, by 2 when they are more than 35, to which annex one cipher; divide the whole by three, and cut off three right hand figures for cents and mills, the left Land figures will 1 be dollars. 90 FEDERAL MONEY. EXAMPLES. 9. In 34 18 9 how many dollars, cents arid mills ? 3)349400 $116,46,Gf Ans. $116,46,6f. 10. In 93 11 4 how many dollars and cents ? Ans. $311 90. CASE VIII. To reduce dollars to pounds and shillings. RULE. Multiply the dollars hy 3, doubling the right Land figure for shillings. EXAMPLES. 11. In g!28 how many pounds and shillings ? * 38 8 Ans. 38 8. 12. In $74 how many pounds and shillings P Ans. 22 4. CASE IX. To change dollars and cents to pounds, shillings, fyc. RULE. Multiply the dollars and cents by 3, and cut off three right hand figures ; the figures on the left hand will he pounds, and those on the right decimals of a pound, which being multiplied by 20, 12 and 4, (as in Case IV. Reduction of Decimals,) each time cutting off the three right hand figures, will give the answer ; or the value of the three right hand figures maybe found by inspection, (as in Case V. of Decimals.) EXAMPLE. 13. In $344 48 how many pounds, shillings, &c. ? 3 103,344 Or by 344.48 20 Inspec. ' 3 s. 6,880 103.344 12 6 10.i=value of ,344 by in. d. 10,5GO 4 qrs. 2,240 Ans. 103 6 1CU. FEDERAL MONEY. g CASE X. To reduce dollars, cents and mills, to pounds, shillings, pence js. RULE. Multiply the given sum by 3 and cut off four right hand figures, and proceed as in Case IX. EXAMPLE. 14. In $116,46,6f how many pounds, &c. ? 3 34,9400 20 s. 18,8000 12 d. 9,6000 4 qrs. 2,4000 Ans. 34 18 9J. CASE XI. To change Sterling to Lawful Money. RULE. Add i to'the Sterling the sum will be Lawful. EXAMPLE. 15. In 347 Sterling, how much Lawful ? 3)347=sterling. 115 13 4 added. 462 13 4=lawful. Ans. 462 13 4. CASE XII. To change Lawful to Sterling Money. RULE. From the Lawful subtract , the remainder will be Sterling. EXAMPLE. 16. Reduce 462 13 4 Lawful to Sterling. 4)462 13 4=lawful. 115 13 4 subtract. 347 00 0=sterling, Ans. 347, g*j FEDERAL MONEY. CASE XIII. To reduce New-England, Virginia, Kentucky and Tennessee currency to Federal Money. RULE. Add a cipher to the pounds and divide by 3. NOTE. If there are shillings, pence, &c. given in any case, they must always be reduced to the decimal of a pound and annexed to the given pounds before dividing by 3 ; and in all such cases three figures must be cut off at the right hand for decimals of a dollar. EXAMPLES. 17. Reduce 36 to Federal Money. 3)360 120 Ans. $120. 18. Reduce 45 16 to Federal Money. Ans. 8152,66,6f. CASE XIV. To reduce New-York and North- Carolina currency to Fed- eral Money. RULE. Add a cipher and divide by 4. EXAMPLE. 19. Reduce 44 New-York and North-Carolina curren- cy to Federal Money. 4)440 110 Ans. jgl 10. CASE XV. To reduce New-Jersey. Pennsylvania, Delaware and Mary- land currency to Federal Money. RULE. Multiply by 8, and divide the product by 3, the quotient will be the answer. EXAMPLE. 20. Reduce 243 New-Jersey to Federal Money. 8 3)1944 648=federal money- Ans. $648. FEDERAL MONEY. 93 CASE XVT. To reduce South-Carolina and Georgia currency to Federal Money. RULE. Multiply by 30 and divide the product by r, the quotient will be the answer. EXAMPLE. 21. Reduce 300 South-Carolina and Georgia to Feder- al Money. 300 30 7)9000 1 285,7 l,4f=federal. Ans. $1285,7J,4f . CASE XVII. To reduce Canada and JVova Scotia currency to Federal Money. RULE. Multiply by 4, and the product will be dollars. EXAMPLE. 22. Reduce 150 Canada or Nova Scotia to Federal Money. 150 4 ( 600=Federal. Ans. $600. CASE XVIII. To reduce Livres Tournois* to Federal Money. RULE. Multiply the Livres by 4 and divide by 21. EXAMPLE. 23. Reduce 1000 livres to federal money. 1000 4 21)4000(190,47,6/r. Aug. $190,47,6^. * The term u Tournois," when applied to money in France, is of the same import as u Sterling" when applied to money in Eng- land. 9 FEDERAL MONEY. CASE XIX. To reduce Federal Money to New England, Virginia, Ken- tucky and Tennessee currency. RTTI.F.. Multiply by 3, and cut off three right hand fig- ures, the left hand figures will be pounds, the figures cut off, decimals of a pound, the value of which may be found as in Case IX. EXAMPLE. 24. Reduce $345,69 to Massachusetts, &c. currency. 345,69 3 103,707=103 14 1|. Ans. 103 14 If. CASE XX. To reduce Federal Money to New York and N. Carolina currency. RULE. Multiply the dollars and cents by 4 and cut off three right hand figures for decimals, the left hand figures will be pounds. EXAMPLE. 25. Reduce $961,54| to New York and N. Carolina cur- rency. 961,541 4 384,619=384 12 41. Ans. 384 12 4. CASE XXI. To reduce Federal Money to New Jersey, Pennsylvania, Delaware and Maryland currency. RULE. Multiply by 3 and divide by 8, cut off three right hand figures for decimals. FEDERAL MONEY. 95 EXAMPLE. 26. Reduce $382 98 4 to New Jersey currency. $382 98 4X3~8=143 12 4i. Ans. 143 12 4. CASE XXII. To reduce, Federal Money to South Carolina and Georgia currency. RULE. Multiply by 7 and divide by 30, cut off three right hand figures for decimals. EXAMPLE. 27. Reduce $530 01 to South Carolina and Georgia cur- rency. 530 01x7-*-30=l23,669=Ans. 123 13 4|. CASE XXIII. To reduce Federal Money to Canada or Nova Scotia cur- rency. RULE. Divide by 4, the quotient will be pounds and decimals. EXAMPLE. 28. Reduce $494 50 8 to Canada or Nova Scotia cur- rency. 4)494.50,8 123,627 123 12 G-\. Ans CASE XXIV. % To reduce Federal Money to Liures Tournois. RULE. Multiply by 21 and divide by 4, the quotient will be livres. EXAMPLE. 29. Reduce $190 47 6^ f to Livres Toiirnois. 190 47 6^X21-^4-^1000. AIIS. 1000. 96 FEDERAL MONEY. ADDITION OF FEDERAL MONEY. RULE. Place the several denominations under each oth- er, and add them as in whole numbers, or decimals. TABLE OF FEDERAL MONEY. 10 Mills marked m. . . 'make 1 Cent marked e. 10 Cents 1 Dime . . . d. 10 Dimes 1 Dollar $ or dolls. 10 Dollars .1 Eug!e Eaj NOTE. When the number of cents is less than 10, a cipher must always be written in the place of dimes ; as ,09=nine cents, &c. EXAMPLES. Add 8 eag. 6 dolls. 4 dim. 8 m. ; 7 dolls. 6 dim. 7 cents, 8 mills ; 8 dolls. 8 dim. 9 dim. 8 cents ; 4 eag. and 8 mills together. Eag. $ d. c. m. $ c. m. ' 8 6 4 8 . - 6 40 8 7 6 7 8 1 7 67 8 8 8 $ 8 80 9 8 It 98 4 8 c 40 00 8 O 14 3 y 7 4 C/3 i $143 87 4 * NOTE. The second method is preferable, and is adopted in this work. PKOOF. As in whole numbers. SUBTP^JICTION OF FEDERAL MONEY. RULE. Place the several denominations and subtract them as in whole numbers, or decimals. EXAMPLES. 1. 2. 3. $. c. m. $. c. m. C. c. m. From 873 28 2 48 348 43 3 Take 87 34 7 7 38 4 97 785 93 5 40 61 6 i. From 2 eagles take ,49 3 mills. 251 43 3 Ans. 1 9 50 7 rn. FEDERAL MOXKY 0r MULTIPLICATION OF FEDERAL MOXEY. CASE I. To multiply the several denominations by any given number. RULE. Place the given numbers and multiply them as in whole numbers, or decimals, and point off in the pro- duct as in the multiplicand. NOTE. In multiplying no regard should be paid to the decimal points. EXAMPLES. 1. 2. $. c. m. $. c. m. Multiply 4 83 6 Multiply 35 32 4 by 8 by 11 $38 68 8 $388 56 4 3. Multiply 8 24 by 24 Ans. $197 76. 4. . . $34 83 4 by 36 1254 02 4. 5. .... 74 8 by 49 36 65 2. 6. . . 09 7 by 700 67 90. CASE II. To find the value of goods in Federal Money. GENERAL RULE. Multiply the price by the quantity, and point off in the product, as in the given price. EXAMPLES. 7. What will 8 yards cloth cost a g3 44 8 per yd. ? 3 44 8=given price. 8=quantity* g<27 58 4=value of 3 yds. Ans. g27 58 4. 98 FEDERAL MONEY. Questions. 8. What will 12 Ib. cost a 80,09,3 m. per Ib ? yd.? 9. 10. 11. 12. 13. 14. 24 yds. ,83,8 77 yds. 149 Ib. ,34 7,30,3 200 yds. ,11,2 1345 yds. . ,23,3 3480 Ib. . ,29,1 81 11 6. 20 11 2. yd.? 26 18. "Ib.? 1088 14 7. yd. ? 22 40. yd.? 313 38 5. Ib. ? 1012 68. CASE III. When goods are bought or sold by the cwt. To find the value. RULE. Multiply the given price by 112, or by 7, 8 and 2, and point off in the product, as in the given price; when /there are more hundreds than one, multiply the price of one hundred by the given number of hundreds. EXAMPLES. 15. What will 1 cwt. cost a S3 24 2 per Ib. ? 3,24,2=given price. 112=lb. in cwt. 38904 3242 363,K),4=value cwt. Questions. 16. What will 1 cwt. cost a 81,08 . 17. . . 1 cwt. . ,34,3 . 18. 8 cwt. . . 3,34 . 19. 12 cwt. . . . ,84,2 . . 20. 24 cwt. . . ,34 . . . 21. 98 cwt. . OQ,7 . . 22. 180cw-t. ,8 mills Ans. 363,10,4. ^Answers. $120 96. 38 41 6. 2992 64. 1131 64 8. 913 92. 954 91 2. 161 28. CASE IV. When articles are bought or sold by the thousand. RULE. Multiply the price by the whole quantity and cut off three right hand figures for decimals, the left hand figures will be the answer in the lowest denomination men- tioned in the given price. FEDERAL MONEY. gg NOTE. When the quantity is a greater number than the price, it will be more concise to multiply the quantity by the price, the re- sult will be the same. EXAMPLES. 23. What will 24570 feet of boards cost a g!8 75 perM. ? 18,75=given price. 24570=quantily. 131250 9375 7500 3750 460,68,750=Ans. Ans. 460 68 7. U. What will 78455 bricks cost a g3 25 per AI. ? Ans. $(347 2 5 3|. '25. What will 43480 feet joists cost a g!5 30 per M. ? Ans. g665 24 4, CASE V. To find the value of parts of any quantity. RULE. If the numerator of the fractional part is an unit, divide the given price of 1 Ib. 1 yd. &c. by the denomi- nator of the fraction ; but if the numerator is more than 1, multiply the price by the numerator, and divide the pro- duct by the denominator, the quotient will be the answer. EXAMPLES. 26. What will | of a yard cost a $4 84 per yard ? denominator 8)4,84=price 1 yd. ,60,5=value of \ yd. Ans. gO 60 5. 27. What will of a yard cost a 4,84 per yard ? 4,84=price 1 yd. 3=numerator. denominator 8)14,52 gl,81 5 5=value off yd. Ans. 81,81,5. 28. What will || of a dozen cost a g9,50 per dozen ? Ans. g8,70,8i. 29. What will T V of a Ib. cost a $8,12 per Ib. ? Ans. gO,81,2. FEDERAL MONEY. CASE VI. When the quantity is a mixt numler. RULE. Multiply the price by the whole number, and for the fractional part, work as before 5 or reduce the mixt number to an improper fraction and proceed as in Case V. EXAMPLES. 30. What will 18 yards cost a $3,84 per yard ? 3,84=price 1 yd. 3,84 Or, ISf^f 1 . 18=whole number. 7=numer. 3,84x1518 = $72,48 as before. 3072 denom. 8)26,88 384 $3,36=value | yd. 69,12=value 18 yds. added 3,36= value yds. $72,48= value 18| yds. Ans. $72,48. Questions. Answers. 31. What will 24 yards cost a $3,24 per yd. ? $79,38. ,84,6 36,16,6$. 4,38 3,08 ,13,3 32. 33. 34. 35. 36. 37. 38. . 42| yds. 69f yds. . 139| yds. 294| yds. 500 yds. 348| doz. . lOOOfyds. 4,00,8 304,95,7^. 430,76. 39,1 9,0|. 2005,00,2. ,8m.pr.dz. 2,79. ,34,8 . 348,21,7$, DIVISION OF FEDERAL MONEY. CASE I. GENERAL RULE. Place the numbers and divide them as in whole numbers, or decimals, and the quotient will be the answer in the same denomination as the lowest in the dividend, which may be reduced to its proper denomination. PROOF. By Multiplication. NOTE. When the quantity is a composite number, divide the price by the component parts, which make the quantity. FEDERAL MONEY. 01 EXAMPLES. 1. Divide $34,48,4 by 4. 4)34,48,4 2. Divide $434,88 by 12. 12)434,88 $8,62,1 Ans. Dividends. Divisors . Divide $197,76 by 24 36,65,2 10,50 67,90 by 49 by 125 b 700 $36,24 Ans. Quotients. $8,24 ,74,8. ,08,4. ,09,7. CASE II. To find the value of 1 yd. 1 Ib. $c. in Federal Money. RULE. Divide the whole value by the whole quantity, and the quotient will be the answer in the lowest deuouii- nation to which the dividend was reduced. EXAMPLES. 7. If 8 yards cost $27,58,4 what will 1 yd. cost ? whole quantity 8)27,58,4=value of the whole quantity. $3,44,8=priee of 1 yd. Ans. $3,44,8. Answers. Questions. 8. If 12 Ib. cost 1,11,6 what will 1 Ib. cost ? $0,09,3 9. 24yds. 10. 77 yds. 11. 149 "ib. 12. 1345 yds. 13. 200yds. 14. 3480 Ib. rn 20,11,2 26,18 ,83,8. ,34. 1088,14,7 313,38,5 22,40 1012,08 . 7,30,3. ,23,3. . . . ,11,2. . ,29,1. CASE III. When goods are bought or sold by the cwt, To find the value of 1 Ib. RULE. Divide the given value by 112, or by 7, 8 and 2, the last quotient will be the answer, in the same denomU nation, to which the dividend was reduced. 103 FEDERAL MONEY. EXAMPLES. 15. If 1 cwt. cost $363,10,4 what will 1 lb. ? 112)363,10,4(3,24,2. 336 271 Or thus- 7)363,10,4 8)51,87,2 2)6,48,4 $3,24,2 as before. 470 448 224 224 Questions. 16. If 1 cwt. cost $120,96 what will 1 lb. cost? 17. 1 38,41,6 18. 8 2992,64 19. 12 1131,64,8 20. 24 913,92 21. 98 954,91,2 22. 180 161,28 Aus. $3,24.2. Jlnswers, $1,08. ,34,3.* 3,34. ,84,2. ,34. ,08,7. ,00,8. CASE IV. When articles are bought or sold by several thousands, to find the price of one thousand. RULE. To the given price annex three ciphers, and di- vide it by the given quantity, the quotient will be the price of one thousand, in the lowest denomination in the given price. EXAMPLES. 23. If 24570 feet of boards cost 8460,68,7$, what will 1 M. cost? A ns. $18,75. 21. If 78455 bricks cost $647,25,33, what will 1 M. cost ? Ans. $8.25 25. If 43480 feet joists cost $665,24,4, what will 1 M.cost? Ans. $15,30. CASE V. When the quantity is a fraction to find the value of one. RULE. If the numerator is an unit, multiply the given value of 1 lb. &c. by the denominator of the fraction ; but FEDERAL MONEY. if the numerator is more than 1, multiply the given value by the denominator and divide the product by the numera- tor, the quotient will be the answer. EXAMPLES. 26. If } of a yard cost $0,60,5, what will 1 yard cost ? ,60,5=given value. 8=denomiuator. $4,84,0= value of 1 yard. Ans. $4,84. 27. If | of a yard cost $6,43,2, what will 1 yard cost ? 6,43,2=given value. 4=denominator. numerator 3)25,72,8 $8^57,6= value of 1 yd. Ans. $8,57,6. -23. If |i of a dozen cost $8,70,8*-, what will 1 dozen cost? Ans. $9,50. 29. If T V of a Ib. cost $0,81,2, what is it a lb.? Ans. $8,12. CASE VI. When the quantity is a inioct number, to find the value of 1 lb. 1 yd. #c. RULE. Multiply the whole number by the denominator of the fraction, adding to the product the numerator; place it over the denominator, then multiply the given value by the denominator, and divide the product by the numerator. the quotient will be the value of 1 lb. &c. EXAMPLES. 30. If 18 y ar ds cost $72,48 what will 1 yard cost ? 18 = whole number. Then 72,48=given value. 8=denominator. And, 1 f 1 8=denominator. 144 numerator 151)579,84(3,84=value 1 yd. 7=numerator added. 151 new numerator. Ans. $3,84. Q'iostions. Jln&werz. 31. Ii'24 yds. cost 79,38 what will 1 yard ? 83,24. 32. 421yds. . 36.16.6$ . ". . ,84,6. 33. 69f yds. . 304,95,7^ . . . 4,38. 34. 139f 'yds. . 430,76 . . . 3,08. 35. 294|yds. . 39.19,0f . . . ,13,3. 36. 500| 'yds. . 2005,00,2 ... . 4,00,8. 37. 348$ doz. . 2,79 .... ,8. PRACTICE. PRACTICE. PRACTICE is a contraction of the Rule of Three, when the first term happens to be an unit, and is a concise method of finding the value of goods. Perhaps no method can be more simple and concise to find the value of goods in Federal Money, than the general rule of multiply- ing the price by the quantity, as given in Multiplication of Federal Money ; therefore, the application of this rule to Federal Money is almost useless. Yet as English merchants, trading with Americans, make out the invoices of their goods in sterling money, an acquain- tance with this excellent rule is necessar}- to every one, employed in mercantile pursuits. Questions in this rule are performed by taking the aliquot, or even parts. The following table, therefore, should be committed to memory, or, at least, the rule for making it well understood, by the scholar. TABLE OF ALIQUOT, OR EVEN PARTS. Aliquot parts of a shifting, j Jlliquot parts of a penny. \ d. qrs. is equal to T V of a shilling. is equal to f of a penny. Jlliquot parts of a ton. CU't. _10*is equal to of a ton. ~ 5= - - - I - - - Jlliquot parts of a pound. \ 4= . s. 1 is equal to J T of a pound. * (> 21= * 1.4= To ' 1,8- - - ^ - - - - j jMquot parts of a cwt. ~ To" ' ' - ' 'qrs. Ib. 2,6= - - J. - - . . 2 or 56== . . i of a cwt. 3.4= - - i - - - - |i or 28= - - - - - 4 = 5 = 6.8= 10 = 14= - - | - - - i T 16= - - * 7= - - A 4= - - > PRACTICE. 406 Rules to find the aliquot parts which any given pence, shillings, pounds, &c. make of a s. . ton, cwt. or cwt. To find the aliquot part of a shilling. RULE. Divide I2d. by the given number of pence, the quotient will be the aliquot part of a shilling. EXAMPLE. What part of a shilling is 4d. ? -Mt=i Ans. To find the aliquot part of a pound. RULE. Divide 20s. by the given number of shillings, the quotient will be the aliquot part of a pound. EXAMPLE. What part of a pound is 5s. ? 20-7-5=^ Ans. To find the aliquot part of a ton. RULE. Divide 20 cwt. by the given hundreds, the quo- tient will be the aliquot part of a ton. EXAMPLE. What part of a ton is 5 cwt. 20-7-5=i Ans. To find the aliquot part of a cwt. RULE. Divide 112 Ib. by the given number of Ibs. thfc quotient will be the aliquot part of a cwt. EXAMPLE. What part of a cwt. is 16 Ib. ? 11216=^ Ans. To find the aliquot part of % cwt. RULE* Divide 56 Ib. by the given pounds, the quotient will be the aliquot, or even part. EXAMPLES. What even parts of \ cwt. are 14 Ib. 8 Ib. and 7 Ib. ? 56-r-14=i Ans. 56-r-8=4 Ans. 56-r-7=j Ans. NOTE. By these rules the preceding tables may be easily made, or the aliquot part of any given price be found ; that is, by dividing the integer by any given number of the same name, which will divide rt without a remainder, the quotient will be the even or aliquot part, 10 106 PRACTICE. To find the value of goods. GENERAL RULE. 1. Suppose the price of the given quantity to be Id. Is. I ,. per yd. &c. ; then the given quantity itself would be the answer at the supposed price. 2. Divide the given price into aliquot parts, either of the suppose'! price, or of one another, and the sum of the quotients belonging to each will be the true answer required. CASE I. When the price is farthings. RULE. Find the value of the given quantity at a penny per Ib. or yd. &c. then divide by the aliquot parts of a pen- ny ; and by 12 and 20, the last quotient will be the answer. EXAMPLES. 1. What will 4678 yds. cost at I, -h and | per yard ? d. 4678 a i per yard. 12 1169J 2,0 9,7 4 17 5i Ans. 4678 yards a per yard. 4678 yards a f * per yard ? Ans. 9 14 11. Ans. 14 12 4. * In all cases where the given price is not an even part it must be reduced into even parts, and the sum of the quotients will be the answer. CASE II. When the price is pence. RULE. Find the value of the given quantity at Is. per . Ib. &c. ; then divide by the aliquot part, or parts, and yd. Ib. fey 20 : the last quotient will be the answer. PRACTICE. 107 2. d. .6 EXAMPLES. d. d. d. d. J. d. What is t'?e value of 8745 yards cloth a 1-1-0-2-^-4-5 d. d. d. d. d. -7-8-9-10 and 1.1, per yd. d. s. w. < . 1 i TV 8745 yds. 4 1 3 8745 yds. a bd. 2915 2,0 72,8 9 1 \ 723 9 36 8 9 Ans. 2.0 364 ,3 9 n 1 8745 yds. 182 3 9 Ans. 2,0 109,3 H Questions. Answers. 3. 8745 \d a 6d. 54 13 1| Ans. 218 12 6. 4. . . .aid. 2 * 87 15 yds. 255 1 3. 5. . . - a 8e?. 2,0 145 ,7 6 291 10. - 6. . . . a 9d. 72 17 6 Ans. . 3^7 18 9. 3 JL 8745 yds. 7. ... a Wd. _ 364 7 6. 2,0 218,6 3 8. . . . a lid. , 400 16 3. 109 6 3 9. 87433 a 9d. 4 l 3 8745 yds. 327 17 7|. 10- 840} a lOd. 2,0 291 ,5 35 7*. . 11. 3800 Ib. a Hi. 145 15 Ans. 1 S182 1 8. CASE III. When the price is shillings and pence. RULE. Find the value of the given quantity a l per yd. Ib. &e. then divide by the aliquot part or parts, the quotient will be the answer in pounds. 108 PRACTICE. EXAMPLES. S. S. S. S. S. 12. What will 8845 yards cosl a 1-2-3-4 and 5 per yd. H . fa 8845 yds. 442 5 Ans. Questions. 13. What 14. , . 15. . . 16. . . 17. . 18. . . 19. . . 20. . 21. . . Answer*. cost 5674 Ib. at 3 4d. perlb. ? 945 13 4 . 7484 Ib a 6 80?. 2494 16 8. . 8450 Ib. a 9 8rf. 4084 5 9. . 7484| vds. alold. 4939 16 8. 8796 ^b . a 17 4d. 7623 12 8. . 3000 Ib. a 2 6rf. 375. . 734 a 16s. 587 12. , 8040| a 16 8rf. 6700 12 6. . 1250 a 18*. 1125 4 6. To" 8845 yds. 884 10 Ans. TU i 8845 yds. 884 10 442 5 1326 15 Ans. J 8845 yds. 1769 Ans. J 8845 yds. 2211 5 Ans. CASE IV. the price is pounds, shillings, pence and farthings. RULE. Multiply the given quantity by the pounds ; for the rest take parts. EXAMPLES. 22. What will 8464 yards cost a 3 6 8 per yard ? t.d. " | 6 8 || I 8464=quantity. 3=given pounds. 25392 2821 6 8 28213 6 8 Ans. 20213 6 8. 23. What will 7848 Ib. cost a 2 7 1H per Ib. ? Ans. 10818 17. TARE AND TRET. 109 24. What will 2157 yards cost a 3 15 2$ per yard ? Ans. 8108 19 5, 25. What will 4374 Ib. cost a 7 10 H per Ib. ? Ans. 32836 1 9*. CASE V. When the price and quantity are both of several denomina tions. RULE. Multiply the price by the integers of the quan- tity and take parts of the integer for the rest. EXAMPLES. 26. What is the value of 7 2 14 Ib. a 3 10 14| per cwt. ? qrs. cwt. 3 10 4i=given price. 7=integers. 14lb 26 16 7* Ans. 26 16 7*. 27. What will 4 3 24 Ib. cost a $4,48 per cwt. Ans. $22,24. 28. What will 12 1 18 Ib. cost a $8,36,8 per cwt. Ans. $103,85,2. TARE AND TRET. TARE AND TRET are rules for deducting certain al- lowances, made by the seller to the purchaser, for the weight of the thing which contains the goods. These allowances are made either at so much for the box, bag or barrel, at so much per cent, or so much in the gross weight. 1. Tare is an allowance for the weight of the box, bag, or barrel, containing the goods. 2. Tret is an allowance of 4 Ib. on every 104 Ib. for waste. 10* 110 TARE AND TRET, 3. Cloff is an allowance of 2 Ib. on every 3 cwt. made t<* the people of London only. 4. Gross weight is the whole weight of the goods, togeth- er with the thing containing them. 5. Suttle weight is when part of the allowances is de- ducted from the gross. 6. Net weight iS the pure weight of the goods, when all allowances are deducted. CASE I. When tare is so much per box, bag, or barrel, <$*c. RULE. Multiply the number of boxes, bags or barrels, &c. by the tare, and subtract the product from the gross, the remainder will be the net weight. EXAMPLES. 1. What is the net weight of 24 hhds. of tobacco, weigh- ing 143 2 1.4 Ib. gross ; tare 84 Ib. per hhd. and what is the value at $7,25 per cwt. ? 84ajfarc. 143 2 14=gross. 24==nuniber hhds. 18 0=tare. 336 125 2 14 lb.=net. 168 !12)2016(18=tare. 112 896 896 A 025 2 14 lb. Ans ' J $910,78,1*. 2. In 241 barrels of figs each weighing 3 19 lb. gross; tare 10 lb. per barrel; how many pounds net, and what is their value at 15f cents per lb. A C 22413 lb. A I $3530,04,7$. CASE II. When tare is so much in the whole gross weight. RULE. Subtract ibe given tare from the gross, the re- mainder will be the net. TARE AND TRET. EXAMPLES. 3. Having deducted the tare, what is the value at $6,50 per c\vt. of 83 hhds. tobacco, weighing 137 cwt. gross ; tare 678 Ib. in the whole ? Afl > 851,15,l|i. | 130 3 22 Ib. 4. At 10 cents per Ib. what is the value of 184 boxes of raisins, each weighing 33 Ib. gross 5 tare 152 Ib. in the whole ? A S $606,80. CASE III. Wlien the tare is so much per cwt. RULE. Divide the gross by the aliquot part, which the tare makes of a cwt. as in Practice ; subtract the quotient from the gross, the remainder will be the net. EXAMPLE. 5. What is the net weight of 24 boxes of sugar, each weighing 7213 Ib. gross ; tare 14 Ib. per cwt. and what is the value at $11,75 per cwt. ? 7 2 13 lb.=l box. 30 1 24=weight of 4 boxes. 6 ). cwt. 14U 1182 3 4=weight of 24 boxes. I I 22 3 ll=lare. 159 3 21 lb.=net (159 3 21 Ib, ?g!879,26,5f. 6. At $10,50 per owt what is the value of 12 hhds. su- gar, the gross weight being 93 1 19 Ib. ; tare 18 Ib. per cwt.? A < $823,26,5f . s -}78 1 17 J Ib. 7. What is the net weight of 443 cwt. tallow gross ; tare 17 Ib. per cwt. and what is the value a 10 cents per Ib. ? A C375 3 1 Ib. 3 ' 1 84418,92,5, CASE IV. When tret is allowed with tare. RULE. Deduct the tare as before directed, tlen divide the suttle weight by 26, (which is the aliquot part that 4 TARE AND TRET. Ib. make on every 104 Ib.) am! the quotient will be the tret, which subtracted from the stittle, the remainder will be the net. EXAMPLES. 8. What is the net weight of a hhd. tobacco, weighing 14 3 27 Ib. gross ; tare 16 Ib. per cwt. ; tret 4 Ib. per 104 Ib. ; how many pounds net, and what is the value at 6| cents per Jb. ? 14 3 27=gross. 4 59 28 Ib. cwt. 16 C 1383 14 oz. 479 120 1679=gross Ib. 239 13oz. 1439 3=suttle. | | 55 5=tret. Ib. 1383 14oz.=net. 9. What is the net weight of 4 hhds. sugar, weighing as follows; viz. No. 1. 8314 Ib. 2. 4 2 19 3. 7 1 14 4. 14 2 23 gross ; tare 19 Ib. per cwt. and tret as usual, and what will it come to a $12,25 per cwt. ? A 528 1 21 Ib. s> I $348,35,9 f CASE V. When doff is allowed with tare and tret. RULE. Deduct the tare and tret as before directed, then divide the guttle by 168 (it being the aliquot part which 2 Ib. make on every 3 cwt.) the quotient will be the cloff, which subtracted from the suttle, the remainder will be the net. DUODECIMALS. 113 EXAMPLE. 10. \Yhat is the net weight of 15 3 20 Ib. gross; tare 7 Ib. per c\vt. ; tret and cloft'as usual. Ib. cwt. 15 3 20=gross. 3 27 8=tare. 14 3 20 8=suttle tare. 2 8 5=tret. 14 1 12 3=suttle tret. 9 9=cloff. 14 1 2 10=net. Ans. 14 1 2 DUODECIMALS, OR CROSS MULTIPLICATION. DIMENSIONS are taken in feet, inches, and parts called seconds. Glaziers' and Masons' work is measured by the foot. Painting, plastering, paving are done by the yard. Partitioning, flooring, slating, rough-boardfng, by the square of 100 feet. Stone and brick work by the rod of 16 feet, whose square is 272 : }. Bricks also are laid by the thousand. GENERAL RULE. 1. Under the multiplicand write the corresponding de- nominations of the multiplier. 2. Multiply each term in the multiplicand, beginning at the lowest, by the feet in the multiplier, setting each re- sult under its respective term, observing also to carry for every 12 from each lower to the next higher denomination. 3. Pro *eed in the same manner, and multiply the multi- plicand by the inches in the multiplier, setting the result of each term one place more to the right hand of those in the multiplicand DUODECIMALS. 4. In the same manner multiply by the seconds (parts) in the multiplier, setting the result of each term one place more to the right of the last, and so on for thirds, fourths, &c. NOTE. Shillings and pence may be multiplied as feet and inches. EXAMPLE. 1. 2. 3. 4. feet. in. feet. in. s. d. s. d. Multiply 3 4 6 3 2 3 1 6 by 7 10 8 6 2 3 1 6 23 4 50 4 6 1 6 294 3 1 6 6 9 9 feet. 26 1 4 feet. 53 1 6 s. 5 9 s. 2 3 APPLICATION OF DUODECIMALS. 1. Measuring by the foot square, as glaziers- and masons' work. 5. There is a house with 4 tiers of windows, and 4 in each tier, the height of the first is 7 2 in. (lut second 6 8 in. the third 5 9 in. the fourth 4 6 in the breadth of each 3 10 in. ho-v nany feet square are in the windows, and how much will the glazing come to a 20 cents per foot ? Fi^tlier y 2 in. " feet 24 l=height. Second 6 8 4=numb. windows. Third 5 9 Fourth 46 96 4 3 10=breadth. feet 24 1= whole height. 289 80 3 4 feet 369 3 4=whole contents, 20 cents per foot is $73,86,6f . Ans e *> 4 "^73,86,61^ II. Measuring by the yard square, as paviers', painters', plasterers' 1 and joiners'* work. NOTE. Divide the square feet by 9, the quotient will be square yards. DUODECIMALS EXAMPLE. 6. A room is to be ceiled, whose length is 74 9 in. and width 11 6 in. what number of yards square is in the room, and what will the work amount to at 25 cents per yard ? Ans III. Measuring by the square of 100 feet, as rough board- ing, slating* shingling, flooring, and partitioning. RULE. Multiply as before, and cutontwo right hand figures in the integers. / EXAMPLES. 