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Les diagrammes suivants illustrent la mdthode. 1 2 3 1 22t 1 2 3 4 5 6 - r . &f I IS; I i r e (V r ^A TREATISE ON COilMIICIilL ARITIIIIIiTlC TO WHICH ARE ADDED PRACTICAL COURSES ON MENSURATION AND BOOK-KEEPING DESIGNED FOR HIGH SCHOOLS AND ACADEIvIIE: By The Christian Brothers. ]S 11/) t*. ■ f u I 'I. h i ( " 1 i '\ •I *) II \\. ii II I 1 _ Sanctioned by the Council of Public Instruction. MONTREAL 44 COTE STREET, 44. /n r Hi Entered, according to Actof the Parliament of Cann da, in the year one thousand eight hundred and seventy-two, by Ephrem Gagnon, in the office of the Minister oi Agriculture. #K*f ACE. Our o^ec , » ,*> ,5«*ii,,»i„„ „f ,y, ^„,.^ ., ^^ P y our H>g-h *<*«(;*, Ml Academies in the Dot^inio. ol Canada, w* » .Wxlerate-si.ed book containino ™'^".'7*'^f^-*^t*'»tf Poetical Tr,atiseson Com° av „g, th,.rel,y, fe. lfiw,:,.u«. ,ho expense of scve": within the read;. «l (fii,. Hi,|io„„j, ^i^^^^^ As decimals l^(sw "fa»d introduced in numeration Though we iiM,^ ^^i„ll f^ii^^^j ^^^ system, yet. the,^«,,Awl has not been neglected Amongst lis »wi»«* ^vficular features, this work otters the i«iw„to4 «**antage of proposing a far greater number ^1>««»,^, q„,,,i„„^ ,^^,„ ^° ^^ of he same s,«. ^ ^, ,,,„ „,„„,,^.„, ^^^^ ^^^^^ will hnd in It .Mil *^ W*,.„,a«„„s requisite to qualify them for the po^^l^W Ml accountants or business men Some pers<«M, f>f^ ^ ^^^ ^^^^ ^^^^^ pl^^ t' lii^i^ PREtfAOK. ^ merous examples oF application, having for principal object to render the pupil iamiliar with figures. Some desire the answers placed immediately after the examples, and others desire them omitted. Both methodshave their advantiig-es and their disadvantages. In order, therefore, that pupils may receive the advant- ages of both methods, the answers to nearly one third oithtj examples in this book are omitted. They will be found, together with clear solutions of ail the exam- ples, in a Key to this vvoik, prepared for the use ol teachers and private learners. jipal after Both iges raiit- :liird will sam- se ot CONTENTS. SIMPLE NUMBERS AND DECIMAIvS. Paob Definitioiii 9 SigM 10 licman Notation n Arabic Notation , 13 Numeriition Table ]4 Rule for Notation 14 Rule for Numeration ]5 Daoitnals jg Appiioiition of the Principles of Nu- meration 18 Addition 22 I Pa4IC. Subtraction 28 Multiplication 3fl Contractions in Multiplication 44 Division ^ .,,, 5(, Cnntraotions in Dirision sy lJ>ciiiiiil Currency 53 Hediifliion ^asure ^ ^ " "' I '^""•7«"' Long MeMurfc. „. 117 118 I J I ▼1 CONTENTS. FRACTIONS. PaOK. Definition!:, itce Sfi Reduction of Fractions 88 Addition of l?ra' ions 94 Snbtraotlon of Fractions 95 Multiplication of Fractions^ ........ 9fl Pa«r. Division of Fractions 9!» flrnatest Coni. Divisor of Fractions. 103 Lea.st Com. Multiple of Fractions.. 104 Practice by Aliquot Parta I0& Mipcellaneoas Probiama 19V DI'.NOMINATE NUMBERS. DeflnUions, Ac 113 Old Canadiftn Money 114 Knglisb Money 114 United Stntes Money 1 1 I French Money 11') Troy M'eight Jir) Apotboonries' Weifiht ll'i Avoirdupois' Weicjht ll'i Linear or Loni: Measure 117 Surveyors' Long Measure,.... ...., !!'■! Squfiro Measure IIS Surveyors' Square Measure 120 Cubic or Solid Measure 120 Liquid Measure 122 Dry Measure ....- 122 Maasureof Time 12:{ Circular Measure 124 Miscellaneous Tables 126 The Metric System of Vfe\ghtg aod Measures 126 Reduction of Compound Numbers.. 1.14 Reduction of the Old Canadian Cur- rency to the Decimal Currency.. 141 Re<]uotion of the Decimal Currency to the Old Canadiah Currency... 142 Addition of Compound Numbers... H'i Subtraction of Compound Numbers. 144 Multiplication of Comp. Numbers.. 14tl Multiplication of Compound Num- bers by Aliquot Part" 143 Division of Compound Numbers... 15.'< Longitude and Time 15& Duodecimals 150 Multiplication of Duodecimals 1S7 Division of Duodecimals.... 158 Miscellaneous Examples 169 RATIO, PROPORTION, AND PERCENTAGE. Ratio 1»3 Proportion 1''4 Simple Propiirtion , Ifi5 Compound Proportion 108 Percentage 171 Misc-llaiieous Examples in Per- centage 17.'> Bituplo Interest ~ 1^^ Partial Payments - IS4 Frobiems in Iirtofest 186 Promiscuous Examj los in Simple Interest '■''' Oompound Interast > 191 PromlMory w ♦!».••>»»......■..•.....»• ivw Forms of Notos...MM'«.c ~ ••••• IM Profit and Loss 1U7 Commission and Brokerage 200 Firo and Marino Insurance 20.'5 Assessment of Taxes 209 Custom-House Business 207 Discount and Present Worths 209 Bank Discount ^ 212 Promiscuous Examples in Disoount 21fi Stocks - 218 Partnership 223 i'^xohan^e 228 Foreign Exchange 230 Equation of Payments 233 'nvolufli KvnUith] Square f CuUd no ^rithmol Qnotnetri M«n«ur«r MiicolUn Account* Omtttl A DtCnitUnt il(M«uratl< ficos ., P"mifco«i •al Hurlii Mensaraiici ttcDfral l'r»i Doo«i,»: ^f.H^ Iwfru(;fion« liny Book,,,, Jnurnal .„., •^gw Forms of JJ.il Proceiis of C) Order of (;|,,i Pfsftfical Rx. D(ni«j,K B«'(| Dai, l>fw-l, JonrnaJ Trial Ualadci Statement Cash Bo-ilr ,„ Bill Book OofflBisaiofl H Piaa. «',» ictions. 103 ctioiu. 104 106 1«« btoaad 125 mbers.. IM an Cur- •rency« 141 irrency ■eney... 142 ibers... 142 iinberp. 144 mber?.. 14t( I Num- 143 ibcrs... 16."< 15ft 156 als 1S7 168 ■ •«M ••••■ JIVv 1«7 200 5 20;5 205 , 207 th 209 212 >i8oount 2](! 21S 223 228 230 233 ''ONTUNTS, MlSCELLANli;0US. .^"'^""'n ^fi*rnnU^"Z l.r 'nvolufion,,, ''''' R»''^iUrm,.J.'.',',",' 24i Squnri- Root'"'.'.','.* ^^' Co»(o Root,,.. "" •••••••••••• 242 245 24« **'•*«"•"«';•; K«'.mpi„..z'::::' 254 2«5 •••••■.• ..... 2fi; <■» m fcciilin- •'•■•oraiiwj of ci^Ji »r Surface*. 914 317 325 •'>27 PromJpcuoug Rxamplw in Circular f^urfaoos.,..,. _ Definitions of Solids •nstiration of .-otitis Miscellaneous I.:xa,npIe;i'n8orrd';; lablo of Chords... . SS4 3.37 34* 355 SM BOOK-KF^EPING. ;-«rtptiri, ,,r p,,„,, , y^ Oen?r«l I'nncif.j©. J ?""'-' '•:«r«r,-8r;T I .;;; j in»fru"UBLK KNTRr,— .srt in, 19 Coma»if.ioii ^»imUt^ Rem.irkf Journal Pay l;ook7.".*.;; " Trial Balance and I'nVenfory" Invoice B'lok Sale,'! Book ""[ Commigsion Sales Book Account Sales Check-Book ;,";;;; Receipts, Notes, ic".*.**',".'.".* Letter Book ~ Practical Exercises...;;;;"*;;; t)otjBLR i'-N7RY,— sbt'iv;;;;;; Remarks ""* Routine. ' Domestic Invoice Book!!;;;.;.;;;*;" Foreign Invoice Book... 8»lat Book.........^ """" "*"" u 51 M 5e n 05 «7 •» 11 U u 11 u 84 00 »• »1 93 M ^ •;•. Tin J0NTRNT8. Paok, <'n'h nook ,...„.. „ 104 U'll li.M lOS IrTPtit.iry 11 ok 110 Jcmal ni B i'»noo ^heot m Si>G',R Kntrt lift Rr-j-arkj I in bkj Bok 117 PiOR. Cash Book « V.'« UJ-or 121 Statement , 124 Chanoinq Sixqlk to D0CBf.K Ex- TIIY I2A l'rncti>:al Ezerci 131 COMMEiiClALAIIlTHMETIC J)EPINITIONS. *» 'ViS-^'^^J^*' i' *^' ««^«"o« of numbers. ?■ M ^"^.^ " *"""• °'' • "»"^'« thin- i..ci« of wt'e" ^"'"'^'y' •« *"^ ^"^^-^ *h'^t will acl.it of 6. JJ°o;berfl in general, are either abstract or concrete u aVpa'SSS!!.? r;:ru?r'?"„n' "^'^'->-™ ■ The, .r, diviJcd into IT.^iaLj*""'-^'"' •"""'J'^"^ «raa aeci„.U fraction., X'.^uZl'^Y.' ""'' "^ "'"<«' "^ >». Concrete Wumbers m .mmbo™ u^d .itk .■ »•» paruoular thiog or qatDtit, Tbu. J[^ «terM06 to 10 D1FINITI0N8. I I They are also subdivided into threo olassefl : poinds^^'"'' '''"'^' '^"**'"° ""^ «°bdivi8ion8, as «> yards, deven /fJ"i;//I''T"''V''^i:*''^*°°^'"P*"'*'^^'*^ ^'C''"*' subdivisions, as fioe dollars twenty Jive cents. =«""«, »s 3rd. And la.stly, those which contain decimal subdiviMong onJv ao twtntyfioe cents ($0.25). ^' *' O. A Simple Number is either hd abstract or a concrete number of but one denomination; as, two, m hats. 10. A Compound Number is a collection of concrete units whose subdivisions are not decimals, but represent several deno- mmations, taken collectively; as, «x pounds /our shillin-a nine pence, three ftctfivc inches, etc. "* 11 . A Power is the product arising from multiplying a num- ber or quar.tity by itself, or repeating it any number of times aa a tactor. .^ 12. A Root is a factor repeated to produce a power. 13. A Demonstration is the prooeeg of reasoning by whioi r truth or principle is established. 14. An Operation is the process of finding, from given auan. titles, others that are required. ^ 15. A Problem is a question requiring an operation. 16. A Rule is a direction for performing an operatioa. 17. Analysis, in Arithmetic, is the process of investigstiiu principles, and solving problems, independently of set rules! \H. The Principal or Fundamental Operations of Arith- metic arc, Notation and .Nuuieration, Addition, Subtraction Multiplication, and Division. ' SIGNS. 19. A Sign is a ^mbol employed to indicate the relations of numbers, or quantities, or operations to be performed upon them. (.) is the decimal sign indicating that the number after it is a oecimaL I lueaos dollar. ». ir*aiii«gimpI,auiBb«rt- 10. »fA«< ». aoompound nuiaberT-ll. WkM . r"--- — ■■•----- .•••'^- • — '<" 'r««« w a aemoasirauon T — 14. Wkai wotatiow. 'J'hns -h the sign oi addition, is renrt plu, be added to 8. tob;M!£Sd^rr^'^'--^-^«-Thus.8 11 7 siprnifips that 7 is to 7 signifies that 7 is ^4, „ „, i. , , - 1+,,^'^ x^ . f n: i;"- '-uf fi>niirf,^,b.fi)rctlio».i„Jir,rj I .! P«.n""I'««. ba« b»m mr- Thn,, [(8 XT) + U1 i T"^'i*''e°'««'l«<*cbrackeu. = 70; 70 +V= M-' "^ *'»»-'"8 X 7 -= »«; S6 + ll ..d u tdtifjr- ^'"'' ' = * ■"'•"• *« »'■» »f » •» 4, >»,".»..». IJ, M read, 6 l» '« 9 as 8 is to 12, NOTATION AND NUMERATION. e.p**. "b"""" " '"^ ■"^'"' -' '«^'"» ■""■"«™ when .ifhs^T™™""'' "' ''°""'°" •" '" «»'-"»" ""- "■• ««a« ROMAN NOTATION. nun.bers, viz : ' ""^''"^'^ *^''*'» °^P^*^1 !«"«" to ^express ^ ^ * t D M l^r., Un, fifty. u °^ , , "»• «>• hundred, hundred, thowand. r» IS HOTATION. I It will be seen from the following Table, that al! numbers may be expressed by the mo of these letters, cither by re|>etition8 or ooDioinatioris. U\ Eyery repefifion of n letter repeats if^ valne: thus II represents two; ITI, represents thrrr ; XX, (wentf/, etc. ' ' 2n(i. Wnen a letter of any value is placed after one of greater valud, it ad(I« its own value to the .greater; but when placed before, its value is to be subtracted ; thus, VII represents seoen ; XI represents eleven; while IX represents nine, or one les, thai ten ; jLL, forty, etc. 3rd. A bar or dash (-) placed over a letter, increases its value » thousand-fold; thus V denotes Jive thomami ; TV, four thou- $and; X, ten thotuand, eto. I II Ill IV , V , VI VII VIII.... IX X XI XII.... X II... XIV.... XV XVI. . XVII.. xvni. XIX.... XX XXL... XXII.. XXtll. XXIV. XXV... u (( i( (( (( li (( 18 Ono. Two. Three. Four, Five, Six. Seven. Eight. Nine, Ten, " Eleven. " Twelve. " Thirteen. " Fourteen. " Fifteen. " Sixteen. Seventeen, Eighteen. Nineteen. Twenty. Twenty -one. Twenty-two. Twenty-three. Twenty-four. Tweaty.five. WAMLM. XXVtl i, XXIX. " XXX .. ' XXXVI " XL •• XLIX •' L LX ' LXX .. ' LXXXT " XC. . XOIV c coc CD.... D DC... CM.... M MC... MD... MM... " MMM. - X - M « .'( >< >( It « etition8 or 1 thU8, II, to. of greater ica placed ints seoen ; I hat than 58 its value four thou- le. (1. red. cA id. i '.d. 1(1. [red. Ired. id. [ind. 1 1. Six. 2. Right. .^. Ten. ^- Thirteen. 6. Fifteen. "5. Seyenteea. 7. Nineteen. 8. Twentj-five NOTATION. BXBRCrSES IW ROMAN NOTATION. B«pre8. tf.e following nu.nhers by letterBt An». VI. 13 ajx. 9. Thirty. 10. Forty-^ix. 11. Fiflf-four. 12. Sixt>. 13. Sixty-eight. 1*- Righty-four. 15. iVinety-nirie. 18 ^ "J".'l""'*r^ ^''d nineteen. }8. Jight hundreA^' is called „, /I "^'^u""' '''"°*^ «^.^'"'fi^« /"9"-- Th 26 In ordt ? i T'' ^'"''^"^^ ^' '^"^ "^ value of its own Thus, the fir«^eZsen^Th.-^^u" ^^' P^''' '* ^'"''"P'^^ third,, the A.,./ X the fourth C *^^ r^"**' *^« ''"' '^ each succeeding. fiuVe to th«,jy/r'-^^^^^^^^ ^"^^ ^^^ o--'. the unit of which Trt^nfoM^hl . '""/'"^"^ *^ ^ distinct orde, the riaht. '^ '^^ ^''•"^ ''f » '^"it of the order f pen"druptV.!';,:ttL''irtr™^"'-'p''""^^^*^^ e^^- ^e 14 •nniKRAtioK. S'nr«!. ?nr/ ^T"*^ ^^ * ^"'" "««<^ inoorabin.tion with other fiK'ures and deKendin- upon the place the Qcmre oecutj^s ThI Cipher be,V3me8 significant when 'eonneoted with other ti^eu;s ollt by filhng a place which otherwise, would be vucan7(No 28) ^'^' hand^JrJn/l*^', '''I '"?P'' ^*'"« ^^ *•'« first. figure on the -eft iureofthrlrthn';;?' ^*r ^ "r^^^^ 'l^o»"and«f because iti.. andfts local valn^^" ' v^^'' """P *^ "*'"« ^•^' ^^« ^^ird H^ure i« 4, eirnple value of h/fiT-' ^°»"?.'' '? « «g»re of the 2nd o?d.r ; the NUMBRiTION TABLE. i «M '-S O H *> «t-i .2 3 g K 'si o 3 " c 2 c e o T a •^ o CE ~ s :=; S D « a o ^.2 45 ® o a « = a o o ^ 2 ° 0:3 a cs us O B 3 O cog 1 2 7, 8 9 4, 2 3 7, 8 6 7, 5 2 3, 6 7 a> «♦, <« fc> o c a ^-^ W'^ r-*" i=; ki « -= = 5 s a •- s,!' s^^ 5s^' s- •^i-f SsS ^ RULE FOR NOTATION. 28. To write in tigureg any number without difficulty of I"u;!t;on"iitn',the?i?L""S°'''l"'^^^^ *^« « '« *^« -der in the order of hund^s of iniS" i^f *''^^**"' k^^ thousands, the 6 places. Thus ^^'^'^ "^^ "'"'^ •«'^ P"* ciphers in the vacant 4 006 020 ftOO 1. 3. 3. 4. 6. 8. 1. 2. 3. 4. 5- 6. as. Wkt^i»tkaritU/m- U»**Jiamf = « a NITVKUriOIf. RULE FOB NUMERATION. »». To r^ad numbers represented by figures JJ'^tn at th. right hand, and point off Z 7' - of three placet each. The first .Cw ■ .; ^^'"''* *"'« P«^A thousands; the third, .£ lovs 1^/"/ "^.?"^"«' '^«^''«>»rf, mK TRILLIONS, &c. yA* w ^',; /t.lT'^' ^''^^^^-^^J '^« i5?*. The number 345 678 907 654 \7^ ""' '''"''fiacres. «n»aner: three hnndred ami fortvL f •,',' '""^ '■" 'he followmg r/S^T^* l[iilioi.«, nine hldre7a^7,,^"j^»«?,,«« ''""^''^d anf -d fi%-four thousand,, three hunl^f ^^rweSj-^'unl' '""'^^ EXERCISES IN NUMERATION OF SIMPLE NUMBERS. 400 6004 80067 670005 9006014 92100121 7. 8. 9. 10. 11. 12. 800800003 87974015 35000918 30150900 70S000549 4050300 28764105 1000500 3008727 605054045 78592835 106405021 EXERCISES IN NOTATION AND NUMERATION OP SIMPLE NUMBERS 1. Twentj-eeren, forty-eight, si^^ty-five 3 or S'lS r 1 f '^"^' ^''' ^-d-d- 4. Thre hu dred a,5'Skv"' ^'""^'^'^ *"'^ ^wenty-four. 6. Four hur. 'ed and nfarnnV'"*- ^"l^'^''^'^ ^"'^ '^^o- 6. One thousand Z. one Ke hllnl ^T^''^^ *"^ "'°«- 7. Eight tliou^and one lu/r.S ^aid S *"'^i '^'■^*- 8. N.ne hundred and sevenS Sfotrntfi'v /"^^-r i^^"^'^"^. 9. SercD hundred and eiditPPn H?^. . , " ^""'^reJ and two. CD CMfV DCCXXX CMXLLY XlX MM 39 What u the ruU/or num^ratitn t mn 1^ li DBCIMALS. DECIMALS. » th?' ^^?^'^^"»a^S arc meant, parts ten times, ., hun-lred times t thousand tnnes. etc, smaller than the unit ., which are TnS cessivelj ten tin.es smaller than the other ' **f^. A whole number and deeimaln in « <^;, i " ■ constitute a Mixed Number ' '""'' ^•■^P--'""- «i^i huSr^s,r;'^s^ j;;^"':::^ "I'^r d^^^^V' ''"^ ;^^^'"'^' and eight thuu.sandth6. •*'"^' '^"'^'' '"^'•^ a»J decimal two hundred NUMERATION TAHLE »Oa WHOLE Nl'MBElis AND DBCtMAI.S. ISOK.VDINQ rROGKRSBION. 1>E8CKNDIN0 PtOORWSlOf. 8. 9 3. sandths. ionihs. ioiths. •As 18 easily seen, decimals," with regard to their order folh.™ inver.oly the systen> of numeration of whole nuXs the ? Ij n^ times .nullor than the unit, wherea. ^e„ is tre unit cpe^ted Tit a^nll^'l'ff'^^^P'"^^'^'^ '^' hundredth pa toTh« unit, and a hundred, the unit repeated hundred ti.u.s &o r wit iT^ m:^:/S"S^ ''■ '^"' ""•"•^ -• ^••^ "> -^-^ --^ - 32. DMOIMAIM. It au Huule tin: jtii-ii^ • ■ the teiuli ^.,,,'^, ■,7'*'*^ '»to ten enual nans p..„i • point ; tic,riim/l(fr''J^ '*T**'"' "/'''''• "^hich place th. l , 6. Three ^W^Jfki'fi, Lp L ' , ^""^''■*''^'''«- «»^#^t»tt, a„,j a,, huadredth.. 18 THE PRINCIPLES OF NUMERATION. P. Twol,„„rl,.o.l an.l Mvc.tv. n,,,! nino lunulrcl-thoimndths. 10. One thousand an.l six, and five ten-thouPandth* 1. Joi.r tliousan.l and seven, and three hundred-thou^andtlw. .o* ^.''^^■"'n^ «*"'! twent/.two millionth^. 3. hji^hty-two, an.l thirty-BJx hundred-n.illionths. 14. higi.t lmndre.1 and fifteen, and sixteen thonsandthi. 15. Iwenty-seven, and one hundred and two biUionths. lb. Twenty thousand and ten, and thirty milliontha. BJU-HMS ORALLY AKD WR.Ti: IX WORD„ THK rOLLOWjNO IflXn mruBKRa ajtd sisolk decimal*. 1. 2. 3. 4. 1. 3. 3. 4. 6.90 9.908 641.400 703.2004 0.004 0.000607 0.005 0.00OT0O7 Mijted number*. 6. 354.0064 6. 352.06046 7. 76.26007 8. 375.60050( Singlt decim^ila. 0.4072 0.401950 0.9540626 0.075003 9 10 11 12 9. 10. 11. 11 41.004064 452.010778 7657.008007 1898.04 0.69804445 0.736050210 0.000500019 0.00000501 •PPLicATioN OP thk: pkinciples of numeration A8 LAID DOWN IN N08. 27 A 31. it fo^owt°''°"^'"° '"^ *^^ principles laid down in No8. 27 & 31, 1st. That, to render a who/e number, ten, a hundred, a thousand times greater, we must write at the right-hand side of he number one, two, three nau-hts or ciphers (1). numoer, tl. Jfi "fL*?' "?'"^'' ^*^ ""'^'' ''""'''"^'^ 260 in adding a cipher after the b, that ,s, ten Un»e« greater than the first, since the units becomi tens, and the ten«, hundreds; or, in otherwJrds, thefl'ur of tbeTst order becomes a figure or the second order, and that onhe second we obtarSn ' ??»re of the third order. If we ^d another cTphet we obtain 2600 which is a hundred time, greater than the first num^ ber since the 260 units have become 26 hundreds. ^ Thus, 26..S5 beoome/i tea Umes greater if written a«3.6. tixM tk« tenths become unit*, the units tens, 4c. ' ** fraatar Y- 3«. Do. A uhoi. N«Mi^.r witA a d^Mmal •mumIV ^■*'** '^^ Uiiy T''"',?"'"' "'ti "" '"»■'*' "«»t.iD.(i, «qa»U ton. a hondrwl d.^ A. 1. !«» 2" 3'» 4" *" «WO»LM or NDMERATION. •"'.', two, throo, &J., jg„™'- "• "'" »a from the right-hand side Thus, in the nuiDher 99*; . if place of the units. ^ """ °"= ^main to talte the numbers beco,,;, O.0O8 8,"d o o02fi'« ""f ■ 'T""' '^'«^; ZTZ &sr*^'"''-4re^s:S"brsri^hrj^ir 1. 1" 3" 50 PRACTICAL EXERCISES Render the whole number 38 10 100 1000 lOOOO 100000 «* 1000000^ times greater. Afu. Ans. dns. Ant. Ans. Ant. 380. 38000. 3000000. V,'i so THK PBOPRRTIBS OF NUMKllATION. 8. Render the mixed niimber 42. 1 064231 1«» 2" 40 «° 60 10^ 100 1000 10000 100000 1 000000 >■ times greater. 3 Render tiie mixed number 4.20 1 1» 20 3» 40 5" 10 100 1000 10000 100000 times vreater. 6° 1000000 j 4. Render the decimal 0.05 2«> 3" 4» 60 10^ 100 1000 10000 lOOOOO tiniea greater. fio 1000000 5. liender the whole mini her 6705415 l* 2" 30 101 100 1000 10000 100000 I 1000000 J • times greater. ©. Render the mixed number 7610438.06 10 30 6« lO'i 100 1000 10000 100000 1000000 timef smaller. 7. Render the mixed number 5.45 1» JO 40 6* 101 100 1000 10000 190000 •• IfMOOO tiracR smaller. Ann. An«. Aug. An:i. Ang. Ans. Ant. Ans. '■ns. Ans. Ans. Ant. Ans. Ans, Ans. Ans. Ans. Ans. 4210.64231 421064.231 42106423.1 iS. 42000. M 60. Ans. Ans, Ans. ^n*.67054150000. Ans. Ans. Ant. Ans. Ant. Ant. Ant. Ant. Ant. Ana. Ant. Ant, 76104.38M 76.10438M •.•dS4f Ant. 2* 4* »• / «" JO 10. Jl 14. 19. 1«. 17. IS. 19, 80 81. 8a 84. 85. 8«, 87. 88. 8». 80. 31. »8 88. •4. ISMKifci;.< iiJtaba!8{MM«lii"j'J;yi «. '*«"'«'' '»" rl.cimal 0.05 KM 100 1 0(10 1 0000 r 'injefi «ri,a|ler » 00000 I 'OO'^OOO j 81 »• ''"'"iT r.H. mucd n„„.ber 206.007 An§, Ana. Aug. A}ig. An 8. Ans. 0.000006 2* 101 /oo J 000 1 0000 '00000 , 'ifiw fMialUr. ^J" i 000000 J A7)8. Ans. Ana. Ana. Ans. 101 100 1 000 J 0000 f ""•«"< "tnaller. '00000 I '000000 J 19, 14 19. 1ialler. a greater. H»na]ler. greater. f'tnaJJer, 'e«t«r. Alls. An..'. Ans. Ans. Ans. Ans. Atui, A71N. An.i. Ans. An,'<. Ans. Ans. An.'i. Ans, Ana. Ans. Ans. Afia. Ana. 0,074 4.50. 0.00005 6060.0867 22 ADDITlOir. ADDITION. OPBRATIUN. 428 635 874 193 7 ber^of- 1^"*?^""?"/' " P"x-« of un.tinj: together wreral num- Sum t Amount • ^ "* ^« ^-^ * -'^''« nu,„ber called th. de,H>!!!i,.!;!- f "'• "' '^' "'"•' '^'"' '''"" ^^^^ ^*- ^^« "- ForinHtance, .lollar- cur, be tt» n">ober«, so that all th« flret ad.l the oolnmu ..t «n«V* ,• thug, 8 and fire aiti 13. and 4 arel7 un,t, .^ I te„ a„d 7 units. Wo writ, tho 7 "iniU under the column ot uniui. and erUe 'h -., nd.-r,ath, if it be Us. than ten. ,1.: /V^ *"? "^"".^ "•'"'" ^* '«•» ^ ^'-^ ^^«» ^««, ^rite the umt figure only, af.{ .../„ 'h, ten or te.: to the next oolLmn.. IV. Write the whole sum of the laet cobunn. w uiMiNMm to «• immmmMdt^ 41. Wka$ w tk« tm m-m i nUe/m- mddHim t 5)^V " ' 'fi: - i' ^ ^y ] "\ ^~i""-' — — m^ r^ . by a pointy ,, ^,„,^ drriZr' ^1'"' '^'. "//-m th. //t« number areciths, 4682 uni* , l> i .T" """» 7'. l.,m.lr,.,W„, and Orit, CATION. »S79.26 46 8 2 i) 7 3 78 56 ^n*. 1 6 6 9 I . c o which is road in the following 05 75 HO 86 hundr«dlha'JTi*;";„^/r« '". «nri 5 are (5 write the 5 hundr,d!h! *. ''"'"''•<"''»>«• VVe than two. "•'*'''' '"^^ ^ .^''•^'ater nuniber of parts Ana. OPSRATlOjr. 128.24 349 00 5(1 >5 I49.d4 __967^ "1645715 PliOOF-. ?flt. Part. 123.24 349.00 472.24 2n.i. Part. 5G.25 149.34 967.32 1 172.91 Addition of partial io/uia. 1172.91 __47l\^24 1645715 which k read 1645 unita 15 hunc^redthl USE op ADDiTrnv iJi'i- number.: the whol^^Tstt t rthT Z^ '"^^^'^ -- ^^-voral pan-a. are given. The selli g p'^^ ^S^ P"°« -'^ other ex- pr^t are given, iTTo?r. n 'i^^'l and thirtv-tw. . :..::_°"**''...V>o»«and and fifteen, + on. hun 2i.40.()n 4- 104.8 + 100.-..025 + 7.;J87ri7 22. 0.4 + 0.20 + o.O.O. , ,,0, ^ o:'2ro +'^.^1' VS*"'''^" 23. COo + 0.00012 + lio ^ ,1 •..;'"*• V-^^"*** ten-thousandths. 2 . G.% + ;^.99 ^ g 7 \ Jfi.V^''^^^ +0.0001005 + 1 + 'SSO. ^ ' ■'■' + ■'.■i> + 7.77 + 3.7S+ 9 0- 26. 4.95 + 9.54 ^ « ,,, ^».. 1 1 7.929 tl„„„.„dTh8: tw™t.v.(i,, lhoa,"tl., "1 «"''''• f ""' ."■»-an,i .l,r <.„„?,' .nd , ^0. Kequirfd the «„ni of f„„r L».k "P' ^"»- 1167.:i2:-.. hundrt.,! f.„.,i 1. '.''"" '«»"", -r twenty tlmu««i,dt|„, + Jjii-ce hundred ten-llmu,indth«' * „„„ 1. ', "rV ■""■"»"iiiii«, + ^ • Required the mm of four hn„,7. "'; ''8l"«n liundreiltli,. '''"3^^=' + "'"etren thou^saldthr **""^'^^-^^0"«'*ndth«. + eiglu bill ^- h„ndreatn?h'3,;:^^ ;-ndred.tho««.ndch^ , sand hundmUh,, 4- thirlMnl^tJ hundred tenths, + one thou- e>^'ht Imndredth. -f- ele«!f u "' '""."T^****' + ^''^"ty miliicnthri -nd ni ,,,„ ,^ili^^;^^- hu„,ired-thou«»„dth^ . ^hrie thoi'.knd ^4. Kequired th« sum of nn. .i i ^""'- 40.174529. thousandths ^ two thSandCdS"'^ tenth., -f- f.„r hun.l ed 4- twenty thou,.and miIJioath« Tten tr ''"•"*" ''""-Jml tenths, faousandth., + one thoS 'and fl.V r'^lr **";' ''^^'^^ '^""^reV' thousaad raiilionthB ? *'' ^^^ *«^"-«n»ll'onths + one hundred •»o- What iH tht? ■»>?. ^r u,„ ,.,,. ■ seven miliionths: one hn Jrl) f'""!.'''^ nuna>er« ; twenty-five an.i jwandth«, on;rndr:f:if:tf:r;flt '-^'-^ -^d'rc!!;;:^^ dnfdthH; »erenteen, and three h»n?5^ ' /"'' ^''^''ty-nine hun tkouwndths? *"'"" ^""dred and forty .i^ht hu^j^J viiM. 3(;.^.63«487. 'I I ki ADDITIOn, PBACTICAL PROBLEMS OR QUESTIONS IN ADDITION 1 56 2 3 8 * 2 7 6 4 3 Ans. 2. I bought some merchandise for the sum of S94.'; fi*;. i must I sell them to gain $25.20 ? «^45.65 ; how much $ \T5T5 ' equate" h;7it?03t";.l S It r wK" -^^ \P"°' 25 .20 245.66 + 26.20 = $^70 85 LlUng pri^e "" ^'"" ' ''" "• » 2 7 . 8 bAns. thano1.MtlriSj2"o^rt «4.75; onTueadaj, $1.15 more spent duringSseXedtsT '^'" '" ^""'^^^ = ^^^^ "'«°»^ ^*« the'^7''8'p?nr4;7^ +"*[ IfAV-KnT f Tuesday and Sunday. On Tuesday. «69;l'rj;l{,;r7liS' t^'f-^'^^' the butcher, ^16 ; th^^ shoe-maker, famiV owe i^ 111 ? ' *»J f«'' houHe-rent, 145; how much does th^ 6.' Th"e"'^;j;.Sn"of Mo' '" t*' ^?^ ^"' '^ '^ ^^''^-fold ? Quebec, 64^, Se^Rifers sto' f'"^ '•^•^.O;? -»'«» that of Levis, 6300: Screl 5250 Shirhl ?.' h,3^^T^^'^ ^^^'^'^ P^^'^t- Pulat.c>„ of tLos;:ev:n-io;n''r'"^'^' '''' = ^^"^^ '^i'- .^^'^ P^' $45ooV}^t:':orn^!7/5S'';^^^^ owes $92. How much did he'o^e'l'fir* '/•''' '%:^'t^\r ^>eforetheeng^ageme„t? re„.a,„mg. How many had Vo v 86iSmi;Th72rd"mo^;*i;rtL«?r«^^^^^^^ ^'^- -"'^■■- there in the army? ' ^ *''* •^'^- '^^^^^ ^T '"^''^^ "'«» "<" „ui:;.I\«ori'^^'^^^-/>^- o, weigh 390 poun1reach??hr;;- . nc gmined »176. How much did h» sell thora for? An$. $486. ABDinOM. 27 10. How miiQv v^u.r>i piurv^^j !• •''-•»"' ' An$. .^7240 hush. .ujr^i n84,e.iS;;;?£iS^^^^^^^ which oc "• .^ Powon who WM bova ia lijl dlS^ ifJu °^ ^^"^ Christian era ? year did ahe di« ? ' **"*' *•<* •* '!»• «ge of 37. In what tkio ^^^ ^'' o^^he Dominion of P«n.^. • "*"*• *3174.55. ' Jh« Province of Ontario iSnL'^V* computed a« follows- bee, 210000 .quaremfea the pZr"';';^'' ^^•^'ovince af Quei »»nat 18 the whole area? aJ^^ \oilli^ ^"*''« ""'les. !»• A tanner bouirht 25 hide« fnr *%. ^»». 4J7360 square mile*, g-epared them, he e^old tLm for Ju2 67°^'*^^^^'' ' ^'^" J'^-^ng How,auehd,dhe«ellthemfor? ^" '"""" '^•'i ^^'^ t»ad paid^ 20. A «„-*„ . ^„,_ $277.40. ''"• -*■ certain sun, of moner wm h;-;^ ^ "**"• *277.40. '^ved$65;thT2nJT6-in "r^^, ^hree persons : tk.lst.,rece^ „^.^^^ J32. more than the geeond ^M the sum divided f ^i*. i8t. $65; 2nd $91 3fl. 21. A merchant in fl«Hm» Jf^^'.^^^M^' ^^o'e sum ^279 70 1143.40 bj the ba gaijf hoVm^^^^^^ "'""""^ '' $6218 So", lost . 22. At the censul of im tT " *'^ P*^ f"'' ''' 1409430 inhabitant that iri^^ Papulation of Upper Canada wa« fOOOOOj New Bra„a«^^J Is^om/ ""h r^' '''''^' ^-^tit tbere in those four ProvinnJ.lu ^"'^ "'^"^ inhabitants were o*' Canada? '^"'''""''' ''^'°»» «on'POHe the pre<«nt Dominion 23. The battle of Marathon took niai"/:.r;^*^.^?^® '"^^^itants. 9"/ ^pf*!:' '''"°^ *^»t period to 1868^? "^ ^'5^'" ^^"«'- How 24. Eighteen tanned honw-hideswelh ^«fi ^Z'" ^'^'^^ ^^"s. 324 pounas ,n being tanned WJa7H55 thl^""'^''- l^'^ ^^'^^ '<>«» 26. A number ia such thaf ;<"!!•• *f , '^"^ ^^"^ weight? 5976. What is the nut ber ? ''^'™'""''^ ^^ ^^^^ th"^ remains but io. Kawwooi is worth ^n 'r« . *'*««. 1246'? *2.45. What is the price !f k n ^^Ti^"*^' *^''" P«-^P*red .t aulrnenta , 27. The populatiuTof EnJon.""^ ''• ^''^'''^ ^^ooU An^^^To that of Nort'i Anieirc;l3^8a8''Z':>f1 ' Vh^'*'"' '"•-^''•"^« - that of Asia, 5H8700000 • thltlr a r . ^""*** America, 22007823 • 20600000 : That of A u!:.U,:?^'^/4f"«^. WO.^5000; thaiofO.eapr.a What IS the whole pop'uiltrcU^'o^rhe^g'loreV"' of Polynesia. ;r90o1: Ant. 1020360878 inhabitant.. •" SDBTRAOTION. SUBTRACTION. between two numbers of the eame kind. ,1,/ ^•^"■'^J """'^\'' ^"* ^^'^t ^'''«^ '■« t« be diminished, is called tt fc:i;"' ^'^ ^'"'^"^^' - ^^-^ -'-»^ « ^ ^e -btracted, cerordl^erTnte!'""^'""''"""^^^^ ''^ remainder, ex- tk^J'fl^ ^r'"^"" «"6W »/;/i.7. each figure in the mbtmhend i$ leu than the figure alove if in the minuend. Ex. From 547 take 324. ortv.kriov. Minuend 6 4 7 Subtrahend 3 2 4 Remainder 2T3 w» writo in hundreds' >«I9, Mid 3 uniti, or 2 AvAi.Y^rs-Wowrit* the leaa number under the Rreuier, ,.., tb«t uuiu of tbe same order shall (taad in the same column; thoD, wo begin nt th« right and f)rnoec^T""'°« "tth" right-hand Proceed ?'r»l7K"'!^ r-l'iee below. Wo than above. ^ but ?h' "*" ^ '"^^ ^'•"'» »h« 2 tons equals JO hundreds, learini; 9 above tha oi- pher anladd the 1 hunl^od equ,!l to ij ten.., to the 2 ton., makin - 12 ten.- 7 ten« f fj; ni 9 I.ares 5. which we write In hu^dVeii'n? ' 'l"V "'^'"^^ ''^' ""'•' "°der ; ' th-;usand from the 3 thousands 2 thn,",n^ ^ *"■" ^®'^*- ^^ ''• h'^ve taken wh,ch we write under. We cS take 6 I 1^"^" '"^ J """S^t from 2 leave, 2^ so from the 8 hundred-thousSwe take 1 h ; 5*""^"^^' ^'""^ ^ tea-thousands ton-thousands, ,.nd adding them tl the 5 ten »h '^■'^"''»"'^' "^'^'^'^ «q"al- 10 « ten-thousands fr.n, 15 ton-thou?ands l«a« q ?* '"u"' '"'''*« ^^ ton-thous.nds: und.r Having taken J hu.dredXu^S fL^'^V ''''2'^f^^' '^'''^^^^ ^« ^"te h mdrel-thousands are left; 3 hundred hnn,"'; ^ ^"'''''«'' t^o sands, 7 leave 4 hundred-thousand,, which we wJft^uM?,'^' 'Tu ^ '^""I'-oJ-thousaids or reinamder, to b.' 492554. ° '"*^"^' "'"^ t^"'" SnJ the dirwence Minuend Subtraliend fieniainder •3 a " e 9 S° • H 6 3 2 y 3 6 0475 47nrT54 OPKKATION. 8 53029 3_6_0^4 7 5 4 9 2 r5~4 METHOD BY ADDING lU. S:to2t^--^^-s-^;^-^p:^i?;:\a 5 ten,. But havng .iJdded i, UL °' f""^'" ^^ tens leave « mousand, to the minuend wn sKmII k„ ' ''^ °^^° added 10 hunflr«,il unless we add 1 thousand to the of ,h ^h ■' * ':?'".»'°J«'- 1 thous.ond tooJaTi' tte°.oM"" >^ t^>-\VotandT£e"'ir?en'^"''""J' t^'-tbo^usI^dT ' 6 ie^ t^nrmakSr/hunlLVi^' '" ''^ --i.-^ ^ "rPen-^e 4 hun^,,a J,^J2f ed-t ousands and subtract theVf^m'tl^'^th^f '^'^■ before. ■^»>"«' w. flad the remainder to be 492554;' the simr? *L-i"' trrr '"""r'-"^ "^ ^^^'^ "- '^"--« c Wkt^ i, tk >- y : ■ — — . «' ^'^^i't^m^for^traciumt m #1' It r ' 80 IITBTBAOTIOIt. IT. Commmnng at the right-hand, take each figure of the mh- ^rahendfrom the figure above it, and write the rZlt und'rneTth III. If any figure in the subtrahend be greater than the corre*. oondmg figure abooeri add 10 to that upper figure beforTsl imS; " " "^ "" '^' '""'' Wt-hanrfigure Iftl ll PaOOF OF SUBTRACTION. 4S. We make the Proof of Subtraction in a.JJin:,. the re- .nainder to the subtrahend, their sum will bo o(,ual to tlie minuend. «t the work la correct, ' Ex. From 35678 take 27899. Rem. Proof 356 78 2 7 8 9 9 7 7 7 9 3 5 6 7 8 Akaitsis — ToproTethij operation, we ada the remainder 7779 to theaubtmhend 27899. and obtain 35(578, whiohsnmisequalto the minuend or greater number. Henoe we coaolude that the operation u correct. This method of proof depends on the principle, that the greater 0/ any two numbers %s equal to the less added to the differlr,c». ■ Use of subtraction.— ^«6^rac on goods; what we still owe on a turn of money of which we have already paid a part; in general to find the 'sufilus of a nvmber over another; the difference between two numbers, dec. We know that the solution of a problem requires a subtraction when wemustfind the difference between two numbers, or the excess of a number over another; and when it is required to find one of two numbers forming a total, that total or amount, and one of the numbers, being given, '' EXAMPLES FOR PRACTICE. (1.) Minuend 76518 Subtrahend 49359 (2.) 57813 .38675 19138 Proof 57813 (3.) 13042 9176 (4.) 250143 176158 Remainder 27159 .3866 Proof 13042 73986 Proof 76518 Proof 250143 48. Uvm d* yon prore tubtraetion f 6. i. 7. 8. 9. 10. II. 12. 13. 14. 16. 16. ly. 18. 19. 'M. tl. a. as. 24. 26. 26. 2t. 29. 36. 31. 39. 33. 34. 36. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. .'0. JI. J2. 53. a. ( u u « « U u u u u u u it u a it ti « It it u a a « ti a n a it a «< »-SU m 6. I Frpip 7. 8. 9. 10. II. 12. 13. 14. 16. It. ir. 18. 19. ^. tl. 32. 33. 24. 26. 26. ar. 29. 36. 31. 39. 33. 34. 36. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. ;'0. 51. J2. 53. »<. (I « it u (4 (4 U it u a M U il a M H it u u ti M u u u u it it it it it it it n n a it ti it ti It n it ti 11 ti « it «4 .#00 46U9 l^iW'-,40 mm .mma mmm mmm mmm fWBTEAOTlOIf. take mwm mmm w>^mm fMmm (I « it it tl (I (( it It It (t It It .( tt it a tl tt if ft it II ft tl it It tl ft it tt ft It rt" tV iV ft ft' ti' it & tV & iV ft' .1* 351 15574 16134 30409 97J25 179127 471097 198576 55595 608578 4137976 988827 154379 737898 14550045 49876579 4007.S049 91791994 4590489 64834795 9068073 1300476 27740761 15007.34 3740056 6475904 74375676 97050654 277451794 9737.350 476294474 49.5647562 676489672 475207454 45612495 798435496 1&4289778 93457897 i>8047775 71904267 677469579 276499619 203405604 93235945 7456,:$yaa5 39787496 746855472 ^78809709 17073969 1977988S 31 »«. ^49 33895 63772 160131 14-7415 268973 3';882!i 388374 48I2'00 130I449« 16835321 20792702 83110009 2969.35925 62608006 185463520 689840100 939476 126030680 3902S9G89 805265.154 484533172 77.3277878 753019798 2693,v5?«I 91272751 18180721)2 88437502 474868620 411088255 77671553 668807729 58P006779 360796512 377406:75 176507908 881264755 93767519 ^078f.U81 *o83&.J74 4006736236 *6e722070S !• H 31 ilTBTTl.AOTION. \P SUBTHACTiON OF I)ECr\fALS. f^r. From «(;.? take 6;).3r)4. OI'ERATlo.V. •^6.700 i 7 . 3 4 C Rttt E - T ir • nuiab«r. 6. 6. 7. 8. 9. 10. 1]. i2. 13. 14, 15, 16. 17. 18. 19. 20. 21. 22. 33. 24. 25. 26. 27. 28, at. at. EXAMPLES B-oa PftACTIOl. From Take Ans. 1.3581 From 28.98S08 « « It « « M M 90.49 109.191 5409.0r.5 764907.05 '^97450.07 4(JiJ742.6 !?70079.04 400048. 2i;i6 409004.9099 670075. yo04 49.1019 610011.050 ' 71079.0013 < 79073.07 « 12G001.0001 *> 191279.9709 '- 40IG45.1005 9.965 0.44449956 0.00338041 ..in r '" "'""' ""^ -«« «'«« ™ »,d for «638. ^ba. ,. ,,. op*:ratio». $26 2 8 $2 3 fi $268 ing tho coat Drioe S2 whole of it for fi Si"*.*?"" difference between 70401 and fiOi9 . ^''*- *^227. 6. What ,3 the difference between fi^V^o aV. » -*»«• ^3459. 6. I owe.i J1628 : 1 mid «q7] • f,"i ^^V","* ^**^8- ^'W- 30952. ^ 7. The greater of twriuilera is nn"^"'^ .^° J "^'^ ^^^ ^ what is the smaller » °«»»fera is 1302, and their dUFennce is Dsi . 8 A merchant sold in one dav '?9';7i in _u '^"*- *21. s-by o,«„d . p.,a. „r »Af 'i,'.r:;rd?i tK IS -^ ■"any year. ti„, ,i^, ,«„;« /»-nd„d by Cha,„pl.i„ i„ ,5„3 ^ ^„ n. iiie area of the Provinnf ^.f /» • ^'"' 262 years, that of the Provuice of oXno iSOOn^n" '' '' ^^'^^"<^ »quare^u Ss • mi es does the fonner exceed Se latte ' '^' "^ = 'i^'"" "'^y «1-- 12. A father was 28 years old .* Vj,L u--.i. . '*"*• 30000 sq. m J*. What namh«r mn^ u jj . jt^ais oia , ^7,, 57 „. .»'^ Jr*"' """"'*' "■"" •- 'JJ-l .0 4 unit. 5 l^JX! n*.,. •» ^«J». 1769. 9% •VBTKAOTION. "♦• What number inuat be ad.l«d .« -4 .. , " '^'^'•^'' "'*•" hiindre-lthfl? °^ ■*^'^*' '*» ^ Hiousttndtl.H, to hare 12 London 28(J,SU1 • how mn^V Yi^^ inhabitants and that of that of Paris ? ' ^^^ '""^'^ ^^•'^ '*'* population of London exce^ „ 21. Alfred the Great .lied in 901 at th« "*' l^to^^ inHabitant«. 24 years: in what^e^i tt helln ''" •*" "' "' ^j » '^^^ of . f ^- Oharlemagne was hnm in -7^9 i. •^'••' ^^^^ he, lat. at his coronation as king- 2nd il . ^T "'"^ ^^ age did he die; and 4th how m J, ^"P^^-orj ^rd. at what until 1869? UmU? oY ^u" *^»P^ fr^^*" hi. death at $1 1 7000 and adjud|ed fo ^e pH' gT ^"*'^^ knocked^dm t ■n the museum of the louvre ^uTred?h^^ *^« P'«c«i ^ l8t. and the last bidding ? «^"»«d 'he difference between the 24. The population of Montreal in iTan . •. , ^'»'- fHTOOO. 'tant8; in 1861, it wa« 57715 In 'l856 f^^^r?^"'''*",^ "^ ^000 inhab, '" 1868, about 136000. What i« thf i ^^' !•" ^^^^' ^0000 5 aad 1851 to 1868? *^''"^*'"«''^*«eofthepopulationVroM 25. A farmer reaoed 1689 h»ak^i , ,' ^^^^^ '"habitants. oat« He sold his CigLS John 89? h^r!' ".""^ ?'^'' '-^»^«'» of bushels oats, and the rema3«,. t , hu^shels of wheat and 478 97 iT„ 1 r *i^^ '""' "' *°^ second ? -..Id have $75 lel{; how mVh have J^ ' ^'^' «^ *J0I6.80, and 28. A merchant sold ti ifian It <• , ^"*' ^^582.30. dit it cost ? °"°" "^ ■" '"J P«"i i' «300 lore. How mSok hJL S.'^f""'" "M in.Mted in the jeu nia u "*?' *'^'^°- b.fo« th. „„.ntio, o( prioUns, -iich .X 1«1 ', ''i':,''i'i« ;^^''» PRACTICAL PROBLBMai cOMBmmO ADDITION aT SUBTRACTION. -ond^.':?ilKrt7V^8^^ !!;«.<'--^or change; on of $43.2? .ndUi^'mo 76 fo°\«lPr * «*" of SSS-.o/anotl.:, •MMMns to him in cash » .«» -r •llT"^ «pen«w, and then there M» hu Moounto right ? ■UBTRAOTION. Xl.t;a^Srw\"ir :ii". !r..^ '-"» "-^ ««•<» •' b, had ri I««> Si'.'J, 4»,'i« f 7».H6 4. 68,46 4. «« J. 128 80 -U f.A ar, < aft not paid 7:^.16 -.|J30. nhimlil bo left Ant. $0.50 Hgainat y,l^ •*»l».l>» «. 9IM.6O ; diffarenofl 160.60 — 160 bow ;„i;;'';;*i:2n t' •"**••' ^^' *" '"'^'^" 2*' *°^ ^^--^^^^^r 6 ; ^- A Htntleumn having 11128, lost i«a8 And b~.„» •it!^? triMch |„j,| 1,^ rM,uvn]w'^ ' «P«nt $172: how ;J. Tf.e water, of the'^St. Lawrence eorer an area of 5G500n*»n"* >i..''e«, twoof.tstributaric'fl, the Saguenav and St Man. ^""* 70.30; for the 2nd., $3674.60; for the "/rd -ii .^" u" r*" '""" »'»"' '"' ^'»" *»«"• Christ, lie left Eainl ■.t'l;t^;"'i'«.'trf'"fV''''°"-''u''"''' •■"' ^-j -mS u YL» » " •'^••' '*°^ '^^'"« Christ. What age was he IaL »>..» hel«ftK^pt, 2nd. at hiB death; and 3rd. how log from tht rJriod «rk3« death to the jear 1871 of the Christian era? ^ ' j4n#. l«t. 80 years; 2nd. 120 years; 3rd. 3222 years E Wtif ?k ?7u^u*^' the 3rd., he gamed $685.30 ; the 4th. Wa^rS Ivn ^***'' »»«g*'"«d $4320.95 ; and the 6tl ., he los •gau, 1.1000, I).-U.r.i5ainorlo«e, andhowmuch? Ans. $169.651oe8 10 A ow«« a .u,.. of fC90, plus $5.5.20 for intere^. He reimbursed -d,ffi««tum« $87.50, $210.00, $318.45; how much doe^ he Stll ♦«4 ?/7J;^it2;:^8\r?Jir.'s^'rT' .*»•!-" Jliiitt a Bank lin* /y « nnn A if- t 1®* *^°*"^' »° «*"''««» he gave 'M\ ! <>»e C0.1 »4.{o 7 ^^ kMwing " ihop Wore hi/lM ,,',,~h.„ S •" ■"" '•■" i'*'f "h" I", bi^l i. hospital.. Having Lked 3500 mLTh™ ^•''*r "^''«*'^ *° '«»^« "' AIM. Io730 niMi. MULTIPLICATION. OA. Ihe multiplicand and mnltini;-. „p- „!!-» «^-^ because they ;,.orfa« or m«feth7-pr,;& '^"^'*' MULTIPLICATION. MULTIPLICATION TABLE. ^1 i 38 l\^ IHTLTTPLTOATIOIf. no^^^c'i'12^''^'''""*"^^^'^-^^^^^ ^he multiplier doe. ^^ Multiply 642 bj 7. OP«RATIOW. ^Multiplicand 542 Multiplier Product 7 3794 *42^re?L";? ??,«^^^^^^^ "quired to t»k. ' ' ■"« "8 product u 3794 Multiplicand Multiplier Product EXAMPLES FOB PRACTICE. (6.) 16812 (8.) 68607 3 4 4 5 6 8 7 9 11 9 12 X X X X S = X 7 = X 11 = X 12 = 10. 873 n. 946 12. 4731 13. 5607 14. 6924 16. 8667 16. 27693 17. 61786 18. 45678 19. 36397 20. 634576 0a8r TI.. owA 12. Eof. Multiplj 478 OPERATIOK. Multiplicand 473 Multiplier 34 Partial ) "TsTI products. { 2868 Kntire product 30692 ' Ant. Ant. Arts. Arts. Ana. Ans. Ans. Ans. Ant. Ans. Ant. 2619 3784 16924 28035 41544 69256 193851 466074 502458 327573 7614912 21. 22. 23. 24. 25. 26. 27. 28. 76394 &7631 266532 83545G 541378 367542 426985 - 576483 29. 6932574 30. 397466 31. 3745178 71, .«^ ^n».., by 64. 8 unita »re 32 onita i P~«««d tfiug. Four time, the 2 unit, in rpC'oftit?!';"!.'!' ''« ^^^ to the nrodi./,* »P*i.I.- .t """'» and add the 3 t<.«= ^TFTTrPLrOAlHw. 3f (4.) 8634 6 51804 19 hnndrels, wUieh we writ* in it. «- obu.ned by this .Dulfiplioation. in WnSf„ $• *7 *' ""*• *»•• «Mt fl«;a« hpi.er; and. addin,- tho ;,ar• two mmdp&o^, N<.TR:,-.When there ure oiphen betwrnin th- ■ •« plier. paw orer them in the JTr^ioi «nd Sf.iH*!"''!*** '»"•" '^' the ■«!«. rfraw « fine underneath. ^^ ^*^ '^ '^ther, and n Multiply tach figure of the multiplicand bw ea^ 4^ . PROOF OP MULTrPUCATIOlf. •??; . '^'l^ P'OOf of multiplication is generallT m,,A^ k, *.. Miultiphcition (1) in which onp nf .,," 7 T™'^ "»***« ^J another the third, or the fourth etc ofon«lm .7 T"'^ ^'^^ ^^^^^ and the other equals t^t^^^Ztrt^^^^^^^^^^^^^ faotor of the operation. Or. "i^r umea, etc., the other In multiplying the multiplicand by the multinlipr M - - l j by 1. and to the product addin. the multipSd Tf tt "^ Jhe^same as the product by tho".hole of ntZ^^^::^ USB Of il^hTlPLlCATlON.— Multiplication ,BrvPM tr. . / numherno man, time, greater ; to takeZ7al7:Z%a:t;:i' to find the value of several units or part, of £, L L **""**^i. ihem is known; to bring a number^eZressL T^, T *"** ^-^ mature to another nunZ .x/rmL S Xa ' "-^^ .^r'«^« of the first, d;c. presnng umts which are subdivisions Omtrally tee knov) that the solution of a nmhl^ tn. ...,,. oj .e..n,. «.- rcqairea, or that of some parts of the unity . 4U ■I, ^ 4. 6. I. 7. 8. 9. 10. 11. 12. 13. 14. 16. 16. 17. 18. 19. 20. 21. 22. 23. 24. 26. 2C. 27. 28. 29. 30. 31. 32. 33. 34. 36. 36. 37. 38. 39. 40. 41. 41. 43. 44. Multiply (1.) 8621 47 60347 344S4 AlU. 406187 976 697 749 8386 7.5.S537 1.^4679 824956 984765 66r)4 97248 €89834 867894 807497875 84966 643966 96824 43208 90480 43 76496 7674 3696 69421 4321 766849 908708 4916 766420H 80097 X 900007 X 4300407 X 460004 *'■ 960076 X 690800 X 7006924 X 786530746 x 4i6.'i4Z0Uo X 898302466 x 496307429 x 767489007 x 879407864 X MtTLTIPLIOATION. EXAMPLES FOR PRAOTIOK. (2.) 37216 65 X X X X X X X X X X X X X X X X X X X X X X X X X X X 186076 223290 An*. 2418976 27 34 46 67 68 79 387 766 789 866 943 996 966 7649 9475 4696 4962 9007 89006 87969 12478 819162 21764 987664 74323 70469 69678 20963 74269 700608 700608 99804 90708 456007 640(JK6 36781)4 987405 94376f> 936704 900076 698765 ' An$. « «< « « « « it u « ti II u « «( (( u u It u tt u « u u tt tt tt tt tt tt tt tt tt tt tt if It It tt (3.) 167034 304 668136 60I1(;20 Ans. 50778336 26362 23698 34464 478002 61240516 10639641 319257972 744482340 6250006 84119520 650513462 864422424 779235449372 6499049.34 6163983100 464686604 214398096 814953.360 3827268 €729276624 95766172 3027622762 1610184434 4267652934 66261288227 69109612052 342637048 160465162304 694872409.'{ €30562104266 3012899647466 46910239216 87086673808 315009635600 3784.341 5654 6< "•■'■■T^-fs.stovrjVzi 411098671149.525 845888887386840 46.3956449974016 681797676464532 €1449942(1100310 MVLTIPUOATION. 41 a) ■ 167034 304 668136 11(20 778336 26352 23698 34464 478002 61240516 10639641 319257972 7444S2340 5250006 84119520 S50513462 364422424 236449372 549904934 153983100 164685604 114398096 14953360 3827258 29276624 95766172 27622752 10184434 57652934 51288227 )9512052 12537048 •5162304 -8724093 2104256 9547466 0239216 6673808 9635600 155546< icui- ;;;:■} 1149626 ^^86840 •974016 464532 ioosie 45. 964907089 X 46. 457907842 X 47. 856407809 X 48. 674396856 X 49. 1864321 X 50. 2465783 X kl. 72400.36 X 62. J08007004 X 600789 796807 305407 285679 609649 3686407 4029008 500123 u ti a u ii n 673697675093221 364864173860494 261552939723263 192661019425224 1136581433329 9089879711681 29170162964288 46411618686U92 MULTIPLICATION OP DROIMALS. Et. 1. Find the product of 4.35 by 8.26. ^ ANALT3I8.— We multiply m in whole numben. and poiat off on me right-hand of the product ai many fignreti for deoimalf a« there are decimal places in the multiplioand and multiplier. The reMon for pointing off Jie deoimala in the product la. that in multiplying 4.35 by 8.26, or by 82« hundredtho, which ii the same thing, wo take 826 times the hundredth part of 4 36 but we obtain the hundredth part in removing the point two fi- ,-Qaift A l"""' *"''*■'*'' *>' '1" (*^"' "' 2nd-) which will gire 0.04S5; i6.9310 ilns.there remains then but to repeat 826 times thia hundredth part to obtain the product required. Ai the number repeated oon- mak nfth. aan,-"*^ of ten-thomandths, the product will bo composed of deci- matoofthe same nature; to separate the n hits it ia then necaesi^ to take its fcSjL'^UmaU^atL'rUi^lir""'" '"P""*"* '*-- "^^ ^"•' If the factors are decimalg only, we multiply aa usual and cut off M many decimals m the product as there are in both factors; but if the product does not contain a sufficient number of figures, we fill up the vacant places by ciphers, placing one alec for the unite. Ex. 2. Multiply 0.054 by 0.066. ANALT8ffl.-MultipIying 54 by 5«, we oktaia 3024: bat as .J? VI i'^'^^a's «n th« two factors, we place two oiphen at the left aide of the product and having put the decimal point, we place another cipher for the units, and thus we find the number 0.003024, which ia iwad 3 thouaandtha 24 mill- lontha. •PBRATIOV. 64 56 324 270 f.003024 (54. Henoe the following Rule.— I. Multiply as in whole number$, and point of eu ffMUiiJigures/or decimals, in, the product, as there are decimal, %n the multiphcand and multiplier. II. If there are not a« many figure* in the product at tk*re ar^ ^cimal places %n the multiplicand and multiplier, supply the d^ Jiciency by prefixing dphtrt. ^ ft- 3 Won.— To multiply ^at&maiM by 10. 100. 1000. eie, (Me. M). I 42 MULTIPLIOATIOW. olr/-"" """'" "" "»■"« »■ '» maUipli,..i„„ of whoU EXAMPLES FOR PRACTICE. 3807.4/) 489.04 X X X X X X X X X X X X X X X X X X X X 9. 98. «75. 66. 976. 696. 4.C5 6.96 3.95 9.475 7.789 2.967 6.694 28.9005 60.705 13001.4 42S1.45 13808.927 5321.807 37.00845 P:JACTICAL PftOBLEMS IN MULTIPLICATION »*• 137.43 622.3 6001.7* 11042.64 95403.76 41588.88 4403.55 6048.24 1362.75 640.076 6122.154 1109.658 63.39218 1140.702736 41066.32546 521913.456 41175089 9806 93749640.72768 20262510.2547 18098.612388 9 ieekaV"'"'^'''"" '"" *15 per week: how much wil he eara m tain the mux wquired « 15 vT« ifl' '''«'?f°'^«'n multiplying by 9 we ob- 2. How much W.J1 126 yard, of cloth coBt at |3.25 a yard ? drSJir.^yiTcoftf'''^^^''^^^-^^' ^- ^"Ch will 75 h«. o'^"'*S"'^'- '*«<»!^'"^' ;."!'%?t'L''r™'^^ "^» ^"^ -i" •>. 0.76. w. Ui the ,« ,.,,i^ ^2.£xQ.7i - /l 80™' '""'"P'^^"* *2.40 by 6. What will 6679 bSheirofSheat L/ *; «f ^^^^ ^' *28260. 7. How many pound, olflm.ra^i'- *oo^ '^^"^'^ * b"«^el ? 198 pound, in ew'h bSS^fr *^*'* '" ^^^ ^*"^^«' '^^^^ being coLSi UaY liSTr"' ***"* '" • ''^^""'^ :i^" 7 ^ ^ pa^sMSif ^ag. 9. A booM haa 296 windovii ^i^a -,o.,u j ^ l*^^-"^*! letters. •rgu., bow -r,«rxrkori,rrz°.i^„^^r- MULTIPLIOATION. 43 10. Required how many trees in a nursery composed of 95 rows, if ^ach row contains 1 78 trees ? Ans. 16910 trees. 11. The circumference of the earth is dirided into 360 deerewi and each degree into 69.6 English miles ; required how many miles •'ound the earth? i4fM. 25020. 12. Required how many hours in a year of 366 days ? An$. 8760. 13. How many days in 1000 years? Ans. 36600o! U. A man deposit* $15 every week in aSaTiogsBank ; how much does he deposit in one year or 62 weeks ? Ang, $1S0. 16. A ream of paper oontains 20 (|«irea; how many quires an there in 672 reams? /Iim/ 11440. 16. If a cask of wine oontains 213 qnarta; required how many quarts m 136 casks ? Ant. 28968 quarts. 17. How many eggs are there in 37 doaen ? Ana. 444. 18. How many days has a person aged 84 years lired, reckoning 3«6 days to the year ? An$. 30660 days. 19. How many pens are there in 200 boxes each containing a ltuss ^„1**P«'^«^ _, , ,, , ilm. 28800 pens. 20. How many days elapsed from the birth of J. C. till the Slst. Dec 1869 inclusively? (Nc , counting leap years.) ^Iim. 682186. 21. Europe produces yearly 3466 pounds of gold; whatis the value in dollars knowing th»t a pound of ttis precious metal is estimated •*J}"8.60? iliM. 16966321. 22. A library is composed of 76 shelves and each shelf contains 86 Tolumes; how many pages are there in all the Tolumes supposing each volume to contain on an a«^erage 420 pages ? An$. 2709000. 23. A speculator has purchased 268 horses and 274 times as many sheep ; how many sheep has he purchased ? An$. 73432. 24. There are 12 hags of wheat on a trick, each bag containing 3 bushels ; how many pounds are there in the whole load, if the bushel weighs 50 pounds? Ana. 1800 pounds. 26. A workman earns $8 a week : how much wiU he earn in 7 7e^^„ , ;, ilfw. 12912. 26. How much will 240 pieces of cloth, each oouMining 44 yds. cost, at $6.40 per yard? An$. $67024. 27. How many pair of shoes can be made in 265 days, in a factory in which 86 pair can be made in 1 day ? 28. If, at one load, a span of horses can draw 2997 pounds; how many pounds can they draw in 327 loads ? 29. A field of 7 acres of land yields 46 bushelaoats per acre ; what is the value of the crops of the 7 acres at $0.40 aJt)U8h. ? Ant. $126. 30. Supposing a sheep gives 6 pounds of wool a year ; how many pounds will 28 sheep give in 3 years and what sum would it bring at 24 aentu rM>r munH ? J... •■ on ae 31. What is the value of the crop of a field containing 4 acres, if aa acre yields 62 bush, oats worth 46 cents per hush. ? Ant. 11160 eta. 32. A laborer thrashes 46 sheaves of wheal per day, giving 16 pecks; how many sheaves could 14 laborers thrash in 9 days, and what would be the quanUtv of crrain obtained ? A»t». 6670 sheaves and 1890 peeks grain. «1| Hi If- HA MUL^IPBIOATIOWi ' CONTRACTIONS IN MULTIPLICATION, OR MULTIPLICATION BT FA0T0R8. 6. 15, l^,are^eo.posUe numbers; for dL 3 X 2??! ='6'">5' mufMieKhlr^^lu^rr^" '" '^' l^^«^^^ nun^bers which, or 2 and 3 and 4 (2% 3 xl = 24)'' * *°^ ^ (* X 6 = 24) ; whn'"?^^ ^« » «=on>po«ed .« «^nS 4, % i f i' £ \l Z ^*) •' »»>«• the jJt', i7*. 1. What will 46 acres of land cost, at |367 an acre ? kr bought. H«o, th. foirow", ^' " ** •*='-' '^^ ««- fr® ■^^"r'; '^'5''''''''* '** m«/rt>/i«. into tu,o or more fact^ ■ZAlfFLJBS FOR PRAOKOB. 2. Multiply 2T45 by 28 ^ 4 x 7 3. Mnltinlr Rf^^Ao u. «< *.^ '1 An*. 7C860. ilii*. 6618692. -i««. 2979423. An$. $9968. 3. Mttltiply 65742 by 36 - 6x7 4. Multiply 78036 by 72 - 3 X 3x 8 6. Multiply 36783 by H. 7.- wJ;t';;ii4l5\rKir,i!i?j.^«.«-^' . .. ^«. i99«8: 8,. What will 64 7>^dBoime^nT'Z.r"\^^ ^^ *"'"^ * ^""^^^l ? 9: In 1 mile there" e 6336 o"nir^Y *' ^^ °*"**' * ^^ ? miles?- 2nd. in 64 Ss? ' **"'' '""^ •''*^'^««' l«t- i" *« Xr-= ._. ^'W- let. 28.51200 ; tf 3N, t, aa it will ing togeth- er, Thus, 6 = 6X >ers which, the factors 6 = 24;; nb«r. Thai, Ills the jmrtt >lier u a if we mul- f 6 acres ; 8, w« eri- I Uie aua- '/aetan. ind that en u$ed. vw order (860. 8692. 9423. 9968. heir mTLTITLIOATIOll. 46 aAt^Z^^K*^^,^'^^''^^^^^*^^*''^ '»o* ra*"^ hours, Ist. lu DO. ;/ Jllfili''!!!!""*" ' '-^^^'^ P^""'^" «^ *»'«•- '» «°« day ; how many pound, wxl ^^wm\s* oon«um«, Ist. in 72 days?- 2nd. in 96 ? 19 A«-«.- >-,i An*. l8t. 897804; Sni TfVliS^'^r*** '^^^^ •^^^ = what will cost, 1st. 15 acres ?- 2nd. TOiw^jt^.^, 144acre8? A„,. i^,. 7125; \M\^tl^.fjf^'^^^^^^P^^^^^*^^^^ '^« multiplier i»\0, 1"^' lv09,.^- ((1^.36, l9t,). ^* ^ii^^^fiw; to d 112 X 100 =. ^^^.rfWr* H900 X 10-112000, the same reiolt as In ^he - i^i'fftff tlitf rtiywdinp' illTiatration we derive the following a^?^'7^^Ji^ '''O^^MntJiguret of the multiplier under *t*^'^ of ^,iem^lfl^a^J, and multiply them together: To their product, urmf^mmy dpher, a, there are on the right of both n^^%3^m^\4m^m!dtipiier. if j »* mm^ MAMPLIS for PttAOTIOX. M^STOoooo 13069S0000 600800 4. MuUjpU'^l^pJ^lly 700500. J. Mutipfy mm$ by 7007000. 6. MutjpUrj^^y^^kji^iijy ^0302000. 1045560 T84170 785215660000000 An: 427606215000. Ana. 21515743249000. iiiM. 814249517400000. j-ll * J 5}?f }r'**3''^l»t millioofl find four thousand, by three hun- -J. ^^ 8541220000000. -i/ii* rIlX?ff^*^ '**'"''*"'' ■•'«°t*'o«''»nd and six hundred, by ^«^i^*ftP*WWiIuttd«d and sixty. Ana. 660114005776000. M»»ftt hundred, 'i 760000. landred, bj 7264000. ** th4 mut. the malti- )art8, 32 (en* ' which the lotor of the 20, is equal aultiply by )ro'luct for Now, as hat by the obtaining iroducts of Itiplier f a larger ralpar. 6768. ^985, !904. 544. !n the to the f-rs if BXAMPLKs FOR pkaotioe (p. 20 and 21). Cask Nl.~T,> .fed thr maHipUcatinn ofdecivinU when it w :Sl;S" -^ .Aa' all the decimal places of ie pr..lu.t Zm ^ S.6628 687.5 OPBUATIOK. 32814 = - 6.562 X 5 4594- ^6.56 X .7 + 2 52.'! = :6.5 X .08 + 5 39- •6. X .006 + 3 37.972 Product. ♦k «*''"'" — ^* "Terre the order oT the figures of the multiplier and write them undor the multiplioand ; and, sinoe thousandths is the lowest decimal figur* to be retained in the product, we place the uni«' (igure of the mnltinlier under tho thousandths' figure of the multipli- oand. Then, the unit of the product U any ligiireot the iiiultiplu:iui(I by the fig- ure of the muUiplier that iHlls under it will be thousandths. When there are figures in the multiplicand on the rlKht of that immediatelv abovn th- «<,„,- „p >?*^"''®*, .'■",. ° '""'tiplicand on the right fig-e being exSe'JruSLfc Sders" th^n^hS^a ^d^'*"^' "^ '\'' '"^^ lected. except for the Bumose of firwiin^ Jk * '°'>^. 'no"8atidths, may be neg- figure from their product^ ^^^^'^'^i what must b« oarried to the thou««dtli' 63. From this illustration we deduce the following RULK.— I Write the multiplier, with the order of its finurm reversed, and wU. the units' place under that figure if hem^ phcnnd which ts the lowest decimal to be retained intheprTdv^ /^n,!!" ^Y'^ *^' P/f^f fj'^f figure of the multiplier by the figures above and to the left of it in the multiplicand increasiZ each purtud product bv as many units as would have been ccZ7d Aom the rejected part of the multiplicand, and one more 2^ the highest figure m the rejected part of any product is 5, or grZTr than 5 and write these partial products with the lowest fiTe of each in the same column. j'-y'*re III. Add the partial products, and from the right-hand of the result point off the required number of decimal figures. ^ NoTB.— 1. Should the number of decimal niaoea in tha miiif!«ii-..,j u . th^n^the number requ,r,.d in the product. s^rpl/tV'd'eS'n^^ran^ex^nl . l'^:rXt:t:Til^^,r^^,;^i^^^^ product it plication should commenQe at least two places to the right, v.. When the number ot units in the highest order of the rpiecfftrl nort r.f ,i. 'If 48 *i ■fTTLTIPLlOATIOll. EXAMPLES FOR PRAOTroB. tai plactiH OPKKATION. 472.350 _646:{.46 283411)0 188940 14170 2834 189 23 3040.256 orKK.inoN. .^.657.389 3246.360,0 182869"" 10972 2194 146 T _^ 1^ I.9C189 9 »* , . I.9C189 3. Multiply 751.2037 bv 3H ri9« i- he^;;fir ^^^-^^^ ^^ 0-«0^K retaini., only t^Ji^^. in th ^"'t'P'y 1.7323152 by 3962 57302 ,-» ^"*' ^-^l 9.^095. «n the product. "^ o»o4.o7d02, wtamiug 8 decimal places 1. The hide of an ox costs «fi i <; . * »«-l*+»2+(|0,8xfl«$l.63) ^«». $2.38 gain, ^ board, MULTIPLICATION. ^'^^!t^t':^^^i ti:^- -^ *'«^ «>^ other «pe„..: ^ bojv rn„.h will th. rnercluf^t r e/i r?" ''* *"'''' «"'^/ ^'i" ^^^^^^ «'»••» at «1.20; L'4.s at ftmn ^^t "^^ ^oo^^as follows.- l2o vol. HniJo„r.re.p.ctivel,.andh:lVnfrtVeUr^^ have Pete? 1». A merchant f-on^Jais'Siecfs'IJli'^''*'",' ^"^^^ ' ^'"^ *"• *600. '^'«, •».] 12 pieces of I. acHjot . ««:i! °^''"''. *•»*"' co»tai,ur.g 37 jar '(>. if HC<>ir cost §28 a hoMP « r. *'°'^" altogether ? •* rna.h .Mh. C(>w and C*e t t?h ^' ™"'^'' andalarn. y times '^^•vilithe farmcoHtthaosTor L^^^^^^^^^^^ ^^'^ J^ow „,uS 1 1. A H'f.oro.ale ,,r„c.r bouiht 4^ ? , '^''"'^' ^^ '^^ «anie rate ? WI ; h. «.Id ,4 »rarre?Hof tS at $Sf 'V^'""^" '''^ ^^'-^^ ^ bu^hfl. of i,«ed ; it i« requ red t'knowtni ^*'""*''^ ^''<^*« ^"d 11 how i„.f,j bush. 0/ .eed will 7 tTJ , "'*"-^ P"""^'« of flax and ftl l^-.-^.. per U,h. ? An,. 2534 pounlsflaf 77 k^?"^ ^"^ ^'^^ ^''^''^J I.{. In a Wa,ry, there are 27S Jotf ' 7^!"^ -• '''^'' ' ^'^-^^-Sa. U T' ^/'.'* ('<>""dH of butter wha eZ wm^'f.^ ^?' ''''^'' «» ^n io^«)).nghii»!.utter»t?0.18anou„dy i ^he da.rj^.n.an make it. A [arrner desire, to manuTl « m A"*' ^^'■^'^'^^^ mauur. worth $4 the bundrTdSh? S ''^ ' ^^ f '•^ «^ '^nd with »upp««f,g h0 requires 2 hundrj wi f. ^'"' ^^ "'""»'« ]. is Held . '-'. A cabinetmaker earns dailTS'^if^"*^^ /^ '^n,. mo.HO ' tlMWion*, f 0.65 each- hown^m^K ^ ^ hinyfiie. !f!120 : and his d«.r#Jpe„.e«ofth?;h'olefrm7;beir4V^^^^ by every week, tie f^«i*2, .Arm 4 times as much as the Lt^ ''^^ ^^ '^« ^'"ount of »i»e retnaiiider in cash • how m.fl bank , tuck- $1938, and nays .r *'«' .-t >-''*^'*' b^-'^W a cc^tat ll ?»^ ^ ^^ ^ ' ^»'- ^^S fM0 7«f;c.r pound ; had he bou"h?S*^ ofivorjat the rate of ^!u '';? '"•'^^^^doneeig uh SSwlSr."^^^^^ '^'^ °"-^^ ^««Jd H. The repair, and super it'enZ.^ t '^"^•^' P'^^ ^«' ^''^ '^orj ? «&y3 per in le ; the cxr.f rfl« r • •*• ^'^ * fajlroad tract co.st yearly »«••<'*! /Ofljf 7 - ./ — P^'^stinifB for a track 132 -y. A pJu,„b«rfurni«hM ti,— b 1 . . ^n*. $136045. tit ^'"^ \ 2 inches r^oXe'rlarf'r ''^- V^.' ^'^''"^^^ tM4i wa (he third, 8 iDchesat «0%fi .1 '"':, ''°^P**' ^ '"^^es at I •"»'aeeati|)0.y6per)'ard. The first kind jp ■i..i •i 60 DiyrsioN. ;;j:?'«i::ri-™sv;r5.x,«..-s: ^'M. $244. DIVISION. nu^wS^^SJdL'^^^^^ --T tia.ea one the factors, the product and tJ«'n*if ^^ P'°^ °^ fi"l ^ "^"^ ^^'^ «euial«Uer. ^*. 1. How many twnw ,e 7 contained in 994? OPBRATION. Divisor 7 ) 994 Dividend 142 Quotient. >d •'•4 moi« bor fi>r )„•. *li4.64. •tJpio.r)*' ? expenses J ► dozeu of n? '• $244. times one ng one of n. Thus, Itiplied by be iiiulti. Divisor. nuiubei iuder. 2. > quotioat • on the MO them d; then, 7 is oon- remain- he 7, ita ) of the qjual 29 aining ; laininjf, liike 14 ljure of 'i divi- 'Heath (tieot? DiTmow. II '•^ 'M prL^l tV ''T';*' 'tV^^'^-iing any figure, r.n,ukr before''^ '^' "'*' ''^'^ «/ '*« ^»'»'**«<', ««'/ ^t'^tofe « equii to the dividt^Tht' woTk Is ZU^J ^'^ '""'^ ^^^'^^^ »- pliSnTcM)"*''"* "' P"«^ '°"'''- f~» di-W« Wnt the ™^r.. „r «alti. BXAMPLK8 roi PftAOTIOS. 1. DiTide 8164 bj «. OPKgATIOV. Dirisor 6 ) 8164 Diridt^L (3.) 5 ) 714326 142866 1. Divide 8. Divide 9. Divide 10. Divide 11. Divide 12. Divide 13. Divide 1359 QuotiMU S ) 893rM rsoor. 1869 QuoUeok 6 Divisor. 8164 Dividend. 6376 by ft. 5692 br C. 38776 bj 8. 174321 bj 9. 1643784 b7 12. 46216796 by 11. 63412632 bv 12. t ) Nfllt lamfi (6.) 4 ) 662846 QaoMenti. 127.0. 932. 12347. 19369. 136982. 4201436. 14. 1ft. 16. 17. \x. 19. Divide rv;_.- J Divide Divide Divide Divide 10. Divide 2271582 hy 7. I i. 15721 2 by 6. 4056360 by 9. 12980400 by 8 4208479,5 by 6 4607060 by 12. ^023620 bf M. 6. 2. C. t. 4. BITmON. FRACTICAL PROBLEMS. 1. Fine jurda of silk velvet at,ai *T'> u J«fti? '^*"''" ^^^^ *^2; how much did it cost • Alf AI,T«I8.— If the Drioa nfm^w.^l 7ald obtain $72; thep^w 72 TA^r!!;^ ^°u'"'; '" '^^"'«P'ri"g it by 9 wt of a 7»rd. Then/in dirE 2e nro C^T u^'T^i *''*'" f^*»" " »nd the pri« of • r»rd , 72 ^ i = ^w §8 j?r ''^. ''•"" ''"*«'• *•• "e obtain the E wtain thu prioe of m yard. ^ ' "'"°' '" diT'ding 72 by «, w« .hilii=p? """'"«• "•*• • ■'■>"•' i 1"- m».y JollT, in 8890 ^4. Ho, „.„y barrels of «„„,„„. ^,_ „,„ ^bof/if-,^, 6. If 12 inches make onp fnnt . i. . ^ .'^"*- ^^ barrels. $1152? "^ ^""o »t> a cor.i ; how many oorde will be had for 10. A person wishes to distrihnu ifiQ „ i "?."'• ^^^ cords. ^«.";«»1'.^" ^'•^ ''''«'• P™<»- Of "« '^te in the quotient; 34 x 1—34. which we write undtr dTe 47; « — 34 « 13, to which brin/rine down the next figur, of the di? I??"f,5'"«*> '" 3. we form 133; 34 in 133, 3 timei. The 3 we Remainder. JT^/'^'" *^« S'^^wnt ; 34 x » u. u . r ..i "'"''*' ''^ write under which bringing down tfcan«»f «»,..- f*i. i- . ,^"« *"; 133 — 102 -, ai II 133 U)2 318 306 l2 «6 vino7i, ..^:^^^rr-t.lt^2--- ''^*«* •• '*• ml* «• iWwtfa »»f„ 14, 4j^j^^ , 1911 •'«^^ iid it cost • ? it by 9, we «nd the price btflin the prjoe yard wiil eoat '« 72 bj «, w« krfl in 8890 8 dollars, ildren; how i#. $9958. bought for 5 barrels. 164 inches? 'erage sum ns. $2:n. ing 4 cento Ans. 66. did he re- Iw. $62. be had for '2 cords, ong 4 bojs Ans. 24. >o is termed g 47 aun- irtial diFi- ontained in e write in ' - H ir the 47; h bringing of the di- form 133: rhe 3 we .34 X » >te under « 31, t* in 318, 9 ite under Bft ondi- mpletiiiff ^lidend. tfrrmton. •• II. Take for ihtprtt pt^rtial dividend the yn»f *««.A^ ^ ^ the. ««( «™, „/rt, dh{A,nd,/0T the .u^d p.,rli,a. divi. 7' J/^^^y jx^rtial di^iaerui will not eonfain the divi^,or place J.Ji' /'*"■' '' ? '""^'Wtr o/Ver AVWinj „« th, figure, of the PROOV.— It is the same aa in short diviBion. DIVISION ACCORDINO TO THK FRENCH MBTHOD. Ex. Divide 11812 by 72. OPIRATION. Dirideod 11812 (J^2 Divi.-^cir. !!. iGi^"" Quotient. 461 432 292 288 4 Remainder. Omkbtatioh.— We lee by ti.. ex- ample m the margin, that the dirisor M placed on the right of tlio dividend and the quotient below it. This mode JiTei the work a more compact and ■eat appearance, and posieisieR the adTantiigo of haying tho ligares of the quotient near tho dlTisor, by which means, tho practical aiffijulty of mul- tiplying the (lirigor by a figure placed at a distance from it, ij reraored. ABBREVIATION OF LONG DIVISION. «7 By the following method, we avoid writing the products in ic... r division, as m the example of Case II, above. Ex. 1. Divide 8764 bj .365. Analtsis.— In this operation, wo say : 3 is «)ntaiacd2time«in8; we write 2 at the quo- OPEIUTIOV. 365 ) 876.4 ( 24 146 4 ... 4 remainder. tient and multiply the dirisor saying : 2 " times 5 are 10, which sabtracted from I« (because wo iiioroaae the « by 10), laarcs tf irhich ■■)itr»«tfy„eo/. He j^^^, <,«..«*, remainder. ^ ^^*^'^' ^•^ths, hundr^ths, *e. cNo. T),' an'd;r:cVdt;a'r: ''^'"^ *^ ^- C>iven6to be divided by 25,. hat ^„ Bet., operation. OPKRATION. 25 ) 6.0 ( 0.24 1 00 in J?a"SoUonTa?:5"^we'rr *1«i«"»«. we«y: » the quotient. S' ^ JIH^^VjP*.'"- -^d • point Jl fay placing a oil'her at thVrirtr-hanVr',!? '"" *•""» 26 ,n 80 J, contained 2 and ?0 tonS/ '*' V»d "7 •' pher, and say : 26 h lOO IntZ'^T}'''^ hnndredths by Uie !d5?Mo»"!:r ^» 2. 3. 4. 5. 6. 7. 8, S». 11. 12. 13. U. 16. DIT18I0N. form th« 8«Qoa4 we write at fh* n the second pM- be added to t^ t in the unktl lotimt Jigun, nderneath the 8 next figure oceed as with the figures of lia remainder, ind continue ta, we place a the aecond other cipher; iodioatad bj I rtmaiat 7* rritlnj a af.' ^» point a» Bat w then a aonber t» iphnr. Mai. Ithataothin* utheeoiTC^ ■on oipk»r. le diriflor,. thacther» ndend ti*. ktionf we»ajr: » 1* point at >n tenth* ' ud lar ; on of a «u therefore, 66 Use of my isicm.— Division seruM t^ Ai^A. i « *o» ^ny Unu, a numUr i, contained into aZLTuSnk t "hal »am6,r muMi a given number be muHi„lZl?rZ^' '"■'"'"''* Siven number. Division serve, aZ rJni'ttZ^fT"'''T EXAMPLES FOR PRAOTrOE. i. Find how many timea ie 72 coataiaei ia 2S50Q. ^ . Divid'd. I>'v.8or. 72 ) 23596 ( 327 Quotient. 216 ~T99 144 666 604 62 Bomaiiider. Paoos- By MULTIPUOATIOM. ^27 QuoticDt. 72 Divisor. 654 2289 23544 . ^ Keniainder 23596 Diviiiend. 2. 3. 4. 5. 6. 7. 8. 9. 10. ii. 12. 13. 14. i6. 27939 38582 406683 743241 964992 173469 497699 218579 ox J ^00 41126 432606 845002 8«7632 sum 16 18 20 26 30 o6 40 42 47 49 60 63 69 CO Quotients. 1746 2143 20284 31833 12442 13006 8662 14703 ftem. 3 8 3 16 2 21 19 n 4 16 5 23 66 41 56 DnrisioN. 1^ 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. I 52 53, 54. 55. 56. 57. 68. 5y. i «0. 4968 940025 445124 4728 39006 1679407 4306404 167008 7466029 6717890 64 68 70 75 79 80 86 87 90 98 (juotieata. 77 6358 493 60663 82844 To ealculate with two decimals in the quotient. 67980 432101 470896 680094 666648 767642 124674 964321 7246579 7H90645 9120128 687621 3466604 4268901 2486930 *l0712d 81267904 69267421 8IMJ640IO 6947:^0210 468904008 389006753 86742807 707070709 654380316 987664321 8606000041 61247680241 742.^8961401 9649646664 8674289646 4247698734 63 .' 241)0086 45t)»010ti007 378942UU4$ 96 69 72 67 441 386 126 216 <12 367 637 4691 1279 1467 7614 7614 617* 7186 7908 9087 7064 d004 8906 4260 49060 49068 6004: 74086 48647 42867 74651 S4672 59866 300462 9S7684 Quotients. 708.12 6262.33 10150.66 1511.67 989.47 4464.44 21500.39 146.68 2909.96 539.41 9639.21 76463.74 48601.64 166979.03 20129.09 826721.74 225106.64 44867.62 162037.95 4i0 61 64 3 69 47 4f 66 %9 98 H«m. 48 23 16 46 163 380 78 196 328 187 153 1422 240 435 4532 6126 3592 6794 184 7462 6768 2684 5914 4120 37440 39106 49042 13310 11893 32712 48424 88056 46810 186360 88764 s. \ 4. 6 6. 6. 7. i 8. 9. 1 10. DITmiOR. DTVISrON OF D8CIMAI>8. M». 1. Divide 3.466 by 2.4. M OFBRATION. 1.4)5.466(1.44 An$. 24 IM N H M». 2. Diride 0.626 by 7.6. AifAi.T9T».--W« diTld. M i. vrhftle nura- n Jk*"?!. *'^'"' *'*• <*'^'»'"' »ud quoU»nt r / . '^° f*«»*»". »'bioh. being multi- plied together, produce the d.Tidend. w« to «*• uabcr te th« pndNet « (tfridewL OPfiRATIOK. TfM ) 626.00 ( 0.07. 626 00 .dend«oeed tfco.e in the d,W, w Lake fe.m equal b7 npnexing two ciphers to the 2^ AL'V* '"'^"» P">o«eded in the divUioQ oVT ^' '.P;1*' '"'^ ''°*^ *• quotient to be 9.t7, or ff unit 7 hundredths. «7. Prom the preoediog illuBtrations we deduce the following Rui,« I.-Z?tt;irf«- «* »n «,^fe numherM, and point off as manv 2^.e of the divisor; hut if thw$ ar0 mt as many, mmply th, de- fiotmey bi/ prefixing ciphtrs. '' '^^ Or, Rule }l~lf the dividend and divie^ hawe not the ,amt number of decimal,, annex cipher, at the right^de of the term ^l^Unur^bL ''"'^' "*''*'•" '"^ '•^^'^''^ tothepointra, in »OTB l.-To diride deoimali bjr !•, 100, ItOO, .i*. (jr.. jy^, ^mooF.-The proof i. the .ame a« in diyision of whole aam- ■XAMPLB8 FOR PRACTICE. s. 79.1 4. 67.8032 6. 2.3421 €. 0.338 7. 14. 8. 0.21318 S. 10.86 10. 0.1728 2.6 U.4 42.2 0.16 Quotients 31.64 4.174 0.055 0.7852 8.34 17. 0.0776 0.012 140. N tu 8 0610 400 «7. What i, «^ rule /or tht dMtion of dediMta f 58 DivwroN. To calculate ^hh five decimals in t) • *• '*"' '" tue quotient. Quotients. 1.62745 1.19201 8.23846 «. 78318 1.62197 0.189IH 0.13680 PRACTICAL PROBLEMS Ham. 34 740 18478 6984 296 1998 528 960 17178 34 240 4 1. If 4.') yards of cloth co8t SI 2^ fn i »4 . .70 ? * oo per d»j ; ,„ ij^^ ^ in«4T7n ■~^''P»ny"'M«*,«2 8S fi, • . ^'«»- 18 days, in f 47.70, u many davn wni k *'*•''*' «« pnoe of a day's UKn, j: One Of" ^''rS^;*''^ t"!r"""ir* "^ " -"u" '/oS* , Other factor ? »« *• /& and their product 4222 fS PinH ft ^M. 182 milM. BTTMIOII. 59 int. '.8. 5 Kam. 34 740 18478 6984 296 1998 528 960 17178 34 240 4 yard cost 7 t by 46, we otors 45 and f » yard = •«». 12.76. iJl he eaFD 18 days. ■ oontained 70 by 2.65, . 18 days. umbers ia »• 7777. re 70344 7 Find the redths. that per )76? r*69? can be r. 215. pages? *. 80. bought ards? ^" will ». 32. I work, r. 23. howlkr nilM. <»it.«mf6yp. ii^i'J^it^^^Ysilj,^^^^ r^**^ '° • kiln which ihe value uf ii^^ijiS? Sfo \?^ " ''^^"^^ <«>' ^^^e operatioa and of 10.28 per ^ff^Lf^S'.^ '« *«*>™««d at $231.14, aUhe rate prf^%*A^7*^ '"" ""'^^ b^ahelsof coal have b^ ength»8abowt#/S^ ftirr^uirjr^ <'" F^'^^'^a, the meat die yearly, 4wJ^, ^TTour .i/eTrrll^^ l^ow many person. for6every44<«?i«rifi.y ^ "*^"'» ^^ •»•»•/ minutt ^^^S^^i^^lTONS IN DIVISION, ng 28 person. .r«A.:/ ^^ facto., an. 7 ) 39? I ■lii' '•*?«»m/ quotient. ""'^' ^^' ^' ?««<»■««/ will beZ 2. 3. 4. 5. 6. BXAMPLE8 FOR PaxOTlOB. Divide 4536 by 14* a x 7 Divide 9774 bj 18 =r 3 v « Divide 14560 Jj 35 =Vx*V Dividel26375br76 -3 V fi r - Dir de «9384 Ht 49 --.3x6x6. ». Diride 57456 br 72' "'-"^ '^' ^*«'^"- «. Divide 246792 by «4 ""'"^ '*•" **^'""- ». Divide 2962876% 1^5"?^ ^^.^*«'«'»- <"o Dj U6, Being It* factor*. iliM. 324. An». 643. ^n#. 41 «. -4««. 1686. ^»»«. 1662. ^»». 79a Ant. 2938. ^fM. 2370S. ,4 6 3 = 12 3 = 9Q 103 , „. . «IA"»L«S rOB PRAOTtOi. • 4,j:f ^"^ '"'• »-« «.. '«- . .„. ., .„, ,„, .,. ^ -T — '. niin the "*•— nt loill he the Ant. 334. An$. 643. Ana. 41 «. Ans. 1686. it.*. 1663, An$. 79a ln«. 2938. M. 23701. DITIBIOII. fl I the opm. ^Qd 7, and ■Diridlag lo T« A quotient •maiiuler of in diridond, part of tho Tho 3Stf4 •rising froa « unita %t% io Talus M lave a quo- . it muat bo >s makM« 7, wo hkTo be uQita of S3; there'- » dividend, oom dirid- > true r*. aU tht the tnfe rl::^:lT '^ ''' "-« »^« ^-tor, 3, 4, .nd 7, and find th. thetrS^;f:;,LS^ '^ ''^ -^-^ ^^^ ^^-^ 3, 6, a„d 6"r,i^ta i^^e^S^' '^ ''' --S»^e ^-tor, 2, 6, and .""aJd^Ld V- -ii^c^^^^^ '''' "'^"' ^^« ^-- ^' '' *^ -d ,t';/Ld «-e Sdtf ^ '^ ^^^' -^"^ '^e ^--« 3, 6, and 9, a;?.r^'.!^/tb. C TT ******* *• (No.3?,i;t7^'''*"'^"«'*«'«"»"»^^%10, 100, 1000, etc 1. Divide 87 by 10. 2. Divide 5813 bj 100. 3. Divide 7009 bj 1000. J- Pl'^iJe 510040 bj 10000. 6. Divide 200371 by 100 BXAMPLB8 FOB MAOTld. Atu. 2003^ £». 1. Diride 85726 by 4600. 46100 ) 857126 ( 19^yy^. 45 407 405 226 ReiDUQder. »r the entire quotient Isi^^JL III. Place the entire . fij °",:''^" J •'^d « there itre to be 'wXet''"/ 7''' '^°'*"> diTisor, oountine them fmm 1 ^ 7* "^-^de «t fint bv fi« « '^ <>f deoimals, |t and r.jecti4tliVfi^Tre« ?«'•'*' 'T'* '"»»^<». the "kK JL,»«"''?' ''^ *»»• given le abb»«iia»,4 T"7?r'"*«d with anarejectiii»thefiiriirB<.^T" "**•■<*« the ri^ht th... • °' '"• «»ven vifior bj iU anoii.»f « ^^' ®" *•«» "ght. In in., H»i • "*' ""°« ^^^ 23.647 the abbKnii»;»9 ._a ^^'"■"'ea with the oommnn .i~*u-j ' P ^')- 'raJ«to«m«rt8, 14. WoS!^ *••'***•' '^""''•"^ <»' ^-<*°"-' qunner-dollar, din.e, Th^„.cA./coina are the 5^nt,3^nt,2-cent, and 1 -cent pieces. weight of gold and 1 part •# « XJ ^Tl^Mn i ' ? . ~'" ~""**'' *» ?"•*« ^y TABLB OF TH« DNITID 8TAT«a OTBEINOT. }J Sn^"^^"!^ ! r*' '^^ let. ore 10 dollar. « i^K,' " li? Ja^aPd\r;;Stir.;^^'/r;^^ centt, and mi/t'.. «wuaw are kept in dollarg, Dimes, o^nts, and miUa. bcioff tr^tinnm nf - j«ii from th. doJIw kj lb. CiiKlJ T.f fc i ■;', '"'•'^""^i are written I-V236. nunarea thirtj-five luills, To exprrjB any number of centa I07 «0. Reduction is the procons of chuntrin" a .iumi.>, of r -.. II. Tochmg,. dollars ,o mill.,, „nnex Ihre,- cipher,. HI. lo change cml$ to mill,, annex on,, cipher. Conversely, * ' U ^n-'!'"^^" ^^.<^^^'«^« '•««<« 'o rfo^^ara, r/twWe 6« 100.- ntof two Jigures/rnm the right ^ "", «rta« TTT ^''''^"["d'' mills to dollars, point off three fynret. All. lo change mills to cents, point off one figure, EXAMPLES POH PHAOTIOE. !• In $7 how many milln ? -^7000 mlllr^" *' '^"*' "" '""« '"""' "^ '° «' »»«"« *" ' time. 1000 ndlk 2. In 3"j6 cents how many dollars ? Analysis.— In $1 there aro 100 oents. therefore i nctu«. u •quale the n«n.bor 01 dollar, ^^ onit-tl^ """'" "''""*' 3. Change $464 to cents. 4. CJiange 612 cente to dollars. 6. Reduce $3.10 to mills. 6. Reduce 35 cents to mill*. 7. Reduce 704.5 mills to dollars. «. Change 10426 cents to dollars, y. tieduce $4005 to mills. !''• In 20GI liiillg h<.\v many ceuitJ ? Ana. 46400 cts. Ana. $6.12. dnllart in cr».'« onrf MM* to dnlUirit— . -~J«™.«r..-fvs«K-»»Ta.-i-.':.'3^V' S6 PRAfTrCALPK-ORLEMS COM PRAOTTOAL PROULBMH. 1- A broker bo RULEs'^"^'' 'i'HE FUNDAMENTAL 2. m -ugiit stocks lor .•3);^729.90, and ii'w much (lid he gain? sold tlieni for An.9. $43«.2;{.j wa^e- ain.miit to?^^'*^^*' """^"'** "'' •p.'.'.iju, wnai will 12 mouths' co.r; ^ '*""' "' ""•'"•be™e» cost $0.9376, »hal will I ,„„. h»w ,n»,,y of each 't H S .."..; 'j' ""'^ ">/ ««;«« " «^ c..„., eacl, . how ,na,7of e;o-h'w;;d ZZ^^J^ An, 15 a i:,,n.ri,f u Y, •" '^^'^" '^'nd did he te gain by ti,e bargain ?'' *•''■ '^''** '* °«^'; how much did I . '• ^^'"^'ifi"!?! J ;^5 bushels of wheat at !Rnfi9oK . ;^"«-;^^235. -t *().:^7.-. a pound, and he ?ema ni^ • ^1""*^^ ^'^ P*^"'"^'^ ^<" coffee he receive ? ' '^ ^ejuainder in cash ; how much ca.sh did ^- I'' a gentleman's incom*. ho i^'mnn . , .'^"*- *66.586. <5l:iO; andto he8eco;7J2TI^^^ *« the «rst he gare the third receive? ' *^ '^'' ^''*" '^ *^« ^"1: how mucli did 10. A lumber merchant boucrht «8n ln„. f m "*"'' ^^^O. what i,s the price of each 10^?' '*^'^°'' *^« «"'» o*" *'^644.80, li. With a Bank note of Siinnn i -j ., ■^"*'- •'^S.se. my shoe„.ak.r's of srfand m^'o, se'rfnt 7s8?5"h ''" ^*' *'^«' lar.M have I left ? ^ ^"' °* *^'5 5 liow many dol- 12. If a hat cost $4.25. how mi,ol> .„iii a j '^"'- '^202. cost ? ^ ' '*°* '""<5^' ^^'" five dozen of similar hate ^3. Anarmv comnosed of fi2]fifi ,„»„ ^ .i_ -^ns. $255. 13708 men lesfafterTleenial^ern^ '"' °^ ^ battle, has in the army? engagement; how many men are there yet 15. Uow much £ I sellllod ''?'';!'''' ^'^^^ *'^^ ^ ? ^- ^-^«- in giving ,^18 comnZtn ? ^ '"^ ""'' "^' ^^^^ '^ ^^^ «76 1 1>. Jo.oph bought 73 casks of t^vrun at S'^iQ fl « , ^",*- *^^^- again for §,-,2 ; what is hi« nn 'fit ? ^ *^ "*® ^'-''''' ^'"^ ^^'d them 17. A IJauker is to receive .'Sl^^'fin i^ »u ■ -• --• an.ouutingto^aHOO, and he se^tud Z S^^lo^^'T"'' './^^ «^^» Hit of the third? second, to |.4.^20 j what will be the '1 Ana. $3830. "ozen of similar amount of the third? oue'-cit?''" '"■" ''"'''' ""''■''' »-^ »""«'» -ill ^ 19. I bought 150 applea for «1 0^ u ^'"' '^'^^^'S*^- - ' -■ """ ^ ""7 lor 20. A banker received dnrin.r »j.^ a * '^"*' 2656. H2769. Ho paid out duriL tt wi vear ^P^^T"*^ "^^^ '^«''^»» niuch he lias fell supposing le had «ii-4|^?^ •V96843 ; required how of the year ? *^^ * *** ***^ '-^^^^ « bis »aA» at the b^nniac OMENTAL them for 43H.2;{.). 2 iiiuuths' IS. $426. 5?1H? IJ 1 quart Ji0.062o. md geese, le geese at ins. 15. 3 of it at ich did I $1235. i received H of coffee cash did 66.586. iseH$4.20 t he gave luoh did $120. .S644.80i .«5.36. )f $348 ; any dol- $202. far hatfe $256. ttle, has lere yet 8392. U.80. ;aiQ $76 $380. Id them 5949. he firat be the 5830. similar 3.80. 'iij for I66d. during fourth, (1 how pafd 52 Tu ;?K TY *. ^"'*'"'' ^^ '^^'^^^'^ **f bft'-'^y ♦«' which I had ^^22. Frank was bora m 1857, in what year will he be 21 year- the age of the non when the father will be 75 year, old?' ^^.4 24. An omnibus able to seat 18 per-on. ,nakes 12 trm^ oer .lav how many travellers will it carry io one vear ot 365 day^s .^on SL that there are always 1 8 persons at each irip ? T..' 7f?40 2o. If we can buy a yard of tiannel for $1.76 ; how many yards of the sarne quality can be got for .$626.56 ? ' A J Si lJr.m^,^ZTV''\r'!'''^ ?"/^^ ^ '^'^"^'•^*'' the" distance bemg i«y uide^. he ^^Iks during 5 days at the rate of 27 miled ner V ^q^'red what distance he has yeUo go? ^n,. ^fmiles^ remains vet'.'?!;r "'"A '^PT*^'" ^''' ^^«^'^^'^ «»*-'' «24 all^ th'ere remams j et * {6.40 ; what is that sum ? Ans. $2004 40 28 I bought 15 yards of linen at $0.25 a yard, 37lJ lo, "^-'oU at 29 Ahfu'^T^'i^ '•«1»«'-«d/lie amount of my Bill? ^. $123.81. earn p'; dly ? " '^*^' '^ '^^ *^* """'^ = ''^^^ ™"°i' '^'l' J»<» • ealio?*I lo!t^"» n' * ^"7' ?'''^'' contaming 28 gallo1.r Jt^ 'lo^.^b SefiSn d 1 if '"' ^y. '^^kage and sold the remainder for |l.20 per gahori ; did I lose or gain and how much ? Ans. Gained $4.20. «»i ofl?l3"s" Y:^l'^ ^T^ *"'* *'^'^ *"^ '"*^'"g repairs for he L^t I fell 'it ? '* ' «t 80 as to gain $60o1 foriiow much 32. What sum of money is required to pay 34 wu-l^^n^fleh* of whom has worked during 28 day^ at$0.80^^r /^.n/.. I^ft u " -'W'a''^r !Hc«ai»,- afier paying herb ^8 wiaf ll ?•' .'•«'^'"«°^ money had she? !j,,«. $1.55. t.W6 ? " '^•'^Klend when thc^ divisor is 3061 and thequoUent At, A i^.,^ „ . 4iM 198,966. "^ntH ; what proflt does h« ,„ake or. I 76 pounds ? 4*m. $5 25 LfH^i^- i 5>f.^, ' ^-.g;^ MAOnOAL raoB n 48. How much will 3550 laths cost at 22 ceuM ner hT.^'ri ? $13^0^?"'' '"*"^ '"■'^' °** '^^^ ^' *^-=^5 * ««'d did I buy for co^t^^f2^r;sr ^' ^^-^^^ ^- ™"^ i,w^ 53. A cabiaet-.naker km earned $45 in a certain number of dav. 35tdT'^" ^rS^^" '^ "- -^^ ^vear« old, wlrJ^hrXLi was mother^"' "" ' "^*' ""'' '^^ "''"*' *S^^ ^^ »^« f^*^^'^»^ thfratfo7'^?75rrH"'"'rfa'"\''^^'^'^''^»' ^ bouglu 'tfo ^f^J^s 'at ttie rate of «l7o0 each, and 19 shares of Bank Stock at $103 iJr 57 In celling cloth for $610, a merchant gained a« ^mch^^frthe cloth cost hun, lesH $5)0 ; what was the cost? i^ *656 58 Althou,rh I wa« robbed of $25, yet after havin«^id $546 which I owed, I haTe $17 left; how mui mowy hi J? ^ * *^ BILLS AND AOOOUNTe. ff BILLS AND ACCOUNTS. 82. A Bill, in business transactions, is a written statement of articles bought or sold, together with the prices of e,ich. and the whole cost. N0TK8.