a 3 ow re 4 i y> ‘ 3 4 1 ? > : BO y's 7. * = a aa te : ae Ne % ewig aes ae eee Se > a ee oe Rd ee ree ee a ie me ig Sees +s ae THE UNIVERSITY OF ILLINOIS . LIBRARY BH Siz T498t5 ee wT + _ - n ee q e* / aTreeraric’ LIFT Ly PRA TANK HB GS fe to ee Ae rh a BP i 19 3 Pe Bim asaerik oy 4 : : LE Oe. x L3 LL7PA UF oa hugs ; aN | gh I eS : tee LL. SGN I! he Gf 3 CS LZPAEZ I: sf Di fee woe 3 x % Dp yl Sf ff Ape ? Pa 5 f%, 7 : * 7 CLC MCI. LG Spgh de A \ I 8S FPAETCHLE Og a 4 fap A, : ? ey Ti J ia | Ma x fh ee lly "£4 a Me ie ye ee ana Pp 7 bo fF, . i “a * TREATISE *-- OF: PRACTICAL ARITHMETIC Book- heeping,. SINGLE ENTRY, OED ES II LASS Se SESE TE # THE FIFTH EDITION, .MUCH IMPROVED. BY WILLIAM TINWEL,S , TEACHER OF THE MaTHEMATICS. -H8Me@ (HUI eke, Witit” eee ein a Spetucastle : PRINTED BY M. ANGUS anp SON, FOR THE AUTHOR. SEES 1805. ) Loss PREFACE Ee TA 48 T HE intention of publifhing this fyftem is io render the »» jfludy of Prattical Arithmetic. as eafy as poffible, and to , xemove thofe redundancies which are too often found in bcoks \ of this kind. For every difcerning teacher will allow, that the principles of any art cannot belaid down in too eafy and plain a manner, In purfuance of this defign, cave has been taken, efpecially in the fir/t fimple rules, not to harafs the fcholar with any thing foreign to the rule: he is learning. Addition, Sub- tratlion, Multiplication, and Divifion, are treated juft in wtegers ; where the f{cholar is troubled with nothing but merely to- add, fubtrad &s*c. after which the manner of arranging the queftions according to the rule is taught: and | faftly, the numbers in the gueflions are given in avords at length, which not only exercife the two jirft parts, but alfa exemplify Notation, i As a further exercife, a large promifcuous collection of | _gueftions ts given to the firft jive rules. _. In Reduétion wiil be found a great many queftions different rom thofe commonly given, all tending to inftruct, but none to “puzzle the learner, 2) Then follows a promifcwous colletion of queftions to Wluftrate alt the parts of ReduGion. The compound rules come next in “corder, at the end of which will be found feveral bills of parcels, f and book-debts, together qwith a number of queftions for exercife, “in the Rule-of-I bree a rational and plain method is viven to ‘work all the queftions belonging to it, whether dirc& or inver/e, This rule-is of fuch extenfive ufe, that the utmoft care foould ~ be taken to render it familiar to the young accountant. The - Rule-of-Five, as it is here entirely founded upon the Rule-of~ LDhree, will be found, upon trial, very ea/y. v PraGice, Po * Pe th AV EES | PS lp ef ‘ere | 1 1Ve- PREFACE. Praéhice, being of fuch material ufe in real bufinefs, iz very amply handled ; as is alfo Tare and Fett and Bills of Parcels. It muft be allowed, that, according to the proper order of teaching, Vulgar Frattions fhould have been put~ before Praélice, as the reafons for the operations in that rule are entirely founded upon them. But as there are a great many who bave not time to learn.a complete fyftem of — Arithmetics fuch ought to be taught thé order of the rules as they ° fallow one ancther, and then Book-keeping by Single Entry, avbich 1s fufficient for common bufine/s. But in order to make.a perfor expert in calculations, Vulgar Fractions are abjolutely neceffary, for which reafon-they are very copioufly treated, and. the. various methods laid down ina clear - manter. In Decimal’ Fraétions, befdes what is generally giveny » fingle circulates, or repeaters, are introduced, as. they occur fp often in meafuring by feet and inches. Exchange qwith foreign countries will be found more: full and extenfive than ufual. Duodecimals is followed» by a number of ufeful queftions in fquaring dimenfions, the utility of awhich is obvious. Bock-keeping- by fingle entry, although it is placed at the end of the Arithmetic, may be learned as foon as the [eholar has gone through the promifcusus collection of quef> tions after Praétice. The feweral accounts in the Day-book’ are fo colleé?ed and arranged as to ferve for a general exercifé to all the praétical rules, therefore very much care fhould be taken to make the learner well acquainted with them.—J ‘ finall. Appendix is added, containing Receipts, Promiffory Notes, and Bills of Exchange, with-proper exercifes. This Edition 1s very tauch improved, as well with refpect to a great number of new queftions being introduced, as in the. order and difpoftion of the foriner.ones. PRACTICAL ARITHMETIC, DEFINITIONS. RACTICAL, ARITHMETIC is the art of com- puting by numbers. 2. A Unit is any thing confidered as one. 3. An Integer is-any whole thing. oe 4. Integers, or whole nur mbers, are fuch. as exprefs any num. ber of things, each of which is a unit. s.. An eyen number is that whofe half is a whole number. 6. An odd number is that which cannot be divided into two equal whole numbers. 7. A fimple number confifts only e@6ne genomination. 8. A compound number confifgs of feveral denominations. g. A fraction, or broken number, is one part or more of an_ integer, and is exprefled by two numbers, the one abeve and the other below a line drawn between them; the number yell is called the denominator, and the number above the numerator $ Thus 4 Numerator. 7 Denominator, 10. A mixt number confilts of a whole number and a frac: tion, as 44 The following Signs are ufed in this Work. = The fign of equality, and fignifies that the nunbers it is fet between are equal, as 16==16. +- The fign of addition, and fignifies that the numbers it is fet between are to be added, as 8-+-2=10. — The fign of fubtraGion, and fignifies that the numbers it is fet between are to be fubtrated, as 8—2=—6. x The fign of multiplication, and fignifies that the numbers it is fet between are to be multiplied, as 8 x 2=16. - The fign of divifion, and fignifies that the numbers it is fet between are to be divided, as 8+-2=4.° a NOT A E10:N. 4/ The fign of the Square Root. 34/ The fign of the Cube Root. sf tste Signs of proportion, as S6 is E532 30245. NOTATION. By notation, any number is exprefled by words or fpures, From the ten fingers of the hand, on which, in ancient times, it was ufual to compute oanikers) the ten figures were called digits. \ Their form, order, and value are as follows. f J, 25 35 4, 5 6, 7 8, os AO - One, two, three, four, five, fix, feven, eight, nine, cipher. The value of every figure i is altered according to the place it ? fiands in. Thus 2 — a % L LT & 6 ra — ee hao | ye = Ba a) ew a ez) a Bt 2 A wd: bo EM 0) rt 4 + 4 a4 4 4 A, figure in the firlt place has only its.own value, in the fecond Gt has ten times that value, in the third a hundred times. that value, &c. It is plain, from the above, that 4 in the firft place denotes 4 units, in the fecond four tens or forty, ‘in the third four hundreds, &c. me A cipher, which of itfelf fignifies nothing, being placed on the right of a figure, increafes its value tenfold. So 50 ftands for fe tens, or fifty. . For the convenient reading of any number, begin at the right hand, and divide it into periods of fix figures, and each period into two equal parts, as in the following TABLE. hot we htt acs oh ect. we he bets hilt. obs. te Ui 2 37%643 9535675 ~ Quadrillions. Trillions. » Quinguillions. Billions. Millions. Whence, to exprefs any number in words, this is the Rute.—Divide the number as in the Table, then begin at the left hand, and exprefs hundreds, tens, units, as you come to the places where thefe figures are; at the end of the firlt part of each period pronounce thoufands, and at the pres end the name of the whole period. | Exprefs in words the following numbers. 14——29—48 79—123——524—-896—-1784—- 3704 — 6735——74067 267231—-— 4678927 12340678 — 406987072 -456700865 72146. 14607307215831 £40783 200673567674 2107614324°°7148672 —7.21 48605 Si gCy OE ETELS Fo 861427467 —9: 4.3: GoS2z7 $4129 4go4sgz1 S64 FO 44.24 1.8. 12345678907200061522601 00008 5 27946 To exprefs any number in figures. Ruxe.—Put ciphers to as many periods and places as are mene tioned in the given number ; then begin at the left band, and write the fignificant figures in fuch periods and places as the queftion direéts, Exprefs in figures, Seventy—Six hundred—Nine ae ae Three thoufand—-Seven thoufand—Forty thoulfand—E ghry thoufand—-Nine hundred thovfand—Eighteen— Lhirty- pated Seven hundred and feventy-three—One thovfond feven hundred and eighty-four— Twenty three thoufand feven hundred and fifty ——Four millions two huadred and {eveaty—Thirty five thoufand- three hundred and forty millions—Four hundred and forty thoe-° {and billions, three thoufand and eighty millions, fix hundred and forty three-+four tboufand and fifty trilions-—Seventy four billions, one hundred thoufand and ten millions, nice thoufend and four—Seventy quadtillions, forty five thoufand and piNnery thillions, Gxty fix thoufand and eighty three, A2 a 4 SIMPLE ADDITION. SIMPLE ADDITION. IMPLE Addition teaches to find the fum of two or more fimple nambers. “ Ruve 1.—Place the numbers under each other, fo that units may be below units, tens below tens, hundreds below hundreds, &c. 2. Add up the right hand column, and fet down the units which are in the fum, carrying the tens to the next. 3. Add up all the columns in the fame manner, till you come to the left hand row, at which fet down the whole fum. To PROVE ADDITION. Begin at the top, and add the queftion down the fame way as you added it up, if the fum be the fame as before, the work as right.- Tre TABLE. Precer sb ay Stool 71 Sl ve PT zg ak ar sd 6 | TE 81 ote 21 3) 4 5] 6b 7) 8h of ety st 41 5)7 617) 8] 9] 10 fas | 12 4i 5} 6] 7] 8] ofs0firfiz] 3 5{ 6] 7] 8] gfrofirjiz| 3] St 71 8) of rof er] t2 | 13] 14 fis 71.8) of rofir faz [13 }14] 15 | 16 Sf ob} ro Pit 2h 13444 larg | 1619 FOO BTS OSU fot gare 397 BEB 7 O48 Fipo-gg 8) eg eg 6 6 40°95 (94.1 goa 33 eo OS EO Par Sy TT eat ae SP 3 7 ay Ome ee a eke G69) sah 7 Bees 4 ge Se hg Brg gg ee Lone Sas 9839 6 661 2 964 2681 9784 6:3 23% 269 4 | 9.483 »:-35 fs EO eg Bape Bon) gn BS g Mt BB | a Oe p22 ES BED 0234 4a ye eee . eh Boe es Ga8 9 445 0 4 2 6.433 ~~ ‘ iIMPLE ADDITION: eg : ea ag i REIT [OA MO RO HtHD HES CH= At (OS MATAR! ANTO MYO FH HAW ADOW ola t¥oO nN Hoo HH RDO A ++ HO] [O+H+ m Minn mn @ neraeal pees ieee +O tam st —“—™~ a NNO + Wrest le wnao tno an ao a Oma O- may > ABintg¢rana HO AH EO 8 A TMOOMNrANADOO NS STrOHDIUIMENtTAA AD Oma me SeSO tome ato OFACH| |OtHTENO MOO ROO YO MH Nero -— + NWMAs HHO HAMAD H. Oo 4 = AANMMHRO!l PMH AOAFANAR MENT A = On NtoO nan Nw O fot tO Nn mn alec NOWO +H pMO NEMO HOD ATH $r +t mrmee Ht OO nr. TH+ mMroont trons a= HE $mecan Oo On» WO StMWB NOR = Awntn DOPTAtAMMIO Nt toto An ao — Nw <= am tind MN AO BOD + tr AO mn AKA NO ARTH aMHARO taAw st Wry FOnAtA UO BOD AA WON FOO N MHIND MeN A mOco =~ O FO Pe r taAna0d MEA AQ tA = Aw H+ OC ola Ho am Hs OMF Hada lant CONTRO YR +H LOO Hee om lly ards inad, sean\ J oti lonwo « mmo Aa howol ltingun ~_ RNASE MIND HOO RH EA, DM rHNROAAMAEHRA WO m0 Atwas aWOw + 5-00 eno Otten ee AO anna bai sick GeO NE an paceses ROB mre HO Mm +} ma a =— SN Ye me DS MN ~ At OAM = om +ATAWD ATO HN OL Ow wt le 046 wa Sel lradsiaam n 20 = ym 92 0 >t ge a A REORCAE NOR Hc ae UME Se WS ay, 428 6428 ES OO: BPO SG: 246 69 43. °°) B.F6 8309. 4) Se ie iss 74389 ro8764 4296 m4. 42.6034 1 0 Sp. 38 O84 7164 4.8.9 6 rot 5 ¢. VON eo $294 5764 487 9 Required the fum of 748695487, L793 40 91278437, 123, 754689, 748, 143, 67, 7262, and 461732? What ts the fum of 127, 76524, 78594 335578, 672184326, 7514, 2615846, 723, 714,62, and 8? What is the fum of 96, 5786, 41380, 7695, °S16, 748672, 425784361, 716726, 12345, 8, 42, and 9? Required the fum of feven hundred and forty five—Three thoufand and fifty four—One hundred and feventy fix thoufand _ -—Eight millions, three hundred and forty thoufand, two hua- dred and ninety—Six thoufand and twenty millions, feventy three. thoufand and fifily—Three hundred thoufand millions, eighty thoufand and thirty two—and feven millions, feven thoufand and feven? Required the fum of fixteen—-Ninety five—Eighty thoufand —-One hundred and fix thoufand, three hundred and forty— . Seveaty millions—#Cbree millions, three thoufand and three—= Ten thoufand five hundred and fifty two-—and fix. huadred and forty three? W hat is the fum of feven billions, thirty. Bye thoufand and four, millions—Nine hundred and forty feven millions, nine hundred and eight—Eight thoufend and fixty five—Five millions, and: ninety fix—-Six huodred and two thoufand, three hundred and fout—Forty thoufand.and feventy fiye-and thirty. four thovfand, three huadred and five? Rew eee ee eee eae ee SIMPLE SUBTRACTION: WIMPLE Subtraficn teaches to find the Disiabeciah chcke cy kJ two fimple numbers. Ruwe 1.—Set the lef number under the greater, in fuch-order, that units may(be below units, &c. z. Begin: atthe right hand, and-take each under figure fron, that which ilands above it, placing down their difference. SIMPLE. SUBTRACTION. 3. When the under figure is oreater than the upper, take the under from ten, and to that difference add the upper, fetting down the fum, remembering, in this cafe, to carry one to the next under figure. To prove SuBTRACTION. Add the difference and lefs number together, if their fam ‘be equal to the greater number, the queltion is right. Fue TABLE. ae ee ea ee ae [tif OF fae 2 aah ed SSeS 8. Lo. Li hod pee tell Sewell WME ad Rk es Dt Doe coal ee Be (Obs OBR RE Rep oe [omen oie pe Pete bed Sah sb 5 i ATG See WRN Boe er DEE sk ee A 6. ee tet Se fof) hl 213 | 4 7 | - - < te OU Sh as We Bl iak ae . Abe bs po yond. 2 >| = hg © = aoe bOmaar lO - - - at 5 | © 7214688 G50 e436 28g OR eg AL Rok Os Sie ot, OP tee 2613322 9485677 6279874 8847217 3 3 7 6.4 3 6 24625 63 4759274 #267846 . 6745557 4 8974023 Ree) Oe oe a: 2°6°1 4.9 6 38627 8 6728690 7d FR a SI Stig, G2: 8 4860827 1872860 6805 626 What is the difference between 740865726 and 4057 336m What is the difference berween 1764075324 and 579043 How. much dees 2784500764 exceed 934307842 3 SIMPLE MULTIPLICATION. How much does feventy five thoufand three hundred and* twenty-five, exceed nine thoufand five hundred and twenty ? How. much does fixty-fix millions, three hundred thoulands,. exceed ninety four thoufand three hundred and feventy ? What is the difference between feven thoufand millions, eight hundred and two thoufaad,—and fix millions, thirty feven thou... fand and-ninety eight? SIMPLE MULTIPLICATION... IMPLE Multiplication teaches how to increafe the mulish: . cand, or number to be multiplied, as often as there are units - - ia the isc agad or number you. multiply by, and the nuapber arifing from thence is called the produd,, Sometimes the.multic - plicand aod muluplier are named /adars.:. MULTIPLICATION TABLE,. Mel. ) to | my | bap: [16] ui 20 | as us 2 eae eal aat 225 hh 30 | 33 | eee bie a 44|_; ene 60) 66 | 72 1 70+b 77 eg l Sol 88] 96 b54fo3) 72 Lgot) 99 4-108 | $< | 70 | 80 | “90 | toe | 110] tac 111225331441 554 66( 771 88} 99 | tro f ta. 1 132l e2 $24.)-36 | 48 | Cod 72 |e fot] acd | tac f132 | imal { NTRS Sip rk ae To multiply by any, number lefs than thirteen. Rure.—Set the multiplier under the unit’s place of the multi... plicand, and multiply every figure in it by the multiplier, fetting . down the units aid carrying the tens, as in {imple addition. Multiply 7643058921 by every figure between-two and thire, teen.- Py : CASe Be fo auultiply by any number greater than twelve. — Revver 1. Place the multipher under the mult pangs in fucts ‘: p | order, that asics may me under units ) tens under. tens,. 4 SIMPLE MULTIPLICATION. 8 =. Begin at the right hand, and multiply by each figure in the . m ultiplier, i in cafe fut, obfer ving to place the firft fipare of each produc under the figure you aré multiplying by. 3. Add up the feveral products, in the fame order as they ftand, and their fum will be the produst required. To prove queftions in multiplication, invert the factors and multiply as above, and if the product be the fame, the quettion is \ Fi ‘ght. I. y60s433804 by a5 —dif. 190135947350 2. 5720764839, by 34-—- 9194506004526. 3. 4007387258, by 67 ——= 2684949462806. 4. 45375158, by 125 ——— 5797019750. 5. 62704395, by 475 29847292020. 6. 726158569, by 9481 6884712236983. 7» 51828976, by 406073 ——- _21046347771248. 8. 642758409, by 730064 469254775108176. 5- 726834933, by 64060938 4656175810521434. 10. Multiply feven billions, thirty five thoufand three hundred and eighty four millions, thirty fix thoufand three hundred and Sixty two; by feventy thoufand three bundred and nine. Anf. 494650816212575858. It. Maliply fixty five thoufahd three hundred and eighty four millions, eight bundred thoufand two bundred and feventy ; by nine millions, forty fix thoufand two hundred and five. Anf. 5914843071 26475 350. 12. Multiply thirty one millions, feven hundred and fourthou- dnd, five haodred and ninety two; by two hundredeand forty feyen thoufand aad fifty. four.—An/, 7832746271968. Case 3, 4 “4 When ther are. ciphers on the right of-one or both faGors, _ Rvrz— —Negleét’ the ciphers, and with the remaining figures peter as in the former cafes: obfervinp. to anaex as many. ciphers to the right of the produdt.as were negleSed, J. aah Saud by 320 —— dnf. 2453396400. | 2. 46127900, by 4700 210801130000. 3+ 123456000, by 1230065 Per1Sso8Socoao0. 4. 5000430000, by 600 -———- 00385 80c0900, 5. Required the product of fix millions, thirty eight thoufand ti nie bundred ; by ninety four thosiagl 2+ Anf. sb Gob220c%. AL 3 | MPLE DIVISION. 6. Multiply feven thoufand three hundred millions, forty thou- fand and eighty, by one bundred and five thoufand. Anf. 786504208400000. WE Multiply feven billions, thirty milhons, two hundred and thirty thouland, by fix hundred and fifty four thoufaad. An 4578019770420000060, ro SIM IMPLE Divifion teaches to find how often one number is contained in another, or to divide a fimple number into a certain number of equal parts. In divifion there are four parti- , cular thi Ngs, viz. 1. The dividend, or number to be divided. 2. ‘The divifor, or number to divide by. 3. “The quotient, or naum- ber of times the dividend contains the divifor. 4. The remainder, or What remains after the work is finifhed. SIMPLE DIVISION. | : DIVISION TABLE. a TELL ae | 80 gil 9] 18] 27] 36] 45 | 54 | 63 | 72 8 | 8 | 16 | 24] 32 {| 40] 48] 560 | 64 Ti 7 [ta | 22 | 28 135 | 42 | 49] 56] 6: 6} Of 12] 18] 24] 30 | 36] 42 | 48) 54 “Oks Protas [20 [25 30] 35; 4of 45 is ha #1 4]. 84 baapr6| 20] 24] 28 | 32 | gb 4 Bla te, SERRA IRE | oe ae fee ela a i Rome BL Oc a oe 9 Case ‘1. To divide by any wumber lefs thaa thirtern. ' Rere. Place't? se divifor on the left of the dividend, and con- fider how ‘often it is ‘contained in as many of the left hand figures ‘of the dividend’ as will cawrain it lefs than ten times: fet the ) a 25- Divide 1735684 by 173¢ 0 ‘anf. 10127444 | REDUCTION. REDUCTION. | EDUCTION teaches to bring numbers of one name, to © ee others of a different name, retaining the farne value. Hig Rure.— When the redaction is to a lefs name multiply, when to a preater divide, by as many of the lefs as make one of the greater. When a compound number is to be reduced to its low- _ eft denomination, begin at the higbeft, and bring it to the next lefs, and fo on to the lafl; obferving to add: to each product thofe numbers of the fame name with itfelf which are in the given quantity. In reducing to a greater name, the remainders will always be of the fame.denomination as their. dividends. Of MONEY.. Farthings | Pence | _ 4 i Shillings | 5 San Seat ee eee ee ae MRA Colle ne Cee De LL. ftands for pounds. . ‘ D. ftands for pence. Sd. fhillings. Qrs, - farthings, ftands for one farthing, or one fourth of any thing. “two fartkings, or one half of any thing. three farthings, or three fourths of any thing. momen § phe WIN pf . Sb. SORE wy A guineais — 1 1 A crownis — 5 o Amoidore — I 7 AA mark — 13 4 Anasgel — O10 A noble — 6 8 1. In'61 Pyuads, how many fhillings, pence, and farthings ? anf. 1220s. 14640d. 5856097rs. 2. In 58560 farthings, how many shillings, and pounds ? anf. 1220s. 611, 3- How many fhillings and pence are there in 74 puineas? ; anf. 1554s. 18648d, 4 How many fhillings and guineas are there in 186484. ? y _ Of ASS45. 74g. | 5. In 20 pounds, how many crowns, fhillings, fixpences, and i pence? anf. 80cr. 4005, 800/4x. 4o00d, ' | B2 a aa Yt Gs Ee aA j fo Ee d “ r Flare oe wane: e- REDUCTION. 6. In 514. how many fhillings, groats, pence, halfpence, fix- pences, threepences, and farthings ? anf. 1020s. 3060gr.. 12240d, 2448o0halfp. 2040/ixp. 408othrerp. and 48g6ogrs. 7- In 25 motdores, how many fhillings, pence, twopences, ‘fixpences, crowns, halfcrowns, threepences, and farthings ? anf. 675s. 8100d. 4050twop. 1350/ixp. 135cr. 270ba/fer. 2700thbrecp. 324009rs. 8. Bring 60 guineas to half-guineas, fixpences, crowns, {hil- lings, pence, twopences, groats, and farthiags ? anf. 120halfg. 2520fixp. 25acr. 1260s. 15120d. 7560; wop. 3780gr. and 60480¢rs. | y. In 126/ how many half-crowns,: fixpences, ,half-guineas, quarter-guineas, threepences, pence, fhillings, and guineas ? anf. 1\008halfer. 5040fixp. 240half-g. 48oquarter-g. 10080 threep. 30240d. 2520s. and 12094. 10. In 252/. how many angels, fhillings, groats, halfpence, farthings, threepences, halfcrowns, crowns, pence, tenpénces, and nobles? anf. soqang. 50408. 15120gr0. 120960halfp. 2419209rs. 201 60tbreep. 2016balfer. 1008cr. 6o480p. 6048 tenp,. 75600. 11. In roogu. how many feven fhilling pieces, fhillings, fix- pences, three fhillings and fixpence pieces, threepences, farthings, twopences, groats, and halfpence? anf. 300/feven-s. 21005. 4200/imp.. Oocthree-s. 8400threep. 100800grs, 12600twop. 630cgr. and 50400ha/fp. 12, In 42d. 75. how many fhillings ? anf. 847. 13, Reduce-7/, 19s. to pence? anf. 1908. 14. Reduce 14/135. 7d..to pence? anf. 3523. 15 In 14% 175. 84d. how many farthings? — anf. 14280. 16. In 14289g9rs. how many pence, shillings and pounds? 17. In 21gu. 178. '4id. how many halfpence? anf. 11001. 18. t10o1hal/p. how many pence, fhillings and’ guineas ? 19. In 16/4cr. 2s. 4d. how many farthings? anf. 16192. - 20, Bring’16192 farthings to pence, fhillings, crowns, and pounds? - | TROY WEIGHT. 24 I | Ounces | 3 g80.. | ax20 1 | Pound 5760 | ee ee BE. REDUCTION. 17 Grs. ftands for grains. Oz. ftands for ounces. Dwts, ——— pennyweights. | Lid, pounds.” Full wetght Gold and Silver. dwt. grs. A guinea ought to weigh - 5° 9%3f4) A half guinea - ° - 2 1694(3) A Crown : r - 107, eae) A fhilling - .- - 3 2075(21grs) Note. A guinea mutt not weigh lefs than 5dzwts. 8grs. Note. 22 carats of fme gold, and two carats of copper melted to- _ gether is accounted the ftandard for Gold. Alfo, Itoz. 2dwiés. of fine filver, and 18dzvts. of copper for ftandard filver. Gold is valued at about 4/. an ounce, and filver at 5s. By this weight are weighed gold, filver, jewels, corn, and all kinds of liquors. : 1. In 7245. how many ounces, pennyweights, and grains? anfw. 864.0%. 17280dwts. 414720815. 2. Bring 414720 grains to dwts, oz. and. lib. 3. In 74d. 100%. 12dwis. 13grs. how many grains? anfw. 45421. 4+ In 45421 grains, how many pounds. 5..In 7 bars of filver, each weighing 4/5, 202. 13dwts. how many dwts ? anf. 709 tile & * APOTHECARIES WEIGHT. Grains | Scruples | poe Kot Dranis fs. 60 |. 3 bh s {| Ounces] Geek eae f Grs ftands for grains Dr. ftands for drams. Scr. ——— fcruples. Lib. pounds. Note. . By this weight the Apothecaries compound their medicines. t. In 7/6. 20%.. 1dr. afer. 17grs. how. many grains? anfw, 41397. 2.. In 41397 grains, how many pounds? La ere: ae [fe Quarters bi | | ae Ue oer 1 | Yard ° BBO 1. 218 fret ao ee | gare. make 4 ell Fiemih. ~ 6qrs. make 1 ell French. 5 1 ell Enplih, 4qrs. 12 inch. 1 ell Scotch. REDUCTION: AVOIRDUPOISE. WEIGHT. : SR a a RY Rea ee Drams | Ounces | : 16 |, 1 | Pounds | 256 | 16 |. 1 | Quarters | 7168 [44h | 28 | 1 | Hundreds | ° 28092 17 W992 (fe. liz rede i | Ton | 573440 | 35840 | 2240 | © Note. ra4lb. make a ftone in almoft all places in England, but. at Lon--—. don $lb make a ftone of butcher-meat. Cwt. ftands for hundreds. § ‘flones make a ewt. 194 cwt. make.a fodder, or fother ; 30 pounds of wool make a tod in Yorkfhire, and the other northern counties ; but in Norfetk and the fouthern .ceunties only 28]b. . # The pound. avoitdupoife is fqual to 14020 1idwis.: 154 gts. troy. re ‘The ounce avoirdupoife is equal to 18dais. 5igrs. troy. Bread, tea, coffee, foap, tar, /&c. and all metals, except gold » and filver, are weighed by. this’weight. “a. In 14cwt. sgr. 17/6. 140%. how many-drams? * anf. AL3152«: 2, Bring 413152 drams to-ounces, pounds, quarters, and cwts. 3. In 6 hogtheads of tobacco, each weighing 1 3caw#s. 2gr.1710. how many pounds? - - anf. 9174. ~ 4. In 19 barrels of raifins; each weighing 2ewt: 3gr. 440. how many pounds? - - anf. §928. s5.. How many pounds are there in 10 hogfheads of fugar, each . weighing Licwt. 3gr. 2111d..? - 3 anf. 13370 » CLOTH MEASURE... REDUCTION. 19: Inc. ftands for inches. E. Fi. {tands for ell Flemifh. Na. —=<=— nails... EE. Fr. ell French. ell Scotch, ' Yds. yards, E..Sca. E. £. ells Englifh. Note. Scotch and Irifh linens are ‘meafured by thé yard ;—Dutch linen by the ell Englith ;—and tapeftry. by the ell Flemith. 1.:In 72yds. 1gr. Ina. how many nails? © anfi-1157 nails. 2..I1n 670 ells Englifh how many nails.?. anf. 13400 nails. 3. In 16482 nails, how many quarters, and ells Flemifh ? by anf..1373E/. File. tgr. 2nd. 4. How-many nails are there. in 7 pieces of cloth, each -meafuring 17yds. 29r. Ina... anf. 1967 nails. 5. In 4712 nails, how many yards, -ells Englifh, and ells Fiemifh ?. anf. 294% yds. 2352 LE. 39228. Fh LONG MEASURE, - Bo Corns | Inches | Pal 3 | I Peet | 36 | 12 | i | Yards i 108. | 36 | 3 | I | Poles | 594 |. 198] 165 |) 5a]; 1] For 60 | .220 : ~ | °23760| 7920| 6 220,)4°40:| ) baf\Mep abt BAR FI 1 ae OGL 2AS bs Note. Geographers and-feamen r-ckoh 60 miles to a degree 3; but its true lengtlf has been found to be 694 miles. The circumference of the earth, being 360 degrees, is by geographers yand feamen .reckoned 21600. miles; but by the true circumference,. it _is 25020 miles. ' 4 Inches make a hand, 2 yards a fathom, and 12 foot a cubit. » 80 chains make a mile; the chain being 22 yards long, is divided into Ya hundred egual parts called links, each iink is 7425 mches. It is cuftomary to allow 18 feet to'the pole in fens, aid in forefts 21 feet. 1. In 42707616. barleycorns,; how many-inches, feet, yards, - poles, furlongs, and miles? anf. 224 miles, 5 fur./18 poles, 1 yd. 2 feet, 8 inc. 2. In 224 miles, 5 furlongs, 18 poles, 1 yard, 2 feet, 8 inches, how many barleycorns ? 5 j $A0 §7y TE +6 REDUCTION.” 3: In 19 miles, how many furlongs, poles, yards, and inchés? anf. +52 fur. 6080 poles, 33440 yas. “1203840 tues 4. Bring 1203840 inckes to miles. SQUARE MEASURE, . Sqr. Iuches S. feet | 144 | I S. Yards | 1296 | 9 | i | 5. poles | WigGaOE Ye) aa" yea ita! a enn 1568160} 10890 | 1210 @ 40 | 1: | Acre 6272640 | 43560} 4843 | 160 |. 4.[.1 Note. Ten chains in length and oné in breadth make an acre. 640 > fquare acres make'a {quare mile. By this meafure land, or.any fuperficies, is meafured. 1. In 7 acres, 2 roods, 16 poles; 20 fquare yards, how many fquare feet? anf. 333236 fquare fects 2. In 331236 {quare feet, how many acres? 3. Suppofe a field meafure 14 acres, 2 roods, 8 poles, how ~ many fquare yards will there be-in 20 fields of the fame dimen- . fions ? anf. 1408440 for. yds. WINE MEASURE. . Pints | Quarts | 2 1 { Gal. | ea 4. cpr i terres S801 M168 amie Ss | Hhds | Oa 2624 63 bee f Pan. 672 [336] 84 [2 ROOF NG SOA RIDE Vg J 2 2010 |; waes qaeg | aa Pe aio Seon ae eee ¥ tun of wine weighs 18cq#t. and one gallon contains 231 cubic inches. lone (oe) = wh Mis. ftands for quarts. To gallons make an anchor of Brandy or : Gall. —— gallons. rum. Tir. tierces. 13 — a runiet.° Fbds hogfheads. 314) ——— a barrel. Pun. puncheons. - 236 ———— a tun of {weet oil.- 8/26. is the ftated weight of a gallon, but 74 is commonly allowed as the weight. Wines, brandies, rum, honey, oil, vinegar, &c. are. meafured by thie - mealtre. —_- Dare eS barrels, REDUCTION. ay 1. In rz puncheons, how many tierces, gallons, and quarts? anf. 3Atir, 1428gall. 5712918. 2. In 5712 quarts, how many gallons, tierces, and pun- cheons? 3. In 71 tuns, 2 hogfheads, 1 tierce, 19 gallons, how many pints ? anf. 144632. ALE and BEER MEASURE, Pints | Quarts | 2 | 1 | Gallons | ‘isc MT 130 |. (“O8bmg Pao pea Y Bartel || 272 | 7136 | am 4 [2 | 1 [Bhd 6 408 | 204| 51 ORC TR, LEBEN Oe: 232 cubic inches are contained in ene gallon of ale or beer. At London 9 gallons make a firkin of beer, and 8 a firkin of ale. Fir. ftands for firkins. B. bbd, ftands for hogfhead of beer. Kild, kilderkins. A. bhd. hogthead of ale. ™s In Scotland. 4 gills make a mutchkin. @ pints make a quart. 2 mutchkins a chopin. 4 quarts a gallon, 2, chopins 2 pint. 16 gallons a hogfhead, The mutchkin is about $ of the Englifh pint, two pints and a quarter of a gill Scotch being nearly equal to three Englifh quarts. The Scotch pint is Ios cubic inches. 3 Englifh pints = 21135 cubic inches. 2 pints and 3 gill Scotch == 21143 = 1. In 141 barrels, how many firkins, gallons, and pints ? anf. 564fr. 4794gal. 3835 2pintse _ 2. In 38352 pints, how many barrels ? 3. In 14hhds. Scotch meafure, how many gallons, pints, and mutchkins ¢ - anf. 224gal. 1792pints, 7168mutch. 4. In 7168 mutchkins, how many pints, gallons, and hogf. heads ? Sg a 7 a SS I I eA AY nM ‘ 4 , we ; ; ire j wa His Ze en REDUCTION, DRY MEASURE, 2 | ¥ | Gal. | 76 | Shy ae 1 { Buth. | 2501 428.[0) gah RO age x | Quar. | 512 |> 250 | 64] 32] 8 | a{ 1 | Weys | 2560 | 1280] 320| 160} 40° | TO) eo 1 | Latt 5120 |. 2569 | Caste there a The ftandard bufhel is 182 inches wide, and 8 inches deep. The gallon, dry meafure, contains 2684 cubic inches. 