*->.^< IMAGE EVALUATION TEST TARGET (MT-3) I.I 11.25 I 1.4 12.0 iSk i.6 V] P%T J> *^ ^v.^^ ^ ^ > /^ ^ :^ .^^ s^. 'W V Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 K^vi* ^. CSHM/ICMH Microfiche Series. CIHM/ICMH Collection de microfiches. Canadian Institute for Historical Microreproductions / Institut Canadian de microreproductions historiques ^ Technical and Bibliographic Notaa/Nota* tachnlquaa at bibliographiquaa Tha Initituta haa attamptad tu obtain tha baat original copy available for filming. 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This item is filmed at tha reduction ratio checked below/ Ce document est film* au taux de reduction indiqu* ci-dessous. 10X 14X 18X 22X 26X 30X / •J 12X 16X 20X 24X 28X 32X tails du sdifiar une nag* Tha copy fiimad hara haa baan raproducad thanks to tha ganaroaity of: McLtnnan Library McQill University Montreal Tha Imagaa appaaring hara ara tha baat quality poaaibia conaidaring tha condition and lagibiilty of tha original copy and in Icaaping with tha filming contract spacificationa. L'axamplaira film4 fut raproduit grica A la g*n*roait* da: McLtnnan Library McGill Univartity Montraal Laa imagaa auivantaa ont it* raproduitaa avac la plua grand SvVn. compta tanu da la condition at da la nattati da raxamplaira film*, at an conformiti avac laa conditiona du contrat da fllmaga. Original copiaa in printad papar eovars ara fllmad baginning with tha front covar and anding on tha laat paga with a printad or illuatratad impraa* sion, or tha back covar whan appropriate. All othar original copiaa ara fiimad baginning on tha firat paga with a printad or illuatratad impraa- sion, and anding on tha laat paga with a printad or illuatratad impraaalon. Loa axamplairaa originaux dont la couvartura an paplar aat imprimia tont filmia an commanqant par la pramlar plat at an tarminant aoit par ia darniira paga qui comporta una amprainta d'Impraaaion ou d'llluatration, soit par la sacond plat, salon ia eaa. Toua laa autraa axamplairaa originaux sont fllmte an commandant par ia pramiira paga qui comporta una amprainta d'Impraaaion ou d'illuatration at an tarminant par la darnlAra paga qui comporta una taila amprainta. Tha laat racordad frama on aach microficha shall contain tha symbol —^^ (moaning "CON- TINUED"), or tha symbol y (maaning "END"), whichavar appliaa. Un doa symbolaa suivants apparattra sur la damiAra imaga da chaqua microficha, salon la caa: la symbola -» signif ia "A SUIVRE". la symboia ▼ signiffa "FIN". Mapa. piataa. charts, ate. may ba fllmad at diffarant raduction ratioa. Thoaa too larga to ba antiraly includad in ona axpoaura ara fiimad baginning in tha uppar laft hand comar, laft to right and top to bottom, aa many framaa aa raquirad. Tha following diagrama illuatrata tha mathod: Laa cartaa. planchaa. tablaaux. ate. pauvant itra fllmte i daa taux da rMuctlon diffirants. Loraqua la documant aat trop grand pour itra raproduit an un saul clich*. il aat film* i partir da I'angla sup^riaur gaucha. da gaucha i droita. at da haut 9n baa. an pranant la nombra d'imagaa nicaaaaira. Laa diagrammaa suivants illuatrant la mAthoda. rrata o :elure. 3 32X 1 2 3 1 2 3 4 a 3 ■ p ■ 1 ^•^--^. ' m m f ' ■"■ K' ^ 1 ^^1 B "** 1 ^M ^ ^^Kr y ■ V E * ■■ ' \ ^K^^ ' * / * • * 1*» i, \ mmmmmm CONCISE INTRODUCTION TO PRAeTICAL ARITHMETIC: FOR THE USE OF SCHOOLS. BY THE REV. JOHN STRACHAX, RICTOII OF CORNWALL, CPPtR-CAI»A*A. 5 m MONTREAL, PRINTED BY NAHUM MOWER. I60 9»~ ■k^:^ ^ * .* r .«^ ^^i vnEPJLCt, '/; ON my arrif al at Ringiton about ten jreart afo ia*»i perintend the £ilMtion of a select nmnber of Popiliy I Mpcriencfid mocliHiconTenieBce from the want of School* Books. —To supplj this defect I was uoder the aecessity of compiling sc? eral treatises on difi'erait sabjects, and a« mong the rest, the lollowiDg on Arithmetic, which I am DOW induced to publish for the greater conTcnience of najr School.— The great ad? antagcs of well digested Text Boo^a both to Master and Scholar are too etident to require proofs* Id rcTisiog this little work for the Press, I hare eodeaTOurcd to make the rules and definitions as simple as possible consistent with perspicuity, a quality which n^ust never be lost sight of in any work, particularly those of an elementary kiod.->I am sufficiently awaro that little reputation can be acquired by the publication of a School. Uook on a subject already more perfect than Any of the other sdcnccs, 8i which has been so well treat- Mi by abler hands* — But my desire to bejiscful to. my Fopils iodocad me4o uBdertake the work, wfieh^l Chooght might without any great eiertion of entellect, though not irithoot much labour, be made more useful for thiscouo* try than any other publication on the subject* There is a dificrance of opinion among Teachfts as to thiD order of Teaching thePrimany rules, some giring the simple and then returning to the compc and, others Teach, ing both at once. — I have been in the habit of giving all the simple rules to young Pupils before they proceeded to the compound, bnt to young Men of discernment, I have seldom found it necessary, as they commonly understood the compound with as much facility as the simple. But If the Pupils are carried through all the Primary rulen before Ihey beg^ to write them down in their Books, it becomes a matter of indiHerence which arrangement be chosen.— It should however he laid down as a principlo that tto Boy can do any thing right the first time, but that he must learn by the help of his Teacher, so as to be able to do it himself ev^r after.— The strict obserrai^e of thift .*■«■' II Jill II Wl n*i^ ^V^Wi mmmmiimmm «» Jy no« only oTKriMc, but of wy otJi., ,„6j„,.- ^IiKLT'I''''''''^ '"''''' •"•'•»''"''» of Timber i» wo„„, .M .'' ■"«•»'"«-• "•ny who rcq-iirelhi. knowledge «in Subtraction ; & i.,Di,i,ion, Book-iebti atrfform. of ^on^Pfy^T'T/" •''T""""' *''» common d"'„c. tion of Direct and Inierse has ben rfiictid o.ri « r,.i- jnrcn That comprehend, both.-The «mo utroxtend"^ «>"<» operai.oD, .erres forDonbte Pronordon ami l. 'cry easily «n,kr,.ood by Boy, who aTtol yU; ,o ■ 3u™ !.,»'?' * "'" ""^ '•™' »•"' '""hci. U Intro- «'u<«d, M hirh will frequently be fonnd more conren ™I than ero„ MHl.ipHcalion.-tare ha, been ukr in Vu^ S ifoTkra';r^'t*'''""""i. ''^y "f"""----!.:'; and to Uke a«ay that seemms abstrBsenes. >o frequently «om„ laiucd ,,f _/„ the arrangement of Decimal Fract on, hLll -il'l",' '™P»"')'ofther,.!e,, something T J hoped, w.ll be found worthy of apprul,atio.,._8in fl'e I, . t.r.t comprehend, several rule, which differ in name ra, 1 *'^f"p f""^'P *' """" '•'•Ic, are introduced of great «e 1.. Practice and sereral thing, entirely new.-I„ Com ^easVTairh"' Tf'"' »"—»"=— are retdet eo easy, and although it was necessary to contract this s.: ij'rj,!;!;:^-^ "■""'"" p-""« '--y tMi^f re:; th,Irv'a,'.d w""!' fr*"'"' ' »°'«"jcovcr that the questioRf are chiefly new, and such as will frequently occur in busi. ness.— Not that I attach any merit to the composition of iuch questions for I frequently write thera out as they are wanted, and this every person ought to be able to do y^ho teaches Arithmetic, or at least he should have a great collection, that he may give his PujHis a sufficient varietv to prevent copying. -The few notes added on Survey. ing are not intended to supersede a more acruratestudy of that subject.— The Problems concerninL' the Gregorian Calender belong to a very short system of Chronology used in the School, and they are added here for conve. niencc— they may perhaps be found useful to othcrs-^for although the calculations in the Nautical Almanac are much more correct, these Problettis will be found suffici- ently so for common use.— I have added by way of Ap- pendix a few forms very useful in business.— Upon the whole it is hoped that this treatise will answer the pur- pose of a Text Book in this country better than an other publication on the subject. Before concldinjii this Address, I bca; leave fo notice my method. of teaching Arithmetic, as it may be of use to those Teachers who have not yet acquire^ much experi- ance.— In a new country like this, a variety of branches must be tmight in every respectable School.— Young Mdn coming from a distance at a very considerable expence are anxious to get forward as fast as possibljfe and even — — . imy»^iiMs,%i Av> M*u icaiiicu p^ult•^^iuas 316 SCiOOtt aU A 2 sppsisvssai ?• PREFACE. lowfd (he (imo reqabite for tequlring (li« kftowledge pi«»^ ▼ionuly nt'cesijiry.— These contiUeratioiii inUucoU oie to turn my thought! to the Di«cot«ry of lome sure nnd U the MDie timfjcipeditious method of teaching Arithmetic. — Ihii object I hMve accomplUbea with a njuch srcatef degree of success than I dared to promite myidf. I ditid©, my lupUi into tcparat«5 Cla^iea uccording to their pro. gresa.— Kach Class have one or more sumk to produca cirery day neatly wrouRht upon their Siatct-the work ii careful y examined, after which I command ercry fiimre to be b ottcd out and the sums to be wrought under mr ^ye^lhe one whoml happen to pitch upon first, irircs 7t.^ .^yT^ '""^''l the rules and reason, follreri «ep, and as he proceeds thelrest silently work alon* with Ji'm, figure for figure, but ready to correct hi. * if ha blunder that they may get his place-as soon as thi, one is finished, the work is again blotted out And another call! cd upon to work Vhc question a loud as before while the rest again proceed along with him in silence and to on round the whole Class.-By this method the prlndpSi- are fixed in the mind, and he must be a refy dull Boy in deed who does not understand erery question thoroughlr before he I^fe it.-This method of teaching Arithmetic pofsesses this important adrantage that it may be pursu, cd without interrupting the PupiPs progress in any other useful study. -The same method of teaching Algebra hll been used with equal success. -Such a plan b certaiZ- 7ery laborious but it will be found successful, and he thai " aniious to spare labour, ought not to be a public leacher.— When Boys remain long enough, it Ami beer* tty custom to Teach them the Theorjr and to gire them a namber of curious questions in Geography, Natural Phi tosopby and Astronomy, a specimen of which may beseea in the questions placed before the Appendix. i need not detain the reader praising the subject which 1 have been treating, for who is ignorant of the great ad irantages rcaulfing from its cultitation.-Wha does not t^rr^ f , pkm' ^1 *° H^ ^**" *'*'^^"'^' of Mathema. tics, Natural Philosophy and Astronomy that a thorough knowledgoof It is essential to the man of business, highly le^mte to tho Scholar and ornamental to the GauilemJ , tei T( lOi Wl th< Jin the .f' ABlTHMETia ARrrHMKTIC ii ik. Art or 9d«oc» of Nnwihen NOTATIOK AND NUMERATION, ' TEACflES us to ffaiJ aud write any tum or n,Lh All nu«,ber. may boi,.pro..ed by the blowing Cul''' i*' 465 7 8fln* Oo*. two, three, four, i.c, «x. -».,». ,.^Mt „^ ^ * ^ TABLE I. ^^^ 9 ' 90() ©000 OOOOO Units Tens Hundreds Thousands TensofThousanrfs , --...^ „, tiiuusanns POOOOO Hundreds of Thousands Millions Tens of Millions Hundreds of Millia TABLE II. Th. Uh. Th. Uii.Th. uTtT^th! 1 12 1234^ 12345 12346(|J 12.145678' I mU67HQf fiOOOOOO ©0000000 ©00000000 Periodk Half l»eriodj. rigur... I 483. 671. 5«, <.8,, »«. 393, W:^,'^!^ From thee Table, we majr obsetTe, ^ icnfo/d proportion, from the right iM «• thri.ft ^ '1* fens, Hundreds, &c. * ^^ ' ^ '*"~ "'"'*r lo«l ,^?„1'^"' "8"* '»' "'o "l"", i...«pl.Md it, ♦he sc^itd linfiwtik #l»- II "*»»«>/»»gn|««»»t«prj «, bill lit -.- .Z2„ "°®^*^Pecyphcf joined It sknii!is!ria.*«« *l^ • NOTATION Krm NtJMrRATTO!^. 4. Th§i the r»*tding of nnj Urgi^ number It maiTf rail. «r by difiding it into imi»d» «f tii jkufei, or haif.i.url. odt uf tbre« fi^^tt. Write down four hondrtd and thrpif. Reid 4085. WiiMi tki (y.si» mllUuiii tin himdrvd. Head»,S7agfifi47a WrHe twu tUuvMud mut hundred mid <^i***' * lioad 57597C854768 ^ " "- * V • *- *••• ■ . ^ _ i^ A rmOfttt Of Till KOMAN NOTATION BT tMl UWTm TIB! Oy TttE AI.PMAIET. 1 % 3 4 d 6 7 8 I ir m V VI ' Vlf VllI wx n XI 12 XII IS xui 14 XIV : 15 XV • 16 XVf" *^ 17 XVII 18 xvin ly xjx 90 XX^ * 30 XXX 40 XL ^ 60 L 60 J.X 70 Lx:* 80 I.XXX 90 XC 100 c 5(X) If) or D 1000 Clf) or M 2000 MM or Tf 60f)0 l30 orT 60(0 I>oM orTT -10000 CCl^Q orT *<>000 I^DDor L «00(X) LX 10(X)00 C orCCClQO'l 6(KXXJ0 1^003 . 1000000 Tfi or cccdrJnori sooofxx) SH ^^^-^^^ )BSCRVATION«. ^ 1. As often as «njr character is repeated, so nianr timet lit talne is repeated. t. When a character of inferior value is placed after ^qM of a superior wilue, their ¥alue» arc added ; but when f)laced before, tfee valuo of the superior is lessened by the Taiuo of the ro^or. 3. Every Inverted o,afBs[ed to this character fa (fiOO) iBTCf oaset ict laiue tenf oid. *■ C i i NOTATION AND NUMIBATION. »t 4. RvfTjr tittif nCm^^mn fifteti tt fti* mi of tlii cliaractpr CI;) (lOOO), incrcutt id fiiluf tanfuld. 5. A lint* clmwii gvof ABjr fiiMictif kjcfoiot Ui f*lii9 som Of THE MoiT yiirutr rRortMTiti or itvirRisi. I. Unity ft (hat hy which et^rjr thhif fn oatore it caL« led one ; Ah one house, one horte. t. Number ii thst wHicii U canjioscd of out of nott UDlei. 3. An Intejop or whole number it a unit, or a colUe» tjon of unifi., as 1, 78, 56. Thoy ar« to called to ilii* ttngitifh (hem from Fractions, whkh are broken luimberf^ «r ^arti of nunbrri, a* one third, one fourth, J, |, 4. One number i« laid to measure aaother when U, dU«^ Yidei it without any remainder. 5. And if a mtmber exactly divides two oi mon oitHU bera, it is then called their common measurer. ' - * 6. An even number ii tJuit which caa be halved or di« Tided into two equal parti-^ 7; An odd number is tlttt whkh cannot behaffedor^ which d i tiers fr *m an even i¥nmberl)y unity. 8. A prime number ia that whkh can only beneaiirecl by 1 Of unity. . » 9. A Comi)osIte number is that which aw ivnittvr* €d by ono number greater than unity. 10. A perfect number is^that which if equal to th« len of all ita aliquot parts, as 0, 38, 4Q9, 8128. S oo Pluf, more ; the siun of Addition. Minus, less ; the sign of Subtraction. Multiplied by ; tiie sign of Muttiplicatioii. Dfvided by ; the sign of Division. So is ; the sian of Proportion, as 2 : 4 ; : 8 Greater than. cr Less than. Difference. Square Rout. S^ Cttbaitool. S^nMlitv • Annul in. ^ Itf. i«l> ten in that imm ... ' .""*• "' »"■'. »'••' for cq^lthu, w"h fn'h *"^.' r"""' «'■<' col.B,„ «Jded. Pro! fiXAMPLEa 547685 676901 637439 27683% 84578C^ D;28967 ji. 37S8547 »3673!)» 421762 £4981 567 ■•■■■t S832 I 3310 iVoo/ the re»t cut Ae K^^V' ^°P^»' *he work, bednninff at ih^^^r. join example^ tlu ttbt'^^ffeCr """ *'"'" ""' '""" 1 A I. *^^«'f^0^9 JN SIMPLE ApnmoW ^ ^Z*J^' '^^^^y^s at one time of R -..iiK * COMPOUND ADDITION. !i % Prom Quebec to Montrca? is ISO miles, from thence to Kingston 200 — from thenco to York 149 from tbeiice to Niagaia 78 miles— from thence to Detroit 210. Required the distance froai Quebec to Defroit. Ans : 817 miles, • 3. A Farmer has 13 acres of land sown with wheat, 17 with Indian corn, 9 with pease, 2 planted with pota- toes, 25 ai.- res of meadow, and an orchard containing,! acre. Uow much cleared land has he. Ans : 65 Acres. 4. A M ercliant has in Cash j£356, in j^ood Bills ^476, in Merchandize jf347, and in accoants j^603— what Is *»e worth? Ans.£\«7^. 5, A Farmer purchases a Farm for j^l75--His Horset cost him .t^67— lliji Oxen j£42— His Sheep j£7— Hi« Farming Utensils ^25.—What4id he lay out ? ; , ■ „ j^ns. j£306, o. 11 ow many days are there from the IGth of March to the 8th of August ? ^„,. 145 Days. 7. Kth'land contains 3,331,434 Inhabitants— Waici 541 54G -Scotland 1,599,068, the Army including the Militia 198,351. Seamen in the Navy 126,279, S^men W Registered Ships 144,558- Convicts l,410^Ire^and contains 4,387,354.-~ttcquire^ the population of ihm a A ^;!,"P*'^^- ^nt. 15^300,000. I *c.S; J^ General mustering his Army, finds that he has. 32947 Infantry, or Foot Soldiers, 4l3t Horse, SOtS Dragoons, 2135 Light Horse, 579 Artillery or GJmners. m? Pioneers, 178 Sappers and 235 Miners-How man^ 4We« does he coLamaml. Am» 44 f fSS COMPOUND ADDITION;^ R U L E. 'W^^m PLACE Dcnomiaationa of the same kitidl ttadbt^^ o«ier.-Add the figures ^ the lower Denomfa^^^' '-'•w '^y «a i«4uy a» oiake one of tfle next supl nomination—write the o?epplus, if any, itmi^iw». n n I & 9iarhed. T*-jr/. \ 4 FarfhinM ^- ^^ Pence... OOMPOVND ADWTIOrJ. TABLES.,. ,. -. OF MONEY. d. 4., 14 Qrs n»«ke 1 Penny 4=!,^ * Shilling 4A^i%^u\. ■ 4f. f. * 198 .. 16 .. •246 .. 14 ,. 133 .. 19 .. 448 .. 27 .. ^56 .. 13 ,, 879 *.\14 EXAMPLES. a. n| 8 5} 3i 44 O , ■* '^*?'l«nati orders Ms ««~—» i ... V. . men-, actoants for the lal, H^ t? ''"^^ ''•" *" '"^M- counf come, to ^27 18 « ,^°"^'",— ^'^*'ercer',ac. the Grocer's ^^7 [4 7, ^*-'5« .^-kf" ^J3 18 4i -. ■ tho* Butcher's J29 12 4 h^'"r''"'''-*»7« 1"-- FBENCir MONEY. • i? Peneir or 2 farthing mala. 1 c„i %^e(^. > W 20 shilling, .... 1 j,p„i, „ p^^i^^ ^^.^^-^ I -.1 „^ jU »!t!S v. COMPOUNDt ADDITION^ EXAMPLES. iaS livres. to/i. ^ehl* •CTSS .. 21 .. 19 ., 7 58^1 •• 17 .. 15 .. 9 3936 •• 15 .. Id .. 11 4213 .. 22 .. 13 - S ^^i7 .. 19 •• 14 .. 2 4m "'1 ^4408 1 7622 T .. 1 • » : I • » ■ ^' „'.. ? • •'• • / ; FEDERAL MONEY. in **Mi , Marked ID Mills make 1 Cent Ct 10 Cents .. 1 Dime D/^ JhnT •• lI>olIar Do/. 10 Dollars . . i Eagle Eao' : EXAMPLES. 4576 .. 7 .. 5 .. 4I.. 9 8903 .* 8 .. 2 .. 3 .. 6 6734 .. 3 .^4 .. .3 .. 2 5876 •. 4 .. 8 .. 9 .. 7 8421 •• 7 .. 9 .. 7 .. 5 29573 • • •.. 8 .. -9 '24996 ,. 4 .. 5 ... ., Q i*«». . ^ ^ 29573 .. 2 .. «■> — — .A. « «^ a« ^ ■ a mm 8 Dols. 7 D. 4 Cts. 3 Jk KH ISi^ ^t^ents, 9 M. to C. 529.'.0 pam to A. 767 Eagles, § M. ^e> B; 393 Eac». 8 ■» • Ha^ttircd the sum jjaid 3--9..1, toD tyut. poJ* 6 D. 2 37§..6..# li I ^ 21408 •• 9 •. 0- .. 1 A dralcr purchases 247« )iv«s, 10 sols, H denier's flour «lrTr'~;^"1 '""=•' " '»''' 9 1«* "-"ho? *' 14 COMPOUND Ammian. jiii. w 4 n H OF «. ootD AND ,UVE« coi»i cnaft«r, » ,.,„^ AMEKICA. GOLD COIN. ^'^^'- " ■ Falue. . Antient Actual Cur* CoinK A Guinea A iralfGuhiea Quarter Guinea A Johannes A Half do, A Moidore A Doubloon 1 A Half du. A Louis D'Or, ) coined before > 5 1793 .. 3 A Pistole of 1 France, coin- > 4 ed before 1793 j An American 7 ,, Eagle J 11 6 AHalfKagle 5 15 renc'y. PiecUm French Currency, AW. #, V ' 14 (OfEng, 96 7 Of Port, 48 36 89 8 7 ...I . 44 l4|^^Span if ligaL iio. 27 4 2i 18 Of * France. ConiJ* SILVER coin. 60 ?0/Aincr. 30 3 '^*- Tha Dollar or English Crown 1 he English Shilling ^ he Spanish Dollar The French Dollar coined before 179S TheFrenc^p,eceof4 1ivreslOsol8 rfae French piiBce of 36 sols i ne Amcsrican Dollar - TheSpaaisli Pistaieng Value. *• *. d, Uv, 8» 5 6 ro 12 1 1 |1 6 5 6 5 6 6 12 4 2 5 at 8 2 1 1 1 6 5 6 10. 1 4 I . *;■? -■*!«««- .^w-t^-^aii" ^?*^»^w^flr;:. «^'lg!i*' ' ' "V. ' J. . .li. l l '' * .' jl i » .< in BAITiqi 1. ■ 1. titeti. } ] Of Eng, land. Of Port- ugal. O/Spaio. Of France, ^OfAmcr, I ica. i' iiv, 8. 6 6|0 1 11 6 6 13 6 2 O i 6 6 1 4 I COMPOUND ADJMTIOP^ TROT WEIGHT. On. II t4 Grains make 1 ?cnny weight, dwt t^smi dwt. • 20 Pcnnyweighta • • 1 Ouiic • • • • AVOIRDUPOISE WEIGHT. Marked. />r, 16 Drams make 1 Ounce oi;. 16 Ounces^ ••-••••••• 1 Pound *t7 S. \iiili%i3 ---zzszizi i \^^M.*» «.V» v/i (ill ^ — ~ 4 Quarters or 113 lbs. 1 Hundred weigbl 20 Hundred weight ..1 Ton, T. lA. lb* Ift COMPOUND ADDITION. 16«1 Ounce, Grocery Ware., and .Jm.r ?'.:?''"'""' ^hece, Flesh. Mcept SUve, a„d GoJi * '''' '"'^•'»» «" MeUli J^c./._//, , A.oirdupoise -. ^ ff' ^^'- ' •^- 1 Ounce ^ - H - 11 .. ,5j 7. «, ^'•. 1 Dram H ^S--- 54 Afoirdupoise. » ^'^'^^e i'o)' lieaner ihaa an oonfltt EXAMPLES* ^ "^ ■ ^ I'. 566.. ty..; •:'^- 14-13 566 .. J7.. 3 »i?8. 15.. 1 »y«- 19.. 766 .. J4 ..3 «43 .. 13.. 1 22 19 tt SS 13 15 10 n u 14 15 8 10 Z039 • • 15 • . • . 24 ' iS '. 15. 13 ., 9 U.is n •• 14 9.. f 8.. S 4.>36 •• 19 .. 3 .. •! ^ ~ — — — „ ** ^ ^-^" *'i^ **<>*4». ]*..,, TT^-^ — ^ *'«'«*'«-f*^'«»tevrri «■£.?■ "■W" 't COB. 13ibs. ir. m Je. • ~t- « — bs IS COMPOUND ADDITION, •^ li •" APOTHECARIES WEIGHT. ifarked. , Crs, fr. 20 Grftini inak«» i fCTOpfi 20«1 Srr. #cr. 3 Scruplei •«.... t Dtum ^^^ez^^^iDr. Av 8 Drains 1 Ounct . 4ao««v4«»8««l Ounce. •I. It Ounce 1 pound, lb. 5r60:*,<88«96-i*U«i/l^. This is difisions- pounding Drugs by lbs, 162 640 373 804 £88 796 the same as Troy weight, only having differtnt -Apothecaries make use of this weight in com- their Medicines ; but they buy and sell their Avoirdu|)oisc weight. EXAMPLES. /6#. oz. dr, tcr, grs» ox, dr. tcr, gr, 11 7 2 19 10 4 8 2 9 6 11 5 6 3 1 Id 14 1 13 17 2 18 864 746 10 903 U 324 2fi7 543 9 6 2 la 7 1 16 6 14 9 9 2 18 6 4 13 S 2 1 10 3457 10 6 1 17 .3641 4 1 1 10 3294 10 6 1 18 3457 JO 6 1 17 2776 6 2 1 \l 3641 4 1 1 10 An Apothecary makes a composition of seven ingredf. ents-the first weighed 7lb8. lioz. 3dr. iscr. I8grs.~-tha second 19lbs. 2oz. Odr. Oscr. 3grs. -the third 131bs. 8oz. 7dr2scr0grs.— the fourth lOlb^. 7o8. 6dr. iscr. I3^rs. —the fifth I71bs. 9o8. Sdr. 2scr. 14grs.— The sixth 8Ibs. JOE. idr. 2scr. I7grs. and the seventh lib. 802. 6dr. 1 6cr. 19grs.-.What was. the weight of the whole. • Marked. nl, if/*. CLOTH MEASURE* A^ 4 Nails make 4 rjaiis make 1 Quarter of a yard 3 Quarters 1 yjemiifc Ell ^ 4 (Quarters 5 Quarters • . . . ^'* I Yai'd vd. P Qtiait^rs • » JD2 1 English EH J:: e. I FkmifiiiEll ^\ j^ ■■■IN' COMPOUND addition; l6=«4«UVrf. 754 5 EXAMPLES. I 2 3 -UTdhtC '2"n"'1V^^^?'' ^- » «^- » N. of Check -the fWrd& 9a« 7^ "'.r^^ *'^'"- ^l"" ^N. her of yards. ^*'''' ''"v 1N,-Rcquircd the buo. • • • • w. Harked. ^^^^ MEASURE, t'* ll f *'i!'^ ^^'""' '"^^^ •"e Inch •;• ^li^:^;' • Foot /• llZl Yard wriis t\m 'S * \ 40Pi*i» •••»•• t **5?. . Rod, Pole, or Percli • •»?»#;• •• i^'ttllOD a • mm't m Mi 'V'mr^. CONFOUND ADDITION. » fur, 8 Furlongs make one Mite M» ^ Miltji #••• •••••^ •»#••• Letvue Circumference of the * >»•»'» 60 Geographical or 6^1 ) iratute Miiei ) deg. 360 Decrees .•••#.. Barley cortig. 3i=l/iic4. 21760=71^-'=: ftfiO^'i'iOrrlOrr I FMr//>»e. 1 ttUOSOrrO J3au=5280=: i 76(J=:a20=8=: I itfiif, EXAMPLES. > Dc^. mt'/ef. fur. Futh. yds. 136 58 7 40 ■ 1 283. 40 4 95 1 1^04 44 66 67a 56 3 77 1 065 32 2 58 i 849 26 i 84 /. l>. 2 11 1 8 2 7 i 6 t 10 3503 27 363 3366 29 322 3503 27 363 3 From A to B is 7m. 6fur. 7p.— from B to C l9m. 3 fur. 3 p. 3yds.— from C to O 27m. Ifur. 25p. 4y(ls. — from D to F ll7m. 6fur. 37p. 2yd3.— -from F to G 293 in, ifur. l6p, lyard. FRENCH LOx\G MEASURE. Marked. XiS. in, /• d, Fer. 12 Lines 12 Inches 6 Feet 10 84 1 OiSc Perch Arpent OS 8 make • • • • • •f • 1 Inch. 1 Foot. 1 Toise. i Ptsrch, 1 A r pent. I League. X, so COMPCnffW '"««•« ',*'20 Kr«„ch U'Vr ,«,C 'r;.""" ' *''««*2 « •a.la 1002 iiogli.r* ^°"- *''» »>«idH..reiu •••• Marked, p. WINE MEASUEi;. « Pfuf« 4 Quarts 42 Gallons » 63^ Gallons 84 Gallons 2 Hogsheads 3 Tipea make • • • • • • • • • • • • • • • • • • • • • ••• 1 Quarf. I Gallon, 1 Ticico. 1 J(ogsljeaif, 1 Puncheon, 1 PfpeofBuft t an. jr. 1008 *= '■,04=ri9« !"= H^lPam/i. ;j:afer., Ockr, Mead, P«rry! VinZ 7?.^^*'**'' ^^^^S The wine gallon contLs '11 1?-^^^'' ^'* «"^ HonayJ, COMTOUND ADDrrroif. EXAMPLES. tl r#ii. pipei, hhd. gall, 1^46 •• 1 M 1 .. 69 8y4 •• .. .. 0t 7f)3 .. 1 .. I .. 4^ 30.12 ..' I .. 1 .. 4<| 1480 .. 1 .. 1 .. 30 627 .. 1 ..1 .. ^1 «., 11845 •• * 1 Ok Funck. gntl. ifti, 040 •• 83 •• 3 804 •• 70 •• % 783 *. 54 •• 1 05g .. 40 •• 3 bPi% •• 33 •• ) 301 *. 92 •• 1 p^% - 1 .. I •* 1 .. o 4147 ** 05 *• ^598 •• 1 .* 1 •• 3200 .. 05 •• 7 11S44 •• ^ M 1 .. iS 4147' •«' 05 •• •• A merchant purchases tf». Ihhd. 2T|!«I. 3qt«. lp»'. of SIicrry-64hhd. 22gal. 2qU. ipt. of Maddra^tlbhti. 17gal3qts Ipt. of Poft-73liiul. 6lg(MI. 2ql. Ipt. of' Mala^t-03hhd. 45gal. Iqt IpU ol IJu^odj-aetdx. €d (lie iai» of iU wholes ^ * •• "^ ^T A fintn^r on e«aminllg hii ceOir, foond of Brtn^f | in".«« 'i'^f' ^!i?/-/^^«l*- 3q<»—0f rum 9T. Op. Ihjid. Kiuff ^' ^* 41g4J, 39|«.;^^w laauy ta»i M Viti ALE AND BE£il MEASURE. Marked. pt. 2 Pints 9^' 4 Quarts i^t. 8 Gailoiie 9 Gallons $ Firkins «((• 2 Aiiaurk tns 3 Kilderkius har. 3 Oarreis ^^/. 2 Butts make 1 (^uart. I p Mon 1 Frliin {>< Ale, 1 Firkm of JUeer. 1 Kilderkjag^ _ • i Barrel. 1 Hogshead; 4i. ^a^. I •• I •. I I •. I .. rru Aid, fifk •• I 1 1 •• 0^ 4 5 4 3143 •• 97^1^7?' 7'*^® '° *'»'•«* '"*'"♦*»" WTmif, lb. Ibhd. P«rter-~98r. lb. Ohd. S9gall. iqt. of smail beer-Hoir manjr tuns were brewed in the whole ? A vintner recelrcSi at ^ -nAdhbd. ftr. r^a» Sqls. i of ^hd^^'A n' ^^':/«*»' '' P*- »" -^ another 7 tui.,' • • • • • Marked. ft. 2 Fin^s at. *9. O'.sas-la ^y or hmi^ Id ■• 2 — 5 « I /r«^€fr Meaturt, 5120 —610 -300 -HO -10 «2«lL^4/. Bjr this arc mcasuriHl ill dry wares, as corn, seeds, roots, fruit, salt, coals, sand, olsters, ice. The standHrd gallon contains Sfift} solid inches, and the Winchester bushel 21dO{- cubic or solid inches. EXAMPLES. Last, utt), eoomh.l'ud. Pecks, galL potts, gti. pti. 196 1 9 3 83 1 1 1 a I 480 1 7 1 76 1 1 1 I 643 n 2 84 1 1 1 1 864 1 8 1 38 732 1 5 0. . 65 1 1 1 971 1 3 2 92 1 1 1 3789* i 1 401 1 1* i i 3592 I 2 318 J789 I 1 401 I III] ^ A corn merchant exports 36 lasts, Iw. 4ars. I coom. o&Nso. J pecks of wlieat~7I lasts, 1 way, Sqrs. Oc. 2 bush. 2 pecks of ryo— 86 lasts, 1 way, 3qrs. jcoom. I bush. 3 pecks of beans— and 46 lasts, 6bush. of oats— » Uqw many Itf u were oiported ia the whole i \ X IV: M< .•♦ COJWPOITNB AI)WTIOi£ iimOT OF CANADA. ^ TlZo' ooZLTlX"" \'n.'^."«'-'' cubic J' >« • •« .V, .« - Marked, €0 Seconefg 60 Minutcf 24 Hours 7 Days 4 Weeks TIM B. make I • • • • • •••••• Minute, Hour. Week* ' I ' f J^Months, May, 5WsVnri ^o •^''"^''* '"'^' ^a>8, 6 hours, 49 m'mutes make 1 Yca^ ' '^ ^^* Seconds, 3600= 60=1 ^o«r. 86400=i-l44(>=24=l D«v 604800== J 0080= 1 60=7-1 frceit 24l9200^4O32O«672=«28=4=li/anM, l-IXAMPLES. m. 546 673 754 8S7 980 «?. 2 2 1 3 1 4285 d. h. fW, 9. 1 5 22 66 43 ■ 6 21 43 £8 ■ 4 19 23 36 ■ 2 17 20 19 ■ 1 12 19 13 ■ 18 If 38 1 1 16 I is 1 S738 1 2 17 4 32 10049 4285 I 1§ 1 15 §0MPDirND ADDITIO??, m ^ . ^ SQUARE MEASURE. Mi. 144 Square laches malce one square TnoU f. ©Square Feet ..,, Y«ri| . yd. 30J Square Yariit , p<,|^j^ ^ po, 40 Square Poles ' ' Hood. fif. 4 Roods -., ,,, Acre,tfc, Inches, - ' ' ' ' i4 Decimals •4 •T3 O Faith 'Pence ingj Shili ings fp^ CM "^ 'O »>4 »l 30 •!!• o o o o lO O 40 O o '^ .M c-i — i 0)00 Pounds Docimal! Farthin Pen fe' ce o o o o o o o o 90 O O) O OOOO i-^C^ffOT o^qotj* Troo«^«o o b o Shillings Pounds Decimals Farth Pence Shillings >^ «0 C< 0-^ ;^ O O O jj^ T?« Mc ^:;;^ OOO cooOfloN^pH Wo^ ^^^^ 2^2 0^ Tji ;o 00 OOO eo 0< •-* O OOO O "5» 00 t* OOO 00 t^ © ^ « O 'tjt f-l f-rt »-( f«J !«* o o «-< »H oO'-t^ o 1-H C* <0 C^ X Tf o o o j-4 CO o ©♦ o o o •O O TJ" © o o o ^ 00 flO N. 0> 00 b. ^" wm r^ ^9^^ M Q««> u -».«,.. .». €OMPotrm> AromoTc c« ^e M ll^ C« t« M •(^ (4 |X> M **»*. oooo oooo^ i« en «>4 lU Ot 00 »0 O l« ♦0 I— O >4 flO 0» O cn ►-• W O Ot o o o ^ C^ OO i*fc « *- .{i. |« ?• cc W *-• o\'^ •(HMKlt»-lti^ .00 S- - r CO to I- 2 • oooa^W^^Og O O O O r» «0 o> Q _ 0» CaO »-^ WJ tn SI l« ^-^ O o> oe o Q c b r— r— r- l-« '^ (fi v) ^ o> o «f« o ^o rfk CvC tS ♦— •*4 Ot oe '-' 00 © O ""^ 18 i-i ^ O *- k« Cr» OC O *~^ tSi ^ o o o o ^»> to tS P^ O o» •"* Si. *^ a© r* on ^ I^ 00 *«* en Oft o% o o o o 4*. t« t« *-* •fc^ 03 l« ♦^ f^ 1^ ).«> H^ O 7S l»-ioH talk- ?« O B 4 f-» • OV tOMPouif 0' nmvncm. m 4 3- DeaTeri la WOOL htfo A weight peculiar (o tliemielrM. Tne-Sacky ConUining t Weltllt The Weigh The Tod The StiMie The Ciote » • • • • t 9 • ■ • • 6} Tods ^ ^toaet 3 Ciofet 7 ibi. ^AIso, 19 Sack! make 1 Last^, or4S68 poundff, , ^6 lbs, of o!d Hay or 60 lbs. new Hay, make a TruM,; 40 lbs. of Straw make a Truss. «6 Trusses make a Load of Hay or Straw. 14 lbs. make a Stone, ' 6 lbs. of Glass make a Stone. 34 Stones make a Seam. PAPER. A Quire contains «4 Sheets— « Ream «0 Qulres~a Buiullc2 Reams— a Bale 10 Reams. 