-I. The party who buje, or who receives money, goods, or serrieM. 83. An Account is a registry of debts and credits. friJ^rH'.rV/'' account should always contain the names of both parties in th« if L^Zi'°i' °"*y '"*^« "?^y T «'le. which may be either debit or credit: or It may haTe two sides, debit and credit. . « u.i. , ur 84. The Balance of an Account is the Jifference between the amount of the debit and credit .«iues. 85. An Account Current is a full copy of an account giv- ing each Item of both debit and credit sides to date. ' /«e^"'~"^° -ooount current hiiTing only one side is sometimes eaUeu a BiU mf 86. An Invoice is a full statement in detail of goods sent to a purchaser or agent at the time the goods are forwarded, giving the marks and coatenta of each package, the charges paid? and how sent. 87. The Footing of a Bill is the total amounr, or cost of all the Items. r^^T^T^" ^^^^ •creditor receives the amount of a bill or an account cur- Z :, » If ^°ri^1?^' '^ ^ ^ PT'^.'^J'. »»riting r.t the bottom of the bill or »«. oouni "lleceivedPaymem" and sigi:ing his name. If tho payment be trade aooount by writing the creditor's name first and his own t,ame under it. as in rorm I. ' '" 2. Bills and aocounts are sometimes paid by the debtor -iving to the creditor a promisfory note for the amount. n e, <-" i/iouiun- In the following bills and accounts the abbreviations are : Dr. for debit or debtor. Or. for credit or creditor. yd. for yard. elos. for docen. bbl. for barrel. bush, lor bushel. lb. for pound. cwt. for hundred weight. 82. What w a Bill ?- M-r««i.» ^fl*^*i^"7~ What i, meant by debtor and creditor?- i^v « BUI $1.70 3.25 .67 .12 .18 .30 5.60 3.25 *, fi 54 48 16 40 75 08 Received Pavment, E. P. Hbaley & Co, per N. Ryan. |158|45 Mr a. Seymour, (Form 2.) Montreal, Sept. 17, 1870. Bought of T. McGiiBRVY & Co. May ej 4 June 10 July 21 << 24 Aug. 3 «' 12 Sept. 2 15 3 4 7 15 10 150 boxes Oranges, ^ $ 3.55 " Raisins, rs> 2.90 cheats Black Tga, ^ 25.00 ' Green Tea, /® 28.50 ' Imperial Tea, ^ 45.10 bbls. Coffee Sugar, /© 27.20 sacks Coffee, ^ I8.6O bushels Corn Meal, /© .85 Credited by Cash, Beoeivtd Payment, T. Moaauv Y k Oo. B*^ FORMS OF BILLS AND AOOOUNTa 71 (Foam 3.) Quebec, June 2, 1870. Mr. D. Johnson, Bought of Byrne, O'Brien & Co. No. 2 7 U 10 40lpair Gaiters, ^.^2.30 75 " Rubbers, i^o 72 ;; C^fi; Boots ra> 3!S0 ' ^'"«k " (3) 2.65 tooperage and Cartage, Insurance, 108 67 $ 92 54 410 177 4 1 00 00 40 55 37 30 L. Jackson & Co., Bj " Canadian Express Line." (Form 4.) Toronto, 0«t. 6, 1870. $739 62 To W. Price & Son. Dr. 1870. i u ?Lk„„J*--^ ^ 18.50 1757 Aug. 9 36 chests Green Tea, . . ./a 31.80f| 1144 Or. 1870. '"'^ ?j|^f l^.^ ^*''*^' Bro^'cioth, . . . .® $5.10 " 27 - 76 " Black Cloth, . . . ® 4 67 Aug. 4 ;| 280 « Red Flannel; . . . ® ""Ta < 24 gross Silk Buttons, . . . <© .43 Balance due W. P. A Son •ot 0.1 50 80 $3966 $102000 35025 201 60 10 32 30 $1682 17 Received Payment, jf2384{ll W. Pwoi t Son. s^^SSlSSSS. ''^'::f^:I'Pfiyli- It FOEM8 OF BILLS AND ACCOUNTS. 'O O C5 O SM _^ •^ tO fO 00 CC *^ O 00 O QQ I AOnOUNTS. 71 5, 1 879 1 ; 75 lbs. 3. liutter >otiDg of tilop at m C0( the " Maine Express Line." Amount of Inmce, $^11)3.01. On Form 4. . » ■ i?^w •'; F^" * Brothers, St. John, N. B., p,.1,1, June 1, 1870, toI>. N. WaL^h, 15260 lbs. pork, at 5} cts. ; 72.15 lbs. cheese, at 8, cts. ; July H, llo2l bushels corn, at 50 cts. ;.Julv 10, 15(50 bbls. Hour at $G.12,Ji. On the above are the followin;? credits : June 25, by lloOlbs. cotton, at (Ji cts; June 30, by cash, $750: July 12, H2,jh lbs. maple sugar, at 7 cts. ; 6450 gallons, molasses, at 37i cts. 1 , Vo 9 *™""°' *^*' ^^'^'^ requisite to balance the account on '^^^y ^^f ^ns. 1121)53.78. 0)1 Form. 2. A ^^' P\ ?;n^'^'-' t' ^''"^l'* ?!" '^- ^^^"'Phy * ^°-' publishers, Montreal : Aug. 4, 1870, iii Juneau's Mental Arithmetic, at 15 cts. ; 50 Smith's Practical Arithmetic, at 37 cts. j 2 doz. Miller's lieador, at H.50 : Aug. 12, 60 lleiiry'8 Grammar, at 7 cts. ; :iG Kerney'a Compendium oi History, at 72 cts.; Sept. 1, 30 Walkingame's Priinarv Ah^ebra, at 18 cts.; Sept. 1, credited by 50 Commercial Arithmetic'.. I' the Chris- tian Brothers, at 40 cts. What balance was due A. M. & Co., Sept. 2 ? Ans. $54, 27. On Form 5. 15. S. N. Kelly bought ofH. Hamel & Co., Quebec, Feb. 3, 1870 IB yds. cambric, at 14 cts. ; 60 yds. calico, at 42 cts. ; 39 vds. cassi'- ";\^^*^^t/''i./^f,y«^10 37 yds. cotton, at 35 cts. ; 'e yds. velvet, a H.70; May 2 .^Oyds. uien, at $2.65 ; May 4, 24 yds. merino, at a"" X r N. Kelly's credits are ; April 1, 50 lbs. cotiee, at 25 ct-. • April 9,_7 cords of maple, at $3.50 : May 20, draft on Halifax, $78 t""%«"' ii/.^i' "''' *^-^^- ^^*' balance was due Hamel & Co. June 26, 1870? ^««. $196.12. Let the pupils make out Bills or Accounts, as the case may be, in properform, from the following. 5 ^.^.-O^^IhT ??'''*" ,''*'^'\'''T^'T'''°'*^*« '^"^'" Gossehn, July 6, 870, and I. Kane, his clerk, collected the amount of the bill • 3b bs. map e sugar, at 13 ci^. ; 16 lbs. coilee, at 15 ct.s. ; 13 lbs tea aty8et«.: 13 lbs. chocolate, at 61 ct<*. : ■- >b". --in-4 a ] 7 r^ 47 lbs. cheese, at 9 cts.; 12 lbs. peppe,, .. 19 ct^.f 20 tbs. but^eV at lb cts. ; 2 gal. vinegar, at 68 cts. Footing of the bill, .$40.S ' 17. I'orwarded per the Eastern Line, June 3, 1870, by B. Ellis & S'ol'e S'^^'l^5i^""'''^C-^n^«\ ''^^''' womeVstockings IMo. 6, at 90 ets. ; 16 doa. napkias, No. iO. at 47 ote. : 24 pair men's '■' nlJ! 76 ■ILLS AND AOOOUOTS. V(^ g'.OV packing, $1.60. ' ^ ""'* ^^"^ '•^'^«'; <- cu. ; charges for IH. Sold by J. M O'Roillv nr * , ., Amount . 51101.95. thier- *27w ill ^ "eilly, Montreal, inr 10 Im7(i tr. a 7i tuier. ^7a ibfl. coffee, at .S6 cts • I'i7(i iho i ' , ' ^ A' C^au- oam, at II ota . ifjAVi ', ^^'" 'bs. lard, at 13 cts • hnn ik- 160 bushels oat8, at io cts il '^> *^^'- *g^'«' •' '2 ^♦V • Julia Meredith, andt/e bS pai'd alz^^"^ ?f*'"'^"«' ^ Mrs. •doz.; 2 doz. silver table TO L t^'^'i'^" **^ f '^'^'•^^' "'^^.TS spoons at $18.60 a doz.. if] "/^'ffut^^^^ ^'^''^ tea- doz.j 1 gold guard chain at * I- fi -p '"'^'^ ^""^«''' »t $7.60 a 20 P. Barfy 4 Son Kinlta ;old toT'^u^ 'K^^^' ^394.76. M follows: 2ioave8white"W'52l« ;,!.""' ^*''«*' «» '870, flour, jt $7 80, 9ilbs:l^""^,"itf6i^.*lVlh, ''"'•' ^^''- "^"-^ - lbs. black pepper, at 42 ct« 9ft iku',. '^^- ''*''''"^ «^ !•> otM . ps. at 70 cSf 6 bush bean: aflUO^" Ui' fh 't ''' ' ' ^^^'^^^ I gal. molasses, 60 cts. ' * '^"t]; ^f ^ ^'^^l ^*con, at 16 cts. ; ^ 21. M. Peter Nelson owes D T W. ^^ooj'ng of the bill, $60.83. 6, 1870, 3 gross «hi?t sJud' ^t 85 i^' T^''""??' «« follows: June stockings, at ,$3.18i; 3 doz.\sL fron/;'i«?'ni^' J^ ^'''' ^"^l^n ribbon at 25 cts. ; 30 pair si kl lovef I't Jl^Af '. ^"S" ^' ^^i yds. at $2.85 ; 22i yds ticking at 45 p^I V !• '^^ ' ,* "^^^^ ''"«« towels, ,22. G TurVer & Son §- .btc sold lT"l^ r '^'' ^'i'' '^'"^^ • ^n^ 17 pair boots, at«3.00: March 'l«iq ^' \- ^''■'^"' ^^^ch 6, 1.4o. 80 pair hose, ;t$L20%3 pair IVe^^P^^^^^^ %fl-«8; A'pril 9 A. 1-t^reen, the following as credl^VnWifi 97 «^*^. "''^'''^'^ «<" 20 cts. ; 10 Third Keaderf atTs 9o ." Affn . o^'^"""^ ^otdetB, at at *4. 75 ; 1 9 Golden Cnuat at *^ J?^ • i'p^. ^''"."'"''' I>"^'-'onanes, ot«. Tlie balance due Q T% Son whfij^ ^^""''•^J*" ^"^'^^^^ -t 37 amounted to $44.05. ' "^^'^^ ^'^ Pa« i iu, . . ^i^.: ^ni. S^" r»:r/''««'<--n.aK No.' 22, at\?12'50 Vr |;;.:?fdo;'w« 2S-in., at .?l.7.5; P.ar h;u. No. M at $27 per doz. : .5 urnlfreflal l«7j' iV'"'^^^{ «• W.lliarn^ Quebec, by H S. Con" ily .[.in^, .'^*!'.S'/'i!''' 'r- ' '•"''«l Mo^- al, to J. B. Po«ton. a« follow. doz. Oct pewter-polJHhed biti^, at w, 1870, 4H pair t.,„g^, at .1", ^ ctn.'; ? S^ck n«*rii,ck*t Vr!; l-^rV \ ' h'^'' -shoemakers' awls, at rm-Sc^K I V^ i ; • ,' ^'* P^''J^ets .4 1,1. Hcrews, at 95 ctH ner ^x i, . ^'"'^*'' rcce.yci yf J ,j p^„,^^ account- N.w s 9 7'J' fh**P^l=bi^tt'ki ;?::acr2r'pi^^- i ete,T%? ' ''»«*"^"P*'-'«»«J04? chaVi for packing; car^ . »i ». .t,u . Sent. 25^ 3.^ yh. Bheetiru, at 1 1 cts. ; 3 yards ♦'i ydH. bioadcloin, at $4..S7A; Oct. 29. 20 Wdf tL^^r^f ^""'' '**.'^ ' ^**.V ^^ yi'' n^eriQo, at 70*ct. the foi mmp crwl.t. N.v. 1, by 22 lbs. butt On this bill cherry wyrxl, «t k:iM l»l>or, attl.so. Wl, J) . . --.er ut 20 cl^^ '«c. 4, by cash, «1 6.00; Dec, d. ■MOtlMWMMItMr fiat i uiace wmiIiu N. P. M. k are cords days »t'"n> of ,u prime factors. °»a»ber are its prime factors, or 8om( ^^■■- What are the prime /actors of 15% ? oombi- tho^?s'm?;l^fhf Jt,^-^,2 the least prime (actor, and Proof. Tl . product of .11 tK. ''"^/"^^^/^^^^^^ n'j«„-.^. aumber. ^ '^ '" *^" P"'"^ ^^^tors mil be the given EXAMPLES FOR PRAOTIOE. Required the prime factors of 6. 1140. Am. 7. 3420. Am. 8. 2445. Ana. 9- 2431. Am. 10. 2205. Am. 1. 28 i. 36. 3. 86. 4. 144. 5. 360. .4n/.. 1, 2, 7. Ann. Arts »o. H. 12673. 12. 12496. 13. 21504. 14. 1.3981. 15. 17199. Ans. Ana. Ana. Ans. Am. more innnhern. ?Zl '^-^"fi'"'"^P^--M,or> common u. ,„. •r Ex. What are the prime factors common to 84, 126, , ,d 210 ? OPBRATlOlf. 2|8_4, 126, 210 3|i2r~637 7 it 2, 3, 105. 3^ 6. ANALT8I8 We find 2 1^ !.» divisor of all the numbers it^^ fu" ^'^■'*°' a oommon tn-'tor • Tio ' '^ *• ''»ereforo, the flrstlJ^f quotit "t«?rciTof ttr" ?l set of quotientl. therefore 3 LJ 7 ''°?'^ common factore'of tl, nui" Th! '"'° no exact divinnr nf >>,.. "uraoers. There is prime factors. ^'- "«^ '«« common 98. (F^// 1» «/i(? rule #0 »w»ri/«« « _„ZI ^ T~ ■-- ■ CANOSLLATIOM. 81 EXAMPLES POE PRAOTIOl. Required the prime factors ooramoo to 1. 12, and 24. 2. 48, 96, and 120. 3. 42, 6;^, and 105. 4. 225, 4;«, and 540. 5. 48, 72, and 9G. 6. 140, 210, and 280. 7. 252, 336, and 420. 8. 960, 1568, and 5824. t>. 330, 495, and 165. 10. 2340, 11934, 12987, and 1485J. Ans. 2, 2, and 3. An$. 3 and 7. Ans. 2, 5, and 7. CANCELLATION. lOl. Cancellation is the process of rejecting eouai far-for, fr«.bers sustaining to each other the ^relation^rdiviS Ex. 1. Divide 112 by 56. U2 66 OPERATION. Ll^J.X ^ X 2 ^ X ^ X %ir%~ = ! = «• Analtsio.— The factors of the dividend are 7, 2, 2 2 and 2, The faotora of th« divisor are 7. 2, 2, and 2. Kejeoting the common fac- tors 7, 2, 2. and 2, we obtai. i for the quotient. 2. When a factor is oancellod. I is supposed to take it. place 14^-^18 'xT'^''^'^'"''""*"^' ^ '^ ^ ^=» X 5 by the product of Dividend, t Divisor, OPERATION. 5 \ ■< ^^ X 5 25 Ifil X IS - "F = ^^• Oi».— -W e hare perform- ed this division without factoring the dividend and divisor, by rejecting th« factors that are common t« both dividend and divisor, and writing the remaining raotoM in their proper places. 103 RULE.-I Wnte the dividend above and the. divisor below a horizontal line. aivtsor II. Cancel all the factor, common to ..th dividend and diiftmn: III. Divide the product of the remaining factors of the divid^mA hy the product of the remaining factors o^the d':^^^:^ result will he the quotient. ' Ml. Wht w cancellation T- 102. What m Ifc.TiliT/bi^'i^iii^a^i^ 4* Sf f i. i4 li 11 Ans. j\. Ans. 17|. Ans. Vil Ana. 4. Ans. 6. Ans. 15. •■ DIVISORS 01" KUMBIBS. EXAMPLES FOR PRACTIOC 3. 16 X 24 X 48 -^ 32 X 36 X 38 = 4. 12 X 7 X 6 -f- 2 X 4 X 3. £. 16 X 6 X 10 X 18 -=- 8 X 6 X 2 X 12. f . 84 X 12 X 18 -r- 21 X 24 X i). "• 72 X 18 X 16 -^ 24 X 16 X 9. 'i. '^2 X 9 X 12 X 5^ 3 xll X 6 X 4. 3. 76 X 34 X 96 ^ 17 X 51 X 32. JO. 25 X 7 X 14 X 36 •^ 4 X 10 < 21 X 64. n. 184 X 145 X 80 -^ 23 X 29 X SO. }q* ?o ^ f \!!> X 15 X 18 - 7 X 54 X 7 X 3 X re numbers is their crr/atest tommon divisor. '» '"cir ^reafesi COMMON DIVISOR. 106. To find a common divisor of two or more numbers. B.T. Required a common divisor of 9, 15, and 21, OPKRATION. 9 = 3x3 16 = 3 X 5 21 = 3 x 7 A.VALTais.— Wo resolve each of the given numbers into two factors, one of which is common to all of thorn. In the operation 3 IS the common factor, and is therefore a common divisor of the numbers. lOT. Rule. — ■ Resolve the given numbers into tk eir prime factors, then xf any factor be common to all, it will be a common mvMor. m. What w a eommuB iiymr 1- 104. What it tA« gceatMt ooinmon diTisor T ORfiATIgT COMMON DIYIBOR. 83 EXAMPLES FOR PRAOTIOB. Piad the common divisors of the following numbers i 1. 10, 15, and 25. 2. 15, 18, 24, and 36. 3. 3, 9, 18, and 24. 4. 21. 77, 35, and 42. Ans. 5. Ana. 3. 5. 28, 14, 42, and .S6. 6. 10, 35, 50, and 75. 7. 4, 12, 16, and 28. 8. 82. 118, 48, and 146. Ans. 7. Ans. 6. 108. numbers. GREATEST COxMMON DIVISOR. To find the greatest common divisor of two or more Ex. What is the greatest common divisor of 168, 210, and 252^? FIRST METHOD. OPBRATION. 168 210 84' 252 105 126 28 36 42 Analtsis — First find the y^vime factors common to the numbers, (IW), which are 3, 3, and 7. Therefore the greatest common divisor is 2 v 3 X 7 =.42. (105, VI). 109. Rule. — Find the prime factors common to all the v um- bers (99), and their product will br the greatest common divisor. The prime factors of SECOND MliTHODo OPERATION. 168 = ?, X 2 X 2 X 3 X 7 210 = 2 X 3 X 6 X 7 252 = 2x2x3x3x7 AHAtvsts.— The prima factors common to the three numbers are 2, 3, and 7.Therefore the great- est common divisor is 2x3 X 7 = 42. (105, VI.) IIO. Rule. — Resolve the numbers inio their prime factors, and find the product of the common prime factors. THIRD METHOD. ill. PftixoiPLEs.— I. If the less of two numbers i» a divisor o the greater, it is their greatest common dhrisor. II. .1 divisor oj a number is a divisor of any number of times that number. III. A common divisor of two numbers is a divisor of their sum, and also of their difference. IV. The greatest common divisor of the diference of tw^> num- bers and one of them, is the greatest common, divisor of the tioo numbers. 109. What it the rule to find the grtattH eommon divitor.flrtt method t— Stcond MMhod t — Third mMhod t '.t*W f-rl 5-i Ml 84 LBA8T OOMMOW MULTIPLE. Ex. Required the greatest common divisor of 117 and 1366. fhli! ' ^"^ ''^ * '^'^'sor of 13t)5, it will be their greatest common divisor. J3y trfa^ I17 « found not to bo a divisor of 1365 sinj there is a remainder, 78 of 7b and ?i 7 ^ *^' «:^*'"«' ""'^'"on d'^isor r II IV^ R'f"**. ^'f°' °^ "7 and 1365. OBa.— A knowledge of the PrinoiDles mn »jn u ^°™'~T''« greatest common divisor of fhro^ „, by findmg the greatest common diSr of two of ^^^^^ °«" be found ^ommon d.v^or of this greatest common divlsoraid°r^/'"'' ^^""^ ^^^ S'-*^'»^*«t The laat common divisor will be the g-atr^oro.^tTst^^f^S'thrn'umU: common divisor of 117 and 1365. EXAMPLES FOR PRAOTiOB. Find the greatest common divisors of the following numbers ■ 72andIfiB A^^ ^. .. 6 lumoers. 1. 72 and 168. p. 175 and 455. 3. 169 and 866, 4. 84, 126, and 210. 5- 12, 18, 24, and 30. 6. 385, 462, and 154. 7. 12, 16, and 18. 5. 210, 350, and 770. 9- 70, 105, and 216. Ans. 24. Ans. 35. Ans. 1. Am. 42. Am. 6 10. II. 12. 13. 14. 15. 16, 20, and 24. 4,^^ a 78, 234, and 468. * 2041 and 8476. 286, 429, and 716. 1649 and 5423. ,^ 92, 116, and 124. ?"S.P'/^2^'^"dl386. 17. 49373 and 1477;j 18. 3013, 2231, and 2047. LEAST COaiMON MULTIPLE. ,.n o*;.±°„??"^«^„?^«^<^ipIe ^^ a number exact). A'..:.;u. u. 2)J_ 2)_j 2) i 2) .' as. LEAST COMMON MULTIPL*. PIBST METHOD. ' OPERATION. . ' f V. iu t SECOND MJ^THOD lae second I, :<^c..rAi-r^„ the facfnr 9 «r. 6 in a line undorneath a. before W , ^.^^ '!°"*°'*' ^»« *^« "n Ji^hled'SiVm" •wr, ti 1 the dirisor and r-.»,r j "'^- "J continue 'a divida ht, „ ^"."'^'^ "um- ' 1 1; it 86 r&AOTIOM. IS 118. Rule. -I. Divide hy the smallest prime number that is 'mi-xacfdioisoro/twoor more of the nmnhers, and write the quotients and the undivided numbers underneath. II. Proceed with the restating numbers in like manner, until ffiere is no exact divisor of any two of them. III. The product of the divisors and the resulting numbers will be the least common multiple, sought. lasuo™ Jfi^^e"""'"' '" P""' '' ''"'' °'^'"-' *'»-'' F^'J""* « **"' EXAMPLES FOR PUAUTICK. Required the least common multiples of the following numbers : 1. 24, 36, and 20. 2. 7, 14, 21, and 15. 3. 14, 19,38, and 57. 8, 12, 16, and 20. 32, 34, and 36. 20, 36, 48, and 50. 9, 18, 27, and 54. 12, 16, 42, and 60. Ans. 360. Ans. 210. Ans. 798. 9. 10, 45, 75, and 90. 4ns. 450. 10. 12, 15, 18, and 35. Ans. VZiiO. 11. 25, GO, 100, ami 125. 12. 22, 12, 44, ami 11. 13. 18, 27, 36, and 40. 14. 270, 189, 297, and 243. 15. 64, 84, 96, and 216. 16. 84, 100, 224, and 300. FRACTIONS. 11». A Fraction is one or more of the equal parts of a unit. 130. Two integers are required to write a fraction one to express the number of parts into which the whole number is divided, and the other to express the number of these parts taken. If an apple be divided into 2 equal parts, one of the narts is o«]UA one half; if divided into A equalVt^ on^ of the prrt^f ca ,e5 o^ third, two of the parts two thirds; if divided into 4 equal nartl oZ 01 the parts is called onejourth, etc. ; if divided into fLuT^^t. one of the parts is called one fifth, etc. ^ ^ ' The parts are expressed by tigures ; thus, i One half is written One third »* Two thirds " One fourth " 'i h Three fourths is written One fifth « Four fifths «« Five sevenths « J£pi".t^^r,^ix'^„,Xr3:r*>Arr,.":r: ' rRAOTIONft /..wffhellleT^^'i^^^^ the one munfof thirnf ."^f **^' """'^^^' '^' V^'''' ^°d shows how 124 S f^i^'l^"" ^' ^*^P'-«^^sed by the fraction. T Ti" ^T'^^f^'going definitions, it follows divided the\iti!^^.!^''x'-''"^'^^"^'^^^^ ""it or quantify of i;i:^'^i;:''^^«3^'^? ^--•- " f y^r^-> the part or fractional unit. I i. thi da.onuu«^;3X^S'r '*' ''";^ "P'-^^^-'d or numbered is 5. Si| is the nuu.er*tar^iT„t1 n^ " '?'''""' ^ ' ''^"^' '"*^'«- ^''-« ^.^Pt. "'^''^^'''"^^^^^^ - '^'->>^^> ^W,W, and *74^J-.'''''*'^"''^^'^>^^'^'^^ '« distinguished as P.o;,e. and as l^^-^^^^^^^^^i^'^ i« o°e whose terms are integral ; f ^'^' ^ f ^»f|^^«tion'- fraction of a fraction ; a« 1«^ -^ i4ftft^#ractiOn is one having a fraction or a mixed number ;ip,. 1" ^T ' *^- ^" improper iniction f- -,«««« WWWttWi- 11J8. ^ complex fraction f— 133. ^ nixsd mub- ^'ll . l^M ii ■il ji 68 REDUCTION OF FRAOTIONS. 1»4. Since fractions are expressions indicating the division of one number by another, it follows, 1st. That if the nvmerator he multiplied, or the denominator number ""^ """*^'''' '^'•^''"'■^''^^ *'* multiplied hy the same 2nd That, if the numerator he divided, or the denominator mm£ ""^ numher, the fraction is divided hy the same 3rd. That if the numerator and denominator he hoth multi- plied, or hoth divided, by the same number, the fraction will not oe changed %n value. REDUCTION OP FRACTIONS. 135. The Reduction of a fraction is the process of changini; Mb terms, or its form, without altering its value. 136. Case l.~Tunducea whole or mixed number to an equivalent improper fraction. Ex. 1. Reduce 12 yards to fifths. OPERATION. 5 X 12 = ^, Ans. iJt^"^' ^V^\'~^^Jipi^ '*« wAofc number by the aiven denowu E.v. 2. To reduce 15| to fourths. * ANALTSis.-ln 1 there are 4 fourths; therefore, 4 times the number of whole ones equals the number of .*?*• ^^^^"-Multiply the whole nvmhr by the denominator ANALYsjs.-In 1 yard there are 6 fifth?, and in \Z yar.i8 there are 12 times 6 fifths = 6 0. OeiRATION. 16J 4 1. Reduce 2. Reduce 3. Reduce 9 to thirds. Am. ^. 12 to eighths. Am. »^. 25 to fwurthe. 4. Reduce 36 to fiftlie. EXAMPLES FOR PRACTICE. 136, What whole nnmher Mtm^toaR Reduce 16 to ninths. Ans.^^. Reiiuce 70 to tentlifc;. Reduce 52 to fifteenths. Reduce 35 to sevenths, ^^^ ^Reduce 81 to elevenths. ♦• redaction fa/ra^tionf— 137. What i. ti^ w,i« /■ Z — : eqwvaimt imj»roftr/rattumt '^ rMuemg a 6, 7. 8. 9. 10. Reduc 11. 12. 13. 14. 16. 16. 17. 18. 37|. 2"-i 7 1 'A V y 2, both' terras of this result by 3 and obtain | for tho final result. As 3 and 7 are prime to each other, the lowest terms of Inst ead of drndipg by the factors 2, 2, and. HO. What M the rule /or redvctM n»^.»....i^~.f— ^.— . TT" ■ \, %-\i pi 90 I ! k RSDUCTION OF FRAOTrONS. Dmde both terms hy their greatest common divisor. 1. 2. 3. 4. 5. 6. 7. 8. EXAMPLES FOR PRACTICE. Reduce the following fraction8 to their lowest term, : SiT- 27 lite n- m- m- 143 A- Ans. Ans' ^. Ans. g. Ans. 3?j. 17. 18. IS. 20. 21. 22. 23. 24. 2H8 fNv fft#. .Tn + o* 4n» f. /1ms. I Case lY.—To reduce a fraction to a decimal Ex. Reduce % to its equivalent decimal. 7 _ > FIRST OPERATION. = f"So- = AVV = 0.875, Ans. SECOND OPERATION. 8) 7.000 0.875 annex tlui ANALY3I8.— We firit .,. .^ same number of ciphers to both ticinvj! (;" the fraction; this does not »''«V'"'\ ''^'"°' ('-'^.ard.) J we then /'^.'/ th. proper I Ex. 2. U«. 0.024. <5, o.e.'is, 7. 0.0008. 8. 0.6H. Am. A. ^«''- TlViJ- 9. 0.000125. 10. 0.8|. 11. 4.00075. 12. O.OC'I. 13. 0.57}. 14. 0.1 GJ. 15. 5.62JJ. 4 3 .4n». i 1.4H. Ca«H5 VI. — yo reduce a compound fraction to a sirnole one, ^ ^ r Ex. t li«»lMC. <^ ■J Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14S80 (716) 872-4503 >^^ '%■: , 93 ■•DUOtlOH or FRAOTTONS, II MMIpl^ the remming numerator, together for „ new n,^ merator. una the remaining de„om{natore /oL nJZJo^iZZ EXAMPLES FOR PRACTICE. 1. Whatis Joff of|? 2 3, 4. 6. 6. 7. What is i of|of|? Whatis Jof^ofjof f? Required the value of « of 1 of A of 21 WiS.^h"'"' f * ".^f V'<^ 'oV.unp{e fraction. What 19 the value of | of i of 5 of f' nf 24 ? Reduce A of J of A I a !nnp!efra^tily^ ' 8. Reduce ^ of X of M of 9| to a whole number. 1 n' wu *' • ' '^^ ^^'"« of J of 2i of 1 A ? 10. What IS the value of A of # of A of ii of «3 ? 12. Required the value of J of 7^ of 1t% of ^ of :"(. 150. Casi VII.. nator. Am. ^. Ans. ^. Ans. ^^. Ans. 2^. Ana. |. Ans. ^. -To reduce fraction, to a common dmomi- a CGI »^m„o„1,ro?,;iLr' *'°°'''"'''"''™'°'«l™' -'-• having a l«"lRaT OPERATION. 2 3 3 4 4 6 X 4 4 3 3 3 3 6 6 6 5 4 4 40 60 45 6t! 48 60 ANALTSia.-The product of the denomi- nators is evidently a common multiple of the denominators. Multiplying both terma of the fraction § by 4 and 5, and of | Ly 3 and 5, and of 4 by 3 and 4, does not change the ralueof the fractions (134, 3rcl.), and to- duces them to equivalent fractions having a common denominator. Hence, the SECOND OPERATION. i' *' *» = *8, M, n- 15». RiiLE.~Multipl^ the terniH of each fraction by all the , I a, . 2 ai . f a> 7. 8. ; 9. ; 10. J 11. ; 12. 1 13. } 14 * lo. 1 quotient. ReduoA 1. 2. 16«. s BKBUOTION OF FRACTIOl^g. 93 EXAMPLES FOR PRACTICE. Reduce the following fractions to their comrT,on denominator — i Am S. J»« 1A in . . . ' i and f 2. ^ and a. 3. f and |. 7. 7j. ^, and ^• 3 ft « /Ins 18 2 5 4) 2T' ■"i (I lot 1(7- 1 II li 1 4. ^ and f, ind . and 5. ^ and ^7.. i47l.f. •?§. 25_ 6 '8 Ans. 4i|), 8. 9. 10. 11. 12. 13. 14. IT- ^««- ^. f§) If." 2 ' ,f ' ''3 4 7 V< II' 5, ail' I 1 3' and ^. and .'^. and I or ^"«-Hi, r,M, ^ 2 3 1 ;< ,-! ^• Ans. f2|, ^ ^^8^, 11^. ir. H/i'oTe; and iil ^"*- A^^' A^A, Ifll- JI54. Ca.E VITI._ro r.^«c^/mc.'/on, ^0 their least common (fcnominafor. common 155. The Least Common Denominatni- ^p f„ fractions is the least denominator to"rcrtheVara"be"r duced, and it must be the least common multiplj of their denom- ve.r. Reduce l J, and ^ to their least common denominator. AHALr»iB.~Wt find tb« loaatcom- mon denominator, by (i.i^, to be 24. We then take such a part of it aa i« OPERATION. 637 2)6; 8' V2' 2)37 3)3, 2 X 2 X 3 X 2 = 24-] f = 12 2, 1. Ans. expressed by each of the fractions sep- «ately for their reapectiye new nu- merators.Xhus, to g^t a new numer- ator for |, we take | of 24, the least oommon denominator, by dividing it by 6, and multiplying .he qMotientby 6. He proceed in like manner with each ot the fractions, and write the numerators thus obtnined over the least common denominator. Hence, the ; - - -.-■ "-""• -• -^ "'" ine imst common mult dmominators, for the least common denominator " - 11. Urnde this common denominator by each of th,> ^;, 1 nomi:vUors, and multiply each numerator huthi ^^'''^'h- quotient. The productf Millie theZTZutors. "'""^^"^-^ EXAMPLEH FOR PRACTICE. Reduce the followinL- frufitinns fo thfir Ifaat » 2. I, ^,V audi .«. ^r-»tii^J§- ^2 - U ■ -5« T, - „ """""uior. iienee,the !»>«». RULE.— I. Find the least common multinle nf t\. • nominators, for the least cnr»m^.. .7...!, ".!^""'^'' of the given 156. W^.t.i>^ ru„y«. re4.<,i^J-;~;;^^ n m ^m 94 ADinriON OF PRA0TION8. Ii' ib I 3. I I I, and ^. 4. H- i, f ?. and f ^ /k, A, ^X, and 2f; 6. I I 6, and ,V- I- ih ^, I, and h 7' TT> 'i) and 51. 9- A- e»"5, and 7i. 10. 5/^, 7, 7 1, and 8. 12. i !), 7, 5, and 4. J^- Br T^j, T^, and ^^. Jt- M, 7^5, -li, and A- 15- 1^, A; ^f, and i«. ^«s nU' im. tVa, im- 4mo 2J 20 00 28 --X/IA. ^, yjj, ^^, Ijj. ^n»- m, hm m, ^' ADDITION OF FRACTIONS. NoTES.—l, Fractions, to bo added c subtracteil, must be abstract or of iik« denomination, and must have a common denominator. 2. Only units of the same kind, whether fractional or integral can be added ^together. i Ea:. 1, What is the sum of |, f, and ^j? s ^T^. OPERATION. 9+20+14 24 — 43 Hf, Ans. Analysis.— M'e first reduce the given fractions to a common denominator. And as the resulting fractions, ^Pj., |o, and i.| have the same fractional uuit! we add them by uniting their numerators into one sum, making 43 __ i ^ the answer. ** Ev. 2. Add 7 1, 8^j, and I J. OPBRATION. 7 + 8 + 1 =. 16 I + A + S - _lf 17|, Ans. Analysis.— The sum of tne integers, 7, 8, and 1, is 16; the sum of the frac- tions, f , ^5^,, and 1, is Ig. Hence, the sum of both fractions and integers ie 16 4-1^= 17|. Hjnoethe 157. Rule. I. To add fractions. — When necessary, reduce the /ructions to their least convnon denominator ; then add tht numerators and j)lace the sur.i over the common denominator. II. To add mixed numbers.— ^rft/ the integers and fractiont aeparately^ and then add their sums. Note. — All fractional results should be reduced to their lowest terms, and if improper fraotions, to whole or mixed numbers. 11. 16T. What M «A« general rule /or addin fractiont ? w. SUBTRACTION OF ^XAnTjONS. KXA.VPLE8 FOR PRACTICE. 95 1. 2. 3. 4. 5. 6. t i . 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. Whatisthr ^muufl 3^ ami 3? Wliat IS the sum ui'i, 7.. anil ' •! What IS the sum (A-1,X, * and 1 " Add h /„ I an,| g^' ^' '' ' * • FindthesumofJ, I, §, and||. Finu the sum of i, » ii arui 29 Awll^^' •'- - -^"" '^'J^ V'^. ^2^. and 2A. A;d4i, l.,aad4A.^' Adddofi, 4of^, andr ^ Addf of^, iof^ofl, ami^. Add 254, 327^, and 25^. ' t^'\ 5. I Ar A, and H.* ti>KlthesumofI7|, 18^, and US. Ad.Uuf/rof|2toYof|! '^ Add3^ol5i, 2^ol-7i, am]^,^4. /In.s. 2|J. Ans. 2/5. .ln«. 2Ifg. 4n^. 10^. /Ins. IfJ. Ans. I161f^. 4n.s. Iff. Ans. 40^. SUBTRACTION OF FRACTIONS. ^^. 1. From I take %. Ex. 2. From 24f take I6<. ANALTsis.-We reduce the given fm- tions '0 a common denominator, and have j-^ and /^ which express fractional unita oi the same value, ^hen 9 twelfths less 8 twelfths equal 1 twelfth = ^, the answer. FinST OPERATION. 24^ = 2414 16i=._16|f 7|| Am. A.VALYsrs.-We fir.t reduce tho fractional parts and i. toacommond.n.„.i„„t.r,35. sL'e "e cannot take 2,8 f,o,n 15, we add 1 SECOND OPBRATI«N. 24^ =. i|i = ass w = m- we hi:: fcV^r ^"^''^'^-^' an^subtT^t g we have 7|2 for the entire remainder. duce, he mixed number^Sp^peTfr™: t.on.0. and these tractions to acoKnX Si?""/- ^l" ^''''" subtract the liL frMt.o,. from the groater. and, reduoio* .r M Mk til m f6 >t*<^w->'-- MTTLTTPLIOATION OF FRAOTlonB. 158 RuLB. I. To subtract fractions. - fT/ien necfsmry, re> duce the fractions to theh least common denominator. Subtract the numerator of the subtrahend from the numerator of the min- uend and place the di/erence of the new numerators over the com. mon denominator, II. To 8ubt,act mixed numbers.— /e-Y?«ce the fractional parts too, comrrwn denominator, and thai subtract the fractional and integral parts separateh/. Ov,-Reduce the mixed numbers to improper fractions, then to a common denominator, and subtract the less fraction from the greater. i7i = Ans. An^. I. 2. 3. 4. 6. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 19^ -'m= Ans. 15 33. From 'i offtake J of ^. 34. From I of I take | of i. 35. From ^ of } take f of ^. 36. From « of ^j; take i of ^ EXAMPLE.S FOR PRACTICK Ans. i 21 If- -„ 4 - iH = lof - 4- ^h - H = 8^ 65. Ans. i§. Ana. ^f. Ans. 10 J. Ans. 5^. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 71^ - 13^ =. 75 - 1\. \r ^2 _ 'i — Ans. Ans. ^729 ff?T' ^'"M - ;^A = ^s - 2|. 165J - 77f = h^ - ^^^ = Ul - HI n - 2f = 47 - Ij^. 1015 12-7 Iff- ••^^ = 93i. 63^1 - 342iJ = 25f - 13'i 17| Ans. 24^. Ans. 87^^.. Ans. 3^. 4ns. 4|f. Ans. 5|f /4?i.s-. 291 f. /Iras. j^. 4n. X m. 20. 7i X Hi = 21. Ux,7^. 22. « X 71* = 23. 24. 25. 26. 27. 2H. 2y. 30. i'^llolli 1? w (ll ■Ig X .'j. 12| X IIS = 4i X ^ i X J X i) V 2 Iff ^ 7 I X li X ii X v lit X I X 2 X 5^ ,7 y 4 3 y 54 - 3 _ 5 - V 5 I Ans. 2\. Ang. 2i. 4ns. 60^. Ans. 63|^. /4ns. U7i. Ans. ^. Ans. |. 15. l\ X 21- = /Ins. 5^, 31. Find the value of 2^ times , 32. Kinti the value off of If offg of » 33. VViiat is tjie product of ^ of j of J by 11 ? 34. What is the product of 12^ by 5^ times 6|? PRACTICAL PROBLEMS. Ana.l. Ans. 3^. NoTC. -In buflineBs transiictions it is customaiy to add 1 cent when the fraotion iseqnal to or gie!it€r than a hailof a cent, and to omit it when it is less than the half of a cent. ThL' fraction is retained in the following answer''. 1. 2. 3. 4. 5. Required the cost of (;} lbs. of ham, at 12^ cts. per lb. T^ yds. of tape, at .''>| cts. per yard. 1)5 quarts ol plutiif, at 7| cts. per qt. .'iG lbs, of chalk, at | of a cent per lb. T^ yards of nuislin, at 9 J cts. per yard. 6. 7 A lbs. of beel', ut .0 cts. per lb 7. 6^ bush, of apples, at 74^ cts. per bush. 8. 12^ bush, of oats, at 62^ cts. per bush. Ans. f 0.85^. Ans. |!0.75JJ. Ans. .'5!0.74|. Ans. .'i!4.84J. IW. What it tht rule/W the muUijAieation of fraotion* t 9. 10. 11. 12. 13. U. 16. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 34. 35. 36. 37. 38. 39. 40. DIYIBION OF FRAOTljNS. 79 bush, ol'salt, at J of a dollar per liusb. 6i quarts of nuts, at [)% cts. per quart. 2| yurdrt of cloth, at J ,,f a .iullar per yd. y barrels of vinegar, at $6 J per bid. 15 lbs. of almonds, at U.^ cts. per ib. 8 J yds. of cloth, at S*n per yard. 15 yds. of ribbon, at 2(ii cu^. per yd. 7| lbs. of coffee, at ^ of a dollar per lb. 8S cords ol' woo(J, at .:<2| per cord. 12 cords of wood, at $i;,37i per cord. 42 budh. of apples, at (13^ cts. per bush. 11 cwt. of sugar, at ^'J'l per cwt. 7 J do«. of eggs, at 12i cts. perdoB. llf bble of salmon, at ^^* per bbl. I2| bush, of potatoes, at 37^ cts. per bush. 22f yds. of seiicia, at 87^ cts. per yard. 7 J cords of maple, at $5J per cord. 4i bush, of rye, at $1.75 per bush. 10| yds. of calico, at 15| cts. per yd. 35| lbs. of raisins, at l,s| cts. per lb. 7| yds. of cloth, at $3^ per yd. 75 J bush, of wheat, at *ld per bush. 9 doz. of adzes, at $10^ per doz. 6| bush, of turnips, at 37 ^ cts. per bush. 23| cords of wood, at |3^ per cord. 75ii lbs. of sugar, at 7| cts. per Ib. 212| lbs. of beef, at 7^ cts. per lb. 3| tuns of hay, at $12^ per ton. 14| bbls of vinegar, at $IU| per bbl. 6^ gal. of molasses, at 2oJ els. per gal. 18 handkerchiefs, at J of a dollar each*. 134 lbs. offish, at 'J| ois. per lb. 9» Ana. ?6'Ji, Ans $2.27}^, Ana. $1.42^. Ana. $3.99. Ans. «;221 J. Ana. $26.58. Alls. $0.96;t .ina. Ana. *41f^. Ans. 1.74^. Ana. f 25||. Ans. $i}5|. Ans. $5.85J. Ans. *1.52.|». ^^1 i till 111 DIVISIOiV OF FRACTIONS. 163. Case 1.— To divide a/raction bjf an integer. Ex. Divide f| by 6. FIRST OPKKATION. f I - 6 = A- 8E0OND ePERATION. f I - 6 = H ^ A. Analysis.- In the fim operation, we divide the tidinorator of the fraction by 6, and write the quotient, 2,over thedenoin- inatnr. In the seeond operation, wa tnuU'pl? »he denctuinnt'.r of the fraotion bv the .livi.sor, t), and wriir the pioduot under tlio numer- •tor, 12. Henoe, /•.«f/l?7 '^' numemtor or multiplying the denominator of a fmctxm by any number divides the fraction by that nmnber (1S4) IM DIVWI05 or FRAOnOMB. ■ •4. Cask U.— To divide an integer bt/ a fraction. tiw. /fow many times wilJ 24 oofitain ^ ? riRHT OPKUATION. J4-?- ^= 168 ^ 6 = 28. • f'JCONl) OPKUATION. 24-4-^ = 4x7 = 28. OPK RATION. 3 • i - ; X I = f^. /ANALTHis — The integer 24 will co«- tain j at) many timoa a.« there are *«•- «»'/(» in 24, equal 168 .-uvcuthn. Now, it' 24 contains 1 seventh 168 timt's, it will contain ^ at many timoa u« 168 will contain (i, or 28 tt^ J t" the aei'ond operation, we divide HW*ft " .«r by the numerator of the fraction, am multij^ly the quotient by the •*w^i».m,'.r, which produces the anme re.-.mt aa in the tirst operation. Uonce, thruluiq hji a f, action ajtisists in multlplijing by the dtnomi- miw, and dividing by the. numrrator uf the' dioiior. Id the numerator of the dividend bo divided by the numerator of the mtf*»,i} (biS Will g ve the same result as tho rule. ^' ^P1>*f e»ncellation where practicable. EXAMPLES VOH PBACTIOE. Ann. |. Ans. tj. 4. 23 -f i. 6. J - ^ Ans. H{. 31. ttt,, WhatU Affjjoi.eral rule /or dividing fraetioni f 8. aVV f. 9. 2i^l^ 10. ^ 4- I? DIVISION or l-BAOTIONS. ^«*- m- 1 19. J ^ ^ /ln«. 3. 11. 7 12. J« -. I i:ii = Ans. ':l 13. 7 i 14. § - KIT. 15. 63 -I- X = 5^. 16. 3i 17. i^ ^ 2S 18. i^ -- 49. /Ins. 21. 6 An8. 117. i20. ill -^51. 21. i - ^ ins, 7 _ 1 J — JiJL — 22. hi -f- 08 23. g| * 24. 15 2o. li) in«, 101 :w= I'ft 26. M - 19 27. 93 ^ 47 i:^ if.- '? JJ = Ans. 3J^. 31. Divide J of J by | of}. I X I = A A 29. 81f -f 91 = 4n#. yj^jl A.N4tT«w._The dividend, re- duced to a siiuplo fraotion, is 7 . the divif'or, reduced in like man- "'-''■' '* (h i ^^^ ^2 '^•'■iJed by 2 18 ISf, tho quotii'nt reijuivod. 0? wo may apply the general rul« directly by inrorting both factow rill, , . "i the dirisor. The Moond method of solution has the twofol 1 udTan^igesof givinc- the an.w- by a single ope.at.on, and of affording greater facility for cancellSn " W = IHJ, Am. Or. i X I X J X I = 18}. 33. Divide J of ^ by X of A. 34. D.vide|offb/|?f}.'^ 35. I>|videf of7^jby^j-ofl7f .^(.. t)ivide^(yof4by|of3i. 37. Divide I of II of A by } of jf of j. 38. Divide|^f5iof7by§of3>;. ' 39. D,vide|offof|byiof^o't-A. 40. Divide i of I of 3G by 1} off. 41. What ia tiie value of ^? 8i 8i - ^ 66 9 OP£RATIOM. 28 26 _ ^^ " 3 - V 3 13 ~ V X £5 = — , ^ns. 28 Ana. If -in.*. 11 J. 0»8.— This example IS only another form forcxpressingdivision of fractions; it is call- ed a complex f motion. We simply reduce the upper number or div- idend to an fraction, and the lower number, or dirisor te ui imn,. J ^^""^ !° "" ''"P'oper divide as before. amsor, te an improper fraotion, ancf thVn 42. What is the value of"? 43. Wliat is the value of ^? 44. What is the value of-^? Ans. 6^, m ^^'^ BIVI810N OF KUAOTIONB. 45. What ia tl)« value of' ? Am. 1. 46. What is the value uf - ^ --? ? .,t ;ii 47. What ia the value of ,-— r- ? 5nf^ 48. What is the value of t-JL^ 7 4iolg 4a. Ueduce -i-*^ ^ ,~v — --—i- to ItM sinmk'.-*t Curtu. Ana. {|. 60. KeduceL^J - 1' to its fliinple^it form. '• ^ rr ^tV PRACTICAL PHOIJLHMS. 1. If f of an acre of land sell for .f63, what will an acre sell for at tk« HHine rate ? v4n.s-. $U7. 2. At $1 per bushel, l-,ow many bushels of onions can K" lu»ught for*12? Ans.\6. 3. How many times will IGJ gallons of vinegar fill a vessel that holds .{gallons? Am. j^. 4. At j^ of a cent each, how many apples can be bon;rht tor 84 cents? /Ins. II. ■ ). If 15 pounds of raisins can be obtained for *3f, what will 1 pound cost? An-f. $0.2 1«. tJ. A butcher expended $56f for sheep, giving $1J per head; how many sheep did he buy ? Arts. 47. 7. At $5 per yard of broadcloth, what part of a yard can be bought for f of a dollar ? Ans. A.. H. If I pay 5"^ cents for riding 1 mile, how many miles can I ride for 1134 cents? Ans. 20. 9. How many pounds of tea, at$li per pound, can be obtained for$13i? Ans. 12. 10. li'j men consume | of 'Jf pounds of meat in a day, how much does each man consume ? Ans. | of a lb. 11. A man bought 37| yards of calico for $5.61, how much did it cost per yard? /In.s. $0.15. 12. Huw many tons of coal, at $5| per ton, can bebou^ihi for $57 ? 13. A horse eats jj of a bushel of oats in a day, in how- 1 nan v days will he eat 15| bushels? Ans'. 42. 14. A merchant bought 97 sheep for *1002|, how much did he give per head? " Ans. i^\.04. 15. If a boy earn } of a dollar a day, how many days will it take him to earn ^9|? Ans. 26. 10. I'(.ter paid $513| for a farm, giving $2 1| per acre ; of how many acres did the farm consist ? Ans. 25. 17. If $2f is paid tor 5^ pounds of grapes, how much is that pei pound? Ana. $0.50. 18. per ton 19. , 20. , il. I get for 22. I > yards 2;{. I 21. I would a 2:>. A •31 per 20. a ooTer a 27. H each b(jt 2H. If chased f 29. H • 4 .vards 30. A e*ch, aiK did he ga GRE. 167. tions is t them, gi\ liiH. fractions. Ex. W Greatest ci Least com ANALTBia. least coiumo tors 112, HO. fifth*, their g fifths; then I 1^ aa the an 167. Wm low 6 I nde 18. H per ton ? QREATBST COMMON DIVrsOR Or rRA0TION8. *nyton<,ofUyc.nbepure»,aH.'*^^^' ^i" An$. $4. GKEATBST COMMON DIVISOR OP FRACTIONS. 167. The Greatest Common Divisor nP, tions ,s the greatest number which w re/.cl ^ '-^''^ ?'" them, giving a whole number for a quotient. ^ ^'^' '''^ °'' E». What is the greatest conunon dirisor of^, 1|, .^ ^ , OPEKATION. 3i If, }| = y, y, ^^ ^ ^^ ^^ Greatest comn^on dirisor of the numerators = 4 ) Ore«.-»^ Least common denominator of the fractions = 35 \ d'rZl^i;::, l^^^^stP^^^^^^^^ ,.na, Che tors 112. HO. nn'i -'J *.- h" V """° *n'= ^»»-> 2, 3, -^rberiho&iC/ "^^ '' '^ '''^'^'- - • -«•<* -»»>.. whi.. . faetor AI.IQUOT PART8 OF ONE DOLLAR. 50 cents =^ of 1 dollar. fh cents = i of t dollar. 2a cents = i of 1 dollar. fO cents = ^ of 1 aul!ar. Ib|cent8 = ^of I dollar. }23caits = iof 1 dollar. 10 cents = ,V. on dollar. Hg cents =^ of 1 dollar. t'i cents = ^ig of 1 dollar. cents = ^ of 1 dollar. e^. M .21 ce„« a j,ar,i, „.],»., „i|| 4I6 yards of „,u.li„ co,.T OPERATION. 8) 416 Ans. $52 EXAMPLES FOR PKACTICE. ^1. What will b. the cost of 724 pounds of coffee at ... cts. a 2. What cost 376 yards of calico, at 25 cts. per yf/" ^'''^''^' j6_At.*3.1Gi each,^hat wniti'hitfco.^P"^'-' ^«'- «1«6*- 173. W*ajmh«r» itk »r . • i ' -^ ■:I:I . l! PRACTICAL QUESTIONS BY ANALYSIS. , QUESTIONS INVOLVING THE RELATION OP PRICE, COST, AND QUANTITT. 170. Case I. — The price and the quantity being given, to find the cost. Analysis.— The cost of 5 units must be 6 times the price ot 1 unit ; of 6 unita, tj tiineg the price of 1 unit ; of 4 of a unit, ^ tim^s the price of 1 unit, etc. IIuuos, tho ITT. Rule. — Multiply the price of one by the quantity. ITH. Case II. — The cost and the quantity being given, to find the price. Analysis. — By Case I, the cost is the product of the price multiplied by the quantity. Mow, having « obtained 9 rei 1 V ,• ■^"«- 29 barrels. _^. it I jurd of calico cost 23 cents, what will 3 U yards cost ? • pmul/r''''"^ ^^^^ ''"""'' '*'''^' containing 70^ lbs., at $^ ^5.^ If board for a family be $342.18| for I je«, how much is ii'p^r R VT J - Ant. $0,931, adozenT'"*"^ ^*'" ^^'°*°^' ^"^^'* ^' •*-^*' *^ ^(^iot*- 7. What will 3921 feet of pine boards cost, at $17.25 per Tooo ? ' at $I7| a ton? ""^^^^ ''^^' ''^ "'''"'' *^°^ ^eig^^'ng 162^ Ibfl., Ill's Oiin ^ * ^'"''^^^' ^^'^ ™*°^ '^"''^''''' *^*" ^^^^ °*'* ^* ^°*'«^* ^<* in*Af,-„ . , , 4n«. 75| bushels. iJl'n^L o v" P''"",'^' ^'^'!: ™^°^ ^^""'^ of codfish, each contain- 12" aT^/?.^ ^V''lT'?*'^*^'^?,*PP^^^''^«^»t*^6i per hundred? 12. At 373ct3. a bushel, what will I ot 456 bushels of j^tatoes cost ? lOon . ?«Ti "^"^^"^"'^^ ,^^e P'^i'i ^'-^r 48« feet of boards, at .^20.25 per i?";7.'5j%^rrom"""''"=' "'^-'^^ ''' '"'-^ "'V^fjvr^t;.^^ per barre'r?^ ^"*'^ of Montreal apples cost $97.50, what is the price ^^16. How many acres of land can be bought for *2117.lsi"at '$5| tAinln^l il^ I***, '^^ ^"f ''^"' ^T'' '"^"y ^*"^^« «f potatoe"*" eacSon- I « f «> i )i»''hel9, can be purchased for $50.62^ ? Jlng 54 q w\ ."^ of » barrel of rels be worth $6.42, what is a barrel woKh ? poindsT *"" ' P^'^ ^""^ ^^^ ^^'' ^*" ™***' •' ^'' P" l»""'i'-«d 20 Wha^. cost 1080 lbs. of hay. at $12.75 a ton. a"l'l3«^'ibs'* ol «.h feed at^^l5.50 a ton ? ^^. ^17.487. 1344 feet of siding, at !^1. 62 i per 100; and 2216 bricks' ir$4rpir AHS ^4i H4jI 22 A grocer bought 108 gallons of oil for $145.80, and lo^t'l2 gal. I'ch'didtelL?"^* "''*'' """"'•' •* *'■'' P*' «»l'-5 ^- 1; 4 ;? •I I .ir!M IM. ir4a«M «*• nl9/»rJlnUNTB. fffi 23. A lumber dealer bought 106250 feet of lumber at $14.ST6 per I 000, »nd retailed it out at $1.75 per 100 ; how much was his whole i^ain ? Ans. $;^;!2.0:^ + . 24. A load of plaster weighing 3.360 ponnde cost $6.71 j^, how much will a ton cost ? 25. If |6.97i be paid for 0.93 of a hundred pounds of beef, how much will one hundred pounds cost? 26. A farmer exchanged 42| bushels of barley w(^th ^1^ cts. per bushel, and 679^ lbs. of hay worth 75 eta. per hundred, for 18780 lbs. of plaster; how much was the plaster worth per ton? 27. If 42 yards of cassimere cost $147, what will be the cost of 34f yards? i4n». $121.80. 28. What is the value of 12 pieces of black cloth, each piece con- taining 27'| yards, worth $2J[ a yard ? Ans. $954.50. 29. At .^5 psr bushel, how many bushels of wheat may be bought for 118.90? Ans. 21^. 30. A farmer sold to a merchant three loads of hay weighing res- pectively 2739, 2217, and 2884 llj"-> at $8. "') per ton, and 42i; lbs, of pork, at $5.25 per hundred. He received in exchange 46^ yards c mwthD at $0.09, 9| yards of carpet ui S4.50, and the balance in m' a«y ; how much money did he receive ? Let thepupilB makt out, in proper fornix as the case may 60, the following: 1. Sold by R. S. Gruham, Monkeal, to E. Dudley, as follows : 1870, Jan. 3, 109^ yds. calico, at 18^ cts. ; Feb 11, 430 yds. muslin, at islets. ; March 2, 37i yds. sheeting, at 23^ cte. ; May 16, 75| yds. Irish linen, at 4K eta. ; 43^ yds. lace, at 7K| cts. Footing of the bill, $161,007 -t- . S. T. E. Clark bought of F. Larose & Co., Quebec : 1870, June 10, 731 gal. Irish wliisky, at 86 cts. ; 108^ gal. fine old rum, at $2.12^; 67^ gal. Holland gin, at $1.45; Aug. 14, 89^ gal. old cognac, at $2.67i; 107 gal. brandy, at$1.37i; Sept. 7, 201^ gal. Scotch gin, at f 1.20. T. E. Clark gave in pait payment, Sept. 11,4 chests green tm, each 67 4 lbs., at 56 cts. per lb. What balance was due F. L. A Co., Sept. 12, when the bill was made out? Ans. $867,714. 3. J. N. Webster, butcher, Kingston, sold to A. O'Regan, Oct. 6, 1870 : A illet of veal, weight 16| lbs., at 10^ cts. ; a loin of lamb, weight 74 lbs., ui 17^ cts. ; a leg of mutton, weight 13| lbs., at 6| cts. ; a leg of pork, weight 164 lbs., at 9^ cts. ; a pig, weight 24ilbs., at 124 cts. ; a buttock of Ijeef, weight 374 ^^^-i ^^ 7^ cts. Footing of the bill, $11,314. 4. E. Lemay & Co. bought of Messrs. A. Roche & Son, Toronto, Sept. 3, 1870 : 123| lbs. eutn lac, at $1.15: 65| lbs. quinquina, at $14.10 : 1074 lbs. rhubarb, at $2.40 ; 1 20i^ lbs. sassafras, at lU cts. : 356i Iba. mastic, at 21 1 cte. Footing of the bill, $1415.911. 6. Sold by B. H. Porter, Ottawa, to Miss D. Valcour, Aug. 20, 1870: 27f yds. Dresden lace, at $3.09; 194 jda. Flanders lace, at $1.62^; 83^ yds. gauEe, at 454 ets. ; 364 Y^^- muslin, at 18^ ots. ; iO pair kid gloves, at 32 cts. ; 25{ dosen napkins, at $6. 1 2^. Footing of th9 bill, $335.3«| >*^ .■•sfW3fc'*^'^i- Lowell cot: ton, at 18a ct^- What was the amount due, Aug. 3, to T. & G ? Ana. *1 335.47 MISCELLANEOUS PROBLEMS. ,»indT^** "^'^ ^' '^^"^ *'°''' °^ ^^* P*"""*^' Of honey, at I6| cts. per 2. At $4i per yard, how many yards may be bought "br $ni ?'* 3. Reduce W to a mixed number. ^ 4n/l25i? ^Lwnr '' •' ^' ^"'^ • '° «q"'^*'^"* fT^*°"^ having a common lenominator. Ans. ^ff. .lfat^^\V'''"*;'"° "T^r '" 2378i and'tSlf; &Se,^li^i; A liat IS the greater number? ^^^ 244" U bought fcrlafctr/ ""*"' "" •""" '"'""" "'/"'"l "-t'l" J.t^'ii^^J^'^t^J' ^— '"■^» ^-- ^IK^"" ii: 1 11 110 MTSOBLLANBOUS PROBLXMB. 8. What will 15i cords of wood cost at ^ of $9j per cordr ». H.iw many pounds in 4 b:ig8, the first containing Mcond _680|, the third 296i, and tlie fourth STa,".? 4na. 16 3605, 10. Andrew spent f, J, and \ of his money, am i, and the fourth BTaj^j? i had i?54.r)0 ike h- r-"- 5) 8,' """J s v^i mo iiiuiic^, aim iiaii .to^.oO left t ow much had he at first? Ans. $8H4.70|^. 11. A servant had J of his savings in one bank, ^ in another, and the remainder, which was 877, in a third bank; how much money tad he? ' ^„g jji4Q_ ^ 12. Leo had I of g of 7i times $7862, and paid i of i of" it for" a ," ; how much had he remaining ? Ans. $3.3379. lA-'/o ,,^ bogheads of sugar containing, respectively, 9451 lbs., itAJ^^-' ^^'-^^ '^^-^ ^^''ff' a"'J 899|, how many pounds? i -*•, ^^"''y bought a bale of cloth for $96.87^ ; he disposes of it for I of the cost, and by so doing, loses $2 on a yard : required the number of yards in the bale. Ans: 18,4^. 15. What is the value of 376U acres of land, at $7.5J per acre? _^ lb. If the transportation of 18| tons of iron co.sts $4S.15|, what is u per tea? Am. $2M-X. 17. A man purchased I of a yard of velvet at the rate of $3.62i per yard ; what di.l it cost him ? Ans. $3.11 jJ. I H. Charles has 634 sheep, which is 94 more than i of 3i timea David 3 number; how many has David ? Ans. 243. • ^i^i'."^ ™^" travels 4 miles in | of an hour, how far will he travel m 1 3 hours at the same rate ? Ans. 10 miles. 20. A merchant owned i of a ship, and sold ^ of J of his share for i^^^'vt^ ^^*' ^^'^' ^*^^*' ^*^ ^^^ "'^''^^^ "'o^''' ^ ■^"«- ^1 ^^00. il. What will i (,f lOj tons of coal cost, at ^% of $42 per ton ? . 1^^; }H of * •^'•^8 be multiplied by ^ of itself, and the product di- Tided by i, what will be the ret^ult? Ans. ^A. 23. Band C own 3144 sheep; how many has each, if B has 11 tunes as many as C ? Ans. B 1834, C 1310. 24. Edward has I of a dollar ; he gives Loui-^ ^ of this amount, and then divides the remainder equally among three boys : what part does each of the 3 boys receive ? Ans. f. V.'3. James obtains from two fields 344 bushels of oats ; if the first yielded 4 as much as the second, required the yield of each field ? 26. How long will it take a man to travel 553 miles, provided h« travels 3^ miles per hour, and 9} hours per day ? Ans. 16 days. 27. 1 bought 15 loads of wood, each containing 11| feet, cord meaa. ure, and divided it equally among 9 persons : what did each receive ? 28. A tree, whose length was 136 feet, was broken into two pieces >y ailing; | of the length of the longer piece equaled | of the length •f die .shorter. What was the length of each piece? Ans. 72 and 64 fl. 29. How many bushels of wheat worth 80 cts. a bushel, will my for f o( a barrel of flour at $7i a barrel ? Ans. 7^ bush. 30. Lought i of g of 5^ yards of blue cloth at the rate of $3.50 per yard; what is the onst? Am. $8.02 ' . 31. Ill of » barrel of eels costs $5, how much will 2 tubs ofe'ela «OHt, one containing J of a barrel, and the other f of a barrel ? 32. If,^ of a gal. of porter is worth i of a gal. of ale, and ale is worth $i per gal., how many gal. of porter will $20 buy? Ans. 24. ".0 left; MI8r«LLA,X10US PROBLEMS. wi!Ln;r[;tri"!;:if/^^'-.'«/^!?^ divided 111 remainder, wliich ave 4, John 1, Peter ,»„, Tl '■morit; >« 24 ; what is the wiio! 5 boyg i*n. lipomas ^^. an.] Paul the 34. What Will be the'co t of Hv J« r ' T-'^"''^-' " """ '''^'i''^'^? d 121 v,^« ,..• ,' ^" . ^J '3 y<>8- of calico, at i-'a .-t- ..„- .. nJ I2i yds. ol'nuKl 35. PI !>. at 1x5 ct J'lipovns/^ofa,sin|: per yard ? ;> .>^ c;irM;o, value.] ■3 ots. per vd. owns ^n«. ^, owns $87000: D $2 0^ J $sm^ -n I of a steamboat, and UnV';.''?'^.' .'J"'' ^' *106»00. 45 0o'TJ.l^.^^-'"'-^-d«;il «45000. VVha\ p^rt o ZXa-roaTh ' f,T ^''^''^ to Ow;n for at that rate ? ^ ' "" '^^ stea.nhoat have I left, and what is it worth i. inUef :n' oWoVJ r;;:,:, TJ " f * •*' ■»,»■ "^ P«'^ "^^ BO pay for the coal ? ^ ' ^^'^ ""^"^ PO""^^ were required 39. I have *800 and wish to lav out S'Urt n<-.> • '^"'- ^'"^^ "^'^• • pound, and the remainder in tea at 52' ct! 1 '" 'T^l ^' '^ ""^ pounds of tea do I bu y ? ' ^" * P*'""'' ' ''^«' "lany 40. A merchant expended .^840 for drv .. ^« '' ?^^^^^^ ^^'- house-lots of the same extent ii.t, Lk;m ^i V J , ^^'-' 'argest-sized •nd .1.0 .he „.,„^e/„;s ^^'s v 'fV.tuol'r'rr 'i;'r''"'' 42. A man own ns 135 J acres nf l«n i n 1 ..: ^^r*- ' '*^ '"^s- to his son; what wL the vl'ue of th/ "^ '-^V*' ^"^ ^ acre? ^*^'^* ^^ the renoainder. at $57.80 per 43 A merchant owns 5 of a factory worth >«!4«nr:n'**'l^^^n'''«' hie share to A, and i the renmi .W f^ n if ^^^- ^« ^^l'*^ * ceive from A and S respectiX and . . ^"^T '""^^'^ <^^'' ^ « re- ^ns. From A $25200 p'""' ?.*'' ^'^'^ ^'^ remaining? 44. A drover bou4t 257 sheen L/'''\'^' ^^f^ '' ^'^^ ^^'^^ A- bought348at$1.87fperLad ?hpn ^frf P/^ ^^^'^ 5 lie aft'erward $1.75 per head, and^th'L / L^,;,£^;,« tf.tlje, whole number at and how much? ^^^naei &i $^.12^; did he gam or lose, 45. A mother divided a basfc*.fr,f^-„ ^n»- Lost $,{5. s 7 ^ ters; to the first ehe^e 12 o/a,^^^^ three daugi and to the thir.i as much as to tKfi . . ^""""-^ ' ^* ^''« ^hole, the third have ? ^^^ '''''''' '"'^ ' ^"^ ' "^any oranges did 46. What IB the smallest sum of monev with ,v5^1*' "^^ '^'■*"g^«- purchase a number of sheep at -^2' Ta^K V V''''\>' f^^er couW each,andanumberofyeaiKsa?lAoK"7"'''^'l^^"^'"^« "^^ »4i could he buy with this moneyl ^ ' ^^''^^ ^""^ ^°^ '"*"7 o-^«acb -^. Induing .ef^rdi^-^L-S^tl^^ ^°s: b!. K Hf brofcoTon^?;? I \ ' ^ ^- ^' 31B^"/:"« !■■ 112 MlgOKLLANXOUS PROBLIMf. 49. The le A of a farir. j^re sown with corn ; the A with barley and 50. How n.aMv huHhels of oats at 62^ cents perlnlh' 1^ remSed 61. Ifit requir^ 34 days for a mason and his JnZ nK;v^23 cubic ^ 2 IfTrof 'r 'T^T^' ',' ''^'^^^''^™ ^« ".alee ucuLic yard? n„?r ",,fi.:'f"^?""'''"^'l^^'^"'e8 of Riienish wine cost ,:;j.:U) • how much will .^482 Lotties come to? j„,. " the .'^atne wi ■ 11 1 1 --■-.-"""• •««.'»•. .'§543. 192. Whal will |.e the pnce of 57^ bushels of rye, if 17,31 bushels of me (Ilia if.v f-r.wt ^«A3 9 " ^ > . ' ' i j "": "*^"* O' jiiulity cost $52? Ans. .$;i0.6G . 54 A piece of silk vei;et would bring $210 were .Tllm'er""know •ng^the pnce of a yard to be $7.50, required the fength ^flhe thoTe • 65 A market woman sold the f of a basket of e.m'^a^"addmt'*28 66. A man has an income such, that ifit were au-Mifented t^'^the pr.ce he pau for a mahogany writingdesk, thatis-WlT heluld spend $2 02i per day. What is h.s income ? ^ns. $685. 1 2^* it tI^^A■''T^' ''^'' "'f ^^* y^'"^ '^f >'"en in 1} hours ; how lon^^will It take him to weave : Lu. 15 yds. ; 2nd. 2& yds. • 3rd 44 vd« • il^ ^r'^'^y'}- ' ''^: n of a yd. ?' 'Ans. l'^28i L!; l^'si^h e'tc tHe , and the^ of he sum paid for 93 lbs. be 60 cts. ? Ans. $2.25. 5 ). In mixmg 10 lbs. of bismuth with 6 lbs. of pevtor and 4 lbs of lead we ob.a.n an alloy which melts at the temperature of boiin. water ;requu-ed Ist what quantity of each metal enters into the m ixt^ «fv f h'K',^"'^- li^bs.; 3rd.3|lbs.; 4th. lllbs.; 5th. 27! lbs 2° » Tk r . ?u ^'r,f ^' ^ ^^- ""^ ?«''*«'•' a»d f lb. of lead] 2 *lb.ofb.smuth,/j,lb. of pewter, and ,1^ lb. of lead, etc. 60. A weaving, mac „ne makes 135 yards of cbth per ,ia; ; how many yards wl .t make, Ist. in 3 days; 2nd. in ,7^ of a day; rd in 4idays; 4th. m 15 days; 5th. in 32^ days; 6th. in 47^1 days and 7ih. m 27m days ? Ans. 1 ° 41| ycis. 2^X1 yt eT ' 61. It would require 1800 yards of cloth f yds', wide lolfake cloLs for a regiment 5 but, on delivery, the cloth is found to be too Sarrow the cbthT'"^°' " "^^^""^ "^ ^"^ ^^^^ ^"""^^ -■ ^^^^ ''' ^''^ -iJ^" of remn . ^^^ f!f^-V'' ' ^'''''' ^^ broadcloth of equf HenJ^hi . Z:^1^^ ^..uiredthelengthofa P^-^knotjng tha! 63. The breadth of a painting is but the J. of its height' If ^th« breadth equa the f of 2 -, yar.ls, what is tS height ?It% yds ^6<. A teacher ofa select school has 60 pupils ; 24 of Sm mv Rnw „ "k "1 ^f ^'' ^^^- ^ "*" '"'^ remainder, ;^1.75, and the rest $2.?.0. T^ Tu v^J' ''' '■^^.^''^^ ^"""^ ^'^ P"P'1« '" 8 months ? ^n«. $846. «„'!v.u"?''^"°n''0'»'e between two watches is | of an hoar- LI ri^'"'' ^*K ' ** ""'""i"' ^''' ^^y' ^^"« ^^^ other loses 5', in the same time: m how many day. will they again mark the Mme tu».f 4th. '^7 6 '"21 DlNOMKCATl NtTMllM. Ill " A dealer in poroelam l,oud,t a J,»t '"""'«' ^ *»-64. -'"••■j:..tE~SS;i;;sB»r DENOMINATE NUMBERS. pounds ^ing one bushel ISO are ^o^nav^ of '.'^' '"^"^^""^^ "°i^ fractions '^ ***^' * °^ * yard, etc., denominate „.f;!l^:-^'°°°^^°ate Numbers express Curr«n«| An IVsights, 188. FFia^waijrapI, nu^j^ - ... ■oimnate number T~W/d.aVmJ«j!*^ oompoand aumb«r?- ■88. .i de- JDominato s l< ' •' II • lU lUii flffrl OURBBNOIW. OtlRRKNOIM. 1. Df.MivioN OF Canada Monet (77). li Old Oanabian Monit, ou Halifax Currenct. TABLE. d. §. $. £. 4 t'lrthingfl mak* 1 penny, 12 pence «* I Bhilling, 6 shillings " 1 dollar, 4 d( liars ** 1 pound, d. qr. t. 1=4. $ 1 - 12 = 48. £ 1 « 6 = 60 = 240. 1 = 4 = 20 = 240 = 960. *•■■» •»•*/ id. rf th« old oaiaag* if equal to 6 eenta of the new. III. Enqluh Monet. TABLE. 4 krthingn (far. «» tr.^ make 1 nennr g, ii P^Cf •• 1 Bbilling ,,' W •iMdIififp n 1 pound or sovereign £ or sow. «. £ 1 1 = 20 d. Jar. I = 4. 12 = 48. 240 = 960. I ^"L^t *"*"*'»«« "• generally exprosBed as fraotiona of a peaay: tkui i m^ mmtAHimm oailed one quarter, \qr.) ^^\d.;Z far. wm Id. ' k^S^J^/' tfc» original abbreTiatioD for shillingg, was formerly written ^^ »^H,»»* and pence, and rf. tbo abbreviation for pence, wm omitted! ^JT**;!*' ^'^^ Wf'tton 3/0. A gtraight line is now used in jplaoe of the/, and mtfmmgt ace written on the left ot it, and pence on the right. Thus, 3^6, 7j3, eto. *4jMS*-nT"* ""u"* f ^H •'«"■''"« pound '1 the Dominion of Cani» k 9*^999^, Mttrl fe«Dce the value of an English shilling is 24J oenta. ..«j *tt *?!*••'*■*'*■* *° goneral oiroulation are: the Mvereirn {=., £1\ «Mtt#Wl.»6^ereign^- 10«.), made of gold; the crown (-.5..), tfie fcalf-' *My*J-^(W)^ the io.-in (- 2..), the shilling, the aix-peace. the^our peno., SKfr^UST*?*^' ' ^'^^'P'^^^' "»" haJi-penny, end the far- fc Ifc* gUtodfad gold eeia of Inland ii 11 parts /jure gold and 1 part '^Uoy j^^^ ^ ■ »" \f5 • "" / 1 — --»..-. aim u parw (-1, ;^ ■W^ a^pyw/ M foaee, la eopper coin, wotgh a pound avoirdupoia. rr. Unitw Statu Mon£t ( t f RBNCH MONKT. Ill C«l.ada u,„„,/; "l°'«l »■ '»lue to 80.188 Do,„i„i„„ of TABLE. }0 roillimes make 1 oentini., centimes " I deoime fr ,^ '°'^**^""«^ '• 1 franc. _, OOMPAIIED. •4 «(•«"'■ I centime 1«. WEIGHTS. D. C. I0.00018«. *0.00I86. «0.186. 8Calo8 of weight are usedTZn °'"' ^^"^'^ standard. Three tain, and tho'^Uniid S ates" ^^ .^S'a 'l.^^"^-'^' ^^'^^ «'• - d"po»s. "'*'' ^^^- • A roy, Apothecaries', and Avoir- ^- Troy Weight. TABLE. 24 grains (er. ) kiaIt. i 20 pennywdghta * J'"7''''°'^'' ^"*- "«• '*«*• 12 ounce*. « i °""*'5' o«- I pound, /ft. 'f- 1 = 30= 480." 1 = 12 « 240 = 5760. WoiBa— 1 ©iaoaond*. eto.. ara ••i.k.j u A era. w.igh.4^„H« ^o/^^^r* ' '^ •^'^' ""*>««<-« .f a oar.t -i. in .peaking .f the purity >f Im . ^^ ^ «• A T«v p,«i i. ^, J*]r 3^^^^ ^ ^ ^^^^ ( . 116 II. APOVHEOARIEri' WeIOWT. 1S>4. Aiiotbi-c tries' tUTeight is used b^ physicians in niixiti- medioines; but modiciries, are bought and sold by Avoirdupois weight. TABLE. ipothecaries nnd in the (juuiitity, 20 grains (gr.) make I scruple, sc. or i. 3 acruplcH <• I dram, dr. or s. 1 ounce, oz. or 3 Ik. I 8 dranifl 12 ounces 1 12 n 41 1 pound, lb. ur lb. ir. I 8 i^6 1 3 24 288 fr. - 20 = 60 = 480 = 5760 m ril. AV01B.'»DP()I8 WeIQHT. -«5. Avoirdupois Weight is used tor all the ordinary pur- poses of weighing. 16 drama (dr.) 16 ounces 25 pounds 4 quarters 20 owt., or 2000 lb«., TABLE. make n « 1 ounce, OM. 1 pound, lb, 1 quarter, qr. 1 hundred weight, cwl. I ton, T. r. 1 curt. 1 20 : qr. I 4 80 lb. 1 25 100 2000 oz. 1 16 400 1600 32000 dv. 16. 256. 6400. 25600 512000. NoTt — The long or grot* ton, hundred weight, and quarter, were formerly ia oommon use; but they have now fallen intodiiuse am»ng merchants in Crntid* The Custom-Eouses continue to use it. Farmera and others weigh still some few trtioles by the long tan. LONQ TON TABLB. 28 lbs. 4qr. = 112 1k. aOewt. = 22n miike it I quarter, marked qr. hundred weight, ♦* cwt. tvn. " T. OOMP 1 pD«nd 1 OQBOe : K V 4BLB or WBI0HT8. '!&*:/. ApothaoMict'. AToirdupoU. 6760 grains, = 7000 vubii. 480 " — A9W t^ ,. ■■ 6760 grains, 480 " irs 480 " xs 480 " E 43r.6 " VawtdM, IB 176 pMiBda, = 144 poands. MKASU'KES. or ^mounufaSatS^^ dimension, oapaoitj standard. It majt 'o^r v ZfT^. •"'^^^^'"^ ^ «ome^fixed •res <>f J^-tenaionf and'Z'L'o" Capacit;:"° °'--«-^^^«- *'^'^''^*''*' ®^ EXTENSION. thick,.I;.'^'^^"«^«'» »^- ^'^^ di-nsion«- length, l^eadth and ^ A Sol.d or^BodyhLYhrerd.- ''"'"'''" '^""^'^ ^"^^ breadth. ihickne.8. "^ ^^''' d.mens.or.s- length, breadth, and I. Linear or Long Measure. or Ztce!""'" " ^°"^ Measure, is used in measuring line. I incV (fn.)ss 12 inch's 3 feet H yd., or I6i ft. 40 rofis 8 furlongs, or 320 rod. •^ in Ilea 69J miles (nearly) attv degrees TABLE. 0.3363 French inch, "lake I fo.jt, 1 yard, I rod, 1 furlong, I mile, I league, it (t u « « u u yd, rd, fur. mi. lea. J degree'on the equator, rfS' or • 1 great circle of the earth. ' mi. 1 1 8 : rd. 1 40 320 : ¥d. 1 220 1760 A 1 = 3 = 16i=. 660 = 6280 3 in. 12 36 198 7920 63360 .'?•' F-TH ■■! i; n« MBASUBS6. Sotn.—l. For th« purpon «f mauuriog oloth u4 other goodc soU W ife^ JMrM^'/T'u" *"^'*"^ '°'" '"''^•«' '■°"'*'^»' «'«»»»'»•• "»<» ^i«u*«U« fl* oia table of oloth measure is practically obsolete. 1 f^i.^° ^Miners' Measure, 12 lines make I Mohj4 inches, 1 hand: *5fo#«, 1 lathom; 120 fathoms, 1 cable-length ; 7i cable-lengths, 1 mUe; X of a 'u paper- the square of 100 Square feet j' brX gC -/Sru^aVrL"*;', "'^i*"^'' '"'"« ''^ by the .quare yard, and by tie .quare of foi squZ f^'Jt^ '^' ^°»'"'' '"^cks. 1 I f I »j::^'i,iiiaiae^--.T„'i;;ij£!^_.7.^2.v:?^'" 1^ 1- ISO MIASUftBS. Ih. w.alh:"'*'" '"°«'" "™ °^*'"'»»«'l 'o «-" 1 -quare. being laid i i..h„ to surveyors' SQUAttE MEASURE. TABLE. 626 square links (_tq. I.) 16 poles it 10 square chains u 640 acres « 36 square miles (6 miles square) " make 1 pole, p, 1 square chain, aq. eh. 1 acre, A. 1 square mile, so. rnu 1 township^ '/p^ mUe oflandie also called a""«.-^' ' "^^ «"'°« '"'° ^""««' ^ 8quai« III. Cubic oe Solid Measure. -olH u^^^^ Measure is used in estimating the contents of solids^ or bodies ; as timber, wood, stone, etc. nf ??*^\ p?»*ents, or Solidity, of a volume, is the nun.ber of times It contains a given unit of measure. «numDer tl,P^.™^-^'T"''°5,?''''''*'"P''*^"-«<^"di*y«'-e always taken in the denominations of linear measure. If each of the sides of a cube is 1 foot, it is called a cubic foot fiJn^'' ■|!"V:l^ °'?"'° '•opresents a oubio yard. Since each of the edges of a cubio yard is .rfeeL •uch of Its faocB will contain 3 times .3 equal to 9 «qu are feet. If, from one fane of this ou be, wo cut oflfa p.Goe 1 foot in thiokne... wo evidently hare 9 »oUd/ee(i and as tho whole block is 3 feet tmck, It must contain -i fimoc o _ ot . i; , « . Henoe, " " "' '"'*'' ^°^^ 1yd. ^flnd the $oM contents of a cube, multiphj its length bmrdth «md thickness togethc, ^ • t MEASTntm. 121 1728 cubic inches (eu. in.) 27 culiic leet 40 cubicleet of round timber, or ) f p . ( or manonry. | ''^* 1728 ('ubic inches 21(> c, bic feet 1000 French cubic feet iO(»0 cubic toise-i TABLE 01- FRENCH MEASURES. make 1 cubic fool, cu fi i toise, cu. to. " 1218. 186432 Engl. oi)b. feet. ■• "J745. 491456 cub. yd. th^i;;.^S!j::i:'];:^«^--r;-i^ freight b^ .tc.,of s.ffi'e':p„';/,;;r/u:.t. ''"Brir*"°« ^"S'^'''^"-' '^-". mit.ng their work by oubio me Jb««T Bn«l'l»yers and masons, inesti- wallsofhouees.eelli^^rflto h,?? I!;- ^*°u *''°^*°ce ^o"" '^e corners of the •Btire length of thrwdlo^tbeoJwl™''''' '''"'' ''°^' ''^ '^^ y-'. that i' the ditn^Sra'a^re'^^^m^^'iCu'^^^^^^^^^^ and embankment., take the eomnutation« are made inlet n 1 SI. Ti"""^ decimals of a foot. The yards. In civil enginoo W thH /il ^ri'''^^ •"""' "" "**"°''^ *° *'"^'<' e«a.ationsaBde;,fb..nk"f^tsaVefitli;;tluo^ "'* '" "'''■''' •'^"™''*«« '<>' ~LJ;;^fc^^™rCa5^;^!or^ir;rnn. or tVei,ht,„g. ^ of the solid that will make 36 foot of hewn or sawed dmhL- " 'T'm^ "' ''^^'''S- '^•'">'' '"^ '°g by measurement; but its mrket 'a^e k - .^^^ ** ° "''''' ^"^^^ •awed ti.uber. Henee. the cubic content, ,?fi^« f '^""'/" ^^°"^'° ^''^ «'' '>«^" «' timber, ns estimated for marked are irfentlfaf "^'"°"°'^ '^"'^ *^ ^'^«' "^ '^«'^'' «>ld- by ^hlttir^tVS':::^^^ ''•""^"•'•^- "^^ "- 6--a>'y bought and aej .td'';ke;lr;'e'itSrnrs*^!st^^^^ '.f^''^' "^ '''^ '-'-" o^ th. ATolfdupois. ""• '* ^•l"'*' '" ^«gbt to 62i lbs. or 1000 oi. MEASURES OF CAPACITY, nifies extent of space. "^ "liferent unit«. Capaaty Big. two .IMMS. Mtmmre. of L.y^nrf, and Jf««vr« «/ Dry SuhHan^ i V , - .^P Mil riiiHi ■"— ''"imTrr"'"-" 122 inBABtniRs. I. Liquid Measure. 208. Liquid Measure, also called Wine Measure i« nnw used for measuring all kinds of liquids. ^'^easu.re, is now TABLE. 4 gills (gi.) 2 pints 4 quarts 31 i gallons 2 barrels 2 hogsheads 2 pipes, or 4 hogsheads make tt 1 pint, I quart, 1 gallon, barrel, hogshead, pipe, tun, tun. 1 66/. hhd, I pi' i = 2 1=2 = 4 = 2 = 4 = 8 gat. 1 63 126 252 [j = (ft. 1 ^ 4 = 126 ^ 252 = 504 = 1008 = Ft- I 2 8 252 604 1008 2016 pt. qt. s^al. bhl. Mid. pi. tun. gi- 4. 8. 32. 1003. 2016. 4032. .'-■064. 2o1;*S''«»«'°Tk*"^''°'u*'y!''®^*"''"5 "'"letimes, howerer. in casks of 6 10 20 gala. etc. The beer barrel contains 36 gallon,, anl the hothead! 54 gallon.: II. Dry Measure. aOSI. Dry Measure is used in naeasuring articles not liaaid M gram, salt, fruit, roots, &c. ^ ' 2 pints (pt.) 4 quarts 2 gallons 4 pecks 36 bushels 1 Imsh. 1 M pk. 1 4 144 TABLE. make u n u II gal. I 2 8 288 1 quart, qt. 1 gallon, gal. 1 peck, vk. hush. I bushel, 1 chaldron, ch. qt pt. 1 2. 4 8. 8 16. 32 64. = 1162 = 2304. »a.-»«j«i uec. 31 iii^22 &SSB^^S!Sss^^^m^:,^ ' 124 mBAmiwu. V • 2. Th« J«<, When the time exceeds one year, there must be added 305 days for each yea*. CIRCULAR MEASURE 211. Circular Measure, called also Angular Measure, Is used principally in surveying, navigation, astronomy, and geogra- phy ; for reckoning latitude and longitude, determining locatfoaa of places and vessels, and eomputing difference of time. MI801LLANROIT8 TABL18. 12ft 212. An Angle i$ the differtncc of direction of two lines which meet at a point; thus, A, B. (!, is an ;tii.j;le. The lines are called the sid w of the angle, and the point where they meet is called tlio ' / V. Deo. i 334 i 303 j 275 i 244 i 214 i 183 i 153 i 122 L 91 . 61 » 30 ) 3«& 2i:$. A Circle is a plane figure bounded by a curved line, all the parts of which are ecjuallj distant from a point within called the center. A circumference is the curve line which bounds a circle, and always contains 360 degrees. An arc is any part of the circumference, as C D, D E. Tho are within the sides of an angle whose vertex is on the center of a ciicle is the measure of the angle; thus, the arc C V. IS one fourth of the circumference, and measures the an-'leE B C which contains 90 degrees. "^ ' TABLE. 60 seconds (") 60 minutes 30 degrees 12 sigoa, or .360° 0. 1 ■. 1 = = 12 = 1 30 360 make 1 minute, *' 1 degree, " 1 sign, " 1 circle, » 1 60 = 1800 = 21600 9 o s. c. 60. 3600. 108000. 1296000. of S '■m^aT'^X''-"' "if^' ''"^''' '' °"<'-fo"E'»» of » oiroumferenoe. or an m 01 «()u ; aa A U. 60" is called a sextant, or I of a oircle. 12 units 12 dozen 24 sheets 20 quires MISCELLANEOUS TABLES. COUNTING. 12 gross make 1 great gross. 20 units •« I 8core. PAPER. make 1 dozen, " 1 gross. make 1 quire. ** I ream. 2 reams 5 bundles make 1 biuidle. " 1 bale. BOOKS. A sheet folded in 2 leaves is called a folio. i 16 leaves is called a IGrao. 4 " " aquarto, or4to. I 18 " « an 18mo. 8 <♦ anoctavo, orHvo.i 24 " '< a 24mG I* " " • 12mo, I 32 " « » 32010. lU T«i mTMQ arsTSM. THE METRIC SYSTEM OP WETOHTS AND MEASURES. The metric system of woi>ht8 and measures-so called bpcaase '^^'''%]'^\--^' ^rom ^.hloh the other units of the sptem whether of length, area solidity, capacity, or weight, are derived --originated m France m 1790. It was determined and established as foUows : a very accurate survey of that portion of the terrestrial meridian or north and south circle, between Dunkirk in the Wthnf ^T°'"'">''''^^''°'^ ^^'' measurement the exact hetuatoVtotr' f ^^V'^*"^ "^"^^^'^' ^^ *h« distance from Dart of ?M, ! "°/*^ P"'"' ^"^ ^^"^Puted. The ten millionth Ffo 7 i ?'^ V^ denominated a metre, and from this all the standard units of measure and weight are'derived and deLm ned t1,r? r' 'iJ '^'^"^ ^'« ^•^^"y ™^de the only le4l sZem Mooted W 9°' • ''^'r' ^" ''''' Since th'at time, Thas Deen adopted by Spam, Belgium, and Portugal, to the exclusion of other weights and measures. In Holland^ other weights Tre used only m compounding medicines. In 1864, the Iv t'em wis egahzed in Great Britain ; and its use, either ^s a whole oMn C/^t P'''''^"' been authorized in Greece. Italy Norway Sjreden, Mexico, Guatemala, Venezuala, Ecuador UdtedsTates fn mt^; ^--1' Chili, San Salvador and Argendn RepubHo In 18b6 the use of the metric system of weights and measures was authorized by Congress for the whole of the United States TABLES AaTHORIZED BY CONGRESS OP THE UNITED STATES. MEASUHE8 OP LENGTHS. Metric Denominations and Values. Myriametre,... Kilometra, Hectometre,... Decametre,. ... Mkthb, Decimetre, Centimetrs,.... Millimetr*, ..... lO.OttO metres,- . 1,000 metres,-.. 100 metres,...., 10 metreSi^ ., 1 metre, , ^^ of a metie, y^ of a metro, Equivalents in Denominations in use. 6.2137 miles. 0.62137 miles, or 3280 feet, 10 inches. 328 feet and 1 inch. 3'J3.7 iQehc!». 39.37 inches. 3.937 inches. 0.3937 inch. U.0394 inch. TH* Miraia stitkk. HRASURRS (.p SCRTAOM. 127 Motrio Denominations and Values. Hectare, .. A»«, Centiare,. EquiyalentH in Denotninationa in use. 10,000 squaro metres, 100 gquaro metres, 1 square metre, I I55o"8qVa"reinchei' 2.471 aores. 11'.».6 square yarda. MEASURES OF SOLIDS. Metric Donominations and Values. Decaatere, Stkrb, I>eoist«r*,„. ... 10 cubio metres, 1 cubifl metre, BquiTalenta in DenominatioBa in DM. 13.079 oubio yards. 0.2759 of a cord of wood. 100 cubic deoimetrea,. 3.63144 cubic feet. Mf:ASURES OF CAPACITT. Metric Denominations and V»l ues. Names. Kilolitre, or atero, iieetolitre,.,, Decalitre, LtTHB, Decilitre, Centilitre, .... Millilitre, No.of litres 1000 100 10 1 1 TU Cubic Measure. Bq-iTalents in Denonrioatione in use. Drj Measure. 1 cubic metre, jJjj. of a cubio metre,.... 10 cubio decimetres,,.,. 1 cubic decimetre, ^ of a cubio decimetre, 10 cubio centimetres, 1.308 cubio yd 2 bu. 3.35 pk... y.08 quarts 0.908 quart,..,. 6.1022 cubio in. 0.6102 cubio in. Liquid or wine measure. 1 cubic centimetre,. ...„jo.061 oubio in.. 284.17 gallons -'6.417 gdllona. 2.6417 gallons- 1.0567 quarta 0.845 gill 0.338 fluid 01.. 0.27 fluid dr... WEIGHTS. Metric DenominatioM and Val ues. NMaea. Millier, or tonneau,. Quintal, Mjriagramme, Kilogramme, or kilo. Hectogramme, Decagramme, «.,., GIkaiqik, , Decigramme , CantigraBUBe, ...... MilligranaM,.^..., Number of Weight ofwhat quantity of grammes, w.-vter at maximum density Equivalents in De- nominations in nse. AToirdupoia weight. 1,000,000 100,000 10,000 1,000 100 10 1 fir TffTT ••••••(•• 1 oubio Miecro,. 1 hectolitre, ... 10 litres,. 1 litre, ^..., 1 tlet'ilitre. ,„, 10 cubic centimetrefi, 1 cubic centimetre ^lyOfa oubiooentimetro,. 10 cubic millimetres 1 aubio millimeb'e, 2204.6 220.46 22.046 2,2046 0.3527 15.432 1.543S 0.1643 0.0164 pounds. pounds. pounds. pounds. ounces. ounoe. gr. Tr. W. grains. of a griUn. •fa grain. ^n ( "i- m TfIB MBTRIP STSTKM. MKAfiiraRS OF ANqLBM. 'M'V; rienominationfi nn,] V;iluo!>. EquiTalenta in Denomination* in we. NOMEf^CLATLTRE AND TABLES W^^^ V;iue,, Timet anf^^"^ "'" ^"''^•''' ^'''P««'^'«'S T<«^ i* fhe same S m" • ^ - "'^^ ^'■''- '^^'^« ^^^lo fo • .J^,r,.l ..aie. In iach of X .'^ m"*;-''' r *'' «°"«t^"°ted upon ««i^ i« princVara J '^t'dti;:;:" -^lif -.-Potions of »r# «lM? »t^/y« which i«.f>,oK/.!,- -^^^ principal units dirmly fmrr it The two filuo^ ''^Vf ^f™' *"d those deriveu i^ Mm the menrrr "''"' ""^''' ^'^^''^ «^°"'^ I •!' Tu'"°'P*' unit of lengths. h M*TRR, ... J ^" ^ '** ^*«^ o^^he metric system, and near) v ' • < one ten-mi, honth part of a quadrani ^the earth's meridian. .•<■ Equivalent, 39.3708 inches. n. Am J .i* ?""<^'Pa^ unit of surfaces. ' 1 ^- ^ '"^^''^fe whose side is ten metres. ' ( ^. Equivalent, 119.6 square yards. III. Stbrf I i' a'"'"*:' ^*' ""it of volumes or solids. »T.RB, .... j 2. A cube whose edge is one metre. ' 'i- i-quivalent, 1.308 cubic yards. IV, LiTRi,. 7. WK 'AHifR '» • • f 9' ^""•''P'' ""'t of capacities. I -i. A vertsel whose rolume is equal to a cube 1 q T. *''^?«^ ^'%« '« one-tenth of a metre. Equivalent, .'JOH quart dry measure, or k 1.0567 quarts wine measure. /J- Principal unit of weights. I -2. The weight of acul:>e of pure water whose ed£r*» ia ni nf .^ .^-i. o m, e^ge'8-01 Of a metre, d. 1 he water must be w 4° C, or 39.2° F eighed in a vacuum 4. Equivalent, 15.432 g^ns, CO H Hi D o TWi MFTRIO 8TRTBM. 12f CO Eh t— ( D > i < Id O 1. Q a o o n en u ' "'to tenths, hundmithfl. and tii.iusaii.ltli.s. Z^^T^y con.sMj.ri„g as a u.ut' to,. ,i,„e u time" each of r'hl""' ' •''"r'*"^^ ''"'^-^' ^'"^ '«" ^^»«»'^^»d wmuM, eacii ol the principal unitf. The na.nea of derivative units are formed bv attaching a prefix to the name of the princi- S.nT* ^\T- "'''!'''' ^''^-^ "'■'^ ^'"'^^'J. vvi.ioh indicates their relation to the principal uniu ^'M^r'^i""'"' ?"'' thousandth, contracted M^i. je^am;,/e MiHilitre ^ ^^ of a litre 8 miUilitreH = ^^ of a htre. ^*centr''''i'?l"''p''"- *^"°J'edth, contracte.^ cenu. tux., Centiare = ^^tt of an ar*. • 4 centiare8 = ;j^ofanare. ' ^ 3. Decivims, tenth, contracted deci. Ex De- raeTrr^" = i^ »»etre ; 3 decimetres L ^ a. •r: tn * £ III S s -2 09 a * g oft) CO '^ c « c c i s. '1. Deca, ten. Example, Decametre, = 10 metres ; 5 decametres = 50 metres. 2. Hecaton, one hundred, contracted hecto. 7<^r»^'f''''^'''=^^^^'^^«'^' 7 hectolitre* = 700 litres. a, I.*, 3 o S ^ 3. Kilioi, one thousand, contracted kilo. Ex 2"^ Kilogramme = 1000 grammes. *■ iKn' f^" '^^"'^"^^ ^'^•' Mjriastere = 10,000 steres ; 3 myr asteres -. 30,0U0 steres. ^' J'JIm '" ^^''^^"d "'yria, and the o in hecto I, and kilo, are dropped wh«a prefixed to are. "^'Ifniri"' f^^f'"^ constructed upon a decimal scale, ten The facts in the preceding views being mastered, the tables can be constructed by the pupil at sight. For exampk The „Imc^ of the den.atiy« units are formed by attaching the seven prefi^e^ c - K * S 11 t ! r i iJi I ul i ; f I! f 180 THB MRTRTO STSTRM. in their order to the principal units of the tnblee. The order of pragres«,on bo,n. ten, tho table of cnpa.itio,, will be written TZ^ lOMillilitres =1 Centilitre, 10 Centilitres = 1 Decilitre. 10 Decilitres = 1 Litre. 10 KiloiitroB 10 Litres 10 Decalitres 10 Iloctolitres I Mjrrialitre. - 1 Decalitre. - 1 riccfolitre. = 1 Kilolitre. ^.tit' .^'''^'^"' ^'"^^^^^^^^^ are presented to- gether in a convenient form in the two following tublea :- TABLE OP SQBMlJLTrPLES AND PHINCIPAL UNITS. Names of Units. PREFIX. BASE. 10 Milli. Equal 1 Centi- 10 Centi- Equal 1 Deoi- 10 Deci- Equal 1 Principal Unit. 10 Principal Units Equal IDeoa. ' Metre Are • Stere Litre Gramme f Metre \.'. ■ Stere Litre ^ Gramme ' Metre Are •I Stere Litre . Gramme r Metre Are Stere Litre { Gramme PaoNnifoiATioir. Mill'-e mee'-ter Mijl'-e-ftre Mill'-e-st«r MiU'-e-li'-ter Mill'-e-gram Sent'-emee'-ter Sent'-e-Are Sent'-e-stir Sent'-e-Ii'-ter Sent'-e-gram Des'-e-mee'-ter Dee'-e-ftre Des'e-st^r Des'-e-li'-tw Des'-e-gram Mee'ter .\re St6r Grana Stubolr. »M .A .8 .1^ ,M .A .S .0 iM lA |8 iL .0 M A 8 L O THl M»TniO BTRTiM. TABLE OF MULTIPLES. lai N'amks of Units. PKKFIX 10 Deca- Equal 1 Hectd. 10 Hecto Equal 1 Kilo 10 Kilo- Equal 1 Myria Myria Pronunciation. Dek'-ameeter Dek'-4re Dek'-a-ptdr Dek'-a-li'.tep Dek'-a-gram Hec'-to-meeter Hec'-t^re Hec'-to-stfir Hec'-to-Ii'-ter Hec'-to-gram Kill'-o-mee-ter Kill'-Are Kill'-o-stgr KiJl'-o-li'-ter Kill'-o-grarn Mir'-e-a-mee-ter Mir'-e-are Mir'-e-a-8t5r Mir'-e-a-Ii'-ter Mir'-e-a-gram M Q 2 M G L ABBREVIATED NOMENCLATURE. -.that the na.o. u^XuTfe^t"^^^^^^^^^ tl-ey should be identical in al! kngLti' "" "'' ^*'"' "^^ ^^^^ 1 m 182 fmrn wgMtiK arsTicM. eosraopolitan in its character: it belong to their hn I 13;4 RSDUOTION OF COMPOUND NUMBERS. REDUCTION OF COMPOUND DENOMINATE NUMBERS. 214. Reduction is the process of chanrrinrr numbers from one denomination to another, without alterin-; their value. Keduction IS of two kinds, Descending and Ascending, -v»>. deduction Descending is changing numbers to lower denominations without altering their value; as pounds to shil- lings prds to feet, etc. It is performed by Multiplication. >5if>. deduction Ascending is changing numbers tohi<^her denominations without altering their value ; as farthings to pelioe, inches to feet, etc. It is performed by Division. REDUCTION DESCENDINQ. 217. Case l.—To reduce a compound number to hvovr de- nominations. Ex. Reduce £45 Is. 8d. to pence. OPERATION. £45 7a. 8d. _20 907#. 12_ 10892d. ANALYSis.-Thore ar« 20.. in £i, therefow, 20 times the number of .£ =, the number of ehilluigs. 20 times 45 = 9ii0«., to which we add 7»., and obtain T. iScurt. Aqr. 19/6. l4oz., how many ounces? 6. In 2'm 93 05 29 l:^ gr., how many grains? 6. In I2rd. Hyd. 2ft., how many feet? Ana. 224. 7. Flow manv in/iliaa ji» '? m't A fiiv •-Jl-i-^ l---» « 8. DiGOarp. 7per. Uo. 5ft., how many feet? 214. What IB tedaotioa!— Hoto mant/ kindt of reduction f— 215. What w r«. da^ot. o^ d em^ending?