7. In 175 10 in. long and 9 10 in. high of partitioning how many squares ? Ans. 17 squ. 29 f. 4 pts. ~ 8. What will the slating of a house cost at $2,25 per square of 100 feet ; the roof being 48 feet in length and 14 10 in. wide, and how many squares Ans, 24 yds. SINGLE RULE OF THREE DIRECT. The three methods of proof are only the first question varied, and they will show how any question in this rule may be inverted. A short and easy method of performing questions in the Single Rule of Three is by comparing the three given numbers together ; the true answer will result from the nature of proportion ; for as much greater or less as the third term is than the first ; so much greater or less will the fourth term or answer be than the second. Thus in ex- yds. $. yds. ample 1st. 8:4 : : 24 ; by comparing the third term (24) with the first term (3), it will be found to be three times greater than it ; there- fore, the fourth term or answer must, from the nature of proportion, be 3 times greater than the second term (4), which is 12, ajftd the true answer, as by the operation above. OBSERVATION I. When the second number is of different denominations, it must always be reduced to the lowest mentioned in it ; then multiply and divide as in the general rule, and the quotient will be the answer in the same denomination to which the second was reduced, and which should be brought into the highest for the answer. EXAMPLE. 5. If 8 yards cost 34 12 6 ; what will 32 yards cost ? yards. ,. s. d. qrs. yds. 8 : 34 12 6 i : : 32 4)132968=farthin<*&. 20 12) 33242=pence, 2,0) 277,0 2 138 10 2, 33242=farthings, 32 66484 99726 8)1063744=farthings. 132968=farthings Ans. Ans. 138 10 2. NOTE. In example 5, the second term being in pounds, shillings, pence a^id farthings, is reduced to the lowest mentioned in it ; viz. farthings ; consequently the fourth ...na will be farthings, which are reduced to pounds &c. for the answer, 18* SINGLE RULE OF THREE DIRECT, OBSERVATION II. When the first and third numbers are of different de- nominations, they must be reduced to the lowest mentioned in either of them ; then proceed as directed in the general rule. EXAMPLES. 6. If 7 Ib. sugar cost $1,75 ; what will 7 2 14 Ib. cost r lb. $. cwt. qrs. Ib. 7 : 1,75 : : 7 2 14 4 7)1494,50 $213,50 Ans. g213,56, NOTE. The first numbers being pounds weight, the third number is reduced to pounds. 7. If 7 2 14 Ib. cost $213,50 ; what will 7 Ib. cost ? Ans. $1,75* ' OBSERVATION III. When there is a remainder after division, which is of the same name with the second term, reduce it to the next lower denomination and divide as before ; continue thus till it is reduced to its lowest denomination, each time di- viding by the first term. Should there be a remainder, place it above the divisor, and annex the fraction thus formed to the quotient, observing first to reduce it to its lowest terms* SINGLE RULE OF THREE DIRECT. EXAMPLES. 8. If 7 02. of gold is worth 30, or $30 j what will a golden vase cost, which weighs 7 1 1 oz. ? oz. . Ib. os. os. $. Ib. OB. 7 : 30 : : 7 1 1 And 7 : 30 : : 7 1 1 12 12 95 95 30 30 7)2850 7)2850 407 2 IQAi, $407,1 4,2f. 9.' If 7 11 oz. of gold is worth $ 407 2 10} | ; what is 7 oz. worth ? Ans. 30. 10. If 3 Ib of gold is worth 187, what is 1 oz. worth ? Ans. 5 3 10 f. OBSERVATION IV. When the first term is greater than the product of the second and third, consider the product as a remainder and reduce it as directed iu Observation III. EXAMPLE. % 11. If 48 yards cost 3 or $3, what will 12 yards cost r yfc. ,. yds. yds. $. yds. 48 : 3 : : 12 48 : 3 : : 12 3 3 48)36 43)36,00(,75 c. 20 4 f!5s. 48)720(15 s. " "[,75 et. Here the product of the second and third terms being less than tne first term, it is reduced to the next lower denomi- nation, giving 15s. and 75 cents for the quotients or an- swers. OBSERVATION V. When the question will admit it, multiply and divide as in Compound Multiplication and Division. SINGLE RULE OF THREE DIRECT. EXAMPLES. 12. If 4 yards cost 34 10 8 ; what will 12 yds. cost? yds. , t. d. yds. 4 : 34 10 8 : : 12 12 4)414 8 6 103 12 1 Ans. Ans. 103 12 1|. 13. If 24 Ib. cost 4 8 10 ; what will 96 Ib. cost ? Ib. . s. d. Ib. 4X0=24. 24 : 4 8 10| : : 96 8 8x12=96. 35 11 00 12 4)426 12 6)106 13 17 15 6 Ans. 17 15 6. OBSERVATION VI. When the first term happens to be 1, the operation is performed by Compound Multiplication, and when the third term is 1, it is performed by Compound Division. EXAMPLES. 14. If 1 cwt. cost 3 15 6i, or $12,75 5 what will 12 cwt. cost ? cwt. . s. d. cwt. 1 : 3 15 6| : : 12 12 45 6 6 Ans. 5 45 6 6. $153. 15. If 12 cwt. cost 45 6 6, or $153 5 what will 1 cwt. ? 12)45 66 er 12)153 3 15 6* $~12/75 An(a $3 156f SINGLE RULE OF THREE DIRECT. Having stated all the variety of cases which can occur in the Rule of Three Direct ; and furnished plain examples for their illustration, the following promiscuous questions are subjoined for the pupil's ex- Questions. ^Answers. 16. If 24 yds. cost $0,84,4; what will 72 yds. cost? $2.53,2, 17. 108 yds. . 4,84,6 . . ,643yds? . 29,07,6. 18. . I cwt. . 9,00,4 . . . 4 2 *14 Ibs. ? 41,64,3i. 19. . 7 Ib. . ,38,9 . . . 3 cwt. ? . 18,67,2". 20. . 1 Ib. . 2,33,4 ... 1 cut.? . 261.40,8. 21. .1 cwt. 261,40,8 . . . 1 Ib. ? . 2,33,4. 22. . loz. gold 17,36 ... 1 grain ? . ,03,6. 23. . 3214lb.750, . . . 14 Ib. ? . . 25,86,2/ 24. What is the interest of $874 a 6 per cent, for a year ? Ans. $52,44. 25. A bankrupt's debts amounted to $4800, and his ef- fects sold for only $1800 ; how much could he pay on a dollar ? Ans. $0,37,5. 26. An invoice of goods amounted to $3480 5 what is the commission on the purchase at 3^ per cent ? Ans. g!21,80. 27. A bankrupt, whose debts amounted to $8749, com- pounded with his creditors for ,78 cents on a dollar ; how much did he pay them ? Ans. $6824,22. 28. A merchant bought 6 bales of cloth, each bale con- tained 6 pieces, and each piece 25 yards, at $52 per piece ; what was the value of the whole, and what was it worth per yard? . 5 SI 872 whole. ns 'l $2,08 per yd. 29. In what time will $100 principal gain $75, at 6 per cent per annum. ? Ans. 12 years. 30. A servant went to market with $8, and bought eggs at 25 cents a doz. ; chickens a lib cents a pair, and ducks a gl a pair ; he bought the same number of each kind ; how many of each sort had he for his money ? Ans. 4 of each. 31. A gentleman's annual income amounted to $40000 ; how much can he spend daily, that at the end of the year he may lay up 25000, and distribute to the poor, quarter- ly, $2500 ? Ans. 13,69,8f. 32. A merchant effects ensurance on a vessel and cargo valued at $18545; what is the premium at 44- per cent ? Ans. $834,52,5. 429 SINGLE RULE OF THREE DIRECT. RULE OF THREE IN VULGAR FRACTIONS. The Rule of Three in Vulgar Fractions depends on the same principles as the Rule of Three in whole numbers. GENERAL RULE. 1. Prepare the question as directed in the Rule of Three Direct. 2. Invert the terms of the first number, and multiply the numerate s of the three numbers continually together ; and a!) the denominators ; their products will be the answer to the question. EXAMPLES. 1. If | of a yard cost | ; what will of a yard cost ? yds. . yds. |=first number inverted r o , 8 . 2 . . 7 s .1 j. JL nen -o- -& for the divisor. niirner. A , Il2 _ 14 _ 10 41 i 3X9X8=216 new denom. And> ^6-27-*^ Ans 10 41 }. 2. If f of a Ib. cost | of a dollar ; what will -& of a Ib. cost ? Ans. /o=ll, 2| mills. OBSERVATION I. When the first and third numbers only are fractions ; and the second a whole number. Reduce the first and third to a common denominator, and then rejecting the denominators, make the numerator of the first, the first number in stating the question ; and the nu- merator of the third, the third number, and the given whole number the second ; then proceed as in the Rule of Three of whole numbers. EXAMPLE. 3. If | of cwt. cost 20 ; what will ^ of a cwt. cost ? 6X8=48 \ new DUm - H and f f , Then 21 : 20 : : 48 7x8=56 common denom. 48 to A 135 10 6, to B 145, to C 154 9 DOUBLE FELLOWSHIP, 135 and to 1) 160; the value of his effects is 252 17 6 ; what must each creditor receive and how much will each have on the pound ? A' S 57 12 B'*61 12 65 12 T>'sG8 8 6 T ||- rf. on a pound. 5. A B and C entered into copartnership ; A put into stock 875, B put in 8987 and C put in gll90$ they gained $950; what must each have of the a;ain ? fA's $272,36, Ant. < B's $307,22,4f Iff , (.C's g370,41,2|f DOUBLE FELLOWSHIP. DOUBLE FELLOWSHIP i* Fellowship with time, and ife when the stocks or' partners are continued in trade for une- qual times. RULE. Multiply each man's stock by the time of its continuance in trade, then say, as in Single Fellowship* As the sum of all the products, Is to the whole gain or loss ; So is each man's particular product, To his share of the gain or loss. PROOF. As in Single Fellowship. EXAMPLES. 1. Two merchants entered into trade ; A put into stock $2500 for 3 months ; B 1800 for 5 months; they gained ^875 ; what is each man's share of the gain ? 2500X3=7500=A'S product. 1800x5=9000=B's product. 816500=sum of products. $. $. ^s product. As 16500:875: : 7500 : 397,72,7 T 3 T =A*8 share of gai, $. $. jB'.v product. A* 16500: 875 : : 9000 : 477,27,2 T 8 T =B*s share of gain. Proof. A's share g397,72,7 T \.7 . B's share g477,27,2 T T .S Whole gain $875 . . 436 SIMPLE INTEREST- 2. Three merchants entered into copartnership ; A put into stock 294 14 for 3 months ; B 240 10 for 4 months, and 290 for 6 months ; they gaiued 300 ; what is each partner's share of the gain ? fA's share 73 19 2J Ans. 4 B s share 80 9 6* f ff ^C's share 146 11 2| 3. Three persons entered into trade for 16 months ; A at first put into stock $7400, but at the end of 4 months took out $2000, at the end of 12 months he put in $3000, but at the end of 14 months took out 850; B at first put in $5900 and at the end of 3 months put in $4300 more, but at the end of 9 months took out 40t)0 and at the end of 12 months 'put in $1500, but withdrew $2000 at the end of 14 months ; C at first put in SI 2000, hut at the end of 6 months took out 5000, and at the end of 9^ months put i 3200, but at the end of 12 months took out $4000 ; they gained 8000 ; what must each partner have of ihe gain? f A's share $2219,39,5|fif. Ans. < B's share. $2634,87,Og\Y T - tC's share $3145,73,3ff4. 4. Three persons were concerned in an adventure ; A ad- vanced $4740 for 5 months ; B 2700 for 6 months ; C 4100 for 4 months ; by miscalculations and failures they were involved to the amount of 1800 ; what must each sus- tain of the loss ? f A's logs 757,72,6Hf. Ans. B's loss 517,93,9ff. lC'sloss524,33,3ff|. SIMPLE INTEREST IN FEDERAL MONET. INTEREST is a premium allowed for the use of money. Simple Interest is that which arises from the principal nly ; and both the interest and principal are always the same as at first. 1. Principal is the money lent. 2. The rate per cent, per annum, or the ratio, is the >H . SIMPLE INTEREST. CASE VI. To find the interest for months and days at 6 per cent. RULE. Multiply the principal by half (he greatest even Dumber of months, and J of the given days and the days in the odd month if any ; cut oft' one figure for a decimal, and proceed as in the general rule; observing, that in find- ing the sixth of the days, the remainder, if any, is a vul- gar fraction, not a decimal, by which multiply as usual. EXAMPLES. 30. What is the interest of SI 4,24 for 10 months and 24 days ? 3)10=mo. 14,24 = principal. halfmo.= 5,4= of the days. 5=halfmo. 5696 )24=days. 7120 4=sixth of days. 76,89,6=interest 10 months & 24 days. Ans. 0,76,8. 31. What is the interest of $24,1 7 for 11 months and 29 days ? 24,17=principal. |)ll(5=half even mo. 5.9f =i mo. & % days. 30= days in the odd mo. 21753 29=given days. 12085 2014=| 6)59 l,44,61,7 = int. for given time. 9- = sixth of days. Ans. gl, 44,6. 32. What is the interest of g35 for 7 months and 19 days Ans. $1.33,5. 33. What is the interest of $784 for 9 months and 24 days ? Ans. 38,4 !, CASE VII. To find the interest for months at any rate per cent. feuLE. Multiply the principal by the given number of months, and divide the product by the rate i'or the urne. INTEREST, 141 NOTE. The rate for the time is found by dividing 12 by the give?: rate per cent. EXAMPLES. 34. What is the interest of g748 for 8 months at 6 percent. ? 6)12 748=pnncipal. 8=number of months. 2=rate for the time. 2)59,84 29,92=interest 8 months. Ans. 29,9-. 35. What is the interest of $40 a 4 per cent, for 15 months ? Ans. 2. 36. What is the interest of 874, a 5 per cent, for 9 months ? Ans. $32,77.5. NOTE. When 12 cannot be divided without a large decimal, it will b& preferable to divide by the vulgar fraction, as in the following ex- ample. 37. What is the interest of $874 a 7 per eeut. for 9 months ? 7)12 874x9X7=55062-7-12=45,88,5. 14=V 2 . Ans. 45,88,5. CASE VIII. To find the interest for days at 6 per cent. RULE. Multiply the principal by O f the days, and cut off the right hand figure for a decimal, and proceed as in the general rule. NOTE. This method of finding the interest by multiplying by of the days, is sufficiently exact for small sums ; but for large sums the variation from the true answer will be more, which may be cor- rected by subtracting from the quotient _L_ part of its amount. EXAMPLES. 38. What is the interest of $94850 a 6 per cent, for 45 days ? 6)45 |)94850=principal. 7!= days. 663950 T V)711,37,5=for 45 days. 47425 9,74.4= T V of quotient. $711.37 ? 5=interest for 45 days= $701, 63,1 =true answer, Acs. $701,63.1, 13 SIMPLE INTEREST. 39. What is the interest of $374 for 120 days ? Ans. $17,48. 40. What is the interest of $15 for 75 days ? Ans. $0,18,7*, CASE IX. To find the interest of any sum for any time, at 6 per cent. RULE. Divide the given principal by 2 and the quotient will be the interest for one month; multiply the interest for one month by the months in the given time, and point oft* as directed in the general rule. EXAMPLES. 11. What is the interest of $748 for 8 months ? 2)748=principal. $3,74=interest for one month. 8=number of months. $29,92=interest for 8 months. Ans. $29,92. 42. What is the interest of $475,48,4 for 3 years and 4 months ? 2)475,48,4 =principal. 2,37,7,42=interest for one month. 40= number of months in given lime. $95,09,6,80= interest for 3 years and 4 months. Ans. $95,09,6. 43. What is the interest of $37 for 7 months ? Ans. gl,29,5. 44. What is the interest of $95,24 for 11 months ? Ans. $5,47,6. CASE X. When the principal is lawful money to find the interest in federal money., at 6 per cent. RULE 1. Multiply the principal by 2, and cut off the right hand figure, for parts of a dollar. Or, 2. The shillings in the given pounds and shillings will he the interest in cents. Or, 3. Divide the given principal by 5. SIMPLE INTEREST. 143 EXAMPLE. 45. What is the interest of 225 in federal money ? Rule 1. 225 Rule 2. 225 Rule 3. 5)225 2 20 S45. 815,0 $45,00 Ans, g45. CASE XT. To find the interest on bonds, notes of hand, $c. when par* tial payments have been made, or endorsed on them. RULE. 1. Find the interest of the given sum to the first payment, which either alone, or with any preceding pay- ment, if any, exceeds the interest due at that time, and add that interest to the given sum. 2. From this amount subtract the payment made at that time with the preceding payments, if any, and the remain- der will form a new priucipal ; the interest of which iind and subtract as of the first sum, and so on till the last pay- ment. NOTE. This mode of computing interest is established by law in Massachusetts for making up judgments on securities for money draw- ing interest, and on which partial payments are endorsed. This mode is the most equitable, because the payments are applied to keep down the interest, no part of which, in this method of computation, forms any part of the principal, drawing interest. EXAMPLE. For value received I promise (o pay Mr. Thomas Bor- land, or order, twelve hundred dollars, with interest in six months from this date. January 1, 1810. ANDREW DUNKIRK. On the above note were the following endorsements ; viz. May 1, 1816, received $130. July 1, received $16. December 1, received $24. January 1, 1817, received $400. March 1, received $25. August 1, received $40. October 1, received $100. December 1, received $200. Whjt remained due January 1, 1818 ? SIMPLE INTEREST. The given sum bearing interest from Jan. 1, 1816 - - $1200 Interest to May 1, 1816, to the first payment (4 mo.) - 24 Amount $1224 May 1, paid a sum exceeding interest then due - - - 130 Remainder for a HCAT principal -------- 1094 Interest due on $1094 irom May 1, to Jan. 1, 1817 (8 mo.) 43,76 Amount $1137,76 Paid July 1, 1816, a sum less than int. then due $16 Paid Decem. 1, 181C, a sum less than int. then due $24 Paid Jan. 1, 1817 a sum exceeding int. then due $400 440 Remainder for a new principal ---.--._ $697,76 Interest on $697,76 from Jan. 1, 1817 to March 1 (2 mo.) 6,97,7 Amount $704,73,7 Paid March 1, 1817, a sum exceeding int. then due 25 Remainder for a new principal ------- 679,73,7 Interest on $679.73,7 from Marck 1 to Aug. 1 (5 mo.) 16,99,3 Amount $696,73 Paid Aug. 1, 1817, a sum exceeding int. then due . - 40 Remainder for a new principal -------- $656,73 Interest on $656.73 from Aug. 1 to Oct. 1 (2 mo.) 6,56,? Amount $663,29,7 Paid Oct. 1, 1817, a sum exceeding int. then due - - 100 Remainder ,or a new principal -------. $563,29,7 Interest on $563,29.7 from Oct. 1 to Decem. 1 (2 mo.) 5,63,3 Amount $568,93 Paid Decem. 1, a sum exceeding int. then due - - - 200 Remainder (for a new principal -------. $360,93 Interest on $368,93 due Jan. 1, 1818 from Dec. 1, 1817 1,84,4 Balance due Jan. 1, 18 18. $370,77,4 Ans. $370,77,4. SIMPLE INTEREST. SIMPLE INTEREST LY STERLING MOXEY. CASE I. To find the interest of any sum for a year. GENERAL RULE. Multiply the principal by the rate, and cut off two right hand figures ; the left hand figures will be in the highest denomination given ; the right hand figures must be reduced to the lowest denomination, each time cutting oft' the two right hand figures. NOTE. When there are several years, multiply the interest of one year by the given number of years ; and if parts of a year are given, as months and days, work by the aliquot parts which they make of a year or month, the sum of the quotients will be the answer. EXAMPLES. I. What is the interest of 394 at 6 per cent, per annum 394=prineipal. 6=rate. 23,64=23 12 9Jf- Ans. 23 12 9| f-. 2. What is the interest of 379 12 4^ a 5 per cent. ? Ans. 18 19 7*. 3. What is the interest of 434 for 3 years at 6 per cent. per annum ? Ans. 78 2 4*. 4. What is the interest of 994 10 4i for 2 years ami 9 months a 6 per cent, per annum ? Ans. 164 1 10|. 5. What is the interest of 978 at 3 per cent, for Si- years ? Ans. 82 10 4. C. What is the interest of 84 10 for 7 months and 25 days a 6 per cent. P Ans. 3 6 2. CASE II. To fund the interest in federal money when the principal given is sterling, at 6 per cent. RULE. Add one third to the principal, and multiply by 2, cut off one figure ; the left hand figures will be dollars. the right hand figures parts of a dollar; or divide the sum by 5, or multiply it by 20 the product will be cents. 13* 146 SIMPLE INTEREST. EXAMPLE. 7. What is the interest in federal money of 456 ling ? 3) 456=sterliri2f principal. 152=1 principal. 608 608 By rule 1. 2 By rule 2. 20 By rule 3. 5)608 $121,60 $121,60 gI2l",GO. Ans. $121,60. CASE III. To find the interest for months at 6 per cent. RULE. Multiply the principal by half the given num- ber of months, and cut off as in the general rule. EXAMPLES. 8. What is the interest of 454 at 6 per cent, for 10 months ? 454=prineipal. 5=4 number months, 22,70 20 14,00 Ans. 22 14, J< What is the interest of 38 12 6 for 11 months ? Ans. 2 2 5j. CASE IV. To find the interest for days. RULE. Multiply the given principal by the given num- ber of days and divide by 6083, for 6 percent, (the number of days in which any sum will double itself at that rate) the quotient will be the answer. JS'oTE. To find a divisor for any rate percent, multiply 365 by 100 "and divide the product by the given rate ; thus, for 6 per cent- 365X100-4-6=6083, ; for 5 P er ce nt- 3S5X 100-7-5=7300 ; for 7 per acnt. 365 X 100-^7=5214, &c. EXAMPLE. 10. What is the interest of 28 for 210daysa6 perct. ? c ?SX21Q=5$80-f-6Q83 ? =r0 19 3^ Ans, 19 3| 9 COMMISSION. COMMISSION. FACTORAGE AND BROKERAGE, ARE premiums, at so much per cent, allowed a person called a Correspondent, Factor or Broker, iui assisting merchants, and others, in purchasing and selling good*. RULE. Multiply the given sum by the rate per cent, and cut oft' the two right hand figures as in Simple Interest. EXAMPLES. 1. What is the commission on the purchase of goods the invoice of which amounts (o 870 at 2| per cent. ? 870X2|=23,92,5. Ans. $23,92,5. 2. What is due to my Factor for selling goods, valued 1 834 at 2^ per cent. ? Ans. $45,85. . 3. What is the brokerage on 774 at \\ per cent. ? Ans. 11 12 2.. 4. What must I allow my correspondent for selling goods to the amount of 48450 at 2 per cent. ? Ans. $1 029,56,2^ . 5. I remit to my correspondent $32840, with orders to purchase goods for my account 5 what is the amount of his commission at 2 per cent. ? Ans. &800,97,5|f-, BUYING AND SELLING STOCKS. STOCK is a fund established by government, or corporate bodies, the value of which is variable according to the ex- igency of the times. The practice of buying and selling sums of money in these funds is become common. RULE. Multiply the sum to be purchased by the excess above 100, cut off two right hand figures^ as in simple in- terest, which being added to the given sum will be the amount of the purchase required. If the value is under par, that is under 100, multiply by the rate per cent, and cut off as before directed. EXAMPLES. 1. What is the pnrchase of $14820 bank stock of the United States, .127| per cent, ? Ans, $188955Q. LNSURANCE. 2. The 3 per cent. United States stock, owned by tht .city of New York, amounting to $840,000 has been dis posed of at G8| per cent. What was the amount of the purchase ? Ans. 575400. 3. Manhattan Bank purchased New York state loan of SI, 000,000 of six per cent, stock at 101 $ per cent. ; what was the amount of the purchase ? Ans. $1012500. 4. The three per cent, deferred stock was worth 69 pel- cent, in June 1818; what is the amount of $9745 a t thai; rate ? Aus. 6724,05, ENSUHJ1NCE. 1. ENSURANCE, or ASSURANCE, is a premium at so much per cent, given for the security of making good the loss of ships, houses, goods, &c. which may happen by storms, fire, &c. 2. The amount ensured is called the principal. 3. The money paid for ensuring is called the premium. 4. The " average loss" is 10 per cent. ; that is, if the owner of the property ensured suffer any loss or damage, not exceeding 10 per cent, he bears it himself, and the un- derwriter or ensurer is free. 5. The k< Policy" is the instrument, by which the en- surers oblige themselves to make good the property en- sured, in consideration of a certain premium, at a stipu- lated rate per cent. CASE I. To find the premium for ensuring any swm- RULE. Multiply the given sum by the rate per cent, and cut off two right hand figures as in Simple Interest. EXAMPLES. 1. What is the premium on the amount of a ship and cargo, valued $4844 a 3J per cent. ? Ans. $169,54, 2. What is the premium on a ship and cargo valued $19330 at 3| per cent, from Boston to London, and 2| per cent, from London to Boston r Ans. gl 159,80, ENSURANCE. CASE II. To find the sum for which a policy should betaken out to cover a given sum. RULE. Subtract the premium from 100, and then say, by the Rule of Three, As the remainder, is to 100 ; So is the sum adventured, to the policy. Or subtract the premium from 100; annex two ciphers to the sum to he covered, which divided by the remainder, the quotient will be the answer EXAMPLE. 3. A merchant wishes to ensure his vessel and cargo, valued at $44350 en a voyage to the East Indies; for what sum must the policy be taken out to cover his property, at 10 per cent.? 100 10=premium per cent. Remainder 90 : 100 : : 44350 : 49277,77,7*. Or 100 10 9,0)443500,0 49277j77,7*. Ans. Ans. 49277,77,7*. CASE III. To find the premium, when a policy is taken out for a cer- tain sum, to cover a given sum. RULE. As the policy, is to the covered sum ; 3o is 100, to a fourth number, which Subtracted from 100, the remainder will be the premium. EXAMPLE. 4. If a policy is taken out for $49277,77,7* to cover $44350 what is the premium per cent. ? 49277,77,7* : 44350 : : 100 : 90100=10. Ans. 10 per cent. CASE IV. Having the policy for covering any sum and the premium given> to find the sum to be covered. RULE. Subtract the premium from 100 ; multiply the policy by the remainder and cut off the two right hand figures, the left hand figures will be the sum to be covered, 150 COMPOUND INTEREST. EXAMPLE. 5. If a policy is filled for 49277,77,7^ at 10 per cent. ; what is the sum to be covered ? 100 49277,77,7^ 10==premium. 90 90=reniainder. 44350,00,00,0 Ans. $44350. COMPOUND INTEREST. . COMPOUND INTEREST is that which arises from the prin- cipal and its simple interest, when due and forborn, reckoned together as a new sum ; so that the principal and interest is always increasing. RULE. Find the amount for the first year, and make it the principal for the second year ; and so on for any num- ber of years; subtract the given principal from the last amount, the remainder will be the compound interest. EXAMPLES. I. What is the compound interest of $744 forborn 4 years at 6 per cent, per annum ? $744=prinoipaJ. g835,95,84=prin. 3d year. 6=rate per cent. 6 44,64=int. for 1 year. 50,1 5,7 504=int. for 3d. yr. 744,. . =giveii prin. 835,95,34 . . =last principal, g788,64=amt. lst.yr.&> $886,1 l,5904=amt. 3d. yr. & 6 prin. 2d. yr. } 6 principal 4th. 47,31, 84=int. 2d. yr. 53,16,695424=int. 4th yr. 788,64 . . =last prin. 886,1 1 ,5904 . .=last principal. $835,95,84=auit, 2d. & $939,28285824=amt. 4th. year, prin. 3d. yr. 744 =rgiven principal. $195.28.2 ? 85824=int. for 4 years. Ans, $195,28.2. COMPOUND INTEREST. 151 2. What is the compound interest of 840 for 3 year?, at 5 per cent, per annum ? Ans. g!32,40,5. 3. What is the amount of 256 10 for 7 year at 6 per cent, per annum com. inter. ? Ans. 385 13 7^. A TABLE Showing the amount of l or Ig/rom i to 10 years, at 4, 4 1, 5, and 6 per cent, per annum compound interest. Fears. 4 |?er cew. 4$ per cent A 5 per cent. 6 per cent. 1 2 3 4 5 1,040000 1,081600 1,124864 1,169859 1,216653 1,045000 ,092025 ,141166 ,192519 ,246182 1,050000 1,102500 ,15762'5 ,215506 ,276282 ,060000 ,123600 ,191016 ,262477 .338226 6 7 8 9 10 1,265319 1,315932 1,368569 1,423312 1,480244 ,302260 ,360862 ,422101 ,486095 ,552969 ,340096 ,407100 ,477455 ,551 328 ,628895 ,418519 ,503630 ,593848 ,689479 ,790848 ; NOTE. The ratio, that is, the amount of 1$ or 1 for one year, at any eiven rate is thus found ; $ $ $ RULE. As TOO : 104 : : 1 : 1,04 for the first year. 100 : 104 : : 1,04 : 1,0816 for the second year. 100 : 104 :: 1,0816 : 1,124864 for the third year; and so for any number of years, at any rate per cent. EXAMPLES. 4. What is the amount of g225 for 3 years a 5 per cent, per annum, compound interest ? 225X1, 157625=260,465625=Ans. $260,46,5. 5. What is tke compound interest of $870 for 8 years a 6 per cent per annum ? 1,593848x870=1386.647760 870=Ans. 516,64,7,, 6. What is the amount of 845 12 for 9 years, at 4^ per cent, per annum compound interest ? 