12 Skina OC Parchment make a Roll. 48 Cubic (eet of timber equal 1 Ton. 4 10 Qrs. or 80 Bushels equal I Last of Corn. 17 Cwt. equal a Last of Flax and Feathers. 12 Barrels equal a Last of Cod FUh, HerrioM, &ew 8 lbs. equal a Stone of Fish. ' «^» ***^ *> COMPOUND ADDITroif, ILog *'*'-^SURE8 OP CAPAClTr. 4 Legs = 1 ca" _ i ''*"' * "'"* Cubic Jni.' 9 Hem = 1 Leak =» 20 . . ?',T 1 0,ner - ,v of an £phah« fl . . . . 'f '? ' 164.pha.-l Ho„ef ^ 3OS yj^ tph» 1000 ; a Choner or JlLmeTjo^cJ^o ' ^""^ *°° » JEWISH LONG MEASURE, 9 Palmi «■ 1 Span ^^^^i DecimaK 2 Span» , ^ I Cubit "" ^'^^^ 4 Cubits ;=« 1 fathom " i'f^^ 6 Cubits = 1 Keed *• ^'^»» 80 Cubits » 1 Schcenics "" ^^'^^^ 400 Cubits «= 1 wi "h? *. , ™ ^"^^^^^ 1 i-arasan =- 4 Eng. mUe. & 530 feet^ * ft^ ■ GRECIAN MONEY # j S Drachm, = J nlrf,?"!: *" « » 7# 4 Drachm, ^ \ r^'^'f^l = 1 s! IWDrachJ Z Jif""'"'^ = 2 7* «0 Minas = , t,, x "" 3/47 1 Talent ». jgj ^j ^ 1 Se,ter«u,''°''^^*'»?"°NEY• 10 Se.ter,U SestcrUum - 8 1 5J Ar,./-_A- .^- _ 80 14 7 COMPOUND ADDfriO??. Gbician wd Roman Wkiouti educed toEitaUsh Trow 4 Lentes 9 Siliqua J, Obolj 3 Scriptula ]| Drachma 2 Draciima 3 Sex tula 3 Duclia n Uncia 88:3 1 Lenten xa 1 Siiiqua » 1 Obolus s= 1 Scriptulum =r= 1 Drachma a 1 Scxtula s 1 8i<-iliac9 sx 1 Dueila =s 1 Uncia «= 1 Libra ss /A*, oz. «/lr^ grt, h \t ■0003 9 18 2 6 3 Q 4 IS 6 1 18 5 10 18 13 I rr 1 1^ 9 w ntttltte Men's rh»ta came ,,. ^,-h9 ,7,. 3d.-Th.'o«ue« a, n"'" bt^ « A /•!> ».i . Am. ..(i'ftl.cius. 6il. lo?' /, ^°""»'»«»'-y Ix'.vs U7 barrW. of I'ork, for jf Sid ty no hmls that he dlill has *S75 17». 8d Haw much ".on,.)- had he at fint ? , An" ^i«« j 7. A Me,chant.mp»rh 4.o«. Sl^J-.f '" of Port rfl8 4.. Haddock *H7 18,. lld...Horrin«,.*-»18 ,i. W. What was the value of the « hole consigninent I i • ■ IS " SIMPLE SUBTRACTION. befi«.r^!? SnWracttoi. t-achefh to 8rta ' «e drffercrrM »,ll!!^y.7 . "".k"""""'"- ■^''« «^'« »" called flw ttmuend, the less the subtrahend. • • • » RULE. «nw!T ^''^ »"> lime .€^70 ; af another time 4198, and at a third pay* ment jt*384. How much remains due ? Ans. £'AjS, 6. 1 drew out from the bank at on^ time £l€^ ; at another ;€393 ; at a third 4*295 'y and at a fourth x376 ; and paid in at sundry times 4'UOO. Required tlu; bal. i»nce. ,, Ans. 4 1 32. 6. London contains 864,845 Inhabitants and the ft next lararest Cities in (Jreat Britain, as follows ; Man- chester 84,020, Edinburgh 82,560,' Lirerpool 77,653, Clasjgow 77,385, Berminnhani 73,670. How much doea the population of London exceed that Z IhnM / .''^'- '*'• ^'""" *" 'he value of ^42 6s xiousehold I uruifuro worth j?57 I9j, k,i .„. i ■^^■' "'• Wc debts .#19 OS «,i m" < . • , . • *'"' «•<-■"'"!". by liim ? " '""'^'' ''" '"" "•'•litors loa* oj,, ^.'^"^'ofofan estate receives from A is-g iV, Bid. and from B. ^'a,? 5s. 4d. from C °^3S. 15, jjd {romD. ^109 12s. 3d.-0ut of whirh hf.fll .l^^-- J}?;i J to th^ h.Z ^^^^ •^'* ^i^' ^^^ "!"^h has he to give to the heirs Ans. ^700 Ss. Oid, r. g to (h« »tU ^ub( rail end -quai to tilt (JbMTOUVt) StTBTnACTTOM. •I 1 J i Proof. 9* 3d. and low muclb 17s. 8d. lioR debts, r this siiQi t remaiui 's» 4jd. oods faf. H' Me 6s. lo^d. 38. Od, 1 2s. ©d. K .164 J lis credi, j642 6s. ecovera- ors loan 4id. V29 17s. 5s. 4jd. s h& to oid. 7. A Gefiffcman in Qurbrc poc^ io «n iloric Rjici»| rhure ho gaiiii • prtze q( U) (iuineai, lust by bftclnn «« IgainKt A jt'?9 IH. Id. wmi <>/ B £.10 Vl^. 8d. toit to C I i 1 7 8s. 5d. recovered a debt from K £^1\H 15s. 3d. and IfiH he gae» hum« h« pays debts to the (inioiint of £17 lUf. |6d. and he carried home with him ^iUU Guineai. How [much money ku * he when ho »et out ? Ans. £25 U«. 4d. 8. B of Montreal acrrpt^ a Bill of a £lOO()and upon rxaminii.g hitt Cat*h he tinds the amount £765 12-'. /)d. two good Hills on London, one of t' 1 35 I 5s, the otiu r of £79 4s. 3d. How much did he borrow to pay tho accipfance ? Ann. £|Q Hh. 4, 9. A siitcr.smith purrhaspsfrom A. Mlb. lOoz. 19dwt, 10fi;r.-"from B. i7lb!i. Hot. IHdwt. 22gr.~ and from C. iHlbs. Ooz. I Idwt. 21grp.— of which he makes up into spoons 71b. 3oE. I9(iwt. 23«ri,— and into Indian orna- mentH lUlbs. 4oz. Ibdwt. 21gr8. Jlow much has he on [band ? Ans. 24 U 14 Q. 10. An apprentice U io fin^-te till he is 21 years of age, Mho is now Ift/earSj 7ino. 25d. l7h. 45m. How long has he to serve ? Ans. 4y. 4m. 4d. fih. 1 5m. 11. A merchant receives 1 ton, i7cwt. Iqr. of snjja^ and sold to A. 2.icwt."~to B. 3cwt. iqr. 27ib.— to W licwt. 3qr. l7lb. 8oz. W hat has he left ? Ans. 19 7 n 8. 12. A merchant rocei^crj from one customer 36 bush, of wheat — from anothei 57 bush. 2pk. — from a third 1'29 bush. 3pk.— and from a fourth 2l3 bush —he sells to K. 27bush. l()k. Ig.— to K ilsbubh. 2pk. How much wheat is still on hand ? Ans. 29()b. Ipk. )g. 13. A gentleman has one field of 27a. Ir. I7p. 1 9yd. —another of I9a. 3r. 5 p.— a third of 35a. 2r. 5 p. 3{;)'d. —a fourth of 21a. i7p. l9yd. lie makes a circular field where the corners of the four fields join, containing 43a, if. i5p. 27yd. How much grouwd is left ? 14. Th? earth revolves round the sun in 365 days, 5h, 49m. and Venus in 224 days, I6h. 49m. 24sec. What is tile diflerence of th«ir periudical timef i ■ J.V.r::tlV^^^^^^^^ ^ '>.rrel. of P.I. 4CWC Iq. S4lbs. Ur« J,. 3,2_^':; 5. flcJe 'i^b^i ^' •q. I51b. 4oa.~No 11 Li.^ i- i«ik * *5lbi. tare ^"ir.dth«.^atwdght: ^^ *^"*«i- ^«- 10. A farmer goei to town with a Joarl of wli««# - 1.1-1. ^ «t;ll» at .f5, and he purchase, 1 j II,. of Mirc/^ ^^l"* 4cl j.a or 9.. J lid. twenty bu.hclsof sa t at £1 jl L* *»nd 2 a . of rum for I7.. 8d.--hc .p^ndi 3. yd wtl monvy did he bring home ? ^ * ^*'* *^ **•* 17. Account of household eipciicci :— Jan. 1st. Sd. »» loth. i3th. leth. tfst. S7«h 1^«(h. On hand t'aid fur 3fbi. of tea,at 7/JJ For sugar, I loaf at ti^ lb. I hor J (Olds of wood Rt'ctiTt'd I l*aid the butrhcr l*aid fho baker J*aid for an ax lor a milk cow KrceiTcd Paid the shoemaker I The brevuT I i barrel of pork • • • ■ • • «Tst. I On hand « • • • »« to receive «„.„,. H. .1". ^. „." J^'H^^^^^.-ccouni., and aU rrom •tue 3«. i«i. -l'»/5 C. *'2y3 8J, and to E. jt'i Us. ll. Paid. J. £. $. d. b I 1 6 8 S 1 17 6 7 2 17 (5 1 5 4 J2 6 4 j 1 U 6 I 1 :i 4 3 9 X •Uifl^B MUI7in4C4T|0||t td. lit rfc<^v«i from Y -^310 4i.7id. ffomN jffSS 143 lOd. aiMllM pmf to F jt* 304 6t. Bd. to G jfitft iSi. 34 ilow i|iiiQ)i noac/ Mi t^ 2>erfraiu l^fe. SIMPtE MULTIPI.ICATI0y, MUr-TIPLICATIOMT ir m rwnwi^mi. «rt?,od of addition. The nmnber to fea Miilllpliccl is calU^ tho Multiplicand. Tbc iwiMm?? b/ wliMh jou Mttltiply, the Multiplier ; and Ibo number found, the Product, ti,© Multtplitr aad Muiuplicsad arc abo calkd Fft4;if bread per day. How raanv p^ftds^are necessarjrt? Arrt. 47152 cwt. 2qr/ 10. 1 here is an army composed of 79 battalions, each tmiiBimg of 450 men. What is the number contained ia • • • • • r IF it be required t^ bring numburs from a higher to a lower denorainatiooi .. o ^* ^ m RtJLE, Bf uHiply the ftiTeo number by the next denomination, ii dcnamiuation^ if apy, p^o- tOdl ng in the p»its of SBMPtE MUtTIPtiCATlOlf. ceed in the same ma«n«r tsS*** *!. QUESTrORS. I. 3. y. In 9* inffots of v p«,. i 'w many grSfns ? • • • • gtains ? ' oimcej) dram., ierB{>fcij v^ ATOUDUPOIS ^fem^l^ m' Jn %W*- ^^'- ^^'^' h«W |h,ny drains > wanj drams f 15. Ho then carry 154r.>^ 15. How man^ poumis d.e»B. sAip of 2^ ^an. l,u^ ^ t ••••«» each ittL CmiTOUND MULTIPLICATlOlf- COMPOUND IkTftliPtlCJTlOS. 4f RULE. "- -^ I^LACE the Multiplier under the lowest detioilftn^ lion of theMMlliplicand ; and if it do not eiceed IS, mul« tipl/ the •eTeral denomination8| obserTing tq carr/ ac** cording to the local talue* RULE 2.— When the multiplier exceeds 12, maltipl/ b^ its component parti successively* RULE 3. — When component parts cannot be obtain- ed for the Mfholo multiplier, multiply by th« numbers ii'hose product comes nearest the ^iTen mnltiplier, then hy the difference, and the sum of the product Is the an- •wer. EXAMPLES* '£, s* d. j^. 8. d. £* s* d« 35 13 7i 89 17 8] 9(1 14 3} 79 3 11} ■•♦ M /J 2J , QUESTIONS. 1. What cost Syds. of iineii at Ss. 9|d. per yard ? Ans. 7s. 6id. t. What cost 3 bush, of wheat at 4s. 9d. per bushel I Aos. 14s. 3(lk d. What cost 91b. of sugar at 7id. per. pound ? Ans. 5s. 7jd* 4. What cost I41b8. of tea at 58. 4| per pound ? Ans. 4^3 15s. 3d. ' 6, What cost l71bs. of butter at ]0|d. per pound «? Ans. I5s. 2|d» 6. What cost 27Ib8 of beef at 4|d. per pound ? Ana. 98. 6jd. 7. if a moidore be worth £1 7s. what is the value of forty-six ? Ans. j^62 2s. 8. If a moidore be worth ^1 lOs. what is the Tal«« 0f7&? Agj!- ifilA lA*. 9. What will 29cwt. of Cheese come fo at £i 178. d# per hua(k«d i Ans. £&4 mi. 4i. « COM POUND MULTIPLIC ATIOI*. thlLZY' '" ""' P''^" "< ^^'OOO "«"» «' i>. lojd. per ^^> '; What .in 2,000 fee. of p,a„k eo^r'ejf? i^'i^,. 12. What will ai'sl acres of r.n i'*"'" '^•*'* '*'• «''• ' per acre .' ^ "^^ " '»"'' como to at 6s. 3d. ^13. If the toll ofa.mill be onA""' ^''°T *»»• ^i- l-nshels,bow many b.Xl, in a -^ »'"• a-other 7^ , ,^.4.^IW«a;,to„si.,,«barrr.;fti^,L':,?,^;,^ 15. Wt,kt is the price of Shhds'^nf ^ • '°''' '^'"'• P«r ga;i.,n ? f " o' JfthOs, of wine, at 15s. 7d. per' V m^ttu/reir""*' '"-^" tl'L' et^ , f ;< Ki^nat wiU thcu wa§es aiiiouat to in a yeax ? ^7' A gentleman has ^T^in '^"'- '^ *^^ ^ 6. ' 3«. per d^, Vh:ttef h7sa\r;;^.i;t''"'^ ^' <^-' . 18. How much will a m:ii • j • '*"'• '^'^'''' "^ 6. 3p. a day ? "'" " """ 8"""^ '0 a year af TObusl,; ^9. VVhatisthepriceof78abushofsaU^T.^!"|/ij. .nil "^ ^^"^'^^''-"^aster fi„*?s that he do^thln/^f ioldier cost ^4 17. k.j m, "»/^ "^ cioathing of (yie^ .V uAadJwn 01 756 mea amount to ?. . ^ 21 A r, ,. ^"*- ^3685 10s. ni.-34l b^^hds of indiln / ""''■ "fP™'"' '^"'•h 3, ' too of hay, w« h °i fr r« ?"" '^'"'^ ^'- ld.-andu7- oHhe pro^ceo't^.rek^J^^''- P-rji-^ ^f ;;-ue. se.f tor''i:T9Ttr'''cr"ff '"^"S"^ """^ -"-"^ nmouatto •""•?«":*«• ffow mucli does tht whole ° - * . Ans...:£93 16 3. «b!lM ,7s'B!r* '^"'^-J "'"»>»« and shop for ,9,ycar. COMPOUND rAULTIPLICATION. 43 94. 349 Soldicrc are to have new coats, each cotti to COftUiii 3 ells, 3qr. 1 nail. How muih cloth will serve ? I. Ans. I^D'iycls. Iqr. Ina. '25. Gorernment dischiirged 7115 sailors, cuch claim* inR 18 months pay. Roquirt-a what sum will pay (hcOfc off, allowing £i 7s. Sd, per month I ' Airs. j£l779lO 10. 26. I bought Qhhd. of sugar, each weighing gross 7cw*r Iqr. 11 lb. and am allowed deduction on each hogshead of 2qr. 131b. What is the ueat weight i Ans. 60cwf. 2qr. TOIbv 27. A merchant failing for ^7(i5, compounds with h\9 creditors for 14s. 7d. per pound. What sum at that rata^ will clear his debt I Ans. .€557 l6sk 3d. 28. How much sterling money shall 1 give for 27 French crowns at 49. 6d. each i Ans, £6 Is. 6d. 29. How much sterling money shall I give for 768? pisos at es. 2d. ? Ans. ^^121 10. r 30. How much sterling money may I qivo for 27» millreas at 6s. 8d. each I Aiw. £9% 1 3s. 4d. : 81. A young gentleman coming of ap , demanded the rental of his estate, which was delivered by his guardian', as follows : — I demand his yearly income, reduced, to-* Hionejr -Wheat 5s. 3d. barley 3s. 11 ^d. pease 38. 7id,. eats 2s. 9d. per busheL -- ^ FORM OF A RENTAL.. MONEY. £. A. pays 217 K. • • 318 C • • 456 B. .. 231 i/. • • 192 y. • •• 276 (or. * •' 385 iL • •, 567 s.. 6 12 17 18 15 1 19 8 9 3 11 4 3 1 3 WHEAT.iBARLEY. qrs. b. p 56 47 73 30 45 27 5 2 3 4 7 3 1 2 3 qrs. b. p. PEASE. 13, 1 2 ^fi5n n fi<2Qi 3 2 17 2 19 3 18 3i 13 3 5 4 2 23 17 15 17 3^ qrs. b. p. 14 5 3 16' 4 7 7 1 6.1 7 18 7 1^17 3 180 3 OATS.' 31 3 1 qrs.b.p. 112 7 0' 9 6 0^ 5 % 7 I 9- 1 |3 6 4 3 8 5 1 1 51 6 2 106 I 7 8 2.62^0^; *t COMPOUND MULTtPLICATlO.t, a«. A „,!);„ p*; ",^- f^.^- '»' '"JMre yard ? '^ " board i. worth Si, "ivr^fi. "* J" •*»". •»«« eack *"■""« ^i=*t. « 7id. per pound ? *••*» "•^ . MULT •••••# -^aSf'^^'P'''^'-^^^^ »ojit higher plice. i Ule|L "Sr^JJ; '^ ^« ^o tH. I^rodact one place Bearer eoXn^^ set each Uvlyinti bv the parti set elU J^*** ^"^ ^ »"<« in i»«U ward, tWright W ^ '*'''* ^'"^^^^ ««ther plact .. J p EXAMPLES, ^- 3 a Multi|ilj 4 5 5 ' ^/ 3 2 9 Bjr 10 9 tf *- illurfiply 4 5 ^» Multiply 5g A Mttffipiy 5^ *• MuFtipijr 24 3 *• Multiply 4^7 QUESTIONS. 7 9 by by 4 by S hyl6 ft. in. $ jft s 8 7 6 AttBt Am, Ans. Ans. 15 £0 93 4 9 402 1 9 COMPOUlSf^ Mtttff LICAtlON- 4i %' ft. In. ft. in. . . Si> 6. Multiply (J 4 ^ by 4 3 7 An«. 57 t f to « 7. Multiply 56 I 4 by 48 3 6 Ans. 2700 8 4 8 g. Mnlrtply 68 8 by 9 10 U An«. 080 5 7 4 9. in a board U feet Icwg and 8 inches brdad, hoW (aftMiy iqiiare feet ? Am. 8 feeC. , JO. In a board VI irrehtgy birottd and 16 feBt 6 incW»* long, haw mahy square feet ? Ans. 19 feet 3 in. < 11. In a board ov plank 15 feet 5 Inched long and loin. 6p. bfoad, how many square feet ? > Ans. 1 Jf. otn. 9p. ^ 12. Required tlw cmiCent of a plank 2(^ feet tortg, Iff inchc* broad ? Ans. «l 7 4 6. < i^f ^"^ ana JG luchti, ' '' «« "'Che,, 52, 15a«d 44 iilch« " ^""^""i ^-d % SIMPLE DIVrsiOSt. •"I thf number e»pre,sL ,,1^'"' «'"'«'«. «'"' Wrisor - I from them, ,o the remlL!: "**""■*'' *"•> ^"b 18 Farms,*re. ^uned the nujnbeT of acres iu each ? Ans. 264 acres. 4. iMfty-six Meichants join in an adventure to China i)y which they gain £moo, required the share of each } * A 1^ uf . . Ans. i^200. h.ru -I V''"''»*J* ^^ ^»"d consisting of 64000 acfesis to be^dmded au.ong 1280 men, ^hat will be the share of ,i ' A f, . ,,_ Alls. 60 acres, of (he year to k« rf.28«, how n.uch must each pay ? In IL"^ ^b'-f * *"" "^"^-^ '*''''""'» »»" '^ he .lice 427 Jfltherank, how many in file? ^ns 102 vJL^^ ^"".V'v.,"'! '^C'"*'' '""' "^"^ Puncheon. ? arLiftri « ""' .^y"'"' '='""*"' 9343578 Inhabitants Z.Tmwr'" *'""'' '""' """^ inhabitant, to . lO.^A party of .oldicrs 272 mites from J.<.»d-ana^f.V. "■' **S ^"-■'"-" *" ' " •'"^ '' **"* many inii;;"mo>t they per day i Ans* 17. ..•irraiir'?!' II. A (Upalbreiind(ka«ftr(blnont v«m A«d. *.mfmuc« bri.« 5M«aa »U«.. ii„w mji, ^„ ^ Mhgt ■All t»»»»- K...._ 3 r ' ' "■'•-• ^Ka ■ail tkikv k...._ 3 12. A farmer plaaU 17553(1 hiUi of |p4i»ii cfni ia 4$4 r«wi. Kequkea the numbfr of iOiii ia etdi roit . COMPOUND DIVISIOX :.\ Uiirj^ion— Reduce the reniaiiwler 1^ the next Jowcr dt .noMlnitlon adding in the gUoo wmll^«. of that nami-l" cofiunuc the divifion lo tht' ^oweit drnuminatioru But if dtlT'i^.^ ?! *'f'''°.' ^humiliation,, reduce bath thu divi«or and dividend to the lowest Uenoiiiination, and pro. » - • EXAMPLES, -* . 65 #« * 4. A. 4i 4 4 I 20 . 3 m 13)0Q(5 % ) 32 1 22 i 4^- 12- A3)55(4 62 4 13)14(1 13 .-.1 COMWWNb OlVRIoy If 2'i. If a mail ^ptna rf€;i59 2s. 4ti. hi Uflvc ttiomhs %*hat is that permomh .^ Aiib. ^«t 8s. 0(M ^^^. ^dicrs, w4iat is the share of each ?^ ^ Aas..^'9/'" 21. I f 1 1 2iiTi , ©f W km t cos t' /! f ^ , w h« t i t t ha t*^pef H^ . Anb. XI 2s. Sa. E I ii —nm ». i i ii ' *^ »i i 10 COMPQu.VBUiiyigiox Mw.V.JLIm./'""'*'*'' """»' -t ^^0 ,0.. .i.tl. i>«"pa-Ki.i"gc.ch 3.. ou._j^„ti't;;;;«,;;»<' poor _ 5^. Tfte reVenuef of a ^«mni»*.. - ^"'' ^^' / "" will ue auiiiuliied at Xio l,, ^^h l 29. ITow Ipng „,„„ , Tr.,lM„V,. wo'V'',!.'*!''''™'!- pvrii»y. ■ ' "••'"• ""d K«liu J«. dd. pay for the freight ^072 18». nhul i>\h,,',hJl« V "•'/ 31. rr the f l„a.lii,.< ofai, ari^ ofiinrfM ^'"• Comomc... X-8.3J8 4,. ad. h„„ Lucht thT.'.rmr/ '■ ; - ■. • Am. .161 3s. 6d. Somotioae. it i, re,„ired ,„ bring , ,e.. D.„„„i„,„^ to a i^reatcT. K U L £. DIVIDE by as many of the less n<.n»».f» 4- on« of the Krcitcr, «nd .hu/pr„c"d (^,7'"!''''" I!' """'" it into (he denomination r"quir«d th. t^ , " ''™"''''* remaiudet if any will be the a.,,1;."'" **■""'"" «'"» 'ho QUBSTIONS. r ». la 8018 half peuci., bow mm,y r„„*d, /*"• f *' t: namst'th-'^'- l!"* """•A>own,/An..1i: Si/pe.^JS^',t"'«'' ^7 "*'"' ^r""'"' '""f Crown., r wi «iiu 1 cuce, of caca an equal nainbcr ? ^ Aqj?, 61b. 6qz, lOdwtm COMPOUND mvisiont if r. In 160040 Ortlof, kow mtny Iitgoii wdgning etch 8. la 51789 Scropfen, how many lb. Ani. lOlbf. fog. Idf. tier. 0. In 183808drs. how Mttiiy cwl. A?(>irtInpoit« ? Am. Ccwt. Iqr. i8lbn 10. In MMOlbi. ho^r many Tons. An*, fl Toni. 11. In l'2«DUiiU. how mAuy y«ii. Am. moydil 1% III 1(]irK)nli. how many e»U ? Am. 50 eUi, 13. lit 3y36n||. how many pkcoi of Cloeh 'loj yirdi '^"S ^ Ant. la piecct. 1-1. In 190< 80 barly corns how many ydi. .. - i ' 1 -A"*- 17fiOvardf, 15. la 1301210 Inchei, how many niilen ? * Am. 21 § mllm. 16. ITow many barley corns will reach round ih$ world which li 360 degree*, ca( h degree 694 "»•!«• ^ AnH. 4765801 GOO barley corm. 17. In 7560 polei, how many acres .' Ans, 4 lac. ^^8. In i7il4i5 yards, hjw ipany acret ? Ans, 35ac. 2ro. 20po. J 9. In 53766 gallons, how many bushels and quarters I ^r. T ^<..«* . ^"*- ^^^^1"- 3p. -6720 bushels, ao. In 24507 pints, how many qrs. «, t . ^ ' ^^*' 47qrs. 6p. 3g, I, f. 21. la 120 pints, how many tallons ? Ans. 16 gallons. tl' i" Ty.'' ^"^ '"""^^ '^^"» ^ A"*' 4 Tom. 2 J. in 66i8qts. how many hos^sheads ? • ' Ans. 13hhds. S7 gallons. 24. In 720 gallons, how many barrels, of Beer ? Ans. 20 barrels. 25. In 9216 pints of A! -, how many hogsheads ? Ans. 24 hogsheads. A MM SI ee^A^A 'Wf%r vwvuass n9 CQmovm DivisiOiV. AH IXEUCISI ON THE lOREaoINO KVLU. ^"^ o/^( BritUh Ar my Es tablished by Law, I80A ^ Commissioned OrFiCEns. Marching Kegiments of Foot. Lieutenant Colonel, , ^ , ,, . f I'r o nn, ^• P^ifr, . . . '. _ V: .0 So'"'''^^ Captain, . , ,^ , ^ ■^ f^ Jo fi A Captain baying superior rank' " 0^2 addit nei. Charter Master, , . \ n « ^ t^^^"*"^ Adjutant. - • - - -• 6 6 JVoN Commissioned Officers Ani> FaiTATEi. Dragooru. Infaatr^ of tlj# Serjeant Major, . . . . 3 a nennAm * Serjeant, . 1 ... 2 2 ^ Corporaf, . . - '. ". 1 yi Corporals aft^^r 10 yrars )" serrice, Dragoons, j ^ ^i jJo. after 17 years service, 1 Ql Vo, after 7 years service, Foot^, lio. after 14 years ser^ce, do/ iru;„peter, Drammei^, Fifer, 1 7 Trt ^/. ■-•-•13' f Do. after 10 years sei vice, 1 4' JJo. Hftcr 17 years service, 1 5 IJo. Infantry after 7 years service, 1^0. Do. after 1 i ^ars serVice, QUESTIONS. J K Required how much money a mv-mast^r nf ^ w_ x*.io.. uiuM have to discharge one month's'nav ixf hi^t line. 2 6 per dfeiii^ 1 10 1 4' *■». f*' COMPOUND DIVISION. ^3 ii corporals, 12 captains, U lieutenants, 8 enslgnfi, ^ inajots,'oiie lieutenant colonel, one quaHer.master, onv adjutant, one ourgeen haflog captain's pay, one scrjeant- najor and 1*2 drummerit ' Ans. j6i743. 2. Required the pay of 16 battalions of equal strength with the one in the last question, for 12 months, aUtming 30 days to the month. Ans. jg3346d6. • 3. llequired the pay of the British army for 12 months, consisting of 198560 men, aMowing one colonel, 2 lleut. colonels, 4 majors, 20 captains, 20 lieutenants, 20 en- signs, 2 SugeonH 2 adjutanis, 2 quarter masters, 2 scr* jeant majors, 2e> Serjeants, 40 corporals, 24 drummers and fiftjrs, for 1000 men. Note— A colonel's pay ^t % 6d, per dieuKr < Ans. ^6185959 13. 4, Received from on board the Quebec, 6hhds. of su. «ar. No. 1, containing 7cwt. 3qrs. 27lbs. tare 3qrs. 141b. No. 2, 9cwt. 2qrs. 181b. tare Icwt. 61b.— No.3, llcwt.i Iqr. 2lJb. tare Icwt. Sqrs. 171b.— No. 4, Scwt, Iqr. 131b. tare2qrs. llb.~No. 5, lOcwt Iqr. 51b. tare 2qr. lllb.—No. 6, 13cwt. Iqr. lllb. tare Icwt, 3qr. 261b. Required the neat weight of the whole, and the price at i>|d. perlb. Ans. 54cwt, 20Jb. price .^'240 3 10. 5. A merchant taking an account of his affiiirs, finds that he has in ready money £497 12s. 8d.— 17 Puncheons ofspuits, worth 5s. 9d. per gallon— 16 Pieces of linen vorth ^5 Us. each-3 Pipes red port wine, worth ^45 J8s. per pipe-^ Hhds. of tobacco, worth ^37 10s.— He owes to A. £U7- 8s.-to 13. ^22 6s. 8d. ' llequir. €d:h,s neat stock Ans. ^1569 19s. 0. A tarmer left 756 acres, to be divided equalty amonff 111* three sons. How much had each, and what was thl v^lue supposing an acre ^29 lis.? ^' ' Ans. 252 acres.— ^25 10s. O^-d. .7. A gentleman purchased 27000 acres of wild Lnd at Is. 3d. per acre ; and 20 years afterwards he left it tu be equally divided amouii 5 sons and 1 daughter. ||<. qmrea the value of the legafv^ the i^'uf \u'\t^^ ^...^l .-. 4d pet ,ici;e, 8. A fe'entieman purchases an Ans. j6'2100 value to ea «*»• Cil, 46212 lOi.-Wijatdidhe estate oi 392ac. 2r. {i^r pay per acre I He aividsg^t £2 «4 COMPODND DIVISION* 1 barrel of llo.,r for etery i iZh tr.^TK^^'*, > «'"» 2., ad. What did he g.7n ? '™''- ''^'fJV^l^ /^ *» We, of 6.b. eachrthe flo»r ia/ref^'x'V"""? '«» l»W.„g How »a„; toave, ? '"""^ * ^„;«'«5' « ^'"-/^t^^^ifdrt!:^^^^^^^^^^ -(*•-' 14. How manvvfti^a «f «* .. ^"Z ^1 5S| yards. •>cr of yards excav^«i .»j A .. . .^"'"^ *"« "«ni« yaros excavatol and the .olid feet of stone taken Solid yard. 30555 J-Fect 825000 bushels „rp1J's"cX' lil^T^.V"'*"'" "'•"<"' 360 *ar He h'ad 22 b^htutf'lh^tte" ^ ' ,'.' r^."' 58 of pease. 94 of fnHj..«. „ •'"^'»«t per acre, id of oats^ '^ ' *^ "■ *naiaii corn, and 5 #nn« *^/ i— i tic re.a.„der of hi, U»d »«, fllio"' ' il"; "'a^'aTrr? lo'Ja. ^>ZtZ^:':^,^^^ "'■ f " r'*^'"* '^'«''»- *»io«as and Wf Ssroftthrt^-nlSr '"** ■>w \ *, tie ]B«a to hat© 7s* Sii^ ''^K. BILLS m vjn^amA ii cacli. and the momen fls. Reqtured the number of etch. \d, lleceivtti from London 3 boxes of hatr, t-acri con- taiuivg 4 doceiv, at 9«. Btk—b piices of broad rioth, 105 yards at 19s, 6d. per yard — freight and other chargei j^S ISs. 6d. In what •««» do the goods stated me, and what nill be the ptica oi i yarilol doth, if I put the whole at jeiS» 10s. ^ .i^ii— .iii.i» BILLS OF PARCELS. Mr. James Gordon,, Bought of Anderw YotJifo, June 5th. 1 Pair ofworstcd stocking at 4s. 6d. £0 tS 5 4 14 9 4 1 3 - 5 f> ♦ rs^ Yds. of iilien at 5s. 9d. d do. superfine doth at j€l 119 9 Dozen of buttons at 4s. 8d. 'S Sticks of hair ai 7 jd. 4 Skeins of siik at Cd. . 8 do. thread at Idr :-- 4^9 16 A STATIONER'S BILL. Mr. George Duguir, ■ 1799 Bought of Peter Wilson, March 1, 10 Rcans post.paper at £l 1^ £i6 8 do. fool's-cap at £l 2 6 9 12 do. printing demi at £l 4 14 8 6 do. coarse wrapping atGs. 3d. 1 17 9 .£41 5 A GROCER'S BILL. Mf. Daniel Heid, 1808 Bought of John Fe&ctjsom, ^prii 17, 18lb8, of white sugar at Is. 9d. 28 do. brown, do. at 9d. 9 do, tea at 6c. 9d. " 4 do. tobacco at Ud. 3 do. snuff at Is. 7d, ^ gailous of spirits at 95. Od« 6 ^1 11 5 1 1 3 9 3 S 4 9 S 7 a ^ £B^f ^v iii I 19 BIUS OF PAnctti. rohats, coarse id„^.g7°*-«*»S«.7 14 « ^o White cotton, 3 pL"ce M „. ^ * « " Jul^aX Tolrisfcli,, • i - • 6 > To Si^it,, 27 gallons, a't 7,. k fo 'I « Credit. ^yPoU^h,i ton, 79 11 11 To Balance due, Errors excepted, ^MUEL CArlR, 53 26 11~TI 1808. '• '"' ^" ^^r^a Jam^ison, Dr v,bHpuline,3vard«atl7s.8d.2 13 q "Sfts.. 79 11 11 53 16 g 13 4 ll| 4 IH ?0A. rORMS 01^ aCCOU . ,4 FARMER'S ACCaim^ Mr. JAMES RoswEBt,^ ^.^ Xf B Eir J A5ti If Wagg Qriti^, |lr* , 1808. -V 5C 18. To IS lb. of butler at lOd. £l 3 4 To flour, 3 cwt. at iTs. 6(f. 2 1^ 6 Topork,! hoi^,w(,^50lb.at4s.4 3 4 To ha/, a tons at ^'2 16 4 3 fl809, Jan. 19. To butter, 1 tub, weight 561b. at lOAct . 2^0 To beef, Ifjr. weight 105 at %L I 6 3 1 ^ -tA »<^ . 'J 3 15 3 l5 17 i^ 5* Reccifcd payment In full January 23. 15 17 JQENJAMIN VVAGGOINEa* *««i^« -f-:' .■ ^ ' 'f A CARPENTERS BILI^ Mb. John Dux, To Peter WiisoN^ 1808. for Capenter* work and MateiiaH^ U^y 1. For 500 faet Plaiik at as. 6(1. £l 12 d ^ ^ 700 do. Boaid8at4. 6 1.11 6 6th. GOO Small Nails, at lid. 5 - 400 Large do. at 28. 2d, > • 8 8 22d/ 1 8 day's w qrk, at 7 s. 6d. per day, 6 1 5 \. * .r £10 13 2 A BLACKSMlTtt's BILL » • ♦ • Mr. Dawsojt, To J a 5. Cpo^, For Black-Smith-s work and mat«;m]s, Dr. J1808^ June 1 . To shoeing 2 horses round,at 7/i 15s. Od. To making a crane,. lO 9j To loib. of irouj^at 7|d^ iar Q II I ' I ' ' III III I jj" £uis^ $ .('A * FORMSOFNOTWAWRlctrPTS •••... £ioo. ■ ^ i PROMISE to p,v to J„h "//'"'' •'»"• 1", J 800 • ••»•••# Three months afti^r da*- /^^^"<^^'»^ Is« Jan. Jsop "ion Haefielff *»• V *» * pron. so to nav m t. V •••••, A JOIKT NOTE. We jointly- ;„d ,,,„,„ „,^""'7«', 1st Jan. iRoO. ^DWAlBiD PHtLLIPS. t t foms OP RECEIPTS. . fteceiVed of Paul *..-i "'•""real, tat Jan. iiino JAMES AlTRLV. Rcceired of Sfeplien Millar Y*!!"*"? "'•'^"''- '809. FORMS OP RECEIPTS. §9 fwlioTe Miteeo pounds, and U In full of one yean rent I due mc out of the said farm at Chrwtmass d»y Imt. JONATHAN JORO£N. • • • • • A Receipt FOR fNTEBEtr. Kingston, 3d January, \B09, I in ^ifr^ ''°"' ^'^i''^, •^*"^*^**'" *^« ««™ of "'"e PoMud. in lull for one j^car'., lutcrcit of one Hundred and Fiftr I Pounds, due me on the 1st instant £9 0. ^ JDAVIfi WATSON. , »••♦»• For a Leoact. Cornwall, 7th January, 1809. Receircd of Edward Philips Kxecutor of the tost Will and r^tament of n,y Uncle James Petry d'^L-r^Ll^hn ^«.n of one Hundred and Scventy.fivf PoJidf in^^/o1 lt^7ih "^Tl^"^ '^ ""' ^y '^' ^^* ^i" and Testa' aiettt of the tajd James Potrj. fi . ^ ,, JOSEPH ANGiy^r •••*.. *" o?^"""" ''° "* 'VDOaSED 6., THE BACK or 1%E DEED FOR THE PUHC.iASE MONElf OH EXECUTING A CONVEYANCE. Received the day and year within written, the turn of O,^ HundrcdandlVenty Pound, of «h. wi.hfn Zan : "^ HENRY JACKSON. •-: >r" «) COMPOUK0 mVISKWC. Coneniiiliig (he numb«r of pUnti r«qtilred to plant tn Acrti • of KngKb^ ami Scotch and also the French Acre or Auj pent, from 1 to 12 feet tlistfcnce |)tei?t form plant. *,> Fret lEngfUhlSeotrh ' IG ■ d 11 hid! he B ;ince — lio\V H[ ^f;|i^rt}b2. H ,l>^:.; -■ ^B pfantis "With H as pj^Qi^d H red. ^K r TEACHES to find a fourth from three glfcn tiWmY»erf. Of the giten numbers, two am aUays of the lame aa^t and (i»e of the same name with xka aumber lought. GENERAL RULE. Place that number for the second term which !i of the eaiiMj name with the number souitht. C<#n6Jdcr whether mofc pr less be rciquircd by the cjuestion— If more, place the Jesi of the two rcmaiuiwg terms for the fmt^ arid the greater for the third— But if less be required, place the greater for the first, and tiie less for the third. Mahiply the second and third terms together, and diridc the pro- duct by the first— The Quotient will be the Answer. * •■ « cost _^. EXAMPLE, If 9 yards of cloth cost £6 lOs, what mUI 72 jarda St? • ^-^ .. yds, dB, #.■'■■'- .''^■' •-^'' "^ 10 :-. 72 20 130 .72 260 ma 20 «)93G0(UJ40(£52 Ans. 100 36 36 O 40 40 i.s II cost 2 - - iL ^ QUESTrOXS. 4 yards of clotti cost \c 6d. what will T!5 yards 2. If 16 do, cost £l 16s. what will 6 d Ans. S\ 16s. o, cost ? AflS. 13s. 6d« J ,.«-«"' ■^.sj 01' flilPLE PROPORTIOIf. ' ^ ^J».^If Py.rf, of cloth cc^i 5 4, •...♦wlirw^.rOl 4. It .1 r.r«.. co.t 5^. .h.f ,fei*« rco?,- *--^ 7. If 2ib.. of .»,„ co,t 1,. ou. Hh.t will u:;: e„':. , S. If 3 ui. „f te. coH U. id. wh.t will «4lb. clt f • 11. S„,,,,„,e 1 purchase 4H yard. „f co.rM ' „,h Lr ^17 8., how o>«.j. yard, can'l p„,cha.e f™ iTi.T H. I haro giren £3 3,. for 74 feet of?i"J ''*"';• "...r feet .hall r,et for i6.. M. f '"* An^'sU'"' is. If lealbi. of t.bacco cost ^fslSs loi,i (.»« »>»»/ pound, n-y be bought for ;ei 2, Id!' ? * * *I.U will 541b. 7 OE. 4dwt. .6^rl cohT * *'*''' for 8.. lUd J ^ '*''• '""' ■"■"> P'xnd.n.ay bel.ought * • ' Au.. 16{ lb.. JO. iri purchase 91 cwt. of flour f.r yo • « 1. »uch will ll7barreu id. conui.^ 1 owe. Z- J< ill l»l»t will 19 pK-ce. cost, each containing asj yards ? 18. A.h».raftofboard.whicht"';„1i'V!^A . for e,.ry i03 board., and rcc«i,ed A649 4 f« hU raf, K.^u.rcd the „„„bor of boards. \J, sMos^f *• vr feet it" ^ iO. A, has u«k timber for wMch h« cry oj feet— he received i timber had hei I>. ba$ 9 J banal* of p< 000. How •»"• WM, lOf m ^ Ans. 14054 15 lajr TT- each weighing 44<;wt, iimPLE PROPORTICW. I -rtOIH. (are— and ttilli it fur £% It 6 p«r ewt What it the value of the whoi« ? Am. jtl036 6 8. 31. What li tho intcreit of i€676 19 8 for one year .at 6 per cml I ' Aai. J^3I tl It}. 9^, tl have iftfured goodi f«i the amount of j€378d lif* ifoni Qiitiboc to London at7i guiuMt. What ihail I pay t^e umlisrwrttMra ? Ana. MdB 3 0. 53. What leuKth of a plank 8 inchim broad will make a square foot, wlicii it rcqujritt |§ Indies of a hoard 1 foot broad? Ana. Jainchci. 