2. ‘Bubhels a boll. 36 Bufhels-a chaldron of coals at London. 3 Bufhels a fack, 68 Buthels a chaldron of coals at Newcaftle, and and weighs 2tons. I3cwts, A bufhel, water mieafure, is 5 pecks.—8 chaldrons a keel. In Scotland. 4 Lippies, or forpats, make a peck. | 4 Firlots a boll. 4 Pecks a firlot. | 16 Bolis a chaldron. ‘fhe Scotch wheat firlot is nearly equal'to the ftandard Winchefter bufhel, being in proportion as 100 is to 99. By this meafure, coals, corn, falt, feeds, fruits, oyfters, &c. are meae. fured. 2. In 18 lafts, 3 quarters, 1 comb, how many buthels ? 3. In 146 chaldrons of coals; London meafure, how many buthels and pecks? anf. 5256 bulb. 26280 pecks. 4. In 176425 pecks of coals, Newca{tle meafure, how many chaldrons ? anf. 518 chal. 61 bub. 5. In 174867 forpats, how many pecks, firlots, bolls, and chaldrons? anf. 170 chal, 12 bolls, 1 fir. Op. 3 for. 6. In 170 chal, 12 bolls, 1 fir. op. 3 forp. how many lippies ? 1. In 1468 buthels, how many combs, quarters, and lafts ?< anf. 18 lafls, 3 grs. 1 comb, anf, 174867. | REDUCTION. OF TIM E: Seconds | Minutes | Gor Treo 3600 | 6o | 1 | Days | 86400] 1440] 24 | 1. [| Weeks | 604800| 10080] 168 | 7 | 1 | Momh 2419200] 40320| 672° [28 |.) 4 ene : Note. 12 Calendar months make a year, but 13 months, “r day, ahd 6 hours, or 365 days, and 6 hours, make a Julian year, by which means, every fourth year has 366 days in it, and is called Leap year. i. How many months, days, hours, minutes, and feconds are there in 1784 years? anf. 23192 mon. 649376 da. 15585024 bo. 935101440 mit. 55106086400 fec. 2. In 7 years, 11 months, 17 days, how many hours. anf. 68952 hours. 3. In 68952 hours how many days, months, and: years ? The number of days in each calendar month may be known from the following verfes which are commonly put in books of this kind. Thirty days hath September, April, June, and November, February hath twenty-eight alone, And all the r-% have thirty-one, Except Leap year, and then’s the time, When February’s days are twenty-nine. A Collection of ufeful Memorandums. 24 Sheets make 1 guire of paper. teoo Bricks make 1 load. 20 Quires — ream ditto. 1000 plain pantiles x ditto, 2, Reams —_ bundle. § Lib. £ ftone of glais. ro Reams —_ bale. re Dozen 1 grofs. 60 Skins 1 roll of parchment or vel-/56 Lib. 1 firkin of butter. lum, 64 Lib. 1 firkin of foap, ro Skins 1 dicker of hides. 30 Lib. x-barrel.of anchovies, 12 Barrels 1 laft of pot-afhes, cod- |100 Lib. x quintal of fit at New- id fifh, &c. foundland. | 17 cwts. make ¥ laft of flax or fea- }24 Lib. 1 tod of wool, t thers. roo Acres make 1 hide of land. | 2.400 lib. 1 laft of gunpowder. 40 Solid feet of hewn timber 1 load. 250 Gallons I tun of Greenland {50 unhewn r load, oil, 13% Gallons x barrel.of herring. — REDUCTION. 42 Gallons 1 barrel of falmon. A Dutch mile—33 Englifh miles I cwt. 1 ditto of gunpowder. j|—TItalian — RS! — 20 ftones I fack of flour. — Spanith league - 32 £2, A French league is nearly 23 Eng-|__ Ruffian vert. - "a w Sa lifh miles. — Toife a 62 feet — German mile—4 Englifh miles. | __ Quintal — rope, When by the tables it cannot be found how many of the lefs name make one of the greater. Rure.— Bring the given quantity, and the integer to which it is to be brovght, to the fame name; then divide the greater number by the lefs, and the quotient will be the anfwer. In 148 guineas, how many pounds fterling ? anf. -155/. 8s. In 155/. 85. how many guineas? anf. 148. Tn 168 crowns how many half guineas? . anf. 80. Bring 504 half crowns to guineas. . anf. 60. Bring 128 ells Englifh to yards. : ° anf. 160. In'785 fhillings, how many half crowns? - anf. 3146 In 555 ells Flemith, how many ells E-nglith ? anf. 333. In 216 moidores, how many guineas ? anf. 27°7g5. 15s: In 1008 nobles, how many half guineas? > anf. 640. In 810 angels, how many moidores ! - anf. 3CO. In 864 marks, how many fhillings? . anf. 11520. In 242 fixpences, how many quarter, guineas? anf. 23qr-g. 3d. MA promifcxous Colle&ion of Queflions to exercife ReEpDUCTION. 1. How many months, days, hours, minutes, and feconds have paifed fince the creation of the world, being 5784 years? anf. 75192 mon. 2105376 days, 50529024 hours. 3031741440 mia. 181904486400 /ec. 2. In 147/. how many nobles, pence, fixpences, three-pences, half-crowns, crowns, angels, ag two-pences, half-pence, and fhillings? anf. 441nob. 35280d, § 880/ixp. ay 1176 dale. 588cr. 2g4ang. 8820gr0, E7040fwop. 70560 halfp, 29405. 3- In 100 tons of lead, how many fothers? anf. 102534 4. in 7 tons of wine, how many hogtheads, tierces, and ie lons - “ anf. 28hhds. 4g2tir. 1704gal. REDUCTION. =) 5. In 14607 quarts of wine, how many gallons, puncheons, and tons? - anf. 14tons, 1 pun. 39 gal. 3gts. 6. How many bufhels are there in 142 chaldrons of coals, London meafure? : - ; anf. 5112. 7. Elow often will a coach wheel, whofe circumference is fix yards, go round between Newcaftle and Berwick, the diftance being 64. miles? - . - anf. 187732. 8. How many fpoons, each 20%. 6dwts. can be made’ out of a large old filver veffel weighing 5/3. 20x. 2dwts. anf. 27. 9. A contractor for a regiment of foldiers purchafes 3000 yards of red cloth, of which he defigns to make coats for the men; how many coats, each z2yds. 2grs. can be made out of the 3000 yards? - - - anf. 1200. 10. In 252/. how many fixpences, three-fhillings, nine-pences, pence, fhillings, guineas, half-pguineas, quarter-guineas, three- pences, half-pence, and -farthings ? anf. 10c8ofix p. t68othreefb. 6720nIne-p. 60480d. 5040s. 240gu. 480half-g, bogr-g. 201 60three-p. 120960half p. 2419209rs. 11. How many fmall inclofures, each 8 acres, 2 roods, and 27 poles, can be made out of a common containing 260 acres, and 10 poles? : > - anf. 30. 12.. Bought 61 hogfheads of tobacco, each weighing 15cw#. 2gr. 8/b. how many pounds are in the whole ? anf. 106384. 13. An apothecary made fix different compofitions, each 2/5. — 30z. 2dr. how many fcruples were in the whole? — anf. 3924, 14. How many bufhels are there in 67 lafts of wheat ? : anf. 5360. 15. A fea captain bought 4 oxen at London, which, after they were drefled by the butcher, weighed 120 {tones each ; how many pieces, each 43/4. -can he have out of the fame? anf, 80885. 16. A merchant bought 15 pieces of holland, each piece 100 ells Englifh, how many quarters are contained in them ? anf. 7500. 17. If one cheft of tea weigh reat. 2gr. how many ounces will there be in 12 chefts, each containing the fame quantity ? anf. 32256. 18. How many fodders are there in 117 tons? anf. 120. 19. In 100 hogfheads of brandy, how many anchors? anf. 630. Cc 26 COMPOUND ADDITION. 20. How many three-gill bottles can be filled out of 3 hogf- heads of beer, London meafure ? : anf. 864. 21. In 174 Newcaltle chaldrons of coals, how many bufhels? 3 anf. 11832. 22. How many gallons and pints are there in 3 tons of {weet oil? = ° : anf. 708gal. 5664pints. 23. A gentleman of fortune has a curious cabinet for holding money, which has 30 {mall drawers in it, of equal dimenfions, each holding exa€ty 240 guineas, how many pounds fterling can they bold ? mais - - - anf. 7560l. z4. In 252 dollars, each 5s. 4d. how many guineas? anf. 64. 25. How many quarter-guineas are in 39/. 12s. Od. anf. 151. 26. In 167 barreis of ale, London meafure, how many gal- lons and quarts? - - anf. $344gal. 213 76gts. 27. In 174 French crowns, each 4s. 6d. how many pounds fterling ? . - - anf. 391. 35. 28. In 504 halfcrowns, how many pence, tenpences, crowns, fizpences, haif-ouineas, guineas, fhilhags, threepences, quarter- guineas, three-half.ences, farthings, twopences, and half-pence ? anf. 15t2od. 1512kenp. 252¢r. 2520/ixp. 120half-g. Gog. 12605. 5040threep. 240gr-g. 10080three half-p. 6048cgrs. 7560twop. 30240halfpence. ; 29. How mary tiles, furlongs, yarcs, feet, and inches, is the earth round, when 69% miles make a degree ? anf. 25020miles, 2001 60fur. 44035200yds. 132105 60Gfeer, 1585267 200inches. 3c. How many feconds are contained in the month of June ? anf. 2592000, COMPOUND ADDITION. OMPOUND Addition teaches to find the fum of two or Ly. more compound Numbers., Ruve.—Place like names under each other; then begin at the loweft, and find its fum by Simple Addition, reduce this fum to the next higher denomination, fetting down the remainder and carrying the quotient ; proceed in the fame manner with all the denominations till you come to the higheft, which de as in fimple addition. Mee edeesoseeae SET AAMAS hwWw YD Dw S 3 esecas Ow AnNRw wb F ‘€OMPOUND ADDITION, PENCE TABLE. d.| Pence.. 8} 95 100 105 11o aay 120 125 130 135 140 145 150 155 160 coal) A+ © OWN OWT NOR = Oe eel | as Meal = Sa Na aa Be OAM WN O O RAR NOR 8 2 See % S Beoeee BEE Ere ee al . —_ PHA OW OM ODN LO fF & fot COMPOUND ADDITION. Jats d. 67. 2 104 33 15. 94 25.14 10% O4 12° 9 6— 8% 2%14—- Ovlt” 126 92 15 104 46 12 6% 1417 45 8 fond 71 14 104 13 — of 612 74 4417 43 17 ore 72 10 11% 65 4 7% 2i—-— 67 9 8% 10. — 72 15° 8% 14.17 WF 72.14 8% FAO. 5% 6 14 105 476 2 § 11% 913 45 71 °9 3% 2 IL 94 6 — 10% 8 14 — 3.17 4% 7 Fae ie 9 6117 4% Sys 2uriy 34 16 83. FORDE ope 52.15 24 42.138, 104 66 17.— 2A Ae Ot 8 17.0" 64 re VA 1OF 2516 45 17 4 8% G1 it. Be 20.13 4% 48 17 104 43 18 9% py: ea ae 64.14 11% 85 16 10% & 5 3% 915 44 OOF Eg \8 13° 28 3 15 11% Boge oe 2 16° 115 CEOS 11 14 6% 6 5— BASS 8% 72 4 7% 66 15 — ne 4 104 18.13 Bh 78s: td, 11h. of fugar, at 94d. : : 8s, 1d, 12/70. of beef, at 24d, ° 2 . 4s. Od, Case 2, When the multiplier is greater than a ae and can be found in the multiplication table. Rure—Find the compenent parts of the multiplier ; and | multiply by one of them, as in cafe firft, and that product again | by the other, will give the anfwer. COMPOUND MULTIPLICATION, 35. LP | 36 OW OI QU hw Ww sods . 14 Yards of cloth, at . 15 Penknives . . 16 Handkerchiefs - . 18 Gallons of wine . 20 Dollars . . 24 Quires of paper . 22 Ells of diaper . 24 Pairs of {pectacles a els of oats . 2s of bark . 28 Arithmetics - . 30 Pairs of fhoes . . 32 Bufhels of wheat . 33 Days work . 35 Yards of linen . 36 Gal. of brandy . 40 Yards of ribband . 42/6. of pepper - . 44) Pairs of {tockings . 45 Yardsof lawn - . 48 Oz. of rhubarb . 49 Cocoa nuts - . 0 Yds. Irifh linen . 54 Maps . . 56cwt. of fugar . 60 Norwich fhawls . 64 Barrels of ale 1 . 66 Grammars . 70lb. of tea = pig Acres = . 77 Gal. beer - - 80 Quarts rum . 84 Hats 2 12 . 88%. of cloves 17 . 90 Bottles of wine 2 . 96 Yards filk eee . 100 Watches - 4 19 . 108 Deals - I 10 . 110 Firkins butter 1 15 10 . t20cws. Tobacco 6 14, COMPOUND MULTIPLICATION. me ofS te el FO BS 2 COW fh oH mw ON 63yds Perfian filk i>) — yep OC oe wee ear ee ‘ _~ CoOn~rst = OWN x ss = FO AW +(e BIH wie ioe) a oe Sp ae OW NOOO ahwo RK vit $f Viet pl vie * hie vin leo wo vik NOvsewobh vd DAD 9 ple vis wis & boot et te tt ae oa ie 1 a EET Pg N { a BW OW ww Or m PSI OR m oS iS) b&w vv ~aTh —q ped rere | cop Coun Va wy | oo? 18 oes ESL SLi Li Lee) | eee be le de) eas tee ow tO XO es, | bls vis i a me ae sid. Pag bit NN § 42. 121 Ewes - 6 027-9 — 197.22 040 43. 132 Stones of beef gE ae 23:18 6 44. 144 Egos 2 ae or Czy re %, When the multiplier is lefs than 157, and is not in the mul- tiplication table. Rurze.—Find the neareft number to it in the multiplicatien table ; with which do as in the Jaft cafe; then multiply the head line by as many as it is-greater or lefs than the given number, which add to the laft-produ€& when lefs, but fubtra@ when greater ; and the fum, of difference will be the anfwer. Pe See Pea Ss. de L: sg 4. 1% at trp aoe 3173 .8..9 1st 6.18 7~ a 1046 .-6-“4- 152) beeen os G —— C93 ern 15,3 sree 18 POE ao 88-5 10% 154 ———— 43... Ze HG Of WEIGHTS and MEASURES. 1b. 10cn, 13dwts. agers. by 4. anf. 31d. 60x. iedwi. 1Ogr. 17ton, 14cwt. 2gr. 19lb. by 6. anf. to6sen. Bewt. ogr. 2/0. 3ewt. Igr. 17/b. by 8. - anf. z7cwt. ogr. 24lb. E7yds. 2grs. 3na. by g. = anf. 15$gyds. Ogr. 31a. ntun. 2bhds. 14gal. by 11. - anf, 83tun, obhd. 28gal. I4acr. tro. 19poles by 12. - anf. b72acr. tro. 28poles. 7cewt. 2gr. 4lb. by 16. - anf. 120cwt, zgr. S/d. How many cw#. are there in 18 pieces of lead, each 1ocwt?. 29gr. 17/b. - - anf. \gicwt. 2gr. 26/b. How many yards are there in 24 pieces of linen, each piece meafuring 14yds. 29r..2na. - > anf. 35 1yds. If one hogthead of tobacco weigh 14cw?. ogr. 17/b. how much will 29 weigh? > - auf. 410cwt. tar. 1710. How many gallons are there in 33 cafks of beer, each 14ga/. 2gt. pint? - “ anf. 482gal. 29t. ipint. How many gallons are there in 47 half-anchors, each 7ga/. pint ? = > anf. 334gal. 3qt. vpint, COMPOUND DIVISION. OMPOUND Divifion teaches how to divide either a com- pound or fimple number, into any propofed number of equal parts, each of which {hall confift of faundry denominations. CAS E15 When the divifor is lefe than thirteen. Rute.—Divide each denomination in the dividend as in cafe firft fimpie divifion, placing the quotients under their proper divi- cends; when any thing remains, reduce it to the next infertar name, adding thereto what is ia the dividend of that denomina- tion, divide this number as before; Proceed ia the fame manner through all the denominations. : “Die 40 COMPOUND DIVISION. Moonbear iae Divide 19 10 10 by 8 20 4 97% «9 : REEMA 8 Divide 6 18 98 by 3 : 20 16 8 4 woe «86 25C«dG(C (Gs HSCS 64 #5 — _10 ere 88 FZ 4. 6 6 4 IZ cee eres Ag ae i 9[—— 53 11 — 12 CASE 2. ln When the anions is more than thifteen, and can be found in the multiplication table. Ruzr.—Find the component parts of the divifor, and divide by one of them, as ia cafe firft, and that quotient again by the ether will give thé anfwer. Divide 1/. 6s.- tod. by 14. - anf. 1s. 11d, Divide 6/. 25. 8d. by 16. - - anf. 75. 8d. _ Divide 6/7. 6s. 8d. by 20. ° . anf. 6s. 4d. _ Divide 72/. as. 6d. by 24. - anf. 3/. Os. 24d. If 30 yards of cloth colt, 3h. 1gs. 74d. what was that a yard? anf. 28. bid. \ Sold 36 pounds of tea for 27/. 4s. 6d. what was that a pound ? anf. 158. 12d. What coft 1 yard of linea, when 42 yards coft 6/. os.. led; anf. 38. 1d, Divide 252 108. 5d. equally among 50 perfons. anf. 10s. 24d. Bought 54 ftones of beef,! for Yoket1s. 6d. how much does ‘at coft a ftone? anf. 3s. Lid. Bought a firkin of butter, contathiog 56d. for 14. 15s. what did it coft a pound? anf. 7d. If 60 eggs colt 6s. 3d. what was thata piece ? anf. 14d. lf 63 pair of thoes coft 18/. 12s. od. witat coft § pair? - anf. 58. 11d; Lf 66 chaldrons of coals coft 557. sf 6d. what was that for + chaldron ? anf. 16s. gd. Bought 72 bufhels of wheat, for 2.3/. 4s. what did it coft a bufhel ? ~anf. 6s. 7d, If a puncheon of rum coft 52/, 17s. what is that a gallon ? anf. 125. 7d. A filver-fmith bought an ingot of fives which weighed 99 ounces, for 24/. 12s. 114d. how much did it colt per ounce? oa: anf. 4s. 118d, Divide 11g? 16s. 82. by 1co ode, Gnfe Uh 35, ad. Divide 42/. 6s. by 108 - we anfs 75. Tod. \ i COMPOUND. DIVISION. Divide 6017. by 120 ae Co - anf. 5 eh os 2d. Divide 40/, 145. by 132 oe | tin 63..2d. MA CASE 3. When the divifor cannot be found in the multiplication table. Ruce.-—Divide by cafe third fimple divifion, obferving the Jatter part of the rule for cafe firft compound ‘divilion. Divide 67. tos. 74d. by 19 - - anh, 6s, 108d. Divide 43/. 14s. tod. by 29 - anf. 11. 10, 2d. Divide 30/- os. 8d. by 34 > - anf. 17s. 8d. Divide 502/. 185. by 47 “i - anf. 10le 145. Divide 18/..75. 82d. by 53 ° anf, 6s, 11%d. Divide 38/. ros, 6d. by 67 ernitihe iat 6d. Wha: is cloth pst yard, when 78 Ae colt 18/, 105. 6d. anf. 4s. Od. Bought 87 quarters of barley for 2027. 5s. 67, what was that per quarter ? ; : : anf. 21.68 6d. Divide a prize of 2011/. gs. equally among 98 failors. anf. 201.105. 6d. If a perfon fpend 7o/. 4s, in two years, how much is that per week ? - . - anf. 135, Od. Bought a pipe of ftrong beer, which contained 119 gallons, for nl. 35° gid. what did it cof per gallon ? anf. 1s. 27. If the clothing of 3 companies of foldiers, containing 274 men, colt 308/. 5s. what was that, at an average, for each man? anf. 11. 25. 6d, Suppofe a pres fpend 47/. 2s. 11d. in a-year, how much is that per day ° - - anf, 25. 74. Of WEIGHTS and MEASURES. ccwt. tor. 2716, by 3 261. 120%: 12dr. by 4 Zion. 12cwt. 2gr. by, 5 ib. goz. 1dwt. Ogr. by 6 510%. tdr. ofer. 16gr. by 7 zoyds. 29r.by 8 *. 62yds. Ofeet. ginc. by 9 g5tun. ibbd. 37¢al. by 10 S2days, zOhours, 15min. by 11 Ziacres, 3r00ds, by 12 & = n Icwt, 3¢r. olb. 6/b. ‘110%. 3dr, 4ton. Ocwt. 2gr. Wb, 30%. 1odwt. Ser. 70%. 2dr. ifcr. 8gr. 3yds. 29r. 3na. Opds. 2feet, Ginc. 3tun 2bbd. 108al, 7days, 12h. 45min. 1acr. 3ra. 10 pol, peta t D 3 ere Se 42 COMPOUND DIVISION. 2iewt. 3gr. by 14 30ells E. 2gr. by 16 13cwt. 3gr. 20/b. by 24 173acr. 3r0. 10po. by 30. 435cwt. ogr. 24/b. by 36 878ells Fle. 1gr. 2na. by 42 Licwt. 2gr. 184/b. by 26 igr. 2241). 39cwt. 1gr. 14/b. by 163 264d: As it gfgyieppens in bufinefs that there is either a2, 4, oF 3 in Uantity, to find the value of fuch this isthe Ruise.—After haying found the value of the whole number. by compound multiplication, divide the head line, or price of 1, by 4 for 4, by 2 for 4, and for 3 divide the head line firit by 2 for 4, and that quotient again by 2 for 4, thefe added to the value of the whole number will give the anfwer. Icwt. 2gr. 61h. tell Es age. 2na. 2gr. glb. §acr. 3r0. 7pde I2cwt. ogr. 10/b. 20¢/s Fle. 2gr. 31bs Pri bers Perinat ote Lae ae to, at—— 4% | anf. me OY Om 44 — 16 9 epee 315 44 674 si a SA ex hgh 14 7 11g - — 3 2 eras E2114 15 OF — —87 404 317 9 ote 181 14 9% 353 415 6 — 169 10 3 563 218 7 — 166 4 7 ? 7G 0 12 6 —— 73: S30 36+ 3° 6... 6. een i21 7 3 724 I 12 10 me lig 8 97F 162 r 16 6F a 29.13 QF When there is any fraction in the quantity. ° Ruxe.—The value of the whole number being found, mults- ply the head line by the numerator, and divide the product by the denominator ; the quotient added to the value of the whole number, will give the anfwer. What comes §7/id. to, at 8s. gd. anf. 71. ros. rid. 19iib. of butter, at Lod, . i anf. 173. 52d. 631ib. of beef, at 442. - ° ° anf. 28. 8d 14416. of fugar, at told. 7 © anf, 12% 104d. PROMISCUOUS QUESTIONS. 43 oF yards of linen, at 3s. 2d. : - anf. tl. 2s. 11¢de 34% 3 ells, at 6s. 103d. ° 2 anf. 111. 185. rosd> 5% ftones of foap, at 4s. 24d. * - anf. 11. 4s. 24d: 18% yards, at 175. gd. - - anf. 161. 128. ode 4% "yards of cloth, at 17s. 67, - anf. 41. 58. 33d- 46% yards, at 6s. 7d. - 2 anf. isl. 6s. 11d 157 ftones, at 14s. 63d: = anf. itl. 78. g3de gozewts, at O/. 175. 6d,. = anf, O24/, 18. 11tds The following Qieflions: are to exercife all the ibe force going compound Rules. : What comes: 13° elbow chairs.to, at 19s. rod. a piece ? anf. 171. 175 In the furvey of a certain river from Water-quay to Marfh- acres, the following diltances were meafured, wiz. from Water- quay to Summer-meadows, 2m. 4 fur. 17po. from thence to New Mills, 3 miles, from thence to Paffage Bridgef 1m. 3 fur. 27po. from thence to the Mill-bank fithery 4m. 17pe. from thence to the Ferry-beat-landing, 7 fur. 29p0, and from thence to Marfh-acres, 2m. 3 fur. how many miles were furveyed ? anf. 14m. 1 fur. 10f0. A borrowed from his friend B 1oo/. of which he paid at one time 10/. Igs. 6d. at another time 21/. 18s. at another 17/. 4s. 10d. and at another 40/. how much remains unpaid ? anf. ol. 178. 8d. Required the price of 101 gallons of Rum, at 8s. 10d. per gallon? anf. 441, 125. 2d. A party of 147 foldiers having feized upon a great quantity of ftores belonging to the enemy, their commander, as a reward for their bravery, ordered the value of the ftores to be equally divided among them; each man received 29/. 18s. 104d. re- quired the value of the ftores. anf. 44011, 145, [Eds What comes 73/b. of hops to, at 1s. 8d. a pound? ‘ anf. 61. 4s. 8Eds. A feaman being wounded, and for that reafon difcharged, came to London and received 54/. 18s. for 36 months’ wages, what was that per month? anf. 11. 10, 6d. { If 1 bufhel of wheat Ratt 6s« 5d. shat will be the price of 56. buthels ? anf. 171. 198. 4d. A perfon arias it was ea in Hts will, that he had left to. his widow 450/. to his eldeit fon 1008/ 195. 10d. to each of sie seaman ie Sy ae ’ & { } : a 44 PROMISCUOUS QUESTIONS ; his other three fons soo/.'175. to his two daughters each 3004 14s. od. to five of his near relations each so/. 115. 6d. to his fervants 30. r4s. 2d, and to the poor of the parifh 10/7. 195. 2d. how much was left in all? anf. 38574. 118. 2d. If 336:d. of cheefe coft 72. 7s. what was that 2 pound ? anf. 62a: C borrowed from D 120/: of which he paid at one time 19/. 19s. 6d. at another time 40/. at another 16/. 85. 4d. at another 6/, 178. 4d. and at anot sal 30/, how much has he paid in all,. and what remains to pay? anf. Paid 1131. 5s. 2d: To pay 61. 145. fod. What will be the price of 7 dozens of bottles at 234. a piece? anf. 19s: 3d. A gentleman paid 21/. 6s. for a dozen of mahogany chairs, what was that a piece ? - anf. 11, 15s. 6d. How many cwé. are there in’ 17° hogfheads of tobacco, each containing 16cwt. 2gr. 1770.. anf. 283cwt. ogr. oll. A fhip, in'a Weit India voyage, cleared 75c/ the belongs to 3 gentlemen, who have each an:equal (hae of her; required how much eacly will man receive of the gain? anf. 93). 15s. What may a perfon {pend-a week, out of an eftate of toool. a year? anf. 19l 4s. 7% Suppofe the owners of a fhip at Shields pay 200/. 185. od. for a cargo of 25 keels of coals, what was'that.a keel? aif. 87. Os. od. Divide 1779945. 39r. cially amobs $4 perfons. anf. 2¥yds Ogr. 3na. If 112/8. of tobacco coft g/. 25. what is it a pound? anf. 1s. 7Ed. What is the weight of 97 kits of falmon, when 1 kit weighs 1gr. 141d. anf. 36cwt. 1gr. 14lb, If he clothing of 680 foldiers colt 1181/. 10s. how much ts that for one man? anf. 1, 149. Od, Divide 11/. 19s. od: equally among 12 men. anf. 19s. 114d. Bought a fuit of clothes, which contained 43yds. at 12s. 6d. what will it coft me? anf. 21, 198. 44d. What will 36 {tones of four come to, at 1s. 11d. per ftone? anf. 3l gs. Required the sl agrtes a between cr. 25. 24d, and 2/. 3s. 2groats? anf. il. 3cr. 1s. Igre 14d, Suppofe A was 20 years of age when’ B was born, how old will A be when B is 40 years old? anf. 60 years. aaa PROMISCUOUS QUESTIONS. 4s Divide 26/. 10s. 3d. into-21 equal parts. anf. 1/. 58. 3d. If 13 filver fpoons weigh 1/5. 70x. 13dewts. Ogrs. what is the weight of one? anf. 10%. 1odwis. Ogre A filver-fmith bought 100 dollars for 19/, 114. 8d. what did they colt a piece ! anf. 38. 11d. If'42 pieces of cloth contain 735 yards, what is the length of ‘one piece? anf. W7yds. 2qts Thirteen linen-drapers buy 361yds. 2gr. Ina. of linen among them, and agree to pay equaily for the fame; how many yards will each receive. anf. 24yds. 39r. Ina. If my income be 48/. 15s. a year, how much is that a week ? ae anf. 18s. od. A perfon left 1087/. 142. to his two fons, out of which the youngeft was to receive 471/. 19s. what was the eldeft’s fhare ? anf. 6151. 158. A merchant bought 9 chefts of tea, 4 of which weighed 2gr. 24/5. each, and the other 5 weighed each 2gr. 6/b. how many ewt, are there in the whole? anf. Scwt. 2gr. T4/b, A merchant bought 40 hogfheads of fugar, 15 of them weigh- ed 8cet. 2gr. 14/b. each, 20 more weighed yews. 3gr. each, and the other 5 weighed 7ews. each; how many cwé. were in the whole? anf. 31gcwt. gr. 14lb. A. trader failing was indebted to A 71/. 125. 6d. to B 34/, os. 9d. io C 16. 8s. 8d. to D 44/. to E r9/. 195. to F rif, 2s. 3d. toG 66/. 175. 6d. and to H a fine of thirty marks. At the time of this difafter he had by him in cath 3/. 135. 6d. ——in commodities 93/. 10s.—in houfehold furniture 13/, 8s. 6d. ——in plate 7/. 185. 5d.—in a tenement 56/. 15s.—in recover- able book-debts 67/, 13s. 10d. fuppofing thefe things given Be « CACM a & ROMO 21 yds. of printed linea, at BN per ghee es Gt 37 16 4% A MARKET BILL. : Pon Gn Level de 193/b. of mutton at . O° 4% perl. 0 6 9% 24% beef * - Oo 44 Oo Qh ae 9 fowls eek - Eo Aoi? ACh OL EBs OO 24 ounces of tea - oO. 8 per 0%..0-17. O 74/b. lump fugar - O Of per lb...0,.6. +12 21 epgs Sa - Oo Rane On zones AX, {tones of flour ° 2 4 per floneo 10 6 Si Set O A GROCER’s BILL. Mr Mafierman, | Bought of Samuel Retailer. May 4th, 1783. reef fle Se se abe 44/2. of green tea, at < 16 9 perl. 3 15 4% 4 — bohea - 8. 6cy Pe ay ¢ —— congo te 9.2 AEE se 173 —— lump fagar - ©. 10% (os eR 0 24% — foft fugar > o. 664 O 13 «1% 63 ounces nutmegs * © ,14 peroz.o oO 11% i VOX black pepper - Om 2d. Ccus ry j 194/b. foap | niin : © 83 perlb.o 14° 24 Lie So Mia. or eee a 48 BILLS of PARCELS, &c. A HOSIER’s BILL. = . feud Le & da 23 pair of thréad ftockings, at 6 2apair 7 4 10 9 lamb wool ditto . mtg 210 9 rr —— black filk ditto : 12 OG m——— 617 6 9 —— white filk ditto = Il J7=——5 4 3 19 ——— worlted ditto. ° 3—— 419 9 17 ——- cotton ditto : 6 4——5 7 8 5°.) tse A CORN MONGER’s BILL. : Py) d. 7A So d. 29 bufhels of wheat, at “ 6 gabufhel 9 3 8 92k em MALE te NB Sa 29 12-1 4I = charley Oe! OY Il 1g 9 673 Oats Jo oa ah Os 1k Eos 18 =e peas ° ta 4 11 6 372 ~———— beans + 5 6 7g I0f 72. mame {plit peas > 6 27=—-— 2:63 19.9 84 - Mefirs Sam/fon &9 Spring, | : 1790. To Almon ManufaGurer, and Co. Dr. foe hee fe gyre. Fan. 4. To 20 blue quilts, at Oo 10 113 each 10 19 7 —24.— Qgchintz ditto I 4 9 —— II 2 9g Feb.z4. — 15 p. of fine blacko 17° 82 pp 13 5°79 Mar. 8. — 2” p. of harateen 4 16 10 130 14 6 4 ° May 1. — 19 pieces of cotton2 19 4 —— 56 7 Funetg.— 24 p. of bluelinfey 1 18 O ——— 45 12 Soe : 268 3 of July Ui, By cafh in part 200 Balance 68 -4 of BILLS of PARCELS, &c. 49. Mr Timothy Hardwareman, i Bought of Meffrs Whol th 4 “Fune 30, 1782. So seas ws ree Dad. 17 dozen penknives, at 0.7 63 per doz. 6.8 65 29 fire fhovels OFA Wey Ug alg Cae 16 dozen iron candletticks 0 -3 (14 per-dozm. 2.10 90 4 dozen handfaws - 2 Sh. O $50 08 5 dozen fine fteel {nuffers OP Obs: apiece) 4.42.6 24 —- London razors OF Bivona Ze 29 63 — Kentifh hammers OF OS Caos. 8 Tas As SAA 43 ~~ F. Greatman, E/q. To Nichclas Bricklayer, Dr. 1784. ‘ bc eS, ves sis So de 4p. 15. Yo 17 thou. bricks, at 0 18 g.athou. 15 18 9g — 4 tiles Lice WO A118. 0 — 21 hon. of lime 0:16 «4 aibunt: 17y, 2.48 ——— — i4loadoffand 0 2. FE atoad. 1 16 9 ———— — 70 days’ works 0. 4310, al dayit 3 8.4 — 70 do. foralabourer o 4 ROS a Fune 4. — 2 thovfand bricks 0 17 41 athou. 1-15 10 — 4 hun. of lime OO, capeshan gh ig 4 — 19 days works for felf and !abourer, at at 4s. 11d. a day. ° Al Dae ey 67°92.0'9 Mr Alexander Woollendraper, Bought of Mefirs Indufiry. Mduguft 1, 1784. yds. gets a ae 433 of fuperfine broad cloth, at 17 9 per yard. 38 16 62 100% of common yard-wide 4 Se 24 11 9g 72 of fine narrow q —— 26 80 <9 of fuperfine Spanifh blue 18, 6 —— 22 40 4 of {carlet - i0 6 —— g15 63 ee of fhalloon ! / i 2k eee 12 dozen of twit pudens I, 6 @ doz. 0 180 134 15 64 E BO BILLS of PARCELS, &&*. Mifs A. R. To C. Milliner, Dr. May 4th,-178 4. Ht ae fo tee 194 yards Flanders’ lace, at, I2 10 ayard. 12 13 5% 30 Ribbon, at ay 1 ak Lit $4 38 4. fans - aoe * 6 Oa pete) Te 9 farfnet hoods . : 8 11 40.33 6 pair of lamb gloves . ES ee A 77 mae ONE LE 6 8 kid ditto - 2 1 0 0 244 yards of fine muflin = - 6 10 ayard. 8 5 8% 29 8-11 The Honourable G. Ho To Lionel Silk-mercer, Dr. 1780. yds. hee 5 ERC ag | Sep. 10, To 172 red filk, at Io 2ayard 9 0. 5% — 29, — 20 broe. fatin, at 19 6 19 10° Oo O42. 4, — 14% paduafoy, at 6 9—— 416 23 — 18, — 8 taffety, at 4 2—— 13113 4 — 26, — 204) filk damafk 16 10——— «16 18 «gf — 30, — 264 luftring, at 8 2—— 10 14 44 Nov. 6,,—:197 *Perfia filk, 3 7—— 38 OF ‘—- 10,-——!292 white fatin, 7 QO-—— I! Io 63 ~~ .12, —~30 black ditto 10 4—— 15 10 0 92 14 7% Lady dun Highlife, To Henry Linendraper, Dr. 1982, °°%. rear: f FRR A Se: Mar. 6, To 173 ells of holland, at 6 4 p.eH 5 10 10 — 4oyds of Irifh linen, 6 107.7413 13 4 Apr. 19, — 27 cambrick AOy 9 Te Vor. — 6 muflin 4 3— 1 5 6 27 — 123 — diaper 2-6 2 4 “% May 1, — 60 home linen ere 8’. $.3q AY OQ 2j— 0 4 6 24. bobbin RULE OF THREE. hry Rak Rae ES i coaeeeeeannetetiieemntitl RULE. OF THREE. THIS Rule is called the Rule of three, becaufe in it there are three numbers given, to find a fourth. Ruve. Obferve that of the three given numbers, two.are fuppofed, and on the other lies a demand.* ‘The nuinber on which the demand lies, mult always be the third term in th Rating § 5 of * the other ipekeeg bee will find one of the fame kind, make it the firft, confequently. the remaining nuaiber will be the fecond, or middle term, and it is-of the fame kind with what is required. Reduce each number to its loweflt denomination, and the firft and third to the: fame name: Then confider’ whether more or lefs than the middle term be required ; if more, make the lefs extreme the divifor; if lefs, thempreater extreme, and the pro- duct of the other two terms the dividend; divide, and the quo- tient will be the anfwer in the fame name as you left your fecond number. as ; Note. The firft and lait terms are called extremes. ‘ The number the demand lies on,.may be known by the Miva how much? what will? how leng? what cof? huw many ?. what comes, &Xc. If 7ewt. colt 21/. how.much will sceeut. come to? | anf. 15! 2. If 13 yds colt 162. how much will 3gyds come to? | anf. 48, 3. How much wil! 32/2. come to, when 4/2. coft igs. anf, 91.123, 4. If 27 men can do a piece of work in 16 days, how many can do the fame in 12 days? a men. co Suppofe 4 clerks -can copy a piece of writing In 7 , hours, how many could do the fame in 18 hours? anf, 18clerks. 6. If 4 yds of cloth coft 3s. what will 24 yds colt? anf. Se. 7» How many yards of carpeting, which is 39rs. broad, will cover a room which is 3 een in breadih, and 4 yards in length? anf. 16. 8. If 8 pounds of tea cot 2/, 12s. what will 19 pounds come to! anf. Ot. 35. 04 2 UNIVERSITY OF ILLINOIS LIBRARY, 52 RULE OF THREE. Q. What will 8 pounds of tea come to, when 19 pounds colt 6/. 35. 6d. anf. 21. 125. 10. Bought 3 rounds of hops for’ 2/. 