845,6X1,486095=1256,641932=:1256 12 10 Ans. NOTE. The operation by the common rule to find the compound interest of any sum for several years being extremely laborious, the preceding: table will greatly facilitate tho work. DISCOUNT. DISCOUNT. DISCOUNT is an abatement of part of a sum of money. due some time hence, in consideration of prompt pay, or present payment of the remainder. The sum paid is the present worth, which is such a sum, as, if put on interest, would in the same time and at the same rate, for which the discount is to be made, amount to the sum or debt then due. CASE I. To find the discount. , RULE. As 100 with its interest for the given rate & time, Is to that interest ; So is the giv.-n sum, To the discount required. EXAMPLE. 1. What is the discount of &84G for six months at 6 per cent. ? $ $ $ $ 100 103 : 3 : : 846 : 24,64^. 6 mo. 6U)6,00 $3 r Ans. $24,64. NOTE. From the given sum $846 Subtract the discount 24,64 T 7 Remains the present worth CASE II. To find the present worth. RULE. As 100, with the interest for the given rate & time. Is to 100 ; So is the given sum, to the present worth. DISCOUNT. EXAMPLE. 2. What is the present worth of &874 at 6 per cent, due 4 years hence ? $ $ $ $ 100 124 : 100 : : 874 : 701,83,8 ff. 6 6,00 #r* 24=Int. for 4 years. Ans. $704,83,8f f . NOTE. From the given sum 874 Take the present worth 704,83,8|f Remains the discount $169, 16,1 ^ T NOTE 1. It is immaterial whether the present worth, or the dis- count is first found, for the difference between the debt and either of them will be the other. 2. The general practice among bankers in discounting bills is to find the interest of the sura drawn for, from the time the bill is dis- counted, to the time when it becomes due, including the days of grace ; which interest is reckoned as the discount. This method, Jiowever, makes the Discount more than in justice it would be. BANK DISCOUNT. RULE. Multiply the given sun? by of the days, in- cluding the days of grace, and cut off' as directed in Case VIII. in Simple Interest, Federal Money. EXAMPLES. 3. What is the discount of $1 1540 for 30 days ? 11540 i)33=given days with grace. 5 1 &i=A days and grace. 57700 5770 $63,47,0 Ans. 63,47, 4. What is the discount of 12000 for 60 days ? i)63=given days uith grace. 12000 = days and grace. 120000 6000 Ans- 14 EQUATION OF PAYMENTS BARTER. In the preceding examples for 30 and 60 days, the 3 jlays of grace are added, making 33 and 63 days, which is the customary mode at the banks. EQUATION OF PAYMENTS. EQUATION o? PAYMENTS is finding a meantime for pay- ing the whole debt, when several sums are due at different times. RULE. Multiply each sum by its time of payment, and divide the sum of the products by the whole debt ; the quo- tient will be the equated time. EXAMPLES. I. A owes B $2000, of which $500 is to be paid in 4 jnonths ; 600 in 5 months ; $600 in 6 months ; and $300 in 8 months ; when must the whole be paid at one pavment ? 500X4=2000 600x5=3000 600x6=3600 300X8=2400 The whole debt 2,000) 1 1 ,000=sums of products. 5i mo. Ans. 5 months. 2. A merchant bought goods to the value of $4000, to be paid as follows; -viz. $1200 in 4 months ; g800 in 6 months, and the remainder in 12 months; but afterwards agreed to pay the whole at ane time ; when must the debt be paid ? Ans. 8 mo. 12 days. 3. A owes B $840 to he paid as follows : 1 in 3 months, ^ in 4 months, and the rest in 6 months; at what time must the whole be paid at once ? Aus. 4J months. BARTER. BARTER is the exchanging of one commodity for another, and instructs traders so to proportion their goods of differ- ent kinds, value and quantities, that neither party may sus- tain loss. BARTER. CASE I. When the quantity and value of one article are give}L, to find how much of some other must be given for it. RULE. Find the value of that article, whose price is given : then say, by the Rule of Three Direct, As the pricje of the article required, per Ib. or yd. &e. Is to 1 Ib. 1 yd. &c. ; So is the value of the given article, To the quantity of the article required". EXAMPLES. 1. Two merchants barter; A has 12 2 14lb. of sugar at $12 per cwt. which he wishes to exchange with B for cot- lon at 25 ceuts per Ib. : hovr much cotton must B give A for his sugar ? qrs.' lllb 12=price 1 cwt. sugar. 12 c. Ib. $. 144 As ,25 : 1 : : 151.50 6 ' 1 1,50 ,25)151,50(606 Ib. $151,50=value of A's sugar. B must give A 606lb. cotton for l 2 14lb. sugar. Ans. 6061b. 2. A has rum at Sl;50 per gal. and B has 4 pipes of Madeira wine, containing 125 ga/Tbjis each ? at $3,50 p gal. how much of A's rum can B have for his wine ?^ Ans. 1166| gals. 3. How much coffee, at 23 cents perlb. must be given in barter for 9 chests of tea, each weighing 95 Ib. at gl,75 per Ib. ? Ans. 6505 6 IS^ drs. CASE II. When a trader has goods at a certain price ready money, but in barter advances the price. RULE. Find at what the other ought to rate liis goods, in proportion to that advance price ; then proceed as in Case I. J^OTF.. The quantity of the latter commodity maybe found either by the ready money or bartering price. EXAMPLES. 4. A has raisins at 25 cents per Ib. ready money, but in barter will have 30 cents per lb.$ B has tea at $1,75 per BARTER. Ib. ready money : what ought B to rate his tea at inbarter> and what quantity of tea must be given for 20 boxes ot" A's raisins each weighing 35 Ib. ? 35 700Z6. 20 ,25 ready money price. 7.00=wt. of raisins. 3500 ,30=barter price. 1400 $210,00=value of raisins, $175,00 =alue at, ready at bartering price. money, c. c. $. As ,25 : .30 : : 1,75 .30 .25)5250(2,10 B's bartering price. $ Ib. $. As 2,10 : 1 : : 210,00 1 2, 10)2 10,00(1 00 Ib. tea. Or ready money price. $. ib. $. As 1,75 : 1 : 175,00 1 1,75)175,00(100 Ib. tea as before. A fS2,10 B's barter price, *' 100lb. quantity of tea. PROMISCUOUS QUESTIONS. 5. A trader lias cinnamon at 30d. per Ib. ready money, iu barter must have 3Qd. per Ib. ; B has nutmegs worth ;. per Ib. ready money; at how much must B rate his Tiutmegs per Ib. that his profit may be equal to A's ? Ans. 9s. C. Two traders barter ; A has 120 cwt. sugar at $12 per ,>\t : B has 256 yards broadcloth at $5 per yard; who must receive the difference, and how much ? Ans. $160 difference in favour of A. i. A has 200 yards of broadcloth worth g2 5 50 per yard, lor which B gives him $250 re ady money, and 500 gal- lons of molasses ; at what did B value his molasses per gallon ? Ans. 50 cents per gaL LOSS ^ND GAIN. 157 'o. A has 200 yards of broadcloth worth $2,50 per yard, for which B gives him $250 in cash, and the rest in molasses at 50 cents per gal. ; how much molasses did B give A be- sides the cash ? Ans. 500 gals. 9. A exchanges with B 40 Ib. of indigo at gl per Ib. ready money, and $1,25 in barter, but is willing to lose 10 per cent, to have ^ ready money ; what is the ready money price of 1 yd. of cSoth delivered by B at S3,50, to equa'l A's bartering price : and hew many yards were delivered ? A C$ 2. Say by the Rule of Three Direct, As the price it cost, Is to the gain or loss ; So is 100, to the gain or loss per cent. EXAMPLES. 1. Wheat is bought at $1,25 and sold at $1,50 per bushel? what is the gain per cent, ? $ '- $ $1.50=priee sold for. As 1,25 : ,25 : : 100,00 l,25=price given. ,25 j25=gain per hush. l,25)2500,00(20,0a Aus. 20 per 14* LOSS AND 2. How much per cent, profit, at 4s. on the pound ? Aus. 20 per cent. 3. How much per cent, profit, at 25 cents on the dollar f Ans. 25 per cent. CASE II. To know how an article must be sold to gain or lose so much per cent. ? RULE. By the Rule of Three, say, As 100, is to the price; So is 100, with the gain added, or loss subtracted, To the gaining or losing price. EXAMPLES. 4. If wheat is bought for SI, 25 per bushel ; how must it W sold to sain 20 per cent. ? $ $> $ 100 : 1,25 : : 120 120 $l,50,00=selling price per bush. Ans. SI, 50. 5. If goods worth 450 are shipped and corne to a bad market ; what will be the amount, if sold at 15 per cent. loss ? Ans. $382,50. 6. Bought 150 yards cloth for 45 ; how must it be sold to gain 25 per cent. ? Ans. 56 5. CASE III. To know ivhat an article cost, when there is gained or lost so much per cent. ? RULE. By the Rule of Three, say, As 100 with the gain added, or loss subtracted, Is to the price ; So is 100, to the prime cost. EXAMPLES. 7. If wheat is sold for gl,50 per bush, and there is gain- ^td 20 per cent. ; what did it cost per bushel ? 100 20 $ $ 120 : 1,50 : : 100 1.50 12,0)15,00,0 $l,25=;primecost, Ans, $1,25. EXCHANGE, 8. If goods are sold for $382,50 ; by which there is lost 15 per cent, ; what was the first cost of them ? Ans. $450. CASE IV. To know what would be gained or lost per cent, if goods, sold at such a rate, there is gained or lost so much per cent, if sold at another rate. RULE. By the Rule of Three, say, As the first price, Is to 100, with the gain added or loss subtracted; So is the other price, To the gain or loss per ceiit. at the other rate. NOTE. If the answer is 100, there is neither gain nor loss ; the excess of 100 is gain ; the deficiency of 100 is loss per cent. EXAMPLES. 9. If wheat, sold at gl.50 per bushel, gain 20 per cent what gain or loss per cent, will there be if sold at 1,2-5 per bushel ? S- ? $ As 1,50 : 120 : : 1,25 120 1,50)150,00 $100 Ans. There is neither gain nor loss. 10. If, when tea is sold at $1,40 per Ib. there is lost 30 per cent. ; what is the gain or loss if it should be sold at $1,50? Ans. 25 loss. EXCHANGE. EXCHANGE, considered as the subject of Arithmetic is the method of finding how much money in oce country is equivalent to a given sum in another. "Par" signifies equality ; that is, when a sum of money in one country. is of the same value, or contains the same quantity of pure gold or silver as a sum in another coun- try ; Exchange then is said to be at par. " The course of Exchange" is the current price between two places, which is sometimes above and sometimes below |60 EXCHANGE. par, according to the circumstances of trade, or the de- mands of money. The course of Exchange between two nations is figuratively speaking, a herald, which proclaims publicly the state of commerce and money negotiation* be- twixt them, and which of the two is indebted to the other. Questions in Exchange are answered by the Rule of Three or Practice. Rules for reducing the several currencies of the United States, also Canada ami Nova-Scotia, to a par each with the other, have been given ; see page 92-95. The subsequent relate principally to foreign Exchange. I. GREAT BRITAIN. Accounts are kept in Great Britain and the West-In- dies in pounds, shillings, pence and farthings. 4 Qd. sterling is equal to one dollar federal money. CASE I. To change pounds sterling to federal money. RULE. To the sterling add i, to the sum annex three ciphers, divide by 3, and cut off the two right hand figures for cents, the figures on the left will be dollars. EXAMPLE. 1. In jl26 sterling how many dollars ? )126=sterling. 42 3)168000 8560,00 Ans. $560. CASE II. To change pounds, shillings, pence and farthings sterling te dollars and cents. RULE. Reduce the shillings, pence and farthings to the decimal of a pound by Case II. or III. in Decimal Frac- tions, annex it to the given pounds, add of the sum, divide by 3 and cut off two right hand figures, as before directed. EXAMPLE. 2. Reduce 246 18 4 sterling to federal money. i)246.919 82306 3)329225 $1097,41| Ans. $1097,41$, EXCHANGE. J Q CASE III. To change dollars to sterling. RULE. Multiply the dollars by 3, from the product subtract ^. and from the remainder cut oft' the right hand figure for the decimal of a pound. EXAMPLE. 3. In $560 how many pounds sterling ? 560=given dollars. 3 )1680 420 126,0 Ans. 126. CASE IV. To change dollars and cents to pounds sterling. RULE. Multiply the dollars and cents by 3, from the product subtract , and from the remainder cut off the three right hand figures for decimals of a pound, the figures on the left will be pounds sterling. EXAMPLE. 4. Reduce $1097,41f to sterling. 3 82306,25 246,91875=246 18 4. Ans, 246 18 4, II. IRELAND. Accounts are kept in pounds, shillings, pence and farth- ings. 4 IQi q r8f I r i. s h are equal to SI Federal Money. 1 l the sum will be Irish. EXAMPLE. & In g444,44i how much Irish money ? 444,44i=federal. 3 )1 33333 33333 T V)100.000=sterling. 868 108 6 8=Irish. Ans. 108 6 8. III. HAMBURGH. In Hamburgh accounts are kept either in Pounds, Schil- lings, and Groats Flemish ; or in Marks, Schillings Lubs, or Stivers, and Phinnings or Deniers. 12 phinnings, or deniers, or 2 groats=l schilling-lub, or stiver=l 1-8 penny sterling. 16 schillings-lubs, or stivers, or 32 groats=l mark=l 6d. sterling, 2 marks 1 dollar=3j. sterl. 3 marks 1 rix doll.=4 6rf. ster.=r 1$ federal money. 7f marks >....! pound Flemish. "32 Flemish pence 1 mark. ALSC, 12 groats or pence Flemish ..... 1 schilling Flemish. 20 schillings Flemish 1 pound. The mark banco=33 1-3 cents by the laws of United States. NOTE. The current money of Hamburgh is of less value than that of the Bank. This difference is called the " as " ble, but always in favor of the bank v EXCHANGE. 100 Ib. in Hamburgh = 107| lb< in the United States. 100 ells . . . . = 62 yards. CASE I. To reduce Marks to Federal Money. RULE. Divide the given sura by 3. EXAMPLES. 1. Reduce 155442 marks to dollars and cents, at 33| cts. per mark. 33=! of a dol. 3)155442=marks. g51814 = dollars. Ans. $51814. 2. In 8456 marks 3 stivers ; how many dollars and cts. ? 3)8456 =marks. 2818,06| ,16f =8 stivers. $2818,831 Ans. $2818,83*. CASE II. To reduce Federal Money to Marks. RULE. Multiply the dollars by 3, the product will be marks. If dollars and cents are given, multiply by 3, cut off two right hand figures, for decimals of a mark, which heing reduced will give the stivers and deniers. EXAMPLE. 3. Reduce $2818,83^ to marks and stivers. $28 18,831 3 Marks 8456.50 16 stivers = mark. 300 50 Stivers 8,00 Ans. 845G marks 8 stivers, ASE III, To reduce Hamburgh to Sterling Money. RULE. Divide the given sum by the rate of Exchange, and the quotient will be Sterling. EXCHANGE. EXAMPLE. 4. How much sterling will a bill on Hamburgh, amount ing to 6609 marks 6 stivers, be worth, Exchange at 35 3d per pound sterling ? 35 3d. 6609 marks 6 stivers. 12 32= marks 2 423 13218 12 groats. -19827 12=6 stivers. 423)211 5 )0( 500 . sterling. 2115 Ans. . 500. 00 CASE. IV. To reduce Sterling Money to Hamburgh currency. RULE. Multiply the sterling by the rate of exchange, and the product will be the answer in the same denomina- tion to which the exchange was reduced. EXAMPLE. 5. How many marks should be received at Hamburgh, for .500 sterling, exchange at 35 3d. per pound sterling-? 35 3 423 12 500 423=groats 2)21 1500=groats. 16)105750=stivers. marks 6609,6 Ans. 6609 marks, 6 stivers. NOTE. To reduce current to bank money ; say, as 100 with the agio added, is to 100 bank : so is the current money to the bank money required. Also to reduce bank into current money ; say, as 100 is to 100 with the agio added : so is the bank money given, to the current required. IV. HOLLAND. In Holland there are two banks, the one of Amsterdam and the other of Rotterdam. The bank of Amsterdam is the most famous and considerable in Europe. It was established in 1609, by the au- thority of the States General, under the direction of the Burgomas- ters of the city, who, having constituted themselves the perpetual cashiers of the merchants of Amsterdam, are themselves a security for the bank. EXCHANGL. Various opinion- have been formed respecting the real sum of mon- ey deposited in this bank, but very few have estimated it under 30 millions sterling. It is to this bank the city of Amsterdam owe? its splendor r.jul magnificence, which though it possesses the greatest part of th<; merchants ready money, rather promotes than interrupts their com- merce, by the security and dispatch with which a bank credit is at- tended ; for as business in the bank is negotiated by transfers, mill- ions may be paid in a day, without the intervention of any cash, which is of the greatest consequence in expediting trade that can possibly be imagined.* In Holland, Flanders and Germany, accounts are kept iu Pounds, Schillings and Pence Flemish, divided as the British pound; but they *re kept more generally in Guild- ers or Florins, Stivers, Deniers or Phiuuings. 8 Phinnings . . make . 1 Groat. . . s. value of 1 livre. 67 520 8440 4220= cent. $1561,40 Ans. 81561,40. 2. My correspondent writes me, advising of the safe ar- rival oft he brig Huntress at Bourdeaux, and that he had received in good condition lhe_gods shipped arid consign? j d to him for my account ; that the net proceeds, after de- ducting freight, duties, commission, &e. ; amounted lo 74101 livres 10 sols, exchange at 20 cents per livre; with what sum in Federal money must I debit his account? 71101,5 =^Iivres and sols. 20= rate of exchange. 814820,30,0 Ans. 14820,30. CASE IT. To reduce Federal Money to Livres f . Divide the given 1 sum by 18^ or llie rate of ex ciange, the quotient will be ihe answer. EXAMPLES. 3. Reduce gl 56 1,40 to livres. 18,5)1561,40,0(8440 Ans. "8440 livres NOTE. To change French to Sterling, say, As one crown is to the given rate of exchange ; so is the French sum to the Sterling money ; also, To change Sterling to French, say, As the rate of ex- change, is to one crown, so is the Sterling to the French money. VI. SPAIN. The monies in Spain are of two sorts; the. one is called plate money, by which is understood, silver money; the 'her is called vellon. EXCHANGE, Foreign bankers or remitters at Madrid, Cadiz, Seville., &c. keep iheir accounts in piastres, rials and mervadies, reckoning 34 mervadies to a rial, and 3 rials to a piastre, the par of which is 3 Id. sterling. The shop-keeper at Madrid, the custom-house, and other deal era wiihiti the kingdom keep their accounts in rials and mervadies veilou. The doubloon of exchange is equal to 4 piastres or 32 mis. Accounts also are kept in dollars, rials and mervadies.> and exchange by the piece of eight = 4 tid. at par. 34 mervadies = 1 rial. 8 rials . = 1 piastre or piece of eight. 10 rials . = 1 dollar. The rial plate is = 10 cents, and the rial vellon 5 cents in the United States; therefore, Jb reduce Rials Plate and Rials Vellon to Federal Money. RULE. Multiply the rials plate by 10, aud the vellon by 5, the product will be the answer. EXAMPLES. 1. Reduce 8471 rials plate to dollars and cents,' 8474 10 $847,40 Ans. $847,40. 2. Reduce 8354 rials vellon to dollars and cents. 8354 417,70 Ans. 417,70. London remits to Cadiz .874 12 4 sterling, ex- change at 37frf. per piastre; how much will be received for this remittance at Cadiz ? 37| 874 12 4x8-5-303=5542,1254= 8 5542- piastres 1 rial 203 15* EXCHANGE. 'VII. PORTUGAL. Accounts are kept at Oporto and Lisbon in reas and ex- change on the milrea=5 7$ sterling, at par, or $1,25 in the United States. 1000 reas=l milrea. CAGE I. To change Miireas and Iteas io Federal Money. RULE. Multiply the given sum by 1,25 and cut off three right hand figures for decimals of a cent ; or add to the given sum and the answer will be dollars and parts of a dollar. EXAMPLE. 1. My correspondent at Oporto advises of the sales of goods shipped and consigned to him, the net proceeds, af- ter deducting commissions, duties, See. amounted to 14637 mil reas, 800 reas, exchange at &1,25; how much must he !>e debited ? 14637,800 Or 1)14637,800 1,25 3659450 73189000 $J 8297,25,0 as before. 292756 146378 $18297,25,000 Ans. $18297.25. CASE II. To reduce Federal Money to Milreas. RULE. Subtract ^ from the federal money carrying the division to three places from the dollars, the remainder be miireas and reas. EXAMPLE. 2. Reduce $1 8297,25 to miireas, a &1,25 per milrea. 4)18297,25,0 3659450 1 4637,800 Aus. 14637 tnilreas, 800 reas. VIII. DENMARK Accounts are kept at Denmark in Current Dollars and Skillings reckoning 96 skillings to the dollar. The rix dollar is=$l in the United States, EXCHANGE. To change Danish to Federal Money, RULE. The rix dollars being equal to Federal Dollars, therefore find the value of the parts, aud annex it to the dollars. EXAMPLE. In 14786 rix dollars and 50 skillings how many dollars and cents, exchange 100 cents per rix dollar ? 14786,50 96 814786,48,00 Ans. $14786,48. IX. EAST-INDIA MONEY. 1. BENGAL. Accounts are kept at Madras in Pagodas, Faoams, and Cash. 80 cash=l Fanam. 36 Fanams=l Pagoda. 1 Pagoda=Sl,94 in the United States. To change Pagodas into Federal Money. RULE. Multiply by 1,94. 2. CALCUTTA, Accounts are kept in Rupees, Annas, and Pice* 12 pice=l anna. 16 annas=l rupee. The rupee of Bengal=55| cents in the United States; To change Rupees to Federal Money. RULE. Multiply by 55|. 3. CHINA. Accounts are kept in Tales, Mace, Candareens and Cash. 10 cash ... =1 candareen. 10 candareens . =1 mace. 10 mace . . . =1 tale, which is equal to gl,43 iu the United States. CONJOINED PROPORTION. To change Tales to Federal Money. RULE. Multiply tales by 1,48. NOTE. Those who wish to acquire a more particular knowledge, of Foreign Exchange may find a very extensive and excellent treatise on, the subject, in u Walsh's Mercantile Arithmetic." CONJOINED PROPORTION. CONJOINED PROPORTION is when the coins, weights and measures of several countries are compared in the same question, and discovers their relation, one to another. CASE I. When it is required to find how many of the first sort of coin, weight or measure, given in the question, are equal to a given quantity of the last. RULE. 1. Place the numbers alternately, beginning at the left hand, and let the last number stand on the left hand. 2. Multiply the first column continually for a dividend, and the second for a divisor. PROOF. Make as many statements in the Rule of Three Direct as the question requires. EXAMPLES. 1. If $4 are worth 40s. and 30s. 6 crowns, and 120 crowns, worth 30, and 42 40 guineas, how many dollars are equal to 1300 guineas ? Left. Right. $4=40*. Left 4 X 30 X 1 20 X 42 X 1 300=786240000=cli vidcnd. s. 30=6 cro. Right 40 X6x30x40=288000=di visor. cro, 120=30, . 42=40 guin. And 7862400000~:-288000=2730 dolls. guin. 1300=$ Ans. $2730. CASE II. When it is required to find how many of the last sort of coin , weight or measure, given in the question, are equal to a quantity of the first. RULE. 1. Place the numbers alternately, beginning at the left hand, and let the last given number stand ou the right, ARBITRATION OF EXCHANGES. 2. Multiply (he first column continually together for a divisor, and the second for a dividend. EXAMPLE. 2. If20lb. at Boston are equal to 18lb. at Rotterdam ; 180lb. at Rotterdam, 224lb. at Versailles; how many pounds at Versailles are equal to lOOlb. at Boston ? Left. Boston 20=18 Rotterdam. Left 20Xl80=3600=divisor. Rotterdam 180=224 Versailles. Right 1 8X224 X 100=403200=div. Boston 100. And 403206-^3600=851 121b. ABS. ARBITRATION OF EXCHANGES. ARBITRATION OF EXCHANGES means a method of choos- ing the best way oi' remi'.tiiig money abroad, with the greatest advantage. It is by comparing the par of Exchange, already found, with the present course of Exchange, that the best \vay to remit, or draw, to most advantage can lie determined/ It is performed by Conjoined Proportion. EXAMPLES. My Correspondent at Rotterdam has 3500, which he can remit by way of Oporto, at 840 reas per dollar, from Oporto to Boston at 8 2d. per milrea (or 1000 reas) ; Or he can remit by way of Roehelle at 5 livres per dollar, and from Roehelle to Boston at 6 8d. per crown ; which circular remittance is the most advantageous, and what is the difference ? First. gl at Rotterdam=840 reas at Oporto. Reas 1000 at Oporto .. =98rf. at Boston. 1000x1=1000 divisor. $3500 at Rotterdam. 840x98x3500=288 1 20000=dividend. 2881200001000=288120 pence. 12288120 24010 shillings. g4001,66-,6f by way of Oporto. INVOLUTION- Secondly* $1 at Rotterdam=5| livres at Rochelle, Livres6 at Rochelle=80t/. at Boston. lX6=6==divisor. $35 JO at Roehelle. 80x5fx3500=1512000=divideiH}. 1512000-v-6=25200Q pence. 12252000 6 21000 shillings. S3500 by way of Rochelle ; consequently the rex mittance by way of Cporto is most advantageous, making the difference of 501,66,6f Ans. The difference of the remittance wholly depends on the Course of Exchange at the time; an extensive correspon- dence therefore, is absolutely necessary to acquire a thorough knowledge of the Course of Exchange to make this kind of remittance profitable. INVOLUTION. INVOLUTION is the finding of power.?. If a number is continually multiplied by itself, the sev- eral products are called "powers" of that number; thus, 2 : 4 : 8 : 16 : 32 : 64 : 128 are powers of the number 2.' NOTE. These powers exist in nature, viz. a root is represented by a line or . years old. . . 11 J Eldest 23 J tSio youngest is 2 years old, and the eldest 23 ; what is the difference of their ages, and the age of each ? 232=2181=3 com. diff. of their ages, Youngest 2") 4th 7(h 6th 5th PROPORTION II. The two extremes and the number of terms being given, to find the sum of all the terms. RULE. Multiply the sum of the two extremes hy half 'he number of terms, the product will be the sum of all the terms. EXAMPLES. 3. What is the sum of an Arithmetical Progression, whose extremes are 3 and 33, and number of terms 11 ? 3-|-33=36x51=l 98=sum of all the series. Ans. 198. 4. How many times does a clock strike in 12 hours ? 12-{-l=13x6=78. Ans. 78, PROPOSITION III. The two extremes and common difference being given, to find the number of terms. RULE. Subtract the less from the greater extreme, and divide the remainder by the common difference, the quo- tient plus one will be the number of terms. EXAMPLES. 'j. The two extremes are 3 and 33, and the common dif- ference 3 ; what is tlie number of terms ? 33 3=30-r-3=10-j-l=ll=number of terms Ans. 6. A man starting from Boston to travel to a certain place, his first day's journey was G miles, and his last was 40 miles ; he increased his travelling each day 4 miles , how many days did he travel ? 40 6=34-f-4= 8, i-f-1 =9 i. Ans. 9 A days. PROPOSITION IV. Either of the extremes, the number of terms, and common difference being given, to find the other extreme. RULE. Multiply the common difference into the num- ber ef terms minus one, subtract the product from the greater extreme, the remainder will be the less extreme; or add the less extreme to that product the sum will be the greater extreme. GEOMETRICAL PROGRESSION, EXAMPLES. 7. The less extreme is 3, the greater 33, the number of terms 11, and the common difference 3; either extreme is required. 3x10=30 33=3 less extreme. And 3x10= 30+3 =33= greater extreme. Ans. 3 and 33. 8. A man in 7 days travelled from Boston to New-York, he increased each day's journey by 3 miles, his last day's journey was 45 miles ; what was the first day's journey, and how many miles did h travel ? Number of terras 7 1=6x3=18 45=27= 1st days jour'y. By proposition II. 27+45=72x3i=252=number miles, C 27 miles. ? Distance 252 miles. GEOMETRICAL PROGRESSION GEOMETRICAL PROGRESSION is when any series of nnm- bers increase by one common multiplier, or decrease by one common divisor; as, 2 : 4 : 8 : 16 : 32 ; here 2 is the common multiplier. And 64 : 32 : 16 : 8 : 4 : 2 5 here 2 is the common divisor. NOTE. The common multiplier, or divisor, is called the ratio. In any Geometrical Progression the same things are to be observed as in Arithmetical Progression, viz. 1. The extremes, or first and last terms. 2. The number of terms. 3. The ratio, or common multiplier or divisor. 4. The sum of all the series ; any three of which being known, the others may be found. NOTE. 1. If any three numbers are in Geometrical Prog-re?:- ion., the product of the two extremes will be equal to the square of the mean or middle number, thus, 4 . 8 . 16 ; 4X16=64=8X8=64. 