- 216. Redaotioa'Lcaading?- 218. JFAa/i. ,Wul. /^i Ea:. gal. ii 112 28 MDUOTION or OOMPOTTNT) NFMBRR8. 136 16. How many cubic ih^t in «? <, j , » ^^*' 34080952. ^0. Hov, manj' pints in lOte. S.L*. 7j„, T^' , ' 22-. fnT^'S IS 'LtJ* «'"'<"0"vV.H?bu»h.ls e«h, 2fi TT^I ■ ' oo»^ many seconds ? iln/ 489n94a»' ^6. How many minutes in lUC. IS. l* 1' ? "*' ^^20243 '. 27. Reduce 38tt> 6s 33 l», tolrains. iti». Case Ih^To redu^ a dmominate fraction to one of a lower denomination. ^ gal. JTff 224 112 28 OPBKATIOH. Ex. Reduce ^J^ of a gallon to the fraction of a gill. A»ALTsw.-To redaoe gallons to mllg -• bcM m the scale. And, since the given num bens a fraction, we indicate the p^oew m" m multiphoation effractions; and^Xr fi'a^ celling, obtain ,^. the answe . H „ot the ♦ M tio^f^ihf:u^}7rf^^^^^ ^-f ^^^ ^-9her denomina- the giL and thr "o^^ .^Sfo^^:'' --..,,«?,, 6e...«. 8XAMPLE8 FOB PRACTIOB. 1. What part of a farthing is ^-U of a £ ? j . ^ i ! |W 136 3. 4. 6. 6. 7. RlDUOTfOlf or COMPOUND NUMBBRi. Kec uce ^Jjyj of a lb. Troy to the fraction of a grain. Kednce 4-ff of a £ to a fraction of a penny. Aus. Id Keduce s^f^of a cvvt. to the fraction of an ounce. What part of a puuul i.s ^-^^ of a ton? What part of a link ia ^ of a rod ? ^„, «/ Keduce -j-^^^ of a furlong to a fraction of a foot. * W liat part of a pint is ^f ^ of a bushel ? Ans J.et Keduce f of | of ^/6. to the fraction of an ounce Troy. "^ ' w imt fraction of a yard is f of ^ of a rod ? .421. Case III.— 7b reduce a denominate fraction to integers • • of lower denominations. Ex. What is the value of ^ of a £ ? 8. .9. 10. 11. 12. 13. 14. is; OPKBATION. £ 8.' d. far. ?). 3 Q 8 6 3^, ^n« Ahaltsis— 8 of£l is the same u l ^ =» 8«. 6d. 33/ar. Henoe,.Uie of 22a. livh^.--.Gonsider the numerator of the fraction as so •S^^;;j^^;/'^^^^«^»rfe«omtna^ion, and divide the^ 4 the EXAMPLES FOB PaAOTIOK. 1. 2. 3. 4. 6. 6. 7. 8. 9. 10. 11. 12. ' 13., 14. 15. what , What k the value of ,5rOfa£? I of a bushel ? I ofaehilhng? fofaowt.? I of a yard? f of a lb. Avoirdupois? ^^ of a day? |ofl5cwt.? __ ^ I of 2^ po'inds Apothecaries' weight?* o?6j toTr* ■**"■ ^*- ''■''• ""'• "* ''■''•■^- '"A'j. '». I of a Sign? iln«. 12'> 5P 25"! Jromapiecftof velvfetoontaining Syd. 3gr. I cut 2«rf. 2^1 Vtvt VI ihe wnoie piece did 1 take ? ^ ' Ans. 58. 5d. l^^far. Ans. Ipk. 4qt. ]§pt. Ans. 3qr. 2/6. 12o«. 7^rfr. Am. loz. \ldr. Ans. Ucwt. 85/6 Uoz. &Ur. «a». Case IV.— £0 reduce a denominate decimal to integers V lower denominationik Kt. OPKBATION. ^0.628125 20 12.562500#. I^ 6.750000rf, ———J 3.000000/ar *0 12,. 6|./. Aiu. BW^OTIW OF OOMFOWD N^K„. ofa£ to shillings and pence. deduce 0.628125 137 '"g^S and the refluU^f f.. fH"l'^*'«»^>"■ J. to reduce it J/l'Trl"°S rhr "'"^f '^-^^^ «' 'Ae Uft u>iil he the a«,«,er r?;"^/''''";^""'*'''"- ^^« •«'«!J^e-' £XA':PLfc8 FOR PKAOTIOt What is the value of 1- 0.45iof»£? 2. 0.748 of a bushel? 3. 0.765 ofa pound Troy T 4. (-.7525 ofa mile? ^ 5. 0.659 ofa week? 6. 0.217«? 7. 0.876 ofa hhd.? 8. 0.865 of an aor«? 9. 7.88126 acres ? 10. 0.626 ofa fathom? U. 0.78S75 ofa long ton? 12. 0.R46yofadegi^? * /!»». 9». Id. 21 far Ant. ipk. iqt. Ipt. SASHgi. AnM. 6/ur. ord. 4yd. i/t, '^in. ^*«. 13' 1.2". Ant. 16CV7/ Sqr. 2/M 2.812. ^^'D^OTION A8C1ND1NO OPKKATION. 24 ) 78692^r 20 ) 'S2THpm. 2L*gr, 12) 163os. lapuft. 13/6. 704. IWft. 7««. 18^. 20|T., Jim, A«ALr8is._24fr..ljH;,.. there- »". jJj of the number of grains ^ «6«2 3278;,v,,..a.a2V.reSlin. 01 the number of ,M,nny weights • tK " number of ounoei. ^ of 3278 = 138 ■IN ii I RtDUOTION OF COMPOUND NHMBBRS. ih^^!^' ,?"^«-7-I- ?J^i*^^e the given number hy thM numher of taZ,u ""^ '""^ '"^"'^ '' '". '^' "^^^ ^''0^'' ^'^^^ n^Lf'^l'^'^J'- ^'t '■"r"''" ^^' ^"'''*'^' ^'"'-^ obtained, and so ZttXti\l' *''"^^^ '^ '^'- denornination required. The last ZiTJi, ' ""'''''^ remainders annexed in a reversed order' ^nn oe toe answer. ' Ant. £17 2*. 9rf. Ana. 4ft) 5S IS. EXAMPLES FOR PRACTIOB, 1. In 16462/or., how many £? 2. In 90720 pence, how many £ ? 3. How many pounds in 4253? 4. In 78692^^., how many pounds Troy wei<'ht ? •ach ^,P^y«'Cian who averages daily 5 presc^riptions of 20 grains •ach,^how many pour.ds of medicine will he use ,n one year, or S8o : M;Jr2?^^^^^^^^ .t4lV.r- '''''• 10 At ai. ^ I' ^u'' '"*"-'' ^"'^'"'^ ^ ^"••'- 19*«- ¥^- ip<. 11 ' nil ^J' ^"^^ "'"^'' ^"""P 0*0 be bo.ight for $;184? 11. How many francs in $176.70 ? >i«„ Qsn 1 J- S,'''' ""^"^ ^"^y' •" 9^^^o ««cond8 ? ' ^"''^- 20. How many tons of round timber in 622080 cu. in'r ' n.^k ^•J' • *' T*"'i2/?. by 24j?. is 6ft. high and 1 },n. thick. How 2» T^r,if • -^^i '''^u' *° ""'^^- ^^'- ••^'«'- ^''^^^ i Z8. In 161384 mthes, how mtunj milts ? -easur^T """^ beergallooe M-e then, ia 1*W. i^;. 2^., wi«, 9A- Sii ^^^i?l^'»""* >"«h««' bow many rood« ? "****■ ^^'^• 26. Reduce 20937 minutes to signs. An$ US l«o ^7- * ' 4iM. 13/6. tio«. far. ^1 RBDUCTION OF COMPOUND NUMBBIW. I39 2S». Huw many ^re'^ uf Scafu^ «"'! m.nutefi did ,.he change ? JO. la 13360128 drams, how many tona? 2S7. Case 11.- To reduce a denominate fraction from « foir^?/- to a higher denomination, ^ Ex. Reduce * of a farthing to the fraction of a £. OPERATION. 9 ^ liugs. I 1 1 ANALT«r8.-There are ifar. io Irf., therefore 1 of the number of farthings equali the nnmbor of peme. There are 12rf. in |, therefore ^ of the number of There are 2«.. in ^1, therefore , P*°°^^'i"f '"'»»« ""mber of shil- ber of ^. Hence i/ir 1 1 x ^t 1 ."" "' ^''"°^^ ^l"*"* H "^ 12 "* 20 * £ 1 2160 Ah$. the number of 4; What part of I. a pound Troy i8 I of a grain T ^. a pound IP f of a scruple? i>- a rod is I of a foot? EXAMPLES FOR PRAOTIOB. ' Ans. rhrd. 4. a iDileisSofarod? 5. a hundreJ-weight is f of an ounce . b. an hour 18^ of 20 seconds? 7. an acre is I of a, square foot? a. 6 hhd. 18 i of a quart? 9. 4 days is | of a tiiinute? . 10. a cord of wood is a nile 71 A ]nna 9/> i • u i . ,/' t^^W- 11. a rod is 2| of ^ of an inoL?' ^' ^•^' *"«^' ^"'^ "V^- ^'^e? 2. an acre is ^ of -*, of 9^ square rods ? "*"'• '^• o. Reduce 9.312/«r. to the decimal of a £. An. £o OflQ* i4. Reduce 517.44/i!. to the decimal of a mile. ^^®^^- 22». Cask III.-- To reduce a impound number to afractum of a higher denomination. Ex. Reduce 8.. 6rf. 2/ar. to the fraction of a £. QPERATJOX. 8«. id. Ifat. = 410/ar. 41 1^ = WO/or. ~ 96^' A!^Ai,T8M.-:3yr^uetionofd««ia- >nate numbers (217), we find 8.. M ijar. «= 410/ar., and that jEI „ 9^ ||«ra^ »»ff - til = I ilj: 140 RIDUOTION or OOMTOUMD NUMBSBB. 230. RULK. — Reduce the given number to itt loweet denomi- nation/or the numerator, and a unit of the required denomination to the tame denomination for the denominator of the required /raction. ■* BXAMPLSS FOB PBAOTIOB. What part of 1. »£is 10». lOd.1 2. R ton 18 icwt. Sqr, 12/6. ? 3. an acre is 2/4. 20/)er. ? 4. a mile is \fur. I2rd. iyd. 2ft. ? 5. a hogaliead of wine is iHgai. 2qt.1 Qj. a square rod is 144/jf. ]i)^in.'l 7. 2civt. iiqr. is icwt. 2qr. 20/6. ? 8. :■{() dayti is Sua. llh. lOmin.l 9. a bushel is 1| pecks? 10. a pound Troy is lOoz. I'Spwt. 8gr. ? 231. Case IV. — To reduce a compound number to a decimal • . of a higher denomination. Eit. Reduce 12«. 9d. ifar. to the decimal of a pound. OPBRATION. 3.00/ar. An$. ff . Ans. ^. . 4 12 20 9.7500rf. 12.812508. 0.640625£. Ana. AwALTSia.— Since there are 4 farthingfi in Id., i of the number of farthings equala the number of pence, i of 3 = o.75<^ which added to 9d. « 9.75d. There are 12ii. in 1«., therefore, ^ of the number of pence equals the number of shillings, i Or, 12«. 9d. 3/ar. = 61 r/ar. £1 = 960/ar. = £0.640625, Ans. of 9.76rf.=i0.8126». which added to" t2«." 12.8125.. There are 20«. in £1, therefore, jljj of the number of shillings equals the number of pounds, J^ ot 12.8126 = £0.640625. Hence, the 2i3S. Rule. — Divide the lowest denomination given by that number in the scale which will reduce it to the next higher denom- ination, and annex the quotient as a decimal to that higher. Pro- ceed in the same manner until the whole is reduced to the dcnomr ination required. Or, lieduce the given number to a fraction of the required denomir natwn, and reduce this fraction to a decimal. EXAMPLES FOB PRACTICE, What decimal part of 1. a gallon is '6qt. \pt. 2gi. ? 2. a, week ia bda. dh. 46min. iSsec. ? 3. a mile is 5fur. 35rd. 2yd. 2ft. J)tn. ? An*. 0.V3603219 h- mi 4. a Imehel is Zfk. 6ft. \ft. ? An: 0.9315gal. RBDITDT105 9W 0ITE1UINOIK8. 141 6. a ponnd Troy is lOox. \2pwt. \^gr. ? Ans. 0.8864581/6. 0. a fathom is ^%ft. ? 7. a ton is UcwLciqr. l6A5lb. ? Ans. 0.H857257'. 8. 14 bushels IS 0.t5 of a peck ? r.f.\ ^^]'^"f ^^T* '^''■*^- '^^'■- 20/6. tohundred-weightnand tlie decimal of a hundred-weiglit, .j,,,. .,,f^ 7 1 7]^k£^'^"*'*4 ^2 ^K<^««'-""a' of a pound, 19». 11 |rf., I d.,. ' i)Jd.', " and 1 ^». bia., and find their sum. Ans. £2.710416 1- . REDUCTION OF THE OLD CANADIAN CrjRRBNCY TO THE NEW OR DECIMAL CURllBNCY. £af. Reduce £72 13 9 1 to cents. OPBRATION. ANAtTSia.— We malHply £72 X 400 — 9«snn «.«♦„ ^^ ^y *'"• because each l, Ant. f'' '!!'"» '' '^'^u-' /° .l** °'"'* ' «. n/fs. lastly, we multiply the num- anii ro.fk;„_ u c , ,. . , ber (if farthings in the pence ejaa^ to l*of /cent *'" remainder by 12. because each farthing Ib farThinl!'^'* farthing ia equal to ^^ of. oent, ie evident from the fact that 48 anrl n^f r ^Tv.? '^ shilling) are equal to 20 rents ; or 12 fnrihings equal 5 cents, and one farthing equals^ of a cent. Hence, the following ^ ;. ^?*' ]^^^^'— I- M'lltiply the pounds by 400, /Ae shillings oy ^«», and take five-twelflhn of the number expressing how many farthings there are in the given pence and farthings. II. Add the three results together, and their sum voill he the number of cents required, III. Consider the last two figures as cents, and the result will be dollars and cents. ■ i EXAMPLES rOR PRACTICE. 1. 2. 3. 4. a. 6. 7. 8. 9. How many dollars and centa in £4 3 li? 4n«. $16.62X. 27 16 3^? " 27 16 Hi? Ans. $111,381. 69 15 6 ? 14 8i? /ifw.f 2.944. 77 19 4^? ^ 17 16 6|? .In.-.. $71.29X. 18 18 lOi? " 9 8 61? iifw. $36.69^. 10. £16 6 11. 97 3 12. 46 17 13. 121 14. 12 15. 1 12 16. 173 13 17. 91 8 18. 19 11 Am. $66,231. 7 9 U 2 ? 11^? 7^? Ans. $187.62^. Ans. $49,984 9i? ' 4 ? Ans. $694.66i K ? 4| 7 Ans. $78.27|f . : :! I I 142 ADDTTIOlf O? PfiMPOnivn IVTTMBWRfi. mmwnos of the dkcimal ciiruency to the OLD CANADIAN CURREN(.T. ear, K«(|„ce *246.88 to the old Canadian ci.rn^ncv. <»rBRATION. 20 4Md. 4 Analy8I3.~Wo divide 246.88 by 4. the number of dollnr. in a pound, and lVr,T\v ^"' •*"" " hundredth, ofa pound. We multiply 72 by 20 r24\ he nu.nber of .hillin^^ in a pound, and a 8h llmg. A-am, we multiply 40 bv 12 tijo number of penoe in k' shilling and the rrsult ,s U. and 80 hundredth ofa penny Lastly, wo multiply 80 by 4. the number of farthinp. in a nennv and the resnlM. 3/W,.. anr20 huodSh^,' or ^ of a farthing. Hence, the .^Un^' ^^'l'^---fi"''J^ the given number bi, 4, and thnnotient EXAMPLES FOR PRACTICE. tiedttce to the old Canadian currency :— I, $m.W= Ans. £40 11 6 10.$319.13i. -ins. £79 16 2, 4, 9, mAd Ana. 97 16 lOJ Ana. 20 10 -Ins. 142 5 - of pence in ?ha right-hand column to be 29 pence =- 2.. 5rf. We wr te tbl umn" of'2n- °"'"T "^ ^''""'J '^"'^ """^ 'l^o 2.. to the col- umn of shilhngs; the sum of which ia fin., = fo i«!. fo^^H.'^'io *" '^' ^^*- "°«*" t»»e column of shillinss we ^ to 4 4 in » IH 61 78 17 28 205 "205" 5 8A 6| ADOITIOK or 0OU9eVND NUMBBR6. £.'a:. 2. Add^iTyofaXtof ofaahilling. 143 il OPERATION. /5ora£ = ^ of a a. - 1 1 9». 4d. Oa. Hd. 2^/ar. 10«. Orf. 2^/1?: Or. 10s. Orf. 2^/ar. ANALT8is.-We first find the ralueol each fraction in inteafers of less (ienom- inations (221), and thon add the result- ing or equivalont compound numbers. Or, we may reduce the fiven fraotiona >?„,,^°'.'l"'' "'" '•'• *»">« clenomination (-219), then add them, and find the vol- ue of their sum in lower denomination*. Ueooe, the following aae. RULE.—I if any 0/ the number, are denominate frao. t^omoryanyofthedenonunatlomare mu,ed numbers, reduce the fractions to integers of lower denominations. .nnh, ^?-' !?' ""'"*'''? '"^ '^°' "'**■'' ^/'^^ ««^^ denomination, will stand in the same column. "■"'"w ««iV' ^'^''""'> "'^■^^ ''i* ^^'''^^^ ^?^«.m*««t.2lirr. ? An 2 T I 3 4 , - , „ , 10/6. 7oz. 7/w/. 21^r.?4n». 34/6. \oz. 1 5/Jtrt, I'Spiot, 1 1 1 144 «TT.TaAOTicm o, coim,tm„ ^„,t«ki. ^ ' '^^ ^* *» •» I'fr., 6Ifh I Is 33 2» 3^. *^ ' ■^^vii.7fur.lch.2on ^^'' '^^i- «/«^- «^A- Ird. 16/ l2<'36M7.8",and57.3M ^ 25.7'Mr 18 2", IS. 3o^2' 15.5", , 10. Find the sum of A ofa mi?, i r ^^'- *''^- ^"^ ^^' ^^.S". i«. find th. .„,„ rfi J* i ^»- r?,,"'*- y- .'•?■;?• 1 1.1J.?. m. .15. A farmer recei^JeoVt. Jhi-^'J f'r/r A"?' *■' '""S '"» ""W.. £Jar. I SUBTEACTION OP COMPOUND NUMBERS. Krom £U 6.. 1,W. 1/a,. ,ak. f ,4 15,. ,^ 3^^^_ OPERATION. der the S" T"f"'« '^« «"btrnhend «- dtotn=S£t:ro?i;;a^;r"?- ^/or. from l/«r., we add Irf. or 4; ,/ t« makin. 9,^. ; and id. fJom loTle ve^ 7d ""1-1' ' '^^ '» ">« » '» the sSh ndj Next.n.weonnnottakeI5,.fromr wf';.^!^^^^^ '^f. ""^ i° the remainder IrH^^" .u '^'^'"^•^''''•^■''*.''e subtract i^Sfrnm"^^^;" '^" denomination of •nd wnte the remainder, ^20. under the column of^f' "* '° ""?'• °"""^«". ^.r. 2. From | ofa mile subtract ^ ofa Airlong. OPERATION. |m. =4/„r. 1 7rrf4yrf.0/<. I otn. -y«r. _ ^2 4 2 1 '5 22^ ^n». 3 34 4i 82 ANALTBI8.. \ye perform the '*™f "?"l»«tk)n M in addition of denominate fractions, (234), and hen subtract the lesevalu. from the srealAr, 3/ur. 34rc<. 4iyd?7;»:8|,„. Jl. *j„„,„-„„„(,j ""'"""Xl r:.^- i-i. From 5i66/. tak7l nf u^ ^^'^^ ^o°8- """ ' ^'*' 15. Subtract%;65rw:eU:rnr''l'-o ^^--^^^Ml^./ ,^ -- -"""»««• u.ooy week I'mm •> i „ ■*"*• 4oW. Mp-,,/ 16. Prom a hoffah^aw r • ™ ^ *^^'<^k8 34 davs ^ '" OUtj ^liiiM.Tfi^''' l4lt MULTIPLIOATION OF COMPOUND NVMBBM. PRACTICAL PROBLE]rfS IN COMPOUND ADDITION AlfO SUBTRACTION. onl'ol'l^^nl^^^^^^^^ two bou^-M^ have I remaining ? '^ ' ^* ''*''" ^^- -^^^ ^i'*''- ? »^ov M««^ di«.nc, how fa. ar. Z', a^rt" 1^ 4r .%ir' ^'".'^ ^j^l"* , 6. A man agrees to build 1S6 rd an if.; ^' ^ ^^**' time, he builds 36rrf. 2ft. ^ ^iJoihtr^^^^ ** ^ otherUme, lOrrf. l^/^^^kV mu^r'^JH':: kinT^^-bf^^^^ ** •* 7. A hogshead ofir^ne los^bl Kv J^"' '""'^ '""*'"' ^'^^? including two leap jiws W^ni nf^!!*"^ an average, for5y*«^ mained? ^ ^ ' °°® «'" °^ '"°« a.^^ayj how muci, ,J «, Suppose a person was boro Fehvniry 2! mt l^'' ^«*' anmversanee of hfs birthday will he have ffi on Feb 29 \7uTi^ 9 How long has a note to run, dated ADril 23 1870 i 1 *. payable Dec 9, 1874? ^pnJ ^^J, 1870, and im4« 10. From a mass of silver weighin^z lOfilh « i^" '^■T' '^^' spoons, weighings/ft. llo^^^z^fsUTaUlrdSrLr 14Fr. : a rase. 7/& IIak i^nw 00 *'• > » lansara, oio. Oo^. I3|^ remain.? ' "^' "''*• '*^- ^^^L' ^Tm"*;^?** unv;rouglu 3^ Howlo7gTa;\LTol^rSt,i^:^^^^^^^^^^ How long, if the time is computed by days ? ^^ ^^^' "^ '^'^ «^ * ^n«. let. llyr. 5«io. 25rfa. ; 2nd. 4130 day». MULTIPLrCATION OP COMPOUND N[mBJ5m Ex. 1. Multiply £8 9,. M. by 6. OPERATION. £ ». d. 8 9 6 6 write tho M. wder the pence, .nd addfhe £,'. Jt C fr ."i" Of s»>iling8. 6 times «.. are 64*'.~«Zi 2. aro56».-£2 Iti,. Rewrite the 16# uiidS- the sh.H.ngs and add tho £i with the prodrt^ we wntound« pound.. Tberrfore 6 tia... <|'£* . 'CSiH. Rule T Wr,;. ti , . A7j. 9 wu "''''®''^ these leveral parts. .>p...„oK. -^2 3,. 6rf. per yard ? £ iT -tprod„rtistheanLWe'c •e «. rf. 6 16 9 = value of 3 bbl. "'^ 6 = price of I yard. '^ 6 = priceof5yardfl. £97 n> 2; J *• ^'''•= price of 45 yds. ^•a^. 3. What cost 643 barrpls ,.f a ■»•' uarrejs of flour, at £2 *>« -rw i.t . ' *-" ^*- 'a- per bbl. ? OPERATION. 1 bbl. = 2 5 7, X 3 =. 10 bbl. =--2rrrT^, . 4 == ^''^ i» 4, X 6 = 1367 10 . Analtsis^S . ^ - ''a'«eof643bbl. barrel by 3? I'dZt th '^ ''>«/al"« of 3 barrel ie m?, "^ { **"« '^^'''^ »f •«wer.\eace tt^'''"''"''^'^ P'«e the value of I dozen gold cups, each cud weiffh- ing 9ox. V^pwt. »gr., at $212.38 a pound? ^ ^A^f' K^ ^^'P "*''^ ^** 2*' ^0" F^J" day, how far will she sail in ^",la^« ^ Ana. 204" 10'. 15. One ton of copper ore will buy 17T. I4cwt. 3qr. Wb. 14o«. o| iron ore j how much will 451 tons buy ? ^^i K^^'^ ^'" ^"y "^^ ^'^- -^P^r. 208q. yd. Ssq.Ji. of land, how much wil $4800 buy ? "^ ^ ^Ans. 295^. lOaq yd 17. 11 1 cask of oil contains H{]gal. 2qt. Ipt., how much will 100 casks of the same size contain? . l^r.' J}'^^ '^ *^® °°^* °^* ^°^^^ ^^f^' 9»'»- '0D& and 2«. 3 Am. wide. at $0.05 J per loot? ilns. $2 27711. 19. Bought 17 bags of hops, each weighing icwt. ''Aqr. 7/6.7* at !t)6.«Ti per owt. ; what was t4ie cost ? 20. What cost 27 r. \5cwt. \qr. S^lb. of hemp, at $183.62 per o? A ^,or,, 4ns. $5098.07 + . ^i. At *li5.75 per acre, what coet 374. 'SR. 35rd. ? «q5!; Ill^*^ "^^^f ^^^ construction of 17 mi. 6/wr. 36rrf. of railroad, at $3765.60 per mile? Ana. $67263.03 + . *o. Dougni a iarm containing 14i/i. 3R. 30ocr., at $97 62* ner acre ; what was the cost of the fa^t ? Ana. $ 1 4149 62 + 24. At $9.26 per cwL, what cosf 19cw*. 3qr. 14/6. ofixomt 6 d. 4 d. 3 d. 2 d. lid. 1 d. lo. =; 8 > 2 14 11 ) 2 14 5.) fur. 6 rd. 18- 8 MIILTIPLICATION OP COMPOU.VD NUMBERS SOLVED BY ALIQUOT PARTS. TABLL OP ALIQI'OT PARTS (173). f'arts of 8 n I cwt. (1) Parte of I lb. Parts of lo«. Parts of* ofU2U). Avoirdupois. TroT ^'ansofa "'• year. '56 lb.= l 28 ib.= r 16 Jb.= |: 14 lb.= [ Jb.=-i., I. i<> 802. 402. 2oz. loz. ,ij5p;yt.0gr.=|)6 mo„ae= -^1 Part- ,fiib. -roy. " "= 1 Parts of a [quarter of 281b. '4oz. _ .Soz. _ 2oz. — . Jo*.10pwt.:=||2(;per. loz. _. 1 i/>^ — T? loper. Parts of 1 aere. Parts of a month. = i, 14 lb.= i 7 lb.= i lb.= | Parts of loz. Troy. Parts of 1 rood. lOpwt. Ogr. = ^ lOper. =1 /ar^A%,. -^ ''^'"^S 4 pon.uh, ghUUngs, pence ^ni ^- Find th, price Of 944 pen«, at M. per pen. 944 pens at Irf. = 944rf. = £./ 18 8 /?• "^ ?«!?•; i of £3 18 8 = £719-1 , !«. - j of irf.; I of £1 19 4 « li {9 J = ^T V\t P!f' f i* ^«- m i» -■ « i< IM MITLTIPLMAnON BT ALIQWOT FARTS. «um W?y aTeno?- b Jt^^ ^c/ i^ HZ ''«'°«/'"-^*-?*. "e multiply the glr- it into i AnrK^iS .ttihl ?,7!*" ^^«" P^f j"' * P''""^' we deoompc the half of id St^hen take the I of /"irs f''V/-' '■''" f»"/'h °f a penn/, or then irf orS of id., 't^at b.'oSeValf'ol :£ ' iVl L^iTs^ 'whr '' ^LL' tl ■£1 1» 4; the.ua. the- giv ,£2 IS 0, iJr the ansl^er ' '* "^ ** i7*. 2. What cost ltf38Ib. of Bugar, at 8 id. per lb. T OPERATION. 16381b. at U. = 1638t. = £81 18 Odrf. = iof2rf.; iof£13 12 = ££_8J= n « u ,, ^J. £58 3= " " << " 8irf. pose ii into 6d/2d.,t^d'ilfl'^Ar;rS ^*. 3. Find the price of 252 yards of merino, at 3.. 9^^. per yd. OPBRATIOX. 252 yards at £1 = £252 3». 4 rf. = 1 of £1 0#. 6 d. = J of 3$. 4d. Ot.Oid. = ^^of5d. Ans. Ea^. 4. What cost 694 cwt. of butter, at £5 II 6^ per cwt ? OPERATION. •^694 =priceof694cwt. at£l « £42 = price at 3*. 5 5 0= '< « 0,. 10 6= « « 0,. 4 d. per yd 5 d. « <« O^rf. " « £47 15 r? = «' " 3^ 9^rf. " " 694cwt. X £5 = £3470 = 10s. d. = ^o{£l I 347 = 1«. 3 d. = J of 10s. 43 7 6 = e«. 3 rf. = ^ori«..Srf.i 8 13 6 = Or Oid.=jofO»..'^rf.j 1 8 11 = Ans. « "694 << « £3870 9 11= " " .< « EXAMPLES FOB PRACTICE. " £5 " " 10 " " 1 3 •< " 03" " _0 OOi" " £5 iTej" cwt « 1. 2. 664 X if. Oi = 3. 1984 X %\ i. less X oi £ $. d. 13 10 3 12 2 S 12 8 5. 1078 d. 01 := 6. 1683 X 2A £ ». d. 1 2 6i 7. 2142 X 6|= 61 6 41 8. 1053 X 54= 23 sf U. 6d. = ©«. 5a. = MtrWlPLIOATION BT ALIQUOT PARTS. 9. 10. 5728 54 HO 11. 24.S6 12. 2147 I.>. 7028 14. 2708 16. 5491 16. 49.36 IT. 4967 18. 2522 19. 2897 20. 7509 il, 1870 2244 392 576 465 X 425 X 1349 X 28. 7045 X 29. 2426 X 30. 1454 X 31. 3632 32. 6741 22. ?3. 24. 25. 26. 27. X X «. d. < 71 < a : ■ 6i : 3j: S\z 6| J ^^ = 8| = lOA 11 = 10J = 11^ 9| = l]\ = 1 8 1 9i = 3 7i = 4 111 5 8 = J 7 7 4i= 6 5i 9 7 = 2 6|= ■£ *. rf. 173 8 67 17 6 31 6 2i 241 11 9' 33.1893x0 4 IDA 34. 604 X 8 "J 35.2916x0 5 ll| 151 An»w«rt. •e «. rf. 36. 5.'J48 X 7 ,s^ - 248 10 5 - 868 U 6 X X X X X X X X X X = 171 11 101 = 179 19 2 ■■ 115 11 10 ■■ 129 U 2% 75 19 4i 105 3 9 51 84 5 n 382 4 4 892 1 2J 1740 6 863 1.3 8 91 •^7. .3720x0 10 d 38.1509x0 14 6 39. 878x0 11 4.1 40.4571x0 1.3 41. 54 X 1 2 9' 42. 62 X I 7 44 *3- 17x4 3 11 44. 24 X 3 13 ■': 45. 472 X 6 10 34 46. 1958 X lis 8 - 47.2471x5 14 91- 48. 972x3 15 10 49.1077x7 12 .3 = 50.3714x2 13 11%= i*!. 1415x4 11 10' 52.2150x9 16 1? 53.2175x6 17 10?- 54. 7251 X 8 7 7I 55.6494x6 19 5'L 56.7122x9 13 4^= -^ 1960 15 ^ 1094 6 I _ 3113 19 101 61 8 6 71 6 7 ' 88 2 6 ■■ 3785 9 4 =14179 18 8| = 8198 13 3 ^'0023 18 7i 21083 8 9 l-'818 18 li 45288 17 81 t>!:i860 16 9 Ex. Required the price 0/ 1581 yards of cloth, at £1 2#. 6rf. = £• 6rf. = ^ of 2s. iof£\ 2 11 loflU. 5^rf. Ans OPERATION,^ 158| varde, at £1 2 11 19 15 = price of 158 yd. at 2a. Gd. __8| = 2 11 perjd. i -3 li SSil/?^^^S:^£'S:iX^ (^~?"«» ANOTHER METHOD - I 158 i yards, at £1 2 11. 2a. 6d. = £1 ^.Ba k of 2«. 6d. Atu £158 19 3 15 16 6 £181 19 Oi = price at £1 « n per yard. 28. (id. *t u _0 Us. 5rf. tt u £i~?~rr " «i i H ! ] ( !i it I M 162 MULTIPLICATION BT ALKJUOT FABT8. AntALTsrs.— In this method, we Orst find th« nrin* nt isua j 7ard. Thi«is£Io8 15 0; fo; tho price of SS Ts £168 I^hV' ^ P*' iquarterofa yardbein'^evidentlv 5. it>f thJ^r T I '.^°^' *•"» P"oe of pnce at £1 por%ar,l bein. ^Fsl fs, h tico at 2 Id ^"-f, t}^'' '^^''>' '^'^ ^ 6 U. The sum of these is £181 18 Oi, the whole price,'^» before ' " 1. 2. 3. 4. 6. 6. 7. 187 ^ S28 3 208 5 971 1 675 ] 3714 638 1 EXAMPLES FOR PRACTICE. £ .f. d. 8. 495 J. 917 10. 11. 12. 13. 14. 515 g 63 g 85? 176 1 15. 785 a 16. 239 I 17. 375 I 18. 759X 19. 774 4 20. U9^ X X X X X X X X X X X X X X X X X X X X 17 8 6 6 13 10 15 2 1 3 1 3 3 4 2 3 2 3 15 10 11 8 Ana. Ann. £ 353 106 7 14 4 5 18 9 18 7 2 'a 8 9|: 10^ 4 : 9 : '6 Ans. 3650 Ana. 917 7 1 4 2 9 8 6 3| 10 10 19 111 15 94 11 6 : 19 lOi : Ans. Ana, Ans, Ana. Ans. Ans. '25 1630 «. 2 16 11 14 13 1271 14 249 12 6.54 103 Ans. .Sd9 Ana. 1877 16 2 12 7 d. 6 lOi n I 2 9 9 6 1 34 5i Ana. 7416 16 104 Ana. 6736 ft 9}^ perlwtT^"' '' *^' ^°'^* ^^^^'•^'- 2?r. 15Z6. of tobacco, at £5 12 6 £94: 94tw/, X £5 = £470 10s. {)d. .-.: £^. 2». (irf. =^of io* 2qr.= \oncwt. 10/6. -.. ^of27r. 6/6. ■= ^ of 10/6. 47 11 2 '' Us. " 2s. 6rf. at £5 12 6 ^«* £632 £5 12 f 5 12 6 X 94 = £52815 2 16 U 6 2qr. = ^cwt. 10/6. ,^of2gr. §/6. = |ofl0/6. •4«#. . , .J6632 8 OPERATION. = cost of 94cwt. at £1. 0= cost of {)\cwt. at £5 :r= a il it 15 = << « .< 16 3 = " a 2or. 11 ;^ = " " 10/6. ■ " " 5/6. 8 1^= cost required ANOTHER METHOD. ^ = ooat of I cwt. = cost of dlcwt. 3 = " " 2yr. 3 = " " 10/6. H= " " 6/6. li« per cwt U U at £5 I ii S ucr cwt. << (< «< U u It « « U 41 « M « « « << u M I. 2. 3. 4. 6. 6. 7. 8. 9. 10. 11. 12. 13. 14. 16. "94 2 16 at £6 12 c perciT DIVISION OF OOMPOriNn NDMBEI18. 15S 1. fiBcwt. 2. iHcwt. 3. I'Jcw/. 4. I2'.)cwf. 6. Hlctvf. 7. 2Hr,afr/. 8. 3U\cwt. 9. I Slow,'. EXAMPIEs Foil PHxcTlCK. 2qr. 'qr. ■Aqr. Iqr. 'qr. Iqr. Mfr. \qr. I per cwt (i 6 8 9 (( a ./n.s-. £ 74 u u u u Jns. £ Alls. £ Ans. £ Ans. £ ii2 -A -.',9 G20 '(tfj. at £0 17 21/6. !U £4 14 lUh. at £4 11 l(i/6. at £2 12 S/A. at £4 5 17/6. at £2 15 7/6. at £1 IS 10 4/6. at £1 12 7 lA i^r ■"^'- •''■^^/'- at £2 IH 4 " " 1! 14 7 .051 19 nG4 3 4 2J|. •-'•1+ 4 + . 1|. 4 + . 1 1 15. IM.Ji^. 2Mper.at£l 8 7iperacre. 7 Ans. £ 148 10 DIVISION OP COMPOUND NUMBERS. I £Sel wifgh ?*"''' "^ '"^" "'"'^^ ^'^^■'' ^^^- ^«'*-' ^«^ ™««i^ will OPERATION, owt. qr. lb. fi) 9 1 10 ANAt,Y8i8.-0ne fifth of Qewt. is icvt. audicwt nmldjr. remaining, to which we add the lor ' and hhve U^r. I fifth of 17.;r. ia 3yr. and 2?r. « 1 q ,s *"'*• l,*!"*'?"^' t<> Which we add the lOlb, and 1 3 12 hav, fi0i6.1 fifth 016,1/6. is im Therefore.) fifth of ^met. Iqr. Wb. = lewt. 3qr. UCb. ^bers and each succeeding denommation in the same JZ' %f there be no remainder. mannet, redLVttlJ'l^u'^t aArci«,tVm^ any denomination, ZrTnLi 1 ^ !•"'"' denomination, adding in the given nun^ berof that denonnnuttan, if any, and divide as be/ore. MMv^n/ « T1 '" '^ '^"'^'" *^*'* °^' *^'^ denominations. The several partial quotients will be the quotient required. -.S^^io^^ »-^. w. .., J;crdttt%lS';[.si£;frsr^^^^^^^^^ ^'^•^--» ", pie numfceri. »"»w»»twM, Mia thu division then 18 the &ame as in gim- OPCRATIOV. € ) 67 10 = priM of 24 yardi. * ^ ^ 11 ^ = pri«« of 4 jarcU, rnr-pricof ijHd. 7 We therefore divide the prior bj •ne of these faetorg, and the quo- ^nt arising bj the other. Henoe, Ilh 'I? IJ! : I I i II I "' ! f i 154 24»5. Rule in succeessio?} . Ex. 3, Divide OPERATION. £> 8. d. 173) 360 8 4 14 _20 173^) 288 ( I,. m 115 12 DIVISION or OOMPOUND NUMBBE8. —Divide hy the factors of the composite nwnber £360 8 4 by 1 73. (£2 ANALyaiB.-We dWde the pounds by ITS and obtain £2 for the quotient, and £14 remain- ing, which we reduce to shilling., and add the H». ; and again, .livide by 17.^, and obtain 1«. for the quotient. Tho remainder. 115*., we redi-o. to pence, and add the id., and again divide by I7rf, and obtain 8d. for the quotient. Thus, the method is the same as by general rule (244). 5^ ,"°"IPS the several quotients, we obUur *^ I a, for the answer. 173 ) 1384 ( ad. 1384 Ex. 4. Divide £24 3 8 by £3 5^. OPERATION. ^t^^^L^±J/Sr:__232]Qfar. £ 3 0«. 5d. Ifar. ~ 2^{)2 far. 8. Analtsib.— Rednoing both dividend and divisor to the lowest don aination mention- ed meithei, and then iivid- fng as in simple numbers, we have 8 for the quotient. EXAMPLES FOR Pi ACTIOS. (1.) T. ctfft. lb. T) 45 15 25 6 10 76 lb. 9) 143 (2.) oz. 5 dr. 5 15 14 13 (3.) hhd. gal. at. pt. 12) 9 28 2 49 2 I 1 dayt '"*° •■ ^ '^'"'^^ ^'^^"'^ ^^^"»»' ^/"'••' ^0^ fer doe« he go in 7. Divide 280 51' 27.766" by 2.754. ^'"- Zs 'iT :^^,','i^' % When 96 shares of a cfXin sfockt^v^ K^ t^, what would be the coat of 1 share ? *' hoi;iV3eU"^rro;i.^:?^«'^ r%^%i,^^ f?r' '^'^ 1. Divide 6rr. 19c«,f. 42/6. 14o*. by 123 ' ^^^^''*^' long woulau cake i.i» to walk 1 degree,- allowing -3654 -dlyrt-o"; 13. Divide 916m. 3>r. 30ni. l,fi^^l IfJ!"' ^^^^'«- ^«"*^ 14. Howm»aytiinaB«wje5 10 10 oo.tained in £537 10 10 T LOIfOrrVDl AND TIMI. 166 Ana. 70. lyk. 7^;:f;;L;":^;e7^'?J\°^*«frt*i" "-'nber of farmers Cbu. !«. ftvide 3794c». yd. 20c«. ^ 7094c«. m. by 334. ^"'' ^^' LONGITUDE AND TIMB. 24y Anl , ,.'""*'' P°'«' "-casing the equator at riiht angle™ •rally on the ocean the mlriJu ^^ f^^"*^ <^» ti»'« continent, al.u gen- " the determiS "leSaT AllntS'lT'"^'^*^^ E"g'«"d considered to hare noToS^tude ^ '^'' '''''^^ ^^ '^'« ^*»« »'« w«t of thi. meridian the Z.L£^ '''^^ P'-. -d at place. BMD. "•MDerorenoonj at those east, the time is after 2. The whde circle of the aartli ^nnn u- t. aud in one hour parses i of 3M» I iZ "^'^f^' ^^^' th" sua in 24 hours. One minuto ^ 6D seconds • 1 minute passes iV"^ 1^*^ - M« - i« = Ifi' •>Mo«, in 1 sMond passes O, on6' .. H' „ i' " , .» „ ' °°""""'' ^«no«.^«j^ 14„, g^y^^ the following COMPARISON OF LONOITDDB AND TIMI. 15 of longitude ss 16* of longitude s 16" of longitude s 1 hour of time. 1 minute of tim*. 1 second of time. exprtt'i fndeg^^s' 11' tf 'T '^^T''''^ ^^''^'^^^ tu,o places, their dlfferenc7rtC^^ ^'■"^'^^'^ ^V 15 u^l gioi II Th, rff ''"^^ f pressed m hours, mmut,,, and seconds. ^;«:;..;t?-^'''T'''^'r''" ""' P^*- ^Pre'^^'t '■» hour'- I . IM MWDSOniAIA ^imkTJ^TJL '^^'^^ >»«>« from oMt to wert, when It b ezMtly II !?3iil^.tf^;i '"f K*^f 2^ ^^ °'°'°<"^ *» "" P' "-"^ <"^«t, and be/ore f2 at £■ STttl. at ih^^rll?"^ f 'fforonoo of tiiM betwoeu two plioea. be LbtraJd JSrlrf ff^hin^ff. ^f'*"!'.*^''*''"'^'''" b« "'« li"« *t the westerly EXAMPLES I-OE PBAOTIOB. wL^'iT^l/", '"^t*^!"-^* ^^! ^fi'r"*' »"d Toronto, 79*^ 21' west. wii#i» ,t w l2ro'olock at Toronto, what is the time at Quebec ? 7>^ 21' 71* 16' U)^^-^ 13 32mi. 2Q$ec 15*. 32w». SOMe. AHAtTSM.— The difference of longitude i« »• 5 . Jpmding by 15 and changing to time flTef 32«r,». 20»e«. for the diflTcreDoo of time '^*?'i,**' **o P'o^oes; and, aa Quebec is V* *• "*'™°'"» ^°« '•°>e is later, and we add the difference of time, which giyes 12A. 32m». 20mo. the tiaa at Quebeo. iM L% «!f^"'*l*'* ^••'"'^ '•, •' V^' 3«" ''•«*' •"'^ that of Ottawa «fL2S*i^20^i'w °^y*'^'*'?^>,V'',^.^',^««t, and the longitude > 'JT , .8 the time at Rome? iln«. 23 wm. 28»ec. past 5 P M « wiJ-»^'P^"*^ a « „ An8.1h.20min.52,ec. u iJ /« '* '^, P^*" ^' ^^ Paul'i, Minnesota, longitude 93° 6' west IJ^^Bjn,. U. 37..V 12.ec. P. M., ^l-£the lon^^^^^^^^^^^^^ ut^i'X'^^ of Jeru»l«» !• 360 32' east, and the longiTude of tiZi^Jl, \ ""rl' ''*'*"' •* " ^®y<''- ^- ^- a^ Jerusalem, what ^I'JKf M^^'r **f^^J^."i*Vr 1' ^" ^^'t, and when it S 10 -£f^ i' ^' '" ^^**^"' '* •« 8 o «look »3'.«ii. 574*ec. in Chicago • ^^**f loagriude of Chicago ? aZ. 87^^ 34' 45' ^ ' W^longituda of Constantinople k 28» 48' east, and of Kingston, «^«««dll» 76'> 41' west; when it s 3 o'cl. P. M. at the latter nl*r^« whM Um^ w it at the former? Ans. 9A. rllmii lesecp T ' «»Lp**Ef*"* ♦*?!"** ^''- 'f ^^ J*'' chronometer that it is 3A. 40min. S^Lf:;,K-. **°T'^^' '^u'"!* '* ^*- ^'^^^■"' 4°«''<'- by solar •«»« ©• bo«rd hit vessel j m what longitude is the vessel ? iln*. 370 26' 16" west. DUODECIMALS. ^»», Duodecimals are deaominato numbers, the denomina. »•■•« Which iQcreaae according to the scaU of 12; or denom- MVLTITLIOATIOIf OF DnODlOTMALS. 1B7 west. inate fractions, whose denominators are 1, 12, 144, 1728 etc. In practice, duodecimals are applied to the measurement of extension the foot being taken as the unit. ' TABLK. 12 fourths, marked (""), make 1 third, marked 1'" 12 thirds " I second, « I»» 12 seconds " 1 prime, or inch, " V 12 primes, or inches, " I foot, « ft. The marks ♦, ", '", "", are called indices. 251. Duodecimals are added and subtra(-„a in the same manner as compound numbers. MULTIPLICATION OF DUODECIMALS. Ea:. How many square leet in a floor O/i. 7' long and 7/i. 9' wide? OPKKATION, 74/r ANALT8I3.— Beginning at tha right, 7' x A' = «3" =. 5' 3"; writing the 3" one place to the right, we reserve the 6' to be added to the next nroduot Then, 9/<. x »' + 5' ^ 86' = 7/t. V, w^ich we write in the places of feet and primes. ^Jext, mul- tiplying by 1fu, ne have V x 1ft. = 49' _r 4/t. V; writing the I' in the place of primes, we resei ve the 4/t. to be added to the next product. Then, '.^/^ X 7/t. -f- 4ft. = 67ft., which we write in the place >>, «., r »u J . ■ ,„ Adding the partial products, we hare 3' 3" for the prodact required. Hence, the _7>. 6ijt. ufi: r ^ 2' 3" j7 3' 3" 353. Rule. — I. Write the several terms of the multiplier un- der the cornsponding terms of the multiplicand. II. Midtiply each term of the multiplicand hy each term of th* multiplier separately, beginning with the lowest denomination in the multiplicand, and the highest in the multiplier^ and write the first figure of each partial product one place to the right of that of the^ preceding product, under its corresponding denomination, car- rying 1 for every 12. III. Finally, add the several partial products ; thtir sum will be the required answer. EXAMPLES FOR PRAOTIOE. 1. How many square (ieet in a piece Of marble 12/1. 7' long, and i/l. 3' wide ? Ans. 53ft. 5' 9". 2. What i.« the area of a floor, the length of which is dft. 8' ll" and width yt. V ? Ans. Uft. 10' 11" 6'". ' 3. How many square feet in 10 boards, each \m. 10' lone and l/l. 8' wide? Ang, 313^. 10' 8". lij i %v 158 OIVIHIOIf OF DTTODIOTMAU. 6in. hliih? ^' "'"^ ^^^■^'' ^"»' ^de, with a clone fence 7/? of ceiling K/?.^4' ? ^' ^^**-' '^^'h 24/);. .;m., and hii^.h, Ant. $33.66. DIVrsiOxN OF DUODECIMALS. OPKRATION. •V»-9')8A5;3"(2/<.3', H„,, 11' 3'* ' IV 3" g. xaereiore, tbo marble slab waa 2/V. 3' in width ANALTai8.--3A. M contained i,. dfJiior h^'f^, M>?ltiplying the whole diTisor bj y*. pveH 7/^ 6' fo, the produot. which wo subtractfrom he corresponding denominations of the dividend, and obcain 11' for a re- mainder, to which we annex the next Sr,7"'Sr","f f'"' dividend, and nave 11 d> 4/if- " oontained in IT, •J timi's. The divisor beinit multi- 'A of me ,„„,.«.,, and .,„„., tke .ro.^J/rjfZZv^. """ EXAMPLES FOR PRAOTIOJS. 1. Divide 184/if. 3' by 40rt. II' 4" a .^ 2. Divide 4I/i. 8' 7" 6'" bv 1ft 4' a . ; ^-''-o^' 3. A table who6e length M \y V" h.« ^***- .^^''- *' '^"2'" 11" 2'"; what i8 its width? ^ ' »»*« »° *>•«* jf 28«^./^ ;r and wit /U' V^T?' ^'*" ^^'^^ ^'^^^^ *- - ;^^/'"«' ■^'' '2'", 5 A block of raarble contains 64/?. 2' 5". its ^\dth^&^'f'' a Its thickness 3fi. V • what Ih its length ? ' ^ ^^n^-^W 'of °^ 6. What 18 the wdth of a rectar.miiar r.«„^ u , , '•^- ^ ' 9' 6" aiidarea I076,,.i^^^1f//f -Ir^P^^' "'iVli;^^ ^^l?*^^ 7. A stick of Umber is IW. 2' u,;.]. ■>/> ,,, ,/^"f- ^Vf ^ ^ • 135c«/f. i0'2"l"'. Wliatisits fe„;fh? ^^^' ^"'^ <^""tams -4««. 47 feet. MlSOlLLAIfBOUH SXAMPLIM. BHSCELLANEOUS FilXAMl'LES. 159 boigh^forVs^'/ef'''''"^"'^'' Low many yanlH of linen may be f fft'^'flf ^'^'*'"^"'r""^'^' Apothecaries' weija ^'^''• \ l^^^l'^^^ of wino be bou-l.t f,.r £30 2 of each gallon? 4. What is the value of I5curt '■^qr. lOJ, what is the cost , ,. Am. £1 G (]. I It", of tea, at .■i;9")() per cwt. ? „f « ^ ?■■.';'" *""'."« '^""- 2?r. I'Jrt. of porf , , M ?ro,^i 2i;a 3.- '.i^-oTr^.ti ?^^? ' '""^ °^"™''- •'£"|' S>' 19 Wl,„. :- Y- , .i". .. . Arts. boAi)b>r8, was 39427' fliSMtf l^r. 1/6.; ,» 1869, the same nlines yielded 41017'. Sev^tLmi If copper was worth 20 ct.«. per lb., of l,ow much greater y>i\ul^m til amount province,! in 1«69, than IHf;8 ? * ^«„ *fiS-VjS R'-^'lh"''^'.' ?^ « ^-^'^ * «"^t. How m.ich would be gained hyZmm the whole at 4^ cts. a potnid ? Ans.^n.ui, ^0. bought a lot 2o roda long and 20 rods wide for * 10000. mi %M 9^ «'n^f 'i'- P""" '^^"^'•'^ ^'^"^- How much was n,v .ai»? ^b. Sold 72 yds. carpeting at ^\.?,1\ a yd., and gained %\%, ftw much did It cost me per yar,i? ^ aJ.UA^ ^11 f. f^^y'nany square yards in the walls of a room 40 t^ jJwr •il i feet wide and 1 2 feet high ? ^^ 28. How many tons of hay, at $0.76 per cwt., must bsq, ft, ft^ Wide, and 22i/2. high, at 18 cents doors, windows, and base board ? " ' ^Am. $hf7HL ^h AiltV^ '' ^ ^»V^- *^ * P^*°« 30« east of Greenwich |^ iw l^t'rB„s ^- ''^ " ■'"-'°' ^"'- ^••'^-.t^-.L^ .,/t' ^'"/^!'f,V'*t«ofeq"alsi« contain 159.4. 2/J. 17»«. r<<, 2i5*» worth 50 cts. per square foot? At^. $lHm^.n. .ni *i bu.ldmg lots of ground ; the fir.^t contained 4 of I ^«# acre; the second. 402 rods: the tliir,^ i nr«n o«.». „.,.!. u. l^JT fof| 34. l2oz. 35. the second, 40'| rods; the third, i of an acre; and 'the ImfK of an acre. How much land in the four lots? Ant. 3R. UpJr How much beef, at 7rf. per pound, ought I to receive It tllb. Mo ;. Qn/fnr^"^f "* longitude between London and St. &, Mo., .9 90- 20' 5 at a certain time each day it is as mucfaS noon in London as it lacks of noon in St. Louis. What is th" SZ .nSt.Loui8? 4ns. HA. 59mtn. 20*eo. A, i db. hixpress in acres and the decimal of an acre the area of dS square ots, each measuring 5rd. S/l. Sin. on a side. ^ '^ *» ST. On an acre of ground there were erected 21 buildings occuo*W on an average Ssq. rd. U28q. ft. ^sq. in. How much of *U mK remained unoccupied ? Aa^. ^fiper. 9l8a ft Uaa^ 38. Reduce ^ of i of 45^/6. to the dec-,oaUf a short"ton. ^' ^' dy. A person lived in Montreal until he was I8yr. 8mo. tida,m loronto, 4 as long; in Kingston, % as long as in Toronto, and 4a*l QW -^ao^ -.3 „^)..„j^ j- • , j 1.^*'^ . m in «4ii 40. A farmer owning 19^4. 3//. 38s^. rd. of land,' divided i equally among his four sons. How much did each eon recejyj how mucl! ha.d the father remaining ? ' Am. 364. 2/i. :59|sj. rd. '-ach, and 484. 3ii. Z^8q. rd. x^xnuaing, 41. A steamer, going uom Halifax to Liverpool, t ra versed ll«l degrees of longrtude d«ly. What length of Ume was it froru om mm to tM Mzt 7 Am. 23*. 1«M^ II180EL1.ANJEOU6 IXAMPLB8. 161 I': r„^tTavni!!''fi'l?'.; *°" ''''''' ** 20 cents per pound ? «icu fi cost him per -lord ? '' '-^*--^- iSi^t^Sko^;;:;.!;;^;^s^'^^^^^^^-^-«-'^-■-'^^ «fi ]?«,w'"^"*'" ■^'"'^'''* ^"': '""''^^'^ °"'' a"d 54.1 1| ra/. remained ,jLgs;c zr. taC.%rs''f, "^ t'%4"«"' «-■ -- $5.:^ 2, fa yard? ' '^^^""^^'^ ^*^« value of the remainder at 47. Ifagallonofdistilled water weigh 8^6. 5oz, 6.74dr what "is the weight of 17fi.a/.,39M;,M<,/.? 4n». 14^ 5or'l.r9rfr meturinVle/rS'' ?" ''''' "'^^ "'" '^ ^'^ °^^^ ^^ ^1^13^^' 24o!' i^nr^n" ''^l** i" ;^ortli Uoz., and allows the baker I^ cts. a loaf for his labor, what Bhoula pro7t'taraff^^^'^''-'''-P^^'^"^'^^'' ^^^«-^ ^J ^^« -- «;fi;;o. "[-'""s 7'' '^ T^ ''• ^^'■P^'' '^ ''^•^'" 2iyj!. long, 15/?. wide, 61. What 18 the value of a pile of wood that is lOrd. lon^ 4fi. wide and 1 iyd. high, at $5.75 per cord ? ^n«. $13.3.42 - >IJ "-''t^:^"'''^ /«"ce ..i/i. high. How much will it cJst to paint the fence on both sides at 12 ct... per .q. yd. ? Ana. $93,862 o3 A merchant purchased in Manchester 34 bales of cloth for t-« ly f> per bale ; he dieposed of the clnih at Porto-Rico for 212c«* .^»ga'; at £1 5 per cwt. Did he lose or gain ? and how much ? ; 04. If a person spends in 6 month, what he earns in 4i months : now n,a„v dollars can he lay by in a year, supposing he earns $325 m2i months? "^"^ ° Ana $390 00 A man has a piece of land 201 J rods long and 411 rods wide, which he wishes to lay out into square lots of the greatest possibte ■^ize.^ How many lotp will there be ? .Itw 396 56. If a man can pay his creditors only 48 o«nt8 on a dollar, how ranch can he pay on a debt of $52.50 ? ' 67. How many bricks, ::!tii. long, 4tn. wide, and 2itn. tWck, are required to build the front ofa house whose wall is 3ok long, 24/t high, and 2JI. thick, allowing the doors and windows to occupy i the ^,'^''^*}..^7USgat.2it. of melMnet. at 20 eta. ami., 'm^'fm ou ?«?. 01 It, now uiuHt I m>U tiu wmamder per gal.. wT&a'to reoeirt X'ul ?' "lot '?f* * , ^"-- «0.263+. ,AA A \ . .7 ^^^ ^""°^ °f ™"™ f**"" «75. how much water must be tdrted to It that I may seU it at 60 centa per gallon, and gain $15 in taesaieolit! Am. &Q gai. ■:l F 162 MISOBLLANBOTO EXAMPLKtS 60, Sold 1 25 equal loads of wood, measuring 115Crf. 3cd.Ji. leu. ft. for V 492.50. What is the quantitj per load, and price per eord ? „, „ ^»s. 1 la^cu./t. each load, $4.26'i per cord, bl. How many francs must a merchant in Paris send lo Montreal m payment lur u doht of $15y8t).862 ? (>-i. If a man fill J of a cask with brandy, J with wine, and i with \yaitr. and if it lack 21^ gallons of being full, how manv gallons will tlwt citsk contain? Ans. lOOgcU. b.S, U oy Pellmg cloth at lOs. 6rf., ^ of the price is gain, what part 01 the co.st would be gained by selling it at 138. ? 64. A ship's chronometer, set at Greenwich, points to 6A. 45wn'rt. Msfc. P. M., when the sun is on the meridian. What is the ship's lori^itude? An8.86"2VE. ho. A grocer bought 15 barrels of salt, of 4 bushels each, at ^U a barrel, and retailed it at i of a cent a pint. How much wa^ his whole S*'"/ , . Ans. $4.60. Of). James own8 Aj of a field, and Leo the remainder; | of the difference betweeo their shares is !SA. 3R. l^l^per. What is Leo's ^^'%^\ ,, , . ■ Ans. 20A. .'.R. dlper. t>/. A gentleman desirous of giving Is. 6d. apiece to some needy boys, found that he hi^d not money enough in,hia pocket by od. ; he therefore gave them is. 4d., and had 9rf. left. Required the number of bojrs. jj J^J^g 7 68. A liquor agent has 50 gallons of wine of superior qnalitv, worth ?7..jO a gallon ; he wishes to reduce its quality by the addition of water so that he may sell it at $6.25 a gallon. How much water must he add ? j^^s. 2ligal. 69. A clothier has 960 soldiers' coats to make, each coai contain- ing 2\yd. of cloth ]li/d. wide, and lined with drilling lyd. wide. How many yards of lining will be required ? 70. A ship captain, sailing from London to Portland, found, on taking an observation, that the sun at noon was 3h. 25min. 40«ec. arieniiaii the London time, as shown by his chronometer. How many degrees west had he sailed ? 71. My father's garden is 10 J rods long, and Sf rods wide, and sur- rounded by a fence 7§ feet high ; he has laid out a walk around it, within the fence, 7^ feet wide on the two sides, and 5^ feet wide on the ends. How much remains for cultivation ? Ans. 21296*0. /^ 72. A bi)y having been sent > a store with 5^ doz. of eggs, was directed to purchase with them equal quatitities of sugar, coffee butter and tea; he disposed of his eggs at the rate of 2 for 6 cents, and paid forthe articles purchased 17, 28, 37^ and 1374 cents per pound, respectively. What amount ol each did he purchase T V eord ? per cord. 10 Montreal and \ with L^alions will f. lOO^a^. I, wbat part 6A. Aomin. I the ship'p I" 21' E. 5h, at$l| a IS his whole 19. $4.60. ; i of the at is Leo's orne needy by oof. ; lie be number Ans. 7. ility, worth addition of luch water u coiitaiD- ivide. How found, on in. 40sec. ter. How iy and 8ur- iround it, ■ide on the 6sq.ft. sggs, was IT, coffee, 6 cents, cents per BATIO. RATIO. IM 254. Ratio is that relation between two numbers or quan- tities, wliich is expressed by the quotient arisin. .^inoo in a proportion, the ratio of the first tothesccon(! term is equal to the ratio of the third to the fourth term, the pro- portion, 6 : 3 : : 8 : 4, becomes f = |, multiplying eacb member by 3 and 4, we have 6x4 = 8x3. Hence, In every proportion, the product of the means is equal to the product of th^ exirerues, 270. From the foregoing principles and illustrations, it fol- lows that, any three terras of a proportion being given, the fourth may readily be found by the following 271. RiTLE. — I. Divide the product of the extremes by one of the me. ins, and the quotient will be the other mean. Or^ II. Divide (he product of the means hy one of the extremes^ and the quotient will be the other extreme. NoT«.— \V« will denote tke required term of a proportion by the letter «. EXAMPLES FOR PRACTICE. Find the value of a? in the proportion. 9 : 16 :: 36 : a,'; a? = 16 X 36 = 64, .In*. 1. 2. 3. 24 7 16 What is the value ui x in each of the following proportions; 4. 42 96 42 X 70 14 ; X 10 : 3 . xl 96? 40? x1 Ans. 56. Ans. 16. Ans. 64. X : 15 ^ 3:9? Ana. 5. 6. .17^ $10 :: 366a. -.xbu.'f 7. 2yd. : 8yd. :: $34 . x'} 8. 7.50 : 18 :: xoz. : 7^o«. 7 8IMPLK PROPORTION. SIMPLE PROPORTION. 165 Jlll^Xtl/Z.l''''' '' " ^q-lityof t.o.i.nple ratio-, the^Le'rafJ? "^"^' ^^ '^''^ ""''' *^^' ^^^^ ^'^^ ^2 yards co«t »t yd. 13 $ OPEIIATIOW. yd- I : 42 :: 30 : ___42 60 j20^ 12) mo * = $105, Am. Eldcidation.-To arrange the g.vennumberBin 1 V *on°.u FoP'>''t'on. or "<"<« tht. qwMion, we miiKe iSdO the i-A.rci term, beeause it is of the same kind as the required /owiA term; and, as from the nature of the question the latter raustbe great- er than the third term, we make the greater of the other two numbers the leeond term, and the less tney»r»«; and then, the product of the me» -3 di- ▼ided by the rlren extreme, givws the ^ .oina THB GAME EXAMPLE BV ANALYSIS. Yi^^/t ?f i^®'-n y*^^7'" cost ^j of $30 = $2.50; then, if Ivi 8t^$2..0, 42j.d. will cost 42 times $2.60 = $106, the answer, a. oost before Aa^f'v}' f-^^so'/ljeM consume a certain quantity of flour ia 28 days, how long will it take 70 soldiers to consume it ? OPERATION. tSolJien. Soldien. dayi. 49 ;: 28 70 days. 7 14 5 = 19|, ^IM. Elo«idatiok.— SiDoe the reqaired answer t days, we make the (ivan dajs the -'i term. Then, as the flour wiU nut last 70 soldiera lo lone »« It wiU 4a soldiers, we make 49 mU diers, the snalUr of the two termi, the Hi>cund term, and 70 soldiere the firtt term j and proceed aa in the firei ezaiuuie, ezoept that we ahertea tiH> work by eaneeUatioa. THB SAIIB EXAMPLB IT ANALTSIg. times 28 dai/ TATf ^^" '^f" \^^ ^""^'^ '^ ^"1 "^^^ 1 «-'^ier4. IdU days, 70 soldiers will con.sume it in ^^ of 1872 davH = 19^ day* 27». KuLE.— I. Writ§ the givm numben^ that u •/ th§ imm name or kind a$ the required fourth Urm, or anmer, /^r OU third if.rtrk nf thm 9i#>/».ui ../.'«•. "^ II. Of the other two numbers, write the larger for the eeesnd term and the less for the first, when the answer shmdd exceed ih4 third term; but write the lets for the tecond term, and th* larg» for the JU'tt, whm the amwrnr ehomld be hu than the third tmm. \% s t i f! I .1 ( * 166 WMPLE PROPORTION. III. Multiply the strond and third tenna togethm-, and divitU *Jieir product by the first; or divide the third term by the ratio «»/" ihr first term to the second. N0TK8.— 1. When the first and s.-oond tefus are of diffornnt denfjiainatioE,? they must bo reduced to the same denomination; and when the thir ; terra n % co!i)|miin 1 number, it must be roduced to the Soweat donouiinat^om mei^tiooed io '^'o "u '*"''*'.®'' ^'" ^^. of the same denomimition oa the thinJ term. 2. I'ho pupil should 'perform these questions bf analysis, 3 4 well ae by p»»- portion, and introduce oanoellatioa when it will i tbreviate iiid wvjration. EXAMPLES FOR PRAOTIOE. 1. Six laborers earn $7.68; l.ow much wiiJ 10 laborers tHrn? 3« 'a'^^rer^? Ana.%\2M; $46.08 2. Il2.ilyd. of c!'^;!i cost £25 3 3; how much will 198vil coi't? 12t)yd.? 137y.l.? 3. One-half a bu ..«». £11% 15 ^%^ £139 4 3fJ; £1517 4J|. -"hvii ai «> H coats ^i,S\ eta. ; how much will 16 buphelscost? U buflheic.- T:^, hiuIjplsY 86^ bushels? 90| bushels? 105^ bushels? Am. $14.56; $30.94; $65.62; eu;. 4. TiGlb. of butif-r C6t,v ^^iS.lJb ; how many lb. can be had for 112.61? .125.74? 8o2.b7? -$36.40? An$. 971b.; 1981b. 0. "* 7^cwt. , wu.u. ^ e*c. what is the value of I il a c\v . If a cwt. of tobacco is worth $39.25 : wt. ? 561b. ? 931b. 4oz. V 107|lb. ? Ans. $0.3925 ; $294.37^; etc. 6. The I of a cwt. ofen.a;r,r cost?6.48 ; what will be the cost of *ci :\vt. ? f cwt. '■! ^ cwt. ? ^ cwt. ? An.$. $6.72 ; $7.20 ; etc. -f 7. If 40^ arpenti? of land are worth $215.50 ; what is the value of }} arpents V 70 nerchM ? 90 toises ? 25^ arpeuts ? 10 per. 4 to. 10 ft. ? liOi arpents ? Ana. $31.92^^ ; $3.72|J ; $a,53U ; etc. 8. The 1*^ of an acre produce 18. cwt. 1 qr. 12 i)L of hay ; what quanuiy will 1 Mr« produce ? 8^ acres ? 36^ pert 9. At Is. 8d. per lb., what quantity of coffee can be had for £3 68. ? ^^ }^,^^^H.^ 2i? £14 lOJ? Ans. 39|lb. ; in/^lb.; etc. 16 tons? 3| tons? 18| tons? Ans. $107.45 A ; $24.67 + ; etc. 12. If3|lb. of coflee cost 72 cts., how much must be paid for 74ilb. ? 96ilb. ? 10911b. ? 2lcwt. ? Am. $14.62 f- ; $18.90 ; etc 13. Six cwt. Iqr. lib. of beef cost £13 7 6, what quantitr can be had tor£8 12 3?£1 8?£17 12 6? 14. For 171 days' work, $26.44 were paid ; how much will be paid tor 1 day's ? 45^ days' ? 89^ days' ? Ah$. $1 .44 : $65.52 ; etcT 16. The rent of a farm containing 12A. 2R. .30per.is$ : 13.75 ; what is the rent of another containing 5A. IR.? 16JA. ? 59A. 2R. 20per ■ 10|A. ? An». $47.06i + » $145.24 1 fi. Savon KtiaKAlfi ^^'«n<«A -*^«* ©O *TC: . 1- -v-— 1- *ii 10 «.«,w.. ,,,..,-,-,,,, .!i Tl\ra wcsts;c7. ju j UuW UiUt/U Will I in cost? 18^ bushels? 26J bush etc. 17. In paying $11| for M28 . v of bowda. irkat quantit badfor$119j^? $230.60 : %iU,m Ans. lU54( + ft >^ '-•W. 18. I can get 336 pens for 3«. id. ; how maajr o«d I get Ir^ S.I t 44T£3 10 14? £0 1 1«4? 2944: srMFLIC PEOPOBTIOM. |f^ ^anuxi had l.e worked 6 dayt more ? ^' ' *'"'' much would he have h«i /i -^ P"*«''^« cost as ,„uch a7 7 Hnnl« ^ ^"*- ^^82. be had for H5 peaches? 280 S^^^^^ how „.any applet e.n ti« creditors to pay ^O.e/on the douL K "P^^' r'"Pr-n»i«ed with on a debt of $256;^.50 ? "*'^' ^^''^ """c^ ^i" one receive 26. What will be the orice of 21 A tn on ,^"'- ^1640.64. cost £815 ? P"°® ^* ^^^- 3». 20per. of land, if 36A. 3R. 27. If lOcwt. 2ar Ulh r.e ■^"*- ^187 10 pay for 8cwt. Inr.^U lb ?' '^^'"^*' °^"* ^^04, how much should w. come M P^-S'"""" «, 40 „.,. ti, k„„j,^_ ,^„ ^„ _,^_^^^_^ <»il each creditor rwei.e ? i^ B t« I P?"^/,'^ '■'^^'*»'' = '^^ ""■"l' 33. If a bowl containing 2 cul.io v,i io .• ^ • "*"*• -^^ ^^ 3. / niany hours will b- reaum^d t?. «. ^ " ^""^^'^ '" ^^ miautM; how and 21v,i. deep ? ^"""^ '^ ^'•"P'^ * °'«tern 4yd. long, 3yd. 'wideT 34. One of two pieces of cloth costs &^-i^ ^u .u '^^'- ^ **°"''«- the ,e„,.b „,eact^„o,i„, rtr:S^?f,t^t^»J^-*„^^^^^ ,^ ■• WM„ .t.„,„eo4 «*'.^s.Tk„o.■„g.bat''.re*/;l. . 38. If the raooa mov-a H" in» ^irm • ^ '*"*• ^^0 ^8 6f itp'.rforra its revoIuT.on"? " ^^ "» ^P^ ^*^' '« "hat time will 4L''"T'''' ^'^p'- - condition ir; ?lt 'd-*' ' "i" "".A iif^' ^'**' '"any ehall I receiva?" ' -aou.d receive o per 40. What is the value of 7 b Tin. .<• >'^'- ^«*. 6247. worth $120 T "*• ^^^■- o^goH knowing that 7oz. are 41. The I of a bushel of prune, ao-t fill k * ^»*- «i«28.67f. b« bought for lA ' ^' * P*'* ^'^ • bMheloao m Ji te I IM COMPOUND PROPORTION. !l *^' i,^r**J^'"^ merchandifie for the mm of «5600, Iloat f4.60 ob every $100 ; how mucli did I disburse? »».o^ o« 4H. A pound uf cin.ianu.ii co.st. $1.10; for how much Hhould 1 re- tail It to gam at the rate of $-.0 on every $1000 ? Ant. $1.15A 44. Who,, metallic pens are (V^ cts. a doBen, how much will 101 gross cost? 16J gros.Y 25J gros8? Ans. $H 061 ; etc ^ 4o. When profitH are :j;5U on every 100 yards of cloth, how many yardH jnust be sold to raise a profit of $850 ? Am. 1700yd. 48. Two pieces of cloth are respectively 41 and 36 yards • the first piece costs $46 more than the second ; required the price of each. AQ wi. u . • .J » 4««. let. $369; 2nd. $324. 49. When wheat is sold at Ts. 6d. the bushel, a loaf of bread weighs 9 ounees; what should be the weight if wheat i<, but 6s. the bUBUel J 4njj I 1 1 50. Every soldier in a regiment of 1000 men is to have' a Jatch- wat;eachcoatw.ll take 4yd. of cloth which is 1 5yd. wide, and is be l.ned with flannel, 14yd. wide; how many ya'L of fla. nel wiU V. required to hne the whole ? Ans. 6625yd 61. Jo draw success on my business, I propose to give $5 to thf poor every time I gain $150; how much willYhave gained when Z al.^ amount to §100? ^ A^s. IsX'^ 62. John can plough a certain field in 6 days, and Maurice in 6 days: what time will both take, working together, to plough the 63. A father earns 68. 6d. per day, his son, Ss. T^d ; in whaUimc vnH^they have economised £1 iO 3, if they exjend but 58. ^J 5^*.?"'^'>""*'?,T.^^ ' 5*y ^''' P*^'"g * y*^ ''^•ch i8"'60^5ft*ng and 44ft. wide, if 14258q. ft. cost 5>;!41 ? ^ 65. Two gangs composed of 20 and 30 men respectively, did 1600 vards of a certain work in 25 days ; how much would the/have done had their number been aug nented by 15 ? Ans. 1960 yards. 66. One hundred degreer. of Centigrade are equivalent to 80 degrees 3f Reaumur; to how many degrees of Reaumur will 232 degrees of Centigrade equal 7 ^^. ig^o ^f Laumur. COMPOUND PROPORTION. »74. Compound Proportion h an expression of eqwtlitr oetween a compound and a simple ratio, or between two compound 8 : 4 I ■ * ^* • 6, li » eompound proportion. Tfc*t «, 12)>C8 : 6X4 1 : 24 : 6 ; for, 12 X 8 X 8 =« 6x4x14 OOMPOUND FBOPO»TIO» >st f 4.60 OB 'Ijoiild I re- t. $1.15^. h will 10\ 06i; etc. how manv . 1700yd. nng2|cwt., he smaller a ; the first of each, id. $324. if of bread but 68. the 9. IlioZ. ; a watch- :JOJ ccatetn "^ d- v ^ L mU I* required to make 200 in 27 .lays? ^ ^" i"''^ "!f"^ Jl- »"""^ '?.'''■■'"' •"' 8 hr. each' M laborers were^m'S „ h a fftbe carriage of 5cwt. 3qr. a distance of if i'J^ ''LZs^"^i%H J^./« a fort there are provisions enough for 152r8oldierf for* 6 mmth,. If the garrison be augmented bv 1 00 men, whaVdS ration >wedthflm. ifthevr. uHin i i^ o' ''"«**"'"'/ ranon «*« »* allowed thflm, if they n uain ' , .uc longer ? l<» 1* f3 1 • • '/ / " "«"! ■„ .uc. longer r ikliLi r ^!* ^'^"^ ^^^ ^ ^'^''^^'> weighing 7ioz., when vV, at i^ 4s 2d Sffe^^'i what should a Is. 2d. foafUjh ;hen wheat iest 6d ««•, Kr»6wing that 1500 give $lo interest in H r |«M *»w/f»kJ r plac- at interest to give me $200 in TS * work 86 7 mer hd in 28 day.s, or 10 hr. - ^»iv l6J§«oz. iths, hat'princi- ar l.$2500. ' n work, to do h? ..iw. oda. was Woven with , . .•',-• ""■'-' s "' « yaiii wiuc , was Woven witl f4^,^SrL^;u!.i'lJ7^«^^«f^P'«««i-f«* yard wide: -4fM. .HS^y yards. 171 MROINTAOK. PKRCENTAGB. signify 6 oer>ts of eVerv 100 "'f^'^^o^evcry hundred. a„d may ^^ every 100 cents, 6 dollars of every 100 dollars, ooS.'^'''®*'®''*^'"""'^''- ''" ""^^^'^ '^' Pe'-eentage ig the pI,Z:,^. "" -'"'"""' - "" P'r«ntage, I iU Oifferenc + ■ijrmDoit. Decimals. ^% 1% 4fc 5% 6fc Hfo 10% l^% 75% \QOfc \2b% ^ h7c 1% % of a fm„iber Common fraotions. \7o « « « « « « « <( << <. « « « « .01 .02 .04 .05 .06 .08 .10 .18 .75 " 1.00 " 1.25 " 005 « of it « u it « « « « « « << « « « « t5^ TffO « .0075 " " „ .076 « " = Tffcr TffCf T^f /a 2 t 1 i 1^ «-^^l. Cask T. — Given, the ha.se and raff //» «*>^«i. t.x. What 18 6% of 512 yards of cloth? ■JPEKATIOK. ^-'' *> = 4' Th.«for., 6^ of 512jd. 96 ,ft,'?™T^% =.06. Therefore. 6« «f 61 2yd. li. 08 of 5 12 « 30.72yd. ^ Or ^ J«-^2yd.^«. i.^o/!,^4 ' 3«.7Jyd. 3fe:J«^Sfota, ITl 0», 100% = 612ytl. 1% = 6.12y.l. 6% = 30.72j't^Ll'?-^-, ^^3.^Whati«32^ or.n60.60? 4*^. of 4M^^oP34t?n|Tof ^^4^Whati« 20/. ofOOcwt.? i% off«50? i /Tf " S'sfb jt of 5. What i« 15% of^? 1% of.*80? 2^^^:^'? -rii ^Jfaj, ^g? much did he spend for each ? 6 7»; '^ r sugar, now « A u***; f'"" f* «S92.05; T. $986.75; C. |I776.ir,. etc ml* ^rTi^n*"* v*""^'!' ^^•'^ ^*"«''' o^ '"<'l«««e« for $7125 ; ^adlold for^wia iJcS 'nr'' '?*.f f ' * i'*^'^''- *"d *he remainder tor what It cost. How much did he gam ? An». $1567.60. 2^3. Oasb ll.—aiven, the hate and percentage, to find the rate %. Bx. What per ceot of $450 w 27 ? OPKRATIOK. 100 27 460 ) 2700 ( 6^. An$. 000 Of, A ^ 100^ = 65iJ,4fM. Or, $450 = 10051^ 1= 1% $ 27 = 6^, Aft«. Ahalt«m.-|450 101005^ of itself. $27 i« ^/ij of $450; therefore, $27 is ^2 7 of 100 <^ •r^of27 times IOO5K = 6j'of$450. Jtk^oflOOjij = (J5tof$460. Or, $450 is 100^ of itjelf; therefore, $1 ii ihi^'^'^^H = 1%. "Hi$i27 i» 27 timw 1^ = 65^ of $460. Ueiicethe ' " ^Zy ■^'—'^'^'^'F'y ^"":» «y the percealage and divide by P*^d that part 0/ 100 jper unt. which the percentage . o/th* % 1 % = ik,t eued deei- )0. 15? 75 of i2; etc. lib.? 11% .6; etc. ? 6J,'« of 192, etc. (? 9*% of t5; etc. E20 16 8? B8 to with- for tea; w. How ry; etc. ; and sold 'emainder 567.60. Jind the self. $27 ii , of 100^, , of $450. tharefon, Bfore, $1 if 27 timM livide by tofih* PMUMINTMn. BXAMPLBU FOR PBAOTIOl. ITS 1. At what rate i)er cent. miuhI we place $20 to have f 2 ? |5 to have*0.2y? *1440 to have $2l.G0 .' xlHO 5 to have £12 16 4^? |4to liMve$0.30? Arts. 10^; f,^; etc. 2. Wliat. per cent, of 40 in 15? ut 180 perches in ;Miicr. ? of \^\ ifl "A? ofi IS i? ofy2gal. iH llgal. 2^it.? Ans. 'M^^: ^%; etc. 3. What fK>rc«nt. of 148 i8 24'!? of 30lb. Avoirdupois is Ulb. 4oi.? of 720lb. ie 601b.? of G20jd. in 46iyd. ? of 1401b. is 771b. ? An$. \(yi%; 37^^; etc. 4. What per cent of $578 iu $26.01? of $250 is $H0 ? of I is A? of£.H 15 is.'l^. 9d.? Afif. 4i%; *-ic. 6. Whiit per cent, of $3(iO will give 25% of $72? Ans. ^%. 6. Bought a horse for $840, and wold him lor $560; how much did I Ioa« per ceiit. ? Ans. 'i:\\%. 7. A number increaHed hy 2 equals 14; required the iucreaee per cent. J885. Case III. — Givm, the rate per cent, and percentage, to Jind the hate. Ex. I lof?t $27, which is 6% of the money I had ; how much had I at HrHt ? OPERATION. $27 4- .06 = $^'.0, Ana. Or, $27 -^- A = i*60 An». Or, &% - $ 27. 100% = $460i Afm Analysis.— If 6%, or .06 «f lome number \a $27, that numbar Bust b« $27 -^ .06, or ^, -: $460. Or, 6% of some number ia $27, 1% of it ii J of $27 = |, and 1 tin^, or the whole number, is lOU timet^ 'i » $460. Henoe the 3S0. llULE. — Divide the percent 1% is 12^ much ? 16i is 2^% of how much ? -, etc. Ans. $22.50; etc. 5. Jfthe perceiitage be $.^7.50, ind the rate 2.^%: what is the Ana. $\ 500. annually $145.60, which was 33|%of hie aaoual base? 6. A fkrmer saved ; required hi« ia«om« ? ^ i I iij I i,. 174 pmMmr7A«Hi. 3«7. Case W.—Oivm, the rate per cent, ««wi 10. A shepherd lost, by disease \2% of his flock : how luawy .J,*^ oomposed his pr.n.tive flock, knowing that there rlrnZ TSif^ 1. A clerk sp-nds 20^ of6Gj% ...ore than i of bis incouW-^l-A ic his income, iflie saves $533? '"^vw*», W'MM 12. A gentleman sold two horses at $120 each ; for one Uft^^sA 2b% more, and for the other 25* less tha,. hi« v«l..» • Ji I :^/?^^ 13. A man wishing tr. sell a horse, asked 25i;^r;';ilnr!S! he finally so d It for 15^ less than his asking price,Tnd gSu*d f?£^ H«m much did the horse cost him, .ad wba! iras his m£w «£f Am. cont, $120 ; wkiiii prt5 !iS; 175 omiifftt #f MISCELLANEOUS EXAMPLES IN PERCENTAGE. An :.s\ ] !. 7! jl. J-^;»'^Jf ;'<"70cut. Iqr. im. 2. *lg IS 1% „f what nnm^T? .„, 3.,on 3. P.nd H munler which, .!Hr,ini-he,l bv \i^% of itself ^ive. iJS" nianyremaln? ' ^"''^'' remainder by sickness; how 6. I 8oJd cloth at :£! in q « . j i- , . •^'»«. 819 men. how mucl, did i, "i!. ^L , ^ ' "'"'"' " ''"' "i* "f ""• <=»»' i -hat LZ ;aS."t '"' "'''°'" ■' '■'*«"- "- hi "weetlv ™1 +; baL4'r'hS:tsct:^3fd fo-ii,"^'"' ' """ '^- «^i=o '"''■ tui:\e Jj. Waatp.. cent, of a „,„„b„ ,ive. 3.J« „f ,,e |*„T,f,lt.. did tbe cargo TOtbim? '"°'' """ "' " '»« "f-'-^i li«' •"»ol, H. There remains 2^,' vd fl »; >. *• ■• "*"'''• •^J827..'50. or iy „„a, .™, 0. liX"',,:^';: ,°' ""™' """t;'?i'tV''* ».«; ^.t^M^S or bf ';„,:S'!"" ,'--. .<;.."« tLe'Veattas habitants ? ** population j what is the number of its in- 16. A fi8h.n,onger had 720bbl. offish, and sold 2Sftlf ^ ^T^"^' cent, remamed unsold? ' ^«Hbbl. ; what per {s* Gav- J'^'p'^ ^'^^ «^h"- "'-"V lb. ? .,„, ifSt s'?' lo. viave to aBenovo enf R,,f.;rf,. 901 i i. . I'THI), boz. of my entire crop ■^Z^^^^T^f''^'^^ "'^J'^'' ^^^ I'45^ 19. What per^cent. of ^0"^ o 1 jve^ ? '"'"'"'"^ ^ '}'''' ^^' 20. Joseph having received^aiiiv V • ,- Ano.'lh%. A short tinfe after, hl^^l^lJfSTl"^ 'V^^ "']' '" ^^^°k' remained £1280 17 6- wLt wiV S. o^'^,''^''' ''"'^ ^''"e still 'ji r . . ' wudi was the Giracv ? Ai^i +'9ij'i ik on ?o«fo, oLrirr„r4 L^eur.', rs ■ ,^ ,;''^- ."■ •- -*>* -i^ battle, and 6* 5?S" eLfder di^'n'ni; ^'''' ''^^f. ^" ^''^' ''^^'^ of ' The ditfer«a*betweeri?numbe^onlrH ^^"t^ ''^^ ^'"'^P'^^'^' wounded WM 164, fcow«»lv Z« . ^^!?'^ ""'^ ^'^^ "»"'l«"- ^fth*. «i io» J MOW muv BMB compofltd th* army ? ,*«,. 22d00. 17< PEBetJHTAat. Lef>' r ^r, ce :* Va^ T^^'^^l *^« ^itj. whieh distance i, 9A %o( ^^. Th. taies orr, rca'm&ah 1!''''"^ ^'^''' the co,ui,at ? yearly; tiieVonhe^"^"'*'^'''^^"^^"' *'«^""t to $i^ the value of ih.Clorj ? ' " '''' '*'"' '*''' i«' '^^^^'J" 5 '^i-at i. 30 Mv ..Jn.. .<• . : . .""'^" *'^^ Pa»' more than Leo? jear/aSfZe/aJS 8'^^'" '»^*° 'hVt of last increase at the rate of 271^? " "> oe in 1879, euppoamg it to nnt ^^' V ^«'»" of a nursery in two years wb £2?1% ''f ^'^^• of the second year were 6* ffr«.«f^r *hu« fi! ^/^ *2178 ; the gams ^re thegaia« ofeach year?^ *^^ ^*'** '^"^ y^*-^' *hat i4n« -twiner s % «n :; — o— «••■» wi ratjii year i I4 4j^,2iid.yr. t 2L% then, 349( of q^i T I J 1,X^^' gwnsof ide let. year; £1120 1 much remaios i„ the bank?^ ^'^ °^^^** ' '^1 tro'^'o^"^ what per cen? of hi' rlrenuf ,?;afh'ar"t!^t/' *'! ' 1""J"««. W6 ; remains? T«? 9I 3!^ oroS®' ^""^ "^''^^ P*' cent. 35. Ifanomberbeaugmentedtfli/Jf il/*'^^^^^ ^^*^- whirrs "KS^'V^'^-^^r •" ^»»^ PU'«haL'%oe, the whiHkJy ; but he lost Ji^' ^'^ ^^^J^ «» the -ine *i»d 5% on entire sal JifiS 10 ^hoi1?Jh\^\^*'''.*'' '^««'^«^ *'«>'"»'•« ehaodiaer ' ""**'^ •^'** ^e pay for each sort of mer- Maurice? ^'*^'''^*^«*^?«*her $22320, how much has wiiL\taStf"^5?0o"TtTr 'f ?rn^ ^° ^''^ Ist.'trFtw, er as fuUom Feb Si' .t l v"*^ ^^ '? "^""'h«' I read in his Ledgl S,,,;, 1 ^ ' ^ - '^^ S'"" ' *^"'V' J 3* loft« : A n«ua« .lo< „„:.« ! — ^.- ...J . «»^ain, jNov. 4^% gain; what were the net monthe ? !-■ - /w .^jo, v^cL. ^ijt iruiii: J^ profile o( hi* businesa during the :li nVPLI IJfTlRlBT. SIMPLE INTEREST. in .u*i*'?" 'i**6f®St J8 tbc compensation mado bv the hor«— , t. the lender for the use of money ^ Dorrower to 22?" J''^ P^inciral is the sum lent. of 8100 Jl^4 ^/® per. cent, is the interest paid for the loan %yTyJ '^ ''"' '"""" "^^ *'"^« -hateverfwhioh is ordr No«._The rate par -at. i. ootnmon.y a,pr„,ed d,oia.ally « hundredth.. §22" I^^ Amount is the sum of the principal and interest 2»3. Simple Interest is the sum paid for th« „J T!? principal only, durin,. the tin.e of the lof.' ' "** ^^ '^' It T^nf;,- f ff^ Interest is the rate per cent, established by law It varies m different countries. ^ ^' ?oX-^''2t:^r,lfZZS^^^^^^ ^e ,aws of tl. intended by the partie*. ^ ' "'"'^y* "nd«*"tood to be the one a»5. Usury is a higher rate % than ie allowed by law N0T.._The law prohibit, u.ury and uiake. it subject to a penalty. 296. '^<>Md the interest on any sum, at an, rate %, for any number of years and numiks. " Ex. What is the interest of $780. for 5 v(^'a.t» am< a .l .,. years), at 7515? What is the amount ? ^ •°*^ ^ ™'*°***'' (^* OPKKATION. $780 Prin. .07 Rate. 154.60 Int. lyr. 5i 1273.00 " 5yr. 13.66 <' 3rao. $ 286.65, ,^.. 780.00 Prin. added. >Hyr. ANAtTsrg.-The intereet of ,j,l for I yea- at — :*o^.'jO. If the interont Of $780 for I year Or, jj,j of the principal « the interoat for 1 year at 7^, The amount u found by adding the principal and intermt together. $1006.65, Amount. 397. Rule —I. Multiply the principal by the rate % »• pressed decimally, and the product will give the interttt for <>m^ year, ^ ^** II. Multiply this product by the number o/ year$, and the month* as a fraction <}J a year, for the interegt required The amount {» found by adding the principal and interett to- gether. NoM.-When part of the time for interest >■ giren ia aeBtha er d^n .»onth u eonrider.4 « ^ of a year, aad one day*a. ^ of TmouA ^' "^ 6* t I' 1ft SIlfPLl INTBU0T. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 16. 16. 17. 18. 19. 20. 21. 22. 23. 24. BXAMPLE8 FOB PRAOTIOl. What ie the interest of * lb tor 7 years, at ,9^ •/ J656 for 2 years, at 7^ ? SlUO for 3 years, at 8^% ? M7 I'J Z'"'.* y^ar« 6 months at 856? $76^50 for 2 years 2 months at 5?? |444.44 for ..years, at 6f5«? I2^2i fl/*"/ * r**'' 2 months, at 75^? fIfe7I.32for 14 months, at ()56? What i!^ tlie amount of 181.81 for 8 year« 4 months, at 6%'f $894 for 20 months, at 65U(U for every Sll>1^. Rule. —I. To find the rate —Galle.jpt^ uo.,^ « nc «atrht iimftMT, 17f IL To find the interest :-^„,,y, the pnndpan, eke rate. 27 dryeV "^^'^ '' ^^^ •"^'^«' ^^*«fiO, at 6%, for 3 years 7 months OPERATION. Tnt. offl forSyr. " 7 mo. *' 27 days. " 3yr. 7mo. 27da. = $0,219^ Principal, $660 « « 14 « «< (i = $0.18 = 0.0.S5 = 0.004^ Analtsw,— The intoiwt _?*?;»?.l•;!r.^:..^|■«^'¥J■ ■■- greater „, l«. .k,„ „! . IM h i -' i' '.nil I I '1 I 'i SIMPLE rifTMMT. i.f-Ml.n.1 p„. ,f i,,e,f „ tt. Z; ^imT.".':*"' ';»» "■.'" '"'""• "4 unr When the ,i,„e i, short, b„,i.«, „e„ „,e the following >ou,aMA (TheVirZ a^tir^'f 'tT'''"'^ eeed at in the above rule. "iweat at b%,) Th, r, pro- METHOD BT ALIQUOT PARTS .09 Rate %, Interest for 1 year, jSTTglsO _ 3 Int. for 3 years, #113.8050" Int. for 6ino. = i of lyr. 18.9675 Int. for2mo. = iof6mo. 6.3225 Int. for I5da. = J of 2mo. 1.5806^ !nt. for 3yr. 8mo. I6da. ?140.6756i, An$. AK4LVfis.-HaTingfound the f.pferest for lyr. and then for 2 jr., the int for .''mo. la ohtained by finit taking i of I j0u's int.. tor (imo., ud tboii ji of this last int. for 2mo. And ^mcolSdaygareloflme., or i of 2ino., we take i of imo.V int. for 15 days. The int. ag found for tht fccreral parts of the wholt time, added together, girt the interest required. VnTB wi,« ^i. . tne interest required, ample is called $140.68 *' *''•' '°**'"«*' »" *•>• »koT« ex- II. Anrf ^Ae interest /or the months and day, by aliqxmt na^t. The sum 0/ the partial interests mil he the interest reqXed METHOD BY MONTFLS. Ex. What i« the interest of,m.20 for 4yr.7mo. and 15da. at6^^? f X ^ = $6.7166. ^. The above u th* product of the prin- olpnl, rate percent., decimally oxpru-eed in souths ani «1i»«imaU of a mo«th. dir U«i hy IS <-■ I X i. ^ 12) 1.4520 = Int. fori jr. .1210 XI Int. for 1 mo. 55.6 6050 6060 6050 fCTUMo. lai. 1^ 54 5 ^^ 8UIPLE ranBMT. 181 METHOD BY PKOPORTiON. «f fo .II^'sl " "" '"'"■<'" <"»^2'=»' " ««. for 4 ye.rs 6 „.<.,.tba Sol. 100 , 6 X 4rr. 6„,„. loja. :: ,52.50 ;«, whence the ■XAMPLDS FOR PI'vACTrOB «• n BOLTED BV A«T OF THB ^OVE METHODS. What 18 the interest on i* t3s22''r2l7 ^^"•^»'>d I6da.. at 651;? fi. f H3 for 2yr. and I'rnc, at i^% ■? ;• f**.-^,^ '•^r lyr. and 6mo., at 6. $1425.20 for iyr. and lOda., at4.i%? £319 10 9 for lyr. lOmo., at 4g %? $742.30 for 4yr. 9mo. 19da., at (>l%'i $1370.40 for 3yr. 4mo. 27da., al 7.^ 9^? $160.76 for 2vr. llmo. 4da., at o| %? $1463.60 for 7yr. 7mo. 22da.. at 6^ % ? £184 18 8 for lyr. 9mo. 6da., at 3i ^l What is the amount of An«. $436,596. Ans. £1 11 0i + . ^ns. $233.72 + . Ana. $296.19 + . Ans. $168.30. Ant. $164,888 + . Ans. £34 16 4 + , Ans. $26,037 + . Ana. $:iGI.178 + . Ans. $6.98 + . Ans. $213.35 + . Ans. $102,618 + . Ans. $350.30 + . ^ns. $727.24 + . 51. $0,146 for 9yr. 9nio. and 9da., at 6 ^ ? 52. $1051.60 for 2yr. lOrao., at 7 % ? 53. $168.13 for 8yr. 5mo. 3da., at (i ^? 54. $100.25 for 2mo. and 29da., at 4 % ? 56. $1,011 for lOyr. lOmo. lOda., at (i ^? 56. $1000 for Syr. 3imo. 29da., at 5^%? '".7. $168.60 for lyr. omo. and lOda., at 6i%? 6%. $2000 for Imo. 6da., eX&l%? 59. $0.06 for 20yr. lOmo. 15da., at 8 ^? 60. $326.25 for 2yr. 9mo. 12da., at 6^^? 61. $496.95 for 6yr. 5mo. 6da., at 6| %? 62. £109 3 9 for 7yr. 9mo. 18da., at 3|^? 63. $2560.75 for 4yr. 3mo. 26da., at 6^51^? 64. What is the interest of $1660 from April 9, 65. What is the amount of $175.08 from May 7, ».'^l uv. Jns. $0.23 + . Ans. $1260.045 + . ^«s. $253,119. Ana. $101,241. ^ns. $1183.18. Ans. $2013.12i. Ans. $384.09 + . to November 10, Ans. $50.2S|. 1861, to Septeni- Ans. S204.2r 66. What is the interest of $176.89i fix)m January 6, 1868, tc July 22, 1869, at 6^^? «7. What is the amount of $175«.76 from Jun« 29, 1860, to Febru- ary 12, 1863, at 7 f(? •nfPU INTBftlM. 183 T, «7J»" '"'•'"""' °' ^' 2 « fro., i'aroh 17, to D«>,aib« IMS. Ti%l" ""' '"'"*'■ °'»l"8-'9. ffon- Ma; 7, 1868, tojuly IT, July ..TS,'..'^*?"'""^'' ' ' *°'" S«P««-*^"^ri8«;to EXACT MBTHOD OF OOMPUTINQ INTEREST. 805. In the preceding methods of computing interest, which are in general use, we have reckoned 30 days to the n.on h and 12 months to the year which allows to ea^ch year 3 b" instead oofL^f oor^r'' ""''^ '^'""^' " these calculations are The following exaet method is used hy business men in oom- puting interest when the time is short. p^e^^I'r^*** '*"' "°^ '"•*'' '* " '«" """» • y*'- •■ «■<"««» by the table o> aO«. KuLE.--Jf«/,/y '*," ^AeprodMC^A' together, audfind the intertst or i'heir ntmfr/r one day. m. If the interest is to be paid by the week or month :~ mm%iufe weeks or months for days, in the above rule. £je. 1 . How much principul nnd intercBt have 1 1.> pay on the lol- Kmttg note, due Dec. 29, 181 i .' ^' ^ ^^' Quebec, Sept. 8, 1868. U^^tlZ^'^'r'^J I prun^r . to pay Jame. Carroll, or order, foar hmdf^d Md twenty dollars, with interest, at 7 % ? Tlic.n.aa Brown. On this note were indorsed the following payments :- - Oct. 1, 1869, received, t22 28 Nov. 20 1869, " :;Voo: M»7 8, 1871, " 247.87. OPERATIOK. FfSTO Sept. 8, 1868, to Oct. 1, 1869, there are 388 days. " Oct. 1, 1869, to Nov. 20, 1869, '• '• 60 *' ^ Nov. 20, 1869, to May 8, 1871 " " 534 " " May. 8, 1871, to Dec. 29, 1871, '< " 235 " ,^ .•-.-4r »f *^ *" '^^ ''''^' = »'85682.4« for 1 \ \ V jm ^4S *i^-^f ' ^""K^^' ^^^^' ^^^^^5 -^"1^^' ^87«' ^7.50; Jan. 1, i«n, fiju ; how much was due at the expiration of the given time ? ^fW. i8r,!l.')..Sl+. probli^:ms in interest. 30». It will be observed that there are Jive parts or terms con- nected with each of the preceding questions in interest, viz : the Principal, the Rate %, the Time, the Interest, and the Amount. 1 he investigation of these involves five oases : I. To find the in- terest; II To find the amount; III. To find the princioal : IV. lo find the rate 5*; V. To find the time. The Oases I. and II. have already been solved (296, 298). SIO. Case IU.~ The interest, time, and rate %, being giv«n, to Jin d the Principal. Ex. What principal in .3 years, at 6%, will gain $47.70 interest? OPERATION. .06 int. of $1 for lyr. _3 .18) $47.70 ($265, Ans. By proportion. $100 : ar :: $t; X 3 : $47.70. AjtaIiTSis — We fiad the interest el $1 for 3 yean. Since it require! 3 years from a principal of $1 to g»in 18 cents, it will require a prinoipalof as many dollars to gain 147.70 m $0.18 is contaiued times in $47.70 : dividing, we obtain $265, the required prinoipal. Henoe 311. Rule. — Divide the given interest or amount by the in- terest or amount o/$l for the given time and rate, and the quotient will be the principal. EXAMPLES FOB PBACTIOE. What principal will ia 1. 6yr. .Smo., at t5 %, give $66.26? Jin$ $2*50 2. lyr. 6mo., at 6 %, give $1.2924 int. T Atu. $U46. PKOBLBMs IN INMMat. 3. Jnio 18da., at 4 %, give $27.60 int. ? 7. 8yr. 8mo 12da t/-^' ^"'.^ ^^^•''16 interest? 187 ^»i«. $1800. Ans. $120. -4n«. $342. 8. lOvr lO.nn -ynV *' ^'^'" «'147.9485? ''*{;;' ^^^it is f he sum ? to produce $619.15 ? ^"^ ^^^ *^*^''' »' 7^ eg, 313. Case IV.- iiionth, is $24 for 90 . $400. if- sufficient -The pHndpal, time and int^est beinggiven tojind the Rate %. ' ^-. The i„t,reat of $750 for 4 years is $,80, what is the rate ^. OPaRATION. $750 ^ r^O.OO) $180.00 (65g,^„,. _180^ ^^' proportion. «'00 : $750 :: ar X 4 : $]80. A^Ai.TM8.-Wefindthe5ntereet on the principal for 4 years at 1 % bmce the interest of $1 at 1 % fbj 4 years is 4 cts., the interest of $750 will be 750 times a. much, or *30. Now, If , 'tJO is I %, $180 will be ^3 T'7J' ^ f'f!> '" contained times m $180 J dividing, we obtain 6, ♦he required rate ^ , gence the rate % required. ^ ' ^ *' "'^'^ ''^^ ^"^'^'^'^^ «'^'^^ ^' t^^ EXAMPLES FOR FRACTIOE. Required the rate per cent, if the interest of \'l\lt^^V'^T- '2da.i8$1.3..36. r «i J;; i o ^^'^ ^y**- '^'"o- 'S £3 JO .'-,3. 0. $125 for 3yr. 6mo. is $32..S7A 5' ll5r/'"".^^'"o^'"°- 2'^da- is $274.77. 8. $36 for .Syr. Smo. 19da. is $8,034. .J. i 1 "^^f^ '■"^'' ^ '""'^ «^ or anj other double iieeif in 14a years? / ""•t'r Ana. 9 ^g. Ans. 1 2 %. -^ns. 6 %. Ans. 7 %. Ans. 7f %. 4n«. 5i 95. a«m, be on interest, . .ruu 01 ...10/. oy- whwi % was the dividend ? to 814. Cass V. ■The principal, interest, and rate % given, tofttid the Tim*. being s . ! "! 1 I 1 ' i 1 1 1 1 : 'ji 1' 188 PROBLUU IN INTimiST. Mm. Ib what time will $460 gain $64 inUrest, t,t 6 %7 OPEKATIOM. 1460 M •27.00 ) 154.00 ( 2yr. 54 00 By proportion. •100 : $450 :: 6 X ;f i Ana. $54. AwALTgia.— W« and th« iatcntt oil the given principal for 1 y»r. Since the interest of |1 for 1 jear ij 6 < tBt?, the intercut of 1456 will b* 450 times aa much, or $27. Now, if it require 1 year for the t^ven pri«- cipal to gain «!27, it will require aa many years to }?ain $64 as $27 it contained times in 554j dividing, wo obtain 2 years, the required time. Hence the 315. Ki LJi.~Divi(k ihe given Intere.st bi/ the interest on the principal for 1 year, and the quotient will he the time reonired in years and decimals. ^ aBddliJs~(bJ'2?0)i°"''''*'*°'*'" ^"°^*"*''' "y- ""^y »» reduced to «o.tlu EXAMPLM FOR PRACTIOl. In what time will 1. $26, at 6 %. give $1.95 interest ? 2. $280, at C. %, give $84 inlereet ? 3. $45.25, at, (i %, give $1.81 interest? 4. $98, at 8 %. o;ain .f 25.48 ? 6. $240, at t; %. uint. to $280 ? An$ 6. $70.50, a :) %, give $31. 72^ interest ? 7. $408, at 7%, amt. to $434,18? 8. £120, at 4^ 56, amt. to £140 8 0? 9. $1, or any other sum, double itself, at 5 9{ int. ? Ans '' 10. $2365.24 double itself, at 7 56? ' ^ "^"^ An$. I jr. 3mo, A7}8. 5 rears. Ans. 8mo. 2yr. 9 mo. lOda. Ans. [ 1 mo. PROMISCUOUS EXAMPLES IN SIMPLE INTEKEST. What principal will in 1. 6jr. 4mo., at 4 %, gi^'e $2048 int. ? 2. 6mo. 6da., at 6 %, give £136 3 6 int.? . 3. lyr. 8nio., at 6^ 56, give $97.60 int. ? 4. 9mo. 21da,, at i) %, give £15 15 int.? .4 6. 3yr. 5mo. 18da., at oj^ %, give $288 int. ? 6. Umo. 9da., at 0^%. give £466 2 6 int. ? 7. 4yr. 6mo. 14da., at 5 %, give $150.37^ int. ? «. 3yr. 6mo. I7da., at 5|%, give $1451.52 int.? In what time will 9. $(;25, at C %, give $262,50 int. ? 10. £67 10 0, at 4 %, give £24 6 int.? r •1779, at 6 %, give $296.6C iat. ? Ant. $9600. Ans £5237 10. Ana. $900. ns. £3H9 13 9 + Ans. $1682.42. Ans. £9000. Ana. $675. An$. $7267.71. ^n».7yr. Ans. 9yr. An$. 3vr. 4ii>r PROBLKMb IN UtrBUUBT. 188 Aru. 4 jr. 9nio. 12dA. An*. 2yr. 25dA. An$. Ijt. Ana. 6/r. inu. Ant. HjT. 155. $242, at 4| %. give |55 int. ? 13. £460, at 5^ 9>. give £50 int.? 14. $2178, at 4/, <■/,, give $635.2;-) int. ? 15. £405, at 6%, ,Mve £151 17 6 int.? 16. $481.25, at :> %, give $1 92.51) int. ? Required the rate %, if the intertHt of 17. $978.20 for lyr. is $18.91. An$. 6 %. 18. £110 12 6 for50da. is £1 16 lOA. Anif. 12* Id. $1290 for 124da. is $19.99*. yln» 44? 20. 14340 for Hvr. i8 $.'.85.90. An>i a\%. 21. $675 for44mo. i8$l42.31i. Ana bi iii A % and \ at 6%; eT.ry year he draws as much as will pay the harne-sing of a horse which ha^aess is worth $117.60 j what is ti^- Miiunnt of hia i;i. to Sept. let., 1868, at 6 % ? Ana. «4.214 + . 28. What will be the amount uf £19 15 9, at 1^%, from Feb. 17th., 1864, to Dec. 30th., 1867 ? Ana. £26 10 7 + 29. If $1756.75 is placed on interest, June 29»h., 18«6, what will it amount to Feb. 12ih., 1869, ai 7 ^? Ans. $2078.869 + . 30. What principal, at b %. durinj' lyr. Hnio. 12da. will amount to £231 12 11|? iin*. £21.3 10 0. 31. On Aug. 15th., 1860, I lent $5269, at 6%; what amount will t)e due me on May Ist., 1868 ? Ana. $7092.164. 32. An individual buys 65|^ acres of land at the rate of $509.72 per 100 acres: if he pays only at die end ut iJyr. Imo. 15da., the int. will equal to | of the principal ; what is the rate? Ana. 4 5(. 33. A person placed a certain sum on interest at 4 %, which pro- duced £427 10, in 3 years ; what is the sura ? Ana. £3562 10. 34. What is the interest on a bill of $257.81, dated March let., ^865, and payable July 16th., 1867, at 7 ^ ? Ana. $42.86 + . 