333 3D? A SHORT SYSTEM OF ARITHMETIC AND BOOK-KEEPING. Taw: ,' ) SHORT SYSTEM OF ARITHMETIC AND BOOK-KEEPING. WITH A SUPPLEMENT ; CONTAINING ANSWERS TO THE ARITHMETICAL QUESTIONS. THE EIGHTH EDITION, CORRECTED AND REVISED. BY R. HAMILTON, L.L.D. PROFESSOR OF PHILOSOPHY IN THE MAHISCHAL COLLEGE, ABERDEEN. EDINBURGH: PRINTED FOR ARCHIBALD CONSTABLE &. CO. AND ROBERT ROSS, EDINBURGH ; WILLIAM COKE, LEITH ; AND GEORGE CLARKE, ABERDEEN". By John Brown, Anchor Close. L IsisT "it ENTERED IN STATIONERS HALL. ADVERTISEMENT. THE Author of the following sheets published a fuller Treatise on the same subjects, intitled, An Introdu to Merchandize, some years ago, for the use of an acade- my which he had the charge of at that time. He had occasion lately to revise that work upon the publication of a new edition ; and it has been represented to him by some respectable teachers that it was too long for or- dinary use, and part of the matter not adapted to the capacity of beginners ; and that an abridgment of it might be useful. IN compliance with their request, he has drawn up the present shorter system ; in which he has endeavoured to explain the principles as fully, and introduce as much useful matter, as the limits of a cheap book would admit; and he has given a very minute detail of the operations in the fundamental rules, for the sake of beginners. The matter is, for the most part, the same as in the larger work, and the words are also frequently the same ; but the ex- ercises are all different, that teachers or students, who are provided with both books, may have a greater variety. V THE shorter Treatise is intended for the common use of schools, and the larger for the further improvement of students who desire to acquire a thorough knowledge of these subjects. MarisrJtal College, Aberdeen, 2. 1796. I DIRECTIONS TO TEACHERS. THE Author has also been desired to offer a few hints con- cerning the order of teaching by the help of this book, for the assistance of teachers whose experience in this branch is not extensive. What follows is intended for such teachers only. The beginner should first be instructed in the four funda- mental rules of arithmetic, both in integers and compound quantities ; and should continue to practise them till he ac- quire a tolerable readiness and exactness. The contractions and varieties annexed to the rules should not be taught till the simple rules be well understood. Some of these are in- serted, rather because they serve to unfold the theory of num- bers, than for their actual use ; and more or fewer of them may be explained at the teacher's discretion. The rule of proportion, rules for practice, the arithmetic of fractions, vulgar and decimal, and the reduction of foreign moneys, come next in order for the generality of learners. The articles in the Appendix, and that concerning mensura- tion (which was intended for the Appendix, and separated from it by accident), are only to be taught to those students whose capacity or intended employment points out the propriety of doing so. The rules printed in Italics, are intended to be transcribed by the learner. The answers to the examples immediately annexed to the rules are printed on a separate sheet, as it may- be inconvenient for young learners to have access to them be- fore they have performed the calculations. When the learner lias gone through the rules, and wrought these examples, he may be returned and directed to those contractions and obser- vations that were passed over before, and employed to work the questions annexed as exercises to the rules. The parts print- ed in a smaller type may in general be left to the student's private perusal. The manner of proceeding may be varied at the discretion of the teacher, according to the capacity of the student. Those of slower parts should by no means be per- plexed with a variety of rules, but their attention confined to x DIRECTIONS TO TEACHERS. he may proceed to extend the materials, page 238, or some of the questions in partnership, or any of the sets in the intro- duction to merchandize, or other book of the same kind. The whole of these are more than any one student will have occa- sion for ; but a well employed teacher in this line will find it convenient, to be provided with variety. These materials are first t> be drawn out in the form of a waste-book, the articles separated, the computations perform- ed, and the blanks filled up. From this the journal and led. ger arc to be posted as before. After the student has proceeded a certain length, he is to peruse the sections upon bills of exchange, and other mercan- tile forms ; and then he is to -draw out the bills, &c. that are mentioned in the different articles as he goes along. These writings are to be made out on separate papers, and folded and indorsed in the regular manner used in business. It will also be ;..n useful exercise, to cause him write a part of the letters ihat must be understood to have passed in the eou,rse of the business. CONTENTS. PART I. ARITHMETIC. Page, dotation . 1 \ddition - - 3 subtraction 9 Multiplication . 15 )ivision - - . 21 lule of Proportion - 29 lules for Practice, Computation of Prices . 37 Deductions on Weights - -43 Commission, &c. - - 44 Interest - -45 /ulgar Fractions - - 51 Decimal Fractions - - - 58 fables of Compound Interest and Aunuities - 65 ? oreign Monies - - -69 Holland - - .70 Germany - - - 72 Denmark - . . 73 Poland, Livonia - 74, Eussia, France, Portugal, Spain 75 Italy - - 76 Ireland, America - - 77 Lrbitratiori of Exchange . -78 Mensuration - - 80 Superficial Measure - - 81 Solid Measure - - 83 Methods of taking dimensions - 86 liscelianeous Questions .9! APPENDIX. ECT. I. Algebra - - 108 II. Logarithms - 111 III. P - 113 IV. f . 116 123 xii CONTENTS. PART II. BOOK-KEEPING. Page. SECT. I. Single Entry - . 127 Day Book .' - - 129 Ledger - . 137 II. Double- Entry - 145 Of the Waste-Bpok - . ib OF the Ledger - - 14,6 Of the Journal . - - 1 Directions for writing the Ledger - 165 WASTE-BOOK - - 171 JOURNAL - . 137 LEDGER, - 208 Materials for another Set . 238 Exercises in Partnership . 243 II I. Bills of Exchange, &c. - 246 IV. Bills of Parcels . 251 Invoices - - 353 Account Sales . - , 257 V. Subsidiary Books - 260 SHORT SYSTEMt ARITHMETIC, &c. PART 1. NOT.AtMN..'! V 1. ARITHMETIC is the science which treats of Number. The theory of Arithmetic explains the properties of numbers ; practical arithmetic applies them to the performance of calcu- lations. The first expedient for advancing in arithmetic, is the ar- rangement of numbers into classes. The idea of one or a unit is simple, and admits of no definition. Ten units form a class of the first rank ; ten times ten, or ten tens, form a class of the second rank ; and ten of any rank form one of the rank m'xt higher, without limitation. 2. The second expedient is the invention of proper me- thods for representing numbers ; the use of which is called NOTATION. There are tvro methods of notation now in use ; the Roman method by letters, and the Arabic by figures, which is much preferable. The Roman numeral letters and their values are the following : I. V. X. L. C. D. M. One, five, ten, fifty, one hundred, five hundred, one thousand. Any number may be represented by repeating and combin- ing these according to the following rules : 1st, When the same letter is repeated twice or oftener, its valie is represented as often. Thus II signifies two, XXX thirty, CC two hundred. 2d, When a numeral letter of less value is placed after one of greater, their values are added : thus XI signifies ele- ven, LX.V sixty-five, MDCXXVIII one thousand six hundred and twenty-eight. 3d, When a numeral letter of less value is placed before one of greater, the value of the less is taken from that of the greater ; thus IV signifies four, XL forty, XC ninety, CD four hundred. A 2 - NOTATION. Sometimes If) is used instead of D for 500, and the value is increased ten times by annexing 3 to the right hand. Thus I^ signifies 500 also CP) is used for 1000 5000 CCI33 for 10000 50000 CCCI333 for 100000 thousands; arej represented by drawing a line over the lop-'of the*- niiraepatj *Vbeing used for five thousand, L forfit thousand", ! tjvo/Jiuncjred thousand. ;vjfr:t1te/XndMC iriettfotl*, VrijmbeVs are represented by the ten following characters : 123 4567 89 One, two, three, four, five, six, seven, eight, nine, cipher. The first nine are called significant figures or digits, and represent sometimes units, tens, hundreds, or higher class- es. VN hen placed singly they represent units. When several are placed together, the first or right hand figure stands for so many units, the next for so many tens, the next for so many hundreds, and the others for higher classes, according to the place in which they stand. The cipher (0) has no signification when placed by itself, but it serves to bring the other figures to the proper places on which their value depends. Thus 5 stands for five, but 50 stands for fifty, or five tens, the significant figure being in the second place ; and 500 stands for five hundred, the significant figure being in the third place. The following table shews the names and divisions of the classes : 8. 4- 3 7, 9 8 2. 5 6 4., i 3 8. 9 7 2, 6 4 * 5 05 U2 OT t/3 CO T rn rr W) rr OB CO (/; VI Vj M cccds c a a G a "CS "^ "*O 2 ^ o o o o o c c rt c CC 5 O C: -3 H a JO XI pO ,fl JQ S S S ?, a 3 C c 3 a 3 rf's'si'Sg illli H 1 Ms - g S H == . ^ -a a BILLIONS, d thousand of Q thousand of Thousand Hundred 1 MILLIONS. Hundred th s Q H K -5H S H 3 The first six figures from the right hand are called the unit period; the next six the million period; after which NOTATION; 3 the trillion, quadrillion, quintiilion, sextillion, septillion, oc- tillion, and nonillion periods follow in their order. 4. The operation of reckoning the value of any number expressed in figures is called NUMERATION. It the number be long, it is proper to divide it into periods and half periods, by different marks; then begin at the left hand, and read the figures with the names of their places. The following examples of literal notation may be express- ed in words, and these words again represented by figures : the examples of notation in figures may be expressed by words or letters, for the learner's improvement. Ill CL1V 1763 949 312308051 MMMM XLIX 1489 1865 574740325 XII MXCiX 1286 174-3 4262499752 XIV MCCXL1X 1705 96 210785803 LXVI CDLIV 3799 1386 J00273G07 XCVJI MCMXI 8372 777 56*02$ ADDITION. 5. ADDITION is that operation by which we find a number equal to two or more given numbers. The riuuiber found is called the sum or amount. RULE. Write the number*, to be added, units under units, tens under tens* and so on. Draw a line under the lowrr number, an i add the right hand column : ij the turn be under ten* lyrite it at the foot of the column ; but if it be ten, or an exxct ., number of ten*, write a Cipher ; ij it be not an exact num. ' for of tens, write the excess above tern at Lie foot of the co- lunn ; and /or evert/ ten 'the turn contains, curry one to the next column, and add it in the ..-ame manner as the former. Proceed in like manner to add,' he other columns, carrying (he-tens of each io the next, and mark down thefull sum of the iejt hand column. EXAMPLES. 35782 4235tf 31793 3759 46593 65793 5735 5487 72406 82648 6666 9035 435080 75328 12345 8972 2575 86493 78yO 6543 368 75936 54S21 5278 5 92 804 '12242 A 2 4 ADDITION. Quest. 1. A person has L.I 25 in money, a house worth L. 512, a ship worth L. 728, goods worth L. 932, and the debts due to him amount to L.479; required the amount of his ef- fects ? 2. If London contains 723^65 inhabitants, the rest of England 6231468, Wales 293572, Scotland 1496380, Ire- land 2510685, and the less British isles 237596, how many rants are there in ali the British isles-? 3. From the creation to the departure of" the Israelites from Egypt were 2513 years ; to the siege of Troy, 307 years more ; to the building of Solomon's temple, 180 years ; to the build- ing of Rome, 251 years; to the expulsion of the kings from Home, 244 years; to the destruction of Carthage, 363 years; to the death of Julius Caesar, 102 years; to the Christian tera 44 years. Required the time from the creation to the Christian aera. 4. An array consisted of 12 battalions of foot and 6 squa- drons of horse. Colonel A's battalion consisted of 738 men, B's 439, C's 573, D's 612, E's 751, F's 811, G's 698, H's 723, I's 51 & K's 716, L's 678, M's 508, N's squadroa 32o horse, O's 289, P's ^76,.Q's 268, R's 250, S's 309. How many horse and foot were there in the army ? It is proper to mark under the sum of the column the figures which you carry, as in example 1st, to prevent the neces- sity of beginning again at the right hand column, in case of interuption or mistake. 6. Addition may be proved by either of the following methods. 1st, Repeat the operation, beginning at the top of the column. 2d, Divide ihe account into several parts, add these sepa- rately, then add the sums together. 7. In compound operations, the given numbers consist of articles of different value, as pounds, shillings, pence, &c. which are called different denominations. RUIE FOR COMPOUND ADDITION. Write the numbers of ihe same denomination under each other , add the figures of the lowest denomination, and find how many of the next higher de~ nomination that sum. conlayi*', an.i whether there be any over. Set dow>> ihe excess, if any^ tit the foot of the column^ and ec.rry one. for eaih if the higher denominations to the next column. in the same manner, carrying always one for each of ADDITION. 5 the next higher denomination, till you come to the highest, then carry by 10, as in simple addition. For example, because 12 pence make a shilling, you carry one to the shilling column for every 12 in the sum of the pence column: and because 20 shillings make a pound, you carry one to the column of pounds for every 20 in the sum of the shillings. Again, in adding avoirdupois weight, because 28 pounds make a quarter, you carry one to the quarters for every 28 in the sum of the pounds ; and because 4 quarters make a hundred weight, you carry one to the hundred weights for every 4 in the sum of the quarters. This is called carry- ing according to the value of the higher place. 8- Table of Sterling Money. Farthings pence | The words at the top of each ~J I SnillinW I column are the names of the ar- - , tides, and all the articles on the _J 1 _ found _l same line are of equal value; 960 240 } 20 | _J thus> 900 f art hings, 240 pence 20 shillings, and 1 pound, are all equal. Table of Troy Weight. Grains j Pennyweights | Troy weight is now used "gji"""}"" ~i ' i Ounces I only for gold, silver, jewels, -430 gg ! L- _ , and for comparing different 760 240 1 ound I weights with each other. Table of Avoirdupois Weight Drams J Ounces This weight is used in Eng- land, almost for every pnr- 16 j 1 Pounds 256 j 16 1 Quarters J 7168 i 448 2 1 Hundreds j *&67sf J 1792 | 112 4 1 1 'on j Scotland in 80 \ 20 1 collecting the T h l n*,' P Ch : ,n ' Ihe pound contains 7000 grains Troy. Table of English Land Measure. A 3 o ADDITION. <). We shall give the value of some other articles in a more concise manner., and recommend it to the learner to reduce them to tables of the above form, after he is advanced to 26. Apothecaries Weight. 20 grains i scruple, 3 scruples = 1 drum, 8 arams = 1 ounce, 12 ounces ~ 1 pound. Tins weight is used only by apothecaries in compounding medicines. It is the same as English Troy ; the subdivisions only are different. ticols Troy or Dutch Weight. 16 drops 1 ounce, 16 oun- ces 1 pound, 16 pounds =, 1 stone. This weight is used in Scotland for iron, hemp, flax, meal, butcher meat, unwrought pewter and lead, most Dutch and Baltic goods, and some other articles. The pound contains 7600 grains, 1 c\vt. avoirdupois makes 103 Ib. 2 oz. Dutch. Scots Old of- Trone Weight is still used for butter, cheese, wool, hay, and some other commodities. The pound varies in different places, and for different purposes, from 30 to 21 Dutch ounces; it is divided into 16 of its own ounces, and 1G pounds make a stone. Scots Land Measure. 36 square ells zr 1 fall, 40 falls = 1 tood, 4- roods = 1 acre. The Scots ell is equal to 37} Eng- lish inches, and is divided into 37 of its own inches. Long Measure. 12 inches 1 foot, 3 feet = 1 yard, 5\ yards, or 1 1 half yards = 1 pole, 40 poles = 1 furlong, 8 fur- longs ~ 1 mile, 3 miies = 1 league ; 4 inches =. 1 hand, 6 feet = 1 fathom. Cloth Measure. 2| inches = 1 nail, 4 nails =: 1 quarter, 4 quarters 1 yard, 5 quarters = 1 English ell. English Dry Measure. 8 pints = 1 gallon, 2 gallons =r 1 peck, 4 pecks =r 1 bushel, 8 bushels = 1 quarter. The V\ in- chester bushel, which is the English standard, contains 2150 inches. Scots Dry Measure 4 lippies - 1 peek, 4 pecks 1 firlot, 4 firiots:.:_ 1 boll, If) bolls .-. 1 chalder. The Linlithgow wheat firlot, which is the Scots standard, contains 2! Scots pints i mutehkin, and is also used for rye, pease, beans, salt and grass seeds. It is about 2 per cent, larger than the Winchester bushel. The barley firlot, used dH> for eats, fruit, and potatoes, contains SI Scots pints. English Wine Mca.-ur?. 2 pints 1 quart, 4qunrts 1 gallon, 42 gjilons - I tierce, 63 gallons = 1 hogshead, 84 gal ions 1 puncheon, 2 hds, 1 pioe or butt, 2 butts ^ 1 ton. ADDITION. 7 This measure is also used for spirits, perry, cyder, vinegar, oil, and honey. The gallon contains 2:->l cubic inches. English Ale Measure. 2 pints = 1 quart, 4 quarts r= 1 gallon, 8| gallons =. 1 firkin, 2 firkins = 1 kilderkin, 2 kil- derkins = 1 barrel, 1 \ barrel = 1 hd. The ale gallon contains 282 cubic inches. In London the bar- rel of ale contains 32 gallons, and the barrel of beer 36 gallons. Scots Liquid Measure. 4 gills = 1 mutchkin, 2 mutch- kins = 1 chopin, 2 chopins == 1 pint, 2 pints = 1 quart, 4 quarts ~ 1 gallon. The Scots quart contains 210 inches, and therefore is a- bout ^3 less than the English wine gallon, and about | less than the English ale gallon. Tims. 60 seconds 1 minute, 60 minutes 1 hour, 24 hours = 1 day, 7 days = 1 week, 365 days =. 1 year. The year, according to the Julian style, contains 365 days 6 hours, and is regulated by allowing an additional day to e- very fourth year, or leap year. January contains 31 days, February 28 days in common years, and ! 2Q in leap years, March 31, April 30, May 31, June 30, July 31, August 31, September 30, October 31, November 30, December 31. i 0. The following table of Sterling money may be use- ful to beginners. d S d s d s 1 s 20 - 1 8 2 24 20 = 1 - 30 = 2 6 3 36 30 1 10 40 3 4 4 ~ 48 40 2 -. _. 50 = 4 2 5 ~ 60 50 2 10 60 = 5 6 *-* 72* 60 3 __ 70 . 5 10 7 ~- 84 70 3 10 80 = 6 8 8 96 80 4 90 7 6 9 = 108 90 - 4 10 100 8 4 10 rr 120 100 = 5 110 -r? 9 2 11 * 132 110 5 10 120 Z= 10 12 r= 144 120 = 6 _ _ Examples of Sterling Money. L. s d L. s d L. s d L. s d 12 3 9 47 13 7| 14 10 7f 476 12 3 578 35 19 101 12 19 iji 153 7 7 796 12 16 3 18 18 8| 536 19 3 10 12 3 5 5 36 15 7| 779 19 10 53 8 4 79 19 12 3| 5428 11 3 3 ADDITION. E.78 9 3 L.46 12 3 L.45 12 3| L.4578 3 4 19 3 10 25 lOf li 8 llf ^75 8 S 45 11 7 ]65 19 10 y 9090 9 9 3.9 12 5 35 1'2 9 35 7 5$ 1857 17 7 28 73 48 18 8| 18 6 3f 1375 11 6 45 5 8| 63 5 7 39 JO 5 16 5 37 19 11 99 19 9 78 19 * 1648 3 8 36 12 2 88 11 .71 42 15 3 4257 8 8 48 4 5 36 12 2 7* 11 4 987'.' 5 4 17 18 7 15 7 S 49 19 3 3212 3 5 t Tray Weight. Ib. oz. dwt. lit oz. dwt.gr. Ib. oz. dwt. gr. 25 7 17 15 6 9 15 105 10 15 8 18 5 15 8 5 7 21 2)3 6 18 19 12 3 18 3423 357 7 13 7 17 10 9 7767 48 8 7 9 19 2 7 2889 51 9 9 22 9 9 10 9 S 4 2 119 11 6 12 C. qr.lb. Avoirdupois Weight. Ib. oz. dr. C. qr. Ib. tz. 13 S 15 18 15 2 2 3 22 14 5 2 23 12 8 13 15 1 9 12 2 1 18 767 17 2 11 11 737 575 925 15 129 996 5388 926 3 14 9 1 2 3 10 English Land Measure. A. R. P. A. R. P. Y. A. R. P. Y. 25 2 18 85 2 15 25 125 2 21 12 18 3 12 73 1 22 28 236 3 1 ; 29 28 1 1 86 16 19 251 1 32 22 13 3 15 95 3 8 29 345 15 19 523 17 9 8 276 2 2 23 37 2 19 18 1 12 12 30 3 30 30 SUBTRACTION. A. R. F. 52 3 7 28 28 17 3 27 5 2 35 58 1 24 Scots Land A. R. F. 526 488 5 1 9 828 9 1 7 735 Measure, E. A. R. F. E. 9 99 2 18 28 18 46 3 17 SO 7 128 12 7 15 375 2 35 14 4 777 1 27 19 19 860 21 5 M. Long F P. Measure. Y. Y F. C/of/ Measure. Scots Troy W. in. Y. qr. nls. St. Ib. oz. 5 3 12 5 5 2 7 5 1 3 15 7 3 3 7 16 4 4 1 8 4 3 2 8 14 12 9 5 18 4 8 9 7 2 3 9 9 9 6 5 7 5 9 1 10 3 2 6 5 4 4 4 9 4 7 2 5 2 1 3 8 7 10 Eng. Dry Measure. Scots Dry Measure. Wine Measure. Q. B. G. pis. C/i. B. F. P. T.hdsrgal.pts. 5341 40 513 92 55$ 1533 28 12 23 8 48 5 8255 19 932 73 27, 7 6 7 2 36 14 2 p 2 IS 2 p 4 3 S 12 821 31 21 4? 3662 45 62 4 91 Scots Liquid Measure. Time, gal. pis. m. g. D. II. min. sec. 28 S 2 1 125 13 21 -61 21 7 1 118 ly 24 18 43 5 2 276 8 48 51 17 -2 - 341 2 17 12 36 5 2 3 78 7 7 9 58 6 S 2 69 16 9 26 SUBTRACTION. 11. SUBTRACTION is the operation by whiclvwe tokenless number from a greater, and find their difference. The greater number is called the minuend, and the less the subtrahend. RULE. Place the less numbtr under the greater, units un- der units, tens tinder tens, and so on. Draw a line bcl&w t then 10 SUBTRACTION. begin at the right hand^ ctnd subtract each figure of the less, number from the, figure above it, and place the remainder di- rectly below. When the figure, in the lower line exceeds the fi- gure dbuvs it, suppose ten to be added to the upper figure ; but in i //>., case you must add one to the under figure in the next co- lumn be/ore you subtract it. This is called borrowing ten. Ewmplcs. Minuend 56739 57894 735698 853261 Subtrahend 32416 39586 286709 586793 Remainder 24323 18308 Proof 56739 Qu. 1 A person carried L 95 to a market, and expended there L.37, how much did he bring home ? 2. A person, whose present age is 63, was 25 years old at the birth of his eldest son, what is the age of the son ? 3. The person mentioned in the first question to addition owed L.879; how a.uch is his neat- stock ? 4. The army mentioned in qu. 4th, lost in battle 1315 foot and 726 horse ; how many remained ? 5. Out of a hhd. of wine there was drawn at one time 15 gal- lons, and at another 28, how much remains ? 6. If a Scots quart be taken from an English wine gallon, how much remains? 12. To prove subtraction, add the subtrahend and remain- der together, if theii sum be equal to the minuend, the opera- tion is ri^ht. See Example l.tf. IS, RULE FOH COMPOUND SUBTRACTION. Place like de- nominations under like, and, beginning a1 the right hand, ntb- traci the number of each denomination in the lower line from the number above it, and place the remainder below. But when the under number oj any denomination is greater than the upper, add so many to the upper an make one of the next higher denomination, subtract the lower Jrom that sum, and carry one to the under number of the next denomination before you subtract it. Thus, in the second example, 24 pounds cannot be subtract- ed from 1,> pounds, but 15 and 28 (the value of a quarter) make 43; from wliich take 24, there remain 19. Or, perhaps it may be easier to subtract the number in the lower Jine irom the value of the higher denomination, and SUBTRACTION. 11 add to the remainder the sum in the upper line : thus 24 from 15 we cannot, but take 24 from 28, there remains 4, to which 15 being added make 19. Examples. C. qr. Ib, A. R. P. L.78 1> 9 7 2 15 12 2 28 49 18 3 5 3 24 5 1 39 Remainder 28 17 6 1 2 19 7 29 L.576 12 3 87 9 5 Miles F. P. r, :'5 3 24 4 16 4 82 3 Proof L.375 12 10 29o 19 11 78 15 9 L.3-68 3 8 2594 8 8| C. q. lb. oz. 3258 2 3 16 9 lb. oz. dwt. gr. 5 8 15 12 3 8 17 20 More examples for practice may be taken from the first and second lines of the several examples in addition. 1 4. Before the learner proceed to solve the following ex- ercises, we must acquaint him that it is often necessary to place the sums in different columns, in order to exhi'-ii a distinct view of what is required. For instance, if the vanes of several parcels of gootis are to be added, whan each parcel consists of several articles, the particular articles should be placed in an inner column, and the sum of each parcel extend- ed to the outer column, and there added. If any person be owing an account, and has made sor^e partial payments, the payments must be placed in an inn^i co- lumn, and their sum extended under that of the account in the outer column, and there auhtrccted. 1773 Ex. 1. Jan. 15. Lent James Smith L.50 22. Lent him farther 70 Feb. 3. Received in part L.63 5. Received farther In gold L.10 10 In silrer 13 23 10 86 10 Balance due me L.33 10 -- 12 Ik. 2. SUBTRACTION. Account of House nold Expenses. 1815. Jan 1. 5. 8. 9. 12. On hand Received Paid for butcher meat For tea For sugar For china Baker's account Received Paid shoemaker's account For stone ware Rtr-ceived. Paid. L.I 3 6 - 7 6J 15 3 1 1 15 1 4 6 2 5 6| 1 9 836 7 17 10 7 17 K.)i 5 7 15. On hand I. A merchant had in ready money L.I 8 8 6 ; goods, viz, sugar worth L.42 i 13 6; wine L.512 7 8 ; rum L.270 3 5; tea L.418 3 8. Jaraes Smith owed him L.53 7 10; John Hil! L.I 9 5 8; Thomas Reynolds L.200 5 8 ; Edward Fer- rers i2s 9d. He owed Robert Bell L.I 7 12 9; David Der- roont L.208 : Henry Green L.I 9 9 9; Richard Bi( kerstafl L.I 3 5 7; Honeyman and Company L.I 000. Required his neat stock ? Answer, L.655 15 7. II. A person takes a lease of a toll for L.800 per annum, and draws in January L.80 7 6, February L.70 9 8, March L.60 12 3, April L.72, May L.91 4 6, June L.50 12 8, July L.I 04 3 7, August L.96 4 3, September L.51 3 7, October L.62 19 8, November L.59 4 3, December L.62 7 4; the expence of collecting is L.40. Required his gain or loss ? Answer, Gain L.21 9 3 III A gentleman's rent is paid by four tenants; A pays L...2S 10s. B L.521 7 9, C L.243 12 4, D L.281 5 3. His expences are, housekeeping L.825 14 6, tradesmen's accounts L.204 8 5, carriage and horses L.I 15 9 S, garden expenses L.54 7 8, private expenses L.76 12 7, duties L 28 12 9, improvement of land L.250 Required what money he has savevl, or what debt he has contracted ? Anvver, he has sa- ved L,31^ 9 9. SUBTRACTION. 13 IV. A gentleman pays for ground to build a house, L.200, and pays the mason's bill L.304 7 8 ; the carpenter's L.504 9s. 6d. ; the slater's L.128 7 8 ; the smith's L.I 5 7 4; the glazier's L.63, 12s.; the painter's L.3'} 4 3d, ; the upholsterer's L.45 9 7. Required how much it costs ? Answer, L. 1:500, 18s. V. Required the amount of the gross tare and nett weight of 7 hhds. tobacco, qt. N 1 7 cwt. 2 qrs. tare, 2 qr. 5 Ib. . N 26 c. 3 q. tare, 3 q. 9 Ib. N 35 c. 3 q. 4 Ib. tare, 3 q. 14 Ib. N 48 c. 2 q. 16 Ib. tare, 2 q. 3 Ib. N 57 c. 3 q. 14 Ib. tare, 2 q. 7 Ib. N 63 c. 3 q. 2 Ib. tare, 1 q. 20 Ib. N 75 c. 1 q. tare, 1 q. 6 Ib. ? Answer, gross 45 cwt. 2 q 8 Ib. tare, 4 cwt. 8 Ib. nett 41 cwt. 2 q. VI. Kequired a state of the following debts due to William Faulkener: A bond by R. Boswell L.lOO, and interest L. 15; remainder of a bond by Tho. Rigg L.450, whereof there is paid L.I 50; another by Francis Dove L.I 64, whereof there is paid L.92, and Interest due on it L.3 5 c>. A bill on. Nathaniel Cook L.46 13 6; another on A Wilkinson L.I 56, whereof paid L.56 ; another on J. Greenhill L.179, whereof paid 3d May, L.18, and 7th June, L.32, and 8th JulyL.16. Two others on Thomas Nelthorp, L.45, and L.9, 16s. Ac- counts due by James Neal, L.36 18 4; by William Fletcher, L.I 7 3 8 ; by A. Stubbs, L 12 11 11 ; by John Casanj L14, 2s. 9d. ? Answer, amount L. 884 11 11. VII. A Gentleman is possessed of silver plate, viz. spoons, weight 8 Ib. 7 oz. 9 dwt. knives and forks 3 Ib. 10 oz. 6. dwt. salts 2 Ib. 3 oz. 5 dwt. 12 gr. salvers 9 Ib. 9 oz. 15 dwt. tan- kards 9 Ib. 8 oz. 5 dwt. tea-pot 3 Ib. 5 oz. 6 dwt. 20 gr. vases 1? Ib. 8 oz. 5 dwt. How much did it amount to ? Answer, 55 Ib. 4 oz. 12 dwt. 8 gr. VIII. A farm measures 300 acres 2 roods. There are in wheat 59 a. 3 r. 12 p. ; in barley S6 a. 1 r. 15 p. 20 y. ; in oats 24 a. I r ! 5 p. ; in beans 12 a. 8 p. ; in turnips 28 a. 3 r. 16 y. ; in fallow 32 a. 9| y. ; in garden ground 3 a. 3 r. and the rest in pasture. Required how much pasture? Answer, 103 a. 1 r. 28 p. 15| y. IX. From Edinburgh to Perth is 40 miles 5 furlongs 12 poles; from Perth to Brechin 41 no, 5 f. 18 p.; from Brechin to Abeideen 39 m. 4 f. 2 p. ; from Aberdeen to Banff 44 m. 12 p.; from Banff to Elgin 33 m. 19 p. ; from > Elgin to In- verness 38 ra, 1 f. Required the distance of each of these B 14 SUBTRACTION. towns from all the others ? Answer, 237 m. 23 p. altogether, &c. X. A corn merchant purchases from one person 128 quarters 5 bushels wheat, and 72 q. 3 b. barley ; from another 105 q. 6 b. wheat, and I 04 q. 4 b. barley. He sells to A 50 q. -8 b. 2 p. wheat, and IS q. 3 b. barley ; to B 48 q. barley ; to C 94- q. 3 b. 8 p. wheat, and 38 q. 2 b. barley ; to D 19 q. wheat, how much should there be remaining ? Answer, 70 q. S b. 3 p. wheat, and 72 q. 2 b. barley. XL From a piece of silk which measured 60 yards 3 qrs, there were sold at diflerent times 12 y. 3 q. 3 n. 15 y. 2 q. 3 n. 14 y. 1 q. 1 n. and 12 y. 2 n. How much slieuld remain ? Answer, 5 y. 2 q. 3 n. XII. An Apothecary has 6 pieces of rhubarb, the first weighs 5 ounces 3 drams 1 scruple 18 grains; 2d, 4^732 9 12 gr; 3d, 4 2 3 15 gr ; 4th, 3^63 1 9 18 gr ; 5th, 3 ^ 1323; 6th, 2 17 gr- What is the weight of them al- together ? Answer, 1 Ib 1 1 J 6 3 8 gr. XIII. A plumber has eight bars of lead; weighing, 1st, 5 st. 8 Ib. 9oz. Scots Troy 2d, 5.1. 12 3d, 4.15. 3 4th, 4.9. 12 5th, 4.2. 14 6th, 3.14. 8 7th, 3.12.6 8th, 3 . 15 . 1. He manufactures 20 st. 12 Ib. 12 oz. How much should remain ? Answer, 14 st. 11 Ib. 3 oz. XIV. A horse dealer carries twenty-five pounds twelve shillings and six pence to a fair, and three horses, which he sells, the first for fourteen pounds twelve shillings, the second for twelve guineas, and the third for ten pounds five shillings : He buys a horse for twelve pounds seven shillings and sixpence, another for eight pounds nine shillings, a third for seven pounds fifteen shillings, and a fourth for nine pounds, of which the seller returns him two shillings and six pence ; and he spends at the fair nine shillings and four pence, How much will he bring back ? Answer, L.25 3 2. XV. A young lady had on hand 1st January L.3 139, and received from her father L.3 on the 12th, and L.I on the 18th : she paid, on 'the 3d, for millinery wares L.I 7 3 ; 5th, for sewing silk 5s. 3d. ; 7th to the music-master L.I, Is. 9th, for gauze 17s. 4d. 14th, for ribbands 8s. 2d. 17th, to dan- cing master L.I, 5s. 20th, for repairing trinkets 15s. and for incidental expences 5s. 2|d. How much remains on hand? Answer, L.I 9 6%. 15 MULTIPLICATION. 15. IN MULTIPLICATION two numbers are given, and it is required to find the amount of the former, when reckoned as many times as there are units in the latter. Thus 8 mul- tiplied by 3, or 3 times 8, are 24. The given numbers 8 and 3 are caltedjactors ; the first (8) is called the multiplicand, the second (3) the multiplier, and the amount (24) the product. Before the learner proceed farther, he must have the fol- lowing multiplication table perfectly on his memory. Twice Four times Seven times Eleven times a are 4 4 are 16 7 are 49 2 are 22 3 6 5 20 8 56 3 _ 3S 4 . 8 6 24 9 0'3 4 _ 4 5 10 7 28 Eight times 5 __ 55 6 12 8 32 8 are 64 6 66 7 __ 14 9 36 972 7 77 8 _ 16 Five times Nine times 8 88 9 18 5 are 25 9 are 81 9 99 Tl ioo tinr IOC on 10 JL ui v** I'j.tiAV'tJ 3 are 9 7 _ Ol/ 35 Ten times 1 v/ 11 T _ 121 4 12 8 40 2 are 20 Twelve times 5 15 9 ----- 4-5 330 2 are 24- 6 18 Six times 4 40 3 36 7 21 6 are 36 5 50 4 __ 48 8 24 7 - 42 660 5 ___ 60 9 27' 8 48 770 6 _ 72 9 5* 8 80 7 84 990 8 96 10 100 9 108 10 _~ 120 11 __ 132 12 144 16. RULE I. To multiply ly a single Jigure, write it un> Jer the unit place of tht multiplicand, and draw a line below. Begin at the right hand of the multiplicand, and multiply each Jigure by the multiplier, writing the units of the product below, and carrying the tens to the next higher place as in Addition. B2 16 MULTIPLICATION. RULE II. When the multiplier consists of several figure.?, write it under the multiplicand, units under units, tens under tern, and so on. Multiply first by the units of the multiplier, GS directed above, then by the tens and the other figures in their order, placing the Jirst figure of each product directly under the figure by -which you multiply ; then add the lines thus obtained. The sum is the product required. If the multiplier be 10, the product is obtained by annexing a cipher to the multiplicand j if the multiplier be 100, by annexing two ciphers; and so on. If there be ciphers annexed to the significant figures of either or both factors, multiply by the significant figures, and annex as many ciphers to their product as there are at the end of both factors. Examples. 8576 4259 4278 53720 9 85 S52 30400 77184 21295 8556 21488000 S4072 21390 16116 12834 3620J5 1633088000 1505856 17. A number which cannot be produced by the multi- plication of two others is called a prime number, as 3, 5, 1, 11, &c. A number which may be produced by the multiplication of two lower ones, is called a composite number ; for example, 27, which is formed by multiplying 9 by 3 ; and these num- bers are called its component parts. Contractions and Varieties in Multiplication. 18. I. If the multiplier be a composite number, we may multiply successively by its component parts. 3748 by 35 3748 35 or 5 times 7 7 18740 11244 131180 131180 19. II. If the multiplier be 5, which is one-half of 10, we rnay annex a cipher, and divide by 2. If it be 25, which is one fourth of 100, annex two ciphers, and divide by 4. ;J 20. JII. To multiply by any number of 9's, annex as many ciphers to the multiplicand as there are 9's in the mul MULTIPLICATION. IT tiplier ; and from the number thus formed subtract the multi- plicand. Ex. 17548 by 9999 1. 53724 by 99 2. 63586 by 999 1754-80000 3. 17274 by 9 17518 4. 89459 by 9999 175462452 21. IV. Sometimes the product of two or more figures may be obtained at once, from the product of a figure already found. Ex 76483 Here we first multiply by 9 ; then, because 3 times 9 5427Q are S7 ' we n 111141 ? 1 }' the first line of the P l '^ duct b ? 3 ' y which gives the product by 27 ; and lastly, because twice ' 27 are 54-, we multiply the second line of the product by 688347 27, which gives the product by 54. 2065041 4150082 by 67 by 85 by 79 by 92 by 543 by 787 by 821 by 355 by 361 8 by 5769 by 2345 by 2575 22. Multiplication may be proved by repeating the ope- ration, using the multiplier for the multiplicand, and the mul- tiplicand for the multiplier; it may also be proved by division; and an account wrought by any contraction may be proved by performing the operation at large, or by a different contrac- tion. 23. COMPOUND MULTIPLICATION. RULE I. If the multiplier do not exceed 1*2, write it under the lowest denomination of the multiplicand. Begin by multiplying the lowest denomination, and, for every unit of the next higher ivkich that product contains, carry one to the next denomination t and set down the exce$s,ifany, under the denomination multiplied; B & 4151420757 J. 57486 2. 374295 S. 58485 4. 35798 5. 5412S3 6. 798642 n i 856749 S. 675402 9. 230420 10. 37485 11. 179483 12. 5429381 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 3048 73658 85074 36967 87693 10203 5648 5576 754912 630203 19579 675491 by by by h y K y by by by by by by by 84 144 1728 125 9998 6789 4812 7236 54*279 96328 52575 16896 18 MULTIPLICATION. and proceed in the same manner till yon come to the highest de- nomination, and then carry by 10, as in &imple multiplication, Examples. L. 5 7 8 1. L.130 58 by 8 9 2. 72 6 9 by 1 1 -- 3. 2471 3 2 by 12 LAS 9 21 4. 9 lb. 5 oz. 3 dwt. 12 gr. by 7 CW. gr. lb. 5. 2 ac. 1 r. 7 f. 18 ells by 6 3218 6. 35 miles 3 f. 8 p. by 10 5 7. 7 st. 5 lb. 9 oz. Dutch by 9 -- 8, 8 cwt. 3 q. 20 lb. by 7 18 1 6 24. RULE II. If the multiplier be a composite number, whose component parts do not exceed 12, multiply Jirst by one of the com- ponent parts, and then multiply the product by the other. Pro- ceed in the same manner with the others, if there be morethan two. L. 15 3 8 by 32=8X4 1. L. 17 18 9| by 35 8 " 2. 205 12 10 by 72 - . --- 3. 306 7 8-J- by 125 L.121 9 4 = 8 times 4. 13 cvvt. 3 q. 12 lb. by 27 4 5. 7 ac. 1 r. 9 p- by 84 6. 7 ch. 2 b. 1 f. 2 p. by 63 L.485 17 4 = 32 times 7- 3 tb. 5$. 3 3. by 28 The operation jrnay be proved by taking the component parts in a different order, or dividing the multiplier in a di* i'erent manner. 5 25. RULE III. If the multiplier be a prime number, mul- tiply Jirst by the composite number next lotver, then by the dif- ference y and add the products. Ex. L. 35 17 9 by 67 = 64 + 3 8 64= 8X8 1. L. 17 18 91 by 29 2. 307 7 6" by 58 3. 245 12 8 by 19 4. 17 2 5i by 74 5. 23 4 llf by 68 (). 12cwt.2q. 11 Ib.hy 71 7. 15 3 7 by 47 S. 6 1 14 by 53 9. 3 ac. 2 r. 7 p. by 13 10. 1 boll 3 f. 2 p. by 97 L.287 2 = 8 times . 8 L/2^K> 16 = 64 times 107 53 3= 3 times L.21-04 9 3= G'7 times If there be a composite number a little above the given mul tiplier, we may multiply first by that composite number, and then by the difference between it and the multiplier, and sub- tract the second product Iron) the first. MULTIPLICATION. 19 Ex. L.17 4 5 by 106=1082 11. L.15 12 4 by 47 12 108:=: 12X9 12. 27 8 3 by 82 13. It) 17 5 by 31 L.206 13 14.3cwt.2q. Ib. by Ip 9 15. 15 1 4 by 62 16. 2 ac. 3 r. 12 p. by 99 L.I 859 17 =108 times 34 8 10= 2 times L.1825 8 2 = 106 times 26. RULE IV. If the multiplier be large, multiply by lo, and mul- tiply the product again by io/ by which means you obtain an hundred times the given number. If the multiplier exceed 1000, multiply by 10 again ; and continue this operation farther if the multiplier require it ; then multiply the given number by the unit pLice of the multiplier ; the frst product by the ten place, the second product by the hundred place ; and so on. Add the product s, thus obtained, together. Example, L.34 8 2 by 3435 L. 34 8 2| by 5= L.172 1 7 }= 5 times 10 lOtimesL. 344 2 1 by 6= 2061 12 6= 60 times 10 lOOtimesL. 3441 10 by 4= 13764 3 4= 400 times 10 1000timesL,34410 8 4 by 3=103231 5 0=3000 times L.119232 1 10i=3465 times 3.L. 73 5 8 by 3159 4. 3 cwt. 1 qr. 3 Ib. by 3742 2. 412 12 7 by 64137 5. 7 feet 5 inches by 16897 3. 1238 by 21469 6. 1 acre 3 r. 12 p. by 4321 27. REDUCTION is the changing of any money, weight, measure, or the like, into a different denomination. When higher denominations are reduced to lower, the operation is called reduction descending, and is performed by multiplication. RULE. Multiply the highest denomination by the number of the next law er which it contains t and to the product add the number of the h^ive r de- nominativn, if any. Proceed in lik? manna- till you come to the hw:- nomination. 20 MULTIPLICATION. Example. Reduce L. 46 13 8| to farthings. L.46 It is easy to add the number of the lower at the 20 same time we multiply the higher, thus : 920 shillings in L,46 L.46 1 3 8-J 13 20 933 shillings in L.46 13 933 18 12 U196 pence in L.46 13 11204 8 4 11204 pence in L.46 13 8 44819 4 44816 farthings in L.46 13 $ 3 44819 farthings in L.46 13 8f 1. How many pence in L.375 12 6? 2. How many farthings in L.743265 19 9f ? 3. How many Ib. in 37 tons 2 cwt. 1 q. 17 Ib. ? 4. How many poles and yds. in 15 acres 3 r. 9 p.? 5. How many grains in 23 Ib. 1 1 . 7 3. 2 ^. 3 gr. ? 6. How many gallons in 13 quarters 2 bushels? 7. How many ells in 15 Scots acres 3 roods 12 falls ? 8. How many ounces in 3 cwt. 2 qr. 19 Ib. 3 oz. avoird. ? 9. How many * pounds and merks Scots in L.I 48 Ster. ? 10. How many seconds in 35 days 10 hours 15 minutes ? $i 28. Questions in Multiplication. 1. How many grains of wheat in 123 quarters, when each bushel contains 6? 5000 ? Answer, 664200000 gr. . lL A country contains 45 shires, each shire 73 parishes, each parish 148 houses, and each house 5 inhabitants; requir- ed the number of inhabitants? Answer, 2430900 inhabitants. 3. If an acre of meadow pasture 3 cows, and each co 17 pints of milk a day; how many pints of milk from ajJtadow of 43 acres in 19 days? Answer, 41607 pints. 4. What is the value of 75 yds. of cloth, at 17s. 9d. ? Answer, L.66 US * There are 12 pounds Scots and 18 merks Scots in a pound Sterling. DIVISION. 21 5. What is the value of 23 hhds. of wine, at L.23 12 6 ? Answer L.543 7 6. 6. .. of 38 cattle, #t L.5 9 3 ? Answer, L.207 11 6. 7. of 1385 stones of flax, at L. 13 9J ? Answer, L.955 1 5| 8. of 63 tons of vinegar, at L.I 5 12 6? Answer, L.9S4 7 6. 9. of 4768 yards of cloth, at 13s. 9d.? Answer, L.3278 . . 10. What is the weight of 29 hhds. at 5 cwt. 1 q. 14 Ib. ? Answer, 7 ton 15 c. 3 q. 14 Ib. j 1. __ - of 37 1 planks, at 4 cwt. 2 q. 9 Ib, ? Answer, 84 ton 19 c. 1 q. 7 Ib. 12. ^ of 29 jars, at 3 st. 2 Ib. 7 oz. Dutch ? Answer, 91 st. G Ib. 1 1 oz. 13 of 1000 guineas, at 5 dwt. 9 gr. ? Answer, 22 Ib. 4 oz. 15 dwt. 14. If the inhabitants of a village consume 1 boll 2 firlots 1 peck 2 lippies in a day, how much will they consume in a year? Answer, 581 b. 2 f. 3 p. 2 !. 15. How much corn will 36 men thrash in 45 days, at 5 bushels 3 gallons each man a day ? Answer, 1088 q. 3 b. 4 gr, 16. How many square feet in an area, 212 feet long and 59 broad? Answer, 12508. 17. How many square feet in the floor, roof, and walls of a room, 25 feet long, 18 broad, and 15 high ? Answer, 2190 feet altogether, 18. How many solid feet in a wall, 205 feet long, 3 thick, and 18 high? Answer, 11070 feet. 19. Required the weight of a plank 12 feet long, 2 broad, and Ji thick, at 25 Ib. the solid foot ? Answer, 750 Ib. 20. Required the price of the same at Is. 2d. the foot, and the expence of carrying it at a farthing the Ib. ? Answer, price L.I, 15s. carriage 15s. 7|d. DIVISION. 2.9. IN DIVISION two numbers are given, and it is required to find how often the first contains the second ; or to divide the first into as many parts as there are units in the second. Thus it may be asked, how often 21 contains 7 ; and the a DIVISION. gwer is exactly three times. The first number (21) is called the dividend ; the second (7) the divisor ; and the number ob- tained (3) the quotient. RULE 1st, Write the divisor and dividend in one line, and draw a stroke,) at each side of the dividend, to separate it from the divisor and quotient. 2d, Point off" as many figures from the left hand of the divi- dend as "Mill contain the divisor once or oftener ; find how many times these figures contain the divisor, and place the figure, \xhich expresses the number of times in the quotient. 3d, Multiply the divisor by the figure you have found, and place the product under the figures pointed off. 4th, Draw a line, and subtract the product from the figures above it. 5th, To the remainder anne% the next figure of the dividend, and point it off. 6th, Divide the number that now stands under the line, as before, and place the figure you obtain as the second in the quo- tient. Proceed in the same manner till all the figures of the dividend be pointed off. ... Examples. .... 65)30114(478 365)974932 (267Uy T 252 730 491 441 504 504 Remainder 1. 8725639 by 72 2. 451008 by 54 3. 7531230 by 81 4. 5486256 by 48 5. 506089 by 35 6. 7439455 by 85 7. 2917156 by 397 2449 2190 2593 2556 382 365 17 8. 427935288 9. 78583743 10. 180496548 11. 275764258 12. 52463742 13. 3996341955 14. 54S23715 by 582 by 648 by 7038 by 7294 by 6843 by 74691 by 10305 Note 1st, If there be a remainder, the division is completed by a vulgar fraction, whose numerator is that remainder, and its denominator the dj* DIVISION. 22 visor. Thus in example 2d, the quotient is 2671 and the remainder 17, and the quotient completed is 2671^. 2d, If the product of the multiplication, by any 'igure you have placed in the quotient, be greater than the figures from which it is to be sub- tracted, the figure in the quotient is too great ; and if the remainder af- ter subtraction be greater than the divisor, the figure in the quotient is too little. 30. A number which divides another without a remain- der is said to measure it ; and the several numbers which mea- sure another are called its aliquot parts. Thus, 2, 4, 6, 8, and 12, are aliquot parts of 24-. As it is often useful to dis- cover numbers which measure others, we may observe, 1st, Every number ending with an even figure, that is, with 2, 4, 6, 8, or 0, is measured by 2. 2d, Every number ending with 5, or 0, is measured by 5. 3d, Every number whose figures, when added, amount to an even number of 3's or 9's, is measured by 3 or 9 respectively. J 31. Contractions and Varieties in Division. first, when the divisor does not exceed 12, the computa- tion may be performed by multiplying and subtracting in your own mind, without setting down any figures except the quotient. Ex. 7)35868(5124 or 7)35868 5124 S2 Secondly, When the divisor is a composite number, we may divide successively by the component parts. If there be a remainder from the last division, multiply it by the first divisor, and to the product add the remainder of the first di- vision, if any ; the sum is the remainder required. 