CIHM 
 
 ICMH 
 
 Microfiche 
 
 Collection de 
 
 Series 
 
 microfiches 
 
 (Monographs) 
 
 (monographies) 
 
 Canadian Institute for Historical Microreproductlons / Institut Canadian da microraproductions historiquas 
 
 ._ , Mm^ 
 
Technical and Bibliographic Notes / Notes techniques et bibliographiques 
 
 The Institute has attempted to obtain the best original 
 copy available for filming. Features of this copy which 
 may be bibliographically unique, which may alter any of 
 the images in the reproduction, or which may 
 significantly change the usual method of filming are 
 checked below. 
 
 D 
 
 Coloured covers / 
 Couverture de couleur 
 
 □ Covers damaged / 
 Couverture endommag6e 
 
 □ Covers restored and/or laminated / 
 Couverture restaur6e et/ou pe!licul6e 
 
 I Cover title missing / Le titre de couverture manque 
 
 I Coloured maps / Cartes g6ographiques en couleur 
 
 □ Coloured ink (i.e. other than blue or black) / 
 Encre de couleur (i.e. autre que bleue ou noi 
 
 I I Coloured plates and/or illustrations / 
 
 que bleue ou noire) 
 Planches et/ou illustrations en couleur 
 
 D 
 D 
 D 
 
 n 
 
 D 
 
 Bound with other material / 
 Reli6 avec d'autres documents 
 
 Only edition available / 
 Seule edition disponible 
 
 Tight binding may cause shadows or distortion along 
 intenor margin / La reliure serree peut causer de 
 I'ombre ou de la distorsion le long de la marge 
 interieure. 
 
 Blank leaves added during restorations may appear 
 within the text. Whenever possible, these have been 
 omitted from filming / Use peut que certaines pages 
 blanches ajout6es lors d'une restauration 
 apparaissent dans le texte, mais, lorsque cela etait 
 possible, ces pages n'ont pas 6t6 film6es. 
 
 Additional comments / 
 Commentaires supplementaires: 
 
 L'Institut a microfilm^ le meilleur exemplaire qu'il lui a 
 6t6 possible de se procurer. Les d6tails de cet exem- 
 plaire qui sont peut-§tre uniques du point de vue bibli- 
 ographique, qui peuvent modifier une image reproduite, 
 ou qui peuvent exiger une modification dans la m6tho- 
 de normale de filmage sont indiqu6s ci-dessous. 
 
 I I Coloured pages / Pages de couleur 
 
 I I Pages damaged / Pages endommag6es 
 
 D 
 
 Pages restored and/or laminated / 
 Pages restaur6es et/ou pelliculees 
 
 Pages discoloured, stained or foxed / 
 Pages d6color6es, tachet6es ou piquees 
 
 I I Pages detached / Pages d6tach6es 
 
 I \/| Showthrough / Transparence 
 
 n 
 
 D 
 D 
 
 D 
 
 Quality of print varies / 
 Quality in6gale de I'impression 
 
 Includes supplementary material / 
 Comprend du materiel suppl6mentaire 
 
 Pages wholly or partially obscured by errata slips, 
 tissues, etc., have been refilmed to ensure the best 
 possible image / Les pages totalement ou 
 partiellement obscurcies par un feuillet d'errata, une 
 pelure, etc., ont 6t6 film^es h nouveau de fagon k 
 obtenir la meilleure image possible. 
 
 Opposing pages with varying colouration or 
 discolourations are filmed twice to ensure the best 
 possible image / Les pages s'opposant ayant des 
 colorations variables ou des decolorations sont 
 filmees deux fois afin d'obtenir la meilleure image 
 possible. 
 
 This Hem is filmed st th« reduction ratio checlced below / 
 
 Ce document est fiim6 au taux de rMuction indiqui ci-dessous. 
 
 10x 
 
 14x 
 
 18x 
 
 •7 
 
 12x 
 
 16x 
 
 20x 
 
 22x 
 
 26x 
 
 30x 
 
 24x 
 
 28x 
 
 : 
 
 32x 
 
Tha copy filmad hara has baan raproducad thanks 
 to tha ganarosity of: 
 
 National Library of Canada 
 
 L'axamplaira filmi fut raproduit graca A la 
 gAnArosit^ da: 
 
 Bibliotheque nationals du Canada 
 
 Tha imagas appaaring hara ara tha bast quality 
 possibla considaring tha condition and lagibility 
 of tha original copy and in kaaping M^ith tha 
 filming contract spacif ications. 
 
 Original copias in printad papar covars ara filmad 
 beginning with tha front covor and anding on 
 tha last paga with a printad or illustratad impras- 
 sion, or tha back covar whan appropriata. Ail 
 othar original copias era filmad baginning on tha 
 first paga with a printad or illustratad impras- 
 sion, and anding on tha last paga with a printad 
 or illustratad imprassion. 
 
 Las imagas suivantas ont *t* raproduitas avac la 
 plus grand soin. compta tanu da la condition at 
 da la nattat* da Taxamplaira film*, at an 
 conformity avac las conditions du central da 
 filmaga. 
 
 Las axamplairas originaux dont la couvanura an 
 papiar ast ImprimAa sont filmAs an commangant 
 par la pramiar plat at an tarminant soit par la 
 darniAra paga qui compona una amprainta 
 d'imprassion ou d'illustration, soit par la sacond 
 plat, salon la cas. Tous las autras axamplauas 
 originaux sont filmte an commandant par la 
 pramiAra paga qui comporta una amprainta 
 d'imprassion cu d'illustration at an tarminant par 
 la darniira paga qui comporta una talla 
 amprainta. 
 
 Tha last racordad frams on aach microficha 
 shall contain tha symbol — » Imaaning "CON- 
 TINUED"), or tha symbol V (maaning "END"), 
 whichavar applias. 
 
 Maps, platas, charts, ate. may ba filmad at 
 diffarant raduction ratios. Thosa too larga to ba 
 antiraly includad in ona axposura ara filmad 
 baginning in tha uppar laft hand cornar, laft to 
 right and top to bottom, as many framas as 
 raquirad. Tha following diagrams illustrata tha 
 mathod: 
 
 Un das symbolas suivants apparaitra sur la 
 darniAra imaga da chaqua microfiche salon )a 
 cas: la symbols — »>signifia "A SUIVRE '. la 
 symbols V signifia "FIN". 
 
 Las cartas, planchas, tablaaux, ate. pauvant atra 
 filmAs i das taux da reduction diffArants. 
 Lorsqua la documant ast trop grand pour atra 
 raproduit an un saul «. xhi, il ast fiimi A partir 
 da I'angla supiriaur gaucha. da gaucha 4 droita. 
 at da haut an bas. an pranant la nombra 
 d'imagas nicassaira. Las diagrammas suivants 
 illustrant la mAthoda. 
 
 1 2 3 
 
 1 2 3 
 
 4 5 6 
 
 ..aSfe rrV:i. 
 
MICROCOPY RESOLUTION TEST CHART 
 
 (ANSI and ISO TEST CHART No. 2) 
 
 1.0 
 
 1^ 
 
 ■ 4.0 
 
 2.5 
 2.2 
 
 2.0 
 
 1.8 
 
 ^ /APPLIED IIVMGE Inc 
 
 ^^ 1653 East Main Street 
 
 S^S Roct^ester. New York 14609 USA 
 
 "-Sg (716) 482 - OJOO - Phone 
 
 ^= (716) 288 - 5989 - Fox 
 
FIFTH EDITION — REVISED AND ENLARGED 
 
 CANADIAN 
 
 Commercial Arithmetic 
 
 COMPRISING 
 
 OVER 3,ocx3 PROBLEMS AND EXAMPLES 
 
 WITH 
 
 Clear and Concise Riles, Explanations and Solitiosh 
 
 NuMBEKiNo OVER 300 ; nearly 60 Principal Titles ani> 
 
 ovEF 700 Distinct Definitions, witu jiore 
 
 than 30 Valuarle Tables and 
 
 30 Illustrations 
 
 also new chapter on 
 
 THE METRIC SYSTEM OF MEASUREMENT 
 
 Now legal in Canada, from MS. examined by 
 
 JIR IIIQIRI JOLY, MmiSTRR OF INLAND BEVENUB TOK CANADA 
 
 and a chapter on 
 THE INSTITUTE OF CHARTERED ACCOUNTANTS 
 
 REVISED BT IIARRT VIOEON, E9g., r.C.A., SEC'Y TO TUB INSTITUTE 
 
 with their 
 
 Examination Questions in Mercantile Arithmetic 
 
 making the most complete 
 
 Text Book and Ready-Reference Manual for the Comuss- 
 
 oiAL Student, Mercuant, Accountant, Lumberman, 
 
 Contractor, Artisan and Farmer. 
 
 COMPILED AND EDITED BY 
 
 CLARKE MOSES, 
 
 Public Sou. Insp,, IIaldimand Co. 
 
 R. C. CHESWRIGHT, 
 
 Matu. Mastbr, SiAroRTn H.8. 
 
 TORONTO 
 
 COMMERCIAL PUBLISHING COMPANY 
 
 88 CHURCH STREET 
 
 1902 
 
^ 
 
 *,*Theanirreriti the Pmhlnnf in lhi» Bia>k are printed reparately in J'amj'hht 
 form, anii Kupplied in lih,raljirop»rtionii uithuut extra charge, /or the fi».' 'i' Teaehert in 
 Bntinem Collejei, Schn'i/n anil In»titutiout. 
 
 
 Entered aocording to Act of tho Parliiimciit of Canada in the jfar one 
 thouiiand eight liiindrcd and ninety-seven, by C A. bENOO eo 1 1 , in the 
 ofHco of the Minister of Agriculture. 
 
 rRINTINO AXn litNTINO nT 
 
 Davis k Uksubiibox, Pkixtf.rs and Bindpm 
 578-580 Kino Street West 
 
 lOKOXTO 
 
 'AdK- 
 
PUBLISHERS' PREFACE 
 
 1% 
 
 THIS Arithmetic haa '• 111 so well recelvwl liy Cu^iitle■^^ Colleges, S^liOols, A:- 
 coiiutaiilK, ami llii.- tiitieral I'uIjUc, ami lus lieeii /ouml go thormii;lily iirix<.tiful , 
 ami lalplul, tlmt another edition has bcL-n calln) 'or. Ad', intake haj bieii 
 taken o( thiita't to a<ld s.tv<ril new (eatiiri, anionif thtm a full »iul roni|iletu Iiidtx, 
 for tliu carifulconi|ii!atioriof whicli woareind. I>te<l to Mk. Kuvk.n J. liKvuoi inr. By iiiiamj 
 ol tliiii liiiltv, which liaj bi in arraiiK'i-d Toiiically as well aa Al|ihabclically, the complete 
 I'oiilentsof tha work 'an be rapidly reviewed, A glance over this Index will Illustrate 
 more forcibly than any words of ours the comprehensive character of the Casaduhi 
 Commercial Akitiiiiitic, 
 
 The Metric Ststim havin,' been lc^'alized In Cana a chapter his been added 
 deal;. ({ with this important subject. This chapter is the moi oonipkte and practical to 
 oe found in any work. It has been compiled with special refer -e to i.-Ouiniercial usajfe, 
 and avoids Physics on the one hand, and Hi(;hcr Mathematics o.i the other. The .MS. 
 was submitted for revision to Sir IIksri Jolv, Minister of Inland Ke\enue for Canada, 
 who Is the hi^'hest authority on the subject in the Dominion, liaviiij made a siiecial 
 study of the Metric System, and having (;"nc to the trouble and expense of t,'ettin|{ 
 dia^'rams, etc., from Fraiico, recently. Sir Henri has examined our MS. with care, and 
 offered valuable BUgeestions, and he considers that "the chapter will be very useful In 
 " teaching the Metrical System, and that the comparison between that system, which 
 "appears so logical, with the prcse t sys' •n■^ of measurement, will certainly be a most 
 " useful and intellectual e.xercise for students." 
 
 The new chapter on the In-stitctb op Cihrterbd Accountakts will be of value to 
 all students who aspire to become expert .Accountants and members of the Institute; 
 while the E.xaminatio.'* Qikstions in .MEac.i.xTiLS Akitiimktic, now for the first time made 
 generally public, will give a correct idea as to the scope of the Institute, and will furnisU 
 valuable material for exercise by stu lents. This chapter has been re\ is.d by the Secre- 
 tary of the Institute, Harry Vio':on, V.aq., K.C'.A., who, with the Presiuent, Gkorob 
 Edwards, Esq., F.C.A., and the Treasurer, W. It. Tisdall, Esq., F.C.A., have shown 
 practical interest in the Canadian CoauERCiAu Arithmetic by valuable suggestions. 
 
 A thoroughly practical and scientific arithmetical education can be obtained 
 from this \V -L, ,vhich embraces a treatment of all the subjects necessary 
 therefor. 
 
 Attention is directed to the following features :— 
 
 1. To the clearness and conciseness of the definitions, solutions, and rules, the 
 latter of which are logically deduced from jireceding solutions. 
 
•• 
 
 IV. 
 
 pnEr.vrK. 
 
 •J. Tci iliB iii;.,o ihort iiualioli in ii'Miliofi, iniiUipiiial, »<, ilnisioii «lt. 
 
 .'1. To ilio tiuniKrou* nolntin .-,, at. I uii! Kiru-i' iiiiiiil • r of cxiToi>ie!<, the prn'^i-al 
 churn' tiT <•( will;. «ill i|oiiliIl-« iDiiiiiKiiil thmi to nil teu'hiTi. In ihi< iiii|i.iri.i t 
 |>orlniiUr llic »btlior9 l.ili';v»i a lon^ftll want hi» Iwii Kiiiiplinl. 
 
 4. Tothcthoro htt itmritof I'tTccritau'e, ami in appll.at' ujh in luiiiot, I"!;"- 
 count, l'.irlial r:niiiiiil*, !;.|iiatioii o( Ar<oiint<, i tr. 
 
 Ti, To the rlcar itWoniunt ot the Conimcrial Law nlatini,' to Intornt, |ii<- 
 roant, cli.-. 
 
 lliliivinif that ttii< voluinn In it.. liiiproM it (nrm will fli il an oicr-lncreailni,' ininilicr 
 of faviritts, it is I'liiti'li'n'.ly «<tit (orth. 
 Tr^ntn, NoM^nilnT. Vy<n. 
 
 liN" )hX TO TABLES. 
 
 Acc'iraio Interest, to Ucckon IMl 
 
 Aniii. tii'9 at rnmpoiiinl Int. tor 10 
 
 > cars 332-.3;!l 
 
 Apolhcnripi' Weight and Klui<I 
 
 Mi'uMire. 63 
 
 Avoiriliipois Weitfht 63-54 
 
 Rooks, Sizcf ot rjl 
 
 Caleniliir Months, Rcikoninif Leap 
 
 Vea:' !.'.) 
 
 CiriMil'ir .^'l■a1url' i;u 
 
 Conmonnd Interest, fl;urcil (or 10 
 
 j.'.irs 174-170 
 
 Cu'.iic .M' asurc b'-^S 
 
 n-1'inials, Uelatioii t > Intetrers 40 
 
 Dry Measure 6.'i 
 
 Koreittn Money, Value In Canadian 
 
 C'nr-eni'y 2.->:i 
 
 Grain Measure 04 
 
 Insurance— (Fndowmont) Ratct. 
 — K.vpertatioTi of l.lff 
 " — (.'Straittlil or Whole I.ifel 
 
 Kates . 
 
 Linear Measure 
 
 I.iipiid " 
 
 I.oiiiciludes, Tx'le ot 
 
 Metric iS^steni, various Talili a 
 Money, Currency, Metals an<l 
 
 l'rci"i"H Stones 
 
 I'u'kers' .Meiiturc 
 
 I'ui'er " 
 
 Peroentaye 
 
 Satt-lojfs, Measurement of. .. 
 
 S.(uaro Measure 
 
 Stanilanl Time 
 
 Taxt .", "r ;i mills 
 
 Tinif .Measure 
 
 We ulits. Comparative Table of 
 
 4i: 
 
 I'lK'C 
 
 ;:i4 
 
 :it.'5 
 M 
 
 (14 
 
 4.;3 
 
 ii-.ia 
 (11 
 ei 
 
 84 
 3i>fi.S97 
 
 6ti-:>7 
 
 (13 
 
 i;io 
 
 r>-i 
 :i4 
 
 INDEX TO ILLUSTRATIONS. 
 
 rair< 
 
 Circle, Bhow..„' bsbis of Me.as't . 37J 
 
 Cone Ss' 
 
 " Frustum of "!>.:; 
 
 Cube 370 
 
 Cyliniier 37'.) 
 
 Decimetre— Mel fie System 415 
 
 Hepiatfon ...,.'. 3ii4 
 
 Ilexaifon 3U4 
 
 Institute of Chartered Accoitntants 
 
 - .Seal 424-427 
 
 Kilo-M->-ric.S-. e-n 41'> 
 
 OctiK'on 3iU 
 
 I'arallelouiram U'..') 
 
 Pentagon 3tU 
 
 Prism, Hexascn.al 370 
 
 " TentiL-onal 37;i 
 
 " Krctanttular 37') 
 
 " Trianii'ilar 37 i 
 
 Pyramid H '- 
 
 Krustum of 3>J 
 
 l'.ll.'0 
 
 Quadrilateral ;tij4 
 
 Hecta-.jfle 3ri.''> 
 
 " divide 1 sr.O 
 
 Uhomtioid sil.'i 
 
 Ithombus se.'i 
 
 Uiffht .Anjjle 305 
 
 Sphere ;-is3 
 
 Souare 3t)S 
 
 Trapezium SiiS 
 
 divided 370 
 
 Trapezoid ;ii;5 
 
 Tri ingle 3r.4 
 
 " Kquilateral 3<iS 
 
 " Isosceles 308 
 
 " liight-angled 308 
 
 " *' showijiL' base, 
 
 I>erpenrlicular and hypolt-nuse 369 
 
 Triangle, Scalene 303 
 
 " s.iowini,' Altitude internal 308 
 
 " " " external 3flS 
 
 Mt?i 
 
 
IXDHX TO COXTKXTS. 
 
 ARkANCKI, AMMIAIIKTICALI.V ANL TO|.lCAI.I.V. 
 
 1laj-k-M„i, !,,„„> i„,i„„u pa,,, „u,„/„-r. 
 
 h 
 
 <tre 
 
 riie litU, ,n 
 'I'trc are «;;, 
 
 HMALI, 
 
 parajrn,,hi, nf vhlfh there 
 iwlicntt gtHTul heaiimiji 
 
 '</ Itcliunn, ./ vhlc/i 
 
 ABBRrviATi"Ns M,o,\ in Runincii. 
 AicDrNi,, Avcra«iiiir or K.|ii«iliin 
 
 nf 
 
 AiToiint Saii'n!. .'.".'.'. 
 
 Ai'i'. iiriis C'iiri> 
 
 ADiriri.iN.Sh.rt.Vihmlsin 
 
 Amcji iir rAum ... 
 
 AVKI'ITIKS ..'.', 
 
 I>«nni'inlilt 
 
 Value r»t Simple In: rest ' 
 
 '■ " Coinpaiiriil " .'.' 
 
 ""'fri'iliMl Annuity ..." 
 TaMnnf Aii;iiiili,sntC<impounrl 
 IiiiiT.vit f(ir4i) vi'iis 
 
 Asxiuniiiuiit ( HiMkriiptcyi " 
 
 AvKuAuivi AroH via 
 
 lUsn KiMcouNT ... 
 
 HAVKmi'Ti V . 
 
 HiiH, .Mcasuniii-nt of . * 
 
 Ijrl.-kwork, .Mtasniriinent'cf 
 
 J K'lKKlmiR ANDC-..MlllrtM,..v 
 
 Hull!! and I! .arsoii Stuik K r\\ 
 
 llrSINK-m AllllllKVIATIHVH 
 
 Ciriiintcrimr, .Mea^urfimnt of 
 Casks, (iaiiirin,' of 
 
 ClfAHA'IKXg ANr. AhllllKviATIOVS 
 
 I ircle, Measiirtmeni cf . . 
 
 Cistiriis, " •< 
 
 Co(l"» f„r Mark 
 
 Commissi.. V axi> I5iiokkr\ub 
 
 {'■>mparat ive Tal.le of \\ . ii;h'ts 
 
 C<.Mi-,,iNi>Isr>T(HlthTa')le«) ., . 179.179 
 
 Til. 
 
 205333 
 
 ;i'.);i.:i,iA 
 3u:m. : 
 IS 
 78-77 
 339-.'}34 
 64.i:.'.| 
 Mj. :.;,:; 
 6.'.4.,-.;,> 
 
 332333 
 326 3i:ti 
 209333 
 
 3111 -:)7s 
 326-328 
 
 ma 
 "05-: 11 
 
 111120 
 
 «12t4l) 
 Vll. 
 
 (170-073 
 
 GGTtif.'J 
 
 Vll. 
 
 C36-tl.i!) 
 
 •id'. 
 
 00<Kl9 109110 
 
 111-120 
 
 14:) 
 
 A, 
 
 'iiloicm Ijiitv, toFind 
 
 ■id. I>Mfy, to Find '.] 
 
 11.8 , . 
 
 nitions an'*. Principles .'. 
 
 •!• showinu' relation of ikd- 
 
 ils to Inteifprs 
 
 •tir.nof Krac. tf 
 '• of De. Tials 
 
 U1127 
 
 40 SC 
 
 85-il2 
 
 •ecimals. 
 
 " (con' rait 
 ■»'-'. Circulatlnsr or Inl 
 
 A.i.ii 
 I>ivi». 
 Muittt 
 8abfn 
 Dekomiv i 
 
 DisCO' WT 
 
 I>er,i ii„ 
 
 True l)i„ 
 
 Bank 
 
 Division, Sh. r 
 Doniesti" . • It, 
 IVit I's Spe.-in.- 
 Enilowmenti li 
 
 Hates 
 
 r« Nl-UBKRS 
 
 on , 
 
 89 
 03-04 
 
 » 95-96 
 
 07-98 
 
 99-I0I) 
 
 (conti ..-ted) 101-103 
 . 101-106 
 
 r 
 
 109-113 
 
 - M-73 
 
 69 
 
 73 
 
 72 
 
 71 
 
 7475 
 
 180-197 
 
 i4-350 
 
 li.'-7-3f.1 
 
 ;<>■! 37 S 
 
 16-21 
 
 "77'i73 
 ^85 
 
 y.'i' ATio.'* -,r ArrotHTH. 
 
 I'. (In Hi inland I'ri.iilijl,.,' 
 
 .Sohi(i..ns liy Internt Alstd'od 
 • •• l'r.ii|ij.t •• . 
 r.x'han p, .Stock -".Manri. « " 
 
 "Cullattral-.." Ilypothetn, etr. 
 K\'IIAN.iH, llilltof., ... 
 
 I'l'Hnltions 
 
 Koriiifn Kvihanifo, .'.'..'. 
 
 " Cirdiii„iisKs-liini;.!;'.,4' 
 Inland or l>..nie,ti,. K\ j.anKf 4') 
 f.xpirtation of Ufe (Tal.le of( " " 
 
 (• VITORISO ■ " ,, 
 
 Ilil-'hestConiinon l'«(,.„, 
 I.>'.i8t C nnnon Multiple. . 
 IVncmif, Mta»irt-nient of Vk 
 
 <'i«es) 
 
 Firo Insuranoe 
 Kurciiin, and 
 
 Kxchan^fe 
 
 Krai Tio.Nij 
 
 Heflnltlons .,', 
 
 • ji'neral Principles ., 
 
 Kinds of Kractioni. .. in i! 
 
 I •■ liietion of '^^ ,!', 
 
 „ Inteirers ,| ) 
 
 .. " Mixid Xiiinbcra.. . c.') 
 
 " 'ni|"""Pir Krac's... . ci 
 
 Tra.'n to llijfher 
 
 20S333 
 
 :iH3-3-:i 
 
 206 317 
 
 207 310 
 
 41.'-t n 
 
 368 2'<3 
 
 4lL.'-l.'i,; 
 11:3- I^J 
 
 23; 
 
 . : I.-. 
 4()-l>i 
 
 ixer- 
 
 I'riivfo Circuitous 
 
 40S406 
 
 2:i:;-:',';t 
 
 401- M 
 37 39 
 
 49-.-.I1 
 
 o' Fr. to Lowest 
 
 Ternm . . 
 Ucluction 
 
 Terms 
 
 Ueijuition of 1>. to'Dc. inials .' ' 
 Kcduction to C.nin.rm Denon ' 
 
 mator -, 
 
 Addition of Fractiong',! «y 
 
 -Siibtrartion " an 
 
 C5 
 
 (in 
 93-04 
 
 Multiplication 
 Uivision of Frao'us (l,y Iiitii.'er)' 
 ^. . .„ " (liy Fr.ufn). 
 (•reatcst Common .Mta-iure 
 
 Funds, Sinkint- 
 
 Gain or L -ss i 
 
 7:!-73 
 7i»-,S4 
 337-339 
 /. ,-.-;■■-■ ■"''•ncrihip ..5J;i-f.3i 
 
 (jooiIs, How to ..lark ... loQ iin 
 
 Greatest Common Measure 
 
 • ntesrtrs) 43 ,. 
 
 <.rc„ est Common Measure (Frac- 
 tions) »., -^ 
 
 OROIND KKNT3 940-141 
 
 HiuirEsi CoMMOK Factor 'ilnlc- 
 
 „ e^"> 43-45 
 
 llioiiEST t MMo.v Factor (Fr ) 73-7S 
 
 nlandorDopiestio Fx.hant'e.. ■457.4C> 
 
 l.NSriTDTE op ClIARTKRKD AcCOf.VT- 
 
 , A^'TS 4''4-4'>7 
 
 'Tirr'" 12»-^M 
 
 I-ife, Whole and Endowment 34''.S47 
 
 •Mirinc wnoT, 
 
 Accurate Interest 334-3:i.i ; ' 5«-"o 
 
 n « ■ Reckoninir.. . . 336 
 Deflmi.ong _ .'.Sfi-^-jj 
 
 I 
 
vi. 
 
 ISDKX. 
 
 iKTtNMT, Si< !••' ' '«nt. M«tliO<l. . . 
 C' Mpouiid 
 
 " for 4i) \ .':»r« at I to In /, 
 i.ul"' mliiinif, Mf»»iirniii of . . 
 
 !«iihiinf, Mi'anuritiiiii't "'' 
 
 LlA»r (.■..y>i"!« Mii.riiLK, (In- 
 
 If-Sprs) 
 
 I.«4«Tt'.Mi("X Ml uriiLi!, (Kr.) . 
 
 ^„l-.i.'.J 
 17».iTil 
 
 .■s» 
 
 «MS 
 
 Osi.t;'.)'! 
 30"-:ill 
 
 lOB-no 
 
 (JUO-T'it 
 Ut I- 
 
 6(l-|.ti' 
 007-WJ 
 
 LiKi l>'Cn«M * 8tt-l47 
 
 iK'tlniiiiin!! £p«i-ri'>i 
 
 K»(wUii.iiiof ',if« (Table of).... i'J 
 
 Whole I.it« lniiir»iu'« (Tal)li! of 
 
 Kite.) „. ■,•■■, 
 
 Enilnvniunt lii'iiiuiira (Table "' 
 
 llal.n) 
 
 LOXdin III AMI TiuN , , 
 
 SimnilardTiiiii', («ilbTaM') 
 To KinJTimofr'im l.oi.ifii'i'l''. ■ ■ 
 •' l.iiu'itiick- tr..ni Time.. 
 
 Table of Lonnitiiik" 
 
 Lumber, Muiuni" liitof 
 
 Marine Inmirar. 
 
 M>HKIMHl'>'ll"*, ilt'u.le< . 
 
 Maminry, Miasuriin' lit of 
 
 MtAHi'Kr.^, drain, Li<iiruU, Linear. 
 
 tic 
 
 Mls»iK*Ti(i.s, I'KAi ricAL JW-41* 
 
 ItelinitioiiH 0U6-tJl]| 
 
 SurlaitH— UuailrilatiraU, (il3-ii'-3 
 
 " -Trianu'lcJ 024 ■;3J 
 
 " -I'ohtfiiiij <J3j 
 
 " -.fip'le 630<aii 
 
 S"liili-l>"tlMilioiH ..tl0045; 04H.i;:>l 
 
 " — I'rimii or C'vlindcr 
 
 " — I'jrramiil or Cone 
 
 " — SplnT.' 
 
 Cubli'al I Cinliriis anil 'Jim.. 
 
 Contcnti f Casks, Gaii^'ini; ot.. 
 
 Measurement of Carpftini;, Wall 
 
 I'aiifr, Saw Lo^s Lumber, 
 
 ShiiiBllnif, Fentliii;, raintint;, 
 
 Pavinof. Lalhintf, Plasttrinif, 
 
 Stone-Work, Bri.k-Work 670-.U 
 
 Mbrcaktil* Aritiimi'.tu -Institute 
 Char. Afcnt. Kxaiii. Ques- 
 tions 428-480 
 
 Mftric Svktim or Mkas't ^'"^H 
 
 M18CIU.LANK01H I'nOHtKMS 78-83; 
 
 [).43-iea; 840-247; U»'M 
 Mn5KT AND CiBiiKNtv, with Tables llll-KU 
 Ml LTirLiCATioN, Short Methods in. 4-15 
 Paintiiii; »nd Kawomininif, Mtaa- 
 
 urtinciitof f"*^' 
 
 Papcrini{(\Vall) Measurement of . C74-C. 5 
 Pariial Pavmknts, how Beik'd.. 198-204 
 
 Partner.s ii- 807-328 
 
 Definitions • 611-y-S 
 
 Division of Gain or Loss, equal 
 
 time • 
 
 Division of Gain or Loss, unc<)ual 
 
 tiuie 
 
 To And Net Uiin or Loss 
 
 ' ' each Partner's Interest . . 
 
 Parintf, Measurement of 
 
 Pkrce.staub (with Table) 
 
 Peri>etual Annuities, to fir (I Value 
 
 PlaaterinR, Measurement of 
 
 Powers a.vd Roots 886 363 
 
 Definitions 6>;«-5'.i6 
 
 Square Koot 597-m) 
 
 Cube " eOl-601 
 
 529 
 
 530 
 
 5:n 
 
 632-5:i4 
 
 t;;it 
 
 84 89 
 
 o.'.0 
 C95-r.!»» 
 
 Vta'-' al Mennuratlon 864-414 
 
 PH.HT AMI L"w» a^^ 
 
 Phihohti im WJ-306 
 
 Miintili, l'rti|iortloil .,.'''11 
 
 Conipound " 601-MW 
 
 Distributive" 5>iU..M0 
 
 "I'uts'and"! «lls"oii bt... k Ex. 41'.' «0 
 
 i^iianlilin, Ki'l "lion oJ ''"''2 
 
 llAiio. Dellnltii i.sof 184 
 
 Umii^TloN of Kractioii* C2 lu 
 
 " " yiMntiliit, Asiind- 
 
 Injr and Dewen-llii: i^Ji"!! 
 
 Root— .S.|U«re and t lUie 886-863 
 
 tiiwloifs, Miamireiofiit of ("^Hi 
 
 Tablet 'j''/* 
 
 .Shuiirlinif, Miasutemmt ot tul 
 
 isiioar MBTiions in Addition .5 
 
 '• •' " iMvixion ..... I .1 
 
 <• •• " Multi|ili'atioti.. >• 
 
 •• " '• Deiimals — 
 
 Multii'li'-ation lii'Lo 
 
 SisKixoKi NU». . . . 837-o3» 
 
 Miihire, .Mi-asureimiit of C'J Iiti4 
 
 •sLrAKKHoor W"-'>"" 
 
 SfAMJAiiiiTiMii, hiiw Uei konid .. Is3-l»» 
 (Stn.k Triiiisai tiont, how Ueik- 
 
 ,,ii,.,i 248-867 
 
 Stoi i>s, Ho> A, i>r! Ksn iiKs, 6i<\ 848-267 
 
 liennitioiisofTirma tlS-VH 
 
 ,si,Kk Kxrhin-e, Metlnxls 01 
 
 l-urrhase and Sale 429-440 
 
 Sl.Kk Kx.haiiL'e, Kulei to Fin I 
 V.1IU0 of aiiares, Dividend, 
 
 Income, cti- l^tVJi. 
 
 Stocks 248-280 
 
 STOCK ExciiA.NoH 841-267 
 
 Bliort Metho<i» in Decimals — 
 
 Livision 10.-103 
 
 Shrrt Method* in Calculations <6-_il 
 
 Stone-work, (easureniint of f.!)'.t-704 
 
 STOHAoRiin irage Keccipts . 284-231 
 Straiubt o. .le Life Insurance 
 
 (Table* 69« 
 
 TaiilksofL TIDB J«.i,„ 
 
 Taxks (with Table) l^'"? 
 
 Time, Standard, how Hcckoiied . . l"^-''^ 
 TB*D«I>iscot-»T, with Problems .. 94-108 
 
 IKtlnitioiis . 312-3iO 
 
 Tax Table at 3 n. .Us , ■ . • ,^, 3-'5 
 
 TRfB I>l»corNT, how Keckoned ... 3S,-3OT 
 
 Wall I'aiier, Measurement Of 074 C78 
 
 WmoiiTS AND Measi KK.S 81-61 
 
 Money and Currency (with 
 
 Tillies) . 1"-134 
 
 Apotliecuries' Weight and Mea. 13j 138 
 Avoinlupois " (with Tab.) 139-142 
 
 Comparative Table of Wu'ts 143 
 
 (5rain Measure (Table) 141 
 
 l,rv ■• " HS-l-'O 
 
 Lii'iuid '• " i:il-l5J 
 
 Linear " includ. Surv.'V- 
 
 or's (Tables) 1.55-153 
 
 Square Measure, includ. Survey- 
 or's (Tables) L'-g-m 
 
 Cutiic Measure (Talib ) li;-,-ltW 
 
 Time " (Tables) 169-179 
 
 Miscell. Tables— CoiintinK 18'" 
 
 " " -Paper 181 
 
 •• •• —Books 182 
 
 Whole Life Insurance (Table of 
 
 Bates) ^5* 
 
ClIAKAC'rr?;s ASU Al;rT?EVIATION^ 
 
 USED IN in SI s.s. 
 
 r 
 
 0/ 
 
 1 
 I 
 
 f 
 
 IMTlrO 
 
 At 
 
 Account. 
 (Vnfi!. 
 
 I'll- Cl'llt. 
 
 XiuiiImt. 
 
 Oriii iin I onc-qimrtor, 
 • 'no ftiirl line half, 
 ' iiioaiiil thrfc ijii.irtiTH, 
 (Ik i-k ninrk. 
 Ily, n^ 14 . IS inches. 
 It..ll...s. 
 
 I'miiihI sterliiij'. 
 Kii(,'li>h BhilHiijjn nni 
 ft. fivciucntly written in" tliH 
 niaiiti.-r, tho shillin;,'s on tlio left 
 <-f th.) iilopiiig li, ,^ ai.,1 thoi«.n<:.i 
 «nl \i> litiht, thu aluivo meaning, 
 fl Kli 'lings ami 3 iwuce. 
 * 'iiy In -21. The day of niaturit v, nn 
 vpressud inaii,,te, and tlio'la.st 
 V of glare aio indicated l.y 
 wutingthe first on the left and 
 the soconl on the right of the 
 sli'ping line, 
 lodoz. §/„ .^,",, a,^^. Fifteen do/.., 
 .1 of whi( h are Sl-J per doz., 5doz. 
 at $I.j, and 5 doz. at §18 per do/.. 
 
 • 1 'W pounda gross 
 hlul. Sugar, weiuht, I.m ll.s. tart-, 
 ',".'? „ „ "^ weight of hhd., 
 _'■'■> !'-l->lb»., <JJ5 lbs., nit weignt. 
 421 '''^*' numbera in 
 
 I , „u , the bracket are the 
 n-^" yia. number of yards in 
 .' cai;h piece respec- 
 
 tively. 
 i G 1-\(a 3 ti. 4 doz. No. 
 •> (" 2 sinllings pur doz. ; doz. 
 A o. 8 C<i 3.I. GY. i)LT doz. 
 
 W. W. and similar characters 
 and letters are placed on pack- 
 figcs to designate a particular 
 I'lt or shii)nient. 
 
 i';;""N:ir..iiimil.or»fl.iriilmark.M) th.it tli.'vm.iv 
 K- Uidtln4,'u,,ln,d With,, jt luliiut,. closcrii'ti.'ii , ^ 
 
 7 X 9, or 
 
 long. 
 
 4ps.| 
 
 10 d 
 
 by 9 in. 7 in. wide, 9 in. 
 
 •^ ' First cla ». 
 
 •^'^^^ Account. 
 
 ■^''^' AdM'fiiiiii'. 
 
 [ -^tft Agent. 
 
 ••^'"' Amount. 
 
 •^«»«i Assorted. 
 
 H-^ Rillbook. 
 
 V Halunee. 
 
 *'' liarrel. 
 
 '"■• liundles. 
 
 " '« Hags. 
 
 '"l" Haskets. 
 
 Rtk \\W\i.. 
 
 Ws Hales. 
 
 "ot Hought. 
 
 KL. oris. o(L. Hill of Lading. 
 
 ' » V HillH payable 
 
 '"'•J<t"-' Bills receival.le. 
 
 '"k Bank. 
 
 'rot Brought. 
 
 B<1'10 Barque. 
 
 Jlr Brig. 
 
 Bin Busheli. 
 
 Bxs Boxes. 
 
 ^ Cents. 
 
 (J or centum . . Hui..lred. 
 
 ^'■•^ Cash book. 
 
 <k Check. 
 
 ','"? Capital. 
 
 '']"• • • Company. 
 
 ?V-P Colle<t 0.1 delivery. 
 
 </'ld Colored. ^ 
 
 ^''' Creditoi. 
 
 Com Comr 
 
 Cons't 
 Cs.... 
 Cwt 
 
 niis8ion. 
 Coneignment. 
 
 Cases. 
 
 \y^'^ Hundredweight 
 
 C/o Caroaf. 
 
 ^, Pence. 
 
 ^}^ Draft. 
 
 i^!^' Dividend. 
 
 Disct Discunt, 
 
vni. 
 
 CHARACTERS ANU ABBUEVIATIOXS. 
 
 Do. or DiUn. The same. 
 
 l)oz Dozen. 
 
 Dr Debtor. 
 
 Ds r>ays. 
 
 Ea I'^ch. 
 
 £. E Krrora expected. 
 
 e1 & O. E Errors and omissions 
 
 exccpUd. 
 
 Eng English. 
 
 EntM Entered. 
 
 Ex Without, as ex-divi- 
 dend. 
 
 Exch Exchange. 
 
 Exps Expense:?. 
 
 EmbM Embroidered. 
 
 Fig'd' Figured. 
 
 Eir Firkin. 
 
 E. o. b t ree on board. 
 
 Fol Folio. 
 
 F'wd or for" wd. Forward. 
 
 Er From or French. 
 
 Fc Franc. 
 
 Fr't Freight. 
 
 Ft Feet. 
 
 Gal Gallon. 
 
 Gro Gross. 
 
 Guar Guarantee. 
 
 Hdkf Handkerchief. 
 
 Hhd Hogshead. 
 
 Hund Hundred. 
 
 j_ JJ Invoice-book. 
 
 In. or" Inches. 
 
 Ina Insurance. 
 
 Insol Insolvency. 
 
 Inst. (Instant). This month. 
 
 Int Inl rest. 
 
 Inv Invoice. 
 
 Invt'v Inventory. 
 
 I. O.'U I owe you. 
 
 Lbs Pounds. 
 
 y\ Thousand. 
 
 Mdse Merchandise. 
 
 Mo Month. 
 
 Mols Molasses. 
 
 M. 't Empty. 
 
 Xet . Without deduction. 
 
 Xo Number. 
 
 X. 1' Notary public. 
 
 0. I. B Outward invoice-book 
 
 Oz Ounces, 
 
 Paym't Payment. 
 
 F'd Paid. 
 
 Pkgs Packages. 
 
 Pr. or Per .... Hy. 
 
 Per cent By the hundred. 
 
 Pp Pages. 
 
 I'r Pair. 
 
 Preni Premium. 
 
 Pros (Proximo)Tlie next month. 
 
 Ps Pieces. 
 
 Pts Pints. 
 
 Qr Quarter. 
 
 (^ts (Quarts. 
 
 Qtls (Quintals. 
 
 Rec'd Received, 
 
 Recpt Receipt. 
 
 R. R Railroad. 
 
 Rs. or Rla Reals. 
 
 R. W Regular way. 
 
 g Shilling, 
 
 Shipt Shipment. 
 
 Shs Shares, 
 
 Schr Schooner. 
 
 S.S Steamship. 
 
 .S(j S(juare. 
 
 Stor Storage. 
 
 Stb't Steamboat. 
 
 Sunds Sundries. 
 
 Super Superfine. 
 
 Str Steamer. 
 
 Tes Tierces. 
 
 Ult. (Ultimo) . .The last month. 
 
 Ves Vessels. 
 
 Vs Against. 
 
 Viz Namely. 
 
 Wt Weight. 
 
 W. I West Indies. 
 
 Yds. . 
 Vr. . . . 
 
 Varila 
 .Year. 
 
 fT^^^H^^M 
 
ADDITION. 
 
 1. Rapidity and accuracy in addition are of the first 
 •mportance to the commercial student. 
 
 These can be acquired only by a thorough familiarity 
 ^v.th the simple combinations of numbers, and a proper 
 practice with these combinations. ^^ 
 
 The following Tableo exhibit all the combinations of 
 numbers and the attention of the student is especfalh 
 
 Combinations ending with o. 
 
 12 3 4 
 
 9 8 7 6 
 
 5 
 6 
 
 
 10 10 10 10 
 
 10 
 
 
 Combinations ending with i. 
 
 
 
 i ^ 3 4 
 9 8 7 
 
 6 
 6 
 
 
 1 11 11 n 
 
 V 
 
 
 Combinations ending with 2. 
 
 
 
 12 3 4 
 
 10 9s 
 
 2 2 12 12 
 
 6 
 7 
 
 12 
 
 6 
 6 
 
 IS 
 
 Combinations ending with 3. 
 
 
 
 2 8 4 6 
 10 9 8 
 
 6 
 7 
 
 
 13 
 
 IS 
 
 18 
 
ADDITION. 
 
 Combinations ending with 4. 
 
 » Q a 6 
 
 4 6 
 
 9 
 
 6 
 8 
 
 7 
 7 
 
 -; 1 4 14 14 14 
 
 Combinations ending with S 
 
 H 4 •'> 6 I 
 
 2 1 _0 _9 J 
 
 11 5 15 16 
 
 Combinations ending with 6, 
 
 c 
 
 
 
 7 
 9 
 
 1 6 6 6 16 
 
 Combinations ending with 7- 
 
 i: 7 
 
 8 
 16 
 
 4 
 8 
 
 2 
 
 
 1 
 
 7 
 
 
 7 7 7 7 17 
 
 Combinations ending with 8. 
 
 4 5 « 7 8 
 1 3 2 1 
 
 1 8 8 8 8 18 
 
 Combinations ending with 9- 
 
 ,. rr J 
 
 5 
 4 3 
 
 7 3 9 
 2 1 _0 
 
 1 9 9 
 
 iff.r the Student becomes familiar with the foregoing! 
 eo^b:;:aS::M:^atto.Uonisd.eoteatotheuseoftlK. 
 
 enain-a. Frroxnmple: 
 
 . V. 17 t r. - -^3 27 A G - 33, 37 & 6 = 43, Ao. 
 
 n::;;;: llir-s^; ■».:.-: a,.-.-.«,-. 
 
 i e the .um ../ any two nuMa-,. »n« 0/ which e«,h mtk 
 
 CO inhi nations. 
 
ADDITION. 
 
 8 
 
 a. An effective drill may be given to the student by the 
 ase of the following diagram : 
 
 
 The teacher places any number within the circle and 
 requires the pupils to add to it any number or succession 
 of numbers to which he may point. 
 
 Rapidity and accuracy in addition can be gained only 
 by adding columns of figures. 
 
 ». In adding ledger columns, accountants frequently use 
 the foilowiug devices : 
 
 EXAMPLB 1.— 
 
 892G42 
 
 41). '(8 
 
 07.84 
 
 81ij.'>5 
 
 481)7.89 
 
 0ili74 
 
 61S7.45 
 
 $14222.87 
 4454 3 
 
 The figure to be earned is placed under the column to which 
 II bclou'is 80 that in case of interruption or mistake it niay be 
 used for reference. 
 
ADDITIOH. 
 
 4. EXAKPLB a.— 
 
 93746 
 2386 
 91642 
 28735 
 82614 
 79186 
 
 257S8 
 8721)4 
 19283 
 63127 
 68432 
 
 82(;91 
 35117 
 63.i29 
 48703 
 21734 
 
 3283M 
 
 203846 
 
 252134 
 
 784288 
 
 The column to be added is divided ^-^^ ,e^.ralJan^ 
 
 These parts are added and the sum of the results then taken. 
 
 5. Addition of two or more columns at the same time. 
 
 ExAUPii 8— ^^ 
 
 76 
 47 
 
 247 
 Mbthod of Addition— 
 
 47 & 6 make 63. 53 & 70 make 123. 123 & 9 make 182 
 132* 80 make 212, 212 & 5 make 217. 217 & 30 make 247. 
 
 Columns of three or four figures may be added in the 
 same way, or by adding two columns at a time. 
 
 The methods employed in Examples 2 and 3 are exce^ 
 lent tests of the corractness of addition performed m the 
 ordinary way. 
 
 «. To find the sum of any series of numbers which 
 have a common difference. 
 
 BUUI. 
 
 Multiply the sum of the first and last terms by the number 
 of terms and divide the result bif 2. 
 
ADurnuN. 
 
 BzAMPU l.-Add. 16. 17, 18, 19, 20, 21, 23. 28, 84. 25, 36, 37, 
 Opkraiion. Common difference is I. 
 
 16 first term. 
 27 laBt term. 
 
 43 
 
 12 number of terma. 
 
 8 ) 516 
 2a8 
 fiXAMPLB 8.— Add, 48, .56, 64, 72, 80, 88, 96, 104, 118. 
 48 
 113 Common difference i> ft. 
 
 160 
 9 
 
 IM440 
 
UULni'LlOATIOH. 
 
 MULTIFLJCAriON. 
 
 SnORT MRTHOOS (S itur/npucATios. 
 
 7. To multiply by any of the numbers from li to ic 
 Inclusive. 
 
 Multiply 4026 by 14. 
 
 4625 
 14 
 
 64750 
 
 nnST MBTTIOD. 
 
 6x4 ^ 1Q carry 2 
 
 2x4 + 2 (carried;' • i » 15 " 1 
 
 6 X 4 + 1 ( " ) + 2 = 27 " 2 
 4x4 + 2( " )+C = 24 " 2 
 
 2 ( " ) + 4 = 6 
 
 The student will observe thnt wo multiply by 4 iu the 
 ordinary way, but in addition tu the ordinary number to 
 be carried we also carry tiie tlgure to the rignt of the figure 
 multiplied. 
 
 82C0ND MKTHOO. 
 
 4C25 X 14 
 18500 
 
 64750 
 
 Multiply by i, placing the product one place to the right 
 and add. 
 
 Note.— This method may be applied when the multiplier has one or 
 more ciphers between the two iif^urcs, by writing the product two or 
 more places to the right, and addinj,'. 
 
 EXERCISE I. 
 
 Multiply — 
 
 1. 796'.i6 by 11, 12, 13. 14, 15, 16, 17, 13. 19. 
 
 2. 87295 by 102, 104, 105, 107. 
 
 3. 49273 by 1003, lOOG, 1008, 1009. 
 
 WM^^ 
 
MULTU'LlCATloS'. 
 
 7 
 wifi i^"" """^"^^^ ^^ *"^ """^^^'- °^ two figures ending 
 
 Multiply 84G by 41. 
 
 WB8T METIOD. 
 
 S^lf C X 1 _ 
 
 6 4 
 
 « X 4 + - (carried) j. t _ oo •• « 
 
 8x4 + 2 " =34 
 
 The Student Will Observe that we place tl^e units figure 
 the mult.phcand as the units figure of the product 
 
 ber'toT" '/' '"' " ^''"^"^ *" ^^« ordinary num.' 
 
 g^g ., SECOND METHOD. 
 
 8384 
 
 846S6 
 
 anf aid'''' ""' '' '^'''°« *^' P'""^"'^* °"« P^^°^ *° t^« '«« 
 
 Pliu^e. to the S; *"' '^"" 'y """"^^ ^^« P-'*-* *- - -or. 
 
 aruitipiy- ^^'"^•SE 2. 
 
 1. e427N by 21, 31, 41, 61, 61, 71. 81, 91 
 
 9. 873% by 301, 501. 601, 801. 
 
 8. 93254 by 2001, 3001, 7001, 9001. 
 
 ». To multiply two numbers in which the unit* 
 
 ExiitvLB 1.— Multiply 74 by 76. 
 
 74 
 
 76 
 
 I5i;ai 
 
 METHOD. 
 
 4 X 6 = 24 
 
 (7 + 1) X 7 = 56 
 
 Multiply 123 by 127. 
 
 ^^ET^OD. 
 3 X 7 « 21 
 (12 + 1) X 12 . m 
 
UULTlI'llCATWS. 
 
 
 
 
 EXERCISE 3. 
 
 
 
 
 84 X Si6. 
 
 7. 
 
 92 X 9H, 
 
 13. iia X lis. 
 
 19. 
 
 153 X 157. 
 
 
 55 X 55. 
 
 8. 
 
 OJ X ftl 
 
 14. V2A X 127. 
 
 20. 
 
 101 X 499. 
 
 
 V'2 X 78. 
 
 9. 
 
 °5 K H.'). 
 
 15. 101 X 106. 
 
 21. 
 
 694 X 69o. 
 
 
 05 X 65. 
 
 ]0. 
 
 .t" X <X:. 
 
 16. 10'. X 105. 
 
 22. 
 
 22.5 X 225. 
 
 
 (Yi X 67. 
 
 11. 
 
 78 X 72. 
 
 17. ioi X 10'.». 
 
 23. 
 
 392 X 398. 
 
 6. 
 
 3) X M. 
 
 12. 
 
 91 X W. 
 
 18. ■-iCJ X 298. 
 
 24. 
 
 173 X 177. 
 
 lO. To multiply two numbers in which the units 
 figures are the same. 
 Multiply 46 by ij6. 
 
 
 46 
 
 
 
 
 
 METHOD. 
 
 
 
 
 66 
 
 
 
 6 X 
 
 6 
 
 
 - 86 
 
 carry 8 
 
 
 3036 
 
 
 
 (4 + 
 
 6) 
 4 
 
 X fi + 3 (carried; 
 X () + 6 ( " ) 
 
 = 63 
 = 30 
 
 carry 
 
 
 
 
 
 EXFR 
 
 ■.ISE 4. 
 
 
 
 1. 
 
 21 X 51. 
 
 7. 
 
 64 
 
 X ••4. 
 
 
 13. 19 X 29. 
 
 19. 
 
 105 X 126. 
 
 2. 
 
 53 X 53. 
 
 8. 
 
 8'i 
 
 X :}';. 
 
 
 iK 27 X 47. 
 
 20. 
 
 113 X 13:;. 
 
 3. 
 
 ■io X 25. 
 
 9. 
 
 47 
 
 X ^7. 
 
 
 I,-.. 3t; X 56. 
 
 21. 
 
 114 X 144. 
 
 4. 
 
 67 X 57. 
 
 10. 
 
 ,"K 
 
 X ■1'^. 
 
 
 \^i. 81 X 34, 
 
 22. 
 
 IP.O X l-.M). 
 
 5. 
 
 28 X ;i« 
 
 11. 
 
 81 
 
 X 91. 
 
 
 17. 83 X 73. 
 
 23. 
 
 125 X 135. 
 
 6. 
 
 92 X 72. 
 
 12. 
 
 42 
 
 X 72. 
 
 
 18. 110 X 140. 
 
 24 
 
 117 X 197. 
 
 II. To multiply two numbers in which the units 
 figures are unlike, the remaining figures being alike. 
 
 ExAMPLi 1.— Multiply 78 by 73. 
 78 
 72 
 
 5616 
 
 Mktiiod. 
 8x2 ■: 16 cnrry 1 
 
 (8 + 2) X 7 + 1 (carried) = 71 carry 7 
 7x7 + 7 (carried) = 56 
 
 ExiMPLB 2.— Multiply 126 by 122 
 126 
 122 
 
 15372 
 
 ;\fLruoD. 
 
 0x2 = 12 carry ] 
 
 (6 + 2) x 12 I- 1 (carried) = 97 carry 9 
 
 12 X 12 + 9 (carried) = 153 
 
 EXERCrjE 5. 
 
 1. 
 
 37 X 35. 
 
 7. 
 
 68 X 01. 
 
 13. 
 
 18 X 43. 
 
 19. 
 
 110 X 113. 
 
 2. 
 
 54 X 52. 
 
 8. 
 
 74 X 78. 
 
 11. 
 
 20 X 27. 
 
 20. 
 
 121 X 125. 
 
 3. 
 
 75 X 76. 
 
 9. 
 
 85 X 84. 
 
 15. 
 
 57 X 59. 
 
 21. 
 
 i:!0 X 134. 
 
 4. 
 
 83 X 82. 
 
 10. 
 
 91 X !)2. 
 
 IG. 
 
 38 X 37. 
 
 22. 
 
 117 X .Ml. 
 
 .5. 
 
 27 X 29. 
 
 11. 
 
 74 X 72. 
 
 17. 
 
 01 X 69. 
 
 23. 
 
 157 X 159. 
 
 6. 
 
 46 X 45. 
 
 12. 
 
 63 X 65. 
 
 18. 
 
 78 X 74. 
 
 24. 
 
 323 X 322. 
 
ilUI.TlVI.l'MioS. 
 
 W\ 
 
 12. To multiply by means of cross multiplication. 
 
 ExAMPLJ' 1 - Multiply 6G by Oa. 
 
 •JO METUOO. 
 
 03 0x3 -IS, carry 1 
 
 — — 5x3+1 (carried) + 6 x G = 52, " 6 
 
 3.J2S "i X ti + 6 ( " ) 85 
 
 Kx.'.v:m: •-'.— .\Iiilti[ily Hi;! by 23. 
 
 JIKTIIOD, 
 
 6x3 = 19, carry 1 
 
 4x3 + 1 (carried) + 6x2^ -i't, " 2 
 
 310 
 
 \. 
 
 ■i. 
 3. 
 •1. 
 5. 
 
 31) X 32. 
 
 ■:: y 21. 
 
 7,1 X 1."). 
 
 ■^7 X '.>7>. 
 
 •.:•' X 51. 
 
 8 X 3 + •_' ( 
 8 X 2 + 1 ( 
 
 EXERCISE 6. 
 
 6. 45 X 02. 
 
 7, 39 X 74. 
 f.'. 82 X 61. 
 9. 37 X 22. 
 
 10. Ii5 X 2'). 
 
 ) + 4 X 2 = 10, " 
 ) - 7 
 
 11. .340 X 4.3. 
 
 12. 008 X 37. 
 18. 54.1 X 23. 
 
 14. -•■■O X 48. 
 
 15. 32r,8 X 7J. 
 
 1 
 
 i:». To multiply by a number Ciiding with 9. 
 
 r.ci.i:. 
 
 Multiply by 1 more than the ijici-n inidtiplier and snlstract 
 the multiplicand. 
 
 Multi-jly 2(53 by 60. 
 
 OPEIUTION. 
 
 18410 (yradurt by 70) 
 203 ( " " 1) 
 
 on) 
 
 
 16117 ( " 
 
 1. 
 
 2. 
 i. 
 
 EXERCISE 
 Multiply— 
 3704 by 79, !9. 
 4G251 Ijy :J9, 50. 
 37284 by [)'.), 09. 
 2'..0:;.- by 80. 20. 
 
 5. 1^250 by 119, 399, ino. 
 
 6. 47:i:i5 by 2:ii), U'M. 709. 
 
 7. 27034 by U9, 240, 189. 
 
 8. 1 71^^25 by O'.W, 409, 139. 
 
 ? f . To multiply by a number v/hich is a little less than 
 ICO, 200, 300, 400, etc 
 
 RCLE. 
 
 Multiply the muliipViraiul hy the .U(feunce between the 
 multiplier and 100, 800, 300, or etc., and suLilract the pro- 
 duct from the V'-"dnr( of tlie multiplicand by ICO, 200, oOO. 
 or etc. 
 
 ■3 
 
10 
 
 UULTIPUCATION. 
 
 .Multiply 676 by HV. 
 
 DPr.IlVTtOM. 
 
 676"( diuHluct by 100) 
 202.i I •• " 8) 
 
 1. 
 
 a 
 
 B 
 4 
 
 6647:, ( • " 97) 
 aERCISE 8. 
 
 ''8'ci!4''br "^. '■■■'>■ »* 5- •^'■'"«2by9'J3. 796, 990. 
 
 41623 by it;J, '.'•';. 97 6. lUU;iby988, ■,.■!. 791. 
 
 ^7186 by 296. DS. 7. 802.^7 by 989. w:i,m 
 
 8124 by 794. H97. 8. 17b24 by 9'..2, iW.K '.m 
 
 15. To multiply two numbers, one of which is more 
 and tlic other less than lOO, looo, etc 
 
 Thf complement of a number is the ditTcreiiCo between 
 that number and tbv uuit of the nest higher order. 
 
 Multiply the tumofthennmhen is» the unit of comparUon 
 by the unit of comparison, and from the product iubstract the 
 product of the exce»y and tiie. comph'ment. 
 
 Multiply 108 by 94. 
 
 Unit of comparison is 100. 
 
 
 
 I>8 .. .. 
 
 8 excess. 
 
 
 
 
 
 '.14 .. .. 
 
 6 complement. 
 
 
 
 
 
 10200 
 
 48 
 
 product of the excess and 
 
 METHOD. 
 
 oompl 
 
 ement 
 
 
 10153 
 
 
 
 
 
 108 - 6 =. 102 
 
 
 
 
 
 
 or 94 + 8 = 102 
 
 
 
 
 
 or 
 
 108 + 94 " 100 r. 102 
 
 102 X lO) = 10200 
 8x6= 48 
 
 
 
 
 10153 
 
 
 
 
 
 EXERCISE 9- 
 
 
 
 1. 
 s. 
 
 8. 
 
 4. 
 
 6. 
 
 107 
 105 
 113 
 103 
 106 
 
 X 97. 
 X 96. 
 
 X 88. 
 X 94. 
 X 92. 
 
 6. 112 X 91. 
 
 7. 115 X 93. 
 
 8. 108 X 96. 
 
 9. 114 X 95. 
 10. 104 X 87. 
 
 11. 
 12. 
 IS. 
 14. 
 16. 
 
 1012 X 994. 
 1015 X 988. 
 1032 X 998. 
 1064 X 993. 
 
 1025 X 989. 
 
MULl LlCAtluy. 
 
 1 
 
 iH. To multiply two nu ib^rs of the sam«? i. umber oJ 
 figures over and near lOO, coo, etc. 
 
 From the iiim nf tin' HUin''c < sii'nttritft th/^ unit of campin 
 Kon, and to the riijht of th> > mlt write thr product of tl. 
 I'xceaet. 
 
 NOTVa. 
 
 1. When there wre fewo^ tif^nrm ic the proiluot of f>ic eioesstn tin 
 cipbere in tLe unit of coMipariiioD. wri! - ci^iliura in th rtsult to eappiy 
 the deAciincy. 
 
 m 
 
 'i When tliere fcr^ 
 
 ik^jf s in t ' product of the exceesea t 
 
 cipliere in thi it ■ 
 
 »* 
 
 iBou edd «xiM>aH on the left Land to 
 
 first part of thu reit, 
 
 
 
 B Aft<:r practice, 
 
 'ingo!' the (!< 4>kmeuta or Uie ezoeeeai 
 
 ezunipleo whore M><" 
 
 
 I ma be nui ed. 
 
 Multiply 11'.: 
 
 4 
 
 KS-THfTB. 
 
 m .. -i^ 
 
 .SP 
 
 iia -f- 6 s 118 
 
 106 ., .. « 
 
 M 
 
 « '1 + 12 = 118 
 
 11872 
 
 
 ^ 112 + lO'' - 10 » ^ 118 
 12 X = 72 
 
 Unit al oompar 
 
 i» 1 . 
 
 
 
 ' HC Z 10. 
 
 1. ll'i X m 
 
 ». 
 
 ii< y lOs 11. lOOC, X 1003. 
 
 2. 108 X iLil. 
 
 
 in^ X Hi. 12. 1017 X 1003. 
 
 8. 116 X liW. 
 
 it 
 
 X im. 13. Il;i5 X 1009. 
 
 4. IIH > 4. 
 
 ij 
 
 . 108. 14, 10:ii X 1005. 
 
 6. 105 > «. 
 
 10 
 
 . X 1 • 1.5. 1075 X 1012. 
 
 17- To multiply bv reans oi complements. 
 
 From either mimhu r set the complement of the other, 
 anil to the right nfthf rrM-, 'vrite the product of the comple- 
 mentt. 
 
 NoTB. — The notes of At 16 apply ir; 'lieae problems if we aabititate 
 the word " oomplementa " in place of " Lj,.cussea." 
 ExAMTLB 1.— Multiply 94 by 03. 
 
 94 .. .. 6 complement. 
 
 98 .. 
 9219 
 
 HETnoD. 
 
 94-2 
 or 98 - 6 
 OI 34 + 98 
 
 92 
 
 92 
 jt92, omit the 1 
 
19 
 
 MULriPLlCA I ion. 
 
 
 KzAMrLi a— 
 
 ExAurLi ^-> 
 
 
 9r7 • • •• 9 
 
 «85 
 
 .. .. 818 
 
 
 99-J .. .. 8 
 
 »06 
 
 .. .. 4 
 
 
 9eOO'J4 (Me Note 1.; 
 
 OM-iCO (•MNotflS.) 
 
 
 EXERCISE 11 
 
 
 
 1. 
 
 97 X »«. 6. S8 X 03. 
 
 
 11. 903 X 09S 
 
 3. 
 
 96 X 'J3. 7. H7 X 88. 
 
 
 19. 997 X 9M 
 
 S. 
 