35. Find the amount of $17041.20, at 4^ ^, for lyr. 7mo. 28d». 36. What sum is that which will give an interest of 1900, in lOyr., ai4.i%? iln». $2000. 37. A principal of £112 10 was put on interest, and at the end of 8yr. amounted to £144 ; at what rate was the principal placed? 38. A boy has accumulated a sum of money by his savings, and wishes to obtain an annual revenue of $140; if the rate is b%, wha. principal must he have ? Ana. $2800. 39. A merchant borrows the aum of £938 12 3, which is owned by a minor aged 15yr. 3mo. 20da. He keeps it until the owner is 21 yeurs old ; what sum will be then due, at 6 % simple intere«t T ill. ito PROBLKMB IN IMTUlHt-. |{ 40. What will be the Interest of $326, from June 6th., 1866, Julj 4th., 1868, ftt7i%? - -■-' - u. Ana. $49.02 + . 41. A merchant eayw that his gain, during the nine years he car- ried on business, equals the price of 3659 yarda of cloth at |2.08 a yard; what was his annual revenue, supposinK he phiced his t'ain on.nterestatS^? ^'^ !l,»,. $380,536. 4J. l^rom I85< to 1867, the population of Syracuse augmented 24|5g; Knowing the Jasiyear'H number of inhabitants to be 102295, tell ne what was the population in 1857 ? ,1ns. 82000 inhab. rcot ,}^!^\ ^"'" '"»«t be placed on interest, at 4 %, to amount to a1 a '" ^^'- *^"'° ^^'^^'^ ^»»«- ^563 2 1^. 44. A man assures me that if he places on interest a sum equiv- alent to 968 yd. of cloth at $3.18 a yard, he will secure an annual rev- '"Vr <^y ^•''•^•''^li 5 wJiat must be the rate ? Ans. 6 %. 4o From an investment of $35680 in commercial concerns, I withdraw a gain of $223 per month ; what is the annual rate of the IT^^ Ans. n%. \^' ^J^^P^^'^y^'^ ^»^'^ for £2830 ; the conditions were £mO in cash, £87 in 6 months, £625 in 10 months, and the remainder in lyr. 3mo., with interest &tT %; what was the amount paid ? • ,"\!L';^*"*^*^'°S raised, during the 6 years of his business, *ooW o'.$29b5.10, desires to know in what time he will receive $88y.u3 as interest at 5 ^g ? 4„g_ g-r 48. An individual borrowed £3750 at 7 %, and then lent it at 6 5^ • • .*' ^o .n ^. '°^^ '" ^^^ ^*y«' ''■ th" y^^h f'^r tl^e first transaction, coii- sists of 360 days, and that of the second, 365 days ? 49. During what time must a certain sum be on interest at 4A % to P'^^cs I olit? Ans. 17yr. 9mo. lOda. 50. In selhug merchandise at 12s. the yard, 1 make a profit of 61 5fe : what 18 the price per yard ? Avs. lis. 31 t- d. 61. Ihef ofaeumofmoney i8lentat4SlJ, andthe*,at5^; what IS the sum, knowing that the annual interest is $28.82 ? Ans. $655. 62. An apparatus for astroncmical purposes cost £49 ; but, as this sum could not be paid before 3vr. 9nio., the price was augmented A of Its primitive value ; what was the rate ? Ans. i %. 63. A man placed on interest, at 4 ^, a certain sum of money which produced m 6 years the funds requisite for the purchase of 368 lbs of preserved tamarinds, at 46^ cts. a lb. ; what wtw the sum? 64. A merchant has invested in business a capital of $21840 which produces him 12^% annually 5 but, for sanitary reasons, he retires from mercantile allairs, and loans his monay at 7^5)^; how much will ^f «V1 ^^^' ^"'^- ^^'^^' ^y ^^^ ^^^^"S^ ^ Ans- 12636.86 J. . n'^ -n '? ^''*' principal the ^ of which at 6%, and the remainder at 7 %, will give $4340 interest? Ans. $70000.00. 5b. A speculator desires to purcha.se a tract of land, containing 450 t^u' ?."?? ^^ ^- ^^^ Wire, and, for this purpose, borrows money at 65 >y- ..t tl-.e expiration of -ijf. llmo. 20da., he sells the f of the land at £fc 10 an acre, and the i-emainder, at £8 2 S the acre ; how much does he lose by ihe traueaction ? lu CUU- OOMFOUICD INTBBB8T. COMPOUND INTEREST. 1»1 itl«. Gomponnd Interest i? interest on both principal and itil. n>t, when tlie Inter is not. piiid when due. doman" i """ '"^^'^^ '^ ''''-' *'^*'"«" «f """y- but cannot i*v"% /•;.r. What is tlie compound interest or$390 for 3 years, at r)%7 OPL-RATION. 1390.00 $-iU9.60 $429,976 1390.00 .06 = J_»^50 |40'J750 .05 = 20.476 Principal for I at. jear. Interest for Ist. jear. Principal for '2nd. year. . Interest for 2nd. yeur. $429.97& Principal for 3rd.' vear. .05 z= 21.^*9 875 IntereHt fur 3ril. year. $451.47375 Amount for 3 years. $390.01)000 Given principal. $ 61.47375 Compound intsrei^t. 317. EuLE. — I. Fitvl the amount of the given principal at (he gmn rate /or one year, and make it the pnncipal for the sec- ond ij ear. -IT J }l- Fmd the amount of thi« new principal, and make it the principal for the third year, and so continue to do for the aiven number of years. III. Subtract the given principal from the last amount, and the remainder will be the compound interest. (a^^u^^r^' ^^«° *!»« ''™o contains yeari, months, and days, find the amount ond interval, pjoceed.ng in all respect, as when the interest U pajablo year!?? EXAMPLES FOR PRACTICE. 1. What is the compound interest of $970 24 days, at 6 5g ? 2. What is the compound interest of $520 3. What is the amount of ^128 for 3 years at 6 %. compound interest? 4. What is the compound interest of $340 payahle semi-annually, at 0^? 6. What is the compound inteiMt of $737 -li-annualij, at 7 f( f for 2 years 9month8 and Ana. $173,295. for 3 years, at 5 qg ? 6 niontlis and 18 daye, Ana. $156,717. for 2yr., interest being Ant. $42.67 + . 76 for 2^ years, payable I ■ k\ 'hi 1«2 OOWPOVND IirTKRn*. 6. What will $900 amount to in 1 year, at 7%, compound interest, payaMo (juarterly ? Ans. $*.)64.67 + 7. VVliut IS the amount of $')00 for lyr., intereat payable every 3 monthH, coiiipuuiiil interest, at 8^? 8. Find I he cuinpoiind interewt of $94H for 3 years 4 months and 18 day^atG^? .Ins. $207,051. iilH. Compound interest may be computed more expeditiouslv by the use of the following TABLE Shoimng the amount o/$l , or £1, at 3, 4, 6, fi, 7, and 8 per cent., compound inltrest, for any number ojf years from 1 to 34. ^^Hh- Years 1 t 3 percent. 4 per MDt. 6 per oent. 6 per oent. 7 per oent. S per oent. ^^Hh:;^ 1.030000 1.040000 1.050000 1.060000 1.070000 1.080000 2 1.0l>ii900 1.081600 1.102500 1.12;560O 1.144900 1.166400 3 1.092727 1.124864 1.157625 1.191016 1.225043 1.259712 ^^^■i .^.'i ^^^^^^^^H 1 4 1.125509 I.169H59 1.215506 1.262477 1.310796 1.360489 ^^^Hi ; 6 1.159274 1.216653 1.2762.S2 1.338226 1.402552 1.469328 ^^^^H^ 6 1.194052 1.265319 1.340096 1.418519 1.500730 1.5S6S74 7 1.229874 1.315932 1.407)00 1.603630 1.605782 1.713824 I t « 1.26(i770 1.368J69 1.4774,55 1.593848 1.718186 1.850930 ;■ i " 9 1.304773 1.423312 1.651328 1.689479 1.8.38469 1.999005 I'l 10 1.343916 1.480244 1.628895 1.790848 1.967151 2.158925 11 1.384284 1.539454 1.710339 1.898299 2.104852 2.331639 , ■ '* 12 1.425761 1.601032 1.795856 2.012197 2.252192 2.518170 r ; 13 1.468534 1.605074 1.885649 2.132928 2.409845 2.719624 ,r\' 14 1.512590 1.731676 1.979932 2.260904 2.5785;H 2.937194 ^ 15 1.557967 1.800944 2.078928 2.306558 2.759032 3.172169 , ' 16 1.604706 1.872981 2.182875 2.640352 2.952164 3.425943 i' " 1 17 1.652848 1.94790L 2.292018 2.692773 3.158815 3.700018 i ! ^ . 18 1.702433 2.025817 2.406619 2.854339 3.379932 3.996020 - ■ i . 19 1.753506 2.106849 2.526950 3.025600 3.616528 4.315701 ^^^^^^H :.i 20 . 1.806lil 2.191123 2.653298 3.207136 3.869685 4.660957 " i ' 21 1.KG0295 2.278768 2.78596:> 3.399564 4.140562 6.033834 i :; : 22 1.916103 2.369919 2.925261 3.603537 4.430402 5.436540 [■•. ' • 23 1.973587 2.464716 3.071524 3.819750 4.740530 5.871464 1|- 24 2.0o2794 2.563304 3.225100 4.048935 5.072367 6.341181 ^^^^^H ^ * 25 2.093778 2.665836 3.386365 4.291871 5.42743!J 6.848475 26 2.156591 2.772470 3.555673 4.549383 5.807353 7.396353 { ; 1 27 2.221289 2.883369 3.733456 4.822346 6.213868 7.988062 i" ! r 28 2.28792S 2.998703 3.920129 5.111687 6.648838 8.627106 ' i j ' 29 2.356566 3.118651 4.116136 6.418388 7.114257 9.317275 i ; 1 5 1 30 2.427262 3.243398 4.321942 5.743491 7.612255 10.062G57 ^H^^^l. 1 I' 31 32 2.500080 2.575083 3.373133 3.508059 4.538040 4.764942 6.088101 6.453387 8.145113 8.715271 10.867669 11.737083 HHI i' ' 1 ^1 1 i 33 2.652.^35 3.648381 5.003189 6.840590 9.325340 12.676050 ■' • 34 2.731906 3.794316 6.253348 7.251025 9.978114 13.690134 - ' Hj L\ ll itk*«b •Mtokto. iHtm. •t f J? ^^^^ '" '^^ compound intewetof |9() for 7 years and 6 mon OPIRATIOir. Amt. of$l for Tyr., |l Principal, Amt. $[){} f^r 7vr., Interest of $1 for 6 mo., ,605782 90 Int. of amt. for Gnio., Amt. added, Amt. for "yr. 6mo-, l^rincipal euttracted, l'14.52"0:}so 4.;«50TU .7226019 Analtsib, — We find tht •mount of $1 for 7 yearg in the table, and multiplyiiiofit by the giTen |irincipal. olirain the »- mount of the .j;'.i() for 7 year*. Wo then (inJ vu thi,» auiount tho intorest for tho « months, and add it to its prinoifial. From the hist nmouut snbtriicf.- int; the orij,'inal principal, we have left the compound inter- est required. Ueuoe ttia 6.0582 1 :i'l 144.5 20:^.80 149.57859^.^ Comp. int. forgiv. time, $59.57 + , Ant. »19. RvLE.-MnlfipI^ fhr amount of $1 for the. given mh cnuitcme, as found m the table, by the given prind.pal, an,] the product xodlle the amount. Subtr, J the principal frmn tht aowunt, and the remainder will be the compound interest. EXAMPLES FOR PRACTICE, at 7^^^*^ '" *^^ •''^'"Pound 'ntere.st of $60 for 8 years .and 6 months, 3. What IS thecomp(.und int. of $3000 for 2yr. 6mo. ISda., at 6^? 6. To what mm will $7.5, deposited in a f^aving.s bank amo.mf at jampouud mt«re8^ for 17 year«^ at «%, payable feud annual];?^ PROMTSSORY NOTES. »20. A Promissory Note is a written or printed en-aee- ment to pay^ a certain sum either on demand or at a specified Time «i.?fj?' 7f,^akerorDrawerofa note is the person who signs It and thus becomes responsible for its pay.uent when due. 33t2. The Pavfifi of » note ^h *1i'> n-rsu-- i-.-^'-, . ^ \ order it is made" payable." ^ "'^""' ""' *°^^'^^ »23. Thelndorserofa note is the person who si-ns his Dame on the back of it, and by so doing guarantees its puyLnt m«le« he wnta. " WiUiout fiiwurae "%ver his name at the Z«' 194 PROHI880RT NOTBS. l! I 1 fa'l • 11 ! ' » S24. A Xegroilable Note is a promissory note which is made p.-iyable to Ijourer or the ordor of some person (ifee Notes ForviH, 2, 3, 4). r \ , in.lSSm!" ^^ " ""^* '■ '""^*''* *° *'"' ***'"'^''' '* """^ ^ neifocintcd without H i^'-n^."°So!:[d'!J w,"!';:;: i;^ r^t;;.:^""" "''^"^■"' "• •^"'^ ^'''' «"■» ^^ '"^'^^ .•?25. A note nmy U, miide i);iyiihle on demand, as in jPrrrm ivo. 1, or at the expiiMtion of a certain timn iirt,>i' its dale us in Forms No. 2, 3, and 4. A note may he made i)ayal,le to a particular person, as in Form No. 1 ; or to any person who is the hearer or holder of it, as in Form. No. 2; or to the order 01 a person named in it, as in Fonn No. 3 ; and may be made payable at a particular place, as in Fonn No. 4. The Not", For7n No. 1, is due when the payee demands its l)ayment from the maker of it. llKMARK.-lf no time is fixed, in a note, it is payable on dornnnd. The Note, Fonn No. 2, is payable to the holder of it at the expiration of six eal.-ndar months from its date. The Note. Fonn No. 3, is due at the time specified in it, to the •jayee .vl,,. uhi.,r>t.s ,t. Jos. A. VViilter nuiv iiMur-,. ,1,,. „n,ein Ma„k }„IU,u-H'*^r'^''"*!^''"^'»«'a"dthus make any person law' thlVX; X '' "*• '''/^' P'^y'"' °''' ^' '"^y indorse it payableTo Inntt * particular person, i^ which case such person can make ftoother person the payee, w Jo«. A. Walter could, by indorsinHhe note m blank or otherwise. ^ un {■■fee Notes, Ifocintcd without 10 eum for which , as in Form : its (hx\('., (18 l)ayiil)le to a eison wlio is to the ovdor uay be made demands its id. L" of it at the I in it, to the iiHic ill Miihk, person law- t payable to ion can make ndorfiing the nanaed in it.' ' allowed by )f the time of the dayr 3, the interect If the timn r tnonthe an %, it bears vhioh does not ^ of InWireit tha same day to pay It if «i«atb*4af Poun 9W IM »id?r?t*n ?"'^"f "« ?0t« ^ • note giren for a valuable con- W«e or to an.'? k'" '^' '";''^*^ ''^^'^ ^^' *^« »»<»""* to the P»jee, or to any subHequcnt bou„JiJe holder. payee but Sll ; r u '" ""^ '''"^^'" ^^" '''^^'' ""ble to the .oX"o„-ti::Sr\'i?r^^^^^^^^^^ r if - ^ «''»^'- *•" p-^- ^ ^^ A?.?eraCte^±^jl 7 ''' P"^'"^"*' ^ "^'^^""^ «-^ ^'--^a to f fpToifi'td^" ouSf. ^''' " ' """^'^ P"'"^«« ^« ^«'^-^ ^^ «.o?^;rttferuivl?^ ^^ ^ ^«^^ ^- i- to f!fut fh.^n?^ '' f 7'""" Obligation, authenticated by a seal. aXer^:nSrrti\r;''"°"^^^ p-^~- - proSc,fve??ol^'''^^';[^^'*^^8^^^«^^^^ ^ conveyance of dition twlJ '"'"' *^' P"y"^"°* ^f ^ bond or debt, on con- ^Z^az^' ^'''' ''' '''''"''''' '' '-'' -•* FORMS OP NO i ^S. Far7n No. 1.— Demand Noti. $ 64 r%% -^^ee, ^nuat.u. /5t/i. , /<9'/0. ^a^ Msce^^^U OtAMP.) ^£cu^ u IM rOEMB OF KOTJB8. I Form No. 2. — Notk Payable to Beaker (Neqotiable.) Forrn No. 3. — Note Payable to Order (Neootiable), C/ne yeca oAei f/a^e, Q/ ^iornt^ ^o Aaii. lo ^e (•TAMF.) S S^. :^^^. Form No. 4., — Note Payable at a Bank (Neqotiabi-e.) G^oUy e^z^ aJI(gl (/a^, Q/ /iio?^nt^e lo /lo/u tc ..^unA, &igfovU'iic'Vc7i diici, j^A ooiiuM. '^o'cicue iec^f/ifect. ^afovu ijnAiaf.) lon^ ^i)oua^ itr lOTIABLE.) (9'/0. dtiable). )TIAB1-E.) '•<»'» AMD LOM. Form of Produce Note. Form of Dm Bm. $103. (nAMp.) fUU PROFIT AND LOSS. 336. Profit and Loss are coinmeroial t«nii« x,^a f^ the gam or lo« in business transaotions ^^^ ** "^^^ PrKd^Lt" ":. t"^ ^""^ ^' ^^-«*i- *• »- oooridered i. 2^d The ^^5' ''""^ "T^^""' ^^^•^ » the Base. ^ Thf /? ^ •4^'^*" °'' '^**' ^hi«h i« the Rate 4 4th. The S^Uns Price, which is the Amount' I)iffere«>a Tie questions follow the same rules as in Percental. Own = Stmng Frice - Co*t. "I, r Its PBOVR AMS U>^^ ' I EXAMPLES FOR PRAOTIOK. 1. I bought cloth, at $2,.'»0 per yard, and sold it eo as to gain 26 %i tor how much did I ficli it a yd. ? Ans. $HA2^. To folre this Example, «ee Case I., 282, KuLl. 2. A farm was bought for $4500, and sold eo as to gain $900 1 how much was the gain % V Ans. 20 %. !• Mlve this Example, m« Caa* II., 384. Ritli. 3. By sellinr a building lot, a man gained $175, which was 12 % of the coBt ; what was the cost? Ans. $1458.3;il. T»Mlve this Example, tee Case III., 2M, KvLi. A. A genileman sold a horse for $180, and thereby gained 20%; what was the cost of the horHe ? Ans. $150. V» aolTa this BzMBple, «m Case IV., 288, Rulb. f. A merchant lost 15 % oi» his old stock of goods ; how nuich did Im lose on those that cost 12^ ota., $6§, .SBJ cts., 334 ctfl-, and ilSf^l Ans. 15 cts. : $1 ; 5| cts. ; etc. %. Bought Bugar, at 12 c4ii. a pound, and sold it so as to gain 1^ •to. a pound ; required the gain %. 7. Sold butter at | of a dollai a pound, which was at a gain of K % ; required the cost per pound. .4ns. ()6| cts. 8. A market woman sold oranges so as to gain | of a cent un each orange, which wa« at a gain of 33^ % ; what was the cost of an orange ? Ans. 2 cents. 9. SuJd a horae at 33J % gain, and with t]>e money bought another horse, which I sold for 15: . 20, and lost 25 %. Did 1 gain or lose by my trading ? and how much ? 10. If I make a profit of 15^ St by selling papor for '0.85 above the cost per ream, how nmch m«at be added to the selling price to realize a profit of 32^ % ? Ant. '^^ cts. 11. What ^llould I sell a barrel of flour for, thatcust me £1 2 6, to gain \^%'t ' Ans. £1 6 3. 12. A neighbor offers his house, which cost him $6900, for 20 % less than cost ; what is his price ? Ana. $6520. 13. A merchant eellfl cloth for $6 a yard, which cost him $3.76 a jard ; what is his gain per cent. ? Ana. 33^ %. 14. I bought 640 yards calico at 15ots. per yd., and sold it at a leduoed prioeof 2i5|J; what did I lose? Ana. $2.40. . 15. A grocer selU coffee at 7Jd. a lb. which cost hiTii 'JJ. ; what is his loss per cent, f Ans. 1 7Z %. 16. A merchant buys at auction $»562,60 worth of goods;" it he sell them at an adranoe of 20 % on the cost, what will be his net profits; deducting $600 for expenses? Ana. $1312.50. 17. How much ehooU I sell dilereat qualities of sugar which cost Me MX 16^ £2 1 3, aad £2-12 C the owt., to gain n\%'i KiOFTP ASi IN freight .nd other wpeasea $5 33 Vhlt In ^"''"^ *^*t ^ P»S St i>^-Buught ahorse for $130 Da;,r*«f u- ^n«' $28.2175 5 wecka, and then sold hi« fc^ IJil ?t£f,^'> noorishmeat da in; tae whole cost ? '^'^ **20 j what^ ^^ jo^, p.^ ^JJ'^J -su. i5oij^.|,t codfish at $4 2'i fi.^ ^ . . ^*^' fO.ll 11 ''»«"':^ gain por cent, y^^-'^'^^^^^^^^d sold it at $4 93; what whioL coft?/;. «,:;iV^? ."'S'^fa -? •> lid. for 3«. 9d JrTb !?• wa. h,sg,i f,,/-Jt^fcT;tfeV-i^' 6 for ^TsV; X mj at 12 ^ advance : what waJ f f, » - * m selling a certain onan ^ 24. A merchant bonJl.t « K . ^'"^"'•* «old ? ^n* Tl qn? ^7. % selling cloth at .|4 the vaff T 1. on ^ ^«*- -^^^i 56- *1- Fm, sold at 26 « loa« i. (h ^!« iT *" "* ••W oo>t f or lo™ per cot in selfng^^Vu « "liV ''»""'"« b, .he g.i. q« A . -<4fM. Iflt hnw... ^^ /^ ^.x'" 2 ^"**'' u"i each 38. A speculator sold the «,«?« nf^^!^^ ^'^^ ' ^'»'^- i^or«e £52 Is '.S'M' ifif''! Il MISf )KBRA4M. . fif^^J.t*iP"r ^^J^""' r"" '^ **-^^ P«'yd., by which I mak« aprofit of 3.^i ^ I sdl lOO^d. b) wholeaale at 30 ^ reduction on the retail price. Wlmt w my gain or lose per cent., aud how much do I receir.ayard? ^«.. 6i ^ lose; $8.32^ a yd. 40 A merchant shells linen 2^ cts. more than the cost and realizes * P , A °* '^ ^ ' '''^^'^ >« t^« coHt of a yard ? .4ns. :: I i cts. 41. A grocer deuianded for a certain quantity of prunes a price 22 % above the co8t; but being a Httle musty, he sold them at 10* less than his first demand, and thus gained $98 by the sale : what was hid hrst demand? j^ $1220 42. At what price should I sell codfish t/hich costs 168." r>*d. mr Gwt. to realize a profit of 12^^ on the cost, after deducting 1 2 A ^ of ttie price/ Ans. £[ I 2U. 4.^. J^ught a quantity of cheese at 12 cts. apound. Supposing the weiglit to be 0^ less than that calculated, and 10 % of the sales to be m bad debits lor how mueh must it be sold a pound to make a net proht ui ] 4 % on the cost ? Ans. 1 6 cent, a pound. *u J— Y'^'ian &Co. bought dry goods for the amount of $6840; ifc""^ I *' ^? * P'^^^' * *' ^^i %. i at 20 %, and the remainder at J^i % prohi ; what was their total profit ? Ann. $1482.00. COMMISSION AND BROKERAGE. »;$S. Commission and Brolcerage are the percentages paid an agent, or broker, for the transaction of business, and is esti- mated at a certain rate per cent, on the amount of the sale pur- chase, collection, etc., effected. ' ?»f ^- ^ Agent, Factor, Broker, Collector, or Com- mission lueroliant, is a person who transacts business for an- other. NoTOS.— I. An agent may be n S])fe[al AgfiU,—i\txASf, authorized to transact only suchbuBine.s as i88| eoified,-- cr a Geiieral Agenty who, ae suob,oaa trat.g. act any biJsiness of the pergon who employ! bin. 2. iVieichaudise and Produce sunt to a ]ier?on for Baloor euperiatendenct, art !&\A. to he comipced. The peit-on sending them is termed » Contignor ; th» person to whom they are sent, ii lermed a Consignee, 3. A oonsigDfi'; whose bu.-inega oflQje is remote from a consignor, is romettmeB termed a CorresjioiideHt, and usually aota «• agent of the lirm consigning hira the goods. 4. Broliers are oktssified aMordinK to the nature >f the sales and oontraots they effect. Ihiig, a Bill Broker is one who n.gotiates the uiscount on bilif (f exchange, etc. ; a.Real-Eita(tBrol:fr\s.onQ whonegotiiitesthe saieol' houses and landn ; luxmuhcr. Bmker, SJnj» Broker. Stock BruLcr, Paivii Bioka; etc. i). A ooUccior m ly hare the business of settling accounts between indivi- duals, or he may bean officer of tho gove»nineDt, at a CoUector of Hie Port, whose business is to eulleot dutiea ; a Collector nf Taxet, eto. fro m a 840. The Net Proceeds is the amount received •ale or collection, less thtf commission and other changes. Questions on CMnmission and Brakcrage foilow th« same rules M those in Percentage. ■X.iMPH!8 FOR PRAOTXOK. 201 '• "^^^ ^"^ ■«»»FK -. Cm, I.. 28^ B«* wiit^rarotts^St*'^'^^*^*^- -»'•»« wood, .t5U; ^••. $1675. IW «,!.. tfci. B..,^ ^ 0«. UL, M,, ,1^^ » -ol*. Aim Bx«ip»e, «, Om. IV., 288, Hvl,. ■16^? "'" *l«ron $309.10 at 5if*; on $4706.2? •1.^40.40, at T^Tofffiifl'^^'i'.^'L"'** <^^*^H It U?of 8..Soldi„er;baBd.«. a. follow,. I.t foT'JlfA''.^''^^^^'^ «^- Mission; 2nd. for £16 1 1 « .» * ^ q_7 . ^*^ ^^ 0, at 4^* com 9. What amount of brokSLl '^^r '"'"• ^ ^»'- ^^ 7 5 + biMJks, as follows: $590 tTr^Sri-?.^^ ^^' e-changing^g^n. «*»d-|wluuitffbwkS;i^rr^^ '' >nre8t,ng $11730, ia Ontaria liow »Mk HMk Zl k. bv? '^*^°* ■'*^'' ^' * * brokerage , •10095.36 toKmJtttplr ^ ^ «« "^l^'^^^-- »»d r»«itt.d -11 ♦u "^^^ owi^r tu, the a«t proceeds; for what nrW ^w i,. -.. .„. px^pcrv, aad what was iii« oomin.MJon ? " "~ ""' k* purchase? "««hii««ob, z^^, how manj •<>«• did 15. A nierckant kairiag on kand 470f !^,r^. .#• '^**' ***' Ti '^ jp "f -cinfi^ n , wttatare the n«t|j>/i>,}e«ds, if soW at Si$ a hkL T i:l 209 COM MISSION AND BOOKlKAffB. If I 16. I p«rehM«d 6000 bash«la of wheat ia Bmflklo, at il.ST^ shipped the eame to my agsnt in Kiugstun^ who ftolol it at $1.62L Uoiw much did I make, after paying $543 forexpeoM* and a eommia- «ioa of 2^-%? Ant. $723. 17. A broker eharged ia« G^^^for the ezAhaage of £681 4 10 in ^eeiibacks ; what was his brokerage ? Ann. £35 16 34. 18. A comniiseion merchant sulci a consignment ol oats for $12686. He charged $66 for storage, and 6^91^ commiusion ; what were the net proceeds? ^n«. *11827.r2i. 19. An architect charges I % tor his plan and Burvey of a building which cost $24000, and l eeived $38S6.12| as the net proceeds; what was the rate of oob- misflion? Ana. 1^%. 28. I remitted $5500 to my l»x)k«r with adriec to invest in Bank stock, after deducting his brokerage at } ^ ; what was the investment ? 29. The net proceeds of a sale were £1408 16, and theeommissioa, .£28 15; what was the rate of commiseioD ? Ana. 2 %. 30. In charging 1^% for the investment of a oertaiu sum, a broker realised $286 ; what was the amount of the investment? A. $19000. 31. My agent in Cincinnati gives me information of the purchase of 4000 bushels of Indian meal at 80 cts. per bushel, and desires me to remit a check on New York which he can sell to a broker aX \% nrotnintn • arka.t oKniilH t.h* Anmnnt rkf tlia <«li«r>lr \\a Kia no»^>v,;.^ow,,, beings^? Ans. $3271.464. 32. A ftctor received £6 12 for the sale of grain at I % commis- sioa ; what was the amount sold ? n. fteoeiyed from A $700 in specie; paid 3^ % Ans. £140. for changing it to fUB AND MARINE INSURANOB. 203 gold; and, after deducting the commission sA2%, employed the bal- ance in the purchase of fruit ; what was pai.l for the fruit: and what wa« the oommi.-sion ? ^.ns. ^iWil.^l), fruit; SKI.-) I commission. S4 lleniitted to my correfipDudent at Rouen £265, for the pnrchaBe of calico at 'M. per yard, after deduotirg his commission at 2 96; how many yardn will I receive ? Am. 6666iyd. .^5. A speculator rec >e« $4113.60 an the net proceeds of a sale, allowing 5 % commission ; what was the ralue of the property ? 36. A cciiiiinission merchant who oharges 5 % commission on sales and inveHtiiients, receives 260 owt. of cheese, at 6d. per lb., and £748 10 6, m cash, with advice to purchase a cargo of cotton for the whole amount ; what will be his total cou mission ? Ans. £97 1 ' 1 U 37. A Halifax aj^ent buys 34 box28 of chocolate; he pays $7.50 for freight and cartage, and his commission is l\ Bured, varying according to the degree or nature of the risk aa- mmed. at %% FIRE AND MARINE INSURANCE. 346. Insurance on property is of two kinds: Fire Inturanmf and Marine lasuiance. 34T. Fire Insurance is an indemnification of damage and loss caused hy fire or lightning. (1) lift iofuruM wiU b* trMto4 of later. Iji, i 9N 'IM AMD UArnn INMntAIfOS. an?b^c,Shwr'''"T®",*" «'*^™»'fi<»*««n of damage priDdjL: '"''"'*"""' '^" «*'*'"'^*'«»'' are tM««lon the following TT* Z^^^^^^ ^* P^c^t^ge. (278) II. The sum insured is the ba*e of prcmin*. in. The sum coTcred by insuraaoe is rfifertnee, BXAMPLB8 POB FRAOTIOB. ftMOBat 2.50. To solve this Example, me Cue 1., MS, VmUL To solve this Kxampie, m« Omo II., SM, Ina. • w^'JiV'L''''"'""*^'f""".«***"''"^ <■«'!<>''*• value, at 13«. WM$14.,.bO; requ.re.! the valueofthe tWDery. Am,. $11648. To solTe this XiAMple, m. C«w III., Ml, WmA 4. What must J)e paid for an insuranoe of $6728 at 11*? 7. A hotel ralued at £8760 i« insured for i of its value at ?'* 'heiit^r? *"^^*^ ^^^'^ ^--^"^ - chtrwyir; :L't t eur«l\j'ri*2?'*'''^.u"*''*^'"'**-^'^"^^«= ''»»•* «um muV'Jia. 9 {fk ?^ ^. *''''^'' ^^'^ P'^'P*"*^ *»^ premium ? An,. $<;500 9. What IS the premium of in«uring£t;s)5 11 8,ati5 13 9«T a i ;f Iif*^ """T^ ** ' insurance fo? my library,' and this sum is jCS i« 8^? P«™ujn for an msuranoe of £1486 13 9, at .ui^ 4 *"S-Zir%X^.tl'i''?;^ ""'"*' oft^f gel! tltmW $2000 of Me «to«k IrkJfV!!!*!*' '^,'u ' «o°«ag'-ation, he saves but ]o ^ *°« « w«« re^ lo«a will be sustain ? Ans. $472 «. to .oi^^fh! r." "I"" ' ''"''**'. '*'""*' *^ '^^^^^^ be injured, at lA *!? M ! *"*"* '"***' '^ **"* '* •" destroyed by Are ? 4. $8400 14. My goods are worth £1563 12. For what sum m.l« T 7 .h.^jp„o„,, i„o«,.f !«.,. both pr^J^'lTp^Zy, r« li). rh(. premium Ota echool-hou«,iB«ared at li^k islfiVn. V., whirt sum was it insured ? » area ai ij % , , ^50 . for '"""" • iiw. $360. AMKSSMBirr OF TAXK8. 2«S of damage e following he aaioaBl $112.50. lii house f $11648. 'fffiMl and 2 14 + . wrecked ; 887.50. 5 what is J 15 0. ist be io- $6500. [3 9%r 8 eum 10 >uot? 13 9, at H+. them in- iaves but «472. red, at 1 A P8400. I iu8«rc ^ at £2 ilGOO. 8*50; for ^4000. of build- balaoce $360. oJl:^^ ''"' "•."" «"'^« ^^*^'^*' *1938 12 « be injured to cow both ppcinmm and g(,bd8 la case oflo».H, the rate beiuK 6««? IH. A .rig estimated at $40000 is injured for % of it« value at H% and Its cargo, worth $H6000, at | ^ ; what is the insurance ? •Jf^; ^ '^''"'''T'^ P""' «I450 tor premium ofinmirance on a cargo of cotton com.ng from Uavana, the rate of insurance being 2^%; What «J™i.. '^ * ^"''*" »n«"«-anoeof$1200: what is the rate of the pretnium ( a . , ^ ofJlLll^il^i.^f.]^' '^^ 7i 5* commission, and find the insur*,;ce of tae sum, at 4J % ? ^„^ ^.^7 5 4^ + . ftnl^"r ,.!*"'' l'f!i"S a cargo of SOObbl. flour, has it insured for Klce LTte ? '* ^' ^""^ P*'^ *^"^-2^ ^«' P'-^"*'"'" 5 what was tae price per bbl. ? ^na.$8.26. R«t 1 r ^"■P-ow"?'' Ji^s two of his vessels insured for $1^0000 in the rn' !/ill^'"''"1! ?^-' f ^ ^' *"'^ f-^"" *45000 in the Colonial Insurance 9** A*r ' *"*^'8 to^ rate of premium for the whole insurance ? . i!4. A house estimated at £300 was insured for I .jf its vahie, dur- «£)!?"' fu ^ P^*" *?'*"'"• Towards tl»e end of the third vear, it ZZ J\^ ^^ I ^""^ ' '"^^^ '^ ^^^ *<^^"^' Jo«« o*" ^'i^' proprietor without any allowance of interest? ^ /Ins £106 «.!?<» J *^-5 V"** •* '^. P'^''^-^ ^""^ P'*»«' and g ^ premium ; every ^3 t"»f ^/m' ^ P^'^ J^ P'-«'"''^"'- The house having been de^ hlvS'K n >'^^^ "'•'at was the loss of the insurance, no interest flaring been allowed? j-,„ 419m- ok ^t.. 1 paid $46.75 for insuring a store for the i of its value, at I , % } wha IS the store worth ? ^„8 $,;hoo. a„ 300 polls, e tax ; that 'a tax who I A's tax. I the 0Ame t. $ pays for 3 is personal $1628.()5. i amount of 1.06, which 'ate of taxa- niaaioD vas 38ii.C9 + oiwrmf-HousB bdiinim. CUSTOM-HOUSE BUSINESS. Mt „nn^^?' ?,"^*®^' **' Customs, are taxes levied on imported fnduSry" ''' '''^^'' of govorn.nent and the proteotl 7home 861. A Custom -House is an office pst'>hli-«]ir>,i 1^, ment for the transaction of business Snt Sut c. \fr2 cars attached toitarecdUed(7««.c,..^o,.e|^atT^^^ s to »°«Peotthecargoesof allvesselsenteringatanyof hese^^^^^ to inspect the invoice of goods, collect the duties et^. ^' etc ; thase oLrge« are oaH.dh«"4r dues '^ "'°"' °^ ""'""« '*"» P«'*' 2. To carry on foreign oommeroe secretly, without •.»„,„,. *i, ^ .• • by law, is tnugglin^. ""'^uy, mtnout paying the duties imposed 868. Ad Valorem Duty is a certain per cent on thTeo«t ofgoods, as stated in the I'nyoice. ^''^ 864. Specific Duty is a tax computed on the wei-ht or measure of the goods, without regard to their cost Lee alow anoes are made before computing the duty. ' 865. An Invoice is a statement of goods, from the sellf-r tn the^uyer, or importer, showing the qua'ntity^nTp"f th^ 866. In the United States Custom-Houses, certain Wal al "ra^elSiZS Vca' f^'.^-^^^S^' ?*«•> be/o^re^Tptifi bc,xes, etc., containing tL goodsf and Velak^^e'y gaTgin^ tt .pe^rdT^e?aTefarJSj;frSX^a^^^ the oniy articles upon which 867.— To compute ad valorem duties. Ex, What is the ad valoram dntv ai i » i^ ^. « • whinh «o«r «^fi« fio » "*^' •* ^ « »' on »n invoice of ich coat OPERATIOir. $a5«.60 X .18 a: $46.17, An$. men BO A»ALTSM._. According to Case I, (MS), we multiply the invoice, $2,^650 which le the ba»« of the duty, bv the IJTeB ratt, uui <■ in the duty, $46 17. H? m »h 111' OUWOM-HOOM BuanMo. th!^^^ls ^l'';^:~f''''^^^' Pfrcenta^e on the invoiced value a/ ««/.ir« r^ ^'"'" "'^^ ^/^'^-i^. -*^ '^« »•««/' ^tW be the orf 3«!> To com}.ute spfci/ic duties. <«'...,"^::J;*^,i7, .tct.-.tu.^'^ .iTi/"' ■"'■^'"■« OMRATION. J 9J •'* = 716.811... tare. ♦40.^. J X .02|=.|I2I.()H«, ,f„ty. Analtsw.— We first find the whole weight of the inroice which u 612()lb. From this amount we deduct the allowimoe for tare, 716.81b., and ocaijiiite tha duty on the remainder. Henoe the folluwing KXAMPLKS FOB PftACTIOK. _ 1. What is the ad valorem duty, at 19 * nn is-rsn ik <• invoiced at 15 cts. per lb ? *' ^^ *> 00 16780 lb. of cordage, llsVso? " *'' '"^^ ^^ •'•'*' - «* bale of HoUaud linens which cost 6. What is th« dutv at 20 od ^„ • • ^^- ^525.85A. cc«t in Liver, ulS' 1 th^' 5° ""T^""! ^^ broadcloth which 6. What thetScdu^riOor'" -oh weighing I20T; tare % J ? '''' P'' ^^'^ ^" ^^ *=^««t« of te'a, aot%j^ir^1j-^r„?untrtoXt"s^^ was the wine invoic^ ? ^ ' *' ''***^ P"«e Pe»" gal- Ht',i6urt„"g^;dSvSTt'^^^ Jf4 ^J on goods'i„voicJar$33lo^1h'e\^1iettV:rth. tj^ 16%; goods invoiced at «4800. were free ,,f rl„Tv o 1 ?^® *^^ nianxler, the duties were at the Zi^nff,^ ^ J' """^ ^n the re- amount of the duties? of -^0^; what was the whole . 10 What is the duty at 18,^ on 60 ke.s af nr..^J:'::'{^r ' l?^" '"^«'cea at if cts. per lb. ; tare m31%? ' ^ ^eighmg i value if ^ ht the ad weighing Sret find the nToice which 9 amount we oe for tare, te the dutj Hence the I compute ' cordage, 1449.73. egs of to- re? ) hhd. of diich cost 25.85^. th which t$4.86|? ts of tea, is 12250, 15%. ', 42 gal. per gal. invoiced the rate rate of the re- 3 whole JO.tO. eighi °g pieces ■y24c,j; Ben, at •>'8r «>. ru^r!L'':if^^^^^^^^^^^ clebt, payable at . rayabieiaYy;;;^,'^'*'^-^^^'^ -"d discount of $25.44, .t 6^ OPERATION. $ 1.06, amount Of $1 ■^5.44-^ LOG = $24. ' 2o.44, given sum. J±^, present Worth. ^ 1-44, discount $25.44 will be M mn„. I ii^° P''®'«"' ''O'^h of worth vrhich. subtr.. oted f?,.m ii" ■ '^ '''" P'"«*«°» $1.44 diacou'nt. H^c^ S:"!?/;!" ""' *''" WORTH "^ '^''' '""^ ^^' 9^i*^t will be the present n. ASMiimci ♦>. on 4 moH.' oml.t, ^^.^.^What ,. .he present worth of .5117.60, puvaM.. i„ ,' year, "at h.nc;,'lt'?r/'' ^'■""' -'^t^ of a debt of £96 6 OJ, .iueT„.'l'?L. 2;s. What Hhould be the discount on 1373.7.'-, nu.T i I nf "L"/ theterm of maturity, at 6i«? •^'•i-'-'. pui^l ''*>• before 24. What iH the diBcouMt on £200 12 6 at 7' <^ "" n'"-^^ ,■*" * 26. A note of $139.94 m pa^ble in 9 mon hi' ^' 1^'^>'.^'' « '" »r- ? worth, .liHcount being f,*?'^^ ™onH'^; wimi^istheprewni 26. Discounted a Jote of £76, payable in 4 year""' ! f'T \ 8uai shall I receive? ^ " m * years, at o,^; what i^^, *' ^'^ ""mediate payment ? \i;i. *„ in^ month, is allowed ? ^ ^^' '**''^ Ai^£\'^''Tlt^' «q?ikL*'''^ M*''*"'^ ''^"^ *^«* '"• *2964.12 readv money *fbr ¥3660.20 payable in lyr. 6mo. : what w.ll h. ...„ ,.„;„ . •_.' ."'•^' '""^ by oiscountinK at 8 at? 90 T 1 1 . ,1 '*. liat will be my gain, in ready monev Ana. $.i08.3^. ^ i ^ 32. I bought Hilkftbr $43713.60, on 15 months' 1?;iif'®£;f\ payiug before the time due, I will obtain 5 * ,1 scount hTwL ^ ? should I pay the debt, so an 1. disburse bur^i" illS" ' ' V.^:!^:'' ^ 33. A tlour-mill was offered for $2.5000 cash. ,,r for jftM^Tna ^ ?. « Ji*: ^<^"'« bought goods to the amount of £82 6A on 20 mn« ' credit; at what time did he pay, knowing that he oltk^ned i tTr,' count per month, and that he disbursed but £75 19 ? jLK^o .«. A merchant gave out two notes : the tiret of «'M'A« . i May 6th., 1867, the second, of $178.64, i^yal'elei^^^^^^ what^sum IS required to pay th. two notes^'ct. 1 utf^seeTisl^oum % ^^\' quantity of produce must be bought at Ss. ner Ih on 22 months' credit, in order to oar but £50 1 9 ini 4p- jH^f- ' the discount at 7 ^ ,' " ' ^ 5; »»s«?i acduv^iug .37. On 9 months' credit, I bsaght 120 bales of cotton p^^k v-.i w^glung 4881b., at 5Ad t\e lb. ^Selling a i^^ZSyVte^'l oaeh,^I paid my own d-bt, and r.^ved 6% discount ; Lw niuch did Ant. £390 8. '^ 212 ■AifK Dnoouirr. 38 I paid $320 for a sum 1 owed ; what w*8 this sum, knowing that f>\% discount was allowed ? Arts. $386.80. 3!). Paid £23 15 for 50yd. of cloth ; having received '> 9^ dipcount, how much did it cost me per yard ? Arts. Oa. ll^V- 40. Ih it more a fi montiia' credit, or at $6.50 on 9 months' credit, discount being 8 ^ ? Ana. Flour at $6.25 is the more advantageous. |i 1 1 ■ y .1 1) m BANK DISCOUNT. 374. A Bank is a corporation, legally established for the purpose of receiving and loaning money, and of furnishing a paper circulation. 375. Bank Notes, or Bank Bills, are the notes made and issued by banks to circulate as money. They are payable in specie at the banks. Obb.— A bank which iggueB notes to circulate ae money, is called ». bank <> ia*w»; one which lenda money, a bank of ducount ; and one which takes ohitrge of money belonging to other parties, a hank of deposit. Some banks perform two and some all those duties. 376. The Capital of a bank is the money paid in by its stockholders, as the ba.si8 of business. 377. The affairs of a bank are usually managed by a hoard of directors chosen by the stockholders, arid tho principal officers are a president, a cashier, and one or more teller^. Obb.— The president and oaahler sign the notes issued; the cashier superin- tends the blink accounts; and the tellers receive and pay out money. A lj>,nk eheok is an order, payable to bearer and drawn on the cashier for money. 378. Bank Discount is the simple interest of a note, draft, or bill of exchange, deducted from it in advance, or before it becomes due. Thus, the ha?ik discount on a note of $106, pay- able in 1 year, at 6 %, i.s $6.36 ; while the true discount is but &6. The interest is computed not only for the specified time, but for three days additional called dai/s 0/ grace. *^.^'T-L' "^^^ tlifferenoe betweeu bank discount and true diicount ia the same as the difference between interest and true discount. 2. The legal rate of discount is ordinarily the same as the legal rate of interesU S7». The Proceeds, Avails, or Cash Value of a note is its face or amount minus the discount. 880. Case I.- ■The face of a note being given, to find the ditcount andprotMtU, 1, knowing *3H6.80. 5l5y '•^« page 1S3, must be followed^ ^ ' "'' ** "^^hod of computing intertst, EXAMPLES FOR PRAOTIOB. •lioo^tS'r^o'da"^^^^^^^ Of a note of ^ 2. WhatistheprlintlrtLfaTo^eo?^^^^^^^^ pro. $989..50. and discounted at the Quebec Bank ? ' ^^^^ '' '" ^" '^^^^ ^. nesirintr to loan £9fin ,^<• a/ . i ^ ^n». JE1979. I aJd to o„,„plc.„ the „„„„„, l;Ee7 '^''.^""r?'^ """' 5. Find the d»y of mat.iritv M,. ♦• ^ j- ^"*- ■'•''-•^'^- ^ ^"^ + • of the following note.!- ^' «"»« of discount, and present value £40 2. Quebec, Dec. .3rd., I8G8. Bank of Quebec. ^ ^ *'"^ ^*^ shillings currency, at the «* ae Juoe s j 6 1869; tern, of disc. 64da. 5 pra, m 13 6^ + . rr.ji 214 BANK WSOOUNT. $10(50^^,^ Montreal, A.pril 19th., 1869. i i Ninety days afier ilate, we promise to pay C. Simson, one thousand »ixty-six and ^^{\^ dollars, at the Union Bank, for value received. Rappe, Wkbueb, & Co. Discounted May 8th., at 7 %, Ans. Due July 18 | 21 ; terra of disc, 74da. ; prooeeda, $1061.40 + 6. What is the difference between the true disco'unt and bank dis- count of .1950, for '^mo., at 7 ^ ? 7. What is the ditierence between the true discount and the bank discount of £2000 9, for 6 months, at ;^ %? tiH*2. Case ll.~ The proceeds of a vote being given, to find the face. A'.r. What i5< the amount of a bill, payable in 60 days, which dis- counted at a bank, at 6^, gives $989..0O for the proceeds? OPBRATION. Analysis.— Sinoe $0.9896 is tJio pro- $1.0000 oe«d8Ci'.i>l, the noteof which $989.60 is Int of $1 for 6^ davn 01 nr. ^^^ proceeds, mu.st be as many dollars as ini. oi J|>1 lor b.i days .0105 $o.9895 i« contained in $989.60. Honoe Proceeds of $1 $0.9895 the 989.50 -=- 0.9895 .- $1000, Ana. . 3^3. Rule. — Divide the proceeds of the note, by the proceeds of $1, for the time and at the rate mentioned; the quotient will b4 the face of the note. By proportion. IW - (6 X ;ft^) : 989.50 :; 100 : *= theface. EXAMPLES FOB PRACTICE. 1. What sum, payable in 90 days, and discounted at 7 * at a bank, will give £170? j^ns. £173 2 7i. 2. A merchant desires to draw $5000 from a bank, and for this Eurpoee discounts his bill, payable in 90 days, at G%; what should e the amount of it? ^ns. $5078.72 + . 3. The proceeds of a note, due in 4 months, and discounted at the bank, at (i %. are £407 18 ; what is the face of the note? 4. Bought goods at Toronto for the sum of $1486.90, and gave ia payment my note at 4 months, at 749J discount: what should V- the amount of the note? 4>M. $1526 + . 5. A merchant wishes to borrow $750 in a bank ; what should be the face of his note, payable in .SOda., allowing 1 % .lisoount per mo T 6. I gave my note at 60 days for a debt of £16* 1«; tf dtMount i* UK aMtUj, wkat waa tka fiMt •f Ik* »otoT T> iud the bank 216 disoounte^Cey^?" '"'^ of interest of a ooie payable in 90 dajH and ^r he given time and rate yields M Its proceeds $0.9845. Then, if OFKKATION. W-«« ^ 0.9845 = 0.06^, ^„.. _. intere«t*f* J? '.'"pooeeds $0.9845. Then.it « manl*' • S!'^"'; ^''•^S^^ in the same tiu. wi 1 viSiru ""'' ^''^ » "^^^ ny per eent. « the given rate, .06, oontaln. 984T ' '^"" '"'•"'*' '^ ^Jf proportion. VXAMrLlS roB FBAOTIOl. ^TWlf%- I- What rate of int«reMt in imu,^ -.u Ascounted at 6 5^ ? "* '* **•** ^*'«'» * note payable in 30 days is 2. A note payable in 2 moBtba .^ j- . , ^»*- 6,?*, ^ 7^f T ""^ *^« interest f^" '^ 7*^.?^ ^. ^'^o7ik , 3 A note, payable in 1 year, wasdigconnfj?"*^^^ annually. ^. 5. Whm was the rate oer amnt L-. . ^"*- ^^Ui- <£, 0. tvijat 18 the rate of interest Lm^JH j?^8V%, 12f«f jg. etc. «.-„., on . bill .„ i„ .oto.'IC^CX'ofl.l'^ '». '2« •MBATIOlf. A„.. '^-^ »0 day. + a d^. = „ d.y^ Int. for 93 days, • P»»oe*af »OmiOOOU8 MXAMPLiCti IN DISCOUNT. 'li «i^7* KuLE.— I. Find the interest and the amou7it of $1 or ^mjorthe time the note has to run. il. Dii>ide the intereet by the interest of the a':nount at 1 % for »M $ame time. tip proportion. 10# + (J4 X ^) : 100 :: 24 : * - 22^1*, Am. EXAMPLBS FOB PELA.OTIOE. 1. At what rate of bank diacouut must « not«, payable in 60 days, b« diBOounted to obtaiu (i % interest? Am 5UW« t.5„ « i '^l'*^ -^o* '""'^ * "*'**' ^"^ ^» 30 days, be di80ounted to ob- rWSn « r ''^ i""^* * °*'^' P^y*^'« •" 120 day.., be digested t„ obtain 8 ^1 mterent T Am 7 »<^»SJX■• •'"'^'x to $1310.25, P.41.:'r„1,jrt if ••'^"--ed Sept. T.h.,'^aro*:,l^„:-t1l-^eio, p4a■.??r^,S^f^ ^-"-^ Ap., ,,,., a„,,, ,f/,,»^'JJ-, pailFr^^al'c?'^-""-— ~?^lo&;»0, pa^:L,fr^*!ri;t^;?4f-'''"-^""--.-?;.--5«Ve, 21. OnMnroU ]9th ,' . , . ^n«. A2091 5 51 + . payable nL'V.M;hr^^^^^ •^•.> .7.' ,,-"*•' what .«uiii , lid I receive? /Itj,.? .*«92 54.fi 4- 23. The contr ct Z ^ tnlvr. \^ ' /''''* ^^'^ ^^* ^lut. of ihe bill ? ordered to do ext work for «I52J' if '"^ ^f '"f ^"'^'^^'^' ^^^ ^^s -a.^0 that e.e co^^^r^l^^.^^^^^ -— ^l!: diec'ount being oi^TaVr;? '^' "'"^ '^.l'/ 1^^,« ^'''H -^«' 25. I owe the sum of If -> 1 4. 22 as follows •«';n^^9 . 1 • f ."*" " ^'. vvjiat IS the present worth nf -kTkq «n j. ^u "^*^- 10 -'5. hence, at 6 ^ ? ^ #769.60, due .^ vfara and 5 months 14 « ':li ; ' ''M I' I lit only £98 • dhi T .-Thtlf ?■ . ^^' **^® discount amounted to After 16 montKl^lSfeO a^^^^ %^rr"' '^f »*• remainder, knowi„g^hH^l'dl!ied\S^08:5lvered benSr, Jn. iT 1'*? '"^^^ purobased the makincrs of 8 V^ n^-t' f ^ ^*yd. lor each, at $1.80 per yd.? A #(i6'\7< -u STOCKS. 8S' •*«''' ''"' ««"' $1.06 By proportion. 106 : lOO :: 7 : *. div^:;d';nrwSwt 8"'^'t'™h^^^^°^ -d ---•d a did he purchase? '^ "" *^'« investment; at what price $0.0* -h •PERATION. $0.08i=$i08, .4n*. ^iu», the purohase prioe. By proportion. 8i : 100 :; 9 jr. share, of ^0 eL, a S'Ztl'^MWdS'iSrrr?"' "^ T^r"' .de^J will he receive a„„„all/? "" '°°'' ^* jtT&r'Vi' i"" IS. If aoo shares of ihe Oitow. Bank sell f™ .^nnilj I *' ■ the pren, um, e«>h share being tlOOf A^ ^1 """" " _ 14. When the nominal ™loe of .took is ^ei •) iTJ ?.f "'""""• is $100 per share ? '"'"" "" "'""'"''' "»'»' "f "I'ioh 1«. Bonghlwock at par, and sold i. »i 1 a . ^'" "-^ 'Im 3 '«r 3 1 t*^ yh 222 !' "^^ •■«*"'«^o*l bought, at the rate of $188.76, a namber of ekares in the Pictou coalmine company, the annual income of whicli is $10 per Hhare. With the income he purohases $2(;0 wortli of .'ooWs ; wiiat was hia mve8tiiVprfl ,« K ^\% Ana. $6,923 -f ;e oeisg ai. A banker owba 150 shares in the Quebec Insurance Company nkWPNUlflHTP. 2]f Charge rne ' «i I ?i,^ "*?,*"" *^» "»«, >cnewiHK th*t the a.-.-nt w,., 32 % fl " * ^''"."^^'^g^ / .In,-*. «1 5966.26. he buv. fc' 4Vi1 °*'? ''"[ ^'l" ""'^""^ «''*'*^ •*'•'*'>• ^'^1' ihiH «un, m*" an! ..!« -^2 . / '''"*^' produce an an.nial incuiiKM.f $18, at ♦kJ*' *?•' •"« -^^ hoiKls, pruduch.K annually -^20 at 64 J « With what av*rR«« J-»^ I. ?V ^^ *''^''' ''® ^".^^ '^ ^ '«»"'» at 68i % ■ at 33 Tm h..l^ ^ '^! *.^* "*'"* quantity of rerenue ? Ana. $98.43 + 110425 a? S^oTrlt'" **^*. ^^r^-^' ^«'"P^"^ <*"' the value tf • ferm'er se^ur/ 1 ' '*"'* Producing $H6 for interest and lividend, oflheik^r 1 • "''?"• "'Z*'^'*^- ^»»'-«"^ the market valu« or me stock per share, and at what rate he let out hi. money ? 34 In J.n iQ..a ^ ^n§. lst.$6\}5; 2nil$5.?i'.//j. £37801 9fl'ifi™?'^» 1848, the total amount of British con ho Is was annually? ' ^'•*^ ''«« t^e amount of interest paid on the,,. He,„i. belt tt''9Tr*:'t''" ^"" V''' '' ^-^-*' 7^Tih1 mISt Miue 95uV whlt^r.i» TJ^u • ^T '^*-^'' '°"«^' ^h^n stock risea to teinerl i:.Jm * i^ *^"^.^* r*»'*«*^ ^^at los. would he have nua- 36 A mi'o?h „-w Q«- ^ ^r- *22.75 gain, and $17.60 loss. deHires to in3 M ^'^ '^'■^^- ''^ * ^*" ^^ «21.80 per 8q. yd. He interest aJddivid^'n J '^^ •"*' *^^^^ '^^^ ? ^^"-'^ P'^^^c^ *200 as Kdence Pn th \*"'^ *'" "/r^'*'*^ "^ *« * pren.ium. In the Sar?dd,V?l.,H '*'T'^'"'^^^^^**<^^' they produce $50 as in- tt7nK?s adlaS ^"^ *"■! "^gotiated at 45 ^Dremium. Which are he Drclm.l?n at "'iu*"^ ^y ^^'^^ '""^l* ^ i* How ,„any shares can he s^ c« e r ^« tT **Jf T'' advanUgeous, and what revetiue could 3 aEs^'andlSo'^rrevTnuT ''' """ -^vantageous by 1.478^j il PARTNERSHIP. 401. A Partnership is an association of two, or more ner ions ,n busmess, each of when is called a Partnrr Suda an^ vocation IS called a Oompan,,, Firm, or HoZe! ** 402. Cask I.-T^o/.^.a./^ ;.,h.V,. .,Wa o/ the profit or A> O'fl Whole 8took, $276 " 475 " __ r>oo OPIRATIOV. f2T5 X 0.12 - I 33, A's profit. 476 X 0.12 ^- .07, IJ'm profit. .OOO ^ 0.12 - _60, C'h profit. Pr-.of !«!ir)0. ACliole profit. 1250 - $0.12. pmlii, ,)n$l. Akaltsib.— Since I ho whole atook i.i'flJSK, dti.l ilm wholo i,rofit. $151), the pro It on every $1 of«t„ck vTillbo as many .ioll us ii.s 150 contain-, tiinon 1250, or *U.I^ on every $1 of stock. Then, each merchant's stock niulti|>liod by .lli jfives oi8 part of the whole prolit. The s-ame result ul.so may be obtained, as follows :— By proportion. 276 i + 475 J =: 1250 + 500^ 160 ;'.i75i (!?:«, A'spr 475^ : .r = Ans. < 57, H'n. pr 500) ( (iO, (."^ pr 8 profit. .tit. ■ofll. Proof, $150, whole profit- 40J$. Rule. — The whole profit or loss, divided by the number denoting (he whole stock, will give the profit or loss on each dollar of stock; and each partner a stock, multi plied by the number de- noting the profit on 81, will give his share of the whole profit or lots. Or, As the whole stock is to each partner's stocky »o it the whole frofit or loss to each partner's profit or loss. II I EXAMPLES FOR PBAOTIOB. 1. With £200, two men gainai £50 ; the flret man contrlbuaa £125, the second, £75: what part of the gain is each entitled to? Ans. The first, £31 b; the second, £18 15. 2. Four merchants ap.suciated and rallied a capital of .^145000, to which each man contributed equally. At the expiration of the part- nership, the capital was found to be augmented by $20877. What •ball be the part of ea^'h man, knowing that the Ist. ought to have 13 parts; the 2nd., li ; the .3rd., 8; and the 4th., 7? Ans. Ist., $23959; 2tid., $20273; 3rd., $14744; 4th., $12901. 3. Three men associating together, gained £287 10; the let., put in 400 yd. of velvet at £1 per yard ; the 2nd., 350 yd. of cloth at £2 ; the 3rd.. 450 yd. of cassimere at ISs. ; what part of the gain should each have? ^ -4fl«. £80, £140, and £67 10. 4. Four persons having joined in partnership airree that the ! wt. put in £1250 ; the 2nd., \ more than the first; the 3rd., as much as the two others togetiier ; and the 4th., his industry during the vcar, which' was estinoated at £2000 ; what share of the profits, £1625, hliali tMk reo«ve? Ana. £260, £312^, £6«24, and £400. PAftTNRMHlP. 826 eachn-ceive? ' j„ i! '' IL^-' ^- H"w much will . 6- The firnt of five ,„en a^.^" l""' ^•^'•''*' '['^''i' '">'' *■•'»<'• oiiii; am ho on witli iJ.n ', ""^•' ^'^^' """'i' than tlu- «i,c 7. Three «pt.culaU;rH hav« t^«rl?t'" *''^*^'^' *-^^'*' **^''"' *■<'"'' *»-'^-'- fc'am, tAe 2n.|., $206 and the 3rd ftLt. w.'' *"' ''"*''^' "'' ""^ voyage 6:>(.\o,.sw.rrtl XoveXaH °*''" ''' ^'"'^'^- ^^'"-'"y ^'"^ arofle. If 250 ton. were Zi led 1. *^" accm'"' of a storn, which J. -i^nree ta?inerM h^nvlif i^u ^i «. ^nw. oi,} auii .i7;> tons. each receive ol' the profits? iJ«/!oi'^'''' ' '"'^^ '>'"«•' ^'i^l the second" £527 6 104 the thir I , '-"*" «"»tr.buted £400 lA 7*; received, however, £98 I's il: hi T"^ P?'"! >-^ "^t known, but he contribution of th; third nerclt^ru t^^'? fl '''! T ''^^^^ '^'^'" "'^ 'he the price of the -'aplingspr hundred ? ^ A *^%1"^' "'^''"'' «'« share £494 I 3. Tl,: pK of l!. ^c-, » ^f'-Jhird .Merchant's £\IS 9 per hundred!^ '" ^^^ ^ ^i' 2nd., £105 9 4^; and' JvTr Bkt:;;' £U2'?S'LVirn;^ ''' ^^^-'^^ fox £ 18 10 more than the second ^L T fi^ '' "i^ ^''' ^^'^'" *J^a"ced ISfton the buying pr!<^^^^^^^ a profit of gave, and the third fJ^„i«hed*o?^lltrf ? ''^^''"' ^''^ ^-"^^ wha^^w^thecontributio„7eL^'''r$^^ that the 1st. fuihed ^^^Sit"" : 'tS In'd' T^-^rh ^"'^-"S not meniioned, and that the ?rH ?,?, u , ".' f"f'"-^he. Exchange is the process of remitting; money from one place to another by Drafts and Bills of ExchariL'e. NoTR. — For a full treatment of this and of the following anbjecu, •«« the Com- meroial Arithmetic. F* ot»»er two are worthlew. Eaoli draft the old pnr of o..ha„.e. inS „f "'thLew pt'" ■*' ""'^ °° was fixed at f4.866. NoW tho ,«,« « ° **'.'.*''® ^*'"« "^ **>» PO"nd sterling old par, thatl;.*4 ^44 I 9 ,v XflU' "H^t'-*" '^^ "''^P^'' P''" »* ^^ of thi fJreat J^ritai,}. must reach the nom Lrf^Liam or Si T^T\f- °'^°'^» ""^ cording to the new standard. ?««»>"«, or 9^ % before it u at par, ao- for the bill of eX,^L? * premmm. How mnoh must h. pay OPERATIOir. $V X 1.11 =$4,931: £.j60 3 6 = £o()0.176; £560.175 X 4.93i = $2763.63, J^n», ANAtTBig.— .Slnoe th* old par •f £.\ Rterlins >= $4,444 or $^, we multiply $^0 by 11^, •r$1.11, the giTonrate, deci- mally erprewed, and we obtain rate ; multiplying the faoe of the bilL :£fi«0 1 A }^^\ *' °*** "^ ^^ *' ''"'^ rORHON IZOHAiraB. <,ll I Ex. 2. What will be the fao« of a bill of exohMiff* on Lirerpool, purcbMed in Montreal for 95537.40, «x«b«ng« being at 1 ^ premium t OPBBITIOH. $5537.40 *:- 4.88| ^ £1133 IS t. AxuLYvn. — We find, as in the preoedin;; example, tbe oost of £\, »ttbe ^Ton rate of exchange ; then we diride $55S7.4I, th» {pren cost, bT the oo8t of exohange for jQ, and oMafa £1132 IS 0, the faee. ^x. 3. What i« th« oost in ToroDto of • WU oa Paria, lot 1780 (htaoa, tJMkange being at 2) ^ dinooantr OPEBATIOV. CSonnMrcia) value of the fraoo, => ••.IN IMnot 2^ % diflooant, e.004M Valuf of 1 fhuM, ....... $0.1818* $0.1H135 X 1780 s $321,803, itiM. 43S. From these illustrations we derive the following Rule.— I. To find the oost of a bill, the faoe being giren.— Mwltiphf thtface by the cost of a unit of the currmcy in which the bill is expressed. II. To find the faoe of a bill, the oost being given. — Divide the pnen cott by the eo$t of a unit of the cwrren^ in which the bill i$ Co be expretned. RsDUCTioN or THE Stbrlino Monbt to thk Old as to TH« New Oanadian Ourrbnot, niw par. '. fiodttoe £500 3 4 nterliug, to Old Canadian CurroiMy. Amaitsib. — The pound ■torling m, $i.8«§, and the Old ourreBO|- peand ib $4; diff., p.8«}. Then £1 stcr. ourreney. JS«w, ^ of a num- ber =^ plu£ ^ ef J of that BBmbsr. Hesss the •PiaATlOK. £560 3 4 4- 4 of £560 3 4 3: US 8 + J^ol 112 8 - 9 6 8| £081 10 81, Amt. Aad in Decimal Currency, £081 10 81 (233) = $2726.131- 4SS4. RuLB. — To reduce tteriing money to Old Canadian Curroney, new par, — Add to the fivm $um iti fifth pitu one tmlfikofihefifik. I Uyerpool, i premium ? od, as in ^he the ooBt of £1, cohange; then th» girtn cost, Iff* for £1, Mid the fa««. M. for 1780 ■QUATION OF PATMBIfTt. BXAMPLEiS FOR PRAOTIOB. S38 ring »g given.— / in which —Divide the h the bill is LD om TO A. — TIm pound .8«i, and the p«and _ $4; Then jEI stcr. - Xl^ oJd «^of anum- >^ «r ^ of that ss tks i Oauadian 'h pltu ont « t/pi:S ^ ''' «°"' '" «-"*' "f « k^°» B°^ "., for ,2000, 35 Ota. ? '•*'''* a^ve par, the mai-c banco being equal to on Lyons amounting to 49S36 fr 20 Inf """ i""^«oy» ^r a bi" txohange below par"? ^^ centime. ; what waa the irate of 10. Received from L. Nelflon * r« t j i .'^*'** *0-053 + . £381 5 0, o« J. Chllter.'&'Sot Qu^l^^'^iLf i«1Ll:i"'""^^ ''"^ mal oonrencj of Canada, at 9 5« preTnS ^'CimoS + !'' BQUATION OF PAYMENTS be^™*d«^ ^""' ""■••""* '' "■' •^"» <» "•[««= before . deb. onoe ,rith»at lj.s to debtor or ereditor! ' ^ ** ''"'' " de?tf*./b^^frrb7XV-r """°'' '^^ ""-" i % i I I 1 ^ ' s * i 11 ' 1 " 1 f ■ 1 , vf ll TP '. i '.' '» ; a ! i i 'f, I. '! > 23* laco 300 ■QUATIOM OF PATMVIfTS. •ra&ATioM. X 30 = 7500 X 60 = 12000 X 90 = 27000 46r)00 9750 41600 -*. 750 = 62da., ayerage term of credit. March I + 62da. = May 2, Ans. the interest of $1 for 7500da. -\- r^uOOda. -f 27000da. — ,,,«„ «„ Jl nquire 46500 days to gain a certain sum, $260 -\- $200 + $300 AwALTsn. — The interett ef 9SM for 30 days is the same u tlM interest of $1 for 7500 days ; ud of .^200 for 60 days, the saue M of $1 for 12000 days; and of 9390 for 90 day., the same fts of $1 for 27000 days. Hence, the interest of all the suns to the time of payment is the same aa '" ""^ 4(i000 days. Now, if - ,- „ ^- , ,— , $750 will require ^ of 46600 days; 46 JOOda. -;- 750 « 62 days, the averag* term of eredit; ana, Maroh I, the date at which the orodits begin, -f- 62da. ■» May 2. the equated time of payment. E:c. 2. Bought of D. I. Lyons several bills of goods, at different times, and on ▼arioua terms of credit, aa by the following statement What ifl the equated time for the payment of the whole ? Jan. 1, a bill ainountiug to $1^00, on 4 months. Feb. 7, " " " " 185, on 6 months. March 16, " " " " 280, on 4 montha. April 20, « « << <• 210, on 6 months. Due M*7 1, July 7, July 16, Oct M, M OPBRATIO*. $300 X 6T X 75 X 172 12396 21000 .36120 69515 days. «»516 -i- 915 = 71^ days. May 1 + 71 days = July 11, Ans. Amaltsis.— We first find the tim* when each of the billi will beoome dtw. Then, since it will shorten the operation and not change the result, we take the flr»t time when ply its amount by 67. Proceeding in the same manner with the remaining bills, we find the average term of credit to be 71 days, and July 11, the equated time of payment. 4t30. KuLG. — Multiply eadi payment by its own time of credit, and divide the aum of the producta by the eum of the pay- ments. NoTB. — If the date of the average tia« of payment U requited, at in Ex. 2, find the time when each of th» »tim»oe«ome» dme. Uu/tiply eaeh ntm ky the numbm' mf day* intervening between the (UUe o/ite beooming dine and the earlieet date ^ • -*•». Hmo. 24d». th, «p,r.t,on „f « ,„i„,l,8, ,h.|| I „,eth'. baling ?^ '" "*""'■ "^ OPKEATION. 30 X 4 = 120 *0 X 2 = 80 ^, 70 200 „^, •I80-$70 = $llo. 200-5-110 = lmo.25da.,Un*. AiTALYSM.- Iha i,tere8t on the 230 f«r 4 month. >. .,„., eo the intewsrofjl Sf 12« months, and the int . of $40 for Imonttl U .4ual to that of iil for 80 mo„thf- an^ Jaa the .nt on both PHtrnZymlnts^ To equ , ,,,, ereSu otintl"fb"arrf fe main unpaid, after the 8 „oneh. ^ ,^^0 t'^lr^l^^tt ^ce r.n.nmn, un^ii ; and tHe V^ui^itt: J^!^ RXAMPLES FOR PRAOriOE. ^ equated time of the b«kiM«- '^ for «33 gal. Required "'*'^ iiMt 12 na 22 d». fs^ I ,!, t36 ALUOATTOW. i;if ( 1(1 • I 2. Bought of C. Lyon«, at 6 mo. £432 worth of goodn ; tX the end of 1 1110. I p»u\ him £7r^, ami 4 mo. after £200 more. How \oug after the t-xpiration of the 6 mo. nhoulii I paj the balance? Ang. 3 mo. 20 da. 3. A grouer bought $2829.75 worth of coffee whicii he desires to pay in three diiUrent paynitrits : the drst is to the necond aa 4 is to 6, and tho third is etiuai to iialf the second. The first paynient should be made in 4 mo. ; the second in 7 mo. ; and the third in 1 year. Hut at the end of « mo. he paid $975, how long can he keep the balance? 4mji. 7 muo. 18 da. 4. An undertiiker built a house for £f/0.35 payable in 15 mo. ; but being in want of nome money, the proprietor pays liim £2847 10 eight monthH before the time. How k)ng, in equity, can tlie proprietor keep tke balance to compensate the advance he made the undertaker? Ans. 22 mo. 4 da. 6. Andrew havuiji; tuAd $8400 worth of linen, at 12 mo. credit, received the ^ of the prio* only 15 mo. after. Wl en did he receive the I ? Ans. In 10 ino. 15 da. 5. I owed $6U0 al i;^ months; I paid 'i of this sum before it was due, so that I can ki ep the remainder 2 years without -njuring my creditor. Required liie time when the | were paiil ? A. '/mo. 15da. 1. A trader owes $3000 payable in 6 mo.; $4500 payable in 8 mo., and 19500 payable in 10 mo. At the end of 5 mo. he pays $12000. How loBg can h» keep the balance? Ant. 17 mo. 24 da. ALLIGATION. 4S3. Alligation treats of mixing or oompouudinji, articles oi ingredients of different qualities or values. It is of two kinds — Alligation Medial^ and Alligation Alternate. ALLIGATION MEDIAL. 434. Alligation filedial is the process of finding the mean or averaze rate of a mixture composed of articles of different qua- lities or values, the quantity and rate of each being given. 439. To find the average value of several articles mixed, thi quantity and rate of each being given. Ex. A grocer mixed 2cwt. of sugar worth $9 per cwt. with Icwt. worth $7 per cwt. and 2cwt. worth $10 per cwt. ; what is Icwt- of the mixture worth ? Analysis.— Since 2owt. at $9 per cwt. is worth «1U !«.i?f ot *7 i%ap «wt- ia worth *7. and 2cwt. at |10 per cwt. is worth $20 ; 2owU + Icwt. 4- 2cwt. =o 6ewt. IB worth $18 -f $7 -|- $20 -^ $46 ; and Icwt. is wocth M maay dollars a« 46 •rataiiu tinMi 6, or $9. OPERATION. 9* X 2 = $18 7 X 1 = T It % % = M 1 4) ia AXJJOATIOII. 237 How louK D. 20 da. he denires jnd afl 4 is t payment third in I %Q he keep ). 18 da. n>o. ; but t7 10 eight rietor keep taker ? no. 4 da. 310. credit, he receive 0. 15 da. ore it was juring my ID. 16da. e in 8 mo., ya $12000. 0. 24 da. articles oi > kinds — the mean ■erent qua- on. nixed, tht vrith Icwt. is Icwt- of owt. is worth 7. and 2cwt. ffU + Icwt. 57 + $20 ^ loUuB u 46 di^L ^""''"--f ?^ '*« ^«'"* 0/ each of the article,, and fhTnJ^ ""tf '^'^.^^i^ h 'f^ ^'umhe, denoting the mm of ihe arttcies. Tht q,u>Umt will be the averagt value of the mixturi BXAMPLB8 rOB PRACTICE. 1. A farmer mixes together 10 bush, of oata at 40 cts ner bu 15 bu. of corn at 60 cte. per bu., and 26 bu. of rye atrS c.f per bu • woat .8 the; -alue of a buHhel of the mixture?^ Am 58 cts ' 2 If I ,n,x 20 pounds of tea at 70 cts. per pound with "5 ^und^ at value 01 1 lb. of this mixture? j^„g 4. j<, , rXn J;I J • f • " ^'?"; *'"' ^^ «»•• •* *^-10; how much IH a gallon of the mixture worth? ' i^. «o 7' i 4. A man bought :i| dozen of eggs at 12 cts. a dozen, '4 doze"' at lOi cts a dozen 4^ dozen at 1 1 cT.. a doz., and 5i doz at 10 en a h^rec^vVpt dte": ^ " *° '"^'^ ^^ ^ ^» '^« ^'^ ' J^ -,-•" '^ fl ^" A.^'^J'lu'"^"' '^' ^®^ *<^ compound 3 lb. 6 or. of gold 2i clrata fine with 4 b. 8 oz. 21 carats, .3 j'b. 9 oz. 20 carats, aniTib 2 oz of alloy; what will be the fineness of the composition? ^n*. 18 cara?;. ALLIGATION ALTEBNATB. 437. Alligation Alternate is the process of finding the proportional quantities to be taken of several articles or in-n- diente rt"o?;ui; ^"^'"^^ ''' '"^^^" '^ ^°- ^ "-^- ^'^^y^ in^^dtnf^L-^^'lj.^^ i>ropo./tona/ quantity to be used 0/ each ingredient, v>hen the mean price or quality of the.rnixtaro. is given. »nf Sover I^ed^lorth'J? T h"?'f «'"*'™«t»^^ ««^^ -orili s2 a bn.hel, wortr$5 a bushd? ''""'' ^"''^ ''' ^'"'"'" ' "'"'"'••^ OPERATION. mini'-- ANALTSig. — Since on every ingredient used whose price or quality is lest than the mean rate thero will be a gain, and on STery ingredient whose price or quality be a loM, and eince tho ./nin. .r.w 1 " ^«'"e'' than the menn rate there will quantities used of each a bfsur^^^ be exactly e,,ual. the relative one bushel of ti.nothy seed lrth%2 ft%r?h?r!"^ "■^^ "°'' f Vo^""'- ^^ ^»'"S $1 would require 4 n^f/bu-h°r"hf;Hli^-*''™''^..S^^^ "^f^^-' '^"'1 ^« «•"» bushel of closer seed wor«i«7'f;,-?rif''"''""fP"'" ^**" ^- -"^ «eiiin- one -quire i Of a°bua:;K'e';;^i .ij;:^;: ^b?; ''' *' ' "'^ ^ '°^'^ *' -''••^ •••d. V.0 take iTa btShel offllo^; V'^r* ^'^ '**'"' * of a bushel of timothy :f '.ail III 288 ALLIGATION. |i ' J 2 H 4 5 :\ 1 8 4 4 4 ^ 1 1 7 1 2 2 [ 10 i 3 3 i7;r. 2. Wlmt proportions of ooffeea worth reepeotiyely 3, 4, 7 and 8l.illings u puixud, must be taken to form a mixture worth 6 shil- Imgs u pound ? oPKftATloN. Analtbm.— To preserTe the •quality of gu'DR and Iomos, wo must alwayncotn- piiio two prioes or .-iinplee ino greater and ono /««« than the uieanmte. and treat eaoh pair or oouplof, as a separate ezaiu- plo. In the given example we form two couplois, and may compare either S and 10, 4 and V, or ;i and 7, 4 and 10. We find that J of a lb. at 3i. must be ,- . , , , taken to !,Min 1 ghilling, ami i of a lb. at 108. to lose I shilling; also j of a lb. at 4b. t.. gain 1 «hilling, and 1 lb. at 7u. to looe I shilling. Thooo proportional niunbc^ra, obtained by comparing the two couplets, arj placed in column,.? 1 and 2. If, now, wo reduce the numbers in columns I anil 2 to a common denominator, iind use thoir numerators, we obtain thu intPgrnl number.- in columns 3 and 4, which, being arranged in oolumu 5, give the propoitionni quantities to bo taken of eacH. It will bu .^con that in co!ni)aring tho simples of any pair or couplet, one of which IS gi-oatcr, and the otli^i- loss tli.ui fho mean rate, the proportional number hnally oljtiimctl for cither term is the diirrronco between the me'in rare and the other term. Tims, in comparing :', and 10, the proportional number of the former is 4. whrh is the dilFerenoo between l(» and the nionn rate 6: and the propor- tional number of the latter is ;{, which is the dinVronce between .s and the moan rate. The same is true of every other couplet. Hence, when the simples and the mean rato are integers, the intermediate stops taken to obtain the final pro- portional numbers as in columns 1, 2, 3, and 4, may bo omitted, and the same results readily found by taking the difference between each simple and the moan rate, and placing it opposite the one with which it is compared. From the foregoing examples and analyses we derive the fol- lowing 4311. Rule. — I. Write the several prices or qualities in a column and the mean price or quality nf the mixture at the left. II. Form couplets hy comparing any price or quality less, with one that is greater than the mean rate, placing the part which must he used to gain 1 of /he mean rate opposite the less simple, and the part that must be used to lose 1 opposite the greater sim- ple, and do the same for each simple in every couplet, III. If the proportional numbers are fractional, they may be reduced to integers, and if two or more stand in the same hoH- zontal line, they must be added; the final results will he the pro- portional quantities required. NOTBB. 1. If the numbers in any couplet or column have a oommoa faotor. it may be rejeoted. 2, We may also multiply the numbers in any oouplet or column by any mul- tiplier we choose, without aflFooting the equality ot ifie gains and loises, and thui obtain an indefinite numbar of resulte, any one of which l>aiDg taken will aire a eorreet final result. li 1 .. ' 3, 4, T and irortb 6 8hil the equality t alwayBcotn- I ina greater I lite, nnd traat parato eznui- we form two cither S and QdlO. ; 9(. must be d i of a lb. at I 1 lb. at 7,j. jra paring the the Dumbortt nieralors, we ij;od in oolumu jplet, one of :ional number rare and the of the former the propor- .ud the moan simples and bhe fanal pro- nd the same and the mean 76 the fol- ilities in a ! the left. / ?ess, with Kirt which 'ss simple, 'eater sim- ey may he \ame hoH- be the pro- V}* faotor, it t)jr any mul- let, aod thus I will glTc a ▲LUOAnOM. BXAMPLEH FOB PRAOTIOS. 1. A grocer ha-s Mu<»ar» worth 10 cents, 11 centn, and 14 centH oer P'T Ur U v''" ■;''"'"? u'"'*^ he mix them toforn. a >...xt„re worth -. VVhutpr.)portion«ofwateratno vaUie, ami wine wi-rth $1.20 a gallon, nn.Ht l.e .i.se.l to form a mixture worth 90 centH a gal- V \ ♦•... . 1 u i^' ' "*'• «»'■ water to i^'al. of wine, ■i A Jarn.er had sheep worth $2, $2^, $.{, and U per heagre-^ ^^bor; the ,„an n.a.y days d,d eacTh lab.r ? ^ AnsVhl.nl ' ''rHpectively ; how boys 24, 4, and 12 daya respectively " ^^ ^^•>'''' ^'"^ the INVOLUTION, many times it is used to produce the powe?-^ ' ^'''' ^'^^ Thus, \ 3» ^ = the first power of 3, or the root. " 3 X ? ^ ?' ^'*?,f««nd power, or square of 3. .(I) - i X i X j X i X j = ,«^, thefitih power of|. Menw, from th.M iereral powers of 3. we derive the following 447. RvLJi.— Mult iplu the qiven nwmher h,, it^^lf ^- 1* Square 25. 2. Square 79. 3. Cul)e4r. 4. Cul)e 39. 6. 24* = ? 6. (1.2)6 = ? KXAMPLE8 FOE PRACTICE, Ans. 225. Am. 6241. ^ns. 103823. Ans. 59319. 4n«. 331776. i4«*. 2.48832. 7. (1.06)* = ? 8. (i)» = ? 9. (5)3 = f 10. (2'^)* = 7 11. (lf)« = ? 12. (2J)» = ? Ans. 1.263476 Ana, A /"»• m Am. Soif, Am. 167*^* 44S. Evolution is the prooeas of ertrfl«.t;no. ♦!,- * « ° «»" The s;tr„;.r 7 ^« '-'--■-ftv„r«r • M2 SQUARS ROOT. 451. The Second Root, or Square Root, of a number, u one of its two equal factors. Thus, 4 is the square root of 16 = 4X4. 453. The Third Root, or Oulie Root, of a number, is one of its three equal factors. Thus, 4 is the cube root of 64 = 4 X 4X4. 453. The Radical Sign is the character, V, which, placed before a number, indicates that its root is to be extracted. 454. The Index of the root is the figure placed above the radical sign, to denote what root is to be taken. When no index is written, the index, 2, is always understood. 455. The names of roots are derived from the corresponding powers, and are denoted by the indices of the radical sign. Thus, V 36 denotes the square root of 36 ; ^/ 36 denotes the cuhe root of* 36 ; V 36 denotes the fourth root of 36 ; etc. 450. A Rational Root is a root which can be exactly obtained. 457. A Surd is one which cannot be exactly obtained* M,, SQUARE ROOT. The roots of the first ten integers and their squares are i 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. 1, 4, 9, 16, 26, 36, 49, 64, 81, 100. KoTM. — 1. It will bo obgerved that the second power or square ofeaohoftht ■nmbers ouatains twice a* many figures as the root, or twice as many wanting sne. IJence, to ascertoin the number of figures in the square root of a given %nmheT,—Btginning at the right, point it off into ng mnny perioiU ii$ poBtible, of Iwo figures eneli ; and thare will be as manyfigweB in the root at there are jperiodt, 2. When the given number contains an odd number of figures, the period ai Ifc* left can contain but one figure. Ex. What ia the square root of 40M T oraaATiov. 4M«I 64, Am. 1S4 y. Analtbu.— Beginning at the right, w* 8«f •rala th« number into periods of two figures aaoh, by plac« Ing a point (.) over the right-hand figure of each period. Now, the greatest square of 40, the left-hand eriod, is 36, th« root of which is 0. Placing the fl oi I right c^ th« aomber, we subtract its square froa the period 40, and to the right of the rennainder bring 4own the next period. We then double the 6, the aert of ths rod aire^* found: ftsd^ pl^u^inir i| on the left ef the dividend for a partial divisor, we pereeif* tt is iTtrieiMJ la the dlvUlend, (oautting its right-hand figure), 4 times. Plaeing the 4 ea tke right df tba Not, ako eo the rigtit of the pnrtiRl diviaor, we multipiv (he diviaer thM ooaiploted 1^ 4, aad ■uMrMt the piodaet fron the iivideaC fhe reel or eaevethiMt 49« 4M ms lumber, is tofl6 = ber, is one 4 = 4X jh, placed jd. above the I no index esponding n. Thus, he root c^ )Q exactly led* ire: 0. 0. f eaoh of th« tiny wanting it of a given • poBiible, of are jieriodt. le period t4 IT* ssfiaral* toh, by plM« ure of each ,he left-hand oingthe 601 equart from ainder bring I the 6, the ificr 11 on IMc wfl pareaif* lei. PIa«iDg «• multiply le divideiM. fefeps^^ia& 243 figu^rs each counting from units' place tou>ard the. Inland right. wrtte Its root on the right for the first figure in the mot. veriod n.J7''!i *^"'"T ''^^^' root figure from the left-hand JV' n 7>7 r ''^«»"^^^ '"'"«»: ff^e next period for a dividend. and\:.r ^""^^ "-^ '*' "'"^ "'^'^^V /««"^ f'>' ^ (rial divisor, TftCri2rjJ''^'' *' *f ^•""'^"■"'''^ '^ «^' dividend, exclusive of tZ Z^M-hand figure, and write the quotient as the next divisor 0/ the root and also at the right of the trial dimmyr. vTJ' T^ '^^'"'"■'^ ^^' product from the dividend. ^ continue in /At« manner until all the periods are used. • after all the periods hare been brought down. be decimals? ^ ^ *°""'^' '^"'^ ^''^ fig'"-"' "^ »»>« '^ot thus obtained riH root^■!«'lrS°i^t{^o^'Ii'"'*''™^^^ * *^°'« °"'°»>" «°d a decimal, v*,. > point over every^cond hVurl ^^"^Tv,""" ^,!'^'^" ^^^°'« °"'°»«^' ^ P»'«^ ««} period, if IncL'plS with" '^rphS *'' "^''' '"" ''' ^''P"'*'"*' ^'""« '''• .qLe r^JtfonhrnulraToTnT [^ """ T' '^ "'''"^«" ''^ "'^"^"^^^ »»>• KXAMPLES FOR PRACTIOB. I. What ia the sqaare root of 133226 ? of 62.8 T % X % 3x2 66 X 6 36 X 2 726 X 6 X 6 =r OPKRATION. 133226 ( 365, Ans. ±_ 7x 6 6 ) 432 7 X J96_ 14.9 X 72 6) 3626 7.9 x .2^15.82) 3626 15.82 x M =, ' r = 2 -=14.9)13:80 .9- LS.41 OPCRATIOV. 62.80(7.92 + ,4. 49 .3900 .0104 T0736" .T^,i'«ii%'s;i?',oTL'';,'fr_.".';,,"" •"■. '^^r „, ,4«, , Of 3249? o<-40»6? of 6329 7 of 6724? or 9801 ? ononis ? 13, 24. 35, 49. 67. U, 4 I ^'•^^u^iimi^^js:ti^^Ajimmmm.-'.->>^» tM SQtTABS BOOV. h ' 1i i 1.* ill 1 i I ;' J I II .1. • K t 3. What i3 the nquare root of U1009? of 454276 7 of 605621 ? of 637821? of648132V of 738417? of80»aij? m 927748? of 977137? of 9999[)9? Ans. 247, 674, 711, 798, 805, 859, 899, etc. 4. What is tl square root of 234.09? of 5.4756? of 17.3056 ? of 256.6401? of 0. J24 ? of 0.120409? of O.O0008836? of 609151. 761 GO? Aru. 15.3, 2.34, 4.16, 16.02, 0.32, 0.347, 0.0094, 780.481. 5. What is the square root of f? of fiw^r? of ^AA, ? of 60J»? of ^? off? of28||? ofjf? ofWJf? ofSsVir? Atu. 0.86602 + , 2^. ^, 7|, \, 0.7746 + , 6|. 0.868 + , 1|» 'I- APFLICATIONS OF THE 8QCA.RE ROOT. 1. Whnt ip the lenjjth of one side of • square (ami •ontaining 98 •cres? At%8. 120 rods. 2. A certain general has an army of 141376 men ; liow many must he place in rank and file to form them into a square ? Ans. 376. 3. A company of persons spent $75. «9; each Hpeiuhng as many cents as there were personp in the company. How nuich did each exiiend? AnM. $0.87. 4. Bought 200 yard>< of carpeting 1 i yards* wide ; what is the length of one side of the square room which this carpet will cover? A. 45ft. 6. A man owns three piecew of land ; the first is 125 rods long, and 63 wide; the second is t;2^ nxls long, and 34 wide; and the third contains 37 acres : wiiat will be the length of the side of a square field whose area will be equal to the three pieces f Ans. 121.11 + rods. 6. Purchased 2 house-lots ; the first is 242 feet square, and the second contains 9 times the area of the firat; how many feet square iu the second ? Aiu. 726 feet. 7. Required the sides of a ri'>cungnlar court-yard haviag an area of 432 reds, and whose breadth is only the | of the length ? 8. A certain field contains 48020 square rods ; the length exceeds the breadth by 49 rods : what are the sides ? Ans. 246 rodr long; 196 rods wide. 9. A dchool-nia«ter says that the number of his pupils multiplied by I of itself is 2523 ; how many pupils has he? Ans. 8". 10. How much will it cost to roughcast the walls of a garden, having a surface of 8100 yards, at Bit, cts. per yard, the walla beiiyi 2^ yd. high? ^n». $1449. 11. Tiie greater of two numbers is 40, and Ih* sum of their squarM 1625; what is the smaller number? Ans. 5. 12. A clock-maker sold three watches whoie prioes are as 5 is to 6, and as 6 is to 9; the sum of the squares of the prices is $3550. What is the price of each watch ? Ans. $25, $30, $45. 13. What is the price of a raking machine, knowine that the price added to its square giyea $186 tor result 7 . Atu. $13. 13 A. 4 of the number it«elf 1 obtaia $96 for result. How many barrels of codfish, at $4 per burel, oaa I buy witk the inoBey I poaeese 7 fibanek *vn Kooc S45 CUBE ROOT. The root, of the first ten integers and their cubes are:- > '> 3, 4 5 A n o 1» 8. 27. 64,' 125,' 216.' 343,' 512,' 729,' 1000." ^-^''^^n.'airS.^^^^^ of the „u«. P«2'.rf*».po^Afeo/«AreeA^«,.«^'''^«'2^^ i< o/ tnfo a. many •^ « the^ear^pe^. ^ '^ *^' "^ ther^ **Ul U a, ma*y figure, in t£ Ej-. What le the cube root of 157464 ? S4 X 4= , p«oor. 54 X 54 = 157464 167464 ( 54 125 32464 J2464 ~0 °"'^"«"- .AxALTs,8.-Begin- ■ing at tho right, we •eparate the given number into periods, by placing a point over the unita' figure, then over thousands. Since the number of periods is two. the root will consist of two fig. ures, tens and unita. Then 157464 =. the oubeoftens,plusthree times the square of piM thrw timed the tens into the Miiar* nf*K- . •. . ^'>« tens into the units, Jhe cube 01- ten. .. thousand^. andStheref"-'^' f""'^- ° u**" °^ "^° "°'^ the number. The greatest nunTSerSnlwh/l ^,°'* '" **»^ thousands of sands is 6, which we write « thel^M fh^^J f ' ! ^"^.'^oef. not exceed 167 thou- 125 thousands, the cube of 5«st?rfcu"/S? 5,^^^ ^^° then "ubtract th. 82 thousands; and, »nne«ing th. nwt no^iS i k ''"''*°i'' *"'* *''"« '«°>ain S24'«« times three times tho square ot^e tens nhf, rhri r^*" **£ ^^^ ""*'«• ^'^ '^^ Pr«d"Ot of the square of tho\nits, mul iJ^Ted tX^'ZT'lflwT 'T.-'''' «"'^^' ?'"» three times the square of the tens >f f !,« ,1? J dmdmg this reiaainder by «omewhatt«,oIarle. Although it may irti,Ta*r«'r ''" ""J^' °' * ""'»»«" the remainder 32464 cont.uns no onl? thre^iirJ^hl?*""''* bo too small, since anit«, but three times t he tens into SeVauL^T*., "l"*"^. "^ '•"« '«"» *"'» 'be units. We therefore make three times t?.erul.«„f^K'^; '''"' ^^''^ ""''« "^ th« hundreds, a trial diyisor. with whiTw„ r *5 .^° ~^/^® ^^"^ "t-'he root, o= 76 der, disregarding the 64 uTiS Sc. th«™ ^ ^^ ''^^ ''""'^''^^^ "^ 'be remain- the squarf of the%ons by .^e iS ThL^H^nffi™ ""^Kr!"* f ^'^^ P^"<'"<""f units fig,:re of the root, or a number somewha l^rJ' '« ^"'•^' ^' •"""* '"^ ""• oon^ lete the diyisor on the supj Jtirh;:;'^^^^.-^:^.""..:?.^-^]^?-^ '» root, wo add to tho 75 hun-ired^^Vhefr^^i^ ^f^*' 'J"'"''"' "^ ""''« *" '^e root into the 4 uuits, plus che squii^S? J ^^i""'". '-^^ ^ '"» «f '»>• divisor 81 n«, thus fiUc^ by \rLDitaaL^L?J* ■"'"P'yi"? the tru. from the ni«rtnd«,th«»i;it,SL"££' Slr^fi?£? ""> ET^"*". 32464. M *teMMb» VMt -««iiHi •«». MMo% 1674C4 is a pmrfeot eobo, And !1 '^ ill »h» ill I > i If ^ 'A' S4« 4IS9. Rule. — I. Point off the givm number into periotk ^ three Jigures each, counting from wUts place toward the left and right. II. Find the greatest cube that does not exceed the left-hand period^ and write it$ root for the first figure in the required root ; iubtracf the cube from the left-hand period^ and to the remainder bring down the next period for a dividend. TIL At the left of the dividend write three times the square of the first Jig i( re of the root, and annex two ciphers, for a tried div- isor ; divide the dividend by the trial divisor, and write the quo- tient for a trial figure in the root. • IV. Add to the trial divisor three times the product of the tens figure of the root by the units figure with a cipher annexed, and the square of the last figure, for a true divisor. V. Multiply the complete divisor by the trial figure ; subtract the product from the dividend, and to the remainder bring down the next period for a neu^ dividend. VI. Multiply the square of the root figures already found, by 3, and to the product annex two ciphers for a new trial divisor ; and proceed as before until all the periods are brought down. KoTB.