30114 by 63 6)75825 by 42 9)30114 7)12637 rem. 3 -j 7) 3^46 I 16 rem, Quot. 1805 rem. 2x6 J Quotient 478 33. Thirdly, When there are ciphers annexed to the di- visor, cut them off, and cut off an equal number of figures from "he dividend ; annex these figures to the remainder, 24 DIVISION; Ex. To divide 378643 by 5200, S2]00)3786]43(72f ig 1- S5 728 by 420 564 2. 50395 by 3700 3. 23462 by 9000 146 4. 58437 by 6700 104 4213 The reason will appear, by performing the operation at large, and comparing the steps. To divide by 10, 100, 1000, and the like; cut off' as many figures on the right hand of the dividend as there are ciphers in the divisor. The figures which remain on the left hand compose the quotient, and the figures cut off compose the re- mainder. 34. The tendency of the operations of multiplication and division are exactly opposite, and each of them furnishes a way of proving the other. To prove multiplication, divide the product by either factor* If the operation be right, the quotient is the other factor, and there is no remainder. To prove division, multiply the divisor and quotient to- gether ; to the product add the remainder, if any ; and, if the operation be right, the sum will be equal to the dividend. Otherwise, divide the dividend (after subtracting the remain- der, if auy) by the quotient. If the operation be right, it will quote the divisor. COMPOUND DIVISION. $ 35. RULE I. When the dividend consists of different de- nominations^ and the divisor is a simple number, divide the highest denomination as in simple division ; and reduce the re- mainder (if any ) to the next lower denomination, taking in, or adding, the given number of that denomination. Divide, this surt\ and proceed in ihr same manner with all the denomina- tions. The several part" of the, quotient thus obtained are of the same names as those of the dividend. DIVISION. 25 Ex. Divide L. s. 72)465 12 432 - 33 20 72)672(9 648 , -- 24 12 . - 72)296(4 288 L.465 12 8 by 72 d. L.s.d. 8 (69 4 1. L.9494 19 5 by 37 2. 5294 14 7 by 121 3. 45532 13 4 by 77 4. 76943 1 9 by 125 5. 345 cwt. 1 q. 8 lb. by 22 6. 214 cwt. 3 q. 9 lb. by 17 7. 1 09 acres 1 r. 35 p. by 31 8. 845 ac. 2 r. 11 p. by 13 9. 1 lb. 5 oz. 17 dwt. by 72 10. 12 lb. 9oz. 6 dwt by 39 11. 25 miles 6 f. 1 p. by 41 12. S7 m. 2 f. 25 p. by 19 13. 38 years J45 days by 7 14. 209 st. 12 lb, 3oz. D.b 99 8 Rem. If the divisor be a simple figure, the quotient may be placed at once under the several parts of the dividend. If the divisor be a composite number, we may divide suc- cessively by the component parts of the dividend : Thus* 8) L. 465 12 8 by 72-.8Xy 9) 58 41 L. 6 9 4 36. RULE II. When the divisor is in different denominations, re- duce both divisor and dividend to the lowest denomination, and proceed as in simple division. The quctient shohich is an aliquot part of both ; then reduce that by division to the denomination required, Ex. 1. Reduce L.31742 to guineas. 31742 Here we multiply by 20, which re- 20 duces the pounds to shillings ; and di- . vide the product by 21, which reduces 2 1 ) 634.840(302 30 the shillings to guineas. 48 42 6* 63 10 Answer, 30230 guineas and 10 shillings. JEar. 2. Reduce 15632 Ex. 3. Reduce L.I 472 to ' guineas to pounds. * merks. 15632 1472 21 3 15632 2)4416 half merk?; 31264- 2208 merks, 20)328272 shillings L. 16413, 12s. * A merk is two-thirds of a pound. 28 DIVISION. 1. How many guineas in L. 524798, 8s. ? 2. How many pounds in 847932 guineas ? 3. How many merks in L.54-698 ? 4. How many pounds in 54621 merks? 5. How many in 75189 moidores at.27s. ? 6. How many in 52396' Joanneses at 36s. ? - 7. How many Joanneses in L.I 1772? S. How many moidores in I .1^824? <). How many miles, &c. in 37985 yards ? 39. Questions in Division. 1. If 7412 eggs be packed in 34 casks, how many in each Answer, 21 2. How many casks will contain 175665 herrings, if eac] hold 735 ? Answer* 23 3. Divide a prize of L.I 5303 3 6 into 317 equal shares. Answer, L.48 5 6 4. A piece of silk, containing 37 yards, costs L.I 12 9 what is the price of a yard ? Answer, 5s. 9d 5. A farm is let at L.I 5 6 an acre, and the rent amount ti> L.388 176. How many acres does it contain ? Answer, 305 acres 6. What is the price of 1 Ib. flax, at L.4, 1 8s. a cwt. ? Answer, 10|d 7. If 1 5 tons of tobacco be equally packed in 26 casks, hov much will be packed in each ? Answer, 1 1 cwt. 2 q. 4 2 8 5 Ib 8. A pound of silver, Troy weight, is coined into 62 shil lings; what is the weight of a shilling? Ans. 3 dwt. 20-| gr 9. A pound of gold, Troy weight, is coined into 44- J guineas; what is the weight of a guinea ? Answer, 5 dwt. 9f -5 gr 10. A farm of 565 acres is let for L.466 2 6; how mucl does it pay an acre? Answer, 16s. 6d 11. What is the weight of a peck of corn, when 5 bolls firlots weigh 7 cwt. 3 qr. 6 Ib. ? Answer, 9* Ib 12. A field of 29 acres produces 160 quarters, 6 bushels, 7 gallons ; how much docs it produce an acre ? Answer, 5 qr. 4 b. 3 g, 13. A rectangular field of 7 English acres is 242 yards long; 'what is its breadth? Answer, 140 yards, 14. A cistern is 35 feet long, 19 broad, and contains, when full,. 73 15 cubical feet of water; what is its depth ? Ans. 11 RULE OF PROPORTION. 40. THE Rule of Proportion, (sometimes "called the Rule of Three) directs us, when three numbers are given to find a fourth, to which the third has the same proportion that the first has to the second, RULE. Multiply the second and third terms together, and divide their product by the first ; the remainder is the number required Ex. Required a fourth proportional to 273, 315, and 351 ? 273 ; 315 : : 351 351 273)110565(405 Answer. 1092 1365 1365 I. 399 : 3.57 : 874, 2. 3465 : 4351 ; 8130 3. 3311 : 2233 : 1204 4. 525 : 786 : 858 5. 9 : 17 : L.1Q 9 9 6. 25 : 39 : L..2.4 10 6 7. L.10 116: L.22 18 3 : : 6 8. L.109 10 9 : L.60 171:: L.50 5, RULE for stating the terms of a Question, 1st, For the third term of the proportion, write down, towards tha tight hand, that term which is of the same name with the number re* quired, and prefix 4 points, (thus : : ). 2t], Consider from the sense of the question, whether the answer ought to be greater or lev than the number you have written. Jf it ought to be greater, place the /fast of the other numbers towards the left hand, 3f thefrst term, and the remaining one in the middle, as the second ttrrr.* r* o C3 .'30 BULK OF PROPORTION. - if'?-, hi t-ivo points (thus : ). But if the answer ought S^. 3 !f,s, p.' .. f !lie snater term fir.it, ners, we repeat the rule in that manner, for the accommodation, of such teachers as incline to use it. 1. Write down that term which is of the same name with the number required, as the second term of the proportion,, and annex four points f them contains more denominations than one, they must be re- duced to the lowest denomination before the qtietion Is' 'wrought. 2. Reduce the third term to the lowest denomination, and the answer will be obtained in that denomination. When the third term is in more denominations than one, muliply by the second, according to the rule for compound multiplication, and the answer will be obtained in the different denominations of the article required, as shewn in compound di- vision. 3d. When there happens to be; a remainder after the division ; 'f the nature ..of the thing required admits of lesser denominations, reduce the re- jnainder.to the next lower denomination, and continue the division. 4th. When th'e rinmbers ar 3 and 3. s. d. 4 )126( 3 16 6th. If the first measure either the Second or third term, TVC may divide that term by the first, ad multiply the quotient fiy the remain? \i\g term. The nrod uct is the number required, 32 RULE OF PROPORTION. 6. If 12 acres 3 roods produce 78 quarters 3 pecks, how much will 35 acrers 1 rood 20 poles produce ? Answer, 216 qrs. 5 b. 1-J p. 7. If 5 acres 1 rood produce 26 quarters 2 bushels, how much will produce 47 quarters 4 bushels ? Answer, 9 ac. 2 r. 8. If a piece of plate, which weighs 5 oz* 16 dwt. cost L.'^ 10 9; how much will a piece that weighs 6 Ib. 7 oz. cost? Answer, L.I 8 63. 9. If a piece of plate, which weighs 2 ib. 5 oz. cost L. 12 8 li, what weight of plate may be afforded at the same rate for L.I 5, 9s. ? Answer, 3 Ib. 10. If a person , whose rent is L.I 45, pays L.12 13 9 of parish taxes ; how much should a person pay whose rent is L.378, 10?. ? Answer, L.33 2 4. 11. If a person whose rent is L. 500, pays L. 2 7 1 8, how* much is that person's rent who pays L.35 ? Answer, L.646 3 0}f 12. What is the value of 1 cwt. 2 qr. 17 Ib. of wool at 7s. 4d. a stone of 14 Ib. ? Answer, L. 4 16 lOf. 13. What is the value of 137 cwt. 2 qrs. lead, at L.9 18s, a fodder of 19| cwt?. Answer, L.69 16 l\l 14. If a garrison consume 38 7 ^ quarters of corn in a week, how much will they consume in 73 days? Answer, 401 J. 15 If 365 men consume 75 barrels of provisions, how n uch will 500 men consume in the same time ? Answer, i02f [ 16, If 36 men perform apiece of work in 12 daw, in what time will 16 men perform it? Answer, 27 days. 17- If 18 men perform a piece of work in 5 days, working 17 hours a days ; in what time will 27 men perform it ? Answer, 3 days 4 hours. 18 I borrowed 1 85 quarters of corn, when the price was 19s. how much should I pay to indemnify the lender, when the price is 17s. 4d. ? Answer, 202f ^ qrs. ly. If the carriage of 7 cwt. 2 qr. for 105 miles he L .1, 5s, how far may 5 cwt. 1 qr. be carried for the same money ? Answer, 150 miles. 20. How much land at 15s. an acre should be given in ex- change for 360 acres, at L.I 2 6 an acre ? Answer 540 ac. 21. A garrison has provisions for 8 months, at the rate of 15 ounces to each person a day, how much must be allowed a day in order that the provisions may last 9 months ? Answer^ 12] f 07. RULE OF PROPORTION. SB 22. A garrison of 1200 men has provision for 9 months, at the rate of 14 ounces a day, how long will the provisions last at the same allowance, if the garrison be reinforced by 400 men ? Answer, 6| months. 23. - How much must the daily allowance be, in or- der that the provisions may last 9 months after the garrison is reinforced ? Answer, 101 oz. 24. If a quarter of wheat afford 60 ten penny loaves, how many eight-penny loaves may be obtained from it ? Answer, 75 loaves. 25. How much tea at 8s. 4d, a Ib. should be given in bar- ter for 140 Ib. at 5s. 5d. Answer, 91 Ib, COMPOUND PROPORTION. 42. Sometimes the proportion depends upon several cir- cumstances. Thus, it may be asked, if 18 men consume G bolls corn in 28 days, how much will 24 men consume in 56 days ? Here the quantity required depends partly on the number of men, and partly on the time ; the question may therefore be resolved into the two following simple ones : 1st, If IS men consume 6 bolls in a certain time, how many will 24 men consume in the same time ? Answer, 8 bolls, 2d, If a certain .number of rnen consume 8 bolls in 28 days, how many will they consume in 56 days? Answer, 16 bolls. But instead of working the simple questions separately, it will generally be better to proceed by the following RULES, i-t, Write down that term which is of the same name as. ibc number required, for the third in the proportion, as directed in the simple rule. ad, Take two terms that are of the same name with each other y and state them for the first and second terms, as explained in the sim' pie rule. 3d, Take other two terms of the same name with each other > and ; tat e them in like manner directly under the former ; and if there be more terms in the question^ state the corresponding ones in the same manner- 4th, Multiply all the terms of the first column into each other for a di-visor ; and multiply all those in the second column into each other-, and thtir product by the third term ; the lust product is the dividend, and the quotient arising from this division is the answer, in the satziQ name as the third term, 34, RULE OF PROPOTION. The above question, according to this rule, is wrought as follows : Men 18 : 24 : : 6 bolls Days 28 : 56 114 36 144 120 Here we multiply 18 into 28 for a divisor, and 6 into the product of 24 by 56 for a dividend. 504 1344 6 504)8064(16 43. The following contraction is often useful. Having stated the proportion, write all the numbers which stand in the second and third columns (which are multiplied together for obtaining the general dividend) above a line, with the character X between each, and all the numbers in the first column (which are multiplied for the general divisor) under the line, with the same character between them. Then if the same number occurs above and below the line, dash i( out from both; and if there be two numbers, one above the line and the other below it a which have a common measure, di- vide them by that measure, and dash them out, placing the quotients directly above or under the numbers so dashed ; lastly, multiply the numbers that stand above the line together; and also those that stand under it, and divide the former pro- duct by the latter. Ex. Jf 18 men consume L,30 value of corn in 9 months, when the price is 16s. a boll, how many will consume L.54 value in 6 months, when the price is 12s. a boll? Value 30 : 54 : : 18 men 9 3 4 Months 6' : 9 #f X# X /# X IS Price 12:16 - 30X;&/^ 10 3 Here we observe/ that 6 under the line measures 54 above it, so we dash them out, and write the quotient 9 above, 54 ; next, because SO and 9 are both measured by 3, we dash them out, and" set down the quotients 1 and 3 ; then because 12 and 16 are both measured by 4, we dash them out, and set down the quotients 3 and 4 ; lastly, because there is now 3 both above and under the line, we dash them out. After &ULE OF PROPORTION. Which, 9, 4, and 18, remain above the line, and their product 648 being divided by 10, the only remaining number under the line, quotes 64-^ which is the answer. The same contraction may be used in every computation which requires several multiplications and divisions. 44. The monies, weights, and measures, of different conn- tries, may be reduced from the proportion which they bear to each other. Ex. If 112lb. avoirdupois make 104 Ib. of Holland, and lOOlb. of Holland make 89 of Geneva, and 110 of Geneva make 117 of Seville ; how many Ibs. of Seville will make 100 Ib. avoirdupois, and how many Ibs. avoirdupois will make 100 Ib. Seville ? oia ^j Qu. 1. 112: 104:: 100 Qu. 2. 104 : 112 :: 100 JOO : 89 89 : 100 ,-fo 10 i 110 : 117 117 : 110 In arranging the numbers, the terms of each proportion must be of equal value; and when the question is of the first kind, the antecedent, or first term of each proportion, must be of the same name as the consequent or second term of the for- mer one : thus 104lb. of Holland is the second term of the first proportion, and 100 Ib. of Holland is the first term of the second. But when the question is of the second kind, the con- sequent of each proportion must be of the same name as the antecedent of the former one. <) 45. Qu. 1. If 50 men consume 15 bushels of corn in 40.: days, how much will 30 men consume in 60 days ? Answer, 1S| bushels.' 2. On the same supposition, how long will 50 bushds iimm- tain 64 men ? Answer, 104^ days. 3. Bow many men may be maintained on 33 bushels for 80 days ? Answer, 55 ineih 4. If the interest of L.100 for 12 months be L.I, 10s. how- much is the interest of L.;<65 for 7 months? Ans. L.9 II ?i. 5. If the price of lo oz. of bread, when corn j> at 4*. 8d. a bushel, be l|d. what will be the price of 8 oz. when con is at 5s. 6d. ? Answer, Id. Iffq. 6. _ what will be the price of corn when the (> oz. loaf is sold for Id'.? Au**tr, ,Ss. ifd. 7. what will be'the weight of the sixpi me k>a* when corn is at 6s. ? Answer, 31% oz. RULE OF PROPORTION. 8. If the carriage of 12 cwt. 3 qr. for 36 miles be 17s., hovr much will be the carriage of 2 tons 5 cwt. for 81 miles ? Answer, L.6, 15s. 9. How far may 2 tons be carried at the same rate for L.5 ? Answer, 67| miles. 10. What weight at the same rate may be carried 20 miles for L.2, 5s. Answer, 3 tons 3 qrs. 11. If 2 horses consume as much corn as 5 oxen, and 12 Irorses consume 7 qfs. in 20 days, how much will 18 oxen con- sume in 25 days ? Answer, 5 qrs. 2 bushel?. 12. If a chest, 12 feet long, 8 feet broad, and 5 feet deep, hold L.54 value of corn, at 10(1. per peck, what value of corn, at yd. per peck, will a chest 10 feet long, 7 feet broad, and 6 feet deep contain? Answer, L.52, 10s. 13. If 98 feet of Paris make 92 of Lyons, and 105 of Ly- ons make 90 of Milan, and 80 of Milan make 104 of Den- mark, how many feet of Denmark in 1 00 of Paris ? Answer, 104-fQf. 14. * how many feet of Paris in 100 feet of Den- mark? Answer, 95||f. DISTRIBUTIVE PROPORTION. 46. If it be required to divide a number into parts, which have the same proportion to each other that several other gi- ven numbers have, we add these numbers together, and state the following proportion, As the sum t is to the particular numbers ': : So is the number required to be divided: to the st'veral parts sought. Ex. 1 Four partners engage to trade in company; A's stock is L.I ,0, !> 's L.320, C's' L 350, D's L.500, and they gain L.730. Il qu red how much belongs to each, if the gain be divided among them according to their stocks ? Rem. A's stock L.I. 50 1320 : 150 : : 730 : B's 320 1320 : 320 : : 730 : C's 850 1320 : 350 : : 730 : D's 500 1320 : 500 : : 730 : L. 82 19 1 120 1-6 19 4960 193 11 2720 2?6 10 3840 Whole stock 1 820 Proof L.730 This acn. i i, proved by adding the gains of the partners; the sum oi which will be equal to the whole gain, if the ope- RULES FOR PRACTICE. Cation be right ; but if there be remainders, they must be ad- ded, their sum divided by the common divisor, and the quo tient carried to the lowest place. If the money furnished by the partners had been employed for different times, each sum would have been multiplied in- to its respective time. I 2. The sum of L.200 was given for encouraging the culture 7 of flax, to be distributed among 6 persons who should raise the greatest quantities, in proportion to what they raised. A raised 456 stones, B 376, C 368, D 352, E 272," and F 224 ; what premium should each receive ? Answer, A L.44 K) 71, B L.36 14 4|, C L.35 18 9, D L/34 1 6, E L/26 11 3, F L,21 17 6. 3. Four merchants trade in company ; A advances L.550, BL.400, C L.270, D L.I 80, and they agree to divide the gain or loss in the same proportion. They buy goods to the amount of their stock, send them to sea, and insure L.1000. The goods are lost at sea, but they recover the L.I. 000 insu- red. How much should each receive, and what loss will each sustain? Ans. A recovers L.392 17 If, B L.285 11 CL.192 17 If, DL.128 11 5i; and A loses L.I 57 2 10?, B L.114 5 8f, C L.77 2 lOf, D L.51 8 6'f. 4. A advances L.I 00 for 5 months, B L.80 for 6 months, and C L.60 for 9 months. How should the gain, which a- mourits to L.44 16 2, be divided among them ? Ans. A L.14 14 9|, B L.14, 3s. C L.15 18 4 1 ,. RULES FOR PRACTICE. 47. The operations explained in the foregoing chapters comprehend the whole system of arithmetic. It remains to point out to the learner the rcudiest methods of applying them to the various sorts of computation which occur in business. SECT I. COMPUTATION OF PRICES. RULE I. J tfier :/>; jwn consists oj jariltinss < /; ; if it It farthing* tab ufouftb of the quantity ,- if a halj -n,'.- t tu -e a i-.- t lf ; ! f three favtbingi take a half and a jounb of the quantity* and 38 ItULES FOR PRACTICE. them. This gives the valuz in fence ; ^.vhich is then rt nn to pounds. Ex. 1. 4)37843 at -'d. 12)9460 f pence _ 2|0)78|8 4d. At >d. 3628* L.39 8 4| At id. 18141 12)54423d. *2jO)453|5 3 L.226 15 1. 786947 at >d. 4. 25894 at id. 2. 549829 at =}d. 5. 159872 at fd. '3. 723754 at |d. 6. 123456 at Jd. 48. RULE IT. JPfo/z the rate consists of pence only. If if be an aliquot part of a shilling, divide the quantity by the number of arii- rles that may be bought for a shilling. If the rate be not an aliquot part of a shitting divide it into tivo or more aliquot parts , and calcu- late for each separately; the sum of their respective values is the an- swer in shillings, which may be reduced by division to pounds. 1 penny is ^ of a shill. 5cl. is the sum of 4d. and Id. 2d. is of ditto 7d. is the sum of 6d. and Id. 3d, is i of ditto Sd. is twice 4d. 4d. is i of ditto 9d. is the sum of 6d. and 3d. 6d. is | of ditto lOd. is the sum of 6d. and 4d. lid. is the sum of 6d. 3d. and 2d. Ex. 1. 7423 at 4d.=|sh. Ex. 2. 4856 at lid. - -- - Or thus: 3)7423 at 6d. = ? 7 of Is. 2428 at Is. 4S56 2|0)24?|4 4 3d. = J of 6d. 1214 at Id. 4048 L.123 14 4 2d.=r|of6d. 8094 . ---- . 4451 4 4451 4 L.222 1J 4 L.222 11 4 The second example is wrought by adding the values at 6d. 3d. and 2d. or by subtracting the value at Id. from the value at Is. 1. 53784 at Id. 7. 9372 at 7d. 86 at 3d. 9. 0999 at 9d. 4. 98765 at 4d. 10-. 17053 at lOd. 5. 54321 at 5d. 11. 781(io i:t lid. 6. 5^221 at 6d. 12. 2068 at Sd. RULES FOR PRACTICE. 39 49. RULE III. When the rate consists of pence and farthings, find the value of the pence by the last rule, and that of the farthings from the proportion they bear to the pence , then reduce the sum to pounds. Ex. 1. 2842 at at 3d.=i of Is. .=i ofSd. 7106 177 7J Ex. 2. 2772 at 7d. at 6d. =i of Is. 1386 Ji 7 d. = i of 6d. 346 6 2|0)88|8 l.| 2)0)173)2 6 L.44 8 li L.8G 12 6 In the computation it is sometimes convenient to join some of the pence to the farthings : Thus, in Example 2d, we reckon the value at 6'd, and at lid. which make 7 id. 1. 278:, at 6Jd. 2. 5479 at 4ld. 3. 5372 at 7f d. 4. 86285 at 5. "4298 at 6. 57392 at 9f d. 2|d. 50. RULE IV. When the rate consists of shillings oa/y, multiply the quantity by the number of shillings* and divide the product by 20 / Or, if the number of shillings be even, multiply by half ths number, and divide the p' o- uct by 10. Ex. 1. 4573 at 1 3s. Ex. 2. 7543 at 14s. 13 7 1|0)5280]1 L.5280, 2s. This answer might have been set down at once, by doubling (for shillings), the unit figure of the first multiplication, G. 32648 at 15s. 7. 13782 at 4s. 8. 12345 at 12s. 9. 67899 at 18s. 10. 13579 at 17s. 2|0)5944|9 L.2972, 9s. 1. 35786 at 16s. 2. 31490 at 13s. 3. 25735 at 11s. 4. 89642 at 8s. 5. 77777 at 7s. 51. RULE V. When the rate conoids of shilling t and lower deno- minations, multiply the quantity by the shillings, and find ths value of the lower denominaticnsfrom the proportion they bear tQ the shillings ; then reduce thsir sum to pounds. RULES FOR PRACTICE. . 4-258 at 17s. 3d. Ex. 2. 5482 at 12s 17 12 2-9606 65784- 4258 3d.- | of Is. 1370 6 of Is. 10646 )d. = of3d. 685 3 2jO)7345jO G 2|0)6783J9 9 L.3672 10 6 L.3391 19 9 1. 36598 at 8s. 7d. 6. 678421 at 6s. 9|d. 2. 5427S at 4s. 8d. 7. 43266 at 13s. 8d. 3. 37581 at 15s. 4d. 8. 7860 at 4s. 4f. 4. 13759 at 12s. 7|d. 9. 14896 at 12s. 2*-d. 5. 23581 at 5s, lOjd. 10. 478 at 15s. 6jdi $ 53. RULE VI. /f7ii? /,6 68. PROBLEM I. To reduce mixed nu./ibers to improper fractions : Multiply the integer by the denominator of the fraction* and to the pro- duct add the numerator. The sum is the numerator rf the improper fraction sought, and is placed above the given denominator. Ex. 5f y -1. 123-f 5 integer 2. 76^ 3 denominator 3 555 1 4. 1207| 15 product 5. 63 J& 2 numerator given 6- 17 numerator sought. Integers may be expressed in the form of improper fractions E 2 52 VULGAR FRACTIONS. Laving any assigned denominator ; the numerator is obtained by multiplying the integer into the denominator. 69. PROBLEM II. To reduce improper fractions to whele or mixed numbers .* Divide the numerator by the denominator* Z*. W=6H I- W 17) 11 2(fi{? 2. \y 102 3. 5 5 * fS 10 5. YV 7 $ 70. PROBLEM III. To reduce fractions to lower terms : Divide both numerator and denominator by any . number which measures botb> and place the quotients in the form of a fraction. E*> m=*j=i- Here we observe that 1 85 and 360 are both measured by 5, and the quotients form f J, which is a fraction of the same va- lue as ||, and in lower terms. Again, 27 and 72 are both measured by 9, and the quotients form , which is still of e- qual value, and in lower terms. The observations 30 will be useful for discovering the measures, To reduce a fraction to the lowest possible terms, we must divide the numerator and denominator by the greatest number which measures both. To find the greatest common measure of t\vo numbers, divide the greater by the less, and the divisor by the remainder continually, till nothing re- mai-n ; the last divisor is the greatest common measure. Ex. What is the greatest number which measure 475 and 589? 475)589(1 475 114)475(4 456' Ans. 19. -- and 4| is reduced to the lowest 19)114(6 terms, by dividing the,numera- 114 tor and denominator by 19, which comes to ||. $ 71. PROBLEM IV. To reduce fractions having different ^nomi- nators to ethers of equal value tbat have the same denominator : ist, Mult -ply the numerator of each fraction by all the denominators except its own. The products are numerators to the several new frac- tions sought* VULGAR FRACTIONS. 53 id, Multiply oil the denominators into each other ; the product is ths common denominator* Ex. |, J,andf = S$8, f|g,andjjg. 4 X .9 X 8 = 288 first numerator 7X5X8 = 280 second numerator, \ 3X5X9= 1 35 third numerator. 5x9X8 = 560 common denominator. 1. Reduce f and T 7 g to a common denominator. 2. Reduce , f , and T 4 T to a common denominator. 3. Reduce f , , ^, and T 2 ^ to a common denominator. If we can find any number that is measured by all the given denomi- nators, that number may be placed for the common denominator ; and* in order to obtain the new numerators, we divide the common denomi- nator by the given denominators of the fractions, and multiply these quo- tients by the given numerators. If the articles given for any operation be mixed numbers, they are re- duced to improper fractions by problem I. If the answer obtained be an improper fraction, it is reduced to a mixed number by problem II. And it is convenient to reduce fractions to lower terms, when it can be done, by problem III. which makes their value better apprehended, and facili- tates any following operation. The reduction of fractions to the same denominator by problem IV. is necessary to prepare them for addition - to a common denominate? j add the numerators, and place the sum above the denominator. Ex. 1. J-+? = fJ + i jsjr.2.. f + i + f = i and by prob. II. = Iff, 1. What is the sum off and ^ ? 2 off land 12? 3. of |, f , and T y > 4. of s, , arid T ^J .5. off, |, f, and f *> 6. of 3|, 4f , and 10 ? SUBTRACTION OF VULGAR FRACTIONS. 73. RULE. Reduce the fractions to a common denominator ; sub- tract the numerator of the lesser fraction from the greater t and place the remainder above the common denominator. Ex. Subtract f from A. Remainder J|. E 3 5-i VULGAR FRACTIONS. To subtract mixed numbers, proceed with the fractions by the fore- going rule, and with the integers as in simple subtraction. II' the nu- merator of the fraction in the subtrahend exceed that in the minuend, rlbrrow the value of the denominator, and repay it by adding 1 to the u- nit place of the subtrahend. When the minuend is an integer, subtract the numerator of the subtrahend from the denominator, and place the remainder above the denominator, for the fraction of the remainder re- quired. i - *n 7 ~ Is f F -*- 5J J Ex. Subtract 145^ from 248f . 24*f? b 7 problem IV. 71. 145f I02f| 1. What is the difference between f and f ? 2. -- : -- between *f and T 5 5 ? 3. --- between / T and T T ? 4. --- between 12 j and h ? 5. --- between 19 and 5$ ? (>. -- s -- between 15] and 12^ ? MULTIPLICATION OF VULGAR FRACTIONS. 74. RULE. Multiply all the numerators together for the numerator oft/H' product j and all the denominators together for the denominator of tb ' roduct. Note 1st. To multiply an integer by a fraction, we multiply it by the numerator, and divide the product by the denominator. 2d, To multiply an integer by a mixed number, we multiply it first by the integer, and then by the fraction, and add the products. 3d, To multiply a mixed number by a fraction, or two- mixed num- bers, we reduce the mixed numbers to improper fractions, and proceed by the general rule j and, if the product be an improper fraction, re- duce it to a mixed number. 4th, When two or more fractions are connected by the word of, as f of JJ-, the expression is called a compound fraction. It is reduced to a sim- ple fraction by multiplying all the numerators together, and all the de- nominators together. 5th, When several vulgar fractions are to be multiplied into each other, 'it may be convenient to abbreviate the terms, as directed 43. 6th, When the multiplier is a proper fraction, the product is less than the multiplicand. Ex. 1. j X ? = J? Ex. <1. Sf X 7f ~ J IS 2 = 65 2 V 2 X 5 = fo num. 8f ~ 4 , ; - by prob. I. 3X7 = 21 denom. 1\ = V by ditto. 42-X-31 = 1302 num. 5 X 4 = 20 denora, VULGAR FRACTIONS. 55 1. -I by j. 4. 75 by f. 7-721 by f. g. 'by T 7 . 5. 12 by 7. 8. 5 by 7?,. s. iV 5 ! by T i T - 6 - 121 b y ^ 9 - 12 A ^ 6>, DIVISION OF VULGAR FRACTIONS. $ 75. RI/LE. 1st, Multiply the numerator of the dividend by the denominator of the divisor. The product is the numera- tor of the quotient. 2d, Multiply the denominator of the dividend by the numerator of the divisor. Thi' product is ike denominator of the quotient. Or. invert the divisor , and proceed am in multiplication. A fraction is said to be inverted, when the numerator is pla- ced for the denominator, and the denominator for the numera- tor ; and the fraction obtained is called the reciprocal of that from which it was formed. Thus | is the reciprocal off, Ex. Divide f by J Quotient Jf 3 X 9 - 18 5 X 7 - 35 Note 1st, When the dividend is an integer, we multiply it by the de-* nominator of the divisor, and divide the product by the numerator. . 2d, When the divisor is an integer, and the dividend a fraction, we multiply the denominator by the divisor, the p-odurt is the denominator of the quotient, and is placed under the given, numerator. 3d, When the divisor is an integer, and the dividend a mixed number, v.e divide the integer, and annex the fraction to the remainder; we then reduce the mixed number, thus formed, to an improper fraction, and multiply its denominator by the divisor. 4-th, In other cases, when the given terms are mixed numbers, wo re- duce them to improper fractions. 5th, When the divisor is a proper fraction, the quotient is greater than the dividend. 1. Divide f by f. 4. 72 by f. 7. 326 & by 7. 2. -A by T V 5. 148 by f. 8. 3 by 2f. 3. IB! by M. 6. Ijby5. 9. S|by2|. APPLICATION OF VULGAR FRACTIONS. 76. PHOB. I. To reduce lower denominations and their fractions to fractions of higher, place the given number for the numerator, and Me value of the higher for the denominator. Ex. 1. Reduce 7d. to a fraction of a shilling. Ans. T 7 g . 2. Reduce ?d. to a fraction of a pound. Ans. r | 5 . 3. Reduce 15s. 7d. to a fraction of a pound. Ans. ||J. 4-. Reduce | of Id, to a fraction of L.I. Ans. or , 56 VULGAR FRACTIONS. Ex. 5. Reduce 3d. to a fraction of a pound. Ans. ^ or 7 ^. 6. Reduce 2 q. 7 lb. to a fraction of 1 cwt. Ans. /y^ or T s s . Note 1st, If the given quantity be in more denominations than one we reduce it to the lowest: thus,, 15s. 7d. in Ex. 3d, is reduced to 187d, ; and 2 q. T lb. in Ex. 6th, to 63 lb. 2d, If a fraction be given, we multiply its denominator by the value of the higher denomination. Thus, in Ex. 4th, we multiply the denomina- tor 9 by 24*0, the value of a pound, and the product 2160 is the denomi- nator of the fraction sought. 3d, If a mixed number be given, we reduce it to an improper fraction, and proceed as directed in the last note. Thus, in Ex. 5th, we reduce 3| to *-f of a penny, and then to T T T % of a pound. 1. Reduce 13s. 3d. to a fraction of L.I. 2. Reduce 3s. 9|d. to a fraction of ditto. 3. Reduce 1 Is. 5Jd. to a fraction of ditto. 4. Reduce 3 q. 21 lb. to a fraction of 1 cwt. 5. Reduce 3 oz. 18 dwt. to a fraction of I lb. Troy, 6. Reduce 1 rood 17 poles to a fraction of an acre. 77. PROB. II. To find the value of fractions of higher deno- minations in terms of lower ones, multiply the numerator by the value of the given denomination, and divide the product by the denominator : If there be a remainder, multiply it by the value of the next denomination, and continue the division. Ex. 1. Required the va Jue of I tf of L.I,? 17 20 _ s. d. 60)340( 300 5 8 Contracted. 40 12 60)340. "I 5.40 ^__ 12 ( 5 60)480 480 f 60)480 I 8J Ex. 2. Required the va* lue of | of 1 cwt. ? 8 4 qrs. lb. 9)32( 3 15f 27 5 28 9)140 9 50 .45 * of L.I. * |s of ditto, S. 4. |1 of lib. Troy, VULGAR FRACTIONS. 57 5. li of a ton, 9. of a yard. 6. |f of an acre. 10. -f- s of a year. 7. ^ of a mile. 11. Jf of a quarter corn. 8. f'of a guinea. 12. ^ of a foot. 78. Any question, where the given numbers are in differ- ent denominations, may be wrought by the arithmetic of vulgar fractions, by reducing the lower denominations to frac- tions of the higher, and performing the operations necessary for the solution of the question, according to the above rules. In the rule of proportion, whether simple or compound, the questions are stated as in the arithmetic of integers, and the multiplications and divisions performed as directed in the arith- metic of vulgar fractions, $74, 75. Questions in Vulgar or Decimal Fractions. I. What is the sura of f, 4, if, and | of L.I ? Answer, y c 5 , or L.3 8 9. * 2. A pillar is built of 4 stones, weighing 4| cwt. Si cwt. 5^ cwt. and 6^ cwt. ; how much does it weigh altogether ? Answer, 19^, or 19 cwt. 23 Ib. *' 3. Required the weight of 4- pieces of plate, weighing 3| oz, 4| oz. 7f oz, and 8^ oz, Troy ? Answer, 23ff oz. or 1 Ib. 11 oz. ISdwt. lgr. * 4. From a cask of wine, containing f of a h.d., there was drawn } of a hd. and afterwards | of a hd. how much re- mained ? Answer, ^ 5 5 ,' or 5 gallons. * 5. What is the difference between f of ^ of a pound and ^ of a shilling ? Answer, T1 \ L. or Ifd. 6, What is the value of | of an acre, at T 9 S of L.I an acre ? Answer, L.J, or 8s. 5|d. ' of> i 5 s J ards at z5 of L.I a yard ? Answer, L.I 5 5 5 , or L.I 2 llf. * 8. of 2f yards at ^ of L.I a yard ? Answer L.|f, or ?s. ld. * 9. of 55^ yards at f of Is. a yard ? Answer, 30fs. or L.I 10 11||. 10. What is the weight of 12| bolls, at 8^ stones, Dutch weight, a boll f Answer, 1 lOf J st. or 1 10 st, 14 Ib. 12 J oz. II. Required the value of a carpet 5\ yards long, 3^ broad, at 3s. a square yard ? Answer, 66 Js* or L.3 6 6. * 12. How much tonnage in 30 boxes, each 5 feet 5 inches long, 2 feet 3 inches broad, and 14 inches deep, allowing 40 cubical feet to a ton ? Answer, 10j 8 3 5 F tons. 5S DECIMAL FRACTIONS. * 13. What will IJi Ib. cost, at the rate of L.6 a cwt.? Ansv.er, i 4 . 5|d. 14. Divide L.3- 8 7 - into 49f shares. : n,wer, ^ or Is. 3d. a share. 15. Divide 7^ acres into 5| shares. Answer, l T 5 ff . or 1 ac. 1 ro. 10 p. a share. * 16. Divide ^ of 1 cwt. into 12| shares. Answer, T ^ cwt. or 10 2 6 , oz a share. I?. What is the breadth of a roof whose length is 1 ; i feet, and ar >a 2:8| feet ? Answer, 121 f ee t. 18. if J of 1 Ib. cost f i of L.I, what will 1 cost ? Answer, L.$j, or 15s. 3|d. 19. If 2| yards cost 4|s., what will -fa cost ? Answer, fls. or 4s. llfd. 20. If 12 men perform | of a piece work in 6| hours, in what time will 20 men perform the rest of it ? Answer, 1 hour 18 minutes. DECIMAL FRACTIONS. NOTATION. 79. In decimal fractions unity is supposed divided into ten parts, and each of these is subdivided into ten parts, and so on. The notation of decimals is the same as that of in- tegers, only they are distinguished by a point called the deci- mal point t or separatrix, placed to the left hand, which sepa- rates them from integers, when they are connected together. The figure on the right-hand of the decimal point signifies tenth-parts, the next hundredth-parts, the next thousandth- parts, and so on. .7 Signifies seven-tenth parts, .07 seven- hundredth parts. .37 three-tenth parts, and seven-hundredth parts; or thirty- seven -hundredth parts. .259 two tenth parts, five-hundredth parts, and nine- thousandth parts ; or 259 thousandth parts. 3.7 . three of an integer and seven-tenth parts. 3.007 three of an integer and seven-thousandth parts. Note 1st, Ciphers placed on the right hand of a decimal fraction have no signification ; but when placed on the left hand, each cipher diminish es the value ten times. DECIMAL FRACTIONS. 59 2d, Decimals may be expressed in the form of vulgar fractions, by wri- ting the given figures for the numerator, and 1, with as many ciphers an- nexed as there are decimal places, for the denominator. 80. PROB, L To reduce 'vulgar fractions to decimals, annex a ci- pher to the numerator-, and divide it by the denominator , annexing a ci- pher continually to the remainder. x. 1 Jf =.16 Ex. 2. ,&= .083 Ex. 3. 8 ^= .148, 75)120(.l6 60)500(.083 27)M)(.143, 75 480 27 450 *200 130 450 180 108 * 20 220 216 *40 Note 1st, From these examples we may distinguish the several kinds of decimals. Some vulgar fractions may be reduced exactly to decimals, as hi Ex. 1. and these are called terminate decimals. Others cannot be exact- ly reduced, because the division ;'lv-.a>3 leave a fettu-.inder. These are call- ed interminate decimals. If the same figure returns, they are called re- peaters, as in Ex. 2. If two or more figures return in regular succession, they are called circulates, as in Ex. 3. If this regular succession goes on from the beginning, as in Ex. 3. they are called^.we repeaters or circulates. If otherwise, as in Ex. 2. they are called mixed repeat t->* or circulate.';, and the figures prefixed 10 those in regular succession are called the finite parts. Repeating decimals are commonly distinguished by a duaL through the re- peating figure ; and circulates by a cow?//, or other mark, at the begin- ning and end of the circulating figures. 2d, ! f it be necessary to annex more ciphers than one to the denomina- tor, before we can begin the division, we prefix as many to the significant figures of the quotient. This is done in Kx. ;. 3d, In like manner, v.htu there is a remainder Jeft in the division of in- tegers, we may extend the quotient to a decimal, instead of completing it by a vulgar fraction. 12 7 8 7115 8 11 25 SI> 25 9> 5tf> T 1T> JI* $81. Fsi-ii'-rM ... .- i iMeiower denominations to decimals of higher. her i lower ti nomination and .--"v :e <7 by the 'value of the f-i^bfr 1 1 hi* there <>r i. . r^t ... rtom'.ii.tiom, oegin at the low- tsi . i.- '- !< . viluct 5 c\vr. 2 qr. SI li' to ;. t-.i-ci:),'! of r ton. 20J . ' 75 ilt . r to rf-ciui . :,' . . ';U- 60 DECIMAL FRACTIONS. nex a cipher, and divide by 28, the value of 1 qr. This gives c75 ; to which we prefix 2, the number of quarters. Then we reduce 9.75 qrs. to a decimal of 1 cwt. by dividing by 4, the value of 1 cwt. and it comes to .6875. Lastly, 5.6875 cwt. is reduced to a decimal of a ton by dividing by 20, and comes to .284375. 1. Reduce 5s. 9d. to a decimal of a pound. 2. 7s. 10|d. to ditto. 3. 3 cwt. 3 qr. 14> Ib. to a decimal of a ton. 4. 9 oz. 12 dwt. to a decimal of I Ib. Troy. 5. 2 oz. 3 dr. to a decimal of 1 Ib. avoirdupois. 6. 3 r. 17 poles to a decimal of an acre. The examples for the corresponding rule in vulgar fractions, 76, may also be reduced to decimals, and the above exam- ples to vulgar fractions. 82. PROBLEM III. To value a decimal fraction in lower denomina' tions : Multiply it by the value of the given denomination^ and cut off as many decimals from the right hand of the product as there are fi- gures in the multiplicand The figures on the left hand are integers of the next lower denomination ; multiply the figures cut off by the value of the next lower denomination, and proceed in the same manner till you. come to the lowest. Ex. What is the value of .425 1. .375 of L.I. of L.I ? 2. .4-965 of ditto. .425 3. .789 of ditto. 20 4. -3375 of an acre. . 5. ,009375 ofatoD. sh. 8.500 6. .03125 of a Ib. avoird. 12 7. .015625 of alb. Troy. 8. .4125 of 1 oz. ditto. d. 6.000 9. .315 of a cwt. Ans. 8s. 6d. 10. .24 of a mile. ARITHMETIC OF TERMINATE DECIMALS. 83. The value of decimal places decrease like that of in- tegers, ten of the lower place in either being equal to one of the next higher; and the same holds in passing from deci- mals to integers. Therefore all the operations are perform- ed in the same way with decimals, whether placed by them- selves, or annexed to integer;-, us with pure integers. The DECIMAL FRACTIONS. ^ 61 only peculiarity lies in the arrangement and pointing of the decimals. 83. In ADDITION and SUBTRACTION, set down the num- bers, placing the decimal points under each other ; by which means tenth parts will stand under tenth parts, hundredth parts under hundredth parts, and so on; then proceed as in integers. 32.035 from 13.348 from 12.248 116.374 take 9.2993 take 10.6752 12.3645 4.0487 1.5728 321.4035 1. What is the sum of 13.357, 149-82, 1.0009, -235, and .027 ? 2. the sum of 237.5, 23.75, .2375, .0273, and 7230? 3. the difference of 13.375, and 8.649 ? 4. the difference of 19.002, and .7456 ? 84. In MULTIPLICATION, allow as many decimal places in the product as there are in both factors. If the product has not so many places, supply them by writing ciphers on the left hand* Ex.1. 1.37 Ex. 2. 43.75 Ex. 3. .1572 1.8 .48 .12 35000 .018864. 17500 2.466 21.0000 1. 19.25 by .324 5. .012 by .034 2. .356 by 9. 18 6. 13.5 by .72 3. 123.4 by .053 7. 3.9 by 5.02 4. S2.5^ by 7.48 8. .05 by .002 To multiply decimals by 10, move the decimal point one place to the right j to multiply by 100, 1000, or the like, move it as many places to the right as there are ciphers in the multiplier. 85. In DIVISION, point the quotient, so that there may be an equal number oj decimal places in the dividend as in the di- visor and quotient together. Thejirstjigure of the quotient is always at the same distance from the decimal point, and on the same side as thejigure of the dividend, which stands above the unit place of the first product. x F DECIMAL FRACTIONS. Ex. .12) 17.28(144 ]. .12) 1.728(14.4 2. .12) .1728(1.44 3. .12)1728. 4. 1728.00(14100 5. 1.2)17.28(14.4 6. 12).1728(.0144 7. .19).323 .27)33.75 8.4).3l6008 123).979326 .52)38896 1.25)1137.5 6.4)15.32 Note 1st, If the division leave a remainder, the quotient may be ex- tended to more decimal places ; but these are not regarded in fixing the decimal point. 2d, To divide by 10, 100, &c. move the decimal point as many places to the left hand as there are ciphers in the divisor. APPROXIMATE DECIMALS. 86. It has been shown, 79, that some decimals, though extended to any length, are never complete; and others, which terminate at last, sometimes consist of so many places, that it would be difficult in practice to extend them fully. In these cases we may extend the decimal to three, four, or more places, according to the nature of the articles, and the degree of accuracy required, and reject the rest as inconsiderable. In this manner we may perform any operation with ease by the common rules, and the answers we obtain are sufficiently exact for any purpose in business. Decimals thus restricted are called approximates, and are denoted by placing the mark + after the last figure. If the next figure would exceed five, the approximate is more nearly expressed by adding I to the right hand place, and annexing the mark ; thus, 7348, re- istrictedto 3 places, is 734 + or rather 735 . 87. To multiply approximates. Ex. To multiply .8278+ by .2153-f. Meth. 1. Meth. 2. .8278+ .8278 .2153+ .3512 16556 In Method 1. we have begun at the higher place of the multiplier. All the figures on the right hand are uncertain, because the carriage from the omitted figures of the mul- tiplicand would change them ; and therefore they may be left out in the operation. This is most con- veniently done by inverting the multiplier, as in method 2, and be- ginning each line of product by the jnxtltiplication of that figure in the multiplicand, which stands above the 41390 24834 413 24 .1782J2534 .1782 DECIMAL FRACTIONS. 65 figure of the multiplier we are using, including always the carriage from the right hand place. The same method may be used when the factors are terminate, if only a few places be required in the product. It is necessary to extend the product one place further than the number of place? required, because the last figure cannot be depended on. 1st, Multiply .7653 by .3512, so as to obtain 4 decimal places in the product. 2d, Multiply 14.251 by 9.103, so as to obtain 3 decimal places in the product. 