2. If four numbers are in Geometrical Progression, the product of the two extremes will be equal to the product of the two means ov middle numbers j thus, 81 . 27 . 9 . 3 ; 81X3=243=27X9=243, 3. If many numbers are in Geometrical Progression, the product of the two extremes will be equal to the product of any two means that are equally distant from them ; thus, 2.4.8. 16 . 32 . 64 ; 2X 64=1 28=4X32== 125=8 X 16=128. 4. If the numbers are odd. the product of any two extremes will be equal to the square of the mean; thus, 2 . 4 . 8 > 16 - 32 j 2X 32=64=4 X 16=64=8 X8=64, GEOMETRICAL PROGRESSION, PROPOSITION I. The two extremes and common ratio being given, to find the sum of all the series. RULE. Multiply the greater extreme by the common ratio, subtract the less extreme from the product, and di- vide the remainder by the common ratio minus one, the quotient will be the series. EXAMPLES. 1. What is the sum of a geometrical series, whose ex- tremes afe 2 and 4374 and the common ratio 3 ? 4374x3=131222=1312031=6560 Ans. 2. A gentleman marrying, received from his father-in- law one dollar, on condition, that he was to receive a pre- sent on the first day of every month for the first year, which should be double still to what he had the month before 5 what was the lady's fortune ? Aiis. ^095. PROPOSITION II. The less extreme, common ratio, and number of terms being given, to find the greater extreme. RULE, Raise the ratio to a power denoted by the num- ber of terms minus one, and multiply that power by the less extreme, the product will be the greater extreme. EXAMPLES. 3. The less extreme is 4, the common ratio 2, and num- ber of terms 10; what is the greater extreme ? 2 9 x4=2048=greater extreme. Ans. 2048. 4. What debt will be discharged in 12 months by pay- ing gl the first monih, 2 the second, each month paying double to the preceding payment, and what will be the last payment ? 2 1 1 2048X2 1=2048 last payment. By propo. I. 2048x2=4096 l = $4095=the debt. PROPOSITION III. The greater extreme., common ratio, and number of terms being given, to find the less extreme. RULE. Raise the ratio to a power denoted by the num- ber of terms minus one, and divide the greater extreme t>j that power, the quotient will be the less extreme* GEOMETRICAL PROGRESSION. EXAMPLE. 5. The greater extreme is 2048, the common ratio 2, and the number of terms 10 ; what is the less extreme ? 2 9 = 5122048=4 less extreme. Aus. 4. PROPOSITION IV. The two extremes and common ratio being given, to find the number of terms, RULE. Divide the greater extreme by the less, and raise the ratio to a power equal to the quotient, add one to the index of that power, and the sum will be the number of terms. EXAMPLES. 6. The two extremes are 4 and 2048, the common ra- tio 2 ; what is the number of terms ? 2048-7-4=512. 2 9 =512. Therefore 9-f 1 = 10 Ana. 7. In what time will a debt be discharged by monthly payments, the first of which is $1 and the last $2048, the ratio being 2 ? 2048-r-l=2048 . 2^=2048. Therefore 11+1 = 12 ino. An. PROPOSITION V. The two extremes and number of terms being given, to find the common ratio. RULE. Divide the greater by the less extreme, and ex- tract that root of the quotient, whose index is denoted by the number of terms minus one, the root will be the com- mon ratio. EXAMPLES. 8. The two extremes are 4 and 2048, and the number of terms 10 ; what is the common ratio ? 2048-r-4=512. Therefore 512 9 =2 com. ratio. Or 512 3 (8 3 =2 com. ratio Ans. 9. What will be the ratio of the scries in discharging a debt in a year by monthly payments, the first payment of which is $1 and the last 8204*8 ? 2048-r-l=2018. Therefore 204*1* * 2 common ratio. POSITION, POSITION. NEGATIVE ARITHMETIC, called the Rule of False, is that, by which a true number is found out by supposed num> bers. Position is either Single or Doable. SINGLE POSITION. RULE. Suppose any number at pleasure, and work it according to the nainre of the creation. If the result fully agrees with the conditions of the question, the work i*s dene, and the number supposed will be the answer ; but if not, proceed thus, As the result of the supposition, Is to the number supposed ; So is the given number in the question, To the true number, or answer. EXAMPLES. 1. A gentleman had a certain number of dollars in his purse, the sum of the third, fourth and sixth part of them made 54 ; how many were in the purse ? 60=supposed number. Then, as 45 : 60 : : 54- 54 20=i O f the supposed numb. = ditto. Proof 3 10=i ditto. 45=rsu m of supposition 72 240 300 24 18 45)3240(72 dolls. 12 54 Ans. 872. 2. Three persons conversing about their ages, said the first, I am so old ; said the second, I am as old again as that ; and said the third, I am as old as the first and half as old as the second ; their ages taken together make 108 vears $ what is the age of each? ("First 21|. Ans. Second 434. (.Third 431. DOUBLE POSITION. DOUBLE POSITION requires two suppositions, which must be used ai-eor^ing to the nature of the question. If either of the supposition* answer the question, the work is flone, but if not, observe the following rule.. POSITION. 187 RULE.. Compare the conditions of the question, with the results of the suppositions, and find whether each sup- position is greater or less than the true answer; if greater mark the excess with + if less, with , and set down both suppositiens and their errors with the signs opposite to them ; then say, As the difference of the errors, if alike, or sum, if unlike? Is to the difference of the suppositions 5 . So is either error, To a fourth number ; which, being added to or subtracted (as the case may re- quire) from the supposition, opposite to the error which is used, will be the true answer. EXAMPLES. 1. A person, being asked the age of each of his sons, re- plied, that his eldest son was 4 years older than the second; his second 4 years older than the third; his third son 4 years older than the fourth, or youngest ; and his youngest son was half the age of the oldest ; what was the age of each of his sons ? First. sup. error, Suppose the youngest 8 years then would the ages of 8 2 the other three be 12, 16, and 20. 18 -f 3 Half of 20=10 and 10 8=2=the first error, and less. 10 5 Secondly. Suppose the youngest 18 years, then would the other three be 22, 26 and 30. Half of 30=15 and 18 15=3 second error, and more. As 5 : 10 : : 2 : 4-f8=12. Or 5 : 10 : : 3 : 6 18=12=the age of the youngest, and the ages of the other three are 16, 20, 24, Ans. 2. A boy, stealing apples, was taken by the owner, and, to appease his anger, gave him half of what he had, and the owner gave him back 10 ; going a little further, he met a man and was compelled to give him half of what he had left, who returned him back 4; going further he met an- other person at whom he gave half of what he then had, and who gave him hack 1 ; at length getting safe away, he found, that he had 13 left; how many had heat first ? Ans. 60. ALLIGATION. ALLIGATION. BY the rule of Alligation, questions, relating to the mixing of different simples, are resolved, it is either Me- dial or Alternate. ALLIGATION MEDIAL Is when there are given the quantities and prices of the several simples to be inixt, to find the price of some quan- tity of the mixture. RULE. Find the values of all the given quantities of the simples to be mixt, at the given prices, and then say, As the sum of the quantities to be mixt, Is to the sum of their values ; So is thatparf, or quantity of the mixture whose price is sought, To its value. EXAMPLE. A grocer, wishing to mix currants, takes 18lb. at 5 cents, 30lb. a 6 cents, and 12lb. a 8 cents per Ib. 5 what is the value of lib. of the mixture ? 181b. a 5c.= 90 30 . . 6c,=180 12 . . 8e.= 96 60Ib. . 183,66 Ib. $ Ib. As 60 : 3,66 : : 1 : 6,1m. Ans, ALLIGATION ALTERNATE. Alligation Alternate admits of several cases, but it is of very little use in business. RULE. Take the difference between each price, and the mean rate, and set them alternately, they will be the answer; which will be as various as the different modes of linking them together. EXAMPLE. How much tea a 16s. 14s. 9s. and 8s. per Ib. will com- pose a mixture worth 10s. per Ib. ? 8 - . 6 a 8s. 2 16s. Ans. 4lb- a 8s. 6 a 9s. 2 a 14s. and lib. a 16s PERMUTATION. PERMUTATION AND COMBINATION OF NUM- BERS. BY the Combination of numbers is meant the different orders, into which any number of things can be disposed, cither by Permutations, Elections, or Compositions. CASE I. To find the number of changes any number of things can undergo. RULE. Assume the natural series of numbers, 1,2, 3, &c. up to the given number of things, and multiply them continually into one another, the Jast product will be the answer. EXAMPLE. How many changes can the three first letters of the alphabet undergo ? 1X2x3=6 Ans. Proof. 1. a b c. 4. b c a. 2 a c b. 5. c b a. 3. b a c. 6. c a b. CASE II. To find the number of Elections of a less number of things from a greater number. RULE. Take the natural order of series 1, 2, 3, &c. up to the number to be elected, and multiply them continually together; then take a series of as many terms, decreasing by otie, down from the number out of which the elections are to be made, and multiply the terms of it continually together; divide the latter product by the former, the quotient will be the answer. EXAMPLE. How many choices of 2 are there in six different things ? Suppose a b c d e f , the things proposed, 1X2= 2. 30^-2-15 Ans f ab > ac ' ad ' ae afj==5 6X5=30. 3 Ans ' I be, bd, be, bf,=4 The elections are <{ cd, ce, cf,=3 de, d=2 15 17 1 90 PERMUTATION. CASE III. To find the number of Compositions of any number of thing* in an equal number of sets, the things being all different* RULE. Multiply the things in every set into one an- other continually, the product will be the answer. EXAMPLE. Suppose 4 companies, each consisting of 10 men, how- many compositions of 10 men each can be drawn out from them. 10X10X10X10=10000. Ans. 10000. Application of the preceding cases. 1. Five travellers came to a public house, and agreed with the landlord to stay with him, as long as they with him could sit in a different position every day at dinner; how long must they stay to fulfil the agreement ? Ans. 720 days. 2. A butcher, wishing to buy some sheep, asked I he owner how much he must give him for 20 ; on hearing his price, he said it was too much ; the owner replied, that he should have 20, provided he t vvould give him a cent for each different choice of 10 in 20, to which he agreed ; how much did he pay for the 10 sheep, according to the bar- gain ? Ans. $1347,56. 3. How many changes are there in throwing 6 dice ? Ans 4665G. 4. How many changes can be rung on the 8 bells belong- ing to Christ Church in Boston, and how long will all the changes take in ringing once over, allowing 8 changes to be rung in a minute. * 5 40320 changes, ' ? 3 days, 11 hours. 5. Two gamesters one day, at dice they would play, And being full merry in wine, Says B. unto A. what odds will you lay, I cast not all the six faces this time ? Says A. then to B. ten to one I'll lay thee, With six dice the six faces you cast not. Pray, gentlemen, shew, and soon let them know, For the odds on the cast, Sirs, they know not. Ans. A.'s chance to that of B, is as 45936 to 720,* orasG/33to 1. SIMPLE INTEREST BY DECIMALS. SIMPLE INTEREST BY DECIMALS. NOTE. 1. Let P = the Principal, or sum put to interest. R = the Ratio, or rate per cent. T= the Time. A = the Amount. I = the Interest. 2. The ratio is the simple interest of $1 or .1 for one year at the rate per cent, proposed, and is thus found ; ratios. As 100 : 4 : : 1 : ,04 = rate at 4 per cent. 100 : 4,5 : : 1 : ,045 = . . 4 per cent. 100 : 6 : : 1 : ,06 = . .6 per cent. 3. All the various cases which can possibly take place in Simple Interest, may be expressed by five theorems, which will be annexed to each case. 4. When two or more letters are joined together like a word, they are to be multiplied continually together. 5. When shillings, pence and farthings are given, they must be re- duced to the decimal of a pound by Cases II. or III. in Decimals, page 82. When cents and mills are given, there is no need of re- duction, as they are in their nature the decimals of a dollar. CASE I. When the principal, time, and ratio are given, to find the Interest. RULE. Multiply the principal, time and ratio together, the last product will be the answer. Or the proposition and rule are more concisely expressed thus, prt. = I. EXAMPLES. 1. What is the interest of .945 10 for 3 years at 5 per cent, per annum ? 945,5=prineipal, ,05=ralio. ,C.141,825=.141 IT Ans. .141 NOTE. When the interest is for any number of days only ; multi- ply the interest of $1 or .! for one day at the given rate, by the principal and given number of day?, the last product will be the an- SIMPLE INTEREST BY DECIMALS. Table of Interest for $\ or . 1 for one day. IPerct. ~ 4 Decimals. Per ct. Decimals. .00008219178 ,00009539041 ,00010958904 ,00012328767 5 6 7 8 .00013698730 ,00016438356 ,00019178082 ,00021917808 The preceding table is thus made ; days. day. As 365 : 06 : : 1 : ,00016438356 365 : 03 : 1 : ,00021917808, &e. 2. What is the interest of g240 for 120 days at 4 per i'ent. per annum ? ,00010958904X240X120=,003,13,6,1 6435200. Aus. $3,15,6. CASE II. Whm the principal, rate, and time are given, to find the amount. RULE. Multiply the principal, rate, and time together, the last product will be the interest, to which add the prin- cipal, and the sum will be the amount. Or, prt.+p.=A. EXAMPLE. 3. What is the amount of $279,50 for 7 years at 4$ per cent, per annum ? 279,50X,045X7=88,04250-J-279,50=$367,54,2|. Ans. NOTE. When there is any odd time given with whole years, re- duce the odd time into days, and work with the decimal parts of a year which are equal to those days. 4. What will 273 18 amount to in 4 years, 175 days, a 3 per cent, per annum ? Ans. 310 14 13,335080064 qrs, SIMPLE INTERST BY DECIMALS. 193 Table of the decimal parts of a year, equal to any number of days, and quarters of a year. Days. Decimals. Days. Decimals. Days. Decimals. 1 2 3 4 5 6 7 8 9 ,002740 ,005430 ,0082:20 ,010959 ,013698 ,016433 ,019178 ,021918 ,024657 10 20 30 40 50 60 70 80 90 ,027397 ,054794 ,082192 ,109589 ,136986 ,164383 ,191781 ,219178 ,246575 100 200 300 365 ,273973 ,547945 ,821918 1,000000 i year =,25 * . . = ,5 1 . . =,75 CASE III. Wlien the amount, rate, and time are, given, to find the principal. RULE. Multiply the rate by the time, add unity to the product, for a divisor, by which divide the amount, the quotient will be the principal. Q f a. _p EXAMPLES. 5. What principal put to interest will amount to $367 ? 54,2 in 7 years at 4^ per cent, per annum ? ,045x7=,315-fl = l,315=divisor. 367,54,21-4-1,315=279,5=8279,50 Ans. 6. What principal will amount to 310 14 1 3,35080064 qrs. in 4 years, 175 days, at 3 per cent, per annum ? Aus. 273 18. CASE IV. When the amount, principal, and time are given, to find the rate. RULE. Subtract the principal from the amount, divide the remainder by the product of the time and principal, the quotient will be the rate. Q ^zEi^R rt. 17* COMPOUND INTEREST BY DECIMALS. EXAMPLE. 7. At what rate per cent, will g279,50 amount to $367 ? 54j2| in 7 years ? 367,54,2i~27950=8S,04,2| 279,50x7=1956,50=divisor. 88,04,25--1956,50=045=4| Ans, CASE. V. WJien the amount, principal, and rate per cent, are given, to find the time. RULE. Subtract the principal from the amount, divide the remainder by the product of the rate and principal. EXAMPLE. 8. In what time will g279,50 amount to 367,54,2^ at 4 per cent. ? 367,54,25 -279,50= 88,04,25=dividend. 279,50X,045= 1 2,5775= divisor. 88,04,25-r-12,5775=7 years. Ans. 7 years. COMPOUND INTEREST BY DECIMALS. Let A=the Amount. P= Principal. T= Time. R= Ratio, that is, the amount of gl or .1 for a year, at any given rate. NOTE. For rules to find the ratio, also a table showing the amount of $1 or .1 from 1 to 10 years, at 4, 4, 5 and 6 per cent, per annum, with rules for its construction, see Compound Interest, page 151. CASE I. When the principal, time, and ratio are given, to find the amount. RULE. Raise the ratio to a power, denoted by the giv- en number of years, by which multiply the principal, and COMPOUND INTEREST BY DECIMALS. 495 the product will be the amount, from which subtract the principal, the remainder will be the Compound Interest. Or p.Xr'.=A. EXAMPLE. 1. What is the amount of $225 for 3 years at 5 per cent, per annum ? 1,05X1,05X1,05=1,157625X225=260,465625. Ans. $260,46,5. NOTE. The raising of the ratio to a power, denoted by the num- ber of years given in the question, being extremely tedious, the ta- ble, alluded to above, will greatly facilitate the operations in Com- pound Interest by Decimals. CASE II. When the amount, rate, and time are given, to find the principal. RULE. Divide the amount by the product of the ratio, raised to a power, denoted by the given number of years, the quotient will be the principal. Q r a - _p r r . EXAMPLE. 2. What principal, being put to interest, will amount tt $260,46,5,625 in 3 years, at 5 per cent, per annum ? l,05xl,05Xl,05=l,157625=divisor. $260,46,5,625-1 ,1 57625=225. Ans. $225. CASE III. When the principal, amount, and time are given, to find the ratio, or rate per cent. RULE. Divide the amount by the principal, the quotient will be the ratio raised to a power, denoted by the given time ; find the root of this power, and it will be the ratio. Or =r t B which, being extracted by the rule in Evolution, will be the ratio. EXAMPLE. 3. At what rate per cent, per annum, will $225 amount to $260,46,5,625 in 3 years ? 260,46,5,625-5-225=1,157625, the cube root of which, it being the 3d power, denoted by the 3 years, gives 1,05=5. Ans. 5. 106 COMPOUND INTEREST BY DECIMALS. CASE IV. When the principal, amount., and rate are given, to find the time. RULE. Divide the amount by the principal, the quotient will be the ratio, raised to a power denoted by the given number of years, which being continually divided by the ratio till nothing remains, the number of these divisions will be the time. Or =r t . which must be divided aceor- ing to the rule. EXAMPLE. 4. In what time will $225 amount to $260,46,5,625 at 5 per cent. ? 260,46.5,625225=1 ,1 57625. 1,157625^1,05=1,1025-7-1,05 = 105-5-1,05 = 1,05. The number of divisions being three gives 3 years. Ans. 3 years. SHORT AND PLAIN SYSTEM BOOK-KEEPING, CALCULATED FOR THE USE OE RETAILERS, MECHANICS AND FARMERS. BOSTON, SEPTEMBER, 1818, BOOKKEEPING. BOOK-KEEPING is the art of recording mercantile transactions. Two methods have been generally adopted, viz; 1. Single entry. 2. Double entry, commonly called the Italian method. The method by single entry is used principally by traders in retail business, and is calculated to answer all the purposes of the mechanic and farmer, that a just and exact state of their less extensive pecuniary concerns may at any time be known. As this method is by much the more concise and simple, it will be explained first, that the scholar may have a dis- tinct view of the subject, and be better prepared to com- mence the more complicated and perfect method by double entry. Single entry requires two principal books, viz; , 1. The Waste, or Day-Book. 2. The Leger. NOTE. There are several other books used by Merchants, for a description of which, see Double entry. The form of the Waste-Book. This book is ruled with two columns on the right-hand for dollars and cents, and one column on the left for insert- ing the folio of the Leger, to which the account is trans- ferred. It is ruled with a top line, on which is written the month, date and year. The articles are separated from each other by a line, and the transactions of one day from those of another by a double line, in the centre of which is the day of the month. For a better description of the Waste- Book, see the specimen annexed. BOOK-KEEPING. The use of the Waste-Book. This book commences with an inventory, containing all the ready money, notes, goods, and every other kind of property, owned by the merchant; als all the debts due by him to others. Then follows a particular detail of every transaction in trade, by which new debts are con- tracted, or former ones discharged; the whole related in a concise and simple style, in the order of time, in which they occur, with ihe quantities and prices of the goods, purchased or sold, with every circumstance, necessary to render the transaction so plain and intelligible, that satis- factory information may be readily given to any interested inquirer. It is of the greatest importance, then, that the Waste- Book be kept wiih particular accuracy, as it contains all the materials composing tfie Leger. Moreover, in cases of disputed accounts, this book is exhibited to judges, and referees for inspection, that they may ascertain the cor- rectness of the entry, as well as the nature of ihe demand, and be enabled to form an equitable decision between the parties. In entering an article in the Waste-Book, the following circumstances should be carefully observed; viz. 1. The date, and on the top of each page, the merchant's place of residence. 2. The person with the title Dr. or Cr. annexed, as he may become Dr. or Cr. in the transaction.* 3. The part of the transaction which belongs to the merchant. 4. The terms of payment. 5. The quantity, quality, mark, &e. of the article. 6. The price. 7. The amount, in the money columns. 8. The folio, or page, to which the article is refered in the Leger. In the Waste-Book, the name of the person, with whom the merchant has dealings, is written over the account in a large round hand, or text, with the term Dr. annexed when he receives any thing, but with the term Cr. when he (the customer) pays, gives or parts with ai?y thing. The titles of Dr. and Cr. may be easily distinguished by the following rules : viz. * The term u transaction"' is applied to all mercantile business, BOOK-KEEPING. 1. The person to whom goods are sold on credit, is Dr*t9 the goods expressing the quantity and price. See Day- Book, January 12, James M HUMID, &c. 2. The person, of whom goods are bought on credit, is Cr. by the goods, expressing the quantity and price. See Day-Bonk, January 22, Rufus Perkins, Cr. &e. 3. The person, to whom money is paid, is Dr. to cash, mentioning whether in full or in part. See Day-Book, Januaiy 31 and April 27. Amos Penniman, Dr. 4. The person, from whom money is received is Cr. hy cash, mentioning whether in full, or in part. See Da\- Book, January 25 and March 4. John Grant, Cr. 5. The person, to whom the merchant, in any way he- comes indebted, is entered Cr. 6. The person, who in any way becomes indebted to the merchant, is entered Dr. 7. The Receiver is Dr. and the Giver is Cr. 8. In Dr. Out Cr. The initials of which form the word idoc, which may assist the scholar's memory. THE LEGER. THE Leger is the merchant's principal book, as in it are collected the scattered accounts of the Waste-book, and disposed in spaces assigned for them ; each with the Debt- or placed on one side of the folio, and the Creditor of the same account on the opposite side of the same, folijj, by which disposition the several transactions, connected with each account, appear together at one view. TJte form of the Leger. Each folio, or page of the Leger is ruled with a top line, on which is writ tea the title of the account, and marked Dr. on the left hand, for receiving all the debited articles, and on the right Cr. for receiving all the credited articles of the Waste book. On the right hand of both Dr. and Cr. sides are ruled two columns for dollars and cents ; one column for the folio of the Waste-book, and two on the left- hand margin for the month and date. BOOK-KEEPING. The Leger has an index, in which the (ides of the ac- counts are arranged under their initial letters, with the number of the folio in the Leger, where the account may be found. Rule for Posting the Leger. Enter the several transactions on the 13r. or Cr. side in the Leger, ^as they stand debited or credited in the Day- book. NOTE. When several person!? or things are included in the same transaction, they are distinguished by the term, "Sundries." Balancing Accounts. When all the transactions are correctly posted into the Leger, each account is balanced by subtracting the less side from the greater, entering the balance on the less side, by which both sides will be made equal. The balances being added to the cash on hand and the value of the goods un- sold, the sum is the net of the estate, which compared with the stock at commencing businessexhibits the profit and loss. NOTE. When the place assigned for any person's account i? filled with items, the person's name must not be entered a second time, but may be transferred to another page in the following manner, viz. Add up the columns on both sides, and against the sum write, u Amount transferred to folio " inserting the number of the folio where the new account is opened. After titling the new account and entering the number of the folio in the index, write on the Dr. side of the new account, u To amount brought from folio " inserting the number of the folio from which the old account was" brought, and on the Cr. side " By amount brought from folio " inserting also the folio where the old account was ; and place the sums in the proper col- umns. See the accounts of Trask folio 2 and 3. When the first Leger is filled up, a new one may be opened as fol- lows, viz. At the end of the preceding Leger, draw out a balance ac- count, entering the debits and credits on their respective Dr. and Cr. side and transfer eaclf unbalanced account to its respective Dr. or Cr. side to the new Leger. The first Leger anay be marked A, the second B, and so on in alphabetical order 18 JOURNAL. Boston, January i, 1817. Inventory of ready money, goods, and debt due to Aaron Richardson, merchant, Boston Money on hand .... $740 John Grant owes me .... 140 Thomas Moore ..... 175 William Young ..... 224* 75 yards broadcloth a 3$ . 225 121$ yards of linen a ,75 . 91,31 20 cwt. sugar a $10,75 . . . 215 800 Ib. coffee a ,20 . . . . 160 List of debts owed by the said Aaron Rieh ardson. To Thomas Andrews, as per account . $32( Amos Penniman .... 7i James Trask 132 David Eaton, Dr. To 5 yards broadcloth 6 do. linen 20 Ib. coffee a $4,25 a ,80 a ,29 12- James Munson, Dr. To 8 yards broadcloth 2 cwi. sugar 30 Ib. coffee a $4,25 a 12,7 ,29 15 Thomas Andrews. Dr. To Cash, paid him in part 22. in f us Perkins, Cr. By 3 chests hyson tea containing 2301b. net, a $1,20 3 do. bohea tea containiag 2701b. net a ,75 N. B. By single entry goods bought are entered either in an in- nice book, kept for that purpose, or posted immediatdv into the egrer, from the invoices or bills of parcels. This mode, howev- r, is not adopted here, but credited the seller at the time/ and "terward* transferred to his accnunt in the Leger. c. 1970 31 530 31 68 140 478 2] % JOURNAL. Boston, January 25, 1817- 203 L. F. 3 John Grant, Cr. By Cash received from him in part op $- 32 C, 3 James Anderson, Dr. To 6 yards linen ... a ,80 a ,29 31 10 60 Amos Penniman, Dr. To Cash, paid him in part 40 1 Joseph Hurd, Dr. To 25lb. hyson tea .... 2 yards broadcloth 14 Ib. sugar .... a $1,40 a 4.75 a ,10 6 49 11 1 Benjamin Gould. Dr. To 40 Ib. bohea tea ..... 12 Ib. hyson .... 50 Ib. coffee .... a ,85 a $1,40 a ,29 in X 65 30 1 Jonathan May, Cr. By 1 hhd. molasses, containing 110 gallons 1 pipe of gin, containing 124 gallons 20 qumtals fish .... IT a ,45 a $1,75 a 8,25 331 50 2 Thomas Chandler, Cr. By 2 boxes candles, containing 901b. 80 Ib. mould do a ,19 a ,25 A 37 10 2 Thomas Moore, Cr. By Cash received from him in full o- 175 1 David Eaton, Dr. To 75 Ib. coffe$ . , . a ,28 3 14 Ib. sugar a $12,50 31 94 JOURNAL, Boston, February 28, 1817- JL. F. 1 David Eaton, Cr. By Cash, in part on account March 1 . . $. 