6s. 6d, what will 60 pounds come to? anf. 41. 10S. tr. If 60 pounds of hops.coft 4, 10s. how much will a pounds coll ? anf. 21. 6s. 62. 12. If 43 yards of cloth colt 57 75. 6d. how many yards may be bought for 16/. 25. 6d. anf. 12G. 13. If 42 men can perform a piece of work in 36 days, how many men will it take to finifh the fame in 6 days? @af. 252. 14. Suppofe r/Z. 4s. 8d. be paid for 8 flones of beef, how - much will 23 {tones come to? anf. 3/1. tos. 114. 15. If‘a certain number of men take 6 months to build a houfe, when they work 12 hours aday; in what time would they build it, if they work but 9 hours a day ? anf. 8 months. 16. What comes 27 pounds of filver to, at 5s. 3d. the ounce ? . anf. 85l. 15. © ¥97- How much filver will 85/. 15. buy, at 5s. 3d. the ounce? anf. 2702. 18. If rot yards of cloth coft 1/4 115. 6d. what will 27% yards come to? ‘anf. AL 3h. 3d. 1g. If 16 men inclofe a garden with a brick wall in 31% days, how many could do the fame in 72 days? anf. 7. 20. What will 34 ftones of cheefe coft, at 2/. 5s. 4¢. per. cave. anf. 19s. 10d. 21. I¥ it take 70 yards of paper, which is 2 feet 5 in. broad, to bea aroom; how many yards will it take of 1 foot 8 in. broad .» ante 1QIz 22. How many ; quills will 172 158. 4d. purchafe, at 6s. 10s. per hundred ? anf: 5200. 23. How many cwt. of beef may be bought for 18/. 10%. when one ftone coft 3s. 1d. anfvrs. 24. Elow long will I take to lay up roool at 1/ 5s. per week? anf. 15 years, 20 weeks. 25. How many yards of fhalloon, which is 3 grs. broad, will line 25 yards of cfoth, that is Sgrs broad? anf. 41%. 26. What will 39r. 3na. of tapeftry come to, at 6s, 8d. per” eli Flemith? anf. 8s. aids 27. How many yards of cloti., ‘at ns. 6d. per yard, moit be given for 72. yards, at 6s. 3¢. per yard? anf. 60. 28. If 1yd 2grs of velvet colt 14s. 6d. how many yares will 212,355. 6d. buy ? anf, A5yds. OF agge ts — RULE OF THREE. 53 29. How much is a géntleman’s eftate worth a year when he pays 500/, 15s. land-tax, at 3%. gd: per pound? anf. 26701. 135. 4d. 30, If a paftare can maintain 7 horfes, 6 weeks; how long would it maintain 35 borfes? « anf. 1% week. gt. If 1co/. gain a certain fam in 12 months, how much will it take to gain the fame in g months? - anf. 133/, 6s. 8d. 32. How much will a thip’s cargo, of 22 keels of. coals, come to, at 15s. gd. per chaldron ? anf. 1381. 125. 33. A fabric was reared by 120 men in 8 moaths ; another is required to be reared in 5 months; how many men ‘will it take ? ‘anf. 192. 34.. How long will 1 take to fpend 3o/e 155. at 10s. 3d. a week 2 anf. 60 weeks. 35. If yews. 29r.- of. tobacco colt 24/. 175.'od, what will 22cavi. Igre come to? . anf. 711. gs. Od; t-8r9r. 36. Suppofe.a perfon can perform a journey. in. 24 days, when the day.is.42 hours.tong ; how many days will he take when the day is but 7 hours long ? anf. Aly 37. A perfon owes 100c/.-but not being able to pay the whoie, he compounds with. his.creditors for ios. 6d. a pound ; how much will they receive ? anf. 525/. 38. Ifa merchant owe 1500/.and his effes amount to 7872, 1os. what will his creditors receive per pound? = anf. 10s. 6d. 3g: If the fixpenny loaf. weigh 2/2. 110%. when wheat is 6s. 44, the bufhel 5. .how.much will it weigh when wheat is 5s. 2d. the buthel ? ; anf. 31d. 40%. vizgdrs, 40. Suppofe 18 pioneers can make a treach in 7 days, how many wili it take.to do the fame in 13.day? auf... 2. 41, What will 67c4al. 17bu/h. of coals, Newcaltle meafure, come to,- 72123 .— 018 oO — 649 12 43 Ges olde aieen nO.) ale ee! (ON ee 18 ack 6. 419 — O 511 —— 124 0. 4% 97. 1417 — Q17 O —_—— 120412. 447 8.17465, — 1 2 6 Se 1964 6 10% 9. 4264 — 4 8 —— 1891. 8... Ua= 80: 344yy — O's 4d Tarot n 92. 3 3% Ile 1574, —.0. 0 6 ——. Ce ei fe 12. 71485 -—-~ 0 © If ———. 4413. 64 13. (617% °— 2:17 .'6 or 1157 58-28 Leo 207 e ope 2.53,1 4 a 470 12 0 Case 8. When the quantity confifts of feveral denominations. Ruie.—Multiply the price by the number of integers, if they be lefs than 157, but if greater, find their value by the former cafes; and for the other denomination of the quantity, take even parts of the price of the integer, or of each other, and add them to the value of the integral part for the anfwer. Note. ‘To know which are the integers, obferve, when the price is at fo much per cevt. then the number of cats. in the quantity are integers; vhen at fo much per yard, the yards are integers; when at fo much’ per ounce, the ounces are integers, kc. yds, gr. nae fue de Lee Le DEORE 00 athe 019 per yara 12) 2 40% Bel ve Oubide 13> meee IO a 2 t2 ce 2. oO 3 22 — 48 © 16 3% 4 2119) 3 0 meng TTS Go og ae PRACTICE, 61 yds. qr. na Se ade Si ele So OTE a 2. at 9 7 per yd. 294.10 1% gal. gt, pr 6. Pah sie ee S- 3 6 per gal O15 33 7s 7 2 0 -=—— gris Lio. 7s ey To SF ie 2 62% 2S 5 OF QQ. 18-39 OF 9.752 al 2A 1Q PAL 10. O° 3 Fo — 2 4 -_————— O°, 2. oe II. oO 1 14 — i Ore Bur ores gr. buf. p. ZL: 12. rR Bak Pte er i her or. TA 215 wh 13. 2 aR A ae sa a et ee 14. PR UN re ie ae Ey O 14 Cry ee 6.32 — 0 6 4° per bufh Ya 16. OO at OF ge 1 8 44 17. See ig see Oe ——— O F405 .O-. 0%, dwt. gr. 18. 715 O — O § 22 per ox a Orn ay 19. 4 612. — o4 73 12,0, De 20. Oo1917 — Oo 41t —— QO. 4.1074 ft. Mb ae ces 21, 08 It). 7 “at 3 11. per flone vere Poe acs 1 em or. lib, est. de 3 e256) SAE SO) mo FO USO per cwt Liz” 8 "38 Bee 7s TAO oe ed Oe o. 9% 24. 18014 — O17 65 Pas i 3G 25. 9218 — OI14T! —— ye ea 26. 189 2 7 — 0 5108 ———— 1 Ae oe oy 27. 217 2 108 — O19 :0 a 200: 14 3% 28. 90 290 S$. 40%2 29 —_—— 29 17 114 29. 0318 —10 6 4 ee 9° 7 104 30. o1r2z2ii— 4 6 7 an 118 23 Ca $5.19. When the given quantity is not of the fame name with the integer whofe price is given. Rurs.—Reduce it to the fame name, then, if it be below 157, find its value by compound multiplication ; but if above, by prac- tice. : : F TARE and TRET. $e the | Lobatse i7bhds, wine, at 7 2 per gal. 383 15 6 34.— of beer, London . meafure - 1.1 TOS Fee mcwt. 7 vind at 2 93 ine 31 7 O ¥4 —— Of tiax, at 9 er fione 37 1 Oo 65 tons of tallow, at yee A 381 6 8 ocwt. of beef, at aia Io 10 O 2oanc. brandy, at Ir 6 per gal. Pry OO 6pun. rum, at 190.9 270 18 Oo. : Cold. of tea, at ~ O95. per 0%. 30 0 O y, 8 ftones of bacon, at 0 5% © per Ib. rae Be Uy, of foap, at o Gt —— 6 3114 19 gallons of gin, at 2 si per quart 9 610 4 lafts of wheat, at 10 6 _ per boll. $4..0,.'O 7 thoufand quills, at 2 9 per hundred G12 a. 21 reams of paper, at I 3. per quire BO Ie i iakee 25 fodders of lead, at 5 6 per quarter 536 5 © 16/2. of cloves, at ~ 1.3), perez. iGo 9 17 chaldrons of coals, t : (Newcaftle meafure. ) a 1 a heh dag: =} 5 i 27doz. of candles, at oO 64 per ib. 815 6 6 lafts of barley, at 3 4 ~~ per bufh. $0 0 Oo x9 flones of leather, at o 10% per lb Il 12 9 160 lafts of wheat, at ro rid per doll. 3287 10..0 “8doz. pair of gloves, at 1 5 per pair 616 0 tcwt, of tea, at 4 54 -per bb. MG FE i ENS | ‘TARE and ‘TRET. bw ROSS weight of goods, _ is the weight both of the com- (S modity and of the cheft, hogfhead, barrel, &c. in which they are contained. Tare is an allowance made by the king to the importer, or by. the feller ta the buyer, for the weight of the cheit, hogthead, barrel, bag, &c. in which the goods are packed. ; Tet is an allowance of al. on 10476, or an abatement of the 26th: pare of what remains after the tare is taken from the grofs, on goods fubject to watte. Cloff is an allowance of 2/8, for 3cwt. mae to the retailer, to make the weight hold out. - TARE and TRET. 63 Neat weight is what remains after all the required deductions are made. Suttle is what renvains after the tare is takea from the grofs, when there are more dedudtions to be made. Note. Tare of feveral goods is regulated by the book of rates; and fometimes the cheft, hogfhead, &c. is weighed before the goods are packed, and their weight inierted in the invoice along with the grofs. Case 1 When the allowance is only made for tare. Rure.—Subtraét the whole tare fromthe whole grofs; and the difference will be the neat. weight. When: the tare is at fo much per cheft, hogthead, &c. multi- ply the tare of one cheft, &c¢. by the number of cheits, hogfheads, é&c. and the product will be the whole tare. When the tare is at fo much per.cwt. take even parts out of the whole grofs, as.in practice. . = 1. Suppofe 3gr. 17%. tares to be allowed on 27cw#. i al grofs, what will be the neat. weight? : anf. 26ew#. igr. 1140: 2. Grofs 100cw#. tare 2¢wt. 17d. how much neat weight? anf. o7ewt. 3gr. tilb. 3. What is the neat weight of 1obhds. of fugar, weighing ia all 130cq#. grofs, tare at 2gr. 16/0. per hogfhead ? anf, 123cwt. 2gr. Blb. 4. What is the neat weight of 21 hogfheads of tobacco, each weighing r3cwd. 1gr. 20/0. grofs, tare on the whole 12cce. 1¢r. anf, 269gcwt. 2gr. 5. What is the neat weight of five barreis of Indigo, weighing 2s follows... . ewt. grb. Ib. No. 1. 4 4 13 tare 18 — 2. 2317 — 16 TAS e Cae Rr ect e — 4 21 2 — 14 — 5 § 327 -—- 20 Seat: Gohes — gr. lb 18 3. 7 grofs. 85e3. 1 ; 6.3 1 fare 158 0 6 neat. 64 TARE and TRET. 6. Bought 20 bales of Smyrna filk, each bale weighing 2cw. -agr. 17/6. grols, tare at 16/). per bale, how much neat weight ? anf. 45cwt. ogr. z0lb. 4, What is the neat weight of 74cw?. zgr. 12/2. grofs, tare at 14/d. per cwt. anf. Oscwt. 1gr. 35/0. 8. How much neat will there be in four bags of hops, weigh- ing as under, at 44/). per cat. for tare? ‘ cwt, gr. lb, No. 1. 7.1 18 — 2. 4 3 20 ee Be Oe Sy | —4 7 2.0 anf. 25cwt. tgr. O16. 9, In 5 cafks of oil, weighing 30cwt. ogr. 173/b. grofs, how many gallons, allowing 18/2. per cavé. for tare? anf. 378. CASE 2. When tare and tret; or when tare, tret, and cloff are allowed, to. find the neat weight. -Rure.—When tare and tret are allowed, divide the futtle by 26, and fubtraé the quotient from it, the difference will be the reat weight. When tare, tret, and cloff are allowed, divide the difference between the tret and the futtle by 168, fubtract the quotient from that difference, and the remainder will be the neat weight. 1. What is the neat weight of 1gewt. 1gr. 14/6. when 18%. ‘per ew?. is allowed for tare, and 4/b. per ro4Jb, for tret? anf. 1scwt. 2gr. 15706. 2. A merchant bought 4 cafks of oil, which weighed 3cwé. rgr. 19/b. grofs per cafk, tare at 1654/8. per ‘cat. tret 4/b. per FO4/b. cloff 2/8. per 3cwt. how many neat gallons were in the whole ? anf. 166-3; 3. Required the neat weight of 4 hogfheads of fugar, weigh- ing as follows? : ewt.gr. 1b. Not, 2) 2°) 290 Tare at r2/b. per cw#. tret at — 2. 8 2 14 4/0. per 104/d. and cloff 2/4. per — 3. 10 (0 Of 3cwt. — 4. 6 27 anf. Taee. 2gr. 181d. 3 4. Grofs 43cwt. agr. ahd tare 2cwt. 2gr. 17/b. tret and cloff as ufual, how much neat ? anf. 39cwt. ogr. 21ilb BILLS of PARCELS and BOOK-DEBTS. - 65 5. A merchant bought 6 hogfheads of fugar, whofe weight is. below, how much will they coft, at 2/. 2s. the neat czw/. cet. gr. Ib No.1 PIB PUTS tare 2gr. 27/6. each. — 2 Onvgy 2 See ek: ~— 4. 8-0. 17 oie 6 3 94 — 6. 2B £6 anf. 861. 133.' 3a. 6. Bought 8 bags’ of cotton, each bag ‘weighing 3cw?r. orgr. lb. grofs, tare at 174/b. per be ‘what/ will they come to, at rs. 34d. per 1b. anf. 182i. 128. 10d. “BIL LS of PARCELS , ts. BOOK-DEBTS. Mr Dick, Corn-monger, , Kinga a gf ata dd 0 George Farmer,” Dr. 1784... gr bub, hs, ad. oni ed Fune 20, To 15 7 of wheat, att 10 4 per gr. 24 1 6 Fuly 16, — 20 34 of oats, - 0 19 10 BOM gag buf. pe. 27, — 27 3 of peafe,- 0 4 1201p. bu. §°14 54 Aug. 6, — 4 24 of tare, - 0 2 14 Oo 9 8 19,— 724%. of hops, - o 2 4h per ld. 8 12 gh SO. 3) 94 “The Right Honourable Earl of M— Sn ee Robert ‘Jeeller, Dr. 1784. 7 ee é. d. Mar. 16, To a large filver ‘cup; wjetstl Ayox. a a atin ! 7 16dwts. at 7s. 6d. per ounce. / 17. 18 6 May 19, —- a punch-bowl, weight 1602, > | 17dwts. 12grs. at.6s. 104d. p. 6z. ive ey June ~ 6, —. 3 dozen iilyer fpoons, wt. 300%. 9S 1). 18dwis. at 7s. 2d. per ounce © ° Ee ETS g —~— 23, —4 large candlelticks, wt. 510%. a4, 4 4é¢wis. Ogrs. at 7s. $d. per oz. 18.19 93 “F3 66 BILLS of PARCEES and BOOK-DEBTS! Aug. 17, ead gold plate, wt. 1002, t gibets. 1g Ser. at 57. 145. Od. per oz. “61 9 BE: — — 10 filyer plates, weight. 670%. 13dwts. at 6s. 7d. per ounce oy Mil fis : 13711 13 Mr Fohn Grocer, | ae Bought of Aferchant and Co. May 18, 17843. Le ac di 4 hogfheads of fugar, weight 43cwt. 29r.. EGibss ; | : at 2/. 165; 4d. per cae. 122.18. 65. 6 chefts of tea, weight gcwt. 2gr. 14/0. at a 2 29/. 6s. per cwt. 282: 07° 3 19 barrels of raifins, weight 3ocw#: tgre7lbs 7 at 1/, 198. 10d. per cw. ; GO. 9.05 oe 7 pockets of hops, weight 32¢ws 2gr. at | 6/. 145. gd. per cwt... 218 19 45 Pepper 1cw#t. 2gr. 18/b. at 4s. rid. per lb. 18. 4 3 Cloves 3gr. 14/b. at 4s. od. per Ib. 5 wh eee *) 3 hogfheads of tobacco, weight 34cwt. 1gr. 16/0. , at 3/175. 10d. per cw. 133 16 ro3. Soap, 4cw#. 2gr. 19/b, at 21. 115. 8d. perce = 12 EB March, 16; 1784. fr John Newcaftle, Bought of Robert Cheefemonger and Cos: ro Chefhire cheefes, wt. 3cw#. 2gr. 17/5, Lis. at 2/. 19s. 10d. per ewe, - 10 318 5% 4°Glocefter cheefes, weight 1cwt. 39r- 14/b. 7 at al, Fos. 6a. per cwt. 3 6 62 12 Suffolk cheefes, weight 4cw2. 16/d, at 125. 7id, per cwt. patch 8 bk ty 27 Yorkthire cheefes, weight me ae 2008. Wis at.1/. 135. Od. per cwt. ¥E § 4% 13 Firkins of butter, at 1/. 125, 6d: a firkin, ‘2h 2.6 1 Flitches of bacon, wesieht 30f; 32/5. at §s. Sd. aftone se. He 8 14 93 Sir Charles Loveliquor, Fulys 6 2784: 6 dozen of red jport,.at 14% gallons of madeira, at 1 pipe of clares 17 gallons of canary 1% hogthead of lifbon 6 anchors of brandy 2% puncheons of ram Mr Fohn Innkeeper; April ro, 1784. Av leg of mutton, weight’ A fore-chain of pork. A firloin of besk A hind qr. of veat: AP round of beef Beef-fteaks AY quarter of lamb: Madam Lovely, beg Box BILES' of PARCELS. aid’ BOOK:DEBTS. 67 Bought of Fobn Redport. Re A 6 18 6 a@ dozen. Saths O Io 9 agallon. 7-15 108 8 10 ESS Gi 0 a) 2 6.14 e. Fz 9: Poem 5 ae O83 12-4 20 GO 234 15 84 eh of George Butchers lb. Zoned, »142"at o a POND Oh, Fe roZ ato 43 O. 44 1s voxiat 3 11 perf o.3g BE ig ato 33 perlb. O 5.114 (Orato 4 Le t60 8 7 ao 4us—— 0 2 4 2 ato 6 ——— o 6.6 219 9% eG To al bts Canton, Dr. Lon OE Bes, ak ° 1784. : ! Feb. 17, To 4 fets of china, ati 2 14° 9 each Fo rg —— 27, —- 24 dozen plates on ey 617 Mar. 9, — 14 ‘coffee Cups © 10 6 pidot..o 12 3 o—— 27, — 6 curious difhes O¥2 ath ‘3 ¥F5--6 pr. 9, — 7 large punch bowls o 4 10 May 4: By cath in part 6? BILLS of PARCELS asd BOOK-DEBTS. Newcaftle upon v yn, Fuly 26; 1784. Mr Fohn Merchant, Bought of Fobnflon &F Co. 7 hogfheads of Jamaica clay weighing as under, what will they coft, when 18/. per cat. is allowed for tare, at 4/. 1s. 6d. per neat cwe. cwt. gr. lb. No. 1. weighed 6 1 14 — 2. a°53 °C — 3. 7 O18" — 4. “mS 2 («6 - — 5. eS 1 20 CG: 6's 26 sgn | For: si Ve 1. Oprofs.- 3-0. san orneie ' ! seis — PaCR rs 43. 0: o._ 6neat at4al. 1s. dag per cut, 175 9.4% - Leeds, Feb. 14,1794. Mr George Andrew, ‘Bought of Mefirs Leck F Robfon. ieces. yds.) $. ih sy te be 6 broad cloth, each 46 atts 9 « peryd. *%:.217 9,..0 4 narrow {57 at’ 5 97% 64) 21-6 2‘Scarlet ~ 21at1I9 6 —— 40.19. 0 7 Flannel 25 at £24 ae 10 11 5% 5 Velveteen Iz7at 36 —— 14,17 6 9 Prince’s Stuff 16at 4 25 —— 30 6 Oo 2 Buckram gat o 8 ——— — 12 9 378 16 2% Dublin, May 14, 1794. _ Mr eer Lee ‘Bought of Mr Fohn Smith, 8 pieces of Lrith Linen, Viz. yds. Gt. 1a. fo he Ee No.1, 4653, 2 at 4 9 per yard, Wigs EAE shale? — 2, 17 0 3 at 5 O 45 ts — 3. 29 2.0 at 3 105 *; 14 3% ceils be RR Ar eae Ve SEE 6 4% —i5. -18 2 1 at 4 38 _——— i oO oa — 6 30 3 3 at 4 2 eee 6 8 103 we Je. 43 +F 2 at 4 8 ee Io 4 az ‘by at. 309 een meaner 10 16 rt — 8. 60 -63 18 6% PROMISCUOUS QUESTIONS, 69 Lancafter, March 16, 1795. Obadiah Kay, Bought of Grievfon &F Co, pieces. yds. by di eek Salt Ge 50. German ferge, each. 19} at 2. 13+ peryd.. 102 § 3% 243 Shalloon 27 atr 48 460 12.9 27 Printed cotton 25 at2 4 ——— 80 If 5% 61. Camblet | 3t ati 10h —— 177. 5 74 4 Bombazeen 362 at3 65 —— 2619-2 294 Scotch linen 24 atl 64 —— 55 — 9 17, Irifh ditto 34 at 2 1 ame 69 42 547 17 13 Cer ‘London, Yanuary 16, 1795. Fames M’ Lean, To Fobn Clarkfon, Dr. ees Fave, Yan. 14. To 17% pieces Holland, each 35yds: Oa oie at 25..75d. per ell Z, Mar. 19. To 29% pieces of tapeftry, each 1O4 yds. at 4s. 10d. per ell £7, May 4 To 12 pieces holland, each 293 yds. i at i 1d. per ell LE. 44 7 Fune 7. To 14 pieces of tapeftry, each 21 yds. bag hE at 3s. 2d. per ell £7. Aug. 17. To 21 pieces Irif linen, each 244 yds. at 25. 114d, per yd. ; 7 Ne 141 19 10% Se ee 399 7 9% Dec. 4. By cath * 300 O 0 Balance 90 7 9% enemas dd promifeuous Colledion of Oisfidae; to exercife the foregoing: Rules. 1. How long would it-take to-count-four hundred’ millions. of guineas, fuppofing 100 to be counted in a minute, 10 hours per day, and the year to confit. of 365 days? anf. 18years, 96days, 6ho. 4.0mins. - 90 PROMISCUOUS QUESTIONS. 2..Sixty hogfheads of beer, London meafure; were ordered to - be put int 30 wine-pipes; but upon trial it was. found that the Wine-pipes would not hold the beer; how many-ale gallons mutt the cafk hold that contains the difference? anf.'143gal. 23379ts. . 3. What is the futh and difference of fix dozen of dozens, and half a dozen of dozens? atf..Sam 936. difference .792%-. - 4+ A’ merchant bought 242 yards-of broad cloth, for 2014. 125. 8d. he paid 13s. 4d. per. yard for. 86 yards of it; how much did he pay per yard for the reft? anf. 18s. 6d. g.. A’ regiment of foldiers,- confilling of 1000 men, is to have - new coats, cach ty. 2grs..of 6 quarters wide, and they are to be lined with ihalloon that is yard-wide ; how many yards will it take to. make-the coats,.and how many to line them ? - anf. 1500yds, to make the coats, and 2250yds. to line them. . 6: A gentleman’ has’2 dozen table fpoons, each zox.. 14devt. three .dozen;tea-fpoons, each 14dwit. 12gr. four. cups, each 130z. 17dwise two:tankards, each’ 2302. 13dwts. how much is the weight of the whole? - anf. 16/b. 10%. 12dwts. 7« Suppofe 69333 dozen pair of flockings to be purchafed~at i/, 10%. pet degen, and the-expence of exporting them to d.ffer- ent countries to'be\2993/. 5s, OW» required the colt, and how . much would bé gained by felling them, on an average, at 2+. Ofd. per pair? anf, colt 1039991 tos. gained 1000c% 8. A butcher buys an ox for, 10/, 16s. and after feeding him with 24 pecks of oats, at 18s. per \quarter, and 20 truffles of hay, at is. 4d. per trufs, flaughters him, and fells the beef, being-40 ftones, at 5id. per 1b 6 Stones of tallow, at 7d, per (0. and the hide for 17. 5s. required his gain or lofs ? ; anf. 3/: Vas. 6d. gain, 9. An-ordinary of too men drunk z0/. worth of wine, at 2s: 6a. per bottle’; how many men, at the fame rate of drink- . ‘ing, will 7/. ferve, when’ wine is-1s. gd. per bottle? ¥s ik anf. 50 men. . 10. What will #30 loads of potatoes come to, at 6s. od. per load ; and how much will they weigh, each load being 14.7. ol. anf, price 4.3/. 175. 6d. weight I1tom, 17cwh Z3gr. 22/6. . 11. How many ells Englifh are there in 146 ells Scotch ? , : anf. 1205546 12, A thip of war, havirig on* board. 178° feamen, befides officers, 100k a prize, whofe cargo confifted of 71 bags of cot- ton, worth rol. 14s. per bag, 4c barrels’ of {picery, worth 50/, 16s. 6d, per batrei, 157 yards of cloth, worth 1/. 35. 3d. per . PROMISCUOUS QUESTIONS. a8 yard, and feveral other .articles to, the value. of 148/. 18s. od. what will each man receive, after the officers have deducted one-fifth of the whole for their thare ? anf. 14ly xs. 4rd, 13. How mach will 112-bolls. of wheat come to, .at 115. 9d, per boll,.and how much will they weigh, when one boll weighs of. 7b. anf. price O5/, 165. weight Ofop,..13cwt. 14. How many Scotch pints are there in 174 gallons Eng- lith meafure ? anf. ABT zs. 15. A perfon purchafed a floop’s cargo of potatoes, at 5s. 8d, per load; the floop’s burden was 75 tons,.and the. load weigh- ed 14/7. 10/6. required the price and number of loads ? anf. price 2311.15. 4d. 145o5gr- number of, loads 81535%- 16. Suppofe.a perfon purchafe 500 turkies, for. 125 guineas, and fells 40\.0f them for 5s. gd. each, 60 at 6s..2d.. 150 at 6s. gd. and. the remainder, at 7s. 6d.. each, how, much would he. gain? anf. 431.25. 6d. 17. Required the price and weight of 129 quarters:of wheat, each weighing 4cevt. 2gr. 121). at-1/. Los. 4d. per quarter? anf.. price 1951. 138. weight 2gtons. 14cwt.. rgr. 8b, 18. Bought 6 facks of flour, at 2/ 5s. per fick y required the price of the whole, and the rate per {tone ? anf. price 13/. 0s. rate per ftone 25. 3d. 19. Required .the. tonnage of a fhip that carries 110 lafts of wheat, fuppofing the bufhel to weigh 44 ftones ; and what will be.the price, at'7s..4d. per boll ? anf. tonnage 2612, price 1613/. 6s. 8d, _,20. The Roman emperor Albinus had fo voracious an appetite, that he fometimes devoured for his breakfaft 500 figs, 100 peach- es, 10 melons, 20/b. of grapes, 100 {mall birds, and 400 oyfters; what would fuch a breakfaft coft, valuing the'figs at 23d. the peaches at 53d and the melons at, 4s., 93d. :each,..the grapes;. at 1s. 114d. per./b. the birds, at 63d, each,: and the.oyfters at.3.a penny? anf..14l. 165. 33d, 21. Seppofe four fir-loins of beef to. weigh .282/b. 3723/6... 4545/6. 563/. and to be purchafed at 3s. 44d.. per ftone.of| 8/2. how much would-be gained, by felling them at 74d. per Jd. | anf... 17s, 74d: 22. Suppofe, a fheep, weighing 19% fones of »8/b. was bought of acarcafe butcher, at 3s. 22d. per ftone, and.retailed)at. 5d. per /b, what would be gained by the fale? And if, the. purchafer fold two fuch theep every working day, throughout the year, what would his gain be at the expiration of that period ? 42 PROMISCUOUS QUESTIONS. anf, 115. 93d. gained by one fheep : and 360/. 1+. 7d. by the annual fale. 23. Twenty-fix wedges of gold, weighing in all 34/5. 302. 1idwts. 14grs. were brought to the mint to be coined into gui- - neas; required the weight of each wedge, admitting them equal, and how many guineas may be made out of the whole, fuppofing an ounce of gold will make 33 guineas? anf. weight of each wedge, 1/b. 302. 16dwis. 147%;975. and 154322 guineas. 24. In 57 guineas, 33 half-guineas, and 48 moidores, how. many pounds ? anf. 1411. 195. Gd. 25. Suppofe the fea allowance for the common men to be 5/2. of beef, and 3/b. of bifcuit per day for a mefs of four people, and that the price of the beef be to the king 24d per Jb. and of the bifcuit 14d. per 7d. fuch was the fhip’s company, that their beef coft the government 12 guineas per day, what did it coft per week for bread ? anf. 351, 5s. 7d. OF43 qr 26. A perfon laid out 100/. upon ferges and fhalloons, the value of the fhalloons was 6o/. and the quantity of ferge 236 yards; and for every two yards of ferge there were three of fhalloon ; how many yards of faalloon were there, and what was the value Sd each per yard? anf. 354yds. fhalloon—Serge 35. 4d. 255-59rs. per yard—Shalloon, 3s. 4d. 23249rs. per yard. Ww hen it is required to have an equal number of pieces, vane . &c. in any given quantity— Add the feveral pieces, parcels, &c. into one fum, bring this fum and the given quantity to the fame name; then divide the one by other, and the quotient will be the anfwer. 27. How many pieces of 132d. 12d. od. 6d. and 4d. and of each an equal number, can be made out of an ingot of filver, value 14.7. 19s. 3d. anf. 798. 28. How many parcels of 14/b, 1216. 8/b. 6/8. and 2/b. can be made out of gcewt. 14/b. anf. 11. 29. How many bowls, each 2/3. 80%. tankards, each 1/b. Goze. — falts and’ pepper boxes, each soz. 5dwts. and {poons, each 1oz. 18dwts. and of each an equal number, may be made out of 16 | ingots of filver, each 2/b. 7oz. 4dwts. anf. 8. 30. How many guineas, crowns, half. “crowns, fhillings, and | pence, and of each an equal number, are there in 1990/. 16s. $d, anf 1352. PROMISCUOUS QUESTIONS. 73 31. How miany guineas, half-puineas, crowns, half-crowns, ie {ixpences, and threepences are there in 999998/. 175. an]. 490797. 32. In 364% yards of cambrick, how many handkerchiets, each 2 of a yard, 1 yard, 1} yard, and 1% yard, and of each an equal number ? anf, 81. 33. In 50 pieces of diaper, each containing 20yds 2gr. how many parcels of 5 ells Englifh, 6 ells French, and 7 eils Fle- mifh, and of each an equal number ? anf. 50, 34. A butcher goes to Smithfield-market with 116/. 14s, and buys cattle at the following prices, viz. oxen at 10/, cows at ol. calves at 1/. 108, and-fheep at 19s. each, and of each the fame number; how many of each fort ? anf. 6. 35. It is faid that 50,000 firkins of butter are yearly fent to London from Cambridge and Suffolk, fuppofing this quantity to be purchafed at 7d. per /b. and the expence for carrying it 1f¢, per 2b. how much would be pained per cent, and how much upon tiie whole, if it were fold at “Léndd, at 11d, per 1b. anf. 251. 148. 3d. 14gr. gain per cent.—26250/. gain upon the whole. 36. If 1728 wine plaffes were bought for 65/25. how much muft they be fold for per dozen'to gain 10 guineas on the whole ? anf. tos. 6d, 37. Bought 12 facks of flour for 27/. how much did they colt per ftone, and what mult they be fold for to pain 3/. upon the whole ? anf. coft 2s. 3d.—muft be fold for 2. 6d. 38. A merchant bought at Oporto, 46 tons of wine, for 579/. 12s. the freight colt 46/ the loading and unloading 6/, cuftoms 10/. charge of the cellar 4/7, how much mutt he fell it per ton to gain360/, by the bargain? anf. 21/. 179: 2d. 2320rs, 39. Suppofe a glover fhould purchafe 50 dozen of gloves, at 185. 6d. per dozen, how mutt he fell them per pair to gain 20/. per cent. anf. 15. 107d. 40. If 50 pieces of flannel, each containing 48yds, were pur- chafed in London, at 2s. 2d per yard, and the fhipping of them to America coft 10/, 10s. befides 12/. per cent for infurance ; how muft they be fold per yard to gain 25/. per cent? anf. 35. 1d. 2424ars. 41. A quill merchant bought 20 thoufand quills, at gs. per thovfand, he paid three fhillings per thoufand for having them drefied, and 4s. 6d. per thoufand for having them made into G 14 PROMISCUOUS QUESTIONS. pens ; how miuft he fell them per hundred to gain 8/. 10+. anf. 2s. 6d. 42. If 2 hogtheads of perry, wine-meafure, were bought for 10/. 10s. and bottled off into quart bottles, how mutt they be fold per dozen to gain 3/. 135. 6d, anf. 6s. Od. 43. Bought a quantity of cloth, for 412/. tos. 85 yards of which being damaged, were fold at 15s. per yard, by which rieans 6/. 7s. 6d. was loft; required the quantity bought, and how much per yard the undamaged part muft be fold for to gain 174, 16s. 8d. upon the whole? anf. Quantity bought roopds—175. 8d. per yard undamaged part. 44. A contragtor agrees to fupply a thip (whofe crew con- filts of the captain, 8 officers, and 160 failors) with provifions, on condition that he receives 15s. per month of 28 days, for each failor, three times as much for each officer, and fix times as much for the captain. He provides 35 barrels of beef, at 35s. 6d.—16 of pork, at 525.—8ton, 1 5icwt. of bread, at 255. per cwt.—82 bufhels of peas, at 5s.—26cwt. 2gr. 21/b. of cheefe, at 30s.—18cw?t. 3gr. 16/b. of butter, at 3/, 145. 8d.— 25% quarters of meal, at 19s. 8d.— 8cw#. of fifh, at 26s.—and cther {ma!] charges to the amount of 1/, 75. 33d. at the return of the fhip he finds his profit to be 1857. 15s. 5d. how long was _ tue voyage ? anf. gmonths, 2\days. 45. The rent of a certain fifhery is 360/. the tenant of it em- ploys 8 men, at 10d. per day, and an overfeer at double that fum; the filhermen -have alfo 3 of the fith caught during the — feafon: The fithing continues 249 working days, and they catch, on an average, 250 fifh in 8 days, weighing one with another 8/5. The expence for boats and nets is 6o/. the fifh are packed in barrels containing 300/b. each, price of the barrels 2s. 64. a piece, falt 1s. 6d. per barrel; required how they muft be fold per barrel that the tenant may gain one fifth of what they are — fold for ? anf. 41. 3s. 10d. 2449rse 46. A privateer, whofe crew confilted of the captain, firlt and fecond mates, a furgeon, carpenter, 52 failors, and 42 ma=_ rines, took a prize worth 312352/. of which, according to agreement, the proprietors are to have 73; the captain is to have g fhares ;. the firft mate, furgeon, and carpenter, 64 fhares each ; the fecond mate 5 fhares; each failor 12 fhare ; each marine $ of a fhare ; how much wil! each receive? — anf. Captain’s fhare, 699/. 6s.—Firft mate’s, &c. 492/. 25.—Second mate’s, 388/. t0s.—LEach failor’s 97/. 2s. 6¢.—~LEach marine’s 66/, 125. VULGAR FRACTIONS. 47. A, B, and C, open an account with a banker, 11 Jan. 1797, and put into his hands’as follows, viz. A 172 175. B 34/. 115. 6d. C 28/. 18s. 10d. on the 21{t A draws 9/. Io.. and C advanced 12/. 5s. the 24th, B called for 6/. ros. the 30th, C wanted 19/. 8s. 4d. February the 12th, B depofited 12/. 13s. and three moidores ; the rgth, A fent for 5/ anda noble ; but on the 24th returned 42/. March 2d. C paid in 20 guineas, and B drew 6 guineas; the 14th, B fent in 17), 8s. 8d. the i7th, A drew 12/ 2s. 6d. on the 10th, they fent for five guineas each; the 14th, they returned that fum and ro marks a piece more ; how much did their-banker owe them jointly and feparately in March 25th? arf. To A 39h 115, 2d. to B 62/. 115. 6d. and to C 49/. 85. 10d. Jointly 15rd. 11s. 2d. ; cee me VULGAR FRACTIONS. . DEFINITIONS,» fe Fraction, or. broken number, is one part of more. of an integer: and is exprefled by a number above and another below a line drawn between them; Thus, 4. The number below the line is called the denominator, be- caufe it denomipates, or fhews, into how many paris the integer is divided ; and the number above is called the numerator, be- caufe it numerates, or fhews, how many of thefe parts the frac- tion contains. The sumerator and denominator are called the terms of the fraction. 2. There are two kinds of vulgar fractions, fimple and com- pound. 