 94 X 95. 8. 84 X 92. 
 
 
 13. 095 X 998 
 
 4. 
 
 99 X 94. 9. 7r. X 96. 
 
 
 14. 0' 788 
 
 S. 
 
 98 X 02. 10. 9a X 85 
 
 
 15. 991 X 885 
 
 I.H. To multiply by means of factors. 
 Thf factors of a miiabor are the numbcis whoBe product 
 is tqual to that niiinhor. 
 Multiply 865 by 35. 
 
 86 - 7 X 6 
 
 806 
 7 
 
 UITUUO OUITTINa UCLTIPUIM. 
 
 865 
 
 6055 produced by 7 
 5 
 
 80276 
 
 6055 product by 7 
 
 30275 
 
 626 X 36. 
 327 X 64. 
 496 X 48. 
 878 X 77. 
 
 S. 
 
 6. 
 7 
 
 8. 
 
 13. 
 14 
 l.V 
 
 ir>. 
 
 " •• as 
 
 30687 X lO.V 
 209.^0 X 121. 
 41378 X 154 
 ?ir.254 X 226. 
 
 " 85 (6 times 7) 
 
 EXERCISE. 
 
 296 X 90. 9. 13:.l X 42. 
 a 13 X 72. 10. 41 04 X .35. 
 764 X 66. 11. ,127 x 126 
 82/ X 45. 12. ,1174 x 'Vi 
 
 I1>. To multiply when one part of the multiplier is a 
 factor of the other. 
 
 liTTue. 
 Multiply by the part <f the multiplier which i$ a factor of 
 another part, plinng the Jirit figure of each partial product 
 under the right hand ^figure of the multiplier which produced U. 
 ExAMPLK 1— Multiply 457 by 348. 
 467 
 248 
 
 3736 prodaot by 8. 
 11208 •• •' 24 (8 times the jroduot by <). 
 
 115816 
 
MULJir'.K Auon. 
 
 ExA^fLc 2— Multiply ei3 by 430. 
 4.10 
 
 2r,Ti product by 4. 
 
 '■^'" "* ■' " "15 (9 tiniM tn« product l>y 4). 
 
 2H()a48 
 
 Exiupuc .'i Multiply 8247 by 843. 
 a.M7 
 842 
 
 C\'\{ product by 3 
 
 *" '■'^'^ " " 4 (2 time* the product by 2). 
 
 36976 <• «• 8 (2 " •• 4). 
 
 18 
 
 
 3733974 
 
 
 EXERCrE 12. 
 
 
 
 1. 
 
 Mi X 120. 
 
 8. 
 
 31»Vl X 427. 
 
 15. 
 
 872S1 X 833 
 
 3. 
 
 47.) X 27l». 
 
 9. 
 
 4275 X 240, 
 
 IC. 
 
 418M5 X Tf. 
 
 8. 
 
 «0a X 142. 
 
 10. 
 
 8137 X 189. 
 
 17. 
 
 G3587 X 618 
 
 4. 
 
 857 X 857. 
 
 11 
 
 2'J5Pi X 284. 
 
 18. 
 
 4!»l'jr, X 428. 
 
 5. 
 
 U43 X 420, 
 
 12. 
 
 47i;5 X 927. 
 
 19. 
 
 ()4-27;) X 535. 
 
 a. 
 
 854 X 3C9. 
 
 13. 
 
 8259 X '.>nCu 
 
 20. 
 
 47821 X 1683. 
 
 7. 
 
 875 X daa. 
 
 14. 
 
 4371 X 1«3. 
 
 21. 
 
 45314 X 2468. 
 
 ao. To multiply by a mixed number. 
 
 ExAuixii 1— Multiply oC3 by CJ. 
 863 
 
 90j product by J = 3C3 + 4 = 00 
 3178 " <• 6. 
 
 22(;sf 
 
 Example 2— Multiply 3426 by 5J. 
 8426 
 _5s 
 
 i:!70j^ product by f = 3426 x 3 .f k 
 17130 " <• 6. 
 
 183001 
 
u 
 
 MULTIPLICATION. 
 
 
 
 
 EXERCISE 13. 
 
 
 Mrltiply— 
 
 
 
 1. 
 a. 
 
 3. 
 
 4. 
 
 812'i by 3J, 
 4.!71 by 15|, 
 2l;i7 by 41f 
 ■iCAo by 22j3i-, 
 
 5J. 
 
 in, 
 
 21f 
 
 353, 
 
 8}, 17f, 13J, llj, lOJ. 
 
 25J, ?.::l 
 
 42f 02f. 
 
 5. 1310 by 161^. 241^, llOrt-, <J5^. 
 
 21. In multiplying by a mixed number, it is often a 
 shorttr method to reduce the mixed number to an improper 
 fraction and to multiply as in fractions. The following 
 exercise contains multipliers of this kind. 
 
 Multiply 689 by 33J. 
 
 C89 X 33| 
 
 -.suxi0J> 
 
 3 
 
 68'.)i)0 
 3 
 
 := 2-."J(5C5 
 
 
 
 
 EXERCISE 14. 
 
 
 
 Multiply— 
 
 
 
 
 1. 
 
 3904 by IJ, 
 
 1?. 
 
 H, 9A. 
 
 11}. 
 
 3. 
 
 1375 by It?, 
 
 33§, 
 
 18A, 228, 
 
 28f 
 
 3. 
 
 4137 by iJOg, 
 
 42J, 
 
 J 33 J, 57f 
 
 
 4. 
 
 31')4 !)y 44|, 
 
 3<¥i. 
 
 71 », 55f. 
 
 45A 
 
 6. 
 
 221 by 8of, 
 
 ^iA. 
 
 233 J, 77^, 
 
 63A 
 
 6. 
 
 iiy:! by 2GGj, 
 
 114*, 
 
 88|, 72 ^j, 
 
 128f 
 
 7. 75Jby 81,V33:jJ, 142?, lllj, 90^. 
 
 32. To multiply by a number which is a convenient 
 aliquot part of lo, lOO, 200, 300, etc. 
 
 Multiply C3S by 2^. 
 
 Since 10^4 = 2J, thoroforo to multiply by 2^ we multiply by 10 and 
 diviilu the resalt by 4. G38 x 10 -5- 4 = 1095. 
 
 The following list comprises some of the multipliers that 
 !!\ay bfi UF.ed in this way. All tho raultipliers used in the 
 preceding exercise are examples of this class. 
 
.yULTIFLICAritKW 
 
 U 
 
 1. 
 
 IJ = 10 ^ 
 
 8. 
 
 2. 
 
 !§ = 10 -r 
 
 6. 
 
 S. 
 
 2J ^ 10 f 
 
 4. 
 
 4. 
 
 5 ». 10 -r 
 
 2. 
 
 «. 
 
 3J = 100 -7- 
 
 12. 
 
 f>. 
 
 12} = 100 f 
 
 8. 
 
 7. 
 
 ir,J = 100 ^ 
 
 G. 
 
 8. 
 
 25 = 100 •=- 
 
 4. 
 
 9. 
 
 37i = ::I00 -i- 
 
 8. 
 
 10. 
 
 75 = 300 -f 
 
 4. 
 
 11. 
 
 41 1 .-= 500 4- 
 
 12. 
 
 12. G2i = 500 -S- 8. 
 
 13. 58J = 700 J. 12 
 
 14. S7i = 700 
 
 15. UC,^ = 700 ^ 
 
 16. 175 = 700 -i- 
 
 17. 112.4 = 1:h) 
 225 .•= iH)0 ^ 
 
 S3 J = 1000 
 125 = 1000 
 1603 = 1000 
 
 18. 
 19. 
 10. 
 21. 
 
 8. 
 6 
 4. 
 8. 
 4. 
 12. 
 8. 
 6. 
 
 333i = 1000 
 
 EXERCl'iE 15. 
 Multiply— 
 
 1. 34f5by IJ, 13, 2J, 5, 8J. 
 25S by 12}, I63, 25, 37}, 75. 
 512 by 41§, 62}. ,WJ, 87}. 
 515byll6j, 175, 112}, 225. 
 357 by 83}, 125, IGOj, 333J. 
 
 23. To multiplj' by 75. 
 
 Multiply by 100 and subtract one quarter of the product. 
 
 EXAUPLB— Multiply 863427 by 75. 
 
 75 = 100 - 25 (one-fonrth of 100) 
 Opfration- ?r,342700 - proiluct by 100. 
 
 21585675 - one-fourth of tiio prodnci. 
 
 64757025 
 
 94. To multiply by 125. 
 
 125 = 100 -t- 25 fonc-fo-rth of 100) 
 
 Muiiiply by 100 and .idd one-fourth of the product. 
 
 i:x.ou'T.B-M:ilr!ply 12317'">0 by 125. 
 
 OpiaaTioN— 12i:!7''r)0ll - j:ro(i!i.?t !.y JOO. 
 
 31091225 - on.- fourth of t'ho product by 100. 
 
 
 1554711 
 
 25 
 EXt 
 
 "RCISE 16. 
 
 
 
 I. 
 
 2. 
 
 -I 
 
 3672.58 X 66J. 
 
 43729 X 95. 
 
 27364 X 975. 
 ■'76298 X 950. 
 
 
 
 5. 
 6. 
 7. 
 8. 
 
 36254 X 105. 
 
 27'.»36 X 133} 
 478256 X 150. 
 236471 X 1025. 
 
-iT 
 
 1« 
 
 Diviaioii 
 
 DIVISION. 
 
 DIVlSUnUTY OF NUMBERS. 
 
 25. A. nura})or is said tc be divisible by auotber number 
 wh'Iu tbe latter will divi lo the fonuer without a remainder. 
 
 2tt. An even number is a number of which 2 is an exact 
 iivisor. 
 
 27. An odd number is a number of which 2 is not an 
 exact divisor. 
 
 28- Any number is divisible — 
 
 1. By 2, if it is iin even uu:nber as 2, 4, 8, 26. 
 
 2. By 3, if the sum of its digits is divisible by 8, as 
 
 741, 7 + 4 + 4 = 15, 15 is divisible by 8. 
 B. By 4, if t'tiL wo ri^ht hand figures are ciphers, or 
 ' express a number divisibl ^ by 4, as 1500, 
 7323. 
 
 4. By 5, if the right hand figure is or 5, as 60, 95. 
 
 5. By 6, if it is an even number and has the sum of 
 
 its digits divisible by 3, as 848. 
 
 6. By 8, it the three right hand figures are ciphers, 
 
 or express a number divisible by 8, as 4000, 
 9218. 
 
DIVISION. 
 
 17 
 
 ^' ^^' ^' !f-?u?"'° '^ ^*' ^'S'*^ '^ ^^^'^'ble by 9, as 
 
 8. By 11 if the difference of the sum of the digits in 
 
 tl^e even ,,hu-os, and the sum of the digits 
 in the odd places is 0, or is divisible by 11 
 as 415203, 459173. ^ ' 
 
 9. By 25, if the two right hand figures are ciphers or 
 
 express a nunil)er divisible by 25, as 4700, 
 
 10. By 75. the same as for 25, providing also that th< 
 
 Bum of th. digits is divisible by 8. as 3900. 
 
 prod^ucte" ^^'"^' °"' ""™''''" ^y^"°ther leaving out t.e 
 
 R0LE. 
 
 Subtract the several rm^ncts from the next number greater 
 ^ndtng wtth the correspon^Ung figure in the dir.tend ani 
 
 rxr "" ''^' '"''-'^"" '^''' '""'"-^ ^ ^^ '-^ 
 
 Divide 42343014 by 973. 
 ordi.nars- method. 
 »73 ) 42343014 ( 43618 lkavtv- «^ 
 
 quQO t-BAVIN,-) onx THE PRODCCTS. 
 
 _ 4-.'3 13014 973 
 
 3423 
 6040 
 1751 
 7784 
 t JO 
 
 I 43518 
 
 8423 
 2919 
 
 5040 
 4865 
 
 1751 
 973 
 
 7784 
 0000 
 
 UXTBOO. 
 
 leaves 2. Write 2 in the relSe;2.dTrr:VTlr "T' t" '' 
 
 1 carried makes 2?., wLich subt, w w '^ *"°^^ ^ *** ^' '^^'^ 
 
 . wLici. sabiiHoted from .S3 (the next number greater 
 
Diviaios 
 18 
 
 9 are i6 and 3 carrel '- -' '^ jjj '^i'' ^ ,„btraoted from 4 leaves 0. 
 number greater eu.h...' with 2). '^^^ ^^id Bo proceed until the 
 
 Bring down 3 th^ .'.oxt figure m the dividend, oo v 
 division is comploieJ. 
 
 EXERCISE 17. 
 
 1. 743-J'.)7 -r 527. 
 
 a. 11839 -r 860. 
 
 8. 87Gii4 T "13. 
 
 7. 
 
 4. 
 6. 
 6. 
 
 8fi287 + 667. 
 64925 + 784. 
 34G81 x 4W. 
 
 Livide 3642739 by 625. 436. 8173. 2106. 
 
 :^0. To divide by a mixed number. 
 
 PlilNCirLK. 
 
 MaWplyino both divisor and dividend by Ou same numbe, 
 does not alter the quotient. 
 Divide 786 by 5|. 
 
 5i ) 738 ( 
 
 8 
 
 8 
 
 1. 
 
 2. 
 3. 
 
 17 ) 2208 { l2ttH 
 17 
 
 60 
 84 
 
 168 
 153 
 
 15 
 
 EXERCISE 18. 
 
 Divide^ 
 
 475 by 3i. 4i,7i. H, ^f, SJ. 
 ?(;24byl3i. 4i9^,31J, 4f 
 6712 by 7J, Hf, 2^, 6^, lOf. 
 
 •U. To divide when all the figures m the divisor 
 except the first on the left hand can oe changed to 
 ciphers by using a convenient multiplier. 
 
 Example 1— Divide 624395 by 35. 
 35 ) 62 1395 { 
 2 2 
 
 7P ) 124^7910 
 "TvSliO - fg 
 
DiyiSlON. 
 
 ExAUfPUi 2— Divide l.T I7ti bv 16». 
 lf>f I MJTO ( 
 6 U 
 
 l ^P ) 8 ()Hgg 
 
 19 
 
 ^.^°"-~" *^® ''"^ remai.ider is required it may be obtained by 
 dividing the remainder found by the number by which we multiply th. 
 divisor. ^ ^ 
 
 1. 4826 -f 6. 
 
 2. 3827 -5- 25. 
 
 3. 9109 -r 75. 
 
 4. AMV.S -i- 175. 
 6. 3798 -r 225 
 6 8306 -i- 45. 
 
 7. 
 
 8. 
 
 9. 
 10. 
 11. 
 13. 
 
 EXERCISE 19. 
 
 32008 -f- 12J. 
 68934 + ^. 
 32165 + 1|. 
 
 8327i i 83J. 
 
 49328 -5- 33i. 
 
 9306 + 62J. 
 
 13. 
 
 14. 
 
 15. 
 
 16. 
 
 17 
 
 18. 
 
 2139(! + 
 
 9201 + 
 
 7345 -5- 
 
 6287 -r 125. 
 
 41|. 
 67f 
 
 312'', i ^ 
 31907 4- 
 
 87J. 
 142f 
 
 »3. To divide by any number that can be changed to 
 a convenient divisor by increasing or diminishing it by 
 an aliquot part of itself. 
 
 BULK. 
 
 After dividing by the divisor so increased or diminished, 
 increase or diminish the quotient in the same proportion. 
 Divide 1920 by 24. 
 
 Opebatio."*, 
 
 3P ) 192p 
 
 4 "rG4 
 16 
 
 80 the quotient. 
 Explanation. 
 
 iof 24 = 6 24 + 6 « 30 
 
 
 
 
 1920 
 
 ■5- 30 = Gl 
 
 
 
 
 
 
 i of 64 = 16 
 
 
 
 
 
 
 
 80 the quotient. 
 
 
 
 
 
 
 EXERCISE 20. 
 
 
 
 1. 
 
 2. 
 3. 
 4. 
 
 1845 J- 
 3040 -5- 
 2322 -f 
 15210 H- 
 
 45. 
 
 35. 
 
 54. 
 48. 
 
 
 6. 7704 -^ 24. 
 
 6. 8343 -t 27. 
 
 7. 41472 -^ 81. 
 
 s. inieo ^ loO 
 
 9. 
 10. 
 11. 
 
 24300 -J. 18| 
 
 24300 -r 87i 
 337500 -J- 75. 
 42;.100 -r 125. 
 
 ■■f^'2^H 
 
 "^'M^ihi .-Vf^^w^, 
 
20 
 
 DIVISION. 
 
 33. To divide by means of factors of the divisor. 
 
 ExAiiPLK 1.— Divide 25380 by 108. 
 
 108s9x4x3ort)x6x:ior9xBxa 
 
 108 ) 2.'<:;80 ( 235 
 210 
 
 378 
 324 
 
 510 
 
 r,40 
 
 3 ) 2r,:N0 
 
 9)2115 
 ~235 
 
 8 ) •2r,,i80 
 6 ) 81iib 
 6)1410 
 
 2;f,3 
 
 9 ) 25380 
 
 6 1 'Jn-JO 
 
 2 )470 
 
 235 
 
 ExAMPLK 2.— fiviM • (i326 by 75. 
 
 75 = 3 X 6 X 6. 
 
 8 )J):!26 
 5 \2iOS . . 2 
 5 ) 421 . . 3 
 84 .. 1 
 
 2 
 
 3x3= 9 
 1 X 5 X 3 = 15 
 
 or 
 
 1x6 + 3= 8 
 8 X 3 + 2 = 26 
 
 21) true remainder. 
 
 Non 1. — To find the trne remaindor. take the product of each remain- 
 der by all the divisors preoeiiiu;> the oi:u that produced it. The sura 
 of these products with the first remainder will be the true remainder. 
 
 2. Take the product of the last remainder by the divisor prooedinf^ the 
 one t'.iat produced it. To this product add tlio preceding remainder. 
 Multiply this result by tlie next divisor and add the next remainder. 
 Continue this process uutil the first divisor has been used as a multiplier. 
 
 1. 25380 -J- 36. 
 
 2. 178584 -r 48. 
 
 3. 23741 -=- 42. 
 
 4. 43165 + 64. 
 
 EXERCISE 21. 
 
 6. 31279 + 72. 
 
 6. 43827 -i- 81. 
 
 7. l'J375 -: I-'-,. 
 
 8. 41(543 -r lo5. 
 
 9. 43716 -f 168. 
 
 10. 29373 + 81. 
 
 11. 41658 + 45. 
 
 12. 23725 + 96. 
 
 31. To divi-^e by cancellation. 
 
 35. Cancellation is the process of shortening operationB 
 by rejecting equal factors from both dividend and divisor. 
 
 36. The sign of cancellation is an oblique mark ( / ) 
 drawn through the number from which the factor is 
 rejected. 
 
Division. 
 
 Divid 
 
 IJ 
 
 e 18 X 16 X 28 by 12 X 7 X 14 
 3 ^ 
 
 '* ^ "' >< ?? ■'« X 16 
 
 /;^ X 7 X ;> * —7— = C^ or 
 
 RCU. 
 
 2| 8 
 7 i 16 
 
 
 Divide 
 
 1. 
 2. 
 
 5 X 9 X 
 
 80 X 56 X 
 3. 70 X 39 X 
 4- 'iS X 49 X 
 3 X 6 X 
 
 EXERCISE 22. 
 
 7x11 Ijy 7 X 
 
 by 
 
 5 X 
 
 3 X 
 
 18 
 
 13 by L.M X 21 X 
 
 '^^ by 7 X 15 X 
 
 8 X 72 by 2 X 3 X 
 
 3 X 11. 
 4x6. 
 
 7. 
 
 6 
 
 ;• 74x12 X 14 X I.;by/sx72x 24 
 
 7 12x27x178 by 51 X 63 X m. 
 
 8. 2_. X X 72 by 44 X 32 X 18 
 
 » J3o X 12 X 29 bv 97 V IS X 154 
 
 10. 46X63X144 by ,2 X 24 X a 
 
 84. 
 
 1 X la 
 
 ^i^m^T'\'^sm^''r^c.'"fmrmi^w9ssmmi 
 
22 
 
 yACTuiU.SU. 
 
 FACTORING. 
 
 i-3 
 
 
 3T. A Factor, a Measure, or a„ Exact Divisor of a 
 
 R.veu num .ori8 an integral number tliat will divide the 
 given nural)er without a remainder. 
 
 3». A Prime Number is a number that hns no factors 
 pxcopi ust'if and 1, as 3, 7, 13. 19 
 
 facr/. ^ ^""'' ^^''°'" " " ^'""^^ °"°^'^''" "«^^ *« • 
 
 lO. A Composite Number i. a number that has other 
 lactora btsiiios iisolf and 1, as 24, 82, 70. 
 
 .^o!:^'2^ "" "™™' °' ""'""'' "'^ '-'»" of . 
 
 4a. To revive a number into its prime factors. 
 
 KULB, 
 
 Divide ,k, .,nn„„r ,.„ „„ ,,„., p„.„„ „„ 
 
 r;t " ""'■^ '■'"' "•■"" ""'""■• '-«■' "« '"" sS 
 
 are I'/j^ ;</;/«? fartont. ^"""ewt 
 
 Fiud the prime factors of 120. 
 
 2 ) 420 
 
 2) 210 
 8 ) 10.1" 
 6 ) 35 
 ' 7 
 
 <20 = 2x2x8x6x7 
 
 2, 3, 5 and 7 are the prime faotori. 
 
 EXFRCISE 23. 
 Find the prime factors of— 
 
 1050. C. .';n,^ 11 ,,,10 
 2t')25. 7, 4(;:.o. lo ^-y^ 
 
 1. 
 2. 
 
 3. 1820. 
 
 4. 1IS5. 
 6. 1155. 
 
 8. 
 
 9. 
 
 10. 
 
 is^ic. 
 ■|i:i2. 
 7000. 
 
 i;;. 
 
 14. 
 16. 
 
 ).;20. 
 
 17(iS. 
 1848. 
 
 16. 
 
 17. 
 18. 
 
 1906. 
 1858. 
 1478. 
 
 19. 2956. 
 20 2406. 
 
 21. 2620. 
 
 22. 2978. 
 
 23. 2992 
 
 24. 3936. 
 2^ 8430. 
 
J 
 
 maiitisT COM HON factor. 
 
 •8 
 
 HIGHEST COMMON FACTOR. 
 
 48. A Common Factor of fwr^ «. 
 
 nu.W.,a. .,n e..ct,I ■i.tcH-nC.rr:;' 1"," 
 or 12 1. a common factor of 24 nrrl 36 ' 
 
 «iirA r.t *■ divisor oi Greatest Common Mm 
 
 sure, of two or more niimlx-ra is Hw> r,. . "'"^o" Mea 
 
 45. To find the H C F nf ♦^ 
 
 n. o. 1^. of two or more numbers: 
 
 Divide thf! greater wmhrr In, the ■<•»<, nu,l ti , 
 hy the remainder, if any, and so Jj^^, 'J^. "' ;i"t" 
 divisor by the /«.,. rmnnd.r vnti f ^^' ^"'^ 
 
 ne list divisor. iinJZn;:';';; "'"'" - - — ■«^-. 
 
 If more than two nnmhers are, ^in>n findih^ U n v, 
 Find tl,« H. 0. P. of 1385 „,„j ^j^, 
 
 1386 
 
 nr.ST METHOD. 
 
 -'2o8 ( 1 
 138S 
 
 882 ) 1.386(1 
 
 882 
 
 604 ) 882 ( 1 
 
 604 
 
 878 ) 504 ( 1 
 378 
 
 8BC0NI) MRTirOD. 
 
 QUOTiENTb I 2268 
 
 1 
 1 
 1 
 1 
 
 8 
 
 H. C. P. 
 
 12fJ ) 378 ( 3 
 378 
 
 NoTB -Obserre that the -„k1 mothn,! io »i, 
 
 work being arranged so aa no. o ne Jta ! I" ''"*' " **^^ ^''^'^ ^l^- 
 more than once. necessitate the xvnt.ng of the divisor 
 
 The column for quotients may be omitted. 
 
 y - T 
 
24 
 
 UlUUEST COMilUS FACIVH. 
 
 BObtracI 
 downwards. 
 H. C. F. 
 
 TllIIU) MKTIIOD. 
 
 > MCi.rn'L.taits 'l:A% 
 13M-. a 
 
 IL'O 
 
 ll"2 iubtract downwards. 
 
 METHOD. 
 
 In this raethoil we us« Buch a inuit |>iii r for TWO »i will (riv« k pr' 
 dact nearuHt to 2':08, that is 3. From th.; pr.nhict 'J772 '.I'lV ■2-26S, which 
 leaves IV n.iuftiri lor .lOI N'tt tsku as a nrilupli.T of .'.Oi nuch a number 
 as will give a product uuarcat to 13d ', tiut ii S, eto. 
 
 ronniH MBTIIOD. 
 
 By means of prime factors. 
 
 PntMB TACTi BS fODND. 
 
 FUIMB rvCToKH AlUlANOfiO. 
 
 la^u = 2 X 3 X a X 7 X 11 
 
 22M 3-2 X 2X0x3x3x8x7 
 
 Coinmoii pr.ni'' "art ra nmltiplied. 
 2 X 3 X 3 X 7 - l-O = II. G. F. 
 
 2 
 
 1380 
 
 2| 
 
 'j'.!Oa 
 
 8 
 
 0'.»3 
 
 2 
 
 ii;u 
 
 S 
 
 ■M 
 
 8 
 
 .-.1,7 
 
 7 
 
 77 
 
 8 
 8 
 
 ih;> 
 
 
 11 
 
 G3 
 
 
 
 8 
 
 21 
 
 « 
 t 
 
 2 
 
 l.'iSO 
 
 2'.'i;d 
 
 S 
 
 "T;'.i;i 
 
 1134 
 
 8 
 
 ~ii:U^ 
 
 378 
 
 7 
 
 77 
 
 1-J6 
 
 
 11 
 
 "18 
 
 Reaolve thf iiiren numbi r» into th ir priiiu'. ftidnrt ; th, 
 product of aU tlif pri.ne factors connnuii tn them is the II. G. F. 
 
 1 IFTll MKIIiOD. 
 
 By means of common prime factors. 
 
 2 X 3 X 3 X 7 = 12C II. 0. p. 
 
 BCLI. 
 
 Dividi' the (jiven numbem i>if the. prime factors common to 
 each : the jirodnct of these prime factors will be the H. C. F. 
 
 EXERCISE 24. 
 Fin I the IT. C F. oJ 
 
 001, 1178. 
 
 ',:i:>:u r.?45. 
 
 410') 'iT^O. 
 
 T.'ii.s .;7«4. 
 
 HS7<'., 1983. 
 
 7'.i,V,, 70i;8. 
 
 ',)8i;i, !I523. 
 
 1. 
 
 323, 
 
 425. 
 
 8. 
 
 2 
 
 228. 
 
 h;i'.». 
 
 9 
 
 8. 
 
 (•,15. 
 
 735. 
 
 10. 
 
 4. 
 
 810, 
 
 1)45. 
 
 il. 
 
 6. 
 
 949, 
 
 871. 
 
 12. 
 
 6 
 
 82.-., 
 
 %0. 
 
 13. 
 
 7. 
 
 CSl), 
 
 1575. 
 
 14. 
 
 16. 
 
 45, 
 
 57. 
 
 81. 
 
 16. 
 
 03, 
 
 99, 
 
 90 
 
 17. 
 
 72, 
 
 84, 
 
 96, 
 
 18. 
 
 30C, 
 
 408, 
 
 510. 
 
 19. 
 
 420, 
 
 402, 
 
 84. 
 
 20. 
 
 540, 
 
 462, 
 
 883. 
 
 21. 
 
 900, 
 
 930, 
 
 2520. 
 
LA AST COHjUON MLUIl'Lli. 
 
 35 
 
 LEAST COMMON MULTIPLf, 
 
 40. A Multiple of a miniher is one tint is exactly 
 diviiible by that numhor. i\n\^ 30 is a multipl,. „f (;. 
 
 47. A Common Multiple of two or innie mniilicrs is u 
 number which is exactly (Uvisible by eat-h of them, thus 18, 
 86, 72, are commou multiples of 2, 3, 6 and 9. 
 
 48. The Least Common Multiple of two or more 
 numbers is the 1< uHt miinher whicli Ih exactly divigible by 
 each of tlipm, thus 18 is the least common muluplo of 2 8 
 6, and 9. ' ' 
 
 Find the L. C. M. of IS, 28, 42. 
 
 FIRST jii'Tnon 
 
 By means of prime factors. 
 
 18 = 2 X ;i X 3 
 
 28 = 2 X 2 X 7 L- C- M. = 2 X 8 X 8 X 8 X 7 - 863 
 
 4a :k 2 X 3 X 7 
 
 KHLK 
 
 Resolve ihp given numbers info their prime factors ; the 
 product of the ditTerent prime factors taking each the greatest 
 number of times it appears in any of the numbers will be the 
 L. C. M. 
 
 BKCOND METnOD. 
 
 Find the L. 0. M. of 9. 15. 18, 16, .^, bO, 46. 
 
 2 i_?, J,l 1«, IB. 12, HO. 15 
 
 2 I ?, 8. 0. ;iJ, J5 
 
 I ""i. 3, 45 
 
 2 X 2 X 4 X -1 ) = 720 L. C. M. 
 or 
 2. 2, 3 I J^_16, 18, 16, 12, 30, 46 
 3. 4, 1, fj, 15 
 8 X 2 X 3 X 4 X 45 = 720 L. C. M. 
 
26 
 
 LJiASJ COMMON MVLTtPLK. 
 
 vjha. 
 
 Write, the nvm^wrn in a haricontnl line, eaneellin^ $urh of 
 the HnuiUer numhern 'i$ ,tre factors of the lari}er,nn(l diiide by 
 any prime factor or prime facturn that will exactly divide two 
 or more of the liven numhern. Write the qnuticnl$ and the 
 undirided iiumhrrs, if any, in a liite heneath. 
 
 Continue this proccus instil the reiult$ arc prime to each 
 other. 
 
 The prodwt ot' all the dicisora and the ntimbert in *he lant 
 line will he the L. C. M. 
 
 i 
 
 
 EXERCISE 2S. 
 
 
 
 
 
 rmd tho L. C. M. 
 
 of 
 
 
 
 
 
 
 I. 5, 'i, 15. 
 
 
 11. 
 
 87, 
 
 94, 
 
 16. 
 
 
 2. 7, U. 21, .28. 
 
 
 13. 
 
 (,^. 
 
 27. 
 
 84. 
 
 
 3. J. 8. 12, 16. 
 
 
 13. 
 
 12, 
 
 61, 
 
 68. 
 
 
 4. 5, 7, 15, 21. 
 
 
 U. 
 
 s-i. 
 
 63, 
 
 72. 
 
 
 .5. 8, 14, 21. 28. 
 
 
 16. 
 
 9. 
 
 12, 
 
 14, 
 
 210. 
 
 6. 9, a, 0, 18, 24. 
 
 
 16. 
 
 60. 
 
 16, 
 
 24, 
 
 26. 
 
 7. 8, 7. 12. 21, 24. 
 
 
 17. 
 
 54. 
 
 81. 
 
 68, 
 
 14. 
 
 8 6, 2, lo, 7, 35. 
 
 
 18. 
 
 *f' 
 
 27. 
 
 80, 
 
 68. 
 
 9. 3, 6, 'J, 54. 
 
 
 19. 
 
 22, 
 
 27, 
 
 64. 
 
 loa 
 
 10. 7, 9, 12, U, 86. 
 
 
 20. 
 
 964(3. 
 
 ()3G4. 
 
 U3ta 
 
 
FRACrioSS. 
 
 FRACTIONS. 
 
 49. A Fraction is one or more of tin- pqual pnrts of h 
 unit, or anvtliing rc^'.inled as a wliol,. ; tluis. on. -)i,i!f. 
 fwo-thiidB, tlii-oefourtlis. are fractions. 
 
 rtO. Tho miit of the fraction is f!ie unit whicli is 
 dividod. One of \]n- . qnal parts is the fractional unit. 
 
 .11. Fra-tions obtained by tlie division of tij" unit inio 
 t .'.itljs, bundredtlis, tlioiis;indtlis, etc. ari> called Decimal 
 Fractions. All other li-.ictions are calltd Common 
 Fractions. 
 
 .1**. A Common Fraction is expros^od by two numbfiH, 
 called the Numerator and th.' Denominator, ♦'■ > mor 
 writl'/n over the latter, with n Vuv iietweeii th 
 
 Or. -third is writtfin ^ I Five-Pixtli.-i la wn, 
 Three foiirthe •■ J j S. v. n tliii tc< ntha " 
 Tlir.o ei^liths " | ; Klevoniu.-.itiethB '• 
 
 i: 
 
 5a. The numerator and the denominator are called the 
 terms of a fraction. 
 
 54. The Denominator of a fraction, written below the 
 line, shows the number of equal parts into wliich the 
 unit is divided aud also names the unit : thus in ^. 8 is 
 the den>"n:nator and shows that the unit is divided into 
 eight equal parts, named eighths. 
 
 5.">. The Numerator of a fraction, written a!)ove tbe 
 line, shows the number of equal parts taken to form tlie 
 fraction ; thus in |, 7 is ilie numerator, aud shows that 
 seven of the eight equal parts are taken or expre.^^sed i'v 
 the fraction. 
 
 56. Since Jie denominator of a fraction shows how 
 many fractional units in tlie numerator are equal to one 
 integral unit, it follows 
 
 111 
 
 
lKKs«feie,^^l^k.V% 
 
 28 
 
 FRACTIONS. 
 
 That <i fraction if an expriis-^^ion of unperformed division. 
 The numerator is the dividend, the denominator it the divisor, 
 and the value '■' th^ /ruilifn in the quotient. 
 
 57. QESKi.::. riii.\firL:\-; of fractions. 
 
 I. Multiply -.1 the v';>n< i ttor or diridimj the denominator 
 by any number muUipiics the value of the fraction by that 
 ninnher. 
 
 If we multiply the numerator of the fraction J hy 3, the 
 result is ?, which is throe times as great as |. If we 
 divide the denominator of \ by 2, the result is ^, which is 
 twice as {,'reiit as \. 
 
 II. Dividini] the unnirrator or mnltivlying the denominator 
 hy any numher divides the fvactina by that nuiaher. 
 
 If we divide the niiniriator of the fraction f by 2, the 
 result is ^, v\iuch is ^ as greiir as J. If the denotiiiriator of 
 I is multii^ied bv 2, theresu t is i, which is ^ as great as i. 
 
 III. Multi<!fii)i,i or dividing loth numerator and denom- 
 inator of afvartion hij the same number does not change the 
 value of the fraction. 
 
 If we multiiily both the num* rator and the denominator 
 of ^ by -J, the retult is f, which has the same value as ^. 
 If we divide hotli numa-ator and denominator of i by 2, 
 the result is |, which has the same value as J. 
 
 5S. A Simple Fraction is one whose terms are both 
 integers, as |, \\. 
 
 5!>. A Proper Fraction is one whose numerator is less 
 than its denominator ; hence il.s value is less than 1, as J 
 rV. 
 
 60. An Improper Fraction is one whose numerator 
 equals or exceeds ils denominator, as i V. ^• 
 
 61. A Mixed Number is a number composed of an 
 integer and a iraction, as 3^, 51. 
 
 ■a: 
 
 I; 
 
 -M' 
 
"PA\ 
 
 FRACTIONS. 
 
 29 
 
 fa 
 
 EXERCISE 26. 
 
 A. A. 1^ ij, i^. ryvi. ip. jr;:}}, fof|. 
 
 2. Espreas the follDwiM- in ^i-nrfs- 
 one third; " 7 
 
 tenr^v«M,,.. four,..,/,., 
 
 thirty ... /,«../..,/.,:,,^,,., ,,, . ^7" !■'■" ;-""'// '/'-'/^ . 
 twelve hun,?,- .1 • ? V ' f'"-^-^^.''"-e-//i««.vu«,/,/j8, 
 
 tv\eive UiiiKliL'd 'n>irt>i-th,,ii<ini.ll'H ■ 
 
 IhToeserenths oi niueieen/o;7^ ///>/', 
 
 8. Write : 
 
 three and a hilf • r , 
 
 »:->;yfive .„, .;e„,v.H.ee/,,,::':l:,r"'' " ^""""^ 
 eighteen and eleven ehiht^/./ourfhs'. 
 
 REDUCTION. 
 
 i 
 
 ea. Reduction of Fractions is tlw ehan-in, „f tl„i, 
 fonu mtho»l clM„gi„g thoir value. ' ' 
 
 fra"c'o„^° "'"" '"'^^^" ""■'''^ -"-bersto improper 
 
 ExAMPLK l._In 18 units how many fifths? 
 Solution. 
 In 1 nnit thero are 5 fifths 
 " 18 onita " 18 timos o fifths 
 or 90 fifths (ij^) 
 Hence 18 = 9^ 
 
 BXA^.B 2.-Redaoel8? to an i.nprop.r fraction. 
 
 SoLUTIOff, , , 
 
 ^ (Example 1) is = oo fifths 
 
 J~ g = 3 jftlrn 
 
 isjj = trnlTfths («i) 
 
 BULB. ' 
 
FRACTIONS. 
 
 
 
 EXERCISE 27. 
 
 
 
 • friu^tiona — 
 
 
 
 III. 
 
 m. 
 
 18i}. 
 
 IV. 
 
 27f,. 
 
 5;,. 
 
 V. 
 
 »». 
 
 51. 
 
 19B 
 
 112i5 
 
 so 
 
 L II. 
 
 71. 2J. 
 
 at- sfr 
 
 « I. To reduce an improper fraction to an integer or 
 a mixed number. 
 
 ExAMPLK. — Ueduoe -^ to a mixed number. 
 Solution. Explamatiox 
 
 6 ) 48 Since ^ express.33 an nnperformed 
 
 9J division (Art. 5(j), tlierefore by performing 
 
 the division we obtain 9| for quotient. 
 
 EXERCISE 28. 
 Reduce to mixed numbers — 
 
 1. 
 
 II. 
 
 III. 
 
 rv. 
 
 V 
 
 H" 
 
 w 
 
 W 
 
 ¥ 
 
 4^^ 
 
 ^» 
 
 ajj 
 
 V 
 
 W 
 
 HJ^ 
 
 V5* 
 
 ^ 
 
 H^ 
 
 4F 
 
 »IF 
 
 *fjA 
 
 Vs' 
 
 ^ 
 
 w 
 
 iJ.'i. To reduce a fraction to higher terms. 
 
 EzAUFLE. — Rednoe i to sixteenths. 
 
 EXPLWATIOH. 
 
 Solution. 
 
 3x4 
 4x4 
 
 3 4 12 
 
 Since it is required to change } to six- 
 teenths, (i.e) a fraction whose denominator 
 is 16, we must multiply the denominator 
 4 by 4 ; then by Art 57, III., so as not to 
 ohauijo tho value of the fraction, we mast 
 multiply the numerator 3 by 4. 
 
 RDLB. 
 
 To reduce a fraction to Inijher terms, divide the required 
 denominator hy the deiin))iin.'itnr of the given fraction and 
 wnltiply both terms hii tlie quotient. 
 
 ":Z ■.•i/'.ifc ,;iA i<it c-^tViii 
 
Beduce — 
 
 FBAVTIONS. 
 EXERCISE 29. 
 
 Bl 
 
 1. 
 
 2. 
 3. 
 4. 
 6. 
 
 6. 
 7. 
 8. 
 9. 
 10. 
 
 i. h h i 
 
 4. h i. i 
 J. h i, i 
 
 3. i, ,1, h 3 
 
 5. I .'-,. f. S, 1 
 
 »• «. % A. A 
 
 to twelfths. 
 
 to eij,'lite(.ntl)8. 
 
 to eiiihths. 
 to twunty.foartbs. 
 to seventy-seconda. 
 to sixtooiiths. 
 to tfty.fourths. 
 to forty-fift!i3, 
 to forty-eii;;itha, 
 to thirty-sixths. 
 
 66. To reduce a fraction to its lowest terms. 
 
 Solution. „ 
 
 16 = itri - I ^^ ^^- •"• "I ■ '^^ may divide both 
 
 „/ * °°'n'^'-ato>-an.l<l..nominator by 4 without 
 
 112 3 ohanymg the value of tlio fraotioix. 
 4 
 
 I 12 
 
 11(5 
 
 3 
 4 
 
 BITLI. 
 
 JZ1\ of the fraction successively hy all the 
 
 pnm factors corn non to the two, or hy the continued product 
 
 ru G fT""' ' ^'"'^ '^'''" ^'^^"'' '^^"'"'"" •^"^''«'•• 
 
 NoTE.-A fraction is in its lowest terms when th« numerator «nH 
 dcmoinmator hava no common factor. numerator and 
 
 EXERCISE 30. 
 Reduce to lowest terms — 
 
 I. 
 H 
 il 
 H 
 A 
 
 H 
 
 II. 
 
 II 
 
 III. 
 H 
 
 it 
 A\ 
 
 nr. 
 
 HI 
 
 kU 
 
 m 
 m 
 
 m 
 
 V. 
 
 an 
 
 iHl 
 
 TTTf 
 
 H.-?''* 1°. '■^'^"^^ ''^'* °'' '^°^« fractions wbfrh have 
 
82 
 
 FRACTIONS. 
 
 
 hflf rent donominator (Art. 65), therefore the common denominator mnsi 
 soutain each of the (ieiioniinators of the uiven fractions exactly The 
 least uu.uhor that will o..ut,iin each of the .:ivon denominatorg'ig .heir 
 L C. M. Thcreforo the least ooinm.jM .lenoininutor of the fractions must 
 bi the L. C. M. of tlieir denominatora. 
 
 KxiMPi,P.. -Change J, f | to equivalent f actions having a least 
 3"mmon dunominator. 
 
 SOLVVIOS. 
 
 The least i;o!iiinon denominator 
 = L. G. M. of 2, 3 ,8 = 24. 
 
 i = U 
 1= H 
 
 Explanation. 
 We first find tlie T-. C. M. of tlie 
 t-'iven dfimminatdrs which ia 24. 
 This must be the Icas^ common 
 denominator to whioli the given 
 fractions can be reduced (Note Art. 
 67.) Reducing each fractioE to the 
 denominator 21 , Art. 65), we obtain 
 U' I'i- j'j- as results. 
 
 BULK 
 
 7. Fi,!d the L. C. M. of the nircn dn,.minator» for the 
 least ci'iiiiiion (Icnuininatur. 
 
 11. Divnie the cominnn dntnniinatnr hy each of the given 
 de.nominitors, and multiply the uumcraior and denominator 
 of each fraction hy the corre.ywndinr/ quotient. 
 
 EXERCISE 31. 
 to their least common denominator. 
 
 Redact' 
 
 1. h 
 
 2- f 
 
 3. i, 
 
 4. 
 
 6. 
 
 6. 
 
 7. 
 
 3, 4, 
 
 ? of I, 
 
 9 
 1 J- 
 
 A- 
 
 42. 
 
 H- 
 
 8. 
 
 9. 
 10. 
 11. 
 12 
 13. 
 It. 
 
 I. J- 
 
 '.1.1 n 1 2 r 
 ■< -■■J' T7f Ji 
 
 I. 
 
 f. 
 
 i of J, 
 A A. 
 
 A- 
 
 *of i. 
 
 A. H 
 
 ADDITION. 
 
 U.S. EXAMPLB 1. 
 tJOLUTIOfi. 
 
 24ths. 
 
 i 
 
 A 
 
 18 
 21 
 
 10 
 
 il = Sj^ Ana. 
 
 •Find the sum of J, |, ^. 
 
 ExPIiANATIOir. 
 
 In order that fractions may be added 
 they must have like denominators and 
 be parts of like units. 
 5 = 18 twenty-fourths. 
 J = 21 twenty-fourths. 
 1^ = 10 twenty-fourt hs. 
 
 49 twenty-fourths = 4| - ?g^ ia«. 
 
 ;•■-•■.? 
 
 ■'■s'^lii; '.\ 
 
 
21ths. 
 ^^1^ 21 The 8,„n of the fraction , ^^ 
 
 nvhx. 
 
 88 
 
 - 19 
 
 -laV Ann. 
 
 I fry "ui*«. 
 
 • ro add FntrtinnM nn 
 
 '0 Mr u.,„ «„ j;;:;;,t;;"T'-' 7,'7 '«^/™«-". 
 
 F,-n,l M EXERCISE 32. 
 
 *ina the sum of— 
 
 1- i. I. i. 
 
 3- §• ?. ». 
 
 5. 
 6. 
 7. 
 
 
 2A. 
 
 ■'*•?• -Jl- 5|, 6f. 
 
 4- J. I. I 
 
 ?. J. !. A. 
 
 8 
 9. 
 
 m. 
 11. 
 
 '3- 2 If 13i, 45, 70. 
 
 3i. )?, 
 
 i,V 
 
 
 V. 
 
 SUBTRACTION. 
 
 "^""^^ ^-^'-'^ "-^^^^-nce between ^a„d I. 
 
 Partsofthesa-nounit. ™'"'^'""^'^^" 
 ^ = tJ twei.ty.fourtha (Art. fi5 ) 
 _. t_^ J '"-cnty.foui th8, 
 
 E^.P.K 2.-Fin1 tL nT ' '"■"'^-^■•^'"-"- = A An., 
 ticnxxo.. '"'"""^ ''^'^-^ ^3.V and 4.5: 
 
 I 24th8. „ 
 
 83iV 114 "^ "tu j.„ Expmxatio.v. 
 
 88/, .Vns, '■^''^® '■''8"" » 38^ Aug, 
 
 ^MvmssicvsRy^ irf 
 
 J^iiZ^SSUSi^ 
 
^ « 
 
 34 
 
 FRACTIONS. 
 
 I f 
 
 ! I 
 
 BoLUTiu;*. 
 
 Irttha 
 
 36| 
 
 191 
 
 16 ', Ana yV 
 
 4 
 15 
 
 hxAsiPLB 3. —Find tho di£ferenoe between 36| and 19f. 
 
 Explanation. 
 Yon can't tako f J from f»^ Borrow unity 
 from 36. ReJuc" it toeighteentha.and then 
 add result to ^ wliioh maku^ fj 
 H fi"m JJleivoa ^. 
 19 fi- 'rn :i-') leaves 16. 
 Reaiilt, Hi,'^. 
 
 RCI.R I, 
 
 To subtract fractions. - When necessary, reduce tlu 
 fractions to their leant common dennmi-iator. Subtract the 
 niimerntor of 'he subtrahend from the numerator of the min- 
 uend, and place the difference over the common denominator. 
 
 RULE II. 
 
 To subtract mixed numbers. — Reduce the fractions, if 
 
 necexsary, to a common denomiuiifor. and if the fraction in 
 the -iubtriihend is smaller than that in the minuend, subtract 
 one fraction from the other, and the smaller whole number 
 from the larger whole nuinlnr. But if the fraction in the 
 subtrahend it larger than thit in the minuend, borroiv I from 
 th'' wh(de iiumber. After changing it to the name denomina- 
 tor as the fraction, add it to the fraction in the minuend. 
 
 Then subtract as 
 
 before. 
 
 EXERCISE 33. 
 
 
 
 
 
 Find the diflference betwoon— 
 
 
 
 
 
 1. f and i. 
 
 8. A and ^. 
 
 IS. 
 
 8f 
 
 and 
 
 ■r>t. 
 
 2. { and }. 
 
 9. A and ^. 
 
 16. 
 
 3A 
 
 and 
 
 i»- 
 
 3. 1 anu H 
 
 10 A an.l ^. 
 
 17. 
 
 5tJ 
 
 and 
 
 ■n\i. 
 
 4. U and i. 
 
 11- 16J and 7J. 
 
 18. 
 
 VJ 
 
 and 
 
 H- 
 
 5. H and i^. 
 
 12. 3f and IJ. 
 
 19. 
 
 11,=!} 
 
 and 
 
 7.5J. 
 
 6. A and U- 
 
 13. a J and 1^. 
 
 20. 
 
 ■^m 
 
 and 
 
 u:ifV 
 
 7. H and H 
 
 14. 6J and 2H- 
 
 21. 
 
 m 
 
 and 
 
 5». 
 
 MULTIPLICATION. 
 
 TO. ExAMPLH 1.— Multiply J by |. 
 
 Solution. Explanattoh. 
 
 a 3 3x2 6 1 '^^^ nuraoratora are mnltii- iod 
 
 ~i~X~3 * 12 " 2 ^""^ * ""'''^ numerator and the ri . 
 nominators for jv ti.-w denominator. 
 
 4 ** 8 
 
fftACTloys. 
 ExAKPt. 2 Multiply i hy , .y , bv I 
 
 85 
 
 '■Mii.i; rio.v. 
 
 " a 
 
 
 ^ !l = 
 
 2 
 
 nrtE. 
 
 Kxj'I,.VNATIO!l. 
 
 Soo Art. 36. 
 
 fieri tice luteqers ami mly.i , 
 
 ft^ simplest form '"""'^nator. Reduce the result fa 
 
 Nox..-Cancellation Often shorten, the operation. 
 
 EXERCISE 34. 
 Find the product of— 
 
 i 
 I 
 i 
 } 
 
 
 
 I 
 
 I 
 
 I 
 
 i- 
 A. 
 
 8. 
 
 9. 
 iO. 
 11. 
 
 
 « X 
 
 * X 
 
 4 X 18 
 
 M X ;; 
 
 '^ 'i X 
 
 A X 
 
 X 
 X 
 
 X 
 X 
 X 
 X 
 
 i 
 
 i 
 
 .1 
 
 S 
 
 I % 
 
 » 
 
 X 
 
 X 
 X 
 X 
 
 X 
 X 
 
 X 77 
 
 16 
 
 18 
 
 X 
 
 X 
 
 X 
 f X 
 
 A X 
 r, X 
 
 ♦ of 20. 
 
 ? X ai. 
 
 S- X 27. 
 
 '.': X J. 
 
 DIVISION. 
 
 ■'j X 
 
 A X yi. 
 
 7I.Tbdivideafractioabyanintegen 
 
 Ex>«rLE l.-Divido ^ by 3. 
 
 Soli- rjcv. 
 Hi . , 2W 3 7 
 23 5i5 « 25 
 
 Example 2.— Divide J by 2. 
 
 SoLDTtON. 
 3 3 o 
 
 * 4 X 2 » 8 
 
 ExAMPLB S.-Divil. :]ii by 11 
 
 SoLDTXnv. 
 
 34 + 11 = 3. rem. 1 
 
 1-- 5 
 3 " 3 
 
 « i. 
 
 83 
 
 Art. 57. Q. 
 
 ExPI,A^•^rI,.s 
 Art. 57, a. 
 
 o 
 
 ff + 11 
 
 E.Xl>r,ANATIOM. 
 
 3 fjf'*'"/"'*-^«-'''y'^ quotient 
 fraction maJtes 1|, ,,, ^, ^ 
 
 -'■'nuir. 
 
 3.T7T Ant. 
 o3 
 
 ooitfi. 
 
aa 
 
 t'ji.icnUiWs. 
 
 or 
 
 2 
 84-3 + " 
 
 lot 
 
 3 
 
 101 
 33 
 
 ^ 11 - 
 
 104 
 3 X 11 
 
 Exi>r,ANATION. 
 
 Rc(l'i'-e tho inixcl number t'. an 
 inii .,.,,• fj-aclini uud proceed ai in 
 example a. 
 
 Ans, 
 
 Diviile — 
 
 I- 51 y 4. 
 
 2. ? l>y tJ. 
 
 8. ,\ l.y 8. 
 
 4. S by 7. 
 
 EXERCISE 35. 
 
 0. 
 
 7. 
 8. 
 
 !^ I'v 11. 
 ii by (i. 
 
 It;: by 
 
 10. 4-2\ by ;i 
 
 11. 07J hy 6. 
 
 12. lUi by 8. 
 
 13. l.lj |,y 7. 
 
 11- H,V by U. 
 
 IS. 21 J by 6. 
 
 72. To divide a fraction by a fraction. 
 
 BxAUPLis.— Divide { by }. 
 
 Exi'LAN'ATION. 
 
 * -5- ! = 
 
 & <il'tI:-< -j- 2 thirds 
 
 Solution. = (i:u.:nth9 ^ lu i,:\ .enths Art. 65 
 
 I + I = i y J = A = .'5'- =■'>'■*_ ^ .i y 
 
 ^ io ."> X 2 ~ 5 ^ •! ~ iT) ^^'"'^ 
 (f.f) J inulfjli^.j by J, (tiio divisor inverted). 
 
 RCLK. 
 
 ^ 7^imt f/if dhisor ami pron:ed us in multiplication <■! 
 friUtinns. 
 
 ex: CISZ 33. 
 
 Divid 
 
 i by 
 ? by 
 iV by 
 
 I'j by 
 
 A. 
 
 A. 
 
 2| 
 
 2l' 
 
 1. 
 ■i 
 
 3. 
 4. 
 
 5. 
 
 6, 
 
 7. t If /r by 
 
 8. ^ X 7i by 3 
 ^- " ^y J X 0^ X 7. 2.' V, X A 
 
 ^*'' 1*5 by f. 23. 1 of 13 A 
 
 "• « by J. 24. 44 
 
 la. 73 bv - 
 
 
 ■f A. 
 
 14. 
 15. 
 
 IG. 
 17. 
 
 IS. 
 19. 
 
 CI. 
 21. J 
 
 73 
 
 13. 
 
 6i by j. 
 
 2.5. 
 2G. 
 
 of 
 
 « 
 
 by U. 
 
 by 41?. 
 
 by ,^vv• 
 
 V't by ii X iij X n 
 by i- 
 by I V. 
 by ai. 
 
 by tV X ,v. 
 by S of ^,. 
 
 by J of 12,»,. 
 
 fy f of A- 
 
 by ,",,. 
 
 27. 13011 l-y ?,nl 
 
 18f by 4t?. 
 
2 
 
 PliACTIOyfl. 
 
 87 
 
 78 A^M^'"'"^^^ COMMON MEASURE, 
 ilonce, *• ^''"- '-'""tamed in it 8 timen. 
 
 TO. A fraction is a common mcasiirp off,. 
 
 «.-«;t«l ,.o„„„o„ laeasuro of i and / ' ' '^' " "'" 
 
 Hence, ■*' 
 
 t«r„; ™tl::,;;:",': r^^ "™»°n measure «, 
 greatest c„„„^.o:';t!,nr.i:.,'r::- 7 '" '": 
 
 •iven denominators °"""°" '"'""P'= "' "- 
 
 The G. C. M. of 5, 5 and 15 = 
 The L. C. M. of (3. 12 and 10 = 
 
 <^- -u. of the 
 
 Therefore the G 
 
 48 
 
 1 liOoi'. 
 
 ,'iven fr.vctioaa is f; Ana. 
 
 The 
 
 
 = 8 
 = 4 
 
 'l'-ti,„<.., 4 and 9 are prince to each other. 
 
1,j^Um-sij^ \^\:*4 
 
 dfl 
 
 FIl ACTIO XS. 
 
 Find tile 
 
 1. I. 
 
 2. 
 3. 
 4. 
 6. 
 6. 
 7. 
 8. 
 
 ni 
 4,-., 
 
 f 
 
 3, 
 
 liil 
 
 i. 
 
 From thi'He principles lui.l iiluHtrations we derive tin 
 : -llowiiig rule : 
 
 BCLR. 
 
 I. /e^'Z/jr*- ,r/to/c and mix.;! nnmhe:» to improper fraHiont 
 and >ill /nil tinim to their lurrsf tcnnt. 
 
 II. Find the ure.itent rnm^uon m,',i8ure of the (jiren numer 
 aton for a luuc uuimmtor, and th,- leant ronuiwn muUiph- oj 
 the,jivc„ dninminntors for a „.;r .1. nominator. Thu fraction 
 will be the greatest common measure 8ou<)ht. 
 
 EXE'CIS; 37. 
 -T -Ht r common measure of— 
 I 4. 
 ?l 
 a- 
 
 i' i 4. f 1. I. A. 
 
 LEAST COMMON MULTIPLE. 
 7». A Multiple of a fraction is any number that con- 
 tains til., fraction an exact integral niunbor of times; thus 
 i is a nniltiple of ^, since i contains ^ 3 times. 
 Hence, 
 
 ««. A. fraction is a multiple of a piven fraction when its 
 numerator is a multiple of the gl/eri numerator, and its 
 aencmiiiator a measure "f the given denominator. 
 
 Hi. k Common Multiple of two or more given fra.-tions 
 is anv niinibor that contains each an exa-t intogral 
 numhei of times; thus, § is a common multiple of ^ly and 
 i, containing ^ 8 times, and ^ 6 times. 
 Hence, 
 
 «!». A fraction is a common multi))le of two or more 
 given fractions when its numerator is a common mi-lH-le 
 of the given numerators, and its denominator is a common 
 measure of tb i given deuominutors. 
 
 
\V-^^^^^M% <«>i 
 
 riucTio.\s. 
 
 89 
 
 H9. The Least Common Multiple of two or more given 
 
 rmctions .B the K„s( ..u.uU-r that c.ntaius each an e c 
 
 Honce, 
 
 »J. A fraction is the least common multiple of two n,- 
 more given fracfons when its numerator is tl .■ least com 
 
 tor the greatest common measure of the given denomina- 
 
 Ex.„P,.._Fi„d the leant co.nmon multiplo of f A. and M. 
 
 SoLCTION. 
 
 L. C. M. of 3. 5 aiiii 15 = 16 
 G. C. M of 4. 12 and 10 = 4 
 TLerefore t),o L. C. M. of the ^iven fractions . V 
 
 PllOOP. 
 
 ¥ + } =. 6 
 
 V f A = 9 
 
 V V H - 4 
 
 The quotientH 5. !) and 4 .xre prime to each other 
 
 Fron. these iniuciples and illustrations we derive the 
 following rule : 
 
 iirLE. 
 
 I. /J../«c. t.Ao/. and mixed n,nnhcrs to improper fractions 
 and all irr thus to their lo.rcst terms. jraaion$ 
 
 II. Find the least common muhiple of the giren numerotur, 
 for a new numerator, and the greatest amunon measure of the 
 given d,,,nnnnators for a new denominator. Thi, frLion 
 will be the least common multiple sought. 
 
 EXERCISE 38, 
 
 Find the least common multiple of— 
 
 1 
 
 2. 
 
 B 
 
 4 
 
 6. 
 6 
 7. 
 
 A. 
 A. SI. 
 
 «• i i ^. 
 
 
 A. 
 
 
 A. J^ 
 
(LCp* . i I 
 
 
 40 
 
 DKCIMALS. 
 
 DECIMALS. 
 
 ■ ^» v^« 
 
 «». A Decimal Fraction. o.)i,)monlv callAr? n« • . 
 
 «w. '^"icotliodetiouiiiiiit ll•8of(lpcimn^^,.„«*• 
 or dcHMoaso by th« uniform scale c^^f 10 m '""'"''' 
 
 «imilflr to that of intc;.s '^ ;,,*, T"' "^ °°*"""" 
 J "'° P^siiiou, till; ( k'ii(iruii|:it()r nf f|,,. iv.. *• . . 
 
 »«. I his 8y.r.m of notation will be best cvplaine.i l,v th 
 following exaiuj-los : '-m^'-uuui uy tij, 
 
 A i« wr.tten .^. and is read ;j t-nths 
 
 rtlni .003. " <• a ti 
 
 i«'' numerator alone in writ' ... , ; <• 
 
 Narkh. 
 
 Unitb 
 Ordxrr 
 
 r3 to 
 
 o " o 
 
 •S'O ~ • 
 
 © 5 ~*' "J 
 
 h -. ::: 
 
 2 2 2 
 
 •*a •.^ 4^ 
 Ci X t^ 
 
 00 
 
 fl 
 
 III 
 
 5 - = 
 
 I 
 
 If 
 
 .X3 
 
 ^ 2) ♦J ,.3 
 
 5 ^ 
 
 ■a 
 = 3 a g 3 
 
 il 
 
 ♦a r^ 
 X o a d 
 
 o i a 
 
 HchM 
 
 2 2 2 2 2 2.22 222 
 
 -*3 -M «A 
 
 — '"S f 
 
 C I. M -< H 
 
 M :o -I ;; ^l; 
 
 -a jo.a 
 -c •? 3 
 
 3 a^ 
 
 = a 9 
 
 2 2 3 
 
 ■asiA 
 «> «j ta 
 I- X S» 
 
i 
 
 UhClMAl.S. 
 
 41 
 
 Prom this it appr-ar-i that 
 
 822.' 22a - 2000 + 200 + 20 + 8+.. l.x_. 
 
 00. r<!,, raethol of rcprosoMfin^ .Irrimal fr.,eti.>,.fl jh 
 
 merely an extonKion of the uu-thod l.y whirl, -nt.-c.,- nre 
 
 repr.sj.nto<l, hI,,.... th. local value of o.uU d:.if i^.c-n.nse^ 
 
 ton ol,l as wo a.hance from ri^-ht to left, and also .l.rr-a.os 
 
 n thesa.no . ...tir-n aH w a.lvar.ce from left to ri-^ht. 
 
 From the foro^joing we derive tho f„Ilon-i„!T priuciples : 
 
 fniNCIII.KS. 
 
 91. 1. Denmals ar. normu,! h, thr ..„,,- h„v of loca, ndue 
 th'tt fjnreniH III,- nutation 0/ iutan'i-x. 
 
 2. Thr dijrrrnit onlcr» o/,}.n,n„l ,„nts .Irrrcasr ,)■<„ <rft 
 l'> rujht mul inrr,-n.efr,nn rinht tn Irft in „ tr.fnl,/ rntio ' 
 
 8. rhr rain, of am, .Icrinn,! jl,u,r ,hpcu,h npu„ th. place 
 U occv;.,-, at thr ri,,ht of the dniwnl ,. .i„t 
 
 4. EnrI, removal of a .Urin,ai o:,l.-r one i,,ace to th. Irft 
 tnr ream's its ralui (rnfohl. 
 
 6. Each remoral of a i.rinud order one j.lace to the >■„/,, 
 decreases ttt value temhld. 
 
 6. Prrfirinff a eif.h.r to a decimal di„n,nshr, its v<r;e tn,- 
 'Old, suu-e U r.„.orr. ever, ,lecinrd fojure o,.^ ;,/,„.„ „> ,hc ,u,ht 
 
 7. Annenu.j a nj.her tn a d.ri.nal doe. nut all. r its ralne 
 nmce xt d>cs not ehuuy. the ,>aee of any n^ure in thedeei.nai 
 
 EXERCfSE 39. 
 Express in deciinal form and rea.i— 
 
 I. 
 