— The observationa made in Notee 1, 2, 3, 4, and b. and«T .he rule for ti»e extraction of the stjuaro root (458), are equally applicable to the extraction of the cube root, except that two ciphers must be placed at the right of a true dirisor when it ia nut oontiiinod in its oorreaponding dividend; and, ia pointing off'deoimab, each period must contain three figurM. Hi f EXAMPLES FOR PRACTIOB. 1. What is the cube root of 12326391 ? OPKRATIOX. 4 ,x,> ,M !'ij. 2» - Trial divisor, 3 x 20» - 1200 3 X 20 X 3 = 180 3« = 9 True divisor, 1389 Trial divisor, 3 x 230* = 158700 3 X 230 X 1 = 690 1« - 1 1 232ISf 1 8 3s True divisor, 169391 X I = 432fi 4167 SSI 169391 16 939 1 2. What is the cube root of 1331 1 of 3375? ol i21ST? of 32768 7 of 110692? Ans. 11, 16, 23, 32, etc. 3. What is the cube root of 1861MT of 272144? of 456633? of 704969? of 970299? Aim. ^7, 64, 77, 89, eto. ovmm EOOT. 347 APTLicinoNa IN am goor. i« height, and X™™ .h "filutl/'T TJ''? "^"'f '« '"« contents of the box. '* """' "« "'*'>. Required the 6. How much miut he ni.,d fnr . „—■ f*"*" '"' ""b' '". ««l, bought at i5Mnt,nS^lhl°"^."*'° '■"■»'*' of pouiid. or lin- theiumllrequal^Sgi?!,^-'''""'""**" "" » "^ "« ""b^ of >».cubee,„.,Aff'jtl':k'Re''^TrJ*^.l4^''"' 7. Required th« value of the artiVl*. -^ * • j • '^***- '^1S3.80. r^T' " ""^ -c'«.:''.^siStrr.^ cLf a?°a'-5 8. What ia that number, whose 1 I -„-j i i"^***" *156.26. give 9 for product ? *' ■' •"'^ i multiplied together, 9. Bought $164.64 worth r»f ^-„ . -^na. 6. "-•-"n"-, each ZSw^g Sf L'T'S' "'' '■■ " -"«"' there are boxes; »nd each oraui ooS. twio. .. ^^ °""'S™ « •" boxe,. Bequired the »«mblr on.oxerL"™^""'*' " '""• !«• In dividing the cube of » ™».i«i„ '''* .''' t"""*' ^'8 oranges. jrj^.-..e uu„L, w.?b;:Sn%TaTo^e;?f K ?f ^1.3 11. A rwerroir, whost lenirth i. t^ ;.. k-„^.u _ ... ^n«- 9- aeptn «a 13 is to 8. contains QOsin 7 i7 "''"•^lu sts i3 la to 6, »nd dimewions of the CJvdr ? ** '"*''*' *** ^^^^^'J ^^at ar'e *he 12. Some merohaolT forS V "/rt^"' ^k**^^'^^ ''^ '''' '^^P^'^ ^4 ft. -MMv wwMB M ti»ere wdn wsooiateB. Hari^t^adc .11: I S4t A»ITHlfBTIOAL PROORUMOH. It . ' ' rf!.''^*^,f *' ^^'y ^""^ >*^«t tW have gained the half a. mi.«h the com anv ? "^ "' '^"''*"**'"'' ^"^ ™»'^J^ partnew were there ia •HI ^A ^^ lu'*^^"", ^^"?^^* certain quantity of pearl-shella ; by^^jing rh;\\ff!"J;;-T^™"'''p'-^T*^^ «»»" heiaiiSutb? the f of Itself, It gives a product of 59049. Required the number of 108. he bought ? j^„ oc r. m ij TT,* , , , iln.f. 35A. 'b. a^rtlin n?,^" ..u'f* V"^'"''.**^"' P*^' ** ^S °e"t8 per lb!/ for a ^,li Tu^f ""u ^*'*' ^^ «'^"'' «»«*^ ^*'*' containing Uo lb., che number ^ba eg bemg such that in multiplying together its J, i, and I, the product will be 8640 ? r j s, & ^^ $3828. PROGRESSIONS. ARITHMETIOAL PROaRBSSIOM. 4«0. An Arithmetical Progression is a series of num. bers n.cieasino; or decreasing by a constant difforenoe. formed Terms of a series are the numbers of which it is m*i mf"® Extremes are the first and last terms, tJ? i ■ m ^®a^S are the intermediate terms. 4«»4. The Common Difference is the number added or sub- tracted, m order to form each sucocHsive term. 4«5. An Ascending Series is produced by adding the common difference to each term successively ; as 13 5 7 Q 11, 13, 15, and 17. J »'.♦'.«',*, », *®*' ^J^escending Series is produced by subtracting the common difterence from each term successively ; as, 17 is' 13 11, 9, 7, 5, 3, and 1. ' ' > 467. Thesumoftheextreii . is equal to the sum of any two terms equally distant from tium, or to double the middle term. Thus, 13 5 7 9 U 1_5 IJ 1 1 9 18 18 18 FS r'8 .^*?^' J.'^'^ following are the Jive quantities considered, three ef which being given, the other two may be found :— 1. The first term, denoted by 2. The last term, *< ** 3. The common'differenoe, « « 4. The number of terms, " « 6. The sum of all the terms, " « Nort.--Hftlf the imi of mj two auubtn it MU«d their AriiAuutiwl Mtmt. a. I. c. n. §. MUKtAJti* er« th«rt ia Ana. 8. ; bypajiog laid out bj Dumber of r lb., for a 40 lb., che i aad iS 9' «. $3828. 18 of nam* hitih it is led or sub- dding the 5, 7, 9, icting the , 15, 13, n of any le middle red, three a. 1. c. n. 8. alMtmm. ABITHJirBTioAL FIlO«RMg,o„. 4«». Case l-— Given the /ir,t ferm ,j. 18 ^ 19 _ 1 J- ns iy , ^i,at in the last term ? 18 =1: 19 -_ I 68, the last term. iMt term ^4 T?8 ifl T°^' "*"• Therefore the Hence the Formiia « T**/'^ ° '*,"'"°" difFerenoe. '"■^ '*■ — 1) C =- 1, or the ■XAMPLBS FOR PRAOTIOE. width ofthe wide end? ^ '^^'^ '" '^"gth. What is tS I t.l\^u^ a"t term of an aacendine eerie- be i th- « ^""'- ^ ^^ '"• I, aud the number of tenne 20, whaYfeX'Taft^i'r^T'li^ii^^ll^^ 471. Ca8« IL--(»^ ,a, ^,,^, ■ >'>•'• of tenna i;^?;-^.^ 3. A man has 1 eons : the Tounaeet in ft . ^ »u . . ^'»»- 3. oW; their ages inoreaae o aritwS^ ' '"'^ ^^ «''^««* 44 rears Aftrenoeofthairafear •"'^'"^**«^ ProgreseioB. Required thll |1» ^••' *7««w. J. 81 L' I' !!■ 1 ( " 'i 1 11 PI ll I 1 I "5" ^B«?S'i/. 859 AlWTHlOmOAL F»0<111W8T0W. 4.gif the extremes ar^ and 2^, and the number of termn is 18, wliat is the common difference ? ^»t*- A' 473. Case III.— Given the extremes, and the common dif- ference, to find the number of terms. Ahaltsib. — Since, a + (M — 1) C « 1» H 1-a -f. 1. HoDoe, the 474. Rule. — Divide the difference of the extremes by the oommon difference, and increase the ^juotient by 1. EXAMPLES. 1. The first term is 8, the last term 203, and the oommon difference 6; what ia the number of terms? -^n*- ^O. 2. A man going a journey travelled the first day 7 miles, the last day 51 miles, and each day increased his journey by 4 miles ; how many days did he travel^ '****»• 12. 3. The extremes are 2^ and 40, and the common difference is 7i ; what is the number of terms? ^»w. 6. 4. In what time can a debt be discharged, supposing the hrstweek 8 payment to be $1, and the payment of every succeeding week to in- crease by $2, till the last payment shall be $103 ? ^— ""* "—^'^ Ann. 52 weeks. 475. Case IV.— Given the extremes, and thenumber of terms, tn find the sum of all the terms. Analysis— Sinoe, the sum of the extremes of an arithmetieal progression ta equal to the mm of auy two terms equally distant from them, it follows that the tornifl must average half the sum of the extremes. Henoe, § « J (a + 1) H. 476. RWL^.—Midtiply kalf of ilu sum of the extremes by the number of terms, BXAMPL18. 1. The extremes of an arithmetical series are S and 19, and the number of terms 9 ; what is th: sum of the series ? Am. 99. 2. A man bought 16 acres of land, giving $1 for the first acre, and 1121 for the lastlvere; the prices of the successive acres form an ar- ithmetical progression. How much did the 16 acres cost? Ans. $976. 3. A «^entlenian wishes to disoharse a debt in 1 1 annual payraenta such that tlie last payment shall be $220, and each payment greater than the preceding by $17 ; what is the amount of the debt, and the first payment ? Ans. 1 st. payment, $50. 4. A merchant bought 20 pieces of cloth, giving for the first, $2, and for the last $40 ; the prices of the pieces form an arithmetical series ; how much did the cloth cost ? Ana. $420. 5. If 100 oranges are placed in a line, exactly 2 yards from each other, and the first 2 yards from a basket ; what distance must a boy travel, starting from the basket, to gather them up singly, and return with each to the ba»ketT an is 18, rion dif- Henoe, the \s by the differenoe ln«. 40. !, the last ilea; how [ru. 12. ce 18 7i; Ans. 6. rst week's jek t(j in- I weeks. of ternu, agression ii )W8 that the fc + 1) n. iremes by \ and the Am. 99. acre, and )rm an ar- is. $976. payraenta mt greater t, and the ent, $50. ; first, $2, rithmetical 19. $420. from each must a boy and return OIOMITRIOAL PROORISSION. 26t GEOMKTRICAL PROGRESSFON. SnnlT"^" '^ ^®0™elrical Progression is a aeries of numbers inoreas.nn: or decrea.in^^ by a constant ratio. ^^"^ Sfi' Z'^® "^"0 IS the constant multiplier or divisor. thafl'^.f2.t8'"G".^'li*t^P^°'"°«'^^^-^-*-«-ter lesf th,?n l^ ?sT *" i ? f 'K^r'""' "'^° ^'« ^""^ •« ^twi rp'. 7. t; 2'. t. t- tV» a. A» etc. wKr„?k' . ■^'^^**^'''^^|"f? i^re the>e qnanHde, considered <*rMof which being given, the other tioo may be '. md ,_ ^' '*^'*°* 1. The first terra, denoted by a. ^. Ihe last term, « i« « 3. The ratio, «• «« *' 4. The number of terms, « « n' 5. The «nin of all the terms, " " „* IkSTTriTJi" ^'•'^••^^ ^-« between two a«nb«. ta the ,,„.„ ^^ 4«a. Ca8I I.^GStW ^^,/..,, ,erm, the ratio, und the num. ber 0/ terms, to Jind the last term. " ''*"**^ ^^iJ^:^'^:^^'^^^'^^^^^^^^^ and the ratio is 3 , A...vsis.-The «rsuerm ^^ . 4, and from the nature of the series, The third term = 4 x '^a «„,, The fourth «„„ , \ I l. , , ^."^-^^^ ^^ •na 80 on. Hence, the last term, 1 =- a X r""^' ../**?■ "^^.^^--^^Mplif the first term by that power of the ratio denoted by the nnmher of terms, less one ^ ^^'"^'^'l^:i^TZ':^tX'^^^^^ «d the EXAMPLKS. ^rZ^r^:^-\^:^^T^^ --^r of teru.^-.., 1 ™illt 7"?!*" ^"^?* ^ ^Sg«' ^^^^''g t*^ W 1 mill for the fejt tg a mills fur the second, and so on , what did the last e^ oost her ?^' Am. $0,266. - I 'J If r tM aOMKTBIOAL PK0«UU1I0M. I.; I >.J,. liii&J.i. ^^^^B 1 ^B^^^B Iji^ii,; V ..-J- r ! i. 4. If the first term of a eeriM k M, the ratio l.tf, and ttie nanbw •f terms 6; what is the last term? An*. 40.146787328. 5. A person traveling goee 2 luileH the first, 4 mileH tke Hfcood, B miles the third day, and no on, increasing in geometrical progression Jor 10 days. How tar did he travel the last day ? Ant. 10';.4 miles $. Bought a lot of land ooniaining 15 acres, agreeing to pay for the whole what the last acre would come to, reokoning 5 cts. fur "the flrnt aore, 16 cts. for the second, and so on, in a threefold ratio. What did tlM lot ooet lue ? Ans. .i;L»;^9 148.46. 4S4. Case IL— Given the txtremet and ratio, to find the turn of all the termt. B». The first term ie 2, the last term is 128, and the ratio 4 1 1*^ quirvd the euui of ail the terms. 8 -». 3a + 128 -♦■ 612 = 4 1 + 8 + 32 + ris OPiaATIOll. X snm of the series. = I X sum of the seriea. 612 — 2 = 3 X sum of the i^eriaa. Hence »",- » = 170, the sum of the series. AWALT8IS.— Since 512 = Ir, 2 = a, and 3 =■ r — I a = ^'' ~ • Hen«e, the ' |. _ 1 • 485. B.VLE.~~Midt:ply the latt term by the ratio, mhtrnei thefirsttermfrom the product, and divide the remainder by the ratio lett one. NotM.-l. If the ratio it leas thM 1. the product of th« last term. maltipHed by the ratio, must be subtracted from the fint term} and, to obtain the divW the ratio must be aubtraoted from the unity, or 1. 2. When a doBoending Heriea if oontinuei to infinity, it becomes what is oalUd an Isnuvn aniKS, whose last tern ranst be regarded as 0, and iu ratio as • traeiion. A ^? ^^1*^" ' T *'^- *° a"*'"''^ Seriei,-i>Hri«<« tkeJtrH fn» 6y a mmU dimimMMd 6y th»fram*«n demitmg the ruHo. BXAMPLE8. 1. Tha ilTHt term of a series is 4, the la.it term is 62500, and the ratio 6; what is the sum of all the terms ? Ans. 78124. 2. If the first term of a series is 12, the ratio 3, and the number of terms 8 ; what i>^ the sum of the series ? Ant. 39.S60. 3. The first term of a decreasing serie8 is 102, the last term 4 and the ratio ^ ; what is the sum of the .series? Ans. 151. — " — -^^-^ , " "^~-= i~ ", tiie ratiu |, Skud tne number of terms 6 ; required the sum of the Hcriet^. ^n^. 1 31A&. 6. The first term of a decreasing series is 106, the last term t Oand Ike raiM i ; r 8. «. 8. . lr-« " r- 1 • , subtract I, mnltiplted the (iiTu«r, bat is oalUd ratio aa • and the , 78 124. number of H9360. rin 4, and IS. 151. umber of m • 0, and iM. 13U. Irllfi-i-fWHlB-li' -^'^ MIAHURBMINT Of LUMBH. 2(|S memJ?nteunfit"rL7nrn "'""''" *'''''>' di-chargad bj monthly pay first n.orith h? il »^"*''-^ '"^* "^ * "^''^ f^r 6 "'onthn. For th« were lo '^re.H d 1,^'?. ' '' ""'' T*' ;^"°««^*'i°K -onth'^ wa^t! thelein/ttgreed to 3 1 *i f 7 ''^; '^^ '"" '"^^ * price ; he, never- for the'thfrd. aud Ton ."«*"" V'f, '''■"' "'K"^^ ^ *'"• ^»'' "•^^"J' !« cost hiw ? ' ' '° ' ^''"'^^'^ '■•^<> 5 bow much did that ground Am. $34S>5.25. MPUSUREMENT OV lu.V BER. J™";'",:,!;!'" ■' "°"'"'"«" ""•"""'' •^ "« ">°. -"i ~".«im™ bj 4»^i. To find the contents of a board thSthT'' ''' ''"'*'' " "*''«"°=' "''^^ ^-^f "tf -- of the width of its endB fo, ,if?- '• ^'>^^-«^J- contents of a board .36 feet long, and l^feet J. What are the conteota of a board 24 feet lonf 'and' Jl S. 3. What are the contents of a taperiu.. board 2^1^^^} '"'^' ^'u' ends are, the one 24 i„(^e«, and the other 13 [n^hes wfde ? "=' ''^''* 489. To find the contents of planks, beams, joists, eto. in S^f^'&,:J;,,:ff ;f ^ ^« -cAe., t, the tkickness, w/tnf7hi^*SdstS;o''wS*^^^^ '" r'*^ *'»''« ^'^^- «"•« of the thicknes..th« common ru^ZbtaSnf/fh^^^^ "'^^^ '^nd the ^tk. ««H of tk. ar^ o/^L CSiifirS? »« «"bio feet i«, to ««/ay^ In I hi 354 I ' ' ( I I f VnOILLANBOITS BXAMPL18. •nf f inoheTJhtk? *^' *""*•"*" "'' P'*"*^ ^^ '^^J^^^g' 2 feet wide, 4?:s:3 ti^r sr ^^^-' -- -^ S^ 4»0. To find the contents of round timber. fomanfThf'^^'^^^ fA« ?«n,9#^, taken in/eef, by the square of one 2dhv{A "^T ^*"1' '"*''* *« *"''^^^'' ^nd,thi4roduct,div xded by 144, ?<,i?^ ^rftre the coni^ts in cuhic/eet. i II ,1 MISCELLANEOUS EXAMPLES. doJ; ht SeeV? "^ ^* ^"" '''"* '•^' ""'^^ P*' *^°S ^' ^'« «-• .«™ ^11 be fi!"?'^' '■' ^''* ^ ^^«^' '^^^ ^^'^ * of ATit'efn^th. 3. A gentleman boughi 95 yard^ of cloth, ? of ayard widtX'Ahn •nd gav. the .ame and $2f for cloth of the'sLaqSri i^S li3J' How many yards did he buy 7 ^ Zl on i ^ 4. A father devined ^ of bis estate to one of his ,om' an^ 2* «/ the residue to the other, and the remainder to his wife ' The ^C ence of h.s sons' U.^acies was found to be £257 3 4 What mf «v did he leave for h.s widow? Ans £635 Tim ^ 6 How many bncks S.inches long, 4 inches wide, and V?&„, feet^hirkV"''"^'^"""'^"*" '' '''' '•^"g' f f-t hig,- -di 6. Ifan.aneanpaini4 ..uare yards in one h^ur^'ln^filTK <^.^40 .ec. .. painting two aides'of a wall 7 feat high X 4 1 Jitt^ WTOBLLAWBOUS BXAMPLM. 7 B • *** titj p«rdS^ bmff fVofl k for* RH^"!?'''i«r°,^3« °° ^^•q-"- on the 8a,.,e quantity . How Tnanv hnlJ' * ^"^^^''' ^ «f'*" g»'" ^42 ^. A groce? bought a hoXa/nf l^ f '^!'fo^"Sht? Ans. 240. must be added to reduce th^£uo 35 .'t^*^^-'Ti.^^''^">"<^^ ^*ter 9- A father, dying, left his snn I i * " P^"" «*'• ^ ^"»' 18 gal months: 1 of the'WnfirL'J^^^^^^ «P«"t^o 8 which he had only «410 left Wi!!! ^ ^^ month8 Jonger, after hitn? ^♦410 left. What amouut did his father ber «Qnft . ., "*"*• '^2^ mo. he takes in C as a partner, and auireSoVR** '^?.'"? ^f l^monthe _. -.1,, .n*. o, t«f year, wimt rent must each pay ? •■''° ^• 23 A person mixed 12 cwt. of slTar^lf «ij' witf ? ' ^ *'^*- •-d 8 owt. at m , how much was fowt^of Ih"; mSure";^^ *'*' I'li 256 MISOXLLANBOTTS BXAMPLM. 24. A shipment of wheat was insured at 2^%, to cover | of its value ; the premium paid was $44.07 ; the wheat being worth 80 cts. per bushel, how many bushels were shipped? Ana. 2825 bush. 25. A stack of hay will keep 24 cow8 or 18 horses one week. How many days will it keep 5 cows an(i o horses? Jni^. 14f da. 26. C. of Montreal, remits to D. of Quebec, a bill of exchange on Liverpool, the avails of which he wishes to be invested in goods on his account. D, having disposed of the bill at 11^% advance, received $9675 ; and, having reserved for himself J % on the sale of the bill, and 2 % for commission, he invests the remainder. What is the amount invested, and for how much was the bit! drawn ? Ana. Investment, $9461.58^; the bill was £2025. 27. What per cent, is gained by buying oil at 80 cents a gallon, and selling it at 12 cents a pint? Ang. 20 %. 28. A merchant pays $10050 for a stock of goods ; he sells them ftt an advance of SiiJ % ; the Expenses connected with the business are $1760. How much does he gain? Ans. $lfiOt). 29. What o'clock is it iwh«»n the time from noon is ^^ of the time to midnight? Ans. 6 o'cl. 24 min. P. M. 30. A merchant receives on commission three kinds of flour ; from C he receives 20 bbl., from D 25 bbl., and from E 40 bbl. He finds that C's flour is 10 % better than D's, and that D's is 20 % better than E's. He sells the whole at $6 per bbl. What in justice sliould each man receive? An$. receives SslSym; D, $158^; E. $211^f?-. 31. For what sum must a note be drawn at 4 mo., that the proceeds of it, when discounted at bank, at 7 %, shall be $875. 'ii ? 32. If 2^ yards of merino If yards wide cost $3.37|. what will be the cost of 36^ yards 1 ^ yards wide? Ans. #52.779. 33. What must be the face of a note at 60 days, the proceeds of which, when discounted at Bank, at 6 %, are$100 ? Ana. $101.06 + 34. A merchant sold a piece of clotii for $24, and thereby lost 26^6 ; what would he have gained had he sold it for $34 ? Ana. &\ %. 36. A bankrupt compromises with bis creditors for 37 ^^(i how much will he pay on a claim of $3656 ? Ans. $1371. 36. A man, dying, left $3565 to be placed at interest for bis son who was 16 vr. 5 njo. 15 da. old ; how much will he receive when he ia 21 years old, allowing 7 % interest? Ana. $4698.37 + . 37. A garrison, consisting of 360 men, was provisioned for 6 months; but at the ei. of 6 months they dismissed so many of the men that the remaining provision lasted 6 months longer ; how many men were sent away ? Ans. 288. 38. What sum must I invest in the New Brunswick 6 % stock, selling at 2i % premium, to secure an annual income of $840 1 Ans. $14350. 39. A grocer divided a barrel of flour into two parts, so that the smaller contained \ as much as the other; how many pounds were there in- each? ^n«. 78f lb., U7f lb. 40. A sportsman spends i of his time in smoking, | in cunning, 2 ho. per oay in loafing, and 6 ho. in eating, drinking, and sleeping ; how much remains for useful purposes ? Aiu. 2 ho. ii. Exchanged 250 whares uf 6 ^j^ stock, at 1^%, for stock bearing 8 96, ai 120 9( ; what x* th« di£ter«n«e is nj income ? Ana. $333. 33^. ver I of ita orth 80 ctH. ?25 buflh. week. How '. 142 da. ^change on ;ood8 on hie !e, received of the bill, the amount ,8 £202i. 8 a gallon, w. 20 %. sells them »u8ines9 are 9. $1600. )f the time M. from Hnda in. P. iiur ; He better than hould each he proceeds lat will be $52,779. proceeds of ;I01.06 + /lo8t 265g; n». 6i %. ;7i%; how s. $1371. for hie aon I e when he 198.37 + . oned for 6 any of the ; how many ins. 288. lock, (telling [.$14350. BO that the ounds were , 117f lb. in gunning, d flleeping; ins. 2 ho. Mik bearing 1333. 33^. M180BLLANBOU8 EXAMPLBS. 257 42. Purchased 100 barrels liprrin(rat1o,;T roS;'*''','^ "" ^ lie mav make a clear gaia of 24 « L i ,. Sf,''' "^f l;'»,"'P™»e«, money beiog worth Oj? '* '"' ^"' T' >" "« gooJs, plaid^'o' a\'5*Xne''.Zt o"""'" °f ■'"'' °" ''^^ ,ii^i;crtrd."::driiT:,rat^3i!f.-T^,;r-'^^^^^^^^^^ m »t what did be give An$. $600. i I I I ri) If If I MIWILLANIOUS KXAMFLW. to tL!!!fl ^''^•'»'.>»boring 7 hours a day for 16 days, were able .'Jn. k^ ■ u-^nl "* *'°'' "'^"-^ '^^^' c»o they complete the res- aumber r'^'' ** "'" * •^*^' '*" * workmen be a.Med to their fn/v ^*^*^*»««? 50 Ontario boads of $1000 each, at"^*i^piSm, he SL'r vT? ^"^' f ^^'^^ **«^' «* ^ * P'^'"''^"^- How many ot me latter did I receive ? ^„, 3jq i.fwr'i '''"^ * friend $700, which he kept 20 .nonths. Some yekra ih^favor r'"" " *^°® ' how long^ehould I keep it to balance ea u ' L. . ,. Ans. 46 J months. on^ft -?''"* A ™«^°h«»ndiee as follows: July 3, if 85. 26; July 4, $48.65, Z^n, ?f •;' A"^- ^^' ^^-^^ 5 ^^P^- 12, «60. What is' due on the ac^ count Oct. 12, interest at 9 5l5 ? Ans. $142.60. 7 „,« *;«"'* certain «"« of money to A, and at the ev.d of Syr. T mo, 20 da.. I received for interest and principal $1000: what sum «1 rnV «.,.„, An.. $820.79 + . «f „J ""'' "•'?' '"^''f 25 yd. of cloth, liwide, how many poundi of wool are required to make 116 yd. of cloth 1 yd.' wide? Ans^ZA. and th« r!^ • ^^"^^ ^o' *^^"?' * Pt?^*^^« '•» 3 ™<^"*'^«' * '" 6 months, and the remainder in 9 months. How much ready cash ought r to Purchased a quantity of oats, April 1; May I its value ha(^ ncreased 2.^ ; June I it. value wa. 30 % more than May 1 , July 1 1 sold t for .u^ less than its value June 1, receiving in payment a luSi ?°^*A^^'«^ I ««' discounted at a bank, a* ^ %: receiving «? r^o.V How much was my profit on the oats? i4»<. $3238.52. .ff:, fi? i " • ^"^ u ""^'^^ °/ •***^ ''^'S^ 1^ 'b-' '•^quired the i^imber of feet of lead pipe that can be made ^m 80 lb. of lead, the caliber of the pipe M) be 1 inch, and the thiokiieRs of it i of an inch. cfi t\ .u J .. iiiM. 10.35 + feet. b6. Une-third of a quantity of goods was sold to gain a certain «. .one-fourth to gan, 4 times as much %, and the remainder to gain 2* thlwhouT'' ^,. I}'""' 'I '^' «^" * "» «^^ Par^ the gaif upon the whole being 21 %V ^n#. Ut.. 12sSj 2nd., 18%; Srd'VsO^T . *J' ^ '"erchant in Kingston has 6000 francs due him on account bni a.'T.i3 .r *"*° r''^'" ''" ^?^ ^'"' ^^'^ ''"'^'"'^ »»d negotiate the u^ Llit I f ^' P®"" fra»V o^ he can advise his correspondent in Pari» to wmit adraft on Canada, purchased with the sum due him, exchange on Canada being at the rate of 5 fr. 20 centimes per dollar Wh|t sum will the merchant receive by each method? Aru. By drafi on Paris, $970 , yy remittance from Paris, $961.5:^ 67. A mil m IS required to grind 160 bushels of provender, worth $1 a bushel, from oat« worth $.40, corn worth $.80, barley -., i; $.90, and rye worth $1.10. and wheat worth $1.30 pei^ bushel, now voAnj bushels of each Kind may he take? ««. H.- ^„^ ..fl., .JrJ?':^P.* 20, 60, and 40, respectively, of siVupTat $;7T;S^W ^•'"' • ■"" """ ^ ^''"' 'iJ'2T[,'b^' 69. A servant draw« off a gallon on each day, for 20 days, from a Jilriwv"*^^'^ ^'''Ir ^'■'^°*' •aohtimesupplying the deficiency hjr ih« addition of a galk>o of w«ter j and thea. tS !»ia^ de.eoUon. b^ MIMHLLAN10U8 BXAM»L„. '4. Jij working 9 bourg a Hov <'^> is. j ^ns. $386 67 Wuetl ^?f ^ ^-" A Sinti;^^^^^ "^'^ wL able to ■due be finished in 15 daye more if^h^ ^kJ'*^*^"*'^°' ^"^ t^^e rP«. r hours adaj? ^ '"°'*' '^ '!»« laborers are employed only 'o. At a certain time bptwpon 9 „ j r. . ■^ns. 4 men was between 3 and 4. WirhTn L^J^ ^ "1*^^^^' »l»e .uinuSnd mmute-hand had exactly cWed^^^^^^^ the hour-hand aad * the prece t,.e when th'e hanlst^ir S VS^^^ ^'" ^^^ 76. D and E traded together • n '^"^* ^«^^- ^^ '"'n- 56t«A 8«j '7. If stock bought at 8^ dispni.»» n "4«». •t.)20 .t what rate shoulJ it be L^h ri^'te? ^ * - the inve.t,fen^ aJ^K iL"f P^'^' ^^^^•i clotli to a wffieiai? I . ^"'- '^^'^ * '^'«ct- i^ Jm'^^^ ^**^«' ««^*1 it to a cloThier 2 ! ^i^"" f ' ' ^ * ^•^^ance : "* "^'d It at a farther advance of 25 ^ 1 !?^ * ^^^^nc^ ; the cloth' much d,d.t cost the importer^ ^^^ *°^ '«<^"'«d |I452. How •7an /^ , '^ tl*« difference between »h- • ^^' ^^'^ «6S. $730, for 5 yr. 9 mo., at 8 jT? « * •°**'**^ *"ld m order to losers % Z tt'tifof .^'^ °°^ '""'^^ the renfai„der S invest tr.::ll":?*d'-^->'^ -,Montrealcitvr.-,.tl%'^'f-^- , 8Ta'?*/^1^^' whatwastheamountoflfr ^F ^o^'t leaving in- «-«. A tailor bought 40 vanl^ of T. J^ . i>^ divxlend ? 4. $1000 """3f.«'''''«^'-'''i°Ctil^^^^^^^^ 2ivd. wide* but on I width. on« nail ^^A - T.-iP ">^*" every 4 yd. i'lilfn quarter a d ^this cloth, '" the whoJ« 82. A tailor bought 40 vards of L J" i™? ^'"''^^"^ ? 4- $ sponging i^ it shrunk in Ct^L^*"*^'^^*^' ^i yd. wide* m width o'ne nail aad L haff^reVVr^'fi V^' ^"' ^ <^"-«, I».bou^tfUn„.U,uarterswi5:,\^Jfe^UiCwerJ;u^^ I tm ^ II fll SM MUOILLANBOTTB BZAMn,!!. i M ■ ■mi i. ■ir ^^H' si . .- : ■l 1' ' •. |. ^1 \i $' I ^^Hi^ iii V i ■iPfiiii ^■1 ■Jiniy width on eyery 20 yards in I«i,^h, and in width it shruni half a nail. Required the number of rards of flannel used in lit.; jg ihf 83. Stock purchased at 5 % pivniium paya 65^ on 'die inv« (..nent, what % will it pay if purchased tu 15 % discount ? .ins. 7,1 %. 84. A riKTcliant failing' in business can pay 70 eta. on li dollar, ile oflfers, to pay his whole indebtedneBS without ix', rest in 5 ycar.s if his creditors v/iU allow him to go on w.th his b>; In ■•js; his otl'er beir>g Jiccepted, how much will his crediiore lose in ii\e 6 years, money being worth 7 %1 Ana. 5'^.02e on a dollar. 80. Purchased a quantity of wine for $675. 32^, a^, 85 cento i>fT gaLon; but a part having ieaked out, the remainder wr.' sold'iM 40 ^advance, s/k! the oii(,;inaI cost was realized. Wha; quantii,^ leaked out? ^ns. 2;i7gai. 86. A owes B ^i'm .'ae in 4 months, and $840 due in 6 months: B owes A $1600 duo ij» 7 months, ff A should make present payment of hia debts, wiieaoi;, au!! in jviBtice to pay A? Ana. In 2in-- lO^da. 87. How muny T ii.'ds of sugar at 8, 13, and 14 cts. p x- pound, may be mixed with 31b. at n cts., 2 1b. at 8^ cts., and 4 1b. at 14 cts. alb., 80 aa so gain 16% by selling the mixture at 14* cts. per lb. ? Ana. 1 lb. at 8 ; 8^ lb. at 13 ; 8 lb, at 14. 88. What IS the dift'orence between the true and bank discount ol $3000, p^iyable in 120 days, at 8^ ^ ? Ana. $4,467 - . 89. A general, forming his army into a square, had 284 men re- maining; but increasing each side by one man, he wanted 25 men to complete the .square. How many men had he ? Ana. 24000. 90. C bought a house of i), and gave him his bond for $6000, dated April 1, 1866, payable in 5 equal annual installments of $1200, the ti-i St to be paid April 1, 1867; C took up his bond April 1, 1869, eenM-annual discount at the rate of 7 % per annum on the payments due afttr April 1, 1869, being deducted. What sum cancelled th» bond Y Ana. $3365.94 + 91. I have a plank 42i feet in length, 24 inches wide, and 3 inches thick; required the side of a cubical box that can be made from '*!.o T-^ * 4n#. 48 inches. 92. IfB owes $500 due in 6 months, $400 due in 4 months, and $300 due in ? months, and pays | of the whole in 3 months, when ought the remainder to be paid? Ana. In 10| mo. 93. A wholesale merchant seni a quantity of goods into the country to be sold at uuctiun, on a commission of 4^ %. What amount of goods must be soil, that his agent niay buy produce with the avails to the amount of $1910, after retaining a commission of 2^? Ans. 94. If the annual rent of 23 A. 1 B. 27 per. of land be $18' much will be the rent of 71 A. 20 per. ? An 95. A Halifax merch; ■, . hipped 1000 barrels of saiu.jn v. in New Orleans, diivctii) m to fcell it, and invest t cotton; his agent sold the salmon at $14 per bbl., paiu v !■• uumges, and bought cotton at $.65 per lb., charging '6% comraisficK morselling the salmri and 5 % for buying the cotton. How ma 7 rvu.-isof wtton did he buy ? An$. 1M85. .b. '0. lOW 56t). ' ' H aofpnt .■•■;i'eds in ■?'< charges, 3nSffln.LAlflODS MXAMKJm. he finds that tm^'JTL^^Z'h ^'^'^l!"* ^«'"g »"«^«<^ ^t s'j? owe ? * " "^^^^ ™°°«y ^'JJ pay the debt ; how much did he -ne,,p,u«,,,lr-,^-^Dj^B^^^^^^^^^^^ to E. quired C's stJck aK°s an!l B 's'sain"! ^"^ ^ ' '^^'^ "'^^ *''*«• ^ 100 A ^'»*: C'e stock, $10000'; A'Bgain «3'-}6 • R'« SRsn^ iUU. A man havinw Inst « ^V k;„ ' " g»iu, ipaao , tj s 5>504. only ,672; ho/mich td-hfattsT^^' '^""'^ '^^ '^s'^S'^' aelling tLTstt^' a^el-i^T^^^ - railro^J-st^ocHV b7 investing tl e remaiader he'^ ^L'*^ f'^T,^' ^^f ' ^ ^^ ^""^ iavest.nent^ money he had remS" wJich Li hi ' ""^^ ^*^'7"'''^ '"^^ '^' «*" '^^ much did he invest ?^' ^'"^ possessed of $480 ; how 102. Bought a certain number of horses for 3;2fiOft 1"*! f u ^'^V gain ? * '^^^ P"*'- What per cent, profit was his The oonsigoM pays $1 20 40 for tS , - *' °" !"<"=«'* '>y =>'■>»• «8.40 per bbl./oi;i»» 2' « ^™^ ^ """ «{«"»=«. sella the flour at •vey 2 ho,«,, 1 acre olpMurt?""'' ' "^^ '"'''T' tj' ""' ''"" gain on the whole? * *'''• ' '""'" "'"ch did I 1 09. I paid *93 16 0, at tij- rate of 9 . ci f ■ '''"'■ **"• ^'?7vV''"™-°'»aetheHL^'*;etV°'""°°'°° " *« ' 4 i*. What WM my aain ? *^ ^ '^ * premium, brokerage ' * iliifc £26. Ml 'I B**!*- ( i ^ ^"ir 15 ! i / ( i i VTSOHLLAinOUS BXAMPLli. 112. The londtudeof Paris is 2" 20' 22" E., and of Constanti- nople, 8° 59' E. When it is I A. M. at the latter place, what time is it at the former? .4ns. 33 niin. 25 j^ sec. past midnight. 113. Having placed a bill of $775 in the hands of a collector, who succeeded in obtaining 75 % of it, and charged 8 % commission, how much did I receive ? i t> o # 114. Suppose that the earnings of the Grand Trunk R. B. for December 1870 were $472240, wliich was an increase of 11J% oyer the earnings for the same month in 1869. How much was the in- crease? ^ ^na. $47224. 115. In a cask containing brandy and water, | of the whole +3 gal. 18 brandy, and ^ of the whole + 2 gal. is water ; required the number of gal. of each. Ans. 43 gal. brandy, 17 gal. water. 116. Hamel, Perry, Lane, and Garneau are partners; Hainel takes \ of the gains or losses; Perry \, Lane ^, and Crarneautherenminder. At ihe close of the year, the resources of the firm are : Cash $10312.50, Merchandise $13447.50i Bonds and Mortgages $1147", Bank Stuck $4500; Hamel has drawn from the business $900, Perry $o25, and Lane $285; the liabilities are : Notes outstanding $5460 ; Balance in favor of Ross & Co., $1120 j Balance in favor of J. L. Murphy, $3'J67.50; Hamelinvested $9547.50, Perry $7905, Lane $6270, and Garneau $.'^480. What is eaclx partner's interest in the business at the close of the year? Ans. Hamel, $9877.50 ; Perry, $8302.50 ; Lane, $6723; Garneau, $4279.50. 117. What is the difference in cost between a draft on Toronto o! $17302.80, at li^ premium, and one on St John, N. B., for the same amount, at ^ ^ discount ? Ana. $302.80. 118. A mechanic received $3.75 a day for his labor, and paid $1.26 a day for his board; at the expiration of 100 days h'- ^-^ ' • ved$200 j how many days did he work? ^l"*- ^^ ^^'J^- 119. For two successive years, a merchant annually contributed $100 for charitable purposes, and added yearly to that part of his cap^ ital not thus expended, a sum equal to its half; at the end of the sec- ond year his capital was dq^bled. Required his capital. Ana. $1600. 120. A merchant in Halifax purchased 350 bales of cotton, each containing 450 pounds, at $.80 a lb., and shipped them to Liverpool at a cost of 16 % for freight and duties. How much in Canada currency did he gain by selling them at 28. lOd. sterling per lb., rate of exchange 171^? ^***- ^23416. 121. A piece of merino cost $.80 per yard ; at what price shall it be marked, that the merchant may sell it at 10 % less than the marked price, and still make 20^ protit? Ana. $1.06iJ. 122. A merchant in Quebec gave $2000 for a bill of exchange of £400 to remit to London ; what was the rate in favor of England f 123. What yearly debt can be discharged by monthly payments, the SrHt being «2, llie second $6, and the thii-d $18, and so on. id geometrical progression ? Ana. $631440. 124. A farmer sold one hog, weighing 250 lb., at 4 cts. per lb. } • e'eoond, weighing 300 lb., at 4^ cts.; and a third, weighing 369 lb., at ots. ; what was the average price per lb. for the whole 7 A. 4f^ ots. ' tii^'iaiiMkil Cet'Htanti- ;vhat tim« idnight. •ctor, who sion, how R. R. for llj^oyer an the in- $47224. whole + 3 quired the I. water, aiiiel takes renminder. 810312.50, a.nk Stock $525, and Balance in . Murphy, S6270, and 3usines8 at ^302.50; Toronto o! B., for the $302.80. paid! 1.26 ■ ved$200; )J dajrR, contributed t of Ilia cap- l of the eeo- 8. $1500. )ttoD, each Liverpool at la currency )f exchange $23416. e shall it be he marked (. $1.06"j. xchange of England f payments, I so on. in $631440. per lb.; • /369 lb., at 4tHot^ 1IIB01LLANB0TJ8 BXAMPLRg. 3^ goods. * *^' Required the cost of the exchange ? ^ ' '^^'"^ *2o70.89. What was the course of 129 A man gave \ of his estate to his wife 1 ot^Z ri^JH"^' . his oldest eon. I of the rAfliWno t 1 • 1 1 ' * , ^"® remainder to what then renminedwWclwaifKon'' '''M ^^"-'>*^'' '^"^ ^ of Mc«i^iSr^;= waL't^ie teTh^isT^iS/r ^^"^^^'"^ ^ '^'^ «^ *i^«« ' ^hat price supposing he should make &%. Did he 1^^0710^ ? '^"^ abIe'i;2%rrrTi:'at;Trh/Lf'«'' '''> ^^^^^^^^.y. S^elrSp-bi^h^e.^^^^^^^ ^-^^'^-^-'^^^^^^^^^ 6, i'p;o±o'r;t^f?;r;^^ - Pa1^n;nt!-i'pril counted at theCk, IpT'lt^ll J^S-'^^f '"^'^T^ «"d had dis- ceive? •'^ ' ^^ 7%; how much cash did I re- 136. Suppose bank stock is purchased at ... ^ ^"••.«344.93 f . bank declar^a dividend of 9 /per Z^^ ^^"'^ *•»« price of the stock ? ^ » Per snare, what % la that on the cost 137. A person, wishing to buy wheat with fh» «.^^^^* y*^* sends to his agent 32 bales, each weigh n^ 380 Ih ^ T^^^' of cotton, the cotton at 26 cts. per lb for wS l.I^.i? "'"o. ^S"^ ^8^"' «ell8 pay. for freight and ch .- a *-Ti fif ! f^'^^^ ?** commission; re8shiscon.mis«in.«f'r:-T,f;/4Y^^^^ .«*Pends the remainder! bushel, for whichhe ch ir.e f »"i rn7^"^'- '° ^u*'"'*^ '^^ «^ ct«- Per obtained through this Sr ? ^^ ^ ^«"''»'««'««; how much wheat is 138. A pole 63 feet lone in falUn^r »aa u i. • ^^^^ + bu. ^«. le and 46 ft. k:j 164 imOBLLAItmtVft IZAMFLia. I ! 139. A farmer heA Hfln rv 4'\ 'SOWS, each fbrnishing 18 qt. of milk a day, from whi.;h he rstAiC 40 tubs of butter of 60 lb. each in 30 (lays. Ho made a cc'Utract to deliver 100 tubs of 96 pounds each •n 80 day^^. How mm.y cows mu8t he add ti 50, and Cliilda put in £500 more. At the end of the third year they dissolved partnerflhip, and found that their joint prop- erty was £7125. What was each partner's share? Atu. Andrews', £2393 .0 4^ ; Baker's, £1597 4 5^ ; Childs', £3134 5 2J. 142. If T buy 50 sharefi Grand Trunk railroal stock at 141 %, and 60 shaies Canada Central railroad stock at 139 %, the former paying % semi-annual divi(Jend of 4^ijj %. the latter of 5 ^ ; what rate of in- terest shall I realize on my mvestment? Ana. Q^%. 143. What is the cost of a bill on Lone* m for £800 17 6 sterling, when the rate of excliange is 9 J % premium? 144. J. Sheridan bought of L. H. Miles & Co., the folic -wing bills of goods; Not. I, 1870, a bill of $760, on 6 mo. credit ; Dec. 16, 1870, a. bill of $300,on 5 ino.; Jan. 1, 1871, al)ill of|425, on 4rao.; Feb. 6, 1871, a bill ot ?275, on 2 mo. What sum would settle the account, May 29, 1871, interest at 7 ^? Ans. $1760.10. 145. When exchange on England is at 10 ijlj premium, itnd freight at Is. 3d. sterling per Winchester bushel, how much can be paid in Montreal for wheat per bushel, in an«w<;nn<; an ordir from Lon ion limited to £3 10 per Imperial quarter? 146. The duty on an -oiceof ,{00 do? « London porter, at 30^ was $190,512; break a^ , 2%. Required the invoiced price per dozen. Ans. $2.1(). 147. Three merchants ha''e *n interest in a steam vessel ; A puts in $9fii) for 6 montiij; B, j.sua unknown, f"T 12 monti^; C, $640 for a time not known when the accounts \ -re settled ; A received $1200 for his share, stock and profit : B, $24u0 'or his, and C, i,ii040 for his. What was B'a stock, and C's time ^ Ans. B's sto-\ $lv.OO; C's time, 15 mo. 148. Merrill, Wells and Roche we' rtp s inthe gi'ain b" inesa ; Merrill had invested \, Wells ^, and ne of the capital. They were to sbar.' equally the gains or It 's. , he business not being »n<^cessful, the partnership was dissol.ed at tiie close of tlif' "ear, when the resources of the firm were found to be: Cash, $l78a , bar •ey ou hand. !*i'2n00: corn, *1 722; rye, $.350; oats, $1650: wheal. $5000. Tiie liabilities were: Notes outstanding, $1562; they owed P Myler, $1200, and P. Riley, $1875. The net losses were $730. What was the net capital of the firm at conamenciog, and what was lach partner's net capital 7 ^■Wt-m^jk,, A00OUNT8 Of HT0RAO«. ACCOUNTS OP STORAGE. 26fi oJil? '% n"* """''""''" '"^^^^^ °f computing stora-e The andratP«7^r'"''"' 'I '^' '^''^'''^^' cities, -Hlopt such ruleJ and rates for storage as they dee.n equitable. Th. ch rJs fo, •itie. an fractional ,.art« of r.^th^a.^' ^ISored fUlfrnonth;"""''' *" *«"• bu.intsBXTr?ieTvt?a"dTii::lra th'e'.r "rr^- --'"-oa.a,i.«ion « k. pt. .bowing the date and number cfbS^ ' J'' °' "'• ^^ '"''snor. an aooount number sold or delivered. In cZn, ti^nrth^^^ roc,i,ed, and tbe aate and customary to avcnM-e the time nnThlrS *'"''''^* "" '"'^*' »" account it la It- there i/a fraction"a. par of ^ ba^ef et^o i^„ 't^""' '" '" f'?'". """"'^ "* ^" ^^J^"' oat J of parta of months above. ' ' ° ""^ "''^'^'^S^' 't >^ treated 8^ in the OP' RATION. da. X 15 1871. May 1, Rec. luu " 16, Deliv. 600 Eal. "500 X 10 " 26, Hec. 2000 Bal. 2500 X 6 June 1, Deliv. 1000 Bal. 1500 X 11 " 12, Deliv. nOO Bal. 400 :< 20 » prod. . 16000 5000 12500 16600 8000 Analysis. — The srora'o o* 1000bbl.forl5da., + .50UbW: for 0d,)., + 2500bbl.for5da.. + loOObbl. for II da., + 400 bbl. for 20 da., is the f-ame as the stora ire of 57000 bbl. fnrl da orl'JOO bbl. for a month ofao days. Ai.d the storage of IDufl bbU at 6 ots. each « ^114, Jm,, July 2, Deliv. 400 3|0 ) sTooJO -.» s,ore,/,om eaa, dale to Ih, mu next Hlowhl^it hZL T T /«• wM^i Zm ^Z ,T ''"'"fl"'l h "" rale o/,lcr„a. If I .i; ?1I tet OINIRAL AYBRAOB. r ! t ■XAMPI.RS Fori PRAOTIOB. 1. What will be the cost o{ storini: salt at 2 etc. per barrel, reoeived and deli veretl a« fol lows: J ine 6, 1H71, lanbhl. ; June IH, 14<>bhl. ; Jnnc'ifi, GOO bill.; July."), HOO bbl. ; July 16, IHu bbl. ; Jnlv 20, ifiO 1.1)1. All delivered Au'^. 1. /Ins. $21.44. 2. What will be the ntoraj^e of flour at .'» oenta per bbl. per month, received and delivered as follows? li«ceived Jnlv I, 1871, 400 bbl.; Julv 15, M^O bbl.; July 26, 4.50 bbl. Deliverc 1, July 12, 200 bbl.; Julv 20, 400 bbl. ; Aug. I, 200 bbl.; and Aug. H, 40) bbl. ' Ans. $2.5.10. '^. Received, and delivered, on account ot JameH O'Neil, sundry bales of cotton, aw follows: Received, May 1. 1871, 1848 bales; May Ki, OtibaIc«: June 1, 210 1 alea. Delivered, June 12, 800 bales; July 1, 480 bales: Aug. H. H2(i bales; Aui?. 10, 2:)0 bales. Required the number of bales remaining in store on September 1, and the coat of storage up to that date, at the rate of 5 cents a bale per month. Ans. In store, 334 ; cost, $240.75. 4. Received. July .3, 1871, 256 ca«ks of wine, on storage, and on JnJy 1.5, 381 more were ad.iedj July IS', delivered 261, and July 26, 312aisk8; July 30, received 321 casks, and Aug. 8, 163 casks: delivered, Aug. 16, 208 casks, Aug. IS, 103 casks, and Aug. li), 116 casks; received, Sept. 1, 320 casks, Sept. 2, 106 casks, Sept. 7, 342 casks; delivered, Sept. 12, 250 casks, Sept. 18, 321 cask.s, Sipt. 21, 133 casks, and the balance, Sept. 27. What was the cost for the stor- age of the above, the charge being 6 cent.^ per cask monthly? i If I r GENERAL AVERAGK. 49JI. General Average is the process of computing the loss to be sustained by the owners of the ship, cargo, and freijrhl, respectively,— when, owing to common peril at sea, any portioo of the property has been dani:iged or destroyed for the common safety. 404. JetSOn is the portion of th« cargo or of the equipment of the vessel thrown overboard. 4»5. The Contributory Interests are the three kinds of property whicli are taxed to cover the loss. These are, 1st. the vessel, at its vdue before the loss; 2nd. the cargo, inoluding the part Bacrificed ; 3rd. the freight, le.sa j^ as an allowance for seamen's wages. 406. The loss which is subject to general average includes, 1st. Jetson ; 2ud. Repairs to the vessel ; 3rd. Eipeuae of de- tention to which the vessel is subject in port. N«TK8.--1. The goods, whether saved, injured, w deitroj) d, are estimated at uieir valne at *he port of degtiuation, except when the adjuatment of the eeneral aTerageiHiui - at the povt of lading. MNR«AL AVBRAOE. 267 .^■J?. The Hhip « ArMie,|« '> ^„ „ *• w.tl, a car^fo of silk, tea e o ' v "i T^""-^^' ^''''"' '^''^'^"••'^ '-^ Q'^^bec gaie. and the captain v. i co,;;;.?, l!,"' ^^ '''' r""^' '^ '-'< '" ^ her cur^.o value.! at .?^",- 692ir,.00 ^'^^^'^'^t ... C400.00 .,„ ^^'^^^ n(m75 , j-,,,^, $7030.75 -f- $14061) - P'i . . S/r.nnn y^"'''-' - -05, rate per cent, of loss. 9>i 1' i ^ -Murphy. & Field. 1155.75 =V;;SKtS%^:--'-''n^'^^ $500 ^ the general Iosm i.s .^•.^750 - §'g:,,-, 75 -- .-?^„ ,■■;':' '""^t conirilaue to other owner, of coniributory interests TutX;. •'^"/'"'='' "'" ^''« f;°»^\^''« amount of hi, pa/,,;;;r'jj^^^^ '" ^'^'^ •''*''"'^'«'^ ^'Sio:'''^^^^^*^'^;'''^^;--'- « . freight. " account when equated, to stand as follows: Dr. Cr. ^% Nov, 21, 1871, $660. j D«« Oct 10, 1871, |876« AVERAGINO OF ACCOUNTS. 271 Creaks* '' $87?""''^ ''""' ^'' the pay.ent of the balance ? Debits, 650 f;^ ^ ^V -^ 2::r. = U3 dav.s. — Halance due 1(];5 .lays previous to Balance, !i!225 '^' ' ^^^^' "'^''"'' ''' J»>ie II, 1871. Difference in time, 42 days. toJfrTa'tdTt^^^t&tTom Vr".rif '^^^ ""Z- ''-J^' -«-^'' -^'« »' equal "de of the account may beTry.reLdiJL .^'' "^ '^^ '^^''^''- Th«t the d'obit of the account must be re4rTed ' if fiV?"''' "'""•"' "f i.i.rost. tho balance Or tkm : ™oaraoa as duo 163 days p,-ev!oua to Nov. 2J , or June 11. Jays. L N. ?^ ,t en^M.J, '^J^ ^e 're^t-of V'^,.'^'';;^'^^';! '^ "^ <'f^^r^^?^ Hence, the balance must he rei^rdec Is l! if -^f ^^° ''■''"''"> ''"• '«•'* ^'-^ys. simple question is : How lon^^mn,/ t'";- ? ^^ ^'''^' /"-em-.u, t.,. Nov. 21. The J!875 fo?4L' days. '""^ "'"'' *"^^ ^'^ «« "ifor«'t to equal the interest of evlT^r/nJt; mus7be*d?ted Juie Tl'^87t'' '^''' ""'^ '"' ^"^^ ''*"""'«' ^^ « accl!!?;«,v"^^~^''''*'-^'''^ ^'"' '''.'/ ''*« haiZ'o/ttt:!:^^^^^^^^^^ t?'' f-;>.w^.ri, ,f: LARa4,:r7«?rfi,Ht. '^""' ""'^ "'^^"^^^^'^ -^^^^ '^^ ;j»frf f^^^^J^Ji^^^^^^^^ smalle. «".« of ^'•.-.^ -« . j; i E;?r;t^;/srs;fi?st '"""^"'^ ^'- "■" ^• ANOTHER METHOD Due, 1871 July 3, $220 X 2 = 440 Oct. 1, 126 ;; 92 = usoo Nuv. 15, 200 X 137 = 274i:0 Feb. 24, 140 x 238= .S3320 April i, ii;0 X 274 $876 660 $226 Due, 1871 July 1, $200 X = Oct. H, i/,o X 04 = 14100 l>ec. 20, 300 X 172 = .01600 II /' / 272 AVBRAOrNO 0» AOOOUNTS. ExPLAXATioB.-We assume July 1, 1871 (the earUeat date upon which any Uombeeomesdue , as the «rne upon which aU the items of the Loount become due. The interest of tho debit items, from this assumed date of maturity to the time thoy respectively booome due, equals the interest «( $1 for 124720 days • the interest of the credit items equals the interest of $1 for 66700 days. Henee' the b.lanooofinfcrestiB favor of the debit side enuals the interest of $1 fo; 59020 day., or $225 for ,^J^ of o9fi20 days « 262 days. Since the balance ot .tem« ,s also m favor of the debit side, it is evident it can remain unpaid 262 da mthout mterest, or will become due 262 days from July 1. 1871, whi h is March H ,o 9P r, •"''*°°* °^"®'"' ^"^ ^««° °° *»»» credit side, it would have been due 262 d:)ys previom to July I, 1871. 501. Rule.— I Assume the earliest date vpon which my Hein of the account becomes due to be the time ofmaturitu for all the Items. ^ •' II. Multiply each item by the nnmber »f da i/s in fervenitw be- tween ths assumed date and the date upon 'lohich it brcomesdue ^'^^J'^y/'yi'"^ of these products on each side of the account. Ihni divide, the uiFFrRKNCB lefwecn the sums of the debit and aedit products hj the bahince of the account; the quotient loill be (ue time for co7isidiO(ftian. III. Whm the d:ff,'tence of products and the balance of the account fall on the same side, count FORWARD; when on opposite SldtS, COWlt BACKWAIin. Notes.— 1. Tho latest date may be used as a startirg-polnt. n .™ . 1"'^'"'=' "^ ""3^ «f '^ *LT' '''"'" '^« '^^'^^♦''' 'f ""J"' '"-e less than 5». reject ti em } whoL more, ad J $1. The work will ha .ufficiertiy accurate. KXAMPIES FOR PRACTICE. i. J. Mar|«hy has wim C. Duval an account, which, when each side fe equaled, eiaitdaaa follows: Dr. Q^ Dae, Sopt. 5, $1542. | Due, Sept. 24 $12%. What 18 the equated tiiue of payineit for tlie lal. ? Am May 28. 2. L. N. Carroll has with Simina & Norris au account, the debit and credit ndes of wtiicli, wlien equated, are as followa : Dr. cr. Due, Feh. 8, $650. ) Due. Feb. 12. $2180. WhAi inu^t be the date of a note for the balance ? Ans. Feb. 14. 3. What is the equated time for the payment ofthe balance of an accoautj which, wh?n the two n^des are equated, tianu? a« toiiows. ^r. Cr. ' ' Due, June 12, f 540. | Da*, Aug 1. *960. Ans. Oct. 4. AVBHAOINO or ACWOCNM. Dr. Due, Oct. 20, $2528. Cr. I Due, Nov. 25, $1800. • Wl,at „ the balance of the foH„.i„g .„„„„„, .„, „,^„ ., .^ ^^^ Dy T JOHlf WOODLKT. fy June 15( '« Mdge., ifol II *^^^ I I J!! f P"J 25 By Cash ||615 yu June 10 " <■< I ion 00 II July 20 1 " Mdse. 540 00 00 Ans. Balance, $615; due June 2M87l7 Z>r. C. Rtan ,k ^cot. with N. Mi,,kr & Co. Or. Feb, Allrch 20 I u ,; I f8 | 00 || May .. - " - ' ' ,;^f 50 June 14 " « 106 00 << 22 To Mdse. $ 44 7n P.. L 24 '< « oo !" ^^^- * By 20 w « ?8 00 May 16 40 \i I; ;■ *rM El i 274 AVEIRAGIiro OF JLCOOXKI'TB. Dr. S. Thomas & Son in acct. whh R. Hill. Cr. 1871 1872 May 11 To M(lse. .•*680 56 Jan. 11 By Cash. $400 00 June 16 u u 272 60 " 29 « it 352 00 July l.'j <( (< 144 20 Feb. n « « 80 00 Aug. 23 (( u 400 00 " 25 U H 784 00 «' 30 « it 272 32 Sept. 9 « « 64 00 Ana. 808 days back of Feb. 7, 1872, or on Nov. 21, 1859. 9. What is tlje balance of the following acct., and when is it due? Dr. L. Murphy in account with A. Kelly. Cr. 1871 1871 May 1 To Mdse. $218 00 May 25 By draft, at 60 da. 1200 00 June 12 a li 274 Oil June 6 " Cash 325 00 Sept. 16 '* Sundries 156 00 Aug. 20 " draft, at 30 ia. 100 00 Nov. 14 <' Mdse. 268 00 1 Oct. 3 " Cash 42 00 Am. Bal., $249, due Sept. 22, 1871. 10. Suppose the following account was settled May 6, 1871, by draft on time, how many days' credit should be given ? Dr. P. Robinson in acct. with O'Neil & Co. Cr. 1871 1871 1 1 Feb. 1 To Mdse. $ 73 44 Feb. rO By Cash $197 44 March 1 t< « 96 50 " 21 (t u 51 68 April 17 « <( 144 72 April 23 " Sundries 30 34 May 1 « « 196 96 May 6 " Mdse. 17 92 An8. 19 days ). 11. When shall a draft for the settlement of the following account be made payable? Dr. S. T. Mitchell in acot. with R. S. Lee. Cr. 1871 June 1 July 14 Aug 16 Nov. 25 To Mdse. oa 2 mo, " " on 40 da, '' Sundries $108 56 191 52 72 1)0 44 1871 Sept. 1 Oct. 15 Nov. 10 " 20 By Cash •' draft, at 30 da. " Cash $100 60 250 300 Ana. Feb. 10, 1872. 12. When shall a aot« be madf payable to b»lanct! the following wcount ? Dr. $400 00 352 00 80 00 784 00 1869. is it due ? Cr. dk. 1200 00 ;J25 00 \. 100 00 42 00 ,2, 1871. 1871, by Cr. $197 44 51 68 .30 34 17 92 19 days. >g acco unt when v^i] the baJannlTA"" *"' *^^« "«'"« to and wishes to diXrAi' ir ^r""' l^> ^"<^ ^15uf, dueNoJ 1« at an interval of 40 d^,f ,ft^^«»^,^ two equal p^ymen^ n. d^ 16. A merchant holds 3 notil ^^ i'^ '"^^ payments be made? -^ace, !j,1080; maturity Aug. 6. CASH BALANCE. ''mmmmmf:- 0A8H BALAN(». OPBRATIOIT Debits. 88 = 14080 68 = 29920 51 = 5100 43 = 4730 31 = 10230 28 = 10360 11 = 2420 OrtdiU. 100 110 330 370 220 X X X X X X X Due, March 7, $ 270 " 28, 200 Ma7 2, 440 20, 720 $1730 6 ) 76840 Sum of debit items, " " credit items, $12,807 $1730 1630 it Daift. 86 = 65 = 30 = 12 = 23220 13000 13200 8640 $1630 6 ) 58060 Interest of debit items, " " credit " $9,677 $12,807 9.677 Balance of items, $100 Balance of interes*, $3,130 True balance June 1, $100 + $3.13 = $103.13. Explanation. Since each item of the debit side of the account was on interest from its date to the time of settlement, the total interostof the several debit items equals the interest of $1 (or 7(5840 days, which, at 6%, gives $12,807. (The int. of .-S I for 6 days is 1 mill; hence, the interest of $1 for 76840 days is found by dividing 76840 by 6, and pointing off three decimal places.) The total interest of the several credit items equals the interest of $1 for 68060 days, which is $y.677. Now, instead of imreaaing each side of the account by its interest, and then finding the balance, this same result may be obtained by finding separately the balance of items and the balance of interests. If the two balances fall en the same side of the account, it is evident the true balance will bo their turn ; if, OD iifferent sides, their dijerence. METHOD BY INTEREST. I 1 1 ■ 1 JF^ ■ Wp I Dv», Daye. Int. March 5, $ 160 for 88 = $2,347 April (. May <« u 25, 440 " 68 = 4.987 11, 100 " 51 = .860 19, 110 " 43 = .788 1, 330 " 31 = 1.705 4, 370 " 28 = 1.727 21, 220 " 11 = .403 $1730 112.807 Due, Oaye, ht. March 7, $ 270 for 86 = $3,870 " 28, 200 « 65= 2.167 May 2, 440 " 30 = 2.200 20, 720 " 12= 1.446 « $1630 $9,677 Balance of items = $1730 — $1630 = $100. " " interest = $12,807 — $9,677 = $3.13. True balauu«) ;ipliiO ■^■ «i3.l3 = $l03.io. NOTK.~Tbe " Method by interest " will generally be found most eonveiuenk •ither for finding the equated time for the payment of the baienoe of aooouatt, or (■ iadiag tbe oaw Ma-'^^ •ASH avrAWOl. f' 6 = 23220 5 = 13000 = 13200 2 = 8640 6) 58060 $9,677 9, $12,807 9.677 $3,130 as on interest A debit items 7. (The int. 8 is found by otal interest l^s. which is interest, and ig separately 8s fall en the : ium ! if, oo •, Int. < = $3,870 = 2.167 1= 2.200 = 1.446 $9,677 13. t eonveiMent aooouBta, or 277 Mar. 6 ToMdse. " 25 April 11 * 19 May 1 4 21 June 1 Jjyint. EnroK excepted, Quebec, June i, i87i. AsDREws 4 Son. ANOTHER METHOD BY INTfiBMT. *!f-,ilT?i»^'-.«fa"acot.$100 ;; l5;;Ca^,paiddraft -fiO Mdse. on 6 mo. By Mdseon 6nio..$I60 8# ,, J^«!» 10900 .uX'"^ u.e cash ™.„. of 'i^^i^^r^;::;;;::^;;:;:^^ OPERATION. Mar. I " 15| Sep. 20 ^,¥JJ-i5 + .3.l38 10.'J.288 15|180.86~. 4621180.398 .April 1 157 'llJuiie 1 96 '("""15 !oot. 10 324.846 JOJ-00 + 2.617 102.617 120.00 + 1.920 121.920 inl]«n'SJ+ -"^'^ ^0.033 351 80.G0~ .'G7| 79.533 • dan J of interests. cashbalan^ 'Z'l T^""" ''' ''^^'^*''^ ^^d^ of the account, the duft\t'r''''i' ''^V'^ 'temfromthe dateon which it becomes t2^VsonZ\flT^T'^ ,7^5 ;A:^b,..ce between the sumZ} JKAe« //ie lala, ce of interest falls on thi same side as the balance of, te,ns the cash balance will be their SVM tolZ ol "PP0>>,te sides, their mvftMESCt:. Or ' 0/ ^hT'add^^'^""' T "'.f '■'• "'^•^"'" ''^^ <^^-'-^^J^onding interval ^(/c^ each cotwiiu of cash values, and the difference of th. amounts will be the cash balance required. '^'•^*^'^"^" ''f ^f"' EXAJIPLES FOR PRACTIOE. 1. The following account was settled Nnv ifi ib-ti uru . Ih^caA balance, i.e.«. being corpSdt"e'ao'h «™V,„?jr« /J- T TH ^"«- *2 15.54. ^r. John Fbaseb ly acct. with L. R. Barry. Or. 1871 Feb. iITo Merchandise 4 « a 22 " u 19 " Cash 22 «< Merchandise 10 « <. ]^|*' 6a/. new acc't. April May July <( Oct. Abv. $ 72 187 250 60 300 125 00 00 00 00 00 00 1871 I ^~ Feb. 16 By Cash March 241 " " April IG " <• " 20 " Mdse. June 27 " « Sept. s\ " Cash ^ov. 161 '< bal.ofint. $100|00 160 300 90 360 200 00 00 00 00 00 Errors excepted. Quebec, Nov. 16, 1871. L. R. Bahrt. ^ Detc r,' Ma^rT '"ZTT' '"'f"' "^^ '^^^"^^ * ^^^ ^^ f^'^^^- .- A-;'9 tn m^L ' Q ' ^ inerchan.ljse, on 3 months, $721.50 • .48 , July 14, to indse, on 2 months, $470.60. Credi or Mam 71. by cash on acct., «600j May lo', by iM^epUace at 30 day^ II 21 ACCOUNT OF 8ALM. ^ *'^°-"'i"- -^ -"-nfa o'„"i/;i^, -■.. o" .00,., ,;o„ Cred.tor, April ., l^Tl/by cash "mo ''/""." ^' ^^ '"d.^e,So 75' ^n»- »23.52, ACCOriNT OP 8ALES. -f K^ ^.-5s^^: ^^S!oi^„:^;^-ent of the ,..n,:e, ne proceeds, which n cormulXnl^'X^f "" '^'' ^.'^^■^' ''^"'^ »»>« to his employer or consignor ""^'^^hant or consignee wakes aft^ ^UhCt ^d& I? jii^V''^ ^:?^'^^^^ '^ «-'^'ed at the equated ti„,e of the different 'Tes ^''"""^' ^'' ^"« '' «^«1» ^ate. I Purchaser. 1871 Jan. 30 Feb. .s " ](i **■ 28 Marcli 20 April 9 May 7 " ;^o L- N. Maguire KeiJer & £ee J'- A. Thibodeau i>' L. Morris Vanner & Simins o. h. Ljnian A. Hamilton H. F. iJurton 1*. Sullivan Description. Wheat, white Wheat, Ont. Corn Oata Wheat, white Corn it Wjieat, Mied. 190.00 704.00 880.00 450.00 600.00 S86.00 >03.2« 216.00 687.60 l$53US0 IMAGE EVALUATION TEST TARGET (MT-S) 1.0 I.I ^1^ 1^ ^ i^ 12.2 •yuu Hi 120 L25 II 1.4 m 1.6 irvr'^ Sciences CoipoiBtion 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 ^ i-C V \\ ^\ ^■a>^- 1^' £^. i/i 1 I 2W AOOODNT OF 8ALM. Charges. ComnoiseJon on $5316,80, at 2^^ Way 30, Freight on 764 bushels of wheat, Drayage and sacks. Advertising in " Mercury ", $182.92 38.20 40.S0 6.26 218.17 Net proceeds to credit of C. Morgan k Co., $5098.63 Errors excepted. Quebec, June I, 1871. JoHK Laird & O'Nbil. Ex. 2. AoconKT Sat.es of 1300 barrels of flour, sold for E. A. O'Dow 1, Moitreal, P. Q. 1871 March « u 23 27 28 500 I arrels Flour, at $6.00 cash 400 " " 6.00 60 d " 6.00 60 days $500.00 Ca^h 700.00 200 " 200 " i< 3 months CHARnxs. Storage on 1300 Ibis. 1 mo., at 3 cts. CoiLiuisijion on $7850, at 2\%, Net proceeds, due. K. E. Quebfc, March 30, 1871, L. RussfiLi. & Co. Per Louis Bllodeau. a as fei •S3 ■H eS O) m h3 ■< O < 4 ACCOUNT OF iALM. 218.17 $5098.63 t) & O'Neil, M for B. A. 1250 7850 00 7614 75 c 03 eS 0) CO u 00 02 h O o ?-^ ■o a o u c J3 CO 00 4) 9 Z, -• 9> OJ ■* s 01 « .5 2 "t/J o a c8 CO •*3 CO ■iu ig !J3 - 3 - 2 ■» •• <« —'■—<•—< i—( -< csi esi -H C^ 00 »— * CVl "— • c:; »— i ^-' c^ r<4 ivi ivi Cs 1— 1 Cs| •* i.-j O C? O Oi C5 «^ CM e^ e<4 5S, o SM o o CM 5M c: a, fC — ^ i Bilodeau. .4 u fi ;. •il » m H i I lil i ! MPTTg^ *C" i!-''nQftig*TJ ' •& gimjg 282 EXCHANOl — fORBION OOIWi. BXAMPLES FOR PRACTICE, Montrea , by L. J. McGreevj A Son. Quebec, viz. : July 2 I87i to Jo,^ Wlute. 400 bb . Ohio extra, at $8.30, 19 bbl. fine"i $5 : Ju ; 5 oSweeuey&Co 125 bbl. Canada extra, at $7.50. 'charges as fol- «in J. i ' ^'"'S^** P,"" Steamboat " Quebec ", 544 bbl. It 16 cts., in Is f ^'"^?' °'' 'ilfTrV '^^'■^«"' 3 *'*«• P^'" bbl. ; insurance ai^'fl i f «;»'"'^«'"" «" ^P?,¥^' *^ '-^^ ^ ^'^^"'••^'^ 'be net proceeds and the date when they shall be accredited to the owner 9 T Rn /i?*^^^*P''«ceeds,.f 4 139.46; due, July 10, 1871. .f k, ; P^ fa?*"- *?^ ^^'•on'"?' received into their store an Invoice of Fru.t per Grand Trunk, from the United States, on acct. of T. A Kane, New Orleans, and sold it as follows: Aug. 3, 1871, 100 boxes raisins, at ^3, cash, 52 boxes lemons, at $3, cash ; Ad<^. 4 25 boxes oranges, at |3, and at 60 da., 200 jars olives, at $0.50, and at 60 da.^. Tn^'T' :^-T^''' f* *''^' ^'^'b: Aug. 9, 25 boxes oranges, at *3, and at JO da., 20 boxes lemons, at it:3, and at 90 days; AugTlO, 150 boxes oranges, at $0 cash llO boxes, lemons, at $3.80, Sash 220 jars T ih^i !^0.50, cash. Sold at auction the three last items amouniino to .>1278; auctioneer's commission on .>1278, at 3A *. deducted" Aug. 10, 4000 lb plums, at $0.50, and at 4 Months' \7llttl were: duties and permit $340; freight and primage, $108; cartage and labor, !t,12 ; relunded for damages, $55 ; storafe and advertising, $.2.54 ; commission on $4314.27, at 5 %. Required the net oroceeds ffid when due? Ana. Net proceeds, $3531.22; due, Oct. 24,*1871 TABLE OP FOREIGN MONEYS OR CURRENCIES, W..fl THE PAR VALUK OP THE DNiT, AS FIXED BY OOMMEROIAL USAGE. Cities and Countries. Argentine Rep. Austria. A zores. Baden. Batavia. Bavaria. Belgium. Denominations and MetaL I 100 centesimos = I real; 8 reals = 1 dollar (silver) 60 kreutzers = 1 florin '* 120 " = 1 rix-dollur '» 60 batzen = 1 ducat (gold) =s 1000 reas = 1 niilrea (silver) = 60 kreutzers = 1 florin " = 48 stivers = 1 rix-dollar '• = 60 kreutzers = I fl rin (silver) : crown, " dacat, (gold 100 oentimM = 1 frano (ulTer) ■ Value. $1,016 0.485 0.971 2.278 0.830 0.397 0.782 0.395 1.072 2.274 0.186 nand 4 Co., 2, 1871, to $5 ; July 5, larges as fol- )1. at 16ct8., ; insurance, let proceeds, 10, 1871. e an Invoice ;ct. of T. A. , 100 boxes 4, 25 boxes \d at 60 da.. 3, at !?3, and 0, 150boxee b, 220 jars i amounting , de.ducted ; riie charges 08 ; cartage advertising, let oroceeds 24,'l871. rHB Ali ns^QE. Value. $1,016 0.485 0.971 2.278 0.830 0.397 0.782 0.395 1.072 2.274 0.186 «xoiiA:,MK--roREioN concB. Cities ftnd Countr'es. Denominatirns and Metal. Bolivia. Brazil. Bremen. Bruno wick, f^hili. China. Columbia. DarmstiJt. I^enniark. Egypt. England. France Frankfort. Genoa and Piedmont, } ^ r^M= ^ dollar (silver) - I doubloon r„\ul ~" bnnkt'tcT "° ^"''''"' ''''■ «'-ling per milrea in Spr:firi-?--OP-0 core. j 100 cents* I dollar " - i . doubloon Ccrnlfl^ 'Oca«h,,candaruif?Jern.) ^ Thr "i"*^®' 10 mace = I tael i C'^'Iver) for'?n?|;?„^K?,a^r'^°"'' ^^- «d-. -re orl«s. j ''^ ^.^^'f .-^ 1 doUar (silver) - i douWoon (sold) . 60kreutzers»Ig„iMer(„,ver) = n.ark,rri:lrarUltt:i^^^^^^ Frederick "or fcro hh ^ Jxchange on London U 9^n,.bank~' daler for £1 2r.f rer^rK^f t<^-'^) f- f- 2.60 to fr. r^reaTSerlJ^^'^^'^^'^-'^-.i i'.xohan on for £1 .teWing ^' ^'^ ?'*«'«•"' "o^e or less. Exchange on Paris ".ll •> qoa f l2penc^=rSC"320a.pperl00fr. I f/l"i;ing8 = i;iet;i.ling.C(.oId) I .£1 or 1 sovereign = C I n'New^tr'^"" '^„*^-««5 in Canada, ill i\ew icork u is usually 7 to \i),- . > sterling in London is wor'h «4 j//' t'^*" ''"'""^ addiUonal, in New York * ''' '»"'i ^ to 10 % 100 centimes =1 franc (silver) = ^xchange on London, fr. 25 50 fnr J^i =» .• ^ Excha^nge on Na. York f^d^^^a^ 1v.^"& to ti;^^^;;^:^rS; or tloria (silver) = £1 8te,lin|. ^*"^ ^^-^^ '"•'^' "Hre or less, for Bxdiange on Pgd*, 31 y^ ^ ^^ ^O. 28a lVali»*. , l.&M )15.580 0.830 0.788 0.692 1.011 15.660 « 1.480 1.022 15.617 0.397 1.051 3.932 4.866 0.186 * 'II ■■ 'i I ' II- ;• 11 h ft « i 1 '' ' I ■ 5 Hi 284 EXCHANOB— FOBKICMI OODII. 4;. ^1 Cities and Countries. Greece. Hamhiirg and Lubeck. Denominations and Metal. VaIm. Hanover. Hindot-tan. Holland. Italy, Florence, IjOghorn, Lombardy, [ Venice. J Japan. Madeira. .Madras. Mecklembur2. Mexico. Monte Video. Naples. Norway. Persia. Peru. Port,u<'ul. 100 lepta = I dragma; 1 dra-^nia (silvar) - ( 12 pfennings = 1 skilling; 16 .^killings > 1 < mark banco (silver) - ( 1 ducal (gold) = less, tor jbl sterlin'T. ^^^^^^''ange on PfTfis, fr. 1.60 to fr. ].70 per mark j 80 groshen = 1 florin (silver) » I ;^0 groschen = I thaler '< > j 12 pice = 1 anna; KJ anna« = 1 rupee(sil.)-: ( 16 rupees = 1 niohur (gold) = lof ^"''"r?? "" London, at^ Uoinbay, 28., more or less, for 1 Comiiany'.s rupee. j 100 cts. = 20 stivers « 1 guikier or florin ( (Sliver) =» Exchange on London, 11 g. 80 ots., more »t lots, tor ±1 sterling. ' guHdeJ""^^ °" ^'"■''' " ^''* ^" "*'•' ™°'^ " '"«' P«' 100 centesinii = 1 lira (silver) = Fxi'hango on London, 30 lira, more or less, fcr £1 }V ■ '"/«"' '° "nd Milan; 30 lira, more or less, per ±1, ui Horence and Le.,'horn. Kx(;han,^e on f'nris^, fr. 85, more or less, 100 lira, in V.nicoandjMilan; 80 to 85 centimes per lira, in J lorence and Leghorn. ^ ' 10 mace = lOO candarines (silver) — 1000 reas = 1 milrea <* » 42 fanams = 1 pagoda (gold) -i 1 florin (silver) - S S reals == 1 dollar « „ ^ 1 doubloon (gold.) ■= J 100 centesimos = 1 rial; 8 rials =- 1 dollar ( or 4 pesos duro «■ ^^Kxchange on London » 52d. aterling for 1 peso ' 10 grani = 1 carlino; 12 carlini = 1 scudo (silver) = 10 carlini =. 1 ducat; 3 ducat = 1 ounce (golil) = 1^ xchan.^^! on London, 575 grani per £1 sterling, hxcha.igo un Paris, 22 a 2a grani per L fr. V lb skdliiigs = 1 mark; ) , ., I 6 marks = 1 rix-dullar j ^^''^^^) = 100 n)aravodis= 1 tomaum (gold) 1 8 reals = i dollar (silver) '100 reas == 1 cruzado; 1000 reas — 1 mil rea (silver) •= 1 crowu (gold) «■ 0.1 cs 0.3»0 2.25T 0.04) 0.694 0.445 7.109 0.400 0.16S 0.T60 1.000 1.H40 0.641 1.005 15.534 1.000 0.960 2.485 1.051 2.233 1.005 1.120 5.813 Cities and Countries ■XOHANOR-FORKICN COINS. Denominations and iMftai. 285 iValue. Prussia. Rome. Russia^ Sl Domingo, Sardinia. Saatony. Sicily. Smyrna an(i Ihe Levant. ISEF?^"^-":s-. I grosjipn: ;io Irea. per ^Tosjien = Spain. for^J?t"r; ^°"^°"' « '»>»'-■' 25 ,.., .ore or ,es., b.e'^Sr^^'^ "" ^°"^-' ^-'o- ^^^'^^ to 42C1. for , „>„. roS'sK."" ^^"«' ^-- ^- ^.10 to 4.20 per 100 centime.s =. 1 dollar = 100 ccntesimi = I lira Csilvor'i :. (iTo^oT'"^- °" "'""'"'^ ^"'^ ^-'« - for Genoa. ilf'*'^'''"r ^ thaler ^silver) - ii-xobango on London, thal«. 0^'' " ^ or less, per £1. ' '"'"'" -^ 'iroschen. more j30/ari=lL';^^^'^^'7~'--li(s^^^ Like Constantinople. " ^^ ~ i In the Levant are likewise u^o.i f , Spanish dorars and Dr.tch H.^n •" ' """^'^ «^'ent, ducat?. Likewise Ge man r^""''"'^ '""' '''^^'''i'i^" $0.96 to $, being sul?:7,t:S^ tl.aler = r 4 reals vellnn — i . f * * par piaster, I 1 doubloon /• . ,. ^ I 1 pistole ^"''/.'J) = Exchange on London, 40d sfori;„» ' "^ per peso^duro or Spanish .oiuf^'g.-- ^i-' du^^Sar''''"^-''-^-^^'^^^- 5 30 per peso 'C4S.kHlu^.e marks. I nx-doilar specie ( 12 n.arks = J j^cat (gold) = S:o::K°r;^^^if^^'"f-^-on.^,«^.. Kxchanc^o ot Ba«Io on I i'"'"'"^ = le«8.for£l. '" °" ^^°"don. fr. 17.5, more or li'xchange on Piu-iH fv i -„, 0.227 1.000 0.7;j4 o.:i«i3 0.186 0.61)4 O.9.S.) 2.4U0 1.059 2.267 ( 286 EXCHANGE — FOUaiON OOINB. I I Tripoli. Tuni8. Turkey. Tuscan V. United States. Wurtenibur'T 120 paras = 1 utchlik (silver) « 16 carobas = 1 piaster '* » 100 aspers = 1 piaster '< = 20 piasters = 1 yorniilik (gold) = Exchanj,'o on London, 104 piasters, more or lew. for £1. Excb. on Parirf, from 400 to 410 piasters for 100 fr. ' 12 soldi = 1 florin (silver) =. 1 crown or corona '* =» 1 ruspone (gold) -= 1 sequin << m NoTA.— For Exchange on Lonaon and Paris, f«M Italy.) ^ i 10 mills = 1 cent; 10 cte. — I dime; 10 I dimes = 1 dollar (gold) «= £ ftO kreutzers = 1 guilder (silver) «= < 1 crown •< oa ( 1 ducat (gold) =. Excliango on London and Paria, the same m for Frankfort. 0.149 0.124 0.026 0.877 0.262 6.92d 2.301 1. 000 f..H95 1.070 2.236 EXAMPLKS FOR PRACTICE ON KXCHANGE (see 406). . « / '^''^^- "^^ Toronto cost £187 lOs. in Liverpool, exchange being at 8 ^ prennum tor sterling ; required the face of the draft ? ^ Wiiut IS the cost of a draft on St. Perersbouri,' for 6i)1.5 roubles 50 copecks, exchange being at 74 cts. a rou ble ? Ans. $5 1 1 7.47. 3 Received of J. Walter & Son, Glasgow, a bill on Messrs. S. Ross t?Z'L f^"^''^^'-^'''i^^'^^ ^^'' W^^^ ^«« •*« value in Canada currency, the premium being y% in favor of sterling currency ? A WK * ■ .1. ,• ^"»- $5540.833 + . 4. What 18 the value in francs of a bill for $976.60, allowing a premium of 3 ^, and ;-i^ fr. to the dollar? Ans. 6359 fr. 29TeQf o. A merchant in Halifax has 8250 guilders 5 stivers due him in Amsterdam, and requests the remittance by draft; what sum will he receive, exchange on Canada being in Amsterdam at 2^ guillera ^ . . , •:, . « ^ AnS' $3666.77+. 6. A broker paid m Ottawa $8030 fbr £1650 draft ou Dublin- at what percent, of premium did he purchase it ? Ans 91%, vT^l , ^' is the value in Canada currency, of 2000 florina in the Welherlands, at 2^ ?« premium ? Arts. *.S20. ». Iwenty days alter the date of a draft drawn at Genoa, Dec. 3 ib. I, at muety day-s, for 1820 bras 15 soldi, C.Jenkine to whose orda .'t was drawn, requo.sts payment, and proposes for prepayment a iisoount of 3 %. What id the value of the same in Canada curreacy alldwing that the «oroDa bears a premium oi5%^ Am$. $1948.11. ARBITRATION OK EXCHANa*:. ..gy lor tin. .„,„. .,a the rate of Sd. 'ter n / ni ?L 1''/ '''" P^'-ol^ased 'f'- f- O'lJrieiK.fMontro'il 1>^;. • . ^"*- i^"'Jf"» liras. ;;; :£<-0(), to IVne & ^^^'1i,^^"f "S' , ^ '^'^^^ °^<^ats. val„e,l >aoetlK^.a..etoU;ra£^;;,l';^^^^-^i^-Krauss, 11301.50, and Toronto, Sept. 14, 1871 Yours &c. „^Naple.s, Jan. 3, 1871 ^*'"'" °^^ 'T""''''^ What i.s the value of ihe above ,^rnf> v "^'^ "f'^^« * Omim. ■'^ dwoouut of 2 5^ being a lowed for n^. '^ ^'''^ "^^ '^■^^ ^^'^ ^^te, at '"andingaprenuumofsiT Prepayment, and the scndi c^,»- ^w«. |208;igJy. AliBITliATION OF EXCHANGE. Putl^tct't^e'^b'tl^^^^ - *^« P-eas of co^. clrawn on one ^r .norr"t^re!l1i;r&" ^' '''^ °'^^°^-^« ?. "Iiat must a neraon in ir!»> °' ""= ^'o »f '2-5 guililen tn f 1?I Ol'KRATION. *' Or thus : ' ^ I $40 X 1.096 • * = $4«7.2fiL -Analtsis.— Since it takes £i in 12.5g,ade„on Amsterdum.it^m '^'^^ T2T *" ''"y a «>ill for 1200 guUder8;bnta bill on London for :£! costs m Montreal 1^x1.095(42?). Moi?l!S! "•"""V"™ ''• draw a rer- Meal line, ^d pli^f, .qaividento wUk M ft 268 ARHITaATlO.N OF RXnHANQK. I :'■ Squared a?i,Mv^r^r°/'^ °PP^"^ ""*> "*^«'' »>«'^"nl''(f with that oflh. tennru^,?r ??i ^' * *•• ^1'. '":"!«"!«"<'<' i^ 'l<"n"t«d by «, and so arrange tha first on^lr St .T"'k?",'''\''''^' '^'^' ''° "f 'ho same denoraination as the ■0 on should there be a Enrcator number of terms. Eof. 2. A morchant in Toronto wishes to remit 8000 franoa to Pari« Jy circular o.xcl>an-e throu^'h Lotvlon. If exclnn-e at Toronto on 1 ans 18 at the rate of 5 francs :{0 cc-ntirnos to the dollar, that at iZu ,r^" '''"' ^^'''^ "^^'^ "'■ ^^'' '''^"^8 20 centimes to tl.o £, and tlmtHt Toronto on London at 9 % premium, how much le-^.s thin by airectexclian^^e, will It coat him, kuowing thut he pay.s his a^ent in Liondon i 91$ commission? ° A\Ai-YSi?.— The cost of the 'lireot exohanj^o would be an many ilollnrs as .SOdll contiiitis 5.3 == lo()'.).43. To (ind tlio cost of the oirculnr ex- chan'j;o we [iroooed as in A*, l.ex-ept that in ihis cajie the factor I -(- ^ c^ == 1.005, iiuiift bo in-iluded amoni,' the ftictorfl on iho right of the virtinal lino to cover the commission paid to the agent in London. OI'EIUTION. W = *150',u;i + . thecostof direct exchuncje. t:t I HdOO fr.' 26.2 fr. I £ 9 £ !P40 < i.o<> ' 1.005 $T = IS14S6.6I +. $1609.48 — *148().f;i = ^522.82. — difference in favor of indirect exchange. 50« lltiLE.— 1. Draw a vertical line, and place the equivalevt sums with the characters denoting thrir rer,pecfive units direetJu oppns%teeach other on the left and right of this line, representinq the required sum hy x, and writing it first and on the left, and arranging the other terms so that the second on the hft shall he of the same denomination as the first on the right, the third on the left the same as that of the second on the right, and so on. II. When a commission is allowed for remitting, put 1 plus the rate on the right (Ex. 2) if the cost, and on the left if thr proceeds, 0/ the^ exchange is required. When a commission ' ts nUowed for drawing, put 1 minus the rate on the left if the cost, and on the right if the proceeds, of the exchange is required. III. Divide the product of the terms on the right hy the product of the terms on the left, and the quotient ivill be the answer. rinI^Z'"Jh-rP°''T'"'"^''i'P''''^«"'''Soon the price the agent who T^h^UL f^u^t,"/^'"'^''"^^' ""'^ oommission on drawing i. a percentage on the value of the bill at the place where the agent besides. t-ain.ige EXAMPLES FOE PRACTICE. h When exchan-e at Quebec on Liverpool is at 9 % premium, and at Liverpool on Brusseln 25 francs per £ sterling: what wilUe^he Ilh that of the so arranjje tho aination as tho the right ; and inca to Parifl Toronto on lar, that at [) tho .£, atui le' ami ren.it,, the ,Hiiie to l,h u -,.„ „ p i'"'';'"' "' ' V""»<"» "f » % i *, '.ow ,„„„,. ,„„, Z:^ e„'l-- ^.n.i .1.; «l,i.l.^- |;;H,r,*,.„,,e •''• When evohinrfo ;« c. i ™ '^^'«- $33(i,".s7 ; on H„,i,,„ aTl'^" -: i4"„ :,f ^? ™ J;X'" "."' •■ '^ '"^""""'' »"'l Toronto i, at parri.ow m ,oh betler i/th ^ " ■, '"■'™ ''"'"''"' ""'I n.oney, allo"„ing *^ to be eu ,al VTp"?""' ""<""" "' '° «'"'i"S pound stcrlin-? "•""' •" '^ f""'««; »">! 2l ihinos, to 1 -'Miv^"e"„L?is: rnd'TiS", °" """"I" ^- -'^'-^ (liscount; howmuchwllK-. IT *^""'^''' <^" UamiUon Lsl'^g af 4 56 Prerni'm allow J'lLfi;;.'^^*^ «» '"" '^gent in Tort.^to di.scouatrbrokera<.eat i2? ^ "^ '" ''''*'"' ^° Humiltun at 1 ^g 9. A banker in°Quebec romit^ If - .w v, ,. . '^"■'- *' ' -f*-"^ "- - as follows: first to Lyonrat 6 fra , .,^0^* ^'^""'^"'•g- ^y arbitration, Hamburg at 181.50 fmScs per iSo ma,lr";l'"'' ^'' ^' '' *^^"°« '^ 3o stivers per 2 marks- then J !^ ^f f' *^«nce '<» Amsterdam at sterling. &ow "^S «le Sg ^^ne^tu h?."' ''' ,^^'r" P" ^ burg, an,, what .vill be ^i.^^:^;:^^^ ^I^tl^^!-, 4«, S Proceeds in Etiimh.,,,. ^..1,^ prem urn I Ans. \ P'-?ceeds in Edimburg, d^ ""Tu § Gain Kv afKW..o#.... ° i , , .-: .*'?' ;" Ottawa, and for that purSbrs a ll^nT^'l'* "'^^''^^ ''^^^'''^^ the rate of 2 francs per mS banco wS i ^-^^i^ange on Paris, at brokerage ^%. Allowing Sfi tTrofl' L*\ ^^ '"""^ards to Ottawa, ooet him ? ^"ow»ng *J6 to 100 mark bancoe, what di.i the hill 12. A of Barcdona owfti H «r r. . '^"'' 1^884 francs. eeionaoww B of Urerpool, £lyoo. BofLirerpooJ m sLai r 290 ABUITRATiON OF MKUCUANDISR. (-'■' ?wn 4 '''^'""*?'"^*'"' ^ ""^ Amatenlam on I) of Bonfeaux, and DofnoHeaux on A of BarceJona. Allowing £1 oxohan^.e" f .M2 flor.n«; I9f!onnHfor4()fmnc«. and 100 frHMO« for 1 !> Spun idoN lar«, how many .loNars will pay the bill ? ^„/ -J«!| -Id I.^. IwiHUtoreinit fruin Glasgow to Qupboo £127:. I "..s.' VVlmt w I r.e Its value in Canada ourn^ncy, reinittin-,' tlvrou-l, r'aris at tlie fo iow.ngrates: £1 eqnal« 26 francs 80 centimes; and 5 francs ce.tnnefl, equal SI ? ^„,. $fi2l0.25' . 14. A merchant in Halifax wishes to remit to London !?f)2r)0 so as to receive the largest possible returns for the name. Ff he reinits di- J 2 ^TM ?V'® ^^«''''">? currency will command a premium of f M 'Vn "-*' f't*:'^; 'f '""^t ^>P at the rate of", franca 20 centimes o the dollar, and 2., francs .so ©entimes to tlie pound; but if ti.rou-h per A4. VVhicli iH tlie moM desirable cour-e ? ylrj,-*. The course through Hamburg is preferable by £8 1 1 31 to the direct course, and by £39 23, to that through France. ARBrTRATION OF MRRCriANDTSE. 50r Arbitration in Merchandise consists in compnrin- tho wci-hts and measures of different countries; also, in Hnrlini^ rem the value of any particularweightor measure of one countrf the value of the corresponding weight or measure of another country. By tlio operations herein involved, the merchant is enabled to determine in what way he can most advantageously export or import any species of merchandise. The operation obviously con- sists, not only in the comparison of the weights and measures of different countries, but also ia the exchange of ourreneies. tablb op the principal weiohtb and measuee8 of the most IMPORTANT COMMERCIAL COUNTRIES IN THE WORLD REDUCED TO THEIR ENGLISH EQUIVALENTS. AUSTRIA. (Chief commercial cities, Vienna and TiiiKnTK.) i 100 commercial lb. = 123.6 Avdp. i Htaro = 2.34 Winch, bu. 1 polonick = 0.861 " " 1 aimer = 15 wine gal. 1 bMril* s 173 " •< 1 ell, woollen meas. =2C.6 in. 1 ell, silk =2i).2 " BADEN AND BAVARIA. (Principal com'.iercial city, Alusuuiio.) I pound = oiU) gram. French « 1.25 lb. Avdp. 1 Aug8b«rgmark=3643gr. Troy. >rtfeaux, and lanires for I 2 Spanish s. Wlrat Pari.H at the 5 francs MO 210.25 f. ?r)2.')0, Ko a.H 10 rejnitH di- prcmiiinj of 20 centimoH t if tlirough nark ban COS i 11 ^, to oe. comparing in (in ling le country, of anotlier enabled to export or iously con- leasuifes of es. IE MOST = 2C.6 in. = 2a.2 <' ARIA. al city, French « t gr. Troy. = 11.8 in. = .33.75 in. = S-Tf) fiH't. = 6.i2r) I foot 1 elJ 1 klafter =r fifrpt 1 flche/fi?! for c<,rn 1 eitner of wine 1 maan . ."RLOIUM. {Hrincipnl commercial city, Antwkkp.) WWWV WrrORTR AlfD MLARim*,. im. = 14.062 .^al = l-'^TDpint. WeightH an.l Meanuros the same } M in France . , HRAZTL. (/ nncipal commercial citu It'o l)K JaNKIIU) ) Weights an.l Mea^nres ti,e san.e as in Portugal. (U/ie of the/our Free Cities ef Germany.) { f ""'' = 1.09 a,. I centner __ hq ^ 1 viertelofwine =1.9.-, .^.J' 1 anker = 5 vierteln 1 oxljoft .-- 6 ankers 1 scheffel of grain 1 last = 40 shettel.s 1 s;one llax CHIXA. {Principal commisrdal city CXHTOS.) }f"^, =i.;{;nb, * P««"i = l;^3.3;J ib. 211 !&=:i?.^"^,,7,V«^'• — -4.00 in. KfiVPT. (FrtnctpaJ nmmercial city Al.K'XA>DHIA.) 1 rotolo Ajrforo ~ j ,r, ^^ rotoJo zaiiro = 3;5..]:j n-A. y.G.l gal. = 5^ gui. = 2 l,u. = -SO. 70 l.u, ~ -'0 11,9 I covid = U.62 lU. CUiU. {Principal commercial city Hatana.) .quintal = 101.75 lb. 1 arroba of wine = 4 1 ^^j 1 feuega of grain -'alu' ^ara ~ 33.34 in' DENMARK AND NORWAY {Principal commercial cities' LoPKNHAGKN and Chujstiana.; fP'-"-^"'^ =i.iu"ib. i centner = lOU lb. = lio.2,s|(, I riertel of wih = 2.04" ./al' I anker of wine =' lo ^ai 1 rotolo za(lino =r 91 -n-yr ,.„ rotolo ,n urn = 2(1.714 oz. I 'l"'ntaIcom.oinC!iiro=l(i;j,,;|i, f^ = ;;.2,{:. II,. Tr.' -Inigma =,,.,.,,. ^,^^,^^ pik ot corn = 2,i.8 in. robebe ot corn ~ 3,; „j,,^ ^ "^''^'^^ = ;!y gal. ^„ . EN'nr.AND. {I^nncipftl commercial cities Lo.vDoN a?)rf LivKiiiMioi,.) ' The EngliHJi Weight. m,d Meas. urea are tho same us j,; Canada. FRAN(^E. {Principal commercial cities, rAiiis. Lyons, and Maksku.i.ks.) Weights and 'Aia-\\i\-<,see p. 1 2(;, FRANKFi)RT .„, the Main. AND TH!-; 8oL-MI|..(iX I'AKTrf OF (-ieUMAXY. 1 II'. heavy = iT.G.'j 02. Avdp, lb. light = 1 -,.0o oz. Tr. [ '"^"'^ = J25 oz. Tr. 1 cwt. of 100 heavy, or lua li-dit lb. = Hi Jb. Avdp. 1 carat of jewels = I.32I dwt. Tr. '•f^^ =11.25 in. I ^1' , . = 21.555 in. 1 J?rankf. Brabant ell = 27.(;GG in. I maker of corn = 3.1.5() bu.sji. 1 sinuner " = (i.312 gal. i uiaasof wine ^ 3.156 pints, f J?^"" - 31.312 gal. I tuder - 6 ohtns ^ loT.S?;-; gal. HAMliCJRG AND LUJf>.CK. {Commercial cities o/Uki;kany.) i P^^'iiJ - 1.068 lb. % i [■ r. mh. B92 rORKfON WEIGHTS AND MRASUIUCS. ' I 100 commercial lb. = lOiJ.838 lb. } '■"^^t «= 11.289 in. 1 ahrn oJwiiie ^ .S8.2o t^al. 1 ftuler = (j Hlini.s = 22D.5 gal. I last 01' grain = 8i>.64'bu. 1 stocks l\ laht = l;u.4 bu. 1 Brabant ell = 27.58 in. lilNDOSTAN. (Principal commercial cities, BoAiiJAY, Hkngai,, Cai.cltta, and Madras.) I maund «. 74.625 lb. Avdp. I seer « 29.875 oz. Avilp. 1 Sicca =x 178.666 gr. Tr. 1 cubit, or 1 covid =^18 in. } g"z = 36 in. 1 C0.S8 == 4000 cubits = 1.125 mi. 1 palhe of corn - 9.5 lb. Avdp. 1 candy = 500 lb. Avdp. 1 gareeofcora « 135 bu. 1 candy of corn = 24.6 bu. HOLLAND. {Principal commercial etfiM, Amstkkoam, Haaklkm, The HAeiE,itoTTBRDAM, LbJYDEIi, etC.) |f"?ot -11. 