54. A bankrupt has effects to the?aiuc of £'ZH^iU l^f. 3d. a^d debts to (he amount uf X'225C ) 18. How uiucti can he pay4n the pounii ? e^. Wk0b is the interest of 0579 pounds for 4 yrarf, it 6 per ceut ? , Ans. £1315 16. 26. How many yardi of carpeting t fcef 6 i'^hcn broad^ wUi cover a^oor that is 28 feet long and 19 broad ? Ans. 70) ds. 3qr l^, ^7. A plain of a certain extent sup Oied 6000 nors« 'with furaite for 21 days. How long would the same plain Lave supplied 2(^00 horse ? ' - Ans. 63 dnys. 28. The p,ovi*rnor of a besieged plar having provisions for 48 days, at the rate of Ijib. of bread, but wishing to prolong the defence, in hopes of succour^ to 80 days.*— What must the ration bo ? Ans. 1,'^. 29. A merchant purchasti 162 pieces of Holland, for 270 pounds. How must he sail it per piece to vain 16 per cent ? Ans. ^l 18 4. 30. A grocer bought 9cwt. of brown sugar for £31 14s. 8d. but finding it to bo of a worse quality than ex- pected, he is wiiUng^to loose 12| per cent. How must he retail it per puond ? Ans. 9d. 31. If 6 men or 8 women (ut dowr? a field of wheat in 28 hours, bow long will i man and 1 woman be in doing the same ? Ans. 66 hours. 82. How many yards of shalloon 3qn^ wide, will line 83. A merchant bought 4 tons of Madeira wifie for €40 pounds — it leaked out 4B gallons. At what shall he ««U it j[)fir g^an^ so ai^o. be ao loser ? Am. X3f» 4d. 4M SIMPLE PROTORTIOtr. , * **a» «»« pric« per ell Kn^llih » 4j per cent ? » v iJ/ pounds for oiif )reiir,tt ^ 36. How nturh cloth at ?. «^.»i^"*/^ ** ^1' ;rr •; •"•^- ----'^ - =h ct ,;;L-" 40. A /mrcd of W will kmn u« i_ > A lis. 8. IheprovisimisUstfi months" ' "«"«-(! to make p-pau. in u rr'oi^i";.;'r.""'^' '^'"; .rT'i^.i-'- 44. A certain 1WrPt»^ «i.»*i« ^^Z'^* ^^- «n«hc8. rhts, when m/can^3 f, f f*?^"^ ''''' ^f'^^^'- ^ ^*^^'^ 2 in. «^ ore feet /inX' Wh!/" 'M" L''"^;'^ ^^^* ^ «»^«d- ,et ? '""^"^ • *^ h*t was the keight of the Tur. 45 c » .. ^^^^' 73 yanls IJ inrh«o si_ paicl in Ci'ut i a gooclMo tkcTalueof^^ioslo'bo )'ca« tkuc. VVJm< is the disco Ans. le discount at 41 per iv^^ ^TLE PfiorCRTION. m 46. A Merchant bougM 6cwt, 3qrt. of CloTei at loa rtt« of «s. 4cl. \m lb. 4 fold thiin for jtlOS Bi*. WheUi- •f did ii8 ltti« or iam by Ihc bargin tnd bow Binch ? r^ . Am. Gained ^17 4». 47. A Merchant Import! Ifl balct of Cloth, each bale bad 4 parceli and each parctd 10 plecM of 26 yardi each. He paid £4 l6n. for every 6 yardi : what came tho 10 balef to and what wAi the price poi yard ? They came to ^l3Jl*i --price Ifli. per yard. 4«. A Merchant bouMht 872 yardi of broad Cloth at 8s. 6d. per yard and aold it again for lQ§. 4d. What did ho gain by the 87i yards ? Am. £79 l8i. 8d. 40. A Goldnmlth bought a wedge of Gold which ivcUhcd 44lbi. 3o2. 8dwt. for jfi5i4 4s. What did ho pay |M!r ounce ? Am. j€3. 60. Thfliun performs an entire retolution or 360 de- grees in the space of 365 days 5 hours 48 minutes and 57 •ecodds of time. How much does it move in one day ? Ans 60' 8" Itt". 51. I brought 5 pieces of Holland each containing 56 ells Flemibfa at 38. 2d. and sold it out again by the ell English so as to gain £J 6«. 4d. What did I sell the ell English ? Ans. 68. 8d. 6^. I bought, 96lbs. cff Cloves for j^68, but finding: them damaged I sell them for 7id. per lb. How much did I lose ? Ans. ^8 Sn. 5;i. I purchased 11 puncheons of spirit at 5s, Gd. At ■what shall I sell it to gain 26 per cent and how mucl» shall I gain on the whole ? Ans. gain .^90 15—69. 10} per gallon. 61. I sold 35 acres 2 roods 12 poles of Land for 7$, 9<]. per acre, which 1 bought at 4s. Od. What do I gain per cent ? An^. d^QJ-ly. ' .55. I purchased 3cwt. of Leather at Js. 8d. and gave It for 166 bushels of Wheat, which 1 sold for 5s. 6d. What did I gain ? ' Ans j^l4 l8s. 66. Bought for ready mo'i?y 400} yards of Flannel at Is. 8:1. per yards — 51.1 yards of Siiallon at is. 6d.— 20 c»?t. of Hour at Ms. Oj— lOlbs. of CloTCr Stcd at Sid,— f 2 14 itones of Iron fl* «o mi jaireoiae price Of the wjiple/ * •^ fi'- It ^100 sain rf« In ,/"'• "f",* IW"- "?(!. I s». Insiu-ed Goods in . cm t. ■*"»• ' W» cwt ' Wrecked and the good, da™«J '^"' ?"*-""« SAipiiM / :r nM to I get per cent for my moley ? ' """^ Ads. j^lO lig^ 7^ j,^ HAPPENr*^'^^^^^ PROPORTION <»estion, ana arcomnlfr"!. "■'•='"»»tanecs enter Into *1U • • • • HULK. the? miM^l^ !^ . 'trOlS two an^ *.j,^ f«. -^^ *^"^ COMPOUND FROPORTIOie. H QI/£STIONS. F Iff fmilf of 1$ peifons eipenjj j£^ in iS weck», |iow nach will icrTC a family of 32 persons 16 w.«jlp I Gevesal Stating* Persons. S Persons. 24 :: 32 ^ "■'6 16 >1* 102 32 512 24 • 2048 1024 £ 144)12288(85 1152 8. ^. 768 720 •• 48 20 144)960(6 864 96 12 144)1 J 62(a ' '- JigBMI^^^^^^^^Mt^^ - 1; ■ • '^^^^^B- y 't% ea 18 COMPOUND PROPORTION, tilt SAMt »y tiro OP2R4TI0N8. ^ Pr. 21 St 3« 8 ^e B. d. 20 \ • « 48 ^ 8)768(42 13 4 72 48 3S 12 20 ^8)240(13 i8 no 54 (T 12 ^^8)72(4 72 853 12 I 10210 18 61440 1024t) 8)163840 12)20480 2,0)^70,6 8 ^85 6 SAqs. I EXAMPLES. ^ ^7i glif K iUlT ^'^ ^*^" ^^^ ^"*^-'' -^^* will i2 — 9 j Ans. ^S 7s. 6d. -. 2. If ^100 in 12 months paiH ^6 inten^s^ x.i,«* . Cipal >viil ,ai„ ^3 7s. 6(1. i/o months? ' ""^"^ ^"°' ^^ : 4.100 :: ^'3 7s. 6d. > . £7 frif£\00phm £eiai2 5 gaiu ^3 75. 6ti, - months^ in V hat time will Ao , 9manths, X. ttSmiBUTIVE PROPORTtON. «t 4. If the iiitereit of £7S for 9 month be £3 Ts. fid. Required the rate per cent ? Ans. X0#^ 5: If 6 horses In 14 days eat 7 bushels of oats, what ouantitv will serfC 24 horses 52 weeks ? / , i . Ana. 7*18 busKoIs. 6. A Lumber Merchant has 900 plank 2^ inches tijiofc and 14 feet long, how many boards arb they equal to 1^ feet long and 1 J i.ich thick ? Ans. I75p boards. 7. If I pay £2 2s. for the carriage of 3 cwt. 160 milei —I demand how much I must pay for the carriage of 7c wt. Sqrsr 141b. 60 miles M the ^uie rate ? - > r, A^. £^ *s. Sd. 8. If I pay £4 for the labour of 8 moii for 5 days, vhat will be the wages of 32 men for 24 days I , A«s. £76 16. 9. If 4 horses^ plough 4i acres in 3j d^ys^ when they . work 8 hours a day— hojv many jacre*. wiH 24 horse» plough in 38 days when they work lOj hours per day ? Ans 384. acres 3p» 10. If 16 masons build a wall 40 feet long and 14 high in 12 days, in how many days will 48 masons build a wall 400 hct long 4 thick and 16 feet high I Ans. 9ldays4 U. If 3 men in 16 days, when the day. is 15 houri long, finish 18 poles of ditching— how many will 8 men fifiish in 4 dp s when the day is 9 hours long. Ans. 7 ^t-h 12. If a family of 7 persons drink 32 gallons 4f Ale in 12 days, how many will a family of 14 personshdrnk la 3 days I Aus. 42 gallons. DISTRIBUTIVE PROPORTION. RULE. HI Ciiis rule, 5JerCT:ciiiiS liictuiug in J. f»rbii6« Snip «3Ci^r« tain their gain or loss in Proportion to their share of thes joint Stock— feaakrupts esiates are ditided and iegacfe» adjusted. ^''^ORTlQjr. ■^0 tWSXRlBOTji n ti. ' . * ««rt3n ""'« «f the gain or C, ' '""'^ '» «"* I>.olo Stock. • <">« .. 7«0; 960 U',^.,^ ^«n f"^ ^ J"'" S'ock_A put. Jn J-^ f^^'^ ^"^f- «*80 for 5 monfli. .* .f ^ '" **0 for 4 nion*Ji. n sainni II """"•»> at th( end of wM/.-!. 41! """""w— B *"iK!d. Haw mu,t ii bediTidwl ? "'*'^ *'"«' "^W mere 60 jo -J * Ti. ^'*^ + 400 ~ 640 a^hen„^640:96 7?|^- ..., , _^ ' 96 Proof. , 1. Three Pb,,„, n ,„^^ - • -b»tB has .i:,oo for' ma„l„ !■•* <3"«"r coi.cen.e.1 ..chrece.>eof.£,876nr^;r"'""- ^Vhat sha.e nUl Sl^hat Stack ha. nT>.'^ "'*^^ *«<> y^* 12 o.r "ifP f»o\i«t »f to ^i,rdend" ''""""'' * sfiaresand wl. "-- Pw^«esses5siiaresandw~hat ividend tlie -^6235. 1 'Progtdm^j X. WSTRIBUTlVE'PKdPcmTION. rt' ^, .. , 5. A'khd^ftclearXiOO by trading with a Capitol of; | Lf fOOO of Which 'A paid -£050 and B i*360. Required |th«} share of eack ? An». A ^104, B i60. 4* A Bankrupt fails for *f7*00 and his cftt-cts are onlf korth i3400^A had given him Credit fori^l200— B for Lf r400— C for^^OOp and D'for of2600. What is th« |sh(iro of each. Ana. A ^^566 13 4, ,B d66\ % 2J ^\, \ * ^ C ^544 8 lOi ♦land Djf 1227 15 61 H-i 5. Tli'ree partners, A. B. and C. join in an adventura. |A. gate goods to the value of £*104p -B. 2080— and C. |169d<«-Thej .gained £'800. What is ihe share of each ? Ans. A.'b£l72 12 Hi— B.'s 345 5 llj ) C.»s 282 1 Ol y 6. A. B.'C and D. ship for Portugal, goods to the |Tal«ic of 22400— A. had J, B. J, C. J, and D. the re- mainder — The ship was taken. What was the loss of each, after they had received o£700 which had been insur. «d ? Ans. A. loses .£*12-*B. •£425-.C. 2566 13 4 > 1). 2495 16 8 3 7. Three merchants join in partnership^ A. putsMn 2450 foi- 4 months — B. 2170 for 8 months— and C. 2800 for 5 months— they gain 2533 J4 6. What was each man^s share. Ans. A. gained 2l34— B> ^101— C. £298. 8. Two merchants enter into partnership for 16 mouths. A. puts in at first ^250, and at 8 months' end he pats in 80 more—B. put in at first £360 — ^^at 12 months* end took out 90-*They gained 2510. What is each man's share? Ans. A. 's 2235 13 llJ—B.'s 2274 6 0|. 0. A. and B.'join in company — A. puts in 21259 on the 1st Januaiy ; but B. can advance nothing till the 1st May. What must B. then put in, to be entitled to ait equal share of the profits at the year's end ? Aa^. 21888 10. 10. A company of soldiers plunder a ♦fillage of money and effects to the value of 21000^ which they agree ta divide among tiiem according to their rank and the^tima they have Served, The oflicers and non-commissioned officJers have served 6 months, and the soldiers 3— the of- SccCJT have iOwi^et moath^ the uoa««oifimissloiied oHlcers I'l »l»llll iplpll ir'r ' PiRACTICE. • * 308. and the pr!vafr>t <><>■ ^«.* ii. . ^ as ■ rs * "■ -'•"'• uiwr«7urcr t Here arc ^ »!!?<««.•' V ^'Answer. Each officer's share .f 15 2 5 t* Non-commissioned officer 17 fl oaW* \ Each soldier • 6 7 s**i'' to diwdc the sum aruong -^ captains, 3 lielitena»l«^ •urgeon, 8 warrant officers, and 120 mp^t^ » 'u captain 24 share, the lieute'nams a^ s^ij l?^^^^^^ €».*, and the warrant officers 3 shares clcJ!^ "'' Auswen A saflor's share ^14 5^1* Warrant oificcr'5 4^ 17 iff Lieutenaat 174 g gJi I ' PRACTICE • IS so called from its extensirc use in business. Of a shilling. • ^' s. 1 is » 3 IB i 4 6 TABLE, Of a pound. o I if i i 1 - J S = 2 = 2 6 == 34 = 40 « 5 == « 8 ^ 10 = Ofacwt, 56 is i 28 -i Quotknt wiU ^e ih^in :"^ri;^^^ '-^ ^^^ th^ '""■mm^-^ X.^"'' QUESTIONS* 1, What Is tlie price of 45^6 7 #1 jirds of Bobblti} at id. ? 2. 3. 4. 5. 6. 7. %. 9. JO. II. 12. 13. 14. 15. 16» 17. • • • • m • • • • •** • I • • « t • • • -• • • • « • • • • • • • • • • • t • • ■• • . • • « • « 2«6S 5621 325 «G8 969 4898 3643 6430 878 8684 7986 979 4897 2368 4893 2143 at • • Ant. £4 14 3j| 31 5 8 3 • tf • • 4 23 4 7 12 •, • id. Id. ' lid. 2d- 3d. 4d. 6d. 8d. 18. Is. 8. 28. 38. 4d. 48. 58. 6s. 8d.** 1631 10s, ..1071 . • . . • . 81 91 213 43 357 798 163 979 592 14 8 4 2 12 -B 1 9 10 8 8 O 12 3 4 8 10 a o o Rule 2.— Wlien the prioi j^ iiot an aliquot part, dl* f.ide it into aliquot parts, ikpCL the sum of their leTcral quotients will be the an8%^ required. 1. What is the price of 1241 doien of lemons at 5d. ! Ans. j€25 17 1. 2. 128 pairs of buckles at 7d. 3. 842 lbs. of sugar at 9d. 4. 1212 lbs. of saltpetre at lOd.' 5. 896 doz. of buttons at lis. 6. 842 lbs. of candles at 3s. 7^ 543 worsted stoc^^Sat 6s. 8. 9768 pairs of silk*gfove» at 7f. 9. 412 gallons of oil at 8s. 10. 789 yards of cassimere at 9$. 11. 891 yaids of lace at lis* 12. 401 yards cf paduasoy at 128» 14., 986 doz. of Port wine at 149. 15. 487 qrs. of barley at 15s. 16. 216 iirkins of butter at 16s« 17i 5S6 cheeses at 17«. Q 3 11 9. f^H 31 11 6, ;SI 50 10 '' ^^1 41 1 4* ^1 126 6 ^1 162 18 ^1 3413 16 S 164 16 ^1 305 1 Hi 490 1 HI 8 JO 12 ^^ « 1 K 1 a .x /i^H 610 M^_ 305 $ ^1 172 A " Bi '* PRACTICE. 18. m y«rds of cloth at 18«. An* ^n* * la.t rule. ' ' ' ^ '"^^'H', M directed by (be two 1. What will 206 cwt. of ,uga, como to at ;C3 13 9 ? a. What wU.244hhd,.of„ola„e,t;':ef:f.%'?,*i ? ^^;^. What .n, 3.. pieces of ,i„«„ cor'to-^'it^.i^ 4. What will ua lAd.. of tobacco tre^'r^'tfl ? 5. What wil, 412 cwt. of potash clct'aV^li, "PI Alls, ^1977 12 «f Vk^m^ '^*^" ^^^ ^^^^^ consists of an eren numLr 1. What W.H 241 ciu of doth come to at 8.^ per dl ? g..l J"*' '"' ^ «« «•"- »^ ^'-E- come" t^lr per . 3. What .m 482 lbs. of tea come to at^ 12/^! it ? pefpa?;' '"' "° "»'' •" "'-^^-«' -«• t-t I4.. ^^5, What will 484 do. of wiae come to^^t' at!*^ p e r.!. Ans. i:411 8. KciE 5 -Should (he RiTcn quantity consist of sereral denominations, value the whole number by the fZrl^l 2. Wfa/ »iii h„ ;u„ *_.. , , . ... Ans. ;e515 I9. London fn n.;„K;; ':: irr»r-_7 .^** *""' .'^owt. from t» at <^'d 6 I Ans. ^^a U 31 !• WtACTICf . jpt. 71 4. What will SGewt. I y. S4ilbs. of f.«ncd uigar com. toatiiSb? ' Am. Xm 10 81. Sey^ral other conclw mcthodi may be adU^a for ihd tx- frcisc of sludenti. If the uumher of articles be fO, each BhUllng of tli« price makes a poinid of the amount. _;,„ «^v«. • "^ If the number bo I*, each l^onuy of the price makei ft •hilHng of the amount. ^' < ^ .k* If ^240, each penny of the price makes a pound erf l^ . amount. If 120, each penny makes lOs. If 4B0, each half.penny makes a pound. If 900, each farthing makes a pound, &c. The expert accountant will frequently discoter mcth. ods of workin.4 particular questions with great facUity, which can be reduced to no gencrul rule. Rule 6.— When the given quantity is feet, inches, icC. multiply the length by the number of feet in the breadth, and take the aliquot part for the iuchea— add them togeth^ •r for the answer. 1. What is the product of 16ft. Sin. hj 5ft. Sin. ? *^ Ans. 87ft. 6in. 2. What is the product of 8ft. Sin. by 6ft. 3in. ? Ans. 52ft. 7in. 3. 3. What is the superficial content of a plank 18ft. 6in. l)y 1ft. 2rn. ? ■^"''- ^*^*- '^*'™' 4. If a room be 45 feet 6 inches long, 38ft. 7in. broad, •what is its area in square feet ? Ans. 1755ft. 6in. 0. 6. How many squa'^e yards of painting are cantainod In a room that measures SOft. 6in. in circumference Jand ©ft. Sin. in heiahth ? Ans. 82yds. 6ft. 7m. 6., 6. How many solid feet in an oak raft confcimmg 40 pieces of 1 ft. 6in. broad, 1ft. Sin. thick, and I6ft- 3in. long > Ans. 121 feet inches. 7. If a window be 3ft. Sin. 9 in hcighth, and 1ft. 4in. ©p. kow many sauar*; Awt of glass ? r ^ t^ ■^ ' ^ Ans. 5Xt. tin. 6p. 4. I \ f^ TARE AND TRET. *« mam w I-, TIRE ♦ TRET. i^«f-I. .„ allowance .fter T.ro Jd -■'^ ''»•'»'" "'•• frotTcr:*""' ""'J'P-'or he .„„,..„ j,,^^^^,^ «^'. lake ali,,.,„, parhoH tib.f '' .** """"'^ V*t EXAMPLE. 3 17 • «8 1 1^ 4 S5 1 II 112)353 536 19(1 7lbu 17 P^rbag. How con man/ poimafi ^eil ? tafning 2icwt— tar# #4^* ^«^». 191 lib/. TAHt ANDTRrT, # 1. fLm^irtd thonrtt wfigbiof '7^^^*- ^h«; •-- • *^ Ant. d5lcwt. Sqrs 26lbi^ y^ 4 Whit If i\ie iifat weiiiht of 5 hogsheadi of Tubac cq weiiilna W<*wi. ^qrs. 8lb». grofs-taro 7lbf. ptr cwt* Ans. 85c^ 2qri. I 'M. «. What h the neat weight of a punch m of Prum^' i. S«pposc a Merc hant buys 12 hoi^thcads 'f Tojbac^, each weighing 9cwt. Iqrs. Ulbf. grost--tare lillb«. ptr cwt —tret ai Uiual How morh neat i ^ In 8 bat^s of Cotton larn, each weighing 4cwt. % ^^^^}U, gPoss-tar ^4lh . per cwt^^tret as usual, llow much neat ' ght ? Ans. 27cwt. ♦Zqrs, 8lb8. xr- 8. In 28 baTrels of Indigo, ejt-h weighing 2cwt. 3qir», 14lbs. crroS8-tare244Ibs. per cwt -trc( 41bs. per 104 •s usuai. How n.ach «-t -igh^^ ^^„, ,,j,,, ^^. 0. Whath the neat weight of 32cwt. 3qrs l«lbf. gti -tare I4lbs. per cwt. tret 4lbs. "«'^1^,* »";'£»«* Sbs. pcf 3 cwt. Ans. 27cwt. U «• ^Slbs. Uo». 10 ^viiat ii t. - mmt weight of 64ewt. 3qr». groM— tare 8lbs. V& C«..-trct and Cloff as u ua! ? Ans. 50cwt. Iqrs. 24lbi. \ ofcr. 11. In S6 c lests of Sugar, each ^f^^*»g ^^^^J*' ^^YJl letbs gross-tare a nbs. pe cwt.-tft^. and cloff as usy. fti. Howmtti' scat weight? _ •^ J Ans. 346 ft. lqr». 25ib5. ^}. -^ * »r,^T,^«A Knvi 6 hnsilie04» o' Tobacco, nach containinff per hogsl d— tare and as n&u al. ilow mn^h neat •weight i Ans 48cwt, 2qrR. 4UJS. 1* ^^^'* a 3 # .11 »OMISCUOUS QUESTION^ •■'J disponing ,i, pm« Cd ''""',«P«»ce of repairi,,, •"num. VVI.»« . ' *" '"'•'"at ^rtn. ! 1 1 ««on«i.i.Ua,j, ? ""'"•' "'^J' '■•'•got W eh/„„de;,ltr >-«, H» hvt high and 3fi w^f, f ? '"« « """« 44 f„t "••-pullmg ;e3 l8l_„nen?Af »*»— *cfding 4:, ;-«here being „„ „i„ hcget.Tl 1 ?""« " ^0 '»'• ^jT „ 4. Suppose the Farm,, 7. . ^""^ ■*■*" 3s. 8d. tai- ;^Obu,h^, PoraJr :. 'L'-'-TL^:!'™' """""U «wci;(n bushel, sent «h.. ivi, . . "" — "»" shine «riT» •"ery 5 bushel 'lew s„™ K '? ■"'" »"«' '«« *ed fo^ «ro.„U WWi., ,,, sann":r!;:''Xt1 "' """"'"« '^ ««i...d by W,H.a. ^23 ,2,. 8d. PaU= aught ..cin,aT(M,rofilem! ^•"^McUdi a qii^ nti(y of I 35 II 2 S4a;er.c.U^l\.f*-'-i^-Ut^ ««• -f 16 I3s. 00. tflOMISCUOUS (JUE^IONS. n -' % Bomht » OoU\ Ufpomter for 50 Guincis ansS^iold h for £50, VV »iat did 1 loio ? Am. ^*4 p. 7. If I buy L»nen .t 5.. per yrd. What will I g*i« per cent if 1 icll it tt fli. 6cJ. ^I!f V^,' u t Sold broad Cloth at IHs. p«r yird, by which I galiu •d 134 IW cent. Required the prime cmt ? Atfi.ed. In the pound profit, what is guinwl per cent ? '^"■' ''^^^ *^'' 10. What quantity of Tea at 8«. per pound must I tlte in barter for Icwt. of Coffee at 2a. Ans. inibl. 11. A deliTercd 504 yirds of Cioth to B at 5s. p«r yard for (J hogsheads* of Wine. What was th« Wine pet gallon? * :%. '' Ans.Cs. 8d. 42. A bath cloth at fl«. 4d. per yard, ready money but In barter iie vill hare lOs. per yard-B hath Slialoon at 20d. per yard, ready money. How must he rate his Sh*, loon to bti no loser in bartering with A ? Ans 2s. per yard. IS Bought 7 hogsheads of Spirits at Ss. 9d. per gal. Ion, but dibcofering that Tj gallons had lealied out of each hogshead-l am willing to sell the whole for what U cost me. How much will ihut come to per gallon ? An». 6s. 6jd. -^Vf 14. At what shall I purchase 3 cwt. of Cochineal— when I7lb8. cost mei£'i3 m. 3d. ^ _ ,. ,^, Ans. 4£'466 13«. lOd. 15. A Merchant purchases 3 pipes of Madeira Wine for j£2B7 I2s. 8d.— but finding it of a worse quality than he expected ho is wiHin<» to lose ^56 1 9s. in the purchase. At what shall he sell it p^r gallon ? ^ Ans. 12s. ggd. .16. What shall I pay for 3 puncheons of Rum, when •5tJ puncheons «ost ^£93 8s. 8d. Ans. o£ll2. 17. What shall I pay for 67yard. Which „»y -JT" '"' '"'"' '«" for Gain by matin .T? '^- P™"**"''" ? i>oA;:eVi:4^- 1^ ;^ I' .54. A F.rn,!,trj,"J--; of Linen , f^j". lie luay sow vtith Whtnt 1 I i '^^''''' °^ Land wl.id, I; f ' or-^ "Sinr^f, ''■ ^ "- S. "; i?Zt: '■■r K <* o **f*ii ii 11 s'L- III . i --King A bu.hcis cach/h; ^Lrii:;™! of Cambrio ^ard to gaiti ?3 48. 6d. lis of Win# it a year hf ■f cent bjr )s. 6d ) 19s. ^(J,f Cotton at ' Cloth 5§ the CJoth ^ of goodi yard^he uantitjr of 3r cent. o/" Fara ciud for fit of 26i I per j^d. expencu sell for i table ? « 6i, 1 which pbugh* ^eat tht ushel — )ects to plants md the cFuu of •ve cK) PROMISCUOUS QUESTIOfJfS. «t I buslieli per acre, worth Ss TJ ^,^'^,^^5:17 '^7 7"^ 2 6. Balance in favonr of Corn 11 15 0. 25. A Merchant liurchases a parcel of goods for ^87^ 12s. 8d —which he exchanges for 6 J Tons Potash. H« • ships the Potash f^r London and pays freight £9 I7i. 6d. per ton— he has no returns befortj l^ months when h« pcts j^Sl 12s. pt^ ton. I demand what he got per cent deducting « per cent because the transaction continued one year? Ans. ^18 I4s. lOid. 26. A London Merchant gircs his son j€576 for an adventure, the young m;»a pure bases goods for the Canad» market—he receives at the Custom-house as much draw back as paid the freight to Quebec. His Personal ex- pence ^57, the goods he exchanges for Staves at £19 lis. 8d. 11 allifax— having first put on an advance of 33j on the rea! cost of Landing them h. Quebec— his Staves cost him £63 5s. per 1000 to bring them to London incidenU alcxpences tS^i lOs. per thousand— he gets a brokor to sell them for jg 126 Stcrrmg per thousand. I demand what h-; made by his adventure allowing the broker 24 per cent ? Gain £678 7s. 6ld. Sterlings 27. A Lumber Merchant contracts to deliver 207 Masts at Quebec for i£4t Halifax Currency— the Masts to b« 90 feet long and of sufficient thickness, the Merchant hires 24 men at 1 dollar per day for 3 months and an ovcrsf«r at 2^ dollars per da/— their provisions and tools cost hJm Is. Gd. for each per day— he gets the Masts drawn to th« bank of the river for £5 17s. 6d. each— expencesof raft, ing every 15 jf29 16s. 8d.— he allows 4 men for everjr Xp at the above wages and provisions^, they arc 9 weeks on their way to Quebec and cost him for incidental ex- pences 7^ dollars per Mast, wfcen thry arrive at Quebec 1 Mast out of every 9 is rejected; I demand what tht Merchant gains by his contract ? Gained £3448 16s. 7|d. 28. A Manufacturer purchases £397 Halifax Curren. cy worth of Goods, which he carrwe to th« mstauge n 99 PROMISCUOUS QUESTIONS. per biisliiWc __ w. • '^.j , "^?! '^^'^ Ashes at 6d, In ,, ."' *9 lis. 3d.-he purchases tir^J .^. '"f '"' ^shes f,J Cooler, at 5s. M.^/'h, T, "?h v' .""' '^"^ -^'^ ««'h, » Ma.„u charge, for /ixi.^/h.^ KcUri^f;' -"' '^s.-t'h. "■at " require, 600 bJhloflhJf^^ 'f»— hofiad, foUth, the oxi-enco of Manufac.. ,- •," ?*'"' " Ton of carno, the Potash, when made "«' "^^ '-«*• SJ- He le gam or lose ? "'"''•J, P" <<""• What dL Manufacturer T,^lt7t: Z^T' '\ '" "■« '-', th, the rate of Jid. pe. ,^0 ? C!",!;, ^."'«^^- cas'h at 30. A black Smidi «. > ^'^^- -f 10-13 7, per lb. ^h,^ jg zcwf. of Iron at 6id. fach which Hill be worth 15dn X"^ '^'^ <^ Ok oz. »« them he loose, ^ of the 'n"^"/ J"* i but in ^ork. 20,000 nails worth^ijd peMcto"',, ,\""^ ""^'^ ^ *"'» JoaKer makiug the nails ban th?.'l, ""' he 3 d at ^3 per acre- ilcre- T^€| than cam thdr waiies »i» »a ^ ii "" "*' ""»« niore oversee hi„,elf. 1„ England he J^d 1 a."' delred ,\" per cent on h,s capital and li»i^ at hi> ca,e Aft- I 7i»n fce find, tl.at J,e has 246 acres cle^redTorth if ' •crc-tbe remainder i, „ow »orth 4 d^ ar,^r ac^ hi iouse »nd barn are worth ^'30 |es, than Sf.'v co^'"' ^ tXran"d'? " '"' ""=" ^•'"'^ '- "- '» "-« -.ii^ Ans Better to fcave remained in England by ^307 ,n 40. A colony of 376 families emigrated from Srn.lA I leg their passage, w hich comes to.f 54 each familv aV' climate and .he fever of the country /.If ^T "' their farms to relieve them frld Jt, aid the the" el" " ineir - apital-if we suppose the unsold farm, irorth J} w •t the end of S years, whether would there haTlbee^ A,? T1!' ""T* """" '•*'' "'"? ™'»»"'<«l at home ' Aus. Better to have rem.iue.l at'home by ^gmTl 3 weti; ^,'"'Pt<^»™Pany <:onsi.ti„s of 27 men use 1,1 7 *,.« • , r • "°* '""'^^ "' «''« 8aii«! articles will b« lifi'o^n '"' ")" ""'Plifflents of a first rate Man of Wat With 939 men for llj weeks ? (VVine 389l.lids. eigalls. Iqts. Aus../ Water y89S Butts. (Flour 771 CHt. Iqrs. 8lb. y^O men with Ciotii of /iqrs. wiUe, lie found that 1^7^'ib, )N1 ?r acre T^^l louse and barri »tis on account «do little more njonth, and in eel to work and ve cleared 12J[ case. After 7 I worth £3 an s per acre— Lis ' thij cost.— to have remain, 'byoifSS? 10. from Scotland Jch after pay. family. Thvj cacii, but they building a hut om change of forced to «ell he the remain, iupports their niMht have got I'y maintained 3 per cent to 8¥rorth o£l50 re hate beea at home ? 9220 11 3. men use in 7 lour and 17^ rticlea will be Man of War ;alls. Iqts. . 8lb. 1PR0MISCU0US aUESTION^ h l^yard wide was sufficient (pj ^9 mm», I require ihn tutaniitv txf t*h\fh QACnKSarV ? A^»> 4*^(^7 vArrja -' 43. I send a cargo of Goodi to tny friead, which ha 'sells for i?3798 12 4. ^Vhat is his Commission -di 2^ percent^ deduction 7s. 3d. per ceot to the Broker he employed ? . Ans. ^«i 2 lo. '44.' What lithe interest of ;j€78 5 12 4 from the 12th of Narcmber to the I6th of Jutie, al 6 per cent ? Ans. j£26 18 Sj. 45. A Merchant In Quebec receives from his Corres- pondent in Londou, Goods to the amount of £3985 12 per Invoice with direction^ to stll them at an advance o£ 27A per cent'drt'd toJiund him Potash in return. Uequirec^ the Commission at fl per cent on the salds and 2-| per cent on the purchase ? a^«' f Gnthc sales £^54 1 7{, X On the purchase 120 1 3 9i. 46. A Btokcr is employed to oet a Cargo insured, a. mounting to XT^Af 12 at lO giaineas per cent— the Brc<» ker to get 3s. 2d. per cent, P^quired what money th« Insurer had to pay the Broker, the tax on the policy be- in|; 5s. 6d. per cent Ans. .^20 15 1^. 47. A Riercliaiii rqcelyes a Consignmcjot of Good» worth ^4738 \^ 4 to sell at 2 J pgp cent Commission or at 5 per, cent, if he run the risk of the sales— it is proba- ble, that he may lose in bad debts £^179 19. Whicl| will be t^e more profitable Xo the Merchant I - Gain at 24 per cent ^11 8 S 5j. Gain at 5 per cent • ' 56 19 Ui. Ans. 'ji" Loss by taking the risk 61 9 6 J. 48. I wish tocovcr ^-§2689 12 on a ship coming froin the Wi'^t Indies at 10 guineas per cent. What will the In* surancc conic to and what sum shall I Ir.swrc I 4y. Snipped G bods for Jamaica to the a;i)outit of ^C57<3S IH. I d^'and what it will cost tocover thjpr^- IHrfy out and bomb at 3 guineas ? , Ans. ^6277 l5^ ^f* ^^ be Insured out Sr home. 50. A Mftprchtnt ST» L>nd.^a eMus f/>r Ch.az-^^.-. Gai^(ilifu a f/(iant;ty <^f doorfs «mount pv^rlnvdic im. ^nsttiui o|S;*^uia:3'?s-.Soiivof t4x pet iillMxon Js) |J I i WP"t- TROMTSCUOUS QUKStidX.^ FMlht wfis^3^5. id. His agents sold them of ^t an atf; Tance cent for ComnusMon-Cottoii ..ool at ^s. per lb cur it>. What is ^ahu:<\ or Ibkt by (bo aaventuie ? «. . rr , . Alls. '4£'4768 19 7J gained. ^oi«, io ,'7'' V**'' ^'*«'"*^ ^'"'*^"^'«« ^^<*» a ^'«pital of *t;>iG4 18 J-he Insures daring the first year of his business, on di/feieat ships to West Indies ^'3708 13 a » gMuvas per^ ce»i-on ships to the Levant £U57 at 4i giincas-^ua ships to thq Kast Indies VSUJ 19 at 73 ju-neas- at the end of the Jirst year h« h obliged to pay on recount of the loss of a West India Tussel i'307 18 nna some othcH loses on the other vessels eamc afiainit him Ih VTF ^i ^''' '''"^' ^^^^ «"'" «*• '««« had he at IrnfiTif r .^'**' ^^"^ ''^^^^''' ^^'^'^J »^ ''^^c l>et" more i^h^K "' '''''' *° ^""^ ^'^^S^' '"^'^ *h^^ ^""^«» ^hereho ducUoa'?^^ P''«curud 6| per cent without any ribk of de. ^ If Lost hy Insurance £94 5 7», Ans.^ Ml^ht have gained by 7 ^ * t I)urehasin)i^ S.tock j '^^ ^ '^t' 5^. An Underwriter has s. Capital of ^67854 12 9, on ^.?.f/''"^^^ ""^ '^^'•^'^ ^® ^^^'^rc^ on a ship for China ^^6854 19 at a premium of llj guineas and on a vessel hound to Quebec i,3984 11 at 6 J guineas i^ith convoy and upon a ship for Trinidad ^'2867 n without convoy lor 9i guineas per cent~in case of loss he is to receive a deduction of ^£"5 per cent~in' the mean time he places his Capital and premiums in the bank at 5 percent and re- ceives accounts in 9 months, that the ship for China had fieen damaged in astoim to the amount of j£6768 12 her ivhote value with the Cargo is estimated at £27864 12 3 ofuhlchhomust pay his share—the other vessels arrive «afe at their ports. Hequired his gain ? i:, , « Alls. £391 8 5| gain. jiollaod 75 Cl.ft.t8 of Tea, each containing Sbilb». at 2fl. i*. per Jl. iiid 27 pip« »£ Wlise »t $#, 6d, jper gaUon-. PRp>IISCUOUS mftSTIOXS. i? tfieMnchant Ifinuret Mt pro|ierty at *2j per ccnt-li« payi at the Custou lliiu!»e » ft J» |^r curt! on tik- Hro«»-¥i4lir ueofhUOootIs, the fivight U .€if, l^ mM he leHi Mi Goods of fio^prr rent fti^fUucc iinOitUJt^ Vrsmc «^r.-%* The smiikiKler losei^O Che^t!l df iVn iimi fi i 1)h'« of \YkH0 Mh\ft\ were sioictl by theCiistoln M<»u«e (nucer* anil he is obliged to sell he remainder fc<^#ef1y nt ah mlviinei' of 37J per cent on the prinio oo»f. Whlth has fhognatur profit ? . ] jMtnh.i.if . al i*- .t \m 4 »?. 54. Two young men w^ctbn JJ\.^7Q tW t^chrcnieof them purchased wild fjiihd* Ht *is. 64 '«Jif<^pt I' (Arm of 108 acren rhi? ifreafi-r pirrt of xihic-h Was elt^ari-d wljh • lioiisc upon it, which cost him logellier with 8 clear gaiiMa do. 5fi. A piirdiases a Mill Seat fur ^218 12 S, „noa i.'h.ch he erects a MHI at an e^pence of .