3- A fimple fra@ion confifts of a numerator and a denomi- nator, as 3, and is divided into two forts, proper.and improper. 4. A proper fraction is when the numerator is lefs than the denominator, as $. - 5. An improper fraftion is when the numerator is either - equal to, or greater than the denominator, as 4, or +t. 6. A compound fraction confifts of two. cr more. fraétions joined together by the word of, as, 7 of 3 of 4. 7- 4 mix@oumber confifts of a whole number and a fimple fraftion, as 9 #.. G2 16 REDUCTION of VULGAR FRACTIONS. When the numerator is equal to the denominator, the fraftion, is equal to the mteger ; thus, gal. And when the numerator is greater thas the denominator, the fraction is greater than the integer, as === 14. Note, lf the numerator and denominator of a fraction be either multiplied or divided by the fame number, the product or quo- tient will be a new fraction, equal in value to the former : Thus, Yn 2=%, OF aX 3=25%) all of which, have the fame. value, = Wegeenttsa prmmatas: Gi 7 z= $>To° REDUCTION of VULGAR FRACTIONS. Casein 'To reduce fraétions fo their leaft terms. Ruie.—Dhiyide the greater term by the lefs, and that, divifor by the remainder, the next divifor by the next remainder, and fo on- reba dividing the next divifor by the next remainder, till nothing remains; the laft divifor is the greateft common meafure 5 by which divide the terms of the fraction for the atlwer. Reduce to their leaft terms. WNO DH 2 anf. anf. an 379 42 315 3 832 A qt Penne heali nel Bie cept ee Ht ‘ 2:67 9 bit, & = ra 5 ao E mo Te eet > 22 | 4. 497 aOT O.. AGO 20 Crais § 42: To reduce fraétions to lefs terms. Rurs— When the terms cf the fraction end with 5 oro, divide by 5; when with an even number Or a-cypher, divide by 23 when there are cyphers at the end of each, cut off as many as are common to both ; and when any number will divide both numerator and denominator, without a remainder, divide them by it. J 4 " r, “Reduce > 242] 5. ‘Reduce aa68 g. Reduce 4722 2 $4 0 6 5 10 478 & 700 e Keyes e ae oR 235 67.2 40 18 3o———- 50, oo rey Vi Ts : R25 46 2 Ay omens | BE By a ee [By len i\ ] + i j | i -_ iy p == cena RP a { Nal) Oe 4 REDUCTION of VULGAR FRACTIONS... 77 C 4-3-8?) 3, | To reduce improper fractions to their proper parts. Rute—Divide the numerator by the: denominator, the quo- tient will be the whole number, the remainder, if any, a numer- atur, to the divifor a denominator: annex this fraction to the whole number. Reduce to their proper parts. ) » 8 iy q fog StL! a > 102457 | 7: 3 ene at 2. 14 = 8 5. 3 ed 1 3 8. es i I 2a 8 HE) it 178 7 2.073 159 $i er OFT [Ke tt del Ds Ge. gap ertia Soa x | Case: 4. To reduce mixt numbers to fimple fractions. Rurs.—Multiply the whole number by the denominator, to which add the numerator; this fum placed over the denominator will form the. fraction required. A whole number is.reduced to the form of a fradtion by. put- ting 1 for-its denominator. Reduce to fimple fractions. anf. anf. anf, 67 A 25 3 3135 t. 67 - A Das GE 0 -* @ [Te Sate Uae 2. 4g sd > Se ie = mM & 1Gy'g be ae 19 rm 3 x : 319 Reet sa Fp OMT PS) ie Bil DeeBlOse.c7) 28 * Case 5. To reduce a whole number to a fracticn of a given deno-: minator. Ruie,—Multiply the whole number by the given denominator, and the product will be the numerator to the fame denominator. i. Reduce 3 toa fraction haying 5 for its denominator. anfrs. 2, Reduce 11 to a fraction having 9 for its denominator. anf. °. 3.. Reduce 27 to a-fraction having 14 for its denominator. a 378 G3 anf. ree - 78 REDUCTION of VULGAR FRACTIONS. C4“ sg 6 To reduce compound -fractions to fimple ones. Ruvr.—Reduce whole or mixt numbers to: fimple fraétions ; - and if the fame number be in both numerator and denominator; omit them, alfo divide thofe numerators and denominators which are. divifible: by. one another,. or by. the fame number*’; then multiply all the numerators together for a numerator, and all the denominators for a denominator of the fimple fraction required. Reduce to fimple fractions. Gnf. ah} e be Sof fF Ob gio ed ba FR of 2) of pee: aR 2: a eee eye we Lite) Ok BR OF By ire ee gu. OF Pore for + SoS? of 2.) ob a sof ro ts* Ae ie OR OE ON a Rdg. 68 vdhogs OF Te. ie Ae? Ses vy 0f Soft. 5 of 8... 3 bre. 2 ofS of 2208s 2 * As the cancelling or abbreviating of numbers is of very preat wfe where multiplication or divifion of fraGtions is concerned, the following is given as-an example how.to proceed in. fucir cafes. Draw a line through the two fixes becaufe they are equal ; alfo draw a line through the 1o°and the 5, becaufe they divide one another without a remainder, and fet the quotient 2 above the 10; for the fame reafon draw a line ‘through one of the twos and the 8, and put the quotient 4 below the 8°; laftly,. . draw a line through the remaining 2 and the 4, and put the . quotient. 2 below the 4; there being now only 7 in the nume- rator, and’2 and 3 in the denominator; multiply the 2 and 3 > together for the denominator, and the anfwer will be’ 314. * Case 7. To reduce fractions of different denominators *to others of equal value, that have a common one. REDUCTION of VULGAR FRACTIONS. 79 Rute 1.—Reduce them to fimple fractions, then multiply each. numerator, by. all the denominators except its own, for each new. numerator, and all the denominators together for a common dee. nominator. Redice to a common denominator, » tie ye & 5. anf ns a : $6 12 2. 5 & F- tine tre & yrs 6 3. & 9 gir 240 © 220 g 252 a> mF To to). yo X 33S 2 t & 2 Sf 24. & 108 abe SS Sai oe aa 38 gy ahs 2 2 - o 7 & 45 << Jam jo +5 & Fs s ae a a Se pS 2: AS: £28 & 594 9 i Z bi : ” 62 2 of 3 & 22. BAS SEN ni a4 es & TF ° 3 ¥ rgz > z a g 1 2 of 2% & 4 56230 780 18 & 150 Oe SE iy DEIN ies ES oa mest Lib 9. 125,7 of XU poet Ie 2 So 5k AS oe 2s Rute 2.—When of two fra@ions the one.denominator can. divide the other without a remainder, multiply the terms of that. which has the defs denominator by the quotient. Reduce-to.a common denominators _. anf. * anf 3 7 6 4 4: 5% 6 3 J. +S & 3 2 75 & a 4. ‘3 & yi = 2 & Pe rod I = 7 y 2 we & ZG ° vo Ms fhe a ek OS th aa od 4 3. ae & 4 e sr & ae 6. 5 & ~ = > & o CASE 8; a Of two given fradions:to find which has the greater value. Rure.—Multiply each: numerator into. the other’s. denomi- nator, and if the produéts'be equal, fo are the frations ; other- wife the numerator of the fraction that-has the greater value multiplied by the other’s denominator, will give the greater pro- duct, . Whether has the greater value. »- anf. anf. anf. - I wi 6 t | 3-27 Orgy - 27/5. xe Ors’ equal I 2 a. Shore o$4| 4. tt on gt 48 |'6, G29 ard do, CASE g. To find the value of fimple fractions of a given integer. OL eae aS REDUCTION of VULGAR FRACTIONS. /Rure.—When the fraction is a proper one, reduce the nu-- merator to the next inferior name, and divide by the denomi- pator; if any thing remain, reduce and divide in the fame manner * as far as convenient, or tul ‘nothing remains. 4 if i ' | t | i a i i it What is the value of TA af — ys. 6d. | ‘ gr. [b. 0%, dre Bal iad,» — 13 4 | 8. syewh —— 2.15 4 5x2: 3. eetb- — — 9 Qs asyuile —~ 2 furlongs. 4. tguinea,— 16 4ars. _ gal. pts. 5. 43 mode — 20 7347-10 ~Lhhd. wine — 28 24- Og a.d. yrs. gre nd, ria gud, cloth-m. —— 2° 2 12. +sacre; —= 30 poles. 6. oe, Ef OY 5 — 10 § 17> ds ~50%. av. ——~ 143drams, Ruve 2.. When: the fraSion is an improper one, divide the nun:erator by the.denominator, the quotient will have the fame name as the integer; thea reduce the remainder, if any, and: divide as'in Rule 1. yh Se d. a sy ad. rs. > 6 : ‘ al 5 Iq. as Le oo G A 8 3] aan fae —- 2297 2 ot Be: Ae Scent, ne “owt. days, hours, 4s yds. ogrsi nay Vi 5.°.3 P2.dag, .— 5126 2.8 3. *Pyd, cloth-m. rae gftte aa eF a8 Re BV.m—=1 21d, L4 ors CASE -10. To reduce money, weights, and meafures to fractions of a - given integer. Rus.—-Reduce the given quantity to its lowelt name for a numerator, and the propofed integer to the fame name for a de- nosninator. : Reduce Sib ide : ie. to 4 tothe fraction Oba 6. anfe. 43f,. ree Whaley Sr ar pound. Yash: 3. — 11s —_ guinea. a roeE Zuie 4. —— Ot — failling. —-- ay 8h. Eee fore ce —- moidore. - ae zi mots. 6. 40%. 13dqwis. lb. troy. ee salt. SSnsancnneicier tbat acted 7 ". 2gr. 14/b.to the frationofacwt, —— Scwt. 3. 2gr. gna. — yard. —— +e yard. 9. 2yd igre — ell. E, —— Sell, E. lo, 29rn 13, — CW, me r2,6Whe CiA.SiB5 dels To reduce fractions of one integer to equal fradtions of ande Ruzte—When there is a certain number of the lefs integer contained in one of the greater, multiply the numerator by that number, when to a lefs integer, and the denominator when to a greater. When there is not a certain number of the lefs integer con- tained in one of the greater, bring the given fraction to fuch an integer whereof a certain number is contained in the integer to which the fraction is to be brought; then by the firit part of the rule bring this to the fration required. Reduce 1. 4/. to the frafion of a sh. anf. AP Se 2. gsi _- Luinede ay Lute 3. $l. ~ crown. —— Acrowns be Paths — fixpence. —. 2 fixp. 5. 4moid. — shilling. ——— ve ae Gs. eb Wte “ae Id. ial CL 275, We alee i —- nail, ——— nail, 8. 354. — Luineas — zr kule 9g. gosh. — halfa-crown) —— 3 ohalf- chs to. 32. £: —~ yard, ——~ +5 ya ii. og — guinea, a a7 guts 12. ~rbalf-a-gui.— shilling, a Ue? iD. 13. 7 of 6s. 8d. — pound. ——s Gls 14. Sanch ry — bhd. a aa bhd. 15. 4 of go”. ~~ 3 sh. isos spathree-sh. 16. +2moid. — pound — $4. 17. ¢groat, — Sixpence, —— ve fix-p. 18. ffix-p —~ half a guinea, ——— a sbalf-gu. $z ADDITION of Vurcar Fractions. ADDITION or VULGAR FRACTIONS. Ruxs.—Reduce the given fraftions to fimple ones, to the fame integer and denominator, then place the fum of the numer-~ ators over the common denominator for the fraction required ; which if an improper one, reduce to its proper parts, *or if of a . given integer find its value, What is the fum of ; ted as : se ap a 51g Ge IG PS arg RS 5 ee Og ee §: an. a $$ 244 | 6. 67,584 — acted ial Se $5832 FISH | 7 tsk Te — STE & 13,4 of & & 8 anf. soe ml late 9. % of 15, 85 & 4 PE ge — 1, = OGae 10. 7 ofa thilling,. & ve of apenny» — 54.9 d tod, t.. 2 ofa guinea, and ofp Ora ws — sl. 8s. 6d. 12. if- wu & Ge, TAS te oyh 14s. Od. 259rs 13. 4 of xo of a £, and 734d. Sh a adios Bueae rae: 14. 2 ofacwt.and3ofalhe — ?35b.3qr. 14/b, 120% : mes 1h. + of ¢ of a yd. and 1% of 2 nae a me 3420 16. ighour, + of 32days, & & Of 7 min. — if him 12h. 54 ahs . Note. Whea mixt numbers of the fame integer are to be added ; firft add- the fraGtions and then the whole numbers.: Add 32, 4% & 10% together. 3 3s 7 & = s ko 1x3 S824 4: 1xX2x8=16 . 10° TM oe 7 ool > Sale — 7 — 14 whol¢ numberss : 58 152, fractions, wwe 29 ee y_S a T—— 2pm AZAR 24+3X8=48 18%, anfwer PT mmm sien tat ana - from the fraction, and the whole number from the whole number: nunierator of the fraction to be fubtra&ted be greater than the ether, take it from the denominator, and to that difference add the other numerator, FURT RAGE OMAK Vurear Fractions. 2. Add 74,9 3 & 65% together. 2 4 Fe we x5 2X5 xX 10=1!100 i AX3X% 1O=3 120 6 TXSX 3105 4 . 22 whole numbers. 325 2% fractions ——= i= Vez 3X5 X10=150 6 24% an{wer. 3. Add 2 Ors Svs & 7} together. anf. 21835. 4. Add 124, g & 6} together. 19346 SUBTRACTION of Vuicar Fractions. ULE.—Reduce the fraftions as in addition ; then place the difference of the numerators, over the common deno- minator, for the fraction required. What is the difference beeween 1 3&3 anf. B13 1s &% anf. 2° Bes BER cc oe es | 4.7 & 3 of f — 1 =63. 5. 44 & L of Z anf. $15 = 315 6. 4, & 7 Ol Iz He 276—327's° 7- of 7 & of 35 rr gos 2588" 8. Lof Z0f OF RK Zof4zof7 .— Foe = 19 1'ee 9. + ofa f. & 3 of a hhilling. — X.=qs. 11d. 23¢9r. S. d. qrs, 10. 7 6 ofapuinea& 4 ofapenny *933d.=17 10 34, Lise Ofee. Of af. and 6d. — 245. =65. 2d. 12. re moidores, & 2 of 9 pounds -— 433 n=605. 57d. cwt. gr. lb. oz. 13. 1Zcwt. & 94 of 110z. — 212h3cewtmi 2. 21 6F Note. When mixt numbers of the fame integer are to be fubtracted, reduce the fractions to a common denominator, then take the fraction If the for the required numerator ; remembering in this cafe to carry 1 to the units’ place. 84 MULTIPLICATION of Vutcar Fractions. 1. From 67 take 2}- 2. From 10§ take 84. 7 S38 24 S §& 854 & 55 oes cre) 7° oF iaan oe oS 1 $5 2 x 03 £iX OY eae AEs 1 gy anf. q 4 by 35 3. From 19+ take 175 | anf. 135, 4. From 1083 take 925 —- Nod Tris i MULTIPLICATION of VuLcar FRACTIONS. HIS Rule is the fame, word for word, as that to reduce, compound fractions to finiple ones. What is the produ& of 3&4 anf. i 4 2 ‘ 2. tof 3 & 3 Tae 3. 72 & ~% of 5 of 10 375° | be 5 5 & of oes Di Sas 6. FofZofs& 15 0f 33 of rr = ———— GaSe DIVISION of VuLGAR FRACTIONS. ULE.—Reduce. the given fractions to fimple ones, then if the terms of the divifor will exaétly divide the terms of the dividend, their quotient will be the anfwer; but if not, mul- ; tiply the dividend by the divifor inverted. _ Note. 2 inverted becomes +; 4 inverted becomes 2; and 5% ; becomes +. What 1s the quotient of I. +o by } anf, Sait |-6. 2 by Ys > anf. a He Ae BY ah oh S17 poy a 3° bye GR Tar | 8. gi by 5 —' 08 ee) i $=119. 47by 5 — TP S18 5. @ by + — $i= 147] 10. fof $by 4, — ie It. 4.of 33 by +% of 10 anf. 225) 12. ¢ of 4 of 9 by | of $ of 3 3, RULE or THREE in Vurcar Fractions. 85 RULE of TOREE in Vurcar FRACTIONS. y ULE.—State the queflion and fiad the divifor, as in the “A. Rule of hree of whole numbers. Reduce each term to a limple fraction, and the firft and laft to the fame integer. Then multuply the divifor inverted by the other two terms, and the product will be the anfwer of the fame integer as the middie term. 1. If 3 of a 2. coft 3% of a fhilling, what’ will +3 of a J. come to? anf. 74. 259!5- 2. 1f 3 of a yard coft 12s. gd how much will 2§ yards came to? anf. 11. 18s. 3d. 3.-If 2 of a/b. coit ss. 6d. what will 423/b. of the fame colt ? anf. 15/1. 10s. Ode 4. If 62 yards coft 18s. what will 94 yards come to ? anf. 11, §s. 7d, 14759" 5. What will be the price of 7icwt. of raw fugar, when > a cwt. colt 145. 4d. anf. 51. 198. §a.. 149r. 6. If 2} yards, which is 14 yard broad, will make a fui of clothes ; how many yards will it take of 1¢yd breadth ? anf. 4t yds 4. Suppofe + of 4 of a Jd. coft 6s. g$d. what colt 1 caw. anf. 761. 1s. 44. 8. How many bufhels of wheat, at 75. 6d. per bufhel, miuit be given for 174% bufhels, at gs. 4d. per bufhel ? anf. 1234 54bufb. g What is the value of 1/3. qox. 17dwis. of gold, at 42/, per cunce ? anf. 721. 4s. 3d. 14qr. 10. What will #3 of a cw#. coft, at 10/. 4s. gd. per fother of rolcwt. anf. Us. 44. 2449rs. 11. If 27 men can do a piece of work in 74 days, how many days would 13 men take to do the fame? anf. 1523, days. -- 12. What comes 7% of 4 of a ton of wine to, when 14 hogf- head coft 45-+%/. anf. 221. 195, 13. lf 33/b. of gold be worth 1003/. what is a pennyweight worth ? anf. 2s. 54. 1yqr. 14 Eiow much bank-ftock can be bought for soo/. at 10/47. » fterling per cent ? i. anf. 4941. 85. Ogyist of SERB et i ir ath eid eel eee Sera EPO eee ae JX al sath 86 RULE or THREE im Vurcar Fractions. 15. Suppofe I have g of a fhip, and that I fell 3 of my fhare for 300/, 175. 6d. what is the value of the fhip ? anf. 4581. os. 6d. 149r. 16. If a perfon fell 4 of 3 of a fhip for 314/, 175. od. what is the value of the fhip? anf. 1469/1. 9s. 6d. 17- Suppofe +4, of a fhip be worth 514/. 195. 6d. how much will £ of & of Ler be worth ? anf. 3581. 128. 10d. t4gre 18. If < of 2 of a fhip be worth 358/, 12s. 10d. 14gr. what part of her can be bought for 514/. 19s. 6d. anf. ~<"y. 19. If a perfon take 3 of 10% days to travel a journey of 207; miles ; how many days will he take to travel 674-2, miles? anf. 22°20-days. 20. If I pay a certain fum for the carriage of 107 cwt. 7 of 4+ miles; how far may I have zojcws#. carried for the fame gnoney ? anf. 14524 imile, The RULE or FIVE in VuLear FRACTIONS. Ep ULE.—State the queflion and find the two divifors, as ii in the Rule of Five of whole numbers. Bring each term io a fimple fraction; the firft and laft, as alfo the fecond and foarth, to the fame integer; then multiply the divifors inverted. by the other three terms, and the product will be the anfwer of he fame integer as the middle term. 1. If 2 men mow = of an acre in + of a day; how many acres will 6 men mow in 34 days? anf. Lijacres. 2. If 4 men can finifh 123 rods of ditching in 3% days, how ynany rods can 18 men do in 145% days? anf. 2564rods. _ 3. If when wheat is 52 fhillings per bufhel, the fixpenny loaf. weigh 52/5. how-much mult be paid for 527/. when wheat is Sis. per bufhel anf. 7s. 6d. 1SS49r. 4. If 264 men, in 5% days of 112 hours long, do a piece of work, in how many days of 9% hours long, will 30 men do the fame ? anf. 5934days. 5. What is the intereft of 873/. 17s. 112d. for 74 weeks, ati 42/1. per cent per annum ? anf. 6l. 8s. 8d. 37¢7529rs. 6. If a reginient of foldiers, confilting of 975 men, make ufe of 17% quarters of wheat in 44, of a month ; how many foldiers will 71 quarters ferve 2;*5 months ? anf. 50. PRE LEE EA OL A A DL RE ON AOD Tar eae, QueEsTIONs fo exertife VutGar Fractions $7 7. What principal will gain 494/. gwss. in 1075 years, at 44/. per cent per annum? anf. 95 54, Queflions to exercife Vulgar FraGions. 1. Whether has .? or 34’; the greater value ? . 2. Reduce 63 of 74 of fixpence to the fraétion of ten fhil- lings. anf. “33. 3. What is the value of 75 of 7Igui. 145. 9d. . anf. 3gut. 208. 7d. 349qrs. 4. Suppofe 1 buy $ of a lottery ticket, and fell 4 of my thare 5 what part have I left? anf. ss. 5. Bought 2 of a thip at one time, and -2, of her at another, and I am now determined to buy all the fhip; required how much I have to pay for? anf. x. 6. If the quotient of a divifion be 2, the divifor 3 of 9+, and the remainder 4, what is the dividend? anf. 243. 7. What number divided by 3% of 7, will give 20? anf. 455. 8. If 3 of +4 of an eftate be worth 107/. tos. required the value of the whole? anf. 4141, 128. 10d. 149r. Q. Four threes may be fo placed as to make 343 how is that done? anf. 33334. 10. If 4 of a valuable colliery belong to one gentleman, + cf it to another, and +4, whofe value is 1000/. to another ; required . the value of the whole colliery, together with what the firft and fecond gentlemen’s fhares are worth? anf. The firft gentleman’s fhare is worth 8000/. the fecond’s 3000/. and the value of the whole colliery is 12000. 11. A perfon left 3 of his eftate to his eldeft fon, 4 of + of % to his other fon, and ihe reft to his relations; the eide{t fon’s fhare was worth 607-%,/, what was the va'ue of the eilate, and what did the youngeft fon, and relations receive? anf. 91t/. 17%. the value of the whole eftate; the youngeit fon got 227/. 195. 3d, and the relations 75/. 195. gd. 12. If 1% herring coft 14d, how many can I buy for 11d. anf. 1k. 13. What number is that, to which, if you add 4 of 73‘, the fum will be 10? anf. 72% 14. If the produét of a multiplication be 7%, and the multt- plicand 4 of 653 what isthe multiplier? — anf. 42-0 HH 2: SI ati ll i pe a a i ae se 88 DECIMAL FRACTIONS. 15. Suppofe M has + of a thip, and fells to N 4 of his thare, and that N fells O 4 of his part; what fhare has O of the hhip, and what-part has M and N left? anf. O has 4, M has left 3, and N 2. 6. How many yards of paper, that is 14%, feot.broad, will hang-a room which is 593 feet long, 123 feet broad, and 13% feet high ? duds 33457 594s. aye FiO dap moidores will purchafe rooj yards, at 4/. 175. for 27% ells Flemifh ? anf. 12m. 228. 4fSod, 18. A prollemén left an eftate to his three fons; the eldeft. got + of 4 of it, the fecond got 3 of 2, and the third 1007447. what was the value of the whole ethnics and how much did the firft and fecond fons receive ? anf. 8639/. 2s. vod. 14gr- value of the eftate: the firft fon received 5039/. ios. and the fecond 1591/1, 14s. rod. 139r. 19. There is a ciftern which holds 110 gallons of water, it has four cocks, the Jarget ef which can empty it in 14 hour, the none in 14 hour, the third in 24 hours, and aN fourth in % hours; required how long they will be in emptying it, when fe are all fet open toge' her? anf. 28min. 56z3x/ec. 20. Place 4 nines in fuch a manner as to be equal to 100. anf. 993== 100. DECIMAL FRACTIONS. DEFINITIONS. 1. A DECIMAL fradion has always a unit, with one cipher if or more for its denominator : as xo si es 2. The numerator only in decimals is expreffed ; the deno- minator being always 1 with as many ciphers a as there are fae in the numerater. 3. Decimals are difinguithed from whole numbers by a poirt on the left of them; thas °5 ftands for 3%, °75 for ri°5) 125 for’ 34, 4nd 4276 for ae 4. A mixt number is when there are lake both on the right and left of the point; thofe on the left are whole numbers, and on the right decimals ; thus, 7°42, 61°14, 100°72. 5. Ciphers on the right of decimals do not alter their value, but being placed on the left of them, with a point prefixed, de- cereale their value in a tenfold proportion, 4 DECIMAL FRACTIONS. - 89 6: A finite decimal has a certain number of places. 7. A repeating, or circulating decimal .is when one,or more figures are continually repeated, 8. A fingle repeater is’ when one figure continually repeats 5 as, ‘666, °3333- dads: ne sigh eri} g. A compound repeater is when two or more figures continually repeat ; as, ‘617617617, ‘424242, «714714. Note. If a vulgar fraction can be reduced to a decimal fraction without a remainder, the decimal is called finite ; if not, the decimal is called in- finite, or a repeater. ; erway | aad The Notation of Decimals will appear from the following TABLE, spurjnoyy, = spaipunpy: > Sua T, sup, & syed quay, sjied uipoapunpy + sjied qipurjnoyy,~ spurynoyy jo suay, ~2 sjaed qipurjnou) ua y From the table it appears that decimals decreafe in the fame proportion towards ‘the right hand, as whole numbers increa‘e towards the left. To exprefs any decimal in words. Rure.—Put 1. with as many ciphers as there are figures in the decimal for a denominator ; then exprefs in words what that fraction is, which will be the value of the decimal. Exprefs in words ‘74——"007—"1 76-—"007 8-— 8 100761 —'001073— 617—"007 2 l—10703-—0007014—"01 6, To exprefs any decimal fraction io figures. Rurs.—-Exprefs it in the form of a vulgar fraction; then if the numerator confift of as many places as there are ciphers in the denominator, fet it down with a point. on the left of it. But if the numerator have not a fufficient number. of places, ciphers, with a point on the left of them, muft be prefixed to fupply the defget, H 3 Jct MNRAS koe a aes 90 Appiti0n and Susrrdction of Decimars. Exprefs in figures three tenths—Five tenths—-Twenty five hundredth parts— Seventy five hundredth parts—Five hundredth parts—Sixiy feven thoufandth parts—One hundred and forty nine hundred thoufandth’ parts—Twenty nine tea thoufandth parts——Cwo thoufandth parts—One, hundred and four thou- fandth parts—Seventeen ‘hundredth parts—Ninety five millionth parts—-One thoufand three hundred and four ten millionth parts. ADDITION axp SUBIRACTION of DECIMALS. To add or fubtraét finite decimals. Ruve.—Place down the numbers in fuch a manner that tenths may be under tenths, hundredths under hundredths, &c. in which order the decimal points wall ftand directly under each other; then add or fubtragt as in whole numbers, and put a point in the fum or difference ftraight under the other points. 1. Required the fum of 253, +725, ‘80761, °43, °7615, "41764, ‘0821, and ‘006. 2. What is the fum of +142, ‘4, "10765, ‘00714, °27, °17545 "10072, 167228, and *14800543. | 3. What is the fum of 672, 14°4, °1728, 16°704, 146 | “0724, 1976°217, 1007'2, and ‘1748? ) 4. Required the fum of 1°75, '4867, 27 615, 7214, °6724, 149°8, 74:6724,.971°614, °718053, and 1007. 5. What is the fum of ‘oo61, 34, 06, 174°55, °2764, "071, 4865°5786, 107607186, and 178°376. 6. What is the fum of eighteen hundredth parts—Seven hun- dred and. forty five hundred thoufandth parts—Nine thoun- fandth parts—Forty three millionth parts—Five, hundred and eight thoufandth parts—One horidred and thirty two thoufandth parts~One thoufand and forty four ten millionth parts—Twen- ty five hundredth parts-—Five tenths—and fix huadred and_ five thoufandth parts! EXAMPLES in GUETRACTION. 1, What is the difference between 71'286, and 8:437? 2. What is the difference between 786, and 29768? a a ar ae ETS. MULTIPLICATION of DECIMALS: gt 3- Required the difference between 16, and 199761? 4. Required the difference between. 81°76, and -008176. 5. What is the difference between feven/ hundred aad fifty fiye thoufandth parts—and ninety nine ten thoufandth parts. To add fingle repeaters. Ruxs.—Repeat the circulates till their right hand figures ftand under each other; if there be a finite decimal in the queftion confifting of more figures than the circulates, repeat the circulates till they have one place more than it, then for every nine in tke right hand column carry 1 to the next, and proceed with the re{t as in addition of finite decimals: the right hand figure in the fum will be a repeater. Note. A repeater is marked with a dafh, thus, 6. 7. Required the fum of +72, *274, °3, °217, °728, 6°01734, "4.2%, and 47°62. : 2. Required the fum of 21°64, *6, 274°376, 7°32f, :007682, 72, 100°%, and °z. 3. What is the fam of 4:7583, ‘006, *784278, 87°48x, ‘4; 1748, 398 of; and “oog. To fabtract fingle repeaters. Ruxre.—In placing the lefs number under the greater, obferve the rule for fingle repeaters in addition ; then fubtraét as in finite decimals ; but if the under figure of the right hand column, be — greater than the upper, borrow nine; the reft as before. The right hand figure of the difference will be a repeater, What is the difference betweea #. 67°2408, and 95434? =| 3. 8-76 1427; and "94278? 2. 3°671569, and +78623? | 4. ‘620378, and ‘3? MULTIPLICATION. of DECIMALS. Cee 1 To multiply finite decimals, _Ruve.—-Multiply as ia whole numbers, and point off in the product as many decimals as there are in both multiplicand and multiplier ; but if the product does not contain as many figures, fupply the defeét by ciphers on the left, gn MULTIPLICATION of DECIMALS; What is the prodact of 161942, by 3°26? anf. 2012'78922 . 2. 12764 by 96? 26'5344." . 3.174 by "149? | cor 25°920. 4. 62°348 by ‘co1p2? —_—- "10773856. 5. °0783' by *461? ——- - "0360962: 6: 706948 by +0087? ° —- ‘000604476,’ 7. Required the produc ‘of ‘one thoufand and thirty eight=- millionth parts, by feventy feven hundredth parts ? anfe *00079926.' CAsSs8: 2° When the produ will contain more decimals than are-necef- > fary, contraét the work by the following. Ruce.—Put a point over fuch a place in the’multiplicand as + you defign the-right hand one of your produé to be ; then fet the - units’ figure of the multiplier uncer the pointed one of the mul+ tiplicand, and the reft ofthem in an inverted order. In multi- plying begin at that figure of the multiplicand which flands . dire€tly above the figure you are multiplying by ; fetting the right - hand figures underneath each other; obferving to increafe thein by carrying from the produét of the multiplier and the two figures of the multiplicand which are upon the right of it: thus, 1 from § to 15°; 2 from-15 to 25; 3 from 25 to. 354 4 from 35 to 45; &c. When the multiplier has not the units’ place fupply it : with a cipher. : Multiply 1.°47°61270 by. 3°728653 limiting the produdt to 5 places of - decimals. anf. 17-7°5 3123." 2. 73°g42 by 1'16489 limiting the product'to 3 places of © decimals. anf, 86'018. 3. 7°06487 by -37°600543° limiting the product to 5 places » of decimals. anf. 265°64294. 4. 14°7261 by ‘4372 limiting the product to 4 places of: © ' decimals. anf, 6°4382, 5+ 42652 by *6178 limiting the produ to 5 plates of deci- - mals. anf..°26351. 6.076148 by 1084374 fienuiog the product to 7 places of decimals. anf. *0064244. MULTIPLICATION ‘of DECIMALS. 93 - '00143678 by *00678735 limiting the produé to ro places of decimals. anf. "0000097519. Case 3. When the right hand figure of the multiplicand is a fingle res peater. Ruve.—-Multiply es in cafe firft, only carry at nine for the firft figure of each produ@; then before you add the lines toge- ther, repeat them till their right hand figures ftand dire@ly under each other ; and in adding, carry at nine as in addition of fingle circulates. anfwers. Multiply 61-4326 by °7 — 43700284. Multiply 5°724.3$ by 1°42. — 81286322: Multiply -648737 by °4867. = *3157406764, » Multiply -06142783 by :064876. — °00398519211532, fa YO bd me Case 4. When the right hand figure of the multiplier is-a fingle reo peater. | Rutz.—Multiply by the repeater as if it were a finite deci- mal, removing the produét one place farther to the left, and divide it by nine, continuing the Quotient (if needfu!) to a circulate ; then perform with the other figures in the multiplier as if they were whole numbers. : Note, Begin at that place in the produ, which is directly under the... . right hand figure of the multiplicand, to reckon for decimals, ; anfwers. - Multiply 64°2973 by. 4°3782. —_ 281°50786768: » Multiply +4278 by °273. — "110932. » Multiply -0376 by 06788. _- "002551786, . Multiply 46786 by 090374874. — 17°538875 737+ hW hh Casey 5. ‘When both the multiplicand and multiplier have a fingle cite culate on the right. Rure.—Multiply the circulate as in the laft cafe, carrying at nine on the ripht; then perform with the other figures of tlic. multiplier as directed. in. cafe third. 94 DIVISION of DECIMALS. anfwers. 1. Multiply 4°7467 by +436. — 2°07275 0629. 2. Multiply 9 63282 by ‘04872. — "469 3330463. 3. Maltiply -735874 by ‘00378. - °062788146506172839. DIVISION of DECIMALS. Cars Bi) By T'o divide finite decimals. Rutt.