 II. 
 
 rwTJs 
 
 III. 
 
 ? :. o 
 
 1 .-, u u 
 
 IV. 
 
 "no 
 
 A 
 
 .!'.-.r. 
 
 V. 
 
 nn 
 
 E.xproHs in the form nfa fniction a.il read- 
 VI. VII. vTfi. jx ^ 
 
 •• -'^ 8-7 .000-. ,,,04 
 
 •^ 0^0 -130 .912 86.003 
 
 ?.-. 
 
42 
 
 DECIMALS. 
 
 Expre83 as decimals— 
 
 XI. Five-tenths, „, . 
 
 eleven tenthoiuandtlu. 
 AlJ. Thirty, and .sc(i<;/i.r<'?u/ii f„„,* 
 
 »i5. A Complex Decimal has a fraction in its right 
 and place .12^ which is read 12J hundredths, fhe 
 fraction not hem^ counted as a decimal place. 
 
 Express as co,amon fractions in their lowest terms- 
 
 XIV. .75, .72, .625, .024, .00.32, .12. 
 XV. .13J. .103. 571, .661, .44iJ, .024f 
 
 tt3. To reduce a common fraction to a decimal. 
 
 Keduce f to ita equivalent dooimil. 
 
 ^ Reason. 
 
 8)J^000_ 3-g^^-5 = -JL" 
 
 ''■^^ 1000 = S = •«''« 
 
 folK.tn!":;ef'^ "' ^^"""^^ ^^^'^^^^^ - ^--e the 
 
 RULB. 
 
 that the division is not compir'or t " avL ' "T^"^ "^ "^^ 
 decimal. ^^^ *^ expressed as a complex 
 
 on?;, th^^tdi:"- .::rt:r^:° '^ ^r^^ ^° ^ ''-- ^-^-^ 
 
 the dononnnator co^ZZnToZr Zr^'J^^'r '"* ' '^'^'^ ^- " 
 end. The decin^als thu Zlu d a^e Ta,l2 «' "■ """°" "'" "°» 
 M>e figures repeated, AVp.Jr; ^ '''^""""^ I^ecin.als, and 
 
 EXERCISE 40. 
 
 Reduce to equivalent decimals— 
 
 ''• A 6. ^3 10. I 
 
 *• « « I 12. iJ 
 
 18. 
 
 14, 
 16, 
 
 16 
 
 12f 
 
 16! 
 
 311 
 
DECIMALS. 
 
 43 
 
 3^ 
 
 ADDITION. 
 
 »5. Since intpgers and decimals increase and decre'iHo 
 uniformly by the scale of 10. it is evident tliat decimals 
 may he added, subtracted, multiplied and divided in the 
 ?nrae majiut-r as integers. 
 
 Add l.i.n. 5.034, .3172, 14.52. 
 
 Explanation. 
 
 ^■^■'' W the decktifU poim.s are in the same 
 
 ■^•;'.^ vertical line it will necessarily brins 
 
 •'t, *^""'^ "°<ier tent!-..,, !u.n Iredths under 
 
 L'ir^ hundreaths, etc., ,and the numbers nmy 
 
 •■'^•^ '^2 therefore be added aa in integers, 
 
 «6. Write the numbers su that thrir dcnmal points are 
 in the same vertical line. A^.l as in inteo'^rs, and place the 
 decimal point in the result direct!,, under the points in the 
 u umbers added. 
 
 EXERCISE 41. 
 
 Add— 
 
 1. .8R12, 26.0.T5, .0037, 3.4, 017 
 
 2. 41234, 17.013, 3.3, 400.2, 0045 
 8. .0120, 40.871. .7251, .0021, 311 6 
 
 4. .061, 3.80,j.^ 40.036, .00319 
 
 «. .004J, 3602^, 7.34, .37J. 
 
 «. Ninety.8even/m«<ir.dt;,., four hundred and three t;,.,«ar.d( A, 
 thirteen ten.thow,andth», sixteen, and meenhumlredtht ' 
 forty-aeven, three hundred and twelve, and 
 
 sixty.four thuusaiidtlit. 
 
 SUBTRACTION. 
 
 ?>7. From 13.65 tak- <).3i;,^2. 
 
 1R fi^nn . NOTE.-The i,ffixi;,>. of cipliers to ri-ht of the 
 
 18.6500 deemed does not alter its value. In practice 
 
 930.52 we omit ti,o decimals, and merely conceive 
 
 4.^818 them to be annexed, subtracting as other- 
 
 wise. 
 
 KDLE. 
 
 »8. Write the numbers so that the decimal places shall 
 stand directly under each other Subtract as in whole 
 numbers, and place the decimal point in the result directly 
 under the points in the given numbers. 
 
44 
 
 l>i^OIJUALS. 
 
 EXERCISE 4Z 
 
 Find the diflVrenco Lravron- 
 
 1- 1V.205 and 1;16. 
 2 1 0;i7 and .•2T.i!i. 
 8- 37.(KI( ;,,„i |il.,Ti2-,3 
 4- ■100.7 and .ontca' 
 
 •'• I'-rom o.ufis take .0187 
 
 ,• '''■'^'" '^OT^ take .29053. 
 
 7. .Sub„-,.cct.m8<;.l and .•;o.,W2 
 
 8 f'-btnwjt .003J716 and oi2o 
 
 MULTIPLICATION. 
 
 «». In mulfiplieation of ckrinnl. H 
 clonm.l point in the nio.lu.t ^''^ P^^'t.on of the 
 
 I'rinciples : ^ ^"'^ '''''^^"''^ "Pon the following 
 
 1; TJie n urn her of ciphers in th l 
 
 •'--1 . .uo the nL... ; ,:i,: :;;;;:-^«-^ « 
 
 n^any ciphers as ther a e I^^f''""'''^'^ ^""^ contain a. 
 Therefore, *''""'^' l^''-^''^'^ i" both factors, 
 
 3. The product of two deeinTila « 
 ^orm must cont.-.in J ^nlZJ ""TT^ "' ^^' '^'''^^^^ 
 decimals in hoth factors ^ ''"""' ^'^"^'^^ *^ ^^'^^^ are 
 
 Multiply .3i,j !,j. 23. 
 .314 
 
 9f.> 
 
 .07222 
 
 Not. TI,o number of decimal plac. 
 .n-oth factors i« 5 ^ho n„,„L ^f 
 fi;:"'-i« m tl,c. pro,l,„.t ip onlv Tl i 
 
 Mnltij)ly— 
 
 1. .75 l,y 
 
 2. .410 by 
 
 3. 5 7o by 
 
 4. 7J1 bv 
 
 EXERCISE 43. 
 
 A. 
 .32. 
 .38. 
 .025. 
 
 6. 3.-ii; by 40.4. 
 
 RDLK. 
 
 '"' 01.") by .003. 
 
 7. 2..'i7l by .i!i8. 
 
 8' .4.'{.> by 1.203 
 
 10. .oOt X .2 X.03 x.2.'> 
 
 
 'Jk«. 
 
DECWALS. 
 
 u 
 
 CONTRACTIONS IN MULTIPLICATION. 
 
 I«l. Muh\i,W O'i.ST'lie by 2.lim'j 80 as to r<-t;iin only 
 1 places of decimals. 
 
 Obdi.n'aiiy Mi:tiiod. 
 02.;t71I6 
 
 _2.:iji(;o 
 
 f.(ii!;;i;7Jl 
 871 -' MUG 
 
 24!il!)|(;c,J 
 
 I87i2-'!n 
 
 12}7H.;l2 
 
 iii; ut;o'j|i07;iol 
 
 Cos I llACTKb ^Tk ruoD. 
 
 62.871 IC 
 
 9(;r i:t.2 
 
 i2i7i ..r « (;L>;i7.l X 2 + 1 
 
 0::..71 X 3 
 
 'i-':i7 X 1 + 2 
 
 <;-:i y 1 + 1 
 
 <jii X »; + 2 
 
 0x9 + 2 
 
 187122 
 24:io0 
 
 371 
 
 r.o 
 
 146 riouTi 
 
 lOtJ. It fmiueiitly happens in muitipHr.ition that a 
 greater number of decimal fj^'uros is obtained in f),e pro- 
 duct than IS necessary for practical accuracy. This may 
 be avoided by contracting each partial product to the 
 required number of de. i.nal places. 
 
 103. From this principle and illustrations similar to 
 the foregonig example we derive the following: 
 
 RULE. 
 
 Write the multiplier with the or.hr of the figure, reversed, 
 and tnth the units place under thatfujure of the mnltipU,a,ul 
 whieh ts the lowest decimal to he retained in the product. 
 
 Find the product of each f,,ure of the wnltiulier by the 
 figures above and to the left of it in the nndtipUnnul, incrensinn 
 each partial product by as many units as uo.ld have been 
 carried Jrom the rejected part of the vndtiplieand, and one 
 more when the highest jiaure in the rejreted part of auv 
 productis5orc,reatcrthaa5s and write these partial pm- 
 ducts with the loivestfiffure of each in the same column. 
 
 Add the partial products, and from the rirjht hand point off 
 the required number of decimal Jif/ures. 
 
 NoTK 1 -In obtaining tl.e nn.nb.r to l.e crirriod it is generally necessary 
 to mu,t,,ly (n.entaliy) only one ti,aru at the ri»„t of the figure ^eZ 
 
 ^rwr 
 
'i \ 
 
 46 
 
 DECIMALS. 
 
 EXERCISE 44. 
 
 4.af.7S le'ainiMi,' 2 docuii.'.l places 
 
 .O->J4.0 " 4 ■. .. 
 
 .731.53 <• 
 
 .127:.y .. .. .. 
 
 .02786 
 .693817 
 
 1. 
 2. 
 3. 
 4. 
 
 6. 
 
 3tj.'J7.> 
 41. .3075 
 
 17.i"i0.liT 
 
 .t3_'i;i 
 
 .Oo;tti47 
 G. 700.37.5 
 7. .371.^25 
 
 X 
 
 X 
 
 X 
 X 
 
 K 
 X 
 X 
 
 3 
 5 
 
 DIVISION. 
 
 PRINCIPLE. 
 
 104, MuUiphnng both divisor and dividend by the same 
 riumlx'r does not alter the quotient. 
 
 105. Multiplying a decimal expression by 10, moves the 
 decMm pomt one place to tlie ri^^ht; by 100, two places to 
 
 he nght; by 1000. three places to the ri,hi. etc.' Ther! 
 fore, moving the decimal point iu divisor and dividend the 
 same number of p aces to the right, multiplier each of them 
 by the same number. 
 
 ExAMrLE 1.— DivMe 16.57S by 6.4. 
 
 ' ■ "^ V Explanation. 
 
 -Multiply the divisor and dividend 
 by 10 and we obtain 64 as divisor 
 and 166.78. Now 54 will divide into 
 16.5, 3 times, and therefore 3 is tlie 
 integral part of the quotient. 
 
 61 ) 1(55.78 ( 3.07 
 _162 
 378 
 378 
 
 BxAMPLB 2.-Divi.3e .736644 by 234"6 
 234 6 ) .73C.a44 ( 
 2346 ) 7.3(!';.lt ( .00314 
 
 7 1 '3a 
 3284 
 
 U384 
 9384 
 
 Here in dividin« we use as tlio 
 first partial dividend 7.306 or 7366 
 thousandths, and hence our first 
 quotient a^^ure 3 thousandths which 
 expressed aa a decimal la 003 
 
« 
 
 f 
 
 i 
 
 I 
 
 DECIMALS. 
 
 •17 
 
 ni;LB. 
 
 <inlthe sa,ne nnrnh.r o, place, to the ri,,ht in the divid.n,l 
 < >»'■';/. ... vn svnple division, placing the decimal point in the 
 quotrent as soon as the ttnths figure is used or brought dou^n 
 
 NOTB.— If the flividond dooa not contain »i manvHop;„.oi i 
 
 EXERCISE 45. 
 
 1. 48.501 + .06. 5. .0771 -=- HO 
 
 2. 2.56 + .00,^3. 6. 21 3 i- 37 5 
 3 1 + .025. 7. 202 4. .01. 
 
 8. -100.8 4- "oiV 
 
 3. 
 1. 
 
 .0012 -J. 1.6. 
 13. Div' Irt 1.21 
 
 9. 10 !;o 
 
 10. I -,.77 
 
 11. 1:^1.25 
 
 + .10, 
 + 75 
 
 14. Divide 
 
 by 11. 1.1, 
 
 036 by 1800, 180, 
 
 1:^ .7,J32ii +33. 
 
 • 11. .011. .0011, .00011. 
 l*^. -H, .018. 
 
 CONTRACTED DIVISION. 
 
 01 '"tar"" '"'"'"' "*' ■^"''^^' -"-' '" '»- p"- 
 
 Ordikary Method. 
 2136-12 ) 7031(10.3 ( 35.7205 
 
 6iOH2''.. 
 i2221.1jG 
 10082 1 'O 
 1530lj(l3 
 14954 Jot 
 430,'i;90 
 427j284 
 12[l0iW0 
 10!(;,S210 
 1172390 
 
 CONTRACTKD MbTHOO. 
 
 218642 ) 7';31 1163 ( 86.72O6 
 
 i:i0026 
 
 122215 
 
 IO1U21 
 
 i:..J>J4" 
 
 14955 
 
 430 
 
 427 
 
 13 
 
 U 
 
 1 
 
 BULB. 
 
 I08 Compare the highest or left hand figure of the divisor 
 'nth the nmts of like order in ,he divrdid, and deterZe 
 how manyjrgures will be required in thr .quotient. 
 
 For the first contracted divisor take as nun,, significant 
 figures from the left of the given divisor, as there are pUcel 
 
48 
 
 DECIMALS 
 
 quired in the quotient, and, at each sui.e.uent division reiect 
 one place from the riyht of the la,t preceding divisor. 
 
 In nudtiplyin., by the screral quotient figures, carry from 
 ike rejected j^gures of the dirisor as in contracted mJtipZZ 
 
 Divide — 
 
 1. 27.3782 by 
 
 487.21 by 
 
 8.47326 by 
 
 .Hlri7i;64 by 
 
 478.325 by 
 0. 8J7-J.436 
 7 1 
 
 2. 
 3. 
 4. 
 6. 
 
 EXERCISE 46. 
 
 4.3 Ji. 7 correct to 3 decimal places. 
 
 8. 
 
 1.0u.,ij7j 
 75.43 
 .07.-.G37 
 1.13^ 
 by 7.">ii..!i.">2 
 by 1.0u7l;33 
 
 .903728 by 44.73054 
 
 REPEATING, CIRCULATING OR INTERMI- 
 NATE DECIMALS. 
 
 10». In reducing common fractions to equivalent deci- 
 mals, refereuce was made in Article 94. Note 1. to he 
 u^ethods of ex,re.ssm, the decimals in cases where the 
 dms.on does not terminate. But if the division we. 
 earned fur enough (never to number of places in tie 
 quotient greater than the nuu.ber represkted by the 
 dmsor) a remamder would he obtained which had occurred 
 before and hence a figure or set of figures in the quotient 
 would be repeated in the same order in a neve 'en Ih"! 
 succession A decimal of this kind is called a repeating 
 or circulatingr decimal, or simply a repetend. ^ ^'"^ 
 
 llO. When a repetend consists of a sinsle fimir^ if • 
 .ndieate,. b, a p„i,H place,, „v. it,- .heat ooC ^f 
 more t„an one l,«„e a point is placed over the firat and 
 one over the )a.t ligu.e repea-ed. Thus the circutt1"g 
 
 Ki2r^S^i»i^l^. 
 
UJiCHJUALS. 
 
 decimals .4444 . and .324324324 . are written .4 and 
 
 , tbem to decimals, we obtain " ''^'''' '^'^ '' 
 
 I'rom the^e and thnilar examples ttr infer that all n«e -k. " 
 repetends ..« thus ,e ,ern-e,Jrom fraXn:\Z^^^^^^ 
 ators are the repeat,,,^ ji^ures, and whose ^ten nZf 
 as many 9^s a, there are repeating figr J,, "'"^ ^»«'''«''* ^'"^ 
 Example l.-Expreas * as a repeating decimal. 
 7 M f .714285711295 + = 7140S5 
 
 as ) 18 ( .40428.71428571 + = 4.;i2857i. 
 
 lia. Decimals in which all the firrnrps ,^o ««♦ 
 called Mixed Circulating Decimals' ^^''' *•"' 
 
 E^x^ 3.-Expre88 .25 as a common fraction. 
 .25 = 33 
 Explanation. 
 
 •25 = .252525 + 
 V 100 times .25 = 25.252525 + 
 Add 1 times . 25 = .252525 -»- 
 Subtracting 99 times .25 s 25 
 
 •■■ 25 = ^ 
 
 Jjora similar examples to this we derive the following 
 
 BULB. 
 
 Omit the points and deeimal Sign and write the /inures of 
 the repetend for a numerator and as many 9's as there a/' 
 places tn the repetend for a denominator. ""' 
 
 ExAwia. 4._Express .2456 as a common fraction. 
 
 SOLCTION. 
 
 2456 
 
 24 
 
 2432 
 
 HU Ans 
 
DECIMALH. 
 
 LXfLANATION. 
 .215t5 ; 
 
 V 10000 timt-a .•21^6 : 
 And 100 times .•iiiij 
 
 .245P>56566H -f 
 
 ■2166.r)65t)")tl + 
 
 _ 24.565G.')6 f 
 
 Snbtractinf,' 9900 times .245& = 2432 = 2158 - 24 
 
 2jnr, -2\ 
 
 O'JOO 
 
 .245(5 = 
 
 Prom examples similar to the preceding?, we derive thu 
 following rule for reilueing mixed circulating dt'ciraals (those 
 in which only a portion of the tigurea in the decimal repeat) 
 to common fractions. 
 
 RDLB. 
 
 Subtract the part of the decimal which dot's not repeat from 
 the whole decimal as if each were whole numhers, and place 
 the remiiinder as a mmu-rator, and for a denominator as 
 many 9's as there arc Jl/nres rrpeaiiuf], followed by as many 
 O's at there are figures in the part irhich d es not repeat. 
 
 EXERCISE 47. 
 
 Express as circulainig ducinmla — 
 
 1- h h h Ij, I'j. -?. f, ?, ^i, A-. 
 
 2. H. ,V. H H- ij, ,V ih H- 
 
 Exprt'H- as fijictions in Liieir lowest tc ms — 
 
 3. .7, .57, .806, 4'5, .360. .162, .2635. 
 
 4. 27, .47, ..SI, .235, .215, .34734, .712n. 
 &. 036, .00-247, .0356. .8510, ,0357, .71..*. 
 
 I 
 
WEIQUIH A.\D MKdSUIiES. 
 
 51 
 
 WEIGHTS AND MEASURES. 
 
 CANADIAN CURRENCY. 
 
 118. Money is the measure of value. 
 
 1 14. Currency is the money praploye.l in trade. 
 
 llli. Coins or Specie aru specioa of m.^tal of Jiuown 
 pur.ty and ^e.^ht, Htatnped at the Muic. and authorized by 
 the Governraent to be used a^ money at lixed value. 
 
 U«. Bullion IB uncoined gold or silver, and includes 
 bars, gold-.hist, etc. 
 
 117. Paper Money is a substitute for metallic currency 
 it consists of Dominion Notes issue 1 by the Qoverument 
 and Bank Notes issued by Chartered Jiaaks. 
 
 IIS. Canada money is the legal currency of the Do- 
 ininion of Canada. It is fouu.led on the Decimal Notation 
 and Its denominations are, Dollars, Cents and Mills. 
 
 lltt. The Silver coins are the fifty cent piece, the t wenty- 
 five-c C V -ce, the twenty-cent piece, the ten-cent piece 
 and tl.a hv.^-cent piece. 
 
 ' he '' .nper coin ia the cent. 
 
 Xhei are no Canadian gold coins ; those of England and 
 the United States are a legal tender. 
 
 TAHLB. 
 
 130. 10 MillB = 1 Con» 
 
 100 Cent3 = 1 Dollar 
 
 et. or ^. 
 dol. or f , 
 
62 
 
 WEIUIITS AND UEASUIiSa. 
 
 UNITED STATES MONEY. 
 181. U. 8. Money is the legal currency of the United Statea. and if 
 often called Federal Money. Ita denominatione are Eagles, Dollari. 
 Diniei, Gents nnd Mills. 
 
 laa. The Gold coins are the double eagle, eagle, half -eagle, quarter- 
 eagle, three-dollar piicc, and dollar. 
 
 laa. The Silver coins are tie dollar, half-dollar, qnarter-doUar and 
 dime. 
 
 The Nickel coins are the one-cont and three-cent {.icces. 
 The Bronze coin is the one-cent piece. 
 
 TABI.B. 
 
 124. 10 Milla . ,1 Cent . et. 
 
 10 Cents . . ml Dime . d. 
 
 10 Dimes or 100 Cents = 1 Dollar . dot. or f 
 
 10 Dollars . . =.1 Ea-le - E. 
 
 ENGLISH MONEY. 
 
 laS. Eiitiliah or Steiliug money ia the currency of Greal 
 Britain. 
 
 126. The unit is ihe Pound Sterling, which is repre- 
 aented by a gold sovereign, is equal in value to $4.8666. 
 
 TABLK. 
 *■••• ■» i-ariiuincs lor. or r/ir 1 ^ i I'onno j 
 
 = 1 Penny 
 
 = 1 Sliilling . ,. 
 
 » 1 Pound or Sovereign /*. 
 
 = 1 Guinea. 
 
 4 Farthings (qr. or far.) 
 12 Pence 
 
 20 Shillings . 
 
 21 Shillings . 
 
 laS. The gold coins are the sovereign, and the half-sovereign. 
 
 ,0 *«??:J^f-.?"''^''"'"^ *" *^^ "°^" (' ^*-)- ">« half-crown 
 (i: ed.), the shuhnj?, and the sixpenny piece. 
 
 1»0. The copper coins are the penny, half -penny, and farthing. 
 
 1.31. The 8tauu.u J purity of the gold coins of Great Britain is 22 
 c.rats fine ; that is \\ pure gold and ^ alloy. That of the silver coins is 
 f } pure silver and ^ alloy. 
 
 TROY WEIGHT. 
 182. Troy Weight is used in weighing gold, saver and 
 jewels ; in philosophical experiments. 
 The measuring unit is the pound. 
 
 i 
 
 ifiim^i.:^^ 
 
 ■ ■*i*.2R*^^m^b^*» ■• 
 
WEIGHTS A.Vn MEAWRE3. 
 
 n 
 
 188. 
 
 TABr.il. 
 
 «Orain.f^.) . , Ponnywoi«ht d^t. 
 80 Ponnywei^hU . 1 Oat.oe . „ 
 19 Oiincoi ... 1 Pound . »" 
 
 A carat is the weight of four Rrains. 
 
 APOTHECARIES WEIGHT. 
 
 I3«. Apothecaries Wei;,'ht is used by dru-^iats and 
 phyB,c,an. m compounding modicinos. but drugs;'! 1 inedi 
 cines are bought and sold by avoirdupois weight 
 
 The measuring: unit is the pound. 
 ^J^he pound, ounce, and grain are the ,nme aa in troy 
 
 TABLB. 
 
 20 Grains = l K.niple 
 
 8 Scruples = l Dram 
 
 8 Drams s l Ounce 
 
 la Ounces a l Pound 
 
 1^0. 
 
 ic. or 3 
 dr. or 3 
 oi. or 5 
 /ft. 
 
 13S. 
 
 APOTHECARIES' FLUID MEASURE. 
 
 137. Apothecaries' Fluid Measure i. used in mixinc 
 hquid medicines. mixing 
 
 TABLE. 
 
 •« ;f"'7'°'^'-°l'M»») = 1 Fluid Drachm /3 
 
 »?F ,n ™' ■ • = 1 I'''"i'l Ounce . fl 
 80 Unid Ounces . . = i pj^^ . . ^3 
 
 8 Pints . . _ , ,,„,, '^ 
 
 • • - 1 Ijalloa . . Cong. 
 
 AVOIRDUPOIS WEIGHT. 
 
 13». Avoirdupois Weight is used for all the ordinary 
 purposes of weighing. oramary 
 
 The measuring unit is the pound. 
 
 Taule. 
 
 16 Ounces (0.) . . = j p,,„, . ^ 
 
 100 Pounds . . _ 1 ir„„i •■ , 
 
 9nnft i> 1 \./ • ~ I Hundred weight mrt. 
 2000 Pounds, or 20 cwt. = 1 Ton ^ 
 
64 
 
 141. 
 
 14a. 
 
 !' J 
 
 148. 
 
 m!nkj.vjia;n 
 
 tti-JOllTS AND MEASUIiES. 
 
 LONO TON TABI,«. 
 
 18 Oanci'g (oi ) =, 1 Pound . . jft 
 
 lia Voiiudi . m 1 llii,ilru.iwoi^ht ewt 
 
 «210 I'omid. . m 1 Toil ■ ■ - r. 
 
 ■PEcui, 4?oinDPPoiH WKronti. 
 
 100 lU Nsils . m 1 Kog. 
 
 100 //«, Dry Fiih . 1 Quintal. 
 
 196 lit Flour . a 1 „rrel. 
 
 800 Wt. BeoforPork = 1 IJarrol. 
 
 COm-AKATIVR TABLK OJ' WRrOHTB 
 
 Twoy » oiiiuui'on 
 
 ! Pound > 67»lO Grairn m 7(>i)0 Omnia 
 
 1 OoDoa ■ 4so •' :> 137J 
 
 175 Ponnds = 144 Pound* 
 
 CHAIN MEASURE. 
 
 APOTlTKCAnUH 
 
 17110 (i rains 
 480 
 172 Puond* 
 
 144. 
 
 Wk 
 
 1 
 
 TABLX. 
 
 
 
 14 lb». Blue Grass Soed 
 
 :ai 
 
 1 Bn 
 
 84 lbs. .ta 
 
 ^ 
 
 1 
 
 86 Ibt. Malt 
 
 s. 
 
 «i 
 
 40 n^K. Ca=itor Beans 
 
 _ 
 
 M 
 
 44 Uij. llom|) Hoed • 
 
 SE 
 
 (1 
 
 48 Ihi. Uirley 
 
 S 
 
 • 1 
 
 48 Ihs. liuckwhcat 
 
 _ 
 
 II 
 
 48 lb/. Timothy Seed 
 
 _ 
 
 !• 
 
 50 lbs. Flax K.,.,i 
 
 „ 
 
 11 
 
 66 lb». Indian Corn • 
 
 3 
 
 It 
 
 6(5 lbs. i;.o 
 
 _ 
 
 >< 
 
 60 lb. Wheat • 
 
 ss 
 
 II 
 
 60 lbs. Beans - 
 
 ss 
 
 >l) 
 
 60 lb>. Red Clover Seed 
 
 s 
 
 *4 
 
 60 lbs. PotntooB 
 
 3 
 
 • • 
 
 60 Iht. Turnips 
 
 9 
 
 •« 
 
 60 Ibt. (Carrots 
 
 a 
 
 M 
 
 60 lbs. Parsnips 
 
 , 
 
 •1 
 
 60 Ibi. Beets 
 
 a 
 
 •• 
 
 60 Ibi. Onions . 
 
 3 
 
 «i 
 
 70 tb$. Bituminous Coal 
 
 a 
 
 U 
 
 
WHOUTS AND MEASVUUa. 
 
 M 
 
 DRY MEASURE. 
 
 145. Dry nKftsuro is nm\ in meiiHuring substancM not 
 lujuid, aB grain, fruit, Halt, roota, etc. 
 
 146. a Pint- ipi ) = 1 (^.!vrt 
 
 4 (.) i.irtH = 1 (i.i.I.jn 
 
 8 0:ill..|lfl 3 1 I fck 
 
 4 PuckH m 1 liiisliul 
 
 9«. 
 gal. 
 pk. 
 
 hii.h. 
 
 147. The Imiicrial Ktan.lnr.l (.J.dlun, for liqui.iH and nil dry sub- 
 HfuucoB, is a mottauro tlmt will .Mnta.ii l(t |mu!uI« nvoinitij.nirt of distilled 
 waUir. weif-iiod in air at tia' Faliri'iilioit, tlie l.u.. ii tur iit HO iuoheB 
 
 I \H. The Imfjerial (Jallon contains 277 271 cul)ic inches. 
 
 I4». Tho Inii)erial Stuu.lird Bushel is equal to 8 gallons or 80 
 oounds of dislillud wator, wdf;licd in a in iiinor above duscribod. 
 ISO. Tho Standard Bualiol contains 2218.192 cubic iodiM. 
 
 LIQUID MEASURE. 
 
 151. Liquid Measure is uko I in measuring liquids; as 
 liquorg, molasises, water, etc. 
 
 TMii.i:. 
 
 152. 
 
 4 Gills (gi.) 
 
 
 
 = 1 Pint - 
 
 pt 
 
 2 Pints . 
 
 
 
 = 1 Quart - 
 
 </'■ 
 
 4 Qiia'-ts . 
 
 . 
 
 . 
 
 = J n.illon 
 
 gal. 
 
 81i G;illuii3 . 
 
 . 
 
 . 
 
 = 1 Barrel 
 
 bbl. 
 
 8 Hairtl.s, or 
 
 (13 
 
 Millions 
 
 = 1 H );^9lioatl . 
 
 hhd 
 
 158. Tlie following denominatioiiK are also in use ; 
 
 42 Gallons ... =1 Tioroe. 
 
 2 Ilot^sbeada, or 126 Gallons = 1 I'ipe, or Bntt. 
 2 Pipes, or 4 no{,'8heada = 1 Tun. 
 
 Note.— The tierce, hogshead, pipe, butt, and tun, are the names of 
 casks, and do not express any fixed delinite measures. They are 
 usually panged, and have their capacities in gallons marked on them. 
 
 154. A Measure is a standard unit esiahlished by law 
 or custom, by which exteiit, dimengion, cap!t-''.ity, amoi-nt, 
 or value is estimated. 
 
■ I 
 
 If ■ 
 
 56 
 
 WEIGHTS AND MEASURES. 
 
 MEASURES OF EXTENSION. 
 
 155. Measures of Extension are those used to ascertain 
 how long a hue is. or in calculatin;^ the size (extent) of a 
 surface or sohd. 
 
 A line has only one dimension— length. 
 
 LINEAR OR LINE MEASURE. 
 In measuring length, linear or line measure is used. 
 156. 
 
 TABLE, 
 
 12 Inches (in.) . = i p'oot 
 
 8 Feet , . a i Yard 
 
 6i Yards, or lO} ft = i Rod 
 
 320 Rods . . = 1 Mile 
 
 ft. 
 yd. 
 rd. 
 mi. 
 
 1 Mile a t20 Rods 
 
 EQniV.U.KN rs. 
 
 = 1760 Yards := 52S0 Feet 
 SURVEYORS* MEASURE. 
 
 C33G0 Inches. 
 
 137. Gunter's Chain, used by land surveyors, is 4 rods. 
 01^66 feet long, and consists of 100 links, each 7.92 inches 
 
 ISH. 
 
 TABLE. 
 
 7.93 Inches 
 
 Z5 
 
 80 
 
 Links 
 
 Rr-rls, 
 
 Chains 
 
 = 1 Link 
 = 1 Rod 
 
 Ik. 
 rd. 
 
 or 66 Feet = 1 Cliain . eh, 
 
 = 1 Mile 
 
 mi. 
 
 SQUARE MEASURE. 
 
 I5». Square Measure is used in measuring surfaces : ai 
 of land, boards, painting, plastering, etc. 
 
 160. Area or Surface has length and breadth only, and 
 IS the space or surface inclu.led within any given lines. 
 
 161. A square inch, square foot or square vard is » 
 square, each side of which is respectively. 1 inch; 1 foot, or 
 1 yard in length. 
 
 3 
 
 ! i 
 
 I L™,. 
 
i 
 
 31 
 
 1«3. 
 
 WBiaUTS AND MEASVRB3. 
 
 TABI.1. 
 
 144 Sqnare Inches {sq. in.) = 1 Square Foot 
 
 9 Square Feet . . = 1 Siu.^reYard 
 
 80i Square Yards . . ■ 1 Scjuare Rod 
 
 160 Square Rods . . a 1 Acre - . 
 
 640 Acres . . . . ■ l Square Mile 
 
 57 
 
 iq.fi. 
 
 *q yd. 
 
 sq. rd. 
 
 A. 
 tq. mi. 
 
 Artificers eatiraate their work as follows : 
 
 By the square foot : glazing and stone-cutting. 
 
 By the square yard : painting, plastering, paving, ceiling, 
 and paper-hanging. 
 
 By the square of 100 square feet : flooring, partitioning, 
 roofing, slating, and tiling. 
 
 Bricklaying is estimated by the thousand bricks, by the 
 square yard, and by the square of 100 square feet. 
 
 NoTKS 1.— In estimating the painting of moldings, cornices, etc., the 
 measuring-line is carried into all the moldings and cornices. 
 
 2. In estimating brick-laying by either the square yard or the square 
 of 100 feet, the work is understood to be 12 inches or IJ bricks thick. 
 
 8. A thousand shingles are estimated to cover 1 square, being laid 
 6 inches to the weather. 
 
 SURVEYORS' SQUARE MEASURE. 
 
 163. This measure is used by surveyors in uumputing 
 the area of land. 
 
 TABUI. 
 
 164« 625 Square Links = 1 Pole ... p. 
 
 16 Poles . . = 1 Square Chain - $q. eh. 
 
 10 Square Chains = 1 Acre - . . ^. 
 
 640 Acres . . = 1 Square Mil* . tq. mi. 
 
 CUBIC MEASURE. 
 
 1«5. Cubic Measure is used in measuring solids or 
 ▼olume. 
 
 166. A solid is that which has length, breadth, and 
 thickness. 
 
 iSPmaHPaBige^ 
 
68 
 
 » WOifrs AND M£:ASVJtES. 
 
 "ess are egual to c„cl, „tbe,. ^' "''"'"'^ ""'I 'Wck- 
 
 I A 'ABU. 
 
 ««8. 1728 Cnbic Inches («...„) 
 
 27 Cubic Feet ■' • • = 1 Cubic Foot . eu ft. 
 
 40 CubicIVet.f Rou„d Timber ;r, ' ' ^^"^'« ^""-d ' «i.yrf. 
 fiO Cubic Feet of Hewn .. ' « 1 Ton . . 7, 
 16 Cubic leet ^ ^• 
 
 8 Cord Feet, or 128 Cubic Feet T J r'"f f °°' ' "^•■^'■ 
 241 Cubic Feet = ^ f'ord of Wood Cd. 
 
 „ ^*^' = ll'orchofStone) „ 
 
 2 Taiir'. ^ ^'^'^ ^■"' °' ^"^'^ '■« -"«^ - load ""' '^'^^^"^ ' '^'^'- 
 ^. "•"'road and transD-jrts»;«„ 
 
 6 Joiners, bricldavers KnA ,« 
 '^-rs. etc . Of one . Jf tb^ op Xr; "^ - allowance for windows. 
 
 ZT' '" ^^'""^''"g "-- work VcUnl:"""- ^'"^^-y-» and 
 for the eorners of the walls of bouses celkrs . Ti '"''^ "° ''"°^^'^«« 
 
 by the ,rMbat is. tbe entire lengtb'^te^aton'lt^^^ 
 MSASURE OF TIME. 
 
 revolution around the sun. "^ °° '*^ *-^'« i tbe latter by Hi 
 
 171. 
 
 60 Seconds (see.) 
 60 Minutes 
 24 Hours . 
 7 Days . 
 
 865 Days 
 
 866 Days . 
 
 12 Calendar Months 
 100 Years . 
 
 TABIiB. 
 
 = 1 Minute . . 
 » 1 Hour . . . 
 * 1 I^ay . . 
 « 1 Week 
 " 1 Common Year 
 
 ■ 1 Leap Year . 
 
 ■ 1 Civil Year . 
 « 1 Century 
 
 min. 
 hr. 
 
 da, 
 
 »*. 
 c yr. 
 l.yr. 
 
 yr. 
 
 O. 
 
WEIGHTS AND MEASURE^ 
 
 years, and is divided into 12 Calendar Mcuih., viz. : 
 
 January (,/a« ) 
 Ftibruarj {Fchy) 
 
 In Leap Year 29 
 March (Mar.) . . ^ 
 
 May (May) ... , g^ 
 ■'^me(June) .... 80 
 
 31 Days. 
 2S "' 
 
 July (Juhi) . . 
 August (Aug.) . 
 September (Sept., 
 October (Oct.) 
 November iXov.) 
 December (Dec.) 
 
 31 " 
 
 30 " 
 
 31 • 
 30 •• 
 3-' " 
 
 173. The Dumbors of days in each mouth may be 
 easily remembered from the f.Ilowin.^ lir.es : ^ 
 
 " '^^''■'y days hi . September, 
 April, June and November; 
 Febrnary, twonty-eij-ht .done, 
 All th^ rest have thirty-ouo, 
 But in leap year, then is tlio time 
 When February Las twenty-nine." 
 
 LEAP YEAR. 
 
 6 Ar. 48m,-„. 49 T.^ "'^ "' '"'^'''' ^«"' '' "^^'^""-V 366 cto. 
 
 da/JiifU'' ''' ''•" '^ '■""'"^'' " '""^ ^^"-^^^ *-«•- - the calen- 
 Inl Year - . 5;^,. is min. 49.7 sec. 
 °^ " • • 23 /.r. i.5m,„. I8.8 „,, 
 
 da^HeTc:'" '°^' ^" ' •^"" -^^ '-■' "'' '' -■"• ^^-^ - of , entire 
 
 cafendrjrbt '"' '^ "'''°'^^' "^ '''' '-'' '^^ ''- ^^^"^^1 in the 
 
 J;,*^f", • ■ ■ """•«• 41.2«c. 
 ld?y *HL;^"^''"^''"^''^^---'"^-'^only... 22 «.•„ 50... of 
 
 in 400 . . aiAr. 31m,„. 20»«e. 
 
 ^ThetuaethuB,ostin400year.,aol.only2/.r. 28..„. 40,«.ofld.,. 
 
60 
 
 ^EIOHTS AND MEASURES. 
 
 In inn V • 
 
 ^n 400 Yeaw 
 In 4000 •• 
 
 2Ar. 28 mtn. 40««8. 
 ^ihr. 46 min. 40 we. 
 
 -•'«. to mm. 40 tee. 
 
 176. The folJowinff ruJe for ).„ 
 render the calendar correTJZl^^. ^I"" ^'" '^«'«'ore 
 4000 years. '"* ^'^ ^'*^^" ^ day for a period of 
 
 BUtdl. 
 
 y^'*'-*. -^ • *"' ''^^''' y^'^r, are common 
 
 II. Every centennial year thnt v. 
 
 lya- ^. , ^^'*'^' '*'^'' common years. 
 
 **V^. Circular Measura in n=^ • 
 astronomy, and geograZ f^r^'f*"^ '" ^"'-eying. navigation 
 
 TiBLB. 
 
 179. 
 
 60 Seconds (*) 
 60 Minutes 
 80 Degrees 
 12 Signs, or 360" 
 
 ' i ""rinute 
 i iJejree 
 
 1 Circle 
 
 B. 
 
 a. 
 
 11 
 
 ■i^m^i 
 
 w>^/ 
 
WEIQUTS AND AIHASUiiKS. 
 
 $1 
 
 ISO. 
 
 181. 
 
 MISCELLANEOUS TABLEa 
 
 COUNTING. 
 
 12 Things = 1 Dozen. 
 
 12 D )zen = l Gross. 
 
 12 GrosB a 1 Great GroM 
 
 80 Things = 1 Score. 
 
 PAPER. 
 
 24 Sheeta = i Quin. 
 20 Quires = i Ream. 
 
 2 Reams = l Bundle. 
 
 5 Bundles = 1 Bale. 
 
 BOOKS. 
 
 2 Leaves = 1 Folio. 
 
 4 Leaves a 1 Quarto, or 4to. 
 
 8 Leaves s 1 Octavo, or 8vo 
 
 12 Leaves = 1 Duodecimo, or 12mo. 
 
 ia2';h*r;!rlV"^'*°',°'^^^°' "^^""^^ the Humbert i«.v.b 
 
 -w wnion a gheet of paper ig folded in makiug booka. 
 
 1S2. 
 
62 
 
 LO.SQinjDE AND TIMM. 
 
 LONGITUDE AND TIME. 
 
 ' } 
 
 ^ ill 
 
 ii 
 
 t 
 
 STANDARD TIMa 
 
 pi^z u^ir^r :x.*:;r ,-ri'™^' -' 
 
 are east ami 7J- aro we,t nf thl "'T"' '* "' "l"«h 
 
 Lon,loD, E„,.l»„d a„r ,1 ,f '^""'"■'^•'' Observatory, 
 apart. lhere"i. a di ." „ e il "11"";'"""' ''' J"»' "• 
 between any one of th m „„d M "''"'' ""'' '■<"" 
 
 the one neion the "17- ll,« , T ','"' "" ""^ ""'*• "' 
 ti.eea,t being o^e how fa" /iT te"''"'"" ""' - 
 west one hour slower TtT „ "'" ""' <"' "'« 
 
 ho... .he ,.• n™r„r,":r„o'-'' -.Tor-s'';';!.'' ""' 
 
 \.lantica„,,H,ePa M Oo a '''•"''r/ '™° '"^"'"'" '"« 
 Centra,, M„„n,atfn;, pS "^ ' '"'^'°°'°"-'' •=-'-• 
 
 par\!t,,'^d:r■:n?';■^'t,''^''™'^'' '"•" '"» «^™' 
 
Lusonubt: Asi) riin<:. 
 
 68 
 
 equal parts called hours, it fono.v.s that the earth on revolv 
 jng on itH axis passes thn.u.h ^\ of 360* „r IS* of 
 longitude m one hour; throu-h V of lon-itirlo in A of 
 an hour, or 1 minutes, and through 1' of lonyitude in A 
 ot 1 minutes or 4 Heconds. ^ 
 
 185. 360* of Lon};itade 
 16* •• 
 
 1 UII.R. 
 
 ■ '» Jr ■iirsorl Day of time 
 » I Hour of time 
 • 4 >[in!itc9 of time 
 4 Socoi.ila of time 
 
 ill. 
 
 hr. 
 
 mill. 
 
 tec. 
 
 Solution. 
 
 r 18' 
 i_ 
 
 29 min. 13 ue. 
 
 - see. 
 
 IH«. To find the difference in time between two 
 known"" "'"■''^''"' ^^'° '^' ^'"■^'■^"^^ ^^ longitudels 
 
 EjtAypiJI — 
 
 If the dilTerence in longitude of two places be T 18' 
 what must be their difference in time ? 
 
 ElPLA.VATIOJJ. 
 
 Since each inin.itu of distance equals 4 
 second, „f ti.e, IS .ninutea of distance 
 will eqnal 72 s^'cond^, or 1 minute 12 
 Seconds of time. 
 
 Since each degree of distance equal 4 
 minutes of tin,o, 7 (legrecs will equal 28 
 minutes, plus I minute, gives n minutes. 
 
 RCLB. 
 
 ^fultipJythedhtancebeturen the two places expressed in 
 ' vy/r. and minutes by 4, and the result is ihe difcreuce in 
 une e pressed in minutes <ind seconds. 
 
 N0TKS.-I If one place be in east and the other in west lon<^itude the 
 dilTerence o longitude is found by adding their longitudes Id f e 
 sum be greater than 180 degrees, it must b. subtracted from 3W 
 
 2 Since the snn appears to move from east to west, when it is exactly 
 
 resulfwUl be"th?!lmf a 'I Sc'r ; 7": .tnd^ifTl V^' ""^ 
 arfHpH ♦«»>,„*• i..i "^'y P '^*'' '>'°a if the difference be 
 
 isterly ^ ""'"''' '''" *'" "^"" ^'" ^ "'^ ''"^ »* '^^ 
 
e* 
 
 LoNonii.f: jut) Tins. 
 
 Ill] 
 
 known. ^° '^® difference of time is 
 
 EZi](PL»_ 
 
 iixvi,Ain.no». 
 Since 4 minatea of tlmo .nn.i i j 
 of longitude 28n,.«.; f ^^ ^ "^^"^ 
 lonKftude ' "**" °' ""« '^'^ '• of 
 
 longitude. "* *^'' "^"^ «' of 
 
 _^ , BUM. 
 
 SoLonoa. 
 7* 6' 
 
 IHS, Toronto, 
 Kingston, 
 Ottawa, 
 Winnipeg, 
 Chicago, . 
 
 Calcutta, . 
 
 Montreal, . 
 
 London(Can 
 
 New York, . 
 
 P«tti8, . . 
 
 TABLE OF LONGITUDES. 
 
 79' 21' 16» W. 
 
 • 76* 28' 26* W, 
 
 • 75* 40' 36* W. 
 
 • 97' 30' 42* W.* 
 87* 37' 45* W.' 
 88' 19' 2* E. 
 75° 28' 15" W 
 
 •) 81« 15' 6* 
 
 74* C 3» 
 
 2' 20' 22* 
 
 ir 
 
 71' 
 W 
 
 W. 
 
 w. 
 
 E. 
 
 BelleviUe, 
 Qaebec, . 
 Berlin, . 
 
 Philadelphia, 76* 
 Victoria, . 123« 
 Hamilton, . 79* 
 London (Eng.) o* 
 Regina, . . 105- 
 Brantford, . 80* 
 Halifax, . qq» 
 
 26' 12* w. 
 
 31' 35* W. 
 
 23' 46* E. 
 
 10' w. 
 
 12' 16» W. 
 62' 80* W. 
 
 «' 38' W. 
 
 2' 26' W. 
 28' 38* W. 
 36' 42' W. 
 
 EXERCISE 4a 
 Find the difference in longitude between- 
 1. Toronto and London (Eng ) 
 I Quebec and Calcutta ^ 
 «. Ottawa and Victoria. 
 4- Hamilton and Berlin 
 f. Brantford and Winnipeg. 
 6- Kingston and Taris 
 
LOAOITUDE AND TIUK. 
 
 Find the differenc-o in aolar time between— 
 
 7. 
 8. 
 
 9. 
 10. 
 11. 
 12. 
 
 Toronto and Gn-enwioh. 
 
 Kin^,'ston and Winnipeg. 
 
 Ott:ava and Victoria. 
 
 Montreal and Utf,'in!i. 
 
 London (Can.) and I.undon lEnjj.) 
 Philudelphia and Calcutta. 
 
 Find the difference in Htandnrd time between— 
 
 18. 
 14. 
 
 15. 
 16. 
 17. 
 18. 
 
 Quebec 
 
 Montreal 
 
 Toronto 
 
 Kingston 
 
 Montreal 
 
 Halifax 
 
 and Ottawa, 
 and Victoria, 
 and Winnipeg, 
 and HeL;ina. 
 and Winnipeg, 
 and Victoria. 
 
 Find the difference between the standard time and tb. 
 •olar time in the following cities : 
 
 19. Toronto, 
 
 20. Jlcntreal, 
 
 21. VVinnipej,', 
 
 Ottawa, 
 
 Victoria. 
 Halifax. 
 
 ZZ T ; V"; ^''■'" ^° P-*"- ^^ fa^^hronometer. Greenwich 
 time ; what is hia longitude 7 
 
 28. When it is 6:40 a.m. at Halifax, what i. the time at Victoria ? 
 
 M. If the difference of solar time between two plaoee i. 1 fe- 18 mi. 
 4 .«.. what U the ditTerenoe of longitude ? *^ " ^ '^^ " "•"•' 
 
 26. When it is Monday 10 p m., solar time, at Toronto, what day and 
 time IS It in London (Eng.) (Greenwich time) ? ^ 
 
LONQITUUE AND TIMM. 
 
 :? t 
 
 REDUCTION. 
 
 ISO. Reduction i^ tlio process of changing the denom 
 .nation of a quantity without changing? its value. It is of 
 two kinds, Descending and Ascending. 
 
 190. Reduction Descending is changing a number of 
 one denomination to another denomination of less unit 
 ▼alu« 
 
 l»l. Reduction Ascending is ciinnrring a number of 
 one denomination to another denomination of greater unit 
 *alue. 
 
 I»3. To reduce Higher denominations to Lower. 
 
 EzAUPiM.—nedaoe 26 bol. 8 gal. Sqt. to qii irts. 
 
 Solution. 
 26 66/. a gal. 8qt., 
 
 4 
 
 8311 9U. Ann. 
 
 EXThKSKItOS. 
 
 Since .SIJ ,/-,/. make 1 66/., there are 
 
 Blj times as mnnv i,'iill(;ns as barrels, 
 and 819 1- 8 = 827 callona. Like-' 
 Wiso, thfre arc i 'irues as njdny qnarte 
 »9 .,'allons, and (S27 x 4) + 3 a 3311 
 quarts. 
 
 BULB. 
 
 Sf»Jt;plj, the hiphp^t denomination by the number required qt 
 the mxt lower to make a unit of the higher, and to the product 
 add th> lower denomination. 
 
 Proceed in thit mann-r with the tuccessive denominations, 
 till the one required it reached. 
 
Loauiruoi-: asd timk. 
 
 67 
 
 EXERCISE 49. 
 
 1. Is ndyi. 18 An. 37min., how miny i<<!Condat 
 
 9. Reduoe 12 mi. Srd. Hyd. '2 ft. to iiictiea. 
 
 S. Reduce 243 (6. 8o<. 6dwt to !; ruins. 
 
 4. In 63e.ydt. Low many oubio inches? 
 
 5. jfl33 6». 8rf., how many farthinjM? 
 
 6. How many ponoo krotheru in i'lHi fu. 0^4.1 
 
 7. In 481 sovereigns how many ponce ? 
 
 8. Ia4m<. 120 rd. 2 yd. Ht. Qin., how iminy rods 7 ykids? f^et T 
 
 inches? 
 
 9. Bednoe 16 T. 8 ewt 86 lb. to pounds. 
 
 to. Redao«18i<. M$q.rd. 2!iiq.yd. to square feet. 
 
 11. How many ({rains in 16 {b. AviMri1iiii')is? 
 
 12. In 2 mi., in 3J mi., in | mi., how mmy ro'U? yirds ? (eet ? inohesT 
 
 13. In 47 (juinotis how many poun I') atiii sliilliiii^'s ? 
 
 14. In 12 lb., Troy, bow many drams, A)ioth<jL'ario87 
 
 16. Find the cost of 2 bl. Hbun. Irm.iqr. 21 "heets of paper, at 
 33.87i a ream. 
 
 193. To reduce Lower denominations to Higher. 
 
 EiAimia.— Kedaoe 167540 minates to wtcks. 
 
 BoLtrrioM. 
 60 ) IS?.*) 10 min. 
 24 ) 2025 hr. + 40min. 
 I'ym da + 9hr. 
 ibvk. -f ida. 
 
 16 irk. 4da. 9kr. 40min. Ana. 
 
 KXPIJINATION. 
 
 Dividing the given number of minutes 
 by 00, because there are ,'5 as many hours 
 as minutoii, we obtiin 2G25 Iiours pins a 
 remainder of 40 n^nutes. 
 
 We next divide tlie 202.') lioura by 24, 
 because there are ^ as many days as 
 hours, and we find thit -HVl't liours = 
 100 (Liys plus a remainder of hours. 
 Lastly, we divi.le the li>9 days by 7. 
 because there are } as. ni*ny weeks is 
 days, and we ftml that lOy days =» 1" 
 weeks plus a remainder of 4 days The 
 last ([uotient and the several remainders 
 arnuiL'od in the order of the succeeding 
 denominations form the answer. 
 
f ^ 
 
 1 -I * 
 
 M 
 
 LOmiTUDE AND IIMM. 
 
 n. 
 
 22. 
 23. 
 
 24. 
 
 2.1, 
 
 IMUM- 
 
 EXERCISE SO. 
 
 1. 
 
 a. 
 
 B. 
 
 4. 
 
 101 SWl onnoM 
 97'J-iO urMM 
 
 437«i9 
 ■27150 
 
 6. ;)-'70 
 
 6. 
 7. 
 8. 
 
 1817fl0 
 278(.JS 
 32469 
 
 9. 4789i;0 
 10. 
 
 iiicliei 
 
 pinta 
 ■econdi 
 cubic iiic!ios 
 
 W3ol0 «ho..taol t>ipor t.) r,. 
 
 to tnni. 
 to lbs. 
 to tnilea. 
 to hup toni. 
 to gallons. 
 to days, 
 to oub:o yarda 
 U) £ 
 to oords. 
 
 11. 24C8 poi.co 
 
 la. 23760 grains, Tr-.y, 
 
 18. 15630 mills 
 
 14. 180035G link* 
 
 16. 43G2 pints 
 
 16. 20430 rodi 
 
 17. 1020300 • 
 
 18. 70 
 
 19. 350 
 20 
 
 ' 18. 
 
 to hiilf-iTOWDJ. 
 
 to Ihi 
 
 to (lollart. 
 
 t') inilea. 
 
 to bualiolt. 
 
 to miles. 
 
 to S. 
 lbs. Avoirdupoi? to Iba. Troy, 
 o^- Troy to oz. Avoirdnpois. 
 
 ''"^-^O «nu„8, Apoth. to lbs. Avoirdapou. 
 J.nd he valuo of 9210.0 /. of coal at 31.75 j.r long ton 
 .«dthopncoof4«2.,«,.23/6,. of .I.eat a 950. a blel 
 low many b,.,.o,« are there in 5100,,. of timothy Z 
 What ,s the freight on 628 bushels of corn at 32. l^ 
 
 What 18 the freight on 16 r. 17 cic/ 20 m / i .. 
 of 2240 lb». 7 ^° '*■ °' '^'^J »» »l-20 per to. 
 
 Find tbe amount of the following bill of grain- 
 
 2?, r: ^ ^'^c. a bushel. 
 
 IJli,, /,.-■. of barley fS r,8o. 
 
 6160/6*. of boans j^t ; i qo m 
 
 2la0/i,,. ofrye (,^ ^go. 
 84(i8 Ibt. of wheat @ 98^. 
 
 
 iSMil 
 
DJiA'uJIi.\dTJi MUMUJihd. 
 
 6i) 
 
 DENOMINATE NUMBERS. 
 
 i 
 
 Itt4. The proceBs of adding, subtracting, multiplying 
 and dividing (ienominate iiumbcra ia based on the aaine 
 principles that (govern simihir oponiMoiis in simple num- 
 bers ; the principal dilfTonce boiii}^ tha^ denominate 
 numbers have an irregular hchIh of increase and decrease, 
 while simple numbera have a uniform ilecimal scale. 
 
 ADDITION. 
 
 Find the sura of 3 U>. 7 oz. 10 diet. 12 (jr. ; 17 lb 5 oa. 
 ^8dwt. Iz/r. ; and 12 /i. 11 oz. d diet. 15. '/r. 
 
 BOLnTIOM. 
 
 lb. 
 
 8 
 
 17 
 13 
 
 OM. 
 
 7 
 
 6 
 
 11 
 
 dm. 
 10 
 
 13 
 9 
 
 3416. Om. i8 dwt. 
 
 Explanation. 
 
 gr. Write the numbers of the aame anit 
 
 12 value in the same column. Beginning 
 
 4 with the lowest denomination, aild as in 
 
 16^ simple numbers, and reduce to higher 
 
 7 yr. donominations according to the scale. 
 
 EXERCISE 5t. 
 
 li 
 
 Add— 
 
 (1) 
 bush. pk. qt. pt. 
 3 
 
 91 
 14 
 17 
 68 
 9 
 
 (2) 
 
 £ t. 
 
 14.5 
 
 109 17 
 
 175 14 
 
 IGO 1.5 
 
 1199 5 
 
 d. 
 
 n 
 
 8 
 
 U 
 
 8| 
 
 10 
 
 (8) 
 
 hhd. gal. qt. 
 
 0'2 3 
 
 69 2 
 
 13 2 
 
 4 1 
 
 27 
 
 79 
 
 3 
 
 61 
 
 159 
 
 66 
 
 pt 
 I 
 
 1 
 1 
 
 
'Hi! 
 
 70 
 
 DENOMINATE NUMBERS. 
 
 mi. 
 
 50 75 
 
 791 11 
 
 87 315 
 
 75 173 
 
 15 29 
 
 (5) 
 ^; »? p. ly.yi 
 
 30 
 15 
 31 
 29 
 13 
 
 15 
 11 
 16 
 
 30 
 
 26 
 
 <^- Add 7r Ur,«. 25 « 14 7- ... ,„ 
 
 12^«'^. and 5c.. 10 "Vr" *' '"'- '«"''• "«-. "T. 
 !'• Find the sum of I2wk a i - t 
 
 '"■--'— -^..-. »»..,, ..,„^,.„,,^^ 
 
 la- A grocor received an invoice of 7 */ , . 
 
 hefo„rth.l2c...; the fifth. llLg*-' ""J"''' '"^•'- ^«^ ^ 
 thesoventh.l3.«„. Ho^vmachd^ithlf !"'"'' ^^'- 24»; 
 
 13. A person has 5 pi.ees of .round ^T ''"'''' "'''*^'* ^ 
 
 ■econd, 17^ 1,.,,, ,. ^'^ ' '^« ^"-st contains 16 J Srd.fv. 
 
 the amount of tll^^^^/ '^"^ '^^•^"^. « ^. 7.,^' w^ 
 li A person owes several snn a ,. • 
 
 to another, IC„. 33,; . .„ , ., '• ^"-^ '■ : to another. £12 sw 
 jni , . *"•' to another. £i-^fi i. . * *'''• * 
 
 10H-: to another. £^0 1. ,?,, w: \ "' '° ^""'her. £31 6, 
 
 !•- ■^P-ontrave]hn,,on,.o./io , . '^ "^« ->>ole amount ? 
 
 ^. the seco.rL,r;;:,^ ^^";^";-;;;^y;J^8.. ^A. 9n*. 
 12 «, the fourth day ar,^ ^V K ' *^^ *'^''"'^ day; 26m.- 
 
 Ho.f«rdoe.he«od^uH„rthe1:-4r "^'- '^^ «'^^ C 
 1«- A jeweller receives on o„.. dav 11 M fi ! 
 
 10/* 50. 20,r ; on anotl, fi '/^ °' ^J^" <»> another day. 
 mnoh does he receive in all ? ■*•"' ^^ '^«"- 16^r. How 
 
 W^^^^^is 
 
 
 ■Sil- 
 
 m: 
 
DENOMINATE NUMBERS. 
 
 71 
 
 SUBTRACTION, 
 
 EzAMPLi. — Sabtract 
 I6dvt. 12 gr. 
 
 lb 
 97 
 12 
 
 SOLCTIO!!. 
 
 OM. dtet. 
 6 16 
 
 9 11 
 
 UlA. 8 01. 4 diet. 21 gr. 
 
 12 lb. doi. lldwt. 15 gr. from 27 ». 5oz. 
 
 ExPIiANATION. 
 
 Write the numbers as for simple 
 anbtraction; take each subtrahend 
 term from its correspomlins^ minuend 
 term. In case any subtrahend term 
 be greater than the minuend term, 
 borrow 1 as in simple subtraction, 
 and rediioo it to the denomination 
 required, etc 
 
 gr- 
 
 12 
 
 15 
 
 
 
 
 EXERCISE 5t 
 
 
 
 
 
 (1) 
 
 
 
 (2) 
 
 
 
 
 (8) 
 
 
 £ 1. 
 
 d. 
 
 {6. 
 
 OM. 
 
 dwt. 
 
 .</'■• 
 
 
 evt. 
 
 lb. OM. 
 
 dr 
 
 136 4 
 
 ^ 
 
 114 
 
 3 
 
 16 
 
 12 
 
 
 68 
 
 16 2 
 
 5 
 
 98 11 
 
 n 
 
 91 
 
 4 
 
 12 
 
 19 
 
 
 27 
 
 •20 1 
 
 6 
 
 (4) 
 
 
 
 (5) 
 
 
 (C) " 
 
 
 A. sq.p. 
 
 »q.yd. 
 
 lb. 
 
 5 
 
 3 
 
 3 
 
 9r- 
 
 rd 
 
 yd. ft. 
 
 in 
 
 75 14 
 
 n 
 
 68 
 
 1 
 
 7 
 
 2 
 
 12 
 
 IC, 
 
 5 1 
 
 11 
 
 73 10 
 
 16 
 
 15 
 
 
 
 7 
 
 2 
 
 15 
 
 14 
 
 6 2 
 
 9 
 
 7. A person owes £78 3». 2Jd. ; he pays £17 17r \%d. ; how much 
 
 does he still owe 7 
 
 8. K. owes B. for 2 invoices of merchandise ; one worth ^17 16. 
 
 ^d., the other £11 2». 9d. ; he pays £26 16.. id. ; how muoh 
 does he still owe 7 
 
 9. A farmer has a farm consisting of 2000 acres. He gave his eldest 
 
 son 109 J. Zrd. iQ/q.p.; to his second son. 48 ,^ lrd.\ tlie 
 remainder he gave to his third son. What was the remainder ? 
 
 10. How long is it from June 2l8t. 1886, to December 14th, 1888? 
 
 11. Thfl latitude of Hamilton is 43* 12' 40*, of Quobeo, 46* 60* 10* ; how 
 
 many degrees is Quobeo north cf Hamilton ? 
 
 la. The latitude of Brantford is 42* 21' 22* ; how far is Brautfor J from 
 the North Pole? 
 
 18. A merchant bought 3 pieces of cloth ; the first measnrod 47 yd iqr • 
 the second, 43 yi.; the third. 41 nd. 3qr ■ when he came to 
 examine it, he found liyd. worthless; how much good cloth 
 was there? 
 
72 
 
 DENOMINATE NUMBEliS. 
 
 I ■ 
 
 ! 
 
 I 
 1 
 
 I : 
 
 
 Ih. 
 17 
 
 SOLUTIOK. 
 M. dvt. 
 
 6 18 
 
 16 
 7 
 
 MULTIPLICATION. 
 
 ExPLANiiTIOS. 
 
