T1|orosoife«Srlti?ii|€tical I ^■Nnhbh *&*/&$ 8. TnoMsm £Jk 11 ■ nw Anderson's Historical Series, A Jur hundreds A Grs and illusi maps, mj A Pic trated w: A Po] serted as Americai •with msn coiv For Introc In Exehar Books or in any part a mew to int receipt of tlu UO.ll H1JW notes, ei tory. \ ited with nnotated J than forty ally illus- :h are in- eminent Uustrated D 3 cts. irate , with er on York. ,tates His- 3. 734 BROADWAY, NEW YORK. A TREATISE ON PHYSIOLOGY AND HYGIENE. FOR EDUCATIONAL INSTITUTIONS AND THE GENERAL READER. By Joseph C. Hutchison, M.D., President of the New York Pathological Society; Vice-President of the New York Academy of Medicine; Surgeon to the Brooklyn City Hospital; and late President of the Medical Society of the State of New Yo/k. Fully Illustrated with Numerous Elegant Engravings. 12mo. 300 pages. 1. Tlie Plan of tlie Work is to present the leading facts and principles of human Physiology and Hygiene in language so clear and concise as to be readily comprehended by pupils in schools and colleges, as well as by general readers not familar with the subject. 2. The Style is terse and concise, yet intelligible and clear; and ail useless technicalities have been avoided. 3. The Range of Subjects Treated includes those on which it is believed all persons should be informed, and that are proper in a work of this class. 4. Ihe Subject-matter. — The attempt has been made to bring the subject-matter up to date, and to include the results of the most valuable of recent researches to the exclusion of exploded notions and theories. Neither subject— Physiology or Hygiene— has been elabo- rated at the expense of the other, but each rather has been accorded its due weight, consideration, and space. The subject of Anatomy is in- cidentally treated with all the fullness the author believes necessary in a work of this class. 5. The Engravings are numerous, of great artistic merit, and are far superior to those in any other work of the kind, among them being two elegant colored plates, one showing the Viscera in Position, the other, the Circulation of the Blood. 6. The Size of the work will commend itself to teachers. It contains about 300 pages, and can therefore be easily completed in one or two school terms. The publishers are confident that teachers will find this work full of valuable matter, much of which cannot be found elsewhere in a class manual, and so pre- sented and arranged that the book can be used both with pleasure and success in the schoolroom. " Many of the popular works on Physiology now in use in schools, academies, and colleges, do not reflect the present state of the science, and some of them abound in absolute errors. The work which Dr. Hutchison has given to the public is free from these objectionable features. I give it my hearty commendation." — Samuel Q. Armor, M.D., late Professor in Michigan University. "This book is one of the very few school books on these subjects which can be unconditionally recommended. It is accurate, free from needless technicalities, and judicious m the practical advice it gives on Hygienic topics. The illustrations are excellent, and the book is well printed and bound. "—Boston Journal of Chemistry. "just the thing for schools, and I sincerely hope that it may be appreciated for what it is worth, for we are certainly in need of books of this kind."— Prof. Austin Flint, Jr., Professor of Physiology in Bellevne Hosspital Medical College, Neto York City, and author of " Physiology of Man,'''' etc., etc. "I have read it from preface to colophon, and find it a most desirable text-book for schools. Its matter is judiciously selected, lucidly presented, attractively treated, and pointedly illustrated by memorable facts; and, as to the plates and diagrams, they are not only clear and intelligible to beginners, but beautiful speci- mens of engraving. I do not see that any better presentation of the subject of ?hysiology could be given within the same compass." — Prof. John Ordronaux, *rofessor of Physiology in the University of Vermont, and also in the National Medical College, Washington, D. C. The above work is the most popular work on the above subjects yet published. It is used in thousands of schools with marked success. Published by CLARK & MAYNARD, New York. Digitized by the Internet Archive in 2007 with funding from Microsoft Corporation http://www.archive.org/details/commercialarithmOOthomrich THOMSON'S MATHEMATICAL SERIES. tyv Qt^e^l A COMMERCIAL ARITHMETIC; Academies, Hioii Schools, Counting Rooms ; EMIES, t^fGHtfeCHO^LS, CoUN*T\ >\^ BUSINESSK.O G \* LLEGES James B. Thomson, LL. D., AUTHOR OF MATHEMATICAL SERIES. NEW YORK: Clark & Maynard, Publishers, 734 Broadway, THOMSON'S NEW ARITHMETICAL SERIES IN TWO BOOKS. I. First Lessons in Arithmetic, Oral and Written. Illustrated. (For Primary Schools.) II. Complete Graded Arithmetic, Oral and Written. In one Volume. (For Schools and Academies.) Key to Complete Graded Arithmetic. (For Teachers only.) THOMSON'S MATHEMATICAL SERIES illustrated table-book. new rudiments of arithmetic. complete intellectual arithmetic, new practical arithmetic. KEY TO PRACTICAL ARITHMETIC. (For Teachers only.) HIGHER ARITHMETIC. PRACTICAL ALGEBRA. KEY TO PRACTICAL ALGEBRA. (For Teachers only.) COLLEGIATE ALGEBRA. KEY TO COLLEGIATE ALGEBRA. (For Teachers only.) COMMERCIAL ARITHMETIC. Copyright, 1884, by M, C. Thomson. Smith & McDougal, Electrotypees. 82 Beekman St., N. Y. o=> I o Teachers. " o ^ =^» TF1HE present work has been prepared with sole reference to a business education in its higher departments. To this end, subjects which have been fully explained in the author's elementary works, or an equivalent, and with which the student is supposed to be familiar, are omitted, and he is introduced at once to the subject in hand. All irrelevant matter is rejected, and that which helps towards the accomplish- ment of the object is adopted. A large amount of valuable business information is embodied in a concise form, and presented in a manner to be easily understood. In the fundamental rules, many labor-saving methods of operation are given under the appropriate name " Counting Room Methods," so called from the fact that rapid computations are so generally practiced by expert account- ants. These methods may be applied, not only to the examples given for illustration and practice, but to every operation involving the simple rules, and will often greatly facilitate arithmetical calculations. A variety of business forms are introduced, and their nature and uses explained, in order to assist the student to an understanding of what constitutes an important part of a practical business life. The manner of keeping Book Accounts, Averaging Payments, Partnership Settle- ments, etc., are fully explained and illustrated by examples from actual business transactions. The chapter on the Metric System of Weights and Measures is made prominent in the body of the book, and includes all the latest recommendations of the Metric Bureau. Examples involving a knowledge of its applications are freely scattered through the book. The subject of Analysis, the business man's specialty, enters largely into the elucidation of every subject, and has an entire chapter devoted to its various applications. The facts and methods given on many commercial subjects, have been procured from reliable persons who are thoroughly versed in their several IV To Teachers. departments. They are therefore authentic business facts, and in accord- ance with present usage. Special care has been devoted to the chapter on Stocks and Bonds, and to Stock Exchange business, which is a full and reliable summary of affairs as now conducted on the New York Stock Exchange. The examples embrace true specimens of daily operations in Wall Street. The chapters on Banking, Clearing Houses, and Custom House busi- ness have also been subjected to the most careful scrutiny, as also, Life Insurance, Annuities, Sinking Funds, etc. The Commercial Arithmetic is intended to follow the author's Com- plete Graded, or the Practical Arithmetic, taking up some subjects and carrying them forward to their higher applications, and treating of others which are beyond the limits of the more elementary works. In subjects which are identical with the Complete Graded, the same definitions and principles are retained. In the discussion of new topics, the same clear- ness, conciseness, and accuracy of style have been strictly adhered to. The examples are all new, and have been selected with a special view to their practical application to business, and not as a trial of the mathematical skill of the learner. Many thanks are due to the gentlemen of the Stock and Produce Exchanges ; to the Collector of the Port of New York and his associates ; to the Bankers, Brokers, and Lawyers who have so kindly given valuable information and suggestions. It is hoped the Commercial Arithmetic will creditably fill the niche for which it was designed, and that it will commend itself to the good judg- ment of teachers, the understanding of learners, and the approval of busi- ness men. The kindly criticisms of all will be gratefully accepted, and their continued favor highly appreciated. New York, March 1, 188k. CONTENTS PAGE Counting-Room Exer- cises 7 Addition 8 Subtraction 9 Multiplication (Short Methods) 11 Division, Contractions 16 Divisibility of Numbers 18 Factoring 18 Cancellation 20 Greatest Common Divisor 21 Common Multiples 23 Weights and Measures. . . 26 Weight per bushel of Grain and Seeds 31 To Change Dates from 0. S. to N. S 37 United States Money 38 Canada Money 39 English Money, French Money. 40 German Money 41 Metric System 42 Metric Reduction 50 Foreign Weights and Measures 53 Reduction 55 Denominate Fractions 57 Reduced to Lower Denomina- tions 57 Reduced to Higher Denomina- tions 58 Addition of Compound Num- bers 59 Subtraction of Compound Numbers. 60 Exact Time between Two Dates 61 Compound Multiplication 62 Compound Division 63 Longitude 63 Time and Longitude 65 •PAGE Applications of Weights and Measures 66 Measurement of Rectangular Bodies 69 Cisterns, Bins, etc 70 Measurement of Lumber 71 Masonry 73 Applications of IT. S. Money 73 Methods by Aliquot Parts. . . 74 Bills of Merchandise 78 Entry Clerk's Drill 80 Percentage 81 Applications of Percentage. . . 88 Profit and Loss 88 Trade Discount 89 Commission and Brokerage. . 91 Insurance. 94 Adjustment of Losses 98 Taxes 100 Interest 103 General Method 104 Six per cent Method 107 Method bv Days 108 Banker's Method 109 Accurate Interest Ill Annual Interest 112 Partial Payments 116 U. S. Rule 117 Mercantile Method 118 Connecticut Rule 119 Vermont Rule 121 New Hampshire Rule 122 Interest on Sterling Money . . 123 Compound Interest 124 True Discount 127 Bank Discount. 128 Commercial Paper 130 Forms of Notes and Drafts.. . 133 VI Contents. PAGE Averaging Accounts 137 Rules. — Product Method, ) * .^ Interest Method )" 140 Cash Balance 149 Rule for Product Method 150 Rule for Interest Method 151 Account Sales 154 To Find Due Date 156 Partnership 158 Bankruptcy 169 General Average 170 General Analysis 172 Ratio 178 Proportion 180 By Cause and Effect 182 Compound Proportion 184 Partitive Proportion 187 Exchange 189 Domestic Exchange 190 Foreign Moneys of Account. 192 Quotations of Foreign Bills. . 193 Foreign Exchange 194 Duties or Customs 199 Custom House Business 200 Import Entries 203 Course of Import Entry in N. Y. Custom House 204 Banks and Banking 206 Bank Account Current 208 Bank Checks 209 Clearing Houses 211 Savings Banks 212 Stocks 216 United States Bonds 218 National Debt of U. S 219 Funded Debt of Foreign Countries 220 Stock Exchanges 220 Quotations. — Seller's Option, ) 9Q „ Buyer's Option ] Stock Investments 223 PAGE Produce Exchanges 232 Storage 234 Life Insurance 236 Table of Rates 238 Annuities 241 Annuities at Compound Inter- est 243 Sinking Funds 248 Powers and Roots 251 Square Root 253 Cube Root 256 Similar Surfaces and Solids . . 258 Mensuration 261 Area of Plane Figures 262 Area of Triangles 264 Circles 265 Solids 268 Gauging of Casks 273 Tonnage of Vessels 275 Grain Measurement 275 Lumber, Doyle's Rule 276 Test Questions 278 Appendix 286 Drill in Percentage 287 Metric Drill 289 G. c. d. of Fractions 290 L. c. in. of Fractions 291 Table of Prime Numbers 292 Property of the No. 9 293 Contractions in Mult 293 Table of Time, in days 295 Mortality Table 297 Life Estates 298 Northampton Table 299 Business Information 300 Letters of Credit 304 Instruments under Seal 304 Book Accounts 305 Statute of Limitations 306 Stock Clearing Houses 307 Abbreviations (Stocks) 308 Miscellaneous Examples 309 Commercial Arithmetic Art. 1. The student of Commercial Arithmetic is presumed to be familiar with the ordinary operations of Common Arith- metic. For this reason, the four fundamental rules, fractions, decimals, etc., are omitted in this work. COUNTING ROOM METHODS. 2. Facility in adding is of the first importance in commer- cial life. It can be acquired only by constant practice, and a thorough acquaintance with the simple combinations of num- bers. 3. In adding ledger columns, accountants frequently use the following methods : (Ex. 1.) (Ex. 2.) $784,306 $346.82 9.348 204.36 751.675 56.07 0.384 207.00 814.25 95.832 862.741 2204.206 26.35 460.48 1.76 $4708.492, Ans. 763.48 1252.07 232 323 Ans. $2066.32 Explanation. — Ex. 1. Write the units' figure of the sum of each col- umn under the column added, and the tens, or figures carried, below as in the example. In adding, name only results. Ex. 2. The second method divides the columns into parts, adding each part separately to find their sum. 8 Counting Rooyn Metlwds. 4. Principles of Addition.— 1°. Only like numbers and like orders of units can be added one to another. 2°. The sum is the same in whatever order numbers may be added. 3. Add the numbers from 1 to 29 in a column. From 29 to 109. From 109 to 199 inclusive. 5. Adding two or more columns at a time. 4. Find- the sum of 29, 48, 37, and 56. Explanation.— To the number at the bottom add the tens, then the unitsaLthe next number above it. Thus, 5G and ^0 are KG, ,n < 7 arc 93, and 40 are 133, and 8 are 14jS Bo afVilifflrand 9 are 170, Ans. 527, 432, and 245, at the bottom, 245, the units of the next are 645, and 30 are , and 20 are 1197, and 30 are 1834, and 9 are OPERATION. 29 48 37 56 170 Ans. S£pJ ind the sum Kins at a time EXPLANATIO add the hundreds, pfPfoer above it ; thus, 675, and 2 are ?»rol204, and Ine following, in like manner 24 32 27 23 42 91 26 34 12 67 21 53 26 78 25 82 93 54 62 58 53 24 66 J 2 26 87 72 65 (8.) 46 32 17 81 28 52 23 20 71 39 18 42 73 24 519 271 436 587 333 745 52 158 232 464 643 27 235 103 (10.) 607 232 211 380 578 231 145 605 760 357 544 276 803 725 adding three OPERATION. 639 527 432 245 Ans. 1843 (n.) 253 12 849 436 551 349 763 37 155 676 844 232 383 918 Counting Room Methods. 6. To Add Numbers Horizontally. It is sometimes convenient to add numbers, when written horizontally, instead of under each other. 12. Find the sum of 428 + 253 + 647 + 926 + 425. Explanation. — Beginning at the right, add the units of all the num- bers, then the tens, then the hundreds ; the sum is 2679. Arts. 13. Find the sum of 2345 + 621 + 2417 + 385 -f- 6457. 14. Find the sum of 325, 4623, 435, 2843, 7546. Note.— To insure accuracy, the addition should be performed by differ- ent methods, or in different directions, in order that mistakes made by one method may be detected by another. 7. Principles of Subtraction. — 1°. Only like numbers and like orders of units can be subtracted one from the other. 2°. The difference and subtrahend are equal to the minuend. 3°. If two numbers are equally increased, their difference is not altered. 15. From 3427 subtract 1235. Ans. 2192. 16. A has 8268 more than B and $150 less than C, who has $4580; D has as much as A and B together; how much hasD? 8. When the Sum and Difference of Two Numbers are given, to find the Numbers. 17. The sum of two numbers is 283, and their difference is 35 ; what are the numbers ? Analysis. — The difference subtracted from the sum will leave twice the smaller number, and 283-35 = 248 ; half of 248 is 124. the less num- ber. Again, the difference added to the less must be equal to the greater number, and 124 + 35 = 159, the greater number. Hence, the Koxe. — From the sum subtract the difference ; half the remainder will be the less number. TJie difference added to the less will be the greater number. 10 Short Methods in Multiplication. 18. The whole number of votes cast for the two candidates at an election was 15564, and the successful candidate was elected by a majority of 1708 ; how many votes did each receive ? 19. A lady paid $350 for her watch and chain ; the former being valued $52 higher than the latter ; what was the price of each ? 20. A and B found a pocket-book, and returning it to the owner, received a reward of $500, of which A took $138 more than B ; what was the share of each ? 21. The sum of two numbers is 4487, and the greater is 653 more than the less ; what are the numbers ? 9. The Complement of a number is the difference between the number and the next higher order. Thus, 2 is the complement of 8, also of 98 ; for 10—8 = 2, and 100-98 = 2. 22. What is the complement of 87 ? Of 125 ? Of 3284 ? 23. By how much does the sum of 6 and 4 exceed their difference ? 24. By how much does their complement exceed their dif- ference ? 25. Victoria was bom in 1819, the Prince of Wales in 1841 ; how old was each in 1882 ? 26. A poor-house had 133 inmates, consisting of infirm and able-bodied 70 ; able-bodied and children 105 ; children and officers 63 ; officers 5 ; what number of each class ? 27. A basket held oranges, nuts, and eggs ; in all 1769 arti- cles; there were 1696 oranges and nuts, and 1262 nuts and eggs ; how many more nuts were there than oranges ? Short Methods in Multiplication. n SHORT METHODS IN MULTIPLICATION. 10. Peikciples. — 1°. The multiplicand may be either ab- stract or concrete. £°. TJie multiplier must be considered an abstract number. 3°. The multiplicand and product are like numbers. 4°. TJie product is the same in whatever order the factors are taken. 11. To multiply by I with a significant figure annexed. 1. If one city lot costs $3245, what will 17 lots cost ? Explanation.— Multiply the multiplicand by the operation. 7 units, and setting each figure of the product one place oZ = 1 acre, A. 160 sq. rods \ 640 acres = 1 sq. mile, . . . sq. mi. Notes. — 1. The Rood of 40 sq. rods has fallen into disuse. 2. A Square, in Architecture, is 100 square feet. 58. In Surveying Government Lands a parallel of latitude called the Base Line, and a meridian called the Principal Meri- dian are first established. From these other lines are run at right angles, six miles apart, which divide the territory into rectangular tracts six miles square. These tracts are called Townships. Since the surface of the Earth is convex, all Meridians converge as the latitude increases. Hence, the Townships and Sections are not exactly rectangular, which creates a necessity for occasional offsets called Correction Lines. 59. Townships are designated by their number N. or S. of the base line. Cubic Meastire. 29 60. A line of townships running N. and S. is called a Range, and is designated by its number E. or W. of the prin- cipal meridian. Thus, T. 39 N., R. 14 E. 3d P. M., describes a township in the 39th tier North of base line, and 14th range East of the 3d A sectkjn. principal meridian. 61. A Township is divided into Sections each 1 mile square and con- tains 640 acres. Thus, 1 Sec. = 1 mi. x 1 mi. = 640 A. \ Sec. = 1 " x|" =320 " \ Sec. = 1 « x i " =160 " jx J Sec. .-= 1 " x I " = 80 " \*\ Sec. = 1" x T V " = 40 * The sections are numbered commencing at the N. E. corner, and running W. in the North tier, E. in the second, etc. Each section is divided into 4 quarter sections, called N. E., S. E., N. W., and S. W. quarters, each containing 160 acres. Thus, S.E. \, sec. 10, T. 39 N., R. 14 E. 3d., P. M., is read, " Southeast quarter of sec. 16, tier 39 north, range 14 east of third principal meridian." 1 MILE SQUARE. A TOWNSHIP. N W 6 5 4 3 2 1 7 8 9 10 11 12 18 17 18 15 14 13 19 20 21 89 23 21 30 20 2S ~7 26 25 31 32 33 34 35 36 6 MILES SQUARE. CUBIC MEASURE. 62. Cubic Measure is used in measuring solids or volume. 63. A Solid is that which has length, breadth, and thickness ; as, timber, boxes of goods, etc. 64. A Cube is a regular solid bounded by six equal squares called its faces. Hence, its length, breadth, and thickness are equal to each other. 65. The measuring unit of solids is a Cube the edge of which is a linear unit. 30 Weights and Measures. Table. 1728 cubic inches {cu. in.) = 1 cubic foot, . . cu.ft. 27 cubic feet = 1 cubic yard, . . cu. yd. 128 cubic feet = 1 cord of wood, . C. 66. A Cord of wood is a pile 8 ft. long, 4 ft. wide, and 4 ft. high; for 8x4x4 = 128. 67. A Cord Foot is one foot in length of such a pile ; hence, 1 cord foot = 16 cu. feet; 8 cord ft. = 1 cord. Special Cubic Measures. 100 cu. ft. = 1 register ton (shipping.) 40 cu. ft. in U. S., or, ) . .. . ■ 42cu.ft.inEng. \= 1 fre ^ ht ton - Note. — A cu. foot of distilled water maximum density weighs 62| lbs. avoirdupois. LIQUID MEASURE. 68. Liquid Measure is used in measuring milk, oil, wine, etc. Ta ble. 4 gills (gi.) = 1 pint . . . pt. 2 pints = 1 quart . . qt. 4 quarts = 1 gallon, . . gal. 31 J gallons = 1 barrel, . . bar. or bbl. 63 gallons == 1 hogshead, . hhd. 69. The Standard Unit of Liquid Measure is the gallon, which contains 231 cubic inches. The British Imperial Gallon contains 277.274 cu. inches. Notes. — 1. The barrel and hogshead, as units of measure, are chiefly used in estimating the contents of cisterns, reservoirs, etc. 2. Casks varying in capacity are often used in commerce, called tierces, pipes, butts, tuns, etc. Their capacity is determined by gauging or measurement, and the number of gallons each contains is usually marked upon it. 3. A Carboy holding about 12 gallons, is sometimes used for corrosive and other liquids. 4. Beer Measure is practically obsolete in this country. The old beer gallon contained 282 cubic inches ; the barrel 36 gallons ; the hogshead 51 gallons. Dry Measivre. 31 DRY MEASURE. 70. Dry salt, etc. Measure is used in measuring grain, fruity Table. 2 pints (pt.) = 1 quart, . 8 quarts = 1 peck, 4 pecks, or 32 qts. = 1 bushel, . 36 bushels = 1 chaldron, qt. pk. bu. ch. 71. The Standard Unit of Dry Measure is the bushel, which contains 2150.42 cu. inches. The British Imperial bushel contains 2218.192 cu. inches. Notes. — 1. The Eng. Quarter seen in, prices current, is equal to 8 bu. of 70 lb. each, or to 560 lb. = \ of a long ton. 2. Stricken or Even Measure is used in measuring grain, seeds, etc., the article measured being scraped off level by a straight instrument called a strike, or strickle. 3. Heaped Measure is used in measuring vegetables and fruit, as potatoes, apples, etc. 4. A heaped bushel is equivalent to a Winchester bushel, heaped in the form of a cone, the height of which is 6 inches. Four heaped measures are about equal to five stricken measures. 72. The standard weight, Avoirdupois, of a Bushel of different kinds of grain and seeds, as fixed by law in the several States named. Table. commodities. Wheat Indian Corn Oats Barley Buckwheat Rye... Clover Seed Timothy Seed . . . Blue Grass Seed Flax Seed Hemp Seed 60 56 52|56 32 50 1 i | IN 60 5(^52 | i 60 60 60 50 56 33 - 1 i 1 60| 60 GO 60 60 60 66 56 56| 56 52 56 32 30 ! 46 32 35 30 48 48 52 50 48 56 56 56 60 64 45 14' 56 5Dj5£ 44 60 60 54 56 .32 is 5C, CO 60 56 56 861 32 45 48 42 42 56 56 60 60 46 !56 I 32 Weights and Measures. Notes.— 1. Beans, peas, and potatoes v.re usually estimated at 60 lb. to the bu., but the laws of N. Y. make 62 lo. of Leans to a bushel. In Illinois, 50 lb. of common salt, or 55 lb. fine, are 1 bu. In N. J., 56 lb. of salt are 1 bu. In Ind., Ky., and Iowa, 50 lb. are 1 bu. In Penn., 80 lb. coarse, 70 lb. ground, or 62 lb. fine salt are 1 bu. In Maine, 30 lb. oats, and 64 lb. beets or of rutabaga turnips = 1 bu. In New Hampshire, 30 lb. of oats are 1 bu. 2. Grains, seeds, and small fruit are sold by the bushel, stricken or level measure. Large fruit, potatoes, and all coarse vegetables by heaped measure. TROY WEIGHT. 73. Troy Weight is used in weighing gold, silver, jewels, and in philosophical experiments. Table. 24 grains (gr.) = 1 pennyweight, . pwt. 20 pennyweights = 1 ounce, . . . . oz. 12 ounces = 1 pound, . ... lb. 74. The Standard Unit of weight in the United States, is the Troy pound, which contains 5760 grains and is equal to the Imperial Troy pound of England. 75. The Value of Diamonds and other jewels is estimated by carats, grains, and quarters. Thus, 4 quarters = 1 grain, . . gr. 4 grains = 1 carat, . . . car. AVOIRDUPOIS WEIGHT. 76. Avoirdupois Weight is used in weighing coarse articles; as hay, cotton, groceries, etc., and all metals except gold and silver. Table. 16 ounces {oz) = 1 pound, . . . lb. _ j cental, or . . ctl. ^ 1 hundredweight, cwt. 2000 lb., or 20 cwt. = 1 ton, . . . . T. Note. — The long ton of 2240 lbs. is used in calculating duties, in weighing coal at the mines, and in a few other cases. Apothecaries Weight 33 77. Comparison of Avoirdupois and Troy Weight. 7000 grains Troy = 1 lb. Avoirdupois. 5760 grains " = 1 lb. Troy. 437^ grains " = 1 oz. Avoirdupois. 480 grains " = 1 oz. Troy. Special Avoirdupois Weights. 100 lbs. Nails = 1 Keg. 100 lbs. Dry Fish = 1 Quintal. 196 lbs. Flour = 1 Barrel. 200 lbs. Beef or Pork = 1 Barrel. 240 lbs. Lime = 1 Cask. 280 lbs. Salt, N. Y. Salt Works = 1 Barrel. 150 lbs. Potatoes, as freight = 1 Barrel. 6| lbs. Crude or Refined Petroleum = 1 Gallon. A ton (2000 lbs.) of Lehigh white ash coal, egg size = 34| cu. ft. A ion of white ash Schuylkill, " =35 cu. ft. A ton of pink, gray, and red ash, " =36 cu. ft. A ton of hay upon a scaffold measures about 500 cu. ft. ; when in a mow, 400 cu. ft. ; and in well-settled stacks, 10 cu. yards. APOTHECARIES WEIGHT. 78. Apothecaries Weight is used by apothecaries in mixing medicines. Table. 20 grains (gr.) = 1 scruple, . . sc, or B. 3 scruples = 1 dram, . . . dr., or 3 . 8 drams = 1 ounce, . . . oz. t or § . 12 ounces = 1 pound, . . . lb., or lb. Notes. — 1. The pound, ounce, and grain are the same as Troy weight. The only difference between them is in the subdivisions of the ounce. 2. Drugs and Medicines are sold at wholesale by Avoirdupois weight. 3 34 Weights and Measures. APOTHECARIES FLUID MEASURE. 79. Apothecaries Fluid Measure is used in mixing liquid medicines. Table. 60 minims, or drops (TR. or git.) = 1 fluid drachm, . fl . 8 fluid drachms = 1 fluid ounce. . . /§ . 16 fluid ounces = 1 pint 0. 8 pints = 1 gallon, .... Cong. Notes.— 1. Ott. for guttoa, Latin, signifying drops ; O,iovoctarias, Latin for one-eighth ; and Cong., congiarium, Latin for gallon. 2. The symbols of this measure precede the numbers to which they refer. Thus, O. 2 "f §6, is 2 pints 6 fluid ounces. 80. The following approximate measures, though not strictly accurate, are often useful in practical life : Table. 45 drops of water, or a common teaspocnful = 1 fluid drachm. A common tablespoonful = -| fluid ounce. A small teacupful, or 1 gill = 4 fluid ounces. A pint of pure water = 1 pound. 4 tablespoonful s, or a wine-glass = £ gill. A common-sized tumbler = \ pint. 4 teaspoonfuls = 1 tablespoonful. Abbreviations.—^, recipe, or take; a, aa, equal quantities; j, 1; ij, 2 ; ss, semi, half; P, particula, little part ; P. aeq., equal parts ; q. p., as much as you please. CIRCULAR MEASURE. 81. Circular Measure is used in measuring angles, latitude, longitude, etc. 82. A Circle is a plane figure bounded by a curve line, every part of which is equally distant from a point within, called the center. Time. 35 Table. 60 seconds (") = 1 minute, . . '. 60 minutes = 1 degree, . . °, or deg. 30 degrees = 1 sign, . . . S. 12 signs, or 360' = 1 circumference, Gir. The Standard Unit for measuring angles is the Degree. 83. A Degree is the angle measured by the arc of -jj-g- part of the circumference of a circle. A degree at the equator, also the average degree of latitude, adopted by the U. S. Coast Survey, is equal 69.16 miles, or 69| miles, nearly. TIME. 84. Time is a measured portion of duration. Table. 60 seconds (sec.) = 1 minute, . . rain. 60 minutes = 1 hour, . . . hr. 24 hours == 1 day, . . . d. 7 days -- 1 week, . . . wk. 365 days = 1 common year, c. yr. 366 days = 1 leap year, . I. yr. 12 calendar months (mo.) = 1 civil year, . yr. 100 years = 1 century, . . 0. Note. — In most business transactions 30 days are considered a month. 85. Time is naturally divided into days and years. The former are measured by the revolution of the earth on its axis ; the latter by its revolution around the sun. 86. Days are divided into Apparent Solar, Mean Solar, and Civil days. An Apparent Solar Day is the time between the apparent departure of the sun from a given meridian and his return to it, and is shown by sun dials. A Mean Solar Day is the average length of apparent solar 36 Weights and Measures. days, and is the Standard Unit for measuring Time. It is divided into 24 equal parts, called hoars, as shown by a per- fect clock. A Civil Day is the day adopted by government for business purposes. It begins and ends at midnight, and is divided into two part^ of 12 hours each ; the former are designated A. M., the latter p. m. Notes. — 1. The difference between the apparent and mean solar day is called the Equation of Time, and varies from 16£ min. to nothing. This difference is owing to the obliquity of the ecliptic, and the unequal velocity of the Earth in its orbit. 2. The Astronomical Day begins at noon and is counted on through 24 hours to the next noon, and corresponds to the apparent solar day. 3. We have seen that the pendulum which vibrates seconds, is the standard of the English and American measures of extension, capacity, and weight. But the length of the pendulum is determined by the mean solar day ; hence, the mean solar day is the ultimate standard of all our weights and measures. 87. Years are divided into Civil and Solar years. 88. The Solar Year is equal to 365 d. 5 hr. 48 min. 49.7 sec, or 365J d. nearly.* *In 4 years this fraction amounts to about 1 day. To provide for this excess, 1 day is added to the mo. of Feb. every 4th year, which is called Leap Year. Note. — Every year that is exactly divisible by 4, except centennial years, is a leap year ; the others are common years. Thus, 1876, '80, etc., were leap years ; 1879, '81, were common. Every centennial year exactly divisible by 400 is a leap year ; the other centennial years are common. . Thus, 1600 and 2000 are leap years ; 1700, 1800, and 1900 are common. 89. The Civil Year includes both common and leap years, and is divided into 12 Calendar months, viz : January (Jan.) 31 days. July (July) 31 days. February (Feb.) 28 " August (Aug.) 31 " March (Mar.) 31 " September (Sept.) 30 " April (Apr.) 30 " October (Oct.) 31 " May (May) 31 " November (Nov.) 30 " June (June) 30 " December (Dec.) 31 " Laplace, Somerville, Baily's Tables. Miscellaneous Tables. 37 90. A Calendar is a division of time into different periods, adapted to the wants of society. 91. The first Civil Calendar worthy of notice was estab- lished by Julms Caesar 46 years before Christ, and continued in use until the adoption of the Gregorian Calendar in 1582. Dates prior to the adoption of the Gregorian Calendar are called old style, and are marked 0. S. ; those since are called new style, and are marked N. S. 92. To change dates from Old Style to New. From 1582 to 1700 (1600 being leap year) add 10 days to Old Style. From 1700 to 1800 add 11 days ; from 1800 to 1900 add 12 dajss ; and from 1900 to 2100 (2000 being leap year) add 13 days. Note. — Russia continues to use the Julian calendar, or Old Style ; hence., Russian dates are now 12 days behind ours. MISCELLANEOUS TABLES. 12 things = 1 dozen. 12 dozen = 1 gross. 12 gross = 1 great gross. 20 things = 1 score. Paper. 24 sheets = 1 quire of paper. 2 reams = 1 bundle. 20 quires = 1 ream. 5 bundles = 1 bale. Books. 2 leaves = 1 folio. 8 leaves rs 1 octavo, or 8vo. 4 leaves = 1 quarto, or 4to. 12 leaves = 1 duodecimo, or 12mo. Notes. — 1. The terms folio, quarto, octavo, etc., denote the number of leaves into which a sheet of paper is folded in making books. 2. In copying legal papers, recording deeds, etc., clerks are usually paid by the folio. Thus, 100 words make 1 folio in New York. 72 words " 1 folio in com. law in England. 90 words " 1 folio in chancery in England. 3. In printing books, 250 impressions or 125 sheets printed on both sides, make 1 token. 38 United States Money. UNITED STATES MONEY. 93. Money is the measure of value. 94. Moneys of Account are those in which accounts are kept. 95. Currency is the money employed in trade. 96. Coins or Specie are pieces of metal of known purity and weight, stamped at the Mint, and authorized by Government to be used as money at fixed values. 97. Bullion is uncoined gold or silver, and includes bars, gold-dust, etc. c - 98. Paper Money is a substitute for metallic currency. It consists of Treasury Notes issued by the Government known as Greenbacks, and Bank Notes issued by banks. 99. U. S. Money is the legal currency of the United States, and is often called Federal Money. Its denominations are Eagles, Dollars, Dimes, Cents, and Mills, which increase and decrease by the scale of ten, and it is thence called Decimal Currency. Table. 10 mills = ' 1 cent, . . ct. 10 cents = 1 dime, . . d. 10 dimes, or 100 cts. = 1 dollar, . . dot., or $. 10 dollars = 1 eagle, . . E. 100. The U. S. coins are gold, silver, nickel, ana bronze. 101. The Gold coins are. the double eagle, eagle, half eagle, quarter eagle, three-dollar piece, and dollar. 102. The Silver coins are the dollar, half dollar, quarter dollar, and dime. 103. The Nickel coins are the 5-cent and S-cent pieces. 104. The Bronze coin is the 1-cent piece. United States Money. 39 105. The weight and purity of the coins of the United States are regulated by the laws of Congress.* Notes. — 1. The gold dollar is the Unit of Value. Its standard weight is 25.8 gr. ; that of the quarter eagle, 64.5 gr. ; of the 3-dollar piece, 77.4 gr. ; of the half eagle, 129 gr. ; the eagle, 258 gr. ; the double-eagle, 516 gr. 2. When pure, gold is said to be 24 carats fine. If it contains 18 parts of pure gold and 6 parts of alloy, it is 18 carats fine, etc.- Gold for manufacturing purposes varies from 14 to 18 carats fine. 3. The weight of the standard silver dollar is 412| grains ; the half dol- lar, 12| grams or 192.9 grains ; the quarter dollar, 6^ grams, or 96.45 gr. ; the dime, 2£ grams or 38.58 grains. 4. The weight of the nickel 5-cent piece is 77.16 grains, or 5 grams; of the 3-cent nickel, 30 grains; of the cent, bronze, 48 grains. 5. The standard purity of the gold and silver coins is by weight nine- tenths pure metal, and one-tenth alloy. The alloy of gold coins is silver and copper; the silver, by law, is not to exceed one-tenth of the whole alloy. The alloy of silver coins is pure copper. f 6. The 5-cent and 3-cent pieces are composed of one-fourth nickel and three-fourths copper ; the cent, of 95 parts copper and 5 parts of tin and zinc. They are known as nickel and bronze coins. The diameter of the nickel 5-cent piece is two centimeters, and its weight 5 grams. 7. The Trade Dollar of 420 grains is no longer coined. 106. Legal Tender is money which, if offered, legally satis- fies a debt. Notes. — 1. All the gold coins, and the silver coins of $1 and upwards, except the trade dollar, are legal tender for all payments. 2. Silver coins less than $1 are legal tender to the amount of $10 ; nickel and bronze pieces to the ambunt of 25 cents. CANADA MONEY. 107. Canada Money is the legal currency of the Dominion of Canada. It is founded on the Decimal Notation, and its denominations, Dollars, Gents, and Mills, have the same nominal value as the corresponding denominations of U. S. Money. Hence, all the operations in it are the same as those in U. S. Money. * The United States adopted the decimal system of currency in 1789. Since then it has been adopted by France, Belgium, Brazil, Bolivia, Canada, Chili, Denmark, Ecuador, Greece, Germany, Italy, Japan, Mexico, Norway, Peru, Portugal, Spain, Sweden, Switz- erland, Sandwich Islands, Turkey, U. S. of Colombia, and Venezuela. t Report of Director of the Mint. 40 Weights and Measures. ENGLISH MONEY. 108. English or Sterling Money is the currency of Great Britain. Table. 4 farthings (qr. or far.) = 1 penny, . . . . d. 12 pence = 1 shilling, ....*. 20 shillings, or i 10 florins W , = 1 Pound or sovereign, £. ^ __ 21 shillings = 1 guinea, . . . . g. 109. The Unit of English Money is the Pound Sterling, which is represented by a gold Sovereign equal in value to $4.8665. The guinea is no longer coined. Notes. — 1. The standard purity of the gold coins of Great Britain is 22 carats fine ; that is, \^ pure gold and -fa alloy. That of the silver coins is 1 1 pure silver and -fa alloy. 2. The silver coins are the crown (5s.) ; half crown (2s. 6d.) ; florin (2s.) ; shilling (12d.) ; the six-penny, four-penny, and three-penny pieces. 3. The copper coins are the penny, half-penny, and farthing. 4. Farthings are commonly expressed as fractions of a penny, as 7|d. FRENCH MONEY. 110. French Money is the national currency of France. The system is founded upon the decimal notation ; hence, all the operations in it are the same as those in U. S. money. The denominations are the franc, decime, and centime. Table. 10 centimes (c.) = 1 decime, . . d. 10 declines = 1 franc, . . fr. 111. The Unit of French money is the Franc. Decimes are tenths of a franc, and centimes are hundredths. French Money. 41 Notes. — 1. Centimes by contraction are commonly called cents. 2. Decimes, like our dimes, are not used in business calculations ; they are expressed by tens of centimes. Thus, 5 decimes are expressed by 50 centimes ; 63 fr., 5 d., and 4 c. are written, 63.54 francs. 3. The legal value of the franc in estimating duties, is 19.3 cents; its intrinsic value is a trifle more. 112. The Coins of France are of gold, silver, and bronze. The Gold coins are the hundred > forty, twenty, ten, and/ve franc pieces. The Silver coins are the five, tivo, and one franc pieces, the fifty and twenty-five centime pieces. Bronze coins are the ten, five, two, and one centime pieces. The gold and silver coins of France, like those of the U. S., are ^ pure metal and ^ alloy. GERMAN MONEY. 100 pfennigs = 1 reischmark. 113. The Coins of the New German Empire consist of gold, silver, and nickel. The Gold coins are the 5-mark piece called half krone (half crown), the 10-mark piece called krone (crown), and the 20- mark piece called doppel krone (double crown). The Silver coins are the 2 and 1 mark pieces. The Nickel coins are 10 and 5 pfennigs (pennies). 114. Reischmark {Royal Mark) is the Standard Unit. It is equal to 23.85 cts. U. S. money, and is divided into 100 equal parts, one of which is called a pfennig. Note. — The coins most frequently referred to in the United States are the Silver Thaler which equals 74.6 cents, and the Silver Groschen equal eteio System.* [& Definitions. 115. Metric Weights and Measures increase and decrease regularly by the Decimal Scale. 116. The Meter is the Base of the System, and is one ten- millionth part of the distance from the Equator to the Pole, or 39.37 inches, nearly. Note. — The term Meter is from the Greek metron, a measure. 117. The Metric System has three principal units, the Me'ter (meeter), Li'ter (leeter), and Gram. To these are added the Ar and Ster,\ for square and cubic measure. Each of these units has its multiples and subdivisions. 118. The names of the higher metric denominations are formed by prefixing to the name of the unit, the Greek numerals, Dele' a, Hek'to, Kil'o, and Myr'ia. Thus, from Dek'a, 10, we have Dek'ame'ter, 10 meters. " Hek'to, 100, " Hek'tome'ter, 100 " Kil'o, 1000, " Kil'ome'ter, 1000 * Myr'ia, 10000, " Myr'iame'ter, 10000 " * This system had its origin in France near the close of the last century. Its sim- plicity and comprehensiveness have secured its adoption in nearly all the countries of Europe and South America. Rs use was legalized in Great Britain in 1864, and in the United States in 1866. It Is adopted hy the TJ. S. Coast Survey, and is extensively used in the Arts and Sciences, and partially in the Mint and Post Office. t The spelling, pronunciation, and abbreviation of metric terms in this work, are the same as adopted by the American Metric Bureau, Boston, and the Metrological Soc, N.Y. Metric System. 43 119. The lower denominations are formed by prefixing to the name of the unit the Latin numerals, Dec'i, Certti, and Mil'li. Thus, from Dec'i, y 1 ^, we have Dec'ime'ter, T ^ meter. " Cen'ti, yi^, * Cen'time'ter, T £ 7 « Mil'li, T ^, " Mil'lime'ter, ^ " Note. — The numeral prefixes are the Key to the whole system, and should be thoroughly committed to memory. METRIC LINEAR MEASURE. Tab le. 10 mtt'li-me'ters {mm.) — 1 cen'ti-me'ter, 10 cen'ti-me'ters = 1 dec'i-me'ter, . 10 dec'i-me'ters = 1 METER, . . 10 me'ters = 1 dek'a-me'ter, 10 dek'a-me'ters — 1 hek'to-me'ter, 10 hek'to-me'ters = 1 kil'o-me'ter, 10 kiVo-me'ters = 1 myr'ia-me'ter, em. (jU »»•) dm. ( T V m.) m. Dm. (10 m.) Hm. (100 m.) Km. (1000 m.) Mm. (10000 m.) Notes. — 1. The principal unit of each table is printed in capital letters ; those in common use in full-faced Roman. 2. The Accent of each unit and prefix is on the first syllable, and remains so in the compound words. 3. Abbreviations of the higher denominations begin with a capital, those of the lower begin with a small letter. Common Equivalents. 1 cen'timeter = 0.3937 inches. 1 dec'imeter = 3.937 " 1 me'ter = 39.37* " 1 kil'ometer = 0.6214 mile. 4. — Merchants usually reckon the meter as 1 T V yard. ONE DECIMETER. i t 1 1 1 T 1 1 1 1 1 1 1 1 f 1 1 1 1 1 1 1 1 1 1 T 1 1 1 1 1 « 1 1 1 1 i f I II i il 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ii 1 1 1 1 1 Li 1 1 1 1 1 1 f 1 1 ■ 1 1 H 1 1 Ti 1 1 1 1 1 1 1 1 1 1 100 Millimeters. * Established by Act of Congress in 1866. 44 Weights and Measures. 120. The Meter is the Standard Unit of length, and, like the yard, is used in measuring cloths, laces, short distances, etc. 121. The Kilometer, like the mile, is used in measuring long distances. * >. 122. The Centimeter and Millimeter are used for minute measurements, as the thickness of glass, paper, etc. Note. — The compound words may be abbreviated by using only the prefix and the first syllable or letter of the unit , thus, centimeter, milli- meter, centiliter, milliliter, centigram, decigram, may be called centim, millim, centil, decig, etc. 123. The approximate length of 1 meter is 40 in.; of 1 decim., 4 in.; of 5 meters, 1 rod; of 1 kilom., § mile. Note. — Decimeters, dekameters, hektometers, like dimes and eagles, are seldom used. 124. Since meters, centimeters, and millimeters, correspond to dollars, cents, and mills, it follows that metric numbers may be read like U. S. Money. Thus, 28.375 meters are read 28 and 375 thousandths meters, or 28 m. 3 dm. 7 cm. 5 mm., or 28 m. 37 cm. 5 mm. 1. Read in meters 15 'Dm.; 78 Hm.; 355 Km.; 49.237 dm.; 3.54 Mm. 125. To write Metric Numbers decimally in terms of a given Unit. 2. Write 9 Hm. 4 m. 6 dm. 8 cm. in terms of a meter. Explanation. — We write meters in units place, operation. on the left of the decimal point, the Dm. in tens 904.68 m., Ans. place, the Hm. in hundreds place, etc., and the decims. in tenths place, centims. in hundredths, etc., as we write the orders of integers and decimals in simple numbers. Hence, the Kule. — Write the given unit and the higher denomi- nations in their order, on the left of a decimal point, as integers, and those below the unit, on the right, as decimals. Note. — If any intervening denominations are omitted in the given number, their places must be supplied by ciphers. Metric System, 45 3. Write in terms of a meter 15 Dm. Ans. 150 m. 4. Write in meters 254 Dm. 42 cm. 5. Write 385 Hm. 24 mm. 6. Write 172 Hm. 32 Dm. in meters. 7. Write 8 Km. 9 Hm. 6 Dm. 8 mm. 8. Write in meters and decimals 4 Mm. 15f Dm. 7 cm. 5 mm. 9. Write in Km. 37 Mm. 64 Dm. 37£ m. 8 dm. 7 mm. 126. To reduce Metric Numbers from higher denominations to lower, and from lower to higher. 10. Reduce 352 meters to millimeters. OPERATION. Solution. — Since 1 m. = 1000 mm., 352 ^52 m. meters = 352 x 1000, or 352000 mm., Ana. 1000 Ans. 352000 mm. n. Change 843000 millimeters to meters. Solution. — Since 1000 mm. = im. 843000 mm. = as many meters as 1000 is contained times in 843000. Pointing off three decimal places divides a number by 1000. Ans. 843.000 m. Hence, the Rule. — Move the decimal -point one place to the right or left, as the case may require, for each denomination to which the given number is to be reduced. 12. Change 75.25 Km. to meters. Ans. 75250 m. 13. Change 8427.83 meters to Hm. Am. 84.2783 Hm. 14. Change 9723.8 m. to Km. Ans. 9.7238 Km. 15. Change 83605.24 cm. to meters and decimals. To Dm. 16. Change 75842 mm. to meters and decimals. To cm. 17. Reduce 187.62 dm. to meters. To cm. 18. Reduce 61.75 Km. to cm. To mm. 19. Reduce 158364 mm. to Hm. 20. Reduce 28.53 Km. to dm. 21. Reduce 153 Mm. to Dm. To cm. 46 Weights and Measures. METRIC SQUARE MEASURE. 127. The Measuring Unit of Surfaces is a Square, each side of which is a Linear Unit. Table. 100 sq. milli-me'ters (sq. mm ) = 1 sq. cen'ti-me'ter, sq. em. 100 sq. cen'ti-me'ters = 1 sq. dec'i-me'ter, sq. dm. 100 sq. dec'i-me'ters _ jl SQ. METER, . ( or cent/ar, . . sq. m. ca. 100 sq. me'ters j 1 sq. dek'a-me'ter, ( or Ar, . . . sq. Dm. A. _ ( 1 sq. hek'to-me'ter, ( or hek'tar, . . sq. Hm. 100 sq. dek'a-me'ters Ha. 100 sq. hek'to-me'ters = 1 sq. kil'o-me'ter, sq. Km. Common EQU 1 VALE NTS. 1 sq. centim. =a 0.1550 sq. in. 1 sq. decim. = 0.1076 sq. ft. 1 sq. meter = 1.196 sq. yd. 1 ar = 3.954 sq. rods. 1 hektar = 2.471 acres. 1 sq. kilo = 0.3861 sq. mile. 128. The sq. meter is used- in measuring ordinary surfaces, as floors, ceilings, etc. ; the ar and hektar in measuring land ; and the sq. kilometer in measuring States and Territories. Note. — The term ar is from the Latin area, a surface. 129. The approximate area of a sq. meter is lOf sq. ft., or H S( l- jd- > ai *d- °^ ^ ne hektar about 2 J acres. 130. The scale of surface measure is 100 (10 x 10). That is, 100 units of a lower denomination make a unit of the next higher ; hence, each denomination must have two places of figures. Sq. Centim. Thus, 23 Ha. 19 A. 25 ca., written as ars, is 2319.25 A., and may he read "2319 ars and 25 centars" If written as hektars, it is 23.1925 Ha., and may he read "23 hektars and 1925 centars," Metric System. 47 22. Express 86.34 A. as centars. As Hektars. 23. Write 75 sq. m. as sq. mm. As sq. dm. 24. In 8234 ca. how many A.? 25. In 184.38 A. how many Ha. ? METRIC CUBIC MEASURE. 131. The Measuring Unit of solids is a Cube, the edge of which is a Linear Unit. Table. 1000 cu. mil'li-me'ters {cu. mm.) = 1 cu. cen'ti-me'ter, cu. cm. 1000 cu. cen'ti-me'ters = 1 cu. dec'i-me'ter, cu. dm. 1000 cu. dec'i-me'ters = 1 CU. METER, . . cu. m. 10 dec'i-sters = 1 STER, . . . . st. 10 sters = 1 dek'a-ster, . . Dst. Common Equivalents. 1 cu. centimeter = 0.061 cu. in. 1 cu. decimeter = 61.022 cu. in. 1 cu. meter = 1.308 cu. yds. Note.— The ster = .2759 cord is seldom used. 132. The cubic meter is used in measuring ordinary solids, as timber, excavations, embankments, etc. When applied to fire-wood, it is sometimes called a Ster, and is equal to about 35J cubic feet. Note. — The cubic decimeter, when used as a unit of dry or liquid measure, is called a Liter, 133. The scale of cubic measure is 1000 (10 x 10 x 10) ; hence, each denomination must have three places of figures. Cu. Cm. 26. Express 18000 cu. mm. as en. cm. Ans. 18.000 cu. cm. 27. Write 28 cu. m. and 15 cu. dm. as cu. meters. Ans. 28.015 cu. m. 28. Write in centimeters 256 cu. dm, 34 cu, cm. 89 cu, mm. 48 Weights and Measures. 29. In 38450 cu. dm. how many meters ? 30. In 253 cu. m. how many cu. mm.? Cu.-em.? METRIC DRY AND LIQUID MEASURE. 134. The Liter is the principal unit of Dry and Liquid Measure, and is equal in volume to a cubic decimeter. Table. 10 mirii-li'ters (ml.) = 1 cen'ti-li'ter, . . . cl. (ikO 10 cen'ti-li'ters = 1 dec'i-li'ter, . . . . dl. (tV *0 10 dec'i-li'ters = 1 LITER, . . . . . 1. 10 li'ters sb 1 dek'a-li'ter, . . . Dl (101) 10 dek'a-li'ter = 1 hek'to-li'ter, . . . El. (100 I.) 10 hek'to-li'ters = 1 kil'o-li'ter, . . . . Kl. (1000 I) 10 kil'o-li'ters ss 1 myr'ia-li'ter, . . . Ml. (10000 I.) 1 cubic centimeter = 1 milliliter of water. Common E QUI VA LENTS. 1 liter bb 61.022 cu. inches. 1 liter = 1.0567 liquid quarts 1 liter = 0.908 dry quarts. 1 hektoliter = 3.531 cu. feet. 1 hektoliter = 26.417 gallons. 1 hektoliter ss 2.837 bushels. Notes. — 1. The Centiliter is a little less than | gill, and is used for measuring liquids in small quantities. 2. The Liter is used in measuring milk, wine, and small fruits, and is about equal to a quart. 3. The Hektoliter is used in measuring grain and liquids in casks, and is equal to about 26| gal., or 2f bushels. • 31. In 128.653 ml. how many dl.? How many cl.? 32. Write 35 1. as cl. As ml. As Dl. 33. How many liters in a cistern measuring 2 cu. meters ? 34. How many Dekaliters in such a cistern ? How many HI.? Metric System. 49 METRIC WEIGHT. 135. The Gram is the principal unit of weight, and is equal to a cubic centimeter of distilled water at its greatest density, viz., at 4° Centigrade, or 39.2° Fahrenheit. 10 milli-grams (rng.) = 10 cen'ti-grams = 10 dec'i-granis = 10 grams == 10 dek'a-grams = 10 hek'to-grams = 10 kil'o grams = Table. 1 cen'ti-gram, 1 dec'i-gram, . 1 GRAM, . . 1 dek'a-gram 1 hek'to-gram, 1 kil'o-gram, dg. 9- Dg. Hg. Kg. (tV or Y S 1, — IT 8 1, denominations, and to a common denomina- -| gi. = T 4 ^ gi. tor, then added. Am ^ gi> 6. Find the sum of £J f s. Jd. in integers. 7. Add f lb. |- oz. f pwt. 9. Add f wk. { d. If hr. 8. Add J gal. f qt. 2£ pt. 10. Add £| |s. 4|d. SUBTRACTION. 11. From 18s. 8d. take 13s. lOd. Note. — Since lOd. cannot be taken from 8d., it be- 18s. 8d. comes necessary to add Is. = 12d. to 8d., making 20d., jcj iq and 10 from 20 leaves lOd. Then 17s. - 13s. = 4s. -— The remainder is 4s. lOd. ^ *-®> Ans. 12. From 24 mi. 7 fur. 8 rd. 12| ft. take 15 mi. 6 fur. 30 rd. 4| feet. 13. From 1 lb. take 10 oz. 17 pwt. 18 gr. 14. From £2$ take 7f shillings. 15. A barrel (31^ gal.) is £ full ; if 7 gal. are drawn off, what part of the contents will remain ? Subtraction. 61 157. To find the Exact Number of Years, Months, and Days, between two dates. 16. What is the difference of time between Sept. 12, 1882, and Dec. 25, 1884 ? Analysis.— The time from Sept. 12, 1882, to Sept. 12, 1884 = 2 yr. The time from Sept. 12th to Dec. 12th = 3 mo. The time from Dec. 12th to Dec. 25th =13 d. Ans. 2 yr. 3 mo. 13 d. Hence, the Eule. — First find the number of entire years, next the number of entire months remaining, then the days in the parts of a month. Note. — 1. The day on which a note or draft is dated, and that on which it becomes due, must not both be reckoned. It is customary to omit the former and count the latter. 17. How much time between Nov. 10, 1876, and May 15, 1883? 18. A note dated Dec. 12, 1871, was paid Oct. 1, 1884 ; how long did it run ? 19. Wellington was born May 1, 1769 ; how old was he at the date of the battle of Waterloo, which occurred June 18, 1815? 20. Find the exact number of days between Apr. 10, 1879, and Aug. 25, 1880. Note.— 2. In finding the operation. exact time by days, write Apr. 10, '79 to Apr. 10, '80 = 365 d. down 365 d. as the time Apr. 30-10 = 20 d. May has - 31 d. June <•' 30 d. days remaining in the first " u ty «H ". and each succeeding month ; Aug. " 25 d. the sum is the number of An S 502 d days required. 21. How many days did a note run dated June 1, 1879, and paid Sept. 28, 1880 ? 22. How many days from June 13, 1869, to Sept. 30 fol- lowing ? from the first date to the same date the next year then write in a column the 62 Compound Numbers. 23. From May 6, '81, to Aug. 11, '82 ? 24. From Apr. 24, '82, to July 4, '83 ? 25. From Jan. 28, '75, to Feb. 6, '76 ? 26. From Dec. 25, '82, to Jan. 31, '83 ? 27. The latitude .of Cape Cod is 42° 1' 57" N., that of New York is 40° 42' 43"; what is the difference of their latitude? Note. — 3. When two places are on opposite sides of the Equator, the difference of latitude is found by adding their latitudes. 28. The latitude of Havana is 23° 9' N., that of Cape Horn is 55° 59' S. ; what is the difference ? 29. The latitude of Valparaiso is 33° 2' S., that of St. Au- gustine is 29° 48' 30" N. ; what is the difference ? MULTIPLICATION. 158. l. Multiply 2 lb. 8 oz. 5| pwt. 4 gr. by 8. Explanation.