88. To divide approximates. Ex. To divide .79864327 4- by .3724- + .3724+)79864237-K.2144 Or thus: .3^)79864237(.214i 744J8 7443 53*84 538 37J24 372 16602 166 14896 148 7063 18 4896 14 2167 4 Here all the figures on the right-hand of the line are uncertain ; for the right-hand figure of the first product 7448 might be altered by the carriage, if the divisor were exterided ; and all the remainders and divi- duals that follow are thereby rendered uncertain. We may omit these useless figures; for which purpose we dash a figure on the right hand of the divisor at each step, and neglect it when we multiply by the next fi- gure of the quotient, but we include the carriage. 89. Shillings, pence, and farthings, may be easily reduced to decimals of three places by the following rule. Take one half of the shillings for the first decimal place ; and for the two next places, the number of farthings in the remainder increased by 1, if it amount to 24, or upwards; by 2, if it amount to 48, or upwards ; and by 3, if it amount to 72, or upwards. Ex. L.3 12 3| = L. 3.614 1. L.5 7 3| 5. 17s. lOd. 4 8 9| 4.44 2. 8 4 9| 6. 15 5 17 2 .858 3. 3 11 31 7. 13 7| 11 101 .592 4. 5 18 10 8. 18 5J 90. Decimals of Sterling money of three places may easily be reduced to shillings, pence, and farthings, by the following 64 DECIMAL FRACTIONS. rule. Double the first decimal place for shillings, and if the second place be 5 or upwards, add 1 thereto for shillings, then divide the second and third decimal places, or their excess a- bove 50 by 4, first deducting 1, if it amount to 2 or upwards ; the quotient is pence, and the remainder farthings. Ex. L.3 .639 = L.3 12 9J 1.L.4 .581 5. .738 .719 14 4| 2. 2 .408 6. .977 2 .861 2 17 2| 3. 2 .4-53 7. .041 1 .191 1 3 10 .4. 7 .447 8. .228 $ 91. As the arithmetic of INTERMINATE DECIMALS is a suh- ject of curiosity rather than of use, we shall only at present give the rules by which they are reduced to vulgar fractions ; and by means of which any question where they occur may be wrought according to the arithmetic of vulgar fractions. RULES For reducing interminate decimals to vulgar frac- tions. I. If the decimal be a pure repeater, place the repeating fi- gure for the numerator, and 9 for the denominator. II. If the decimal be a pure circulate, place the circulating figures for the numerator, and as many 9's as there are places hi the circle for the denominator. III. If there be ciphers prefixed to the repealing or circula- ting figures, annex a like number to the 9's in the denominator. IV. If the decimal be mixed, subtract the finite part from the luhole decimal. The remainder is the numerator ; and the de- nominator consists of as many 9'*' as there are places in the circle, icilh as many ciphers annexed as there are Unite places before the circle. Til ll<5 ", ^ fiO 25." C 7 in us, tdOyVsCf 6 From the whole decimal 23562 we subtract the finite part 235 and the remainder 23327 is the numerator. For a practical exercise in decimal fractions, the same ques- tions may be taken as were proposed in vulgar fractions, o 78, and the numbers reduced to decimals. In those marked *, some of the decimals are interminate; and the questions may be wrought by approximate decimals. TABLES of COMPOUND $ 92. TALE I. Amount INTEREST and ANNUITIES. of L.I Compound Interest. K CD 3 P. Ct 4 p. Ct 5 P. Ct. 1 1.03000 1.04000 105000 2 1.06090 r. 08160 1.10250 3 1.09273 1.12486 1-15762 4 1.12551 1.16986 1-21551 5 1-15927 1.21665 1.27628 6 1.19405 1.26532 1.34010 7 1.22987 i'3i593 1.40710 8 1.26677 1.36857 1.47746 9 1.30477 1-42331 I.55I33 1C 1.34392 1.48024 1.62890 ii 1-38423 t-53945 1.71034 12 1.42576 1.60103 1.79586 13 1.46853 1.66507 1.88565 14 1.51259 1.73168 r-97993 15 r -55797 1.80094 2.07893 16 1.60471 1.87298 i 18287 *7 1.65285 1.94790 1.29202 18 1.70243 2.02582 2.40662 19 I-7535I 2.10685 2.52695 20 1.80611 2.19112 2.65330 3 3 p. Ct.| 4 p. Ct, 5 P- Ct. 21 1.86029 2.27877 2.78596 22 1.9161,0 2.36992 2-92526 23 1-97359 2.46472 3.07152 24 2.03279 2.56330 3-22510 25 2.09378 2.66584 3-38635 26 2.15659 2.77247 3.55567 2 7 2.22129 2.88337 3'73346 28 2.28793 2.99870 3.92013 29 2-35657 3.H865 4.11614 30 2.42726 3.24340 4.32194 31 2.50008 3-373I3 4-53804 32 2 575O8 3.50806 4.76494 33 2.65234 3-64838 5.00319 34 2.73191 3-7943' 5-25335 35 2.81386 3.94609 5.51601 36 2.89828 4.10393 5.7918* 37 2.98523 4.26809 6.08141 33 3.07478 4.43881 6.38548 39 40 3.167094.61637 3.262O4I4.8OIO2 6.7047.? 7-03999 TABLE II. Present Value of L.I Compound Interest. K s 3 P- Ct. 4 p. Ct. 5 P. Ct. I .970874 961538 .952381 2 .942596 924556 .907029 3 .915142 .888996 .863838 4 .888487 .854804 .822702 5 .862609 .821927 .783526 6 .837484 790315 746215 7 .813092 -759918 710681 8 .789409 .730690 676839 9 .766417 .702587 .644609 1C .744094 .675564 .613913 ii -722421 .649581 584679 12 701380 624597 556837 *3 680951 600574 530321 14 .661118 577475 505068 15 .641862 555265 .481017 i 6 .623167 533908 458112 '7 605016 513373 436297 18 587395 493628 415521 J 9 .560286 474642 395734 20 553676 45638? 376889 K S 3 p. Ct.| 4 p. Ct. 5 P- Ct- 21 537549 -438834 35894* 22 .521893 .421955 341850 23 .506692 .405726 325571 24 491934 .390121 310068 *5 .477606 375II7 295303 26 .463695 .360689 281241 27 450189 .346817 267848 28 .437077 333477 255094 2 9 424346 320651 .242946 3 .411987 308319 231377 3i 399987 .296460 .220359 3* 388337 285058 .209866 33 377026 274094 .199873 34 .366045 .263552 J 9Q35^ 35 355383 '253415 .181290 36 345Q32 .243669 .172657 37 334983 234297 .164436 3S .325226 225285 .156605 39 .315754 .216621 .14914$ 4C I 306557 .208289 .142046 TABLE III. Amount of L.I Annuity Compound Interest. .? 3 P- Ct. 4 p. Ct. 5 P- Ct. J I.OOOO J.OOOO I.OOOO 2 2.0300 2.0400 2.0500 3 3.0909 3.1216 3-1525 A 4.1836 4.2465 4.3101 5 5-3091 5 4163 5-5156 (, 6.4684 6.6330 6.8019 "t 7.6625 7.8983 8.1420 8 8.8923 9.2142 9-5491 9 10.1591 10 5828 11.0266 JO 11.4639 2 O06I 12.5779 ii r 2 8078 13.4864 14.2068 12 14- = 920 15.0258 15-9171 J3 rj 6178 16.6268 17.7130 14 17.0863 18.2919 19.5986 *5 18.5989 1O.O236 21.5786 16 20.1569 21.8245 23-6575 J7 21.7616 23-6975 25.8404 18 23.4144 25-6454 28.1324 19 25.1169 27.6712 30.5390 zo 26.8704 29.7781 33.0660 K .-1 3 P. Ct. 4 p. Ct. 5 p. Ct. 21 28.6765 31-9692 35-7I93 22 30.5368 34-2480 38.5052 *3 ^2.4529 36.6179 41.4305 44 34-4265 39-0826 44-5020 *5 36.4593 41.6459 47-7271 26 38553C 44.3H7 5I.H35 7 40.7096 47-0842 54-6691 28 42.9309 49.9676 58.4026 29 45-1189 {2.9663 62.3227 30 47-5754 56.0849 66.4388 31 $0.0027 59*3283 70.7608 3* 52-5028 62.7015 75-2988 33 55'0778 66.2095 80.0638 34 57-7302 69.8579 85.0670 35 60.4621 73.6522 90.3203 36 63-2759 77-5983 95-8363 37 66.1742 81.7022 101.6281 38 69.1594 8 5-9703 107.7095 39 72.2342 90.4091 114.0950 40 75-4013 95-0255 1x0.7998 TABJLE IV. Present Value of L.I Annuity Compound Interest. ^ ea 3 P- Ct. 4 p. ctji P. ct. J 0.9709 0.9615 0.9524 2 i'9i35 1.8861 1.8594 3 2.8286 3-7751 2.7232 A 3-7I7I 3-6299 3-5460 5 4-5797 44518 4.3295 6 5-4I72 5.2421 5-0757 7 6.2303 6 OO2I 5.7864 8 7.0197 6.7327 6.4632 9 7.7861 7.4353 7.1078 10 8.5302 8.1109 7.7217 j i 9-2526 8.7605 8.3064 1 2 9.9540 9-3851 8.8633 33 10.6350 9.9856 9-3936 I* 11.2961 10.5631 9.8986 Ij 11.9379 11.1184 iQ-3797 l( 12.561} 11.6523 10.8378 1? 13.1661 12.1657 11.2741 1 8 13-7535 12.6593 11.6896 J 9 14.3238 13.1340 12.0853 ao M.8?75 '3-5903 12.4622 K BD 3 P. Ct. 4 p. Ct. 5 P- Ct. 21 15.4150 14.0292 12.8212 22 15 9369 14.4511 13.1630 23 16.4436 14.8568 13.4886 24 '6-9355 15.2470 13-7986 25 17-4131 15.6221 14-0939 26 17.8768 15.9828 i4.375i 27 18.3270 16.3296 14.6430 28 18.7641 16.6631 14.8,981 29 19.1885 16.9837 15-1411 30 19.6004 17.2920 '5.3725 3' iO.OOC4 17-5885 15.5928 32 20.3888 17.8736 15.8027 33 20.7658 18.1476 16.0025 34 21.1318 18.4112 16.1929 35 21.4872 18.6646 16.3742 3 11.8323 18.9083 16.5469 3? 22.1672 19.1426 16.7113 38 22.4925 19-0679 16.8679 39 ',2.8082 19-5845 17.0170 ^:*3.ii4 8 19.79^ 17.1501 TABLE V. Value of an Annuity of L.I for a single Life, ac- cording to Mr de Moivre's Hypothesis ; viz. that of 86 chil- dren, born at the same time, one dies each year till the whole be extinct. Age. 3P-C. 4 p.C. 5P-C. 9.10 19.868 16.882 14.607 8. ii 19.736 16.791 14-544 7.12 19.604 16.698 I4-48 13 19.469 16.604 14-412 6.14 I9-33I 16.508 14-343 15 19.192 16.410 14.271 16 19.050 16.311 14-197 5-17 18.905 16.209 14.123 18 '8.759 16.105 14.047 19 18.610 15-999 13.970 4.20 18.458 15.891 13-891 21 18.305 15.781 13.810 22 18.148 15.669 13.727 83 17.990 15-554 13.642 3-34 17.827 15-437 13-555 35 17.664 I5-3I8 13.466 26 17-497 15-197 3-3 75 37 17.327 15.073 13.28* 28 17.154 14.946 13.186 39 16.979 14.816 13.088 3c 16.800 14-684 12.988 3.31 16.620 14-549 12.855 32 16436 14-411 12.780 33 16.248 14-270 12.673 34 16.057 I4-I26 12.562 35 15-864 '3-979 12.449 36 15.666 13-829 13-333 3 7 15-465 13-676 13.214 38 15.260 I3-5I9 12.091 I '3 9 15 053 I.W59 11.966 40 14.842 13.196 11.837 41 14.626 13,028 11.705 42 14.407 12.858 11.570 43 U .185 12.68.} 11.431 44 13-958 12.504 11.288 45 13.728 12.322 11.143 46 '3-493 12.135 10.992 47 13-254 11.944 10.837 48 13.012 11.748 10.679 49 12.764 11.5^8 10.515 Age. 3 p.C. 4P .C. 5P-C. 50 12.511 U-344 10348 51 12.255 II - I 35 10.176 53 11.994 10.921 9.999 53 11.729 10.702 9.817 54 n-457 10.478 9.630 55 11.188 10.248 9437 56 10.902 10.014 9-339 57 10.616 9-773 9-036 58 10.325 9-527 8.826 59 10.019 9-275 8.6n 60 9.727 9.017 8.389 61 9-419 8-753 8.161 62 9.107 8.482 7.926 63 8.787 8.205 7.684 64 8.462 7.921 7-435 65 8.132 7.631 7-179 66 7-794 7-333 6.915 67 7.450 7.027 6.643 68 7.099 6.714 6.362 69 6-743 6.394 6.073. 70 6.378 6.065 5-775 6.008 5.728 5.468 73 5-631 5-383 5-15* 73 5-246 5-029 4.826 74 4-854 4.666 4.489 75 4-453 4.393 4-143 76 4.046 3.912 3784 77 3-632 3-520 3.415 78 3.207 3.111 3-034 79_ 2.776 2.707 2.641 go 3-334 2.284 2.235 Si 1.886 1.850 i 816 82 1.429 1.406 1.384 83 0.961 0.950 o-937 84 0.484 0.481 0.476 85 o.ooo 0.000 o.ooo 68 93. USES OF THE TABLES. THE Tables contain the particulars mentioned in the titles in pounds, and decimals of a pound. 1st, To find the interest or present value of any sum, or the amount or present value of any given annuity ; take the value of L.I for the time and rate proposed from the tables, and multiply the same by the given sum or annuity. 2d, To find the interest or present value of any sum for s greater number of years than the tables extend to ; take twc or more numbers from the tables, corresponding to the num- bers of years whose sum may be equal to the given number ol years ; the product of these numbers is the interest or present value of L.I for the time proposed. Ex. What is the amount of L.I in 60 years, at 4? per cent. : amount in 30 years 3.2434 multiply by the amount in 30 years - 3.2434 amount in 60 years 10.5196 3d, To find what annuity for life or years may be purcha- sed for a given sum ; divide the given sum by the value of ar annuity of L. I, the quotient is the annnity required. In like manner, if the amount or present value of an un- known sum be given, with the rate and time, the sum may be found, 4th, To find in what time a given sum or annuity will in- crease to any proposed amount, when improved at a given rate of compound interest ; divide the amount by the sum or an- nuity, and look for the quotient or number next lower in the tables, against which you will find the number of years in the column of years. When you do not find the number exactly in the table, the number of days to be added to the years may be found nearly by the following proportion : As the difference between the next lower and next higher numbers in the tables : is to the difference between the number looked for and the number next lower in the tables : : So is the number of days in a year, or 365 : to the number of days required. In like manner, the sum and amount, or present value ol an annuity, being given, the time may be found ; and an an- nuity for life, together with the value, being given, the age oi the annuitant may be found. FOREIGN MONIES. G9 Qu. 1. What is the amount of L.365 in 25 years, at 4 per cent, compound interest ? 2. What is the present value of L.239, due at the end of 37 years, at 5 per cent, compound interest ? 3. What will an annuity of L.25 amount to when 12 years in arrear, at 4 per cent, compound interest ? 4. What is the present value of the same annuity for 12 years, interest at above ? 5. What is the value of an annuity of L.25 on a person's life whose age is 52, upon De Moivre's hypothesis, interest as above ? 6. What is the amount of L.100 in 73 years at 3 per cent, compound interest ? 7. What annuity for 33 years may be purchased for L.500 at 4 per cent, compound interest ? 8. What annuity may a person, aged 48, purchase for L.500, upon De Mo;vre's hypothesis, interest as above? 9. What sum will amount to L.500 in 36 years, at 5 per cent, compound interest ? 10. In what time will L.42 amount to L.IOO, at 4- per cent, compound interest ? 11. In what time will an annuity of L.15 amount to L.IOO, at 3 per cent, compound interest ? 12. At what age may a person purchase an annuity of L.20 per annum for life for L.250, upon De Moivre's hypothesis^ compound interest at 6 per cent. ? FOREIGN MONIES. 9^' THE kinds of money used in Europe are very nume- rous. Some are real, as guineas, shillings, and pence, which are current coins of gold, silver, or copper ; others are ima- ginary t as pounds, to which there are no single pieces of mo- ney corresponding. Some kinds are used in common accounts, as pounds, shillings, and pence ; others only on particular oc- casions, as merks and crowns. The par of the money of one nation, compared with that of another, is the intrinsic value of any piece or denomination, estimated by the weight and fineness of the gold or silver of which it consists. The rate of exchange is the current value allowed for mo- 70 FOREIGN MONIES. ney of one country, when reduced to the money of another. This rate is not always the same as the par or real value ; neither is it alike at all times. For instance, the just value of a French crown is 29|d. ; yet sometimes 32d. are allowed in exchange, sometimes only 28d. The reason of this is, that foreign payments are transacted by bills of exchange, which rise and fall in price, like other commodities, according to their plenty and demand. But this variation is confined with- in certain limits ; for, if the course of exchange were to dif- fer much from the true value, the merchants, to whom this difference was unfavourable, would have recourse to the trans- portation of real money, which no prohibition, contrary to their interest, would be able fully to prevent. The course of exchange also differs, accordine to the time at which a bill is payable. Bills at sight only should proper- ly be valued at par ; bills payable otherwise should be valued lower, in proportion to the distance of the term of payment. There are particular kinds of money fixed by the practice of merchants, for regulating calculations of exchange. A variable sum in one country is allowed for a certain species in the other. The monies for regulating exchange are often imaginary, and sometimes different from those in which ac- counts are kept. At Amsterdam, and several other places, money deposited in the bank is of superior value to the current money of the country. This difference is called agio, and is liable to varia- tion. Accounts are kept in current money ; bills of exchange are generally transacted in bank money. 95. The following general rules will direct the attentive student in computations respecting the comparison of monies. 1. Reduce the given sura (if necessary) to that kind of mo- ney by which exchange is computed. 2. Reduce this according to the given rate of exchange to the corresponding money of the other country. 3. Reduce the exchange money thus found (if necessary) to the kind of money required. 96. HOLLAND. Accounts are generally kept in flo- rins or gilders, stivers and pennings. Exchange with Bri- tain is transacted by allowing so many shillings and pence Flemish for the pound Sterling, the value of which at par is about 36s. 7d. Flemish. The course of exchange varies from FOREIGN MONIES. 71 Sis. to 38s. Agio at Amsterdam varies from 2 to 5 per cent. 1 gilder = 20 stivers. 1 stiver = * 1 6 penning s. 1 L. gross = 6 gilders = 20 sch. gross, 1 schilling gross = 6 stivers 12d. gross. 1 penny gross = 8 pennings or J stiver. 1 rixdollar =r 2| gilders. 1 dollar 53 2 gilders- 1 ducat = 51 gilders. Ex. 1. How much Sterling money in f.54*6 current, ex- change, 36s. 3d. agio 2^. J02 : 100 : : 54-76 Ex. 36s. 3d. 205 : 200 : : 12 5476 435 205)1095200(5342 8 banco 40 L. s. d. 435)213696(491 5 1 Here we first reduce /.5i76 current to/.5342 : 8 banco by the propoiv tron 102: 100. Secondly, Because 40d. Fgross make a gilder, we multiply by 40, and thus reduce it to 213696d. gross, taking in 16 for the 8 stivers. Thirdly, We also reduce the rate of exchange, 36s. 3d. to 435 pence gross. Lastly, We divide the sum of the pence gross, 213696, by the rate of exchange reduced, or number of pence gross in a pound Sterling ; and t his quotes the, value in Sterling money, L.491 5 1. Ex. 2. How many current gilders in L.I 000 Sterling ? Ex. 34s. 8|d. agio 2 per cent. L.1000 at 34s. 8Jd. 34708 4 34 6 34000 20)208250 stivers banco 4d. 333 4 /10112 10 banco 4d. 333 4 208 5 agio |d. 41 8 ./10620 15 current 34708 4 sch. gross. First, We reduce L.I 000 by practice to schilling gross. * The imaginary monies are marked in Italics. 72 FOREIGN MONIES. Secnmlly, We multiply the schillings by C, which reduces them to sti- vers banco. Thirdly, We divide the stivers by 20, which reduces them to gilders banco. Lastly, We calculate and add the agio, the sum is the answer in cur- rent gilders; the agio is calculated according to 56. These computations might Imvc been done by decimal arithmetic. Qu. 1. How many current gilders in y]3760 banco, agio 4jV Ans./. 39179 2. How many gilders banco m/2650: 11 current, agio 31 ? Ans./.2567 2. 3. How much Sterling money in L.I 000 Flemish, ex. 35s. 6d. ? Ans. L.563 7 7. 4. How many pounds, &c. Flemish, in L.325, ex. 34s. lid. ? Ans. L.567 7 11. . How much Sterling money in/.lSOO, ex. 35s. 2d. ? Ans. L.I 42 $ 7. C. Row many gilders in L.287 Sterling, ex. 35s. 3d. ? Ans./ 3035 0| st. 7. How much Sterling money in ^4650 : 1 1 current agio 3| per cent. ex. 35s. 4d. ? Ans. L.424 18 6. 8. How many gilders current in L.90 Sterling, ex. 35s. 6d. agio 3 per cent. ? Ans.y:987 5. 9. How many pounds Flemish in L.I 322, 10s. Sterling, ex. 35s. 8id. ? Ans. L.2359 16 8f Flera. 10. What is the value of the gilder banco when the ex- change is 36s. ? Ans. L.22|d. The exchange between many countries in Europe is gene- rally transacted by way of Holland. 97. GERMANY. At Hamburgh accounts are kept in marcs and schillings lubs. 1 marc lubs = 16 schilling lubs. 1 schilling lubs = 12 phenings. 1 pound gross = 7| marcs lubs, or 120 schillings lubs. 1 schilling gross 6 schillings lubs. 1 penny gross = \ schilling lubs, or 6 phenings. 1 rixdollar = 3 marcs. 1 dollar = 2 marcs. J ducat = 61 marcs. Exchange with Britain is transacted by allowing so many schillings aid pence gross for a pound Sterling. The compu- tation is nearly the sau.e as with Holland; observing that the marc lubs contains Id schillings lubs; whereas the gilder con- FOREIGN MONIES. 73 tains 20 stivers. Agio varies from 15 to 25 per cent. The par is about 35 sch. 6d. gross current per L. Sterling. The course of exchange varies from 33 to 36 sch. banco. Exchange with Holland about 33 stivers banco per dollar of Hamburgh. In Austria, Hungary, Bohemia, Swabia, and Franconia, they reckon by the rixdollar of 90 cruitzers^ In Saxony and Hanover by the rixdollar of 24 gross. In Brandenburgh and Pomerania the rixdollar contains 3 florins, and the florin 30 gross. The value of the rixdollar in all these places is about 3s. 6d. A hard dollar =r 1| rixdollars. A ducat = 2 hard dollars. These places exchange with Holland and Hamburgh, and also with each other, on the rixdollar, at so many per cent. With Britain at so many pence per rixdoilar, but common- ly by the way of Holland or Hamburgh. Qu. 1. How much Sterling money in 1328 marcs lubs cur- rent, agio 20 per cent. ex. 33s. lOd. ? Ans. L.87 4 5. 2. How many marcs lubs current in L.I 08, ex. 33s. 4d. agio 15? Ans. M. 15521 lubs. 3. How much Hamburgh money current \uf. 1223 current of Holland, agio there 3 per cent. ex. 32|, agio in Hamburgh 18? Ans. M. 1711 3 lubs. 4. How many current gilders of Holland in 1000 marcs lubs current, agio in Holland 4 per cent, in Hamburgh 25 per cent. ex. 32? Ans./ 665 12. 98. DENMARK. Accounts are kept in rixdollars Da- nish, marcs, and schillings. 1 rixdollar = 6 marcs. 1 marc = 16 schillings. 1 ort =4 marcs. 1 ducatrzll marcs. Exchange with Britain from 4 to 5 rixdollars pur L. Ster* ling. Par 4s. 6d. Sterling a rixdollar. . with Holland, about 110 rixdollars Danish for 100 rixdollars banco. with Hamburgh, about 250 marcs lubs banco for 100 rixdollars Danish. Qu. 1. What is the value of 244 rixdollars in Sterling mo- ney, ex. 4> ? Ans. L.57 8 2, &c. 2. What is the value of 264 rixdollars in current gilders of Holland, ex. 108, agio 4 ? Ans./ 635 11 G 74 FOREIGN jftONIES. 99. SWEDEN. Accounts arc kept in copper dollars* marcs, and ures. 1 copper marc = 8 ures. 1 copper dollar = 4 copper marcs. 1 silver dollar 3 copper dollars, rixdollar = 3 silver dollars, rixdollar = 48 skillins. skillin r= 12 runstics. silver dollar rr 4 silver marcs, ton gold = 100,000 rixdollars. Exchange with Britain, at so many copper dollars for L.I Sterling. with Holland and Hamburgh, at so many silver marcs for a rixdollar, or by the rixdollar at so many per cent. Qu. 1. How much Sterling money in 17425 copper dollars, ex. 41 ? Ans. L.425. 2. How many gilders banco of Holland in the same, ex. 12i silver marcs for the rixdollar banco ? Ans./ 4646f . $ 100. POLAND AND PRUSSIA. Dantzic. Accounts are kept in Polish florins or gilders, and gross. 1 florin = 30 gross 1 ducat =: 8 florins 1 rixdollar = 3 florins 1 Frederic d'or = 5 rixdollars. Exchange with Britain at so many pence for a florin, par Is. 2d. with Holland, so many gross for L.I Flemish banco. with Hamburgh, so many gross for the rixdollar banco. Qu. 1. How much Polish money in L.150, ex. Is. Ifd. ? Ans./ 2618 5 Polish. 2. How much in/ 1575 current of Holland, ex. 306, agio 5 ? Ans./ 2550 Polish. 101. LIVONIA, Riga, &c. Accounts are kept in rix- dollars albertus> and gross. 1 rixdollar ~ 3 florins 90 gross. Exchange with Holland and Hamburgh by the rixdollar at so many per cent. The value of the rixdollar is about 4s. 9d. Qu, 1. How many gilders of Holland in 372 rixdollars al- bertus at the rate of R. 98 alb. for R.' 100 of Holland ? Ans.y. 9*49 nearly. 2. How many rixdollars albertus in 765 marcs lubs, ex. R. 99 alb. per R. 100 of Hamburgh ? Ans. R. 252 40 gr. FOREIGN MONIES. 75 ' 102. RUSSIA. Accounts are kept in roubles and copecs. ] 00 copecs ~ 1 rouble. Exchange with Britain at so many pence a rouble; par 4s. 6d. with Holland, about 50 stirers a rouble. with Hamburgh, about 110 copecs the rixdollar lubs, Qu. 1. What is the value of 378 roubles, at 4s. 5d. ? Answer, L.83 9 6. 2. What is the value of the same in money of Hamburgh, ex. 105? Answer, 1080 marcs lubs banco. 193. FRANCE. Accounts are kept in livres, sols, and deniers Tournois. 1 livre or franc = 20 sols. 1 sol =12 deniers. 1 Louis d'or =r 21- livres. 1 ecu or crown 3 livres. Exchange with Britain on the crown from 28d. to 34d. par 29Jd. with Holland about 28 stivers banco a crown. Qu. 1. How much Sterling money in 1620 livres, ex. 29|d.? Answer, L.66 18 9. 2. How many livres in L.49 15 10, ex. 29f ? Answer, 1200 livres. 104. PORTUGAL. Accounts are kept in milrees and rees. 1 milree =1000 rees. 1 crusado of exchange = 400 rees. 1 new crusado = 480 rees. 1 moidore = 4800 rees. 1 Joannes = 6400 rees. Exchange with Britain 65 to 70d. per milree, par 6?|d. with Holland about 50d. gross per crusado. with France about 430 rees per crown. Qu. 1. How much money of Portugal in L.70 6 3, x. 67|d. ? Answer, 250 milrees. 2. How much money of France in 568 milrees, ex. 432 ? Answer, 3944 livres 9 sols nearly 105. SPAIN. The monies of Spain are distinguished into vellon and old plate ; the latter bears to the former the proportion of 32 to 17. Accounts are kept in rials and G2 76 FOREIGN MONIES. marveclies. Shop-keepers reckon by vellon, and foreign dealers by plate money, in which bills of exchange are always tran- sacted. 1 rial = 34 marvedies. 1 piastre rr 8 rials plate. 1 dollar = 10 rials plate. 1 ducat = 375 marv. or 11 rials 1 marv. plate. 1 pistole of ex. = 4 piastres. 1 pistole =r 5 piastres. Exchange with Britain 40 to 45d. a piastre, par 43d. with Holland about ll()d. gross a ducat. with France about 18 livres a pistole. with Portugal about 630 rees a piastre. Qu. 1. How much Sterling money in 4500 rials plate, ex. 42 d. ? Answer, L.98 8 9. 2. How much current money of Holland in the same, ex. 112, agio 3 ? Answer,y. 1176 13 current. 3. How much money of Portugal in the same, ex. 640 ? Answer, 360 milrees. 106. ITALY. At Venice accounts are kept in lires, sol- di, and picoli, sometimes in ducats and grossi ; exchange is transacted by the ducat, agio is 20 per cent, and upwards. 1 lire = 20 soldi. 1 soldi =r 12 piculi. 1 ducat current ~ 6^ lires 24 grossi. Exchange with Britain, about 50id. per ducat banco. with Holland, 93d. Flemish per ditto. with Hamburgh, 89d. Flemish per ditto. with France, 100 sols Tournois per ditto. . with Portugal, 744 rees per ditto. with Spain, 318 marvedies per ditto. At Genoa accounts are kept in lires, &c. as at Venice. Exchange is transacted by the pezzo of 5| lires. At Milan, Parma, and Modena, accounts are kept in lires, soldi, &c. and exchange transacted by the ducat or scudi of 117 soldi. In Tmcamj accounts are kept in the same manner, and ex- change is transacted at Florenceby the crown of 7| lires, value 3s. 2 id. and at Leghorn by the piastre of 6 lires, value 4s. 2d. In the Pope's Territories accounts are kept in crowns and julios. I0julios=:l current crown, and 12 julios = 1 stamp^ FOREIGN MONIES. 77 ed crown ; exchange is transacted on the stamped crown, va- lue 6s. At Naples accounts are kept in ducats, tarins, and grains, 1 tarin = 20 grains, and 1 ducat=5 tarins; exchange by the ducat, value 3s. 4d. In Sicily accounts are kept in ounces, tarins, and grains, 1 ounce = 30 tarins, 1 tarinrrSO grains, 1 ducat=13 tarins; exchange by the ducat, value 3s. 4d. In the Sardinian dominions accounts are kept in lires, &c, exchange by the scudi of 3f lires, value 4s. 6d. Exchange from one place of Italy to another is generally transacted by reducing crowns, ducats, or pezzos, at a certain allowance per cent. Qu. 1. How much sterling money in 1264 ducats banco of Venice, ex. 5 Id. ? Ans. L.268, 12s. 2. How much French money in 4025 lires of Genoa, ex. 107 sols for a pezzo ? Ans. Lrs. 3745 Tournois. 3. How much bank money of Holland in 3627 livers of Mi- lan, ex. 101 d. Flemish a ducat ? Ans.f. 1565 10. 4. How much money of Spain in 36? 5 lires of Florence, ex. 380 marv. a crown ? Ans. 5476 rials 16 marv. 5. How much money of Portugal in 1896 current crowns of Rome, ex. 1025 rees for a stamped crown ? Ans. 161 9| milrees, 6. How many pounds Sterling in 736 ducats of Naples, ex. 3s. 3d. ? Ans. L.I 19, 12s. 7. How much current money of Sicily in L.41, ex. 3s. 5d. a ducat ? Ans. 104 ounces, 8. How much current money of Sardinia in L.I 00, ex. 4s. 5d. scudi ? Ans. 1630 Irs. 4 soldi nearly. 107. IRELAND. Accounts are kept in pounds, shil- lings, and pence, Irish, which are inferior to Sterling. Their real coins of gold and silver are the same as the British, but they have halfpennies and farthings of their own. A shilling Sterling is 13d. currency, consequently L.I Ster- ling L.I 1 8 currency, and a guinea passes for L.I 2 9. The value of L.100 Sterling at par is L.108 6 8 Irish. The course of exchange varies from 6 to 12 per cent. 108. BRITISH AMERICA. There is some of the British money in circulation in the United States and British colonies ; but Spanish and Portuguese money is more common, especially in the West Indies. The quantity of these being G3 78 FOREIGN MONIES. still insufficient, paper currency has been substituted in place of real money ; and accounts are kept in pounds, shilling, and pence currency, the value of which is very fluctuating, but al- ways inferior to Sterling. In the West Indies, the exchange is about L.I SO currency for L.100 Sterling. In many places of Britain, bills on London, if payable at sight, or on a short date, are negotiated at a premium, which seldom rises so high as 2 per cent. Bills at a long date pass tit par, or at a discount. Qu. 1. How much Sterling money should be allowed for L.600 Irish, ex. 7 per cent. ? Ans. L.560 14? 11, &c. 2. How much Irish money for L.95 10 6' Sterling, ex. 9 percent.? Ans; L.I 04 2 5, &c. 3. How much currency of Jamaica for L.I 20 Sterling, ex. 3^.140 currency for L.100 Sterling? Ans. L.16S. 4. How much Sterling money for L.500 Jamaica currency, ex. 135 ? Ans. L.370 7 5 nearly. 109. TURKEY. 1 Asper=about f of Id. 1 paistre^SO aspers. EAST INDIES. 10 fanamszrl rupee, value 2s. fid. 36 fanamsrrl pagoda, value 8s. gd. A lack of rupees is 100,000, A crore of rupee? is 100 lacks. ARBITRATION OF EXCHANGE. 110. If the courses of exchange were always at par, or corresponding to each other, there would be no advantage in transmitting money through different countries, and the di- rect conveyance would be preferred, because attended with less expense and delay. But the courses are always fluctuat- ing, and often in such a situation, that money may be drawn or remitted to more advantage when it passes through several places. In order to carry on this business, we must compute the rate of exchange which should prevail between two places in correspondence, with the rates between these places and a third. For example ; if^he exchange from London to Am- sterdam be 35s. Flemish for one pound Sterling, and the ex- change from Paris to Amsterdam be 52 id. Flemish a crown Tournois ; then, as the Flemish money, which is equal to a pound Sterling, is to the Flemish money which is equal to a French crown; so is L.I to the corresponding rate of the crown. That is. FOREIGN MONIES. 79 s. Fl. d. FJ. L. 35 : 52J : : I : halfpence 840 : 105 : : 240 : 30d. Sterling. Thus, the value of the French crown, if the money were circulated through Holland, would be SOd. which is called the arbitrated value, or the rate by arbitration Now, if the course of exchange from London to Paris were SOd. a crown, no gain would be obtained by circulation ; but if the course be higher, suppose 32d. a dealer in exchange may remit 1000 crowns to Paris, by way of Holland, and draw for it directly, by which he will gain 2d. a crown. If, on the other hand, the course will be lower than the arbitrated value, suppose 2Sd. he may remit the money directly to Paris, and draw for it by way of Holland, by which he will also gain 2d. a crown. If the exchange from Britain to France had been given SOd. and to Holland 35s. the arbitrated rate between France and Holland would have been computed by this proportion ; d. Sterling, 240 : 30 : : 8-10 : 105 halfpence Flemish. If the exchange from France to Britain had been given SOd. Sterling, and to Holland 52^d. Flemish, the. arbitrated course between Britain and Holland would have been thus computed ; d. Ster. -SO : 240 : : 105 : 840 halfpence Flemish = 35s. Money may be circulated through several places for the same purpose. The method of computing the value is explain- ed 44. This is called compound arbitration. Allowance must be made for commission to the factors at the different places, vvhic,h is generally \ per cent, to each. Qu. 1 . What is the arbitrated rate of Exchange from Lon- don to Hamburgh, when the rate between London and Hol- land is 35s. 6d. and between Holland and Hamburgh 33 st I Ans. 34s. S^jd, 2. What is the value of the rouble, when the exchange be- tween Britain and Holland is 35s. 4d. and between Holland and Russia L.48 st. ? Ans. 4s 6||d. 3. What is the arbitrated value of the milree, when the^ex- change between Britain and France is 30d. and between Por- tugal and France 420 rees ? Ans. 713-d., 1, What is the arbitrated rate of exchange between Spain 80 MENSURATION. and Portugal, when the exchange between Spain and Britain is 4-5d. and between Britain and Portugal 66d. ? Ans. 681 T 9 T rees. 5. What is the value of 325^ rixdollars albertus, drawn on Holland at 105 rixdollars albertus for 100 rixdollars banco of Holland, and from Holland on London at 35s. 2d. ? Ans. L.73 p 2, &c. 6. What is the value of the same drawn on Hamburgh at 102^ rixdollars albertus for 100 rixdollars banco of Hamburgh, and from Hamburgh on London at 34s. lOd. ? Ans. L.72 18 7f, &c. 7. Money may be remitted from London to Amsterdam, ex. 35s. lOd. from Amsterdam to France, ex. 28 st. from France to Spain, ex. 1 8 Irs. Required the rate of the piastre by ar- bitration ? Ans. 46f d. 8. A debt of 500 ducats, due at Venice, may be drawn for directly, ex. 50id. or the value may be drawn on Holland, ex. 35s. from Holland on Portugal, ex. 48d. gross, from Por- tugal on Spain, ex, 640 rees, and from Spain on Venice, ex. 320 marvedies. Required which is most advantageous, and the difference ? Ans. It is most advantageous to draw by Holland, &c. if no commission be taken into account ; and the difference w L.2 7 1. MENSURATION. 111. MENSURATION, is of three kinds; lineal, superfi- cial, and solid. In lineal mensuration, the length or extent in one direction is the only thing attended to; and this is under- stood when we inquire the distance of a city, the length of a street, the height of a mountain, or the depth of a well. Su- perficial measure respects breadth as well as length ; and is understood when we inquire the extent of a field, the size of a window, or a picture, ^olid measure respects length, breadth, and thickness ; and is understood when we inquire the size of a plank or stone, or the capacity of a cistern. Lineal measures are taken by applying a rod, ruler, or line of a known length. For many purposes, it is reckoned in feet, inches, and parts or lines of ^ of an inch. A superficial foot is either a MENSURATION. 81 square, which measures a foot in length and a foot in breadth, or a space of equal extent in any form; for example, two feet in length and six inches in breadth. A square fo >?. nay be divided by lines drawn in one direction into 12 parts, each a foot long and an inch broad ; and these may be divided by 'cross lines, each into 12, or altogether into 144 square in- ches. In like manner, a square yard may be divided into 9 square feet ; and, in general, if we multiply the lineal value of any measure into itself, the product gives the superficial value. SUPERFICIAL MEASURE. $ 112. Superficial measure is computed from lineal measure by multiplying the length by the breadth. The twelfth part of a superficial foot is termed by artificers, though improperly, an inch, and is divided into J 2 parts, each part into 12 seconds, and these are again subdivided as far as necessary, the value of the places decreasing regularly by a scale of 12. Hence it is evident, that if a foot in length be multiplied by a foot, an inch, or a part in breadth, the. pro- duct must be a foot, an inch, or a part of superficial measure ; but if an inch of length be thus multiplied, the product will be 12 times less than that of a foot ; and if a part be thus multi- plied, the product will be 12 times less than that of an inch: From which we may infer the following practical rule : Multiply each denomination of the length by thejeet of breadth^ and place each product under the denomination of the multipli- cand from which it arises, carrying^ token necessary, by 12 to the higher place ; then multiply by the inches, and set each product one place farther to the right hand. Lastly, multiply by the uarts, and set each product another place towards the right hancL F. In. F. In. P. JEx. 1. Length 7 3 Ex. 2. Length 73 9 2 Breadth 5 9 Breadth 28 3 2065 4 8 18 5 3 6 Surface 41 8 3 Surface 2083 911 6 }n Ex. 2. we must multiply the lower denomination by 28 separately, and divide the products by 12, to discover thQ 82 MENSURATION. carriage and remainder. In like manner, we multiply 73 by 3, and divide the product by IX. This method of working it called duodecimal multiplication. $ 113. We shall work the first example by several other methods, that the learner may judge which is preferable. Decimally. By Reduction. By aliquot parts. F. In. F. In. In. F. In. 7 3=7.25 7 3 = 87 7 3 5 9~5.75 5 9^69 5 9 783 5 Feet, 36 3 522 6 Inches, 376 3 Inches, 199 12)6003 41.6875 12) 500 rem. 3 41 8 3 12 41 rem. 8 8.2500 12 3.0000 In the first of these methods, we reduce both factors to de- cimals ; in the second, we reduce them to inches, and mul- tiply these, whith gives the answer in square inches or parts ; in the third, we multiply by the feet, and take half the mul- tiplicand for the value of six inches in the multiplier, and one-fourth of it for the value of three inches. $114-. If the measure be required in yards, or in any other denomination greater than feet, we may first find* it in feet, and then reduce them to yards. Ex. What are the contents of an area, 6 yards 2 feet 6 in- ches long, and 4 yards 2 feet broad ? .F. In. Length reduced, 20 6 Here we divide the super- Breadth reduced, 14 ficial feet by 9, which quotes . the superficial yards. 9)287(31 yards, 8 feet. Questions of this kind may also be wrought by multiplying each part of the length into each part of the breadth, pro- MENSURATION. S3 vided we attend to the value of the products, and reduce them when necessary. Thus, Yds. F. In. 6264 yds. X 2 feet= 8 4 yds. X 6 in.~24 4 2 6yds. X 2 feet =12 3 3)20(6 yds. 72 18 2 feetX 6 in. 12 2 X 3=6 feet 12)84(7 31 8 Here, because any lineal denomination, multiplied into itself, produces squares of the same, we first multiply the yards by the yards, and the feet by the feet. Then we multiply the yards in each factor by the feet in the other factor ; and these products added amount to 20, being so many ob- longs, each a yard long and a foot broad : This, divided by 3, gives square yards, and the remainder^ multiplied by 3, gives square feet. Then we multiply 4 yards into 6 inches, which gives 24 oblongs, a yard long and an inch broad, or 72 oblongs of a foot by an inch ; which, added to 12, the product of 2 feet by 6 inches, makes 84 such oblongs, or 7 square feet. In general, like denominations multiplied by like, produce squares of the same ; and the products of unlike denominations, divided by the value of the greater, quotes squares of the greater ; and the remainder multi- plied by the same value, quotes squares of the less. Length. Breadth. Surface, f. in.pts. f. in.pts. f. in pts, 1. 5 3 4 2 21 10 6 g. 17 10 15 3 271 11 6 3. 18 6 52 95 7 4. 32 5 7 9 251 2 9 5. 43 8 2 5 5 236 7 2 10 6". 739 428 30 10 6 Yds. f. in. Yds. f. in. Yds. f. 7. 52 7 1 41 5 8. 418 3 2 16 6^ 9. 72 2 6 324 275 1J SOLID MEASURE. $115. Because a square foot contains J44 square inches, it may b. -vith the like number o; , h square, anil uv; inch high. If these be covered with other* MENSURATION, till the heap be raised a foot high, it becomes a cubical or so- lid foot, arid contains 12 times 144, or 1728 dice, or a like number of solid inches. A solid yard contains 27 solid feet; and, in general, if the lineal value of any measure be multi- plied twice into itself, the last product is its solid value. Solid measure is computed by multiplying the length l)y the breadth, and the product by the thickness : Or by multiplying the superficial measure by the thickness. As solid feet are divided by artificers, like superficial ones, into inches and smaller parts, decreasing by a regular scale of 12 ; the computation, when the dimensions are given in feet> and parts of a foot, may be performed by duodecimal multi- plication. Ex. Required the solid contents of a wall, IS feet 6 inches long, 5 feet 8 inches high, and 2 feet 7 inches broad ? By duodecimals. By aliquot parts. F. In. F. In. Length 13 6 13 6 Height 58 5 67 6 9 - Surface Breadth 76 2 6 44 7 6 Solid contents 197 67 6 4 inches 4 6 4 inches 4 6 76 6 2 153 6 inches 38 3 1 inch 646 197 7 6 $ 116. Measures given in yards and feet, or in any other denomination, may be reduced to the lowest denomination ; and the solid contents being found in that denomination, may be reduced again to higher ones. Ex. What is the contents of a cistern, 9 yards 2 feet long, 6 yards 2 feet broad, and 3 yards 2 feet deep ? MENSURATION. Length Breadth Surface Depth F. 9 6 F. 2 2 or or F. 29 20 _*_* 580 14 2320 58 Here we find the solid con- tents 8120 feet, which we di- vide by 27, the number of so- lid feet in a solid yard. 27)8 120 feet Content* 300 yards 20 feet. Questions of this sort may be also wrought by multiplying each'terin of the factors together, and attending to the value of the factors. Y.F. Length 9 2 64 yds. 4 Breadth 62 2 feet 4 Thus 9yds X2feet=18 54 6 X2 =12 S)SO( 10 Surface Depth 64yds. X 2 feet 4 feet X 4 yds. 3)128(42 12 08 .6 9)16(1 yd. 9 2X9=18 feet. 300 20 Contents Here the superficial contents of the base of the cistern is found 64 square yards and 4 square feet, by the method explained 112; and it is required to multiply this by 4 yards and 2 feet the depth. It is ob- vious, that 64 superficial yards multiplied into 4'yards of depth, give 25t> solid yards ; and 4 superficial feet multiplied into two feet of depth, give 8 solid feet. We have >ext to multiply 64 superficial yards by 2 feet of depth, which gives 128 spaces, a yard square, and a foot deep ; and, since 3 of these make a solid yard, and each of them contains 9 so- lid feet, we divide the product 128 by 3, which quotes 42 solid yards, and multiply the remainder 2 by 9, which gives 18 solid feet. Lastly, we multiply 4 superficial feet by 4 yards of depth, and this produces 16 spaces, each a foot square and a yard high. It requires 9 of those to make a solid yard, and each Qf them contains 3 solid feet ; therefore we H 85 MENSURATION. divide the product 16 by 9, which quotes 1 solid yard, and multiply the remainder 7 by 3, which gives 21 solid feet. In adding the solid feet we carry by 27 to the yards. In general, if the superficial and lineal measure be of the same deno- mination, the product is a solid of the same. If the superficial measure be of a higher denomination, ^he product, divided bv the value of the same, quotes solids of the greater ; and the remainder, multiplied by the square of that value, produces solids of the less. If the lineal mea- sure be of a higher denomination, the product divided by the square of its value, quotes solids of the greater, and the remainder, multiplied by the value, produces soJids of the less. Qu. 1. Required the solid contents of a block of marble, S feet 6 inches long, 2 feet 4 inches broad, and 1 foot 5 inches thick? Answer,/. li 6 10 2. of a wall 42 feet 8 inches long, 7 feet 3 inches high, and 1 foot 7 inches thick ? Answer,^ 489 9 4. 3. of a box ."> feet nine inches long, 3 feet 2 inches broad, and 2 feet 8 inches 4 parts deep ? Answer,^ 4o 8 10. 