€1657 18 Z year with another £S5 ^ ; at th. end of ii5 years (ho bushels of Wheat e.ery lawful day of which J, h .ivou for Grmding. What li,fere*t does A get forli. money >alu,n« e,ch bu.hels of Wheat at 5s. or if he chose t a t.lw.!; f ^*^'^*^*'^* «* Q«^'^c piirchasvs 6^85 l^ushcls of •wheat for 6s. 3d. | and sf^nds it to Mill to be ground, ho ^ecnres cwt Sqrs. for erery 5 bu.hef- ; ejpences of tZT^\'' ^^'u *"^ ^''^ i^; »^«' b"«^«» batrels cost c ve OA H;.r** ' packing 2.5d. per barrel-he may re. ceive 9i dollars per barrel of Icwt. 3qrs. ar he may send It o Jamaica at 7s. 6he same amount,.a^,5 percent, and lost on, iy A days reserving J pec j^^^t comraissi<^n ; and at the end ot these 3 months, he discounted bills for 2 months ivr iua oxiuii amount at 5 jpcr cent, taking 1 per ceui fRACTIONS. %9 A «t>miniition and loiiiif; only 4 diiyi. Required what he gaiocd by the depoitit at the end o( the year. , ' 60. 31 Gentlemun KuiiHCiib« ^'dOcO »«'«ic:h, to make «• Stuck for rarryiH'i on th** buMn*?»»>oi Bankifiii • they d«'- po»if J each, to reuinin in »|wci»» in their faults— iJiry purchase a home and ofllC4tf for ;t't(7G8, ami ihu ckpunc.ts of comluoiinic their biitiiuc5«t i« ^yvo i'i perdiiuuin -tlu^jr discount biilM to the amount, of their nominal Stock i»itti their notes at ft ner cmt-*they find that nolel^^ the a. mount of ^'1439 one year with another are lost and that they lose by Uiscountin^ bad bills £%79 12 8* 1 demund* liow m"ch \}{ir cent they got for their money supposing the btiildin, » worih what was glfeu for them, dtnlucttng only the InieretJt ? Am, £\4 7 S. 90. There h a company whose Slock amounts to ;€86984 18 ; divided into i()4 share — they laini'd in o'le- year £{'iSV(i lu i A has 9i iharesi. liequind his Khar©; •f the proiits ? ' Ans. ^M178 1^^.. FRACTION Si. FRACTIONS or broken nnmhprs express f»ny part or parts of an iinif. —If, for i»xainpli when th«'Nnmer«tor il equal or i! realty thrvithe l> 'nomitmtor ah,|,, ^, f. A compoiHuJ Kractiott is the fraonon oi a fraction a^ f of I ; to explain this— if one of the ^tixfhs^nto whidi w«* supposed tiieappli! out were a-ain (iivided into 6 arts,, two of these subdivitfiops would 4>v iouf expressed, ^.of '^ @1 th*i !*iiu'e * /■' **< I REDtJCTrOi>^ OF REDUCTION OF VULGAR PRACTIO S CaiSi 1-To Rttluce Frictions to tht Ir low i t. rwi •nH #?!*;;^^'^'P*'^ *'•* DenoBrfnmor by th, ^u »eri ch inrt that DiTWor by the remainder cuiiti.m«llv till ootfci t tTTl"; n^Y***" bu.h Numerator ii„d DenLlnator ' J itnarATT' *".' '^«"-"«"-^- by any number a pleasure that will pro its lowebt terms, 7. Reduce ^y/^ to its It west terms. 18)^^\(-.| Auf. Anf« T7%t Ans. 'J An?*. vhr* Alls. ^^. Ans. RuiE. -Multiply the wfrbfe nnmber by the DenonJfn- «or, adding in the Numerator, and altCeflii* Mia ©fee lAe ^iTcn di»9iai^9tor» ••^ r*.^ »te »11Bi}li«t tMl ftCtlou bf iiriu CTIO ^ ow t ti row. Iil0 i^tt o«r. .>. to till iiatkir^ nominator * r tiisure, or Iji. ny number at •»! Ani» Ani. l^ii. An«. ^^U Alls. ^^, Ang. y. An«. JJi^ A no 2 09 \ an iuif) roper > he Denonftiu tltis »iiia o?er TUrXJAR FRACTIONS. V^ c% t\ to »n ini »§« rac Hon. 6X ' 50-fl««V ^"■^ clioM. Alls. \*^«. Afii. I, RHuee ft|5 to an improper I «. lieducc ni'toan lmpro|ii?r fraction. 3. ' Hjuce 7J to an iniprope. A Mot 4, I clinch 174 to an im|t#r|H'r fr. rloi, J I- ' o^ to an improper fractiuit. (^ 1 to an improper fraction. 7. , • *ib\ to an improper fraction. Case 3. -To Hcdttcc inu>roper Fr.iction to whole or mlicil numbert. 5^. .'.*? !^* UuLi.— Difida the Nnmfrator by the Dflnomlnitor.. EXAMPLES. Reduce V to a whole or mixed number. ^ . 6)3 1 (G| Am. SO A"**. III. y. Ani. ^^. An*. i|*. 7f 17f. 8lf. ' 1. Reduce Vr' *** * whale or mined number, Ans. 8|J. a. RitluCi' y to a whole or mixed unmher. 'S^. 3. Reduce y to a wnole or niixed miw >er, 4. Reduce y to a w holt) or mixed number. 5. Reduce ^ to A whoioo^ miied number. . 6. Reduce ^l* to a w hole or inixeil number. 7. Reduce ^\^ to#whdleor miied number. Case 41— To r«il«ic^j[r«€tionB to a common Deuomio. •tor. * Rr5LE.— Multiply each Numerator into all the Dewo. minatui'8 except its own for a new iNumerator and all tint Donouiiuators to^ulhcr fur a ccwnmon JDenammator. . EXAMPLES. •' " -^ Reduce J, ^, and ^ to a rotnmon denominator. 3>C^Xy«=5t ,. ,♦ iN^* i\ 2X1X9=72 1. Reduce l^atid \ to a cooioioti deiiomlnaf^. -r^rv IMAGE EVALUATION TEST TARGET (MT-3) V- {./ 4^ V. 1.0 ^1^ ^ ^ 1^ 12.2 iiiB - 1^ I.I u m S IIM IJ4 % /A 7 /A *>v>^ .^ ''^ Photographic Sciences Corporation \ ^^ •s^ \ \ ^<^ V ^ o^ Ij' '<*> 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-450 J :zyr» TBOf> ItiBT* to a €ut*isatM» ui'».M',iiin;no!. A>na '♦* "2®® •••^ 5i Reduce f\y, |, -i*; and -fy to arominoin]»'nc»: jurttor. Arik -77<5o _?400 jl»oo 3640 "^- T2nS-o- a simple fraction. W.. 3. Reduce J of { >r' f of ^ to a simple fraotsoni^f^^, 4. Reduce •/ olH 10 a simple fraction. |J|. 6. Reduce ^ of 7 (o a simple fraction. |^,. 6. Reduce \^ of }J of || to « simple fraction, jili* Case 6. — To reduce fractions of** 'ohe denominatiou tO' another retainin>>, the same Talue. Rule.— tf it be from a higher to a lo^rer, multlpl^r th« liumerat'>r ^y the inft^rior denominaton — If from a I6wer lo a higher, multiply' the denominator.- ^ EXAMPLPX, Reduce |^ of tf penny to the fraction of a pound by C6ro|)arin:.,at— it btcotncs |. of ,"j of s'-o which 1 educed < by the last *cascv is j^^j^t V 1. Heduco l^ of an ounce to tlie fraction of a pound A-vordupoiie* -■ - Ans. ^, 2. Reduce I of a^^ony to ihe fraction of i^ po«|UiU 3s, litdiiey;^7d. to the fracUofi of a uouud. wmmm VULGAR FRACftONS. ^ '4. Reduce 12lb. to the fraction of a ton. ^ 6 Reduce i of a pound to the fraction of a guinea, 6* Reduce ^ of a f^irthmg to the fractioij^of a shdlin?. S Reduce | of a pound to the fraction of a ton. „ j^ S. Reduce ^U of a £ to the fractioa of a penny. ^^ 9 Reduce ^ vd. to the fraction of a mile. irtrc' 10. Reduce ^ of a £ to the fraction of a RuinCa. ^^^y. 11 Rediicef o,f an dunce to the fraction of a cwt. ^079 1% deduce 3 bush. 3* pk. to the fraction of a qnarter. 13! Reduce 4 furlongs to the fraction of a league. Case 7.— To find the raltfe of FfkWons. Rule -:* Reduce the numerator to the next inferior dfi^ nomination, and diwdc by the denominator. If there bo a remainder, reduce it to the next donooiinatKin aUd 01* virions hf>foru ■ ■"•'.>: Tide as before EXAMPLESii J^Qgulred the f alue of 4 of a j^ 20 .a .1 *> 4)60 15 158. Att9* f: Reflulred the Value of | cwt. ^ Aas. iqr. 21lb.l2 .7dr.'^ % Required the Tatuc of | of a .£. 13s. 4d. i. Rcqiired the talue of ^ of a j^. ^ 12s. 6cl. 4. Required the value of I of an «!! Enghsh. 3 qr*. 5. Required the value of j^^ of a mile. 6. Reouired the value of I lb. Avoirdupoise. 602. 134 drs. 7. Required the value of f lb- Troy. ^ 6 oz. ^ dwts. *20^ dr. 8. Required the value of I ell English. 1 qr. 3i i^U«* 9. Required the value of ^ of * "***®' 10. Required the value of | of a hhd. of wine. '.^" '- . 62 gal. 2 qts* I If' J : > S ! ! I , 84 REDUCTION OF VULGAR FRACTIONS. 12. Roqutred the value of \ of a da^. 14 honrs^j »; 13. KequTfd flio value of /j of a too. Scnt.Sqrs, Case 8.— Turfed ucej*rixed FfftiittotH to single ones. Wlsen/lju- nuincratof is the ntegrdl parf^KuLE i Mtfl- i\,\y the nuiueralor of thi fi*0a^i by the dtnoiuinaioi' of the fractional part, to which add itn niiinerator for a lu^vy numerator. 'J'Ijoji mu4lif)ly the denominator of the frac- tion b}' ilie dunouunator o( |ha/xaciional part for a ucw aeuuffiinato^'. *. / ' Reduce ♦ to a sin^ilf fraction. 'v . fiX4 -K '24+3 S I 97 Now Nuraeratof 8X4 ^* ^ 9^ New DcDominaior» EXAMPLES. 1. Reduce ^ to a siipple fractioo^ 8 Ans^lJ^ 85 A us* -^j* ). Reduce _I to a simple fraction. 9 3. Reduce ^3- to a simple fractiofi. When the depon)inator is the integral part, R ULE.— M u Itiply the denominator o^ the fractijon Jby i)ic denominator of the fractional pairt, to which add it» numerator foj- a new denontinHtor— then multiply the numerator of the fraction bv the dc|i^i|iiuator of thefj^iLOto tional part, for a new numerator.^ '" ^ - !* Reduce - . _i: * Reduce — to a simble fraction. - ' 8 X S^24 7X2z=^i;fl=:5i to a eim|}lc fraction. 4X5 — 20 .. 8^ 'a ^' i. M ADDITION 6F VU LG a'R Fit ACTIONS. 9i fxAMPLES. .-K ' 1. Reduce 8 ?r,* to % simple fraction. Ana, 14 { lit -»,..■-, t. ^^oco 31^ to a simple frwt^j|f^ papje i •■■ ■ 3. Reduce j-^ to a siqapje fraction. ADDITION OF VULGAR FRACTIONS. RULE. REDUCE the fracdons, when necessary, to a commta denominator. Add the auuierv .orsaud place the sum oFcr the comaioii denumiuator. EXAMPLES. Add I and J t^ji^ethcr. 5X3=15 23 1 /s-g- A.ns. 6X4=20 1. A^d ; of a £, and | and 4 of a penny. ^- ■:-^-vc-. . ;.;; J'^ Ans. 13s. lid. | 4. 1 2. Add 1 of a auinea to i of a crown, ^ of a siul.ing, I jenny. .^ ^ ^ .Ans. 12 1 -^y. ^ of a foot, ^ of a yard, and J of a wile to- Aui*. 1 540 jards, 2ft^. 9in. 5f yards, 4 J ells English, and ^ of a nail to- Ans. ll>ds. loa. |. § of a day and ^|: of an hour together. Aus= 8 hours. 12 min. 30 sec. ari(f $ of a 3. Add getMr. 4. Add gethcr. 5. Add a. Paid lo A. ;637jj to B. £g5i\ to 7J, Require£th« ftmount. Aus.-t59 15 10, 'i M SUBTRACTION OF VULGAR FRACTIONS. 7. A. pucrha!if!i iV of • ^*"^ stock for .€8168, and ho Hishei to i)ur« h«»« i Ut JtUSUS. What will be hl8 tharg aitU the price f Atii. |Jj.— 4fe'a067U. SUBTRACTION OF VULGAR FRACTIONS. nuLK. PRKPARE the ffflftipns a§jjl|cct.pd in Addition— then act ono numerator from the other, uiidrr wluch write the common denominator. «u EXAMPLES. From } of a j£ Uike | of a shillinjj;. 4 of ij°=:V 5 Ct^X« 5X^ 300 10 lllfa II ». 5xC=z30>^6()(Hfl.8d. An> m- .50 30 J2 . T 11 30)210(^8 ^240 1. From 5 of vi guinea fake J of a .£. An§. 2s. 4<|. ■a. From ff of a ton take ^ of an cm t. An«. io cvi't. ^ qrs. 2^ lb. ;^y. 3. From i of a chaldron take |J of a bushel. * i: ' • Anfc. 17 ?)Ubh. { of a pk.. 4. From 5- oz. take |- of a dwt. 6. From si{ cwt. take id,% lb. A us. 3 cwt. 1 qr. 12 lb. ,\j. 6. Four merchants build a ship— A. tak -s J, B. |, and the remain. 'SVLdtib tieshareof l>, yi,lo ge Aqs. li l^ pmiP me ruHJam- "^VWON or TULCAR ntACnONS. V9 ^MVlTiPLlCATiOif Oi VULGAR FRACTIONS. RULE. MULTIPLY jHc ©8«€nK©ri Infathor for a new nu» pcratar, and lli« ^^MtoviAmm* i^f » n^w ilisaoaOiittoc. 1XAMPLR8. Ilultlply I by f . 8>c4=rH I Aqc Aoi* !}• Am, 7iV Ang. ,'^ Am. 337I4 4X7:b)f I. MoMlply I bj 1*. / . «. MttUiply i of 7J by |of3J. 3. MulUplyJofibyi. 4, MultlpJy ^t by 7. - . «. Whtt colt 14J yards at £iJ ? A»^»- 4»3 *^/i' «. Wbut Is the urice of «7l y^rds of scarlet at ^ij f. . * . Ans. £91 15 lU* KoTi.-Ia murtiplylii|lf ffroilfcr Fractions, the prcW 4QCt is always less than the multipHciind ; for i^in^muu tipl>lii« by fi'miM Airfther Increases ni»r tleCiHsises tht •nultiplicand, roumplyin|j >y less than a unit n»ustde. crease the multiplicand : thus, luulUplyUig by | Of | # the same as difidio^ by S 4|f |f ,^ ^ DIVISION pF VULQAR FRACTIONS. WLTIHiirA* »«iiKrator of theatTldetid by iH ^fltfnoiiiinator of thedifisor for a new nunier»tor, and th« 4ien*M»mator of fhe di«ideod by the numerator of the di- ▼isof, for a ncn deriotninator— or In? ert the ditisof aa4 IftwmA as m BitiHipikatioH. : v ^' ' JBXAMPLES. " .St... WJ^ I by S. 1.. DiF&l i by |. ' Am, i,t, A us. ||» Alii, vf » £«rfE»'4j. *»•• 2 « Au3. i*i4i» il •H M f ROPORTION OF WLQAK rRACTIONH. 7. Diride 456J Sj. , . Ant. 13041. 8. Divide »i by i of A. Ai.i. 3H**!. D. l>if Idti A |>rao of 4&490C} Into 8C| shariss. AuB. *60 1*1 il^Vp 10. ]>Wlde £47 imon^ 7 bcggart, 3 raen, % fvoincti % 1 boys ; (ihiiig tiie w^iutii | • lUAu'ii tibare^aod the boys § a uronaati^tf. 11. Divide 37} yards of scarlet among 4 men and a tt»y> giving the boy | a man*8 share. l%lHo\iJi^7^ qxukUctHot wheat for j£59,\. What wai ^hat ^r. qudf ter ? NoTK.-~If von ditlde by a fraction lesi than unity the quotient will be greater ♦hau the dividend, because an/ iiumlnr contains mure thirds, fourths or fifths than ir does units. '■ ^ kp ^ . #t'<" - PitOPORTlON OF VUi^GAR FRACTIONS, ^^;^i'#' ■ RULE, ■'''t-;-' ' ^ • ; STATE the terms as directid in Proportion of wtiolg nuinburs j invert the divisor and proceed" as in Multipli. cation. EXAMPLES. f *' I. If 51 yards cost £6 8 loi 4, what will I yards cost! )d.H: ''*^P t:i Ans. if 3. If /i of a ship cost Jt.760 X 3, what will J cost I Ans. 46446 15. 3. If j£{ purchase J of a yard, what^ will 3»| «II« Fiuinish coat ? , , . , Ans. ^10. 1 1 8. 4. When 3d purchases «qr. what quantity uf ^old witl X01| sterling purchiibej; , ^ Ans. 1| lbs, 6. If 50 trees, each coniainlii^«4| solid feet of tim« ber, be fold for £b% 18 7i, what will 40I solid feet \m y^i^^^^ ' Ani j^l 19. 6. When 5hhds. of sngar, each containing Sli^wt. cost ^16 17 6, what will 3^ cwl. cost. ? Ans. £5 5. C T: There i^' a c(Ai m-i-^ »*ftp*K =^«eA* « A'' kimiL sksss^ .What is the i niuii oi i v.f ia» ^hiire ? Aos. iiri. f tm Tf 9| yards 6( cloth I) yards broad bcsuflRddiit for %1^dier's coat and waltitcoat, What quaotity of cloth it required f»r a rtogiment of 897 fnoo ? 9. HoK^ much^ In Isaigtirthftt is 4^ lochti |q breadth, 'Will make a foot square ? , , -^ BECIMAL FfiACTlONS. AN unit may he (divided into ten equal parts and each of these again into t parti* jm liEXHJCTiQri of decimau. Anj Decimal baj be radueed to a Vulgar Praetfo**!^ placing I beluw it witk at iiiaa| cjrplicn aonexMl aa tliei# irtf lUmcii in ike Ijtximak REDUCTION OF DBCmAtf. €Ait I.--T0 reduce ViUgarto Dcdraat Fracti^nf. RULK. Annex cypliiira^tii the a«acraCgr aod difjii |i/ tde deoomiiuitur. . EXAMPtKg. . 1. Eaduco I (o a dccimal,^ S)iOOO(|125 Aiii# ,..,». Br . ' . S-* SO 40 "~ t: n^QCt }t If ), iy I, I, to decifliatf* I. iieduc« ^, 1^^, |}, \^y to decimall. Cass 2.-*To reduce numbers of different denomfnattbn* iodcchnal ffaUiuns. HULE--Reduce it to a fuigftf IractiOQ iad^work t>y the last rule. , EXAMPLESv RcduGB Sd to the (Tedma! of a ^. »|^)8 ■♦j':£ !• Reduce IBs^ 0|d. totbe decimal of a sS* 4 , ?it ff* Ani» ;£ ,778125. $« Redujce Sd« to the decimat ol a ;g. An». jg ,<)375» 9. H^ttce 8»» 6d. to the decimal of ajfi. An»»,jg ,425« 4. Raducfi 1^. i|d, to tiie dfefsoUil of a suitiea. REtoucrnoN or Wecim am. las i. Reduce did. to tie dcdm«l oft th. Aw. ,W «. 6. Reduce S(^. Itdwli, lOg". <«/^« ^'!5j^jl"^l^ Troy. . -A". ,719W^**« 7. Redace Sqri. iSife- to the dcclssals of a ^^t. Am. ,tt4«857*-*. 8. Redaee toydi. tfeetel^cli. to the decimal of « mll^ Am. ,0118371 Hi*. Am. ,6to^^ 10. Reduce 1 rood Spoils to tiM decimal of an acre. Am. ,37d« 11. Reduce Sbnih. 1 peck to the deeimil of a quarter.* Am. ,40(»6, tf . Reduce 6| inch%i to the decimal of a foot. Aoi. ,56«4. Caii S.— -Toftnd the Talue of any titen Decimal. RULE. Multiply' by th«f neit infeiior denominator, cot off ai many placev from the right hand as there are pla. ces in the aifen Decimal ; Multiply the figures pointed off by the next Denouiinator and cut off as before. Proc^ thus till you come to the lowest. EXAMPLES. 1« What if thft Taloe of fii of a 4^« 85 «0 17^QO«17«. Atii. -i / * f . What is t^ Talue of ,098126 of a £. Ans. 6}iT. 3. What is the Talue of ,1875 of a j€, Ans. 3s. 9d^ 4. What is the Talue of ,1^5 of a sh. Ans. 1 id, 5. What is the Talue of ,6845 of a cwt. Ans. ^qrs. SOlbs. lO^rs. Mrs. alA*. 6. What is the Talue of ,131 of a Tun uf Wine. Ans, 30^18. Spts. aJ^, 7. What is the Talue of ,03125 of a barrel of !i(- r, Ans. Igali. tpt* t. What is tho Talue of ,28 of a Mile. Ans, 2fur. 9p. 3yds. toin. 2b. ±2. Case 4. — To find the Decimals of Shillirit?*, pence and l«rtlmig8 by i&s|pefiticu.*~HULE. jAka li4f tht^ObqiPlior I % I I REDUCTION OF DPiCIMALi. of fhltUngi for tho firit Decimal, tlien thenwmher of firt*. inf(i in Ihf rrmaiiidor inrri'tsit! Hy I for e? ery f4, will Ims the twoneit Duclmil placcf. To compkl^ theDctimal call these 5 ^aures or Jfoeir eacefts sbora 25, 50, 75, peace, the farthing! in them IncreaMsd by 1 for ef«T/ 94 givo other ^ Aguret ; coutiaue Uiis method till the dcclinali i»o4 or re|)eat. / find the dcdmal of I0f. 4ld. by iiisp«€tioii< i -^AofttN. • * 18»eFartliiagiln4id. 818 Find tHe decimal of lOi. 8jd. by inspection. 5-«i of lOi. Y - #1 farthiogii in 8id. increased by I for 44/ #7 Caccii of 34 abovo %5 turiiad into farthings tn.. **► ■ ' vi EXAMPLES- Add %i^, 18f, 17| and 14f topctheii Thus 24^ « 24,333 l»i *= l«,12d ^ 17| =* 17,g33S .14J« 14,1111 7441=74,4027 fteduce j^l4 13 4,£l7 6 8, £9 Jf 4, j^4 10 tl, HBlS 13 8, ;ei7 6 4, «£9 7 2 and add them toijether. * Ans. j^lse 10 5y£ 166,62083. RULE.— Wh^n the given Decimals (ern'inate in a cif, -de make all the circles similar and cunt'^irminous-^find th« number of nines in the left hand <;/ «umn of circles— add them to the sum of the right hand column and proceed at In finite Decimals. NoTE.~Similar circles consists of an equal "nnmbcr of places.— Dissimilar circles may be made Kimilar- thus, find tiie least multiple of the number of places in the given circles and extend each of them to as many places as there are units in the k»ast muUiple,, Thus 3,27 and 78,3476 •re uisitimilar because the one contains tvi.o places and the other three but as 6 is the least multiple of 2 and 3, extefldi Uem to 6 places and they nvJU b« nioular* . SrUBTR ACTION OF DECIMAU, EXAMPLES. 6,434443 T*47847S ©,353536 tdl 44,317845 23,909090 41,307307 I rta ,0384ft»5S i| = ,f57857l45J ^r « ,27^27^747 ^»,14814S14 1,495U5124 ftfiduce & add £^2{u ^45^\, £68^\, £57^^, £6f^l ■- ■ _ 1, ( • M ■/ ^ ■ ( f M ■ SUBTRACTION OF DECIMALS. • • • » BUTJS 1.— A rrana^e the numbers as taught io AddU liQD, aad proceed as io whole numbers. ' ^ EXAMPLES. i From 56,1275 , 18,7684 ^^'L^ Take a7,843« g>893a 17,987 *28l283«» 8,8752 6,U3 ' Find the ditferencc between ^0 yards, ^ quarters and 45^5 yards. Ans. iO yda. 3 qr^ 2 na. ku LE 2.-Wheit yr>u hare repeaters make them simi^ ilar and conterminous, and subtract as uBual---but if th# repetend of the minuend be less than that of the subtra- iend, take 1 from the ri^ht hand figure of the remamdet, ^ ' EXAMPLES- From 987,333 721,0375 ^f,^\^^\i Take 18 125 676,77777 97,41665 969,207 144,25972 From £29 13 4 take £l3 16 S, Fron^ j6'218 11 2 take ^25 18 6» 344j8373? MULTIPLICATION OF DECIMALS. ••••*• RULE K^Proceed as in -l-l^J^^^!^!;^^!^ IP 5oJ so many figures, add cyphers on the left h^d. / yF^~^. '"^... .:mm ): 1,1 % dW MIT -^^PLICATION OF DECtMAH ,075^ ,064 EXAMPLES. 300 450 »004dOO Am, 4306t 9470 ^. .. , : r«,7d686r Afvli. Multiply 74567,8 by ,343. Ads. 35735,8910„ 87,65 by , 125. Ana. 10,95620. : ^^®^ ^')' ^^^'^^ Am, ,0161 33 75. RULE «.— To contract the operation so ^s to rctatii M maoy places in the product as are necessary ~ I n?ect the multiplier and make the units place stand und^r tAo place of decimals which you want to retain in the pro* duct— then In multiplying reject all tho figures to th« right hand of the multiplying digit, and set down their products so that their right hand figures may fall in a strait line below eajfa other, observing to increase the first fi^jure of erery line by carrying 1 from 5 to 1 5, 3 from 1$ to 25, &c. from the preceding fitjures when you begin to multiply, and the sum is the produc^t required. EX:AMPLES. : V Multiply 27,14985 by 92,4^035, and reMn 4 plac^ of decimals in the product Contracted. ' Common way*. «'?'^H986 27,14985 53,01420 92,41035 24^34874 542997 308599 2715 81 14 13 574930 81 44958 2714 108599 6*2997 94434874 9860^ 44 2 -«' «.i 26*^8,9280 2508,928^650616 v Multiply 2>38a45 by 8;?175 and retain only 4 «?eci. mal placei. , , .An*. 19,6107. k.^V,, x DITISION OK DECiMAM., lor Multiply »«5, 13768 by 16,7 324 and retain only 4 de. •imal pUicI'8, Am. 6*i7fi,«dtiO, Multiply 395,3755 by ,7564^2 and retain only one de« dmat pfactJ4 - • Aus^ 290,1. ' ,-RlJLK 3. T-rWIitn the Rifen numbers arc rvpeti^iidft. redute then] iiatu their equivalent vuli^ar fractious, and hnd iko product of thesis fiactiuiis— Heducu the fractiuu expre«8jug the pfoduct to a deciuiaf, aud it will b« tilt auswer, ,, .EXAMPLES, JIuItiplY 33 by 26. ff Xt*=s::A\=>0^8 Ans. Multiply 37,25 hy W. , i Ans. 9,92«. Multiply 7,7^ by «07. Ans. 2,267. MuUit>iy 84,76 by 84,0. Ans. 8023,57* DIVISION OF DECIMALS- •H • ♦ • RULB 1.-- Proceed as in whole numbers, and from the quotient point off as many decimals as the decimal places in the dividend exceed those in the divisor — If the quoti'^nt has not so many places, su^^ply the defect 1^ cyphers. EXAMPLES. PiYide 45,S4fl6 by 3,68. 3,68)45,3496(12,32 ^H 36 8 854 736 1180 1104 «5G} 730 120 ^m^ ' I? i ICt ttTKIOK Of MCIMAtS. tivi^c t4,6W by ,45^ . Aas.^4,1 DWide84O0 by ,640. Am. 16660*^. Di?lde,2l4()8b)'2,5. An*. /)868r^. Diflde ,80468 by ,073. ^m IC^7^". HUL£ a.— Ttt coiitraA dWision— lUflng found (Im 0r8t figure of the i^uotieii* In ttae common way, f^r every lifter figure difidc the last remainder, ooiittinu « figure it each stop on the right of the dif isor, but rememburing to carry for the increase of the figurea— cutoff w taught ia J^uUiplication. *" Contracfed. Common way, 1«,269)744,34738(€1,4,8 J2,209)7 64^84738(01, 4i 73614 78614 1820 1227 693 490 103 98 1890 Iti6i9 Wi 598 490 76 ■»•<■ 108 98 83 6 4 I>iVideH,l69^WT>y 3,141 5» and retain 6 placc«^ lecin - in thequotient. ^ Ans. 3,87377. Dividu 25,1367 by 217,3543 and retain five places of decimals. An|, ,11564. DiTide 514,75498 by 12,34254 retaining 41,705757. RULE ^i^When you meet with a repetend, change the dijisor and the dividendinto their equivalent vuljiaf factions—find the quotient— reduce it to a decimal; and U will be the answer required. Divide 33 by 26. EXAMPLES, y y ' . 3 3 and 1 3 "^ n^^TTf — Mil Divide 234,6 by 7. . Aw*. 301,7l438t* Divide 8l,96i by 4,35 ^ Ans* i8,^83fl^. l^Mi |d^93|86C03&6 by 4^5^281219^. A^. 464^4 idi^Jtmii^O^S ^'ESTIPNSW FRACTIONS. .•*■. , X* a, 1AKE ♦ft dMT. ^"-.^ -«^; ,- ^. „„. it* ^««e«*iht fmrelMsOT S| plecctof wkki each pkce .ioii€aliii»ir 44^ |*r4i*t 68. |d. r)«r yard. I de««nd tb« ^aliM of 81^ irteceB at that rate. Ans. £1b 14 J fy. 5. A UNfCllaiit hiw Tmat 8|i. 9^ lb. %Mch he wishes ta Biift«f f^ Sfigar at 6J per lb. I demwl how much .gwgur he ^ ni fei!ifihrc4or Alike »»». ' '^ ^^^JV*' *f *, ,, 4. B«ttgh« liOMH. •*'Tia at6|9.pwrlb. and soldU 'Jo* jiero. WftAt Wis ^ fiWfl per cent. Ans. £35 l> 34 tJIt' 6. If fl. ytttdi^ df «^ Sfi the intar^*t fof*\ nWe vi^ar — if thB interest be required for sereral jr *** ■1 for one year by months or dayS| iPfOp9jrtioii« isear at o SI14PLE INTEREST. Ill N* B.— ComwHslwiv Broliaie^ Inturanct, picoimt and purchMing af Stocks may be all calculated by thb Rule. 1 % QUESTIONS. 1, What b ^ Inif r«t of £96 it per cent 05 6 5,70 >* 14,00 ea j£5 141. Att«. #5867 10 6 :f 17,87 10 17,50 6,00«:;f 17 17«. W. Am. S. What 1^ the Interest of £\i05 for 3 years at pe? Uent^ Ans. £^17 Us. 4. What Is the intefeifof ^815 at 8 percent for years. Ans. £391 4. 5. What is the interest of £978 12 for 4^ years ^at 7 percent. Ans. £308 5 2tV^' .6. What is the interest of £845 10 for J year at 5 per cent. Ans. £10 11 4i. .,,^^ 7. I hare at interest £1765 12 at 6 per cent— j^845 ^^8s. at 7#er cenit and i can always make 6 per cent up- on £2678 w^wrut rimntag any risk. At what can I af- ford to live per annum. Ans. £344 7 9J. 8. A Merchant in London sends his a^eni; in Quebec, C« tHttMflSf, «.. f • What il the eemmMdii on £S4(^ it f f p^ ce^.' 10. What 18 the comoiission on £478 1^ 4 at 4 t^\ cent. Am. ^ % lOf 11. A Cpramiswow Merchant transacts busmm wU^' another id t\ni itikt tt Jt^B^Td 19 4 ik M iikrH^e^ commisskia of 3 per cent, liequired Mis neat profits per " annum. Ant. j£869 0. 12. What is due my Broker for fTnding sale for Goodt> to the value of £l5fZ at 4s. Gd. per cent. 13. What is the brokagft of £Q4b M I per cent. Ans. £i 12. 14. Negofiated fiills fot my cmpfoye? to the amount of jfi^l8786 18 4 at i per cent. What do I hjeeiW. Ans. £93 It'T'J. -• ■ - 15. A and B dispute aboifl tlieir ftins—- A does com- mission business to the amount of £38458 10 per annum* — which yields hira nt »ti arerage 2f per cent— B is w Broker .lad not only does A*8 iHisi^ess, but IT other Merchants, whose concerns ar€f is extensire as those of A and his contin^jent Brokagc is equal to 3 more and h» chariieB 1 per cent* Which of thetivo pains more. 7 A gains £961 8 3. ^ '* ] B gains £2018 19 affV THE foHowiiig TabTe calculated for tkc 9 digits, wfri §!▼% tlic Interest or Commkiuon of any smn pf oumf^ ey, at seieral rates, with great ease* T A B L E. ,01 Ans. 1 ,y25 ,0* ,076 ,100 ,125 l&O 9 Z 4 b 9 ,u3 ,035t"^,045t,05 ,06', 07 ,09 ,16 ,105 ,f2 ,140 ,175 IRL216 ,O^,0^i,lO ,12t,^35[,15 ,16 ,20 .24 ,055 ,110 ,16^ ,1801,20 ,Vm ,24|,260 ,28 ,225 j, 25 .2701.80 ,06,0651,07 jlf j^*^14 ,18^195 ,21 ,275 .S3oL36 53q',S2£ 16 ,24 ,32 0{ ,2r ,38 ,40 ,4^^ mftrm wtatt** lit ^ j4bknff^ Ae U^ttzt of i£H% H for 4 ycirl al 7i vCTWnt-Ae tibulir number oppoiUtj 4^ t^ l^t »^o<* ./ RdttUired < h« intfcreit of i0476 for S yiJtH fct« per cent. ^ ^f6X64*304,64«£304 1» 94. What to lh« Intfrwt irf^M ffH* t yf^ft at 4f per c*nt. f4Xi3(^«7i90«i:7 6 9j. Tbe imtebetl lii the right himi c^ltimn ^ejM%S#nt the Itnw or the priift •»«> /or tens, hundreds, or Ihousanda by remoting the Decimal point one, two, or three place! to the right hand -thus the in. Iferert of j^l for 4 ftm it per eelit It, ,Jfl and by re* «loTins( the DeeinMil point two placet i£««, it bccomeii tlie interest of jeiOO for the same time and rate. Required the Interest of jfiSiS 6s. for 13 yearts at fou» fer cent per annum. .< w '^ d?S48 6Xfft«=4l83> BY THE VABJiBr 4itK)0»160,(> J00« 4,0* £167,328 or£W 6 0| Inf crest. IP0 Galeulate Interest at fire per cent for Days. KULE.— Multiply the principal by the number of , days, and divide the prodnct by 7300 and for any other fate, tahc a proper propotioo— OP, To Calcuhite Incstest at anf rate per cent for days. RULE.—Multipry the principle by the number of jt--, - ^^J j_s-i>ij- ^.f t~\^f>^ ft^f* '^f»«» #»aiv* 4-Ken' liiridy the DfO* r ttiajr i»iiu m«»«5»«%» *** iw^. •••S'r |.«.i" ~^ — -y ** i duct by 73000. QUESTIONS.,; 1, What is the inte.gsi of ^641 at 5V5 ^^fn'^l^^* n« to- for 50 days. •- K2 114 r ^. \Tb«iii 4 p«r cent. 3. WhfttU ^ per cent. 4. Whtt U 5 per cent. 6. WhatU per cent. 6. What it cent. 7, What is 19th at 5 per SIMPLE INTEREST. th« amoantcf £5300 15 8 for 150 ddjrs a$ Ans. Ji'5965 ^ 4 ||. the iatemt of i^lOOO 10 for L2 daj i at Am. £i 1% lOi. the intcreit of £378 14 for ii7 days at Am. £6 11 9. the tntereft of jei7 6 for 117 day 9 at 4j Am. £0 6 3. the intcreit of £0»O for dO dayi at 5 per A0«. j£7 11 ^1. the IntcMrett of £92 from May 14th to Not. cent. Am. j^S 8 IJiif. WHEN PARTIAL FATMSNIS ARE MADB. RWLte.— Multiply the pHncipal and the different baT- ancef by ihe number of dayi they are at Interest-radd the prodacts and divide the sum by 7300, remembering U lakt a proper Proportion for any otber rate. A Bill of 4^400 was due April 20th, of wWch £lN) •was paid Junelftth^ ^28 August 4th and the balance October the 2d. Required how much iatfircst ii due ai G per ceut. * April 20th 400X56 =« ^240( June 16th paid |S^X50 August 4th paid ^YaX^^ 1 15438 6^368 Add f being 6 per cent 10471 • : 7300)62829 ^£8 12 Ij Interest. Lent A NoTCmber ll(h, 1807, £800, which I rcceiTod In the following partial payments— January ISth, 1808, £250 ; April l7vh, £l52 ; June 18th, jSiOO ; Au^iist 19th, £125 ; JjepteniUer «2bth, s^ccived the uai»«w«. Reqaired the latcrcst ftt Aj^cr ceot. ' . ^ ^ Ans. jC25 1 4i t'j. 8IMPLS INTEQ^Ii "f To tU firtt day, ltc> t4S SI73 S03{384S«5 ll m\ ^4 30 ThuTlbi; wu. b, found '7^;;«^f J- it^lSl'^'r t„e.t in accouuU «»"«"' °'P"V&/-«f one mon.lv ru^s^:^\s^stbrLrof!s;''ott "■«---. -* »ccn by iotpection, „», , t /„, l-ha,, from Ut Jul, to t,t AP'" "•.^'^r'""'' J^J July m the left hand and opposite under ApHI. y»» j^'';^ 274 the number sought. -Froift March 10th ta Auguat l,t,=lS3-10=l4Sday8. A runs a cash accoun. .«ith a Banltcr^ta th, «t.M oT J500 at S per cent i~ '"'=""""l"T^'„^^ „'-,» In A"* ker allow, only 4 per cent for «0=!' "*''"?'' ""TLe fofc favour. What interest is due and by ^hom o»i the lot- lowing account. til' I I Jtntjtry 8, dr««f far jr*«6, Ma?