—Divide as in whole numbers, and point off as many decimals in the quotient as the dividend has more than the divifor; but if. there be not as many places in the quotient, put ciphers on the left to fupply the defe@; and if the dividend have not as many places of decimals as the divifor, annex ciphers till they be equal; or by annexing ciphers continually thereto, the divifion may be prolonged till nothing remains, till the quotient circulate, or as far as may be judged neceflary. Divide 1. 74°687342 by 6°35: 4. "76438 by 7'4273 2. 642973 by “479 5. "089725 by 67349 3- 49677426 by *72386 6. 100617483 by °00741 Note. To divide by 1 with any number of ciphers on the right of it, the quotient will have the fame ficures as the dividend, with the decimal ~ point as many places farther to the left as there are ciphers in the divifor. Divide 1. 742'°637 by 100% 3- 49651 by 10000. 2, 417°0 by 1000, | 4. 7618 by 190000 CASE 2, When the divifor confitts of many figures, contra the work by the following . Ruxze.—Set the divifor regularly under as many of the right hand figures of the dividend, as will contain it lefs than ten times ; and put a point over that figare in the dividend which ftands Straight above. the units’ place of the divifor. The firft figure of DIVISION of DECIMALS, the quotient will poflefs the fame place as the pointed figure of the dividend; then from the nature of the queftioa onfider how many figures the quotient muil contain ; take as many of the lef. hand figures of the divifor, and an equal number of the left of the dividend, if they will conjain it, if not, take one place more, rejecting all the other figures. In dividing, account each re. mainder as a dividend, omitting a figure from the right of the divifor for every divifion ; obferving to iscreafe the fir figure of each product for the omitted figures, as ia cafe fecond multipli- cation; proceed in the fame manner till all the figures of the divifor are exhaufted. 1. Divide 326°4270 by 8'97482, retaining four places. of decimals in the quotient. anf. 36°3714. 2. Divide 167248367 by 2°61489736, retaining 5 places of decimals in the quotient. anf. 6°39598. 3. Divide 1247°61523 by 54'61786, that the quotient may contain 3 places of decimals. anf. 2.2°342. 4. Divide 7486°235 by *096789735 retaining 2 places of decimals in the quotient. anf. 77345°34. 5. Divide 2°6007300 by 07486378, retaining 3 places of decinials in the quotient. ey anf. 34°739. 6. Divide :00764872 by :008729643, that the quotient may coatain 6 decimal places. - anf. *876177, Ca se 3. When the dividend has a fingle repeater on the right. Ruxe.—Divide as in cafe firft, only inftead of annexing ci- phers to the remainder, when all the dividend figures are taken down, ennex the circulate, and continue the divifion till the quotient circulate, or is exaét enough for the prefent purpofe, ‘1. Divide 743°728 by 43°674. 2. Divide 46736 by 4°6728. 3. Divide 7°43 by °672876. CASE 4. When the divifor isa fingle repeater, or has one on the right of it. Rure.—Multiply both the divifor and dividend by nine, and confider the produéts as another divifor and dividend, with which do as ig cafe firlt. ; 96 REDUCTION of DECIMALS. t. Divide 72-486 by ‘3. 4. Divide 67243 by 7-214. 2. Divide 6°7948 by ‘4. 5. Divide 2°4367 by 07652. 3. Divide 74653 by 7274. 6. Divide 74.6724 by 6°4374. REDUCTION of DECIMALS. Case «1. ‘To reduce vulgar fraGtions to decimals. Ruvz.—lIf the fraction be not a fimple one, reduce it thereto, in its leaft terms; then add one cipher or more, with a decimal _ point on the left to the numerator, and divide it by the denomi- _mator, the quotient will be the decimal required. Reduce each of the following fraions to a decimal. Te 5 + t oa 6) 7 a & 9 7. 5 of 3. anf. “he 2. 3, a $ $s o & x5 8. + of £, — ee 3- rag: anf. c41G | +9. 2 Of ZB. — Bei 40 3h 60759494 | 10. 5 of a — 05625. 5- 135 —— «10377358494 | 11. 4 of F of 4. — "25. 6. £ of $.— “375. (12. 2 of ¢ of .— Ret - Mr Colfon’s method of reducing a vulgar fraction, whofe de- nominator is a prime number™, greater than 11, to a decimal, of a confiderable nufiber of places, is fo much to the purpofe, that _ his manner of doing it is here fubjoined.— Let 375 be propofed: then by cividing as taught above till the remainder be a fingle figure it will become 35 '03448,%, then multiply the numbers on each fide of the fign of equality by the numerator 8, and it will give 3; '27586.¢,, this fubftituted — for 4°; makes 4%== 03448275 862%5.. Again, multiply the num- bers-on each fide of this fign of equality by the numerator 6, and it will give {6=-2068965517,%, this fubftituted for <% makes 3*5=='03448275862068965517+3. Again, multiply the numbers on each fide of this fign of equality by the numerator 7, Note. When -} is put after any anfwer, it denotes that it may be carried © farther. * A prime number is that which can only be meafured by itfelf or a unit; that is, no other number but itfelf er a unit cam divide it without @ remainder. REDUCTION of DECIMALS. 97 and it will give ='5=='2413793103448275862029, this fubltitu- ted for =4 makes 455="034482 75862068965 5172413793103 448275862035, &c. CASE, tae To reduce money, weights, meafures, &c. to decimals, Rue 1.—If the quantity to be reduced confift of one de- nomination, divide it by as many of that name as make oné of the integer to which it is to be brought, and the quotient will be the an{wer. 2. If the quantity be a comjpound number, fet the denomina- tions under each other, beginning at the Jealt, for dividends, and on the left of thefe, place oppofite to each dividend, fuch a num- ber for a divifor, as will reduce it to the next fuperior denomina- tion, then annex one cipher or more, with a decimal point on the left, to the upper dividend ; and divide, placing the quotient of each on the right hand of the following dividends, as a deci- _mal-part of it, and the laft fum will be the anfwer, Reduce 1. 140%. to the decimal of a| 7. 195. gid.- L. — 88q58>. cwt. — anf. *0078125, | 8. 175. od. — £. — 8875. 2. 7d. — gut. — °027. |g. *Iday - year °002739726+4- 3. Linc. - mile - *O0001§ 7828. |. 10. 2re. 17p0. 144 yds. = acre. 4. 2na.— yard — ‘1245. anf. ‘60919 +- a, 6s. 43d. - £. — °3177083. | 11. gr. 16/).- cwt. *392857 + oz. dwt. © 12. 12bufb, —. Newcaltle chal- 6. 4.17 - ib. troy — “40416. dron “= "17047+ Case’ 3. To find ¢ the value of decimals of a piven integer. Rure.—Reduce-the given decimal to the next inferior name, and point off in the produé as many places of decimals as are in the given number; then reduce thefe to the next inferior name ; proceed in the fame manner to the loweft pame required ; and the feveral figures on the left of the points will be the value of the decimal, J » RULE of THREE ins DECIMALS. What.-is the value of oe anf. anf. Re PRL 15s. | 9. °723 0f a Lon- ane, ' 2. "125moid. — 3s. 42d. | don chal. of coa! o hha Pe 3. O25gui. -—— 135 19d, | to. -75 Of a New si bush ; 4. 2a —— 8d. 3 go4grs. | caltle chal. of coals ek i - : ae, ‘66 é hon yt “Si2scwt. 140%. | 11. 66676 of t poDEB/L | ‘ 6. a Gehne wine - 3'1185ga. | yard:lonp mea. . if 7. °375bush. —~ 1 peck, tgal.| 12. ‘95LIlE. — gr. 3na. . a 8. ‘671875 of a ihe Cioth | 13. °1875yd@. /g.m. - Lf. ggin. i Meafure —— 2gr. 23na. | 14. *41875acre — iro. 27p0- 2 7 i : 5 “The RULE or THREE in Dectmats. if | R ULE —State and work the queftion asin whole numbers 3 only inftead of red jucing each term to its loweft dtnominds ‘tion, PA air numbers and vulgar fractions to decimals, f.3/b. colt +404. how much will 73/b. come to? anf. 7d, 259rS-- Note. Take: all the queftions int the rule of three in vul gar factions. FR Re ne re re TS SRE Kh eee The RULE or FIVE in DecimaLs. NETS role! te’ the very fame as that given for the tule of three in decimals. 1. If 2 men mow § of an acre in 3 of a day, how many acres will 6 nien mow in 32 t dae? anf. 11tacres. Note. Take all the queftions in the rule of five in vulgar fractions, | EXTRACTION of the SQUARE ROOT. HEN any number is multiplied by itfelf, the product ; is called the {quare of that number; as, 7x 71249 the’ ; {quare of 7. Therefore to extract the fcuase root of any quantity, is to find fuch a number, which being Big be by. 7 a N Parremetemnme sete seen Na ee TE LR TE TLIO ELIT LN eT cata CeO FG a SE ey 5! % EXTRACTION of tbe SQUARE ROOT. 69. itfelf, produces the given quanity ; thus, the fquare root of 19 is 7 Lips 7% 72249. Square root of 36 is 6, becaute x6= sy O6Ge 1 4] sit 6 AS ON ET wy. piston Role Taine mI Rue for Exrractine the Square Roor. ~ Point the given number into sales of two figures each, beeniag at a units’ place, going to the left for integers, and to the right for cimais.* - Find a oe e number either equal o, or the next lefs than the left hand period 1; and place its root in the quotient s fubtrad the fquare number from the firft period, and to the Ai feence bring down the next period for a dividend. 3. Double the quotient figure for the firft part of the divifor, and fee how often it is contained in the dividend (excepting the units’ place) fet the number of times in the quotient, and alfo on the right of the firft-part of the divifor, which completes the divifor; multiply the whole divifor by the laft quotient figure, and fabtrad the product from the dividend ; to the remainder annex the next period ; ; then double the right hand figure of the + lait divifor, which, together with the other figures belonging 10 it, will form a new divitors with which proceed as before. \ Note. There muft always be an even number of decimals in the quantity to be extracted. Extract the {quare root of 1.256 —— 16} 6. 12345°729 —— Viti. 2. 18769 ~— 137 | 7. 718672137 — 26°80806-4- 3.734 —- 23.) 8. 507823 —- > 741°2617-4 A 7590 417129— 87'123 | g 12 bes 374.044 1 | 5..67897°0186 —260°57-+ | 10. 101 —= -10'04987 56-44 ) SS * There will be as many integers, as there are periods of integers, and as many decimals as there are periods of d lecimals. etl ea 100 Extraction of the Square Roor ofa Vulgar fradion. To Extrad the SQUARE ROOT of a Vutcar FRACTION. ULE.—Reduce the fraftion to its leaft terms; then find the root of the numerator and denominator for the an- {wer.. Bat if the root of either the numerator or denominator « cannot exaétly be foutid, reduce the fra€tion to a decimal, and extract its root. - What is the fquare root of i} lay anf. aie | 4. ooe anf °78214-+ | 2. 335 okie al "7270-4 a 2 — ee] 6. f¢ aks it Le. 3 a The Use of the SQUARE ROOT. N the right angled triangle A BC; “A C is called the Hypothenufe, A B the Bafe, and B C the perpendicular. A right angle is formed by one ftraight line ftanding upon another in fuch a manner, that it does not incline more to one | fide than another ; as B C upon A DB. Cc } t E — ay E | a ~ Loy ben 'C | WY, e! Gras. © Py A Ae Rc ak DL NE Oe pg TET The Ufe of the SQUARE ROOT. 101 i CAS Bit \ Having the hypothennfe and bafe given, to find the perpen- die dicular. Ruxe,—Subtra& the fquare of the bafe from the fquare of the hypothenufe, and the fquare root 6f the difference will be the anfwer. Given the hypothenufe 225, and the bafe 180; required the perpendicular. anf. 135. Case 2 Having the hypothenufe and perpendicular given, to find the bafe. Ruxre.—Subtra& the fquare of the perpendicular from the fquare of the hypothenufe, and the {quare root of the difference will be the an{fwer. Given the hypothenufe 225, and the perpendicular 135; re. quired the baie! anf. 180, (Cod 8 (35 Having the bafe and perpendicular given, to find the hypothe- Hv c. Ruxe.—~Add the fquares of the bafe and perpendicalar ‘to- gether, and the fquare root of the fum will be the anfwer. Given the bafe 180, and the perpendicular 135; required the : x hypothenufe ? anf. 225. \ The following Examples are founded upon the three foregoing GC ajes 4 1, Required the length of a ladder that will reach from the edge of a ditch, which is 18 feet broad furrounding a fort, to the top of the fort, which is 34°82 feet high? © anf. 39°19. 2. Required the length of a fhoar, that is to ftand 54 feet from a building, which will fupport a jamb 11°9 feet from the ground ? Ahad anf. 13-b. 3. Wanting to find the height of a rock, which was nearly perpendicular, 1 flood 554 aes from the bottom, and found 5 caer ED 1 wk cl saa cs Vorb e.g rO2 The Ufe of the SQUARE ROOT. _ that the diftance from the place where I flood to the top of the rock was 140% yards; required its height? anf. 129'07 yards. 4 A. ladder, 40 feet long, may be fo placed, that it will reach a window 33 feet from the ground on one fide the flreet ; and, without moving it at the foot, will do the fame to a ‘vin- dow 21 feet high on the other fide; required the breadth of the {ireér ? anf. 56°64 feet. . 5. A ladder, 65 feet long, was flanding upright again a wall of the ne height; but the workmen having occalion to dele window, flid the ladder 25 feet from the building in- order to accomplith their aa beste new much the top of the ladder full frém the fummit of the wall ? anf. 5 feet. 6. | here arethree towns M, N, and P, ie gare that N lies 240 miles fouth of M, and P 180 miles weft of M; required the diftance between N and P? anf 300 miles. 7 There are two towers on a plain, th 1e one 240 feet high, and the other 180; a ladder placed i in the line of diftance be- tween them, 215 feet from the bottom of the loweft, will touch the top of both towers; required the length of the Jadder, and the diftence betweens-t the towers’ anf. 280'4 feet the length af the ladder, and 360 feet the diftance between the towers. 8. Ifthe femi-siameter of the earth be 4000 miles, and the heipht of a mountain be 3 miles; at what diftance will it be feen at fea, or on plain ground, the eye of the f{peétator being fuppofed ° on the furface ? anf 1 55 males nearly. g. There are two,columnsin the ruins of Pe rfepolis left flan de ing upright : the one is 64 feet above the plain, and the other 50; ina [lraight line between the fe two, ftands an ancient fmall eae the head of which is 97 feet fronr the fammit of the higher, and 86 from the top of the lower, the diflance of the bafe of which column tothe cencer of the ftatute’s bafe is 76 feet ; required the diffance between the top of the columns? anf. 157-4 fect. to. The height of an elm, gro wing in the middle of a {mall circular ifland, 30 feet in diamter, is 53 feet, and a line ftretch- ed from the tep of the tree to the outlidg of the water is 112 feet ; La is the breadth of the water furrounding the ifland ? anf. 83:6 feet. - 11. A may-pole, whofe top was broken off by a blaft of wind, ftruck the ground at 15 feet from the pole: what was the length of the whole may-pole, ; FepdeGhe the broken piece to be 39 feet ? Pbcgh anf. 75 feet. Sl ntti é , F Extradion of tte SQUARE ROOT... 103 Ty G dthe mean p Orth | bette WO cive imbere io hnd.the mean proportional between two civen numbers. Ruve.—Multiply the two numbers together, and extract.the {quare root of the product for the anfwer. What is the mean proportional. between 49 and 64, What is the mean proportional between 16 and 256? é : anf. 64; 3.. What is the mean proportional between, 16 and 36? anf. 240 4. A gentleman has a garden in the a of a parallelogram, whofe site 28 fide is 64 Fat es and the fhorteft 36, which he intends to change into a {quare of the fame area; required the fide of tied fquare ? anf. 48 fathoms. 5. Suppofe a general had an army of 567009 men; and he would form them into a {fquare, how many muit be in rank and file? “2 anf. 75 3. eneieciaiemeaiaaieal een To Extract the CUBE ROOT. HEN any number is multiplied by itfelf, and that pro- dud by the firft: number, he lat ie i is called the cube; thus, 8 x 8=-64 % 8=512=—cube of 8. Therefore to ex- tract the cube root is to find fuch a number that being multiplied _ by itfelf and the product again by the firft pumeery produces the given number: thus, the cube root of 125 is 5, becaufe_ 5 X5.X 5125. The cube root of 343 is 7, pak > au ay 2 — 343° ; } ag tay Ta ia eae eek a, ee SFP lrath power tlaco6|s3144t}16777216 AAT 40625124 767823 361 TABLE of the firfl twelve towers of Numbers. iit power |i 2 BI oes 4. § 6 7 8 - G ad power | I 4 oe 16 25 36 49 ay 4 eee 3 manne | | ES | TT exe ence sa | ccm ee SS ee ee | eee — rl See Re cot 3d power | I e 27 64 125 216 43 $12 729} ath power | 1} 16 81 256 625 1296 240T 4096 , 6561 sth power | I} 32] 243 1024 3125 7776 16807 32768 59049 ewe || Cee ed eee | eS ee eer ers EE SSR | T_T 6th power } 1] 64 129 4096 15625 26056 117640 262144 53441 ath power | I} 128} 2187 16384) 78125} 2.79936 823543. 2097152 4732969 8th power | 1 256 6561 655 36 390625 1679616 5764803 167792761 43046721 I 5u aii. uae: 1953125| 10077696 40353607 13421772% 387420489 Gp Ap aS i Bae RTO ee Petes 60466146) - 282475249] 1073741824) 3486784401 mn RD ee ee gth power roth power E 1024} 59049 1048576] 9705025 I |2048|£77 47 4194304 43828325, 362797056 19773267431 85899345921 31381059609 |— an ee ES eer pn eee) | re ee een ees | ne ee I gbas 287201 68719496736 2824205 36481 Ree SEA OR EI AE EAI rith power | eee eee Be SESS: SS ALS SP iE hie AR Te OBE RE To Extrad the CUBE ROOT. —_—S tes Ruxie.—Divide the number to be extracted into periods of three figures each, beginning at the units’ place, and find a cube number either equal to, or the next lefs than, the left hand period 3 fubtrac&t the cube number from the firft FErOM, and to theidiffer- ence bring down the next period, which call a dividend. Find the divifor by multiplying the fquare of the number in the uotient by 300; confider how often it is contained in the divi- dend, and put the number of times in the quotient 3 multiply the divifor by this quotient figure; then add a cipher to the number which was {quared to find the divifor bys and multiply it by 3; and that produ& again by the {quare of the laft quotient figure ; cube the laft Soren figure. Place thefe three fums regularly under the dividend, add them together, and call their fum the Ae See which fubtraé@ from the dividend, and to the differ cé bring down the next period 3 proceed in the fame manner i 1 all the periods are brought down, Note. ‘The fubtrahend muft never be more-than the dividend, 1s RROSOSO7 6 anf. ®) 225) SO0125'725 — 92°8-. 2. 76765625 -— 42°59. 1220615227232 — 4968. 3+ 4149°995543— 16°07. | 7 401719179 = — 737-5 Extra the cube root of | 4. 27407028345 anf. 3015. = 6. = To EXTRACT -the CUBE ROOT of a VULGAR FRACTION. ULE-—Reduce the fraction to its loweft terms: then ex: tract the cube root of the numerator and denominator for the anfwer. But if that cannot be done, reduce the fraction‘to a decimal, and extraét the cube root of it. Extract the cube root of 3. 3 anf, "9085 +. 6 8 saa I. t6a5 anf. a 14 a 1937+ a ee a RLS TR oe RE ae a SR SK Sa eRe ges AEE SSE TT Sf bers. The USE of the CUBE ROOT. O fied two mean proportionals between two given num: Rure —Divide the greater number by the lefs, and extra the cube number will give the leat greater number wi il} give the greatelt. What are the two mean proportionals between 5 and 320 2% 2 $12? z. What are the two mean proportionals between 7 and a) 15379? Sa Pa root of the sees which root: multiplying the lefs- mean proportional, and dividing the, 4 “ anf. 20 and 80. . What are the two mean proportionals between 64 and aah 128 and 256. | anf. gt and 1183. Having the dimenfions of any folid body given, to find the . dimenfions of a fimilar one, that will be greater or lefs, any number of times. Rure.— Multiply or divide the cube of each of the given dimenfions, by the number of times that theirequired folid is to be greate# or lefs than the given one ; product or quotient wi 4, Swe BARA | the 2, There much? ilk sa UR is a eifte rn anf. 5 -feet. long, 4 broad, and 3 deep, wherein is contained a ae quantity of water ; dimenfions of another. cillern that_avill contain 5 ofect long, 7°2 br then the cube roct of each e the dimenfions_of: the folid requ tired. 1, There is a cubical veffel, whofe fide is t2 inches ; required anf. 17°300-4-. 3. Suppofe the length of a fhiy’s keel be 44 feet, the mid- fhip beam 15, and the depth of the hold QO: dimenfions of another fh times the burdeng ip, of the \ requircd the - fame form, that nae carry three required the 822 tines as oad, and 5°4 deep,. Gde of a fimilar yeffel that .will contain three times as much? anf."Vhe length of the keel 63°46,.the-midthip beam 21: 639) rem. 3, and the depth of the hoid 12°97S/feet, rem. 18. 4 Required the fen will hold of "S 8000 oranges, each of whofe fho 2'179 inches, and the longelt 3°375 ©. length, 44°58 59 in bre anf.'67°§ adth, and 43°58 in depth. rte(t diameters i193 th, breadth, and depth of a box, that. inches in ’ The Ufe of the CUBE ROOT 107 5. If a thip’s keel be 125 feet ong the midfhip.beam 25, and the depth of the hold 153; required the dimenfions of een fhip of the fame form, that wiil carry but half the quantity ? anf. 9972 feet, the keel, 29°84 the midfhip beam, and 11:9 the depth of the hold. 6. Lf a fhip’s reat be'4g feet, the breadth 173, the depth 8:7, and her burden ig tons ; required the dimenfions of a Gimilar fhip whcfe burden is 360 tons? es Length of the keel 76°95 feet, midihip beam. 29°53 d depth 1 14°$77. 4 sd \ Note. The folidity of like fizures are in proportion to each other, as the cubes of their fimilar fides or diameters. 7. If a ball of four inche é diameter weigh ¢ oi/b. required the weight of a fimilar one whofe. diameter is 7 inches? anf. so'old. g ae Wa S. If a eube* of filver, whofe as is 3 inches, be worth "8h; 7a 6d. required the fide of a cute of the ae filver, whofe value fhall be three times as much? f. 4°326, &c. b. Suppofe there is a fone 20 iaches long, Ke "cae and & deep, which weighs 217/b. required the length, breadth, and depth of a like ftone, which weighs 1000). anf, 33°28 inches long, 24:96 broad, and 13°312 deep. 10. There are 3 chelts, the firft contains 10000 folid inches, the fecond. 16656, and the third 20000, required the fide of a cubical cheft fiat wil contain as much as all the three? ; anf. 26 inches. 11. If a fhip of 300 tons be 75 feet long in the keel; re- cuired the burden of a fimilar fhip, whefe keel is 1q@0 feet long ? anf. 71x tons. 12. If a thip of 72 tons burden be 45 feet long in the keel, 17°3 and in breadth, 8-7 depth; required the dimenfions. of a fimilar fhip that will carry 5 times as much? anf. Length 769, breadth 29°583, depth 14'877, t To find the TONNAGE of SHIPS, Re 1.—Multiply the Jength of the keel, taken within board, fo much as the fhip treads upon the pround, by the fength of the midihip beam, within board, taken from plank to 108 To find ithe TONNAGE of SHIPS. plank, and that product by half the breadth, taken as the depth, then divide the laft produ@ by 94, and the quotient will g pivenhe tonnage. 1. IF the length of a fhip’s keel be 80 feet, and the midfhip- beam 30; required the tonnage ? anf. 382°9787 +1 2, If the length of a fhip’s keel be 87 feet 6 inches, and the midthip-beam 28 feet 8 inches ; required the tonnage ? anf. 382'476 tons. Rue 2.—Ship-wrights take the dimenfions on the outfide of the light mark, as the fhip {wims being unladen, to find the content of the empty fhip. But if the m nk of the fhip be taken from the light mark to her full draught of water,-when laden, it will give the burden of the fhip: And then the length, breadth, and epth multiplied together, and divided by 100 for men of war (which gives an allowance for guns, anchors, &c. that are all burden but no tonnage) and by g5 for merchant ee gives, the tonnage, "ty N. B. A hundred folid feet make a ‘ere Required the tonnage of Noah’s ark, whofe length was 300 feet, breadth 50, and depth 30? anf. 47364St0ns. Rue 3.—At London, fhip-wrights multiply the length of the keel by the extreme breadth of the fhip, taken from outfide to outfide, and that produdt by half the ss redduh and this they divide by 94 for merchant fhips, and by 100 for men of war; the quotients are the tonnage. Required the tonnage of an eighty-gun fhip, the length of sehbts keel is 149 feet 4 inches, and her extreme breadth 49 feet 8 inches ? anf. 1841°86-+4., 2. Given the length of the keel of a feventy-four, 138 feet, and the extreme breadth 46 feet 9 inches; required the tonnage ? anf. 1§08'038125 tons. 3. Required the tonnage of an Eaft Indiaman, the length of whofe keel is 132 feet 8 inches, and the extreme breadth 38 feet? Af BO FO7O8s The following method is ufed in the royal navy. Rue 4.——Let fall a perpendicular from the forefide of the ftern | at the height of the haw/e holes, and another from the back of the a main port at the herght of the wing tranfom: from the length bes | tween thefe perpendiculars deduct ? of the extreme breadth, and’as © MULTIPLICATION of DUODECIMALS. rog many times 24 inches as there are feet in the height of the wing tranfom above the upper edge of the keel, the remainder is the length of the keel for tonnage. “I’hen multiply the length of the keel by the extreme breadth, and that produ& by half the breadth; divide this produ& by 94 gives the tonnage. r. Given the lenpth-of the keel 68 feet, the extreme breadth “223 required the tonnage. anf. 195 47 2, Required the tonnage of a thip whofe keel is 78 feet, and the extreme breadth 241 feet. anf. 2490s 56 3. Given the length of the keel 70 feet, extreme breadth 24 ; required the tonnage. anf. 21434, MULTIPLICATION of DUODECIMALS. HIS Rule is chiefly ufed by artificers in taking the dimen- fions of their work. Feet multiplied by feet give feet. Feet multiplied by inclies give inches. Feet multiplied by parts give parts. ~ Inches multiplied by inches give parts. Inches multiplied by parts give feconds. Parts multiplied by parts give thirds. 12° Fourths 1 Third 12 Thirds ® 1 Second 12 Seconds “x 1 Part 12 Parts =) 1 Inch 1z Inches 1 Foot Rue 1.—Place feet under feet; inches under inches; &c. then multiply the loweft denomination of the multiplicand by the higheft of the multiplier, fetting down the produéts according to the above table; proceed with. the lefs denominations of the multiplier in the fame manner. x. Multiply 7 feet, 4 inches; by 4 feet, 2 inches. anf. 30 feet, 6 inches, 8 parts. 2, Multiply 6 feet, 7 inches; by 9 feet, 3 inches. cs 60 feet, 10 inches, 9 parts. 110 MULTIPLICATION of DUODECIMALS. 3. Multiply 12 feel 5 inches; by ‘ feet, 9 itches. anf.-58 feet, 11 inches, G parts. 4 Multiply 11 feet, 10 inches; by 12 feet, 10 inches. anf 151 fect, 10 inches, 4 parts. 5., Maltiply 17 feet, 9 inches; by 13 “feet, 6 inches. anf. 239 fect, 7 inches, 6 parts. 6. Multiply 6 fe et, 4 inches, 7 Pparts.; by 6 feet, 7 7 inches, 3- parts. anf. 42 feet, 1 inch, g parts, a ieckaalet 9 thirds. 4. Multiply 26 feet, 3 inches, 4 parts; by 10 feet, 6 inches,. 7 parts. anf 277 feet, 2 inches, 3 parts, 1.1 feconds, 4:thirds. 8. Multiply 180 feet, 7 inches; by § feet, 7 inches, 8 parts. anf. 1018 feet, 3 inches, 5 parts, 8 fecondse 9. Maltp! ly 20 feet, 8 inches, 4 parts; by 8 feet, 7 inches, anf. 177 feet, 7 inches, 6 parts, 4. feconds. o. Multiply y 175 feet, 6 inches, 3 parts; by 16 feet. anf. ii 4. inches. Kuve 2.—If the number of feet in both multiplicand and multiplier be great, take even parts for the inches, parts, &c. as in ae A Prec. feet. ince feet. inch. fetta tnt. pas, y. Multiply 871 9 by, 29 M1. anf. 26079 10 3. 2. Multiply 187. 4 by:174%) 9. 9293901 .0— 0% q. M im, ts 63% 1ObDy 317 4. —— 196059: 1 4. 4. Multiply -197' 6 By 200 5. —— g582.° 3 5. Multiply 413 7 by t57 8 —— 65208 3 6. Multiply 178 11 by 307 1.5 —— 54942 3 11. Rue 3.—When there are yards in the queftion, multiply: by the number of them, and take parts for the lefs denominations. yd. fe. in. — yd. fe. in. a fein. pa. fe: tr. Multiply 9 2 7 by 4 2 10 anf. 2°33 Be 2..Muluply 24 1 oby 12 1 6 so 0:6; 2.0 a, Multiply 37 28by 72 4 —— 29420108 4- Multiply 48 0 7 byett « 6 —— 55408 60 5. Maltiply 120.2 oby 72 4 -—— 093816 80 @. Multiply 67 1 y 6 OO Fen 24 oe n OP TR ged SQUARING DIMENSIONS ULE.—Muiriply the length by thebreadth, and the pro- CA duct will be the anfwer. aM Required how many fquare yards are in a room floor, whofe length is 30 feet, 6 inches; and the breadth, 25 feet, 4 Fates : anf. 85 yards, 7 feet, 8 inches, 2. If a pane of plafs be 4 feet, 8 inches, g parts long; and 1 foot, 4 inches, 3 parts broad; ‘how many feet of glafs does it contam?. anf, 6 feet, 4.inches, 10 parts. 2, 3. 3. What is the value of a piece of timbe ry whofe length Is 27 re i 6 inches; and breadth ‘10 feet, 11'inches; at 25.-74d, er {quare yard ¢ anf 4l. 75, 62d, a tlow. many {quares are contained in a partition that is-64. et a Pa , 6 inches Jone.; and 12 feet, 2 inches: broad ? o> anf 7 /quares, 90 feet, 1 inch, § parts. Note. 100 fu: are feet make a {qu 1are, ; . cs. Ifa ceik ng be 54 feet, 9 inches long; ang 22 feet, 6 inches es broad, how many {quare yards are contaijed in it ? anf. 3 36 f iq. dee ie feet, 10 inches, 6 6 parts. A 6. A round -pillar-is to be painted, whofe height is 18 feet, 4.inches, and the girt 10 feet, 5 inches ; how many yards are in it ? anf. 21 SV: ae ds, 2 feet, 6 inches. 7. What will the glazing of a large window come to, at rou, per-foot. whofe breadth is 12 feet, 6 i inches, and height 16 feet, g inches? anf. 8. 14s. 54d. 8. What is a marble flab worth. whofe length i sug feet, 7 inches; and breadth 1 foot, 1 Lo inches, at 6/b, per foor? anf. 31s. sd. g. Ifa ee have 3. tier of windows, -4 in a tter; and if the Height of the firft tier be 6 feet, 3 inches; of the fecoud 5 feet, 4 Rae and of the third 4 feet, g inches; and the breadth of each 3-feet, 6 inches; what-will the glazing come to, at 15d. " per ‘Hey , anf. 141. 5s. Lod, 10. One has paved a rectangular court yard, sis test, g inches in breadth, and 68 feet, 6 inches in lenpth; and in wt he has laid a foot-way the length of the court yard, and 5 feet, 6 inches broad ; the foot-way is laid with purbick ftone, at 3s. 6d. per yard, and the ref{t with pebbles, at gs. per yard; what will the whole come to? : anf. 491. 