— Multiply each 2 lb. 8 oz. 5| pwt. 4 gr. denomination separately and unite % g like denominations as in addition. Or the multiplicand may be reduced Ans - 21 lb - 6 oz - 5 P wt - 8 g r - to the decimal of a pound by Art. 154. Note. — If a fraction occurs in the product of any denomination except the lowest, it should be reduced to lower denominations, and be united to those of the same name as in Compound Addition. (Art. 156.) 2. Multiply £12 8s. 6d. by 6. 3. Multiply 17 gal. 3 qt. 1 pt. 2 gi. by 8. 4. Multiply 48 mi. 3 fur. 10 rd. by 12. 5. Multiply 2 hr. 45 min. 17 sec. by 25. 6. Multiply 48° 25' 17" by 28. 7. Multiply 28 bu. 6 pk. 5 qt. by 13. 8. Of 36 persons visiting the Crystal Palace, London, 17 spent 16s. lfd. apiece; each of the rest spent 8s. 10-Jd, more than each of the 17 5 how much did they all spend ? Longitude. 63 DIVISION. 159. 9. A man paid £15 12s. 6^d. for 8 chests of tea ; what was that a chest ? Note.— Since 8 chests cost £15 12s. operation. 6Jd., 1 chest will cost j as much, and 8 ) £15 12s. 6^d . £15+8 = £1, and £7 over. Reducing An§ £± 19g Q(L g, far> £7 to shillings and adding the 12s. gives 152s., which divided by 8 is 19s. The pence cannot he divided by 8, but 6£ d. = 25 far., which +8 = 3^ far. Am. £1 19s. 3± far. 10. Divide 12 gal. 3^ qt. by 5. 12. 18s. 3£d.-r-5 == ? 11. Divide 24 bu. 3| pk. by 7. 13. 83° 19' 9"-f-15 = ? 14. How many cords in a pile of wood 196 ft. long, 7 ft. 6 in. high, and 8 ft. wide ? 15. Paid £1 7s. 7Jd. for a boy's coat and vest ; the price of the coat was double that of the vest ; what price was the vest ? 16. If a franc is $.193, how many francs equal $1500 ? 17. An importer paid £48 7s. 3d. for English files, at £1 6s. 6d. per dozen ; how many dozen did he import ? 18. If a rail-car goes 17 mi. in 45 min., how far will it go in 5 hr. at the same rate ? • 19. In 4 mi. 3 fur. 28 rd. 4 yd., how many kilometers ? LONGITUDE. 160. The Longitude of a place is the number of deg., min., and sec, reckoned on the equator, between a standard meridian (marked 0°) and the meridian of the given place. All places are in East or West longitude, according as they are East or West of the Standard Meridian, until 180°, or half the circumference of the Earth is reached. Notes. — 1. The English reckon longitude from the meridian of Green- wich ; the French from that of Paris. Americans generally reckon it from the meridian of Greenwich ; sometimes from that of Washington. 2. When two places are on opposite sides of the Standard Meridian, the difference of Ion. is found by adding their longitudes. (Art. 157, N ( . 3.) 64 Compound Numbers. 161. Comparison of Longitude and Time. 162. The Earth turns on its axis once in 24 hours ; hence, ■fa part of 360°, or 15° of longitude, passes under the sun in 1 hour. Again, -fa of 15° Ion., or 15', passes under the sun in 1 min. of time. And -fa of 15', or 15" Ion., passes under the sun in 1 sec. of time, as seen in the following Table. 360° Ion. make a difference of 24 hrs. of time. 15° « " « lhr. " 4 mm. 1' " " " 4 sec. 1" " " " T Vsec. 163. To find the difference of Longitude between two places, the difference of Time being known. 1. The difference of time between St. Petersburg and Wash- ington is 7 hr. 9 min. 19£ sec. What is the difference of longitude ? Explanation. — Every 15' of Ion. operation. makes a difference of 1 min. of time ; 7 hr. 9 mill. 19 J sec. hence there must be 15 times as many 15 min. of Ion. as there are min. and „ seconds of time, and (7 hr. 9 min. 19£ sec.) Ans ' iU7 iy 4y * x 15 = 107° 19' 48f". Hence, the Kule. — Multiply the difference of time, ex-pressed in hours, minutes, and seconds, by 15 ; the product will be the difference of longitude in degrees, minutes, and seconds. (Art. 162.) 2. A ship sailing westward reached a point where its chro- nometer at noon showed the time at Greenwich to be 6 hr. 45 min. 28 sec, p. M. ; what was its longitude ? 3. If the difference of time between two places is 19 min. 12 sec, what is the difference of longitude ? 4. The difference of time between New York and Chicago is 54 min, 30J- sec What is the difference of longitude ? Longitude. 65 5. If the time at Greenwich is 4 hr. 56 min. 4^ sec. when it is noon at New York, what is the difference of longitude ? 164. To find the Difference of Time between two places, the Difference of Longitude being known. 6. When it is 2 hr. 36 min., A. m., at Cape of Good Hope, Ion. 18° 24' E., what is the time at Cape Horn, Ion. 67° 21' AY. ? Explanation.— The difference of longitude 18° 24' E. between two places on opposite sides of the g^° 21' W. standard meridian is found by adding their Ion- — • gitudes. As there are ^ as many hrs., etc., as -^ / "^ ^ ^ l ^ there are deg., the difference of time is 5 hr. 43 min. Ans. 5 hr. 43 min. Again, 12 hr.— 5 hr. 43 min. = 6 hr. 17 min. Adding to this the time before 12, 2 36 Gives the hour before midnight. 8 hr. 53 min., Ans. Hence, the Eule. — Divide the difference of longitude, in degrees, minutes, and seconds, by 15 ; the quotient will be the difference of time in hours, minutes, and seconds. Note. — Add the difference of time for places east, and subtract it for places icest of a given meridian. 7. New York being 3° E. from Washington, and San Fran- cisco 45° 25' W., what time will it be at New York when it is noon at San Francisco ? 8. The difference of Ion. between Albany and San Fran- cisco is 48° 41' 55" ; what is the difference of time ? 9. Constantinople is in Ion. 28° 49' E., St. Paul 93° 4' 55" W. ; when it is 2 o'clock p. m. at St. Paul, what time is it at the former place ? io. Mobile, Ala., is 88° 1' 29" W. Ion. ; Cambridge, Eng., is 5' 2" E. Ion. When it is noon at Mobile, what time is it at Cambridge ? n. How much earlier does the sun rise in Boston, Ion. 71° 3' 30", than in New Orleans, Ion. 90° 2' 30" ? 12. Than in Astoria, Ion. 124° ? St, Louis, 90° 15' 15"? 13. Than in Chicago, Ion. 87° 37' 45" ? 5 66 Weights and Measures. APPLICATION OF WEIGHTS AND MEASURES. ^AD- MEASUREMENT OF SURFACES. 165. A Surface is that which has length and breadth only. 166. An Angle is the opening between two lines which meet at a point, as BAC. The Lines AB and AC are called the sides ; and the Point A, at which they meet, the Vertex of the angle. 167. When two straight lines meet so as to make the two adjacent angles equal, the lines are Perpendicular to each other, and the two angles thus formed are called Right Angles; as, ABC, ABD. 168. A Plane Figure is one which repre- sents a plane or flat surface. 169. The Perimeter of a plane figure is the line which bounds it. 170. The Area of a plane figure is the quantity of surface it contains. 171. The Dimensions of a plane figure are its length and breadth. 172. A Rectangle is a plane figure having four sides and four right-angles. (Art. 168.) 173. When all the sides of a rectangle are equal, it is called a Square. 174. When its opposite sides only are equal, it is called a Parallelogram, Measurement of Surfaces. 67 175. The measuring unit of surfaces is a Square, each side of which is a linear unit. 176. To find the Area of Rectangular Surfaces. 1. How many square rods in a field 28 rods long and 12 rods wide ? Solution. — A rectangle 28 rods long and opekation. 1 rod wide will contain 28 sq. rods. And a 28 rods, field 28 rods long and 12 rods wide will con- -j o tain 12 times 28, or 336 square rods, Ans. Hence, the An ^ 336 sq. rods. V Kule. — Multiply the length by the bj^eadth. ( 1. Area = Length x Breadth. Formulas. — •< 2. Length = Area -^ Breadth. ( 3. Breadth = Area -+■ Length. Notes. — 1. Both dimensions should be reduced to the same denomina- tion before they are multiplied. 2. One line is said to be multiplied by another, when the number of units in the former are taken as many times as there are like units in the latter. (Art. 10, 2°.) 2. Bought a rectangular farm 245 rods long and 88 rods wide, at $75 per acre ; what was the cost ? 3. How many yards of carpeting, 27 in. wide, will be required to cover a floor 22 ft. long and 15 ft. wide ? Note. — This and similar examples admit of two answers, each of which is correct ; the one in a mathematical sense, the other in a com- mercial sense. 1st. There are 36| sq. yds. in the floor; to cover this requires 48f yards of carpeting, 27 in. wide. 2d. The exact number of sq. feet in a floor does not always correspond with the quantity of carpeting which must be bought to cover it. Since 6| breadths, 3 qrs. wide and 7^ yds. long, are required to cover the floor, and the fractional breadth must be as long as any other, it will be necessary to buy 7 times 7| yds. = 51^ yards. 4. A building lot is 150 ft. front and contains 2 A. ; how far back does it extend ? 68 Weights and Measures. 5. A man bought a rectangular field containing 3750 sq. rods, the length of which was 75 rods, at $15 per acre ; what was its breadth and what did it cost? 6. How many rolls of paper 25 ft. long and 18 in. wide will be required to cover a wall 26 ft. long and 13 ft. high? 7. What will it cost to concrete a court that is 268 ft. square, at $3.86 per sq. yard ? 8. How many sq. inches in a flat roof 54 ft. long and 25 ft. wide? 177. To find the Area of an Oblique-angled Parallelogram, the Length and Altitude being given. Multiply the length by the altitude. Note. — If the area and. altitude, or one side are given, the other factor is found by dividing the area by the given factor. (Art. 30, 3°.) 9. What is the area of an oblique-angled parallelogram whose length is 60 ft. and its altitude 53 feet ? Ans. 3180 sq. feet. 10. A grove in the form of an oblique-angled parallelogram contains 80 acres, and the length of one side is 160 rods; what is its width ? Note. — The area of a square, a rectangle, a rhomboid and rhombus is found in the same manner. 11. How many sq. feet in a piece of land 13 rods square? 12. One side of an acre of land in shape of a rectangle is 9 rods long ; what is the length of the other side ? 13. What cost a field 77 rd. long and 41 rd. wide, at $18.60 an acre ? 178. To find the Area of a Trapezoid, when its Parallel Sides and Altitude are given. 14. The parallel sides of a trapezoid are 26 ft. and 38 ft., and its altitude 14 ft. ; find its area ? Solution.— The sum of the parallel sides 26 + 38 = 64 ft. ; \ of 64 = 32 ft., and 32 x 14 = 448 sq. ft., Ans. Hence, the Measurement of Rectangular Bodies. 69 Rule. — Multiply half the sum of the parallel sides by the altitude. 15. What is the area of a board 13 in. wide, one side of which is 24 in., the other 28 inches ? 16. The two parallel sides of a field are 85 and 90 rods, and the distance between them 54 rods ; how many acres were there ? MEASUREMENT OF RECTANG-ULAR BODIES. 179. A Rectangular Body is one bounded by six rectangular sides, each opposite pair being equal and parallel ; as, boxes of goods, blocks of hewn stone, etc. 180. When all the sides are equal, it is a Cube ; when the opposite sides only are equal, it is a Parallelopiped. 181. The Contents or Volume of a body is the quantity of matter or space it contains. 182. The Dimensions of a rectangular body are its length, breadth, and thickness. 183. To find the contents op volume of Rectangular Bodies. l. How many cu. ft. in a box of goods 4 ft. long, 3 ft. wide, and 2 ft. thick ? Solution. — Since the box is 4 ft. long and 3 ft. wide, there are 12 sq. ft. in the upper face. If the box were 1 ft. thick it must have as many cu. ft. as there are sq. ft. in the upper face. But it is 2 ft. thick and therefore con- tains (4 x 3) x 2 = 24 cu. feet, Ans. Hence, the Rule. — Multiply the length, breadth, and thickness together. (Art. 30, 3°.) Notes. — 1. When the contents and two dimensions are given, the other dimension may be found by dividing the contents by the product of the two given dimensions. (Art. 30, 3°.) y y y y a > /^j I ji.n.1 1, |-||: n^i7Fpr 70 Weights and Measures. 2. Excavations and embankments are estimated by the cubic yard. In removing earth, a cu. yard is called a load. 2. What will it cost to dig a cellar 40 ft. long, 32 ft. wide, and 8 ft. deep, at 25 cts. a cubic yard ? 3. How many cu. meters in a mound whose length, breadth, and height are each 6.4 meters ? 4. How many loads of earth must be removed in digging a cellar 40 ft. long, 20 ft. wide, and 8 ft. deep ? 5. How many cu. ft. in 10 boxes, each 7| ft. long, If ft. wide, and 1J- ft. high ? CISTERNS, BINS, ETC. 184. The Capacity of rectangular cisterns, bins, etc., is measured by cubic measure, but the results are commonly expressed in units of Liquid and Dry Measure. 185. To find the Number of Gallons in Rectangular Cisterns, etc. 6. How many gallons will a rectangular vat 6 ft. long, 5 ft. wide, and 4 ft. deep contain ? Solution.— The product of 6 ft. x 5 x 4 = 120 cu. feet ; and 120 x 1728 = 207360 cu. inches. Again, in 1 gallon there are 231 cu. inches, and 207360-^-231 = 897f* gal., Ans. (Art. 69.) 7. How many bushels will a box 8 ft. long, 4 ft. wide and 3 ft. high contain? Solution.— 8 x 4 x 3 = 96 cu. ft. and 96 x 1728 = 165888 cu. in. Since 2150.4 cu. in.=: 1 bu., 165888 cu. in. = 165888^-2150.4 = 77$ bushels., Ans. Hence, the Eule. — Find the number of cubic inches in the object measured, and reduce them to liquid or dry measure, as may be required. (Arts. 69, 71.) 8. How many gallons would a cistern 7 ft. long by 6 ft. wide and 11 ft. deep contain ? 9. At 30 cts. a square yd., what would be the cost of plaster- ing the bottom and sides of such a cistern ? Measurement of Lumber. 71 10. If a reservoir 45 ft. long, 28 ft wide, contains 45360 hhd., how high must it be ? n. At $1.12! a bushel, what is the value of a bin of wheat 9 ft. long, 7 ft. wide, and 4 ft. deep ? 12. A farmer had a bin 8 ft. long, 4£ ft. wide, and 2£ ft. deep, which held 67| bu.; how deep should another bin be made which is 16 ft. long, 4£ ft. wide, that its capacity may be 460 bushels ? 13. How many hogsheads of water will a cistern hold, which is 5 ft. 6 in. square and 8 ft. deep ? MEASUREMENT OF LUMBER. 186. A standard Board Foot is 1 ft. long, 1 ft. wide, and 1 in. thick ; that is, a square foot 1 inch thick. Hence, A Cubic Foot is equal to 12 board feet. 187. A Board Inch is T V of a board foot ; that is, 1 inch long by 12 inches wide and 1 inch thick. Hence, Twelve board inches are equal to 1 board foot. 188. Sawed timber, as plank, joists, etc., is estimated by cu. feet ; hewn timber, as beams, etc., either by board feet or cu. feet; round timber, as masts, etc., by cu. feet. 189. To find the Contents of Boards, Planks, etc. 1. How many board feet in a board 13 ft. long, 18 in. wide, and 1 inch thick ? Explanation. — Multiplying the length operation. in feet by the width and thickness expressed 13 X 18 X 1 =■ 234 in. in inches, we have 234 board inches. Divid- 234-^12 = 19i ft. ing this product by 12, the result is 19.1 board . i qi -Pf feet, Ans. MS ' L ^ U ' 2. How many board feet in a scantling 14 ft. long, 6 in. wide, and &| in. thick ? Solution.— Multiplying the length in feet by the width and thickness expressed in inches, we have 14x6x2§ = 210 in., and 210 + 12 = 17£ board ft., Ans. Hence, the 72 Weights and Measures. Rule. — Multiply the length in feet by the width and thickness expressed in inches, and divide the product by 12 ; the quotient will be in board feet. Notes. — 1. The standard thickness of a board is 1 inch. If less than 1 inch, it is disregarded ; if more than 1 inch, it becomes a factor in find- ing the contents of plank, scantling, etc. If one of the dimensions is inches, and the other two are feet, the 'product will be in Board feet. 2. If a board is tapering, multiply the length by half the sum of the two ends 3. The approximate contents of round timber or logs may be found by multiplying | of the mean circumference by itself, and this product by the length. 3. How many feet in a board 14 ft. long and 18 in. wide, and of standard thickness ? 4. Find the contents of a tapering board 15 ft. long, 16 in. wide at one end and 11 in. at the other ? 5. What cost 125 boards 11 ft. long, and 15 in. wide, at 4£ cents a board foot ? 6. What cost 28 joists whose dimensions are 4 in. by 3J in. and 11 ft. long, at 25 cts. a cu. foot? 7. How many cu. feet in a log 65 ft. long, whose mean circumference is 12 ft. ? 8. How many cu. ft. in a beam 24 ft. 6 in. long, 1 ft. 9 in. wide, and 1 ft. 2J in. thick ? 9. How many feet of boards would be required to build a fence 4 ft. high and 126 ft. long, and what would be the expense at $2£ for 100 feet? 10. What cost a ship's mast 56 ft. long and 9 ft. in circum- ference, at $1. 12 J per cu. foot ? 11. How many boards 12 ft. long and 4 in. wide are required for a floor 36 ft. by 27 ft. ? 12. How many feet of boards would be needed to make 9 piano boxes, the interior dimensions of which are 6 ft. 8 in., 5 ft. 7 in., and 3 ft. 6 in. respectively, the boards being 1 J in. thick ? Masonry. 73 MASONRY. 190. Stone Masonry is usually estimated by the perch ; Brickwork by the thousand bricks. Notes. — 1. A perch of stone masonry is 16| ft. long, \\ ft. wide, and 1 ft. high, which is equal to 2 4 J cu. ft. It is customary, however, to call 25 cu. ft. a perch. 2. The average size of bricks is 8 in. long, 4 in. wide, and 2 in. thick. In estimating the labor of brickwork by cu. feet, it is customary to measure the length of each wall on the outside ; no allowance being made for windows, doors, or corners. But a deduction of ^ the solid contents is made for the mortar. 1. In the walls of a cellar, the thickness of which is 1 ft. 6 in., the height 8 ft., each side wall 52 ft., and each end wall 25 ft. ; how. many perch (25 cu. ft.) ? 2. At I4.87J a perch, what will it cost to build the walls of the above cellar ? 3. How many bricks are required for a building the walls of which are 58 ft. long, 25 ft. wide, 44 ft. high, and 1 ft. thick, making no allowance for windows, doors, corners, or mortar ? 4. At $3.75 per M. for bricks, and $4.25 per M. for laying them, deducting ^ for mortar, what will the walls of such a building cost? APPLICATIONS OF UNITED STATES MONEY. 191. United States Money is added, subtracted, multiplied, and divided like Decimal Fractions, and requires no special rules. 1. A man has farms valued at $56850, city lots at $86960, a house worth $12800, and other property $8750 ; what is the whole worth? Ans. $165360. 2. If a student's expenses are $198 for board, $37.50 for clothes, $150 for tuition, $35.87 for books, $27.37£ for inci- 74 United States Money. dentals, annually, what would it cost a year to educate 4 boys at the same rate ? 3. The cost of laying the Atlantic Cable was as follows : 2500 mi., at $485 per mile ; 10 mi. deep sea cable, at $1450 ; 25 mi. shore ends, at $1250 ; what was the whole cost ? 4. Bought wheat at 94 cts. a bushel to the amount of $59.22, and sold for $70.56; what was the selling price per bushel ? 5. In selling 86.55 tons of coal, at $5. 64 per ton, a merchant made $100.63 ; how much did it cost him a ton ? 6. Paid $2225 for 180 sheep, and sold them for $2675 ; what should I gain on 1500 sheep at the same rate ? 7. A man bought an acre of land for $1250 ; he afterwards sold 100 ft. square for $1000, and divided the remainder into lots of 25 x 100 ft., which were sold at $500 each ; how many lots did he sell, and how much did he make in the transaction ? METHODS BY ALIQUOT PARTS. 50 cts. = $4. 12J cts. s= $4. 40 cts. ss $| 334 cts. = $f 10 cts. ss $ 1 l 37J cts. = $| 25 cts. sa $J. Si cts. = $ T V 62J cts. = ! 20 cts. ss $-§. 6£ cts. = $^g-. 75 cts. = I 16 1 cts. = $f 5 cts. s= $^. 87 J- cts. = I 192. To find the Cost of a number of like things, when the Price of one is an Aliquot Part of $1. 8. At 33 J cts. each, what cost 576 Grammars? Analysis.— At $1 each they would cost $576; but the 3 ) 576 price is 33J cts. = $^, and 576-J-3, or x| = 192. Hence, the jins. $192 Eule. — Multiply the given number of things by the fractional part of $1 which expresses the price of One; the result is the cost. (Complete Grad. Arith., Art. 208.) 9. What cost 17 chests of tea of 59 lbs. each, at 33| cts. a pound ? Aliquot Parts. 75 10. Sold 18 bbl. pork of 200 lb. each, at 12£ cts. a pound ; what did it come to ? 11. Find the cost of 158 tons coal, at $5.33£ a ton. 12. 170 lb. soap, at 8 J cts. a pound. 13. 264 lb. raisins, at 25 cts. a pound. 14. 295 lb. 8 oz. butter, at 33| cts. a pound. 15. 756 yd. calico, at 20 cts. a yard. 16. 275 doz. eggs, at 12£ cts. a dozen. 17. 1260 pine apples, at 16f cts. a piece. 18. What cost 4 lb. 5 oz. 6 pwt. of gold dust, at 75 cts. a pennyweight ? 19. A man gave 87-J cts. a sq. rd. for 503 A. of land; what did it cost him ? 20. What would be the cost of enclosing a square lot of 160 acres with a fence costing 75 cts. a yard ? (Art. 621.) 193. To find the Number of Like Tilings when their Cost is given, and the Price of One is an Aliquot Part of $1. 21. How many pounds of coffee at 33J cts. a pound can be bought for $84.50? Analysis. — Since the price is %\ a operation. pound, $1 will buy 3 pounds, and $0.33^ = $J $84.50 will buy 84.50 x 3 = 253.5 lb. 84 50 x 3 = 253 5 Or, at §1 a pound $84.50 will buy as Qr m / 5Q ^ $i _ gg^g lb . many pounds as $| is contained times 6 in $84.50, or 253.5 pounds, Ans. Hence, the Rule. — Divide the cost of the whole by the aliquot part of $1 ivhich is the price of One. 22. How many lb. butter at 33-J- cts. can be bought for 56 lb. tea, at 62£ cts. 23. What cost 3 bu. 2 pk. 3 qt. of peas, at 87J- cts. a peck ? 24. If a man can pay 62-J cts. on a dollar, how much can he pay with $1352.50 ? 76 United States Money. 25. Bought 14 bbl. salt of 4 bu. each, at $1.40 a barrel, and sold it at 10 cts. a peck ; what was the gain ? 26. At 6J cts. a foot, how many planks each measuring 26 ft. 9 in., can be bought for $36.78£? 27. How many bales of cotton of 450 lb. each, at 37J cts. a pound, are equal in value to 15 hhd. sugar of 1800 lb. each, at 8-J cts. a pound ? 194. To find the Cost of a number of articles, the Price of one being $1 plus an Aliquot part of $1. 28. At $1.25 a bu., what cost 568 bushels of wheat ? Analysis.— At $1 a bu., the cost would be $568. 4 ) ^68 But the price is $1£, therefore 568 bu. will cost 568+ 142 143 (i of 568) = $710. Hence, the |^ 10 j_ ngt Rule. — To the number of articles, add its proper frac- tional part ; the sum will be their cost. 29. At I1.37J- per sq. rd., what cost 263 A. of land ? 30. Bought in Michigan 300 bu. of oats, at 1\ cents a pound ; what did they cost ? (Art. 72.) 31. Bought in New York 286440 lb. wheat, what is its value at$1.87iabushel? 195. To find the Cost, when the price per 100 or 1000 is given. 32. What cost 2925 lb. sugar, at $12.50 a hundred ? Solution.— 2925 lb.=Yinr of 100 lb., and ??=Lj£— = $365. 62|, Arts. 33. At $4.33£ per M., what cost 2367 bricks ? Solution.— The price per M. = $4^; then 3)2367 (2367 x 4 ) + (2367-^3) _ 4 looo- -- cost ^ Or, multiply the number of bricks by 4, add \ of ~oq the same number to the product, and divide by 1000 by pointing off 3 figures in the result. Hence, the $10,257 Aliquot Farts. 77 Kule. — Multiply the price per hundred or thousand by the given number of things, and divide the product by 100 or 1000, as the case may require. (Art. 10, 4°-) Note. — In business transactions, the letter C is put for hundred; and M for thousand. 34. What cost 536720 bricks, at $8.75 per M.? 35. What cost 125268 feet of boards, at $31.25 per thou- sand ? 36. At $5f per hundred, how much will 25345 pounds of flour come to ? 196. When the cost of 100 or 1000 articles, pounds, etc. , is given, the price of one is found by simply removing the decimal point in the given cost or dividend, as many places to the left as there are ciphers in the divisor. (Art. 264, Com. Grad. Arith.) 37. If pine boards are $21.63 per 1000 ft., what is that per foot? Ans. $.02163. 38. Bought wheat in N. Y. at $3.1 2 \ a cental ; what would 6410§ bu. cost at the same rate ? 39. If 12£ cw.t. of sugar cost $140, what is that a pound ? 197. To find the Cost, when the price of a ton of 2000 pounds is given. 40. What cost 5460 pounds of hay at $8.50 per ton ? Explanation.— At $8.50 a pound, 5460 lb. will 5460 cost $46410. But the price is per ton of 2000 lb. ; § 5q therefore dividing by 2, and removing the decimal point 3 places to the left, will give the answer. 2000 ) 46410 .00 Hence, the £ nSm $23,205 Eule. — Multiply the price of 1 ton by the given num ber of pounds and divide the product by 2000. 41. What is the freight, at $5.40 per ton, on an exportation of 9654 pounds of cotton ? 42. Bought 26 sacks of wool, weighing 560 lb. each, at $26.50 per ton ; what did it cost ? 78 United States Money. BILLS OF MERCHANDISE. 198. A Bill is a written statement of goods sold, or services rendered, with their prices, etc. Note. — Bills should always state the names of both parties, the place and time of each transaction, the name and price of each item, and the amount. 199. A Bill is Receipted when the words " Received Pay- ment" are written at the bottom, and it is signed by the creditor, or by some person duly authorized. Exam ples. Copy and extend the following bills : (l. Bill of Dry Goods.) Boston, Jan. 28th, 1883. Mr. James Mitchell, BoH of W. Starbuck & Co. (Cash after 30 days.) 23 yds. silk 15 yds. broadcloth, 23 yds. cambric, 13 doz. buttons, 26 skeins sewing silk, 14 yds. wadding, 47 yds. bl. muslin, 35 yds. Can. flannel, 42 yds. calico, 12 doz. Brooks' cotton, } doz. fancy hose, 8 pr. kid gloves, @ $2.12} @ 3.75 @ .12} @ .25 @ .06J @ .08 @ .12 @ .14 @ .12} @ 1.08 @ 10.00 @ 2.00 Amount, - - Bec'd PayH, W. Starbtjck & Co. Bills of Merchandise. 79 (2. Books.) Messrs. J New York, May 15th t 1883. C. Griggs & Co., To Clark & Maymrd, Dr. 1883. May 1 For 150 U. S. Histories, © I0.62J « 72 Rom. " @ 1.15 " 96 Grammars, @ .65 " 200 Com. Graded Arith., @ .75 " 125 Prac. Algebras, @ .83 " 65 Col. " @ 1.05 " 84 Physiologies, @ 1.10 Amount, - - Redd PayH, By Draft on Boston, Clark & Maynard. (3. Statement of Account.) San Francisco, Oct. 3, 1882. Messrs. Robert Standart & Brother, In Acct. with Scott & Merwin, Dr. 1882. June 4 a 15 July Aug. Sept. 8 10 20 July 1 20 Aug. Sept. 10 25 165 tons R.R. iron, 25 cwt. Steel Wire, 48 doz. Axes, 125 Saws, 342 cwt. Lead, $45.25 21.50 10.40 3.75 7.40 Or. 500bbls. Flour, @ 5.40 456 bu. Wheat, @ 1.17 Dft. on JSTew York, 112 shares Mining Stock, @ 75.00 Bal. due, - - Rec'd PayH, Scott & Merwin, 400 Per Charles Kingsford. 80 United States Money. Entry Cler k s Drill. 200. Enter the following memorandum, made at Detroit, Mich., and find the amount of the bill : Mem.— A. B. bought of 0. D., Apr. 15th, 1883, 624 lbs. Java coffee, at 25 cts. ; 420 lbs. green tea, at 75 cts. ; 648 lbs. gran- ulated sugar, at 12£ cts.; 528 lbs. brown do., at 6J cts.; 350 lbs. bar-soap, at .05; 428 gal. linseed oil, at 87| cts. Common Form Messrs. A. B., Detkoit, Mich., Apr. 15th, 1883. Bought of C. D. 624 lbs. Java Coffee, @ 25 cts. 420 lbs. Green Tea, @ 75 cts. 648 lbs. Granulated Sugar, @ 12 j- c. 528 lbs. Brown " @ 6£ c. 350 lbs. Bar Soap, @ 5 cts. 428 gal. Linseed Oil, @ 87£ c. Amount, - - Redd Pay% 5. W. A. Sanford, Esq., of Philadelphia, bought, June 3d, 1883, of James Conrad, 28 yds. of silk, at $1.75 a yard; 42 yds. of muslin, at 56 cts. ; 16 pairs of cotton hose, at 87J cts.; 35 pair of silk hose, at $2.10; and 25 pair of shoes, at $3.25. What was the cost of the several articles, and how much is due on his account ? 6. Holmes & Homer of Cincinnati, bought, July 1st, 1882, of H. W. Morgan & Co., 100 bbls. flour, at $5.50 a barrel; 50 bbls. pork, at $8.25 ; 25 bbls. beef, at $9.75 ; 112 kegs of lard, at $3.25 ; and 25 bu. corn, at 74 cts. What was the cost of the several articles, and how much is due on his account ? ^^ r° » ... EROENTAGE. 201. Percentage is the method of calculating by hundredths, 202. The term Per Cent (from the Latin per and centum), means by the hundred, or simply hundredths. 203. The Rate Per Cent is the number of hundredths to be found or taken. It may be expressed by the sign %, by a deci- mal, or by a common fraction. Table. Sign. Decimal. Fraction. Sign. Decimal. Fraction 1% .01 =3 TOO" i% .005 — T0~0 5% .05 = * H% .025 = A Wo .10 = tV Wo .0025 — loo 25% .25 = i H% .0625 = A 50% .50 =s i m% .1875 = A 75% .75 = f 3H% •33i = i 100?/ 1.00 = i im% 1.125 = H 204. Since hundredths occupy two decimal places, every per cent requires, at least, two decimal figures. Hence, if the given per cent is less that 10, a cipher must be prefixed to the figure denoting it. Thus, %% is written .02; 6%, .06, etc. Notes. — 1. A hundred per cent of a number is equal to the number itself; for }£§ is equal to 1. 2. In expressing per cent, when the decimal point is used, the words per cent and the xigit ( +PUU. UU Ans. 4000 81. What number diminished by 25$ of itself is 4560? Analysis.— Since 4560 = 100% -25%, it must be 1 — ,35 = ' 75 75% of the number, and 4560-=-.75 = 6080, the num- .75 ) 4560.00 ber required. Hence, the j^T qqqq Eule. — Divide the amount by 1 increased by the rate. Or, Divide the difference by 1 diminished by the rate. „ d _ i Amount -j- (1 -f Rate). ~ \ Difference -^ (1 — Rate). What number plus What number minus 82. 12f$ of itself = 24129 ? 86. 36% of itself = 3360 ? 83. 10$ of itself = 1540 ? 87. 5$ of itself = 3078 ? 84. 33J% of itself = $3680 ? 88. 25$ of itself = 450 ? 85. 25$ of itself = 5000 ? 89. 7-|$ of itself = 6475 ? 90. Sold 1900 bbl. flour for $11520, which was 20$ above cost ; what was the whole cost and the cost per barrel? Percentage. 87 91. A dealer sold 1600 bbl. beef for $24000, which was a loss of 25$ ; what did the whole cost, and what did he get a barrel ? 92. A builder sold a house for 18250, which was 12$ more than it cost him ; what was the cost? Exam ples. 1. What is the cost of a house which sells at a loss of 7£$, the selling price being $11500 ? 2. A merchant owes $12575, and his assets are $7500 ; what per cent can he pay ? 3. Sold 2 city lots at $1500 each ; on one I made 15$, on the other I lost 15$ ; what did I gain or lose ? 4. If 15$ of what is received for goods is gain, what is the gain per cent ? 5. Sold goods for $29900 and made 15$ after deducting 5$ for cash ; what was the cost? 6. 240 is 33^$ more than what number ? 7. A collector who has 8$ commission, pays $534.75 for a bill of $775 ; what amount of the bill does he collect ? 8. What is \% of $1728? 9. What is 9|$ of 275 miles? 10. What is the difference between 5£$ of $800 and 6£$ of $1050 ? 11. Bought 300 long tons coal at $3.75 a ton and sold it at $4.60 a short ton ; what is the per cent profit ? 12. Bought a barrel of syrup for $20 ; what must I charge a gallon in order to gain 20$ on the whole ? 13. Sold 25 tons coal at $5.64 per ton, and made $62; what did the coal cost, and what per cent was the profit ? 14. A quarter section of land was sold for $4563, which was 8$ less than cost,; what was the cost per acre ? 15. What $ of a number is 25$ of 3 fourths of it? 16. \% of 1258 is \% of what number? 17. What % of a number is 20$ of f of it ? 88 Percentage. APPLICATIONS OF PERCENTAGE.* PROFIT AND LOSS. 219. Profit and Loss are gain or loss in business transac- tions. They are calculated by percentage. The cost is the base ; the per cent of gain or loss, the rate ; the gain or loss, the percentage ; the selling price, the cost, plus or minus the gain or loss. 1. A man paid $650 for a carriage, and sold it for 8% more than it cost him ; what was his profit ? Analysis.— 8% = .08, and $650 x .08 = $52.00, Arts. 2. A musician bought a piano for $570, and sold it for $624.15 ; what per cent was his profit ? Analysis. — $624.15 - $570 = $5415 (gain), and $54.15 -f- 570 = .095, or9|%, Ans. 3. A provision dealer made $500 on a cargo of flour, which was 20$ of the cost ; what was the cost ? Analysis.— Since $500 are 20% of a number, 1% of that number is *V of $500 = $25, and 100% is $25 x 100 = $2500, Ans. Or, since $500 = £ (20%), f = $500 x 5 = $2500, Ans. 4. A merchant tailor sold a quantity of goods for $750, on which he made 25$ ; what did the goods cost him ? Analysis.— $750 is the cost +25% of itself; and $750 -f- 1.25 = $600 the cost, Ans. 5. A grocer sold a quantity of damaged goods for $400, which was 20$ less than cost ; what was the cost ? Analysis.— $400 is the cost -20% of itself, and 100% -20% = .80, $400^-. 80 = $500, the cost, Ans. * The Applications of Percentage in business transactions are numerous and impor- tant. Special pains should therefore be taken to have the subject thoroughly under- stood. Trade Discount. 89 Or, | - \ (20 f ) = % ; since § = $400, \ = $100, and | = $500. (Art. 215, N. 2.) Hence, the " Profit or Loss = Cost x Bate. Bate = Profit or Loss -^ Cost. Formulas.— { Cost = Gain or Loss -j- Bate. j Selling Price -f- (1 -f Bate), or " [ Selling Price -r- (1 — Bate). Note.— It often shortens the process to take the fractional part of the base, indicated by the given per cent. TRADE DISCOUNT. 220. It is customary for merchants and manufacturers to have fixed price lists of their goods, and when the market varies instead of changing the fixed price they change the rate of discount. The fixed price is named the list price, and the deduction made from it, is called the Trade Discount. Note. — Profit and Loss are calculated on the actual cost of goods, or sum invested ; trade discount on the list price. 221. Dealers usually announce their "terms" upon their "bill heads" thus, Terms 3 months, or 30 days, less 5%; terms 60 days, or %% discount in 10 days, etc. Note. — When bills are paid before maturity, merchants usually deduct the legal interest for the time, on amount of bill. 222. To find the Net Amount of Bills when discounts are made. l. A Bill of goods at list prices amounts to $105 ; what is the net amount, the trade discount being 10^, and 5% off for cash ? Solution.— $105 x .10 = $10.50, and $105- $10. 50 s $94.50. Again, $94.50 x .05 = $4,725, and $94.50 -$4,725 = $89,775, Ans. Hence, the Eule. — Deduct the trade discount from the list price, and from the remainder take the discount for cash. 90 Percentage. Note. Observe that the first rate of discount only is deducted from the list price, and the subsequent rates are deducted from the remainders. The result is not affected by the order in which the discounts are taken. 2. What is the net amount of a bill of goods, the list price of which is $435, sold 5$ off for cash, trade discount 8$? 3. Sold books on 3 mo. amounting to $854.75 at a discount of 12$ from retail price, and 10$ off for cash ; what is the net value of the bill ? 4. The gross amount of a bill is $236.37; the rates of discount are 15$ and 8$ ; what is the net amount? 5. Find a direct discount equal to a discount of 12-§-$ and 8%. Ans. 19£$. Note. — To find a direct discount equal to two or more taken in succession ; from the sum of two discounts subtract their product. 6. What direct discount is equal to a discount of 25$ and 17$? 7. On a bill of $625, what is the difference between a discount of 30$ and a discount of 25$ and 5$ ? 8. Bought books at a discount of 20$ on the retail price, and sold them at the retail price ; what per cent did I gain? 9. What per cent would I gain at a discount of 33£$ ? 10. With a trade discount of 8$ and 5$ for cash, goods were sold for $825 at a profit of 15$ ; what was the cost ? 223. To Mark goods so that a given per cent may be deducted and leave a given per cent profit. 11. Bought cloaks at $75.10; what price must they be marked, that 15$ may be deducted and leaye 25$ profit ? Analysis.— The selling price is 125% of $75.10, and $75.10x1.25 = $93,875. But the marked price is to be diminished by 15% of itself, and 100%— 15% = 85% ; hence, $93,875 = 85% of the marked price. Now $93.875^-. 85 = $110.44, the marked price. (Art. 217.) Hence, the, Rule. — Find the selling price and divide it by 1 minus the given per cent to be deducted ; the quotient will be the marked price. Commission and Brokerage. 91 12. A bookseller wishes to mark up the price of a book which he now sells for £2, so that he can deduct \§% and yet receive the present price ; what must be the marked price? 13. A merchant sells cloths for $268 by which he gains 23%; how must he mark them so that he may deduct 4$ and make the same profit? 14. Bought diamonds at $920 ; how must I mark the price that after abating b% the profit may be 25% ? 15. What must be the price of an article from which you deduct 20% and leave 20 cents ? COMMISSION AND BROKERAGE. 224. Commission is an alloivance made to agents, collectors, brokers, etc., for the transaction of business. Brokerage is Commission paid a broker. Guarantee is the % charged for assuming the risk of loss. Notes. — 1. An Agent is one who transacts business for another, and is often called a Commission Merchant, Factor, or Correspondent. 2. A Collector is one who collects debts, taxes, duties, etc. 3. A Broker is one who buys and sells gold, stocks, bills of exchange, etc. Brokers are commonly designated by the department of business in which they are engaged ; as, Stock-brokers, Exchange-brokers, Note- brokers, Merchandise-brokers, Real -estate-brokers, etc. 225. Goods sent to an agent to sell, are called a Consignment ; the person to whom they are sent, the Consignee; and the person sending them the Consignor or Shipper. 226. The Gross Proceeds of a business transaction are the whole sum received. 227. The Net Proceeds are the gross amount received, minus the commission and other charges. 228. Commission and Brokerage ■ are computed by Per- centage ; the money employed is the base ; the per cent for services, the rate ; the commission, the percentage. 92 Percentage. Note. — Brokerage is computed on the par value of stocks, bonds, etc., as the base. 1. Find Z\% commission on sales for $8168. (Art. 215.) Am. $285.88. 2. What is the commission at %\% for selling 875 bushels of wheat, at $1.25 ? 3. An agent collects $2850 ; how much does he pay to the owner after deducting b% commission ? 4. A commission merchant sold goods amounting to $2875.50 ; the charges were %\% com., %\% guarantee, cartage, storage, etc., $18.50 ; how much was due the owner ? 5. Paid $375 to an auctioneer for selling a house ; his com. being %\%, for how much did he sell it and what did the owner receive? (Art. 217.) 6. An agent received $864 with which to buy goods ; he was to have 2\% commission on the amount of purchase ; how much was his commission and what the amount of purchase ? 7. A commission merchant received $654; he charged %\% commission and *Z\%~ for guarantee ; what were the net proceeds ? 8. An agent charged %% commission and $58.60 expenses for selling a house, and sent the owner $16350 ; for what did he sell the house ? 9. What is the brokerage, at \%> on the sale of stock, the market value of which is $5250 ? 10. Paid a broker $25 for buying bank stock at par, com- mission \% ; how much did he invest ? 11. The sum of $25365 sent to my agent, includes invest- ment and commission at 3f % ; what is the investment ? What is the commission ? 12. My agent bought tea at \% brokerage, and was paid $450. He afterwards sold the tea at a profit to me of $6150, deducting 1 \% commission on the sale ; how much was his commission ? 13. A man wishes to draw on New York for an amount sufficient to cover expenses of %% exchange and 2\% commis- sion, and leave him the sum of $5242.50; for how much must he draw ? Brokerage. 93 14. What number diminished by ty% of itself is equal to 895 ? 15. A bill of $875 was placed in the hands of a collector, who obtained 75% of it and charged 8% commission ; how much did the owner receive ? 16. A man invested $6350 in U. S. bonds at 105$, broker- age 1 1%, and sold them at 115%, brokerage If % \ how much did he gain ? 17. On what valuation is $18.25 the commission, at \% ? 18. On what sales is $825.50 the commission, at 7%%? 19. A merchant sold on a commission of 8^%, 200 bbl. pork, each weighing 200 lb., at 12J cts. a pound ; what was the amount of his commission, and how much did he remit to the owner ? 20. A lawyer received $6.80, being 8% commission for col- lecting a note ; what was the face of the note ? 21. A real-estate agent bought land for which he received 2|% commission for buying and $48.50 for charges. The whole cost of land, commission, and charges was $8450 ; what was paid for the land ? 22. A commission merchant sells 60 bbl. potatoes at $3.25 a bbl., and 42 bu. beans at $2.50 a bu. ; how much is due the consignor, the commission being 2f% ? 23. An agent who charged 2J$ for selling a house, paid the owmer $12360 ; what did he get for the property? 24. On what amount of sales is $241.75 the commission, at 15%, after deducting $18.20 for expenses? 25. An agent received $67.50 for collecting $4500 ; what was the rate ? 26. A man sends $3246.20 to an agent in Boston to buy shoes, deducting his commission at 2% ; what was his com- mission ? How much did he spend for shoes ? 27. A New York firm sell for me goods at 6% commission ; how mucli must be sold that my broker can buy stock with the proceeds to the value of $6250, after deducting his com- mission of %\%t 28. A dealer in pork cleared $1565, charging 10%' commis- sion ami paying $850 expenses of packing ; if the pork cost him 7 cts. a pound, how many pounds did he pack ? 94 Percentage. INSURANCE. 229. Insurance is security against loss. It is distinguished by different names, according to the cause of the loss or the object insured. Thus, Fire Insurance, Marine Insurance, Accident, Health, Life Insurance, etc. (See Life Ins., Art, 566.) Note. — Risks of transportation partly by land and partly by water, are called Transit Insurance. 230. The parties who agree to make good the loss, are called Insurance Companies or Underwriters. Note. — When only a part of the property insured is destroyed, the underwriters are required to make good only the estimated loss. 231. Insurance Companies are of two kinds: Stock Com- panies and Mutual Companies. 232. A Stock Company is one which has a paid-up capital, and divides the profit and loss among its stockholders. 233. A Mutual Company is one in which the losses are shared by the parties insured. Note. — Some companies combine the principles of Stock and Mutual Companies, and are called Mixed Companies. 234. The Premium is the sum paid for insurance. 235. The Policy is the written contract between the insurers and the insured. They usually run from one to five years. 236. A Valued or Closed Policy contains a certain fixed value on the thing insured ; as of houses, goods, etc. 237. An Open Policy is one in which the value of the article insured is to be determined in case of loss. 238. The rate of premium charged depends on the nature of the risk and the time for which the policy is issued, the rate for long policies being less than for short ones. Insurance. 95 239. Rates for less than a year are called Short Rates. Notes. — 1. Policies are renewed annually, or at stated periods, and the premium is paid in advance. In this respect insurance differs from com- mission, etc., which have no reference to time. 2. When a policy taken for a year is cancelled prior to the end of the year, a Return Premium is paid to the party insured. 240. Premiums are computed by the rules of Percentage. Rates of premium are a per cent of the sum insured, or a num- ber of cents paid on $100. Thus, 25 cts. on $100, is \ of 1 % ; 75 cts. on $100 is f % . 241. An Insurance Agent is a person who acts for Insur- ance Companies iu obtaining business, collecting premiums, adjusting losses, etc. 242. An Insurance Broker is a person who negotiates insur- ance and receives a percentage from the company taking the risk. Note. — Insurance Brokers are regarded as agents of the insured. 243. The Surplus of an Insurance Company is the excess of its assets above its liabilities. 244. To find the Premium, from the sum insured and the rate. 1. What is the premium for insuring a store and goods valued at $12000, at \\% for 1 year ? Solution.— $12000 x .015 = $180.00, Am. Hence, the Formula.— Pr em i um = Sum In. x Rate. (Art. 215.) 2. What is the cost of insuring goods worth $4000, at 80 cents per $100, the policy and survey being $1.50 ? 3. If I take a risk of $12000 at a premium of 1|£, and re-\ insure it at \\%, what will be my gain ? 4. Insured a cargo from Liverpool worth £850 10s. 4d., at a premium of \\%\ at $4.86 to the £, what is the premium in U. S. Money? 96 Percentage. 245. To find the Rate, from the sum insured and the premiumc 5. A man paid $215 for insuring $8600 on a tenement house; what was the rate ? Solution.— $215. 00 h- $8600 = .025, or 2*-%, Ans. Hence, the Formula. — Rate = Premium-?- Ami. Insured. (Art. 216.) 6. A grocer paid $40 annually for an insurance of $5000 on his goods ; what was the rate? 7. If the owner pays $2800 for insuring a steamer worth $42000, what rate per cent does he pay ? 8. Paid $25 for an insurance of $3000 ; what was the rate ? 246. To find the Sum Insured, when the premium and the rate per cent are given. 9. A merchant paid $1200 premium, at 2\%, on a ship and cargo from Liverpool to Baltimore ; it was lost on the voyage ; what amount of insurance should he recover ? Solution.— $1200.000-*-. 022 = $54545.455, Ans. Hence, the Formula. — Sum Insured = Premium-?- Rate. (Art. 217.) 10. If I pay $254 premium on silks, from Havre to New York, at 1\ per cent, what amount does my policy cover ? 11. A gentleman paid $62 annually for insuring house and furniture, which was 2\% on half its value; what was its value ? 12. How much insurance can be obtained for $125 on a store and contents, at 1-|% ? 13. Paid $287 to insure half the value of a cargo at 2f % 5 what was its total value ? 247. To find the sum to be insured to cover the value of the goods and premium. 14. Goods bought in Paris for $7594, were insured at 2\% ; what sum will cover the value of the goods and the premium ? Anatasis. — The sum insured is 100% of itself, the premium is 21' < of that sum, and 100% -24% = 97|%. Now $7594-:-. 97i = $7788.72, the sum required. (Art. J518.) Hence, the Formula. — Sum Insured == Value -f* (1 -— Rate), Insurance, 97 15. If a warehouse is worth $266250, what sum must be Insured, at %%, to cover the property and premium ? 16. What sum must be insured, at 3%, on a consignment of tea worth $4200, to cover property and premium ? 17. A merchant sent a cargo of goods worth $25275 to Canton ; what sum must he get insured at 3%, that he may suffer no loss, if the ship is wrecked ? 18. The premiums paid for insuring two stores, are $98.25 and $146.50 ; the rate is lf% ; what sum must be insured to cover the property and premium ? Examples. 1. What is the annual premium on a policy insuring a house for -jj- its value, at \% ? 2. If $125 are paid annually for insuring $24000, what is the rate per cent ? 3. What premium must be paid for insuring $6500 on a store for 3 years at %\% ? 4. A house is insured at f%, and the premium is $93.60; for how much is it insured ? 5. A shipowner insures a ship and cargo for $89325, at 4-|%, the policy covering both property and premium ; what is the value of the property ? 6. What will it cost to insure a factory worth $26000 at \%, and machinery worth $16800 at \%, with $1.50 for policy? 7. Paid $350 on a shipment of goods to insure \ the value, at 2>\% ; what was the whole value ? 8. A company had $125 premium for insuring property worth $18000 ; if similar property worth $45000 were insured at the same rate in another company, what would be the premium ? 9. A dealer insured a stock of goods for 1 year, at \\%\ if the short rate for 6 mo. was 83 cents on $100, and the policy was cancelled at the end of that time, what should be the return premium, the goods being insured for $3500 ? Note. — Multiply the sum insured by the difference between the given rates. 7 98 Percentage. ADJUSTMENT OF LOSSES. 248. Losses may be partial or total. In ordinary cases of partial loss, the insured is entitled to indemnity only for the actual loss. If a total loss occurs, the insurers pay the full amount of their policy. 249. If the policy contains the "Average Clause," the com- pany pays only such a proportion of the loss as the amount insured is to the value of the property insured. Thus, a person who has a policy with the " Average Clause " for $1000 on property worth $2000, would receive Note. — It is customary for Insurance Companies to reserve the right to repair or replace the damaged property. 250. If the loss is partial, but amounts to more than half the value of the property, the owner has the right to transfer to the company what remains, and claim the full value of the property.* This is called the right of abandonment, and the company cannot refuse to take it, unless specially named in the policy. 251. When a partial loss occurs to a vessel, the companies pay such proportion of it as the sum insured is to the value of the property. It is an established rule that one-third shall be allowed the insurers for the superior value of the new material used ; that is, " one-third off, new for old." 252. A total loss may be actual or constructive. An Actual Total Loss is one by which the property insured is entirely destroyed by fire or water. (Art. 230, N.) A Constructive Total Loss is one in which some portions of the property are saved, and are transferred by the insured to the insurers by abandonment. * American Cyclopedia, Adjustment of Losses. 99 253. In such cases the insurers pay for the whole, and hold the salvage or property saved as their own. 254. To estimate proportionate losses. 1. A merchant insured $2500 in a Mutual Co., $1500 in the Howard, and $3500 in the Phoenix; a loss by fire of $6000 occurred ; how much should each company pay ? Explanation. — The total sum insured was $2500 M. $7500, the loss was $6000. Dividing $6000 by -^qq jj $7500 gives 80 % , proportion of insurance to loss. 3500 P Share of Mutual a $2500 x .80 = $2000.00, _oOW r. of the Howard = $1500 x .80 = $1200.00, $7500 Sum Ins. of the Phoenix - $3500 x .80 = $2800.00. 6000-^7500 = .80. Hence, the Kule. — Divide the loss by the total insurance, the quo- tient will be the per cent which each must pay. 2. The loss by fire on a piece of property was $8000, of which $2000 was insured in the Howard, $3000 in the Phoenix, and $3000 in the Manhattan Company ; how much did each com- pany contribute ? 3. The loss by fire on a store and contents was $4525 ; the property was insured $2500 in Franklin Company, $4000 in Mutual, $2000 in Phoenix, and $3000 in Hanover Company ; how much should each pay ? 4. A shipment of silks valued at $25000 was insured for $15000, with a policy containing the " average clause ;" if the goods were damaged to the amount of $5000, how much would be paid by the company ? 5. A cargo of oil worth $30000 was insured for 18 months at %\% ; at the end of 12 months the policy was cancelled ; if the short rate for 6 months was 65 cts., what should be the return premium ? 6. A real-estate owner insured $75000 at the average rate of \% a year for 12 years ; the entire property being at the end of 10 years destroyed by fire, the company paid the loss in full; how much was the real loss to the company, the insurance having been regularly paid ? 100 Percentage. TAXES. 255. A Tax is a sum assessed upon the person, property, or income of citizens. 256. A Property Tax is a tax upon property. 257. A Personal Tax is a tax upon the person, and is called a poll or capitation tax. Notes. — 1. A Poll Tax is a specific sum levied in some States upon all male citizens not exempt by law, without regard to property. 2. In Mass. a poll tax is assessed on every male inhabitant above the age of 20 years, whether a citizen of the U. S. or an alien. Rev. Stat. 258. A License Tax is the sum paid for permission to pur- sue certain avocations. 259. Special Taxes are fixed sums assessed upon certain articles of luxury ; as carriages, billiard tables, gold watches, etc. Note — The Internal Revenue or Stamp Tax upon perfumery, watches, proprietary medicines, etc., was repealed by Act of Congress in Oct. 1882. 260. Property is of two kinds, real and personal. 261. Real Estate is that which is fixed ; as, houses and lands. 262. Personal Property is that which is movable; as, money, stocks, bonds, mortgages, etc. 263. Assessors are persons appointed to make a list of taxable property and fix its valuation for the purpose of taxation. 264. A Collector is a person appointed to receive the taxes. 265. Property taxes are computed by Percentage. 266. An Assessment Roll is a list of all persons in the dis- trict liable to be assessed, with their taxable property and its valuation. Taxes. 101 267. To Assess a Property Tax, when the sum to be raised and the valuation of the property are given. 1. In a city whose property was valued at $2500000, a tax of $15000 was levied ; there being 250 polls, each taxed $2, what was the rate of the tax, and what A's tax whose real estate was valued at $8000, and personal at $5000 ? Explanation. — The sum to be raised is $15000 solution. less $500 on the polls, equal to $14500 on the Town tax $15000 property; and $14500 -*- $2500000 = $.0058. or 5.8 p H « 500 mills on a dollar. OKnnnnn \ AnS ' Rule. — Divide the given amount by the amount of $1 for the given time and rate. 17. What sum loaned at 1% a month will amount to $600 in 1 year ? 