ri M' IXTrTwrnm. USINESS Digitized by tine Internet Arciiive in 2008 with funding from - IVIicrosoft Corporation http://www.arcliive.org/details/crittendencommerOOgroerich ;■■/■ THE CRITTENDEN COMMERCIAL ARITHMETIC AJSfD Wnmm Mmml DESIGNED FOB THE USE OF MERCHANTS, BUSINESS MEN, Academies, and Commercial Colleges. BY JOHN GROESBECK, C0N3ULTINO ACCOUNTANT, PRINCIPAL OF CRITTEND?JJ'8 PHILADELPHIA COMMEECIAL COLLEGE. 3'vd\i ^bilion, 'gtbm'H anb (gnlargtb. SAN FEANCISCO: H. H. BANCROFT & COMPANY. 1868. " Knowledge Is the guide of practice." "If a man's wits be wandering, let him study arithmetic."— Bacon. "Washington studied the intricate forms of business. Ho copied out bills of exchange, notes of hand, bills of sale, ireceipts, and all the varieties of the class, witli a precision and elegance that were remarkable." Entered according to Act of Congress, in the year 1868, by JOHN GROESBECK, in the Clerk's OflBce of the District Court of the United States for the J Eastern District of Pennsylvania. >>iK EDUCATION DEPT. STXBEOTTPED BT MACKELLAR, SMITHS k /OSSAIT, PHILADELPHIA. FBINTED BT J. B. BODOKBS. PREFACE TO THE FOUETH EDITION. The object of this book is to impart that practical knowledge which is daily required in business life. Business is based upon comprehensible principles and facts, a knowledge of which will promote efficiency in actual transactions. Practice only can impart skill in application; but practice enlightened by knowledge sooner acquires proficiency, and is saved from many errors and much useless labor. Among the qualifications necessary in mercantile pursuits, none are more essential than a thorough ac- quaintance with the methods of calculation employed, and a familiarity with the various forms of business papers. The limits of the text-books on Arithmetic in com- mon use prevent that extended explanation of com- mercial customs and regulations, and the presentation of the requisite details, necessary for a clear understand- ing of the manner in which the calculations are to be applied; and, while the principles of numbers are ivi349332 4 PREFACE. fully elucidated, the shert, practical, and labor-saving methods actually used by business men are omitted. -The pupil frequently finds, when he enters into active life, that he is poorly prepared, and that he must learn more expeditious and varied methods of calculation than those he has been taught at school. Success and advancement in any pursuit depend in a great measure upon the qualifications possessed when entering upon it, as the exactions of active life leave little opportunity to remedy deficiencies of preparation. He who would succeed must not wait until surrounded by the bustle, demands, and complications of actual busi- ness, any more than the captain should defer obtainmg a knowledge of navigation until his vessel is at sea, or the physician put off the study of medicine until called upon to prescribe. He should go prepared into the busy walks of life, ready to surmount every difficulty and to excel in every thing he undertakes. The calculations presented in the following pages have been selected as the best and most important in actual use in business circles, and which are daily be- coming more and more necessary to be well understood by those who wish to make an efficient preparation for the employments of the counting-house. Several of them, it is believed, are now published for the first time. Not only the principles, but the mechanical processes, should be completely mastered, in order to acquire that readiness, rapidity, and accuracy of appli- PREFACE. O cation which are essential to secure an eminent posi- tion as an accountant, or to become a competent business man. The forms of papers are those with which every per- son should be familiar, and include a greater variety than has yet appeared in any one collection. They are accompanied by explanations of their nature and use, and the obligations and relations of the parties to them, and will impart such accurate ideas of business practices as will be of great service to those of limited experience. Many subjects have been introduced which, though rarely taught in schools, are of great importance in the counting-room and in actual life. The student of book- keeping especially will find much to aid him in his attempts to acquire a knowledge of that science. The author has been connected for the last eleven years with Crittenden's Philadelphia Commercial Col- lege, for which this manual was primarily prepared, and, in addition to his knowledge of the wants of the student, has been frequently consulted by merchants and others upon difficult questions that have occurred in their practice. These difficulties have been care- fully noted, and many of their intricacies are here solved and explained. He takes this opportunity to acknowledge his in- debtedness to numerous friends for their valuable assist- ance in the preparation of the work, and to render 6 PREFACE. them his sincere tlianks. He would also express hia obligations to the officers of numerous banks and mer- cantile houses, of the Mint, the Custom-House, and of various public and private establishments, for the opportunities afforded him of obtaining reliable in- formation on many subjects of interest and value. Three large editions of the work having been ex- hausted within a few months, it has been carefully- revised and considerably enlarged, and no effort has been spared to render it worthy of its very favorable reception. To those who have kindly favored him with their communications, — as invited in the first edition, — the author tenders his thanks, and would here repeat that he will deem it a special favor if business men, teachers, and others, will communicate any suggestion, new or improved method of calcula- tion, or useful information on business f^opics, that may add to its accuracy and completeness. CONTENTS. COMMEBCIAL ARITHMETIC. caaeacters and abbreviations. 12 Methods of Addition 13 Balancing Accounts 19 Cancellation 20 Fractions: Rules frequently used 21 Denominate Numbers 26 Practice 30 Contractions in Multiplication 31 Contractions in Division 40 Calculations used in Particular Branches of Business... 43 Proportion 45 Simple Proportion 46 Compound Proportion.. 47 Diatributive Proportion ..« « 48 Compound Distributive Proportion 50 Medial Proportion 61 Percentage 66 Commission, Brokerage, &c 69 Storage 64 Insurance .w,. 66 Marine or General Average 70 Taxes 73 Interest 76 Computing Time 77 Accurate Interest , 81 Interest on Government Bonds .........<.. 81 Interest in England. .....v.-.ii.v..iiii..i....w 82 Problems in Interest. ..^...ii.i.j. < 83 True Discount 84 Banking , 85 Merchants' and Bankers' Interest Accounts. i.... 89 Partial Payments , 95 7 8 CONTENTS. Piai AvBBAaE OP Payments: Abbreyiated Methods 99 Average op Accounts: " " ; 108 Time Table lU Money, Weights, and Measdees 116 Relative Value of Gold and Silver 117 United States Gold and Silver Coin 119 Foreign Gold Coins... 121 Foreign Silver Coins 122 Weights and Measures 123 Money, Weights, and Measures of United States 126 Money of Great Britain 130 Weights and Measures of Great Britain 131 French Metric System 132 Foreign Moneys of Account 136 Foreign Weights and Measures 186 Comparative Tables of Weights and Measures 136 Exchange 138 Domestic Exchange 139 Foreign Exchange 140 Explanation of Exchange Quotations 140 Exchange on England 141 Shipments of Specie 142 Bankers' Rules for computing Sterling Exchange 143 Sterling Table, at Premium 145 Sterling Table, at Par 146 London Course of Exchange 147 Exchange on France 148 Custom-House Business 149 Profit and Loss 154 Total Gains and Losses 154 Gains and Losses on particular Goods 155 Premium and Discount 158 Gold and Currency Table 159 Discounting Bills and Invoices 160 Price Lists 163 Advanced Cost of Invoices 164 Importers' Advance Table 165 Quick Sales and Small Profits.. 171 Marking Goods 172 Annual Product op Gold and Silver 173 CONTENTS. 9 Paok Pabtnership Settlements 174 To find each Partner's Share of the Gains and Losses 176 To find each Partner's Share at closing 177 Detecting Erkors in Trial Balances 184 Finding the True Weight with Fraudulent Balances 185 Dividends and Investments 186 United States National Debt 188 Description of United States Bonds 189 United States Treasury Regulations 192 National Debts 193 The Stock Exchange 194 gtock Quotations 196 Stock Interest Table 202 United States Bonds in Europe 203 London Quotations 204 Paris and Frankfort Quotations 205 Compound Interest 206 Compound Interest Tables 207 Annuities 211 Tables of Annuities 214 Building Associations * , 217 Life Insurance 220 Carlisle Table of Expectation of Life 221 Life Interest Table 223 The Cental System 224 Square Root 225 Lumber Measure 226 ^Gauging 227 Testing the Accuracy of Measures 228 Grain Measure 228 Calculations in Natural Science 229 Mechanical Powers 229 Falling Bodies 232 Specific Gravity 233 Light and Heat 237 Strength of Materials 240 Properties op Numbers 242 Miscellaneous Rules 242 Rules of Mensuration 243 10 CONTENTS. BUSINESS FORMS AND INFORMATION. Taoi Business Maxims 246 Payments and Leoal Tendek 247 Receipts 250 Book Accounts 257 Bills, Invoices, and Statements 258 Bills of Lading 264 Account Sales 267 Accounts Cubeent 269 Oedeks #271 Checks 272 Checks payable in the future 274 Certified Checks 274 Certificates of Deposit 275 Teansactions with Banks 275 Rules foe detecting Counteefbit Bank Notes 277 Desoeiption of National Bank Notes 278 Desoeiption of Teeasuey Notes, oe Geeenbacks 279 Due-Bills ! 280 Peoducb Notes 281 Peomissoey Notes 281 Negotiable and Non-Negotiable 282 Presentment and Protest 285 Aocommodation Notes 286 Collateral Notes 286 Joint and Several Notes 287 ^ Judgment Notes 287 Form of Protest and Notice 292 Deafts and Bills of Exchange 293 Indoesements 298 Acceptances 301 Agency „ 802 Powers of Attorney 304 Sealed Insteuments 307 Bonds 308 Common Form of Bond 309 Clauses for Bonds 809 Release 810 CONTENTS. 11 Paoe CONTEACTS 312 General Form of Agreement 314 Agreement of Sale « 314 Bill of Sale, and Affidavit for Goods sold 315 Guarantees 316 Partnership 318 Partnership Agreements 320 Partnership Notices 324 Landlord and Tenant 326 Forms of Lease 327 Security for Rent 328 Mercantile Correspondence 329 Mercantile Letters 334 Offering Goods 334 Declining Offer to purchase 334 Declining to purchase 335 Order for Goods f. 335 . Enclosing Invoice and Bill of Lading 335, 336 Advice concerning Shipment 336, 338 Acknowledging Receipt of Invoice 337 Consigning Goods to be sold on Commission 337, 338 Enclosing Account of Sales 337 Enclosing Note for Discount at Bank 338 Enclosing Account Current 339 Enclosing Remittance 339 Acknowledging Remittance 340 Asking for Settlement 340, 341 Enclosing Draft for Acceptance, and Answer 341 Enclosing Statement of Account 342 Advising of Draft 342 Enclosing Notes for Collection 342 Letter of Introduction, and Recommendation 343 Answer to Advertisement 343 Application for Situation 344 Order for Book 344 Instalment Receipt 345 English Exchequer Bill 345 Certificate of Stock 346 Certificate of Scrip Dividend 347 United States Five-Twenty Bond... 348 CHARACTERS AND ABBREVIATIONS USED IN BUSINESS. f At. Account. Cents. Per cent. Number. One and one-quarter. One and one-half. One and three-quarters. 1» 16 doz. i^j, i^j, lyi^j. Fifteen doz.. 5 of which are $12 per doz., 6 doz. @ $15, and 6 doz. at $18 per doz. Ihhd. Sugar. ^^^^P^^^'g^r linn weight, 155 lbs. tare, or weight of hhd., 945 lbs. net weight. « The numbers ^^o "" I 1QQ ^.lo ^'^ ^^6 bracket 4p8.28J-138yds.^^^ the num- ber of yds. in 1100 155 9451b8. 42] 36 I 32 J each piece respectively. 10 doz. I @ 2/- 1 @ 3/6. 4 doz. No. 5 @ 2 shillings per doz. ; 6 doz. No. 8 @ 3«. 6rf. per doz. 7 X 9, or 7 by 9 in. 7 in. wide, 9 in. long. ^ W.W., and similar characters and letters, are placed on pack- ages to designate a particular lot or shipment. (Goods aro uumboroil aud marked, that (boy may be diutiuguishud without nii- oute description.) Acc't. Account. Adv. Adventure. Am't. Amount. Ass'd. Assorted. Bal. Balance. Bbl. Barrel. Blk. Black. Bo't. Bought. B. L.,orB. ofL. Bill of Lading. Co. Company. Cr. Creditor. Com. Commission. Cons't. Dft. Disc't. Do. or ditto. Doz. Dr. Ea. E.E. E. &0.E. Exoh. Exps. Fig'd. Fol. Forw'd, or fwd. fr. Fr. Fr't. Guar. Gal. Hhds. Ins. Insol. Inst, (instant) Invt. Int. Mdse. Mo. Net. No. Pay't. Pd. Pk'gs. Per, or pr. Per cent. Prem, Prox. (proximo) Ps. Rec'd. Ship't. S.S. Sunds. Ult. (ultimo) Yds. Yr. Consignment. Draft. Discount. The same. Dozen. Debtor. Each. Errors excepted. Errors and omis- sions excepted. Exchange. Expenses. Figured. Folio. Forward. From. French. Freight. Guarantee. Gallon. Hogsheads. Insurance. Insolvency. This month. Inventory. Interest. Merchandise. Month. Without deduc- tion. Number. Payment. Paid. Packages. By. By the hundred. Premium. The next month. Pieces. Received. Shipment. Steamship. Sundries. The last month. Yards. Year. 12 d COMMERCIAL ARITHMETIC. METHODS OF ADDITION. 1. Addition constitutes the greater part of all the calcu- lations of business and common life ; and the ability to add with rapidity and accuracy is of more practical utility than all the other arithmetical operations combined. This ability, however, can be readily acquired by the exercise of memory and the right kind of practice. A regular method should be pursued ; encumbering the mind with amounts to be carried from one operation to another should be avoided ; and a prac- tical familiarity with the sums of combinations of numbers should be cultivated as much as possible. Any thing which lessens the number of operations to be performed promotes rapidity. By closely adhering to the following methods, a short time only will be required for acquiring considerable proficiency. 2. In writing numbers, care should be taken to make the figures clear and plain, so that a 3 will not be mistaken for a 5, or a 7 for a 9 ; and also that the figures in one line do not run into those in the line below, and that all the figures of a column be placed directly under each other. 3. Commence at the foot of the column and add upward, and, if the column is long, always set down the carrying figure. This relieves the mind from apprehension of loss of time, from being compelled, by interruptions which often occur in busi- ness, to leave the work when nearly through the addition of several columns of figures ; and then, if necessary, any column may be re-added without the trouble of adding the preceding. Always add the carrying figure to the next column on commencing. 2 13 14 METHODS OF ADDITION. 4:, The following methods of retaining the carrying figure are adopted by most accountants : — FIRST METHOD. SECOND METHOD. ^13213.30 15 15 25342.13 12468.31 27 1143.13 27 35321.34 20 13476.21 23 2113.13 10 103077.55 103077.55 2 22 2.1 I In the first method, the figure to be carried is written small immediately under the figure to which it belongs. In the second method, the whole result of each column is set down by itself, the sum of each column being written one place to the left under the sum of the column preceding it; then, when all the results are written, the right-hand figures, including all the footing of the last column, will give the total result. 5, If the figures are not set doicn in regular order under each other, instead of trying to follow the column upward, take the figure which is the same number of places from the right hand as the figure with which you started, not regarding whether it is below tens or hundreds, or very near the right- hand figure, or at some distance from it. For instance, if you wish to add a column of hundreds which have been set down irregularly, instead of looking for the next figure above, look for the next figure which is three places from the right. This method will save time, and avoid perplexity and uncertainty. 6. To secure accuracy, the addition should be performed twice, — in dificrent directions : this gives new combinations, and, if there has been a mistake, is a preventive of its repeti- tion, which is likely to occur, especially when the mind has been too long engaged. METHODS OF ADDITION. 15 7. If the columns of figures are long, it is generally better to place the footings on a separate piece of paper and test their correctness, before placing them in ink on the book ; as mistakes can then be corrected without defacing the page by erasures. 8, Familiarity with the totals of combinations should be th3 object of all practice. Counting is not adding. It is quite as easy, and considerably quicker, to say at once, 8 and 7 are 15, than to count 8, 9, 10, 11, 12, &c., up to the result 15 ; and also to say, 3, 6, 10, 15, than to say, 3 and 3 are 6, 6 and 4 are 10 10 and 5 are 15. COUNTING-HOUSE DRILL TABLES. Drill Table No. 1. 20 20 20 20 20 20 20 20 20 20 19 19 19 19 19 19 19 10 19 19 18 18 18 18 18 18 18 18 18 18 17 17 17 17 17 17 17 17 17 17 16 16 16 16 16 16 16 16 16 16 15 15 15 15 15 15 15 15 15 15 14 14 14 14 14 14 14 14 14 14 13 13 13 13 13 13 13 13 13 13 12 12 12 12 12 12 12 12 12 12 11 11 11 11 11 n "11 11 11 11 10 10 10 10 10 10 10 10 10 10 9 9 9 9 9 9 9 9 9 9 8 8 8 8 8 8 8 8 8 8 7 7 7 7 7 7 7 7 7 7 6 6 6 6 6 6 6 6 6 6 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 O 2 2 2 2 2 2 2 2 2 2 1 T 1 1 1 1 1 1 1 1 2 3 4 5 G 7 8 9 10 11 1 I 1 16 METHODS OF ADDITION. Drill Table No. 2. 20 21 22 23 24 25 26 27 28 29 30 19 20 21 22 23 24 25 26 27 28 29 18 19 20 21 22 23 24 25 26 27 28 17 18 19 20 21 22 23 24 25 26 27 16 17 18 19 20 21 22 23 24 25 26 15 16 17 18 19 20 21 22 23 24 25 14 15 16 17 18 19 20 21 22 23 24 13 14 15 16 17 18 19 20 21 22 23 12 18 14 15 16 17 18 19 20 21 22 11 12 13 14 15 16 17 18 19 20 21 10 11 12 13 14 15 16 17 18 19 20 9 10 11 12 13 14 15 16 17 18 19 8 9 10 11 12 13 14 15 10 17 18 7 8 9 10 11 12 13 14 15 16 17 6 7 8 9 10 11 12 13 14 15 16 5 6 7 8 9 10 11 12 13 14 15 4 6 6 7 8 9 10 11 12 13 14 3 4 5 6 7 8 9 10 11 12 13 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 The above columns should be added until the addition can be easily performed and without hesitation. 9. In the following columns, add all the figures enclosed in each bracket as one number, and name only results in the same manner as when the figures are taken separately. Thus, in adding column No. 4, say 7, 11, 16, &c. 10. When a figure is repeated several times, count the number of times it occurs, and multiply by the figure. Thus, if the figure 8 occurs seven times in a column, multiply 7 by 8 for the result, instead of adding seven 8*s together. 11. When three figures occur in regular order, — as 4, 5, 6, or 6, 7, 8, — three times the middle figure will be their sum; when five figures occur, take five times the middle figure. When there are four figures in regular order, take METHODS OF ADDITION. 17 twice the sum of the extremes; when there are six, take three times the sum of the extremes. (1.) (2.) 324 678 235 789 143 976 421 899 312 989 234 988 343 878 423 673 225 789 123 968 334 887 212 987 324 798 123 976 431 687 212 997 (3.) 3)3 4 3 4)5 4J6/3 3\7\7 7J8i4| 4\6\6i 2J8/1 8|3171 2/9/3/ 3-)0 5\ 4^5\5/ 5J5il\ 2\3)9J 3/7i5\ 71615/ 3/4/2 4419 13959 72 1 2 ADDITION OF SEVERAL COLUMNS AT ONE OPERATION. 12. To add two or more columns at one operation. To the lower number add first the units of the next num- ber above, then the tens, then the hundreds; and so continue. 23 OPERATION. 31 22 + 5 = 27, 27 + 10 = 37 24 37+4 = 41,41 + 20= 61 15 61 + 1 = 62,62 + 30= 92 22 92 + 3 = 95, 95 + 20 = 115 Ans. 115 234 OPERATION. 112 322 + 3 = 325 + 20 = 345 + 400= 745 423 745 + 2 = 747 + 10 = 757 + 100= 857 _322 857 + 4 = 861 + 30 = 891 + 200 = 1091 Ans. 1091 2* 18 BALANCING ACCOUNTS. Practice will enable a person to add amounts of two or more figures at one operation : thus, 22 + 15 = 37, 37 -f 24 = 61, 61 -f- 31 = 92, 92 -f 23 = 115 Ans. As soon as the combinations become familiar, addition by this method can be performed without diffi- culty ; but, for ordinary purposes, one column at a time is sufficient. In Ledger accounts, when the last two or three columns are not all filled, they may be added at one operation with advantage. 13. Very long columns of figures are sometimes added in the following manner : — FIRST METHOD. 247 362 228 436 1273 128 326 121 1848 121 316 405 SECOND METHOD. 247 362 228 436 1273 128 326 121 575 121 316 405 842 2690 Ans. 2690 Ans. ADDING HORIZONTALLY. 14. In some branches of business the ability to add num- bers which are written horizontally instead of being placed under each other, is often required. Thus, — 824 + 325 4- 652 = 1801 All the units are first added, then the tens, and then the hundreds. A little practice will soon overcome any diflficulty which may be experienced at first. Add434, 216,4217, 3217. Add 216, 1231, 432, 1800, 2167. Add the following numbers as they stand : — 325 116 365 431 275 218 Ans. 1730. BALANCING ACCOUNTS. 19 BALANCING ACCOUNTS. 15. It is frequently of advantage to the accountant to find the difference between two sums by addition, instead of by Bub traction. For example, if he wishes to find the differ- ence between 2427 and 1235, instead of taking the trouble of placing the smaller number under the larger, he will add, mentally, to 1235 a sum that will make the whole equal to 2427, writing the figures as he proceeds under 1235. 2427 1235 1 1 92 — balance. When both sides of an account contain several amounts, first add the larger side in the usual manner ; then commence at the top of the columns, on the smaller side of the account, and add doionwards, inserting the necessary figures to make the required balance. Thus, to find the balance of the following account : Dr. V. I. Andrews. Or. 1867. Jan. 3. " 10. '' 24. To Mdse. n u u a $84.00 72.00 43.00 $199.00 186T. Jan. 10. By Cash, a 17. " « Balance, $45.00 67.00 8 7.0 First, add the larger side; then say, 5-|-7 = 12, and 7, the figure required to make the balance, =r. 19. Set down 7 and carry 1. 1 -|-4 + 6 = 11, and the remaining figure of the balance =19. To test the accuracy of the work, add the whole of the smaller side, and include the balance. Dr. EXAMPLE II. George L. Burtis. Or. 1867. 1867. Feb. 9. To Mdse. $187.37 Feb. 15. By Cash, $150.00 " 26. u u 37.42 Mar. 10. « " 437.75 Mar. 4. CI 11 260.38 Apr. 9. a a 720.16 May 6 u a 132.50 " 9. a cr 350.00 20 CANCELLATION. CANCELLATION. 16. Cancellation is the process of shortening operations in multiplication and division by rejecting equal factors. 17. Cancelling, or rejecting a factor of any number divides the number by that factor. 18. Cancelling a number is the same as dividing that number by itself, and, consequently, the quotient is 1. 19. Dividing the multiplicand or multiplier will give the same result as dividing the product. 360X24 = 8640, 8640 -f- 6 = 1440. 360 -V- 6= 60, 60 X 24 = 1440. 24 -f- 6= 4, 4X360 = 1440. 20. If the dividend and divisor be both multiplied or both divided by the same number, the quotient will not be changed. 32 --8 = 4 32X5 = 160, 8X5= 40, 160h-40=4. 32 --4= 8, 8--4= 2, 8-f- 2=4. 21. Dividing the divisor will give the same result as multi- plying the quotient. 14)126(9, 9X2 = 18. 14-^2 = 7, 126-j-7 = 18. 22. Dividing the dividend will give the same result as dividing the quotient 14)126(9, 9-^ 3 = 3. 126-3 = 42, 42-- 14 = 3. 1. Divide the product of 6, 8, and 9 by 4 times 3. 2. A merchant bouglit 27 yards of cloth at $2.25 per yard, and paid for it in tea at 75 cts. per lb. How many pounds were required ? ,Ans. 81 lbs. 3. What will 28 pieces of cloth cost, each piece containing 27 yards, at 25 cts. per yard ? FRACTIONS. 21 FRACTIONS. RULES FREQUENTLY USED. 23. T 3 multiply whole numbers by fractions. Rule. — Multipli/ hy tJie numerator, and divide the product by the denominator. EXAMPLES. 1. Multiply 464 by f . 464 X 3 = 1392 ; 1392 -^- 4 = 348 Ans. 2. Multiply 12672 by 18|. 12672 181 4) 38016 — product by 3. 9504 — product by f . 101376 " " 8. 12672 " " 1. 237600— product by 18f . 24. To multiply a fraction by a fraction. Rule. — Multiply the numerators together for a new nume- rator, and the denominators together for a new denominator. Multiply § by 4. 2. Multiply i by y\. 2X4 = 8 3. - if" |. 5X7 = 35 Ans. 3V 4. - f, " if. 25. To divide by a fraction. Rule. — Invert the divisor, and multiply as in the previous rules. 1. Divide f by |. 6. Divide A by f . 1 inverted == | 7. 1 (C 1 4 2" 5 X 4 = 20 8. i " h 9X3 = 27 Ans. -HO. 9. ^ of 21 by y5_. 2. Divide 4 by f . 10. i of 4 by /o- 3. " A by |. 4. " 3^ " f. 11. i of ? by j%. 12. /5 by 4. 5. " 9 ^' |. 22 DECIMALS. 27, To divide by a mixed number. liVLE.—^ Multt2)/f/ the whole number in the divisor ly the denominator of the fraction, and to the product add the nu- merator. Multiply the dividend hy the denominator of the fraction ; then divide as usual. The remainder, if any, must he divided hy the denominator of the fraction to ohtain the ttnie remainder. 1. Divide 480 by 5i. 5i 480 1 _2 11) 960 2. Divide 2675 by 18|. 3. « 18992 by 133J. 4. " 425 by 311. 5. " 341 by 7f 6. " 1227 by 97 J. 87jVor87,lJRem. 28. To reduce a decimal to a common fraction. liuLE. — Write the decimal as it stands, omitting the deci- mal point, for the numerator. For the denominator j write 1 with as many ciphers annexed as there are decimal places in the numerator. EXAMPLES. 1. Reduce .25 to an equivalent common fraction. Ans. -p^\, which reduced to its 2. Reduce .375 to a common fraction. Ans. -/y^j, which reduced to its lowest terms = ^, Anq 37 5 3 Ans. JQQJJ g. 3. Reduce .1875 to a common fraction. Ans. j\. 4. Reduce .625 to a common fraction. Ans. ^. 29. To reduce common fractions to decimals. Rule. — Annex ciphers to the numerator, and divide hy tJie denominator, prefixing a point to the quotient. Tliere must he as many places in the quotient as there have heen ciphers annexed; if not enough, prefix ciphers. Note. — For practical purposes, it will bo sufficiently accurate if the division be carried to four or five places. DECIMALS. EXAMPLES. 1. Keduce | to a decimal. 4)3.00 .75 = f^%Ans. 2. 3. 4. Reduce |- to a decimal. « 6 (C (i « Jt U li 5. 11 2 U IC 23 Ans. .375. Ans. .8571+. 30. MULTIPLICATION OF DECIMALS. Rule. — Multiple/ as in whole numbers, and from the right of the product point off as many figures for decimals as there are decimal places in both multiplicand and multiplier. Jf there are not figures enough in the product, prefix ciphers. EXAMPLES. 1. Multiply 4.25 by 6.5. 4.25 6.5 2125 2550 27.625 Ans. 2. Multiply 84.5 by 4. 84.5 4 3. 4. 5. 6. 7. 8. 9. 0. 338.0 Ans. Multiply 6.425 by 4.25. « 18.5 '' 6.75. " 12.575 " 9.375. '^ .25 " 6.0025. .275" 3.0025. « 18.625 '^ 5.25. What is the cost of 12| lbs. @ ^ cts. per lb. ? What is the cost of 7| yds. at 18| cts. per yd. ? Note. — It is sometimes more convenient to change ccmmon fractions i9 docimala before multiplying. 18| X 12i = 18.75 X 12.6. 24 - PRINCIPLES OF FRACTIONS. 31. DIVISION OF DECIMALS. Rule I. — When the decimal places in the dividend and divisor are equal, divide as in wJiole numbers; the quotient will be in whole numbers. Rule IL — When the decimal places in the dividend exceed those in the divisor. Divide as in tchole numbers, and from the right hand of the quotient point off as many decimals as the decimal places in the dividend exceed those in the divisor. Should there be a deficiency of figures in the quotient j it must be supplied by prefixing ciphers. If there be a remainder, annex ciphers, and continue the division as far as desired, each cipher annexed being equivalent to one more decimal in the dividend. Rule III. — When the decimal places in the divisor exceed those in the dividend. Annex ciphers to the dividend, and proceed as before. EXAMPLES. 1. Divide 156.25 by 6.25. Ans. 25. 2. " 234.70525. by 64.25. Ans. 3.653. 3. " .8727587 by .162. 4. « 6.25 by .1875. 5. " 3271 by 4. PRINCIPLES OF FRACTIONS. 32. Numbers written in the form of a fraction denote division, the numerator being the dividend, and the denomi- nator the divisor. 33. Multiplying or dividing both the numerator and denominator of a fraction by the same number does not change the value of the fraction. 34. Multiplying the numerator, or dividing the denomi- nator, of a fraction multiplies the fraction. 35. Dividing the numerator, or multiplying the denomi- nator, divides the fraction. REDUCTION. 25 DENOMINATE NUMBERS. 3G, A Deuoiuinate Number is composed of simple numbers of different denominations. 37. Reduction is the process of changing numbers from one form, or denomination, to another, without altering their values. (For Tables, see Weights and Measures.) REDUCTION DESCENDING. 38. To reduce numbers from a higher denomination to a lower. Rule. — 1. Multiply the numhcr of the highest denomination hy the numher which one of this denomination makes of the next lower. 2. Add to the product the number in the next lower denomi- nation^ if any. 3. Proceed in the same manner through the lower denomi- nations to the one required. EXAMPLES. 1. Reduce XIO 7s. lOcZ. to pence. 10 20 shillings in a pound. "200 7 207 shillings. 12 pence in a shilling. 248^ 10 Ans. 2494 pence. 2. How many pints in 22 bushels, 6 qts. 1 pint ? 3. How many inches in 6 rods, 2 yds. 8 ft. 6 inches? 4. How many minutes in one day r' 5. How many pounds in 1 ton, 3 cwt. 3 qrs. 10 lbs.? 6. Reduce 75 bushels to pints. 3 26 REDUCTION. REDUCTION ASCENDING. 39. To reduce a number from a lower denomination to a higher. Rule. — Divide the given number hy the numher required to make one of the next higher denomination. Divide the quotient thus obtained as be/ore, and so proceed to the denomination required. Note. — The remainders, if any, are of the same denomination as the numbers divided. EXAMPLES. 1. In 1275 pence, how many pounds? 12) 1275 20) 106s. 3^. £5 6s. Ans. £5 6s. 3d. 2. Reduce 15485 lbs. to tons. 3. Reduce 632687 feet to miles. 4. In 7846 grains of gold, how many lbs. ? 40. To find the value of one denomination in numbers of another denomination having dijQTcrent relations. Rule. — Reduce the given numbers to a denomination which is common to both, then reduce the residt to the denomination required. EXAMPLES. 1. How many Ells English in 600 Ells French ? REMAnK. — Both denominations can be reduced to quarters. 600 Ells French =z 3600 qrs. 3600 qrs. reduced to Ells English = 720, Ans. 2. Estimating a gallon wine measure to contain 231 cubic inches, and a gallon beer measure to contain 282 cubic inches, how many gallons beer measure are there in 640 gallons wine measure 't 3. If a dollar is worth in Can ten 4s. 4(f.j how many dollars are equal in value to £1500? DENOMINATE NUMBERS. 27 FRACTIONS OF DENOMINATE NUMBERS. 41. To reduce a fraction of one denominjftion to wliole numbers, or to an equivalent fraction, of another denomina- tion. Rule. — Multiple/ or divide the fraction hy the same num- hers that would he employed in the reduction of whole numbers. EXAMPLES. 1. What is the value of -f^ < Df £1? 1% X 20 : fix 12 = 9d. Ans. 2. What part of £1 is | of a penny? Ans. -gl^. 3s. M. 3. What part of a bushel is | of a quart? 4. Reduce -l^ of a day to lower denominations. 5. Add I of a pound to | of a shilling. Ans. 15s. 10c?. 6. Reduce | of a lb. to the fraction of a cwt. 7. What part of an acre is | of a rod ? 42. To reduce a denominate number to a fraction of another denomination. Rule. — Reduce the given numbers to the lowest denomina- tion mentioned^ for the numerator, and a unit of the denomi- nation of the required fraction to the same denomination ^ for the denominator. EXAMPLES. 1. Reduce 7s. 4c?. Ifar. to the fraction of a pound. 7s. 4c?. Ifar. = 577/ar. £1 = 960 '' Ans. IJJ. 2. Reduce 1 pint to the fraction of a gallon. 8. What part of a bushel are 3 qts. ? 4. What part of a week are 3 hours? 5. What part of a mile are 5 feet ? 28 DENOMINATE NUMBERS. DECIMALS OF DENOMINATE NUMBERS. 43. To reduce a denominate number to a decimal of a higher denomination. Rule. — Annex ciphers to the lowest denomination , and divide hy that number ichich will reduce it to the next higher denomination, and annex the quotient as a decimal to that higher. Then divide that higher denomination as be/ore, and so continue dividing until the whole is reduced to the denomi- nation required. Or, Red^ice the given number to a common fraction of the de- nomination required J and reduce this fraction to a decimal, EXAMPLES. 1. Reduce £7 15s. (Sd. 3far. to the decimal of a pound. Sfar. = .75 of a penny. G.75f7. = .5625 of a shilling. X7.778125 15.56250s. = .778125 of a £. Ans. £7.778125. 2. Reduce £617 Is. Id. to the decimal of a pound. 1.0000 4 3.00 12 6.75000 20 15.5625 12 20 1.0833 £617.05416. Ans. Note. — For a shorter practical method for sterling money, see page 43. 3.* Reduce 3 bus. 1 pk. 3 qts. to the decimal of a bushel. 4. Reduce 3 qrs. 12 lb. 8 oz. to the decimal of a ton. 5. Reduce 2 gals. 1 qt. 1 pt. to the decimal of a gallon. 44. To reduce a denominate decimal to whole numbers. ,RuLE. — Multiply the given decimal as in reduction of whole numbers, and point off in the product as in multiplica- tion of decimals. The numbers on the left of the decimal point \cill be the whole numbers required. Note. — Only the decimal part of each number should bo multiplied. DENOMINATE NUMBERS. 29 EXAMPLES. 1. What is the value of .625 of a pound? .625 20 12.500 12 6.000. Ans. 12s. Gd. 2. What is the value of .875 of a ton? 3. What is the value of 1.875 of a bushel? 4. What is the value of .425 of a pound troy? 5. What is the value of 2.19375 of a year? MISCELLANEOUS EXAMPLES. 1. How much money is required to pay for the following ? 32^ yards muslin, at 16| cts. per yard. 18| lbs. tea, @ $1.15 per lb. 17A lbs. coffee, at 221 cts. per lb. 15| lbs. lard, at 16| cts. per lb. 23-| lbs. chrome yellow, at 37^ cts. per lb. 19 j\ feet brass, at 23| cts. per foot. Ans. 2. If a piece of land is worth $317.50, what is | of it worth ? What is | ? What is | ? 3. A man sold 4| acres of land for $320. How much did he receive per acre ? 4. A United States, or Winchester, bushel contains 2150.42 cubic inches : how many cubic inches in 13| bushels? 5. What is I of j% of $117? of $585.? 6. Bought i5| tons Russian hemp for S4325.50: what was the price per ton? 7. What is the cost of 3 metres gold chain, at $3.25 per inch, each metre cpfltaining 89.371 inches? 8. What is the valine of 15 gals. 1 qt. 1 pt. of wine, at $3.75 per gallon ? 3* 30 PRACTICE. PRACTICE. 45. Practice is a brief method of ascertaining the total value of a quantity by combining the values of convenient aliquot parts. 4:G. An Aliqnot Part is some fraction of a quantity "whose numerator is 1. EXAMPLES. 1. What is the value of 336 yds. cloth, at 18|cts. per yd.? 12'/ = I of a dollar. G| = i of 12A^. 8)$336 value at 81 per yd. 2)42 " " 12^/" ^' 21 " '< _6^/'^ " Ans. $63 " '' 18|>? " " 2. How much will 1232 bushels wheat cost, at 81.31J per bushel ? 1232 1.31-1 4)1232 cost at $1.00 per bu. 4) 308 '^ 25/ 77 " 6|/ Ans. $1617 " $1,311 « '< 3. What will 28 bus. 3 pks. 4 qts. clover-seed cost, at $3.50 per bus. ? $98.00 = cost of 28 bus. ^ of 3.50 = 1.75 = " " 2 pks. I " 1.75 = .87^= " " 1 " I " .87i = .43j = '' " 4 qts. Ans. $101.06^ = « " 28 bus. 3 pks. 4 qts. 4. What will 270 yds. silk cost, at £1 5s. 6d. per yard? Ans. £344 5s. 5. What will 326 bbls. flour cost, at $7.87-^ per bbl. ? 6. llequired the cost of 12 gals. 3 qts. 1 pt. of molasses, at 62^cts. per gallon. CONTRACTIONS MULTIPLICATION AND DIVISION. The following contractions are useful for imparting readi- ness and dexterity in the mechanical processes of multipli- cation and division. If thoroughly mastered, they will be found to be of great service, and will amply repay the time and labor expended in acquiring them. They include, in a condensed form, nearly all of practical value that has yet been published, together with some methods which, it is be- lieved, now appear in print for the first time. The labor of making out bills and invoices, entering sales, taking account of stock, and many similar operations, may be much lessened by their use ; as extensions can be made without writing out the operations, while the liability to mis- takes is diminished, because there is less labor, and fewer figures are employed. 31 ■^It 32 CONTRACTIONS IN MULTIPLICATION. CONTRACTIONS IN MULTIPLICATION. 47. To multiply two numbers of two places each wliea the units or tens are alike. Rule. — Multiply units hy units ; <^w, IE the units are ALIKE, multiply the sum of the tens hy the units, and the tens hy tens. If the tens are alike, multiply the sum of the units hy the tens, and the tens by tens; in all cases carrying as usual. EXAMPLES. 1. Multiply 34 by 54. 34 4 X 4 = 16 54 5-f-3= 8X4 = 32 4-1 (carried) = 33 3 X 5 = 15 + 3 (carried) = 18 1836 2. Multiply 45 by 43. 45 5 X 3 = 15 43 5 + 3= 8X4 = 32 + 1 (carried) = 33 4 X 4 = 16 + 3 (carried) = 19 10. Multiply 36 by 34. 1935 4X4 = 3. Multiply 44 by 64. 4. u 32 ^' 72. 5. (( 28 " 18. 6. u 45 " 35. 7. a 123 '^ 33. 8. a 65 ^' 55. 9. a 124 " 34. 11. 64 " 64. 12. 35 « 34. 13. 72 " 73. 14. 37 " 35. 15. 45 " 45. 16. 6Q '< 66, 45 X 45 = 5 X 4 with the square of 5 annexed. 75 X 75 = 8 X 7 " " 5 48. This rule includes the multiplication of two numbers whose units or tens are ones, the squaring of numbers, multiplying when tlio units are alike and the sum of the tens is ten, &c. As it is capable of several hundred applications, its valtte is ob- vious. A little practice will give the ability to write the products witliout setting down (he figures to be multiplied. It is believed that this is tlic first time the above rnje has appcardl in print. CONTRACTIONS IN MULTIPLICATION. 33 49. To multiply by numbers, the half, third, or fourth of which is a convenient multiplier. EuLE. — Middply the half of one number hy twice the other, or one-third of one number by three times the other, ounds to itself y and point off one decimal. EXAMPLES. 1. ITow many gallons in 675 lbs. ? 675 225 = i of 675 90.0 Ans 90 gals. 2. In 1846 lbs. how many gallons? in 075, in 339 lbs. f PROPORTION. 45 PEOPOllTION. 75. Ratio is the relative magnitude of two numbers of the same kind, and is found by dividing one by the other: thus, the ratio of 3 to 12 is 4. 76. A ratio is denoted by two dots similar to a colon : thus, 5 : 15 expresses the ratio of 5 to 15, and is read, As 5 is to 15. 77. It may also be written in the form of a fraction : thus, ij^ expresses the relation of 4 to 16. 78. The two numbers compared are called the terms of the ratio, the first being the divisor, and the other the di- vidend. 79. The first term is called the antecedent^ and the last the consequent. 80. The terms of a ratio must be of the same kind, or such as may be reduced to the same denomination. We cannot compare 3 yds. with- 6 dollars, but we can compare 3 yds. with 5 feet, because we can reduce yards to feet, and say. As 15 feet are to 5 feet. 81. Multiplying the consequent, or dividing the antecedent, multiplies the ratio. 82. Dividing the consequent, or multiplying the antecedent, divides the ratio. 83. Multiplying or dividing both antecedent and conse- quent does not alter the ratio. (See Oancellation, Art. 20.) 84. Proportion is an equality of ratios. Thus, 2 : 4 : : 10 : 20 expresses that the ratio between 2 and 4 is the same as between 10 and 20, and is read, As 2 is to 4, so is 10 to 20. The first and fourth terms are called the extremes; the second and third, the means. 85. In every proportion the product of the means eqiials the product of the extremes. From this principle, having three terms of a proportion, we are enabled to find the fourth. 46 PROPORTION. SIMPLE PROPORTION, OR, RULE OF THREE. 86. A Simple Proportion is expressed by an equality of two ratios, and consists of four terms. When three of the members of a proportion are given, two of them must be of the same kind, and the other must be of the same kind as the fourth term, or answer. 87. For finding the fourth term, we have the following HuLE. — Place the given number which is of the same kind as the required answer^ as the third term. Then, if from the nature of the question the number sought should be larger than the third term, place the greater of the two remaining terms for the second term, and the less for the first) but if the number sought should be less than the third term, place the less of the two remaining numbers for the second, and the greater for the first. Reduce J if necessary/, the first and second terms to the same denomination, and if the third term, is a compound number^ reduce it to the lowest term mentioned in it. Then multiply the second and third terms together, and divide the product by the first term : the quotient will be the fourth term, or answer. EXAMPLES. 1. If 25 barrels of flour cost $165, what will 35 barrels cost? 25 : 35 : : 165 35 25)5775 231 • Ans. $231. Since dollars arc of the same kind as the answer sought, we place $165 as the third term. Then, as 35 barrels will cost more than 25 barrels, wo place 35, the larger number, for the second term, and 25, the smaller, for the first. Bi/ Analysis. — If 25 barrels cost $1G5, one barrel will cost f 6.60, and'35 barrels will cost 35 times $6.60 = $231. PROPORTION. 47 2. If 7 yards of broadcloth cost $24.50, how much wilJ 12 yards cost at the same rate? 3. If 18 bushels of wheat cost $27, what will 50 bushelsf cost? 4. What will 27 yards of cloth cost, if 48 yards cost $3G? 5. What will 100 shares of railroad stock cost, if 175 shares can be bought for $125? 6. If 12 men build 16 rods of a wall in a day, how many rods will 9 men build ? 7. How much will 14 yds. 3 qrs. of cloth cost, at the rato of 10 yds. 1 qr. for $20? 8. What will 22 gals. 2 qts. of wine cost, at the rate of $15.50 for 6 gals. 1 qt. 1 pt.? 9. If I of an acre cost $320.25, what will | of an aero cost, at the same rate ? COMPOUND PROPORTION. 88. A Compouud Proportion is one which involves two or more simple ones. 89. Every example in Compound Proportion can be solved by two or more simple proportions. 90. All the terms of a compound proportion appear in couplets, except one, which is always of the same kind as the answer sought. Rule. — 1. Write the numher which is of the same hind as the aiiswer sought^ for the third term. 2. Arrange the two terms of each ratio separately, as in imple proportion. 8. Multiply the continued product of the second terms hy the third term, and divide the result hy the continued prO' duct of the first terms. Note. — The work may frequently be much abridged by cancellation. EXAMPLES. 1. If 12 men in 30 days earn $270, how many dollars will 18 men earn in 36 days? 48 DISTRIBUTIVE PROPORTION. 12 : 18:: 270 30 : 36 360 : 648 : : 270 648 360)174960($486 Ans. 1440 3096 2880 2160 2160 Or, by cancellation, §270 13 the same kind as the required term, 18 men will earn more than 12 men, and more can be earned in 36 days than in 30. 12X30 = 360. 18 X 36 = 648. 9 3 3X9X18 = 486, Ans. J3i/ Analysis. — If 12 men earn $270 in 30 days, 1 man will earn ^j of $270 = $22.50 in 30 days, and ^i^ of $22.50 = 75/- in 1 day. If 1 man earn 76^ in 1 day, 18 men will earn 18 times 75/, or $13.50, in 1 day, and 36 times $13.50 = $486 in 36 days, men. men. Bij Simple Proportion.— 12 : 18 : : 270 : 405. days. days. 30 : 36 : : 405 : 486. Ans. $486. DISTRIBUTIVE PROPORTION. 91. Distributive Proportion is the method of dividing a number, or quantity, into parts which are proportional to given numbers. Note. — This rule ia also called Fellowship, or Partner aTiip, the Pule of Proportional Division, and Partitive Proportion. For Partnership, see 2HKJC 174. 02. The principle of this rule can be easily applied to the Bolution of numerous questions of a practical nature, such as determining the profits and losses of partners in trade, ap- portioning the shares of participators in prize-money, finding the relative proportion of ingredients requisite to form a given quantity of a compound, apportioning taxes, school- rates, averaging, &c. DISTRIBUTIVE PROPORTION. 49 Rule. — Multiply the whole quantity to he divided hy each proportional number^ and divide each product hy the sum of the proportional numhers. Or, use the following formula : — Sum of the pro- ] ^ Quantify or num- 1 . . f Each propor- portional numhers ) ' her to he divided ) I tional number. EXAMPLES. 1. Divide 300 into two parts which shall be to each other as 3 to 9. 3 + 9 = 12 12 : 300 : : 3 : 75 the less number. 12 : 300 : : 9 : 225 the greater number. 300 proof. 2. Divide $600 proportionately among 4 men whose shares are to each other as 3, 4, 5, 6. 3_|_4 + 5 + 6=^18 18 : 600 : : 3 : 100 first man's share. 18 : 600 : : 4 : 133i second " " 18 : 600 : : 5 : 166| third " " 18 : 600 : : 6 : 200 fourth " " 3. Divide 450 shares of railroad stock among 3 persons iu proportion to the number of shares already held by them, A. owns 400, B. 200, C. 300. What number will each re- ceive ? 4. A., B., C, and D. invest $50,000 in a shipment to Cuba. A. invests $15,000, B. invests $20,000, C. invests $10,000, and D. invests $5000. They gain $30,000. What is each partner's share of the profits? 5. A., B., and C. do a piece of work for $140. A. does J, B. Jq, and C. -^Q. How much ought each to receive? 6. Gunpowder is composed of 76 parts of nitrate of potass, 14 of carbon, and 10 of sulpliur. How much of each in- gredient will be required to make 12 cwt. gunpowder? Ans. 9 cwt. 13li lbs. nitrate of potass. 1 cwt. 2 qrs. 20^^^ lbs. carbon. 1 cwt. 22 1§ lbs. sulphur. 7. A., B., and C. engaged in trade, and agreed to share the gains and loi^ses in proportion to the amount each invested, A. invested $5000, B. $8000, C. $7000. They gained $6600. What was each man's share? oO DISTRIBUTIVE PROPORTION. COMPOUND DISTRIBUTIVE PROPORTION, OR, DOUBLE FELLOWSHIP. 93. In Compound Distributive Proportion, each share is affected by different periods of time, or by different quantities or rates. lluLE. — Multiply each share hy the time^ or quantity^ or rate, hy which it is affected, and the products will be the pro- portional numbers. Then proceed as in Simple Distributive Froportion. EXAMPLES. 1. A. and B. entered into partnership. A. invested $100 for 2 months, B. invested $200 for 3 months. They agreed to divide the gains and losses in proportion to the capital of each and the time for which it was invested. Their gains were $280. How much was the share of each ? $100 X 2 mos. = 200 for 1 month! $200 X 3 " =: 600_ " 1 " 800 : 280 : : 200 : 70, A.'s share. 800 : 280 : : 600 : 210, B.'s share. 2. If an iron enameller manufactures a mixture worth $100, which he applies with equal thickness to the following lots, what does the mixture on each of the plates cost? 14 plates, 8 in. wide, 10 in. long. 8x10= 80 sq. in. each. 10 '' 10" " 20 <' " 10X20 = 200" " " 20 " 15" " 20" " 15x20 = 300" " " 14 plates each 80 sq. in. = 1120 sq. in. 9120 : 100 : : 1120 : 12.27+ 10 " " 200" " =2000" '• 9120 : 100 :: 2000 : 21.92 + 20 " *' 300" " =6000" " 9120 : 100 :: 6000 : 65.78+ 9120 100 : : 9120 100 : : 9120 100 : : 9120 $12.27, the cost of 14 plates. 1 plate costs 88 cts. nearly. 1 sq. inch costs |§ or \^\ cts. nearly. 3. A., B., and C. hired a pasture for $45. A. had 15 cows pastured 2 months, B. had 8 cows pastured 3 months, and G. had 9 cows pastured 4 months. How much should each pay? MEDIAL PROPORTION. 51 4. If 4 oz. gold 22 carats fine be mixed with 8 oz. gold 18 carats fine, how much fine gold will there he in 6 oz. of the mixture ? Note. — ?'Ae Jineneas of gold is uaually expressed by saying that gold it to many carats fine ; that is, that so many parts out of 2J^ are pure gold. 4 oz. X If = If oz. fin 3 gold. 8oz.XM = W" " " II + V¥ = ¥?^ = ¥' ^^^ quantity of fine gold in 12 oz. 8 + 4 = 12; then, 12 oz. : %^ oz. : : 6 : 4f. Ans. 4f oz. Or, By Analysis. — If there are ?/ oz. pure gold in 12 oz. of the mixture, there is -^^ of ^ or ff oz. in 1 oz. of the mixture; and in 6 oz. there are 6 times || = 2^^ or 4| oz. MEDIAL PROPORTION, OR ALLIGATION. 94, Alligation is the process of finding the value of a compound or mixture of articles of different values, or of forming a compound which shall have a given value, or one in which the articles shall be in a given proportion. 95. To find the average value of several articles when the quantity and rate are given. Rule. — Multiply/ each quantity hy its rate, and divide the sum of the products hy the sum of the quantities. The quo- tient will he the average value. EXAMPLES. 1. If 25 lbs. of tea worth 60/ per lb. be mixed with 25 lbs. worth 36/ and 40 lbs. worth 75/, what is one pound of the mixture worth? OPERATION. 25 lbs. @ 60/ = 15.00 25 <' " 36 = 9.00 40 " " 75 = 30.00 90 lbs. are worth S54.00 1 lb. is worth $54.00 -f- 90 = 60/. Ans. 52 MEDIAL PROPORTION. 2. If I luix 100 lbs. sugar worth 10/ per lb., 3G lbs. worth 15^ per lb., 80 lbs. worth 12/ por lb., and 40 lbs. worth 9/ per lb., what will one pound of the mixture be worth ? 