142 in. \ f " , = 27 083 in. 1 last for corn « 85.25 bu. 1 aam of wine =" 41 gal 1 »at = luu kan - 1 hectol. Fr* ^ 26.42 gal. 1 muddle = luO hop- 1 hectol. ^ 2.84 bu. 1 pound . 1.08 lb. 1 i^r. kdogramme — 2.20 lb. 1 last, marine -: 4410 lb. LOMBARDY (Italy.) {Principal commercial cities, VKNJCi; A; Milan.) 1 libra = 1 kilogramme =» 2 lb. 3J oz. Avdp. The Mea.Mures are equal to th« French. NAPLES (Italy.) {Print- i I d commercial city, Naplk.s.) I rottulo = ],yg ]^,_ I cantaro groeso =» 100 rottolo = 196.50 1b. - 106 lb. - 42.75 gal. = 264 gal. = 52.20 bu. = 8C ID. 1 cantaro piccolo 1 aalma of oil 1 carro of wine 1 carro of grain = 1 canna PORTUGAL. {Principal commercial city, Lisbon.) 1 libra or arratel = 1.01 lb. I arroba = 22 arratel8 = 22.2G lb. 1 quintal = 4 arrobas = 89.05 lb. 100 libra.sor arratelo= 101.191b. I almude of wine = 4.37 gal. 1 tonelado «= 227.25 gal. 1 Canada . 13. 06 pints. 1 moyooftorn — 23,03 bu. 1 vara = 43.20 in. PRUSSIA. {Principal commercial city, Bbki.in.) 1 pound = 1.03 1b. 100 pounds Dantzic = 103.3 lb. I quintal. = 110 lb. 1 eimer of wine 1 ahm 1 sclieffel of graua 1 laat of grain 1 Berlin ell 1 Prussian ell RUSSIA. {Principal commercial cities, St. PKTERSBLRa and Warsaw.) 1 pound (funt) = o.90 lb. 1 pood = 40 pounds = 36 lb. 100 pounds = 90.26 lb. 1 wedro of wine -= 3.25 gal. 1 eorokovy = 40 wedros = 130 gal. 1 chetwert of corn 1 arsheen 1 sashen SARDINIA (Italy.) {Principal commercial cities, Gkkoa and Tl'uin.) 1 peso grofiPo (Genoa) = I2.1(J6 oa. Avdp. 1 libra (Turin) = 13 oz. Av;Ip, 1 pahiio (Genoa) = 9.75 in. 1 minaufcorn '< = 3.50 bu. 1 barileofwine " «= 16.31 gal. 113.42 1b. = 18.14 gal. = 39.66 gal. = 1.52 bu. = 91 bu. ■■ 25.5 in. = 26.28 in. = 5.95 bu. = 28 in. = 7 feet. bar le of oil « = 14.35 „al I P|edelipran.lo(Turi.i)= 20.5 in f piede juaneJle " « 12 75 n raso (ell) . ^ Jlf j^' J ^acco lor wjne '« = 25.5 gal. .-, . SAXONY. (I^rtnctput commercial cities IJRESDEN and Leipsic.) ' {pound - 17.625 „..Avdp. 1 ell i'.»75 jij. J^c,,*,ofco.„ .-|j- " bu. 3.5 pinta. 7= ;!3 gal. 3.5 pinta. 1 foot I ell 1 stab or staff 1 malter of corn 1 iinniir of << , ohm of wine - maas << ^ TURKEY. (Principal commercial city Constantinople.) Jpound,chequi,-ll..33uz.Avd. ^^^ « 14 02. Avdp. 1 pile, commercial = 27 i,i I kilJow of corn — 7 5 y multiplying by 1.(195, and tinally the brokerage is added by multiplying by 1.0025. £;.... 2. A merchant of Toronto ,^ends lard to Hamburg at f 10 per cwt., and orders remittance throuL^li Liverpotd, expen.se of remittance to he paid by N. Ashley of Hamburg. Allowing !iK7 excliange for 20 mark l.ancos, and l."^^ mark bancos exchange lor £1 ; also, that the bterimg £ bears a premium of 9 96 in Toronto, and that 105 lb. Ham- burg equals 112 lb. Toronto. Wliat is the cost of 1 lb. Hamburg, charges for cotmnissioo being 2 %, insurance 1 %'i AVAI.T3T8. $10-1.105 =. price of 1 lb. Hamburg in C.ma la currency, which X j^g or £1, flinl j.'Jg makes the re- quired deduction in favor of Sterling currency ; then the remaining value X j^n, is increased by the percentage of expense, siml thatvuluu so increased X 13^ or y ia exchanged to mark baniofl ; ifJ^l =1.3i^ inark.s, £7 =. 96 m.irka; and the marks X l<^ skill, k 4 fikilliogs 6-f- pfenniugs per lb., A*». OPEKATtO.V. 105 40 109 100 7 X 10 9 100 103 96 16 4 skiilings 5+ pfennings per lb., Ana. EXAMPLES FOR PRACTICE. 1. A merchant in Quebec ships 2000 lb. of butter to Bremen, and Bells the same at 12 grotea per Bremen lb. The total receipts are remitted to Paris, and the merchant of (Jiiebec draws on his agent there. For how many francs at 6.25 to $1 mupt he draw, allowing hie agent in Paris charges 2 % commission ? Ana. 1 290.44 v fr. 2. L. Enrigiit of Halifax imports from Lisbon 18 quintals of raisins, tor which he pays 50 reee per arrated. He sells the same in tht yti . ; ■i-^;-. .vi2;?5.'."J!L"XZ^Z!!i!^_llj FORErON WEIOHT8 AND MBA8UR18. what we have 295 Hie .sau.e, allowing a Brommm of 8 ^' n 'T"^'^' V c^^'P?-"'' '° »^^>' ^^'^ and 25 francs to Jt I ? IZ L i • ^ t^ '^'"'J'' "'^ '^^^'"''"g currency, that R. N. B. PoM tl e flax for's'."S ^^ "'^^ ^'^'''^ "'''^^^'•^^«' ^"^ did he gain on the total cost? ''"" "'* ^""'^' ^'^^^ P^^ °«"t- 4. Maple .n-ar is Whf]I/ nl? be rcnmted, an.I 29 % gained. to Naplel android a ' 5 carii^i n^^^^^^^^^^^^ ^ P"""''' ^^^^^^P"^'i tI>rou>rli Pari., the exc £1?? ?, ^ ^ ''''■> '""^ re.nutance is ordered rateor24grui 1 (W^ ^n'^'^^' '^"'^ Paris being at the of 5.25 francs toll A low "^ \'IT ^-'V ^"^^^'^"^ «^ ^^e rate ^-nce. etc., a.no.nf l^^^^ 1^^^^:^^^^^- £ ^^ wih'cSt^!tlJ;;t^;^r^^tft [ ^"^ that'-^SftSre centinies. Alluui^^^riremium o jt":^ »""' "^/c;^"?- '^ '"^^^"'^'^ ^'"^ and 5.25 francs lo the dollar T i • f ^''7''^ "** ^^'^'■^'»^' currency, advantageous,, ^^^^^^^l^^^X^^f^t^^ S'pP^^^ 6. Having a ouantitv of^wLpA^ '^'l' P^ ^'^- •''! ^^"'"' «^ ^i^'-'rpoul'. market, I .n"ake^ inmS a' i fiJ^^^^ ^? ^'^P^" '" ^'"^ ^''^^^ ».ost faVorabie placera'l nLjll ^ '^'"' *"'^ A.nsterdun, the two »..Hi it«. I find thS A Lit J % ^"^ '"vest.gate tlu ir comparative and ren.itta. ce can £ d Icted U^^ '* conunands 127^ tlorins .er last, to 80 IVancs, 5!20 L.u^ bet^ oSo l^"' 1 ^he rate of 37 florins is -^J*^. 4d. 8terlin.r ner hn«»f«1 °nce Is u contract in which a companv *t pulates to pay a certa.n sun. of u.oney on the death 7thJ nually. or^u/r.erirnt^rdingtofgrTement '^ '' '"^'^"'^ '*°°"^"^' ^^'"'■a- ^. The maured may designate to whom tbe amount of the policy shall be paid u^^7'p'^^ Insurance Policies a.e of the followin-^ kmd.- 1^ An E,uhroment Insurance RAiry, that is, a contract \u which an Insurance Company agrees to pay to the party insured a snec biX T " '''''''' T^ '' ^° '"^ ''^'"-^^ should hi. death concur befo e that age, on condition that he .shall pay an annual pemium untd the policy matures ; 2nd. .1 mn-Zhrfeito,. ]ik or Z T -^^ Pohc, IS one in which, even though the parfy insu • d .litid fail to pay his annual premiun.s after the first, the company a xree. l?fhY;;;ioT' '^ """^ '' ''^ ^"" '"^^^'^^ ^" ^^^ "''''-^? The Expectation vf Life is the avarage number of yea.vs that )\S. the year f.lO; more, tlian on last (lay of the is -oldiera ; on 'lays lie niul- iber, knowing Ans. .1. price iw equal tlie l.Jth. term inn. 50 cts. n the last day ate ul' C cents the preceding ns. 23328. leured $650; f increase per Ana. 3. LIFE INRURANei. 299 a company eath of the the insured of tbe insured, years, when ic :mium at the ally, setni-aa- shai) be paid. nnu; kinds: ctiii which red ;i spec- leath occur 1 1 premium or End >!.■}■ lied should any agrees ni.iturity years thai etermined In^reJ nm ;,.J» f fu P^O'"'"'" ""'^t be «uch a sura n.s will, when put at Bnai IS easUy foand upon tho prinoipio of Life Annuities. ^ Bnv flt![°ii°.!^,''""''^^'**'"''•"'''^^*■'^° ^■^'•'«' ^howing the premium to be pai.l at B.ny ago to scour.) ad annuity cf i^ioo, during tho rern.^in.lor of life. ' Dir1."tion"n? Thr/w'"' '' 'r^° "* '^ '^^"« °f tho polioy, and another at tho ex' C.' I I ii \i I i^ge at ibsue. 14 15 16 17 18 ly 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 64 65 UFB INSUKANOB. LIFE TABLB. ANNUAL PREMIUM ON A POLICY OF $100. Payments during life. $1.4707 1.5105 1.5516 1.5940 1.6377 1.6829 1.7296 1.7780 1.8280 1.879S 1.9335 1.9891 2.0470 2. 1 07 1 2.1696 2.2346 2.3023 2.3728 2.4464 2.5232 2.6034 2.6873 2.7752 2.8674 2.9641 3.0658 3.1729 3.2.S56 3.4046 3.5303 3.6632 3.8038 3.9530 4.1111 4.2782 4.4549 4.6417 4.8393 5.0486 6.2708 5.5067 6.7577 Payments To cease at 6t Payments . To cease at 60 Payincnt.s . Tc)ccasoat5( Asfo nt . i^sue. $1.4999 $1.5238 $1.6150 14 1.5422 1.5683 1.6681 15 1.6861 1.6145 1.7240 16 1.6316 1.6625 1.7826 17 1.6786 1.7124 1.8444 18 1.7275 1.7644 1.9096 19 1.7782 1.8186 1.9785 20 1.8310 1.8753 2.0516 21 1.8859 1.9344 2.1292 22 1.9431 1.9963 2.2118 23 2.0027 2.0612 2.3000 24 2.0648 2.1291 2.3944 25 2.1300 2.2007 2.4959 26 2.1981 2.2761 2.6054 27 2.2695 2.3555 2.72.^8 28 2.3444 2.4395 2.8525 29 2.4230 2.5284 2.9928 30 2.5058 2.6226 3 1466 31 2.5930 2.7228 3.3163 32 2.6851 2.8296 3.5044 33 2.7824 2.9436 3.7142 34 2.8856 3.0657 3.9503 35 2.9951 .11971 4.2182 36 3.1117 3.3:W7 4.5251 37 3.2361 3.4919 4.8807 38 3.3692 3.6584 5.2981 39 3.5120 3.8402 6.7959 40 3.6654 4.0393 41 3.8311 4.2588 42 4.0106 4.5021 43 4.2055 4.7735 44 4.4181 5.0782 45 4.6512 5.4235 46 4.9075 6.8180 47 6.1902 6.2?26 48 6.50,38 6.8032 49 5.8536 7.4317 60 6.2470 51 6.69:^6 62 7.2061 53 7.h01T 54 8.504^ 1 55 ts Aafo nt t5t . isi?ue. 14 1 15 [) k; t) 17 t 18 VJ 20 21 22 i 2.i ) 24 [ 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 62 53 54 65 UK INSDRANCW. ENDOWMENT AS^URA^VCR TABLE. (Ago at Polioydua j isgae. at 40. I> 1 i; ■> 16 $3,356 17 3.545 IH 3.752 IS 3.978 20 4.228 21 4.504 22 4.812 23 6.156 24 5.544 25 5.985 26 6.489 27 7.082 28 7.752 2!) 8.558 30 9l 9.526 .1' 32 33 34 36 36 37 38 39 40 41 42 43 44 46 46 47 48 49 50 61 62 63 64 *5 LIFB INHtTRANOB. NON-PORPEITINQ TABLE. ^B^^~:^j^^^;'^^^ on fnr «anh '.. V • ""«:»"^'«n. »r one-twontieth of tlio sum 1 III! Five I Ten Paytn'>i|P*w»n»g i 21 .'3 21 25 20 27 28 29 30 31 32 33 31 35 $7,696 7.8481 8.020 8.193 8.374 8.55fi 8.758 8.962 9.154 9.316 9.488 9.660 9.842 10.258 |14.400| Fifteen Paym's «4.294 $3,190 4.3«(; 3.2(;0 4.482 3.;! 32 4.582 3.412 4.690 3.494 4.79S 3.574 4.914 3.(5G6 5.030 3.750 6.138 3.838 6.234 3.908 6.330 3.980 6.430 4.060 6.540 4.152 6.658 4.246 5.782 4.334 Twenty Paym's $2,656 2. 7 hi I 2.77.8 2.844 2.914 2.986 3.002 3.138 3.210 3.274 3.338 3.408 3.480 3.558 3.640 Five Paym's 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 !?1 0.470 10.702 10.9;!6 11.178 11.422 11.664 11.886 12.110 12.332 12.566 12.808 1.!.063 1.3.336 13.648 13.9841 Ten I Fifteen Payra's'Pnym'd .'?5.914 6.050 6.190 6.336; 6.478 6.612 6.738 6.862 6.988 7.1221 7.262 7.410 7.574 7.762 7.972 .•?4.434 4..-)46 4. 648 4.758 4.870 4.972| 5.0621 5.1641 5.266^ 5.3661 5.478 5.610 5.752 5.914 6.10G wenty Payrn'j $3,726 3.816 3.i)06 4.002 4.096 4.186 4.276 4.366 4.462 4.564 4.676 4.800 4.936 5.092 5.274 EXA.MPLES FOR PRACTICE. $2750 OPERATION. X .023728 = 165.252, Ans. ANAtvam. - We multiply the face of the policy, $2750. by the rate <7f found opposite .SI ye.irs , liable at t'tcr niiL' premium, n assured, ami ao ^remiuiBj will b« Fifteen Twenty ! Faym'i Piiyrn'j .«4.4;i4 ^3.726 4..-)46 ;:;.H]6 4.648 3.906 4.758 4.002 4.870 4.096 4.972; •^.186 5.0(121 4.276 r..lGli 4. .366 5.2(J(3^ 4.462 o.HiiOi 4.564 5.478 4.676 5.610 4..'^n9 5.752 4.936 5.914 5.092 6.100 5.274 surance Com »t the igsue of B uaultiply the $2750, by the site .'il yeiirs -n xpre3sed deci- ; what IS his '. $28,197. cy for .•f35t.U), 27 .veara ? ?e policy for ; how much policy for the . $265.40. ANNDTTIB8. «-, ft A a"^\i.e/:r,t''!:etT"r'lh? ''"I'^rr -" '"« "^^ •• «- a^e o, 26 an.,.„„t 01 insurance iha.! ? •**'''• '"'" "'"'^^ 'e^« will ^11?; Ant 'KO.^^r^ il/t«. $26^0. AXNIITIK8. is for a J.tto"„Sct"?v™s''"°' "'■'''' P'™"' "•■oo.mnuanoe con,i:„« ilre'r""' *""""»' °' P^Petutty, is o,a. which e»ci, pay,„e„t of an annuu/ „ a„ '" "T' '" !" ''' '■™'» -b. became d„,, ,„yr;°aV, "S '""■""• '■™'" "'^ '-' -»'" •.-'!\b'':„^'o*<'rpi:i71r i-T'.'^' " -"po""-' '»■ preset worth olit, floal^X TtMlf ^r""^' °' "■» compound interest, wiU amoun »! ,1,/ ,• , "i""' P"' O""" Ibe annuity, ,0 its 'finaUalue' '™o of the expiration of rl-i"^- ■"•"-".-••'. ".6"^^^^ 'iJ the ordia-jry rates of inter«rt. * '^'^ * «"«° omaber of y,*,)* I III i i' ,M| if r f !)?« JN Hh \lk ii'jj TABLE ''"'"'"5»/rL?T"**' ''^"" T^'-'J^^' "^*^ ^''^ ""'""'»• "' compound i»fjrestforany number af y,i,in nul e:vcetding fifty 7 per oeot. Ij 3pcre«nt. |8^ pececnt. 9 4 5 6 7 8 9 10 1) 12 J3 )4 lu 16 17 18 19 !20 v!l y3 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 i.ouifooe ;JAl3iiU(>0 .'J.O'JOJUO 4.l.-;i(i27 5.309136 i;.4»384IO 7.(ii)ilti2 1^.892336 IU.ir)9l()6 ll.4C,H79 i2J07796 14 1 921)30 15.617790 17.0r)0324 I8,./J89I4 20.156d81 21.761588 23.414435 25 nG"5G8 2d.o7o:i74 2:*.i;76486 1 OOIIOUO 2.035000 3 ii'(;22r» 4.21494: 5 3(W4ti6 6.5.'.Uli 7.779408 9.051687 i0.36d496 II 731393 4 per cent. 45j 4H 47(J 48 49 &9 30.536780 32.452884 34.426470 36.45!)2i;4 38..553(»42 4(1.709634 42.930923 4r).-Jl9rr50 47.575416 50.01 '2678 52.502759 55.077841 57.730177 60.462062 63.271944 6C. 174223 69.159449 72.234233 75.401260 78.663298 82 023190 a5.483b92 •3S).048409 ^~2'.)s6l ;d'. 'v ! . ' i^A^p ^; OS..VJ, :;4w' 13.141992 14.601962 IJ.n3ii3o 17.676986 19.295681 20.971030 22.705016 24.490691 26 357100 2d.27:iL82 30.269471 32.32«9(;2 34 460414 36.666528 38.949=57 41.313102 42.75906{.' 46 290627 48.910799 51.622677 54.429471 .57 334502 60.341210 63 45315 66.67401 70.007603 73.457869 l.oiiui''"' S0400UU 3.121600 4.216464 5 41632.1 6,632975 7.byrt294 9.214226 I0 5d2795 I2006I07 9 p«f oent. I percent. 77.02889r 80.724906 84.550278 88.509537 92.607371 96.848629 I0I.23S33I 105.7*1673 13.486351 I5.025s0i 16 626835 18 29)911 20.u235-:8 2i e24531 2:; 697512 25 64.'4I3 27.6TI . j}^ 29.77(r()79 31.969202 34.24797U 36.6 1 7 -r) J 3<».0b2604 41 645908 44.311745 47.084214 49.9675^3 52.966286 56 084938 59 323335 62.701469 66.209527 69.857909 73.652225 77.59=314 b 1.702240 95.9703:i(; 90.4091.50 95.025516 99.826536 104,819598 110.0123/^2 M.5.4 12877 121.029.392 !26,>7n56-:- 11. r, 3509731132.945390 iV0.3^8297!i:"').^G3206 125.601»4Ci :.>.833734 1.(1001100 2.0.")0000 3.152500 4 31 01 25 5,52.')63I 6 801913 8 142008 9.549109 1 1 ,026'64 12.r)77^93 I4.20(i787 15.917127 17 7 1 -,'983 1959=632 2 1 .57e564 23.657492 25 840366 a-', 132385 30.539004 3,3.06.5954 35.719252 3b.50.52 1 4 41 430475 44 501999 47 727099 51.113454 54.669126 58.402583 62.322712 66.43::; 848 70 7G0790 75.298r29 80 063771 85.06()959 9(t,320.307 95.S36323 101.628139 <07.7W)54t) 114 095023 I.OOOiiOO 2.(60000 .3.183600 4374<>I6 5.637093 6.975319 8393838 9.d974f^8 II 491316 I3.1ci0795 14.97 1(i4:i I6.8(i9'.»4l I8.8-1'J|;W 21.0l.-)0i;6 23,275970 25.6705281 28.2128t<0 30 905653 120.799774 127.83'J763 135.231751 142 993339 151.143006 159.7001.56 16^.6^5164 178 119422 IH8.025:{93 198.426663 33.75999 36.7tt5591 39.992727 43.392290 46,995828 50 815577 54. =64512 59.156383 63.705766 68 528112 73 639798 79.05=1=6 84 801677 90.889778 97.343165 104.183755 I.OiMlOOO 2 '170000 3 214900 4 43:i,M3 5 7.i073!» 7 l.'.3'29l ^ 654021 1 0.25981 (3 1 1 9779=9 13816448 l57»,Joy9 17.888451 20. 14064 J 22. 5504 88 25 lJi^022 27.9=;054 30.P402I7 33 9hiyii3J 37..<7By05 40 995492 44.c(j5I77 49 005739 53 436141 58 |7o6rl 63.2490,30 68 6764'0 74.4=3->3J 80,69T(;i.»| =7.346529 94.460786 102.073041 no •21=154 1 18.933425 128 258765 111.434780 1 3e,i;36878 I19.I2086-! 18.1M3460 127.2681 li>i J 'jO,;i3';4(jO 135.9042f/>i ti^;,,! ;ii) 45.058..'. ;' j4\.^i>i 154 761966 16,j.047684 175.950645 187.597577 191)758032 212 743514 226.508125 241.098612 256..->61.')29 .>72.9.5d401 i 130.99991 0|la2.6C70t>4[209!34797t>ja90.'3k5905 199.635112 214.609570 230.«)32240 247 776496 266.120851 285.749311 3ii(! 751763 32.1.224386 353.27(1093 378.999000 406.528929 46 47 48 49 50 TAIii.E Showinxr the present tvnrth ,,1 ,n annu,/ r-vi ., 305 3 p. eent. 0.97087.1 J.yia47(i t'.82dGIJ ;V7I70!W 4-.7;)707 5.417191 (».5«U-,'8'J 7.onhm 7.786109 9.-.i52(iy4 9.9.-)4004 I(».6:549.->5 ll.-3.-) '■■i.ofi 11(12 I;j.l0(ill8 i:«.7r);{r,i.'} 14.323799 14.87747,'-) 15.4150'.>4 Il3.93(;9l7 Iti44;i()(;8 HJ.93r)r)42 I7.41314H 18. 32703 [ 18.704108 l'J.J6S455 19.(300441 •20.000428 0.9(;r>IH4 1.89:»G!)4 2.8(»u;;!7 3.()7.'J07;i 4.r.ir)052 5.328.-.5:! 6.114541 6.8739,-()| 7.C07G87 8.3IG605 9. 00 1 r>r) I 9.663334 10.302738 10.920.-)20 n.517411 12.0.94117 12.651321 13.1896S2 13.709837 14.212403 14.697974 15.16712.^) 15.620410 16.058368 16.48 1.'-) 15 .876842 16.8903.V2 1 'J.»->noi !•» <-».-.,..„_ 17.28536c 17.667019 i8.03r)7(;7 I A 392045 18.736276 .'0 338766 19.068685 20.765792 21.1.1J837 '1.487220 5l.>i32v.. 22 ir.7235 '22.492462 122.808215 •23.114772 23.412400 19.390208 19.700684 20,00l)t)6l 20.290494 2'».5ro525 20.841087 21.102500 21.355072 2I.O99104 23.701359 2 l.«;J4883 23 981902122.062689 24.2542741 •24..''>|f^7!; 24.775149 V 024708 25.266707 25.5016.57 r-25.729764 '2-2J8279I 2. t9,";45i; 22.700918 22.899438 23.091244 23.270564 23.455618 ".96 1. 538 1 .8r«(J09." 2.775091 3.629895 4.45182i 5.24213'/ 6 0020.55 6.7.32745 7.435332 8.110896 8.760477 9.385074 9.;»85648 10..563123 11.1/8387 11.652296 12.165669 12,6.59297 13.133939 13.590326 14.029160 14 451115 14.8.56842 15.246963 15.622080 15.982769 16.329586 16663063 16.983715 17.292033 17.588494 17.873.552 18.147646 18.411198 18.664613 18.908282 19.142579 19.3678641 19.584485 19 792774 19 9930.52 20.185627 2(1.370795 20.548841 20.7ii0040 20.884654 21 042936 2I.195J31 21.341472 21.482185 1 1.9.52.38 1 1 1.1.59110 3.515951 4.329477 5.075692 5.786:i73 6 463213 7.107ft2->| 7.721735 8 306414 8.8(532.521 9..39357:{ 9.6!)8641 I0.37i)6,58 10.837770 11.274066 11.689.587 o.943:{9(; , 1.83:!:fi)3 2.72.V248I 2»;730I2 3.465106 4.212364 4.917.324 5.5s-j:wi 0.209741 6.80J692 7..360()87 7.886^*75 8..3S3814 8.8.52i;8;! 9.294981 0.712219 10.lO.5vS9.-, 10.4772(io i.>,ij.;..;'.i!^'^~'^*''"V"-'-''''""" 2.08;>. 21 I J58Ji(;i0..3:!.5.578 12.4fi22lo ll.4{;9.12l 10.593')')7 12.821 1.53I 1 1.76-107; ' 12.04 i5-<-J 0,9,14579. I.SOMJI? 2.(;.'13|4 3.3-^72(»!» 4.100195 4 7665371 5.3?928l) 5.97l29ri 6.5I582-* 7 023.577 7.498(i(i9 7.912(;7I 8.3.57635 8.745452 9.J07S9> .0.44663-2 9.76:!20(i lf».059O7O 13.16.3003 13.488571 13 798642 14.093945 14.275185 12.30.3379 l-.'..55035> I2.78.335ti I3.003l(!(i 14.64.3034 13.2 1 0.-.34 14.8981-7 13.406 KH 15 141074 13.590721 15.372451 13.764.^31 15..5928II 13.9290.S6 15.802677 14.08401;! 16.(102549! l4.23o-'30 16 192204 14.30814 16.374194 |10.8!5527 11.061241 11.272187 11.4693.34 ll.().5.3.83 11.8257791 11.9,'^6709 12.137111 12.277674 12.409041 r2..53l814 I2.64(m55 -7')o| 12.854009 14.498^!46 12-947672 1 6.546852 1 4.620987 13.0.35208 0.71 1287 14 730780 13.117017 10.86/893 I4.84(>019 13 1J)3473 17.017041 14.949075 |3.2(;49->8 I7.1.59/ir:'6jl5.04()297 '7.2943(;8il5.13eoi6 17.423208 17.545912 17.662773 17.774070 17.88(»067 17.981016 18.077158 18. IIJ87S2 15.224543 15.3()617.') 15..383I82 15.455832 15.524.370 15..589()28 15.650027 15.707572 13.331709 13.394120 13452449 13.506962 13.557908' 1^.605522 13.650020 13.6!)1608 13.730474 13.766799 18.2559251 15.76l86l|l3.8Q0746 f Si < % t i '■> ] m i ' VH f' ' 3M AWWniTtRH. u *m^. To find the amount, or final value, of an annuity certain, at compound interest, in arrears, or forborne, Ex. An annuity of $400 a year remained unpaid G years ; what re the amount due, at 6^ compound interest? OPERATION, $6.975319, amount of SI for 6 years. (See Table). 400 $2790.1276; " $400 NoTT.— When the annuity draws timple iuterett, the amount is found as in amutal interest. 52T. Rule. — Multiph/ the amount, or final value, of an an- nuity q/'$l for the given rate and time,f()uiiei>t value of her interest, at 7 %, compound 'oterest? Ans. $42(;!. 8. A yearly pension, unpaid for 12 years, at 6%. wjmpound int., amoiinted to $1)550.2762 ; what was the pension ? Ans. $1 1 :!9.1 2 + . 9. What sum should be paid for a perpetual annuity of §1500, pay- able semi-annually, interest being at 6 % ? Ans. $25000. 10. A lease, whose rental is $()00 a year, is left to a son and a daughter. The son is to receive the rei>tfor8 years and tlie daughter for the 1 2 yr. succeedmg. What is the present value of the daughter's interest, allowing 5 % compound interest? Ans. $8599. 3'J -f . 11. What will an annuity of 840, payable semi-annually, amount to, in arrears for 5 years, at 6 ^ ? Ans. $458.55 + . 12. I w>:^h to purchase an annuity which shall secure to my ward, at 5 5t compound interest, $300 for 15 years. What must I deposit in the annuity oflBtee? Ans. $3113.89 + . 13. A laborer agreed to work for 1 year and 6 months at the rate of $25 payal>le monthly ; he was paid only at the end of the 18 mo. ; how much did he receive, being allowed 6% simple interest per an Q»'"? Ans. $469.12^. 14. A merchant being desirous to secure a dowry k>r liis son. de- posits annually a sum which, placed at simple interest, commencing at his 1 2th year to his 23rd., amounts to $630, and that due for dowry, to $5580 ; find the value of the yearly deposit, and the rate %. Ans. Deposit, $300 ; rate, 30 %. 16. A founder wishes to economise $360 in 5 years; wliat swn Bhall he have to deposit at the end of each year so as to have the required sum at the end of the 5Hi. year, comprising both capital and compound interest, at 5 % per annwa? Ans. $63.16. 16. What is the amount ofanannuityof$45. payable semi-annually, for 3 years, at 7 ^ compound interest ? Ans. $294.75 + . 17. A servant leaves his yearly salary of $250 in the hands of hi& master, on condition that he will allow him 4^% interest, per annum, to be added to his capital ; find how much will be due the servant at the end of 15 years. Ans. $5196.01. 18. A marbler buys divers blocks of marble measuring altogether 4.850 cubic yards at $1 16 a cu. yard ; lie pays $122.60 in cash, and settles the remainder in 4 annuities; what ia the amount of each an- nuity at 4^^ interest. Ans. $445.99. 19. Find the amount of an annuity of $225 fbr 5^yr. payable every three months, interest -dt l^% also quarterly. Ane. $5729.62 4. 20. An oi! merchant bought 32 bbl. of euperfine olive oil, fur which he paid'yearly $190 for 1 years. If money was worth 6 ^ per annum compound int., what was the cost of a barrel ? Ans. $43.70. 21. A planter agrees to pay $598 in 13 payments, in such a maimer that 6ach succeeding pa.yment shall be greater than the preceding one bj 9 6 ; what will be hu first and last pajmeot 7 Au$. Last |ti2. red 6 jr., 4.43 + . "or 15 vr. l29r).6S. lually, for compound $42(1!. lound int., ;0.12+-. 1 500, pay- S25000. son and a ! dau-gjhter laughter's 9.3'J + . f, amount 8.55 + . my ward, 1 1 deposit 3.89 + . : the rate 5 18 mo. ; set per an :69.r2^. is fcon. de- uniencing for dowry, e, 30%. iv\\&i som ) have the ^pital and $63.16. •annually, 4.75 + . nils of hi& ?r annum, servant ax 196.01. altogether cash, and f each an- 445.99. ible every 29.62^. for which er annum $43.70. a mai»er eding one l8t|62. AffWUITnM. 309 tl^f capital deposUed wlm canifll '^^ f f '^T ' '' ^ P"' aunum on calculateciatl^i^gyearrv ' d ff S^. '*J!1 '^T'''' ''■ '"^^est Z 18 years and UnoSf' '^ ^' ^'""^^^^^ I'^'-^^ioo of hi« life b^ 24. A laborer, from the acre of Ifi ♦. «n ^"'^- ^^^^^ *2 5A. 23. A mechanic boucht tools fn,- tu^ , *-^"'- *'*15-45i. m yearly, so as to cance] hird/bt in I ''*™ ""l f L^^® = ^^^^^^ ^'d he pound interest ? ' ^^"^ "* ^ ^^a^^' at 5 Jg per anmim cora- 26. I have deposited $5000 at 5 <*; intPPP«* ^ :^"'- *^' ' -27. withdraw only .$150 yearly, and tha flT ' °".«o»dit.on that I will win be added to tj/e cap^ af wha? Vilf i!T''^'' «*" '^' '"»«^«t years ? ^'*^""' ' "^^^^ will be due me at the end of 12 27. When dvin? a forfKo- ua . ^^s. $6591.71 a boy and a giH " yeSt oTd V, ''""^ "^'"^^^^^ *« 1"^^ twin chi Id L deposited at 7%, If;^„^^;,,VrdtSVo?r"'^^ ''' ^^« ^oy -a« 'nterest, payable semi-annually • the IfJZ^'^^'h ^^ ^ ^ compound bemg 13 3.ar5«wide and twicJ as S 'r ' '" 35 window^ each $3.37 J per square yard, but oServe that a -THRRM0Mli:TER8. Pi .' (■;-;■ ' i ! 1 1 1 1' ?8 in a Savings Bank, a,i'S^%; and continues the same for 20 yeafs, comuicricmg at the age of 26. What will Ite his capital at the end 8? Ana. 1»$135; Z'' 3808.74; 3» $94.3.Ib + . TEMPB]RATIJRE— THERMOMETERS. (586. Temperature is a term employed to denote the con- dition of a body in respect to heat, or cold ; it al«>o expresses the greater or less capacity of a body to excite i« us tiie sensation of heat or cold. NoTW.— Heat and cold are correlativa terms ; that is, as the former inoreaises in a body, the latter decreases, and the converse. Tom|)erakure generally nten to tho amount of sensible heat in a body ; eold being regarded as the absence of heat. SST. A Thermometer is an instrument used to measure tl e" scales Tr''"'"^?*" ^^"'^ ««^«« filling the tbTo.oteSr'."''"*'"' '^'^ - ^'-''o. inlt;af of Seru^fS'^o" Since th« interval between th. a. * divided into 100 eqnarpartefn «,/',"« ?"'' '','"""8 Po^" »f "ater ■ahrenheifs, and 80 Mual Mrl, il'l,.*-™'*?*' ISO equal pans?' SS,K'."i^'™- ■» ."«ktd!20.'';L"Lft„t-A»i':».-a,e t^e 1 i ; •\ ! l>! '12 TKMP«RATUai5-THMlMOMBTIR8. »44. To ehange fi^om Reaumur's to Fahrenheit's eoale. o9?Y'1;~^'f '^'y f^j^^'^rees on Reaumur's scale hy |, and add heif^scale '''^' '"'^ ""'^^ ''" *^'' temperature hy Fahren- 545. The degrees on the Centigrade, Fahrenheit's, and Re- aumur s scales, corresponding t) temperatures differing by 10° Centigrade between the freezing and boiling points of wat^r, are given in the following tablo : ' Ceutigraat. 0" Zero = 10" = JO® 30» = 40" = 60" = 60« = 70O = 80» = 90» = lOOe = Fahrenheit. 32^ Freez'g. = 50'^ = 68" = 86° = 104" = 122" = 140" = 158" = 194" = 212" = Reaumur. 0" Zero. 8" 16" 24" 32" 40«» 48" 56« 64" 72" 80" By means of the rules (641, 542, 543, 544,) the atudent can readily extend this table above and below these limits. EXAMPLES FOK PBACTIOE. 1. What temperature bj Fahrenheit's Hcale corresponds to 176" Centigrade? 'Jna 348*° 2. When the temperature of a body by Reaumur's thermometer is 7» , what IS It by I'ahrenheit's? j^„g 20"'" 3. What temperature by Reaumur's thermometer answers to 834° Oentigrade ? ' 4. What temperature t)y Centigrade's soalfi norre-oorids to 45" Fahrenheit? ' " ^ ^^^ ^^^ 6 When Fahrenheit's thermometer indicates —13°, what should ttie Ceati^fradK Mi Reaumur's indicate ? 4Wf Qwtigrade, —26" j Beaumur, ■-20''. "^yr*^Tj^i»->g^qi| A Mktrb '^ KlI.OMIITK An Abh, «QrriVAL«.Tfl or mrthio measures. « 39.37 — 3.284 = l.OQSfl ( '■» I <«-^«3 C =.< 7 -ifl^-.T'-^''""'^ C — .^.953-f- yq rods _ =«= 39.37 inches...... .28-f- feet.... .09S« + yards! 313 An inch A foot A yard flfj^^t 10 inches I^y^rd A »q. yard A iq. rod ~ n- ■(]. A Hkotaub i = 2.47J acres. ? = .0038»-f sq. mii;' T *"''° -T- 04. miie ^ A sq. raifo ■■i:a,tet ^«i--h ^^■" Asq. foot A Stkbk. -^ a cubic raoter.. I * . . ..3i1[!t°;:S/a:::;."L'„":?r — •22»'l+ meter. = .3048-f tneior. *" •9141-1- meter. » .OOflilH kil,.m. « l.609-f- kilom. *= '834-1- cent! are «= .2629+ are. -= .4046-f- hect. « 258.99-f- hect. =-=.0006454- cent. = .0929-f cent =.0000163-f8ter9 «= 3.62-f 8tere. sz .7H4-J- stere. = ,0283+ stere. A IdTKa. / ♦• * •»M«ttr« 0/ capacity , I = a cubic dooimetcr I a 1 "= •"«8+ of a „T„^/"n:::V;- I ^ °^ f£<^'. = 23.32 liters. •JOB I "°"""«"'r.. ^oi.oi+oubicinfihes A flKOT»i,rr«B,. ^ ■" ^•''^•'^-f bushels ' =3.a317l-loHbicfeet AaRAJi,. .. ( ~ (35^ ^'■■*°'' ^'•°^ ^' •• A grain C ~ i».d6+ ounce, At. Wl ' A ;.r n ., = ^H.^2 liters. A& = 3.78+ liters. A fluid o«. », .02958+ liter Acu.„ich =..,M63-fr,ite'r"- A bushel A ou. foot .352+ hectol. .283+ hectol. .0648+ gram. A &.,>«««.... j - S?t S: l;: »S- ^° -ojr. lb. ^ .4530+ kilo. ^ - 2.679 1 Troy VV^ght ( l-^,--^- ^ -J^S^f kilo°|. ^ T^"'^"*" J r ??„1;i'»> At. Weight..... f — i,ivi-j- tons An avoir, lb. ; A ton ilog. = .000453+ ton. : .907+ tonneau 100 grades. ' A ton A Gradr S **« measure of anaUii • * • u. J =- .9 of a dog«e^^ f "S"^' «»?'« - - ,.„_ ° A de^-ree =■ i n "'"■ NoTBs — 1 Th "II • '='*"I' grades. MENSURATION. i i I i ' •Mi ij < I i DEFINITIONB, 546. Mensuration treats of the meaearement of lines but faces and solids. ' 547. A Point is that which has place, or position, but not ma-jnitude. ^ ' r j 548. A Line has length without breadth or thickness, and may bo straijrht or curved. 549. A Surface is that which has length, or breadth, without height, or thickness. There are three kinds of surfaoes; viz plain, convex, or curved, and concave. ' 550. A Plane Surface is one, every point of which is touched by a straight line, extended over and upon it. 551. A Curved Surface is one that ha« length and breadth without thickness, and is constantly changing its direction. 5S-S. A Concave Surface is the reverae of the curved, and constitutes the interior surface of a hollow sphere. L ^??" ^?^^}h Volume, or Body, is that which has length, breadth, and^ thickness. Length, breadth, and thickness, are called dimensions. Henoe, a solid has three dimensions, a surface two, and a una one. ANQLBS. 554. An Angle is the diyergenoe 6f two straight lines from a common poiat; as the angle A. Also read 1? ^* '^^^ ^^'^ straight lines are called the sides of the angle, and the common point of intersection, the wr/«E. 555. A Right Angle is an angle formed by a straight line and a per- pendicular to it, and contains 90°- as the angles ABE and E B 0. ' 556. An Acute Angle is one less than a right angle ; as the angles 557. An Obtuse Angle is one greater tiian a right aagle : ae the an- gle A B D. — / VftUNQLKfl. Hnee, stir n, but not kness, and li, without Mies; viz., which is d breadth on. rved, and as length, jiesa, are a surface [▼ergenoe common Jso read lines fire , and the le vertex. an angle i a per- ns 90°; tc. ) is one le angles ) is one I the ao' 315 lie^??);^"*"®i.''"^««'-«^»^''««th'''t ^e in the sanie direction ; they are other ; as A B and C D. POLYGONS. it. mr&c. " ^"^ "'■ " "sure is the number of equare units in TRIAN0LB8. 56«. There a„ eev.r.1 kind, of triangle,, „.„»),.. e,L.*" """"""^ friangl,, the three sides of whioh .„ . In lie right-angild trianrie tlfj J^ """* ?"° "Slit angle. is oaUed thehi^LnZ^ ' *" '"''' °''1'°^"« ""= --igh "angle, fciquilateral leoseeles. Scalenui NoT«.-Ih« aottod li«« «.p,^„ ^^ ^^^^^^ ^ ^^ ^^ Kight-anjled. m ? m 11 U' 816 OF THR nrnrLi. QUAIIRILATEKALS. m 1 1 I I k . I . 567. There are three kinds of quiulrilateralfl, namely : o" ^t® Parallelogram, wliicli has its opposite sides para o mi J'^^P^O^d) ^'I'cli li''f^ only two of its sides parall 3. The Trapezium, which has none of its sides parallel. Parallelogram. Trapewid. Trape«uai. ^56S^ Ther e are four kinds of p;.rallolograms, nauiely: 1. The Square, whose sides are equal, and whose angles are right angles. 2. The Rectangle, which is any right angled parailf ic^rani. ' 3. The Rhombus, or Lozenge, whose sides are equal, and whose angles are not right angles. 4. The Rhomboid, whose opposite sides are equal, but its angles are not right angles, and its length exceeds its breadth. ISquaro. Reotnngle. BhomJiUB ^<^mboid. OF THE CIRCLE. 569. A Circle is a plane figure bounded by a line, every part of which is equally dis- tant from a poiat within called the centre as A G H B C E D. The Circumference of a circle is the line that bounds it. It is divided into 360 parts called degrees. 5^0. An Arc is any j.ortioii of the circumference ; as A D, 3J1. A Radius is a line drawn from the centre to the cir- cumference ; as A, or C. 57a. A Diameter is a line which passes through the centre and IS terminated by the circumference ; as A B. MBIVSOIATIOV op suaPAOBB. — 317 •rc^^f D 0°"'"' '" * ""«'" ""« J'»""'« ">« -femUio, of „. drolei »> the ,,",t A * K A "•» P'--"""! chords of . S79. A Lune, or Orescent .o ♦!, fpaco contained be ween the !r^!' of . ' intersecting circles. ''' °^ '^° whfsf L;Lf Sf: .5et'7 '^ T pentagon ABC D E ^"''^' "^ '^*' MKNSUKATICN OF SURPACBS. Probf.km T. To find the area of any paraUelogram. ■> n- , . * '^ * ~ ^ " square yards /It,, 4th ,476 00^4 ykTUlm/,'^'^ «^«-' /J- > .-.1"5w'4'o|-,%"^.j:,^-'^«^^U.«o.^. ; )3 ^ ;* i. i 1 . 1 i li ■li Mi n n a A E H p Q1Q ° «»NiUBATlON Of 8Ca»A0BH. 3. Find the area of a rectangle A B C D 01 wlucl. th. I,a.e A [i = 7 yard.H, and th^ iiltitiide A I) = 4 yards. Ol-KRATION. 7 < l = 2H flq. yd., -!»|«. 4. What is tlie height, or allituda, of a recta..;rle who-e l.aso is II yards, and aren, i IZ rtquare yards? 14 =. s yards, ^«.. ^ * ''®"°°' ""»* ^°'«^»' •'hoild bo eqiml to 112 + ■dna. 1st 72 1. 5 1 i sq. yd. ; 2nd 10997.248 eq. yd., etc. n M ^^''^"^ '^ "'^ ^'■^* °^ ^^^^ rhombua A B L p of which the base A B is 12 feet, aad ahitudeE D, 4 feet? Operation. 12 x 4 = 48 sq. feet, Atu. 7. Find the area of the rhombus whoae - 4n 99 v^ 1? n oo -.^'^ ^"'-^ »'tiMi.les are as follows : 1st A B q^q-f'^^ y i^A^u'^ 32.,oyd.; 2nd D C = 105.75 yd., C P = 86.95 yd. ; .^rd A B = 145.20 yd., E D = 127 54 vd -4/11110 — /)«.. UtW.n.Z(lo«i.yd.; 2nJ 9194.9625 .q.ViSfd 18518.8080 Q wu..* ■ *i ja. ■ /!»». 110 8q. ft. 10 eq. m. .n 1*fW nf J' t'^^f'S^^fenoc between the area of a floor 50 feetsquare, ^^•n1 r ?^''''' t^*"^ ^^ ^""^ ^"^-^^^ ^««- 1250 feet. ' lU. iind the bases of rectangles containing each 19208 sq. vd S'2 8(?v) /h 7n"f.n'''?''/r> ''* 100 y^-' ^»d 7,24 yj., 3rd iJ52.80 yd., 4th 705.fa0 yd., 5th 940.80 yd. M TT. 11 "^"n ,^''*- ^^^-^^ y*^- 5 2nd. 85.75 yd., etc. 11. How many boards will be required to floor a room Ifi yards loDg by 8 yards wide, .f each board is 3.90 yards long by .32^ard 10 A -4 11 o- V „ . . ^w*- 102.56 board's. 12. A side-walk .3.) i\. 3 :n. long by 2 ft. 9 in. wide is to be orer-laid with a nuxture ot bitume and sand. What will be the cost at $2 92A a square foot? ^n... §283.54 + .' l.-i. Ihere is a square whose area is 3600 vd. ; wh^it is the side of a square, and the breadth of a walk along each .side and each end of the square, which sliall take up just one half ..f the v-hoie' fl ^A**- ^ Hi ^\*^.o*" the .square; 8.78+ yd., breadth of the walk. \\ piece of land in the form of a parallelogram is 2i;4 yd. loa^' and Its width is^j of its length ; how many bushel, of wheat will ^ required to sow it, it it takes 1 4 bu. per 1000 sq. yd. ? Atu. 43.56 bu ■K'^nsATroN OF nvHTAm, PROBLRM n 319 aa L» «'• I'ltiu tJie area «;„„„ '?«'« ™»( of Ihe product, which * "~ ^^ half ,UBa . 22 — 8 s: 13. f 320 i' i. ; 1 1 I i 1 ' 1 1 i i 1.1! I. ! r MwisuBATioif ev mKrAgle ABC, = 15 feet, 26; 400 + .C. £ II the brink I of the pond line which iiast to the ►.24+ a. 3 ««-.««„,„, „ ,„^^_^^^^ ^^^ yorda: finf) ff °f " '"""S-lar field ,, ?„„,.„. „'<"•' lOl/rPfr. 4 Tl, " ■'"^'^''"<'" ' "'"""« I acre and 3 r „:j • A, 'adder 50 feet Inn., .„:>, __ . Am. U:^^^ 007 ' ^ fiide-walk. :l?l'.^^«'''?eNit will rP.nl, „ L"'_"r ^'f'. 'acMer over to ^n.9. J4.^7I .897 yd. '!^e other .ide c7the st'ree't l^'S,^"'^ ''> -' tl>e^aS:oretV?iJ'^'^'^^ . ■'^. What.;nSV''f^^!-^'2^eet? Ans. 21.1 (eet. '^ I'ouse, in theW. ' " ,..e, if Ans. I7.G7 ft, on each side were 17.< ^"« 24.78 ft. ^ -'^- What would u''f'''!'!^2^eet? feet? ^"'^'^'^''^^^'dtb, if the rafters Proble.m V ''•'en the h,p„,|,e„„,e ^^^ one sidl „f u '*•• i. in the rieht- " - riven A f <.. ., "6"' given A C ~? '>?!• '''^^'<-a".?Ied (Wangle A R d ^. , 2 ■Vr'V''"'' '"'=■'«« i «25 - 400 = 225 . ^2-^ 9n fa^t — "J f^'-.i^uuse era / 4l ,''^^* ,'« t'^e ba.se ? . ^. ■4n*. 06 feet. ong. anditsoppolitevokpL^',.?* ''"^ «^ t^ie rafters be \( fl Problem VI. -^ "^e area Of a trapezoid. Orijj. Rule Mth' 1 ^^ t-o: the quotient wiulTtt^X'^'^-divi^^ fi ! '1 )1 I , I . ■ 1 1 . 1 ! ! i si' j Mf J ii 322 MBI^SURATION OF SDRFACES. Ex. I. What is the area of the trapezoi*^ A BCD, having given A B = H4 yards, D C = 26 yards, and D E =» 20 yards? Operation. (34 -5- 2 = 600 eq. yd., 26)x20= 1200; 120C Ans. 2. Required tlie area of trapezoids who^e perpendicular heights auJ bases are: 1st H = 16 It., B = 24 k. and 36 ft. ; 2nd B = 20.15 ■>i.2f) yd. and 62.49 yd. ; 3rd H = 36J ft., B = Ib^^ fi. vd., B and85ift.: 4th H = 55 A yd., B = 106.iyd. and 134j»'„ yd. : 5lh 1st 480 sq. ft. H = 7(1^ ft., B = 145J ft. and lODj a. Ans. 2nd !)74.65u5 &q. yd. ; .3rd 2923.15 sq. ft., etc. 3. What is tlie area of a trapezoid, the parallel sides of which are 12.41 and 8.22 chains, and the perpendicular distance between Jhem 6.15 chains? . Ans. 5 A. 1 R. 9.956 per. 4. The parallel sides of a piece of land having the form of a trape- zoid, are 2482 and 1644 hnks, and their perpendicular distance is 1030 links: find its area. Ans. 21 A. R. 39.824 per. 5. A field in the form of a trapezoid whose parallel sides are 76.28 and 60.72 yards, and the perpendicular distance 4(i yards, was sold for $18768 ; what shall be the cost of another field o( the same kind having a rectansular form, who#e base is 115 yards, and altitude 76 yards? ' Ans. $51760. Problem VII. To find the area of a quadrilateral. 500. Measure the four sides of the quadrilateral, and also one of the diagonals: the quadrilateral will thus be divided into two triangles^ in both of which all the sides will be known. Then, find the areas of the triangles separately, and their sum will be the area of the quadrilateral. Or again, Let fall on the diagonal two perpendiculars drawn from the vertex of the opposite angles ; multiply the sum of those perpen- diculars by the diagonal, half of the product will be the area. n E^' i. Suppose (hat in the quad- rilateral A B C D, the diagonal A C = 88, the perpendicular D B = 27, and B F = 25 ; what is the area? Operation. 27 + 25 = 52 ; 62 x 88 -r- 2 = 2288, Ans. 2. In the quadrilateral A B C D, the side A B <« 12 lieet, the side B C => 16 ft., the Hide C D >^ 10 ft., the eicU MENSURATION 01" 8DRPA0E8. 323 e trapezoi*^ yards, D C 200; 120C leightp and 1 = 20.15 = 75j'(» n. '„ yd. : 5lh I) gq. ft. ; r wbicb are weeo them 956 per. o( a irape- listaace ih ,824 per. s are 76.28 ii, was sold eame kind [)d altitude $51750. ', and a ho ivided into be known. their Hum I from the one perpen- i the area. a the quad- igonal A C D E = 27, je area? 2; 62 X 88 ^ B C D, the side B C =. t'l., the eida AD = 1 P ft., and the diagonal A C = 22 ft. ; what ia the area ? 9 «,, , . , ^ns. 174.02 aq. ft., .i. What 18 the area of a quadrilateral whose diatronal is 40.25 feet and the 2 perpendiculars 12.25, and 15.05 ft.? 4.' 549.4125 sq ft ' 4. Kequired the area of a quadrilateral whose diagonal is 108 feet b inches, and the perpendiculars 5« feet ?, inches and 60 feet 9 '"^>^|;. , ,^ Am. 6347.25 sq. ft. .0. i;ind theareaofeachof !he follow! n^r quadrilaterals: Ist dia<'- onal 65, perpendiculars, 28 an03.5. E«l> = I:-J -' ^n _i_ '> __ ^KK l5o;- X oi EyD = 13 y. 70 455. 52 X 61 2 = 65(5, BwtoC = 96 X (32 + 61> -^ 2 + 456 + 66C , iiU^lm - 1441.8.6 ,q. yi., or 2.M6+ Je^lt the regular 3e sides A B, erpendicular 570 ft., Ana. he following •, perpendic. 12^, one ol 3rd 2916. T polygons, lar, 24 feet ; ar, 12^ feet ; ch side, 22 3 feet, etc is: Ist of a rhose side 's line? ch. ; etc. gon, the side 3 long by 4| avementfl. MENSURATION OP .-DRPA0E8. (tnd trape- \e Proh. II area of the area of the !DEFGH 1= 33 yd., yd., pq «= Am = 41 == 52 yd. ; yd., Yp = wiB = 32 = 84 X (32 274. FdoE - 2 « 455, l> -^ 2 « he polygon I + 1503.6 acres, Ana. as 2. Suppose the same irregular polygon A B follows; Am = 10ft. fin.,L = 32 ft ft. 4 in. /« — 0/ A n • ' „ "-' "" 325 C D E P G H to measure 6 ft. 4 in., In = 21 n. 9 V:' Tp Z % l' V"-' oU = 28 ft. ; Al ■= 4 ft. 10 in.; Bm = 10 ft ;^. 7. l" ^-'.^^ = lift. 6 in. oD Qn = 16 ft., FP - 4ft!Vk,%rJ^^- 2.n ; ^^ T '^"- ^ -' "V ^q la ft. 8 in. ; what is its area ? Ans. 1297.82+ eq. ft. PROMISCUOUS .XAMPLBS I» R.CT.UN.AL .,™p«E». 4 yards high; allow- ceilin„ ? P" ^^"^'^^ yard for Uie walls, and fin nf= e^°. le ceiling ? ''^ *'" "^"^'■'^ y^''^ fo' tiie walls, and 60 cts. for tlL 2. Some paper 15 inches lon^r an,i 10 • u • .'^"*- $1^5.56. quire; what will a quire of the LmT ^^'"«^«« wide, costs 1 6 cts. a long and 13 inches wide ? ' ^"^''^^ "'''' ^h'«'' >« ^^^ >nche« 3. The panelling of a room is 191 t^- 1 .'^"*- ^-^'il- what must'^be paid for It Cwin^ ?hi? h' ^^"^ ^""^ ^ ^°'«^^ high: I8a. 4d. a sq. toise, and tlie naTnJL r,f o^^, ^^rpenter'n work cSsts 42yar..s? * ^ ^"^"^'e, whose sides are 20, 30, and „^^- ThehypothenuseofatriancJe is 4^; fo.f a ^'^"5" ^^^-^^ yd. 25 ft.; what is it3 base? "**"«'* '^ ^^ «et, and its perpendicular 32 ft. long and ISmchesZJ^^i^X 1 f''''^'' ^''^'"' ^he rolls bein"ir at $1.75 Iron ? '^''' ' ^°*^ ^^^'^^ "^"^^ bo paid for the whole 9 What is the surface of a <^hepf nf -i 30 rolls; |52.60. wide? uii^ceota sheet of paper | yd. long and | yd 10. The sides of three sauares Rr» q a A ^"^^ ^''^•> °^ "'i ^q. ft. 12. A 6ide.walk 6iyardslon-andlAvaHJl^!J' pavin.-tile.. with stones, each stan% has a aurfaco o 70 sauarlt'.;' ^ ^l P*^^'^ b3 the cast of the whole pavement at the rat2 of ?1h' a'' ' T^'^S^^^ etonea? ''*'' '"^ '^^'^^ ol i5>18.i)0 per hundred J 3. What ia the area of a panlpn in tl,^ »Uo * ,"^^*" ^32.5 »" to lower •ud 5.2o yd. h,«h, at the r«teof $i.ia tha^. yd. 7 AZ%lt88+' 326 MENsnaAxroN of surfacbs. I'r I j L ' i 17. What cost a piece of cloth 12^ yards long and I A vards wide, at the rate of.$1.90 a yard in length? Ans. $23.15. 18. What is the area of a trapezoid, whose diagonal is 45.10 yards long and the two perpendicular?, 15,80 and 20 yards? ,„ . , , Ans. 807.29 sq. yards. ly. A man plastered three ceilings each 7.35 yards lono- by 5.40 yards w:de, and painted 6 doors each 2.05 yards high by L05 yards wide ; what sum must be yet paid him, if he charges $1.22 a sq. yard for tne ceiling, and fO.HG a sq. yard for the doors, havinir been paid already $22.40 on account? ^ 20. Find the side of an equilateral triangle equal in area to a square whose side IS 8 feet. Ans. 12.15 + ft. 21. Find the area of a piece of land comprising three trapezoids, and one triangle ; the parallel sides of the first trapezoid are 36 and 54 yards, altitude 19.50 yards; those of the second are 110 and 75 yards, altitude 126 yards; those of the third 186 and 141 yards, altitude 219 yards; the base of the triangle i.s 69 yards, altitude /9 A%n u 1,,-. ^ns. 10.244+ acres. IZ. A field whose parallel sides are 630 and 436 yards, altitude 80 yd., 18 let for $200 a yr. ; how much is it per acre? Ans. $22.70 + . 23. A room 12 yards long by 7 yards broad was floored with boards rf yards m length ; the waste made on employing those boards was I oMheir gross surface, and they cost $.25 per sq. yard, gross surface. Ihe work was done in 12 days at $1.10 a day, and the nails used amounted to $2.50. Find the whole cost of the floor. Ans. $39.70. 24. A man wishes to plant 1815 trees at an equal distance Jrom one another, so as to form a rectangle whose length is to its breadth as 5 18 to 3 ; how many trees should he plant on eacli line ? ^5. Ihe g of the cost of a barn gate being paid, there still remains I of that cost plus $23.40 to be paid. Suppose the barn to have two gates each 3 yards in width and 5.40 yards in length : what cost the square yard? ° ^^^ ^4 26. Some earth was brought and levelled upon a field whose area equals that of a regular heptagon, the side of which measures 42 yd. ; i^hat cost the work at 4d. a sq. yd. ? Ans. £40 1 3 + . 27. What will be the cost of roofing a building with sheet-iron at $1.22 a sq. yard, if the roof comprises two equal triangles whose bases are 9.40 yd. and altitudes 6.32 yd., and also two equal trapezoids whose parallel sides are 25.48 and 16.08 yd., their altitudes bein r° ^^"^^' ^^^P^^-^'ds •qnal triangles wh..seba,;es are Ifi20^v'' i-jT V'"' ^'^^ ? 2" two l-'ps each being lo.so v ..Ton 'hv Vv V f "^T'"^ ^''^^ ^^^ ' ^'«° '^ ^l"".!,' the gutters; the'siafes wK,.?*" {!:>''*;'' P'"« ' '"'^"^ '^f'slates 0.21 7 yd.,"and ar'e ZrZo 19^ vd" h ^) ^- 'V"''\"'^' ^ ''^'^ ^y are paid .r sundr? e.pe^ %^iSS Xfe io^stTtlKo? ^^^ 4ns. $265.22^. Problem X. To find the circumference of » circle, the diameter being given. ° wcf Will be the circumference. N0T^4,« is the cireumferenoe of a circle whose diameter i. 1. . ■^•^- ,^* What is the circnrnterenre nfo circle whose diameter is 18 yards? Op.R. 3.1416 X 18= 56.5504 yd., 4„,. 3. What are the circumferpnPf.a r.e ■ i ' , Io7.7106 yd., etc. ^n». I 265.46o2 yd. ; 2" 422.482368 yd., etc. Problem XI. To find the diameter of a nimio ♦!,« • •luccer 01 a circle, the circumference being 594. RVLK-Bivide (he circumference hy 3.141(; and th. qmtunt will he the diameter. ' ' 1^%i'J^V''^'^'^'^''^' ^^^ «'r«'« -hoee circumference is Operation. 25.1328 - .3.1416 = 8 yards .!«« ^^^t^r^V^^f^ who. circun^,.n;es are ^ yd': Ki;2:;^;liJ22?'2o^"'^?^r?^"T"^^«-^ '^^9.2. 60 it 6' 3" ? ^ ' 4«. 1-1/0.;,'.? i '• I ^*^- ' "' *H y^- ; P" iiw. 1 11.02146 yd. ; 2«' 24.2105 + yd., et^. e M 1 328 I 1 J ! 1 1 ■1 1 It 1 ^M ■ * ^^^|H ■ i! 1 MKN!!5i;nATrON OP SCTllKAOliS, PR'BLKM XTT. To find the length of a circular arc, whea the number ol degrees which it contains, and the radius of the circle are known. n^*'}J*' 1^''^^K.— ;)//(// /y,/y fJir. vinnhpr of degrees hy the decimal .01 ^•lo, and the product arising, hy the radius of the circle. E.v. I. Suppose the arc A B to contain D 120 degree.-, tirui the railius A C be 10 teet j what is tlie length of the arc ? Oper. .01745 X 120 X 10 ^ 20.94, Ana. 2. What is the letjgtli of an arc containing 25°, the diameter of the circle licing 15 ft. ? Ans. 3.2718 11. E .S. Required the lengtli of each of the fol- lowing aros: 1 1120 10',(]iainetei- 20 ; 2nd 10" 15', diameter 68 ; 3rd 670 17' 44i", diameter 25 ; 4th 60''. radius 14. Ans. Lst 2.123 +; 2nd 6.0813 +, etc. Problem XIII. To find tho length of the arc of a circl ), the chord and ridius being given. S06. llnr.E. — I. Find the chord of half the are. II. From 8 times the chorda/ half the a'C. subtract the chord of the whole arc, divide the remainder by 3, and the quolieat will be the length of the arc, nearly. Ex. 1. If the chord A B, fig. of Prob. XIl., equals 30 feet, and the radius A C be 20 feet ; what is the length of the arc A D B ? OpEiiATioN. First draw D C perpendicular to the chord A B ; it will bisect the chord at P, and the arc of the ciiord at D. Then A P = 15 feet. Hence, AC^ — AP^ = oF^, that is, 400—225=176 and V 175= 13.228 =_ C P. Then D C — CP = 20 —13.223 r== 6.772 = D P. Again, A D = V A P^ -h P D2 = V 225 i- 45.859984. Hence, A D = 16.457 =■. chord of the half arc. 16.457 X 8 — 30 Then, r^ == 33.885 = arc A D B, Ans. 2. Tf the chord A D of half the are A B I), %. of Prob. XII be 30 feet, and the churd A B of the whole arc. 50 feet; what ia'the length of the uro ? Ans. 031 feet. /E^ lumber oi fthe he (decimal circle. to contain be 1 teet ; 0.94, Ans. containing g 15 ft. ? ;.27I8fl. of the fol- er 68 ; 3rd + I etc. )rd and the chord quotient it, and the 9 lAB; it rhen A P 25=176 84. Ana, >. XII, be lat is the ik feet. MENSURATION OF 8DRPA0E8. 329 Ans. 64.42. PttOBLE.M XIV. To find the area of a circle, the diameter, or the circum- ference, or both, being given. ^597. nvLE.-AIuItip?^ the square of the diartiefer by .7854. ^'^ultjply the square of the circumference by 07958 Or Ex. 1. What is the area of a oiroie whose diameter is 12 yards? i. Fmd tlie area of a circle whose circumference is 12 yards OP.a. .07M8 X 12> - .07958 x U4 = U.459I ^. yi.', An.. and.h^?£*;aX°"'"'°'= """'' ™"fere.ce is 37.70 yd., 0,ERi„„„. 37.70 X 8 _ U3.10 sq. yd., An.. low'^M^^ir, .'srvr s?iL'Si t™^ 4° 86.59035, etc. *"• ^■''•' ^ "^''"i 3" '9«3-50i PaOBLEH XV. Oiven a circle, to find a .aiiitre i.,k,»i, .k.n v._. . equal area. SB Ji?lJ:"~'- "■*" *"°""^ X -8862 = .ide of an ,^ II. f A. c,>ra^«.3K» X .288J = «a. ./■,„ eyui,^, ^«,„ «r,>| 330 MENSURATION OP SURFA0E8. ,1 i 1 n I If f ill 111 'i II ' ,1 I: f- 1 ill III • 'ill I Ex. 1 The diameter ofaoircwlar field is 650 yards, what would be the side of a square field of an equal area? OptRATioN. 6o0 X .8862 - 676.03 sq. yd., Ans. 2. The circumference of a circular fishpond is 200- what is the 3)de of ;i .square of an equal area? Opkuation. 200 X .2821 = 56.42, .4ns. 3. Find the sides of squares of equal areas to circles whose circum- ference^-are l"250yd.; 2^ 300 yd. ; 3" 412.50 yd.: 4" 135.75 yd.: L '«;..'!>'-"• J ^"*- 1° 70.525 yd. ; 2» 84.63 yd. ; 3« ll6.:{(i(;2D yd,, etc. 4. What are the sides of squares of equal areas to circles whose io\ToT ff ^'^ 2^ ^^-5 2° 30 ft.; .3« 73.10yd.; 4« 45 ft. 8 in.: o! f ^*?^ /.'^- ^ . ^"»- 1° 22.155 yd.; 2^ 26.5860 ft. ; 3" bb.5536+ yd., etc. ' Problem XVI. Given the diameter, or the circumference, of a circle, to find the side of the inscribed square. 5»». Rule.- L— The diameter X -071 = side of the inscribed square. II. The circumference X .2261 — side of the inscribed square, Ex. 1. The diameter A B of a circle is 300 ; what is the value of A C, the side of the inscribed square? Operation. 300 x .7071 - 212.1.S, Ana. 2. What are the sides of the inscribed squares, if the diameters of the circle are 1«312; 2«400; Z^ 150.20: 4° 225.,S0 yd. : 5" 170 ft. 8 in. ? ' ' ^ ^"«- I'' ;^20.6152. 2" 282.84; .so 106.206 + , etc. •• Hequired the sides of the inscribed squares of which the circum- ipivncos of the circle are 1^ 718 yd.; 20 180.40 yd.; 3^ 368.10- 4" 1.!;).70 yd. ; 50 800.20. Ans. l^ 161.6218 yd. ; 2= 40.608 + yd! i .-1'^' «2..^5y31, etc. ' PliOBLEM XVII. To find the area, nf a ttt^p.tnr nf a n\To\»t 600. Rdlb.— I. Find the length of the arc by Problem XII VII II Multiply the arc bjf one half the rad»U9, and the prudm^ II be the orta -f.Ti-v'i-.f'ir' ' f^^Sffifcti" MKNSURATION OP rtUKFACE.S. , whnt would what ie tbe 331 ,J. Find .he area era, actor „.„,, ,„<„„, ,. I'^anfufel;^;!,: „,■ 5. Wl,a. i. the area of a «„ioirole i„ „,„■„, ,b. J,"„'k ilTjf " C- What i« the area of a .ertnr „f , k- i .l ''"'■ ''53-874r,. •nd the r.h„, of the droit 1"l7' °' """='■ "" j}^,^; '^ o'o^sVoe' k "' Problem XVIU. To and the area of the segment of a circle. 111. V f he segment it areaier fhnn tJ.^ • • , area. /.^.,A,,; L, ij. /^r L ;?Lf / /r*'"'"^'; '^/'^ '^^ ""^ either case, will be thiareareqXd ' ""'^ '^' ''"'^^ *" Or use the following """ '-• -: -» • "-i" ^^.hf s Of .r-e-A ^o^ rj Operation, "^ ' " =~^=^ of C P. ofPD. -AD: iiieasure nieawure I 26.7309, the measure ■ I I, .1 332 MRNSURATION OF SURI-AOEH. Jd. 20 ftniSVp^ 'n?i ^^^'^'•.a'^'"^ - 257.309, area of the «ector A D B C; JSrvrm .,?, - //o'' CAB- aroa of Reginci.t .v D I{ ; that is. 267..^()J _ 1!)2 - 6r,.309, area ro(,uire.l. It is alnc cbvious that the area 8 40 yards, and the conjugate axis D B • *r I Ib is 25 yards? Operation. eq. yd., Ans. 40 X 25 X .7864 = 786.40 oA^;„^®*l"''"^'^ ^^^ ^^^^ ^^ *^« ellipses whose axes are 1«» 5 and 4 vd • yd. 60 70.40 and 4- 66 yd. Ana. !<> 16.708 sa vd - 20 6S.1269 eq. yd. ; 30 98.1934 «,. yd., eta ^' ' ' )r A D n C} i> ; and the • 15; that ia, iUH, tliat the whole circle degroes, the — ^60° =1 = 76.79 yd. >6 = 25.71 segt., Ans. adius is 10, segment =» 6 X 20 X d. or [360<^ = iy.l93; of the seg- ; being 10, 5 sq. vd. !7 atid the J2.31 + . the radius 28.27 + . reas of ihe 75 ft. ; i" sq. ft. ; given. leir prod- area. garden in t^erse axis axis D E = 786.40 tnd4yd. ; md 34.18 1- y^' i MBNSURATION OF SURrAOES, Phoblem XX. 833 Given the area of an ellipse and one of its axes, to find the other axis. Phoblem XXI. To find the ciroumfe, , of an ellipse, the two a«, being given. o„rf^^, ''"'-^-^""'f'.'/ 'he mm of the two ox,, h, 1.5708, and the product ,„n gtu, ike drmmfjence, warly. Op™*t,o»^ (20 + 16, X 1.5708 = 66.5483, nearly. An.. Problem XXII. To find the area of a circnlar ring, or of the space included between two concentric circles. ^ 605. '^m.^.-Midtiply the, sum oftke two tUnmeter-^ hi *Ji-!r rifr'o;,""" '^''P'''^'''' «^^"^' % -7854 for the i^reanfhL fr^)lZ '^^,^"'^*^ 'if'^<'<^^ ring, siihtract the square of the /ess 6y the decimal .7854, thejtroduct will be tht area. . . „ . , An$. 75323 lb. fn \L S'"Jw ^!,^'^* "} ^\'^ ''"''" '^''■°'« of the earth corresponding o the 49» of atitude north, knowing that the value of each degree of longitude, in that latitude, is 80018.43 yards. 18. The diameters of two concentric circles are 45 and 30 ; what is the area of the ring f n-med by those circles ? Ans. 883.575. c^ : oT*^"^ I"^7 ""P*' ^ '"'^^^^ '" '^^•^'"s, can be drawn from a tin on li'"°j.'^^' '°"S by 15 inches wide ? Ans. 205. 20. J he diameter of the bottom of a ba,sket is .46 yd., an! the cir- cumference of its top is 2.262 yd. ; what difference is there betn-een the area of the lower base and that of the upper base ? Z' .„ c' . , Ana. 0.240977 sq. yd. ^l. trom a iinc sheet 28 inches long by 25 mche.s broad, how manv ""If ^ml ^®.*i'''*w" who.se diameters are 2^ and 3^ in. ? Ans. oil. ' 22. Ihe circumference of a circle is 314. 1 G yd. : what is the rac'lins of a concentric circle half the urea ? Ans. 35.35 yd. .ul^li^^*''?*^?.**^^*"''^'*'^ ""'"^ "'' ^ circular parterre, "knowing that the exterior diameter of the parterre is 18.40 y.l., and the breadth 5^* ""S 80 yd. ? Ans. 44.233728 sq. yd. Z4. W^at Utile Side 01 a. square equal in area to a circle whose diameteria4? ^J^g 3.544 + . 25 The exterior diameter of a circular pond is 15A yard.s, the breadth of the ring j»^ yd. ; required 1 ^ the area uf the ring ; 2« what will be paid to have it paved in tlag-.stuues, at tiie rate of §4.16 a sq. yd. Ans, $171.72. 26. A circular garden whose diameter is 26.5 yd., is enclosed l"y a fli^^^if'"' "'^ '^'^' ^^"^'^> '^^^ '"*"y bundles of gras.s, each weighing' 3b. 64 b., can be gathered from this ring, knowing that when the grass dries up, it io.ses 56 % of its wei>iht, and gives 2056 lb. of hay 27 Ihe radius ot a circular pond is 12 yd.; what must be the width of a grassy ring around the pond, that contains the same ftr**' Ans. 4.97 yd. 28. A triangular meadow wiiose sides are 6420, 6280, 340U yd., eneloseH an eliiptical pond wliu-e diameters are 195 and 348 yd. Find the worth of the hay produce. I by that meadow, if 5056 lb. are cut per acre, and sold at 4 cents per l.undle of 10 lb. Ans. 138246.29 + : 29. A man has a ci«tern wliose diameter is 3 ft. 10| in. ; its ed"e, which 18 23| in. broad, is to be covered with tin-plate at the costVf W.lOasq.yd. Find the ooet a»». *b.3ti -t- , ll !■'•; I' i r ■1 iii. I' ri 336 PROMIBOUOTJS KXAMPLE8 TN CIRCULAR 8URFA0M. he own .(ill ? ^ °' ^^ P™''/' '" diameto. What part doei The field p^uMssfoolhoJh' °'^""' '"'°',"'' ^M a>"l 328 yd. whi s^ireSJa^riirf r-""" -t i"--^ i- '«e.d beine nart of /pS„ ^- '^^"'«"^ the arc ol" which is J70« .h; «dtf of'.LVet^T7°/6'vr" "";■"" i™!?' ««'» i» s" and KS^i^',?^^^^^^^^^ - ^LVthetdi^jTS ^m^:. -itr-''' kOEB, .50 a sq. y angles are un^uT °° °"""' """^ """"^ «'"'^» n>aneq^Cai?s^fer:ir:he:/°7 7"''^f ^"^ - «17. Ti'«'«8»i«loM«Wr«i,.«*i«„^tt„g^,„,^ 338 tJ i| MENStrRATION OP SOLIDS. hi ■I if % 'I In . > Ri fc t i e.|ual and sirailar triangular pyramids, whose vertices meet in I lie centre ot a sphere supposed to ; iicumscribe it, »'l"'- polyhedrons are the prism and „„ *?*• /■ P"™, '■■' » %iro whose bases, or ends, are any similar cIm ?;,-,i7il.'''"°" "^'^ '^ perpendicular to the base, is ©as. An oJ^Hc prism is one whose axis IS not perpendicular to the base, 624. The height, or altitude of a prism, in an „b„,„ „„ ,, „„,„,„ ;, ,^^ perrndiatf'r^'il' ««- r^'"' """"^ l'JP»«>enuse is the aris. " „.;?*• ^ •"""S"'"'-. quadrangular, pentagonal, hexaKonal etc rS^onX""" '"' '^ " '"""«'=■ aquadrilatiral, a-penL;!:;: alle?o?r™.'* ^"»"«">P'Pe'Jon « " P™">, whose base is a par- anS?'^],^*?"^*'"^'' 'V-^''^ "^S"™ contawed by several tri. »m«oa verL " "" "" '" *' """° "'""=' """* "'™'' >■"» one *«r»'*' pjrrjwiW, P7t-/rftmid ices meet in MKN80BATI0N or SOLUM. 339 nn^^i- T^® ''•'^** of the cone is the perpendicular drawn from its ton to w»s.», ihe generant or side ofthp »o„c ,. th. hypo,he„„se, which" by the revolution of the riohuiigled t iaCio to the plane of itst^aTdt 2 ■L;:,^'^ "^■» '^ -'■-<' Small oirde. *s»« m, 635, The/.«,^:,r;i of «'i cone, is the portion re- maininij when an upper section is removed. e:56. A Spheie is a solid, bounded by a curved surf'icc, every part of which is equally distant trora a point within, called fSie^ Ti,« J- /. '^c centre. to a^pJ^I£fZ:L' ^f''='« '^ " '™ -i™" from the centre thS Jtt:?: jtS;s ^ ticts -^ " "- ^-'°^ betre^tw^Lrpire;' Sh r:^";: ,i:. --™ '--- Circular Spindle is a o VA ,1. /. ' Spindle 18 a solid, th<; %urc or shape oi' which IS marked by the revolution of tl- arc of a circle about its chord, which remains stationaiy. (Jreat circle. :& S40 MSIfSVRATION or SOLIDS. Sector. Segment. Spherical Wedge. T^ Segment with two bases. 643. A Spher- ical Sector is a solid generated by the rev- olution of a sector of a circle about one of its radii. 643. A Spher. ical Segment is a portion of the sphere cut off by any piano. The plane is the hase of the segment ; the perpendic.ilar distnncc from the centre of the base to the convex surface, IS the height of the .segment. 644. A Spherical Wedge is the portion of a sphere com- prehended between the halves of two ^rroat circles. 645. A Spheroid, or Ellipsoid, is a figure produced by the revolution of a semi-ellipsis about oi a of its rxes, that axis re. maining fixed. When it revolves about its t. ansverse axis, the figure is said to be prolate ; and when about its conjueate a'sis. It 1.S called oblate. J ' = . Problem I. To find the surface or area of a prism. 646. EvLE.—Muffiply thepenmeter of the base by the alti- tude, and to the product add the area of the bases : the sum will be. the surface. Ex. 1. What is the sur- face of a rectangular prism who.-e base is 3 by 4 yd., and altitude 5 yd. ? ' Operation. The perim- eter of the base is (4x2) + (3 X 2) = 14; 14 X 5 = 70 yd., convex Hurface ; 70 + (4x3x2)=94yd.,yln». ^.r. 2. Required the entire surface of a pentagonal prism, when each Hide ot the base is 10 feet and the heightSO. Operation. 10 x 6 x 30 = 1500 so ft., convex surface: 10" x tabular number, or 100 x 1.720477 = 172.0477, area of one base. 1 hen, convex surface = 1500, square feet, lower base =r 172.0477 " " upper base = 172.0477 « " ; I B»4iTC sar&oc 1844.0964 « MlNSUaATION OF SOLIDS. 341 ri^^^^^^r^UrilugC^ ?'•'«"'» whose ba«e is an heiglit 2a feet? ^ ' '^^ ^* ^^'°»' measures 20 inches, and ii . 4. What is the waIl-8nrfi,/>o ^r "*' ^^"^ ^^- ^- ■'''^ "Q- in. 16/eet long and 1 St fjSf ? "^^ '"l''^'' '^-"^' -''"«^ «ides a?e each o. A rectangular Dri,sini« •? v,^ 1 r , . ^««- 71^ sq. vd. what is 1° the conve^r, rface ^^ "^' • •'•^- ^'■^'^'^' ^"'^ « ^d. h.Vh; Its two ba.es ; 3° he side r a ^ .. ^"""' ' • ^^ ^''^ ^^'^°'^ m,rface of 6. What extent of 8.,r/ace is ^n oVi; '^■- ^''^' '/^ ^-^"^ «q- ^d- are hexagonals, each side ,'ea 'initio '-''7' ''f ^"'^"^ ^''^'hich pri^n. 20 feet, and the pe WtS ofTL • '"^''''•' .^''" ^'^'^'ht of the 4^ feet ? perimeter of a section perpendicular to the sides 7. Required the entire suriace of an .,,,,^"^- ^•^•60843+ eq. ft. ' whose base is 15 and altitude 12 feet ""^j^"*' -E'Tj '^« '''^'^ «^ Prohlem TI. To find the solidity of a prism. fee., a^d it, l.JgfriSfeer'wi.a.t &S.:T'' * ""»*"""S ^ Upkration. 32 X 2 /iq9n7fi9 v. 1= .,,. J 2. What is the «ohdi v !f ! . " ''^'^'^^ "^ ^^'^'^ ^^^'^ ^ns. eral triangle, eal^idf MENgnRATION OF 80LID8. II. To find the slant height of a regular pyramid from it» superficial area, and the side of its base. 6..,?^,?*/ r""-:? "TT^'"'''^ '/'^"'^^^' "'''"■ '"^'^^'^^ the area of th, bct^se^ and divide the remainder by one half the perimHer of the III. To find the side of the base of a regular p] xamid from Its superficial area and its slant height, the area of the base not being included. ««!?*^^; ^^j-J^'—^''!''^^ (hegmn area by half the slant height, and that quotient again by the number of sidesf ^ ' Ea^. 1 . What is the entire area of a trian- gular pyramid, the slant height of which ie iO feet, and each side of the base 4 feet ? Operation. 4x3=12, perimeter of the base; 12 X ijjO = 60 sq. ft., area of convex surface; 42 x .4330127 = 6.9282, the area of the base.; 60 + 6.9282 = 66.9282 sq. ft., entire surface, Aru. 8n^^"n!,")Ti'^ ^r^r^'l \ '''^^".'^'" '"a"g"lar pyramid is 31.732052 sq. tt., an(i the side of its base 2 feet ; what ie its height? -_°,lo'nr7-^,?;.^'^^^'"^^ 1.732052, area of base; and 31.732052 eter J thets7= io':ee;,'Z.' ""• '''" '' ^ '' ^^'^ '"^^ P^""" E.V. 3. The superficial area of the sides of a regular trianmilar Sferu'i^'Jf if "XT '"'""'' ""'°'«" ""•'"^ -'aUalrfi Operation. 30 -^ 6 = 6, and 6 ^ 3 = 2 feet, Atu. 4. The slant height of a regular pentagonal pyramid is 40 feet anH 6. The area of the sides of a regular heiagonal DVpamiH i« qfio .irs'i&V"" '" •"'°' "''«'" '' '^«' -l'at1,7he''ESt'e^ 7. What is the total area of a regular heDtaeonal n^^rJ^ ^^^ slant height is 21 feet, and the meJnreofiKA^UZ^j ''"°'* - ^•J^^.:?^«V^*'eg«Ja''l»eptagonal pyramid i8"483°9rMu2e W and the side of its base 6 feet; ;^ MiUmlaoi height? ^ ** 2jm. 96.17+ X lid from itft e. , • area of the meter of the amid from area lant height, a of a trian- of which ie 4 feet ? neter of the a of con vex 2, tlie area )282 sq. ft., 31.732052 131.732052 the periin- triangular I the liDear feet, and ', and also 6 sq. ft. ramid, the f. 160 ft. lid is 360 r measure 3|feet. lid, whose 58? 3 sq. ft. |uare feet, 17+ ft. ■■NSFRATION OF SOLIDS. Problem TV. 343 T. am the „rfao. of a, tm.tnu of . regnU, py,.„M. i^.r. •• What is the superficial area of th« fill 91? , on^' "PP" perimeter. Then (36 + 24 -. 2 = .30, and .30 x 18 = 540 vd lflfi«Hj-;<7o „, area ot the sides. Again. 6 x 2 -iqwnTft') -1' I5.5884.)72, area of lower base, and 4 x 2 598n7fi9 -. i n onio" = what 18 its wliole surface ? ^•' ^".^ "** S,^ top 4 ft. • 3 What is the convex surface of the frustum of^T; f '*^-,^- amid whose ^lant heijrht is 50 fppt ^^,.1/0^ ^.u P "^Ptasonal pyr- of the upper ba.e 4 feet? ' '''^' of the lower base 7, and Ans. 1925 sq. ft. Problem V. I. To find the solidity of a pyramid. pentangular, etc , pyramid, from it, solidity and ha^it and r^lrac, the sq,mre root o/,kesZ,Z ^ "''"'"'' "'"»'*'•. in. To find the height of a regnlar pyramid from the .ide 01 tie base, and its solidity. <*e ruuli bfS ^ 'net^mn o/ ilu ,uU ofm &,„, and mukify hi 344 Ut^MSURATION Of 80LID8. * I h' 1^'- m n Ea:. 1. Wha* is the eoluiiljr of a triangular py»amid, the h^Tgbt of wliich is 20 feet, and each side of the ba-e 4 (Wt ? Opkrat»on. 4" X .4330127 x y = 46.188 cub. ft., Am, Ex. 2. Ifthesolidity.ot'areg. ocfasoiuJ pyramid be 2133. r)273088 soU-J feet, and its height 42 f«et ; waat is th« meaHur* of oae of itt •quai eiiies ? OfERATioti. 2433.5273088-7- Vj=173.R233792 ; 173.82^3792-*- 4.8264272 {See Table)=:36, and V 30= 6 ft., side of the base required' Ex. 3. A rej^ulur octagonal pyramid contains 2433.5273088 solid feet, and one of its equal sides measures 6 feet ; what is its iiei"ht ? 0PER4TI0K. 2433.5273088 -f- 4.8284272 = 504, and (504 -t 62) X 3 = 42 feet, Am. ^ 4. Find the soJidity of a regular pentagonal pyramid, its height being 15 feet, and each side of its base 2 i feet ? Ana. 53.7649 sq. ft. 5. How many cubic yards in a i.riaii.;ular pyramid, the height of whk;h is S.CS yards, and the three sides of its "base 1.5, 1.9. and 2.6 yards? Ahs. 1.6669 cu. yd. I. A regular pentagonal pyramid contains 45.879297 solid yarda and it« aides measure 6 feet ; what is its height ? Ans. 60 feet. 7. How many solid yards are there in a pentao-onal pyramid, the sirle of wluch, at the ba^p, measures 6 feet, and \U hei'jht GO feet ? Am. 45.8794 + cu. yd. 8. What is the measure of one of the sides of a regular pentagonal pyramid, containing 4678.56 solid feet, and having a height of 64 feet? Ans. 12.29+ feet. 9. An octagonal stone monument has a perpendicular height of 45 feet, and the linear measure of its side is 5 feet 10 inches. Also, each side of the inner cavity measures at the base 4 feet 1 1 inches, and its perpendicular height 41 feeU How many yards of stone does the monument contain ? Ana. 32. 1 973 + cub. yd. Problem VI. To find the solidity of the frustum of a pyramid. 653. Rule. — Multiph/ the areas of the two basea together, and extract the square^ root of the product. This root will be the urea of a base ichich is a meri(l be the conie:, snr/ace ; and fo this add the areas of the two bases, when the enfj.^fnce isre^Jred, II. To determine the area of surface in a cylindrical ing. 657. Rule.— rr, the thickness of the nnq add the inner Ex. 1. What is the entire surf, of the cylinder in which the .iianieter of tlie base is 10 feci, and the altitude 24 feet ? Opkuation. .3.1416 X 10 = 31.416, circumlerence of the base J 31.416 x 24 = 102 y imi—iRKA o- fLi . 753. ys4, convex surf. Also, = 911 064 ^T. ft fir" °'""' '^'"'' ^'"'"- "■■■■'•'»* ^ <"*•" ' 2) 6 Wliaf io ^K^\ . '^"*- 325.6968 8q. in. !! t I ( - 84S «*««.: WENSnRADCON Of SOUJM. .. How much must be pmd lor the painting of the wall and oeiline oi i\ c r«ular room, whowe .lianicter is MO and height 1.' fret, at *2.50 *« x .78iJ4 = 78.54; 628.32 + 78.04 = 706.86 eq. ft., Antt. i3'^: '^' ,^*'**.*? ^^^ diameter of the ba«e of a cone, if its solidity be i* feet, and its ahitude 12 feet? Opkkation. V(24-f-.7854^ V) = 2.764 feet, nearly. Ana. Ex. ?,. If the solidity of a cone be 36 feet, and its diameter at the base .^ feet; what is its altitude? Opek. 36 -^.7854- .3a = 5.0i)29 ; 5.0929 x 3 = 16.278 ft., An$. 4. Acquired the entire surface of a cone whose side is 36 and the diameter of Its base 18 feet. Ans. 1272.348 sq. ft. , 5. If the solidity of a cone be 72 feet, and its altitude 30 feet; what 18 Its diameter? j^^„ 3 027+ {-.et. hpi,;Ji%77."'"T"''^''f^''' •'*'" ""^ * cone is 9.50, and the slant 7^ wf ' "* ^'^^ ^"^""^ «urface ? Ana. 105 744 + i«; 7>at will it cost to tin a circular steeple, the base of which is 16 feet in diameter, and the slant height 48 feet, at 7.-. ctn. ^er -quare 8. l?ind the convex burtace of a cone, whose slam hei-^ht is 40 feet andthecircumferenceat its base 12 feet. ' 9. If the solidity of a cone be 3684 feet, and its diameter 30 feet ; what IS Its altitude? ^n«. 15.635+ feet Problem X. To find the solidity of a cone. 662. Rule.— J/«/^ipZy the area of the base bij the altitude • and divide the product hy 3, the quotient will he the solidity. ' Ex. 1. What is the solidity of a cone, the diaineter of who^e base 18 4 feet, and altitude 5 feet? mSnZ ^\ l-^lTlir ^P.^^^-'^q^^re feet, area of the base; (l/.&bb4 X 5) -r- 3 = 20.944 cub. ft., Ana. Ex. 2. What is the solidity of a cone whose side is 2.5 yards, and the radius ol its hiue 1.5 yu4a ? .' "» •*"" fP Tf?f '^^sitt0^mmmemtmm I > V' f 1 j f " 11 ! i i 1 1 ' 1 1 m 1 ■f^ ■I if ^^H' 1 i 1 1 > 1 1 1 MBMHURATION 0» SOMDB. Find first the altitude of ttie couo. The altitude, radius, and side of the aon. 2 v^l' Vd'il "I'^r =% i-^^ ~ 2-25 = 4 yd. ; hence, A = ^Th: I ^J\ ^;IV K ¥ f ^•^'^^^ ^'l- y*^-' *^^* »f ^lie base; 7.0fi86 x i = 4.7124 cub. yd., Ans. ' 8. The circumfejenoe of the base of a cone in 40 ft., and the altitude /■ Wk f '!»!'' ' r!,^''^ ^ ^"'- 254(;.66 ci,b. ft. Rf TL vil '^ ^^® '"''"i'^ of a circular pyfan.id. thedia«,eter of which at the ba,e measures 4 ft., and its height 18 ft.? Ans. 75.3984 cu. i\. 5. VVhat 18 the solidity of a cone whose height is 1.35 yd., and the area ol the base 3.40 sq. yd. ? Ans. 1.530^ub yd 6. Requiradthesohdityofacone who.se altitude is 1.23 yd., and the circumlerenoe of its base 1.98 yd. Ans. 0.127913 cub. vd. altttude 4 yards ? ^„^. ^^^gyg^ ^u^j. ;d. i Problem XI. To find the surface of the frustum of a cone. 663. RVL^ --Add together the drmmfennas of tiie two bases ; and multiply the sum hy half the slant height of the frus- aZi fP'f'''' ""f *f ^^'^ <^onvex surface, to\hich add the areas of the bases, when the entire surface is required. A „ ^^- 1- What is the entire surface of the / \ Iruf^^umofacone, the slant height of which 18 J feet, and the circundorenues of the bases S and 6 feet ? Operation. (8 + &) x ^ = 70 sq. ft., con- vexKurtace; B^ x .079.58 = 5.09312, lower f"''J.n'^/'^'P= 2.86488, upper base; 70 + 0^.512 -^ 2.86488 = 77.958^^^. ft., entire surface, Ans. ' h.Lr T y^ the convex surface of the frustun. of a cone, the side being .7 yd., amd the radii of the bases .3 and .95 yd. ? s wu^tic*\. .. -4ns. 2.7489 sq. yd. is 210 Td thlt oTZr T r ?''^*"t' vvhose diameter of the bottom M ^lU yd., that of the tu]. 2..^0 yd., and slant height 3.84 yd. ? A Ti, • » Ans. 26.5402 sa. vd , 4. Ihere i^ a feustum of a cone, whose slant hei-ht is 12 leet th*, Probi.km Xli. To find the solidity of the frustum of a cone. 664. Ruus.-. y'kci the sum of tko areas if the two ends, mU II. MENSURATION OP SOLIDS. 349 I of thfl aone, me ; let A be ■ = VT^ 7.0fiH6 X he altitude cub. ft. r of which !4 cu. th I., and the sub. yd. 3 yd., and jub. yd. ^ards, and zuh. yd. iiie two ' the/i-us- h add the ace of the ; of which the bases |. ft., COD- 12, lower base ; 70 ft., entire , the side sq. yd. le bottom I.? s({. yd. i leet, the id 9 feet ; eq. ft. ids, cKid ofageometrkal mean between them ; muUlph, the i^rime hv nn. third the altitude, and th. product Jill he tl 1?/?% '^ Ex. 1. If the diameters of the two base^ of thp frii«f,..» .*• be 24 and 20 feet, and tbe altitude .30 feet ; wl.at iJ^t" soHj;tv^''"' . Opkration. 242 ^ .785,1 ^ ^-.^^^^ ^^^.^^^ ^^,^|_^ ^^^^^^^ • ' .90 yd. the area of the lower base 2.25 sq. yd, and of t..e upper I "f .{. How many cubic feet in the frnstum of a cone, whose altitude is 28 feet, and the diameters of the Liference of the lower ba.-^ 1 445 v and 01 he upper .628yd. ^„,. .coo,.5 ' cub.^'vcf .■^- Wliat IS the height of the frustum of a cone, the convex surLe of which IS 84 sq ,t.. knowing that the area of ihe upper 1^ "si eq. ft., and of the lower base 12 sq. ft. ? JfJ^,. 12 feet PttOBAEM XIII. I. To find tte area of a wedge. U^?mo^t^l'^'~^'T^ ^^'^- r« '^ '^' '^^«^^' ^^l"«h is a paralle- ^A« reqmredarea. ^ ^^'''' '''''''' «''^'«« "''^^ ^« II. To find the a»ea of a prismoid or frustum of a wedge .TIT:-^ '.""'- ^^ "i- "'■■ »- »f "- '''•d, and n . ,0 „...! .1 "^- '°:t "«» "' '!« '"o sides: V 12' — n "- li ob a«d 2 inclies, the length^and tre^lth nJtL 'r "" ^"^'"^"^ "« ^^ 1 inches, and the lenSh eq. in. f the base and that J III be the I wedge. 'voo ejids, i equally 8 breadth B inches ; iohe8, or I follows : i parallel inches. : 4 = 24 length of e central e area of ■■ Hi26 + g :^.ft- by indicular iib. in. 4. If the length of the ba.se of a wedge be 24 inches, its breadth 7 niches, Its edge 32 inches, and its height 33 inches; what is its solid- '^y' Am. .'^OSO cub. inches. Problem XV. I. To find the surface of a sphere or globe. C6S>. Rule. — Fiml the arm of a ci me of the same, diam- eter as the sphere, and midtiply the same h\j 4. Or, Multiply the diameter by the circumfireiice of the sphere, the product W'll l>e the surface. II. To find the diameter of a sphere from its surface. 670. Rule. — Divide one fourth the area by .7854, and ex- tract the square root of the quotient. III. To find the surface of a spheroid or ellipsoid. 071. Rule.— Multiply Ihe product of the two diameters by .7854, and that product by 4, th.i result will be the surface. IV. To find the convex surface of a segment or zone of a sphere. 07S. Rule. — Multiph/ the circumference of the sphere c;' which the segment or zone forms apart, by the height of the seg- ment or zone. Ex. 1. What is the surface of a globe 50 inches in diameter ? OpERATioi;. The surface of a great circle is .7854 X 602 .= 1963.50 sq. in. Hence, the surface of the globe is 1963.5 x 4 = 7854 eq. inches. Ans. Or, 50 x 3.1416 =» 157.08, the circumfeience of a great circle : 157.08 X r)0 = 7854 sq. in., surface of the globe, Ans. Ex. 2. If the area of the surface of a sphere be 24 square feet : what is its diameter ? Operation. (24 -i- 4) -f- .7854 - 7.6394, and V 7.6394 = 2.76 an ellipsoid be 6 feet, and the feet, shorter 5 feet Opkbation «q. ft., Ama. he longer diameter of what is its surface ? (6 X 5) X .7864 =- 23.662; 23.662 x 4 =- 94.248 852 MKNStTBATlON OF SOUDB. 1 It ; ;i' ,i_i ;. i. Eat. 4. Ff the diameter of a sphere be 50 inches, what is the couTex surface of a segment of the name 10 inches high? Operation. 50 x ;5.1416 = 157.08, circumference of the circle, and 1,)7.08 x 10 = 1570.8 sq. in., area required, Ana. 5. What in the surface of a sphere, the circumference of wliose great <'''"°'«J!,« 't-'J;! yd. ? Arts. 7.4506 sq. yd. b, 1 he diameter of a sphere is 21 inches; what is the surface of a zone whose height is 4^ inches? Ans. 296.8812 sq. in. 7. If the surface of a sphere be 6.16 square yards, what is its diam- Q rru , ,. ^««- 1.40 yd. 8. ihe longer diameter of an ellipsoid is 18 feet, and the snorter- 15 feet; what is its surface? 9. Required tiie surface of the segment of a sphere, comprised be- tween two parallel plans at a distance of 1.25 yd. from each other, the ,n°^mf*^^ ^P'*^''^ ^'^^"= ^-^^ yd- ^ns. 27.489 sq. yd. 10. The radms of a sphere is 3.08 yd. ; required l" the circumfer- ence of a great circle ; 2'-^ the surface of that sphere. ,, _,, ^rw. 1^ 19.852 yd.; 2o 119.2098 sq. yd. 11. Ihe area of a zone IS 2.85 sq. yd.; required the entire surface of the sphere, the height of the zone being .45 yd. ? ,o 1. , • ., ^^' 12.742 sq. yd. 12. lieqnired m miles the surfece of the two frigid zones, allowing 327.1i)6.-i7 miles for the height of each of them, and 39.'^5.82986 miles for the radius of the sphere. I f n''*"7^° ^^^ '■*'° ^"''f'>'"'s of irregular solidB, or bodies, the following process J jIV ^'^^"^' """^ °0'°P'>sed of plane faoes.^nrf the area of each face, ana add them together for the whole surface of the solid; if oompo^ed ot circular taoes, eftmcie theee tnto a number of faces infinitely great, eo thtt each might be eonndered a plane. Then proceed as above to obtain the entire surface. PuOBLBSf XVI. I. To find the solidity of a sphere. 673. Rule.— Multipli/ the surface hj one third of the radius, and the product will be the solidity. Or, Multiply the cube of the diameter by the decimal .5236, and the product will be the solidify. II. To find the diameter of a sphere from its solidity. 674. Rule. — Divide the solidity hy .b2^Q, and (^.'v^ ct the cube root of the quotient. m. To find the solidity of a spheroid or ellippoid. 