18. What principal at 7%, loaned from. Apr. 9th, 1881, to Sept. 5, 1883, will amount to $1477.59 ? Problems in Interest. 115 19. What sum at 1% will amt. to $221.07 in 3 yr. 4 mo. ? 20. What principal at 9% will amt. to $286 in 3 yr. 4 mo. ? 21. What principal at 6% will amount to $3695.04 in 1 yr. 4 mo. 18 days ? 22. What principal at 8% will amount to $442.71 in 2 yr. 2 mo. 24 days ? 295. To find the Time, when the Principal, Interest, and Rate are given. 23. In what time will $1500 gain $198 at 6%? Analysis.— The int. of $1500 for 1 yr. at 6% is operation, $90 ; hence, to gain $198 will require the same prin- 90 ) $198.00 cipal as many years as $90 are contained times in 77T jT'o'vj. $198 ; and $198-=-$90 = 2.2, or ty years. Hence, the '. * * " Eule. — Divide the given interest by the interest of the principal for 1 year at the given rate. Formula. — Time = Int. -^ (Prin. x Rate). Notes. — 1. If the quotient contains decimals, reduce them to months and days. (Art. 153.) 2. If the amount is given instead of the principal or the interest, find the part omitted, and proceed as above. 3. At 100%, any sum will double itself in 1 year ; therefore, any per cent will require as many years to double the principal, as the given per cent is contained times in 100%. 24. In what time will $850 gain $29.75 at 7$ ? 25. In what time will $273.51 amount to $312,864 at 7%? 26. In what time will $240 amount to $720, at \%% ? 27. A man received $236.75 for the use of $2820, which was Q>% interest for the time ; what was the time ? 28. How long must $204 be on interest at 6% to amount to $217.09? 29. How long will it take $500 at 5% to % gain $500 interest ; that is, to double itself ? OPERATION. Explanation.— The interest of $500 for 1 year at 5 % , 25 ) 500 is $25 ; and $500-*-$35 = 20. Ans. 2$ years. ' Ans. 20 yr. 116 Percentage. Tab le. Showing in what time any given principal will double itself at any rate, from 1 to 20 per cent Simple Interest. Per cent. Years. Per cent. Years. Per cent. Years. Per cent. Years. 1 100 6 161 11 «¥r 16 H 2 50 7 14f 12 81 17 5tf 3 33i 8 12J 13 7* 18 H 4 25 9 11* 14 7* 19 5A 5 20 10 10 15 6* 20 5 30. How long will it take $10000 to gain $5000, at 6 per cent interest ? 31. A man hired $15000 at 1%, and retained it till it amounted to $25000 ; how long did he have it ? 32. A man loaned his clerk $25000, and agreed to let him have it at 5% till it amounted to $60000 ; how long did he have it ? PARTIAL PAYMENTS. 296. Partial Payments are payments at different times of parts of a note or bond. 297. Indorsements are receipts of payments written on the back of notes and bonds, stating the amount and date of the payment. 298. To compute Interest on notes and bonds, when partial payments have been made. $ 965 - New York, March 8th, 1880. l. On demand, I promise to pay George B. Curtis, or order, Nine Hundred Sixty-jive Dollars, until interest at 7 per cent, value received. Heniiy Bbowx, Partial Payments. 117 The following payments were indorsed on this note : Sept. 8th, 1880, received $75.30. June 18th, 1881, received $20.38. March 24th, 1882, received $80. What was due on taking up the note, Feb. 9th, 1883 ? OPEBATION. Principal, dated March 8th, 1880 $965.00 Int. to first pay't, Sept. 8th, 1880 (6 mo.) 33.7 75 Amount due on note Sept. 8th. 998.775 1st pay't (to be deducted from amt.) 75.30 Remainder, or new principal 923.475 Int. to 2d pay't, June 18th (9 mo. 10 d.) 50.278 2d pay't (less than int. due) $20.38 Int. on same principal from June 18th to March 24th, 1882 (9 mo. 6 d.) $49,559 - $20.38 = 29.1 79 Amount due March 24th, 1882 1002,932 3d pay't (being greater than the int. now due) is to be deducted from the amount 80.00 Balance due March 24th, 1882 922.932 Int. on Bal. to Feb. 9th (10 mo. 15 d.) 56.529 Bal. due on taking up the note, Feb. 9th, 1883 $979,461 United States Rule. Find the amount of the principal to the time of the first payment, and subtracting the payment from it, find the amount of the remainder as a new principal, to the time of the next payment. If the payment is less than the interest, find the amount of the principal to the time ivhen the sum of the payments equals or exceeds the interest due; and subtract the sum of the payments from this amount. Proceed in this manner to the time of settlement. Notes. — 1. The principles upon which this rule is founded are, 1st. That payments must be applied first to discharge accrued interest, and then the remainder, if any, toward the discharge of the principal. 2d. That only unpaid principal can draw interest. 118 Percentage. $ 650 - Boston, Jan. 1st,. 1882. 2. For value received, I promise to pay John Lincoln, or order, Six Hundred Fifty Dollars on demand, with interest at 6 per cent. George Law. Indorsed, Aug. 13th, 1882, $100. Indorsed, April 13th, 1883, $120. What was due on the note, Jan. 20th, 1884 ? ^ ^9S.9 ^ Trenton, April 10th, 1874. 3. Four months after date, I promise to pay James Gar- field, or order, Two Thousand Four Hundred Sixty Dollars, with interest at 6 per cent, value received. George G. Williams. Indorsed, Aug. 20th, 1875, $840. Dec. 26th, 1875, $400. May 2d, 1876, $1000. How much was due Aug. 20th, 1876 ? $ 5000- Indianapolis, May 1st, 1875. 4. Six months after date, I promise to pay John Folger, or order, Five Thousand Dollars, with interest at 5 per cent, value received. John Adams. Indorsed, Oct. 1st, 1875, $700. Feb. 7th, 1876, $45. Sept. 13th, 1876, $480. What was the balance due Jan. 1st, 1877 ? Mercantile Method. 299. When Partial Payments are made on short notes or interest accounts, business men commonly employ the follow- ing method : Find the amount of the whole debt to the time of set- tlement ; also find the amount of each -payment from the time it was made to the time of settlement. Partial Payments, 119 Subtract the amount of the payments from the amount of the debt ; the remainder will be the balance due. $■^16- Rochester, March 21st, 1880. 5. On demand, I promise to pay to the order of Henry Patton, Four Hundred Sixteen Dollars, with interest at 7 per cent, value received. Johk Martin. Keceived on the above note the following sums : June 15th, 1880, $35.00. Oct. 9th, 1880, $23.00. Jan. 12th, 1881, $68.00. What was due on the note, Sept. 21st, 1881 ? SOLUTION. Principal, dated March 21st, 1880 $416,000 Int. to settlement (1 yr. 6 mo.), at 7% 43.6 80 Amount, Sept. 21st, 1881 459.680 1st pay't, $35.00, Time (1 yr. 3 mo. 6 d.), Amount $38,103 2d pay't, $23.00, Time (11 mo. 12 d.), Amount 24.530 3d pay't, $68.00, Time (8 mo. 9 d.), Amount 71.292 Amount of the payments 133.925 Balance due Sept. 21st, 1881 $325,755 6. A bill of goods amounting to $850, was to be paid Jan. 1st, 1880. Received June 10th, $145 ; Sept. 23d, $465 ; Oct. 3d, $23 ; what was due on the bill Dec. 31st, 1880, int. 6% ? 7. An account of $3200 due March 3d, received the follow- ing payments: June 1st, $310; Aug. 7th, $219 ; Oct. 17th, $200 ; what was due on the 27th of the following December, allowing 7% interest ? 300. Connecticut Rule for Partial Payments. I. When the first payment is a year or more from the time the interest commenced : Find the amount of the principal to that time. If the payment equals or exceeds the interest due, subtract it from the amount thus found, and considering the re- mainder a new principal, proceed as before. 120 Percentage. II. When a pay't is made before a year's int. has accrued : Find the amount of the principal for 1 year ; also, if the payment equals or exceeds the interest due, find its amount from the time it was made to the end of the year ; then subtract this amount from the amount of the principal, and treat the remainder as a new principal. III. If the payment be less than the interest: Subtract the payment only from the amount of the principal thus found, and proceed as before. $ 650 ' New Haven, April 12th, 1879. 8. On demand, I promise to pay to the order of George Selden, Six Hundred Fifty Dollars, with interest, value received. Thomas Sawyer. Indorsed, May 1, 1880, rec'd $116.20. Feb. 10, 1881, rec'd $61.50. Dec. 12, 1881, rec'd $12.10. • June 20, 1882, rec'd $110. What was due Oct. 21, 1882 ? SOLUTION. Principal, dated April 12, 1879. . . . , $650.00 Interest to first payment, May 1, 1880 (1 yr. 19 da.) 41.06 Amount, May 1, '80 691.06 First payment, May 1, '80 ... 116.20 Remainder, or new principal, May 1, '80 574.86 Interest to May 1, '81, or 1 yr. (2d payment being short of 1 yr.). . 34.49 Amount, May 1, *81 609.35 Amount of second payment to May 1, '81 (2 mo. 20 da.) 62.32 Remainder, or new principal, May 1, '81 547.03 Amount, May 1, '82 (1 yr.) 579.86 Third payment (being less than interest due) draws no interest. . . 12.10 Remainder, or new principal, May 1, '82 567.76 Amount, Oct. 21, '82 (5 mo. 20 da.) 583.85 Amount of last payment to settlement (4 mo. 1 da.) 112.22 Balance due Oct. 21, '82 $471.63 Partial Payments. 121 301. Vermont Rule for Partial Payments. I. When payments are made on notes bearing interest, such payments shall be applied, " First, to liquidate the interest that has accrued at the time of such payments ; and secondly, to the extinguish- ment of the principal" II. When notes are made " with interest annually." The annual interests ivhich reviain unpaid shall be subject to simple interest from the time they become due to the time of settlement. III. If payments have been made in any year, reckoning from the time such annual interest began to accrue, the amount of such payments at the end of such year, with interest thereon from the time of payment, shall be applied : " First, to liquidate the simple interest that has accrued from the unpaid annual interests. " Secondly, to liquidate the annual interests that have become due. " Thirdly, to the extinguishment of the principal. H 500 - Montpelier, Feb. 1st, 1878. 9. On demand, I promise to pay to the order of Jared Sparks, Fifteen Hundred Dollars, with interest annually at 6%, value received. Augustus Morse. Indorsed, Aug. 1, 1878, $160. Nov. 1, 1881, $250. Eequired the amount due Feb. 1, 1882. SOLUTION. Principal $1500.00 Annual interest to Feb. 1, '79 (1 yr. at 6%) 90.00 Amount 1590.00 First payment, Aug. 1, 78 $160.00 Interest on same to Feb. 1, '79 (6 mos.) 4.80 164.80 Remainder, or new principal $1425.20 122 Percentage. Remainder, or new principal $1425.20 Annual interest on same from Feb. 1, '79, to Feb. 1, '82 (3 yr.). . 256.53 Interest on first annual interest from Feb. 1, '80 (2 yr.). . $10.26 Interest on second annual int. from Feb. 1, '81 (1 yr.). . . 5.13 15.39 Amount 1697.12 Second payment, Nov. 1, '81 $250.00 Interest on same to Feb. 1, '82 (3 mo.) 3.75 253. 75 Balance due Feb. 1, '82 $1443.37 302. New Hampshire Rule for Partial Payments.* I. When on notes drawing annual interest, Find the interest due upon the principal, and the annual interest at the annual rest \ next after the first payment, from date of note. II. If the first pa) T t. be larger than the sum of interests due, Find the int. on such payt. from the time it was made to end of the year, and deduct the sum of payt. and int. from the amount of principal and interests. III. If less than the annual interests accruing, Deduct the payment without interest from th e sum of annual and simple interest, and upon the balance of such interest cast the simple interest to the time of the next rest. IV. If less than the simple interest due, Deduct it from the simple interest, and add the bal- ance without interest to the other interests due when the next payment is made. Proceed thus to the end of the year after the last pay- ment, being careful to carry forward all interest unpaid at the end of each year. * Abstract of N. H. Court Rule. Report of Hon. C. A. Downs, State Superintendent, t The time when the annual interest becomes due from year to year. Partial Payments. 123 10. A agrees to pay B $2000 in 6 yr. from Jan. 1, 1870, with interest annually. On July 1, 1872, a payment of $500 was made; and Oct. 1, 1873, $50. What was due Jan. 1, 1876 ? SOLUTION. Principal $2000.00 First year's interest $120.00 2 yr. simple int. thereon 14.40 134.40 Second year's interest 120.00 1 yr. simple int. thereon 7.20 127.20 Third year's interest 120. 00 2381.60 First payment, July 1, 1872 $500.00 Int. thereon from July 1, '72, to Jan. 1, '73 15.00 515.00 Balance of principal $1866.60 Interest on same for fourth year. $111.99 + Second pay't (less than the int. accruing during the year) 50.00 Balance of fourth year's interest unpaid 61.99 + Annual interest on balance of principal for fifth year 111.99 + " " " " sixth " 111.99 + Simple int. on unpaid bal. of fourth year's int. for 2 yr 7.43 + Simple interest on fifth year's interest for one year. 6.71 + Balance of principal 1866.60 Amount due January 1, 1876 $2166.71 303. To Compute Interest on Sterling Money. 11. What is the int. of £175 10s. 6d. for 1 yr., at 5 per cent ? Explanation.— Reduce 10s. 6d. to the £175.525 Prin. decimal of a pound (Art. 154); then -05 Rate. multiply the principal by the rate, and £8.77625 int. 1 year. point off the product as before. The 8 on 20 the left of the point is pounds, the figures 15.52500 s. on the right are decimals of a pound, which must be reduced to shillings, pence, 6.30000 d. and farthings. (Art. 153.) Hence, the Ans. £8 15s. Q\d. Eule. — Reduce the given shillings, etc., to the decimal of a pound; then -proceed as in TJ. S. money. Reduce the decimals of a pound in the result to shillings, pence, and farthings. (Art. 153.) 12. What is the int. of £56 15s. for 1 yr. 6 mo., at 6% ? 13. What is the int. of £96 18s. for 2 yr. 6 mo., at A\% ? 14. What is the amt. of £100 for 2 yr. 4 mo., at 5% ? 124 Percentage. COMPOUND INTEREST. 304. Compound Interest is the interest of the principal and of the unpaid interest after it becomes due. 305. To Compute Compound Interest, when the Principal, Rate, and Time of compounding it are given. I. What is the compound interest of $5000 for 3 years, at 6%? Principal $5000 Int. for 1st year, $5000 x .06 300 Amt. for 1 yr. , or 2d prin 5300 Int. for 2d year, $5300 x .06 318 Amt. for 2 yr., or 3d prin 5618 Int. for 3d year, $5618 x. 06 337.08 Amt. for 3 years 5955.08 Original principal to be subtracted 5000 00 Compound int. for 3 years $955.08 Hence, the Eule. — I. Find the amount of the principal for the first period. Treat this amount as a new principal, and find the amount due on it for the next period, and so on through the whole time. II. Subtract the given principal from the last amount, and the remainder will be the compound interest. Note. — If there are months or days after the last regular period at which the interest is compounded, find the interest on the amount last i obtained for them, and add it to the same, before subtracting the principal. 2. What is the compound int. of $1450 for 3 yr. 6 mo., at 6%? 3. What is the compound int. of $8500 for 4 yr. 6 mo., at5%? 4. What is the amt. of $9500 for 6 yr. 3 mo., at b%, com- pound int. ? Compound Interest 125 Table. 306. Showing the amount of $1, at 3, 3|> 4, 5, 6, and compound interest, for any number of years from 1 to 20. n Yrs. 3%. 3|%. 4%. 5%. 6%. Ifc 1. 1.030 000 1.035 000 1.040 000 1.050 000 1.060 000 1.07 000 2. 1.060 900 1.071 225 1.081 600 1.102 500 1.123 600 1.14 490 3. 1.092 727 1.108 718 1.124 864 1.157 625 1.191 016 1.22 504 4. 1.125 509 1.147 523 1.169 859 1.215 506 1.262 477 1.31 079 5. 1.159 274 1.187 686 1.216 653 1.276 282 1.338 226 1.40 255 6. 1.194 052 1.229 255 1.265 319 1.340 096 1.418 519 1.50 073 7. 1.229 874 1.272 279 1.315 932 1.407 100 1.503 630 1.60 578 8. 1.266 770 1.316 809 1.368 569 1.477 455 1.593 848 1.71 818 9. 1.304 773 1.362 897 ; 1.423 312 1.551 328 1.689 479 1.83 845 10. 1.343 916 1.410 599 1.480 244 1.628 895 1.790 848 1.96 715 11. 1.384 234 1.459 970 1.539 451 1.710 339 1.898 299 2.10 485 12. 1.425 761 1.511 069 1.601 032 1.795 856 2.012 196 2.25 219 13. 1.468 534 1.563 956 1.665 074 1.885 649 2.132 928 2.40 984 14. 1.512 590 1.618 695 1.731 676 1.979 932 2.260 904 2.57 853 15. 1.557 967 1.675 349 1.800 944 2.078 928 2.396 558 2.75 903 16. 1.604 706 1.733 986 1.872 981 2.182 875 2.540 §52 2.95 216 17. 1.652 848 1.794 676 1.947 900 2.292 018 2.692 773 3.15 881 18. 1.702 433 1.857 489 2.025 817 2.406 619 2.854 339 3.37 993 19. 1.753 506 1.922 501 ! 2.106 849 2.526 950 3.025 600 3.61 652 20. 1.806 111 1.989 789 ! 2.191 123 1 2.653 298 3.207 135 3.86 968 Note. — Compound interest cannot be collected by law ; but a creditor may receive it, without incurring the penalty of usury. Savings Banks pay it to all depositors who do not draw their interest when due. 5. What is the compound int. and amt. of $200 for 10 yr., at 3^? SOLUTION. Tabular amount of $1 for 10 yr., at U% $1.410599 Multiply by the prin 200 Amt, of $200 for 10 yr 282.119800 Subtracting the prin 200. Compound int. for 10 yr $82.1198 126 Percentage. Eule. — I. Multiply the tabular amount of $1 for the given time and rate by the principal ; the product will be the amount. II. From the amount subtract the principal, and the remainder will be the compound interest. Notes. — 1. If the given number of years exceed that in the Table, find the amount for any convenient period, as half the given years ; then on this amount for the remaining period. For example, the amt. for 20 years by table .at 6% =3.207135, this multiplied by 1.123600, amt, for 2 yr. gives $3.603537 the amt. for 22 years. 2. If interest is compounded semi-annually take £ the given rate and twice the number of years ; if compounded quarterly, take \ the given rate and 4 times the number of years. Thus, the amount of $400 payable semi-annually for 3 yr. at 6%, is the same as the amt. of $400 for 6 yr, at 3%, payable annually. 6. What is the amt. of $3500 for 5 yr., at 5% com. interest? 7. What is the amount of $1350 for 12 years, at 1% ? 6. What is the com. int. of $1469 for 15 years, at 3%? 9. What is the com. int. of $2500 for 24 years, at 6% ? 10. What is the com. int. of $1650 for 30 years, at 3£$? 11. What is the amount of $1800 for 3 yr., at 6% compound interest, payable semi-annually ? V12. What is the amount of $1500 for 2 years, at 12$ com- ound interest, payable Quarterly? 3. To find the principal or present vvorth of an amount at compound interest: Divide the given amount by the amount of $1 for the given time and rate at compound interest. 13. What is the present worth of $6036.25 due in 8 years, at Q% compound interest? 14. What principal at compound int. will amount to $2375.92, at 5%, in 14 years? 15. What is the present worth of $2521.81, due in 14 years, at 6$ compound interest ? 16. What principal at 10$, will amount to $265.33 in 10 years, int. payable semi-annually ? True Discount. 127 . TRUE DISCOUNT. 307. Discount is a deduction from a stated price, or from a debt paid before it is due. 308. The Present Worth of a debt, due at some future time without interest, is the sum which put at legal interest will amount to the debt when it becomes due. 309. True Discount is the difference between the face of a debt and its present worth. 310. To find the Present Worth and True Discount of a time note. 1. What is the present worth and true discount of $478.06, due in 1 year and 8 mouths, at 6%? Analysis.— The amount of $1, at 6%, for 1 yr. 8 mo. = $1.10. Since $1.10 is the amt. of $1, at 6% for the given time, $478.06 is the amt. of as many dollars, for the same time and rate, as $1.10 is contained times in $478.06, and $478.06 -^ $1.10 = $434.60, present worth. Then, $478.06- 434.60 = $43.46, the true discount. Hence, the Rule.— I. Divide the debt by the amount of $1 for the given time and rate ; the quotient will be the present woHh. II. Subtract the present worth from the debt, and the remainder will be the true discount. Find the present worth and true discount of 2. $950.25, due in 1£ years, at 6%. 3. $3272.50, due in 2 yr. 3 mo., at 7%. 4. $6895, payable in 3 years, at 5.%. 5. $8650.75, payable in 3£ years, at ±\%. 6. $10000, due in 4 yr. 5 mo., at %\%. 7. What is the difference between the interest and true dis- count of $52250, for 1 year, at 6% ? 128 Percentage. 8. If a note for $2500 be given with interest at 7% per annum for G mo., what will it be worth 3 mo. from date ? 9. When money is worth 6%, which is preferable, $15000 cash, or $16000 payable in 1 year ? BANK DISCOUNT. 311. Bank Discount is simple interest, paid in advance. 312. The Proceeds of a note are the part paid to the owner; the Discount is the part deducted. 313. The Maturity of a note or draft is the day it becomes legally due. In most States a note does not mature until 3 days after the time named for its payment. These three days are called Days of Grace. Notes. — 1. As interest is charged by some banks for the day of dis- count as well as for the day of maturity, this with the 3 days grace makes the time for which discount is taken four days more than the time named in the note. 2. If the last day of grace occurs on Sunday or a legal holiday, the note matures on the preceding business day. Thus, if a note matures on Monday, and that is a holiday, it is payable on Saturday. 314. The Term of Discount is the time from the date of discount to the maturity of the note. Note. — In computing interest and discount on notes and drafts the practice is not uniform as to what constitutes a year. Some compute it on the basis of 360, and others of 365 days to a year. On Stock loans in Wall Street, interest is computed on the basis of 360 days to a year. 315. To find the Bank Discount and Proceeds, when the Face of a note, Rate, and Time are given. l. What is the bank discount of $568 for 3 mo., at 6% ? What are the proceeds ? Solution. — The face of the note = $568 Int. of $1 for 3 mo. and grace at 6% = .0155 Discount = $8,804 Proceeds, $568-$8.804 = ^559.196. Hence, the Commercial Paper. 129 Rule. — Find the interest of the note at the given rate for three days more than the specified time ; the result is the discount. Subtract the discount from the face of the note ; the remainder will be the proceeds. Note. — If a note is on interest, find its amount at maturity, and taking this as the face of the note, cast the interest on it as above. 2. Find the proceeds of a note of $850, due in 3 mo., at 6% ? 3. Find the proceeds of a draft of $885, on 60 days, at 6%. 4. Find the maturity, the term of discount and the proceeds of a note of $5250, on 60 days, dated July 1st, 1880, and discounted Aug. 21st, 1880, at 5%. 5. Find the difference between the true and bank discount on $6000 for 1 year, allowing each 3 days grace, at 7% ? 6. A merchant bought $6800 worth of goods for cash, sold them on 4 months, at 15$ advance, and got the note dis- counted at 6% to pay the bill. How much did he make ? 316. To find the Face' of a note, that the proceeds may amount to a given sum, when the Rate and Time are given. 7. For what sum must a note be made on 4 months, that the proceeds may be $6400, discounted at 6%? Solution.— The bank discount of $1 for 4 mo. 3 d. = $.0205 The proceeds of $1 = $l-$.0205 = $.9795 Therefore, The face of the note is $6400 -=-$.9795 = $6533.945 Hence, the Rule. — Divide the given sum by the proceeds of $1 for ,p. (St.iip.ti, f.i.m.p, n.n.rl, vn+.p the given time and rate 8. What must be the face of a note on 6 months, discounted at 7% that the proceeds may be $900 ? 9. The avails of a note were $8350.90, the term 3 months, and the rate of discount 8% ; what was the face of the note ? io. How large a note on 90 days must I have discounted at 6$, to realize $5460 ready money ? 9 130 Percentage. 317. To find the face of a draft that may be bought for a specified sum, when the per cent premium or discount is given. 1. How large a draft can be bought for $2040, at 2% premium ? Solution —At 2% premium, $1.02 will buy $1 draft. Aud $2040h- $1.02 = 2000. Ans. $2000. 2. How large a draft can be bought for $2910, at 3% discount ? Solution.— At 3% discount, $0.97 will buy $1 draft. And $2910^.97 = $3000, Ant. Heuce, the Eule. — Divide the given sum by $1 increased or diminished by the rate of premium or discount. 3. How large a draft on San Francisco can be bought for $5200, at a premium of 2-J$ ? 4. What is the face of a draft on Chicago for which you pay $8250, at \\% discount ? 5. A merchant invests the proceeds of a sale, amounting to $3250, in a draft on Chicago, which he can buy at a discount of \\% ; how large is the draft ? 6. What is the face of a draft on New York which costs $2850, at \\% premium ? COMMERCIAL OR BUSINESS PAPER. 318. Commercial or Business Paper includes Promissory Notes, Drafts, Bills of Exchange, etc. 319. A Note or Promissory Note is a written promise to pay a certain sum on demand or at a specified time. Notes. — 1. A note should always contain the words " value received ; " otherwise it is not valid, and the holder may be obliged to prove it was given for a consideration, in order to collect it. 2. A note as a gift is void from want of a consideration, unless it has passed for value into the hands of an innocent third party. Commercial Paper. 131 320. The Maker of a note or draft is the person who signs it. The Payee is the person to whom it is to be paid. The Holder is the person who has the note or draft in his possession. Note. — A note becomes void when founded upon fraud, or when any material alteration is made, as in the date, amount, or time of payment. 321. A Collateral Note is one given with stocks or other security, empowering the holder to sell, if the note should not be paid when it becomes due. 322. A Joint Note is one signed by two or more persons. Notes. — 1. The Face of a Note is the sum whose payment is promised. This sum should be written in words in the body of the note, and in figures at the top or bottom. 2. When a note is to draw interest from its date, it should contain the words " with interest ; " otherwise no interest can be collected. For the same reason, when it is to draw interest from a particular time after date, that fact should be specified in the note. 3. All notes are entitled to legal interest after they become due, whether they draw it before, or not. 323. A Negotiable Note is a note drawn for the payment of money to "order or bearer," without any conditions. A Non-Negotiable Note is one which is not made payable to "order or bearer," or is not payable in money. Notes. — 1. A note payable to A. B., or "order," is transferable by indorsement; if to A. B., or "bearer," it is transferable by delivery. Treasury notes and bank bills belong to this class. 2. If the words " order" and " bearer" are both omitted, the note can be collected only by the party named in it, and is not negotiable. 3. When a note is given for any number of months, calendar months are always to be understood. 4. If a note is payable on demand, it is legally due as soon as presented. If no time is specified for the payment, it is understood to be on demand. 132 Percentage. 5. If a note has been lost or destroyed by fire or other accident, its amount may be collected upon sufficient proof. 324. An Indorser is a person who writes his name on the back of a note and becomes security for its payment. Notes.— 1. If an indorser of a note, draft, etc., does not wish to guar- antee its payment, he writes " without recourse " over his name at the time of the indorsement. This does not affect the negotiability of the note. 2. Sometimes notes and drafts are drawn to the order of the maker, to facilitate their transfer without the indorsement of the holder. Such notes are negotiable by delivery. 325. An Indorsement is the signature of a person written upon the back of notes and other commercial instruments. (Art. 297.) Notes. — 1. A note made payable to A. B., or order, may be collected by any one to whom A. B. may order it to be paid. This order is written on the back of the note and is called an indorsement. 2. If A. B. writes his name only on the back of the note, it is an indorsement in blank, and is equivalent to " Pay the bearer." 3. All the parties who write their names on a note are liable for the amount due, but only one satisfaction can be recovered. 4. No days of grace are allowed in Alabama, Georgia, Kentucky, or California, except the note is held by a private banker or by a bank. 326. A Draft is a written order addressed by one person to another, directing him to pay a specified sum of money to a third person, or to his order. Notes. — 1. A person accepts or promises to pay a draft, by writing the word accepted across the face, with the date and his name under it. 2. To honor a draft is to accept or pay it on presentation. 327. A Protest is a written statement made by a notary public, that a note or draft has been duly presented by the holder- in person for payment or acceptance, and was refused. It protests against the Maker, Drawer, Drawee, Acceptor, Payor, Indorser, etc., for all interest costs or damages incurred through refusal of payment thereof. Note. — A protest must be made out the day the note or draft matures, and sent to the indorser immediately, to Jiold him responsible. Commercial Paper. 133 Forms of Notes and Drafts. 328. No. I. — Time Notes without Interest. (Negotiable.) $850. New York, Jan. 10th, 1883. Tliree months after date, I promise to pay George Ban- croft, or order, Three Hundred Fifty Dollars, value received. Henry Lincoln. What are the bank discount and proceeds of this note ? Note. — When no rate of interest is mentioned, the legal rate ( ate is always understood. 329. No. 2.— Time Notes bearing Interest. (Negotiable.) $ 500 ' Philadelphia, Feb. 15th, 1883. Sixty days after date, we promise to pay H. Foot, or order, Five Hundred Dollars, with interest, without defalcation, value received. John Richards & Co. Required the bank discount and proceeds. Notes. — 1. When banks discount time-notes bearing interest, it is cus- tomary for them to compute the interest till maturity, and take the amount as the face of the note. 2. In Penn. negotiable notes must contain the words " without defalca- tion." In New Jersey they contain the words " without defalcation or discount." 330. No. 3. — Demand Notes. (Negotiable.) $ 120 - Chicago, April 15th, 1883. On demand, I promise to pay W. H. Seward, or bearer, Tivelve Hundred Dollars, value received. Daniel Webster. What was due on the above note June 21st, at 8% ? 4. What would be its amount at H% ? At 5% ? Notes. — 1. Notes on demand are entitled to the legal interest of the State in which they are made from their date to their payment. 2. If the words "or bearer" were omitted, the above note would not be negotiable. 134 Percentage. 331. No. 5.— Notes without Grace. (Negotiable.) $Ji.25 T %%. Baltimore, July 1, 1882. Fifteen days after date, without grace, I promise to pay George Brabburn, or bearer, Four Hundred Twenty-five -ffy Dollars, value received. Silas Weight. What was the amount due on this note at maturity ? 332. No. 6.— Notes on Demand op on Time. (Non-Negotiable.) $ 700 ' Indianapolis, May 31st, 1882. On demand after date, I promise to pay Robert Carter, Seven Hundred Dollars, with interest at 8%, value received. John Hancock. Eequired its amount at sixty days. 7. What would be its amount, if the time were 3 mo. and the rate 1% ? Note. — Notes of the above form are not assignable, and can be collected only by the drawee. 333. No. 8.— Joint Notes. S1600. Sl , LouiSj Aug . 6> i 883 . Two months after date, we jointly promise to pay Horace Holben, or order, Sixteen Hundred Dollars negotiable and 'payable without defalcation or discount with 6% interest, value received. A. H. Stebbins, John Wakd. Find the amount due at maturity. Notes. — 1. The signers of a "joint note " are equally responsible for its payment, and must be sued jointly. 2. The signers of a "joint and several " note are individually responsi- ble for the whole amount, and either promisor may be sued alone. Commercial Paper, 135 334. No. 9.— Notes Payable by Installments. $ 8°°°' Richmond, Va., Oct. 16, 1883. For value received, I promise to pay 67. C. Davenport, or order, Two Thousand Dollars, with interest, in the following manner, viz : Five Hundred Dollars in two months after date, and the balance in installments of Five Hundred Dollars every two months until the entire amount is paid. G. L. Bennett. What was the amount of each payment, at 6%, without grace? 10. What would be the interest and amount of the same note at 7^? At 5%? 335. No. N.— Sight Drafts. $3000. New Orleans, Oct. 3d, 1883. At sight, pay to the order of J. B. Hamilton & Co., Three Thousand Dollars, value received, and charge the same to J. C. Saunders. To T. J. Sawyer, Boston, Mass. Note. — Drafts are drawn payable to the order of a person named in them, and are therefore not to be paid until indorsed by him. 336. No. 12.— Time Drafts. $ 3560 - Grinnell. Iowa, Dec. 22, 1883. Ninety days after date pay to the order of Calvin Selden, Thirty-five Hundred Sixty Dollars, and charge the same to the account of Sam'l Barrett & Co. To S. Ball & Co., Trenton, N. J. Notes. — 1. If a draft is payable at a specified time after sight, the date of acceptance and the time of the draft determine its maturity. 2. The laws of N. Y. do not allow " grace " on sight drafts, nor on time drafts if drawn on a bank or banker. 136 Percentage. 337. Find the date of maturity, discount, and proceeds of the following note, offered for discount June 10th, at 6%. $ 750 ' New York, May 8th, 1882. 13. Sixty days after date, I promise to pay George E. Fisher, or order, Seven Hundred Fifty Dollars, value received. Seth Low. Solution. — Sixty days from May 8th is July 7th, and 3 days grace make July 10th. The above note was offered for discount June 10th ; hence, the term of discount was 30 days. Int. at 6% for 30 d. on $750 = $3.75 Discount. $750 -$3.75 = $746.2 5 Net proceeds. Proof. $750.00 Date of maturity July 10th. 14. A note of $475, dated June 20, 1882, payable in 3 months after date, was offered for discount Aug. 11th ; what were the net proceeds at 6% ? Find the date of maturity, the discount, and proceeds of the following notes : $ n6S - Newark, N. J., Dec. 1st, 1882. 15. Four months after date, I promise to pay to the order of Claflin & Co., Eleven Hundred Sixty-three Dollars, without defalcation or discount, value received. James Edsok. The above note was discounted Feb. 15, 1883, at 6%; what were the proceeds ? $2500. Knoxville, Tenn., Apr. 12th, 1882. 16. Ninety days after date, ice promise to pay to the order of Wm. Day, Twenty-Jive Hundred Dollars, value received. Monroe, Lockwood & Co. The above was discounted May 15th, at 6% ; what were the proceeds ? Averaging Accounts. 137 AVERAGING ACCOUNTS. 338. An Account is a record of business transactions. 339. The Average of several unequal numbers is their sum divided by their number. Thus the average of H, $6, and $8, is $18-5-3 = $6. 340. A Day Book is a journal of accounts in which are recorded the debts and credits of the day. 341. A Debtor is a party who owes another. 342. A Creditor is a party to whom a debt is due. 343. A Ledger is a book to which a summary of the accounts of the " Day Book" is transferred for reference and preservation. 344. The Debits or Debts are placed on the left, marked Dr. ; the Credits or Payments on the right, marked Cr. 345. An Account Current is a running account containing a record of the mercantile transactions between two parties, showing the cash balance due at a certain date. The items usually draw interest from their date, or some specified term of credit, to the time of settlement. Notes. — 1. It is customary for merchants, bankers, and brokers, to render their accounts at stated times, as monthly, quarterly, semi-annually, or annually. 2. Whether the items draw interest depends on custom or agreement between the parties. Among wholesale merchants and jobbers, it is cus- tomary to charge interest on accounts after six months. 3. Among retail dealers, mechanics, farmers, etc., the items seldom bear interest ; hence, in settling such accounts, it is only necessary to find the merchandise balance. 346. The Commercial or Merchandise Balance is the differ- ence between the debit and credit sides of an account. 138 Percentage. 347. The Cash Balance is the sum required to settle an account at any given date. 348. The Average of an Account is the equitable time when the payment of several debts due at different times may be made at one time without loss of interest to debtor or creditor. 349. The Average Time is called the mean or equated time, and the process by which it is found is often called Equation of Payments. 350. The Term of Credit is the time between the contrac- tion of a debt and its maturity. (Arts. 157, 313.) 351. The Average Term of Credit is the time at which debts due at different times may be equitably paid. 352. Averaging Accounts depends upon the following: Principles. 1°. The rate and time remaining the same, Double the principal produces twice the interest. Half the principal produces half the interest, etc. 2°. The rate and principal remaining the same, Double the time produces twice the interest. Half the time produces half the interest, etc. Hence, 3°. Tlie interest of any given principal for 1 year, 1 month, or 1 day, is the same as the interest of 1 dollar for as many years, months, or days, as there are dollars in the given principal. 353. To find the Average Time, when the items are all debits or ail credits. l. A bought a farm July 15th and was to pay $500 down, $300 in 2 months, $400 in 6 months, and $600 in 8 months ; what is the average term of credit and date when all these payments may be equitably made at once ? Averaging Accounts, 139 By the Interest Method. Interest of $500 cash, for mo., at 6% = $0.00 Interest of $300 for 2 mo., at 6% = 3.00 Interest of $400 for 6 mo., at 6% = 12.00 Interest o f $600 for 8 mo., at 6% = 24.00 Ami of pay'ts = $1800 Int. = $39.00 Taking the date of the transaction, viz., July 15th, as the time for pay- ing all the items, the debtor would lose the int. of $300 for 2 mo., $400 for 6 mo. , and $600 for 8 months. Therefore, the sura of items ($1800) is entitled to a term of credit equal to the time required for $1800, at 6%, to gain $39. Now, the interest of $1800 for 1 mo. = $9; and $39-i-$9 = 4^ mo., term of credit ; and July 15th + 4| mo. as Nov. 25th, date of payment. By the Product Method. The first payment being cash has no solution. product. The next payment was due in Items. Time. Product. 2 mo. and its interest for 2 mo. equals the 500 X = 00 mo. interest of $1 for 600 months. (Prin. 300 X 2 = 600 mo. 1°-) 400 x 6 = 2400 mo. The interest of $400 for 6 mo. equals ^q^ q 4800 mo the int. of $1 for 2400 mo. , and the int. ~~ of $600 for 8 mo. equals the int. of $1 for 1800 ) 780 4800 months. Therefore the amount of ^Y^ ^j m g 4.1 m o. interest due on the sum of items, equals the int. of $1 for 7800 months, and $1800 is entitled to a term of credit equal to T J 7 _ f 7800 months, or 4} months. July 15 + 4$ mo. as Nov. 25th, the date of payment. Note. — This method is the same in principle as the interest method. 2. Bought a bill of goods Apr. 20th amounting to $6000, on the following terms : £ cash, -J- in 4 mo., and the balance in 6 mo. ; at what date may the whole be justly paid ? Am. Av. time 3£ mo., or Aug. 5th. 3. On a certain day A bought a horse for $175 on 30 d., 3 cows for $120 on 45 d., 80 sheep for $250 on 60 d., and 5 tons of hay for $130 on 90 days; what is the average term of credit ? 4. Bought a ship for $30000 ; the payments were $5000 cash, $8000 in 4 mo., $7500 in 6 mo., $4500 in 8 mo., and the bal- ance in a year ; what is the average term of credit ? 140 Percentage. 354. To find the Average Time when the items have different dates and different terms of credit. 5. .Required the average date at which the following items may be paid at once without loss of interest to either party : April 10, merchandise on 30 days, $40. May 1, " 40 " $54. June 15, " 30 u $70. " 30, " 40 " $80. I. By the Interest Method. Due. Time. Items. Int. at 6#. May 10 (from May 1st) 9 d., $40 = $0.06 June 10 « 40 d., $54 = 0.36 July 15 " 75 d., $70 = 0.875 Aug. 9 " 100d.,_$80= 1.33 3 Int. at 6% for 1 day of $244 =.04 ) 2.628 65.7,or 66 d. Ans. Date of pay't is 66 d. from May 1st, or July 6th. Explanation. — The earliest date at which any item matures is May 10th ; therefore, taking May 1st as the standard date, and finding the interest at 6 % on each item for the number of days from this date to its maturity ; the sum of int. = $2,628, the sum of items = $244, which is entitled to a term of credit equal to the time required for it to gain $2,628 interest. The int. of $244 for 1 day, at 6% = $0.04, and $2,628 -f- .04 = 65.7, or 66 d., the av. time. May 1st + 66 d. = July 6th. Hence, the Eule. — Take as the standard the first of the month in which the earliest item matures; find the interest on each item- from the standard date to the date of its ma- turity, and divide the sum of interests by the interest of the sum of items for 1 month or 1 day, as the case may be. The quotient will be the number of months or days from the standard date to the average date of payment. Add this number to the standard date and the result will be the equitable date of payment. Notes. — 1. If the earliest due date is the standard, its item has no product, but it must be included in the sum of debts. Averaging Accounts. 141 2. If the fraction in the quotient is £ day or more, 1 day is added ; if less than \ day it is rejected. 3. In computing by the interest method, the rate forms no element of the calculation ; hence, any rate may be used. The most convenient is 6% or 12%. At 12% the int. for 30 days, or 1 mo., is .01 ; and for 3 d., .001 of the principal, or \ as many thousandths as days. 4. Any date may be assumed as the standard, but it is generally more convenient to take the first day of the month in which the earliest item falls due, or the last day of the preceding month. Some prefer the earliest or latest date of any item, or the earliest or latest maturity. II. By the Product Method. Assuming May 1st as the standard date, the term of credit for the first item is 9 days. The 2d item due June 10th, the time from May 1st, is 40 days, etc. Arranging the items as below and multiplying each by the number of days from the standard date to its maturity. Due. Time. Items. Products. May 10, 9 d. x $40 = 360 June 10, 40 d. x 54 = 2160 July 15, 75 d. x 70 = 5250 Aug. 9, 100 d. x _80 = _8000 Sum of items, $244 ) 15770 d ays. Av. time, 64 T ^ d. May 1st + 65 days = July 5th, date of pay't. Hence, the 355. Rule. — Find the date when each item matures. Take the first day of the month in which the earliest item becomes due as a standard, and find the number of days from this to the maturity of each of the other items. Multiply each item by its number of days, and divide the sum of the products by the sum of the items. Tlie quotient will be the average term of credit. Add the average time to the standard date, and the result will be the equitable date of payment. Notes. — 1. When an item contains cents, if less than 50, they are rejected ; if 50 or more, $1 is added. 2. In averaging accounts, it is customary to consider 30 days a month. But when the terms of credit are given in months, calendar months are always meant. 142 Percentage, 6. A grocer sold the following amount of goods : June 3d, $380 on 90 days' credit; June 10th, $485 on 30 d.; July 21st, $834 on 70 d. ; July 28th, $573 on 40 d. ; Aug. 2d, $485 on 40 d. ; what is the average term of credit and date of payment ? EXPLANATION. — D ue ' Time. Items. Products. The second item is due Sept. 1, G2 d. X $380 = 235G0 July 10th. This being July 10, 9 d. x 485= 4365 the earliest date on g t ^ gQ ^ x ^ = mQQ S^SWS S ^ * 67 d. x 573 = 38391 for the standard date. Sept. 11, 72 d. X_485 = 34920 Finding the number 2757 ) 176296 of days from this date to the maturity of 63.9 d. each item and proceed- July 1st + 64 d. = Sept. 3d, Date of Pay't. ing as in Ex. 2d, the average time is 64 days. ' Date of pay't, Sept. 3d. Note. — When several bills are bought on common terms of credit, find the average date of purchase, and add to the result the common term of credit. 7. Sold goods as follows on 4 months credit : Aug. 20th, $975; Sept. 4th, $1150; Sept. 16th, $650; Oct. 3d, $846; Oct. 19th, $578; Nov. 19th, $1240; what is the equitable time of payment ? 8. Bought the following bills of goods on 4 months credit : March 10th, 1879, $250; April 15th, $260; June 1st, $540; at what time is the amount payable ? 9. If you owe a man $84 payable in 4 mo., $120 in 6 mo., $280 in 3 months, what is the average term of credit? 10. If you owe one bill of $175, due in 30 days ; another of $812, due in 60 days; another of $120, due in 65 days; and another of $250, due in 90 days; what is the average term of credit ? n. Sold goods as follows: May 17th, $560 on 30 d.; June 1st, $435 on 45 d.; July 7th, $863 on 60 d.; Aug. 13th, $1000 on 15 d. ; what is the equitable time of payment ? 12. Bought March 5th, a carriage on 6 mo. for $750 ; March 10th, a span of horses for $560 on 4 mo.; April 1st, a set of double harness $275 on 3 mo. ; May 10th, a wagon $160 on % mo.; what is the average term of credit ? Averaging Accounts. 143 356. To find the Extension of Credit, to which the balance of a debt is entitled when partial payments have been made before they are due. 13. A sold B a bill of goods March 12th, on 6 months, amounting to $1740 ; July 10th, B paid him $500 ; Aug. 6th, he paid $700 more ; to what additional credit is B entitled on the balance ? Explanation.— March 12th + 6 operation. months equals Sept. 12th, the due $500 X 64 = 32000 date. From July 10th to Sept. 700 X 37 = 25900 12th, is 64 days. From Aug 6th _~ } — to Sept. 12th, is 37 days ; there- L fore the int. of $500 = int. of $1, 1740 107f d. 32000 days, and the int. of $700 = g . £^h 1Q7 d = p^ m ^ int. of $1, 25900 days ; both pay- r ments equal the int. of $1, for 57900 days. Therefore, B is entitled to the use of the balance ($1740—1200) = $540 for ^fa of 57900 days, or 107| days additional time, or extension of credit on the balance. The equitable date of payment is Dec. 28th. Hence, the Eule. — Multiply each -payment by the time from its date to the maturity of the debt, and divide the sum of the products by the balance remaining unpaid. TJie quotient will be the equitable extension of credit. Note. — If a partial payment is made before a debt is due, equity requires that the debtor should have an extension of credit on the balance, equivalent to the interest of the pre-payment. But the creditor is not always willing to allow this and is not required to do it, by law. 14. A man bought a bill of goods on 90 d., amounting to $2340.75 ; if he pays $1000 down, what extension ought he to have on the balance ? 15. A man owes $1569.75, payable in 90 days ; 60 days before it is due he pays $350.86, and 30 days later $211.89 more ; what extension ought he to have on the balance ? Note. — In finding the average date of payment some accountants omit the cents and units of dollars, using only the nearest number of tens in the multiplication. Thus, the numbers in the last example would be $157, $351, and $212. This shortens the process materially. 144 Percentage. 357. To find the Average Time when an account has both debits and credits. 16. What is the average time and date of paying the follow- ing account : Dr. Geo. Bancroft in acct. with Miller & Co. Or. 1883. 1883. May 21 For Mdse. 3 mo. $500 May 24 By Cash. $300 " 28 a a a 250 June 8 " Sundries 60 d. 400 June 9 " " 30 d. 160 July 21 " Cash. 100 Dr. Product Method. Or. Due. Items. Days. Prod. Due. Items. Days. Prod. Aug. 21 $500 112 56000 May 24 $300 23 6900 " 28 250 119 29750 Aug. 7 400 98 39200 July 9 160 69 11040 July 21 100 81 8100 $910 800 110 96790 54200 $800 54200 ) 42590 ( 387 T *r days, or 390 d. Ans. Bal. $110, due in 390 d. from May 1st, or May 25th, 1884. Explanation. — Having found when each item of debt and credit becomes due, by adding its term of credit to its date, we assume as the standard date the first day of the month in which the earliest item on either side of the account matures, viz.: May 1st. Multiply each item on both sides by the number of days between its maturity and the standard date, and divide the difference between the sums of the products (42590), by the difference between the sums of the items (110). The quotient is the average time of payment. Since the time from May 1, 1883, to May 1, 1884 = 1 year, the date of payment is 390 d.— 365 d. = 25 d. Hence the bal. $110 is equitably due May 25th, 1884. Dr. Interest Method. Cr. Due. Items. Time. Interest. Due. Items. Time. Aug. 21 $500 112 d. $9,331 May 24 $300 23 d. " 28 250 119 d. 4.95| Aug. 8 400 99 d. ' July 9 160 69 d. 1.84 July 21 100 81 d. $910 800 $16.13 9.10 $800 Int. $1.15 6.60 1.35 $97lO Int.at6%on $110 fori d, = ,018)7.03 ( 390 days from May 1, '83, or May 25, Averaging Accounts. 145 Explanation. — Taking the interest at 6^, there is a bal. due at the assumed date, May 1st, '83, of $110, and a loss of $7.08 interest. To bal- ance this loss of int., the payment must be deferred till the int. of $110 shall be equal to $7.03. The int. of $110, at 6% for 1 d., is .018, and $7.03-r- .018 = 390. Hence, the time of payment should be 390 d. = 1 yr. 25 d. from May 1st, '83 = May 25th, 1884. 358. From the preceding illustrations we derive the fol- lowing Rules. 1. Product Method. — Write the date at which each item on both sides matures, and assume the first day of the month in which the earliest item on either side becomes due, as the standard date. Find the number of days from this standard to the maturity of the respec- tive items. Multiply each item by its number of days, and divide the difference between the sums of products by the difference between the sums of items ; the quotient will be the average time. If the greater sum of items and the greater sum of products are both on the same side, add the average time to the assumed date ; if on opposite sides, subtract it ; and the result will be the date when the balance of the account is equitably due. Notes. — 1. In finding the maturity of notes and drafts, 3 days grace should be added to the specified time of payment. 2. When no time of credit is mentioned, the transaction is understood to be for cash, and the payment due at once. II. Interest Method.— Find the interest of each item for the time from the. standard date to the maturity of the respective items, and divide the balance of the interests by the interest of the balance of items for 1 day or 1 month ; the quotient will be the number of days or months, as the case may be, between the standard date and the time of settlement. When the balance of account and interest are both, on the same side, add this to the standard date ; if on oppo- 10 146 Percentage, site sides, subtract it ; the result will be the date of set- tlement. Note. — The average time will be the same whatever the rate of interest. 359. It is advisable for the learner to solve the following examples by both the preceding methods : 17. Balance the following account by both methods. Dr. J. H. Strong & Co. in acct. with Smith & Crane. Cr. 1883. Mar. 25 To Mdse., 60 d. $560 Apr. 30 By Sundries, 30 d. $450 Apr. 7 a (( a 830 July 13 " Cash. 500 May 2 a a {( 730 Aug. 31 " Dft., 30 d. 260 Note. — In this example the bal. of items and excess of products being on opposite sides, the average time is subtracted from the standard date. 18. What is the balance of the following account and when due ? Dr. H. Morgan in acct. with Lockwood & Co. Cr. 1880. 1880. July 20 To Sundries. $760 Aug. 26 By Flour. $520 Aug. 10 a (( 540 Sept. 12 " Stocks, 30 d< 300 Sept. 15 a a 850 Oct. 1 " Cash. 385 19. Find the average time of paying the following account : Dr. George Jenkins. Vr s 1881. 1881. Mar. 1 To Mdse,, 30 d. $500 Apr. 12 By Draft, 20 d. $400 Apr. 5 " << 3 mo. 700 May 10 " Cash. 540. May 20 " " 4 mo. 850 June 4 a, a 60O Averaging Accounts. 147 20. What is the balance of the following acct. and when due ? Dr. Wm. H. Jackson. Or. June 1 To bal. of acct. $745.37 June 10 By grain, 30 d. $545.60 " 20 " silks, 30 d. 1050.83 July 12 a (( tt 675.31 July 14 " wh. g'ds," 971.55 " 31 " cash. 900.40 Aug. 3 " sundries," 1260.10 Aug. 15 " note, 30 d. 1000.00 21. At what date can the balance of the following account be equitably paid ? D W. H. Hendeickson. Or. 1882. 1882. Apr. 7 To Mdse., 2 mo. $300 May 1 To Mdse., 60 d. $350 July 5 " " 3 mo. 500 June 10 " M 30 d. 500 Aug. 10 " "I mo. 400 Aug. 30 " Cash. 250 360. In the following examples different dates may.be assumed -as the standard. 22. What is the balance of the following account and when equitably due ? Dr. A. P. Holmes in acct. with Lord & Taylor. Or. 1878. 1878. Aug. 14 To Sundries. $1100 July 5 By Mdse. $585 " 21 a (( 950 " 18 a a 640 Sept. 1 a a 760 Aug. 11 a <( 965 * 10 <( (4 1000 Sept. 20 a a 800 Am. Bal, $820, Due Oct, 28, 1878, 148 Percentage. 23. Find the balance of the following acct. and when due : Dr. A. B. in acct. with 0. D. Cr. 1880. 