96. To find what quantities of ingredients of different values will form a compound of a given value. EuLE. — Find the gain or loss on one of each ingredients then take as much of any ingredient as will make the gain and loss equal. Or, At the left of the column containing the rates, write the mean rate. Then connect each rate that is less than the mean rate with one that is greater, and write the difference opposite the rate with which it is connected. If more than one difference stand opposite to any numher^ add the differences together. The differences, or sums of difference^ written opposite any rate will denote the quantify of the ingredient to he taken at that rate. Note. — I. If any article is of the mean rate, it need not be linked, as it is of the average value, and will not aflfect the rate. II. Every pair of numbers joined, forms of itself a compound of the right proportions, whether taken separately, or in connection with others. This operation only gives the ratios of the several in- gredients. If all the quantities found, be multiplied or divided by the same number, they may be increased or diminished at pleasure, without affecting the proportion. III. When part, or all, of the numbers contain fractions, they may be reduced to a common denominator, and their numerators used. IV. A variety of answers may be obtained by linking differently, all of which will be correct. EXAMPLES. 1. In what proportion must a grocer mix coffee worth 15 f, 18/, 20/, 22/, and 24/ per pound, that the mixture may be worth 21/ per pound? MEDIAL PROrORTION. 53 FIRST OPERATION. By selling at 21/^ 1 lb. worth 15/ I gain 1 lb. worth 2 (( (< 18 20 Total gain, 10 22/ Hose 1/ 24 " " 3 Total loss, 4 To make the gains and losses equal, instead of lib. he can take 6 lbs. at 22f , or 2 lbs. at 24/. Or 3 lbs. at 15/ and gain 18j^ 3 " " 18 " *' 9 9 " " 24 " lose 27 SECOND OPERATION. £1 15— 18— 20 22j 24— 1-3 17 Proof. 3 lbs. @ 15 = 41 17 18 '■' 20 ■' 22 u 24 = 54 = 20 = 22 = 2.1G 21/ =$3.57 2. If a grocer wishes to mix tea worth 70/, 80/, $1, and ?>t.lO per pound, that the mixture shall be worth 90/ per pound, how many pounds of each must he use? Ans. 97. To find what quantity of each of the other ingredients must be used to make a compound of a given value, when the quantity of part, and the value of all, are given. E.ULE. — I^ioid the proportional numbers as in the last case, and divide the given quantity hy its proportional numher. Multiply each remaining proportional quantify hy the quo- tient so obtained, and the several products will be the rcquirec^ quantities. EXAMPLES, 1. How many poup^s of sugar, worth 8/, 12/, and 24/ per pound, must be mixed with 40 pounds worth 20^, that the mixture may be worth 22/^ per pound? 64 MEDIAL PROPORTION. OPERATION. Ah 24 JjJ 14-1-10 4-2 = 26 32 Then 2X20= AO%%f= 3.20 2X20= 40 "12 = 4.80 2X20= 40 "20 = 8.00 26X20 = 520 "24 =124.80 Ans. 640 "22 =$140.80 10, the limited quantity, divided by 2, the proportional quantity of sugar at 20 cts., = 20, the ratio. 2. How much wine worth $1.25, $1.30, and $1.40 per pallon must be mixed with 40 gallons worth $1 per gallon, 10 gallons at SI. 20 per gallon, and 5 gallons at $1.70 per gallon, that the mixture may be worth $1.35 per gallon? OPERATION. 40 gals, at $1. =40.00 10 " " 1.20 = 12.00 5 " " 1.70= 8.50 55 60.50 fl.lO — ,3, 11.25—, 1.40 5 6 5 25 + 10 + 5 = 40 55 Average price per gallon, §1.10. 55, the limited number of gallons, which average $1.10, divided by 5, the proportional quantity, gives 11 for the ratio. Then 5X11= 55 at $1.10 = $60.50 5X11= 55 " 1.25= 68.75 5X11= 55 " 1.30= 71.50 40 X 11 = 440 " 1.40 = 010.00 605 "$1.35=816.75 Ans. 605 gals. 1)8. To find the quantity required of each ingredient to make a compound of a given quantity, when the value of the ingredients is given. Rule. — Find the proportional parts as hcfore^ and divide the quantity of the mixture hy the sum of the proportional parts. Multiply each quantity hy the quotient thus obtained, and the several products loill he the required quantities of each. MEDIAL PROPORTION. 55 EXAMPLES. 1. A merchant received an order for 460 lbs. of sugar, at 15^ per pound. He has in his store sugars worth 10^, 12/, 20/, and 25/ per pound. How much shall he take of each to fill the order? OPERATION." 10 X 20 = 200 at lOf =$20.00 5X20=: 100 " 12 = 12.00 3 X 20 = GO " 20 = 12.00 6X20 = 100 " 25 = 25.00 23)460 460 " 15 =$69.00 20, average quantity. Ans. 200 lbs. at 10/, 100 lbs. at 12/, 60 lbs. at 20/, 100 lbs. at 25/. 99. If a quantity is at tlio average rate, it may be disregarded until the other quantities are found, and then enough of that quan- tity taken to make the whole equal to the required compound. 100. As each combination is perfect in itself, if the result is in mixed numbers, when whole numbers are required, we may select some multiple of the pairs, and thus make up the quantity sought. MISCELLANEOUS EXAMPLES. 1. What is the fineness of a composition consisting of 2 lb. 8 oz. gold 18 carats fine, 3 lb. 6 oz. 14 carats fine, 1 lb. 6 oz. 22 carats fine, and 1 lb. 6 oz. alloy ? 2. A cask contains 30 gallons wine worth S3 per gallon. What quantity will the cask contain after pouring in water until the contents are worth but $2.50 per gallon ? 3. A farmer wishes to mix rye at 70 cts. per bushel with corn at 90 cts. and oats at 50 cts. What quantity of each 1 :ust he take to make the mixture worth 75 cts. per bushel ? 4. A merchant wishes to fill a barrel which will hold 200 lbs. with sugar worth respectively 8 cts., 12 cts., and 14 cts. per lb., so that the mixture may be worth 13 cts. How much of each must he take ? 5. A man bought 50 bbls. flour for $500, — some at $8 per bbl., some at $9 per bbl., and some at $12 per bbl. How many of each kind did he purchase ? 56 PERCENTAGE. PERCENTAGE. 101. Percentage is a method of computing by means of a fraction whose denominator is 100. The term jjer cent, is an abbreviation of the Latin per centum^ which signifies hy the hundred. 102. The Rate per cent, is the number of hundredths. Thus, 8 per cent, is eight-hundredths, and may be expressed tS,, or .08, or 8%. ^y^ ==| „f _jj =^j, = .00125. Per cent, is simply the proportion of a hundred, and is not any of the denominations of Federal money : 10 per cent, is not 10 cents, nor 10 dollars, but ^^^ ; 10 per cent, of $50= $5 ; 10 per cent, of 85bbls. = 8Jbbls. Percentage is used in most commercial calculations, such as In- terest, Commission, Insurance, Profit and Loss, &c. 103. Case I. — To find the percentage of any number or "juantity, the rate per cent, being given. Rule. — Multiply the given number hy the rate per tent., and divide hy 100 (i.e. point off two decimals). EXAMPLES. 1. What is 8% of $640? 640 X 8 = 5120. Ans. $51.20. 8 % of 640 = -i-8^ of 640 = \y^o = 51.20. The percentage on sterling money and denominate numbers ia found after reducing the numbers to the lowest denomination given, or to tlie decimal of the highest, and then proceeding as in nimplo numbers. (See Decimals of Denominate Numbers, p. 28.) 2. What is 6 per cent, of £15 05. Qd. ? By Art. 43. 9s. 6^. =z £.475 15.475X6 =.92850 20 18.57000 12 0.84000 Ans. 18s. ^^Q^d. £15 9s. 6c?. = 37140^. 3714 X 6 = 22284 222Md. = 18s. 6j%%d. PERCENTAGE. 57 101-. Case II. — To find what rate per cent, one number is of another. Rule. — Annex two ciphers to the percentage, and divide hy the number on lohich the percentage is reckoned. Example. — What per cent, of 40 is 8 ? 800 -f- 40 = 20. 8 = ^5 of 40; f^ of 100 = 20. 2. A student at an examination in which 50 questions were asked answered 45 correctly. What per cent, did he answer ? 105. Case III. — To find a number when the value of a certain per cent, of it is known. llULE. — Annex two ciphers to the percentage^ and divide hy the rate per cent. Example. — 42 is 25% of what number? 4200 -f- 25 = 168. 2. A man sold a house, and gained $2850, which was 12} per cent, of what he received. How much did he sell it for ? 106. Case IV. — To find what number is a certain per cent. more or less than a given number. Rule. — When the given number is more than the required number, annex two ciphers to the given number, and divide by 100 PLUS the rate per cent. When the given number is less than the required number, annex two ciphers to the given number, and divide by 100 LESS the rate i^er cent examples. 1. What amount of gold, at a premium of 25 per cent., can I buy for $720 in currency? 100 + 25 = 125 ; 72000 -f- 125 = 576. Ans. $576. 2. Purchased merchandise and sold it for $1680, thereby losing 20 per cent. What did the merchandise cost ? 100 — 20 = 80 ; 168000 -- 80 = 2100. Ans. $2100. 68 PERCENTAGE. EXAMPLES IN PERCENTAGE. What is 6 ^ of S2G.45 ? 2G.45 X 6 = 158.70. Ans. $1.58/^. Note. — The figures on the left, after pointing off, are of the lowest de- nomination in the number multiplied. If there are cents in the given number, two more places must be pointed off for cents. 1. If a merchant who buys goods on 6 months' credit is allowed a deduction of 5 % for paying his bill within 30 days, what can he save on a bill of $560 ? How much on $3650? 2. If a man fails to pay his water rent until he is charged 12% for delay, how much will he lose if his water rent is $18.75? 3. If 1 % per month, counting from the time of payment, is allowed on all taxes paid before July 1st, and 1 % per month charged on all taxes remaining unpaid thereafter, how much more does A, pay than B., if B. pays his taxes Feb. 1st, and A. pays his taxes Nov. 1st, their tax-bills being each $180? 4. A merchant owes $6500, and his property is worth only $5425. What per cent, of his debt can he pay? 5. A man shipped 3800 bbls. of flour to England, and during a storm 19 bbls. were thrown overboard. What per cent, was lost ? 6. If a man pays an income-tax of $177.50, the rate being 5%, what is the amount of his income above the deduc- tion allowed by the government? 7. If I have $374.50 in currency, how much gold can I buy when it sells at a premium of 7 ^ ? 8. The population of a certain village increased in 5 years from 6000 to 7800. What was the average rate of increase per year ? 9. What is the difference to a salesman between selling a bill of $1000, on which there is a profit of $100 of which' ho receives J, and selling the same amount for a commission of 1 J per cent. ? What will be the difference to the firm if the goods are sold for $950 instead of $1000, and what the difference to the salesman ? 10. A merchant sold a lot of cloth at $3 per yard, and thereby gained 20 per cent. What per cent, would he have gained if he had sold the cloth at $3.75 per yard ? RATES OF COMMISSION. 69 COMMISSION, BROKERAGE, &c. 107. Commission is the charge made by Factors, or Com- mission Merchants, Brokers, and other agents, for buying and Belling merchandise, stocks, &c., making collections, or trans- acting any other business for another. It is usually calculated at so much per cent, on the amount of money received or ex- pended. 108. A Broker is one who makes a bargain for another, but who has not the goods in his possession. 109. Guarantee is the charge made for assuming the risk of loss from non-payment by the purchaser. 110. The Consignment is the quantity of goods sent to be sold; the person who sends them is called the Consignor; the commission merchant, or person to whom the goods are sent, is called the Consignee. (See Account Sales.) 111. The excess of the amount of sales or collections over the charges, is called the Net Proceeds. 112. Stocks are usually bought and sold at a certain per cent, on their j^ar value, or at so much per share. (See The Stock Exchange.) 113. Bates of Oommission adopted by Philadelphia Merchants. The charges for selling flour, grain, seeds, and other produce shall be 2\ per cent, on the gross amount of sales, and the incidental expenses, handling, cooperage, measuring, fire insurance, &c. sliall be charged in addition. That, in order to secure uniformity, these incidental expenses shall be as follows, viz. : — On flour, not less than 3 cents per barrel for labor, 3 cents per barrel for inspection and cooperage, 3 cents per barrel for storage. (See Storage, page 64.) On wheat, when received by rail, not less than 1 cent per bushel for measuring, storage, and labor. All other grain, when received by rail, 1^ cents per bushel for measuring, storage, and labor. 60 RATES OF COMMISSION. On wheat and other grain, when received afloat, 1^ cents per bushel for measuring, and actual expenses incurred when stored, which shall not be less than the charge made by rail. On seeds, dried fruit, butter, dressed hogs, feed and meal in bags, and other miscellaneous produce,, 2^ per cent, commission, and 1 per cent, for storage, measuring, &c. A charge of not less than |^ of 1 per cent, for fire insurance shall be added in all cases, except where sales are made afloat. After the first mouth shall have expired, the charge for storage shall not be less than 3 cents per barrel per month on flour, and ^ cent per bushel on grain, with ^ of 1 per cent, per month fire insurance. Rules. — In all cases where acceptances are made on produce, in anticipation of sales, the commission merchant shall be at liberty to sell, in order to meet the drafts at maturity. Delivery will be accomplished on the part of the seller when he places at the door of his warehouse flour or meal in a position to be removed by the purchaser's porters or stevedores ; and grain, when pointed out to the purchaser or his agent. The expenses of towing and wharfage of boats and vessels shall be paid by the purchaser of the cargo, when moved for his accommo- dation. RECEIVING COMMISSION. Cents. Bacon 50 Bark 50 Beef 50 Butter and Lard 50 Clay 50 Clover-seed 2 Coal 10 Corn Meal 3 do 12 Dye Woods 25 Flour 3 Grain, all kinds 1 Hemp 6 Hoop Poles 20 Indigo 8 do 4 Iron 20 Leather $1.00 Lumber 20 Nails 20 Plaster 10 Seeds 1 •^ ton. bushel. (( barrel. hhd. ton. bai-rel. bushel. bale. 1000. chest. ceroon. ton. ton. 1000 ft. ton. ton. bushel. Cents. Shingles 20*1^1000. Shot 6|^ keg. Soap, foreign 4 box. Staves 20 1000. Steel, in bars or bundles 20 ton. Sugar 15 hhd. do 5 barrel. do IJ bag. Tallow 25 hhd. Tea 4 chest. Tin, block 15 ton. Tobacco 25 hhd. do 6 bale. do. manufac 2 box. Whisky 25 hhd. do CJ barrel. Whiting 25 hhd. Wine 25 pip^ do ().J cask. Wood, dye 30 ton. Wool 12.; sacjs. RATES OF COMMISSION. 61 COMMISSIONS FOR PURCHASING. On produce generally, one-half the charges made for selling, and 2| per cent, on all other goods. COMMISSION FOR RECEIVING AND SHIPPING HENCE TO OTHER PORTS. Cents. Cents. Flour and Meal 6^"^ barrel. Corn Meal 25 hhd. Flour and Meal 31 hf.bbl. Grain, all kinds 1 %1 bushel. Peas and Beans 1 " Seeds, all kinds 3 " COMMISSION FOR LOADING MERCHANDISE IN CARS AND BOATS. On store goods and merchandise generally, 75 cents per ton. LEAKAGE AND BREAKAGE. On spirits, 2 per cent. ; ale, beer, and porter, in bottles, 10 per cent. ; all other liquors, in bottles, 5 per cent. EXAMPLES IN COMMISSION. 1. Received $245 for selling goods at a commission of 5%. How much did I sell ? 245 X 100 = 24500 24500 -f- 5 = 4900. Ans. $49.00. 2. A broker purchased for me 50 shares of railroad stock, of the par value of $50 per share. His charge was J%. How much did I pay him ? 3. A country trader buys through a commission merchant an invoice of goods for $2550. The commission merchant charges 2^ % for buying. How much must the trader remit to *pay for the goods and commission ? 4. Thomas & Sons sold for me, at auction, a lot of goods to the amount of $14,500. Their charges are as follows : — Com- mission, 2^%; guarantee, 2^%; advertising, $22.50; dray- age, labor, and storage, $32.50. How much is due me ? 5. A house was sold for $2400, which was 80 fo of its cost. What was the cost ? 6. Paid a broker $24 for investing money in bank stock for me, soiling at par at a commission of |%. How much did he invest ? 6 62 COMMISSION. 7. Paid a merchant 3 ^ commission, and received $3880 as net proceeds. What was the amount of sales ? 8. What number diminished by 3% of itself is equal to 796 ? 9. Received, as net proceeds of a consignment, $760, after paying 2^ ^ commission for selling. What was the amount of sales? 10. Received S224 dividend on 50 shares railroad stock, which cost $3200. What was the rate per cent. ? 11. An agent sold property for $18,240, and received $121.60. What was the rate of commission? 12. If I pay a commission merchant $125 for commission and guarantee on a sale of $2500, what rate does he receive ? 13. A commission merchant wishes to buy exchange with the net proceeds of a sale amounting to $714. The rate of exchange is 2%. How large a bill can he buy? Ans. $700 14. A Cuban merchant wishes to draw on New York for an amount which will leave him the sum of $6141.39, after pay ing a premium of 4^ % for negotiating and exchange. Foi how much must he draw ? Ans. $6430.77. 15. A merchant received $525, with which to buy goods He is to receive a commission of 2^% on the amount of pur- chase, for buying. How much is his commission, and what is the amount of purchases ? 16. I have remitted $3600 to my agent in Montpelier, with which to buy wool, first deducting his commission of 3^ for purchasing. How much will he expend for wool? How much will be his commission ? 17. Invested in wheat the proceeds of a consignment of flour, less my commission on both at 3%, which amounted to $60. What did I sell the flour for, and what did I pay for the wheat ? Ans. Flour, $1030, Wheat, $970." jn.o _ ^^^ =r^9j'7^, net proceeds of the flour. fgg of wheat + y«^ com. =f^^ of the wheat. Then yVff ^^ ^^^^ ^0"^ = loff <^^ ^^^® wheiit, and ^Vj ^^ *^6 flour equalled the wheat, and j^j of the flour equalled the commission, $00. 18. A commission merchant sold goods for $6262, and re* ived $150, which included a charge fo What rate of commission did he receive? ceived $150, which included a charge for freight of $9.34. COMMISSION. 63 19. Sold lumber on commission at 5%. Invested net pro- ceeds in dry goods at 2% commission. My wliole commission was $70. What was the value of the lumber and the dry goods ? Ans. Lumber, $1020, Dry goods, $950. Suggestion. — Net proceeds of lumber equal ■^^■^, or 95%. Com- mission on dry goods equals yf^ of 95% =l|f%. l^A -j- 5 = 6|f. Then, if 6ff % equals $70, 5% equals $51, 2% equals $19. 20. J. B. Myers & Co. sell for me a quantity of dry goods on commission at 6%. How much must be sold that my agent can buy flour with the proceeds to the value of $5400, after retaining his commission, for buying, of 2 * % ? Ans. 21. Sold goods at 2^% commission, which I invested in sugars, and sold them at a profit of 15 per cent., realizing a gain of $240. How much commission did I receive, and how much did the goods sell for ? 22. A merchant bought an invoice of grain, which, in- cluding 1| % commission, cost $5050.62^, and paid $15.25 for freight. He sold the grain at a profit of 15% on its first ^ost, and invested the proceeds in sugar, which he sold at 5% profit, receiving a note due in 48 days, including grace. This note he had discounted at 6 % , at bank. What was the cost of the grain, and how much were his profits ? Ans. Cost of grain, $4994.43; total profits, $916.66. The following transaction occurred in a Philadelphia com- mission house : — 23. A commission merchant received an order to purchase merchandise worth $1000, on which he paid $50 for drayage. He was to efi'ect insurance at the rate of 1% on 10% advance of total cost of merchandise, drayage, commission for buying, and cost of insurance, and was to receive 3% commission on total cost of merchandise, drayage, and insurance. What was the amount insured, and how much did he receive for commission, and how much for insurance? Ans. $1203.28, Com. $31.86, Ins. $12.03. Suggestion.— \% of 3% ^.0008, which added to 1%=.0103, which increased by 10% of itself equals .01133, the rate of insu- rance on $1. %\OoO increased by 3% of itself equals $1081.50, which increased 10% equals $1189.65. Then, to find the amount to be insured to cover $1189.65 and the insurance, or .01133 of itself, we divide $1189.65 by $1 less .01133, which gives us $1203.28. G4 STORAGE. STORAGE. Storage is chi.rged at a certain price per barrel, bale, box, etc., according to regulations adopted by the Chambers of Commerce or Boards of Trade of the different cities. All goods stored are subject to one month's storage. In some places, if they remain any part of a month they are charged for a full month ; in others, after the first month, if taken out within fifteen days, a half-month is charged ; if after fifteen days, a whole month. The owners of the goods pay for putting the goods in store, stowing away, and the expenses of delivery. When goods are received and delivered at the pleasure of the con- signor, the dues for storage are usually determined by an average. To compute storage. Rule. — Multiply the number of barrels, or other articles, first entered^ by the number of days between the time of entrance and the time of the first delivery, or second entrance. Then Multiply each balance by the number of days it cojitinues unchanged. The sum of all the products will be the number of articles in store for one day. To find the number stored for one month, divide the sum of the products by SO. Example. — What is the cost of storage, at 1/ per bushel per month, of wheat received and delivered as per following account, closed Oct. 2d, 1866 ? Account of Storage of Wheat received and delivered for account of A. Y. Rodgers Sf Co., St. Louis. Date. Received. Delivered, Balances. Days. Prodncta. 1866. July 2 200 ^00 9 isoo «» 11 150 60 6 250 «« 16 350 400 5 2000 " 21 300 100 20 2000 AURUSt 10 400 500 5 2500 '« 15 450 50 6 250 «« 20 50 0000 Septemb'r 5 200 200 6 1000 «« 10 100 300 5 1500 " 15 200 100 17 1700 1250 1150 30)13000 Bal. on hand :t.2, 100 433i 1250 1250 433i X ¥ = •?'•"-. Ans. INSURANCE. 65 INSURANCE. 114. Insurance is a contract of indemnity by which one party engages, for a stipulated sum, to insure another against a loss or injury to which he may be exposed. 115. The Insurer is the person who takes the risk. He is sometimes called the Underwriter, from the custom of individual insurers writing their names, together with the amounts for which they will be responsible, under a descrip- tion of the property insured. 116. The Premium is the sum paid for insurance, and is a percentage on the amount insured. 117. The Policy is the instrument containing the contract, and describes the property or person insured, and the terms on which the insurance is effected. 118. Insurance companies are generally incorporated bodies ; but persons, such as commission merchants, shippers, and others, insure, at times, as well as companies. 119. Mutual Insurance Companies are those in which the persons insured become members of the company, and liable to a certain extent for its losses; they also share in the gains of the company, if any. 120. Policies are of two kinds, — Open Policies^ and Closed or Valued Policies. 121. A Valued or Closed, Policy is one in which the amount insured is definitely determined at the time the insurance is effected. Houses, furniture, and goods in store are insured in policies of this kind. 122. An Open Policy is one upon which amounts yet to be ascertained and insured may be entered at different times. (See page 69.) They are used by persons who insure goods which are to be conveyed from one place to another. The person taking an open policy gives a note, called a Premium Notr^ to the insurance company, as security for the premium on the amounts he anticipates insuring before the Jate on which 6* 66 INSURANCE. the note matures. This note at maturity is returned to him on payment of the premiums on the amounts he has had in- sured. A nominal premium is mentioned in the policy when made out, but actual premiums are fixed at the time the risk is reported, and are regulated by a scale of prices arranged by the company. When the insurance is on goods to be imported from a foreign country, the value of the currency of that country is also stated. As it is customary to insure for about 10% more than the cost of the invoice, this is included in the valuation of the foreign currency. English money is thus estimated at $5.25 per pound sterling. When the insured ships goods, or receives information of goods shipped to him, he must notify the insurance company as soon as he is in receipt of bill of lading or other advice of shipment. Some open policies which insure invoices shipped abroad, contain the clause that "no risk shall attach until the amount and description of the same shall be approved and indorsed thereon by the company, and to be valued at the sum so in- dorsed;" but open policies designed to cover goods to be re- ceived will cover all consignments if reported immediately on receipt of bill of lading or advice of shipment. In all open policies, to the description of the property are added the words "lost or not lost," so as to include all goods not known to be actually lost. 123. To guard against fraud, property is not usually insured for its full value, and no more can be recovered than the amount of actual loss. The party insured must also have an interest in the property insured, and, when goods or furniture arc destroyed, must be able to give a full enumeration or description of the property. Dwelling-houses, and permanent property about the value of which opinions differ, and which deteriorate in time, may generally be insured for from one-half to three-fourths their INSURANCE. 67 estim&ted value ; goods at sea, or in transportation, from 5 per cent, to 25 per C3nfc. more than their cost or invoice price, in order to cover the expenses of freight, insurance, and a share of the profits; goods in store, at their cash value; but the goods are not usually specified until a fire has occurred. 124. Insurance companies will not insure more on any one risk than a stated amount, which usually ranges from $3000 to $20,000, according to the capital of the company insuring, and the hazard of the risk. They will frequently, however, take a larger amount, and then reinsure themselves for part in another company. 125. The rate for insuring varies according to the degree of risk incurred, either from original liability, or from the difficulty of preservation or recovery when fires take place ; and some property is so hazardous that insurance companies decline to insure it at any rate. On private dwellings the rates are about 2 per cent, for a perpetual policy, and 1 of 1 per cent, annually; goods at sea, from I per cent, to 3 per cent. The following rates are taken from those adopted by the New York Board of Fire Underwriters : — For insuring $100 in dry goods, groceries, boots and shoos, crockery, furs, leather, paper, wine and liquors, dry drugs, carpets, jewellers' stocks, from 55 to 95 cts. Retail stocks of tobacco and cigars, books and stationery, music and prints, organs, wood and hollow ware, hats and caps with manufac- turing, cabinet ware, paints and oil, toys, vessels in port, from 90 cents to $1.20 per $100. Wholesale drugs, steam tug- boats, steam and sail vessels, lumber-yards, from $1.25 to $1.65. Tar, naval stores, sugar-houses, from $1.50 to $2.50. 126. The advantages to commerce from insurance are im- mense. " Without the aid that it affords, comparatively few individuals would be found disposed to expose their property to the risk of long and hazardous voyages; but by its means inse- curity is changed for security, and the capital of the merchant whose ships are dispersed over every sea, and exposed to all 68 INSURANCE. the perils of the ocean, is as secure as that of the agricultu- rist/' The dangers from not being insured are so many and BO great that none but millionaires can afford to remain un- insured; and it is considered by some a moral duty to insure in all cases where the interests of creditors or of one's family are in danger from the omission of it. EXAMPLES IN INSURANCE. 1. What is the premium for insuring $4500 @ 1- % ? 4500 X 1^ = 67.50. Ans. $67.50. 2. What will it cost to insure a house for $2600 at a pre- mium of 2%, the policy and survey costing $1.50? 8. Effected insurance on a cargo from Liverpool, worth £1872 lis. 5c/., at a premium of 1^%. What is the pre- mium, the pound sterling being valued at $5.25? 4. If the premium on a perpetual policy is 2^, which will be returned on payment of 5% of the premium for every year the policy is held, what is the difference in the cost of a perpetual policy insuring a house valued at $4000, and returned at the end of four years, and an annual policy taken *t a premium of i of 1% per year for the same time? 4000@2%=80. 5%of80=r4. 4x4 = 16. 4000@i%=10. 10X4:= 40. 40 — 16 = 24. Ans. $24. 5. What is the cost of insuring furniture worth $3000, at a premium of 80 cts. per $100, the policy and survey costing $1.50? • 6. A merchant insured his goods to the amount of $5000 in one company at a premium of 1-%, and $2800 in another company at a premium of 1'%. The policies cost SI each. What did he pay in all? 7. It* I take a risk of $10,000 at a premium of 1^%, and reinsure it at 1^%, what will be my gain? 8. If I take a policy covering goods in my store for 1 year, to the amount of $15,000, at a premium of 1^%, and within that time I insure consignments to the amount of $23,000, at the same rate, how much do I gain ? 9. At i of 1 % per month, what will be the cost of in- suring goods worth $2800 which remain in store 3 months? OPEN POLICY. 69 o I. ►^ HJ CO B ^ a o p. C3 o. O 1 w p a V^ >-i o o : 9 o W o Oi fD O o P* H 1-8 n O P 2, < c> o P^ CJ- : ^ ^ t:^ S3 •< O K •< E2 t3 !3 2 o O ^ - O^ p o_ B 2, '"' : 2 t2j 2 !i^ hi o 2 fD Bt 1^ ^ 5'i" p p p &- i-< cu •- ►^ Pu P a> p o p O p o2, -i ^ i?r - ^ ^ T. - :: - :: p s a2H 1— » to 1— ' f-t to CO Is, O 03 OT CO >;^ OT CO H- ' ^5 to CO ?>5 fill ^i*^ px ^to ^p JO px o i«f:s "bO o ^ CO Oi b 00 "to b o o Ci v*^ o o -I Ox o "^ "^ ^ S. o o o o o o en o o "! ^ CO €6 to ^ on to = 5' Ox - ►1 - :; - - :: OM §s CD CO O O HJ !:> >-i *< M, ^^ >-j ^ -m oS"|►:? 2" o o\ ^^ ^1 C5 Ox b en ~Cn 2! CO CO to o CD Ci g o o on on pi o CO to 5 O-S O- o b b b b b ^T b-i b 'r' S o 3 P 3 o o o o o o OT o o \-t l_l K* ^ to y_l ^_, HJ H^ ^ lOjl-' ^ "^ S 1 ^ H3 to 1— ' CO h- ' ^;^ CO o •M )— 1 o to Ot o OT CD B S" 5 Oi to ;-i "-i 'i 1^ •^ 1-^ ■-s '-! R ■-J 2 S3 as a £3 p » P ^ p S *< «-rj •^, ^ Y- w^ ^ «^^^ 1 70 MARINE OR GENERAL AVERAGE. MAKINE OR GENERAL AVERAGE. 127. General Average means a contribution made by all parties concerned towards a loss sustained by some of the parties in interest, for the benefit of all. In such cases, the loss arising from the contribution falls within the provisions of the insurance policy. 128. No general average takes place unless it can be shown that the danger was imminent, that the sacrifice was volun- tary and considered indispensable for the safety of the rest, and that the portion which was saved icas saved hy reason of the sacrifice. 129. Particular Average Is any partial loss, without being voluntarily encountered, and is borne wholly by the owner of the property damaged. In cases of particular ave- rage, the indemnity is to be adjusted upon a comparison of the gross proceeds of the sound and the damaged goods, 130. Jettison (from the French jeter^ to throw) is the portion of goods thrown overboard. 131. Salvage is an allowance or remuneration made to those by whose exertions ships or goods are saved from the dangers of the seas, fire, or enemies. 132. The cargo, including the part sacrificed, is valued at the price it would have sold for in cash at the port of desti- nation. The ship, and freight, and every thing on board which pays freight, contribute to general average. The wages of seamen do not contribute, that they may have no interest in op- posing a sacrifice necessary to the general safety. From the freight | is usually taken (in New York X) for seamen's wages, pilotage, &c., to find its contributory value. In the valuation of repairs, masts, cables, &c., it is cus- tomary to deduct 1, — thus estimating the old as worth | the value of the new. MARINE OR GENERAL AVERAGE. 71 Statement of General Average of the " Fairweather/' Pereak J. Cooke, blaster, from New York to New Orleans, in consequence of losing part of her rigging hij a violent gale, in getting aground on Stirrup Key, and by throwing part of her cargo overboard, as appears by protest, &c. Amount of Losses. Paid Geo. Burton and Wm. H. Taylor, of the sloops Emily and Shamrock, for assistance in getting Tessel off, as per agreement, Protests, postages, stamps, Ac, Value of goods thrown overboard : Fosdick & Co.'s goods, G. Porchs' " Gustav Piaggio's " Freight of goods thrown overboard, A(^ustment of average, and certificate, $1800. 3840. 4000. 9640.00 6000.00 26.00 Total losses, $23670.00 Contributory Interests. Ship Fairweather, valued at Goods of Fosdick & Co., $12500. " " G. Porchs, 17250. " '« Gustav Piaggio, 4000. " " J. Burnside & Co., 5250. Total cargo vahied at, as per invoices, Freight, $24000, less %, = Rate of contribution, 23.67 per cent. $45000. pays $39000. $16000. 2958.75 40S3.07 946.80 1342.08 $100000. Particular Average on the Ship. Repairs, new masts, yards, &c., as per bills, Less J^ for new. Ship's value, $45000, at 6^^ per cent. =± 4275.00 1425.00 $2850.00 9231 3787 23670 20 GO The different parties, if fully insured, can recover from the insurance companies the amount contributed to the general 72 MARINE OK GENERAL AVERAGE. 133. The rules for adjusting averages — with all the inci- dents of general average, salvage, and the like — are different in different countries. In most commercial ports the calcula- tions are made by Adjusters of Averages, — a class of men who have a knowledge of the customs of the place and an ex- tended experience, both of which are necessary in order to have a full understanding of the subject. The proportions of general average are calculated as follows ; — 134. To apportion general average. Rule I. — Divide the sum of the losses hy the sum of the contributory interests, and multiply each contributory interest by the quotient thus found; the product will be the contribu- tion of each interest to the general loss. Or, lluLE II. — By Proportion. Sum of the \ . fsumof the! .. /each contributory") , f sum to be contributory interest/ " ( losses J " (. interest / " (contributed. MISCELLANEOUS EXAMPLES. 1. What sum must be insured, at a premium of 1' %, to cover the total loss, insurance included, of a cargo valued at $2731.25, charges $10.25, policy $1 ? 2. What will it cost to insure goods worth $3500, at a pre- mium of f ^, if the policy includes 10% advance on the value of the goods ? 3. I paid $32 for an insurance on goods worth $4800, shipped from Boston to Philadelphia. What rate did I pay ? Ans. 4. A merchant shipped a cargo valued at $15,000 from New York to Cuba, which he insured at 2^%. The addi- tional charges were $425. For how much must he sell the cargo to gain 20 % on the entire cost ? 5. Insured a cargo worth fr. 97,500, shipped from Havre to New York per the Marie Pierre. What was the cost of insurance at 1^%, if the franc was valued Tit 25 cents and the cost of policy was $1 ? Ans. $427.56. 6. Insured in the Girard F. & M. Insurance Company goods valued at $17,000, and paid $127.50. What was the rate if TAXES. 73 TAXES. 135. Taxes are sums of money assessed on persons, pro- perty, incomes, or products, usually for some public purpose. 136. When assessed on persons without regard to property, they are called Capitation or Poll Taxes; and in some places the payment of a poll tax is required before the privilege of voting is granted. 137. Property Tax is assessed on real and personal estate, and is sometimes apportioned at a certain per cent., but usually as so many cents on $100, or so many mills on $1. Real Estate includes immovable property, such as houses, lands, &c. All other property, such as money, notes, stocks, mortgages, furniture, tools, cattle, &c., is called Personal Property. 138. Taxes are also assessed by the United States Govern- ment on incomes, manufactures, sales, &c. 139. The persons who estimate the value of the property to be taxed, and apportion the taxes, are called the Assessors. MO. Before assessing taxes, it is necessary to ascertain the sum to be raised, including expenses for collection and the proportion which it is expected will be uncollectable. 141. To find what sum must be assessed to raise a given net amount. Rule. — Subtract the rate allowed for collection from fl, and divide the net amount to be raised by the remainder : the quotient wiU be the entire sum to be assessed. EXAMPLES. 1. What sum must be assessed to raise $950,000 net, allowing 5 % for collection ? Sl.OO — .05 ==: .95. $950000 -- .95 = $1000000, Ans. PROOF.~5%of$1000000 = $50000. $1000000 — $50000 = $950000, 74 TAXES. 142. It is also necessary to find the number of persons liable to pay a poll tax, if any; to estimate the value of all property, both real and personal, to be taxed, and to make an inventory of it ; to determine what portion of the tax is to be raised upon the polls, or articles of property upon which there is a specific tax (if any), and to divide it equally among them. The amount to be raised by a specific tax must be deducted from the total amount of tax to be raised. Then, 143. To find how much must be paid on each dollar of taxable property to raise the remainder of the tax, we have the following Rule. — Divide the amount to he raised, hy the amount of taxable property , less that part on which nothing can be col- lected : the quotient will be the answer. EXAMPLES. 1. The tax assessed by a certain town is 837,500; its pro- perty is valued at S2, 500, 000. What rate per cent, is the tax? and how much will be paid by a man whose property is assessed at $12,000? 37500 -- 2500000 = .015, or, 1^ cts. tax per dollar. 12000 X U% =$180, Ans. Proof. — When a tax list is made out, the amount of the taxes of all the individuals in it should equal the whole tax assessed. TAX TABLE AT THREE MILLS PER DOLLAR. % $ $ $ $ $ $ $ 1 pays .003 10 pay .03 100 pay .30 1000 pay 3.00 2 pay .006 20 ' ' .06 200 " .60 2000 " 6.00 3 '' .009 30 ' ' .09 300 '' .90 3000 '^ 9.00 4 " .012 40 ' ' .12 400 " 1.20 4000 <* 12.00 5 '' .015 50 ' ' .15 500 " 1.50 5000 " 15.00 6 '' .018 60 ' * .18 600 '^ 1.80 6000 '^ 18.00 7 '' .021 70 ' ' .21 700 '< 2.10 7000 " 21.00 8 " .024 80 ' ' .24 800 '' 2.40 8000 " 24.00 G " .027 90 ' ' .27 900 '^ 2.70 9000 '' 27 00 10 '' .080 100 ' ' .30 1000 '' 3.00 10000 " 30.00 TAXES. 75 2. A tax of $5130 is to be raised by a certain town; the property to be taxed is assessed at $430,000. There are 240 polls, each taxed $1. What amount must be levied, allowing 5% commission for collecting? what will be the tax on $1 ? and what will be the tax of each of the following persons? A., who pays a tax on $6000, and 1 poll. B., <' " " " " 5400, " 2 " C, " " " " " 1550, " 4 " OPERATION. Tax to be levied on the town, $5130. Rate of collection, 5%. 100 — 5 = 95. 5130 -^ .95 = 5400, the amount to be as- sessed. 5% of 5400 = 270, amount paid for collection. 240 polls at $1 = $240. Total amount to be raised, $5400 Less amount of poll tax, 240 Amount to be raised on property, 5160 5160 -- 430,000 = .012, or 12 mills on a dollar. A.'s tax, $6000 @ .012 ==« $72 1 poll, 1 Total, $73 B.'s tax, $5400 @ .012 = $60.80 2 polls, 2.00 Total, $62.80 O.'s tax, $1550 @ .012 = $18.60 4 polls, 4.00 Total, $22.60 3. How much tax will a person pay whose property is assessed at $6400, if he pays l|-% city tax, and 1 of 1% State tax, be- sides paying 5% United States tax on an income of $1800? 4. What rate of tax is required to raise $27,500 on pro- perty assessed at $1,850,000 ? 76 INTEREST. 5. What amount of taxes will a person pay whoso income is $12,800 per year, from which a deduction of S1900 is allowed for expenses, 5 ^ being charged on all incomes less than $10,000, and 10% on all over that sum; his city and State tax is 15 mills per dollar on property assessed at $75,000, be- sides paying a tax of $2 on his gold watch, a tax of $6 on his carriage, and a license tax of $10? INTEREST. 144. Interest is compensation for the use of money or value. The sum for the use of which interest is paid is called the Principal; the sum of the Principal and Interest is called the Amount. 145. Legal Interest is the rate established by law. Usury is interest greater than the legal rate, and is prohibited by law. In some States, however, parties are allowed to give and receive higher than legal rates by special contract. All interest in ancient times was called usury. 146. When no rate is mentioned, the legal rate is always understood. Debts of all kinds draw interest from the time they become due, but not before, unless specified. Interest on interest remaining unpaid is considered illegal. 147. The legal rate in most of the States, and on debts due the United States, is 6% per annum. In New York, Michi- gan, South Carolina, Wisconsin, Georgia, and Minnesota, it is 7%; in Alabama and Texas, 8 ^ ; Louisiana, 5% ; Cali- fornia and Kansas, 10%; and in Oregon, 12J%. 148. The legal rate in England and France is 5%; in Canada, Nova Scotia, and Ireland, 6%. 141). In Pennsylvania, commission merchants and agents of parties not residing in the State are authorized to enter into an agreement to pay a rate not exceeding 7 % on balances of "money remaining in their hands, and to receive a rate not exceeding that amount, for advances of monoy uiado by them COMPUTING TIME. 77 on consignments from persons living and transacting busi- ness beyond the limits of the State. 150. In Arkansas, Illinois, Iowa, Michigan, Mississippi, Mis- souri, and Tennessee, interest as high as 10% can be taken by special contract; in Louisiana and Florida, as high as 8%; in Minnesota, Texas, and Wisconsin, as high as 12 ^; in Califor- nia and in Massachusetts (since July 10, 1867), any per cent. 151. Most merchants settle their accounts semi-annually, or oftener, and the interest is calculated for days. The interest on Notes and Bonds which have some time to run, is gene- rally calculated for months and days. COMPUTING TIME. 152. To find the time between two dates, omit the day of the date and include the day of maturity. For instance, if Tuesday is the tenth day of the month, to the next Tuesday, the seventeenth, is seven days; but if both Tuesdays are included, we have eight days, if both are omitted, only six days. 153. When months are mentioned, they are construed to mean calendar months, by which is meant the time from one day in one month to the same day in another month. Notes or securities falling due on the 30th or 31st of any month which has only 28, 29, or 30 days in it, are considered to be nominally due on the last day of the month, and there- fore legally due on the 3d of the following month. For in- stance, a note dated November 30th, payable 3 months after date, falls due on the last day of February, and three days of grace make it payable on March 3d. Less than a month is reckoned at the rate of 30 days to the month, 154. When it is required to find the difference between two dates in years, months, and days, it may be done as in Sub- traction of Co npound Numbers. 78 COMPUTING TIME. EXAMPLE. What is the difference in time between July 15th, 1865, and September 19th, 1862 r* The earlier date is placed under the later, and the numbers of the months are written instead of their names. Tr. mo. da. 1865 7 15 1862 9 19 2 9 26 155. As the number of days in the different months varies, counting time by days is the only exact method, when the dates are less than a year apart. From Jan. 1, 1867, to July 1, 1867, is 6 mos., containing 181 days. " Sept. 1, " " Mar. 1, 1868, " 6 " " 182 " " Apr. 1, « " Oct. 1, 1867, " 6 " " 183 « « Mar. 1, " " Sept. 1, " " 6 " " 184 " 156. The number of days between two given dates may be found as in the following example : — What is the number of days between January 5th and July 3d? In Jan. 26 days. " Feb. 28 " dd the number of days in January " Mar. 31 « after the 6th to the days in the " Apr. 30 " intervening months, and the three " May 31 " days in July. " June 30 " " July 3 « Total, 179 157. Or, call each month 30 days, and correct by adding one for every month intervening which contains 31 days, and subtract two for February, except in leap-years; then but 1. In the example already given, from Jan. 5th to July 3d, there are five whole months, two of which contain 31 days, and one, February, contains but 28. They consequently average 30 days each, making 150, which, with 26 days in January and 3 days in July, make a total of 179. Time Tables will bo found useful fur ascertaining the ti'ue between different dates. (See Time Table, page 114.) COMPUTING TIME. . 79 158. It is sometimes desirable to know for what time to draw a note so that it will not fall due on a Sunday or a holiday. After finding the number of days, divide by 7 to obtain the number of weeks and days, then count the odd days from the day of the week on which the note is dated. In the example given, 179 days = 25 weeks and 4 days. If January 5th was on Monday, then July 3d will be four days from Monday, or on Thursday, 159. The following may be useful to those who have fre- quent occasion to draw notes : — 33 days = 4 weeks and 5 days, 63 days = 9 weeks, 93 days = 13 weeks and 2 days : therefore, A note at thirty days will fall due five days later than the day of the week on which it was given. A note at sixty days will fall due on the same day of the week. A note at ninety days will fall due two days later. 160. It is customary among business men, in reckoning in- terest, to consider the year as consisting of 12 months of 30 days each, or 860 days. As there are 365 days in a year, this gives -gl^, or y^^^ too much. The difi'erence is so small, however, that in ordinary transactions it is not noticed. The mercantile custom has in many cases been sanctioned by law. In New York, the law on this subject (Rev. Stat. vol. ii. p. 182) reads as follows : — "For the purpose of calculating interest, a month shall he con- sidered the twelfth part of a year, and as consisting of thirty days ; and interest for any number of days less than a month shall be esti- mated by the proportion which such number of days shall bear to thirty." INTEREST AT 6 PER CENT. 161. The interest on $1 for one year or 12 months = 6 cents. 2 " =1 cent. 1 month or 30 days = J cent, or 5 mills. 6 " =: 1 mill. Therefore, one-half the number of months equals the interest on 1 dollar, in cents; and one-sixth the number of days equals the in- terest on 1 dollar, in mills. 80 INTEREST AT SIX PER CENT. 162. To compute interest at 6 per cent. If the time is in months or years. Rule. — Multiply the principal hy one-lialf the number of months, and point off tivo decimah. If there are centa in the 2?rincipal, point off four decimals; the remaining figures will he the interest, in dollars. If the time is in Rule I. — Multiply the principal hy one-sixth the numher of days, and in the product point off three decimals. If there are cents in the principal, point off five*, the remaining figures vnll he the interest, in dollars. Or, to avoid multiplying by fractions : — Rule II. — Multiply the principal hy the numher of days^ and divide the product hy 6; then point off as in the pre- ceding rule. (See Cancellation, Art. 19.) 163. When the time is less than 1 month, the cents in the principal may be disregarded; when less than 2 months, all under 50c.; when less than 3 months, all under 33c. EXAMPLES. 1. What is the interest on $1875 for 7 months? 1875 X 3^ = 65G2^ Ans. $65.62*. 2. What is the interest on $4250 for 24 days ? 4250 X 4 = 17000 Ans. $17. 3. What is the interest on $5650.37 for 27 days ? 4. " '' $7250.45 " 3mos. 29days? 5. " '' $364.50 " lyr.4mos.12da.? 6. « " $1575.25 " 9mos. 17days? The notes, accounts-current, interest accounts, in another part of the book, will afford additional examples for practice. 104. To compute interest at any given rate. Rule I. — Find the interest at six per cent., and divide it hy 6; the quotient will he the interest at one per cent.; then multiply this interest hy the given rate. Or, INTEREST ON U. S. BONDS. 81 Rule II. — Find the interest at six per cent., and add to it or subtract from it in the same ratio as the given rate is greater or less than 6. For 7% add ^. " 8% " I «' 9fo " h or divide by 4 instead of 6. " 10^ take ^^ by annexing one cipher and dividing by 6. " 12^ multiply by 2, or divide by 3 instead of 6. For Sfo take |, or divide by 12 instead of 6. ** 4:fo subtr, i, or divide by 9 instead of 6. " 5% '♦ f Note.— As the interest for 60 days at 6 per cent, equals 1 cent for every dollar, interest at tliat rate can be found by add- ing or subtracting as the time is more or less than 60 days. EXAMPLES. 1. Find the interest on $1285. for 33 days at 7%. 2. " " $4825.60 " 90 '^ "9%. 3. " " S2726.35 " 3mos. 18 da. " 10% ACCURATE INTEREST. 165. To compute accurate interest. Rule. — Find the interest as in the preceding rulesj and subtract from it ^^part of itself ; in leap-year subtract ^j. NoTE.