178. o4d, A 2 312 LOSS and GAIN. 11. Suppofe a brick wal!, round a garden, meafure 974 feet, round, and 9 feet, 6 inches high; what did the building of it come to, at 52. 15s. 62. per rod of 2722 {quare feet. anf. v96l. 53. 6d. 22. What is the value of 5 oaken planks, at 34. a foot, each 37 feet, 6 inches long, and whofe breadths are two of them each 1 foot, 1 inch 6 parts in the middle, the third 1 foot, 6 inches, in the middle, the fourth 11 inches, 3 parts, and the fifth 1 foot 2 inches 3 parts? anf. 11. 5s. 84d. LOSS and GAIN. A S this rule is only the application of the Rule of Three, to : find the gain or lofs upon goods, the following obferva- tions, together with the knowledge of that rule, wall be fufficient for the folution of the following quettions. Osservation 1.—When the gain or lofs upon any quantity of goods is required. Say, as the quantity, whofe gain or lofs is - given, is to its gain or lols; fo is the quantity whofe gain or lofs .18 required, to its gain or lofs. . 2. When the gain or lofs is given at fo much per cent, make -100/, with the gain added, or lofs fubtra&ted, the middie term of the flating. When required, fay, 2s the prime colt of any quan- tity is to its gain or lofs ; fo is 100/ to its gain or lols. ae 3. To find the prime coft of goods; fay, as the felling price of the goods (whofe prime coft is given) is to their prime coft ; fo is the felling price of the goods (whofe prime coftis required ) to their prime colt. 1. At is. 6d, gain per 1/ fterling, how much per cent ? anf. 71. VOs: 2. Bought tea for os. 6d. per /b. and fold it at 14s. per Jb, how much will be gained by felling 1o0/b. at the fame rate ? anf. 221. 10s- 3. Suppofe I gain 22/. tos. by felling 100/4. of tea, how much was that per J. eo anf. 4s. 6d. 4. By felling cloth at u2s. per yard, I gain 15/. per cent; what thall { gain when I am obliged to fell it at 10s. 6d per yard. anf. 125. 6d. gain per cent. BARTER. I 13 5. Bought tobacco at 7/ 16s. per cat. and fold it for 12/ 12s. per cw what was the gain per cent? : anf. 611. tos. Opa. 6. A merchant bought a quantity of raifins for 187/. but they proving not fo good as expected, he is willing to lofe 5/7 per cent; how much will he lofe upon the whole? an/. Ol. 7%. 7. Sold filk at t2s. 6d. per yard, and thereby gained Le 10s. per cent; what did it colt per yard? anf. Vis. 7d. 2gsgrss 8. Suppofe 1 buy fugar for 3/. 175. per cw. how m uft I fell it per /b. to gain 1o/, 10s. per cent? anf. 9235d. 9. if by retailing a large cafk of beer, containing 718 gallons, I gain 117. 195. 4d. what did it coft me per quart ? anf. 3d. Note. Beer is commonly fold :at.qd. per quart. 10. Sold 100 gallons of brandy, for 61/. 135. 4d. and by. fo doing, gained 12/. 10s. per cent, what was the prime coll of a gallon? anf. 10s. 11a. 23qrSs. tt. Being under the neceflity of difcharging a bill, I fold a large web of linen for 4o/. and thereby loft 72. tos. per cent, whereas, according to the common rate of bi tiie, I ought to have gained 10/. per cent ; required how much the web was fold under its proper value? anf. 71. Vis. 4574. ¥2. By felling hops T gained 57. 155. a pocket, which is the of what. they coll me; what was the gain per cent? . anf 16/. 135. 4d, 13. Sold 120 bufhels. of wheat; at 5s: tod. per bufhel, by. which I loft 9:/. per cent; but the market rifing, I fold an equal quantity for 6s. 114d. per bufhel; whether did I gain or lofe by the latter quanti:y, and how much in the whole? anf. Gained 3/, 55. by the latter quantity, but loft 5y. in the whole. 14. By felling cloth I gain is. 4d. per yard, which is the 2 + of what.1 paid for it, what isthe gain per cent ? anf. 14). 54. 8d. 24grs. BARTER. * f 4 ARTER is the exchanging of commodities, and teaches perfons who barter, how to proportion. the value of goods, fo as neither party may fuffer-lofs. K 3 zm ey . + ica ENE SITE ae cen: marl EE EIS OT Ie Oe Te 7 \ 114 BARTER. CASE tb. To find how much of one commodity muft_be given for ano» ther. This is done by the Rule of Three. Case 2% When the quantities of two commodities, of unequal value, are given for each other, to find the balance in money or in goods, _ Calculate the value of the given commodities, by their pro- per rules, and their difference will be the balance in money: . when the balance is to be paid in goods, find what quantity of them this: balance will purchafe. In bartering, goods are often rated above their true value : therefore having the ready money and bartering price of one commodity given, as alfo the ready money price of another commodity piven, to: find its bartering price; fay, asthe ready money price of the one, is to its bartering price, fo is the ready money price of the other, to its bartering price. 1. How much barley, at 5s. 6d. per buthel, willbe received for 100 buthels of wheat, at 6s. gd. per bufhel? ‘anf. 122 ¢bu/fh. 2. How much fugar, at 4/155. ‘per ew#. will be got for zocwt. of hops, at 7/ 12s. per cw. anf. 46cwt. 1gr. 165900. 3 How many hogfheads of ‘obacco, at 12d. 10s per hogf- head, mutt be given in barter for‘ 1000 el!s of holland, at gs. 6d. ‘per ell? anf. 22bbds. 4. M and N barter: M ‘has 60 yards of fupetfine raven grey, at ros -6d. per yard, for which N- would give him 102 “yards of commen yard wide, at 4s. 3d. per yard, and the’ba- Jance in monéy : how much money muit'M receive ? anf. 361. 16s. 6d. ‘sg. A and B’barter: A has 2eqw? of tea, at tos. 6d. per Jd. for which B would give him 300/. of coffee, at 4s. 3d. per 7. and pay the balance in fugar, at-ro§d. per 7d.-how-many-/b.. of fugar muft be given? ~ anf. 123051. 6. What was cloth per-yard.“when 66 yards of it were given. for 70, grofs of buttons, at 84d. per dozen? anf. Oasis 7, Diand C barter: D has 27 reams’ of paper worth t2s. “6d. per team, ‘but ‘ia’ barter “he charges 13s. qd. Chas: quills worth tos. 6d. per thoufand ; required “the ‘bartering price. of the quills, and how many of them muft be given for the paper. SIMPLE INTEREST. Ly anf. 11s, 27d. per thoufand ; 324 thoufands muft be given for . the paper. e : 8. P has 249 yards of Irifh linen, at 4s. 4d. per yard, which - he would barter with Q for 20 guineas ready money, and take the balance in home made linen, at 1s. 11d. per yard; how much » oftit will pay the balance ? anf. 34332yds. g. A gentleman has 1290z. 15dwts, of old filver, which he - values at 4s. 3d. per ounce ; and he propofes to add 83/. 2s, o3d. thereto, in order to purchafe a very curious and valuable piece of - plate, weighing 2600z. 1odwis. Required how. much the plate - was rated per ounce? anf. 8s. 6d. to. Evhas 79 yards of muflin, at 6s. od. per yard, but barters at 7s. and receives from F chintz;iat 5s. $d. per yard, which . was only worth 5s. sid. whether has the advantage in the barter, and how many yards of chintz.muft. F give E ‘for his‘ muflin ? anf. 97yds. 244grs and F has the advantage, and_his bartering price fhould only have.been 5s. 7d. 3349rs. SIMPLE: INTEREST. | os *-NTEREST is a fum allowed by. the borrower to the lender, ~ for the ufe of the fum lent, at fo much per cent per annum. Simple Intereftis.that which arifes only from the fum lent, - and fhould never, legally, exceed 5/. per cent, per annum. The fum lent is called the principal. The principal. and. intereft. added together are called the amount. Case 1, s To find the intereft of any fam of money, for any number of years. Rure.—Multiply the principal, time, and rate per cent, toge- ther, and divide the product by tco, the quotient wiil be the anfwer. . t. What is the intereft of 145/. for 1 year, at 5/. per cent, -per annum ? anf. 7h. 55 2. What is the intereft of 1087/, 18s. for 6 years, at 4/. per Cent. per annum? anf. 2611, 18. Tinred. ‘ a 116 SIMPLE INTEREST. B. Required the intereft-of 75/ 18s. 6d. for 3 years, at aah. per cent. per annum ? anf. 10l. 48. Lid. 3329rs6 4. Required the interelt of soo. for 10 years, at 43/, per cent. per annum?! an/. 237/. 108. 5-. Required the intereft of 262. 16s. tod. for 8 years, at 322 per cent, per annum ? Ath, a]. 10s. 3d. 3r9rs 6. What is the interelt of 751. 15s. for 3 of a year, at s/. per cent, per annum ! anf. 21. 16s. 93d. 7. What is ‘the intereft ‘of 10007/. for 7% years, at 4t/. Per cent, per annum ? Es 3299). 78 8, Whatis the intereft of 106/; 16s. for 54 years, at 43 a! oe cent, per annum? anf, 201. 125. 7d. 3359086 “ ae a ees ' I Ad G ie t CASE: (2¢ When the intereft is required for Weeks or days. Rure.—Find the intereft for a year; then for weeks ; fay, as 52 is to the intereft of a year; fo is the number of eek: whofe tereft is required, to the liek: For days; fay, as 365, isto » che inveret? Of a year; fo is the number of days whofe intereft is required, to the Meshes wy SIMPLE INTEREST. Dec. A TABLE forewing the Number of Days from any Day of one Month to the fame Day . of any oiker Month. Ee From any Day of | Jan. | Feb, | Mar. | Apr. Apr. {2 May | June | July | Aug. | Sept. | Oct. | Nov. | Dec. 306 | 275 | 245 | rit 184 ¥-053 | 122°] 92 [Mot | gt 53] 123 303 | 273 | 242 | 212 [r22 oz} 6 [ arf 365 | 334 | 304 | 273 | 243 a | 243 | 212 184 | +53 | 123 {92 | 92 | 62'| “3 [365 | 335 | 304] 274 t. | 273 | 242 | 214 [183] 153 [122] 92| 6t| 30] 365 [334 | 304 Noe 304 | 273 | 245 | 214 | £84 | 153 | 123] 92] 61] 31 | 365 | 335 [334 | 203 | 275 | 244 | 214 ot {| 6: | 30] 365 153 [122 | ot] 6r] 30] 365 To any Dao «f Note 1. If it be leap year, and the month of February included in the time, one day muft be added to the number in the table, Note 2. Divide the year by 4, and if nothing remain it is leap year, 1, for 07 weeks, at-s/. per cent, i. What is the intereft of 137 per annum 2 anf. 215 4s. Od. 149r- 6. weeks, at 48/, per. cent, er cents 81/. 10s. 3d. Eeegrs ays, at 5/. p d aifs 4 t to, in 4 2. What will 750/.:amoun per annum ? anf. 10%. 3. What is the interelt of 1000/; for 74 per annum? 1 Sp a NR ag Mo a gmp Sete ene os rri8 INSURANCE, BROKERAGE, &e.. 4. What will roo?, amount to in 19 years and 50 hai: at anf. 190 163. 12°37 9rs- s/. per cent, per annum? ary 6th, £0 Dhteriak: 5. What will 5co/, aniount to, from. Fanu ber 34, 1780, at 43/. per cent, per annum? ans pape On 30d. 3-27 9rse. 6. What ts the intereft SE g7l. from February gth, to Septem= ber 20th, 1788, at si. percent, per anna?» unf, 21. 1.98. 6d. 143297. 7. If 1occo0/. were laid to interett March 7th, 1745; and continued to May 14th, 1752; how. much mult be received for principal and interelt, at 47? per cent, per annum? anfe 132741. 10s. Ade 373 7tSu INSURANCE, BROKERAGE, on COMMIS-. ‘NSURANCE is an agreement made in writing, called a policy, houfes, &c. expreffed in it. whereby, for a certain fom, the infarers apree to. make good the value of the property, whether of lhips, goods,. Brokerage, or commiffion, ts an allowance to brokers at home,.- or. agents abroad, for the buying or felliag of goods for orl Siocks are the public funds of the nation, fuch as bank Rock, india fto:k, South+fea flock, &e. Note. The following queftions are. calculated by Simple-, Tntereft. What imuft be paid for infuring tocol: at 44/1. per cent. anf. 45%. 2. What will the infurance se a Welt-India fhip’s cargo, va-% lued at 7481/4 Igs. come to, at 73 per cent mit 561d. 29. ee j . 6d... come to, ate anf. Bl Ys. 23d 4 . What is the brokerage of 71 6/, Vgs. tod) at 548. pet rents anf. iL 1gs- 4ide Iaougre 3., What does the con mmiffion of Aye. 18 a4 per cent. Mie COMPOUND INTEREST. ’ 119 5. How much will purchafe 1189/. India ftock, at 1083. per cent. anf, 12881, 115. 6d. 329rs. 6. Flow much will purchale 1786/. bank-{tock, at 98¢/. per cent. anf..1765!, 18s. id. 350% 7. My agent fends me word that he has bought goods, on my account, to the value of 61:97 17s. 6d,. what “will his: coms mi li come to, at 24/4. per cent. pany: bS4 Sse Linde How much will purchafe 1200/ of Southfea ftock, at Sc per. cent. anf. 11501 ros, 9. What is the brokerage of 467/, 15. od. at 6s. per cent? Ae, oh Bs od. 345 pat Se 10. My fattor’s fales, per the Good pee amount to 91 7/, 34s. 11d. what is the coamiflion thereupon, at 24/) per cent? anf. 201. 128. 11d. 34 b9rse 11. An agent negociates a bill of roro/. how 1 cominife fion will he re ceive, at 14/. per cent. anf. 171. 135. 6d. 12, In time of war, 1 infured an Faft-[ndia-m an, Matt value was. 17972/. at 154/. per cent; how much will the infurance come to? anf. 27851, aa 2d. 129r. 63. How much ftock will 381/.:135. 10d. purchaie at 77-4/. flerling per cent? an. “4001 a5, ew COMPOUND INTEREST. OMPOUND Intereft, or intereft upon intere, is that C which arifes from both principal and intereft, that 1s, the intereft, fo often as due, being added to'the principal, becomes a new principal. . Rure.—Divide the principal by the part which the intereft ‘is of 100/. thé quotient will be the intereft for the firt year, which add to the, given principal, the fum will be the principal for the fecond year ; divide the fecond year’s principal in the fame nian ner, and add the quotient thereto, this wil) give the third year’s principal ; and fo on for any number of years. Note. If the intereft be not an even part of 100/. divide as in Practice. What will r000/. amount to. in 4 years, at 5/ per cent per annum ? 120 EQUATION of PAYMENTS. ‘5 | a | tooo Given principal 50 Firft year’s intereft 5 | a's | 1050 Second year’s principal 52 ro Ditto intereft “gs | oh | 1102 10 Third year’s principal es 55 26 Ditto interelt 5°} ts | 1157 12 6 Fourth year’s principal 57 07 7% Ditto intereft en 1215 10 14 Amount 1000 Principal 215 10 :£ Whole intereft * 2. What will 1784/, amount to in 6 years, at 5/. per cent, per annum, compound interelt ? anf. 2390l. 14s. 63d. 3: What will the compound intereft of 750/ come to in.7 years, at 5/. per cent per annum ? anf. 305/. 6s. 53d. 4. How much will roo/, amount to, in.8% years, at 5/1. per cent, per annum? 5 anf. 1511. 8s. gd. EQUATION or PAYMENTS. Bias of payments is the finding of a mean time to pay feveral debts, which were due at different times, with- out lofs to either debtor or creditor. Rure.—Multiply each fum by its time, and divide the fam of all thefe produéts by the whole debt, the quotient will be the mean time. 1. What will be the mean time to difcharge a debt of 260l. payable as follows, viz. 70/, at 3 months, 100/. at 5 months, and and go/. at 6 months? anf. 4 months, 3 weeks, 1+yday. 2. A owes B 1s 0ccol. to be paid as follows, viz. 5oo/. in 6 months, 1oo/. in 7 months, and the re& in 12 months ; but fome time after they agree that the whole is to be paid at one time ; required the mean time ? anf. 8 months, 2 weeks. er nr th A NI AOE OO LRT DISCOUNT. eee. 3 3. C bought goods from D to the value of 750/. and agrees to pay 300/. at 3 months; 400/. at 6 months, and the reft at 8 months; but they agree afterwards to make one payment of the whele ; 1 demand the equated time for the payment ? : anf. At4months. 4. A certain debt is due as follows, viz. $ at 3 months, 4 ab 5 months, 7% at 7 months, and the reft at 12 months ; Now if it were agreed to pay the whole at once, what would be the mean ime ? anf. 65months, DISCOUNT. iy Seater is an abatement of a certain fum for the pay- ment of money before it is due. The prefent worth of any debt, or the ready money paid for it, is fuch a fum, that if it were put out to intereft for -the fame time and rate per cent, the difcount is allowed for, it would amount to the given debt. Rure.—Say, as one year is to the rate per cent, per annum; fo is the given time to the intereft of 100/. for the given rate and time. Add this intereft to roo/. then fay, as this fum is to the intere{t of 100/. for the given rate and time ; fo is the given fum or debt, to the difcount. When the prefent worth is required, make 100/. the middle term. 1. What difcount muft be allowed for the prefent payment of a debt of g17/. due 8 months hence, at 44/. per cent, per annum? anf. 261. 148. ard. 2.. Required the prefent worth of 175/ 15s. payable 10 months hence, at 5/. per cent, per annum ? anf, 168) 14s. 4d. 329rs. 3. What ready money will difcharge a debt of 535/. 175. 62, due in 4% months, at 43/. per cent, per annum ? anf. 5261. os. 11-43 4d, 4. A tradefman fells goods to a merchant for 1000/. to be paid in 6 months; but the merchant is willing to pay ready money, provided he has an abatement of 5/. per cent per annum, how much ready money mult be paid? | - anf. 9754-128. 2d. 1t59r, = ~ - pe aR - SS th Wa 6 - to 4 122 COMPANY. 5. What is the difcount of 140/. 18s. for 150 days, at 434 per cent, per annum ? anf. 21. 8s. 4d. 12.133pr. 6. How much ready money will I receive for a bill of 500/. due “11 months hence, when:l allow for difcount.33/ per cent, per annum? anf. 4831. 75. 8472,d. 7 Aclegacy of 800/. is left me by an uncle, to be paid 9 months after his deceafe; but 1, being-in want ne ready money, agree with his executors, to allow them 5 per cent, per annum, for prompt. payment, how much will I receive ? . anf. 7712 1s. 8207, 8. Required the difcount of 420/. 17s. from May 7th, to December 15th, at 44/. per cent, per annum ? anf 111. 4s. 2d. 3554429rs. 9. What is the prefent worth of 1786/. payable as foilows, viz. 500/. in 6 months, 700/. in g months, and the reft in 12 inonths, at 32/, per cent, per annum? — anf. 17391. 135. 6d. 3% SiosezoIy COMPANY. Y this. rule, the accounts of perfons in partnerfhip are ad- julted ; and’ each partner’s fhare of the gain or lofs, isin proportion to the fum he has in‘the joint ftock. 3 Rure.—As the whole ftock, is to the whole gain or lofs, fo is each perfon’s particular ftock, to his particular gain or lofs.. 1. Two merchants, A and B, apree to trade together; A puts in 270/.-and B igo/. they gain 100/. required each man’s fhare of the gain? anf. A’s 58/. 139. 10d. 332%¢rs. B’s 41k 68. 1d. offgr. 2. Suppofe three perfons, D, E, and F, make a joint ftock of 144/. of which D puts in 487 E 30/. and F 66/. they gain 1261, required how much each man will receive of the gain? anf. D 421. E 261. 55: and F 57/. 155. : _ 3. A, P, and Q, trading together, had the misfortune to lofe | che 12s. A’s flock was 56/) P’s 6o/. and Q’s rool. tos. how = i much mutt each perfon fuftain of the lofs? anf Aral. 17s 11d. 2388ore P 15/. 19s. 3d. OF i and Q 26/. §4s. od. oF349¢r. a 4. Four merchants, M, N, O, and P, whofe ftock is 1200/, | COMPANY with TIME. 123 of which M put in 150/. N 200/. O gool. 18s. and P the reft ; gain by trading 2077, ngs. 1 demand each partner’s fhare thereof ; anf. M 25/. 19s. 103d. N 341. 139. 2d. O Ogl. Qs. 5a. pesagr. and P.79/. 165.64. of sar. 5. A, B, C, and D, make a {tock of 1800/. and in the courfe oftheir trading they gain 202/. 10s. of which A received 75/. B 60/.C 45/, and D22/ 10s, required each man’s {tock ? anf. A’s {tock 666/, 135. 4d. B’s 5337. 6s. 8d. C’s 400). and D’s.200i. 6. Three merchants, A, B, and C, bought a Welt India: hip; whereof A paid 3, B 4, aod C the. reit, which amounted to 786/. 18s. 10d. in a trading voyage, of two years, they gaia 1786/. after paying all expences; bow much is each man’s (hare of the gain? anf. A’s fhare to7i/. 12s. B’s 4761. 58. 4s, and C’s 2387. 25. 8d. 7- D, E, and Fy put into trade equal fums of money; they gain 1000/. of which D was to have 6 per cent, becaufe he acted . as agent for the whole: E and F were only to receive 4 per cent each : I demand each-perfon’s fhare of the gain? aif. I's thare 4281 118. 54d. E’s 2852. 145. 33d, and : F's 285/. 145. 34d. - COMPANY with TIME. Y this rule the gain or lofs is divided-among the partners, in proportion to the fum, and the time of is continuance, in the joint {tock. Rure.—Multip!y each man’s ftock by the time of its con- tinvance: then fay, as the fum of thele produéts, is to’the gain or lofs ; fo is each of thefe produats, to each man’s gain or lofs. 1. [wo perfons, A and B, enter into partnerfhip: A put into the {tock 97/. for 6 months: B 1o0o/. for 8 months: they trade, and gain, 40/. 185. required each man’s fhare of the pain? anf, A’s thare 17/. 45. Sd. 32%32¢rs. and B’s.23/. 13s. Od. ogSiqr. | 2. D pats into company 700!, for 11 months: E 472/, 18s. for 13 months: and F 604/. for 12 months: they gain 672/, 18s, rod. | demand each perfon’s thare of the gain! L.2 ‘ i 124 EXCHANGE. | anf. D’s thare 246/. os. 10d. 3294%°ars, E’s 1961, 82. 10d. 13737939". and F’s 230). gs. od. 234082 ars, 3. Three perfons ‘agree to make a joint ftock: A puts in 170/. for 12 months: B 300 guineas for 10 months: and € 2374 10s. for 6 months: they gain 487/ 19s. 8d. how much 1 did each man receive of the gain? anf, A 150/. 9. Qa. - | rzar9"- B 232/. 7s. sd. 2prars. andC tos. 25. 54. o24gr- 4. Four merchants, P, Q. R, and S, agree to trade together for 18 months; P puts in 300/. and at 8 months’ end 400/. more ; Q puts in 6oo/. at the end of 4 months takes out 200/. and at the end of other 6 months, puts in 3007. R puts in 700/. which continues the whole time; and S puts in 275/. and at the end of 12 months 1677 more; they gain 1000/. what is each man’s fhare? anf. P's thare 245/. 15. 11d. 2-4 59rs. Q’s 2711. 35. Sd. 1 559r R’s 3284 105. 8d. 2494ars. reid ei Shi. 35. ak 24 559TS: Ve}ene) EXCHANGE. 7 XCHANGE is the paying, or receiving, of cafh in one country, for an equal fum in another. | The par of exchange is the real worth of money in one coun- try, compared with that of another. The courfe of exchange is fometimes above, and fometimes — . below par, according to the circumftances of trade between the two nations. : The agio is the. difference’ between the bank and current money: The bank money, in fome places, being of more value ~ phan the currency. In thofe places where the agio is ufed, the exchange is always made with the bank, With FRANCE. England exchanges with France upon the imaginary crown of three livres Tournois. nt oi 12 Deniers 1 Sol = oO of8 20 Sols te 1 Livre = o 9f 3 Livres < 1 Crown “=n 2 52 8 Crowns 1 Lous d’ore = 19 6 EXCHANGE. ALSO Sd 3 Deniers v 1 Liard fe Oo OF 5 Liards ta} t Patard ~ so Oo OF zo Patards 7 1 Floria a rio Note. The real French crown weighs 19 davis. 142¢rs, and its value is $s.. 447d. Note. The following queftions are folved by the Rule of Three. 1. How much fterling will 7874 livres, 10 fols, amount to, exchange at 314d. per crown, Tournois? » . anf. 344). Yos. 21d, 2. How many livres will 344/. 1or.:2d. {terling amount to, exchange at 314¢: per crown, or ecu? anf. 7844 livres, 10 fols. 3- Paris remits-3419 crowns, 49 fols to London ; how much {tering mult be-received there, exchange at 309d. per ecu? anf. 4391 18s. 10d. 3y3o9rs. 4. Loadon remits to Paris 439/. 185. 10d. 3x43.9grs. fterling ; _ how many. crowns muft ke received there, exchange at 307d, per crown? | anf..3419 crowns, 49 sols. With SPAIN, ». In the principal towns of Spain they keep their accounts in piafters, rials, and mervadies; and exchange with Britain, com- monly on the piafter, whofe par is about 3s. 7d. and fometimes on.the ducat, whofe par is about 4s. 113d... $6 Udi or. 1 Metvadie . = oO o*0S} 34 Mervadies--€ 4 ) > v Rial oe O «gad 8 Rials }ah 1 Piafter = Zi 7 0 375. Mervadies & t Ducat oe Tad @ ce a eae t Piftole Se ORs LO 1. How much fterling will I receive for 1728 piafters, ex- change at 4444. per pialter? anf. 3231. 25, 2. How many piafters muft be given for 323/. 2s. exchange at 449d. per piatter ? anf. 1728 pioflers. 3. An Englith gentleman being im Spain, wants to exchange a bill of 700/. fterling, into ducats, at 4s. 9d. each ; how many will he receive ! anf. 2947+4'5 ducais. : L, 2 | 4. ier pieces of eight, each 404d. how many pounds rlirg anf. 28761. 40s. 3d. i a hange 2876/. 10s. 3d. into pieces of eight, at 40rd. - each? anf. 1704.6. Malaga, December, 24th, 1783. Invoice of wine laden by George Jackfon, on board the Suc- cefs, Thomas Meanwell, matter, for account and rifque, as per advice from William Merchant in Briftol, the mark as per margin. {te pia. le me. To cof of 12 pipes of wine, Bot. of Sig. ] nes Minho, at 26 piaffers sper pipe 3 To cuftom at 10 rials per pipe isin Ao W. M. To porterage, and boat-hire : 1: 07.0 To brokerage, at 3 per cent - 0 6 23 To commifion, iy 2 per cent - 6.5.23 Piaflers: 242 2 12 Errors excepted, -. George Jackfon. Required how much fterling the above invoice will amount ‘to,. exchange at 454d. per piafter? _ anf. 64), 7s 2zFed. With PO RTUGAL. In Portupal they keep their accounts in reas and milreas: - and exchange upon the milrea, which is imaginary, whofe par is 58. 72d, Se tore 2.7 | | t Rea ae Ov OP’. 400° Reas u 1 'Crofidee } = ie vials 1d00. Ras Eo rt Milrea® gieiy 1.. How much fterling money will pay a bill of 825 milreas,~. exchange at. 644d. lter. per milrea? anf. 222/. 28. 11d, 24grs. 2.. How many milreas will 222/. 25,’11d, 249rs. amount to, . exchange at 643d. per milrea! anf. 825 milreas. . -A merchant in London draws upon his'‘correfpdndént at Lifton, for 759/, how many milreas will the ‘merchant’s’agent : Feceive, exchaoge-at 5s. 15d. fterling per milrea ? anf, 206132 milreds. BA es How much fterli mg will 296134 milreas ‘aniount’to, ‘ex. change at 5s. 144. per milrea? anf. 759l. EXCHANGE, 124 Wih HOLLAND, FLANDERS, jand. GERMANY... They keep their accounts in thefe places, fometimes in'pounds, .. fhillings, and pence, asin England; and fometimes ja»guilders, . ftivers, and pennings; and exchange with Britain on the pound Flemith, whofe par is 36s. 6¢. Flemifh banco,.or 385. 13d, currency, per pound flerling in ‘Holland ; but ‘in Hamburgh 35s. 63d. At the bank of Amiterdam, bills are negociated ‘by transfers, without paying any. cafh, which ferves greatly to €x- pedite bufinefs, fo that bank payments are reckoned from. 4 to 6 per cent. better than payments in cafhh. The cafh of Holland Flanders, and Germany, is diftinguifhed by the name Flemifh, | in the fame manner_as Enghih money is diftinguifhed by. the . name fterling. . , The following TABLE flews the value of the current money. . bce. ods ight. 8 Pennings: , _ 1 prot, or penny < ues solo, vo. foe 16 Pennings Tots l: Mpotivedie endelyresdiie wold 4 Oz 6 Stivers | 1 filling flemifh §=. -O- o »6 133 zo Stivers. 2 | cr opuilder or'florin $aez 00 1 1g) 27 6-Guilders ( & ae pound femihh =» O10 9 2% 5 Guilders 1 ducat, filver See a GO 24 Gnuilders 4 a nxdollar om) -0 4 6:0 20 Guilders 1 ducat, gold = 1sr6;. 0! : Jn Hamuurcu. 6. Phennings 1 -Grot, or penny = = 90 0#5 12 Phennings 1 Shilling lub Si On he 6 Shillings lubs 1 Shilling flemifh © = io: 68 16 Shillings Jubs 23 1 Mark — th 1.6 2>Marks (egy a SDollae «ie a ek Ya) 3 Marks 1 Rixdollar — 9 «=: 4.6 6% Marks t ‘Ducat _ sg 8 4k 7% Marks - 1 Pound ‘flemith POs oF 1. How much: fterling, money~ will, a, bill of .15.28/. smarke. 10s. /ubs. amount to, exchange at. 55..3d. flemith;per /..{terlmg ? . anf. .300l, 2. How many pounds flemifh will goo/. fterling amount’ to, exchangeat 355..$4.-flemith per /. fterling ? anf, 5281, Smarks, 108, lubs. 128 EXCHANGE: 3.‘How many guilders will I receive for roo/. ferling;-ex- change at 36s. 6d. flemifh per pound fterling ? azf 1095 guilders. 4.. How-much flerling will a bili of 1095 guilders amount ; ton exchange at 36s. 6d. flemifh per J. fterling ? anf. tool. flerling. » T turn currency into bank money, fay, as 100 with the agio added; is to,100; fo 1s the given currency, to. its. valuein bank ; money. 5. Change 1007 guilders. currency into. bank moneys agp at } 4% per cent. anf. 963305 6. Change. 963434 guilders.bank money into. currency,’ son 4% per cent. anf. 1007. 4. How much fterling will a bill of 17489 ftivers currency amount to, exchange at 34qs. per /. fterling, the agio 6 per cent £ anf. 78. 16%. 11d, 2° eaeengs: 8. How many ftivers currency will 78/, 16s. 21d Zarate 79ts fterling amount to, agio at 6 per cent, and the.exchange at 347+. fiemifh per / fering) anf.-17489. 9. How many. pidciers will 100Q/. fterling amount to, ex- change at 38s. 7d. flemith per Z. fterling ? anf. 4630 rixdollars. 10. How much fterling will be received for 4.630 rixdollars. exchange at 385. gd. per./. ¥, anf. 1ooo/, Hamburgh, March 19th,1784. 11, Invoice of-20 pieces~of cambric, and 15 pieces of hol- Jand, laden by me John Careful, on board the Swallow, Roger Seaman, matter, upon the account and rifque of James Trader, | merchant, in Neweaf{tle, under the mark per margin.. The con- = tents,-cofls,.and charges, as follow, viz. _ guils ft. po 20,Pieces of cambric, qt. 6172 ells Englith, ; at 1 guil. 6 fivers per ell. 803 1 8 15:Pieces of holland, qt.572-eils Englih, at + a 1 guil. 16 livers per ell : ead pont beaks j. T. Cuarces, To cnftom and brokerage of the . — guil.. jt. » cambric, at 5 purl. per piece 109 0 To ditto holland, at 6 gutl. per piece go. oO}. To charges.in buying, and warehoufe » room, Xc.. - PP EQIS To boatage and porterage, &c:. 40g FO EXCHANGE, eee 129 guile” fi. p. 2034 10 8 To my commiffion, at 2% per cent 50 17 4% 2085 7 12¢ Errors excepted. From your humble fervant, Fobn Careful. How much fterling will the invoice amount to, exchange at 355. od. flemifh per 7, fterling ? anf. 1941, 85. 10745d. With VENICE, There are three kinds of money at Venice of different values, viz. bank money, currency, and picoli. The bank money is 20 per cent better than the currency, and the currency 1s 20 per cent better than the picoli. } They exchange on the ducat banco, whofe par is 4s. 44, fterling. s. d. nt? Sold Sees Oo oO Sh 6 Soldi 3 } 1 Grofs = 0 lig 24 Grofs EQ: Ducat = 3 ‘9334 Current Money. s.. a 1 Soldi = 0 07% 5x Soldi 1 Grofs =o 1332 24. Grofs 1 Ducat = 3, 533. : Note. Accounts are kept at St George’s- bank at Genoa; and alfo at Leghorn, in deniers, fols, and livres, as in France; but they exchange upon the piafter, which at Genoa is 5 livres, and at Leghorn 6. make 1. How much fterling will anfwer a bill of:476 ducats, bank money, exchange at 5o4d. per. ducat? anf. 1001. 35. 2d. 2. How many ducats, bank money, will be received for 1oo/. 35. 2d. f{terling, exchange at 503d. per ducat? anf. 476 ducats. 