4. .. of a beam 12 feet 6 inches long, 2 feet 3 inches 8 parts broad, and 1 foot 5 inches 6 parts thick ? Answer,/ 41 48113 5. of a rampart 15 yards 2 feet long, 5 yards 1 foot broad, and 3 yards 1 foot Q inches high ? Answer, 299 yds. 3f feet. 6. the cavity of a ditch ISO feet long, 7 yards broad, and 90 inches deep ? Answer, 758 yds. 9 feet. METHODS OF TAKING DIMENSIONS. $ 117. The value of materials is proportioned to their quantity, and therefore should be charged according to their solid measure ; and the expense of building, or any other la- bour, which is proportioned to the quantity of materials used, should also be charged by the solid measure. But la- bour bestowed on the surface of materials, such as can-ing, polishing, or painting, should be charged according to the Superficial measure. However, if solid work be all of the same thickness, it is sufficient to take the superficial measure by the length ami breadth, and adapt the price to the thick- ness ; and sometimes, although the thickness be unequal in different parts, the superficial measure is taken, and the thickness reduced to a" common standard, by proper allow- ances on. such parts as are thicker or thinner than others. MENSURATION, 87 For example : If the side walls of a house be two feet thick, and the end walls three feet thick, we may add to the super- ficial measure of the end walls one half the same, which brings it to the standard of the side walls. Glass, slates, and other materials, whose thickness cannot properly be taken, are charged by the superficial measure. $ 118. MASON WORK. Ruble work is generally estimated by the rood, which contains 36 square yards; but, in some places, roods of other dimensions are used. The most com- mon thickness is two feet, and walls of any other thickness are either reduced to that standard, or charged in proportion to the thickness. Different methods are used for taking the dimensions of a house, according as the tradesman engages for workmanship only, or for materials and workmanship together. In the first case, the measure taken round the house on the outside is considered as the length, and is multiplied by the height of the wall from the foundation : The vacancies for doors, win- dows, and the like, are nr/t deducted: One foot is added to the height of the side walls, as an allowance for levelling, and the same for every belt. In the second case, the breadth of the house is measured on the inside, deductions are made for vacancies, and the allowance. for levelling is given at the rate of workmanship, Gable ends are measured by taking half the sum of .their length, and the length of the chimney stalk, which is consi- dered as the length of an upright wall of equal contents, and is multiplied by the height, taken from the level of the side walls to the foot of the chimney stalk. The breadth of chim- ney stalks is estimated by adding their breadth to their thick- ness ; and this being reduced to standard thickness, is multi- plied by their height. An allowance for carrying up the vents is given by the li- neal foot, which is measured by dropping a plummet down the chimney. Arches and circular work of any kind are estimated double measure. c, 119. HEWN WORK is generally measured by the superfi- cial foot. The dimensions are taken by a line, which is bent into all the hollows, and over all the projections, in order to ascertain the extent of the surface which has been shaped by 83 MENSURATION. the tool. This way of taking the dimensions is called gird, ing, If the measures be taken after the stones are built, an allowance is made to the outward surface for any hewn work in the joinings. Stones for hewn work are estimated by the cubical foot : Marble Jacings generally by the superficial foot, two inches being the standard thickness. Digging for foundations or vaults, is measured by the cu- bical yard. Paving and causeway, are measured by the square yard. 120. BRICK WORK. When the thickness of a wall con- tains the length of one brick and the breadth of another, or brick and half, it is reckoned of standard thickness. Other walls are reduced to standard thickness, by multiplying their superficial measure into the number of half bricks in their thickness, and dividing the product by three. Brick work is measured, in England, by the square rod, which is 16| feet long, and consequently contains 272 f square feet, but 272 is generally reckoned exact enough in computa- tion. Brick work, in Scotland, is measured by the yard square. Chimnies standing by themselves are girt round, and that measure is reckoned their length, and multiplied into their height. Chimnies connected with a wall are measured on the breast and two flanks ; the sum of these is taken for the length ; and the part above the wall is girt and computed separately. If a chimney hath two or more funnels, the measure of the bridges that separate them must be added. No allowance is made for the vacancy at the fire place. 'Vacancies for doors, windows, and the like, are deducted. Brick arches are estimated work and half ; groined arches double. ' 121. CARPENTER and JOINER WORK. Flooring and roofing are measured, in England, by the square of 10 feet, or 100 superficial feet. In Scotland, generally by the square yard. Joisting should properly be measured by the cubical foot. Sometimes joisting is charged by the superficial measure of the floor in squares or yards, with an allowance for the part of the joist that rests in the wall. Vacancies in a floor for stairs or the like, are deducted, but no deduction is made for hearths, because the extraordinary MENSURATION. S9 work in the border is reckoned to stand for what js saved in the boarding ; neither is any allowance given for sky-lights in a roof. In measuring roofs, the breadth of the wall-plate on which the rafter rests, is added to the measure of the sloping sides. Sometimes the breadth of the house within the walls, added to half the breadth, is considered as equal to the two sloping sides. Partitions are measured by the square yard. The height is taken by girding over the mouldings ; but, in taking the length, the straight line only is regarded. Doors and -windows being wrought on both sides, are charged as work and half. Barred doors are measured by adding the breadth of the bar to the heighth. Vacancies for chimnies, windows, and the like, are deducted. Sashes are charged separately, and mea- sured by adding the checks to the day-light. Cornices, door and window frames, lintels, skirt boards, and the like, are measured by the superficial foot ; the dimensions being taken by girding them over the mouldings. Sometimes they are measured by the lineal foot, the breadth being agreed on, and charged accordingly. 122. TIMBER-MEASURE. The method of measuring squa- red timber, equal at both ends, is obvious. Unequal squared timber, which is larger at the root end than the upper end, is generally measured by taking the length and breadth at the middle. * Round timber is measured by girding it about the middle with a small cord ; one fourth of the girth is considered as the side of a square beam of equal dimensions. Tapering limber should be measured by supposing it di- vided into parts of 8 or 10 feet long, which are girded and computed separately as above. None of these methods are accurate ; and they are some- times considerably erroneous ; but, being established by long practice, they are universally used in business, and will not easily be laid aside. 1 1 23. SLATER WORK. Slating is measured, in England, by the square of 100 feet; in Scotland, by the rood of 36 yards. The eaves, or projections, which are generally 9 inches, sre allowed double measure. In pavilion roofs, half the length of the eaves added to H3 SO MENSURATION. half the length at the top is taken for the mean length. An- allowance is given for hips and valleys, by the lineal measure in length, and reckoned at a foot and half in breadth. Tile roofs are measured like slate ones, but no allowance is given for double eaves; but if a tile roof have a. slate edge, 4- inches are allowed for joining, and 9 for double eaves. 124. PAINTING aud PLASTER WORK. Printing is mea- sured by the square yard wherever the brush touches. The height of rooms is taken by girding over the mouldings ; but the length is measured in a straight line, as in joiner work. The painting of the bars of windows being trouble- some, is reckoned equal to the whole surface; aud railing Is reckoned equal to the whole surface painted on both sides. Enriched cornices, and the like, are charged as work and half, or double work, according to the nature of the car- ving. Plaster work, whether on roofs or partitions, is measured by the square yard. Deductions are made for all vacancies. 1 C 25. GLAZIER WORK. Glass panes and windows are measured by the square foot. A small foot of 8 inches was formerly used by glaziers in Scotland : but that practice is now laid aside. Windows round at the tpp are measured as if they were squared to their full height ; also round, oval, or irregular windows, are measured by their greatest length and breadth, on account of the trouble and waste of ghiss they occasion, 126. LAMD MEASURE. The area of a rectangular field is computed by multiplying the length into the breadth: the area of a triangle, by multiplying the base into half the perpendicular ; for a triangle is equal to the half of a rectangle on the same base, and of equal altitude. Fields, bounded by straight lines, in whatever form, may be divided into tri- angles, and computed accordingly. The measures of the ba^ ses ar.d perpendiculars may be taken on the ground ; but it is more usual to make a plan of the field, by methods, which this is not the proper place to explain ; and to measure the bases and perpendiculars with compasses, on a scale adapted to the plan. Land is commonly measured by Gunier's chain, which is divided into 100 equal links. Ten squares of this chain make .in acre; and, because each square of the chain contains lOjOOQ square links, therefore, if the product be obtained in. MISCELLANEOUS QUESTIONS. 9t Square chains and links, it is reduced to acres and lower deno- minations, as directed y 8-2. The length of the English chain is 66 feet ; of the Scots chain 74 feet. 4 Scots acres are nearly equal to 5 English, 80 English chains make a statute mile. $ 127. If a field be not bounded by straight lines, we must measure the most convenient straight lines within it, and mea- sure the offsets or distances between the straight line and boun- dary at the end of every chain, or as often as the irregularity of the ground requires. The sum of the offsets divided by their number, may be considered as the mean breadth of the space between the straight line and boundary ; and this being multiplied by the length, the product is the area of the space between the straight and curve lines, which must be added to the area comprehended by the straight lines. ., If the boundary of a field be bent inwards, it is sometimes more convenient to measure a straight line on the adjoining ground ; in which case the area between the straight and curve line must be subtracted from the area contained within the straight lines. When the boundary is very irregular, it may be necessary to measure a straight line, partly within the field, and partly without it. When this is done, we must carefully distinguish the offsets taken outwards or inwards, and regulate the computation accordingly. For exercises in the several kinds of Mensuration, see Mis- cellaneous Questions, LXII. LXX1V. MISCELLANEOUS QUESTIONS. I. THE rent of a gentleman's estate is L.I 25 in money, 154 quarters wheat at 35s. and 99 quarters barley at 2(>s. ; land- tax, and other burdens, amount to L.43, 4s. How much does the neat rent amount to ? Answer, L.480, II. A labourer receives JOd. a day fer every work day, from 5th February to llth November, inclusive, and 7d a day du- ring winter. How much do his wages amount to in the year ? Answer, L.I 2 2 7. III. A gardener receives L.8, 8s'. for his yearly wages, be- sides 6\ bolls meal al 13s. 4d., ]| bolls malt at 18s, and a cow's grass valued at L,l, 5s. How much does it amount to? Answer, L,15 68. 92 MISCELLANEOUS QUESTIONS. IV. How much would he gain or lose, if, instead of the a- bove articles, he received Is. each work day in the year ? Answer, He would gain 6s. 4d. V. A mercer sells 21 yards at 15s. 6d. and 3 yards at 14s. lOd. and on receiving payment allows 5 per cent, dis- count for ready money. How much did he receive ? Answer, L.I? 11 6. VI. How many trees may be planted on an English acre, at 6 feet distance ? Answer, 1210. VII. A merchant imports 1000 quarters of wheat, prime cost 3?s. a quarter, freight and charges L.31, 5s. on the whole quantity. What does it stand him a quarter ? Answer, L.I 17 7. VIII. From Aberdeen to London are 505 miles and 37 sta- ges. Required the expense of travelling at lid. a mile, Is, 6d. additional each stage, and L.I 12 1 altogether for tolls? Answer, L.27 10 6. IX. If 3 persons travel in a post chaise, as above, in five days, how much does it stand each, including 5s. each a day for maintenance ? Answer, L.10 8 6. X. How much cheaper is it to each than if only 2 persons had travelled, and their expense for maintenance on the jour- ney had been 7s. each a day? Answer, L.5 1 9. XI. A gentleman, whose estate is L.500 per ann. pays L.40 for house-rent, and his daily expense besides is a guinea and a quarter. How much does he save or overspend in a year ? Answer, He overspends L.I 9 1 3. XII. How many hogsheads, containing each 63 gallons, and each' gallon 231 inches, will be held in a vessel 9 feet long, 7 broad, and 5 deep? Answer, 37/ 3 3 T , XIII. What is the length of a road, which is 33 feet broad, and contains an English acre ? Answer, 1320 feet. XIV. How much ground in a road of the same breadth and a mile long ? Answer, 4 acres. XV. If the road from Aberdeen to London be 33 feet broad, one place with another, and 5' 5 miles long, and the value of the land L/20 an acre, how much is the value of the land which the road occupies ? Answer, L 40,400. XVI. A spring of 'water, which furnishes 16 gallons every minute, supplies a city of 5000 families. How much water has each fanr'y a day? Answer, 4fg gallons. XVII. A tradesman engages an apprentice for 5 years, and MISCELLANEOUS QUESTIONS. 93 receives L.25 of apprentice fee. He agrees to maintain him, the expense of which is reckoned at 8d. a day ; and to allow him, for clothes,. L.3 the three first years, L.5 the fourth, and L.8 the fifth. Now, if nothing he reckoned for his work the first year, but the second year the value of it amount to L.G, the third year to L.I 2, and the two remaining years always to L.6 more than the year preceding, what does the master gain or lose by his service ? Answer, He gains L.2 3 4. XVIII. A farmer manures a field at the expense of L.3 an acre ; and the first year it produces 2 quarters of corn more every acre, the second year, 1| quarter, and the third, | of a quarter, price 1 8s. a quarter ; after which the effects of the manure are exhausted. What does he gain or lose by manu- ring it ? Answer, He gains 16s. 6'd. an acre. XIX. If a cow yield 20 quarts of milk a day for 240 days, and 25 quarts make 1 Ib. of butter ; how many Ibs. of butter will be obtained in the season, and what does the value come to at 7 Id. a Ib. ? Answer, 192 Ib. value L.6. XX. 'Part of the earth from a rampart 70 feet long, 18 broad, and 12 high, was taken to fill up a ditch 50 feet long, 20 broad, and 9 deep, how many cubical yards of the ram- part remain . ? Answer, 226 yards. XXI. I carried to market 48 guineas, 17 half-guineas, 13 quarter-guineas, 7 moidores, 3 quarter- moidores, 9 eighth Joannes, 17 half-crowns, and 23 shillings. I sold there 3 cows for 5 guineas each. I bought 450 spindles yarn at 2s. 3d., 114 ditto at 2s., and 107 ditto at Js. 9|d. ; also 150 yds. linen, at Is. 9|d. My expenses were L.I, 18s. Required how much I brought home? Answer, L.7 6 Oj. XXII. A silversmith buys L.I 00 value of silver at 5s. 2Jd. an oz. ; he makes 6 dozen of spoons, each weighing 2 oz. 4 dwt. and 6 dozen small ditto, each weighing 12 dwt. and 6 pieces of plate, weighing, No. 1 1 Ib. 3 dwt. 10 gr. No. 2 1 Ib. 1 oz. 13 dwt. 4 gr. No. 3 1 Ib. 6 oz. 15 dwt. No. 410 oz. 2 dwt. No. 5-^6 oz. 13 dwt. 6 gr. No. 6 5 oz. 14 dwt. 2 gr. How much silver has he still unwrought ? Answer, 9 Ib. 7 oz. 7 dwt. 2 gr. XXIII. I bought 500 quarters of wheat at 39s. and 350 quarters of barley at 23s. I have delivered in return 235 yards of cloth at *12s. 9d. 312 spindles of yarn at 2s. 3d. 73 half-guineas, 19 moidores, 250 dollars at 4s, 5d, and the seller 94 MISCELLANEOUS QUESTIONS, agrees to abate 5 per cent, in consideration of some damage which the corn sustained. How much do 1 owe him ? Answer, L.I 004 10 7. XXIV. A sold to B 34 lb, of congo tea at 4s. 9d. 12 Ib. of bohea at 3s. 6'd. and 18 lb. of hyson at 7s. 4d. He bought from him 1 82 lb. of sugar at L.3, 6s. a cwt. and C 245 lb. of hops at L.4, 16s. a cwt. What is the balance, and to which party is it owing ? Answer, B owes A 1 8s. 3d. XXV It is required to divide a prize taken at sea, value L.20370 106, among the captain, 2 lieutenants, the surgeon, the purser, 4 petty officers, and 90 private men, allowing each petty officer as much as 2 private men, the surgeon and pur- ser each as much as 8 men, the lieutenants each as much as 16, and the captain as much as 50 men ? Answer, A private man's share L.I 03 18 7|> &c. XXVI. If 125 quarters of wheat at bis. 6cl. are delivered in barter for barley at 18s. 9d. a quarter. Required the quan- tity of barley ? Answer, 210 qrs. XXVII. A delivers to B 15 yards of cloth at 17s. 6d. and 12| yards at 14s. fid. in barter for wool at Is. 6d. a lb. What quantity does A receive ? Answer, 305 lb. II VI 11. I gave 63 gallons of brandy at 7s. 4d. in barter for 56 gallons of rum. What does the rum stand me a gal- lon ? Answer, 8s. 3d. XXIX. I gave 95 firkins of beer at 8s. 6d. in barter for 5 cwt. 3 qrs, 2 lb. of tobacco. W ; hat does the tobacco cost me the lb. ? Answer, Is. 3d. XXX. If 12 cwt. 3 qrs. of tobacco be bought at 5 guineas a cwt. and retailed at 1 3d. a lb, how much is gained upon the whole, and what is the gain per cent. ? Answer, L. 10 8 3, and 15| per cent, XXXI. A grocer buys sugar at L.3, 15s. a cwt. What must he sell a cwt. for, to gain 5 per cent, and a lb. for, to gain 10 per cent.? Answer, L.3 18 9, and 8d. 3 T 5 5 q. XXXII. If 16 gallons of rum at 7s. 6d. be mixed with 4 gallons of water, what is the value of the mixture ? Answer, 6s. XXXIII. If 18 gallons of rum at 8s. be mixed with 14 gal- lons at 6s. what is the value of the mixture ? Answer, 7s, ld. XXXIV. A grocer mixed 4-6 lb. of tea at 7s. 6d. with 54 lb, at 5s. 2d. 28 lb. at 4s. 6d. and ?2 lb. at 4s. 2d. what is the va- lue of the mixture ? Answer, 5s. 3d, MISCELLANEOUS QUESTIONS. 95 XXXV. If 75 quarters of wheat at 30s. be mixed with 125 at S6s. ; at what rate must it be sold a quarter, that the owner may gain 5 per cent. ? Answer, L.I 15 5|. XXXVI. How much tea at 6s. 8d. must be mixed with 25 Ib. at 9s. that the value of the mixture may be 7s. 6d. a Jb. Answer, 45 Ib, XXXVII. How much tea at 4s. must be mixed with 50 Ib. at 5s. 4d. and 74 Ib. at 6s. 8d. in order that the cost of the mixture may be 5s. ? Answer, 140 Ib. XXXVIII. How much corn at 38s. a quarter, must be mix- ed with 120 quarters at 30s. that the owner may gain 12| per cent, when he sells it at 36s. ? Answer, 40 qrs. XXXIX. If 3 cwt. of hops, bought at L.4, 18s. a cwt. be mix- ed with 2 cwt. at L.5, 3s. and 2 cwt, 16 Ib, at 1 Id. a Jb. what must alb. be sold for that the gain may be L.7 68? Answer, Is. Id. XL. A corn-merchant sells wheat at 30s. a quarter, and gains 5 per cent. How much will he gain per cent, if the price should rise to 32s. and how much will he lose if the price should fall to 26s. ? Answer, gain ! 2 per cent., loss 9 per cent. XLI. A barters with B 120 gallons of rum at 8s. 4d. and 76 gallons of bivndy at, 7s; 9d. for 1500 Jb. oi cotton, and re- ceives L.I 6 6 as the balance. What is thf; value of alb. of the cotton Answer, Is. {ji ( J 4 XLII. A. owes to B upon separate claims L. 1500 Scots, 12400 merkt* Scots'and ' . ! 00 Sterling, with 3 years interest on the first debt, 2 years on the second, and 9 months on the third, at 5 per cent.; in payment of which he gives .95 Joanneses, 75 nioidort- s, 27 dollars, at 4s. 3d. 29 guineas, and 17 half-guineas. How much does he still owe ? Answer, L.76 16 1. XLIII. A gentleman had three daughters wno all died be- fore him : the eldest, A, leaving two daughters ; the second, B, three ; and tin- third, C, five. The rent of his estate was L.6.59* an(i it v\as sold for 30 years purchase : his moveable subjects amounted to Lt83QO, iiis debts and funeral expen- ses to L.450. Required what provision each of his grand- children will have when his eti't. ts are divided according to law, viz. his e^iute per xtirpesy or an equal share to each fa- mily - but Jus uioveable> pt. capita, or an equal share to each person ? Answer, A's children L.3jOO each, B'sL.2435, C's L,1583. 06' MISCELLANEOUS QUESTIONS. XLIV. Required the expense of keeping a chaise per an- num, the cost of the chaise being L.90, two horses at L.25, allowing, besides legal interest, 5 per cent, for the wear of the chaise, and 15 per cent, for the wear of the horses ; and supposing each horse to consume daily a stone of hay at 5|d. and 1^ peck of oats at 24s. a quarter; duty L.8, servant's wages L.10, and maintenance ?d. a day, stable and shade rent L.3, 10s. and the farrier's account, L.2, 10s.? Answer, L.106 2 3. XLV. A butcher buys an ox for L.10, 16s. and after feed- ing him with 24 pecks of oats at 18s. a quarter, and 20 trus- ses of hay at Is. 4d. slaughters him, and sells the beef, being 36 stones, at 5|d. a Ib. 6 stones of tallow at 7d. a Ib. allowing 14 Ib. to the stone, and the hide for L.I, 5s. Required his gain or loss ? Answer, gain L.2 8 10. XLVI. A and B traded in company, A's share being three- fourths. At the dissolution of the copartnery, the goods be- longing to the company amounted to L.2564, and the debts due to them to L.3658 6 8. A agrees to take the risk of re- covering the debts for an allowance of 12 per cent., and B tak^s off the goods at 5 per cent, discount. How will accounts stand between them ? Answer, B owes A L.I 022 4. XLVII. A peasant possesses 5 acres at 24s. an acre, one half oi it is in grass, and the other is sown with wheat and barley in equal parts. He receives the seed from the lord of the manor, wheat at 3 bushels an acre, price 32s. a quarter, barley 2| bushels an acre, price 3s. 4d. He pays him 5 gui- neas, and works for him 22 days in time of harvest, at lid. a day, and as many days more at 9d. a day as discharged what he owed. How many days did he labour ? Answer, 27 days, besides the time of harvest. XLV1IT. The ship Diligence, burden 120 tons, value L.6, 10s. a ton, sails from Aberdeen to London, and makes five voyages out and home in a year. The freight of goods is 2s. 6d. a barrel bulk, whereof 6 make a ton : and in the voyages to London, she has at an average two thirds full, and three fourths on the return . insurance one guinea per cent, each trip ; ttar and wear, and other expences, L.35 a voyage out and home; captain's wages L.6 each trip ; mate's L.3 each ditto ; 6 mariners 30s. a month, and I boy 15s. a ditto, reckoning 13 months to the year ; victualling for 8 men at 8d. a day, MISCELLANEOUS QUESTIONS. 97 each during the whole year, interest on the value of the ship at 5 per cent. Required the gain or loss ? Answer, Gain, L.47 4, XLIX. Required a number, which being added to the 17th part of 765, the sum shall be equal to the square root of 2601? Answer, 6. L. Required a number, from which if you take two-thirds of four-fifths of itself, the remainder shall be equal to T ^ of & of 560 > Answer, 90. LI. Required a number, from which, if 7 be subtracted, and the remainder divided by 8 ; the quotient multiplied by 5, and 4 added to the product ; the square root of the sum ex- tracted, and three-fourths of that root cubed, and the cube divided by 9, the last quotient may be 24 ? Answer, 103. LII. Three persons purchase a ship. A pays for f , B for f , and C pays L.270 for the remainder. Required what A and B paid, and what part of the ship C had ? Answer, A L.480, B L.450, C &. LIII. Ground was feued for building, at the rate of 3s. O'd. a foot in front, and 80 feet in breadth ; besides a payment of 25s. a foot in front. Required the value of an English acre, estimating the feu-duty at 25 years purchase ? Answer, L.3062 16 3. LIV. A fair trader imports 48 pipes of wine, prime cost L.28, 12s. a pipe, freight 22s. a pipe, duty on a ton of two pipes L.28, 14s.; and he sells it for L.49 a pipe. A smug- gler imports an equal quantity, but pays, for freight, 80s. a pipe ; the expense of smuggling comes to L.I 2, 12s. and one- third is seized by the custom-house officers ; and as he is obli- ged to sell the remainder in a clandestine manner, he only ob- tains for it L.47 a pipe. Required which has the advantage, and by how much ? Answer, The fair trader has the advantage by L.I 91. LV. The price of a pipe of French wine, including char- ges, is 486 livres, exchange 29d. a crown, duty L.51, gs. a ton, freight and charges 39s. and it runs 54 dozen bottles, &c. 2s. 6d. a dozen. For what may a dozen be sold, that the importer may gain 20 per cent. Answer, L.I, 4s. LVI. A farmer pays L.100 rent, and on obtaining a new lease, agrees to pay it in barley, at an average of the prices for the six last years, which were 17s, 25s. 2 is, 6d.-~ J9s, 98 MISCELLANEOUS QUESTIONS. 21s. and 22s. 6d. a quarter. Ho\r much barley should lie pay ? Answer, 93 3 ] =- quarters, LVII. 1500 quarters corn were purchased at 35s. and be- ing kept 15 months, lost 8 per cent, in measure, and were sold for 41s. granary-rent and charges L.25, interest 5 per cent. Required the gain or loss ? Answer, Gain L.I 4 18 9. LVII I. The sum of L.200 being given to encourage the culture of flax, was distributed among 6 persons, in propor- tion to the quantities they raised. A raised 456 stones, B 376 stones, C 568 stones, D 352 stones, E 272 stones, F 224 stones. \Vhat premium should each receive ? Answer, A L.44 10 7|, BL.36 14 4J, C L.35 18 9, D L.34 7 6, E L.26 11 3, F L.21 17 6." LIX. A gentleman's estate consists of 130 acres arable land infield, rent 1 7 } bolls barley at 14s. and 2 pounds Scots in money an acre ; 312 acres outfield, rent 3 firlots oats at 11s. and half a merk Scots in money an acre ; 25 acres meadow at a guinea ; 280 acres pasture at 2s. 6d. ; the mansion-house and gardens are valued at L.500, and the wood upon the estate at L.3360. Required the value at 27 years purchase ? Answer, L.I 087 >, 18$. LX. A wine merchant imported 8 pipes wine, which cost him L.31 a pipe, and which were bottled into 52 dozen each, bottles and charges 2s. 3d. a dozen. He sells it at first for 15s. a dozen; but as that kind of wine became scarce, he raises the price 6d. a dozen after he had sold 100 dozen, and raises it as much after selling each 100 dozen. Required his gain ? Answer, L.33, l6s. LXI. A clergyman's stipend is paid as follows : A pays L.25, and 10 bolls 3 firlots barley ; B pays L.I 2, and 6 bolls 1 firlot 2 pecks meal; C pays L.13 6 8, also 9| bolls meal^ and 7 1 bolls barley ; D pays 12 b. 2 f. 3 p. meal, and 6 b. 3 f. .2 p. barley. Required the amount, converting the barley at 1 4s. and the meal at 7 pounds Scots a boll ? Answer, L.84 8 If. LXII. Required the number of squares flooring in a house of 3 floors, 54 feet by 26 within walls, deducting from each floor the vacancy for the stair, 12 feet by 7 feet 10 inches ; each square containing 100 superficial feet? Required also the value at 45s. the square ? See 121. Answer, 39 T 3 S squares, value L.88 8 6. LXIII, How many yards of wainscot in a room 64 feet MISCELLANEOUS QUESTIONS. 99 in circuit, and 10 feet 9 inches high, allowing for a dooi* 6 feet 8 inches by 2 feet 9 inches, and 2 windows with shut- ters, each 5 feet 6 inches by 3 feet 4 inches, the door and window shutters being charged as work and half, and deduct- ing a vacancy for a chimney 6 feet by 5 feet 3 inches ? See 121. Answer, 76 yards. LXIV. How many yards painting in a wall 18 feet by 9 feet 4 inches, deducting the chimney, 4 feet 6 inches by 3 feet 4 inches ? and how much does it corne to at Is. 7d. a yard? Answer, 1? yds. L.I 6 11. LXV. How many yards plastering on a wall 1? feet 8 inches long, 10 feet 6 iriches high, deducting the door, 6 feet by 2 feet 9 inches ? and how much does it come to at Sd. a yard ? Answer, 18| yds. and 12s. 6fd. LXVI. How many deals 12 feet long 7^ inches broad are required for a floor 7J yards by 5, with a vacancy 7 feet by 5 ? Answer, 40 deals. LXVTI. How much should be charged for the workman- ship of a house 40 feet long and 25 broad within walls, the side walls 2 feet thick and 24 high from the foundation, the gables 3 feet thick-and their height above the side walis to the foot of the chimney -stalks 8 feet ; two chimney-stalks 7 feet broad, 3 thick, and 8 high, at 30s. a rood, reduced to the standard of 2 feet, including allowance for levelling the side walls? See 118. Answer, L.^3 7 4|. LXV1II. How much should be charged for the same house, at L.6 a rood for materials and workmanship, deducting a door, 7 feet by 4 feet, and 1 5 windows, each 5 feet 4 inches by 3 feet, and including the allowance for levelling the side walls, at 30s. a rood ? Answer, L.82 1 5 7 7 . LXiX. What is the measure of a brick- wall 48 feet long, 22 high, 2| bricks thick, in which there are two doors 7 feet by 4, and 10 windows 5 feet by 3, and 46 feet Q? arched work above the doors and 'windows, the arched work being accounted work and half, and the whole reduced to standard thickness, and reckoned in squares or yards ? See J20. Answer, 5*-ff squares, or 161 yards 6 feet. LXX. How many feet of hewn work in 9 pair chimney- jambs, 3 feet 4 inches by 15 inches; and 3 ditto, 2 feet 4 inches by 10 inches; 9 lintel?, 4 feet by 15 inches; 3 ditto, 3 feet by 15 inches; 9 hearths, 4 feet by 2 feet 10 inches ; 3 ditto, 3 feet by 2 feet 6 inches ; and 24 steps of stairs, 4 feet 100 MISCELLANEOUS QUESTIONS. 8 inches by 1 foot 6 inches ; and what is the value thereof at lOd. a foot? Answer, Feet 420 ^, value L.17 10 4. LXXI. How much slating in a roof 46 feet long, and 18 feet from the coping to the eaves ? and what is the value at L.5, 8s. a rood, or at 33s. a square ? See 123. Answer, 5 roods llf yards L.28 150 17| squares 28 9 3 LXXII. How much timber in around tree 18 feet long and 68 inches in girth in the middle? See 122. Answer, 36| feet. LXXIIT. How much timber in a tapering tree 32 feet long, and girth in the middle of each 8 feet, the girths being 64 inches, 56 inches, 52 inches, and 48 inches? Answer, 42| ft. LXX1V. What is the measure of an irregular field of 8 sides, divided into 6 triangles, whose bases and perpendicu- lars are as under ? See 126. Bases. Perpendiculars. Bases. Perpendiculars, ch. links. ch. links. ch. links. ch. links. 1st, 3 12 2 20 4th, 3 12 2 96 2d, 2 14 1 54 5th, 4 50 3 12 3d, 1 56 2 70 6th, 2 27 3 20 Answer, If measured by the English chain A. 2 39 8 Eng. If measured by the Scotch chain 2 39 10 Sc. LXXV. A church is built for L.I 200, which contains 1500 persons. One-third of the seats are let at 2s. 6d. another at '2s. 6d. and the remaining third at Is. The minister's salary, L.100, is paid from these rents, and the remainder applied to reimburse the expence of building. How much per cent, does it pay annually ? .Answer, 6| per cent. LXXVI. A person purchases 1500 quarters barley at 24s. 6d. and converts it into malt. He pays for malt-house rent L.22, 10s. for servants wages L.56, for malt-duty 9|d. per bushel malt, and the malt is sold at 28s. a quarter. Ke- quired the gain or loss, supposing each quarter barley to pro- duce 9| bushels malt ? Answer, loss L.I 3 1|. LXXVII. 100 quarters rnalt at 28s. are distilled into spi- rits, and produce 12* gallons a quarter. The operation con- tinues 60 days, and the daily expences of fire, rent, service, and wear of utensils, is 13s. 4d. duty 2s. 6d. a gallon. Re- quired the cost of the spirits per gallon ? Answer, 5s. 4-?,-*d, JLXXVI1I. If a still of 100 gallons be required to distil the spirits from 16 quarters malt in 6 days, the produce being 12 * MISCELLANEOUS QUESTIONS. 101 gallons a quarter, what duty upon she still easb gallon will be equivalent to a duty of. 6d. on. the gallon spirits, suppo- sing the still to be employed. 3 quarters 'oat meal, at 18s. 9d. ; 7 cut. stock- iisli, at 2 l 7s. i cocperi^c pncl. charges, L.9 4 5. The ship re- turns^Ukr.a yoyi'^-j of ,- i:;<;Mi:s and 7 days,' and the con- tractor sells the remaining provisions for L.4.3. Required his gain or-lo.'-s? At Fwer, gain L.I iy 11 ?*. LXXXIIJ. An estate consisting of 130 acres, at 15s. an acre, 200 at 1 2s. and 250 at y*. is to be divided between two sisters. The elder gets the best ground, but allows in return, a greater quantity to the younger, so as to render the value equal. How much land has each ? Answer, elder, 242 1 acres, younger, 337 j? acres. LXXXIV. If two-fifths of the inhabitants of Great'Britain (the whole number 8,000,000) be consumers of snuff, and be distributed into five classes, in proportion to the numbers 1, ?', 4, 5, 7 ; the first class consume 6lb. per ann.thc second 4lb. the third Silb. the fourth 21b. and the fifth lib.; what quan- tity of tobacco will be consumed, supposing the waste in ma- nufacturing -| of the tobacco ? and what will be the duty at Is. 3d. a pound ? Answer, 8,9(50, 000 ib. or 4000 tons, L.560,000. LXXXV. The rent of a salmon-fishing is L.260. The te- nant employs 6 men at 8 guineas for the season, and an over- seer at double wages. The fishermen also have 1 of the sal- mon. The fishing season continues 24S work days, and they catch, at an average, 100 fish in 3 days, weight at an average, Sib. each. The expence for boats and nets is L.43 1,5 4. The fish are salted and packed in barrels which contain 400lb. each, price of barrels, 3s. 6d. salt and charges, 2s. 8d. a bar- rel, and sold at such a price as that the tenant's profit is ex- actly one-fourth of the value. Required the price each barrel? Answer, L.4, 8s. LXXXVJ. The manager of a theatre pays for rent L.SOO, for scenes and dresses L/250. He engages the first player, for the season, at 43, 1=^=8. 3. A number prefixed to a letter is called its coefficient, and is understood to multiply the value of the letter. Thus 5a=60, 7A--21. When letters are placed together, the quantities they re- present are understood to-be multiplied into each other. Thus, ab - 36, ac = 24, be = 6, abc -72. Jf the same letter be repeated twice, or oftener, its value is understood to be multiplied into itself as often. Thus, 00 144, aaa=z 1728, 666 = 27, bbbb = 81, ccccc = 32, aaccc = 1152. 4. Instead of repeating the same letter, it is common o mark a small character above it towards the right hand, which points out that k is to be understood as repeated as often Thus, at or aaa = 1728, a 2 b* or aabbb = 3888. Quantities produced by the successive multiplication of an- ether are called powers of that quantity. Thus a z (144) is the square or second power of a (12); a* (1728) is the cube or third power of the same ; a 4 (20736) is the fourth power or biquadratic ; a s (248832) is the fifth power or sursolid ; and so on. The simple quantity a (12) is called the first power; and the small figure which points out the order of the power is called the index or exponent. 5. Quantities which produce a given quantity by suc- cessive multiplication, are called roots of the quantity pro- duced. Thus, 2 is the square root of 4, for 2X2iz4 3 is the cube root of 27, for 3X3X3=27 5 is the biquadratic root of 625, for 5X5X5X5=625 K 110 APPENDIX. V* or 2 \/ , denotes the square root of the quantity to which it is applied. Thus, ^/9=3, */al>~6. V denotes the cuhe root. Thus, 3 ^ 125=5, *+/~ac+b=:3. 6. The following are mixed examples of algebraic notation. i j_^~! /77 d ^ In Ex - l - bd or sx *= * c ^ d 12, which divided by c de -}-/>* c or 2, quotes 6, the value 2. abc -- - - = 69 of the first term ; of or 12X9=108, from which 5 subtracting^, or 8, there remains 100, which divi- oi ded bye? or 4, quotes 25, * the second term ; then = 130 /<* or 9X4=36, whose 6. a6+cxTHT d = S3 S( l"are root 6 is the third a-\-b f c tcrm ' an( * e terms ^ e ' ^' - /?~ == ^ ing added, because con- nectedbythesign X,the sum 37 j s t h e value of the expression. In Ex. 3. the numerator and denominator are both under the radical sign ; therefore we first divide, and then extract the square root of the quotient. In Ear. 4. the numerator only is under the radical sign ; we therefore extract its square root, and divide the root by the denominator. 7. To illustrate the use of algebraic notation in directing computation, we shall take the example of the rule for finding the value of an annuity of L.l for a given life on Mr de Moi- vre's hypothesis. See Table V. Let the difference between the proposed age of and be re- presented by n, which is called the compliment of life, the rate of interest by r, the present value of L.I due at the end to n years by a and the value required by v. a-^ZTiXr-r-a 1 The algebraic expression is v - ^ - The rule in words is, Find the present value of L.I due at the end of the compliment of life, to which add the compliment of life less one; multiply this sum ly the rate of interest, and to the product less one ; add the present value of L.I, the sum is the dividend. f V LOGARITHMS. Ill Multiply llie square of the rate of interest by the complement of life f the product is the divisor. Divide these terms, and the quotient is the value sought. From the brevity and distinctness of the algebraic expres- sion in this and other cases, algabraic notation deserves the student's pain to acquire, although he should not pursue that study farther. SECT. II. LOGARITHMS. 8. LOGARITHMS are artificial numbers, by the help of which several operations in arithmetic are performed with more ease ; and addition, in particular, supplies the place of multiplication. As tables of logarithms are arranged in different forms, we cannot here give directions for finding the logarithms corres- ponding to any number, or the number corresponding to any logarithm ; but the student must be made acquainted with the manner of using his own tables before he proceeds to the fol- lowing rules. The figure on the left hand of a logarithm, separated from the others, is called the index, and shews how many integer places there are in the corresponding number ; which is al- ways one more than the index. Thus, in numbers under 10, the index is ; in numbers between 10 and 100, the index is 1 ; between 100 and 1000, it is 2 ; and so on. The logarithms of decimal fractions have negative indexes. If there be no ciphers after the decimal point, the index is 1. If there be one cipher, the index is 2 ; and so on, A negative index is added when the logarithm is subtracted, and subtracted when the logarithm is added. The logarithms of mixed numbers are found in the same manner as those of integers ; but the index is regulated by the integers only. Thus the logarithm of 7328 is 3.864985, . of 732.8 is 2.864985, and of 73.28 is 1.864-985. The logarithms of vulgar fractions are obtained by subtract- ing the logarithm of the denominator from that of the nume- rator. 9. PROBLEM I. To perform multiplication by logarithms, add the logarithms of the factors ; their sum is the logarithm of the product, K2 12 APPENDIX. Ex. Multiply 125 by 72. Log. of 125 = 2.096910 Log. of 72 = 1.857332 Product 9000 3.954242 10. PROBLEM II. To perform division by logarithms Subtract the logarithm of the divisor from the logarithm c the dividend ; the remainder is the logarithm of the quotient. Ex. Divide 8928 by 279. Log. of 8928 = 3.950754 Log. of 279 = 2.445604 Quotient 32 1.505150 jll.' PROBLEM III. To find a fourth proportional to three given numbers, or to work the rule of three by logarithms : Add the logarithms of the second and third terms, anc from their suni subtract the logarithm of the first ; the remain- der is the logarithm of the term sought. Ex. 8631 : 7371 : : 7946 : Log. of 2d term 7371 = 3.867526 Log. of 3d term 7946 = 3.900149 7.767675 Log. of 1st term 8631 = 3.936061 4th term sought 6786 3.831614 12. PROBLEM IV. To involve numbers by logarithms: Multiply the logarithm of the number by the exponent of the power ; the product is the logarithm of the power. Ex. What is the cube of 21 > Log. of 21 = 1.322219 3 Cube 9261 3.966657 13. PROBLEM V. To extract roots by logarithms: Di- vide the logarithm of the given 'number by the exponent of the root ; the quotient is the logarithm of the root. Ex. What is the square root of 3969 ? Logarithm of 3969 - 3.598681 Koot 63 * = 1.799340. PROGRESSIONS. 113 Ex. 2. What is the cube root of 9261 ? Logarithm of 9261 = 3.966658 Root 21 = 1.322219 SECT. III. PROGRESSIOXS. 14. AN ARITHMETICAL PROGRESSION, or SERIES, is a rank of numbers that have equal differences. Thus, 2, 4, 6, 8, is an ascending arithmetical progression, where the com- mon difference is 2 ; and 30, 27, 24, 21, 18, is a descending arithmetical progression, where the common difference is 3. L " ,' r^tesf ^ term ' I " So} ^ ~ d the common difference, 2 or 3 n the number of terms, 4 or 5 s the sum of the series, 20 or 120 Any three of these five being given, the other two may be found. The sum of the first and last term of an arithmetical series is equal to the sum of the second and last but one, or of any two terms equally distant from the extremes ; and if the number of terms be odd, the middle one is equal to half the sum of these pairs. Upon this principle most of the opera- tions in arithmetical progression depend. 15. PROBLEM I. Given the greatest and least terms, and number of terms ; sought the common difference, and sum of the series ? KULE 1. Subtract tJie least term from the greatest t and sub tract I from the number of terms, divide thejirst remainder by the second ; the quotient is the common difference. RULE 2. Multiply the sum of the first and last terms by half the number of terms ; the product is the sum of the series. The algebraic expressions are d=^TZf, and s=a-f2 x ' 721 2 Ex. Given the first term 20, the last 100, and number of terms 17 ; sought the common difference and sum ? Answer, Common difference 5, sum 1020. 16. PROBLEM II. Given the extremes, and difference ; sought the number of terms, and sum ? K3 !M APPENDIX. Ex. Given least 24, greatest 144, difference 6: Sought number of terms and sum ? Ans. Number 21, sum 1761, $17. PROBLEM III. Given the number of terms, difference and sum : Sought the extremes ? Ex. Given number of terms 12, difference 4, and sum 300 : Sought the greatest and least term ? Answer, Greatest 47, least 3. 18. PROBLEM IV. Given either extreme, difference, and number of terms : Sought the other extreme and sum ? 1 X 2 Q. 1. A person spent L.I 90*8 in 12 years, and the expence of each year was L.8 more than that of the year preceding. How much did he spend the h'rst and last years ? Answer, L.I 20 and L.208. 2. The youngest child of a family was 6 years old, the eldest 21, and there was an year and a half between the age of each. How many children were there ? Ans. 11. 3. What debt can be discharged in a year, by paying 6s. the first week, 6s. the second, and a shilling more each week than was paid the preceding, and what is the last payment ? Answer, L.79, 6s. and L.2, 16s. 4. What is the value of a wood divided into 21 hags or parts, whereof one has been annually cut, allowing for each hag at the rate of'L.5 per annum, since the last cutting ? Answer, L.I 155. 5. A journeyman gains L.25 in the tenth year of his ser- vice, and his gain each year was 15s. more than the former. What did he gain the first year and altogether ? Answer, L.fs, 5s., and L.216, 5s. 19- A GEOMETRICAL PROGRESSION, or SERIES, is a rank of numbers, each of which bears the same proportion to the number immediately following. The successive terms are ob- tained by multiplying or dividing the preceding term conti- nually by the same number, and the multiplier is called the PROGRESSIONS. 11 J common ratio. Thus, 2,4,8, 16, is an ascending geome- trical series, whose common ratio is 2; and 21 6, 72, 24, 8, is a descending geometrical series, whose common ratio is 3, or rather J. The product of the first and last terms of a geometrical se- ries is equal to the product of the second and last but4, and its root 8 is the- first (Zf. o{b5 figure of the quote ; then we subtract 64 Gl from 7?, remainder 8, to which . the : cond period 25 being annexed, 165)825 makes up the resolvend 825. Then t *; Ae-fim 126 APPENDIX. 1 ac. 1 r. 14- p. ; in exchange for which the heritors agree l give him a square field equal to all the three. What is the side of the square ? Answer, 39 poles. 2. A square plantation, where the trees are 12 feet distant, contains 108900 trees. What is the length of the side, and how many acres does it contain ? Answer, 3960 feet and 360 acres. S. There are two circular ponds in a gentleman's pleasure ground ; the diameter of the less is 100 feet, and the greater is 3 times as large. What is its diameter ? Answer, 1?3.2 feet nearly. 4. * A wall is 36 feet high, and a ditch before it is 27 feet wide. Required the length of a ladder that will reach to the top of the wall from the opposite side of the ditch ? Answer, 45 feet. b. Glasgow is 44 miles west from Edinburgh; Peebles is exactly south from Edinburgh, and 49 miles in a straight line from Glasgow. What is the distance between Edinburgh and Peebles? Answer, 21 1 miles nearly, 28. RuLES^r extracting the CUBE ROOT. 1. Having divided the number into periods, as directed 26, Aprj.Jind the greatest cube number contained in thejirst or left hand period^ and place the root of that number as the first figure of the root sought. 2. Subtract the cube of that figure from thejirst period, and to the remainder bring down the next period. This makes up the Jfrst resolvend. 3. Multiply the square of the part of the root you have found ky 3, and to the product annex two ciphers. This makes up the trial divisor. 4. Divide the resolvend by the trial divisor , and place the quotient as the nextjigure of the root sought. 