675. RULK. — Multiply the longer axis by (he square of the shorter one, and ihe product by ihe decinvd .5236. the result wiU be the required Molidity. ' '"taWtfi^'i 9 the coDTex )f' the circle, wliose great )6 sq. yd. surface of a 12 sq. JD. ia its diarn- 1.40 yd. the siiorter- niprised be- h other, the 9 eq. yd. circurnfer- 8 sq. yd. tire surface 2 sq. yd. 3, allowing; 29:^6 miles ^ng process >/ each face, i ot circular ch might be \e radius, I, and the lidity. ■ 'v a the Old. irr of (he zsuk will MKVSURATION OF '30ITD8. 363 IV^find the solidity of the segment of a sphere. «T«. "^^hw..-!. From, three rime, the _ h'ght afthe segment ; mnltlpU, the rema^l ^qnnre of the radius of'JJ.'eq^n^'lZ^'J^ tlJZ' .t V. To find the solidity of a 7or of a sphere «TS. Rule.-!. To the. sum of the squares of the radii a, bJt soiUUr^' ""'^ ''^''''' ^ ^'^^^^' and the last resuLevl , ®^®. ■RULE.-.2. For the middle zone of a sphere: I\om the Z'ZX''^'TT'^'^''P^"^'' ''/-'^-^^ ^e zone is Z^, snho net one third the square of its height, and multiply tU rl mmnder hy the height, a >d also hy .7854. ^^ VI. To find the solidity of a spherical sector. incS'does'u contn f '' "' * ^^^'^ ^« ^^ '-^-' '-- '-"7 ^ohd Operation. 3.1416 v lo =, 5:,.!c foot of caat-iron weighs 450^ lb. Ana. 0.6973 ft. 8. If tU? ;iiar.ctfr of t'je baHC of the Pegnientol a sphere be ;>0 feet, and the he-^^ht ..vftbe sause 5 feet; what is its solidity? Ana. 18;?2.(i cub. ft. 9. yjh&i 's t>;e 8o]i(i:;ty of a sector of a sphere 2i leet in diameter, the SfifmLu- jjaae of which is 4 feet distant from the r.i'ntral flection ? Ans. l6n;'.5616 cub. ft. 10. The surface of a sphere is 55.44 square yard.-; . what is its sol- iJHy? Ans. 38.8, '! + cub, yd. 11. What is the solid content of a spheroid, the longer axis of which is 16 feet, and the shorter 12 feel? 12. What is the solidity of the torrid Kone, thediameU-r of the earth being 7957.75 miles, and the height of the zone 8173.14565052 "iJe-s? Ans. 149455081137 cub. miles. 13. The diameter of a sphere is 24 feet, what is its solid contents? Ans. 7238.2464 cub. ft. 14. What is the solidity of a spiierical segment whose height is 2 feet, and the diameter of the sphere 10 feet ? Ans. 54.4544 cub. ft. 15. Required the solidity of the middle zone of a sphere, the top and bottom diameters being each 4 feet, and its height 6 feet ? Ant. 188.496 cub. ft. 16. The height of a spherical segment is 8 inches, and (he radius of its base 14 in. ; what is its solidity? Atu. 2731.0976 cub. in. 17. If the eoli(iity of a sphere be 4'.62 cub. yd,, what is 1° its diam- eter ; 2" the circumference of its great circle ; 3° its whole surface ? 1^. Required the volume of a spherical sector, the cuxsular base o' .which is .25 yd. distant from toe central section, and the diameter oi the sphere .84 yd. Ana. 2.2167 1 2 cub. yd. 19. The height o{ & spherical segment 16 .42 yd., it? sarlace 1.6632 eq. yd.) what is 1° the radius of the sphere; 2<» t» ^lidity ofthe sphericHl .sector ? ^n«. 1« .63 yd. ; 2«> .3< .; cub. yd. '■^^- ^j)»|; '■'' the solidity of a Bone whose greater ■ v jeter is 25 ft., between theiu i height Am' vf908 oub. ft. Pkoblkm XVII. To find the solidity of any regular i*oij i oil eurpsr radlre 1buljd contents ? 464 cub. ft. se height is 2 544 cub. ft. ahere, the top feet ? t96 cub. ft. id (he radius 76 cub. in. ) I" its diam- ale eurfax^ ? xsular base < e diameter o. 12 cub. yd. jrfice 1.6632 'lidity of the cub. yd. eier is 25 ft., 1 08 onb. ft. -OIL MISC1LLANI0U8 MAMPLK IN sOLlDg, 355 tJ^ solidity. ^ ^^^<^ed ,pkere, m,d the product will U «?««« ";Mj/!:.i;'iv!'L'„7"i'!^;"{ any irre,^.ular body. suol. .« a «tnne, a chain A. tnehes, Ang. ^ n'e . lone is ^7.7274 x 12^ = 346.5925 cub. fe .m^ersedVnXnttefou'r" rl'^ '%'"^'' ^'"' -^'«'' «» object 34 gallons. WhatlsMtdSty ^^^^^^^'^^^ ^ '^- -J, ia Opkration. 5 — 35 «: I ,t ,, *' hence 277.274 x I.5 , 415.91 i u,^ll!'7°f "'"'^ '''^'''^-^ ««h- i«- I W;raSror%\tSfd8 wS ,';'7 .ti.'""^'' ''^. ^'^'^*°- «hem into • division consists in taking for the Vfirfov el ^*^''^ ^^ reckoned. The easiest fohd, and for base the side ophite A-, n^° P^'"'"^'^' ^^' '-^'^'^^^^^ angfe of £ kinds of pyramids, is to proXoe the, h ''T J"".°°''«^' '" ^^^d the he). -hr of all irfn thin plane board, anKrutr is /;.?!'' ''''^ " '"'^^" ^'^ '^^ base, by means »ve (he hwghtof the pyramid. ^® '"^^^ ^"'' "^'« P^^e wilfevi-lentty MISCELLANEOUS EXAMPLES IN SOLIDS. anJ-th^\'id^SelVar^^^ ^™ - 71.1126 cub. vd 1*-; 2» the altitude She pritl^r^'' ''^"'^^*^ ^^ ^J^« a''^- Vth^ i What is the solid contentT^f^r IV^^^ f*" ^^- ' '^^ '^■■^^^ jd. of whose base is 12 i^ aS it" lu t.tief 177'^?'".?! ,^^ ^^'■^'-^- 3. A room 9.25 yd. Ion- i fi^ v •) , "*" •^'-^•I'J-l cu. ft. Papered; the rolls of tSer are^ 2 ^f ', ^"^ ?-80 yd. high, is ^^ be {•^12.25 ^. ,d. ,,, thi^aPtu's in^|;e'3,>;;:^7^'- -^^ Allow- be required, and what will be ti lie C'ist at 75 ct, lis, liowr many roll« will L^?'^;!l^"^!:f*.''"^'^«^<^f^^cyiin. -^ns. 20.51'! roll per roll ? w f-'* yil., and ite altitude 3 of ih ;^ A -...11 ■> o . . ft . ' *•" , . 'p» and $15.38 + . er, the ratims of who«e base eoircunif. Am. 185.707 +. .^q. yil. cuiuferenoe? """-"er ujwe b leet in Ipi,^,!. o,..j i ...... leet in length and I foot Ju cir- Ana. 96.1^76 lU 356 MIStOELLANKOnS KZAHPLKH IN BOLIBS. I! 'I !'■ r 6. Wliat is tiie w^iglii of a i^quare bri^ pillar whose aide is 0.7S yani>, ami lieiglic 4.75 yards, if I cubic yard of brick inaBimry weiiilia 3(1 civt. ? " Ant. 96.1875 ib. 7. Tlie filaiu lieiiihl ol a regular he^caguiial pyramid is 8 yd., and iba side of its base t> vards ; what is its whole surface ? Ans. 237.5307 sq. yd. 8. A man had a wall built for $186, which was $3.20 a cub. yd. What \s the height of that waJI, knowing that it is 14.5 yd. long and •70 thick? iln*. 4.18 yd. 9. A rectangular basin is 12 to. long, 2.5 to. wide, and 1.6 to. deep; how many barrels of 3! ^ gal. each does it hold, there being 231 cu. in, in a gallon ? Ans. 2811.9 + bbl. 10. The convex surlace of regular triangular pyramid is 45 sq. yd., the slant height is 6 jd. } required the length of one of its side-edgee. An8. 6.50 yd. 11. The lower base of a pile of stone is 26 by 12 yd., the upper on« 16 by 8 yd., and the pile is 3 yd. high : find its cubic contents. 12. What is the convex surface of a right cone, the radius of whose base is 1.4 yd. and its side, the | of the circumference of the base? Ans. 29.0167 + sq. yd. 13. I desire to get a cylindrical tub made whose depth will be 3 ft. ; what must be its diameter that it may hold twice as much as a similar tub whose depth h 5 ft., and diameter 3^ ft. ? Ans. (5.38 tt. 14. What is the slant height of the frustum of a cone, whose convex surface is 12.26 square yards, and the radii of the two bases 1.71 and 2.2 yards? Ans. .998 yd. 15. How many cords in a pile of wood whose length, breadth, and height are respectively 15.5, 4, and 7.25 yd. ? Ans. 94.81 + . 16. What mu-^t be "the radius of a cylindrical basin holding 110045 gallons, its depth being 5 yd.? Ans. 5.^39^+ yd. 17. How many solid feet in the frustum of a pyramid whose bases are regular octagons, the sides of which are respectively 21 and 9 in., and the perpendicular distance of the bases 15 ft. ? Ans. 119.20+ cub. t\. 18. What is the surface of the base of a quadrangular prism, whose altitude is 1.15 yd., and its solidity 4.25 cu. yd. ? Ans. 3.6956 sq, yd. 1 9. Find the solidity of a beam whose length, breadth, and thickness, are respectively 12.76, 0.35, and 0.25 yd. Ans. 1.115625 cu. yd. 20. A man gets a cemenieil cistern made iu the ground that will hold 3000 gal. ; what will be its depth, the length and breadth being respectively 1.8 and 1.75 yd. ? Ans. 4.715 yd. 21. What is the solidity of a regular hexagonal pyramid whose al- titude is 3.6 yd., and the side of the base 3.6 yd. ? Ans. 40.405651 cub. yd. 22. What is the convex surfece of the frustum of a triangular pyr- amid whose ba-^es are parallel, knowing that the sides of the lower bate jire 2, 3, an i 4 ft. ; the corresponding sides of tho upper base ,0.95. 1.20, and 2.10 i\. ; and the height of the three traj^zoids 5, 6, and 6.45 feet? Ans. 40.4537 sq. ti. 23. What are the dimeDaione of a barn whose capacity is 810 cu. elcrf '-""rail area 01 half on acre; what will bi- ih , liatn- -7. Whali8the,«iirra(!i.nf » .«. . . 'tis. 66.50 yj. jcal Hector who.e soM^'ifi "sX ^ ""b id"'';'.'' "^ ?• '^^V? « ^^^^^ being 1.5 vj.? ^ *^""- J^'^-' "'« railius of the spltert ,, .^^Wl.t i. the surface of the earth, its ra.Hu. I'^^^at^ ^,, 29. Find the8oHditvofaIo..9^rv/f '^"^'^'f •^.^*^-^^<^'^^q- '"'"• ••^O- What must be the th.Vkn«. r Z^- '^•^^•«»'062 cub. yd. aruJ external surfaces a e fand ff/v.^J/ '' '"" ^P'^^'^^^^^^ internal •■5i. A basin hold, log- 7^ ;^: 12 yards? /i;,^,. q^ . •^2. Keqinred the convex «nrF«?. .• a 5 ' ^"'' '^'^ dimensions. un.^ respective,, ,.«4 and /^^afltte^irhSI^^^I^,:;: :^^--- 35. One no.,n.J JA i ' "<^"^ J*^"^' was the wire? ^Hect^ cylindricairwlS-w:;; •;j:^l:^,rf^'^ «-^^^ -•' -d the wire of each part? a' Is 9^-«9^^''' ""/^^^'-^ *''« <^«^^^e^ «"rfaoe 37. What i8 the wefX" nf '^^'^ ''^•/'^'- ' 2"'' ^^-''^^d sq. yd. thkkness, if LexS d,/. ^''PPr.'P^''''^^' «'^^^' 0.985 inch in weight of'a ouU:Z^£^r^l^,^^ ^P'-e is 1.35 yd., and thS oou^yt^rS:^^-;;^- eIlipticai'fisl.pond to be digged io hie eiTiaJlaxis 12.75%.! H?^^ tliat li.h-pon.l ,3 to measure 15 yd., the digfe^ing it, if the co u alV^chle 'l "^ ""' ^^fq""-^"V^ ^''^ ^'' ^^' or the maaonry. at $15.45 p^cfb^d.^'s?'?^ ' " '^"^ ^^^^* the oapacity of tus pond. P^^ *^"'^- ■y'^- ' -^ '''e whole cost; and i^ the t«^r'bls!'i8 6^'LSf SL ^.''■"^'""' ,K ^i cone who.e radiu. of »ad itfl depth 16 inJw t'fiS^ w,thT7 '' '^^'/'^^'T/. ^^*^^^ ^' '"'^^^^' ^f that acfd. ^i, U wSlh /i'^ct'^'qurr '^^"' ^'^t,i t.if ^ ' !' 'I 358 TABL» O? OHORDS. •9 l 40. Supposing' t>»e Moon m oe a perfect sphere, what is her surface, her diaiDeUT Lvi.-,' t/> .Ii.vt ci the Earth asH is to 1 1, and the diameter of the Earlh I>eing 7912 miles? Ana. H(]2&158^ pq. mi. 41. A fbiiinK'r wishes to cast a semi-sphericfll lioiler whose internal diameter sliall he (i^ feet, its thickness 2j^ in. Required the weight oJcaHt-iron ii will lake, if we allow 10% waste in melting, knowing tliat tlie hpecitic weight of cast-iron is 7.208 Ans. 8608.3(;+ lb. 42. The interior space of a blo' >.-..Hvt v.. nsist* of two conic frua- tum« uniting at their larger base whose diameter is } of the height of the furnace. The altitude of the upper frustum is I of the height of the furnace, its less diameter is i of the greater. Tiie altitude of the lower frustum is .^^ of the height of the furnace, its less diameter is ^ of til > greater. If the furnace is 15 yards high, what is its interior cap-icity? y47i». 41.921 cub. yd. 43. A fountain in the fomi of the frustum of a cone is filled with water. Required 1'' how many gallons it contains, if the circumfer- ences of its bases are 16.95 and 15. 8& yards, and its depth 5.35 yd. ; 2° in how many hours it will be emptied, if the water is let out by tJiree pipes, of wiiich the 1st empties l^gal. in I minute; the 2nd, 11 gal. in 8 min. ; the 3rd, 13 ^;al. in ^i^ hr. ; 3" what time would each pipe take to empty the whole founta n by itself? ■' II TABLE OF CHORDS. Tn the table of chords, the radius of any circle is represented by 1 ; and in tlocinial of the radius, is represented the length of chords that subtend arcs of 1', 2', 3', &c., up to an arc of 180«*, which is itself a semi-circuui^jrence. Any chord which is not a diameter, subtends two arcs, one of wliich is less, and the other great - than a semi-circumference; but their sum eq As the Iroumfc noe. In all problems treating of arcs, the smaller arc is always im- plied, unless otherwi?? mentioned. 1st Rule.— To obtain the chord ( t any arc greater than a semi- circumference, avbtract the degrees oj the gioen arc fro-.i .m'^ . and find m the table the chord that corre"/ '. ms with the difference. Ex.—Wh&t is the chord of a -.re o^ U0° ? 360° — 310° - 60°. Intl oV he chord of 60^ s 0.8452. 2na Rule.— To find the leng. of au cliord in any £;iven ci muitxply the radius of the given circle by the chord in? table. ted in the A'.r.— How long is the chord of an arc of 24o in a circle whose radius 18 20 yd. ? The chord of 24» in tb« table ie 0.4158; U x 0.4158 - 10.395 'f-'wismi B her fiurface, the diameter 8^ pq. mi. 'hose it)ternal ■ed the weight ing, knowing 08.36+ lb. vo conic fru8- the height of the height of kltitude of the diameter is ^ is ita interior II cub. yd, is tilled with he circiunfer- pth 5.35 yd. ; ' is let out by ite; tlie 2nd, 16 would each represented he length of arcof 180», arcs, one of Bumference ; 3 always im- than a semi- a 360''. and Terence, s 0.8452. given ci;ole, ited in the circle whose 8 - 10.395 TABLR OF CHORDS. 3ft9 yafr;u]!e;lsrLo%no'*1o'V' ' ''''^' '" which a cl>ord ofl? yJi^AZ'' ^'''^ ^'' •" '''' '^^'^ ^^ 0-^502 ; 134-0.,S502 . 34.20. ing with tUtquotuZ ' ^ '" '^' '"^' '^'^ ''«^'"* corresponl ^^^^l^ S^,t "' ^^« ^'-- «»>-' - 4-24 yd., if 4.24 - 20 ^ 0.2120; 0.21: m the table indicates 12° 10' An, tended to any n'un.b^r ^ l^S'lX^t''''' '^ "" '""'^' ''^ *''• TABLE OF CHORDS. 21 22 23 24 0,0175 '>,034:) 0523 0(i!)8 0,0872 0,10-47 0,1221 0,1395 0,1569 0,1743 0,1917 0,2091 0,2264 0,2137 0,2611 0,2783 I 0,2956 I 0,3129 0.3301 (1,0029 0,0204 0,0378 0,0553 0,0727 0,0901 0,1076 0,1250 0,1424 0,1598 0,1772 0,1946 0,2120 0,2293 0,2466 0,26.39 0,2812 0,2985 0,3157 0.3330 0,0058 0,0233 0,0407 0,0582 0,0756 0,0931 0, 1 1 05 0,1271) 0,1453 0,1627 0,1801 0,1975 0,2148 0,2322 0,2495 0,2668 0,2^41 0,3014 0,3186 I 0,0087 0,0262 0,0436 0,0611 0.0785 0,0960 0,1134 0,1308 0,1482 0,1656 0,1830 0,2004 0,2177 0,2351 0,2524 0,2697 0,2870 0,3042 1 0,3215 0,0116 0,0291 0,0465 0,0640 0,0814 0,0989 0,1163 0,1337 0,1511 0,1685 0,1859 0,2033 0,2206 0,2380 0,2553 0,2726 0,2899 •,3071 0,3244 0,0145 0,0320 0,0494 0,0669 0,0.^13 0,l()ls 0,1192 0,1366 O.IjIO .,1714 0,188-5 0,2001: 0,2235 0,2409 0,2582 0,2755 0,2927 0,3100 0,3272 ih\ '4 i ii it- !»'' n P aeo TABLfi OF cnORnd. D. 0' 10' ,, 20' 30' 40* 50" • 20 0,4499 0,4527 0,4556 0,4584 0,4012 0,4011 28 0.483-< 0,4-^07 0,4895 0,4923 0,4951 0,4979 :?o 0,r)l7G 0,521) t 0.5233 0,5201 0,52m9 0,5317 32 0,5.-) 13 0,5511 0,5509 0,5598 0,5025 0,5052 34 o,r)sn 0,5875 0,5903 0,5931 0,5959 0,5980 36 0,(UH0 0,6208 0,0230 0,0203 0,0291 0,0319 38 0,6511 0,6539 0,0500 0,6594 0,00 J I 0,0019 40 O.fiStO 0,6808 0,0895 0,6922 0,0950 0,0977 42 0,71(;7 0,7195 0,7222 0,7249 0,7270 0,7303 44 0,7492 0,7519 0,7546 0,7573 0,7000 0,7027 46 0,78 1 5 0,7811 0,7868 0,78'J5 0,7922 0,7948 50 0,8452 0,8479 0,8505 0,8531 0,8558 0,8584 54 0,9080 0.9100 0.9132 0,9157 0,9183 0,9209 58 0,9090 0,9722 0,9747 0,9772 0,9798 0.9823 62 1,0301 1,0320 1,0.151 1,0375 1,0400 1,0125 ()6 1,0893 1,0917 1,09 U 1,0905 1,0990 1,1014 70 1,1472 1,1495 1,1519 1,1543 1,1507 1.1590 74 1,2030 1.2'>60 1.2083 1,2106 1,2129 1,2152 78 1,2586 1,260;) 1,2632 1,2654 1,2077 1,2699 82 1,3121 i,314{ 1,3105 1,3187 1,3209 1,3231 86 1,3040 1,3601 1,3082 1,3704 1,3725 1,3746 90 1,4142 1,4163 1,4183 1,4204 1,4224 1,4245 94 1,4627 1,1017 1,4667 1,4086 1,4700 1,4726 98 1,5094 1,6113 1,5132 1,5151 1,5170 1,5189 100 1,5321 1,6340 1,5358 1,5377 1,5;}95 1,5414 104 1,5700 1,5778 1,5790 1,5814 1,5832 1,5849 108 1,6180 1,6197 1,6214 1,0231 1,0248 1,6205 112 1,6581 l,05i)7 1,6613 1,6029 1,0045 1,6662 116 1,6961 1,0976 1,6^»91 1,7007 1,7022 1.7038 120 1,7320 1,7335 1,7350 1,7304 1,7378 i;7393 124 1,7659 1,7673 1,7086 1,7700 1,7713 1,7727 128 1,7970 1,7989 1,8001 1,8013 1,8026 1,8039 132 1,8271 1,8283 1,8294 1,8306 1,8318 1,8330 136 1,8544 1,8554 1,8505 1,8576 1,8587 1,8598 140 1,8794 1,8804 1,8814 1,8824 1,8833 1,8843 144 1,9021 1,9030 1.9039 1,9048 1,9057 1,9065 148 1,9225 l,923i i;9241 1,9249 1,9257 1,9265 152 1,9406 1,9113 1,9420 1,9427 1,9434 1,9441 156 1,9503 1,9569 1,9575 1,9581 1,9587 1,9593 160 1,9696 1,9701 1,9700 1,9711 1,9715 1,9721 164 1,9805 1,9809 1,9813 1,9817 1,9821 1,9825 188 1.9S9') 1,9893 1,9896 1,9.899 1,9902 1,9905 170 1,9924 1,9920 1,9929 1,9931 1,9934 1,9936 172 1,9951 1,9953 1,9955 1,9957 1,9959 1,9961 .174 1,9973 1,9974 1,9975 1,997 1,9978 1,9980 176 1,9988 1,9989 1,9990 1,999. 1,9992 1,9992 179 1,9999 1,9999 1,9999 . 1,9999 1,9999 1,9999 180 2,0000 -i CULLING AND MBASUllINO. 861 50' • 0,4(>H 0,4!)79 {),fhm 0,5052 0,5!)S(; o,G;n'j o,(]Gi:t 0,6t)77 o,7;{o;? 0,7027 0,7'J48 0,H584 0,9209 o.;)82;5 1,0125 1,1014 1.1590 1,2152 1,2699 1,3231 1,3746 1,4245 1,'4726 1,5189 1,5414 1,5849 1,6265 1,6662 1.7038 i;7393 1,7727 1,8039 1,8330 1,8598 1,8843 1,9065 1,9265 1,9441 1,9593 1,9721 1,9825 1 9905 l',9936 1,9961 1,9930 1,9992 1,999» Culling and Measuring of Timb.r, Masts, Spars, Deals. Staves and other articles of a like natari. (Pioiu the Consolidated Statntes of Canada. Cap. 45.) ^ Doals^-. A Quebec Rtn,i,]a,d D.,,! h 12 fc-t !on- 11 inches broad and 2^ inches thick, and contains 2. fr » i„ G^ts ^hi^ ?"4Kd'a?r'''" Standard contain 229 'ftr's i^^cihTc o"; u;;ill7ttchThi:k'.""''"'' '' '''' '-'' '^^'''^^ ^--'1 One Quebec Stunl.rd is 100 pieces oP 12 ft. hv 11 i„ hv 21 in an-ys equal to 1 hd. 1 c^r. 16 pes. of St. Potcrsbur's idLi^ and 240 Quebec Standard Deal, are equal to 11 loa.Fs ' 1- tt'lf t'f 'Ii'''"'"';'l ^"•^'■^ '^ oquaUol20 PCS. c^ A Load of Deals is 600 square feet by one in'^b in thickn,«. equa^to^SO cubic feet J or 300 square fit oV 2 the' oV4^^ ar/andllinntl II t'' (^'''l^'^ inches, Quebec Stand- ard and equal to 36^ St. Petersburg Standard deals. t^K ^ °:T'"'^ Quebec Standard Hundred into St Pe- 30 TrXters. ^ '^""^'^ ^' "'^ remainder, divide U hy i«ct: "^"miir '''''-'' '*^^"' - ^^"^^ ^° ''' ^-^ 9 ^(PZ ^."'^^•i/"d seventy-five Standard St.aves are equ«l to Owing to the vari«tion.s in breadth and thicknass of Staves. to KSr'^ °'' ^^'''"' ^'"^"° ^^^""'^^^^' *« t)e equal h=..^^lwS^"~^"' ^''^ of Latbwood is 8 feet long and 4 feet fiigii, iiingiish measure. * ■n rf Hi 1 ; 'I'.'l I'.. •l) ,* U M 'jHIi i I' : 1 1 J . 1 362 CTJI-tlNG AND ME.ASURTNO. CUSTOMARY ALLOWANCE FOR FREIGHT AND BROKEN STOWAGE. Deals.— A Hundred St. Petersburg Standard, at twice the cliiirged rate for timber per load. _ Staves. — A Mille Standard, at six times tbe rate cbnro-ed foj- timber per load. A Mille West India, at twice the rate charged lor timber per load. Lathwood. — A fathom of Lathwood, at the same rate as charged for timber per load. FREIGHT AND SHIPPING. To find Freight measurements, or cubical contents of pnckages, Rdlk. — MuUiphj length, breadth and thichness together /for surfaces, length and brctdth only. For Stowage.— 97 quarters of Wlieat, or 140 barrels of Flour, or 80 barrels of Ashes, are considered equal. For Grain.— 42 oul)ic ftet equal 1 ton of shinping. One bushel is equal to 60 lbs. 2218^ cu. in. are equal man Imperial bushel. 8 bushels are equal to one quarter =17745 cu. in., or 1Ot^^0 cu. ft. Therefore, 1 ton will take 4rV quarters 1 bushel being = 60 lbs. ; 1 quarter = 480 lbs. ; 1 ton = 1968 bs. A ship of 200 tons measurement can, therefore, carry 820 quarters \ but it can generally carry much more. ^^ CUBIC OR SOLID MEASURE. 42 solid feet equal 1 ton of shipping. 40 solid fett, round or unhewn " 1 ton or load. .50 solid feet, hewn or squared timber.. " 1 ton or load. 50 cubiefeet " 1 barrel of flour. 8 barrels " 1 ton. 5 quarters " 51 J cubic feet, 5 quarters , ,. " 1 loud. SQUARE MEASURE {seep. 118, 119, 120). Engi.ish. ' Fhgnoh. 36801.7 Square Feet equal 1 Square Aipent. 0.845 " Acres " 1 «' " 2.471 " " " 1 « Hectare. i " Foot " 0,0929" Metre. »!^^7it-iiyy. fW!-'~ iiSSm ■M 6PE01PIC GRAVTTT. !G3 T AND twice the hnro'ed foy te charged le rate as rpnckages, efher ; for barrels of img, One n Imperial on. in., or S 1 bushel 68 bs. A ) quarters ; f shipping, r load, r load. \ of floor. )ic feet. ENOH, re Aipent. Hectare. " Metre. 1 3 955 Prchcs .. u j ^^..^^^ The side of a s,,,^,re acre is 69^ yards i„ jen.tl,, and is ofton .,>.'-t^d by Irench-Canad.ans as a unit of length I'or short Iv 1 French foot is equal to 12ff) English Inches. 104 lbs. arc " to 112 " Po^ndg I Canadian Minot is " to 1.054 Imperial Bushel! The following rules for Timber Calculations may be found useful by the trade. ""'"^y "^^ Sqm're^''^""' ^*^"'''' ^'"'^''' "^ ^"^^'•«"t ^^^es, to an Average contrnts of (he whole fo parts ; divide 'he product by the total ^alfeet; the square root of the quotient will he L average sgu'ire, in inches. "I'c/ci.ye To find the Cubic Contents of Round Timber. ^/wy''7"Ti'^"'"V''V^'r*'''''' '^"^('Pf,y (he product hy 11 and tT 'I 'f "^''^^.^ '^' result by the length of the. L ■ ^hen TABLE OP SPECIFIC GRAVITIES. In estimating the weights or specific gravitfes of bodies rain- That n '' 1-"T"^ l'^^" "-^ '^'' ^»'''"^="'^- ^^^Poriment has show that a c..b,c foot of rain-water weigh. 62^ pounds Avoirdupois' OOsfieVsurV^' We follows that- a'cubic inch wei^h; " bo V h n 1?- "5 "^ ''r"f • V' '^''''^''''' ^^' ^"^^^ific gravity" of ci bod) bo muluphed by the above decimal, the" product r.ill be whicTm tt^r'^^r.' :;^'^^ '^'^ in poundTirolrdu o^ dupoi:: nsibs' Trot ' '' '''' ^"" ''' ''^- ^^^"■ f ; vl^rti -n V' f ^Tb'^«^t of«"J one of the - "in^ ariicies ic in uutices Avoudupois. lii»» h. SPECIFIC ORAVITY. 11'^ Woods (Dry). Ash 845 Apple ,. 793 Box-wood 1031 Beech 852 Birch 567 Butternat 376 Cedar 561 Cherry 715 Chcsnut 610 Cocoa, ,....,.. 1040 Cork 240 Cypress 614 Ebony (American) 1331 Elm..... 570 Fir, White 512 Haokniatiick 592 Ilazcl...., 860 Hemlock 368 Holly 760 Liirnum vitaa. , 1333 Lime 804 Logwood 913 Mahogany (Honduras). 560 Maple 750 Maple, bird's eye 576 Oak (Canadian) : 872 Oak (English) 932 Pear (i61 Pine, White. 554 Pine, Ptod 590 Pine, I'ellow 461 Pine, Pitch 660 Plum 785 Poplar 383 Spruce 500 Taraiirack 383 Walnut, Grey 671 Walnut. Black 550 Willow. 585 Liquids, Metals, &o. Alcohol, pure, 60°, Brer Brandy , Blood (human) , Bees-wax Brass, c;ist Brick, fire , Coal ( Anthracite) Coal (Newcastle)... Coke Copper, cast Earth, onmmon Glass, window Gold, 22 carats Granite (Scotch). .. Guttapercha Honey,..., Iron, cast Lead, oast Lime, hydraulic... Marble (Vermont) Milk Petroleum Plaster of Paris. ... Platinum, native.... Quicksilver Salt Sand, common Silver, pure cast.... Soap, Castile Starch , Steel Plates Tallow , Tin, pure „..., Turpentine Water, common.... Water, saa,. =„,.„, LZinCj roUed.t»«t.... 794 1034 924 1054 965 8396 2201 1436 1270 1000 8788 2194 2642 1748<: 2625 980 1450 7207 1825 11352 2745 2650 1032 878 1176 16000 13568 2130 1670 10474 1071 950 7806 941 7291 870 1000 1026 7iyi iS, &0. 794 10H4 924 ]Uo4 965 8396 2201 1436 1270 1000 8788 2194 2642 17486 2626 980 1450 7207 1825 11352 2745 2650 1032 878 1176 16000 13568 2130 1670 10474 1071 950 7806 941 7291 870 1000 1026 7iyi BOOK-KBEPINa neyiNiTioiw. 1. Book-Eeepiug is a syatema tie record of buameeg trane- actions, or the art of keeping aocounts. Every penon, engaged in busines 6 for himself, should ke^) a book of some kind m which to record all his buBin«>8S transactions. The mechanic, the farmer, the )>r»'cf8ional man, etc., should keep an account with every person with whom thty denl. For no one should trust transaotionB of a pecuniary nature to his memary atone. 2. All business transactions consist in an eschangc of values. 3. There are two methods of Book-keeping in general use, distinguished as Single and Double entry. 4. The Double Entry is conceded to be greatly superior to the Single Entry, particulaily from its more excellent tests for deptermining the correctness of the work. 15. Single Entry embraces only the accounts of persons, and consists of 6)<^ one debit, or one credit. 6. Double Entry is derived from the fsct that every business transaction must be entered to two or more Ledger accounts, as two or more persons or things ar^^ affected thereby. T. Two books appear indispensable in Single Entry ; via., the Day Book and Ledger. 8. The three main books used in Double Entry are the Day Book, Journal, and Ledger. The Day Book aud Journal are sometimes combined in one. O. The number and char.j'^ter of the auxiliary books depend somewhat on the nature and extent of the business, but more on tiie amount and kind of information desired. Those most in use are the Cash Book, Bill Book, Invoice Book, Sales Book, the Oommission Sales Book, etc. 10. The Day Book is that in which are entered the busineai traneactions in the date and order of their occurrence. This book should be plain, ooncise, and unequivocal in its statemeatc. Ab the records in it are supposed to be made whan the transiietions and all the circum- stauMes connected tberewith are fresh ia the mind, it is tb* only book allowed in court, Ml oases of litigation. 11. The Journal is a book in which the buMness transactions rreordcd in the Day BoiMcare prepared to be entered in tiie Ledger, by ascertaining the projKJt debits find erodits involved in each ii j'.n.^action. This process is eallfAjmumaUvmg. 1*. The Ledger is the book of retuh*, — *he final book of entry. 1 $ li f. 4 BOOK-KBRPtNO. rn this book, nndor approprirrte h&a*. ocUfed R• made te ibow as important rMuUo( itself. trang«d all tfa« ten ; Inoladinjyt, .distinct record jedgor \e called he sums of tion rehiting or paying the 'cash on hand, k at the end of the next day's iption of all 1 their datee, i of Recfeivable, ed all bills of 3 our posses- • daily, weekly, the original in- 11 goods sold c, either daily, [e, they are de- n this book we nutedeeorip- ok, iind frotn it e for whom we ling to some to the trane- by a nanie, a Creditor ; oreditfi must m ae importaot BOOK-KEBPINO. il" \ ?^??S?® •' '"""y ^"'^ ""^^^'^^ belonging to the concern. tt' n ^.^^H"y '"^ ""y '^^^^ '^wif'S by the concern. -*». tasa IS the title to (losignate money. ite?^itWl SuJ^Vmon^'L. ^''^ !^'^^'^'''"^ f''^ '^" ^^''^'P" '^ <^'"', and cred- tima, oxhibUare^mfrl^f ih '^'^^''^noe between the two .idee must, at any of rL=h „. a roeouroe of the exact amount of cash on hand. The croJit aida 1 Sn^T^5r°°' "°''' ''' "''■'' ""' "'''-' '■■'"'' ''»'"^°' bo paid out than 24_ Bills Receivable are written obligations ofwh'itever heZ'cHved!' P^^^^^'*""' ^""^ ^^'""^ ^ ««'"*^^" specified amount is to th^ debS a5/L I • ^^"-^ /"'lu""'' °^"°''«'^- The oxceg., if any. must be on trie debit side, and will indicate thnt portion of our rosouroes consistinj,' in note.: „T??' ^^*^?/?yable are written obligations of the concern, for which a specified amount is to be /nld. B,Mhtilitiir.tTp^e; 'rrTse'n^ed'Ld credited with ite returns. ^ ' "^P™«»ntea, and 27. Real Estate relates to such property as houses and lands and the account is similar in its objects and teachings to that of Merchandise. 38. Bank Stock, Railroad Stock, etc., are not accounts dissirniar to Merchandise and Heal Estate, inasmuch as stocks of all kinds are bought and sold at their market value, rather than the value written on their face. 2». Shipment or Adventure is but another h ime for Mer- chandise, and is used to distinguish bpt,veen property in store and out of store. <,.,fh^l"/'"'*P^'''^''"*'''''r^^'>^'*'^'*!^'»y " '^g«°t fo' "*. we should disdn- guishufrom our merc-..ad>'e;u store by ffivine it a siirnificRr.t .,«,»« mT. "Shipment to Halifax. ,>r -SLipment I lrofrliIent?or""tn^r^?"t^''ch1 With their procoeds."the oiflereno^'being'a gair;r ir«I:' '^'' '^ '^'^'*^ SO. Feraonai Accounts, that Is, accou.its representintf per- sonal indebtedness, and designated by the uropei nameb- of such •11 / 18' ''f llllk' bfel BOOK-KGEPINO. fi ■ii ! 1 1} ' '•t ... persons a^ sustain relations of debtor and creditor to the oonoera, aro capable nf showirts: either resources or liabilities. Personal Accounts aro liebited with such suras as, from time totlme, the persou miiy become indebted to the oonoern, or the concern has pidd them, and eredhea wttli what they have paid the concern, or the concern may have beoome indebted to them. ♦51. Stock, used as a Ledger title, means simply the proprietor of the business, or the stockholder. There would bo no valid objeetion to using the proprietor's name inatead; but as nfl real good would result from the change, authors, taftchers, and praotio«l accountant?, accept (he term which custom has suggested. This account is usually the first opened in the Ledger, and ia important to show the nut investment. It i^ generally credited with the whole investment, and debited with snsh liabilities as the concern assumes to pay for the proprietor. The difference is the not investment, or what the concern owes the proprietor. Fiotii the fore the oonoern, ime, the p)er80Bk in, and eredtted >eoome indobted he proprietor ae infltead; bat , and praoUoftl portant to show ]vegtment, and the proprietor. > proprietor. m principles ho will thor- diffioulty in any business uld be cred- so for his or y should be ill! or them, r them, aod BOOK-KBEPiNo. ^.— Bills Palpable. Bills Payaole account should be cr«^few «♦!. anoes, or written promises to n«v »T!^ !u ^^ ^n^ notes, aooept itecl when they ar^ paid or^d':eU " *''^ "" ^«^' ^^ ^^ ^•—Persons. or the, get „u, „f „„ ^R "'""' "' ''»°»°'« i» » I ■T IDOUBLE3 El^TI^Y. SET 1. (INITIATORY.) DAY BOOK, JOURNAL, AND LEDGER. RKPRE8EKT1NG THE BUSINESS OP A SINGLE PROPRIETOR. WITH KXPLANATIONS FOR JOURNALIZING, STATEMENTS, BtO. INSTRUCTIONS FOR SET I. The following set comprises the most simple transactions in business ; the main purpose being to illustrate the foregoing prin- Biples, and to initiate the student more fully into the proce'sses of Book keeping. The general instructions given in connection with this set, will apply with equal force to the succeeding ones . They ghould, therefore, be properly heeded. The transtictions are first recorded historically in the Day Book, in the order of their occurrence ; from thence transferred to the Journal, and from thence to the Ledger. In journalizing a traas- action. the first thina* tn Yu^. annaJAoraii la tV,a nr^^~^^„ »- tu: affected ; next, m what manner aflfeoted ; and 'aslaj, the proper application of the principle. The check-mark (V) is uinde oppoiHte the Day Book entry, immediate^ upon its b«ing journaUted, IT. DGER. :ETOit. rs, BTO. 3sactions in egoing prin- processes of lectioii wJth ones. They ! Day Book, Ti-ed to the sing a traos- 'D or Lx^Uig the propor ide oppodto T>AT BOOK.—SBT I. ftilness, and notE t ^' '"''' ^°^«^«''' a°d constant watch- errors in postin. = "^"'^ '°™"^°° ^'*»> "^w beginner, thaa «?h^Sg^:tt*Llt "r -f'tH*'^ •'°"^"^'' -^ -•»« >* the debit or'crediljol^U ^PP^'^^' ^e in mg side in the Ledcrgr u^ino- 1. • "^ '* °" *^^ correspond- entry. Suppose fofeiannle th." "''^'T''' '^'' ^PP^^'^^ J«"^°«' disc Dr. To Cash '' T^ i ' *^'J°!^^"a ^"try to be " Merchan- Merchandise is to be debh^dTndT ".''"^^^ 5 «<^""«' ^^^^^ chandise account in the Led .'er on P^!'t T'^-?'^- ^^^'' ^^'" Cash," and carry the amounftn fi? ' '^'*'' f'^'' ""' ^^^' " To Cash account on^heV.T /^ we^r^^Bf.r-. ^i" ^.'''' carry the amount into the or ,}Z^?' -^y/^^erchandise," and Journal, be careful to en to in , hi. i ^'"'""- u ^? P°^*^"g ^'^^ '^^ thep^ge of the Ledger to whlhT"'"" "I '^' ''^^ °^ '^^ «^°^^"°'. t>pon ill being entered in The tedger ^''''^' '"^^'^^^^^^i DAY BOOK,— SET I. (JPEBEc, January 2, ]67i ''^ r ^S'„L7.o '.". ':"'"•' ""^ ■'•^ C..1. ^''°'tTLf;r°»^'"-'^'"-''»^'p'ij -Bough, of A. L,„<,l,|.„, (,»,!,, $4500 350 16731 it 1 ^- .1 i 1 1 i.'«f i>AY BOOK,-~SBT I. JuBBEo, January 12, 1871. V V V V V V V Amount brought forward. Sold Jos. Murray, on fc^ 16 yds. Biack Cloth, (a) $6.5'J 17 Bought of N. S. I'ower, on our uoie due Feb- ruary 22, next, 21 yds. Black Satin, /S) $i. 10 20 Accepted R. Green's draft on us at 16 days' eight, favor of M. Duval, 26 Sold J. N. Benson, on hiw note payab'e Fel». 27, next, 86 yds. Canada Gray Ciulh, fd) $5.40 31 Paid Ca«b m follows: Fc\- .''-■.;■: ting of Store, Eci r ;;,,',■ ;iy Expenses, Fus S'Vu'. of Store, one month, February I 115.75 42 60 30.00 Received Cash of Jos. Murray, on %j Bought of Myler & Lee, at '?, months, 432 yds. Irish Linen, (d) §.45 Lent Cash to D. Murphy, until 15th inst., 6 Sold W. S. Reid, 84 yds. Gray Cloth, /® $5.50 Received in Payment, .3 Shawls, rti) $60, fl80 His Note at 40 days, for 200 Balance on 5i^, »2— 462 Paid our acceptanc*, ftivor of M. Duval, in Cash, |720!> 97 86 360 302 8d 60 194 120 462 70 60 10 40 35 350 $9310 40 46 "^■X'- |720!» 97 70 50 86 3dU 302 10 4-0 88 60 194 120 462 35 40 DAir BOOK,.-43BT I. Quebec, FEBRUAar 10, 1871. Amount brought fory,ard, \ Beceired Ca.h of Joe. Murray, ia full of %, _ 15 "*'th'io«t^°'^' ''"'*'*'"' '" '"" '"^ "^"° '' 18 Gave my Note ^ 60 clay«, for 250 Bounce on f„ 245_645 22 PuiJ^CuHh for mj Note in favor of N Power, now 25 Exehanged Notes with L. White for our mutual accon.modaticn, each drawn at 40 days, TfSTo 47 120 645 50 27 Received Ca-h for J. N. Bencon's Note pdvt due, ■ « Bought of I.. A. Tavlor, 500 yds. French Merino, /® $.75 bave in Payment, Ciix ^^''''^ ^""^^ ^^ ^^ ^^^^^ ^""^ ^'^^^ Order on W. S. Reid, in full pf «fe, _J5-375 __ 28 Paid Cash for gtoie Rent to date " Family Expenses, etc., $30 48.50 86 300 302 376 10 40 78 $11264 50 95 " h 35e $93101 45 ^^^o. IMAGE EVALUATION TEST TARGET (MT-3) y^ 1.0 I.I w^ 12.2 WUu id. 116 =d <^ /). Phntnorpnlnip Sciences Corporation 4. ■^ iV ^k is debited for the liability assumed by thL' eonpern, Prin. 1. R. Green is ered- iteii according to Prin. 6. ft lei.'t i * MtRCHANDfSB Dr. i ' To Cash. 1673 Merchandise roH $1673, and is debited, PriH. '}.-Giwh was paid for merchandise, and irf credited, Prin. 2. 8 686 70 1 Cash Dr. 2 To Merchandise, Cash is debited for its receipts, Prin. 2 Merchandise is credited for its proceeds, 6S6 " 12 97 fiO 3 Jos. Murray Dr. 2 To Merchandise. Jo«. Murray Dr., Ptnm. «.— Merchandie* Of,, Prim, .3= 97 50 1 $7307 20 $7307 '' 10 Or. ;f45()0 350 1673 70 686 TO 50 20 97 $7307 51) 20 JOURNAL,— SET I QuKBBo, January 17, 1871. Z)^ AiERCHArJDISK Ancunti brought forward, Dr. Tfi Bills Payablr, Crl%"°?'" Dr., Prin. 3._biiu Payable 20 To Bills Payable. have ««ncW«rf our inJobtedness to him by prom.MO« to ,,ay the amount to another pe^^on whom ho has authorized to receive ir new h .bi ity thus assumed, Prin. 6. ,»,i . "^ ^ *'.'"'"8^ wrought in our affairs hy ih u transaction is the transfer of a liability ^^11 a ,,ersona: account to a note. We rT °";i"l^''' "^" Obligation at its matu! protUIeS* ^'^'"""'^ ''■^ ^"'°S our paper 26 Bills Receivable Dr. To iVIerchandise. •1 BxPKNSi; Dr. To Cash. fc;«p«'j» Dr., Pr.«. 7.-Ca8hCr., Prin. 2, ■ February I CAtitJ Dr. To Jos. 1VIURRAY= CMh Dr., Prxn. 2.~Jo$. Murr.y Cr., Prin. 6 u I7307I 20 8G 10 Cr $7307 86 20 10 302 40 m i — ii 1 I •r i: in \ > < I i, ■' \l I) JOURNAI^— SET I. Quebec, February 2, 1871. Dr. Amounts brvvght forward, Mtt ^OHANDISE Or. To Myler & Lee. Merahandise J>r., Prim. 3— Myler A Le« Cr., Pnn, 6, D. Murphy To Cash. D. Murphy Dr., Prin. «.-CaAOr., Prin. 2. 6 Sundries Dr. To Merchandise. Merchandise Bills Receivable W. S. Reid Merchandise Dr., Pnn. 3. Bills Reeeiy- able l>r., Prm. 4. W, S. Reid Dr., Prin 6 Merchandise Cr., Prin. 3. The term Sundries is here used for the first time. It means, simply, Sundry Ac ooimtt, and is convenient as a Journal ex- pre.-'. ion, and to avoid the necessity of enu- inerjiiing the items which comprise the totals cafncd to the Ledger accounts. — 7 Bills Payable Dr. To Cash. Bills Payable Dr., Prm. i,.-Cagh Cr.. Prm. 2. ' 10 1 1 Cash 3 Dr. To Jos. Murray. o^« '*'■•• ^'^- 2— •'<*• Murray Cr., $8184 194 120 180 200 82 06 40 350 47 50 $9357 Or. 18184 194 05 40 rjo 462 350 47/60 ?..!.. mill, imui yiwiii jju^A.,- l« t 96 $9357 95 SS*SfS^^^^g*5^^!^ pp^tsh^^^-,,-^^^,^ Or. 18184 1»4 Ofi 40 120 462 350 47i S9367 60 »6 !' ■ I Ill U llr II I J I IJJi l j JOUBNAL,— SBjx l QlTEBEO,'PBBBrAaT 15, 1871. Dr, Atnoxmf i-rought forward, Br, Cash To D. MuR«>Hy. Sane Pri* as for the preceding entry. 18 $9357i ;».•) 120 Memchandisk Dr. To Sundries. To Cash. "' Bills Payablk. " C. Phelan. Merchandise Dr., Prin. 3. — Cash Cr Pnn. 2 Bills P„yabIo, Cr.. />«« 5 j d' Pheian Cr., Prin, fi. ' 22 Bills Payable Dr. To Cash. Bins Pay. Dr., Prin. S.-Cash Cr.. Prin. 2. 25 Bills Ukceivable Dr. To Bills Payable. B. Rec. Dr., Prin. 4.-B. Pay. Cr., Prin. 6. . 27 Cash j),.^ To Bills Receivable. Cash Dr., Prin. 2.—B. Kec. Cr., Prit. 4. (( Merchandise Dr. To Sundries. To Bills Receivable. " Cash " W. S. Reid. Mdse. Dr., Prin. 3.— B. Reo, (.'r Prin 4 • Caah Cr.. Prin. 2; W. S. SeiJ Cr:'. S^^'.V. 28 EXPE.NSE Dr. To Cash. BzpaD8« Dr., Prim. 7._Ca«h Cr.. i>rMi. 2. 18 646 86 10 300 302 40 376 78 50 $11264 y a*. !j!y357 120 95 150 260 246 3ft 10 300 302 200 140 35 40 78 60 $112641 96 S'fv ^^t i^sfl ' iHn^^l ■HHI liEDOER,— SET I. (5 f I I i I ]. iii. §e IS| 2 1 o w n s^ M ;& ■* s - IS ?0 ^^ eO r^ r-l O 1 -a o 13 K a 5J o o a It e a. — NW^ST»l>^^r»< ei 00 Si! c,a 1-5 £ti ^5 d I o w .£3 OS „ C3 3 -M ri. M : 5 : 5 : 3 lftl-^^^-0C?^^»OO_ o s oo o o o t- o o s « IS O «C o [» o M O X) ^ •<»1 M o o s o 1 c c « i-i N CO Tf Tj( o H5 04 00 2S 45 ^ ■ § «r ,a 5^ ^1 h ^ o ^ 5 "B w . =! ! mS^ - QJS 23 o M»— o>rtt- — i-H cs; ^^ • I- . t 2 q j» % ^ --s^s«« 1 a 14 «5 IS 1 OS o CO r" ! -^'■V^^ijjfv^.^n ,-. ■ •«s^<» 1 < O d 3 o ■*n< 1 ^■^ «« CO 6» cs ro oo y . £? ..5 ^ flO « ® *« O fri ' ' - i ", ■cb> e^ « 00 2&; 00 a ^ .i « o •« 8" n J ^q ffi ^ o ■^ r^ 00 cs C 3 * 16 ^' m i:«£!DQ£}JEl, -SfiT I. 3 2S§i I2i « O 3 S I O 00 o .o = I 55 r*:: N N ^ ■* a > a> -S ja cj 'S o V C4 SaSSog s ««• O 30 m >-H CS -^ T^ o (tf n 00 cj J © J -9 Ck» O O =1 O — o 1 = o tc o lO 00 >o 35 PS ■^ ID e I. s< ..-■>» CO So.a '» i :s I s f) 6» N« CO s 2§ "-s o M ?«• ft CO o o H 3 <^ 16 39 2 33 -a 3 ^ o H XI 2 «Jii&mmmmm^ 'C^tl 3 §S? IS 6» N.-O 1 LEDGER,— SET I. a5s ^1^ 3 1 => 1 - r- - s 1 >o 00 1 (A «e SO ■ c « 11 w^ o h: OO « (M ' ••* «-2 -2' S9SS 12 ■O 1-1 M M •a 12 O a a •a n — ^ «o o 3 1 "" •o x> o O lo « o t- eo '^t ri => * OS o wj M n lO «» o« It c:i a^. mMmmmmm 29SS 12 = •^ «o « O 31 »«t M o « M ec is*- 00 •« O O I -o us O O I M = o t- 05 M 0-* oro M C4 x> s .£:-9 53^ 3 : : s < .fl 2 m " O ° S .S-3^ <- 5 2 O T ii!fil 00 •a n OS « o a is o JS 2 o J ® ^ y ° o -, 5 * 7; (t-i >' • "-■® ^ S 8 c o >,a) 1.5 ±>^^ 1, 1 fc - ^a~ 3 O O V . - gg 0) . -3 fc a = •' '^5 £ §.2s 5 « S »• * ■ o a V S - .a -o - J; S S°£ (-3 w CS w •=£§§ ^ P ■ s fa S js ^'■ ^ 1; _ "w ** £>^ ! "3 c = .o a <« -3 "SgSo'Sg.s* .a. s V _ V a> s § « « C O c c -2 .— ^ * S'S OS "5 -O J^ JQ J3 01 .a o ® 03 •— M N lO If IL« a> o a m" o ._ o E- ■n if ii i>\ii wi 301 to bal foej pro pro res{ and I are LlA and Rep •o *- T» en w •a • :2 • CO 35 •r) t- n C«J CO "f O o e- CO T 1^ ■S 9 S PROOEWS or CLOSING. I'ROOESS OP CLOSING. 3r)0 570(;|fi0 80241) "131; I oi 3,-)0 9700 166 Soi 120 «2 Steele, Casli, Mcrclmruliae, Bills IJeceivablf, i'ill.H Payable, H. Green, Jos. Miiiray, Expcn-^e, Myler & Lee, I^. Murpby, «'. Phelan, VV. S. Reid, 11264 95j[ Equilibrium, !onc usivo cvidptieo tl,,, •,! ,1 „ . ■ ''^""•"•'1; ivliicl. ;ilK>nls ^ the Le,j''T::i:i^T;'s::^:r^j^^ ^^^^y;^y now proceed to cToi:''rtyn:c rn^^'^^'v^:^'' 7^^ for-otten that the object of closin- t T o i • ^'' '^ "°^' ^^ pi-opor manner both f ],« « T" J • ^'^*^"'''" >^ *« pi'oscnt in a resources and liabilitie^^amM « ; i"^" ^^ * ^'■'^* ofits and losses. "'''"'^''"' '^"'^ '^^ P'ogrcss, by a list of its gains Bj an examination of the fants ,> v-i!' V -p-. n d are shown by an excess of the Dehii side of K??t ^"'"«''<'^» LiAB.MT.Es by an oxce^ of thV^.w / ^j r^» accounts, and and that Lnsss are Twn K '^'^ ''^" of Rkai. accounts: ^lu^TATim accounts, and G't.in* by an excess of the Credit 21 h '-*'^ s I M iimK ii PR00E88 OP CLOSING. side of RkprEsentativr accounts. This will su2:a;eHt the pro- priety of opcnitig two accounts for these general results: one to contain the rcsouiccs and liabilitie?, and the other the gains and losses. We will now open these accounts nndor the titlrs of " Loss and Gain," and '• Balance," the former to contain the re- sults of the Ueprksentative, and the latter of the lli:AL ac- counts. Before proceeding to elose the accounts, we must ascertain if they are all ill a condition to show the results desired. The Merchandise account, as it now stands, shows an excess of the debit side, and would therefore represent a foss, if the merchandise were all sold. The account itself does not show whether the pro- perty is all sold; aiii the only means of ascertaining the facts in the case, is to take an actual inventory, or a valuation of that which remains unsold. This we now proceed to do, with the fol- lowing result : INVENTORY. Merchandise remaining unsold, February 2S, 1871. ISC 93 yards English Black Cloth. l&$5 $ 465 21 ♦* Black Satin, «' 4.10 8(5 10 432 " Irish Linen, « .45 194 40 86 " Silk Velvet, " 7.50 (i45 600 '« French Merino, « .75 375 3 Shawls, " 60.00 180 $lii45 50 Hence, we see that the unsold nierohandiso is worth Si 945 50, which amount we enter on tlie credit side of Merchandise account in red ink, * and transfer the same immediately to Balance ac- count. The accounts are now in a condition to close ; and wc will take them in their order. The first account (after Stock, which is the proprietor's own account) is Cash account. This aooount represents a resource consisting of cash on hand ; the debit side showing the money received, and the credit side that disposed of. We close the account by entering the difference, in red inJa, ou the credit side, and footing up the sides, drawing double lines underneath. The red ink entry, or balance, is trans- ferred immediately to the debit side of Balance account. The Best account, Mcsrchandise, shows a g'ii», and the balance is trans- * An entry In redink on the Ledgor, denotes that the amount thus written it to be irf the Kkal ac- tvemust nscertain ts desired. The i an excess of the ' the merchandise ^vhether the pro- ining the facts in valuation of that do, with the foi- !8. 1871. ) $ 465 t.io 80 10 .46 194 40 r.5o 045 .75 375 ).00 180 $11^45 50 worth Si 945 50, chandise account 7 to Balance ac- to clo?e ; and we it (after Stock, account. This 1 on hand ; the credit side that the difference, in sides, drawing balance, is trans- ! account. The ; balance is trans- lount thus written m ir position under the e oppotUe aide from oxoesti of that lide. PBOCWfiS OP OLOSINO. «oa„ balance., and we close it by simply ,-uli„„ the do ,2 1 ne" *ow, a «<,„„., .„d is .ransfened to thelj.VoV BaL V.'^rn" .helc- d TrT *" 7f'-' °f."Ji "■" "<"=»""'» exhibited unJ°r been plerlv r? ^1' 'l^ "''"""''■ "»'' '^ '^e balances have « next take . T-iai Balance of ^^^'ZoJ^^^ SECOND TRIAL BALANCE. Dr, Cr. Stock, Loss and Gain, Balance, I $4500 340 60 989 40 .tt:;: Z !;^t"l?tr Sd rfff^^r^ side, decreasing the investment The S.A '°''' •" ""' '*"'''' the capital invested inc'aaed b> ^'^^IZhZ'TJT''" equal tho/,fMra( worlh, as shown hv the R J , ' »' <"""■*. now close 'stoclc account in^ Bala/ce whwTusI?""/ '^' eju ,b™„ „f the Balance account ; a^d cotlct" i 't^^^-t^unT t.iy euurd 01 resources and liabilities. " ' " -account, b Jness ,hich it occupied'atr oil ;:C^^^^^^^^ the not investment, or net intae- of tile pIv^Li ' ' "'"« I , ! ORDER OP OLOeiNQ. ORDER OY CLOSING. Th« student will <\o woW to observe particularly, and to follow out in prnctioe, tlie foUowin- order of closin.i,' tho Lcd,;?er. First.— Open ;in account with " Loss and Gain," (if not al- ret.ay opened,) and aaotiier with " Bulanco " ; the former to exhibit tho losses and gam-t, and tho latter the renoarces and ha- bxll/ie.t. Second.— Ascertain from the inventory if any property remains unsold ; and, if so, credit each account lor which such property was oriu'inally debited with the value of that unsold, makinp; the entry in red ink. •' By Balance," and transferrin^' the amount directly to the debit side of Balance account, making this entry in black ink, " To Merchandise," or "To Real Estate," or any other account from whicli tht^ amount is tranaferred. The Ledger accounts will each show, now, one of tho four following results; viz.. a Resource, a Liability, a Gain, or a Loss. iThird. — Omitting Stock account, (or Partner's accounts,) commence with the first account in the Ledger. First ascertain which of the above results it shows, and make the closing entry accordin"-ly. If the diiference represent a resource or a liability^, enter upSn the smaller side, in red ink, «' To " or " Bi/ Balance " as the case may be, and transfer the amount in black ink to the opposite side of Balance account. Tf the difference represent a gain or loss, enter on the smaller side in red ink, " To " or " By Loss and Gain," and transfer the amount, in the same manner, to Loss and Gain aocount. Close all the accounts (except Stock or Partners',) and transfer the balances as directed. The Loss and Gain account will now show, on the debit side, all the losses, and on the credit side, all the gains, the difference being the net gain or net loss. The Balance account will show on the debit side all the resources, and on the credit side all the liabilities, (excepting the result of Stock or Partners' accounts,) the differ- ence being the real interest or present investment of the proprietor or proprietors. m • i -n i Fourth.— Take a " Second Trial Balance," or a TriaJ Balance of the remaining open accounts. Stock or Partners', Loss and Gain, and Balance. If the balances have been properly trans- ferred, the debits and credits of these accounts, taken together, must be equal. . Fifth.— Close the Loss an;! Giin account into Stock, or, it it be a partnership business, into the partners' accounts, dividing the gain or loss according to agreement. Tho Stock or Partners' ac- counts will now show the original investment, increased by the gain, or decreased by the loss ; the difference being the jyvesent 24 j^, and to follo\» Lcd,2;er. lin/' (if not al- the I'ormer to Honrces and Ua- roperty remains I such property old, iniikinnj the [ill the amount iking this entry h]st;ite," or any i. The Ledger lowing results; ler's accounts,) First ascertain he closing entry ce or a liability, " Bj/ Balance," ')tt« 30 Vds. Clotfn,. Val,.-.t „» ,:. <. i' . .« " ",,'3-. *— >"J''1 l>- ^t. Just. Received ance. s. 6d. ceiled in pa,n,en., cihr^f 10, alid'tirriaC"' «' I'l;.;::'- ,"«" 100 yds. Cassiinere, at 8s. H!,l _!« C3„i,i ,^ y, v i ' ca«h, for l,al. ot account n.^- due, £6 7 ti.-lS. Aooeuted C. Vt7;. kin's Draft Received of E. G. Ir on me at 8 day.-^, in favor of A. Svk vine, cash, on %, £1 5.-~31. IJ epted C. Har- e.-J, for £8 8.— SO. on ,ny note at 2 months. I0,s v,].. Dutch I K Aiid.bert 140 yd... Elbeuf Cloth, at £1 !i, at £i I !o't ofS. McGill, lien, ut 28. 8d.— 16,'«. Suld uote at 16 da., for £150, and cashVor the S 5. Rec'd in payiu't iii.s 26 bal.~84. Takeu from the i') Il niAOTICAL EXERCISKS. Store for my own use, '4 Silk hiinclkerchiefa, at 8s. Gd. — 35. Sold D. N. Fatten, 28 yds. Silk Velvet, at £2 15. Received in paynnent, 100 yds. B!- e Cloth, at 15*., and ca-li for the bal. — 30. Received of B. Morency, 50 yds. Yellow Cotton, at Is. 4d., on %.— 37. Bo't of D. St. Just .'50 yds. Sedan Cloth, at £1 2 G.J. Gave in payment his note of the 12th instant, for £10; the balance on "/c — 38. Lent F. Audibert, cash, £12 10, until lOtli of February next.— 30, Paid cash for acceptance fiivor of A. Sykes, 19th inst.; on the same day, received cash of \V. Dixon, in full of ^. — 31. — Paid cash for sundry expenses, £G 10 t. Take the detailed Inventory of the Merchandise unsold on Jan- n&ry iiisty and quoted at the cost price, the amount of which is £872 6 e. £ 2G6 11 2 Net Gain realized on January Slst, My Net Capital M (I 1465 6 2 \ '■ I ! if timtstt Mi 'i MEMORANDUM II. February 1, I continue the same business with the following, resources and liabilities, shown in Balance account oflast month' Ledger; viz.. Resources: Merchandise, us per Inventory, $1489. S3. Cash, $2982. SG; Bills Receivable, MGGT.oO; E. G. Irvine's account, §3.70; B. Morency's do., ^235.41 ; F. Audibert's do., $50 ; Liabiu ITIES : Notes outstanding, for !?4SG.83 ; Bedard and Jordan's acct, ?35; D. St. Just's do., $'J5.25.— 3. Rec'd cash of F. Audibert, in fub payment of the oan of last January 28tii. — 3. Gave D. St. Just, an order on B. Morency for $G(), to be p li 1 in cash. — 4. Paid cash for Insurance in the Ruyal Insurance Co., un Merchandise amounting to $1400, at li% premium.— O. Sold Kelly & Shea, at H months, 20^ yds. Elbeui Cloth, at $5.60 ; 217 yds. Belgian Linen, at G2icts. ; 57yd3. Cassimere, at$1.70; 69 yd^. Indian Cotton, at 22^ cts.— 7. Rec d cash of L. Newton, in full for his note of $1067.50, due this day.— 9. Sold H. T. Perry, 65 yds. American Cloth, at $2.70; 24^ yds. Gray Cloth, at S2.75 ; 20| yds. Merino, at $1.45; 31 j'ds. Yellow Cotton, at 82^ cts. Received in payment his note at HO days,'' for $150, his order on F. Audibert, for $80, and cas)\ for the balance. — lO. Rec'd of F. Audibert, in payment for his note of January 28, last, amount'g to $600, and due this day; viz., 82 yds Silk Velvet, at .^9.80, and cash for the balance.— 11. 'Bought of A. Gibb, 218 yds. White Flannel, at 87^ cts. ; 195 yds. Red Flannel, at 92 cts. Gave in payment my Draft, at si^ht, on B. Morency, for $150; the bal. at 1 month.— 13. Sold G. S. Convey on %, 7iyds. Silk Velvet, at $10.70. — On the same day, sold to sundry persons, lor casli, 8, yds. White Flannel, at $1.12 ; 87^ yds. Blue Cloth, at $4.20.-14. Rec'd for my portion in my aunt's l>equest, $■•60.75, in ca-h, Vrhio:! I !;ave depos- ited in the Union Bank. — 15. Paid in ca.^h my note in favor ol H. Simon & Co., for $120, due this day.— 17. Sold C. R. McGruth, :u 8 days, 8 Silk Handkerchief-, ai 85 cts.--lJ»-. Bo't of A. Lane & C--.. 2i5| yds. Black Watered Silk, at $1.86. Gave in payment H. T. Perjy's note in my favor, for $160; my note, at40 days, tV;i tsOO , 26 Gd.— 25. Sold I'ed in payment, —30. lifccived %.-27. Bo't hive in payment %.— 38. Lent ext.— 30. Paid the same day, cash for sundry ! unsold on Jan- nt of which is 206 11 2 465 6 2 ith tlie following of last month' itory, $1489.83, [rvine'p account, 0., $50 ; LiABiij 1 Jordan's acct, Auilibert, in fuh rave D. St. Just, I. — 4. Paid cash mdise amounting a, at 3 months, linen, at 62^cts. ; , at 22^ cts. — 7. 1067.50, due this 1, at $;2.70; 24i 5; SlyJs. YeUuw at ;-iO daya,'' for for the balance, te of January 23, is Silk Velvet, at . Gibb, 21Syds. at 92 cts. Gave 150; the bal. at I Velvet, at §10.70. ih, 8J yds. White 14. Itec'd for my i«;i I have dopo'-s- ote in liivor ol H. I. R. MoGrath, tii of A. Lane & C'.. n payment II. 'i\ days, f« taOO , PRACTICAL BXERCrSfcS. and cash ibr the balance -ai» * - ;ack watered Silk, at '^^ i\ * ^•'^'^•-24. Sold f^^r cu^^h ,i' vd. yJ"- Sedan Cloth, at .s' 30 ^0' ^^ ^'^'- ^'^ ^'^""^1- at .^1. o'-^2i anee of 20th in.'t, ftnr^r /'f'"'^''^-^' Di-^courit.d mvaccep «ale at auc;;^-o Tl :*£'Sr^"' '" T'' - the?:t proc^^d'of'te Store on the 24th i sL-38 R^c'd ^^^ '"■'" *!i« «^« ^'"^^ destroved my cash, $1400, amt. for wh^h my \li' h^" /''^ ^°^?' ^"^"rance Co., J "ly^viert'liandise was insured. BALANCE ACCOUNT. MEMORANDUM III. March I f A J h 11 i -^7, to my Dry Good bu.sfne^s Mv r' ?^ J"'"^^ F^-^^uce and Gro- 'allows : Cash on hand, £755 3% .fc. '""['''' ,^"'^ Liabilities are as ^^ per Inventory, £486 7 G ■ V 's j^'^'^" »'«"^. ^75; Merchandise Notes outstanding amt'e to £r7; 7;, ^r^ "'^"'^ '»« on %, £11 is' and C. Pheian, £61 5 io„ f ^"' ^ «^e Mvler & Lee £4S 9 yds. Sdk Velvet, at £2 2 6 _o u '^,'^^"<^" Merino, at 48. 6d • 5' I bbls. Superfine Flour cPu»„ J ' , "'^- ^^'^a Pour, at £1 J. « pV;"? ^0 bush, i'eas, at 4s 6d • '^n 1 1 ^,' , °^^^' Oatmeal, at ^"glish B ack Cloth, at £1 16 s- vVl «, P^^"*' ^^ %, 12 yds. tco 'J^^^t ^"P^^'^"^ *^Jo"r. atii 6 2 ^""^'^r^^PJor Flour, at r^n^''^^^'^!'^"' ^ Jo^en Fet hats JT**:,,^/*^^^- Crawford I ! i l! 1 PRACTICAL EXBBC18M. Maurice fov Ca«h. 1 bbi: fi»t.a Snr>eric.r Flour, M l9.-0n the pa.ne day, Accepted Myler & Lee^s DrafY on in- at 10 .lays. »" J^^^r of 1. lJ.el,fbr£;^7 10.-8. Reo'.i of J. B. Davi"- ?;ri' •,""-,?;,/ "J^' -Onthe8amr.day, 13o'tf)rca.'.h<>fSMUth & O'Ne.l ..0 lbs- coffee^ at Is. 2d.; 20 U.S. Tea, at 2h. fid.; 60 X,3. Brow"^u?ar at S^.h , 16 lbs. Chocolate, at 1h. .5d.; 24 lb.. Cboe^e. at '-i'l-^' S^J^p,^' Rolland, at one month. 15 yds. Iri.h Linen, at 38. ; .30 yd.. Red Flan- nel, at 4m. 4d.~10. Bo't of A. Haniel & Co. .54^ yd.. Alpaca, at is. Id. : 1 LSI yds. F»ench Me»no, ai 53. .Sd. ; 6 Carpetbags, at 5.s. 6d. ; 3 doz. handkerchief, at lOs. 5d. Gave in pay"^"<^^njy note at 90 daTs, fori:20 10; Uie bal on %.-13. Rec'd of W S. Reid, m cash, £11 15, in full of %.-!». Paid £3 H 9 in cash for the purchase, oartage etc., of 2^ curd, of fire-wood.-ll. Sold B. Jones on hi8 note at 2 months 70 vds. Red Flannel, at 4s. 7d. ; 15 y;li Black Cloth, at £1 16 9^: 28 yds. White Flannel, a^/^-Jf •-:1%^°,'*/ for cash, 16 lb'.. Butter, at U. ; 5 bu. IJarley, at 68. n;l--l«- B^« '' of J. B. Davis acheck on C. Howard, for£17 1, payable to the l^earer, which was paid me this day, in cash, in full of ^.-IT. .^old ix. i.e- niay, 2 bblsT Superfine Flour, at £1 7 ; 2 bbls. Extra buperiur Hour, atil 17 8:1 barrel Oatmeal, at £1 1 1 : 40 lbs. Butter at 1 id. Rec'd in payment, cash, £2 10 6; the balance on acct.-lO. I aid L. Crawford & Co. cash, in full of %.-SO. Paid cash for acceptance favor olT. Lebel, 7th inst.-31. Paid cash for a horse and harness, £43 5.-22. Bought of F. R. Meredith, 6U yds. Cassiniere, at 9s. 3d. Paid in cash, £18; the bal. at 20 days.--2a.. Bo't of Myler & Lee, 78i yds. Woolen Carpet, at 2s. 7d. ; 85 yds. Printed Calico, at lO^d..; 18 pair Cotton Gloves, at Is. l^d. ; 15 yds. Welsh Llannel at 2s. bd. • 6 Silk Umi on his note payable U the rnrin';; '''r^: ^^^"' ^- »• Col -On the same day SoMP L f ' ^"^.^^.thout interest, .>f60 Bank Stock, at ^^ .t!on he^TeTaV R. ''.^''' *? i^'^'^^"'^ ^^^''^^^^ in full of acct.->10. Sold J M f if ' '^u- T^' ^'■'''" ^^- ^^^''-^'H Superior Flour, at" 12.45 •'> hbi^Fw ^''pf '*^^'"^'^"'^' ^ l^bls. Extra perfine Flour J6.40 1bbi. Oatmeal ?s'^^ ^,'*^^' ^ b^'' S"- 40 lbs. Brown Snea,' at iii o^t Tl m' 1 ^ '"'' ^^''''''^'' ^^^^-m; in payment, 100 bu. potatoes at'4linl""oT'i'"- " ' '"' R^^c'd the balance,-On the^samedkr pLt{' o'^ ^Jf "«^ «* 60 days for the above Invoice in cash S2^^^ ^1 ^o ^f*"^ Jrunk for freight of in full for his Sof Mu ci^2> -i^"s Jl^^^ i^ I' «: Merfd.th, Black Cloth, at $7.72 i- yds" RkTw Q ^'"' ''^.'^ ^^ >'*^«- ^"g'isS Velvei, at J8.65 "5 Fd hLs afll •',) vi *n ^^'^^S ^^ ^^- ^ilk in the Un.on Bank.-l4. Rec'd of PrR^f ?T''^'^ ^^«^' °'«h, if- if i li PRACTICAL EXER0I8B8. $17.28 on the Union Bank, in payment of his account. — 20. Rec'd $84 in cash for 6% dividend on 14 Shares Montreal Bank Stock. —21. Rec'd of J. Beaudry, Sorel, loO bu. Oats, at (iO cts. ; .'500 bu. Rye Meal, at 90 cts., which I Hold immediately with fHO profit, to E. Stephens. R*c'd in payment of the latter, a note at 2 ) days, lor $200; cash, $120; the balance on %.— 23. Bo' t for cash lu bWs. Extra Flour, at $4.80; .T) bbla. Fancv Flour, at $4.70; H bbl.s. Su- perfine Flour, at $4.60; ■i bbls. Oatmeal, at $6.— 24» Lent cash to P. Fremont on hia note at 40 days, and without interest, endorsetl by A. Sauran, $65.-25. Rec'd cash of G. S. Convey in payment for his note of the 9th inst., due this day.— 20. Sold C. A. Simpson, 8 Simres Montreal Bank Stock, at $112. Rec'd in piiyment, 128 yd«. Eibeiif Cloth, at $6 ; and cash which I deposited in the Union Bank.— 27. Sold N. O. Day on his note at 2 months, 35 bu. Peas, at $1.13 ; 17 bu. Barley, at $1.29; 20 lbs. Cotfee, at 30 ots.; 4 bbls. HerringH, at $7.85.— -28. Paid cash for Myler A Lee's Draft, in iavor of C. May- nard, $62.45. — On the same day, Gave the carpenter an order on N. Graham for $5. 10, for repairs of Store Fixturec^.— 30. Sold J. S. O'Brien, 200 yds. Irish Linen, at 90 cts. ; 40 yds. Silk Velvet, at $9.20 ; 12 Felt Hats, at $1.98| ; 12 Black caps, at $1.90. Rec'd iu payment, Neil & Roche's note, at 40 days, for $240 ; cash, $203 ; discount allowed for the payment in cash, $3.80 ; the bal. on ^.— On ihe same day, Paid canh for sundry expenses; viz., Taxes and Gas, $5.63, Family expense.^, $24.35; Rent of Store, $26. Take the detailed Inventor}/ of the Merchandise unaold April 30th, and quoted at ihe cost price. The Merchandise amounts to $22^2.96. The Shares of the Montreal Bank Stock, to 624.00. BALANCE ACCOUNT. t BKBODBCKS. ■jr, LIABILITIES. S 840 ^■j: ( Cash, $ 83,' Bills Payable, 10 ^H ' i ( 1 M«rcliandise, 2232 95 C. Phelan, 245 00 ^H M $1 1 Bills Receivable, 1285 45 A. Haiiiel & Co., 72 47 ^■1' J. Bell, 14 86 J. Beaudry, 3(;0 00 ^^^^^^^H ! A. Smith, 42 50 Stock, •4821 0',^ ^^^■f-' ' Montreal Bank Stock, 624 00 ^H liH I \ B.Nolan, 26 98 [ Union Bank, 1 H. Collins, 910 46 72 90 ^H . i Hi N, Graham, i i E. Stephens, 125 \l\ 00 ■1 " IIL '- ^ J. S. O'Brien, 1 147 85 59 5 % ^^^^^H '< i*G^^H H ] 1 $6338 $6338 59 u L_ ; 9 SKT I[. DAY BOOK, JOURNAL, CASH BOOK, BILL BOOK, COMMISSION SALKS BOOK, ACCOUNT SALES. it,.] DAY BOOK,— SET II. QuEBKc, April l.st, 1871. J. Byrne and F. O'Reilly Imvc tl,i. ,Iay ontore.l BTRNfc, & Reilly, toconrluct a Produce, Grocery Domestic Shipping business, and for l.uy.n" IS 8el mg Real Estate, Steamboat Stocks, etc : ~Tl e parties to invest equal amounts of net capital ad to share alike in gains and losses. ^ ' J. Byrne's Resources are as follows : une-half d the Tow-boat Nestor, valued at 7800 One-iourth of the Tow-boat Levis, *' «« 6400 His Liabilities are: A Note, favor of Barclay & Co., due April II th, which the Finn assume, J. L. Eraser, amt. due him. Making his Net Capital $20200. $8750 250 20200 1 If m 00 9000 00 s DAY BOOK, SET II. Qr.f.Hiso, Apiul 1st, 1871. V. O'Hcilly'fl Resources are: Casl) on liathi, $19600 A Note in liis favor, drawn by 1.. Clint, due May 25tli, 4230.60 His LialiiliticH, which the Firm assume, are Young & Talbot, anit. iliie them R. Fisher & Son, " " " Makinfj; his Xct Capital $20200. fl068 2.502.60 1 Deposited Casli in the National Bank, 2 Bought of C. Ross & Bro., Storo ami Fixtures, at Paid thern,CliPck oil National B'k, $2000 Bond and Morlgiige for balance, 4000— $6000 Solil i of thft Tow lioat Nestor for cash dl•J.o^ilfd in the National Bunk, Bonjiht of L. II. O'Connor & Co., IFiQ bhlH. Snpwfine Flour, ^ !? 120 ♦' Extra Mfjsa Pork, " 720 " MfSH B.'ef; \'l! Piinic Beef, (iO «< Bed llamH, 6(t " Pearl Ashes, 8 hhde. Sugar, 8800 lbs., (< (1 Gave in payment. Our two Notes— 1 ^> 10 da., fur 1 ® 3 nio., for Our Check on the National Bank, for Balance on ^, :"). to 10.00 12.00 !).00 KL.^O .').50 .07i $2000 4000 $810 1200 Hfi40 1 1 2.5 9!)0 27.5 H60 .3700 4000— $ia700 Drew Cash from National Bank, per Check, 32 2.S830 3630 60 60 18000 6000 00 00 4200 00 1.3700 00 4C9 00 DAY BOOK,— SET II. QuHBEc, April 6, 1871, Paid cash for \ Repairs of Tow-boat Ley is, 90 00 a.H r?sk, ' ^^""■'^«'' '0 be eol.J on our ^ 200 bbl... Mess Beef, ^$12 2400 •^0 " Prime " <( ij 270 4 hhd8. Sugar, 4400 lbs., " $.07^ .S30-3000 4 Paid drayage on same in cash. 8 Bo't of E. S. Pierce, a House, 24 St. Louis street, for Gave in payment, A of Tow-boat Nestor, for $2200 Uieck on the National Bank, f:)r 1.000 liond, secured by Mortgage, payable '" <• nio'ill'f^, tor .S.S00~700n Received per Ora„d Trunk R. R., from L. Sha^v & Co loronto, to b,^ sold on their % «..,! risk, (•00 bush. Wiieat, invoiced /?» .fl.do "00 •• Corn, »• «« (ig 4200 Iba. Butter, '< <« "14 Paid transportation charges, in casli, 10 W Z nf f "'"' ?" ^f '?"*' ^^"'^' ^f Lewis & Wright, of this city, (heir Bill of Exchange at «.gl.l on Watson & Co., Montreal, and reimtte the same this day to Young & Talbot, in full ol Faid ,n cash, i % Pretn. for the Bill, *^"^2.C7 .■?00i 7000 00 00 9.0 00 1070 II .! I DAY BOOK,— SET 11. Quebec, Apku. 12, 1871. Rfoeivr'i ifii.'l' ''•nee (Imt the Tow-l>.iaf Lovn* Mink ^estenlaj in tl, St. Lawrence river, near i. ""en Inland, uml lia> Jicen dt'livercilover to the Under- writers. The boat being insured fnr $21 ')00. we liave reci'iv- ed ill Casii, (wliicli we liave deposited in the National Bank,) rmiu tiie Qnol)ec Ins. Co.. nnr \ of same, $5:17;'). !.s« Expenses $110, = f52t»ii Lost the Bal. of our Share ol'the cuat of eaid Boat, ($5400 + *l)0 - $52(j.')) = 225 13 Rec'd per Steamer Anna, from F. J. Ray, Halifax, N. S., to be HvUi on liis % and risk, 400 lil.ls. Codfish, invoiced ffi) *4.r)0 (iOO " Mackerel, " " 6.50 500 " Herriogs, " '* o.OO Paid Freight and Insurance, in cash, 15 Bought of A. Stars & Co., per Check on National Bank, 30 Sliarea National Bank Stock, ^ $48 per S. 16 SoldB.W. Hardy, for cash, from L. S. ConsigDuient, 4200 ll- Butter, i9 $.\6 800 budb. Corn, " .80 & Co.'s $(172 640 Cloped L. Shaw & Co.'e Consignment, and rendered them an Account Sales of the same. Our charges for Storage and Adver., $ 20.00 Our Conn-iiasion on Sale?!, 64. IM L. Shaw & ' ';.'8 net proceeds, 2152.87 Boughl, at Aucuon, I- :)f ot^amboat S' rel, for 34 5400 0(1 150 00 1440 00 1312 00 ^ 2237 6400 00 00 DAY BOOK,- SET II QUKBKC, APIML 17, 1871. "I'M) ()(i 1.^0 00 1440 00 1312 00 22,-^7 6400 00 00 (^>avo ill payment, The Note or L. Clint, favor of P. O'lteillv an.l .liie 2;, 1, i.r.xiino, .':;42;{0.7lO Our chpoko'i National B'k for inoo.OO tu^li U,f Sal. inclmJHjg tlisci, •^"N.ie, GfH;.l!)-642(i.7!i The di^ct. on Note, $4230.60 for .'{8 day.s, is it Gave oi.r Note, ^ 40 day,, to the QneI.ec In.s. Co ^i'riTl'\''Y ■^'""''' *^^^''" Stea.Mbout Sorel, fur *0500, ^ 2 ^ = $i:;o, a,„| Policy )?[. 18 ^ W fr '"^''i^-'b^^-'^t Alfre,!. a„.| coM.i,ne.J tu % and risk!' ^"^'''"' '""'''"' '^ ^^ ''^^''^' «» -"r 50 bb!s. Pearl A.^hes, fron) Store, valued f<2>$7 !? im 4 hhd*. -1400 lbs. Sugar. " <• I 600 bblH. Mackerel, (F. I. R'^ Consi..„. Paid ca T' V^ *^5" ■ ° 4500 i-aul cttflh lur Ins.^Preujium and Policy, 20 19 The SteaMiboat St. Alban, on which we shipped puds to McLean & Co., Montreal, got on fiS a her , rnval in p..t. and our go, J.,= which w'i resc .; ,„ a (hunaged condition, and upon which there was no in.surance, were sold at auction lor 2H 79 Shipped, per St»>an)boat Glory, to W. S. Kellv ^iniiJrr' ^tt^^ ^^ ^"^ ''''^''^ -^"^ -^^ i''^ % •'0 bbls. Superfine Flour, /a $ (5.12 3GG ■■50 '< Extra Mess Purk, " U.oo 650-9IG Paid drayage on same in cash, 131 00 5266 00 2500 00 920 00 m.^ in i i ■lit 6 DAY BOOK, -SET IL Quebec, April 20, 1871. Sold E. G. Henry, for cash, 400 bbls. Codfish, (F. J. R'8 Con.) ^ |5 2000 500 '< Herrings " " '< 6 3000 Closed F. I. Roy'a Consignment, and rendered him an Account Sales of the same. Onr clirtrires for Storage and Advertising, 50.00 Our Commission on sales, 287.50 F. I. R. net proceeds, remitted in cash, 9062,50 22 Sold to J. L. Fraser, 25 Shares National Bank Stock, at fn) $52 Received payment as follows : Canceling tor our indebtedness to 5''"'. $250.00 Iiilcrest on same allowed by us, 1.50 Cash for the balance, 1048.50—1.300 23 Received from G. Doyle & Son, Ottawa, to be sold on their ^ and risk, 1000 bush. Wlieat, SOO *< Oats, 200 bbls. Tallow, Paid i'^reight in cash, 24 Sold our House, No. 24 St. Louis street, toR. Fisher & Son, for Offset, as part payment, the am't which we owe them on %, $2502.60 li^cM their Note at 1 8 months, fieciired by Mortgage on Prop- ^ ^r^y. for 5000.00 And Cash, for the balanoe, 437.40—8000 25 '\ Sold E, F. Andrews, at 40 days, on % 200 bbls. Tallow, (G. D. & Son's Cons.) /© ?8 5000 00 9350 1300 00 100 8000 00 Od IfiOO 00 SS l»te«,. due o„ sSrialr'^ *»"£» ' 0.75 27 Cash paid, I»ificount off- to May 1 7 ' '^^^■^'^ 29 Received advice from Price & Tr. w . pale of 50 bbls. Pearl A.i '.^'"S^'o"' o^the -;j 600 l>bi.;MackLet'S:iLl'^V'"'"^^'-' ISlhinet. ' snipped ihein on the Net proceeds remitted in casli, 30 1000 bush. Whear <^pn t, o . /a $1.40 ' ^^- ^' * ^^^'^ « Coneignment) CJofieiJ G. Doyle ,^„,,^ 8758 00 Pa.d sundr, expenses this month, in cash, JOURNAL,— SET II. QuKBKC, Ai>iuL 1st, 1871. Dr. Gr. • The term "Mortgage Payable » i« but another name for BilU Payable : the ad'ount! mZ b" kept ^separate or together. There is a dist.uctjor, between a SomiSorrnote nnd^ mortgage on real estate ; and the majority of business ■to would pr»fer to h«T9 U»»t distinction prwwved in tbwr aooouHts. Sundries Dr. To J. Byune. S29200 00 National Bank $16000 00 Tow-boat Nestor Stock 7800 00 Tow-boat Levis Stock 5400 00 J. Byrne Dr. To Sdndrie*. 9000 00 " B. Payable. 8750 00 " J. L. Fraser. « 250 00 Sundries Dr. To F. O'liKiiXY. 23830 60 Cash 10600 00 Bills Rkckivabie 4230 60 F. O'Reilly Dr. To Sundries. 3630 60 " yocNG& Talbot. 1068 00 " R. Fisher k Son. « 2562 60 National Bank Dr. 18000 00 To Cash. 2 .. , 600( 00 18000 00 Real Estate Dr. To Scindries. " National Bank. 200( ) 00 «' MobtoagePay.' i • 400( 1 00 Gr. 00 00 00 00 129200 00 60 60 00 8750 250 238:^0 00 00 60 00 00 1068 2562 00 60 18000 00 2000 4000 00 00 r BillB Payable : tha listinction betwoen a majority of busineas MOOUBtS. JOURNAL,— SET 11. Quebec, Apiul 3, 1871. ypr Or. Nationat, Bank /;,. To Tow-boat Ne.stou Stock. 4 _ Mekchan DISK Dr. To Sundries. To BiM.s Payabi,).:, " Nationai, Bank. " L. R. O'CONNOK & Co, — •■•- _. 5 Cash Dr. To Nationai, Bank. -esent <^ particular IS as though wo had sn.'d same in this advent aod cash credited our m tire. c'^Jnn,? ""i" f'*^ distinction. It norchandi^e for 7 nn ) f '-'^^ ""''''""f' invested thi 80 cost and morohandiae ■f w- ' — 1 1 )i ;; i- i JOURNAL,— SET II. Quebec, april 9, 1871. Br. 8 L. Shaw & Ce.'s Cons. * Dr. To Cash. 10 SCNDRIE3 Dr. YOCKG & Tai.bot Premium To Sundries. ToIa onal Bank. .« Cash. 11 BiLLK Reckivabi.e Dr. To L. Shaw & Co.'s Consignment. 12 Sundries ■''**• To Tow-boat Levis Stock. National Bank Loss and Gain . 13 F. L Ray's Consignment Dr. To Cash. 15 Or. $ 95 National Bank Stock Dr. To National Bank. 1068 2 00 1020 00 G7 $ 95 00 62G5 225 150 1440 00 00 00 00 1068 2 00 1020 5490 GO 67 00 00 150 00 1440 00 rKoae. m effect, as wouia db au a^ receive, as comm ssion morchaots, •t:';;ir"'L''t:a7C'efore ff Kur^ -count ^th the ,-. % Ih. pro^rty, we d«bU it onij with what it haa eoBt u.. 40 JOURNAL,-SET n. Quebec, April 16, 1871. /v. To L. Shaw & Co.'s Cons, << I- Shavt & Co.'s CoNsioN. Dr. To Sdndiues. " Storage & Adfertisino. " CoMMisaio>f. " L. Shaw & Co. St'NDRlES />». rr,^ o '-'^' io Sundries. Steamboat Sorel Stock DlSOOONT To Bills Receivable. " National Bank. " Cash. Steamboat Sorel Stock Dr. To BiLr,8 Payable 18 Shipment to Kingston To Sdndries. *' Mdse. " F. I. Rav's CoNriGw " Cash. "Jeir CoDeignmentlocounf . " ^^*'*'* '*' ^'^r business wit"h'^h"''* tbe aet amt. their nronertv a/i\ "^ ""* "«ef^ «'> »how fhl #■ ? "° '^^™ «<> f*r ; and m When iKS'o:,^ °3„d "^f '" '^ '''8'^r^nce Se7n T/'^-h''*'^ ;'^ ''"tUled to! -ui. to the a.sw«ir,i'-i- '^^ coLgi', ru;t!"::d?;4-:^- -u't.totheac=^'g^J':,^- 41 ; \i 1 1 I I [i JOURNAL,— SET IL Qdebeo, April 19, 1871. Dr. Cr. Cash Dr. $2500 00 To Shipment to Mont heal (1) $2500 00 W. S. Kellt (2) Dr. To Spnoribs. 920 00 '* Mdse. 916 00 " Ca3B. 4 00 90 t Ca8h Dr. 6000 00 To F 1 Rat's Consignment. 6000 00 « 9360 00 F I. Ray'8 Consignment Dr. To SCNDBIES. " Storage & Advertising 50 00 " Commission. 237 50 •' Casb. 9062 60 •>2 Sundries Dr. To National Bank Stock. 1300 00 J. L. Frasgr 260 00 Interest 1 50 Cash 1048 60 (1) Shipment lo Montreal is treated precisely as any property or represent- ative aocouni ; baviog been dabiled with itn costs, we now credit ii witii its proceeds. The difference will be, in this case, our losf. (S) Here the good« are not shipped for our account, but for the account of another party who oxtered them. This is therefor* a regular sale. 42 "•acfteaiu. Gr. 10 00 $2500 00 !0 00 916 4 00 OU 00 6000 00 00 50 237 9062 1300 00 50 50 operty or represent- » credit i( with its for the acoouDt of rtal*. 6 JOURNAL, -SET n. ^Quebec, Aprm. 23, 1871. /)^ TE. G.DOTI.E& Son's Consign. Dr. To C^sH ■ 24 i/r. lo Real Esta H. FisHKK & Son MORTGAOK HeceiVablb Casb ■ — - 26 E. F. Andrews ^„ To G. Doyle 4 Son's Cons. 26 $ 100 00 2662 5000 437 1600 Or. $ 100 8000 Shndries Dr. To National Bank. Bills Payable (]; Interest 60 00 40 00 00 00 J 600 27 Bills PATABLM2)i)r. To Sundries. " Cash. " Interest. 8760 00 8 75 00 8768 76 2000 00 1993 34 66 wrlti^i^n'ttS^'^^t/ thf J'ar':*^',!" '"' ^'"^'"'^ '^-^ credited with the .... est wi h'-.h^^* "'^'«^'"-« debit Bi'ls Payabl JithtS'^""'*?!'** P^y. *» ordor^ est with the amount we pay for Interest. *°*' ''^ ^° "°*e' "Wd inter- arioyg"eKrp:;^',r,lV'$%*i^'r'V^*^^" ••• «Fe.aedvaiue a. w. here debit BillSPnvublowkh the fapf' T^'f'' " **•" >«S8*^han iJC "w. ;^Jtbe.n«t.e amount produced by ir.&^'t^'irv'^;':^'^^'^:;:^ 4S il^;, ^mi JOURNAlw, - SET n. QuEBKc, ApiiiL 29, 1871. Dr. CA(?n Dr. To Shipmkxt to Kingston. 30 $5100 00 Cash Dr. To G. DoYi.K & Son's Cons. G. DoYi B & Son's Cons. Dr. To SrNDKiKS. " Stobaoe &, Advertising. " Commission. " G. DoTLE & Son. u F O'Reillt u EZPENSB Dr. To Cash. Dr. To ClBH. 1400 2900 00 00 200 ISO 00 00 Cr. $5100 00 1400 30 75 2796 00 00 00 00 200 150 00 00 We have omitted the Ledger in this Set, believing the student to be fully capable to post the accounts without assistance of this kind. Wo shall adhere to this plan hereafter, except in cases wlicie some new principle or application may be otherwise more clearly shown The student wHl make his Ledger conform to the following Trial Balance, and close it in accordance with the Statement hiob follows w '. ^■^^»-ft?;iff^:^^ff,-. ving the student issistiince of this , except in cases ! otherwise more to the following the Statement rooi-ing.s. 23098125 140U TRIAL BALANCE. LEbGKJi ACCOUNTS. J- HVIIIL- National Hank Tow-boat Ntvstor Slock low-boat Levis Stock Bills Payable' •»• L. Fraser Bills Receivable Cash Youni;; & Talbot H. FJHlier & Son Real Estate Mortgage Payable Merchandist L- li. O'Connor & Co. Shipment to Montrtai L. Shaw& Co.'sConsi.r,, Premium, Disc't, & [..t L0H8 ami Gain F. I Ray's Consignment National Bank Stock i^toragean,! Ailvfrh,^,,,;: Coiiiiiii8ision L, Sliaw & Co. Steamboat SoreJ Si,oc4f SliipmeiU lo IiHj.u«icn W. S. Kelly <;. Doyle & Son's Cons. Mortgage Keceivable i^- F. Andrews G. Doyle & Son Expense INVENTORY OF Ux>^SOLD PROPEKTY. T.)t:ll 2:)2(i() 2;v>;:{(i|i;i) 2(i;?(;(; (>i()(i 5l!)() J4syi 2o() 423(i|i;i) 31)50 7J7() 1()()S 2oG2|i;() HOOO 7;^()() 'I (it; 2 40(10 2500 2332 11500 1300 100 376|(i:-! 2152S7 Uulanoeg. 202001 20000 4i;^l 7300 4000 100 370 03 5100 3000 2152 87 Merchandise, I ofTmv-boat Nestor Slock, Keai Estate, ' I Steamboat Sorel Stock, 5 Shares National Bank Stock, ^$30, $9325 1050 6300 6531 250 00 00 00 00 00 ,4 45 $24a56JU0 STATEMENT,— SET U. LOSSES AND GAINS. ^^^^^^^^^^^^H! ^^^m I: r TTT. 1 225 ( 504 33 Oi 166 00 150 00 1645 58 2723 r.3 «. Qaini. Tow-B(i,\T Nksto« Stock,... i'ro«et!ds from rales. 6400 Valuf of unsold 1950 8860 Cost 7810 65t )0 1300 . Gain 650 1 00 on Tow-B/)AT Lkv»8 Stock, Coat 5490 ^H' Proiceedg from Ins 5265 Lofs. 225 ^^^^^^^^^M 1 f ( I i 1 t Real Esjatr, .....Proceeds from siiles..''000 Value of Unsold 6300 14300 Cost 13000 OnAn 1300 1 t 1 1 .MRRGBANDI3R li'roceeds from B.ileo 4662 Mdaeun3.(porInv.).9325 139S: Cost 13700 287 » 110 100 376 i 2723 f i 00 1 ^^^^^^^H ' Gain 287 fcHIPMBNT TO AlONTBIiSAIi,. ....Cost 3001 Proceeds 2500 Loss 504 ^^^^^^^H ' Prkmium, UISO'T, l.\TEREST,..Oosr. 3'J 71 Proceeds 6.f)6 Loss 33.05 ^^^^B 'J Natjonal IJA.NK Ktook, Prooceds from sales.lSOO Value of unsold 250 1550 Cost 1440 ^^^^^^H ^^^^^^^H Gain no 00 ^^^^^^1 STORAGE AND ADVERTiaiN0,..PrOC6edS 90 ^^^^H '.H' SUl C()M,MI8S[0N, " 33 ^^^^V ' ^'jHHI Shipmr.vtto Kingston, Cost '5266 ^^^H tfli Proceeds 5100 ^^^^^H S^H Loss , 166 ^■■■■M ! iJiriMM Jfc.XPKN«B^ Cost ^^H 'if WW Net gi»in • 1 53 ^g^^g 46 Lamm. 225 00 Qain 550 00 130000 287 00 504 33 GO 05 110 100 376 166 150 1645 2723 00 00 58 fi3 2723 00 00 63 IIESOTJRCES AND LIABILITrES. '''■"'" ''W'en/oriM of Unmld Property. Jifi- Liul.il, Tow BOAT Nebtob Stock,, HkaI, ESIATR, Na no.vAL Bank s;ock:::. "■^• Steauboat SoREt, Stock,.." 63 From Ledger Aoeountn. CASH '"'" ^'"'""" MOKTOAUE PAVA8I.R..;:;::0utsta hand. 'Hiinj' Notes. l' iuZvn^"*" ^ ^^«-'-We owe them w. s. kkllt,..:.. ";;::;;:::J™° '^"^ G.^.ov-u:A«uN We owe th;-;;:::;™::::: ' ' rawn out 200.00 His half of net gain 822.79 622.79 His present interest in the eonoern- 20822.79 87 2795 21022 79 62224 45 62224 46 20S22 79 his B.Lce a Juft ;hLV;o ei^/i'V^-i-f 'V 'f""- - .ouroos a.d Liabilitios therelLwa, ">e bead of lie- 4T I'M V s 1 I CASH BOOK, Cash Ukciivbd. 4l ti ti i( April; !;To ['\ O'Reilly KecM of him as cupital. " I 5i " National IJank, . . . Uec'd of it. " 16 " USIjdw&Co'sCon- sigiiineni,.. . ilecM for fale of this date. " Ship't to Montreal,. Rec'd for sale at auction. " F. I. liay'wCoiidign- nienl, HecM for gale of lliifi date. " iVtit. Bank Stock, liec'd the lialarice of sale of this date. *' Keal Ef-tate, Rec'd for Lai. of s.ale. " Ship'l to Kirigstcn, . Keo'd tor sale of ciwda. •' G. Doyle A Son's Comigtiiueiit, . . Kec'd for sale of this date. To Balance, Kroni old %. BILL BOOK, Bills No. WUon n'c'd. Drawars. lit whose favor. For what received. Where pay. 1 2 I.Sil April • > 1 11 L. Clint, H. VV. CooiKf. F. O'Reilly. Ourselves. Investment. Merchandise. Our Offioe. BIIJ.S No When iM(l Mat. A pill Drawer^ 18' )vriit', .1, I Ourselves. In wliOhe favor. Hurjlay & Co. L. R. O'Connor & Go. u Quebec Ins. Co. 48 For what given. To Hal. «;^ Md /t- .»e. Where payable. Quel>ec. Insurance. u ital. f 19600 7 90 C230 20 Where pay. Our Offioe. . (< << wliat 'en. il "■'. aace. Where payable. Queliee. u -SET n. Cash Dlsbursed. " , ,. '"."■■•",«""vi-.Sl..d<..P„Tl for rfoair. li ti (( n u It <( << lOi );{ Ii7 18 19 20 2;! 27 ;!() ;{u ■M) ' ai'l (or Drayaijc. Paitl K:»r net j)riiceevl3, '^nipin t to ]iin<»s{oM PiM / .- i " W. S. Ivelly, = ^"'l.^"' ''Jf i'l.-nrance \\ !;'• f- ^''f^ conVi^',, ■ tr. Doyle & Son's Con Hills Pavable -M./br Freight. F. O'Keillv '''."'"'"