1880. Aug. 11 For Mdse. $160 Sept. 2 By Sundries. $75 Sept. 5 a u 240 Oct. 10 " Note, 30 d. 100 Oct. 20 (( 1 horse. 175 Nov. 1 " Cash. 110 24. Find the bal. of the following acct. and when due : Dr. Wm. Gorham in acct. with John - Hendrix. Cr. 1880. 1880. Feb. 10 For Mdse., 4 mo. $450 Mar. 20 By Sundries, 3 m. $325 May 11 <.( a o (t 500 July 9 " Draft, 60 d. 150 July 26 a a o li 360 Sept. 15 " Cash. 400 25. Average the following account : Dr. James Green & Co. Or. 1882. 1882. Jan. 10 To Mdse., 3 mo. $450 !jan. 1 By Bal. of Acct. $485 " 25 " " 30 d. 265 Feb. 10 " Note, 3 mo. 2500 Apr. 20 « " 3 mo. 850 Mar. 1 1 u Draft, 30 d. 360 \I 26. Balance the following account : * Dr. C. J. Hamilton. Cr. 1880. 1880. Jan. 20 To Sundries, 30 d. $500 Jan. 20 Byrealestate,60d. $400 Feb. 12 60 d. 340 Mar. 1 " Draft, 60 d. 200 Mar. 1 30 d. 300 : " 20 "Cash. 400 Cash Balance. 149 27. Average the following account ; Dr. Henry J. Raymond & Co. Or. 1882. 1882. Aug. 10 To Mdse., 60 d. $150 Aug. 25 By Mdse., 30 d. 1500 Oct 1 " Cash. 350 Sept. 20 " " 30 d. 350 " 18 " Dft., 30 d. 250 28. Find when the balance of the following account becomes due: A. B. bought of C. D., July 16th, 1883, merchandise $350 ; Aug. 11th, $465; Sept. 9th, $570; Sept. 14th, $850; Oct. 18th, $780. The former paid August 1st, $360; Sept. 30th, in grain $340; Oct. 5th, cash $500; Oct. 21st, $625. Cash Balance. 361. To find the Cash Balance of an account, at a given date. 29. Find the cash balance of the following acct., due July 15th, 1880, at 6% int. : Dr. Thomas Packard in acct. with Henry Selden. Cr. 1880. Mar. 10 To Mdse., 30 d. $650 1880. Apr. 20 By Bal. acct. $500 Apr. 1 " Cash. 1000 May 13 " Dft. on 90 d. 940 May 26 " Note, 60 d. 1260 June 1 " Bank Stock. 1000 OPERATION. Date. 1880. Apr. 9 " 1 July 28 Days. Items. Products. Date. 1880. Days. Items. 97 $650 63050 Apr. 20 86 $500 105 1000 105000 Aug. 14 -30 940f -13 1260* June 1 44 1000 2910 28200f 2440 2440 196250 Bal. of items, $470 103380 6 1 000 ) 92J870 Balance of products. Bal. of int., $15,478 And $470 + $15.48 = $485.48, Cash balance. Products. 43000 44000 16380* 103380 150 Percentage. Analysts. — Taking the given date of settlement, July 15th, as the standard, we find the maturity of each item, as before, in days. The third item of debits is a note on 60 d., with 3 days grace ; hence, it is not due till 13 days after the settlement, or July 28th. This is indicated by the sign — , and the item being entitled to interest for 13 days, its product is placed on the credit side of the account. The second item of credits is a draft on 90 days, with 3 days grace, and it is not due till Aug. 14th, 30 days after settlement, which is also indicated by the sign — , and its product is placed on the Dr. side. Since each item is multiplied by its number of days, dividing the balance of products by 6000 gives $15.48 = interest of bal. at 6%. And the bal. of items, $470 + $15. 48 = $485.48, the cash balance required. Hence, the Rule for Product Method. Find the number of days from the given date to the maturity of eaeh item. Multiply each item on both sides by its number of days ; if the maturity of any debit item extends beyond the date of settlement, place its product on the credit side ; if the extension is a credit, place its product on the debit side. Divide the balance of products by 6000, and the quo- tient will be the balance of interest at 6%. J¥7ien the balance of items is on the same side with the balance of interest, add the interest to the items ; if on opposite sides, subtract it; the result will be the cash balance required. Notes. — 1. In settling mercantile accounts interest is not always reckoned. This matter is regulated by. previous agreement. When interest is charged it is calculated from the time the account is due. It may first be found at 12% as in averaging accounts, and the result changed to the legal rate. 2. The reason for placing the product of an item on its own side when it becomes due before the time of settlement, is because it is entitled to interest for the intervening time. In like manner, if a credit extends beyond the settlement, equity requires that interest should be allowed on that item. Hence, its interest for that time must either be subtracted from its own side, or be added to the opposite. The latter is the more convenient, and therefore adopted. Cash Balance. 151 362. The amount due on an account current at a given date may be found by the interest method, or by the product method. When interest is not charged it is only necessary to find the merchandise balance. (Art. 346.) 30. What is the cash balance on the following account, July 1st, 1881, interest at 6% ? Dr. A. B. in account with C. D. Or. 1881. ! 1881. March 1 For Mdse. $120 ! April 2 By Sundries. $300 May 10 a a 340 " 20 " Cash. 450 May 22 " " on30d. 560 June 8 " dft. on 30 d. 120 Interest Method. Items. Days. Int. Due. 1881. Items. Days. Int. $120 122 $2.44 April 2 $300 90 $4.50 340 52 2.95 " 20 450 72 5.40 560 10 0.93 July 11 120* -10 1020 0.20* 870 $9.90 870 6.52 6.52 $150- $3.38 = $146.62 ca ish balance. Ba 1. of Int. , $3.38 Due. 1881. March 1 May 10 June 21 Kule for Interest Method. — Take the given date of settlement as the standard and multiply the respective items by the number of days between this date and the due date of each item. Find the interest on each item at the given rate, and the difference between the sums of debit and credit interest will be the balance of interest. WTien the balance of items and the balance of interest are both on the same side, add them, when on opposite sides, subtract them, the result will be the cash balance. Note. — Interest tables are much used in making out accounts current. After an account is balanced it is considered the same as cash and draws interest on the amount. 152 Percentage. 363. Second Form of an account current including interest. Br. A. B. in % current with 0. D. Cr. 1881. Days. Int. Items. ! 1881. Days. Int. Items. March 1 Mdse. 122 2.44 $120.00 April 2 Sundries. 90 4.50 $300 May 10 (i 52 2.95 340.00 1 ■ 20 Cash. 72 5.40 450 May 22 " as June 21 10 I0.93 560.00 July 11 Dft. on 30 d. -10 120* July 1 Int. on dft. 10 0.20* July 1 Bal. of Int. 3.38 U u Bal. of Int. 3.38 11 " M Acct. 146.62 Balance. 9.90 1020.00 1 9.90 1020.00 ii ii $146.62 Note. — Since the date when the draft is due, is 10 days beyond the time of settlement, interest is charged for that time to the Dr. side. As the balance of interest is on the Cr. side, the draft is credited to items on that side and charged to interest on the other. 31. Find the cash balance of the following %, Aug. 5th, 1882, at Dr. \o/? Geo. Bancroft in % with H. Greely. Cr. 1882. June 10 To Mdse. $200 1882. June 15 By Cash. $100 * 30 a a 300 " 30 a a 150 July 11 a a 120 July 6 a a 200 " 24 a a 250 " 30 a a 300 32. Find the cash balance of the following i, Oct. 30, 1882, at Dr. James Morris in % with John Jay. Cr. 1882. Jan. 5 To Mdse., 60 d. $182 1882. Feb. 1 By bal. of %. $300 Feb. 12 u " 30 d. 270 Mar. 30 " Cash. 250 Mar. 7 " " 30 d. 480 Apr. 20 a a 200 Apr. 15 " " 60 d. 640 June 15 " Note, 30 d. 300 May 9 " " 60 d. 530 Aug. 1 " Cash. 400 33. Find the cash balance of the same account at Averaging Accounts Current 153 34. What is trie cash balance of the following acct., Dec. 31st, 1809, at Y/o ? Dr. S. Parkhurst in acct. with G. P. Putnam. Or. 1869. ! Sept. 10 To Mds., 30 d. $1250.15 1869. Sept. 25 By Mds., 60 d. $1560.50 Oct. 1 " " 60 d. 1015.60 Oct. 10 " " 90 d. 948.30 " 23 " " 45 d. 1500.85 " 30 " M 40 d. 1430.65 Nov. 15 " " 60 d. 1743.44 Dec. 15 " " 30 d. 1365.42 35. What is the cash balance on the following acct., Jan. 10th, 1882 ? Dr. S. B. Chittenden in acct. with A. T. Stewart. Or. 1881. Aug. 4 To Sundries,3 m. $1400 July 5 By Mdse., 3 mo. $685 * 20 a a a 1050 " 18 a <( tt 840 Sept. 10 a a a 780 Aug. 11 a (( a 960 " 24 a a tt 1300 " 18 " Draft, 30 d. 800 36. Reduce the following transactions to the form of an acct. bearing interest at 6%, and find the cash balance : Feb. lith, 1870, C bought goods of D amounting to $1250; March 14th, a bill of $2160 ; Apr. 10th, a bill of $1700; Apr. 30th, a bill of $1070 ; May 6th, a bill of $2000. March 1st, 1870, sold a bill to D of $1640 ; March 20th, a bill of $1160; Apr. 15th, a bill of $1600 ; May 1st, a bill of $1340 ; May 21st, a bill of $1000 ; what was the cash balance June 10th, 1870 ? 37. What was the cash balance due July 20th, 1869, on the following account, at 1% int. ? s(Dr. George Clark & Co. in acct. with Chas. Anderson. Cr. 1869. Mar. 1 For Mdse., 3 mo. $500 1869. Apr. 5 By Mdse., 3 mo. $350 " 20 " 2 mo. 750 " 20 " " 2 mo. 900 Apr. 10 " 5 mo. 410 May 1 " " 4 mo. 620 May 21 " 1 mo. 600 " 22 " Cash. 200 1 54 Percentage. 38. Find the balance due Sept. 1st, at 6% on the preceding amount. 39. Find the balance of the same account due Nov. 1st, at 6%. 40. Reduce the following memoranda to the form of an account, and find the cash balance due Jan. 1st, 1879 : Aug. 1st, 1878, A bought goods of B amounting to $560 ; Aug. 26th, $840 ; Sept. 21st, $1000 ; Oct. 12th, $1370 ; and Nov. 1st, $600. A sold B, Sept. 11th, 1878, wheat amounting to $350 ; Oct. 1st, wool amounting to $760 ; Oct. 31st, $400 worth of butter ; and Nov. 16th, paid him $1000 cash. Account Sales. 364. An Account Sales is a record of the goods sold by an agent for his principal, with his expenses and charges. Notes. — 1. The charges include freight, cartage, storage, advertising, insurance, commission, guaranty, etc. 2. The invoice or sales form the credit side of the account, and the expenses the debit side. l. H. Standart, of Detroit, sold March 12, 1883, the following consignment of goods for J. L. Starbuck & Co., of Boston : 150 pieces Merrimac prints, at $4 ; 135 pieces shirting, at $7.50; 1 case of 85 Bay State shawls, at $8.75 ; 65 pieces flan- nel, at $12.50; 300 pair shoes, at $2.25; 150 pair boots, at $4.20. Charges for freight, $35.00 ; cartage, $3.50; storage, $5.00 ; insurance, $6.50; commission and guaranty, b%. What were the net proceeds ? Averaging Accounts Sales. 155 Account Sales of Merchandise for acct. and risk of J. L. Starbcjgk & Co., Boston. Mar. 12 To J. Smith, 150 pes. Mer. pr. @ $4 " 135 pes. Shirt.® $7.50 Hoyt & Co., 1 c. 85 B.S.sh.@$8.75 " 65 pes. flan. @ $12.50 L. Wood, 300 pr. shoes @ $2.25. " 150 pr. boots @ $4.20, Charges. Freight, -------- Cartage, - - Storage, --.----- Insurance, -- - Commission and Guaranty, 5$, - Net Proceeds, - - $600 1012 50 743 75 812 50 675 630 $4473 $35 3 50 5 6 50 223 69 273 $4200 75 69 06 2. Put the following into the form of an Account Sales : James Scott, of New Orleans, sold on account of J. Hamil- ton, of Cincinnati, Nov. 16th, 1882, 300 bbls. of pork to W. Gerard & Co., at $27 ; 1150 hams, at $1.75, to J. Ramsey ; 875 kegs of lard, each containing 56 lb., at 12 cts., to Henry Parker, and 750 lb. of cheese, at 18 cts., to Thomas Young. Nov. 30th, 1882, paid freight, $65.30; cartage, $15.25; insurance, $6.45; commission and guaranty, at 5%. What were the net proceeds ? 3. Samuel Basset, of New York, sold on account of James Field, of St. Louis, Dec. 3d, 1882, 85 bales cotton, at $96.50; 63 barrels of sugar, at $48.25 ; 37 bbls. molasses, at $35. Paid freight, $45.50 ; insurance, $15; storage, $35.50; com- mission and guaranty, 3 \%. What were the net proceeds ? 365. The Commission and other charges are considered due by some at the average date of sales ; by others at the average maturity of sales. This is usually settled by agreement. 156 Percentage. Note. — The method of averaging an account sales is the same as that for averaging an account having both debits and credits, except in the matter of adjusting the date for the commission and other charges. 366. To Average an Account Sales, and find when the net pro- ceeds are due. 4. Average the following, and find the due date of net proceeds: Eeceived on consignment, 1000 bbl. flour from B. & Co., Chicago. Sales. July 11 Aug. 5 u 20 Sept. 2 July 1 u 1 a 3 200 bbls. flour, sold on 30 d. 350 " " " 10 d. 250 " " * 30 d. 200 " " " 60 d. Charges. Freight, - - Cartage, Storage, - Commission, 2\% on $5920, • Commercial Balance, - 55.50 6.20 6.00 5.75 |$1100 00 2170 00 1500 00 1150 00 $5920 $450 25 30 75 150 00 148 00 779 $5141 00 00 00 SOLUTION. I. Find the average date of sales Date. Due Aug. 10 " Sept. 19 " Nov. 1 Items. $1100 2170 1500 1150 $5920 Days. 40 45 80 123 Products. $44000 97650 120000 141450 ) 403100 Av. time of sales, 68 days. Sales due July 1st + 68 d. = Sept. 7th. Averaging Accounts Sales. 157 II. Find the average date of Charges : Date. Items. Days. Products. ue July 1 $450.25 $00.00 u u 1 30.75 00.00 « 3 150.00 2 300.00 " Sept. 7 148.00 68 10064.00 779.00 ) 10364.00 A v. time, 13 days. Charges due July 1st + 13 d. = July 14th. Averaging the sales and expenses, they now stand as follows : Date. Items. Days. Prod. Date. Items. Days. Prod. Due July 14 $779 13 10127 | Due Sept. 7 $5920 68 402560 _779 ^0127 15141 ) 392433 Av. time, 76 d. Net proceeds $5141 due July 1st + 76 d. = Sept. 15. Hence, the Rule. — I. Find the amount and the average date of sales. The date of sales will be the date of the commis- sion and guaranty. (Art. 357.) II. Find the average date of the charges, make the charges the debits and the sales the credits, and find the average date for paying the balance. 5. Put the following items into the form of an account sales, find the net proceeds and date of payment : A. B. Harrison, of Buffalo, sold a consignment of goods from Chase & Co., Chicago, as follows: Nov. loth, 1882, 135 chests tea, at $45, on 30 d. ; 'Nov. 20, 75 sacks coffee, at $28, on 2 mo.; Dec. 1, 256 kegs lard, at $4.50, 30 d.; same date 285 tubs butter, at $18.37, on 2 mo. Paid freight Dec. 1, $23.75; cartage, $5.40; storage, Dec. 10, $7.80; commission, 2J$. 6. Same parties sold Sept. 1, on 3 mo., 3520 lb. sugar, at !12J; Sept. 15th, 25 chests tea, each 85 lb., at .98, on 2 mo.; Oct. 2, 28 half-chests Oolong tea, 42 lb. each, at $1.05, on 2 mo. The charges were paid Oct. 15, freight and cartage $85, commission and guarantee 5%. 1 AET^ERSHIP. fe- 11 -^- 367. Partnership is the association of two or more persons for the transaction of business. 368. The persons thus associated are called Partners. 369. The association is called a Firm, Company, or House. 370. The Capital is the money or property furnished by the Partners. 371. The Assets or Resources of a firm are various kinds of property belonging to it. 372. The Liabilities are its debts. 373. The Net Capital or Worth of a firm is the excess of its property above its liabilities. 374. The Insolvency of a firm is the excess of its liabilities above its property or resources. Note. — The Net Insolvency is the difference, made by the gains of a firm, between its present and former insolvency. 375. The Net Gain or Loss is the difference between the total gains and total losses. 376. Partnerships are General, Special, or Limited. 377. A General Partnership is one in which not only the property of the firm, but the private property of each of the partners is liable for its debts. 378. A Special Partnership is one in which a person puts in a certain amount of money, and loses only that amount in case oifailure* Partnership. 159 379. A Limited Partnership is one in which, if certain things are done, a person's private property shall not be respon- sible for the firm debts. Notes. — The things required in most States for the formation of limited partnerships are : - v 1st. The arrangements must be in writing, signed and recorded in a cer- tain public office. 2d. There must be at least one general partner. 3d. The special partners can take no actim part in the business, and their names must not appear in the firm name. 4th. The amount which the special partners contribute must be actually paid in and duly advertised. If any one of these requirements is omitted* the partnership becomes general. 380. The gains and losses of a firm are divided according to the previous agreement between the partners. Thus, In some cases the gains or losses are divided in proportion to> the capital, or the average investments of the partners. In others the inequalities of 'their investments are adjusted by allowing each partner a specified salary, which is taken from the gains of the firm before they are divided, no interest account being kept. But the more common practice is to credit each partner with interest on his capital and charge him interest for sums he draws out ; then divide the gain or loss according to certain percentages or fractional parts. Notes.— 1. Upon dissolution the partners are individually liable for the existing debts of the firm. 2. If a partner assigns his interest in the business, the word " release" must be used in order to pass the whole interest. 381. To find the Net Gain or Loss of a Partnership. l. A and B commenced business with a capital of $8000 cash and $3000 merchandise, and bills payable $1450. At the end of the year they had $5500 in banfc^$4500- ij% goods, and $2950 in bills receivable, and debts ow<£t by firm $9$). What was the net gain or los§ of the firm ? 160 Percentage. Assets at Commencement. Cash $8000 Mdse 3000 Assets 11000 Liabilities 1450 Net capital $9550 $12000- $9550 = $2450, Net gain, Ans. Hence, the Assets at Close. Cash in bank $5500 Mdse 4500 Bills receivable 2950 Assets 12950 Liabilities 950 Net capital $12000 Rule. — To find the Net Gain. — Subtract the net capital at commencement from the net capital at closing. To find the Net Loss.— Subtract the net capital at clos- ing from the net capital at commencement. 382. To divide the Gain or Loss in proportion to each partner's capital, when employed for the same period. l. A and B formed a partnership ; A furnished $3000, B $5000 ; they gained $2000, and agreed to share the profit or loss in proportion to the capital of each ; what was each partner's share ? 1st Method.— $3000 + $5000 = $8000 Capital of firm. f $$=§» hence A ' s share=$2000 x f = $750 A's gain. 5ooo_5^ m B's share = $2000 x § = $1250 B's gain. Proof.— Whole gain = $2000 2d Method.— The gain $2000-=-$8000 (cap.)=.25, or 25%. (Art. 216.) $3000 x .25 = $750 A's gain. $5000 x .25 = $1250 B's gain. Proof. — Whole gain-' 3d Method.— $8000 : $2000 : : $3000 : A's gain, or $750. $8000 : $2000 : : $5000 : B's gain, or $1250. Hence, Rules. — I. By Fractions. — Make each man's capital the numerator, and the irliole capital the denominator of a common fraction ; multiply the whole gain or loss by these fractions, and the products will be the respective shares of the gain or loss. Partnership. 161 II. By Per Cent. — Find what per cent the gain or loss is of the whole eapital, and multiply each man's capital by it. III. By Proportion. — The whole capital is to each part- ner's capital, as the whole gain or loss to each paHner's share of the gain or loss. 2. A and B buy a store which rents for $950 a year ; A advanced $3500, B $4800; how much rent should each receive ? 3. A and B form a partnership, A furnishing $2200 and B $2500 ; they lose $800 ; what is each one's share of the loss? ^4. The net gains of A, B, and C for a year are $12800 ; A furnishes $25000, B $18000, and $15000 ; how should the profit be divided? 5. A invested $12000 and B $8000 in a business. A's share of the gain or loss is to be § and B's -J. At the close of the year their resources are $25000 in goods and cash, and liabilities $15000 ; what is the net capital, and what each partner's share of the gain or loss ? 6. X, Y, and Z bought a ship on speculation ; X put in $30000, Y $20000, and Z $15000 ; they sold it at a loss of $7500 ; what was each man's share of the loss ? 7. A, B, C, and D form a partnership with a capital of $57000 ; A furnishing $10000, B $12000, C $5000, and D the remainder ; they make 15% of the joint stock ; what is each partner's share of the profit ? v 8. The shares of the joint stock of a firm consisting of three partners, are as £, -J, and J ; they divide a profit of $3900 ; what is each partner's share ? 9. A put $7500 and B $6000 into a land speculation ; and A's share of the loss was $225 ; what was B's share ? 10. Two men formed a partnership, the former furnishing 3 times as much capital as the latter ; they gained $12500 ; what was each one's share of the gain ? 168 Percentage. -4- 11. A, B, and entered into partnership; A furnishing £, B \ and C the rest of the capital. On winding up the busi- ness, O's share of the profit was $4518 ; what were the respec- tive dividends of A and B ? 383. When each partner is allowed to withdraw a stated sum, and no interest account is kept. (Art. 380.) 12. A and B form a partnership, investing $6000 each, and agree to share the gains or losses equally. A drew out $1200 and B $1000. Kequired the gain or loss of each at the end of the year, their books showing the following results : Resources. Cash $7000 Mdse. per inventory 7200 Bills receivable 2400 Debts due per Ledger 5000 Total resources $21600 Liabilities. Firm owes per Ledger $3000 Bills payable 1600 Total liabilities $4600 Net capital at closing is $21600- $4600 = A invested $6000 Less withdrawal 1200 $17000 A's Cr. balance. B invested $6000 Less withdrawal 1000 A's i net gain = $3600. $5000 B's Cr. balance. $9800 Net gain of firm $7200 B's ^ net gain = A invested $6000 Withdrew _1200 4800 A's £ net gain 360 A's net cap. at closing $8400 Proof. B invested $6000 Withdrew 1000 5000 B's I- net gain. 3600 B's net cap. at closing $8600 $8400 + $8600 = $17000, firm's net capital. Notes. — 1. Amounts withdrawn are sometimes considered resources. But money withdrawn by a partner cannot properly be said to belong to the resources of the firm. 2. When a partner has a fixed salary it is generally considered a part of his investment. Partnership Settlements. 163 13. A and B formed a partnership ; A furnished $15000, B 11250, and agreed that A should share J of the gain or loss, and B f. During the partnership A withdrew $600 and B $400. What were their gains or losses at the close, their resources being $21000 and liabilities $30000, no interest acct. being kept. OPERATION. Liabilities £30000 Less resources 24000 Firm's net insolvency. ...... 6000 A's floss 18750 B's § loss 12500 Total loss $31250 A's investment $15000 Lessarnt. withdrawn 600 $14400 B's investment $11250 Less amt. withdrawn 400 10850 Firms net investment 25250 Add firm's insolvency 6000 Firm's net loss $31250 A's | loss $18750 less net invest. $14400 = $4350, A's net insolvency. B's f loss $12500 less net invest. $10850 = 1650, B's net insolvency. Proof.— $6000, Firm's net insol. 14. A, B, and C formed a partnership; A put in $5000, B $4000, and C $2500. A withdrew $1000, B $800, and C $500. They agreed to share the gain or loss in proportion to their original investments, no interest account being kept. At the close, what was each partner's share of gain or loss, and the net capital of each, as shown by the following statement : Resources. Cash in bank $3475 Mdse. per inventory 5150 Bills receivable 4225 Debts due firm . . . . . 3150 Total resources $16000 Liabilities. Bills payable $3000 Rent, etc 700 Debts firm owe 2300 Total liabilities $6000 15. A put $10000 into a partnership and B $5000. They agreed to divide the gain or loss in proportion to their original investments, and to keep no interest account. During the year A withdrew $800 and B $500 ; what was the net capital of each at the close of the year, their resources being $25800 and their liabilities $18500 ? What per cent of their investment was the gain or loss ? 164 Percentage, 384. When one or two partners are allowed a fixed salary and no interest account is kept. 16. A and B formed a partnership, agreeing to share the gains or losses according to their investments; A furnished $20000, and was to receive a salary of $1000, B furnished $15000, and was to have $750 salary ; what was the gain or loss of each and what his net capital at the close, by the following statement : Resources. Liabilities. Cash on hand $6000 Bills payable $14000 Mdse. per inventory 5000 Rent, etc 1500 Bills receivable _3500 Total liabilities $15500 Total resources $14500 Liabilities $15500 Resources 14500 Firm's net in sol 1000 A's 2 loss 215711 Total loss $37750 A's invest Add salary 1000 $21000 B's invest 15000 Add salary 750 15750 Firm's net invest 36750 Add firm's net insol 1000 Firm's net loss $37750 A's | loss, $21571.43 less net invest. $21000 = $571.43 A's net insolvency. B's f loss, $16178.57 less net invest. $15750 = 428.57 B's " Proof $1000.00 Firm's net insol. 17. A and B each invested $6000. A received a salary of $1000 a year, and B $1500 for services. A drew out $650, B $500. What was each partner's interest in the firm at the end of the year, by the following statement : Resources $48500 Liabilities 1250 Firm's net cap $36000 A's investment $6000 A's salary 1000 7000 Less amt. withdrawn 650 A's credit balance 6350 B's investment $6000 B's salary 1500 7500 Less amt. withdrawn 500 B's credit balance 7000 13350 Net gains of firm $22650 Partnership Settlements. 165 A's credit balance $6350 B's credit balance $7000 " i gain 11825 " net capital " Again 11325 " net capital $17675 385. To find each partner's interest at the end of the year or close of the partnership. 18. A and B formed a partnership Jan. 1st, 1882, and agreed to share the gains or losses equally. A's capital was $6000 and B's $7250 ; each partner was allowed 6% on his capital and charged 6% for the sums withdrawn. March 1st, A withdrew $300; July 9th, $250 ; Sept. 10th, $200 ; Dec. 18th, $150. B withdrew Apr. 17th, $100; Aug. 4th, $400; Nov. 23d, $250. "What was each partner's interest in the business Jan. 1st, 1883, their resources being $26500 and liabilities $6000 ? Resources $26500 Liabilities 6000 $20500 Firm's net capital- A's amt. withdrawn $900 ; Av. date July 7th, 178 d. to Jan, 1st. B's " " $750; " " Aug. 27th, 127 d. " " A's capital - $6000 Less withdrawn 900 $5100.00 Int. on cap. 1 yr $360 Less int. on $900, 178 d 26.70 333.30 A's credit balance $5433.30 B's capital $7250 Less withdrawn 750 $6500.00 Int. on cap. 1 yr $485 Less int. on $750, 127 d 15.87 419.13 B's credit balance $6919. 13 Firm's net capital $20500.00 A's credit balance $5433.30 B's " " 6919.13 12352. 43 Firm's net gains $8147.57 B's credit bal $6919.13 " igain 4073.781 " net capital $10992.9H A's credit bal $5433.30 " i gain 4073.78^ " net capital $9507.08^ Firm's net capital, $20500. 166 Percentage. 19. C and D formed a partnership with a capital of $12000 apiece. They agree to share the gains or losses equally, each receiving interest on his capital and paying interest on all sums he withdraws. At the close of the year they had cash in bank $8000, merchandise $32500, bills receivable $2000. They owed bills payable $4000, other debts $5040. During the year C drew out $2015, the int. on which to the end of the year was $40.50. D drew out $4100, the int. on which to the end of the year was $32. How much did they gain or lose, and what was each partner's net capital at the end of the year ? 20. A firm of 3 partners commenced business with a capital of $6000 each. The gains and losses were to be shared equally, each was to have interest on his capital and pay interest o*n sums withdrawn, which sums were considered as taken from the gains and not from the capital. What was the net gain or loss, and what each partner's net capital at the end of the year, when their accounts were as follows : Assets. Cash $4250.00 Mdse 16500.00 Bills receivable 1000.00 Debts due firm 4120.67 Partners' withdrawals with interest. Adrewamt 1027.72 B " " 2070.11 C " " 3242.04 $32210.54 Liabilities. Bills payable $500.00 Personal debts 630.35 Cap. with interest 19080.00 Net gain 12000.19 A's± gain... $4000.06 Drew out.... 1007.57 A's bal 2992.49 B'sigain.... 4000.06 Drew out.... 2049.6 1 B's bal 1950.45 C'sigain 4000.06 Drew out.... 3213.92 C's bal $786.14 $32210.54 21. The firm of A & B formed a partnership Jan. 1st for 1 year, investing $8000 each. They were to have 6% interest on their capital and be charged 6% on sums withdrawn. The gains or losses were to be shared equally. Apr. 4th A drew out $500, July 10th $400, and Sept. 5th $200. B drew out May 6th $700, Aug. 12th $300, and Oct. 4th $400. What was each partner's net capital on closing, the net gains being $3850 ? Partnership Settlements. 167 386. To divide the gain or loss in proportion to each partner's capital, when employed for different periods, or by Averaging their investments. Note. — An Average Investment is a sum invested for a certain period, equivalent to several investments for different periods. (Art. 348.) 22. A and. B enter into partnership ; A furnishes $4000 for 8 months, and B $6000 for 4 months ; they gain $2300 ; what is each one's share of the profit ? Explanation. — In this case the profit of each partner depends on two elements, viz. : the amount of his capital and the time it is employed. The Int. of $4000 for 8 mo. - Int. $4000 x 8 = $32000 for 1 mo. And " $6000 " 4 mo. = " $6000 x 4 = $24000 " 1 mo. Whole capital = $56000 They gained $2800; and $2800 -=-$56000 = .05, or 5%. $32000 x .05 = $1600.00, A's share. $24000 x .05 = $1200.00, B's share. Hence, the Rule. — Multiply each partner's capital by the time it is employed. Consider these products as their respective capitals, and proceed as in the last article. Note. — The object of multiplying each partner's capital by the time it is employed is, to reduce their respective capitals to equivalents for the same time, or to average their investments. (Art. 353.) 23. A, B, and C form a partnership ; A furnishing $1500 for 9 mo., B $1700 for 10 mo., and C $1400 for 15 months ; they lose $1600; what is each man's share of the loss ? 24. Jan. 1st, A, B, and C form a partnership ; A puts in $4000, but after 6 mo. withdraws $1000 ; B puts in $3000, and adds $500 after 4 mo. ; puts in $2000 for the year ; they gain $1800 ; what is the share of each ? 25. A, B, and began business Jan. 1st, when A put in $7500, and July 1st he put in $2500 more ; B put in Jan. 1st $12000, and May 1st withdrew $4000 ; C put in Jan. 1st $10000, Aug. 1st he added $3000, and Oct. 1st he withdrew $7000. At the close of the year the profit was $8500 ; how much ought each to have, the gains being divided according to their average investment ? 168 Percentage. OPERATION. Jan. 1st, A invested $7500 x 12 = $90000 for 1 mo. July 1st, A « 2500 x 6 = 15000 $105000 Jan. 1st, B " 12000 x 12 = 144000 May 1st, B withdrew 4000 x 8= 32000 112000 $217000 Jan. 1st, C invested 10000 x 12 = 120000 Aug. 1st, C " 3000 x 5 = 15000 135000 Oct. 1st, C withdrew 7000 x 3 = 21000 114000 Total average investment for 1 month = $331000 A's share of profits, $8500 x iff = $2696if f B's " " $8500 x iff = $28763 4 3 4 T C's " " $8500 x H 4 - = $2937j|f Proof.— $8500, entire profits. Explanation. — Each investment and withdrawal is multiplied by the number of months between its date and the time of settlement. The products of each partner's withdrawals are subtracted from the products of his investments, and the remainder is his average investment. The sum of the average investments is the denominator and each separate invest- ment the numerator of the fractions which indicate each partner's share of the gain. Note. — The same result may be obtained by either of the preceding methods (Art. 382). When the first method is used, the fractions should be reduced to their lowest terms. 26. A and B formed a partnership and divided the gain or loss in proportion to their average investments. A put in $6000 for 12 months, and afterwards $4000 for 6 months. He withdrew $3000 for 4 mo., then $6000 for 2 mo., before the close of the partnership. B put in $7000 for 12 mo., then $6000 for 8 mo. He withdrew $4000 for 5 mo., then $8000 for 2 months. They gained $4560; what was each partner's share ? 27. X, Y, and Z formed a partnership ; X putting in $3000 for 1 year, Y $4500 for 8 months, and Z $5000 for 6 months ; they lost $4000 ; what was each man's share of the loss? 28. Three men hire a pasture for $87.50. A put in 10 cows for 7 months, B 60 sheep for 5 months, and 12 horses for 3 months ; 5 sheep being considered equal to 1 cow, and 4 horses equal to 5 cows ; how much should each pay ? 29. A and B are partners, A putting in $4500 and B $2500 ; after 6 mo. they take in C who furnished $10000 ; their gain for the year was $5000 ; what was Mie share of each ? Bankruptcy. 1G9 30. Two men entered into speculation and their profits dur- ing the year were $6240. At first A ? s capital was to B's as 3 to 2 ; after 4 months A withdrew £ of his and B £ of his ; how ought the gain to be divided ? 31. A firm commenced business with a capital of $15600, and doubled it in 1 year. A put in ^ for f of the yr., B -f for £ of the yr., and the balance for f| of the yr. What was each partner's interest in the concern at the end of the year ? 32. A and B are partners, each furnishing $10000 ; after 4 mo. A took out $1000 and B $1500 ; 4 mo. later each took out the same sum as before, and at the end of the year the assets of the firm were $15136 ; to what share was each entitled ? 33. Three men form a partnership and contribute $20000, $30000, and $40000 respectively. A drew out $3000, B $4000, and $5000 a year and in 3 years the assets of the firm were $120000 ; how much belonged to each ? BANKRUPTCY. 387. A Bankrupt is a person who is insolvent, or unable to pay his debts. 388. Bankruptcy is the state of being insolvent or a bankrupt. Note. — After the assets of a bankrupt have been applied to meet his liabilities, he still remains liable for them unless discharged by a Court of Bankruptcy, or by a compromise with creditors. 389. The Assets of a bankrupt are the property in his possession. The Liabilities are his debts. 390. The Net Proceeds are the assets less the expense of settlement. They are divided among the creditors according to their claims. Note. — The claims of a certain class of creditors, as employees and others, are paid in full up to a certain amount. These are called "Pre- ferred Creditors." 170 Percentage, 391. To find each Creditor's Dividend, the Liabilities and Net Proceeds being given. l. A merchant failing in business made the following state- ment: Liabilities. Notes outstanding $1200 A. Booth & Co 2500 Bliss &Co 8750 Total $12450 Assets. Cash $2737 Real Estate 1500 Merchandise 2950 Total 7187 Expenses of settling 215 Net assets $6972 The net assets $6972.00-*- $12450 liabilities = .56, or 56%, rate. Dividend to creditors is $1200 x .56 = $672 on notes, $2500 x .56 = $1400 to Booth & Co., and $8750 x .56 = $4900 to Bliss & Co. Hence, the Rule. — Find what per cent the net proceeds are of the liabilities, and multiply each creditor's claim by it. 2. A bankrupt owes A $6500, B $4600, and D $3800; his assets are $5950, and the expenses of settling $1700 ; what per cent and how much will each creditor receive ? 3. A R. R. Co. went into bankruptcy, owing $48500, and having $13300 assets ; the expense of settling was h% of the amount distributed to creditors. What per cent and how much did a creditor receive on $8350 ? (Art. 216.) 4. A manufacturer failed, owing A $12260, B $13850, and C $14560 ; his assets were $28350, and the expenses of settling were $1250. He owed $850 to employees who were to be paid in full ; what per cent and how much did the other creditors receive ? GENERAL AVERAGE. 392. General Average is the equitable apportionment of losses at sea among the owners of a cargo, when the safety of the vessel required a portion of it to be thrown overboard. Notes.— 1. The voluntary sacrifice of property for safety is called Jettison. General Average. 17i 2. The parties whose goods are sacrificed are not paid in full, but bear their proportion also for the loss sustained. 3. Insurance companies bear their proportion of the loss, as found by general average. 393. To establish a valid claim for a general average, three things must be made apparent : 1st. An imminent common peril, and necessity for sacrifice. 2d. A voluntary sacrifice oi apart to save the remainder. 3d. The success of the effort to save a part, as a result of the sacrifice. Note. — The jettison is included in the contributory interests, and bears its proportion of the loss. 1. A, B, and C freighted a vessel with flour from New York to New Orleans; A had on board 1800 barrels, B 1200, and C 600 ; on her passage 600 barrels were thrown overboard. Beckoning the value of the flour at $5.50 a barrel, what was the average loss ? Note. — Find the per cent of loss as in the last Article, the sum of the values of the contributory interests being as the base. (Arts. 219, 254.) 2. In a heavy storm, the master of a London packet threw goods overboard to the amount of $15000. The whole cargo was valued at $74000, and the ship at $38000 ; what per cent loss was the general average ; and how much was A's loss, who had goods aboard to the amount of $16000 V 3. If an Insurance Co. had assumed a risk amounting to $12000, at 2|% on the vessel and cargo mentioned in the above example, and paid a general average loss, what would have been its real loss by the disaster ? (Art. 215. ) 4. The sloop Huron, from Chicago, carried 3000 bushels wheat for T. Hamilton & Co., insured in Co. B. for $3000, at 2% ; 2500 barrels flour, valued at $5 a barrel, for G. Standart, insured in Co. C. at 2\% ; and 500 bu. corn, valued at 50 cts. a bu., for Gardner & Co , insured in Co. D. at \\%. The vessel was insured for $25000, \ its value, in Co. A., at 3%. During a storm the flour was thrown overboard ; what per cent was the general average, and what the loss of each. (s^^ 394. The arrangement of problems under different heads, as Profit and. Loss, Commission, Interest, Proportion, etc., is convenient for reference and review, but experts perform most of their business calculations by Analysis. 395. No specific rules can be given for the solution of problems by analysis. Common sense and judgment are the best guide. 396. The reasoning in general proceeds from that which is known or self-evident, to that which is required ; from a part to the whole, or from the whole to a part ; from a given cause to its effect, or from a given effect to its cause. 397. Like Numbers only can be compared. When fractions have a common denominator, their numerators are compared like integers. 398. In finding what part one number is of another, the number denoting the part is the numerator and that with which it is compared the denominator. Note. — If either or both the given numbers are fractional, they should be reduced to a c. d. ; their numerators are then compared like integers. l. A merchant made $8368 in two years, and the differ- ence in his annual gain was $986 ; what was his yearly profit ? Solution. — The sum minus the difference equals twice the less number. Therefore, $8368-$986 = $7383, and $7382-5-3 = $3691, the less. And $3691 + $986 = $4677, the greater. General Analysis. 173 2. Bought a span of horses and a carriage for $1856 ; the • horses were worth $268 more than the carriage ; what was the price of each ? 3. To what number must 962 be added 3 times to make 8472? 4. Bought a horse for $465, and sold it for $240; what part of the cost did I get ? Solution.— $240 = ffg, or H oi $465 ; hence I got |f of $465. 5. What part of 112 yards are 96 feet? What part of 112 rods ? 6. Wliat part of ^ is -J^ ? Note. — Reduced to a c. d. the given fractions become £ £ and §§, which are like fractions. Now 22 is f § of 35, Ans. 7. If y\ of a ship cost £273 2s. 6d., what will g% cost ? 8. What part of £f is ^ ? 9. What part of 46f is 18| ? 10. A merchant lost $5367, which was ^ of his capital ; what was his capital ? Analysis. — Since $5367 = T 3 ff of his capital, ^ of it was \ of $5367, or $1789, and \%, or the whole, was $17890, Ans. 11. A drover being asked how many sheep he had, replied, 2149 are equal to T 7 g- of them ; how many sheep had he ? 12. A man being asked his age replied, If you add to it its half, its third, and three times three, the sum is 130; what was his age ? 13. | of a number exceeds \ of it by 20; what is the number ? 14. A real-estate agent sold a house for $7265 ; what was his commission at 3% ? Solution. — Since his commission on $1 was $ T f TT , on $7265 it was $7265 x jf, = $217.95, Ans. 15. A house valued at $8241 is insured for f its value at \%\ what is the premium ? 174 General Analysis, 16. A country trader buys a stock of goods amounting to $3450 ; the commission charged for buying was %\% \ bow much must he remit to pay for the goods and commission ? 17. An auctioneer sold a lot of goods amounting to $15600 at %\% commission, and 2\% for guaranty ; the charges were, for advertising $25.50, for storage, labor, and cartage $34.50 ; how much was due the owner ? 18. A miller bought a cargo of wheat for $12600, and sold it at a profit of 15£% ; how much did he gain ? Solution.— 15^% is .155 of $1. Therefore, on $12600 lie gained $12600 x .155 = $1953, Ans. 19. Bought a quantity of lumber for $5200 ; paid for freight and cartage $85, commission $135. I gained 28% on the entire cost ; for how much was it sold, and what was my profit ? 20. If 12% of $97.50 be lost, what amount will remain ? 21. A man owning f of a bank, sold 35% of his share ; what per cent of the whole was left ? 22. 24 is f per cent of what number ? 23. A man owned -f of a mine, and sold f of his interest for $1710; what was the whole cost? 24. What is the interest of $840 for 2 yr. 8 mo. 24 d. at 6%? Analysis.— The prin. $840 x .06 = $50.40, int. 1 yr. Int. for 2 yr. at 6% = $50.40 x 2 = $100.80 Int. for 8 mo. (f yr.) = $50.40 x f = 33.60 Int. for 24 d. (f mo.) = $4 20 x § = 3.3 6 Int. for 2 yr. 8 mo. 24 d. = $137.76 Or, the int. of $1 for 1 yr. is $.06 ; for 2 yr. 8 mo. 24 d. = 2\l yr., it is SH x .06, or 41 ?g 06 , and the int. of $840 will be *H**£X ^M- = $137.76, Ans. 25. What is the interest of $1165.50 for 5 yr. 3 mo. 9 d. at n ? 26. What principal on interest from Apr. 9, 1881, to Sept. 5, 1883, will amount to $1477.59, at 7 per cent f General Analysis. 175 27. If #600 at simple interest amounts to 8684 in 2 yr. and 4 mo., what is the rate per cent ? Analysis.— $684, arat.— $600, prin. = $84, int. The interest of $600 for 1 yr. at \% = $6.00. The interest of $600 for %\ yr. at 1 % = $14.00. Since $14 int. require the prin. at 1% fy yr., $84 int. for the same time will require as many per cent as $14 are contained times in $84, or t h e un k. nown te rm. is money, make $54 the third 3 term, 18 chairs the first term, and ^-iir^ = $432, Am. 144 the second. The product of PkOOF. ^t =■ Ai or 1 \ . the means divided by the given extreme gives the other extreme, or unknown term. Hence, the Rule. — I. Arrange the numbers so that the third term may be of the same hind as the answer. II. When the answer is to be larger than the third term, make the larger of the other two numbers the second term; but when less, -place the smaller for the second term, and the other for the first. III. Multiply the second and third terms together, and divide the product by the first ; the quotient will be the fourth term or answer. Notes. — 1. The factors common to t\\e first and second, or to the first and third terms, should be cancelled. 2. The first and second terms must be reduced to the same denomina- tion. The third term, if a compound number, must be reduced to the lowest denomination it contains. II. By Cause and Effect. 429. A Cause is that which does something. An Effect is something which is done. Notes. — 1. Men or animals and machinery, goods bought or sold, money at interest, time, etc., are causes; for the increase of either, increases the effect produced. Work done, provisions consumed, cost of goods, etc., are effects. 2. In examples of freight, distance and magnitude may be regarded as causes, producing money for their effect. 3. A little practice will give great facility in distinguishing between causes and effects. Simple Proportion, 183 430. 2. If 8 men mow 24 acres in 1 day, how many acres will 25 men mow in the same time ? Analysis. — In this example the statement. 2d effect is required, which is an ex- tstC. 2d C. IstE. 2dE. trenie. Put X in its place. 8 m.: 25 m. : : 24 A. : X A. 8 m. (1st cause) is to 25 m. (2d cause) as (25 X 24) -v-8 =c 75 A., Ans, 24 A. (1st effect) is to x A. (2d effect). Since the product of the means equals that of the extremes, the prod- uct of two numbers and one of the numbers is given, to find the other number or unknown term. (25 x 24)-s-8 = 75 A., Ans. 3. If 25 bushels of wheat make 8 barrels of flour, how many bushels will be required to make 54 barrels ? Analysis.— In this example statement. the 2d cause is required, which *•*<*• 2d c - lstE - 2 <1E. we represent by x bu. The 25 bu. : X bu. : : 8 bbl. : 54 bbl. product of the extremes, or x = (54x25)-^8 = 175 bu., Ans. perfect terms, divided by the mean, gives the required term, which is 175 bushels. Hence, the Kule. — Make the first cause the first term, the second cause the second term, the first effect the third term, and the second effect the fourth term ; -putting x in the place t of the unknown tej*m. If the unknown term is an extreme, divide the prod- uct of the means by the given extreme ; if a mean, divide the product of the extremes by the given mean, (Art. 424, 2°, 3°.) Notes. — 1. All the elements contained in one antecedent or cause must be in its consequent, and all the elements in one consequent or effect must be in the other as factors. 2. In inverse proportion, 1st C. : 2d C. : : 2d E. : 1st E. 3. In continued action, causes embrace both an agent and time. 4. An effect may be a simple result, or both a result and time, or it may embrace length, breadth, and thickness. 4. If a ship has sufficient water to last a crew of 28 men for 18 months, how long will it last 25 men ? 18.4 Proportion. 5. If 18 ounces of silver will make 8 teaspoons, how many spoons will 24 pounds of silver make ? 6. If a railroad ear runs 225 kilometers in 8 hours, how far will it run in 12f hours ? 7. If 20 yards of cloth, £ yd. wide, are required for a dress, what must be the width of a piece 12 yds. long to answer the same purpose ? 8. If the interest of $675.25 is $55,625 for 1 year, how much will be the interest of $4368.85 ? 9. What cost 11 lb. 4 oz. of tea, if 3 lb. 12 oz. cost $3.50? 10. Find the value of the unknown term in $4 : x : : 9:16. 11. If I own f of a farm and sell f of my share for $2300, what is the value of the whole farm at the same rate ? 12. If 14 acres of meadow yield 32| tons of hay, what will 5J acres produce at the same rate ? 13. If 36 horses eat 92 hektoliters of oats in a week, how many hektoliters will 55 horses eat in the same time ? COMPOUND PROPORTION. 431. Compound Proportion is an equality between a com- pound ratio and a simple one, or between two compound ratios. Thus, . " > : : 24 : 63, and \ ' > : : j ' > are compound proportions. For, 7x3x24 = 2x4x63, and 2x3x9x4 = 4x2x3x9. It is read, ' ' The ratio of 2 x 4 is to 7 x 3 as 24 to 63." Note. — The value of a compound ratio equals the product of the simple ratios of which it is composed. Thus, £ x § = § x |> 432. The terms of a compound ratio may be considered in their relations to each other as causes and effects, as in Simple Proportion. Notes. — 1. All the terms of a compound proportion are given in pairs of the same kind, except one which is of the same nature as the term required. 2. The order of the terms and of each ratio is the same as in Simple Proportion. Compound Proportion. 185 l. If 4 men mow 60 acres in 10 d., how many acres can 6 men mow in 8 days ? Analysis.— In this problem the statement, 1st cause is 4 men and 10 days, the l8t c - 2d C. 1st E. 2d E. 2d cause is 6 men and 8 days, the 1st 4 m. : 6 m. ) _ . . effect is 60 A., the 2d effect z A. is 10 d. : 8 d. ) '' '' '' required. Dividing the product of the means by the product of the extremes gives 72 A., the term required. The factors may be arranged in 2 6 the form of a fraction, and the 6 X $ X $0 work much abridged by cancella- x — ^ x 10 = Ans. tion. 2. If 8 men can dig a ditch 60 ft. long, 8 ft. wide, and 6 ft. deep in 15 d., how many days will 24 men require to dig a ditch 80 ft. long, 3 ft. wide, and 8 ft. deep ? Analysis. — In thi s statement. problem the causes and lstc - 2dc - lstE - 2dE effects are both compound 8 m. : 24 m. ratios. The required term w *"* ' ^ i : : J 8 f t. : 3 ft. x is the 2d cause and is one lo d. I X d. J f P -ft • Q ff of the means. Dividing the product of the extremes + r - AlA A ^ & by that of the means gives x = * * ** * W * * * » = 20 = 31 d . x = 3* days, Am. Hence, U X 00 X $ X 6 the 4 Rule. — Arrange the causes and effects as in Simple Proportion, putting x in the place of the required term. When all the means are given, their continued product is the dividend and the product of the extremes the divisor. When the extremes are given, their product is the dividend, that of the means the divisor, and the quotient is the answer. Equal factors in the divisor and dividend should be cancelled. > Notes. — 1. The terms of each couplet in the compound ratio must be reduced to the same denomination, and each term to the lowest denom- ination contained in it, as in Simple Proportion. 186 Proportion. 2. When the same quantity is an element of both causes or of both effects, or when both antecedents or both consequents are the same quan- tity, it may be represented by the figure 1. 3. If the wages of 75 boys for 84 days were $68.75, how many days could 90 boys be employed at the same rate for $41.25 ?. 4. If 25 persons consume 300 bu. of wheat in 2 years, how much will 139 persons consume in 6 years ? 5. If a stack of hay 1 6 ft. high contains 12 cwt., what will be the height of a similar stack containing 6 tons ? 6. If a man pays $30 for freight on 90 bbl. flour to go 160 miles, what must he pay for 360 barrels to go 90 miles ? 7. A quarter-master wished to remove 160000 lb. of provi- sions from a fortress in 18 days; it was found that in 12 days 35 men had carried away but 25 tons, how many men would be required to carry the remainder in 6 days ? 8. If 6 journeymen make 132 pair of boots in 4J weeks, working 5-J days a week, and 12f hours per day, how many pair will 18 men make in 13| weeks, working 4 J days per week, and 10 hours per day ? 9. If 4 lbs. of yarn will make 12 yards of cloth 1 \ yard wide, how many pounds will be required to make a piece 200 yards long, and If wide ? 10. If $800 will earn $11.50 in 168 days at 6%, how much will $640 earn in 192 days at 9% ? 11. From a sheet of paper 25 in. long and 18 in. wide, a printer cut 30 pages for a book. How many of the same size pages could he cut from a sheet 24 in. long and 20 inches wide ? 12. If 3 men can do a piece of work in 6 days, working 10 hours a day, how long will it take 16 men to do twice the amount of work, when they work at it 9 hours a day ? 13. If 2 compositors can set 50 pages in 6 d. of 10 hr., when each page contains 36 lines of 48 letters, how many compositors will be required to set 192 pages, each having 40 lines of 54 letters, in 4 days of $ hours ? Partitive Proportion, 187 14. If $1200 will earn 819.20 interest in 6 mo. 12 d. at 6%, at what rate will $240 earn $14.40 in 4 months ? 15. If 100 horses consume a stack of hay 20 ft. long, 11 ft. 3 in. broad, and 31 ft. 6 in. high in 9 days, how long will a stack 18 ft. long, 5 ft. broad, and 14 ft. high supply 80 horses ? 16. Bought a pile of stone 24 ft, long, 12 ft. high, and 9 ft. wide for $120, and gave a note for $300 for a similar pile 12 ft. wide and 36 ft. long ; how high was the second pile ? 17. If 5 pumps, each having a length of stroke of 3 ft., working 15 hr. a day for 5 d. empty the water from a mine, what must be the stroke of each of 15 pumps which would empty the same mine in 12 d., working 10 hr. a day, the strokes of the former set of pumps being four times as fast as those of the latter ? PARTITIVE PROPORTION. 433. Partitive Proportion is dividing a number into two or more parts which shall have a given ratio to each other. 434. To divide a number into two or more parts, when the ratio of the parts to each other is given. l. A and B divided $396 in the ratio of 5 to 7 ; how much had each ? Analysis. — Since A had 5 opebation. parts and B 7, both had 54-7, (396 -r- 12) X 5 = $165, A's part, or 12 parts. Hence, A will ( 396 _^_ 12 ) x 7 = $231, B's " have -/a and B ^ of the money. Now fl of $396 = $165, and T 7 ¥ of $396 : IstC. 2dC. IstE. 2dE. Or, Sum of parts : whole No. : : each part : share of each. Hence, the Rule. — Divide the given number by the sum of the pro- portional numbers, and multiply the quotient by each one's proportional part. 2. Divide 624 into three parts which shall be to each other as 6, 8, and 12. 188 Proportion. 3. Divide 450 shares of stock among 3 persons, in propor- tion to the number of shares owned by each ; A holds 400, B 200, and C 300 ; how many shares will each receive ? 4. Three men engaged in trade agreeing to share the gains or losses in proportion to their investments ; A's capital was $6000, B's $8000, C's $10000; they gained $8800; what was each man's share ? 