€h 10, paM ^3^, I^ir 16, drew far^JlO^Julv tO, pakl ,£^0, Septembor 10, •Ircw for •T^IO, NovfinWr 0, paid JTfK), DeeeraBiHO, drew for jr«6# ; in JaAuM^ i^ a«ttled atconi'ti. How -"-- U lUHd. .»»; 1800. fcr. br. fe: l>r, Cr. Cr. Dr. 0». *.<' I f »f. f 6». $b0 flfO itso tio 10 410 4^ 00 260 lIX) 61 00^ 66 6^' litidoJ 105|0 49^^ ^•^^ICO S040 42960 14776 00O(y l\W 4^tl^ M0D)281^^ 18170 880' AfiS. ^3 17 2f 14776 A owed )it!» Banter on the 3Jst of JX»c. 1807, > o£86 3s. andaist of August ^140 and 10*ii -uWAi- ^4'< 1 O l*a al»f.. ~»*.j.t^^. ^--tTy M «"» -A 11,1 ---I- *r200 and 12th May oTSCO and 8lh Aug. cf320 and l2th Oct. J76 59. and IQtb Nov. ^ig. Required the state of the accounts and interest to the 3 1st Dfcc. 1808, al- lowing 5 per cent, when the balance is in fa? or of the Jkukcr and 4 per cent, i^hen a^ain«t him. STMfLR W1HIIF.8T. f# Or Mr. B. hi. .ccount r.,mnt with Mr M. C^. t.c princiiml, und th.n f.,m tW .mou«i aeduCt the W- .t 5 ;^" r, ana ..ade p.rthl pay--t, «« fuUuw. He- quired the st*t« ¥( tHe iffwr Auf . 14, 190^ lti«r««t fiit I ywtt: «ft«J «9 «i} Juii« l« AMowWil OcU8. I Paid in part » ' # Balance Interest for 1 year imd Sfl ilay» 1804. Jan. I. jLtaount 1067,671 «fa * 817,671 50,4 S68,07t 408,07 i ■4 Paid in part Bsitatftd 460 Idtcmt for 1 jM kiif 42:6 davi 37 , l7t 1805. I ■ A""***! *S m bear interest a1 6 ^jcr Cetit. Receited 1»* t itv a year anU 45 days, 1 desire to know 'the ec^uatea 190X^1^=77900 4^0)107680(224{ ! t ■ 11 i^ W 1 I ^» 1^ IQiJATION OF FAYJUEItll Method ^$L WHttle debt £^m \ 40r=l IttOO' I>4id At 40 (la)ia QO 420 Paid at 96 days im r4jE!jMda4Swada^s SO 104=2i96a aiOnSftftOpk 480) 107)586(224 In tU wcaod method wc subtract each payment as it falls due from the whole dibL We thea multitxlyt thfi respective balance's by the niunber i4 vho engage to make good the loss if ships, houses or merchandize, happening from storms, fires, &c. The per ccntajie given is called the Premium, and tht paper in which the contract is written the Policy. . What"*is the Insurance of a parcel of goods, Taluf ^1000 at 10 guineas jier cent ? 1000 105 6000 ICCO jif 105000 Aris. T\0^. To "tor& ptoperty is to insure the premium as well as th« value of the cargo— in this case we subtract the pre- mium from ^100 — then as that remainder is lo cf 100 so Is the value of the property to ili^ sum which covers it. What sum must be insured to coier ^5370 iJtemiuin^ ten guiueas per cent ? h f I I* I I 1 ^ PURCHASING OF STOCK^ 100 10 10 £ £ gy 10 : 100 ; ; 6370 100 89,5)337000(6000 sum fo be ingurcd. 1. What is the insurance of j£000 at 8 per cciit ? Ans. a£72, 2. What is the in«urance of of 600 at 7| per cent ? 3. What is the premium on £l870 at 4 guineas ? PURCHASING OF STOCK. STOCK is a general name for the capitals of trading companies, and also for the debts of government. TABLE. 09 0-) O- "1 Ti re c ~ tn a- A "■; ft Cn 'a ft •^ a ?f"ff<5 l-~l s - UA " ^ >-> »--fc ^"^1 ^ ^.- '^J ^ ^■^ •* ^l 1^ -1 46 46 46| 48 49| 51 32.^ 34 55^ 57 co' 6U. 63 64^ 00 S7i (9 70 1 62^ 60 53J'61| 51|'62 56 J64 57j;66 594*68 70 \7% 74 614 63 64$ np< 66.^176 68|»78 70 jSu 71i82 73^|84 75:1 86 77 78f 80^ 821 75 I 76f| 77i 80 82 J 85 87i 90 90 92 93 96 99 102 105 108 9u 92 94 92i 111 95 !14 97i\ud}f 100 jl20 102| 123 105 ;126 I0r^'l29 I JO U32 105 1150 I07j|l53.J 1C8U55 112 160 115J165 li9 122^ 170 175 126 jl80 12Cfl85 133 [190 136jh93 140 !200 i43|205 147 [210 I50|215 i 220 19^ VMlfpnn* 189 194;1 19< I 204| 210 21 5 J 220^ 225| r23 i 112^135 !l57i225 [236 115^ 138 ll6l j230 :241 1171141 U64^'235 ;246f'23 5. 1 57^: 15 16 161* 15 15 .1 162 ..... 168 16 16 173111 6ij6 178x117 [5 5 r/A '8 \5 1 8i-'5 19 h 20 20i|4 21 2I-i z'2 22j 23 13 10 9 5 1 17 14 11 8 5 2 17 15 13 H ot 7i H H H 3 6J H 2 4 4 } iU ilf 4 8 10 4 6 11 4 5 1 ■^ PURCUASING OF STOCK- nw fi 13 4 5 10 8i B 9 p; fi 5 6 1 21 5 17 7i 5 14 3i 5 11 H 5 8 Ij 5 6 3 5 2 6J 5 oi 4 17 6f 4 15 2 4 13 10 10 4 8 10 4 6 11 4 5 1 All questions relative to Stock arc expeditiously ans- t^ert'dby the help of this Tabic. First it may be observ. €d that the mar.ner of purchasing StocT;, is to give a real sum for a noannal one -thus if the 4 per cen be ^80, I pay this sum for £100 Stock and rixeive a dividend ot £\ per annum, which is equal to £5 per cent, on ha sum actually paid. When you can purchase into the three per cents at £60, &c. you are said to purchase at par and uet T) per cent for your money— if you purchase any of tluvse securities lower than the sums mentioned you hare more than 5 per cent, if you purchase higher, &C-. vou have less than 5 per cent-thus, if 1 purchase £100 Stock in the three per cents for £45 my interest amounts to jea 13 4, if I pay TUf for ^100 Stock, I have only £4 5 1 interest for my money.— As the different 1^ u nils ^ary in their prices so do they sometimes vary in the pro. portional value they bear to one onthcr, so that it is Ire- qnently profitable to sell one kind of Stock and purchase another-lthns, If 1 find that ^100 of three per cents caa be purchased for ^46^ and that ^100 of 5 per cents, sell at ^95-it is my advantage to sell ^f ^Y') ^f"" cents and purchase 3 per cents, because 1 find ^^om the Table that at ^95 per cent, they produce only ^5 5 3 per annum, while the 3 per cents at 401 per cent produce £6 9 8| j)er cent.-From this Table may also be learn, ed the proprotion which the purchasing into the l^uads bear to landed Estates or life annuities, QUESTIONS. ' \, What is the purchase of j€313 lOs. 03 per cetit annuities. Ans. £^3 U It- 2. What does £1200 Capital Stock in the 4 per cents come to at 844 P^"^ cent. Ans. ^1008 lOs. 3. What is the purchase of £640 8*. India Stock at 120 per cent. Ans. ^^768 9 7f . 4. What is the purchase of £926 Bank Stock at 130^ ner cent. Ans. £1208 8 7i. *^ 6. My Broker informs me that he can purchase into the 3 per c:nts for £66, or into th« 5 per cents at £U2|. Which is the more profitable* # M m EXCHAlVfm. 6. I hare ^1700 Bank Stork which I nlay fell at tSCf percent and puidiase 3 per cents at j655j per cent. Ilequircd the dilicrencc of the Dividends. 7. I am offered an Kstati at T3 years purchase or I can purchase lUnk Stock at 4*140. * How shall I decide. 8. A Gentleman pui phased ^'ItdOO of East Indi^ Stork at £\S9 and. soon after tlie Funds rising, he solA out at 06*231. What did he gain. EXCHANGFT TEACHESl t» find what sum of the money of one Country ii' equal to any gifcn sum of another according to a certain given course of Exchange. Par of Exchanye is the Standard to which the course is compared and points out the intrinsic value of the monejf of diilerfnt countries compared with eojch other, cstimaU. ing by their weight and fineness.. •!>« AIJN*. oa 1' t asterung valuMi, 34 Marvedtcs make 1 Rial, .^ j£o d|. 8 Rials ••.. 1 Piastreor pieceof 8, 3 10 Rials .... 1 Dollar, 4 32 Rials •••%.! Pi«tole of ExcTiangc, 14 375 Marvedics • ' • • 1 Ducat, 4 Par 43d « Ste/^ing per Piastre* PORTUGAL. •, ;, , Sterling value* Milrea make 1000 Reas, ^€0 5 7|. 100 Reas, Gj. 400 Reas, 2 8^^ 480 Reas, 2 Sj- 4800 Reas, 1 7 0. 6400 Reas, 1 16 0. 7, 6. 4. llj^ 1 4 1 1 1 I • • • • Testoon Crusado of Exchange New Crusado Moidore Joannis Par 67 Jd. per Milrea, HOLLAND. Sterlirg value,. 16 Phennings make 1 Stiver(or2d. Flem.)£0 ly|^ 20 Stivers .... 1 Guilder or Florin, O 1 9|. Si CfUiUUrs ...• iRix Dollar, 4 6^^ (^ Guilders •••• 1 P par 4 2i . Britaiu^^^ -^ P...o«55d.. par 4 6. perron 5Sd. par 4 6. Piatre=«=6 lircs par 4 4._ €rorm--7ilivrespaT 5 2^. Bucat=a5 tarins par 3 4^ Seudi==6 Urcs ,par 4 6. I)ucat=13tarins=: 3 4. BENM ARK^ & NORWAY. make 16 Shillings, .... 1 Rix Dollar, .... 1- Ort, .... 1 Ducat, Far 4s. Cd. Sterling Per ^i*-^,^^^^"- , gj Poterburgh exchange b^y/^^jll".^:,^^^^^^^^ 9d.: lt.!:"Thc Rix.Dollar of Uollnnd, Hamburgh, Austru,, Genoa Leghoriv Florence Naples " Sardinia Sicily 1 Mark 6 Marks 4 Marks 11 Marks Par 4s. Sterling; value, £{) 9. 4 6. G 3 0. ^ a 8 3. Hj) u^ 14« EXCHANGE. Denmark and Brazil. — The Dollar which not only pasKs ill Spain, Portugal and America^ but also in Barbiirjr^ Morocco, Arabia and Egypt. Were Exclianjte entirely guided by the intrinsic TaU ve of coins, the dollar would be, in many cases, a safe and easy mcd urn— And in some instances, it may be used ■with advantage : — For example, in America where so many different currencies are used, any given currency may be turned into any other currency required. -^ '^ RULE. -^Express the dollar in shillings or pence in each of the currencies, in the form of a fraction, of which let the given currency be always the numerator.-— Then multiply by any sum of the currency given by th« denominator, and divide by the numerator — the quotient is the answer in the curfency required. Examples. How many pounds New-York currency are equal t# S 100 Halifax ? Hereadollar=5s, Halifax, &r=:8s. New. York currency^ The given sum lOOX 8= 800-f- 5=^^160 aus. Haw many pounds sterling in ^400 Halifax ? Here a Dollar, JjO six.pences Halifax* And 9 Sterling. *€400X9=3600-j-iO=j£360 Aus^ OH, A Dollar 60 pence Halifax. And 64 Sterling. i400X 54^^^1600-7- 60= rf£3a0 An J. !^ EXCHANGf. A TABLE. IV ^liew'ina how to Bedace Halifai Currency to any of th« ''r«lcles in North America or th. W.t Indies, .„d also into Irish money ; .nd Vice .crs.-LlkewUe the amount of JCiQO Halifax or StetUng iu the wreral Cur- rencies. , Jfnlifax to Sterling or {hi iifferml Currencies, ^ contr». £00 I »«cr Sterling. 1 — t'w ^697 10 i£l26 Irish. I — ik Jamaica. ^100 Halifax £no 4-4 + i •^ rv l£no Virginia v^ N. Hampshire Rhode-Island I Connecticut I Massachusetts + i - i -i ^IftO New.Jersey Pennsylvania Delaware Maryland New- York N. Carolina e i - 4 4.8-4-5 +-5 -s-S , Georgia U93 6 8;s. Carolina - iM + ^i a «E Si 8 £^0 EXCHANGE A TAULE, &c. coNTiKUBD. Sterling to llalif'ux t)r the etiftf'' •»• Cnrreneteh 4[ coHtrm, Halifax. fl £. i. d. Sterling. Ill 2 2} 1^667 10 £\^& jgiltO irbh. 106 6 8 + 4 "4" ti "■■ ui Jwnaif a. j 1 38 1 7 8^ + J + j! ,7« Virgin in N. llamfjshirD tihode.fsiiand Connecticut Massachusetts las 6 8 i£l50 £160 I '4693 6 8 iV*'w- Jersey PennsyUauiA Delawaro Maryland N«v-York N. Carolina + J -i 1«6 W 4 X5^3 X3-^5 Georgia iS. Carolina* 177 15 efxie-roxo-t-io 103 ic 05, + ^v I From this table wo may turn Sterling or Ilalifftn into fach other, or into any of the currencies with facility.— For example, to reduce Halifax tP Sterling wc deduct -^^--to reduce Sterling to Halifax we add ^—to rcduro . Halifax to Irish wc deduct ^^^—to reduce Irish to Haii. fax we add ^ — the currency of Georgiu and South Caro- lina is exactly of the same value as army pay. 1. In ^465 Jamaica currency, how many pounds Halifax. To Reduce Jamaica currency to Halifax, I find by tbe^ X*ble that I must deduct f. 6)165 93 j6372 Ans», F f. U £m Jama.c* currency^how many pounO* Sterling? BytheT»blemultii>lyby,7«. - . 465 * "^30 1^56 334,80 16,00 i^334 16s Ant. • t. £400 Hftlifa*->>o^ many pon^di IfUU« By the Tabl« deduct :,!«• 40)400 10 £3Q0 Irtsli, Anf.^ ■'M j^fOO Irish— how many pounds Sterling ? *• ^'^ ^' Bv the Table deduct Vt* « „ < ^^ Ann. ^390-.,V-»/360 Stcrllfir. ^ In £860 V.r/inU, &c. currcncy-how many pounds SCeraug ,;^t,.,,, ,ed«ct t- j£860-i=.€645Slerlin?, Ans. 6. In ^450 lIaUfax--how many pounds N. Jersey, &c. currency; ^^^^^ ^,, ^^ ' ^ £460+i«J^675 Anf. 7. In 0^675 N.Jersey, &c. currcncy--hi,w nony 675 6)202f £405 Sterling,^ JHiO^ im tXCflANOt. UmIkI^^^^ Georgia curreocjr--hoir nunf potiiuls By (ho Tables add ^ ». In ^140 Georgia currcncy-^how man/ poundi Sterl ing, deduct 5^. QUESTIONS. 1. A M(^rcliiint in Madrid draws upon hh corrfipon- dent at London, for lim I Piastres. What do.-, the bill •mount to in Sterling money eichangc 6()d. SterlinH o...rM.cr^ pound MerU 15 In £557 Ifi Stcrling--how many Piastres ol Leghorn Eichanj^c 471d. per PiaHtrc ? ** Aug. 'i8'25 Fiastcrf »3 »oi» 4 den. 16 In j€*15 17 1 Stirling— how many tliRats Cufp rent In Venice agio ^3 pw cent ftud Eichau^^c 53d. pet ducat. BILLS OF EXCHANGE. AS no part of a mercantile education admits of greater rariety than that of Exchange, i*o there i» ..o part uf great/r importance. Eve.y person should be. acquaint*^ Hith the nature of Bills of Ki change or Nites of Hand, whether merchant, gentleman, or shop-keeper. A fenr ptneral observations, therefore, relativo to them will not be useless. A Dill of Exchange Is a Rhort order for money to bo receiTed in one place or country for the value paid in a. nolher, to which men of credit pay the strictest regard. When a merchant wishes to remit money to any distance, he draws two and sometimes three bills of the same date, (each excepting against the others :) these are sent by different conveyances, and if one reach the place of destu nation and Is paid, the others are of no force. A bill of exchange should be immediately tendered for acccptauco upon couiing to hand. Acceptance is performed on a bill after date by the v»nrc,».i nn xrhom it is druwo. writiun his name at the bot- tom : But when it is a bill after sight, the acceptance must likewise mention the day of the month in writmg >vhen accepted, in order to ascertain the time of payment. 132 BILLS OF EXCHANGE. ii .■ li -.... -I H i Indorsing. — A bill is endorsed whQn the pcrwetBOt writes his name ^crohs the back ; Uy this he becomes ac countable for ^^ payment to any perbon to nhom ht "Bhall pay it away. Protesting takes place in case of non-acceptance^ «nd is (he business of a Notary Public ; or where there Is none of a substdntia! person, in the prejionre of two creditable witnesses. The holder of the bill can then have rec( irse to the drawe: and all the endorsers, not only for the valueof the bill hni also for interest or dam. ages, but if he neglect to rrolest he has no claim. All bills of exchange are j a) able to/he person in whose fa- Tour they are drawn, or to 11^ o'rder (even tho' ilie word order should not be wientioued m the b(idy of the bill] and are, according to the custom of merchants, in^orsa. hlii ; — it is however more correct to insert the words *' or order." Payment of a bill sTiould be made dxactly wTien due.— In order to deternune when a bill falls due, it is necessa* ry to be acquainted with Usance *ad Days of Grace. Usance is the customary time allowed for the payment of foreign biUs, and is more or less according to the cus- tom of ditfrrcnt places. Usance between Canada and London, 3 months. Between Britain and France, 1 month, do. d{». the Netherlands, 1 month, do, do. Sixain, 2 months, do. do. Purtnoal, 3 months, do. do. Italy, 3 months, Amsterdam allows Spain, Portugal & Italy, 3 months. do.' do. France, Flanders, Geneva, I month. Double Usance is doubJe the customary time* It is usual wiih merchants to grant a certain number of days to the acceptor after the bill becomes due, called Days of Orace. In BiiJuiu o days are anowCu — Hi noaHTiiij Portugal and Veiice, 6 — Naples, I3enmark and Norway, 8— France, Dantzick and Koninysberg, 10— Ilamburgti »ad Sweden, 12--Spain 14— Hwbwj 15, wTien due.— r to the cus- I Bnxs OF E:scflA!^GTe/ iw anp.e to Samue Biakc, or Order, two thousands Siix hAimJred and iifty sit^ marcs lubs, value received and place the sam* to my ac*?. cqimptac jxer advice, .> tm» TiIj^WM*SS R¥A^iiij a To Mr. John Gordon, Lortdq|i, No. 4. l-isl^on, 5th June, \s6^'. :, S50Milreaft„;..: ■;■.- 'j^ .' Ju'l^U^J^ ^ ^_, ^ . . At double iisance pay iMa my first of Ilxchaiige to aI.^ r\^.i^^ .^jf iif_ A 1^ >'-- T)~'>->~-'-. i-i > ii..n.)r^^l isiA fifty rallreaF atiiTC shiflinjf iud'sii irt!iiclip^^i^i^5t.ya'u«. receiv( iv'accoto'M To Mr. James Logan, London. M 114 COMPOUND INl'EREST. BTOQUfsrsToufaiiis. Paris, Qili August,. IgOOi- At usance \idy Uu» my firbt bill of KA-i;iiifjQ^e t^^Mr*^ Bobtii-I i)uun, or Order, the suip a( eight thou^^od seven bttiidrt'd livres Tournois, valuQ received aitd plajpo i^^ i^O^ to my tccompt as pejc 44vic€i. JA^QB MASp^. To Peter HiU, £bq. LondoQ. ARBITRATIOxV OF EXCHANGE. AS the course of t^x^hai^e between ditiereiit nations is alniofit continudtiy varyinti. Arbitration toaches to re- rait to, or draw upon turei^n places in such a ujahirier a* shall turn out the niOKt profitable. In Simple Aibitrat'itMf three places only are concerned — for Kxainple if i lie Ex. change from Montreal to London, bt* lapoiindsfor & pounds Sterling and from Lisbon to London, 64d. per milrea. Then as ^'9 Sterling is to the Quebec currency' So is 64d. Sterling to the value of the milrea. A Merchant in Montreal wishes to pay £500 Qhehe^ currency, to his correspondent iu Dublin, which he may remit direct at ;^97 lOs. Irish per £ 100 Currency, or he may purcha&e a bill on London at ten per cent and from London to Dublin, he may r^mit at; a discount at 12 per cent. Which is the more profitable. j^500 Currency ==460 Sterling. Th«n ^lOii&teir. : 4\ 1« : : £450 ! : £504 Gain j6'l4.Irish by remit fmg through London. Money may be circutatetf through several places fqf 4lie same purpose — this is called Cinnpound Arbitration, AM Questions tn Sfoipte or Com{M)Hml Arbitration may be ^loxmed by otto of more statings in the Rule of Three, COMPi»UNO INTEREST IS calciiltted 1/ ro«kiiig the nmount at mh s^M iM> nf inyineat the pfinci])ai for the next. < i ^ It ^ iwi9ttal «l ^iuO ia 3 ywti »t £i per cm^t edWW*^^D iOTEREJf . ISA 20 16 «d year's inter. 500 4 620 4 J i6,692cryciir2^63 4 ^*v. / I f ■< 7,68 4 2,7^ j^SO « lit year's intereit 20 lf6 « 2d do. at k2 7i 4|«* 3d do. . 'JR Jbi J662 8 Oi if Ans. [An«. £57 17 6 J; t. 'W'hat is th^lnteirests of £4l0 for 3 yeiiftat4j pf ct. When Compound Interest is calculated by Decimals, t^o usual method is to find the annount of one pound for a year at' fhe given rate per cent. Ii^rolfe the amount thus found into such a power as is d^tn^He^ *y the num. fcp of yearfli and the product multiplied by the gif en »»tii of principal will give the amount required. To find the Interest, subtract tHe principal frOm the amount. ' What is the compound interest of £364 for 4 year* ai 6 per cent ? . idso •""t,lt)2.1 -■'^:; 55125 tiesisa 1215506V5 496^64500 7^9303750 5646^1875 ■ Wi n . ■» II I w iii^wi— — 443,444^7600 364 r8,444«7600«=^78 8 10| Au». l,3i5506S5s=4s. power of 1,05. I ,,- In ^OMPOU^IIINTERES'R A TABLE or tife amount of jfil por oke yijOi; ties [ llates j»er cent 3 H 4 4 Annuities' I Rates ! A«muities ! Rates of ^1. I per cent of ^l. 1,03 U035 1,04 J ,045 1,05 Eer ct. 5i G 7 71 1,055 1,06 1,P65 1,07 1,075 8 8i 9 10 Asmultift 1,085 1,09 1 ,093> 1,1 A TABLE^ Shewing the times }n ^hich any sum doul)rIe» itself at Tari. ous rates per cent. Rotes per ctut. % 3 SJ 4 4i Doubles at Simp. Interest years 40 a3* 25 22$ I)oi;1}le8 «t Componnd Intere»t. RAtes per cent. Doubles at Simp. Interest. Doubles at) Compound Interest, 35,0028' 28,0701 «^,4498 520,1488 17,0730 15,7473 5 6 7 8 9 10 , years ^ 20 12J 10 f >* 14,2067 11,8957 10,2448 9,0065 8,0434 7,272:i As computations are Tcry tediousin Compound In fe. rest and Antiuitiss, Tables are camraonTy us£d in buw- ties.^i- ■ -''••_■■■ ^ _ '^^ ^^r^Ani'z iJt-^sfieits the amonnt of ^1 at 'Componnid Ihteresf.— .Table 1st is thus made, 1,03 XI, 03-:::: 1,0609, amcmnt of £ l for 2 yekrs, X ^ ,03;:;: 1 ,092727 amount for 3 years, '&c. The other rates of interest areiioTolved ' in i\i^ sake manner. EXAMPLES. ^ 1. What will ^3C0 amount to in 3^liirs at 5 per ceat per annum ? ^ l,05Xl,05X l,Of=l;167625X300=347,287500 20 >^ 5,750000 «A 9,00C0C0t =£347 5 9. .4. if' 5 ' T^\:: .f.w'er '-i;;nL''.o find th, .io«»t Luiply Ctab-la' »Lbi. f« th. gWea «f «.d time by U» n"'^«?'H^ U th. »o.n« or ^TOO ro^Sj^yea,. .t^5^pe. *'V.m.tUtbe««o«ntof^a r».^7^ years »tfl^p^ •"i! What is tie amooBt of £M0 for 15 ycais at 6 pM CMDt compouncl interests To find the principar ditide tfte araiouot by the tabulw nombcr for the given rate and time. I. What principal at e i>er cent iatwwt for 7 yearf amounts to ^^30,0720 i 80,07i(l Tabular number 1,50363=:£20. ^ What prirtcipal put out at 5 per cent compot ail fcterest will amount to ^€243,2025 in 4 years^? ^^^ J. What ptlndpal put out at 4 per cent Compound li^^ ferest will amount to ;e:iO39,2O«0 in U ^"^^^^ ^^^r^ To ind the rate p&r cent— Difide the amount by thq ' Drincipal and the quotient corresponds with the taljular Lmber opposite the flme and under the rate louftht. ^^ • EXAMPLES^* - ^ t* If /€200 in 4 years amount t» ^6245^2025, what Is the rate per cput ? 2100)243,2026(1, 21 6rr5 per cent. 2. If j£5(K) in » 5 tears amouLit to ^ »039,465 what is tbe rate per cent I -^ -r^ ^ns. 5 per cent. To find the time— Divide the amount by the principal and the qnotient willcorrespoad to ore of the number* nuder the i^ivea rate, opposiso to which' you will tind tha 4Jm- ' EXAMPLKS. 1. In what lime will ^300 amount io j£500 at 5 pcf cent ? lis - 1 i<5666G corresponds to rO years & Vferri = ^ >C232. IW COMPOUND mTERBST. Nt)T8.— Wiftbtlie miinber ioe§ not coiteipatid Id ik« tabftf, the niiinlivr of daj s to be added nmy be found by this propoHion— as the dtflfcrence bttweeD the next Jowcr iMid Qcjtt higher iiui^bers In tlielable is to the ditTerenee of the given number and the next lower, so is 365 diy« to. the days nearly, ^ 2. In what time will £200 amount to 243,2025 at « ^l'?*'^ , . Ans.4jear». 3. In what time will £500 e -♦ to £1039,465 at S^ ^r**"*^ _ ^ An*. 15 years; iVuTe. — To nnd the amount oi any »um for a greater mimlwr «f yoars tto are to he found in the table— taJto two or more numbers fron^ the tj^Ie whose sum is etiuafc to the |^?en number, of veara and muUiply xh^^js^, iiit« eacb i>ther ; the product is the amount proposed^ lle^uired the amount, for 40 years. Amount for 20srS,2071 35 /or 20=131,207135 Mk* *. * ■ -^ , Fof 40=:;10,28i77 Table 2— shews the pre«jent valne of j€1 componn^'^ ihterest— This taWe i^ constructed by di?i^ng £\ by iti^ amount for one year, for the present worth the first year •nd th^ present worth for the totyear divided by the fmcuat gives the stcond, &c. Thus, 1^.1^58s:i952381 first year tk 8152381 -f- 1,05=5 W033=2d year, and 90703-3- ^05=r863838=i3d year or divide a^l by the nunbcrs in the. 1st table successively, and the quotient's will be the numberain the secomil^ A ifentiemaR leaves his godso« j£600 to be paid him wh^p: he comes of agcr— the boy is now four year's old and the executors wish to pay him at preseiH'-«-fe%i|ire|| the present worth at 5 per cent, . . Multiply the tabular number fdVtfie rate and time - - 436296 By theannuify 500 218)148000 Or divide ^500 by 229201 8 the correspoadin^ luimbtt |a table I8757,485W(000 By Table ^d-Amouflt je757,4864^ X ^y tabular number ,752091 599,9994»=Ijf60a - •• •■*- ADJNyiTLfiS. AN Annuity i« any periodical incomf^ arising fraw money lent or from houtoi, lands,, f^alAries, pensions, &c. payable yearly erery hatfyeair or quarterly to continue for a certain number of years, far life, or forever. When anani -ty continues unpaid after it falls due, it is tfeco, sgidlo be in aprears/ VVheo U does not cooimtuce for «ome time after, it is said to be in reversion. Annuities arocommanly comRUiedat.cowH}Qund iiitefcst— thismtJth, od being m ore equitable both for the buyer and seller.— The amounts of aiMiuito, or their preseoi values, a r» ^8ie»t found by llie two foaowing tables for the annuity of £l. ' ._. -^' >v- / - ^ . TABLE 5. Ta male tbis table, take the first years amount, nrhioh U ^l>-^multiply it by 1,05^1=3,05, the second year's amount, at ft per eeit^, which a^n multiply by 1,054* 1=3,1525 =«third year's amoJint. Or to j£t, the first year of this table, add the first year iA Table 1st- their sum Is the second y««r of this table, to which add tbe sec* ond year uf Tabic ist -their sum will be the third year. To and the amount of an Annuity^ forbortie any num. ber of years. Take out the amoun t of £\. for the proposed time and ratcpf intcrest^theii multiply it by the given annuity-^ the product will be tho amount;; f40 ANN0KTIE9. r 1 . Find tire Mnon ht of ao anDuiiy of £50 forSoribi i^ years at 8 per cmt. On Uie line of 20 ytari and column cf 8 per cent fitaiida 3ears ? * Ans. £348;8G39; H^ Sottgl!* tfie yearly annnity which In the »|>ace of 1* years wiU amount to iif 10©0 at 4i per cent. Ans. ;^48,fl4'. 3. In what tfme w Hf afn yearfy amiutiy of ^^'48,114^ aoiouut to ^100 at 4) pet cent^ Conpoond Interest ^ Ans. 15 year.. TABLE 4.* To make ffiis Tatle divide j£l, by t,05=952^# tft 5 #k.A;^ :«iill 4- / ff ykM ., ,.*t.. 'k^«.**%J« «*«>k.K> "J t.!iM>i i'U.i.v preient wt>rth .d then to contmue SO ycr., „ to termuiate 50 yeari hcoco at ft P« =urit A o# aiM t of .6 1 50() for Bo>m at4.i per <;f. i?Klfl-48,94f «#?• amittity for &t) y«;ari it'Sm^'iij A'i amoniit ctfcrtli that of B b) 16 1 ,^ | g Ikt) prmiu worth of n^iich U jfe' iT^gli ft. How ToRg may « leaie of rf30 he kid for ^CI §7 § 5 toitni '^ i*^** * ^^"^ ^'^ ^ ^^"^ *" •" ^'^***® •'^ ^^^ V^ ntr. ter a' ' * ''^'^*''^*^"» o* tHe «an»e t•»*»•^t• 14 ycam af. •nip' C ^•^'^ « fur'h*' rtSferniort of 31 yean afrrr A 4A n • *^"8*»^***® prweiit worth of the diibrcnt termi «| *J per cent, Mtely as.f they had been to run the whole period, th.t i, C for 49 >e.r,, B for SI .„d A for 7, .ubtr«rl n« ,h, •econd from the first .nd the third from (he second aSd we l>aTeAworth^a»4,«S«-B=i:375,e01-C=a66,B4ia! -i.^' i.^.''"^'" "" "'"«o' ■ freehoM estate the rent of » r -^'.f *' '1 P^" '"" ' ;*4|=^4985,7An,. a. A gentleman porchasen an esute for j£l4)0OO at ^hat yearly rent mutt be let H to baf o 4 per cent for 'hhi 9. An estate which cost *PgOOO is fet for ^360 a vcar ■ought the number of years purchase and what rat« of io. lereit the purchaser has for his money ? Ahs. 22,22 years purchase and 4 J pw certl itv^h.^r?*!* thefment talne of a retersion »n per,>attt. ity which ,s to commence 40 yeaw henco the ycaHy re»4 ^f which is £70 discounting at 4 per cr*t ? ^ ;^ * . ' Presant value ^^364,5. ^ ^11. SuppdS^ tfcenatldn&l debt January i. imQ.tnha W ^7^3 "iffions-in whatthhe wilt ii be eitk^^sh^a if i siatihg fund of Q miliioM. Ana, 37 yews ncarlyT ^^Hl 1 PEPKNDojMiiewiouaMinfiwof iome particular Mfa -, liftjti ; Ihdr f4fci«iu <|i*il»»;a ffiviutwu cifciini»UMC4»s— i So tfitvrisst of munty mid iho clmiicc uf tiipoccaliouof th« contiiiuaocfk of, i*f«. T>ia T»*M*3ti v/ animilki alrmly cjren piAke na iiratiaiuo'fartuy fuiitiunciwy jbut Uie «ix. pecfttloo of lift' l>«i'i« a thing not c^rtaiii and only pon, 8ei$iiiii( a certain chance~ii w iifideiU that iho value uf a ffffrtain ttfinutiity muit be dluiitusliiHl in pruportion, as this cipL'cUtioii is baluw ceruiiity. ThiiJ* if the present value uf an atiiiuity c«»rfaia be any huo», wippoie ^lOQ awdthe faluu or expectancy of life \^^ then the value ot the life annuity would be only half the Conner or £bQ ; and if the value of that life be only J , the value of thf. life annuity will be } of £iOO (hat is 1133 6 8, &c. Calculations on Lives are deduced from tiie cumparisott of bills of mortality f.>r tbediffiercat ages. Thus if 50 persons die out of 100 in any proposed inne, then half the numlier only remaining aliv^, anyone person has an equal cUunii.' t« live or die In that time or the f alue of hit life for that time is i, but if J of the number die then the value of any of llie survivor's lives is J, and if J die (ho value of any of the survivor's lives is 4, &c. Consequent- ly the probabiltty of life is greater or less according as thwre appear* more or fewer, chanC4?8 for a person's living Off dyin^at any ^iven sta/e of life. Thus the probabili- ty that a person now 40 shall live to (SO is -ili by the LiMidort bills ol Mortality, andf J}| by the Northampton, and the chance of his dying |J4 by the former, }JS^/ the latter. The extremity o( life Is that period beyond which there i%no probability of suriifin^. This pgriod i* iuted at 97 years in the Northampton Tables. The comfileweiifc of Life L th» number of years which a person's a e waaU of (ho full extremity— thus the coo- plement of an a^^e of 40 is 67. Kxpertation of Life is the number of years that a man of any given age may hop • to^live, or U is the number of ypi^r's p^#-cl|ase irti.tw 1.