25 C 3 John Grant, Cr. By Cash, received from him in full . 2 . 108 G James Dean, Dr. To 8 Ib. candles ..... 12 Ib. coliee 7 Jb. sugar ..... a ,22 a ,29 $1 10 6 24 4 Wiliiam Greenwood, Dr. To 24 Ib. coffee .... 3 Ib. bohea tea ... 10 Ib. candles .... a ,29 a ,86 a ,22 1P 12 1? 2 James Traxk, Dr. To Cash, paid him in full . ' . .. 07 . 132 o ? Rufiis Perkins, Dr. To 12 yards broadcloth cash, paid him on account Q1 a $4,75 a $149 206 4 Jonathan Boylston, Dr. To 42 Ib. susrar" 34 Ib. coffee 1 3-| Ib. bohea tea 8 gals, gin i a ,15 a ,29 a ,85 a $2,25 45 85 3 John Grant, Dr. To 14 Ib. sugar .... 10^- gallons molasses 4 gals, gin .... 4 Ib. candles a ,15 a ,55 a $2,25 a ,22 17 62 4 William Greenwood, Cr. By Cash, received from him on account - 10 4 a 95 23 75 31 1 Benjamin Gould, Cr. V By Cash, received from him on account 54 50 7-. . _ 4 1 Benjamin Gould, Dr. To 24 Ib. bohea tea . . . a ,85 12 Ib. hyson ... a $1,40 10 gallons oil , . a 1,10 35 Ib. coffee ... a ,29 58 35 3 Thomas More, Dr. To 8 gals, molasses . . a ,55 5 gals, brandy a $2,50 6 do. rum ... a 1,25 24 67 1ft 2 Thomas Chandler, Dr. 4 To 12^ Ibs. hyson tea . . a.r ^1,40 34 Ib. coffee a V ,29 30 yards linen a ,95 3 gals. Lisbon wine . . o 1,50 60 36 1 James Munson, Cr. By quarter cask cont'g. 34 gals. Lisbon wine a $1,25 42 50 JOURNAL. 207 Boston, June 15, 1817- JL. F. $. 1C. 4 William Young, Dr. To 15 gals, gin a $2,25 3 quintals fish a 4,-: 18 Ib. boheatea . a ,81 10 gals, mola&ses . a ,55 15 do. Madeira wine a 3,75 124 30 3 John Grant, Dr. To 20 Ib. mould candles a ,28 14 Ib. hyson tea , a $1,40 l cwt. sugar . ^ Thomas Henshaw, Dr. To 65 yards superfine broadcloth 3 Leghorns .... dozen pair silk hose 2 silk vests a $6,50 a 2,50 a 3 a 2,50 $- 72. William Greenwood, Cr. By his bill for repairs on house Cash, received from him on account 10 si Samuel Tuckerman, Dr. To 8 gallons Madeira 5 do. brandy 10 Ib. Hyson tea 8 gallons rum 50 Ib. coffee 15 Ib. mould candles 4 cwt. sugar .... a $3,75 a 2,50 a 1,40 a 1,25 a ,28 a ,28 a 12,30 133 John Grant, Cr. By Cash, received from him on account 31 90 Thomas Chandler, Cr. By Cash, received from him on account . 90 Joseph Bri^ham, Dr. To 4 pieces Nankins 64 yards superfine broadcloth 12$ do. calico ..... 5 do. black florentine 1 piece bandannas 63 yards black lustring a $1,25 a 6,bO a ,65 a 1,10 7 a 1,50 77 James Trask, Dr. To Cash, paid him on account . 350 * JOURNAL. Boston, August 8, 1817. David Eaton, Dr. To 8 yards superfine broadcloth 8 yards calico . . . 100 chapel needles 1 piece of India bandannas 3 pairs thread hose 2 do. silk gloves 10 a $6,75 a ,65 .' a 1,40 a 1,50 73 William Greenwood, Dr. To 8 gallons molasses 28 Ib. sugar . . . . . 5 gallons rum 5 Ib. candles 2 Ib. bohea tea it a ,55 a $12,25 a 1,25 a .22 a ,85 James Munson, Dr. To 6$ yds. superfine broadcloth 11 yds. white flannel i Ib. sewing silk 6 yards florentine 13$ do. bombazet a $6,75 a ,66 a 1,80 a 1,10 a ,42 i 63 Benjamin Gould, Cr. By his Check on Union Bank . 70 James Trask, Dr. To Cash, paid him on account . 200 Thomas Andrews, Dr. To 13$ yards calico 6| yards black- lutestring pieces Nankins 6 pair silk hose 3 pair silk gloves 3 Leghorns a .65 a $1,50 a 1,25 a 3 a 1,45 a 2,50 51 10} JOURNAL. 211 Boston, August S8 ? 1817. William Bradley, Dr. To 1 piece Canton crape, 18 yards 6^ yards coloured lutestring 8j- do. satinet 8 do velvet .... 100 chapel needles i lb. coloured sewing silk a a a a $18 1,50 ,60 ,40 1,80 g William Bradley, Dr. To 2 ivory combs 4 lon^ crooked combs (J yards bltxck florentine 3 pieces Nankins jj dozen pciir silk hose 2 pair silk gloves a a a a a a o> ,30 ,25 $1,10 1,10 3 1,45 2 50 2 silk vests .... 3^ yds. superfine broadcloth 1 .piece of bandanna handkerchiefs *>i a a 2,50 6,75 7 Samuel Tuckerwan, Dr. To 10 gallons gin .... 2 quintals fish . ... 5 gallons Lisbon wine a a a $2,25 5, 1,50 Srnt CT James Dean, Dr. To 8 gallons Madeira wine 100 lb. coffee 10 lb. hyson tea 15 lb. mould candles 5 gallons rum .ft 4 do. gin . m 2i cwt. sugar t . 5 t - a a a a a a a $3,75 ,28 1,40 ,28 2,50 2,25 12,25 Rufus Perkins, Dr.f To 10 gallons Madeira/ 3 do. gin / . 1| quintal fish / 16 lb. mould candles a a a a, $3,75 2^5 ,2* $. 49 c, 55 76 34 40 125 28 JOURNAL. Boston, September 8, 1817. . F. 5 i 1 3 1 1 1 3 i 3 Thomas Gibson, Dr. To 9 yards broadcloth a 1 silk vest .... 2 pieces Nankins . a 3 pairs silk hose a 4 pairs silk gloves ... a jo $4,50 2,50 1,25 3 1,45 60 A ,75 ,42 $1,2* 16 44 50 John Grant. Cr. By Cash, received from him on account O/J 28 Jonathan May, Dr. To 3 pieces Nankins . a 8^ yards broadcloth . . a 15 yards linen .... a 6 do. black Florentine . . a 4 pair silk gloves .... a 4,75 ,95 1,10 1,45 70 77 James Munsou, Cr. By his check on the Union Bank for Qf) . 112 Benjamin Gould, Dr. To 5 gals, brandy *. . a $2,50 2,25 5 12,25 l quintal fish .... a ^ cwt. sugar .... a 38 19 Jimes Anderson, Cr. By Thomas Winslow's acceptance of a draft for 50 >0 AJM Penniman, Cr. Sftash, received from him on account J 12] JOURNAL. Boston, Octobers, 1817. L. F. 1 David Eaton, Dr. To 1 piece bandannas , 6 yds. coloured lustring 7 do. calico .... 200 chapel needle^ .... $7 a 1,50 a ,75 a ,40 * 4 Ib. sewinsr silk 4 pair silk gloves . . . a 7,20 a 1,45 31 2 Thomas Chandler, Dr. To 10 gals, brandy .... 4 do mm . ... 3 do. Lisbon wine 8 Ib. bohea tea .... a $2,75 a 1,25 a 1,50 a ,85 10 43 2 Thomas Moore, Cr. By Cash, received from him on account . 4 4 William Greenwood, Cr. By Cash, received from him on account . 20 3 James Trask, Dr. To 15 yards -white flannel 4 yards black lustring 4 long crooked combs . 4 pair silk hose .... 2 silk vesta 11 a ,66 a $1,50 a ,25 a 3 a 2,50 35 2 James Dean, Dr. To 7 yards florentine 10 yards bombazet 1 dozen tape .... 10 yards white flannel 8^ yards broadcloth ------ 16 a- $1,10 a ,42 ,75 a ,66 a 4,75 61 4 Jonathan Boylston, Dr. To 12 yards durant .... 8 do. velvet . ... 20 do. white flannel a ,38 a $2 a ,66 3C JOURNAL. [13 Boston, October 18, 1817. I*. f William Young, Cr. By an order on David Newman for ... 00 ft 124 C. 25 4 Samuel Tuckerman, Dr. To Cash paid him on account 200 00 4 Jonathan Boylston, Cr. By Cash, received from him on account pc 99 o Thomas Henshaw, Cr. By his Check on Massachusetts Bank for oq 75 00 t Joseph Bri^ham, Cr. By Cash, received from him on account n- 67 87 5 Thomas Gibson, Cr. 3y a bill on James White a! 10 days 54 50 Thomas Moore, Dr. To 2 lb. coloured thread . . . a $1,25 2 lb. white do. ... a 1,20 20 yards Scotch shirting . a ,30 2 ivory combs .... a ,30 4 long crooked do. . a ,25 4 silk ve?ts ..... a 2,50 00 22 50 1 Senjamin Gould, Dr. To 20 gallons rum .... a $l,2. r - 10 do. gin . ... a 2,^r> 30 yards Scotch shirting ... . a ,30 900 chapel needles . a ,40 QA 50 10 1 fames Munson, Dr. To 12 gallons oil . ... a $1,10 1 quintal fish .... 5 20 yards Scotch shirting . a ,30 2 lb. white thread . - - a 1,20 ~9J 60 JOURNAL. Boston, November 1. 1817. Joseph Brigham, Dr. * To 2500 chapel needles a ,40 ^ dozen ivory combs . a' ,30 1 dozen long crooked do. a ,25 3 silk vests .... a $2,50 Is Ib. sewing silk a 7 10 yards durant a ,38 36 66 3 I - Samuel Tuckerman, Dr. V To 22 gallons Madeira wine a $3,75 15 do. Lisbon .... a 1,50 20 do. gill . t a 2,25 . 150 00 ! Thomas Henshaw, Dr. To 9 yds. white flannel a ,66 1 Ib. coloured thread $1,10 1 Ib. white do. 1 3 pieces bandannas a 7 5 pieces Nankins a 1,25 13 yds. broadcloth a 4,75 4 silk vests . ... a 2,50 10 108 23 Thomas Gibson, Dr. To 12 pieces Nankins a $1,25 1 doz. silk hose a 3 3 silk vests . - . ft 2,50 5 yds. coloured lustring a 1,50 66 75 JO David Ramsay, Dr.. :1 o 2 cwt. sugar .... a $12,25 100 Ib. coffee .... a ,29 15 gallons brandy . . a 2.75 10 do. rum .... a 1,25 10 Ib. hyson tea .... a 1,40 121 1 25 JOURNAL. f!6 Boston, November i5, 1817. I.. F. ; R. C. 1 James Munscn, Dr. To 1 piece bandannas . $7 14 Leghorns a 2,40 7 pair silk hose a 3,25 1 dozen tape ,75 1 Ib. coloured sewing silk . 7 1000 capel needles a ,40 2 pair thread hose a 1,50 IP 78 10 4 William Young, Dr. To 50 Ib. coffee a ,29 20 Ib. bohea tea a ,85 8 gals. Lisbon wine a gl,50 43 50 Oft 3 James Anderson, Dr, To 1 piece Canton crape . . $18 16| yds. satinet a ,60 16 do. velvet a 2 25 do. twilled coating a 1,25 dozen crooked combs a ,25 2000 chapel needles a ,40 100 80 5 Joseph Rrigham, Dr. To 8 ivory comb? a ,30 1 dozen crooked combs n , 25 yds. twilled coating 1 Ib. coloured thread a 1 2000*. 75 1 Benjamin Gould, Cr. is Check on Manufacturers' and Mechanics' Bank at Boston, for ... Oj 8T 44 4 William Brad l-y, Cr. ,.v Cash, received from him in full ' 8 09 1 . , .. ^ ,,, ,.,. ^, Jonathan May, Cr. By Cash in full " ' 70 77 4 William Young. Cr. By Cash, receivf d from him i^ full "6 186 50 5 Thomas H^u^uau. Cr. By Cash, received, from him in fall - . 105 98 320 LEGER. [1 Dr. David Eaton, 1817. JF ; lo Sundries .... 50 10 211 94 Dr. Jonathan May, 1817. May 18 4 To Cash in full .... 331 50 Sept. 24 11 Sundries 70 77 402 7 LEGER. Cr. 1817. IJFj $. C. Feb. 28 By Casli, in part 3 25 May 2 Cash .... 4 30 Sept. Dec. 121 Cash 19 Cash, for balance 11 17 80 33 50 54 - 169 04 Cr. 1817. May 5 By Cash, in part 4 55 June Sept. 12 26 34 gallons Lisbon wine . a $1,25 Check on Union Bank, Boston 5 11 42 112 59 Dec. 20 Cash, in full 17 75 16 ! 1284 66 Cr. 1817. 15 By Cash .... 4 45 Dec. 24 Cash in full .... 18 117 75 f !lC2J7 Cr. 1817. j May Aug 31 :o By Cash . ... His check on Union Bank I 54 70 50 Dec. 24 His check on Mechanics' Bank 18 87 14 |211 194 Cr. 1817. I < b. By Sundries, as per Journal 21331 50 L'er,. 25 5 >5 223 Cr. C. 50 55 1817. June Dec. 3 By Sundries as per J. By his check on Boston Bank -TF 17 $ 271 27] 543 05 Cr. 1817. Feb. 15 By Sundries as per Journal 2 37 10 July 31 Cash .... 8 90 81 127 91 Cr. 1817. Feb. .< By Cash in full 2 175 Oct. 10 Cash .... 1'2 4 07 Dec. 31 Account at folio 1 ieger B. 42 >o 222 17 Cr. 1817. Jan. April 1 15 By balance on former account Sundries \ Amount transferred to folio 3. 9U3J7 Cr. 1817. Jan. 1 By stock .... 1 320 Dec. 21 D. Standwood's acceptance 17 51 -2i 371 25 Dr. LEGER. Kufus Perkins. 31 1817. j>'j March 27 3 To Sundries as per Journal 206 May " 8 4J Sundries .... 270 56 Sept* 5 10. Sundries . . 56 79 533 35 Dr. John Grant, * 1817. Jan. 1 1 To balance of okl account 140 April 7 o Sundries .... 17 62 June 20 6 Sundries .... 43 57 July 5 7 Sundries .... 57 50 Dec. 18 17 Sundries 108 19 3G6J88 Dr. James Anderson, 1817. Jan. 28 2 To Sundries as per Journal 10 00 April 4 Sundries 5<5 '21 July 12 7 Sundries .... 38 H7 Nov. :>0 15 Sundries .... 100 80 7P J 48 Dr. Amos Pennimun, 1817. Jan. 31 2 To Cash in part April 27 4 Cash in full June 27 6 Sundries 75 Dec. 5 16 Sundries 47 5i 155 30 Dr. James Trask, 1817. j o amount brought irom ioao 2 482 Aug. 24 9 To Cash .... 2^0 Oct. 12 12 Sundries .... 35 0* Dec. 31 account transferred to folio 1 leger B. 186 72 903 vfc LEGER, Cr. Ibl7. Jan. Dec. 22 By Sundries, as per Journal Cash, in full JF 1 17 $. 478 54 C. 50 85 533 35 Cr. 1817. Jan. March July Sept. Dec. 4 27 20 22 By Cash in part Cash in full Cash on account Cash on account Balance .... 2 3 8 11 17 32 ' 108 90 28 108 50 3S ; 366 83 Cr. 1817. May Oct. Dec. 12 1 22 By Cash on account ornas Winslow's acceptance for his Check on Boston Bank 4 11 17 60 50 102 48 212 48 Cr. Jan. Oct. Dec. 1 7 23 By Balance due on old account Cash on account Cash in full 1 11 17 78 28 48 50 80 155 30 Cr. 1817. By amount brought from folio 2 903 75 903 TS Dr. LEGER. William Young, 1817. .Tan. June Nov. De. 1 15 JF 1 6 17 To balance of old account 224 124 43 141 C. 50 95 75 Sundries .... 533 Dr. Samuel Tuekerman, 1817. July Aug. Oct. Nov. Dee. 23 31 20 3 31 1 8 10 13 13 133 40 200 150 33 90 46 _ Cash Balance transferred to folio 1 Leger B. 557 36 Dr. William Greenwood, 1817. March May Aug. Dec. 12 25 10 2 3 5 9 16 To Sundries ..... 12 18 16 78 17 27 51 75 125 70 Dr. Jonathan Boylston, 1817. jr March Oct. Nov. Dec. 31 16 27 31 15 To Sundries Sundries . . . . . 45 33 106 24 85 76 67 71 99 To Balance transferred to folio 1, Leger B. 210 IDr. William ttradley, 1817. I 1 | Aug. 28 10 To Sundries - - 29 10 Sundries 4954 7634 LEGER, Cr. 1817. April Oct. Dec. 20 18 -25 By Cash in full An order on Cash in full D. Newman . JF 4 13 18 $ .224 124 185 t 25 50 533 75 Cr. 1817. July 2 3 By Sundries, as Sundries per Journal 7 7 307 249 50 86 36 557 Cr. 1817. April July Oct. Dec. 10 IM 10 31 By Cash Sundries Cash Balance clat jut trim*., to ibiio 1, Legtr b. 3 2 1C 15 7 125 7 if 70 Cr. 1817. July Oct. 10 21 By a draft on J. Nicholson' Cash on account 7 13 150 .60 210 99 99 Cr. 1817. April Dec. I If* 25 By 124 gallons oil Cash in full I 4 18 117 8 30 an 125 Dr. LEGER. Thomas Hens haw, 1817. July Nov. IJF 15 8 8J14 1 To Sundries I Sundries .... $. 72 108 180 C. 75 23 98 Dr. Joseph Brigkam, 1817. Aug. Nov. 2 1 25 8 14 15 To Sundries .... Sundries .... Sundries .... ~~ 173 62 ^0 o5 87 Dr. Thomag Gibson, 1817. Sept. Nov. 8 10 11 14 To Sundries .... Sundries .... 60J30 66J75 12705 Dr. David Ramsey, 1817. | Nov. |12|14|To Sundries .... 12125 Dr. Benjamin Franklin, 1817. Pec. (10 16|To Sundries .... 252J82 Dr. Balance, 1817. Pec. 31 LF 2 4 5 5 5 5 To Thomas Moore, due to me William Greenwood Joseph Brierham Thomas Gibson . , David R;imsey Benjamin Fraitklin , 4? 79 106 72 121 252 675 50 % 55 25 82 00 LEGER., Cr. 1817. JF $ C. Oct. 00 By Check on Massachusetts Bank 13 75 Dec. 26 Cash in full 18 105 98 180 98 Cr. 1817. Oct. 23 By Cash .... 13 67 87 Dec. 31 Balance due to me transf. to folio 1 Leger B. 106 173 87 Cr. 1817. Oct. 25 By bill on James White at 10 days 13 64 50 Dec. 31 Balance due to me transf. to folio 1 Leger B. 72 55 127 05 Cr. 1817. I Dec. |3l|By Balance transferred to folio 1 Leger B. I I I 121(25 Cr. 1817. Dec. |31jBy Balance transferred to folio 1 Leger B. 20* I 252182 Cr. 181 ;. Dec. 31 By Jonathan Boylston, due to him James Trask Samuel Tuckerman LF 4 3 4 23 1R6 33 71 72 46 243 89 30 LEGER. [1 LEGER B. Dr. Thomas Moore, "181871 LF/ j JJTJC. Jan. II j To balance at folio 2 Leger A. . . | 42|50 Dr. William Greenwood, 1818. I I I *~ ~~\ Jan. j l| (To balance at folio 4 Leger A. . . | 79|9. r . Dr. Jotmthau Boylstoii, 1818. '\ Dr. James Trask, Dr. Samuel Tuckerman, 1818. .Dr. Joseph Brigham, Tirnn | i j [~ Jan. j 1| [To balance at folio 5 Leger A. . . (106| Dr. Thomas Gibson, 181.8. Jan. l| (To balance at folio 5 Leger A. | 72(55 j) r . David Ramsey, i i"~ Jan. Mi |To balanqe at folio 5, Leger A. . . | 121|25 Dr. Benjamin Franklin, Jan. I T ITo balance at folio 5 Leger A. ) LEGER. LEGER B, Cr. IJFJ $. )C< I I I Cr. Cr. 1818. j j 1 I I .Ian. I 1'By balance at folio 4 L^ger A. ..II 24i7l Cr. 1318. . , Y i i Jan. I IJBy balance at folio 3 Leser A. . . I Cr. Jan. | l|By balance at folio 4 Leger A. ! 33146 Cr. Cr. Cr. Cr. T~T LEGER. (Book-Keeping by . single entry does not show what goods are unsold or the profits or losses, except when the transactions are very few. The Leger containing nothing but the accounts of persons dealing on credit, only shows the merchant what debts are due to him, and what he owes to others. If therefore he wishes to know what goods remain unsold and what his profits arid losses by the whole or any part of his business, he can- not obtain this knowledge by single entry without u taking account of stock, 1 ' that is, by weighing or measuring every article remaining unsold, which are commonly valued at prime cost. The value being added to the money on hand, will exhibit the net of the estate, which, compared with the original stock, will show the Profit and Lo?s. Hence it appears evident, that Book-keeping by single entry is essentially defective in its not giving the merchant a correct knowl- edge of the state of his affairs, without the laborious task of u taking account of stock," which is very subject to error, and can afford no adequate means either of preventing embezzlement or detecting fraud. ' Fortunately, however, for the wholesale merchant, and the less extensive trader, these objects are attained by the Italian method of double entry, as effectually, perhaps, as the ingenuity of man can devise. Every scholar, therefore, who wishes to become a complete ac- countant, must be conversant with that system, which being upon universal principles, and clearly understood by the pupil, will easily lead to the invention of other plans more conveniently adapted to any particular purpose.) 238 UYDEX TO 1 A. Fol. i Andrews Thomas . . JB-| Anderson James . . 3 ?HE LEGER. B. Fol Balance .... 5 Boylston Jonathan . . 4 Bradley William . 4 Brigham Joseph . . 5 c. Chandler Thomas 2 D. 'Dean James / 2 E. Eaton David 1 F. Franklin Benjamin . 5 G. Grant John Gould Benjamin Greenwood W. Gibson Thomas 3 1 4 5 H. 'Hurd Joseph Henshaw Thomas 1 M. Munson James . . May Jonathan . Moore Thomas 1 1 2 P. Perkins Rufus . fenniman Amos 3 3 H. Ramsey David 5 T. Trask James . . -2, X Tuckerman Samuel . . 4 Y. Voung William INDEX A. 4 TO i ^ LEGER B. B. Brigham Joseph Boylston Jonathan . 1 1 E. F. Franklin Benjamin . . . 1 G. Gibson Thomas Greenwood William l l M. Moore Thomas 1 R. Ramsey David .. 1 T. Trask James \ Tuckeriuau Saiuuel . 1 \ NEW AND CONCISE SYSTEM OF BOOK-KEEPING, BY EXTRT1-, FOR THE USE OP WHOLESALE, DOMESTIC AND FOREIGN TRADE, AS CONDUCTED IN THF, UNITED STATES, The whole designed for the use of Schools and BY D. STANIFORD, A. M. BOOK-KEEPING. EVERY mercantile transaction has two parts, or be- longs to two accounts, and requires its distinct entry on the Dr. of the one, and on the Cr. of the other, to show the change of property. From this circumstance arises the distinguishing title of this method by Double Entry. The art of Book-Keeping by Double Entry consists, 1. In recording, correctly and intelligibly, the transac- tions in the several books. a 2. In transferring; the several accounts from one book to another, with the corresponding Drs. and Crs. 3. In the method of balancing and closing the accounts, There are three primary books used ; viz. 1. The Wate, or Day Book. 2. The Journal. 3. The Leger. The secondary or auxiliary books are, 1. The Gash 2. Bill 3. Invoice 4. Sales 5. Account-current 6. Commission Book. 7. Sbip's-account' 8. Expense 9. Letter 10. Postage 11 . Receipt 12. Check .Book. To which may be added, the Numero, or Ware-house Book, and Memorandum Book. Part, or the whole, of the preceding books, are used by merchants, as the extent and nature of their business ma* require. WASTE-BOOK. FOR the form and use of this book, see (he Waste, or Day Book, in Single Entry. BOOK-KEEPING. $37 THE JOURNAL. THE Journal is a fair transcript of all the transactions, recorded in the Waste Book, compiled in the same order, but differently expressed. Here the two parts, which be- long to every transaction, in the Waste, are clearly distin- guished by their proper titles with their mutual relation of Dr. and Cr. to facilitate their transfer to their separate ac- counts in the Leger. The form of this book is similar to the Waste, with this only exception, that on the left hand, there are two col- umns for references to the folio of the account in the Leger. the first for the Dr. and the second for the Cr. See speci- men annexed. An experienced book-keeper can easily dispense with either the Waste book,, or Journal; but the young book-keeper needs them both, for simplicity and clearness. The art of Book-keeping, by the Italian method, wholly depends on a correct discrimination of the Dr. and Cr. of each transaction. The mode of ascertaining them, in double entry, is the same, in effect, as in single. But here things, as well a* persons, are made Drs. and Crs. and one thing, or person, is made Dr. to another thing, or person, asCr. DEBTOR ^JTD CREDITOR. The following rales, for distinguishing the titles Dr. and Cr. with the explanations and notes, will greatly assist the young book-keeper in making the Journal entries from the Waste book and posting from the Journal to the Leger. RULE I. When goods are sold on credit, the Purchaser is Dr. to goods ; and Goods Cr. by the purchaser. See Waste and Journal, Jan. 2. Sold Charles Lee, sugar. Explanation 1. As the sugar is sold but not paid for, Charles Lee must be made Dr. to sugar ; and Sugar Cr. by Charles Lee, for the quantity and price. NOTE 1 In all cases of selling, the goods, sold and delivered, are Cr. but the Dr varies according to the terms of sale. RULE II. When goods are sold for cash, make Cash Dr. to goods sold ; and Goods Cr. by Cash. W. and J. Jan. 7. Sold rum for cash. Explanation 2. As the rum is sold, and the money received at the time, it is not necessary to know to whom it was sold, but the money received, that is, Cash is Dr. to the rum, for its value } and the Rua Cr. by Cash for the quantity and price. BOOK-KEEPING RULE III. When goods are sold for part cash and part 0.11 credit, make Sundries Dr. to goods sold; viz. Cash, for the sum received, and the Purchaser, for the rest ; also Goods sold Cr. for the whole amount. W. and J. Sept. 27, Sold Winslovv Lamb, tea. Expl. 3. This case is the reverse of Feb. 22. Here Sundries are Dr. to tea; viz. Cash, for fne money received, and W. Lamb, for the rest ; then Tea is Cr. by sundries. RULE IV. When goods are sold for part cash and partbills, make Sundries Dr. to goods sold; viz. Cash, for the money paid, and Bills receivable* for the rest, or value of the bill ; also the Goods sold Cr. by sundries, specifying the price and quantity. W. and J. Jan. 27. Sold A.Eastman, lands, for cash and bills. Extol. 4. In this case make Sundries Dr. to laad for its value ; TJZ. Cash, for the sum received, and Bills receivable, for the rest ; also Land Cr. by sundries for the same value. NOTE 2. If you sell a house, or ship, &c. ; make the entry as in selling goods ; viz. Cash, Buyer, &c. ; Dr. to house, ship, &c. ; for the value. Aug. 18. Aug. 19. Dec. 25. RULE V. AVhen goods are sold, and payment received by a bill or draft on another person, make Bills re civ able Dr. fo goods sold; and Goods, stating the pr-c-e and quantity, Cr. by bills receivable, expressing on \vhom drawn. W. 8c J. Feb. 25. Sold N. Freeman linen for a bill on A Young. Expl. 5. Here Bills receirable are Dr. to linen, and Lintn Cr. fcy bill on A. Young, for 600 yards a $1.20. NOTE 3. When several sorto of goods are sold, there will be sun- dry Crs. viz. the several sorts, each for its value ; but the Drs. will be the same as in Note 3. ' Thus., dish Dr, to sundries, if sold for cash, Buyer^ if on time, Bills Ttztivable, if for bill. RULE VI. Goods bought for ready money, are Dr. to Cash, and Cash Cr. by the goods. W. and J. Jan. 15. Bought port wine for cash. Expl. 6. The port-wine being bought, and the money paid, Port- wine must be nu.de Dr. to Cash, for the quantity and its value ; and Cash, Cr. by port-wine for the same value. As port-wine was a p:u % t of your stock, therefore when the same sort of goods are purchased of several persons and at different prices, it is convenient to have some mark to distinguish them, that when the account of such goods shall be balanced, the prime cost of those, which may remain unsold, can be known. NOTE 4. Buying is the reverse of.selling, and has the same variety of cases, in all which the goods bought and received are Dr. but the Cr. varies according to the conditions of the purchase. The rules for buying and selling merchant goods is to be applied in buying and sel- ling any thing else ; a. c , plate, jewels, furniture, ship, house, lands, &e. BY DOUBLE ENTRY. 239 RULE VII. Goods, bought an credit, are Dr. to the sel- ler, and I he Seller Cr. by good*. W. and J. Jan. 18> Bought of A. Newman, linen. ExpL 7. As the linen is bought, but not paid for, you become Dr, to A. Newman for the same ; but as you must not open an accoun* -with yourself, and because the linen has become apart of your stock, which represents you the merchant, the linen must be made Dr. to A. Newman, for the quantity and its value ; also A. Newman Cr. by linen, for the same value. RULE VIIT. Goods, bought for part cash and part cred- it, are Dr. to sundries ; viz. To Cash, paid in part, ami to Seller for the rest. \V. and J. Feb. 22. Bought of W. Lamb, broadcloth. P,. Here broadcloth must be made Dr. to sundries, express- ing tlie quantity and price ; and Cash, Cr. by broadcloth, for tin? money paid and W. Lamb. Cr. by broadcloth for the rest ; viz. $o75. RULE IX. When ^oods are bought, part for cash and part for bill, make Goods Or. to sundries; viz. To Cash, for the sum paid, and To Bills receivable for value of the bill. W. and J. April 15. Bought of R. Lakeman, sun- dries. ExpL 9. This is an entry, complex in both its terms, that is, tws Drs. and two Crs. Therefore in this, as in all similar cases, the best rule is to resolve the case into two entries; viz. First, make the Goods, that is, Sundries, Dr. to the Seller, R. Lakeroan, for their full value, as if they had been bought on credit ; then make the Seller, R. L. Dr. to sundries ; viz. To Cash, for the sum paid, and to Bilk receivable, for value of the bill. See directions for writing in the Journal, complex entry. NOTE 5. When goods are bought, part for cash, part credit, and part bill, make goods bought Dr. 1o sundries ; viz. To Cash, for sum paid, To bills receivable, for value of the bill, and To seller, for the rest. RULE X. When money is paid, the Receiver is Dr. to Cash; and Cash Cr. by the receiver, for the sum paid. W. and J. Jan. 12. Paid James Lewis in full-. ExpL 10. By the Inventory it appears you owed J. Lewis $140, and consequently he stands credited by this sum in the Leger ; there- fore as no erasures or crossings are allowable in mercantile books, you must discharge the debt, by debiting J. Lewis to Cash for the money paid him in full ; also Cash Cr. by J. Lewis. . NOTE 6. In all cases of paying money Cash, is Cr. but the Dr. varies according to the terms on which the money is delivered. NOTE 7. In paying money you mu.