5. A, B, 0, and D commenced business with a capital of $18500; A invested $800 less than B, and invested $1000 more than A, and D $900 less than C ; how much did each invest ? 6. Divide 560 into parts, so that the second may be 4 times the first. Analysis. — The 1st part + 4 times the 1st part equals 5 parts. Since 5 parts equal 560, 1 part = 560 -f- 5 or 112, and 112 x 4 = 448 the 2d part. 7. Divide the number 582 into 4 such parts that the second may be twice the first, the third 21 more than the second, and the fourth 54 more than the first. 8. If C has twice as much money as B, and if $12 be taken from A's money, it will be equal to \ of B's ; how much has each, the sum of their money being $645 ? 9. If 6 lbs. of coffee cost $2,40, and 20 lbs. of coffee are worth 12 lbs. of tea, what will 120 lbs. of tea cost ? 10. If 8 grammars cost $6.40, and 9 grammars are worth 6 geographies, 48 spellers 10 geographies, 3 arithmetics 18 spellers, 15 readers 9 arithmetics, how much will 8 readers cost ? n. A, B, and C are in partnership; A puts in \ of the cap- ital, B T 5 ¥ , and C the remainder ; they gain $2150 ; what is the share of each ? 12. If | of A's money and £ of B's equal $900, and f of B's is twice § of A's, what sum has each ? 13. A father divided $18500 among 3 children, so that the portion of the second was greater by one-half than that of the first, and \ the first was equal to \ of the third; what was the share of each ? jXCHAN GE, 435. Exchange in Commerce is of two kinds, Domestic or Inland and Foreign. 436. Domestic Exchange is making payments between different places in the same country by Drafts, or Bills of Exchange. 437. Foreign Exchange is making payments between places in different countries, in the same manner. Note. — In commercial law, the different States of the United States are considered foreign to each other. But for the purposes of the present work transactions between them will be treated under Domestic Exchange. 438. The Par of Exchange is the standard by which the value of the currency of different countries is compared, and is either intrinsic or commercial. 439. Intrinsic Par is a standard having a real and fixed value represented by gold or silver coin. 440. Commercial Par is a conventional standard, having any assumed value which convenience may suggest. Note. — The fluctuation in the price of bills from their par value, is called the Course of Exchange. 441. A Bill of Exchange or Draft is a written order direct- ing one person to pay another a certain sum, at a specified time. 442. A Sight Draft is one payable on its presentation. 443. A Time Draft is one payable at a specified time after date or presentation. Note — Drafts or Bills of Exchange are negotiable like promissory notes, and the laws respecting them are essentially the same. 190 Exchange. 444. An Acceptance of a draft is an engagement to pay it. As evidence, the drawee writes the word accepted across the face of the draft, with the date and his name. Note. — Days of Grace are allowed on time drafts unless otherwise specified, but the number varies in different countries, from 3 to 12 days. DOMESTIC EXCHANGE. 445. To find the Cost of a Draft, when the Face and Rate of Exchange are given. l. What cost the following sight draft, at 2\% premium ? $ 2 7°°- New Orleans, Jan. 30th, 1882. At sight, pay to the order of James Calkins, twenty-seven hundred dollars, value received, and charge the same to the account of Selden" Bros., & Co. To S. Bliss & Co., New York. Explanation. — The remittor of the above sight draft is James Calkins, who bought it at the bank and had it made payable to his order. He owes J. Smith of New York $2700. He writes on the back of the draft, " Pay to the order of J. Smith," and signs his name. When Smith receives it he signs his name also on the back and takes it to S. Bliss & Co., for payment. Solution.— At Sj% premium, the cost of $1 draft is $1,025, and $2700 will cost $1,025 x 2700 = $2767.50, Ans. 2. What cost a sight draft on San Francisco for $2500, at 2\% discount. Solution. — A draft of $1 at %2\% discount will cost $0,975, and $2500 x .975 = $2437.50, Ans. Hence, the Rule. — Multiply the face of the draft by the cost of $1. What cost a sight draft for What cost a sight draft for 3. $8515, at \\% premium ? 9. $4265, at \\% discount? 4. $6845, at \% premium ? 10. $8500, at \% discount ? 5. $9875, at \% premium ? 11. $8763, at 50^ discount? 6. $7365, at 2% premium ? 12. $4562, at 75^ discount? 7. $3876, at 25 premium? 13. $8423, at \% discount? 8. $8245, at 50^ premium ? 14. $9654, at \% discount? Domestic Exchange. 191 Notes. — 1. On time drafts, both the rate of exchange and the interest are commonly included in the quotation prices. Brokerage is usually included in the rate of exchange. 2. When the rate of exchange exceeds the cost of shipping gold or cur- rency by express, one of them is sent instead of drafts. 15. What is the cost of the following time draft, at 1 \% pre- mium, and interest at Q% ? $5000. Philadelphia, June 4th, 1883. Sixty days after sight, pay to the order of George Wil- liams, five thousand dollars, value received, and charge the same to the account of H. Avery & Co. To S. Pakkhurst, Baltimore, Md. Explanation. — The above time draft, purchased by G. Williams from H. Avery & Co., is sent by W. to a creditor, A. B„ in Baltimore, with the indorsement " Pay to the order of A. B.," with signature. When A. B. receives it he takes it immediately to S. Parkhurst, who writes or stamps the word "accepted" across its face, with date and signature. The maturity of the draft is 63 days from the date of acceptance. Solution. — The cost of a sight draft of $1, at 1\ % premium=$1.0125 Subtracting the interest on $1 for 63 days (3 d. grace), at 6 % = 0.0105 The cost of $1 draft = 1.0020 Multiplying by 5000 Cost of draft for $5000 =$5010. 0000, Ans. Note — 3. Since the bankers in Philadelphia have the use of the money for 63 days before the house in Baltimore will pay the draft, the interest for that time, at the given rate, is deducted from the cost. 16. Find the cost in Denver of a draft on New York at 90 days sight, for $6265, at 2% premium, interest being 6% ? 17. Bequired the worth in Lexington, Ky., of a draft on Bos- ton for $4500, at 30 days sight, at 1% discount and interest 6%, 18. What is the worth of a draft of $5600 on St. Louis, at 30 days sight, premium 1-J$, including interest ? 19. A commission merchant in Chicago sold for a firm in Detroit a consignment of French china. The sales amounted to $10500, the commission was b% on sales. He sent a 30 days draft at \% discount in payment of the net proceeds; what did, it cost him, interest being 6% ? 192 Exchange. FOREIGN MONEYS OF ACCOUNT. 446. The value of the money unit of Foreign Countries in United States money is published annually by the Secretary of the Treasury. The following is the Report Jan. 1st, 1883. Country. Austria Belgium Bolivia Brazil British America.. Chili Cuba Denmark Ecuador Egypt France Great Britain. . . . Greece German Empire.. Hay ti India Italy Japan Liberia Mexico Netherlands Norway Peru Portugal Russia Sandwich Islands Spain Sweden Switzerland .... Tripoli » . . Turkey . . ... . U. S. of Colombia Venezuela Monetary Unit. Florin Franc. Boliviano Milreisof 1000 reis... Dollar Peso Peso Crown Peso Piaster Franc Pound sterling Drachma Mark Gourde Rupee of 16 annas Lira Yen Dollar Dollar. Florin Crown Sol Milreis of 1000 reis. . . Rouble of 100 copecks. Dollar Peseta of 100 centimes. Crown Franc of 100 centimes. Mahbub of 20 piasters. Piaster •. . Peso. Bolivar Standard Silver. . . G. and S Silver... Gold.... Gold.... G. and S G. and S Gold.... Silver Gold G. and S, Gold G. and S. Gold G. and S. Silver.... G. andS. Silver.... Gold.... Silver. . . . G. and S, Gold Silver Gold Silver Gold G. and S. Gold G. and S. Silver.... Gold Silver G. and S. Value in U. S. Money. .40,7 .19,3 .82,3 .54,6 $1.00 .91,2 .93,2 .26,8 .82,3 .04,9 .19,3 4.86,6| .19,3 .23,8 .96,5 .39 .19,3 .88,8 1.00 .89,4 .40,2 .26,8 .82,3 1.08 .65,8 1.00 .19,3 .26,8 .19,3 .74,3 .04,4 .82,3 .19,3 Foreign Moneys. 193 Notes. — 1. The Franc of France, Belgium, and Switzerland, the Peseta of Spain, the Drachma of Greece, the Lira of Italy, and the Bolivar of Venezuela are the same in value. 2. The Peso of Ecuador and of U. S. of Colombia, the Boliviano of Bolivia, and the Sol of Peru are the same in value. 3. The Crowns of Norway, Sweden, and Denmark are also the same in value. Quotations of Foreign Bills of Exchange. Sterling, 60 d., $482$. Reichsmarks (4). sight, $485. For long sight, .94f @ .94^ Cable transfers, $4.85 @ $4.85 J. For short sight, .95 @ .95$. Commercial, $4.80 @ $4.80$. Amsterdam, 60 d., .39$. Francs, 60 d., 5.23f @ 5.23$. " 3d. sight, .40$. Notes. — 1. Bills at 60 days are generally less than sight bills, because of the interest on them for the time. (For intrinsic par, see Table, Art. 446.) 2. Cable Transfers signify the method of sending funds to persons abroad by means of the Atlantic Cable. Payments are often effected by telegraph between distant places in the United States. 3. Commercial Bills are drafts drawn upon merchants. 4. Exchange on Paris is quoted by giving the number of francs and centimes to $1. The same applies to all countries where the franc and its equivalents are used. 5. Amsterdam quotations give the number of United States cents to the guilder or florin. Intrinsic par of 1 guilder = 40 r 8 T cents. 6. Quotations in Reichsmarks are based on the cost of 4 reichsmarks ; hence, .94| @ .94$ signify the number of cents to be paid for 4 marks. 447. The value of the unit of foreign moneys of account being given as in the table (Art. 446), the cost and face of bills are easily found by Analysis. 448. To find the value of Sterling money In U. S. money. l. Change £410 12s. 8-|d. to U. S. money. 8.5d. 12.708 Explanation. — Reducing the 12 shillings and pence to the decimal 20 of a pound, as in the margin, and multiplying by the value of £1 as 410.635 + given in the table, the result is ^10.635 X 4.8665 = 11998.355. $1998.355, Ans. 194 Exchange. FOREIGN EXCHANGE. 449. Bills of Foreign Exchange are commonly drawn in the money of the country in which they are payable. 450. A Set of Exchange consists of three bills of the same date and tenor, called First, Second, and Third of exchange. They are sent by different mails in order to save time in case of miscarriage. When one is paid, the others are void. Note. — Exchange with Europe is chiefly done through the large commercial centers, as London, Paris, Geneva, Amsterdam, Antwerp, Bremen, Vienna, Hamburg, Frankfort, and Berlin. 451. A Letter of Credit is a draft made by a banker m one country, addressed to foreign bankers, by which the holder may draw fnnds at different places in any amount not exceed- ing the limits of the letter of credit. Note. — Travellers generally prefer letters of credit to bills of exchange, because they can draw at any time and at different places such, sums as their convenience may require. 452. Sterling Bills or bills on Great Britain are quoted by giving the market value of £1 exchange in dollars and cents. 453. To find the Cost of Sterling Bills, when the Face and Rate of Exchange are given. l. Eequired the cost of the following bill on London, at $4.8665 per pound. £875 16s. Baltimore, Jan. 10, 1882. At ten days sight of this First of Exchange {Second and Third of same tenor and date unpaid), pay to the order of Peter Cooper, Eight Hundred Seventy-five Pounds Sixteen Shillings Sterling, value received, and charge the same to account of Henry Hayward, Jr. To James Kent & Co., Bankers, London. Analysis. — Reducing 16s. to decimals of a pound, the face of the bill £875 16s. = £875.8. Since £1 is worth $4.8665, £875.8 are worth $4.8665 x 875.8 = $4262.0807, the cost. Hence, the Foreign Exchange. 195 Kule. — Reduce the shillings and pence to the decimal of a pound, and multiply the face of the bill by the given rate of exchange. (Art. 446.) 2. An importer owed a manufacturer in Sheffield, Eng., £1740 10s.; what cost a bill on London for the amount, exchange being $4.87-$-? 3. When exchange on Manchester is $4.88, what cost a bill of £3520 ? 4. A merchant in New York gave an order to a broker to remit to Liverpool £15000. With exchange at $4.89^ and brokerage \%, what did it cost him in U. S. money ? 5. What cost a bill of exchange for £2800 15s. 9d. at $4.85 ? At$4.82J? 6. What cost £3560 18s. 3d. at $4.80? At $4.89£? At $4.83-|? 454. To find the face of Sterling Bills, the cost and rate of exchange being given. 7. A merchant paid $4256.40 for a sight bill on London ; exchange being $4. 86, what was the face of the bill ? a a *Aoa it*. oi i 4.86 ) $4256.40 Analysis. — Since $4.86 will buy £1 exchange, i $4256.40 will buy as many pounds as $4.86 are 875.8 contained times in $4256.40, or £875.8. (Art. 20 153.) Hence, the . « OWK .. f , ' . Ans. £875, 16s. Ecjle. — Divide the cost of the bill by the given rate of exchange ; the quotient will be the face of the draft. Reduce the decimals, if any, to shillings and pence. (Art. 153.) Note. — When the cost and face of the bill are given, the rate of exchange is found by dividing the latter by the former. (Art. 216.) 8. An importer paid $15265.40 for a bill of exchange on Birmingham; exchange being $4.87, what was the face of the bill? 9. Paid $25275 for a bill on Edinburgh; exchange being $4. 87 J, what was the face of the bill ? 196 .Exchange. 10. Paid $8500 for a bill on Dublin, exchange at $4.88; what was its face ? n. The cost of a bill on Liverpool for £825 16s. 6d. was $3964.50 ; what was the rate of exchange ? 12. The cost of £492 17s. 6d. was $1850; what was the rate ? 13. On an invoice of £850, what is the difference between its valuation at the Custom House and an exchange rate of $4.80? - 14. At $2946.50 for £600, what was the rate ? Note. — The cost of imported goods is generally estimated by adding the charges of importation to their value in the money of the country from which they come. 15. An English merchant consigned to an agent in New York the following invoice : 188 pieces of broadcloth, 37J yards each ; 165 pieces of silk, 52 yds. each ; 68 pieces velvet, 21 yds. each ; the agent sells the cloths at $4.93 per yard; the silks at $1.27 ; and the velvets at $2.62-§- ; pays 35% duties, and charges 2\% commission; $83.25 for storage, and sends his principal a draft on the Bank of England for the amount ; the rate of exchange being $4.85-|, what was the amount of the draft in sterling money ? 16. A merchant imports 160 pieces of broadcloth, 24 yd. each, costing $2.75 per yd. The duties and other charges amounted to $650. What must be the face of a sterling bill of exchange to pay for the goods, and what price per yard must he sell them to make 15% profit ? 455. Bills of France, Belgium, and Switzerland are quoted by giving the value of $1 U. S. money in francs and centimes. Note. — Centimes are commonly written as decimals of a Franc. 17. Required the cost of a bill on Paris of 3000 francs, exchange 5.25 fr. to a dollar. Solution.— Since 5.25 fr. will buy $1 exchange, 3000 francs w: 1 buy as many dollars as 5.25 are contained times in 3000, or $571 42, Ans. Foreign Exchange. 197 18. An invoice of goods costing 8324.50 fr. was passed through the Custom House ; what is the difference in U. S. money between its custom-house value and the exchange rate 5.22 ? 19. Paid $600 for a bill on Geneva ; what was the face of the bill, exchange being 5.16 fr. to $1 ? Analysis.— If $1 will buy 5.16 fr., $600 will buy 600 times as many, and 5.16 x 600 = 3096 francs, Am. 20. Bought a bill on Havre for $4500; exchange being 5.23, what was the face of the bill ? 21. What cost a bill on Antwerp for 1200 francs, at 5.20 fr. exchange ? 22. What is the difference between exchange at 5.24 fr. and the custom-house value on a bill for 68000 francs ? 456. Bills ou Germany are drawn in marks (reichsmarks). They are quoted by giving the value of four marks in U. S. cents. The intrinsic par value of 4 marks is 95.2 cents. 457. Bills on Austria and Netherlands are drawn in florins or guilders, and are quoted by giving the value of 1 florin in U. S. cents. 23. An agent in Amsterdam remitted a draft on New York for which, including brokerage \%, he paid 975 guilders; what was the face of the draft, exchange at 40.2 cents to a guilder ?. 24. What cost a bill on Frankfort for 840 marks, exchange being $.94$ ? Analysis. — Since 4 marks are worth $.945, the worth of 840 marks is 840 times \ of $.945, or $198.45, Arts. Note. — Multiply the exchange value of 4 marks by the given amount and divide the product by 4, or divide before multiplying. 25. What cost a bill on Berlin for 3800 marks at $.96 J ? 198 Exchange. NOTE. — When the value of an invoice at the Custom House is required, multiply the given amount in marks by the intrinsic par of 1 mark 23.8; the product will be in cents. 26. What is the face of a bill on Hamburg when exchange is .94J and th e cost of a draft $1856 ? 458. The method of finding the face of a foreign bill of exchange is essentially the same as that of domestic bills. 27. Eequired the face of a bill on Hamburg for which $2500 was paid, exchange being 95 cents. Analysis. — Since 95 cents will buy 4 marks, $2500 will buy as many times 4 marks as .95 is contained times in $2500 or 2631 j^, and 2631^ x 4 = 10526 T 6 ¥ marks, Ans. 28. What would be the Custom House valuation of the same bill ? Solution.-$2500.00-j-23.8 cts. = 10504 T 2 T \ marks. Ans. 29. Find the face of a bill on Frankfort costing $1762 in gold, exchange at .95 \. 30. Paid $2800 for a bill on Berlin, exchange .93|; what was the amount of the bill ? 31. What is the cost of a bill of 3800 florins on Amsterdam, exchange being 39§- cents to a florin ? Analysis. — Since 1 florin costs 39| cents, 3800 florins will cost 3800 times as much, and $.395 x 3800 = $1501. Hence, the cost of the bill is $1501. 32. What is the cost of a bill of 2500 roubles on Russia, exchange being 65.8 cents to a rouble ? 33. What is the value of an invoice entered at the Custom House for 8750.50 florins ? 34. A bill for 8500 guilders cost $5355.00 ; what was the rate? 35. Bought at par 375 rupees of India, 385 Austrian guilders, 850 crowns of Denmark, brokerage \% ', what was the cost in U. S. money ? 36. Sold 954 Russian roubles at par, and paid \% brokerage ; what was the net sum received ? Duties or Customs. 199 DUTIES OR CUSTOMS. 459. Duties or Customs are taxes imposed by Government on imported and exported merchandise. 460. A Tariff is a list of goods alphabetically arranged, with the rates of duties, drawbacks, etc., on them, charged and allowed on the importation and exportation of articles of for- eign and domestic produce. 461. The Free List is the list of imported articles which are exempt from duty. 462. Duties are of two kinds, Specific and Ad Valorem. A Specific Duty is a fixed sum imposed on each article, ton, yard, gallon, etc., without regard to its value. An Ad Valorem Duty is a certain per cent on the cost of goods in the country from which they are imported. Note. — On some goods both a specific and ad valorem duty is charged ; as on statuary marble $1 per cu. ft. and 25% ; on woolen goods 50 cts. a pound and 85 % . 463. In estimating specific duties, certain allowances are made, called tare, draft, leakage, and breakage. Tare is an allowance for the weight of the box, bag, cask, etc., containing the goods. Draft is an allowance made for waste and impurities. Leakage is an allowance for waste on liquors imported in Breakage is an allowance of a certain per cent on liquors imported in bottles. Notes. — 1. Tare is calculated either at the rate specified in the invoice, or at rates established by Act of Congress. 2. Leakage is commonly determined by gauging the casks, and Breakage by counting. 200 Custom House Business. 3. In making these allowances and in estimating weights and curren- cies, if the fraction is less than $ it is rejected ; if $ or more, 1 is added. 4. The Long Ton of 2240 pounds is used in computing Duties. 464. Gross Weight is the entire weight of goods and packages. Net Weight is the weight after all allowances have been deducted. CUSTOM HOUSE BUSINESS. 465. The United States are divided into various districts, each of which has a Port of Entry and a Custom House. 466. A Custom House is a building or office established by Government where duties are collected, vessels are entered, cleared, etc. The larger Ports have a Collector, a Naval Officer, a Deputy-Collector, Surveyors, Appraisers, Inspectors, Weighers, etc. 467. On the arrival of a vessel in Port, the Master is required to present his manifest and invoice to the Collector or Consul, and pay his entrance and clearance fees. 468. A Manifest is a memorandum signed by the Master of a vessel, giving its name, its tonnage, its cargo, with the place where he received it, and the names of the shippers and con- signees. 469. An Invoice contains a description of the goods with their cost, in the weights, measures and currency of the country from which they are imported. The invoice with its marketable value, must be authenticated by a Consul of the U. S., or by one of a country in amity with the United States, or by two respectable resident merchants. 470. Ad Valorem duties are assessed only on the actual cost or general market value of the goods in the country from which they come. Specific duties, on the quantity landed. (Art. 462, N.) Note. — The law has recently been changed which made the dutiable value of merchandise include the cost of transportation, commissions, etc. Duties or Customs. 201 471. The Entrance Fee is the annual tax paid for permission of a vessel to enter Port. It is based on the measurement, or tonnage of the vessel. 472. The Registry of a ship is its enrolment at a custom house. 473. A Bill of Lading is & formal receipt for goods taken on board a vessel, signed by the master, binding himself to deliver them in good condition, for a certain remuneration or freightage. Note. — Bills of lading are made out in triplicates ; one is sent by mail to the consignee, a second is sent by the master of the ship, and the third is retained by the consignor or shipper. In all cases the bill of lading is the evidence of shipment, and title to the goods shipped. 474. A Bonded Warehouse is a building for the storage of bonded goods on which the duties have not been paid, but have been secured by bond of the owner in double their amount. Note. — All goods remaining in bond, are charged 10% additional duty after one year, and if left beyond 3 years, are regarded as abandoned to the government, and sold under regulations prescribed by the Secretary of the Treasury. 475. A Drawback is money refunded for import duties previously paid, or for internal revenue tax paid on such articles as fermented liquors, medicines, etc., when these are exported. Excise Duties are taxes or licenses for the manufacture or sale of certain articles produced and consumed at home ; as tobacco, whiskey, etc. 1. A merchant imported 610 gallons of olive oil ; allowing 2% for leakage, what was the specific duty at 25 cts. per gallon ? Solution. -2% of 610 gal. = 12.2 gal., and 610-12.2 = 597.8 gal. Finally, 597.8 x .25 = $149.45, Ans. 2. What is the specific duty on 825 lb. soap, at 15 cts. a pound ? 202 Duties or Customs. 3. What is the duty at 30% ad valorem, on an invoice of English goods amounting to 4)1500 10s. 6d.? 4. Find the duty on a bill of English carpeting amounting to £6250 5s. 6d., at 35% ad valorem. 5. Taylor & Co. imported 2 cases of goods, each weighing 175 lbs., costing £1215 10s. and paid a specific duty of 30 cts. per pound and 35% ad valorem. What was the amount of duty ? What did the goods cost him ? 6. A. T. Stewart imported goods from Paris amounting to 28425 francs. What was the ad valorem duty at 35%, in United States money ? 7. What is the duty at 40% on an invoice of French jewelry, amounting to 8560 francs ? 8. The value of an invoice of French china is 19285 fr. ; what is its cost in New York, at 50% duty ? 9. What is the duty on an invoice of books from Vienna the value of which was 6429 florins, at 38% ? 10. Find the duty on an invoice of woolen cloths from Germany valued at 8437 Reichsmarks, at 45%. / n. What is the duty on an invoice of linens amounting to £3256 sterling at 27%, allowing $4.866£ to a pound ? 12. What is the duty on an invoice of 650 yd. of broadcloths which cost in London 16s. 6d. per yard, at 40% ad valorem, the value of a pound sterling being as above ? 13. Find the duty at 33% ad valorem, on 1 case of shawls valued at £42 5s., 1 case of linens at £37 10s., duty 40%; 1 case prints at £8 5s., duty 20% ; incidental expenses £1 5s., commission 2|% ; consul's fee 15s. What is the total cost in TJ. S. money? 14. Required the duty and total cost of 1 case of French silks, value 3500 francs, duty 50% ad valorem ; 1 case velvets, value 28000 francs, duty 50%, expenses, cartage, shipping, etc., 625 francs, and commission 2J%. 15. What is the duty and total cost of 2500 pieces bleached calico, 33 yd. each in length, and 1J yd. wide ; price 6d. per yd., duty 4 cts. per sq. yd., and expenses at Liverpool £65 10s.? What is the amount of a bill of exchange at $4.87 to cover the cost ? Duties or Customs. 203 476. What is the total cost and amount of duty on the following invoice, at the rate of 50%' for silks and 35% for broadcloths ? l. Invoice of two packages merchandise purchased by A. J. Smith, London, for account and risk of H. B. Clafltn & Co., New York, forwarded per Steamer " Alaska" from Liverpool. Marks. o> Nos. $875 $876 Packages and Contents. 1 Case silks, 10 p'c's, Av. 45 yd. each Discount 6 % 1 Case Broadcloths, 12 p'c's, Av. 48 yards each Discount 2| % Consul's fees . . . Com. 2£% Cost Silks Charges Ins. and Freight Packing and Cartage . Charges for shipping. £440, 13, 8 10, 8 Yds. Price. £ s. d. \ 450 6,6 576 10,8 2, 15, 6 4,3 14,0 Cost. £ s.d. 146, 5,0 8, 15, 6 137, 9,6 307, 4,0 7, 13 , 7 299, 10, 5 137, 9,6 3, 13, 9 £440,13,8 Broadcloths . . . Charges on £441, 4, 4 .. £137, 9, 6 .. 7, 7 , 2 £144,16, 8 . . £299,10, 5 .. 7, 7 , 2 £306,17, 7 11, 0,7 £451, 14, 3 £ 68, 14, 9 104, 16, 8 10,8 £625, 16, 4 Or, $3045.53 ) Duties £173, 11, 5 at $4.8665 = $842.92 \ Duty on Silks 50% " Broadcloths 35%.. Consul's fees Total cost Note. — Each invoice is accompanied by a proper Bill of Lading, signed by the master of the vessel, stating the number of boxes or packages received, their marks, weight, and size, the names of the shipper and consignee, the prices charged for freight, primage, etc. 204 Custom House Business. IMPORT ENTRIES. 477. Goods are entered at the Custom House by marks and numbers which should correspond to those on the Invoice and Bill of Lading. 478. The principal entries are 1. Merchandise for immediate consumption. 2. Merchandise for storage in a Bonded Warehouse. 3. Merchandise for immediate transportation in bond to another part of the country. 4. Merchandise for transportation in bond to a foreign country. 5. Merchandise for export of imported goods, or of goods made in this Country, for the benefit of a Drawback. Course of an Import Entry in the New York Custom House. 1. The Entry is made in duplicate, one copy for the Collec- tor's Office, the other for the Naval Office. It is a fair statement of the cost of the goods mentioned in a foreign invoice, the name of the Importer, name of the vessel, date of arrival, etc. 2. The Collector's Entry Clerk endorses the Invoice with the value of the goods in the currency of the country from which they were imported, notes the rates of duty, the deduc- tions to be made, etc., and places the Collector's Stamp on it, which notes the name of the vessel and date of arrival. He then marks the duty on the face of the Collector's copy of entry, and makes out a Permit for the goods mentioned in the Entry to be landed. 3. The entry is then taken to a Record Clerk in the Collector's Office, who charges it to the Naval Officer. The Naval Office Entry Clerk examines the work of the Collector's Entry Clerk, and if correct, endorses it and checks the permit. The entry is returned to the Record Clerk, who charges it to the Deputy Collector. Import Entries. 205 4. The Deputy Collector sees that the oath on the entry is taken, designates the packages to be sent to the public store for examination, signs each invoice under the steamer stamp and the numbers of packages, and returns the entry to the Record Clerk, who charges it to the Bond Clerk for the draw- ing of a Bond if necessary. The entry is then sent to the Delivery Clerk for the Importer. 5. The Importer takes the entry to the Cashier's Office for the payment of duty. The Cashier checks the duty statement of the Collector's Entry Clerk, etc., and gives the Importer the permit and the Naval Office copy of entry. 6. The Importer presents copy of entry, etc., to Naval Officer, who checks the papers, records payment of duty, and gives the Importer a permit signed by himself and the Deputy Collector. The Importer then presents the permit at the store where the goods are, pays storage, and receives packages not marked for appraiser. 7. The Appraiser, with the designated package before him, compares the goods in it with the invoice, verifies and determines the quantity and value thereof, and makes his return to the Collector. 8. The entry and invoice are charged to an amendment or liquidating clerk, who in accordance with the Appraiser's report, makes up a statement of the duty as it should be, in the invoice. If the ascertained duty is found to be less than that originally paid by the Importer, the excess is refunded; if greater, the deficit must be supplied. . 9. At the closing of a vessel's account, all the entries, with the manifest of the cargo and the Inspector's return, are placed on file. Note.— Much of the labor of making entries, obtaining permits, etc., is done through Custom House Brokers, who are familiar with the necessary steps. 206 Banks and Banking. BANKS AND BANKING. 479. Banks are Incorporated Institutions which deal in money. There are two classes, National and State-banks. 480. Banking has three departments of business : 1st. Receiving money for safe keeping, subject to the order of the depositor. 2d. Loaning money, discounting notes, drafts, etc. 3d. Issuing notes or bills for circulation. 481. The Income of Banks is chiefly derived from loans and circulating notes. 482. Banks make no charge for keeping deposits, and pay no interest on them, except in rare cases, at a low rate. The privilege of loaning a portion of them is a large source of income, and ample equivalent for the care and responsibility. Notes. — 1. According to the laws of the U. S., Banking Associations may be formed of any number of persons not less than five. 2. No association may be organized with a capital less than $100000, with the exception that in places whose population does not exceed 6000, they may be formed with the approval of the Secretary of the Treasury, with a capital of $50000. 3. In cities the population of which exceeds 50000, the capital must not be less than $200000, the stock being divided into shares of $100. 483. A National Bank is required to transfer and deliver to the U. S. Treasurer an amount of Kegistered Bonds not less than one-third of the capital stock paid in. These are held as security for the circulating notes delivered to the banks depos- iting them. Notes. — 1. Banks having a capital of $500000 are limited in their circulation to 90% of the par value of the registered bonds deposited at Washington ; those having a capital between $500000 and $1000000 to 80%; between $1000000 and $3000000 to 75%, and above $3000000 to eo%, Banks and Banking. 207 2. By act of July 12th, 1870, no National Bank organized after that date can have a circulation above $500000. 3. A Bank reducing its circulation may deposit with the Treasurer, legal tenders or specie in sums of not less than #9000, and withdraw a proportionate amount of the bonds previously deposited. 484. National Bank notes are redeemable in lawful money by the banks which issue them, and by the Treasurer of the United States. Note.— By act of June, 1874, every National Bank is required to keep on deposit in the treasury of the U. S., a sum equal to 5% of its circula- tion for redeeming its bills. 485. A Reserve Fund equal to 25% of their deposits, is required to be kept by National Banks in the cities of New York, Boston, Philadelphia, Albany, Baltimore, Pittsburgh, Washington, New Orleans, Louisville, St. Louis, Cleveland, Detroit, Chicago, Milwaukee, and San Francisco, and 15% by all other National Banks. Note. — These are called '" Reser ve Cities," and the excess above the requirements is called the Surplus Reserve. 486. A Surplus Fund, of the net earnings of the Bank, is also required by law to be set aside, before the usual semi- annual dividends are declared, until this fund amounts to 20$ of the capital. 487. An Annual Tax of 1% is paid to the United States by National Banks on the average amount of their circulation. Notes. — 1. The circulation of State Bank Notes ceased after Aug. 1, 1866, when a tax of 10 Jo was imposed by Congress upon each issue. 2. A Stockholder of a National Bank is liable for an amount equal to the par value of the Stock he holds. 3. The Revised Statutes require National Banks which go into voluntary liquidation, to deposit in the Treasury within six months, an amount of lawful money equal to their outstanding circulation. The law also requires that a sufficient amount, thus deposited for the payment of circulating notes, must remain in the Treasury until the last outstanding note shall have been presented. Hence, it will be seen the Government derives the benefit of notes which are lost or destroyed by fire and water. 208 Bank Account Current 4. Savings Banks and private bankers do not issue notes for cir- culation. [For the organization and regulation of National Banks, see Revised Statutes of U. 8., and for State Banks, the laws of the different States.] Exam ples. 488. l. What amount of Bank Notes is a National Bank allowed to issue, which deposits $500000 in U. S. Bonds to secure its circulation ? What is its redemption fund? (Arts. 484, 483.) 2. If a National Bank reducing its circulation, deposits with the U. S. Treasurer $27000 in legal tenders, and sells the Bonds withdrawn at 115-J, what are the proceeds ? (Art. 483, N. 3.) 3. What is the semi-annual tax upon a National Bank whose average circulation is $925460 ? 4. A capitalist has on deposit $450000, of which lh% is coin, 45% greenbacks, and the balance is National Bank notes ; what is the value of the bank notes ? 5. A bank having failed was placed in the hands of a Eeceiver, who declared a dividend of 45% in favor of the depositors. A's balance was $6526.50, B's $8417.95, and C's $4562.87 ; how much did each receive ? Bank Account Current. 489. l. Daily balances at 6% interest, to Apr. 26, 1883. Bank Account Current. 1883. Dr. Cr. Jan. 1 800 5 300 " 31 200 Feb. 6 300 March 4 500 Apr. 8 100 " 16 300 " 26 Bal. 1113.28 Int. 13.28 $1813.28 $1813.28 Daily Balances. Items. 800 500 700 400 900 800 1100 Days, x 4 = x26 = x 6 = x26 = x35 = x 8 = xl0 = Int. at Q% Products. 3200 13000 4200 10400 31500 6400 11000 6 ) 79700 $13,283 Bank Checks. 209 Explanation. — On J.an. 1, $800 were credited, and remained till the 5th, when $300 were debited." $800 being on int. 4 d., the product is 3200, that is, the int. of $800 for 4 d. = the int. of $3200 for 1 day. A debt of $300 being made Jan. 5, there remained a balance of $500 on int. till the 31st, or 26 d., when a credit of $200 is added, making $700 till Feb. 6, etc. The int. by Art. 284, is $13.28, which is added to the credit side of the account. The bal. due is $1113.28. Hence, the Rule. — Multiply the debit and credit balance for each day, by the number of days between it and the next debit or credit ; add the products and find interest by Art. 284. Notes. — 1. The balance of interest must be entered on the debit or credit side of the account as the case may be, after which it draws interest like the other items. 2. If the balance of items is sometimes credit and sometimes debit, take the balance of products before dividing. 2. What is the balance due on March 1st, for the following account current at 5% ? The National Exchange Bank, in acct. with S. S. Carlisle. Bank Account Current. Daily Balances. Products. 1833. Dr. Cr. Dr. Cr. Days. Dr. Cr. Jan. 1 200 " 18 150 " 28 250 " 31 125 Feb. 4 150 225 " 12 250 BANK CHECKS. 490. A Check is an order for money drawn on a Bank or Banker, payable at sight.* 491. When a check is drawn payable to bearer, it is trans- ferable without endorsement; when drawn payable to a person named, or his order, it must be endorsed by the person to whom it is made payable. * The law requiring that every check have a two-cent revenue stamp placed upon it, was repealed July 1st, 1883. 210 Bank Checks. Notes. — 1. The payment of a check may be countermanded by the drawer, at any time before it is paid or accepted by the Bank. 2. The holder of a check should present it without unnecessary delay, otherwise, if the Bank should fail, the drawer will not be responsible. 3. A check should be dated on the day it is drawn, and state the day when it is to be paid, if payable in the future. 4. The amount of a check should always be written in words, and the same amount in figures placed in the left-hand corner at the bottom, the cents being written in the form of a common fraction, as §8 T %%. 492. A Certified Check is one upon which the Paying Tel- ler or Cashier writes or stamps the word "Certified" or "Good/' and under it his signature. The bank thus guarantees payment. JTo. 873. JJew York, Oct. 29, 1883. ®lje €l)emical National Bank.^ (Pay to Alfred J. Pouch J$ w „ or Order Three Thousand ^L-Q^ollars ^ -V. W. Hunter. 4* 493. A Certificate of Deposit is a written or printed state- ment issued by a Bank, certifying that a certain person has deposited in it a specified amount of money. Brooklyn, Qec. 12, 1883. (Commercial Bank. George Brown has deposited in this l^ank. Four Hundred Dollars to the credit of Himself, pay- able on the return of this Certificate, properly endorsed. John J. Vail, Cashier. Note. — Certified checks and certificates of deposit are often used in making remittances, instead of drafts. Clearing Houses. 211 CLEARING- HOUSES. 494. A Clearing House is an Association of Banks, whose representatives meet for the purpose of daily exchanges of checks and drafts, and the settlement of balances. 495. The New York Clearing House is composed of 45 Na- tional Banks, 12 State Banks, and the U. S. Sub-Treasury at New York. The other city banks, both National and State, make their exchanges through the agency of some member of this Association. 496. The New York Clearing House, established in 1853, is the oldest institution of the kind in this country. Since that time 22 others have been established in different cities. 497. Each bank is represented every morning by a messen- ger and a settling clerk. The former brings the checks, drafts, etc., upon the other banks, which his bank received the day previous. These are called the " exchanges" and are assorted for each bank and placed in envelopes. On the outside of each envelope is a slip on which is listed the amounts of the various items which it contains. These envelopes are arranged in the same order as the desks for the several banks. 498. At a signal from a bell struck at ten o'clock precisely, each messenger moves forward to the desk next his own, and delivers the envelopes containing the checks, etc., for the Bank represented by that desk, to the clerk on the inside. The clerk receiving it, signs and returns it to the messenger, who immediately passes to the next desk, delivering the exchanges as before, and passes on until he has reached his own desk again, having delivered his entire exchanges for all the Banks. This occupies about ten minutes. 499. The messengers then receive from their several clerks the envelopes containing the exchanges, and return to their Banks reporting their condition. The clerks then report to the Assistant .Manager the amount they have received. They are allowed forty-five minutes after the delivery of the exchanges to enter and prove their work. 212 . Savings Banks. 500. The debit Banks are required to pay their balances to the Manager before half-past one o'clock the same da}', and immediately after that hour the credit Banks respectively receive the amounts due them. Notes. — 1. A record is kept of the daily transactions of each Bank, and a statement of the loans, specie, legal tenders, deposits and circulation made weekly to the Manager of the Clearing House, so that the move- ment of each Bank can be determined, and its condition pretty accurately estimated. 2. The rapidity with which exchanges are made by this method is a marvel. The business of a single day has amounted to $295,821,422, and the exchanges during the year preceding Oct. 1, 1881, exceeded $48,000,000,000. SAVINGS BANKS. 501. Savings Banks are institutions which receive small sums of money on deposit, and place them at interest for the benefit of the depositors. 502. They usually declare a dividend of the interest due the depositors, semi-annually, on the first days of January and July, which, if not withdrawn, is passed to the credit of the depositor on the books of the Bank, and bears interest the same as a new deposit. Hence, Savings Banks pay Compound Interest. 503. Some Savings Banks allow interest to commence on deposits on the 1st day of Jan., April, July, and October. Others, when deposits are made on or before the 1st day of any month, allow interest to commence on the 1st day of that month. This method is preferable for persons having a small income. Notes. — 1. No interest is allowed on any sum withdrawn before the 1st day of Jan. or July for the time between the last dividend and the withdrawal, and no interest is allowed on fractions of a dollar. The smallest balance remaining on deposit the entire term is entitled to interest. 2. Deposits are usually paid on demand, though the Bank is entitled by law to 60 or 90 days notice. Savings Banks. 213 504. The laws of the State of N. Y. do not allow Savings Banks to have on deposit for one individual a sum exceeding $3000, exclusive of accrued interest, unless such deposit was made before May 17th, 1875, or by order of a court of record, or of a Surrogate. Notes. — 1. Savings Banks are restricted to 5% per annum regular interest; but if their surplus earnings amount to 15% of their deposits, they are required to declare an extra dividend once in 3 years. 2. Savings Banks in this State are allowed to pay interest on sums deposited during the first ten days of Jan. and July, and the first three days of April and October from the first of these months. 505. In the following examples deposits draw interest from the 1st of Jan., April, July, and October, at 5%, unless other- wise mentioned. l. A man deposited in a Savings Bank, July 1, 1882, $175 ; how much interest should be credited him Jan. 1, 1883 ? and $175 x .02^ = $4.37* , Am. 2. A man deposited $320 in a Savings Bank Jan. 1, 1881, and July 1, $240 ; how much was due him Jan. 1, 1882, allow- ing 4% interest ? Analysis.— July 1, Int. on $320 (6 mo.) = 320 x .02 = $6.40. New Principal July 1 = $320 + $240 + $6.40 = $566.40 Int. 6 mo., Jan. 1 * = ($566 x .02) = 11.3 2 Amt. due Jan. 1, 1882 = $577.72 Note. — Though interest is not reckoned on the fractional parts of a dollar, in finding the amount at the close of a year these are included. 3. Jan. 1, 1880, a clerk deposited in a Savings Bank $150 ; March 12th, $48; June 17th, $125; and Sept. 30th, $150. Withdrew Apr. 10th, $25; July 12th, $34; Oct. 10th, $50; what was the balance due Jan. 1st, 1881, int. 4% quarterly ? Note. — In order to determine more easily the quarterly balances entitled to interest, the account may. be arranged in the following form, showing the amount due at each regular interval, the time, and the int. on the successive amounts. 214 Savings Banks. ir * Date. Deposits. Drafts. I Bal. Time. \ Int. 4%. 1880. Jan. 1 March 12 Apr. 10 150 48 125 3 150 6 $482. 23 34 57- %5 34 50 -$109 = $c 150 173 267 3G7 173.57 3 mo. 3 mo. 3 mo. 3 mo. Ans. 1.50 1.73 June 17 July int. 12 Sept. 30 Oct. 10 3.23 2.67 3.67 July 1881. Jan. 1 int. 6.34 J a n. Explanation.— $150 draws int. 3 mo. The 2d dep. ($48- $25) + $150 (Apr. bal.) = $173 draws int. 3 mo. 3d deposit ($125 + $3 July int. —$34, dft.) + $173 (July bal.) = $267 draws int. 3 mo. 4th deposit ($150-$50, dft.) -f $267 (Oct. bal.) = $367 on int. 3 mo. The sum of deposits with interest, less the sum of drafts gives the balance due. 4. A deposited Jan. 1, 1881, $125 ; March 15, $140 ; July 5, $65. He withdrew Feb. 15, 1881, $30; Apr. 10, $12; Oct. 15, $20. What was due Jan. 1, 1882, interest being ±%, payable quarterly ? Date. Deposits. Drafts. Balances, 1881. * Jan. 1 $125 1 Feb. 15 $30 | | $95 • Mar. 15 140 Jj- • . - Apr. 10 12 128 *H£ * *. 1.90 (6 mo.) •' 1.28 (3 mo.) July 5 65 $226.18 due, July 1, 1881. Oct. 15 20- 45 . . 1882. ' Jan. 1 Int. 5.42 (6 mo.) $276.60 Amt. due. Savings Banks. 215 Note.— The drafts are usually deducted from the last deposits made. Thus, the draft of $30 taken from $125, leaves a bal. of $95 on int. from Jan. 1. The draft of $12, Apr. 10th, leaves $128 on int. from Apr. 1, etc. (Art. 504, N. 2.) 5. Jan. 1," 1883, B deposited $120 in a Savings Bank; Feb. 20, $60 ; Apr. 1, $150 ; May 30, $80 ; what interest pay- able semi-annually at 4$ was due July 1, 1883 ? 6. On the 4th of Jan., 1881, a mechanic deposited $84 in a Savings Bank ; March 25, $50 ; Oct. 9, $96. He withdrew May 1, $12, and on the 20th of Oct., $21 ; allowing deposits to draw interest at 4$ from the first day of every quarter, how much will be due him Jan. 1, 1882 ? 7. Balance the following, Jan. 1, 1884: deposits Jan. 1, 1883, $250 ; Feb. 6, $58 ; Apr. 10, $64. Checked out March 15, $50 ; May 13, $75, interest beginning from the first of each quarter. 8. What would be due a depositor at the end of the year, who had a balance of $563 in bank Jan. 1 ; Jan. 8, he added $75 ; March 28, $65 ; May 15, $84 ; Apr. 12, withdrew $15 ; Oct. 11, $60, int. allowed from the 1st of the month following a deposit ? 9. The balance due n clerk Jan. 1, 1882, at a Savings Bank was $150 ; April 1, he deposited $75 ; July 2, $87 ; and Oct. 3, he drew out $25; how touch did the bank owe him Jan. 1, 1883, interest payable semi-annually "A « . V * • k io. Balance" the following pass-book Jan. 1, 1883 : * r, . Dr. Dime Savings Bank in acct. with J. Hamilton. Cr. Jan. 1 Mar. 31 Oct. 1 Three hundred fifty dollars One hundred twenty dollars InJ. to July, at 5%. Three hun. seventy-five dol. Int. to January. Aug. 1 One hundred twenty dollars Oct. 15 Sixty-five dollars. Stocks 506. Stocks represent the capital or property of incor- porated companies. 507. An Incorporated Company is an association authorized by law to transact business, having the same rights and obliga- tions as a single individual. 508. The capital stock of a company is divided into equal parts called Shares. Note. — The par value of a share varies in different companies. It is usually $100, and will be so regarded in this work, uuless otherwise stated. 509. A Stock Certificate is a paper issued by a corporation, stating the number of shares to which the holder is entitled, and the par value of each share. 510. The Par Value of stock is the sum named in the certificate. 511. The Market Value is the sum for which it sells. Notes. — 1. When shares sell for their nominal value, they are at par; when they sell for more, they are above par, or at & premium; when they sell for less, they are below par, or at a discount. 2. When stocks sell at par they are often quoted at 100 ; when at 1% above par, they are quoted at 107, or at 1% premium ; when at 15% below par, they are quoted at 85, or at 15 fc discount. 512. A Preferred Stock is one which is entitled annually to a stated per cent dividend out of the net earnings, before the common stock dividend is declared, and may be cumulative or not. Note. — When cumulative, if the earnings are not sufficient to pay the dividend for any year, the holder of preferred stock is entitled to the back dividends before any other payments are made. Stocks and Bonds. 217 513. An Installment is a payment of part of the capital. 514. An Assessment is a sum required of stockholders to replace losses, etc. 515. The Gross Earnings of a company are its entire receipts from its ordinary business. 516. The Net Earnings are the remainder after all expenses are deducted. 517. A Dividend is a sum divided among the stockholders from the net earnings of the company. Note. — Companies sometimes declare a Scrip Dividend, entitling the holder to the sum named, payable in stock at par value. 518. A Bond is a written agreement to pay a sum of money, with a fixed rate of interest, at or before a specified time. The term is applied to National, State, city, and railroad bonds, etc. Notes. — 1. Bonds are named from the parties who issue them, the rate of interest they bear, and the date at which they are payable, or from all united. Thus, "IT. S. 4's of 1907," means that these bonds bear 4% interest, and are redeemable after 1907, at the pleasure of the Government. 2. Bonds of States, cities, corporations, etc., are named by combining the rate of interest they bear with the name of the State, corporation, etc., by which they are issued ; as, Ohio G's, N. Y. Central 5's, etc. 3. Convertible Bonds are those which may be exchanged for stock, lands, or other property. 519. Bonds are also known as first, second, etc., Mortgage bonds, Income bonds, and Consols. 520. A Coupon is a certificate of interest due on a bond, to be cut off when paid, as a receipt. Notes. — 1. Income bonds are those on which interest is paid, if earned, and are not usually secured by a mortgage. 2. The term "Consols" is applied to Bonds issued in place of two or more classes of outstanding bonds, which are thus consolidated into one class. The term originated in England. 218 Stocks and Bonds. 521. A Mortgage is a conveyance of real estate or other property, as a pledge for the payment of a certain amount of money. Note. — If either the principal or interest is not paid when due, the mortgagee has a right to take or sell the property. United States Bonds. 522. United States Bonds are known as Coupon Bonds and Registered Bonds. 523. Coupon Bonds have Interest Certificates or Coupons attached to them, and are negotiable by delivery. For this reason they sell higher in foreign markets than registered bonds. Registered Bonds are those payable to the order of the owner, whose name is recorded in the office of the Register of the Treasury, at Washington, D. C. They can be transferred only by assignment duly acknowledged. Notes. — 1. Letters relating to the transfer of registered bonds or the payment of interest on the same, should be addressed to the Register of the Treasury. 2. The transfer books are closed for 30 days previous to the day for the payment of dividends ; and stockholders desiring the place of pay- ment changed, must give notice to the Register one month at least before the dividends are due. 3. When bonds are sent for transfer, state where the interest is to be paid, inclose the stock of different loans in separate envelopes, and name on each the amount of stock and the date of the Act of Congress authoriz- ing its issue. 4. Powers of Attorney for the assignment of U. S. Bonds, and the assignments, must be properly filled, before transmission to the Register. 5. Powers of Attorney to draw interest should be addressed to the First Auditor of the Treasury. 6. In quotations of bonds, the accrued interest from the day of closing the transfer books, is included in the price. Stocks and Bonds. 219 NATIONAL DEBT OF THE UNITED STATES. 524. The National Debt of the United States is divided into Bonds, Funded Loads, Refunding Certificates, Navy Pen- sion Fund, debt bearing no interest, etc. No nation has a common name for all its debt. Funded Debt Bearing Interest. Bonds at 6% continued at 3 J $149,682,900.00 " at b% " " 401,503,900.00 " at 4\% 250,000,000.00 " at 4^ 738,772,550.00 Refunding Certificates, 4% 575,250.00 Navy Pension Fund, 3% 14,000,000.00 $1,554,534,600.00 Debt bearing no Interest since maturity 11,528,265.26 Non-Interest-bearing Debt. Legal-tender Notes $346,681,016.00 Certificates of Deposit 9,590,000.00 Gold Certificates 5,188,120.00 Silver « 68,675,230.00 Old Demand Notes 59,920.00 Fractional Currency 7,075,926.92 437, 270 ,212.92 Total principal $2,003,333,078.18 525. Bonds to the amount of $64,623,512, known as "Currency Sixes," were issued to the Pacific Railroads, and the interest on them is payable by the United States ; but they are not included in the above estimate, as the Government holds mortgages on the roads to cover the amount. Note. — These took their name from the fact that the interest on them is payable in currency or any legal tender. All United States Bonds are exempt from taxation. 