5 Multiply the part of the root formerly found by 3, and multiply the product by the last figure placed in the root, and an- nex a cipher to the last product ; this makes the second part of the complete divisor, and it is written under the trial divisor. 6. Under this write, the square of the last Jigure placed in the root ; which is the third part of the complete divisor. * The square of the hypothenuse or slanting side of a right angled frK angle, is e^ual to the sum of the squares of the other sides* EVOLUTION. 121 7. Add these numbers to the trial divisor ; the sum is the complete divisor. 8. Multiply the complete divisor by the last figure placed in the root, and write the product under the resolvend. 9. Subtract the product from the resolvend, and to the re- mainder bring down the next period, wliich makes up the second resolvend. 10. Proceed in the same manner with the second resolvend, find with the following ones, till all the periods be used. Ex. 1. 373248(72 root. Trial divisor 14700)30248 resolvend 420 4 Complete divisor 15124 2 Ex. 2. 45118016(356 27 First divisor 2700) 18118 first resolvend 450 25 3175X5= 15875 Second divisor 367500) 2243016 second resolvend 6300 36 373836x6=2243016 , APPENDIX. Example 3. 74-778091597(421; 64 4800) 240 10778 first resolvend 5044X2 r= 529200) 1260 1 10088 690091 second resolvend 530461X1 = 530461 55172300) 37890 9 159630597 third resolvend 53210199X3 = 1596305^7 In Ex. I. the nearest cube number to 373, the first period is 343, and its root 7 is the first figure of the root sought ; then 343 subtracted from 373, leaves a remainder of 30, to which we bring down 248, and this makes up the resolvend 30248. The square of 7 multiplied by 3, with 2 ciphers annexed, is 14700, the trial divisor; and the resolvend being di- vided thereby, the quotient is 2 ; then 3 times 7, multiplied by 2, with a cipher annexed, is 420 ; and the square of 2 is 4 ; and these numbers being placed under the trial divisor and added to it, make up 15124, the complete divisor; and this multiplied by 2, produces 30248, which is e- qual to the resolvend. Therefore the root is exactly 72. In Ex. 2. the first trial divisor 2700 might be get 6 times in the re- solvend ; but if we work with 6 according to th rule, the product of the complete divisor will exceed the resolvend ; therefore we diminish the quote by 1, and try 5, which answers. The second trial divisor is the square of 35 multiplied by 3. Required the cube roots o the following numbers ? " 1. 157464 Ans. 54 2. 397065375 735 3. 340068392 698 POSITION. Required the cube roots of the following numbers ? 4. 21024-576 Ans. 276 5. 253395799552 6328 6. 27270901 301 7. 1953 . 125 12 . 5 rein. 8. 195 .3125 5. SO 2005 9- 19 53125 2. 5-966141 10. 7584, 19. fJ4,S*706S< 11. 8888 2. 07*3*57 ' Qu. 1. -The side or a cubical altar being 1 cubit, it is re- quired to find the side of one of the same form, and of twice that size ? Ans. 1.259921 + cubits. 2. Required the side of a cubical mound, equal to one 288 feet long, 216 broad, and 4<8 high ? Ans. 14-4 feet. 3. If a ball 6 inches diameter weigh 13|lb. what will be the diameter of a ball that weighs 62 ^lb. ? ' Ans. 10 inches. 4. If 25 grains of gold gild a wooden ball which weighs 729 ounces, how many will gild one of the same kind that weighs 1728 ounces ? Ans. 44 j grains. SECT. V. POSITION. 29. IN position, we take any number, and perform the same operations with it which the question directs to be done with the number sought. The number thus obtained is call- ed the result. If the result be the same as the given num- ber, the assumed number is the number sought : If not* we proceed by the following rules, according to the nature oi' the question. In SINGLE POSITION state the following proportion, As the result : Is to the given number : : So is the position or number supposed : To. the number required. Ex. A general increases his army one-fourth by recruiting, then loses ^ by death, and of the remainder in battle ; af- ter which there are 1170 men remaining. How many were there at first ? L2 J24, APPENDIX. Suppose the army consisted at first of 1200 men. recruits | or 300 1500 lost by sickness Jg 150 remainder 135O lost in battle 225 result 1125 Then 1125 : 1170 : : 1200 : 1248 Ans. 30. In DOUBLE POSITION, we try two numbers as above, and find the errors or differences between the results and the given number. If the errors be of the same kind, that is, both greater or both less than the given number, we take their difference; but if the errors be of different kinds, (one greater and the other less than the given number) we take their sum. Then As the difference or sum of the errors : Is to the difference of the positions : : So is either error : To a fourth number, which number is called the correction ; and being added to, or subtracted from, the position producing that error, the sum or remainder is the number required. Ex. To divide the sarn of 310 between A, B, and C, in such a manner that B's share may be L.20 more than of A's, and C's may be L.I 5 more than % of B's. First, Suppose A's share was L.90, two thirds of which is 60, therefore B's share is 80, and three-fourths thereof 60 ; consequently C's share 75, and the sum of their shares or result 245; but it ought to be 310, therefore the error is 65. Secondly, Suppose A's share 108, B's will be found 92, and C's 84; therefore the result 281, and the error 2G\ As the results, being both too small, are of the same kind, we take their difference 39, and the difference of the position is 18 : Then 39 : 18 : : 26 : 12, the correction or error of the second position. And because the second position was too small, we add the correction, and obtain 120 for A's share ; which, being tried according to the. conditions of the question, answers. POSITION, 125 Er. 2. A and B began to trade with equal stocks. A added to his stock each year one-fourth of what he had at the begin- ning of that year; B increased his stock by an equal sura each year; which was less by L.75 than A's gain the third year; and at the end of three years A's stodk exceeded B's by L.99. Required what stock they "began with ? First, Suppose they began with L.480. A's gain the first year is L.120, the second year L.150, and the third L. 187, 10s. and his stock at the end of 3 years L.937, 10s. B's gain each year L.I 12, 10s. in all L.337, 10s. and his stock at the end of three years L.817, 10s. Therefore the excess of A's stock above B's, or the result is L.120; but by the question it should be L.99 ; therefore the error is 21. Secondly, Suppose they began with L.640. A's stock at the end of 3 years will be found L.I 2 50, by proceeding as above, and B J s L 1165; difference of their stocks or result L.85; error L.I 4. And because one of the results is greater and the other less than the given number, we take their sum 35 ; and the differ' ence of the positions is L.I 60 ; then 35 : 160 : : 14 : 64, the correction of the second position ; and as it appears from tho operation that when the positions are increased, the results become less; therefore the second position, which produced too small a result, is too great, and the correction being subtract-* cd from 640, the remainder 576 is the original stock required. Note 1. Questions in which the results are proportional to the posi- tions, are solved by single position. 2. Questions in which the results are not proportional to the positions, and which produce simple equations, when solved by algebra, may bt= solved by double position. Of this kind are questions where some given number is adtled to or subtracted from the position in the course of tlu operation. 3. Although the rules of position cannot solve questions which, when treated by algebra, do not produce simple equations, they generally afford a good approximation. 4. In the single rule, 1 may always be taken for the position, and in the double rule 1 and may be taken for the two positions. o. Questions that fall under the single rule may also bs solved by the double rule. The following are arranged promiscuously for a trial of the learner's skill, in referring them to the proper rules. Qu. 1. Required a number to which if a half and a sixth be added, and then a tenth of that sum subtracted, the re- mainder may be 216 ? Answer, Hi, L 3 126 APPENDIX. 2. A person mixes 50 Ib. of tea, part worth 6's. Id. and the rest worth 4s. so that the value of the mixture is 5s. Requi- red how much of each ? Answer, 24 Ib. at 6s. Id. and 26 at 4s-. 3. A and B began to play with equal sum's of money ; A won 20 guineas from B, and then lost of what B hud re- maining, and lastly, won 5 guineas, after which B had 10 guineas more than A. What did they begin with ? Answer, 80 guineas. 4. The number of scholars in a school was 80 ; there were one half more in the second form than in the first ; the num- ber in the third was f of that in the second, and in the fourth | of the third. How many were there in each form ? Answer, 12, 18, 30, and 20. 5. A field was sown with wheat at 5s. a bushel, and pro- duced 8 return ; the crop was sold at 4s. a bushel, and after paying for the seed, there remained L.33, 15s. How much was sown ? Answer, 25 bushels. 6. Four persons comparing their ages, B observes tliat he was 5 years older than A ; C that his age was | of the sum of A and B's ; D that his age was f- of the sum of the three others. Now the sum of their ages was 120 years, Sought their ages ? Answer, '20, 25, 30, 45. 7. A farmer kept a servant for every 40 acres he possessed ; and on taking a lease of 120 acres more, he engaged 4 addi- tional servants, after which he had a servant for every 36 acres. Required the number of acres and servants he had at first? Answer, 240 acres, and 6 servants. 8. One third of a man's life was spent before his first mar- riage, and the time he lived with his first wife was i of his life ; after being a widower 4 years he married again, and the duration of the second marriage was of that of the first. He isurvived his second wife 14 years, Kequired his age ? Answer, 72 years. PART II. BOOK-KEEPING. SECT. I. SINGLE ENTRY. 1. BOOK-KEEPING is the art of recording the occurrences of a merchant's business, in such a form as to exhibit a dis- tinct view of the state of his affairs; the debts due to him, and the debts he owes to others. The method by single entry is the simplest and shortest, but not the most perfect. It is generally used by shop-keep- ers, and requires two principal books, aDAY-BooK andLEDGEii; the form of which is shown in the following specimen. The DAY-BOOK begins with a list of the debts due to the owner, and of the debts due to him by others. Then every transaction by which new debts are contracted, or former debts discharged, is entered as it occurs, with the quantifies and price of goods bought or sold, or other circumstances necessary for explaining the transaction. When goods are sold on credit, we write A. B. [the purchaser] Dr, and then mention the article, or articles with the rates and amount. When we pay money, we write C. D. [the receiver] Dr to Cash ; when we buy goods, E. F. [the seller] Cr for the articles purchased ; when we receive money, G. H. [the payer] Cr by Cash. If debts be contracted or discharged by any other means, the person who becomes indebted to us, or to whom we pay a debt we formerly owed, is entered Dr ; and the persons to whom we become indebted, or who pays a debt he formerly owed, is entered Cr, and the nature of the transaction explained. 2. The LEDGER contains an account for every person with whom there are dealings on credit; where the articles for which he is accountable to us, and those for which we are account- able to him, are placed on opposite pages of the same toiio ; the Dr articles on the left hand page?, a.nd the Cr articles on '.he right hand pages, 128 BOOK-KEEPING. To post the ledger; allot a space tor every person or com- pany, whose name occurs in the list of debts, at the beginning of the day-book ; write the title, and enter the debts on the proper side, referring to the page of the former ledger wtiere the account was : and enter the names in an index prepared for that purpose : then proceed to post the articles from the day-book in their order, in the accounts of the person they be- long to, allotting a space for the account and writing the title, if it was not opened before. The date of the article is written on the margin, and the transaction is entered on the Dr side when the person is marked Dr in the day-book ; and on the Cr side when he is marked Cr in the day-book. When a single article is bought or sold, we mention it, with the quan- tity and rate, in the ledger ; but when several articles are bought or sold at the same time, it is more usual only to enter the sum of the whole, writing To Sundries, or By Sundries, and referring to the day-book for particulars. The number of the folio in which each article is posted, is marked on the margin, of the day-book. If the space assigned for an account be too small, it must be transferred to another folio. See Miss Ca- pel's account, transferred from folio 4- to folio 7, in the follow*- ing specimen. Instead of entering the Dr. and Cr articles on the opposite pages, some enter them all on the same page, and rule two sets of money columns, one for extending the sums of the Dr arti- cles, and the other for the sums of the Cr articles. 3. Besides these books, a CASH BOOK is generally kept for entering the sums of money received and paid on opposite pa- ges of a folio, in the form of the ledger ; and an INVOICE BOOK, in which invoices or accounts of goods purchased are transcri- bed, and which makes it unnecessary to enter the particulars of such purchases in the day-book. 4. It is easy to collect a state of all the debts due to the owner of the books, and those due by him, once a year or oftener ; from which, together with an inventory of the goods on hand, and ready money, the neat stock of the owner will be known ; and this compared with the neat stock at the be- ginning of tiie year, found in the same manner, shows the gain or loss upon his trade during the year. $ 5. Some shop-keepers enter ail their sales, those for. ready money as well as those on credit, in their day-book, j and when this is done, a column is generally ruled in the BOOK-KEEPING. 129 day-book, for extending the cash- articles, and the amount of money received is entered once a-week, or once a-day, in the cash-book. This method is not followed in the following spe- cimen ; but we recommend it as the preferable one, when, the articles are not very numerous and minute. 1. The first Day- Book and Ledger are entitled A, the second B, and so on. The balances of the accounts of each ledger supply materials for opening the new books. The an- nexed set, being supposed the second, is entitled B. It be- gins with lists obtained from the supposed balances of ledger A, and the balances with which the ledger is closed are to be transferred to ledger C. In order to. give the learner some practice in calculation, the values of the articles are not set down in the specimen of the day-book. When several articles are sold at the same time^ the amount only is placed ; and when a single article is sold, the value is left blank in the day-book, but will be found in. the ledger. DAY-BOOK. J-rf o. M LIST OF DEBTS due to James Ncale, Shop- keeper, Aldergate, L. s. d. .1 Samuel Remington, Chelsea 18 12 .1 Will. Floyer, Hackney 25 16 .1 Henry Cox, Cornhill 39 12 6 .1 Woodward and Jackson, Fleet-street 51 10 2 John Symons, Esq. of Haughton 739 2 Fred. Page, Hampstead 21 .2 Gco- Lewis, Aliiermanbury 33 2 .2 Anth. Walsh, Wood-steeet 18 197 14 3 LIST OF DEBTS due by said J. Neale, L. s. d. ,3 To Harris and Jones, Lombard-street per bill - - 100 .3 Edward Herbert, Ludgalehill 24 .3 Jo. Goring, Poultry 55-,- i > 129 5 < * 1S. 10 s 12 15 D 15 a. 9 6 1 8 "= Will. Fidding, Pall-mall, Dr. To 15 yards white silk, - at 25 yards cotton, SO - s. d. 7 4 9 Frederick Page, Cr. I... By cash, in full - ^3 Abated him s. d. 10 2 6 Miss Capel, Dr. To 12 yards lawn, at 3s. 9d. 5 - - - -^-rr, Edward Davies, Canon Street, Cr. By linens, per invoice book Thomas Dimsdale, Richmond, Dr. To 3| yds. superfine cloth, at 19s. George Carey, Dr. To 18 yds. linen, at 25 yds. ditto, 36 yds. ditto, 28 yds., ditto, s. d. 3 6 2 9 1 10 1 4 Jo, Goring, Dr. To cash, in full - 16- Miss Capel, Dr. To 15 yds. muslin, at 3| yds. persian, s. d. 4 6 2 4 Mr* Barron, Hanover Square, Dr. To 6 pair glo\es, - - at 12 pair silk hose, s. d. 1 2 12 DAY-BOOK. .6 6 .6 .7 Henry Cox, Cr. By cash, in full 07 . 20 5 10 56 14 ( t 12 6 Geo. Lewis, Cr. By cash, in part - Hugh Lloyd, Dr. To cash, in part - John Butter, Thames Street, Dr. To 4f yds. superfine cloth, - at 6 yds. second ditto, 2 hats, 3 i S. ( 19 = 12 16 ' i> . East India House, Cr. - 3y teas bought at sales, per invoice book East India House, Dr. 'o cash, paid deposit j ,15 - Robert Evans, Adelphi, Dr. V> 12| yds. cotton, at 15i yds. ditto, 7| yds. muslin, 16 s. d. 3 9 3 2 4 10 Miss Capel,Dr. 'o 6 Ib. ^ouchong tea, - at lOlb. congo ditto, s. d. 9 4 6 .3 Edward Herbert, Dr. 'o cash, in part - .7 Francis Apsley, Bloomsbury, Dr. 'o 7| yds. superfine cloth, - at 12 pair silk hose, - - 12 pair worsted ditto, -12 pair gloves, - s. d. 18 11 4 3 1 4 DAY-BOOK. 133 March's 8, 1787.' Mrs Barren, Dr. To 1 damask table cloth April 2.- Samuel Remington, Dr. To 22 yds. iinen at < 36 yds. sheeting 28 yds. diaper 5. John Radcliffe, Dr. fo 20 Ib. Souchong tea, at 9s. 2d. 9. Woodward and Jackson, Cr. 3y cash per order on Henry Hill : ll. Sir Thomas Morgan, Whitechapel, Dr. To 16f yds. silk, at 11s. 3d. 16 , 3y Cash in part Cha. Alien, Cr. 18. Jo. Goring, Dr. \> 2 pair silk hose, at 12s. 21. _ Richard Knight, Morpeth, Cr. >y hats, per invoice book y cash in full Geo. Lews, Cr. Miss Capel, Cr. y cash in part William Snoiue, Dr. o 20 yds. cottons, at 5s. 3d. ; 4. _ _ 6 Robert Evans, Dr. o 21 yds. linen 6 11). Souchong tea 12 Ib. congo tea M s\ d. 1 9 9 5 * 2 s, d. 13 20 134 DAY-BOOK. .8 A .3 .3 .1 3 .7 i V 8 .S Henry Norton Bel/ord, Dr. To Si yds. superfine cloth, - at 9| yds. cottons, 10 s. d. 18 6 5 George Carey, Cr. L. By cash - - 17 Abatement - - s. d. 9 1 Harris and Jones, Cr. By a year's interest on my bill Harris and Jones, Dr. To cash, paid them And granted them a new bill for L.50 19 William Floyer, Cr. By cash, in full 00 Anth. Walsh, Cr. By cash, in full Miss Capel, Cr. To 5 yds. fine linen, at 11s. *. .--,-.,- June John Butter, Dr. To 3 yds. muslin - at 12| yds. lawn, 1 s. d. 9 2 3 James Meadows, Piccadilly, Dr. To S| yds. cloth, at 18s. *7 . By cash, in full 11 Erftt-crd Herbert, Cr. By an assortment printed cottons, amount voice book per in- L. 5 17 77| 55 1C 18 10 10 DAY-BOOK. Henry Norton, Dr. TO 17/5 y ds - silk > at 14s - Richard Knight, Dr. To cash, paid their bill to Matthew 1 1 ult. 1 mdt, in full Honeywood William Fielding, Dr. To 22i yds. linen, at 7 pair worsted hose . 3 - - - j s. d. 2 3 4 2 Thomas Dimsdale, Dr. To 2| yds. muslin, 9s 2d. John Symons, Cr. By cash, in full Edward Davies, Dr. To cash, in full ' . James Meadows, Cr. By cash, in full Abated . . L. s. d. 3 Robert Evans, Dr. To 105 yds. linen, at 3s.' 135 3. d. !92f 7 60 INDEX TO LEDGER B, A Allen, Charles 3 Apsley, Francis 7 B Barren, Mrs 6 Buller, John 6 Balance 8 c Cox, Henry .- 1 Capel, Miss 4.7 Carey, Geo. 4? D Davies, Edward 5 Dirasdale, Tho. 5 E East India House 6 Evans, Robert 6 F Floyer,Will. 1 Fielding,' Will 5 G Goring, John 3 H Harris and Jones 3 Herbert, Edward 3 I K Knight, Rich. 7 L Lewis, George 2 Lloyd, Hugh 5 M Morgan, Sir Tho. 7 Meadows, Ja. 8 N, Norton, Henry 8 P Page, Fred. 2 Q R Remington, Sam. 1 Radclifte, John 4 S Symons, John 2 Snowe, Will. 4 T V W Woodward & Jack- son 1 Walsh, Anth. 2 X y Z LEDGER. 137 1 1 1 1 "SS ^ O j O O "- 1 | -H rH * 1 s ** !CO <3 ^ *^ **3 G^l rh O ' O o S y f a' . $ a Si tS ** ^ S ^ a ^_^ . "2 -2 44 3 3 g 8 ^g .2 ~^* ** f . *^ C3 ,3 ^ -^ *S M 35 -fl 3 "S 8 I y C^ C3 S M* a & ^ && 33 *& Oi O 3 G S-fr 00 . j>.a w^ -> rt s ^ tu *"* < ^ || 1 1 1 1 * T 1 o? co o o Jwj 2 * S s , G?^ | ^ f 1 <1 IM ^. e" <1 g ci So C*s yj K^ S) i-S "o 2 1:2 J2 r2 .2 l.o" C^ ' "^ 1 <2 1 1 3 fl.S c itfj w^ ^ * 3 ** 3 S s- ^ . 8 S3 O "O q |f2 ^ 13 ,^-NJ^ ^ (^ t- ^ j^. -H 00 b- ^ - ^ ^ QO ^ oo j.: cc ^ t G OH -^ M3 LEDGER. 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SO 0) -* 3 3 00 0) i^ g H nil CO I co in i-ild | i-iRi o? co i 10 I o 1 1 O< CM iO Ci _: I"- G<> 1 Gi | O CO CO ^O !> O I Ci ^ ^ 1 S | GO i 1. 1 1 * *5 (^ * ' ta ' S W i o ^ to 03 V K J-2 QJ "S o> O ^ *j r H ^Q "*rt '! ^ "l 1 "o aj*.2 ' ' a o f-< en ^ ^ -2 ' M S O> CO r2 \ t oj oj O ^) C3 G^ _OJ ^ TJ G) ^ - c 2> p C C 3 3 ^.|| 'v; |J w O Q fl 03 f*\ CJ *2 O O ^S Q Q ^H A Q H o O O HH HH H H E- 1 H H < GO CO O3 CO O 10 ^ o b- t- co l^- -H CO < V"" N QQ ^ * CO . 0) co . a) OO " t>^ O N*^ I""" ..O Z^ ^- es G *>- a & J^ C^ C^* C ^ fe S rH fcrl 3 *"' S 3 ^ g ^ ^ LEDGER. 143 Hi 3 o , 3, ns u CO O s-> O> I I S "^ "i 45 OD -Q^T 2 ! .-W S J 1 - % t3 -3 ft r.H< O s i- 0< 01 LEDGER, i- I M I 3S I | O CO O O) > r-i *O CO Oi "* I 00 S I & it- CO oo a> S ff CO CO WO sO " ' 1 ^g wast! a>.c-e as oo H H c2 r o o o o o HHHH r o H f2 O O O HHH o o HH o H o H , . > rH ^ OO (if t- a rt 3 is ioo F y I 145 SECT. II. BOOK-KEEPING BY DOUBLE ENTRY. 7. THE books of a merchant ought to contain every parti- cular relating to the aSairs of the owner, and be disposed in such an order as to afford ready and complete inforriatKm in every point for which they may be consulted. Ttie matter which they should exhibit may be reduced to the three fol- lowing heads : First, The debts which are owing to the owner, and the debts which he owes to others. Secondly, The goods and other articles of property which belonged to him ; the quantity and value sold, or otherwise disposed of; and the quantity and value which still remain in his possession. Thirdly, The amount of his stock when the books were opened; the profits he has obtained, and the losses he has suf- fered-since ; and the amount of his stock at present. The method of book-keeping by single entry answers only for the first of these. The Italian method by do'uble entry comprehends them all. It requires three principal books, the Waste-book, Journal, and Ledger. Of the WASTE-BOOK. 8. The WASTE- BOOK, or DAY-BOOK, contains an exact register of all occurrences in business in the same order as they take place. It begins with an inventory of every tiling be- longing to the owner, a list of the debts due to him, and of the debts he owes to others : It is carried on with a full rela- tion of ail the money he receives, or pays ; of all the goods he buys or sells; arid of every other occurrence *io his business. Each article should be entered as soon as the transaction takes place aud'sliouid be clearly expressed in the plainest language. It should r. > supply from the accountant's memory, but shoiud be fully intelligible to any person:, 'however un- acquainted with the busings. At the same time, the book should be written with all convenient brevity ; and therefore som times may refer to invoices and other accounts for pant- - cui;;r>. The accountant's first care should be to have nothing defective or ambiguous ; his second, to have nothing super- fluous. N U6 BOOK-KEEPING BY DOUBLE ENTRY, In entering sales, the packages, quantities, rates, and value of die articles are mentioned. In articles relating to Bills, the date, drawer, accepter, and time of payment, are narrated. In insurances, the ship, master, voyage, and rate of the pre- mium : and the particulars relating to other articles in the same manner. The date is written in text on the top of each page. The articles are separated from each other by a line ; and the transactions of one day are separated from those of another by a double line, in the middle of which there is left a blank space for inserting the day of the month. Of the LEDGER; 9. The LEDGER is a book in which articles of the same kind are collected together ; and for this reason it is divided into many accounts, under which the different branches of the business are arranged. The general form is pretty tnuch the same in the Italian method as in the method by single en- try, but the matter is much more extensive. Accounts in the ledger are of three kinds, which answer to the three purposes of book-keeping mentioned 7. 10. First, PERSONAL ACCOUNTS, which contain on the Dr side all debts due to us when the books are opened, and during the course of the business, whether arising from goods sold, money lent, or otherwise ; also the payments made by us of debts which we owed. On the Cr side, they contain debts due by us at opening the books, or contracted during the course of the business, and payments made to us of debts that were owing us. The balance shows what is owing when the books are closed. It, in the course of the business, a variety of debts be owing us by bills, in order to save the trouble of opening an account for each debtor of this sort, a general account is kept for them all, under the title of Bills Receivable. All bills due to us are entered on the Dr of this account when received, and on the Cr when paid, or otherwise disposed of. The balance shows the amount of bills on hand. In like manner, an account o/ bills payable is kept for en- tering the bills we owe to others. It contains, on the Cr the bills whicb we accept; and ton the Dr the bills which we pay; and the balance shows what bills we still owe. BOOK-KEEPING BY DOUBLE ENTRY. 147 The account of Bills of Exchange contains foreign bills, when bought, on the Dr. and the same, when sold, on the Cr. H. Secondly, REAL ACCOUNTS. By this we understand accounts of property of whatever kind, such as ready money, goods, houses, lands, ships, shares in public companies, and the like. The account of ready money is entitled Cash. On the Dr the money on hand at opening the books is entered, and after- wards every article of money received. On the Cr there is entered every article of money paid out ; and the balance shows how much ought to be on hand. Accounts of goods are generally ruled with inner columns for entering the quantities. When the books are opened, the goods on hand are entered on the Dr of the respective ac- counts ; the quantities being placed in the inner, and the va- lues in the outer column. Goods bought are entered in the same manner, and goods soid are entered on the Cr ; the quantities and values being placed in the proper columns. Charges laid out on goods are entered on the Dr ; and when an incidental advantage arises from then:, ^-\\ -^ public bounty, it is entered on the Cr. If the sums of the inner columns on the opposite sides be equal, it appears that the goods are all sold, and then the ba- lance of the money column shows the gain or loss. If rhe sum of the Cr be greater, it is gain ; if the Dr be greater, it is loss, If the sum of the inner column be greater on the Dr side, it appears that part of the goods are on hand ; and their value must be added to the sum of the Cr, in order to deter- mine the gain or loss, Accounts of ships, or shares of ships, contain on the Dr the value of the ship when the books are opened, and all expen- ces laid out thereon ; on the Cr all freights received, ui like manner, accounts of houses or lands have the vahc of the subject, and all repairs, or other charges, entered tm the Dr, and all rents, or other profits received, on the Cv If the subject be sold in whole or in part, the sale is entered on the Cr. And, after valuing the subject, the balance on hand, (if any) shows the gain or loss. Accounts of property in the public funds, or shares in com- panies, public or private, contain the value, or monev paid in, on the Dr, and the dividends received on the Cr, and are balanced as other real accounts. N2 US BOOK-KEEPING BY DOUBLE ENTRY. Some persons open accounts for household furniture, plate, jewels, books, or the like. In general, real accounts contain the value of the proper- ty, and all charges on the Dr, and the sales and other returns on the Cr. When the account is to be balanced, if any pro- perty remains, the value thereof is placed on the credit ; and then the balance shows the loss or gain, according as the Dr or Cr side is the greater. 12. Thirdly, ACCOUNTS of STOCK, PROFIT and Loss, and its subsidiary accounts, which are sometimes called Fictitious accounts. The stock account contains on the Dr the amount of the debts which the owner owes when the books are opened ; and, on the Cr, the amount of ready money, goods, debts, and property of every kind belonging to him ; therefore the balance shows what his neat stock is ; or, in case of bank- ruptcy, how- much his debts exceed his effects. There is no- thing further entered in this account till the books are ba- lanced ; and then, if the business has yielded profit, the neat gain is entered on the Cr ; if it has been unsuccessful, the neat loss is entered on -the Dr ; after which, the balance shows the neat stock at the time the books are closed. The Profit and Loss account contains every article of gain on the Cr, and every article of loss on the Dr. The balance shows the neat gain or loss. This account is partly compo- sed of articles that occur while the books are running. For example, legacies received are entered on the Cr ; goods de- stroyed on the Dr. The rest of the articles are those of gain or loss, arising from the real accounts, which are collected when the books are balanced. 13. It has been found convenient to open several subsi- diary accounts, in order to shorten and methodize that of profit and loss. These contain certain articles of gain or loss which may be reduced under distinct heads. They are in effect so many parts of the profit and loss account ; tr.id their balaaces are entered on the proper side of that account when the books are closed. The chief of these accounts are the following : Interest account, Which contains on the Dr sums paid or incurred for interest; and on the Cr sums received, or become due for the same. Commission- account, Which contains on the Cr articles of BOOK-KEEPING BY DOUBLE ENTRY. 149 gain received, or owing us, for our trouble in transacting business for others. There are seldom any entries on the Dr. Charges merchandize. Which contains on the Dr all char- ges paid or incurred on the business, which do not belong to any particular account, as shop rent, public burdens for trade, clerk's wages, postages, and the like. If any of these should afterwards be charged to some other account, the sum so charged is entered on the Cr, Proper expences, Which contains on the Dr money, or any thing else, withdrawn from the trade for our private use. There are seldom any entries on the Cr. The amount of this account, as well as the former, is not properly loss; but as it has the same effect in diminishing the stock, it is placed in the same manner to the Dr of profit and loss. Loss by bad debts, Which contains on the Dr such debts as we reckon desperate ; and on the Cr any of these which may happen to be unexpectedly recovered. Account of abatements, Which contains on the Dr discounts allowed by us on payments received; on the Cr discounts allowed to us on payments made. Insurance account, Which contains on the Cr premiums received, for making insurance; and on the Dr losses sus- tained on the same. The balance shows the gain or loss which arises from dealing in insurance. More or fewer of these accounts may be used, according as the articles are frequent ; and others may be invented to suit the purposes of the business which the books are kept for. 14. In FOREIGN TBADE, When goods are sent abroad at our risk, and consigned to a factor to be sold in trust for us, it is necessary to open several accounts which do not occur in domestic trade, to show what goods we have at sea, whether outward or homeward bound ; what goods we have in our factor's hands ; what debts are due to our factor for our goods sold on trust ; and what is owing to us by our factor, or by us to him. For these purposes the following accounts are kept : . Voyage to B, Which contains on the Dr the value of the goods sent to sea, with charges, and on the Cr the value of the cargo when it arrives at the place of destination, or whea the adventure otherwise comes to an issue. The balances of 150 BOOK-KEEPING BY DOUBLE ENTRJT. these accounts show what property we have at sea in voyages outward. W. L. (the factor) my account of goods, which contains, on the Dr the value of the goods in the factor's hand, and on the Cr the disposal of the same. The balance shows what goods remain on hand ; and, when the sales are finished, it shows the gain or loss. W. L. My account of debts, or My account on time, which contains on the Dr the debts owing for goods sold by our factor, in trust, for us, and on the Cr the payments received by him for the same. The balance shows the extent of out- standing debts. W L. My account current, is a personal account between our factor and us. Voyage or adventure from B, which contains the value of goods shipped for us, on the Dr, and their value when they come to hand, or are otherwise disposed of, on the Cr. The balance shows what property we have at sea in voyages home- ward. 15. A FACTOR is a person employed to sell goods, or transact any business for another. His books ought to exhi- bit a distinct view of the state of affairs under his charge ; and, for this purpose, his ledger must contain the following accounts, besides the usual ones respecting his proper busi- ness. A. H. (the employer) his account of goods, which contains the charges paid out on the Dr, and the goods sold on the Cr. It may be ruled with inner columns, and the quantities received entered on the Dr, the quantities sold on the Cr, in order to show what remains on hand. A. H. His account of debts, which contains the debts due for our employer's goods on the Cr, and the payments of the same on the Dr. A. H. His account current, which is a personal account between the factor and his employer. These accounts are counterparts to those kept by the em- ployer; the Dr of the one corresponds to the Cr of the other. 16. In PARTNERSHIP the following accounts are used: E. M. (the partner and manager) my account in company , when we have any business under the management of ano- ther partner. Oar share of the goods or other property in the BOOK-KEEPING BY DOUBLE ENTRY. 151 hands of the manager is entered on the Cr of this account, and the returns obtained from the same are entered on the Dr. The balance shows what property \ve have in the com- pany ; and what gain or loss has arisen from it, when the business is concluded. Goods in Company, Voyage in Company, Factor my account of Goods in Company, and others of the same kind, are kept by the partner who manages the affairs of the company. Their contents and balances are of the same nature as in domestic trade. 1 7. Other accounts may be CAOvenient on some occasions. Among these are the following : Suapence account, which contains on the Dr goods sent off without orders ; and on the Cr the same goods, when return- ed, or when notice is received that the person to whom they were sent intends to keep them. Goods bought on contract, which contains on the Dr goods bought on contract or forehand bargain, but not yet received ; and on the Cr goods received in fulfilment of these bargains. Goods sold on contract, contains on the Cr the goods we sell on forehand baigain ; and on the Dr the goods delivered in fulfilment thereof. Account of bad debts, contains on the Dr such debts due [to us as are reckoned desperate. It serves to distinguish them from the effective articles of our property, and saves the trou- ble of transferring the particular debts from one ledger to another. If any of these debts happen to be recovered, the payment is entered on the Cr. 18. Every simple transaction in business belongs to two accounts, and must be entered on the Dr of the one, and on the Cr of the other. Thus, when a person becomes indebted to us, the article he owes must be entered on the Dr of his account ; and if it be for money paid him, it is also entered on the Cr of cash ; if for goods sold, it is entered on the Cr of the account of goods ; if for any thing delivered him by another person at our desire, it is entered on the Cr of the deliverer's account ; if for any wager or bargain, by which we are gainers, it is entered on the Cr of profit and loss. Thus, in whatever way the debt arises, it is entered on the Cr of some other account, as well as on the Dr of the per- son's account who owes it. In like manner, when we become indebted to any person. 152 BOOK-KEEPING uv DOUBLE ENTRY. the article we owe must be entered on the Cr of his account. If it be for money received, it is also entered on the Dr of cash ; if for goods bought, it is entered on the Dr of .the ac- count of goods ; if for any thing delivered to another person at our desire, it is entered to the Dr of the receiver's ac- count ; and if it be in consequence of a losing bargain, it is entered on the Dr of profit and loss. Again, when goods are received, the transaction is entered on the Dr of the account of goods. Jf they be bought for ready money, it is also entered on the Cr of cash ; if on trust, it is entered on the Cr of the seller ; if they be exchanged for other goods, it is entered on the Cr of the goods delivered ; if they be obtained without any return, it is entered on the Cr of profit and loss. * When goods are delivered, the transaction is entered on the Cr of the account of goods ; and if they be sold for ready mo- ney, it is also entered on the Dr of cash ; if on credit, it is entered on the Dr of the purchaser ; if exchanged for other goods, it is entered on the Dr of the goods received ; and if they be given away gratis, or destroyed, it is entered on the Dr of profit and loss. Thus every article in any account corresponds to some other article on the opposite side of a different account. % The same sum is entered on the Dr of one account, and on the Cr of the other ; and it follows from this, that, If all the ac- counts in the ledger be added, the amount of the sums of the Dr will be equal to those of the Cr. Of the JOURNAU $ 19. The JOURNAL is a fair record of all the transactions compiled from the waste-book, in the same order as they stand there ; but expressed in technical style, that it may be trans- ferred to the ledger with more ease. When we are to enter any article in the journal, we must consider which accounts in the ledger it will require to be placed to, both on the Dr and Cr, and write [the former ac- count ; Dr to [the latter account}; then we annex an expla- nation of the article, and place the sum in the money column. Example. Waste-book.) Sold for ready money, SO yards linen, at 3s. L.4 10 Journal.) Cash Dr to Linen, Sold 30 yds. at 3g, 4 10 (,) BOOK-KEEPING BY DOUBLE ENTRY. 153 Here we consider, that the article must be entered on the Dr of cash, because money is received; and on the-Cr of linen, because linen is delivered : Therefore we write Cash Dr io linen; to which we annex an account of the transaction. The article thus entered is called a Journal post'. Cash is called the Dr Linen the Cr f the words Cash Dr to Linen the En- try, and the following words the Narration. The learner will be able from this example, to enter any simple article in the journal, providing he knows the accounts to which- it should be posted on the Dr and Cr of the ledger. The knowledge of this must be collected from the description of the ledger accounts already given, and is summarily com- prehended in the following general rules : I. Every thing received, and every person accountable to us, ZA Dr. II. Every thing delivered, and every person to whom we art accountable, is Cr. The journal should be written by one person, in a fair hand, and at leisure hours. The articles are separated, and the titles and dates marked in the same manner as in the waste- book, 8. The entries are written in half text, for ornament and distinction. In the inventory, the designation of every person is mentioned ; and the same is done the first time that any name occurs in a journal entry. 'The narration should be complete, without referring to the waste-book ; and so clear, that every person acquainted with the style ofr the journal may understand it with ease. When the post is written we mark a dash / against the article, on the margin of the waste-book, to show how far the writing of the journt il is advanced. 20. As the whole art of writing the journal consists in a proper choice of Drs and Crs, we shall first give some rulos for the most common cases of simple posts, and a few exam- ples for the illustration and practice of each; then we shall ex- plain the nature and form of complex posts ; and lastly, lay down some further rules for journalizing transactions which frequently occur. RULE I. The person to whom any thing is delivered is Dr to the thing delivered^ when nothing is received in return. Therefore when money is paid, the receiver is Dr to cash. 151 BOOK-KEEPING BY DOUBLE ENTRY. When goods or other property, is sold on credit, the pur- chaser is Dr to the thing sold. Thus, Waste-book.) Paid John Bell in full L.52 Journal.) John Bell Dr to Cash, paid him in full 52 Waste-book.) Sold 50 yards cloth to J. Hill, at 12s. 30 Journal.) J. Hill Dr to cloth sold him 50 yards, at 12s. 30 Ex. 1. Sold James Selwyn, 12 puncheons rum, at L.41 L.492 2. Paid Aaron Hill, in part 73 12 3. Lent Thomas Trader per note on demand, 150 4. Sold Berry and Jenkins, 1200 yards linen, at Is. 6d. 90 $ 21. RULE II. A thing received is Dr to the person from tokom it is received, ivken nothing is delivered in return. Therefore when money is received, Cash is Dr to the pay- cr ; when goods are bought, the goods a*e Dr to the seller. Thus, Waste-book.} Received from Thomas Gay in full L,72 Journal.) Cash Dr to Thomas Gay, received in full 72 Waste-book.) Bought from J. Hawley, 60 Ib. wool at 9d. 250 Journal,) Wool Dr to J. Hawley, bought 60 Ib. at 9d. 250 Ex. 1. Bought from James Hanway 100 qrs. wheat, at 24s. L.I 20 2. Received from D, Carew, in full 77 12 6 3 Borrowed from H. Lombard, per bond, 1000 4. Bought from Fr. Mariner, one third share of ship Enterprise, value L.I 700 56613 4 2%. RULE III. A thing received is Dr to the thing given for it. Therefore goods bought for ready money are Dr to Cash. When goods are sold for ready money, Cash is Dr to the goods. When goods are bartered, the goods received are Dr to the goods delivered. Thus, Waste-book.) Bought for ready money 10 hds. wine, at L.I 5 L.I 50 Journal.) Wine Dr to Cash, bought 10 hds. at L.15 150 BOOK-KEEPING BY DOUBLE ENTRY. 155 Waste-book.) Sold for ready money 100 gallons rum, at 9s. L.45 Journal.) Cash Dr to Rum, sold 100 gallons, at 9s. 45 O Waste-book.) Bartered 3 lids, wine, at L.I 5 for 100 gallons rum, at 9s. 45 Journal.) Rum Dr to Wine, received 1 00 gal- lons, at 9s. in barter for 3 hds. at L.I 5, 45 Ex. 1. Bought for ready money, 31 cwt. 2 qrs, 14 Ib. madder, at L.6, 8s. per cwt. L.202 8 2. Sold for ready money, 75 Ib. tea at 6s. 4Jd. 23 18 1 3. Bartered lOOOlb. allum, at 6d. for 200 bu- shels salt, at 2s. 6d. 25 4. Paid for one fourth share of ship Adven- ture, 20 hds. wine at L.22, 10s. 450 23. RULE IV. Goods and other real accounts are Dr for all charges laid out on them. If money be laid out, they are Dr to cash ; if any thing else be delivered, they are Dr to the thing delivered; if the charge betaken on trust, they are Dr to the person to whom it is due. Thus, Waste-book.) Paid for repairs to Ship Traffic, L.I 8 Journal.) Ship Traffic, Dr to Cash, paid for re- pairs 18 00 Waste-book.) Delivered wood from my timber- yard for repairing the Angel-Tavern. 