^^i^- equals a little less than 1^ cents for each dollar of interest. Or, Multiply the interest on the given sum for 1 year by the num- ber of days for which interest is required, and divide by 365. The quotient will be the required interest. This rule is equivalent to the following formula : — As 365 1 fThe number of ^ ("The int. on the) ( The > : ■< days for which > '• ■{ given sum for V : -^ required ) (_ int. is required j ( 1 year J (^ int. INTEREST ON GOVERNMENT BONDS. 1G6. By the ordinary metlio(Lpf computing interest at 6 ^ , the interest on $6000 is $1 per day, and the principal will double itself in 200 months. The difference to the United States Government between paying interest at the rate of 360 days to the year, and paying accurate interest, or at the rate of 365 days to the year, is $5 per year for every $6000. 82 INTEREST IN ENGLAND. The Five-Twenty Loan is over $950,000,000, and the interest on it more than $155,000 per day. The difference, on this loan, between usual interest and accurate interest, is nearly $2250 per day. The formula under the preceding rule is employed in the Treasury Department at Washington. EXAMPLES. 1. What is the interest on U. S. Bonds of $15000 from May 1st to July 17th, at G% ? From May 1st to July 17th = 77 days. Int. on $15000 for 1 year =: $900 ; 900 X 77 = 69300. 69300 -f- 365 = $189.86 Ans. 2. What is the interest on a Five-Twenty U. S. Bond of $1000 from Nov. 1st to Feb. 3d? Ans. $15.45. 3. What is the interest on a Ten-Forty U.S. Bond of $1000, bearing 5% interest, from March 1st to Aug. 10th? Ans. $22.19. INTEREST IN ENGLAND. 167. The legal rate of interest in England is 5 per cent., and parts of a year are counted in days at the rate of 365 days to the year. To compute English interest :— Rule. — Reduce the shillings and pence^ if any ^ to the deci- mal or fraction of a pound (see Art. 72) ; the7i — For Years — Midtiply the principal hy the number of years, and the product will he the interest, in shillings. For Months — Multiply the principal hy the number of months, and the product will he the interest, in pence. For Days — Multiply the principal hy the number of days, divide the product hy 73, and point off two decimals: the quo- tient will he the interest, in the denomination of the principal. Example. — What is the interest on £425 for 1 year, 3 months, and 10 days, at 5% ? 425.S., interest for 1 year. 106.25 " " 3 months. 11.64 " '^ 10 days. 542.89s. = £27 2s. llc^. Ans. PKOBLEMS IN INTEREST. 83 PROBLEMS IN INTEREST. 168. To find tlie principal, when the time, rate per cent., and interest are given. Rule. — Divide the given interest hy the interest on one DOLLAR ybr the given rate and time. EXAMPLES. 1. What sum invested at 6^ for one year will produce $360? Interest on $1, for 1 year, at 6% = .06. .06)360.00 = 6000 Ans. $6000. 2. What principal in 2 years at 7% will give $3556 ? 3. " " 3 " 6 mos. at 6% will give $470 ? 4. " " 6 " 8 " ^' 8% " $540? 5. « " 3 '■' 4 '' " 6% " $540? 6. What must I pay for real estate, producing $750 per year, that I may receive 6% on my investment? 7. What must I pay for stocks, paying a dividend of $345 yearly, that I may gain 9 ^ ? 8. What reduction must I obtain that I may purchase stocks of the par value of $8000, paying 6 % dividend yearly, to receive 8 % on what I invest ? 169. To find the rate per cent., when the principal, time, and interest are given. Rule. — Divide the given interest hy the interest on the prin- cipal at ONE per cent. EXAMPLES. 1. A house which cost $4800 rents, above expenses, for $264 per year. What per cent, does it pay on the invest- ment? Interest on 4800 at 1 % = 48. 264---48=:5i Ans. 5^%. 2. If I invest $3500 for 1 year, 2 months, and receive $490, what rate do I receive per year? Ans. 12^, 170. To find the time, when the principal, rate, and interest are given. 84 TRUE DISCOUNT. Rule. — Divide the given interest hi/ the interest on the prin- cipal, for ONE day; the quotient will be the required time, in days. EXAMPLES. 1. In what time will $5530.42 produce at6%? Interest on $5530.42 for 1 day = .921)30.42(33+. 2763 i 630.42 .921 + interest 2790 2763 Ans. 33 days. 2. How long will it take a sum of money to double itself at 6 ^ simple interest ? At 7 9^ ? At 8% ? 3. Invested $6000 at 6%, for which I received $750.42. How long was it invested ? 171. To find the principal, when the time, rate per cent., and amount are given. PtULE. — Divide the given amount hy the amount of ONE DOLLAR for the given rate and time. EXAMPLES. 1. What principal will amount to $1120 in 2 years, at Amount of $1 for 2 years at 6% = $1.12. 1120 ^ 1.12 = 1000 Ans. $1000. 2. What principal will amount to $1500 in 1 year, 3 mos., at5%? At7%? TRUE DISCOUNT. 172. Discount, as usually calculated, is the same as Simple Interest; but true discount is a deduction from an amount which is equal to the interest on the remainder at the same rate and for the same time for which the deduction was made. 173. The Present. Worth is the sum paid, or tlie value of the note, or debt, after the discount has been deducted. BANKING. 85 174. To find the Present Worth. Rule. — Divide the given sum hy the amount of one DOLLAR for the given rate and time. To find the discount, subtract the present worth from the given sum. EXAMPLES. 1. What is the present worth of $1360, due 6 years hence, @6%? Int. on $1 for 6 yrs. = .36 LOO Amount, 1.36)1360.00(1000 Ans. $1000. 2. What is the present worth of $1248, due 8 months hence, @ 6 % ? What is the true discount ? 3. What is the present worth of $162.50, due 6 months hence, @ 7%, and what the discount? BANKING. 175. Bank Discount is computed in the same manner as simple interest. It is deducted from the amount or face of the note when the note is discounted, and the remainder, called the proceeds, is placed to the credit of the person for whom the note is discounted. As the person offering the note can obtain the money immediately, and the note may remain unpaid until three o'clock on the day of its maturity, banks, generally, in reckoning time, include the day on which the note is discounted, as well as the day on which it matures. This, with the three days of grace, for which discount is also taken, makes /oMr more days than the time mentioned in the note. See, also, Transactions with Banks. 176. To compute Bank Discount. Rule. — Multiply the amount hy i the number of days, in- cluding the day of discount and the three days of grace, and in the product point off three decim,als. The above will give the interest at 6%' For any other rate, add or subtract in proportion as the given rate is greater or less than 6*^, as in Art. 164. 8Q BANKING. EXAMPLES. 1. Robert F. Hay, on May 2d, offered the following note, properly indorsed, for discount :— $525. Philadelphia, March 29, 1867. Sixty days after date, we promise to pay to Robert F. Hay, or order, at the Union National Bank, Five Hundred and Twenty-Five Dollars, without defalcation. Value re- ceived. * R. J. BiRNEY & Co. How much will he receive as the net proceeds of the note ? 60 days from March 29th is May 28th, which, with the throe days of grace added, gives May 31st. From May 2d to May 31st, including the day of discount, is 30 days. Interest on $525 for 30 days == 2.63 discount. 625 — 2. 63 = 522.37 net proceeds. Face of the note, $525.00 2. On Nov. 4th, offered for discount a note for $350. dated Oct. 15th, payable 3 months after date. How much cash will I receive? Find the time, discount, and proceeds of the following notes : — 3. DiscoTinted Nov. 4th, at 6/^. $750. Pittsburgh, Oct. 15, 1866. Three months after date, I promise to pay to the order of Jas. Dunlap & Co. Seven Hundred and Fifty Dollars, at the Citizens' National Bank, without defalcation. Value received. John F. Chase. 4. Discounted Jan. 12th, at 7%. Sl250./„»^. New York, Dec. 10, 1865. Sixty days after date, I promise to pay to S. H. Crittenden & Co., or order, Twelve Hundred and Fifty y^o Dollars, for value received. Henry T. Stewart. Discounted July 6th, at 6%, $450./^Qo . Trenton, N.J., May 10, 1866. Four months after date, I promit.e to pay at the First National Bank, to the order of Samuel T. Brown, Four BANKING. 87 Hundred and Fifty f^^ Dollars, without defalcation or dis- count. Value received. HaYWARD, GtLEASON & Co. 6. Discounted Sept. 18tli, at 6; $1875. Chicago, Aug, 15, 1866. Ninety days after date, we promise to pay to the order of Charles Manning & Co. Eighteen Hundred and Seventy-Five Dollars, for value received. H. Evans & Co. 177. To find how large a draft, at a given premium, may be purchased for a certain amount. Rule. — Divide the given amount hy ^i, increased hy the rate of premium. Note. — To find how large a draft may be purcTiased, when sold at a discount, divide the given amount by $1, less the rate of premium. EXAMPLES. 1. How large a draft may be purchased for $2020, at a premium of 1 ^ ? 1.01)2020(2000. Ans. $2000. 2. What is the face of a draft on New York to cost $18500, at 1 J % premium ? 3. For what amount may a draft on Cuba be purchased with $6430.77, at a premium of 4i% ? 4. A commisrsion merchant wishes to invest the proceeds of a sale, amounting to $4840, in a draft on St. Louis, which can be purchased at; a discount of f %. How large a draft can he obtain ? 178. To find the amount of a note that shall produce a given sum when discounted at bank. Rule. — Divide the given sum Inj the proceeds of ^1 for the given rate and time 88 BANKING. EXAMPLES. 1. For what sum must a note be drawn so that the discount for 63 days at G% may be deducted and the proceeds will be $1295 ? Interest on SI for 63 days = .0105. $1.0000 .0105 .9895)1295(1308.74 Ans. 2. llequired the amount of a note that may be discounted for 33 days, at 6 % , and $5500 received as the proceeds. 3. How large must a note be made to obtain $425.50 from a bank, for 42 days; discount @ 6% ? 179. Banks, by deducting the interest in advance, obtain a larger rate per cent, than they would by taking true discount ; and this rate increases in proportion to the time for which the discount is taken. The advantages of short credits, however, are generally considered to be more than an equivalent for any such excess that might be gained by extending the time. The following table shows the rates of interest obtained by banks, including the advantage from compounding the interest, when they discount notes at 6 and at 7 per cent., for any num- ber of months from one to twelve. It will be seen that when the time is less than two months — the usual limit for which notes are discounted in cities — the excess is inconsiderable. RATK. d a a a CO § a s a 8 a t- 00 a o 1 C4 6 per cent. 6.200 6.216 6.232 6.248 6.264 6.281 6.298 6.316 6.332 6.349 6 366 6.383 7 " " 7.272 7.295 7.317 7.339 7.362 7.385 7.408 7.432 7.456 7.480 7.505 7.627 At the nominal rate of 6 per cent., a bank receives, when it discounts a note for 1 month, -gl^, or .5,^-^''^ of 1 per cent. (^Il^of 1 percent, more than 6 per cent, per annum = J of ONE CENT on $99.50); when for 2 months, ^\, or 1^^^ per cent. ; when for 1 year, ^'^, or fi] 2 per cent. INTEREST ACCOUNTS. 89 INTEEEST ACCOUNTS. 180. In the settlement of mercantile accounts, interest ia calculated or not, according to custom or the agreement of the parties. Amounts are considered due at the time they should be paid in cash, or when they are equivalent to cash. 181. Bankers, Saving Funds, &c., charge and allow interest on dealers' accounts according to regulations which vary in different places. After the time is adjusted, interest is gene- rally calculated by one of the following methods : — FIRST METHOD. By Interest on each amount to tlie time of set- tlement. SECOND METHOD. By Product of Days. THIRD METHOD. By Daily Balances. 182. By the First Method, interest is reckoned on each amount from the day it is due to the day of settlement, and the balance between the debit and credit interest is added to that side of the account on which the amount of interest is the largest. When an amount is not due until after the day of settle- ment, a discount is allowed, and entered on the opposite side of the account in the interest column. The labor of making out such accounts is much lessened by the use of Interest Tables, such as Price's and others. 90 INTEREST ACCOUXTS. 183. By the Second Method, each amount is multiplied by the number of days from the time it is due to the day of settlement. The interest on the sum of the products for one day equals the sum of the interest on each amount taken separately. The interest on the balance of products for one day equals the balance of interest. When an amount is not due until after the day of settle- ment, it is multiplied by the number of days from the day of settlement to the day when it becomes due, and the product is placed in the column of products on the opposite side, in the same manner as discount is treated in the first method. 184. By the Third Method, the balance existing at any time is multiplied by the number of days it remains un- changed. The interest on the product for one day equals the interest on the balance for the number of days it con- tinues ; and the interest on the difference between the total daily balances for one day equals the balance of interest be- tween the debit and credit sides of the account, calculated on each amount separately, as by the first method. AVhen the rate of interest on one side of the account is different from the rate on the other, the interest is calculated on* the total daily products of each side separately for one day, and the balance of interest is taken. If the rate of in- terest on both sides of the account is the same, the difference between the footings of the debit and credit sides of the total daily balances may be taken first, and the interest reckoned on that for one day. This method is used by many bankers. Besides saving much labor, the total daily balances may be entered without delaying for any particular day, and can therefore be kept in readiness, and the account completed with very little addi- tional trouble, whenever the day of settlement is determined. For practice, nil the accounts given may be made out in each of the different methods, and may also be averaged by Compound Ave- rage with the same results as above. INTEREST ACCOUNTS. 91 OO o ^ £_i_j CD (-"JB C<5 ® ffl U O !z! a -* ^ g. "•-T' d y 2 g. 3 £ £ & 3 § ITS a,? ^P P'S' • g ll§ 8 S I B\^l o o ^ ., hi ^ ^^^^i9 ^!^ w . 2 S 2=-? "g ® 81 S 4331 4 5962 500 1 1 i ISISSSg g 8 8 8 r*- g; CO g g ^ p kJ .2 ^ H W u tri Ul t?d |I^ t^ w {^ ^ s p ^ 9i INTEREST ACCOUNTS. H Cl W !^ 1 P S ^ N o s? o w £3 C/J H « P o w =y .4 g s s CO O rl ?. ^ g ?? 3 ^ 8 88 -%— ^ISII s 1 %l l_ i II 'A'.'X. £ " « rt Si g5 1867. Feb. 5 May 23 July 5 9 1867. Feb. 6 May 10 June 2 July 1 67875 23400 10184 i r-l •g 1 S S IS ">* *; 8 "8 8 8 8S Sll s a ^ S S W >* o :(§)g@g(§)gfl £ PI- 00 c 1? 'S s s; » » >4 INTEREST ACCOUNTS. 93 THIRD METHOD.— BY DAILY BALANCES. The Western Saving Fund In account with Henry J. Rodgers. Interest to Feb. 28tli, 1867. 1867. 1867. Jan. 2 To Cash, 100 00 Jan. 7 By Check, 50 00 " 12 " " 250 00 " 22 " " 100 00 I'eb. 11 « (( 30 00 Feb. 1 « C( 40 00 •' 21 (I « 200 00 " 2i « u 50 00 i< 28 " Int. to Feb. 28, '67, 1 62 " 28 " Cash on settle- ment of acct. 341 62 581 62 __ 681 62 Balances. Time. 100, from Jan. 2 to Jan. 7, 5 days = 500 for 1 day. 60, " 7 " *' 12, 5 " = 250 " *' 300, u 12 " " 22, 10 *' = 3000 " «' 200, « 22 '* Feb. 1, 10 " = 2000 " " 160, Feb. 1 " *« 11, 10 " = 1000 « " 190, *' 11 '« " 21, 10 «' = 1900 '« " 840, " 21 '' «* 28, 7 " = 2380 '' « 11630 Total daily balance = $11630 for 1 day. Which, at 5% interest = $1.62. 3. What is the balance due on March 1st of the following account : — The National Saving Institution In account with Porter A. Florence, Dr. Amts. Cr, Amts. Days. Daily Balance. 1867. Jan. 2 17 To Cash By " 300 00 100 00 (( 27 To - By - 250 00 150 00 Feb. 6 7 To " 250 00 350 00 94 INTEREST ACCOUNTS. O O (— > ^ o o o o CO o o O o o o o O CO s o o o o o o o o 00 a O lO o o o lO o iO io k o t>- »o -^ CO (M »0 t- '^ O 00 tH (M ia 00 CO -* cq « rH -rH r-i t- CO 1-1 Si -rt M OI>l>»0'^OiOCO r-( tH (M CO CO rH O O O O O O O O O iO ^ O O l>THT-lCOCO(Mr-(lO -^^M rHIMCO rHrHrHi— I ^ r-< O ^- en 1 i; CO ' . A 1 ? fl -o b ^ a W 0^ ^ PARTIAL PAYMENTS. 95 PARTIAL PAYMENTS. 185. Partial Payments are payments made at different times of part of a Note, Bond, or other obligation, and should be indorsed upon the back of it. 186. When a partial payment is made before the deht is due, it cannot be apportioned part to the debt and part to the interest; but interest is allowed on the payment as well as on the principal to the time the debt becomes due. 187. Interest is not allowed to form part of the principal. BO as to carry interest. 188. The following rule for computing interest when partial payments have been made has been adopted by the Supreme Court of the United States, and by New York, Massachusetts, and most of the other States of the Union, and is called THE UNITED STATES RULE. I. The rule for casting interest when partial payments have been made, is to apply the payment, in the first place, to the discharge of the interest due. II. If the payment exceeds the interest, the surplus goes towards discharging the principal, and the subsequent interest is to be com- puted on the balance of principal remaining due. III. If the payment be less than the interest, the surplus of in- terest must not be taken to augment the principal ; but interest con- tinues on the former principal until the period when the payments, taken together, exceed the interest due, and then the surplus is to be applied towards discharging the principal, and interest is to be computed on the balance as aforesaid. Decision of Chancellor Kent, Johnson's Chancery Rep., vol. i. p. 17. Or, 189. Apply whatever payments may he made to the dischai^ge of the interest then due, and the surplus, if any, to the dis- charge of the principal. Note. — The principal remains unaltered when the payment is less than the interest at the time due. 96 PARTIAL PAYMENTS. 190. It will be perceived that, by the above rule, if a person owing the debt makes a payment less than the interest, he loses the use of it until the time when the sum of the payments exceeds the interest. For instance, the interest on $1000 is $5 per month. If $5 per month is paid, at the end of the year $1000 would still be due, while the interest on the payments, $1.65, would be lost. 191. The Connecticut rule differs from the United States rule only in this respect, that if a payment greater than the interest at the time due be made before the principal has been on interest one year, the person making it is allowed interest on it to the end of the year. If settlement be made within one year, interest is allowed on the payments from the time they are made to the time of settlement. EXAMPLES. 1. A bond was given for $1500, dated July 1st, 1863, pay- able 1 year after date, with interest. The following indorse- ments appear on the bond : — July 1st, 1864, Received Fifty Dollars. Jan. 1st, 1866, " One Thousand Dollars. How much was due at the time of settlement, July 1st, 1866 ? Original sum named in the bond, $1600.00 Interest from July 1st, 1863, to July Ist, 1864, First payment, a sum less than interest. Interest from July 1st, 1864, to Jan. 1st, 1866, Second payment, a sum greater than interest, 1000. 825.00 Balance for new principal, 675.00 Interest from Jan. Ist, 1866, to July Ist, 1866, 20.25 Amount of principal and interest due July 1st, 1866, $695.25 2. $3500. New York, Aug. 17, 1862. For value received, I promise to pay to Henry L. Barnes, or order, on demand. Three Thousand Five Hun- dred Dollars, with interest. Robt. H. Wilson. Indorsements. March 17th, 1803, One Hundred Dollars. July 17th, 1863, Fifty Dollars. Nov. 17th, 18G3, Three Hundred Dollars Feb. 17th, 1864, Fifteen Hundred Dollars. How much remains due August 17th, 1864? PARTIAL PAYMENTS. 97 192, As it is customary among merchants to settle their accounts yearly, or oftener, the following rule is much used by them, and is called THE merchants' RULE. I. First find the interest on the principal fi om the time it becomes due to the time of settlement, and add it to the prin- cipal, II. Find the interest on each payment from the time it was made to the time of settlement, and add the sum of the interest thus found to the sum of the payments. III. Deduct the sum of the payments and interest thereon from the amount of principal and interest, and the difference will he the balance due. Note. — This is substantially the same as the First Method for finding Interest on Accounts Current. (See Art. 182.) EXAMPLES. 1. $600. Philadelphia, June 12, 1865. For value received, on demand, I promise to pay to the order of Andrew W. Dawson, Six Hundred Dol- lars, with interest, without defalcation. Chas. C. Kunyon. Indorsements. August 12th, 1865, Keceived One Hundred Dollars. November 12th, 1865, '' Two Hundred and Fifty Dollars. January 12th, 1866, *' One Hundred and Twenty Dollars. How much was due February 12th, 1866 ? Principal, Int. from June 12th, 1865, to Feb. 12th, 1866, 8 mos., $600.00 24.00 Amount of note to Feb. 12th, 186G, 624.00 First payment, Aug. 12th, 1865, Interest 6 months. $100.00 3.00 Second payment, Nov 12th, 1865, Interest 3 months, 250.00 3.75 Third payment, Jan. 12th, 1866, Interest 1 month, 120.00 .60 Amount of payments and interest, 477.35 477.35 Balance due February 12th, 1866, 9 $146.65 98 INTEREST TABLE. 2. $350. Cleveland, May 9, 1865. Six months after date, I promise to pay to the order of James Brown & Co., Three Hundred and Fifty Dol- lars, value received. Edward S. Long. Indorsements. July 12th, 18G6, Received Seventy-Five Dollars. Oct. 27th, 18G6, ** Two Hundred Dollars. How much was due Jan. 3d. 1867 ? TABLE Showing in how many years a given principal will double itself. AT COMPOUND INTEREST. AT SIMPLE BATE. INTEREST. Compounded Compounded Compounded Yearly. Half-Yearly. Quarterly. 1 100. 69.666 69.487 69.400 u 66.66 46.556 46.382 46.298 2 50.00 35.004 34.830 34.743 2i 40.00 28.071 27.899 27.812 3 33.33 28.450 23.278 23.191 3J 28.57 20.150 19.977 19.890 4 25.00 17.673 17.502 17.415 4J 22.22 15.748 15.576 15.490 5 20.00 14.207 14.036 13.946 5i 18.18 12.946 12.775 12.686 6 16.67 11.896 11.725 11.639 6J 15.38 11.007 10.836 10.750 7 14.29 10.245 10.075 9.989 7i 13.33 9.585 9.914 9.328 8 12.50 9.006 8.837 8.751 8J 11.76 8.497 8.346 8.241 9 11.11 8.043 7.874 7.788 n 10.52 7.638 7.468 7.383 10 10.00 7.273 7.+ 7.+ AVERAGE OF PAYMENTS. 99 AVERAaE OF PAYMENTS. 193. The average of several numbers is that number each would be if their sum was divided equally. Thus, the average number of yards in four pieces of cloth, one containing 24 yards, one 36 yards, one 38 yards, and one 42 yards, is 35 yards. The total number of yards equals 140, which, divided by the number of pieces, equals 35, — the average number of yards in each piece. 194. Average or Equation of Payments is the method of finding the time when the payment of several sums, due at difi"erent times, may be made at once, without loss of interest to either party. 195. Accounts are settled both by the methods given in Interest Accounts and by averaging. When several bills of goods are sold on credit, and become due on different dates, instead of settling each bill separately as it becomes due, it is customary to average the time, and settle the amount of all the bills at the averaged time. This saves the labor of com- puting interest on the several bills. 196. When all the amounts are alike, the average time is found by adding the different terms of credit together and dividing their sum by the number of the amounts. This, however, is seldom the case, and other rules have been found necessary. 197. To find the average time when all the terms of credit begin at the same time. Rule. — Multipli/ each amount hy its term of credit, and divide the sum of the several products hy the sum of the debts; the quotient will be the average time of credit. 100 AVERAGE OF. PAYMENTS. EXAMPLES. 1. A merchant purchases goods, January 6th, amounting to $900 : $300 i)ayablc in 6 months, $300 in 8 months, $300 in 10 months. ^Vhcn may the whole be paid without loss to either party ? $300 for 6 months == 1800 for 1 month, 300 " 8 " =2400 " " 300 "10 " =3000 " " 900 )7200 " " Ans. 8 months. $900 at the different terms of credit equals S7200 for 1 month, or as many months as $000 is contained times in $7200, which is 8 times. Therefore, if the merchant gives his note payable 8 months after January 6th, it will be equivalent to giving three notes payable according to the terms of credit first proposed. Note. — If the result contains a fraction less than a day, reject it; if it is more, add one to the number of days. Also, when the cents are less than 50, disregard them; when more, call them $1. 198. The accuracy of the above rule has been questioned. The author of this book has in his possession eighteen differ- ent Arithmetics, some of them excellent ones, in which the rule is stated to be erroneous. The following example is generally used to illustrate its inaccuracy : — "If a man owes me $200, $100 payable now and $100 pay- able in 2 years, what is the equated time ? Ans. 1 year." It is said that this is incorrect, because I lose the interest on $100 for 1 year, which is $6; but for the other hundred I gain only the true discount, $5.66-|-, making a difference of nearly 3-1 cents. ^ Or, for the first payment I should receive $100 and interest for 1 year, which is $10G ; and for the $100 paid 1 year be- fore it is due, I should receive the present worth of $100, which is $94.33|i, making a total of $200.33|J, or 34 cents more than I receive by the usual method. The fallacy is in supposing that $5.66 is all that I gain for the $6 which I lose; lor if I receive the discount 1 year be- fore it is due, it is clear that I gain the interest on it for 1 year; and the interest on true discount is always equal to th.o AVERAGE OF PAYMENTS. 101 difference between true discount and interest. Interest on $5.6.& for 1 year = 34 cents ; $5.66 -\- .34 = $6.00. Again, if I am not paid the $100 due now until 2 years have elapsed, I ought to receive as interest $12; if I receive $200 at the end of the first year, I gain the interest on $200 for 1 year, which is $12, the same as before. Interest on $200 for 1 year is the same as interest on $100 for 2 years. ^ 199. The following has been given as the true rule for the Equation of Payments: — ^'■Find the present worth of each deht^ then find the time at which the sum of the present worths will amount to the su7n of the debts; this gives the true time." EXAMPLE CALCULATED BY THE "TRUE RULE." Interest at 4- per cent. Amount. 1080 G960 Time. 2 years 4 " Present Worth. 1000 6000 8040 7000 7000 1040 disc't. Interest on $7000 for 1 year, $280. 280)1040(3 yrs. 8f mos. For $7000 to gain $1040 will require 3 yrs. 8 mos. 174 days. SAME EXAMPLE. Interest at 40 per cent. Amount. Time. Present Worth 1080. 2 years 600. 0960. 4 " 2676.92 8040. 3276.92 3276.92 4763.08 disc't. Interest on $3276.92 for 1 year = 1310.77. 1310.77)4763.08(3 yrs. 7 mos. 18 days. Difference in results, 29 days. 9* 102 AVERAGE OF PAYMENTS. As the rate of interest ought not to affect the result, the accuracy of this **true" rule is questionable. Even if it were correct, the amount of labor required to find the average time by this method is BulBcicnt to prevent it from coming into general use. The present worth is not in exact proportion to the time and amount due. The true discount of $500 for 1 year is not the Bame as the discount of $100 for 5 years. MISCELLANEOUS EXAMPLES. 1. If A lends B $300 for 4 months, how long ought B to lend A $G00, to equal the favor? Ans. 2 mouths. 2. If I owe $400, payable in 6 months, and pay SI 00 im- mediately, how long may I keep the balance as an equivalent? Ans. 8 months. 3. A man bought goods at different times to the amount of $10,000, which are due per average July 1st. He wishes to give 4 notes in payment, due 1 month apart. When ought they to mature, to equal the average? Ans. May 15th, June 15th, July 15th, Aug. 15th. 200. To find the average time when the credits begin at different times. Rule I. — Find the date when each debt becomes due. (See Time Tables.) Find the time intervening between the earliest of these dates and the date of each succeeding amount. Multipli/ the amount first due by 0. Multiphj each succeeding amount by the time intervening betiDCcn the earliest date and the time the amount becomes due. Divide the sum of the products by the sum of the debts; the quotient will be the average time required. Add this average time to the day of maturity of the amount first falling due, for the day of payment. Taking the time from the date of maturity of the amount first due, and the terms of credit as extending to the dates when actually due, makes the process similar to that of the preceding rule. AVERAGE OF PAYMENTS. 103 Note. — ^When a purchase is made for cash, it is due on the day of the purchase. "When the term of credit is the same for each amount, labor may be saved by averaging the dates of the purchase and adding the term of credit to the average date so found. When all the debts have the same term of credit except one or two amounts which have no credit, add inter- est to those amounts for the general term of credit, and then average as before. For finding the timej see Interest; also Time Table. EXAMPLES. 1. Required tlie time wlien tlie amount of the debts as below stated becomes due per average. Jan. - 6, $300 G mos. July 6. Apr. 10, 200 6 " Oct. 10. May 7, 400 3 «« Aug. 7. Time from. July 6 to Aug. 7, 32 days. July 6 to Oct. 10, 96 days. Statement arranged. Due. Amount. Time (in days). Product. July 6, 300 00000 Aug. 7, 400 X 32 12800 Oct. 10, 200 X 96 19200 900 ) 32000 (35f Ans. 36 days from July 6th is August 11th. 20L ABBREVIATED METHOD. The cents and dollars may be disregarded, in averaging, without any important change in the result. EXAMPLE. Due. Amount. Time. Amount, omitting dolls, and cents. Product. Jan. 5, $372.50 X $37 — 000 " 15, 264.25 10 X 26 = 260 " 25, 227.50 20 X 23 = 460 " 30, 329.10 25 X 33 119 ^=^ 825 )1545(12ii;. 1U4 AVERAGE OF PAYMENTS. USUAL METHOD. 372.50 X = 000000 264.25 X 10 = 264250 227.50 X 20 = 455000 329.10 X 25 = 822750 1193.35 )1542000(12ifl|98o. Ans. Jan. 18fh, by both methods, the difference being only about -J f g of a day. 202» By Interest. — Find the interest on each amount /or the time obtained as he/ore ; then Find how long it will take for the whole debt to gain that amount of interest, the result loill he the average time. Note. — The equated time will be the same, whatever may be the rate of interest : we can, therefore, take that rate which is most convenient. Interest tables can also be profitably used. EXAMPLE UNDER RULE I. Due. July 6, Aug. 7, Oct. 10, Amount. 300 400 200 $900 Days. 32 96 Int. at 6^. 000 2.133 3.200 S5.333 Interest on §900 for 1 day = .150. For $900 to gain 5.333 requires ($5,333 ~ 150) 35//jj days. 36 days from July 6th = Aug. 11, Ans. as before. 2. Calculate the above at the rate of 12 per cent. 3. When shall a note to settle the following account be made payable ? Henry Field To James L. Edwards Dr, 1867. Mar. Apr. (< May 3 4 IG To Mdse @, 3 mos., 30 days, 60 " CO " as per bill rcndei (( (( (( (< •ed, 250 100 300 420 1070 00 00 00 00 00 AVEIUGE OF PAYMENTS. 10^ Due. Amount. Time. lut. at 12 per cent. May 4, 100 000 June 3, 250 30 2.500 June 15, 300 42 4.200 June 30, 420 57 7.980 For $1070 at 12% to gain 14.680 will require 41 days; 41 days from May 4th is Jane 14tli. By taking J of the number of days as a multiplier, interest at 12% for 1 day on $1070 = .356f . 203. ABBREVIATED METHOD, BY INTEREST. Labor is saved by the use of the following rule in finding the lime when due. Rule. — Count the time from the FIRST day of the first month given. Set opposite each month the numher of months intervening between it and the first month. This numher added to the term of credit, with the day of the month opposite to which it is set, will give the time for which to calcidate interest. TJien calculate interest for the months and days thus found, at 12 per cent., in the same manner as in the previous rule. example. Date of Sale. Time of Credit. Amount. Jan. 6, 3 mos. $300 Feb. 12, 4 " 400 Mar. 18, 3 " 250 statement. A^«„r.t No. of Months Total Time, Amount n -, . , ' from 1st mo. mos. days. $300 3 6 400 1 5 12 250 2 5 18 Int. at 12 per cent ■ .600 = Int. 6 days, 9.000= " 3 mos. ' 1.600= " 12 days. 20.000= " 5 mos. ' 1.500= " 18 days. 12.500= " 5 mos. $950 Total Int. 45.200 106 AVERAGE OF PAYMENTS. Interest on amount of debt, $950, for 1 mo. @ 12 fo =^$9.50. 9 50)4520(4 mos. 3800 720 30 days in a month. 950)21G00(22f^ days. Average time, 4 mos. 23 days, which, counted from Jan. Ist, gives May 23d, Ans. BY USUAL METHOD. Amount When due. Days. Product. $300 Apr. 6 000 400 June 12 67 2C.800 250 " 18 73 18250 950 950)45050(47 days. 47 days counted from April Gth, gives May 23d, as before. By the abbreviated method, all the labor performed appears in the operation ; but in the usual method only a part of the work is written. The abbreviated method is used to a considerable extent in New York, Philadelphia, and Boston, on account of the labor saved in counting time and in reckoning interest. Some have claimed that results may be obtained by this method with greater facility than by the use of Equation Tables. In some instances, the result will not exactly agree with that obtained by the use of days for the time between the dates when due, from the fact that some months contain more (lays than others ; but in ordinary cases the difference will be .but a trifle, while the labor of averaging is very much diminished. The correct time may be obtained by addiii Tj;^"',^^"- Int at 12 per c.„.. Jul7v2, 3mos. 35100 1 4 12 { «*'«o^ '"''i^* r^ Aug. 15, Cash 260 2 2 15 { ?;°fo " i| Z ' r 24.500 " 7 mos. Oct. 10, 3 mos. 350 4 7 10 j 1.050 " 9 ds. $700 t .117 '< 1 day. Total credit interest, $36,317 112 AVERAGE OP ACCOUNTS. Timo of Credit. Am't. 1866. June 15, 3 mos. $200 Aug. 9, 3 " 400 Sept. 18, 1 " 300 900 700 DEDIT SIDE OP THE ACCOUNT. No. mos. from Total Time. earlieat mo. mos. days. I"*' ** ^^ per cent n Q ir./ 6.000 int. 3 mos. „ K 0/20.000 " 6 mos. "^ o yj J 200 ♦' 9ds. n . TQ? 12.000 «' 4 mos. "^ * ^"t 1.800 " 18 ds. Total debit int. 42.000 " credit " 86.317 Bal. of account, $200 Bal. of interest, $5,683 Interest on $200 for 1 month = $2. 5.683 H- 2 = 2 months 25 days. 2 months 25 days forward from June 1st is Aug. 25th, Ans. For additional practice, average the examples already given by each of tlie dilFerent methods. Average the following Account Sales : — Account Sales of Merchandise for joint account of Newhall, Hart & Co., H. Foster & Co., and Ourselves. 1866. April Sold Leonard Barker & Co., @ 6 mos. : — <@> 15 hhds. Cuba Sugar, 25,422 lbs., @ 16c. <^ 32 half-chests Oolong Tea, 1805 lbs., tare 480 = 1325, @ 1.10 CHARGES. Fire Ins. on $0000 @ 1^ % , $90.00 Cooperage, AVeighing, Labor, &c., 17.37 Com. and Guar, on $5525 @ 5%, 276.25 Net proceeds due per average, $5141 I Paul & Thompson $4067 1457 $5525 383 E. E. New York, April 9th, 1866. Note 1. — Take the sales as the credit side, and the charges as the debit Bide. 2. Accounts Sales are averaged to know when the proceeds maybe paid without charging interest to cither party. AVERAGE OF ACCOUNTS. 113 Average the following accounts :- Dr. Parker Burton. Dr. Ans. Balance $100, due per average, E. P. Lossing & Go. Cr. 1866. 1866. — - May 22 To Mdse at 3 mos., 500 00 May 25 By Cash, SCO 00 " 29 u u 250 OC June 9 " Sundries, 400 00 June 10 " 30 days, 150 00 July 2 " Cash, 100 00 Ck. 1866. 1866. Mar. 10 To Mdse. (net) 250 75 Mar. 20 By Cash, 250 75 " 15 " " @ 3 mos., 187 50 " 2 " Draft @ 30 days. 120 00 Apr. 14 " " 4 " 262 25 Apr. 26 " Cash, 150 00 May 24 « " 3 " 465 60 May 24 " Sundries, 50 00 The following table will be found useful when averaging accounts. To find the time between two dates : — Look on the left for the month contai^iing the earlier date, and on the same Hue, to the right, for the month containing the later date : the number of days under the name of the month, or the number of months at the top of the column, will give the required time, if both dates are on the same day of the month. If the day of the month of the later date is different from that of the earlier date, add or subtract, as the case may be. To find the day which is a given number of days after a certain date : — Find the number of days in the table, opposite the month, containing the given date whicb is next larger than the given number of days ', subtract the given number of days, and count back from the same day of the month above the number taken, as the day of the month of the given date. For example, to find the day which is 144 days after June 28th, look opposite June for the number next greater than 144, which is 153 in Nov. 144 from 153 = 9; and 9 days back from Nov. 28th brings us to Nov. 19th, the required date. 10* 114 TIME TABLE. ^ I I ^1 CJ so ill So ^ CO = 52 .:-§ ^4 J*CO s« 3C0 tfco i s GO Ii Ii 1^ SpcO i ii 64 a4 f^ ^22 S^^ ll n o s to 1 ll ^3 ^ CO i4k4 Is pi i s §■■8 Si IS ^B as /•s 44 ^c4 sf^ i ll ^1 1^ la 1 j4 ej-a ,^^ /^ 1^ ^^ '^B Is -r-5 Ii i =1 ll >-SrH 05 It It ll ii 4 JSP sg i as-o a-c ll fHl -IS it CO to |t 4 o tH the gramme. 251. Silver is the legal standard of value in France. The franc in silver is valued at 9.384 pence sterling. The value of the franc in gold is 9.516 pence sterling, giving fr.25.22 for £1 sterling. The United States Custom-House valua- tion of the franc is 18.6 cts.; United States Mint price, 19.6 cts. 252. The mint standard for both gold and silver is y^^ pure and y^^ alloy. The gold coins are the napoleon, of 20 francs, and the 100, 50, 10, and 5 franc pieces. A kilogramme of standard gold is coined into 155 twenty- franc pieces. The silver coins are the silver napoleon, of 5 francs, and the 2, 1, J, and \ franc pieces. The copper or bronze pieces are 10, 5, 2, and 1 centimes, weighing, respectively, 10, 5, 2, and 1 grammes. 253. Accounts were formerly kept in livres tournoise, with its subdivisions of the sou and denier. 12 deniers = 1 sou or sol, 20 sous = 1 livre tournoise, 24 livres = 1 louis-d'or^ 3 livres = 1 ecu or crown, 81 livres = 80 francs. WEIGHTS. Gramme = 15.432349 grains Troy. The kilogramme (1000 grammes) is the weight most fre- quently us«d in commerce, and is equal to 2.679227 lbs. (2 lbs. 8 oz. 3 dwt.) Troy; or, 21.204621 lbs. (2 lbs. 3 oz. 4.652 dr.) avoirdupois. A kilogramme is generally taken as 2^ lbs. 373 J grammes = 1 lb. Troy. 453| grammes = 1 lb. avoirdupois. 1 cwt. = 50.80234 kilogrammes. 100 myriogrammes = 1 ton, 20^ lbs. 1 quintal m^trique =1 100 kilogrammes. Note. — At the U. S. Post-Office, 15 grammes are taken as i oz. 12 131 WEIGHTS AND MEASURES OF FRANCE. MEASURES OF LENGTH. 1 METRE = 39.371 English inches. 1 decimetre = 3.9371 " 1 kilometre = 0.62138 miles. 1 Eng. mile= 1.609036 kilometres. Old Measure. — 1 aune = li yds. 1 brace = f yds. See Art. 73. Merchants usually reckon the metre as one and one-twelfth yards. MEASURES OF SURFACE. 1 ABK = a square decametre = 119.6046 sq. yds. 1 centiare = 10.76441 sq. ft. 1 " = 1.196046 sq. yds. 1 hectare = 2 acres, 1 rood, 36 perches. 1 acre, Eng.=: .40466 hectares. 100 sq. ft. = 9.28987 sq. metres. MEASURES OF CAPACITY. 1 LiTKB = 61.02803 cubic inches. 1 " = 2.1135 wine pints, or 1.7608 imperial pints, or 908 qts. dry measure. 1 hectolitre = 3.53171 cubic ft. = 22.01 imperial gals., or 26.419 wine gals., or 2.839 Winchester bus. MEASURES OF SOLIDITY. 1 STERE or kilolitre = 35.31714 cubic feet = .2759 cord. 1 *« r= 1.308042 " yds. 100 cubic inches =16.38592 " centimetres. 2M:, The terms of the Metric System are now generally used by scientific men. Congress, by act of July 27, 18G6, aade it lawful in contracts and in legal proceedings to employ ihe weights and measures of the Metric System; and Great Britain, in 1861, passed an act authorizing it3 use. FOREIGN MONEYS OP ACCOUNT. 135 SYNOPSIS OF FOREIGN MONEYS OF ACCOUNT. 1 florin = .40 1 florin = .40 M°°^y ^* Dolls, eta. Amsterdam, 5 cents = 1 stiver, 20 stivers = 1 guilder or florin. Berlin, 30 silver groschen = 1 thaler. 1 thaler = .69 Bremen, 5 schwaren = 1 grote, 72 grotes = 1 rix-daler, 5 rix-dalers = 1 louis-d'or. 1 s. daler = .79|- Calcutta, 12 pies = 1 anna, 16 annas = 1 rupee. 1 rupee = .44J Christiania, 120 skilling = 1 specie-daler. 1 s. daler = 1.06 1 banco rix-dollar = .39|. Constantinople, 40 paras = 1 piastre, 100 pias- tres =1 medj idle. 1 medjidie =3.35 Copenhagen, 96 skilling = 1 rigsbank daler. 1 s. daler = 1.05 1 banco rix-dollar = .55. Frankfort, 60 kreutzer = l Zollverein florin or guilder. Genoa, 100 centesimi = 1 lira Italiana. 1 lira = .18j«^ Hamburg, 12 pfenning = 1 schilling, 16 schil- ling =1 mark. 1 m. banco = .35^ Lisbon, 1000 reis =: 1 milreis. 1 milreis = 1.12 London, 240 pence = 12 shillings = 1 pound. 1 pound = 4.86 Madrid, 34 maravedis = 1 real, 20 reals = 1 duro. 1 duro =1,00 Naples, 10 grani = 1 carlino, 10 carlini = 1 ducat. 1 ducat = .80 New York, 100 cents = 1 dollar. Palermo, 20 grani =: 1 taro, 30 tari = 1 onza. 1 onza = 2.40 Paris, 100 centimes = 1 franc. 1 franc = .19^^^ Pekin, 1 tael = 10 mace = 100 candareens =: 1000 cash. 1 tael = 1.48 Rio de Janeiro, 1000 reis = 1 milreis. 1 milreis =: .51^ Rome, 10 bajocchi = 1 paolo, 10 paoli =: 1 soudo Romano. Is. Roman-o= .99 J JSt. Petersburg, 100 copeck = 1 silver rouble. 1 s. rouble =: .75 Stockholm, 12 runstyken = 1 skilling, 48 skillingar = 1 daler in banco. 1 daler = 1.06 Venice, 100 centesimi = 1 lira Austriaca, 8 lire Austriache = 1 florin Austriaco. 1 lira = .16 Vienna, 100 kreutzer -=i 1 gulden or florin. 1 florin = .48J 186 FOREIGN WEIGHTS AND MEASURES. COMPARATIVE TABLES OF WEIGHTS AND MEASURES. 1 Imperial Gallon = 277.274 cubic inches = 1.2 Wine Gallons. Wine Measure, 1 quart = 67f " 1 gall. =231 cubic inches Dry " 1 " =67j " 1 «' =268 Beer «' 1 " =70j " 1 " =282 ♦♦ rx-5 weight, } 1 po-" = ^^«« «--• Avoirdupois " 1 " =7000 " 175 lbs. Troy = 144 lbs. Avoirdupois. Dry Measure, 1 Bushel of U. S. (Winchester bu.) =2150.42 cub. in. *' 1 Imperial Bushel of Great Britain = 2218.192 " " 1 Bushel U. S. heaped measure =2747.7167 «' FOREIGN WEIGHTS AND MEASURES FREQUENTLY MET WITH IN REPORTS OF MARKETS. Ahm, in Rotterdam . (nearly) Almude, in Portugal . Almude, in Madeira Alquiere, in Madeira . <' in Bahia " in Maranham " in Rio Janeiro ** in Pernambuco . Anna of rice, in Ceylon . Arroba, in Portugal . " in Spain " of wine, in Spain (large) «' «« " (small) Arroba, in Malaga Arshecn, in Russia Bahar, in Batavia (large) . " " (small) Bale of cinnamon, in Ceylon (net) Barilla, in Naples . Cantar, in the Levant " of oil, in Leghorn " of brandy " *< in Malta ** (grosso) in Naples " (piccolo) " . ** (grosso) in Sicily . " (sottile) " Carro- in Naples <* of wine, in Naples 40 gallons. 4.37 '« 4 to 8 gallons. If to 2 pecks. 1 bushel. 1 to IJ bushels. I to IJ " 260.4 lbs. 32 25 4.246 gallons. 3.34 " 41 28 inches. 4J piculs. 3 104f lbs. II gallons. 118.8 lbs. 88 120 " im " 196| <« 106 " 192J " 176 " 52.2 bushels. 264 gallons. FOREIGN WEIGHTS AND MEASURES. 13^ Catta of tea, in China .... IJ lbs. Cayang of rice, in Batavia . 3581 lbs. Chetwert, in Russia 5.95 bushels. Fanega, in Spain . 1.6 Hectolitre, in France . . . 2.84 bus. or 26.42 gallons Kilogramme, in France and Netherlands . 21 lbs. Last of grain, in Amsterdam . . 85^ " " " in Bremen .... 80f '' *« of salt, in Cadiz .... 75| bushels *' or moyo of salt, in Portugal 70 « of grain, in Dantzic (nearly) . . 93 " <' in Flushing .... 92J '* « " in Hamburg 89.7 " " " in Lubeck 91 «< " in Rotterdam . 85A " " in Sweden 75 «« " Utrecht 59-f " -^ Lispound, in Hamburg .... 14 lbs. Mark, in Holland 9 ounces. Maund (factory), in Calcutta 74f lbs. " (bazaar), 10% heavier . 82.4 " Mina of grain, in Genoa .... 3.43 bushels. Moyo, of Lisbon 23-f *' '* in Oporto 30 Oke, in Smyrna 2.83 lbs. Orna (or eimer) of wine, in Trieste . 14.94 gallons. " of oil 17 " Palmo, in Naples lOJ inches. Picul, in Batavia and Madras 136 lbs. " in China and Japan .... 133^ " Pipe of wine, in Spain .... 160-1- gallons. Pood, in Russia 36 lbs. 1 oz. 10 drs. Quintal, in Portugal .... 89.05 lbs. " in Smyrna 127.2 «' " (of 4 arrobas), in Spain 100 «* in Turkey 124J " " of cotton (45 okes), in Turkey 127.3 " Rottolo, in Portugal 12^ Rottolo, in Genoa 24 " in Leghorn 3 ** Salma of grain, in Sicily 9.77 bushels. " (general) " .... 7.85 " ** of wine " . . . . 23.06 gallons. Scheflfel, in Germany 1^ to 3 bushels. Ship pound, in Denmark . . . 352 lbs. '* " in Hamburg .... 299J " Staro (or stajo), in Trieste 2.34 + bushels. Tale, in China 1 J ounces. l| yards. Vara, in Rio Janeiro . . (nearly) •* in Spain 9i " 12* ] 38 EXCHANGE. EXCHANGE. 255. The term Exchange, in commerce, signifies the giving or receiving of one currency for its value in another; or, the method of making payments by means of written orders without the transmission of money. See .Bills op Ex- change. 256. Excliaiige is of two kinds, Domestic or Inland^ and Foreign. 257. Domestic Exchange includes the exchanges made within the limits of one country. 258. Foreign Exchange relates to the transactions be- tween different countries. Foreign Exchange comprises Nominal Exchange and Real Exchange. 259. Nominal Exchange has reference to the compara- tive market value of the currencies of different countries. 260. Real Exchange is that which relates to the inter change of commodities without reference to the precious metals. 261. The Trne or Intrinsic Par of Exchange be- tween two countries is the exact equivalent of pure metal in the coined piece which forms the unit of price of one country compared with the currency of the other. The alloy is reckoned of no value. 262. " Thus, according to the mint regulations of Great Britain and France, £1 sterling is equal to 25 fr. 20 cent., which is said to be the par between London and Paris. Exchange between the two countries is said to be at par when bills are negotiated at this rate; that is, when a bill for £100 drawn in London is worth 2520 francs in Paris, and conversely. When £1 in London buys a bill on Paris for more than 26 fr. 20 cent., the exchange is said to be in favor of London and against Paris; when £1 in London will not DOMESTIC EXCHANGE. 139 buy a bill on Paris for 25 fr. 20 cent., exchange is against London and in favor of Paris. 263. " Exchange is made to diverge from par by any discrepancy between the actual weight or fineness of the coins and the mint standard, and by the variations in the demand and supply of bills of exchange. "The cost of conveying bullion or coin forms the limit within which the rise and fall of real exchange is confined ; for if a mer- chant can send a bill for less than the expense of sending gold, he will send a bill, but if sending a bill would cost more than the ex- pense and risk of sending gold, then he will send gold." 2G4:. The Commercial Par of Excbange is the market value of the currency of one country when sold for the cur- rency of another. 265. The Course or Rate of Exchange is the current prices of exchanges, or the variable price of the money of one country which is paid for a fixed amount of that of an- other country. DOMESTIC EXCHANGE. 266. The calculations connected with Domestic Exchange require only the ordinary applications of Percentage. EXAMPLES. 1. What is the cost of a bill for $240 on New York, pur- chased at li% premium? Ans. $243. 2. What is the cost of a draft on New Orleans for $1800, at 1 1 ^ premium ? 3. Sold $375 uncurrent money at 2i% discount. How much did I receive ? How much did I lose ? 4. Exchanged $600 in bank notes for gold at 5% premium. How much did I receive ? 5. Bought goods, $1250, and sold them at a profit of 25^ ; purchased a draft on St. Louis, with the proceeds, at a dis- count of f %. What was the amount of the draft? 6. Shipped goods to Havana, and received a draft for $2500, which gave me a profit of 20% ; sold the draft at 4^ ^ pre- mium. How much did I gain by both transactions ? 140 QUOTATIONS OF EXCHANGE. 7. A commission merchant sold goods, the net proceeds of which were S2750. How large a draft can he buy to remit to his consignor, if he pays i% premium for the draft? How large a draft if he purchases at i ^ discount ? FOREIGN EXCHANGE. 2(i7, In Foreign Exchange it is usual to reckon the money of one country as fixed, and the other as variable. The country whose money is calculated at a fixed price is said to receive the variable price, while the other country is said to give the variable price. Thus, if I buy a bill of exchange on Paris, I receive so many francs per dollar, — the dollar is the fixed price, and the francs the variable price. If I buy a bill on Hamburg, I pay so many cents per marc banco ; the marc banco is called the fixed price, and the cents the variable price. In quotations of exchange rates, it is usual to give only the variable prices. 