3. How much fterling muft be given for 1000 ducats cure | rency, exchange at 5034. per ducat banco? anf. 1741, Os. 10d. 34grs 4. How many. ducats currency, will fatisfy a draught of 1747. Os. £Od. 34ars. fterling, exchange at 5ojd. per ducat ? anf. 1000 dueates. 5. How many livres will be received in Leghorn for 178/. 175. fterling, exchange at 4s. 42d. per piafter? anf. A905% heures FR0 EXCHANGE. 6. Genoa is indebted to England 17867 livres, 14 fols, how much {tering has England a right to receive, exchange at 45. ag. per piatter ? | gafengil. os: 2d. Os sqre With IRELAND, and the WEST INDIES... Accounts are kept in thefe places in pounds, fhillings, and pence, as in England, and they exchange on the 100/. fterling ; the par is about 108/. 6s. 8d. Irifh, per rool. fterling; but the courte of exchange is from 5 to 12 per cent, according to the balance of trade. In the Welt Indies the fcarcity of cafh, has. forced them to make ufe of paper currency, which fuffers a great difcount, 140/. of it being given for ‘100/. fterling, and often ‘more, according the nature of the trade. t. How much fterling will 1407/0 15s. Weft India currency amount ‘to, exchange at 142/, per cent. anf. ggtl. 7s. 5d. 25 79rs. - 2. Dublin remits to London 1250/. Iriih; how mach tere ling will it amount to, exchange at 1103/ per cent. daf. 11321. 10.5%. 3. How much muftbe received at Dublin for 1132/7, 10,525. fterling, exchange at biog per cent: anf. 12501. 4. Boughtia quantity of fugar at Jamaica, for 748/ currency, paid for factorage. and other charges 54/. per cent, how much flerling will the fugar come to, exchange at 1387/. per cent. anf. 5681. 48. OF Perd. amaica, December 19th, 1785. 5. Invoice of 15 hogfheads of fugar, and 10 puncheons ofrum, laden by me Robert Fagor, on board the Weft Indiaa, Theo- bald Jenfon, commander, for the account and rifque of George. Atkinfon, Efg. merchant io London, marlved as per ‘margin. | . Cw. grs. lb 15 ffhds. of lugar, wt. 157 3 profs, tare 18-per cw. 25. "LTS tare: We A 132 1 16% neat, at'gh Ve. per cwé. currency £4:575 18> 63° ro Puncheons rum, at 147, 1cs. per pun- cheon, currency bite ‘ 145° 6 ‘Charges, and my commiffion on the whole, at 43/. per cent. . 34 4 IOk-. EXCHANGE. r3t How much fterling will the foregoing invoice amount to, exchange at 140/. per cent. anf, 5391. 85. 255d. Wih DENMARK and NORWAY. Accounts are kept in thofe places in rixdollars, marks, and fhillings ; and they exchange upon the rixdollar, whole paris.4s. 6d. flerling. ait § 3: Penins 7 fe Danifh fhilling = 9 Ov 16 Danith fhillings | 4 | 1 Mark oe e 9 4 Marks Vs 1 Dollar — 3.8 1% Dollar | E | 1. Rixdollar = 4 6 14 Rixdollar @, { Double Rixdollar = 6 0 tr To how much fterling will 85,4 rixdollars,” "3 marks, amount to, exchange at qs. vd. fterling per rixdollar ? pi nit 165: 51d, 2. How many rixcollars will 195/7..16s. 524. amount. to, exchange #t 4s. 7d. per rixdollar? anf. 854. rixdollars, 3 marks. With SWEDEN. In Sweden they. keep their accounts in copper. rixdollars, copper dollars, copper marks, and runiticks; they. exchange with Holland upon the .copper mark, whofe par is 14d. but when they exchange diredtly with England, it is upon the cop- per dollar, whofe par is 63d. tole. coed, 8 Runfticks o (1 Copner mark & OW LIS 4 Copper marks 3 \: Copper dollar = Oo 6% 6 Copper dollars Ed: Copper rixdoilar ‘2 30 15 1 Copper dollar 1} Silver mark = Oo 44 3 Silver marks itv’ 1 Caroline i 2 4. Silver marks & 1 Silver dollar = 1» 63 3 Silver dollars 1 Silver rixdollar an 4 8 1. Change 7148 co. rix. 2-do. § run. to fterling money, at 74d. per copper dollar ? anf. 13841. 195. 10d. 2539rs. 2..How much fterling will a bill of 18740 copper dollars amount to, exchange at 407 dollars per /. {terling. . anf. 458! Os. Srad5¢. 3. In 4587. os. Sz35¢. flerling, how many copper dollars, exchange at 407 dollars per pound? anf. 18740 co. do: Mors, . EXCHANGE. With DANTZIC, and KONINGSBERG. Thefe places exchange, for the moft part, with Britain, by way of Amfterdam and Hamburgh ; they exchange with Hol- and and Hamburgh by an uncertain number of Polifh grofs for a pound Flemifh, or rixdollar. When they exchange directly with Great Britain, it is upon the florin, whofe par is 1s. 2d. fterling. Se Ode 4 Deniers, or pence, © 1 Shelon == OQ OF 3 Shelons ) ( : Grofhen a O Os 5 Grofhens | | 1 Couftic a QO 2F 3 Couttics 3 T Tiofe = ay | 2 Trufes FS 1 1 Florin or guilder = 12 3 Florins | t Rixdollar ro g: 6 2+ Rixdollars sey Ducat 4 9 4 13 Ducat 1 Frederic d’or = 17 6 Note. The ducat is rated at gs. 4d. fterling, but it is only worth 9s. 1. How many rixdollars will anfwer a bill of 4764 florins, exchange at 125 grofhens per rixdollar of Hamburgh ? anf. 11433% 2. How many florins will fatisfy a draught-of 741/. 19s. 6d. fterling, exchange at 165d. per florin? anf. L071 1% fi» 3. How much fterling will 10711-3,2, florins amount to, ex- change a at 163d. fterling per florin? anf. 7411. 198 6d. With RUSSIA. Rauffia exchanges with England by the medium of Holland, | very feldom direétly ; they exchange upon the ruble, whofe par - | is 4s. 6d. fterling. te iods 2 Polufcas “) {1 Mofcofque — =-.0o of 2 Mofcofques 1 Copeack — = 0. O's 3 Copeacks | 1 Altin — = o 133 3+ Altins- = 31 Grive’ oo Se Oy ee 2} Grives = | 1 Polpoltin a sf eet 2 Polpoltins t Poltin -— = 2 Poltins J 1 Ruble oe Say 2 Rubles 1 Ducat ee Ss igice 1.. In 14867 rubles, how much fterling, exchange at 572d. flerling per ruble? anf. 35461. 7s. 1134, 2. In 3546/. 7s. 113d, a eR how many rubles, exchange at 5724. per rubie ? anf. 14867 rubles. e ej °o 138 Ze gr. {terlin bles, 67 copeaks. rest vv 4260 amount to, exchange at 58 anf. 43821. 8s. 6d. 1 anf. 17864 ru Note. The following fpecimen of accounts fhews how Britain exchanges with other countries through the medium of Holland. EXCHANGE. 3. To how much fterling will a quantity of hemp, whofe va- 4. rubles, 67 copeacks, flerliog per ruble ? ) lue is 178¢ 4. How many rubles will 4382/. 8%. 6d. come to, exchange at 584d. per ruble? g. 2--18ih beer 21 90 Sunparsfup *paidagxe SOL ie eteceea* b g1 § a $19119] Jo a3ejjod oF, Gg ¢ -TS$ub “sappy *pueynoys [ae a: sad ff or w 9 Mae Geek fe3 | ou 03 anp aouejeq Ag ‘fbr nk zbol g “1 zbol Uo, oseIDyOIG. OF, ——e "3099 Jad s43Aq}y z1 01 L$ waosod 248 3 ony 1 or SE . 4 OF Ww. Sajoym ay ao "ET “HT 01 ‘pt . uompunutos Aw oT, cA gee, Foss ye 041 ka "S 'BOl, 6 1602 3 NP 2 Soup Aq 30} g § 421 awa aod Ff 1 oy 977 umesp EoLlor O}, Oz “Fg ‘af 2 0} ; ‘orip v ‘oitp Aq. So aide ae yok kg Sz ‘Sny\? te bf sopumeip Lior 07 61 say Or z zg was sod S7E ye oy “1efWOPXu “UOPUG'T Ul “Ay aad -1/f'0S 1 “unod. Cr Sora NAIA JO nosey ut oO .o1 zLgr< -oe anof uo Yye1 7, S.* 8° nok uo umep ‘pyr ay Aq atu uo umeip J nf yn LesSE ve pgds Aq sor aunt | soxf pF C ssejopxu 6vL os, “% oval “bolt Polt 9 p41u0y tynzy fo ‘uvupooy 4]y “47 ‘uvmpoon apy prof qt 09 “9Siyy fo offs f, apy | quof spoo8 sof Synzy fo unupoon apy 4of edo Sunpaseyfiuy fo yunor syonpung L ay — we | | ARBITRATION. | ARBITRATION. ..RBITRATIFON teaches how to negociate bills through feveral pleces.. As the courfe of exchange is continually varying, the merchant ought: to have an extenfive knowledge con- cerning the rate of exchange in foreign parts; that he may under- {tand haw to remit and draw to the beft advantage. SIMPLE ARBITRATION. In fimple- arbitration the rates of exchange from one place to two others are piven; to find the arbitrated rate between the two aria . If the exchange between Spain and London be 42d. fterliog per piafter, and the exchange between Spain and Wamburgh 7o7d. flemifh per piafter ; what is the arbitrated rate between ‘Hamburgh and London ? anf, 33s. od. flemifd per 1. ferling. 2. If the rate of exchange between Hamburgh and Spain be "ogd. flemith per piafter, and the exchange between Hamburgh and London 335. gd. flemifh per /. {terling ; what is the par of arbitration between Spain and. London? anf. 42d. flerling per piafter. 3*. If the exchange between London and Paris be 32d. ; fferling per crown, and to Amfterdam god. flemith per / Sterling ; and if by advice from, Holland to France, the courfe. of exchange between A'mfterdam afd Paris*be fallen to $24. femith, per crown; what may be gained per cent, by drawing on the one place and petuieing to the other. anf. 31. 165. 117yd. 4. Paris draws. gon Boadén for 3600 crowns,at 55d.-fter- ling,. per crown 3. for which London ‘draws upon Paris at ‘56d. {terling per crown, and is allowed = x per cent, for commifiion ; Whether did Paris gain or lofe by this tranfaSion 3 : and. 46 crs. gained by Paris. a 5. Holland was ordered to-remit to Spain} at 943d. Flemith * Marr and Hutton give different anfwers to this queftion, the reafon is, Mair draws on Paris for 100/. and then remits to Amfterdam ; but Hutiod semits 100/. to baa ang Bere and then draws upon Paris Mair’s anfwer is 3/. 14s. o8d, Zz Hutton's anfwer is 34.165, Ish. ARBITRATION. per ducat ; now:if the exchange between London and Amfter. dain be 430d. flemifh per /. {terling ; and between London and Spain 384. flerling per piafter, how much will Holland gain or lofe per cent, by remitting firft to London and then to Spain ? | anf. 18s. 8id. gain. COMPOUND ARBITRATION... NOMPOUND Arbitration is when the rate of exchange - _y between three or more places is given; to'fiad how much ; a remittance pafling through them will amount to... Ruve,—Diftinguith the. rates into antecedents and. confe- quents,” and place the antecedents in one row and. the confe- quents in another, oppofite each other; fo: that eachyconfequent may be-of the fame name with the next antecedent, and the firft antecedent..with the afi confequent, which. muft. be the fum whofe value:in exchange is required.’ If there: be a- fra¢tion ia any of the numbers, multiply both the antecedent and the confe- quent by the denominator ; and if the fame number be in both antecedent and confequent, it may be left out; then multiply the antececents continually together for a divifor, and the confe- quents for a dividend; divide, and the quotient will be the value of the fum, required. . . . 1.; London was ordered to remit 1500/. fterling to. Spain, by the way of Amfterdam, at 420d Memifh per /. flerling.; thence to France, at 58 prots per crown; thence to Venice at 100 crowns per 60 aucats ; and from. Venice to Spain, at 360 merva- dies per, ducat ; how many piatters wili it amount to in Spain ? : anf. 8625444 piaffers. 2. Paris was ordered to remit to’ Holland 546 crowns; bat not liking’ the direét exchange, they are firft fent to England, at 30d. per crown; from thence to lialy, at 65d. per ftamp crown; from Italy to Venice, ata 100 flamp crowns per. 140 ducats; from Venice to Leghorn, at 100 ducats per 100 pia- fters ; and from Leghorn to Holland, at 864. flemith per pia- fler : how many pence. will be received at Holland? : aif. 30340% pence. 3- A merchant in London wants to draw upon Leghorn for 2040 piafters, from whence he has advice that he can draw at god. per piafter, but not chufing the direct rate, they are order- ed firlt to Venice, at 94 piaiters per 100 ducats; thence to 2 136 ' ALLIGATION. Spain, at 320 mervadies per ducat; thence to Portugal, at 630 reas per 272. mervadies.; thence to Holland, at 50d. flemith per 400 reas; thence to France, at 56d. per crown ; and laftly, te Britain, at 314d. fterling per crown; now fuppofing he pays % per cent for-commiffion at each place, how much will the circular remittance be better than: the direat? anf. 321, 2s. 114d. nearly. 4 A merchant in Holland was ordered to remit to London 1500/. flemith at 36s. 945d. flemith per /. fterling ; but refolving to try the circular way; he fends them firft to Paris, at 56d. per crown tournois ; thence to Italy, at 100 crowns per 56 ducats ; thence to Hamburgh, at rood. per ducat; thence to | Portugal,. at 45d. per. 400 reas; and from thence to London, at 5s. 3d. per milrea ; now fuppofing 4 per cent for commiffion was allowed at:each place ; how much will be gained by the cir- cular remittance ? anf. 81. 145. 114d. ALLIGATION. LLIGATION teaches how to mix different forts of fiinples together, fo that the compofition. may be of a jnean quality, or price; and it is divided into four parts, called medial, alternate, partial, and total. ALLIGATION MEDIAL. Y this rule the mean price of any mixture is found, when the particular quantities, and their prices are given. Ruir.—Maultiply cach price by its quantity, and divide the fam of the produéts by the fum of the quantities; the quotient will be the mean rate of the mixture required. “1. A vintner mixes 17% gallons of wine, at 6s. 4d. per gal- lon 3; with 20% gallons at @s. rd. per gallon; 14 gallons at 4s. titd. and 27 gallons at 5s. 2d. what is a gallon of the mixture worth ? anf. 68. 1d. 3>ys9rs. 2. A farmer mixes 17 bufhels of wheat at 6s. 8d. per buthel, 16 bu‘hels of rye at 4s. 6d. 10 bufhels of barley at as. 3d. and 4 bufheis of peas at 2s. 1034, required the worth of a bufhel of the mixture ? anf. 55. 17d. per bufad, , | ALLIGATION ALTERNATE. 58% 3: Of what finenefs is the compofition, thatis made by-mixiag 22 oz. of eae of 21 caracts fine, 40x: of 22, 6oz..of 224,. and 3402. alloy ? anf. 175 y caratis fine. Note. The finenefs of alloy is reckoned nothing in mixtures-of this. kind. 4. A fpirit-merchant mixes 19 gallons of coniac brandy, at 145. 9d. per gallon, and 17 gallons. of wine-brandy, at.115. 24, with 10 gallons.of another fort, at 8s. 10@. what is a gallon of . the compofition worth? anf. 125, 14. 2497s. . A malfter mixes 70 buhhels of malt, at 55. 4d. per bufhel + 100 ‘buthels, at 6s. 1d. 50 buthels, at 4s. 11d.and 37 buthels, at Gy. 6d. per bulhel, what is the mixture rate of a pulbel anf: §s. 8d. Zot ars, 6. What is the price of a cwt. of the following compolition, viz. 7 cwt. at 31, 45. 6d. per cevts 10 cet. at 1d. 198. tod. 6 cwt, at 2/. 10s. and 32 cats at’ 5/. anf. 31.73. id. 2%Zqrs. ALLIGATION ALTERNATE, By this rule we find the particular quantity of each of the m= gredients, whofe rates are given, that will compofe a mixture at a piven price. . Rure.— Reduce thé rates to one denomination, and fet them under one another ; then link together each rate that is greater than the mixture price with:one that is lefs; place the difference between the mixture rate, and that of each of the ingredients oppofite the rate it is linked to; if only one difference be fet deain{t any rate, it is the quantity belonging to that rate; but if there be feveral, take their fum for the proper quantity. . A grocerwould mix fugars, at 10d, 7d. 5d. and 4d. per ib. to make a quantity to fell at 6d. per 4d. how much of each fort muft be ufed ? anf. 2lib at 10d,. ib. at 7d. 1b, at 5d. and 4éid. at-4d. or any other quantities in the fame proportion. - 2. How much corn:at 45. 7d. 3s. 8d. 25. 11d.:4.,and 3, id. per bufhel, muft be mixed together to make a compofition worth 3s. 10d. per bufhel ? anf..20 at 4s. 7d. 2 at 3s. 8d. 2:at 4s. Q at 2s. 11d. and g’at 3s. 1d, . 3. Wanting to fell brandy ae gd. per gallon, and having 3 138 .ALLIGATION PARTIAL. feveral, quantities worth tos. 6d. os. 11d. 11s. 4d. 125. and ~ 16s. per gallon; how much of each fort muft be ufed ; anf. An equal quantity of the firft four forts, and 23> times as much of the laft. 4, A goldfmith has sold of 17, 19, 21%, and 22 caraés fine, out of which he wants to form a compofition of 21 caracts; how much of each fort muft be taken ? anf Yat 17, 4 at IQ, 2 at 214, and 4 at 22, or any other quantitiés in the fame proportion. 5. How much tea at 6s. 6d.—75.—8s. od.—t10s. 1d. and 12s. 11d. per lid. will compofe a mixture worth 10s. 6d, per /ib. anf. An.equal quantity of the firft four forts, and 4 times as much of the lat. . ALLIGATION: PARTIAL. Alligation Partial is when the quantity of one of the fimplesis . given, to find the feveral quantities of the reft in proportion to » the one limited. : Ruie—Find the difference between the mixture rate and each » of the fimples as in the laft rule; then fay, as the difference of that - fimple whofe quantity is given, is to the given quantity ; fois « each of the other differences to its proper quantity. . How much tobacco at 15d. 18d, and 20d. per 4d. mult be-= Mint with soo/b. at 2s. per Ub. that the compofition may be: - worth 194. per ld. anf. 125 at 15d. 25 at 18d. and 25 at 20d. . 2. How. many gallons of brandy, at 8s. 10d. and 115. 2d. per gallon, muft be mixed with 19 gallons at 15s. per gallon :: ; that the. mixture may. be worth 12s. per gallon? © | anf. 14% at 8s. tod. and 14% at its. 2d. © cf “A merchant has 140 gallons of excellent gin, worth 14s. -. per gallon, but finding he cannot get that price, mixes it with « ‘other’ gin, ‘at 85: os; 6d. and ros. per gallon; required how ~ much. of the laft three forts he:muft take, that the mixture may © ‘be worth ros. 62. per gallon ? anf, 122% gallons. ALLIGATION TOTAL. Alligation Total is when*the whole quantity of theingredients « to be mixed is piven; to find: each ingredient in proportion. SINGLE POSITION... 139 Ruie.—Find the feveral -differences:as before; then fay, as. the fum of the differences, is to the:total quantity: fo is each. : particular difference, to its proper quantity. = 1. A diftiller would make’ a-compofition of §55: gallons, -. worth gs. 6d. a gallons. out-of brandy at 12s. and tos. 6d. per gallon, and cyderat.2s.:per gallon: how much of each fort mult. he take? anf. 22¢gal. at 128; 225-at ross 6d. and: Losgal. of cyder, 2. A goldfmith has gold of.18, 20, and 24 caraéts fine, out of which he wants to form a compofition of 12002. of 22 caraéts fine : required how much of each fort he muft take ? : anf. 24 at 18, 24 at 20; and 72 at 24. 3. A grocer has fugar at 7d. 8d. and 11d. per Uid. out of which he wants to make a ect. worth 10d. per /id. ‘how much of-each fort muft be taken? - : anf, 16). at 7d;-1640. at 8d. and 8ohb. at 11d, POSITION... HIS rule is called. Pofition, or Suppofition,.becaufe with °- the help of fuppofed numbers, and by reafoning from them according to the nature of the queftion, we find the. true ones. This rule is divided. into two parts, called Single and Double: . in the firft of which, one fuppofition is ufed, and in the laft two. . ~ - SINGLE POSITION. : Ruxz.—Suppofe any number at pleafure, and work with it as - if at were the true-one:. then if the refult be either too little or too much.: fay, as the .refult of the pofition, is to the pofition: . fois the given number, to the. number required. 1. Three-perfons, A, B,.and-C, difcourfing about their ages, find that A is as old again.as B, and B is three times as old as - C, and the fum of their ages is 210 years ; required each. per- fon’s age? anf. A 126, B63, and.C 21. - 2. Divide 10000 guineas among: three perfons,° William, Andrew, and James ; and give William 645 more than Andrew, and Andrew go lefs than James. anf. Andrew 30883, James 31733, and William 37334: 3. There is a ciftern which has three cocks :. the preate{t cock can. empty it in 14 hour, the fecond in 3 hours, and the 140 DOUBLE POSITION. third in 4% hours: how long would théy take to empty it, if the cocks were all fet open together? anf. Phour.= 49 7;minutes.: 4. What number is that, to which if the third, the fourth, and the feventh of itfelf; be added, the fum will be: 580? anf. 336. 5. One:being afked his.age, faid, if 3 of the time I have lived be multiplied by 8, and $ of the product be divided by 4, the: quotient will be 45 what was his age? / anf. 60. . 6. A gentlemea bought a coach, two horfes, and harnefs for 150/. the horfes colt 5 times as. much as the harnefs, and ‘ the coach.as much-as.both horfes.and harnefs: how much did. he pay for each? | anf. Harnefs 12/."1os.:horfes 62/> 10s; and coach 75/. ”, Divide 10852. among four. perfons,. A, B,-C, and D, in - fuch a manner, that B may have twice as.much as.A, and 6o/. more: C.three .times- as. much as.A,. wanting roo/. and D five. times as much as A, and 4o/. more? anf. A-o8¢yl, B:25 73,1. C-ig522l. and D. 533-24. - DOUBLE POSITION. :. Ruxz.+—Makeé two pofitions,- and proceed With each accord- ing to the nature of the queftion ; find hew much the refults are ' different fromthe. given number: then multiply each of thefe differences,.or errors, by thé other’s pofition: and if the errors : bé both too much, or too little, divide the difference of the pro- duéts by the difference of ‘the errors: but ifthe one error be too : — much, and.the other too little, divide the fum of the produéts by ~ the fum-of the-errors, and the quotient will be the anfwer. 1. James, Andrew, and. Thomas,-playing at hazard for. 1296 crowns, difagreed about the game, and the money being upon the table, each feized as much ashe could: Andrew -got 60 » more than James, and “Thomas-+ of ‘both their-fums;: required how much each got ? . _anf. James‘got 510, Andrew:570, and Thomas 216. 2. A farmer fold a number of fheep-and lambs‘to a butcher, . for-128/. and was paid for every weather 205. for every ewe 16s. and for every lamb 4s.—-Now there :were twice as many ewes as weathers, and-as.many lambs as both ewes and weathers: . required how many there were of each fort ? anf. 40 weathers, 80 ewes, and 120 lambs. . DOUBLE POSITION. 3. When firft the marriage knot was ty’d Betwixt my wife and me, My age did her’s as far exceed As three times three does three : But after ten and half ten years, We man and wife had been, Her age proportion’d was to mine, As eight is to fixteen. Now pray, What were their ages on the wedding day ? - anf. Ye was 45, and fhe 13. 4. A gentleman had two horfes, Chefnut and Swift; and a faddle worth so0/. which fet on the back of Chefnut, makes his value double that of Swift; but fet on the back of Swift, makes his value treble that of Chefnut: required the value of each horfe ? unf. Chefnut 30/. and Swift 40/, 5- A perfon bought Irifh linen at 6s. per yard, and home. made linen at 3s. per yard; and paid 6/. gs. for the whole, which was 32 yards: required how many yards there were of each fort? anf. 11yds. of Irith, and 21yds. of home-made linen. _ 6. ‘There is a fith, whofe head is 9 inches long, the tail as long as the head, and half the body: and the body as long as both head and tail; required the length of the whole fifth? ! anf. 72 inches. 7. A veffel, that holds 60 gallons, has 4 cocks: if they all be fet open at once, they will empty it in 24 hours; now the fecond cock can empty twice as much as the firft ; and the third three times as much as the firft; and the fourth 5 times as much as the firft, during the fame time: required how many gallons are emptied by each cock ? anf. 5gal. by the firft cock, ror? by the fecond, 1634 by the third, and 27+’; by the fourth, 8. Four men have each a fum of money, which altogether make 250/. if to the firlt man’s money be added 8/. it will make juft as much as the fecond man’s money decreafed\ by 8/, and as. much as.8 times the third man’s money, and but 4 of the fourth man’s money ; how much had each man? ; anf. Firft 1654/. fecond 32§$/. third 344/. and fourth 197 gr. g. A gentleman gave to A and B rool. for the ranfom of a prifoner ; but they falling out about parting the money, each fnatched up as much as he could: upon agreement, B pave A ¢ of what he fhatched up, and A gave B > of what he {natched 142 ARITHMETICAL PROGRESSION. up; this done, each had. 5o/. required how much each fnatched up? anf. A O4l. 5s. 83d. and B:35/. 145, 33d. ARITHMETICAL PROGRESSION. . N Arithmetical Progrefion, or Series, is a rank of num- bers which continually increafe or decreafe, by the adding or fubtracting of equal numbers, called the ratios, or common cifferences; thus, , 4, .8; 12, 16, 20, ZQ, 16p 12, 8, 41, 9, 29 dhs i: Og? ts 30s Le, 12,10, 8, 6, 4, 2s t Common difference is 4 : i Common. difference is 2 - In an arithmetical feries the fum of. the extremes is equal to. the fum of any two means equally diftant from the extremes; thus, 2 + 12 = 4 +--.10 =.6 + 8. And when the number of terms are odd, the fum of the extremes is equal to double the middle term ; thus in the feties 3,5, 7, 9, 11, 13,15, the, double of p= 1834155413 7+411. In arithmetical progreflion there are five things to be obferved, ; 1. The Jeaft term. Ex: . 2. The greateff term. t seach 3. Fhe number of terms. a 4. ‘The common difference. - 5» The fum of all the terms. PROPOSITION: 1... When the extremes and. the number of. terms are given, to > find the fum of all the ternis.. Rure.—Multiply the fum of the extremes by the number of < terms, and half the produét will be the anfwer. « 1. If the greateft term be 12,:the leaft 2, and the number of ternis 6; required the fum of the feries? * anf. 42. 2. A perfon bought. 20 yards of cloth, and agreed to pay 6d. for the firft yard, and.19s. 6d. for the laft;, how much did the cloth coit him? - i anf. 10l, 3. How mapy ftrokes does a clock {trike in 10, hours ? anf. 55 frrokes, , ARITHMETICAL PROGRESSION. 143 4. If so:eggs were ‘placed in a ftraight line, at-2 yards dif- ftance from each other, and the firfta yard from a bafket. how ~ much ground does a perfon go over, who brings them one by one into the bafket? anf. 5000 yards, or 2 miles and 1480 yards. PROPOSITION 2. When the extremes and the number of terms are given to find the common difference. Ruuz.—Divide the difference of the extremes, by one lefs than the number of terms, and the quotient will be the anfwer. 1. If the extremes be 2 and 12 and the number of terms 6; required the common difference ? anf, 2. 2. If the extremes be 6 and 234, and the number of terms 20% required the common difference ? anf. 12. 3. A man‘has 10 children, the youngelt is 5 years old, and the eldeft 274, they increafe in arithmetical progreflion ; what is the common difference of their ages ? anf. 23> PROPOSITION 3. When the extremes and the common difference are piven, to find the numberof terms. ) Ruve.—Divide the difference of the extremes, by the com- mon excefs, and add one to the quotient for the anfwer. 1. If the extremes be 2 and 12, and the common difference 23; what is the number of terms ? anf. 2. A perfon being afked how many children he had, replie the youngeft was 5 years old, the eldeft 274, and the common difference of their ages was 2% years; how many had he? ine anf. 10. 3. A man going a journey, travelled the firft day 5 miles, and increafed his journey every day 3 miles, til! his lait day’s tra- vel was 38 ; how many days did he travel ? anf. 32. PROPOSITION. 4. When the leaft extreme, the number of terms, and the com- mion difference are given, to find the gtéateit extreme. oe £44 ARITMETICAL PROGRESSION. Ruve.—Multiply the common difference by one lefs than the number of terms, add this product to the leaft extreme, and the {um will be the term required. 1. Given the leaft extreme 2, the number of terms 6, and the common difference 2 ; required the greateft extreme? anf. 12. 2. A man going a journey of iz days, travelled the firft day § miles, and increafed his journey every day three miles: how many miles did he travel the Jaft day? anf. 38. 3. A man clears a debt at 10 payments, in arithmetical pro- greffion, the firft payment was 12/. and the common difference s/. what was the laft payment ? anf 57), PROPOSITION 5. / When the greateft extreme, the number of terms, and the common difference are given, to find the leaft extreme. Rure.—Multiply the common difference by one lefs than the number of terms: fubtraét this product from the greateft ex- treme, and the remainder will be the leaft extreme. 1. Given the greateft extreme 12, the humber of terms 6, and the common difference 25; required the leaft extreme ? anf. 2. 2. A man going a journey of 12 days, increafed every diy "journey 3 miles, till his laft day’s journey was 38 miles; how many miles did he travel the fir{t day ; anf. 5 miles. “3. A perfon clears a debt of 345/. at 10 payments, increafing g/. in arithmetical progreflion, till the laft payment amounted to - 57/, how much was the firft payment ? “anf. 121, GEOMETRICAL PROGRESSION. A Geometrical Progreflion, or feries, is a rank of numbers. which continually increafe or decreafe, by the multiplica- ‘tion or divifion of equal numbers, called the ratios ; thus, © 2, 4, 8, 16, 32, 64, here the multiplier or ratio is 2. 64, 32, 16, 8, 4, 2. the divifor or ratio is 2. 3> 9s 27, 81, 243, one 243, 81» 2%) 95 3: the ratio is 3. In a geometrical feries, the product of the extremes. is equal to the produ& of any two. means equally diftant from the ex- GEOMETRICAL PROGRESSION. 145 tremes; thus, 2X 644 328 X 1622128. When the num- ber of terms is odd, the fquare of the middle term is equal to the product of the extremes, or any two terms equally diftant from the middle term. | If over a feries of terms in geometrical progreflion, when the firft term is equal to the ratio, be put an arithmetical feries, whofe firft term and common difference are each one: then the addition or fubtraétion of the terms or indices of the arithmetical! feries, correfpond exadtly with the multiplication or divifion of their refpective terms in the Geometrical feries ; thus, he eae Per A Pa oe », Indices. 31 9» 27, 81, 243, 729, 2187, Here 3-+4=7th arithmetical feries. So 27 x 81=22187=7th term Geometrical feries. Here 7—3= 4th term. So 2187-~-27=81=4th term. : If the geometrical feries begin with one, the firft term of the che arithmetical feries mutt be a sia sige Sabie a Patani ident , Indices. B58). tay By F410, = 32, i When the terms of the arithmetical feries begin with a cipher, the fum of the indices made choice of muft be one lefs than the number of terms given ia the queftion; for 1 ftands over the fecond term of the geometric feries, 2 over the third, &c. Here 2-4-4==6th term, arithmetical {eries, So 4x 16=64=7th term, geometrical feries, If the firft term of the geometrical feries be greater than 1, and different from the ratio, then the firft term of the Arithme- tical feries muft be a cipher ; but, in this cafe the product-of any two terms in the geometrical feries, mult be divided by the firit’ term, to make it anfwer to the fum of the eorrsfponding terms im the arithmetical feries ; thus, O; qT, 25 3, 4s 5» 6, 5) 15, 45) 1352 405, 1215, 3645, Here 2-+-4=-6th term arithmetical feries. So 45 X 405=218225 53645 ne term geometrical fe. ries. In geometrica! progreflion, there are alfo the following five particular things to be obferved. 