-l ?.hvay~ mention whether in full or in part. BOOK-KEEPING RULE XI. When you lend money on security, make the JSorroiver, Notes, or Bills receivable.. Dr. to Cash, naming the srum and security ; also Cash Cr. by the borrower^ note, or bills receivable, naming also the sum and security. W. and J. Feb. 2. Lent S. Tyler, on bond, &c. ExpJ. 11. You need only make S. Tyler Dr. to Cash for ths principal received, and Cash Cr. by S. Tyler, for the same sum, emitting the interest, until it shall be paid. NOTE 8. When you borrow money, make Cash Dr. to the lender^ notes, or bills payable ; and the Lender, Notes, or Bills Payable Cr. by cash. RULE XII. When you pay charges on goods, repairs or reimbursements on a ship, taxes or repairs on a house, &c. f make Goods, Skip or House Dr. to Cash ; and Cash Cr, by 3ooo ths. Person Cr..by bill or note renewed. W. and J. Dec. 20. NOTE 15. When you pay cash for a bill, note or acceptance due from you to another, make Bills payable Dr. to Cash, naming the per- -on ; ad Cash Cr. by bills payable, naming also the person. W. and J. June 10. Aug. 25. Oct. 30. This case is shtxil^r to paying- money under Rule X. BOOK-KEEPING RULE XIX. When you give a bill or note in payment fifr goods purchased, but not booked, the Person to whom the bill is given is Dr. to bills payable; and Bills payable Cr. by the same person. W. and X. April 12. RULE XX. When you give in a note or bill to be dis- counted, make Sundries Dr. to bills receivable; viz. Cash for the net sum received, and Profit and Loss Dr. for the discount; also Rills receivable Cr. by sun- dries for the whole value of bill, W. and J. Feb. 26* Discounted A. Young's note. Expl. 17. Although you did not receive the whole value of the note, it must be discharged the same as if you did, therefore, Sundries must be Dr. to bills receivable, viz. Cash for what you received, and Profit and Loss Dr.. for the discount, and Bills, receivable^ Cr. by sundries for the, whole face of. the note. NOTE 16. This, rule will apply in all cases where discount is made .'or prompt payment. NOTE 17. When you discount a bill to another person, make Bills receivable Dr. to sundries ; viz. to Cash^ for. net sum paid, and .Profit -. s Dr. fov the discount. RULE XXI. When a person fails, and compounds with his creditors, make the Bankrupt Cr. by Sundries, for the wliole debt due by him ; and Cash Dr. for the sum received' in the composition ; also Profit and Loss Dr. for the Loss. W. and J, Dec. 14. A. Newman becomes a bankrupt, &e. NOTE 18. This case is much like that under Rule XX. therefore it needs no farther explanation. RULE XXII. When you receive the freight of a ship, or charter of a vessel, or the rent of a house, make Cash Dr- to the ship or house, for the sum received, and Ship or House Cr- by Cash, for the freight or rent. W. and J. Nov. 27. Received from Jones & Penniman fre%htrof the frhip Massachusetts. NOTE 19. Debit and credit here asunder Rule XIV. RULE XXIII. When you pay cash for ensurance on a ship, goods or cargo, make the Ship or Goods or Voyage to - -, Dr. to Cash, for the ensurance money 5 and Cash Cr. by ship or goods or voyage to , for the same sum. ^Y. and J. Feb. 23. April 10. Expl. 18. The charge of ensurance being an additional expense on the ship, goods or cargo, they must be debited for Cash ; and~ therefore Cash Cr. by ship, goods or cargo, for the same sum. BY DOUBLE ENTRY. RULE XXIV. When you pay money for charges on a voyage, make Voyage to or from , Dr. to Cash, ex- pressing for what ; and Cash Cr. by voyage to or from . W. and J. Nov. 15. Entered at the Custom-house my goods from Bourdeaux, and paid duties, &c. Expl. 19*. As this, like Rule 23, is a farther expense on the voy- age, you must make Voyage from Bourdeaux Dr. to Cash, for the du- ties and other charges ; and Cash Cr. by voyage from Bourdeaux, for the same charges. RULE XXV. When goods are bartered for others of equal value, make Goods received Dr. to goods delivered : and Goods delivered Cr. by goods received, naming the price and quantity of each. W. and J. Jan. 20. Bartered sugar for coffee. Expl. 20. When one commodity is sold, or exchanged, for anoth- er, it is called Barter ; and when one sort of goods is exchanged for another of equal value, as in this case, make the Coffee received Dr, to the sugar delivered. NOTE 20. When one sort of goods is received for several sorts delivered, make Goods Dr., to Sundries ; viz. To the several sorts of goods, delivered, for their respective values. NOTE 21. When several sorts of goods are received for one sort de- livered, make Sundries ; viz. the several goods received, each for its value, Dr. to goods delivered. RULE XXVI. When several sorts of goods are bartered for several others, and that whether the goods, received and delivered, are equal in value or not, make two entries; First Make the person with whom the barter is made Dr. to sundries ; thai is, to each sort delivered, for its respec- tive value ; Secondly Make Sundries, that is, each sort of goods, received Dr. to-the person with whom the barter is made, for its respective value. W. and J. April 4, Bartered with R. Means, &c. Expl. 21. This is a case complex in both its terms,, and requires two entries, therefore, First, make Robert Means Dr. to sundries ; \dz. sugar and rum delivered him, and Sundries ; viz. Sugar and Rum Cr. by the goods delivered secondly, make Sundries ; viz. Ashes and Tow-cloth, received, Dr. to R. Means, and Robert Means, Cr. by sundries, viz. ashes and tow-cloth received, See directions for writing in the Journal, complex entry. RULE XXVII. When goods are shipped off, for your own account, from your ware-house, and consigned to a factor, make Voyage to , Dr. to sundries ; viz. To the respective goods, for their prime cost, and To Cash, for shipping and other charges ; also Sundries ? viz. the re- BOOK-KEEPING spective goods, and Cash, Cr. by voyage to W. and J. May 8. Shipped on hoard the General Hamilton for Oporto and consigned to F. Alvardo & Co. Expl. 22. As the goods are consigned to F. Alvardo & Co. for your own account, you must make voyage to Oporto, consigned to F. Alvardo Si Co. Dr. to sundries, for the whole cost and charges ; and the several articles of goods shipped (entered in the books) Cr. by voyage to Oporto. NOTE 22. Foreign trade comprises three things ; viz. 1. The ship- ping off the goods to a factor. 2. Advices concerning them from the factor. 3. The returns made by the factor to you. NOTE 23. In all cases of shipping off goods to a factor, Voyage to , is always Dr. but the Cr. varies according as the goods s'hipped off are booked, that is, taken from your warehouse, or presently bought, which may be either for cash, or on credit. RULE XX VIII. When you ship off goods bought on credit, make Voyage to s Dr. to sundries; viz. To seller or sellers, for value of the goods at prime cost, To Cash, for shipping charges, also Sundries, viz. the Seller orSellersCr. by the voyage to , for the value of goode, and Cash Cr. by the voyage to , for the charges. W. and J. April 10. Voyage to Bourdeanx, &c. Expl. 23. This case differs but very little from the preceding rule, and therefore is easily posted, make the Seller or Sellers Credi- tors, instead of the goods as above. NOTE 24. Voyage must be debited for all charges which incref>- the cost, and credited for whatever lessens the cost ; such as boun- ties or drawbacks on exported goods ; thus- for bounties, make CaJi or Custom-House Debentures, (as you may receive money, or pro- cure a debenture-bill) Dr. to voyage. When you receive paymeivt of the debenture-bill, make Cash Dr. to Cu.stom-House debentures. NOTE 25. For drawback?, make Cash,, or Custom-House Bonds, (as you may receive cash or take up your bond) Dr. to voyage, or to goods exported. RULE XXIX. When intelligence, with the account of sales, is received from your factors-advising that he had re- ceived and sold your goods, make Factor my account current Dr. to voyage to , for the net proceeds, and that whether the goods are sold for cash, credit, o^part both; also make Voyage to , Cr. by factor my account cur- rent, for net proceeds. W. and J. Nov. 8. Received ac- eount sales from C. Leroi, of the net proceeds of the cargo consigned to him. ErpL %4. As the cargo was consigned to C. Leroi, for your ac- count, so he becomes your debtor, whenever he advises of its arrival and sales ; .therefore you must make Charles Leroi. my account cm-- BY DOUBLE ENTRY. rent Dr. to voyage to Bourdeaux, for the net proceeds ; and Vojage to Bourdeaux Cr. by C. Leroi my account current, for net proceeds. NOTE 26. "When the ship or goods arrive, make Goods received Dr. to voyage from , also Voyage from , Cr. by the goods. W. and J. Sept. 3. Nov. 18. NOTE 27. If the return cargo is- sold on the wharf before the voy- age is discharged in the books, make the Buyer, Bills receivable, Cash, %f the Things received, Dr. to voyage from , for the quantity and value ; also Voyage from , Cr. by the same, for the quantity and value. W. and J. Nov. 25. Dec. 15. RULE XXX. When your factor makes a remittance in goods to you, having givpn you previous notice by account sales, or when the same arrives, make Voyage from -, Dr. to factor my account current, for cost and charges of the cargo, per invoice ; also Factor my account current Cr. by voyage from > for the same suui. W. and J. Sept. 3. Nov. 12. NOTE 28. A factor is the person employed by the merchant. RULE XXXI. When your factor, for goods consigned to him, remits to you a bill, payable at single or double usance, or any other time after date or sight, upon getting the hill accepted, make Bills receivable, stating on whom drawn, Dr. to factor my account current, for value of the bill; also Factor my account current Cr. by bills receivable. W. and J. Dec. 6. NOTE 29. When the payment of the bill is received, make Cash Dr. to bills receivable ; and Bills receivable Cr. by Cash. Dec. 8. RULE XXXII. When you have goods consigned to you by your employer, on which you have paid charges, as freight, duties, &e. ; make Employer his account of goods Dr. to Cash, stating for what ; and Cash Cr. by em- ployer's account of good*, for the same sum. W. and J. March 1. Paid freight on Henry Lee's tobaeco. Expl. 25. As you have the tobacco in your own hands, you need ..nly make Henry Lee's account of tobacco Dr. to Cash ; and Cash Cr. by H. Lee's account of tobacco, for the charges. NOTE 30, When there is but one kind of goods, name it as in H Lee's account of tobacco. NOTE 31. Employer is the person who employs the merchant to transact business for him. NOTE 32. Factorage comprises three things, 1. The receiving of the employer'* goods. .2. Selling them. 3. Returns made for tjiera.. BOOK-KEEPING RULE XXXIII. When goods consigned to you by your employer are sold for cash, make Cash Dr to Employer his account of goods, for the sum received ; and employer his account of goods Or. by Cash for the same sum. W. and J. March 14 and 24. Expl. 26. As the Dr. and Cr. applied to ercploj-er's account of goods admit the same varieties as proper trad'e, therefore no further explanation is necessary. NOTE 33. When you sell your employer's goods, for a bill, make Bills receivable Dr. to employer his account of goods ; and Employ- er's account of goods, specifying the price and quantity, Cr, by bills receivable, for the bill. W.- and J. March 4. RULE XXXIV. When your emp3o\ers goods are all sold, balance his account of goods, that is, charge Employ- er's account of gaods Dr. to Sundries; viz, to Cash, for any charges paid by you and not yet booked ; and to Com- mission account, for your commission ; and to Employer his account current, for nel proceeds; also make Employer's account current Cr. by his account goods for net proceeds, and Commission account Cr. by his account of goods, for commission. W. and J. March 30. Leger, EL Lee's ac- count tobacco. RULE XXXV. When you remit money to your employ- er, make Employer his account current Dr. to Cash ; and Cash Cr. by employer's account current. W. and J March 31. RULE XXXVI. When your employer draws a bill on you, payable at usance, which you accept, make Employer's account current Dr. to bills payable, for value of the bill ; and Bills payable Cr. by employers account current, for the acceptance. W. and J. Aug. 25. RULE XXXVII. When you buy up goods on credit, and ship them offby order for your employer, make Employer his account current Dr. to sundries; viz. to seller or sel- lers> for prime cost of the goods, to Cash, for charges, a* custom, ensuranee, and to Profit and Loss, for your commis- sion; also each particular article Cr. by employer his ac- count enrrent. AV. and J. Oct. 9. Vender Effingin of Amsterdam, &c. Expl. 27. As the goods were shipped for the account and risk o V. Effingin and not your own, so whether they arrive safe or not, you must make V. Effingin his account current Dr. to sundries for the whole cost; and each article, when entered in the books as in this Case, otherwise the seller, must be made Cr. for its respective value,.. BY DOUBLE ENTRY. RULE XXXVIII. When you buy up goods for cash and ship them off to your employer, nvtk? Employer's account current Dr. to sundries ; viz. to Cash* for prime cost and charges paid, and to Profit and Loss, tor your commission. NOTE 34. If you procure drawback or bounty, as this belongs to your employer, make Cash Dr. to employer his account current. NOTE 35. If you receive money, bill or bond, at the custom-house, by "bounty or drawback, make Cash. Custom-House debentures, or Custom-house bonds, Dr. to employer's account current. RULE XXXIX. When good* in company are bought on credit, make < wo entries; first, make Goods in Co. (naming partner) Dr. to the seller, for the value of the goods bought; and the Seller Cr. by the goods bought in Co. ; secondly, make each Partner his account current Dr. to his account in Co. for his respective share: also each Partner his ao- eount current Cr. by his account in Co. for his respective share. W. and J. Nov. 30. Bought of R. Means pot ashes in Co. with D. Whitman and self, each half. E.rpl 28. As the ashes is in Co. you must first make ashes in Co. witft D. Whitman and self, each half, Dr. to R. Means, for the quan- tity and value ; also make R. Means Cr. by ashes in Co. with D. Whitman and self, each half, for the same sum. Secondly, As 3"ou have a partner, make his Account current Dr. to his account in Co for his half of ashes ; also your Partner's Ac- count in Co. Cr. by his account current for the same sum. NOTE 36. Goods in Co. or Voyage in Co. are debited for all charges paid upon them, and credited for every article of profit. NOTE 37. Partner's account current shows what partner owes to the company, or the company to him ; instead of which some use '" partner's account proper." NOTE 38. When you receive partner's share of goods, or cash for the goods bought in Co. make cash Dr. to partner his account current for the sum received ; and Partner's account current Cr. by cash, for the same. June 21. Dec. 2. NOTE 39. In paying for goods bought, or receiving payment for goods sold in Co^ or Voyage in Co. the entries are the same as in proper trade. NOTE 40. When you pay partner his share of net proceeds, make Partner's account in Co Dr. to cash ; and cash Cr. by partner's ac- count in Co for the same. Dec. 4, 5. NOTE 41. After goods are brought into partnership there is no further occasion for second entries, as some merchants practice ; and the entries not only as it respects payments, but in every other trans- action will generally, under similar circumstances, be the same as in proper trade. BOOK-KEEPING RULE XL. When goods in Co. are sold for cash, make cash Dr. to goods in Co. (naming partner.) and goods in Co. Cr. by cash. W. and J. Lee. 2. NOTE 42. When goods are bought in Co. and each partner pays his share in ready money, or if he bring in his own share of goods ; make, Goods in Co. Dr. to sundries ; viz. To Cash, or to Goods, for your share, and to each partner's account in Co. for his share. NOTE 43. If the goods shipped have been formerly brought into Company, make Voyage to , Dr. to sundries viz. To goods in Co. for their value. To Cash ; for shipping charges. RULE XLL When goods in company are all sold off, balance the said account, that is charge Goods in Compa- ny, Dr. to sundries ; viz. to Cash, for all charges not yet booked ; to Commission account,nr your commission; to eaclv partner's account in Company, for his share of gain, and to Profit and Loss , for your share ; also make sundries ; viz. Cash, for charges not yet booked, commission account for your commission, Partner's account in Co. for his share of gain, and Profit and Loss, for your share of gain, Cr. by goods in company. See Leger, ashes in Co. with D. Whitman and Self; also voyage to Copenhagen in Co. with S. Dean and Self. RULE XLII. When goods are bought on credit in Com- pany, and shipped off, make two entries, viz. First, make Voyage in Co. Dr. to sundries, viz. To seller or sellers, for the value of the goods, to Cash for shipping and other charges ; also make ^Sellers Cr. by voyage, for the value of goods, and CashCr. by voyage for charges; Secondly, make each Partner his account current Dr. to his account in Co. for his share of goods bought in Co. also Partner's Ac- count in Co. Cr. by his account current, fer his share of goods bought in Co. W. and J. June 20. Expl. 29 Shipping goods in Co. is so much like bringing goods inte company that attention to Rule XXXIX and others respecting " goods in Co." will be sufficient explanation respecting Voyage in Co. NOTE 44. The entries, upon the advice and returns of the factor are the same as in proper trade. RULE XLI1I. When you receive the account sales from your factor, or receive returns of the goods in Co. consigned to him, make Factor our account current Dr. to voyage ia Co. to i f for ilie net proceeds ; also Voyage BY-DOUBLE ENTRY. in Co. to - (the place) Cr. by the fuctor our account current, for the same sum. W. and J. Nov. 6. RULE XLTV. When cash is remitted by factor, make Cash Dr. to factor our account current; and Factor our account current Cr. by cash ; for the same sum. W. and J Dec. IS. RULE XLV. When you receive a bill or note for goods sold, make Bills receivable. Dr. to the buyer ; and the Buy- er Cr. by bills receivable, for the same. March 24. De- cember 26. DIRECTIONS FOR WRITING IN THE JOURNAL. 1. In a simple entry, the Debtor should be first nam- ed, then the Creditor, all in one line ; after which the narration or cause of the entry, concisely and intelligibly expressed in one line, or more if necessary. Thus. Joseph BrighamDr. to Port wine, For 5 hhds. at $55 per hhd. $275 Journal Feb. 21. 2. In a complex entry, let the sundry debtors or cred- itors be written in the first line, and expressed by the word * Sundries," with the sum total short extended, ail in one line, under which let each of the several Crs. or Drs. with their respective sums be subjoined, each in a line by itself, which being added must'be carried to the money columns; Thus, Broadcloth Dr. to Sundries $1750 For 500 yds. at $3,50 To casn, paid in part $875 Window Lamb, for the rest - 875 Journal February 22. 1750 Sundries Dr to Richard Lakeman $12100. Fish merchantable, at $3,50 3400 quintals $11900 Oil, at &10 per barrel 20 barrels 200 Journal April 15. 12100 N. B. Every transaction of the Waste-book, thus en- tered is called a " Journal pnst or entry" For example, see J. February 12, "Joseph Brigham" is called the Dr " Port -wine" is the 6V. -The ' words " Joseph Brighnm Dr. to Port-wine" is called the entry, and the words whirh follow, the narration. 250 BOOK-KEEPING When two or more persons or things are included in th same account they are expressed by the term " 4 Sundries," or " Sundry accounts.'' A simple entry is that which has only one Dr. or one Cr. as Cash Dr. to rum. Journal January 7. A complex entry is either when one Dr. has two or more Crs. as Broadcloth Dr. to Sundries, or when two or iore Crs. have only one Dr. as, Sundries Dr. to Richard Lakeman, or when several Drs. have several Crs. and then the entry is said to be complex in both terms. In such cases of com- plex posts, it is preferable to make two separate Journal entries, so that the first may have only one Cr. and the second only one Dr. This mode will prevent the confusion attending a single entry, and avoid the improper ambig- uous, titles of " Sundries Dr. to Sundries." Bartered with Robert Means IS cwt. su- gar a SI 2,50 per cwt. $225 Waste April 4.- 120 gals, rum a g>l,25 For 20 casks of pot Ashes 45 2 4 Ib. net a $4.94 / r per cwt. 500 yds- tow cloth a 150 $37, ,25 225 125 350 f Sundries Dr. to Robert Means $375. I Ashes, 45 2 4 Ib. net | a 4.-94-/ r $225 I Tow Hoth, 500 yd. a } 25 125 Journal Entry <( Received in Barter. ^350 April 4. Robert Means Dr. to Sundries 375. To sugar 18 cwt. a $12,25 $225 To rum, 120 gals, a SI, 25 150 ^Delivered in barter. 375 NOTE 1 . In complex entries the sure total should be short-extend- ed, and annexed 1o the word u Sundries/' 2. In mentioning the several Drs. and Crs. the Cr?. have the word " To" written before them, but 1hc ITS-, are expressed wlth- eut any word prefixed. ee preceding Journal entry. POSTING THE The first Journal i r.rv ru, Mains Ihe *>i'lsfance of tfee Inventory, which is divided into two parts ; VKS. BY DOUBLE ENTRY. 1. All the money on hand, the goods, notes, or bills re- ceivable, furniture, houses, lands, ships, debts due by bond or mortgage, accounts, and every other kind of properly which the merchant possesses. The difference of these t\vo parts shows the merchant's net stock, or how much he is worth after all his debts are paid. The first entry i* " Sundries Dr. to Stock." The particular D'rs. are, Cash^ Goods, Bills receivable, due to him, and the Persons indebted to him. 2. The second entry is made, " Stock Dr. to Sundries." The particular Crs. are the Persons, to whom the mer- chant stands indebted, Rills payable accepted by him pay- able to others. NOTE 1. Sbo& is a term used to represent the merchant or owner of the book?. '2. The Debtors and Creditors should be written in large round hand, or text, both for ornament and distinction ; and the figures of to the folio, much smaller than' those of the dute or LEGER. The Lesjer is the merchant's principal book, to which the several transactions, dispersed through the Waste-book, hut collected and prepared by the Journal entries of the ti- tles with the relation of Dr. and Cr. are transferred each to its proper account. The Leger is ruled in the same manner as in single en- try, with the exception, that in this, inner columns are rul- ed in accounts of goods, and a folio column both on the Dr. and Cr. sides, for references to the folio, \\here the corresponding Leger entry of each article is made; for in the method of double entry, every article is twice entered in the Leger ; viz. on the Dr. side of one account, and*Lgain on the Cr. side of some other account, so that the figures have a mutual reference from one to the other, which also greatly facilitate the labor of examining the accounts. In posting the Leger, the following circumstances muit he carefully observed. On the Dr. side must be written, 1. The date, in the first and 2d left hand columns. 2. The Journal folio, in the 3d column. 3. Each creditor title, the cause of the entry, in tl do. 1. The transaction, belonging (o the title, in 4th do. BOOK-KEEPING 5. The quantity &c. ^in account of goods, in inner col- 6. The quality &c. umns, ruled within the 4th do. 7. The Leger folio of the creditor, in the Sth do. 8. The amount in dollars and cents, in the 6th and 7th do> On the Cr. side must be written, 1. The date, in 1st and 2d columns. 2. The Journal folio, in 3d do. 3. Each debtor title, the cause of ihe entry, in the 4th do. 4. The transaction belonging to the Leger title, in the 4th do. 5. The quantity &c. 5 in inner columns ruled in accounts 6. The quality &c. of goods, in the 4th column. 7. The Leg** folio of iM Debtor, in the 5th do. 8. The amount in dol$. and cents, in 6th and 7th do, NOTE. Besides the seven columns, there should be othar inner columns, ruled between 3d and 5th, for number, weight, measure, mark, exchange &c. when these are considered. In filling up the Leger, assign a sufficient space for each account, in the order hereafter arranged, beginning with Stock 9 $c. The titles of the accounts are written over the account? with Dr. prefixed on the left hand page, and Cr. annexed on the right ; below which are the articles with the word " To" prefixed on the Dr. side and " By" on the Cr. side. Upon the margin are recorded the dates of the articles in two small columns allotted for that purpose, and one for a reference to the Journal folio. The titles are inserted in the index under their initials with the folio reference, as soon as they are written in the Leger. In entering the Dr. article, write on the line the name of th in the third or fourth columns of the trial h*. !. e, as i may properly belong, a?id at the same t.mt inserting \\i\\\ peiicii mark, the difference ou ihe less side of the ae- 260 BOOK-KEEPING count in the Leger ; which being added will balance, that is, will make both sides equal, at closing the books. Add up the third and fourth columns of the trial bal- ance, and if the sums agree, the Leger is proved to be cor- rect ; otherwise the books cannot be brought to a balance, till the error is corrected. The correctness of the Leger being thus proved, the clos- ing of if remains to be done, which may be thus performed. 1. Form a Profit and Loss sheet, like the oue annexed to the Leger. 2. Take from the Leger. or the trial balance, all the ac- counts which *lo*e with Profit and Loss, and enter the halanee of each on its respective Dr. and Cr. side of the Profit and Loss sheet ; and to the Profit and Loss sheet add the debits and credits of the Profit and Loss account 3. Add up both sides and subtract the less from the greater, the balance will exhibit the gain, which must be debited if the Cr. side be the greater, ' To stock for net gain," and will balance both sides of the Profit and Loss sheet, in case no error is committed. Transcribe the Profit and Loss sheet .into the Waste hook, and from that, by the usual method into the Journal and Leger. The next thing to be done is to make a " Balance (LC- count," similar in form to the one following the Profit and Loss sheet. Take from the Leger, or trial balance, all the accounts which close with " Balance," except that of Stock, which will be taken from the Dr. side of that account in the Le- ger when the sides of the balance sheet are to be added up ; and must be carried to the Cr. side of the balance sheet. This will make both sides equal, if there is 110 error. The next thing to be done is to transfer the " Balance sheet'' to the Journal, by making ' Balance account Dr. to Sundries," taking the particulars from the Dr. of the Bal- ance sheet ; also by making *' Sundries Drs. to Balance ac- count." taking the particulars from theCr. side 'of the Bal- ance sheet, including the stock account. See J. p. 13. Each balance must then be transferred to its proper ac- count in the Lesjer, inserting in the column of the Journal the number of reference to the folio in the Leger. BY DOUBLE ENTRY. OF CLOSING THE ACCOUNTS IJV THE LEGER. Having added up the money columns on the Dr. and Or. sides as before directed, make both sides equal by adding the difference of the two sides to the less ; and thus pro- ceed with cash account in the Leger, and the accounts will be closed. In forming a new set of Books, make out an inventory in the Waste-book from the balance account of the Leger. The entries in the new Journal will be " Sundries Dr. to Stock /' the particular debtors being taken from the Dr. side of the " balance account." Also, " Stock Dr. to Sundries /' the particular creditors being taken from the Cr. side of the " balance account." Thus by the Balance of the Leger will be found, 1. What stock there is to begin another set of books. 2. What the gain or loss has been since the commencement of trade ; and from the balance sheet, which is an account formed with the Dr. and Cr. the stock is ascertained. The gains and losses are found in the account of Profit and Loss ; the several articles transferred into the accounts of "Stock'' and " Profit and Loss," are found by balancing or closing every account in the Leger. Some accounts balance of themselves ; some are closed with " balance" only, others with " Profit and Loss" only ; Balance, also Profit and Loss are closed with "Stock ;" and Stock balances of itself, in case no errors are commit- ted, which is the best proof of the correctness of the books. WASTE-BOOK. Boston, January 1, 1817. J. F. 1 Inventory of the estate of Thomas Russell, merchant. Ready money, deposited in the Union Bank $4000 House in Hanover-street, value - 2500 Land in the county of Washington, in the Province of Maine, 750 acres, a ,75 - 562,50 Ship Massachusetts, value - 7000 Household furniture 1500 Jacob Thomson's note, dated Nov. 10 last, payable to my order, at 6 months $350 David Jones' note, dated Dec. 3, last, payable to my order, at 3 months 410 760 Broadcloth, 250 yds. a $3,50 per yd. - - 875 Linen, 400 yds. a ,80 320 Port-wine, 7 hhds. a $45 per hhd. - - - 315 Sugar, 20 hhds.w'g. 240 cwt. a $10,50 pr. cwt. 2520 Rum, 12 puncheons, a $125 per pun. - 1500 Thomas Lamson, merchant, Boston, owes me 400 Amos Locke, carpenter, Salem, owes me 275 1 List of debts and notes owed by the sak Thomas Russell. To James LeAvis, merchant, Boston, - $140 L. Samson, mer. Boston, payable on denVd. 