— T» ilia t«i« prbbtbitlty or jtroporflon of ^•fiC4! that II [MN-toii of A ^feti ago cantiKUCi Uvrng i propot»«<) niimhtT of yean. Let iho age bote ami ctie yean propoful 18. In the London tabfe afalnftt 30 /cars itantli 404 iatid against 38, 341 ; which sh^wi that of 404 persons that attain the a^e of 20, ohiy 541 attain the age of 38— coito •fqiit»ntly'i53 die bet^^een the ages of ItO and 38. The chance therefore Js an 3|l : IAS. When sciffsral pcrsoiu are given, find thdr chances separately and then multiijly them into one aiiother^ Pnoa. «l.— To Uiid the t alac of an tniioHy for a pro. posiHl life—Take from the tables the ralue of £l for th« Mge and rate of interest proposed, and multiply by the MVfCfi anouitr. EX^^tPLKS; ^1. What U the talue of an aii annuity of £^0 wi a ]]orson's life H'ho!>e age is 6(^ at dp^r cent h . Value of au age of 60 from the tables 8,39 ,j 260,70 V 33 £250 14. f n solving the differeni caws "vre use the ^('#rthaInpton Ubks as better adapted for general ^actice« ^ Proa. 3.— To find the tafue of an aunnity durinp the joint lives o( two persons, and to cease wheu one of thea dies. EXAMJPLE. ^ - - • - What is the talue of j^SOO anndi«y for the joint lirei ©f two persons j THe one S5 ami the other 65, interest 6 per cent. Value of t#o Joint lives 35 & 65=»7)85 < 9nrk iNltm. 4.-*-T& fin^ the V4\tfe of an anoCiily to eontlnue during th« longest of two li?cs^"-*-Subtract the t»Iu9^ the ANKVITIBS ON Ur%% 1# jlrilil Hfct fromtlic iia^ af the f aluf of the twajkes, ^rl^indcf li the f *lu« uf aa annuity f^r £l m Ut« |«ii|«t4 of the two Um. EXAMPLE. Whit If thfi*?a1u« of £m tnaulty upon the lo8g«* of iwo lit ft, the one 45 and the uth^ 05 y«ar8, mt«r€ii © ^ ' Value of a Uft of 44 yearf 1S,B7 i .. ^of 05 ymi 7,2S «0,85 6,6t - #/ T Paoi. 6.— To find llie ▼»'«« of An wtate in perpetnUy •rt«r tlic death of the persent poshcasor-Find the lalue of the estate, subtract the yaluc of the life erf the pcfiou m possesion, the remainder is the ? alue of the rotc^MoWi A Person has th - perpetuity of an mt^^o of -i^BOO nUe ih^ death of the powessor aged 65. What |^ the f alut of the rtTcrsiori ? ^i f *i* Value of the eattkie ^t 5 per c^nt, 5(V yeafSU of the life of the posseisor '?,'28 ^ ^f i- 151,7^" 800 *; . , J . [v> 8,99 1' I fr ' X by the Annuity 3,58 » 30 [meni Diride by the?alue of the joint 7 -^- ^n— , cj««i ««„ ' ,. ji. « > ai«il07«40=a single pay* lives lucreased by 1 J m ' * *^ -^ 0,92==£l0,82 an- ^nual payment TABLE of the rates of assurance of a singlclife in theso* ciety for equitable assurances — the sum assured ^100. For I For Ty^art atan- jFor the whole life opf year. | naal pajrnient of. jannual pa yinentof > to 10 15 20 95 30 96 1^0 45 50 55 1 1 1 1 2 9 11 6 13 11 17 7 8 2 19 3 11 65 4 5 5 7 4 19 6 7 9 1 i £ s, d, £ 1 10 7 2 1 1$ 7 2 1 16 2 2 2 3 2 8 3 2 14 2 I 3 3 5 1 4 3 18 6 5 4 11 2 5 5 11 7 6 6 16 10 7 8 13 10 s. dt 2 10 (^ 12 10 9 8 U 17 9 7 U 12 II 9 3 17 7 3 9 SELECT QUESTIONS. 1. What will £246 amount to in 30 years ti 5 pet l^t } Ans. ;^1063,1978. t«ri-_i. •- Ai .—...A. ^f ^-t Kf\ ^ ' n« S An^. £12715,932495. Note. — As the Table is calculated only for 30 years, tl^e %^J wjLVQJ^m wiu^^i sun ii 9i and multiply theii SELECT QUESTIONS. 14? I fabuHir numbers continually into etch c*her and that product by the given aum.-ThU la»t product is tUe ju nimint— For example the number corresponding 7o%0 .nd 30 year, mulf.pli«l together give 1>, 4674000 to 30 and 91 Jear. d". 8"« 7,3910881 And these multiplied give the anionnt) ^g^ 7gggg33 for 91 years ) j-.r , . Multiply by - V; ^^^ ?t-r £12715,03^493 8. What is the present worth of jBMQ due at the end of 30 years allowing 5 per cant compoui^ ^"^T^' !« ' An3. £56,9189. 4. What is the present worth ot^/O 7 1,2048 du« 7 yews^ence at 5 per cent Compcmn^ ^^^^'^f * ^.^ ' ^ '^ Ans. £60. . 5. What sum will iClOOo atnonnt to at 4^ per cent ^er annum in 6 years ? Ans. ^62246 3 7^ 624. 6. In what time will jf 500 become j£607 15 Oi*t 5, per cent Compound Interest ? Ans. 4 years, 7. My Servant James Ainold, receiTCS on the 18th ot July, 1808, from Mr. WUliam Jarvis, forty poun4# in full of an account delivered. What receipt ought he Jo give. , i. T 8. Mf friend Peter Careful, lends me on the Ist Jan. tary, 1809, je550, which I agree to repay l^im in two months. Reqnired the form of the promissory note. , . 9. Mr. Joha Torgan, gives me on the 7th Fcbuary, 1^09, fifty six pounds ten shilling in part payment of a debt he owes me. Required a copy of the receipt. 10. Mr. Thomas Paris pays on the 11th of December, 1808, twenty Ave pounds, fifteen shillings and eight pence by a bill on Simon Taylor, Merchant in Quebec, bi^ io^ part of a debt. What kind of a receipt shall I give him J 111. Mr. Samuel Craig, of Liverpool owes Simon Sny- der, of Montreal, two hundred and ninety six pounds I8s= which Craig draws for at three months sight. Re- quired a copy oif the bill of Exchange. r\ 12. Nathan Patterson, of Quebec owes James Demps. ifit of Montreal, £l97 125. which PattWBon, draws Ut 148 SELECT QUESTIONS. on the 17th November, 1808, payable to Pdter WharJ' ton, or Order at one nioiith. 1 dematid a copy of the- l)ill of Exchange and the receipt that Wharton sould givo Pemp&ter who receWed the above on account. 13. Richard Moorston, receives from Jacob Campbell, on the 11th of July, 1808, twenty seven pounds on ac count for the use of his son. I demand a copy of tho receipt. • 14. On the 25th of October, 1808, William Provost, receives df AHtfti Morrice, eighty pounds twelve shillings in money, and also an assignment on William Sangsterfor the same sujrt. I demand a copy of the receipt that Pro, vost must give Morrice who received it for half a years annuity. 15. On the Sd of February, 1809, Patrick Lawrence, receives of Georgfc Philips by the hands of Joseph Wag- goner twenty three pounds iu full for an account deliver- ed. I demand a copy of the Receipt. 16. What will an annuity of ^£40 per annnm amou%l to in 3 years at 5 per cent ? Ans. j^l26 2s. 17. What will the same annuity amount to in 15 years. Ans. i'863,l4^^;lOO, 18. What will an annuity of j^75 per antiiim amount .OQ7QQ7 i 77246913,555672 4,549382 5,80730 2 883368 3,733456 4,822345'6,2 1 386 2,99870313,92012915, 111686 6,6488 3,118651 "''' 3U2- 42726213,24339714,321 9 4215,743491 4ai6l35l5,4l8387 7,li425jy,3l/z7 7,39635 7,98806 8,62710 7;'3l225|lO,C626 N2 J50 TABLES OF COMPOUND INTEREST. I TABLE IT. m THE PRESENT TALUB OF £l COMPOUND INTEREIT. I| 3pgr cen: .\4per cent, \npereent. [6 prr Cfnt^7ner rentA8verr^t 1[ OTrmT 1 IWitfc'dol /ter^J' A. #^!.^,^..^ ^L. ■ - ' ■ 4 6 7 8| 9 10 II, 970874 ,942596 ,915142 ,888487 ,862609 ,837484 ,81309^ ,789409 ,766417 ,744094 9615381,952^811,943396 ,9^4556 ,888996 ,854804 ,821927 ,790315 ,759918 ,730690 ,702537 675564 ,907029 ,863838 ,822702 ,783526 746215 ,710681 ,676839 ,644609 ,889996 ,839619 ,792094 ,934579,925920 ,873438;,857338 ,816297,793832 ,762895 ,747258,712986 ,704961 1, 666042 665057,622749 ,527412 ;582009 i|,591898j543933 11,7224211,649581 12,701380,624^7 13,680951 ,600574 14 66ni8',577475 15^641862|,655265 16,623167,533908 17, 6050] 6, 513373 18 ,587395,495628 *9,570286',474642 ,6139131,558395^508349 20 21 22 «3 24 25 26 27 28 50 ,558676 ,537549 ,521893 ,506692 ,491934 ,477606 ,456387 ,438834 ,421955 ,405726 390121 ,375117 ,584679,526788 ,73502^ ,680583 ,63016^ ,583490 ,54026>l ,500249 ;463193 ,556837 ,530321 ,505068 ,481017 ,458112 ,436297 ,415621 ,395734 376889 ,3589^*2 ,341850 ,325571 ,310068 ,496969 ,475092 ,444012 ,468839,414964 ,44230! ,387817 ,417265 ,362446 ,393646 ,338734 ,371364 ,350344 ,330513 ,311805 ,294155 ,277505 ,261797 ,246979 ,295303\232«99 ,463695^,36068i),281241*,2198lO ,450 1 S3;,3468 1 71,267848 ,207368 '"*"""' ""^'' """ " 195630 184557 ,316574 ,4288^ ,397113 ,36769» ,340461 ,315241 ,291890 ,27026J^ ,295864,,250241> ,276508',231712 ,2584191,21454a ,241513,198655 ,2257 13, 18394a ,210947,170315 ,1 97146, I5769£r ,184249,146018 ,172105;,135201 ,160930;,12518ef ,150402], 11 591 3 , 140562^, 107|^7 ,4ilP87i,308319,231377;,l741 10 ,1313,671,099177; 'ALLIGATION. 131 ALLIGATION TEACHES to mx two or more simplei of different ... comwosition may be of a middle qual- r;r::i — oVZ Mud. = aV- M«IU1 .a* AUigatiou Alternate. • • • • ^.ALLIGATION MEDIAL IS when the quantities and prices of several things ar« giyen, to find the mean price of the compound. ^ RULE. Multiply each quantity by its price-add the products and divide their sum by the whole compositiOQ-the quo- tient giTes the price of the compound. EXAMPLES. 1. A corn-dealer mixes IQ bushels of wheat at «s. per bushel, with 12 bushels of rye at 4s. 7d. P^'^f he) »nd 18 bushels of barley at 28. 6d. per bushel-What is th« ▼alue of 1 bushel of the composition ? Bushels lOX 6s. =:60s. value of the wheat, — 12X48. 7il.=55s. — — Tye. — 18X^8. 6d.=45s. — — barley. — C value of one bushel 40 ) 160(48. < of the mixture. 160 .^ ^. A vintner mixes 6 gallons of wine at 4s. lOd. per •allon wi^h 12 gallons at 5s. «d. and 8 gallons at Cs. 34d. What is a gallon of this composition worth ? Ans. 5s. 7d. 3. A goldsmith melts 4 ounces of gold 22 carats fine, 10 oz. of 21 carats fine, and 6 oz. of 18x:arats fine— Re. «uired the degree of fineness of the composition. Ans. SOfV'Ca'^^s* ''4. A composition being made of 5 lbs. "of tea at 7s. per lb. and 9 lbs. at 8s. 6d. per lb. and 14| lbs. at Ss. lOd. J. ,K > A ••'• fi" 1 rii.il per ib. — what is ouc pouuu wuii.t r -.^"=. --■ =-'^''=. S. A grocer mixes 18 lbs. of raisins at 4d. per I ^;- with 28 lbs. at 6d. per lb. uad 12 lbs. at 8d. per |b. — What » the prSb of ft ib, of the mUtuje ? Aus. 6^d. per ib. 1*- m ALLIGATION ALTERNATE. ^ALLIOATION ALTERNATE IS the method of finding what quitntity of each of the itigr«;dients whose rates are giTen, will compose a mix- ture of a giYen rate. RULE I. ].. Write the rates of the simples in a column under «ach other. 2 Connect or link with a continued line the rate of each simple which is less than that of the Compound with one, or any number of those which are greater than the Compound, and each greater with one or any number of the less. -t 3, Write the difference between the miiture rate, and that of each of the simples opposite the rates with which they are linked. 4. Then if only one difference stand against any rate, It will be the quantity belonging in that rate ; but if there be several, their sum will he the quantity. Note. — From this Rule it appears that many of the quotients will admit of a variety of answers, by increasing or decreasing the quantities in any proportion. EXAMPLES. I. A yintner would mix 4 sorts of wine at 128. pet gallon, at l8s. per gallon, at 24s. per gallon, and at 26s. jper gallon — What quantity of ep h must be taken ? |12 ,6 at 12=: 72 20 18 24 [26 — , 1 at'l8=t ~kl2 at 24= — * 8 at 26 s: =t 72 48 208 20 ) ^0 12- 1.8-1 24-! ^0- 400 ( 80 Proof, 400 4 18 at l2:r= 48 at 18=108 at 24=192 Sd. on ■u at 2t)== 6% 20 ) Proof. 12-- 44.6==: la IS— 64.4=10 '124—8+2=^0 126— '248=10 In the last of tliese 400(20 be numbers are doubly combined, ALLIGATION ALTERNATE. rtV %. I wo»W i"\'"*^',;j„;„ .t 8». What quantity .hall I i.»e«rc»cK ? An.. « lb- '"'^^ gj. ^ 4,. .^lat 4.%a^Trr.t,r,tt!:i.t5io«.f '.♦•''' .b.co». 48. ©a. p*5«^ "" iQ . ^ bushel ? , n"'. Tit ^» 6d -* . 3'. la -3 .t 4.. & S »t 4.. 8d. per lb. """'h" •'"':„» X of tach, to «11 hi. com- What quantity must ne lai^w «• > pound at lOs. a*Us -~iife: at 9s. Sd.> at 8s. carats fine^ roust be taken to mak« u^ a *-"» k> '':1^8*"^i7, 18, an^^g, and 3 at^l & ^Scaratifine: RULE II. . fouud by Unking to the required quantHy pf eacn. EXAMPLES; ' - H, » •****^ - 6--., « Thenasar2::50:8j 15< 12 : 1 : : 50 : 4^ 12' 50 Proof. e A crocer has currants at 4d. at 6d. at 9d. and at vv5-±K «rtd he wou4d make ainixture of 2402bs.^ so ihat it might be aft'ordcd at 8d. per lo. ^-^-^^■^ A Itt -£''^Jlf each sort must he take Ans. 72 lbs. at 4d.-24at 6d.— 48 at9d. and96at lld» V ^^ SINGLE POSITION, 3. A merchant bas tea at Sii. at 6§» at 8i. and at ^. »d. per lb. from which he wishcii to make a rnisture of 87 lb. to besoldatrs. perlb.—How much mutt be taken of each sort ? Ans. 29 lbs. at 5s.— 2aat 9s.— 14 J at 6s. Sc UJ at gi. ' 4. A goldsmith has gold 25 caiats fine, some 22 and •ome 18 carats fine, of which he wishes to make a mix. ture of 60 ounces of 20 carats fine— How much must hn ^ take of each? Ans. I2 of 24, 12 of 22 & 36 of i« car. fine. RULE III. Whcm one of the ingredients is limited id a certain quan, tify — Take the il ifi'er en ce between each price and the mean rate as before : then, as the difference of tliat simple whose quantity is giren is to the rest of the difterences se? craL ly, Eb is the quiifitity ^yfm to the screral quantttiei re- quired. EXAiMPJ^ES. 1. Ifo^mnch wine at i2i- and at 8». sfiall I mix with 40 gallons at A 58. per gallon, to.be able to scU the mil* Ituo at lOs. per gallon ? I to 16— ,2 12—12 ! 8— *6+2=:a 2 2 2 2 2 2 9 • • 40: 40 40 : 40 40 : 160 12 2. A tobacconist has (obaeco at it. at Od. and at 7d. per lb. — how much of each must he take to mix with SO lb. at 24d. per lb. ? Ans. 12 lb. of each sort to mix with the 30 lb* SINGLE POSITION TEACHES to resoWe a Yariety of question* that ea«- »ot be wrought by any of the former rules. The results are always in proportion to the supposition. RULE. Talro •«« i» vinMi KoM aA «\T uaa n r/% An n ir»4M»#^«* »:#Y> :* thi •onditions req^iired in the question. Then as the false result <|ue§tiim to tht; true number. to the supposed number, so is the r«SttU in Ike llKOtf! positioiC EXAMPLES. IM I.. Three merchMti join in an adfentare, wi J « •»€!« •f jeiOOO-of Hii» A. g«" • certain .urn, ti.htV «. much „ 1 wd C. u much M both-how much did each con. *"'&!«. A. gaw £500, then B.=^i06 AC|.=:^MO, the.um ofalUhcihare.;s^aOO-butit.houldh»,c been ^1000— therefore, I say if j£6O0 £200 j£1000 1000 600)200000(333^ A'8 sWf. 1800 166^ B'8 shire. 500 C'i share. 2000 1800 1000 Proof, 2000 ^ 1800 200 2 Two gamWcs qnarrelliiig about their game, each teizdi as many of the guineas on the table as he could--. B. found that he had } of the number, which exceeded ^\ the share A. got by 18--Requlred the number of guineas on (he table. An*. 54 guineas 3 What number Is that which being increasctl by $, J, and'i of itself, the sura will be lOO t / Ans. 48. . 4. A gentleman distributes 68. 6d. among some poor people, consisting of men, women and children, lo each man he ta,c 6d. to each woman 4d. and to each child 2d.-~there were twice as many women as men, and twice as many children as women. How many were there ©f each ? Ans. S men, 6 momcn, 18 children. 5. What sura of money is that from which £5 oeing subtracted J of the remainder will be 40 ? Ans. £65. A A and H havino received eaual sums of money ,> A.V'd out of his £25,"ai^ B. of his £60-and then it ppearcd that A. had jist twice fts inu«h money ad B — how much did each receiTe 1 Ans. £95, ^^ pomiM fospiM, it sam is f hat wHotc ) pmrt, } part, mi I ptrt, jlher, iJial I amount to JS94 ? A ns, Jlso. 7. What Aiidcd tcgcti 8. There wat a dolicioai Cake among iht Greeki, call. «d Thfioin, J of which wai of the ane»t flour, | of Eggs jpnd I of Lard and Ho««y, to these wore added Q ounces of Milk. Reouired the wcicht of the whole Cake aod of Reqt each ingredient ? Am. %4Q omuaM iii ail. I'- ll DOUajUl} fOSlTION^ TFACHKTfl to resolfc queitioni by two luppoiUioni of faUe uumbcrs. RULE. 1, Take any two numbers and proceed with thera ac« eording to ihc conditions of thequfstion — ftnd the differ, cnces or errors between the resuUi and the given number. 2, Multiply each of these crrprt into the others sup. position, and if both are of the same kind, that is both less or both greater than the giten number, divide the difference of the products by the difference of the errors. 3, But if the enors are not of the srme kind, that is, If the one be greater, und the other less, then di?id© the 8um of the products by the sum of the error^j the QuotU €nt will be the answer. v r.^^ . , ^ EXAMPLES. ^. Thirce persons discoursing about their ages — I am 18 years of age says A— I am as old as A and half as old as C, says B, and I am as old as you both sdid C*^ ^*^ quired their respective ai»f^. Suppose C's age be 40 SupposcC'aageto be 60 Then B must be 20 the half 30 . And A's age added 18 add 18 38 B's age* add A's age 18 add A's- •uHract C»s 40 48— B'sagflk ■AS 60 la hU «fror« 1^ Othe^rioff DOUBLE POSITlOiV. m 40 ao X 10 60 40 000 '240 'J40 J I 2. I (liiMk yonliarc ',H) Gccse this year s.iUI A to B— no S.I id n, l»ut if I had a^ many as f have and half a* many and twoGcesr and a h.ilf, thun 1 should just hare tsveiify —how injuiy had ho, AnR. 7. 3. A Drunkard goei — how much money did each snatch up. "- f^ ^ y« .^ .^ ^ .^ '3* j\: MO/ IKJSi D= 62 10 o £100 Ans. \Bn PERMUTATION OF QUANTITIES. 7. A nmn sleaiinji appU-i ^a'^ n^"t by A. who took hilf h\* applei and rclurntMl \% he Hun met B who <;»ok half 0f what hn hail .m1, his value is trij^lo that of tin. firit- ;whAt is the value of each horse. Au«- ^^^O and X 10. ». ( PERMUTATION OF QUANTITIIiS DISCO VERH how many wiiys any glfpn ntiihWr may be plaeed or changnl. • • * • Multiply all the terms in their natutAl order from on« to the given number. i:XAMPLr.:v lion- many changes mi^ht be r'ng in f. rnxmc bolls ? • lX'2=:^Xo— 5X1=24 ;< 5—1% X<:=:720Aj|f.. o. How m:iny cUan^tn n.ay be rung in Vi bell«, ami Hhal time would it reciuire, supposing U) <^*»^;«.^' ♦" ^" rung »a one minute, aul the year to consist of JG5 dnys 5 hours and AO minjiles ? Ans. 470OC16OO changes ; and 91 year?, 2G I days, ^2 hours, 41 minutes. ) 3.' In hoTv Tiany positions may a family «^f J p^e"0"« be placed ' ^"^- 362880. ^ i Agcnflcmangivrsaninkecpcr^lOO for liberty t(». lod.<^in his house as long a<^ he could place (ho anuly, consisting of 7 porsous in ditrerent positions at table- Thc innkeeper accejvted the omr -^fSow supposini^ swv^ silt dow n ;tt table 4 tinu."? a dny— how long would the gen loroaa remain according to his ag Ans. 27 years, recment .' months, I daj, * ,.-> . sotTAiiE root; BV OLUTION 1 o., EXtlUCTION OF ROOTS. ■JO VKTUAVr Vl'lKsqUAllE UOOT. 1 DIVIDK. Ili« Birr" •'"•nbrr Into i.t-rlcdr Of-JJW figure. .acU, l.cgl..i..g »l SQUARE ROOT OF VULGAR J'UACTlpNS. RULE.* •*^' - REDUCE the fractious to their lovrest terms-tbcii extract the square root of the uutnerator fir a m-^w uu- inerator, and the square root of the tknoininator lor a new denominator-or reduce the fraction or fractions to deuimaU, and extractthe root as in whole iiunjUeis. What is the square root t)f {\ I '^ ' The square root of 16= ± ^jj^^^.f^ do. of 25=; i> What b the square root of 1| ? do. doi of 64 of «*4 ? l5 4F ' 160 SQUARE ROOT. I i; Before you proc^^d to the following questiaos, iUostrft* tivu of the usu of the square rout, ob&x:r?e the following rules — ' 1. To find a mean proportional between any two num» ^ei» — multiply tho two nuaibi^rs lo\^ethcr anil ej^tract tho square root. 'i. To find the side of a square equal in area to any g';vL9M 037 6 4^61(6090 ■ 218 . &9n037 rcBolvtnd 60* X 300 =1080000 CO X^X30= l^^O^ 9 X9 81 1096281 9==986652r 44508643264 resoWend. 6C90»X300 =11126430000, 6090 X4X30= 730800 4* =' 16 11127160816 4*=44508643264 What is the cube root of 696787 1 ? Ans. 1 91. of 7880599 ? 19^- of 456533 ? 77. of 85184 ? '^^• of 163039787817 ? M63. of 94996712418f) 19125 ? Ans. 456285. . To find the side of a Cube equal in solidity to any gir- Ud solid.-Extract the cube root of the solid content. EXAMPLES. , The Solid con.tent of a marble stone is 35937. He. quired the side of a cube of equal solidity ? *^ 35937(33 Ans - 27 3* X 300^2700 3 K 30= 270 -9 8937 2979 S.=^937. 164 CUBE ROOT. :i The solid 6otitcnfs of similar figures are to' ODe aiiodNr as (he cubes of tluir dranietcrs. . If a leaden bullet 4 inchcis diameter virvigh 18lb. What' ifiil a bullet 7 laches weigh ? 4 4 7 7 16 4 40 7 04 : 18 : : 343 la 2744 313 • 64)5-174(9a,4684)r- 576 414 584 300 266 440 38i 560 612 48 To find the diameters of a solid body, haf ing those of another similar one given either great^sr or less. — Cube the dimension giveu— augment or dimir ah them accord. iii» tr\ A ball wliose diameter is 10 inches, weighs 6^1 lbs. iRequired the diameter of another ball whuse ^ei^ht it ISI lbs. 10 JO. 100 10 623 : 1000 :: 135=210 root 6 inches, ^. The circumference of a cable being 7i Inches, one fathom weighs 16^ lbs. How many pounds does one fathom of a cable weigh whose circumference is Di inche«. square, pounds. square. pounds. As 52,5625 : 16,25 : 1 13ia»,0625 : 42,68i8 Ans. To find two mean proportionals bet\reen an/ tw<» gir- £n numbers—divide the greater extreme by the .tss and the cube root oft he quolientmnl^iplied b^j; the less rslrprn« tives the less mean ; multiply the same cube root by nio fcss mean and the product is the greater mean proportional.. EXAMPLE. What arc the two mean propqition^s between 4 & 500». 4)500 125(5 cube. 4 ^ IcssmeaQo 5 100 greater mean. ARITHMirriCAL PROGRESSION. ANY^tank of numbers that increase or decrease, by a Jommon difference are said to be m Arithmetical Progres- t€rm3 MU1II. aa. tA. 11 >l! 180 .. 180 198,0 Ans. 198. : 1. A man bought 7 }ards of Cloth and gave for thei first yard 3s. and for the last,27s. What did the 7 yards amount to? Ans. j^5 5s. 2. How many strokes does a clock strike in 12 hours ? ^ Ans. 78. 3. How many strokes doth the Venitian clocks strike in a revolution which go 24 hours ? Ans. SCO. 4. If 100 stoneare placed in a line .exactly 1 yard as. sunder and the first a yard from a basket. What length of ground will that man -go over who gathers J»»cm up singly, and returns with them one by one io the basket . Ans. 1| mile, and 120 yards. PftOB. 2.— Given the extremes^ and the number of terms to rind the rommon difl'erence. _ t « RULE.^Divide.the ditfereute of the extremes vy one less than the uumb^Tof terms, tUe quotient '^ the c gin- mo a ditfarence. CEOMKTRICAL PROGRKSSION. i«r EXAMPLES. Let the extreme, be 4 and fiH and the number of t«r«>» 17. Required the common d.ffcrence. 68 I 'I DWlde by 17 - \^-l6)(itO common differeTiCc. 64 <2 If a person purchases 7 yds. of Cloth and gives for the first yard3s. and for the last 27s. VV hat is the com. mon ditrJrcnce of the price of each yaad ? Ans 4s. PiiOB. S.—Giren the extremes add comWon difference to find the n I) mbcr of terms. ,,*!»« RUI V —Divide he dift*ercnce of the extremes hy the common ^'liflVrcncc- the quotient increased by 1 is the number of terms. . 1 Let the extremes be ^ and 56, and the common dif. fcrence 3. What is the number of terms ? M>-2=54-4-3=184'l=l9 Ans. o If the rxtremes be 3, and 33, and the common dif- ference J What are the number of terms ? Ans. 1 1 . Piion 4 —Given one extreme, the common difference and the number of terms, to find the other extreme and the sum of the series. llUhV. — MultipW the comtnon difference by the number of terms less' one, and (ho product will be the dilVerence of the extremes. Add this product to the less extreme for the greater, or subtract it from tli*; greater for the less. , . The !a«t term is 56, the number of terms 19, and tlie common difference 3— what is the iirst term ? 3 1« 5 4 56 S:i ^ less extreme. 54 56 greater do. 168 GEOMETRICAL rilOGRKSSIOX. 'ill : If the greatest term be 70, th(* common differpncn 3, and the nunibrr of terms 21 — What in the least term and som of the scries ? Ans. 10, the last term^ & the sum 8 |a A debt can be discharged in a year by payinji< 1 shil. ling the first week, 3 shillings (he .second week, and so on always 2 shillings more every week— What is the debt, ond what will the last payment be ? Ads. ^'135 4s. the debt, and the list payment £5 ii, GEOMETllICAL PUOGRESSJOX. •"When any rank or series of ntimbers \t\c/^p''^ by oni common multiplier, or decrease by one comm.in dirisor, it is said to be in Creonietrical Profc»resssion — thus, 1,-1, \6 04, '256'j &e. ; here the comrnon^a^ftiplier or ralii) is 4 und 81, 27j i>, 3, &c. j here the common diviH)r ©r ratio is 3. PiioOLLM I. — Given th^* exfrenle and ratio to fmJ the nim of the scries. IILJIJO. Multiply the last term by the ratio, and «nbtract the tirst term from the product the remainder divided by the ratio less one, will fiva the bum of the sopics. EXAMPLES. 1 . The cTjIremes of ^geometrical i)rogrr«^ion ore 2 and 8192 and the ratio 2—^ hat is the sum of .he series ? 8192 ' 16384 2 2 — 1 )16382(=r: ices': An«?.l(J3«3. 2. A gentleman S(»l(l 800 acres of land for which he got 2s. for the 1st 100 arn's, and far the last 3i7r)8s. ; ratio was 4— what were the 800 acres sold for ? 20)4369,0 the ^£2184 10s. Ans. 3^1 A noblemaa demands of a JeweUer the price of a casket containing 12 very brilliant diamonds— the jewel. CEOMCTRICAL BROGRKSSION. 189 ,er demanded 5s. for ^.^ ^^^^ ^ ^^^^^ ' pgo». %^GhBn the first (firm, the ratio, and number Af terms to ftnd any term assigned. RULK I. -Find a few of the luadlng terms afcr>»hicli pUcc their indices, W'gining with a cypher. . ^ a Find wW ftgnres of the iitcliceii when addetJ togeth. tr, give the Indexlss bfone than that of the term sough . 3: MuUiply the numbar^ standing »"der such indices, into ea^h other M ««»**© ^^« \^odtict a dividend. 4. Raise the first term to a power whose indei h one \vM than the number of terms -multiplied, and make tfti result a divisoi'. •- , . ., . 5. Divide the dividend by this di? iior and the qaotiwt *is the term sought. . . ^ Note.— The '»nd*tC/B9 mqst begin irlthan unit, whem the first term »f the series Is equal to the ratio-aad mi thii case the product of the different |erro«i, matcad of being only a dividend, would be thp t^m sought* EltAMPLES. 1. A Jeweller wishing to purdhase 9 rich pearls, a- •reed to give 1 guinea f^ the first, 2 for the sccoid, &c. ^doubling the ^>f iCiJ/feach tbno. as he proceeded to tli« last. What was thei|>?ice of the pearls. ^ '^^^\ 1. 2, 4, 8, 16, 32, Terms* C 54.3 =i number of terms leaa one. * ^"^ I sax 8 ==456 Guineas. Arts, 256 guineas i. There is a Geometrical series whose .first term is S and second term 6,-— required the 12th term* * • 4^^=!^ the cominon ratio. • CO, 1, «, S, 4, 5, 6, Indices. I 3, 6, 12, 24, 48, 96, 102, Terms. nnu__j S.*^ e Ty.^f»w **x f n*li tt%rrn__ Apd lS2,X?6==18452~the dividend which in this case isi iiirided by 3 th0 first power of 3, because the uumbet ^ , terms multiplied being only 2 aod a — 1 «*i P 170 MENSURATION. Ui i f i I' u the power in mhi«h 3 h to be ralictl— therefore lS*JJo« 6144 thii lt»riii rcipiii^d, ^herwiie. 4*^ i?^1-f./l^lndeit of i'iih p«v<»r. 12X 1WK'>''-^'^'J*»90-J- by lh»i «qimr« of thr«», 1)(*raiisein (i¥^ t^v. ms «re uswl and ^ y^j — iiUiai EXAMPLES, 1. An Indian huflng lirH* iliscofored tlic jjame jf Ch( ' •hewed it to his kuig, who was »o dallghted h ;h the iu. TiiUion, that ho bid him lit wiiAihO would, a^ t rem \ fur his ingc-nuiU ; upon which he rcquustt^ i ^aln of wheot for the hrst square on the Choss board, 'I for the second, 4 for the third, «&c. doubling continually to ()4 the whole nunOH?r of squares. The Kifti; astoni«hf^d at the apiarcnfc insiguincance of the request, commanded thi whv^i to be givert him. Now supposing 040,000 tjraim »a bunhcl. It is required, how many ships of ^00 toni burthen, wer^tiecessary to carry off the m heat— allowing 40 bufeheN to make a t..ii ? Ans. :ieiy tiia SlidJog Hulo now to b«i described. SLiniNG RUT.K. »T«fTr<^ :,*5*»j.^0n* cf>nfi«ts of two Diece? of n foot ifl teij'gtlVeat;li, which are connected tugelher h^ a bi iss joint On the sliding side of this rft fc ar^ fof>r iiheidt, num bers, mar C ara apuM .t k«l A, B, C, D,-i;ift! ivfo *iA-lle oiif*'W am Uo sllikf. thfejBf these liiie* A, B aiM < MENSURATfON. Ifl 1 U^ lMV»ft»i# tlier proccccj from ©ne >ro4uct»t «ir two num, S,.t 1 upon A. »o one «f the ""'" ''"..V.Tfl^a ,h« «. ,,|.»t th. ther number u,.on A.. w.U l> found th« tJ.. Urns .eel. ,i o» the othe, p»n U tkuliut and ,ncrea.