1. The leaft term. tremes. 2. The greateft term. t Extremes 146 GEOMETRICAL PROGRESSION. -3. The common ratio. 4. The number of terms. .§. The fum of all the terms. PROPOSITION ‘. ‘When the extremes and the number of | terms are given, to, find the ratio. Rurr.—Divide the greater extreme by the lefs, and extract fuch a root of the quotient, whofe piety is one lefs than the num- ber of terms. 1. Given the extremes 3 and 2184, and the bumber of terms 73 required the ratio ? ‘anf. 3. 2. Given the extremes 5 and 36459 and the number of terms 7; required the ratio? - anf. 3. 3. Suppofe a perfon buy -10-acres of Jand, and agree to pay 3d. for the firlt acre, increafing the payments in geometrical pro- grefion till the laft acre’s. price amount to 246/ os. gd. re- quired the ratio ? Bed a - PROPOSITION 2. When the extremes and the ratio are given, to find the; fam of all the terms. - Rure.—Divide the difference of the extremes by one lefs than the ratio, and to that quotient add the greater extreme for the anfwer. . Given the extremes 3 and 2187, and the ratio 33 re- shes the fum.of the terms ? _ anf. 3279. 2. Given the extremes 5 and 3645, and the-ratio 3; re- quired the fum of the feries ? 3 anf. 5465. 3- A gentleman, who had a daughter married on new-year’s day, gave the hufband towards her. portion, one guinea, promif- ing to double that fum the firft day of every month, during the firtt year, of 12 months; he got 2048 guineas, on the fisit day of the laft month ; required the young lady’s portion ? anf. 42991. 15s. PROPOSITION ' 3. When the lefs extreme, the ratio, and the number of terms are given, to find the greater extreme. GEOMETRICAL PROGRESSION. 147: Rue.—Find fome of the terms, by means of the ratio, and over them place a feries in arithmetical progreflion ; when the fir{t term is equal to the ratio, add fuch numbers of the indices together as will give the term required ; then multiply into each other the numbers of the geometric feries, which anfwer fuch in- dices, and the lait product will be the term fought. But when the firlt term is different from the ratio, add fuch indices together as will make one lefs than the term required, and, as before, multi- ply into each other the numbers of the geometric feries which anfwer to fuch indices, and confider the laft product a dividend ; ,then raife the firft term to fuch a power, whofe indice is one lefs than the terms multiplied for a divifor, and.the quotient will be the anfwer. ? ) r. Required the r2th term of a geometrical feries, whofe — firft term is 3, and the ratio 2? anf. 6144. z. Given the firft term 3, and the ratio 3, required the 2oth term ? anf. 3486784401. 3. Required the 16th term of a geometric feries, whofe firft ‘term is 1, and the fecond 2? anf. 32768. ' 4. A gentleman going to.a fair to buy fome good horfes, fiw a horfe-dealer who had 20 very fine ones, for which he afked 20 guineas a-piece ; the gentleman thinking they were over dear, the horfe dealer told him, if he would give him but a fingle farthing. for the fir(t, and double that price to the 19th, he would give him the zoth into the bargain: this being immediate- ly accepted; required. how much they were fold for, and whether the gentleman paid more or lefs than 20 guineas a head. — anf. They were fold for 27/1, 6s.. 1d. 2549rs. a head. 5. A fervant agreed with a mafter to ferve him 11 years with- - out any other reward for his fervice but the produce of a wheat corn for the firft year: and that produét to be fowed the fecond, and fo on from year to year, until the end of the time, allowing the increafe to be in a tenfold proportion: required the fum of the whole produce ? Note. 7680 wheat-corns will fill a pint; and fuppofe the wheat fold for 3s. 4d. per bufhel. anf. VATLALIA1I1O wheat corns—226056% buthels, 376762. os. 5d. the reward, 6. An Indian, called Seffa, having invented the game of chefs, fhewed it to his king, who being highly pleafed with it, bid him afk what he would ae for the reward of his ingenuity, See 2 SS 148 anf. 48 hhdss - 21. A and B barter, A has 42cwt..2grs. of fugar, at 3/. 155. per cwt. and 12 yards of cloth, at gs..1d.-per yard; B has 333+ yards of Holiand, at 8s. 34. per yard; required: who muft. pay the balance, and how much? ax/: B muft pay 27/65. 6d. balance. «. 22; Two men depart from’ the: fame »place; the one:goes = directly north, 14 mules a day, and the other fouth, 22 milesa = : day; how-far are they afunder on the 24th day? anf. 864 miles. . 23. A gentleman has'an orchard of fruit. trees; 4 of which » bears apples; + pears, 4 ‘plums, and 50 of them cherries; how « many trees are there inthe orchard? anf; 600. trees. 24.-A. linen-draper bought a certain: quantity: of Irith «and Scotch linen for 29/. 15s. 64.*the quantity of Irifh linen was 48 yards, at 45.44; per yard ;.and for every 2 yards of Irifh he ; had 5 of Scotch; how many yards of Scotch linen had he, and what-did it coft him-per yard? © - anf. 120yds. at 35.240, 25. A» gentleman: dying; left his eldeft fom5280/.:and his - youngelt + of that fum-;, 4 the father’s property was equal 14, times’ what he had left his eldeft.fons required how much the gentleman died poffefled of? « anf. 110001, 26. A fhip being overtaken by:a ftorm, the feamen, in order to lighten her, threw overboard 17 hogtheads of fugar,. worth 341. per bhd. the value of which was + of the indigo they threw: A’ Promiscuous Convection or, QuESTIONS.. Ist: out; they were alfo obliged to throw £3 cannons each. worthy’. 18/, tos. ‘overboard; the value of all that was caft.into.the ‘fea: . amounted to: 4 of 4% of the fhip. and cargo; withthe reft they»: got fafely to land; required. the value: of the fhip and cargo. » before. the ftorm, A Paomisevous Cottectron’or Qusstions~ batters wich B for two forts of goods, the one at gd. the other at 8d. per /id..to have + in money, and of each fort.of goods an equal quantity ; required how many 2. of each fort.of goods he... muft have, and alfo how much money ? anf. 139444. of each fort, and 37/, 15s. 6$d.-in money. 35. Suppofe { buy fugar for 3/1 1552 per caus and fell it for 4l. 6s. 3d. per cet. payable in 18: aieanegh ; how much do I gain per cent, per annum? © anf. tol. 36. A merchant in Londonexports goods to America, amounting to 57848195. 6d.« which are fold far 9261 83,5. currency + the factor dedudts 5/. per cent, for commiflion and charges, and remitssthe remainder at 130/.. per cent, how much is pained by the’adventure:? anf. 981. os. 3d. 37 1fthe‘exchange between Holland and Hamburgh be 67d. fiemith per-dollar,and between Holland and Germany at 70d. flemith:per florin ; tata the par of exchange between Hol- land and-Germany anf: 73~°,d. per florin, g82°T he quae of {choiars in a certain {choal is as Follows; : +g learn fluxions, =% learn algebra, .x’5 learn geometry, 3 arith- metic, and 9 Jearn furveying 3 paoaciin the number of each ? anf. 5 learn fluxions, 12 algebra, 24 geometry, 30 arithmetic, and g furveying; total 80 {cholars. 39. Lent, on Chriftmas 1780, the fum of sooo/, at 4% per cent, after,which I lent feveral fums at the fame rate, and drew upon: the borrower as occafion required, viz. on March 25th, 1781, I drew for 194/--55..0n June 25th, [lent 676/. and drew for 700/, on: September 25th: following, 1 lent . 5692 175. required how much remains due to me? anf. $516l. 11s. 62d, 40, Three perfons, D, ns and: F, buy a fhip, of which 'D paid 4 of 9, paid of +3, and F p40/. how-much.did D and E pay, Sccd elias part-of the fhip had I? anf. D: paid 3054 gsetged. E 26h. 58. 5d, 12igr. and ¥F had $5 of the fhip. 41, Suppofe L gains 26/,in 6 months; M 36/..in 5 months, ‘and N :46/. ing, months with a ftock of 155/. what was the general ftock ? anf. 5041. 15s. 254d. 42. Bought. a quantity. of goods for 480/. 12s, upon. ex- amining them, 4 of the whole was damaged: fo that 1 could only fell the damaged part for. 5s. 6d.’ per yard.:\and by fo doing loft 48/. 18s. at what rate per ell Englifh muft 1 fell the undamaged part to make:upmy lofs? : .anf.-nes.2d, 1i2S tor. A Promiscuous Cottection OF QuESTIONS. 153 43. There is a crown weighing 60id. which is made of gold, filver, copper, and brafs;.the weight of the gold and filver to- gether is 40/5. of the gold and copper 4544. and-of the gold and brafs 36/:. required how much gold was ia it? anf. 30%/b. 44. There isan Ifland 73 miles round, and 3 footmen all {tart together, to travel the fame way about it? A travels 5 miles a day, B 8, and C 103; when will they come. together again? _ | _ ‘anf..73 days. 45- G and H barter: G has fugar worth 8d. per 4d. but in barter rates it at 13d. and gives g months credity.H has tobacco _ worth tod, per “id. but in barter infifts on 17d. required how much credit H muft give to make the barter equal ? anf. 6 months. 46. Two merchants, C and D, buy a fhip. worth 1800/. they have unequal fums of money, for C fays to D, lend me + of your money, and 1 will be able to pay for the fhip: and fays D to C, lend me-4 of your money, and then I can pay the value of the fhip : how much had each perfon?. anf. C 12001. and D-gool. 47. Divide 222/, 16s. 13d. among 3 men, 9. women, and 17 boys, and give each man as much as 3 women, and each woman . as much as 5 boys! Sein Te’ anf. Vhe men mutt receive 93/.. 14s. oid. the women. ., 93/. r4s. od. and the boys 35/7. 75. 113d. 48. A merchant in London fent over to his correfpondent at: - Amfterdam 1000 moidores, the charges for fhipping and.come . miffion came to 5/1. 19s. 6d. when they came to. the place con- figned and were weighed, they amounted to. 14209¢4.,.14,f% currency ; I demand the value in fterling money, and how much the merchant gained or left by his moidores, the .agia being at 5 per cent, and the courfe of exchange 345. 6d, flemith per /, fter-__ ling ? anf. of. 6s. 32d. loft. 49- A gentleman left a handfome portion to his two daughters, _ the elder had 4 of 3 of his fortune, and the. younger. had 50004/. which was juft + of the elder’s portion: required how much the father died worth ? » anf. 1754 4b. 50. A merchant bought 14000 feet of mahogany, Spanifh meafure, for 609 dollars, each 582d. and paid x60. for freight, - commifion, and other charges ; what did it.coft him per foot Englifh, one Spanifh foot being to. one Englifh, as 1-004 to 42. anf. §°218d, g1. Hiero, king of Sicily, ordered his jeweller to make him 154 A Promiscuous Counecrion OF QuESTIONS:. a crown, containing 63. ounces, of, pold; the workman thought fubftituting part filver. therein: a proper. perquifite, which coming - to the. king’ sears, he. ordered the famous Archimedes to-examine -it, Who putting it-intoa veflel of water, found.it contained 8°2245 cubic. inches, and having‘found that a cubic inch of gold weighed 10°36 ounces,-and of filver 5°85 ounces: he found what part of his majefty’s: gold had been changed, and you-are defired to re=_ peat the procefs.. anf. There was 3402. 3dwis. 22}. grs. of gold, and 280%. . 16dwis. 129r. of filver in the crown. 52-.A, ‘in order to put off 720 ells of holland, at 6s. 8d: per | ell, phick is only ‘worth «4s. propofes,-in cafe he has half the value: in money, to give B a difcount of to/. per cent, and to take the reft in faffron; B, apprifed of A’s intention, rates in . juttice his faffron. at 3Os,.per pound: required what it was really worth, and what quantity of it muft be given to. A? anf- The faffon was worth 20s. per 44. and A mult receive mand. of it. 53.-A merchant having fold tobacco at 15d. per Ub, loft 10 . per cent, refolving ‘to make up his lofs-and fomething over, he fold’ too/, worth® of another parcel, and gained thereby 4o/.. Pet Sent, required how many /#6. weight there. were-in the laft parcel, and what he oe it for per 45: anf ro28Slib. at234d. per lid. - 54. Bought -hofe at’ London for 3s. tod per pair, and ‘fold them afterwards at Dublia at 5s. 6a. per pair s.now taking the - ‘charges at an average to be 13d. per pair; and confidering I mutt lofe 84 per cent, by remitting my money home apa ; ‘what will gain per cent. anf. 351,-t4 part of the thip’s cargo ; his ftock had the fame proportion to. his part thrown overboard, that the whole cargo had to the whole. thrown overboard, and 3% times the quantity calt overboard "was 34 times the whole fhares of A and B. When they cameo land, A fold his remaining part for Al. 4s. per cat. and found binifelt 4 loler of 10/. per cent, B advanced the remaining part of his fugar 20/. per cent, and C gained 4s. 8d. per cw. ‘by the: quantity he faved ; how much did each perfon lofe by the woyage:s the charge of which amounted to 500 guineas ? anf. A 83l. si. B 30042. rps. C1g74l. 9s. 6d. 66. There were 25 coblers,: 20 taylors, 18 weavers, and 12 combers, fpent 6/. 13s. at a meetings to which reckoning 5 coblers paid as much as 4 taylors, 12 taylors as much as 9 weavers, and 6 weavers as much as 8 combers, nay much did each company pay, and hi each man? d. 5. ~ anf. Coblers 11 re o each 1 4# Taylos 115 © — I 9g Weavers 2 2 0 — 2 4 Combers 1 1 0 —— 1 Q 67. A had 15 pipes of Malaga wine, which he parted with to B for 44/. per cent profit. B fold them to C for 38/ v1. 6d. advantage ; and C made them over to D-for 500/, 16s. 8d. and thereby gained 64/ per cent. What did the wine coft A per pipe? i anf. 271, 143. Bf2E404, a eas ez t58 A Promiscvous Correction or QuesTions. af . . 68. A town is fupplied with water brought in pipes from 3° different fountains at the diftance of 14 mile, 2$ and-24 miles; each foot of pipe weighs 12/. at 23d. per lib. expence.of lay- ing them 13d. per yard; cifterns and other expences amount to 4¢4/. fix hundred of the inhabitants agree to pay as much annu-— ally as will amount to the intereft of the money expended at 5/. per cent, how much will each perfon have to pay ?_ anf. (Ose 69. Suppofe the diameters of the bores of the pipes in the above queftion to be 42, 52, & 6% inches; andthatthefirftruns 4 gallons per minute, and the others in proportion to the fquares of their. diameters; Now it was found that the number of fa- _ tilies ia the whole town was fuch, that each would haveexa@ly as many pallons per day, as the firft pipe run per minute; How many families were there? anf. 6640. © nS Lal? ie iS ‘ on Se ORS : Wee gay ; i, : ‘a ‘ ( * : % Book-Keeping by Single Entry. a6 1D5N, a! Na @ yon 7 OR Lk cr i Ry Book-keeping by Single Entry, only two books are necef- fary ; day-book and ledger. In the day-book are recorded, promifcuoufly as they happen, what goods are fold on truft, and what goods or money ts‘re- ceived. In the ledger are inferted the feveral accounts belonging to each different. perfon, which Jay difperfed in the day-book, and are arranged in their proper order of Dr and Cr. ‘ihe left fide of every page being appointed for the Dr. and the right for the Cr, ° An aiphabet is prefixed to the ledger containing the names of the perfons whofe accounts are therein. Direéions for the Learners Copy into the day book one month’s accounts, and calculate them by their proper rules, which will be of preat fervice to the jearner. [hen begin with the firft account of the day-book, and poit it into the ledger, leaving a convenient fpace below it to contain more accounts; and if it confift of more than one article, write, To /undries, if Dr. or Ly fundries, if Cr. next enter the name in the alphabet under the firtt letter of the furname ; and laltly write the page of the ledger, where it 1s placed, oppofite the account in the day-book. Do the fame with all the firft month’s accounts; and then copy the fecond month’s into the day-book, and poft them in the fame manner : proceed thus till the whole be finithed. Obferve to Icok ‘into the alphabet before you poft any account, to fee if the name be there. If it is, place the account in the fpace under the name. When any place is filled up, the balance of the account mult be transferred to another page. The DAY-BOOK. Newcastir, January 1, 1798. Mr William Pelafe: Br. To 29 buthels cf wheat, at 6 per bufk. malt, — 8 _ barley, — 5§ Oats; — 4 aM Robert, Jenkinfon, Dr. | i Pearle cloth, qt. 1074 yds. at 6d. 3 ee “Me r Foi ofeph I. akefeld, Dee APE eg Tid. Been téa,.. at 16° 9. per: Be. $—- bohea,y — 8 9 , 0%. nutmegs, -——- O 14 per oz. — black pepper,— On 27 19% lib. foap, — 0 83 per id, 15— Mr ‘ecaibiin Wi interton, pe TNE & To ‘5a dat of brandy, . * 14 10 per gal. —— red, port, Hee & —— malaga, — hfbon, mountain, 24— Mr eee Goof, Dr. $, od, AUF, at 10. 6 per gal. gin, Preheat ei 9— DA¥.BOOK.” Neweaftle, January 26, 1798. ¥} Mr Andrew Tomlinfon, Dro $+ de To 11 pair of black filk ftockings, at 12 6 p. p. —— 9 white filk ditto, —16 7 =——} © — 19 - worlted ditto, — 5 3-——| — 17 cotton ditto, — 64 —j| _| an Fobn Weflerley, Efg. Dr. ey Pega f To 27 pair of red harrateen, at 4 16 10 p: p. — 19 cotton, — 219 4———- 2 ne 2 Mr Faslua H irene we - bush, pec. To 27 3 of peafe, at in mn per bufh. — 4 242 tares, ° ~~ 2 If February 1 2b Mr Humphrey ee Dr. d. To 7thoufand quills, - at 2 .g per dund. — 21 reams of paper, — 1 3 per guire. 2 Mr Thomas Barrowman, Dr. To 17 {tones of foap, at 62d. per fb. 24.2] Mrs Arabella Furhnch, Dr. Se 12 10 per yd. No 193 yds Flander’s lace, » at — 30 —— ribbon, —__ — 4° fans, ° — 5 6 each — 9 farcenet hoods, — Ee OEE Sa eas leads Perret tess tates 3 The Hon. Lord George Mountain, Dr. To 17 bbds. of wine, at 7s. 2d. per gal. Ore. 162 DAY-BROK: Newealftle; February 21, 1793. —— taffety, 4 green filk dace 16 } 3 Lady Luring, Dr. -- 5. Gs To 6 pair of lamb gloves, at 2 3% p. pair. i 8 kid ditto, —2 6 — 24% yds of muflin, — 610 p. yd. 3 Mifs Loui ifa ols bos, sate To 173 yards red filk, at 10 2 per yd. es 26 brocaded fatin -- 19 6 14% paduafoy, — 69 2 Q Pett mee ome 20% March 4——.- Mr Fofeph Wilmot, Dr. To 8 ftones of bacon; at sd. per iid. 4 eee 4 Sir Henry Grain, Dr. die. a cies To 4 table fets of china, at 2 14 9 each — 24 dozen of plates, —-o 4 7 a piece — 14 coffee cups, — 010. 6 per doz. — 7 large punch bowls, —.0 14 10 each 4\ | Lr Gregory Emerfon, Dr. he! [To 28 Hutten’s arithmetics, at 2 33 a piece —- 16 Euchid’s Elements — 76 ——. | fy i. 4 Myr George Kidman, Dr. . {To 32 bufkels of wheat, at 6s. 1d, per buth. « DAY-BOOK: 163 j————-———-Newcafile, March 30, 1798.——--_—— Datel de 4 Mr James Newcafile, Dr. fo dein, To 17 dozen pen-Knives, at 7 6 per doz. — 29 fire fhovels, —.3 7 each — 16 doz, plain iron candleft. _ 3 1% p. doz, | Tare April 4 sa Pas ed 5\. _ Mr Alexander Penrith, yeh bode To 96¥ yards. nankeen,,; at 1 8 oper yd. - — 334 blue cloth,, —- 5 o —— — 274 —— drabclothh ~—-5 o0 —— — 24. , red cloth, — 7.6 ——— 32! 5\10 10 Sania Mr Thomas Barrowman, Cr. ss cafh in full. = ° - - - 6 3/112 (hae EE | 31 Mifs Louifa Darlington, Dr. To 33% yards of figured filk, at 4s. per yard. 6.13} . April 20- Mrs Arabella Farmer, Dr’ Sel cae _\To 120 yards ribbond, at 7 6 per dozen — 36 do. camblet, — 1.9 per yd. — 36 do. crape, wh gp rg apa seas — 60 do. bombazine, — 4 °0 — 40 do. grey ftuff, — 19 —— 25 alo we ee 2 He Mr William Ogle, Dr. : fe e [fo 28 yards fine blue cloth, at’ 16 0-per yd. —— 15% do. blue grey, —138 —— I 284. - do. raven grey, —136 —— 1 DAY-BOOK. « —Newcaftle, April 27, 1798: Sir Henry Greatmaa, Dr. oz. dwt..gr. -s.. d. To a filver cup, wt. 47 16 oat 7° 6 p. ox} -— a filver punch bowl 16 17 12 -- 6 10% — — 3 doz. {poons, 30 18 -O-- 752 ey 3 candleiticks, Sk 4 Oe 5 me —— 10 plates, 67 13 0-6 7 — SSS Se RS a PRS Seat gainers Sen ge LS 20— The Hon. Lord Geerge Mountain, Cr. By a bill on Mefits Dougias-and Co. for 4 Lady Luflring, Dees Lae per yd. 1To 20: yards mantua, at ° - perfian, — 8 . dawn, eee 6 he fe) aeambnicy. xb es May. 1-——- Myr George Trader, Dr. To 894 yards of check,. at 72d. per yd. —— 183- do..of .do. -—-10d. —— — 434 do. of do. — told; »—— — 253 do. of do. — od. —— Mr William ebajoy Cr. By cafh received By abatement My, ie rep 5 Mr Nickolas Cheefemongers ae i ewt. grs. lib. To 3 2 17 Chefhire cheefe, at .2 é LO p.cw. — 1 3 14 Glocefter ditto. — 1 15. 6 -— — 4.0 16 Suffolk dito. 012 JE — 6 2 20 Yorkshire ditto. DAY-BOOK. Newcaftle, May 6, 1798.- Mr Mofes Greenwell, Dr. Se To 31 yds. worfted white fhag, at I 9 p. yd. . — 30 — ditto blue, — 110 — — 3ci— ditto ditto, — tr — — 31 — ditto fearlet, —2z2 8 — — 16 =< ditto bluehar: —5 g — IZ Mifs Louifa. Darlington, Dr. were tase 3 x To 24 yds of ducape, at 7 6G per yd. j— It do. brocadey —— gQ 8 -——— — 104 do. luftring, —- 5 3 —— — 4 do. perfan, —- 1 9 —— 19 — 3. Mr Fofeph Wakefield, coh So [o 4 lib greentea, at 17 6- p. Hid, — 12 do. bohea, | 9g do. pepper, 8% do. coffee, —~ 77 0%. mace, ee. 27 Mr Robert Fenkinfo 1 By cafh in full = - June 6 —— Mr Foshua Houfekeeper, Dr. | $y sy er. To 6 quarters oats, at 2 4 per bush. —- 318 buthels peafe, — 3 9% hag 12 bean, —4S —— i 19 ——— tares, — t10 — — 7 quartersmalt, — 3 15 —— cae 5 lib, hops, — 1 § per th, . DAY-BOOK. —Newcattle, June 11, 1798. Mr Erafmus Gordon,»Dr. To 14 cwt. of ah 6s. 94. per ftone “ Mr Hemp drafongy | oe : By cafh in full os 19 . , “Mr William Fobnfon, Dr: To 6 las bs baricys at 34. 4d. . 25 Mr Andreas Farrifon, De. d. Ta 2” calf fins, at 9 — 75 fheep ditto, —_ 7 — 36 ditto ditto. — 1 8 ——— — 15 buck ditto, — 6 —— per fkin« 17 Rufha hides 120 lamb fkins, ———- Ful Mr -Fohn Montague, Dre Fa Sh a ta Ob $e {Co 19 gallons of gin, at 2 5% per quart - -— 20 anchors of brandy, 11- 6 per gallon \ 1 NORD pa eS ~ i2 Mr T hosed Merchant, Dr. cwt. gr. lib. SY Bot damn.) hae To 1 2.18 of pepper, ato 1 irk p. Xb,. —9O 3 14 cloves, —0oO 4 9 30, 1° 7 vaiGns, —4 1 19.20 “p.cws. I— 4 2.19 foa—p, —2 18 8 —— : 1 : Mr % ofhua Houfelecpr, te To 27 dozen of candles, at. 64d. per (id. ~ : ed ee ee (24| 610. | 2. DAY-BOOK. | Newcaftle, July 14, 1798.- 4 Sir Henry Greatman, Cr. $0) ds By 20 lafts of wheat, at 10 114 per boll — 14 — ditto) —10 6 Bie ag ay se ee ee 2 O 43 The Hon, Lord George Mountain, Dr. '|To 6 puncheons of rum, at 105. 9d. per gallon. |270|18) © 3 Mifs Loutfa on eae Dr d. 10% yds, fattin, at 6 6 per yd. 15 —_ brocade, ee EO OS 11 fcarfs, — 10 0 each i— 14 yds. Genoa velvet, -- 17 4 per yd. [ 10 — Juftring ni 5 bes SRO aR ee aE 2. FS Mr Harty Goodfellow, Cr. "|By cafh in full - - : - S re as dr George Candleftick, be To 6% tuns of tallow, at 7s. 4d. per ftone ———___ —___—-- Auguft 1-.. ae Mr Fofeph ine rae To 3cf. 1245. of bacon, ato 5 8 per flone — 13 firkins of butter, — 1 12 6 per fr. 29|17) 42 Mr William Ogle, Dr. 5 Se ° ‘1To 434 yds. broad cloth at 17 9 p. yd. — I1coy—- common yd.w.— 4 oe oo — 72 — fine narrow, 3 — pen 7 — 24 — fuperfine Span. blue 18 6 _ 168 t DAY-BOOK. ‘(nme Newcaltle, Aupult 4, 1798. Se Sesh Ay 6 Mr Thomas scl uaa Dr. t. gr. lid. ha “dd; Io t 10 3.18 offugar, at 2 16 10 p. cut. } J eich as coin: —29 6 o — ae o 17% —raifins — 1 19 10 ~ 14 .— hops — 614 9 —— Ic —— Sir Henry Greatman, Dr. To a plate of gold, wt. 100z. t4dwis. Sgrs. at se 145: Od. per ounce Mr Fonathan Wi ee tat Gr. By cath i in full . cay r Ahn tsi OREN Cece r Sere Ge ces Gee a Mr Fames Newcafile, Dr. d. Hy y } i i ‘ } ty 2, To 5. doz. fine feel fnuffers, at 1 62 a piece — 24 —. London razors. --2. 4 — 63 — Kentith hammers, - 5 64 a doz. id 2 Ome ee Mr Febn We gflerky, Cr. By cafh in part —s = ar ike 6 Seeeuserecme eee Fy Mr Fofoua Heap eer, Dr. d. To 26 blue quilts, at 0 10 113 each — Qchintz ditto, —r °— ‘;— 16 pair of fine blankets, o i Bz per pair Sept. 6 2 i Mrs rdbill F armen, Cr. Bycehiin fall DAY-LOOK. 169 Newcaille, September 6, 1798. LMr Fofhua Housekeeper, Dr. To 181 buthels of oats, ai 2s. gid. per bubh. barley, - 45. gd. Le) {2 lwo PRIDE TNE A SaaS, Pe Oa GE SE Ea dea ok i 4 Sir Henry Greatman, Dr. : Mies To 34 hhds. of beer, at 1. 12 per pal. , — 10 gal. of gin, — 2 5% per quart | L222): 2 4 -- 12 fdr Fobn Wefterly, Cr. SeEEraneeeess oe w ae By cath in full Y - _ 871 tro wal IE pn al ~loO—s ——- 5 Mr Nicholas Cheefemonger, Dr. | ewt.g. lid. Bis ys [o21 7 Chefhire, Be ne Mia 05 0 cut. — 30 Ig Glouceiter, roe kA 8 | — 6 1 16 Stilton, —I1 8 Darcey — 7 0 14 Suffolk, —O 14 10 25] ta} 53 PIR) pone tr sala ale La 3 Mis Louifa Darlington, Dr. | Co 693 yds. diaper, at ts. 64. per yard 5) 41 72 20 I Lr Faeph Wakefield, Dr. Co 60 4b. of tea, at 74d. per ounce 30} O] © Mr Fofeph Wilmot, Cr. 3 By cafh in full ° - - - - 32| 8| 73 27 Mr Fames Neweajlle, Dr. 4 aornds [o 5 quarter$ oats, at 2 3. per bufh. — 7 bran — 1 10 — 9 bufhels beans, — 4 10 — 19 tares, — iil —— — 16 peas, — 3114 ——, ——— } RP v6.15 tk ti pen ceihitiinirdeieet 170. DAY-BOOK. --Newcaltle, Odtober 2, 1798.- The Hon. Lord George Mountain, Dr. O%. Abs! O0an . 52s Toa fil, fet of caftors, wt. 25 10 10 at 7 9 pro. plates, -- 85 14 15-6 6 — ——iea pot and jamp, -- 29 16 15 - 6 4 — eS eue See ee *3- , Mr Alexander Penrith, Dr. To 185 yds. {carlet, at 10 6 per yard — 200 — fhalloon, oe aes + 12 doz. twift buttons, -- 1 6 per. crat | Mr George An Gr. By cafh in part “ - - i : Lady Lnfirings ar ee To 62 yds ducape,- hat 6 is per yard — 53: — brocade, — $8.10 He: it — Perfian, . — 1 22 ————— — 213 — luftring, — Do Beh es URES 7 REE ato Aaa. Mr George Trader, Dr. To 19 {tones of leather, at 1o%¢. per Ud. 2 Mr Foshua Sonlttnheo Cr. By cafh in full . - 2 ASNT AAT A ns a Mr Thomas Mabie De NeSvge Hb. A wee To 45 fs ro of fugar, at 2 7 6 percat. 12 Sir Henry Greatman, Dr. To sue ih of mountain wine, at 4s. Y per gallon - - - P Y > DAY-BOOK. ry -Neweaftle, Oober 16, 1798..—— ' £. {5 | Mr Fofeph TE Cr. By’cath in part : # Y Mr Andrew Tomlinfon, Dr. | ‘ | s 15 pair of cotten hofe at 3 2 worlted — 3 18 ~—— ftrawberry, — 4 mute, — 2 —16 16 —— filk gloves, 74 Norwich hofe, 11 —— filk ditte, bE EP 18 6 Mr Fobn ri alae Cr. By cafh in full - - . Mr Thomas Merchant,. Cr. - cw, g. fea a By 19 3 hops, at 5 5.10 per cwt i LO, Py — 419 O news Mifs Lout/a Darlington, Dr. Y ell flee |: $c; he To 17. «1 of Flanders a at 19 Se pelt, neloal ia Mr Gregory Enerion Cr: ‘By cath in full : - - - gi 4) 2 (Ph oR Gang ar > eearass wea mama wc 7, ee 6h Mr George Candleflick, Cr. yds. q. na. so By 13 14 0 of Irih linen, at 4 84 p. 7d — 87 01—muilin — 87 — Lf - i 3 ne Nov. 1 a 5 Mr William Ogle, Cr. By 379r- 7bush. of oats, at 14s. gd. p. quarter. |. 2713) 75 3 i Lady Luftring, Cr. f By catia fall 9 je ai a oS Og ay ae DAY-BCOK. Newcaiile, Noveniber 1, £768. Mifs Des ifa Be ie Cri. By cafh in parts - i Mr Fofbua Havhebeepons Dr. cw. gr. lib. EEA Ne" & To 28 2 17 coarfe fugar, at 2 19 43 p. cut) Ake Fofep? gees OF. CE reece ge naa eae sa ET Mr Mofes Greenwell, Cr. By cahh in full ‘4 4 : if ——_———12 The Hon. Lord George Mountain, Dr. meee To 112 dd. of coffee, at. -§ 4. per Ab. —~ 52 {tones of fugar, — 7 6 p. ftone ry Air Era/mus Gordon, Cr. By 7 grofs of buckles, at 1s. 24d. per pair 1 Gene en Mr George Faminfon, Dr. Todds d. To 4 frails ¢f raifins, wt. 448 at 32 p. J, 6 cy Raa «i eager — 1 puncheon of prunes 604 --. 74 —— 3 bags of pepper, 1774 = 9 —— eed 20 Mr Andrew Tomlinfon, Cr. . oy 181 yds of cloth, at 2s. gid. per yd. ec al * arene ae cece 4 The Hon. Lord George Menai Dr: d, To 137 gallons of rum at Ss 2 per gal. > WP ns meen paceatelrcamts yy Meceend! beac 4 DAY-BOOK. 173° Newcaltle, November 26, 1798. | 4 Mr Fames Neen Cr. By cafh in full °° - > > 40,15, 18% aay 8 Sir Has Fafa cia, Dr,. To B71 ¢ oz. of plate, at 5s. 4d. per ounce |232! 5) 4 December 6 5 Mr Alexander Penrith, Crs By cafh i in full : - - - . 5) ty OF Cana GRR ESTAR 8} Mr Danlél Roberts, Dri- MBM i To 171 yds. thalloon, . at 2.7 per yard — 173— — 211 - — 175 — Yorkth. cloth —-4 9 — 177 fine.narrow, — 7 10 . 158} 4| t ah Mr Fofhua ; Hoag, Cr. By cafh in ful - - . ton a 84 g} = Mr Ambrofe Patrfn, Be Waves ia!) Sa Oe ro 12 pi. ribbon, meafuring 7g at 1 6S p.y. => 20 rio STE Sa tar Sas ONT aet Taner — 16 ———, -§- —————_ 821 — 1 ok — sce aay ieee, iauseamencench erty suammewnnte ui lec bua beer Peaeed en hess mee: 6% —12 I Mr William Fobnon Cr. By cafh in full’ - ° > Bo] Oo} O Mr Nicholas Cor enanects or By cath i in part - - 40) O}.0 : 16 - 6 Mr Andrew Harrifon, Cr. By cath i in full - - - : 381171 5 7 Mr George Faninfon Cr. By cafh in. part wt id ~ * 80i ol Oo 2 P 3. | ee | SED To 743 yds. linen, at 3 — 873 — muflin, —6 8 DAY-BOCOK. —Newcaltle, December 20, 1798. Sir Henry Greatman, Dr. Se 26 &. 4 per yard The Hon. Lord George Moumies Cr. {By cafh in full - he Mr William Holdioess Dr. To 350 razors, ; at 1 33 each \—- 420 penknives, — o 9g — 950 pair of fciffors, -. —- oO 2% p.p. — 230 — — —o 44 — “Mr LUPE: Hates Gr. By caf in full Soe CE Mr George ia ae Cr. By cath in full * -29 Mi ifs ace cabs Stak ee Cr. - By cafh in full Mr George Jeet Cr. 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O37 snp VOsUTTLUO 7 AV OF ih Setuupany oO} “47 er and Tret ils of Parcels Queftions Vulgar Fractions Reduétion Addition Subtraction Multiplication Divifion Rule of Three Rule of Five Queftions Simple Addition, a ANotation of Decimals 4. | Addition and Subtraction go 6 | Multiplication . 8 | Divifion to | Reduction 13 | Rule of Three 15 | Rule of Five 24 | Square Root 26 | Ufe of the Square. Root 32 | Cube Root 35 | Ufe of the Cube Root 39 | Tonnage of Ships 43 | Duodecimals 46 | Squaring Dimenfions gi | Lof and Gain $4 | Barter 56 | Simple Intereft 62 | Compound Interefé 65 | Aquation of Payments 69 } Difcount 75 | Company 76 | Exchange 82 | Arbitration 83 | Allegation 84 | Pofition Progr effi on 85 | Quefiions 86 | Book-Keeping by Single 87 Entry Decimal Fractions ‘~ 88 | Appendix 103 106 107 10g III 112 113 115 11g 120 TAI 122 124 134 136 139 142 148 | 159 187 a