15 00 Journal.) Angel-Tavern Dr to Timber, delivered for repairing the same 1500 Waste-book.) Due to William Carpenter for re- pairs to the Angel-Tavern 12 Journal.) Angel- Tavern Dr to William Carpenter due him for repairs 12 Ex. 1. Paid duty on 18 tons iron, L.2 16 2 50 11 2. Due Thomas Smith for freight of the same, at 25s. per ton 2210 3. Delivered from my warehouse 400 yards sail-cloth, for the use of the ship Neptune, be- longing to me, at lOd. 16 13 4 Paid for 500 bushels lime, at 6d. for impro- ving the farm of Sunnyside 12 10 24* RULE V. When rents of houses or lands, freights of ships, bounties on goods, or any other profit sjrjm rc< i amounts, are received, Cash is Dr to the account Jrom which the profit 156 BOOK-KEEPING BY DOUBLE ENTRY. arises: If any tiling besides money be received, the article re* ceived is Dr: IJ 'they remain unpaid, the person who owes them is Dr. Thus, Waste-book.) Received freight of the ship Traf- fie for a voyage to London L.35 Journal.) Cash Dr to ship Traffic, received freight to London 35 Waste-book.) Received 100 barrels salmon, being the rent of Inver-fishery, at 52s. 260 Journal.) Salmon Dr to Invcr -fishery, received the rent, being 100 barrels at 52s. 260 Waste -book.) John Public owes me a year's rent of the Angel-Tavern 52 Journal.) John Public Dr to Angel-Tavern, for a year's rent due by him 52 Ex. 1. Received a year's money- rent of the farm of Sunnyside 120 2. Received 50 quarters wheat, being the part of I he rent of the farm of Sunnyside, pay- able in grain, at 36's. per quarter 90 3. Henry Powel owes me for freight of the ship Neptune from London to Lisbon 70 25. RULE VI. When an article of loss occurs, Profit and "Loss, or some subsidiary account, is Dr. If the loss be paid in ready money, it is Dr to cash ; if it be paid in any thing else t it is Dr to the thing delivered. If it remain unpaid, it is Dr to the person to whom it is owing. Thus, Waste-book.) Given my daughter at her mar- riagc L.500 Journal.) Projit and Loss Dr to Cash, given my daughter at her marriage 500 Waste-book.) Taken for family use from my , granary, 3 boils meal, at 13s. 4d. 200 Journal.) Profit and Loss for proper expences) Dr to Meal, taken for family use, 3 bolls at 13s. 4d. _ 2 Waste-book.) Due James Rich, for a year's in- terest on L.I (.-00, at 4 per cent. 40 Journal.) Profit and Loss (or Interest 'Account) Dr to James Rich, due him a year's interest on L.1000, at 4 per cent. 40 BOOK-KEEPING BY DOUBLE ENTRY. 15? Ex. 1. 3 Barrels raisins are stolen from my Ware house, at L.2, 15s, - L.8 5 2. Paid H. Lombard a half year's interest on my bond of L.1000, at 4- per cent. 20 3. Due Thomas Benson for a year's rent of my ware-house - - 30 4. Taken, for my own expences, anno 1787 500 26. RULE VII, When an article of gain occurs that is not immediately connected ivith any real account, Cash, the article received) or the person accountable for it, is Dr to Profit and Loss, or to some subsidiary account* Thus, Waste-book.) Received in a gift from my father L.100 Journal.) Cash Dr to Profit and Loss, received from my father 100 Waste-book.) Received in like manner at opening shop, 100 yards cloth, at 12s. 60 Journal.) Cloth Dr to Projit and Loss, received from my father at opening shop, 100 yards at 12s. - 60 Waste-book.) James Barbour owes me a year's interest of L.1000 50 Journal.) James Barbour Dr to Projit and Loss, [or to interest account] due by him for a year's interest of L.I 000 - - 50 Ex. \ . Received for my trouble in settling John Payne's affairs - - 220 2. My uncle, John Friend, has left me a lega- cy, payable by his executp^r John Fell 100 3. Received a pipe claret wine in a present from my correspondent at Bourdeaux 32 4. Thomas Harvey owes me for commission on L.I 200, at A per cent. 300 27. RULE VIII. When one person pays money, or delivers any thing else to another on our account, the person luho re~ ceives it is Dr to the person who pays it. Thus, Waste-book.) James Goldsmith has paid the Bank of Scotland on my account - L.100 Journal.) Bank of Scotland Dr to James Gold- smith, paid them by him - 100 Waste-book.) Arthur Young has delivered James Baker ] OU quarters wheat, for which I am to account to him, at 30s. - - 1 50 O 158 BOOK-KEEPING BY DOUBLE ENTRY. Journal.) James Baker Dr to Arthur Young, for 100 qrs. wheat, delivered him on iny account, at 30s. - - L.I 50 Ex. 1. William Hunter has paid Thomas Fisher on my account, per receipt 65 2. William Telfer has received from A." Smith, in consequence of a letter of credit from me, 100 3. Delivered Richard Hawke my bill on Will. Aislabie, 30 ddt. - 50 4. John Gurney has drawn a bill on Sam. Sim- inonds on my account, 2 oidt. - 3.50 28. A COMPLEX POST is one that contains either more Drs or more Crs than one. The form of these will appear from the following examples. jE.v. 1. Sold William Drapier, 25 pieces cloth, at L.I 5 apiece, L.375 130 stones wool, at 5s. 6'd. a stone, 35 15 L.410 15 If the two articles sold to William Drapier were entered separately in the Waste-book, and transferred to the journal by RULE I. they would stand thus : William Drapier Dr to Cloth, sold him 25 pieces, at L.15, ' - - L.375 William Drapier Dr to Wool, sold him 150 stones, at 5s. 6d. - - 35 15 And if these were posted to the ledger, there would be two articles placed to the Dr of William Drapier, one to the Cr of Cloth, and one to the Cr of Wool. But the sales may be entered in the form of one complex journal post, as follows : William Drapier Dr to Sundries, To Cloth, for 25 pieces, at L.15, L.375 To Wool, for 130 stones, at 5s. 6U 35 15 . L.410 15 And then there is only one article on the Dr of William Drapier in the ledger. Ex. 2. Sold 10 pieces cloth to William Drapier, at L.I 5, L.150 12 ditto to John Mercer, at do. 180 22 L.330 BOOK-KEEPING BY DOUBLE ENTRY. 159 This example also falls under Rule I. But whereas there was one Dr and two Crs in the former example, there are two Drs and one Cr in this. William Drapier and John Mercer, the purchasers, are Drs for their respective quanti- ties ; and Cloth, which is the only thing delivered, is Cr for the whole quantity. The journal post is, Sundries Drs to Cloth, Will. Drapier, for 10 pieces, at L.15, L.150 John Mercer, for 12 ditto, ditto, ISO L.330 22 Ex, S. Bought 50 qrs. wheat from J. Tull, at 35s. L.S7 10 12 from E.Ellis, at 36s, 21 12 L.I 09 2 62 Journal, Rule II. Wheat Dr to Sundries, To J. Tull, for 50 qrs. at 35s. L.8? 10 To E. Ellis, for 12 qrs. at 36s. 21 12 L.I 09 2 62 Ex. 4. Sold 150 qrs. beans to A. Arnot, at 13g. 4d. L.I 00 75 ditto to S. Berry, 13s. 4d. 50 18 ditto, for ready money, 13s. 2d. 11 1? 243 L.161 17 Journal, Rules I. and III. Sundries Drs to Beans, Alex. Arnot, for 150 qrs. at 13s. 4d. L.100 S. Berry, for 75 13s. 4d. 50 Cash, ^ for 18 13s. 2d. 11 17 L.161 17 24-3 29. ADDITIONAL RuLES^or JOURNAL ENTRIES. 1. The journal entry of the inventory at opening the books is Sundries Drs to Stock ; Cash for ready money, Goods, Voy- ages, &c. for the articles of property belonging to you, and Debtors and Bills receivable for debts due you. 2. The list of debts due by you is entered thus, Stock Dr to Sundries, To Creditors, and To Bills payable. 02 J J 160 BOOK-KEEPING BY DOUBLE ENTRY. t 3. When an account of l?ills receivable is kept ; if you sell goods upon a bill, enter Bills receivable Dr to Goods. 4. If you lend money upon a bill, Bills receivable Dr to Cash. 5. When you receive payment of a bill entered as in the two last posts, Ca&h Dr to Bills receivable. 6. If you discount a bill entered as above, Sundries Drs to Bills receivable ; Cash for the money received, and Interest account for the discount or interest deducted. 7. If you deliver tke bill on trust, or in payment of a for- mer debt, Receiver Dr to Bills receivable. 8. If you buy goods or borrow money on a bill, when an account of bills payable is kept, Goods purchased, or Cash Dr to Bills payable. 9. When you pay a bill entered as above, Bills payable Dr to Cash. 10. When you receive from your correspondent a bill on another person, you may enter, Bills receivable Dr to tic Re- mitter ; and then when the bill is paid, Cash Dr to Bills re- ceivable ; but if no entry be made when the bill is received, the entry at payment is Cash Dr to Remitter. 1 1. When you accept a bill drawn on you by your corre- spondent, you may enter, Drawer Dr to Bills payable ; and then when you pay it, Bills payable Dr to Cash; but if no en- try be made when the bill is accepted, the entry at payment is Drawer Dr to Cash. 12. If you draw a bill on one person, and deliver it to an- other upon trust, or in payment of a debt formerly due him, -Receiver Dr to the person drawn on. 13. But if you receive money, or any thing else for the bill, Cash, or ihe thing received, Dr to the person drawn on. 14. If one person draw a bill on another on your account, Drawer Dr to the person on whom he draws. 15. If you purchase a bill of exchange with an intention to sell it again, Bills oj Exchange Dr to Cash, if bought for ready money ; or to the person from whom received, if it be not paid for. 10. When you dispose on a bill of exchange entered as above, Cash, or person to whom delivered orient, Dr to Bills of Exchange. 17. When you cause insurance to be made on a ship or BOOK-KEEPING BY DOUBLE ENTRY. 161 cargo of your own, Ship N. [or voyage] Dr to Cash, if you pay ready money ; or to the Insurer or Broker, if on credit. 18. If a ship, which was partly insured, be lost, Sundries Drs to Ship ; Insurers for the sums insured; or Cash or Bills receivable, if they give ready money or bills ; and Profit and Loss for the value of the part lost. 19. If you agree to underwrite upon, or insure a ship for another, Cash, if you receive ready money, or person insured if on trust, Dr to Insurance account. 20. When you settle a loss upon a ship you have insured, Insurance account Dr to Cash, if you pay ready money ; or to Bills payable, if you grant your bill for it. 21. When you receive payment of a debt with interest, Cash Dr to Sundries ; To payer, for principal, and to Interest account for interest. Or you may tirst charge the payer Dr to Interest account for interest; then Cash Dr to the payer for the whole. 22. When you pay a debt with interest, Sundries Drs to Cash ; Receiver for principal and Interest account for interest. Or Interest account Dr to Receiver for interest, and Receiver Dr to Cash for the whole. The alterations in this and the former article, if the debts be constituted by a bill, are ob- vious. 23. If your debter becomes bankrupt, and you accept a composition in full, Sundries Drs to the bankrupt ; Cash for money received ; Bills receivable if bills be received, and Pro- Jit and Loss, Loss by bad debts, or Desperate debts for balance. 24. If you receive goods of several kinds in exchange for other goods of several kinds, either of equal value, or where the balance is paid in money, enter twice thus : first, A. B. Dr to Sundries, to Wine and Rum delivered, and to Cash if money be delivered. Then Sundries Drs to A. B. Tobacco, Sugar and Cotton, received, and Cash if money be received. Although no account is necessary for A. B. this method is the best, as the entry otherwise would be Sundries Drs to Sun- dries ; and complex posts where there are both several Drs and several Crs always occasion some confusion, and it is bet- ter to avoid them. 25. When you send away goods in expectation of their being kept, Suspense account Dr to Goods. If your cor- respondent I, S. advises he is to keep them, /, S. Dr ta 03 1(>2 BOOK-KEEPING BY DOUBLE ENTRY. Suspentc account. If he sends payment, Cash Dr to Sits* pense' account. If he return them, Goods Dr to Suspense ac- count. 26 When you contract to purchase goods, e. g. tobacco, to be delivered at the time agreed on, Goods bought on contract Dr to M. N. the seller. When you receive it, Tobacco Dr to goods bought on contract. If the bargain be passed from by mutual consent, M. N. Dr to goods bought on contract. 27. When you contract to deliver goods, e. g. linens, to be delivered at u future time, 72. F. the buyer Dr to Goods sold on contract. When you deliver them, Goods sold on con- tract Dr to Linen. If the bargain be passed from, Goods sold on contract Dr to R. F. 30. JOURNAL ENTRIES in FOREIGN TRADE. 28. When you ship goods, and consign them to a factor to sel! on your account, Voyage to B. Dr to Sundries. To Goods formerly your own. To Seller, or Bills Payable, for goods bought on trust. To Cash) for goods bought for ready money, and for charges shipping. 29. When your factor W. L. advises that he has received them, W. L. my account of goods Dr to voyage to B. 30. When your factor advises that he has sold goods for- merly entered as received, on credit, at your risk, W. L. my account debts Dr to ditto my account goods. 31. When he advises to have received payment of goods for- merly sold and entered as above,- W. L. my account current Dr to ditto my account debts. 32. When lie advises to have shipped goods in return, Voyage from B. Dr to W. L. my account current. 33. When the goods homeward are received, Goods re- ceived Dr to Sundries ; to Voyage from B. for prime cost, and to Cash for charges. But it is seldohy that,go many. entries will be needed, as the advices received may iqclude several particulars. Thus, if the first advices be^tliat the goods are sold for ready money, W. L. my account current Dr to Voyage to B. And if no- thing be entered from the shipping ot the goods till goods be shipped in return, Voyage from B. Dr to Voyage to B. Se- veral other cases may occur, which can admit of no difficulty, if the above be understood* BOOK-KEEPING BY DOUBLE ENTRY. 163 31. JOURNAL ENTRIES in FACTORAGE. St. When you receive goods in consignment, to sell for your employer and pay charges, A. H. his account goods Dr in Cash. 35. When you sell your employer's goods*, Cash, if for ready money ; and Purchaser, or Bills receivable, if on credit, Dr to A. H. his account qf goods. 36. If you take any of your employer's goods to yourself at the current price, Goods Dr to A. H. his account of goods. 37. When the sales are finished, and account of them sent to your employer, A. H. his account goods Dr to Sun- dries. To charges merchandize, for ware-house rent, &c. To commission account, or Profit and Loss for the factor's commission. To A. H. his account of debts, for debts (if any) out- standing. To A. H. his account current, for balance due to his em- ployer. 38. But if you agree to answer for the debts in considera- tion of an allowance granted you, the entry will be A. H. his account goods Dr to Sundries. To charges merchandize, and commission account, as above. To insurance of debts, or Profit and Loss for allowance. To A. H. his account current for neat proceeds, whether paid or not, 39. When you receive payment of a debt due for your em- ployer's goods, which you had not insured, after the account sales are sent off, two entries will be necessary, as it not only has a reference to your account with the debtor, but also to your account with the employer, -Cash Dr to Payer ; and A. II. his account of debts Dr to ditto his account current. 40. When the factor ships goods for his employer, A. H, his account current Dr to Sundries ; To goods, formerly be- longing to the factor ; To seller, or Bills receivable for goods bought on trust ; and To Cash for goods bought for ready money, and for charges, and to commission account for com- mission. 32. JOI/RNAL ENTRIES in PARTNERSHIP. 41. When *OUR PARTNER T. W. is THE MANAGER, and you 164- BOOK-KEEPING BY DOUBLE ENTRY. pay in your share, T. W. my account, in company Dr to Cash, or, To Goods given in, or To Seller, for goods bought on cre- dit. 42. If you advance your partner's share as well as your own, Sundries Drs to the thing given in ; T. IV. my account in company for your own share, and T. W. my account proper for his share. 43. If your partner advance your share, T. W. my account in company Dr to T. W. my account proper. 44. If you receive advice of the goods in company being sold, T. W. my account proper Dr to ditto my account in company ; and then when you receive your share, Cash, or the thing received, Dr to T. W. my account proper. 45. But if you receive payment when the goods are sold, Cash, or the thing received, Dr to T. W. my account in com- pany. 33. In PARTNERSHIP when YOU ARE THE MANAGER, two entries are sometimes necessary ; one for the transaction as it relates to the person you deal with, and another as it relates to your partners. 46. When goods are brought into company, enter, Goods in company. Dr to Goods, if formerly your own; to Cash, if bought for ready money ; to Seller or Bills payable, if bought on cre- dit ; and to Partners, if furnished by them. Then enter each partner Dr to goods in company, for their share. 47. When the goods are sold, Cash, or the Buyer, Dr to Sundries ; to goods in company for your share, and to each part' ner for his share. 48. When goods are bought and presently sent to sea, Voyage in company Dr as in article 46, and each partner Dr to Voyage in company, for their share. 49. When goods formerly belonging to the company are sent to sea, Voyage in company Dr to Sundries; To goods in company for your share only; and to Cash, for charges if paid by you ; or to partner, if paid by him. Then each partner Dr to voyage in company, for their share of the charges only. 50. When the factor sends account sales, W. L. our ac- count current Dr to Sundries ; to voyage in company, for your own share, and to each partner for his share. The entries for other cases in partnership are either analo- gous to the above, or the same as in proper trade. BOOK-KEEPING BY DOUBLE ENTRY. 165 The method of keeping partnership accounts in the hooks of the ma- nagers here given, is different from that in the introduction to Merchan- dize, and shorter. By this, the accounts of goods and voyages in com- pany, contain only the share of that property which belongs to the own- er of the books ; by the other, they contain the whole value belonging to the company. But neither of these methods, nor any other that has been proposed, are free from being liable to some objections, and they are sel- dom used in business, and that only in occasional and short concerns. The proper way of keeping company accounts is in separate books ; and this is the constant practice in fixed companies. 34. It appears from what has been said, that some ar- ticles may be journalized in different ways with equal pro- priety ; but when a second article relating to the same subject occurs, there is no room for choice ; it must be journalized in strict conformity to the former ones. Hence the following rules. 1st, When any kind of property is entered on the Dr of a ledger account, it must be entered on the Cr of the same account, tbhen it is disposed of or altered. 2d, When any debt contracted is entered on the Cr of a led' ger account, it must be entered on the Dr of the same account, when paid or compensated 3d, When one article is exactly opposite to a former one (as in the case of returning goods bought) it must be journalized by reversing the former entry, i. e. by making that account Dr which was Cr before, and that account Cr which was Dr before. DIRECT loxsjbr WRITING the LEDGER. 35. The titles of the accounts are written in a fair text hand, and entered in the index, and as much room allotted for each as is thought necessary. When the space is filled up, the account is transferred to another folio. The journal post which expresses Cash Dr to Linen, implies at the same time, Linen Cr by Cash ; and all others, whether simple or complex, are to be understood in the same manner. (i 36\ In posting the ledger, proceed by the following di- rections : First, look for the Dr of the journal post in the index, under the proper letter, and this directs you to the fo- lio of the ledger where the account is, if it be already open- ed: if not, you must allot a space for it, write the title, and enter it in the index. Then enter the article on the left hand page of the account under the title, or the former article, by 166 BOOK-KEEPING BY DOUBLE ENTRY. writing the date on the margin, and the name of the creditor on the line, with the word To prefixed, and a narration of the transaction annexed ; and inserting the sum in the money co- lumn, and the quantity, it' it be an account of goods, in the inner-column. Then turn to the account of the Cr of the journal post, and enter the article in the right hand page, pre- fixing the word By to the name of the Dr. This being clone, turn to the journal, and mark on the margin the numbers of the folios to which the article is post- ed. The figures which point out the references to the Dr and Cr folios are separated by a line : For example, if the Dr entry be on the third folio, and the Cr entry on the fifth, the reference is f . There is often a reference column ruled in the ledger, for pointing out the other entry, corresponding to any article. In this column, the folio of the Cr entry is marked against the Dr article, and the folio of the Dr entry against the Cr article. In a complex post, where there is one Dr and several Crs, enter in the account of the Dr To Sundries per Journal, and insert the whole sum of the article in the money column ; then turn to the several accounts of the Crs, and enter in each By the common Dr, annexing a narration, and inserting the sum only which belongs to that Dr in the money column. When there are several Drs and only one Cr, turn to the account of each i>r in their order, arid write To the common Cr, placing the .sura belonging to that Dr in the money Ca- lumn; then turn to the account of the common Cr, and enter By Sundries par Journal, and insert the whole sum of the ar- ticle in the money column. An article in the ledger is generally comprehended in one line. The narration should be as full as can be contained in that bounds. If it cannot be narrated completely, the journal is referred to, for further particulars, by writing per Journal. 37. The books should be written up as frequently as can be done conveniently, so that the journal may keep pace nearly with the waste book, and the ledger with the journal. Each book should be carefully revised, and compared with the book from which it is posted. In comparing the ledger, observe the following directions^ Begin with the first journal post, and turn to the folio of BOOK-KEEPING BY DOUBLE ENTRY, 167 the ledger where the Dr is entered, which you are directed to by the marginal reference, and compare the date, entry, and sum. IF you find them to correspond, it is well ; if not, the ledger must be altered till it correspond with the journal, Then place a dot before the reference figure in the journal, and a mark " before the sum in the ledger. Proceed in the same manner to compare the Cr of the journal-post, and all the following posts in their order. The dots in the journal show how far the comparison is advanced, and the marks in the ledger show what articles are compared. It will be more convenient if two persons assist each other in comparing the ledger. One has the journal before him, and reads the reference figure, titles of the account, and Dr or Cr; the other turns to the account, and reads the ar- ticle. 39. In correcting errors in the ledger observe the fol- lowing rules. 1st, If an article be omitted, do not attempt to interline it at the place where it should have been ; but insert it under the last article when you discover the omission, and mark a cross X against it on the margin, and another at the place where it should have been. 2d, If you discover a mistake immediately when committed, correct it without cancelling any thing, as in this example. To Cask, say, To James. Spiers received to ace, ; 3d, If you have written a line entirely wrong, or in a wrong place, write the word Error at the end, prefix a cross, and omit or cancel the sum. 4th, Cancel errors, by drawing a line lightly through them, so that the old writing may still be legible ; by which it will be evident, that the book has not been vitiated for a fraud u- le.nt purpose. The same method should be followed in cor- recting errors in the journal. When the comparison of the books is finished, glance over the ledger, to observe if the mark oi comparison be af- fixed to every article. If not, you must turn to the journal, and observe if the articles be right which had jiot been marked. 40. Merchants generally balance their books once ; The design of this operation is, to collect the various b;anclies of their business diffused through the books into a concise ab- 168 BOOK-KEEPING BY DOUBLE ENTRY. stract ; to ascertain their gain or loss since the last balance ; and exhibit the present state of their funds. For this purpose, prepare two sheets of paper, ruled with money columns, in the form of Dr and Cr ; write Profit and Loss as the title of the first, and Balance as the title of the second. Add both sides of all the accounts in the ledger, and subtract the lesser sum from the greater ; place the difference on one of the sheets, and on the side corresponding to the greater sum. If this difference appear from the nature of the account to be gain or loss, it is entered on the profit and loss paper. If it be any article of property or debt due to us or by us, it is entered on the balance paper. If there be ar- ticles only on one side, the sum is entered on the proper pa- per. More particularly, In personal accounts, enter the difference, which is the debt owing to you, or by you, on the proper side of the ba- lance sheet. In the Cash account, enter the difference, which is the mo- ney in hand, on the Dr side of the balance sheet. In accounts subsidiary to profit and loss, enter the differ- ence on the proper side of the profit and loss sheet. In accounts of goods or other property, if there be nothing remaining on hand, enter the difference, which is the gain or loss, on the proper side of the profit and loss sheet. If the whole be still on hand, enter the value on the Dr of the balance sheet ; and, if this be different from the prime cost, charges included, enter the difference in the proper side of the profit and loss sheet. If part be sold, and part on hand, add the value of the quantity on hand to the sum of the Cr. This sum is the whole return that will be obtained, if the rest of the goods be sold at the estimated value ; and this being compared with the sum of the Dr, which is the whole expence, shows the gain or loss. Enter the same in the proper side of the profit and loss sheet, and enter the quantity and value on hand on the Dr of the balance sheet. When you have collected all the balances, add the sums of both sheets, and add to the profit and loss sheet the sums of the profit and loss account in the ledger ; then subtract the lesser sum of each sheet from the greater. This being done, mark down the sums of the stock account, and add thereto the balance of the profit and loss sheet on the WASTE-BOOK. London, JULY 5, 1787. 179 Sold for ready money, 5 pipes Lfsbon wine, at L.23 10 L. 60 baskets Florence oil, at 2 9 6 2 puncheons rum, at 38 10 -6.- Paid bill to N. Brent, March 3, 4 mdt. L. To M. Drapier, May 3, 2 mdt. 10. Sold to M. Wilson, per bill 6 mdt. 8 bales thrown silk L.386 15 bags C. Oliva's wool, qt. each 180lb. is Ib, at 2s. 4d. 5 hds. sugar, qt. each 8 cwt. at L.3 2 6 16. Paid H. Meredith's bill to W. Wade, 23d ult. 20 ddt. L.246 13 .. J. Manners, in full 450 Manners having abated me L.I 5s. Contracted with P. Manners for 1000 quarters bar ley, to be delivered me on or before Jan. J5 next, at 24s. 6d. Bought from P. Hill 40 pieces, qt. 840 yds. muslin, at 7s. 9d. Delivered him in barter 230 gallons brandy, at 5s. lOd. And my note at 2 months for the balance London, AUGUST 1, 1787. Received advice from Tho. Aubrey, Jamaica, th* he has received the cargo per the Sea Hors Jones,, and sold the same, neat proceeds, per ac count sales, L.I 640 currency, ex. 60 per cent. 368 65! 69 180 WASTE-BOOK. London, AUGUST 1, 178?. Whereof paid Outstanding Currency. Sterling I.. I 1G8 L. 472 L.1640 Thomas Aubrey has shipped per the Dolphin, Har- ris, 20 hds. sugar, 25 cwt. coffee, and 40 torn logwood, amount per invoice, L.I 376 currency ex, 60 per cent. Made insurance at J. Hazard's office on L.80C .value in ^oods, per the Dolphin, Harris, from Jamaica to London, at 5i gs. per cent, policy 10s. 6d. Shipped for Lewis Necker, Rochelle, per the Bien- faisant, Perraulr, 400 qrs. of my own barley, at 26s. 9d. 600 ditto bought from J. Whitbread, at ditto, per bill, 3 mdr. Commission on the last, at 2 per cent. . Paid charges shipping L.I 3 9s. Shipping also per said ship, consigned to L. Neck- er 150 qrs. wheat, at 38s. Charges shipping, L.2, 2s. Made insurance at J. Hazard's office on L.I 380, value in barley, per the Bienfaisant, to Rochelle, on account of Lewis Necker, at 2 per cent, share policy 7$. And on L.290 value in wheat, per said ship at ditto, share policy, 3s. 6d. 15. Drawn on L. Necker to J. Appleby, for ready mo- ney, usa. Lrs, 18000, ex. 29d. WASTE.BOOK. London, AUGUST 24, 1787. 181 Paid Francis Groset, in full John Hazard to account Sam. Archer, in full L.276 10 100 116 10 Sent Will. Dashwood, Ipswich, 4 bales thrown silk, L.I 93 5 pieces, qt. 105 yds. muslin, at 8s. Desiring him to keep them at these prices, or re turn them at my charges. London, SEPTEMBER 1, 1787. Sold the remainder of C. Oliva's wool as under, 18 bags, each I80lb to W. Dashwood, at 2s, 3 id 5 ditto ditto to N. Spence 2s. 4d. The last for Spence's bill, 4 mdt. Advice having been received of the loss of the Dol phin in the voyage from Jamaica, I have settlec for the sum insured ; which deductingi 2 per cent per agreement, is L. Received one half in ready money. And the underwriters * bills 3 mdt. for the balance. Sent C. Oliva account sales of wool. Charged ware-house rent, and incidents during sale, L.3 17 10 Commission on L. at 21 per cent. Insuring debts, at 1^ per cent. Neat proceeds - - .... . Remitted C. Oliva, my bill on L. Necker, usance Lrs. 16633 5, ex. 29d. , : 12. Bought from Will. Nugent, 150 barrels rice, at L 3, 3s. 20 bags hops, qt. each 3i cwt. at L.3, 15s. * The particular bills should be specified here. Q 553 476 1024 182 WASTE- BOOK. London, SEPTEMBER 15, 1787. Received payment of bill on A. Asgi'l, May 12. 4 mdt. William Dashwood advises me that lie keeps the thrown silk sent 27th ult. at my oft'er, but has returned the muslin. Paid J. Vanlow's bill on me to R. Hill, l6'th ult. 1 mdt. on account of H. Meredith - 00. - Received from Raikes and Thomson, Petersburg!!, per the Empress, Bloxam, to sell, on their ac- count, 30 tons iron, .300 bobbins flax, Paid duty on iron, at L.2 1 6 2 per ton L. Freight on ditto, at 13s. per ditto on flax, at 2s. 6d. per bobbin, Charges unloading - - L.8 16 -27. Paid note to P. Hill, July 24. 2 mdt. _ 30. Sold William Jennings, Snowhill, 12 tons R. and T.'s iron, at L.I 8 5 40 baskets "Florence oil, at 2 8 20 barrels rice, at - 35 London, OCTOBER 1, 1787. Shipped per the Minerva, Greaves, for Hamburgh, a cargo consigned to Thomas Calvert, merchant there, on account and risk of James Fielding, Walbrook, Charles Drake, Crutched-iriars, anc myself, each one-third concerned, 130 barrels rice, at L.3, 5s. 30 casks logwood, qt. each 5 cwt. at 18s. bought from J. Hahday, per bill, 5 mdt. Tobacco furnished by Ja. Fielding, L.620 Woollen stuffs, furnished by C. Drake, 418 Paid charges at shipping 9 1 ~ 1605 WASTE-BOOK. 183 London, OCTOBER 1, 1787. Made insurance, at Jo. Hazard's office, on L.1600 value in goods, per the Minerva* Greaves, to Hamburgh, in company with J. Fielding and C. Drake, at 3| gs. policy 10s. 6d. Sold W. Nugent the following goods belonging Raikes and Thomson, 6 tons iron, at L.I 8 10 50 bobbins flax, at L. 4 12 10. Delivered James Eden, Watling-street, 40 pieces muslins, qt. 840 yards, to be sold by him on our joint account, each one half concerned, at 7s. 9d. Sold Raikes and Thomson's flax, as under, 100 bobbins for ready money, at L.4-, 12s. 80 ditto to W. Dashwood,* at L.4; 15s. 70 ditto, damaged, to R. Thurston, per bill 2 mcit. at L.3, 15s. Received payment of J. Dalton's bill on M. Pope, 7th August, 2 mdt. remitted me by H. Mere- dith _ 15. J. Eden has furnished on our joint account 1800 yards cambric, amount, per invoice, L 625, 10s whereof my one half share is 20. Paid James Eden in full James Fielding in full L.150 65 4- 6 25. Charged H. Lambert a half-year's interest on his bond of L.500 at 5 per cent. 31. Settled accounts with Honey wood and Co. The interest due them is L.30 113 And the balance due them L. to Cr new account Q 2 150 184 WASTE-BOOK. London, NOVEMBER 3, 1787- Thomas Aubrey advises me that he has received payment of the outstanding debts, to the amount of L.S52 currency, ex. 60 per cent. And the remaining L.I 20 he reckons desperate. 5. Lewis Necker has received and sold the wheat per the Bienfaisant, and has remitted me, as the va- lue of the same, his bill on D. Green, 15th ult. '3 mdt. 7. Honeywood and Co. have paid C. Oliva's bill on them on my account, 4th ult. 1 mdt. Sold for ready money 8 tons R. and T's iron, at L.18, and taken the remaining 4 tons on my own account, ditto Sent Raikes and Thomson account sales. Charged warehouse rent and incidents L.5 'Commission on L. at 2| per cent. Amount of outstanding debts Balance due them 9 1 10.-. Discounted at the Bank of England, my bill on M. Wilson, 8th July, 6 mdt. L. Received - - - L. And the discount is Paid bill to J. Whitebread, 8th August, 3 mdt. 20. Sold Thomas Kenrick, Blackfriars, 12 pipes Lisbon wine, at L.28 26. Received from P. Manners, 500 quarters barley, in part of the quantity contracted for, July l6th, at 24s. 6d. 275 312 WASTE-BOOK. 185 London, DECEMBER 1, 1787. James Eden acquaints me that he has completec the sales of the cambrics and muslins, and that th< amount, deducting charges, isL.1029; where of my half share is Received payment of the underwriters bills, Sept 5, 3 mdt. L, And from James Eden, in part - 200 _ 1 3 Received payment of bill on R. Thurston, 10th ult 2 mdt. 14. Paid P. Manner's bill to Ch. Gould, 1st cur. 10 ddt. H. Meredith's bill to N. Home, st. JL.612 150 18. William Nugent having failed, I have accepted composition of 15s. per pound on his debt, and discharged the same. The composition received is - L. And the balance lost L. whereof for my own debt, L. For Raikes and Thomson's Thomas Calvert, has sent me account sales of the cargo per the Minerva, Greaves, in company with Fielding and Drake, neat proceeds, merks lubs 29233 current, agio 15 per cent. M. banco, ex. 33s. 4d. Drawn on Thomas Calvert, for ready money, to J. Priestley, usance, merks lubs 17250 current, agio 15 per cent. M. banco, ex. 33s. 4d. Bought for ready money, W. Napier's bill on P. Meninski, Petersburgh, usance, and remitted it to Raikes and Thomson, roubles 3600, at 4s. Id. Q3 186 WASTE-BOOK. London, DECEMBER 24-, 1787. Paid J. Fielding, in part - L.400 Ch. Drake, in part 250 John Hazard, in full - 82 10 Paid small charges on my business for 6 months - L.36 5 4 and my own expences ditto 260 Sent account current to H. Meredith, Charged him interest - L. Commission on L. at i per cent. Postages - - - 86 Balance due by him L. to Dr. new account. Inventory of goods on hand, Dec, 31, 1787. 500 quarters barley, at 24s. 6d. 3 puncheons rum, at L.38 3 pipes Lisbon wine, at L.28 20 bags, 70 cwt. hops, at L.3, 10s. the price having fallen since purchased. 4 tons iron, at L.I 8 And I estimate the present value of my share o ship Traffic, at L.220. 1S7 JOURNAL. .1 .2 .2 .2 ,2 .2 .3 .3 ~5 ,1 Ts .3 .4 A .1 ,1 ij .4- ~~c London, JANUARY 1, 1787. 526 2160 1764 207 250 500 366 1035 3 13 9 9 4 -MM 1 Sundries Drs to Stock, L.6808 6 1 Cash, for ready money Wheat, for 1200 quarters, at 36s. Claret, for 36 pipes, at L.49 Cotton, for 15 bags, qt. each 3 cwt. 1 q. is 48 cwt. 3 qrs. at L.4-, 5s. Share of Ship Traffic, Tho. Stout master, for \ Hen, Lambert, Westminst. per bond, due Apr. 25 Elliot and Clive, Leadenhall-street, per account Bills receivable for the following, D. Bell on J. Harris, 12 ult. 3 mdt. L.320 My bill on W. Smith, Oct. 9, 6 radt. 715 9 6808 6 Stock Dr to Sundries, L.2713, 2s. To Honeywood and Co. London-wall per account, settled Dec. 31. To J. Kempenfeldt, Amsterdam, f.7560, at 22 d. To Bills payable, for the following, To J. Hill, 12 Sep. C mdt. L.175 ToR. Turner, 15th Sep. 8 mdt. 369 12 1475 693 544 2713 10 12 2 3 Linen Dr to Cash, L/225 Bought 1200 yds. at 3s. 9d. 225 166 13 4 Cash Drto Elliot and Clive, L.I 66 13 4- Received in part Geo. Floyder, Southwark, Dr to Wheat, L.585 Sold him 00 quarters, at 39s. 585 T _ 188 JOURNAL. London, JANUARY 10, 1787. .1 jf Linen Dr to Samuel Archer, Milk-street, L.1760 Bought 30 ps. 720 yds. at 3s. 2cl. L.I 14 20 ps. 500 yds. at 2s. 6d. 62 10 50 1220yds. .5 Salmon Dr to J. Kirman, Berwick, L.I 387 10 Bought from him 300 barrels, at L.4 126 15 Cash Dr to Claret, L.306 Sold 6 pipes, at L.51 -18. Honeyiuood and Co. Dr to Cash, L.600 Paid them to account 24-.. Sugar Dr to Claret, L.520 Received 20 hds. qt. each 8 cwt. is 160 cwt. a L.3, 5s. in barter for 10 pipes, at L.52 30. London, FEBRUARYS, 1787. Sundries Drs to Wheat, for 500 qrs. at 38s. 6d. lash, received in part - L.500 Bills receivable for W. Davenport on W. Aston, 3 mdt. 314- 10 W. Davenport, Chatham, for ba- lance - - 148 7 oyage to Leghorn, per the Dispatch, Bayley, Dr to Sundries, for a cargo consigned F. Alcara To Salmon, for 200 barrels, at L.4 12 6 L.925 To Linen, for 600yds. at 3s. 9d. 112 10 To Bills payable, for 1250 Ib. leather, bought from W. Ellis, per bill, 4 melt, at Is. 2d. Carried forward 72 18 4 L.1110 8 4 1387 306 600 520 10 176 10-r 962 10 JOURNAL. London, FEBRUARY 7, 1787. 189 Brought forward L.I 110 8 4 To Cash, for 300 yards broad cloth, at 15s. f 225 For insurance of L.I 300, at 3 gs. with policy, 10s. 6cl. ! 41 6 And charges shipping 271 19 6 10. Sundries Drs to Sugar, for 10 hds. qt. each 8 cwt is 80 cwt. delivered in barter, atL.3, 10s. L.280 Brandy, for 300 gallons received in barter, at 5s. 9d. L.86 5 Cash, received balance - 193 15 15. J. Kempenfeldt, Dr to cash, paid his bill on me to R. Barbour, 12 ult. usance, being value of 3306 6, ex. 35s. 8d. agio 3 per cent. 17. Cash Dr to Sundries, To Salmon, for 100 bar. at L.4-, 16s. To Wheat, for 150 qrs. at L.I 17 9 To Brandy, for 120 gallons, at 6s. To Linen, for 250 yds. at 3s, 8d. L.480 283 2 6 36 45 16 8 20. Wheat Dr to Sundries, for 800 quarters from Je thro Tull of Belfield, at 37s. L.1480 To Cash, paid in part L.4.50 To Will- Davenport, for my bill on him, 1 mdt. 100 To Jethro Tull, for balance - 930 Jo. Kirman Dr to Cash, paid his bill to N. Comp ton, 21 ult. 1 mdt. J. Kempenfeldt Dr to Cash, for D. Smith's bill on W. Hoorn, usa.fA253 14 current, ex. 35s. lOd 1382 10 280 300 844 19 1480 200 395 4 6 190 JOURNAL. London, MARCH 3, 1787. Voyage to Jamaica, per the Sea-Horse, Jones, Dr To Sundries. To Linen, for 350 yds. at 3s. 9d. L. 65 12 6 and 720 ' at 3s. 2d. 114- 1070 To Bills payable, for 2500 yds. cottons from N. Brent, per bill, 4 mdt. To Fr. Grosset, Sheffield, for hardware To Cash, for charges shipping To Jo. Hazard, Royal Exchange, for insurance of L.800 on above, at 5 gs. policy 10s. 6d. Consigned to Th. Aubrey, Kingston. -7.. Barley Dr to Sundries, To Jctliro Tull, for 500 qrs. at 26s. L.650 To P. Manners, 700 qrs. at 25s. 9d. 901 5 1200 9.- Cash Dr to Sundries, To Claret, for 6 hds. at L.5I, 10s. L.309 To Brandy, for 150 gallons, at 5s. lid. 44 7 6 12. Cash Dr to Voyage to Jamaica, received drawback of excise on 250O yds. cottons, at 4d. ] .5. Cash Dr to Bills receivable, for bill on J. Harris 12th Dee. 3 mdt. : 17. Bills payable Dr to Cash, paid bill to J. Hill, 15th September, 6 mdt. Sills receivable Dr to Sundries, cw t. qrs. To Cotton, for 5 bags, 1 G 1 , at L.4, 1 Os. L.73 2 To Sugar, 5 hds. 40 atL.3 76 135 Sold J. Lascelles, per bill, 4 mdt. ... 179 378 276 42 10 6 10 88! 1551 353 41 13 320 208 JOURNAL, 191 London, MARCH 29, 1787. /. Rinnan Dr to Cash, paid his bills, viz. TV A. Hunter, 26th Jan. 2 mdt. L.250 To W. Pearee, 26th ult. 1 melt. 350 London, APRIL 2, 1787. Fr. Alcara, Leghorn, my account of Goods Dr to Voyage to Leghorn, for the cargo per the Dis- patch, Bayley, received by him Voyage from Leghorn, per the Dispatch, Bayley , Dr to Fr. Alcara, my account current, for a car- go wine, oil, and silk, shipped by him, amount per invoice, Lires 24672, ex. 4s. 3d. per piastre WilL Nugent, Fish-street, Dr to Sundries, To Cotton, for 8 bags, qt..26 cwt. at L.4, 8s. L.114 8 To Wheat, for 100 qrs. at L.I 18 3 191 5 To Claret, for 9 pipes, at 51 15 465 15 Sundries Drs to share of Ship Traffic, for my share profits since Sep. 1. last, Cash, received in part L.20 Bills receivable, for Thos. Stout's note on demand - - 24 14. Geoffrey White, Oxford-street, Dr to Sundries, To Linen, for 500 yds. at 2s. 7|d. L.65 12 To Cotton, for 2 bags, qt. 6 cwt. 2 qr. at L.4, 6s. abating 10s. - 27 9 To Claret, for 4 pipes, at L.51 12 6 206 10 Sundries Drs to George White, Brandy, for 200 gallons, at 5s. 3d. L. 52 10 Rum, for 5 puncheons, at L.39 195 Cash, received balance - 52 1 600 382 873 771 j 29! 299 192 JOURNAL. London, APRIL 18, 1787. Sundries Drs to Dills receivable, for the following bills discounted at the bank of England, W. Davenport on W. Aston, 3d Feb. L.314 10 jVJy bill on J. Lascelles, 21th ult. 4 radt. 208 2 6 L.522 12 6 Cash, received for above Interest-account, for discount L.519 3 12 6 19.- Cash Dr to Sundries, To Elliot and Clive, in full - L.200 To Geo. Floyder, in part 385 To Bills receivable, for Tho. Stout's note on demand - - 24 Sundries Drs to Cash, J. Kirman paid his bill to R. Lloyd, 16th Jan. 3 rndt. in full //. Meredith, Liverpool, his account- current, paid his bill to C. Golding, 17 ult. 30 ddt. L.58V 10 300 24.- Jethro Tull Dr to Honeywood and Co. delivered him my order on them London, MAY 3, 1787. Ben. Gomez Lisbon, his ace. cur. Dr to Sundries, for goods shipped per the Diana, Blackney, on his ace. To Wheat, for 800 qrs. at 38s. L.'l520 To Barley, for 800 qrs. 26s. pd. 1070 To Bills payable, for 350 yds. broad- cloth, from M. Drapier, per bill, 2 mdt. at 16s. 280 * T'.> P r Jit and Loss, for commission on cbi;K at 2i per cent. 7 To Cash, paid charges shipping 16 5 6 * Or, To Commission account. 522 12 609 887 10 1000 2893i 5 JOURNAL. 193 London, MAY 7, 1787. Fr. Alcara, my account current, Dr to ditto my ac count Goods, for neat proceeds of the cargo pe the Dispatch, Bayley, per account sales, Lire 43686, ex. 4s. 3d. per piastre , 1 12. Bills receivable Dr to Voyage from Leghorn, Sold A Asgill the wine on board the Dispatch, pe bill, 4 mdt. 15 Cash Dr to Sundries, To William Davenport, in full To Geo. Floyder, from H. Moor L.48 100 18. Bills payable Dr to Cash, paid bill to R. Turner 15th Sept. 8 mdt. Cash Dr to H. Meredith, received for J. Dyer or R. Lamb, 29th ult. 20 ddt. Sundries Drs to Voyage from Leghorn, Florence oil, for 100 baskets, value L.I 86 - - Thrown silk, for 12 bales, value 412 16 Sundries Drs to Cash, Florence oil, paid freight, duty, and charges - L. 72 5 Thrown silk, paid ditto * 136 10 28. Honeywood and Co. Dr to Fr. Alcara, my account current, for my bill on him to them, usance, Lires 19014, ex. 4s. 3d. per piastre London, JUNE J, 1787. Cash Dr to Sundries, To Bills payable, borrowed from A. Leslie, per bill, 1 ddt. at 4 per cent. L.250 To Geo. Floyder, in full - 1 00 R 154 2?5 148 369 21' 598 208 67 194 JOURNAL. London, JUNE 3, 1787. Carlos Oliva, Bilboa, his account (>f Wool, Dr to Cash, paid freight of 50 bags Spanish wool, qt. 6ach 180lb. is 9000 Ib. received per the Sove- reign, Penning, to sell on his account, at 2s. 6d. per bag - - L.6 5 Charges 368 Cash Dr to Sundries, To Bills receivable, for bills on W. Smith, 9th Oct. 6 mdt. L.715 9 To Interest Account, for 2 months int. 519 3 10. Bills payable Dr to Cash, paid bill to W. Ellis, ?th ib. Feb. 4 mdt. 12. Honey-wood and Co. Dr to Ben. Gomez, for my bill on him to them, usa. milrees 2000, at 5s. Gil. Will. Nugent Dr to Carlos Oliva , his account oj Wool, for 12 bags, qt. each 180lb. is 2160 Ib, at 2s. 3d. 20. -, Sundries Drs to Cash, H. Meredith, paid his bill to H. Bishop, 10 dst. L.115 10 P. Manners, paid him to account 450 30. Sundries Drs to Cash, Proper Expences, for personal and family expences for 6 months - - L.200 Charges Merchandize, for 6 months charges - 15 10 Proper Expences Dr to Claret, taken the remaining pipe for my own use 721 18 550 565 10 215 JOURNAL. London, JULY 1, 1787- Jethro Tull Dr to Honeyiwod and Co. for my or- der on them to him in full Lisbon wine Dr to Sundries, To Ben. Gomez, for 20 pipes received per the Dia na, Blackney, amount per invoice, 846 milrees, at 5s. 6d. - - L.232 13 To Cash, pd. duty, atL.28, 18s. p. ton T L.289 Freight, at 25s. per pipe 25 Charges unloading j 368 L.317 6 8 Sundries Drs to Ben. Gomez, Honey-wood and Co. for my bill on them, usa. ex 5s. 6d. - M. 4000 L.I 100 Cash, for my bill to N. Dove, do. 3675 101012 6 7675 Cash Dr Sundries, To Lisbon icine, for 5 pipes, at L.28 10 To Florence oil, for 60 baskets, at 296 To Rum, for 2 puncheons, at 38 10 Bills payable Dr to Cash, Paid bill to N. Brent, 3d Mar. 4 mdt. L.378 to M. Drupier, 3d May, 3 radt. 280 Bills receivable Dr to Sundries, To Thrown silk, for 8 bales - L.386 To C. Oliva, his account of Wool, for 15 bags, qt. 2700 Ib. at 2s. 4d. 315 To Sugar, for 5 hds. qt. 40 cvvt. at L.3 2 6 - - 126 Sold M. Wilson, per bill, 6 mdt. R2 5S< 195 1 54Q 19 2110 142 148 f it 368 12 658 826 196 JOURNAL. London, JULY 16, 1787. Sundries Drs to Cash, Hen. Meredith, paid his bill to W. Wade, 23d ult 20 ddt. - L.246 IS 4 Pat. Manners, paid him in full 450 Pat. Manners Dr to Barley , for abatement Goods bought on Contract Dr to P. Mannners, For 1000 qrs. barley, to be delivered on or before J 5th January next, at 24s. 6'd. 24. Muslins Dr to Sundries, for 40 pieces, qt. 840 yds. at 7s. 9d. L.325, 10s. To Brandy, for 230 gallons, at 5s. 1 Od. L.67 1 To Bills payable , for my note to P. Hill, 2 mdt. ... 