 Write the multiplier under the low 
 eat denomination of the multiplicand 
 
 123'*. T^-i-i^i^nr... thus r'''''' "' ^" ^"'^^^^ -'-'-"' 
 
 '""itoM""'^^-^''^'-^^^^ Put down icu.der,r. Carry 
 ISrftrt. X 7 + {4du>t. carried) - fl-i^™* 
 
 1« under J. Carry 4 to LT °" " '''""• ^^^ '^•'^ 
 
 6a». X 7 + (4o*. carried) » 39o* - s za , 
 
 8 under M. Carry 3 to /6. ''""' " ^ '*• ^ "'• Put down 
 
 17/6. X 7 +(»«». carried) - lio ih v . :, 
 
 «airieaj _ i22 lb. Put down 122 under lb. 
 
 EXERCISE 53. 
 
 1. Multiply 88 lb. dot. ndwt. by 17. 
 
 2. Multiply 19 r. newt. 18 /fc. by 19 
 
 3. Multiply 3/6. 4 5 23 13 17^r. by IL 
 
 4. Multiply i-ya. I ft. 11, v,, by 21. 
 
 5. Multiply 17„„-. 2rrf. 16/t. by 28. 
 
 6. Multiply 15, d. 2yd. l^i. by 29. 
 
 7. Multiply 144^. 17*j.p 19 ,^;. yd. by 6. 
 
 8. Multiply 17 c. 69c».A 718c« ,„. by 18 
 
 9. Multiply 73AW 61^a/. 3jMp,. by26' 
 
 10 If one cord of wood cost £1 16,. ^a., what will 25 oorda cost • 
 11. If you can bny3 6u. 3«i 3„, #„, «, u -»" ooMa cost < 
 
 bought for «79 ? ^ *^' ^"'^ '"'^'^y bnahelB can b. 
 
 -if.oucane.chan/one^a";r:t:::7':;^:Tr''r" 
 
 how many acres of pasture can you .'at fori, ^^'^' f ^'''"'"' 
 ,. -a ■,.,, . -^ fe®*'""^ 41 acres of wliftii.*? 
 
 14. Bought 16 pieces of lace, each containing 62 yards at £1 , ^ 
 
 yard, and sold 7 pieces for i^i i <: , ' ^^ "*• 2<*- P* 
 
 -«.. .M p., , J, Zli' ^ZS?- "" •""—'" 
 
'i 
 
 DESOMINAT:'! SUilBERS. 
 
 DIVISION. 
 
 7b 
 
 BZAMFU — If 122 lb. ioz. lodmt. ir.g,. of silver be made into 
 7 bars of equal weight, what will bo the weight of one bar ? 
 
 Solution Explanation. 
 
 tt. Of. dwt. gr. Write the diviiliid and divisor 
 
 '' ) ^^^ ^ ^^ 18 M in sliort division, and divid.j as 
 
 17Z6. 6ot. 13Jirt. IGi/r. in 8im|)lG niirnbt rs, tlius: 
 
 if of 122 ;6. a nii. and an undivided romain I r of 3 lb. 
 Reduce this remainder t»o«.; addtheSoz of dividend m 39o«. 
 f of 39 ox. 3! bot. and an undivided remainder of \ot. 
 Reduce this remainder to diot. ; fcdd the 15 dwt. of dividend m 9', ,hci. 
 if of 95(it«(. « VAdwt. and an undivided remainder of 4 Jict. 
 Reduce this remainder to gr. : add the IQgr. of dividend a IVigr. 
 \ of 112 ffr. « Ugr. 
 
 EXERCISE 54. 
 
 1. Divide £91 12«. 6(/. by 6. 
 
 2. Divide 386/6. Qoz. UdwU 2Zgr. by 29. 
 
 3. Divide 9 T IG cwt. 16 i6. 3 o«. 1 (Jr. by 17. 
 
 4. Divide di ,-> ^ (5 43 03 Ugr. by 36. 
 6. Divide 78 wi. 14;-. by 31. 
 
 6. Divide A yd. I ft. Uin. by 15. 
 
 7. Divide V386l.iq.mi. ITJA. 20sq.p. 11 tq. yd, by M. 
 
 8. Divide 138cu yd. -lOcu.ft. 1100 ew. in. by 399. 
 
 9. Divide 20Wi(i Higal. ^qt. Igi. by 147. 
 
 10. Divide n5bu»h. Spk. Iqt. lp(. by 07. 
 
 11. Divide 1 circle by 128. 
 
 12. Divide 3R5da. Ar. by 210. 
 
 13. If 16 bushels of oysters cost £75 17«. 4d., what will one bushel cost ? 
 
 14. If one yard cost 2». fid., how many yar.ls can be boiij,'ht for £180? 
 16. If you can buy 15 square rods of land for £1, for how many pounds 
 
 can you buy one acre ? 
 
 16. Divide a square mile into 15 equal parts. 
 
 17. A man travelled 1249 mi. 36r,Z. in 61 days ; how far did he travel 
 
 in a day ? 
 
 18. Acartman carried 117 cd 110o«./t. in 100 loads ; how much did 
 
 he average a load ? 
 
 ..-.J'.. 
 
74 
 
 DE NOMINA TF. FB ACTIONS. 
 
 DENOMINATE FRACTIONS. 
 
 lua, A Denom-nate Fraction is a fraction whose 
 integral unit ia a .1. no,ni„,ite number 
 
 special ruL are nisslVrthel"^^^^ T'^T-^ therefore.no 
 
 e.^p.es are ,ve. to .jy e^p.::^^!^; ^tru^ri;:;;^:^ " 
 
 I»«. To reduce a denominate fraction or decimal to 
 integers of lower denominations. 
 
 ''"''loZllT' ^'"^ '-''''^ "^ "*''^"" °^ "^^^^^ denomination. 
 £A X ¥ x__ V =■ ,05i. £.4376 X 20 X 12 = i06d. 
 
 lOrx/. = 8$. 9d. 
 or 
 £.4375 
 
 20 
 
 •. 8.7500 
 
 12 
 
 d. 9.0000 
 .-. £.4375 « 8*. 9<i. 
 
 105(i. = 8». 9d. 
 or 
 £A X ¥ » y = 8^,. 
 
 i«. X 1^ ^ ud. 
 
 .: £A = ^«. od. 
 
 or 7 
 
 -?? 
 16 ) MO ( 8». 
 
 128 
 
 12 
 
 12 
 
 16 ) IK ( Od. 
 141 
 
 I »7. To chang:e a fraction or decimal of onn m^«^ • 
 nation to a higher or lower denomtaation " °'"'" 
 
 u= - Oliaiit,'e A (.9) of ac mch to tho fr ution of a yard. 
 
 Opeuaticv. 12;_^9/«. 
 
 A".. X A X J = ^y,i. Ana. 3 ) .07? 
 
 .025 or ^yd 
 
DBNOMINATE FJIACTIONS. 
 
 75 
 
 1»«. To change one denominate number to the 
 fraction or to the decimal of another. 
 
 ExiMPLB l.-Roluc. .< jf I J>t. to (1) the fraction Of a gallon (2) to 
 
 ttif docima! of a tjallon. * ' 
 
 ^""-"'O^- SOLDTION. 
 
 TO A JuaMON /lUCTION. 10 ^ DKCIMAU 
 
 :!./'. Ipt. = 7pt. a ) 1.0 pt. 
 
 ExAMii.K 2.-_Ue,luoo lot. W. 3/ar. (1) to the fraction of a £ (2) «« 
 =ho Jucimai of a £. i /• •■ 
 
 Solution. 
 to a decimal. 
 4 )^ 3/ar. 
 12 ) G.ind. 
 20 )_15..-,i;25 «. 
 
 ^778125 of a £. 
 
 Hoi.r r.'oN. 
 
 TO A COMMON- FliACTIOS. 
 
 Iai. OJii. 3 747 /ir. 
 £1 = 9C0 ;ar. 
 
 .-. 747/ar. , £JiJ . ..,.,..„„.„.. 
 
 , .., f,'^^'''"-3— R'^'lu'^e*! 3.. 4d.(l)to the fraction (2). to the decimal 
 of Jtl 17». id. 
 
 SoLDTIiiN 
 
 £1 3«. l(i. = HHOd. 
 £1 17o. 4r«. = 44H,i. 
 .'. £1 3>. id. = ,jj^ of £1 17«. id. 
 = g of 
 = .625 of •• 
 
 EXERCISE 5!«. 
 
 1. Reduce ,^ of « mile to the fraction of a yard. 
 
 2. What iathevahie of .>*'y2:> of a £ ? 
 
 3. Reduce Jf of a penn ywoij,'ht to the fr letion of a pound, Tnw. 
 
 4. What part of 3 weeks is 4 (ia. \i\ hr. aO min. ? 
 6. Wliat part of l\ bushels is .45 of a peck ? 
 6. Re luce .425 of a foot to the fraction of a mile. 
 
 It.' luce fifiU Is. l,i. to the decimal of a £. 
 
 What 13 the vahie of J of a tiiiie 1 
 
 Whiit part of an iiicli is /g of a yard ? 
 
 What [(art of a lb. Troy is .75 of a grain ? 
 
 Reduce 3 biuh \pk. .5 qt. to the decimal of a bushel. 
 
 Reduce 2.333J years to intej^ers of lower denominatiooi 
 
 Refluce £14 15». 9d. to the decimal of a £. 
 U. Reduce § of a hundredweight to the fraction of an ou«o«. 
 16. Reduce J of a mile to the fraction of J of a rod 
 16. Beduoo £2 10*. OJd. to the decimal of £2 17, 'id 
 
 7. 
 
 8. 
 
 9. 
 10. 
 11. 
 12. 
 IS. 
 
7tt 
 
 AUt^Uul i'AUia. 
 
 ALIQUOT PARTS. 
 
 I 
 
 exact dimor ol tlint numljcr or cjimulily. Xlius 3 i. ,n 
 aliquot pari of 20 ; asj of 100. iius o u an 
 
 Manybu.i„e,8 calculation, may l,e shortened by com 
 bm.ng tl,„ values of conveni.nt ali,,uot „a,tH. 
 
 *"'"•'■'= ' -W"' "'" "6 y.rd. of cloth .„, .. .5,.„j . j.„j , 
 Solution. 
 At«1.00peryard. the price would be 5,-,.70 
 
 " --'^ " iof .50 .. .. -•'' 
 
 :l_J'-l4 " iof .25 .. .. ^It 
 
 i:- SAMPLE 2 What will 7 /j»..;. q«z. « . * , 
 
 baahel ? '' '^^^^ ^3'- °^ ^^^^^t co.t at »1.60 a 
 
 Solution. 
 
 7 bushels ^ 81 eo = 
 
 2 p-'cks = } busliol _ 
 
 1 pock = \ biialiel _ 
 
 4 <iiiart9 z J peck ~ 
 
 _2^iii;irts^^j^ofJ^peck « 
 
 ?11.20 
 
 .80 
 
 .40 
 
 .20 
 
 M 
 
 n-2.~Q Ana. 
 
 per 01 
 
 ExAMPLB 3.-rind the cost of 972 o. of gold du«t at £3 l,.. ^, 
 
 At £3 
 
 " 10». 
 " S*. id. 
 " lOd. 
 " 6(i. 
 
 £S 14«. 
 
 Solution. 
 1 «* *. ^^^ "'• '''^ P'"''^ '"""''l ^e £2010 0.*. O-i 
 
 « J of 10. ;•; 
 
 - i of 3,. 4d. " « .. ^ : " 
 -J of 10.. .. . .. : ^ ; 
 
 ^'^^ " ** " ^E3C2irion7. Ans. 
 
 IjTP"**^- ",-■. ^j,- -iS^Erw- •"' ' 
 
*LIQU0T FARTS!. 
 
 U.O^:Z:Z'-^'''' ^"' '"""'■ ^^*- "/^ or clover.^ co.t a, 
 
 HoI.fTION. 
 
 1153 00 = Uo.t of 31 6«*/, 
 
 2 25 , .. „ . 
 
 ...,, .. 
 
 ^^ *n__ 
 
 84 hiuh. Spk. 4 jt." 
 
 i of 34 50 . 
 iof 2.25 « 
 iot 1.12} . 
 
 •I5(j.l)3f 
 
 EXERCISE 56. 
 
 Wh»* is the cost of— 
 
 1. 75 <6,. of ooffoe at 33 Jo. a lb. 
 
 2. 120 tt«. of sngar at 12.Jo. a /ft. ? 
 
 8. 84 yards of carpet at $l.j:jj a y^rd ? 
 
 4. 144ba8heleofwheatat»l.l6jabasl,eir 
 • ^^^^ '~'^" °' "'•'^"^'es at 15.. !,i,i. a bo,x ? 
 
 6. 886 pieces of silk at £9 6. 7H a piece? 
 
 8 eifiV^T' ''""•"' "''""''' '•^^-^•''^ 'on' 
 
 8. 616^. 152pr. oflandatSini.SOanacre? 
 9.43ft„M^2,,.7^,„,„^^^^^^^^^^^^^^^^ 
 
 0. 2/ft lOo,. 14..,. of gold at £63 12.. a pound » 
 
 11. 270 yd.. Bilk at £15,. 6j. per yd 7 
 
 12. 326 Aft/., flour at 87.87i per 66/. ? 
 
 13. 15J. 3r.20rd. land at ?60 per acre? 
 14- 12 7-. Ucwt. freight at 84 per ton? 
 
 15 W3,r.l2/ft.at?61..,0porlon,toor 
 
 16. 27 y<i,. of cloth at 3.. gjd. per j,d •> 
 
 17. 84c„.yd,. 24o«./t at ?2.o0 per <•„ yd ? 
 
 18. 13., a/. 1,,. I pi, wineat?:!,,erj,<,y./ 
 W. 17«r«. 2 jr. at 87.60 per ton ? 
 
 iO. J do^. elbows at 32.75 per do., r 
 
78 
 
 UiaVELLANEOUi) PliOIiLKMH. 
 
 
 MISCELLANEOUS PROBLEMS. 
 
 EXEKCISE 57. 
 
 \ 
 
 !• 
 
 1. Find the total distance around a rectangular field at 1,728 feet loii« 
 and 1,683 feet wide. * 
 
 2. A manufacturer nells 23(5^ barrels of flour on Mm, lay A 124 barrele 
 on Tuesday, idj barrels on Wodut^day, 30:52 barrels on Thursday 25 6 
 barreb ou Friday, and 33^ barrel, on Saturday How many barreU did 
 he sell durint,' the wook ? 
 
 3. A certain b..ildinf{ contains 74 windows, each window containing 8 
 panes of slass. Fir.i the cost of tho glass at 14 cents por pane. 
 
 4 How many pounls of wire will it require to fonce a field 304 feet 
 square, the fence boin;. 6 wi.o. hij-h. if 10 feet of the wire wei"h one 
 pound ? n uo 
 
 5. A man deposited in a bank 98,752 ; he drew out at one time 94 234 
 at another, $1,700, at another, »'.I02, at another, »4!). How much had he- 
 remaining in the bank ? 
 
 6 A man invests in tra.ie at one tirao ?680, ut another time «820 at 
 a third t.me, «1,580, and on a fourth occasion, $420. How much must'he 
 add to ihu sum of these thnl the amount may be $5,000 ? 
 
 7. A merchant bought 240 barrels of flour for »1,920, and sold it at 
 810.50 a barrel. What did ae gain ? 
 
 8. A farmer exohaii-jd 75t bashels of wheat, &t.81.25 a bushel for 78 
 barrels of flour, at 82 pur barrel, and received the balance in money 
 How much money did he receive? 
 
 9. A man bought 15 acres of land at »38 an acre, and 76 acres at S47 
 an acre, and sold the whole at 845 au acre. Did he gain or lose, and how 
 much ? 
 
 10. The cost of tho Atlantic Telegraph Cable, as originally made was 
 as follows : 2,500 miles »t ^4^5 per mile, 10 miles deep sea cable at $1 450 
 per mile, and 25 miles shore ends at $1,250 per mile What was its 
 t^)ti».i cost ? 
 
 WB^^^^Kmssmm^^^ 
 
U ISC ELLA MMU.'i PROIlLKMn 
 
 711 
 
 II. 
 
 Jvli ?.r •n:::,:,L":,',',r''""' " "'■" ^-^ - "o" ■• •« . -. 
 < o '.^."turrrer r r ;" ■' '- ■» > '•"■" ■" '•• ." <..^ 
 
 «ain ? -" •*""• now many oonts will she 
 
 horses at ^lO.J ? ' °"^'* *' "'>•'. "sen at ?70, or 
 
 ho soli ? ''" ** »^-'^^« ^ ^i- ton. How many tons did 
 
 9. How many times is tha Q. M of il fii -„ 
 
 in the L. C. M. of the same numb";,? *' *' ^* *'^'* ^A contained 
 
 10. If 3j3, tons of coal will last as lon-r „» aio „„ j , 
 
 tons of coal will l«t a. ,on« as 13 ^ ^ oVlf'^ "' "°°'^' ^"'^ ^-'^ 
 
 III. 
 
 1. What will 46 JimA Snk 1 nt ^* u .. 
 
 2. Wishin, to travoln a ■ at nw r T "' '''' " '°^^«' ' 
 -oney. How m.ny pou" ij did I r^'^e \ °"'""^"'^ '''''' '- ^n^'isb 
 
 3. What will 25 T. Dcict 01 /;,i; «f ^ i 
 
 ^ t;. "^ °°*' <>ost at 90.40 a lonn t«„ • 
 
 revolutions iu T distance oVe.l'niLT''""''"""' "'" ""^^ '-^ """^ 
 7. If 6i lb». of ooffeeoost ?V,. what will 27^/6.. cost? 
 
 I of a brZ'ltrg?4 yC r°'^'" -"^ * °^ "^ «^"- »- ^»ed Iron. 
 
 ER!V 
 
so 
 
 UISCELLANIAWS PROBLEMS 
 
 9. A o' • certain nombcr exceeds If of tlie saiiin number by IM. VVh»« 
 ii th* nmnlier? 
 
 10. A oprtain number multiplied by a.5 and divided by S.aproUuo*- I 
 Wliiit i« tha uumb«r 7 
 
 IV. 
 
 1. Divide the sum of .(>75 and .0075 by the difference of 7.8 and .76. 
 
 2, Find the leaat common mnltiplo of J, ^, || and A. 
 
 8. Divide «2,000 between two persona so that one should have } as 
 
 raiiuh as tho uthar. 
 
 4. Boujht a cord of wood for 94.nj5, a cheese for »7.r.(i^, and 14^ /6*. 
 of butter at 250. per lb. What was the cost of tlie wiioio ? 
 
 5. At U\ a bushel, how many bushels of wheat can be bonuht for 
 S:!7.68j ? *^ 
 
 6. 1/ a lb. of tea be worth J.62}, what is .8 of a /6. worth T 
 
 7. Who* is tho value of 720 poiindB of hay at 812 75 a ton, and 912 
 (Dunds of shorts at 815} a ton? 
 
 \ 8. BouKht I2yd$. cloth ttt ? 87 J per yd., and agreed to pay } the cost 
 in butter, at S.inj per lb.; \ in money and the remainder in eRgH at ».12} 
 a dozen. 11. w many pounds of buttor and dozens of eggs were required ? 
 
 V 9. What is tlie value of 1,046 pounds of beef at 94^ per cwt.T 
 
 10. How many pairs of pants can be made from 48.6 ydi. of cloth 
 allowinj; 1.8 yd. per pair ? ' 
 
 W \ 
 
 ^ 1! 
 
 T. 
 
 1. Sold 126 equal loadsof wood, measuring 116 erf. ied.ft. leu. ft., for 
 1402.50. What is tho quantity per load, and price per cord T 
 
 V 2. If I buy 120 gallons of rum for »7'. how muoh water must be added 
 to it that I may sell it at CO cents a j,'allon, and gain »15 on the sale of it ? 
 
 3. What part of a short ton is J of a long ton ? 
 
 V 4. I have a field 90 rods long and ,.0 rods wide. How muoh will it 
 cost to build a fence around it at J.12.J per foot ? 
 
 5. A. owns A of a field, and B. the remainder; f of tho difference 
 between their shares is 6 ^. 3 rdt. l^pr. What is B.'s sharef 
 
 6. What part of ■ cord of wood is a load lyt. long, 2J/t. high, 8i rt. 
 wide ? 
 
 7. Reduce |^ of a long ton to the decimal of a short ton, 
 
 ^ 8. A farmer sold 8 loads of potatoes, averatjing 27 btuh. 
 each, for t.45 a bushel. How much did he receive ? 
 

 MlSCELLdy^OUa PHObLKMS. g, 
 
 9 A miTdiani in iollinK' Urooeriei aellH 14,i),a« for » tt ■ how m».i, 
 doe. h. cheat a custo-n.-r wh s..l Mm to t'ho amou, t , si? 
 
 10. If th.- loMKitudf of Bulkville is 77* 2«' la" VV whiit will Iw. .i 
 t.m. .n that ,h.o« wh,a it i. 3 .r. 85 ,nin. ..m. U. London Ku" '" 
 
 VL 
 
 ...oL^raT'' '"■f,"' ~°'' «°''*»i""'8 '21* cubic inches, can b« 
 (itioKea in 3 cubic yards? 
 
 •wry jr. lind at what rate per hour tho train i. travHiui,. ? 
 
 8. What i. tho ooBt per hoar of liKhting a room with J "humors each 
 
 nJai i;r^;;i"^;:;i;irsc:t;:i:^ r- '- - "- 
 
 *,n!; ^ '" '!!"■ ^^' '^^ ^■"'^' °' "'°"'' ''■"'^ ''*"«^ ''^ «'«hcs to cat an 
 e.iaaJ numbor of coats, pants an.i vests. What number of each can 1 « 
 out if they contain respectively 3 J, 'ij, ) ^ yards ? 
 ^^6. Boaght 13 r Scu,t. 70 lb,, of .agar at |8.26 per .... What was th. 
 
 7. How many bale, of cotton, of 400/6. each, at 86 cents per W ar. 
 
 8quali.ivalaotoie/,W.ofsu,.ar,ofl..500/6.each. at 8 cents per M.? 
 
 * 8. Wliat part of 6 da. 28 Ar. 68min i,i da. 6 hr. r.Omin.? 
 
 9. Thirty -two raen afp-eeto build 14 m.-. 384 rd. 6 ft. of road. Winn 
 
 the work Ks J done, they employ 8 more men. What diBtance does each 
 
 man construct '( °" 
 
 X 10 I wish to put 111 bush. 2pk. 4 qt. of prain into bags that should 
 contain 3 bu,h. Ipk. i qt. each. How many ba,s will be r^uired ? 
 
 VII. 
 
 time, how long will he be m travelling around the world ? 
 
 2 St. Thomas is 81' 15'. and Halifax 63' 3(5' West Londtude. WheL 
 It 1. 13 o olook noon at St. Thomas, what is tho time at Halifax ? 
 
 > 8. The ice on a pond, whose area is J an acre, is 10 inches thick. How 
 manv ton. of ice may be taken from the pond, supposing a cubic foot of 
 ice to wt-:;^;i ul} ponnds ? 
 
:-,t'H*,:'^^^.M'\\i''] 
 
 vVlU.'. 
 
MICROCOPY RESOLUTION TEST CHART 
 
 (ANSI and ISO TEST CHART No 2) 
 
 A APPLIED IIVHGE Inc 
 
 ^^ 1653 East Ma,n street 
 
 B%a Rochester. New York 14609 USA 
 
 '"^ (716; 482 - 0300 - Phone 
 
 ^= (7'6) 288 - 5989 - Fa« 
 
E i 
 
 H 
 
 IV 
 
 :f 
 
 82 
 
 MISCJiLLASEOUB PROBLEMS. 
 
 ] \ 
 
 I i. If the regular fare on a railway is 3 cents a mile, bat ( is allowed 
 o£f full faro when return tickets are bought, find the distanoe between 
 two places if a return ticket costs J1.80. 
 
 6. 450 leaves of a certain kind of paper make an inch of thickness 
 
 i ind the thickness of a book 6 inches bj 4 inches, in which 10 square 
 yards of the paper are used. 
 
 I 6. It costs 523.10 to fence a square field at 3J cents per yard. How 
 many acres in the field ? 
 
 7. From 10 acres take 8 i4. 159pr 30yd. 6/t. 103 tn. 
 
 8. Wliat is the result, when 500 is divided by .25, the quotient by .026, 
 the second quotient by 60? 
 
 9. Bxpiess 3.74976 minutes as the decimal of a week. 
 
 10. What is the least number from which l,2i34 and 1,656 may each be 
 taken an exact number of times 7 
 
 VIII. 
 
 1. If water in freezing expands ^, find the weight of a onbio foot of 
 ice, a cubic foot of water weighing 1,000 ounces. 
 
 2. Find the difference between 9A. 159 pr. 80 yd. 2ft. 36 in. and lOA. ? 
 
 3. Divide »760 among A. B. and 0., so that B. may have 1160 more 
 than A., but $50 less than 0. 
 
 4. How far may a person ride in a carriage going at the rate of 8 
 miles per hour, so that if he walked back at the rate of 3 milea per hour 
 he may be gone 6} hours 7 
 
 6. What will it cost to dig a ditoh on each tide of a road i miles 80 
 chains long at 40 cents a rod 7 
 
 6. Walking 4J miles an hour, I start after a friend whose paoe is 3 
 miles an hour ; how long shall I be in overtaking him 7 
 
 7. How many square rods are there in 100 square chains 7 
 
 8. A man owns .1875 of a mine ; he sells .17 of his share. What 
 fractional part has he left ? 
 
 9. Beduce | of an hour to the decimal of } of 48 minutes. 
 
 «^ 10. What will it coat to fence a square 10 acre field at 80 oents a rod 7 
 
 IX. 
 
 1. At »2.40 per rod, what will it cost to fence a piece of land 84.6 rods 
 long by 24.76 rods wide 7 
 
 2. A ship with its cargo is worth $340,000, f of the value of the cargo ia 
 worth f the value of the ship. Find the value of each 7 
 
 m 
 
i 
 
 MISCELLANEOUS PROBLEMS. g^ 
 
 3. Divi(?e 6 dy. 17 hr. 11 min. by ^^. 
 
 4. How many reams of paper will h, required to supply 7 ."00 -i', 
 scnbors with a weekly newspaper for a year, allowmy a sheof for one 
 
 > 6. Tele-raph polos are placo-l 8 ro'ls anart, and a train pa:,. 9 n-,e 
 every 4} seconds. How many miles an l.c.r ia the train t.av.'llin - ' " 
 
 6. A man charged me 15 cents for a settle of coal, when coal' wa. 
 selhns at ?7 per ton. IL.w many pounds ou-'ht the scuttle to hold ? 
 
 > 7. Divide 382.60 amon. 27 men and 37 boys so that each m u, mav 
 nave three times as much as each boy. 
 
 lo«<?hrLT"'"! 7.,t*'' "•^•'*' " y^"^' ' ^*'" 11°°"'^ more than I 
 9. If i of an estate be worth £-m, find the value of ^, of the estate 
 
 i?l 
 
 12 J*.t:. r; •„" r' "'" *'' """'^ '^^^ °' * "^*^^ «° "°-^ - 
 
 2. Divide «C00 between two persons, so that one shall have 3 as much 
 as the other. * oiuuou 
 
 3. A regiment marching ,9J miles an liour makes 110 stens in » 
 minute. What is the length of the step? P -n a 
 
 ^ 4. I bought 20 pounds of opium by Avoirdupois weight, at 66 cents 
 an ounce, and sold by Troy weight at 60 cents an ounce. Did I gain or 
 lose, and bow much ? ^ 
 
 ,6. The G. C. M. of two numbers is 12 ; their L. 0. M. is 72 ; one of 
 th* numbers is 24 ; find the other ? 
 
 c/^'u^'"!.^^'^'*.^ """""^ ^- ^- *"•* ^•' ^ "'"* B ^"1 receive »5 for A 's 
 H while C. receives »6 for A.'s 15. ''^r a. s 
 
 7. Which is the greater' .0025 of a mile or -79 of a rod ? 
 
 8. How long will it take a train 20 rods long, and going at the rate of 
 15 miles an hour, to cross a bridge 15 rods long ? 
 
 ^ 9. When an ounco of gold is worth «19.45, what is the valae of .04 of 
 a pound 7 
 
 -^10. A coal dealer bought a quantity of coal at 96 a ton, and sold it for 
 48 cents a hundredweight, gaining thereby »43 20. How many tons did 
 he buy ? j •• «"« 
 
84 
 
 PEliCKSTAGK, 
 
 PERCENTAGE. 
 
 200. Percentage is the method c f calculating h^ 
 hundredths, or it is t!..' bvm i\\)iAm\ t.) suflh coiuputationH 
 as involve the miinber lOu ;,s the Icisis or unit of measurf 
 
 201. Per cent, is an ubbieviation of the Latin phras:c 
 per centum, and si-nifiep on or ly the hun^ln-.l. Thus 4 per 
 cent, means 4 of every hun.lred nu..] may signify 4 cents of 
 every 100 cents, $1 of <.'\vvy rOGO, 4 lbs. of every 100 lbs., etc. 
 
 20t:. The biyn % btantls for the phrase per cent. ; thuB 
 8 per cent, is written 8%. 
 
 20.3. To express any per cent as a decimal or as a 
 common fraction. 
 
 Since any per coat, is some number of hundredths, it 
 is properly expressed by a decimal fraction, or by a com- 
 mon fraction. 
 
 Since 6 % means six-hundredths, therefore 6 % » .06 = ^ , 
 
 TABLK, 
 DECIMALS. 
 
 ■muoLs. 
 
 1% 
 2% 
 
 4% 
 
 «% 
 10% 
 
 25% 
 
 40% 
 100% 
 12«% 
 
 i% 
 
 i% 
 
 12 J % 
 
 m% 
 
 .01 . 
 
 .02 m 
 
 .04 
 
 .05 = 
 
 .10 
 
 .25 = 
 
 .40 
 1.00 s 
 
 l.M 
 
 .00} = .006 m 
 
 .OOJ = .0076 » 
 
 .14 m .125 m 
 
 .83) « 
 .14^ 
 
 COMMON 
 
 FRACTIOI 
 
 TOTJ 
 
 
 TTO 
 
 = A 
 
 riv 
 
 = A 
 
 ro!r 
 
 = A 
 
 Air 
 
 = A 
 
 I^,At 
 
 = i 
 
 a;. 
 
 = i 
 
 m 
 
 = 1 
 
 3 2r, 
 
 1 i,n 
 
 = f 
 
 i 
 
 1 
 
 100 
 
 ~ 200 
 
 3 
 
 -1 
 
 lUO 
 
 3 
 
 ~ 400 
 
 12J 
 
 1 
 
 100 
 
 '^ 8 
 
 33J 
 100 ■ 
 
 1 
 ~ 8 
 
 I 
 
 11! 
 100 
 
PJERCENTAOE. 
 
 86 
 
 ■ 
 
 en 
 
 f 
 
 The stwhnt will ohern- that a,,,, per cent h expns.,,/ as a 
 decimal by r.moviug the derimd point two phnrs to the left 
 in the number expressing the rate per cent., that is, dirldin., 
 the rate by 100. 
 
 EXERCISE 57. 
 
 What decimala and what coiumon fraetiona are eouivi- 
 
 k'Ht to — 
 
 1- •'^%. 7%, 17%, 50'^ 225%. 7 
 
 2- i%- ?%. 1%, A%. i%. 8. 
 J^'^- 2i%, 18] %, 374%, 31J%. 9. 
 
 4. 43}%, ;^G}%, 02i%, C8i%. 10. 
 
 .^- 81i%. 8|%, 16j%, 14?%, 22J%. n 
 
 «• 41|%, 581%. 66}%. 83i7o. 
 
 Sf^tX, 60%. 5r,5%. 75% 
 
 «■'?%, 87i'/, 91}%, Gj... 
 
 10? %, 35 ;,. 3,^..^. 23i ■,. 
 
 !'i%, 175 ■.;, 70%, !t.3j-, 
 
 775%, 57f%, 15J%, 80%. 
 
 12. 13,5 7i, 130^, ,,^Jy^^ ^.,^, 
 
 2<M. To change a decimal or a common, fraction to 
 an equivalent per cent. 
 
 203. Since any per cent, is changed to v-n equivalent 
 decimal or common fraction by espressiuir it as so many 
 hundredths, that is by dividing: it by 100, it follows that 
 any decimal or common fraction can be chan-ed to an 
 eqmvalent per cent, by multiplying such decimal or frac- 
 tion by 100. 
 
 ExAMPLa 1.— What per cent, ia e.iuiv'aleat to .06? 
 Solution 
 .06 3 f.06 X 100) % = 6% 
 ExAMPLB 2.-What per cent, is e.^uivalent to the fraction f ? 
 Solution. 
 S = (S X lOOj % . 76% 
 NOTK.-A decimal is multiplied by 100 by removing the decimal point 
 two places to '„he left. F"*«»» 
 
 EXERCISE 58. 
 
 What per cents, are equivalent to the following fractions ? 
 
 1. 
 2. 
 
 -j.3. 
 4. 
 6. 
 6 
 7. 
 8. 
 9. 
 10. 
 
 i 
 
 J. 
 
 i- 
 
 h 
 
 A. 
 
 A- 
 
 A. 
 
 A- 
 
 * 
 
 i. 
 h 
 h 
 h 
 
 A, 
 
 S 
 
 A. 
 A. 
 
 f. 
 
 i. 
 
 ?. 
 
 }. 
 
 A. 
 
 A. 
 
 A' 
 
 r' 
 
 A 
 5"t 
 
 f. 
 
 i. 
 
 I'r, 
 I 
 
 J*. 
 
 I 1 
 
 I ; ^■ 
 1 
 
 1 n>,1Sf SVn 
 
 4 
 
 Tff' 
 
 A. 
 
 t. 
 
 8 
 
 I r> 
 
 : !'r,- 
 
 f. 
 
 A. 
 
 9 
 1 1 • 
 
 'J. 
 
 
 'jA^rlfi 
 
86 
 
 PERCF.NTAQE. 
 
 \i \ 
 
 1^ I 
 
 Kt i 
 
 i 
 
 Wb--^ per cents, are equivalent to the following decimals " 
 
 12. 0... .064. .09. .01. .001. 3875, .O.ii;5. .0,3126. .0025. 
 18. .0.3J. .028^, .004. Oo.i. .or,§. OOOi. .-Ml .oilj. 
 
 nrT,*"\T° ^""^ '^'^ ""^'"^ °^*"y P^'' ""t- o^ a number 
 or quantity. 
 
 ExAMPLK.— Find 8% of 625. 
 
 SoLDTlOM 1. OPEIt.\TIOl(. 
 
 SoitunoN a. 
 
 625 
 
 8 
 
 50.00 
 
 OPEiiAriox. 
 62u 
 .08 
 
 ExPLANATIOS. 
 
 ■ l%(rH)of63«. 
 
 « 8% " •« 
 
 Explanation. 
 8% of 025 = .on of (or times) 626 
 
 50.00. 
 
 Find— 
 
 1. 20% 
 
 2. 2.-.% 
 8. 4% 
 
 of 
 of 
 
 60.00 
 
 .SOLCTION 8. OpEKATION. iOxPLANATION. 
 
 r#^ X 62.-, = 50 8% of 625 = ,3^ of 625 . 60. 
 
 EXERCISE 59. 
 
 5, 25, 45, 75, 125, 96. 
 
 4. 36, 76, 96, 12S, 210. 
 
 of 25, 75, 125, 250, 300, lOQO 
 
 4. 12i% of 64, 96, 160, ?.-iO, 480, .",00. 
 
 6. 163% of 6, 36, 7>, 84, 132, ;i24." 
 
 6. 8J- of 12, 72, 60, 24o! 252,' 372* 
 
 7. yih% of 80, 32. 48, 75. 90. 724 
 f ■'%% of 9, 27, 7-,, 336_ 47^ 520] 
 9. 6.i% of 32, 64, 256, 90, 750. 
 
 10. 31 J % of 48, 80. 144, 75, .380. 
 
 11. 87J% of 16, 72, 108, 350, 968. 
 
 12. 22=0^ of 27. 45, 63, 507, 656. 
 
 13. 28f% of 21, 35, 50, 987, 770. 
 
 14. 7A% of 26, 39, 78, II7, 273.' 
 
 15. 75% of 24, 32, 28, 264, 760. 
 of 70, 110, 40, .^50, 660. 
 Of 86, 475, 373, 254. 
 of 374, 228, 937, 8321. 
 
 °* i- h 8. A, A- 
 i 20. 126% of 57.50, »376, 436 bushels, 328 toni. 
 
 ^S" f^ °^ ^^*' ^^*' ^7*' ^ 4J. 33J. 
 aa. 6% of 350yds., 450 men, 376 lbs.. 580o«. 
 
 16. 90% 
 
 17. 31% 
 18 44% 
 19. 50% 
 
 1 
 
PEJiVhyTAGE. 
 
 87 
 
 . ^^T*.?*''*'" ^^* ^*^"*^ °^ *"y per cent, of a number, 
 to find the number. 
 
 ExAMPM.— ai ia tt% of what mimbor? 
 SoLOTioa 1. 
 
 Op: 
 .08 ) 
 
 21 ( aoo. 
 
 Solution 3. 
 
 Opkiiation. 
 V X 100 » 300. 
 
 Solution 3. 
 
 34 
 
 OPtl.ATIOK 
 
 X H« - 300. 
 
 Expr.ANATio». 
 Tl!0 ((ueBtion is 0-> «: wliat nmnbor 
 ■ 24. If 24 IB tlip product of two 
 factors, ono of which is .OS. tho othur 
 factor may L» found by dividing 24 
 by .OH. 
 
 KXPLANATION. 
 
 If 8% of the D'lmber = 2 J 
 tlien 1% - .. « j^„f .ji ^ 3 
 " 100% •' " » 100 X 3 = 300 
 
 I'Sl'LAV'.TluN. 
 
 The qnestioii is ^j(, of wlmt nunibor 
 
 » 24. If 21 is conipofi tl of two fao- 
 
 tori, ono of whioli U ,,h. the other 
 
 factor may bo found by dividinj,' 24 by 
 
 rhs- 
 
 EXERCISE 60. 
 Find the numbers of which — 
 
 1. 60 is 4%, 
 96 is 20%, 
 640 is 12.5%, 
 
 3. 
 
 3. 
 4. 
 
 6. 
 
 6. 
 (7. 
 
 8. 
 
 9. 
 10. 
 11. 
 
 32 ia 
 320 iB 
 252 is 
 105 ia 
 
 84 ia 
 35n ia 
 220 ia 
 
 48 ia 
 
 8i%, 
 161%. 
 30%. 
 
 m% 
 
 41|%, 
 15%, 
 771%, 
 24%, 
 
 8%, 
 
 25%. 
 
 160%, 
 
 35 ?4. 
 40%, 
 37i%, 
 58i%, 
 35%, 
 3i%, 
 16%. 
 
 2%, 
 
 50%, 
 
 225%. 
 
 7 » </ 
 
 «♦%, 
 60%, 
 
 66J%, 
 'i5%. 
 
 12%, 
 
 75%, 
 
 ifio%, 
 
 7f%, 
 
 14?%. 
 
 'J0%, 
 
 87i%, 
 
 12?%, 
 
 o5%, 
 
 23J%, 
 
 :o%, 
 
 6%. 
 90%. 
 H0%. 
 
 6|%. 
 12J%. 
 70%. 
 3 J%. 
 
 63%. 
 83i%. 
 
 2t "' 
 
 5|%. 
 36%. 
 
 a08. To find what per cent, one number is of another. 
 
 ExAMPLs.— What per cent, of 60 ia 15 ? 
 
 Explanation 
 As 15 is U of (io, and as the frac- 
 tion ij oxprp.ssud as % is (f J x 100)% 
 ■ 25% Art. 205, it follows that 16 ia 
 25% of 60. 
 
 SOLCTION 1, 
 
 H - (H X 100)% - 35%. 
 
HS 
 
 Pi-UChMAUi;. 
 
 8or.nnon a, 
 .6 ) 16 ( 25 
 1% X 25 . 
 
 SoLtrrioN 3. 
 60 ) 15 ( .25 
 .26 a 25%. 
 
 K'cn.wui'i.N. 
 1 % of 00 = .0, 
 '^' 15 is 2'. lim.s .C and 
 
 tLLr.>f,,ri>5 times 1% of 60 
 
 Tho 'I'vMioii IS CO X what %> 
 
 - ■ = 15. If l.">i.^t],.,„.j,l,Kt()ftWO 
 
 factora.one of w!ucii ih »;o, tlie othtr 
 factor can be found by di wdin^' 16 by 
 60. 16 + 60= .25. and .25, 25%, 
 
 EXERCISE 61 
 
 1. What % in 30 of fiO ? 12 of 48 ? ir, of 45 7 7 of .T5 7 of 03 ? 
 >2.mat%ofl2is2?30is.07 35is28?40is.,'7-^S' 
 
 ^5 vT "^^ J"'' ''' "''' '«' ^0' '■'' '•^'^ 1'"^? 1^-'? 300? 
 5. What % of 200 is 25 7 75 ? 125 7 250 ? 1 ■" 9 h71 ? i ,•2 9 . ,, o 
 
 7. What % 18 49.5, 5(1.25, ."8.50, ,m, 14(of2o-,? 
 
 8. What % is .024J, .4». <i :^, .0:.J, .25 of 2}?' 
 ^•'f[^^^%oiii^-^l A? A?:j?|? J7 U? 
 
 10. What % of 18.79, 187^, 2H1.«5. 319.43. .S;.1.59of .1879? 
 
 209. To find a number, which, if increased or 
 diminished bj a certain per cent, ofiiself, wil be equal 
 to a given number. cquai 
 
 300 7 """"" '•" '''•'* '^''"'•^^ ''^'^'-^'^^^'^ "^y ''' % of itself Will equal 
 
 Explanation. 
 Solution 1. », 
 
 125% of required number = 300 " any number be i„- 
 
 Thereforethe " •< . m x 300 „^ "^'^^^'^ '^^ '' %of itself 
 
 See Art. 207 ^^ " '"' *^' '■^""^"•"' "^^^O^^^ 
 
 + .25%) = 12.-, o/ of the 
 original number. 
 
 SoLonoN 2. 
 t of required number =: 300 
 Therefore the •• " = | x 300 = o-q^ 
 
 EXPI.ANATI0.N-. 
 
 25% = J. AnumbLT 
 increased by J of itsbif 
 will be equal to f of it- 
 self, that is (I + J) of 
 itself. 
 
Mor 
 
 
 •y IJO , of iUolf will ,,,u„l 
 
 S0% of rcvjnin d numb, - SfiO ""/, ""'"'"-■' '"" '' 
 
 Therefore th« " .. « v' x Sfio ... ^'^'"'^''y-" -'itsdl 
 
 - ■■^"'^. = '^H';,. -f till) 
 oriKiii.t! miinbcr. 
 
 Boiirrrnv a. 20 ■v _ i , , 
 
 ♦ of required nuui.or . :m:o a " ~ A ^ '''"^''""" 
 
 Therefore the " " = . „f . 'n ... aeon •ised by ^ of itwlf 
 
 a J ot i,,0 « 4-.0. will Iw ;i - J) » J of 
 
 itfolf. 
 EXERCISE 62. 
 
 What number increased hy— 
 
 1. 
 2. 
 
 8. 
 
 4. 
 
 \«- 
 6. 
 
 7. 
 
 8. 
 
 9. 
 
 10. 
 
 > 11 
 
 12. 
 
 10% 
 
 7.'-)% 
 62} % 
 
 21i % 
 83i % 
 16% 
 36% 
 100% 
 6% 
 22% 
 
 §% 
 1% 
 
 of itself 
 
 of its.'If 
 
 of itsrlf 
 
 of its'.'lf 
 t)f itself 
 of itsulf 
 of itself 
 of itself 
 of itself 
 of itself 
 of itself 
 of itself 
 
 eijnalH 
 P'luals 
 
 e(jii.ils 
 
 equals 
 
 eqUiils 
 
 equals 
 
 ec)UalB 
 
 equals 
 
 ecju'ila 
 
 oquila 
 
 equals 
 
 i 
 
 What numi)* '• diminished 
 
 13. 
 
 U. 
 
 15. 
 
 16. 
 
 17. 
 
 It). 
 19. 
 20. 
 21. 
 22. 
 \28. 
 ^ 24. 
 
 110? 
 
 >^lL'0? 
 
 587.12? 
 :! \r> ? 
 •-'._i.s A. ? 
 H4.«cwt. ? 
 1272? 
 
 ?r,49? 
 *;t.06 7 
 
 »81.72? 
 
 65 % of itself 
 50% of itself 
 10? % of itself 
 
 4 % of itself 
 37i% of itself 
 
 5% of itseif 
 20% of itself 
 
 9 % of itself 
 S7} % of itself 
 
 6*% of itself 
 ?% of itself 
 
 j% of itself 
 
 by- 
 
 equals ?2,5n0 7 
 equals 28.5 feet? 
 equals 1,035 miles r 
 equals ?4fir).r,0? 
 equals S20:).37J7 
 
 equiils ~';,r,.5? 
 
 equals SO ■? 
 
 equals 'J^? 
 
 oiiualg 10? 
 
 equals n.-ij*, ? 
 
 equals 07.957 
 
 equals 216.38 7 
 
99 
 
 fhum Atib Loas. 
 
 PROFIT AND LOSS. 
 
 aiO. Profit and Loss are commorcial terms used to 
 express gain or losa in busini'ss tranBactiona. 
 
 all. Gaim and lotsei ar> mnalhi -siiiiiuted at tome rate 
 per cent, of the coxt of the (inr„l» inHuiling the erprnaea. 
 
 212. To find the Gain, Los.., or Selling Price, the cost 
 and the rate per cent, of gain or loss being given. 
 
 ErAKPM 1 — A raer. liini uold cloth which cost 41.75 por y»rd, so 
 MtoRain8%iniehin«. VVl.at was the .'aiii and Bulling prio«? 
 
 Solution 
 Ccft 
 
 Gain - 8% of J1.76 > 
 Selling price . 3 
 
 81.75 
 .1 4 Art. 206. 
 
 J1..S9 
 
 ExAMPLK 2 —Goods which cost ?J.40 are bold at a loss of 5%. Find 
 Ihc loss and the Bellin;,' ju je. 
 
 SOLDTIOS 
 
 Cost . . . = 
 Loss » 6 % of 52.40 « 
 Sellinf; price . . s 
 
 «2.40 
 
 12 Art. 206. 
 
 ?2.28 
 
 21». T: find the Cost Price, the Selling Price, and 
 the rate per cent of gain or loss being given. 
 
 Example 1.— By selling goods for *132, I gain 10%. What is the 
 oon p.-ice ? 
 
 Solution. 
 
 100 % Cost price m Cost price 
 10% " = Gain 
 
 .*. 110% Cost price = Selling price 
 ;. 110% Cost pr=ct = SlH'2 
 
 Cost price = \1l of »182 = »190. Art. 207. 
 
 1 
 
 i 
 
 -i 
 
1 
 
 PROFIT 4ii LOSS. gj 
 
 ,TTu . ,**t""* '""^ *'"* "'" '"y "*""• ■ *" *«'"!• '<» »1 80 I low nr 
 >V hat II the ooji. price 7 
 
 l"'OI,0TIO!«. 
 
 100 % Cott prio« m Gout prioe 
 
 10% J: ^ - Lmm 
 
 .. '.»o % CoHt price m Rollinjj prioe 
 
 ■ :'0';, (^oMt jirico a 51. SO 
 
 Cost price ..- W 0*11 80 . «'nn. Art. 907. 
 
 till. To find fheCost Price, the Gain or Loss and 
 the rate per cent, of gain or loss being given. 
 
 of ?H50. Kiiil the coat of farm 
 
 Soi.tTTIOM. 
 
 30% CoHtof farm » 88.0 
 
 .-. CoBtoffarm > W x ?850 7 ? 1,250. 
 
 ExAOTLi a— A yacht was . )ld for«1.2001o.s than it ooat.itiiow.ar 
 thereby I aiut; 12J % of the cost. What was the oo»t ? 
 
 Solution. 
 13)% of tbeoMt « tl'200 
 
 the coat « J-^ x 1200 . »9600. Art 207. 
 
 ai«. To find the rate per cent, of gain or loss, the 
 selling price and the cost price being given, 
 
 ExAMPLM l.-Qoods which co.t 96 are sold for -7. What ii u 
 g»in%? 
 
 Exi'LANAI'ON. 
 
 ?7 - S5 » »2 tjain Since the <?.un 
 % : - computed on the cost, the question 
 bciomes, «2 i:^ what % of 85. 
 
 By Art. •>(! , »2 i8(}of 100)% « 40% 
 of .?•'> (the cost). 
 
 Eji.»ipu a.— Good! which cost J7 are sold for »5. What is the 
 
 tvsv ^ * 
 
 ExTLiNATIOy. 
 
 97 - 95 = ?2 loss. Sines the loss % 
 SoLunoN. is computed on the oost, the qnoBtioa 
 
 (f X 100)% •« 28f%. Ant. becomes. 82 is vhat % of |7. 
 
 By Art. 208 52 ia (f of 100) % « 
 28f % of the cost (97). 
 
 BOLCTION. 
 
 (I Of 100)% « 40%. Ans. 
 
i>'2 
 
 PROFIT ASD LOSS. 
 
 ai«. To find uiie Soiling Price, the Cost Price and tht 
 gain or loss per ceni. of the selling price being given. 
 
 KxAMixr l.—For wlu.t rnuHt I gcil au arti'^lo whkii oo*l »a.W •oim 
 tot^uin 26% of thoiiullln« [Hiuo? 
 
 8elliIl^' prioo « 100^ RcIImR prio*. 
 Gain ■ 26% •• •• 
 
 Cost price - 75 % SellinK prio*. 
 
 .'. T5% Stllinj^ price m j-j.as 
 
 SolluiK price - W » 9.25 - »8.00. Art. 207 
 
 ExAUPu a— I aold j^oods which coBt «2.6ii, lo th»t I loik 2« oi 
 the lellinti price. Find t\w gelling price. " 
 
 Solution. 
 
 Selling' price m 100% Selling prioa. 
 I'f]^ ■ 26% " <• 
 
 Cost > lL'r,<;„ Sullinj? price. 
 •*• 128%of the selling price m S2..')0 
 
 the Belling price « f J) of 2.60 ■ »2.00. Art. 207. 
 
 i i I 
 
 EXERCIf« 68. 
 
 I ; 
 
 Find gain or loss ai.cl selling price- - 
 
 
 COBT. 
 
 1. 
 
 J8.00, 
 
 2. 
 
 s.'i.eo. 
 
 8. 
 
 «4.20, 
 
 4. 
 
 »■> 60, 
 
 6. 813.20, 
 
 20%. 
 10%. 
 16%. 
 
 m%. 
 
 40%. 
 
 Find cost price — 
 
 81 IXINO FBICI. 
 11. ?7.50, 
 
 13.00. 
 $4.59, 
 I6.60, 
 H.66. 
 
 12. 
 18. 
 14. 
 16. 
 
 OAIN%. 
 
 60%. 
 30%. 
 28f%. 
 22|%. 
 
 14 °<;, 
 
 COST. 
 
 6. flfi.fiO, 
 
 7. 814.76, 
 
 8. ?13.t;o, 
 
 9. 810 80, 
 10. S4..50, 
 
 UIXINO PBIOa. 
 
 \ 16. -4.75, 
 
 17. $r,M, 
 
 18. 812.00. 
 
 19. 824.30, 
 
 20. 85.61. 
 
 toss %. 
 87* %. 
 
 4%. 
 62t%. 
 16s %. 
 38J%. 
 
 I<088%. 
 
 6%. 
 60%. 
 
 4af%. 
 86%. 
 
 8i%. 
 
 . 'ii. UAwr. . L 'iki 
 
ttiotn A b l.usa. 
 
 «» 
 
 Find t,'.iii) or luss ",; 
 
 ■Bf.l.I'.', illlcK, 
 
 21. :li'..n, 
 
 aa. iim, 
 
 28. ? 1 ), 
 
 24. 8,).0 1, 
 • 26. 87.u0. 
 
 Find cost — 
 
 OAI.V. 
 
 30. «.l 00, 
 SI. t;Oo., 
 8a. 37 }o. 
 
 38. (5.<i0. 
 
 cosr. 
 Shoo. 
 •5.00. 
 
 f 1 III). 
 
 11.00. 
 
 •6.oO. 
 
 OAIN %. 
 
 40 '](,. 
 
 Mhxr iMi |.|(ici 
 
 27. rr,/,o, 
 2H. S: ; -0. 
 3i<. 810.110, 
 
 84. 
 
 3.-,. 
 
 .4 si; 
 
 rJ -0, 
 
 ■: ; >o, 
 
 JI.L'O, 
 
 ;37. e.'i.oo. 
 
 COST, 
 
 f8,on. 
 
 »7.50. 
 81. '.00. 
 •12.U0. 
 
 80%. 
 
 a-l ■ a- 
 
 oy 
 
 1 88. GoodB w,^h ,,>,.,o wore so, , .o .. to ,.in 25% of t,.' ^U.«, 
 
 price, tixxa tile st'llin - pii, o " 
 
 «9. An article which c.st <:i.50 was h,,-!,! «,, ti„.t 121 <»• of rl , 
 
 w..-.. lost. Fin,l tl.o se-lin, „no.. of , li. iLtfi^ "^'^' 
 
 iO. What . the .ollin. pn. a l.orso which co.t ^i..,. aud which 
 was .old M a» to .aiu . ^ of the prooo^ia. 
 
 :^:«Ar:ziBhK ..£ 
 
94 
 
 TliA.DE DiacOUNT, 
 
 i 
 
 I; 
 
 ! ', 
 
 '; ! 
 i 
 
 ^ J- 
 
 TRADE DISCOUNT. 
 
 'JIT. It is customary for merchants and manufacturers 
 to have fixed price lists of their goods, and when the 
 market vanes, instead of changing the fixed price they 
 change the rate of discount ^ 
 
 fhfJf * T'Jn^ .?T""* '' * percentage deducted from 
 the face of bills, the list prices of goods, or from the amount 
 of a debt without regard to time, and is expressed by the 
 term per cent. off. ^ 
 
 219. Thus 20 % off. means a deduction of 20% from the 
 nominal or asking price. 20 and 5 % off, means a discount 
 of 20 %, and then 5 % from the remainder, etc. 
 
 The result is not affected by the order in whica the dis- 
 counts are taken. 
 
 ^.^^^*' P^'^l''' ^'""^^^y ^nrionnce their terms upon their 
 bill heads thus, Terms 8 months, or 80 days less 5 % 
 meaning that a credit of 8 months is given, but if the bill 
 be paid within 30 days a discount of 5 % will be allowed. 
 
 321. Goods are marked by wholesale dealers or jobbers 
 at a i-ate % above, which will allow a certain per cent, of 
 discount from the list or marked price, and still realize a 
 margin of gain. 
 
 222. The net price of goods is the list price less the 
 
 trade discount. 
 
 228. To find the net price, the list price and discounts 
 being given. v.uuuu. 
 
TliADE DISCOUKT 
 E ^^ 
 
 Solution. 
 9640 
 
 -1^ - 25% of 8610 
 9480 
 
 1^ " 10%of84H0 
 
 1432 
 
 _21.60 s 6% of 8432 
 
 9410.40 = Net price. 
 
 or mo«Irs«u'!.4':° "'"^'^ '""™"' "'"'™"=«t to two 
 
 SOUJTIOM. 
 
 Pet list price = 8100 
 
 Ist Discount =__20- 20% of 9100 
 
 80 
 tod Discount =. _j8 , 10% of 880 
 Net price = 872 
 Total discount on 8100 = 8ioo'- 872 « $28 
 .•. discount a 28%. 
 
 «ail. Prom similar examples we derive tha M)^ ■ 
 
 BUIiB. 
 
 From the sum of the discounts subtract ^ of their product. 
 
 10 - 
 
 luo "y mctf pruauct, 
 
 ,*^to rr ^" ^^' '^°'' '""'"P^^ *^« discount » 20 ^ 
 100 ■ 2Q% 
 
 Thus, If discounts of 20. 10 and 5 % off are given 
 From the preceding illustration. 20% and in<v 
 equal to a single discount of 28 %, co.binZig 28 ^ n"^ T^^ 
 we get a discount of 28 + 5 - lili! - q,.V\^ ^ ^* 
 ai.eo„e e,„al to .he d,.c„a„ts ofTo, l"o a"'*'., 'ft ""'" 
 
96 
 
 TliADK DISCOUNT. 
 
 227. To mark goods so that a given per cent maj 
 be deducted and leave a given per cent, profit. 
 
 KxAJiPL'.— At wliat prico niu.-^t I mark an article whioh oost 94.00 
 so tliat, after deducting 20%, I miiy still have a profit of 25? 
 
 Solution. 
 SellinR price a ?4.00 + 25 % of ? 1.00 a 85.00, 
 and 20% less than tho marked prico a: Kelling price J6.00. 
 .•. 80% of marked price = u.OO. 
 
 markod prioe = Y^t x 5.00 « 86 26. 
 
 1: I 
 
 
 
 EXEiiCiS 
 
 E 64. 
 
 
 
 Find cash price of — 
 
 
 
 
 LIST FKIOR 
 
 TB\I)K DISCOn.VT. 
 
 LIST PHtOH. 
 
 TBADB DiaCODNT. 
 
 |1- 
 
 8360. 
 
 6 and 20 % off. 
 
 9. 
 
 .S3i;o.tio, 
 
 10, 5, and 3 % off. 
 
 2. 
 
 ♦475, 
 
 80 and 5 % off. 
 
 10. 
 
 i?-'142.1.5, 
 
 5, 2 J, and J % off. 
 
 •3. 
 
 8«00, 
 
 20 and 10 % off. 
 
 11. 
 
 ? 102.18, 
 
 20. 5, and 2^ - off 
 
 4. 
 
 »75i, 
 
 10 and 8 % off. 
 
 12. 
 
 5075.36, 
 
 10, 8J. and J% off. 
 
 6. 
 
 ;S1000, 
 
 40 and 20 % off. 
 
 13. 
 
 3171 25, 
 
 40. 10, and 6 % off. 
 
 6. 
 
 81750. 
 
 25 and 10 % off. 
 
 *14. 
 
 f:!',)i; i;o. 
 
 50, 30, and 1 % off. 
 
 7. 
 
 81840, 
 
 30 and i % off. 
 
 15. 
 
 $4;iG-^.50, 
 
 20, 10, and SJ % off 
 
 8. 
 
 83200, 
 
 40 and i % off. 
 
 16. 
 
 83169.20, 
 
 33J, 20, and 10 % off. 
 
 What direct discounts are equal to discounts — 
 
 17. 6%and20%; 30%and 6%; 20%and 10%; 10%and6%. 
 '18. 40%and20%; 25 % and 10%; ;iO%and J%; 40%and J%. 
 
 19. 10 %, 5 % and 3 % ; 50 %, 10 % and 5 % ; 40 %, 20 % and 10 %. 
 
 20. 10 %, 10 % and ' % ; 20 %, 1 % and 5 % ; 10 %, 5 % and 5 %. 
 _^31. 10%,8J%Rndi%; 33* %. 20 % and 8J % ; 5%,2J%andi%. 
 
 .^ 22. What is the difference on a bill of $425 between a 
 discount of 50 % and a discount of 30 % and 20 % ? 
 
 • 23. A bookseller wishes to mark a l)ook which cost $2.00 
 that he may allow a discount of 25% and still make a 
 profit of 20 %. What must be the marked price ? 
 ")<^ 24. If the list price of certain goods is $12 per gross, 
 what will I gain or lose by buying of Mr. A., whose dis- 
 counts are 25% and 10%, instead of from Mr. B., whose 
 discounts are 20, 10 and 5% off? , .■ ^ 
 
THADE DlSVOUm 
 
 97 
 
 a profit of 26 % ? ^"^ "^' and still have 
 
 MISCELLANEOUS EXERCISE 68. 
 
 50% of what wa, imtii rr f *' "" ''"""' ■■ 
 
 iow much .id he p„, tor the whole ,1™;; *°" '" '*"' ^ 
 
 conl-.t.fonMsttd'/r;:'""'' "- ■•-"^ POO. 
 vation, which paid f„ H^^ifi^f,'""^™" "'""^f"! oalti- 
 
 -».r...„„th.xssir---t;e',: 
 wn!r,zt::h:-riv:::r:r.aVrr 
 
 many mmates are there now ? ^^ ^°^ 
 
 age. freight, etc. \vhat mus/he Lirihe"?"" ^"^ «"*- 
 on the whole cost ? ^^^'^ ^^'^ *« gaiu 40 «^ 
 
 ^6. In a mixture of alcohol and water m^ ■ , . 
 How many gills of alcohol in 8 gal'ol of .f ^ •'' *''"^°'- 
 how many gills of water ? ^ " °^ *^" '"^^^^'-e. and 
 
 6. 560 bushels of wheat, bought at $1 m 
 wore sold at a profit of 10 %. What d^c i^ ^ ^" '^''• 
 
 ^ '^nat did the wheat sell for ? 
 
98 
 
 THADE VlSCOUNr. 
 
 fni; 
 
 ; . . 
 
 .7. Bought a bill of goods amounting to $875.50, from 
 \vhii;h was deducted 6%. Wbat was the percentage 
 tillowed, and the amount paid ? 
 
 8. Having $10,720, I invested 25% of it in land, and 
 12 J % of the remainder in fencing it. What remained ? 
 
 9. Two men engaged in trade, each with $;3,5iO. One 
 of them gained 33^ of his capital, and the other gained 
 60%. How much more did the one gain than the other ? 
 
 10. A little boy who has 8 apples gives 25 % of them to 
 his brother, 12.}% to his sister, and 50% to his mother. 
 What per cent, and how many has he left ? 
 
 11. Charles sold his sled, which had cost him $1.75, at 
 20% below cost. How much did he get for it ? 
 
 • 12. A lot of damaged calicoes are to be sold at 75% 
 below tho marked price. What prices must be asked for 
 those that are marked 8c., 10c. , 12ic., 16c., 20c., 30o. ? 
 