268. Nearly all the bills of exchange drawn in this coun- try are drawn and negotiated on one of the following places : viz., London, Paris, Bremen, Hamburg, Cologne, Leipsic, Frankfort, and Amsterdam. QUOTATION OF FOREIGN BILLS OF EXCHANGE, By Drexel & Co., Bankees, Fhilada., June 1, 1S66. Explanation. Premium (on old par of 4.44|), from 9 to 9| per cent, on bills at 60 days' sight. Premium from 9|.to lOi per cent, on billi at 3 days' sight. At 5 francs, 11 centimes per dollar. " 5 " 8 " 80 cents per rix-dollar. " 37 " " marc banco. " 73i " '« thaler. " 74 " " " 42 " " guilder or florin. From 42 to 42| cts. per guilder. 269, Bills of exchange are drawn in the money of the country in which tlicy are made payable (See Forms of Bills op Kxciianhf..) Exchange. On London, 60 days, 109 @109| « « 3 " 109t@110i " Paris, 60 " 5.11 <{ 44 3 " 5.08 " Bremen, 60 " .80 " Hamburg, 60 « .37 " Cologne, 60 " .73i " Leipsic, 60 « .74 « Frankfort, 60 " .42 " Amstordaii , 60 " .42®. 421 See, also, London Course OF EXCOANGE. PAR OF STERLING EXCHANGE. 141 Exchange on England. 270. By the usage of bankers for ages, the pound sterling has been valued by the old Spanish Carolus pillar dollar, now entirely out of circulation in Europe and America; of these, $4.44| were equivalent to the pound sterling. This rate originally represented the true par of exchange between the two countries. In 1834 the eagle was reduced in weight to 258 grains (see Tables of Coins of TJ. S.), and now contains 232.2 grains pure gold. The English sovereign is the coined piece of which the pound sterling is the money of account, and contains 113.001 grains pure gold. Standard weight of sovereign, grains 123,274 Alloy, xV part ..... 10.273 Fine gold in the sovereign . . 113.001 By the proportion — 232.2 grains : 113.001 grains : : $10, we find that the equivalent of the pound sterling is $4.8665 ; and, allowing for the wear of coin, we have $4.84, the value established by Congress in 1842, and the rate at which duties are estimated in the Custom-Houses. It has been found convenient to retain the old value as the basis of exchange, and to express the present exchangeable value by a premium on this basis. It requires the addition of 9 % to make the Custom-House value, and the addition of about 05 ^ to equal the intrinsic value, of a pound sterling in our currency. Old par value of £1. = $4,444 9% premium, = .399 Custom-House value, $4.8443 Old par value, $4.4444 ^% premium, .4222 Intrinsic value, $4.86G6 Exchange quotations refer to the old par. When, there- fore, exchange is quoted at about 02% premium, there is in fnct no real premium, but the true par has been attained. When nothing is said to the contrary, the quotations are for bills at usance^ or 60 days' sight and 3 days of grace, 142 SHIPMENTS OF SPECIE. which, at 6 ^ interest, involves a loss of more than 1 % be- sides the time of transportation. On the other hand, 1% is about the cost, including freight, insurance, &c., of shipping gold; and as one of these items balances the other, the real par of exchange on England is 9J%, at which rate it is as well, or better, to remit good 60-day bills as specie. PRO FORMA ACCOUNT OP A SHIPMENT OP MEXICAN DOLLARS FROM NEW YORK TO LONDON. 10000 dollars purchased in New York at If prem. . . 10175.00 Packing Charges, Shipping, &c. Insurance at J^ on 10175.00, and Policy $1 . Total cost in New York . 7.50 51.87 $10234.37 Value in London, 10000 dollars weighing 8660 ounces, and sold at 58J pence per ounce Charges in London, Freight, J^ Primage, 6^ Landing Charges, Postage, &c. Brokerage, ^%, Com. J^ = |^ = Net Proceeds, Cash, in London Add Interest for 63 days, at 4% . £ 2097 «. d. 6 11 £ «. d. 6 4 9 5 2 13 9 13 2 2 19 5 11 2078 1 14 10 11 £2092 11 11 Par of £2092 lis. lie?. = $9300.43. This amount drawn at GO days' sight, to produce the above $10234.37, would establish the rate of exchange on London at 110.04 per cent. Gold is sometimes exported when exchange is quoted below the true par, by bankers who have branch-houses and there- fore no commissions to cover, and who insure their own risks ; by those who can save a guaranty commission on commercial bills, and by those who are compelled to procure specie. Exports of Specie from New York for the week ending June 2, 1866, to Liverpool^ Southampton, Havre, Bremen, and Hamburg, May 80, Amoricau Gold, $2,715,700 " " French " 0,208 " " Spanish " 9.492 " 31, Ainericftn " 4Sr),000 June 1, " " 1,645,197 " " Gold and Silver bars, 14,800 « " Sovereigns, 02,920 " 2, Gold and Silver bars, S2,500 6,021,817 Amount bro't forwa'd, $5,021,817 Juno 2, Foreign Coin and Ame- rican Gold, 1,179,408 ' Gorman Silver, 2,000 ' Mexican " 40,S28 ' Silver Coin, 20,000 ' American Gold, 606,834 ' Foreign Coin, 60 Total for the week, $6,870,991 EXCHANGE ON ENGLAND. 143 RULES FOR COMPUTINa STERLING EXCHANaE, USED BY BANKERS AND DEALERS IN EXCHANGE. 271. The par value of a pound sterling, $4.44|, equals $4|, or 'y^ dollars; and as there are 40 sixpences in a pound, 1 sixpence is equal to ^ of a dollar. To find the real value, a premium must be added. 272. To FIND THE VALUE OP STERLING MONEY. Rule I. — Reduce the pounds and shillings to sixpences^ hy multiplying the pounds hy Jfi and the shillings hy 2; to their sum add i, if the pence equal or exceed 6; divide hy 9, and to the quotient add the given premium^ and 2 cents for every penny exceeding 6 in the given number of pence. EXAMPLE. 1. What is the value in U. S. Currency of £540 7s. *ld.y at a premium of 9* % ? 640X40 = 7X 2 = «. 7 = 6 + 1 = 9 )21615 2401.6667 11% 216150003 12008333 228.158336 Premium. 2401.6666 2629.824936 Value of \d., 2 $2629.84 Rule II. — Reduce the pounds and shillings to sixpences^ and to their sum add ^ the number of pence ; then divide hy 9^ and to the quotient add the given premium. 144 EXCHANGE ON ENGLAND. EXAMPLE GIVEN UNDER RULE I. 7-4-6= 1.166 7X 2= 14 540 X 40 = 21600 9 )21615.166 2401.635 Par value 9^ per cent. 216.15165 12.00842 228.16007 Premium. 2401.685 Ans. $2629.845 2. Reduce £1872 lis. 6d. to dollars at par. Ans. $8322.54. 3. Reduce £617 Is. Id. to United States currency at 9^ premium. Ans. $2989.28. 4. What is the value of £1500 at 8% premium ? 5. What will be the cost of the following bill of exchange at 8f % premium? £150. New Yobk, June 13, 1866. Sixty days after sight of this First of Exchange (Second and Third of same tenor and date unpaid), pay to the order of R. J. Milligan One Hundred and Fifty Pounds, value received, and charge the same to account of Brown & Bros. To Beown, Shipley & Co., Liverpool, England. 273. To reduce Federal money to Sterling. Rule I. — Divide the given amount hy the value of £,1 at the given premium. Rule II. — Multiply the given amount hy P, and divide the product hy 40; annex two ciphers to the quotient^ and divide hy 100 increased hy the premium. EXAMPLES. 1. A commission merchant wishes to remit ^7071.57 to STERLING EXCHANGE TABLE. 145 England. How large a bill of exchange can he purchase at 9% premium? 7071.57 9 1591.1033 100 40)63644.13 109)159110.3300 1591.1033 1459.7277 20 14.5540 12 Ans. £1459 14s. 6^^. 6.6480 2. What amount of exchange can I buy for S3567 60 at 81% premium? £739 16s. Qd. 3. Purchased a bill of exchange, at 9t% premium, which cost $4275. How large was the bill ? 4. How large a bill of exchange can I buy for S2850, if I pay 9J% premium? The cost of goods imported from England is often estimated by adding the proportion of charges to the value of the pound or shilling. For example : — An invoice amounts to £2400, which, with Exchange at 9 % premium = Duties, freight, and other charges, amount to Making the total cost Then, if £2400 cost $12227, one pound cost 12227 -T- 2400 = $5.09^ nearly, and 1 shilling costs 25i cts 1 penny 2^ cts. Cloth at 16^2. per yd. would cost 33 cents. $11626.66 600.34 $12227.00 TABLE Showing the value of £1 sterling from on the old par of ? Old par 4 per cent. 5 5J 7 n to 12^ per cent, premium $4,444 4.622 4.644 4.667 4.689 4.711 4.733 4.756 4.767 4.778 7f per cent. |4.789 8^ (Eng. fr"ts) 4.800 8^ per cent. 4,811 8^ " 4.822 8| " 4.833< 9 (Cust.-House) 4.844 9^ per cent. 4.850 9i- " 4.856 9| '' 4.861 9| " 4.867 13 9| per cent. 9f 10 m m 11 Hi 12 12^ $4,872 4.878 4.883 4.889 4.894 4.911 4.933 4.956 4.978 5.000 146 EXCHANGE. STERLING TABLE. Oakulated at the Far Value of ^4,-444 ^ ^^ Sterling, £ $ cts. m. £ $ cts. m. £. $ cts. m. Shill'gs. Icts.m T 4.44.4 41 182.22.2 81 360.00.0 1 0.22.2 2 8.88.9 42 186.66.7 82 364.44.4 2 0.44.4 3 13.33.3 43 191.11.1 83 368.88.9 3 0.66.7 4 17.77.8 44 195.55.6 84 373.;i;j.3 4 0.88.9 6 22.22.2 45 200.00.0 85 377.77.8 6 1.11.1 6 26.66.7 46 204.44.4 86 382.22.2 6 1.33.3 7 31.11.1 47 208.88.9 87 386.66.7 7 1.65.6 8 85.55.6 48 213.33.3 88 391.11.1 8 1.77.8 9 40.00.0 49 217.77.8 89 395.55.6 9 2.00.0 10 44.4i.4 60 222.22.2 90 400.00.0 10 2.22.2 11 48.88.9 61 226.66.7 91 404.44.4 11 2.44.4 12 53.33.3 52 231.11.1 92 408.88.9 12 2.60.7 13 57.77.8 53 235.55.6 93 413.33.3 13 2.88,9 14 62.22.2 54 240.00.0 94 417.77.8 14 3.11.1 15 66.66.7 65 244.44.4 95 422.22.2 16 3.33.3 16 71.11.1 56 248.88.9 96 426.66.7 16 3.65.6 17 76.55.6 57 253.33.3 97 431.11.1 17 3.77.8 18 80.00.0 68 257.77.8 98 435.55.6 18 4.00.0 19 84.44.5 59 262.22.2 99 440.00.0 19 4.22.2 20 88.88.9 00 266.66.7 100 444.44.4 20 4.44.4 Pence. $ cts. m. 21 93.33 3 61 271111 22 97.77.8 62 275.55!6 200 888.S8.9 1 0.01.9 23 102.22.2 63 280.00.0 300 1333.;3:3.3 2 0.03.7 24 106.66.7 64 284.44.4 400 1777.77.8 3 0.05.6 25 111.11.1 65 288.88.9 600 2222.22.2 4 0.07.4 26 115.55.6 66 293.33.3 600 2666.66.7 5 0.09.3 27 120.00.0 67 297.77.8 700 3111.11.1 28 124.44.4 68 302.22.2 800 3655.55.6 6 0.11.1 29 128.88.9 69 306.66.7 900 4000.00.0 7 0.13.0 30 133.33.3 70 311.11.1 1000 4444.44.4 8 9 0.14.8 0.16.7 31 137.77.8 71 315.55.6 1100 4SS8.R8.9 10 0.18.5 32 142.22.2 72 320.00.0 1200 5333.3.'{.3 33 146.66.7 73 324.44.4 1300 6777.77.8 11 0.20.4 34 151.11.1 74 328.88.9 1400 6222.22.2 12 0.22.2 35 155.55.6 76 333.33.3 1500 6(J66.f.().7 36 160.00.0 76 337.77.8 1600 7111.11.1 i 0.00.5 37 164.44.4 77 342.22.2 1700 7555.55.6 38 168.88.9 78 346.66.7 1800 8000.00.0 0,00.9 39 173.33.3 79 361.11.1 1900 84'W.44.4 40 177.77.8 80 355.56.6 2000 8888.88.9 0.01.4 (See, also, Importers' Adv.ince Table.) To find the value of any given amount not mentioned in tho table, take the sum of those numbers that will equal the given amount. EXCHANGE. 147 liOuclou Course of Excliango. 274. Loudon has been called the great clearing-houBe of tlie world. Nearly all the foreign trade of the United States is settled through England and France. LON DON RECEIVES FROM, OR GIVES . TO, Variable, according to the ex changes, Amsterdam 12 florins and 3 stivers for £1 sterling. Bremen 609^ rix-dollars ( £100 sterling. Berlin 6 dollars, 25 silver groschen * £1 Christiania 4 specie-daler, 30 skilling f { (( 11 Constantinople 140 piastres ( (( (S Copenhagen 9 rigsbank daler, 10 skilling ' <( (( Frankfort 121 Zollverein florins £10 Genoa 25 lire, 35 centesimi £1 Hamburg 13 marks, 12 schillings <( (t Milan 25 lire, 40 cents (( (( Leghorn 25 « 50 " It (( Paris 25 francs, 21 centimes ii it Rome 46 Paoli (t a Stockholm 12 dalers in banco, 1 skilling * (t tt Vienna 13 florins, 70 kreuzers ( (( i( Calcutta 23 pence sterling for 1 Comp . rupee. Gibraltar 48J " 1 duro, or hard dollar, or Spanish dollar. Lisbon 531 .1 1 milreis. Madrid 50J " 1 hard dollar. Naples 39| « 1 ducat New York 49J " 1 U. S. dollar. Palermo 119J « 1 onza. Pekin 78^ " a thousand cash. Rio Janeiro 30 " 1 milreis. St. Petersburg 381 u 1 silver rouble. Venice 47 u 6 1ir e Austriache. 5ee, also, Synopsis of Moneys of Account.) 148 SHIPMENT OF SPECIE TO PARIS. Exchange on France. 100 Centimes make 1 Franc. 1. What is the cost of a bill of exchange on Paris for fr.10277.76— exchange at fr.4.89 per dollar ? Ans. $2101.79. 2. "What must be paid for a bill on Paris for fr.3875.50, at fr.5.19 per dollar? 3. What is the difference between the Custom-House value of 18.6 cts. per franc, and exchange at fr.5.19 per dollar, on a bill for 58000 francs ? 4. Estimating fr.5.21 to be the par value of 61, what is the premium on gold when exchange for currency is quoted at fr.3.4-5 per dollar ? PRO FORMA ACCOUNT OF A SHIPMENT OF MEXICAN DOLLARS FROM NEW YORK TO PARIS. 10000 dollars purchased at If premium, 10175.00 Packing Charges, Shipping, &c., 7.60 Marine Insurance, at ^% on $10175.00, 50.87 Policy, 1^ 51.87 Total cost in New York, . ^10234.37 Value in Paris 10000 dollars sold at fr.5.34 fr.53400.00 Charges in Havre : — Import Duty and Permits, fr,6.40 Cartage, Cooperage, &c., 10.10 Freight, ^fo on $10000, 25.00 Primage, 10^, 2.60 160.87 409.25 570.12 Atfr.5.25, $27.50 = Charges in Paris : — Freight, fr.72.25 Viewing and Delivering, 3.25 Brokerage ^fo, Com. ^% = g%, 333.75 = 144.37 Net proceeds, cash, in Paris, fr.52829.88 Addlnterestfor 63days, at4%, 369.80 Total, fr.53199.68 This amount drawn at 60 days' sight, to realize the above $10234.37, will require the rate of exchange to be fr.5.20 per dol- lar. Without commission in Paris, the rate would be fr.6.22J: or J% lower. CUSTOM-HOUSE BUSINESS. 149 CUSTOM-HOUSE BUSINESS. 275. Custoin-Houses are houses or offices established by government for the collection of duties on commodities entered for importation or exportation, where bounties and drawbacks upon such importations or exportations are paid or received, and where vessels are entered and cleared, &c. 276. Ports of Entry are places at which custom-houses are established ; and it is lawful to introduce merchandise into a country only at these places. 277. Vessels arriving at any port of the United States must report at the Custom-House within twenty-four hours after their arrival, and within forty-eight hours must enter, or make a further report, which shall contain all the particulars required to be inserted in a manifest. 278. Manifests, or invoices, must be produced, containing particulars of goods, with their cost in the currency of the country from whence imported. When no invoice has been received, and the owner or consignee has testified under oath that such is the case, the goods are entered by appraise- ment. When the value exceeds $100, permission must first be obtained from the Secretary of the Treasury to enter in this manner. If the invoice or entry does not contain the right gauge or measurement of the goods, they must be weighed, gauged, or measured at the expense of the importer. When the value of the foreign currency is not fixed by any law of the United States, the invoice must be accompanied by a consular certificate, showing its value in specie, or United States dollars ; and in default thereof, a bond for the produc- tion of such certificate will be required. 279. Specific Duty is rated at a specified amount upon each article, ton, yard, lb., &e., without regard to its value. 280. Ad- Valorem Duty is rate4 at a certain per cent. 13* 150 CUSTOM-HOUSE BUSINESS. upon the cost of the goods in the country from which they wore imported. 281. In estimating duties, certain allowances are made for the package, waste, or damage, as it is the design of the gov- ernment to tax only so much of the goods as may actually arrive and be available in the market. 282. Tare is the allowance made for the weight of the package containing the goods, in the manner prescribed by law. In some cases it is reckoned at so much per package, sometimes at a certain percentage, and sometimes by actual weight or measurement. 283. I>raf t is the allowance made for waste or impurities. 284. L-eakage is an allowance made for waste on liquids. Breakage is an allowance on liquors imported in bottles. 285. Gross Weight is the entire weight of goods and packages combined. 286. Net Weight is the weight after all allowances have been deducted. 287. Tonnage is the amount paid per ton on the vessel for permission to enter port. 288. Warehousing is the placing of goods in public store, or bonded warehouse, in charge of the government, when the importer does not wish to withdraw the goods or pay the duties immediately. All goods so deposited must be withdrawn, or the duties thereon paid, within one year; and all goods remaining beyond three years are regarded as aban- doned to tlie government, and sold under regulations pre- scribed by the Secretary of the Treasury. 289. A €ustoin-IIouse Broker is one who attends to making the proper entries of goods at the custom-house, for merchants. As there is a great variety of points involving special questions for each separate invoice, style of merchan- dise, and form of entry, the services of a responsible custom- house broker will materially aid those who are inexperienced CUSTOM-HOUSE BUSINESS. 151 TABLE OF FOREIGN MONEYS, As fixed by laiu for estimating duties at the United States Custom- House. For all others a consular certificate is required. Ducat of Naples Florin or Guilder of Austria, Augs- burg, and Bohemia Florin or Guilder of Frankfort, Nu- remberg, and Southern Germany. Florin of Netherlands Florin of Trieste Franc of 'France and Belgium Lira of Lombardo-Yen. Kingdom... Lira of Sardinia Lira of Tuscany Livre of Leghorn Livre of Genoa Livre Tournois of France Louis d'or, or Rix-dollar of Bremen. Marc Banco of Hamburg Milreaof Azores 83J, Madeira 1.00, Portugal 1.12 .' Onza or Ounce of Sicily Pagoda of India Pound sterling of Great Britain and Ireland, and Jamaica Pound sterling of Canada, British Provinces, Newfoundland, Nova Scotia, and New Brunswick Pagoda Star of Madras Real Plate of Spain Real Vellon of Spain. ...^ Rouble (or Ruble) Silver, Russia.... Rupee of Company and of British India Specie dollar of Ucnuark Sj)ecie dollar of Norway Specie dollar of Sweden Tael of China Thaler or dollar of Bremen, of 72 grotes Tl Taler or Rix-dollar of Prussia, Ber- lin, Leipsic, Northern Germany, and Saxony Dollar of Mexico, Peru, Chili, Cen- tral America, and Cuba .80 •48M .40 .40 .481^ .16 .18A .isk 2.40 1.94 4.84 4.00 1.84 .10 .5 .75 1.05 1.06 1.06 1.48 .71 Lower Denominations. 10 carlini 60 kreutzers.. 60 kreutzers.. 100 centimes. 60 kreutzers.. 100 centimes. 100 4 reali 20 soldi 20 " 20 " 72 grotes 16 schillings.. 1000 reis. 30tari 36 fanams 20 shillings... 20 42 34 maravedis 34 100 copecks. 16 annas 6 marks 6 « 48 skilling.... 10 mace 72 grotes groschen.. shillings. , 10 grani. 4 pfenningSf 4 " 4 " 20 solidi. 12 denari. 12 " 12 " 5 schwaren. 12 pfennings. 20 grani. 48 jittas. 12 pence. cash. 12 pyce. 16 skilling. 16 12 oefre. 10 candareens. 6 schwaren. 12 pfennings. 290. The ton in all cases is taken at 2240 lbs. In weights and currencies, less than one-half a pound or one-half a dollar is dis- regarded; more than one-half is taken as one. 152 CUSTOM-HOUSE BUSINESS. 1. What is tlic duty to be paid on the following invoice, a*: the rate of 35 % ad valorem and 50 cents per lb. specific duty ? Invoice of Merchandise purchased by Bell & Co. for account and risk of Cade, I?kothI':ks & Co., rhiladelphia, forwarded to Liverpool for shipment per steamer "Persia^' IIUDDERSFIELD, ESQ., 10th Dec. 1867. <^ 547 7 pieces 50 inch Fancy Coatings (aU wool). *'ll28 46i ^1130 431 1130 45 1138 45J 1131 m 1161 46i 1137 45i damage, Deduct ^7 overmeasure, 7 ps. making up, Sample Card, 3/-, Case, 23/-, Carriage, 6>:, Commission, 2i per cent., 2i per cent, discount on £173. 19. 1., Consul's certificate. Gross Weight, 654 lbs. Net " 539 " Cash, l)ec. 10, 1867. yds. Zl9i 317f 309i 173 1 175 4 180 4 175 £176 Extract from Hill of Lading. ^O 547 F.jot. 35- @ 45/- per ton, £1. 9. 8 Primage, 1. 11 £2. 1. 7 Shipped by Weston & Co., on " JPersia" from Liverpool to New York, one Case, marked ;is pr. margin, and consigned to Cai>e, Bros. & Co., Philadelphia. Liverpool, 13th Doc. /67. Note. — The ton is a ton measurement, 40 cubic feet ; the Case is 35 cubic feet 3 in. 35i -^ of 45 shillings =;£1. 9. 8. for freight. Shipping Charges. Charges on Case ^ ^ 547, shipped by Weston & Co. pr. Persia for New York, con- signed to Cade, Bros. & Co., by order of Bkll & Co., Huddersfleld. Dues and entry at Customs, 1. 11 Bills of Lading, 1. 6 2. 9 Commission, 2. 6 Cartage, £8. Liverpool, 13th Dec. /67. CUSTOM-HOUSE BUSINESS. 153 Duty. Invoice Value, £176. Deduct Consul fee, not dutiable, 175. Liverpool charges, 5. 4 10. 4 15. 8. 8 £176. Woolcng. 3. 8 £176. 3. 8., at $4.84, = $853, duty 35 per cent., $298.55 lbs.— 539, " 50 cts., 269.50 Put}', $568.05 2. Imported 25 bags canary-seed, weigliing 5920 lbs., the tare of which was 75 lbs., and paid duty of ^1 per bushel of 60 lbs. How much did I pay? 3. Imported from England, per brig "Wellington, 24 sacks wool, weighing 2560 lbs., invoiced at Is. 3art- ner's share. Then, III. Ih each 2)ortners original investment add any addi- tional investments or sums to ivhich iie may be entitled, and his share of the net gains, if any ; also, deduct the amounts loithdrawn by him, and obligations assumed by the firm for him, and his share of the net losses, if any. 178 PARTNERSHIP SETTLEMENTS. Tf the orujuial agreement entitle him to any other sum, or make him responsible to the firm for any sum, add or suLtrarf^ as the case may he. EXAMPLES. 1. A. and B., having been in business 1 year, dissolve partner- ship. B. retires, leaving A. to continue the business and liqui- date the debts of the firm. A. invested 312,000, B. $10,000. Each is to receive interest on his investment, and share the gains and losses equally. How much did each gain? what is A/s capital at closing, and how much should he pay B. ou retiring, the resources and liabilities being as follows ? Resources. Liabilities. Cash on hand, $5,000 Personal debts firm owe per Ledger, $8,170 Personal debts due firm, per Bills Payable, 4,200 Ledger, $12,000 Interest on notes and drafts, 130 Less 25 per cent, for bad debts, 3,000 9,000 Total Liabilities, $12 500 Mdse., as per inventory, 16,530 Hills Receivable, 3,500 U. S. 5-20 bonds, 4,000 Accrued interest on 5-20 bonds, 120 Real Estate (store and lot), 6,500 . Store fixtures, 350 Total Resources, $45,000 OPERATION. Total resources, $45,000 ♦« liabilities, 12,500 Firm's net capital at closing, $32,600 Interest on A.'s investment, $12,000 for 1 year, = B.'s " 10,000 " = $720 600 Firm's net capital at closing, A.'s investment, $12,000 Interest for 1 year, 720 12,720 $32,500 B.'s investment, $10,000 Interest for 1 year, 600 10, GOO Firm's net gains in business, 23,320 $9,180 A.'s investment, $12,000 B.'s investment, Interest for 1 year, 720 Interest for 1 year, His I net gains, 4,590 His J net gains, $10,000 600 4,590 A.'s net capital, $17,310 B.'s net capital, $15,190 A.'s net capital, $17,310 B.'s " 15,190 Firm's net capital, as before, $32,600 PARTNERSHIP SETTLEMENTS. 179 2. J), and E. are partners ; each invested $3000, and agreed to share the gains and losses equally. During the year, J), drew out $600, and E. $500. What were their gains at the end of the year, their resources and liabilities being as follows ? Jtesoicrces. Cash on hand, $3,500 Mdse., as per inventory, 3,600 Bills Receivable, 1,200 Debts due firm, as per Ledger, 2,500 Total resources. $10,800 Liabilities. Debts firm owe, as per Ledger, $1,500 Bills Payable, 800 Total liabilities, 2,300 Firm's net capital at closing, $8,500 D. invested $3,000 Less amount withdrawn, 600 D.'s credit balance, $2,400 E. invested 3,000 Less amount withdrawn, 500 E.'s credit balance, $2,500 Balance of investments, 4,900 Firm's net gains, $3,600 PROOF. D. invested Withdrew $3,000 600 E. invested $3,000 Withdrew 500 ^ net gains, 2,400 1,800 2,500 ^ net gains, 1,800 D.'s net cap. at closing, $4,200 E.'s net cap. at closing, $4,300 D. E. 's net 's capital, $4,200 4,300 Firm's net capital, as above, $8,500 3. A., B., and C. form a partnership; A. invests $15,000, B. $12,000, and C. nothing. They share the gains and losses as follows, — viz. : A. 2, B. ^, and C. i. A. draws out during the year $800, B. $900, and C. $400. What is each partner's 1§P PARTNERSHIP SETTLEMENTS. capital, and what are the gains at the end of the year, when their resources amount to 840,000, and their liabilities to $44,000 ? OPERATION. Liabilities, Less resources, $44,000 40,000 Firm's net insolvency, $4,000 A.'s investment, $15,000 Less am't withdrawn, 800 $14,200 B.'s investment, 11,100 12,000 Less am't withdrawn, 900 A.'s ^ loss, B.'s I " C.'s i " Total losses. $14,450.00 9,033.33 4,816.07 $28,900.00 25,300 Less am't withdrawn by C, 400 Firm's net investment. Add firm's insolvency, Firm's net loss, 24,900 4,000 A.'s investment, $15,000 Less amount withdrawn, 800 A.'s ^ loss. Net investment. B.'s investment, Less am't withdrawn Less his |- loss, B.'s net capital. 11,100.00 9,633.33 $1,466.67 A.'s insolvency, C.'s $28,900 $14,450 14,200 $250 $4,816.67 400.00 C.'s net insolvency, $5,216.67 $14,200 A.'s net insolvency. $12,000.00- C.'s I loss, 900.00 Add am't withdrawn. Deduct B.'s net capital. Firm's net insolvency. $250.00 5,216.67 5,466.67 1,4 66.67 $4,000.00 4. hi which a salary is allowed each partner. No interest account kept. A., 13., and C. entered into partnership January 1st, 1865. A. and B. each invested $7000, C. invested $14,000. A.'s share of the gains or losses was i, B.'s i, and C.'s J. A. was to receive a salary of $1000 per year, B. SI 500, and C. S500, for services. A. drew out $650, B. $450, and C. $900. What was each partner's interest in the firm January 1st, 1866, when their resources were $54,500, and their liabilities $13,500 V PARTNERSHIP SETTLEMENTS. 181 OPERATIOX. Resources, $54,500 Liabilities, 13,500 Firm's net capital, $41,000 A.'s investment, $7,000 Add salary, 1000 Less amount withdrawn, A.'s credit balance, B.'s investment, Add salary. Less amount withdrawn, B.'s credit balance, C.'s investment, Add salary, Less amount withdrawn, C.'s credit balance, 13,600 29,000 Firm's net gains, $12,000 A.'s credit balance, $7^50 B.'s credit balance, $8,050 C.'s credit balance, $13j600 " igain, 3,000 " i gain, 3,000 " i gain, 6,000 Net capital, $10,350 Net capital, $11,050 Net capital $19,600 Proof. — A.'s net capital, $10,350 B.'s " 11,050 C.'s " 19,600 Firm's net capital, as above, $41,000 5. Li lohich amounts withdrawn are averaged^ and interest is charged and allowed. A. and B. entered into partnership January 1st, 1864. A. invested $12,000, and B. $14,500, the gains and losses to be shared equally ; each partner to be allowed 6 per cent, on his investment, and to be charged at the same rate on sums drawn out, A. drew as follows : — March 1st, $300 ; July 9th, $250 ; September 10th, $200 ; December 16th, $150. B. drew, April 7th, $100; August 4th, $400; November 23d, $250. What was each partner's interest January 1st, 1865, their resources and liabilities being as follows ? 16 8,000 650 7,350 $7,000 1,600 8,500 450 8,050 $14,000 500 14,500 900 13,600 182 PARTNERSHIP SETTLiixME M: Resources. Casli, ^8,600 Tersonal debts due firm, 16,000 Bills Receivable, 1,400 Mdse., as per inventory, 26,000 Penna. Central K.ll. Stock 6,000 Total resources, $53,000 Liahili'.ies. Personal debts firm owe, $1 1,500 Bills Payable, 500 Total liabilities, 12,000 Firrn^s net capital ^ /; ! ." '> '> $53,000 Average date of amounts withdrawn by A., July 0th. " " " B., Aug. 26th. A.'s investment, $12,000 Less amount withdrawn, 000 Interest on investment, $12,000, for 1 year, 720 Less interest on $900 withdrawn, from ave- rage date, July 6th to Jan. 1st (178 days), 267 A.'s credit bahince. Sll,100 453 $11,553 IJ.'s investment, $14,500.00 Less ani't withdrawn, 750.00 $1G,750.( Int. on investment, $14,500, for 1 year, 870.00 Less int. on $750 witli- drawD, from average date, Aug. 26 to Jan. 1 (127 days), 158.75 7n.25 B.'s credit balance, $41,000.00 $11,401.25 Firm's net capital, A.'s credit balance, §11,553.00 B.'s " 14,461.25 26,014.25 Firm's net gains, A.'s investment, less amount withdrawn, $11,100.00 Credit balance of int., 453.00 His \ gains, 7,492.88 A.'s net capital, $19,045.88 $14,985.75 B.'s investment, less amount withdrawn, $13,750.00 Credit balance of int., 711.25 His \ gains, ' 7,492.87 B.'s net capital, $21,954.12 Firm's net capital, as above, $41,000. 6. A., B., and C. commenced business with a capital of $6000 each. The gains and losses were to be shared equally, and each partner was to receive interest on his capital, and to pay interest on all sums withdrawn. At the close of the year they had— Cash on hand, 84250 ; Merchandise, 816,500 ; Hills Receivable. SIOOO ; Personal debts due them, 84120.67. The firm owes— Bills Payable, 8500 ; Personal debts, 8630.35. During the year, A. drew out 81007.57, the interest on which to the end of the year was 820.15 ; B. drew 82049.61, on which the interest was 820.50 ; C drew 83213.92, the in- terest on which was 828.12. How much did they gain or lose, and what was each partner's capital at the end of the year 'i NoTK.— When books are kept by Double Entry, the above results can be obtained with very little trouble. PAPtTNERSIIir SETTLEMENTS. 183 7. When the capital of the firm or company is kept separate from the accounts of the partners, and the amounts withdrawn are to be considered as taken from the gains and not from the capital, the following forms of statement are generally adopted : — • Assets. Real Estate, Miichinery and fixtures, Cash, Mdse., as per inventory, U. S. 5-20 Bonds, Accrued int. on do., Bills Receivable, Central Paciiic K.R. StocK, Partners' withdrawals and interest, — James L. Hart, Robert Hunter, Philip S. Weston, $45,000 7,000 2,500 8,500 G,000 120 12,000 .J, 5,000 8,400 4,880 3,500 Liabiliiics. Bills Payable, $15,750 Debts, per Ledger, 14,250 Capital Stock, 50,000 Net gains, 22,900 Jas. L. Hart's \ gain, $11,450 Less am"t withdrawn, 8,400 Balance, $3,050 Rolit. Hunter's \ gain Less am't withdrawn, , $5,725 4,880 Balance, $845 P. S. Weston's \ gain, Less am't withdrawn. $5,725 3,500 Balance, $2,225 $102,900 $102,900 8. A. and B. commenced business as partners. A. invested $20,000, and B. $10,000, A. sharing | and B. \ of the gains and losses. No interest account was kept. A. drew out $1700, and B. $2150. Their assets at the close of the year consisted of— Cash, $4200; Bills lleccivable, $8800; Mdse., $26,000; and Personal debts, $16,000. 10 per cent, of the personal debts are considered bad. Their liabilities are — Bills Pay- able, $3250; Personal accounts, $11,250. If B. should re- tire from the firm, how much ought he to receive ? Assets. Cash, $4,200 Bills Receivable, 8,800 Mdse., 20,000 Personal accts., less 10%, 14,400 $53,400 Add amount drawn out, 3,850 $57,250 Liabilities. Bills Payable, Personal accounts, Capital invested, Finns net gain, $3,250 11,250 $14,500 30,000 $44,500 12,750 $57,250 A.'s Acct. B.'s Acct. Dr. Drawn out, Balance, Drawn out, lialance. $1,700 26,800 $28,500 $2,150 12,100 $14,250 Capital, I net gain, Capital, \ net gain. $28,500 $10,000 4,250 $14,250 184 DETECTING ERRORS IN TRIAL BALANCES. DETECTING ERRORS IN TRIAL BALANCES. 322. The Trial Balance is the best short test of the correctness of account-books that has yet been devised. It is not, however, entirely reliable ; because its etjuilibriuni is not affected by posting into the wrong account, or omitting to post both a debit and a credit of equal amounts. When the Trial Balance is not in equilibrium, to discover where the error exists, — 1. Ascertain the exact amount of the error. • Omitting to do this has led to prolonged search for what did not really exist. 2. If the error is of large amount, examine whether the amounts have been entered in the Trial Balance correctly. Many mistakes are made in transferring amounts from one place to another. For this reason, some book-keepers always post with their Ledger on their right, to prevent reading the figures backwards. 3. Examine the Cash Balance: it can never be on the credit side, and should agree with the amount actually on hand. The balance of Bills Receivable should never be on the credit side, nor the balance of Bills Payable on the debit side of the account. 4. If posts are made directly from the Cash Boo'i:, see whether the balance brought down from the previous montJi has been deducted from the debit footing before posting to the debit of cash. The total debit footing, less the balance from the previous month, is the proper amount to post. 5. Examine the books, to find an amount corresponding with the error, or with half the error; an amount posted to the wrong side of an account will produce an error in bal- ancing equal to twice the amount. 6. Divide the error by 9. It is a principle in figures that the difference between any number and the same number DETECTING ERRORS IX TRIAL BALANCES. 185 transposed in whole, or in part, may be divided by 9 without a remainder, and the sum of the figures in the difference will make 9's. Thus, the difference between 753 and 735 = 18 -V- 9 = 2, and 1 + 8 = 9. 9753 9753 9753 9753 7953 9573 9735 3579 1800 180 18 6171 Errors in transposition are among the most difficult of de- tection. 7. See whether the footings of the accounts and the bal- ances are correct. If the error is in one figure only, it is generally an error in adding, carrying, or transferring. If the error is in the dollar column or cent columns only, the columns on the left need not be re-added. 8. If, after the above examinations, the error remains undiscovered, examine each post separately, and check the amounts both in the book from which postings are made and in the Ledger, and then examine the amounts to see if any remain unchecked. If the entries are made correctly, and the amounts are in equilibrium before posting, by following the above suggestions the error will soon be detected. FRAUDULENT BALANCES. 323. To ascertain the true weight with fraudulent balances, when the weights are accurate. Rule. — Find what weights balance the substance to be weighed; then transpose them, and find the weight that will 2)roduce an equilibrium; then multipli/ together the two weights thus found, and extract the square root of the j^^'oduct. Example. — If by the first weighing the article weighs 8 lbs., and by the second it weighs lOg lbs., the product is 81, the square root of which is 9, the true weight. 16* 186 DIVIDENDS AND 11 VESTMENTS DIVIDENDS AND INVESTMENTS. 324. stocks is a general term applied to the bonds of the Government or State, and to the bonds and shares of incor- porate companies. They are usually bought and sold, through the medium of brokers, at the Stock Exchange. 325. Bonds are obligations or deeds securing the payment of a certain sum of money on or before a future day ap- pointed. When issued by governments or corporations, they are made in denominations of convenient size, bearing interest usually payable semi-annually. They frequently have coupons or interest-tickets attached, bearing date, amount, signature, &c., which are due at the expiration of each successive half- year; these are cut off as they are paid, and held as receipts. For temporary loans, Treasury Notes have also been issued by the United States Government, payable with interest, some with and some without coupons. Exchequer Bills have been issued in England in the same manner. 326. A Joint Stock Company is an association of men having a capital that is divided into shares of equal value, which are transferable and may be bought and sold like any other property. 327. Certificates of Stock are issued to each stock- holder, indicating the number of shares to which he is en • titled. The first or original value f the shares is called their nominal or par value. When they sell for more than their par value, they are said to be above par, or at a premium; when for less, below par, or at a discount. 328. An Instalment is a certain portion of the capital paid at a particular time. 320. An Assessment is an amount for which the stock- holders are called upon to make up deficiencies or losses. DIVIDENDS AND INVESTMENTS. 187 330. The Gross Earnings consist of the entire receipta of a company. 331. The Wet Earnings are what remains after the ex- penses are deducted. 332. The Dividend is the sum divided among the stock- holders from the gains of the business. 333. Sometimes, in addition to the cash dividend, which is payable at a stated time, the company declare a Scrip divi^ dend^ for which certificates are issued payable on the contin- gency that the affairs of the company continue prosperous This Scrip bears interest, or not, as the company may deter- mine. (See Form of Certificate of Scrip.) 334. A Mortgage is a conveyance of property as a pledge for the security of a debt, and becomes void when the debt is paid. 335. Ground-Rents is a term applied to leases of build- ing lots, the rent of which is considered equivalent to the in- terest on the valuation of the land. The payment is gene- rally secured by a claim on the building erected on the land occupied. By a recent law in Pennsylvania, no new ground-rent can be made irredeemable, but may be extin- guished upon payment of a sum the interest of which is equal to the rent annually paid. 336. Building liOts are sometimes sold at so much per foot. The price is obtained by dividing the interest per annum on the valuation of the whole lot by the number of feet on the front ; the quotient is the price per foot. Thus, a lot valued at $3000, with a front of 20 feet, is said to be worth 19 per foot; the interest on $3000, which is $180 per annum, being divided by 20, the number of feet on the front, gives $9 as the price. J137. The value of an investment depends upon its security, its productiveness, its permanency, its facility of transfer, and the readiness with which the income derived from it may be collected. 188 THE NATIONAL DEBT. National Debt of the United States. The following is a statement of the Public Debt of the United States on the 1st op March, 1866 : — Debt bearing Coin Interest. 6 per cent. Bonds, Dec. 31, 1867, and July 1, 1868 . $18,323,591.80 6 per cent. Bonds, Jan. 1, 1874 .... 20,000^000.00 6 per cent. Bonds, Jan. 1, 1871 7,022,000.00 e per cent. Bonds, Dec. 31, 18R0, and June 30, 1881, called 6'8 of '81 282,693,100.00 6 per cent, b-20 Bonds, May 1, 1867, or May 1, 1882, int. May and Nov 514,780,500.00 6 j.er cent. 5-20 Bonds, Nov. 1, 1869, or Nov. 1, 1884, int. May and Nov 100,000,000.00 6 per cent. 5-20 Bond.s, Nov. 1, 1870, or Nov. 1, 1885 61,263,000.00 5 i)ercent. 10-40 Bonds, March 1, 1874, or March 1, 1904 - . 172,769,100.00 s 6 per cent. Bonds, Oregon War., July 1, 1881 . . 1,016,000.00 $1,177,367,291,80 Debt bearing Currency Interest. 6 per cent. Bonds, Union Pacific R.R. Co., Nov. 1, 1895 $1,632,000.00 6 per cent. Bonds, Central Pacific R.R. Co., Jan. 16, 1895 2,362,000.00 4, 5, 6 per cent. Temporary Loan, ten days' notice after thirty days 118,577,039.50 Certificates of Indebtedness 1 year from date . 62,264,000.00 1 and 2 year 5 per cent, notes, 1 and 2 years from date - 8,536,900.00 3-year Compound Interest Notes, 3 years from date, 174,012,141.00 3-year 7-30 Treasury Notes, 3 years from date . 818,044,000.00 $1,185,428,980.50 Matured Debt not presented for Payment. Texas Indemnity Bonds $618,000.00 S-year 7-30 Treasury Notes 167,3.i0.00 Bonds 81,2(18.00 Treasury Notes 118,161.64 •.'omporary Loan, coin 1,200.00 $985,979.54 Debt bearing no Interest. ; Sed States Notes $423,435,373.00 '.•^ tioiial Currency 27,52.V^^4.52 told Certificates of Deposit 12,627,600.00 $463,.'>S6,707.62 Total Debt $2,827,868,959.4« THE NATIONAL DEBT. 189 Tine Public Debt of the .United States on the 1st of March, 1867:— Debt bearing Coin Interest. 5 per cent. Bonds $198,091,350.00 6 per cent. Bonds, '67 and '68 ... . 15,679,591.80 6 per cent. Bonds, 1881 283,745,250.00 6 per cent. 5-20 Bonds 954,839,000.00 Navy Pension Fund 12,500,000.00 $1,464,855,191.80 Debt bearing Currency Interest. 6 per cent. Bonds $12,922,000.00 3 year Compound Interest Notes .... 141,308,830.00 3 year 7-30 Notes 632,798,050.00 $787,028,880.00 Matured Debt not presented for payment 14,576,689.07 United States Notes $376,235,626.00 Fractional Currency 29,514,722.32 Gold Certificates of Deposit 18,376,180.00 424,126,528.32 Total Debt $2,690,587,289.19 Amount in tbe Treasury. Coin $107,271,031.12 Currency 52,552,368.27 159,823,399.39 Amount of Debt, less cash, in Treasury $2,530,763,889.80 The foregoing is a coi^rect statement of the public debt, as appears from the books and Treasurer's returns in the Department on the 1st of March, 1867. (Signed) Hugh McCulloch, Secretary of the Treasury. Reduction of debt in one year $137,281,670.00 Amount in Treasury. March 1, 1866. March 1, 1867. Coin $55,736,192 $107,271,031 Currency 60/282,767 52,552,368 Total $116,018,959 $159,823,-399 Debt, less amount in Treasury March 1, 1860 $2,711,850,000 Debt, less amount in Treasury March 1, 1867 2,530,763,890 Actual reduction of debt in one year $181,086,110 At this rate of reduction, the entire debt could be paid in fifteen years. Receipts and Expenditures of the United States for the year ending June 30th, 1866. RECEIPTS. j EXPENDITURES. From Customs . . . $179,046,630.64 Civil, Foreign and Mis, . $41,049,965.96 From Public Lands . 665,031.03 From Direct Tax . . 1,974,754.12 From Internal Revenue 309,226,812.81 From Miscellaneous . 65,125,966.46 Total , . . $556,039,195.06 Pensions and Indians . 16,253,300.44 War 284,449,701.82 Navy . . ... 43,519,632.21 Interest .... 1 .33,074,737.27 Total . . , $518,347,337.70 Total receipts $556,039,195.06 Total expenditures .... 518,347,337.70 Excess of receipts $37,691,857.36 190 THE NATIONAL DEBT. UNITED STATES BONDS. 338. The term "Five-Twenties" is applied to the G% gold-bearing bonds of the United States^ to which twenty years' half-yearly coupons are attached, but which may be paid off in gold by the Government, on due notice to the holders, at any time after ^fc years. 3:39. The 5-20's which were issued May 1, 18G2, called "Old 5-20's," because they were the first issued, are redeem- able after May 1, 1867, payable May 1, 1882. They bear interest at 6 % payable on May 1st and November 1st. 340. The 5-20's of 1864 were issued November 1, 1864. Interest payable May 1st and November 1st. 341. The 5-20's of 1865, November Issue, bear date November 1, 1865. Interest payable May 1st and Novem- ber 1st. 342. The 5-20's of 1865, July Issue, are issued in exchange for 7-30's, and bear date July 1, 1865. Interest on them is payable January 1st and July 1st. 343. The term "Ten-Forties" is applied to the 5% gold-bearing bonds of the United States, to which half-yearly coupons are attached for 40 years, but which may be paid oflf in gold, on notice to the holders, at any time after 10 years. Interest on them is payable, on the $500 and $1000 coupon bonds, and on all the registered bonds, March 1st and Sep- tember 1st; and on the $100 and S50 coupon bonds yearly, on March 1st. 344. The *« Scven-Tliirties" represent a Currcnci/ Loan having 3 years to run, then convertible at the option of the holder into a gold-interest 6% stock having 20 years to run, but with the right reserved to the Government of paying off the loan in gold at any time after five years. The term " Seven-Thirties" is derived from the rate of interest M'hich these thrcH' years' foiu crtililo Tintos bcnr, to wit: 2 cents per UNITED STATES SECURITIES. 191 day on each $100, or for 365 days, seven dollars and thirty cents on each $100. The First Series 7-30 Treasury Notes are dated August 15, 1864, and interest on them is payable in cur- rency August 15th and February 15th. Second Series 7-30 Notes, the same as first, except that they bear date June 15, 1865, and interest is payable June 15th and December 15th. They are convertible June 15, 1868, either into 5-20 bonds or money, at the option of the holder. The Third Series 7-30 Notes, same as the first two, except that the Government reserves the right to pay the interest at any time at 6% in gold instead of 7/^ in cur- rency, convertible 3 years from their date, viz., July 15, 1865, into 5-20's. Interest payable July 15th and January 15th. 345. The 6 per cents, of 1881, sometimes called the long or unconditional 6^ gold-bearing loan, cannot be re- deemed by the Government at all, except by purchase, until after the year 1881, making this the most desirable of all the United States loans as a permanent investment. Interest on them is payable January 1st and July 1st. 346. The terms "Greenbacks" and " Legal-Tenders'' arc convertible. All the Greenbacks are legal tender. All gold-bearing bonds are either coupon or registered. All the coupon bonds are issued in denominations of $50, $100, $500, and $1000. Registered bonds the same, with $5000 and $10,000 additional. The 7-30 Notes are issued in sums of $50, $100, $500, $1000, and $5000, all with coupons attached. Any coupon bonds will be exchanged by the Government for registered of the same issue. 192 TREASURY REQULATIONS. UNITED STATES TREASURY DEPARTMENT REGULATIONS. MH. Instructions to Correspondents. — "Letters re- lating to the redemption of public securities, the conversion of 7-,^Q Treasury Notes, or the exchange of coupon bonds for regis- tered certificates, should be addressed to the Secretary of the Treasury. Letters relating to the transfer of registered stock, or payment of interest on the same, should be addressed to the Register of the Treasury. The transfer-books are closed for thirty days previous to the day for payment of dividends, and stockholders desiring the place of payment changed, must give notice to the Register one month at least before the day of payment. When bonds are sent for transfer, stat« where interest is to be made payable, and always inclose stock of difierent loans in separate letters. When specifying the difierent loans, or referring to the interest, name the amount of stock, and describe the loan by the date of the act of Congress authorizing it. Powers of attorney for the assign- ment of United States stock, and assignments, must be pro- perly filled before transmission to the Register, as no blanks can be filled in his office. Powers of attorney to draw interest should be addressed to the First Auditor of the Treasury." 348. The National Debt of Great Britain is of two kinds, funded and unfunded. When a certain portion of the public revenue is appropriated for the payment of the interest on the debt, it is called funded, and it is called unfunded when no such division is made. Exchequer Bills (see Forms), which are somewhat similar to United States inter- est-bearing Treasury Notes, are a part of the unfunded debt. England has effected loans at different rates, 5, 4, 3 J, 3 per cent., &c. ; and one of the conditions of such loans is, that while the stipulated interest is regularly paid, the Gov- ernment cannot be called upon to return the principal. NATIONAL DEBTS. 193 349. Consols are a 3% English stock, which had its origin in the act of Parliament consolidating several separate Government stocks, called in the act Consolidated Annuities , and commonly quoted, for brevity, " Consols." The stock, from its amount, and the immense number of its holders, is more sensitive to financial influence than any other. Its dividends are payable semi-annually, — January 5th and July 5th. 350. The other kinds of stock, bearing 3%, are the Re- duced Annuities^ which formerly bore a higher rate of in- terest, and the New Three per cent. Annuities. NATIONAL DEBTS. Great Britain, United States, France, Austria, Russia, Italy. Spain, Netherlands, Turkey, Prussia, Portugal, Hamburg, Greece, Debt. $3,999,010,695 2,827,868,959 2,000,000,000 1,580,000,000 1,395,000,000 770,000,000 745,000,000 425,000,000 255,000,000 215,000,000 165,000,000 23,000,000 20,000,000 Population. 30,000,000 35,000,000 36,500,000 75,000,000 68,932,000 21,770,000 16,000,000 3,619,000 16,440,000 18,000,000 4,000,000 222,000 1,000,000 Average Amount per capita. 133.33 87.70 54.79 21.06 20.23 35.37 46.56 117.43 15.51 11.94 41.25 103.60 20.00 1. What is the annual interest on the debt of England, at the average rate of 3 a- per ccut., and what is the proportion for each inhabitant to pay ? 2. What is the annual interest on the debt of the United States, as per Statement March 1st, 1867, and how much is each person's share ? How much must be raised by the Government annu.ally to pay the interest and cancel the debt in 30 years ? 