« Pn(.ii,2.-XolniJeono niimfier bjr anolhti, ai OM ''^s!; the di.Uor « on A.''o '/on B. th«n against 864 on ^•iV.,':.^:^hen'l r.de;d ™n,'W^ond O.e en,, of «).« li.,et 4inT.nl.!i It 1 i or UX) time, to w.*lc it lafTon A. a il increasfc the t^uotfCui accorduif 'jr. HU r>'-Set V « p-n I). to 1 ., ,.on C. ih^n ag."^""' ^^ upon D will bo the square mb on V, „ i, ,„ »_ If V, Woild square <2iO, cV.m the V on V. i» hf 100, then Ih. ' ohC, wUl bw iOO and the p.oduu W ^^Piuia. 4,--To entwt t>»e s. vre root of uny mVr^ «w 1 9 Off ■ HUl-»r'4. 4t l'up( C. to I upon D. then aRalast 129() tba «.imher uiion C. is 36 on D the true root. E|OB. E~ r» pt-rform fopariion n^ ilit 3uu*i.^ ruv. M i irt MENSURA ■RULE — M the flr»t num TIOfT. ber fl'upon A. to th« ifedm! 34 the thinl numbfr 5$ on A. U ion H. then ai^ainit tnS lOiifth pfOpOrtiiJnai ^4uf • Note.— When ooe of the mMd1« numbpf* mm off the Iftot, t«ke tlie lOth pari tof it «nly, ind »ifffn«tit tlie an, •W«f» ti»n limfi— To find a tMrtJ proportional In ciactly the name, (he sucond niimbi'r Mnn twice rcp«»tid. Thii^i suppoM! a third proportional wai re^ujftjd lo a and 4^— Set the first 26 on B. to the second 4« »« J^* then against (he ic«>'. e.ch bring ITi '?> '7' ,'^J^t ' " d" , ««.« of H^ !„«;« 1" .1.0 b,o..ler end, and U4 M •"^-'"--'^j. |»Ho» 9 -To Bn« Ih* xrtWl'y of »q..«r«d «r '««" '•"';'J rnoB .J. ■ MnlliDiv lh« n..iiU a small cord-then J of fhe « rt is taken for the side of tke square. I^pering t «be. i. measured by girding it in two or "jore places and dividing the sum of the girts by theu number for the "T What is the solid content of a round tree 25 feet ion, and the girt ia the midd,e^45 inch. :^ 9fl. Stn. girt by lity, ex- uarc. >rt in the , yearly • ARTIFICERS estim.a« or compute the value of their Avork by difl'ercut measures. • ♦ • • BRlCK-LAYER-s WORK. BRICK.LAYK'.IS Measure their work by *''^ '"f »( 16J feot, wl.«se square is 272 J and thesUndard h ckn.M (hey rec'kon a brick and a half thick, (lo th.s tbakn*. other dimensions must b« re-'«ced, wn.clr is done t^y mu - tiplving by the half bricks in the thickness aciV-Uiruling by 3 half bricks or the standard thickness. • • • • MASON'S WORJC. TO Masonry all sorts of Stone Work beloiHS ; and themcasure mad. use of is a foot, either sohd or super- .... „ .- _! .U-, .„i,:r«i.«v-ni.>£es4 &c. are meas- urod by the superRcial foot-Walls, blocks of marble oc stun.!, columns, i:c. arc measured by tnc solid Joot. X7^ MENSURATION. GAUPENTER's & JK)rNER'« WORJC TAllPEN I'ER^s a«d Joiner's Work cousi*ts of flomc i„g,t)artiUo;ing, roofing, &c. »nd is me^ured hy if^ sqoacc of 100 feet. • • « SLATER'S & TILER'S WORK. . THK content of a roof i» found by multipTymg the len^HllfThe ridge by the yrt f.o» eve to eve ; and .n ulatinK. allowance must be made for the doub e row at he bo torn ; and double measure Is commonly al owed for gulters, Tallies, &c. but no deduction, are made foe chimnie*. • • • • PLAIHTF.RER & PAINTER'. WORK ♦f AISTERlNGand Painting are measnr d by tnc iquwe yard-dedl.ctio« are made for all vacanc.es. • • •■• GLAZIER'S WORK. , . . , GLAZIERS take their dimensions in feet, ^<^<^J"^ pX and estimate their work by ^'^^^''^''^Jli!;, Jln«s of crcrv form are measured a» if they were squirts, on accouTof thi w aste attending .he c utting ut the gla.. PRACTICAL QUESTIONS. 1. THERE is a wall 72ft. 6.n. long, »««• ^ "• "'="' Jn bricks thick-Required ^"^^;::::'\,n. 1. If a wall be ^45 feet 9 inches long and 16^ hi ^h and «|b.icks thick, ,eq«i..d the ^^^ ^^^t^:^^: '"s." I wish to buUd a house 45^ ieet l*..g and , 5 feot broad within the walls, the "-f '" b^^f ,t, •>« .^^^ oal.lcfi feet hifih above the wall,th ""oic >k s thick-Required the content u. rods An -J^, 7 4. Required the solid feel in a stone «»" '"^^ 6in. long, 18f.. 3in. high, and2tt. 3.n._.h.cW.^^^^ ^^_ What is the Talue of a marWe slab «ho^« '^"f ' 7s. 6d. per «q"are toot h IS 6ft. 9ijB. bieadlhaft. 4in. at Ans» £'7 3 9. **3# MENSUaXTION. lit « T „t,h tenter «ndcri.¥e. *« »>»'ld a ho»^ ,„„g, the brcaJth 44 feet and ^'^^i^'^^J'^Jlf'^oiA, sjuare. Wiiat will it cast I Ans. «»i * of a true ,..tch. What will it "^^^^^i^^^,. , ,id. per square. v„„„ how nrnnv squares there 10. A Tiler wishes to know n"".™""/ '^ . .,e?n a roof40i feet in length and g.rt 4^'i^'-^ j,^^. inches on each side r .,.,.. tu^t m^^asurea 1,. There is a quantity »' l- "^f ^^f Mgh a d'?s 234 feet 8 inches »''«»' '"^^-^.J^Jhing and plastering rendered betweeu quar ers , the """'8 ^, j „m 8d. per yard and the wlating 2d. P^J^^'^ ^jj. the whole come to? •^"''• NyTE.-In rendering betwee- quarters, yon ded»et J and in whiting and colouring you adU J. 13 If a cicUn. be 59 feet 9 inches Ions and 24 feet 6 n. II a "«»"- "^ jj are in that room J inches broad. How many y"™^^^ ^^^ y.,^^, 5 fe.f. ,4 If a room be paintc.! wl.o.e hel,hJ is .6 feet iu- ehes. How many y4«t> *'« »' * aI^TO yard t feet.' • 1 ■; A hbn^e has three rows of « indow»/(ivs in a row, the Ut'oT'eVrn is 5.^.^0 inche,, the s^ond 5 ee 3 inches and (he third 4 feet 9 mcnes, the ^!^^_ , Cinches. Required the number of feotand the expcnce r:i..iiBff-.4*9*d: Ber aqiLire foot . An^.'l93fcet0mch€f5 I^^pence h*\ Ifi SURVEYING. OARPKNTEa^S ACCOUN' lA¥Et BrKBN£B, £eO. D9. 1808. To Dan IF I. ThompjiPm. July 15. To 753 yds. 3 ft. 8 hjcIim of FboRing at ^i< ■ ■» *i ^swer o^!^l3G 17 4^^% LAND sun V IKYING. r KO man can be a skilful surveyor, who is npt comf, pictely master of arithmetic, geometry, and tii^'onomitry. Here therefore, wc can only give a few practical n*iPS which may be usefiil to the pcnth man or farmer, who may bedesifous of linding the true content of a piece of ground. 0A>' THE CHAIN. LAND is measured with a Cham^ called Guriter»s chain, (from its inventor,) of 4 poica or 2^i yprds or 66 ipet in length. It consists of 100 fq^al Jli^^k*-^ and the Jenntb of each link is therefore ,V^ of a yard or ^% of a foot OF 7,^2 inches* ,. a • Land iM estimated in acres, roods, and perches. Aft acre is equal to 10 .vpiare* chains— that is, 10 chains in length and 1 in breadth-or, it ii> ^20X'::2r=48^40 square yards— or, it is 4(>X1=:'^0 square poles— of, it .s 1000X100=100000 square links ; these beiniir all tha lame quantity. A square pole, or the square ,0^^ H yds, long, or the square of J of a chain, or of 25 Uuks h Qlb square links. In measuring linti. It U best to set down the links a* integers, and when the content is found it will be in square li!iks J then cut otf & of the figures op the right hand for decimals, and tho rest will be acres^The decimals cut ott are multiplied by 4 for roods, and by 40 for perches. A cross staff is bk feet long, made sharp at one end to cufer iJii'^-tnc {iiwunu /-\_ Mfvsi r^■ A laratfi t^liltfi t>r a pkc*j-yf WMod if pUcc*. If. tbe plate be brs^ss^ it i% d /hrats nlilte StJRTfiYINe. 170 f^rmshea with sights : If U be of wo^d, saw two s^Jckt H rtuartef of an inch deep, at rl>..ht angles. This st«ft • useful to njeasurespiall and cmok.d pieces of «ro«nJ, and t^iy't-ii.^e' perp^naitularfi. W ben cliaitims^ in the field, if vou ha^e occasion to raise a pcrpitidlcolar to any as. siencd point or corner, your eye cao inform yoo, if you are near the place, on 4hich it sho.ld fall : 'Uen stick down voor cross staff perpendicularly, iixmg one of its lines directly over your chain & parallel tn it r Apply voiir eye to the other end of the line on the staff head- ind h^oklflR along the flame, if you perceive the assigned poiut in a direct line ^ith thit which you .ook along, vou have found the plice ; hui if the mark lies to th« right or left;, you must moTe your staff, and place it ac- ^" An offlsCt staff, divided into ten links or 6] feet, is ^ yerv useful instrument for laeasuf-ing off. sets and other jhort distances. , Ten ^ifrall arfows, or rods «»f sron or wx^o^, are used to mark the end of every chain's leagth in Pleasuring lines. PftOBLEM l.-To fihd JhVconteut ofa square piece of land Measure orfe bf the sides with the chain, which beins LHiTtiplied into itsfelf, gives the content «-eq«»rcHl' 'E7.ampl4 v. Wh(^t is- the tont«nt of a square |aidii| nhose side is 4 chains 5 liuks ? , % 4.05 3§2S 1600 •'4 .■*• 2^6100 40 »?,44000 5 It All. 1». 2r. 2^]>. *y4«. l80 WJRVEYING. ' y^oB. a.— Toifind the content of a rectangle, or long equare. iMuUiply the length by the breadth ; the product U the content. , ; i»^V , Example, There i8 a field A0 chains 54 ImVfl > length, and 7 chains 44 links in breadth— What is the area ? Ans. 12a. Ir. 20jp. Prob. 3.— To find the content of a trianjiular piece of ground. • • . .Chain aloor, the base : Find by the cross.staff, where the perpendicular fails, and measure its length j Thenmuiii'ly half the base into the perpendicular, for the content' or the whole base into the perpendicular^ and half the product is the answer. E;3tAMrLE. There is a triangular pic^c of land, whose base is 14 cluins, and the perpendicular 7 chams^lS links. Hequired the area. Ans. 6a. 3r. Iftp. 36. The area of a triangle may be found without th« help of a i>€rpendicular. Add the Vides of the triangle into One sum -from the half of this suni subtract each side respectitijly : Multiply these three ditferences and tb? half sum into one another :— The squ^e, root ^f the product is the area* Problem 4. » TO MEASURE OFFSETS. Let the following figure represent the side of a large Field beio£ a right lined offset. Required the content ? In order to measure these offsets— place yourself at A and fix upon a mark in the opposite -hedge at K— then measure the perpendicular A B— enter A in your field book, return to the point A and as you are chaining the base line A K, take up the several perpendiculars, R C, Q D, P E, OF, N G, M H, L I.— To find the true area of all theoffsets thus taken up, obscrvethe following -m I IVCJjCa* A»»ui».H'*/ ««ftW 19 U .«. ^^» ' "■•/ itermediate distance upon the base '^ Liae— ai^ iialf the product is the content. pendicttlars, by the i«1i^r>«>nf r\l*Tm tnalonftth or distance from the follow.a«-for ""'»"<;' ?;* Sm^liatc distance between '^e t-f^ -'^ '« ^ 1-- ,.*,dicnlttr»i» found by subtracting lO 40 (»*»'" ""^^ » chain., 40 UnkB counting from A ) fjom ^^ »;«^' » - inks, the remainder I chain 40 l.rtk, .» the h tormea.M distance -in like manner n.ay the rest bo found. Chains. Li»h. Vmunsiom. i-iains. LwKU S jNo. 4 (0 No. 5 -3 No. 6 I No. 7 g No. 8 I No. » a No, 1 No. 2-2 3 No. 3 a 10 14 19 20 24 28 ^2 ^O^'lsfperpeadicular" 0^20 2d i^crpendicuUr. o;20 2d do. ^.^Idl^d do. *^o><\lBjim ' f' ' ' 2»7'2 Sum. I:t2 ^mediate diatanec^)?^ I20 • 2176 260 19^>^^> !r80 '-^. . 1*^52:^76 «,1 1 20 in tlie same mariuer may the other aiicai he Ittuad, and the scf erai pfoducts will be as fv*liv»)ft » i 8,1 rm 12,eS60 7,5GOO 4,fi2(«X) 13,3221 8,7920 1,4336 4 . . „,■,/>?•* 3,06672 "t^omo Anii 3a. Sr. 3p» ft ir I" .L fl' ri H>ai Proii. 6.— To mcafiurc an Irrejsufir (IcM.— H^qutreJ r aI.- i>„ii t»„ ti.AA In Mfra* rdXttAn. &e, iioliAA.. Proii. o. — To mcafiurc an irrej^uiar nciu.—- ivr4uiir« ChecuQicut of ike foliowlni field, ia ncres, roods, & i»ol»j», You are supposed to enter the field kt C, and as yoa cbain from C to E take up the South «ff-««tts to the left hand-^Nfxt chain the second statioH from «^*<>*'*"^ take up the West olf.setts^ Chain «f^m F to G, taking up the North off-set-and then chain from G to C, tak ing up the last off.set- Lastly, measure the 1 rapeztt.m € It! f g' by chaining the baie Une C F,.& Uke the r.ghi hand off-sett X G, and the it'ft Y E, DIMENSIONS. SoHtIi of' Weit of-Hiit. North off-ietU East ofsetU •^ y^ I-., j.^.-^ I,it hnMi Utt hand Silts left Ujthand iaml, lit Sttifion. fd Station. Uji haAd l^Jt '«<*"<* «.08 4.46 .6.80 10:50 16.00 1,66 1,5« 0,60 1.80 160 0,20 1.66 1.66 47« 9,60 11.96 14.94 15.90 l.«0 0.00 1.60 1.14 1,90 0,00 Content 3d Station, 1,*4 1.44 $.54 0,— 10,80 3,32 15.30 3^54 18.40 3,66 19,90 0,— Content 4«fc Station. t,7t 1.86 400 1,10 6.70 «.00 8.?0 2,00 11,32 0,^ 13,40 0, Content Trapetiufn, 8.80 10.?6n » 15,30 U,70l.i t4.86 0, Cofitent 4566^ Perch^* 54 245 3-4p«rc/i. 6Sf5\ptrch€t. "Q* Prrchet, JO'O z.Tff l7.ftO 0,00 l9.«6 0,94 19.96 0,00 ^tm iU33-4|K^fftit «t?llVF,TlN«. lis I 246; 65 5j |«0)6153(38«. If. Stp. 4n». 480 1353 W80 40)73(1 40 S3 ^ u SomHlrars «ucli a figure as that abotc is compnfcrt Dy fiidma « mean breadth uad nieati len^ih. Bat however expcdiuoui this melhod may appear, it u always false , Ihoufth the error diminishes according to the number or breadths and lengths from which the measures are taken In this field the mean of fourlcnuths wab formed 2 1, 74 and the mean of G breadths 18,33. These t^o "umbcrs multir plied into each other, give an area oi 39a. 3r. l7p. which IS aiere than the trnth by la. Ir. 54p. ^„*.„„«4 The ffeneral flatness of this country and the continwed i^oods render the more elegant and scieutiftc methods of fur^ying in some degree useless. The townshipt arc commonly laid out in right lines, and if attention be paid to the compass the business of the sun eyor is rather a labor of body than of mind. Great care, however, should he taken of the Tariation of the iompass and of the back sight. When any minerals appear to disturb the ma net! stakes should be used. In fine the surrey or who is ambitious of co-i .-ctness, must never spare labor -- lie m^tst not go round large trees or other impediiueutsr ITfticU hfe fiuUa itt his way. if it fe« passible te nmoia ihQm \M4 A «ENERAL EXKRCISB* J GENERAL EXERClSSt »V1 1. HKQUTRED the ig* ofiU world at the time of tK* Flood from ihc 6lh Chapter «f Gciwsia and the 6th fciso of the 7lh Chapter— aUo the length of time from th6 Flood to the call of Ahraham, f^^ora the 10th and follow lug verses of the 11th Chapter and Ist verses of the I7u CJiapter ? Ans. 2047 years. *>. From the Creation to the Flood were 1G56 years— to the call of Abraham 4'16 years— to the departure of the Urailitcs 430 yeais— to the siege of Troy 307 ycarl —to the building of Solomon's Temple 180— to Homer's lime y7-~to (he eMablishment of the Spartan j?OTcrnment hy Lycur^iw ^3— to the tirst Olympiad 108— to tha buiUluigof Konie53-lo the Jewish captivity 147--ta the rolurn of the Jews 70— to the expulsion of (he Kings from Rome 27— to the bcoiuuing of the Frluponnebiua var78— to ihe burning of Home by the Gauls 41 — to the conquest of Tcrsia ky Akiauder 57-~to tht first l^unic nar C9— t.' the desirnction of Carthaj^u 118— to Ihe death of Juliui. Casar 101— to (he Christian Ara44— «ind from the Christian Aratothe p.esent time 180t Years. Hcquired the timt f^ooi the Creation to the prc- ttnt ? Ans 581 ^^ years. 3, The Marriners compass was invented in 1302 j JPrintin^ in 1440-^uul America was discovered in 1492. 31 ow many years m ere there between each of these dis, •overios? ^ An.. ^8, 62, IIK). 4. Ganpowder was invented in 1344- Ganpowor plot vas discovered in 1G05. How many years between, and bow many years are there since each o. these events i ^ ^ Ans, 2Gl, 464, «03. 6. If the human heart heat 70 times in a mhxute, aud each pulsation transmit 4ui. Avoirdupoise of bIo<*d and the whole blood be ,V part of the wei^^ht *>« .^^^ bucy. In what time will the blood of a man v^hose weight isl4U lbs. circurale throu»/h the heart } Ans. ^4 seconds. C. A General eommandina; an army of ipKi u.en, trJi^cU huitMJrgasud i by rccruUm^ .afterwards H iQiH ' X n timeoftKl e 6th fcrdo from thd ind follow of the I7u 47 years. 56 years— jparture of 307 ycarl to Huinor'i government 08— to th» ity 147— to tt (he Kingi luponnebiui) luls 41 — to to tht first a^u ll8~to vi\ Artt44-^ time ]80i tu the pre* il^ years. 1 iu 1302 J td in 1492. jf these dis« 62, lyo. upon or plot )elween, au(| events ? 464, «03. minute, aud of blottd and of the body, M tight is 140 4 seconds. tV c1 we And 4 of the remnlnder fell m btt('«. Hoir kV TZ^ ft' An^- »0,5(K)mcn. r . X »n^ , the pSrafli •♦«»'» 7U ,>.ces e*ch^ feet fi ioch^ net liuuute. Hequircd e i..>fe.n««t pet hourl Alts im 7f. 1}). ^vUi. g The Qttiek tl«e rotrehing U « pacei per second— r quired h w i -ny luibi tiiat is per hou ? Ans. 3m. Sf. 1 'p. • «»• A* df '■on* ^C earth measure* t4yi1 u.Jet ^ low long wo. » ..»J '«ke to sail round it at the ale of A .ailes au 6ou J 't met with uo iutirruption ( IC \ Own beloii fired at 13 wiles distance, the report b hea.d a minute after the fire ii seen, HiHjtiiml how far sound moves in a second ? Ans. I '44 leei. 11. A Baker purchasi.8 17qrs. of Wheat »^6^i/»•'- iing. which lie r.udH into 49cv.t. of flour, W»"« ;^ .^^ td illar Vt of < >*^*« -eipence of ^^^yiug it afc I I i*. fed.-^h.T bakes It into qua-om loaves of4i,lbs. tach, which he sells at I ijd. tM eM'^-^ice f ,»>«^»"R ^^ ^^^™ 68. 4d. pec cwi. 1 Uemaud ho^ much he looses or gaias ^u^rVwi , Ans. 6h. 3d. percwt. loft. 12 AOentlcmati ships to Jamaica, goods to thMU mount of ^'4708 l2« hil. which he covers by . surmg utt)l Guineah^freight46'3 47 lO^'.-his aKcnt. sells tht Goods at 106 per cent currency advance in the luvoice-- i:xoUan^e-4'4P per cent and reta.iiing 6 per cent comims. sion- he purchases rum at 2i. 3d. per ga Ion Jama^^^* «uriency-the freight cost him l^d. per gallon, Sted n^ *^hc sells it in London for 8s. 6d. per t;allou. What Mas liie state of the adventure? ^.niA ,, «hi ; , Ans. Clear gain £4016 3s. 8lu. ' 1lTli!erer annum ^( '24 yews purchase, th< re was a marsh intK^ urounds which ho got drained at jL 17 lOs. per acre, con- Lm^of.Syi acres-rents it at iJl lU. 3d. V^^J'J^y he builds iarre houses and fences to the value of ^.J78^ 18s. and he then r.uscs his rents J, soon atter, he so.d the wh >le fur -^5 years purchase. Hequircd hi. P*-^^^ /^"« ^ hat interest he had for his money, alter tiuishuv all Hi* imiirmemeRts^ while he retained the Ksute ? 14 s{ ^ ^ « ■? .£-. ^ ^ ^ V^.K.% V^. V IMAGE EVALUATrON TEST TARGET (MT-S) y A // ^'^ FHotographic ^Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 1458? (716) 872-4903 5 m A G&NBRAL BXPHCl^l. - • f 14. A Gciitlewao purchases «7689 acr^p of Laiwl f(f^ J dollar \wf acres, and kept »* IT years— li# tkim selb f trams, cuittaiwng 208 acris^ f»ch, at t^ cMlwf per aew-, twoyiars afUT ho s^td the re»t at 21 dollars. He might h^Te l^«it Qut hi« mofiejr »t^ per c^. ii«^uip«d wUc^ mould hjtrc prodwced th^ uwt© prafiti J^CMit iflaid OiiUt Interest i^4871 5«. 7dr Gaitted by s^Min^ Ldod d^ll 93 1 1 89. Q^^ 1^. A country M«rc^it goes to MoAtrefti on (irSd •# Jiin«» 1799, and pujrdui8e« jfilOOa wotlli ol (^>i»d8, ai 13 momhs credit-M>ii the 3d July, hetemitr ^i56 in good bilh -oiithe^ofAfiril k« sends 5| tons Potftslr ■worth' je55 per toa--on tb« ^th Jwit fav^Mfnds 94 barrels of floiir at 10 dollars per kkrrel and orders Goods to ihv am^ont of j£980^on September I8tb, he remks £m% in money and furs to the amount of j^lda^-^-on April 7th* 180. , he sends 317 btvrels flaurnN^rtb^S^doliars^^'pei' bar*^ rel and itt July he orders k fresh assortment of Goods tO' thife araoun4 of c! 17«5 wblirb wefe seot bim i^4y mhy on l^th Octobtr, he sends t3 tons Potash woriildf4# per foii;j--onApril9t*>, I80a, the MoatreftI Merchant maket up hfs account. Eeq4iired how it 8tood> giring^tbe conn. tryMerchunt Credit for bis remittances at^ per centy. " •'iwglng him 5 per cent upon the l^aiance against him I Ans. Due hi» Creditor j^l dT3 1 8s, 4|di Iff* A Mercbaik pn rthases^ j63768 #ortb^ of n heat at 4s. 9d. per Caoadimi niinot and Manufeetures it Intd flour at the rate of !^ Winchester buebels for erery barrel of flour, containing Icwti 3^rs.— piice of barrel and pKclcing is. 34-.-^^^^ fto^ir r«iiiiafntQg » months* on hand »pon iospeei^on.^ was sour an& sold for ^ dollars per barrel, at Quebec— the remainder n^AS exchanged for Spi- rits at 4«. per gallon,. 11 galione for 1 barrel offlUur^ tbe spirits remained on hand one year and^' tiieff soldal 6s. 6d. I dea>anu what the Merchant gained by tho transaction I Atts. ^d089 1 1 s. 1 1 4d. caini 17. A Merchant purchased 81 tons of Potash a|^r 1»8. €d. with the riew of shipping it to London, but' Sliding the Market low, he kept it in bis ware-house 1 81 senilis -at lf>r^^h.h» £tlt« Ili«rkel i>ric© was slill low— H ua« sold for Imb Linen at »». 9il.— Check 2i. 7d, a>»ii broad Cloth I5«* 7d. aleath, J thcFt. Th^ cs|«jncc of SKiiding th« ashes to London wa« ;CtS 108. jier ton »ii4 ti P«' c««t is [md for fion.*«;s8iorf *-the goods arrtfed in Monirea! flf n3(>!Hh<» afar th« »hip- ment of the PotHbh and it was 10 months before tlitf Linen, check, and broad Cloth were s^ldy the prices bchi^ for the linen ^s. 2d. check 4s. 3d. an* broad cloth 18»4 4d. — the ex pence of fright out Oforn London and attend! ance was 5 per com* What was Nie lo8« or gain in thgf whole ? Ans. pain ^48^ l Is. 2|d. la A GentleiikanM^ecjuiret hts ai^nt in London ta pur. chase him g78r Oid^ *« * * BILL S^.NT home; CoENWAtL^ 1st Jamiaty, fochtwtgc for £47G8> Sterlings iit Seventy thrfee ^y« sfght of this ray first of Ex*» ehange (second, third and fourth of thfe me tenor anrf date unpaid) Bease to pay to Jas. Brown, or Order, ih^ turn of four thousand, seren hundredy and sixty eight pounds Sterling, value receired J and plafce it to my ac* Compt without further adr ice fromy Sir, your obedient Serrent,- U ' %^ ADAMSMITm Mdwrl. Frasers & fco. tonlofi* • • • « 10. A Nobleman pnrchases a tract of land in Canada of 80,000 acres, at 1 dollar per acre, and brings out at colony Of bi families ; each family areraiin^ b persons, at the expense of 4^9 12 6 each person -~I4e engages to ffiafe i^hh nf the head* of the fannly 60 acres nu cleared Wirti »t lhd^ettd*# 5 -fms^f ^ix^^^mH 4iwi^' to<^ ««^ wm^i 16» GENERAL EXERCIsTE Jamcly east, him ^37 JS 9 per ,.n„m. They lettf. bo.e lt»a«^ntJfv . f » !'»/» 4.437 per ...num. We»ui). ik \^ q«..ntif| of Wool lo mcrea-.o I every vtar cluruiir the r oriRrtial c„,t and ^?a per «.,„un, ...ore. K*auiroS an it J •^"*' ■^169« 10 fi Jolt 20. A London AldermM left a l^^acy of jfilOOwOOo' t« be divided among hi, three .on., in the p'ropoTt o,?^ u .'.* ? "; ?.'' i^'" ^— •"" t;- baTing died, it i. rtauir! rJ/^lr^t^Vrr-" "--"A.^-Sb. .id whS Ans, A.'s sharo^57l42 17 1§ 1 ^1. A gentleman wishing (o make a fish- pond elact^r ^6 perches in diameter and 9J fevt deep. Hequired h. number of cubUal feet of earth throwd out, and whaJ quantity of «round ji took up. \ ^ f Ans 2631665 ^t68 cubical feet, & nearly Ca. ir. 7p. f*- .V« "t^r (jraufecs discharges into the Sea 400 Ooo »«b.cal fe«t o water per s.cond, in the rainy season, X2 continues during i of the y.ar, and 80,000 f^t per sec- ond during the r.ma,nd >oldiei> beso placerf that the nujnhcr infill k SENEGAL EXERCrsft fi» * HI. let SfiOOiatdiers be drawn up hi the form btu |t|uare, so that the distance in file may be 7 feet and iit rank 3 feet, lietiuired how many men form the side of the square. • Antf. 9^4* *" ^^^^ ^ ^^4" i^V^'^* '^6. Let 8450 men be drawn hi an oblong square, th* Qne side of which shall be double the other. .- , A n3. 130 in rank and 65 in file. ' ar. T.aW out on musHn ^600 ; but ending .J damaged, I wai ualigcd to 9eil it at ds. per ^ard^ and by su doing, lost jf 50 —At what rate per dt must 1 soU the undama. ged^ part to clear £5i)on the whoie ? Ans* Us. 7?d. 28, The amount of a sum of money which hadbeeii^ put out to interest is Jt' 100, aud the prmclpal is just ST times as rorch as the interest. What is the principal I ^ i»* Ans. j£87 lOs. ?9. A person dying worth ^€5460, left his wife witL •hild, to whom he beqweafhed, if she had a son, f of hit estate, and the ^i'st to hJi son— bnt if she hiid a danghter I to herself and ^ ta h: dauii^hter^Now it happened that •he had both a son and a daughter. How must th^ estaKf he divided to answer the father^s intentions I Ao% The daughter tets £780— the son £3X30 > ^ Tlw mother 4^1 560.t -f 30. A general drawteg up Ws army in square battle^ inds he has 284 soldiers o?>er ; b*U; inereasing ; each side by one soldier, he wants 2$ to fill up the square. Re- quired the number ot soldiers in the army. Aos. 24000. 31; Suppose the sea allowance for the common mon ta be 5ib. of beef tind 3lb. of buiscuit a day for a mess of 4 people, and that the price of the beof is 2|d. per pound and of brmd l^d.-^ndw if tha ship's company be such that the meat th*»y eat cost J^ guineas per day, what must Ihey pay fof their bread i>er week ? Aus. *6'2S 4. 32. A person paved a ^jourt^yard 42ft. 9in. in fronlk find 68 feet 6 inches in depth, and in this he laid a foot- path the depth of the court 5ft. 6in. in breadth— the foot path was laid of tine stonj; at 3s. Od. per yard, and thf rest with pebbles at Ss. per yard What will the whole sametta ? Ans, £4Q 17 h Id, *«• A «ENE11AL EXBR€fSR i^^a'iu^tal'T * "^""" * ^^ " «"^'. .hare, and « bay ^ A"s. A bajr'8 shareXl 12 ^id. i^ ; ^, ,7 gjd .-> . a wooiaii'ii ; ^3 ^ 7 u «y a .^».:.-^** > J?«»mg the dwtauoj to b« 95 injiliooa of milei. ^ 35. What is the ralia of the felc^il/ofXht^l^lf^of iinuter? ^^ fc»***si"g fi-am the liii.. t« the earth m 74 ea th measured on the parallel of latitarfe is about 16550 uirii T ." '^' '*''^ *"'■'*• '**»"** ''^ 2^ ^*>»*r« 66 tnin. ^^y ^u T "™ '''"*^*' ****^ A»»* 640m. •i,rr;.;J ^*"'^^^^*'"**^»''^*^> ana attraction are re. fJ^l^fu^ P'*P<^rtu,nal to the sqaaret of their dktancet xrcwi the centre wJience they are propagated. Su|)po8yigibedistaiiceofthe fttw-rrom the earth 9$ fcTrl?!^.!! *"u'^^'''^"'^*^"«''«* ''^^ d"»*nc« from *im another body must be traced 10 as to reeeire li^ht •nd heat quaUruijle ta that of ibft earth, * ,. •- ;. . Ana. 47i millions of milet, «i* If the mean distance of the sua from us be 10ft of Its diamitters ; how much hotter is it . the surface ef the #an fhan under our equator ? Am. 11236 times hotter. 3V. iiu(>pose the piaiiet Mcrciiry to be 37 millions of ■Mies digtaat from the sun— Venns 68 mitlions^the Ear4li 95 millions— Mars 144 millions-- Jupiter 49a millioBs— Saturn 900 miliionr-Georgiam Sidus iSOO millions.-^ Kequued the Sun's heat, liuht, and attraction on each of W&9 bodieft-adroittiiig the earth to hare lOOparts—thett Mercury 66S Jupiter 3,7 Venus 101 Saturn 1,1 ^ «-, ^'ars 43 Geo. Sidus OjS'^d 4a. There are 2 columnsin the rains of Persepolig left ^andins upright^ the^oue is 64 fe^ sh^vp ihs i^J^r ^ftA P^Qth^t 50— III a right, fine bttweea ibm m»4$-0 A CRNC^AL mCl^tlCISR. tvlkiilt RMinrstalu*, the head ^ ^hldi is 97 fctt from orti6n of their sur. laces and also of their solidities^ supposing them both Globular as they are yery nearly. . C TlieSurfacca are as 13^ to I neatly, ' Ani. I ^.^^ SoKdities as 49^ to I nearly, < 45. The battering ram of Vespasian weighed 11 J,000 pounds; and was mo red with such velosity at to pass through 20 feet in a second c^time, ivhich Was found stif. icient to demolish the walls bf Jerusalem. Required what Tcloeity giren to a cannon ball of 3%ibs. would pro* duce an equal effect^ Ans. 62600 feet 46. What weight win a mari be able to raise who pres* ses with the force of n hundred and a half on the end of an equipoised hand&r;i'Le 100 inches lon^, nieeting with a conventeot prop 7 J inches from the lower end of the Ma* chine? Ans. ^072lbs. 47. A weight of ijlb. laid on the shouldersr of a man is no greater burden to bini than its absolute weight or ^4 Otiuct:», what uiiTercnct; wiii he feci between tne 9aiu If ei^ht applied near his elbow «t 13 laches from the shouk A GENERAL EXERCISE ^cr, and iha palm of his hand 28 inches from the saMCkf- »nd how much more must his miiscU-s thtm draw to 8up«i port k at ri^>ht anglc8| (hat i.*i having his arm stretched right out ? Ans* 24il)s. Aroirdupoisc. . 