• Note Xo. 2. ''expense, p,,;, " "" ^i' ^'^"c«; ::::::::: ;^;^^""-'T.'-^pe...e.. —SET II. Reoeivabli. ':"« I Time of Note. to run April lu GO days. j,,^ |,T ^^-, -; .i^..^..^ .'.-,v,.ip.-Hi,.-g:A-jfJ^ »feB Dr. COMMISSION SALES L. Shaw & Co.'s i 1871 April u 1.40 14QQ " 30 •re due. will be foo^U in the Com tneroial Arithmetic from p. 2fi«to 279 61 ACCOUNT SALES,— SET U, Account Sales -!, 600 bii. Wheat, ) SO) " Corn,' > on % and ri»k of 200 |l>s. Butter, > L. Shaw & Co. I, :/■ !' il- ! 1871 April 11 16 9 16 ii Sold H. W. Cooper, on his Note ^ 60 days, 600 lin. Wijeat. <® §1.70 $1020.00 Sold B. W. Hardy, for cash, 4200 lbs. Butter, r® $.16 672.00 800 bu. Corn, fed .80 640.00 2332 179 1 00 <« << . Charges Paid Freight, in cash, 95.00 Storage «& Advertising, 20.00 Comiiiiseion, 2|% on $2.S32, 64.13 1.8 L. Shaw & Co.'s net proceeds, Due by Equation, May 13, 1871, E. E. Byrnb & O'Rbilly, Quebec, April 16, 1871. Per J. Maguire. $2152 87 Sales of Goods by order and for % of F. I. Ray. 1871 April II II II n 18 20 Taken to our account, 600 bbls. Mackerel, ^ $7.50 $4500.00 Sold for Cash. 400 bbls. Codfish, (d) .*5 2000.00 500 " Herrings, rd) $6 3000.00 -Charges . Paid Freight & Insurance, in cash, $150.00 Storage & Advertising, 50.00 Commission, 2^ % on $9500, 237.')() F. 1. Ray's net proceeds retuitted E. E. Btrnk & O'Eeiily, Quebec, April 20, 1871. Per J. Maguiri 52 9500 487 $9062 00 riO 50 md risk of 00 I 00 00 2332 00 00 00 13 179 IS *2152 87 re. I. Bay. 00 00 00 9500 00 00 no 4M7 ■)0 $9062 oO 'ri'. i(f^'??^--*'"^!,>i.. ■!•;•:«'■ PEA0TIC4L EXEROrSES.—SRT „, Sales of 5 200 bbls. Tallow, ) « «/ - „ ^ I 1000 bu. Wbeat. ( ^°^ ^ 0^ »• Doyle & Son. April 2; •' 30 u u u SI 600.00 li 1400.00 23 30 Sold E. P. Andrews, fa) 40 davs 200 bbl.s. Tallow, ra)$S' ' oold for cash, 1000 bu. Wheat, /® .$1.40 Charges Paid Freight, in cash, Storage & Advertisinsr. Commission, 2^^ on'^ISOOO, G- Doyle & Son's net pro. due May 20, 1871, E.&O. E. Byrne &0'Reiu,y, Quebec, April 20, I87I . Per J. Maguite. $100.00 .30.00 75.no MEMORANDUM. the prosecut on of a vrodurp o-i,!: ""^ "'^'» Oj tiAi.L & Guifkin, n and^br buying and Sri^/nTS/cf T'^ ^"^'"^-' the Capital &s agreed. A. J HaH i/ f i * ^^'7- ^''*' *^ ^'"'•"'•^»' Griffin, twcthirlsofthegaL or OSes 1'7 H ii "L^' ^'"^ ^^- »• Liabilities are taken from tL Ral a *^* "^"^"^ Resources an.J April, Memoran,lum IV, ;" so R rrwr-""!/'' ^'''^ ^^^^^S^"- ^" bihties are as follows; Cash Ssr.^T^n" i'r , " ,^^e^"»rces and Lia- at 40 days, L $150 ^he balance L 7'"' ' '''''' ^^"*^''^'* ^«^^ Sold J. Morgan & Co J 50 bWs 1^. p "lontks.-Un the same dav, ^0000 ibs.. a^6i cts ' R^ ^fin pav,^:ent'hYf ?-'^ ''''''''' '^'^ at 6 cts. ; R. S. Griffin's note tlS Zor 1 J''^'' f P'"', ' "^^^ i'^'''- commencing business, due 2t th S foSlS ""^ ^''' l'^'' ^''•'^' ^^ eale and for discount on note .f 2^T7'-, n- ^^^ ^ ' an'l cash for bal. of for 27 days is $6.76.-3. SaveR l^Li.^'^V ^'" ^- ''^- ^'^^'^'^ "ot, Hull's note thei. favor, due this dkJ^TJh,*.?^?: ? Pa^'^^ntof A. J. cash for the balance, 5r^30 _ffih« 1 ^ ^''^'•f ^'^ ""''• > and meucingbusi^es., date^Fe^ ,fary" t 'atfl l^lS ^^ '^' ^''"J' ^ «^™' Amu of Note, $738.36. Theint for 9?,1 fLJ VI' '^''^^ "''' ^'""''^ date. 44.~Onthek.nedayBo'tofO c^^^^^^^^ fine Flour, at $4.25f'l00 bWa E^^trk M ''^/,^^,"^ ^^^'' ^^ira S^pe^ 53 f irriPT -n— —««-—»■ J' i1 PftACTIOAL BXRR0rSE8^-r-8«T II. Hamfl, at$16; 50 bbls. Pearl Ashes, at $4.30. Gave in payment, 3 bbls. Codfish, at $3.60 ; 100 buphelfl Potatoes, at 48 10 ; our check on the Union Bank, for!?250 ; bal. on "/c — 2;J. Sliij)i)ed per Steamer Laval, to S. Larue & Co., Caspe, for their %, and pursuant to their order, 150 bbls. Mess Beef, at $11.50. Paid CH.'^h lor drayage, .$4.75.-34. Sold to ndry persons, for cash, 3 barrels Herrings, at $7.50 : 3 bbls. Mackerel, at $8.40; 10 bW*. «4 - 7 $7 ; alsoto the PBAOTIOAL aX8K0l8B8,— 8«T «. oil the 14th i„st.,wa. wrecked 1^1^; a ;!.'''°A^%™^« »» Shipm't 20th in8t.,-Steamer and Ca/.o to^f In il^^L Lawrence o'the ceptance of the 18th i, st at ?0 li ^'?T*«- '^''^coiintefj o.ir ao- Bal. paid in ca8h.-28. Paid R q rl^fflf ?', """ '^^*^'^*^' '-^ «*-l7 -On the same day. .old ^. How!'. lo C F 'p P^'^^*^ "''«' '^^OO. Red Flannel, at 80 cts., and 2' v^i!'r1o V" a.-^''"®*' °" %' -^^^ yds. Stea.uer Victoria, which was Sreoft • W^ ^'"/i*" ^^^^^li inst^ per '\^. 20tl» inst Amoul^S'luTed $2608%] '«?" .1^^- ^-^"enc'e'ia which we received our note of l!«l • . -^^* I« ^ = $2(>0.86, for ca.h l:.r balance.-orthe 'ame d.v '" " '?'' ''*^'' ^^'^-^'^ ? ^ "^ i- J. W.isun, St. John N. T of PeLHT^ ^" Account Sales'from the 7th mat. Net proceeds #2976 If Iw? T' ^^f «^"t him on by them, on Viger & Roy, ^t eight Vfo; ..frt n . f t-^^^' '"'"'•"^d paid in cash $I500.-.3O Rec?l «n a ^ P'-'^^eeds) which has been & Kelly, Halifax, of 2?0 bbfs Mess Bfet'Z? «^^«^<•'•om Blanchard of 4th ,n.t. Net proceeds, $2;/80 86 -On ^1^^'"^' ? ''"^'^ '« ^''«"' dry persons for cash, 15 ibs. Brown SuTar^iM'?'" '^^^' ^"''^ ^^ ''»»• at 30 cts. ; 44 lbs. Butter at in^^fb'h T f-'n ^^'' Chocolate, 3 bbls. Beef Hams, at $18 • 2 bb??" l?v, ^* ^"^'.^° ^^'•"' ^t ^0 cts. j -31. Paid cashVor Rent of S^rel'! ^1"^''^^ Jl""'"'^ ^' ^^^'^' Laborers, $38. ^^ **^' ^^^i" Clerk hire $100; for INVENTORY OP UNSOLD PROPERTY. Merchandise, Shipment to Halifax, balance of Mdse Shares of the Montreal Bank Stock, ' The net losses, May 31, am't to ?,^ry*'^^^'^- Hall's third Is AndR s Griffln-.two-thirda, A. J. Hall's capital is ^ «. a. trnffin's capital is fl477.22 4!>2.4l i^«4.HI 432H.6I 8457.23 $275381 601 76 20800 $3563166 6ft LI. '• ''M SET III. JOURNAL DAY BOOK, INVOICE BOOK, SALES BOOK, COMMISSION SALES BOOK, ACCOUNT SALES, FORMS OF NOTES, DRAFTS, LETTERS, ETC. PARTNERSHIP BUSINESS. BsMABE. — The Se«e of books thue far phown in this work, have all been condwcted upon the IlraUan method of hi»towcal Day Book, with separate Journal. We did so ou account of its greater eimpliciiy, and not to distract the mind from more important considerat-ions which it was neoesffiiry to inforce. The student being now more thoroughly grounded m the science, we shall henceforth give a little attention to the more practical forms in use, and to a greater variety of entries than heretofore. We wish him particularly to note the peculiar form of the Journal Day Book introduced in this Set, that he may be able to express, in this manner, any conceivable transaction, combining all the eaeential points of the separate Day Book and Journal. Where mo»e severely practical forma — for the purposes of condensation — are not in use, the Journal Day Book meets with great favor, ae being both plain and practical. In the transactions of this Set, we have introduced a new featuie ; vi«., Mdse. Co. transactions. It will, of course, be understood that by "Merchandise Companies" is meant the temporary copartnerships existing between the consignor and consignee, having reference to the sale of particuter conpignments of merchandise. The nature of this epecies of eoRartnership differs from, that of a general copartnership only in its duration, and the manner of conducting its sales. In Mdse. Co. business, one of th« partner s — the consignee — is the commission BQ^vchaat, and, in that capacity, receives and disposes of the property 66 I! ^OXmHAL DAT-BOOK,— TOT HI. •8 he would (rf a wmple conatonmpnr . A. ^i ^ur, he IS mterested in the ssAns^tl ^ ^^ drfftwnce being tJiat ^ »e^ and which are^^ly mt 2^" -^ ^ '^""^ '^''^'^' ^'"^ '^ $Pfn»ng and closing eni-Z? In I« i' ^'^"* f "'^ ^ '•^g^^^s the Mrse. 5o. a,^^,^ t fr^^. In th^ n^ethod-exen^^ified by Lorhe & Bro. an inveice to be «o f "on • " / J^''" ^' '"^^^'^e from C. A " With the invoice and exSn«io • '"^ ,^' ^^ ^l^bit " Mdse. Co. cost of the invoice, til nEom?! ''■'^" '^^^ Consignors with th^ ^ though it were kli our ofn °T e IT-'^'^^"''^'^ ^^^ ^^^^ Property the 6a„,e principle, will beTo de J L Si?"'' !^*''^' **' recognizing ohandise. In the second rnefhod tl^p%£ ' 'f ^"^''*' °'^''^* o^'l^e mer- ^'r of the property is reZ„mbIe ^tT^^' ^f ^Snized is that the C.Lortie& Bro., mdse to beS . • -^"^ when, we receive from A ' witb o«r ot^Xre only a^d^J';! ^^' ^^ ^^^'^ "^dse. Ca ««•'« entry, in this case, tf m2de ^o of'^ '^'' consignor. The .consign- debt us for our share, and u |,j-L*;n?rp'^ ^''^* T'^ ^°»'J be°to •hare. ' " oiiipment in Co. to Quebec " for liis »re!cep?bytre/?rsShortl^^ P^'-'*' interested, if the accounts ^euSs/co. aSnT;- M'tettir'e'c'sf"^' ^'°"^*^' ^ before debS? credit the consignor with their f?uIlT-~'V'''''^ ^'^'^ expenses-and «ha.e, aad any ^other ^frty ^ ^1 \ e/S"? ^"^ <3onsi|nor's) joint consignor would, in auch a case dSf Jl '?'' *^^'' «^««'- The Bhare, and each W the othorTaV^Jt,' .?-''"''^"l' ^^'^^ their joint other parties would, if makLTnentrv?/'' "' ^^f «^*^'«- ^he ejgnee and credit the consignor t^oH^v^ correspond, debit the con- Where there are more tC ^ ^""^ ^'^ ^'^^ "^'^re. are kept by the «eco^rf7ne hod 7he^'n''-'"'"''l^'^' «»d the accounts Co.>ccount/orAwot;nS.td aK^^^^^ '^'^'^' "^dse. consignor for his (the consignee's Zrpf ru '^'^'-g^^' and credit the liand, should debit each of the n«r f f ' u^^ consignor, on the other ; Ship't in Co." for hfs own share F«^^^^^^ «^«r««' and debt "Shipment in Co.," and c'dit f^^^^ ^^^^^ parties shouJd •hare. ' ""'^ ^^^^^*- the consignor euoh for his own JOURNAL DAY BOOK,-SET HI Quebec, Mat 3rd, 1871. offgrLSSd'stfni- ^?^-,^-«' P--ticles B^tsranTlrlfc?^^^ 5r ma 1 t I \\> I I u . I %p JOURNAL DAY BOOK,-SET HI. Quebec, May 3rd, 1871. SuNDums Dr. To C. S. Mitchell (1) For Effects invested : Cash Deposited. $9000 Bills Receivable Notes in his favor ; via., one ""*' drawn by P. Racine, duo May 28, • . 1^00 Another drawn by S. Lewis, due June 6, WOO Balance of ?i^. _^ $12000 P. Allard oe a SrNURlES Dr. Cash Bills Receivable MeIIC'HANDISE A. RlNKUET For effects invested •. Deposited. To R. A. HuDON. $8000 Ship't to Montreai To Merchandise '« Cash Nolo in his favor, drawn by D. Aylwin, due Juno 1 1000 As per Inventory, Inv. B. 2700 Balance of %. _^ _ 4 Dr. To Sundries. 12000 12000 00 00 Shipped per Steamboat Quebec, and consigned to G. S. Walls, Montioal, to be sold for our %. Inv. of produce, as per S. B. $573 Paid Freight and Drayago 2 12000 575 06 00 S. White & Co.'s Consignment Dr. To Gash Paid Freight and Drayage of nn Invoice of Flour, as per I. B., amt'g to §1018.25, rec'd from S. • White&Co,tobosoldoDthefr%. 575 0(1 00 n\ TW« l« .uuTMMod 10 b« two ooUbu- lor doIUn aU o«»-rided llnoa £w II. 1) ooo 500 000 600 6120C0 06 ON. iOOO 1000 2700 300 12000 12000 00 00 TGS. ebeo, k'alls, $573 2 12000 575 08 00 of nn I. B., omS. 675 0(1 10 00 fit»— reded lines for Pi«t of roouj, ^ JOURNAL DAY BOOK,-SET HI QuBB-Ec, May 7, 1871. Dr 8 To SUNDRIEH. 156l{l0 Mkrchandme Kao'd perSteamb. Champlain.from i>. C. Peachy & Son, Montreal, and consn^ned to u.. for our aoot. an Idv. of Wines, as per I. B jTo D. C. Pkachv & Son For amount of " Cash $1549.60 Paid for Freight & Dray. u.5i) . 8 National Bank To Cash ' Dr. 156110 Deposited. « Spndriks X)r. Cash Dmooittt To Bills Iieceivable. I Discounted D. Aylwin's note, far. K. A. Hudon, due June 1st. 10000 looobo Proceeds of note Amount of 24 ds., at «^ . 10 $•90 4 L. DOUOLAS ic Co. [To Mdsb. '< Cash " Commission 100000 ^r. To Sundries, | 1272 Forwarded per Grand Trunk R R pursuant to their order, an"ln- voioeofAJdse., as follows! Sundry produce, per 8. B. $1240.00 Paid Freight and Ins. 30.20 For Expedition ud Ins. 2.48 ■ li - 1272 68 Bills R,gnEfyjiBi,B To S. White A Co. 'a C Dr. iONSIONMENT. 62400 Im JOURNAL DAy BOOK,— SET HI. QuKEKO, Mat 12, 1871. Cami Dr, To S. White * Co.'b Consionmbnt. [ For RaU) of Flour, as per C. S. B. S. Whitk a Co.'s Con. Dr. To Sundries. Cloaed S. White it Co.'s Consign- ment, an' I rendered them an Account Salea. To Storaqb & Adver. Our charges $ 18.50 30.20 1149.30 " Commission 2}% on $1208 *• S. WniTE & Co. Their net p»ooeed« 14 Merchandisk Dr. To Sundries. Bo't of L. MoCord, produce, as per r. B.. amt. $2581 90, and paid OS follows : To P. Am,ARD Oar order on him, for $300.00 " National Bank Our check, for 750.00 " Bills Receivable S. Doran's note of the Hih Inst., for t)24.00 " " Payable Gave our note, at 30 d's, lor 500.00 " Discount Allowed on the bal 12.30 « Cash For balance* 895.60 " 15 . C. S. Mitchell, Private Dr To Cash. Drew oo private ^ . 16 Dr. Mdse. Co. a. To SuNoriES. Rec'd from C. Lortio & Bro , Hali- hn Riild OP our joint acct. to and risk, each i, .Mdse. as }«r I. B., amount $3550. To C. LorTIB & Bro. Their invoke as above Cash Paid freight 60 $35J0 40 584 09 1198 00 1198 2581 00 90 2681 30 .S590 90 50 00 3590 r JOURNAL DAY BOOK. -SET III Qdkibc, May 17, 1871. 8- W»TB ,k Co. To Shipiukt to Montbkal. Received an Account tn lO -* -H !r) o5 o ' t- '~0 t- t~ -rf CM a> — TC 't «. £ OJ = "^ c- tJ il^OjCOj/joJ fQQdotaooa 1 00 m 1 '^ -"tOIMOOOTj-Cvl 1 ^ Oi C5 i-O — ■ CD fo >n lO kO t-ooc>»ecc^?fiie^ (M fC IX OS 1— 1 •— ( fC aS' ^ >• *: c ^ . ^ . 1^ >-.■::> " 2= -^^^^ £-3- — -SO TT § - § .= . --S .2 2 at 0) 0) a> CO « « C C ^ C B c^ ■; . ^ •* c8 o U3 »o CO P- CO 0^ rl( a> •— 1 CO 10 a» ^ „_^^__.^_ ic I^ t- e$.\0 Jy«'» " Ham, 60 bbl8. Apples, 66 " Extra Superior Flour 4b " Fancy Flour, 60 bags, 7000 lbs. Coffee, 8 ca.sks Bordeaux Wine. 120 hollies Champagne Wine, 22 gala, Cyprus Wioe, .13 3.72 5.50 4.50 .15 " 50.00 " .80 " 5.00 (I $ 74.00 247.00 186.00 330.00 207.00 1050.00 400.00 96.00 110.00 Quebec, May 1, 1871. Signpd R, A. Hddon, Invoice of Flour sent per Grand Trunk R. R and consigned to Mitchell & Hudon, Quebec, to be sold on our % and risk: 80 bblt?. Superfine Flour, fS) $5.00 70 " Oatmeal, ^ 6.10 45 « Rye Flour, " 4.25 $ 400.00 427.00 191.25 Ottawa, May 4, 1871. $101S.25 S. White & Co. Into CE of Merchandise shipped per Steamboat Champlam Capt. Ricard, consigned to Mitchell fu i°"' S^^^^°> pursuant to their order and for tnejr %, viz. : — 50 bble., 1600 gals. Coal Oil, ® $ .60 $900.00 20 660 •* Linseed Oil, " 1.00 660.00 15 Herr.ncrs u 535 7375 Herrings, — Charges.. Insurance (8) ^%oa $1650, $7 ?<; Montreal, May 6, 1871. $1538.75 10.8,5 D. C. Pkachy & Son. "^7 $2700 00 If 1549 fiO i X! W U itf > '! ; i! } I o . M.H. M.H. BODS INVOICE BOOK, -SET HI. Quebec. Mat 14, 1871. Quebec, May 14. 1871. Messrs. Mitchell & Hcdok, Bo't ofL. McCoRD. 1600 bush. Red Wheat, td f.90 1200 " Oats, " Mi 360 «• Peas, " .80 42 tubi, 1846 lbs. Butter, " .15 $1350.00 675.C0 280.00 276.00 Received lajiuent, 16 L. MoCoRD. Shipped per Brig Victoria, consigned to Messrs. Mitcbell & Hudon, Quebec, to be sold oo joint %, each i, VIZ. : — 250 boxes, 5000 iba. Soap, /© $ .07 $ 350 160 " 4000 " Chocolate, " .20 800 30S " Sperm Candles, " 8.00 2400 Halifax, Msy 7, 1871. $3560 C. LORTIE & BrO. 21 Shipped per BngVaudreuil, consigned to Messrs. Mitchell & Hudon, Que-jec, to be sold on joint % of E. Gary & Son, Rnd themselves, each ^, viz.: — 36 bbis,, 1441 lbs. Plums, ^ $ .08 $ 115.28 90 '♦ Green Apples, '' 3.60 324.00 176 " Gray •' " 4.12 721.00 Montreal, M>iy 14, 1871. $1160.28 Q. QuiNN k Co. M B 12581 9v L. MJ mmmm,,. *■■■ •"- VS._1, 12081 9v M. SALES BOOK,— SET in, Quebec. iMay 4 1871. QuZ''Sa''n7r K'n"'"'^' ''■''PP^'^ P^'- Steamboat MontSl^rf U u"'' "°^»'"»«'' to G. S. Walls, aionireai, to be sold on our %, viz. : 3 bbls., 620 lus., Lard, /5)$.10 '='' Apples, <« 3 5Q 20 bags, 2800 ibs., Coffee, •' .'is —Charges. $ 62.00 91.00 420.00 $573.00 M.4H.I Drayage, Mitchell & Hudon Quebec, May 4, 1871. — ■ iO 2.00 676 L. D. A Co. M.4H, Invoice of M.rchand.se sent per Grand Trunk Li2 ,v, • ^^''^'g"^'! '0 L. Douglas & Co., pi,r ^^ S t^lheir order of the 4th inst" and for thS7%, 6? '^' Extra's"' """"n '^ * -16 $ 262.40 22 bags 3088 JIv'^'pT ^''"'" '' ^'"^ '^-^^O-OO oags, dU8S Ib:^., Cotiee, '« .20 _G17.60 -Charges. .^ Paid foi Drayage, $ ,^^ Insurance, roi 2% pre- niiuni on §1245, "^ 24 90 Our Coi«in,8. for Ins. an J Exped._2A8 ,S2.68 $1240.00 Quebws, May 10, 1871. MiTCHKI.L & HCDON. $1 61 II i " 1^ '; I i: - SALES BOOK,— SET HI. QiiRBicc, May 19, 1871. Invoice of Merchandise shipped per Steamer dirtier, Capt. Roy, and coni?igiied to M. Blanchct & Co., Pictou, to lie sold on joint %, each i. Z9 e.AG. 40 bbls., 1200 gals. Coal Oil, fa) $ .60 $720.00 20 " 560 " Linseed Oi>" 1.00 660.00 $1280 9 00 Chnrgps. Paid for Dray age, $2.76 " »• Ineurance /a ^ijif on $1290 6.45 20 $1289 •20 s MiTCHfcLL & HdDON. Quebeo, May 19, 1871. B. B. biTOicK of Merchandise per Brig St. Maurice, consigned to J. N. Carbray, Three Rivers, to be sold on our % and risk. J.N.C. 40 sacks, 160 bu. Red Wheat, rd) $.90 $144.00 90 " 360 " Oats, ' '' .45 162.00 $ 306 00 Charges. Paid for Drayage, etc., Mitchell & Hcdon. 4 50 $ 310 5t Quebec, May 22, 1871. 1 B. E. FW*"*- 1% mier cbot 0.00 0.00 $1280 00 2.75 6.45 9 20 • $1289 20 nslsneiJ to J. N. and risk. I o o pq CO o M GQ o a <0 o O O 4J A ^ ui ."2 43 o * fL K ! 'f ^ vt i o o o o •h Ma 5.0 0.0 5.0 o o ^ j>e^ oo CO »t (C >» Or! 0 Tf — O — -— 1 •* lO — . CJ Cv| 1— » cc t €^ ^ m C. sold each 2 to rges. gain. CO w C4 "0 ^ K ^ £ O ^ 2i n »ndered May 'a net procee ay 29, 1871. -< H o . o Account Sales n C. Lortie & Bro. 767.25. Due M E. E. O ,. ^ > « V. m «o <. en ^ ^ ^ — " N ^ - - I S* 3 3 3 3 3 72 '^-^'"•^Aj&kiiUWi^MH cc 03 C4 Ol ^ l>H o L3 03 r/1 •«Q r! • ^ ^ W5 ^ «o ^o?: ^ I: *i- ; I B ti <-j. 4> u X JS « -"• Q ffQ oj ,^ 62' 2 >• £ £ o; O a; i •— o8(/} o o o o or 'o > aj3 m = !:! ^-5 So > 00 C — I a '3 oj <" ir tc a . "^j-r-go '» 33 ,_, !r /','- — >• », Q CM -- " ^^W OJ a. I 00 O 3 03 Ci 1^ >ii;rf3 ■«! re !00 «j ;a >* T*< O »ft 00 o o c^ -*< ^ ^"^ 09 •^ S S-. T* «i a, b ,^ ®rJ ea |5 nt 00 S=l ' 78 II : the 7b r •@ 2 «e X'^WS'' as RECEIPTS, NOTES, DRAFTS, &o. UECBI1»TS. (Prom traiMuotion of Jm. 31, p. 8.) Quebec, .Tiinnary 31, 1871. :^::i°'l'±± """' ''l"'V Dollar., in full f„r o„e ,„o„th'. rent of Store, up to date. E. R. T HI' DEL, $250. ^ (Frwn trangaotlon of Feb. 18, p. 9.) Quebec, Fel-uary H, 1871. thisdav e neither more nor less than the transcript of a man's thoughts, or what he vvoulil say were he to speak with care and deliberation. As no ( o men ever think or talk exacU*- «like, so vo two men oorild be expected to vnrrte alike. 78 LETTER BOOK, — SET III, ttoa Rorogs tko idvo signed. May 2fl, p. 63.) V 26, 1871. ■ji' Mitchell A 1, and charge Urbrat. lie 2, 1871. of exchange r to the order pence, value "vant, 1T0HB1.L. I bweiness let- Hut letters actions c^Set n their way. letter, that ia, i would for an )uld consider 1 aocontplish- igh niuch Hid igenient, and Individ uwity; less than the 'e he to speak r talk exacU** There are, in bueinese letters, certain qualifications which are equally essential to all, and with reference to which, general instruc- tions may he given. We will enumerate a few of these points:— let Like all other documents in manuscript, a business letter should be, chiroirraphically, well written, so as to commend itself at once to the reader. Ne^itness and legibility are the chief requisites in a hand- writing. 2nd The grammatical construction should be faultless; and, above all, nodocument should be disfigured with misspelled words. 3rd The subject matter should be immediately apparent, stated with- out circumlocution, and in terms not to be misconstrued. A business document should be written in brief terms, and yet explicitly. There is no qualification which will more surely commend yowig men to the favor of an employer than proficiency in Business Corres- pondence. (Circular.) QvvAu c, May 1, 1871. G. S. Walh, Esq., Montreal. Sir:— We, the subscribers, respectfully announce to you that we have formed a copartnership under the firm of Mitchem. & Hitdon, for the prosecution of a wholesale Grocery, Wine Business, and General Commission. We take the liberty of assuring you that all business intrusted to our care, shall receive from us, personally, prompt and faithful attention ; in a word, that we will correspond to the coa- fidenoe placed in us. Very respectfully, Your obedient servants, Mitchell & Hcdomt. Messrs. Mitchell 6f Hudon, (Quebec. MoNTRKAL, May 2, 1871. Gbntlemen :— In reply to your circular of tlie 1st inst., I beg leave to solicit the favor of your patronage fur a general commission business, and pledge myself for the strict <lvice. We find it conformable to the Invoice, amounting to $1018.25, which we hvve placed to the credit of your %. We beg leave to assure you that we will pay all possible attention to your orders. Offering you our sincerest thanks, we remain, Your obedient servants, * Mitchell k Huoom. Messrs. D. C. Peachy dj- Son, Qumeo, May 7, 1871. Montreal. Gents : — We are in receipt of the goods you consigned to ue, pursuant to our order of 3rd inst., and of wliich you gave advice by your favor of oth inst. Save a few barrels of Herrings whose quality appears to us inferior, the rest is satisfactory. Your account is credited for the amount of Invoice, $1649.60. Very respectfully yours, Mitchell & E0OON. Messrs. L. Douglas 'e:,i;'s'; wis r^Lre-t it'^f Your obedient servant, G. S. Walls. QuEBjcc, May 19, 1871. Messrs. M. Blanchei ^ Co., Pictou. l.H.e debited ^ .oK'rhe'rtl"; UUif" "" """' *• ^' y«ur outtulile 8ervant«, MiTCHELL &, Hrdon. 1 [ bCYSDR BOOK, — 8BV IH. Mtsart. Aikcheit d^ Hudon. ' Quebec. Montreal, Ms^ 14, 1871, Gents : — We acaept witli pleasure your proposition t© j«iii in a Company Speowlatio«. We, accordingly, ship you, per Schooner Vautireuil, wliich is to saU to morrow, Mercliandise, as per enclofeed Invoice, to be sola in joint account with yourselves, B. Oary Jc Son, and ou/seives, eaeh one tliird. We kave debirca you ft: 4 of Invoice. Witching you c«Mi|»lete success in the salea of them, we beg t« subscribe ourselves, Very truly yours, G. Qdinn & Co. J. N. Corbray. I'jSq.y Three Rivera. Quebec, May 22. 1871. Sir : — Youss of the 16th inst. is at hand. Your proposiUoae are gratefully accepteii. In accordance ilierewith, we phip you per Schooner St. Maurice, 40 bag? lied Wheat, and 90 itags Oats, as per eneloHcd Invoice, amoniifelflg to $810.50, which we consign to you to be Bold on our % and rif S; Meisrs. C. Lortie Sr Bro., Hclifax. QoEBEr, May 23, 1871. Genti.bmkn: — We send you enclosed. Account Sales of the Merchandise forwarded on 7th inst. We have been quite successful in the sales of tliww, and we are of opinion, from actual appearances, that the good jwarket s^Jiall continue for sometime. If you think advisable to risk a new conf^ignment, we shall be happy to join you in it, or to sell for you on Conmiission. Very reepectftillf, Mitchell k HuDoir. Pi«*oi!, May 23, 1871. Ms»srs. MUdiell S( Hudon, Quebec. Gkvts: — E-nclosed, please find Account Sales of the Mer- tshandine y«u shipped us on the 19th inst. Your aei proweds i« 92 »y U, 1871, )SJtion t» j«in in ju, per Schooner as per enclofeed E. Cary it Sod, them, we beg U X3, DINK & Co. May 22. 1871. 'oiur proposiUoM we phip you per nags Oats, as per 9 consign to you remain, sir, fully, L & HUDON. May 23, 1871. )unt Sales of the II quite succesHful tnal appearances, e. If you think appy to join you IV, L & HcDoir. May 23, 1871. ilea of the Mer- r Bfli proseeds is r-KT-fFB boor:.— SBT in. ToaIu \VV."^*': '•'""' ^^'''"*'''" '^' ^he sale of the like goods. Please iivil u'JR^r •'"'" ^'?f",^'" ^'" ^^^ reasonable amount. F lease au vi.se u,- thereupon, and believe us, TjTjly yours, M. Blanchet & Co. *HREE Rivers, May 24, 1871. i^ssps. Mitchell ^ Hudon, Quebec. but vonr p"' '"■'" ^'''''' *^" ^'"^ -''^ '•-'«^- ^'he car.o war avo " proceX ' *"^^^»^<='^' 0" National Bank for |I15; ae n. Yours respectfully J. N. Cakbray. QrEBKc, May 26, 1871. •. A'. Carhray, Esq., TfiTHj Rivers. b^gof J;.?c;r„/roe?r£LT ""'"■""•« *'' '"'' -^ Bel,e« us «er disposed to hoDor you .ill, our c.nfl,lence, Truly yours, Mitchell «fc Hrnox. Quebec, May 28, 1871. Messrs. G. Quinn (f- Co., Montreal. .oieeo^s^^n::it'°'^^^*°^^''' ^^^^""^ ^^'- «^^-- ^n- Hop ing you will fipd iJ.e reH4,!t satisfeetc eciuibe ourfielves, Gentlemen we b •eg to sub Very fcr uly youBs, I I sit 88 iMMiiMUHil .M^^^... Pi lCTIOAL EXERCIH18, — SET III. Messrs. L. DougUts ^ Co., Qckbkc, May 30, 1871. Toronto. Gknt3 : — We are in receipt of v'uir favor of the 27th insi., oontainihg a draft at sixty days oi» A. Siiii.ns & Devaiix, Tjoad(jii, foi $1272.6H, which is placed to your credit. Please accept, Gentlemen, the pinctre thanks of Your obedient pervants MlVtHEI.l, & ili DON. Meaarif. D. C Peachy ^ Son, Montrt'i-L. QuEBKC, May 31, 1871 Gents :--Enclosed, yon wir find a Dalt at eight days' pi^jht on N. Caron for ^'260, tor which cou vvill plea.se to credit us. We Lave the honor, Qeia.s^Meii, to remain, YoiivK gratefully, Mll'CHELb & HUUON.. t I M']\ Efi MfiMORANDUM I. June 1, We, Mitchell & Hudon, continue our business w*h the Re^-oiirces and Liabilities taken from our Balance Sheet p. 66. — SS. Receiv'ed advice ffom Douglas & Co., Toronto, that they have pur- chased, as per agreerwent, KO bbls. Extra Flour, to be sold on our joint %, ( ich i, and that they have debited us for ^ the cost price which, as per bill, amounts to $585. — 3. Shipped per Brig St. Hu bert, and consigned to S. McManus, St. Johns, Newfoundland, to be sold on our % and risk, produce, (S. B.) amtg. to $1864. Passed our note No. 3, at 6 mos., to the North Insurance Co., for ins. on !?2010, at 14 %, and paid m cash tor Policy, $1.25. — Rec'd per Grand Trunk R. R., frorn L. Dion, Montreal, Bordeaux Wines (I. B.) amounting to $120 ; and accepted his draft oa us, favor Jones & Co., at 20 days' eight, for the amt. of invoice,— 4. Gave Merchandise (S. B.) in pay- ment of an order from P. Allard, tor $369.20. — Exchanged eur note No. 6 with E. Gary & Son's, for our mutual accommodation, each drawn at 30 days, for $320 ; discounted theirs at the National Bank, and rec'd in cash, $318.24. Discount was taken for 33 days, at 6 %. —5. Bo't on joint acct. with G. S. Walls, each ^, 5000 lbs. Chocolate, at 25 cts. We are to receive 5 % c»tnmisslon on the sale. Paid in cash for our half, $625. — 6. Rec'ii of S. Lewis, in payment of Ins I for tIOOO, due this day, Merchandi.se (L B.) utnlg. to $500, XT_ UULC i.1IU and cash fo" the bal. — T. Rec'd pf"* Hrig Culumbia, Capt. Riif^se.!^ fc-om C. A. Mtlson, Limewck, pm^i- nt to our order and for ol • ?-! Mdse. (1. R.) due in Liaierick on . . let next, amounting to i JO, Gave our bonds to th« Ctutom-house for duties, at 3 and 6 moM., ?? 84 May 30, 1871. jf the 27th inst., iiix, LoadiJii, foi of infs & tl! DON. VRAGTrnAL RXERCI8EH,— SF.T HI. ^l t40 ; jni.J Freight in eash, $74. RecM at tl mu,e]:r:,f Columhia from C. A. Mol an>t. .¥;!(■:>, to be 8oM on h le f-'amn rinip bv the C'listo son, 50 ca«k-s Sicily Wine (L V,.) F. (C Laru S. B '1 : hou.se foKlnties at l^ IS % and risk. G av(.' our bond- (o the months, for 8160r,.40; paid Frei^'l :.7()— « «!,i,i v'j, ■■"" ^\ ."" '-^'a""-*"; paid l'reit,'ht m vhe 5 '^^sh q •, T' "'" •';^""^*' ^^ 2 n.o.., endorsed by Xli ilay 31, 187!. It days' pi^jUt on t us. HUUON.. upiness w*h the beet p. 66.-2. '. they have pur- be sold on our ^ the cost price per Brig St. Hu foundland, to be 34. Passed our ir ins. on .*2040, er Grand Trunk !.) amounting to Co., at 20 days' ! (S. B.) in pay- lianged (jur note inodation, each National Bank, 33 daye, at 6 %. lbs. Chocolate, e sale. Paid in payment of his .) atiug. to,f500, , Capt. Ri'iJse.l, ' and for ot ■ % , mting to f JO. and 6 mo*., 'b? ''S. B.) iuuUr to «2^« 7^ o I T "^"-^ ^vicrciianiiise Ironi our Store . "•■'.•"'"«• lo ^^i)«.75, and an Invoice of Oaf ^ /T «: n \ i^?* /> O. Mane 1 wmir;;, '■'',".""• *'2(i ; an.l ca-l, lor ti.e b»I.-I3. .l.eh- drnli;™ Upai 1 Ga ',, "f r iir,';!;'" n "■■"■• '"■ ''?-''"''"" °' we ii.ive g.ien our ncceptance, at 40 days, due J.xpc.MM for loading, etc., aint. CoSloli. -Our July 2(i, fur .'^.OOiid. cou.nmsion is $77.33 -1 J rJ „t „ ^^' ^"'■\''.'"'- ^o !?lo(,. • Our Bradv each ' Ml V .t ,"> x ^'^^*"*^^"^'"' ''" J^'"t»<^connt with P. ui^i)' f ,t 1)^' 1 '*■ ^^' ^^•>' ^'"'S- to §«)700. Our A purchase in Co -i i pIh r? f"' "'"■ ''«<=^P^^^"«<^ at ;;0 days, iJovclmut & dt th^' •lav.-lT'B^ro'H'e.riv^- ^^'^ ^I-^^^Cord. for$.foo* ainfinn „i • i •? ' Healy & Cameron, the Bri'^ MaWa f.r Bla:2h;;i'?^.:^'^|?^S;^l!:^-= -- draaat 30 days' ^iJJ'S M^ on National B^nk for the^.fl-^i « "t" f ' 'r ^'^^-i^ ^"'1 ""'"^'"^^'^ S. White .t f\. n. ; ^'^'-—IS- Sent per Grand Trunk R. R., to C A M'« r ^'''^' P"'-''"^"^ to .«heir order, Mdse. (C. S. B.) of No. 2, in their fUvor fi ^ m% ^n t { n '" '^ '" P^^^ ment, our note al -Itt vl^U n■{I^ f '^^'-^.-^.-^O^ and their note at 40 days, for the lrPn^\fL j^' for .repairing Brig Maria, ^33.10.-30. ShioDed n '^ ot 'hh?, .?f R^'h''^ 1° ''•.^- '^^^^^-^^ Limerick"to beS »n .1 ic /c of himsclt, H. Brook, ami ourselves e'loh ' ' - " h-om x\ld.se. Co. E -.^^ - ^ —- ■ .- • ,'. ':''.'^" 3 bal per on J Suifa. etc.. .$20.60 amt at 2 u)o.a . o.o-> ,. o. lOT. Wi.ite to .VtS.;0. Paid casl, fur loading, , lorin.s. on .i;.JOOO, at ^ %. Our com>ni,s.sion on^^iS? ) 6' at " ^j^ .^MVai' "" •'"""•''. ''^ ^ %• Our at ' <^ ;. «iVrn w I -. .^ ^^^;onrcommssonlbriiis at , %. 1^ * 1 2.;.0. We charged for the Frei-ht hv onr Bri.^ M-rh '"^i' H. hruuk-.s ^ i« ;>] 703.285- ; C. A. Moi^^on^ I '^iliVi }li^5 ' $1703.2S|.J!2i. I„,ured%'ur Bri^l^i^ "S in th! G U f *' """^ ''A""'' ii:e'Fiti-b;^5t i^tr otr 2^,^ i/^;:^!;; .?^"t: thr amounting to *^97.7'J. Our i i««jj.n hT „ ] •' '^ ** ' t'le proceeds o *> ^i.< ;. uur i 18^448,85, and our net gain, $156.35. i 9: ■'; i' I i ' ! I ! I ( • j i j ( f 1 m\ 1 1 i^' PRAOTICAI- EXERCISES, — SET III. —34. Rec'd of S. .McManu^, St. .Tohnp, Newfoundland, Acaount Sales of the Mrlse. consi.stncil to Ihiin by Brig St. Hubert. Not pro- ceeds anit,2. to $2120, Reo'd in payment an Invoice of Fish (1. B.), anitg. to §2120. Paid for l-'rei^ht. and other expenpes, in caah, Sfil .34, Clo-ed our Invoice to St. John'p witli a .cain of $229.25.-35. P;iid casli for our accpptance of L. Dion's draft, favor of Jones —38. Rec'd from C. Lortie & Bro., Halifax, Account Sales of the Mdse, shipped them from C. A. Molson's Con- pjgnment. Net proceeds, $2962 for which wo rec'd their draft, at 60 (lavs, on Hamel &, ]?ros., which was accepted. — Taken to our %, at 2 mo.s., the remaining 10 casks, of C. A. Molson's Consignment, at ?I28. Closed C. A. Molson's Consignment, and rendered him an Account Sales of the same. Tlie expenses for Duty, etc., to this day, amt. to $1725.85. Our Commission on Sales, at 5 i^, is $354.10 ; Storage and Advertising, §12. Net proceeds due C. A. Molson, on , $4990.05.-30, Rec'd from C. Lortie & Bro. an Account iales of our shipment of the 10th lust. Lj Brig Victoria. Net proceeda, $843. Rec'd also a draft from them, at 10 days' sight on Garneau & Co. Pail carfi for clerk hire and other expenses, $104.75. BALANCE ACCOUNT, JUNE 30. BE30TTRCE8. 1 70 LlABU.lTIES. '• Rills Receivable. $ 4415 Rills Payable. $13266 90 Cash. 14185 58 G. S. Walls. 192 80 National Bank. 1210 00 D. C. Peachy & Son. 16 10 Merchandise. 12000 00 C. Lortie & Bro. 5359 25 P. Allurd. 569 20 E. Carv & Son. 405 46 A. Rill fret. 300 00 1 G. Quinn & Co. 792 22 M. Blanchet & Co. 55 20 C. A. Molson. 4886 K\ L. Douglas & Co. 156 35 G. Morin. 180 00 N. S. Robertson. 5233 C. S. MitcheU. 13500 97i H. Brook. 1703 m R. A. Hudon. 13531 474 Brig Mctria. 1 0000 no Sh'pt to Limerick. 1703 J. Merault. 600 00 ■ 1 .•P52131 931 $62131 93| 86 Klland, Acaonnt nbert. Net pro > of Fish (I. B.X in cash. .?fi 1.34. '.25.-35. Piiid Jones Si To., for 3m Mil p. Co. D, )ld R. Wood.", on Co. P., at 40 eta. ^alls an Account ing. etc., $2'!. 60 ; t gain, $218.20. & Bro., Halifax, \.. Molson's Con- their draft, at 60 ken to our %, at Consignment, at rendered him an etc., to this day, 5^, is!?3r)4.10; !. A. Moleon, on 3ro. an Account 1. Net proceeds, [it on Garneau & 04.75. — ■» $13266 90 192 80 Son. 16 10 5359 25 405 46 792 22 48H6 7(;j 180 00 13500 97i 13531 47i $62131 931 praotioa: exercises,— set m. MEMORANDUM II. panSip'^I ^^:^l^;,^T^^ir 'f/ -»-- -to CO h^'l L.Moore's invc«tme„r i . u T 'T^^ mve-.tmont is on Bo't of F. Belmonrhi "SI fote 5^" T " "^^'-'^ ^'''"'^•-»- niortga^.eonf]iepronert.for$%Too S r /" 'i^-X'"^"'' ^^^'^'Hned to date «12(^ ; pa^l Jasl >o the barV^^ t r' 'f '^^ "" '^''^'IP''^ on %, 10 hhds; Surrar 1 rAn il * *«l-''t.— Bo t oi Fremont & Co. .S.3^30; 15000 l«/e ,i'it'' ^fc «-lia'rca'l'%^''" '''''' f* work and painting, $1 12 ".O -i Ro^' . J ^^ ' ^^"^ carpenter's Toronto, to be sold on o, r"7(ifnt ^/ ':^ ^'T '^^""'"- * S°". Extra Flour, at $6; l.?o ml pt/v l""^ P'J^^ ''''^' ^' ''"" ''b's' same, in cash, ^t^O.-Re^ iro^;?^ i^^ ' Pi^''' '"'•^'■ghl o. 300 bbls. Extra PIm r ?i^i^ o . *"'^' "" ^"'^ "'^^e at ,".0 days. Pork, (Mdse Co A.' 'at iTs'^lciosn'^ "' ^'■'' ' \'' ^'''- l'^^"' & Son, and renderp/j .'^*'^— Closed company sales with Bennir,^ for Storage n;Stnr«l?.T""-"^'^%^"T ^" «''^^4 « our ^ net 2ain S '?"^R ' Conimission 2^ ^ on sales $ . . company with J. Arnold A Tim if; '* '''^•35.— Closed sales in Acciunt Sa'es. Our chat e/ for ^^'"S'^**^"' ^"'1 /f "d.ered tiien, an himself P T? nL i ' ^ ,'^' , ^^^' ^o be so d on joint ^ nt SSruLV;, pS^'tTl''. ™ cTlr^ '"■"'.'' ^' per oon,?4' p^ "& e s a net gain, ;j;510 : P. E. O- . v' o«rCo,nm,...,;.24<«o„.lles,?;i75.0^j:n gam $5 -ir.. Sold W. J. Lyo, h, for clsh i&n',K^ <>*— !«• Bo't of Jorda.' '^'^'' ^ 30000 lbs., at 9 cte. • p^jd in cash vs 4 net .rain. *519: our J net Ian & Sewell, 30 J.hds. B hhds. Su'-ar, 11250 'rown Sugar, 11200; bah on i:i,S.S I I! > PBAOTIOAL RXBROIBIS, m. cai?h as follows : for wlt-ek hire to ^., $225.-30. H.A. (Jliakners 15tV \x\nU, $T6 ; t* L. Moore, •n < ■** 3 it ' , di«ooui)tetl hie note 111 our favor, du. July 12th ; proct'eds «i'tLc lote *149fi.68 ; (MecouiU off, for 22 ilayn. ^ti.'H).— RecM of '• ArnoH k Bro., an Aocount SaleH of rt»e Mdse. t^3()0.— Paid J. .'v.lu •; bi>>'H (h -t on us, favor of C. RukpoII, per check on Quebec Bank, for $1453. 12.— 28. Rec'd cash fur rent of part ol our Store ■^«2;7(). Per statement rendered this dav, our share of earnings of lust trip of Steamboat Eupopa, ai.its. to *.H75.— 29. Paid cash for sundry espenees to date, 38.50.— 30. Ro'd from P. E. Onslow, Accouut Sales of the Sugar shipped him on the '.'2nd met. Our ^ net loss, 3172^50. P. Beknont has h= i day inve^aed in the firm, irn cash, $40o,n.35.— July 1st. Rc3 d irom C. R. Kerney, Halifax to be sold on hi*i and ■ ui- joint ^, «ach i, 150 bbls. Mackerel, invoiced at $7 : 40 bbls. Ilepnngrt, invoiced at ^'4.50 ; 75 bbls. Lini-e«d Oil, invoiced at $40 ; puid Freight per check on Quebec Bank, $75. Deposited cash in the Qnebto Bank, $1-2750.— 2. Shipped P. Gilmonr & Co., St. John, N, B., to be sold on our joint %, each ^, 200 b.ls. Thin Mess, at $*.S.5b; paid Dravage, i'n cash, $27.-3. Sold R. S. Venner, for cash, 150 bbls. Mackerel, (Mdse. €o. D.,) at 87.50. »> Effected iti- .-urance for $750(», at | f^' on any property that may be in our warehouse, $50.25.— 4. Shijped J. O'Regan & Co., Montreal, as per t^ieir order, at 60 days, the folIowingMerchandi.se; 75 bbls. Linseed Oil. (Mdse. Co. D.,) at $45 ; 40 bbls. Herring.s, ^Md.^e. Co. D.,) at $4.50.~Closed Mdse. Co. D., and rendered C. R. KerH( m Account Sales of the same. Our charges for Storage, Adv- rtising & Insurance, $15 ; our Commi.ssion, 2^ % on Sales $ C. R. Kerney for his .i Invoice, $2115. and net gain, $? ;.50. Our ^ net gain, i^ —5. Paid by check Quel Ma,«s(»n & V)., Sandwich, to be sold on theirs and our joint acct., e&ih i, 500 bbls. Prime Porft. at $13.50 ; 250 bbls. Lard, 50000 lbs., at 7^ cts. ; paid Freight per check on Quebec Bank, $750.- '..>. Sold J. N. Miles. Quebec, 150 hhds. Brown Sugar, (M'^' e. Co- K.,) ai *;f6. R"c'd in payment, J. Mountain & Go's, note, ad ' irch 3, 1871, due one d.iy after da'e, for $7500 ; due to dat- i Sfc note $lS5.'i0 ; and cash for balance— Close Effected in- niay be in our >., Montreal, as ndise ; 75 bbls. ngs, #lMd>e. Co. J. R. Kerm. an ;, Adv. rtising & y $ 0. R. .50. Our ^ net vertising bills of foly, Hamilton, and ourselves, )aid Freight per Map'-c'ti & Mj., ftih i, 500 bbls. bs., at 7^ cts. ; *». Sold J. N. o. K.,) at $15. \*arch 3, 1871, note$l«o.20; videred Kane & !. Our char>?;es n "i.j 96 on sales, ler's, $3381.25; i' note, due taia ik. $6000.— l* PRACTICAL EXBR0r8E8.^„ ,„. •flltOO ()7 ^- * • *' '^'^ Jays sicht fL J, •''^ Sold our draft q,^ ;-"i^red li. Et-„ l\^-'l^\ '• cts.-Closeci AmS '^^ «¥''' ''." t>'ir cliarL'es fl.rQ* ' ^*"J'^'«h, an Account «ii ?',*^-' '^^'i fi;? o„X,f "B%i«n^««' etc.T7^'/'tr Cof """" $li)50utJi'n ^*-^'» ^^"^ i'- I. Nolan's n.?*''V''! *""'' ^^ «cot- ^!:^^^C'W^'^^^ ^^^"O^t^i^ bbls S£ McGinn I- • Kernel's note on , « .,? ™ P/""""*'" »1200._3e S" f: ."""i?,"" ''■■", ».wi..-8y''S ,"«'"■ '»'"'°'^" amr. changed to . '.l^^^' ^""'""^ '-^ I•^ "hn^rf '! ^cfV^ '^^''''^" * '1^- a..:t. cC4a to 'T'^ ^'"^*- P^^^^'i o St k ace? rrir *^« JNVE ,RY, JULY 31. Store, valued /© r!f "»bo^^ Europa Stock fntfrest due us , n V...„ . fn 7 J '^"ropa stoc i &t;,il- -\^ote. I21..95 , -1.37 { 21. REsoaRCfis, i^ess, interest due from us BALANCE ACCOUNT, JULY 31 $22500 15000. 00 00 192.68 Real Estate. Cash. QMeb, c Bank. Bill? Heceivable. Interest Receivable. Sieaiub Europa c,--i- gtearnboat Europa. f. (xiknour & Co. LuBir.iTifcs. Mortgage Payable. Bills i'ajable. interest Payable. J. D. Roe. I*. E. Onslovv. Kane & Joly." A. C. Miller. E. Belmont. L. Aloore. I 6750 11>17I 21 8010 00 50 37 00 2932 ,> a 1 1 . I i ! i SET TV. JOBBFNG AND IMPORTING BUSINESS, EMBRACING AS PIUNCIPAL BOOKS, CASH BOOT{. DOMESTIC AND FOREIGN INVOICE BOOK;>, SALES BOOK AND JOURNAL; AND AS ATTX1UARIB8, INVENTORY BOOK AND BILL BOOK. WITH A ROI'TINE TAKBX FitOM AN EXTENSIVE BUSINESS HOCSS. 1,1- ' 3i? , Remarks. — Thr partionlir feature of this set consists in the manner uiid form of original ontrios, wliich are made in separate books, — cNcwhero used as ;iuxiliarie3, — from which they are either jonrnilizftd, or passed directly to the Ledger at stated pe- riods. Tiiis method has many advantages over consecutive en- trios ill the Day Book, an'], in one form or other, is adopted gene- rally in till largo establi>hiiients. The labors of the Book-keeper are thu.-; divided up, and the separate departments of the business receive such special record as to present all the facts in their clearest light. Thus, if any particular information is desired res- pecting purch.ises, all the facts can be found at once in the In- voice Book; in the sime manner, the facts and condition of the sales can be found in the Sales Book; the receipts ;ind disburse- ments of casli, in the Cash Book, etc. In thi' previous sets, those books are represented ; but they are used only as auxiliaries, the entries of the business being made in the other books without reference to them. This plan, it will be evident, although possessing some merits, involves a large amouiA of unnecessary labor, whieh v.ould prove a great objection in ex- tensive houses. The special l.onks themselves, however, are so essential in evtry well-regulateil h;,isiness, that they would receive favor, even at the expense of this additional labor. If, t refore, K^as HOVSK. '«;;r-un> their adaption. ^■'^^''^'- ■'''•g^'ncnt woi.l.] b. „oe,lo,T AW sales and Durchases .o/lTrt ' ^ *^'''.""'''''''^''^ ''"-'•^"or *° ^'^ ^^^'^-r J «'l others, iZkoLAS:^ '"'" *'^"« ^-'''^« ROUTINE FOR AUGUST ]87I NOTB Tosctthpfnl I and reduction of curronnil. u-^" '"*'"'«o '''ook, involt n,, ^ '""'^'<-''f- T'"' fended with the inv "ice b .^ "'^''""««. which beirur ,.a rJ n"* u ° '"'^•'' "'■" 'sporting houses thn H^lr '""^''"^ ''"""» tlio Ca^li hIoI ,''"'''• "^^' ""' ''x- tbe CashVk ' "'"'^"'"'^ '^^« "ote.tend.u in tht {, voice '^f^T' '" '"■"'v °"" "^'^1*. but only in Cooic copled-Cash' ^7''' "'^ P^-* ^^^ -Journal entrv .T fee ved per Sto,„„ ke" oSau LT^*;,?^*' C- B.-B ij jiiV I JOBBING AND IMPORTING BUSINESS. $15.60, (C. B.— B. B.)— 20. Sold Stein & Co., St. Mary, P. Q., oc their note, at months, Invoice of Prints, $1425.48, CS. B.— B. B.^ Paid T. J. Colston on private acot., $100, (C. B.)— SI. Sold Mdse. for cash, per Petty Caool, Invoice of Goods, $188.62. Paid duties in cash, $2«.29, (For. I. B. — C. B.) . . .Bought of Bell & Archer, on our note at 6 months, Invoice of Cloths, $1926.14, (Dom. I. B.-B. B.V . . .SoldN. B. Roy, Levis, for cash, Mdse., $923.40, (S. B.— C. B.)— 23. Sold Mdse. aa per Pettv Cash Book, $1S0, (C. B.)— 25. Sold E. Curran, Richmond, for cash^ Invoice of Gloves, $460.75, (S. B.— C. B.) . . Paid Postage, Porterage, etc., in cash, $12, (C. B.)— 27. ^old Lee & Strang, To- ronto. on their note at 8 mos., Invoice of Mixtures, $3303.71, (S. B. B. B.) — 28. Sold T. Hoss & Co., King.^ton, on 8 months note, Invoice of Goods, $578.52, rS. B.— B. B.)--30. Sold A. R. Jacob, Batiscan, o« note at 3*months, Invoice of Goods, $100, (S. B.— B. B..) ' Sold Mdse. per Petty Cash Book, $125, (C. B.) ...pAiJcasb in full of Drayage acct., $20.75, (C. D.) 98 BOMISTIO revoiOE BOOK. WMESTIC INVOICE BO0K.._SKT IV. This book contains copies of .,11 ; • chased from importers anrotSers „ nr"'' ^^ "^^^chandise par t'ons of all such purchase. fZI .*'"', "^""^^3^' ^^^th the condi- by sorue peculiar marL which Ts "f ^'f'"' '"« distin.uisred ^^''v.n. an important purpo e in ch i!^'"''! '' '^' ^^^'^^^ 17c. 239.9(5 ^K' '* " " 13892 " 18 250.11 36 « J5rowii " 14153 <' 25 353.88 42 '< W. li. Diaper, 21691 " 7^ 162.69 Note at G inos. from Aug. 10. .^ II N. Casey & Bro. (8 months.) 750 751 753 754 CM. K. A. Vj. a. D. C. E. N. EG. 381)2 5788 6202 4187 5630 5685 4 cases 4.4 Bleached Shirting, 40 17322 40 1736 40 1755 40 17312 6955 yds. at 9i ots. Note at 8 months from Aug. 11. 26 L. Power &. Co., 52Print8,973 1858 52 1)65 1834 53 " 967 1895* 5587 Vd.® 8c. 446.98 51 " 972 1924« 49 " 968 19542 49 " 971 1920 5808 yd. /®8ic. 49.3. 6S Discount off 6^ 940.66 47.0;i C. B. 893.63 Purchases on time (taken to Ledger), Cash jjurcba6es (entered iroiu C. B.), Total for the month, 1303 76 893 1006 64 660 73 63 1667 2197 .3864 :;7 39 76 9* ET IV. 303 76 1006 64 660 73 393 63 1667 21 DT 3864 :!7 76 DOMESTIC INVOICE BOOE,_SET IV. QUKBEC, SEPTf-MBKR 20, 1871. Beij. & Archer, i( (6 nionthe.) I88?!.M ""«'";: °"™"=. I «»' 1178a 1137 1094« 11513 1268 1J68 1279» 12618 }906|.0Sebastopol Checks, 11 683 12452 = 14191 vda. ^I'Hg. $1915.78 3.00 189630 1915)28 190.3 o'O a 1737 .3 World's Pah-, I77o.i0 it 1823 33 a 1834 33 1845 30 « Cooperage Note at 6 mo-nths. To.al^„,3se for ae„„. (taken .0 t. ■ I B t a O B =: I :: <» (M B o g to B o "» OS o 3 I! o O PQ «tj CO CV5 "C o> CO «o O iO I rr, »o 00 ffo o -* 00 I— 4 c 02 CC OC n CO o o OS CO C^ C^ r-l VO 1—1 ^ QD cc m '^ 9^ Cfi (^ ^ '^ "^ <^ en u a, > o u •13 @ o ai" so o w «o «o 00 OD ^j t^ IK a? (« oi o m c^ — e^ 'M CO >0 O to r-C -^ C^ @ a s ^ 1 s — ^ s^^ o a^ ^ "" •z; - - - ^ - to 4> 00 Ol S 1 2 H « V. •* s* o - ■» -B H« tn o oi eft •a m cS" o '|'"o eo «o 1 :: 1-^^ 1 F-l -E «■ 8: ^ «> ■a ts e « w s ^ o m aa s » 00 —I -H ^O ■ «-. 5^ .^ • ■c ■■« ^-^ J* «o r 2 ^S 0/ « " "o r KlO 2i W) M t: jn t, gpH ^ go — u K 9J I) ai A £ «s J o ee «; '■■if 8ALM BOOK. SALBS BOOK. This book contains all the reo;ular pales, either for cash or on time ; tiie cash sales beinsj extended in the inner column, are, of course, not included in the amount for which merchandise is cred- ited from the Sales Book. These sales, to<■■ y sales not entered on the Sales Book, are posted from the Cash Bo<)k. The total credit of the merchandise account for the month will agree, in amount, with the monthly leeapitulation in the Sales Book. Quebec, August 1, 1871. R. F. p. AOe. 192 1289 71 46 46 1 € 68 100 101 L. Beacdry, St. Thomas, P. Q. 1 case Black Velvet, 796 yds. at 36 cts. $286.56 10 pea. Fancy Cassimeres, 275 yds. at 70 cts. 192.50 110 Robes, at $2 220.00 Note at 3 months from Aug. 1. 12 .. F. Peters & Co. Three Rivers. 25 dot. Ladies' Whit* Cotton Ho«e,®$l $25.00 20 29 I 1 4 2 8 6 6 1.25 25.00 1.13 32.7' Pearl Spun Silk Hose, 8^ 8.00 " " 9 8.00 Black " 9 $7.50 .38.00 Pearl *< 20.09 40.00 Ladies' Lisle Gauntlets, 4.60 36.00 " " 4.75 23.75 " *< 9.00 45.00 Note at 6 noe. frotn Ang. \%. A«)0unt forward. 699 0« 273 91% 6% §2 br cash or on (lumn, are, of ndiee is ored- rith the pc y oni the Cash Por the month n in the Sales 699 OS 273 62 97)68 SALES BOOK, -SET IV. QUEB 'W iF . 'li SALES BOOK, -SET IV. Quebec, Septembbu 1, 1871. A. M. RooNET it Co., Montreal. U.M. 62 I bale Brown Sheeting. 663» yards at 14 CIS. $ 78.89 .00 doz, GeuV^ Linen Hdkfs., at !?5 2.'i0.00 R.X. 2.S1 1 case Cotton Damask. 540 yds., at 20 eta. 108.00 Ifipcp. Black Bombasin, .558 yda. at 11.25 710.00 1 case Silecia, 2200 yds. at 13 c. 286.00 1432 89 Note at 6 ino«. S. D. HioofNS, Quebec. 231 10 pcH. Black Boinbagiin, 350 yards, at !PM0 $385.00 19 20 pes. Duck, 710 yds. at 20 cts. 142.00 527 00 Note at 8 mos. ft J. F. Nestor, St. Thomas. 1 bale Stark Brown Sheetings, 829 yds. at 10 cts. .i; 82.90 130 1 bale 4-4 Shatvr Finnuel, 3372 yds. at 5i) ai'-. 168.75 12 pes. Grei; Vfj; Barege, 200 yards, at B.) ets. 70. UO 1066 I case Solid Check Ginghanns, 2394 yds. at 18 cts. 430.92 752 57 Note at 8 mos. 1ft S. R. Woods, Ottawa. 4 cases Harop Prints, M. 481 246 1332 G. 491 1262 15812 M. 509 1108 1222 M. 97 1276 17152 5851 yds./® 12 cts. $702.12 2 bales Brown Globe Drills, 1141 10.328 1147 1029 20613 yds./® 10 cte. 206.17 908 29 Note at 8 mos. 9.0 N. B. Rot, Levis. 9 oases Cotton Bama^k, 4868 yards at 20 cts. $972.00 5 % off, 48.60 923 40 Received cash. Amounts forward, 923 40 1 3620 76 ifta SALES BOOK, SET IV. QtTEHKo, Sbptembib 25, 1871. Amounts <^»rwaril, of';- ^J'"/*^' RicJimoni, 5 n ^^",'J'<'8'I'i;>e Gauntlet.", ^$5 *450 1432 89 S. i Krd (jlovoi, 5% Off, Reaeiyed ca.sli. 27 00 *7 36,00 485.00 24.'25 923 40Jj .S620 4(>0 76 527 00 m' V\f . \^'^' Toronto. 32|»0i ''< (< nucK 1^ oo dO» 1 1. ooj./. 1 . V/irtn9 // '^•^^' '49. 9K A/l« rw 2^653 14 c. dO put! s.plnoM.Miatijre?,2«772 27 c. Note at 8 nionfefae. 41.-).fl« 416.2? 415.1ol 4I.'i.24 41.5.17 776.y2J 752 57 — 28 T. Ross & ( 0., 4 ps. White Piques, 75 1 ) 130,3 71 674 I 18 19 64|60| ps. Larellas, 15 30281 fa> .? Note at 8 montlis Kingston. (iH $75.25 1.25 18.75 • I'i 484.52 30 908 29 923 923 40 40 3620 76 A. R. Jacob, Bati.<: f '^'^f • '^ie^'B Nov,- Silk Shirts, ^'S $10 I 5786J a tt « n It 26 30 35 Note at 3 months. — Sales on time, i Sales for caeh, entered here anrl nn«^.^ I iroTii V. u ' i lOOOO iroTii C. a Pettj sales entered al on« on C Total sales for the loi" ^%. .^. w. ^7'^%^o. IMAGE EVALUATION TEST TARGET (MT-3) A [/. 1.0 I.I ■ 50 '•"^" Ui u. |40 2.5 2.0 IL25 ■ u iiiiim 6" 1.6 Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 V iV >^ M ^9) V •^ ^ ^ ^^ ? .V i/.. CASH BOOK, This ifl the mos<) convenient form for a Cash Book to be kept in connection with a general merchandise business ; the feature of special columns may be extended, if desirable. It will be .een that all cash entries, debit and credit, are taken to the Ledfrer, either through the Journal or directly, from this book, toiretb-3t with all accounts producing or costing cash. Tho amounts difr tinguiahed as *- per petty Cash Book," are entered here from a Dr. Cash. [ (> ., j 1' '■' JJ .! 1871 Au ' e 8 14 JI5 '18 V ,21 25 2h 27 30 31 Mdsb., 6. R. BOTCK. Loam, 6. K. UoYep, MrsE., BiLi,8 Rkc'bi.k, Mdsr., Bills Ubo'blk, Mdse., Mdsb., Bills Rbo'blc, AIdsk., Mdsb., W. B. GBAf, Ammmt on hand. Sales, per Petty C.-Bouk. Reo'd on acct. Return from J. B. Law- rence. Rec'd in full of acct. Sales, r,er F per Foreign I, B J^f'ijase and J'oitenic-o ' I'lUies, as per JA,roign 1. B D..conntonPorr.n'rnote Un P.wvato asct Note favor rt.n".v.-i,i,|,,j„^ iJinics, por i-'oreiijn f U Ck'rk hire, $;^0; $20 Discount on Stein J^ Co. '8 note On private acct. Mase. purchased for Cash ^m'^n?h'^^"''^'"''"'"°S">« BaJanQe on hand 105 Bi Fi Dr. IR71 Sopt 1 3 'i 7 12 17 •20 t.{ 25 3U| Belanee tm hand, Mdsr.. Sales, per Petty C.-Uook iNTBRTTgT, Disc'f on note fav, A. G. C. Bnii.8 Kro'blk, DiPc-t A. M. Kooney k Co. 'a note MDSfc., Sa as, per PeMy t -Book Mdsb., Sales, per Petty C.-Hook Mdsi., Snles, per Petty 0.-13ook M i)8«i., Sold N. JJ. Roy, per S. B. MosB., Sales, per Petty C.-Book Mdsh., Sold E. Curran, per S. B, ftlnsB., Sales, per Petty C.-Book ' Mdae. Salefl for Cash Total Cash reo'd during; the montb Oach Mdte. SwMlr. Bal. 70 20 L'SOjOO 21S!50 3(52 40 923!4I» 180'0l 4(i0|75 125! 00 29 1432 2i90 25 1462 2490 3962 89 8031 8S 3Hft2 12584 89 72 106 Oach Simdr. Bat. 29 1432 1462 249U 3952 89 8631 83 Sv*.*)! 12684 8» TJ Book. 1871 Septj 1 V Bjcpbnbe, 2 V Loan, fi V Bills Patablk, 0|V jlNTlRBST, 0( j.MDse., V iBxpRNan, V fi- A. HoDu.t, AIdsk., V KXPKNSB, } Porterage Paid Drayage. «8.50 Lent L. Morgan Diso'td Note favor A. Q. Cook LUsoonnt ou A. M. H. A Co 'b note l>ulies, at per For. I. B ' Pnid Drayajje, on aoct. ' Pmd OD privHte acct. I>utle?, as per For. I. B Paid Drayage in full Mdae. purohiised for Ua*h Total Cash paid for the month timance on htmd 304 1760 600)00 150000 49 1200 20 76 2414 304 2719 12584 ' BILL BOOK, The Bill Book can never, with advantage, be made a principal book, from which to post The form presented below is the best Bills No. 1 2 3 4 5 6 7 8 9 10 11 12 l.S 14 When Keo'd. Aug. (I Drawer or Endorser. W. H. Ellison. D. Atkinson. H. AI. & Co, Sept. 1 5 H 15 J. 27 H 2H 30 1 1 1 12 14 20 J. R. East. 28j H. M. & Co. << it a J. 0. Moss. H. M. & Co. Drawee orlMaker. J. N. Gait. S. T. Perron. L. Beaudrj. F. Peters & Co. Hazel & Poy. Stein (t Co. C. E. Lawson. A. M. Rooney & Co. S. D. Higgiiis. J. F. Nestor. S. R. Woodis. Lee & Strang. T. Rush & Co. A. R. Jajob. !' I Bills Nil. When Drawer or Endorser. Feb. 20 G. H. Shills. April 1 S. A. Pugh. May 1 2 A. G. Cuok. Aug. 1 P. McHugb &: Co, " UN. Caeev & Bro. Sept. Bell & Archer. 108 Drawee or Maker. 11. M. & Co. u « BILL BOOK, —-SET IV. nade a principal below is the best for general purposes, althou^rh the example is more comprehensive. arrangement in the former Receivable. e«oriVIaker. > or Maker. Date. t. 1871 on. Feb. 11 ■y- April 12 &Co. Aug, 1 ^oy. " 12 3. " 14 'son. " 2n ney & CJo. " 28 ;ins. Sept. 1 << r. or. 5 da. " 8 ng. " 15 Co. " 27 b. " 28 " 30 When and How dipposed of. PaiJ. Discoiintod. Difioounted. Discounted. Payable. It9 hi INVENTOIiy BOOK. Ths book is used to ermmernte the different articles of unsold merchandise, at such times as ,n.y b., deemed desirable. It is on hnn !"k •"''•' T:;^^, ^' f"^"'"'^- tho amount of merclw,ndise on hand being included m the opening journal e„try. Inventories are frequently copied into one of the Invoice Books: but a sep- arate book is preferable. ' ' M -de. on hand, August 1, 1871. Marks. H. M. R L. B. V. P. A. B. R.&X. N. A. Nos. 192 1 8 197 2.S1 19 1289 62 M. 190 4 B. S. 130 1066 4595 3624 1 bale Brown Sheetings I case Black Velvet 1 case Paper Cambrics 21 pairs Wliitc Blankets 41 pea. Black and White Tweeds 21 " Fancy Cassi meres 17 •' Black Satinet 1 case Woolen Shawls 20 pes. Black Bombasin 37 « Duck Canvas 2 bales Black Wadding. . ,loz. lIORobea 1 case Cottonades 10 cases Cotton Damask 150 doz. Gent's Linen Hdkts 160 pes. Diaper 60J Play Linens 1 case Black Alpacas 1 " Opera Flannel 100 doz. Men's Gloves 140 « Ladies' Lisle Gauntlets 6 " " Kid Gloves 1 bale Stark Brown Sheet! nir« 1 " 4-4 Shaker Flannel 12 pes. Green Veil Ban ..rp 1 case Solid Check Gin;:iiun>- 25 pes. Coburgs 1 case Silecia 1 " Linaeys 1 " Corset Jeans 1 '' Delaines 1 *' D. Bege 110 Yih. : Prioo. 7!tfi 2()0f) l.Sf)93 576' 469 60 900 i;^92 80 687^ 5400 19313 910 750 829 3373 200 2394 625 2200 i2(;6'^ 17251 3(1(1 864 .11 .263 .06 1 3.43 25 .60 .522 4.89 .872 .15 .22 1.50 .222 .16 4.50 .90 .17 .272 .372 2.50 4.46 6.25 .082 .45 .29 .14 .60 .091 .172 .06 .25 .11 Amount. fil 212 125 7-' 342 345 24 G 293 787 208 17 165 154 864 675 135 328 98 93 Of) 03 37 75 22 +0 50 80 60 00 63 00 00 00 35 250|25 281 25 25000 624 31 7U 151 5M 3;:!5 2G2 208 221 lOH 325 85 40 25 46 .S8 00 n; ou 50 64 5! 00 04 8299 4( firtides of unsold dcsinible. It is, if of meiclwiiKlise try. Inventories ookfl ; but u sep- t71. s. Price ' .11 . Amount. :] 61 9.S f. .26'^ 2I2!);i .OG' 12. ■) 00 3.43 •7 . J 03 .)' ' .25 34i J 37 S' .60 ■m:- > 75 i .522 24 C 22 3 4.8y 29;- +0 ) .872 787 50 ) .15 208 80 ) .22 17 60 1.50 165 DO •1 .222 154 63 1 .16 864 00 4.50 675 00 .90 135 00 a .17 328 35 .272 250 25 .372 281 25 2.50 250 00 4.46 624 40 6.25 31 25 .082 7U 46 a .46 151 S8 .29 5S 00 .14 3;s5 16 .60 202 ji) .091 203. 5G .172 221 ( i4 ,06 103; )1 .26 325 1 )0 .11 95 04 i )299 4 rC JOURNAL,— SET IV. QuKBRc, August 1, 1871. Cash Mkrcha.noise BiM.s Rec'ble Store Rent S. R. BOYCE W. E. Gray Resources ,,n.| Liabilities of A. .J "all,O.S.Mitci)ell,an,iK.A.H„: ??.'?• r"^[f"«" in tho firm of. 'llnll. MchellA Co." doing n,-ene,; Jn )l,ing and Importing l,u8ino=^ n.m 'th'"S f ^'""'«°^ - '^^^ Amt. on hand, per 0. Book .$738(»..')0 " I"''' " S2i)».4i1 Notes on hand, per Uni » 2084.00 Advance payment for rent 1600.00 Balance of account 2040.00 « JJ80.20 22864ir To Bills Payable Notes outstanding, per B. B. 8500.00 " R. P. Davis B.alance of account A. J. Hall Net Investment " C. S. Mitchell " « " R. A. HlIDON " « 31 __ Mercbandisb To SUNDRIKS. To Bills Payable For the fniirmin™ r =. ror ine to h, wing Invoices per Dom i'lie ""lO ""^ ^- '''^"""gh A Co., From .\. Casey & Bro. A ug. n 660.73 "l667.3r 22364 2,574 98 JOURNAL,— SET IV. Qdebrc. Aiioust 31, 1871. HiM-a Rkckivabt.k To Mkrchandise. Snlet for tho month, perSalM Book : L. Beiiudry, Auj;. 1, $fl99.0« K. Peters A Co., " 12, 273.52 HaielAFoy, ■- M, 869.38 Stein A Co., «< 20, 1425.48 0, B. Lawson, " 28, 171.04 <( Cash To SCNDRIES. rr, ., Keceipts per Cash Book : J o MD8E. Total Sales for Ca>h 1062.60 S. R. BoTCE Roc'don ncct.,$flOOi $1410 2040.00 ^■'''*^ Return from J. E. Lawrence MOO.OO " Bills Rec'ble Received on Notes, *12(J4; $800; .$1425.48 " W. E. Gray Iq full of acct. 3489.48 1480.20 Sundries Mdse. EXPENSI Loan A. J. Hall R. P. Davis Interest T. J. CoLSTOK Bills Payable C. S. Mitchell To Cash. Disbursements per Cash Booi : Purchases, etc., for Cash 23i'2.0« As per Items, ,'$15.25 ; $7.50 : $25; $50 Lent J, E. Lawrence Paid on prirate aact. In full of acct. y7.75 80U.00 8U.00 175.00 Per items, $15.ti0 ; $50.44 66.04 Paid on private aoot. 100.00 Hn^lcotned noto favor G. ]]. Shills 3800.(10 Paid on private acct. l.'^O.OO 112 .345)8 48 3438 8872 48 IS 8872 18 7620 86 rc'ifl 85 JOURNAL, -SET IV. QiiKij|.:o, Skptkmbkk 30, 1871. Mdsk. To Bii.r,8 Patabi I- ? ■ '^ATABr.fc Involoe per Pen., l. B ' '• W. MeadkAPo !''"""':l'''^^'"'".-«"Pt.20 I»2«.I4 ' iiEADfc&Co. Inv..fi!e,.t.,0.,,e,F.I.U. N6;U9 " J. Baii,kv&S()n " 20, 188.62 ! 3667 BiLta RecjcivABi-B To Mpse. I 7602 Sales for the month, as nor S. D. • A. M. Roone.v A Co., Sept. I, U.f2.S9 J- F. Ne.^tor S. K. Woods Lee ifc Strang T. Ko.<:s A Co. A. R. Jaoob <( " 5, 527.((0 " 8, 762.57 " 15, 90S.29 " 27, 6393.71 " 28, 678.62 " 30, 100.00 Cash 7602 93 To SnNDRiEy. i 3952' Rppoiptf., per Cash Book : Trtal Suli's for Oiish 2490.26 To MnsE. " ^'"■'■•' ^^'^"''"'^« R'-'-l - "0*- 1432.89 SrN'jr^RiBS Mdsk. fixPBNSE Loan Bii.i.s Patabi 3952 89 nifburgeiiient.s per Onsh Book : Porch.'.ee^ oto., for Cash 3(14.39 I'er Items, $17.60; $76; 112 • $3«.76 ' ,25 26 Lent L. Morgan ^OO 00 To Cash. 27 IS 24 E Inti lltJES'l' R. A. HcD Disc'W note f«r. A. 0. Cook 1500, "iso'tonA.M.R.&Co.'8note .00 ON raid on private aect. 49.80 '■! ! 140 00 !; 113 .Dr. HALL, MITCHELL A OO.'S Balances of their Resources in Casu, Mdsk., SroitK IIkvt, Uii,i,s Hkc'ule, Loan, T. J. Colston, Resources. Balance on hand. Hularice on lian I, per Inventory, Advance payment. Balance on liand. Balance due tliein. Balance iu liieir favor. $9865 7810 16011 818M 600 100 128 16.' 48 61 00 09 00 00 18 Dr. Balances of their Losses I J' \-r^ Lossen, EXPENSK, Interest. A. J.Ham/s C. S. MlTCHEl,!,'s H. A. HuDOJj's Loss. Loss. 9 net gain, i net gain, s net gain, Net Gain, $1661.05 1661.05 1661.05 $ 22.3 85 00 89 498;i $.J292 15 Oi 114 ELL & CX).'S eir Resources 'their Losses $ 223 00 85 89 1.05 1.05 1.05 498;i 15 $.^292 Oi BALANCE SHEET, SET IV. and Liabilities. Or. VV. Meadb & Co.. ■'. I!aim;y & Sun, J. IlAi.r.'s, S. MiTC'flEM/s, A. Ht'DON's. iJalunce in their favor. Halance in their favor. Share of capita), SJiareofcai)ital, Share of capital, Net Capital SG.TIO.?') =»-^0«, whh intercut ut 6^, Less interest added •^' A. T. Hl-gh.«, % Casli oil ;% 1 j C. I. Lane, ^y 40 l.blfi. Fancy Fiour, rci ,$7 ■ ■ . 26 S2I0,0.S 2.08 ' -^ pi ss„fgi:!' -,--.: 3 1 A. T. HcGHE8, By his Draft at 3 davM «,«!,► r r^ accepted " S'^'' °» ^' Dplorma, To Storage o» 30 lb)**. OommissiouoDlISO, at 4 ^ To Lit* Draft on u- <»♦ in -lo L- Water, accept'e? ^"^^ ^'S'^^' '^ ^^vor of lp:% \ I i . mi CASE BOOK,— SINGLE ENTRY. Dr. Or, 1871 July • 4 <« l< il (I u Aug 18 20 22 2H 26 t« 31 Amount of Cash on hand at commencing bui^inees Paid for 300 bu. Wlieat, /TO 72 ota. " for Freight and other expentM L. P. Clark ao a Ioun C. I. Lane on % for Freight ami Dra^age on an Invoice of apples fron* G. N. Rollaud S. Fraeer & Co. on % C. I. Lane on % for Freight and Cattau'e RecM of L. P. Clark, for loan of Uth invt. " of L. P. Clark as loan •' for eale of 1 2 bbls. exlra Flour, /© |7 Paid for Advertising, etc. *' L. r Clark for loan o» if,th Kec'd of S. J. Pierce, (or balance ol % Paid for Stationery Kec'd of A. T. Hughet^ofi % " for Sales ol Roilaud'*. apples Paid G. N. Rollaud in full o(% Balance on hand 13000 (I « It Balance from Julj 31, 1871. 200 76 84 39 liO 180 c. OO 3698 00 00 00 20 00 00 216 2 200 81 6 50 20 3 Q. 00 CO 00 25 50 00 00 40 2 75 50 00 30 293fi 20 35 39 2996 3698 30 36 20 120 'RY. I>r. Of, c. 3000 Oft 200 75 84 39 vm 180 3698 00 00 00 20 00 00 20 35 21 b' 2 200 81 6 50 20 3 2 76 39 2995 3698 e. 00 CO 00 25 50 00 00 40 50 00 30 30 3ft 20 Q il« ! t h ^il III !l 1 i Vif ►o %• Cj C4 s n «* ^ ^ CM R- r- 00 00 3 '* d tf d 8 O) (33 CM 1S71 July <= = o CM O f^ §1 t» ec c. r-4 o 00 r- CC fc M ec Q) So u M «, s •"« t- £ '£/ t? esi to o - CO ■* 00 's "- 2 1 X 3 COO coo c o OCX o e>4 o ■X «» www 1 c a C! 5 rs • 08 '3 ^3 W - . - H- - c« It — " C. 1 59= 5 -•Hi ll 'ti:'mtti0k;h'!s^;i iitlW^T 8TATBMENT II 'i, BHOWma TH£ OONDITION OF THE BUHIITISB I On tho 31st of July. : i I il i I .-.,] Resourcu. 1. From Ltdgmr /4ccott»»to.-— Balance due bj A. T. Hughes %. From Cask floo/c.— Balance of Cash on hand «. From Bill Book. S. J. Pierce's Note, due September let A. T. Hughes' Draft, due August 8 4. From Jnvmtory. —Merchandise on hand. . Liabilitiu. I. From Ledger i4c(>.iHite.— Balances du4 to Ct L Lane J> K. Eirouac J. Gleasoa t. From Bill Book. Note faror R. J. Vincent, flue Aug. 1 2 " " 8. Fraser & Co., " Sept. 13 " " C. I. Lane " Aug. 15 " " S. Fraser & Co., " Sept. Ist Present worth or net capital Mj capital at oommeDCing business wac Net gain rwJieed July Slst 80 2995 100 105 1188 0. 00 36 oe 00 93 4469 2S 80 318 167 105 120 180 210 00 00 04 00 00 00 08 1380 13089 13000 89 12 IS 00 U 124 CHANGING SIN-GM?. TO DOaBLB ENTRY. to Doulh Entry, PrEPARATORT STATEMlflT. •o'^Ta^;r24.'"''' ''"°"'°" ^"'^ ^biW., «Ucen < le.|| $ Btsourct$. — LiabiixtitM. BnJ!"p^^ Accounts Payable (already postod) clJtS?.*''''' out8tanding,pr BilJ Lok ^ tapiUl at commencing business Net gain realized in buMons SOfOO! ' 29953S 20500 1188 93i 565|04 HlolOH 3000 00||4380 4469|2« 1) 80 18 will lack Just the ai^ o'^'n^et'l^VsTietof ^^^^^^^ Opening ,a the j^edger an accountVii; nami J J^T""-?' credit, my capita at commencin^r h,L^/ f' / ''"**''■ ^« »*« ment of a Double Entry Ledger ^^'^^ *^' commence- Merchandise, and Bills Payable Thl; nf- ' "' J^^^^'vabie, Je" change'," and will 8eC%eA Se„Tv,rrr*%T '*''''" *^ iSft I %c O TO 3 "5 CO fC — -5 CQ 00 m s «» tx I u-5 O <» O 0) o CQ lO €» OC — » a a 0) c3 w n -1 K — ^ t: ^ 2 s 30 ~' 126 Ne -HACTicAi, EXEncis.s I^^ si.r«x,.,, ei^thv. '^"RTUit Isf, lJi7i r i> M I ' ai, n ouHl, as follows : to W uTi / l '* P'""* ^^^ '-M cents -4 ^r^akle, 2 da^s' Work at 5ci. %' ' a *''^ ^^'''^ ^' ^'-Sf) to H • ^ai,l them m part in Cash ft5^ D^r P'"' a"'"nr.ti„.r to »5'> o ■» '^ighte 10 by 16, a -25 ct s!^- ^'' p'" ^•'^"'^™«- '^''^ forG zi„' per Hgxeement, $15.-15 Gar 'a J>'r'^"° '^ ^«'^«'«- ^ Coa h a^ Grand Trunk R. R. Co* for *H it* ^/i«H,*,^°- *» o'rder o, the Paint at 25 cts — ■« t/ ^ f;"""''^- Rec'dca^h for 17 IK^ j. at «f'*'?ii^L*««' "^ ^^-SO^Paiif H lilt '"'^ ^T ^ ^'>'^^^ ' '> ^'v atfi.__ao. Rec'd cash of T R.. i^^V'^' ^ ca'-h, 6 days' \V',,rir cte.-.Paid ca.h for Cair« of Shon S vJ ^!^ ^^'' ^^ite Paint u I Glover, for Stained oC as ,' J „ '*''^' ^^ follows : '"V J painting Church, $210.-l2S^ V*' *'"'*"f' i^^'^- ofC. HaniV,;,; New Sash at Ma'nLact^ry t feV « ""^ ""'^"'^ *"•' ^i*' = for ,;! J '6, *t 9 ct8. ; 1 -jy Liffi'o W^ agree.nent, to wit. 56 Li^l.t. ' |^? 110 Wioduw Frames, at 46 cts^fyLttn' P '"'"'"♦ ' '^ ■"' ' , lor fainting Reception Re JonesGdays' Work, at,?l, Walter, 5^ day.s' Work, tor Pa in tine '?P-,^ndry, 4 plays' Work $j;j.iS*^,^ Cloth tress Coil »t$1.50jioH.Te t" H. leakle, 5 days' Work, at .*l at 75cta.~27. B 'o'tof L. S. l; P-- J « ^"'" '^'■«*8 Coat, $16- ] PfliTni , r> ' ^- '^- ^-'gers, 1^ iw ounoiy Jobs, m i>er Rill, ir 127 per Bill, in PlAOTtCAL KXRUCfWES IN SINGLE KNTRT. OMh $22.fin._as. Paid ciVHh for I ft ^aN. Linflpp.! Oil, at $1,624.- a». Reo'd ouch for Tin Sij^n, $10. Pai.l casJi for Tin and Jaf^nntng, f4.26. — 30. Uur ly A fJulj owe riip for Painting i Hico. as per a^r*^ ment, $80.— Pai(l H. TcakiW, in i;a«h, f. .iays' Worlt, at *!.— 31. r^id (or Kent of Shop one m«; "»b, Id oahIi, $16.67. Balances of the Resources and Iilabilitles. If . ! I t«. .11 ; I y ,; Resoiircu. Caah, balanoe on hand Stock oftoolii, as per In- ventorjr-Book Stock of paints, etc H. Young J. WilHon & Co. Grand Trunk R. R. Co. Citj Hall Hardy dc Gait 1540 08 7.-) 00 65 50 1.3-1 l:i •) 00 1 8 61 16 ('0 70 00 911 31 Liahilitiea. L. S. Rogers J. O'Farrel) W. G. McLean Balance. — My net capital 16 3 140 159 751 .38 00 00 .38 9.3 91131 '^'huat My net oapjtal, on Sept. let, i.•^ $7;-)!, " " " at commencing husinc'88 was only 575, 93 00 My gains in bunnesa hare been MEMORANDUM IL $176.93 Sept. 1, 1871, I eomratnce businesp with the following re^ souroei: Cusb, $Bol..34; Mtrehaodiie, $5120; Bills Receivable, $1386.60 ; E. S. Burronghs owes me. on %, $167.04; L. N. VeMon. $120.98; T. A. Maguire, $96.40 ; C. N. Darid, ^1.64.-1 owe a/5 follows: On Notes, $350 ; to Poston dc Co., on ^IJ, .;>.:. J. 12; to Gar- neau ARoy, $180.88.— Paid L. l^avis, forrepairson t i.' S( , 18.74. —Sold C. N. David, on cr«lit, 2 bbls. Flour, at V.2o.-'Z. ;JoId L. N. Veldon, on %, U gals, of Sperm Oil, at $1.60 ; and 50 lbs. Pow- dered Sugar, at 10 ds. per pownd.- 3. Bo't of Poston A Co., on %, 8 boxes Havana Sugar, 3284 lbs., net wtight, at 74 cts.— Paid in cash, '■;• a Set of Account Books, $20.50.-4. T. A. Maguire ha« paid me \ \ 03 hi8 old aooonnt— Sold D. S. Raymond, on account, 60 lbs. Cn; \ t •ucsur, at 10 «t«. ; and 100 lbs. Brown Havana Susar. at SJ c*t.- ". i?o'< (ri'Garnftdu t Eoy, on % Goods amounting 10^*406.58. I'Md l-m v:.iOO in ms'h —8. Bo't of W. C. Lord, for cash, Merchan- dis..' ^aiViPting to$2k^* ...lU.— L. N, Veldon has paid me !?40 on %, -^. C. d. Dftvid h'j Utn |>ainting in tb« store f* wvh kL $1.26, for 128 60 r. at $l.62Jj|.~ 1(1 Ja[«tining, as per agre** , al $1.-31, itles. 16 3H :i 00 140 00 159 38 pital 751 93 911 31 751.93 575.00 176.93 bllowing re- Receivable, , N. VeMon, I.- -I owe as 12; koGar- . !8.74. Z. Oold L. 50 lbs. Pow ; Co., on %, ^aid in eaali, hsM paid me )unt, 60 Ibfl. 5u2ar. at 8J to !i;406.58. h, Merchan- ■ !?40 on %. ut $1.26, for "»v Note at '2 ,,. L r- a'"onntiri.' io ^•tflQ, ,''"''' '>f ^ eS atts;?®-""^?^'^ ^' ^' ^^fcn mi. 7u^^"'' ^«'- Clothing, ■uay, amountin,' (,, >;(J3 Note, dated I vu. ■>a;o. •{olj's Note, No. 2, ^Y: on, I „i- " ^ •'• ^•^- liurroii, li in urrou^hj ^ft.'y^^^as.fss £r "^±-;."-;-i;^r -as- T. A. Ala". Note, on demand, week amounted to ^590.;i2. . , .^. *5lJ — ao n ""' ^""'^u "e ii*| pre- I2d -HO. Paid ■■*^^^^tej»saa PRAOTICAL BXER0I8KR IN SINOLE EN'TIIT. Popton & Co. $100 on account, in casli.— Paid my Clerk's salary for the month, in cash, $60.~Cash Sales for the week", $338.96.— Having taken an Inventory of the goods in the store, I find the amount to be $5086.41. I have Nates ai^'ainst various persons, amtg. to $1 127.46. I owe Not*8 amounting to !fir)14.36. On September 30th, my Net Capital is $7528.73, and my Net Gain, $!■;«. 73. t s MEMOFUNDUM III. Oclober 1, 1871, W. S. Drum, Cabinet-Maker, ast-'ociateswitli himsHf T. A. Graham ; — Drum transferring to the firm sucli portion «>f his resources and liabilities as is mutually agreed upon, and Gra ham investing tlieir equivalent in cash. The parties are to share alike in gains and losses. W. S, Drum invests in tl)o business, as follows: Cash, 100; Sun dry Notes which he holds against other.s, per B.-B., $700; E. Miles' balance of account, his ftvvor, 81I1.50; J. R. Nesbitt's balance of account, liis favor, $74.80; Materials and Unfinished Work, as per Inventory, $71:5; Stock of Furniture, as per Inventory, $420.86 ; Stock of Tools, as per Inventory, !ji>302.40. W. S. Drum owes; viz., Sundry Notes, as per B.-fe., amtg. to $842 ; L. McTntvre & Co., bal. 01 acct., $1.34; N. Percy & Son, bal. ofacct., $150.40. T. A. Gra baiu, invests inthe business, in cash, $1206. 16. — 2. Bo'ttorcash ofC. Vallee, Planks, as per Bill, *i5I.2ti.— ». Sold K. Miles 2 Hair Clotlu .Mahogany Sofas, at $20. Rec'd iVom the same on account, in cash) $120.-4. Sold Mrs. C. Nelson, on acct. ; viz., 18 Mahogany Chairs, Cane Seats, at $1.25 ; 12 Mahogany Ciiairs, Hair-Cloth Seats, at $3 ; 4 Cherry Dining-Tables, at $G ; 2 Maple French Bedsteads, at $4.25; 2 Maple Low-Post Bedsteads, at $2.75.-5. Sold P. McGee on acct., per wife, 2 doz. Windsor Chairs, at $12 ; 1 doz. Windsor Chairs, for $15; 1 doz. Windsor Chairs, for $10; 2 Spring-Seat Black Walnut Sofas, at $21.-0. Paid for Wages, per Tuny-Book, in cash, $15.— 8. Sold for cash, 2 Bureaux, Maliogany Veneered, at $22. Paid as follows: A. Patry, for repairs ot Shop, in casli, $103 ; S. Jones, for Painting Shop, in cash, $44; L. Mclntyre & Co., in full ofacct., in cash, $134; lor Glazing 2 Lights of Glass, cash, 70 cts.— 9. Rec'd •ash for B. Motley's Note, Drunrs favor, $250. — Bo't of N. Percy & Son, Lumber, for $270. Gave in payment our Note at 30 days, in full of all acct. — Sold E. Miles, per daughter, on acct., 2 Black Wal- nut Footstools, at $1.50.— Sold C. T. Renaud, on acct., 6 Patent Pivot Chairs for Otnce, at $5. — II. Sold for cash, 2 Arm-Chairs for Office, $10. — Sold E. Miles, per wife, on acct., 2 Black Walnut Extensio.'i Dining-Tables, at $40.— 1». Sold P. D. Flood, on acct., 4 Children's Higli Dining-Chaire, Maliogany, at $2. — Sold Miss Anna Roy, on acct.; viz., 6 doz. Windsor Chairs, at $11 ; 2 Rocking Chairs, Sec- ond-Hand, at ^'J.— Paid cash for Wages, 87o.—l«5. Sold for cash 2 Pints of Varnish, $1. — E. Miles assumes P. McGee's account, trans^ ferred to him, for .$91.-10. Boudit of L. Mclntyre & Co., Paints, Varnish, Brushes, etc., as ner Bill, anitg. to $350.52. Paid to them eash, in part, $100,— 17. keceived |i)r Staining Cupboard, in cash, 130 T. rk'fi salary for 8.9G.— Having ! amount to be T. to? 1127.46. inj Net Gain, ist-'ociateswilU I) sucli portion pon, ami Gra 8 are to share sh, 100; Sun 00; E. Miles' tt'a balance of Work, as per ory, $420.8G ; n\ owes ; viz., re (fe Co., bal. . T. A. Gra L for cash of C. 2 Hair Clotii,. o>Mit, in cftshj oguny Cliaira, Seats, at $3 ; ads, at $4.25; jQee on acct., :or Ciiairs, for Black Walnut 1 cash, $1"). — ^22. Paid aa S. Jones, for ill of acct., in Ls.— 9. RecM 3f N. Percy & at 30 clays, io 2 Black Wal- I Patent Pivot lirs for OtHce, mt Extendion , 4 Childrea's Lnna Hoy, oa Chairs, Sec- j!d for cash 2 3Count, tranS" ■ Co., Paints, aid to them mrd, in cash, HI>TS AS TO RESOUHOES AND LIABILITIES. '•-h2 0,..oma,^, u$7-iJS,'F"f,f''''''--^' '' ^''■~^^- Sold S ■ •• • ' ^J"- ^''''' J*--- Miles, per aon, on account, 2 Hat- , ... .lu, ^ nocKini' u lairs. at .«!I9. o a> iJr.un's Nu.e. F. Walter's Lor 1%. P^^"^f"^ ^^^OO.-Pald cash for '•■•OM. da.e, ,0 Dec. 0th an^um^^^to ^^ i'i'^P '^^ D''^^^""' acct., ,n ca.h. *20.-Bo't of I l/h, ^3.-^.{. Pa.,1 W. S. Drum on •*1 92.80.-24 Paid oZu o /i*. "=' ^" '>^'Cotinl, Lumber, ner Bill ^ct., 2 MahogaV Bureaux, Sit^hSIa^^f-a?*', ^^ ^VJ ""'^' ^» Wap:e«, a, per Time-Book, S73.30 -20 ^j' -r^^', ^""^ <^^'' ^r hogany Hccking Chair« I'i ,< ;. , ^•^'•' <«r cash ; Tiz., 4 Ma- MapIeFrenchBtd8(eaT'a/^0 2 ''^^^ at$l2.o0; 2 Birds'-Eye f 4; 2doz. Child's Hl'-hCliiV.^ ;;'=^^,^;."«t:?'^^'""^Chairs/a Chairs at ^ps.-P.idoaahasf ho;,: for B^i/of ^^^^ ^"^'^'"^ to T. A. Graham, on acct. SJO- fnrR» Vr ^"^"'"gfJSl.go- to Mis. Anna Uo;, onaoat iklZfT''^''^^''^^' .OOct^-Solj P. D. Flood, oaLt.. TbILoI W:te'[r,„f;^7«»,^33.-.ao. Sdd j^BuaRo/haa returned the Maho^av B^fl' . if' *^=^''^- Mis« lastaBt, beoaitsa it wa- too large f^rLr^^^^^^ ^'^^ ^'^'h The Stock of furniture on hand am't. r ;; ;; ;; ««.«„ .„a3atuS wS,'?.'- ''^'■- ',? «'^j-'-^» tools, depreciated br use - ., '*^^-^'* Tbe'«mount ofBilla Roc. in possession of thoH " 283. 'JO Jiilia Payabla outataadiog m ., ^^^^-OO ' " 862.40 dlNTS AS TO RESOURCES AND LlABrLlTlMs. ;i«r::.:fs;;5;i^;j^.::^i^^;^;;- -- e.t.siveiy in ,,. .ea. business has been forcibly 4t beS L f .''"° "rV" condition ol tTse tliat certain Ledger Aocour k • i ! '^'l''"'^' ^^'^ ''^s been tau<'in oUiers to show liabilhS and thai' u.e'co"" 'T'^^"' '''''' '''^^" , ttnu tiut the correspondence between the HINTS AS TO RBSOUROiSS AND LTABILITIIS. repourceB and liabilltien thus shown must agree in a certain sense, with the accounts phowinf» gains and losses. Any careful observer, however, must be aware that all classes of resources are not equallv valuable; and that,' in the course of trade, persons may become in- debted to ue both on note and account who will never pay ; the re- source thus represented bein^ absolutely valueless. In estimating the condition of a concern, therefore, it is well to know whether the books are truthful; that is whether the rt$ourcea exhibited on their pages art' a'tisolute or fictitious. The liabilities are always presnmed to be genuine.) The importance of this precaution will be apparent when we consider that al gains in business, as shown by representative ac- counts, are predicated upon the integrityof the resources. Forinstance, suppose we sell A, $300 worth of Merchandise, and take hie note for it. In recording the transaction, w« credit Merchandise, and debit Bills Receivable. In estimating our gains and losses, we, of course include among the proceeds of Merchandise this amount, which adds $300 to our gains. Our Merchandise account is closed, and the result finds its way into the Loss and Gain account, thus having an impor tant bearing upon the apparent prosperity of the business. But sup- pose this note should prove toorthleaa. It is now evident that the $300 credited to Merchandise account was not a legitimate product, and that all gains predicated upon it are necessarily fictitious. But tliejo are other resources represented in the Ledger, the exact value of which is uncertain, — they may be worth their face, or half of it, or nothing. How shall they be treated in a general exposition of aflUirs? Shouli], we consider thein all valueless, and close them into Loss and Gain the error may be a« great as to permit them to remain and represent actual worth. The most approved method of diaposing of this class of accounts, is to permit them to remain upon the Ledger, but to neu- tralize their effect by opening an aooount showing fictitious liabilities of the same account. Aa appropriate title for this account is ** Sus- pense." When therefore doubtful resources exist on our Ledger, and we do not wish to represent anything more than actual gains, the process should be to debit Lose and Gain, and credit "Suspense" with the amount of the doubtful resources. If any of these are after- wards paid, or their value becomes tangible, it is very easy to restore them by debiting Suspense and crediting lioss and Gain. This method is far preferable to the more usual one of closing up all doubtful ac- count into Suspense. The Suspense acc«unt in the latter case would represent either a loss or a resource. If a loss the amount may as well go at once to the Loss and Gain aooount; and if a resource, it had much better remain under its own more appropriate title. But the chief objection to this course would be the exhibitng ot accounts as clo&ed, which are yet owing and may be paid. If Mr. A, forin- stance, wliom we thus consider doubtful, ahould desire to see hie ao- count i?i our Ledi^er, that he may pay it, it might be awkwaid to iulbrm him that, iwving considered his account worthless we had carried it into Loaa and Gain. He might not desire to change ov estimate of the value of his iodebtedneee. >ITRS. a certain sense, careftil observer, 9 are not equally may become in- <}er pay ; the re- [n estimating the hether the K)ok8 ;d on their pagea i presumed to be B apparent when epreeentative ac- es. For instance, take his note for mdise, and debit es, we, of course lunt, which adds d, and the resnll laving an impor inesH. But sup- ent that the $3(iU ate product, and ious. Bat thei'c :t value of whicli of it, or nothing. atfairs? Shoulfj, I Loss and Gain in and represent ?ing of this class dger, but to neu- titious liabilities ccountis "Sus- our Ledger, and tual gains, the lit "Suspense " f these are after- Y easy to restore n. This method I all doubtful ac- atter case would amount may as if a resource, it riate title. But itng oi accounts If Mr. A, forin- tre to BM hie ao- be awkward to trthleas we bad to Changs om