17 194 THE STOCK EXCUANOE. THE STOCK EXCHANGE. »]51. The Stock Exchange is an association organized for the purpose of buying and selling stock. It is governed by stringent regulations, to prevent improper persons from being admitted, and to insure fidelity in the performance of en- gagements. The members are elected by ballot; if a certain number of black balls appear against a candidate, he is re- jected. In Philadelphia, five are sufficient to prevent his becoming a member. The admission fee varies: to the New York Stock Ex- change it is $3000; to the Philadelphia and the Boston Stock Exchange it is $2000. In London the admission fee is 20 guineas, besides a yearly subscription of 10 guineas. The fee to become a member of the New York Open Board is $2000 ; to the Gold Board it is $2500. There are no dues to be paid in addition, but members are fined for non- attendance. Rules are enacted by which the proceedings of the Exchange are governed, disputes settled, and by which the prices and terms in buying and selling stocks are regulated. The charges in our large cities for buying and selling United States bonds are i per cent., or 12^ cents for a bond of $100; for other bonds, } per cent., or 25 cents per $100; for shares of com- panies, } per cent., or 25 cents per share when the par valuo of the shares is $50 or more ; when the par value is between $5 and $50, J per cent., or 12 J cents per share; when $5 or less, G} cents per share. In London, the commission on the sale or purchase of stock in the English or foreign funds is i, or 2.s\ Cxi. per cent. ; on exchequer bills, Is. per cent. ; on railway shares, when over £50 in value, i per cent, upon the value. Stock is bought and sold during the sessions, or '' boards," as they are termed, at which time a clerk calls the names of THE STOCK EXCHANGE. 105 the different stocks in the market, and the members offer to sell or to buy at a price which they mention. A charge against a member is instantly investigated, and, if he is found guilty of misconduct, or fails to fulfil his en- gagements, he is expelled. The Stock Exchange has a language peculiar to itself. A stock " broker'' is one who receives and executes orders for persons who are not members of the exchange. A stock *' jobber" deals in stocks for his own account. A "stag," or *' outsider," conducts his transactions outside the Exchange. A " bull" is one who operates for a rise in prices, — so called from the nature of a bull to toss with his horns. He is usually one who has agreed to purchase stock, without any intention of holding or' paying for it, but with a view to sell out again before "settling-day" arrives. A "bear" is one who en- deavors to depress prices, — so called from the nature of a bear to tear down with his claws. He, generally, has agreed to deliver more stock than he possesses, and is consequently obliged to buy in order to settle his account. A " lame duck" is a member unable to fulfil his contracts, and is therefore expelled. '^ Opening-day" is the first day the books of a corporation are opened after a dividend has been declared. The term " selling short" is applied to sales of stock which the seller does not own, and over which he has no control. Securities sold in this manner are generally deliverable at a specified time, not exceeding 60 days. If the contract is for a longer period than three days, the seller receives interest. " Seller's option" gives the person selling the privilege of making delivery at any time intervening before the expiration of that mentioned in the contract, by his giving one day's notice. " Buyer's option" gives the purchaser a claim for delivery at any time before the maturity of the contract, by a similar notice. The contract must be settled at least by maturity, unless extended by mutual agreement. The transactions are 19G STOCK QUOTATIONS. adjusted by delivery of property, or the payment in cash of the diflferencc in prices. A postponement of settling-day is termed a " contango." By a law in Pennsylvania, contracts for the sale of stock to be executed or performed at any future period exceeding five judicial days next ensuing the date of such contracts, are prohibited under heavy penalties. The "cornering" process, or "getting up a corner," is the act of a combination of operators, and is always the result of short sales. All the floating shares of a company are bought for future delivery, and when the stock has been rendered scarce in this manner, the shares thus bought are suddenly called for, to the loss of the short sellers, who are obliged to buy at an advanced rate, or pay the buyer the difference in price. The following extract was taken from the United States Gazette : — REPORTED BY JAY COOKE & CO., BANKERS. 26000 U. S. 5-20 bonds, 100 Reading R.R., 2 da., 100 " " 5w.n. 300 Reading R.R., b. 30, 300 N. Y. Central, b. 15 and int. 35500 U. S. 6's, 1881, lots, 100 U. S. Treasury 7-30 F. & A, 300 Catawissa prof, s., w.n., 2000 Penna. R.R., 2d M., 6'8, 100 Punna. 6's, int. off, 100 " 5's, 400 " R.R. ex. div., 600 Pliila. & Erie R.R., b.o,, 300 " " " B.O.. 103* 51i 1000 Camden & Amboy 6'8, 18S9 308i 671 103 109i lOOi 104 31 EXPLANATION. 5-20 bonds at $3.62J premium. Railroad stock sold at 2 days' credit. " " to be delivered before five days, without notice. 6 per cent, bonds, due in 1889, at S^ per cent, premium. To be delivered before 30 days. " " before 15 days, with int. U. S. 6 percent, bonds, duo in 1881, sold in lots, aggregating ^l^.-SOO. 7-30 bonds, interest payable in February and August. A. & 0. moans Apr. & Oct. Catawissa preferred stock, without notice. Second mortgage, bearing 6 per cent. int. Penna. 6 per cent, bonds, the interest last duo having been paid. Penna. 6 per cent, bonds, bearing 5 per cent, interest. Penna. R.R. shares without dividend. 500 shares at $32, at buyer's option wlien to take the stock. 300 shares at $.'U, at seller's option when to deliver tho stock. The value of a given number of shares is found by multi- plying the number of shares by the price per share. NoTK. — Tn finding the cost of bonds, the rate of brokcrnRe may b« added to tho price, as tho brokerage and price are both calcuUited on the same amount. DIVIDENDS AND INVESTxMENTS. 197 Example 1. — AVliat must I pay for 100 sli:ires of Chicago & llock Island R.R. stock, purchased at $112.50 per share, brokerage at I % and revenue stamp included ? 100 shares @ $112.50, $11250. i% on $10000, par value of 100 shares, " 25. llevenue stamp, Ic. on every $100 of sales, 1.13 $11276.13 Ex. 2.— What will I receive if I sell 300 shares Cleveland & Pittsburg II. R. stock, @ $72.00, after paying for revenue stamp and brokerage @ i % per share ? $72 X 300 = $21000 300 shares at 1% per share (par value, $50) = $75.00 Revenue stamp, 2.16 $77.16 $21000 — 77.16 = $21522.84, Ans. To find the dividend on any given number of shares of Btock. Rule. — Multipl>j the par value of the stoclc hy the rate of dividend^ and divide the product hy 100. EXAMPLES. 1. If I own 100 shares of Penna. Railroad stock, the par value of which is $50, how much will I receive when a divi- dend of 5% is declared? 50 X 5 = 2.50, dividend on 1 share. 100 X 2.50 = 250, " ^' 100 shares. Ans. $250. 2. How much will a stockholder of the New York Central Railroad Co. receive of a 4% dividend, who owns 500 shares, the par value being $100 per share ? 352. To find the rate of dividend- Rule. — MaMply the dividend hy 100^ and divide hy the 'par value of the sioch. 198 DIVIDENDS AND INVESTMENTS. EXAMPLES. 1. The receipts of a mining company in one year are 8170,000, clear of all expenses. The company has a capital of $500,000, divided into shares of 810 each. Reserving $50,000 as a contingent fund, what rate of dividend can it declare for the year ? what per month ? and how much can be paid on each share of stock ? 170000 — 50000 = 120000, amount to be divided. 120000 X 100 = 12000000 12000000 h- 500000 = 24 Ans. 24% yearly. 2% monthly, 20c. per month on each share. Proof.— 24% of 500000 = 120000, dividend to be declared. 2. A man subscribed for 300 shares of stock in a manu- facturing company, the par value of which was plnced at $50 per share ; but, after paying three instalments, amounting to 75% per cent, of the par value, a dividend of 3% was de- clared. How much will he receive, and at what rate per cent, on the actual cost? 3% of 50 = 1.50, dividend on one share. 1.50 X 300 = $450, dividend on 300 shares. 75% of 50 = $37.50 1.50 X 100 = 150.00 150.00 -- 37.50 = 4 Ans, $450. Total dividend = 4% on actual cost. 353. To find what rate of income will be derived from a given investment. Rule. — Multipli/ the income hy 100, and divide the product hy the amount invested. EXAMPLES. 1. If I buy railroad stock at a premium of 6 per cent., and pay \ per cent, brokerage, what per cent, of income will I re- ceive if its annual dividend is 7 per cent. ? 7X100 = 700 700^106J = 6}o Ans. 6}?%. 2. What per cent, will I receive if I buy stock, wliich pays 4 % dividend, at a discount of 20% ? 100 — 20 = 80, amount invested. 4X100 = 400 400 -J- 80 = 5 Ans. 5%. DIVIDENDS AND INVESTMENTS. 199 3 If I pay 106 for United States 6% bonds, having 15 years to run, wliat per cent, will I receive if I keep them until they mature, and then obtain the principal ? 6 % per year for 15 years = $90 interest. Principal, 100 Total amount received, 190 Cost of bond, 106 Total income, 84 To find what rate is required for 106 to gain 84 in 15 years, see Art. 79. 106 at 1% = 1.06 X 15 = 15-90, interest at 1% for 15 years. 15.90)8400(5.283-1- Ans. M^^fc 7950 4500 3180 13200 12720 4800 4770 Note. — The interest on the semi-annual payments of interest is also ta be considered. 4. What rate per cent, will be gained if I purchase United States 5-20 bonds, at a premium of 8%, if they are paid at the end of 6 years ? Ans. 4|f . 354. To find the price to be paid for stock to obtain a given rate upon the investment. Rule. — Annex two ciphers to the rate per cent, which the stock produces^ and divide hy the required rate; the quotier4 will he the price to be paid. EXAMPLES. 1. At what price must railroad stock be purchased, whi/»h pays 6% on the par value of $100, in order to obtain 7^ income on the investment? 600--7 = 85.71f Ans. S85.71. 2. At what price must I purchase railroad stock of ihe par value of $50 per share, which pays a dividend of 6%. that I may obtain an income of 8% on the investment? Ans. $37.50. 200 DIVIDENDS AND INVESTMENTS. 3. If T receive 9% on my investment in a company which pays a dividend of 6 % , at what price did I purchase ? 4. At what price must 5% stock be purchased in order to obtain G% on tlie investment? 5. At what premium ought an 8% stock to sell, to equal 6% stock? Ans. 33J. 0. At what rate must G% stock be purchased to equal 8% stock? to equal 10% stock? 355. To find what rate must be obtained, that a given sum invested may bring a given income. Rule. — Multiply the given income hy 100, and divide the product hy the sum invested. EXAMPLE. If I invest $5000, what rate per cent, must I receive to obtaiu an income of ^325 per year? 32500 ^5000 = 6,^ 9J. 356. To find what sum must be invested, that a given in- come may be obtained. RuLE.-7-Z)tyw7e the required income hy the rate of income per share, or per ^100, for the numher of sluires or bonds re- quired, and multiply the quotient hy the given price. EXAMPLES. 1. "What sum must be invested in United States 6% bonds, ftt 108, to realize an income of $1200 per annum? $G = income per $100,— $108 the price of $100 bonds. 1200 -^ G =: 200, the number of bonds of $100 each. 200 X 108 = 21600. Ans. $21000. 2. What sum must be invested, at $65 per share, in rail- road stock which pays a dividend of 10^ on the par value of $50 per share, in order to obtain an income of $520 ? 10% of $50 = $5, income per share. $520 -V- $5 = 104, the number of shares. 104 X $05 = $0700. Ans. $0700. DIVIDENDS AND INVESTMENTS. 201 3. If United States Ten-Forties are selling at 93, how much must I invest in them to obtain a yearly income of 11800, after paying 5 % income tax ? 357. To find the par value, when the premium or discount is given. lluLE. — Divide the given value of the stoch hy 1 increased hy the rate 'per cent, of 'premium,^ or diminished hy the rate per cerit. of discount. EXAMPLES. 1. Bought Mechanics' National Bank stock for 29, at which price I paid a premium of 16%. What is the par value? Ans. $25. 2. Sold Worcester & Nashua Railroad stock for $91.66i, and received 10% above the par value. What is the par value? Ans. $83.33i 3. Bought Philadelphia & Erie Railroad stock for $47, which is 6 % below par. What is the par value ? 4. Bought Fulton Bank stock at 500% premium, for $180. What is the par value of the shares ? Ans. $30. 858. To find at what price a bond, having several years to run, must be purchased, that the interest and final payment will be equivalent to a given rate per annum on the investment. Rule. — I. Find the Amount of the given bond. II. Find the present worth of this amount at the proposed rate. Note. — No account is taken in this rule of interest on the annual pay- ments of interest. EXAMPLES. 1. What shall I pay for a bond of $100, having 5 years to run, with interest at 6%, in order to make it an 8% invest- ment? Amount of $100 for 5 years = $130. By Art. 84, 130 -^ 1.40 = 92.86. Ans. $92.86. Interest on $92.86 at 8% for 5 yrs. = 37.14. 92.86 -f 37.14 =r 130. 2. At what price must I buy United States 5-20 Bonds, if they are paid in 4 years, in order to gain 7% on my in- vestment ? 202 STOCK TABLE. 3. Bought Kentucky State Eonds, bearing 5^ interest, payable in 3 years, and received, when I obtained the prin- cipal, 6% on iny investment. What did I pay? MISCELLANEOUS. 1. What rate per cent, will the purchaser of Philadelphia Bank stock receive on his investment if the premium on the stock is 35% and the bank pays an annual dividend of 8% ? Ans. 5||. 2. Which is the most profitable, — United States 10-40 Bonds purchased at 95, or the 5-20 Bonds purchased at 105 f* 3. Which is the better investment, a ground-rent bearing 6% interest, purchased at 98%, or railroad stock purchased at 10% premium, which pays an annual dividend of 7%? and how much ? 4. What interest will a person receive who purchased United States 5-20 Bonds at 104, if he sells the gold re- ceived for interest at a premium of 30 % ? STOCK TABLE, Showing the rate of Interest received on Stocks purchased, from 25 per cent, discoutit to 25 per cent preynium. KATE RECEIVED ON STOCK BEARINTQ INTEREST AT Purchase Price. 5 per cent. 6 per cent. 7 per cent. 8 per cent. 10 per cent. 75. G.666 8.00 9.338 10.666 13.333 80. 6.25 7.50 8.75 10.000 12.500 85. 5.882 7.143 8.235 9.411 11.764 90. 5.555 6.6G6 7.777 8.888 11.111 95. 5.263 6.316 7.263 8.421 10.526 97 50 5.128 6.156 7.179 8.205 10.256 100. 5.000 6.000 7.000 8.000 10.000 105. 4.7G1 5.714 6.6G6 7.019 9.523 no. 4.545 5.454 6.3G3 7.272 9.090 115. 4.347 5.130 G.086 G.95G 8.G95 120. 4.1 GO 5.000 5.833 6.GGG 8.333 125. 4.000 4.800 5.600 G.400 8.000 UNITED STATES BONDS IN EUROPE. 203 UNITED STATES BONDS IN EUROPE. The Five-Twenty Bonds issued in 1862, called the "Old'' 5-20's, were the first known in Europe, and for that reason are in greatest demand, causing an advance over the issues of 1864 and 1865 of 1^ to 4J per cent. The real value of the different issues is the same. The quotations in London, Paris, Frankfort, Hamburg, and other places, are the prices of $100 bonds in American gold. Thus, "Frankfort, Feb. 9th, U.S. 5-20's 761," signi- fies that $76.25 in U. S. coin is the price of a bond for $100. The interest which has accrued at the time of purchase forms a part of the value of the bond. The principal causes of the difference in the quotations on the same day are the fluctuations in the rate of exchange and the difference in the basis of calculation. It is necessary also to know whether the " old" or " new" issue is meant. The telegraphic report frequently omits the date of issue ; in the Stock Exchange Circular, the prices of both are given. To understand the subject fully requires a knowledge of exchange and stock calculations, and an acquaintance with the customs and manner of dealing among bankers. Foreign Stock Quotations. (per ATLANTIC CABLE.) London, Mar. 1. U. S. 5-20's, nh Illinois Central E. R., 76^. Erie R. R., 36i. Paris, U. S. 5-20's, 821. Frankfort, " u u 76i London, Mar. 23. li a Uh Frankfort, " U li 77h 204 UNITED STATES BONDS IN EUROPE. L.ondon Quotations. — The price quoted in London is at the nominal par of 4s. 6d. per dollar, or 84.44| per pound sterling. To this about 9J% must be added for the differ- ence between the old par and the present value of our coins. To obtain the currency value, the premium on gold must also be added. EXAMPLES. What is the value of $1000 in U. S. 5-20 Bonds when quoted at 70 and the premium on gold is 35 % ? 1000 70 700.00 Nominal par value. 9^% 630000 35000 66.5000 Exchange premium. 700 766.50 Value in American gold. 35% 383250 229950 268.2750 Premium on price in gold. 766.50 1034.7750 $103.48 in United States. To a resident of the United States a purchase in London like this would require an addition of 1^ commission, and interest equal to ^^ more, which increases the price to $105.03. The proceeds of a sale would be $1.55 less than $103.48 = $101.93. 2. When gold is at a premium of 33%, what will be re- ceived from a sale of $5000 U.S. 5-20's, at 72, allowing commission and interest at 1^% ? 3. How much will a 5-20 Bond for $5000, purchased in London, cost, in currency, when exchange is 109, and gold is at a premium of 30%, allowing commission at 1% ? UNITED STATES BONDS IN EUROPE. 205 Paris Quotations. — In Paris the price of exchange affects the quotations. On the Paris Bourse the bonds are estimated on the conventional basis of 5 francs to the dollar, while the actual value of a dollar in exchange transactions is 5.10 and 5.15, equal to a difference of $2 to $3 on $100. London quotations, being based on the old par, require the addition of about 9?% and the difference between the Paris Bourse rates and actual exchange rates, to give the corapara- tive value of both places. Example.— February 23, 1867. London, U. S. 5-20's 731; Paris, 83i Premium on $73.75 @ 9^%, = $7.00 Difference between Bourse and exch. rates = 2.50 To be added to London rate, 9.50 73.75 + 9.50 = 83.25 Paris rate, as above. Note. — The difference between the Bourse rate and the exchange rate should be taken from the Paris quotations to obtain the real price in Paris. In Frankfort, when American gold is not paid, the value is computed at the rate of 2 J guilders per dollar. 1. On March 1, 1867, the quotations per Atlantic Cable were: London, U.S. 5-20's 73i; Frankfort, 76i In New York, exchange on London the same day was 109. Value of $73.25 in London, @ 9% prem., 79.84 Price in Frankfort, 76.62 Difference between London and Frankfort, 3.22 With exchange on Frankfort at tlf, the difference is but a trifle. 2. On the same day, Illinois Central R. R. stock was quoted in London at 76^^, Erie Railroad at 36^. What are these prices equivalent to in U.S. currency, gold being at 140? 3. What is the value in United States currency of a bill of exchange on England, when quoted at 153, which includes the exchange premium and premium on gold? 18 206 COMPOUND INTEREST. COMPOUND INTEREST. 360. Compound Interest is interest on both principal and interest, 361. To compute compound interest. lluLE. — Find the interest on the given principal to the time the interest becomes due, and add the principal. Then find the interest on this amount for the next period, and add as before, and so continue for each successive period to the time of settle- ment. Subtract the given princijml from the last amount, and the remainder will be the compound interest. When the time is for years, months, and days, find the amount for the years, and the interest on this for the remainder of the time. When interest is payable oftener than once a year, find the amount for each interval in the same manner as when the interest is pay- able yearly. EXAMPLES, 1. What is the compound interest of $500 for 3 years, at $500 Given principal, .05 . 25,00 Interest for first year. 500 525.00 Principal for second year, ,05 26.25 Interest for second year. 551.25 Principal for third year. ,05 27.5625 Interest for tliird year. 551.25 578.8125 Amount for three years. 500 Given principal. $78.8125 Compound interest for 3 years. 2. What is the compound interest of S t25 for 4 years, at Tfo ? of $275.50 for 3 years, G months, at 7% ? COMPOUND INTEREST. 207 362. The labor of computing Compound Interest may be much abridged by the use of the following tables. TABLE I. Showing the amount of One Dollar at Compound Interest, from ^ to 4^ per cent., for any 7iunfiber of years not exceeding twenty. i per cent. 1^ per cent. 2 per cent. 2i per cent. 1 1.005000 1.015000 1.020000 1.025000 1 2 1.010025 1.030220 1.040400 1.050625 2 3 1.015075 1.045670 1.061208 1.076891 3 4 1.020150 1.061350 1.082432 1.103813 4 5 1.025251 1.077270 1.104081 1.131408 5 6 1.030377 1.093429 1.126162 1.159693 6 7 1.035529 1.109830 1.148686 1.188686 7 8 1.041207 1.126479 1.171659 1.218403 8 9 1.016413 1.143375 1.195093 1.248863 9 10 1.051&45 1.160526 1.218994 1.280085 10 11 1.056904 1.177934 1.243374 i.312087 11 12 1.062188 1.195603 1.26S242 1.344889 12 13 1.067499 1.213537 1.293607 1.378511 13 14 1.072836 1.231740 1.319479 1.412974 14 15 1.078199 1.250216 1..345868 1.44S298 15 16 1.0S3589 1.268969 1.372786 1.484506 16 17 1.089007 1.288003 1.400241 1.521018 17 18 1.094452 1.307323 1.428246 1.559659 18 19 1.099924 1..326932 1.456811 1.598650 19 20 1.105424 1.346835 1.485947 1.638616 20 3 por cent. 3^ per cent. 4 per cent. 4^ per cent. 1 1.030000 1.035000 1.040000 1.045000 1 2 1.060900 1.071225 I.OSIGOO 1.092025 2 3 1.092727 1.I0.S718 1.124864 1.141166 3 4 1.125509 1.147r.23 1.169859 1.192519 4 5 1.159274 l.iS76:-:o 1.216653 1.246182 5 6 1.194052 1 .229255 1.265319 1.302260 6 7 1.229874 1.272279 1.315932 1.360862 7 8 1.2G6770 1.310809 1.368569 1.422101 8 9 1.304773 1.302S97 1.42.3312 1.486095 9 10 1.343916 1.410599 1.480244 • 1.552969 10 11 1.384234 1.459970 1.539454 1.622853 11 12 1.425701 1.511069 1.601032 1.695881 12 33 1.408534 1.563956 1.665074 1.772196 13 14 1.512590 1.6180^5 1.7.31676 1.851945 14 15 1.557967 1.675349 1.800944 1.935282 15 16 1.601706 1.733986 1.872981 2.022.370 16 17 1.652848 1.794676 1 .947900 2.113377 17 18 1.702433 1.8.57489 2.025817 2.208479 18 19 1.753506 1.922501 2.106849 2..307860 19 20 1.806111 1.989789 2.191123 2.411714 20 208 COMPOUND INTEREST. TABLE II. Showisig the amount of One Dollar at Compound Interest, from H to 12 per cent., for any number of years not exceeding twenty. 6 per cent. 6 per cent. 7 per cent. 8 per cent. 1 1 1.050000 1.060000 1.070000 1.080000 2 1.102500 1.123600 1.144900 1.166400 2 3 1.157625 1.191016 1.225043 1.209712 3 4 1.215506 1.262477 1.310796 1.360489 4 5 1.276282 1.338226 1.402552 1.469328 5 6 1.340096 1.418519 1.500730 1.586874 6 7 1.407100 1.503630 1.605781 1.713824 7 8 1.477455 1.593848 1.718186 1.850930 8 9 1.551328 1.689479 1.838459 1.999005 9 10 1.G28895 1.790848 1.967151 2.158925 10 11 1.710339 1.898299 2.104852 2.331639 11 12 1.795856 2.012196 2.252192 2.518170 12 13 1.885649 2.132^)28 2.409845 2.719024 13 14 1.979932 2.260904 2.578534 2.937194 14 15 2.078928 2.396558 2.759031 3.172169 15 16 2.182875 2.540352 2.952164 3.425943 16 17 2.292018 2.692773 3.158815 3.700018 17 18 2.406619 2.854:5.39 3.379932 3.996019 18 19 2.526950 3.025593 3.616527 4.315701 19 20 2.65:3298 8.207135 3.869684 4.660957 20 9 per cent. 10 per cent. 11 per cent. 12 per cent. 1 1.090000 1.100000 1.110000 1.120000 1 2 1.188100 1.210000 1.232100 1.264400 2 3 1.295029 1.33100C 1.367631 1.404908 3 4 1.411582 1.464100 1.518070 1.573519 4 6 1.538624 1.610510 1.685058 1.762342 6 6 1.677100 1.771561 1.870414 1.973S22 6 7 1.828039 1.948717 2.076160 2.21 0C81 7 8 1.9925G3 2.143589 2.304537 2.475963 3 9 2.171893 2.357948 2.558036 2.773078 9 10 2.367364 2.593742 2.839420 3.105848 10 11 2.580426 2.853117 3.151757 3.478549 11 12 2.812065 3.138428 3.498450 3.895975 12 13 3.005R05 3.452271 3.883279 4.36:J492 13 14 ;'..:U1727 3.797498 4.310440 4.887111 14 15 3.6-12482 4.177248 4.784588 6.473565 16 16 3.970.".00 4.594973 5.310893 6.130392 16 17 4.S276.33 6.054470 6.895091 6.866040 17 IS 4.717120 5.559917 6.64.3551 7.6S99fti 18 19 5.141(i01 6.115909 7.2«W42 8.612760 19 20 5.60J411 1 6.727500 8.062309 9.0462<.H 20 COMPOUND INTEREST. 209 363. To find the amount of any sum by tlie tables. Multi- "ply the amount of $1 for the given rate and time hy the given 2^rincipal. Example. — What will be the amount of $590 for 10 years, at 6% compound interest? Amount of $1 for 10 years at 6% = 1.790848 500 Amount of $500 = $895.424000 $895.42 — $500 = $395.42, the compound interest. 364:. When the time extends beyond the limits of the table, find the amount for a convenient length of time, and use this amount for a new principal for the remainder of the time. Example. — $1.790848, amount for 10 years, at 6%, mul- tiplied by 1.338226, amount for 5 years, equals $2.396558, amount for 15 years. 365. When the intervals are less than a year, find how many such intervals occur in 1 year, and divide the given rate by the number of intervals thus found; then under the rate shown by the quotient, and opposite the number show- ing the total number of intervals, will be found the amount. Examples. — 1. The amount of $800 for 3 years at 6 per cent, compound interest, payable semi-annually, is the same as the amount of $800 at 3 per cent, for 6 years, payable annually. If the interest was payable quarterly, it would be the same as the amount of $800 for 12 years at IJ per cent.; if payable monthly, the same as for 36 years at J per cent. 2. What is the compound interest of $950 for 3 years, months, at 12%, payable semi-annually? 3. What is the compound interest of $4600 for 2 years, interest payable quarterly, at 6 % per annum ? 366. Comjwund Interest, and also the Compound Amoiuif, vary in proportion to the principal. 367. To find the principal or present worth at compound interest, the amount, time, and rate per cent, being given Rule. — Divide the given amount hy the compou7id amount of ^1 for the given time and, rate. 18* 210 COMPOUND INTEREST. Example. — What is the present worth of §306.26, due 3 years hence, at 7 % compound interest? Amount of U for 3 years at 7 %, $1.225043. $306.26 -^ 1.225043 = $250. - Ans. $250. 368. To find the principal or present worth, the compound interest, the time, and the rate per cent, being given. Rule. — Divide the given interest hy the compound intercut on ^1 for the given time and rate. Example. — What principal at 7% compound interest will produce $351.81 in 15 years? Compound interest of $1 for 15 years at 7% = $1.759031. $351.81 -- 1.759031 = $200. Ans. $200. 369. To find the time or rate, when the other quantities are given. Rule. — Divide the amount hy the principal, and look for the quotient in the Tahle, under the given rate, or opposite the given time. 370. To-icompute compound interest by the use of loga- rithms. Rule. — Mnd the logarithm of the amount of $100 for 1 year or the time specified, and reject 2 in the index. Then multiply it hy the given numher of years or time spe- cified, and to the product add the logarithm of the principal; their sum will he the logarithm of the amount. EXAMPLE. What is the compound interest of $340 for 7 years at 6 ^ '/ Logarithm of $106, rejecting 2 in the index, 0.02531 Number of years, 7 .17717 Add logarithm of $340, 2.53148 Logarithm of the amount, 2.70865 This logarithm gives, $511.23 Deducting the principal, 340.00 Compound interest of $340 for 7 years, $171.23 ANNUITIES. 211 ANNUITIES. 371. An Annuity is a yearly income or sum of money to be paid regularly at stated periods. 372. A Perpetual Annuity is one that is unlimited in duration, or which can be terminated by the grantor only on the payment of a sum whose interest will equal the annuity. 373. An Annuity Certain, or Terminafele Annuity, begins and ends at a fixed time. 374. A Contingent Annuity depends upon some par- ticular circumstance, as the life of one or more individuals. Life Insurance, Dowers, and Pensions are of this kind. 375. A Deferred ilnnuity, or Annuity in Rever- sion, is one that begins at some future time. 376. An Annuity forborne or in Arrears is one on which the payments remain unpaid after becoming due. 377. The Amount or Final Value of an annuity at compound interest is the sum to which all its payments at compound interest will amount at the end of the annuity. 378. The Present Value of an annuity is the sum which at interest would amount to its final value. ANNUITIES AT SIMPLE INTEREST. 379. To find the final value of an annuity at Simple In- terest. KuLE. — Multipli/ the interest on the amiuity for 1 year Inj the numher of years less 1, and this product hy one-half the number of years ; then Add the product of the annuity multiplied hy the nmnhcr of years. 212 ANNUITIES. EXAMPLES. 1. What will be the amount or final value of an annuity of ai50for Syearsat 6%? Interest on ^150 for 1 year = $9. 9 X 7 = 63. 03 X 4 = 252 150 X 8 = 1200 Ans. 81452 2. The rent of a house, which is S300 per year, has re- mained unpaid for 5 years. What amount is now due, allowing interest at 7 % ? Ans. $1710. 380. '1 J find the present value of an annuity at Simple Interest. ^ llULF.- -Find the final value of the annuiti/^ and then find the presf'tt value of that amount. EXAMPLE. 1. What is the present value of the annuity mentioned in the first example under the preceding rule ? Final value, $1452. Present worth of 81452 for 8 years at 6% =$981.81. ANNUITIES AT COMPOUND INTEREST. The amount of an annuity of $1, at 6% Compound In- terest, for 1 year = $1.060000. 2 yrs. =$1.123600. 3 " =$1.191016. The final value of an annuity of $1 for 2 years. .3 years. 4 years. $1.00 $1.0000 $1.000000 1.06 1.0600 1.060000 $2J06 1.1236 1.123600 Final value for 3 years, $3.1836 1:1?15H' Final value for 4 years, $4.374616 The final value of $300 for 4 years = $4.374616 X 300, = $1312.3848. ANNUITIES. 213 881. To find the final value of an annuity. Rule. — Multiply the amouPit of ^1, as given in Tahle /, hy the annuity : the product vnll he the final value. 382. The final value may also be found by obtaining the principal required to produce an amount of interest equal to the annuity, and then multiplying this principal by the com- pound amount of SI for the given rate and time. 383. To find the present value of an annuity. IluLE. — Divide the amount or final value of the anmdty hy the amount of ^1 at compound, interest. Or, Multiply the present loorth of ^1, as given in Tahle IT., hy the given annuity. Example. — Find the present worth of an annuity of SI for 3 years at 6%. The final value of $1 for 3 years = S3.1836. Then, by Art. 3G8, Compound Interest, the present value of an annuity of $1 for 3 yearsz=$3.1836^1.191016 = $2.673012. The present value of S500, at the same rate, for the same time, would be $2.673012 X 500 = $1336.506. 381. To find the present value of an annuity in reversiou. KuLE. — JF'ind the present value of an annuity of ^1 to the time the annuity commences, and also to the time it termi- nates; then multiply the difference hetween these present valuei^ hy the given annuity. Or, Find the present worth of the final value of the annuity from the present time to the time it terminates. Example. — A father leaves an income of $500 per year to his son, to commence in 5 years and to continue for 10 years. What is the present worth of the legacy, at 6 per cent. '/ By Table II., present worth of $1 for 15 years, $9.712249 " " $1 '' 5 " 4.212364 $5.499885 $5.499885 X 500 == $2749.94, Ans. 214 ANNUITIES. TABLE I. Showing the FINAL VALUE of an Annuity of One Dollar per anmim, Compound Interest, from 1 year to JfO, inclusive. i 3 per cent. 31^ per cent. 4 per cent. 5 per cent. 6 per cent. 7 per cent. ' 1 1.000 000 1.000 000 1.000 000 1.000 000 1.000 000 1.000 000 2 2.030 000 2.035 000 2.040 000 2.050 000 2.060 000 2.070 000 3 3.090 900 3.106 225 3.121 600 3.152 500 3.183 600 3.214 900 4 4.183 027 4.214 943 4.240 404 4.310 125 4.374 616 4.439 94.3 5 5.309 136 5.362 466 6.416 323 5.525 631 5.637 093 5.750 739 6 0.468 410 6.550 152 6.632 975 6.801 913 6.975 319 7.153 291 7 7.662 462 7.779 408 7.898 294 8.142 008 8.393 838 8.664 021 8 8.892 336 9.051 687 9.214 226 9.549 109 9.897 468 10.269 803 9 10.159 106 10.368 496 10.582 795 11.026 564 11.491 316 11.977 989 10 11.463 879 11.T31 393 12.006 107 12.577 893 13.180 795 13.816 448 11 12.807 796 13.141 992 13.486 351 14.206 787 14.971 643 15.783 699 12 14.192 030 14.601 962 15.025 805 15.917 127 16.869 941 17.888 451 13 15.617 790 16.113 030 16.626 838 17.712 983 18.882 138 20.140 6^43 14 17.086 324 17.076 986 18.291 911 19.598 632 21.015 066 22.550 488 15 18.598 914 19.295 681 20.023 588 21.578 564 23.275 970 26.129 022 16 20.156 881 20.971 030 21.824 531 23.657 492 25.670 528 27.888 054 17 21.761 588 22.705 016 23.697 512 25.840 360 28.212 880 30.840 217 18 23.414 435 24.499 691 25.645 413 28.132 385 30.905 653 33.999 033 19 25.116 868 26.357 ISO 27.671 229 30.539 004 33.759 992 37.378 965 20 20.870 374 28.279 682 29.778 079 33.065 954 36.785 591 40.995 492 21 28.676 486 30.269 471 31.969 202 85.719 252 39.992 727 44.865 177 22 30..536 780 32.328 902 34.247 970 38.505 214 43.392 290 49.005 739 23 32.452 884 34.400 414 36.017 889 41.430 475 40.995 828 63.430 141 24 34.426 470 30.606 528 39.082 601 4-1.501 999 50.R15 577 58.170 671 25 36.459 264 38.949 857 41.645 908 47.727 099 54.864 512 63.249 030 26 38.553 042 41 ..313 102 44.311 745 51.113 454 59.156 383 68.676 470 27 40.709 634 42.759 060 47.084 214 54.669 126 63.705 766 74.4S.3 823 28 42.9:i0 923 46.290 027 49.967 583 58.402 583 68.528 112 80.(i97 C91 20 45.218 850 4X.910 799 52.906 286 62..322 712 73.6.-)9 798 87.;uo ,V>» 30 47.575 416 51.022 677 56.084 938 60.438 848 79.068 186 94.460 786 31 50.002 678 54.429 471 69.328 335 70.760 790 84.801 677 102.073 041 32 52.502 759 57 ..334 .Wi 02.701 469 75.298 829 00.899 778 110.218 15-4 33 55.077 841 00.311 210 06.209 527 80.063 771 97.313 165 118.933 425 34 57.730 177 6.'!.453 1.52 69.857 909 85.006 959 104.183 755 1-28.258 70,-) 35 60.402 082 00.074 013 73.052 225 90.320 307 111.434 780 138.236 878 36 63.271 044 70.007 003 77.598 314 95.830 323 119.120 807 148.913 460 37 66.174 223 73.4.^7 809 81.702 246 101.028 139 127.268 119 160.337 4(K) 38 69.150 440 77.028 SOi) 85.070 iWO 107.709 546 135.904 206 172.561 020 39 72.2;u 2:J3 80.724 906 90.409 150 114;005 02:3 145.058 458 1S5.640 2ii2 40 75.401 260 84.550 278 95.025 516 120.799 774 154.761 966 199.635 112 ANISUITIES. 215 TABLE II. Showing the PEESEXT WORTH of an Annuity of One Dollar per annum, at Compound Interest, from 1 year to J^O, inclusive. OT 3 per cent. 3}/^ per cent. 4 per cent. 5 per cent. 6percent. 7 per cent. 1 0.970 874 0.966 184 0.961 538 0.952 381 0.943 396 0.934 579 1 2 1.913 470 1.899 694 1.886 095 1.859 410 1.833 393 1.808 017 2 3 2.828 611 2.801 6,37 2.775 091 2.723 248 2.673 012 2.624 314 3 4 3.717 098 3.673 079 3.629 895 8.545 951 3.465 106 3.387 209 4 5 4.579 707 4.515 052 4.451 822 4.329 477 4.212 364 4.100 195 5 6 5.417 191 5.328 553 5.242 137 5.075 692 4.917 324 4.766 537 6 7 6.230 283 6.114 544 6.002 055 5.786 373 5.582 381 5.389 286 7 8 7.019 692 6.873 956 6.732 745 6.463 213 6.209 744 5,971 295 8 9 7.786 109 7.007 687 7.435 332 7.107 822 O.bOl 692 6.515 228 9 10 8.530 203 8.316 605 8.110 890 7.721 735 7.360 087 7.023 577 10 11 9.252 624 9.001 551 8.760 477 8.306 414 7.8S6 875 7.498 669 11 12 9.954 004 9.663 334 9.385 074 8.863 252 8.383 844 7.942 671 12 i;5 10.634 955 1()..302 738 9.985 648 9.393 573 8.852 683 8.357 635 13 14 11.296 073 10.920 520 10.563 123 9.898 641 9.294 984 8.745 452 14 15 11.937 935 11.517 411 11.118 387 10.379 658 9.712 249 9.107 898 15 16 12.561 102 12.094 117 11.652 296 10.837 770 10.105 895 9.446 632 16 17 13.166 118 12.651 321 12.165 669 11.274 066 10.477 260 9.763 206 17 18 13.753 513 13.189 682 12.659 297 11.689 587 10.827 603 10.059 070 18 19 14.323 799 13.709 837 13.133 939 12.085 321 11.158 116 10.335 578 19 20 14.877 475 14.212 403 13.5'JO 326 12.402 210 11.469 421 10.593 997 20 21 15.415 024 14.697 974 14.029 160 12.821 153 11.764 077 10.8.35 527 21 22 15.936 917 15.167 125 14.451 115 13.163 003 12.041 582 11.061 241 22 23 16.443 608 15.620 410 14.856 842 13.488 574 12.303 379 11.272 187 23 24 16.935 542 16.058 368 15.246 963 13.798 642 12.550 358 11.409 334 24 25 17.413 148 16.481 515 15.322 080 14.093 945 12.783 356 11.653 583 25 26 17.876 842 16.890 352 15.982 769 14.275 185 13.003 160 11.825 779 26 27 18.327 031 17.285 365 16.329 586 14.643 0.34 13 210 534 11.986 709 27 28 18.764" 108 17.667 019 16.663 063 14.898 127 13.406 164 12.137 111 28 29 19.188 455 18.0.35 767 16.983 715 15.141 074 13.590 721 12.277 074 29 30 19.600 441 18.392 045 17.292 033 15.372 451 13.764 831 12.409 041 30 31 20.000 428 18.736 276 17.588 494 15..592 811 13.929 086 12.531 814 31 32 20.338 766 19.068 865 17.873 552 15.802 677 14.084 043 12.646 555 32 33 20.765 792 19..390 208 18.147 646 16.002 549 14.230 2.30 12.753 790 33 34 21.131 837 19.700 684 18.411 198 16.192 204 14.368 141 12.854 009 34 35 21.487 220 20.000 661 18.664 613 16.374 194 14.498 246 12.947 672 35 36 21.832 252 20.290 494 18.908 282 16.546 852 14.620 987 13.035 208 36 37 22.167 235 20.570 525 19.142 579 16.711 287 14.736 780 13.117 017 37 38 22.492 462 20.841 087 19.367 864 16.867 893 14.846 019 13.193 473 38 1 39 22.808 215 21.102 500 19.584 485 17.017 041 14.949 075 13.204 928 39 40 23.114 772 21.355 072 19.792 774 17.159 086 15.046 297 13.331 709 40 216 ANNUITIES. 385. To find the present worth of an annuity in per- petuity. This is equivalent to finding a principal the interest of which is equal to the given annuity. Rule. — Annex two ciphers to the annuity, and divide hy the rate. Example. — The annual income from an estate is $250. What is the present worth of the estate, allowing compound interest, at 6 per cent. ? Ans. 386. To find an annuity from its present value. Rule. — Divide its present value hy the present value of an annuity of ^1 for the given rate and time. Example. — The present value of an annuity for 10 years, at 5 per cent, compound interest, is $3000. What is the annuity? Ans. $388,513. 387. To find an annuity from its amount. Rule. — Divide the given amount hy the amount of $1 for the given time and rate. Example. — The final value of an annuity for 11 years, at 7 per cent, compound interest, amounts to $4735.08. What is the annuity ? Ans. $300. miscellaneous examples. 1. What sum of money must a man invest annually at 6 per cent, compound interest, that he may have $5000 at the end of 10 years ? 2. What is the present worth of $500 to be received annu- ally for 6 years, allowing compound interest at 7 per cent. ? 3. What sum invested at 6 per cent, compound interest Will yield an income of $1800 per annum for 12 years? 4. The executors of an estate offer for sale an unoccupied Icnsc that has 6 years to run, for a premium of $300. How much, added to the annual rent, will amount to the same sum ? 5. What is an interest of $250 annually in an estate for 10 years worth, allowing money to be worth 7 per cent, com- pound interest? BUILDING AND LOAN ASSOCIATIONS. 217 BUILDING AND LOAN ASSOCIATIONS. 388. Building and Loan Associations have for their object the accumulation of a fund from which the members can obtain the means to build or buy houses, purchase lands, or for similar purposes. The shares are usually estimated at $200 each, and are paid for in monthly instalments, generally $1 per month for each share. When the accumulated payments reach a certain sum, the funds are offered at auction, and given to the shareholder paying the largest bonus or discount. Interest on the loan thus made is paid monthly, or at the same time as the periodical dues. The loans are generally secured by mortgage on real estate. To prevent delinquency, fines are imposed of 5 or 10 per cent, per month on all sums not paid when due. When the total amount received by the association is sufficient to give each shareholder the amount originally agreed upon, the association closes. As promotive of habits of economy, and as affording means of profitable investment, these associations have been highly successful. The chief benefit, however, is derived from the increase in the value of the property purchased, and in the convenient form in which the payments are made. Practi- cally, these associations have given homes to hundreds who would otherwise never have owned them. 389. To find the cost of a share at simple interest, when the monthly dues, time, and rate of interest are given. Rule. — Multiply the interest on the monthly payment for one month hy the number of months^ less 1, that the associa- tion continues, and, this product hy one-half the number of months the association continues. Then Add the product of the monthly payment by the total number of months. 19 218 BUILDING AND LOAN ASSOCIATIONS. EXAMPLE. What was the cost of a share for which SI per month had been paid for 9 years, allowing 6% simple interest?. Interest on U for 1 month, .005. 108 — 1 = 107 Number of months in 9 years = 108. 108 -~2= 5-1 107 X -005 = .535. .535 X 54 =^ 28.890 U. X 108 == ^108.000 Total cost, allowing 6 per cent, interest, $136,890 390. To find the cost of a share at compound interest. Rule. — Divide the monthly payment^ after annexing two ciphers, hy the given rate of interest^ and find the compound interest of the quotient for the given rate and time. 391. To find the cost of a loan at simple interest. Rule. — Add the present value of a share to the pi-csent value of the payment required for the loan. As it is impossible before the association closes, owing to the variations of discounts, number of borrowers, etc., to know the exact time the association will continue, an approximate value is all that can be found. From eight to ten years is the usual time. EXAMPLES. 1. What is the cost of a loan of $200, the a.ssociation re- quiring $1 interest in addition to $1 as regular payment to bo paid monthly for 6 years, the present value of a share being $50 ? Interest ou $2 for 1 month = .01. 6 years = 72 months. .01 X 71 = 71/. 71 X36r= $25.56 $2 X 72 = 144.00 Value of payments to be made, $169.56 Present worth of payments for 6 years, $124 26 Value of share, 50 Cost of loan, $174.26 Ans. A bonus of 10% on $200 would leave $180. A bonus of 20% would leave $160. 2. Which would be preferable, the above loan and pay- ments, or to borrow $180 at 6 % compound interest? BUILDING AND LOAN ASSOCIATIONS. 219 392. To find the rate of interest paid for a loan. liULE. — From the cost of the loan Huhtract the amount received y then^ Find the rate it will require for the loan to gain this dif- ference in the yiven number of years. 393. To find the amount of fines on dues remaining unpaid. Note.— The total amount of fines is equivalent to the sum of the com- pound interest of the dues for as many months as each payment remains unpaid ; or to the final value of an annuity for the same time, with in- terest at the rate of the fine. Rule. — Multiply the compound, interest of ^1, at the rate of the given fne, hy the dues for one month, commencing ivith the interest of one month, and continuing for the ivhole num- ber of months. The sum of all the p)roducts will he the total amount of fines. Or, by Annuity Tables, From the final value of an annuity of ^1 for one more year than the number of months that the dues remain unpaid, sub- tract one more dollar than there are such months; the remainder will he the fines on dues of ^1 per month. This midtiplied hy the total dues per month, will give the total fines. Or, Multiply the sum of the fines on ^1, as given below, by the dues for 1 month. EXAMPLE. How much must a man, whose dues are S5 per month, pay for fines at 5 % per month, on all sums remaining unpaid, after his dues remain unpaid 6 months ? By Compound Interest. The interest on $1, at 5 per cent.. For 1 month, = .05000, on $5, = .25 u 2 « = .102500, (t « __ .51 « 3 " = .157625, « <( __ .79 " 4 " = .215506, « « __ 1.08 " 5 " = .276282, «c « __ i.y8 « 6 « = .340096, « <( _. 1.70 $1.142009 Total fines for 6 mos., at 5 per ct., ' on unpaid dues of $5 per mo., $5.71 Fines on dues of $1 per month, remain- ing unpaid for 6 months, at 10 per cent, per month. For 1 month, on $1, .10 .21 " 3 « " " = .33 " 4 " " « = .46 " 5 " " " = .61 " 6 " « « = _.77 Total fines for 6 montlis, ) *., ^g at 10 per cent, J 220 LIFE INSURANCE. LIFE INSURANCE. 394. Life Insurance companies base their premiums upon the number of years each person is expected to live after insuring, and the use of money for that time. 395. The EXPECTATION OP LIFE is the average number of years remaining to a person at a given age, and is deduced from tables of mortality, which have been prepared from various ob- servations made in different places and periods, showing, out of a given number of persons, how many complete each subse- quent year, and how many die in it, till the whole are extinct. The Carlisle tables, formed by Mr. Milne according to the mortality observed at Carlisle (Eng.), the Northampton tables, formed by Dr. Price (Eng.), the Wigglesworth tables, pre- pared by Dr. Wigglesworth from data founded upon the mor- tality of this country, and others, are employed. The Carlisle tables are in general use in England, and to a considerable ex- tent here. The Wigglesworth tables have been adopted by the Supreme Court of Massachusetts in estimating life estates : they show a smaller expectation of life than the Carlisle tables. 396. The PROBABILITY that a person of any designated ago will attain any greater age is expressed by dividing the number of survivors at the greater age by the number that attain the given age. Thus, by the Carlisle tables, of 10,000 persons born together, 5642 attain to 30, and 2894 to 60 years of age. The probability that a person now 30 years will reach the age of 66 years is, therefore, HJj, — about J, or 1 chance in 2. The value of a sum of money, the receipt of which depends upon the person being alive at that time, will be reduced by that contingency one-half; so that if the sum to be received is $1000, its value is reduced to only $500. The present worth of $1000, due 36 years hence, interest at 6 per cent., is $122.74; but, depending upon the same con^ tingency, it is worth only $01.37. LIFE INSURANCE. 221 TABLE OJ Mortality based upo7i observations at Carlisle [Eng.] the rate of extinction of 10,000 lives. showing i ■^ O so S t {I to O 00 o . IJ 'A fcfi ?2 || ;5 10000 1539 35 5362 55 70 2401 124 1 8461 682 36 5307 56 71 2277 134 2 7779 505 37 5251 57 72 2143 146 3 7274 276 38 5194 58 73 1997 156 4 6998 201 39 5136 62 74 1841 166 6 6797 121 40 5075 66 75 1675 160 6 6676 82 41 5009 69 76 1515 156 7 6594 58 42 4940 71 77 1359 146 8 6536 43 43 4869 71 78 1213 182 9 6493 33 44> 4798 71 79 1081 128 10 6460 29 45 4727 70 80 953 116 11 6431 31 46 4657 69 81 837 112 12 6400 32 47 4588 67 82 725 102 13 6368 33 48 4521 63 83 023 94 14 6335 35 49 4458 61 84 529 84 15 6300 39 50 4397 59 85 445 78 IG 6261 42 51 4338 62 86 367 71 17 6219 43 52 4276 65 87 296 64 18 6176 43 53 4211 68 88 232 51 19 6133 43 54 4143 70 89 181 89 20 6090 43 55 4073 73 90 142 87 21 6047 42 56 4000 76 91 105 30 22 6005 42 57 3924 82 92 75 21 23 5963 42 58 3842 93 98 54 14 24 5921 42 59 3749 106 94 40 10 25 5879 43 60 3643 122 95 30 7 26 5836 43 61 3521 126 96 23 5 27 5793 45 62 3395 127 97 18 4 28 5748 50 63 3268 125 98 14 3 29 5698 56 64 8143 125 99 11 o 30 5642 57 65 3018 124 100 9 2 81 5585 57 66 2894 123 101 7 2 32 5528 56 67 2771 123 102 5 2 33 5472 55 68 2648 123 103 8 2 34 5417 55 69 2525 124 104 1 1 19* 222 LIFE IN!5UK.\NCE. 397. The expectation of life may be obtained by finding the S2im of the probabilities that the person will live to the extreme limit of life, plus A. The ^ is added on the supposi- tion that, on an average, the life will fail at the middle of the year. Thus, by the table, the probability that a person at 102 will live one year is |, that he will live 2 years is i : I -{- I -j- ^ = J-3 -— 1 30 years. It may also be found by dividing the aggregate number of years which the persons who are alive at one time will live, by the number of per- sons. A short rule, which gives approximate results, is to take J of the number of years between the person's present age and 80. Thus, a person at 20 has an expectation of 40 years; at 50, of 20 years. The value of the probabilities and expectation of life under various circumstances is calculated by actuaries, and involves complications too extensive for an elementary work. From these calculations, tables are arranged, showing the rates at which companies will insure lives, — such rates including all probable losses, expenses, interest, and profits. To all who have limited incomes, Life Insurance ofiers a provision against the accidents of life. By paying a small sum annually, a person at his death may leave his family — which would otherwise be dependent, either from lack of pro- perty, or from having heavily encumbered property — in com- fortable circumstances. By a Joint Policy, two persons may insure and the sum insured is paid to the other on the death of either. By the Endowment Policy^ the amount can be made payable to the person insured at a stated time, — thus making provision against old age. A Life Insurance policy has enabled per- sons of unquestionable character and business ability, who have otherwise been unable to borrow on account of advanced age and the uncertainty of life, to obtain capital with which to conduct a profitable business. VALUE OF LIFE INTERESTS. 