526. Of the funded loans there are registered bonds of the various issues, in denominations of $50, $100, $500, $1000, $20000, and $50000 ; and coupon bonds of $50, $100, $500, and $1000. 220 Stocks and Bonds. The Funded Debt of Foreign Countries. 527. Consols are the leading funded securities of the Eng- lish Government ; bearing 3% interest, payable semi-annually. This debt amounted in 1882 to $3,814,500,000, of which $3,545,000,000 were Consols, or Consolidated Annuities, re- deemable only at the pleasure of the Government. 528. The funded debt of France bears the title of Rentes. The rate of interest is usually 5%. This debt in 1882 was $4,750,337,109. Besides this the "Bons du tresor" amount to $65,000,000. 529. The German Empire has only about $70,000,000 funded debt bearing 4% interest, known as 4% Imperial bonds. 530. In 1882 Austria had a funded debt of $1,450,000,000, the larger part bearing b% interest, known as "Austrian Consols." 531. Russia had a debt of $2,421,417,932, a portion of which bears a nominal interest of 5 and 5|$. They are known as Oriental loans, and are below par. Prussia has a debt of $498,500,000, of which $220,000,000 is consolidated (zuheilung) at an average of 4% interest. Italy has an immense debt, of which $380,000,000 are in " Rentes " of 3 and 5 per cent. STOCK EXCHANGES. 532. Stock Exchanges are Associations organized for buying and selling stocks and bonds and other similar securities. 533. Members are elected by ballot. The qualifications for membership are good character and solvency. 534. The Officers are a President, Vice-President, Treasurer, Clerk, Secretary, Standing Committee, Finance Committee, Committee on Listing Stocks, and a Nominating Committee. Notes. — 1. Every Association makes its own By-Laws, which are stringent and rigidly enforced. The Stock Exchange. 221 2. A system of Arbitration supersedes all appeals to the law for the settlement of disputes. 535. The New York Stock Exchange is composed of 1200 members, the maximum allowed by their By-Laws. It is said that seats at this Board have recently been sold at prices rang- ing from $20,000 to $30,000. 536. The Exchange is open for business from 10 a.m. to 3 p. m. Before any new securities are allowed to be quoted or sold on the Exchange, they are subjected to a rigid examina- tion by the Committee on "Listing" Stocks. 537. There are two lists of Stocks, one is known as the Regular list, the other as the Free list. 538. Ordinarily Stocks and Bonds are quoted at a certain per cent on the par value of $100 per share. Stocks of the par value of $50 are called half stocks, and those whose par value is $25 are called quarter stocks, and the price quoted is the percentage of the par value. The commission for buying or selling Stocks or U. S. Bonds is | of 1% (i%). Mining Stocks are quoted at so much per share, and the commission varies according to the price of the stock. 539. Pipe-line certificates are quoted at so much per bbl. for 1000 bbl. of crude Petroleum oil. 540. Stocks sold " regular way " are paid for and delivered on the next business day. On sales made " buyer three " or " seller three " no interest is charged ; on contracts longer than 3 days, the buyer pays interest, unless otherwise specified. ~No contracts for more than 60 days are recognized. Notes. — 1. "Seller 3," means deliverable on either of 3 d., at the option of the seller. "Buyer 3," means the buyer can demand delivery within 3 d., but must take and pay for it the third day. 2. Quotations are termed "flat" when the accrued interest is included in the price named. 222 Stocks and Bonds. 541. Margin is cash or, other security deposited with a broker on account of either the purchase or sale of securities, and to protect him against loss in case the market price of the securities bought or sold varies so as to be against the interests of the customer. It is usually 10$ of the par value of the stock. Note. — Brokers charge interest on the sums expended and allow interest on the margins deposited. 542. A Bear is an operator who believes the market price of stocks will fall 543. A Bull is an operator who believes the market price of stocks will advance. Note. — Hence a bull will buy stocks in order to profit by the I i /her price at which he expects to sell, and a bear will sell in order to profit by the lower price at which he expects to buy. 544. Hypothecating stocks and bonds is depositing them as collateral security for money borrowed. Note. — The securities must be greater than the loan by at least 10% of their par value, and in every case by an amount equal to 20% of the amount of the loan. This excess is called the margin of the loan.. 545. Watering Stock is increasing the number of shares of an incorporated company without a corresponding increase in their value. 546. A Corner is produced when one or more operators owning or controlling, all the stock of a company are able to purchase still more for either immediate or future delivery. When they demand the stock, the sellers are unable to find it in the market. 547. A Syndicate is a combination of Brokers, Bankers, or Capitalists who undertake to place large loans, and transact other business. Note.— Stock Privileges known as " Puts." " Calls," " Spreads," and " Straddles," are not recognized by the Stock Exchange, Stock Investments. 223 Quotations in Stocks. 548. The following are taken from a report of sales at the New York Stock Exchange in Dec, 1883. The abbreviations which appear will be explained hereafter in the Appendix. 10000 4's, coup 123£ I Cen. Pac. 1. g 104i @ 104£ 50000 4's, reg 122| Erie, 5th 105 800003's, " 101 25000 4£V 114J 2000 N. C. 4's, en 81} 1000 Tenn. f. new S 38 10 sh. Am. Ex. Bank 130 100 Chi. & N. W. pf 142} 100 Mut. Un. s. f. 6's 84£ Cur. 6's,'95 127i Chi. Bur. & Q. 5's Deb 91| N. Y. Central 116 @ 116| N. Y. Elevated 105 Chi. & W. Ind. s. f 106.| N.J. Central 83 £ Va. Mid. inc 63| Seller's Option. 500 Sh. N. Y. EL © 1 5, S. 60. New YorK) Dec . 15> 1883> I have Purchased of Lockwood Bros. Five Hundred (500) Shares of the Capital Stock of the Netv York Elevated Railroad Company, at one hundred five dollars ($105) per share; payable and deliverable at seller's option within sixty (60) days ivith interest at the rate of 6% per annum. H. B. Stevenson. Buyers Option. 500 Shares N. Y. 0. @ 116, B. 30. New York> Dec . 28> 1883 . / have Sold to E. J. Marshall Five Hundred (500) Shares of the Capital Stock of the Neio York Central Railroad Company, at one hundred sixteen per cent; payable and deliverable at buyer's option within thirty (30) days with interest, at the rate of six (6) per cent per annum. C. B. Hatch. STOCK INVESTMENTS. 549. Premiums, Discounts, Dividends, and Assessments, are computed by Percentage. The par value of the stock is the Base ; the per cent of premium, dividend, or discount is the Rate; the premium, discount, or dividend is the Percentage. 224 Stocks and Bonds. 550. To find the Cost of stock, the par value and the rate of premium, discount or dividend being given. 1. What cost 50 shares R. R. Stock, at 6% premium, par value 1100, brokerage \% ? Analysis. — The cost of 1 share, at 6 % premium + \ % brokerage = $106,125. Cost of 50 shares = $106,125 x 50 = $5306.250, Ana. 2. What cost 60 shares of R. R. Stock, at 8% discount, brokerage \% ? Analysis. — The cost of 1 share, at 8% discount, and \% brokerage = $92,125. Cost of 60 shares = $92,125 x 60 = $5527.50, Ans. Hence, the Rule. — Multiply the cost of 1 share by the number of shares. Note. — In finding the entire cost of stocks the rate % of brokerage is added to the rate above or below par, as both are calculated on the same amount. (Art. 538.) 3. What must be paid for 800 shares Telegraph stock, at 25$ premium, brokerage \% ? 4. What are 60 shares Erie R. R. stock worth, at 15J<£ discount? 5. What must be paid for U. S. bonds, par value $5000, at 106, brokerage \% on the par value ? Solution.— 50 shares, at 106 = $5300, and {\% brokerage) $6.25 = $5306.25. 6. What cost 75 shares Union bank stock, at 8f% premium, brokerage \% ? 7. The premium on stocks sold was $858, the par value $7550 ; what was the cost ? 8. The discount on a Mining stock is 15j% par value $50; what is the value of 23 shares ? 551. To find the premium, discount, dividend, or assessment, the number of shares and rate being given. 9. What would a stockholder of New York and New Haven R. R Co. receive, who owns 500 shares, from a 4=% dividend? Stock Investments. 225 Solution.— 500 shares at $100 = $50000 tlie par value, $50000 x .04 = $2000.00, Ans. Hence, the Rule. — Multiply the par value of stoelc by the rate %. 10. A western R. R. Co. called for an assessment of 12\% ; how much must a man pay who owns 350 shares ? 11. The stock of a mining Co. was sold at a discount of 4$$; how much was received for 800 shares, par value $50 a share ? 552. To find the Rate %, the par value of stock, the premium, discount, dividend or assessment being given. 12. The capital stock of a Co. was $100000, the dividend $22000; what was the rate per cent? Solution.— $22000.00 -*- $100000 = .22, or 22%, Ans. Hence, the Rule. — Divide the premium, discount, assessment, or dividend, by the par value of the stoelc. 13. The discount on 75 shares Panama R. R. stock was #725 ; what % was it ? 14. A man owning 25 shares Western Union, was assessed $85 ; what was the rate per cent ? 553. To find the number of shares, when the sum invested and the cost of I share are given. 15. How many shares of factory stock at 6% discount and brokerage \%, can be bought for $76200 ? Analysis. — Since the discount is 5% and brokerage }%, the cost of 1 share is 95%+£%,.or 95J% of $100 = $95.25. As $95.25 will buy 1 share, $76200 will buy as many shares as $95.25 are contained times in $76200, and $76200 -j- $95.25 = 800 shares, Ans. Hence, the Rule. — Divide the sum invested by the cost of one share. 16. How many shares of Mutual Union telegraph stock, at 15$% discount and brokerage \%, can you buy for $13500 ? 226 Stocks and Bonds. 17. Find the number of pipe line certificates at 115J, that can be bought for $15150, brokerage \%. 18. What number of elevated railroad shares at 105, brokerage \%, will $75150 pay for? 19. Find the number of shares of Union Pacific, at 20% discount, that can be bought for $32000 ? 554. To find how stock must be bought which pays a given per cent dividend, to realize a specified per cent on the investment. 20. At what price must I buy stock which pays 6% dividend, so as to realize 8% on the investment? Analysis. — Since the annual income of $1 is .06, this must be T f^ of the price to be paid; then -^ = .06 -*- .08 = $. 75, and £{$ = $75. Hence, the Kule. — Divide the rate which the stock pays by the required rate, the quotient will be the price of $1 stock. 21. What must be paid for U. S. 4's that 8% may be received on the investment ? 22. What must be paid for stock that yields 20% dividends, so as to realize 1\% on the investment ? 555. To find what sum must be invested to yield a given income, when the market value, and the rate of interest are given. 23. What sum must be invested in N. Y. 5's, at 108£, to produce an annual income of $2500 ? Analysis. — The income $2500 -j- $5 (int. on 1 share) = 500 shares, and 108^ (price of 1 share) x 500 = $54250. Hence, the Kule. — Multiply the market value of 1 share by the number of shares. 24. How much must be invested in U. S. 4's, at 123§, to yield $3500 annually? 25. What must be invested in Nebraska 8's, at 75, to yield an income of $3540 annually ? Stock Investments. 227 26. What sum must be invested in stock at 112, which pays 10% annually, to obtain an income of $3200 ? 27. How much must be invested in Alabama 6's, at 85, to realize $2500 a year ? 28. How much must be invested in stock at 106, to yield an income of $6000, the stock paying 10% dividend annually ? 556. To find the % of income from a given investment, without regard to its maturity. 29. What is the % income on bonds bought at 125, paying 1%% interest ? Analysis. — Since the int. on 1 share ($100) is $12, the int. on $125 is fa of $12, and $12-s-$125 = .09?, or 9f#, Ana. 30. Bought 5% bonds at 75 ; what will be the % income ? Solution.— $5^-75 = .06|, or 6|%, Ana. Hence, the Rule. — Divide the income per share by the cost per share. 31. Find the per cent of income on U. S. 4}'s, bought at tut 32. What is the per cent of income on Iowa 6's, bought at 108}, brokerage \% ? 33. Which is the more profitable, $10000 invested in 3 per cents at 101, or in 4 per cents at 122}? 34. If a person were to transfer $29000 stock from 3} per cents at 99 to 3 per cents at 90-| what would be the difference in his income ? 35. A man agreed to take 300 shares of mining stock, par value $50 ; after the third installment was paid amounting to 75^ of the par value, a dividend of 3% was declared ; how much and what % on the actual cost did he receive ? 228 Stocks and Bonds. 557. To find the % income from a given investment payable in a given time. 36. What per cent income will be received if I buy U. S. 4's at 112, payable at par in 16 years? Analysis — Since the bond matures in 16 years, the premium on 1 share ($12) decreases j-f, or $| each year. The int. $4— $f = $3£ income. And $3.25-r-$112 (cost of 1 share) = ^\\\°/c the rate required. 37. Bought Tennessee bonds at 38, bearing ±% int., having 25 years to run ; what per cent will be realized if they are paid at par at maturity ? 38. What per cent income will be gained from S% bonds, bought at 90, and payable at par in 20 years ? Analysis. — Since the maturity is 20 years, the discount ($10) decreases £&, or $| each year. The int. $8 + -| = $8£ income ; and $8.50h-$90 = $.09,*, or 9|% the required rate. Hence, the Rule. — First find the average annual decrease of the premium or discount. If the bonds are at a premium, subtract it from the given rate of interest; if at a discount, add it to the interest ; the result will be the average income of one share. Divide the average income of one share by the cost of one share, and the quotient will be the rate per cent of income. Notes. — 1. When bonds are at a premium, the longer the time before maturity, the greater will be the rate per cent of income. 2. "When bonds are at a discount, the longer the time before maturity, the less will be the rate per cent of income. 39. What rate per cent of income will be received on IT. S. 4J's at 114, payable at par in 16 years? 40. Bought Kentucky bonds at 90, due at par in 30 years, drawing 8% interest ; what is the per cent of income ? 41. In 1882 Milwaukee and St. Paul 6'§, due at par in 1930, were bought for 108 ; what interest will this pay ? /Stock Investments. 229 Note. — Other methods of analysis than those given are often used by dealers in stocks and bonds. Take Ex. 41. The amt. of $100 (1 share) at 6% for 48 years equals $388. Subtracting cost, $388— $108 = $280, total income. The question now becomes, " What per cent of $108 will yield $280 in 48 years?" In 1 year, 1% of $108 = $1.08, and in 48 years $1.08 x 48 = $51.84. If $51.84 = 1 % , $280 = as many % as $51.84 are contained times in $280, or §^ % . 42. If I pay 108 for U. S. 4's, having 15 years to run, what % will I receive if I keep them till they mature and they are paid at par ? 558. To find how stock must be bought which has several years to run, and pays a given % dividend, to realize a specified per cent on the investment. 43. At what price must 6% bonds, payable in 8 years, be bought to realize 4=% on the investment. Analysis.— The Amt. of $100, at 6% in 8 yrs. = $148. The Amount of $1, at 4% in 8 yrs. = $1.32. $148-s-$1.32 = $112j& per share. Hence, the Rule. — Find the amount of $100 for the given time and rate, and divide it by the amount of $1 for the same time, at the rate required. 44. Bought railroad 6% bonds payable in 5 years, and expect to realize 11% on the investment ; what did I pay ? 45. What must I pay for 5 per cent bonds, which mature in 15 years, that my investment may yield 4 per cent ? 46. What shall I pay for a bond of $500, having 12 years to run, with interest at 6%, in order to make it an 8% invest- ment? Practical Examples. 559. l. At what price must a stock paying semi-annual dividends of 2% be bought, to yield 6% per annum on the capital invested ? 2. If the semi-annual dividends are 2\%, how must the stock be bought to yield 5% ? 230 Stocks and Bonds. 3. Which is the more profitable investment, a stock at 120, paying 8% annually, or a 20-year bond at 90, paying 6% annually ? 4. Three companies, A, B, and C, are to be consolidated on the basis of the relative market values of their stock. Thus, A's capital $1,000,000, Market value 100%; B's " $1,500,000, " " 50%; C's " $625,000, " " 40%. The capital of the consolidated company is to be $2,000,000, in 20000 shares of $100 each. What proportion and what amount of the capital should be allotted to each of the old companies ; and how much stock in the new company should the holder of 1 share of the stock of each of the old companies be entitled to ? 5. When 3% government bonds are quoted at 101, what sum must be invested to yield an income of $800 a year ? 6. What is the accurate interest on an investment of $5000 in U. S. 4£'s at 114J, from Jan. 1 to March 1, inclusive ? 7. If a man buys stock at 17% above par, what per cent does he receive on his investment, if the stock pays a dividend of 8\% on its par value ($100) ? 8. A man bought 8 shares of stock at 108|, and after keep- ing it 11 months received a dividend of $7 a share, and sold the stock then at 109£ ; what per cent did he receive on his investment ? 9. How many shares of Mutual Union Telegraph stock at 84J, can be bought for $12000, brokerage \% ? 10. Bought Oct. 12th, 400 Pacific Mail at 42J, and 200 Mich. Cen. at 92 £; Nov. 10 sold the former at 42 J, and the latter at 92| ; what was my gain ? n. Which would be the better investment, $12120 in N. J. Central at 84, paving 3% annual dividends, or the same invested in Chemical Bank stock at 2020, paying 15% every 2 months? 12. A customer deposited $500 margin with a broker Nov. 23, who purchased for him 50 shares Mich. Central at 80. He sold the same stock Nov. 30th at 98 ; what was the gain, brokerage \% ? Stock Investments. 231 OPERATION. Dr. Nov. 23. To 50 sh. Mich. Cen. at 80. . $4000 Brokerage \% 6.25 Nov. 30. Int. on $4006.25, 7 days fa By margin deposited Nov. 23. •* 30. Nov. 30. Note By 50 sh. Mich. Cen. at 98. . $4900 Less Brokerage | % . . . . 6.25 Int. on $500, 7 days —The brokerage, £ of 1% is equal to $12.50 on 100 shares of stock at the par value of $100 each. 4006 25 4 67 4010 500 4893 75 58 5394 $1383 Balance Less margin 500 Gain. . $883 92 13. A man bought 100 shares Union Pacific at 79}, and sold the same at 82f ; what was the gain, less \% brokerage ? 14. Governments yielding $240 a year at 4$ interest, were sold at 108, and the proceeds invested in land at $75 an acre ; how many acres were bought ? 15. What cost 25 shares of 111. Cent, at a premium of 33$ ? 16. What rate of dividend on the above would be equal to 6$ interest on the investment ?• 17. If the N. Y. Cen. declares a dividend of 15$, how much will a man receive who owns 250 shares ? 18. What per cent on his investment if he bought the above stock at 95 ? What per cent if bought at 116 ? 19. Which is the better investment, R. R. stock at 25$ discount, and paying a semi-annual dividend of 4$, or money loaned at 10$, interest payable annually ? What % better ? 20. If the annual dividend on a stock is 15$ and money is loaned at 10$ per annum, what should be the price of the stock? 21. On 84 shares of stock 2 semi-annual dividends were declared, one at 5$, the other at 4$, the investment paid 10$; what did the stock cost ? 22. A man's income from $2000 worth of stock is $75 semi- annually ; what is the per cent per annum ? 232 Produce Exchanges. 23. At what per cent discount must 6% stock be bought, that the investment may pay 9% ? 24. If a stock yields 15$ per annum, what is its value when money is worth 8% ? 25. March 4th, deposited with my broker $500 margin, for purchasing 50 shares Mo. Pacific K. R. stock at 92J. The stock was sold March 28th at 96f . Allowing 6% interest on the deposit, and charging 6% interest on the purchase, and \% brokerage, what was the net profit on the transaction ? 26. Sold "short" through my broker 200 shares Mich. Cent, at 90, and "covered" my "short" at 86|. Allowing \% commission for buying and selling, what was my net profit ? 27. What rate per cent income will be received on U. S. 4's at 108, payable at par in 15 years ? 28. A man's income from U. S. 4's of 1907, bought at 123, and 3's at 101, is $350. If bought at par an equal sum would have been invested in each ; how much was his investment ? How many shares of each stock did he buy ? 29. Paid 86} for stock bearing 8% annual dividends ; and received each year $480 ; what was the investment ? 30. Borrowed $100000 upon 1000 shares N. Y. Cent, at 120. If the market price falls to par, how much more of the same stock must I deposit with the lender to keep up the original margin ? (Art. 544, N.) PRODUCE EXCHANGES. 560. Produce Exchanges, or Boards of Trade, are Associa- tions of dealers in Produce. They make their own By-Laws and are conducted by a Board of Directors, usually including a President, Vice-President, Secretary, and Treasurer, who are elected by ballot. The fee for membership is $1000 and upwards. They have committees on Complaints, Arbitration, Appeals, Trades, Prices, Transportation, Information and Statistics, etc. Produce Exchanges. 233 561. The department which most concerns the public, is the Inspection by their committees of the great staples of food, as grain, flour, the various kinds of provisions, peas, beans, beef, pork, lard, butter, cheese, eggs, and all the important products of the country. To protect the public against fraud and adulterations, they classify these various articles according to quality, after careful inspection, and adopt marks or brands for each, by which they become known in the markets of the world. What the Stock Exchange is to financial securities, the Produce Exchange is designed to be to the staples of food. Note. — Exchanges have already become important accessories of commerce. They facilitate speculation as well as regulate it ; they are courts of arbitration for settling disputes, and are considered almost a necessity to the interests they represent. Many associations have mutual life insurance attachments connected with them. In addition to the stock and produce exchanges there are Real Estate, Petroleum, Cotton, Tea, Coffee Exchanges, etc., each with a separate organization, the avowed objects of which are to advance the interests of trade and commerce. 1. What % do I make by purchasing flour at $7.50 per barrel cash and selling it for $8.25 on 3 mo. credit, when money is worth 6% ? 2. A man has a bin 28 ft. long, 5 ft. 4 in. wide, and 4 ft. deep, filled with wheat ; what is it worth at $1.15 per bushel? Note. — The quantity of grain in bins, etc:, is found by reducing it to cubic inches and dividing the result by the number of cubic inches in a bushel. (Art. 71.) 3. A dealer has 3 bins of wheat containing 700, 950, and 1000 bu. respectively ; he has sold 3 lots of 400 bu., 1 lot of 75 bu. 1 pk. 5 qt., and 6 lots each of 10 bu. 3 pk. 2 qt. ; what is the value of what he has left at $1.15 per bushel? 4. Bought wheat at $1.10 a bushel, allowing \\% for waste and 2 cts. a bu. for storage; how must it be sold to gain 8%? 5. The net proceeds of a shipment of hay, sold at $28 per ton, were $12580 after deducting 3% commission and $500 for other charges; how many tons of hay were shipped ? 234 Storage. 6. A dealer received 10000 barrels of flour to sell on com- mission, and was to invest the proceeds in TJ. S. notes at Y^% interest; he paid $759 charges, sold the flour at $9 a barrel and charged 3% commission on the sales ; what amount of notes could he buy at 36% premium, brokerage \% ? 7. A produce merchant bought 30000 bu. corn at $0.55, paying $450 charges, and $225 storage ; he sold it at 25$ advance on the entire cost on 90 days time ; at what price per bu. did he sell it, and what per cent did he gain at the time of sale, money being 7% interest ? 8. The net proceeds of a sale of 1000 tons of hay at $20 per ton were $18325, after deducting $875 for charges; what was the rate % of commission ? 9. A dealer expended equal sums in wheat, rye, and oats ; on selling he made H% on the wheat, b% on rye, and lost 15$ on the oats ; the whole sum received was $1782 ; what sum did he invest in each kind of grain ? 10. A grain merchant bought 9000 bu. wheat, paying at his option $1 cash per bu., or $1.10 on 3 mo.; which would be the more advantageous, to buy on credit, or to borrow the money at 7% and pay cash ? STORAGE. 562. The business of Storage is done by commission and forwarding merchants. The prices charged are regulated by the Board of Trade of the city in which the Storage is made, unless by a special agreement. 563. The rates are usually fixed at a certain price per barrel, bushel, box, bale, etc., for one month of 30 days. Notes. — 1. In some cities a full month's storage is charged for any part of a month they may remain in store, in others 15 days or less are called | mo. and over 15 days a whole month. 2. On Grain the charge per bushel for storage varies in different cities. Storage. 235 564. Accounts of Storage ordinarily contain an entry of articles received and delivered with the date of each. They are somewhat similar to bank accounts. 565. To Average a Storage Acct. according to actual time. l. Received on storage and delivered the following : May 1, 1883, 1000 bbl. flour; May 26, 2000 bbl. Delivered, May 16, 500 bbl.; June 1, 1000 bbl.; June 12, 1100 bbl.; July 2, 400 bbl. ; what was the cost of storage at 6 cts. a mo. per barrel ? Acct. of Storage of flour received and delivered for acct. of A. Hamilton of Chicago. Date. Received. Delivered. Balances. Days. Products. 1883. May 1 1000 bbl. 1000 bbl. 15 15000 " 16 500 bbl. 500 " 10 5000 " 26 2000 " 2500 " 5 12500 June 1 1000 " 1500 " 11 16500 " 12 1100 " 400 " 20 8000 July 2 400 « 000 " 00 0000 3000 bbl. 3000 bbl. 30 ) 57000 Storage for 1 month for 1900 bbl. 1900 x. 06 =$114.00, Ans. Rule. — Multiply the number of barrels, etc., by the number of days they are in store between the time of entrance and delivery. Multiply each balance by the number of days it remains unchanged. Divide the sum of products by SO, the quotient is the number of articles in store for one month. 2. Received and delivered on account of Samuel Barrett of New Orleans sundry bales of cotton as follows: Received Jan. 1, 1884, 2310 bales ; Jan. 16, 120 bales ; Feb. 1, 500 bales; Feb. 12, 200 bales. Delivered Feb. 12, 1200 bales ; March 6, 800 bales ; April 3, 400 bales ; April 10, 300 bales. Balance the account to May 1, and find the storage due at 15 cents a bale per month. 236 Life Insurance, 3. Eeceived on storage, and delivered the following merchan- dise : Received Jan. 1, 1884, 100 bbl. rye meal ; Jan. 15, 200 bbl. rye meal ; Feb. 10, 300 bbl. corn meal ; Feb. 20, 10 bbl. oat meal. Delivered Jan. 15, 100 bbl. rye meal; Jan 30, 150 bbl. rye meal ; Feb. 28, 200 bbl. corn meal. What is the amount of storage due March 1st, at 5 cents a barrel per month ? Note. — When different rates are charged for different kinds of goods in store at the same time, a separate calculation must be made for each kind. LIFE INSURANCE. 566. Life Insurance is a contract by which a company or party agrees to pay a certain sum of money on the death of the person insured, or when he reaches a certain age. 567. Life Insurance Companies are divided into Stock, Mutual, and Mixed (Stock and Mutual), and Co- Operative Companies. (Arts. 232, 233.) Note. — The first three are defined under ° Insurance." (Art. 229.) 568. In a Co-Operative Insurance Company each member is assessed a fixed sum to meet losses by deaths as they occur. This sum is graduated according to age at the time of becoming a member, and the sum for which he is insured. 569. The Policy is the Contract which specifies the rate of premium, the parties to whom the money is to be paid, etc. Notes. — 1. The money may be paid to any one named by the insured. If payable to himself, it becomes a part of his estate at his death, and is liable for his debts. 2. If payable to another, it cannot be touched by his creditors ; nor can he in his will deprive the party of its benefits. 3. The agreement is not to indemnify the insured for a loss, as in Fire and Marine Insurance, but to pay a specified sum. Hence, a person may insure his life for any amount, or in as many Companies as he pleases. 570. Policies vary according to the nature of the insurance. The more prominent are the Ordinary, Limited, Term, Endow- ment, and Annuity Policies. Life Insurance. 237 Note. — Two persons may insure by a Joint Policy and the sum insured is payable to the other on the death of either. 571. An Ordinary Life Policy stipulates to pay to the parties named in it, a certain sum of money on the death of the insured, the annual premium being paid during his life. Note. — The holder of an Annuity Policy receives a certain sum every year during his life. It is secured by a single cash payment. 572. A Limited Policy is one on which the premium is paid annually for a limited number of years, specified at the time the policy is issued, or until the death of the insured, if that should occur before the end of the period named. Note. — The premiums on this class of policies are payable annually, or all at one time. If they are all paid at once, the insured receives an annual dividend in cash. 573. Term Policies are payable at the death of the insured, if he dies during a given term of years, the annual premium continuing till the policy expires. 574. An Endowment Policy guarantees the payment of a certain sum of money at a specified period, and is payable at the death of the insured, if he dies within that period. It becomes an endowment payable at the end of the period to the insured, if he is still living. Note. — An endowment policy is a combination of a term, policy and a pure endowment. These policies are issued for periods from 10 to 35 years, and may be paid by single payments or by annual premiums. 575. The Premium is a fixed sum paid annually, or at stated periods. It varies according to the expectation of life. (App. p. 297.) 576. The Reserve Fund is a sum which, put at a given rate of interest, with the premiums on existing policies, is intended to be sufficient to meet all obligations when they become due. Note.— The legal rate of interest on reserve funds in the State of New York is 4| % , in Massachusetts 4$ , 238 Life Insurance, ANNUAI PREMIUM RATES FOR AN INSURANCE OP $1000. PAYABLE AS INDICATED, OR AT DEATH, IF PRIOR. Age. At In 10 In 15 In 20 In 25 In 30 In 35 Age. Death. years. years. years. years. years. years. 25 16.91 100.23 62.65 44.46 34.04 27.54 23.30 25 26 17.34 100.27 62.71 44.54 34.14 27.66 23.46 26 27 17.79 100.32. 62.77 44.62 34.24 27.80 23.64 27 28 18.26 100.38 62.84 44.71 34.36 27.95 23.84 28 29 18.76 100.43 62.92 44.80 34.49 28.12 24.06 29 30 19.30 100.50 63.00 44.91 34.62 28.30 24.31 30 31 19.85 100.56 63.09 45.02 34.78 28.51 24.58 31 32 20.44 100.64 63.19 45.15 34.96 28.74 24.89 32 33 21.06 100.72 63.29 45.30 35.15 29.00 25.23 33 34 21.73 100.81 63.41 45.46 35.36 29.29 25.60 34 35 22.42 100.91 63.54 45.64 35.61 29.61 26.01 35 36 23.16 101.02 63.69 45.84 35.88 29,97 26.47 36 37 23.94 101.14 63.85 46.06 36.18 30.37 26.98 37 38 24.78 101.27 64.04 46.31 36.52 30.81 27.54 38 39 25.66 101.42 64.24 46.60 36.90 31.30 28.16 39 40 26.61 101.58 64.48 46.91 37.32 31.85 28.84 40 41 27.60 101.76 64.73 47.27 37.80 32.46 29.59 41 42 28.66 101.97 65.03 47.67 38.33 33.14 30.42 42 43 29.79 102.21 65.36 48.12 38.92 33.89 31.32 43 44 30.99 102.48 65.74 48.63 39.58 34.73 32 31 44 45 32.27 102.78 66.17 49.20 40.32 35.65 83.40 45 46 33.64 103.13 66.65 49.85 41.15 36.67 46 47 35.11 103.53 67.19 50.56 43.07 37.79 47 48 36.66 103.98 67.81 51.37 43.09 39.03 48 49 38.33 104.49 68.50 52.27 44.23 40.39 49 50 40.10 105.06 69.26 53.27 45.48 41.87 50 51 41.99 105.70 70.12 54.38 46.86 51 52 44.01 106.41 71.08 55.61 48.38 52 53 46.16 107.20 72.14 56.98 50.06 53 54 48.47 108.08 73.32 58.50 51.89 54 55 50.92 109.07 74.63 60.17 53.90 55 56 53.55 110.16 76.09 62.02 56 57 56.35 111.38 77.71 64.06 57 58 59.35 112.73 79.51 66.31 58 59 62.56 114.23 81.50 68.78 59 60 65.99 115.90 83.71 71.49 60 61 69.67 117.75 86.15 61 62 73.59 119.81 88.84 62 63 77.81 122.09 91.81 63 64 82.33 124.63 95.08 64 65 87.17 127.43 98.68 65 Life Insurance. 239 577. The true value of a policy surrendered is the legal reserve less a certain per cent for expenses. The market value is the sum the company will pay the holder on its surrender. Notes. — 1. Reserve Endowment, Tontine Investment, and some other special policies, guarantee to pay the holder a definite amount at the termination of fixed periods. 2. Some companies apply all credited dividends to the continuance of the insurance. Others apply the legal reserve to the purchase of term insurance at the regular rates. 578. Finding the annual premium for an ordinary life or endow- ment policy when the rate and sum insured are given ; by the Tables. 1. What is the annual premium for an ordinary life policy of $3000, issued to a person 35 years of age ? Solution. — By the Table the annual premium for $1000 at 35 years of age is $22.42 ; hence, for $3000 it is 3 times $22.42 = $67.26, Am. 2. Find the annual premium for an ordinary life policy of $10000, issued to a person 40 years old. 3. A young man at the age of 25 years took out an ordinary life policy of $20000 ; he died at the age of 45 years ; how much more than he had paid in premiums did his heirs receive ; no allowance heing made for interest ? TABLE OF ANNUAL KATES FOR ENDOWMENT POLICIES OF $1000. PAYABLE AS INDICATED. Age. In 10 years. $103.91 In 15 years. In 20 years. Age. Age. In 10 years. In 15 years. In 20 years. Age. 36 25 $66.02 $47.68 25 36 $105.75 $68.12 $50.11 26 104.03 66.15 47.82 26 37 106.00 68.41 50.47 37 27 104.16 66.29 47.98 27 38 106.28 68.73 50.86 38 28 104.29 66.44 4815 28 39 106.58 69.09 51.30 39 29 10443 66.60 48.33 29 40 106.90 69.49 51.78 40 30 104.58 66.77 48.53 30 41 107.26 69.92 52 31 41 31 104.75 66 96 48.74 31 42 107.65 70.40 5289 42 32 104.92 6716 48.97 32 43 108.08 70.92 53.54 43 33 105.11 67.36 49.22 33 44 108.55 7150 54.25 44 34 105.31 67.60 49.49 34 45 109.07 72.14 55.04 45 35 105.53 67 85 49 79 35 46 109.65 72.86 55.91 46 240 Life Insurance. 4. A man at the age of 32 years has an investment of $15000 at 6% interest, which he intends to leave his family ; what will be its amount in 25 years at compound interest ? How much will his family receive if he takes out a life policy and pays the premium with the interest on his investment ? 5. What annual premium must I pay for a twenty-year endowment policy of $12000 ; my age being 40 years? 6. What is the annual premium on a 20-year endowment policy for $16000; the age being 45 years? 7. How much more is received at the expiration of the 20 years, than has been paid out in annual premiums ? 8. If a person 36 years of age secures an endowment policy for $1000 for 20 years, payable to himself or his heirs, what will be his loss if he survives and pays his premium annually? 9. A man insured his life at the age of 46 years for $15000 on the ordinary life plan. He died at the age of 75 ; having paid the premiums annually, how much had the insurance company received ? How much would a 10-year endowment cost for the same sum ? 10. What is the annual premium for a 15-year endowment policy of $12000, issued to a person 32 years of age ? 11. When 46 years of age a man took out a 10-year endow- ment policy of $10000. He survived the period of endow- ment ; having paid the annual rates, how much less did he receive than he had paid the company, reckoning interest at 12. A gentleman at the age of 45 insures his life on the ordinary life plan for $18000. How much must be put at 5% interest to meet the annual premiums ? 13. If he lived to be 65 years old, would his family receive more, or less, if the premiums were put at h% interest in a savings bank ? How much ? 14. A lady 35 years of age took out a life policy for $5000 for the benefit of her husband, paying the entire premium at the rate of $369.91 on $1000, in one payment. She died in 5 years after securing the policy ; how much less would the company have received if she had paid the premium at the annual rates ? Annuities, 241 ANNUITIES. 579. An Annuity is a specified sum of money paid annually, or at equal periods ; as, semi-annually, quarterly, monthly; to continue a given number of years, for life, or forever. 580. A Perpetual Annuity is one of unlimited duration. 581. A Certain Annuity begins and ends at a fixed time. 582. A Contingent Annuity depends upon some unforeseen event, as the death of an individual, or his arrival at a certain age. Life Insurance, Pensions, Dowers, Leases, etc., belong to this class of incomes. 583. An Annuity in Possession or an Immediate Annuity is one that begins immediately. When the Annuity begins at some future time it is called a Deferred Annuity, or Annuity in Reversion. Note. — The term of reversion may be definite or contingent. 584. If Annuities are not paid when due, they are said to he forborne, or in arrears, 585. The Present Value of an Annuity is the sum which, at the given rate of interest, will amount to' its final value. 586. The Amount or Final Value of an Annuity is the sum which all its payments with interest on each will amount to at its termination. Note. — Annuities, like debts, are entitled to interest after they are due. 587. Annuities at Simple Interest are computed by the principles of Arithmetical Progression, the Annuity being the first term ; the interest of the annuity for 1 year, the common difference ; the time in years, the number of terms ; and the annuity plus the interest due on it for the number of years less 1, the last term. 16 242 At 8i7nple Interest 588. To find the Amount or Final Value of an Annuity at Simple Interest, when the Time and Rate are given. 1. What is the amount of $100 annuity for 5 years, at 6% ? Analysis. — The first annuity is not due until the end of the first year, and draws interest only from the time it falls due. The second is not due until the end of the second year, and draws interest 1 year less than the first ; the third one year less than the second; and so on till all the pay- ments are made. Hence, the arithmetical series 100 + (6x4), + 100 + (6x3), + 100 + (6x2), +100 + 6, +100. 589. The last payment equals the given annuity plus the product of the annual interest by the number of payments less 1. 590. The terms are now the annuity or first payment, the last payment, and the number of payments, to find the sum of all the payments. The sum of the two extremes, 100 + 124 = 224, and 224-T-2 = 112, the average value of all the payments. Now, 112 x 5 = 560, the sum or final value of the annuity. Hence, the Eule. — I. To the annuity add the product of the annual interest of the annuity by the number of pay- ments less 1, for the last payment. II. Multiply half the sum of the first and last pay- ments by the number of payments, and the product will be the final value of the annuity. 2. What is the amount of an annuity of $150 for 8 years, when money is worth 6% simple interest ? 591. To find the Present Worth of Annuities at Simple Interest. 3. What is the present worth of $1 20 annuity for 4 yr., at 7%? Solution. — By the preceding rule the final value of the annuity is $530.40. The present worth of $530.40 due in 4 years, at 7% simple interest — $414,375 (Art. 310). Hence, the Rule. — First find the amount or final value of the given annuity for the given time and rate ; then find the present worth of this amount as in true discount. 4. What is the present worth of $600 annuity for 8 yr., at 6%? Annuities. 243 ANNUITIES AT COMPOUND INTEREST. 592. Annuities at compound interest are computed by the principles of Geometrical Progression, the annuity being the first term; the amount of $1 for 1 year, the ratio; the number of payments, the number of terms, and the annuity multiplied by the amount of $1 for 1 year or period, raised to the power whose index is 1 less than the number of payments, is the last term. l. What is the amount or final value of an annuity of $100 for 4 years, at Q% compound interest. Analysis. — The first annuity is not due until the end of the first year or period ; the second is not due until the end of the second year or period, and draws interest 1 year less than the first ; the third draws interest 1 year less than the second, and so on until all the payments are made. Hence, assuming $1 for the annuity, we have the following series : $1, 1 x 1.06, 1 x (1.06 x 1.06), 1 x (1.06 x 1.06 x 1.06) ; or, $1, 1 x 1.06, 1 x (1.06) 2 , 1 x (1.06) 3 , etc. That is, each successive term = the 1st term xby the ratio raised to a power whose index is 1 less than the number of the term. Therefore, the last term = 100 x 1.191016 = 119.1016. Hence, 593. To find the last term or payment Multiply the first term by that -power of the ratio denoted by 1 less than the number of terms. 594. The terms are now the annuity or first payment, the last payment, and the ratio, to find the sum of all the payments. Since, $100 (annuity) x (1.06) 3 = $119.1016, the last payment, $119.1016x1.06, the ratio, = $126.247696. Then, $126.247696 - $100 (annuity) = $26.247696 ; and $26.247696 -h .06 = $437.4616, the sum of the terms, or final value of annuity. Hence, the Rule. — Multiply the last term by the ratio, and sub- tracting the first term from the product, divide the remainder by the ratio less 1. Note.— The labor of computing annuities at Compound Interest is greatly diminished by the use of the following tables : 244 At Compound Interest. Table I. 595. Amount of $1 annuity at Compound Interest, from 1 year to 40, inclusive. Yrs. 1 8*. 8tf. 4* ft. w. 7%. Yrs. 1.000 000 1.000 000 1 000 000 1.000 000 1.000 000 1.000 000 1 2 2.030 000 1 2.035 000 2.040 000 2.050 000 2.060 000 2.070 000 2 3 3.090 900 3.106 225 3.121 600 3.152 500 3.183 600 3.214 900 3 4: 4.183 627 4.214 943 j 4.246 464 4.310 125 4.374 616 4.439 943 4 5 5.309 136 5.362 466 5.416 323 5.525 631 5.637 093 5.750 739 5 6 6.468 410 6.550 152 6.632 975 6.801 913 6.975 319 7.153 291 6 7 7.662 462 7.779 408 7.898 294 8.142 008 8.393 838 8.654 021 7 S 8.892 336 9.051 687 9.214 226 9.549 109 9.897 468 10.259 803 8 9 10.159 106 10.368 496 10.582 795 11.026 564 11.491 316 11.977 989 9 10 11.463 879 11.731 393 12.006 107 12.577 893 13.180 795 13.816 448 10 11 12.807 796 13.141 992 13.486 351 14.206 787 14.971 643 15.783 599 11 12 14.192 030 14.601 962 15.025 805 15.917 127 16.869 941 17.888 451 12 13 15.617 790 16.113 030 16.626 838 17.712 983 18.882 138 20.140 643 13 14 17.086 324 17.676 986 18.291 911 19.598 632 21.015 066 22.550 488 14 15 18.598 914 19.295 681 20.023 588 21.578 564 23.275 970 25.129 022 15 16 20.156 881 20.971 030 21.824 531 23.657 492 25.670 528 27.888 054 16 17 21.761 588 22.705 016 23.697 512 25.840 366 28.212 880 30.840 217 17 18 23.414 4,35 24.499 691 25.645 413 28.132 385 30.905 653 33.999 033 18 19 25.116 868 26.357 180 27.671 229 30.539 004 33.759 992 37.378 965 19 20 26.870 374 28.279 682 29.778 079 33.065 954 36.785 591 40.995 492 20 21 28.676 486 30.269 471 31.969 202 35.719 252 39.992 727 44.865 177 21 22 30.536 780 32.328 902 34.247 970 38.505 214 43.392 290 49.005 739 22 23 32.452 884 34.460 414 36.617 889 41.430 475 46.995 828 53.436 141 23 24 34.426 470 36.666 528 39.082 604 44.501 999 50.815 577 58.176 671 24 25 36.459 264 38.949 857 41.645 908 47.727 099 54.864 512 63.249 030 25 26 38.553 042 41.313 102 44.311 745 51.113 454 59.156 383 68.676 470 26 27 40.709 634 42.759 060 47.084 214 54.669 126 63.705 766 74.483 823 27 28 42.930 923 46.290 627 49.967 583 58.402 583 68.528 112 80.697 691 28 29 45.218 850 48.910 799 52.966 286 62.322 712 73.639 798 87.346 529 29 30 47.575 416 51.622 677 56.084 938 66.438 848 79.058 186 94.460 786 30 31 50.002 678 54.429 471 59.328 335 70.760 790 84.801 677 102.073 041 31 32 52.502 759 57.334 502 62.701 469 75.298 829 90.899 778 110.218 154 32 33 55.077 841 60.341 210 66.209 527 80.063 771 97.343 165 118.933 425 33 34 57.730 177 63.453 152 69.857 909 85.066 959 104. 183 755 128.258 765 34 35 60.462 082 66.674 013 73.652 225 90.320 307 111.434 780 138.236 878 35 36 63.271 944 70.C07 603 77.598 314 95.836 323 119.120 867 148.913 460 36 37 66.174 223 73.457 869 81.702 246 101.628 139 127.268 119 160.337 400 37 38 69.159 449 77.028 895 85.970 336 107.709 546 | 135.904 206 172.561 020 38 39 72.234 238 80.721 906 90.409 150 114.0D5 028 145.058 458 185.640 292 39 40 75.401 260 ! 84.550 278 1 95.025 516 120.7!)!) 774 154.761 C66 199.635 112 40 Annuities. 245 Tab le II. 596. Present Worth of $1 annuity at Compound Interest, from 1 year to 40, inclusive. Yrs. 1 3*. SK*. <¥. 5*. 6£. 7%. Yrs. 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 2.801 637 2.775 091 2.723 248 2.673 012 2.624 314 3 4 3.717 098 3.673 079 3.629 895 3.545 951 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 7.607 687 7.435 332 7.107 822 6.801 692 6.515 228 9 10 8.530 203 8.316 605 8.110 896 7.721 735 7.360 087 7.023 577 10 11 9.252 624 9.001 551 8.760 477 8.306 414 7.886 875 7.498 669 11 12 9.954 004 9.663 334 9.385 074 8.863 252 8.383 844 7.942 671 12 13 10.034 955 10.302 738 9.985 618 9.393 573 8.852 683 8.357 635 13 14 11.296 073 10.920 520 10.568 123 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 SCO 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 13.590 326 12.462 210 11.469 421 10.593 997 20 21 15.415 024 14.697 974 14.029 160 12.821 153 11.764 077 10.835 527 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.&56 842 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 11.469 334 24 25 17.413 148 16.481 515 15.622 080 14.093 945 12.783 356 11.653 583 25 26 17.876 842 16.890 352 15.982 769 14.275 185 13.003 166 11.825 779 26 27 18 327 031 17.285 365 16.329 586 14.643 034 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 18.035 767 16.983 715 15.141 074 13.590 721 12.277 674 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 14.230 230 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.a32 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 39 22.808 215 21.102 500 19.584 485 17.017 041 14.949 075 13.264 928 39 40 23.114 772 21.355 072 19.792 774 17.159 086 15.046 297 13.331 709 40 246 Annuities. 597. To find the amount or Final Value of an Annuity. Kule. — Multiply the tabular amount of $1 by the annuity, the product will be the final value. (Table I.) Note. —When payments are made semi-annually, take from the table twice the given number of years, and £ the given rate of interest. 2. What is the final value of $600 for 8 years, at 6% ? Solution.— Tab. Amt. of $1, at 6% for 8 years = $9.897468 ; and $9.897468 x 600 = $5938.4808, Ans. 3. What is the final value of an annual pension of $150 for 15 years, at 4$ ? 4. A widow is entitled to $140 a year for 18 years, at 10% semi-annual compound interest ; what is its final value ? 598. To find the Present Value of an Annuity. Kule. — Multiply the present worth of $1 by the Given Annuity. (Table II.) 5. What is the present worth of $300 due in 7 years, at 6% ? Solution.— Present worth of $1, at 6% for 7 yr. = $5.582381 ; and $5.582381 x 300 = $1674.7143, Ans. 6. What is the present worth of an annual ground rent of $500, at 4%, for 12 years ? 7. What is the present worth of an annuity of $500 for 8 years, at 4% ? 8. What is the present worth of an annuity of $3000, at %%, for 20 years ? 599. To find the Present Worth of an Annuity in Reversion. Kule. — Find the present worth of $1 to the time the annuity begins, also to the time it ends ; and multiply the difference between these values by the given annuity. Annuities. 247 9. What is the present worth of an annuity in reversion of $1000, at 6%, which begins in 3 years, and then terminates after 5 years ? Solution.— The present worth of $1, at 6% for 3 yr. = $2.673012 "8 yr. = $6.209744 Their difference $3.536732 x 1000 (annuity) = $3536.732, Ans. 10. The reversion of a lease of $450 per year, at h%, begins in 3 years and continues 9 years; what is its present worth ? li. A father bequeathed his son, 11 yrs. of age, a 5% annuity of $1000, to begin in 3 years and continue 10 years ; what would be the amount when the son was 21 years old ? What is its present worth ? 600. To find the Present Worth of a Perpetual Annuity. Eule. — Divide the given annuity by the interest of $1 for 1 year, at the given per cent. 12. A man wished to establish a perpetual professorship in a college, at $2000 a year ; what sum must he invest in Gov't 5's to yield this income ? Solution.— $2000. 00 -^-. 05 = $40000, Ans. 13. An estate in New York pays $3000 annually, at 6% interest, on a perpetual ground rent ; what is the value of the estate ? Note. — When the annuity is payable for any period less than a year, before dividing by the interest of $1 for 1 year, the annuity must be increased by the interest which may accrue on the parts of the annuity payable before the end of the year. 14. What is the present worth of a perpetual annuity of $250 in arrears for 10 years, allowing ?>% compound interest. Note. — There is now due the amount of $250 annuity for 10 yr. at 3%, which must be added to the present worth of the perpetuity. 15. What is the present worth of a perpetuity of $500, in arrears for 30 years, allowing compound interest at 5 per cent? 248 Sinking Funds. SINKING FUNDS. 601. Sinking Funds are sums of money set apart at regular periods for the payment of indebtedness. They are properly derived from an excess of income above expenses.* 602. To find what sum must be set apart annually, as a sinking fund, to pay a given debt in a given time. 1. A certain town borrowed $20000 to build a Union School- house, and agreed to pay 6% compound interest; what sum must be set apart, as a sinking fund annually, to pay the debt in 10 years ? Analysis.— The amt. of $1 at 6% comp. int. for 10 yrs. is $1.790848, and that of $20000 is 20000 times as much, or $35816.96. (Art. 306.) Again, the amt. of an annual payment or annuity of $1 at 6% for 10 yrs. is $13.180795 ; since to pay $13.180795 requires an annuity of $1 at 6% for 10 yrs., a debt of $35816.96 will require 35816.96-T-13. 180795 = $2717.36, Ans. Hence, the Rule. — Divide the amount of the debt at its maturity, at compound interest, by the amount of an annuity of $1 for the given time and rate, and the quotient will be the sinking fund required. 2. What sum must be set apart annually to rebuild a bridge costing $30000, estimated to last 17 years, allowing 5% com- pound interest ? 3. A railroad company bought $100000 worth of rolling stock, payable in 5 yr. with %% compound int. ; what sum must be set apart annually as a sinking fund to discharge the debt ? 4. The National debt of the United States is about $2,003,000,000 ; what must be the excess annually of revenue over expenditure, allowing 5% comp. interest to pay the debt in 21 years. * Sinking Funds were first introduced into England in 1716, and renewed in H86 by- Messrs. Price and Pitt, who contended that by applying a certain amount of revenue to the purchase of stocks the dividends of which should be reinvested in the same manner a sinking fund would be established, which at compound interest would increase so that the largest debt might be paid. But the fallacy of this idea was proven by Dr. Hamilton, who showed that the sinking fund had really added to the debt, and demonstrated that the only true sinking fund consists in an excess of revenue above expenditure. Sinking Funds. 249 603. To find the number of years required to pay a given debt, by a given annua! sinking fund. 5. A village built a school-house costing $12000, and raised $1700 a year to pay for it ; allowing 6% compound interest, how many years will it require to cancel the debt? Analysis.— Since a sinking fund of $1700 at 6% for a certain time has a present worth of $12000, a sinking fund of $1, for the same time and rate, has a present worth of TT Vir P a *t as much ; and $12000 ---$1700 = $7.05882. Looking in Table (Art. 596) in col. 6%, the time correspond- ing with this present worth of $1 is 9 years, which is the number of whole years required, with a balance due of $738 .51. The amt. of the debt $12000 at 6% comp. int. in 9 yr. = $20273.748 The amt. of s. fund $1700 " " " " = 19535.238 Balance due at the end of 9 yr $738.51 Hence, the Eule. — Divide the debt by the given sinking fund, and the quotient will be the present worth of $1 for the time. Loolc for this number in Table (Art. 596) in the col. denoting the given rate, and opposite in the column of time will be found the number of years. Notes. — 1. If the exact number is not found in the column take the years standing opposite the next smaller number. 