800 James Munson, merchant, Boston, pay- able on demand - 2050 Joseph Franklin, merchant, Boston, pay- able on demand, .... "- 1500 1 Sold Charles Lee, at 5 months. 72 cwt. sugar a g!2,50 per cwt. - i Rule I. | , 7 . 1 Sold for cash, 9 puncheons rum, a $135perpuu Rule II. 12 Paid James Lewis, in full Rule X. 15 _ 1 Bo'tfor eash, 8 hhds. port- wine, '; 42 pr. hhc Rule VI. i 18 1 Bouebt of Andrew Newman, 1000 yds. linen i ,70 ! Rule VI a ,70 per yd. 2252^ 4490 900 1215 14ot 336 i 7001 \\ASTE-BOOK. Boston, January 19? 1817 263 Bought for cash, 84 c\vt. sugar, a gl 0,72.6^ per cwt. ------- Rule VI. 20 Bartered 84 cvvt. sugar, a $12 per cut. lor 4032 lb. coffee, a ,25 per Jb. Rule XXV. Paid Joseph Franklin, in full Rule X. Paid James Mtinson, in full Ride X. 901 1003 1500 2050 Sold A. Eastman my 750 acres of land, acre, in payment of which I have receiv- ed cash, in [ - - $350 And his bill, at 11 months, with interest, for balance ._--__ 475 Rule IV. 23 Paid Lemuel Samson, in full Rule X. 29 Received from Thomas Lamson, in full Rule XIV. 31 Received from Amos Locke, in full Rule XIV. February 2 Lent Samuel Tvler, on bond, at (3 per cent. Rule XI. 5 Rec'd from J. Thomson, payment of his note Rule XVIII. 1 Sold for cash 400 yds. linen, a $1,10 per yd. Rule II. 12 Sold J. Brieham, 5 lilids. port-wine, a $55 perLhd. - -' - - - Rule I. 15 Bo't for cash, 220 bhls. of Hour, a 8,75 pr. bbl. Rule VI. 825 800 400 275 2000 i 350 j 440 : 275 : 1925 WASTE-BOOK. Boston, February 18, 1817. B't of D. Whitman, 1250 Ib. hyson tea, a $ 1,25 Rule VII. 20 Paid W. Hart, for repairs on the ship Mass. Rule XII. 22 Bo't of W. Lamb 500 yds. broadcloth, a 3,50 For which I paid cash in part . . $875 Balance due him is .... 875 Rule VIII. Sold to Nye Freeman GOO yds. linen, a gl,20 for which he has given roe a bill on A. Young, paj-- able in 3 months ..... Rule V. 26 Discounted with the Massachusetts Bank, A. Young's note, at 3 months . . $720 discount . . 11,16 Net sum received .... Rule XX. See Pract. Arith. p. 153. Bank Dis. 28 Effected Ensu ranee, at the Union Ensu ranee Office, on the Massachusetts from Boston to London and from thence to Boston, $6000 at 3 per cent premium . . . . . $210 Policy . . ,75 Rule XXIII. See Pract. Arith. p. 148. March 1 Henry Lee of Norfolk, Vir. has consigned lo me by the brig Favorite, Cupt. C. Hunt, 15 hhds. tobacco, for sale on his account ; on which 1 have paid freight a 2,75 per hhd. Rule XXXII. 4 Sold W. Paterson,per bill payable in 5 months. 4 hhds. of Henry Lee's tobacco, weighing as fol- lows; viz. No. 1. 10 3 14lb. tare 145 Ib. 2. 11 2 16 150 3. 9 3 24 135 4. 10 27 140 42 2 25 Ib. 570 Ib. is 4215 Ib. net, $6,80 per 100 Ib. Rule XXXIII. N. 33. See Pract. Arith. p. 110. _ 7 Sold for cash 100 bbls. flour, a Rule II. WASTE-BOOK Boston, March 10, 1817- J. F. 3 Paul truckage, on H. Lee's tobacco, 15 hhds. a ,75 per hhd. Rule XXXII. 14 3 Sold for cash 8 hhds. of H.Lee's tobacco, w'g. as follows ; viz. No. 5. 8 2 13 Ib. gross, tare 135 Ib. 6. 9 1 140 7. 10 14 138 8. 8 3 15 145 9. 7 3 23 125 10. 9 1 13 132 11.10 14 140 12. 8 2 14 130 72 3 22 Ib. 1085 Ib. is 7085 Ib. net, a $6,50 per 100 Ib. Rule XXXIII. See Pract. Arith. p. 110 Tare & Tret. 3 Paid for repairs on Louse in Hanover-street, Rule XII. 19 Bought for cash 1 20 gals, rum $1 ,25 pr. gal. Rule VI. 20. 3 Sold to R. Means, 150 c\vt. sugar, 12,25 Rule I. 24 Received of Robert Means, his note, to my order, at 9 months, with interest, in full for 150 wt. sugar . . .... Rule XLV. Sold for cash 3 hhds.H. Lee's tobacco, \v'g. as follows ; viz. No. 13. 9212 Ib. gross. Tare 146 Ib. 14. 8 3 27 138 15. 10 1 13 148 23 3 24 4U2 Ib. makes 2812 Ib. net, a $6,90 per 100 Ib. . . Rule XXXIII. See Pract. Arith. p. 110. 27 Paid for weighing and other incidental charges attending the delivery of Henry Lee's tobacco ...... Rule XXXI I. 30 Paid storage of H. Lee's tobacco. 15 hhds. Rule XXXII. 23* WASTE-BOOK. Boston, March 30, 1817- J. F. Furnished H. Lee with account sales of his 15 hhds. tobacco, amounting to 941,17,3 My commission on the same a 2 per cent. 25,88,2 The net proceeds .... 846,79, Rule XXXIV. See Pract. Arith. p. 147. 31 Remitted H.Lee, by mailjinbank bills ot'U.S Rule XXXV April 4 Bartered with R. Means, 18 cwt. a $12,50 And 120 gallons rum a gl,25 suga 225 150 , For 20 casks pot ashes, each weighing 2 2 qrs. gross tare 25 Ib. pr. cask is 45 2 4 Ib. net> a $4,94,^ per cwt. $225 500 yds. tow cloth, a ,25 125 Rule XXVI. 6 Rec'd from D.Jones, pay't of his note $440 Interest for 30 days . . . 2,05 Rule XVI. N. 12. Paid expenses, this quarter, for men's wages and other incidental charges Rule XIII. 10 Chartered the Brig Huntress, Capt. S. Saw yer, for a voyage to Bourdeaux, and laded her with the following goods ; viz. 2200 bushels corn, boHof C. Lee, a $1 $2200 2200 ditto wheat, bo'tof C. Lee, a $1,25 2750 230 bags coffee, bought of E. Nichols & Son, weighing 18400' Ib. a ,25 . Cash paid for dunnage, &c. . . paid shipping charges . . . 4950 4600 175,20 155 Consigned to C. Leroi, Supercargo for sale & returns Rule XXVIII. Made Ensurance, at the Union Ensuratice Office, Boston, on the cargo of the brig Huntress from Boston to Bourdeaux, valued $9880,20 a 3f per cent, premium . . 370,50,7 Policy ... 75 Rule XXIII, See Pract. Arith. p. 148. $. C. 872 67,1 500 350 415 120 05 25 9880 20 371 25,7 WASTE-BOOK. Boston, April 12, 1817. 267 J. F. 5 Granted to C. Lee my note, dated 10th inst.i at 60 days, for 2200 bushels corn and 2200 do. wheat! 4950 Rule XIX. 15 Bought of Richard Lakeman of Ipswich, 3400 quintals of merchantable fish, a $3,50 $11900 20 barrels oil, a $10 . . . .200 For which I paid him cash . . . $6050 And my note, at 60 days for the rest 6050 Rule" IX. Exp. 9. 18 12100 Paid Andrew Newman, in full Rule X. 20 Received from Joseph Brigham, cash in full for 5 hhds. port wine. Rule XIV. 24 12100 700 275 Paid David Whitman in full for 1250 Ib. tea' purchased of him Feb. 18. Rule X. 26 - ! 1562 Paid Winslow Lamb in full Rule X. 28 875 Bought of Joseph Turrel for cash 340 pairs men's shoes, a ,90 per pair . . $306 522 pairs women's coloured ditto, a 1,20 626,40 120 ditto boots, a $3 . . . 360 Rule VI. May 4 Received Rule XVIII. of William Paterson's bill Bo't for cash 8000 white oak staves a $35 pr.m. Rule \ 1292 286 280 Shipped on board the General Hamilton for Oporto, Capt. A. Delano, and consigned to F. Al- vardo & Co. for sales and returns, on my own ac- count and risk, 3400 quintals of merchantable fish a $3,50 11900 8000 white oak staves a $35 . . 280 Paid shipping charges .... 11,50 Rule XXVIII. 12191 C 50 40 62 50 268 WASTE-BOOK. Boston, May 15, 1817. S. T. No. ion 8. T. No. Ia20 Effected Ensurance at the Union Ensurance Office, Boston, on the cargo of the General Ham- ilto'n, from Boston to Oporto and thence to Bos- ton, valued $10000 a 5i pr. cent, prera. $525 Policy .... ,75 Rule XXIII. See Pract. Arith. p. 148. , 18 Bought for cash 3 pipes gin, containing, No. 1. 134 gals. 7 out 2. 129 8 3. 133 5 making 376 gals, a $1,55 pr. gal. Rule VI. 20. 396 20 Bought of R. Means, at 30 days, 20 casks of pearl-ashes, each containing 2 1 26 Ib. net, mak- ing 49 2 16 Ib. a $6 per cwt. Rule VII. 24 Granted to R. Means my note dated 20th inst. payable in 30 days, for 49 2 16 Ib. pearl-ashes. Rule XIX. 31 Shipped on hoard the Galen, Capt. S. Turner for London, and consigned to said Capt. for sales and returns, the following goods ; viz. 17 casks of Ashes, pot, marked as in margin, w'g. 45 2 4 Ib. net a $4,94 JL. pr. cwt. $225 20 do. of Ashes, pearl, marked as in margin, weighing 49 2 16 Ib. net, a $6 pr. cwt. 297,85,7 Paid shipping charges Rule XXVII. 15,25 June 5 Sold for cash 20 hbls. oil, a $1 2,50 per hi. ' Rule II. 10 Received from Charles Lee, cash in full . Rule XIV. Paid Charles Lee my note, dated April 10th, at 60 days Rule XVIII. No. 15. 18 Sold for cash 2 punch, rum, a S132 pr. pun. Rule II. * f * o-j WASTE-BOOK. 269 Boston, June SO, 1817. G Shipped on board the Mary-Ann, Jas. Sco Master, Bale .T. V. Hhds. Ito20 .T. v. I bound to Copenhagen the following goods as marked in the margin ; viz. 1 bale broadcloth containing 3000 yds. bo of Amasa Goodhue a $3,50 per yd. $10500 20 hhds. tobacco containing 240 cwt. bought of Thomas Mackuy, a $5 1200 Paid shipping charges . . 35 Which goods are consigned to Jacob Vantorff, mer chant at Copenhagen, for the joint concern o: Samuel Dean and eelf, each half, Rulr XLII. 2! Received from S. Dean his half of the value of Voyage in Co. to Copenhagen Rule XXXIX. N. 38. DO 7 Sold for cash 3266 Ib. coffee* a ,23 per Ib. Rule II. 25 7 Shipped on board the Pacific, Capt.L. Davis for New-Orleans, 340 pairs men's shoes, a ,90 . . $306 522 ditto women's coloured ditto, a $1,20 626,40 120 ditto boots, a $3 . . . 360 paid shipping charges, . . . 10,2C jOrs-ic.-r.ed to Kinsman Turrel, merchant there, for ej-le and returns on my own account and risk, vritb ; orders to invert the net proceeds in produce, lilulc XXVII. ! 30 7 Sold .Tames Wilson 1 puncheon rum Rule I. July 1 Paid house expenses, and other charges thi quarter. Rule XIII. Received from S. Tyler in part on his bond Rule XVII. u of R. Means, balance in barter XIV. 7 Paid Richard Lakeman my bill, a 90 days Rule XVIII. N. 15. 11735 11?35 5867 914 50 48 130260 132 119 495 25 6050 270 WASTE-BOOK. Boston, July 10, 1817- J. F. Paid Robert Means my bill, a 30 days . . Rule XVIII. N. 15. 12 Paid Thos. Mackay in full for tobacco . . Rule X. 15 Bought of Rufus Perkins 2500 Ib. coftee a 22 cts. .... Rule VII. 20 7jPaid Araasa Goodhue in full for broadcloth Rule X. : 25 7. Sold for cash, G75 Ib. hyson tea, a 1,50 Rule II. 7 Sold for cash, 500 yds. low elotb, 25 cts. Rule II. | 30 Rec'd Interest on W.Paterson's bill, 41 days Rule XV. August 1 8 Granted Rufus Perkins my note, a 30 days Rule XIX. Paid E. Nichols & Son cash in full for 18400 i Ib. coffee ...... Rule X. 15 8 Henry Lee of Norfolk, Virginia, has drawn on me in favor of Charles Lee, for $120 at 10 days after sight, which draft I have this day accepted Rule XXXVI. 18 8 Sold my house in Hanover-street, for cash Rule H. N. 2. 19 . 8 Sold for cash my household furniture . . . j Rule II. N. 2. 20 8 Remitted Henry Lee, the balance of his act. Rule XXXV. ' ! 25 8 .Paid my acceptance of H. Lee's draft in fa- vor of C. Lee. ..... Rule XVIII. Note 15 I- 297 1200 550 10500 1012 125 1 550 4600 120 3000 2300 226 C. 85,7 50 96 79,1 10] WASTE-BOOK. 271 Boston, August %8, 1817. J. F. 8 8 8 8 .8 8 8 8 9 9 Kiugman Tnrrel, writes me of the safe ar- rival at New-Orleans, of the Pacific, with my' goods ; the net proceeds of which amounted to 1405, CO that he had invested the same in! cotton, which he had shipped by return of the' Pacific, on my account and risk, 9 bales weighing 6390 Jb. a ,<2 per Ib Rule XXIX. 1 T $. . 1405 1410 550 C. CO 30 50 05 75 44 80 Sold for cash 120 barrels flour, a $11,75 . . Rule 11. ScYlf 1 i ' , . - Paid Rufus Perkins my bill, a 30 days . . . Rule XVIII. y. 15. c l The Pacific, Lemuel Davis, has arrived from New-Orleans, and brought me m return the net! proceeds of my goods, remitted by K. Turrel, merchant there, 9 "boles cotton, weighing G390 lb.; a ,22 pr. lb 1405 Rule XXX. \ ,.,.' Paid for freight and other charges for my goods in the Pacific from >. . . 134 Rule XXIV. 12. ' Sold for cash on the wharf at auction my 9 bales of cotton, r ^b. Rule II. & XXIX. IS. 27. 1885 833 14 Ii7 876 Sold W. Lamb 575 i for which I received the rest at 60 days Rule !!!. qn Received from Samuel Tyler SI 4 on his bond. Rule XVII. Ocl 1 Paid for men's wages aii'l other incidental expenses this quarter. Rule XIII. r Sold A. Newman 3 pipes g:a, 376 gallons, a $1,80, at 90 days. Rale I. 272 WASTE-BOOK. Boston, October 9, 1817. J - F -l $ 9|Bonght of James Wilson for account of Vender Effingin, Amsterdam, at 30 days, w I 10 hhds. tobacco, weighing as follows ; viz. rvJ No. 1. 1340 Ib. eross tare 84 Ib. 2. 1574 . . . . 90 Shipped on board 3. 1394 .... 89 the Mary-Ann, 4. 1504 .... 96 Capt. Hoffman, 5. 1479 .... 88 for said Effingin 1 s 6. 1584 .... 87 account and risk. 7. 1498 .... 90 8. 1640 .... 100 9. 1549 .... 99 10. 1584 .... 98 15146 Ib. 921 921 Ib. 142251b.net a$4pr.!001b.$569 | Shipping charges ..... 21,10 Commission a 5 per cent. . . . 28,45 Rule XXXVII. 10 9 j Granted to James Wilson my note, dated inst. at 30 days, for 10 hhds. tobacco, bought o him for account of Vender Effingin, for [Rule XIX. 15 9|Received advice from Francisco Alvardo and Co. of the safe arrival of the General Hamilton, al Oporto, that they had received my goods, and had sold the same for cash, amounting, after deducting freight, duties, &c. to 14637,800 reas Exchange a 1,25 per milrea ; that they had ship'd by the re turn of the General Hamilton for Boston,the net pro- ceeds in port wine, viz. 18297^ gals. a800 reas pr gal. Rule XXIX. See Pract. Arith. p. 20 Exchange. 9|Received from S. Tyler, S350 OQ Rule XVII. 05 61 569 9 Sold for cash 400 yds. linen, a ,95 per yd. Rule II. 30 9|S'd J.Wilson 750 yds. b'dcloth a 4,25 for which I received" my note pay'ble to him $569 Cash for the rest, .... 2618,50 I Rule IV. 8297 380 3187 WASTE-BOOK. 373 Boston, November 1, 1817. 10 10 10 10 10 The Galen, Capt. Turner, is arrived from London, and brings me in return for my goods, " Pianos Fortes, valued a l81,12,2f Ster. . , Rule XXIX. N. 26. See Tract. Arith. p. 160. 5 Entered at the Custom House Pianos, and paid duties, freight, &c. Rule XXIV. my Fortes 6 Received advice from Jacob Vantortf, of Co- penhagen, that he had received by the Mary-Ann, Capt. Scot, the goods consigned to him for the joint concern of Samuel Dean and self, amounting to 14786 rix dollars and 50 skillings, Exchange 100 cts. per rix dollar. .... Rule XLI1I. See Pract. Arith. p. 171. Received intelligence from Charles Leroi, Supercargo of the brig Huntress, who advises his safe arrival at Bourdeaux, that lie had sold the cargo, amounting to 74101 livres 10 sols, Exchange 20 cents per livre ; that he had shipped by return of the Huntress the net proceeds in brandy ; viz. 11856-6_ gals, a 6 liv. 5 sols per gal. Rule XXIX. See Pract. Arith. p. 167. 12 The brig Huntress, Capt. S. Sawyer, is ar- rived from Bourdeaux, and brought the net pro- ceeds of my adventure, viz. 11856^ g a ] s . brandy, a 6 liv. 5 sols per gal. .... Rule XXX. 17 Entered, at the Custoni-House,my goodsfrom Bourdeaux, and paid duties, freight, &c. . . Rule XXIV. 18 807 115 16 50 14820 14020 784 The General Hamilton, Capt. Delano, is ar- rived from Oporto, and brought returns of my goods, viz. 18 l 297i callous port wine, a 800 reas per gal. (18297 Rule XXX. 19 5 aid at the Custom-Hoese, duties and other charges for the General Hamilton from Oporto Rule XXIV. 20 deceived from Samuel Tyler g870 on his bond. Rule XVII. 1010 870 48 30 40 WASTE-BOOK, [13 Boston, November Z5, 181?. J. F. 10 10 10 10 10 10 10 10 11 ii 11 S'd. for cash on the wharf my 18297 gallons port wine, a $1 ,76 per gal. being the net proceeds of my adventure to Oporto by the General Ham- ilton. .... . . Rule XXIX. N. 27. Received of Jones & Pennman for freight oi the ship Massachusetts. .... Rule XXII. 28 Received from Winsiow Lamb in full Rule XIV. Paid reimbursements on the Massachusetts to Europe . . .... Rule XII. 30 ; Bought of 11. Means, for account of D. Whit- man and self in Co. each half, 340 cwt. pot ashes, a $6 per c\vt. on demand, myself having the dis- posal of the same. Rule XXXIX. December 1 Paid R. Means in full for our 340 cut. pol ashes, in Co. with D. Whitman and self. . . Rule X. 2 Sold for cash our 340 cut. pot ashes, in Co. with D. W r hitman and self, a $6,75 per cwt. . . Rule XL. Received from D. Whitman his half share ol ashes bought of 11. Means. Rule XXXIX. N. 33. 3 Paid charges on ashes in Co. Rule XXXIX. N. 36. 4 Adjusted accounts with David Whitman in Co. and paid him in part of net proceeds on ashes in Co. . . .... Rule XXXIX. N. 40. 5 Adjusted accounts with S. Dean, of voyage in Co. to Copenhagen, and paid him in part ol net proceeds. ...... Rule XXXI X. N. 40. 32203 14] WASTE-BOOK. 'Boston 9 December 6, 1817. 275 J. F. 11 11 Received from Vender Effingin his remit- tance, per bill on R. Perkins, Boston, for amount of goods shipped by his order, on board the Mary- Ann, Capt. Hoffman, amounting to 1855 gilders 13 stivers, Exchange 40 cents per gilder. Rule XXXI. bee Pract. Arith. p. 166. 8 Received from Kiifus Perkins, payment of Vender Effingin's bill. .... Rule XXXI. X. 29. 9 Sold for cash 10 lihds. port wine, a 851,50 Rule II. 12 Sold for cash 3266 !b. coffee a ,20 per Ib. Rule I. Received from James Wilson in full for 1 puncheon of rum ..... Rule XIV. 14 Andrew Newman is become a bankrupt, and owes me ... . g>G76,80 He has compounded with his creditors, a ,38 on a dollar, which I have received in full of his debt. . . . 257,18,4 Balance allowed him Rule XXI. See Pract. Arith, p. 127. 15 419,61,6 Sold at auction my brandy by brig Huntress from BourcU aux Amount of saJLs $'2C676 From which deduct commission 14 ) n United States duty . - | \ 2 P er ct " 53 Received in ciish . . $13070,24 ( James Henderson's note. Bills ^ at 90 days, endorsed by receivable j William Ponsby $6535,12 ( T. Henshaw's note, at 90 days, endorsed by Tho. Benson . 6535,12 Rule XXXIX. N. 27. 16 $26140,48 11 Sold for cash 3 Pianos Fortes a $115 . . . Rule II. $ 742 742 515 947 14 676 26140 48 525 WASTE-BOOK. Boston, December 17, 1817. [15 J. F. 11 11 Taken for the use of my family 1 Piano Forte Rule VI. N. 4. 12 12 12 12 12 12 12 12 &l the request of Robert Means, I have ac- commodated him by a renewal of his note, due :his day, for 4 months longer, . . J1837,50 His bill renewed for the same. Rule XVIII. obs. Received from Samuel Tyler, the balance due on his bond. . . . g271 Amount of Interest by partial payments 86,34,4 Rule XVI. See Pract. Arith. p. 144. 25 Received from Jacob Vantorff, merchant, at Copenhagen, the net proceeds of goods consigned to him for the joint concern of Samuel Dean and self, each half, by the Mary-Ann, Capt. Scot, amounting to 14786 rix dollars and 50 skillings, Exchange 100 cents per rix dollar. Rule XLIV. See Pract. Arith. p. 171. 20 Sold Vancouver & Sons the ship Massachu- setts, at 4 months ..... Rule I. Received from Vancouver & Sons (heir bill payable in 4 months, for the ship Massachusetts Rule XLV. 27 Sold fnr cash, 2 Piano Fortes, a $210 Rule II. Rec'd. payment of A.Eastman's bill $475 Interest on the same for 11 months . 26,12,5 Rule XVI. N. 12. 30 Paid for men's wages, and other expenses this quarter. ...... Rule XIII. S'd. for cash, household furniture, 1 P. Forte Rule II. Received from Robert Means, Interest on his note, for 9 months and days . , , Rule XV. 14786 WASTE-BOOK. S77 Boston, December 31, 1817- 13 Profit & Loss to be debited for sundries, Expense account since Jan. 1, $499,33 For men's wages and other charges . . . 120,25 ditto 119,24 ditto 127,44 ditto 132,40 Profit & Loss to be credited articles of gain, since Jan. 1, For House, in Hanover-street Land, in Washington Comity Ship Massachusetts Household Furniture Broadcloth Linen .... Port wine Sugar .... Ruin .... Gin Coffee .... Flour .... Tea .... Oil Piano Fortes Commission Voyage to Bourdeaux London . . New-Orleans from New-Orleans Vender Effingin, Amsterdam Voyage from Bourdeaux . . Oporto for sundries, $42916,15,8 . $455,63 . . 262,50 3557,24 , . 810 562,50 520 139 549,50 111 94 303,62 510 283,75 50 347^84 54,33,2 4568,84,3 . 5580 . 153,55,3 103,20 344,75 . 123,71 . 10535,68 12895,51 Profit & Loss to be finally debited per Stock, For net gain since January 1, Balance account to be debited for Stock, For net Stock ..... END OF THE WASTE-BOOK. 24* 42916 15,8 43796 1 92,1 61834 278 JOURNAL. Boston, January 1, 18 iy. Dr. L. F. 1 3 3 3 3 2 4 4 4 4 4 4 5 Cr. L. F. 1 Sundries Dr. to Stock $22527,50 Cash deposited in the Union Bank . $4000 House in Hanover-street . . 2500 Lands for 750 acres in County of Wash- ington, P. of Maine, a ,75 per acre 562,50 Ship Massachusetts . . . 7000 Household furniture . . . 1500 Xotes receivable, J. Thomsons note, dated Nov. 10 last, payable to ray order, at 6 months $350 D.Jones' note, dated Dec. 3d last, payable to my order tit 3 months, 410 760 Broadcloth 250 yds. a $3,50 per yd. 875 Linen, 400 yards, a ,80 . . 320 Port wine, 7 hhds. a g45 per hhd. 315 Sugar, 20 hhds. w'g. 240 cwt. a $10,50 2520 Rum, 12 puncheons, a $125 per pun. 1500 T. Lamson, mer. Boston, owes me 400 A. Locke, carpenter, Salem, owes me 275 $. 22527 C. 50 1 5 5 5 5 Stock Dr. to Sundries g4490 To J. Lewis, mer. Boston, due to him jg!40 Lemuel Samson, mer. Boston, ditto 800 James Munson, mer. Boston, ditto 2050 Jos. Franklin, mer. Boston, ditto 1500 4490 7 4 Charles Lee Dr. to sugar, For 72 cwt. a g!2,50 per cwt. 900 I 4 Cash Dr. to rum, For 9 puncheons, a gl35 per pun. 1215 b 1 James Lewis Dr. to cash, 140 1C 4 1 Port wine Dr. to cash, For 8 hhds. a $42 per hhd. 18 336 4 7 Linen Dr. to Andrew Newman, For 1000 yards, a ,70 per yd. . . . 700 4 1 Sugar Dr. to cash, For 84 cwt. a glO,72,6-JL per cwt. . 901 5 4 Coffee Dr. to sugar, Received 4032 Ib. a ,25 per Ib. in barter for 84 cwt sugar, a $12 per cwt 1008 2] JOURNAL. Boston, January 24, 1817. 379 Dr. L. F. 5 Or. L. F. 1 Joseph Franklin Dr. to cash, Paid him in full ..... S- 1500 Co 5 1 n " James Mnnson Dr. ta cash, 2050 1 * 3 Smuiiies Dr. to land g825 Cash in part for 750 acres land jg350 Biih receivable, bill on A. Eastman, at 11 months, with interest, the rest 475 00 825 5 1 Lemuel Samsaii Dr. to cash, Paid him in full ..... on 800 1 4 Cash Dr. to Thomas Lamson, Received from him in full . : "V^^^H 31 400 1 5 Cash Dr. to Amos Locke, Received from him in full 275 7 1 Samnol Tyler Dr. to cash, Lent him on bond, at 6 per cent, per an. c 2000 1 2 Cash Dr. to bills receivable, Received from J. Thomson payment of his note 350 1 4 Cash Dr. to linen, For 400 yards a 1,10 per yd. l 440 7 4 Joseph Brigham Dr. to port wine, For 5 hhds. a g55 per hhd. 275 5 1 Flour Dr. to cash, For 220 barrels, a $8,75 perbbl. 18 1925 6 8 Tea Dr. to David Whitman, For 1250 Ib. a gl.25 per Ib. Of) 1562 1 50 3 1 Ship Massachusetts Dr. to cash, For repairs, paid to William Hart 00 53 20 4 1 8 Broadcloth Dr. to sundries g!750 For 500 yds. a g>3,50 per yd. To cash, in part . . g875 Winslow Lamb for rest . 875 1750 380 JOURNAL. Boston, February %5 f 1817. Cr. L. F. 4 2 1 1 8 6 1 8 1 1 4 8 8 Bills receivable Dr. to linen, For 600 yds. a gl,20 sold to Nye Freeman, for which I have received a bill on A. Young, due at 90 days ..... 6 Sundries Dr. to bills receivable, $720 Cash, recM. for A. Young's note, disc'd. 708,84 Profit and Loss, discounted 3 mo. Inter. 11,16 00 Ship Massachusetts Dr. to cash, For Ensurance from Boston to London on 6000 at 3% per cent, premium, . . . 210 Policy, . . . ,75 i\Iarch 1 B. Lee's account of tobacco Dr. to cash. Paid freight of 15 hhds. from Norfolk . Bills receivableDr.toH.Lee'sac't tobacco Received William Paterson's bill a 3 months, Cash Dr. to flour, For 100 barrels a $10,25 10 Henry Lee's ac't. tobacco Dr. to cash, Paid truckage 15 hhds. a ,75 per hhd. 11 Cash Dr. to Henry Lee's ac't. tobacco, For 8 hhds. as per Waste, wt. 7085 Ib. net. . 1 House in Hanover-street, Dr. to cash, 10 Rum Dr. to cash, For 120 gallons, a $1,25 20 Robert Means Dr. to sugar, 150 cwt. a $12,25 per cwt. 04 Bills receivable Dr. to Robert Means, Received his note, a 9 months, with interest, Cash Dr. to Henry Lee's tobacco, For 3 hbds. wt. 2812 lb.net, a $6,90 per 100 Ib. JOURNAL. 281 Boston, March 2?, 1817. Dr. | Cr. L. F.'L.F. Henry Lee's ac't. tobacco Dr. to cash, 'aid for weighing and other charges, 30 flenry Lee's ac't. tobacco Dr. to cash, Paid storage, ..... H.L's ac't. (obae. Dr. to simd's. $872,67,3 8 To his accH. current for net proceeds, $846,79,1 9 Commission acH. for ;ny commission, 25,88,2 HL Lee his aecount current Dr. to cash, Remitted him by mail in bank bills, April 4 rl. Means Dr. to sundries. 375 Sugar, 1G cwt. a $12,50 Rum, 120 gallons, a $1,25 Delivered in barter. 150 g Sundries Dr. to Robert Means, g>350 Ashes,pot, 45 2 4 Ib. a $4,94 J T . . 225 Tow cloth, 500 yds. a ,25 . , 125 Received in barter. 6 Cash Dr. to sundries, 412,05 2 To bills receivable, on D. Jones . 410 Profit and Loss, for interest 30 days, 2,05 17 Expense account Dr. to cash, Paid men's wages, &c. this quarter, 10 Voyage to Bnur'x. Dr. to sund's. $9380,2( 7 To C. Lee, for 2200 bush, corn a 1 2200 ditto, 2200 do. wheat a $ 1 ,25 2750 To E. Nichols & Son, for 230 bags coffee wt. 18400 Ib. a ,25 per Ib. Cash, for shipping charges, 4950 4600 330,2< By brig Huntress, consigned to C. Leroi, fo sale and returns. Voyage to Bourdeaux Dr. to cash, Premium on the Huntress 1 cargo $9880,20 a 3 per cent. . . . $370,50. Policy, ,75 JOURNAL. Boston, April 1%, 1817. F. 2 8 1 g 1 7 1 1 1 2 1 6 Charles Lee Dr. to bills payable, Granted him my note 10 inst. a 60 days, . $ 4950 2100 2100 700 275 1562 875 1292 286 280 12191 C. 50 40 62 50 Sundries Dr. to R. Lakeman, $12100 Fish merch'ta. a g3,50 per quin. 3400 $1 1900 Oil, a $10 per bbl. 20 barrels, . 200 Richard Lakeman Dr. to sundries, 12100 To cash, . . . . . 6050 Bills payable, my note a 90 days, . 6050 JO Andrew Newman Dr. to cash, "0 Dash Dr. to Joseph Brighara, leceived from him in full. David Whitman Dr. to cash, Paid him in full for 1250 Ib. tea, a $1,25 $6 Winslow Lamb Dr. to cash, Paid him, balance. .... 00 Sundries Dr. to cash, g!292,40 < Shoes, a ,90 340 pairs, . $306 < ditto, a $1,20 522 ditto, . 626,40 Boots, a $3 120 ditto, . 260 Cash Dr. to bills receivable, Received payment of William Paterson's bill, Staves Dr. to cash, For 8000 white oak, a 35 per M. Voyage to Oporto Dr..to sund's. 1 219 1 ,50 To fish, 3400 quintals, a 3,50 . 11900 Staves, 8000 a $35 per M. . 280 Cash paid shipping charges, . 11,50 Shipped the above goods on board the Genera Hamilton, Capt. Amasa Delano, and con signed to Francisco Alvardo & Sons, mer chants at Oporto, for sale and returns. A JOURNAL. S83 Boston, May 15, 18J7- Dr. L,. F. 10 5 6 8 10 2 10 'r. .F. 1 1 8 2 6 1 6 r r oyage to Oporto Dr. to cash, r or premium on the General Hamilton's cargo, 13 $ 525 582 297 297 533 250 900 4950 26 1173 536 586 5 5,: s," 10,' 50 50 xin Dr. to easli, p or 376 gals, a $1,55 per gal. O Ashes, pearl, Dr. to Robert Means, For 20 casks, wt. 49 2 16 lb. a $6 per cwt. n, 1 iobert Means Dr. to bills payable, r or my note granted him for 30 days, 31 Voyage toLondonDr.to sund's. $538,10,7 (To Ashes pot, 45 2 4 lb. $4,94-0- S per cwt. . . $225 f Ashes pearl, 49 1 16 lb. a $6 297,85,7 Cash paid shipping charges, . 15,25 Shipped on board the Galen, S. Turner master, for London, and to him consigned, for sale and returns, for iny account and risk. Cash Dr. to oil, For 20 barrels a $12,50 per bar. 3ash Dr. to Charles Lee, deceived from him in full, n Bills payable, Dr. to cash, ? *d rny note to C. Lee, dated April 10, at 60 day -to Dash Dr. to rum, For 2 puncheons a R132 per puncheon, . . o Voyage to Copenhagen in Co. with 8. Dean and self, each half, Dr. to sund's. $11735 To Amasa Goodhue, for 3000 yds. broadcloth a $3,50 per yd. . . . $10500 To Thomas Mackay, for 240 cwt. to- bacco, a $5 per cwt. . . 1200 Cash paid shipping charges, . . 35 Consigned to Jacob Vantorff, merchant there. Samuel Dean's account current Dr. to his ac count in Co. for half the above goods. . . Cash Dr. to S. Dean his ac't, current, For his half of voyage in Co. to Copenhagen, . JOURNAL. Boston, June 23, 1817- Dr. L. F 1 11 9 10 i i 2 2 9 5 9 1 1 1 Cr. L. F. A 6 6 1 4 1 7 8 1 1 1 9 1 6 6 3 Cash Dr. to coffee, For 3266 Ib. a ,28 per Ib. 5 $. 