223 VALUE OP LIFE INTERESTS, WIDOWS' DOWERS, ANNUITIES, &o. Extract from Instructions issued by the Treasury Department, Washington, February 15, 1S66. " Whei-e legacies are made paj'able at the expiration of a life or lives in being, the Tahie of the legacy will be estimated by the Carlisle tables of life annuities, whi-ch are appended to tliese instructions. " Where a legacy is made payable on a future contingency, the value of the legacy is to be estimated by a consideration of the time, certain or ascertainable by the an- nuity tables, when the legacy wiU become vested. CARLISLE TABLES. Bi ^SJ'S^ -11^9- .9 ^§3^3^ -al^g'- ^1 •3^28 • § g 00 a c llll!f t2 i! lllil S 2 a, a a w 5 g '-■3'« 9^ |^=o§l.9 W ^ Is 1551 1 2 t^0 ■< ^ Ph (^ < W ^ fk 38.72 14.9202 .104788 41 26.97 13.2043 .207741 1 44.68 15.4325 .074065 42 26.34 13.0737 .215580 2 47.55 15.6225 .062645 43 25.71 12.9395 .223635 3 49.82 15.7521 .054874 44 25.09 12.8032 .231812 4 50.76 15.8008 .051953 45 24.46 12.6576 .240548 5 61.25 15.8252 .050490 46 23.82 12.5059 .249646 6 51.17 15.8213 .050722 47 23.17 12.3454 .259278 7 50.80 15.8029 .051830 48 22.51 12.1751 .269494 8 50.24 15.7742 .053551 49 21.81 11.9889 .280669 9 49.57 15.7385 .055689 50 21.11 11.7946 .292324 10 48.82 15.6972 .058168 51 20.39 11.5846 .304922 11 48.04 15.6523 .060860 52 19.68 11.3701 .317792 12 47.27 15.6055 .063670 53 18.97 11.1481 .331108 13 46.51 15.5573 .066559 54 18.28 10.9201 .344791 14 45.75 15.5072 .069566 55 17.58 10.6805 .359172 15 45.00 15.4558 .072650 56 16.89 10.4364 .373815 16 44.27 15.4028 .075832 57 16.21 10.1839 .388967 17 43.57 15.3501 .078996 58 15.55 9.9287 .404275 18 42.87 15.2956 .082267 59 14.92 9.6788 .419268 19 42.17 15.2384 .085695 60 14.34 9.4368 .4.33789 2C 41.46 15.1778 .089331 61 13.82 9.2154 .447078 21 40.75 15.1151 .093095 62 13.31 8.9900 .460612 2-2 40.04 15.0500 .097002 63 12.81 8.7636 .474183 23 39.31 14.9972 .101248 64 12.30 8.5245 .488530 24 38.59 14.9068 .105592 65 11.79 8.2793 .503231 25 37.86 14.8307 .110157 66 n.27 8.0211 .518737 26 37.14 14.7521 .114876 67 10.75 7.7552 .534690 27 36.41 14.6685 .119892 68 10.23 7.4813 .551125 2S 35.09 14.5829 .125024 69 9.70 7.1926 .568446 29 35.00 14.4982 .130105 70 9.18 6.9022 .585867 yo 34.34 14.4123 .135258 71 8.65 6.5945 .604328 31 33.68 14.3240 .140560 72 8.16 6.3045 .6217?0 32 33.03 14.2343 .145938 73 7.72 6.0341 .637953 33 32..36 14.1366 .151789 74 7.33 5.7S94 .652634 34 31.G8 14.0344 .157932 75 7.01 5.5887 .e046Sl 35 31.00 13.9291 .164255 76 6.69 5.3762 .677427 36 30.32 13.8174 .170957 77 6.40 5.1833 .GsSvtOO 37 29.6i 13.7021 .180796 78 6.12 4.9971 .700173 83 28.90 13.5833 .185000 79 5.80 4.7703 .713420 39 28.28 13.4570 .192530 80 5.51 4.-57 19 .725687 40 27.61 13.3289 .200208 81 5.21 4.3604 .738376 224 TIIK CENTAL SYSTEM. Example. — If a person whose probability of life is l'i.34 years inherits an estate having a rental value of $1000 per annum, the present worth of the annuity of $1000 for that term is 9.43G8 X 1000 = $'J430.80, — the valuation on which he is taxed. THE CENTAL SYSTEM. Efforts have been made by the Boards of Trade in most of our large cities, to introduce the Cental System in place of the bushel, in buying and selling all grains, seeds, and similar productions. The Cental is one hundred pounds. Several articles have been sold for years by the Cental ; and its general introduction would be attended with many advan- tages. Dealings in grain especially — the quality of which is indicated by its weight — would be conducted with much less inconvenience than at present. The weight of wheat, rye, barley, and oats, per bushel, as now estimated among shipping-merchants, may be found on page 228. To find the price per cental when the price per bushel is given. Rule. — Multiply the price per bushel hy 100, and divide hy the number of pounds. Example. — At $1.38 per bushel for wheat of the weight of CO lbs. per bushel, what is the price per cental ? 138 X 100 = 13800 ir'800 h- 60 = 230 Ans. $2.30. To find the price per bushel when the price per cental is given. KuLE. — Multiply the price per cental hy the number of pounds in a bushel, and divide by 100. Example.— At $2.50 per cental, what is the price of a bushel of wheat? 250 X 60 = 15000 15000 -=- 100 = 150 Ans. $1.50. SQUARE ROOT. 225 398. SQUARE ROOT. Rule. — I. Pomt off the given number^ commencing at units' place, into periods of two figures each. II. Find the greatest square in the left-hand period^ and place its root in the quotient ; subtract the square number from the left-hand period^ and to the remainder annex the next period of the dividend. III. Double the root already found ^ for a divisor ; find how many times the divisor is contained in the dividend, exclusive of the right-hand figure ; place the result in the quotient, and at the right hand of the divisor. IV. Multiply the divisor by the last quotient-figure^ and subtract the product from the dividend. Bring down the next period, and proceed as before. When a number is not a perfect square, annex ciphers, and continue the root to as many decimal places as are required. Note. — Mixed decimals must be pointed off both ways from the decimal point. To extract the square root of a fraction, extract the square root of both the numerator and denominator. When they are not per- fect squares, reduce the fraction to a decimal, and extract the root. EXAMPLES. 1. What is the square root of 50964? 50964(225.75+ 4 42 1 109 84 445 " 2564 2225' 4507 33900 31549 4514f 235100 225725 2. What is the square root of 8796, and of 123562 226 LUxMBER MEASURE. LUMBER MEASURE. 399. A standard board is one that is 12 feet long, 1 foot wide, and 1 inch thick, and tlierefbre contains 12 square feet 1 inch thick. In timber for exportation, i inch more is allowed for shrinkage, planing, &c. The length of board.s, joists, beams, &c., is measured in even inches", odd inches not being counted. 4:00. To measure boards. Rule. — Multiply the length in feet hy the width in inches j and divide the product hy 12 ; the quotient will he the numher of square feet. When the hoard is more or less than 1 inch thich^ add or suhtract in 2^roportion. A plank 2 inches thick, 12 feet long, and 1 foot wide, would measure 24 fret j hoard measure. Note. — If the boards are tapering, take half the sum of the two ends for the mean width. Some inspectors measure only the narrow end. 401. To measure joists, beams, &c. Rule. — Multiply the width in inches hy the thickness, and this product hy the length in feet ; divide hy 12, and the quo- tient will he the contents in feet. 4:02. To find the number of feet which a given log will contain when sawn square. Rule. — Square half the diameter in inches, and multijdy hy the length of the log in feet. rractically, it is customary to take two-thirds or -j?^ of the dia- meter of the small end of the log, for the side of the square which ean bo sawn from a given log. 4:03. To find the number of boards which can be cut from a given thickness of log. Rule. — Divide the thickness of the log, minus \ inch, hy t plus the saio-cut (} i7ic]i). GIAUGING. 22T GAUGING. Gauging is the process of finding the contents or capacity of casks and other vessels. Ullage is the difference between the actual contents of a vessel and its capacity, or that part which is empty. The usual manner of gauging is by the diagonal rod, which gives only approximate results, but sufficiently accurate for ordinary purposes. FOR SMALL CYLINDRICAL VESSELS. Rule. — Multiply the square of the diameter^ in inches, hy SJf., and that hy the height, in inches, and point off four figures ; the result will he the capacity, in wine gallons and decimals of a gallon. Ifheer gallons are required, multiply hy 28 instead of SJf. EXAMPLE. A can measures 15 inches in diameter, and is 2 ft. 2 in in height. How many gallons will it contain ? 15 X 15 = 225 X 26 in. (height) = 5850 5850 X 34 = 19.8900 Ans. 19/0^0 gals. FOR CASKS. Rule. — Add -^-q of the difference hot ween the head diameter and the hung diameter to the head diameter, for the mean diameter; then proceed as in the previous rule. Or, Add together the square of the hung and head diametersj and of twice the middle diameter hetween the hung and head. Multiply the sum hy length of cask, and the product hy .1309, To find the contents of ullage casks. Rule. — When the cask is standing — Find one-third the sum of the head, mean, and hung dia- meters, and square the result ; multiply hy the height of the fluid in inches, and that product hy .003.^ for wine gallons^ and hy .0028 for hcer gallons. 228 GRAIN MEASURE. To test the accuracy of dry measures which are in the form of a cylinder. Divide 2738 by the square of the diameter j in inches; the quotient will be the depth for a bushel; one-half the quotient will he the depth for a half-bushel; one-quarter of the qivotient, for a pechy &c. To test the accuracy of measures for fluids which are in the form of a cylinder. Square the diameter , in inches, for a divisor. Divide 294 for wine gallons. " 359 « beer " " 342 '' dry '' GRAIN MEASURE. To find the quantity of grain in a bin or wagon. Rule. — Multiply the height, length, and breadth together, in inches, and divide by 2150.4^ ; the quotient will be the num- ber of bushels. To find the quantity of grain when heaped on the floor in the form of a cone. Rule. — Square the depth and square the slant height ^ in inches ; take their difference and multiply by the depth, and this product by .0005 ; the result will be the contents, in bushels. To find the quantity of grain when heaped against a straight wall. Rule. — Square one-half the depth, and proceed as in the previous rule. WEIGHT OP GRAIN PER BUSHEL, AS ESTIMATED AMONG SHIPPING MEBCHANTS. Wheat, .... 60 lbs Rye, 56 // Barley, .... 48 // Oats, 35 lbs. Corn, .... 56 «r MECHANICAL POWERS. 229 CALCULATIONS IN NATURAL SCIENCE. MECHANICAL POWERS. Power, or Force, is a compound of weight and velocity. Machinery is employed to save either time qx force; but no machine can save both : either force is gained at the expense oi' time, or time is gained at the expense of force. Motion takes place only when the power is greater than the weight or resistance, including friction. It is a principle in mechanics that the power is to the weight as the velocity of the weight is to the velocity of the power. The mechanical powers, of which all machines, however complicated, are constructed, are three in number, — viz.. Lever, Inclined Plane, and Pulley. The Wheel and Axle is a revolving lever; the Wedge is a double inclined plane ] and the Screw is a revolving inclined plane. The Lever. — There are three kinds of levers : — 1. When the fulcrum is between the weight and the power. 2. When the weight is between the power and the fulcrum. 3. When the power is between the fulcrum and the weight. The weight multiplied by its distance from the fulcrum is equal to the power multiplied by its distance from the fulcrum. Example. — The weight on the short arm of a lever is 120 lbs., at a distance of 1 foot from the fulcrum : what power applied to the long arm, at a distance of 8 feet, will balance it? 120 X 1 = 120. 120 -f- 8 == 15 lbs. Ans. When the fulcrum or support is between the weight and power, the pressure upon the fulcrum equals the sum of the weight and power. When the fulcrum is at one extremity and the power or weight at the other, the pressure upon the fulcrum equals the difference between the weight and the power. 20 2^0 MECHANICAL i'OWEllS. The Wheel and Axle, or Uevolvinq Lever. — The power multiplied by the radius (half the diameter) of the wheel is c({Uii\ to the weight multiplied by the radius of the axle. Example. — The diameter of a wheel is 80 inches, and that of the axle 6 inches : what power on the wheel will balance 600 lbs. on the axle ? Radius of wheel, 40 inches; radius of axle, 3 inches. 600 X 3 = 1800. 1800 -- 40 = 45 lbs. Ans. Pulleys. — Pulleys are of two kinds, fixed and movable pulleys. Fixed pulleys do not increase the power, but they are useful for applying it in the most convenient direction. In the movable pulley all the parts of a cord are equally stretched, and therefore each cord from one pulley to another will bear an equal part. Hence the power is doubled for every movable pulley. Example. — What power is required to balance a weight of 1800 lbs., by means of 3 movable pulleys? 3X2 = 6. 1800 -^ 6 r^ 300 lbs. Ans. The Inclined Plane. — The power required to raise a body up an inclined plane, is equal to the product of the height and weight divided by the length of the plane. The Wedge, or Double Inclined Plane, derives its advan- tages from the fact that power can be applied to it by per- cussion or a stroke. As a theoretical rule, it may be said that when two movable bodies are forced apart, the power required is equal to the product of the resisting power mul- tiplied by ^ the thickness of the back, divided by the length of one of the inclined sides. When only one of the bodies is movable, the power re- quired is equal to the product of the resisting power multi- plied by the thickness of the back, divided by the length of the wedge. The Screw, or Revolving Inclined Plane, is an inclined MECHANICAL POWERS. 231 plane wound round a cylinder, and its length is found by adding the square of the circumference of the screw to the square of the distance between the threads, and extracting the square root of the sum. The height of the plane is the distance between any two contiguous threads; the base of the plane is the circumference of the screw. Having the length of the plane and its height, the power required is found as for the inclined plane. If the power is applied at the end of a lever, the cir- cumference of the thread may be taken as extending to the circle formed by the end of the lever. Example. — If the distance of the centres of two threads be i of an inch, and the radius of the lever attached to the screw be 12 inches, what is the power of the screw? The circumference of the screw will be 12 X 2 X 3.14156 = 75 J in., nearly. Therefore, to find the power of the screw, 75 J -f- i = 300|, the power of the screw. The power of a man, it is estimated, on an average, is able to raise 70 lbs. 1 foot high in a second for 10 hours per day. Horse-Power, in machinery, is estimated at 33000 lbs. raised 1 foot every minute. A machine horse-power is con- sidered equal to 4.4 horses. The strength of one horse is equivalent to that of 5 men. A draft horse can draw 1600 lbs. 23 miles per day, weight of carriage included. Steam, under ordinary circumstances, is equal to tho pressure of the atmosphere, or about 15 lbs. on the square inch. A cubic inch of water is converted into about 1 cubic foot of steam, producing a force equal to 2200 lbs. 1 foot high. Its weight is .488 that of the air; or 27.206 cubic feet of steam equal 1 lb. avoirdupois. One cubic foot of boiler will heat 2000 feet of space to an average heat of about 70° or 80° Fahr.; and one square foot of steam-pipe is adequate to the warming of 200 cubic feet of space. 232 FALLING BODIES. GRAVITY OF BODIES. The gravity or weight of bodies above the surface of tho earth decreases as the square of their distance from the earth's centre, in semi-diameters of the earth. Example. — If a body weighs 1800 lbs. at the earth's sur- face, what will it weigh 2000 miles above the earth esti- mating the diameter of the earth at 8000 miles? From the centre of the earth to the given height is 1^ semi-dianie- ter. 1 ^ X H = 2}. 1 800 -^ 2| = 800 lbs. , Ans. FALLING BODIES. Gravitating bodies attract each other with forces varying inversely as the squares of their distances. A body falling freely from rest will descend lQj\ feet the first second, and the space fallen through in any number of seconds equals the product of IGy'^ by the square of the number of seconds. Thus, a body in 4 seconds will fall 4 X 4 = 16 X 16 Jrr = 257J feet; in 5 seconds it will fall 5' X 16^3 = 4021.^ feet. To find the time required for a body to f\ill through a given space, divide the square root of the space by 4; the quotient will be the time, in seconds. Example. — Required the time for a ball to fall from the spire of a church 256 feet high. ^256 = 16. 16 -r-4 = 4 seconds, Ans. The Velocities of falling bodies increase as the times. Thus, at the end of the first second the velocity will be 32 J; at the end of the second second, 64| ; at the end of the third second, 32J X3 = 96A. The 3fean Velocity is found by taking the square root of the space in feet, multiplied by 64 J; or by dividing the space fallen through in feet by the number of seconds. The SPECIFIC GRAVITY. 233 velocity acquired at any period is equal to twice the mean velocity during tliat period. The Ifomentum with which a falling body will descend is equal to its weight multiplied by its velocity. Examples. — 1. What is the velocity of a weight falling 2i feet? 2i X t>4 == 144. -^./144 =: 12 feet, Ans. 2. What is the force with which a weight of 200 lbs. will strike after falling 2i feet? Velocity = 12 X 200 = 2400 lbs., Ans. To find the number of feet fallen through, when the weight and momen-tum are given. Divide the momentum by the weight for the velocity ; then divide the square of the velocity by 64, for the height re- quired. Example. — How high will it be necessary to iliise a weight of 50 lbs. to produce a force at striking of 800 lbs. ? 800 ^ 50 = 16, the velocity. 16^ = 256 -- 64 = 4 feet, Ans. A fiill of j\ of an inch in a mile will produce a current in rivers. SPECIFIC GRAVITY. The Specific Gravity of any substance is its weight compared with that of an equal bulk of fresh v/ater. A cubic foot of rain-water, at a temperature of 60° Faliren heit, weighs 62^ lbs., or 1000 ounces avoirdupois. One cubic inch weighs l^^f ounces. The specific gravity of a body may be found by dividing its weight by the weight of an equal quantity of fresh water. Bodies heavier than water, when immersed, lose the weight of an equal bulk of water. Floating bodies lose weight in proportion to the quantity of fluid they displace. Tables have been constructed showing the specific gravi- ties of most substances. Pure gold, cast, has a specific gravity 20«^ 234 SPECIFIC GRAVITY. of 19 258, or more than nineteen times as heavy as wator gold 22 carats fine, 17.48G; pure silver, cast, 10.474 standard silver, 10.312; cast iron, 7.271; cast lead, 11.352 copper, cast, 8.788; common marble, 2.686; brick, 2.000 cork, .240; olive oil, .915; pure alcohol, .792; air at the earth's surface, .001 1, or g-^^; hydrogen, .070 that of air. Oxygen equals 1.106 of air. Knowing the specific gravity and the size of a given body, we can ascertain its weight; or, having the weight and spe- cific gravity, we are enabled to find its size. Examples. — 1. What is the weight of a cubic block of cast iron, each side being 2 feet? 2X2X2=8 cubic feet in the block. Specific gravity of iron, 7.271 X 8 = 58168 ounces. 58168 -f- 16 = 3635^ lbs., Ans. 2. What is the size of a cubic piece of marble weighing 1200 lbs.? 1200 lbs. == 19200 ounces. Specific gravity of marble, 2.686. 19200 -- 2686 = 7^%\% cubic feet, Ans. To determine the quantity of two ingredients in a com- pound which they form, or the quantity of adulteration, em- ploy the following formula: — As the product of the" (liffereaco between the specilic gravities of the heavier and tho li}j;hter body, multiplied by the specific gravity of the compound, (The weighty -i of the Y (compound, j The product of the dif-" ference between the specific gravity of tlie compound and that of the ligliter body, multiplied by the specific gravity of the heavier body. The weight of the hea.-itr bcdy. To obtain the «veight of the lighter body, substitute for the third term, " Tho product of the difference between tho specific gravity of the heavier body and that of the compound, by the specific gravity of the lighter body." IIow TO Try Spirituous Liquors. — A cubic inch of good brandy, or other proof spirits, weighs 234 grains : there- fore, if a true cubic inch of any metal weigh 234 grains less PRESSURE OF THE ATMOSPHERE. 235 in spirits than in air, the spirits are proof. If the cube lose less, they are above proof; if it lose more, they are under proof: for spirits are lighter as they are better in quality, PRESSURE OF THE ATMOSPHERE. A cubic foot of air at the earth's surface weighs 1.222 ounces; 13.27 cubic feet weigh 1 lb. Water is about 825 times heavier than air The air at the earth's surface, in consequence of the weight of the atmosphere above it, is in a state of compression. At a mean rate, the pressure is equal to the support of 29.5 inches of mercury, or 33.18 feet of fresh water, or 15 lbs. pressure upon the square inch. The pressure of air on the surface of fluids causes them to rise in pipes or vessels when the air is removed above them, but not more than 33.18 feet. A cubic inch of mercury weighs 7.866 ounces, or nearly half a pound avoirdupois : therefore 30 inches of mercury will weigh 15 lbs., and will balance the pressure of the atmos- phere. The air presses equally on every side. If the air was of the same uniform density upwards, we could easily tell its height ; for if its weight is to water as 1.222 is to 1000, then 33.18 feet is in the same proportion to 5i miles, which would be the height. But the air becomes rarer as it ascends ; and when the altitude is in arithmetical proportion the rarity will be in geometric proportion. Thus, if at 7 miles' heigl.t it is 4 times lighter than at the earth's surface, at 14 miles' it will be 16 times, and at 21 miles' 64 times lighter; and, by similar calculation, the atmosphere has been found to reach the height of about 50 miles A column a foot square, reaching to the height of the atmosphere, is equal to 2116.8 lbs. The heights of mountains have been calculated by the use of the barometer, which rises or falls according to the pressure or density of the atmosphere. The following short method is sufficiently correct for all ordinary puj-poses. 236 VELOCITY OF SOUND. Take the height of tlic mercury at the top and at the bottom of the mountain, and then employ the following formula : — Sum of the ) . / Difference of ) , . ( eonnn I . / Height of mountaiu, heights / • t the heights } " \ °-^^ / ' t in feot. Example. — If the barometer stands 29.8 at the bottom of a mountain, and 27.2 at the top, what is the height of the mountain ? 27.2 29.8 29.8 27.2 57 : 2.6 : : 52000 : 2372 feet, Ans. The pressure of condensed air is in proportion to its con- densation. Thus, air compressed into i its usual space will press with a force equal to 15 X 4 = 60 lbs. per square inch ; but, as the pressure outside is 15 lbs. per square inch, the real pressure is 00 — 15 = 45 lbs. per square inch Velocity and Force of the Wind. — At a velocity of 5 miles an hour, wind presses i lb. on a square foot; at 15 miles an hour, H lbs. per square foot; at 30 miles an hour, or 22 feet a second, 4} lbs. per square foot, and is what is called a brisk blow; at 50 miles an hour, the pressure is 12J lbs. per square foot, and produces a storm ; at 100 miles an hour, the pressure is 50 lbs. per square foot, and is sufficient to tear up trees. VELOCITY OF SOUND. Sound travels 1142 feet, or j\ of a mile, per second, or a mile in about 4| seconds. Sound of all kind travels at the same rate, the whisper as fast as the cannon's roar. Sound passes in water at the rate of 4708 feet per second. Examples. — 1. A flash of lightning was observed 5 seconds before the thunder was heard. What w^as the dis- tance of the cloud if A X 5 = if = ly\j miles, Ans. LIGHT. 237 2. The report of a minute-gun at sea was heard 4 seconds after the flash was seen. How far distant was the gun? LIGHT. Light travels from the sun to the earth, 95,000,000 miles. in 8j minutes. The intensity of light at any distance from a luminous body is in an inverse proportion to the square of the distance. Thus, at a certain point, a board 1- foot square will cast a shadow 2 feet square at double the distance, 3 feet square at 3 times the distance, 4 feet square at 4 times the distance. The areas being increased as the squares of the distances, the light, consequently, is decreased in the same proportion. Solids shine in the dark when heated from 600° to 700°. Light from gas, as usually obtained, is not in proportion to the gas consumed. It is more economical to have one good large gas-light than several small ones. An argand burner, consuming five feet per hour, giving the light of 12 candles, G in a pound, when reduced so that only three-fourths of that quantity is burned, instead of giving the light of 9 candles, the proportional quantity, produces the light of 6 candles only, a positive loss of 36 per cent, of light. A burner con- suming two feet per hour gives the light of two and a quarter candles only, while a burner consuming 7 2 feet per hour gives the light of twenty-two candles, the pressure being uniformly r^Q of an inch. A clear glass globe obstructs about 12 per cent, of the light ; a clear globe engraved with flowers, about 24 per cent. ; a globe ground all over with flowers, about forty per cent.; an opal globe with flowers, about 60 per cent. HEAT AND COLD. Heat expands all bodies, with few exceptions, but in diff'erent degrees. It expands liquids more than solids, and 238 HEAT AND COLD. gases more than liquids. The thermometer, by its scale of eqial divisions marked upon the tube, indicates the degree of heat in a given case. The mercury in the thermometer expands as heat is applied, and the scale enables us to deter- mine the amount. The temperature of melting ice is called the freezing point, and is marked 32°. The temperature of boiling water is marked 212°. When the temperature is 68°, it is called summer heat; 98° is called blood heat; 108°, fever heat. This is the scale commonly used in this country, England, and Holland, and it is known by the name of tho inventor, Fahrenheit. Above the boiling point, heat is measured by an instrument called a pyrometer. For very low temperatures, spirit-of-wine thermometers are employed. Mercury, in freezing, contracts, and therefore does not burst the thermometer. The Celsius, or Centigrade, thermometer, universally used in France and Northern Europe, and the Reaumer thermo- meter, used in Spain, commence with zero as the freezing point. 1° Fahrenheit = |° Centigrade = |° Reaumer : so that in making comparisons 32° is to be taken from Fahren- heit, and then that part of the remaining degrees which is expressed by the fractions just given. Common fire is estimated to be at a temperature of 790°. Lead expands at 212° Fahrenheit from 1,000,000 parts to 1,002,848; it melts at 594°, and does not, when cold, return to its original dimensions. Lead pipes which convey hot water or steam become permanently elongated, and leaden linings, where hot water is used, become gathered into ridges. Tin at 212° expands from 1,000,000 parts to 1,001,937, and melts at 421°. At the same degree silver expands to 1,001,909, and melts at 1850°. Gold expands to 1,001,460, and melts at 1983° ; copper, to 1,001,718, and melts at 2160°. Iron expands to 1,001,182, becomes red-hot in the dark at 752°, in daylight at 1077°, and melts at 2754°. HEAT AND COLD. 239 The effects of lieat may be seen in the iron rails on the rail- roads throughout the country. There is a variation of 80° in the temperature between the cold of winter and the heat of summer. This is sufficient to elongate a bar of iron ten inches long, five one-thousandths of an inch, or t^-q^-q part, which would require, to produce the same effect, a force of fifty tons upon the square inch. The tubes of Menai Bridge vary in length with the changes of the air, from half an inch to three inches every twenty-four hours. Iron bars, when much heated, frequently injure masonry, instead of support- ing it, from the same cause. Mercury expands between 32° and 212° from 1,000,000 to 1,018,155, and boils at 662°. Ether boils at 95°. Vinous fermentation begins at 60° to 77°; acetous fermentation begins at 78°. Most metals occupy less space when solid than when melted, and therefore produce imperfect casts. For this reason coins, medals, and ornamental wares are stamped instead of cast, to secure the requisite size, sharpness, and beauty. Alcohol expands -J between 32° and 212°, and, under ordi- nary changes of atmosphere, would increase from 20 gallons in January to 21 gallons in July. It boils at 173°. Water in a vacuum boils at 124° less of heat than when under the ordinary pressure of the atmosphere, or when the barometer is 30 inches. On Mt. Blanc water boils at 187°. The boil- ing point of water, with a pressure indicated by the barometer of between 27 and 31 inches, varies 1.65° for every inch. Water converted into steam occupies about 1700 times as much space as before. In freezing it expands \ of its bulk, and 3^3 for every degree from 40° to 212° : hence ice floats on the surface of water, and close vessels are burst when the water they contain is frozen. Melted snow produces about ^ of its bulk in water. Sea-water freezes at 27°, strong wine at 20°, brandy at 7° 240 CALCULATIONS IN NATURAL SCIENCE. At the depth of 45 feet the temperature of the earth is uniform during the entire year. Freezing Mixtures are frequently required; and the one most convenient for common use, such as freezing ices and creams, is composed of 2 parts ice or sn^w and 1 part common salt. With this a temperature of 5° below zero, or 37° below the freezing point, can be obtained. Another compound, of 3 parts snow or ice and 4 parts chloride of calcium, will produce a temperature of 14° below zero. Heat is absorbed most rapidly and longest retained by dark and dull surfaces, and is generally conducted least by sub- stances in condition of least density. Heat and light are both reflected best by bright surfaces. Compared with a rough, blackened surface as 1, the reflective power of tin is 80, of brawss, polished, 93, of gold and silver, polished, 97. THE STRENGTH OF MATERIALS. The strength of a beam increases as the square of one of its homologous sides, while the weight of the beam increases as the cube ; and therefore long beams are weak from their own weight. A beam twice as broad as another is twice as strong, one twice as deep is four times as strong, and one twice as long has only half the strength. A triangular beam is twice as strong when resting on its broad base as when resting on its edge. If the beam is supported in the middle and loaded at each end, it will bear the same weight; that is, each end will bear half the weight. A beam fixed at both ends and loaded in the middle will bear one-half more weight than it will when the ends are loose. When the weight is distributed uniformly over the whole length of the beam, it will bear double what it will when the CALCULATI02s^S IN NATUEAL SCIENCE. 241 entire weight is in the middle. A beam fixed at one end and loaded at the end projecting, will bear only one-fourth the weight it will when loaded in the middle and supported at the ends. From various experiments, it appears that the ultimate strength of various bodies, an inch square and an inch round bar of each, 1 foot long, loaded in the middle and lying loose at both ends, is as follows : — Square bar. Round bar. Oak 800 lbs. 628 lbs. Ash 1137 893 Elm 569 447 Pitch Pine 916 719 Deal 566 444 Cast Iron 2580 2026 Wrought Iron 4013 3152 One-third of the above weights is considered sufficient in most cases for a permanent load. To find the strength of any rectangular beam supported at both ends and loaded in the middle, or supported in the middle and loaded at both ends. Rule. — Multiply the number in the table by the breadth and square of the depth in inches, and divide the product by the length in feet : the quotient will be the weight, in pounds. Example. — What weight will break a pitch pine plank 16 feet long, 10 inches broad, and 2 inches thick, when supported at both ends and loaded in the middle ? 916 X 10 X 2^ ^^^^„ ^ — = 2290 lbs., Ans. 16 A plank of the same length and thickness, 20 inches broad, would require twice the weight, or 4580 lbs., to break it, and one of th. same length and breadth, twice as thick, would re- quire 4 times the weight. A plank twice as long, of the same breadth and thickness, would break with 1145 lbs., or ij the above weight. 21 242 I'ROPERTIES OF NUMBERS. PROPERTIES OF NUMBERS. Any number may be divided by 1^, 2, 2J, or 5, without a re- mainder, when its right-hand figure may be thus divided. The square root of a number is greater than any of its prime facto-rs. Any number may be divided by an aliquot part of a hundred when its two right-hand figures may be thus divided. Any number may be divided by an aliquot part of a thousand when its three right-hand figures may be thus divided. Any number divided by 3 or 9 will leave the same remainder as the sum of its digits divided by 3 or 9. The difl'erence between any number and the sum of its digits is a multiple of 9. The difference between a number and the digits of the same num- ber arranged in another order is always divisible by 9. MISCELLANEOUS RULES. To find two numbers when their sum and difference are given. Rule. — Add one-half their sum to one-half their difference, for the larger number, and take one-half their difference from one-half their sum, for the smaller. To find two numbers when their sum and product are given. Rule. — Take the square root of the difference between the square of the sum and four times their product ; the result tcill be the difference be- tween the numbers. To find two numbers when their difference and product are given. Rule. — To the square of their difference add four times the produetf and the squart root of the sum will be the sum of the numbers. To find two numbers when their sum and quotient are given. Rule. — Divide the sum by the quotient increased by 1 ; the result will be the smaller number. To find two numbers when their difference and quotient are given. Rule. — Divide the difference by the quotient less 1, for the smaller number. To find two numbers when their sum and the sum of their squares are given rui.es in mensuration. 243 Rule. — From the square of their suffi take the sum of their squares, and half the remainder will be the product; then proceed by Rule above. To find two numbers when their sum and the difference of their squares are given. Rule. — Divide the difference of their squares by their sum ; the quo- tient will be their difference. To find two numbers when their product and quotient are given. Rule. — Divide the product by the quotient and the square root of the result will be the smaller number. To find two numbers when the square of their sum and the sum of their squares are given. Rule. — From the square of the sum take the sum of the squares ; the remainder will be twice the product of the numbers. Subtract four times the product from the square of the sum, and the remainder will be the square of their difference. Extract the roots, and proceed as in Rule above. RULES IN MENSURATION. To find the contents of an irregular body. Immerse the body in a vessel full of water, and measure the quantity of water displaced. To find the area of a rectangle. Multiply the length by the breadth. To find the area of a triangle. Multiply the base by one-half the altitude. Or, From half the sum of the three sides subtract each side separately ; multiply together the half sum and the three remaiiiders, and extract the square root of the product. To find the circumference of a circle. Multiply the diameter by S. 14156, or S\. To find the diameter of a circle. Divide the circumference by 3.14156 ; or multiply it by .318309 To find the area of a circle. Multiply half the diameter by half the circumference. Or, Multiply the square of the diameter by .785398. To find the side of a square equal to a given circle. Multiply the diameter by .S862S7, or h, of y 3.14156. 244 RULES IN MENSURATION. To find the diameter of a circle equal to a given square. Multiply the side of the square by 1.12S38. To find the side of an inscribed square. Multiply the diameter by .707 106^ or y/o ; or the circumference by £25079. To find the side of the largest inscribed equilateral triangle. Multiply the diameter by .866025. To find the circumference from an inscribed square. Divide the side of the square by .225079. To find the diameter of the three largest equal circles that can b« inscribed in a given circle. Divide the diameter of the given circle by 2.155. To find «.he contents of a cube. Multiply three sides together. To find the surface of a cube. Multiply the square of the length of one of its sides by 6. To find the surface of a sphere. Multiply the diameter by the circumference. To find the solidity of a sphere. Multiply the square of the diameter by 3.1416. Or, Multiply the cube of the diameter by .5236. To find the solidity of a cylinder. Multiply the area of one end by the length. A CUBIC FOOT OF PoundB. Ponridfc Loose earth or sand weighs 96 Clay and stones weigh. 160 Common soil i( 124 Cork weighs 15 Strong <( (( 127 Tallow " 59 Clay (( 135 Bricks *' 125 Lead << 708J Marble " 171 Brass << 534| Granite " 165 Copper <{ 555 Sea- water " 64^ "Wrought iron (( 486J Oak wood " 55 Antbraci (e coal (( 50 to 55' Red pine ♦' 42 . Bituminous " <« 45 to 55 While pine " 80 Charcoal (hard woo d)" \^ Charcoal (pine wood) weighs 18 BUSINESS FORMS AND INFORMATION 21* 245 BUSINESS MAXIMS. Endeavor to be perfect in the calling in which you are engaged. Think nothing insignificant which has a bearing upon your success. There is more in the use of advantages than in the measure of them. Make no investments without a full acquaintance with their nature and condition ; and select such investments as have intrinsic value. Of two investments, choose that which will best promote your regular business. Become known, — and favorably known. Never refuse a choice when you can get it. Goods well bought are half sold. Goods in store are better than bad debts. Nothing valuable is lost by civility. By prosecuting a useful business energetically, humanity is benefited. Keep accurate accounts, and know the exact condition of your afiairs. Be economical : a gain usually requires expense ; what is saved is clear. Beality makes no allowances for wishes or bad plans. 216 PAYMENTS AND LEGAL TENDER. The law gives the debtor who owes several debts to the Bame creditor, the right to apply a voluntary payment, at the time of making it, to whichever debt he prefers. If the debtor does not exercise the right, it passes to the creditor ; and if neither party makes an application of it, the law will apply it according to its own view of the intrinsic justice and equity of the case. Payment of debts cannot be enforced after the lapse of a certain number of years, which are specified in the several States in what are called the statutes of limitations. STATUTE LIMITATIONS IN THE UNITED STATES. NAMES OF STATES. < a 1 1 NAMES OF STATES. OQ a BOOK ACCOUNTS. 257 BOOK ACCOUNTS. Entries of transactions should be made at or near the time of their occurrence. The time to make a charge against a purchaser is when the goods are ready for delivery. Entries, to be admissible as evidence, should be made by a proper person, and be without erasure, alteration, or inter- lineation. Mistakes should be corrected by marking the erroneous entry void^ and then making a correct entry ; or, if the entry has been transferred to other books, by making another entry in explanation. Items and particulars should be specified, as a general charge cannot be supported by this kind of evidence. The entry must be made for the purpose of charging the debtor; a mere memorandum for any other purpose is insufficient. As a general rule, copies of all important papers, such as letters, orders, accounts current, and account sales, should be kept, as they may be required for proof or refbrence ; but, usually, a copy is not a voucher, and nothing but the original paper will answer. To collect a debt on the evidence of a book account, from a person in a distant place, a copy of the account should be made out, and accompanied with an affidavit in the usual form, setting forth : — 1st, that the above copy of account is correctly taken from the book of original entries ] 2d, that the charges were made at or about the times of their rcf^pective dates; 3d, that the goods were sold and delivered at or about the time the charges were made ; 4th, that the charges are correct and the account just; and, 5th, that the person named is not entitled to any credits. This affidavit should be sworn to before a magistrate or commissioner, and will save the trouble of producing the books. (See Affidavit, page 315.) 22* 258 FORMS OF BILLS. BILLS, INVOICES, AND STATEMENTS. A Bill is a written description of particulars or items. A Bill of Goods, or Bill of Parcels, is a description of* the quantity and price of goods sold, with the time of the transaction and the names of the purchaser and seller. An Invoice is a full account of goods or merchandise, in which the marks, numbers, contents, and value of each package are described, together with the charges for commis- sion, insurance, packing, &c. A Statement is a synopsis of an account, or a brief enu- meration of bills which have been purchased within a certain time. Some mercantile houses send statements" monthly, or at other regular periods, to their customers who purchase on credit, that a comparison of account may be made, and, that if any error exists, it may be remedied in time. 1. Bill FORMS OF BILLS. -, unreceipted. Mr. Henry L. Stone, Rochester, March 18, 1867, Bought of George S. Thompson. 10 lbs. Java CoflFee, 5 " Green Tea, 12 <* Brown Sugar, 25 yds. Muslin (Wamsutta), 17 " Flannel, 1 doz. Linen Ildkfs., 12 yds Mous. de laine, @ .40 1 20 .14 .23 .45 .20 4 6 1 5 7 8 2 $80 FORMS OF BILLS. 259 2. BUI receipted hy Firm. New Orleans, December 26, 1866, To B. H. Fenton & Co., Ih-, Mr. J. J. Bibb, To 48 yds. u 12 *. u 10 <* « 20 " u 7 u ♦♦ 2 doz " 1 «' « 3^ yds Muslin, Drilling, Gingham, French Chintz, Broadcloth, Spools Thread, Linen Napkins, . French Cassimere © .22 " .18 «' .35 « .40 " 3.25 .75 " 2.00 " 1.90 Rec'd payment, B. H. Fenton & Co. 3. Bill receipted hy Clerh. f Shipped at | I buyer's risk. J Chicago, Feb. 19, 1867, Messes. H. H. Applegate, Terms, Note at 60 days. To JAMES HARRIS SON & Co. Dr. 820 25 boxes Cheese, 82 738, @ .12 $88 56 10 bags Flaxseed, 1206 — 11 =1195 lbs. 2m bus., "3.00 64 02 2 bbls. Eggs, 141 -6 = 135 doz., " .25 33 75 3 kegs Butter, 295 — 31— 6 = 258 lbs., " .35 90 30 5 tierces Leaf Lard, 1620 — 271 = 1349 lbs., " .21 283 29 $359 92 Rec'd payment, STAMP James Hakris, Son & Co., per L. M. Wilson. 260 FORMS OF BILLS. 4. Bill receipted hy Cleric. Mr. Seth W. Osborn, Philadelphia, llmo.y 7, 18G7. 0. B. 65, page 180. Teems, U months. Bought of J. M. & T. H. Saundees. Packages Nos. 305 20 2 doz. Men's BIk. Cassr. Hats, @ $24.00 ^8 00 " 16 « " " Wool « 18.00 108 00 «< 12 3 " Boys' Drab " 15.00 46 00 «« 21 3 " Child's Fancy Wool Hats, " 15.00 45 00 ♦4 17 3 " Men's White Canton Hats, " 13.50 40 50 1320 60 pre. Women's Calf Pegged Boots, " 2.25 136 00 1350 96 " Misses' " " Balmorals, " 1.15 110 40 1216 36 " Women's Morocco Welt '• " 2.10 75 60 1301 36 " Child's Kid Pump Boots, 60 21 60 2 Cases, 1 50 $630 60 Received pajTnent, STAMP J. M. & T. n. Saunders, per J. L. Gurnet. 5. Bill paid hy Note. Please ex.\.mine Packages carefully for Missino Articles. New York, January 13, 1867. Messrs. Geo. W. McWilliams & Co., 0. B. 4, page 75. Bought of Fisher & Collins. — 2 4 1 7 Doz. Edg'd Muffins, 1.00, 1.20, 1.35, 8 15 2 Seta W. Gran. Tea Sots, 40 ps., @ $8.50, 1 1 17 00 2 Doz. Mocco. PitcUers, 4.50, 7.00, 11 60 6 " Table Tumblers, @ 1.25, 10 15 10 10 5 7 50 50 « W. Gran. Dishes, 50, 1.00, 1.50, 2.00, 3.00, 70 00 20 Sets " Teas, @ 1.10, 22 00 u i i i . Doz. Edg'd Bakers, 2.00, 4.50, 6.00, 4 76 Crate, ^'^ Box, ^ and Portei-age, ^ 2 78 $143 65 1 Jloc'd payment by Note at 4 moa. BTAMP Fisher & Collins. FORMS OF BILLS. 261 6. Mr. James L. Eushton, Bills for Services, &c. Worcester, July 7, 1867, To Frederick T. Stojte, Dr. 1867. Jan. 7 M 20 May 10 For Professional Services in Family, " 6 visits to son, Charles Rushton, " 3 " " " Henry L. Rushton, $10 5 3 $18 Mr. John H. Wagner, Buffalo, August 19, 1866. To Wm. H. Turner, Dr. 1867. May For Repairing House, as per Contract, " 800 feet Pine Boards, @ $8, " Lock and Key for door, " Nails, Hooks, Ac, Received payment, W. H. Turner. $25 6 2 1 $34 65 8. Mr. Owen T. Jones, Chicago, July 3, 1866. To Henry G. Langdon, Dr. in English branches, 3 mos.. $16.00 in Latin, " 20.00 Instruction of daughter, Louisa J. Jones, in English branches, 3 mos., $15.00 in Music, " 15.00 Use of Piano, lO.OC Books and Stationery furnished during the Term, Received payment, Henry G. L\\3D0N, per S. Y Lanodon. $35 $78 00 50 262 FORMS OF INVOICES 9. Items of an Account. Me. S. B. Morehouse, Mechanicsville, Jan. 1, 1867, To 0. Tompkins & Co. Dr. 1866. Apr, May June Sept. 5 9 16 14 6 10 11 To 5 bbls. Genesee Flour, extra, @ $15.00 " 10 lbs. Pearl Starch, " .18 « 20 " English Breakfast Tea, " 2.25 » 2 bbls. Prime Pork, " 17.50 Ca. By 17 yds. English Broadcloth, @ $3.00, $51.00 " 25 " French Chintz, " .40, 10.00 " 12 " English Bea\er Cloth, " 3.00, 36.00 Balance due, Settled by due-bill, 0. Tompkins & Co. $75 1 45 35 00 80 00 00 May July $156 97 80 00 $69 80 INVOICES— DRY GOODS. Cincinnati, Jan. 17, 1867. Messrs. Leonard & Curtis, BoH 0/ Joseph Gushing & Co. Terms, 3 mos. Note to your own order. L. & C. 304 312 540 17 137 15 801 4267 No.l 142 2 cases Merrimac Prints, 80 ps., 2804 yds., @ .17 1 case Satinets, 450 yds., " .78 5 ps. Extra Black Cassimere, 120 yds., " $2.75 10 " Satin Stripe Muslin, 200 " " 1.30 40 Check Square Slmwls, " 2.13 6 Imperial Long " " 11.00 3 ps. Solferino Opera Cloth, 90 yds., " .85 12 Ladies' Mourning Long Shawls, 60 X 120, " 9.00 2 ps. Taffota Ribbons, " 1.50 5" BuffOhambrays, 155 yds., " .42 2 « Printed Plaid Flannel, 90 yds., " .52 E.C 46 15 " Plain Mousseline de Laines, metres 674.1 = 730i yds., « .28^ Rec'd payment, Jos. CUSIIINQ A Co., per L. R Taylor MONTHLY STATEMENT. 268 Invoice of TWO packages of Merchandise purchased by W. B. Long- WOETH & Co., and forwarded to B. G. Babcock, Liverpool, for shipment per ^^Kangaroo^^ S. S., bound for New York, for ac- count and risk of MESSRS. Homer, Colladay & Co., Phila- delphia, and to them consigned. 7743 2301 2302 ^j Fancy Wool Long Shawls, " " Square " yf £ Broche Borders, yds. Cases, Packing, Oil-Cloth, &c. J Fancy Wool Long Shawls, Case, Packing, &c. Discount on £241 14s. 4rf., @ 2i, Charges, Cartage, 1/6, Commission li per cent., £3 lis. M., Cash, 1st Sept. 1866, E.E. Glasgow, 11th August, 1866, W. B. LONQWORTH & Co. £ s. d. 70 24/- 84 18 17/- 15 6 12 9/- 5 8 200 1/- 10 200 lOH 8 15 200 M. 6 13 4 19 10 131 2 72 23/- 82 16 48 12/- 28 16 19 6 112 11 243 6 13 237 12 3 12 £241 5 Other invoices may be found under Profit and Loss. MONTHLY STATEMENT. Boston, Jan. 31, 1867, Messes. B. H. Bradford & Co., ^ To A. A. Lawrence & Co. Dr. 1867. Jan. To Mdae., as per Bill rendered, @ 3 months, " " " " " 3 " " " " " 60 days, " " " " " 3 mot ths. $75 132 318 123 $648 264 BILLS OF LADING. BILLS OF LADING. A BUI of Liading is a formal receipt subscribed by the master of a ship, or other common carrier, acknowledging the receipt of goods intrusted to him for transportation, and bind- ing himself, under certain exceptions, to deliver them, in like good condition as received, at the place and to the person named in the bill, or his assigns, for a remuneration or freightage. The bill of lading is the evidence of shipment and the title to the goods shipped, and may be indorsed or transferred to other parties. Three sets are usually made out : one to be sent to the person to whom the goods are consigned, one for the person shipping the goods, and a third to be retained by the carrier, or master of the vessel. The bills of lading contain a descrip- tion of the packages shipped, including their number, marks, weights, &c. Common Carriers are those who hold themselves out to carry all goods intrusted to them, or all goods of a particular kind. They are of two kinds, — inland carriers by land or water, and carriers by sea. They are answerable for all losses which do not fall within the excepted cases of inevitable accident and the acts of the publio enemies of the country. The carrier may limit his responsibility by agreement with his customer; but he cannot exempt himself by notice or agreement from responsibility for actual negligence. He has a lien on the goods carried, and may retain them until he has been paid his freight. Primage is an allowance made for loading the goods. The terra ♦'Average" refers to general or marine average, in which, if loss arise during the voyage, the cargo is required to bear a propor- tionate share. ^ A Manifest is a list containing the marks, description, and num- ber of packages of the ship's cargo, together with the names of tho shippers and consignees, and must be certified by the master of the vessel before tho collector of customs, or the consul. A Consnl is an officer appointed by Government to reside in a foreign country, for the purpose of protecting the commercial in- terests of the subjects of his own nation. Documents of any kind attested by tho consul, under his hand and seal of office, are ad- mitted as evidence in courts of justice. BILLS OF LADING. 