258 8 London, AUGUST 1, 1787. Sund?*ies Drs to Voyage to Jamaica, for neat pro- ceeds of the cargo per the Sea- Horse, Jones, Currency. Sterling. Th. Aubrey my account cur. received by him L.I 168 L.730 Ditto, my account debts, outstanding - 472 295 Ex. 60 per cent. L.1640 Voyage from Jamaica, per the Dolphin, Harris, Dr to Th. Aubrey, my account current for goods shipped by him on my account, viz. 20 hds. sugar, 25 cwt. coffee, 40 tons logwood, Amount per invoice L.I 376 currency, ex. 60 per cent. 696 13 1225 325 10 1025 860-4 JOURNAL. London, AUGUST 1, 1787. 197 Voyage from Jamaica, Dr to J. Hazard, for insu ranee made at his office on L.800 value in goods per the Dolphin, Harris, at 5} 2 gs. per cent, po licy, 10s. 6d. Lewis Necker, Rochelle, his account current, Dr to Sundries, for a cargo shipped per the Bienfai sant, Perrault, on his account, To Barley, for 400 qrs. at 26s. 9d. L.535 To Bills payable, for 600 qrs. ditto, bought from J. Whitebread, per bill, 3 mdt. - 802 10 * To Profit and Loss, for commission on the last, at 2 per cent. 16 1 To Cash, paid charges shipping 13 9 Voyage to Rochelle, per the Bienfaisant, Perrault Dr to Sundries, To Wheat, for 150 qrs. at 3Ss. L.285 To Cash, paid charges shipping 2 2 - Sundries Dr to John Hazard, L. Necker, for insurance of L.I 380, value in wheat, per the Bienfaisant, Perrault, to Rochelle, at 2 per cent, share policy 7s. - L.27 19 Voyage to Rochelle, for insurance of L.290, value in barley, per ditto, ditto, share policy 3s. 6d. 5196 Cash Dr to L. Necker, for my bill on him to J. Appleby, usance Lrs. 18000, ex. 29d. 24 Sundries Drs to Cash, Fr. Groset, paid him in full John Hazard, in part Samuel Archer, in full L.276 10 100 176 10 -~ * Or, To Commission Account* R3 46 1367 287 725 553 JOURNAL. London, AUGUST 27, 1787- Xur>pcnce account Dr to Sundries, To Thrown silk, for 4 bales L.I 93 To Muslins, for 105 yds. at 8s. 42 Sent W. Dashwood, Ipswich, to be kept or return ed at my charges. London, SEPTEMBER 1, 1787- Sundries Dr to C. Oliva his account Wool, W. Dashwood, for 18 B. 3240 Ib. at 2s. 3*d. 2s. 4d. Bills receivable 900 2IJ 4140 The last to N. Spence, per bill, 4 mdt. Sundries Drs to Voyage from Jamaica, having set tied with the underwriters for L.800 insured o the cargo per the Bienfaisant, lost on the voyag homeward, deducting 2 per cent, per agreemen Cash received L.392 Kills receivable, for the underwriters bills, 3 mdt. - - 392 -8.- C. Oliva, his account of Wool, Dr to Sundries, 'fo Charges Merchandize, for small charges L.3 17 1 it and Loss, for commission f 334, at 2| per cent. -j L.25 17 ring debts on ditto, 11- p. c. C 1218 6 * To Profit and Loss, for commission on L.I 034, And insurim iP- To C. Oliva, his account current, for neat proceeds L.38 15 982 C. Oliva, his account current, Drto L. Necker, for m bill on him to him, usa. Lrs, l66'3 , 5, ex. 29 * Or, To Commission Account, L.25 17 To Insurance of Debts, 12 18 6 235 37 10. 476 784 1024 66J JOURNAL, London, SEPTEMBER 12, 1787- 199 Sundries Drs to William Nugent, Rice, for 150 barrels, at L.3, 3s. L.472 10 Hops, for 20 bags, qt. each 3 cvvt. is 70 cwt1*at L.3, 15s. - 262 10 15. Cash, Drs to Bills Receivable, for bill on A. Asgill 12th May, 4 mdt. 17. Sundries Drs to Suspense account, Will. Dashwood, for silks sent 27th ult. kept by him Muslins returned L.193 Hen. Meredith Dr to Cash, paid P. Vanslow's bil on me to II. Hill, l6th ult. 1 mdt. on his accoun 20. Raikes and Thomson, Petersburg!}, their accoun Goods Dr to Cash, for charges on a cargo pe the Empress, Bloxam, consigned to me to sell 01 their account, viz. Duty on 30 tons iron, at L.2 16 2 L.84 5 Freight on ditto, at 1 8s. 27 on 300 bobbins flax, at 2s. 6d. 37 10. Charges unlading S 16 27. Bills payable Dr to Cash, paid note to P. Hil 24-th July, 2 mdt. 30. Will. Jennings, Snowhill, Dr to Sundries. To Raikes and Thomson their account . goods, for 12 tons iron, at L.I 8, 5s. L.219 To Florence oil, for 40 baskets, at L.2, 8s. 96 To Rice, for 20 barrels, at L.3, 5s. 65 London, OCTOBER 1, 1787. Voyage to Hamburgh in Co. with Ja. Fielding an Ch. Drake, Dr to Sundries, for a cargo per th 735 275 235 350 157 258 380 200 JOURNAL. London, OCTOBER l, 1787. Minerva, Greaves, consigned to Th. Calvert on our joint account, each one-third concerned, To Rice, for 130 barrels, at L.3, 5s. L.422 10 To Bills payable, for 30 casks logwood, qt. 150 cvvt. at 18s. from J. Haliday, per bill, 5 mdt. - 135 To J. Fielding, Walbrooke, for tobacco 620 To C. Drake, Crutchedfriars, for wool- len stuffs 418 To Cash, paid charges 9 10 Sundries Dr to Voyage from Hamburgh in Co. Ja. Fielding, for his one-third L.635 Cha. Drake, for his one-third 635 Sundries Drs to Ja. Hazard for insurance of L.1600 per the Minerva, Greaves, to Hamburgh, at gs. policy 10s. 6d. L.59 6 6 Voyage to Hamburgh, in Co. for my l L.I 9 15 6 Ja. Fielding, for his one-third 19 15 6 Cha. Drake, for his one-third 19 15 6 Will. Nugent Dr to Raikes and Thomson their ac- count Goods, For 6 tons iron, at L.I 8 10 L.I 11 50 bobbins flax, at 4 12 230 10. Sundries Drs to Muslins, for 40 ps, 840 yds. deli- vered to Ja. Eden, Watling street, to sell on our joint account, at fe. 9d. L.325, 10s. Ja. Eden, my account in Co, for my one-half, - L.I 62 15 Ja. Eden, my account proper, for his one-half, - - 162 15 160. 1070 341 JOURNAL. London, OCTOBER 10, 1787. 201 Sundries Drs to Raikes and Thomson their account of Goods, Cash, for 100 bobbins flax, at W. Dashivood, 80 ditto, at LA 12 4 15 Bills receivable, 70 ditto, to Il.Thurston,at3 15 250 The last per bill, 2 mdt. being damaged. Cash Dr to H. Meredith for J. Dalton's bill on M Pope, 7th August, 2 mdt. 15. Ja. Eden, my account in Co. Dr to my account pro- per, for my half share of 1SOO yds. cambric, fur- nished by him on our joint account, amount per invoice, L.625, 10s. , 20. Sundries Drs to Cash, Jas. Eden, paid him in full Ja. Fielding, in full L.150 -, 65 4 6 Hen. Lambert Dr to Interest account, for ^ year's interest of his bond L.500, from April 25 31. Interest account Dr to Honeywod in Co. for interest due them ... Honeywood and Co.'s account to be balanced by 162 13s. dufe them to Cr new account, as settled this date. London, NOVEMBER 3, 1787. Sundries Dr to Th. Aubrey my account of Debts, Th. Aubrey my ace. current, Currency. Sterling. for amount received - L.352 L.220 Voyage to Jamaica, for a des- perate debt 120 75 Ex. 60 per cent. L.472 460 380 262 1102 150 31215 215 12 SOU 295 -* 10 10 10 JOURNAL. London, NOVEMBER 5, 1787. Bills receivable Dr to Voyage to Rochelle, for L. Necker's bill on D. Green, 15th ult. 3 mdt. be- ing in full for the cargo per the Bienfaisant, sold by ditto Necker ... C. Oliva ace. cur. Dr to Honey-wood and Co. for his bill on them, on my account 4th ult. 1 mdt. Sundries Drs to Raikes and Thomson their ace. Goods Cash, for 8 tons iron, at L.I 8 L.I 44 Iron, for 4 ditto, L.18 - 72 Ha ikes and Thomson their ace. Goods Dr. to Sundries To Profit and Loss, for commission on L.I 878, 10s. at 2* per cent. L.46 19 To Charges Merchandize, for small charges - 591 To Raikes and Thomson their account debts, for outstanding debts, 1202 10 To Ditto, their account current, for balance due them 466 10. Sundries Drs to Bills receivable, for my bill on M Wilson, 8th July, 6 mdt. discounted at the Bank of England, Cash, received - - L.819 Interest account, for discount - 7 Bills payable Dr to Cash, paid bill to J. Whitebread 8th August, 3 mdt. 20. Thomas Kenrick, Blackfriars, Dr to Lisbon ivinc for J2 pipes, at L.28 26. -, Barley, Dr to Goods bought on contract, receivet from P. Manners 500 qrs. in part of the quantity contracted for 16th July, at 24s. 6d. 312 216 1720 18 802 336 10 61: 12 JOURNAL. London, DECEMBER 1, 1787. 205 James Eden my account proper Dr to ditto my ac- count in Co. for my half share of the muslins and cambrics sold by him Cash Dr to Sundries , To Bills receivable, for the underwri- ters bills, 5th Sept. 3 mdt. L.392 To Ja. Eden, my account proper, in part 200 * 13. Cash Dr to Bills receivable., for ston, 10th Oct. 2 mdt. on R. Thur- Raikes and Thomson my account Debts t)r to ditto their account current, for above Sundries Dr to Cash, P. Manners, paid his bill to Ch. Gould 1st cur. 10 ddt. L.612 Hen. Meredith, paid his bill to N. Home, st. 150 18. Sundries Drs to Will. Nugent, having accepted composition of 15s. per pound on his debt, am discharged the same, Cash, for composition received L.465 6 Profit and Loss, for loss on my own debt 69 17 Raikes and Thomson their account debts, for loss on their debt - 85 5 Raikes and Thomson their account debts Dr to ditt their account current, for their proportion of th money from Nugent 1 20 : Tho. Calvert our account current Dr to Sundries for neat proceeds of the cargo j inerva nierks nibs 29233, agio 15 per ceir.. ---1.2542 banco, tx. 33s. 4d. 514 592 262 262 10 10 762 62( 25j 1035 15 12 201 JOURNAL. London, DECEMBER 20, 1787. To Voyage to Hamburgh in Co. for my | of above L.6?7 T/ To Ja. Fielding, for his of ditto 677 17 To Ch. Drake, for his I of ditto 677 17 22. -. Cash Dr to Tho. Calvert my account current, for my bill on him to J. Priestly, usance, merks lubs 1500 banco, agio 15 percent. M. 17250 current ex. 33s. 4d. , 24. , 2033 1200 Ralkes and Thomson their account current Dr to Cash, For G. Napier's bill on P. Mininski, usance Rubles 3600, at 4s. Id. remitted to them Sundries Drs to Cash, James Fielding, paid him in part Ch. Drake, in part John Hazard, in full L.400 250 82 10 31. Sundries Drs to Cash, Charges Merchandize for 6 months charges L. 36 5 4 PfoperExpences, for 6 months expences 260 ft. Meredith Dr. to Sundries, To Interest account^ for interest due by him L.I 6 4 2 * To Profit and Loss, for commission on L.I 162, at i per cent. 2 18 To Charges Merchandize, for postages 86 Balance due by him to Dr new ac- count L.814, 14s. Or, To Commission Account. 730 296 BOOK-KEEPING BY DOUBLE ENTRY. 169 side which corresponds with the greater sum of that account ; then subtract the lesser sum from the greater. The remainder will be equal to the difference of the sides of the balance sheet if the books be right, and the balances exactly collected. This equality may be proved from the nature of the articles collected. The Dr of the balance sheet contains every kind of property belonging to you, and every debt, owing to you ; and the Cr contains every debt owing by you. Therefore the difference of the sides shows what your neat estate amounts to. The profit and loss sheet, when the articles from the ledger are included, contains every thing you have gained on the Cr, and every thing you have lost on the Dr ; and the difference of the sides is your neat gain or loss. The stock account contained your effects and debts at the time the books were opened; and therefore, when the gain or loss is added to the proper side, it must show the extent of your neat estate fit present. Thus, the stock account and the balance sheet both point out how much you are worth at present ; the one from your former stock, allowance being made for your gains or losses ; the other from a view of your present effects and debts ; and they will correspond, because both must be agree- able to the truth, if the books be correct. 41. The balance being struck, 'your next work is to close the books. Every article in the ledger should be posted from the journal; therefore, the most regular way of finishing both, is by inserting the following articles in the journal, and post- ing them in the common manner to the ledger. 1st, Profit and Loss Dr in Sundries, for loss on the follow- ing accounts. The particulars are taken from the Dr of the Profit and Loss sheet. 2d, Sundries Drs to Profit and Loss, for gain on the follow- ing accounts. The particulars are taken from the Cr of the Profit and Loss sheet. 3d, Balance account, Dr to Sundries, for debts ami proper- ty belonging to me. 4th. Sundries Drs to balance account, for debts due by me, The particulars of this and the former are taken from the re spective sides of the balance sheet. 5th, Profit and Los* Dr to Slock, for neat gain ; or, Stock Dr to Profit and Loss, for neat loss. 6th, Balance account, Dr to Slock, for neat stock, . P 170 BOOK-KEEPING BY DOUBLE ENTRY. Instead of inserting these entries in the journal, some ra- ther choose to transcribe the particulars of the profit and loss and balance sheets in the ledger. 42. When goods of any kind are all sold, it is better to enter the gain or loss, and balance the account immediately, without waiting for the general balance ; and when any per- sonal account is cleared by a payment in full, it must be im- mediately balanced in the ledger ; and when the balance of an account is adjusted by a settlement, it must be balanced in the ledger, and opened again by the sum due, in conformity to the settlement. See Honeywood and Co. folio 3. In the following specimen, the first six months oi' the waste- book are fully given ; but in the last six months, every sum that may be found by computation, or by comparing the ar- ticle with former ones, is left blank for an exercise to the learner. And on account of the narrowness of the page, the figures of reference are only marked in the first month of the journal ; and the folio column is omitted, except in the first folio of the ledger. The narrations, for the same reason, are sometimes rather shorter than they ought to be. When sums are connected by a brace (as in the article ?th February), they ought to be placed in. an inner column, and their amount extended to the column in which they stand. 171 WASTE-BOOK 43. London, JANUARY 1, 1787- INVENTORY of money, goods, and debts belong ing to James Molincux, Merchant, London. Ready money - - 1200 quarters wheat, at 36s. 36 pipes claret, at L.49 15 bags cotton, qt. each 3 cwt. 1 q. is 48 cwt. 3 q. at L.4, 5s. One-third share of ship Traffic, T. Stout master Henry Lambert, Westminster, ovv.es me, per bond Elliot and Clive, Leadenhall Street, per account And I have the following bills, D. Bell on J. Harris, 12th ult. 3 mdt. L.320 My bill on W, Smith, 9th Oct. 6 mdt. 715 9 525 2160 76 207 250 500 366 1035 List of debts due by the said J. M. To Honeywood and Co. London Wall, per account settled 31st December To Ja. Kempenfeldi, Arnsterdam, /7560, at 22d. To Jo. Hill, per bill, l : ;ith Sep. 6 mdt. L.I 75 To Ro. Turner, per bill, 15th Sep. 8 mdt, 369 12 3. Bought for ready money 1200 yds. linen, at 3s. 9d . 5. Received from Elliot and Clive in part 8. Sold G. Floyder, Southwark 300 qrs. wheat, at 39s . 10. Bought from Jo. Kirman, Berwick, 300 barrels sal mop, at L.4 126 P2 6808 1475 69, 544 225 138" 10 13 172 WASTE-BOOK. JUOMuUrt, JAJNUAKY J.O, I/O/. Sold for ready money 6 pipes claret, at L.51 IS 306 Paid Honeywood and Co. to account ,^. 1 ,, ,, Bartered with Geoffrey White, Oxford-street, 500 yards linen, at 2s. L.65 12 6 2 bags cotton, qt. each 3 cwt. 1 qr. at L.4, 6s, abating 10s. 27 9 4 pipes claret, at L.51 126 - 206 10 For 200 gallons brandy, at 5s. 3d. 5 puncheons rum, at L.39 Received the balance in money L.299 11 L.52 10 195 52 1 18. Discounted the following bills at the bank o England, W. Davenport on W. Alston, 3d Feb. 3mdt. - L.314 10 My bill on J. Lascelles, 24th ult. 4 mdt. 208 2 6 L.522 12 Received for the above And the discount is L519 3 12 771 44 29911 522 J76 WASTE-BOOK. London, APRIL 19, 1787. Received from Elliot and Clive, in full L.200 .. from Gex). Floyder, in part 385 . from Tho. Stout, in payment of his note 9th current 24 Paid J. Kirman's bill on me to R. Lloyd, 16th Jan. 3mdt. in full - L.587 10 Hen. Meredith's bill to Ch. Golding, 17th ult. 30 ddt. - - 300 having agreed to open a current account with Ditto Meredith of Liverpool. Delivered Jethro lull my order on Honeywoocl and Co. to account. London, MAY 3, 1787. Shipped per the Diana, G. Blackney, for Lisbon, for account and risk of Ben. Gomez, merchant there, 800 quarters wheat, at 38s. L.I 520 800 quarters barley, at 26s. 9d. 1070 350 yds. cloth from M. Drapier, per bill, 2mdt. at 16s. 280 Commission on the cloth, at 2| per cent. 7 Paid charges shipping - 1656 7. Received from F. Alcara account sales of the cargo per the Dispatch, Bayley, neat proceeds Lires 43686, ex. 4s. 3d. per piastre , 12. Sold Alex. -Asgill, per bill, 4 rndt. the wine on board the Dispatch from Leghorn, for (^Received from W. Davenport, in full L.48 o- from H. Moor on account of Geo. Fioyder - 100 609 887 1000 10 2893 1547 148 WASTE-BOOK. London, MAY 18, 1787. 177 Paid bill to It. Turner, 15th Sept. 8 mdt. 21. _, . ,,., Received payment of Ja. Dyer's bill on II. Lamb, 2pth ult. 20 ddt. remitted me by H. Meredith The Dispatch being arrived from Leghorn, I have brought into my warehouse 100 baskets Florence oil in flasks, value - L.1S6 12 bales thrown silk . - 412 16 Paid duty and charges on oil . on silk L.72 5 136 10 28. Drawn on F. Alcara to Honeywood and Co. usa Lires 19014, ex. 4s. 3d. per piastre London, JUNE 1, 1787. Borrowed from A. Leslie, per bill, 1 ddt. at 4 per cent. * - - L.250 And received from G. Floycler, in full 100 - 3. Keceived from Carlos Oliva, Bilboa, per the Sove reign, Neal, a consignment of 50 bags Spanish wool, each 180lb. to sell on his account, Paid freight, at 2s. Gel. per bag L.6 5 Charges unloading - - 36 Received payment of bill on W. Smith, 9th of October, 6 mdt, L.715 9 2 months interest - - 5193 10. Paid my bill to W. Ellis, 7 February, 4 mdt, 369 12 217 598 208 673 15 350 11 721 IS 178 WASTE-BOOK, London, JUNE 12, 1787. Drawn on B. Gomez to Honeywood and Co. usa. 2000 milrees, at 5s. 6d. 15 Sold 12 bags of C. Oliva's wood to W. Nugent, qt. each 180 Ib. is 2160 Ib. at 2s. 3d. . 20. Paid H. Meredith's bill to M. Bishop, lOdst. - . L.115 10 P. Manners, to account 450 30. Paid personal and family expences for 6 months L.200 small charges on my business 15 10 Taken for my own use the remaining pipe claret London, JULY 1, 1787. Delivered Jethro Tull my order on Honeywoot and Co. in full 3 Received from B. Gomez, Lisbon, per the Diana Blackney, 20 pipes Lisbon wine, amount per in voice 846 milrees, at 5s. 6d. Paid duty at L.28, 1 8s. per ton freight, at 25s. per pipe charges unloading, L.3 68 Drawn on B. Gomez, To Honeywood and Co. usa. M. 4000, at 5s. 6d. To N. Dove, do. 3675 The last for ready money, 7675 550 243 565 21, 55 211 JOURNAL. London, DECEMBER 31. 1787* 205 Profit and Loss Dr to Sundries, for loss on th following accounts, To J. Kempenfeldt To Rum To Interest account * To, Florence Oil To Proper Expences To Charges of Merchandize To Voyage from Jamaica To Voyage to Rochelle To Hops L.2 4 6 IB 511 41 19 122 14 18 17 10 15 1 10 Sundries Drs to Profit and Loss, following account, Wheat Claret Cotton Share of Ship Traffic Linen Salmon Sugar - - Brandy - - Voyage to Jamaica Barley F. Alcara, my account goods Thrown Silk Lisbon Wine Rice Voyage to Hamburgh, in Company J. Eden, my account in Company for gain on th L.186 17 ' 94 5 - 7 15 ! 14 2 1 i 17 10 - 20 8 14 J 109 12 1( 55 164 16 i 29 14 12 10 15 123 1 1C 39 Profit and Loss Dr to Stock, for nett gain Balance account Dr to Sundries, To Share of Ship Traffic . L.220 To H.Lambert - . 512 10 Carried forward L.732 10 S 899 204 206 JOURNAL. London, DECEMBER 31. 1787. 7189 2889 4299 2 18 Brought over L.732 10 To Bills receivable, On N. Spence, 1st Sep. 4 mdt. L.I 05 On D. Green, 15th Oct. 3 mdt. 275 To Barley, 500 qrs. at 24s. 6d. 612 10 To Rum, 3 puncheons, at L.38 114- L. To H. Meredith - - 81414 To Lisbon wine, 3 pipes, at L.28 84 . To Goods bought on contract 612 10 To Th. Aubrey * account current, L.I 44 90 To Will. Dashwood - 944 5 To Cash 623 1 1 9 To Hops, 70 cwt. at L.3, 10s. 245 To W. Jennings, - 880 To Iron, 4 tons at L.I 8 . - 72 To James Eden, my account proper 314 10 To Th. Kenrick - - 336 To Th. Calvert,acc. current M; 11983 833 12 Sundries Drs. to balance account Honeywood and Co. - L.474 14 Bills payable To A. Leslie, 1st June, 1 ddt. L.250 To P. Haliday, 1st Oct. 5 mdt. 135 385 JP. Manners - - 613 James Fielding - 277 17 4 Ch. Drake - - 291 1 10 Raikes and Thomson, account debts 599 Jiai/ces and Thomson, account current 249 5 Stock Dr, to balance account, for neat stock, 207 INDEX. A Archer, Samuel 5 Alcara, Fr. ace. goods 7 Alcara, Fr. ace. cur. 7 Aubrey, Th. ace. cur. 11 Aubrey, Th. ace. debts 1 1 B Bills receivable 3 Jills payable 4 Brandy 6 Jarley 7 Balance account 1.5 c Cash - 1.13 Claret - 2 Cotton - 2 Charges merchandize 10 Calvert, Tho. 15 D Davenport, Will. 5 Dashvvood, Will. 12 Drake, Ch. 14 K Elliot and Clive 3 Sden, Ja. ace. in Co. 14 Eden, Ja. ace. proper 14 F Floyder, Geo. 4, Florence oil 9 Fielding, Ja. 14, G Groset, Francis 6 Gomez, B. Goods boughton cont. 10 H Joneywood and Co. 3 Hazard, John, 6 Hops 13 I Interest account 8 Jennings, Will. 13 Iron - 13 K Kempenfeldt, Ja. Kirman, John 5 Kenrick, Tho. 15 L ^ambert, Henry 2 jinen - 4 Jsbon wine 10 M Manners, Pat. 7 Vitredith, H. 9 Muslins - 10 N Nugent, Will. 8 Necker, L. 11 O Oliva, C. ace. wool 9 Oliva, C. ace. our. 12 P Profit and Loss 8 Proper expences 10 Q R Rum - 8 Raikes and Thomson account goods 12 Rice - 12 R. and T. ace. debts 15 R. and T. ace. cur. 15 S Stock 1 Share of ship Traffic 2 Salmon 4 Sugar - 5 Suspense aceount 12 T Tull, Jethro 6 Thrown silk 9 V Voyage to Leghorn 5 Voyage to Jamaica 6 Vo^ age from Leghorn 1 Voyage from Jamaica 1 ] Voyage to Rochelle 1] Voy. to Hamb. in Co. 13 W Wheat - 2 White, Geoffrey 8 X y Z 208 (1) LEDGER, Dr. Stock, 1787. Fo Jan. To Sundries, per J. 2713 g Dec. 31 To Balance account 15 4299 4 7 7012 i 7 1787. Jan. 1 Feb. 3 Dr. Cash, ] To Stock on hand To Elliot and Clive in part To Claret, for 6 pipes, at L.51 To Wheat, in part Fo 1 r 2 o c 525 166 306 500 13 4 1C To Sugar, received balance fc 193 15 _.^ 17 To Sundries, per J. 844 IS 2 Mar. 9 To Sundries, per J. - 353 7 6 To Voyage to Jamaica, for drawback 6 41 13 4- 15 To Bills receivable, for bill on J. Harris ^ 320 April 9 To Share of Ship Traffic, in part profits 2 20 14 To G.- White, received balance 8 52 1 6 18 To Bills receivable, for sundry bills discounted 3 519 19 To Sundries, per J. - 609 May 15 21 To Sundries, per J. - To H. Meredith, for J. Dyer, on R. Lamb 9 148 217 June J To Sundries, per J. - 350 9 To Sundries, for bill on W. Smith, with interest 721 8 3 July 1 To B. Gomez, for my bill, per J. 9 1010 12 6 ^ To Sundries, per J. 368 Aug. 15 To L. Necker, for my bill on him, per J. 11 725 _ Sept. 5 15 To Voyage from Jamaica, per J. To bills rcc. for bill on A. Asgill, 12th May, 4 mdt. 11 3 392 275 - Carried forward to fol. 13 8658 10 7 LEDGER. (9) 20 9 Contra Cr. ' 1797. T 1 Fo 6808 l Jan. i Dec. 31 By Profit and Loss 8 204 6 7012 7 1737. Jan. 3 18 Feb. 7 15 Contra Cr. By Linen, for 120 yards, at 3s. 9d. By Honeywood and Co. in part By Voyage to Leghorn, per J. By J. Kempenfeldt, paid his bill to R. Barbour Fo f 3 225 600 271 300 19 6 20 By Wheat, in part 2 450 _ 24 By J. Kirman, paid his bill to N. Compton i 200 _ 27 By J. Kempenfeldt, for a bills remitted him 3 395 4 6 Alar. 3 By Voyage to Jamaica, for charges 6 & 7 ff 17 By Bills payable, paid bill to J. Hill, per J. 4 175 29 By J. Kirman, paid his bills, pev J. 5 600 April 19 By Sundries, per J. 887 10 ~_ May 3 3y B. Gomez, paid charges 9 16 5 6 18 By Bills payable, paid bill tp R. Turner 4 369 12 21 3y Sundries, paid freight and charges, per J, 208 15 June 3 10 By Carlos Oliva, his account wool, per J. By Bills payable, paid bill to W. Ellis 9 4 9 72 11 IS 4 20 3y Sundries, per J. 565 10 30 3y Sundries, paid charges and expences 215 10 July 3 6 3y Lisbon wine, foe freight, duty, and charges 3y Bills payable, per J. . 10 4 317 658 6 8 16 iy Sundries, per J. 696 13 4 Aug. 8 By L. Necker, for charges shipping barley 11 13 9 Jy Voyage to Rochelle, for charges 11 2 2 __ 24 5y Sundries, per J. - . 553 Sept. 19 By H. Meredith, for P. Vanlow's bill per J. 9 350 20 iy Raikes and Thomson their acct. goods, per J. 12 157 11 8 27 By Bills payable, paid note to P. Hill 4 258 8 4 Carried forward to fol. 13 8574 15 S B 210 (2) LEDGER. 1787. Jan. 1 Feb. 17 Dec. 31 1787. Jan. ] Dec. 31 Dr. To Stock, at L.49 'o Profit and Loss, for gain 1787. Jan. Dec. 3 1787. Jan. Dec. 3 1787. Jan. Oct. 2 Dr. o Stock, at 36s. o Sundries, per J. 37s. o Profit and Loss, for gain qrs. 1200 800 160 480 186 2000 826 Claret, pipes 36 36 Dr. ]\> Stock, at L.4, 5s. percwt. Io Profit and Loss for gain Cotton, B. 15 cwt qrs 48 3 858 20' 48 3 21- Dr. Share of Ship Traffic, To Stock for one- third share To Profit and Loss for gain Dr. Henry Lambert, Westminster, To Stock, per bond, due 25th April To Interest account, for one half year's interest ? 25 ' 1 26 50 51 LEDGER. (2) 211 Contra Cr. 1 1 1787. qrs. Jan. 8 Feb. 3 By G. Floyder, at 39s. By Sundries, per J. at 38s, 6d. 300 500 585 96210 17 By Cash, at 37s. 9d. 150 283 2 G April 3 By W. Nugent, at 38s. 3d. 100 191 5 May 3 By B. Gomez, at 38s. - - 800 1520 ~~ Aug. 1 By Voyage to Rochelle, at 38s. 150 285 ~~* 2000 3826 17 G Contra Cr. 1787. pipes Jan. 15 By Cash, at L.51 - 6 306 _ 24 By Sugar, in barter, at L.52 10 520 Mar. 9 By Cash, at L.51, 10s. - - 6 309 , Apr. 5 By W. Nugent, at L.51, 15s. 9 465 .'5 __ 14 By G. White, at L.51 126 4 206 10 ... June 30 By Proper expences - 1 51 36 1858 5 1787 Contra Cr. B. cwt qrs Mar. 24 By Bills receivable, at L.4-, 10s. per J. 5161 73 2 6 Apr. 5 By W. Nugent, at L.4, 8s. - 8 26 114 g 14 By G. White, at L.4, 6s. abated 10s. - 2 6 2 27 9 15 48 3 214 19 6 Thomas Stout, Cr. 4787. Apr. 9 By Sundries, for share profits 44 _ Dec. 31 By Balance account - - 220 264 - 1 Contra Cr. 1787. , Dec. 31 By Balance account 512 10 512 10 212 (3) LEDGER. Dr. Elliot and dive, 1787. Jan. ] To Stock, due by them per account 366 13 4 366 U 4 Dr. Bills receivable, 1787. Jan. 1 To Stock, for sundry bills, per J. 1035 9 __ Feb. 3 To Wheat, for W. Davenport on W. Aston, 3 mdt. 314 10 _ Mar. 24 To Sundries, for bill on J. Lascelles, 4- mdt. 208 2 6 Apr. 9 To Share of Ship Traffic, for T. Stout's note 24 ____ May 12 To Voyage from Leghorn, for bill on A. Asgill, 4 mdt. 275 July 8 To Sundries, for bill on M. Wilson, 6 mdt. 826 . Sept. 1 To C. Oliva, ace. wool, for bill on N. Spence, 4 mdt. 105 * To Voyage from Jamaica, per J. 392 _., Oct. 10 To Raikes and Thomson, account goods, per J. 262 10 $Tov. 5 To Voyage from Rochelle, for bill on D. Green 275 3717 11 6 Dr. Honeywood and Co. 1787. Jan. 18 To Cash, in part - - 600 ^ _ _, May 28 June 12 To F. Alcara, account-current, for my bill, per J To B. Gomez, for my bill on him to them, per J. 673 550 8 3 July 3 To B. Gomez, for ditto, per J. 1100 Oct. 31 To Balance, due them, to Dr new account 162 13 3086 1 3 1787. Pec. 31 To Balance account -. 474 14 474 14 ._ Dr. J. Kempenfeldt, 1787. Feb. 15 To Cash, paid his bill, per J. - I/. 3306.6 300 __ 27 To Cash, for a bill rem, him, per J, 4253.14 395 4 6 /. 7560.- 695 4 (> LEDGER. (2) 213 Leadenhall-street) Contra Or 1787. Jan. By Cash, in part - - - 16 1 4 April 1 By Cash, in full - . 20 36 1 4. 1787. Contra Cr ; Mar. 1 By Cash, for bill on J. Harris, 12. Dec. 3 mdt. 320 April 1 Jy Sundries, for bills discounted, per J. 522 1 6 1 Jy Cash, for Tho. Stout's note on demand 24 June 1 By Cash, for bill on W. Smith, 9. Oct. 6 mdt. 715 Sept. 1 By Cash, for bill on A. Asgill, 12. May, 4 mdt. 2 To Nov. 1 By Sundries, for a bill discounted, per J. 826 Dec. 9 By Cash, for underwriters bills 392 .___' 13 By Cash, for bill on R. Thurston, per J. 262 K 31 By Balance account 380 3717 6 1787. Jan. ] London-wall, Contra Cr. y Stock, due them per account 475 April 24 y J. Tull, for my order on them 000 July 1 y J. Tull, for ditto - - 580 Oct. 31 y Interest-account, due them 30 i 3 086 1 3 1787. _ Oct. 31 y Balance of former account, due them 162 3 Nov. 7 y C. Oliva, account-current, per J. 312 1 474 i Amsterdam 9 . Contra Cr. 1787. Jan. 1 y Stock, due them - - /.7560 693 _ Pec. 31 y Profit and Loss, for loss by exchange 2 4 6 1 " ' 695 4 (J 214, (*) LEDGER. Dr. Bills payable, 1787. Mar. 17 To Cash, paid bill to J. Hill, 15th Sep. 6 mdt. 175 May 18 To Cash, paid bill to R. Turner, 8th Sep. 8 mdt. 369 12 June 10 To Cash, paid bill to W. Ellis, 7th Feb. 4 mdt. 72 18 July 6 Po Cash, paid sundry bills, per J. 658 Sep. 27 To Cash, paid note to P. Hill, 24th July, 2 mdt. 258 8 Nov. 10 ^o Cash, paid bill to J. Whitebread, 8th Aug. 3 mdt. 802 10 Dec. 31 To Balance account 385 2721 8 1787. Jan. 3 Dr. Linen, Yds. ^o Cash, at 3s. 9d. - 1200 225 30 To S. Archer, per J. . 1220 176 10 Dec. 31 To Profit and Loss i 2 1 2420 403 11 Dr. George Floyder y 1787. Jan. 8 To Wheat for 300 qrs. at 39s. - 585 585 4 Dr. Salmon, 1787. Par. Jan. 10 Dec. 31 To J. Kirman, at L.4> 12 6 300 To Profit and Loss 1387 17 10 10 300 MMW 1405 - LEDGEU. (4) 215 Contra Cr 1787. Jan. 1 y Stock, for sundry bills, per J. 544 ___ Feb. 7 y Voyage to Leghorn, for bill to W. Ellis,'4 mdt. 72 4 Mar. 3 y Voyage to Jamaica, for bill to N. Brent, 4 mdt. 378 May 3 y B. Gomez, for bill to M. Drapier, 2 mdt. 230 T June 1 y Casn, for bill to A. Leslie, 1 ddt. 4 per cent. 250 , July 24 y Muslins, for note to P. Hill, 2 mdt. 256 4 Aug. 8 y L. Necker, for bill to J. Whitebread, 3 mdt. ^802 Oct. 1 y Voy. to Hamburgh, for bill to J. Haliclay, 5 mdt. 135 721 *MB 8 Contra Cr* 1787. Yds. Feb. 7 By Voyage to Leghorn, at 3s. 9d. 600 112 17 By Cash, at 3s. 8d. * 250 45 8 Mar. 3 Jy Voyage to Jamaica, per J. 1070 179 6 April 14 By G. White, at 2s. 7id. - - 500 65 6 2420 403 8 Southward, Contra Cr, 1787. April 19 By Cash, in part ... 385 _ _ May 1 By Cash, from H. Moor 100 ___ June By Cash, in full 100 585 1787. Feb. Contra Cf. Bar By Voyage to Leghorn, L.4 126, per J. 20 925 1 By Cash, at L.4, 16s. - - , 10 480 30 1405 (5) LEDGER. Dr. 1 787 Feb. 24 To Cash ' P aid his bil1 to N ' DO'TO Cash, paid his bills per J John Kirtuan y . 21st ult. 1 md Mar. 2 April 1 1787. Jan. 2 Dec. 3 1787. Aug. 2 1787. Feb. 3 1787. Feb. 7 To Cash, paid his biJl to R. Lloyd, 16th Jan. 3 mdt Dr. Sugar, To Claret, in barter, at L.3, 5s. per cwt. To Profit and Loss Dr. o Cash, in full Dr. 'o Wheat, per J. Dr. o Sundries, per Jo 16' Samuel Archer, William Davenport, Voyage to Leghorn, LEDGER. (5) 217 1787. Jan. 10 1787. Feb. 10 Mar. July 24 3y 8 By 1787. Jan. 1787. ^eb. May 15 By Cash 1787. Apr. Berwick, Contra By Salmon ftfr 300 barrels, L.4 12 6 Contra By Sundries, at L.3, 10s, per J. By Bills receivable, at L.3 7 6, per J. Bills receivable, at L.3 2 6, per J. 30 By Milk-street, Linen, per J. Contra Chatham , Contra Cr. 1387 10 1387 cwt. 80 40 40 160 Cr. 280 135 540 176 10 Cr. 20 By Wheat, for my bill on him, 1 mdt. per J. , in full 100 48 148 per the Dispatch, Bayley, Cr. 2 By F. Alcara, my account goods, per J. 1382 218 (6) LEDGER, 1787. Feb. 10 Apr. 14 Dec. 31 1787. Apr. 24 July 1 1787. 2VTar. .Nov. Dec. 3 1787. Aug. 2 178T. Aug. ' Dec. 2 Dr. 'o Sugar, per J. at Ss. 9d. 'o G. White, at 5s. 3d. 'o Profit and Loss Brandy, Gal. 300 200 500 Dr. Jethro Tull, Esq. 'o Honeywood and Co. for my order on them 'o Honeywood and Co. for ditto. Dr. Voyage to Jamaica, Te Sundries, consigned Th. Aubrey, per J. To Th. Aubrey, my account debts, per J To Profit and Loss Dr. Francis G reset, Sheffield, Fo Cash, in full Dr. To Cash, in part To Cash, in full John Hazard, LEDGER. (6) 219 Contra Cr. 1787. Feb. 17 Mar. 9 July 24 Gal By Cash, at 6s, - 12C By Cash, at 5s. lid. - - 151 By Muslins, in barter, at 5. lOd. 23C 36 44 6 6 '8 50C 14 9 2 of Belfidd, Contra Cr. 1787. Feb. 20 Mar. 7 By Wheat, for balance of 800 qrs. per J. By Barley, for 500 qrs. at 26s. 930 650 - 1580 - per the Sea Horse t Jones t Cr. 1787. Mar. 12 Aug. 1 3y Cash, for drawback on 2500 yds. cottons, at 4d. By Sundries, per J. ... 41 1025 r < 4 1066 c 1 Contra Cr. 1787. Mar. 3 By Voyage to Jamaica for hardware - " 276 Insurance Brker, Royal Exchange, Cr. 1787. Mar. 3 Aug. 1 8 Oct. 1 ty Voyage to Jamaica, for ins. of L.800, per J. iy Voyage from Jamaica, per J. iy Sundries, per J. - - / By Sundries, for insurance to Hamburgh, per J. 42 46 33 59 4 8 6 G 6 G 6 182 320 (?) LEDGER. Nov. 26 Dr. 1787. Mar. 7 To Sundries, per J. Barky, Dec. 31 To Profit and 1797. June 2C July 16 1787. Dec. 1 31 1787 Apr. Dec. 31 1787. April 2 1787. VI ay 7 To Goods bought on contract, at 24*6. 6d. Qrs. 120( 50( 170 Dr. Pat. Manners, Esy, of Westfield, To Cash, in part To Cash, in full To Barley, for abatement To Cash, paid his bill to C. Gould, 10 ddt. To Balance account Dr. Fr. Alcara, Leghorn, To Voyage to Leghorn, for the cargo received To Profit and Loss -- - Dr. Voyage from Leghorn, To F. Alcara, my account current, per 3. Dr. F. Alcara, Leghorn, fo Ditto, my account goods, for nett proceeds Lires. 43686 43686 155 61! 2218 450 450 90 612 613 13SS 164 1547 87 10 16 54? 547 LEDGER, (7) 221 1787. May 3 July 16 Aug. 8 Dec. 31 Contra Cr. Qrs. Uy B. Gomez, at 26s. 9d. . - 800 1070 1 535 612 5 10 By L. Necker, at 26s. 9d. - 400 By Balance account - - 500 1787. Mar. 7 1700 2218 901 15 5 Contra Cr. By Barley, for 700 qrs. at 25s. 9d. 901 5 1787- July 16 By Goods bought on contract, per J. 1225 1787. May 7 1225 1547 4 My account of Goods, Cr, By F. Alcara, my account current for nett proceeds 1787. May 7 21 1547 4 per the Dispatch, Bayley, Cr. By Bills receivable, per J. - - By Sundries, pei J. 275 598 16 1787. April 2 May 28 873 16 my account current, Cr. Lires. By Voyage from Leghorn, per J. 24672 By Honeywood and Co. for my bill, per J. 19014 873 673 1547 16 8 4 43686 T3 .-:': (8; LEDGER. Dr. Wiluam Nugent, Fish-street, 1737. April 5 To Sundries, per J. June 15 To Carlos Oliva, his account wool, per J. Oct. g To Raikes and Thomson, their ace. goods, per J 1787. April 14 T J787, April 14 T 1787. April Oct. 31 Nov. 10 771 243 34-1 Dr. Geoffrey White, Oxford-street, o Sundries^ per J. Dr. o G. White, at L.39 Rum, 299 195 195 11 Dr, Interest account, I8To Bills receivable, for discount, per J. To Honeywood and Co. due them To Bills receivable, for discount, per J. 12 SOU 41 Dr. Profit and, Loss, 178T. . Dec. 18'To W. Nugent, lost by his bankruptcy 31;To Sundries, per J. To Stock, for nett gain 69 73 204 101 LEDGER. (8) 223 Contra Cr. Sept. 12 Jy Sundries, per J. 735 Dec. 18 Jy Sundries, per J. * 620 8 355 8 Contra Cr. 1787. Apr. 14 By Sundries, per J. 299 11 Contra Cr. 1787. P July 5 By Cash, at L.38, 10s. - - 2 77 Dec. 31 By Profit and Loss - / By Balance account, at L.38 3 114 - 195 Contra O. 1787. June 9 By Cash, for interest on W. Smith's bill 19 Oct. 25 By H. Lambert, for one half year's interest 12 Dec. 31 By H. Meredith, for interest due by him 10 By Profit and Loss 10 41 - 1787. May 3 Contra Cr. By B. Gomez, for commission, per J. Aug. 8 By L. Necker, for ditto 16 Sept. 8 By C. Oliva, account wool, per J. - 38 15 Nov. 8 Dec. 31 By Raikes and Thomson, account goods, per J. By H. Meredith, account-current, per J. 46 2 1! By Sundries, per J. 899 10 1011 13 224 ( 1787. Apr. 19 June 20 July 1C Sept. 19 Dec. 14 31 178T. May 3 1787. May 21 1787. May 21 Dec. 31 1787. June 3 Sept. 8 9) LEDGER, 300 115 246 350 150 19 1181 10 13 10 14 ^ 4- 9 Dr. Henry Meredith , Liverpool, To Cash, paid his bill toC.Golding, 17th ult. 30 ddt. To Cash, paid his bill to H. Bishop, 10 ddt. To Cash, paid his bill to W. Wade, 23d ult. 20 ddt. To Cash, paid P. Vanlow's bill, 16th nit. 1 mdt. To Cash, paid his bill to N. Home, st. To Sundries, for interest, commission, and postages 2893 G Dr. Ben. Gomez, Lisbon, To Sundries, for a cargo per the Diana 2893 6 186 72 Dr. Florence Oil, B. To Voyage from Leghorn To Cash, paid freight, duty, and charges 100 258 o 412 136 29 If 1C 14 Dr. Thrown Silk, B. To Voyage from Leghorn - - 12 To Cash, paid freight, duty, and charges To Profit and Loss 12 579 9 1024 1034 11 IS 8 4 Dr. Carlos Oliva, Bilboa, B. lb. To Cash, paid freight and charges on 50.9000 To Sundries, per J. 50 9000 LEDGER. (9) 1787. May 21 Oct. 10 31 1787. June 1 2 July 1 1787. July 5 Sept. 30 Dec. 31 1787. July 8 Aug. 27 1T87. June 15 July 8 Sept. 1 his account -cur rent Cr. By Cash, for J. Dyer or R. Lamb, 29th ult. 28 ddt. By Cash, for a bill, per J. By Balance account 217 150 814 1181 550 232 2110 3893 14 14 l' j U his account-current Cr. By Honeywood and Co. for my bill on him, per J. 3y Lisbon wine, for amount, per J. - By Sundries, per J. - 148 96 13 10 15 Contra Cr. By Cash, at L.2 9 6 By W. Jennings, at L.2, 8s. By Profit aad Loss - ~ B. 60 40 100 258 5 386 193 Contra Cr. 3y Bil|s receivable, per J. By Suspense account ... B, 8 4 J2 579 243 315 476 5 his account of Wool Cr, B. By W. Nugent, at 2s. 3d. . 12 Jy Bills receivable, at 2s. id. - 15 By Sundries, per J. - 23 Ib. 2160 2700 4140 50 9000 1034 5 226 (10) LEDGER. 1787. June 30 To Dec. 31 Cash, for 6 months expences To Claret, for 1 pipe To Cash, for 6 months expences 1787. June Dec. 31 30 T 1787. July 1 Dec. 1787. July 1787. July Sept. IV Dr. Proper Expences, Dr. Charges Merchandize, Cash, for 6 months charges fo Cash, for 6 months charges Dr. To Sundries, per J. Profit and Loss Lisbon Wine, 31 To 20 Dr. Goods bought on Contract, 16 To P. Manners, per J. Dr. Muslins, 34 To Sundries, per J. at 7s. 9d. To Suspence account, returned 45 Yds. 840 105 9*5 200 51 260 511 51 54919 1210 56210 122, 122. 325 42 36710 LEDGER. (10) 227 Contra Or. 1787. Dec. 3 By Profit and Loss 511 """ * - 511 1787. Sept. 8 Contra. Cr. 3y C. Oliva, his account wool o 710 Nov. 8 3y Raikes and Thomson, their account goods 5 9 1 Dec. 31 By H. Meredith, for postages 8 6 By Profit and Loss 41 911 51 5 4 Contra Cr. 1787. P. July 5 By Cash, at L.28, 10s. , 5 142 10 Nov. 20 By Th. Kenrick, at L.28 - , 12 336 Dec. 31 By Balance account, at L.28 - 3 84 20 562 10 1787. Nov. 26 Contra Cr. By Barley, for 500 qrs. at 24s. 6d. 612 Q Dec. 31 By Balance account 612 1225 - 1787. Aug. 27 Oct. 1C Contra Cr. P. Yds By Suspenee account at 8s. - - 5 10 By Sundries, per J, 40 84C 42 Q -35 10 45 94 367 $28 (11) LEDGER. Dr. Thomas Aubrey, Jamaica, 1787. | Currency Aug. 1 To Voyage to Jamaica, per J. Kov. 3 To Th. Aubrey my ace. debts, per J. L.1168 , 352 1520 Dr. Thomas Aubrey, Jamaica, Currency 1787. Aug. l[To Voyage to Jamaica, per J. L.472 29 Dr. Voyage from Jamaica, 1787. Aug. IjTo Th. Aubrey, my account-current, per J. To J. Hazard, for insurance, per J. 86 4 90 Dr. Lewis Necker, Rochelle, 1787. Aug. 8JTo Sundries, for a cargo per the Bienfaisant ._ To J. Hafcard, foy insurance, per J. Dr. 1 787. Aug. 8JTo Sundries, per J. To J. Hazard, for insurance, p*r J. Voyage to Rochelle, 136' 2" 1394 287 5 293 LEDGER. (11) 229 1787. Aug. 1 Dec. 31 1787. Nov. wy account current, By Voyage from Jamaica, per J. By Balance account 3 By my account of debts, Sundries, per J. 1787. Sept. Dec. 3 1787.' Aug. 1 Sept. 1787. Nov. 5 Dec. 31 per the Dolphin, Harris, By Sundries, per J. By Profit and Loss his account current, 3y Cash, for my bill on him, per J. By C. Oliva, account current, per J. Cr. Currency. L.1376 144 950 Cr. Currency. L. 472 Cr. per the Bienfaisant, Perrault, Cr. y Bills receivable, per J. y i'rofit and Loss 78-1 -f 1221- 906 14 6 725- 275 ..| 89 230 (12) LEDGER, 1787. Aug. 27 1787. Sept. 1 17 Oct. Dr. To Sundries, per J. Dr. William Dashiuood, Ipswich, To C. Oliva, his account wool, per J. To Suspence-account, for thrown silk To Raikes and Thomson, account goods, per J. 1787. Fcpt. Nov. 7 8 To 1787. Sept. 2 Nov. 1787. Sept. 1 Dec. 3 Suspence-accounl, Dr. Carlos Oliva, Bilboa, L. Necker, for my bill, per J. To Honeywood and Co. for his biil on them Dr. Raikes and Thomson^ Pctersburgh, To Cash paid charges, per J. on To Sundries, per J. Iron T. 30 Flax B. 300 30 300 Dr. Rice, To W. Nugent, at L.3, 3s. To Profit and Loss B. 150 235 371 193 380 944 669 312 98? 19 157 1720 187810 472 15 487 10 LEDGER, (12) 231 Contra 1787. Sept. 17 By Sundries, per . 1787. Dec. 31 Contra By Balance account 1787. Sept. 8 By 178T. Sept. 30 Oct. 10 Nov. 1 787. Sept. Oct. 1 Cr. his account current, Cr. C. Oliva, account goods, for neat proceeds their account of goods, By W. Jennings, at L.I 8, 5s. 8 By W. Nugent, per J. By Sundries, per J. 8 By Sundries, per J. at L.18 Iron T. 12 12 30 'lax. B. 50 250 Contra Cr. 30 By W. Jennings, at L.3, 5s. By Voyage to Hamburgh in Co. at L.3, 5s. U 2 300 B. 2 13t 150 235 944 944 98? 219 341 1102 216 187810 48" 232 (13) LEDGER. 1787. Oct. 10 Nov. Dec. 81 1787. Sept. 1: Dr. Cash, Brought forward from Fol. 1. To Raikes and Thomson, their account goods, per To H. Meredith, for a bill, per J. To Raikes and Thomson, their account goods To Bills receivable, for a bill discounted 'o Sundries, per J. To Bills receivable, for bill on R. Thurston lg To W. Nugent, for composition 2g To Th. Calvert, my account current, per J. Dr. Hops, 1787. Sept. 3( 1787, Nov. 3787. Oct. 1 Dec. 31 To W. Nugent, at L.3, 15 bought for ready money, rials 6128, ex. 3s. 8|d. per piastre. 27th, M. Soderini has remitted J. Kempenfeldt on my account a bill of ./8077 10 banco, agio 5 per cent, is ^8481 7 current, being value of ducats 3590 banco, agio at Venice 20 per cent, ducats current, ex. between Venice and Amsterdam 90d. esti- mated at 22d. per current, f. of Amsterdam. 30th, Settled accounts with H. Meredith ; charged him interest L.27, com- mission on L.445, 10s. at | per cent, and postages 5s. 9d. Paid small charges on my business for 6 months L.S1, 10s. my own expenses L.260. Goods on hand, 110 cwt. alum at L.I, and 2 cwt. Jesuits bark, at L.29, 6's. my share of ship Traffic, valued at L.420. The Profit and Loss, and Balance Accounts for these six months, will be found as follows : Dr. Profit and Loss. To share of ship Traffic L.55 To Rum To Hops - 17 K To Insurance account 6 1' To P. Almagro - 4 19 To charges merchandize 17 18 To Proper expences 260 Or. By P. Manners L.IC j-j By Th. Calvert 18 1 By L. Necker 2 15 By A. Luzi 55 13 iiy H. Meredith 1 4 3 By Barley 50 By Lisbon 6 By Iron I 15 3y Alum 5 1? 6 By Interest account 32 16 8 By Spanish salt 2 2 2 By Cochineal 96 6 S .dy Jesuits bark 1 10 By Voyage to Venice 58 5 4 By Cordage 12 . . By M. Soderini, acc.cur. 5 H 1 By Stock t.I 3 365 5 242 BOOK KEEPING BY DOUBLE Dr. Balance- account, Cash 751 3 4 Share of Ship Traffic 420 . Bills receivable onD.WillisL.37868\ on M. Vince 48 6 8 J 426 13 4 H. Meredith 1095 r Th. Auhrey 90 Alum, llo'cwt. at L.I 110 T. ( arpenter 400 J. Hazard 129 12 6 Jesuits bark, 2 cwt. at L.29, 6s. 58 12 Jo. Pennant 245 4 6 Jo. Gale 88 J.Kempenfeldt,/.8481 290 17 4 11. C6mvay 47 15 A. Drugger 30 16 Voyage to Halifaxin Co. 1396 2 3 M. Soderini, ace. goods 323 18 : 5903 14 3 Cr. By bills payable to A. Leslie L.S50 \ to A. Brent By A. Luzi By Stock 620 j 870 757 - 11 427613 4 590314 3 43. PARTNERSHIP. We have subjoined some cases in partnership ; the accounts of which may be drawn out in the method of double entry, as a further exercise for the learner. The entries in partnership, when the accounts are kept in separate books, are in general exactly the same as in proper trade, except the alteration of style to the plural number ; nue, us, and ours, instead of /, me, and mine ; and the like. If the partnership be only occasional, there will be no oc- casion for a stock account, and one account for each partner is sufficient. The partners are stated Cr for whatever they pay in, and Dr for whatever they receive from the funds of the company. As the stock is advanced by the partners, the Cr side of their account will be almost always the heaviest. Xn order to determine what one partner owes to another, find the amount advanced by them all from the balance of their respective accounts ; divide this sum equally, if their shares be" equal ; if otherwise, according to their proportions ; this gives the sums that each ought to have advanced : and the difference between these sums and the sums actually advanced is die balance due to or by the several partners. PARTNERSHIP. 243 If one partner has more especially the management of the business, it may sometimes be convenient for him to open an account of Cask in Company ; but it will generally answer as well to charge himself Dr for all he receives, and Cr for all he pays out, in managing the affairs of the company. 