 13. A grain dealer bought wheat for $9,384, and sold it 
 ai a gain of 4i %. What did he receive for it ? 
 
 -^v 14. If a man owes $2,500, and agrees to pay it in 4 instal- 
 ments, the first to be 50 % of the whole, the second 25 %, the 
 third 15 %, the fourth 10 %. What will each instalment be ? 
 
 II. 
 
 1. A merchant owes $6,500, and his property ia worth 
 only $5,425. What per cent, of his debt can he pay ? 
 
 2. A man shipped 8,800 barrels of flour to England, and 
 during a storm 19 barrels were thrown overboard. What 
 per cent, was lost ? 
 
 3. If I have $374.50 in currency, how much gold can i 
 buy when it sells at a premium of 7%? 
 
TRADE DISCO I J, ST. 
 
 99 
 
 1/ 
 
 4. The population of a certain village incrense.l in 5 
 years from 6,000 to 7.800. What was the average rate of 
 increase per year ? 
 
 5. A man bought 350 acres of land, at $40 an acre, anJ 
 
 oldpartof J for $2,240 at the same rate. Wh.t pe/cent. 
 of the land did he sell ? 
 
 6. An agent received $^7.50 for collecting $4,500. Whit 
 per cent, was his commission ? 
 
 7. Bought sugar for $150 and sold it for $1(>7 50 Wli«f 
 per cent, was the gain ? 
 
 i 8. A merchant owes $8,250, his assets are $:^ 240 What 
 per cent, of his debts can he pay ? 
 
 s 9. Sold ; acres of land for what the whole cost. What 
 wiis the per cent, gain? 
 
 10. What per cent, of 865 days are 30 days ? 
 
 11. Bought a number of eggs, and sold 11 for the money 
 paid for 18. What per ceut. was the gain ? ^ 
 
 ouJtitt s£;"'w,T' '"'" ^''"' ^^*'' ^^' ^^•"' '-^"^ '^-^^ 
 out with 320. What per cent, were lest ? 
 
 13. Of 4,000 acres of land, I sell 140 acres. Wl,at ner 
 cent, do I retain ? ^ 
 
 ^ 14. A grocer sold from a hogshead containing 60o pounds 
 of sugar i of it at one time, and * of the remainder a 
 another time. What per cent, of the whole remained ? 
 
 
 III. 
 
 ^1. A merchant owes $1.5,120, and his assets are ^9 8->8 
 What per cent, of his debts can he pay ? 
 
 2. If $52.50 is paid for the use of $750. 1 year, what is 
 the rate per cent, if $.6.70 is paid for the use of $ir26oV 
 
100 
 
 TRADE mSCOUNT. 
 
 ti 
 
 h 
 
 t i 
 
 8. A man shipped 2,600 bushels of grain from Chicago, 
 and 455 bushels were tlirowu overboard during a gale. 
 What was the rate per cent, of his loss ? 
 
 4. One number is 6% of another. What per cent, is thy 
 latter number of the former ? 
 
 ^5. My furniture is worth §7,200, which is 90% of the 
 value of my lot ; and the value of the lot is 33 J % of that 
 of ray house. How much are lot, house, and furniture 
 together worth ? 
 
 ^ 6. A gentleman who had a yearly income of |2,000 for 
 four years, spent tl.800 the first year, $1,500 the second, 
 $1,200 the third, and $2,260 the fourth. What per cent, 
 of his income did he save during the four years ? 
 
 7. A person expended 16 % of all he was worth in baying 
 20% of the stock of a raining company. If the entire 
 stock of the company sold for $100,000, how much was the 
 person worth ? 
 
 / 8. A merchant, embarking in two speculations, in the 
 first made .£37 9s. 3^., which was 4 % of his investment; in 
 the second he lost £27 16a. 8d., which was 5% of his invest- 
 ment. How much had he uvested in both enterprises? 
 . 9. A.'s yearly income, which is 7% of $27,000, is 160% of 
 B.'s -ncome. If B. receives an income of 10% annually 
 from his property, how much is he worth ? 
 
 10. A leap year is what per cent, of a common year? 
 
 11. C. from an income of $5,840, spends $4,966.20; D. 
 from an income of $2,790.40, spends $2,660.88 ; E. on an 
 ircome of $1,569.50, saves as much ptr cent, as the rate 
 per cent, that 0. saves, exceeds the rate per cent, that D. 
 naves. How much does E. save? ? / / / 
 
 12. What is the cost of a house which sells at a loss of 
 7i%, the selling price being $11,500? 
 
TRADE VISCOUM. 
 
 101 
 
 18. A merohaut owes $12,575, and bis assets are $7,500. 
 What per cent, can be pay ? 
 
 . 14. Sold two city lots at $ 1,500 eacb ; on one I made 16 % 
 on the other I lost 18 %. What did I gain or lose ? 
 
 IV. 
 
 mQ'oi^^'°.?ru° * °""**'° ''"'^''^' 11^ °f J*««^f. ^« have 
 109.835. What would we get. if we subtracted from the 
 same number 11 % of itself? 
 
 • 2. In a certain nursery, 15 % of the trees are pear trees 
 1% cherry trees. 4% plum trees, and the rest, numberin<'^ 
 480. are apple trees. How many trees in all. and bow 
 many pear, cherry, and plum trees does the nursery con- 
 tain ? 
 
 . 3. P. having lost 20% of his capital, was worth exa -tly 
 as much as Q., who had just gained 12% on his capital 
 Q. s capital was originally $15,000. How m ich was P.'s ? 
 .4. A railway company sold 12% of its lard, and then 
 mortgaged 5 % of what was left. It then had ,0, ROO acres 
 unencumbered. How many acres had it orig.jally ? 
 
 .) 5. What number, increased by 2^% of itself, equals 124- 
 diminished by 38J % of itself ? 
 
 6. What fraction, increased by 21 % of itself, equals f H ? 
 
 7. 240 is 33J% more than what number ? 
 
 i8. A collector who has 8 % commission, pays $534.75 for 
 a bill of $775. What amount of the bill does he collect ? 
 
 9. What is i% of $1,728? 
 
 10. What is 9i % of 275 miles ? 
 
 U. Wiiat is the difference between 5*% of $300 and 6i<4L 
 of $1,050? -^ 
 
102 
 
 THALK DISCOUHT. 
 
 % 
 
 %l 
 
 
 U! 
 
 12. 25% of 800 busholB is 2^ of how many busheU? 
 
 13. Sold 105 banelH of potatoes, which was 36 % of all I 
 mised. How juan.v did I raise? 
 
 14. A hirmer sola 7.5 acres of land, wliich w&b 16% of 
 all he owned. How many acres did he own ? 
 
 1. What per cent, of a number is 25 % of J of it ? 
 
 2. i% of l,-258 id ^ % of what number ? 
 
 8. What per cent, of a number is 20 % of f of it ? 
 
 4. A min spends $S25 (50, which is 83.^ o^ of his 8ah,ry. 
 now mucii is his salary ? 
 
 of ti^q 70° t'"" °"* ^ ^ °^ ^'' ^^""^ ^^I^"^'* *° pay a debt 
 of 1243.72. How much had he in hank '? 
 
 J 6. If a man owning 40 % of an iron foundry, sells 26 % of 
 bis share for $1,246.60. what is the value^of the whole 
 loundry ? 
 
 7. A farmer sold 3,160 bushels of grain and had 80 % of 
 his entire crop left. What was his entire crop ? 
 
 8. If a man owning 45 % of a steamboat sells 16* % of his 
 share for $5,860, what is the value of the whole boat ? 
 
 9. The assets of a business man are $135,700 which 
 sum IS 48 % of his debts. What is his indebtedness ? 
 
 ^10. A fruit aealer sold a lot of oranges foi $337.50, which 
 allowed him a profit of 12^ %. What did he pay for them ? 
 
 11. A city lot was sold for $25,500. the gain on the cost 
 being 825% What was the cost ? 
 
 12. A grocer sold 800 bushels of potatoes for $285 
 which was 16§% less than he had paid for them. Ho^ 
 much did they cost him per bushel ? 
 
 I ' 
 
 
TUADE DISCOUST. .^g 
 
 SaoV' w''^ ^"'^t ??, u '"" '^ '^ - 3" P^«fit wan 
 «i.».70. How much did he soil tliom for ? 
 
 percent, that woui.l be gained by soiling them for $840 
 
 ■ 15 I" the scl.oolH of a villain, vegterday there wor« 1.285 
 puj.Us present, which wua 95 o^ ..f th. whole number belon«- 
 Jng. How many belonged to the Bchools ? 
 
 VI. 
 
 •^ 1. Sold a horse for $310, which wag 15% les. than his 
 .alue. vv hat was his value ? 
 
 - 2. A man h:iving incnas.d his ba.ik deposit 40-]^ ,t 
 amounted to $y 10. Plow much had he at first ? 
 
 8. My income tlm year is $2,232. which is 7% l..s than 
 It wa^; last year. How mu -h was it last year ? 
 
 4. A man sold 160 acres from his farm, which was 12ist 
 less thaa the number of acres he retained. How many 
 acres in his farm ? 
 
 ■■'. 5 The price of a single ticket from Princeton to Wood- 
 slock IS 30c., but 20 coupon tickets can be bought for 
 16. What per cent, is av.d by buying coupon tickets? 
 What per cent, is lost by buying 8in,^'le tickets ? 
 '^6. 10% of a flock of sheep were killed by do"s • 64% of ' 
 the rest were lost; 33jo^ of the remaining number were 
 sold and 28 then remained. What was the original 
 number ? ** 
 
 7. At harvest time a farmer sold (iO bushels of wheat 
 wh.ch was 25% of the quantity he sent to miii, and what' 
 he sent to mill was 40% of what he kept over till the next 
 spring. How many bushels had he at first ? 
 
104 
 
 TRADE DISCOUNT. 
 
 i * r. 
 
 II 
 
 Nil! 
 
 > , 
 
 r f I = 
 
 8. When a merchant sold hia goods for $261. he gained 
 twice ae much aa he wo»l<l have In.t had he boI 1 them for 
 
 f ,\. Jl""* ''^^ •"'" 8'"" P" *^'*"'- ? (How nuuiy tlm- ih. 
 lots ii the iifforonoe between jaOl and 8207 ?) 
 
 9^ A grocer sold butter at 12 % profit. Had he sold it 
 for 2c. more per pound, l;e would have gained 20%. What 
 did 60 pounds cos* him".' 
 
 10. A boy buys an old pair of skates for 50c. and sells 
 tliem for 25c. He then buys a pair for 25e. which he sells 
 for 50c. What per cont. did he lose on the first pair 
 what per cent, did he gain on the second ? 
 
 11. If a dealer buys a hat for .$3, and sells it for $4, what 
 per cent, docs he gain ? If ho buys it fur $4 and sells it 
 for |8, what per cent, does he lose ? 
 
 12. One hundred pounds of beef were sold for $6, havinc 
 been bought at 4c. a lb. What per cent, profit ? 
 
 18. A retail dealer in boots and shoes sold 60 pairs of 
 boots for $800, they cost him $6 a pair. What rate ner 
 cent, did he gain ? ^ 
 
 14 A merchant bought goods for $500. What per cent 
 would he gain by selling them for $530 ? For $525 ? For 
 $650? For $540? For $560? For $675 ? For $600? 
 For $1,600? 
 
 VII. 
 1. William buys a penknife for 20c. and bells it to James 
 for 25c. What per cent, does William gain, and what per 
 cent does James lose ? 
 
 fiit ^i ^1^ ? .?'""*'' °^ '°''°''' *'°^' ^^«° *° «<^^89es are 
 8i% of the daily session, how many hours i the session? 
 
 ^. 8. If a book is marked to be sold at 25% above cost, but 
 It IS sold at 20% below the marked price, what was the gain 
 or loss per cent. ? 
 
 VI 41b&'<3|i *a 
 
TRADE DISCOUXT. 
 
 105 
 
 
 4. If ^0 pounds of coffee are exchanged for 120 pounds 
 of BUgbr, what per cent, ia tho coffee worth per pound nioru 
 taan the sugar ? 
 
 5. What per cent, do I gain by sellinf? an article for $3 
 for which I paid $2.25? What per cent, do I lose by buy- 
 ing an article for $8 and selling it for $2.25 ? 
 
 8. A drover sold a horse for $226, and thus gained 26 %. 
 What did he pay for him ? 
 
 7. i3ouKht 800 long tons coal at $3.76 a ton and sold it 
 at $4 60 a short toe. What is the per cent, profit ? 
 
 H. Bought a barrel of syrup for $20. What must i charge 
 a galbn in order to gain 20% on the whole ? 
 
 , 9. Sold 25 tons of coal at $5.(34 per ton, and made $62. 
 What did the coal cost, and what per cent, was the profit ? 
 
 yC 10. A quarter section of land was sold for $1,563, which 
 was 8% less than cost. What was the cost per acre ? 
 
 11. If 16 % of what is received for goods is gain, wliat is 
 the gain per cent. ? 
 
 ^ 12. Sold goods for $29,900 and made 15 % after deducting 
 5% for cash. What was the coat and tho luai-ke I price ? 
 
 . 13. A dealer sold 1,600 bb!s. beef for $24,000, which was a 
 loss of 25 %. What did the wliole coat, an^' what did he get 
 a barrel ? 
 
 14. A builder sold a house for $8,250, which was 12% 
 more than it cost him. What was the cost ? 
 
 VIII. 
 
 \ 
 
 A merch jjd cloth at $3 per yard, and thereby 
 
 gained 20%. What per cent, would he hav" gained if he 
 had sold the cloth at §3.75 per yard 9 
 
106 
 
 TUADK msCOVNT. 
 
 (^ 1. Mr. A. i„ii(l threo timo« as much for »„•« i 
 '"« gig. If he l.a,i paid 15 % m, ro L ,. T" *" ''"■ 
 
 for his lu.r.c, ti.ey von d to.ln '""' "'"^ ^"^ '^ '^'«« 
 
 iw7« ui,. ,. ^°'^ "lane a % on his cantal ftn.i m. 
 
 1873, 8i- on Iiih capital tlius incrci...,! r' ? 
 
 then equaled ^llki W , 1 ^'^J'^^'^' ""^ "-ofit 
 
 whatwu.shi«;..iit;;iH7j; '" °"°'""' ^^^^'^'^'^ 
 
 7. A statue was sold for <%7-.q nr. i • i 
 "^ore than it co.t H- d i 1 ?. 'I '^ ''''' * °' ^^ 
 
 cent, .ould Inuc Loen ,air,. d or io!t ? ^ '' "''** ^' 
 
 X «. Hold goods lor $4,02G,75, at a loss of 8i<ii w. * 
 would tey h u. Ud to sell for to yieldTp^.^n't^-^H 
 
 9. 13. bou,ht a Lo.se for .S200. and sold it at 20% advauc 
 to C. who ..old it to D. at a loss of in ■ , ■ ^'^^"""''' 
 
 i:. lor 5% uaure than it co^t h^ If S LM ^ft " *" 
 
 1... for the horse. would-I.. h^ losfo^«'a^^ed t!'V" 
 pii" ''Lut. ? haiuea, and what 
 
 .^10. k. sold X. some goods for S;q<u «* i 
 
 X. -Id UK..U to v., a, a',„„m „ fj%' "nn T" "' '^^ 
 
 a.ore or 1™, than K., audVow mucb ? '' '"'" ^■ 
 
 r%"- Z It Lj,t« Jlii'r ';r '''^''' "'""-« 
 yield a profit of nt ""' ""■ »"" '""'''»*. '« 
 
 •^^^l^'Tj-^^i^MSiff^ 1^^^ 
 
 aHKrj^^0iiiok '^. 
 
IHAUE mscovsT. 
 
 107 
 
 12. A rlrovor laiM out equal H.jtnH for flhofip, cowa, and 
 liogs. On llic lio-rt he IohI 1%, on tli.. nhoop ho inado 16%, 
 and 01. the cowr ho lost 1%. h- r.r«ivod for the who!,, 
 ?l,r.35, nn<l Imij^rht 25 ho^'H. w)i)it di 1 each ho« cont him ? 
 What did all tlic Hhf'op cost liini ? 
 
 • 18. JonoB t.lT.'rL'd his houne for 15^ ranro tlmn it co-t 
 I'iiu, hut aft. iward Hold it for $16,r,25, which was 10% Ichh 
 than his ori^'iiil olfer. How much did hiH houno cost him ? 
 
 * 14. The population of u certain city in 1H71 increa-.d 
 •1% on tliat of 1S70; in 1872 it iticrmsed 6% on that ..f 
 1871; in ]87;J it incroaHt-d fi% on thai of 1872, an I 
 amounted to 1,889,024. What waa its popuhitiou in 1870 ? 
 ' 15. If a certain nurahor he increased In KirfY, of its'lf, 
 and the aura is diminished hy .'50% of itaolf, 10% of the 
 roraaiodor ia 14. Reuuirod, the nuiubur. ') 
 
 i 
 
 IX. 
 
 1. If a merchant who huya goods on 6 months' credit is 
 allowed a deduction of 5 % for paying his hill wilhiu 30 days, 
 what can he save on a bill of $500 ? How much on $8,0.50? 
 
 2. If a man fuilH to pay hia water rent until h(i is ci.arged 
 12% for delay, how much will he lose if his w.ilor rate is 
 $18.75? 
 
 8. If 1 % per m inth, counting from the time of payment, 
 i!i allowed on all taxes paid before July Ist, and 1% per 
 ramth charged on all taxes remaining uui)aid thereafter, 
 how much more does A. ))ay than B., if 13. pays his taxes' 
 Felruary 1st, and A. [)ays his tuxes November Ist, their 
 tax -hills each being $180 ? 
 
 •1 Wiiat is the net amount of a hill of •joods, the list 
 price of which is $185, sold 5% oil for cash, trale discount 
 8%? 
 
108 
 
 TRADE DlSOOVilT. 
 
 I 
 
 » tt. «e. vl W .he b, ,fr '"' "'*°'"" -••■• wt' 
 
 6. The gross amount of a bill i. «2»fi o, .^ 
 -i'Koune are 16 « and 8 % Wi, ?° .^f ff = «■« rales of 
 7 p,„j J- """ "'oe net amount ? 
 
 J.^F,ndad.eotdisco„„te,„a,toadieeou».„fi2j5, 
 ^^8^ What direct discount is e,ual to . discount „, 25 * and 
 A 9. On a bill of |625 what ;« f», j-» 
 -n. of 30 , and a di^lfn't Inl^^t^;^'^^'" ' ^■•'• 
 
 PH^lSMttm'atlhLeSi™!"' 1*:° '"^ «'«" 
 I gam ? •"" P"^- What per cent, did 
 
 "• What per cent, would I cain «t . a- 
 
 •2. With a trade discount JZ .« °°°'" "''^^^ 
 were sold f„r $825 at a profl.?,? '""^^.f '^ =■«". good. 
 
 13. A bookseller wishes to 1 . ™' ""° """ ' 
 
 which he now sells fo $3 »„ Z' "" "'" """^ "' " "^^ 
 
 ^r - -- -'«" wht rti'^mis 
 
 and make the same profit V ^' '"^^ ^^'^n*'* 4% 
 
 16. Bought diamonds at «QOn rr 
 
 a^«etl:';'a::;tr^,;';™;";-artic.e,rom which ,o„ 
 
MARKISa GOODS. 
 
 109 
 
 MARKING GOODS. 
 
 228. It is customary in mercantile houses to use a private 
 marif, which is placed on the goods to denote their cost and 
 Belhng price. A word or phrase containing ten dillVicnt 
 ;etter8 is taken, the letters of which are used to indicate 
 the ten digits. For example, the word " Sutherland " is 
 selected ; then the letters reprcHeiit the figures as follows : 
 
 Sutherland 
 1234567890 
 
 If it is required to mark $1.75, it is done thus, Sle; 
 47 hi ; 90 nd. 
 
 220. The following are among the words and phrases 
 that may be used : Haliburton, Cbelmsford, Cum' erland. 
 Blacksmith, Now be smart, Strike hard, Cash profit, Black 
 horse, etc. 
 
 2SO. It sometimes happens that the selling price con- 
 tains three figures, while the cost price contains but two. 
 To prevent this difiference from being noticed, the letter 
 denoting the cipher is prefixed to the cost inice. For 
 instance, the cost price was 85 cents, it would be marked 
 dae; and the selling price, sue; thus each price would be 
 indicated by three letters. 
 
 33l> An extra letter, called a " Repeater," is used to 
 prevent the repetition of a figure. Instead of writing see for 
 1.55, which would show that the two right baud figures 
 were alike, and thus aid in giving a clue to the key-word, 
 some additional letter is selected for a repeater, — y, for 
 instance — and then tbe price would be writtf^n sey; 837 
 would be written tyl. 
 
 SS3S. Arbitrary characters are frequently used instead 
 of letters, thus : 
 
 1234 5G7890 
 
110 
 
 ^'-rt 
 
 1 
 
 ^AliKlNO GOODS. 
 
 Cost ?1 JO, 
 1>0, 
 •1.50, 
 1.75, 
 
 2.51), 
 
 1 wn , . EXERCISE 66. 
 
 Dsf, iSI m n . , ^ 
 
 «%, .. ,, ,:" ^'•'J'"'i,' price. 
 
 ^'^fark tlu; Polling, n, ; " r ," '^-■ 
 Chelmsford." ^ '^^^''"^^ usiii-r fi-p . ^ , 
 
 8; wi.... lotto.': w„„';/Cd :r r '^r '•""« "^b 
 
 "I «"glo articlos which wor» I """^'""8 "ic sclH„„ ,„.;,„ 
 
 ™ I at „ p fl. „, ,4 :: ; ;f ; „:7!:f "- «-» -.d 
 
 5. What wonM be tho sell „1 ^' ''^'■''•") 
 
 """f I at ?.i.co, on >LS tlfo':?™ "' '■""™'^'' »'««los 
 purchase prioe, if ti„, .l' , j'^^J^ -e Jo;, „, .,, 
 
 ,.;' \ ^'" ™"M tho selling pWee It J^ 'f !''.°a' ^ 'o(al 
 C 'Sh profit" be used. witlf/Ja re, / ; 1 " '"' 1^'''«» 
 . •>; A merol.aut using as Z,"'' ""■''""■r ? 
 
 '"' -ales the cost per v„ ^ o a nf" ™''', "Chelmsford," 
 TOat mark „.i|| i„,||^,„^' ^ ° » P'oce of ,;„,, j;,,,^ ^ 
 
 ~n':::r,T;:t»n-*--o%i>o..ar,i 
 
 '- "'l'".' pnee anj the sellh™ prij.""™" ""^ '<"' P"ce, 
 
SI 
 
 «OJ/Jiii670^ AND bliOKEHAGk. 
 
 Ill 
 
 I 
 
 / 
 
 COMMISSION AND BROKERAGE. 
 
 234. Commission ia an allowance nuule to agents or 
 commission mercliaiits for transacting biiHiness. It is 
 usually calculated at so much per cent, on the amount of 
 money received for aaks or expended in purciui^e. 
 
 235. A Commission Merchant or Agent is a person 
 engaged in the buying and selling of goods for another, as 
 the purchase or sale of merchandise or real estate, collect- 
 ing or investing money, etc. 
 
 236. An Agent's Commission for sale is computed 
 on the gross proceeds, and for purchase on the prime 
 cost. 
 
 237. A Broker is one who effects purchases or sales in 
 the interest of buyer or seller. 
 
 A broker does not generally take possession of the article 
 bought or Id. He usually contracts in the name of the 
 party from whom he receives his compensation. 
 
 23S. Brokerage is the compensation paid to a Broker. 
 
 23». The Principal is the person for whom the business 
 "/5 transacted. 
 
 240. A Consignment is property received to be sold on 
 commission. 
 
 241. The Consignor or Shipper is the person who ships 
 the goods to be sold. 
 
 242. The Consignee is the person to whom the goods 
 are sent to bo sold. 
 
 243. A Guarantee is the charge made for assuming the 
 risk of loss from non-payment by the purchaser. 
 
112 
 
 iil: 
 
 COM MISSION ASL hIiOKERAGR. 
 
 S44. The Gross Proceeds of a sale or colketion is the 
 total amount received hy the agent before deducting com 
 mission or other charges. ^ 
 
 345. Tlie Net Proceeds is what remains after all 
 charges hav« been deducted. 
 
 h^T'o"" ^"°""^ ^^'^^ '■' '"^ ^'^f c"^ent in detail rendered 
 by the Consignee to the Consignor, shoeing the sale so 
 the consignment, all charges or expenses attending the 
 same, and the net proceeds. ^^"u'"g uie 
 
 mfdt!;th/"r"* ^"''^^'*^ '^ ^ ^^*^''^^ «f-tement 
 auanh- V ^ ^'''^ "S^^^ *« ^^^ Pnncipal, showing the 
 quantity, grade and price of goods bought on his account 
 
 24.S. To find the Commission on a sale of eoods the 
 gross proceeds, and per cent, of commission befnggiVen 
 
 Solution. 
 •fi.OOO X .OJ = 8180. Ana. 
 
 JoTsl^llf^^J^^ Commission on the purchase of 
 
 which trrso'aTJti"':"'"" '°"f * ^^ ^^^ ^^^^ ^^^^ °' ""^- 
 
 I.- """*/*"».»» ft commission of 20°/!; KinH tlm »™«.,«* < 
 
 his commission. ™' ® amount of 
 
 SoLtTTrON. 
 
 JHy 'n?= ««7-10 = Cost of Bilk. 
 5875.00 X .02 = 517.50, Ans. 
 
 nf^rn!!: J° ^""^ *^^ ^"""^""^ °^ ^ Sale when the amount 
 Of commission and the n^r mnf ^r • . ""'" 
 
 given. ^ commission are 
 
 \r. 
 
I 
 
 COMMISSION ASD liliUKEIiAOE. 
 
 E""'"— I^fceived?245for9ellinKaslnpmentofgood8ata 
 ai.88.on of 0%. How much did I receive for the goods? 
 
 lis 
 
 com- 
 
 SOLCTION. 
 
 6% of amount rcccivod = 
 1% 
 
 100% 
 
 ?2« 
 ?215 X 100 
 
 .'. Amount recoi\cd for goods = S4,;)00. Ans. 
 
 2.11. To find the Commission on an investment when 
 the amount sent the agent includes both the amount to 
 be mvested and the agent's commission. 
 
 t. y^ .^""'"''f . 1—^ commission merchant rccHved a clieck for «S5 15. 
 to be .nvested .n tea after de.luctin, his comn.i.siou „f :; ■.,. How uuch 
 money d.d he invest, and what was the a..ount of his coniinissil; 
 
 Solution. 
 
 The amount to be invested is 100% of itself, the commis- 
 810U IS 3% of amouut invested. 
 
 /. 103 % of amount to be invested = 
 1% 
 
 a>,i6o 
 
 103 
 85,i:o X 100 
 
 lOo 
 
 100 ?i '• „ 
 
 .•. The amount to be invested « 85,000. 
 Commission, ?5,150 _ §5,000 = »i5o! 
 
 «Jon T^'""'"t -•7?''^'"^ ^ol-i a conei^mment of cotton on .-»% commis 
 8ion. I am .nstructed to invest the proceeds in citv nrnn rt.. ^""".""'^ 
 commiss,onof 2,, on the price paid for . .e prtLtr^ wTolZ^ 
 n... ..on .3 8200. Find the amount for which t'he coUon sold. 
 
 SoLnTION 1, 
 
 Take the amount for Mhich the cotton sold as a unit 
 
 then ,i-, of the amount of sales = first commi,s;.,i. 
 
 ^'^ " " = ^''»t is l,.ft after deducting 
 
 Ibt Com. 
 
 ^^yf^i^ 
 

 114 
 
 CUMillSSION A^D UROKEIUQE. 
 
 I? 
 
 i 
 
 i^t 
 
 Cn every ?102 of amount left after <le.luctins Ist Com 
 the agent receives $2 for his second comuiission. 
 
 .-. TI.oa«onf.commiH9ion - ,^ of the amount to be invested. 
 Hence ^ of ,»5?j s jJi-y of sales = »ecowl mmmi.i.-<ion. 
 
 •■• (\hi + 11^5,) of Haifa = A-onf a total commission. 
 t8j of sales =s S'.'OO. 
 
 Salea s »4,()S0. Ana. 
 
 Solution 2. 
 3% + 2% = 5%. 
 
 If the 6% commission had been elmrged on the whole 
 *rr- f/ '• "'' '^^'-^^^^^on would have been 2% of 
 f200 - $4 more. ,-.... the entire commission would have 
 been $200 + $4 = $204 = 5% of sales. 
 
 .". 6 % of galea = 8201. 
 
 Sales = 91,080. Ans. 
 
 Again: If the 5% commission had boon taken on the 
 amount of purchase money, the entire commission would 
 have been 3% of .$2(.0 = $6 less than it was. U. the 
 entire commission would have been $2)0 - §(} = $194 
 - 5 % of purchase money. 
 
 .'. •'5 % of purchase money = ?194. 
 Purchase money = 83,880. 
 
 SoLUTroN 3. 
 
 It Will be found that on every $102 from sale there is %5 
 entire commission. Suppose wo allow for commission for 
 ^elhm,, $•> of tj„ ^102, leaving $100. For commission 
 for purchasrn;,, $3 of the $100, leaving $07. The entire 
 commission would be $5. 
 
 In tlh' former case we have char^red 2% of ?>-^ = tJ cents 
 too much. But in the latter case we have charged 3% of 
 $2 = 6 cents too little, i.e., the .."c'..s-.s- .quals the deficit, 
 and we have still $5 entire commission. 
 
 Thnu, i-Jir of sales = 8200. 
 Sales = f4,0S0 
 
 ^^'msagmfi 
 
t 
 
 1 
 
 ■ 
 
 I 
 
 CuilMISSlON J,\V miUKEUAOK. 
 
 lis 
 
 Soi.cTroN 4. 
 
 L -t 100% = Pftle. 
 
 3 % of sile = First CommiBsion. 
 
 r§3 0f97% = lit ",', of sale = S,<ond " 
 
 3% of sale + l}?'iofHale = Total •• 
 
 ■\\\% of s.ilo = Sl'oi). 
 
 100% of B;i;o = uma. 
 From the foregoing Kohitiuiis wc obtain the following 
 If commisBion ou sale is 4% and on purcluise 3^;^, tha 
 
 entire commiasion = ^ "^ '*_ .• e J nf «al#» «,,>„^. j 
 
 100 + 3' *' ro7i °' *^'^ monej , and 
 
 4 + 3 
 
 100^1' *•''•' 96 ^^ purchase money. 
 
 And generally if we have m per cent, on sales, and n per 
 cent, on purchase, tlie entire commission 
 money, and ^q~ of purchase money. 
 
 Ill 
 
 100 + n 
 
 — of sale 
 
 EXERCISE 67. 
 Find the commission — 
 
 1. On the sale of merchandise for $3,150, at 1\%. 
 
 'I. On the sale of a mill for $8,450, at 2'] "{,. 
 
 8. On the sale of 375 bbl. of flour, at $(5.25 a bbl., at 3;}%. 
 
 '. Oil the })urphafle of a farm for $12,870, at 2\%. 
 
 5. On the sale of '2[:o baLs of cotton, each wei"hina 
 6201b., atHJcentsalb., at U%. ° 
 
 Find the rate of commission — 
 
 . When .$78 ia paid for selling goods for $5,200. 
 
 7. When $84 is paid for colle< ting a debt of $4,800. 
 
 8. When $189 is paid for selling a farm for $7,5G0. 
 Find the amount of sales — 
 
 9. When a commission of $360 is charged, at 21"/, 
 
 10. When the brokerage charged is $48, at i°^. 
 
 11. When the agent charges $59.60 commission at 1^%. 
 
 12. When a commission of $57,824 is charged, at U%, ' 
 
 13. ^^hen the net proceeds are $38.70, commission 3^%, 
 
 14. When the net proceeds are $2,444.55, brokerage J%. 
 
no 
 
 COMMISSION A\n imoKHiiAu,.:. 
 
 F'ndthe amount to bo i„v(.Ht..,| H„.| ,,„„„„•,,. ,„, 
 Jr' ![ tl of ""'"""'' •'"''''•^'•'«'^ '■-•••■"'"'--". 
 
 1.'. W hilt weight of wool, at 52 foiitn ,i II. i . , 
 
 -i «. How iuaiiy l.l.ls. oati lio buy? 
 iJl. All apeut sol.l a houso an-l lot for ^m ron 
 
 ■"■"tH o„ ti,„ farm f„r$,>..,,0 „;"■'"' ""l''«- 
 Fin I H.« ♦^i 1 v'''.->u, on a ( oiiiiinHaum of H"/ 
 
 1 lua tbe total amount of his commiHsion. ^"• 
 
 2-4. An aRont m'oivod $(;i2.6() for h,.Ii;„„ 
 commission of Uo/ \vuJ ! "'"f^ «'"'^'"> on a 
 
 I* /o. AVhat was the amount of his sales? 
 
 -i>. A collector's cliar.'OH for colIppf.'n.T . 
 to ^14 10 at a -'/^ 'or coiiectiM^T ,1 ^^^^^^, ji,„„„ j j 
 
 lo -"M-i.iu, at a commisHion of 6<i: \vi,..f 
 
 26. An agent roccivos $12,501 20 to invest in u». n* 
 
 a commiss on of n "/ Fin,! H, " , " "''''^^ "'• 
 
 in wheat. ' '^" ^ "'' '^'^°""* ^^ "^0""y i» vcMtcl 
 
 27. IIow many lbs. of wool af 97^ o n 
 
 - .M.. ir .a; «... . in; ll^;z:- ,!;-'" 
 
 did he l„,, a„d what . Jtal atout cm Z7 '""'" 
 
 ^5%gi'-.i*^ 
 
COiJMISSItiN ANh IlLohEHAUK. 
 
 117 
 
 .1 
 
 29. l'.ii(l a l.n.k.T |iW.IO r„r l.uy,,,^ l-o hJuihih of r.il- 
 roa.l Ht.,„.k. ,.t Ur,\ % ft Hharc. VVliut wiih tl.o r.ite of inn 
 
 HO. An unrtd in \f„„tr..al ntrnitf.-i $:»,7!>r..r,f; on a h-.N, 
 of r,l() |,„rn.|M „f (|..ur, at $7.2r. a Im.rd. What w,,,h I.jh 
 riit(( of coniniiHHion ? 
 
 ^ Ml. A mil ,.Hl,alo hrok.,r clia^-nH $IH2.}M for invf-Htinq 
 »r2.l.0(; in a fnrtory. VVIiat waH Ihh miu of l,p.k...a '/ / 
 82. I H...II throi,;:!, my i.rok. r 7 toriH of l'„a/.,| nutH al' 
 »7.60 inr cwt. J low uim-h .lo I rocoive if tho l,rokor 
 charges 1% for Holling? 
 
 f 88. Sent $114 to an a«ent in Tr.ronto to hf invrHted in 
 pnnlH. at 12^ - entH a yar.l, after taking out his comrniHaion 
 of 3i %. How many ynr.lH ran he pnr.haHe ? 
 
 t 31. My attorney coll...-te.lH()% of a note fr.r $1,200 and 
 charged 6i % cornmiHBion. What amount hI,ouM he' r,av 
 me ? . ' -^ 
 
 85. An agent Hells a conHignment of Hour for $7 r>l{2 80 
 and then purehanefl 1,840 buHlieJH of wheat, at $1 40 a 
 buHh.J.hiH eommisHion being 2^%. What sura muHt he 
 remit to the conniguor? / 
 
 80. An auction-rr, who ohMi-ed 2% for Belling, found his 
 commiHHion for the huI., of a certain houne jUHt suflieieiit to 
 pay for a Cyclopuidia in 1(5 vohimos. worth ^G.SO a vohime 
 What did the house Hell for ? 
 
 • 87. A commission jnerehaut received a reniittfinr-e of 
 $1,000 to he invente.l in sug.r, after deducting IiIh eonirnia- 
 Bion of 2% The sugar costing Sgc. a lb., how many 
 pounds could he buy ? 
 
 88. How much does a house bring, for which the owner 
 receives $21,2,^.5, 1 -^ of the purchane mo-.ey having been 
 first deducted for the ac^.nt who sold it ? 
 
 W^ 
 
 
118 
 
 CUilMlsSlChW ASl) UlioKERAOt:. 
 
 'Ar: 
 
 V •- 
 
 '.\ f 
 
 mi 
 
 r ■ 
 
 furls M -Mr"'' '""''•^''".'^f ^""'"' »' -^S...), can be bought 
 nlao to he pnid out of this huhi ? « k 
 
 40. A cou.miHsion morcbant sol.l 500 ll.s. „f butter at 
 18c per >.. and invested tbe proccedH in oats at 42,- a 
 JHisbel. I .'. charged .:]% for soUing and Ur, for buying 
 
 o"::irb?;::r^"'-"'"^^^^^^^ 
 
 ^41 A fruit bn.kor .old $G80 worth of apples, ond after 
 'oductmg 0- connnission and 20% for freight and o te 
 c arg .„,,,, ed the bahu.ce i. oranges. How .nuob 
 lie .nve.t .n orangeB if he charged 2 o^ for buying? 
 
 >|^42. My agent in Brantford hoIIs for me a quantity of dry 
 goods on comm.8s.on at li o^. How much must be sold tha^ 
 
 $5,400. after retammg his commission, for buying, of 2i ? 
 48 Sold goods at 2^ % commission, which I invested in 
 
 l^did thtooTstl^rrT^'^'^ ''' ' '---' -' '- 
 
 44 A merchant purchased an invoice of grain which 
 mcludmg a commission of IJo^. eost $5.ofo 65 T 
 
 01 150^ on he entu-e cost, and invested the proceeds in 
 sugar wha, he sold at a profit of 50^. What wa t le 
 amount pa.d tor commission? What the entire cost of the 
 gram, and how much were his profits ? 
 
 .46. A commission merchant bought goods for which he 
 roce.ved 5 56 commission for buying and $63.25 for charges 
 
 Iv2-n W^ °' '""'^' commission, and charges was 
 $3,2o0. What was paid for the goods? 
 
COMUIS.siuN ASU liliuKLliAQK. 
 
 Hi) 
 
 n 
 
 48. An agent boui;lif coflffK at 3"!:, ItrokeruKe, and received 
 $350. He afterwanlH Hold thi; cotft-u at a profit to hia 
 priuciiml of $o,l(;o, after deductiiij,' 1^% (■(HiwiiisKion on 
 the amount for wliicb it wua Hold. How much whb bin 
 oomniisHion ? 
 
 47. I received from Day k Son, of Chicago, a phip load 
 of corn, which I sold for (10c. per huHliel, on a commiHsion 
 of 4% ; and, by the slnitpor's instiuction.s, invested the net 
 proceeds in barley, at 75c. p.r bushel, chaining 5% for 
 i)uying; my total commi.sbion waH .§1,350. iluw many 
 bushela of corn did l»ay \- Son ship, and how many bu.shela 
 of barley should they receive ? 
 
 48. A ButTalo brewer remitted $21,500 to a Toronto 
 commission merchant, with uistructions to invest 40% of 
 it in barley, and thp remainder, less all cliar^^cs, in hops. 
 The agent paid 60e. per bushel for barley, and 2()c. per 
 pound for hops, charging 2 % for buying the barley, 3% for 
 buying the hops, and'5% for guaranteeing the quality of 
 each purchase. If his incidental charges were §187.50, 
 what quantity of each product did he buy, and what was 
 the amount of his commission ? 
 
 > 49. A Toronto factor received from Cinoinatti a consign- 
 ment of corn, which he sold at 75o. per bushel, on a com- 
 mission of 6%; and by instructions of tho consignor 
 invested the net proceeds in wool, at 2Uc. per pound, 
 charging 2% for buying, and 3% additional for guaranty of 
 quality. If the total amount of the agent's commission 
 and guaranty was $l,64u, now many bushels of corn were 
 received ? 
 
 - 60. My Memphis agent sends me an account purchase 
 of 850 bales of cotton, averaging -180 lbs. each, bought at 
 16c. per lb., on a commission of 2^ %. His ehaiges, ulher 
 than for commission, were: frei;:ht advanced, $126.60, 
 
 y 
 
 
120 
 
 COUmSilOS AM, UHOKHHAUH. 
 
 1 1 i 
 I if ' 
 
 O»rtn{jo. 158.2/5, and ir.Hiinui.v Al-j 7« vii 
 Ir.mUto,.aythoac..Jur • '^ ''*' --'-»'-'<i 
 
 61. An nsent Hells a conHi«n,no„t of Roods for *.> ino 
 
 re.nitH $2.0-24 77 F i, .7 ! ' ;"'.""- '"" «'""'ui.-*Hiuo 
 *• ."^-i./?. i-.n.l the rato of his coiiunissioM 
 
 commission. With tho nl . ," . ' "'"' ''"""^^^ ^ % 
 
 at 10c. a ynnl. I ! J ^J->,.c.o.1h l.e .,„,« cotton olotl.. 
 
 o4. A commiHBion mprflpinf i,..^ ^ 
 
 am,„mle,i to Siso Wi.l, ,i, "I"'"""/'"- '•'■•iKlit, ilc, 
 
 •< «}c. . lb., ci, ,:i„, aV"' " ■ '" '"'^' '"«"• 
 
 much sugar docs he buy, and what in 1,7 ' ^' /^"'^ 
 commisaions? " "^^ *'"''""' o^ h«8 
 
 I H 
 
CVHTOM UOUSK UVSINKSa, 
 
 12] 
 
 CUSTOM HOUSE BUSINESS. 
 
 *2Si'2. Duties or Customs are taxtH Icsicd l.y t|,e 
 Dominion GovorniiK.iit on imported ^oodH, for ri'venue 
 purposes and for tlio piohrtion of home industry. 
 
 a«:i. Duties are of two kin-ls. ad valorem and specific. 
 
 a«l. All Ad Valorem Duty is a c rtain ptr cent. 
 RBscHHcd or levied ou the lu-timl cost of the «o.hN in the 
 country from which thoy are imporlcd, as shown by the 
 income. 
 
 2a;i. A Specific Duty is a tax HsstKH. ,| at a certain 
 sum per ton, foot, yard, jrallon, or otliur weight or Uitusure. 
 without referencH to the value. 
 
 No«.-Dpon certain Koode both specific and ad vnlurem dutiea ur. 
 levied 
 
 2««. A Custom House is an office established by the 
 Dominion Government for the transaction of business 
 relating to duties, and for the entrance and cluuauce ol 
 vessels. 
 
 2i57. Ports of Entry are places at which custom houses 
 are established ; and it is lawful to introduce merchandise 
 into a country only at these places. 
 
 iiSiH. A Clearance is a certificate given l)v the C<.!!.ctor 
 of a Port after the requirements of law hav,.'l.on complied 
 with, that the vessel has been properl-. . nterod. 
 
 a«». An Invoice or Manifest is a statem.,nt made by 
 the seller or shipper, giving a description of the same, 
 showing aotuai cost, or value of such meiclumdise; showing 
 also, marks, numbers, quantity, eharKes, and other details? 
 
'L^^.^ilkU.^M>LW 
 
 
 
 ^f^^cT 
 
 i , 
 
 122 
 
 CUSTOM HOUSE BUSINESS. 
 
 a«0. All invoices are made out in th. ■ , 
 
 whieh the importation is made °°°'"''^ ''■°"' 
 
 'te value i. „„t fi.edl^^t'h" ' otru.'tb" ""^' ^ "'=" 
 by a cooeuiar cor.ifieale .Lowing it, vlrj ^™P'""«' 
 
 i™uiieXrd'C:a:ii.r:t^^^^^ '^^ »*« », 
 
 e.em"tfr!m to" '"'" '""'"''^ ='-'» <>' «ood. that are 
 
 impoSdtM'?: " " ""°™°"« "'O^'- '- oni,„ida 
 a««. Draft i, an a„o™„„e made for waete or impurities. 
 
 J^de''""" ""■^'" " "■' -'>'■' t«">" any allowance, 
 „,^,r- '*" "'*" '^ "■» "'Sh' «f'- all allowance, are 
 
 
CUSTOM HOUSE JlUSLWKSS. 
 
 123 
 
 'i-l. Drawback—When distilled spirits, form, nte.l 
 liqu .s, and tobacco upon which an oxcipe duty has b.m 
 paic and foreign m.rcha-idise upon which an import .lutv 
 t^a. been paid are exported, the tax or duty upon the same 
 
 Drawback ''^"'" "^ "" ^'' °' ^'"^^' ^'^ '^^^'^^ * 
 
 274. An Appraiser is an officer of the customs who 
 examines imported merclmndise and determines the 
 dutiable value and the rate of duty of the same. 
 
 37.». A Bonded Warehouse is a place for ttie storage 
 of merchandise on which the duties have not b. en paid. 
 
 Notr^s l.-The law requires an entry for t-ocls to be made within thr, « 
 days after arrival. If no entry is made the ,,x„ls mav be onvey d to the 
 Queen s Warehouse, and may be sold after thirty d.y'. for dut^ 
 
 2. In case goods are warehoused, that is. claimed by the importer and 
 ransferred by proper entry to some bonded warel>o.L. they can^t b^ 
 sold \Mthm two years from the date of such transfer. 
 
 taL''i^"thrn' '"?' w* * r°'' "^ ^"'^-^ ''"'^ ^^« unclaimed, they are 
 taken to the Queen's Warehouse, and are subject to sale by aucfon 
 withm tuirty days. The proceeds of thn sale, after payin, all expe.s T 
 
 z^:ir '° """^'"^ ^''^"''' "''' "^^ '^ ^''^'^ -^^ '^^^^^^ 
 
 276. A Custom House Broker is a person who makes 
 entries, secures permits, and transacts other business at 
 Custom Houses for merchants. He is familiar with the 
 tariff laws, and the details and regulations of Custom House 
 business. He usually acts under the power of an attorney. 
 
 277. To find Specific Duty. 
 
 EXAMPLB.-What is the specific duty on 150 casks of alcohol of 60 
 gallons each, at 20o. per gallon ; leakage, 5 % ? ' ^ 
 
 Solution. 
 60 gal. X 160 . 9000 gal. = Gross quantity 
 Less 5% for leakage = 450 gal. 
 
 8:-5;) gal. = Net quantity. 
 20o. X 8650 . 91710.00 - Speoific duty. 
 
 'm^!ms^mm^^r...w^. 
 
) ^isk- 
 
 
 124 CUSTOM HoaSK mrsiSESS. 
 
 27». To find Ad Valorem Duty. 
 
 '- '^n: .rp! ;ui:.:t -::r:--^; « -^ . .0 bo,, o, 
 
 »'.'c.a]b.. taresib. porbox? 
 
 nill.UTION. 
 CO lb. X 120 = COOOlb « Orno • . 
 
 81b. . 1,0, (mo ,b::?,r "«•«'>*• 
 
 '■'O'Olb. = N.twoi«ht. 
 ^ fo. X 5040 = J.1 -.3 60 - vw , 
 
 •^•^•'60 X .,0 = L,2 : i;;;:''"^- 
 
 (li 
 
 ,bV«- 
 
 f i 
 
 I f 
 
 ? i 
 
 it 
 
 I 
 
 
 M, 
 
 f f<! 
 
 
 EXERCISE 68. 
 Find the c,:ecific duty— 
 
 'b., d„.°"3fe'.':';b"'' °' '"• ^'' -" ">■■ '"oieod „. Uo. a 
 
 «"ot-.°"sJ:t.'::T.3irfn;. '■™= «■■«"' >« -b. each. 
 
 5- On 60 packages of ^a. enph t« n 
 per lb., tare 5 %. ^ ' '^'^ ^^ ^^- ^'^^Sht, at 2ic. 
 
 6. Ou 897,120 lb. of bituminous eoal at 7-. 
 
 7. On an importation of 200 bo.l of , T '"^• 
 box containing 20 plates 21 x 48 » ^ ^^^''''' ^''"^^^^ 
 eq- ft. r 1 X 4s,u. jn gj^e, at 25c. per 
 
 '« 
 
 ^^»r.ft3^^^o*i 
 
CUSTOM HOUSE UUSINESS. J2B 
 
 Find the ad valorem duty— 
 11. On 16 tons of Htoil. invoiced at ISc. per lb., at 25 %. 
 U2. On 175 boxes of raiHins, 18 lb. per box, at 17%. 
 
 13. Ou 6.->0 doz. kid gloves, invoiced at $6.50 a doz at 
 62 %. 
 
 . 14. On 600 Ral. sperm oil, of 42 -il. eacb, invoiced at 
 46c. a Ral., at 20% ; 3.i % being allowed for ki.k;.-... 
 
 15. What is the duty at 10% on an invoice of Fren.h 
 jewellery, nmountiiirj to 8,560 francs? 
 
 16. What is the duty on an invoice of books from Vienna 
 the value of which was 6,42f» tl ninH. at 38%. 
 
 17. What is the duty on an invoic- of linens amounting 
 to £'3,256 sterling at 27 %, allowing $4,866^ to a pound ? 
 
 18. Find the duty on an invoice of woollen cloths from 
 Germany valued at 8,4.17 lieichmarks, at J->%. 
 
 19. What is the duty on 1,000 yd. of i.russels carpet 
 27 in. wide, invoiced at 6s. 9d. per yd. ; duty 44c. per sq. yd! 
 Bpecilic, and 35 % ad valorem ? 
 
 20. An invoice of woollen cloth, imported from England 
 was valued at £dn(j (Js. If its weight was 684 lb., how 
 much was the duty, at 50c. per lb. speciiic, at 35% ad 
 valorem ? 
 
 /21. I imported from the United States 7,240 bush, of 
 corn and 17} tons of hay, invoiced at $y.5'i per ton. What 
 amount of duties had I to pay, at 15c. per bush, on the 
 corn and 20 % on the hay ? 
 
 22. The duty, at 19 %, on an importation of satin, is 
 1309.70. What is the invoice of the goods ? 
 
 23. How much duty must be paid on an importation of 
 27.640 1b. of wool, invoiced at t'!,!97 !0s. 4d., if tho rate 
 of duty is 10c. per lb. specific, and 11 % 
 
 /o 
 
 ad valorem ? 
 
i^ 
 
 IJ ! 
 
 126 
 
 CUSTOM HOUSE liUSlNESS. 
 
 i^^ What in tl>. duty a.ul total cost of ii.r,00 ..iec-eg 
 
 «v 1 7 J '^ '^ *•'" a'Jiomit of a bill of 
 
 o HI 5> i.«/ to the i to covtT the cost ? 
 
 '•^5. Fijul the duty on 50 cason of f,.i... . i ... 
 
 ''0 II... and 00.000 iLvannaX I H^^'^^t ""''"^! 
 '^^ ^^75 per M.. the dutv bcinr^SOc 'tr .' ''''"'". 
 I 'a, to and ,S2.50 per lb. specific on the ci-ura and 'iT o/ 
 ad valorem on both. '^ ^ 
 
 lo., tare J ^ What was the rate ? 
 ii7. Eequired (he duty and total cost of ] cubo of Fr^nM 
 
 :it:;.r--rjt.r4" - -- 
 
 Bhiumnc flfp r9- f "^'^"cs duty .50 0/, t^M'enses, cartage, 
 enipl'ing, etc.. (.2o francs, and commission 2^ %. 
 
 28 A merchant imported 80 pieces three-ply carnet 7fi 
 sq. .ya. HI a piece, and paid $2,591 84 <lutv It^r 
 sq. yd., and 80% ad valo em. What wa th ^'' 
 
 IHT yd., in sterlmg nK.ney ? '^' '"'"'"^ ^'^'^^ 
 
 . ■^. A merchant imported 800 pieces of three-ply carnet 
 each p.ece contanu-ng 75 sq. yd., invoiced at oV 61 per 
 H .yd., upon winch he paid a duty of 17c. per so vd 
 specific, and 35 o^ ad valorem. What was tl « f.f^ ^" ^ 
 of duty paid ? - ^ *^® ^"^^^^ *^"^ou"t 
 
 / 
 
 30. On40ease8oftobacco,eachw.ighing65Ib and 20 000 
 
 avana cgars. weighing 200 lb., in^-oiced at $ ''T 
 
 the uty on tobacco being $.80 per lb., and on cLu I'll 
 
 per lb. sm'cfic, and 40 °/ ad valorem. ^ ^ ^ 
 
 Nalued at i42 os., 1 cas. of linens at i'37 IDs., duty 40 % ■ 
 
r'M' Vhi^^ 
 
 cvmoii uuusi: n us in ess. 
 
 W 
 
 I cnne prints at £h r,.., .I„ty 20%; incidental exivns.. 
 
 II OH., comn.,Hs.,.„ 2i % • oon.s.il's fws 158. What is the 
 total cost in Cana.liau money ? 
 
 82. W. A. Murray & Co. imported 10 caeofl of shawlH 
 averaging 216 lb. a case, invoiced at 2IHH.1.10 francn Tj 
 duty l.e.ng ^0. , ,b., and 35 », ad valo^cu. 1 .i ; 
 
 Zd'.; "un '"' "f«-'-"«^-. bought at 5.1. f.-a.. s to 
 
 he doHar. What waH the duty, and what did the shawls 
 
 cost, after paying other charges to the amount of $75 i^U? 
 
-Iw ■" 
 
 'Ml 
 
 INSUHANCB. 
 
 
 INSURANCE. 
 
 n I 
 
 27». Insurance ir a ronf met by wl.i,!, one party 
 
 ^^ nch ,.no,lK.r n.ny s..s,,.i„. u in .liH.in.ui.i..! , 
 
 iZj''"';"- •'•• '''"' '— '-. Accuin.t J...unu.:., 
 
 ana llrnlih Insunince. 
 
 JiHO. An Insurance Company is a company or c.rp,.. - 
 ation wind) insures against, loss or (L.nia^;o. 
 
 to prnir.plos of orKanizution as follows —1 V/ . •/ 
 
 cnnirv?'«f^ f °''' Insurance Company is one in which tho 
 en itvl stock H owned by the mombrrs of the connniiv 
 on od stockhoMors. They alone share tho proatsS' 
 liable for tho losses. 
 
 The bu8i„es8 of a stock company is managed by directors 
 chosen by the stockholders. ""tciors 
 
 a«;j. A Mutual Insurance Company is one in which 
 the^persoua m.ured receive a share or division of the 
 
 2Si. Non-participating policies, the holders of which 
 (10 not share m the pn^^^ts nr I,io-aa nv- • j i 
 ,„„i, I 1 • I " -t^ or losoea, are idsued by certain 
 
 mutual and mixed companies. 
 
IN.SU/iMNCIi 
 
 12'J 
 
 tsnn. A Mixed Insurance Company .« one, whiH. h 
 X^""'' """ '^ -•"'"•"^^' f U... LrM an,. JuZ 
 
 nJHaH Ju" '?"'■"■ °' Underwriter Ih tl.o ,„.rty who 
 'tHMUnoH th. r.sk, or aKr,....H to in.l..n.n,l> a,,,,,OHt Iohh 
 
 i£H7. T\w Policy iH ilj« „H„„. „,.,,li,.,| to tl„. wrifton 
 
 aKr.ouu.ntof.oM,rnotl,,.tw,.„th,,InllnuH.M;o, .," ; 
 
 a.SH. A Valued or Closed Policy Ih o„o in wl.ir-h the 
 -nonnt n.nun.l .« clHioUHy do,..nn,n..,l at tho t 
 '""uran,.o ,H ofT..t,ul. Houhoh, fun.i(,un, an,| «oo,Ih in ' 
 Btor« aro i„Huro,l in poli.i.H of thiH kin<l. 
 
 _ a.S1». An Open Policy ia ono „pn„ which arlrlitionaj 
 .nHurancoB n.ay ho entor,.] at anv ti mo from po.t t 
 
 at rates and nndor conditionn agrood upon. ' ' 
 
 2ttO. TlH. Premium in the amount paid for the ir.suran.o. 
 a»i. Ar. Insurance Agent is a per , on who ropr.sentH 
 on« or more Insurance Companies, and acts for hem n 
 Bohc.tmg husmess. collecting premiums, adjunting Ioboh. et " 
 2«tJ. An Insurance Broker is a pernor, who effc-.t'- 
 insurance for a compensation called brokerage or commit- 
 Bion. 
 
i i 
 
 i ■ 
 
 1 
 
 I 
 
 in 
 
 r! 
 
 i;<0 HKK ISSUUANCK. 
 
 FIRE INSURANCa 
 
 21l». Fire Insurance refers to insurnncn against loss or 
 JaniaKo by lir... Losses may 1.." total or partial. 
 
 a«l. Fire Insurance Losses am imnally adjusted by 
 Iho iiiHiiiaiu-o toiiii.aijy p^yin.^ tlif full amo.iiit of the loss 
 provi.lo.i tl,:.l Hucli losH ihn'.H not i-xnr,l the sum in.sun.l • 
 if the policy, however, contains the "average clause " the 
 payment made is such proportion of tUv Iohh as the 
 amount of nisuranco boars to the total value of the 
 proptrty. 
 
 aSK"5. The Term of Insurance is the period of time for 
 which the risk is taken, or the property insured, 
 
 a««. Short Rates are certain rates of premium charged 
 by the companies when the term of insurance is less than 
 a year. 
 
 2S»7. In case a policy is terminated at the request of the 
 insured, he is charged the "short rate" premium- if 
 however, it be terminated at the option of the company' 
 the lower long rate will be charged, and the company 
 refund the premium for the unexpired time of the policy. 
 
 2»«. To guard against fraud, property is not usually 
 insured for its full value, and no more can be recovered 
 than tlu. Jimount of actual loss. The party insured must 
 also have an interest in the property insured. 
 
 aiMI. Dwelling-houses and permanent property, about 
 the value of which opinions differ, and which deteriorate in 
 time, may generally be insured for from one-half to three- 
 fourths their estimated value; goods in store, at their cash 
 value. 
 
 Insurance companies usually reserve the privilege of 
 rebuilding, replacing, or repairing damaged property. 
 
 ^^^m!Sim^i:sm'<<iM^s^'^'m,£mrd 
 
 'i^M r 
 
 •"■ia/'Vip^-itS^r 
 
MAiaSK ISsUliASCK. 
 
 iUl 
 
 MARINE INSURANCE. 
 
 »00. Marine Insurance rofers to inHuraiic.i of vcs„el.s 
 and their ciir^oes a^uiiiBt tlie (lii!i^,'(T.s of imvi^itiou. 
 
 «OI. Inland or Transit Insurarce rofti-s to in.siinuieo 
 of lULTclmiuliHe wliilo bcin^' tnmsporttMl froiii i,!;i,-,. to placo 
 either by rail or water routoH, or both. 
 
 :I02. Marine Insurance losses are adju.stcd by tiie 
 insurance conii)any payi.i;,' only such a proportion of tho 
 loss as the Hiim inHiircd ia to the <ntiro \aliio of tlit- vessoJ. 
 
 'IO;i. Policies on Cargoes are is.siicd for a (Certain 
 voyaj^'e, and on vesHtda, for a V()ya.,'o, or for a «[. ..-ili,.! time. 
 
 »OI. Salvage is an allowance madu to tlio.s.; reiidf-ring 
 voluntary aid in saving vessels or carf,'oes from in;ui)ie 
 casualties. 
 
 ;«0*"i. When the insured ships goo.ls, or receives infor 
 mation of goods shii)ped to hiu), he must notify the insur- 
 ance company as soon as he is in rtcoipt of bill of hulinr^ 
 or other advice of shipment, that it may be entered on the 
 open policy. 
 
 iiO<S. Goods at sea may generally be insured from 5% 
 to 25% more than their cost or invoice price, in order to 
 cover the expenses of freight, insurance, and a share of the 
 profits. 
 
 307. To find the cost of insurance, the amount 
 insured, and per cent, of premium being given. 
 
 Ex.\MPLE.— A house and its coiitcntn arc insured for 88,500. Wha» 
 is the cost of insurance for one yeitr at li% premium ? 
 
 Solution. 
 88,600 X .015 = S127.50. 
 
 RULB. 
 
 Multiply the amount of insurance by the rate per cent, of 
 premium, and the product ivill he the cost of insurance. 
 
av' .f '%'i'* "'?tm\','f4i9^- 
 
 : 1: 
 
 
 jr.. 
 
 i 
 
 I. 
 
 I 
 
 I ■ 
 
 5 J* 
 
 Jfi 
 
 182 
 
 MAlltSE ISSVliASCE. 
 
 thTH^r ^^^"? ^^"^ ^"""""^ '"^"'■^^' *he premium, and 
 the per cent, of premium being given. 
 
 Ex,m;.K -I pai.i e'70 to innure a sto.:l; „f «„„d. ^r one vear at . 
 pr«u.um 0/2% For what amount wan the ,,ol.oy uuuri? ' 
 
 RoiUTION. 
 
 2% of amount of policy = 6170 
 
 1% " .. „ no 
 
 100% 
 
 ^ 170 X 100 
 
 ■■ ?8./n(). Ant. 
 
 » S8,o00. An«. 
 
 .*. Amount of pnl'r y 
 or 
 
 &170 + .02 
 
 KCLB. 
 
 Duide the premium hy th- rate per cert, of premium, and 
 me qunttent will he the amount tiisnred. 
 
 3«». To rind the rate per cent, of premium, the 
 premium and the amount of insurance being given. 
 
 J.XAMii.E.—l j.aiu ?8.-, i.remiam on a house insured for 9---^ 
 wnat was tho nito per cent, of insurance ? 
 
 SoLnTION. 
 
 Cost of insuring »f.,800 ia 885 
 ,. 85 
 
 81 
 8100 
 
 (ksuO 
 
 83 X 100 
 ' r,800 
 ij %. Ans. 
 
 ■0125, orlJ%. Ana. 
 
 .'. Bate 
 or 
 
 185 -^ 8G,800 
 
 RULE. 
 
 Diride the premium by the sum insured, and the quotient 
 M m tic the rate. 
 
 3IO. To find the sum to be insured that will cover 
 bo h premmm and insurance, in case of loss. th. vaLe 
 of the property and the rate being given. 
 
 EiAMPLB— Fc- ^iii.t iimount must property worth »7 .vin i 
 
 oTtl :o:^'''- ", *'"- •" "'-' °' '^^^' ^""^ 'be prSiuT nd he v.u e^ 
 of the goods may be recovered ? ^ 
 
MAlUNh lHaUlUNCE. 
 
 laa 
 
 HoLCTION. 
 
 To realize 905 we must insure 8100 (8ince5i.pai,l in promium) 
 " 91 » 100 
 
 '.».■. 
 f,«« .. Kill V 7flnrt 
 
 • 98.000. Ana. 
 