914 1302 132 119 495 25 C050 297 1200 550 10500 125 1012 1 C. 48 60 24 85,7 50 96 Voy. to N.Orleans Dr. to sund's. $1 302,60 < To Shoes men's, 340 pairs, a ,90 $30G { do. women's 522 pairs, a $1,20 626,40 Boots, 120 pairs, a $350 . 360 Cash, paid shipping charges, . 10,2C Consigned to Kingman Turrel, merchant there. 30 James Wilson Dr. to rum, For 1 puncheon, a $132 JUIV 1 r- Expense ae't. Dr. to cash, Paid this quarter, for men's wages, &c. . . Cash Dr. to Samuel Tyler, Received from him in part, lent on bond, 3 Cash Dr. to Robert Means, Received from hmi, balance in barter, 6 Bills payable Dr. to cash, Paid to Richard Lakeman my bill, 10 Bills payable Dr. to cash, Paid Robert Means my bill at 30 days, 10 Thomas Mackay Dr. to cash, Paid him in full, . . , 15 Coffee Dr, to Rufus Perkins, For 2500 Ib. a ,22 per Ib. . ' . 20 Amasa Goodhue Dr. to cash, 5 dash Dr. fo tow cloth, For 500 yds. a ,25 ... Cash Dr. to tea, For 675 Ib. hyson, a gt,50 30 Cash Dr. to Profit and Loss, "or interest on W. Patersou's note, ... 8j JOURNAL. 2S5 Boston, August 1, 1817. Cr. L.F. 2 2 2 3 3 2 2 11 F) 2 12 2 11 6 7 Rufus Perkins Dr. to bills payable, Paid my note a 30 days, 8- 550 4600 120 3000 2300 226 120 1405 1410 550 1405 134 1885 833 14 . Nichols & Son Dr. to cash. For 18400 Ib. coffee, H. Lee's ae'f. cur't. Dr. to bills payable, Accepted his draft on me, at 10 days after sight, 1 Cash Dr. to house in Hanover-street, Cash Dr. to household furniture, . . Of) Henry Lee's ae't. current Dr. to cash, Paid him balance in full of his account, . . 05 Bills payable Dr. to cash, Paid my acceptance to H. Lee, K. Torre!, my ac't. cur't. Dr. to voyage to Xew-Orleans, For net proceeds of goods consigned to him, . 31 Cash Dr. to flour, For 120 barrels, a $11,75 Bills payable Dr. to cash, For my bill to R. Perkin?, a 30 days, . . 3 Voyage from New-Orleans Dr. to K. TurrePs account current, For 9 bales cotton, wt. 6390 Ib. a ,22 per Ib. Voyage from New-Orleans Dr. to cash, Paid freight and other charges, Cash Dr. to voyage from New-Orleans, For 6390 Ib. cotton, a ,29$ per Ib. . . CVJ Sundries Dr. to tea, g833,75, Cash in part, . . . 578,75 Winslow Lamb rest at 60 days^ . . 255 <>A .Cash Dr. to S.Tyler, in part, lent on bond, 386 JOURNAL. Boston, October 1, 1817. Dr. ,. F. 10 7 11 9 11 1 1 1 2 7 10 11 11 Cr. L. F. 2 5 9 2 9 2 10 7 4 4 10 2 10 10 Expense account Dr. to cash, Paid men's wages, &c. 5 $. 127 676 -618 569 18297 350 380 3187 807 115 14786 14820! C. 44 80 55 25 50 16 30 48 30 Andrew Newman Dr. to gin, For 376 gals, a $1,80, payable in 90 days, . 9 Vender Effingin his account current Dr. to sundries, $618,55. To J. W. 14225 Ib. tobac. a$4 per 100 Ib. $569 Cash, paid for shipping, . . . 21,10 Commission, for my commission, . . 28,45 Shipped on board the Mary-Ann, Capt. Hoffman, for Amsterdam, per order, and for account and risk of said Effingin. 10 James Wilson Dr. to bills payable, For my note dated 9 inst. at 30 days, Francisco Alvardo & Co. his ac't. cur't. Dr. to voyage to Oporto, For net proceeds of goods consigned, . . o Cash Dr. to Samuel Tyler, Received in part, on bond, 5 Cash Dr. to linen, For 400 yds. a ,95 30 Sundries Dr. to broadcloth, $3 187,50 Cash, in part, . . . $2618,50 Bills payable, my note a 90 days, . 569 Piano Forte Dr. to voyage to London, For 6, valued at 18J,12,2| sterling, . . 5 Voyage to London Dr. to cash, Paid duties at the custom house and freight, . a Jacob Vantorff our ac't. current Dr. to voyage in Co. to Copenhagen, For net proceeds, as per account of sales, amount- ing to 14786 rix dols. and 50 skillings, 8 Charles Leroi my account current Dr. to voyage to Bourdeaux, For net proceeds per brig Huntress, amounting to 11856JL gals, brandy, a 6 liv. 5 sols, . . 10] JOURNAL. 887 Boston, November 12, 18i7- Dr. I.. F. 11 11 12 11 1 1 1 1 Q L. 12 12 8 < < (Jr. L. F. 11 2 11 2 7 11 8 2 8 12 2 12 12 Voyage from Bourdeaux Dr. to C. Leroi my account current, ^or net proceeds of voyage to Bourdeaux, . -19 8- 4820 784 8297 1010 870 32203 5054 255 1208 2040 1020 204C 2295 102C C. 25 40 16 39 20 Voyage from Bourdeaux Dr. to cash, 3 M duties at custom house and freight on brandy, 18 Voyage f. Oporto Dr. to F. Alvardo & Co. For* net proceeds by the General Hamilton, 18297^ gals, port wine, a 800 reas per gal. 19 Voyage from Oporto Dr. to cash, Paid duties, freight, &c. o Cash Dr. to Samuel Tyler, deceived in part on his bond, Cash Dr. to voyage from Oporto, For 182973- gals, port wine, a $1,76 . . 0*7 Cash Dr. to ship Massachusetts, For freight from Europe, &c. 3 Cash Dr. to Winslow Lamb, Ship Massachusetts Dr. to cash, Paid the Capt. for reimbursements, - 30 Ashes in Co. with D. W. Dr. to R. Means For 340 cwt. ashes, pot, a $6, on demand, . David Whitman's account current Dr. To his account in Cc. for his half of the above mentioned pot ashes, Dec 1 Robert Means Dr. to cash, Paid him in full for 340 cwt. p ot ashes, bo 1 t of him in Co. with D. Whitman and self, each half, Cash Dr. to ashes, in Co. v/lth David Whitman and self, For 340 cwt. & ^6,75 per cwt. ... Cash Dr. to D. Whitman, his ac't. cur'( Received hjs half share of our 340 cwt. pot ashes 388 JOURNAL. Boston, December 3, 18 1 7. Cr. L.F. 2 2 2 11 2 4 5 9 7 11 i r 11 Ashes in Co. with David Whitman and self, each half, Dr. to cash, For charges on the same, .... $. 86 1020 6867 742 742 515 947 132 676 26140 525 210 14786 C. 70 50 26 26 14 80 48 43 David Whitman's ae't. in Co. Dr. to cash. F'd him in part for his share of net proc's on ashes, 5 Sam. Dean's account in Co. Dr. to cash, Paid him in part for his share of net proceed?, Sills rec'able Dr. to V.Effingin's ae't. cur. i^or bill remitted, in full for net proceed?, on R. P. Sash Dr. to bills receivable, To Vender Effingin's bill on Rufus Perkins, . ,,. _,. Dash Dr. to port wine, For 10 hhds. a $51,50 per hhd. in Cash Dr. to coffee, For 3266 Ib a 29 per Ib 13 Cash Dr. to James Wilson, For 1 puncheon rum, 14 Sundries Dr. to A. Newman, $676,80, Cash, received in composition, . . $257, 18,^ Profit and Loss for balance, loss, . 419,61,6 1C Sundries Dr. to voyage fr. Bourdeaux,$26 140,48 Cash, in part, for sales of brandy at auction, . D. 13070, '24 ! James Henderson, for his note a 3 mo. endorsed by W. Ponsby, , . 6535,12 Thomas Henshaw's note, a 3 months, endorsed by Thos. Benson, . 6535,1- Cash Dr. to Piano Fortes, For 3 a $175, '17 Household furniture Dr. to Piano Fortes For 1 taken for family use, IS Cash Dr. to J. Vantorff our ae't. current, For net proceeds of goods consigned for the joint concern of Samuel Dean and self, . JOURNAL. Boston, December 20, 1817. Dr. L. F 8 Cr. L. F 12 2 2 2 10 2 2 12 Robert Means Dr. to bills receivable, For his bill given up for renewal this day, . Bills receivable Dr. to Robert Means, For his bill renewed for 4 months, Cash Dr. to sundries, $357,34,4 To Samuel Tyler, for balance principal due on his bond, . . . $271 Profit and Loss, for interest, . 86,34, 25 Vancouver & Sons Dr. to ship Massa. For said ship, a 4 months, 26 , Bills receivable Dr. to Vancouver &Sons For ship Massachusetts, a 4 months, 27 Cash Dr. to Piano Fortes, For 2 a $210, 28 Cash Dr. to sundries, 501,12,5 Bills receivable, Abram Eastman's, Profit and Loss, for iaterest 11 mo. $475 26,12,5 30 2 Expense account Dr. to cash, For men's wages, &c. this quarter, Cash Dr. to household furniture, for 1 Piano Forte, ash Dr. to Profit and Loss, For interest on Robert Means* bill for 9 month and 6 days, 31 . Profit and Loss Dr. to sundries, $499,33 To expense account for men's wages, &c. $120,25 ditto, 119,24 ditto, 127,44 ditto, 132,40 25* 890 JOURNAL. [13 Boston, December 31, 1817- Dr. JU. F. Cr. L.F. $ C. 3 SundriesDr.to Profit &Loss, $42916,15,8 3 To House in Hanover-street, . g 455,63 3 Land in the Coun. of Washing'n. 262,50 3 Ship Massachusetts, . 3557,24 3 Household furniture, . . 810 4 Broadcloth, . . . 562,50 4 Linen, .... 520 4 Port wine, .... 139 4 Sugar, .... 589,50 - 4 Rum, . . . . Ill 5 Gin, 94 5 Coflee, .... 303,62 5 Flour, . . . . 510 6 Tea, .... 283,75 6 Oil, 50 7 Piano Fortes, . . . 347,84 9 Commission account, . . 54,33,2 10 Voyage to Bourdeaux, . 4568,84,3 10 Oporto, . . 5580 10 London, . . 153,55,3 11 New-Orleans, . 103,20 11 Voyage from New-Orleans, . 344,75 11 Vender Effingin, of Amsterdam, 123,7 1 11 Voyage from Bourdeaux, . 10535,68 12 Oporto, 12895,51 42916 15,8 3 1 Profit and Loss Dr. to stock, For net gain sinee January 1, 43796 92,1 12 Balance ac't. Dr. to'sund's. $63444,31 ,1 2 To cash, .... $41561,57,1 2 Bills receivable, . 21882,74 63444 31 1 v*->*i*i*i JJ,4 12 Sundries Dr. to balance ac't. 63444,31,1 | Samuel Dean's ac't. in Co. $1525.74 12 D. Whitman's ac't. in Co. 84,15 1609,89 1 Stock, net of my estate, 6 1 834,42, 1 , . 63444 31,1 1 Stock Dr. to balance account, 12 61834 42,1 BUD OE THE JOURNAL. 1 INDEX. 291 INDEX TO THE LEGER A. ASHES, . . . Page . . . . 6 Al> p Munson, Jame^, age 5 8 9 3 Ashes in Co. . Alvardo F. & Co. my . 12 ac't. cur't. 11 Massachusetts, ship, B. Bills receivable, . Bills payable .... 2 . . . 2 N. Newman, Andrew, .... Nichols & Son, 7 9 Broadcloth . 4 Boots, .... . . . . 6 o. Oil, . . . 6 Brigham, Joseph, Balance Account, ... 7 . . . 12 P. Profit and LO Q S, . . . . . 3 4 7 9 e. Cash, Coffee, Commission, . 12 5 9 Port wine, Piano Forte, Perkins, Rufus, . . . R. Rum, .... 4 D. Dean, Sam. our ac't Dean, Sam. ac't. in . current, . 9 Co. . .9 S. Stock, 1 4 5 6 7 E. Expense account, . . . .10 Effingin's,Vender his ac't. cur't. 11 Samson Lemuel, .... Shoe" F. Flour, Fish, 5 6 ... 5 T. Tea, .... 6 6 7 12 Tow cloth, Tyler, Samuel, Turrel,Kingman,my ac't. cur't. G. ... 9 V. Voyage to Bourdeaux, . . to Oporto, . . to London, . . . to Copenhagen, . . to New-Orleans, . . from New-Orleans, . from Bourdeaux, . . from Oporto, . . . Vantorff, Jacob, our ac't. cur't. Vancouver & Sons, . . . 10 10 10 10 11 11 11 12 11 12 H. House, .... 3 Household furniture, ... 3 L. . . . 3 . . . . 4 Lamson, Thomas, . . . . 4 . . . 5 Lewis, James, . . . . . 5 Lamb, Winslow, . Lee, Henry, his ac't Lee, Henry, his ac't Lakeman, Richard, Leroij Chs. my ac't, . . . 8 . tobacco, . 8 . current, . 8 . . . .' 8 current, . 11 w. Whitman, David, .... Whitman, D. ac't. current, . Whitman, D. ac't. in Co. . Wilson, James, 8 12 12 9 293 LEGER. [1 Dr. Stock Account, 1817. Jan. Dec. 1 31 J.F. 1 13 To sundries, as per Journal. . . . Balance, for net stock, Cr. L.F. 12 $. 4490 61834 C. 42,1 66324 42,1 Dr. Cash 1817. Jan. Feb. Mar. April May June July Aug. Sept. Oct. Nov. 1 7 27 29 31 5 10 26 7 14 24 6 20 4 5 10 18 21 22 2 3 25 25 30 18 19 31 12 27 30 20 25 30 20 25 27 28 1 1 2 2 2 2 2 3 3 3 3 4 5 5 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 9 9 9 10 10 10 10 To Stock on hand, Rum, .... Lands in part, Thomas Lamson, Amos Locke, Bills Receivable, on J. Thomson, Linen, ... Bills receivable, A. Young's disco'd. Flour, Henry Lee's ac't. tobacco, . . Henry Lee's ac't. tobacco, . . Sundries for note on D. Jones & int. Joseph Brigham, Bills receivable, W. Paterson's note, Oil, 4 3 4 5 2 4 2 5 8 8 7 2 6 7 4 9 5 7 8 6 6 3 3 3 5 11 6 7 7 4 4 7 11 3 8 4000 1215 350 400 275 350 440 708 1025 460 194 412 275 286 250 900 264 5867 914 495 25 125 1012 1 3000 2300 1410 1885 578 14 350 380 2618 870 32203 5054 255 71166 84 52,5 02,8 05 62 50 48 50 96 05 75 50 16 39 35,3 Charles Lee, Samuel Dean, his ac't. current, Coffee, .... Samuel Tyler, in part, Robert Means, Tow cloth, .... Tea, hyson, .... Profit and Loss, House in Hanover-street, Household furniture, Flour, Voyage from New-Orleans, Tea, in part, Samuel Tyler, in part, Samuel Tyler, in part, Broadcloth, in part, Samuel Tyler, in part, Voyage from Oporto, Ship Massachusetts, W. Lamb, in full, Account transferred to folio 2d. . . 1J LEGER. 1Q3 Contra, Cr. Dr. $. ) C. 1817. J.F. I..F Jan. Dec. 1 31 1 13 By sundries, as per Journal, . . Profit and Loss for net gain, . . 3 22527 43796 50 92,1 663-24 42,1 Account, Cr. 1817. 12 1 By James Lewifa, 5 140 Jan. 15 1 Port wirie, .... 4 336 19 1 4 901 24 j Joseph Franklin, 5 1500 24 2 James Muason, . . c 2050 28 2 Lemuel Samson, c 80C Feb. 2 2 Samuel Tyler, 7 2000 15 20 2 2 Flour, .... Ship Massachusetts, 1925 53 20 22 2 Broadcloth, in part, 4 875 28 c \J Ship Massachusetts, 3 210 75 Mar, 1 J Henry Lee's ac't. tobacco, freight, 8 41 25 10 2 Henry Lee's ac't, tobacco, truckage, 8 11 25 18 c, House in Hanover-street, 3 44 37 19 Rum, .... 4 150 27 4 Henry Lee's ac't. tobacco, 8 5 50 30 4 Henry Lee's ac't. 8 10 50 3] 4 Henry Lee's ac't. current, 8 500 April 6 4 Expense account, 10 120 ^5 10 4 Voyage to Eourdeaux Ensurance, 10 371 5,7 10 4 ditto, . . Shipping charges, 10 330 15 5 Richard Lakeman, 8 6050 18 5 Andrew Newman, 7 700 24 5 David Whitman, 8 1562 26 5 Winslow Lamb, 8 875 28 5 Sundries, as per Journal, 1292 May 5 5 Staves, . . 7 280 8 5 Voyage to Oporto, 10 11 15 6 ditto, for Ensurance, 10 525 5 18 6 Gin, 5 582 June 31 10 20 6 6 6 Voyage to London, Bills payable, to Charles Lee, Voyage to Copenhagen, 10 2 10 15L25 4950 35 25 7 Voyage to New-Orleans, 11 10 20 July 1 7 Expense account. 10 119 24 6 7 Bills payable, to Richard Lakeman, 2 6050 10 7 Bills payable, to Robert Means, 2 297 85,7 12 7 Thomas Mackay, 9 1200 20 7 Amasa Goodhue, 9 10500 I \ccount transferred to folio 2d, |47433f02,4 291, LEGER. [ Dr. Cash Dr. 1817. J.F. [J.F. $. C. To account brought from folio 1. 71166 35,3 Dec. o 10 Ashes in Co. with D. Whitman, . 12 2295 2 10 D. Whitman's acH. current, 12 1020 8 11 Bills receivable, R. Perkins, . . 2 742 26 9 11 Port wine, .... 4 515 12 11 Coffee, 5 947 14 13 11 James Wilson, . '. 9 . 132 14 11 A. Ne-wman, 7 257 18,4 15 11 Voyage from Bourdeaux, 11 13070 24 1C 11 Piano Fortes, 7 525 18 11 J. Vantorff, our ac't. cur't. 11 14786 48 20 12 Sundries, as per J. 357 34,4 27 12 Piano Fortes, 7 420 28 12 Sundries, as per J. 501 12,5 30 12 Household Furniture, 3 220 30 12 Profit & Loss, for interest, 3 84 50 107039 62,6 1 Jr. Bills Receivable, 1817. Jan. 1 1 To Stock, 760 27 2 Lands, on Abram Eastman all mo. 3 475 Feb. 25 3 Linen, on Alexander " oung, a 3 mo 4 720 Mar. 4 3 H.Lee's ac't. tobacco, for W.P's bill 8 286 62 24 3 Sugar, on Robert Means, a 9 months 8 1837 50 Dec. 6 11 V. Effingin's ac't. cur. on R. Perkins 11 742 26 15 11 Voyage f. Bourdeaux, J. Henderson 1 * 11 653b 12 15 11 ditto, T.Henshaw's note, a 3 mo 11 6535 12 20 12 R. Means, renewed bill, a 4 mo. 8 1837 50 26 12 Vancouver & Sons 1 bill, a 4 mo. . 12 6975 26704(12 Dr. Bills Payable, 1817, June 10 6 To cash paid Charles Lee, 1 4950 July 6 7 ditto Richard Lakeraan, . . 1 6050 10 7 ditto Robert Means, 1 297 85,7 Aug. 25 8 ditto my acceptance to H. Lee , 2 120 Sept. 1 8 ditto to Rufus Perkins, . . 2 550 Oct. 3C 9 Cash, James Wilson, 9 569 12536 85,7 2] LECER. 95 Account, Cr. Dr. 1817. J.F. L.F. $. C. Aug. 8 8 By account brought from folio 1. . E. Nichols & Son, . . . 9 47433 4600 02,4 20 8 Henry Lee, . . ... 8 226 79,1 25 8 Bills payable, H. Lee, 2 120 Sept. 1 8 Bills payable, R. Perkins, . . 2 550 4 8 Voyage from New-Orleans, 11 134 50 Oct. 1 9 Expense account, 10 127 44 9 9 V. Effingin, voyage to Amsterdam, 11 21 10 Nov. 5 9 Voyage to London, 10 115 50 13 10 Voyage to Bourdeaux, 11 784 50 19 10 Voyage from Oporto, 12 1010 40 28 10 Ship Massachusetts, 3 1208 20 Dec. 1 10 Rob. Means, .... 8 2040 3 11 Ashes in Co. with D. Whitman, 12 86 70 4 11 D. Whitman, his ac't. in Co. 12 1020 5 11 S. Dean's ac't. in Co. . . 9 5867 50 30 12 Expense account, . 10 132 40 31 12 Balance due to me, 41561 57,1 107039162,6 Cr. 1817. Feb. 5 2 By cash, Jacob Thomson's note, . . 1 350 26 3 Sundries, as per Journal, 720 April 6 4 David Jones, 1 410 May 4 5 William Paterson, 1 286 62 Dec. 8 11 Rufus Perkins, 2 742 26 20 12 R. Means, bill given up for renewal, 8 1837 50 28 12 Abram Eastman, 2 475 31 12 Balance due to me, 21882 74 26704 12 Cr. 1817. April 12 5 By Charles Lee, my note a 60 days, 7 4950 15 5 Richard Lakeman, 8 6050 May 24 6 Robert Means, .... 8 297 35,7 Aug. 1 8 Rufus Perkins, .... 9 550 15 8 Henry Lee's account Current, . , 8 120 Oct. 10 9 James Wilson, .... 9 569 12536 85,7 2CJ6 LEGER. [3 Dr. Profit and Loss, 1817 Feb. Dec. 26 14 31 31 1 J.F 11 12 13 To bills receivable, for discount on A Young's bill, .... Andrew Newman, for loss by him, Expense account, ae per J. . Stock, for m t gain, .... Cr. L.F 5 "t 1C 1 11 4U 49 43796 16 61,6 33 92,1 02,7 44727 Dr. House in Hanover-street, itn?. Jan. Mar. Dec. 1 18 31 1 3 13 To Stock, Cash for repairs, Profit and Loss, 1 2500 44 455 37 63 3000 00 Dr. Land in the County of 1817. Aug. Dec. 1 31 1 13 To Stock, . . 750 acres, Profit and Loss, 562 262 50 50 825 00 Dr. Ship Massachusetts, 1817. Jan. Feb. Nov. Dec. 1 1 20 28 28 31 1 2 3 10 13 To Stock, Cash, for repairs, ditto, for Ensurance, Reimbursements to Europe, cash, Profit and Loss, 1 1 2 7000 53 210 1208 3557 20 75 20 24 1209ft 39 Dr. Household Furniture, 1817. Jan. Dec. Dec. 1 17 31 1 11 13 Fo Stock, . . Piano Forte, Profit and Loss^ 7 1500 210 810 2520 LEGER. 207 Cr. Ur. 1817. 3.T. L.F. $. C. April 6 4 By cash, for interest on D. Jones 1 note, 1 2 05 July 30 7 ditto, ditto, 1 1 96 Dec. 4 Ashes, in Co. with D. Whitman and self, my half of gain, 12 84 15 in Voyage to Copenhagen in Co. with S. Dean and self, my half gain, 10 1525 74 20 12 Cash, for interest, 2 86 34,4 12 Cash for interest, 2 26 12,5 30 12 Cash for interest, 2 84 50 31 13 Sundries, per Journal, 42916 15,8 |44727|02,7 Cr. 1817. Aug. 10 8 By cash, 1 3000 3000 Washington, Cr. 1817. Jan. 27 2 By sundries, 825 825 Cr. 1817. Nov. Dec. -27 -25 10 K> , 12 5054 69^5 12029 39 39 Vancouver and Sons, i Cr. 1817. Aug. Dec. IP 30 8 12 Cy cash, . . . Cash, Pia v o Forte, 1 2 2300 220 2.320 __ LEGER. Dr. Broadcloth, 1817. Jan. Feb. Dec. 1 22 31 J.F. 1 2 13 To Stock, a g3,50 per yard, . . Sundries, a 3,50 per yd. . . Profit and Loss, . . . Yds. 250 500 Cr. L.T. $ 875 1750 562 3137 C. 50 50 750 Dr. Linen, 1817. -Jan. Bee. 1 18 31 1 1 13 To Stock, a ,80 per yd. Andrew Newman, a ,70 per yd. Profit and Loss, Yds. 400 1000 7 320 700 520 1540 14CO Dr. Port wine, To Stock, a 45 per hhd, Cash, a 42 per hhd. Profit and Loss, Hhds 7 8 15 315 336 139 790 Dr. Sugar, J817. Cwt. Jan. 1 1 To Stock, a $10,50 per cwt. . . 240, 2520 19 1 Cash, a $10,72,6-4 T per cwt. . 84 1 901 Dec. 31 13 Profit and Loss, 54y yO 324 3970 50 Dr. Kum, 1817. Gals. Pun. Jan. 1 1 To Stock, a $125 per pun. . 12 1500 Mar. 19 3 Cash, a $1,25 per gallon, 120 1 160 Dec. 31 13 Profit and Loss, 111 1761 1 Dr. Thomas Lamson, 1817.1 Jai. I li llTe Stock, 400 4] I.EGER. 299 Cr. 1817. Oct. 30 J.F. 9 By sundries, a $4,25 per yd. . . Yds. 750 Ur. --I $. 3187 3187 C. 50 r Cr. 1817. Feb. Oct. 10 -25 -25 2 3 9 By cash, a 1,10 per yd. Bills receivable, A.Youns:, a $1,20 Cash, a ,95 . . " . Yds. 400 600 400 1 2 1 440 720 380 1540 _ 1400 Cr. 1817. Feb. Dec. 10 9 2 11 By Joseph Brigham, a g>55 per hhd. Cash, a $51,50 per hhd. . . Hhd?. 5 10 7 2 275 515 15 790 Cr. 1817, Jan. Mar. April o 20 -20 4 3 4 By Charles Lee, a 12,50 per cwt. Coffee, a $12 per cwt. . Robert Means, a $12, 25 per cwt. Robert Means, a $12,50 . . Cwt. 72 84 150 18 7 5 8 8 900 1008 1837 225 50 324 3970 50 Cr. 1817. Jan. April June 7 4 18 30 1 6 7 4 By Cash, a g!35 per puncheon, . " R. Means, a $1,25 per gal. 120 gal. Cash, a $132 per pun. . James "Wilson, a gl32 . . . 120 gals. i'un. 9 2 1 12 1 1 9 8 1215 150 264 132 1761 of Boston, Cr. 1817.1 Jan. J29 1 2|By Cash, 1 400| 300 Dr. LEGER. Amos Locke, 1317. Jan. J.F. 1 To Stock, Cr. r..F. $ 275 Dr. James Lewis, 1817.1 | t Jan. Il2 l|To Cash, 11 140| Dr. Lemuel Samson, ,1317.1 Jan. |28 2 To Cash, t i i| cool Dr. James Munsori, 1817.1 I Jan. |24i 2|To Cash, I I lU050| Dr. Joseph Franklin, 1317. Jan. 24 1 2|To Cash, l|l500[ Dr. Gin, 1817. Gals. May 18 6 To Cash, a jgl,55 per gal.. . . 376 li 58280 Pec. 31 13 Profit and Loss 94 676 :;0 Dr. Coffee? 1817. Ib. Jan '0 - To c u"rir a, 25 per Ib 4032 4 1000 July 15 7 Ruius Perkins, a ,22 per Ib. . . 550 Dec. 31 13 Profit and Loss, . . . 303 62 1861 62 Dr. Flour, 1817.1 1 Feb. |15| 2iTo Cash, a $8,75 per bur. Dec. 31 13 Profit and Loss, 111925 510 2435 53. LEGER. of Salem, 301 Cr. Dr. 1817. J.T. L.F. $- c. Jan. 33 C) By Cash, 1 275 of Boston, Cr. 1817. Jan. 1| IJBy Stock, 140) of Boston, Cr. 1817.1 j Jan. j 1 l|By Stock, of Boston, leoo! Cr. 1817.1 ! Jan. ! l| l|By Stock, of Boston, 12050! Cr. 1817.) | Jan. | Ij l|By Stock, 1 1500| Cr. 1817. Oct. 5 9 By Andrew Newman, a 1,80 -Gals. 376 7 676 80 676 80 Cr. 1817. Ib. June 90 7 3^66 i Q14 At* Dec. 19 11 ditto, a ,29 per Ib 3266 9 Q47 6532 1861 62 36* Cr. 1817. iBar. Mar. ? 3 By cash, a $10,25 per "bar. . . . 100 1 Aug. 31 8 ditto, a $11, 75 120 1 1410 220 2435 302 Dr. -LEGEil. Tea, ! or. 3317. k* Ib. L.F 'v C. Feb. Dec. 18! 2 3l| 13 To David Whitman, a $1.25 per Ib. Profit and Loss, .... 1250 8 1562 283 50 75 i 1846 25 Dr. Ashes, 1817. Aprfl May 4 20 4 6 To R.Means,a$4,04_fi r per cwt. R. Means, a g6 per cwt. cwt.qr.lb. 45 2 4 49 21G 8 225 297 35,7 95 020 522 i).->,7 Dr. Fish, 1617.1 i April 1 15! 5|To Richard Lakeman, a $3,50 . J3400| 8 r 11900j Dr. Tow cloth, 1817.1 I April 1 4' 4lTo Robert Mean?, a ,2-5 per yd. Yds.] I , I 500' 81 125 Dr. Oil, 1317. Bar. 1 Apri] 15 5 To Richard Lakeman, a $10 . . 20 8 2001 Dec. 31 13 Profit and Loss, 501 250| Dr. Shoes, 1817. April 28 28 5 Frs. 340 522 862 1 1 306 626 932 40 4Q ditto, a $1,20 i Dr. Boots, 1817.1 'o cash, o g3 per pur, IPrs. I I 120' I 1 360* LEGKH 303 Cr. Dr. S- i c. 1017. 7.1'. Ib. L..F July 25 7 By cash i a $1,50 675 1 1012 50 Sept. ~21 C sundries, a $1,45 -575 833 75 1250 1846 25 Cr. 1817.1 May J31 31 jcwt.qr.lb. By voya. to London, a &4,94 T R T per cwt. pot, . . . I 45 2 4 ditto, a 6 pearl, . . 49 2 16 225 297 35,7 85,7 Cr. 1817.1 jQiit.l ]V T ay I 8' 5'By voyasre to Oporto, a 3,50. . [34001 Cr. 1817.1 July 125 7>By cash, a ,25, ifds.j 500! 1' 125 1 Cr. 1817. June By cash, a g 12,50 per barrel* Bar. 20 250 >5o| Cr. 1817. June By voyage to New-Orleans, a ,90 . ditto, Prs. 340 522 862 306 f 626 140 935LUO Cr. 1817.1 June '25' 7 ! Bjr yoyage to ^ew-Orleaas, a ,Prs. j I i .. I 120' I!' seoi 304 LEGER. 7 Dr. Staves, 1817 May 5 J.F M. > To cash, ft 35 per M. 8 Cr. L.F 1 sP* 280 C. Dr. Piano Fortes, 1817. Nov. Dec. 1 31 9 13 P. Fort. To voyage to London, valued, . 6 Profit and Loss, .... 10 807 347 1155 16 84 00 Dr. Andrew Newman, 1817. April Oct. 13 5 8 To cash, . . x . Gin, . . . . . 1 5 700 676 1376 80 80 Dr. Charles Lee, 1817. Jan. April 2 12 l 5 4 2 900 4950 Bills payable, my note a CO days, 5850 Dr. Samuel Tyler, 1817. Feb. 2 2 To cash, lent on his bond, , 1 2000 2000 Dr. Joseph Brigham, 1817, Feb. U 2 4 275 7] LEGER. 305 Cr. IS 17. May 8 I.F. 5 By voyage to Oporto, a $35 M. 8 Dr. r..p. 10 s.,c. 280| Cr. 1817. Dec. 16 17 27 11 11 12 By Cash, a 6175. Homeho'ci furniture, a &210 Cash, a 5210 P. Fort. 3 1 cy o 3 2 525 210 420 6 1155 of Portland, Cr. 1817. Jan. Dec. 18 14 1 " 4 700 676 80 80 1376 of Worcester, Cr. 1017. A pril June 10 10 4 6 By voyage to Bourdeanx, Cash. 10 1 4950 900 5350 of liustou, Cr. 1817. .'ulv Sept. Oct. Nov. Dec. -50 JO -20 20 7 8 9 10 12 By ca&h, in part on his bond, .... ditto, , ditto, ditto, . ditto, ditto, . ditto, ditto, in full of principal, .... 1 1 1 1 o 495 14 350 870 271 2000 of Charleston, Cr. 1817. April 201 aBvca-h, V 275 306 LEGER. 3 Dr. Robert Means, Cr. $ C. 1817. J.F. L.P. Mar. oo 3 4 1837 50 April A /I 375 May 24 6 Bills payable, a 30 days, 2 297 85,7 Dec. 1 10 Cash, p'd him in Co. with D. W. & self, 2 2040 20 12 Bills rec'ble, his bill given up for rene. 2 1837 50 i 6387 85,7 Dr. Winslow Lamb, 1817. April 2G 5 To cash, for balance, ... 1 875 Sept. 27 8 Tea, a 60 clap, .... ti 255 1 1130 Dr. David Whitman, 1817., April [24 5|To cash, ..... 1 1562 50 Dr. Henry Lee, his account 1817. Hhds. Mar. 1 3 To cash, for freight, . . 15 1 41 25 1U 3 ditto, for truckage, . . . 1 11 25 27 4 ditto, for weighing, . . . 1 5 50 30 4 ditto, for storage, 1 10 50 JO 4 Commission ac't. for my com. 9 25 88,2 -JO 4 His ac't. cur't. for net proceeds, 8 846 79,1 941 17,3 Dr. llichard Lakeman, 1817. April 15' 5'To sundries, as per Journal, Dr. Henry Lee's account 112100! 1817. Mar. 31 4 To cash, remitted him by mail, . 1 500 Aug. 15 8 Bills payable, draft on myself, in favour of C. Lee, .... 2 120 20 8 Cash, ill full, 2 226 79,1 846 79,1 LEGER, of Amherst, 307 Cr. jDr. ' $. C. 1817. J.T. L.F. Mar. 24 3 By bills payable, a 9 months, . . . 2 1837 50 April 4 41 Sundries, . . . 350 May 20 6 Ashes, larl, .... 6| 297 85,7 July 3 7 Cash, 1 25 Nov. 30 10 Ashes, in Co. with D. Whitman & self, 1212040 Dec. -20 12 Bills rec'ble, his bill renewed, a 4 mo. 21837 50 6387 85,7 of Salera, Cr. 1817.1 Feb. 22 2 4 875 Nov. |28 ,0 Cash, 1 255 1 11 sol of Boston, Cr. 1817.1 Feb. US' 2'Bytea. of Tobacco, Cr. 1817. Mar. 3 By bills receivable, for Cash, ditto, lihds. 15 286 '62 460)52,5 194 02,8 941|17,3 of Ipswich, Cr. 1817.1 April 1 15' 5'By sundries, as per Journal, 1 '121001 current, Cr. 1817. Mar. 30 4 By his ac 1 t. of tobacco, for net proceeds, 8 846 79,1 ; 846 308 Dr. LrtGER. James Wilson, Cr. $. C. 1817. J.F. L.*. Jfune 30 7 4 130 Oct. 10 9 Bills payable, o 30 day?, 2 509 701 Dr. Samuel Dean, Boston, 1817.1 June 20 6 To his account in Co. for his $ voyage to Copenhagen, .... Dr. Samuel Dean, Boston, 1817. Dec. 5 11 To cash, in part, for net proceed? on voyage to Copenhagen, 2 5867 50 31 13 Balance due to him, 1525 74 7393 24 Dr. Thomas Mack ay, 1817.1 July 12 7 To cash in full, 1 1200 Auiasa troodhue, 1817. July 20 *7 To cash in full, .... 1 10500 Dr. Kufus Perkins, 1817., Aug. 8'To bills payable, a 30 days, Dr. E. Nichols & Sons, 1817.1 I Aug. I 8l 8 ' To cash in full, 2'4600 Dr. Commission 1817. 1 Dec. 31 13 I To Profit and Lo5, 54 33,2 ! ' 5S LEGER. of Lynn, 309 Cr. 1817. Oct. Dec. J.F. 9 11 By Vender Effingin's account current, Cash, in full, .... Dr. "li 2 569 132 701 his account current, Cr. 1817. June 21 By Cash, for his half voyage in Co. to Co- penhagen, .... 2 5867 50 his acoount in (Jo. Cr. 1817. June Dec. 20 18 By his acH. current, for his ^ voyage to Copenhagen, Voyage to Copenha. for his $ share gain, 9 5867 50 10 152> 393 74 24 of Boston, Cr. June 20 By voyage to Copenhagen, in Co. with S. Dean and Self, 10 1200 of Newbtiryport Cr. 1817. June 20 By voyage to Copenhagen, in Co. will S. Dean, and Self, 10 10500 of Beverly, Cr. 1317.1 July 1 15! 7|By Coffee, ! I | 5[ 550| of Boston, Cr. 1817.1 April [101 4| By voyage to Bourdeaux, 10|4600l Account, Cr. 1817. Mar. Oct. By H. Lee's tobacco, my commission, Vender Effingin, 8 2588,2 11 2845 I 54|33,2 310 LEGER. Dr. Expense [10 1817. April July Oct. Dec. ! 6 1 1 30 3.F. 4 7 9 12 To cash, men's wages, &c. ditto, ditto, ditto, ditto, ditto, ditto, |Cr. L.F : i c C $ L 120 I 119 > 127 > 132 j 499 C. 25 24 44 40 33 Dr. Voyage to Bourdeaux, 1817. April Dec. 10 10 31 4 4 13 To sundries, as per Journal, . . Cash, fo*r Ensurance, Profit and Loss, . . 9880 1 371 4568 20 25,7 84,3 14820 30 Dr. Voyage to Oporto, 1817. May Dec. 8 15 31 5 6 13 To sundries, as per Journal, Cash^ for Ensurance, Profit and Loss, 1 12191 525 5580 50 75 18297 25 Dr. Voyage to London, 1817. May Nov. Dec. 31 5 31 6 9 13 To sundries, as per Journal, Cash, paid at the C. house, freight, &c. Profit and Loss, . 2j 538 115 153 807 10,7 50 55,3 16 Dr. Voyage to Copenhagen, 1817. June Dec. 20 18 18 6 To sundries, as per Journal, S. Dean's acH. in Co. for his net gain, Profit and Loss, for my half ditto, . Rolo Xt.T. 9 3 11735 1525 1525 74 74 14786 48 10J LEGER. 3i Account, Cr. Dr. $ C. 1817. J.F. L.F. Dec. 31 13 By Profit and Loss, 3 499 33 Note. Th is account is balanced by Profit and Loss. f\e because the several things which are made Dr. are of no value in a mercantile way, but an entire loss. 499J33 Consigned to Charles Leroi, Cr. 1817. Nov. 8