44. In fixed companies, it will be proper to open a stock account, and two accounts for each partner; one entitled 'A. B. his account in 'company, which exhibits the extent of his concern in the funds of the company; the other, A. B. his ac- count proper, which contains receipts and payments of money, and other transactions between the partner, considered as a neutral person, and the company. In the entries, at opening the books, if any partners have not fully paid in their shares, their proper accounts are charged Drs to Stock ; and Stock is charged Dr to the partner * proper accounts who have paid more ; then Stock is charged Dr to each partner his account in company, for his share of the nett stock. At balancing the books, if it be intended to divide the gain, Profit and loss is charged Dr to each partner his account proper for his share ; if it be intended to apply the gain to increase the stock in trade, Projit and loss is charged Dr to each partner his ac- count in company, for his share ; and if loss be incurred these entries are reversed. I. Thomas Reynolds and George Bourn having agreed to deal in company in the wine trade, each one half concerned, Reynolds furnishes 12 pipes claret, atL.53, 10s. ; Bourn gives in 20 pipes port, at L.28, 5s. ; they purchase from P. .ill 6 pipes Madeira, at L. 12 ; and they commisson from Seville 8 pipes sherry, which J. Carrero ships for them, amount 912 piastres, and draws on Bourn for the value, at 3s. 4d. Rey- nolds pays for insurance of L.I 50 on the sherry, at 3 gs. per cent, and when it arrives, pays for freight, duty, and charges, L.I 18, 10s. Bourn sells the wine as under; 8 pipes port to D. Bridges, at L.31, 10s.; and 7 ditto to Francis Grey, at L.31 ; and 5 ditto to James Holmes, at L.30, 15s.; 4 pipes Madeira to Charles Love, at L.45, 17s.; 2 pipes sherry to George Atkins, at L.36, 10s. and 3 to Henry Miles, at L.36, 15s. and the remainder for ready money at L.36 3 pipes claret for ready money, at L.40 and 4 ditto to F. Grey, at L.42, and 5 ditto to John Wilkes, at L.41. He receives pay- ments from Atkins and Love, but allows Love 8s. discount. He also receives a partial payment of L.I 00 from Bridges. X2 244 PARTNERSHIP. He pays P. Hill for the Madeira, and for cellar-rent and in- cidents L.12, 5s. and charges 1 per cent, on the sales for his own commission. Eacli of the partners takes one of the re- maining pipes Madeira, valued at prime cost. At settling ac- counts, the debts due by Grey and Miles are assigned to Rey- nolds, and those by Bridges, Holmes, and Wilkes, to Bourn. II. A. Rose, B. Smith, and C. Crawford, agree to engage equally in an adventure to Barbadoes. Rose gives in 2400 yards linen, at Is. 2d. Smith gives in woollen stuffs to the va- lue of L. 138, 10s. and Crawford furnishes 500 dozen beer in bottles, at 5s. 4d. a dozen; and they purchase china ware from D. Hicks, value L.I 34, and hardware from E. Wood, value L.207 both per bill at 3 mdt. They ship this cargo per the Unicorn, consigned to Fr. Lindsay, and Smith pays for char- ges and insurance L.42 10 4; after which the partners meet, and make such payments to each other as render their shares of the advance equal. At the end of three months, Rose pays The bill to Hicks, Crawford pays the bill to Wood, and they meet again and equal their advances. Some months after, they receive advice that Lindsay has received and sold the cargo, nett proceeds per account sales L.S41 sterling; and has ship- ped in return, per the Zebra, 16 lids, sugar, amount L.408 ; V 20 bags cotton, amount L.362, 10s. ; and 10 puncheons rum, 1^.2 10, and has drawn on Smith at 2 mdt. for the balance, Crawford procures insurance of L.800, on the cargo home- ward, at 4- gs. per cent, policy 10s. Gd. In due time the ship arrives,and they sell the rum on board to G.Lamont for L.255 ; Rose pays freight, duty, and charges on the sugar, L.I 68, and freight and charges on the cotton, L.I 8, 10s, and sells -ihds. Miuar, qt. 6l cwt. to H. Hawthorn, at L.2, 15s. per cwt. and id lids. qt. 1 48 cwt. for ready money, at L.2 13 6 per cwt. and takes the rest on his own account, the quantity being 32 i.:.wt. at the same rate. Smith sells 5 bags cotton, qt. 1480 Ib. n the first, L.2100 on the second, L.I 200 on the third, at X 3 246 PARTNERSHIP. 3 gs, per cent., and receives bounty on the whole, at 5s. per quarter. Some time after, they receive advice that the En- terprise was arrived at Marseilles, and the cargo sold by Joiu- ville, nett proceeds Livres 70734, and that he had shipped h* return a cargo wine, silk, and paper, amount Livres 81240 ; and drawn on Gurney at usance for the balance, ex. 29d. per crown ; Gurney receives L.600 more from each of his partners, and pays the wheat bought on credit. Urbini re- ceives and sells the cargo per the Adventure, nett proceeds S320 pezzos, of which he remits 7000 to Gurney, at 4s. 6d. per pezzo ; and Thurlow, who has other dealings with him, agrees to account for the balance at the same rate. The partners then receive advice that the hazard had foundered at sea, and only two of the crew were saved, and some time after Gurney recovers the sum insured, deducting 2 per cent, according to agreement. Jn the mean time, the Enterprise arrives, and the partners agree to divide the cargo ; Thurlow takes the silk at L.I 2 14, Inglis the wine at L.I 7 50, and Gur- ney the paper at L.428, and Gurney gives in his account of postages, and other small charges, L.5 710. SECT. III. BILLS OF EXCHANGE. 45. A BILL of EXCHANGE is a written order from one per- son to another, requiring him to pay a certain sum of money to a third person on his account ; and that either on demand or against a specified time : By means of which, money may be easily remitted from the most distant trading countries to each other. If the bill be payable in the same country in which it is drawn, it is called an inland hill of exchange ; if payable in a different country, it is a foreign bill of exchange, Their form and use will appear from the following examples. N I. L.300. Amsterdam, 12th January, 1787. At usance, pay this my first bill of exchange to Mr Richard Barbour, or order, three hundred pounds Sterling, value re- ceived, and place it to my account, as per advice, To Mr Jnmes Molineux, JAMES K^MPENFELDT LONDON. Tp exjplaip the business transacted by this bill, it must be BILLS OF EXCHANGE, &c. 247 supposed that Barbour, who resided at Amsterdam, had occasion to pay money in London, and applied to Kempenfeldt for a bill on that place. Kempenfeldt agrees to supply him, and draws the bill upon his debtor, James Molineux, according to the above form. Barbour, upon receiving the bill, pays the value to Kempenfeldt, and sends it to his creditor, suppose Nicholas Stone, of London, first writing on the back of the bill, Pay to Mr Nicholas Stone, or order, value in account, RICH. BAR- BOUR ; which writing is called the indorsation, or indorsement. When Stone receives this bill, he applies to Molineux, and requires whether he be willing to bind himself to pay it when due. Molineux agrees to this, and writes at the foot of the bill, accepted, JAMES MOLINEUX, and delivers it back to Stone ; who may either keep it till due, and then demand payment ; or transfer the property of it to another, by indor? sing it again ; and thus it may pass through any number of hands by successive indorsements. -Ja. Kempenfeldt is called the drawer of this bill, R. Barbour the indorser, N. Stone the possessor, and Ja. Molineux the accepter. When the bill is paid, the last possessor writes on the back, under the indorsement, Received the contents, NICH, STONE, and delivers it thus discharged to Molineux. Bills are payable either a certain number of days, weeks, or months, after date ; or at sight, or a certain number of days, weeks, or months, after sight ; or at usance, or double or tre- ble usance ; or on a certain day which is neither connected with the date nor presentment of the bill. Usance signifies the ordinary time, according to the customs of the countries where the bills are transacted ; which is one month from the date of the bill, in bills between Britain and France, or the Netherlands ; two months between Britain and Spain ; and three months between Britain and Portugal, or Italy, It is also customary to allow a few days, called days of grace, be- yond the precise time mentioned in the bill. Three days of grace are allowed in Britain. When a bill is payable after sight, the accepter must marl^ the date of his acceptance, in order to fix the term of pay- ment, as in N. IV. If a bill be refused acceptance when presented, or payment when due, it must be protested. A protest is an instrument or writing, taken by a notary public, in presence of two wit- nesses, containing a copy of the bill, a relation that accept= 2i8 BILLS OF EXCHANGE, &c. ance or payment has been demanded and refused, and a decla- ration that all parties shall be liable to the possessor for the value, with damages. If the possessor neglect to protest the bill on the last day of grace, he loses recourse against the drawer and indorsers, and has onlj the accepter to look to for his payment. If a bill be lost by any accident, a second one is drawn to supply its place, in the form of N. V. ; in like manner a third or fourth bill, if necessary, may be drawn. N. II. f. 4253 14 London, 21th February, 1787. At usance pay this my first per exchange to Mr James Mo. Hneux, or order, four thousand two hundred and fifty-three guilders fourteen stivers current, value received, and place it to my account, with or without advice, To Mr William Hoorn, DAVID SMITH, AMSTERDAM, Before Molineux sends off his bill, he indorses it thus, Pay to Mr J. Kempenfeldt, or order, value in account. But to save the trouble of the indorsation, the bill may be originally drawn in the following form : /4-25S 14> London, Pith February, 1787- At usance, pay this my first per exchange to Mr Ja. Kem- penfeldt, or order, four thousand two hundred and fifty-three guilders fourteen stivers current, value received of Mr James Molineux, and place it to my account, with or without advice. To Mr William Hoorn, DAVID SMITH. AMSTERDAM. N III. L.217 Liverpool, fyth April, 1787, Twenty days after date, pay this my first bill of exchange to Mr Henry Meredith, or order, two hundred and seventeen pounds Sterling *, value received, and place it to my account, as per advice. To Mr Robert Lamb, JA. DYER. LONDON. Accepted, Ro. LAMB. Indorsed thus, Pay to Mr Ja. Molineux, or order, value in ac- count, HENRY MEREDITH. * In bills and other obligations drawn in Scotland, or payable there, the word Sterling must be added to the sum, as otherwise Scots money inight be understood, In English bills, &c. that word is seldom used. BILLS OF EXCHANGE, &c, 249 N IV. L.I 15, 10s. Liverpool, 3d June 1787. Ten days after sight, pay this my only bill of exchange to Mr Matthew Bishop, or order, one hundred and fifteen pounds ten shillings,, value in account, and place it to my account, as per advice. HENRY MEREDITH. To Mr Ja. Molineux, 7th June, accepted LONDON, JA. MOLINEUX. N V. L.3I2, Is. Bilbao, Mh October 1787. One month after date, pay this my second bill of exchange, first not paid, to Don H. Padilla, or order, three hundred and twelve pounds one shilling Sterling, value received, and place it to account of Mr Ja. Molineux, as per advice. To Messrs Honeyvvood and Co. CARLOS OLIVA.. LONDON. N VI. Lrs.' 16633, 5. London, 8th Sept. 1809. At usance, pay this my first bill of exchange to Mr Carlos Oliva, or order, sixteen thousand six hundred and thirty three livres five sols Tournois, value in account, and place the same to my account; as per advice. To Mr Lewis Necker, JA. MOLINEUX, ROCHELLE. NVIL i London, 20M February -1787, One month after date, pay Mr Jetliro 'Full, or order, one hundred pounds Sterling, value received, and place it to ac- count of To Mr William Davenport, JA. MOLINEUX, CHATHAM. ' 46. Obligations for debts are frequently taken in the form of bills, drawn by the creditor, and payable to himself; of which the following are examples. L.208 2 6. London, 24th March 1181. Four months after date pay to me or order, at my house here, two hundred and eight pounds two shillings and sixpence, value delivered you by To Mr John Lascelles, JA. MOLINEUX. CONDON, Accepted, JOHN LASCELLES. ' 250 BILLS OF EXCHANGE, &c. L.250. London, 1st June 1787. One day after date, pay to me or order, at Lloyd's coffee- house, two hundred and fifty pounds Sterling, value of To Mr Ja. Molineux, ABRAHAM LESLIE. LONDON. Accepted, JA. MOLINEUX. To bear interest at 4 per cent. A partial payment may be marked on the back of the bill as follows. London, 10th January 1788. Received one him* dred pounds in part of within bill. A. L, 4-7. Forms of promissory notes. I promise to pay Mr James Molineux, or order, on de- mand, twenty-four pounds Sterling, being the balance due to him at clearing accounts. London, 9th April 1787. Tuo. STOUT. I promise to pay Mr Patrick Hill, or order, two months after date, two hundred and fifty-eight pounds eight shillings and four pence, value received. London, Z^th July 1787. JA. MOLINEUX. L.25S 8 4. I promise to pay Mr Ulyssus Usury, ororder, one thousand pounds, at three, six, nine, and twelve months from this date, in equal portions, with interest on each from this date to the term of payment, value received. London, l^th Jan. 1788, TIMOTHY TBADER, 48. Form of an order on a banker. L.580. London, 1st July 1787. Pay Mr Jethro Tull, or order, on demand, five hundred and eighty pounds, on account of To Messrs Honeywood and Co. JA. MOLINEUX, LONDON-WALL. 49. Forms of Receipts. Received from Mr Geo. Floyder three hundred and eighty- five pounds Sterling to account. London, 19th April J787. L.3S5. JA. MOLINEUX, Received, London, 15th May 1787, one hundred pounds from Mr Henry Moore, on account of Mr George Floyder, Southwark. JA. MOLINEUX, RECEIPTS. 251 London, 24M August 1787. Received from Mr James Molineux one hundred and seventy-six pounds ten shillings, in full of all demands preceding this date. SAMUEL ARCHER. A receipt for interest on a bond. Received from Sir William Wallace, baronet, by the hands of Mr James Wallace, writer to the signet, fifty pounds Ster- ling, in payment of one year's interest of a bond for a thou- sand pounds Sterling, due to me by the said Sir William Wallace, dated 1 5th May, javiic and eighty ; and that from the term of Whitsunday javiic and eighty-six, to the term of Whitsunday javiic and eighty-seven ; and I hereby discharge the same. In witness whereof, I have written and subscribed these presents at Edinburgh, this twentieth day of May javiic and eighty-seven. THO. CHARTERS. Receipt for writings. Deceived from A. B. six several deeds or writings, purport- ing to be the rights to the lands of M. in the county of P. in conformity to the inventory hereto annexed ; for which several deeds and writings I hereby promise to be accountable, and re- deliver to the said A. B. on demand. Witness my hand at London, this 25th March 1788. X. Z. A receipt by a land-steward, or factor, to a tenant. I Thomas Trusty, factor to the Right Honourable Earl An- gus, grant me lo have received from John Husband, tenant in Rosefield, one hundred pounds Sterling, which, together with fiv pounds for cess paid by him, for which he has delivered the collector's receipt, is in full of one year's rent of the lands of Rosefield, possessed by him from the said Earl, for crop javiic and sevenly-foar years; and I hereby discharge the same. In witness whereof, I have written and transcribed these presents at Newton, this fifteenth day of May javiic and seventy-five years. THO. TRUSTY. SECT. IV. -V LLS OF PARCELS, &c. 50. A BILL or PA^CL^S is i note of the quantity and va- lue of goody soli:, v:. : ivtiou to the purchaser along with the in tl ing form : 252 BILL OF PARCELS, &c. Mr BENJAMIN HANCOCK London 17th March, 1787. Bought of Henry Higgins. 12 Ib. Opium, at 19s. lOd. per Ib. - L.ll 18 35 Ib. Gura Arabic, at Is 8d. per ditto 218 4 3 2 Ib. Rhubarb, at 32s. lOd. per ditto - 20 10 5 3 cwt. Jesuits bark, at L.I 5, 8s. per cwt. . 46 4 19| oz. Phosphorus, at 5s. 4d. per oz. 55 4 L.86 16 1 51. An account of goods formerly sold is drawn out nearly in the same form. If a partial payment is made, it is placed under the account and subtracted. If several partial payments be made, they are placed in an inner column, and their sum extended and subtracted. When the account is paid or compensated, or settled by a bill, a receipt is granted at the foot, in which the manner of settling it is narrated. Mr HUMPHREY POPE Dr. to GEORGE STATIONER. 1785. June 12, To 25 reams post paper, at L.I, Is. L.26 5 -- 12 ditto foolscap, at 18s. - 10 16 July 12. 120 reams printing demy, at 15s. 90 Aug. 6. 6 reams superfine royal, at L.2, 2s. 12 12 - Sep. 12. 25 reams cartridge, at 14s. - 17 10 . Oct. 19. 5 cwt. pasteboard, at 18s. - 4 10 L.161 13 1785. June 30, By cash, in part, L.20 Aug. 31. By cash, in part, 50 -- 70 -- L.91 13 Abated - 13 Edinburgh, 30th October, 1785, Received bill at 3 months date in full for above, GEORGE STATIONER. BILLS OF PARCELS, &c. 253 1 JOHN PLANTER Esn Hammersmith, 30th Ocfoler 1785. PLANTER, Esq. Bought Qf NlGHOLAS GARDENER. 12 C. plants English oak, at 2s. 6d per C. L. 5 C. American elm, 3s. 2d. per ditto 15 C. - larix, - - Is. 9d. per ditto 5 M. i spruce fir, - 5s. per M. 20 M. hawthorn, - 3s. 6d. per ditto 75 grafted apples, various kinds, 3d. per plant 20 grafted plums, ditto, - 4d. per ditto 50 Ib. lucern seed, - Is. 2d. per Ib. 20 Ib. Saint Foin seed, - lid. per ditto 1784. June 1. To a diamond ring set in gold, L.21 July 15. To an ornamental silver vase, wg. 115| oz. at 8s. 9d. per oz. Aug. 18. To a service silver plate, wg. 325f oz. at 7s. 6d. Sept. 15. To 6 dozen silver spoons, atL.9 per doz. L. Oct. 18. By 236 oz. old plate, at 5s. 6d. L.182 15 9 London, 31st December 1784. Received payment of above in full of all demands, OLIVER GOLDSMITH. III. London, 3d March 1787. Mr James Molineux oought of Nicholson Brent 20 pieces calicoes, 25 yds. each, at 2-. 6d. per yard ; 20 pieces, 14i yds. each, at 2s. 9d. ; 30 pt. _^ yds. each, at 3s. ; 30 ps. 20 yds. each, at 3s. Id. ; 25 p*. IS yds. each, at 3s. 8d. ; boxes, L.I 126. Amount L 378. IV. Mr James Gentle bought of Thomas Farmer, 1 3th Sep- tember 1785, 13 qrs. .5 bushels wheat, at L.2, 2s. ; 15th Oc- tober, 15 qrg. 3 bushels barley, at L.I 3 4; gth Novem- ber, 2 loads, 24 trusses hay, at L.2 7 6 per load of 36 trus- ses ; 22d November, 8 qrs. 2 bushels 2 pecks wheat, at L.1 18 4, and 7 bushels ucans, at 18s. per quarter; 5th De* 254 BILLS OF PARCELS, &c. cember, 5 qrs. oats, at L.I 2 8. Received in part, 30th Oct. L.20, and 18th Nov. L.30. Balance, L.25 5 4. V. London, 15th June 1774. John Gilson bought of Wil- liam Rawlinson 4 Ib. green tea, at 12s. 9d.; 7 lb. Bohea tea, at 6s. 7|d. ; S6 lb. tobacco, at 8 id. ; 8 lb. coffee, at 2s. 4d. ; and 12th July, 17lb. pepper, at Is. 2d ; 6 lb. nutmegs, at 3s. 9d. ; 6 lb. cinnamon, at 23s. 6d. ; and 17th August, 15 lb. sugar, 7fd. ; and 25 lb. fine salt, at 5|d. ; and paid the same 19th December. Am. L.I 7 1 6 J d. VI. Glasgow, 16th June 1774. Mr William Hay bought of Edward Galloway, 3 cvvt. 2 qrs. 12 lb. sugar, at6|d. per lb.; 3 cvvt. 3 qrs. 14 lb. ditto, at 7^d. ; 2 cwt. 2 qrs. 8 lb. ditto, at 8|d. ; 12 lb. tea, at 7s. 4|d. ; 46 lb. ditto, at 6s. 8|d. ; 13| lb. ditto, at 5s. 3|d. ; 12 lb. coffee, at Is. 9|d. ; 3 cwt. 2 qrs. raisins, at 54s. per cwt. ; 2 cwt. 2 qrs. currants, at L.3, 2s. per cwt. ; and 2 cwt. 3 qrs. ditto, at L.2 5 6 per cwt. Amount, L.82 9 2f. VII. London, 16th September 1773* David Grierson bought of John Smith 1 piece flowered silk 32 yards, No. 19. at 19s. ; 1 piece plain white ditto 29 yards, No. 12. at 15s. 6d. ; 1 piece 46 yards black ditto, No. 42. at 13s. ; 1 piece 32 yards damask, No. 17. at 12s. 6d. ; 6 pieces of 136 yards lutestring, No. 14. at 8s. 9d. ; 2 pieces 48 yards Persian, No. 16. at 2s. 9d. ; 6 pieces 156 yards black bombazeen, No. 18. at 4s. 6d. ; 2 pieces 53 yards white ditto, No. 3. at 3s. 9|d ; 3 pieces 45 yards poplins, No. 17. at 2s. lid.; 2 pieces 57 yards superfine black cloth, No. 4. at 17s. 4d. ; 1 piece 26 yards ditto, No 5. at 17s. 2d. ; 1 piece 32 yards freeze, No. 12. at 3s. 8d. ; 1 piece 49 yards scarlet cloth, No. 8. at 17s. 6d. ; 5 pieces 118 yards shalloon, No. 7. at Is. 9d. Amount, L.351 7 4. VIII. Mr Francis Malcolm bought of Dashwood and Co. London, l^th November 1770, 2 hds. logwood, No. 1 qt. 5 cwt. 3 qrs. 24 lb. tare 2 qrs. ; No. 2. 3 cwt. 3 qrs. 24~lb. tare 1 qr. 15 lb. at 12s. 6d. per cwt; 1 hd. alum, qt. 12 cwt.' 'J qrs. 7 lb. tare 2 qrs. 2 lb. at 17s. per cwt.; 2 hds. copperas, qt. No. 1. o cwt. 3 qrs. 20 lb. tare 1 qr. 15 lb. ; No. 2. 7 cwt. 1 qi\ tare 1 qr. 18 lb. at 5s. 4d. per cwt. ; 1 cask madder, 3 cwt. 2 qrs. tare 20 lb. at L.7 12 6 per cwt. ; 5 hds. at 5s. and 1 cask, 4s. Amount, L.47 4 10 1 255 INVOICES. $ 49. An INVOICE is an account of goods sent off, generally by sea, either in consequence of orders from the person to whom they are sent, and at his risk, or consigned to him for sale, at the risk of the proprietor. The form is exhibited in the following example : INVOICE of goods shipped by Thomas Aubrey, per the Dol- phin, J. Harris master, from Jamaica for London, on account and risk of Mr James Molineux, merchant there. 20 hds. SUGAR. cwt.qr.lb. I. M. No. 1 15 3 No. 1. at20 2. ...15 2 7 3. . .16 14 4. .16 2 8 5. .15 1 20 6. .14. 3 21 7. .17 1 7 8. .15 3 12 9. .14 3 9 10. .15 3 24 158 2 161 3 320 1 Tare i 1 q. p. hd. 15 cwt.qr.lb. No. 11. .16 1 12. .16 2 15 13. .15 3 21 14. .15 3 20 15. .16 2 16. .16 3 20 17. .16 18. .16 2 19. .15 2 8 20. .15 2 161 3 20 hds. at 12s. 4 Casks Coffee. cwt. qr.lb. Ib. No. 1 6 3 12 tare G4 2 6 3 15 66 3 6 3 18 67 4 6 2 24 68 305 1 at L., 8s. p. cwt. L.722, 12s. 12 L.734 12 27 1 13 Tare 2 1 13 265 Neat 25 at L.6, 10s. per cwt L.162 10 4 Casks, at 8s 1 12 L.I 64 2 40 tons Logwood, at L.10, 4s... 408 Carried forward L. 1306 14 256 INVOICES. Brought forward, L.1306 14 Charges, viz. Porterage L.I 3 7 Wharfage , 1 10 Customhouse-fees 1 2 3 15 7 L.1310 9 7 Commission on L.1310 9 7, at 5 per cent 65 10 5 To the Drof Mr James Molineux 1376 Kingston, 12th June 1787. Errors excepted. THOMAS AUBREY. Sometimes, when a factor purchases goods on commission, he transmits the bills of parcels for his employer's satisfaction; and in that case it is sufficient to insert the sum of each bill in the invoice. See ft IV. I. William Jones and Co. of London shipped for James Dar- ceville of Bourdeaux, per the Phcenix, William Hay, mas- ter, on the 12th June 1770, 3 bales cloth, qt. N 1. 3 pieces 54 yards black, at 15s. 8d. ; 4 pieces 77 yards scar- let, at 16s. 3d. ; 2 pieces 46 yards grey, at 14s. 9d. N 2. 5 pieces 103 yards blue, at 12s. 9d. ; 3 pieces 62 yards brown, at 13s. 2d. N 3. 4 pieces 83 yards purple, at 15s. 7d. ; 2 pieces 38 yards green, at 16s. 2d. ; 2 pieces 39 yards pale grey, at 12s. 6d. ; charges shipping 15s. 4d.; commission 2| per cent. ; insurance on L.380, at 2 gs. per cent. ; policy 5s. 6d. ; commission on insurance J per cent. Required the invoice ? Amount, L.384 9 8. II. The following goods were shipped by R. Manners from Jamaica to London, 10th June 1 773, consigned to Coney and Gascoigne there, per the Friendship, James Webb master, 6 boxes indigo, qt. N 1. 79 lb.; N 2. 76 lb.; N 3. 78 Ib. ; K 4. 88 lb.; N5. 87 lb.; N 6. 87 lb....tare, 12lb. per box, at 5s. 6d. per lb. boxes 2s. each ; 12 bags cotton, qt. N 1. 3 cwt. 2 qrs. 15 lb.; N 2. 4 cwt. 1 qr. 12 lb. ; N 3, 4 cwt. 2 qrs. 13 Ib. ; M4. 3 cwt. 3 qrs. 15 lb.; N 5. 3 cwt. 2 qrs.; N 6. 3 cwt. 3 qrs. 18 lb.; N 7. 3 cwt. 1 qr. 15 lb. ; N 8. 4 cwt. 5 lb.; N 9. 4 cwt. 1 qr.; N 10. 3 cwt. 2 qrs. 11 lb.; N 11. 3 cwt. 3 qrs. l61b. ; N 12. 4 c*t....tare, 10 lb. per bag, at L.4 3 6 per cwt ...wharfage and cartage. L.2 6 8,..customhouse fees, 10s. Amount, L.311 16 2. INVOICES. 257 III. The following goods were consigned by James Morison of Dundee to James Hargrave, London, and shipped 15th May 1770, per the Active, William Smith, 2 boxes linens, qt. 3 pieces 65 yards, at Is. lOd. ; 14 pieces 387 yards, at Is. 8|d. ; 12 pieces 266| yards, at Is. 6d. ; 12 pieces 243 yards, at Is. 2d. ; 5 pieces 110 yards, at Is.; 1$ pieces 278 yards, at 10|d.; boxes 4s. Gd.each; 1 bale Osnaburgs, qt. 23 pieces of 21 1 yards each, at 8|d. ; sheeting and ropes, 2s. 4d. ; 1 box thread, qt. 14 Ib. at 3s. 4d, ; 32, at 3s. 7d. ; 28, at 4?. 9d. ; 19, at 5s. d. ; and 16, at 7s. 2d. ; box 3s. 2d. ; charges shipping 7s. 8d, Amount L.I 35, 13s. IV. Thomas Dundas, of Glasgow, purchases goods from the following dealers, by commission from David Franklin of Philadelphia, and ships them per the Hercules, William Bridges master, 15th May 1774. From David Bruce, saddler, 2 boxes, qt. No. 1 . 6 saddles, at L.3 12 6; and 6 bridles, at 5s. 6d.; No. 2. 4 saddles at L.2, 15s.; 4 bridles, at 5s. ; 12 whips, at 2s. 6d. ; 12 riding caps at Is. 6d. ; boxes, 4s. each. From William Hunter, ironmonger, 3 parcels, qt. 12 dozen pair hinges, at 8s. per dozen ; 3 dozen large locks, at 2s. 3d. each ; 6 dozen small ditto, at Is. 4d. ; 6 grates, 16 Ib. each, at 4d. per Ib. ; 6 sets fire irons, at 3s. 9d. per set ; 3 dozen bolts, at 4|d. each; 1 jack, L.I, Is. From Oliver and Caddel, 3 casks nails, qt. 5 M. Garrcn nails, at 10s. 6d. per M. ; 15 M. double doubles, at 7s. 6d. ; 20 M. double floorings, at 6s. ; 32 M. single floorings, at 5s. ; 40 M. tacks, at Is. 4d. ; 3 casks, at 2s. lOd. From James Bonnar, colourman, 1 cwt. 2 qrs. white lead, at 4id. per Ib. ; 1 cwt. 3 qrs. 15 Ib. red lead, at 4|d. ; 2 qrs. 12 Ib. Spanish brown, at 5|d.; 18 Ib. vitriol, at 2s. 4dV, box 3s. 6d. Cartage and porterage, 18s. 4d. ; customhouse dues, 5s. 6d. ; pommissiott 2 per cent. Amount, L.96 6 10, ACCOUNTS SALES, 50. An ACCOUNT SALES is drawn out by a factor to whom goods had been consigned, and returned to his em- ployer when the sales are finished. It contains the quantities an.d value of the goods sold, the charges attendingthe salr, y s *5S ACCOUNTS SALES. the factor's commission, and neat proceeds. The form is ex- hibited in the following specimen : ACCOUNT SALES of goods received from Petersburgh, per the Empress, Bloxam, tor account and risk of Messrs llaikes and Thomson, merchants there. 30 Tons Iron. T Sep. 30. W. Jennings, 12 at L.18, 5s. Oct. 8. W. Nugent, 6 L.18, 10s. Nov. 8. Cash, 12 L.18, 30 300 Bobbins Flax. B Oct. 8. W. Nugent, 50 at L.4, 12s. L.230 10. Cash, 100 4, 12s. 460 W. Dashwood, 80 4, 15s. 380 . R. Thurston, 70 damaged 3,15s. 26210 1332 10 300 L.I878 10 Charges, viz* Duty on 30 tons Iron, at L.2 1C 2 freight on ditto, at I8s. , on 300 bobbins flax, at 2s. 6d, Porterage and Cartage "Wharfage Customhouse fees Warehouse and cellar rent Insurance of flax against fire Postages Commission on L.I878, at 2J> per cent. 210 Neat proceeds to the Cr of Messrs Raikes and Thomson L.I668 10 Whereof in cash, L-466 Outstanding 1202 10 London, 8th November 1787. Errors and bad debts excepted. ACCOUNTS SALES. 259 Another Form of the same Account. at L.I8, 5s. L.219 at L.I 8, 10s. at L.4, 12s. 341 at L. 4, 1 2s. 460 at L. 4, 15s. 380 at L. 3, 15s. damaged 262 10 at L.18 216 irsr. Sept. 30. W. Jennings Oct. 8. W. Nugent 10. Cash W. Dash wood - R. Thurston Nov. 8. Cash Iron. 30 T. Flax. 300 B. 50 100 80 70 12 6 12 30 300 L.I878 10 (The title and charges as in the last.) I. Account sales of C. Oliva's wool, see Journal and Led- ger. II. The goods contained in invoice, No. II. were sold by Co- ney and Gascoigne, as follows : 18th Sept. To James Mill, 8 boxes indigo, No. 1, 2, and 5, at 7s. 4d. per Ib. 22d ditto, To James Dickson, 5 bags cotton, No. 1, 5, 7, 8, and 10, at 5 gs. per cwt. 23d ditto, To Thomas Smith, 4 bags cotton, No. 2, 3, 4> t and 11, at L.5, 7s. per cwt. 27th ditto, For ready money, 3 boxes indigo, No. 3, 4, and 6, at 7s. 2d. and 3 bags cotton, No. 6, Q, and 12, at L.5, 6s. per cwt. Charges ; Freight of indigo, 6s. per box ; cotton, 4s. per cwt.; porterage, 10s. 6d. customhouse fees, 8s.; warehouse rent, L.I 3 4 ; commission 2| per cent. Neat proceeds, L.373, 16s. ACCOUNTS CURRENT. J 51. An ACCOUNT CURRENT contains a state of our trans- actions with any person whom we have dealings with, disposed in the form of Dr and Cr on opposite pages. The substance and general form is the same as that of the account in the ledger; only in drawing out the account, the peculiar style of the ledger is laid aside, and where the word Sundries occur in the ledger, the particular articles are specified, and all re- ferences supplied, 260 SECT. IV. SUBSIDIARY BOOKS. 52. THE books described in the foregoing sections are always the principal ones, and, in some cases, may be suffi- cient ; but merchants, for the most part, find it convenient to use several lesser or subsidiary books, for the purpose of abridging the principal ones, or supplying their deficiencies, or exhibiting the same articles in a different point of view, or preserving an exact copy of their correspondence and engage, fluents. The most common of! these books are the following. 53. The CASH BOOK. This book is kept in a folio form, like the ledger, and contains the sums of money received on the Dr, and the sums paid on the Cr. The articles are entered nearly in the same manner as in the ledger, only the particulars of each entry are commonly inserted, instead of referring to the journal ; and the amount of the money received or paid each month, is entered in the ledger, referring to the cash, book for particulars. By this means the cash account in the ledger is contracted to 12 lines, and exhibits, on inspection, a comparison of the sums that pass through the owner's hands at different seasons of the year. Another use of this book is to enable the cash-keeper to check the money on hand as often as he finds necessary. 54. The BOOK of CHARGES MERCHANDIZE. This book is only paged, and serves to abridge the cash book. Some- times it contains every article of charge, whether on particular goods and voyages, or on the business in general. But as it is intended to save the trouble of entering trifling sums in the principal books, such as postages and the like, we think it bet- ter to use it for such articles only; and to enter freights, duties, shop-rent, clerks' wages, and other large articles, in the cash- book at once. The sums of this book are transferred once a month to the Cr of the cash book ; or, if a certain sum, sup- pose a pound at a time, be delivered to a clerk, or shop-keeper, for petty disbursements, it may be entered in the cash book as often as that sum is delivered. 55. BILLS of PERSONAL or FAMILY EXPENCES are also intended to abridge the cash book, and to save the inconve- nience of inserting articles not immediately relating to business. These books contain the articles of expence in a simple forra^ SUBSIDIARY BOOKS. 261 and the suras are transferred, at convenient times, to the cash- book. 56. The POSTAGE LEDGER. Factors have occasion to charge their employers with the postages of letters received from, or from others, relating to their business, and other small charges that occur in conducting their affairs. The par- ticulars are entered in the book of Charges Merchandize, and the amount chargeable to each employer is collected in the postage ledger. This ledger only requires to be paged ; the articles are posted from the book of Charges Merchandize as from a journal ; the titles, references, and index, are written in the common manner, and the sum is transferred to the princi- pal books when the account is settled. Thus, the amount of postages, and other small charges, due by Henry Meredith, is 8s. 6d. the particulars of which will be entered in the postage ledger. When the account-current is draws out, we add the postage account, and write against the sum, Stated to his Dr 31 st December, and transmit a note of the particulars along with the account-current, to our employer, if required. 57. The MONTH BOOK, or WEEK BOOK, is intended to shew the sums of money which we expect to receive, or have to pay, in the order of time, that we may be in readiness to answer the demands on us. A folio may be allotted for a week, and divided into 6 parts, fine for each day, and the articles payable or receivable, whether bills, or of any other kind, are entered on opposite pages, so soon as they are known, on the part reserved for the day they fall due. If the articles be less frequent, those which fall due on the same week or month may be entered promiscuously, and the particular day that they fall due marked on a column reserved for that purpose. In the following specimen the right-hand page is placed under the left hand page, for the conveniency of printing. January 1783, to receive 1 From D. Smith, for wheat . . L.250 12 J. Jones' bill, 9th Oct. 3 mdt. . 175 10 28 T. Hill, for tobacco, 3 months credit . 156 12 6 20 R.Somers's bill on T.Woodlie,17th ult. 1 mdt 500 *+ January 1783, to pay 15 Bill to H. Berry, 17. Nov. 2 mdt. . L.I 15 20 J. Clinton, for linen . . 224 15 J8 Remitt. to T. Van Egmont,/ 1728, 22 Jd. 162 . 18 Bill to N. Millar, 9th ult. 1 mdt. . 77 12 262 | SUBSIDIARY BOOKS. 58. INVOICE BOOK, ACCOUNT SALES BOOK, and ACCOUNT CURRENT BOOK. These books contain exact copies of the ac. counts and invoices sent off. The form of these papers was fully explained 50. et seq. Some merchants also keep books for copying the invoices and accounts received, but if the accounts themselves be carefully preserved, it answers the same purpose. 59 MEMORANDUM BOOKS. These books are of different kinds, as the nature of business requires. A book of commissions may be extracted from the letters of our correspondents, or marked down, upon receiving verbal orders. It contains a distinct note of every affair in which we are employed, whether goods be bought, or other business to be transacted. The opposite page, or a marginal column, may be reserved for marking the execution or impracticability of exe- cuting these orders. The following is a specimen : Aug. 2. From L. Necker's letter, 18th July. To ship per firstvessel for Rochelle 1000 qrs. barley, if under 28s. 1000 qrs. wheat, if under 36s. 8th August. Shipped per the Bienfaisant. Not to be got at the price limited. 60. BILL BOOKS are ruled with a number of columns, for entering the dates, sums, and other particulars of bills, the time of payment, and the event. One register of this sort maybe kept for BILLS RECEIVABLE, where the bills we receive from our correspondents are entered when they come to hand; ano- ther for BILLS PAYABLE, where the bills drawn on us are entered when accepted, and a third for DRAUGHTS or bills drawn by us, in different books, or different parts of the same book. The form of these will appear from the following spe- cimen, being the bills drawn on J. Molineux by his corre- spondents, for the six months of the foregoing set. The bills granted by him for goods purchased, or money borrowed payable to the drawers, are not inserted, as it will be more convenient to enter bills of that sort in a separate register. SUBSIDIARY BOOKS, 263 H-* O Oi Or O OC OOOOO~* 55 i I I Igi l I I I I I I p: S-' p;' fas; ^ p o p | Pill Q ^ > * ? 5 ill I 111 " ^ O O -i O H- ^ CQ H I 2 6 P 5 ^ r 61. PROGRESSIVE LEDGER. When the articles in per- sonal accounts are frequent and extensive, it is convenient to know how much is owing at present, by inspection with- 264 SUBSIDIARY BOOKS. out the trouble of adding the articles in the ledger, and com- paring the opposite sums. For this purpose a separate ledger is used, where one page is only allotted for each account, and the articles are entered as they occur, and added to, or subtracted from, the former balance, as in computations of in- terest ; and columns may be ruled for computing the interest. See Part I. 61. The following specimen is supposed taken from Honey* wood and Go's books : 1786. Dec. 31 Mr James Molineux, Jan. l8Cr. Apr.24Dr May28Cr. JunelOCr. July 1 Oct. 5 Dr. Dr Dr. To Balance By Cash To his order By his bill on F. Alcara By his billon B. Gome2 To his order 3y his bill on B. Gomez To interest 1475 600 .10 875 1000 10 187.5 673 1202 550 10 b 1 q - Q \J 652 580 1 9 1232 1100 132 30 1 1 11 9 9 3 162 13 Day?. Products* A 'WAREHOUSE BOOK is to be kept by factors intrusted with the custody or sale of goods. It contains the different artidrs received into the warehouse, the marks, packages, owner? names, &c 6 on one side, and the delivery of the same on the other. SUBSIDIARY BOOKS. . 265 62. RECEIPT BOOK. This book contains the receipts granted to a merchant for the payments he makes, which are signed by, the receivers. It is intended to save the risk of losing detached papers. For forms of receipts, see 49. 63. LETTER BOOK. Merchants ought to keep an exact copy of all the letters on business they dispatch. A folio book is prepared for this purpose ; the names of their corre- spondents are written in text on the margin, and entered in an index. The letters are usually copied in the order they are written. Sometimes a portion of the letter book is allot- ted for each correspondent, that the state of our transactions as narrattd in the letters may be conveniently inspected. The following specimen may serve as a lesson to beginners in the style of mercantile letters. James Kempenfeldt. 27th February 1787. I was duly favoured with yours 31st December and 12th ult. By the former you transmit me account-current of our transactions last year, balance%x!ue you f.756Q; which I have examined and found right, and stated the same in conformity. By the last, you advise your draught on me to R. Barbour, usance L.300, ex. 35s. 8d. f. 3210 banco, agio 3 per cent. . f.3306 6 which is duly honoured, And I remit you inclosed D. Smith's bill on W. Hoorn, usance - - . ^4253 14 Placed to your Dr /7560 which clears the balance above mentioned. Sen. Gomez. 3d May 1787. I was duly favoured with yours of 28th March, desiring me to ship a cargo corn, and an assortment of cloth, on your account. Being able to execute the same within the prices to which you limit me, I have freighted the Diana, George Blackney, for your place, and transmit you invoice of both, amount L.2893 5 6, placed to your debtor. Blackney has agreed to deliver the cargo for L.I 50. You will please ship for me per return of said ship, 20 pipes of your wine, vintage 1785, which I desire to have of the very Z 266 SUBSIDIARY BOOKS. best quality, although the price should be rather higher on that consideration, and advise me of the same per post. Two months credit are allowed on the cargo ; against which time I expect invoice of the wine, and shall draw as desired for the balance. P. S. Blackney sails to-day from the Downs, with a favour- able wind, and I hope will have a safe and speedy voyage. ftaikes and Thomson. 8th November 1787. We refer you to ours of 10th ult. and having since com- pleted the sales of your goods, we now transmit you account sales, neat proceeds L.I 668, 10s. which we hope will give satisfaction. You will observe the money in our hands is only - - - L.466 . And the amount of outstanding debts - 1202 10 L.1668 10 As we expect soon to receive payment of the greater part of the debts, and the exchange at present is unfavourable, we have deferred any remittance, but you may depend upon re- ceiving one in a few weeks. 64. Farm of a Letter of Credit. SIR, London, 15th April 1788. This will be delivered you by Henry Conway, Esq. of Thistledown, who will spend some time in Holland, in his way for Vienna, whom I beg leave to recommend to your ci- vilities. You will please supply him with what money he may have occasion for, to the extent of J. 5000 on my account, and transmit me his receipts for the same. I am, SIR, Mr Ja. Kempenfeldt, } Your most humble Servant, Amsterdam. J JA. SUPPLEMENT TO THE SHORT SYSTEM or ARITHMETIC AND BOOK-KEEPING. 5. ADDITION. ADDITION. 1. 428556 2. 181750 English Land Measure. 3. 39074 A. R. P. Y. 4. 640174 1. . 176 1 8 Qu. 1. L.2776 2. * 376 1 6 2. 11493666 persons 3. 1266 2 3 14r 3. 4004 years 4. 7766 foot Scots Land Measure. 1712 horse A. R. F. E. 9478 total 1. . 180 18 4115 $10. Sterling Money. 3. 2287 3 12 31 1. L. 8c) 1 6 2. 108 15 5| Long Measure. 3. 102 17 2f 4. 7375 10 2 1. 30 m. If. 26 jo. 2. 36 y. O c /: 3 in. 5. 397 5 21 6. 476 1 gi Cloth Measure. 7- 426 11 6J 23 y. 2 qr. 1 w. 8. 36277 8 4" c0.9 TVw/ Weight. Troy Weight. 48 rf. 12 /&. 6 oz. lb. oz. dwt. gr. J. 103 3 16 2. 46 10 18 9 English Dry Measure. 35 q. 6 b. Oo-. Qpt s . 3. 897 8 11 5 Scots Dry Measure. 183 ch. 9b. Of. 3 p. 1. Avoirdupois Weight. 51 c*. 1 . 22 lb. or2, 11 c&rf. 1 gr. 22 /&. Wine Measure. 42 t. 2hds. 49 g-. 6jp. 2. 57/6. 13 oz. 10 d>. w4/dwt. 12 gr. 5. 20 gall. 6. 21 inches 5. }3ac.3r. 5 p. 6. 354 miles. $ 13. 7. 66 st. 2 /. 1 oz. J. L. 76 12 11 S. 3t.2 out. 2 q. 2. 1173 14 111 3. 489 2 10 24. 4. 2 . 16/6. 15oz. L L.627 17 8| 5. 1 lb.ll oz. 17 dwt. 16 gr. 2. 14806 4 " 6. 18 m. 6f. 32 p. \~y. 3. 38298 11 A 4. 18 f. 14 cut. 16/6. $ 21. MULTIPLICATION. 5. 613cc. 2r. 36 p. 1. 3851562 6. 450 ch. 5 b. 2f. 2 p. 2. 31815075 7. 96 Ib. 6%. 4 3. 3. ' 4620315 4. 3293416 " $ 25. 5. 293916669 1. L.520 4 11 1 tf. 628581254 2. 17827 15 " 7. 703390929 3. 4667 S $. 239767710 4. 1267 41 9. 833659560 5. 1580 18 7 10. 216250965 11. 420887635 T. cittf. yr. Ib. 12. 1 30.80656075 6. 44 14 1 25 J3. ' 256032 7. 37 3 21 14.- 1 Q6067 5.2 d. 16 17 3 I* SHORT SYSTEM OF ARITHMETIC. 269 25. MULTIPLICATION. 9. 46 ac. lip. 10. 11 ch. 56. 3f. 2 p. 11. L.1203 19 8 12. 2247 16 6 13. $15 19 11 14-. ST. Scut. 3 Ib. 15. 47 T. 7cwt. 2qrs. 24/6. 16. 279 ac, 2r. 280. 26. " 1. L.231502 1 2. 26*64796 17 3 3. 261563 19 8 4. T.613 1 2 26 6. M23 5 35 1 11 or, 125319^ 5 iw. 6. A7885 3 12 27. 2. 713535351 farth. 3. 83149/6. 5. 1 3822 3 4 gr. 6. 848 #a//. 7. 91 152 12 5 27 4 7 591 6 8 615 10 10 T S V 15 ciot. 2?. 22/6. V/6. 3 ac. 2r. 5 p. 65 ac. Or. 7 p. 29. DIVISION. 11. 37807 12. 13. 14. 1. 2. 3. 4. 1. 2. S. 4. 5. 6. 7. 8. 9. 10. Soz. ISdwt. 11. 5/1 ;>. 12. 1 m. If 13. 5v. 205f 14. 2 rf. 1 /6. 36. 1. 19 2. Ill 3. 365 4. 5. 255 37. 1. L.1553 11 4 2. 204 12 10J. 3. T.167 12 2 12 4. /6.148 6 21 5. 4c. 56 3 19 20 6. Q, 1718 2 2 7. H<&. 793 41 8. Yds. 104 1 9 9. L.277 15 6? Z5 270 SUPPLEMENT TO THE 38. DIVISION. 48. COMPUTATION or 1. Gr.499808 PKICES. 2. Z,.8y0328 12 10. L.710 10 10 3. M.82047 11. 3582 11 3 4. .36*14 12. 43 1 8 5. .10:910 3 49. 6. L.94311 1. L.78 6 Gf 7. Jo.65.40 2. 97 5| 8. Mo/. 102 40 3. 173 9 5 9. 31.21 4 26 2 4. 350.5 6 6| 5. 696 10 10 j 40. RULE OF PROPORTION. 6. 2510 18 50. 1. 782 1. L.286'28 16 2. 11382 2. 20468 10 3. 812 3 14154 5 4. ItiMflf 4. 35856 16 5. L.37. 15 1 5. 27221 19 6. L.38 5 2/y 6. 24486 7- 13 7- 2756 8 8, L.27 18 4 .8. 7407 9. 61109 2 $ 47. COMPUTATION OF 10. 11542 3 PRICES. 51. 1. L.15706 12 10 3. L.1639 9 5| 2. 12663 14 2. 1718 4 Sf 3. 28890 7 10| 3. 753 18 2i 4. 8685 7 4| 4. 26 19 5| 5. 6902 7 11 5. 499 -12 " 6. 231087 3 6. 257 4 7. 29565 2 $ 48. 8. 1727 11 3 1. L.224 2 9. 9092 15 4 2. 6'28 17 2 10. 371 18 10J 3. 219 16 6 52. 4. 1646 1 8 1. L.17991 10 * - 5. 1131 13 9 2. 912 13 4 6. 1355 10 6 3. , 94 15 7. 273 7 4. 427 16 8. 20817 4 8 5. 10913 10 ft, 574 19 3 6. 952 17 6 SHORT SYSTEM OF ARITHMETIC. 271 52. COMPUTATION of PRICKS. ; 58. INTEREST. 7. 897 4 ~ The fractions under farthings 8. 293 5 rejected. 9. 156 14 8 1. L.4 7 3| 10. 42 12 6 2. 1 12 81 11. 26 7 4 3. 9 19 7J 12. 15 14 4. 6 7 If 13. 22 11 4 5. 25 13 f 14. 70 19 6 6. 15 2 1 15. 18 1 8 7. H 9| 16. S3 5 8. 10 71 53 - 9. 2 15 4J 1. L.9221 6 8 10. 4 1 31 2. 6360 19 9 % 3. 17745 12 2J 68. VULGAR FRACTIONS. 4. 41478 5 11 5. 2991 10 4 1. 6. 3222 18 6 2. Vf 54. 3. 3 8^9 1. L.216 10 3| 4. 10865. 5 2. 846 10 4 5. 3. 1378 1 1| 6. 18235 4. 66 4 2 69. 5, 41 3| I. igi ! 6. 10 8 8| 2. 1 6 1,0 7 11 12 6 3. 43f* 8. 10 4 6 4. 2_i 9. 13 If 5. 21 1 10. 6 19 4} f 70. 1 ^ 7 57. COMMISSION. 2! I 3. 1. L. 9 7 6 4. li 2. 6 5 71 5. 5 5 IT T 3. 89 14 if 6. y 7 s 73- 4. 39 9 9f 01. ;. 5. 6 7 2 1. 6. 7. 30 8 5A 15 5 ^ 2. 3. IN m 2 iif,S 4 i 8. 20 8 10JJ f C or | iY/ Iff!' iYtT?i^ 272 SUPPLEMENT TO THE I. 2. 3. 4. 5. 6, l. 2. 3. 4. 5. 6. VULGAR FRACTIONS. $ 72. ADDITION. 73. SUBTRACTION. ill 1. 2. 3. 4. 5. 6. 7. 8. 9- 10. 1. 2. 3. 4. 5. 6. 7. 8, ^ 13f $ 74. MULTIPLICATION. S6f 650| 42f| 82fS 75. DIVISION. 180 tt If Ut 76. VULGAR FRACTIONS 1. JLf{ 2. "3Vo 3. . |5 4. c-il 5. ^55 6. ac -V- $77. 1. 55. 4rf. 2. 8 d. 3 q. 3. 3 d. 3 q. 4. 4toz. 17 dwt. 12 gr* 5. 6 etc. 3 y. 1 4 /6. 6. 3 r. 3/?. 10^^. 7. 5/27jp. 2|y. 8. 185. Sd. 9. 2/ 6^'w. 10. 85 days. 11. 76. 3 /? 1 g . 12. If zw. DECIMAL FRACTIONS. $ 80. 1; .48 2. .109375 3. .064 4. ^ 5. .30^ 6. .714285 7. .72, 8. .2,037, $81. 1. L. .2875 2. Z. .39375 3. T. .19376 4. Ib. .8 5. &, .13671875 6. ac. .85625 $ 82. 1. i L.*- 7 6 SHORT SYSTEM OF ARITHMETIC. 27$ 82. DECIMAL FRACTIONS. 89. DECIMAL FRACTIONS* 2. L. 9 11 // 1. L.5.365 3. 15 99 2. 8.239 4. 1 r. 14 . 3. 3.563 5. 21/6. 4. 5.941 6. 8 dr. 5. .891 7. 3 rfwrf. 1 8 gr. 6. .77 8. 8 u>. 6 gr 7. .682 9. 1 qr. 7& lb. 8. .921 10. lfur.36p.4jy. 90. 83. 1. L.4 11 71 1. 164.4399 2. 282 2. 7491.5148 1. 29f 3. 4.726 4. 7 8 11| 4. 18.2564 5. 14 8 84. 6. 19 6| I. 6.237 7. 10 2. 3.26808 8. 4 6| 3. 6.5402 4. 234.1 93. COMPOUND INTEREST 5, .000408 and ANNUITIES. 6. 9.72 7. 39.578 1. 973.032 8. .0001 2. 39.300f 85. 3. 375.645 1. 1.7 4. 234.627f 2. 125. 5. 273.025 3. .03762 6. 865.203f 4. .007962 7. 27.552 5. 74800. 8. 42.560f 6. ^910. 9. 86.329 7. 2.39375 87. 10. 11. Z2yrs. 42-^days, 6yrs. 31 days. 1. .2687f 12. 34t%yrs. nearly. 2. 129.72f Brown, Prints, Anchor Close, 14 DAY USE RETURN TO DESK FROM WHICH BORROWED LOAN DEPT. RENEWALS ONLY TEL. NO. 642-3405 This book is due on the last date stamped below, or on the date to which renewed. Renewed books are subject to immediate recall. NOV21 1968 8? O HH LOAN DEPT 191976 1.8 0112576 PHOTOCOPY APR 7 '87 General Library