 " 17.600 
 
 or 
 
 100% - 5% 
 •7,G0O + .!»,-, 
 
 RCLI. 
 
 'J.5 
 SH.OOO. Ana. 
 
 _ DtVtrf^ the value of proprrt>, by 100%, minus the rate of 
 tniurunce, and the quotient will he the sum insured. 
 
 311. To estimate proportionate losses. 
 
 li.!nrt^^r«,'~'^ merchant innurud «l'.500 in the On'ario Matual 
 $1,500 ,n the PLcBn.x. and J;.,r,00 .n the Western. A loss by tire of $6 000 
 occurred. How iiiuch should each company pay? oi^o.vw 
 
 SOLUTIOM. 
 
 12,500 Ontario Mutu»l. 
 
 1,500 l'ha>nix. 
 
 _3..W0 Western. 
 97,500 = Sum insured. 
 
 •6,000 + 7.500 = .80 
 
 2.500 X .80 = *2,000 
 
 1.500 X .80 = 1,200 
 
 8,600 X .80 = 2,800 
 
 R ito of losa on 91. Ex. 
 Share of Ontario Mutual. 
 Phanix. 
 " Western. 
 
 RULE, 
 
 Divide the loss by the total in.virance, the quotient will be 
 '•he per cent, which each must pay. 
 
 EXERCISE 69. 
 
 1. What will it cost to insure a factory worth 1^20 000 at 
 i%, and machinery worth §1G,8U0 at |%, with $l.o() for 
 policy ? 
 
 2. What premium must be paid for insuring $6,500 on 
 a store for 3 years at 2 J % ? 
 
> ■ ■ 
 
 ' 
 
 ' 
 
 1? I 
 
 t * 
 i 
 
 \, 
 
 fi 
 
 i:n 
 
 M.ansi. ISsUiiASCK. 
 
 '■'""•"' •^'- '""• •^"'i'-- ^h- 1>-I<H un.l furniture w.re 
 ...sure fo,- ,s,ooo :a th. h,uuo rate. What did I p a, 
 •'""""ily for iiismMii..,. on Imtli ? ^ ^ 
 
 ^«. II si-JA are pni.! unnuully for insurinK $24,000, what 
 'H iiic nitr per eont '? 
 
 5. I'ui.l :=;:!.-Onn a Hhipment of ;.o,>.Is to insure 3 the 
 v<'l..o. at in :.. What was the whole vuh.c ? 
 
 G A hous.. is insurc.l af j} -. and the pron.iura is $tK).60. 
 i-orliow much 18 it ii.sm-cdV 
 
 7. '''l'" n.r«o of .steamorG;inion. hound for Liverpool ia 
 ^ «. A „,a,iun,..l,,ri„K c™,,,:u,.v ,mi,l S214.80 ,,re>„i„m for 
 
 ^ 10. A merchant sent a cargo of goods worth $25,275 to 
 Canton. ^Vhat sum must he get insured at 3%, that he 
 may Ruffcr no loss, if the ship is wrecked ? 
 
 of !'; wortl! Si" rf '' "'""'' '^ '^' '^^ ^ consignment 
 Of tea worth $-1,200, to cover property and premium ? 
 
 12. A shipowner insures a ship and cargo for $80,.S26. at 
 
 Wli:; , ^7 TT'^ '^"''' ^'-'^''''y ^"d premium. 
 \\ hat 18 the value of the property ? 
 
 13. If a warehouse is worth $266,250, what sum must 
 be insured, at 2%, to cover the property and premium? 
 eo";/^', premiums paid for insuring two stor.e are 
 po.24andW46.50; the rate is 1| o^. What sum must he 
 insured to cover the property and premium ?;^^ J 
 
U A Hist: INHUUANCM. 
 
 185 
 
 ' 16. The loss by fire on a Htorc luid cont. nts wns * t.')2r. ; 
 the property was insiir.).! $•_',;•)(«> in \V. stt^rn. $ ! "tii in 
 Hritirtli Atnerieaii. $i OOO in |'r.,viiici;ii, an. I §:i,(«j() 1,1 
 Royal Canadian. J low iiiuch ishoul.l each pay ? 
 
 16. Tlie loss hy fire on a pi,co nf proii'Tty \v:m >?S,Onn, ,,f 
 which $2,000 wis itisur.Hl in tho Ortiiua A^jriciiltu,..!, 
 $M,000 ill tho London Mutual, and r^;>,(i()u in th. ('it,/,, n. 
 IIow much did uuch I'onijMnv (•oui-'\)\Ui? 
 
 *\7. A block of stores and contents was in^ur<d for 
 $'2'>0,0()0, und hooatno daiua^'ed hy lire and u iKm' t.) tlm 
 nniount of $l.')0,(l()(). <)f ih,. riH'.;," $ {0.0(»(i ^vi, taken l,y 
 the Q;;el.oc Co , §<;.-),000 l>y tie J^riti.sh AuiM-ir 'u, ,«;■.:,. (x^o 
 by th( Western, and the reni;iind(r was .lisided i,|u.i!lv 
 between the Hoyal Canadian and the London Miiluii. 
 What was the net loss of each company, if the premium 
 paid was U%? 
 
 18. A man owin<? J of a ship, insured I of liis infer, st at 
 U%, and paid $9L50 for preminra, and a policy ch;iige of 
 $1.50. If the ship lieeoraes daraa<,'ed to the extent of 
 •712,000, Low much can be recovered on the policy? 
 
 19. For how ranch must a house worth $G,000, and 
 furniture worth $2,000, be insured, at 11%, to co er the 
 cost of the policy, which was $2. the amount of premium 
 paid, and J of the value of the property ? 
 
 20. A schooner is valued at $10,500, and has a carj^o of 
 8,500 barrels of apples, worth $2.10 jter barrel. What 
 amount of insurance must be obtained, at 2>-%, to provide, 
 in case of loss, for the value of the property, the premium. 
 and $5 additional which the owner paid f *r survev and 
 policy ? 
 
 21. The furniture in my house is estimated at one-half 
 the value of the house. I get itoth insured for $7,0875) 
 
 ^or 5 years, at 2^%, and find that in 
 
 case of total destruc- 
 
 flu 
 
186 
 
 MARINE INSUJtANCJi. 
 
 tion the face of the policy will ha r u ■ ^ 
 -..ert.a.p.L,n----^^^^ 
 
 for $62,500 r$s7m TtT '" '"'"^'''' ^'*'^ ^'^ contents, 
 
 stock worth $35,000 A fi I ^ 'T' *"^ ^^^O.OOO on 
 ing and the n^achinor^ ar iT'.' ^^ ^''^^^ ^'^^ ^uild- 
 anaount of §15,000 "'., 'he ^f''''^^^'^' each to the 
 How much is the cj;i.uta 't th " '""'^^'^ ^^^^*'«3^^^- 
 
 pohcy contains the" average cCe?" """'^ ^^ *^^ 
 
 goods ttthTiti::f4: '*? ^^^^^ ^^2'«««' -d 
 
 of their value, at herat oVT ''' L'""^ ^^'^ '°^ ^^^■""r'^^ 
 
 wboaiiows hi. a^::; ;ti7fr'tr"°^'''^^«^-' 
 
 retains 5% himself. How much /. °" "^^P^-^^^'um and 
 the merchant, what does tlTl ^ *^' '"'"^'^"'^^ «««t 
 net premium receivl/^^thel^Xf ^"' ^'^^ '' ''' 
 
 wo?th $1 w'TeIr "r '^' ^ ^' ?^ ^^'"^' '^ ^-^^-^ 
 of 1 %; the second J of T^7^ ^'^'^ * ''" ^•'■^^^' «^ I 
 remainder, at J of J i Fin J I } "^' '"'' ^'''^ ^^^^^d, thl 
 "toij^. find the total premium? 
 
TAXKS. 
 
 18; 
 
 TAXES. 
 
 »ia. A Tax is the sum assessed on the person Dronertv 
 income of an individual for local .mprovLent.' pajme^ 
 of officers, support of schools, and other general purposes 
 
 318. A Poll Tax is a certain sum reauirpd of «o„», 
 ™.ecu..ea liable to u^atioa, .itao.t JZTt Us^pt 
 
 ^**- ,^ f'oP'^'^ T>x is a lax assessed on real or 
 personal estate and is assessed at a given rate per e' o 
 
 Xtr:;","'."'"""^ '' '" ""^ "-" " »'°»' "'■•' 
 
 SIS. Properly is of two kinds,-Real and Personal 
 
 .SnJ-Zn't-ct^::^:-:^-: 
 
 ...oipalU. and l.e XZ t^t^prsrsMS: 
 tHxir* "^ ^°"^'**"' '' ' P'"°° ^PP^'^t^-i to collect the 
 
 y. 
 
188 
 
 TAXES. 
 
 Of tfxatiL^ ii^\]::: ''' ^""^ ^^^^^^^^ -^ ^^^ -te 
 
 the Jrz-ut ::: tiZT ^" " '^-'r °^^^ '^^ "* -«•« - 
 
 for »12.000? *^ ^^ " P''"°" ^ho«e property wa» assessed 
 
 SOLDTION. 
 
 On $1 the tai. is .001125 
 .-. " »12.000 .. .001125 X 12000 - ,185. A„s 
 
 B0LB. 
 
 .WOOO. Wh.. , Jo, JJnwrC rS ''"" "'"^ " 
 
 Solution. 
 On 8229,000 there ia a tax of $5,725. 
 ••. " »1 " .. 5,725 
 
 229,000 ~ **'• •^"■* 
 
 BULK. 
 
 «lned at »12,500, and who pays for 2 polls V ' " ^^^^'^^ "' 
 
 Solution. 
 
 IIL °fff; • ^°'0'>°tofpoiit«x. 
 
 82 
 
 •16,230 
 
 810,000 
 812,500 
 8250 
 
 pn!Sti?* J"" u"^ '^"^ ^""^ assessed, the rate of taxation 
 and the tax being given. "-lAtcioa 
 
 JOxAMPLE.— The tax on a certain property was 8% in a„^ »u 
 
 iJfer;-^is 
 
i 
 
 TAXES. 
 
 SoLniioN. 
 10.00776 is the tax ou U 
 
 " .. J _ 
 
 .00775 
 
 •96.10 - •> 
 
 189 
 
 •1 
 
 5'C.io ,,„ ,„„ . 
 :00775- " •^^■^°°- '^°'- 
 
 »1 
 $38,800 " 
 
 BULK. 
 
 Uiiide the tax by the rate of taxation, and the quotient will 
 be the sum assessed. 
 
 ;?t> 1. To find what sum must be levied on the assessed 
 valuation to raise a i 'ven net amount. assessed 
 
 » .V f ^^^^^f^^"- What sam mast ba levied to raise 833,800 not. allowing 
 8 % for collection 7 "*"» 
 
 Solution. 
 To raise «97 net, 81 - must be leried. 
 100 
 
 97 
 
 100 X 38,e00 
 
 • 97 " " - »40,000. Ana. 
 
 or 
 ei.OO - .03 = .97 
 838,800 -^ .97 = ?10000. 
 
 BDLS. 
 
 Subtract the rate allowed from SI, and divide the net 
 amount to be raised by the remainder.- the quotient will be the 
 turn to be levied. 
 
 825. When the rate of taxation is ascertained, for con- 
 venience a Tax Table is usually prepared ou tliat basis. 
 The following is based on the rate of 8 mills on the dollar. 
 By its use much labor and time may be saved. 
 
 Tax Tablb at Three Mills peb Dollab. 
 
 • $ 
 
 1 pays .003 
 
 2 " .006 
 
 10 pay 
 20 " 
 
 9 
 
 .03 
 .06 
 
 100 pay 
 200 " 
 
 .30 
 .60 
 
 1000 pay 
 
 2-00 " 
 
 « 
 
 3.00 
 
 6.00 
 
 9.00 
 
 12.00 
 
 15.00 
 
 IS 00 
 
 8 " .009 
 4 " .012 
 6 " .015 
 6 " .018 
 
 30 " 
 40 " 
 50 " 
 60 " 
 
 .09 
 .12 
 .15 
 .18 
 
 300 •' 
 400 " 
 oOO " 
 600 '• 
 
 .<)0 
 1.20 
 1.50 
 1.80 
 
 3000 " 
 4000 " 
 5000 " 
 6000 " 
 
 7 " .021 
 
 70 " 
 
 .21 
 
 700 " 
 
 2.10 
 
 7000 " 
 
 21 ■■■■0 
 
 8 " .021 
 
 70 " 
 
 .24 
 
 800 " 
 
 2.40 
 
 8000 " 
 
 24 00 
 
 9 " .027 
 
 90 " 
 
 .27 
 
 900 " 
 
 2.70 
 
 9000 " 
 
 27.00 
 30.00 
 
 10 " .030 
 
 IM " 
 
 .80 
 
 1000 " 
 
 3.00 
 
 10000 " 
 
,4 
 
 H: 
 
 II ;: 
 
 >V i 
 
 140 
 
 TAXES. 
 
 SOLCTION. 
 
 Tax on 82,000 a »6.00 
 
 " 400 = 1.20 
 
 70 « .21 
 
 5 = .01} 
 
 •I 
 
 II 
 
 82,473 = 87.42}. 
 
 EXERCISE 70. 
 1. My property is assessed at $6 400 Af fK. . , «, 
 
 he paya . rate of sTx ? *''°'"' '" ''"""■"" P'oP^'y. » 
 
 a»i.t; ro"::.:': ri/^z-r'-' ^ ''•'^■'^- ^ 
 
 and what was the tflT nn o V * ^""^ ^^e rate, 
 
 ««. was tne tax on a farm assessed at $4 000 ? 
 
 pa. an aa.H«o„. .. ,, , ,„,,, \:^Z.''^;^ 
 collection ? ^ *^'^^^' *"^ P^J ^ % for 
 
 i' he pay. H « City tai, li t:Ti, t r°™' '"°'""^- 
 
TAXES. 
 
 141 
 
 I 
 
 9. A Town-hall, costing $12,250, was built bv a tar 
 assessed upon the property of the town. The tax rate was 
 6 mx s on the dollar, and the cost of collection 2% Wha 
 was the valuation ? ;• — ^ ^^ 
 
 taxa^t'io!,^7 T'^r*^ '•' '"^"''^ "* ^'^■^^' '^"'^ th« rate of 
 taxat on or school purposes is 5 mills on the dollar, what 
 
 does the tuxt^on of each one of my three children c slme 
 If all of them attend the public schools ? 
 From the table find out how much— 
 
 11. Mr. W. h. nun pays on $ 6.000 
 
 <i 
 
 $ 6,583 
 $ 6,354 
 " $10,000 
 " $ 7,534 
 $ 5,821 
 
 12. Mr. M. Howard 
 18. Mr. H. Brierly 
 
 14. Mr. E. Munroe 
 
 15. Mr. W. Galer 
 
 16. Mr. D. Turnbull 
 17. Make out a tax table, rate 16 mills on the dollar. 
 
 -^18. Allowing 5°^ for taxes uncollectable. and 2% for 
 CO lection what sum must be levied that $50,000 mly be 
 realized for the building of a school-house ? : 
 
 J^\ ^l' ^?r'" "^ *^' ^"'"S' °f ^'^"^i"^ ^vish to levy a 
 tax which will net them $18,979, after paying the expense 
 of collection, which will be 8 %. The assessed value of rell 
 and personal property is Sl.260.000, and there are 828 
 polls, each taxed $2. How much will $1 be assessed ? 
 
 wS Im hV H r^ on property valued at $1,856,000. 
 V\hat wll be the tax on Dr. Burns' property, which i» 
 valued at $8,Go0 ? j-, »u«.u u 
 
 21 A bridge costing $18,135 was built by the proceed. 
 of a tax evied upon the property of a town, the rate of 
 taxation being 50c. on $100 (5 mills on $1), the cost of 
 collection being 2^%. What was the assessed valuation of 
 the property ? 
 
 »r9""if». 
 
 warn 
 
142 
 
 I! 
 
 TAXES. 
 
 22. If the assessed valiio of (he roal o«,i 
 property of a city is $80,000 „00„.l a ' f'^^""' 
 desirtul for the constn.etin. '"'""^ ^** '• 
 
 rate of levy to rea i ' ' Oo f^T' "'"' '"'^^ '^ '^' 
 
 allowed for collection aLd 40] of h. T'^'"' '^ ^^ ^« 
 
 aiM 4 ^ Of the levy be uucoilectuble J 
 
 valted'lt%?;000 1'h.V^ "h""1 "''°" '^ ^''^ ^^i' 
 
 p--yth!tratlf';ji:y-:---^^^ 
 
 The .L-SL' ;;^^^^^^^^^^ ^^21.073. 
 
 interest. $6,850; higCy4 $7 seT T''°"^'' ^'^ ^ 
 and continseut expense? lis ttrf v. "■""' •^'■^^^' 
 levied on a dollar toZZ' ^' '"' """'^ ^^ 
 
 fund of $7 00^ r ''^'"''' ""'' P^"^^'^^ » ^i^l'ing 
 
 r 
 
 525r1 
 
MISCELLANEOUS. 
 
 MISCELLANEOUS. 
 
 14a 
 
 EXERCISE 71. 
 I. 
 
 1. A commission merchnnt. whoso rate both for sollinr. 
 and invest ng is 5% receivPH 91 (\(\f\ ik r , ^ 
 
 a lb anrl «q nnn • "''f ''''" f ^'^^^ l^'- of pork, worth 0,;. 
 a Jb., and |3,000 in cash, with instructions to invest in a 
 shipment of cotton. What wil, be his entire comZi:: , 
 
 i- Having sold a conhignm, nt of cotton on 3% commis 
 son I am instructed to invest the proceeds in own" 
 after deducting my purchase commission of 2% Myt^^ i 
 
 ZTsT '' ''''' ^°^ -"^^^ --^ ^^^^ ^--t in 
 
 «oods must be sold, that my ^JtJ^',Z:::l:^ 
 the avails, to the value of $3,500. after retaiing^^ 
 purchase commission of 4 % ? luuiing nis 
 
 J $7 247°"'?'" ""''"i""' ''"' " consignment of wheat 
 for 17.240. He pays $40 for freight and storu^^e and 
 charges a commission of m. What are the net prot^ls ? 
 6. A merchant buys, through an agent. 480 vds of 
 carpet at 80o. per yd., and pays the agent | % comn "ion 
 The freight amounted to $1.92. At whaf L. '°'\- 
 
 must the carpet be sold to realiz; a prolt of 33^%^ '"' 
 
 85o' I Ttr^ ^f^ ^""'^'^^ °^ ^^^^t •" Winnipe. at 
 85c. a bushel, and shipped the same to my a^Lr Z 
 
 Ottawa who sold it at ^1.10 per bushel. How murdid r 
 
 make, after paying $543 for expenses and a comrssiot of 
 
I 
 
 144 
 
 MISCELLASEOUS. 
 
 Dour After deducting his commission of n% and S20 2S 
 for other expenses, ho. many barrels of flou/ at $ a bate 
 will the money purchase ? -^ ^o a oarrei 
 
 8. A flour merchant in Montreal remitted to his corres- 
 
 amn.mf nf +1 ".*«"°'^' ** ^i /° premium. ^Vhat was the 
 
 amount of the consignment, his commission being 2^ % ? 
 
 9 Sold 2.978 bu.hels of wheat at $1.06 a bushel- 
 invested the proceeds in suRar. as per order resLvinf^v 
 commission of 5o, for sellmg and l' % ?or buying and t"e 
 expenses of shipping. $53.87. How much did f invest in 
 
 5^^:.T^ ^^' *° * "''■*'^° ^°^°"°* °° ^ commission of 
 6%. and having remitted the net proceeds to the owner 
 
 ^ib.l6. W hat was the amount of commission ? 
 
 II. 
 «iln ^V"";* ^""-^* *'* "** ^^ brokerage, and was naid 
 
 $M50. deducting ^ % commission on the sale. How much 
 was his commission ? ™"''" 
 
 2. 11.600 bushels of wheat were bought through an 
 8. From a consignment of 8,160 lbs of *«* «nU u 
 
 S74 '"wh":: '"■ '?: "°'"^'-- -' '-^ « -t'oc «- 
 
 for seUi„.^f ,"',"■' ""f""- °' """"■Won «lmrg^ 
 tor selimg, if the cliarges for storage and msuraL. 
 amounted to $61.60 ? b -uu losuranM 
 
■3 
 I 
 
 -J 
 
 3 
 
 -IK 
 
 1 
 
 I 
 
 "'■•'CHLUXLUVS. 
 
 bow .nueh ,;,„« :,e dra. r '""" °' *=•''''■»''• l'"' 
 
 pwce^lflf""! 'T""'"'' '™"> '"■' '"J' "Rem $ ,00 „, ,|,e ,„( 
 l-rocceas Of a shipmont of Inittcr If M,. 1. 
 
 mission is 3«^ delivery rl„„ «rs,/ "f, ""''""" ™™ 
 
 made for guaranty of „ ,"l 7^ .„ , ' ,"'"' '* '^'""' '' 
 pounds, a, 27o. per ]|, ^TZ , '""•"''"»"=■ l'""' ■"»".» 
 commissi,,,, was all,,;;;, T" ""^ ■"•"" ""-'• '"O ''"" muei, 
 
 «3- and U.0 ;::Li\r-„^ - ^^^^^^^^^^ 
 
 celling, a,rd 2*7^, Lr„1, li,™'"'"""™ "^-S^J^fo, 
 
 7. A broker- .;,;-'"'"",'": "Lr°"'" ■ 
 to tbe bale, at ICk I :. J™ ■ ' '"''-''■•■>«"'? 185 lbs. 
 
 charge, 5,79. He in , , rasr!;;",, ™'' '^"'^' ""'' '"' 
 flour for tbe oonsiguo eharrin! ° "" "."" . P'"««'l» io 
 How n.„eU was .ti„'au;tt^TsUrT:'^^'°°„°'/,*^°- 
 
 eiierrrit?-; id%r"'^°"'°^"'-^' 
 
 'or buying tlttr J Teol SV '^ ""','" ""■ ^^'' 
 and he d.arges 26X additi„n'„w ^'°° "'" ''-■■' «22, 
 
 -ss of tbe I,,,, wia 'ri'u[d'r;;:"'°°" f" ''="■■ 
 
 pay for purcl,ases and charges ? ' '' """''' '" 
 
 sigunrlri' "grVsrl^oe'ed '^'f"' ,'° "" °*»- » - 
 oLarges being 'S 0^/ the "' .™' ^'■'"*^' "^^ 
 
 directed the age,tt to °;::f„'tmrtr:r'' '*^- ^» 
 
 i»y himself his coa„i«ion f^r bu, ! m rr"?'''/"' 
 »ame What was the amount i, vi tej an .° °' '"" 
 oomm,ss,on for both transactione ? ' '°'"'"' 
 
 t. 
 
 -Isl 
 
!h: 
 
 
 r I 
 
 
 t 
 
 14U 
 
 illSCELLd.SEOUS. 
 
 10. An arj.Mit sold -i.OOO husliela Alsike clover seed, at 
 $7.85 per Imshcl, on a coinmis.sion of 5%; iiuil l.'iOO 
 bushfls medium red, at $r>.-20 per Luahel, on a conimission 
 of 2S\\.: takinj,' tlio purchasur's 3 month's not.' for the 
 amount of the sales. If tho u«ent chari^vs 4% for his 
 guaranty of the notes, what amount does he earn by the 
 transaction? /,'. 
 
 III. 
 
 1. A consignment of butter was sold for $1,.570, of 
 which $1,0 1(5.45 were the net proceeds. What was the 
 rate per cent, of commisaion ? 
 
 2. An Australian buyer shipped 33,000 lbs. of coarse 
 wool to a Lcmdon agent to be sold on couiiniH.sion, and gave 
 instructions fo" the net proceeds to bt; invested in leather. 
 If the agent sold the wool at l8c. per ' on a commission 
 of 2%, and charged 10^^ for the purr so and guaranty of 
 grade of the leather, wliat was tht .imount of his com- 
 missions ? 
 
 8. Wlint are the net proceeds froiri the sulo of 2,250 bblt,. 
 of flour, at .56.-25 a bbl., if the charges for freight and 
 storage be 50c. a bijl., commission for selling 2%, for 
 guaranteeing paying l^^o? 
 
 : An agent sold, on commission, 1,750 bbls. of mess- 
 pork, at $1(5.50 per 1)1)1., and 508 bbls. of shta-t-ribs, at $18 
 per bbl., ebarging $112..-;0 for cartage, and $5.->o for 
 advertising, lie then remitted to his [irincipal $36,000, 
 the net proceeds. Find the rate of commission. 
 
 - 5. A commission merchant received $1,(340 with which 
 to buy corn, after deducting a commission of 2| %. What 
 is the amount of his commission, and how many bushels 
 of corn, at 62 Jc. a bushel, can he buy ? ' > ■^;j, 
 
 'WM 
 
^isci:i.i..i.\i:,jus. 
 
 117 
 
 6- The hoMer of a .l.uhtful claim of ^^-n i i . • 
 »n n,..nt for collection. H..v..n, "t f Tn'^ " '" 
 
 Kr' ""''''" '■"'■'■^•'■"^ >--''''' ''>-'^-r^ 
 
 • i*- A commission merclnnf cii^ , 
 
 for .^,> •>ifi ir '''''™'^ ^^•"■^ 'I consi-nm<nt of cotton 
 
 ■gn r JV T"""'' "'■ " ^"^'-'o'-neut of wheat was 
 tie mt ' '"'.P'--^'^'^'^^ «'• '-^ consignment of oats, Z 
 
 which ^!7-on '. ^''" ^'^'"'"'-^^i^". was $330, of 
 
 How much '«"r""'"' '"^ *''^ oonHi,muu..t of .h.at. . 
 oats? "'' "" ^^""'^^'°" °- ^^e eonsi^nmeut of 
 
 IV. 
 each al^ifff'T '^"''' "" ' '^'^'"' '^'^'^'^^' '"^"'^^^J at $2l.aO 
 watches. / " ^" *^' '^•^^'^^' ^"'l --^-^^ on the 
 

 148 
 
 iiiaCELLASEOlS. 
 
 IfM 
 
 .: i v'..-' merchant imported casks of wine, and |.iiid 
 $-i-"2 Jm '■. a .-7-2 por fiallou. l('akiij,'o 10% allowed. How 
 u.ii. y !^!;, ^ to ear.b cask, Imd no leukuKu l^een allowed ? 
 
 'J. I'ail ^.Ofid ■ soods which had hocii dnmii^'.d ; 
 
 *^; •^' '^^ Ku is '21%. and tho duty was 21%. 
 
 W. I w.ih lu v< prico of tilt' gooda ? 
 
 4. A'l .n-i)..iU. ; aid $825 duty on nn invoico of silks, the 
 dut^ o< i„u 21 „',. But dama-ps of IT, ;, were allowed at the 
 cus'.-m-hou.se. What was the entire cost of the goods ? 
 
 5. A SI' ; 11- refmer imports 50 hhds. of sugar weighing 
 480 lbs. each, and 120 hhds. of molasses containing G3 
 gals. each. What is the amount of the duties, if" the 
 Bugar pay iic. a lb. and the molasses 8c. a gal., an allow- 
 ance being made on the sugar of 10%, and 2% on the 
 molasses ? 
 
 6. A liquor dealer receives an invoice of 120 dozen 
 bottles of i.ortcr, rated at $1.25 per dozen. If 2% of the 
 bottles are fo md broken, what will he the duty at 24 % ? 
 
 • 7. A merchant imported 56 ca.sks of wine, each contain- 
 ing 3(5 gils. net, the duty at 30 % amounting to $907.20. 
 At what price per gallon was the wine invoiced ? 
 
 8. The duty on an invoice of French lace goods at 24% 
 was $132, an allowance of 12% having heeu made at the 
 custom-house for damage received since the goods were 
 shipped. What was the cost or invoice of the goods ? 
 
 9. A quantity of Valencias, invoiced at §l,6o4, cost me 
 $1,980.50 in sluie, after paying the duties and $12.24 for 
 freight. What was the rate of duty ? 
 
 -^ 10. A merchant imported 50 casks of port wine, each 
 containing originally 30 gals., invoiced at $2 50 per gal. 
 He paid freight at $1.30 per cask, and duty at 30%, 1|% 
 leakage being allowe 1 at the custom-house, and $8 50 for 
 cartage. What did the wine cost him in store ? 
 
*i.Vc-A7./..(.vy.o.7. 
 
 U'J 
 
 <1..' rat,; of :lLiy ," -*" ■'" ">•■ ™'' «^"-2'*. IU,ui,vd! 
 
 .1.0 i„„„r.„,. ;,.cv,>':, ,1:^';- ^l':; "■""■'■ ■'■'■'" '"""- '"'' 
 
 l'".on,, ,uvoice,l ,.l i2.W „o.- box- -.Jl-i^ l""' "' 
 
 ■" =<™. ".voiced a. *:u,0 „.,- box.' ,;:":," '7^ 
 
 «...o„„lof duty, c.,ti„mt„l u .'Ito,, not ;■ 1 *''"''' 
 
 «ml at 8% on lemona „„d or»„„..,? " ' '»'"■' 
 
 • 5 Tlie duty on „„ in,„| , 
 
 ".voiced pnVe i,« dozen ? " *' ''"''"""'■ <■'"' 
 
 6. Imported 12 cjisks nf\v;.> , i 
 ".voiced a. $3.25 p^Z^^T-'i^f 7'T'" '' •""'• 
 
 "' -10%. H, ,„el, A „' .aini'i ■',■"' ' " '"'' 
 
 ?2,747.58 ? ** -^ " *"'"" '' ■ "liole fo, 
 
 .f .ach ca.uo h^vU::; V,, -;;« ."«r„. „.,..,. 
 
 value per lb.? ^^^ ^'' "^vuice.! 
 
 VI. 
 
 and 5>100 for msun,,. (1, funut.u-e. ,^ ) i .^ i Tu 
 
^1 
 
 
 I 
 
 II 
 
 A . 
 
 150 
 
 MISCELLANEOUS. 
 
 2. A canal-boat load of 810 bushels of wheat, worth 
 !tOc. per bushel, is insured for three-fourths of its value, 
 at 1|% premium. In case of the total destruction of the 
 wheat, how much will the owner lose ? 
 A 3. A company took a risk at 2^%, and re-insured | of it 
 in another company at 2^%. The premium received 
 excee.led the premium paid by $72. What was the 
 amount of the risk ?' // 
 
 t4. I insured ray grocery store, valued at $13,500, and 
 its contents, valued at $33,000, and paid $;3oO for premium 
 and policy. If the policy cost $1.25. what was the rate 
 per cent, of premium ? '^ / 
 
 5. A merchant shippedii cargo to London, and to cover 
 both the cargo and the premium, he took out a policy of 
 1100,800, at 3i %. What was the value of the car^'o ? 
 
 6. The steamer Cibola, valued at $90,000, is insured for 
 $75,C00, at 2i%. What will be the actual loss to the 
 insurance company, in case the steamer is dama-^ed to the 
 amount of $20,000 ? ° 
 
 7. Insured for their full value 200 barrels of flour, 
 worth §0.75 a barrel, and 400 barrels worth $0.25, at ^ of 
 1 %. 125 barrels of the first lot and 250 of the second 
 were burned. What was the actual loss to the company ? 
 
 }k8. A speculator bought 2,000 barrels of flour, and had 
 it insured for 80 o^ of its cost, at 3}o^, paying a premium of 
 $429. At what price must he sell the flour, to make a net 
 profit of 10%? 
 
 >^ 9. A vessel is so insured that if lost the owner mav 
 receive both the value of the vessel and the premium The 
 value of the vessel is $9G,084, and the rate of insurance 
 11%. Find the premium. 
 
 10. An underwriter agreed to insure some property for 
 enough more than its value to cover the premium A 
 policy was issued for $25,087.81. The rate being 86c. on 
 $100, what was the properly worth ? 
 
MISCELLANEOUS. 
 
 being 1«?'^*'"' ™™' "''"' "■« P«»ium,,l,e rate 
 7 12. A speculator bouglil 1,000 bbls. of H„„r a„H |,„<1 ii 
 
 So", 2o1^ ?,/,"? ""' '' "" '"' """^ '" '-'- » 
 
 teilo-^n"'"'""'" ^''•"' '" '""""'S - »l'iP ""'1 cargo for 
 
 takeftloooo'atTrr """ *' "' * °"%; " «™ma 
 tates f 10,000, at J of 1 % ; „ tbir.l, $1 J.OOO, at s of 1 % • 
 
 VII. 
 
 1 A town containing $541,250 taxable real estate and 
 f 15 620 personal property, levies a ta. of .009 y^. If 2 ^ia 
 l^djor eollectn.g. what is the net amount realized fr^o^ 
 
 )< 2. In a school section the valuation of the tix.l.Ip 
 property ,s $752,400, and it is proposed to pat e 
 school.house and ornament the grounds at an oxp se ^f 
 $5 000. If old material sells for $073.70, what wil be the 
 rate per cent, of taxation, and what will be B's tax. whose 
 property was valued at $9,400 ? 2.,^. / 
 
 ^ %, 18 to be ru.sf.fl ,„ a certain town. The polls 5G0 Tn 
 number, are ta.ved $1 eieh Therppl ^, " . P°"'' •'^' '» 
 «1 07nnnn ] u ^' '^'"^'^ ^^ assessed at 
 
 f 1,-70 000, and the personal property at ,^130,000 Deter- 
 n.ne^t^he rate, make an assessors' table f;r that ..te nd 
 
162 
 
 MISCKLLASKUUS. 
 
 14. The cost of maintaining the pubh'c schools of a city 
 during the year 1888, waB .$11-2.000, and the taxable ^ '. 
 property of the city was $14,800,000. How many mills on -, ":' 
 a dollar must be assosse.J f„r .school purposes ? If 10 o/ of "^ / 
 the tax assessed cannot be collected, how many mills on a " 
 tlollar must then be assessed ? 
 
 i ■ «rq?nm *''' TT"'^ '^^"' "^ "" **^^°' '•°'^' ^"^ Personal, 
 ih !l^bdO,000, and the town expenses are §3,913 95 How 
 
 much tax must be collect, d co yroyide for town expenses 
 810 n 7 V' - ->'-ti.„. If the same town contains 
 810 polls, taxed $1.50 each, what will be the rate of 
 axation. and how much will be the tax of a man who pays 
 lor two polls and owns property as.sessed at $M„oO() ? " ;, '' 
 \Z' tnV^ f 18.94:^.20 i. assessed upon a town contain- ' 
 
 f2./08 000 and the personal property at $151,600. If ' 
 the polls be taxed $1.25 each, what will be the rate of 
 Property taxation, and what will be the tax of Peter 
 Par ey, who pays for tluve polls, and has real and personal 
 estate valued at $23,760 ? 
 
 $/i97^'on''''T'^ ''^"' °^ * '^^'^ ''' °" ^«^' ««tate, 
 taxof k.o ""t°" P^^-^«"^' property, $432,500. A poll 
 tax o ip.SO ner head is assessed on each of 1,870 persons 
 Jhe town yote» to raise $8,000 for schools, $1,500 for 
 
 an $310 for contingent expenses. How much tax will a 
 milling company have to pay on a mill valued at $46 500 
 and stock at $19,760 ? f^u.ouw, 
 
 Uii 
 
 ^.ih'x^ti'i-rA. 
 
UilJiRliST. 
 
 163 
 
 - /■.Li, 
 
 2 
 7- 'I 
 
 INTEREST. 
 
 82tf. Interest is money paid for the use of money. 
 
 327. The Principal is the mouey for the use of which 
 interest is paid. 
 
 32S. The Amount is tlic sum of the principal and 
 interest. 
 
 82». The Rate is the per cent, of tho principal paid for 
 its use for 1 year, or a specified time. 
 
 Note.— Whea the rate is given, it is to be understood in this work to 
 mean rate per annum, anless otherwise specified. 
 
 85JO. Legal Interest is the rate tised by law for cases 
 in which no rate is specitied in the agreement between the 
 parties interested. 
 
 In all the Provinces of Canada the legal rate is 6%. 
 
 331. Usury is a higher rate than the legal rate, 
 
 882. In computing interest, a legal vear is 12 months or 
 865 days. 
 
 888. Simple Interest is the interest on the principal 
 only. 
 
 j-yskx. 
 
 ''■-.r-Tfea-^v 
 
164 
 
 ^CCURATK INTKIiKST. 
 
 ACCURATE INTEREST. 
 
 (lL'month8or;t.;, di.stoayear). 
 
 rate. ' ''^^<^''»« o^ a year, at a given 
 
 E«.,P,.K l._Fi„d tl. . interest on §660 for 2 ycare at 4 %. 
 
 Solution 1. 
 
 *5'')0 Principal 
 
 _0t 
 $26.00 Int. for 1 yr. 
 
 2 
 
 $62.00 " 2 yrs. 
 
 SoLUTI'lN 2. 
 
 |6.;"iO is int. for 1 yr. at 1 %. 
 4 
 
 " " " •' A O/ 
 
 •26.00 
 
 a 
 
 IOxI'IjANATION. 
 
 Intereet for 1 year is 4% of th« 
 
 principal S(i,W = J(ir,o x .04 a 
 
 »-"'■ 00, and tlie int.Test for 2 years 
 
 ia t^vice tlie interest for 1 year, or 
 
 »2ti.00 X 2 ■ »52.00. 
 
 SOLITTION 8. 
 
 •6.50 
 
 S « 4 X 2 
 
 •52.00 
 
 SOLUIIO.V 3. 
 
 •9.00 
 
 20 = 6 X H 
 
 •192.00 
 
 152.00 " .. 2 yra. " 4 o^. 
 
 J.U,,.. 2.-Fi.d tbe interest on »960 for 3 yrs. 4 mos.. at 0"^ 
 So..aoxI. s,,,,,^^.,_ «^ 
 
 n„ 89.60 
 
 •57.60 ^ Int. for lyr. ^^ 
 
 tinm " "3Jyrs.|3yrs.4mo8.) SlTw'OO* 
 2 1'1'e result will be the same in Fv i ..,1 »» 
 
 EXERCISE 72. 
 
 Find the interest for one year of— 
 
 1- «4o0at4i%. 
 2. ?680 at SJ %. 
 8. S9r.nat7i%. 
 4. 5840 at 5*%. 
 6. •1,720 .It 0§%. 
 
 6. «'2,630at4J%, 
 
 7. 84,920 at 5%. 
 
 8. .?."),0il0 at :ij o^. 
 
 9. «3.r:iO jit .-'.i 'v^ 
 10. S4.(!80at4i°X 
 
 11. •7,428 at 5J%. 
 
 12. ?9,»'.54 at %. 
 
 13. 57.8 -il at6i%. 
 
 14. s^:),(ii3 at 7%. 
 16. •5,4:;0 at 5%. 
 
 ^^^r,^ 
 
 ^^r. • ^'".m 
 
ACCURATE ISIEHEST. 
 
 166 
 
 Find the interest and amount— 
 
 , 
 
 1(3. 
 ^17. 
 
 10. 
 
 ai. 
 
 22. 
 
 23 
 
 24. 
 
 25. 
 
 20. 
 
 27. 
 
 28. 
 
 29. 
 
 30. 
 
 81. 
 
 S3. 
 
 / 83. 
 
 f 84. 
 
 85. 
 
 86. 
 
 . 87. 
 
 88. 
 
 89. 
 
 40. 
 
 41. 
 
 42. 
 
 43. 
 
 44. 
 
 46. 
 
 PK1.NC11'4L. 
 
 »(i()0.00, 
 »70().(I0. 
 
 jriOii.no, 
 
 »!»'<( ».()0, 
 «H(IO.()0, 
 »74().00, 
 81,.JJ().00, 
 t^'.tti()..-,0, 
 
 m'<.m, 
 »:ii;;i.2o, 
 
 • I.Ol'O.OO, 
 
 84,075.00, 
 
 ?4,028.75, 
 
 84,02600, 
 
 8270 :tt), 
 
 8H10.00, 
 
 •lOO.OO, 
 
 8900.00, 
 
 8360 00. 
 
 875i).80, 
 
 847 . 30, 
 
 8328.00, 
 
 1474.90, 
 
 8640.80, 
 
 8143 33, 
 
 8300. '.(6, 
 
 8790.00, 
 
 81,800.0), 
 
 81,080.00, 
 
 8891.00, 
 
 hATI. 
 
 5%. 
 C%, 
 
 7';{., 
 «%. 
 «%, 
 
 8J%. 
 
 10%. 
 
 12%, 
 
 6|'^ 
 
 24%. 
 
 3i%, 
 
 'i%, 
 
 4%, 
 
 8%, 
 
 H %, 
 
 9%, 
 0%. 
 5%, 
 7%. 
 4%. 
 3%. 
 
 6i%. 
 
 8i%, 
 
 6J%. 
 
 3i%. 
 
 12%, 
 
 11%, 
 
 13%, 
 
 10%. 
 
 ^%. 
 
 TIWB. 
 
 ayr 
 
 2yi . 6 mot. 
 r.yr- 
 
 3 yr-i. Srnus. 
 6yrs 
 
 7 yrs. 
 
 2yru 10 moi. 
 ;iyr8. '.1 11108. 
 
 4 yrs. li rrioi 
 Syrs --'ii.n. 
 
 1 yr. 7 iiius. 
 
 2 yrs. 4 luos. 
 6 yrs. 
 
 3 yrs. 2 moa. 
 1 yr. 11 moa. 
 
 1 yr. 9 mcjs. 
 
 2 yj's 7 11109. 
 
 3 yrs. 'i 11103. 
 •') yrs. 4 rnoB. 
 2 yrs. 7 inos. 
 6yr8. 3inos. 
 2 yrs. T) iiios. 
 
 4 yrs •; mo9. 
 
 1 yr. ■ won. 
 G yr- 
 
 2 yrs 
 •'iiyrs. 
 *i yra. 
 2|l yra. 
 3i yrs. 
 
 88«. To find the interest on a sum of monev. for a 
 given number of days, at a given rate. 
 
 Example 1.— Find the interest on 8850 for 02 days at 5 %. 
 
 SOLCTION 1. 
 
 88.50 
 
 5 
 
 842.50 Int. for 1 yr. 
 
 62 
 
 866 ) 2636.00 ( 87 ?1 + 
 or 
 87 72. 
 
 Solution 2. 
 
 CANCELLATK N METHir). 
 
 6.60 X S X 62 ^ 52700 
 *i '? ~73 
 
 78 
 
 :^ - »7.a3. 
 
 mjL^ ' 
 

 156 
 
 ACCUJtATE INTEREST. 
 
 EXPIANATION. 
 
 f^'-''^^^intZltlfi^^^^^^ .-. therefore 
 
 mte,.est for 1 vcar (fisio, by 6^ Ind S, °r' '"^ '""'"P'-V-K th. 
 Solution 1. or by cLellatLn'as irso.'t;:;;".' ^'^ "'"^' ''^ '''' " - 
 
 ExAMPLB 'i. Find tho interest on 8q ■«« / 
 June 18tli, 1801. at ". j^^ a^^^^';*'' °° •'•^^^ ^'°n> April 16th. 1«89. to 
 
 (From April 16th, '89, to June I8th '91 i. 9 . 
 Solution 1. ' ' ^ y^"" ""^ 63 dayg.) 
 
 00 fn » Solution 2. 
 
 32 0xfix^= ^^•^.".i Int. for .3 d, 
 
 32..0X6X2 . 39n.00 .. 3 vrl" 
 
 »423.66 .. 2yr8.63d» 
 
 reference to .he matt^ be lar/.t":'"^ 'T"'"" '■" 
 compute the discount b/days * ■'■" "''" "'"J' 
 
 Time table, showing the number of days; 
 
 #32.60 
 
 (i 
 
 »195r60 
 
 24 
 
 f423.66. 
 
 sW 
 
 From ant 
 Day of 
 
 To THK CORRESPONDINQ DaY OF 
 
 * I ^ ' 6 I 7 8 ; Q ,n ,, 1 
 
 January ...j 355 
 Ftbruary...,' .3.34 
 
 """•oh , 3,10 
 
 April . . 
 
 May 
 
 June .... 
 
 July 
 
 August . 
 
 BepteMili'T. 
 
 October 
 
 November. 
 
 Deoiiiber 
 
 381 ■ 21a i 2i:i ■■ 0:3 
 I'-O I 181 I 210 o|,) 
 
 IVJ 
 
 '.'2 
 
 ISO 
 3:;.-, 
 
 J! I 
 
 ;iui 
 
 ■-.'■"' 
 
 !-.3 
 '■Xi 
 
 11 
 
 3'!i ; 
 .".03 i 
 
 i:<3 I 
 
 ]i? I 
 
 '■1 I 
 
 1. Ho. many days hon, „„,. .g^ j„ ^„^^^^ ~ 
 
 Find " l\r • f^sPLAXATroN. 
 
 Maytothesan^edayinilus '" ''^ ;""''^'- "^ '^'^J- ^n-.n. ai.v .-.v ,„ 
 Augu.t 18. and 92 /lo t T02 days 1^^ '' " ^'^ '^''^^ -- ^i-n 
 
 J 
 
ACCURATE ISTEllEST. 
 
 167 
 
 from^wlucL t.n.e u counted, subtract the difference fro,., the tabula^ 
 
 2. If in Leap Year, and the month of February be incltided in tl.. 
 tun, reckoned, add 1 day to the number of days found by The table 
 
 EXERCISE 73. 
 
 Find interest on — 
 
 raiNoiPAi,. 
 
 1. »3,600, 
 
 2. »4,600, 
 8. 1800, 
 4. 1760, 
 6. »9,360. 
 6. $4,350, 
 
 TIME. 
 
 G5 da.. 
 80 da., 
 90 da., 
 45 da., 
 135 da., 
 219 da.. 
 
 RATI. 
 
 5%. 
 
 7%. 
 8%. 
 
 3*%. 
 
 PtllXCIPAU 
 
 I. :J340.S0, 
 
 8. 8424.-10, 
 
 9. ?(J25.30, 
 
 10. 342«.r,0, 
 
 11. *;i70.75, 
 
 12. S4-20.80, 
 
 TIBfB. 
 
 130 <ia., 
 •JTJa, 
 48 da, 
 
 2'J2da, 
 73 da., 
 6U da., 
 
 BATK. 
 
 3i%. 
 
 4%. 
 
 7% 
 8%. 
 
 Find the amount — 
 
 \18. 
 14. 
 15. 
 
 16. 
 
 17. 
 
 Xl8. 
 
 tl9. 
 
 20. 
 
 121. 
 
 22. 
 
 23. 
 
 24 
 
 25. 
 
 PRINXIPAL. 
 
 »542.00, 
 »0-i4.00. 
 
 8'JGO 00, 
 §1,100.00, 
 »1. 180.20, 
 *1.260.48, 
 $1,010.25, 
 8l,0'.t7 76, 
 
 ?9T().80, 
 
 88;jt;.84, 
 $1,272.24, 
 81,284.96. 
 «1,20 1.00, 
 
 $989.00, 
 
 R.\tB. 
 
 7 o/ 
 
 8%, 
 
 9%. 
 
 10%. 
 
 11%, 
 
 12%, 
 
 8?i, 
 
 6%. 
 
 7%, 
 
 9%. 
 
 10%, 
 
 12%. 
 
 11%, 
 
 12%. 
 
 From 1888 
 
 " 1887 
 
 " 18^2. 
 
 " 18>S'.), 
 
 " 1S8.'), 
 
 " 18-.8, 
 
 " 1890, 
 
 " 1885. 
 
 '• 3KSS. 
 
 " 1887, 
 
 " 1891, 
 
 " 1890, 
 
 " 1888, 
 
 " 1889. 
 
 TIME. 
 
 '', Oct 27, to 1890, May 12. 
 
 Sept. 19, to 1889, June 1. 
 
 Dec. 31, to 1892, Oct 1. 
 J:in. 1, to 1892, Due. 20. 
 
 April 1. to ISSU. .July 28. 
 Au;,'. 31, to 18;)3, Nov. 1. 
 Feb. 20, to 1891, May 10. 
 Mar. l.j, to 1885, Jan. 15. 
 June 19, to 1889, April 7. 
 Nov. 24, to 1887, Nov. 30. 
 Sept. 27. to 1892, Dec. 9. 
 Dec 8, to 1891, May 1. 
 Dec. 25, to Ibl^lO, May 28. 
 Mar. 21, to 1890, June 30. 
 
 27^ A note for $560.60, dated May .'th, 1881, was paid 
 Dec. 8l8t. 1882, with interest at 7 %. What wag the amount? 
 
 28. If 1 have the use of $275 for 4 years 10 months from 
 Jan. 12th, 1883, what amount must I return to the owner 
 allowing 6 % mterest, and what will he the date of mr.turity ? 
 
 M 
 
 W^ 
 
158 
 
 A (JC UJiA TK INTEREST. 
 
 29 Roquired the amount of $108.60 from Aug. 20th to 
 r^ec. 18th, 1886. at 10 % •? ^ 
 
 80 What is the interest on a note for $51.5 6-2 dated 
 March 1st. 1883. and payable July 16th. 1885 at 7 v' 
 
 81. What is the value of a note of $65.75, due with 
 intere.,t for 1 year 2 uiouths, at 6^ '}(, ? 
 
 82. If a person borrow .$875 at 5V,. what will be due the 
 lender at the end of 2 years 6 month.s ? 
 
 wer!'/i nT '"''' u'" ^T^''''^ '°t ^or $12.600 ; the term8 
 vvere, $ 1.000 m cash on delivery. $3,500 in 9 months. $2,600 
 .n year 6 month., and tho bahnco in 2 vears 1 mou ha 
 wUh 6% xuterest. What was the whole amount paid ? 
 
SIX PKii CEHT. iiaiuOD. 
 
 f6S> 
 
 I 
 
 f* 
 
 SIX PER CENT. METHOD. 
 
 «f q^n'''. '^\ ^'f ^^' ^^"^- ^^thod is for.nod on , basis 
 of 860 days to tlie year au.l :iO .lav. t , the uun'l 
 
 3:«.S. At 6% per annum the interest of .'?x. 
 
 For lyr. 12 mo., or 360 .la., is tJo-o.; ,f,, ■ . 
 
 For -I ... f v/ •»., 18 iO- = .01 of the pniuiDiil 
 
 A '".,.. or 1 da.. ,8 im. , .OOOi of the prinoip^l. 
 
 Hence the following— 
 
 PRIXCIPLES. 
 
 5. The inter f St for 60 ,!,n/<, ,-f (!<>/ ;, f ; , 
 
 <*«i:-r;i"ri''"f''''''*' "1 ' '^ '■' ''"""'' '■" """"■'"' "" 
 
 '"" /^0'«t two places to the Ip/'f i„ n.^ ■ ■ , 
 dividing the result hy 2. ^ '" '^" ^''"'"''^^ ^'"^ 
 
 ™o?th; aid dayV« 6'f "" '" """ ""■"^" "^ ^"-. 
 
t 
 
 160 
 
 SIX PER CENT. METHOD. 
 
 ftt 6 "' y'"*"'" ^— ^^'^^t » "'" interest on J450.75 for 1 yr. 8 mos. »1 da 
 
 SOLCTIO.N 1. 
 
 Int. on *l for 16 mo,. - $.075. (Principle 1) 
 
 ~ _?}_::. 21 Jl » .0036^ (Priuciple2) 
 
 Int. on $1 for 1 yr. 3 mos. 21 da. m 8 0786 
 
 .-. Int. ou 81.50.75 for 1 yr. .-J ,nos. 21 .la - »150.76 » .0785 - »,,5. 383874 
 
 yOLDTION 2. 
 
 1 yr. 3 mos. 21 da. = 471 da 
 *J-^'>'^'> » Int. fo r liOJa. (Principle 8) 
 4:'0 " (GO X 7) 
 30 " (00 + 2) 
 15 " (;iO ^ 2) 
 6 " (Principles) 
 
 •31.5025 
 2 25375 
 
 1.12i!^i75 
 .45075 
 
 •35.383876 
 
 Int. for 171 da. 
 
 NoTB l.-For business parposea it is sufficiently e.xict to carry the 
 work to mills, ns in the shorter process. ^ 
 
 2. In tl.is process when the decimal in the fourth places is less than 
 6 .t .s rejected ; when 5 or greater tnan 5. the figure .n the th,>d d"c " 
 place .s .ncreased by one. and th. decimals to the right o the Zd 
 decimal place are rejected. ™ 
 
 »4I. y'o>,/ the interest at any other rate than 6%/,y 
 thxsvuthodj^rstjind the interest at 6%. and then increase or 
 dtvmnsh the result by as many sixth, a, the given rate i, 
 unit, greater or less than G o^. Thus, /.r 7% add *. for 8% 
 add f or i, for 4 % subtract t or i, etc. »' ' « * 
 
 EXERCISE 74. 
 Find the interest at 6 % of— 
 
 1. ??267.27for6rao. 24da. 
 
 2. »14(5 18 for 1 yr. 21 da. 
 8. 8256.84 for 2 yr. 4 mo. 12 da 
 4. 5597.25 for 7 mo, 18 da. 
 6. •418.76 for 1 mo. 25 da. 
 
 6. »309,18for2yr. 24 da. 
 
 7. §38.90 for 1 yr. 1 mo. 6da. 
 
 8. •146.48 for 9 mo. 10 da. 
 8. f 275.50 for 11 mo. 13 da. 
 
 10. »l,29.Hfor3yr. Imo. 27da. 
 
 11. •2,000 for 2 yr. 7 mo. 24 da. 
 
 12. $»,010forlyr. Imo. 13da. 
 
 13. »t)80 for 2 yr. 6 mo. 10 da. 
 
 14. 81,895 for 1 yr 7 mo. 7 da. 
 
 15. S 108 for 5 yr. 5 mo. 1 da 
 
 16. 81,000 for 11 yr.l mo. 20 da. 
 
 17. •645 for 4 yr. 4 mo. 5 da. 
 
 18. 8500 for 3 yr. 1 mo. 27 da 
 W. •895 for 6 yr. 11 mo. 11 da. 
 
 20. H&oO for 1 yr. 10 mo. 23 da. 
 
 21. ;gl,463 for 9yr. 1 mo. 9 da. 
 
 22. »365for4yr. Imo. 25da. 
 
 ..«sfft^;i^:* ijn I iiiMPii'ii' iii|ihiii 'Jia^^mm^s^m^'^^fm 
 
SIX I-KR Lh.Nl. HKIUOD, 
 
 Find the interest and amount- 
 
 161 
 
 HUNOrPM,. 
 
 M. »1.0H0.r.u, 
 
 •9<!0 00, 
 
 8576.18. 
 
 S045.00. 
 
 91.200.00, 
 
 Jl.WOOO. 
 
 Se.'a.oo, 
 
 f<''0().(;o, 
 
 n,V\r,.\l, 
 
 9891.00, 
 
 24. 
 
 25. 
 
 2(i 
 
 27. 
 
 28. 
 
 29. 
 
 30. 
 
 31. 
 
 32. 
 
 83 
 
 M 
 
 ■ATE. TIMR. 
 
 '%• I yi . I) riio 
 
 S'Y.. 2yr II, no. 
 
 !'%. 3 \ r. 4 mo, 
 
 10%. 3yr Omo. 
 
 12%, 6.vr. lOmo. 
 
 '>'%>. Gvr. 3ino. 
 
 10%, Vi yr. Cnio. 
 
 «%. H mo. 1 1;, 1,1. 
 
 fi';'.. 17 mo. 18,1a. 
 
 10%. 2,{mo.Ufia. 
 
 12%. 40 mo. (mIu. 
 
 7%, 14 mo 17,1a. 
 
 ?: -■ iH.no. 
 
 f'.KiO 00, 
 9l,2!«!00. 
 fl.OSdOO, 
 *0. 81,8(10 00, 
 <!• JOOO.OO, 
 »7!)n.0O, 
 
 f8i;'),44_ 
 
 45. 8I.J'.'G.;-,6, 
 
 46. 81. -."J,:. 28 
 
 8fi. 
 8C. 
 87. 
 
 38. 
 .'!0 
 
 42. 
 43. 
 44. 
 
 "*T"' TfMl. 
 
 0- 
 
 9 mo. 25 d». 
 
 1 >r !),„„ n,i,i 
 
 1 .vr. !) mo.?i,i» 
 
 2 jr. .3 mo. 9 da. 
 
 2.vr. 9mo. 21(la 
 
 3yr. Omo. 16 da. 
 
 •1 yr. 7 mo. 18 da. 
 
 ''yr. lOiMo. r, dft. 
 
 7 yr.il mo. 27 da. 
 
 Wyr. 4mo. I7da. 
 11%. lOyr. 5 mo. 1 da. 
 8%. ISyr. 4mo. 39d«! 
 
 8%. 
 
 II" 
 12'V 
 
 '""'„ 
 9%. 
 
 - "Ah *ojfr. tmo. 39d« 
 rmdtl .ntereston8<)72for21Gd.ysatO%. 
 
 SOLDTro.V 1. 
 
 f-0 16 . ., igp .. 
 
 3.3fJ m u .^^ „ 
 _^672 « .. g .. 
 
 •2^19^ - i^Tf^Tsiedi: 
 
 f X 3) 
 (CO .f 2) 
 (Priii( ij)!o 5j 
 
 fioLCTION 3. 
 
 8072 
 .036 
 4032 
 2016 
 934.193. 
 
 KxPLAVATIOIf. 
 
 By Principle / the int-n-.t 
 on II for 21M. .,;„■„: 
 -».O.iO. ... Interest or. >.J7a 
 
 'or-lOday, .5(;72x u.O « 
 •ti.ij2. 
 
 SOLDTION 8. 
 ••672 + 6 a, tlI9 T ^ , 
 
 •^ ••112 X 216 « 82^ : °*'!"J,f-, ;'""-?'<»«) 
 
 Ex.^:,, .._Find the interest on 8760.48 for 17'^ , 
 SoLUTio.N. '•""•to lor 174 days at 6 %. 
 
 •-'^'"i^^J^t. for 60 da. (Pnn-p,e3) '"""'"' ^'"'-'* 
 
 ,76018 . .. '^ .f . ^ 3) 2.7^5 
 
 J__{Principle«) ___7^ 
 
 f22.0oZ 
 
 »22-0539m^n^7T^ 
 
I 
 
 ■ \ 
 
 1G2 
 
 SIX PER. CEST METHOD. 
 
 
 
 EXERCISE 
 
 7B. 
 
 
 Find tlio int 
 
 ormt on — 
 
 
 
 1. 
 
 8l.7r)0.00. for 
 
 1 > ila.vM, Ht 6%. 
 
 IS. 
 
 •6.178.00. for 9d»vii,at 9% 
 
 2. 
 
 Sl,l2.-).0i). for 
 
 21 .iuv^, at 7%. 
 
 19. 
 
 »7:!'.M)ii, for 11 d I vs. lit 6% 
 
 3. 
 
 »74i 50. for 
 
 :U> iliiys. at t\ %. 
 
 M. 
 
 *l,17t.")i. for Vi l.yn. at «%. 
 
 4. 
 
 ?!»iO.0(», for 
 
 II.') ii:ivg. al ("i '}'„. 
 
 Jl. 
 
 Saio.iKj, for 70 day*, at 10%. 
 
 fi 
 
 Si'.f.ii.uO. for 
 
 <l:i .l.ivH. at 8%. 
 
 •21. 
 
 81,478.1)0, for 80 diiys. at ti %. 
 
 6. 
 
 Siai; 4'J, for 
 
 :<:{.h.v«, at 9%. 
 
 23. 
 
 82,150.00, for '.ir> daya, at 4^%. 
 
 7. 
 
 SI. 000.00. for 
 
 '21 iliiyx, at 10%. 
 
 24. 
 
 81,'iOO.OO. for .■.:i .Uy»i. at 6%. 
 
 8. 
 
 I'J.OOO.oi), for 
 
 12 .lii\!(, lit 5'Jt. 
 
 26. 
 
 31,.-00.00. for 87 day*, at 7 %. 
 
 9. 
 
 SlI.M.tM), for 
 
 JO days, at «J%. 
 
 26. 
 
 SIJOOO, f.,r 41 day«, at 6%. 
 
 10. 
 
 »1,:(«H.IMI, for 
 
 ."0 d:iVH. at 3%. 
 
 27. 
 
 5;)i;o.oi, for 81 day 8, at 6%, 
 
 11. 
 
 »'J3.00, for l.-.U days, at G% 
 
 28. 
 
 8a,347..0O, for 18 day^i, at 7%. 
 
 la. 
 
 t>j.j0.00, for 
 
 75 iliiys, at 7 %. 
 
 29. 
 
 ei, 112.49, for 25 dayi», at 8%. 
 
 13. 
 
 «Hf,'.r.O, fnr 
 
 46 days, at 6%. 
 
 30 
 
 81,:i00.00, for 13 days, at 6 «t 
 
 14. 
 
 «800.00, for 
 
 27.1i\y8, at 6%. 
 
 Ml. 
 
 817,000.00, for 8 day*, at 6|%. 
 
 16. 
 
 »l,7a-).(IO, or 
 
 67 days, at 9 %. 
 
 82. 
 
 |195.,<>0, tor 83 days, at 10%. 
 
 16- 
 
 JlvJC.OO, for 
 
 55 days, at 6%. 
 
 33. 
 
 81,050.00, for 43 days, at 7 %. 
 
 17. 
 
 5.1.741.85, for 
 
 Find the iiit 
 
 (1 days, at 7%. 
 
 crt'St in — 
 
 81. 
 
 81,600 00, for 44 days, at 7^ % 
 
 
 fHINCIl'Ali 
 
 FKOM 
 
 
 TO BATl. 
 
 
 86. 13.5.61, 
 
 Nov. 11, 1891 
 
 
 Deo. 16, 1893. 6%. 
 
 
 86. gr.0.00, 
 
 Sept. 4, IH'.IO 
 
 
 Jan. 1, 1892, 8^%. 
 
 
 87. »1)786, 
 
 May 17, 188*5 
 
 1 
 
 Doo. 20, 1893, 7%. 
 
 
 38. 93-25.J8, 
 
 Juno 20, 1882 
 
 1 
 
 Sept. 4, 1884, 8%. 
 
 
 89. «154.76, 
 
 April 10, 1888 
 
 
 Nov. 24, 1888, 6%. 
 