265 BILL OP LADING, SIGNED BY MASTER OP VESSEL. In good order and well-conditioned, by B. Gal- laway, Jr., as Agent, in and upon the good ship called the Kathleen, whereof is Master for this present voyage, IT. E. Roberts, and now riding at anchor in the river Thames, and bound for Philadelphia, via Falmouth, Eighteen Bales Merchandise, being marked and numbered as in the margin, and to be delivered in the like good order and well-conditioned, at the aforesaid Port of Philadelphia {the act of God, the Queen's ene- mies, fire, and all and every other dangers and acci- dents of the seas, rivers, and navigation, of whatever nature and kind soever, excepted), unto Mr. Porter Morgan, Philadelphia, or to his assigns, he or they paying freight for the said goods, £6 lis., in full. Primage and Average accustomed. In ®ittKSS whereof, the Master or Purser of the said Ship hath affirmed to three Bills of Lading, all of this tenor and date, the one of which Bills being accomplished, the others to stand void. Weight and contents unknown; and not accountable for £5115. leakage, breakage, or rust. Freight payable at the current rate of exchange on the day the ship enters at the Custom-House. P.M. P. 18 Bales. # 1/18. Rate 20/-. Freight, 5 Primage, 3 Dated in London, this 23d day of Dec, 1865. Contents unknown. U. E. Roberts, Master. BILL OP LADING SIGNED BY CLERK OP R. R. CO. Oamde] 'gxttxhtt 1 & Amboy Eailroad and Transportation Company. , of Messrs. iPhiiadelphtay Feb. 24.y fS6e, Barclay & Barclay, 30 casks Linseed Oil, Marked — H. L. T.- -^ 1 to 30. To be transported to New York, and delivered to Mr. H. L. Turner, or order, upon the following [Here TERMS: the conditions are inserted.] W. P. Murphy, For the Company. 266 BILLS OF LADING. STEAMBOAT BILL OP LADING. Ilfctibsb by the Wilmington Steamboat Line, in apparently good order, from H. Y. Healu, marked and entered as below (con- tents unknown), which we promise to deliver at Wilmington (breakage and leakage excepted), and not being responsible, if lost, stolen, or damaged, beyond the value of Fifty Dollars per package. 1 Case Merchandise. Marked : — George Danby, "Wilmington, Del. Philadelphia, Jan. 19, 1867. P. T. Simpson, Affent. FREIGHT BILL. POEM No. 69.-SEEIES B. No. 1211S. ^/litadetphiay JVor. S, /S66. Mr. Robert B. Stewart^ To PENNSYLVANIA R. R. CO. Dr. For Freight from Mill Creek on 3 boxes Apples, 4 " Mdse., Weight. Rate. Freight. Expenses. Total. 1935 1450 56 60 10 8 83 70 57 50 11 9 40 20 $20 60 Rce'd payment for the Company, Tnos. Y. MuKR.^T. WAREHOUSE RECEIPT. Syracuse, June f8, fSG?. Delivered to John Cottrell & Co., in good order, for which they liave paid the charges thereon. Marks. Articles. Quantity. Charges. J. C. & Co. X. L. # lto20 ^ 20 " 30 Oswego Flour, extra, Corn Starch, Freight from Oswego, Dray age, Storage, &c., T. & L. MosiER. 20 bbls. 10 " 1 3 50 00 50 ACCOUNT SALES. 267 ACCOUNT SALES. An Account of ISales is a detailed statement of goods sold and the charges incurred thereon, and is made for the purpose of showing the net proceeds of sales. When goods have been sold on commission, the agent or commission mer- chant makes out an account sales, to be sent to the consignor, or person for whom the goods were sold. Account Sales are made out in various forms 3 that form being used which is most convenient for the branch of busi- ness in which it is used. Sometimes they are made out in the form of a ledger account; the quantity of goods sold, with their marks, prices, &c., being entered on the credit side, and the various charges on the debit side. The difference between the two sides exhibits the net proceeds, and is entered on the smaller side, to produce a balance. Another form, and the one which is generally adopted, is to enter the sales, with all the particulars, first, and the charges underneath. When the goods are not all sold, a minute of those still on hand should accompany the account sales. To make out an account sales, turn to the consignment account in the ledger, and from thence to the original entries, to obtain all the items affecting the account. When the goods are sold for cash, or when the consignor guaranties the sale, it is not necessary to give the names of the purchasers; althow^h this is frequently done. A del-credere commission, or guaranty, is a commission charged for becoming responsible for the debts of those who purchase the goods on credit. Account Sales are averaged to find the date when the pro- ceeds may be paid without loss of interest to either party, (See AvERACiE of Accounts.) 268 ACCOUNT SALES. Saks of 5i6o bbi8.ffiurM^^cmri;?er Barque Aurora, /or Account of James T. Hoyt, Berlin, Md. To whom sold. Description. Price. 1RC6. Dec. 19 Jefferson Andrews, 25 bus. Ohio Wheat, 1.15 J28 76 38C7. Jan. 5 R. J. Long, 50 bbls. Elm Grove Fam. Floor, 9.50 47 60 It 8 Chaa. S. Brown, 100 bus. Kentucky Wheat, 1.20 120 00 13 L. S. Harris & Co., 20 " Oliio 1.18 23 60 u " " 75 bbls. Oregon Fam. Flour, Ex., 8.50 637 50 ♦« 25 Henry G. Stone & Co. 55 bus. Ohio Wheat, 1.10 56 00 •( " 25 bbls. Flour, Grant's Mills, 11.00 275 00 $1187 35 Chakges. Freight and Dravago, $46.00 Insurance on $1000, @ IJ per cent., 12.50 Storage and Labor, 7.25 Commission and Guaranty, 5 per- cent, on 1187.35, 59.37 Net Proceeds duo per average, , 1867, 124 12 $1063 23 Leonakd B. Hudsox. New York, Jan. 28, 1807. Account Sales of 75 Bales of Wool received per Pennsylvania Rait- roadj and sold for Account of Messrs. Smith & Williams, Salem, Columbiana Co., Ohio. 1866. Nov. 10 Three-quarter blood Merino Fleece, Net 9238 lbs., @ 60c., 80 days. 6542 80 Doo. 15 Half-blood Merino Fleece, Net 2638 lbs., @ 55c., " 1460 90 (t 1867. Jan. 5 Unwashed Merino Fleece, Net, 240 i disconnt, 80 ICO lbs., @ 55c., 30 days. Common and quarter-blood Fleece, Not 985 lbs., @ 50c., 30 days, 88 492 00 50 $7674 20 Charges. Freight and Drayage, $192.33 Commission, including Insurance, Storage, and Labor, 2 cents per lb. on 13,101 lbs., 262.02 Net Proceeds due Dec. 22, 1866, E. B. Thaw & Walker. 464 S5 $7119 85 PmiADELPniA, Jan. 10, 1867. ACCOUNTS CURRENT. 2G9 ACCOUNTS CURRENT. Accounts Current are statements in detail of accounts wliicli have been open or running from one time to another. They are usually made out twice a year, or whenever circum- Btances require, by the parties desiring settlement. The object of an Account Current is to furnish the person to whom it is sent a statement, that he may know the extent of his dealings, and what balance may be due from him to settle his account. Accounts Current are drawn from the accounts in the Ledger, with which they must agree, and should contain a description of every transaction, with date, items, and amounts, as expressed in the books of original entry, allow- ing for the difference of style. When particulars are not supplied, reference should be made to the entries or papers in which they may be found. Interest is allowed, or not, according to custom or the understanding between the par- ties. The time for which interest is calculated is counted from the date when the amount is due, or equivalent to cash, to the date of settlement. For the different methods of cal- culating the interest, see Interest Accounts. Accounts Current are sometimes averaged as in Average of Accounts. If there are errors in an Account Current received, it should be objected to within a reasonable time, or it becomes an Account Stated, which does not require a proof of items. The letters E. E. and E. 0. E., appended to invoices and accounts, are for the purpose of intimating the right of cor- recting errors or of supplyipg omissions. For additional Accounts Current, see pages 91 and 94 ; and for finding interest on English Accounts, see Interesi IN England. 23* 270 ACCOUNTS CURRENT. m O ^ 6 o - a g S 8 feSIS II 1 a " S fcS g 1 0> r-l <0 0> t^ CO t> O |l -t< IM -t- CO *; 5 8 8 8 8 I8S3ISII I - ^ 1 1 11 i \ » H 6 da «3 1 ■Ob- ja '-( 3 a g § S 5 SIS 1 i:; § S ^ "- ^ 1 1 « " 2 3 s ^ S S S S 1 = ^ t = a < 8 8 8 8 8I8J21SI 1 00 ^ 12 J2 ^ ^ So S.i i ^ J 3 5 5 a J i 1 o*' ;3 s s s 1 h ORDERS. 27 ORDERS. An Order is a written request to deliver money or goods to some person mentioned, or to his order, or to the bearer, on account of the person signing the request. It is used by the person receiving it as a voucher that the person signing it is responsible, and that the thing or things mentioned have been delivered. Orders may be made negotiable; but the persons on whom they are drawn are not under obligation to pay them unless they have been accepted. ORDERS FOR MONEY. Lancaster, Aug. 16, 1867. Mr. James T. Fordley, Please pay to M. B. Brown, ig^ order, One Hundred Dollars, and charge to our account. ^100. Jos. W. Andrews & Go. Messrs. Alfred Slade & Co. Gentlemen : — Please pay to Thomas Brown, or order. Thirty Dollars, due on my account, and oblige Yours, respectfully, Philada., Aug. 12, 1866. Robert H. Jenkins. ORDERS FOR GOODS. Baltimore, Feb. 19, 1867. Mr. William B. Linden, Please pay to Andrew B. Jones, or bearer. Sixty Dollars in Goods from your store, and place to account of Henry W. Wilkins. Albany, Mar. 25, 1867. Mr. Charles Riqua, Please send me, per bearer, Ten Barrels Flour, Genesee Extra, and oblige Yours truly, Henry Burnham. 272 CHECK??. Dayton^ 0., August IG, ISGG. Messrs. L. A. Tiers dk Son, J^ew York. Dear Sirs : Please send imrrudiaiehj Five (5) Half- Clients Imperial Tea, Hugo & Otto, ^7, as per sample sent us, and oblige Yours, truly, Corbin & Walworth. St. Louis, Jan. 3, 1SG7. Messrs. E. C. & J. Biddle, Philadelphia, Pa. Gentlemen: — Please send us, per Adams Express, 60 Crittenden's Book-Keeping, C. H. Edition. 25 do. do. H. S. do. 30 Lynd's Chss-Book of Etyirwlogy. 12 Cleveland's American Literature. 16 Alsop's Algebra. Upon receipt of your Bill, with Goods, we will remit by Draft or Express, ow you may direct. Respectfully, yours, A. B. M. Thompson & Co. CHECKS. A Check is a written order or request, addressed to a bank or banker, by a person having money deposited, requesting the payment, on presentment, of a certain sum of money to a person therein named, or to his order, or to the bearer. When drawn payable to a person or hearer^ it is transferable without indorsement, and the holder is entitled to payment ; when drawn payable to a person or his order, it must be in- donsod by the person to whom the check is made payable ; when made payable to a person without the words ^' or order," or " bearer/' or to a X)articular person " only," it is not nego- tiable. CHECKS. 273 As checks made payable to a person's order compel the payee to indorse tliem, they are, when drawn in this form, often used in lieu of receipts. The drawer of a check may countermand its payment at any time previous to its payment or acceptance by the bank. A check received from others should be presented without unnecessary delay, as the drawer will not otherwise be respon- sible for its payment in case of the failure of the bank. Every holder of a check is liable to every subsequent holder only for the time for which he would be held if originally liable. A post-dated check is payable on the day of its date ; but, as circumstances may arise that will render void a check drawn with a date in the future, some prefer dating the check with the day on which it is drawn, and stating in the body of the check the day when it is to be paid. When made payable on a future day mentioned, different from that of the date, they have been treated as bills of ex- change, and as such are entitled to days of grace, and require revenue stamps, the same as bills of exchange. The amount of a check should always be written out in words. The amount in figures is placed in the corner, that the sum for which the check is drawn may be seen at a glance, and also as a precaution against any alteration which might be made. CHECK PAYABLE TO BEARER. "I ^t. 7. Gincinncbti, jlug. 16, 1S67. ,^au «!^ t—JcMnMe/ "^ya€la* -^^ ^^^^ ^/ ^u/ei, CERTIFIED CHECKS. A certified check is one for the payment of which the bank becomes responsible, upon being certified, or marked " good" by the paying teller, with his signature attached. Certified checks are used to prevent the inconvenience and risk of withdrawing and counting sums of money that are to be im- mediately paid to others. They are also used instead of drafts for making remittances to distant places. "m M |to. 122. I (Philadelphia, :^ipril 6, 1M7. ^u /a J^tyA l'^ J^ia/am, el ^ic/ei, $1000. .=^t.^.1 .0ff^a^/.^J^^^, TRANSACTIONS WITH BANKS. 275 CERTIFICATES OF DEPOSIT. Certificates of Deposit are used when money is temporarily deposited, and no regular bank account is kept. When made payable to another person's order, they are frequently em- ployed for making remittances, in the same manner as cer- tified checks. 1 STAMP. 1 cv. cir\ o/. ^SB^^^aaBK. 1' M MoBton gattond Mnnh. ^^^P M Boston, JUass., Fel. 26, 1S67. M ^^AeiA. -^^J^. .^^ct/vt^ -nati t/e/iodti^ec/ th' -/mJ m t^«^;^^^^,s^..^,^^s^.^,^/.^,^.=:^^*'*«5 -::^j/t<)4*A<^n-07^e 9^housand (Pounds Sterling-^ for Value received, and place the same to account of To Brown, Shipley &. Co., Liverpool, Eng. .^eoye, .=0^^/<^. SECOND OP A SET OF EXCHANGE ON PARIS. %mhm^%^ f@p l@5i@a> FPe iefo iorh, gob. 14, \%m. At Sixty Days' Sight of this S K G O N D J^ of Exchange {First ^ Third of same tenor and date unpaid) Pay to the Order of J0BE(PB: WILBOJT. 2~er2/ 'thousand Two Hundred Francs for Value received, and place the same to account of To Delacroix &. Co., WW /p^ Paris. ^M THIRD OF A SET OF EXCHANGE ON FRANKFORT. At Sixty Days' Sight of this THIRD of Exchange [First ^ Second of same tenor and date unpaid) Pay to the Order of J. :fiZ^EIiQ: GjfiUZjiJTQ -^^•^.^-...■^..-^..^-^^^.^^Five Thousand Florins^ for Value received, and place the same to account of To Grants, Balfour & Co., ^|^ Frankfort. ^^ ^^te^ ^*^a. 293 INDORSEMENTS. INDORSP]MENTS, ACCEPTANCES, &c. INDORSEMENTS. The word indorsement signifies a writing on the back of a bill or written instrument , but it is well settled that this is not essential in order to charge a person as an indorser. The indorsement may be on any part of the note, or on a paper annexed to it, and in ink or pencil ; but it is better that the signature should be in ink, to prevent erasure. When a note or bill is drawn payable to a person or his order, it is properly transferable only by indorsement; nothing else, in law, will hold the parties to a note directly liable to the holder. FORMS OP INDORSEMENTS. 1. INDORSEMENT IN BLANK. John S. Barton. 2. INDORSEMENT IN FULL. Pay to Jas. Jones, or order. John S. Barton. 3. QUALIFIED INDORSEMENT. Without recourse. John S. Barton. 4. RESTRICTIVE INDORSEMENTS. Pai/ Robert Hunter, for my use. John S. Barton Pay to Chas. Harrison only. John S. Barton. 5. CONDITIONAL INDORSEMENT. Pay George Gray, or order, the within, unless before due he receives the amount from my agent. John S. Barton 6. INDORSEMENT BY AN AGENT. John S. Barton, Agent for Howard Chester. 7. A GUARANTY ON A NOTE. For value received in cash, 1 hereby guaranty the payment of the uithin Note. John S. Barton. 1 . A blank indorsement makes a note transferable by mere delivery only, and by it the indorser is made liable for the payment of the note. If the note or bill is lost after such INDORSEMENTS. 299 blank indorsement, any person who should become the holder of it, in good faith, for a valuable consideration, without no- tice, would be entitled to receive the amount thereof. 2. Indorsements in full prevent a subsequent holder from recovering against the antecedent parties, unless he can de- duce a regular title to the bill from the person whose name stands as first indorser. If all the subsequent indorsers are in blank, the holder may 'make himself the immediate indorsee of any one of them, or he may deduce his title through them all in succession. If some of the subsequent indorsements are in full and some in blank, then he must make a regular deduction of title through them all, or make himself the immediate indorsee, under some prior blank indorsement. Persons taking a bill or note subsequently to a blank in- dorsement may transfer it, either by delivery or by indorse- ment. 3. A qualified indorsement is one which affects the liability of the indorser, but not the negotiability of the note. If the holder of a note wishes to transfer it without being held liable for its payment, he can do so by writing his signature and adding '■'■witliout recourse" or other words to that effect. 4. The holder who has absolute property in a bill or note has the power of limiting payment to whom he pleases. A restrictive indorsement will not, however, be presumed from equivocal language, as restrictive indorsements tend to impair the negotiability of bills and notes. 5. If the payee or indorsee of a bill or note annexes a con- dition to his indorsement, before acceptance^ the drawee who afterwards accepts it is bound by the condition. If the terms of the condition are not complied with, the property in the bill reverts to the payee, and he may recover the sum payable in an action against the acceptor. 6. An agent should expressly indorse as agent, or write the name of his principal ; otherwise the indorsement would 300 INDORSEMENTS. be inoperative. When an agent is compelled to indorse notes or bills over to his principal, to avoid responsibility, he should use a restrictive form of indorsement. In Pennsylvania, a factor who remits a bill to his principal, in payment of goods sold on his account, and indorses the bill, does not thereby become personally responsible to Ms prifxipal, if he receives no consideration for guaranteeing and does not expressly undertake to do so. 4 Eawie, 384- 389; 5 Wliart 288. An indorsement in the form of A. B., Treasurer of- Company^ has been held not to render the agent liable as an indorser, but considered as intended only to pass the paper, and as equivalent to an indorsement "without recourse/' 7. An indorsement implies a contract to pay the note if dishonored, if due notice is given of dishonor, and not other- wise ; whereas a guaranty implies a contract, if due notice «? given of dishonor within a reasonxihle time. The guaranty should contain words importing considera- tion, and, unless made expressly negotiable^ is good only to him who first takes the note and advances money upon it. If the guaranty is upon a separate paper, it should describe the note with sufficient distinctness. If, upon proper presentation, payment of a note or bill is refused, the holder must give prompt notice of such refusal to each indorser whom he wishes to hold for payment, and inform him that he will be held for the payment of the same; otherwise the indorser will be discharged. If the holder could delay, he might injuriously aflfect the indorser, and his remedy against other persons. The holder of a note or bill may commence suit against any of the indorsers, or against all of them at once. When there are several indorsers, each is liable to those after him, and should give notice to all parties indorsing prior to himself. Each indorser may require any one whose name precedes ACCEPTANCES. 301 Ilis own to make good to him the loss he may sustain, pro- vided he gives notice of his intention to do so on the day he receives his own notice, or the day after. This notice may be given by any person competent to serve it; but a notary public is usually employed for the purpose. ACCErTANCES. An Acceptance is an engagement to comply in whole or in part with the terms of a bill. When the drawee engages to pay according to its terms, it is called a general acceptance ; when he agrees to pay with some qualification or condition different from the bill, it is called a conditional or qualified acceptance. When a bill is presented for acceptance, the drawee is en- titled to twenty-four hours, if he desires it, to decide whether he will accept it or not. In New York and Missouri, if the bill is not returned within twenty-four hours, it is deemed by law to be accepted. Acceptances are usually written across the face of the bill, and, for distinctness, in red ink. Any words not refusing its request, or the signature of the acceptor in blank, \b prima facie evidence of acceptance ; and when not otherwise provided for by law, the acceptance may be either verbal or in writing, — a written acceptance; of course, being more easily susceptible of proof. In New York- it is held that no person shall be charged as an acceptor of a bill of exchange unless the acceptance be in writing, and every holder may, on presentation of the bill, require that the acceptance be written on the bill, and if such acceptance is refused, the bill may be protested for non- acceptance. The holder may assent to a qualified acceptance, and it will be good as far as it extends ; but he takes it at his own risk, and he must give notice to the antecedent parties, or they will 26 302 AGENCY. not otherwise be held bound by it. The condition of the acceptance should appear upon the face of the acceptance in writing, as any subsequent holder for value, without notice, would not be bound by verbal conditions. The holder is not bound to take any but an unqualified or unconditional acceptance; and when refused, if he wishes to maintain a claim against the other parties, he should treat the bill as dishonored, unless they assent to the proposed condi- tional acceptance. If the holder declines the conditional acceptance, it will be a waiver of all right to hold the drawee. Form of Conditional Acceptance written across the face of a Draft, "Accepted if in funds from consignment shipped us on 3d instant. Roger B. Gray. "New York, Oct. 17/66." AGENCY. An Agent is a person having power to act for another, who is called a principal. A man may do by his agent whatever he can lawfully do himself, and his agent can do for him. A General Agent is one appointed to transact all the busi- ness of his principal, or all his business of a particular kind. A Special Agent is appointed for a specific and particular purpose. A Broker is an agent employed to negotiate between other parties, and is presumed to act in the name of his principal. A Factor or Commission Merchant is an agent to sell goods for his principal, but who acts for several persons in that capacity. lie diflers from the broker in having actual possession of the goods. A Factor may buy and sell in hia own name as well as in the name of his principal. AGENCY. 303 An Attorney is an agent acting in behalf of his client. The authority of an agent may be constituted in three ways : by deed under seal, by a writing without seal, or by mere words. The authority of an agent may be revocable or irrevocable. It is irrevocable when an interest in the subject-matter is conveyed to the agent, or the authority is given for a valuable consideration; it is revocable when no interest is conveyed, in which case the principal can revoke the author- ity at his pleasure, subject in some cases to a claim for An agency may be revoked by the operation of law, by expiration of time, by changes producing incapacity to act, by the extinction of the subject-matter or its complete fulfil- ment, or by the death of the principal. A power of attorney to sell goods or stocks ceases with the life of the principal, and upon his death may become valueless. Where the conveyance or% any act is required to be under seal, the authority to execute it must be under seal also. Verbal authority, ordinarily, is sufficient; but an agent ought, for his own security, to act under written authority, and to disclose his character whenever he executes a con- tract. In signing his name, the mere use of the word "agent" is not sufficient; the name of the principal must also appear. Instead of writing "Henry Grant, Agent," it should be " R. Brown, per Henry Grant;" or, "R. Brown, by his attorney, Henry Grant." If an agent does an act or makes a contract unauthorized by his principal, though in the name of the principal, he is personally Hable; but if the principal, with the knowledge of all the facts, adopts or acquiesces in the acts done under an assumed agency, he cannot afterwards impeach them under the pretence that they were done without authority, or even contrary to instructions. If the principal does not dissent and give notice of it within a reasonable time after being in- 304 POWER OF ATTORNEY. formed of what has been done, his assent and satisfaction will be presumed. "An agent is personally liable if he makes himself so ex- pressly, or if he transcends his authority or departs from its terms and directions, or if he conceals his character as agent, or if he purposely conceals the name of his principal, or, perhaps, if he does not actually state the name of his prin cipal/' It is the duty of the agent to follow implicitly his instruc- tions, and to keep his principal fully and promptly informed in regard to the business intrusted to him. An agent is liable for interest if he has made it on the money in his hands, but not if it has lain idle. As a general rule, an agent cannot appoint a substitute, or delegate his authority to another. But a power of substitu- tion may be expressly given, or it may be inferred from the nature of the act to be performed, or where there is a known and established custom of substitution. POWER OF ATTORNEY. A Power of Attorney, or Letter of Attorney, is a written instrument, usually under seal, by which authority is given to one person to perform some lawful act for another. Authority to execute a deed must be given under seal, and be acknowledged by both husband and wife, and must be done in the name of the principal. Upon the death of the principal, the authority delegated by power of attorney ceases, and all subsequent acts under it are void. The authority intended to be conferred should be expressed in clear and intelligible terms, and be propeily executed, attested, and acknowledged. POWER OF ATTORNEY. 305 FORM OF POWER OF ATTORNEY. j^itob all Pnt bn i^m |wstnts, That I, of , County of , and State of , have made, constituted, and appointed, and by these presents do make, constitute, and appoint , of , County of , and State of , my true and lawful attorney, for me, and in my name, place, and stead, and in my behalf, to (here insert the things which the attorney is to do) ; giving and granting unto my said attorney full power and authority generally to do and perform all and every act and thing whatsoever requisite or proper to effectuate all or any of the premises, with the same powers, and to all intents and purposes with the same validity, as I, if personally present, could (giving and granting, also, unto my said attorney full power to substitute one or more attorney or attorneys under him my said attorney in or concerning the premises, or any part thereof, and the same at his pleasure to revoke ; and) hereby ratify- ing and confirming whatsoever my said attorney (or his substitute or substitutes) shall and may do by virtue hereof in the premises, ^n ^illteSS feljeaof, I have hereunto set my hand and affixed my seal, this eighteenth day of September, in the year of our Lord 18 Signed, sealed, and delivered [Seal.] in the presence of Henry R. Linden, Wm. H. Moult. N.B.— ^By omitting the words in brackets, no power to appoint a substitute is given. SHORT FORM. ^nofo all Pen bg il^tst presents, That do make, constitute, and appoint true and lawful Attorney for and in name with power, also, an attorney or attorneys undei for that purpose to make and substitute, and to do all lawful acts re- quisite for affecting the premises; hereby ratifying and confirm- 306 POWER OF ATTORNEY. ing all that the said attorney or substitute or substitutes shall do therein by virtue of these presents. ^n Wiitnzsz fcljereof, have hereunto set hand and seal the day of , in the year of our Lord one thousand eight hundred and . [l.s.] Signed, sealed, and delivered in the presence of POWER TO TRANSFER STOCK. Jlnofa all Pen bg t^m |r£sntts, That I, K. W. Y., of Oswego, County of Oswego, and State of New York, do make, constitute, and appoint Leonard D. Gray, of the same place, my true and lawful attorney, for me, and in my name and behalf, to sell, transfer, and assign unto Hosea W. Hunter, of said Oswego (or, any other person or persons). One Hundred Shares in the capital stock of the Syracuse National Bank, in Syracuse, State of New York, standing in my name on the books of said corporation ; and to do all necessary acts and to make the necessary acquittances and discharges to eflFect the premises (add, if desired, and I do further empower him to substi- tute any person or persons under him, with like power) ; hereby ratifying and confirming all my said attorney (or his substitute or substitutes) shall lawfully do by virtue hereof. |n WilimsB ia^mof, &c. POWER TO RECEIVE DIVIDEND. ^nobj all Pm bg l^CSe '§Xt$mU, That I, H. Y. Bell, of Oswego, County of Oswego, State of New York, do constitute and appoint Hiram Howell, of Meridian, Cayuga county, to receive from the Cashier of the Oswego National Bank the dividend or dividends now due me on all stock standing to my name on the books of the said bank, and to receipt for the same ; hereby ratifying and con- firming all that by him may lawfully be done by virtie hereof in the premises. TOtncsS my hand, etc. Signed and delivered in presence of, &c. SEALED INSTRUMENTS. 307 SEALED INSTRUMENTS. A contract which is under seal is called in law a specialfij. Bonds are of this class. All other contracts, whether oral or in writing, are called i)arole contracts. A specialty is dis- tinguished from a simple contract by its seal. An impression upon wax, wafer, or, as in most of our States, a scrawl of ink, attached to the signature, is regarded as a sufficient seal. A seal implies consideration, and is in general absolute ; but in New York a seal is only prima facie evidence of con- sideration, which may be rebutted as if the instrument were not sealed. A specialty is not negotiable like a promissory note : it may be assigned, however (see Form of Assignment), the assignee taking it at his own peril, and having only the rights of the original obligee : if the obligor has any set-off or claim against the obligee at the time of the assignment, the assignee will be compelled to allow it. If the assignee, previous to taking the assignment, obtains from the obligor an admission in writing, or in the presence of witnesses, that he has no defence or set-off, the obligor is liable to the assignee for the whole amount. In Pennsylvania, and in some other States, bonds are made legally assignable; and the assignees can sue in their own name when they are for payment of money, and drawn '• to order" or " to assigns," and the assignment is " under hand and seal" and in the presence of two or more witnesses ; the intent of the act being to enable the assignee to sue in his own name and prevent the obligee from releasing after assignment. If they are not drawn in the above form, bonds may be assigned for a valuable consideration, wi'h permission to sue in the assignor's name. 308 BONDS. The indorsement in blank of a specialty does not make the indorser liable as in the case of a negotiable note. An instrument under seal is not barred by the statute of limitations, and, if originally good, is so for twenty years. BONDS. A bond is an obligation for the payment of money, or for the performance or non-performance of certain acts, with a penalty annexed in case of failure to comply with the con- ditions of the bond. It requires no technical words: any sealed writing which distinctly acknowledges a debt is a bond ; but generally there is a condition added, that if the obligor does some particular act, the obligation shall be void, or else shall remain in full force. The penalty in a bond is usually double the amount of the real debt, for the purpose of covering the full debt, together with interest and costs. All that can be recovered of a penalty in a bond, in addition to the amount of the debt, is the interest and costs; but when a specified amount is agreed upon for liquidating damages, it must be distinctly so expressed, and then such specified sum is the amount to be paid. Where it is the intention to bind the heirs of the obligor, the term heirs must be named. Executors and administrators are bound though not named. If the obligation of a bond becomes impossible by the act of God, after making it, the penalty is saved; if it be im- possible at the tiuie of making it, it is said the condition alone is void, and the bond shall stand, single and unconditional. Where several payments are due at difl^eront times on a bond, if one payment is delayed and the bond is so drawn, judgment may be recovered for the whole of the real debt, with stay of execution on the several payments till such specified times as those payments become due. BONDS. 309 COMMON FORM OF BOND. Jlnob all '^m bjj ibcs£ |jixscnts, that I, , in the county of and State of , am held and firmly bound unto , of , in the county of and State aforesaid, in the sum of One Thousand Dollars, lawful money of the United States, to be paid to the said , or his certain attorney, executors, and administrators or assigns; to which payment, well and truly to be made and done, I do bind myself, my heirs, executors, and administrators, and every of them, firmly by these presents. Sealed with my seal, and dated the day of , Anno Domini one thousand eight hundred and The condition of this obligation is such, that if the above bounden , his heirs, executors, administrators, or any of them, shall and do well and truly pay, or cause to be paid, unto the above-named , his executors, administrators, or assigns, the just and full sum of Five Hundred Dollars, lawful money, aforesaid, with legal interest for the same, on or before the day of next, without fraud or further delay, then the above obligation to be void and of none effect, or else to be and remain in full force and virtue. Signed, sealed, and delivered in [ Seal. ] the presence of CLAUSE FOR JUDGMENT BOND. And I do hereby authorize and empower any attorney of an}' court of record in the State of , or elsewhere, to enter judgment against me, my heirs, executors, and administrators, and in the favor of the above-named , his executors, adminis- trators, or assigns, for the above sum, as of the past, present,' or any future term of said court, with release of errors, costs of suit, &c. INTEREST CLAUSE. And it is hereby expressly agreed, that should any default be made in the payment of the said interest, or of any part thereof, on any day whereon the same is made payable, as above ex- pressed, and should the same remain unpaid and in arrear for the space of thirty days, then and from thenceforth, that is to 310 RELEASE. Bay, after the lapse of the said thirty days, the aforesaid principal 8um of Five Hundred Dollars, together with all arrearage of in- terest thereon, shall, at the option of the said , his executors, administrators, and assigns, become and be due and payable immediately thereafter, although the period above limited for the payment thereof may not then have expired, any ibing hereinbefore contained to the contrary notwithstanding. SEALED RECEIPT OR RELEASE. GENERAL RELEASE OF ALL DEMANDS. Jlltob all Pen bg t^cse '^XtStnts, that I, Howard C. Burton, of New York, for and in consideration of the sum of Three Hundred and Seventy-Five Dollars to me paid by George C. Taylor, of Phi- ladelphia, the receipt of which I do hereby acknowledge, have re- mised, released, and forever discharged, and I do for myself, my heirs, executors, and administrators, remise, release, and forever discharge, the said George C. Taylor, his heirs, executors, and administrators, of and from all debts, demands, actions, and causes of action, in law or equity, of every kind, character, and nature soever, against him, from the beginning of the world to this day. |n Ccstimong foljcreof, I have hereto set my hand and seal, this thirteenth day of July, a.d. 1865. Signed, sealed, and Howard C. Burton. [Seal.] delivered in presence of Ethan Young, Alex'r R. Rundle. A Deed is a writing or instrument sealed and delivered. As generally used, it is a writing for the conveyance of pro- perty. In Pennsylvania, a scroll enclosing the word "seal." or "L.S.," is a good and valid sealj but not in all the States. A Fec-Siinplc interest is the absolute ownership in an estate. A Warranty Deed is so called because the grantor cove- nants to insure and defend the lands mentioned against the persons and to the extent specified. SEALED INSTRUMENTS. 311 A General Warranty covenants and warrants against all persons whatsoever; a Special Warranty, only against himself, his heirs, and those claiming under him. Deeds by executors, administrators, or guardians generally contain no warranty ; and every requisition of the law should be com- plied with, to obtain a good title. A Quit-Claim Deed is one which conveys all the interest which the grantor may possess, whatever it may be, in the land specified. A I>eed Poll, or Single Deed, like a quit-claim deed, is made by one party only (for example, a sheriff's deed). A Trust Deed is given to persons to hold for the use of some other person who is entitled to the proceeds, profits, or use of the property. A Ground-Rent Deed conveys land, with a reservation of a certain sum of money in the nature of rent, to bo paid at specified times, and may be for life, for a term of years, or in fee. A Mortgage is a conditional conveyance of property as a pledge for the security of a debt. All kinds of property, real and personal, which may be sold absolutely may be mortgaged. As a general thing, chattel mortgages^ or mortgages on personal property, are not good against third parties or creditors unless the property is actu- ally delivered, or the mortgage acknowledged and recorded. When a mortgage is paid by instalments, each payment hould be receipted upon the record of the mortgage as it is made. When the debt is paid, the mortgagee is bound under a penalty to enter satisfaction on the records within a limited time ; and care should be taken by the mortgagor that it be done. If the death or removal of the mortgagee occur before satisfaction is entered, petition should be made to the Court of Common Pleas that it may be so ordered. 312 CONTRACTS. CONTRACTS. A contract is an agreement, upon sufficient consideration, to do, or not bo do, some specified thing. A consideration may be any benefit to the party promismg, or some trouble or ivjury to the party reedvincf the promise. In general, an offer or proposal becomes a contract as f.oon as it is accepted, and acceptance may be made before the expiration of the time limited, or at any reasonable time before knowledge of a retraction of the offer. In the majority of the United States, no action can be brought against a person upon an agreement not to be per- formed within one year from the making of it, unless some note or memorandum of the agreement be signed by the party to be charged, or his lawfully appointed agent. Persons under twenty-one years of age, married women, and insane persons, are incompetent to make a contract. A minor, however, may contract for necessaries ; so, also, may a married woman when her husband, without good reason, re- fuses to make suitable provision for her. The subject-matter of the contract must be possible ; it must also be lawful. A contract founded upon fraud, or to do an illegal or immoral act, is void. A contract in total restraint of the exercise of a man's trade or profession would not be enforced by the courts, because it is against public policy ; but a con- tract restraining him in any particular city or place is valid. Care bestowed in clearly expressing the contract in plain and unambiguous language, may be the means of preventing lawsuits and the loss of friendship as well as the loss of money. '< Three things should be attended to in writing a contract. 1st. Weigh well your words, and ascertain their exact import or value. 2. Use enough of them to express all that you mean or intend by the contract. 3d. Arrange them in such a manner that they have but one meaning, and that the meaning you intend." — Hon. Joel Jones. FORM OF AGREEMENT. 313 Verbal evidence may be admitted to explain, but not to change, the original contract. Contracts of Sale. — A sale is a contract for the transfer of property for a valuable consideration. The subject-matter and the price must be certain, or capable of being made so, to constitute a sale. The subject-matter should be perfectly identified, ascertained, and designated, so as to be distinguished from every thing else. After the sale is completed, the goods are at the risk of the purchaser. If in a contract for the sale of goods no time be mentioned for payment, the law implies a contract to pay for them on delivery, and the buyer is entitled to the goods only on pay- ment or tender of the price. The buyer acquires a right of property by the contract, but until he pays or tenders the price he does not acquire a right of possession. If the sale be made upon credit and nothing be said as to the time of delivery, the buyer is entitled to possession immediately; although the seller can reclaim the goods if the buyer is insolvent and they are in the hands of a common carrier or have not yet come into the actual possession of the buyer. In the several States, excepting Louisiana, no contract for the sale of any goods is binding, when the price is above a certain sum, unless the buyer shall accept part of the goods so sold and actually receive the same or give something in part payment, or unless some writing of such bargain be made and signed by the party to be charged. The sum required in Massachusetts and New York is $50 ; in Vermont, $40 ; in Connecticut, $35 ; in New Hampshire, $33.33 ; and in New Jersey, $30. In dissolving a contract, the law requires that it shall bo done by the same means that render it binding : if the con- tract was under seal, the release or discharge must be under seal also ; if the contract was required by law to be in writing, it cannot be dissolved by a verbal agreement. 27 314 AGREEMENT OF SALE. GENERAL FORM OF AGREEMENT. STbis 3^prccnunt, made the sixteenth day of February, a.d. 18G8, between Joun T. Evans, of Sandusky, County of Erie and State of Ohio, of the tirst part, and Henky W. Ward, of llouston, County of Shelby and State aforesaid, of the second part, ©litlUSSttlj, That the said John T. Evans, for the consideration jiereinafter mentioned, doth covenant and agree to and with the said JIeniiy W. Ward, that {Jicre insert the agrcerrient on the part of Evans). And the said Henry W. Ward, in consideration of the covenant ^f the said party of the first part, doth hereby covenant and agree to and with the said John T. Evans, that [here insert the agreement on the part of Ward). Kit ^illTfSS lu^CKof, we have hereunto set our hands and seals, the year and day first above written. Signed, sealed, and delivered in presence of John T. Evans. [Seal.] Edv/ard p. Hartell. Henry W. Ward. [Seal.] Thos. J. Turner. AGREE3IENT OF SALE. ^gixemmt made this day between Thomas J. Raymond, of New York City, of the first part, and Leonard Munroe, of said city, of the other part, as follows: — Said Thomas J. Raymond, for the consideration hereinafter men- tioned, doth hereby agree to deliver to said Leonard Munroe, at his store in said city, as the same may be required from time to time, — the whole to be delivered before the first day of May next ensuing the date hereof, — two thousand pounds Old Government Java Coffee, equal to a sample exhibited. In consideration whereof, said Leonard Munroe hereby agrees to pay to the said Thomas J. Raymond twenty cents per pound for each and every pound so delivered, in the notes of the said Leonard Munroe, payable three months after date, to be given at the end of each and every month, for the amount of coffee then delivered under this agreement. ©litncss the said parties, at New York, this day of , A.r). one thousand eight hundred and sixty W. P. Thornton. ) Thos. J. Raymond. T- AT w f Witnesses present. K. M \\n,sr>N. ) *- LEONARD MUNROK. BILL OF SALE. 315 A BILL OF SALE OF GOODS. Jlnobj all P^£ll bg t\}tSZ presents, that l, Jared K. Long, of Buf- falo, for and in consideration of the sum of five hundred dollars to me in hand paid by John Cottrell, of the same place, at and before the sealing and delivery of these presents, the receipt whereof is hereby acknowledged, have bargained, sold, and delivered, and by these presents do bargain, sell, and deliver, unto the said J. Cottrell, One Tliousand (1000) bbls.. Linseed Oil, now in store at Pittsburgh, Pa. %Q l^attC aitb to l^olb the said goods unto the said J. Cottrell, his tjxccutojs, administrators, and assigns, to his and their own proper uae and benefit forever. And I, the said Jared K. Long, for my- self and my heirs, executors, and administrators, will warrant and defend the said bargained premises unto the said J. Cottrell, his executors, administrators, and assigns, from and against all persons ■whomsoever. Witness my hand and seal, this tenth day of March, 1868. Sealed and delivered in the presence of Jared K. Long. [l. s.] Jas. Clark. Henry R. Damon. AFFIDAVIT FOR GOODS SOLD AND DELIVERED. State of , County of , ss. Francis J. Murray, of , in said county, being duly Bworn (or affirmed), deposes and says that'Byron C. Gates, of , county of and State of , is justly and truly indebted unto him, the deponent, in the sum of dollars, for goods sold and delivered by him to the said Byron C. Gates; and that he has given credit to the said Byron C. Gates for all payments and set-ofi"s to which he is entitled ; and that the balance claimed, according to the foregoing account, is justly due; and that the said account is correctly stated. Sworn and subscribed, this day of , a.d. 1868, before me, Henry C. Beach, Commissioner for the State of 816 GUARANTEES. GUARANTEES. A guarantee is an engagement whereby one man, called the guarantor, binils himself as security for the performance of certain acts by another. A guarantee, to be binding, should be for a consideration ; as in law all promises made without a consideration are valueless. Though not always necessary, it is preferable that the gua- rantee be in writing; because the evidence of the fact is then so much easier of proof. In some States, the guarantee must express the consideration for which it was granted. Guarantees of commission-merchants, binding them to warrant the solvency of the purchasers of the goods they sell on credit, need not be in writing. The words of a guarantee should be strictly construed, and not taken to mean more or less than the words clearly ex- press. A guarantor is not liable beyond the scope of his engagement : a mere recommendation or overture to guarantee is not sufficient. A guarantee must be accepted, to make it a contract; and the guarantor must have notice, either direct or implied, of its acceptance within a reasonable time. In Pennsylvania, by act of April 26, 1855, no action shall be brought upon any special promise to answer for the debt or default of another, unless the agreement, or some memo- randum or note thereof, be in writing. This act does not apply to contracts in which the consideration is less than twenty dollars. Guarantees do not continue to transactions which take place after a change is made in the firm to which they were given, unless such change is expressly provided for. In some States, unless the creditor can show that it would be useless to proceed against the debtor, he must first institute proceedings against him before he can resort to the gun^""*^r. GUARANTEES. 317 A guarantor, after paying the debt, has a right to substi- tute himself in the place of the creditor, and is entitled to receive from him all the securities held by him for the prin- cipal debt. Guarantee of a. Debt not yet incurred. PiTTSBUUGii, Dec. 8, 1865. Messrs. Geo. II. Stuart & Bro., 13 Bank Street, Philadelphia. Gentlemen : — The bearer, Mr. Henry G. Layton, of this place, intends visiting your city for the purpose of purcliasing goods. Should you be disposed to furnish him with such goods as he may call for, we hereby guarantee the payment for any purchases he may make within one month from this date, to any amount not ex- ceeding five thousand dollars. Yours, truly, S. T. Humboldt & Co. Note. — The consideration in the above guarantee is the selling of gooda on credit to H. G. Layton. Another. Cincinnati, Dec. 11, 1865. Geo. H. Whelan, Esq. Dear Sir: — I hereby guarantee the payment of any bill or bills of merchandise Mr. J. L. Johnson may purchase from you, the amount of this guarantee not exceeding five hundred dollars ($500), and to expire at the end of three months from date Kcspectfully, yours, Benjamin Patten. Guarantee of a Debt already incurred. Louisville, Kt., Feb. 19, 1 368. Messrs. M. C. Harrison & Co., New Orleans. Gentlemen : — In consideration of one dollar, pai4 me by your- selves, the receipt of which I hereby acknowledge, I guarantee tliat the debt of four hundred dollars, now owing to you by George W. Perkins, shall be paid at maturity. Very respectfully, yours, Leonard H. Morton. 