2. To ascertain the balance due* at the end of the number of whole years, find the difference between the amount of the debt at the given rate for the time taken out, and the amount of the sinking fund for the same time and rate. (Tables, Arts. 595, «306.) 6. The national debt of Great Britain is about £800,000,000; allowing 5% compound interest, how many years would it require to cancel it by an annual sinking fund of £48,000,000 ? 7. The national debt of France is about $4,750,000,000 ; allowing 3% int., how long would it take to discharge it by a sinking fund of $200,000,000 a year ? 8. The Dom. of Canada had a debt in 1881 of $199861537, and a sinking fund of $44465757; allowing 4$ int., how many years will be required to cancel the debt? 250 Sinking Funds. 604. To find the amount of a sinking fund, the rate of interest and the time being given. 9. If a Railroad Co. sets apart an annual sinking fund of $20000, and puts it at 7% compound interest, what will be its amount in 10 years ? Analysis. — The amount of a sinking fund of $1 in 10 jr., at 7%, is $13.816448 (Table, Art. 595) ; therefore, the amount for the same time and rate of a sinking fund of $20000 = 13.816448x20000 = $276328.96. Hence, the Eule. — Multiply the amount of $1 for the given time and rate as found in Art. 595 by the annual sinking fund. 10. What will be the amount in 12 years of a sinking fund of $12000, yielding 5% compound interest ? 605. Sinking Fund Bonds are securities issued by Corpora- tions, based on the pledge of a special income which is fancied for their redemption. Note. — This income is derived in the case of Railroads from the sale of lands, from rents, etc., or from a per cent of the earnings. These bonds are bought and sold in the stock market like Mortgage Bonds. 11. A Kailroad Co. issued sinking fund bonds at 6% for $200000, payable in 10 years; if at compound interest, what sum must be set apart annually to meet interest and principal when due ? (Art. 602.) 12. What would be the amount in 10 years, at 6% simple interest ? 13. If the funded securities were drawing an annual income of 4:% compound interest, by how much would the amount necessary to meet principal and interest at 6% be reduced ? 14. With the above reduction what sum would be needed annually as a sinking fund to pay the amount when due at 4$ ? f OWER8 and 606. A Power is a product of equal factors. Thus, 2x2x2 = 8, and 3x3 = 9; 8 and 9 are powers. Note. — Powers are named according to the number of times the equal factor is taken to produce the given power. 607. The First Power is the number itself. 608. The Second Power is the product of a number taken twice as a factor, and is called a Square. 609. The Third Power is the product of a number taken three times as a factor, and is called a Cube. 610. An Exponent is a small figure placed above a number on the right to denote the power. It shows that the number above which it is placed is to be raised to the power indicated by this figure. Thus, 611. The expression 2 4 is read, "2 raised to the fourth power, or the fourth power of 2." 1. Express the 4th power of 84. 3. The 7th power of 350. 2. Express the 5th power of 248. 4. The 8th power of 461. 612. To find any required Power of a Number. 5. What is the 5th power of 8 ? Solution.— 8 5 -8x8x8x8x8 = 32768, Ans. Rule. — Take the number as many times as a factor as there are units in the exponent of tli e required power. 252 Powers and Roots. Notes. — 1. A common fraction is raised to a power by involving each term. Thus, (f) 8 = T V 2. A mixed number should be reduced to an improper fraction, or the fractional part to a decimal ; then proceed as above. Thus, (2£) 2 = (|) 2 = - 2 ¥ 5 - ; or 2£ = 2.5 and (2.5) 2 = 6.25. 3. All powers of 1 are 1 ; for 1 x 1 x 1, etc. = 1. 613. A Root is one of the equal factors of a number. Note. — Boots are named from the number of equal factors they contain. 614. The Square Root is one of the two equal factors of a number. Thus, 5 x 5 = 25 ; therefore, 5 is the square root of 25. 615. The Cube Root is one of the three equal factors of a number. Thus, 3 x 3 x 3 — 27 ; therefore, 3 is the cube root of 27, etc. 616. The character (y') is called the Radical Sign. Note. — It is a corruption of the letter R, the initial of the Latin radix, a root. 617. Roots are denoted in two ways : 1st. By prefixing to the number the Radical Sign, with a figure placed over it called the Index of the root ; as ^/4, ^/8. 2d. By a fractional exponent placed above the number on the right. Thus, 9*, 27*, denote the square root of 9, and the cube root of 27. Notes. — 1. The figure over the radical sign and the denominator of the exponent, each denote the name of the root. 2. In expressing the square root, it is customary to use simply the radical sign (\/)> the 2 being understood. Thus, the expression * j? 636. A Rhombus is an equilateral rhom- boid. 240 262 Mensuration. 637. A Trapezoid is a quadrilateral which has two of its sides parallel. 638. A Trapezium is a quadrilateral haying four unequal sides, no two of which are parallel. Note. — The line AB is the diagonal of the adjoining figure. 639. A Triangle is a polygon haying three sides and three angles. 640. The Base of a triangle is the side AB on which it is supposed to stand. ad a 641. A Vertical Angle is the angle opposite the base; as 0. 642. An Equilateral Triangle is one haying three equal sides. 643. The Altitude of a triangle is the per- pendicular CD drawn from the vertical angle to the base. AREA OF PLANE FIGURES. 644. The Area of a plane figure is the surface bounded by its perimeter. 645. It is proved by Geometry that TJie area of a triangle is equal to half the area of a parallelo- gram of equal base and altitude. Illustration. — Let ABCD be a parallelogram whose altitude is the perpendicular EB. Connect the diagonal corners by the straight line BD, and the parallelogram will be divided into two equal triangles, the altitude of each being EB. Area of Plane Figures. 263 The area of a parallelogram or rectangle is equal to the length multi- plied by the breadth. The sides mast be reduced to the same denomina- tion before multiplying. Note. — The perimeter of a parallelogram of unequal sides is greater than that of a square of equal area. Illustration. — Let the adjoining figure be a garden whose area is 16 sq. rods. If a fence is put around it in its square form, its length will be 16 rods. Bat if a the width is exchanged for an equal area in the rear, the length of the garden will then be four times its width and the length of fence required will be 20 rods. 4 rods. 4 x 4 = 16 eq. rods. 1. A lot of ground 80 ft. long by 20 ft. wide was cut diagonally by a railroad, leaving a triangular plot of the same base and altitude; what was its area ? 2. What will it cost to pave a roadway 80 feet long and 15 ft. wide, at $1.50 per sq. yard ? 3. What will it cost to plaster a room 15 ft. 6 in. long, 13 ft. 8 in. wide, and 9 ft. high, at 26 cents a square yard ? 4. Two fields contain 10 acres each ; one is in the form of a square, the other is 4 times as long as it is wide ; what would be the difference in expense of fencing them at $2.25 per rod ? 5. If the fence were built 4£ ft. high, of boards 8 in. wide, the lower one raised 2 in. above the ground, and a space of 3 in. between the boards, how many sq. feet of boards would be required for both fields ? 6. How many more for one than for the other ? 7. A piece of land containing 2 acres is 5 times as long as it is broad ; what are its length and breadth ? 8. How many bricks 8 in. long and 4 inches wide will pave a yard that is 100 ft. by 50 ? 9. How many yards of carpeting J yd. wide will cover a floor 27 ft. 3 in. long and 22 ft. 6 in. wide? How many breadths will it require ? 10. If the room were 23 ft. 8 in. wide, how much would you need to buy allowing for waste ? 264 Mensuration, AREA OF TRIANG-LES. 646. To find the Area of a Triangle, when the Base and Altitude are given. Multiply the base by half the altitude. (Art. 632.) Note. — Dividing the area of a triangle by the altitude gives the base. Dividing the area by half the base gives the altitude. 1. What is the area of a triangle whose base is 24 feet and altitude 16 feet ? 2. The base of a triangle is 28 centimeters and the altitude 16 centimeters ; what is the area? 3. A board 16 feet long is 22 inches wide at one end, and tapers to a point; what is the value at 4J cents a sq. foot ? 647. To find the Area of a Triangle, when the Three Sides are given. From half the sum of the three sides subtract each side respec- tively ; then multiply half the sum and the three remainders together, and extract the square root of the product. 4. What is the area of a triangle whose sides are respectively 12 feet, 16 feet, and 18 feet ? Solution.— (12 + 16 + 18)-*-2 = 23 ; 23-12 = 11 ; 23-16 = 7 ; 23-18 = 5. And 23 x 11 x 7 x 5 = 8855 ; ^8855 = 94.1 + sq. ft., Ana. 5. How many acres in a triangular field whose sides are respectively 45, 55, and 60 feet ? 6. What is the area of an equilateral triangle whose side is 24 feet ? 648. To find the Altitude, when the Area and Base are given. Eule. — Divide the area by half the base. 7. What is the altitude of a triangle whose area is 37J square yards and base 5 yards? Ans. 15 yards. Circles. 265 8. At $6.25 a sq. rod, a triangular lot cost $1281.25 ; the base was 40 rods, what was the length ? 9. The base of a triangle is 128 ft., area 298f sq. yd. ; what is the altitude ? 10. A house lot containing 12 A. 56 sq. rods was in the form of a triangle, the base of which was 56 T | T rods ; what was the altitude ? 649. To find the Base, when the Area and Altitude are given. Kule. — Divide the area by half the altitude. 11. What is the base of a triangle whose area is 156 sq. ft. and its altitude 12 feet ? . Ans. 26 feet. 12. What is the base of a triangle whose area is 144 acres and its altitude 60 rods ? 13. Find the base of a triangle whose area is 5280 sq. yd., and altitude 240 yards. 14. A garden contains -J of an acre in shape of a triangle, the altitude of which is 2 rods 4 ft. 3 inches ; what is the base ? 15. A triangular field whose altitude is 70£ rods, contains 12 A. 56 sq. rods; what is the base ? CIRCLES. 650. A Circle is a plane figure bounded by a curve line, every part of which is equally distant from a point within called the center. a 651. The Circumference of a circle is the curve line by which it is bounded. 652. The Diameter is a straight line drawn through the center, terminating at each end in the circumference, as AB. 266 Mmswratim. 653. The Radius is a straight line drawn from the center to the circumference, and is equal to half the diameter, as CE. Note.— From the definition of a circle, it follows that all the radii are equal; also, that all the diameters are equal. 654. From the relation of the circumference and diameter to each other, we derive from Geometry the following Pki^ciples.— 1°. TJie Circumference=the Diameter x 8.U16 nearly. 2°. The Diameter of a Circle = the Circumference -f- 3.1416 nearly. 3°. The Area of a Circle = half the Circumference x by the Radius. Notes. — The diameter of a circle may also be found by dividing the area by .7854 and extracting the square root of the quotient. 2. The area of a circle may also be found by multiplying the square of its diameter by the decimal .7854, or, by multiplying the circumference by \ the diameter. 3. The decimal .7854 is found by taking \ of the area of a circle whose circumference is 1, that is \- of 3.1416. 1. What is the circumference of a disc of 15 inches radius ? Solution.— 15 x 2 x 3.1416 = 94.248 inches, Ans. 2. What is the diameter of a lake 721 r. in circumference ? Solution.— 721 rods-s-3.1416 = 229.5+ rods, Ans. 3. What is the area of a race-course 320 rods in circum- ference ? Solution.— 320.0000-4-3.1416 = 101.859 rods = diameter, Radius = 50.929, and ^ circumference = 160 rods. 50.929 x 160 = 8148.64 sq. rods., Ans. 4. A cistern is 29 feet 8 inches in circumference; what is the diameter ? 5. What is the difference in the perimeters of 2 acres of land, one a circle the other a square ? Circles. 267 6. What is the diameter of a circular piece of land measuring 4| acres ? 7. How many sq. feet in a circular grass plot 45 feet in diameter ? 8. A circular fish-pond is 850 ft. in circumference; what is. its area ? 9. The diameter of a circular piece of land is 84 feet ; how long a fence will be required to go around it ? io. A horse is tied to a post in a meadow, by a rope 45| ft. long ; how much ground can he graze upon ? n. What is the area of a circle whose diameter is 120 rods? 12. What is the diameter of a circle whose circumference is 94.318 yards ? 13. What is the circumference of a circle whose diameter is 45 rods? 120 rods? 14. How many acres in a circular park whose circumference is 2 miles ? 655. The Area of a square inscribed within a circle, is found by taking twice the square of its radius. 15. What is the largest square stick of timber that can be cut from a log 36 inches in diameter ? What is the length of one side ? Solution.— (18 x 18) x 2 = 648 sq. in. = Area. = 25.45+ in., Ans. 16. How large a stick of square timber can be made from a log 20 inches in diameter ? 17. The circumference of a circle is 3 ft. 4 in. ; what is the side of a square of equal area ? 18. What is the difference between the area of a square circumscribed about a circle 18 inches in diameter, and the area of the largest square that can be inscribed within the same circle ? 19. The circumference. of a circle is 3 meters 4 decimeters; what is the area of a square inscribed within it ? 268 Mensuration. 656. To find the side of a square equal in area to a given circle. Rule. — Multiply the diameter by .8862, or the circum- ference by £821. 20. The diameter of a circle is 20 feet; what is the side of a square of equal area ? Solution.— 20 ft x .8862 = 17.7240 feet, Ana. 21. A field is 150 rods in circumference; what is the side of a square field of the same area ? 22. The distance around each of two gardens is 25 rods ; one is in the form of a circle, the other a square ; which contains the more land, and how much ? SOLIDS. 657. A Solid is that which has length, breadth, and thickness. 658. A Prism is a solid whose bases are similar, equal, and parallel, and whose sides are parallelograms. Note. — When their bases are parallelograms they are called parallelopipeds, or parallelopipedons. 659. All rectangular solids are prisms. 660. A Right Prism is one whose sides are perpendicular to its bases. 661. A Rectangular Prism is one whose bases are rectangles, and its sides perpendicular to its bases. 662. A Triangular Prism is one whose bases are triangles. Notes. — 1. Prisms are named from the form of their bases, as triangular, quadrangular, pentagonal, hexa- gonal, etc. 2. When their sides are all equal to each other they are called cubes. Solids. 269 663. The Lateral Surface of a prism is the sum of all its faces. 664. A Cylinder is a circular body of uniform diameter, whose ends are equal parallel circles. 665. The Altitude of a prism or a cylinder is the perpendicular distance between its bases. 666. To find the Lateral Surface of a Prism or Cylinder. Eule. — Multiply the perimeter of the base by the altitude. Note. — To find the entire surface, the area of the bases must be added to the lateral surface. 1. What is the lateral surface of a prism, the altitude of which is 18 feet and its base a pentagon, each side of which is 8 feet. Solution.— 8 ft. x 5 = 40 ft. the perimeter. 40 ft. x 18 = 720 square feet, the surface, Ans. 2. What is the convex surface of a cylinder the circumfer- ence of whose base is 62 inches, and the altitude 3 feet? Solution.— 62 in. x 36 = 2232 sq. inches, Ans. 3. How many square feet of canvas will be required to cover a cylinder 16£ feet in circumference and 25 feet long? 4. How many square feet of surface m a stove pipe 22 inches in circumference and 12 feet long ? 5. What is the convex surface of a log 25 ft. in circumfer- ence and 18 ft. long ? 6. What is the convex surface of a cylinder 3 ft. long and 1\ ft. in diameter? What is its entire surface ? 270 Mensuration. 667. To find the Contents of a Prism or Cylinder, when the Perimeter of the Base and the Altitude are given. Rule. — Multiply the area of the base by the altitude. Note. — This rule is applicable to all prisma, triangular, quadrangular, etc. ; also to all parallelopipedons. 7. The standard bushel of the United States is 18J inches in diameter and 8 inches deep ; how many cubic inches does it contain ? Solution.— The diam. 18^ in. x 3.1416 = 58.1196 in. = circumference. 58.1196^-2 = 29.0598 ; and 18|-*-2 = 9} ; 29.0598 x 9i = 268.8031 sq. in. = area. And 268.8031 x 8 = 2150.4248 cu. in., Am. 8. What are the contents of a log 15 ft. long and 2 ft. in diameter ? 9. The standard liquid gallon is 231 cubic inches; how many gallons in a can 22 inches in diameter and 3 feet high ? 10. How many en. feet in a triangular prism, the area of whose base is 920 square feet and height 20 feet ? 11. What are the contents of a quadrangular prism whose length is 25 centimeters, and the base a rectangle 3 by 5 centimeters ? 12. How many liters will fill a cistern 2 meters long, 5 decims wide, and 8 decims deep ? How many kiloliters of water ? 13. What are the contents of a triangular prism, each side of which is 30 inches wide and 5 feet long ? Fyramicl, Frustum. Coue. Frustum Solids. 271 668. A Pyramid is a solid whose base is a triangle, square, or poly y 07i, and whose sides terminate in a point, called the vertex. Note. — The sides which meet in the vertex are triangles. 669. A Cone is a solid which has a circle for its base, and terminates in a point called the vertex. 670. The Altitude of a pyramid or a cone is the perpen- dicular distance from the base to the vertex. 671. The Slant Height of a pyramid is the distance from the middle of any side of the base to the vertex. 672. A Frustum of a pyramid or cone is the part which is left after the top is cut off by a plane parallel to the base. 673. To find the Lateral or Convex Surface of a Regular Pyramid or Cone. Eule. — Multiply the perimeter of the base by £ the slant height. To find the entire surface, Add the area, of the base to the convex surface. 14. What is the lateral surface of a regular pyramid whose slant height is 15 ft, and the base is 30 ft. square? Solution.— Perimeter of base = 30 x 4 = 120 ft. 120 x 7| (| slant height) = 900 sq. ft., Arts. 15. What is the surface of a pyramid whose base is an equilateral triangle measuring 4 ft. on each side, and slant height 16 feet ? 16. What is the convex surface of a cone, the diameter of whose base is 7 ft. and its altitude 12 feet ? 17. What is the entire surface of a triangular pyramid whose slant height is 25 feet, and each side of the base 10 feet. 18. What is the entire surface of a right cone, the diameter pf the base and the slant height being each 40 feet ? 272 Mensuration. 674. To find the Contents of a Pyramid op a Cone, when the Base and Altitude are given. Kule. — Multiply the area of base by % the altitude. Note.— The contents of a frustum of a pyramid or cone are found by adding the areas of the two ends to the square root of the product of those areas, and multiplying the sum by ^ of the altitude. 19. What are the contents of a pyramid whose base is 144 sq. feet, and its altitude 33 feet ? Solution. — 144 sq. ft. x 11 (| of altitude) = 1584 cu. ft., Ans. 20. What are the contents of a cone the area of whose base is 1865 sq. feet, and its altitude 36 feet? Solution.— 1865 x 12 ft of altitude) = 22380 cu. ft. 21. A monument in the form of a square pyramid, is 2 ft. 10 in. square at base, and 11 ft. high; at 175 lb. to a cu. ft. what is its weight ? 22. What are the contents of a round log whose length is 20 ft., diameter of larger end 12 in., and smaller end 6 inches ? 23. The altitude of a frustum of a pyramid is 27 ft., the ends are 4 ft. and 3 ft. square ; what is its solidity ? 675. A Sphere or Globe is a solid ter- minated by a curve surface, every part of which is equally distant from a point within, called the center. 676. The Diameter of a sphere is a straight line drawn through its center and terminated afc both ends by the surface. 677. A Hemisphere is one-half a sphere. 678. The Radius of a sphere is a straight line drawn from its center to any point in its surface. Gauging of Casks. 273 679. To find the Surface of a Sphere, the Circumference and Diameter being given. Eule. — Multiply the circumference by the diameter. 24. Require the surface of a globe 4 inches in diameter. Solution.— 4x3.1416 = 12.5664 in circumference. 12.5654 x 4 = 50.2656 sq. in. surface, Ans. 25. What will it cost to gild a ball 12 inches in diameter, at 10 cents a square inch ? 26. Required the surface of the earth, its diameter being 8000 miles. 27. The diameter of a sphere is 100 centimeters; what is its surface ? 680. To find the Solidity of a Sphere, the Surface and Diameter being given. Rule. — Multiply the surface by £ of the diameter. 28. Find the solidity of a sphere whose diameter is 12 inches and its surface 4.91 sq. feet ? Solution. — 4.91 x 144 ■= 707.04 sq. in. surface. 707.04 sq. in. x 2 = 1414.08 cu. in., Ans. 29. What is the solidity of the earth, its surface being 196900278 sq. miles, and its mean diameter 7916 miles ? 30. Find the solidity of a cannon ball 3 decimeters in diameter ? 31. The basin of a fountain is a hemisphere 22-| ft. in diameter; what are its cubical contents ? 32. How many hogsheads of water will it contain ? GAUGING OF CASKS. 681. Gauging is finding the capacity or contents of casks and other vessels. 682. The mean diameter of a cask is equal to half the sum of the head diameter and bung diameter. (Art. 339.) 274 Mensw*ation. Note.— The contents of a cask are equal to those of a cylinder having the same length and a diameter equal to the mean diameter of the cask. 683. To find the Contents of a Cask, when its Length, its Head, and Bung Diameters are given. Rule. — Multiply the square of the mean diameter by the length in inches, and this product by .0034 f or gallons, or by .0129 for liters. Note. — In finding the contents of cisterns, it is sufficiently accurate for ordinary purposes to call a cubic foot = 7$ gallons. 1. How many gallons in a cask whose length is 35 inches, its bung diameter 30 inches, and head diameter 26 inches? Solution.— (30 + 26) -4- 2 = 28 in., the mean diameter. (Art. 682.) 28 2 x .7854 = area of base. Area of base x length = contents in cubic inches, which are reduced to gallons by dividing by 231. Instead of using the factor .7854, if we divide it by 231, the number of cubic inches in a gallon, and multiply by the quotient .0034, the operation is shortened, and the result is in gallons. Thus, 28 2 x 35 x .0034 = 93.296 gal., Ans. 2. What is the capacity in gallons of a cask whose length is 26 inches, its head diameter 17, and bung diameter 22 inches ? 3. Find the contents in liters of a cask whose length is 54 inches, its bung diameter 42, and head diameter 36 inches ? 4. Required the contents in gallons of a rectangular cistern 4£ ft. long, 3J ft. wide, and 6 ft. deep. 6. What are the contents in gallons of a cask 36 in. long, its head diameter 26 inches, and bung diameter 32 inches? 6. What will be the cost at 60 cents a gallon of a cask of molasses, whose, length is 16 in., the head and bung diameters 10 and 12 inches ? 7. A cylindrical ash-receiver is 18 inches in diameter and 28 inches high ; how many bushels will it contain? 8. What must be the depth of a cylindrical measure 18| inches in diameter to contain a bushel ? Tonnage of Vessels. 275 TONNAGE OF VESSELS. 684. Tonnage is the weight in tons which a vessel will carry It is estimated by the following Carpenter's Rule. Multiply together the length of the keel, the breadth at the main beam, and the depth of the hold in feet, and divide the product by 95 (the cu. ft. allowed for a, ton) ; the result will be the tonnage. For a double decker, instead of the depth of the hold, take half the breadth of the beam. Note. — A Register Ton = 100 cu. ft. is the legal standard. * m . • m J 40 cu. ft, U. S., or ) ",. A . u A Shipping Ton = 1 . > used in estimating cargoes. 1. What is the tonnage of a double decker with 300 ft. keel and 42 ft. beam ? Ans. 2785^ tons. 2. What is the tonnage of a single decked vessel whose length is 150 ft, the breadth 30 ft., and the depth 12 ft? Rules for the Measurement of Grain. 685. To estimate the quantity of grain heaped in conical form on the floor. Rule. — Square the depth and the slant height in inches, multiply the difference of the squares by the depth, and multiply this product by .0005 ; the result is the contents in bushels. Note. — When heaped against a straight wall, take one-half the product before multiplying by the decimal. 3. A conical heap of grain left by a thrashing-machine was 5-J- ft. high, and the slant height was 9 ft. ; how many bushels did it contain ? 4. A quantity of wheat heaped against a straight wall was 4 ft. high, and its slant height was 7 ft. ; how many bushels were there ? 276 Mensuration. 5. A quantity of grain was heaped in a conical form in a corner, perpendicular height 4 ft. 3 in., slant height 7 ft. 1 in. ; what is its value, at $1.66| a bushel? 686. To measure the height of an object standing in a plane. 6. What is the height of a tree standing in a plane which casts a shadow 50 feet, measured with a pole 5 ft. long, casting a shadow 10 ft.? Solution. — Take a pole of any convenient length, and placing it in a perpendicular position, measure the length of its shadow, which we will suppose to be 10 feet, then by Proportion 10 ft. (shadow of p.) : 50 ft. (shadow of t.) : : 5 ft. (1. of p.) : height of tree. 50 x 5 = 250, and 250^-10 = 25 feet, Am. 7. What is the height of a pyramid, standing in a plane, which casts a shadow of 100 feet, measured with a pole 7-J ft. long which casts a shadow of 15 feet ? 8. The shadow of a tower was 36f ft., and that of a cane 2| ft. high standing near it was at the same hour 9 inches ; what was the height of the tower ? LUMBER 687. Doyle's Rule for finding the number of square feet of boards a round log will yield : For logs 16 feet in length, Subtract Jf from the diameter in inches ; the square of the remainder will be the num- ber of square feet of inch boards the log will yield to each 16 feet. l. How much square-edged inch lumber can be cut from a log 24 inches in diameter and 12 ft. long. Solution.— 24-4 = 20, 20 2 = 400 sq. ft.; 12 ft. = |f = f of 16 ft. ' 400 x | = 300 sq. feet., Ant. Note. — This rule is not accurate for perfectly straight logs, but gives a sufficiently just approximation for the average, and is much used by lumbermen on account of its simplicity. lAumber. 277 2. How many square feet of boards will a log yield which is 36 iuches in diameter and 18 feet long? 3. How many sq. feet of boards can be cut from a log 24 feet long and 18 in. diameter ? 4. How many from a log 18 ft. long and 12 ft. diameter ? 688. To find the number of inch boards which a given thick- ness of log will yield. Eule. — Divide the thickness of the log, less \ inch, by 1{ inch. 5. How many boards may be cut from a log 17{ in. thick ? Solution.— 17£ in — \ in. = 17f in. 17f-t*l£ = 14 boards, Ans. 6. How many boards may be made from a log 16^ in. thick? 7. How many square-edged boards of equal width can be made from a log 18 ft. long and 1G inches in diameter, allowing J inch for saw cut, and what would be the board measure of the whole ? 689. To find the cubic feet in round timber. Eule. — Square { the mean girt in inches, multiply it by the length in feet, and divide the product by Note. — This rule only approximates the exact quantity, something being allowed for crooks and waste. 8. The mean girt of a log is 36 in., its length 40 ft.; what are its contents in cubic feet ? 9. How many cu. ft. of timber in a log 26 ft. long, and whose mean girt is 48 inches ? Note. — The size of square timber that a log will yield may be found by multiplying the diameter of the smaller end by .707. 10. The diameter of the smaller end of a log is 18 inches ; what is the width of the square timber that may be sawed from it ? TJESTIONS FOR REVIEW. 690. l. Add seven hundred thousand two hundred sixty, twelve million twelve, fifty-four thousand four hundred, six million two thousand twenty-seven. 2. From the above sum subtract three million sixty-five thousand three, minus six hundred thirty-eight thousand four hundred nineteen. 3. Add eighty-four million fifteen, sixty-seven thousand sixty-eight, five million ten thousand seventeen, three hun- dred thousand twenty, three million eight thousand seventy- five, nine hundred million twenty-seven. 4. (8143 + 24429) -^-34 x 12 = what? 5. A lady went shopping with $15.50 in her purse ; she paid 28 cents for needles, $2.25 for gloves, $5.75 for a dress, and $2.25 for ribbon ; how much money had she left? 6. If the divisor is 19, the quotient 37, and the remainder 11, what is the dividend ? 7. A> person owning f of a mine sold f of his interest for $1710 ; what was the whole mine worth ? 8. A market woman having eggs for sale, counted her stock and found that T \ of them made 147 ; how many had she ? 9. In a certain battle f of the forces were lost, and there were 9800 men left ; how many were there at first ? 10. If | of f of a ship is worth $9370, what is the whole worth ? 11. What is the quotient of 65 bu. 1 pk. 3 qt., divided by 12? 12. How many bushels will a box 8 ft. long, 4 ft. wide, and 3 ft. high contain ? Test Questions for Review. 279 13. One factor of a number is 11, the other 3708311605 ; what is the number ? 14. If the quotient is 610, the remainder 17, and the dividend 45767, what is the divisor ? * 15. Find the g. c. d. of 192, 744, and 1044. 16. The sum of two numbers is 143J, their difference 17J ; what are the numbers ? 17. Find the sum, difference, product, and quotient of -J and -|. 18. What number multiplied by \ of itself will produce 12£? 19. A man paid $275 for a horse, which cost | as much as his carriage ; what did he pay for the carriage ? 20. At $7f a barrel, how many barrels of flour must be given for 530 barrels of potatoes worth %Z\ a barrel ? 21. Bought a sleigh for $75, which was f of 3 times the price of the harness; what was the price of the harness? 22. A man paid $40 cash for a cow and sold her at a credit of 8 months for $45; how much did he gain, reckoning interest at 6%? 23. How many planks 18 ft. long and 15 inches wide, will be needed to floor a barn 63£ ft. long and 33£ wide ? 24. A man's salary this year is $600, which is J more than it was last year; what was it last year ? 25. If a pipe of 5 inches diameter will discharge a cistern in 12 hours, in what time will a 3-inch pipe discharge it ? 26. A broken tree rested on the stump 20 ft. from the ground, and its top touched the ground 50 ft. from the stump ; how high was the tree ? •27. What is the length of a diagonal drawn on the floor of a room 30 ft. long and 24 ft. wide ? 28. A man sold his horse for $100 and gained 25%; what per cent would he have gained if he had sold at $120 ? 29. What cost six $500 U. S. 6% currency bonds, at 22£% premium ? 280 Test Questions for Heview. 30. Three men hired a pasture for $150 ; A pastured 4 cows 12 weeks, B 6 cows 10 weeks, and 8 cows 15 weeks ; how much should each pay ? 31. In a school of 280 pupils, 12 were absent ; what was the per cent of attendance ? 32. A market woman bought 150 oranges at the rate of 5 for 2 cts., and sold % of them at the rate of 3 for 1 ct., and the remainder at the rate of 2 for 1 ct. ; did she gain or lose, and how much ? 33. If 1^- pounds of beef and 1-^- pounds of flour are allowed for a ration, how much will 560 rations cost if the price of beef is llf cts. and of flour 3J cts. per pound ? 34. How many hektars of land can a man buy for $946, if he pays at the rate of $86 for every 7 hektars ? 35. When brooms are sold at $3 £ per doz., what will be the cost of 16| gross sold at 5% discount on bills over $100 ? 36. If the interest of $1800 for 12 mo. is $108, what will be the interest of the same sum for 8 mo. ? 37. If a tree 50 ft. high casts a shadow 60 ft. long, how long will be the shadow of a tree 80 ft. high ? 38. A number diminished by J of itself is 1140 ; what is the number ? 39. What is the sum, difference, product, and quotient of 263|, and 175f ? 40. A retail dealer's profits this year are $8350, which is ^ less than last year ; what were they last year ? 41. The wholesale price of Grammars is 98 cents apiece ; but for cash they are J less ; what is the cash price ? 42. A merchant fails for $12575, and his assets are $7500. What per cent of his debts can he pay ? 43. What is the value of a house which brings $11,500 when sold at a loss of 7£ per cent. ? 44. If on the day of the battle of Lexington 1 cent had been placed at compound interest at 6%, what would have been the amount on the 19th of April, 1884 ? Test Questions for Review. 281 45. How much do I gain or lose if I obtain at a bank $1000 for 1 year at 6% discount, and then put it at interest for the same time and rate ? 46. The average quantity of wheat required to make a barrel of flour is 4^ bushels ; the cost of conversion is* 56 cts. a barrel. If wheat in Chicago is 98J cts. a bushel, and expense of trans- portation 15 cts. a bu., what would be the profit to a New York miller if 8500 bu. were sent from Chicago, and sold, when converted into flour, for $8 \ a barrel ? 47. How many bushels of grain are in a conical pile 5 ft. high and 26 ft. in circumference ? 48. How many bushels of wheat can be placed in a car 20 ft. long, 8 ft. wide, and 7 ft. high ? 49. How many such cars would be required to transport 8700 bushels ? 50. Two city lots are sold at $2500 each. How much is made or lost if one is sold at a profit of 15 per cent and the other at a loss of 15 per cent ? 51. What is the exact interest on a note of $1175 from September 12th to December 24 ? 52. At a recent examination a student received 83 per cent in History, 94 in Algebra, and 87 in Philosophy ; what was his average per cent ? 53. A man having 4 tracts of land containing respectively 175 acres, 210 acres, 318 acres, and 268 acres, divided it into 4 farms ; what was the average number of acres in each ? 54. The population of New York and Philadelphia together in 1880 was 2053469, the difference was 359129 ; what was the population of each city ? 55. How many centars in a piece of land 145 meters long, and 23.2 meters wide ? 56. How many square feet of glass in 8 windows of 12 panes each, size 10 in. by 14 ? 57. If a staff 3 ft. 8 in. long cast a shadow 2 ft. 6 in., what is the height of a steeple that casts a shadow of 248 ft. at the same hour? 282 Test Questions for Review. 58. What are the proceeds of a note for $750, discounted at a bank for 30 days at 6 per cent ? 59. A R. R. Co. declared a scrip dividend of 6%; to how many shares was a stockholder entitled, who held 50 shares of the original stock ? 60. Sold at wholesale a bill of merchandise at 25% discount, and h% off for cash ; what was the whole discount ? 61. What is the length of a rope extending from the top of a stake 13 ft. high to the top of a pole 40 ft. high, standing 35 ft. from the stake ? 62. A merchant increased his capital the first year by \ of itself, the second year by -f , the third year he lost -f of all he had, and had $15000 remaining ; what was his capital at first? 63. What per cent of an acre is 1 sq. yard ? 64. What part of 8 square feet is 2 feet square ? 65. How many cu. meters in a wall 24 meters long, 8 -fa m. high, and 52 cm. thick ? 66. What would be the cost of building this wall is $4.25 per cu. meter ? 67. If a cistern 19J ft. long, 10J ft. wide, and 12 ft. deep, hold 546 barrels, how many barrels will a cistern hold that is 18 ft. long, 9 ft. wide, and 15 ft. deep? 68. If $500 is deposited for a child at birth, at 1% compound interest payable semi-annually, what will it amount to when the child is 21 years old ? 69. The following payments have been made on a note of $10000 given March 1st: April 3d, $200; April 25th, $10; May 20th, $3000; July 1st, $400; December 15th, $4000. How much will settle the note January 1st ? 70. What must be the inside diameter of a globe that will contain 5 gallons of water ? 71. If a measure 60 centimeters deep holds a hektoliter, what is the depth of a similar measure holding a centiliter? 72. A man owes $2400, \ of which is now due, \ of it in 3 months, \ of it in 4 months, and the remainder in 6 months; what is the equated time of payment ? Test Questions for Review. 283 73. What is the g. c. d. of 529, 782, and 1127 ? 74. For what amount must a 60-day note be written to yield $250, when discounted at a bank ? 75. If a ball 2 inches in diameter weighs 4 pounds, what is the weight of a ball 6 inches in diameter ? 76. A piece of cloth of 14 yd. sold for $61.25, which was a gain of 25% ; what was the cost per yard ? 77. What is the g. c. d. of 1177, 1819, 2782, and 4708? 78. A gentleman has a note due at bank on which he received $575 for 3 mo. at 4% discount ; he goes to another bank and obtains the money to take up the note, for which he pays 6% for 6 mo. ; what was the face of the last named note ? 79. What are the contents of a sphere, diameter 60 inches ? 80. How many hektars in a piece of land -| mile square ? 81. How many hektoliters in a box, length 2.25 m., width 1.75 m., depth 1 meter ? 82. What annuity at 6% compound interest will amount to $10000 in 20 years? 83. What must be the diameter of a cylindrical cup 6 in. high, to hold a gallon ? 84. If a stock is bought at 109J and an annual dividend of 7% received, what per cent is*that on the investment ? 85. A draft on New Orleans bought at \% premium for $12000, was sent to an agent to pay for cotton purchased at 1\% commission ; what was the value of the cotton ? 86. Find the amount of duty on the following: 8 casks raisins, at 11 cts. a lb., gross weight 888 lb., tare 12 lb. per cask, duty 25$ ad valorem ; 12 boxes sugar, 400 lb. each, at 7 cts. per lb., tare 10%, duty 24% ad valorem ; 60 hhd. molasses, at 54 cts. per gal., leakage 2%, duty 20$. 87. Mr. A. deposits $20 twice each year, 1st of Jan. and July, in a savings bank which pays 5% per annum, adding the accrued interest at the end of each 6 months; what sum will stand to his credit in the bank on the day after he makes his sixth deposit ? 284 Test Questions for Review. 88. If it cost $312 to enclose a field 216 rods long and 24 rods wide, what will it cost to enclose a square field of equal area with the same kind of fence ? 89. Three notes bearing interest are dated respectively July 3, 1883, Oct. 9, 1883, and Feb. 6, 1884 ; if a single note were substituted for the three, what should be its date ? 90. Ralston & Baxter received a consignment of 8500 bu. wheat from Jones & Co., Milwaukee. Their account sales is as follows: Oct. 20, 1883, to C. & Co. 2500 bu., at $1.12 on 30 d.; Oct. 22, to D. & Co. 2500 bu., at $1.11 J on 10 d. ; Nov. 1, 3000 bu. to J. & Co., at $1.10 on 60 d.; Nov. 12, 500 bu. to R, & Co., at $1.15 on 30 d. Charges Oct. 15: Freight on 8500 bu., at.l2|; weighing, $42.50; towing, $14; demurrage, $10 ; commission, 2 \%. What is the equated time for the pay- ment of the net proceeds, the commission being due at average due date of sales ? 91. What is the present worth of a reversionary lease of $250, which begins in 12 years, and continues 25 years at 5%, com- pound interest ? 92. A man wishes to inclose a garden 56J feet long and 40^ ft. wide, with an iron fence the sections of which shall be of equal length ; what ie the length of the longest sections that can be used ? 93. What number multiplied by \ of itself equals 32 ? 94. What number multiplied by f of itself equals 54 ? 95. What number is that which if doubled and the product divided by 3, the quotient squared, that square increased by \ of itself, the result will be \ of the square of 12 ? 96. What is the quotient, if the cube of 75 is divided by \ of 1000? 97. What is the profit of buying peaches at 60 cents a hundred, if 10% of them decay, and the remainder sell at 2 cents apiece ? 98. At 40 cents per centar, what would it cost to plaster a hall 76 ft. long, 54 ft. wide, and 18 ft. high, deducting 10% for windows and woodwork ? Test Questions for Review. 285 99. How many bushels of wheat equal 63 hektoliters? 100. What is 75$ of the difference between the square root of 256 and the second power of the same number ? 101. A field containing 6 A. 12 sq. r. is 3 times as long as it is wide ; what are its length and breadth ? 102. What is the smallest sum of money for which you can buy oxen at $85, or cows at $35 each ? 103. What is the distance from a comer of a cubical block to the opposite diagonal corner, the sides being 9 sq. feet ? 104. A field \ as wide as it is long contains 8 J A. 32 sq. r.; what length of fence is required to go around it ? 105. A man paid for tobacco an average of $25 a year from the age of 18 until he was 60, when he died and left $1500 for his heirs ; if he had deposited in the savings bank each year the money spent for tobacco, how much might he have left at b% semi-annual compound interest? 106. The diameter of a circle is 10 inches ; what is the side of the square that may be inscribed in it ? Note. — The diameter of a circle forms the hypothenuse of the two right-angled triangles which equal the square inscribed in it. 107. What is the side of a square equal in area to a circle 150 meters in diameter? 108. In what time will $1265 at 6%, yield $85.25 ? 109. If the interest of $3865 for 8 mo. is $180.03, what would be the principal on which $360.85 is paid for 2 yr. 4 mo. 15 days? no. Find the difference between the square root of the least common multiple of 6, 12, 18, 36, 48, and the square of their greatest common divisor. in. In 15 hektars how many square rods? 112. An agent sold flour at $7.92 a barrel, at a loss of 4%; at what price should it be sold to gain 8% ? 113. In 126589 meters how many kilometers ? 114. How many miles, rods, etc., in the above? 115. If flour sold at $12 a barrel gains 15$, what would be the gain % if sold at $11.25 ? m If * s> j ( _ PPENDIX. (1 g ^15r^ a «* DRILL EXERCISES. 691. The following and similar exercises should be practised till the combinations can be read without hesitation : (1.) (2- ) (3.) M (5.) 6. 59 75 643 74 725 87 8462 34 7425 34, a. 7. 27 82 350 62 842 73 2351 23 6534 23, b. 8. 46 71 128 49 523 27 3162 34 5623 14, c. 9. 28 15 352 73 435 54 4273 43 4731 25, d. 10. 34 63 243 25 327 43 5384 52 5842 36, e. 11. 29 50 455 63 276 32 6275 63 4953 27, f. 12. 68 71 729 31 586 34 3284 32 2586 54, &• 13. 97 53 426 76 235 20 1635 34 4234 62, h. 14. 82 43 623 25 463 52 2586 89 1736 44, i. 15. 64 25 321 35 958 76 7434 26 5398 29, J- 16. 18 12 238 17 386 29 5869 73 1234 56, k. 17. 19 50 125 51 315 46 3276 42 7891 01, 1. 18. 62 25 436 25 434 57 1635 38 1234 16, m. 19. 64 37 536 63 372 46 5913 84 6843 75, n. 20. 53 63 257 47 657 32 6284 35 7616 24, 0. P. a. R. s. Note. — The numbers in the above examples should be added perpen. dicularly for the first five examples, then horizontally through the 20th. They may be taken in columns of two or more figures at a time. Subteaction. — 21, 22. In col. marked "P" (at bottom) subtract 7th from 6th ; 9th from 8th. 23-28. In " T * take b from a ; d from c ; f from e ; g from h ; i from j ; k from 1. Drill Exercises, 287 29-34. In "S" take b from a; c from d; e from f; h from g ; i from j ; 1 from k. Multiplication. — 35-50. Multiply the numbers in " T " by those in "P," begin "a." Division". — 51-65. Divide each of the above products by the numbers in i ■ Q." Note. — These exercises may be continued and extended at pleasure. Drill in Percentage. 692. l. Selling price $95, cost $84 ; required the gain %. 2. Profit $30, cost $128.50 ; required the gain %. 3. Loss 12%, cost $125.25 ; required selling price. 4. Selling price $225.50, loss 18% ; required cost. 5. Cost $120, selling price $160 ; required gain %* 6. Profit $350, cost $800 ; required gain %. 7. Loss $25.50, cost $175 ; required loss %. 8. Selling price $1875, loss 15% ; required cost. 9. Profit 6£%, cost $1200 ; required selling price. 10. Principal $240, int. $26.40, rate 8\%\ required time. 11. Principal $450.75, rate 9%, time 4 yr. 7 mo. 15 d.; amount? 12. Principal $425.45, rate 6%, time 3 yr. 6 mo. ; required compound interest. 13. Insured $6700, rate \%, time 1 yr.; required the premium. 14. Principal $800, interest $32, time 8 mo.; required rate. 15. Tax $12500, property $2400000; required rate. 16. Principal $2500, time 1 yr. 4 mo., rate 7-&%; amount? 17. Difference discount and int. of $900, 3 yr. 4 mo. 20 d.- 6$. 18. Bank discount $168.13, at 6% ; 8 yr. 5 mo. 19. Bank discount $900, at 8% ; 9 months.. 20. Amount £35 4s. 6d., 2 yr. 8 mo., at 6$; 21. Net proceeds 320 A., at $22.50; commission l Q%. 22. Insurance $10000, at \% ; policy $1. 288 Appendix. 23. Cost $400 for 9 cwt. 52 lb. coffee, gain 1%% ; required selling price. 24. Interest $685.50, at 10%, time 3 yr. ; required principal. 25. Paid $6180, brokerage 3% ; required amt. of draft. 26. Discount $1600 for 60 d., 6%; required the avails. 27. Amt. $860 from Jan. 25, 1882 to Jan. 5, 1883, at 9%. 28. Amount of $124.17 for 11 mo. 29 d., at 9%. 29. Interest of $3000 for 6 mo. 15 d., at 7&%. 30. Prin. $860.56, int. $149.63, time 2 yr. 8 mo. 3 d. ; rate ? 31. Avails of note, $8000, at 6%, 6 mo.; required its face. 32. Principal $475, at 6%, amount $57095 ; rate. 33. Present worth of $2500, due in 9 mo., 6%. 34. Cost of bill $2500, discount %\% ', required the face. 35. Principal $750, amount $960.85 at 7^% ; time. 36. Gain $384, at 12-|% J required the cost. 37. Interest of $1200 for 2 yr. 3 mo. $168.75 ; required the rate. 38. Prin. $5000, at 7 T 3 o%, from Jan. 1 to March 1, 1884 ; required the accurate interest. 39. Income is $800 from IT. S. 5's, at 104 ; required the investment. 40. Prin. $860, at 6%, amount $900 from Jan. 1 to what day? 41. Bought bill of goods amounting to $6845, and less charges $65, sold same at 12-§-% advance, took note for 60 d. and with proceeds from 6% discount, bought bill on London at 109J ; required the face of the bill. 42. Goods marked 25% advance on cost, are sold at 15% below the marked price ; what per cent is the gain ? 43. If you hire money at a bank, at 6% for 4 mo., to buy a horse at $180, what does the horse really cost you ? 44. What rate of interest does a man pay, who gets his notes discounted at a bank for 90 days at 6% ? 45. If a bank borrows $100000 at 6 per cent and discounts a 30-day paper for the same amount at 6 per cent, what are the profits ? Drill Exercises. 289 46. The true discount of 81215, due in 10 mo. 20 d., is 890 ; what is the rate ? 47. Which is better, and how much, 6% bonds at 90, or 8% bonds at 130, both due at the same time ? Metric Drill. 693. l. A man sold J of a farm of 170 hektars, which cost 500055 francs, at 3500 fr. per Ha., T ^ of it at 2800 fr. per Ha,, and the remainder at cost; what was the gain or loss? 2. If with 34 kilograms of wool, 25 meters of flannel 60 centims wide can be made, what length of similar flannel, 80 centims wide, can be made with 108 Kg. of w T ool ? 3. How many fields containing 2 Ha. 47 ars each can be made on a farm of 313 Ha, and 69 ars? 4. How many hektoliters of wheat will a bin contain which is 7 meters square and 2.7 meters deep ? What will it cost at $2 per bushel ? 5. Express the rate per hour of a mail train in terms of that of a mail cart, the former traveling 4J myriameters an hour, the latter 135 kilometers in 10 hours ? 6. If 26 men working 10 hr. a day can dig a trench 50 meters long, 4 meters 25 centims broad, and 6£ meters deep in 12 d., how many men will it require to dig a similar trench 125 meters long, 3 meters 6 cm. broad, and 9 m. 35 cm. deep in 18 d., if they work 12 hr. a day? 7. It requires 14375 sq. bricks to pave a path 184 meters long and 4 m. 5 centims broad ; find the side of each brick. 8. What is the radius of a circular bed whose circumference is 3 meters 50 centimeters ? 9. If 13 square meters 20 square decims of canvas are required to cover a cylindrical column, the radius of whose base is 28 centims ; what is the height of the column ? 10. If a pipe 3 centims in diameter will empty a cistern in 8 min., what is the diameter of a pipe that will empty it in 18 min.? li. How many cubic decimeters in a globe 6 decimeters in diameter ? 290 Appendix. GREATEST COMMON DIVISOR OF FRAC- TIONS. 694. The Greatest Common Divisor of two or more fractions is the greatest number that will divide each of them and give an integer for the quotient. 695. To find the Greatest Common Divisor of two or more fractions. I. Find the g. c. d. of -f, if, and 2f . Analysis.— Reducing if to lowest terms, 2f operation. to an improper fraction, and all to the least ^-| — -f^, 2-f- = -% -. common denominator ; the fractions are |f, f f, led = 45. and Y/. The 242 273 304 334 365 30 December. . 31 62 M 121 151 182 212 243 274 304 335 365 l. How many days from May 13 to Aug. 23 ? Explanation.— Find "May" in the column of months at the left; and on the same line under " Aug." find 92, which is the number of days from any day in May to the same dr-f in Aug. But Aug. 23 is 10 days more than Aug. 13, and 92 + 10 = 102 d., Ana. 296 Appendix. Note.— If the required date be earlier in the month than the date from which the time is counted, subtract the difference from the tabular number. 2. How many days from May 13 to Aug. 1 ? Explanation.— From May to Aug. is 92 d., but to Aug. 1 is 12 d. less than to Aug. 13 ; and 92—12 = 80 d., Ans. Note. — If the given date is in a leap year it will be necessary to add cr subtract one more day when Feb. intervenes 708. If it is required to find a day which is a given number of days after a certain date, look in the table opposite the mo. having the given date, and find the number of days next larger, subtract the given days and count back for the required date. 3. Find the date that is 125 days after July 4th. Explanation.— Opposite July, the next larger number than 125, is 153 in Dec; 153-125 = 28, and 31-28 = 3. Hence, Nov. G is tha date. 709. To find the time for which a note must be drawn, so that it will not fall due on Sunday or a Legal Holiday. Rule. — Find the number of days by the Table, and dividing them by 7, the quotient will be the number of weeks and days. Then count the odd days from the day of the week on which the note is dated. 4. A note was drawn on Friday the 1st of Feb., to run 3 months ; what day of the week will it fall due ? Solution. — Three months from Feb. 1st brings May 1st, which by Table is 89 d. in a common year, or 90 d. leap year. 89-5-7 = 12 and 5 d. over. Friday + 5 d. gives Wednesday, or in leap year, Thursday. 5. If a note is dated Tuesday, Apr. 1st, to run 60 days, what day of the week will it fall due ? 6. The birthday of Shakspeare was April 23, 1564; how many years, months, and days from that to the present time ? 7. Suppose a note is made on Wednesday, the 13th of Feb., 1884, payable in 3 months from date; what day would it be due? Life Insurance Tables. 297 LIFE INSURANCE TABLES. 710. The Expectation of Life is the probable number of years a person may live after he has reached a specified age. It is found by dividing the number of those who survive that age by the number of those who attain it. American Experience Table of Mortality. Adopted by the State of N. Y. in estimating life endowments. Com- Number Deaths Com- Number Deaths Com- Number Deaths pleted surviving at in each pleted surviving at in each pleted surviving at in each Age. each Age. Year. Age. each Age. Year. Age. each Age. Year. 10 100.000 749 40 78,106 765 70 38,569 2,391 11 99,251 745 41 77,341 774 71 36,178 2,448 12 98,505 743 42 76,567 785 72 33,730 2,487 13 97,762 740 43 75,782 797 73 31,243 2,505 14 97,022 737 44 74,985 812 74 28,738 2,501 15 96,285 735 45 74,173 828 75 26,237 2,476 16 95,550 732 46 73,345 848 76 23,761 2,431 17 ' 94,818 729 47 72,497 870 77 21,330 2,369 18 94,089 727 48 71,627 896 78 18.961 2,291 19 93,362 725 | 49 70,731 927 79 16,670 2,196 20 92,637 723 50 69,804 962 80 14,474 2.091 21 91,914 722 51 68,842 1001 81 12,383 1,964 22 91,192 721 52 67,841 1,044 82 10,419 1,816 23 90,471 720 53 66,797 1,091 83 8,608 1,648 24 89,751 719 54 65,706 1,143 84 6,955 1,470 25 89,032 718 55 64,563 1,199 85 5,485 1,202 26 88,314 718 56 63,364 1,260 86 4,193 1,114 27 87,596 718 57 62,104 1,325 87 3,079 933 28 86,878 718 58 60,779 1,394 88 2,146 744 29 86,160 719 59 59,385 1,468 89 1,402 555 30 85,441 720 60 57,917 1,546 90 847 385 31 84,721 721 61 56,371 1,628 91 462 246 32 84,000 723 i 62 54,743 1,713 92 216 137 33 83,277 726 63 53,030 1,800 93 79 58 34 82,551 729 ; 64 51,230 1,889 94 21 18 35 81,822 732 : 65 49,341 1,980 95 3 3 36 81090 737 66 47,361 2,070 37 80,353 742 67 45,291 2,158 38 79,611 749 68 43,1&3 2,243 39 78,862 756 69 40,890 2,321 Notes. — 1. Wigglesicorth's tables, prepared from data in this country, have been adopted by Massachusetts in estimating life estates. 