 
 40. «e61.50. 
 
 J Que 3, lts89 
 
 » 
 
 March 25. 1690, 6%. 
 
 Fi 
 
 od the amount of— 
 
 
 
 
 41. 8450.80, 
 
 March 6, 1893, 
 
 
 Deo. 20, 1893, 6%. - 
 
 
 42. »1..5(»0.00, 
 
 May 6, 18it4, 
 
 
 Jan. 20, 1896, 4%. 
 
 
 43. 8137.30. 
 
 Deo. 12. 188». 
 
 
 Jaly 8,1891. 4^%. 
 
 ■^smi^^^-r?^5^^.^i3msm^d^ \wi^ 
 
ACCURATE I. 
 
 '{EST. 
 
 168 
 
 f, 
 
 ACCURATE INTEREST. 
 
 (la moDtlm or 3C5 diiyH to » ytar.) 
 
 843. Since iutorest in Cmmln in ivckonoi ii[)oti n Hhsih 
 of 865 .lays to a year, the interest found by the " Six 1'. r 
 Cent Method." which 18 l,aso.l upon tliu siippositioii that 
 m) .' ivs , -xla. a year i id ;U) days a niontii. is nut ^tri.tlv 
 •ccuf.atff. 
 
 a* I. Si re th-^fear cont lim 865 d,iui>, the iiUnrst, inund 
 hy the Sir Pn '•■nt Mrth.nl for 860 dayi to the year, is .f, 
 
 or ^ part of it.ir'j too Uirje. 
 
 84«. In many States of the American Union ;i 
 reckoned on the basis of 860 days to ihe .vciM- 
 peoplo in Canada etill reckon the interedt ci i. 
 on this basis. 
 
 :{I6. On account of the shortness of ;: ■ <;.; i' 
 Method, many nccountanta prefer to rech : 
 method, and to then make the nocossu.-, . .' , 
 of itself. 
 
 ExAMfLE — r mI tho accurate int.orc>.t on .750 for 90 t. . .: 
 
 i^OLUTION. 
 
 •7.50 3 Int. for t;0 da. at 6 %. 
 
 3.7,"i a " 30 " '• 
 
 75 X " ti " i« 
 
 ~' % " 6%. 
 
 e.-^t is 
 Many 
 
 . --.iH 
 
 ^ "' 3 -K,. 
 
 112.00 
 
 4 00 
 
 810.00 
 
 116.00 
 
 " 98 " 8%. Art. 841. 
 
 ,^ of 910.00 = »i.i.73. Accurate intercit. 
 
 EXERCISE 76 
 Find the interest at 6 % on — 
 
 1. 82,500 for 7-5 days. 
 9. f 750 for 48 dayg. 
 8. 86,253 for 96 daya. 
 4. 84,525 for 47 days. 
 
 5. ?8,3fi0 for 78 days. 
 
 6. $1,780 for 51 days. 
 
 7. 83,051 for 43 daya. 
 
 8. 89,875 for 153 dfcyg. 
 
164 
 
 ACCUIUTE INTEREST. 
 
 Fiud the interest and amount of — 
 
 9. fBIOOO 
 
 10. $945.50 
 
 11. 5378.^8 
 
 12. ?3y4.7:) 
 
 13. SolO.OO 
 
 14. »t31.'>.00 
 
 15. S4.J0.00 
 10. 8120.00 
 17. $.353.00 
 
 for G^^ days at 6 %. 
 for 33 diiya at C%. 
 for 75 days at C %. 
 for 130 days at C%. 
 for G.J days at 7 %. 
 for 93 dayr at (i %. 
 for 78 days at 5 %. 
 for 96 days at 7§ %. 
 for 80 days at 10%. 
 
 18. 
 19. 
 20. 
 21. 
 22. 
 23. 
 
 »670.00 for 
 »7«-).00for 
 »1,200.00 for 
 »2,.500.00 for 
 »1,".I3) :-0 for 
 e2,]:iil.-.,sfor 
 
 24. »1, 000.00 for 
 
 25. ?2,000.00 for 
 Si'5. ?1, 500.00 for 
 
 Find the interest of- 
 
 Pr.INOIl'AJ 
 
 27. »450, 
 
 2R. 5720, 
 29. VJ')0, 
 $540. 
 SlOO, 
 ?900, 
 S240, 
 S.S33, 
 »672, 
 
 86. mo, 
 
 37. ^600. 
 88. §030, 
 
 SO. 
 81. 
 83. 
 83. 
 84. 
 85. 
 
 39, 
 40. 
 41 
 
 S480, 
 8270, 
 $386, 
 
 TIUB. 
 
 From Ang. 10 to Nov. 8, 1885, 
 
 Jan. 25 to April 7, 188,5, 
 
 Feb. 3 to Mar. 19, 1884, 
 
 April 8 to May 18, 1890, 
 
 Jan. 30 to Mar. 6, 1892, 
 
 Feb. 12 to Mar. 4, 1893, 
 
 May 31 to Nov. 27, 1895, 
 
 ! 1 to Nov. 29, 1886, 
 
 S^J. 28 to Oct. 25, 1880, 
 
 June 19 to Nov. 10, 1881, 
 
 July 4 to Oct. 20, 1889, 
 
 Feb. 1 to Aug. 20, 1889, 
 
 Jan. 21 to Dec. 2, 189.1, 
 
 May 10 to July 29, 1894, 
 
 Oot. 13 to Dec. 12, 1895, 
 
 78 days at 5 %. 
 45 daya at 7 %. 
 68 daya at 5%. 
 93 days at 8 %. 
 75 daya at 5%. 
 70 days at 4 %. 
 73 days at 6%. 
 110 days at 9%. 
 219 days at 4J %. 
 
 BATB. 
 6%. 
 
 7%. 
 8%. 
 9%. 
 4%. 
 7i%. 
 10%. 
 6%. 
 
 ^%■ 
 
 12%. 
 8%. 
 
 61%. 
 6%. 
 6%. 
 9%. 
 
 42. A person borrows $3,754.15, being the property of 
 a minor who is 15 years -S months old. He retains it until 
 the owner is 21 years old. How much money will then be 
 due at 6 % ? 
 
 43. A note fur $710.50, with interest aftor 3 months at 
 7%, was given Jan. let, 1884, and paid Aug. 12th, 188C. 
 What was the amount due ? 
 
 44. A speculator borrowed $9,675, at 6 %, April 15th, 
 1884, with which he purchased flour at $6.26 a barrel' 
 May 10th, 1885, he sold the flour at |7| a barrel, cash.' 
 W hat did he gain by the transaction ? 
 
ACCURATE INTEREST. 
 
 165 
 
 of Ul I 'Ih h« I TT '" '''^ ^''^t>ital ; but .,n acc^un 
 
 b ' ~e /'^^ "^"^^ ''- '' ^- ••" ^ ^-« ^ -^^^* 
 
 46. Bought 4,600 bushels of wheal at lil I9i i, u, 
 payable in 6 month, ; I ia,me,liat " :u,* , fo i", ."t 
 bushel ea»h, and put the money at intere at „« ,- 
 
 e end of the 6 n.onthe I paid f'r the wS D d ^'.at 
 or lose by the transaction, and how much ? *^ 
 
 befnf^iv^*"' "" ^"""''^- '"<= '*''. "■»-. »nd interest 
 
 Ex-^PLB 1.— What priuoipal wiU vieW ftiisn ^ . • 
 *mo8. at4%? '^'^ ***" y^eia ?41.80 interest in 2 yrs. 
 
 Solution 1. 
 91.00 
 
 •O'JJ ) 44.80 
 
 _3 3 
 
 .23 ) 13440 ( 8480. 
 
 ■04 
 .04 
 
 _?i 
 
 .09i 
 
 Solution 2. 
 
 9J%of the principal = j;4t.80 
 
 .". the p--:- -ipal = 44 80 X ~ 
 
 = US,. H 
 
 ESI'LANATION. 
 
 Tiio interest on >1 for2yr3 
 4 moa. at 4 % is ^.Ol>i. then fore 
 844.80 must be the interest ou 
 
 as ni.my dollars ;,t 8 OSi is con- 
 tained in ?4i.80 or «.480, Ana 
 
 Example 2.- On what sum of money is 
 days at 5 %. ' 
 
 Solution. 
 
 *T%7bOI the principal = • i.j no 
 
 .-. the principal = iir,A;o y ^^*^ 
 » 84,380. lA 
 
 l^Xn.ANAlIO.V 
 
 The interest each year = 4 % 
 Of the principal, anrl for 2J 
 year. = 4%x 2i = ;,i%ofthe 
 pnnnipal, and tiieixforr It,^"/, of 
 the i)rinci{)al = Ji-i h;i. 
 
 45 00 the interest for TO 
 
 ExPLA.VATr i;;. 
 Interest for each year =. .5 v 
 Of the principal, and "for 70 .lavs 
 = 5% X 3",". = Vjof thej..-;:,. 
 cipal and therefore 1^ % „: Uio 
 principal = ;■ l.-,.(jO. 
 
 liCLB. 
 
 U^anlr^r" *"""" " '" '"""" ■"' *'^-'- ""^-'' 
 
 
166 
 
 ACCURATE INTEREST. 
 
 ^ 
 
 11 i 
 
 M •' 
 
 
 
 
 
 EXERCISE 77. 
 
 
 
 Find t 
 
 10 princ 
 
 iipal — 
 
 
 
 
 lUTE. 
 
 TIMR. 
 
 INTR11B8T. RATS. 
 
 TIM*. 
 
 INTBHR8I 
 
 1. H%, 
 
 1 yr, 
 
 »15J. 
 
 7. .V!^. 
 
 7 yrs.. 
 
 »2<).76. 
 
 2. r,),%. 
 
 1 " 
 
 Uli. 
 
 8. :!A%. 
 
 4 " 
 
 «!M .50. 
 
 ■■'-■ 4i%. 
 
 4" 
 
 «2r,j. 
 
 9. 1%. 
 
 H- 
 
 StiS.25. 
 
 4. 3j%, 
 
 i " 
 
 m. 
 
 10. Ji%, 
 
 If 
 
 »47.2o. 
 
 a «%, 
 
 i" 
 
 »18. 
 
 11. «%, 
 
 58 » 
 
 1H70.00. 
 
 «. 2i %. 
 
 6 " 
 
 »62i. 
 
 12. 3i%, 
 
 4i" 
 
 9130.00. 
 
 Find the principal — 
 
 
 INTEBKST. 
 
 RaH. 
 
 TIMI. 
 
 4.13 
 
 642.70 
 
 7 %, From Jan. 1, 1880, to Sept. 1, 1887 
 
 14. 
 
 »1!»7.80. 
 
 8%, 
 
 '• Jan, 1, 1SS7, to July 12, 1889 
 
 N15- 
 
 J'.'O OS, 
 
 6%, 
 
 " Jan 1, 18S8. to Sept. 9, 1890 
 
 16. 
 
 SC.0.75, 
 
 5%, 
 
 " Jan. 1, 1890, to Oct. 10, H'Jl 
 
 »."• 
 
 S;i)S7.7.5, 
 
 9%, 
 
 " Jan 1. 1890. to .luiy 1, 1891 
 
 ^18. 
 
 »HC)('...32, 
 
 10%, 
 
 •• Jan. 1, 1888. to Out 18, IH'.IO. 
 
 19. 
 
 S'.)0 ((6 + 
 
 11%. 
 
 " Jan 1, 1892, to July 1, 1894 
 
 20. 
 
 8.5()1.56. 
 
 12%, 
 
 •• Jan. 1, 1889, to Oct. 1. Is03 
 
 yai 
 
 >|44.';.iy, 
 
 7%. 
 
 " Jan. 1, 1888, to July 21, l.S'.m. 
 
 tk22. 
 
 ^77.70, 
 
 8%. 
 
 ' Jan. 1, 1892, to Nov. 15, :8l!5 
 
 2^ 
 
 ^' $31."). (M 4 
 
 5%, 
 
 • Jan. 1, 1887. to Aug. 6, 1892 
 
 ^24 
 
 $95.97, 
 
 6%. 
 
 • Jan. 1, 1891, to Nov 1, 1893. 
 
 7 25 
 
 $700.70, 
 
 9%, 
 
 ' Jan. 1, 18110. to Oct. 10, 1899. 
 
 . 36. 
 
 $1,150.86, 
 
 12%, 
 
 ' Jan. 1, 1880, to July 20, 1887 
 
 ." 5 
 
 34H. To find the principal, the amount, time and rate 
 being given. 
 
 ExAJirLB 1.— What principal will amount to $700.20 in 2 yrs. 7 moB. 
 
 »t8%? 
 
 Solution 1. 
 
 $1.00 
 .08 
 .08 
 
 2^ 
 .20^ 
 
 1.00 
 
 $1.20| 
 
 $1.20§ ) $760 20 ( 
 
 i_ 3 
 
 3.62 ) 2280.60 ( $630. 
 
 flxTLANATIuN. 
 
 The amount of ?1 for 2yrB. 
 7 mos. at 8% is 81.20|, therefore 
 the principal will be as many 
 dollars as $1.20§ is contained 
 times in $700.20 or $630. Ane. 
 
 .■ii£WE5> 
 
ACCVIUTK lisiKliEST. 
 
 HM 
 
 SorjTioN 2. 
 100% + 8% X a,7j s i2nij % 
 
 120| % of tlie pr.noipil = STtjo.vi) 
 
 the principal = 87GO.20 x 
 = St'30. Ana. 
 
 Kxi-I.ANATION. 
 
 Iiiti n fit for 1 year = H % of 
 Uio priiHupal and for i vra. 7 
 
 principal, hence the amount = 
 '"" i 'Jf t'lo principal + 2Qi% 
 ^ of tlio principal = 120.J •', of the 
 princijii, theroforo VJii^ ■(, of 
 tho jjrincipal =87';0.v!0. 
 
 100 
 
 EiAMi-LE2.-Wl>at principd «,,!] un.on.t to *2,,^3,5.(!0 in 152 daya 
 
 •t5%7 
 
 SotnTios. 
 100% + 5 X JSJ , 102^,% 
 1027^%of the principal = S2 2:j.-,.(;o 
 .•. the principal = f2,2.J.j.60 x 
 100 
 
 102^^ 
 
 »2,190. Ans. 
 
 IjXPI.ANATION. 
 
 Interest for each year = 5% of 
 tli- principal, and for 152 davi = 
 ■'>% X liij = -'^3% of thcj princi- 
 pal, ana ih.^roforu 10.'^^% of the 
 principal = S2,235.t;u, t,ie amount. 
 
 RULE. 
 
 Divide the given amount by the amount on Si for the 
 given t.me and rate. 
 
 EXERCISE 78. 
 
 What sum must be put out at interest for— 
 
 1. 
 
 2 years at 4% to 
 
 amount 
 
 to f-mo. 
 
 2. 
 
 4 " 
 
 
 G% 
 
 It 
 
 ■?■-', HO.OO. 
 
 <s. 
 
 >') " 
 
 
 n% 
 
 11 
 
 y^jw.do 
 
 i. 
 
 H " 
 
 
 3% 
 
 " 
 
 S87.20. 
 
 6 
 
 10 " 
 
 
 7% 
 
 ii 
 
 5312.00. 
 
 6. 
 
 8 " 
 
 
 5% 
 
 ■t 
 
 ::•:!';. 00. 
 
 7. 
 
 2i .. 
 
 
 2% 
 
 11 
 
 i-y.i.oo. 
 
 ^8. 
 
 a,t " 
 
 
 •J/o 
 
 ti 
 
 $120.00. 
 
 9. 
 
 'i •' 
 
 
 8% 
 
 14 
 
 j!ii;o.oo. 
 
 10. 
 
 i"^ " 
 
 
 3% 
 
 ■ 1 
 
 $'l,3r,:).00. 
 
 ^11. 
 
 !)| " 
 
 
 1% 
 
 l« 
 
 9l7y fiO. 
 
 12. 
 
 6i " 
 
 
 5 "a 
 
 II 
 
 9;ifio.oo. 
 
 13. 
 
 3 yr 1 
 
 mo. 
 
 at 4% 
 
 II 
 
 51,01 1 00. 
 
 U. 
 
 2yr. 6 
 
 mo. 
 
 •• <i% 
 
 II 
 
 8114 i'lO. 
 
 16. 
 
 3 yr. 7 
 
 mo 
 
 • H% 
 
 II 
 
 S3H(5 00. 
 
 16. 
 
 lyr. 8 
 
 1110 
 
 " 3% 
 
 It 
 
 «94.-).00. 
 
 17 
 
 2 yr 2 
 
 mo 
 
 •■ •''!^% 
 
 U 
 
 ? 1,1 30 00. 
 
1(58 
 
 .<< 'I ■<//..(//.; iM'hiiisr. 
 
 IH. 
 
 1 >r, r. 
 
 III'. 
 
 lit 'li'V. I'MiiiKiniil l..'M|0(H>. 
 
 10. 
 
 ■J \ r. H 
 
 IM.I 
 
 " H'\. 
 
 II 
 
 ;> 1 .0:1 ' <K». 
 
 vo. 
 
 1 VI. !l 
 
 III.) 
 
 •• 10 v, 
 
 II 
 
 »'.» 10,(10. 
 
 91. 
 
 r. vr. y 
 
 Illll. 
 
 '• r^' 
 
 II 
 
 »'."■.•'.' 00, 
 
 av. 
 
 M yi 1 
 
 Illo. 
 
 " *<'\, 
 
 11 
 
 ffl.iHr.oo. 
 
 -VM. 
 
 I.-. ,li.. 
 
 
 " 'I'V. 
 
 II 
 
 Ifl.JVO NO. 
 
 2 J. 
 
 If. iln 
 
 
 •• HX 
 
 II 
 
 )ti.o:iK,(io. 
 
 u.">. 
 
 ly .III, 
 
 
 •' :'i'V. 
 
 II 
 
 »y,'.':':i an. 
 
 yii. 
 
 . .!». 
 
 
 " 4'V, 
 
 II 
 
 »I,HC.>, Jll. 
 
 a,- 
 
 10' .III. 
 
 
 •■ r.'v. 
 
 • 1 
 
 Jt.lll.V'O. 
 
 an. 
 
 :WH ,ln. 
 
 
 ■• :i"*, 
 
 II 
 
 ('•.'.■'Ml./O, 
 
 'i'.t. 
 
 v.. 'III. 
 
 
 " >''% 
 
 II 
 
 r.'Mi\ .M». 
 
 .')(). 
 
 I..0 .i.i. 
 
 
 " ■'\'\, 
 
 •• 
 
 S:i.:!|.M 7r.. 
 
 HI 
 
 •'OK ,|„. 
 
 
 '■ H% 
 
 «• 
 
 tfv,.-. 00. 
 
 .'*'.* 
 
 ■'^. .111, 
 
 
 •' f'"., 
 
 " 
 
 »r>ii'i im. 
 
 ;t:i. 
 
 1 . 1 .ill 
 
 
 " ;<.v\. 
 
 II 
 
 »..'.',( 'H. 
 
 ;u. 
 
 Ml'.! ,lu 
 
 
 ■' ••■!« 'V. 
 
 " 
 
 .^If.A'.H',. 
 
 »l«>. Fiiul tlio time, the principal, interest and rate 
 betitK Riven. 
 
 lvM,n,K 1. lMwh.t,u„.,w,il«(;OV,f,0,,i".|,„.n»|;.^,,, „„,.,„Mt,U 
 
 •% 
 
 8..I,C I I'.N. 
 
 6 07*. 
 
 8 
 
 l''xrr,\NA II. .N. 
 Till. int. i.nt, f.ir I voiir 11 1. h% 
 ,, ,, . . idflHid |,„( thoiiit.'r..«ti.. 'IT, 
 
 4-^ CO = l..t.forlyr.«fS<Y, tim... Ms . - „„' („„.' 
 
 4S.(;() , I--' ,•.■, , .. 7, ., . , ■■ «• Mill,' :. 
 
 , ./ ■" . .,■, <iiii.« 1 y..|,r = •^yiH. VinoH. 
 
 ' >' ^ • i ; -'> IS , rni..A. Aiih 
 
 Ex.vM,.,,,- ■... I„wl,:atniu. wUI»Wl pr..'ln,or.,V:.,Mt,.roHtat.»%T 
 
 I'M'I ^NWI.lN. 
 
 Till' ini.Mv.i .-..r I y,.,ir lU 4% 
 
 !^.^^. :. T.U.f.,r,yr.,it4%. only - ;, of U„. s,,.,.. „,„, 
 
 y3Si! ^ ''''''■ "^ '''•' "f'Vvs- Ann. *■'•'' ''""'• '^- -■,,■,;:■, "f I y<„i- =. 
 
 i^A "f •''•■■• 'l-iyi = 10,) .liiya. 
 
 nCLK, 
 
 4 
 
 '"'/''■ princi/iiil /or 
 
 1 year ,it thr ,;//(// ;•(//,. 
 
 an 1 ?"J:t7," ""i ''"^^";"*/'"-«^« "f « f-c.ion, or of a wiiole number 
 
I 
 
 Ai;<ii/u,i 1 1', IN I KUi<:.,i 
 
 KiJJ 
 
 a. If tlm krnnnril) in ((ivrni iiiHl.. a | .,f tlin i.it,.tn»t,, liri>l lli» |,.irt oiriil,l4«i 
 ftnd |irii'i<(i| iin iili'ivn. 
 
 8. At lOO'X,, Miy xrrrii (,( IIKIIloy will ./'■i|/.?c it>i. If in I yii%r . lfi"r< ' mi 
 
 »ny |...r .•,.,,1. will I .„ ,„ ,„„„,/ yr„r, I,. .|,„iI,Im U... prinoi|,»| an U.« 
 
 |iv«a per <i«rit la ii<»iiiiiiin<i tiiiin* in UHi%. 
 
 EXERCISE 79. 
 
 FilKl III.' tllMfl — 
 
 PiiiNcn-Af.. 
 I. SHKido, 
 
 a 8i(»M»(i(), 
 
 8. l\2t) rk, 
 
 4. iHOill-.!, 
 
 6. It.iKi' .00, 
 «. 6(;:,i,()0, 
 
 8H''(» DO, 
 
 tl:.'i no, 
 
 jH'.IL.oo, 
 
 ?v<;h (II), 
 
 filH-JOO, 
 
 7. 
 
 8. 
 
 9. 
 10. 
 11. 
 
 itAm. 
 
 ■lix. 
 
 » ';;.. 
 f-' %. 
 
 7'X,. 
 8%. 
 
 SVO. 
 
 *i.i'4. 
 
 7.^ in. 
 til. 
 8..0. 
 
 e7H 
 m)M 
 
 SMI.H.W. 
 
 5'2H'l.(li. 
 
 B'ur, 7'., 
 
 ?V>fV .;:., 
 «•■'. . 10, 
 ':'iV-t 1,0, 
 
 ^i.o:!/!.'/^, 
 
 }l,l'r n, 
 IK. 8I,)!)>!*.0, 
 20. 91,vO<i.OO, 
 
 •i\. 8i,y';M4o, 
 
 13. 
 
 18 
 H. 
 
 ir, 
 n; 
 
 17 
 
 IM 
 
 RATI. 
 
 :» ■/„ 
 
 ' ' "/■.. 
 
 i< >'■/■.. 
 
 -' ■■/... 
 
 7 %, 
 ;» %, 
 
 IHTJ'riinrT. 
 
 UlH'(,-,i. 
 
 81 IV ()i,r,. 
 
 «i ■'.■;. 1 1.-,. 
 »:■..;•;. ')■,>«. 
 
 ?7",).i';i. 
 
 ♦;%, SI "'foo. 
 
 lO'X, «l /M.\ VI. 
 
 PhfNIIII'AT.. 
 
 a.S. ?l,ir,(i.(i(i, 
 2'1. 8l,ll'.l.-..()0, 
 25. »2,'.i'.!ii.00, 
 
 86. %\,Hi-,m. 
 
 KATR. »M'ir;MT. 
 
 ';•/, ?i i-,i/W). 
 
 7iX, 8l,o:i^i;o. 
 
 4%, |l,'l-.; 10. 
 
 priiN';ip*r.. (ufK. Avior,-, /. 
 
 27. 8»,; 0, fi% «l ni.20. 
 
 2H. 82,1'JO, ^4% ■':>.tV;.V) 
 
 2'.i. ii.r,r,r,, r.'i,. %ir,r^n.r,). 
 
 .'JO. S.'5,28.';, 2i%, 5.i,.;H.7:i 
 
 27. 1'-. Io;i,iio(l $1,(;00 ut M'X u: Ml it. aifiO!int<;(l t,-, .$^,000. 
 What wuH the liiii'! ? 
 
 '28. Mr. Jioper pfu'l $ 18 in'r-r.--!:. For what pf.rio'l did 
 he pay it, tho principal h'.in^^ %iW), anrl ttjo rate 5%? 
 
 29. Borrows/] Jan. let, 1880. $C0 at 6%. to h^- paid as 
 Boon an the ini'-rest amountt-d to ono-hai,*" th.:: i-iincipal. 
 Wiion is it due? 
 
170 
 
 ( \ 
 
 I, 
 
 I 
 
 J 
 
 Ir 
 
 ACaUJUrji INTKliEsi. 
 
 lor ^1,(..,8.80 cash, h,8 profit bein- e.iuivjilpnf fn ro/ 
 
 « .0. c %, () ^ 8 % and 10 % per annum ? 
 
 are "gtl" *"' ""' "'"» """^'P^' '"'""t. and time 
 
 •.«.7at;;«r*' ""' ""■ "^ •"" '" » "»'• » ""'1.. pro.1. 
 
 Solution 
 
 l-'.48 a Tnt. for 1 30?. at 1 % 
 
 2A 
 
 •30. IG = Int. for l',:(, yrs. at 1 %. 
 ?30.1G)!fi;!-,.72(4J 
 
 1% X 4J =.1^;^ Aa^ 
 
 h ;|' 
 
 luoc 
 
 ExriMNATION. 
 
 The interest on fl,318 for 
 »yr9. 6moa. at 1 % = vjO 16 
 but the interest is A^ ti„„ s as 
 Kreat as 830.10. .-. the rut,, por 
 ot-'it. is li times 1% a 4^0^. 
 
 
 f.lj 
 
 j^f 
 
 Fr:^ 
 
 
 EZPUNATION. 
 
 fi.^.";.?? 
 
 Hon (he interest is of the prinoi- 
 pal for -iA years ; this fraction 
 d.Wded by 2 A expresHos what 
 fraction of the principal the 
 Interest is fori year; IIms lattar 
 fracti:-! is expressed as percent. 
 bv multiplying by 100. 
 
 iateresfr"*" '"^^ "'** "^ -^^ •^•^«« - ^6 days, produce ,45.00 
 
 SoLCTioir a. 
 113.5.7a 1 
 
 fl.24S.OO * 2^'' ^^%' H%. 
 
 SoLniioN 1. 
 »4.S.80 = Int. for 1 yr. (365 da., nt I % 
 
 *• •' YbCii nt Jo, 
 
 8912 , '«4.'>tiO( S 
 
 EXPLAVATION. 
 
 interest on 54 isu for 76 da-'n 
 *tl% = eo.l2, but the interest 
 IS o times as t^rwu as 9.12 . the 
 nito is times 1 'v, - r. ,^ 
 
dOOUUATK INIEIIESI. 
 
 171 
 
 SoLDrtO!* a. 
 
 fi'.no 1 
 
 «)'>.i*.0 
 
 Kvrr.ANATioN. 
 
 ti.xi ('•■ tho priiioipal tlm intcreBt i» 
 ^"'■aV^ year; tliia friictir)n ,iivid<-<l 
 ''y aVis oxproasoB wlmt, friction of 
 the priiicitial is for I year; thii 
 latter fraction ii oxpressed ai per 
 oent. by multiplying by 100. 
 
 BCUI. 
 
 Diridt the given interest by the interest of the principal at 
 1 % Jor the ffivrn time. 
 
 Not. -If the amount be given instead of the interest, liud the part 
 omitlud and proceed as abova. 
 
 Find the rate — 
 
 PllIN-CirAl.. r.S-TKKEST. 
 
 f-^OiiOO, 
 
 EXERCISE 80. 
 
 81800, 
 890.00, 
 ?7t> 00, 
 »o0.00, 
 $0i 1.00, 
 
 TtHB. 
 
 lyr. 
 10 yr. 
 6 yr. 
 
 3iyr. 
 2yr. 
 
 2. ? 150.00, 
 
 3. ^ISO.OO, 
 
 4. ?;iOO.OO, 
 6. S'jOO.OO. 
 
 6. 8450.00. 
 
 7. 9600.00, 
 
 8. 81-ji).no, SI8.00, 
 
 9. »2,0ihi.()0, 890.00, 
 10 91,000.00, 8340.00, 
 11. S2..500.00, |;21>.-,.00, 
 12 83,00000, f.'iOC.OO, 
 
 13. ? 1,850.00, 8uH2.00, 
 
 14. 83,.^: 0.00, 8315.00, 
 
 15. 8'.ii',0.00, *8880, 
 
 16. 8790.20. 8171. OS, 
 17 fH;t7,.50, 8251. .HO, 3yr. fi ra 37 
 18. $1,2'24.72, 848104, 5 yr 7 m. 38 
 19.81,152.(10, 8103 20, 3yr. 10 m. .39 
 30 8807 40. «320 94, 7 vr 4 m 40. 
 
 88100. 3yr. 
 839.00, 1} yr. 
 
 lyr. 
 2yr. 
 
 Iftyr. 
 3yr. 
 
 21. 81.2:il.;w, 
 
 22. 880i).00. 
 
 23. 88,4. -.O.OO, 
 
 21. 
 
 25. 
 
 26. 
 
 27 
 
 28 
 
 29. 
 
 30 
 
 31 
 
 32 
 
 33. 
 
 34 
 
 1 yr. 6 tn. 3." 
 
 2 yr. S m .iO. 
 
 8311..^,0, 
 
 . $7J0.0(), 
 
 8000 00, 
 
 5720 00, 
 
 ■53»;i 00, 
 
 «4.is 00, 
 
 858 1 00, 
 
 ?5 11.00, 
 
 8!,l'' ).00, 
 
 Sl.oii.-. 00, 
 
 82,rjo.00, 
 
 *1.K25.00, 
 
 ?J.:!-<0 00, 
 
 82,l:io.oo, 
 
 82.55-. 00, 
 
 6,-! -'.S,: 00, 
 
 8730 00, 
 
 intrhest. timb. 
 
 892:; h-i, 
 
 8lH0), 
 
 81 1> 00, 
 
 82lr'J2, 
 893.73, 
 
 8180 00, 
 .j40 80, 
 370 50, 
 82196, 
 ?!i 28, 
 85 95, 
 810 80, 
 
 ?;-; <;o, 
 S3 :i',, 
 
 8J7 10. 
 80 1, 20, 
 S".0.70, 
 v:;l 50, 
 8.-i;i 75, 
 *'->5 00, 
 
 8 yr 4 mo. 
 
 9 mo. 
 3 moa. 
 
 1 yr. 4 m. 
 
 1 yr. 3 m. 
 
 2 yr. 7 ra. 
 1 yr 5 m. 
 
 3 vr Urn. 
 312 da. 
 17l(. . 
 
 8'. la. 
 •15.1a. 
 I'M.i. 
 I2.ia. 
 87 da. 
 102 d» 
 318 !a 
 75d.i 
 150 i.1 
 200 la. 
 
 41. A house bought for $12..500 paiM .^1,000 rent. If 
 $200 were paid for taxes and r.-pairs whiit rate of interest 
 di-1 the purebasf money yi\.iu ? 
 
i7ii 
 
 COm-UiWL LSTKHEST. 
 
 \ 
 
 \'. I 
 
 i ? 
 
 If 
 
 COMPOUND INTEREST. 
 
 a«l. Compound Interest 13 the interest of ih. • • 
 pal and of the unpaid interest after it be"ls due '"""* 
 
 Notes l._The simple interest may be add«^ r ■ : 
 «m..annually, or quarterly, as the p/rtfos may a«Se'"" ''' *'^""' 
 a. Compound interest can not be coU^nt.i k i 
 
 I. Some Savinas and Loan n^r^ 
 annuuily. '^°*° Companies componna interest semi. 
 
 Solution i. 
 
 ^"nc'pal 
 
 Int. for 1st yr. (?2.000 x 0,5) " ^-O"" 00 
 
 Amt. f.rlyr., ori'nd Pri'ncipal "'^:^ 
 
 Int. for 2nd yr. (2,100 X .0.:) 82,100.00 
 
 Amt. for2yr8., or.Srd Pri,; ,,,,1 ^ ^^'t'^ 
 
 Int. forSrd. yr. (-2,_'0.5 X .o'-i) i'-i.iOXoo 
 
 Amt. for 3rd yr. .. _110.26 
 
 On«i„al Principal to be subtracted ^^-^nOs 
 
 Compound Interest for 3 vrs 2,000.00 
 
 • '• ■• ?315a? 
 
t'UMPuLWV i.SiKHKST. 
 
 SoLrTioN 2. 
 •2,000 
 
 ' "■'> Ann, of n for 1 yr. 
 6'-'- i'*0 Amt. of S2,(j(iu for 1 vr. 
 
 1.05 
 
 »a.205 Amt. of ?2. 100 fori yr. 
 
 1.0,j 
 
 •2,31 -,.26 Amt of 82,20,5 for 1 yr. 
 2.000 Principal. 
 9316.26 Com J. o a nil Interest. 
 
 J78 
 
 SOLDTION 8. 
 
 1.0-. 
 1.05 
 
 l.l6:'.5 
 
 1.0.'. 
 
 1 V.:i\:ll 
 
 _L'Ol)0 
 
 e2.ai.';.26 
 
 2,0(,() 
 
 SmonSi7s%'~^"^ "" '=""""'"'^' "^^^''^^^ °" '''"^0 '« 2 ye»r. 
 
 SOLOTION 1. 
 
 • 1,000 
 
 Principal. 
 
 80 
 
 Int. Iflt yr. 
 
 •1,030 
 
 Amt. l8t yr. 
 
 86.40 
 
 Int. 2nd yr. 
 
 •1,100.^0 
 
 Amt. 2nd yr. 
 
 23 328 
 
 Int. for 3 moa. 
 
 •1.189.728 
 
 Int. for 3 yra. 3 ino3. 
 
 •1,000 
 
 Principal. 
 
 f^OLUTION 8. 
 
 •189.728 Compound Interest. 
 
 •1,000 
 
 l.OS 
 
 •1.0 -io 
 
 1.08 
 
 •l.lfi0.40 
 
 1.02 
 
 Sl.lsj.T'.'S 
 
 1 0(10 
 
 ilsu.728 
 
 Amt. of 91 for 1 yr. 
 
 Amt. of 81 for 8 mos. 
 
 BOLUTIOK 8. 
 
 1.03 
 
 1.08 
 
 1.16<>4 
 
 1.02 
 
 1.18:)728 
 
 1000 
 
 •1189.728 
 
 IIOCM) 
 
 •189.728 
 
 858. The nse of the following table will greatly shorten 
 calculations in compound interest. 
 
174 
 
 COMPOVSl OfTERSaT. 
 
 TiLBU. 
 
 Showing the nmnint of fl or £1. at differan* ralM lor amj number of 
 ycarg from 1 to 40. 
 
 Vrs. 
 
 1 
 
 •i 
 
 •{ 
 
 4 
 
 a 
 
 (i 
 "i 
 
 81 
 12 
 1:! 
 11 
 
 la 
 
 17 
 18 
 
 19 
 30 
 
 'il 
 
 a a 
 
 3,1 
 
 36 
 37 
 
 3S 
 
 30 
 
 31 
 33 
 33 
 34 
 3J 
 
 30 
 
 :i7 
 
 38 
 3«» 
 40 
 
 1 per ft. 
 
 1.0100 000 
 1 (L'Ol 000 
 
 i.o:i(ia 010 
 
 1.04U(i 040 
 l.OalO 101 
 
 1 0G15 2ii2 
 1.0721 351 
 l.Os-iS ^{Jl 
 1.0:)..ti 653 
 l.UiiCi 221 
 
 l.U.'.r, (583 
 1.12.-.S 2o0 
 1.I3.S0 033 
 1.1 11(1 742 
 1.1009 CUO 
 
 1.1725 78t) 
 1.1843 044 
 I.l'JCl 47.5 
 1.2081 I 00 
 1.2201 ilOO 
 
 1.232.! ;tl!) 
 1.2147 l.M) 
 1.2571 030 
 1.2607 340 
 1.2624 320 
 
 1.2025 503 
 1.3082 089 
 1.3212 910 
 1.334.5 039 
 1.3478 490 
 
 1.3613 274 
 
 1.3749 407 I 
 1.388G 901 I 
 1.4025 770 ! 
 1 41t;C 028 : 
 
 1.4307 688 ! 
 1.41.50 705 I 
 1.4595 272 j 
 1.-1711 225 ' 
 1.4b.s8 r,37 I 
 
 li per ft. 
 
 10150 
 
 000 
 
 1.030-' 
 
 •-'.50 
 
 i.ot.-i; 
 
 781 
 
 1.0013 
 
 O'.tj 
 
 1.0772 
 
 .S40 
 
 9 per ct. 3} per ct. 
 
 1. 0113 1 433 
 1.1098 1.50 
 1.1204 920 
 l.i 133 900 
 1.1005 408 
 
 1.1779 489 
 l.i!-5G 182 
 1.2!.i5 524 
 1.2317 557 
 1.2502 321 
 
 1.2i;89 865 
 1.2.SM) 203 
 1.307:i lO'. 
 1.82(;o 507 
 1.3108 :<'>Q 
 
 1.3670 578 
 1 3875 037 
 1.10-:f 772 
 1.4'J.i5 028 
 1.450J 454 
 
 1.4727 095 
 
 1.1918 002 
 1.5172 -'22 
 
 1.6;;9:t 805 
 l.SOaO 802 
 
 1.5865 264 
 1.6103 243 
 1.6344 792 
 1.65tt9 064 
 1.0638 813 
 
 1.7091 396 
 
 1 7347 706 
 
 1.7607 983 
 
 1.7S72 103 
 
 1.8110 184 
 
 1.0200 000 
 1.0 iul 000 
 1.0012 080 
 1.0fi24 321 
 1.1010 608 
 
 1.1261 624 
 1.1480 856 
 1.1710 593 
 1.19.-0 925 
 1 2189 944 
 
 1.2433 743 
 1 26S2 417 
 1.2936 066 
 1.3104 787 
 1.3468 683 
 
 1.3727 857 
 1.1002 414 
 1.42-12 462 
 1.4508 111 
 1.4859 474 
 
 1.51"i; 063 
 1.545.1 796 
 1.570,s 092 
 1.0084 372 
 1.6406 059 
 
 1 6734 181 
 
 1.70(J8 PTl 
 1.7410 212 
 1.7758 440 
 1.8118 615 
 
 1.8475 888 
 1.8845 406 
 1.9222 314 
 1.9606 760 
 1.9993 805 
 
 1 02.50 000 
 1.0.,06 250 
 1.070,s 906 
 1.1038 128 
 1.1314 082 
 
 1.1696 934 
 1.1 8S6 857 
 1.2184 029 
 1.246^ 629 
 1.2800 845 
 
 1.3120 6u6 
 1 3448 688 
 1.8785 110 
 1.4129 738 
 1.4482 931 
 
 1.4845 050, 
 1.6216 lv2 
 1.5596 587 
 1.598b .501 
 1.0386 104 
 
 8 P«T cl. 
 
 1.0300 000 
 1.0009 000 
 1.0.<27 270 
 1.1J.-.5 088 
 1.1.502 740 
 
 1.1910 ,523 
 1.221/8 738 
 1.2667 700 
 1.3047 731 
 1.3439 163 
 
 1 3842 338 
 
 1.4'-',57 608 
 I.i6s5 337 
 1 5125 «97 
 1.6579 674 
 
 1 6<»i7 
 1.6528 
 1.7024 
 17535 
 1.8061 
 
 064 
 476 
 380 
 060 
 112 
 
 3.0398 878 
 2.0806 850 
 2.1222 987 
 2.1647 447 
 2.2080 396 
 
 1.6795 818 
 
 1.8602 945 
 
 1.7215 714 
 
 1 0161 034 
 
 1.70 ;o 100 
 
 1 0735 865 
 
 l.m^l 259 
 
 2.0327 941 
 
 1 8539 441 
 
 2.0937 779 
 
 1.9002 927 
 
 2.1565 912 
 
 1.9478 000 
 
 2.2212 890 
 
 1.9964 950 
 
 2.2879 276 
 
 2.0464 073 
 
 2.3565 655 
 
 2.0975 676 
 
 2.4272 624 
 
 2.1500 067 
 2 2037 669 
 2.2588 508 
 2.3163 221 
 2.8782 061 
 
 3.4326 368 
 
 2.4933 487 
 2.6566 824 
 2.6195 744 
 2.6850 638 
 
 2.5000 808 
 2 57,50 827 
 2.6523 362 
 2.7319 063 
 3.8138 624 
 
 3.8982 783 
 2.9852 266 
 8.0747 834 
 8.1670 369 
 8.2620 877 
 
 " -M^-m^mm^^i'i 
 
 -^? 
 
 ■.•i.7 
 
 "i^^ 
 
 s^0. 
 
 fo/ 
 
 ■=«ilVniiBFC 
 
COUi'VlSb IXTKimST. 
 Tabu. 
 
 I7« 
 
 Vr».!;fi^crri.! i p,., ot. li „<, cl. 
 
 1 
 •J 
 3 
 4 
 .1 
 
 <) 
 
 7 
 
 f) 
 
 9 
 
 10 
 
 11 
 1.1 
 til 
 II 
 1.1 
 
 16 
 17 
 IM 
 
 li> 
 SO 
 
 91 
 
 36 
 37 
 
 39 
 80 
 
 31 
 
 83 
 33 
 •Si 
 3J 
 
 36 
 37 
 3!« 
 3<J 
 40 
 
 l.at.:o 000 
 
 I.OTIJ vf-.i 
 1.HH7 17^ 
 
 1.1 »:.") •j.io 
 l.l»7i'' Ni;; 
 
 1.22'J2 .-,53 
 1.L'7l'2 7!I2 
 1 ap.s 000 
 l..i'i-'S !)7a 
 1.U05 987 
 
 t.4.500 r,97 
 I.-MIO r,.6 I 
 l.oi;;;0 6(io 
 
 l.•!i^O (M.i 
 1.C703 1.S8 
 
 1.7HH9 HfiO 
 
 1.791(1 7r,:, 
 
 1.8574 892 
 1.!I22.''. 013 
 l.!M',(7 88S 
 
 2.059i 314 
 2.i;tl5 115 
 2.2001 Ml 
 2 2.S;j.{ -Ml 
 a.3632 449 ! 
 
 2.4.1.-.9 .-„s,-, i 
 2.5:315 071 
 2.Gi'01 719 
 2.7 US 779 
 2.8007 937 
 
 1.0 mo 000 
 l.O'l.; i,()0 
 1 J 2 n 040 
 1.1 '''.H 5M5 
 i ].21tx, 5J9 
 
 1.2053 190 
 1.31.VJ 317 
 l.-MUr, coo 
 1 !■•■„( 118 
 l.lc02 442 
 
 1.S394 540 
 l.'^nio 322 
 l.(;(,.-,0 735 
 1.7:il ■. 704 
 1.8009 436 
 
 1.0 I'D 000 
 
 l.O'.iJ » 2 ".I I 
 
 1.I4I1 tlOi 
 
 l.I'.i'J5 is, 
 
 1 2iOI Mlu 
 
 i..'inj_' f,oi 
 
 i.aoiH tils 
 
 1.4l'.1 (10 ; 
 
 1.4s M,-,i 
 
 I.e.-.--.' ..91 
 
 l.«22-l 530 
 
 l.Of' ,-1 sill 
 1.7721 :- 1 ! 
 l.K"l9 4<:» I 
 
 1 935-.' 821 I 
 
 a pcrfl. I.^f prr cl. 
 
 1 0":i.) OOO 
 l.lOJ'. 000 
 1 157'; 250 
 1 21.-.-, 003 
 1.2702 610 I 
 
 l..TIO» 
 
 l.ll!. ' 
 
 l.i; : 
 
 1.0-j8:h 
 
 1.7M3 
 
 i.7;'5s 
 
 I.il7!';» 
 2.0789 
 
 !'50 
 "04 
 
 :m;; I 
 
 5i;;i 
 
 4. 1 
 31 fl 
 2si' 
 
 1.8729 812 .i.0223 701 
 
 1.9479 005 2.1].;;i 708 
 
 2.0::58 105 2.'J0si 787 
 
 2.IC08 491 2.3!i7.-5 003 
 
 2.1911 231 2.4117 140 
 
 2S0.-;0 314 
 3.0007 075 
 3.1119 423 
 3.2208 003 
 3 3335 904 
 
 3.45(i2 661 
 3.5710 254 
 3.6!I00 113 
 3.82,53 717 
 3.9592 697 
 
 2.2787 C80 
 2.3099 ls7 
 
 2.4047 156 
 2 5(;33 Oil 
 2 GhoS 303 
 
 2.7721 097 
 2.8S33 i;s5 I 
 2.9987 033 j 
 8 1180 514 
 3.2433 975 
 
 3.3731 834 \ 
 
 3.."0ti0 587 i 
 3.01.S3 811 
 3.7943 103 
 8.9460 889 
 
 4.10.S9 825 
 4.2080 898 
 4.4388 134 
 4.6163 669 
 4.8010 206 
 
 2.5202 411 
 2.0330 520 
 2.7521 00'! 
 2.87i;o l:;.s 
 3.0J51 314 
 
 , 3 1400 790 
 
 ! 3.i'S.'0 096 
 
 I 3.-i'-".i.; 999 
 
 3..-,sii.i 304 
 
 j 3.7463 181 
 
 ' 3.9138 574 
 4 0899 810 
 4.2740 301 
 4.4603 016 
 4.C673 478 
 
 4 8773 784 
 5.09('8 004 
 5.32t;2 192 
 5.50.08 9!10 
 6.8103 045 
 
 2.IS-, 71:; 
 2.2. '-0 l>-3 
 
 2.i-;(; 192 
 
 2. '20;) 502 
 2.0532 977 
 
 2. ',859 
 2.9.,^J 
 3.071.- 
 3.22.'.0 
 3.3600 
 
 02G 
 '■■07 
 238 
 
 '.199 
 519 
 
 3.5.'05 727 
 3.7::' i .'o.i 
 ".I'-'ul 291 
 4.1161 350 
 4.3219 424 
 
 4-5:!'5-'") 395 
 4.7'-.19 415 
 5.0031 S,S5 
 6,2533 4s0 
 6.5100 154 
 
 •^.7918 101 
 O.OsU 009 
 6.;i.S5i 773 ; 
 6.7017 512 I 
 7.0399 887 
 
 •NoT«.-A8 the 5J table is eoldora Z^^H^];;^, 
 iiircc Sgarea. 
 
 1.0,-.-, 
 l.I!3 
 1.174 
 l.-.'.i9 
 1 307 
 
 1.,I7U 
 1.1. '>« 
 1. .-;;., 
 
 !.»,;■! 
 1.7od 
 
 l.vO'i 
 l.-'..l 
 2.0)0 
 2.116 
 2.232 
 
 2.355 
 
 2.'185 
 2.f.21 
 
 2.7(-0 
 
 2.J18 
 
 3.078 
 8.248 
 
 8.420 
 8.0 1 5 
 8.813 
 
 4.023 
 4-211 
 
 4.478 
 4.724 
 4.984 
 
 6.258 
 6.517 
 6.8.V2 
 6.174 
 6.614 
 
 6.872 
 7.2,-0 
 7.0(9 
 8.1 1;9 
 8.613 
 
 we only ciUiad M 
 

 v,r-j 
 
MICROCOPY RESOIUTION TEST CHART 
 
 (ANSI and ISO TEST CHART No. 2) 
 
 ^ APPLIED INA^G E 
 
 '653 Eost Main Slreel 
 Rochester. New York 14609 
 
 (716) 482 - 0300 - Phone 
 (716) 288 - 5989 - Fa« 
 
 USA 
 
I 
 
 ; 
 
 If : ^ 
 
 COMfOUND 
 
 TlBU. 
 
 II 
 
 Yrs. 
 
 1 
 
 9 
 
 3 
 
 4 
 A 
 
 6 
 
 7 
 
 8 
 
 9 
 
 lO 
 
 11 
 13 
 13 
 14 
 13 
 
 16 
 IV 
 18 
 19 
 30 
 
 31 
 33 
 33 
 34 
 35 
 
 36 
 37 
 38 
 39 
 30 
 
 81 
 
 S3 
 33 
 84 
 85 
 
 86 
 87 
 88 
 89 
 40 
 
 6 per ct. 
 
 7 per ct. 
 
 1.0600 000 
 1.1236 000 
 1.1910 160 
 1.2624 770 
 1.3382 256 
 
 1.4185 191 
 1.6036 803 
 1.5938 481 
 1.6«91 790 
 1.7908 477 
 
 1.8982 986 
 2.0121 985 
 2.1329 283 
 2.2009 040 
 2.B965 582 
 
 8.5403 517 
 2.6927 728 
 2.8543 392 
 3.0255 995 
 3.2071 355 
 
 3.3995 636 
 8.6035 374 
 3.8197 497 
 4.0489 346 
 4.2918 707 
 
 4.6498 830 
 4.8223 459 
 6.1116 867 
 6.4183 879 
 6.7434 912 
 
 6.0881 006 
 6.4533 8G7 
 6.8405 899 
 7. 2510 258 
 7.6860 868 
 
 8.1472 620 
 8.6360 871 
 9.1642 624 
 9.7036 076 
 
 10.2857 179 
 
 8 per ct. 
 
 1.0700 000 
 1.1449 000 
 1-2-250 430 
 1.3107 960 
 1.4025 517 
 
 1.5007 304 
 1.6057 815 
 1.7181 862 
 1.8384 692 
 1.9671 514 
 
 2.1048 620 
 2.2521 916 
 2.4098 4o0 
 2.6785 342 
 2.7590 316 
 
 2.9621 638 
 3.1688 152 
 3.3799 323 
 8.6165 275 
 8.8696 846 
 
 4.1405 624 
 4.4304 017 
 4.7405 299 
 5.0723 670 
 6.4274 326 
 
 6.8073 529 
 6.2138 676 
 6.6488 384 
 7.1142 571 
 7.6122 550 
 
 8.1451 129 
 8.7152 708 
 93253 398 
 9.9781 135 
 10.6766 816 
 
 11.4239 422 
 12.2236 181 
 13.0792 714 
 13.9948 204 
 14.9744 678 
 
 9 per ct. 
 
 1.0300 000 
 1.1064 000 
 1.2597 120 
 1 3601 800 
 1.4093 281 
 
 1.5668 748 
 1.7138 213 
 1.85 i9 302 
 1.9990 046 
 2.1589 250 
 
 2.3316 390 
 2.5181 701 
 2.7196 237 
 2.9371 936 
 8.1721 691 
 
 8.4259 426 
 8.7000 181 
 8.V960 196 
 4.8167 Oil 
 4.6609 671 
 
 6.0338 337 
 6.4365 404 
 5.8714 637 
 6.3411 807 
 6.8484 762 
 
 7.8968 682 
 7.9880 615 
 8.6271 064 
 9.8172 749 
 10.0626 669 
 
 10.8676 694 
 11.7870 830 
 12.6760 496 
 13.6901 336 
 14.7853 448 
 
 169681 718 
 17.2456 266 
 18.6252 756 
 20.1162 977 
 21.7245 216 
 
 lO per ct. 
 
 1.0900 000 
 1.1881 000 
 1.29')0 290 
 1.4115 816 
 1.6386 240 
 
 1.6771 001 
 
 1 8280 391 
 1.9925 626 
 2.1718 933 
 
 2 3673 637 
 
 2.5804 264 
 2.8126 <'.48 
 3.0658 046 
 3.3117 270 
 3.6424 826 
 
 8.9703 059 
 4.3276 834 
 4.7171 204 
 6.1416 613 
 6.6044 108 
 
 6.1038 077 
 6.6586 004 
 7.2578 746 
 7.9110 882 
 8.6230 807 
 
 98991 679 
 10.2450 821 
 11.1671 896 
 12.1721 P21 
 13.2676 786 
 
 14.4617 695 
 16.7638 288 
 17.1820 284 
 18.7284 109 
 20.4189 679 
 
 22.2612 260 
 24.2538 868 
 26.4366 806 
 28-8169 817 
 81.4094 200 
 
 1.1000 000 
 1.2100 000 
 1.3310 000 
 1.4041 000 
 1.6105 100 
 
 1.7715 610 
 1.9487 171 
 2.1435 888 
 2.3579 477 
 2.5937 426 
 
 2 8531 167 
 
 3.i;W4 284 
 3.4.Vi2 712 
 8.7974 983 
 4.1772 482 
 
 4.5940 730 
 6.0544 703 
 6.5599 173 
 6.1159 390 
 6.7276 000 
 
 7.4002 499 
 8.1402 749 
 8.9543 024 
 9.8497 327 
 10.8347 059 
 
 11.9181 766 
 18.1099 942 
 14.4209 986 
 16.8630 930 
 17.4494 083 
 
 19.1948 425 
 81.1187 768 
 23.2261 544 
 25.5476 699 
 28.1024 869 
 
 80.9126 806 
 84.0039 486 
 87.4048 484 
 41.1447 778 
 45.8598 666 
 
 ll' -^ }| i i, 
 
COMPOUND INTEREST. j-r- 
 
 NoTBB l.-If each of the nambere in the table be diminiBhed by 1, th. 
 remainder will denote the compound interest of $1. instead of its 
 ftmonnt. 
 
 » J J!;!"*""*!. " <^"P°°'"*«^ eemi.annuaJly, take J the given rate and 
 rmce the number of years; if compounded quarterly, take J the j-iven 
 rate for 4 times the number of years, etc. 
 
 cnLII'Vr"*"!'"' *°^ '""°^^' °^ y^*" °°' Siren in ihe table mav be 
 computed by finding the products of the amounts for any two numbers 
 <M years whose sum equals the given time. 
 
 mnin^? ^1^ ^^^ *.°T* °' "'^ ^^^° principal at compound interest, 
 multiply the principal by the amount of 81 for the time and r.te. 
 
 «. If the time contains parts of a period, as months or da)«. find the 
 •mount due for the full periods, and to this add it. interest for the 
 months or days. 
 
 EXERCISE 8f. 
 
 Find the amount and the compound interest of— 
 
 1. $312 for 8 years at 6% ; $800 for 4 years at 4%. 
 
 2. $640 for 4 years at 6%; $376 for 8 years 8 months 
 and 16 days at 6%. 
 
 a. $1,200 for two years 4 months at ^%; for 3 years 
 8 months at 7 %. 
 
 4. $400 for 1 year 6 months at 7%, payable semi- 
 annually. 
 
 6. $2,000 for 1 year at 8^, payable quarterly. 
 
 6. $1,000 for 23 years at 7%. 
 
 7. $750 for 12 years at 3%. 
 
 8. $920 for 8 years at 5 %. 
 
 9. $2,600 at 6%, from Jan. 1st, 1870, to Jan. Ist, 1891. 
 
 10. $1,410 at 8%, from March SO.u. 1889, to August 
 15th, 18i)4. 
 
 11. What is tlie amount of $3,500 for 6 years at 6 -^^ 
 compound interest ? .> /o 
 
 12. What is the amount of $1,350 for 12 years at 7 %?j 
 
178 
 
 COMPOUND INTEREST. 
 
 13. What is the compound interest of $1,-169 for Iff 
 
 years at at 3%. 
 
 14. Wha*-. is the compound interest of $2,500 for 24 
 years at 6 %. 
 
 15. What is the compound interest of $1,650 for 80 
 years at 8 J %. 
 
 16. What i" the amount of $1,800 for 8 years at 6% 
 compound iutertst, payable semi-annually? 
 
 17. Whftt ie the amount of 1,500 for 2 years, at 12% 
 compound interest, payable quarterly ? 
 
 18. What is the compound interest of $5,000 for 2 years, 
 at 6%, if the interest is due annually ? If the interest is 
 payable half-yearly ? If the interest is payable quarterly ? 
 
 19. By how much does interest compounded semi-annu- 
 ally exceed simple interest, on $400, for 2 years 6 months 
 at 7%? 
 
 20. What is the amount of $2,400 from ^fay Ist, 1887, to 
 Jan. 14th, 1890, interest compounded half-yearly, at 5%? 
 What is the amount, if the interest is compounded yearly? 
 What is the amount, at simple interest ? 
 
 21. What is the compound interest on $7,325 for 2 years 
 2 months at 7%? 
 
 22. Find the compound interest on $3,333 at SJ % semi- 
 annually for 1 year 7 months. 
 
 ■23. What amount was due March 25th, 1886, on $1,612 
 borrowed Jan. 25th, 1885, with compound interest at 1^% 
 quarterly ? 
 
 24. What is the amount of $4,615 at compound interest 
 for 2 years 5 months at 8% ? 
 
 25. Find the amount of $3,500 at compound interest 
 from Oct. 29th, 1888, to Nov. 16th, 1889, at 2% quarterly. 
 
COMPOUND INTEHEST. 
 
 26. How much Rreuter. af eompoun.l than at muule 
 .n^-rest. would be the a.uouut of $1,568 in 3 ,ea.s 8 naonul: 
 
 27. Find the amount due Sept. 18th, 1889 on «i^o 
 loane^^ Sept. 18th. 1886. Intere'st comp'oun.ie'l Z^ 
 
 of '^rnn?^' 'Vt' '"''''"*' ^^"^PO'^^^ed every six n.ouths 
 
 29. What will $16,000 invested Jan Ilth ift^. ./ 
 »oSep.lCth,1893,atlO,,intere^;;2r,:::i;r 
 y^rs old that, on arriving at 21, he may havo .^.5 000 
 It^ul;?'""' '^ "^' ^'" '"^--^'^^ --I--''^'' --i- 
 To Jiud the principal or present worth of an amount at 
 ^p^onn. interest, airide the .iren amount L, the a,nZ of 
 Sljor the gu-en t^ne and rate at compound interest, f i. e 
 Ze:Zr ' '-^"''" ''' '"''''' ""-'''' as i,: simple 
 
 31. What is the present worth of $6,03G.:i5 due in 8 
 yenrs, at 6 % compound interest ? 
 
 jZ-f'^-^Q^t «'i"''^"' ^* compoun 1 interest will amount to 
 |2,ii < 0.92 at 6 % m 14 years ? 
 
 33. What is the present worth of $2,521.81 due in 14 
 years, at 6 % compound interest ? 
 
 What principal at 10% will amount to $265 83 in 
 10 years, niterest payable semi-annually ? 
 
 85. What sum at compound interest at 4%, interest due 
 annually, w.ll amount to $1,000 in three years ? 
 
 36^ What sum would have to be put out at 6%. interest 
 payable every six months, to produce $54a.3456 compound 
 interest in 8 years ? f"""« 
 
 37. At what rate would $500 have to be loaned, to 
 amount to $107940 in 10 years, the interest being com- 
 pounded annually ? 
 
IbO 
 
 70VNT. 
 
 DISCOUNT. 
 
 3«4. Discount is an fl])citciiicnt or allowance in.de 
 from tljo amount of a debt, a note or other obligation. 
 
 SSrS. The term discount is often used without refer- 
 ence to time to imply an abatement at a certain rate per 
 cent, on a 2 rice asked. 
 
 356. When Time enters in as an element, two kinds 
 of Disconr-t are distinguished, viz.: True Discount aud 
 Bank Discount 
 
 TRUE DISCOUNT. 
 
 .357. The Present Worth of a debt, note or other 
 obligation, payable a a future time without interest, is 
 such a sum as, being placed at interest at a legal rate, will 
 amount to the given sum when it becomes due. 
 
 35S. True Discount is the difference between any 
 Hiim of money payable at a future time find its present 
 worth, and is equal to the interest on the present worth. 
 
 Ij.r,n8TRATio!*.— Suppose A. o\VL=i B. SIOiJ payable a vear honoo witliout 
 :r.t..Test. Tlie current rate of intertat being G %, the pre-o :it worth of 
 tlie debt is JlOO, because that sum would amount to $106 in 1 vcar at 
 " %■ 
 
 The tme discount is »10C- $100 or 56, which is evidently the interest 
 on the present worth 5100, for 1 year at 6 %. 
 
 .359. To find the present worth and true discount, 
 the face of the debt, rate per cent, per annum, and time 
 being given. 
 
3 
 
 TRUE DISCOUNT. 
 
 181 
 •l.l60?o"ry"a«mi^* *"""* ''°"'' ""^ """" ^''*"""» ^ * '^''bt of 
 
 Interest on 81,00 for « years at 6% . 
 .*. #1.36 has for its present worth 
 •1. " 
 81,S60 •• M 
 
 » 
 
 81.00 
 
 1.00 
 
 i.ao 
 
 100 X 1,860 
 
 136 
 » 81,000, present worth. 
 ?3G0, true discount. 
 
 11,360 - 81,000 = 
 J- Divide the face of the debt' by the amount of Str r ,t 
 
 SOLUTIOM. 
 
 81.20 has for Us discount 820 
 II u „ .20 
 
 91,781.40 <• 
 
 1.20" 
 1,7h1.4i» X 20 
 
 829G.90, discount 
 
 ^^^i<i« the interest of the deht fn,. ih. ■ 
 
 h the amount of «?/ / '1 • ' ^""^'^ '""* ^"'^ ''"'^ 
 
 «^ «w amo„«f oj SI, ana the quotient will be the discount. 
 
 I?- J .u EXERCISE 82. 
 
 Fmd the present worth and true discount- 
 
 2.Ofe6bI..0at7%daein3vr.9n,o. 
 8. Of^500at5%dueinllu,; 
 
 6- Of »l,57o at 7;i duo i„ i yr. 3,„o 15 j. 
 6.0f§8GOatf.i%du«i„9ol ^ 
 
 7.Of8078 4Oat4i%d.9inlf3u,o. 
 
 ». Of 8990.7oatl0%duoiu7o,la. 
 10. Of ?l,315.45at8%duoin219d«. 
 
182 
 
 TiWK biscouai. 
 
 
 Find tlie true discount on — 
 
 11. 81,600 duo in 3. vr. fi mo. at 6%. 
 