27* 318 PARTNERSHIP. PARTNERSHIP. A Partnership is a voluntary contract between two or more persons to place their property, labor, or credit, or some or all of them, in some lawful business, and to divide the profit, or bear the loss, in certain proportions. (See p. 174 ) A partnership is not constituted merely by an interest, but depends on the joint liability to loss, as well as on the par- ticipation in the profits. A stipulated portion of the profits as mere compensation for labor or services does not constitute a partnership. A General Partnership is one formed for trade gene- rally, without limitations, and comprehends whatever business the partners may engage in. A Special Partnership is one which is confined by the terms of the agreement to some particular kind of trade or business, or some particular transaction or speculation. A Liiniited Partnership is one in which the responsi- bility of one or more of the partners is limited to the amount invested by him or them in the concern. In a limited part- nership the special partner has the advantage of investing where the profits are equal to the gains of actual business, without risking more than the sum contributed. The laws relative to limited partnerships are of a nature to require great care on the part of any one about to become a special partner. The statute law of the State in which such partnership is formed must be complied with literally and accurately. The advice of able counsel should in all cases be taken before entering into such a partnership, in order to avoid assuming the re- sponsibilities and liabilities of a general partner. A person who lends his name as a partner, though he con- tribute neither money nor time, nor receive any share of the profits, or who suffers his name to continue in the firm after PARTNERSHIP. 319 he has ceased to be an actual partner, is liable to third per- sons as such. Each partner has full power to bind the firm by all acts and contracts within the scope of the partnership business. A partner cannot make the firm responsible for his sepa- rate debt, nor enter into engagements binding the firm which are unconnected with, and foreign to, the partnership. Each partner may buy and sell and make contracts for the firm, and may receive and pay money and become a party to negotiable paper in the name of the firm. In signing contracts relating to partnership business, part- ners should always use the proper style of the firm, not merely their own name, nor any other name than the full and exact name of the firm. In general, however, one partner cannot bind the other by an instrument under seal, unless the other expressly assents, is present when it is executed in the joint name, or sub- sequently ratifies it ; though he may execute a release of a debt due the firm. Nor can one partner bind the firm by a guarantee not in the regular course of business, unless it be afterwards adopted by the firm. One partner may discharge himself from liability by giving express notice to any customer, or other person, not to trust one or more of his copartners. A partnership may be dissolved by the expiration of the time limited for its continuance, by the voluntary act of one or all of the parties, by the death, insanity, or bankruptcy of either, and by judicial decree. If no precise period is men- tioned for its continuance, a partner may withdraw at any time; and even if formed for a definite time, a partner may, by giving due notice, dissolve the partnership as to all future capacity of the firm to bind him by contract, subjecting him- self thereby to a claim for damages for a breach of the cove- nant. In cases of a dissolution by death, it is the surviving part- 320 PARTNERSHIP. ner or partners alone to whom belong the right and duty of disposing of the property, collecting the assets, and paying thereout the debts: the representatives of the deceased have no right to do more than to call upon the surviving partner or partners to render an account. A creditor of a partner may sell only such partner's indi- vidual interest in the surplus partnership property, after all claims upon the firm are discharged. The purchaser is not bound to become a partner, nor are the others bound to admit him. The dissolution of a partnership by consent of the parties should be indorsed on the articles of copartnership, and im- mediate actual notice communicated to the parties who have had previous dealings with the firm. Notice in a newspaper is sufficient as to persons who have had no previous dealings with the firm; but it is not sufficient for those who have had, as the law requires express notice to the debtors. Upon dissolution all the members are liable, individually, for the contracts and debts of the firm existing at that time. In general, after dissolution, the power of one partner to bind the firm ceases; but either partner, without agreement as to the mode of liquidation, may sell such property as he may have in possession, and may collect and receipt for debts, being liable to be called to account in a general settlement. When one partner assigns his interest in the firm, the word 'release" must be used, as it alone, it is said, can pass the whole interest. Guarantees given to a partnership do not continue valid to a new firm. AGREEMENT BETWEEN PARTNERS. All jiartnership agreements should be Written, and each l)artner should hold a copy. Although not essential to their validity that the agreement should be in writing, yet un- PARTNERSHIP. 321 pleasant feelings and difficulties, as well as serious pecuniary loss, may be prevented by having the terms embodied in clear and distinct language. Partnership articles should specify the names of the seve- ral partners, and the name or firm under which the partner- ship is to be conducted, the kind of business to be transacted, the time of commencement and intended duration of the partnership, the amount of the capital contributed by each partner, the manner in which the gains and losses are to be shared, whether interest is to be allowed on capital and at what rate, the amount which may be withdrawn yearly by each partner for private use, and the manner of disposing of the partnership effects in the event of a dissolution. Other stipulations may be inserted at the pleasure of the parties. FORM OF ARTICLES OF COPARTNERSHIP. Articles of Agreement, made and concluded this first day of January, in the year a.d. one thousand eight hundred and sixty- seven, between Robert R. Johnson, of the first part, and Charles S. Burton, of the second part, both of Pittsburgh, county of Al- leghany, State of Pennsylvania. , The said parties have agreed, and by these presents do agree, to associate themselves as co- partners for the pui'pose of carrying on the General Hardware Business on the following terms, to the faithful performance of which they mutually bind and engage themselves, each to the other, his executors and administrators. First. — The name, style, and title of such partnership shall be R. R. Johnson & Co., and it shall continue for three years from the date hereof, except in case of the death of either of said partners within the said term. Second. — That the said Robert R. Johnson contributes, as his share of the joint stock, merchandise valued at Ten Thousand Dol- lars ($10,000), a schedule of which is contained in the stock-book of the firm, and the sum of Five Thousand Dollars ($5000) in cash ; and that the said Charles S. Burton contributes the sum of Three Thousand Dollars ($3000) in cash. Third. — All profits which may accrue to the said partnership 322 PAKT.NKitSIIIP. Bliall be divided, and all losses happening to (he said firm, wbctber from bad debts, depreciation of goods, or any other cause or acci- dent, and all expenses of the business, shall be borne by the said parties, in the proportion of three-fourtks by the said Kobert K. Johnson, and of one-fourth by the said Charles S. Burton. FouRTU. — The said 11. K. Johnson and Charles S. Burton shall devote and give all their time to the business of said firm, and use their utmost endeavors, to the best of their skill and ability, to conduct the business for their mutual advantage, and will not, within the period above-named, engage in any otlier trade or busi- ness to their private emolument or advantage. Fifth. — That books of account shall be kept, in which shall be entered a full and exact account of all the purchases, sales, transactions, and accounts of said firm, and which shall always be open to the inspection of both parties, and their legal repre- sentatives respectively. An account of stock shall be taken, and an account between the said parties shall be settled, once in every year, and as much oftener as either partner may, in writing, request. Sixth. — Neither party shall assume any obligation or liability, verbal or written, either in his own name or the name of the firm, for the accommodation of any other person or persons whatsoever, without the consent, in writing, of the other party; nor shall either party lend any of the funds of the copartnership without such con- sent of the other partner. Seventh. — No large purchase shall be made, nor any trans- action out of the usual course of the hardware business be under- taken, by either of the partners, without previous consultation with and the approbation of the other partner. EiOHTH. — The said Robert R. Johnson shall not withdraw from the funds or .pint stock of the firm more than the sum of Piighteen Hundred Dollars per annum, nor more than Three Hundred Dol- lars in any one month; and the said Charles S. Burton shall not witlidraw more than the sum of Eight Hundred Dollars per annum, nor more than One Hundred Dollars in any one month. Each (or neither) party shall be allowed interest on his share of capital in- vested; and if, at the expiration of the year, a balance of profits be found due to either partner, he shall be at liberty to withdraw Baid balance, or to leave it in the business, provided the other part- ner consent thereto. PARTNERSHIP AGREEMENTS. 323 Ninth. — At the expiration of the aforesaid term, cr earlier disso- lution of partnership, the stock or its proceeds, after paying the debts of the firm, shall be divided in the proportion of five-sixths to the said Robert R. Johnson, and of one-sixth to the said Charles S. Burton; but, if the said parties or their legal representatives cannot agree in the division of stock then on hand, it is hereby agreed that the matter shall be referred to the arbitration of II. L., C. II., and D. F. (or three competent disinterested persons, selected as may be arranged); and what they shall direct and determine therein shall be binding and conclusive upon all concerned. Tenth. — And it is further agreed, for the faithful performance of the aforesaid articles of agreement, that either party, in case of any violation of them, or either of them, by the other, shall have the right to dissolve this copartnership immediately upon his becoming informed of such violation. Ijn Milncss fobercof, we have hereunto set our hands and seals the day and year above written. Executed and delivered in presence of Robert R. Johnson. [Seal.] Henry C. Rodgers. Charles S. Burton. [Seal.] John L. Darrow CLAUSES TO BE INSERTED IN PARTNERSHIP AGREEMENTS WHEN DESIRED. Not to be bound, or indorse bills, for others.— And that neither of the said parties shall, during this copartner- ship, enter into any deed, covenant, bond, or judgment, or become bound as bail or surety, or give any note or bill of exchange, or accept any bill, with or for any person whatsoever, without the con- sent of the other first had and obtained. A majority to control. — That in all matters respecting the transactions of the partnership and the management of the business, the expressed opinion of the majority of the parties to this agreement shall govern and be binding on all of said parties ; and in cases of difficulty they shall have power to wind up or sell the concern. Not to trust any one against tbe wisb or a partner. — And that no merchandise belonging to the firm shall be sold to any person or persons after notice from either of said partners that such persons are not to be credited or trusted. 324 PARTNERSHIP AGREEMENTS. Neither partner to asisign his interest.— Ana it ia agreed between said parties that neither of them shall, without the consent of the others, previously obtained in writing, sell or assign bis share or interest in the joint concern, to any person or persons whatsoever. AGREEMENT TO CONTINUE PARTNERSHIP. By Indorsement on the Original Articles. SSI^enas the within-mentioned partnership has expired by the limitations contained therein (or will expire on, &c.), it is hereby agreed that the same shall continue upon the same terms, with all the provisions and restrictions herein contained, for the further term of five years, from the day of f U SStrtncss bl^ereof, we have hereunto, &c. Witnesses. Arthur 15. Clark. [Seal.] Geo. C. HARHiEY. Matthew H. Ralston. [Seal.] M. H. Martin. AGREEMENT TO DISSOLVE A PARTNERSHIP. By Indorsement. We, the undersigned, do mutually agree that the within-men- tioned partnership be and the same is hereby dissolved; except for the purpose of final liquidation and settlement of the business thereof, and upon such settlement wholly to cease and determine. SSillttSS our hands and seals, this day of, &c. Signed, sealed, and delivered in presence of Chauncby S. Douglass. [Seal.] Harvey C. Chester. Keuben H. Howard. [Seal.] Porter L. Fields. PUBLIC NOTICE OF FORMATION OP PARTNERSHIP. Notice of Copartnership. — The undersigned have this day formed a copartnership under the name and style of Gregory, Anderson & Co., for the purpose of carrying on the wholesale dry- goods business, at 689 Chestnut Street, Philadelphia. George W. Gregory. Andrew L. Anderson. PniLA., Jan. 1, 1868. Samuel T. Holden PARTNERSHIP NOTICES. 325 PUBLIC NOTICE OF DISSOLUTION OF PARTNERSHIP. Notice of Dissolution. — The copartnership heretofore existing between George W. Gregory, Andrew L. Anderson, and Samuel T. Holden, under the firm of Gregory, Anderson & Co., i3 this day dissolved by mutual consent (or, has this day expired by limitation, or as the case may be). George W. Gregory is authorized to settle all claims against, or to receive all amounts due, the above-named firm. (Or, Either partner will sign in liquidation.) (Or, The business will be continued by George W. Gregory and Samuel T. Holden, under the name of Gregory & Holden, who are authorized to settle the accounts of the late firm.) George W. Gregory. Andrew L. Anderson. Feb. 1, 1868. SamueL T. Holden. PUBLIC NOTICE OF CHANGE OF PARTNERSHIP. Notice. — Thomas Y. Benton is admitted this day as a member of our firm. The business will hereafter be conducted under the name of Porter, Hudson & Co. Benson J. Porter. July 1, 1867. Jacob L. Hudson. ANOTHER. — ONE PARTNER RETIRING. Notice. — Mr. Lewis N. Dixon retires from our firm this day. The business will be conducted hereafter under the name of Ru- dolph & Hunter. Lewis N. Dixon. Jared L. Rudolph. Jan. 1, 1868. Philip T. Hunter. SHORT FORM OF ASSIGNMENT OF BOND. For value received, I do hereby assign and set over the within obligation, and all moneys due thereon, unto James M. Walters, his executors, administrators, or assigns, without recourse. WatnZBB my hand and seal, this twentieth day of January, 1868- Signed, sealed, and delivered in presence of John L. Rayburn. Milton N. Somers Henry K Park. 326 LANDLORD AND TENANT. LANDLORD AND TENANT. A landlord is one who owns real estate which for a stated period, and at a stipulated rental, is in possession of another, called a tenant. The contract between the two parties is called a lease. It is advisable, in all cases, that leases be in writing, and that each party have a copy. The terms of a lease should be specified clearly; verbal promises are of no efi'ect to add to or vary a written lease : the lease must speak for itself. A lease from year to year is where no definite time is fixed for its termination; a lease for years is every estate which is to expire at a certain specified period. A tenant for years may underlet, unless forbidden by the lease. Where a lease for one or more years expires, and by im- plied consent the tenant remains in possession, he is not a tenant at will, but is considered a tenant from year to year. If no time is stated for the payment of the rent in a lea.se for a year, the rent is not due until the end of the year, un- less the law of the State is difierent. In New York, in the absence of special agreement, the rent is due on the usual quarter days. To terminate a tenancy from year to year, each party is bound to give notice within the time required by the statute law of the particular State. The notice should be in writing, directed to the tenant; if he cannot be found, leaving the notice at the dwelling-house will be sufficient. No notice is necessary to be given to the under-tenants. It is advisable for the landlord to preserve a duplicate of the original notice, with the time and manner of service indorsed on it, and signed by the witness or witnesses. A tenant from year to year is entitled to six months' notice in New York, Vermont, Kentucky, and Tennessee ; to three months' notice in Pennsylvania and some of the other States ; and to two months in Massachusetts. FORM OF LEASE. 327 A tenant is not responsible for taxes, except wlien so speci- fied in the lease; and, when paid by him, ho can deduct the amount from the rental value. A landlord is under no legal obligations to repair, unless he has expressly covenanted to do so ; nor a tenant, in the absence of a covenant, beyond injuries occasioned by his voluntary negligence. FORM OF LEASE. S^^is gigrttment ®illUSSetIj, That Henry T. Morion doth hereby let unto R.obert H. Walters that certain house and lot situated No. 1801 Green Street, fourteenth ward, city of Philadelphia, for the term of one year from the fifth day of June, 1866, at the rent of six hundred dollars per year, to be paid in quarterly portions in advance ; and the said Robert H. Walters doth hereby, for his heirs, executors, and administrators, covenant and promise to pay to the said Henry T. Morton, or his assigns, the said rent in the propor- tions aforesaid ; and the said Robert H. Walters, his executors and administrators, shall and will not, at any time during the said term, let or demise, or in any manner dispose of, the hereby demised pre- mises, or any part thereof, for all or any part of the term hereby granted, to any person or persons whatever, nor occupy or use the same in any other manner than as a private dwelling, without the consent and approbation, in writing, of the said Hem-y T. Morton or his assigns, first had for that purpose ; and at the expiration of the said term yield up and surrender the possession of the said pre- mises, with the appurtenances, unto the said Henry T. Morton or his assigns, in the same good order and condition as the same now are, reasonable wear and tear thereof, and accidents happening by fire or other casualties, excepted. And the said Robert II. Walters, his executors and adminis- trators, hereby agree that all the personal property on the premises shall be liable to distress ; and also all personal property, if re- moved therefrom, shall, for thirty days after such removal, be liable to distress, and may be distrained and sold for rent in arrear ; the said Robert II. Walters, his executors and administrators, hereby waiving all right to the benefit of any laws now made, or hereafter to be made, exempting personal property from levy and sale for Arrears of rent. 328 NOTICES TO QUIT. It is heieby further agreed, that if the above-named Tlobert 11, Walters should continue on the above-described premises after the termination of the above contract, then this contract is to continue in full force for another year, and so on, from year to year, until legal notice is given for a removal. ^n S3IitlWSS fe^crtof, the said Henry T. Morton and Robert H. Walters have hereunto set their hands and seals, the fifth day of June, one thousand eight hundred and sixty-six. Sealed and delivered in the presence of Robert H. Walters. [Seal.] James T. Rodgers. Henry T. Morton. [Seal.] SECURITY FOR RENT. I, George L. Mason, do hereby agree to be responsible to Henry T. Morton, or his assigns, for the true and faithful performance of the above-named contract on the part of Robert H. Walters. ^n WSilhuss fo^ereof, I have hereunto set my hand and seal, the fifth day of June, one thousand eight hundred and sixty-six. Sealed and delivered in the presence of George L. Mason. [Seal.] James T. Rodgers. NOTICE TO QUIT BY THE LANDLORD. Sir: — Please take notice that you are hereby required to sur- render and deliver up possession of the house and lot known as No. 7 Day Street (or as the case may be), which you now hold of me, and to remove therefrom on the first day of next, or at the expiration of the current year of your tenancy. Dated this day of , 1867. To Mr L. N. Selser. J. G. Bond, Landlord. NOTICE TO QUIT BY THE TENANT. Please take notice that on the 1st day of May next I shall quit possession and remove from the premises I now occupy, known as Louse and lot No. 7 Day Street, in the city of New York. Dated this first day of Jan. 1807. Yours, &c., To Mr J. G. Bond. L. IT. Selskr. MERCANTILE CORRESPONDENCE. 329 MERCANTILE CORRESPONDENCE. In all composition, three tilings require attention : — the thoughts, their arrangement, and the language employed. On business subjects, as on other matters, he writes best who writes from a full mind. No one is expected to write well on any subject who has but little acquaintance with it. This is the reason why otherwise well-educated persons fre- quently fail in their efforts to write a good mercantile letter : they are ignorant not only of the technicalities of business phraseology, but of business itself. The qualifications acquired at school are a good founda- tion ; but they will not dispense with a knowledge of business^ dealings and of the peculiar styles of expression employed in commercial correspondence. Familiarity with the techni- calities of the counting-house is gained only by constant practice ; and facility and skill are not obtained until these have been mastered. To a business man, a terse mercantile phrase is as full of meaning as a formula is to a mathematician, and a few words are often all that is necessary to impart what would require from others many circuitous sentences. A well-written mercantile letter furnishes not only a model for acquiring form and phraseology, but is also a record and an explanation of the business transacted. Business letters often partake of the nature of contracts, when mistakes, omissions, or uncertainty would involve serious loss. They should be clear and concise ; there should be nothing ambi- guous, nothing omitted, nothing superfluous. Men in busi- ness are too much occupied to waste time either in reading or writing long letters filled with what is irrelevant or useless. Good writing materials should be selected. It is poor eco- nomy to use inferior articles ; and the who^e appearance of the letter is affected by the quality of the ink and paper used. The date of a letter should be stated correctly and dls- 28* 330 MERCANTILE CORRESPONDENCE. tinctly, as it is frequently a matter of considerable import- ance. In England the day is placed before the month; thus, 11th August, instead of August 11th, as in this country. lu writing from a city, it is well to mention the street and number. The form of complimentary address to be adopted depends upon the degree of intimacy and the relative position of the parties. In writing to a gentleman to whom you are an en- tire stranger, he is addressed as " Sir." " Dear Sir" is used on nearly all occasions, frequently to a stranger, unless a cer- tain formality is required. " My dear Sir" implies a very friendly relationship. A married lady is addressed as " Madam" or " Dear Madam," and an unmarried lady as *'■ Miss" or as " Dear Miss," usually with her last name affixed. " Reverend Sir" is used in addressing a clergyman ; " Esteemed Sir" is usual when some degree of formality is re- quired. Judges and Members of Congress should be addressed by the title of " Honorable." In writing to a firm, company, or any number of persons associated in a body, the address is " Gentlemen." The place where the person resides who is written to, is given, to provide against any accident or attempt at fraud which would destroy the superscription and thus prevent it from being used as evidence. In answering a letter, after acknowledging its receipt, each point requiring consideration should be taken up in order and discussed in a separate paragraph, before any new sub- ject is mentioned. Orders should specify exactly what goods are desired, with full directions concerning them. If a communication on other subjects is also sent, the order should be on a separate part of the letter, or, better still, on a separate paper. In letters containing remittances or enclosures, the amount, or papers enclosed, should be distinctly mentioned, to guard MERCANTILE CORRESPONDENCE. 331 against loss, and that the letter may be used as evidence, if necessary. When drafts are drawn, it is customary to inform the person on whom they are drawn, that he may be pre- pared to meet them at the proper time. Some firms have a printed form of receipt, and also a printed form of letter for acknowledging remittances re- ceived, which they use in order to save the time and labor required in an extensive correspondence. Instructions to agents and commission-merchants should be in the plainest terms, with full directions how to act in any contingency, that there may be no misunderstanding or dispute. Agents should keep their principals well advised in reference to the condition and progress of the business with which they are intrusted. A bill or statement of account is usually sent at stated periods, and should of itself call attention to its settlement. Sometimes the words " Please remit" are written on one end of the bill, for that purpose. Many houses, however, are in the habit of sending out statements which are merely for the purpose of comparing accounts. When it becomes necessary to request payment, it should be done in gentlemanly terms, even if there has been con- siderable delay. A man loses more than he gains when he indulges in rash or insulting language. A bitter word, when spoken, may be forgotten ; but, when once written, it becomes abiding evidence of the irascibility, if not insult, of the writer. A decided yet respectful manner is productive of the best effects. An air of civility should pervade every letter, yet there should be nothing servile or affected. In writing to others on business pertaining solely to one's own affairs or for his own benefit, a stamp should be enclosed, with which to prepay the postage. To persons who have a large correspondence, the postage is an item of some importance. Letters of introduction and recommendation should not bo 332 MERCANTILE CORRESPONDENCE. sealed, that the persons whom they concern may have an opportunity of knowing their contents. In applications for situations in business houses, the hand- writing has much to do with success. It is almost useless for a poor writer to expect employment in a counting-house. Merchants do not wish either the discredit or the inconve- nience of bad writing. When testimonials are required, and it is desired to pre- serve the original, a copy should be enclosed, and marked " copy" at the top of the page. All business letters requiring an answer should receive im- mediate attention. Negligence in this respect is a species of incivility. Every letter, as soon as read and its contents attended to, should be neatly folded, indorsed with the name of the writer and the date of the receipt and answer, and then filed. It is advisable that copies of all letters, and also all papers of importance, be retained for future reference. A facsimile copy of a letter is admitted as evidence after notice to the other party in the cause to produce the original. The mere mechanical folding of a letter is not unworthy of attention. A letter carelessly written, clumsily folded, or ill directed, denotes either ignorance of what is proper, or a want of respect to the person addressed. The superscription should be distinctly written. From neglect of this precaution, thousands of letters are sent every month to the dead-letter office. During the year ending June 30th, 1867, there were received at the Post-Office Department MERCANTILE CORRESPONDENCE. 333 at Washington 4,306,508 letters as unpaid or misdirected. On many the name of the town as well as of the State was omitted from the direction ; on some the superscription con- sisted simply of the name of the town and State, that of the person being omitted, as if totally unimportant; and so care- less had been the writers of others that they had not even signed their names. When sent to a large city, the letter should be directed to the street and number, as well as to the post-office and State. The postage stamp should be placed upon the upper right- liand corner. When it is important to know whether the letter has been received or not within a certain time, a re- quest for its return to the writer, if not called for, should be placed upon the left-hand end of the envelope. J 1 I tyfu€aaemma, Limited space prevents our offering more than a few forms of letters which relate to transactions of the most frequent occurrence. Nearly all of those here given have been taken from the letter-books of extensive houses, and are presented not as models of superior excellence, but for the purpose of aiding those who wish to become familiar with the language and formula of business correspondence. 334 MERCANTILE LETTERS. MERCANTILE LETTERS. 1. Offering Goods. JL. fal S^ /c^ /c^^/. We ^ne Me u^^ {^ encio/Una a ^ew tyT€€taaia. %yAeu aie m ^a^/eind m awte^ /^ 'UtUcM, 'uoa neea anu m Mem, €oe dna« Ae Ac^tAu ^ ieeen^ dc 2. Declining Offer to Buy. Mbssbs. Gkay, Smith & Co. Philadelpuia, Aug. 3, 1866. Gentlemen: — Yours of the 25tL ult. is received. We are under the necessity of declining to fill your order upon the terms proposed by you. On receipt of fifteen hundred dollars, we will ship the goods, with the understanding that the balance will be paid within sixty days from the date of shipment. Hoping that these terms will be satisfactory, we remain Yours, very respectfully, Uenry L. Park & Son MERCANTILE LETTERS. 335 3. Declining to Purchase. Messrs. L. H. Alward & Co., Milwadkie, November 1, 1866. Philadelphia. Gentlemen: — We are in receipt of your favor of the 30th ult., and have likewise received the samples of Poplins, but, having as many goods of this description as we require for our present sales, we must decline handing you an order from samples forwarded. Respectfully, yours, Chandler & Co. 4. Order for GtOods. Memphis, Tenn., August 10, 1866. Messrs. Marshall & Howland, New York. Gentlemen : — You will please ship us at your earliest convenience Three (3) Half-chests Imperial Tea (Andreas, ;^257), same as in last bill ; also, Two (2) Half-chests of best Imperial (Queen of the North, ^9, or something better). Ship by Great Western Dispatch, and mark goods as follows : J. M. Orwiq & Bro., Memphis, Tenn., Care Gould & Linton, Cincinnati, Ohio. Please write across Bill of Lading, *' Insured in consignees' open policy in the Globe Insurance Co. of Cincinnati," and send Gould & Linton the amount of Invoice, that they may enter on our policy book. Your early shipment will much oblige Yours, very truly, J. M. Obwiq & Beo. 5. Enclosing Invoice and Bill of Lading. Per " Wyoming." PHiLADEipmA, March 17, 1867. Messbs. L. M. Seaton & Co., New Orleans. Bear Sirs: — We confirm our last letter of 12th inst., and hand you herewith enclosed B. of L. and Invoice of Cases E, H, ^632 and 633, ordered by your Mr. Carlton, which we have shipped this day on board Steamer Wyoming. Amt., $1250.35(y<>5 ; due June 17th. Should you need any of our qualities of Cassimeres, we shall bo pleased to fill your orders on the best terms possible. Yours, truly. Wells, Fisk & Co. 336 MERCANTILE LETTERS. 6. Concerning Credit at a Banker's. " Edinburgh." Liverpool, 12 Feb., 1868. Messrs. John Simpson & Co., Philadelphia. Gentlemen: — We have your favor of 29tli ult., and, as desired, have confirmed a credit for <£500 to Messrs. F. & B. Brown & Co. Your instructions respecting shipment and insurance have our attention. We are, gentlemen, Your obedient servants, Geeen, Richards & Co. 7. Advice concerning Shipment. Messrs. John Simpson & Co., Liverpool, 17 March, 1868. Philadelphia. Dear Sirs: — We are advised that the under-mentioned goods aro coming to us for shipment on your account, and we purpose for- warding them by the conveyance noted below. Should they not arrive here in time for shipment, a further advice will be sent you. We state the value as given for entry, and remain Yours, respectfully. Green, Richards & Co. Per S. S. ''Delaware," for Philadelphia, sails 22d inst. J. S. C, 1/3. 3 cases, £224, from F. & B. Brown & Co. 8. Enclosing Invoice. Per the " City of Paris." Manchzsteb, 20 March, /66. Messrs. John Simpson & Co., Philadelphia. Dear Sirs: — We have the pleasure to hand you herewith invoice of the packages noted below, which we trust will result in all re- spects to your satisfaction. To cover present shipment, we apply for funds to Messrs. Green, Richards & Co., as usual. Great activity prevails in our market, and prices generally are advancing. We are, dear sirs, Your obedient servants, F. & B. Brown & Co. £220. 18. 0. net cash, Mar. 20/66. J. S. C, 1/3, per steamer " Delaware." MERCANTILE LETTERS. 337 9. Advising Receipt or Invoice. Mr James L. King, Boston. St. Louis, April 6, 1867. Dear Sir: Your favor of March 29th, with B. of L. and Invoice, was received in due time. The goods are all that we desired; and for your promptness and care in filling our order, accept our thanks. Enclosed find in payment Holmes & Bros.' Draft on First National Bank of Boston, at sight, for $1875.t5^'>5. Please acknowledge receipt per return mail, and oblige Yours, respectfully, Thos. L. Smith & Co. 10. Consigning Goods to be sold on Commission. Messrs. Samuel G. Porter & Co., Cincinnati, May 11, 1867. Hew York. Dear Sirs: — Your favor of 7th inst. is at hand. We enclose you Invoice and Bill of Lading of 100 bbls. Mess Pork and 50 firkins of Butter, shipped this day per Merchants' Line, to be sold for our ac- count, as per agreement. We request you not to sell for lesg than Invoice price, and if you succeed in disposing of this lot satisfac- torily, you may be almost sure of receiving further consignments from us. We have drawn on you at ten days' sight, through Phoenix Bank, for One Thousand Dollars. Awaiting your advices, and hoping soon to hear from you, we remain. Very truly, yours, M. Johnson & Co. 11. Enclosing Account Sales. Messrs. M. Johnson & Co., New York, Juno 10, 1867. Cincinnati. Dear Sirs : — Enclosed we send you Account Sales of Pork and Butter shipped us on May 11th. The Net Proceeds, $1750.62, due per average July 2d, we have placed to the credit of your account; the result, we hope, will be satisfactory. We shall bo pleased to receive further consignments from you, and will endeavor to dispose of them on the most advantageous terms. Thanking you for past favors, we remain, Truly, yours, Samuel G. Porter & Co. 29 338 MERCANTILE LETTERS. 12. Advising of Shipment. 45 Calliope Stbekt, Messrs. H. R. Stanley & Co., New Orlkans, Nov. 4, 1867. Cincinnati. Wc herewith enclose Bill of Lading and Invoice of Molasses and Sugars, amounting to $4233.75, which we have this day shipped per steamboat Star of the AVest, as per your order of 27th ultimo. We have taken considerable pains to select such lots as we thought would suit you, and hope we have succeeded. Sugars are advancing. We send with this a list of our present quotations. Awaiting your further orders, and grateful for those received, we remain, Very respectfully. Your obedient servants, W. Morrison & Co. 13. Advising of Consignment. Messrs. T. H. Hawkins & Co., Havana, June 4, 1867. Boston. Gentlemen: — We have this day shipped you, per steamer Juniata, Farington, master, 1200 bbls. P. R. Sugar, T. H. II., and 228 bbls. Cuba S. W. Sugar, L. B. C, to be sold as per our agreement. Please find Invoice and Bill of Lading enclosed. From the present state of the market, we are induced to hope that this lot will meet with ready sale at good prices. Should you suc- ceed in disposing of this Invoice satisfactorily, we expect to send you another early in next month. Awaiting your advice, we remain Yours, respectfully, LiNNARD, Bates & Co., per S. T. Gerter. 14. Enclosing Note for Discount. Chas. R. Coleman, Esq., Cashier. baltimork, Feb. ii, 186S. Dear Sir:—Vfe offer for discount, enclosed, J. Brown's note, Jan. 12th, at ninety days, for $4250.75. By discounting the same you will much oblige Yours, respectfully, Thos. H. Whitman & Co. MERCANTILE LETTERS. 339 15. Enclosing Account Current. Mb. Hbnry T. Morris, Sandusky, 0., Jan. 1, 1867. Nebraska City. Dear Sir : We respectfully call your attention to the enclosed Account Current, with interest calculated to this date, showing a balance in our favor of $3275.^^*'^. If you find correct, please remit us a Draft at sight for the amount, and oblige Yours, respectfully, D. KUNDEL & Co. 16. Enclosing Remittance. Mkssbb. J. T. Anthony & Co., Savannah, January 21, 1867. Manchester, Eng. Gentlemen: Your favor of 2d inst., covering statement of account, is at hand, and upon examination we find it correct. Enclosed please find Richardson & Cowden's 1st and 2d of Exchange on Brown, Shipley & Co. for Two Hundred and Sixty Pounds 7/5, in settlement of account to 1st inst. Please acknowledge receipt, and oblige Yours, very truly, B. F. Moore & Co. per D. B. Martin. 17. Another. Messrs. A. L. Watson & Co., Trenton, Apni 10, 1857. Philadelphia. Dear Sirs : Enclosed find my Check on First National Bank of this city for Twenty-Two Hundred and Fifty Dollars, in payment of Bills of July 21 .... 1262.10 " 25 . . . 872.00 " 28 . . . . 115.90 $2250.00 Please acknowledge receipt, and oblige Yours, respectfully, James Anderson. 340 mercantile letters. 18. Acknowledging Remittance. Bup?ALO, Jan. 12, 1867. Received from Messrs. George H. Jackson & Co., Five Hundred and Fifty j2_.5^ Dollars on account. $650.3^^5^. H. D. Clinton & Co. Messes. Geoeqe H. Jackson & Co., Bowalo, Jan. 12, 1867. Uiica,N.Y. Gentlemen : — Above please find receipt for remittance contained in yours of lOth inst., for which we are obliged. We find in your state- ment a variation in two items, those of December 6th and 19th. Can you favor us with an explanation, as we have no credits reducing the amount of $35 to $26.y5g% or $675.-,^ to %&b^.^j^t Waiting your reply, we remain, Respectfully, yours, H. D. Clinton & Co. 19. Another. Messes. Thos. M. Young & Co., Albany, Nov. 13, 1866. Syraeme. Gentlemen: — We have the pleasure to acknowledge the receipt of your esteemed favor of 10th inst., containing your Notes dated Sept. 1, at 3 mos., for 425.66, " 15, " " 425.66, Oct. 1, '' " 425.67, Amounting to Twelve Hundred and Seventy-Six -^^j^ Dollars, which we have placed to your credit in settlement of your account. Please accept our thanks, and, requesting the favor of your future orders, we remain, Very truly, yours, Chas. L. Riqua & Co. 20. Asking for Settlement. Me. Heney G. Sandees, Worcestkb, May 25, 1867. Concord. Dear Sir : — We respectfully call your attention to our statement of account rendered April 8d, a settlement of which at your earliest convenience will much oblige Yours, very respectfully, Hobaob Boyd & Co. MERCANTILE LETTERS. 341 21. Enclosing Draft for Acceptance. W. B. Perry, Esq., Portland, Dec. 18, 1868. Castine, Me. Dear Sir: — We enclose our draft on you for acceptance, wliich please let us have by return mail, and oblige, Respectfully, yours, James Holland & Co. 22. Return of Accepted Draft. Messrs. James Holland «& Co. Castine, Dec. 25, 1S67. Gentlemen: — Enclosed please find your draft, dated 18th inst., for $400, with acceptance. My absence from the city has caused the delay in replying to your favors. Yours, truly, W. B. Perry. 23. Requesting Payment. Mr. B. S. Vernon, Rochester, June 19, 18—. Syracuse. Dear Sir: — If convenient, please let us have the amount of your bill, March 15th, for $187.50. We desire to close all our accounts by the 30th inst., and have need of all the funds due us. Please remit without delay, and much oblige Yours, respectfully, Lansing, Mason & Co. 24. Another. Messrs. Douglass & Heath. Louisville, Nov. 2, 18—. Dear Sirs: — We are obliged again to ask you for the balance of your account, now four months past due. We are much incon- venienced by your delay, and have waited longer than we think ought to be expected. The account must be speedily settled, and, if we do not hear from you by the 15th inst., will draw on you, at five days' sight. If the draft is not protected at maturity, we shall be compelled to adopt some other mode of settlement. Very truly, yours, W. Randolph & Co. 29* 342 MERCANTILE LETTERS. 25. Another. Mr. H. Y. Henderson, WaMmoTOir, April 6, 18«7. Dover, Del. Dear Sir: Enclosed please find our usual monthly statement, amount- ing to $376.-j^j5g^, for which, if found correct, we shall be pleased to receive remittance by 30th inst. Should we receive no remittance by that time, we propose to draw on you at sight for the amount, unless in the mean time we are otherwise advised. Yours, respectfully, James S. Smith & Co. 26. Advising op Draft. Me. H. T. Hawkins, Clbvelakd, June 3, 1867. Harvard, III. Dear Sir: As we are in want of funds, we take the liberty of draw- ing on you at 5 days' sight for bills of Jan. 10th, $576.00 Feb. 12th, 300.00 $875.00 Please protect, and much oblige Yours, truly, Brown & Woethinoton. 27. Enclosing Notes for Collection. Cashier First National Bank, PHixADixpinA, July 29, 18«6. Cincinnati. Dear Sir : — Enclosed find for collection. Note J. Smith, due Aug. 3/6, 810.20 " J. Jones, " «« 8/11, 600.00 Acceptance Morton & Co., due Aug. 10/13, 920.62 $2320.82 If paid, please remit Draft for proceeds. Yours, very respectfully, Georqe V. Mau». MERCANTILE LETTERS. 843 28. Letter of Introduction. WoKCESTEB, Mar. 2, 1867. Bear Sir: — This will introduce to you my friend Mr. Samuel S. Price, of this city. He intends staying a few days in your place, which he visits on business ; and I take the liberty of recommend- ing him to your kind attention. He is a gentleman of excellent acquirements, and we know him to be responsible to the extent of his engagements. Any attention or favor that you may render him shall be considered a personal favor, which I shall be happy to reciprocate. To Jabed L. Mokton, Esq. Very sincerely, yours, Chas. M. Huntee. 29. Letter of Recommendation. To whom it may concern : — ' Bufpaio, Oct. 13, 1868. The bearer of this, Mr. Edward K. Mitchell, has been in our em- ploy for three years past as salesman and book-keeper, and we have ever found him diligent and faithful in the discharge of his duties, and one who endeavored to make his employers' interest his own. He is correct and reliable in his accounts, and is well qualified to act as book-keeper or correspondent. We cheerfully recommend him to any who may require the ser- vices of a trustworthy and competent person in their counting-house. Very respectfully, J. W. Cresson & Co. 30. Answer to an Advertisement. 315 Olive Street, St. Louis, April 27, 18 — . Gentlemen: — In answer to your advertisement in the "Democrat" of to-day, for an assistant in your counting-house, I respectfully offer my services to your firm. I am without experience in busi- ness, but have a desire to enter mercantile life, am willing to work, and have just graduated from our city High School. If you will give me a trial, I will devote myself to your interests and endeavor to acquit myself to your entire satisfaction. For rC' ference as to my character or ability, I would offer the names of Mr. George H. Bo wen, 116 Washington Avenue, Messrs. J. F. Dwight & Co., 20 South Main Street. Should a personal interview be desired, please address as above. Very respectfully, Herman L. Foster. 344 MERCANTILE LETTERS. 31, Application for a Situation as Book-keeper. Messes. K. K. Langton & Co., Colcmbus, 0., Feb. 19, 1868. Cincinnati, 0. Gentlemen: — Having learned from Mr. Charles K. Minturn that you (Icsii-e the services of a book-keeper, I respectfully offer myself as an applicant for the situation. I have been engaged for two years in the wholesale house of L. R. Bullock k Co. as clerk and assistant book-keeper, and have a good knowledge of accounts. My business acquaintance is extensive in the western part of this State and the northern part of Kentucky, and I could therefore influence considei-able trade. I enclose copy of testimonial from my late employers, and would also respectfully refer you, as to my character and ability, to Messrs. Albert L. Hancock & Sons, Wholesale Grocers, Cincinnati, " Stringer, Burt & Co., Iron Merchants, ♦* F. L. Williams, Esq., City Solicitor, '« Any communication which you may be pleased to make, addressed as above, will receive prompt attention. Very respectfully, yours, Feedeeick K. Johnson, 32. Recommendation enclosed in the above. (Copy.) Columbus, June 1, 1SG7. The bearer, Frederick K. Johnson, has been in our employ as assistant book-keeper for over two years, and we have always found him to be honest, steady, and correct in his habits and deportment, and well qualified for any position of trust in a counting-house. We cheerfully recommend him as a competent book-keeper, and one who will earnestly apply himself to promote the interests of his employers. Respectfully, L. R. Bullock & Co. 33. Order for a Book. Madison, Feb. 26, 1868. Messrs. S. II. Crittenden & Co., Philadelphia. Enclosed find One Dollar and Fifty Cents ($1.60), for which please send me one copy of the "Crittenden Commercial Arithmetic and Business Manual," and oblige Yours, truly, Hkney M. Curtis. INSTALMENT RECEIPT. INSTALMENT RECEIPT. 345 WASHINGTON R. R. COMPANY. Received, Washington, dl;pr. 11th, 1S67, of 8. J. jlndbrews, Qjwo Q^housand Five Sundred 0ollars, being Twenty-Five Dollars per share, and the Q^hzrd Instalment on (Two Hun- dred Shares of the Capital Stock of the WAaHmOTOK nAllROAO COMPANY J for which said shares a full Certificate will be given upon payment of all instalments due thereon, and the surrender of this Certificate. .r^Ban.^ ^l. ^uU^r. Secretary. f^esideni. Copy of aai Exchequer Bill issued in the reign of Queen Anne. £l2 lOJ. EXCHEQUER. A 28/24. Purfuant to an Act of Parliament, Anno 1709, for enlarging the Capital Stock of the Bank of England, &c. This Bill entitles the bearer to twelve pounds, ten fhillings, with intereft at a farthing a day. To be received in all aids, taxes, loans, and payments whatfoever to Her Majefty, and to be paid to the bearer by the Governor and Company of the Bank of England, from time to time, as the fame shall be paid into the exchequer by any receivers or collectors of Her Majefty's revenue, aids, taxes or fupplies ; and be thence reiflued and at all times by fuch receivers or collectors out of any public money in any of their hands, as directed by the faid Act. BANK DEPOSIT TICKET. Deposited, April 8th, 1867 ^ at the MKGHANIGS' NATIONAL BANK. By ^tonAn, ^iU/cz ^ ^^. Dollars. Cts. 675 25 50 325 4e5 00 " " I'a and 2'8 00 Specie 00 Checks, as follows 75 50 $1541 26 346 CERTIFICATE OF STOCK. ls^^^@l>«>e»«M»«»«MMM* CERTIFICATE OF SCRIP DIVIDEND. 347 M^MM^MMTHE OCEANIC INSURANCE COMPANY. ^Or^CiM&P:^^ mmmmmmmmmmmmMmmmm'Mmmmmmmmmmmmmmmmmm ir^iii^i^ 2 jd 111 m >^ cj. ?ft ^ o «^ a M ^ ?;^ s- 5f 1 & o V2 5^' ^ ^ H « ^ g; cT H' _ _ £ij 5 ?* r4.<«^ « ai « 5 a. o o 3-^ S-*^ r^r* c»- o >i CJ ::? » fn OOOOOO60CO SildOad JO 31V0IJIiM30 000000 000^ opooooouooo oMW^iWiMM'^M^MWM^o oooooooo^i 348 U. S. "nVE-TWENTY'' COUPON BOND. YB 3,^^^^ \J^c.U ivi24953S ^P li ^ THE UNIVERSITY OF CALIFORNIA UBRARY ■1 ■:'': 'AVi I i • i i 'i 1;,,