298 Appendix. 2. Among the prominent English tables of mortality are the Carlisle tables by Milne, and the Northampton tables by Dr. Price. The former are generally used in England. 711. According to the Carlisle tables, of 10000 persons born together, 5528 reach 32, and 2771 reach G7 years of age. The expectation of life to the age of 67 therefore, of a person now 32 is §||-|- = \ nearly, or 1 chance in 2. Illustration. — What is the net premium to insure $1 during the year succeeding the age of 60, the present age being 40 ? By Table, the number living at 60 is, ... . 57917 61 is, ... . 56371 The number dying during the year is, . 1546 Pres. w. of $1, due in 20 y. at 4=% (Art. 306, N. 3), . $.45638 Present worth of $1546 = $705,563 By Table, the number surviving at 40 is 78106. Then, 705.563-^-78106 = .00903, net premium. Explanation. — The Table above shows that of 78106 persons now living at the age of 40, 1546 will die during the year succeeding 60. The present worth at 4 % of $1546 payable 20 years hence is $705,563, which divided among 78106 persons now living, gives the premium which would secure an insurance of $1 to each of them in case of death during the given year. LIFE ESTATES AND ANNUITIES. 712. The rule prescribed in New York State for estimating the value of life estates is as follows : 84th Rule of the Supreme Court to ascertain the gross sum in payment of life estates. Whenever a party, as a tenant for life, or by the courtesy, or in dower, is entitled to the annual interest or income of any sum paid into court, and invested in permanent securities, such party shall be charged with the expense of investing such sum, and of receiving and paying over the interest or income thereof ; but if such party is willing and consents to accept a gross sum in lieu of such annual interest or income for life, the same shall be estimated according to the then value of an annuity at six per cent on the principal sum, during the probable life of such person according to the Portsmouth, or Life Estates and Annuities. 299 Northampton Annuity Table. 713. Showing the value of an annuity of $1 at 6%. Age. No. of years purchase the Annuity is worth. Age. No. of years purchase the Annuity is worth. Age. No. of years purchase the Annuity is worth. | ! Age. Xo. of years purchase the Annuity is worth. 1 10.107 25 12.063 49 9.563 73 4.781 2 11.724 26 11.992 50 9.417 74 4.565 3 12.348 27 11.917 51 9.273 75 4.354 4 12.769 28 11.841 52 9. 129 76 4.154 5 12.962 29 11.763 53 9.980 77 3.952 6 13.156 30 11.682 54 8.827 78 3.742 7 13.275 31 11.598 55 8.670 79 3.C14 8 13.337 32 11.512 56 8.509 80 3.281 9 13.335 33 11.423 57 8.343 81 3.156 10 13.285 34 11.331 58 8.173 82 2.926 11 13.212 35 11.236 59 7.999. 83 2.713 12 13.130 36 11.137 60 7.820 84 2.551 13 13.044 37 11.035 61 7.637 85 2.402 14 12.953 38 10.929 62 7.449 86 2.266 15 12.857 39 10.819 63 7.253 87 2.138 16 12.755 40 10.705 64 7.052 88 2.031 17 12.655 41 10.589 65 6.841 89 1.882 18 12.562 42 10.473 66 6.625 90 1.689 19 12.477 43 10.356 67 6.405 91 1.422 20 12.398 44 10.235 68 6.179 92 1.136 21 12.329 45 10.110 69 5.949 93 0.806 22 12.265 46 9.090 70 5.716 94 0.518 23 12.200 47 9.846 71 5.479 24 12.132 48 9.707 j 72 5.241 Rule. — Calculate the interest at 6%, for one year, upon the sum to the income of which the person is entitled. Multiply this int. by the number of years purchase set opposite the person's age in the Table, and the product is the gross value of the life estate of such person in said sum. l. If a widow 42 years of age is entitled to dower in real estate worth $10500, what is the gross present value of her right of dower ? 300 Appendix. Solution.— J of $10500 = $3500; int. 1 yr. at 6% =$210.00. The number of years' purchase which an annuity of $1 is worth at the age of 42 is 10.473, and $210 x 10.473 = $2199.33, Ans. 2. If a man 60 years of age is tenant by the courtesy in the whole of an estate of $8000, what is the gross value of his life estate at present ? Note. — If the annuities are payable semi-annually, one-fifth of the value of a year's purchase should be added to those values. 3. A lady whose estate was valued at $500000 died, leaving her husband, then 45 years old, a life interest in the whole estate ; what was the gross value of his interest at her death ? 4. A man left an estate worth $15000, of which his widow, aged 54, was to receive during her life the interest on J, payable semi-annually ; what was the gross value of her portion in the premises. 5. A gentleman purchased a life annuity of $1000, belonging to a person 20 years old; what should it have cost him? BUSINESS INFORMATION AND FORMS.* R ECEI PTS. 714. A Receipt is a written acknowledgment that a debt is paid. Note. — A man is not bound by laic to give a receipt ; but by courtesy and custom they are always given when desired. 715. A full receipt states the amount received, the date, place, and kind of payment, by whom and in whose behalf the payment was made, by whom and in whose behalf received, and to what debt or purpose it is to be applied. When the receipt is signed by the person to whom the pay- ment was due, his signature is enough. But when the business is done through an agent, he writes his principal's name, and his own name below it, with "per" or "by" as a prefix to signify the agency. * For forms of Bills, Notes, Drafts--, etc., see pp. 79, 118, 133-136. Business Information and Forms. 301 Notes. — 1. Partial payments should be endorsed on the note or bond, and the party making the payment should also take a receipt for it. 8. When a receipt is given by a person who makes his mark instead of writing his name, it should be witnessed. Receipt in Full. S225 T 7 / W . Boston, Jan. 31, 1884. Received from H J. Smith, Two Hundred Twenty-five ffy Dollars, in full of all demands, to date. Osgood & Co., per W. Simmons. For Payment on Account. Philadelphia, Feb. 4, 1884. Received from Wm. Rowland, One Hundred Forty-five fyy Dollars, on account. For a Note. New York, March 1, 1884. Received from Everett Graw & Co., their note of this date, at three months, in our favor, for Eighteen Hundred Tiventy-seven f-fo Dollars, which, when paid, will be in full for account rendered to 28th inst. $1827^° . J- C. Byrnes & Co. Receipt for Interest. New York, Jan. 15, 1884. Received of Ginn, Heath & Co., Two Hundred Forty -six Dollars, in full for six months interest due this day on their Bond to me, bearing date Oct. 18, 1882, for Eight Thousand Two Hundred Dollars. $246. L- E. Clark. Due Bill for Goods. New York, Feb. 6, 1884. Due to Henry Jones, on demand, Twenty-five -ffo Dollars, to be paid in goods from my store. T®Kjr~ K. H. Macy. 302 Appendix. Order for Goods. Brooklyn, May 1, 1884. Messrs. Journeay & Burnham, Gentlemen :— Please pay to John Wood, or order, Sixty- three Dollars in goods from your store, and charge the same to our account. Burtis & Co. Installment Receipt. CD O CD $2000. 400 Share s. Brooklyn (£. E. ft. QTompanrj. Received, Brooklyn, Jan. £9, 1S&4, of A. J. Pouch, Two Thousand (Xollai^s, being Tvjenty-fLve (Dollars per Share, and the Ihird Installment on Four Hundred Shares of the Capital Stock of the Brooklyn Elevated Railroad Company; for which said Shares a full Certificate will be given, upon payment of all Install- ments due thereon, and the surrender of this Certificate. C D , A B , Secretary, (president. Shipping Receipt. Albany, Jfay 9, '84-. JHbany,Jtfay 9, '84- \ Received from Wm. Wfills $ Co., in ,„- . ., , , ■ good order, on board the C. Vibbard Shipped on board ' bound for J\[ew York, the packages Ijound for_ . marked and entered as below : ( ) Mar-hs (Packages \ J & 4 doz. boxes Oswego Starch. JAarks J M> °- 6 barrels Apples. RoU. B. Smith , fig't. Business Information, and Forms. 303 Bank D raft. No. 2350. Auburn ook Keeper. General Form of Agreement. This Agreement made the day of between A— B — of City and State , of the first part, and C — D — of City and State of the second part, WITNESSETH: — That the said G D , party of the second part, in consideration of the sum hereinafter named, doth covenant and agree to and with the said A B of the first part, that (insert agreement). And the said party of the first part doth covenant and agree to pay unto the said C D (insert agreement of A B .) And for the true and faithful performance of all agreements above mentioned, the parties to these presents bind themselves each unto the other, in the sum of dollars as fixed damages to be paid by the failing party. In witness whereof we have hereunto set our hands and seals the day and year first above written. Signed, sealed, and delivered ) A B . (Seal. in the presence of \ C — D . (Seal.) 304 ^Appendix. 716. Letters of Credit can be procured from Foreign Exchange Bankers, by depositing the amount in money or m securities. A small commission is charged besides the regular rate of exchange. (Art. 451.) Circular Letter of Credit. No. B S6581. New yoRK Feb ^ mL Gentlemen : — We request that you will have the goodness to furnish Mr. Henry R. Rusted, the bearer, whose signature is at foot, with any funds he may require to the extent of £500 (say Five Hundred Pounds Sterling), against his drafts upon Messrs. Brown, Shipley & Co., London; each draft must bear the number (No. » 36581) of this letter, and ive engage that the same shall meet due honor. Whatever sums Mr. Husted may take up, you will please endorse on the back of this Circular letter, which is to continue in force till Feb. 22, 1885, from the present date, Feb. 22, 188 % We are respectfully, gentlemen, Your obedient humble servants, Brown Brothers & Co. The Signature of Henry R. Husted. To Messieurs the Bankers, Mentioned on the third page of this Letter of Credit. INSTRUMENTS UNDER SEAL. 717. A Contract is a formal bargain made between two or more persons, upon sufficient consideration, to do or not to do some act which shall be lawful. 718. A Deed is a writing or instrument signed, sealed, and delivered. As generally used, it is for the conveyance of property. 719. A Bond is a sealed obligation for the payment of money, and usually has a penalty annexed in case of failure to comply with the conditions annexed. Book Accounts. 305 720. Ground Rents are leases of building lots, the rents of which are considered equal to the int. on the value of the land. Note. — Bonds and Mortgages on real estate, and Ground Rents are regarded with a good degree of favor as investments. 721. A Fee-Simple interest is absolute ownership in an estate. 722. A Ground Rent Deed conveys land with a reservation of a specified sum of money in the nature of rent to be paid at stated times, and may be for life, for a term of years, or in fee. Notes. — 1. Instruments under seal are not barred by the statute of limita- tions like ordinary debts. 2. In ordinary cases where the consideration is expressed, there is no difference between an agreement under seal or otherwise, except that the former can be more easily proved and is therefore to be preferred. BOOK ACCOUNTS. 723. In order to collect a debt on the evidence of a book account, a full copy of the account must be made out, and it must be accompanied with an affidavit, as follows : Form of Affidavit for Goods Sold and Delivered. State of County of Henry Smith of being duly sworn (or affirmed), deposes and says, that James Brown 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 James Brown ; and that he has given credit to the said James Brown for all payments and set-offs to which he is entitled ; and that the balance claimed, accord- ing to the foregoing account, is justly due; and that the said account is correctly stated. Sworn and subscribed this day of , a. d., 1884, before me Charles C. Jones, Commissioner for the State of . 724. Items and dates should be given in the account, as a general charge cannot be sustained by evidence of this kind. The entry must be made in form at the date of purchase for the purpose of charging the debtor, not as a mere memo- randum. 20 306 Appendix. Note. — In order to be admissible as evidence, entries should be made without alteration, erasure, or interlineation, and by a person authorized to attend to that department. The Statute of Limitations of the United States. 725. The time within which suit must be commenced for the collection of a debt, varies in different classes of cases from one to twenty years, and differs in different States.* For accounts m general it begins from the date of the last item or payment, and in every case the time is renewed by every partial payment. States and Terri- tories. Alabama ... Arkansas . . . Arizona California... Colorado — Connecticut Dakota Delaware . . . Dist. of Columbia Florida Georgia Tdabo Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massacbusetts . . . Michigan Minnesota Mississippi 6 < a o o, O 11 if a Yrs. 1 bo "2 Yrs. Yrs. Yrs. 3 6 10 20 3 5 5 10 2 4 4 5 2 4 4 5 6 6 6 3 6 6 17 17 6 6 20 20 3 6 20 20 3 3 12 12 4 5 20 20 4 6 20 2 4 4 5 5 10 10 20 6 10 20 10 5 10 10 20 3 5 5 15 5 15 15 15 3 5 10 10 6 6 20 20 3 3 12 12 6 6 20 20 G 6 10 10 6 6 10 10 3 6 7 7 States and Terri- tories. Missouri Montana. .. Nebraska . . . Nevada New Hampshire New Jersey New Mexico . . . New York North Carolina. Ohio Oregon Pennsylvania . . Rhode Island. . . South Carolina. Tennessee Texas Utah Vermont Virginia Washington .... W. Virginia Wisconsin Wyoming Yrs. 5 B 4 2 O a Yrs. 10 10 5 Yrs. 10 10 5 4 20 16 6 20 10 15 10 20 20 20 10 4 4 8 20 6 10 20 5 Yrs. 20 10 5 5 20 20" 15 20 10 15 10 Notes.— 1. In the States of Kentucky and Virginia a store account may run two years. In W. Va. 3 years. 2. In the case of notes, etc., if the debtor at any time makes a written acknowledgment of indebtedness, the claim is renewed. * Clark's Commercial Law. Stock Clearing Houses. 307 STOCK CLEARING- HOUSES. 726. A Stock Clearing House is an association of dealers, to facilitate the balancing of transactions in Stocks or Bonds. Note. — Stock Clearing Houses are in successful operation in some of the large cities of Europe. An attempt was made to establish one in New York, which was partially successful. The following is a glimpse of the plan proposed : 727. Each member reports to the Clearing House on a blank form, the names of parties with whom he has had dealings, and the balances in his favor or against him, of all transactions. At 12 : 30 the clerks in the Clearing House tabulate all the balances as reported, and notify each member from whom he will receive, or to whom he will deliver the stocks shown by his report. Note. — A settling price is fixed by the Clearing House for each stock, and members are required to receive only as many shares of any stock as they may have bought more than they have sold. The difference between the "settling price" and the buying or selling prices of the original transactions must be paid in cash. The followir ig is the form ol a Report to the Clearing House : To Receive. To Deliver. Balance. U. P. N.Y.C. Name. U. P. N.Y.C. To Receive. To Deliver. 750 500 J. G. Hewitt C. T. Burtis 800 Chas. S 100 .Andr evvs. U. P. 50 400 N. Y. 0. 800 300 Chas. S. Andrews. . J. G. Hewitt 1 I 500 1 i 1000 1 1 C. T. Burtis. TJ. P. 200 N. Y. C 200 1000 100 C. T. Burtis Chas. S. Andrews..! 1 300 | 1 750 1 J. G. Hewitt. 250 U. P. N. Y. C. 200 Explanation. — These three reports show that 2550 shares of TJ. P. Railroad Stock and 900 shares N. Y. Central were bought and sold ; but the transactions are settled through the Clearing House by the delivery of 400 shares of N. Y. C. stock and 250 shares of U. P. stock. Thus, Andrews' balance shows that he is to receive 400 N. Y. C, Burth and Hewitt each report balances of 200 N. Y. C. to deliver. They are notified by the Clearing House to deliver to Andrews. 308 Appeiidkc. 728o Abbreviations used in Stock Quotations. Ad Adjustments. Allts Allotments. Applied to shares giving the privilege of others, at specified prices. As , Assented. U. S. c. 3's, or 4's U. S. currency bonds at 3% or 4% int. B. c Between calls. B. 30 Buyer's option at 30 d. B. 20, flat Buyer's option at 20 d. without interest. Bds., or b Bonds. " C " before price Cash. Certs Certificates. Com Common stock. Cons., or en Consolidated. Conv., or cv Convertible. May be exchanged. Coup. , or c Coupon. Cur., or c Currency. Deb Debentures. D. s. f. 5's Deb. secured by sinking fund, at 5% int. Div Dividend. Ex. d., or e. d Without dividend. Ex. coup Without coupon. Ext Extended. Fd Funded. Gen General. Gtd Guaranteed. L. g Land grants. L., or 1 Lot, the aggregate of several sales. L. s Land Scrip. Inc. 6's Income bonds, at 6% interest. Mort., or m Mortgage. N. 6's New Q% bonds. Pref., or pf Preferred. Pur. m. fd Purchase money funded. Reg., or r Registered. R. e . . Registered and extended. Sep Scrip. S. 30 Seller's option at 30 days. S. F., or s. f Sinking fund. W. n Without notice. 2d M. s. f . 7's '85 Sinking fund bonds secured by 2d mort., payable at 7% in 1885. Con. M, & s. f. 6's Consolidated mort. and sinking fund, at 6%. V| S^— ' ■ * ■■■♦ 1 ISOELL AKEOTJS JP|XAMPLES. 1. What number is that to which if 16 be added, then 25 subtracted from the sum, the difference be multiplied by 21, and the product divided by 28, the quotient will be 63 ? 2. How many gills, pints, and quarts, of each, an equal number, are there in a hogshead ? 3. A company of 175 men have provisions enough to last 6 months ; if 47 of them leave, how long will the same provisions last those that remain ? 4. A farmer had 45 head of cattle, and hay enough to last them 5| months ; if he buys 13 head more, how long will the same hay last the whole ? 5. Six men bought a ship together worth $45268, for which A paid \ of the whole, B \, and the others paid the balance equally ; how much -did each pay ? 6. A manufacturer hired an equal number of men, women, and children, at 75 cts., 62| cts , and 37^ cts. each per day, and the daily wages of the whole amount to $113.75 ; how many of each class did he employ ? 7. A man bought a drove of horses for $17947, and after selling 62 of them, at $83 apiece, the remainder netted him $51 each ; how many did he buy, and for how much apiece must he sell them to make $2510 by the operation ? 8. A merchant bought 868 yards of cloth at $6.50 a yard ; he after- wards sold 253 yards at $5| per yard to one customer, and 368 yards at $8] to another ; how many yards had he left, and what was the net cost to him ? 9. A man bought 148 acres of land, at $23 per acre, and 260 acres at $17 ; he afterwards sold 300 acres at $25 ; how many acres had he left, and what did it stand him in per acre ? 10. A garrison of 450 men has provisions for 5 months ; how many must be discharged, that the same provisions may last 71 months? 11. In a certain county are 105260 topers, who drink 3 glasses of liquor apiece every day, at a cost to them of 8 cents a glass ; how many barrels of flour would this useless expense pay for, per annum, when flour is $8 a barrel ? 310 Miscellaneous Examples. 12. A grocer having bought 1328 pounds of butter at 27* cents a pound, afterwards sold 263 pounds at 28f cents, and 375 pounds at 29| cents ; how much had he left, and what must he get for it in order to gain $215 by the operation ? 13. A drover brought 1463 sheep, and 285 lambs to market, the former costing him $5.15 per head, and the latter $2.17 per head ; having sold 320 sheep and lambs together at $5| a head, he wishes to know at what price per head he must sell the remainder in order to gain 20% on the money invested. 14. A man bought a lot of silver containing tea-spoons, dessert-spoons, and table-spoons, of each an equal number, weighing respectively 5 pwt. 6 gr. ; 13 pwt. 10 gr. ; and 1 oz. 11 pwt. 8 gr. ; the weight of the whole was 6 lb. 8 oz. ; how many spoons were there of each kind? 15. A man bought a drove consisting of cows, calves, and oxen, in equal numbers, for $3693.375 ; for cows he gave $27i apiece, for calves $4^, and for oxen $43f ; how many were there of each kind ? 16. A liberty pole 108 ft. high was broken in such a manner that its top struck the ground 36 ft. from its foot, the other end resting on the top of the part left standing ; how high from the ground was it broken. (Art. 704.) 17. A man pays $1500 per annum interest on various mortgages, at Ifo ; how much money does he hire? 18. What must be the face of a note to cover the discount for 90 d., at 6%, and yield $472.86? 19. A man spent | and £ of his money and $20 besides, when he had $80 left ; how much had he at first ? 20. A barn was 38 ft. wide at the gable ends, and the ridge of the roof was 5 ft. above the eaves ; how many ft. of boards would cover the gable ends ? 21. Sold goods for $2543.50 at a profit of 5%, and took a note at 60 d., which was discounted the same day, at 6% per annum; what was the net profit ? 22. Which is the better investment, U. S. 3's, at 103|, or Bait. & O. 1st 6's 1919, atll4i? 23. Bought Boston H. & E. 1st M. 7's due in 1900, at 114; what is the per cent income on the investment ? 24. What is the weight of an iron cylinder 15 ft. long and 10 in. in diameter, allowing 4 cu. in. to a pound ? 25. A man having a triangular gore of land, one side of which was 256 rods long, and the perpendicular distance from this side to the opposite corner, 72 rods, exchanged it for a square farm of equal area ; what was the side of his farm ? Miscellaneous Examples. 311 26. An importer bought 1565 yards of silk, at 5s. Gd. per yard ; paid £7 12s. for freight, 25 per cent duties, and remitted a bill on London at 9£ per cent premium ; how must he sell it per yard on 6 months, jn order to make 12^ per cent, allowing 7 per cent interest ? 27. A merchant sent his agent in London 425 bales of cotton weighing 356 pounds apiece, which cost him 9| cents a pound ; the agent paid f d. a pound for freight, £43 for cartage, sold it at 8d, a pound, and charged 2h per cent commission. If the merchant sells a bill of exchange for the amount, at 10|% , will he make or lose by the operation. How much ? 23. "What rate-per cent income will be realized from 8% stock bought at 95, if paid at par in 20 yr.? 29. Four notes of $500 each are due in 3, 6, 9, and 12 months respec- tively ; in how many months may they all be paid at one time ? 30. Which is the greater, an income of $500 per annum for 15 years to come, or the reversion in perpetuity of $500 annuity at the end of 15 years, interest at 6 per cent ? 31. Which is the better investment, 7% bonds, or a house which rents for $240 a year, taxes being $30.50, and annual repairs $40 ? 32. What is the average distance between stations on a R. R. that is 149 m. 234 r. 4 yd. 2 ft. long, the number of stations being 18 including one at each end of the road ? 33. How must goods which, cost 60 cents a yard be marked, that the merchant may discount 20% from the price and still make 20% ? 34. How many shares of mining stock at 80 must be sold, that the proceeds invested in Iowa Mid. 1st M. 8's, due in 1900, may yield a profit of $960 if bought at 108 ? 35. A father left an estate valued at $11740 to 3 sons, whose ages were 15, 13, and 11 respectively, to be so divided that if put at interest at 5%, the amount should be equal as the sons came of age ; what sum did he will to each ? 36. Bought $600 worth of books at a discount of 33^% from list prices, and sold them at regular retail price on 6 mo. credit ; what was the per cent profit, if money was worth 6% ? 37. What must I pay to insure a factory valued at $21000 at £ % ; and the machinery valued at $15400 at f % ? 38. Sold a bill of goods amounting to $1875, of which 15% was payable in cash, 25% in 3 mo., 20% in 4 mo., and the balance in 6 months ; how much cash would pay the debt at once, when money is 6*% per annum ? 39. A miller had 400 barrels of flour worth $6£ a barrel, 15% ©f it was destroyed by a freshet ; he sold the remainder at $8.50 a barrel ; how much did he gain or lose ? 40. Which is the more profitable investment, to buy flour at $8.50 a bar- rel on a credit of 6 months, or at $8.25 on 2 mo. when money is worth 6%? 312 Miscellaneous Examples. 41. A cylindrical tank 30 ft. in diameter and 15 ft. deep is filled with oil ; how many gallons does it contain and what is its value at 4$ cents a gallon ? 42. A merchant's retail price yields a profit of 25% ; if he discounts 10% at wholesale, what per cent does he gain at wholesale? 43. Bought Chesapeake & Ohio 1st pf. R. R. Stock for 26^, the same Stock sold last year for 32£ ; how much would a man lose who bought $5000 worth last year ? 44. At what price must 6 % bonds payable in 10 years be bought to realize 8£% on the investment? 45. What is the per cent income in 1884 on Chic. R. I. & Pac. 6's coup., payable at par in 1917, bought at 123£ ? 46. Divide $1860 among A, B, and C, so that for every $5 given to A, B may receive $4, and for every $3 given to B, C may receive $1. 47. Divide § into two parts, so that one of them is greater than the other by f . 48. A mine is worth $50000 ; a person sold T 3 advance; the second, at 20% advance; and the third at $1.15 a bushel; his expenses were $112.25, his commission 3%; what were the net proceeds ? 86. In the above speculation, what per cent was the grain dealer's gain? 87. A merchant sells goods at different times as follows: May 2, a bill of $800 on 4 mo.; May 15, a bill of $1200 on 6 mo. ; June 1, a bill of $1500 on 8 mo. ; and June 15, $800 for cash ; he then agrees to take a note for the whole, at 60 days with interest ; what should be the date of the note ? 88. March 4, 1884, a note for $1000, at 6% interest, was given, on which the following indorsements were afterwards made: May 1, 1884, $75; July 17, 1884, $15.50; Dec. 1, 1884, $30.50; Dec. 31, 1884, $400; Jan. 31, 1835, $250 ; what was due Aug. 18, 1885 ? Appendix. 315 TABLE I. THE AMOUNT OF AN ANNUITY OF $1, AT COMP. INT., FROM 1 YR. TO 50. Yr. 1 3 per ct. %% per ct. 4 per ct. 5 per ct. 6 per ct. 7 perct. Yr. 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1 2 2.030000 2.035000 2.040000 2.050000 2.060000 2.070000 2 3 3.090900 3.106225 3.121600 3.152500 3.183600 3.214900 3 4 4.183627 4.214943 4.240464 4.310125 4.374616 4.439943 4 5 5.309136 5.362466 5.416322 5.525631 5.637093 . 5.750739 5 6 6.468410 6.550152 6.632975 6.801913 6.975319 7.153291 6 7 7.662402 7.779408 7.898294 8.142003 8.393838 8.654021 7 8 8.892336 9.051687 9.214226 9.549109 9.S97468 10.259803 8 9 10.159106 10.368496 10.582795 11.026564 11.491316 11.977989 9 10 11.463879 11.731393 12.006107 12.577893 13.180795 13.816448 10 11 12.807796 13.141992 13.486351 14.206787 14.971643 15.783599 11 12 14.192029 14.601962 15.025805 15.917127 16.869941 17.888451 12 13 15.617790 16.113030 16.626838 17.712983 18.882138 20.140643 13 14 17.086324 17.676986 18.291911 19.598632 21.015066 22.550488 14 15 18.598914 19.295681 20.023588 21.578564 23.275971 25.129022 15 16 20.156881 20.971030 21.824531 23.657492 25.672528 27.888054 16 17 21.761588 22.705016 23.697512 25.840366 28.212880 30.840217 17 18 23.414436 24.499691 25.645413 88.132886 30.905653 33.999033 18 19 25.416868 26.357180 27.671229 30.539004 83.759992 37.378965 19 20 26.870374 28.279682 29.778078 33.065954 30.785592 40.995492 20 21 28.676486 30.269471 31.969202 35:719252 39.992727 44.865177 21 22 30.536780 32.328902 34.247970 38.505214 43.392290 49.005739 22 23 32.452884 34.460414 36.617889 • 41.4:30475 46.995828 53.436141 23 24 34.426470 36.666528 39.082604 44.501999 50.815577 58.176671 24 25 36.459264 38.949857 41.645908 47.727099 54.864512 63.249030 25 26 38 553042 41.313102 44.311745 51.113454 59.156383 68676470 26 27 40.709634 43.759060 47.084214 54.66'.n26 63.705706 74.483823 27 28 42.930928 46.290627 49.967583 58.402583 68.528112 80.697691 28 29 45.218850 48.910799 52.966286 68.822719 73.639798 87.346529 29 30 47.575416 51.622677 56.084938 66.438847 79.058186 94.460786 30 31 50.002678 54.429471 59.328335 70.760790 84.801677 102.073041 31 32 52.502759 57.334502 62.701469 75.298829 90.889778 110.218154 32 33 55.077841 60.341210 66.209527 80.063771 97343165 118.933425 33 34 57.7:30177 63.453152 69.857909 85.066959 104.183755 128.258765 34 33 60.462082 66.674013 73.652225 90.320307 111.434780 138.236878 35 36 63.275944 70.007603 77.598314 95.836323 119.120867 148.913460 36 37 66.174223 73.457869 81.702246 101.628139 127.268119 160.337400 37 38 69.159449 77.028895 85.970336 107.709546 135.904206 172.561020 38 39 72.234233 80.724906 90.409150 114.095023 145.058458 185.640292 39 40 75.401260 84.550278 95.025516 120.790774 154.761966 199.635112 40 41 • 78.663296 88.509537 99.826536 127.839763 165.047684 214.609570 41 42 82.023196 92.607371 104.819598 135.231751 175.950545 230.632240 42 43 85.483892 96.848629 110.012.382 142.993:339 187.507577 247.776496 43 44 89.048409 101.238331 115.412877 151.143006 199.758032 266.120851 44 45 92.719861 105.781673 121.029392 159.700156 212.743514 285.749311 45 46 96.501457 110.484031 126.870568 168.685164 226.508125 306.751763 46 47 100.396501 115.350973 132.945390 178.119422 241.098612 329.224386 47 48 104.408396 120.388257 139.263206 188.025393 256.564529 353.270093 48 49 I 10S.540648 125.601846 145.833734 198.426663 272.958401 378.999000 49 50 ! 112.796867 130.997910 152.667084 209. 34? 996 290.335905 406.528929 50 316 Annuities, TABLE II. THE PEESEXT WORTH OF AN ANNUITY OP $1, PROM 1 YEAR TO 50. Yr. 1 3 per ct. 3 l / 3 perct. 4 per ct. 5 per ct. 6 per ct. 7 per ct. Yr. 0.97087 0.96618 0.96154 0.95238 0.94339 0.934579 1 2 1.91347 1.89969 1.88609 1.85941 1.83339 1.808017 2 3 2.82801 2.80164 2.77509 2.72325 2.67301 2.624314 3 4 3.71710 3.67308 3.62990 3.54595 3.46511 3.387207 4 5 4.57971 4.51505 4.45182 4.32948 4.21236 4.100195 5 6 5.41719 5.32855 5.24214 5.07569 4.91732 4.766537 6 7 6.23028 6.11454 6.00205 5.78637 5.58238 5.389286 7 8 7.01969 6.87396 6.73274 6.46321 6.20979 5.971295 8 9 7.78611 7.60769 7.43533 7.10782 6.80169 6.515228 9 10 8.53020 8.31661 8.11090 7.72173 7.36000 7.023577 10 11 9.25262 9.00155 8.76048 8.30641 7.88687 7.498669 11 12 9.95400 9.66333 9.38507 8.86325 8.38384 7.942671 12 13 10.(53495 10.30274 9.68565 9.39357 8.85268 8.357635 13 14 11.29607 10.92052 10.56312 9.89864 9.29498 8.745452 14 15 11.93794 11.51741 11.11839 10.37966 9.71225 9.107898 15 16 12.56110 1-2.09412 11.65230 10.83777 10.10589 9.446632 16 17 13.16612 12 65132 12.16567 11.27407 10.47726 9.763206 17 IS 13.75351 13.18968 12.65930 11.68959 10.82760 10.059070 18 19 14.32380 13.70984 13.13394 12.08532 11.15812 10.335578 19 20 14.87747 14.21240 13.59033 12.46221 11.46992 10.593997 20 21 15.41502 14.69797 14.02916 12.82115 11.76408 10.835527 21 22 15.93692 15.16712 14.45112 13.1(5300 12.04158 11.061241 22 23 16.44361 15.62041 14.85684 13.48857 • 12.30338 11.272187 23 24 16.93554 16.05837 15.24696 13.79864 12.55036 11.469334 24 25 17.41315 16.48151 15.62208 14.09394 12.78336 11.653583 25 26 17.87684 16.89035 15.98277 14.37518 13.00317 11.825779 26 27 18.32703 17.28536 16.32959 14.64303 13.21053 11.986709 27 28 18.76411 17.66702 16.66306 14.89813 13.40616 12.137111 28 29 19.18845 18.03577 16.98371 15.14107 13.59072 12.277674 29 30 19.60044 18.39205 17.29203 15.37245 13.76483 12.409041 30 31 20.00043 18.73628 17.58849 15.59281 13.92909 12.531814 31 32 20.38877 19.06887 17.87355 15.80268 14.08404 12.646555 32 33 20.76579 19.39021 18.14765 16.00255 14.23023 12.753790 33 34 21.13184 19.70068 18.41120 16.19290 14.36814 12.854009 34 35 21.48722 20.00066 18.66461 16.37419 14.49825 12.947672 35 36 21.83225 20.29049 18.90828 16.54685 14.62099 13.035208 36 37 22.16724 20.57053 19.14258 16.71129 14.73678 13.117017 37 38 22.49246 20.84109 19.36786 16.86789 14.84602 13.193473 38 39 22.80822 21.10250 19.58448 17.01704 14.94907 13.264928 39 40 23.11477 21.35507 19.79277 17.15909 15.04630 13.331709 40 41 23.41240 21.59910 19.99305 17.29437 15.13802 13.394120 41 42 23.70136 21.83488 20.18563 17.42321 15.22454 13.452449 42 43 23.98190 22.06269 20.37079 17.54591 15.30617 13.506962 43 44 24.25427 22.28279 20.54884 17.66277 15.38318 13.557908 44 45 24.51871 22.49545 20.72004 17.77407 15.45583 13.605522 45 46 24.77545 22.70092 20 88465 17.88007 15.52437 13.650020 46 47 25.02471 22.89943 21.04294 17.98102 15.58903 13.691608 47 48 25.26671 23.09124 21.19513 18.07716 15.65003 13.730474 48 49 25.50166 23.27656 21.34147 18.16872 15.70757 13.766799 49 50 ! 25.72976 23.45562 21.48218 18.25593 15.76186 13.800746 50 Appendix. 317 TABLE III. AMOUNT OF $1 AT COMPOUND INT., FROM 1 YEAR TO 50. Yr. 3 per ct. \SY 2 perct. 4 per ct. 5 per ct. 6 per ct. 7 per ct. 8 per ct. Tr. 1 1.030000 1.035000 1.040000 1.050000 1.060000 1.070000 1.080000 1 2 1.060900 1 1.071225 1.081600 1.102500 1.123600 1.144900 1.166400 .2 3 1.09272? 1.108718 1.124864 1.157625 1.191016 1.225043 1.259712 3 4 1.125509 '< 1.147523 1.169859 1.215506 1.262477 1.310796 1.360489 4 5 1.159274 1.187686 1.216653 1.276282 | 1.338226 1.402552 1.469328 5 6 1.194052 1.229255 1.265319 1.340096 1.418519 1.500730 1.586874 6 7 1.229874 1.272279 1.315932 1.407100 1.503630 1.605781 1.713824 7 8 1.266770 1 .316809 1.368569 1.477455 1.593848 1.718186 1.85093C 8 9 1.304773 1.362897 1.423312 1.551328 | 1.689479 1.8:38459 1.999005 9 10 1.343916 1.410599 1.480244 1.628895 | 1.790848 1.967151 2 158925 10 11 1.384234 1.459970 1.539454 1.710833 1.898299 2.104852 2.331639 11 12 1.425761 1.511069 1.601032 1.795856 2.012196 2.252192 2.518170 12 13 1.468534 1.563956 1.665073 1.885649 2.132928 2.409845 2.719624 13 14 1.512590 1.618694 1.731676 1.979932 2.260904 2.578534 2.937194 14 15 1.557967 1.675349 1.800943 2.078928 2.896558 2.759031 3.172169 15 16 1.604706 1.733986 1.872981 2.182875 2.540352 2.952164 3.425943 16 17 1.652848 1.794675 1.947900 2.292018 2.692773 3.158815 3.700018 17 18 1.702433 1.857481, 2.025816 2.406619 2.854339 3.379931 3.996019 18 19 1.753506 1.922501 2.106849 2.526950 3.025599 3.616526 4.315701 19 20 1.806111 1.989789 2.191123 2.653298 3.207135 3.869683 4.660957 20 21 1.860295 2.059431 2.278768 2.785963 3.399564 4.140561 5.033834 21 22 1.916103 2 131512 2.369919 2.925261 3.603537 4.430400 5.436540 22 23 1.973586 2.206114 2.464715 3.071524 3.819750 4.740528 5.871464 23 24 2.032794 2.283328 2.i 563304 3.225100 4.048935 5.072365 6.341181 24 25 2.093778 2.363245 2.665836 3.386355 4.291871 5.427431 6.848475 25 26 2.156591 2.445959 2.772470 3.555673 4.549383 5.807351 7-96353 26 27 2.221289 2.531567 2.883369 3.733456 4.822346 6.213868 7.988062 27 28 2.287928 2.620177 2.998703 3.920129 5.111687 6.648836 8.627106 28 29 2.356565 2.711878 3.118651 4.116136 5.418388 7.114255 9.3172751 29 30 2.427262 2.806794 3.243397 4.321942 5.743491 7.612253 10.062657 30 31 2.500080 2.905031 3.373133 4.538039 6.088101 8.145110 10.867669 31 32 2.575083 3.006708 3.508059 4.764941 6.4533S7 8.715268 11.737083 32 33 2.652335 3.111942 3.648381 5.003188 6.840590 9.325.337 12.676049 33 34 2.731905 3.220860 3.794316 5.253343 7.251025 9.978110 13.690134 34 35 2.813862 3.333590 3.946089 5.516015 7.686087 10.676578 14.785344 35 36 2.898278 3.450266 4.103932 5.791816 8.147252 11.423939 15.908172 36 37 2.985227 3*71025 4.268090 6.081407 8.636087 12.223614 17.245626 37 38 3.074783 3.696011 4.438813 6.385477 9.154252 13.079277 18.625276 38 39 3.167027 3.S25372 4.616366 6.704751 9.703507 13.994827 20.115298 39 40 3.262038 3.959260 4.801021 7.039989 10.285718 14.974465 21.724522 40 41 3.359899 4.097834 4.993061 7.391988 10.902861 16.022677 23.462483 41 42 3.460696 4.241258 5.192784 7.761587 11.557033 17.144265 25.339482 42 43 3.564517 4.389702 5.400495 8.149667 12.250455 18.344363 27.366640 43 44 3.671452 4.543342 5.616515 8.557150 12.985482 19.628469 29.555972 44 45 3.781596 4.702358 5.841176 8.985008 13.764611 21.002461 31.920449 45 46 3.895044 4.866941 6.074823 9.434258 14.590487 22.472634 34.474085! 46 47 4.011895 5.037284 6.317816 9.905971 15.465917 24.045718 37.232012 47 48 4.132252 5.213589 6.570528 10.401270 16.393872 25.728918 40.210573 48 49 4.256219 5.396065 6.833349 10.921333 17.377504 27.529943 43.427419! 49 50 4.383906 5.584927 7.106683 11.467400 18.420154 29.457039 46.901613 50 Pages 8, 9. 3. 435,5589,14014. 6. 556. 7. 809. 8. 566. 9. 4805. 10. 6454. 11. 6458. 13. 12225. i£ 15772. 16. $8592. iX^es 10,11. 18. 6928 votes, less ; 8636 " greater. 19. $149 ch., $201 w. 20. $181 B, $319 A. 21. 1917 less no. ; 2570 greater. 22. 13, 875, 6716. 23. 8. 24. 4, 2. #5. 63 y. V. 41 y. P. 26. 58 c. 47 a-b. 23 inf 5 Off. 27. 682 more. Art. 11.— 2. 1255440 3. 1562292. 4. 1441073. 5. 1517644. 7. 6950664. 9, 4526818. 10. 5212999. 11. 6047136. 12. 7956585. 14. 67544325. rages 12, 13. 16. 465507. 17. 712236. 18. 27600. 19. 3458000. 20. 17520000. 21. 124704000. 22. 495. 23. 737. 25. 62680257. 26. 8435406375. 29. 25038. SO. 57196. 31. 253377. 32. 323352. 55. 5456256. 36. 860209340. 87. 9067243052. 38. 5153209664. Pages 14, 15. 41. 1873784. 42. 2232321. 43. 33104944. 44. 40858938. 48. 4698. 49. 21760. 50. 182975. 51. 2015898. Page 17. 3. 9626^. 4. 7707*. 5. 1792. 5. 1312AV 7. 46364. 5. 2580|14|. 11. 1104&- lift 9042^. 15. 8325 T V l£ 13400*. Prices 19, 20. 3. 2, 11, 13. 4. 3,41,397. 5. 2, 2, 3, 5, 41. 6. 2, 5, 281. 7. 3, 5, 5, 43. 8. 2, 2, 2, 2, 2, 2, 2, 2, 3, 5. 5. 2, 2, 643. JO. 2, 2, 3, 3, 3, 83. 12. 2. 13. 2, 2, 3. 14. 2, 2, 2, 3. 15. 5, 5. JY/f/es 21-25. 2. m- Q 1503 «*• -'■SUT- 4. 5 T V /r 145 O. ^3 T . 0. 236^. 7. 64. 5. $24. 9. 36bbl. 10. 676 bu. 11. 38 § reams. 12. 6 men. ^Lr*. 39.-2. 144. 5. 2. £ 46. 5. 4. 0. 19. 7. 2. 5. 16. £>. 2. 10. 12. Xg. 4 Acres. 13. 3 ft. X*. 14 ft. 15. 16 yd. ^•*. 45.-2. 210. 3. 100800. 4. 21168. Answers. 319 5. 3360. 6. 9900. 7. 51408. 8. 34650. 9. 1791700. 10. 1388016. 11. 2520. W. 5040. 74. 30. 15. 12 in. i0. 360 peaches. 17. 180 weeks. 18. 2f. 25. $31.68 ; 72 H., 9& A., 88 G. .Prtflres 45-50. 4. 2540.42 m. J. 385 00024 Hm. 6. 17232 m. 7. 8960.008 m. 8. 40157.575 m. 9. 370.678307 Km. 15. 836.0524 m.; 83.60524 Dm. 16. 75.842 m.; 7584.2 cm. 17. 18.762 m.; 1876.2 cm. 18. 6175000 cm.; 61750000 mm. 19. 1.58364 Hm. 20. 285300 dm. 21. 153000 Dm.; 153000000 cm. 22. 8634 ca.; .8634 Ha. 23. 75000000 sq. mm.; 7500 sq. dm. 24. 82.34 A. 25. 1.8438 Ha. 28. 256034.089 cu. cm. 29. 38.450 cu. m. SO. 253000000000 cu. mm. ; 253000000 cu. cm. 31. 1.28653 dl. 12.8653 cl. 32. 3500 cl.; 35000 ml.; 3.5 dl. 33. 8000 liters. 34. 800 DL; 80 HI. 35. 238.47 dg.; 2384.7 eg.; 2.3847 Dg.; 23847 mg. 36. 0.025384 dg.; 0.0025384 g. 37. 2158 g. ; 215800 eg. 38. 0.001 Kg. 39. 31000600 g. Pages 51, 52. 4. 70.925 bu. 5. 19.295 gal. 6. 223.704 mi. 7. .3047328 oz. 9. 199.53325 A. 10. 8829 cu. ft. 12. 2286 cm. 13. 10972.5 g. 14. 2609.7 cl. 15. 3412.28 A. 16. .4046+ Ha. 17. 60.746+ Ha. 18. 1772.04+ lb. 19. 995.334+ p. 2. 10798.22 m. 4. 93 cm. 5. 0.3872 Km. 6. $362. 16829. 7. 99.053 g. S. 25.028+ m. 9. $323. 10. 1.44 fr.; 33.84 fr.; $2.53. 11. $31.70 gain. 12. $38,245 gain. 13. 9 1 sters each ; 7.20 fr. Pages 55, 56. 2. 1535220 sec. 3. 1296000 sec. 4. 762036 in. 5. 3872448 in. 6. 1401264 grs. 7. 328291b. 8. 790294i sq. ft. 9. 13200 ft. 10. $39600. 11. $380250. 12. 41 far. 13. $2104.70|. Art. 151.— 16. 1111b 6oz. 11 pwt. 14 gr 17. 386 bu. 2 pk. 6 qt. 18. 4 d. 10 hr. 50 min 34 sec. 19. 5847 c. 74 cu. ft. 20. 857 bbl. 8 gal. 3 qt. 2gi. 21. 658 A. 90 r. 204 yd. 22. 5907 r. 4 qr. 12 sh. Pages 57, 58. 23. 20 m. 7 ch. 2 r. 24. $60.61. 25. $1790.25. 26. 20 A. 13 sq. r. 260| sq. ft. 27. $1874.04. 30. 200 rods. 31. 1 pk. 5 qt. If pt. 32. f gill. 33. 45 lb. 12.8 oz. 34. 6 d. 6 hr. 46 min. 48 sec. 35. 6 oz. 17 pwt. 3* gr. 36. 9 oz. 15 pwt. 18 gr. 37. 9 hr. 28 min. 4.8 sec. 3S. 6 fur. 30 r. 2 yd. 7.2 in. 39. 5406l T V sq, ft. 40. 64 cu. quar. in. Page 59. 44. .688+ lb. 45. £.733 + . 46. .0004958+ m. 47. T^hi, or .00382 lb. 48. .05625 gal. 49. .0580357 wk. 50. .0131579 ton. 51. $638.53. 52. $59.25ff 53. .0625 d. 54. .2903. 55. .4187. 56. .3808. 57. .03062. 58. .625. Pages 60, 61. 2. 241 A. 1 sq. r. 3. 168 bu. 2 qt. 4. 38 mi. 5 fur. 39 r. 2£ ft. 6. 2s. lOd. 3 far. 7. 8 oz. 13 pwt. 6 gr. 8. 3 quarts. 9. 4 d. 21 hr. 33 min. 320 Answers. 10. 13s. 3d. 12. 9 mi. 1 fur. 18 r. 7 ft 10 in. 13. 1 oz. 2 pwt. 6 gr. U. £1 14s. 9d. 15. j. 17. 6 yr. 6 mo. 5 d. 18. 12 yr. 9 mo. 19 d. 19. 46 yr. 1 mo. 17 d. 21. 484 days. 22. 109 days. Pages 62, 63. 23. 462 days. 24. 436 days. 25. 374 days. 26. 37 days. 27. 1° 19' 14". 28. 79° 8'. 29. 62° 50' 30". Art. 158. 2. £74 lis. 3. 143 gal. 2 qt. 4. 580 m. 7 fur. 5. 2 d. 20 hr. 5£ m. 5 sec. 6. 1355° 47' 56". 7. 385 bu. 2 pk. 1 qt. 8. £37 9s. lOd. 2 far. 10. 2 gal. 2 qt. 2| gi. ii. 3 bu. 2 pk. 1 qt. f pt. 10. 3s. 7d. 3| far. 13. 5° 33' 16|". U. 91| C. 15. 9s. 2d. 2 far. 16. 7772 T f3fr. 17. 36| doz. IS. 113i mi. 19. 7.182 Km. Pages 64, 65. 2. 101° 22'. 3 4° 48'. 4. 13° 37' 42". 5. 74° 1' 2". 7. 3 hr. 13 min. 40 sec. 8. 3 hr. 14 mi. 47| sec. 9. 10 o'clk. 7 m. 35f s. 10. 5 o'clk. 52 m. 26^ s. 11. 1 hr. 15 min. 56 sec. 12. 3hr. 31m. 46 s.; 1 hr. 16 m. 47 s. 13. 1 hr. 6 m. 17 sec. ^Pages 67-69. 2. $101061. 4. 580| ft. 5. 50 r. wide ; $351 T 9 e, cost. 6. 9 f \ rolls. 7. $30804. 51 f. 8. 194400 sq. in. 10. 80 rods. 11. 46010| sq. ft. 12. 17| rods. 13. $367.00125 Art. 178. 15. 338 sq. in. 16. 29 A. 85 sq. rods. Pages 70, 71. 2. $94,815. 3. 262.144 cu. m. 4. 237^ loads. 5. 169 U cu. ft. 8. 3456 gal. 9. $10.93i 10. 303.1875 ft. 11. $227.81^. 12. 7.95 ft. Bages 72, 73. 3. 21 ft. 4. 16 4 ft. 5. $77.34|. 6. $7.48H- 7. 585 cu. ft. 8. 5Hf| cu. ft. 9. $12.60. /0. $318.93f. 11. 243 boards. 12. 2270| ft. Art. 190. 1. 73ff perch. 3. 197208 bricks. 4. $1493.85. Pages 74=, 75. 2. $1794.98. 3. $1258250. 4- $1.12. 5. $4,477 + . 6. $3750. 7. 13^ lots; $6462 g. 9. $334,331 10. $450. 11. $842|. 12. $14.16f. 13. $66. 14. $98.50. 15 r $151.20. 16. $34,375. 17. $210. 15. $799.50. 19. $70420. 20. $2640. £*. 105 lbs. 23. $163, «& $2164. Pages 76, 77. 25. $2.80. 26. 22 planks. 07. 13^ bales. 29. $57860. 30. $120. 31. $895H. 34. $4696.30. 35. $3914.625. 36. $1457.33|. 38. $12020. 39. $0,112 per lb. 41. $26.0658. 42. $192.92. Ptoses 78-81. $163,745. $653.35. $152.98. $977. $241.27. $1588.75. Pages 83, 84. 20. .42, or 42%. 21. .53f, or53|%. 22. .46|, or46|%. 23. .2l|, or21f%. 24. .34ff,or34ff%. 25. .27^, or 27&%. 26. .50, or 50%. 07. .23f, or23f%. 30. 471. 3i. 586.25. $£. 469.84. 33. 313.38. 34. 814.20. 35. 7397.25. 30. 6842. Answers. 321 37. 6.03£. 38. 49.92 sq. r. 39. $24.25 dif. 40. 26.999 miles. 43. 4f%. u- m%- 45. 5%. .46. 6^ 2 3%. 47. m%. 4S. 18|f%. Pr/t. 40. $12525. 41. $0.74i. 4f. 60|§t%- 4c?. $12432.432 + . 44. $6.73243728. 45. $3.83 ioss. #. $5329.03 profit. 47. 71 bu. 45. 8.999+ bu. 49. 967 cars. 56). $115.09 loss. 51. $19.89. 55. 88%. J5. 242| acres. 54. 847170 Phil. 1206299 N. Y. 55. 3364 Ca. 56. 93± sq. ft. 57. 363.73ift. Pages 282, 283. 58. $745,875. 59. 3 shares. 60. 28*%- 61. 44.204 ft. 62. $12000. 63. .00^. 65. 106.08 cu. m. 66. $450.84. 67. 540 bbls. 68. $2120.60. 69. $2760.69. 70. 1019 in. 71. 2.7 cm. ;.?. 3 mo. 73. 23, r/. c. d. 74. $23809.52. 75. 108 lbs. 76. $3.50 per yd. 77. 107, r/. c. d. 78. $599.34. 75. 113097.6 cu. in. 5#. 64.75, Ha. 81. 39.38 + . HI. 82. $271,845 + . 83. 6.3 in. 84. Wh%. 85. $11609.76. 86. $665.37. 87. $127.73. Pages 284, 285. 88. *$1 87.20. ,89. Oct. 16th. 90. Dec. 6th, 1883. 91. $1962.01. 92. 44 ft. 93. 8. 94. 9. 95. 6. 95. 3375. 97. 200%. 9S. $2470.75. Answers. 329 99. 178.731 bu. 100. 49140. 101. 18 ft. wide ; 54 ft. long. ' 102. $595. 103. 5.19 ft. 104. 156 rods. 105. $3405.30, Bank ; $4905.30, all. 106. 7 + in. = 1 side. 107. 132.9+ meters. 108. 1 yr. 1 mo. 14 d. 109. $2174.585 + . 110. 24dif. 111. 1970.80 sq. r. 112. $8.91 per bbl. 113. 126.589 Km. 114. 78 mi. 211 r. 5.332+ yd. 115. Ufa. Pages 286, 287* 1. 75635. 0. 586916. 3. 754108. 4. 6783002. 5. 7388520. 6. 1731704. 7. 1010663. & 948395. 9. 982110. 10. 1183219. £2. 1199035. 12. 725522. !«?. 661945. 14. 549253. 15. 1417691. 16. 974687. 17. 1162790. 18. 379261. 19. 1373105. £0. 1486901. 01. 3193. 22. 1856. 05. 89111. 24. 89189. 05. 88909. 00. 164808. 07. 366185. 05. 665645. 29. 611111. 50. 111109. 51. 89111. * 50. 164898. 55. 484737. 84. 259331. 55. 4436640650. 36. 1817822786. 37. 2626568694. 38. 1331846875. 39. 2023209268. 40. 1398214650. 41. 1777211634. 42. 4130024886. 43. 1431347492. 44. 3468401325. 45. 223702272. 46. 1538746950. 47. 768264600. 48. 4405321875. 49. 4084589512. 51. 68851 T 3 A 9 *V 52. 51846 T 9 T VV T - 53. 2044181HH. 54. 377582£ffff. 55. 83132|ff|f. 56. 30687ff{ft. 57. 24368fffff- 58. 9677 ¥ V3 5 3. tV 11. 51 bags ; 3f bu. in each. 12. 332 lots; T \5 A. each Art. 697. 2. 24. 3. *£ = 15f . 4. isjA - 402f. 5. *-740 = 97!!, 6. 6f davs ; A, 10 t. ; B, 15 t.; C,8t. 7. 5 hr. 20 min. ; meet at stg. pt. 8. 8 hr. walk ; 22 times No. 1 ; 28 " No. 2 ; 33 " No. 3. rages 293, 294. 2. 515944. 3. 45327848. 4- 53837066. 5. 675159828. 7. 2916 ; 3025 ; 3364. 8. 2704 ; 3136 ; 3481. 10. 2025 ; 4225 ; 7225 ; 9025. 12. 11025 ; 13225 ; 21025; 18225. u. 59004. 15. 82852. 10. 29623. 17. 31394. Art. 709. 5. June 3. G. 320 y. 3 m. 8 dys. 7. Friday, May 16. Page 300. 2. $3753.60. 3. $303300. 4. $3177.72. 5. $743.88. Pages 309-314. 1. 93. 155 T X 3 of eac 8 t V| mo. 4.27 mo. A, $11317 ; B, $9053.60 C, $6224.35 D, $6224.35 E, $6224.35 F, $622435. 65 each. 313 horses ; $61 each. 247 yds. ; $1151.25 cost. 108 A. left ; $3 per A. 150 men. 1152597 bbls. 690 lbs. left ; $0,571 per lb. $5,618 per head. 32 spoons of each. 49 animals. 10. 11. 12. 13. 14. 15. 16. 48 feet, 17. $21428.57. 18. $480,305. 19. $240. 20. 190 sq. ft. 21. $94.41 Net g. 22. U. S. 3's = 2ff % ; . B.&0.6's=4Hf#§%. 23. .05 T V 24. 3534.3 lbs. 25. 96 rods. 26. 8s. 101-d. per yd. 27. $10566.43 gain. 28. 8*f#. 29. 71 mo. 30. $500 for 15 yrs. ; $1378.9162 greater. 31. 7% bonds; $10061 better. 32. 8.807+ miles. 33. 90*. 34. 172.66 shares. 35. $4200, 1st ; $3900, 2nd ; $3640, 3rd. 36. 45+ fo. 37. $264.25. 38. $1838.8745. 39. $290 gain. 40. $8.25 on 2 mo; 81 cts. per bbl. better. 41. 79315.2 gals.; $3569.184 val. 42. 12i%. 43. $891,493 loss. 44. $118^ per share. 45. 4,£ T %. 46. $900, A's money : $720, B's " $240, C's " 47. a i«w ; f £ greater. 48. f of the mine. 49. 20 days A; 30 " B; 50. 322 lots. 51. 6^%. 52. 396096 Pop. 53. 43% B; 68% C. 54. 28+ % N. Y. 55. $3438.75. 56. 75%. 57. 66|% Gold; 33J% Silver. 58. 20'books. 59. 26250 oz. gold ; 2916| oz. alloy. 60. 1900, 1st ; 2660, 2nd ; 3420, 3rd. 61. $54000. 62. $65331 63. 21050." 64. $10097|, 1st cost ; $12347y, 2nd cost .012+% gain. 65. 80|%. 66. $12.32 marked. 67. 26iyds. 68. 3691 §f$ times; 14.6608 ft. cir. 69. $18.20. 70. $387.88 + . 71. $450, C's money ; $800, D's " 72. 53 days. 73. $473.45 due. 74. $11560.69. 75. 9%. 76. $53,196. 77. 16|%. Answers. 331 78. $1500, daughter's $1050.85||, C's 82. 486.6 bags. share ; salvage ; 83. H%. $7500, each son's ; $1784.1 lgV, A's loss; 84. $413.50. $10000, widow. $1529.24|f, B's " 85. $2313.72. $1108.88|f, A's $1709.15i|. C's " 86. Wf% gain salvage ; 80. $708.75 di'f. 87. Oct, 31. $945,761-8, B's 81. $189.03 Bal. 88. $287.55. salvage ; ■# o o * A Hand-Book of Mythology : Myths and Legends op Ancient Greece and Rome. Illustrated from Antique Sculptures. By E. M. Berens. 330 pp. 16mo, cloth. The author in this volume gives in a very graphic way a lifelike pic- ture of the deities of classical times as they were conceived and worshiped by the ancients themselves, and thereby aims to awaken in the minds of young students a desire to become more intimately acquainted with the noble productions of classical antiquity. In the legends which form the second portion of the work, a picture, as it were, is given of old Greek life; its customs, its superstitions, and its princely hospitalities at greater length than is usual in works of the kind. In a chapter devoted to the purpose, some interesting particulars have been collected respecting the public worship of the ancient Greeks and Romans, to which is subjoined an account of their principal festivals. , The greatest care has been taken that no single passage should occur throughout the work which could possibly offend the most scrupulous deli- cacy, for which reason it may safely be placed in the hands ot the young. RECOMMENDATIONS. " Fifty years ago compends of mythology were as common as they were useful, but of late the youthful student has been relegated to the classical dictionary for the information which he needs at every step of his progress. The legends and myths of Greece and Rome are interwoven with our literature, and the general reader, as well as the classical student, is in need of constant assistance to enable him to appreciate the allusions he meets with on almost every page. The classical dictionary is not always at hand, nor is there always time to find what is wanted amid its full derails, and the reader is thus often obliged to answer "no" to the question, " Understandest thou what thou readest ? " This handbook, by Mr. Berens, is intended to obviate the difficulty and to supply a want. It is compact, and at the same time complete, and makes a neat volume for the study table. It gives an account of the Greek and Roman Divinities, both Majores and Minores, of their worship and the festivals devoted to them, and closes with sixteen classical legends, beginning with Cadmus, who sowed the dragon's teeth which sprang up into armed men, and ending with a wifely devotion of Penelope and its reward. The volume is not one of mere dry detail, but is enlivened with pictures of classi- cal life, and its illustrations from ancient sculpture add greatly to its interest."— " The Churchman" New York City. ~ " The importance of a knowledge of the myths and legends of ancient Greece and Rome is fully recognized by all classical teachers and students, and aiso by the intelligent general reader ; for our poems, novels, and even our daily newspapers abound in classical allusions which this work of Mr. Berens' fully explains. It is appropriately illustrated from antique sculptures, and arranged to cover the first, second and third dynasties, the Olympian divinities, Sea Divinities, Minor and Roman divinities. It also explains the public worship of the ancient Greeks and Romans, the Greek and Roman festivals. Part II. is devoted to the legends of the ancients, with illustrations. Every page of this book is interesting and instruc- tive, and will be found a valuable introduction to the study of classic authors and assist materially the labors of both teachers and students. It is well arranged and wisely condensed into a convenient-sized book, 12mo, 330 pages, beautifully printed and tastefully bound."—" Jovrnal of Education," Boston, Mass. " It is an admirable work for students who d(j§|re- J to find in printed form the facts of classic mythology."— Rev. L. Clark SeelyeTWUfrSmith College, Northamp- ton, Mass. " The subject is a difficult one from the nature and extent of the materials and the requirements of our schools. The author avoids extreme theories and states clearly the facts with modest limits of interpretation. I think the book will take well and wear well."— C. F. P. Bancroft, Ph.D., Prin. Phillips Academy, Andover, Price, by-Maii* Post-paid, $1.00. CLARK & MAYNARD, Publishers, New York. ID I /^Jo Two-Book Series of Arithmetics. By James B. Thomson, LL.D., author of a Mathematical Course. 1. FIRST LESSONS IN ARITHMETIC, Oral and Written. Fully and handsomely illustrated. For Primary Schools. 144 pp. 16mo, cloth. 2. A COMPLETE GRADED ARITHMETIC, Oral and Writ- ten, upon the Inductive Method of Instruction. For Schools and Academies. 400 pp. 12mo, cloth. This entirely new series of Arithmetics by Dr. Thomson has been prepared to meet the demand for a complete course in two books. The following embrace some of the characteristic features of the books : >m- on, ace i la T35 the ect for ad, div Sec fro bin anc wit Wr two acti roa him inst la- tum ) con . in- cipl jps in tfl ?ar and xne discussion or topics wmcn UBJUllg exclusively to tne nigner uepart- ments of the science is avoided ; while subjects deemed too difficult to be appreciated by beginners, but important for them when more advanced, are placed in the Appendix, to be used at the discretion of the teacher. Arithmetical puzzles and paradoxes, and problems relating- to subjects having- a demoralizing tendency, as gambling, etc., are excluded. All that is obsolete in the former Tables of Weights and Measures is eliminated, and the part retained is corrected in accordance with present law and usage. Examples for Practice, Problems for Review, and Test Questions are abundant in number and variety, and all are different from those in the author's Practical Arithmetic. The arrangement of subjects is systematic ; no principle is anticipated, or used in the. explanation of another, until it has itself been explained. Subjects intimately connected are grouped together in the order of their dependence. Teachers and School Officers, who are dissatisfied with the Arith- metics they have in use, are invited to confer with the publishers. CLARK & MAYNARD, Publishers, New York.