48,. Two Porters carrying h burihiMi of ^OOlbs. hang tipon a pole 4 feet long, the ends of which rest on their •hoiilders — one of them bcinj; « cunning roguo, pushed the weight 6 inches nearer his companion than himself. Jlow much let»s the weijght did he cArry ? Ans. fiOIb. less, 49. Being ordered one ifay to observe how far a batte« ry of cannon was from rae, 1 counted by my watch 17 seconds between the time of seeing the Hash aid hearing the report. What was the distai^ce supposing sound to BiOTO 1 142 feet in a second of time ? Ans. 3 milt ,, f JJJ, 50.. A body weighing 201b. is impelled by such a lorce «8 to send it through icX) feet in a second. With what ▼elosity then would a body of 8lb. weight move if it "Here impelled by the same force ? Ans. 250 lb. 61. A general has an army of SCOOO men» which he Irishes to form into an equilateral triangle. Required the number of men forming the side of the triangle and the liumber forming the perpendicular. Ans. Side iJ88,337 :»' Perpcn. 249,7075. '■} 62. What is the circumference of SatiTro, supposing his diameter 76042 miles ? Here we multiply the diame« ler by 3,1416 and ihe product is the circumference. w*, w; Ans. 248318,3472. {^'53. What is the luperficial content in square miles, cm . hci^urfaoc of Saturn ? Here we multiply the circum. ference by the diameter or the square of the diameter J)y 3,1416. Ans. 1962748^589,3721 miles. 64. What is the solid content of Saturn in miles f— ilMuifipIy the superficial content by J^ of the diameter, or the square of the .diameter by | of the circumference, or the cube of the diameter by ,5236- the product Is th« toUdity. Ans. 253552607187792,6252 miles* 1 3 4 6 6 7 8 9 Mi U dpi 2,f 3,C 4,1 5,1 6,^ 7,< 8,J IO,J 1 1 ,^ 12,1 12 13 14 15 10 14, 16,1 !7,< 18, 'iO, ^^ 23, 19126, 17 18 20 26, 2l;28, 22 30, 23:^2^ 24 34< 25 36; 26,38, 2740. 28 29 30 42, 45 47 K-^ V to 8Up«i stretched u poise* [i8. hang on their , pushed I himself. iOib. less* r a batte* watch 17 I hearing sound to ", fiji. h a lorce ith what ove if it J50 ib. which he [111 red the and tho 8,337. \ '075. j usioif hii t diame* lice. ,3475. Ofiiies, OM ! circum. diaii-eter miles, jiilcs f— neter, or rence, or zi h tb« mile8# f ABLE§, ^W TABLES OF ANNUITIES. TABLE HI. TBI AMOUHT OF if I ANNUITY COMPOUND INTlllESl. 1 per cfnt. 8 ptr rmt frs. Sptrcent. 1 1,000000 2 2,0300(X) 3 3,090900 4 4,183627 6 5,309136 6 6,468109 7 7,66'2462 8 8,89-2336 9 10,159106 10 11,463879 11 12,807796 12 14,192029 13 15,617790 14 '7,086324 15 18,598913 lG'iO,156K81 17^1,761587 18 23,414435 1925,1 ir>868 2026,870374 , 2ll28,676485 4 per cent, 1 ,000000 2,01(X)00 v), 121600 4,246464 5,4irivi22 6,632,3227l.lj73,6397f)h 66,438847i79j058186 E i3,249< 8,6761 71.4838 80,6970 87,34^5 94j4007 73,1059 79.9544 S7,3507 95,3388 103,965 113,283 l^J TABLKS OF ANNUITIKS^. T A n LE IV. ratiENT TALUE or 4^1 ANNUITY COA(|>OUIfD.Ilf|r«R|k»m; I 4 6 6 7 10 TT 2,8'iHfin 4,ri7«;ii7 6,|l7JPi 7,01 U60v' 7,78<)lOi) 4 />rr rrti^ 2,775091 .'3,6^1)886 4,451822 6^2 42U7 65<>02()55 «, 732745 7,435331 8, 1 1 0896 5 pfr cent, 0,1152381 1,859410 2,7232 18 3,5i:)i>51 4,3-29477 5,M75f5*i2 5,786 J 73 6,^103213 7,107822 7,721785 6 ;>«r owf. 7 pfteent. fl ^wr 12 1^ It 1«7 18 W 20 l>,2;ri(j24 9,954(XU 10,634955 1 1 ,29L»U73 11,937935 12,561102 3,166111? 13,753513 U,S23799 U,877*7p 0,043396 1 ,833393 2,673012 3,465106 4,212301 4,91732^ 5,582382 6,20979) 6,801092 7,360r.S7 21 15,115024 S; |5,93G917 2') 16,443^)0^ . 24 16,935542 ',^5 17,4131.18 26 17,876843 27 18,327032 28 18,764108 29 19,188455 3cll^/>0044i 8,70(U70 9,38^K)73 9,1)856-17 IO,5631t2 11,118387 J 1,652295 12,165668 12,669290 13,133939 13,590325 0,9315 0,lj'2jj l,8(*8(; 2,5241 3,3872 4^1001 4,7665 6,389C 6,9712 1 4,0261 5fJ ! 4, 4511.^ 14,856841 15,246962 1 15,622(t79 I 15,082768 1 16,329584 1 16,663062 I 16,9837-131 I7^292032ij 8,306414l 8,863252 9*393573 9,898641 0,379658 0,837770 I ,^274066 1 ,689587 2,08531 1 2,46221( " ■ • 2,82115.^ 3,.lf,J0^)3 3,4K8574 3,798642 4,093945 4,375I«5 4,643034 4,898127 5,141074 5,372451 6,5152, 6,24( 7,0235 1 78i 2,. 57/5 3,3I^( 4,6>J 5,2061 a,74f>l ^6,7H( 7,8808751 7,49^6 '7,I3« 8,38.384 4 7,94'.fl; 7,^Si 8.852683 8,3576' 7,l-(d 9,294984 8,7454 8,244J 9,712249 9,1079 0, 105805 9,4 466 0,477260 9,7632 0,827604 10,0.1)! 1,158117,10,335 11,469921 10,594 11,761077*10,585 I2,()4l582jn,0m (2,30337911,272 2,.550358 2,783356 3,0(^3166' 3,2^^10534 3,406164 3,590721 3,764831 1 » ,469 ll,(i5^ ii,8':5 1 1 ,986 12,137 12,277 12^409 8,55J 8,851 9,rii 9,S7!l 9,603^ 9,Si)t| I0,0lfi 10,200 10,371 10,5':8' 10,674 J I0,8()fl! JO,93« 11,015 Il,i:8. 11,;^57 T\nLBs OF riionAninTiKs of life. 105 T A li L 1: / '. . rnOMAUII ItlLH 01^ LlfC AT I.ONDOPf. m^f. lir'mL'. ttie. ac*. Imna. tlw. our. hiiH^. i/ii-. of f . //» lug. rfk. u It It 15 16 17 IB 19 no UMIO 680 .SI 7 496 46V> 4^« 440 4:W) 4t'i 41.'i 410 40.'> 400 391) .S8> 3H0 37.5 370 .1(J.5 .0 l.>.l jl «7 17 It 10 «l .N 1 ."^ ''I SiAl \ 5 3.*9 S.i.1 tfi) I a.'7 6 87 I 3i^ I t» 'JH .Sl^ 7 19 .10 31 3^ 3:i 34 3> 36 37 3H 39 54 )« 301 1194 '4fU7 VUO «73 V.»9 «37 4< 4J 41 4> 4(i I 47 4a 49 60 i'.»9 19'3 IH.^ , 7 I7tt 171 t »9 40 I «^9 8 3oo 1 51 41 ' «'^2 i a .SI I lIH 147 141 i:i.'> l«9 117 lit 107 10« 64 .5^ .56 .57 SB 69 (iO CI 6/ O.J I 87 . age. living 9766 HO6 8(i60 7283 67Ui 6446 1367 336 h'7 9 10 11 12 13 14 6ii49 ' 184 6066 140 , 69*6 Ilo 6815 10 6735 60 .S675 /.i 6623 60 6673 60 ' 6VAS 60 50 ' <4 «5 «6 i!7 !t8 «9 30 31 S« 33 75 483^ 4760 408,5 4olO 4636 .1460 43H;> 4310 \ 76 75 76 76 16* 17 18 19 20 »»t 6423 6.i73 6320 6-J6i 6199 61.3i 4986 i3 ! 4'^iU 60 53 68 63 67 It 75 76 76 4^36 4160 4085 4010 3»^36 3860 .S78,> 3710 76 76 76 36 ^6 37 38 39 40 4[ 42 43 44 ! :S'i'l6 4> j 3248 j 7 a 4f^ 47 49 60 61 612 i^936 I 79 2867 bl W776 8« 26V4 ' 8« 63 i;(» i 2 :»4 : i?.)30 6A I «448 66 ! $366 67 I $284 3669 348'^ 34(>4 75 76 76 77 78 317U ! 78 3092 ( 7b 30U I 7tt 68 69 60 61 62 63 \ ij4 66 (> 1472 I39li 1312 VVoi 1162 1072 992 82 82 82 82 82 82 8$ 82 82 81 8! 80 80 CO 80 80 80 80 80 80 80 74 75 76 77 78 79 80 81 82 83 84 86 86 87 88 89 90 91 92 94 96 96 912 83^ 75« 675 602 .534 469 406 .'i48 289 2»4 186 146 iU 83 62 46 34 i?4 16 rf/V. 80 m 7,1 ()B 6.11 63 60 57 65 48 41 34 28 21 la It 10 » 3 109 TAHLIvS OF UFF ANXUITirS. T A n L E VU, ▼ ALUI or AH ANMt/liY or £i ON A HI MOM t%rw.. eent. I «#M|. t J^ftf'l /IJ<» fM'f /Htf' ' V"' •/•"» kine at .1 ^i-r r/u<#* ut 4 /»«ri jcAiOf 4* ^^#r { xkaie of ,\^r I'Uim u 1 4 ptr itia»r ut 5 emu '«• J Vurth- J.0H' I S'tt, Ik- hm \ \»rlh\ \l cetti. I I- VHt. utn. I i8,H J u //»/>!. (^o/t, . wn/'f. «4«»M. jaiw^^.i 10.731 I 10 J 1 12 >3 M ».5 »7 iH i() 21 9^ 30 '7' 17.4; 7' '7' 168 16.5 16,3 • 6,1 59 .56 15-4 '5i 18,3 t8, >,2 S.B 1 5' «7 2 r 4, < '6.04 t7.oiji4.t15. 17 •7-6^'M.3'5.a3l '"^3 '4 aiS.^M >7 6«jl4,3*5 14 '7'39,M».U5 04 '7-''5H4.^ 14 91' 7.«o,i4,i i4t d '^'95>40i4,7' ' 5.79 1;,9 14.59 '5'6/;i3 7;,4,46 6,46 •5 3i;i3'4 i3'5 I", I 8h6 7.' 3' 2 MjO •"•031310 i4 7|i5'9i,i2,9 i4>5 14.3^ 14)^' 1 4' •• ' i-^.oi 34 35 3< 38 39 17 08 ^7«- 7'^M .7,^9 »7- i5,o|ib,92 ,4 8;i6,7 H'6'6,54 i4 4'^3i |4i2l 6,14 ,4 i|'5'94 i3'9»5'7;:) i3.7|'5S2 i3i5!»5'3c i3'?|»5^"« ia.2ii4i8'i fill 4 m i4)* I :> '3 134 I 3'^ ,29 ia>7 12.3 12.1 ii'9 1 1- 11)5 ! 20 II .8 •»»7 1383 i3'75 1 3- 66 i:i'5^ I--47 i' H 45 46 49 Cl ''!( »#!• J AW/'« /^M 1 N firth X ^o(i4t^j|n74 rtut, don '4i39i ^.6!n»93 3,69 I'fi I r,o io,H iOi7 »»9,«3''OJo.5 •«*>3'95«o.4 I I, r 13,091013 »4 13 4V,»oti >.aiJ»i8 9.9 13,0a io,c ta .8 a, 66 »»»47 I a, 09 11,89 14,68 «l.47 4 lOt 1 1 .«6 ,06 io||i,98 •7 ii>67 0,5 1 1,41 o ,3.18 i3»o7 i5'8o,i2,7 iS.68i2,(3 i5»56'^«1 i5'44lii»3 «53i i5i8 5 05 .4 Q« /4 78 14,64 »4,50 •4^35 - 4 2') • 4,04 i:?,88 o<»«^»32 .a 1 U> : 65^ 8,oj 8,3c 7>yc 7.6'8 737 0.- 67 7> 68. 7.4 69 7,1 ;o 69 7» 6.7 72 6 6 73 6.2 74 5-9 I75 S.^ t 6 5»79 810,83 91610164 9»4 »0i4'' 9 3 10. 2o 9' * 9*98 8,9 9,7 8<7 9,5 8,6 9.28 8,4i 9'°4 8,2 8( 8 t 8,i5 O' i:J 7'9 7'7 75 7-3 7'' 69 6.7 6,3 5^9 5i4 io»c 9,H i^,7 90 9,4 91 3 I', II. '0.1 '-V 10 I 10, lO' 8,89 8,03 7.76 7'49 8,9 8.8 8,t 8,5 8,4 8.2 8,1 8,0 7'9 7'7 7.^ 7>4 7.? 7.' ,ai 6 ''7 6.93 6,0 6,65 6,.] 6,361 6,y o.c 8: 6 10 5'79| S^» 5'2:'i' 6,4 4>^6, 5,2 9.' 7.J 77 ft,] ^^ 51 hi] I«f. ' Vf «i > » /•»!»* f>rr ifuuf ut )^ ttit. 'Mth r«»n- » Sd f>pt, tlon . J)^ |,02 10, S i',1 1,8^10,1 1 H.i ,fet>io,c ",4 »47 t)it) ",« ,38 9.^ 'M ,09 9'7 10,9 ,89 9-5 1* '",7 ,6S 9,4 J!) 6 .47 9.3 lo'l ,«6 9-' 1 10* ,06 9,0 lO,« ^.83 8,9 q,9 ).64 8.8 9.1 ,4? 8,«» 9.5 i.2o 8,5 |,<)8 8,4 l'7:. 8. a 1 9.! |,5< 8.1 8] ;.28 8,0 86 1,04 7'9 8.1 l.Bc 7'J 8,1 t,i5 7.^ 7.> 1,B9 y^i 7-1 1,03 7.? 7.5 -,7^ 7.« ^'i f,49! ^'9 7.^ r.ai 6,7 6.1 >.93 ^^ 65 ^^5 6,.i 6j S3^ ! 6,. 6,0 ).c8 t),o si >»79 5t'> i-S i.>5i 536 5' ),23' 6h 4? b^^ * 5)2 i?' < o M H Agf*. n: ^ o >^ H »-^ < o D < > 10 36 40 4'> 50 (jU 66 70 76 H)7 cent. I «rMl. I «•»'«<• d,m. : mm. \t ith*' -f ^r'' 'J *'"-: .' **>'*P*"\ !3,oi i/ynn, f!ii'V,(.7 ri,7ls,Hiu, J^il,a() 1^,^.1 ii,:!.*'!!^. H 11,01 ii,«ri,o()lo, ^i\\,m \t,\t>\\0M^2M y, 7,11,30 i:«,63l0,«i'h2,l0' 0, l!lO,U'Z 11,70 0,6 10,0111,08 0,0 0,H'n,04! 8,1 lotll,7 I Mil, J 13,1 11,6 10,7 tn,st I6,7f) 15, m l4,eJH 8,6 7,8 6,0 6,1 6,3 10,05 8,05 7,7'i 6,36 4,00 7,8 7,^2 6,5 6,8 !I,3I 10,86 10,08 0,'i6 8,31 7,«2l 6,01 6,ll 4,72 8, 6 8, 1 7, C 7, 6, 6 4, 10,4* 0,00 0,*26 8,6f> 7,7^ 6,80 6,70 4,6'i 261-2,6 30 1 I ,y 36 ll,*2 40 10,4 16 46 0,6 60 ^.1 11,06* 11,68 11,32 16>l3,0l5,^3;r^,3|13,41|n,lO •2ull3,3 14,66 11,811^2,06,10, 6 L4,'23 11, "2 12,63^10, 1 13,73 10,6 I'^^iM 0, 6|n,0'2 l3,15'lO,Ull,70 0, OjlO,66 1'2,46, 0,Ul,'23| 8, 6 10,^21 11,60; 8, H 10,61 10, 80! 8,'i 0,87 y,86' 7,6 9,08 8,79 7,0 8,17 7,60] ^,4 7,13 6,0 6,'26, 5,7, 5,03 5,2 4,01! 5,0| 4,70 60 66J 7d 75I 8,0 8,^2 7,5 6,8 20 8, 7, 5 7, 6, 0; 6, 4 4, 8 9,ti<» 0,08 8,40 7,62 6,71 5,68 4,50 20!1'2,8|14, 13.11,3 26ll2,^13,74'lO,8 30'll,6| 1 3^^0 10,3 35'10/J.1*2774 0, 12,6 4 10, 1 II, '23 l'2,^23 9, 710,99 11,87 0, 2 10,71 11,45 8, 8 10,36 40lO,'2;t'2,Ky O,'2llO,0'2 8, 4 0,04 45, 9,Vll,37( 8,6:10,38 7, 50; 55 IbOi 7,4 8,8 8,1 3 1 0,5*2 8,0 0,63 7, 4 0,6'2 7,5 8,87 6, 8,60 6,0 8,00 6, 4 0,45 8,8# 8,^2 7,4G I,' ft p/tilf.. f 19S ) I h ^ la o o ti* Value nt 3 per Value, at A pn hb\ 0,7 20 70 6,0 cent. Lon- '. ^orth- i>N. '. Uttipi. 75 25111,8.13,38 30,1 1, 3; I "^j 97 7,14 0,15 Lfin- Um. '. 0,3 J,7 4,83; 5,(; I'afuc atojxr cent. L»n- : Xortk* (Ion. I ampt. nt. A'orth- ampt. 6,9^1 5, 9 6,5» 5,83 % 4 5,5.1 4,6!^) 4, 8| 4y\t 26 fa O 35 40 i5 50 55 ()0 r)6 70 75 JO J 5 U) 15 50 55 60 05 70 75 35 4(a 45 50 35 ' 160 05 10,7 10,0 9,4 8,7 8,0 30 6,6 5,9 5,( 12,46 11,85 11,16 10,36 9,48 10,5,11,94 10,1 11,6^2 9,6111,22 7,3 8,50 7,37 6,10 4,80 9,1' 8,5 7,9 7,4 6,8 6,2 5,0 4,9 10,73 10,16 9,49 8,77 7,91 0,92 5,78 4,59 9, 4;iO,7,0j7,02 5,9 6:j61|5,5'6,2l 5,4 5,77 5,1J5,30 l,8 4,46'4,6/4,'27 I Hi I I f I ■! Ill 458,3; 9,78 507,9j 9,20 507y6 557,2 60 6,7 656,2 7a6,5 76'4,« 556,9 666,5 65 «35'6,0 70 5,4 J75;v "l6©>, » 60^05,2 65 75;4,6 65M 70,4,9 ^^170 4,6 '75 4/2 7,4 8,99(5,7 7,1 8, 50 6,5 7,95 6,2 7^27 5 j8 6,455,4 5,46 5, ( 4,394,5 8,31 7,89- 6,09 5.r^ 4,21 8,7l6,8'8,08;6,27,5!i 8,156,57,59 6,61 5,58 4,47 6,07,10 6,1?6,9& 5,7*6,57 5,76,24 5,3 5,90 5,2 5,314,95,05 4,6 4,2814,414,1 1 6,27,18 5,7 6,74 7,095,9.6,065,56,27 6,33 5,0 5,99 5,2 5,67 5,15,13|4,8 4,89 4,54,1714,3.4,02- ^5,6;6,23 5,2 5,80 5,9/5,3 5,664,95,37 5,144,M,904,64,es 4,194,44,02 4,2 3,87 'Tj7^nT;2b^, 7 4,96 4,78|4'6'4,57:4,44,38 3,96j4;^3,8l4^3^ 4,26^4,44,09 3,60.4,0'3,47 75i75|3,8j 3, VI 13,7 3,02 4,2'3,y3 3,d3,3r>' ERRATA^ AS the DISTANCE of the Author rendered it impowf. Die for hioi to correct the Press, the number of Errata hufe been much increased : But he boues the foliowint iwt coutaina the most wateriah IN COMPOUND DIVISIOX. r«ge 49 Question 3, Divide ^17 3 by 6 « ^S 17 i» — — 12, For ^4 9 Head ^4. 19. — — 15, For 94Jb. Read 84lb. — — 19. For 6». ad. Read 6«. Sd. ^ *-" ^ — ^'^' ^0' o£iJ59 S 4 Read d'^bT t 4. I'age TiO, Qiwiilioti 3. For «47.5l2 Read 8467w lartJiings. _ — -* C.^'wdib. 6oz. IQdwt.readeib. 19o«.idwt. 5cffc Page 51, Question 8, For 51789 Read 5525 «crijple». — •— 17. For 7560 poles, Read, 6560. — — «5, For 9216 Read 9792. xage 5?, Question 1, For i743 Read 1733; — — 2, For 334656 Read 332784. — — 5, For 1569 19 Read 1069 19. P«ge 54,Question 11. For ^65 17 6 Rear} ^65 12 tf. SIMPLE PROPORTION. P*ge 64, Question 36» For l Re^d »— 4. — — 56, For lOib. clover-seed Read 10%^ COMPOUND PROBOKJION. Page 69. Questiou 7, For^l 6 9 Read ^l 16 9. — ~ 12, For 3 Read 8 davs. DISTRIBLilVE PROPORTION. Pag^ 70. For ^750 B.'s Mtock, Read ^.5()0. — Question !> For 897iJ() Rtad ^89784. — — 6. h'»\ui% dtn 10. Page 73, Question 4, For ^4 7 l-2d. Bead ^H 7 1-fl^ — — 11, For Answer Read 307. — — 14. For Answer Read dQ90 4. 74, Question 4. For Answer Read XM6 16. 77, Qaestiou 8* Read 552cwt. Oqrs. 21b. Answer. — -— 10, For 81b. tare Read IBib. 79, Question 17, Read 574>ds. 101, III liie Rule, For denominator Read denomiuation. 104, In tUe Note, For consists Read consist. 11 a, In the Table, For 7 1-2 Read 7. Page Page Page Page Page Page Page 183, QuesUon 11, Lost Isl lOd. .. •> sv iXVzii -jy re:stitiiiij^ uiruugU Loudoa* i^ APPENDIX,. PROBLEMS m CIiaONOLOGY. POPl^ Oregory in t He year IbWi reformed .th«f JuKa* Calenaar or Old Style, which had, heftjrc that time, bcenp «iii!d overall Kurave-AccordmR to J-u lias Caesar j the year coiwisted ol 365 days 6 hoiirs^ or ^\.^h days and a quarter, that is, three years of 366 day» each, and the fourth year of 306 days,— But as the mean tropical ye:ir consists only of 365 days^, 5 hours, 4& minutes and 67 seconds • an- error of 11 minutes 3 second* was |>roduccd every year -This amonnted io t«0 days form the time of the general council of Nice holdeu in the year 3^26 of the Christian TEra, to the year 1682^ Poi>e Gregory added these ten days, aid brought the account of tinreback to its proper day again— At the same time he appointed that every century after a day more should be added, making theyoarsof the complete Centwric* 16130, 1700, 180(^', V900 common' yea^s of 365- days each, instead of leap years of 36G days, which makes the mean Gregorian year 365 days, ^ hours, 45 minutes^, 36 seconds. . This new account or new style termed afte^ its reform, er, the Gregorian Calaflder, was not adopted in Great Britain tilt the^ yeaf 1752 when the Julian account had lost 1 1 days, and therefore the 3d of September was hi that year, by act o? Parliament, reckoned the Uth. Problem 1 .—To find when Leap Year happens, RULE. — Divido the given year by 4, if nothing re- Bafiin, it is leap year; ' PuoB. «.— To find the Golden number. RUL^'.— Add 1 to the given year and divide by 19,, the remainder is the Golddtin amber, if nothing remain^ then iQis the Golden number. What i» the Gold4« Duoibfei' ft^r -1809 • I • %l. 19)1810(95 iiiE^af^*^:'*^ 100 ^5 d Aes, HMhwIW.'!' If d ■> 900 APPENDIX. NoTi.— The Goldefi number or Luntr Cycle Is t pt* riod of 19 years, after which the changes of the moon re turn to the sane days as in tbo former 19 years, though not eiactly to the same hour.. Prob. 3. — To find the Epact, V: RULE. — Take 1 from the Golden number, multiply the remainder by 1 1 and divide the product by 30, the remainder is the Epact. The Golden number for 1809 is 5 — 1^»4X U 3044.1^ SO the remainder is 14*1116 E[)act. NoT£.~A4K Epact is the eicess of the solar year or months abovi' the Lunar year or month— T4ie annual Epact ordilfcience between the solar and Lunar year is about 11 days, for 2 years,^2 day. —for 3 years, SS days, or 3 days rejecting (he 30, for 4 years 14 days, &c. The eicess of the Solar above the Lunar month, wiiL. in common years,, be nearly as follows; Jan. Feb. March. April. May, June. July. Aug. S«pt. Oct. Nov. Dec. 0. 2. 0. 2. 2.. 4. 4I e. 7. 8. 10. 10. V- ^ IN LEAP YEAH Si Jan. Feb. March. April. May. J^ne. July. Aug. Sept. Oct. Nov. Dec. 0. 2. 1. 3. 3.. 6. 5. 7. 8. 9. 10. 11. PoRB. 4.— To iind the Moon's Age nearly. RULE —Add togetht;r the Epact of the year— the Epact of the month, and the day of the month-^the sum^ rciecting 30 if above it, i% the iVioun'8 age nearly. To Had the Moon's age on the I2th l'4;bfuaffy, ISQ.9^ 14 Epftct for the year. i'. 2 Number of the mootbi 12 Day of the month. 28 Moon's age, nearly. NoTB. — The day of the mean new moon ^being known^ add 7i days to it for the mean time of the . first quarter, 15 days for the mean time of full moon and 22| days for the 3d quarter. . Pros. h. — To find the Moon* a «outhIn£ nearlv. nr her comini^ to the MeriiUan. RULE. — Take ^ of her age for her Southing, nearly ■ — if less than 12jt is afternoon — if greater, the excess aboye 12 is the time after last midnight. aWei*!)i*. • *• FOa EXAMPLE. 12th Febrnary, 1809. The Mooii^s ajic is 2ax4««' 1% 4.5»22li. 24iii, — l2=fclOh, l'4iii. inorninr». pROB. 6— To find the Cycle of the Sun. Ry LK— Add 9 to the given year ; . divide the sum by fH and the remainder h the Cycle re«ittircd-~if nothii^ remain the Cycle i» 28. , What U the Solaif CyiU fay the preseat^ y,c^ IBOi)* ^,. Toiaod; Add p: *., 0».^li••^^••v'^-^'^. V-'' ? •i^li ' 168 . . , , • • * * r M Cycle dftTie fain. ^^^^^ T}« tiicdr tM« Cyde is totifiidtheSiuiday or WHAt^ #al Letter,. . r i Prob. 7— To find the year of mdiction. RULE.— Add 3 to the given year ; divide the sum b^ is and the remainder will W thte indictica— if noting r«f» Maitt^ U will be B. TijliBO^' ' ' Add 3 <*:^ fj* •' 80 ..t' , r. The Ti^dktt ' ^t Ro'iian IndicHon li 4 porioia of YS jears lis^ioisly'by thd lionwns pointing out th« )?eriod» I r 1 Prob.'sHTo find Ore JiiliahT^idd, UULB^— Adk 47I3 to th^ giycD yOar and «he sum Ibm tkfl JuHarr Period. v will to^ i APFENDTIK^ WhafyetroftlHj Julian Pfri^ tmwm tc the •eDt^car. F^ 05^2 lfOTE.-^The JhiTian Period is a UoToluHon of 7980 year« and Is proUucnl by the continual multiplication of m tl.rte Cyeles ; %\z, that of the Sun 28 ytars-that of tiio Moon 19 ^eATH and ti.at of the indiction i5 years. ii'{?i"*i;'^'~k^'** **"** ^^ Uumiuical or Sunday Letter. iiVLh.-^Biyide the CMitmiw.by. 4~sul)tract doubt* the remainder fron 6, and. then ada the oild numbet and I'H fo4irfh -difwb this. i>y 7-— subtract the remaiader irom 7 and the number left pojklits out the Letter. THUS FOR THE PUf SENT YEAR ISOQ. Difidc 18 ibe wntoiicsby 4.and 2 is left— (he doubk Of which 4 talcen. from 6 haves % to which add the odd years 9=11 .Jinihthcir 4th pari 'i^l^ diwded.by 7 Icavei « whifth subtracted from Zlca^4«.i-«A the Domini cU H'r-;7^ .^ B^> ^ 3, I> 4, E 5,^ F 6, G 7. ibeUominical Letter goeth backward ia a common year one heltcr j but in leap year two. ,. lKr.L ^ - 'PABLE h wrthe Golden numbers, Kpacts and 0omjaical Lettcw for the! yth Century. APIT.NDIX. ^03 k common TABLli If. J rER?ETU4t Al^f^NAC, inS:r^Vi October f a1 B ['(Hnf) iTTijrjX" XinjJSt rCi'D I E I F 1 e; AJ B February March Nof. | U E | F|JJ_|Al^J4 — ^Auril ^ luif—] 4„,dajr /„ll„w.„g„i„ b„ ,h« • •__ —••'•>« 11^ 30 O 25 lA 8«i}ilii;9t2 16 t«:il6 55 21 7,28 «li 7.28 14 8!^^ 15 30.«j| 9,5016 0[^5 F 1l4|l7 3«4'^o'3ilJtim'3117 18'4:«5.1i.3^18.»l.S«Jb 8«?9Ud. 1 4,U 16 2 23 17 3 18 4 «^i a I«3.119I« l3S4!l()| d • .^ ^^~ . 14 28 91 lA29"2«j 8 9JO«3' 9 10 ol 17 10 Thus for the y 1*1 f » ' i . .i< xr^p A fcETTEa OF CHEDIT. ;«-; *i« ^iH «V ' '• . i *'.• ?!^^*^^'' JanMary '24, 1809. •WM^h twq hundry^^fiud lifty pounds sterliog, in m^cIi s»ma as he shall havfJ oAf^a^s^ion for and require of yon, for "which UkjO his jreQ^ipt^ and draw upon inc as per ad,^fqt;. .,,^';.f.,f J am, Sir, Your most obt. servt.^ A. U, Mr. S^A^i^i^ liiEAffiE, Mercht, Loadon. . •hu jj««uifr«'>tfA; Bffjfc/ OF LADING. U'.^^'*v» ; •'***^ ^ Shlpp«[l,'by>he ^ace of God, in ^ood order and TLbhd'on^ in *nd Upon the ship called «(er J^awfoB, BiJiiit»r» far accanipt and ri»lc •f Mr. J[«ai#f ^S^ai^Mon, tnmtMnt, Moiilre*!^ Niito «Mliftl ami nuoi- IhtmJ ^ yet itiiii-;4tfi^ »ia. IV j BUO^AD CI.OTH, d aAS.fif« (No. I. 118 jwUi. Mil* iNif). 4. log No. 5. . IJ. 15 a a '4 * Gross i)i 3 l3 Tare io 6 -i^hwi 1 a 7 1 » l8 1 1 Jo la u 8^1 % 7 neat If 388..pe^c1rl, i; 55 I g Coet of wrapper and hoxat,, . ': 3 CnARGFS. ICi»tt(«itce on af l»ii> «t 3 per cent, 19 10 Vulicy 3s. ed. per cent, 1 13 London-, 20th March, 1809, ^-^ Irrors excepted, ALluXa. BliOWN. Jii 5-(y ^e^ 4yi40 642 4,0 r APFENDIX. AN ACCOUNT OF SALES. tii MoNTRiAt, l^ehOct. 1801. AV •fcoiint of tale of Ote b^lcs ini|H»rt6n<* broad clotk r^cii*»ul i»or r^« Mitrky Julm Krooiimn, iiia«»(cr, for tc •uuiit uf Juieph VVt;b»ter, merchant, Luodou Uli. nxLVM, |j£. S.D. No. 1- coiitaining I OR yarili, Nu. *i. — IIH — No. 3. — 81 — No. 4. — «0 — ^0, 5. — 10« — 511 yurcHat 10s. 0(1.421 CII4ROE». To freUht and avcra^o - ^11 !^ (To landing charge* 3.s.0d.p«rb.iio 17 To ware-house ront and deliv- ery, 69. 3d. per bale • 1113 To comiiiUs'oii at 6 per cent, 21 13 2i 35 ll» ro the nctt procccth carried to the cred- it of your accompi • PER CONTRA. Sold for ready money,. 45( Ca. 10^ 5 8t 72i 75 Oct. l.'No. I. lOgyarda. ^o.% 118 — 216 at 17s. lOi* Sold James Duncan, at one month, No. 3. 84 yardd. No. 4. 99 — 183at18^. 6d. M^^ ^^ Kept No. 5. 102 yds*, at l8s. Sd.Of.y^T^ »5 42i at ^ months • • • Montreal, 12th Oct. 1809. Errors excepted t PKTKR WILSON. ***^ APPEXDTX FORiM OF A BOND.. •i.'^^/^^y'*'" "''" ^^ ^^^''*' p»fsent«,.tiij,t r, A. B. ofeJtr fiJy of .Moiirfa',.Vleichanr, a.,i ht- Id .ndti.mly lH>uint:- yo ^. L of the «aine cify, Geiitlewan, in ibe sum df on« tnoiisai.d pounds ol ^ood and lanful money of the Pro- viiirc ol Louei C anada, f;(, hi» paid to the said C. K. or tohisctrrai., A'torM,^., Kxeoutors, Admini&*nifors, or Ai.sigfi.s ;. ,or ihe true payment thereof, I bind mywlf,. my llt».a«, Kxrcuturs aod Admini»r the same, then this obligatiou to be void or else td» wmaia in full force.. A, B LETTER OF ATTORNEV. KNOW alj men, hy these presents, that I Samuel Apne, of London, Merchant, for diyers good causes and considerations, have named, constituted and appointed, «tid by these presents, do name, constitute and appoint ay Frienil Allen Jameison, Esqr. of the city of Montre- al, in Lower Canada, my true and lawful Attorney, for we, in my name, and to my use, to ask, demand, recover and receive of A. B. of the said city of Montreal Mer-> ^'hant, the sum of to me due and owing by and from the said A. B. giving and hereby granting to my said Attorney, my full power and authority to take, pur- ine, and follow such legal courses for the recovery and obtaining of the said debt, as I myself might or could' do^ iT«r^ 1 persooaUy present^ and acquittance or other auJU J^rPFNDlX, %\l IciPfrt aiKc1t»r?e in my name, to m^kf an«1 «.Tf, ratif^in?, contirnun. anU nllowin. all and whatnoe.er ii.y Atto.nvjr shall lawfally do or cause to 1). done, in and abu.H tht rremiM^s by tittue of theHc- i.feM>nl...-In ^dRcw whereof 1 hare hereunto set my hand and h.^1 ihi, — day of— - in the forty eighth y.ar of thereun of our No-re.. • Lord Geor.e the Third, Fy the (.r.cc of r,od km^ of the British l«Ies and in the > ear of our Loid oimi thou, •flftnd ei^ht hundred ^ind eight. ARBITRATION BOND. rJt U a .er Canada, to b« paid to the said A. Z. uis Attor.i«v, txecut irs, or Ad. tninistrators. To which erery payment 7»> >*"'^ f*;^^" fully to be made I oblige my Hens, Evecurors and AcU «ii.,istr*tors, firmly by these present, sealed ^f my seal, ^yvd at -— ~ ua tlie — day of «n the year of 4)ur Lord — - and in the forty eighth year of the rc^ia of «ur Soteu'ign Lord VingGeorjie, Th« condition of this bond is such tliat if the aboTC bounden A. B. his heirs, Executorsand Amin.stratois do in all things well and truly stand to, obey, abide by, per- form, fulfil and keep the Award, order. Arbitrament and defermination of X. Y. and B.C. Arbitrators ind^tferent. U named and elected as well on the i>art and behalf of th€ above bonndcn A. B. as of the above named A. Z. to Arbitrate, award, order, Jud,>e, and aekrmine u. an« •uaccrning all aj:d aU »ann<;r of actiou and actions, 219 APPENDIX. ^«u«e Md causes of actions, suits, bill-;, bonds, snettlitlet. Judgments, Kxtcutions, KxttMjts, quarrels, controTcr! »Jts, trespasses, damages and demands whatsoever, at any time or times heretofore bad made, mo?(d, brought, corn! inenced, «ued, prosecuted, suftVrnI, contmiteed or de|)end- |ng by and betwaen (he said piHtie-, so as the ^aid award X»e made and given up in writing binder their hands and Bi^h to the fiaid parties, on or before the next ensu. ing the date above mentioned— then this obligation to b« 'toid or eiu* to ^ en^aiu in fuil force A. U. Sliljoed and Sealed in the perst ncc of, G. IX rOUMOFAN ARBITRATION BOND OR SUB- MISSION USED IN SCOTLAND. ^J^^ ^' «"^ B. by these presents, submit and refer to 1/. D. all controvercies, claims, and competition of right between us of and concerning and oblige us and our «uccvbSors to abide by their decree to Arbitrate to be therein promounced betwixt and the day of — next !• come under the penalty of besides performance. FORM OF AN UMPIRAGE OF AWARD. rO ail people to whom this present writing shall come, •we X. V. and H. C Arbitrators indifferently chosen be- tween A. B. iand A. Z. of . • • ., send greefing. Now knov ye that we the said X. Y. and B. C. having deliberately heard, considered, and understood the griefs, allegations, »nd proofs, of both the said parties ; and being willing, as much aj, in us lyelh, to set the said parties at unity and ijood accord*-do, by these presents, arbitrate, award, deem, Tiecree and jnd^e, that the said A. B. his executors, administrators, and assigns, do and shall well and truly r^y, vra vau.c ly ue paiu uDio me saia a. z,. nis execu- tors, administrators and assigns, the full sum of ....... ©f lawful money of the Province of Lower Gauada, oil AFPENOIX. 9IS Ae .... day of ...• ncxtcn.uinR«he«Jnte of these F«»- ;"(. • and that upon |,ayment thereof, thr. .aid A. B. tnd A. Z -hall, at iU »^n proper cost and charge. ^^Utbtribc, and a, .heir serc-ral '^'^^\^»'' ^'"^'^^^"^ «cl! to the other a general release ... »r,,,ng ^ »» -* - ters actions, suits, causes of actions, bonds, bills, C( to. ia^ls tm."ro»ersi^s and d.^nauds whatever, which euher "„? » en. hath, a.ay «r might have of and »«--'-' other by reason aforesaid, or means "f ""r •»» ''^';;^' ,', ,.r thine whatever, from the beginninu of the "<".'"' IhV ..Ty of . ..- last past, and in (he forty -c.ghlh lea.' ; ti^ ri of ourSovreign'l^ord King George .Vc. *T„ wi ness w'hereof, we have hcreanto s.t mrr hand. and seals, this i« the year of our Lord, one thou. •and cisht hiindted and eight. • V Sealed and Delivered in «ii» ». • preiicnce of L. S. 'G. r. GENERAL RELKASE. ^ ''Tli:as:s"'.nJ j::etr;m^' cti 'a'd J tt: ":::!' ^ of mC »; heirs,'*executors aod adu.i...tia. prtstiHs uu iw , / f.,rever uuit c aim unto A. ... »cal,the •••• dayt)f j &c. ot-S mX^li atJii -.t----- y the presence of i ill APPKXmt. rouM OP A ruoTKsr, wirii av accfptfd liiu. UK fc;xciiA.\(;K aanexkd; El MoNTMEAi.. ]7th Vn* I HAT to »!.,L''l'Th ''-^ '"''''!'. '"^ '''"""'y ""'y •>'" of c,than«, .led ad /If,. ?'•''""; ^■"*V«" "'Irs.he sum uf t»o hun. To V ?■;'" '" ";:' '"'''^'' ^"""' JA*' KS STEVEN, i o Air. CiitB t«AiG, Al.rchanl in London, nv.h- I u I Ac<, lite d- PET KH CRAIG. O.V .h„ day (he ihei*enty.{ont-.h of April. oneVho., .-. H,ht ...n.dred a.ul ei, l,< .. .,,e r v.« \f Da," d «»^cha»«., «l.cr.of a true copy is abo»e written • I fh "? "i'T' "' '"""*""' N-^'^y Public, by rovJ '„ ' said 1,11 ot mchangu „nfo Mr. Pgter Crais, of L,«,d,.n "'-■.•cha,„, ui,o.i Hhom the same i, dra«,t, Uo eu^lo I was answered by Mr. A. ti. his clerk,' that he 1. ■>Mhe c„..,u,.y a„d would re.«,n .o.mor ow, Vhenlhl ...d ,. , «„o,abeccrUinly pa.d ; which an.^cr no. b .* >n^ *a,.sfae,c„.^, therefore 1 the said notary, at the reqnett .fores4..l, have protected, and by these pres^-nts do so^mn airbl rV r r" •«^'-' "■« ^-a-rand acceptor of ,h; co.iiera, forexclian,e, re-exchange, and all cost,. char»e= rf' ..age,, a,,d interest sulf.red, for ,a«t of payment of «he (he said bill of exrhan.e. I'^J'O'-nt of Done and pro(t<8ted in London, in the presence of n» J^d M.,„ and John Davis, „f L„„'don, afo'esaidr^U-feL' xr ,,.^ ^AMKSTUIIAKR, Notary P„bi:r ^OTE.-.Hhe^e no Notary residcsUny suhsfanThI pL>rson of the pl^-e, in the prceucc of tvraLdibli J ( ■csstts may act as su^h. " * ^' FIM?, m''