 12. 83.:.r.() duo in 110 ill at 7%. 
 
 1- $4,'»(;0.76 due in iHmo. ;it ('.J%. 
 14. S'JilO.lOdnoin 7:1 da iit Kt;^. 
 16 Jl>25.i;5 due in 8 mo. at 7j^ %, 
 
 16. Wljich is the In-tt. .-, to buy flour at $S a barrel, on 
 6 months' credit, or |7.50 cnsh, mouay beiu;^ u..rtb b%? 
 
 17. Wliat is the (lillerence between the iuteroat and true 
 discount of $1,();30, at 6%, due in 8 months? 
 
 18. Which is worth the most, $010 in 12 months, $620 
 in G months, or iJiJOO cash, money being worth 8%? 
 
 19. Bour;bt a farm for $2,!)(J4.12 ready money, and sold 
 It again for .58,n(;5.20, payable in 1 year, 6 months. How 
 much would be gained in ready money, reckoning true dis- 
 count at 8%? 
 
 20. Having bought a liouse for $5,048 cash, I at once 
 sold It for $7,000, to be paid in 18 mouths without interest 
 If money is worth 8% per annum, did I gain or lose, and 
 bow much ? 
 
 21. A man bought a flouring mill for $10,000 cash, or for 
 $12,000 payable in 6 months, or $15,000 payable in 1 
 years months. He accepted the latter offer ; did he gain 
 or lose, and how much, money being worth to hun 10%. 
 
 22. Goods to the amount of $510 were sold on 6 months* 
 credit. If the selling price was $30 less than the goods 
 cost, and money is worth 6% per annum, how much was 
 the loss and the per cent, of loss ? 
 
 23. A speculator bought 120 bales of cotton, er. h bale 
 containing 488 pounds, at 9 centF a pound, on a credit of 
 9 months for the amount. He immediately sold the cotton 
 for $6,441.60 cash, and paid the debt at 8% discount ; how 
 much did he gain ? 
 
ThUE Diacuu^T. 
 
 188 
 
 24. How much mnst I,. di^muuWd for t>'e proHont nrv 
 
 01 6 months ; .SM.,...) for H ,„ .nth., uu.l the rHuaindcr for 
 16 months, money hdn- worili lo- ,„>r ann.nn? 
 
 25 A inorch.nt hon^^ht a hill of ;; ..Jh for ,^2 ir.O on 6 
 month^crecUt and the s.ller off,.,! to d.cJunt th'e hi, 
 a 6 %. for I,. If ,„,,ey in worth 7| - p.r. ann.uu. lunv 
 much w.uld the merchant g.in hy accepting the Beliers 
 
 26 A merchant bought a bill of goo,ls on (5 months- 
 credit amounting to $1,-150. What will he gain by ,avs..nt 
 
 nr.:;ir^^^'''^^'^°-^ ^^°^ -•''>• ''^-- 
 
 27. A dealer bought grain to the amount of .^2 700 on 
 4 months' credit and immediate y sold u at an advan.'e of 
 
 M /i ? , ^''''''"^' "^ ^^'' ^^''^ 1'^ l«^i^^ ti'e nres.nt 
 worth of his debt at a rate of discount of 8% per inaum 
 how much did he gain ? 'i"uum, 
 
 28. After carrying a stock of silk for 4 months, I sold it 
 at an advance of 80% on iii.t co.t, , .tending to the ,hi - 
 
 wouh 5 o^ per annum, what was my per cent, of i.roiil or 
 
 for1'J"n'''* *n'"'' ^'' ^^'^^^ '■^^''>' "^^•"^'>' ^°d sold it 
 foi $5,2o0, payable ,n 1 year G months. How much would 
 
 be gamed in ready money, discounting at the rate of 8%? 
 How much, discounting at the rate of G % ? 
 
 80^ The asking price of a hardware stock is $6,4G0. on 
 whch a trade discount of 25%, 15 o^, and 10 % is offe ed 
 and a credit of 90 days on the selling price. If money is 
 
 Tf'i r,w ''^** '""" '^'°"'^ ^' .iiseounted for the pavment 
 of the bill ten days after its purchase ? i . "* 
 

 1 
 
 til 
 
 W 
 
 IU4 
 
 iM.V/i DlSCuV.M. 
 
 BANK DISCOUNT. 
 
 a«l. Bank Discount in n .I.Mluctioii iiHnnlly mndo hy 
 l>niikH for paying a nolo bofon- • h .Inn. This .l,..lucti<)f, is 
 til.' iutorest on the fiico of th.- n^to for tli.' tiiii« it haH 
 to run, inelu.lin« tlirco ftd.li'oinil diiyrt, call.,! I>.,u$ of 
 
 :i«t». Days of Grace ivro tliroo ,.'ayH iisnillv nllowo.l 
 for tlio j.iivnunt of u note, iil. jr tho oxpiritioi. of (lio time 
 Hpeeitiod in tho nolo. 
 
 mill, riui Proceeds of a note is tlio ainoimt rvcch-vl 
 by tho hoMcr from tho bank whop tho note i» ,U>.ouuU>d. 
 It irt tho amount of tho nolo at maturity Iobh tho iutcnat 
 on tliat amount for tho term of di u-oinit. 
 
 Iu,tTHriuTi.iti-A por8..n h,-l.l« » nolo f„r 91.000 imval.le in 7:» .lays, 
 incln.imf; the .lays of «racc Wislii.ij; to ii«o tho inon. v ii.nnr.iiat.ly ha' 
 in.lorHos tho note aiul olTors it to I.Ih bank for diH.nii..t If both umkvr 
 »ncl iiulnrsrr are consiciriv.l n ponsihlo. the banli rrlMJim tl.o nolo ami 
 if the 1, ;:,,! rate i« «%. do.i-ctin- SIJ (tl,o intorost of »I.00() for 7:i cinys) 
 pays over ilio balanco ?;.tW to tli- hohhT. Tho note is thus diBoouutod ' 
 the bank discount ia iV2 ; tho iiroceoda aro 8'. .HH. 
 
 ;i« i. Negotiable paper commonly inchidos all ordeis 
 and promises f..r the paynu. * of money, the {)roi.erty 
 interebt in which may be negotiated or transferred by 
 iudor.soment. 
 
 ima. A Promissory Note ia a written, or partlv writ- 
 ten and partlv printed, agreement to pay a certain sum of 
 money, either on demand or at a specified time. 
 
 3««. The Face of a Note is the sum for which it is 
 given. 
 
 367. The Maturity of a note is the expiration of the 
 timi' ineludinf^ days of grace. 
 
Jijt.\K IHScniJM. 
 
 I.,.-, 
 
 :tilH. Tlu. Time in larik .lis.ount in ,ilwav« ,i 
 
 •'""-" ' '■""■■'" t.n;j:;::::;:;: ,■';;•;:;;:;■';'; 
 
 -r^r;::n:^:™:i::::r ■""•"'"■- • '^ 
 
 a^O. Value of a note ,a itn ,n,,(„ri(y ,. ,h r. 7 » 
 
 «"':::: V:":;:::::;''.,tr':;;r;''"'^ ^ -^ ' •-" - 
 
 '•CO, UM.,1 .ft...r u„annly. fro,,. wl.,H. , ' " ',''"""■"' "" »»>« 
 
 P'T .■..,.t. -..,„ ,.0 r. .„vvn.,| If """■■■ ""■ '•^■■'' ^"^^ - "•« 
 
 "'"" 'i i" -^luioM to thn wol . ; ;;; tt " """■■' "" '■^^^^o' 
 
 W'.r.l. •Mn.til,,Hur'arol,| I ' ^'"; "'^' '■'•'-' t'"> r.N, of _;. t,„ 
 of ,.y.n....t of'note. ot 1 , ' Ji^;"'" --", "" '="^'" -'' »■" '<».« 
 
 -t.fn.„,,„,uu-uytn,p.,,,,,,.,!:j;::'';,/:.:;:i.''' '^"" "^^' *"' '->■ 
 
 -'■ llio |.,,rs.,n who i>roirii...;H to n^v n .I'...! ,i,„ . 
 
 re.pon«n,,.fortho,aj;::::'ltt„'''''" " '''"'•^ '"' '•^'-- -'■' ^^ 
 
 -uat ba hoi. by the ,.ay. ^ ^.tll it ':;;''',;:'"^ '^'"""^^ '^ '^--'-' ' ^ '' 
 
 th!-,:!;:':;:orr"" °"'^ ^''^" " ^^ -"^ ^-^^-^'^ "^ t... .., ., 
 
 .o.„ent endorser ie not ii!!;; ilT^lllJ^i^Sr '" "" '^''''- "^ -'' 
 
 «i:in:uh:rr :;:::•; -;• , :;: ;-- -^ •« --^ • ^^^«. ..,„,... 
 
 reapons.hloforpay.neVt "'"' "" -"'--'"na a. s„d. .s 
 
 7. If the payee writes above his si.'naturo '• P.- , t„ fi 
 
 .t 18 called a/u/i enUor.en.ent. In this case k B 1 , 1 !^ '"^" °^ '^ " " 
 before he can n. .,,ti:,te it. ^^' ^"''^ '° ^"'J'---s« '» 
 
 8. If the payee writes above bis signature. • Pay to A R , ■■ 
 ter.n..,l a rcttricth-^ en.lorPempn* «• i ay to A. B only," u is 
 
 fl 
 
I 
 
 i 
 
 lb6 
 
 BANK DISCOUNT. 
 
 9 If tlio onilorsor (loot not wi<!i ti rcnler hlinm If Un.h\n for |iii\mcnl 
 h« *li')iil<l writo, " Withoot r>!oi)iir«« t.i mn, ' i.ne Ins iiiiiii«. Tuih ii 
 Oulli 'I u quiilififd eiiilorBumonl. 
 
 10. Wlien a noti^ ia iiin<lo pnyalilo to lu'iiror it ia iieijotiubli witln^ut 
 •ndomotnent, (lolivrry boinK nil iln^t i* m-o'flHury. 
 
 11. lu ealculiitiii^.' tlio (lato i>f iiiuturity of ii notu, t1i<- tnn-e dttyit ^'rnoi- 
 m it be alliiwcil after tlie time expresH' .1 tluit in, it f iIIm dm- on tlif lliinl 
 day aftor its turm litu u\|)lrod. T)i« day on wliicli thu iioto i<i dutcd it 
 not counti'd in c-oinputin^ the dat« of maturity. 
 
 12. Wli II a nolo boioiiiiM due wliii:li luippcns on the tliiril day after 
 the time iixj.re <h1, it muat bo pnsi-nt.d for |iayinoiit diinn ■ litniiinHH 
 huurH at tliu (ilaoe nicntionotl in it. If no [ilari> in mIhI i it nIkiuM bo 
 prcHL'iit' d at tliu iniikir'H place nf bii-iiiit>:->) or at hiM rcHidoiice. 
 
 1;H. Sliotild the makur ri'fiise to pay it, the propor d«mniid tn'in^! made 
 it in the duty of the holdi r to 'lire ,lut notice to all tho parties to it. Ue 
 may have it protdstud if he chtiosua. 
 
 371. A Protest is a dcclar-'tion in writing by a 
 Notary Piiblic, giving legal notioo tu the juakcr and oiidor- 
 Bcrs of a note of its non-i)iiym(.'nt. In Uulurio a notu raust 
 be protested on the day of its maturity, othorwise the 
 endoiser.s are rtioastd from all obIij.';ition to pay thf note. 
 
 N'TKs 1. When a nite booDin.'s duo ou Sun lay or a lo;;. ' lioliday, it 
 nmst bo pi: i on the day followin;^. 
 
 2. The person paying; a uoto has a ri<;ht to a reoe.pt, wlii::h ia usually 
 written on the back of the note. 
 
 3 The person who pays a note has a right to it as his voucher, if it it 
 netjotiable, but not otherwise. 
 
 4. Wlion a note is made payable with interest it bears interest from the 
 dato of it, aud not merely from its maturity. In Buoh a case the intcrt'st 
 is part of the debt. 
 
 6. Wlien a note bears interest, tho discount is computed ou the face of 
 tlje uoiu with the interest rdded. 
 
 G. When the term of a note is given in months, calendar montlia are 
 meant and no allowance is made for a deficiency in the number of days 
 iu any month. This being the case the student will see tliat four notes 
 drawn at 2 months and bearing dates. Doc. 28, Doc. 29, 1 )ec 30, Doc. 31, 
 rci^i-fe-tivfily, will beco!'.-.;' i'.'.s on the same day, viz, : March 8rd, of next 
 year. 
 
hASK IHSCOUS'T. 
 
 Ib7 
 
 7. WUn th. tira. U .„pr<,.„. ,„ ,/„;,,. ,1,, day .f maturity i. f., ,H !,, 
 onnt.n,. f.rwar.l r„„. tl.o .late of th. not<, tl. „/,.. „. Z^LJ, . 
 
 »rii. H.mks n> .liHc-ounting notes alwavH n^cKon din- 
 count for un exact nu.nl.cr .. .l.yH from the time of 
 d.HcounhnR to d.to of maturity. TIuh on a note mat.,ri,«« 
 Jnly 5th. and d,...ount<.d May 25th, the tern, of di^^ount 
 would be rtrkont-d ,. fnllowH : 6 days in May, + 80 duvs 
 in June + 6 days in july « 41 duyg. 
 
 not J*** ^^ ^"^ *^* ^^^^ discount and proceeds of a 
 
 fOBl, duo UO days lienoe, »t 7%. 
 
 SoLOTIOS. 
 
 The term of disooont is 93 day^. 
 
 iDterost of »C:i for 93 days at 7% » S12 20 . Bank df-co 
 •081 - »ia 20 = im 80 = Proceedi. 
 
 Er«,rt. a._A not« of $375 dated Octobc-r 2;!r,l. p.vablo in 30dav. 
 with .nterest at 7%. is disoouutod at a bank Novo.ub.r l^'th ut 8^ S 
 ths proceeds. ** *'"" 
 
 SoLCTION. 
 
 The dau of rnitnrity is Novemhur I'Gth. 
 The note bears interest for 34 davs. 
 
 13/76 
 1.875 
 .1875 
 .0l--'5 
 2.125 
 
 $2,479 
 
 Int. for ';Oda. at 6%. 
 " 30 " 
 
 '• 1 11 
 
 " 37 
 
 11 .. ^ 
 
 Int. for 3 Ida. at 7%. 
 
 12.479 (360 da. int.) less ^ of »2.479 » ?2..15 (acta- int.) 
 The amount of note at maturity is 8375 + 82.4.^. x> 8:^77 4s 
 or?47ayr '" '''''^ ^^ ^^' ''*"'' ^'''" November 12th unti'l November acth. 
 
j;i * 
 
 »r 1 
 
 •i ; 
 
 ri ' 
 
 liiW 
 
 Hi 
 
 l-ll 
 
 
 188 
 
 £^i^if DISCOUNT. 
 
 B Int. for 60 da. at 6%. 
 
 = " 12 •• 
 
 -)■ s " ^ " 
 
 « •• 14 » 
 
 + = •• " 2 
 
 = Int. for 14 da. at i"%. 
 
 11.15 (actaal int.) 
 
 •1.1742 
 11.174 (360 da. int.) loss ^ of $1,174 
 
 9377.45 = Amt. of note at maturity. 
 
 l-l" = Disct. for time held by bank. 
 1376.30 = Proceeds. 
 
 ExAMPia 3,— A note of 9760 dated August 4th, 1888. payable in ( 
 months with interest at 6%, is discounted at a bank October 20th, at 7 % 
 Find the proceeds. 
 
 Solution. 
 The date of maturity is February 7tb, 1889. 
 
 The note bears interest from August 4th, 1888, to February 7th. 1889. oi 
 187 days. 
 
 >7.50 a Int. for 60 da. at 6% 
 22.50 s " 180 •• 
 
 .75 s " 6 •• 
 
 .125 = •• 1 •• 
 
 187 
 
 J23.0C (actual int.) 
 
 J23.375 = 
 •23.375 (360 da. int.) less ^ of 823.375 
 The amount due at maturity ia ^750 + $23.00 = S773.06. 
 The note is held by the bank from October 20th, '88, to February 7th 
 '89. or 110 days. 
 
 •7.7306 = Int. for 60 da. at 6 % 
 3.8653 = " 30 
 2.57G3 + SI " 20 " 
 
 •14.1727 a •• iTo 
 ^.3621 + SB •• " 1 
 
 •16.5348 = Int. for llOda. atT%. 
 •16.58 (360 da. int.; Ies3 ^ of S16 .53 = 316..31 (actual int.) 
 •773 06 ai Amt of note at maturity. 
 
 ^31 B Disct for tima held by bank. 
 
 •756.75 = Proceeds. 
 
 EiAMPLi! 4.— Find day of maturity, the time to run, the discount, 
 and proceeds of the following note : 
 
 ^^•^00. Ottawa, February 3rd, 18S9. 
 
 Five months after date, I promise to pay John Craig, or order, 
 the sum of One Thousand Eight Hundred Dollars, value received with 
 interest at 6%. Thomis Cowajt. 
 
 Discounted May 22nd, 1889, at 7 %. 
 
BANK DISCOUNT. 
 
 SoiCTIO.N. 
 
 188 
 
 
 Ab the note, boars interest, the discount n,„ * u 
 .-- Of SI.SOO. fro. rebrua;, SrVto X" * ".t 5317^ "'^ ''' 
 imerest on J, ,S00 for 153 day. at 6 o^ , 345.27 + ' 
 
 The amount of note at n^aturity » 81,800 + $45.27 = »1 8,5 ,, 
 The note is held by the bank from Muv -nd to jl PH f ' 
 
 Interest 6u ?1 815 27 fnr j^ ^ ^ ""'• *"" *" "^a/*- 
 
 ■-u" .,1,010.^7 for .15 days at 7% « 81 loa j- 
 
 Proceeds - 81 845 27 ft, - o . „ ^'wowu. 
 »i,fl-io.^7 - 8I0.92 s SI, 829.86. 
 
 BULB. 
 
 EXERCISE 83. 
 
 Find th« bank di.co>,„t a„d proceeds of a note for- 
 
 9% II 
 
 2. 
 
 3. 81,000.00, 
 4 8110.2.5. 
 
 il 
 
 45 
 80 
 
 w 
 
 6% 
 
 Jui tUe date of inaturit, a„d , .-ceed, of the fo.Win, 
 
 6. 
 6. 
 
 7. 
 
 8. I 
 
 0. i 
 
 10. ! 
 
 D.^TE OF NoTB 
 
 January 20. 
 May 7".. . 
 June 4 .. . 
 July 27 . . . , 
 November 1. 
 ^^■^y '^7 .. .. 
 
 Facb. 
 
 82,500.7 
 81,200.. 
 f 3,G()0 . 
 SS,200. 
 
 80 cnn . 
 84,,s«o . . 
 
 Datb of 
 
 DlSCOCNT. 
 
 January 20 
 ^ay 31 . . . , 
 Ju'y 18 .. .. 
 
 f^^eiitember2. 
 Koveujber 28 
 Aujiust 15 .. 
 
-t 
 
 190 
 
 UASK DISCOUNT. 
 
 Fitid the jirncoids aiwi djito of tuiiturity of the following 
 notcH (liscoiiiilcil lliroiit;li a hioker, iiiu comiiiiBBion buiug 
 J% of til." face of tlie notcH : 
 
 11. 
 
 12. 
 
 in. 
 
 It 
 
 1.). 
 
 1C> 
 
 I>ATK or Nl'TK 
 
 FiluiiiUN 18. 
 •hiiio I .... 
 .Iiiiiiiiiry 10. . 
 Maroli:!., .. 
 i\Iny IS .. .. 
 .I.'iiiiiurv .S . , 
 
 '1 IMl- 
 
 •1 lllilH 
 
 WAa. . 
 
 l:'(» •• . 
 
 Ii MIK8 
 
 r.0.1:i. . 
 
 . 
 
 Kack. 
 
 1"J.tMlO .. 
 
 Si'i.OtKI . . 
 
 (f.")..".(M) . . 
 
 .-.-s TOO . . 
 
 5t-',"^i> . . 
 
 5r'.i,(''t»i» . . 
 
 1>,VTR OF 
 
 I)|:ic.i:nT. 
 
 I'cliiimry 18. 
 Jlllir VI .. .. 
 Jstiiiiii'V 10. . 
 
 Ai'i;l :'.'().. .. 
 Mmv H .. .. 
 
 lUrn or 
 I»lw HUNT 
 
 6%. 
 0%. 
 
 •I'f.. 
 (■.■'.',. 
 
 17. V'uul tlio proc't't'ds of a note of IfHGO, due in 8 luonths, 
 at (•.%*? 
 
 18. Find the proccoda of a draft of $885, on GO days, 
 at ()%■'' 
 
 11). Kind tlio nmtiirity, the term of discount and the 
 procetHls of a note of :{;;">, '2r)0, on dO (hiys, dated July lat, 
 ISSi), and discount, d Au;j;ii.4 'llai, 18.Si), at 5%. 
 
 20. Find the dilTtTonce between the truo and bank dis- 
 I'ount (Ml $r»,Ol)0 for 1 year, allowing each 3 days grace, 
 at7%? 
 
 21. A merchant biui.ijht $('i,800 worth of goods for cash, 
 soM tliem on 4 luontiis, al l.O'o advance, and got the note 
 discounted at % to pay the bill. How much did he make ? 
 
 22. f G52. 15. Ottawa, Jan. 25th, 1889. 
 Five montlis after date I promise to pay to the order of 
 
 Charles Barrett six hundred nnd fifty- two and ^Vff dollars, 
 value received, with interest at six per cent. 
 
 Discounted at 4} %, Mar. 15. WiiiLi.\M Kimb.\ll. 
 
 23. $215. PKTEKBonouGii, Jan. 28th, 1889. 
 Thirty days after date, I promise to pay to the order of 
 
 James Fogg two hundred and fifteen dollars, value received. 
 Discounted at 6%, Feb. 3rd. John Rooeus. 
 
 '-Ifm-.-JSI 
 
BASK OlSCOl/NT. 
 
 i'.n 
 
 2\. $2,017 H5. aAr,r.J,u.. Llth. ih;,. 
 
 Tl.rc.) moritliH after <]ate I proiniHr. (o pay to tin; onler of 
 J"liii I'.rowii two tlioiiHaiid and bovoutocii and ,"• ,|M|i um 
 lu! rcccivcil. 
 
 I)iHr-.ountod at lO'X, Mar. Ist. Tn,.,T„Y li.ci.K. 
 
 -'■ ^'-^OO On,.:,,,..,. Ja,i. If, IHH!,. 
 
 Nincly davM aft.T .latn I pif.MUHe to p,iy („ (|„. ,,,,|,,,. „f 
 Ja,ii<,s I'iko four tlioiiKand hovoh l.u.idn.l and .ixty dollars 
 valuo received. ' 
 
 Disro.u.tod at 7i %, Feli. ir>tli. VV„,r.,AM ( urAu-.s,: 
 
 'iC. !?r,,0()(). BaANTi-oiU). Oct. 'Itli, J 889. 
 
 Six inorilliH after date I proniim, to pay to .John Adnmn 
 or order five tlioiiHand dollai-B, valm, rocoiv, d, uiUi inteicnt 
 at HO veil per cent. 
 
 I»iscou..te.l at 8%, Deo. Slst. W„,,,,am Dunn. 
 
 27. $!t,010. London, Jan. IDtli, 1889. 
 
 Sixty davH from dnfo I promifie to pay to the order of 
 Charles Carroll nino thousand and forty .lollarH, value 
 recoivod. 
 
 Dineounte-l 5] %, Feb. Kith. j,,,,, M.sho,,. 
 
 '^^- ^*'^'^- Bkrt.in. Nov. 9rd, 1888 
 
 Six months from date we jointly and severally pn.rui.4eto 
 pay to the order of Charleb Fall hix hundred aiid fifty dol- 
 laiH, value roceiv. .1, with intereflt at six per cent. 
 Discounted at 7% Jan. 3rd, 1889. 
 
 John Hknderhon. 
 James Hendricks. 
 29. A note for $3,600 with interest, dated Jan. 15th 
 1889. and payable 3 months after date, was diseounLid at 
 a bank Feb. 15th, the legal rate bein- 7%; with the pro- 
 ceeds was paid ou account 40 % of a bill due that day. How 
 much remained due on the bill ? 
 
 ■=-^lfe^ 
 
W2 
 
 UASK lUSVOUSi 
 
 80. A racrcliant sold soino goods that cost hitr $840. iit 
 a |)rofit of 12%, and took in paynu'nt a four-mouth note 
 dated May 15th, which after 52 days lie got dincounted at 
 a bank for 7%. IIow much did ho receive from tlie bank^ 
 
 81. A merchant, having Hold 200 l)arrcls of flour at 
 $6.80 a barrel, and having taken in pay jent a {JO-day note, 
 found, on gettinr; the note diHCounteil at a bank tlie day 
 of its date for 7%, that ho had reah'z. d on the transaction 
 a cash profit equal to 300% on the bank discount. What 
 had the flour cost him por barrel ? 
 
 82. A person owing for 117 A. 5 sq. rd, of land, which he 
 had bought for $32 an aero, i)aid on account the procooda 
 of a sixty-day note for $2,000, which he got discounted at 
 a bank, for 7 %, on the day it was drawn. How much 
 remained due ? 
 
 88. I paid in cash $960 for an engine, and sold it the 
 same day for $976, taking a 60-day note, which I dis- 
 counted at a bank at 8%. Whr.t was my gain or loss ? 
 
 84. Perkins, Ince & Go's bank account is overdrawn 
 $11,510.19; they now discount, at 6%, a 90-day note for 
 $3,976.21 ; a 60-day note for $5,514.25 ; a 30-day note for 
 $1,546.19 ; a 20-day note for $2,540.86 ; proceeds of all to 
 their credit at the bank. What is the condition of their 
 bank account after they receive credit as above ? 
 
 86. W. Darling & Co.'s bank account is overdrawn 
 $12,915.47; they now discouut, at 6%, a 90-day note 
 for $-',428.40; a 60-day note for $6,311.25 ; a 80-day note 
 for $1,120.50 ; a 20-day note for $4,500; a 10-day note for 
 $1,550.50 ; Proceeds of all to their credit at the bank. 
 What is the condition of their bank account after they 
 receive the above credits ? 
 
BANK niSCOUNT 
 
 '93 
 
 374. To find the face value of a note that shall pro- 
 duce a given sum when discounted at bank. 
 
 ..,s ,.i;r:;:;:„i:::„!::r;;;'it;';;;-i£ ;r;;W;,ii;;^r ' - "■ 
 
 .Sni.iri Kin. 
 Hank clisrnunl ..f $i f,,r 75 .1;,), ,1 \ ; $0,,, 
 
 81 - ».016 :. %\m procoeda of »l. 
 8.9^1 = procofda of Jt 
 
 • 1.903 = 
 
 _1_ 
 
 l.'JdB 
 
 82,000. Ana. 
 
 Divide the ijivm sum by the proree<h of S I for the given 
 rate and time, and the quotient will be the face value of tht 
 
 note. 
 
 EXERCISE 84. 
 
 Find the face of n .e or draft— 
 
 PuOCERDa. 
 
 1. *;jf)i..-)i) 
 
 ~ 2. ?.(;m.40 
 
 3. SlI.^Ji) 
 
 5. 87 1 7. so 
 
 » 67'Jfi.'.'0 
 
 Bank Di.scount. 
 
 7. S2..S0 
 
 8. 5:fi;.00 
 
 9. S'J 80 
 
 10. 81.!)0 
 
 11. 6li.C,0 
 Vi. to <i\ 
 
 13. What sum. due 73 days heuce, at 7%. should be 
 discounted, so that the present payment muy be $900 ? 
 
 «f ^t'T^^'t" *^ '^'' °^* °«*° ^' 60 days, the proceeds 
 of which, when di.connted at bank at G%. are $1,276 ? 
 
 m\ 
 
 II 
 
194 
 
 BANK DISCOUNT. 
 
 m 
 
 15. If a merchant wishes to draw $5,000 at bank, for 
 what sum must be give his note at 90 daya, discounting a 
 6%? 
 
 Ifi. The avails of a note having; 8 months to run, dis- 
 counted at ft bank at 7%, were §270.84. What was the 
 face of the note ? 
 
 17. For what sum must a note be drawn at 80 days, to 
 net $1,200 when diycountod at 5 % ? 
 
 18. Find the face of a 8 months' note, the proceeds of 
 which, discounted at 2% a month, are $496. 
 
 19. Owing a man $575, 1 give him a GO day note. What 
 should be the face of the note, to pay him the exact debt, 
 if discounted at 1^ % a mouth ? 
 
 20. James T. Fisher buys a bill of merchandise in 
 Montr.al at cash price, to the amount of $1,486.90, and 
 givts in payix^ent his note at 4 months at 7|%. What 
 mi'st be the face of the note ? 
 
 3T5. Given, the rate of interest to find the corres- 
 ponding rate of bank discount. 
 
 ES.UIPLE.— A broker buys a 70 day note at such a discount that hia 
 money earns him 10 %. What is his rato per cent, of discount ? 
 
 SOLUTIOX, 
 
 70 day note = 73 days' time. 
 
 Interest on ?10o fo 7.> daya at 10 % — 82. 
 .'. Amount of $100 = S102. 
 
 ?102 in 73 days j^ivoa S2 interest. 
 .*. 100 " 365 " SO^J " 
 
 .*. Rate of discount = 9J} %. Ana. 
 
 376. Given, the rate of bank discount, to find the 
 corresponding rate of interest. 
 
 ExAMPM.— What rate of interest is paid, when a note payable is 
 
 70 days is discounted at 10 % ? 
 
'I 
 
 BANK DISCOUKT. 
 
 195 
 
 SOLUTIOM. 
 
 ro d»y note a 73 days' tiroo. 
 
 Intorest 0-1 8100 for 73 H^ya at 10% 
 .*. P'-'ioeod-iof 5100 a ;f99. 
 
 •08 in 73 days gives 52 int^resl. 
 .-. 100 " 865 » 510JJ .. 
 
 :. Rate of interest » lOJJ o^. Ans. 
 
 •a. 
 
 EXERCISE 85. 
 
 30 dn^t'*/'*' ^V".'"'''' '' P'"^'- ^'^^^ «» note payable fn 
 30 days IS discounted at 6 % ? 
 
 2. A speculator discounted a note due in 90 days at 12^ 
 
 z :zT-:z r '"^ ^""' ™" »' '-'-' -^' ^ «« 
 
 8. If a note payable in 8 months without Rrace be 
 
 o J' K ' * "° u ^'''J^^^^' '"^^^^'''S ^" 96 days, without «race 
 re onXesr '-' ''' '-'' ''- '^^ ^-' -^- ^^ the 
 6. A broker discounted a note ,lue in 4 months without 
 grace at he rate of 6°/ per annum, what was Le actuj 
 rate of interest realized on the sum advanced ? 
 
 tot^:^'sSe;e:;r^^"^-*^'«-«^«^^^^^^^ 
 
 pold ZTbT "I t"^ '"^^"^* ^" '' '^^ "°te^ «0"e8- 
 pond to 5. 6, 7. and 10 per cent, interest. 
 
 h^^ZI' •'^^? ^.^'"^ discount exceeds the true discount 
 by the simple interest on the true discount 
 
 Bank discount = Interest on principal. 
 
 True discount , Interest on present worth of principal. 
 
 .. * f°*«^-est on (principal-true discount). 
 
 " " ?^'^^' °° Principal)_(interest on trae disconntt. 
 = (Bank discount)_(interest on true discount). 
 
196 
 
 BANK DISCOUNT. 
 
 .if ! 
 
 or, 
 L«tP ■ Priicipal; t a time; r m rate. 
 •*• P t r « liitorost, or bank diacouni. 
 
 z — -T- « True discount. 
 1 + tr 
 
 P t p 
 
 P * ' - , r- " Di£fbrenoe B. D. and T. D. 
 
 1 + t r 
 
 (P- P )tr. 
 ^ 1 + try 
 
 \i + try 
 
 tr. 
 
 Bimplf! interest on the true discount 
 
 B. D. on 8100 for 1 yr. at 6% s $6 
 
 T.D. " " .1 m 
 
 6 
 
 Differenoo cs (6 — 9 
 
 l.OU 
 
 , 6 
 86 
 
 106 
 
 fifi o 
 
 But 'j^ »■ the simple interest on 8— for 1 year at 6%. 
 ■ Simple interest on the true discount. 
 
 878. If the bank discount or simple interest on a 
 sum of money for a given time and rate is * of that sum, 
 then the true discount will be — -^ of the sum. 
 
 II interest = i, °' principal, then 8a iu interest on ?b. 
 .*. 8b {i.e. principal) + ?a (i.e. interest) = 8 (a + b) = Amount. 
 
 .-. $b is present worth of 8 (a + b). and $a is the true discount of 
 • (a + b). 
 
 /. True discount ia r- of priucipal. 
 
 ft + o 
 
 Thus: 
 Simple interest on 8100 for 1 yr. at 6 % » 80. 
 
 i.e., the intcr.jst ia j-f^ of principal. 
 Then $0 is iaterest on J 100. 
 .'. 8100 of principal + 86 of interest = 810(j. Amt. 
 .*. 8100 is present worth of 8100, 
 and 86 is true discount of 8106, 
 
 i Xitts iiaouaaA « ^^ £2 psassijai, i^.. ^* — of prinoipaL 
 
BAlfK VISCOUNT 
 EXERCISE 86. 
 
 197 
 
 2- The it,tore»t is ts .h,T * F"'<i «"> ITincij,,!. 
 
 'nt-. and .utZ ^fioTLl' "ST '"'™° '- 
 
 4. If the interest is J nf m • ""^ "'® Pr'ncipal. 
 the pnnci,a^ is the true dttT""'"^' '''*' '^^^"°° °' 
 
 TJie^mtnTis $1/0' %TnTthe n? '" ^°^ *^^ P"°^'P*'- 
 
 6. The difference betw en he iT'^'f . 
 
 on a sum of money for u v .''* "^ *^« ^'«count 
 
 «um of mono/ ^ ^* ^'"" ^* 8% is ?18. Find the 
 
 7. Beckoning bank discount at 5<i: - 
 
 receive $21 Jess than thn . • , ^' * P''''°" ^0"^ 
 
 ^- a ,ear to run W ^^ iTl ' " °' ^ "°^^ ^'""^^ 
 
 true discount were deducted ''''''' ^°' *^' "°'^ " 
 S- I have two notpa n J l 
 
 «■ tree ci/scount, llie en,i„ °, !",' ''"™"'"' *'"' "'her 
 
 feoe of the note on^ClJis ?'"« *'• ^'°"" «" 
 »• Tlie interest „n . T """' ™' »"»«<<• 
 
 «=e «isc„..tr 'tH Z'reTs '^IsV'T- '=■ ^■^"' ■"" 
 and rate per cent. ^^®^- ^^"^ 'i^e sum 
 
 ^T^a.!^ at r ^::t:^^r t' r ""* ^^ ^ ^^" ^' 
 
 -how,., ,,-^^^;;^d^^ 
 
 and the dis:ourL°" 1:0":: t"^"^^ f ' ''^'^ '« ^^^0' 
 tbe sum and rate per cent "' '"^ '''' ^^°^- ^^^^ 
 
 12. The interest on a c^^H^n Pn>.> <■ 
 the discount on the same sum fot 1 ™'"'^ '" ^'^^' "^^ 
 rate is $150. Find thHuT '''"'' ^"'^ '*'"* 
 
 11.; 
 
 
 /*•: 
 
 ''i: 
 
198 
 
 PAHTUL PAi'AlESlS. 
 
 PARTIAL PAYMENTS. 
 
 a7». Partial Payments aro part paymcnta made at 
 different times of notes, acceptances, bonds, raort«,'nge3 or 
 other written and interest- ben ring instrummts which the 
 debtor is obh'ged to pay. 
 
 »HO. Indorsements aro the acknowledgments of the 
 payments written on the back of the note, acccjitaiico, etc., 
 Btating the amount and (hite of the payrnont. 
 
 Special reccipta aro Boiuotimea given for partial payments made, 
 indtflad of writing the acknowledgment on tho back of the obli;^ation. 
 
 SSI. The method of computing interest when partial 
 payments have been made is based on the following 
 principles : 
 
 1. Paymenta must be applied first to discharge accrued 
 interest, and then the remainder, if any, towards the discharge 
 of the principal. 
 
 2. Only unp'iid principal can draw interest. 
 
 ExAMPLK 1.— A lu .0 tho face of which was ?a,oOO, bearing' intorost 
 at e%, was given October 17th, 18SJ, and apttled February 14th. 1H80. 
 Find the balance due. tho followinj itid >rsemontg having boon made • 
 March .Srd, 1885, sC.yO; October 2oth. 183 5. 81,000; Docombar 6th 188^" 
 82,400. 
 
 SOLCTION. 
 
 Faoeofnoto »3,C00.0O 
 
 Interest to date of first payment (137 da.) f^^ g? 
 
 Amount of principal and inturc^t at time of llrst paymont .. |5 l\ii\. 07 
 
 First payment (Mar. 3rd, 1885) '.. .. \-,yy(jQ 
 
 Reraaindorafter deducting first payment jTosi 07 
 
 Interest to date of second payment (lyr. 2:3(5 'a.) ;i(il H!) 
 
 Amount due at time of second payment 8.i H^:) 4« 
 
 becond payment (Oct. 2 -,th, 1881!) "./" i|onOOO 
 
 Remainder after doductin;; second payment 82,:i8.j 16 
 
 Interest to date of third p:iyment (2 yr. 42 da.) HO" "2 
 
 Amount due at time of third payment 82 C8S 18 
 
 Third payment (Deo. fit:., H88) ' '.."'.." 2,400 00 
 
 Remainder after deductini,' third payment "8288 18 
 
 Interest to time of settlement (70 da ) 3 3^ 
 
 Balance due at time of 8ettlenic;it (yob. 11th, If'SO) .. .. "829149 
 
PAHIUL PAYUESTS. 
 
 91,000. -, ^ ,, 
 
 r ^ Toroutn, May 16th, 1S8I. 
 
 Oil this note were iM.lorse.i the followin-^ i.avmcnfca. 
 
 October 25th. 1S.1 .. * "''^•f? 
 
 July nth. 1886 •• •• '"'•'? 
 
 Sq.teinber 20th. 1087 .. ' " „.',„, 
 
 Deceinbor 6th. 1888 .. .. " ,^7^ 
 
 N\ Mat remamed due ^fay 20th, 1889 7 
 
 SoLUTIOH. 
 
 F.iL'e of note 
 
 IntcrosttoSopt. 20th. 1882 (I'yr'Ios da) H.OOO.OO 
 
 Kemainder after deduct...^- first payment' v!^"*^* 
 
 Interest fron. flrnt pay:nent to Oct. 2oth. 1881 (aVrsVsS da ) ' " V^ 
 
 Amoant duo at time of ««,on<l u a.ent ' . *' 
 
 ^•econd payment (Oct. 25th. 1884) fl.0H2.l4 
 
 Remainder after deducting Bccond pa'ym'e^t "..".." " 'Z^l 
 
 h-terest from second payment to Deo. 5th. 1888 (4 yr, 'il a[ \ o^- "JJ 
 Amonnt due at timo of fifth pa-ment ' -^^' 
 
 Third payment, less than interest du. ':,.'' ^^'^^'^ 
 
 Fourth '• .. _ p7.).20 
 
 Sutu^of third and VourVh payments.'losVthi; inVerei; ^^^ 
 
 Fifth payment". 8187.30 
 
 Sumofthird.fourth;;nd"fifth payments'*.;* " ~^ .,„ 
 RemaindoraftcrdediictinL' third fo'irth Rn^flni, _»292.30 
 
 B.l..» d.. .t limo of ooWcmsM ,JI»,- 2011,, 1389) .. ' '.. -js,|^ 
 
 Rtn,R. 
 
 the date of the note to the tune of the first payment. IftZ 
 payment equals or exceeds the interest dJs,Hrrct tk 
 mentfrom the amount, and treat the remair ' [[, Z'c 
 principal. "^'^ 
 
 ■ «■>•• 
 «.■ til 
 
I 
 
 ^^^^H'' '• 
 
 ■i • 
 
 ^H, 
 
 > 
 
 ■' 
 
 J^ : 
 
 200 
 
 rAUllAL /•^rj/ivATS. 
 
 <?. 1/ any pay mint i< 1,$$ than the accrued intereat, computt 
 th,- int.reit on the $ame principal, to a date when the turn «/ 
 f/i" piifinentg eqnnU or excce.U th interest then due, and 
 tnhtract th<$umofthe payments from the amount, and reifard 
 the remainder a$ a new principal. 
 
 S. Proceed in the tame manner with the remaining pay' 
 m.nte, until the date of tetllcment. 
 
 EXERCISE 87. 
 
 1. A note of $ 1,560, dated Jan. 22nd, 1837, and drawing 
 intercBt at 7%, lind nayraenta endorsed npon it as follows r 
 Jan. 10th, 1S88, $2,000 ; Aug. Slst. 1888, $500; Jan. IStlii 
 1889, |l,yOO; Mar. 4th, 1889, $8G0. Find the balance 
 due June 15th, 1889. 
 
 2. On .1 claim for $3,000, dated Aug. 12th, 1885, and 
 bearing intorect at 7%, payments were made as follows: 
 Deo. 15th, ^885, $30; April Ist, 1887, S550 ; Jau. 20th,' 
 1888, $85; June 12th, 1688, $1,651.50. How much was 
 dueMay Si'tli, 1889? 
 
 3. I held a bond against Ira Fox, dated May .4, 1885, 
 for $4,")00, on interest at G%. The following payments 
 were endorsol on this bond: May 2l8t, 1886, $800; June 
 10th, 1887, $i.20O; Aug. 10th. U88, $1,500. What was 
 due May Ist, 18S9? 
 
 4. On a mortgage for $5,500, dated Aug. inth, 1882, and 
 bearing 6% interest, the following payments ^are m;.,le: 
 Jan. Ist, 1883, $100; Mar. 2nd, 1883, $25; Aug. 13th, 
 1885, $2,500; Dec. 19th, 1887, $2,500; Mar. ,8t, 1689, 
 $500. How much was required for full Bettieuient, Mar. 
 11th, 1889? 
 
 ■ MiiT \m li ^'^ 
 
 ri M'^ 
 
fAHTUL rAyjit:;Ts. 
 
 201 
 
 for Mil;, «2. at C,%, .latod June 25tl., l^HS. on which » 
 r.i>-m. Mt of ^iir/) 25 was ma-lo Au«. Ist. IHSS. a„,I a ,,-iy 
 tuout o, ?21.iy on the ir,th of each Hubsequcut .nonth! ^ ^ 
 
 6 0„ a w.. of $2,000. made ^rar. 19th. 1885. an.l bear- 
 
 . IP w , may ura, imh8, ^700 ; l-eb. Ist, 18H9. Si 000 
 liow .uuch w,ll bo required for sottl.ruont in full. mJ.Z. 
 
 7. I pave a mortgage for $10,000. ^ray 0th, 1 S,S2. bcarin. 
 ThHS iinJ. A^ ^' ■^''"- ^'^' ^''^^' ^''•'5«0J April 25th, 
 JSSU ? """ ''" "' "' ^'""^ Bcttlcnent, June 2nd. 
 
 8. A bond was Riven Mar. 3rd. 1883. for $8,G50 with 
 mtoros a 8%. Tho following paymentB were r ade on 
 account: A.,nl 17th, 1884. $1,000 ; May lOtn 1885 50 
 
 f88Q ? How much remained duo. May 7th. 
 
 intt jltTc ^' f f ' ''''' '''^^ ''^''' ^^•'^^- ""'' ^--^« 
 
 10. A note of $2,000. dated Jan. 22nd 18S0 nn^ a 
 
 lo.ioAs. May 20th, Ibny. $100; July 20th lafto «qo- 
 i>ov. ^na, i8bJ, $20; Dec. 23rd, 1889 Sio'5 i?,-r, 1 ^1 
 balance due Mar. 1st, 1890. ^ ^''''^ ^^^ 
 
 l.S'iJ5*flBK:- t «■ Sc!.- 
 
 iZ10f.^..¥Tt7' 
 
rfr=*B 
 
 I ' 
 
 h 
 
 802 
 
 PARTIAL PAYMENTS. 
 
 11. A note of §1,6G2.50, dated Jan. 15th, 1888, and 
 dniwing interest at ^%, bad payments endorsed upon it 
 as follows : April 80tb, 1888, §25 ; June 24th, 1888, $25 , 
 Sept. 2nd, 1838, §625 ; Jan. 31st, 1889, §700. Find the 
 balance due May 12tli, 1889. 
 
 12. Oct. Ist, 18S5, a note for §1,000 was Riven, payable 
 in 4 years, with 6% interest. A paymeiit of §50 was 
 mnde 1 year from date; a payment of §250 was made 
 
 1 year 6 months from date ; a payment of §224 was made 
 
 2 years from date ; a payment of §20 was made 2 years 
 8 months from date ; a payment of §110 was made 2 years 
 10 months from date. How much remained due at the 
 maturity of the note ? 
 
 13. A mortgage for $5,400 was dated Strathroy, Jan. 
 let, 188(5, and endorsed as follows: May 22nd, 1887, 
 $1,200; Feb. 9th, 1888, §150; Oct. 28th, 188S, $1,500.' 
 What was due Mar. Ist, 1889, interest 5%? 
 
 14. A note of $302.25, dated Aug. 4th, 1887, and drawing 
 interest at ^ %, bad payments endorsed upon it as fallows: 
 Oct. 14th, 1887, $100; July 21st, 1888, §100; Oct. 11th,' 
 1888, §50; Jan. 18th, 1889, §50. Find the amount due 
 July 22nd, 1889. 
 
 15. On the following note, payments were endorsed as 
 follows; Nov. 3rd, 1887, §50; Mar. 16th, 1888, §50; Oct. 
 Ist, 1888, $50; Dec. 80th, 1888, §1,000; April 1st, 1889, 
 §625. How much was due, if paid iu full, May 8th, 1889, 
 money being worth 6%? 
 
 $1,600.00. Brantfoud, April 1st, 1887. 
 
 Three years after date, T promise to pay to the order of 
 Silas Hopkins, one tl-ousand six hundred .lollars, value 
 J^eceived. j^s. Mcuray. 
 
 16. On the following note endorsements were made as 
 follows: Aug. 1st, 1883, §350; Nov. 3rd, 18b3, §1,000; 
 
PARTIAL PAYMENTS. 
 
 203 
 
 Mar. 20th, 1885, $600 ; Mar. Slst, 1885, $2,500 ; Dec. 
 11th, 1888, $2,000. What was the balance due Jan. 30th. 
 
 188P? 
 
 $6,500.00. Bbockvillr, Mar. 19th, 1882. 
 
 ^ On demand, I promise to pay to the order of T. Gihuour, 
 six thousand five hundred dollars, with interest at 6 %. 
 
 W. HiND.SON. 
 
 17. The following note was settled Oct. 13th, 1888; 
 a payment of $25 having been made Jan. 15lh, 1887 ; one 
 of $;300, July 12th, 1887; and one of $200, April 1st, 
 1888. ]f money be worth 8 %, how much was due at final 
 settlement ? 
 
 *3'^^-50. GAI.T, Aug. 1st. 1886. 
 
 Six months after date, I proraiso to pay to Alex. 
 Buchanan, or order, five hundred eighty-five and tow 
 dollars, value received. F. MoHardy. 
 
 18- ^500. St. TnoMAs, Fub. 1, 1888. 
 
 For value received, I promise to pay D. E. Broderick, or 
 order, five hundred dollars three months after date, with 
 interest at 7 %. • James Monuob. 
 
 Endorsed as follows, May 1, 188S, $40. 
 " Nov. 14, 1888, $8. 
 
 " April 1, 1889, $12. 
 
 " May 1, 188U. $30. 
 
 How much was due Sept. IG. 18«9 ? 
 
 19. $5,000. SxiiATFORD, May let, 1887. 
 
 Six months after date I promise to pay G. T. Smith, or 
 order, five thousand dollars, with interest at 5 per cent., 
 value received. John Adams. 
 
 Endorsed, Oct. 1st, 1887, $700. 
 " Feb. 7th, 1888, $15. 
 " Sept. 13th, 1888, $480. 
 What was the balance due Jan. Ist, 1889? 
 
 ■V*f 
 
204 
 
 PARTIAL PjniEUTS. 
 
 ' .; 
 
 20. $2,460. Trenton, April 10th, 1887. 
 
 Four months after date I promise to pay W. H. Austin 
 or order, two thousand four hundred sixty dollars mti 
 interest at 6 per cent., value received. 
 
 George G. WiLLiAMft. 
 Endorsed, Aug. 20th, 1888, $8iQ. 
 Dec. 26th, 1888. $400, 
 " May 2d, 1889, $1,000. 
 How much was due Aug. 20th, 1889 ? 
 
 ^^- ^^^°- CcELPH.Jan. Ist. 1887. 
 
 For value received, I promise to pay Alexander M„- 
 Kenzie, or order, six hundred fifty dollars on demand with 
 interest at 6 per cent. Geouob lIw. 
 
 Endorsed, Aug. 18th, 1887, $100. 
 " April 13th, 1888, $120. 
 What was due on the note, Jan. 20th, 1889 ? 
 
 1,'i 
 
 '4 
 
 ^^^^^T^^tW^^^^u^^Mf 
 
EQUATION OF ACCOUNTS. 
 
 206 
 
 EQUATION OF ACCOUNTS. 
 
 s^mi. Equation of Accounts, also called Equation of 
 Paymen s, and Averaging Accounts, is the proces" of 
 finding the tune at which several debts due ardXent 
 timee may be paid in one sum without loss of 'ntcnfs to 
 
 wh..n the balance of an account having both debits and 
 credus. may be paid without loss of interL to either party 
 
 ..I *t/w' Equated Time is the date at which the 
 .veral^debts due at different times may be equitably paid 
 
 trS^d^^ir^:^:-;^^"^^'^*^^^^ 
 
 3SG. The Average Term of Credit Ib the time to 
 
 elapse be ore several debts due at different times may all 
 be paid at once without loss to debtor or creditor. 
 
 J.T' -M " ^°'^^ P^^^ '' ^"^ ^•^^"'"^'^ ^"-^^ 0^ settle- 
 ment. with which the dates of the several ac.-^nts are 
 compared for the purpose of finding the equated time. 
 
 N0T.3l._Any conceivable date may bo taken as the focal date- th. 
 most common dates used beina the earlipqt,' ^„f« *i ,'"'***«•"• 
 the first day of the month of t?. 0^^ 1 d.t a:^^ h^^^ 'T 
 
 month preceding the month of the earliest due I'te '"' '""^ 
 
 2. In Equation Tables. Dec. 31st. or Jan. 1st. is taken for all examples. 
 
 day basHr aT^- dVt'^'^'^':' ^^"^ '''' '^' <=-* • ^^ either on 360 
 fw . n -f . ^ ^ "• '^'"'""' ^'"■y'"« *''° 'esalt. prori.lin.. only 
 
 Jhrrgho;^''^'*^ "• "^ "''' '^'''^^' °^ --P^"'^^ ^--'t be ob^rveJ 
 4. The student is recommended to chooqn nno ™«*i, j . 
 
 3S8. Equation of aocounts depends upon the followir-? 
 principles : yf^^ummr ^ 
 
 :■ -■'^r 
 
p 
 
 ; ! ■ 
 
 fir 
 
 ' ! 1 
 
 :fS . , 
 
 ill 
 
 206 
 
 EQUATION OF ACCOUNTS. 
 
 1. The rate and time remaining the same. Dotible the 
 principal produces twice the interest. Half the principal 
 produces half the interest, etc. 
 
 2. The rate and principal remaining the same. Double 
 the time produces twice the interest. Half the time produces 
 half the interest, etc. 
 
 3. Hence, the interest on any given principal for 1 year, 
 1 month, or 1 day, is the same as the interest of Si for as 
 many years, months, or days, as there are dollars in the given 
 principal. 
 
 4. Hence, the interest on any given principal for any 
 number of years, months, or days, is the same a* the interest 
 for 1 year, 1 month, or 1 day, on as many dollars as is 
 expressed by the product of the pive,: principal multiplied by 
 the given number of years, months, or days. 
 
 38!K The Bevera! rules ip equation of accounts are 
 based upon the principle of bank discount, for they imply 
 that the discount of a sum paid before it ia due equals the 
 interest of the same amount paid after it is due. 
 
 390. To find the average time when the items are 
 all debits or all credits, having the same date and 
 different terms of credit 
 
 Example. — A.bouglit a farm June 24th and was to pay }500 down, 
 J300 ia 2 months, f 100 iu G months, and §000 in 8 month j. Find tlie 
 average term of credit and the equated time. 
 
 Solution 1. 
 
 By the interest method. 
 
 Interest on 8500 for mo. at 6 % = SO.OO. 
 " 81300 for 2 » " = 3.00. 
 
 " 8400 for 6 " " = 12.00. 
 
 «« §600 for 8 " " = 24.00. 
 
 Amount of payments = »1,800 Interest = 30.00. 
 
 Interest on »1,800 for 1 month at 6 % » »9. «39 -r »9 » 4J. 
 
 1 mo. X 4J = 4J mo, the average term of credii. 
 Jnne 24th + 4^ mo. = Nov. 3rd, the Ch^aated time. 
 
 Jl 
 
i:(iUATIUN OF ACCOUSIS. 
 
 207 
 
 EXPLISATIOS. 
 
 If we take June 2Uh a? the timo for payment of all the items, A. 
 «v«ld lose the interest of S.iOO for 2 nioutha, $400 for C months, and 
 •SCO for 8 moaths. in all S39 interest. He is tlierefore entitlo,! to the 
 a<*. of ?1,800, the amount of the debt, for such a timo as the interest on 
 u would be eiiu.il to S.JO, and which is shown above to be IJ ni ^ntlia, 
 and 4J months, from June 24th. Rives the erjuiUed time Nov. Hrd. A.' 
 could therefore pay the amo-.iiit of the debt, ?1,800, on Nov. 3rd," 
 without loss of interest either to himself or his creditor. 
 Rui-B FOR Interest MsinoD. 
 Fhid the interest on each item for its term of credit, and 
 divide the sum of these interests by the interest of the sum of 
 the items for 1 daij, 1 month or 1 year as the case maij he. 
 
 The quotient ivill be the number of months or days from 
 the focal date to the equated time of payment. 
 
 Add this number to the focal date and the result will be 
 the equitable date of payment. 
 
 Notes 1.— In computing by the interest method the rate forma no 
 element of the calculati(jn, hence any rate may bo used. The most 
 convenient rates are 6 % and 12 %. 
 
 2. The result will be the same whether we reckon 3G5 days to the 
 year or 360 days to the year. 
 
 Soi.nioN 2. 
 
 By the product method. 
 
 ExrLANATIO>f. 
 
 This methi,' I is the same in prin- 
 ciple a3 tlia interest metliod. Tlie 
 interest on J.iOO for 2 months is the 
 same as the interest on ?1 for 
 000 months; the interest on SIOQ 
 for a raL.'itlis eijuals the interest on 
 §1 for 2,400 montha ; and the inter- 
 sst on SGOO for 8 months equals the interest on 81 for 4,800 montlis. A 
 would therefore h-e the interest on 81 for 7,800 months. Ho would 
 therefore be entitle to the use of 51,800 for such a time as the interest 
 sn It would equal the inter-ist on ?1 for 7,800 monthj, or 4| montha. 
 RnLE FOR Pr.( 2 jcT Method. 
 Multiply each item by its term of credit, and divide the 
 sum of the products by the s?z.>« of the items ; the quotient will 
 be the aver^ *erm of credit 
 
 ITEMS, 
 
 
 TIMB. 
 
 
 PUOl^UCT. 
 
 oOO 
 
 X 
 
 Onio. 
 
 S3 
 
 00 mo. 
 
 300 
 
 X 
 
 2 mo. 
 
 S 
 
 COO mo. 
 
 400 
 
 X 
 
 Gmo. 
 
 = 
 
 2,li:0:no. 
 
 000 
 
 X 
 
 8 mo. 
 
 a 
 
 4,8')0mo. 
 
 1,800 
 
 
 
 
 7,8U0 mo. 
 
 7,800 
 
 -5- 1,800 
 
 ^ 
 
 4i mo. 
 
 
208 
 
 EQUAiion OF Accouma. 
 
 EXERCISE 80. 
 
 1. On a certain clay A. bouf^ht a horso for $175 on 30 days, 
 
 3 cowa for $120 on 45 davfl, 80 blieop for $2.">0 on 60 days, 
 ar.d 5 tons of hay for $130 on 00 days. What is the 
 average term of credit ? 
 
 2. Bouf:;ht n ship for ?30,000 ; the payments were $5,000 
 cash, $8,000 in 4 months. $7,500 in 6 months, $4,500 in 
 8 months, and the balance in a year. What is the average 
 term of credit ? 
 
 8. Sept. Ist, 1891, I bonglit goods, as follows: $200 on 
 2 months* time, $400 on 3 months, and $450 on 4 months. 
 What was the average term of credit, and the average date 
 of maturity ? 
 
 4. On the first day of December, 1890, a man gave 3 notes, 
 the first for $500, payable in 3 months ; the second for 
 $750, payable in 6 months ; and the third for $1,200, pay- 
 able in 9 mon. iS. What was the average term of credit, 
 and the equated time of payment ? 
 
 5. Bought merchandise Jan. 1st, 1893, as follows : $350 
 on 2 months, $500 on 3 months, $700 on 6 months. What 
 is the equated time of payment ? 
 
 6. Jan. 15th, I bought a bill of goods amounting to $900, 
 $275 of which was on 80 days' credit, $300 on GO days, 
 and §325 on 90 days. What was the equated time of pay- 
 ment ? 
 
 7. James Hudson, June 12lh, owes $317.75 due in 
 
 4 months, $216.38 due in 5 months, and $170 due in 
 6 months. Find the average time of payment and date of 
 maturity. 
 
 8. Dec. l-jt. 1894, bought goods to the amount of $1,200, 
 on terms as follows : 25% in cash, 80% in 3 months, 20% 
 in 4 months, and the balance in 6 months. Find the 
 equated time of payment. 
 
 
EQUdTlOS OF ACCOUNTS 
 
 10. Bought a Lill of Koods Ai.riJ Vnn. 
 
 and the balance iu G moJh aV. t T .' ^ '" ^ "^""'^«' 
 l>e juatly paid ? ^^ '"'"^ ^'**« ^^^ tJ^e whole 
 
 who e . , , eaultahl/paid -rot'lnr" "^^^ *'^ 
 
 12. ^\illinm Owens bought a farm „f •!•)/! 
 m acre, , ,,aj.able i„ cash, i ,„ i j' ? " T^' »' «<=8 
 
 ■terns bcin, „, the sa^e^d^'o^'S actS^ "' ^" '"' 
 
 Example.— L O Hiii \ ^ ^ »-v.v»ujjt. 
 
 J400 on 3 n.o„U>s ; An,. To^ *S s/^o"" .'' ""''* ' ''"'^ ^^'''- ^^^O- 
 •600 on 6 .ontU. wLt ia iheequaWur? """*''' ' '^^*- "'^' ^^^^^ 
 
 SoLCTION 1. 
 
 Interest method. 
 
 DOS. 
 
 Aug. 1, 
 Oct. 15, 
 Deo. 10, 
 Mar. 12, 
 
 ITEMS 
 
 ?3.i;o 
 
 400 
 450 
 
 r.oo 
 
 DATS. 
 
 
 75 
 131 
 223 
 
 = $.30 
 
 INTKR19T4T6%. 
 
 SOO.OO. 
 
 6.00. 
 
 9.S2i. 
 22.30. 
 
 e37.I2i iDtewBi. 
 
 Amount = 5i,eoo 
 Intereet on 1,800 for 1 day at G ■ 
 
 37.12J.,30=123ldayr 
 Aug. 1 + 124 days = Deo. 3. 
 
 wonld lose the Zj^VnVttX^"''''' '' *" "»« '*^»'' - 0- HUl 
 
 ^ for 223 days, in all737 SV 'a iltf T 'J"" '" "* ^^^ '^^- 
 
 ^f 'i-sj. -njostioe he should be aUowedtUaw 
 
fliO 
 
 EQUAllOS OF ACC0VNT3. 
 
 >i 
 
 of 11,800 for sach time as the interest will araoutit to 937.12J. or M 
 shown above (or 12-4 dii.}'^. 
 
 Hcuoe the ciimtod tuna h 124 days, after An;;. 1st or Duo. lirJ. 
 RcLK »on Intkiiest Mkiiiod. 
 
 l\ike as the focal date the eirlirHt due datr. Find thr 
 intmst on each itemfro'ti the stind'trd date ti th^- /;/-■ ';/' »(» 
 maturity and divide the sum of the iutrrenta hjj the inter, :^t 
 of the sum of the items for 1 d'Uj. 
 
 The quotient aill be the number of days t'roin the st'unlard 
 date to the average date of payment. A<lil this numher to 
 the standard date and the result will be the equated tiuie of 
 payi/ient. 
 
 NoiKS 1.— If the earliost or latest due data id the focal date, its item 
 has no Interest, bat Buch item must be included in the sum of the debts. 
 
 2. If the fraction in the quotient is i day or more, 1 day is added ; if 
 leM tban } day it is rejected. 
 
 8. Any date may b« assumed as the focal date, the most prefera ^Is 
 being the earliest or latest due date. 
 
 4. In business practice, odd cents and even odd dollars are rejected 
 from the items in the interest calculations. 
 
 6. In the solution given above the «aiu of interest to tiie i ayee on the 
 first two bills, which are to be paid after they are due, equals the loss of 
 interest on the last two which are to be paid before they are due. 
 
 6. In ref^ardto the foregoing problem, it may be urged that a debt Ch.n 
 not be paid before it is contracted, but, it must be remembered, that the 
 object of the solution is really to find at what iato a note, <iiv^.i m 
 settlement of the account, should be dated, in order tliat neither piuty 
 would lose interest. 
 
 7. When terms of credit arc given in nioutha, calendar mouths are 
 
 meant. 
 
 SoLnTioN 2. 
 
 By the product method. 
 Assume August Ist as the focal date. 
 
 I)UB. 
 
 Aug. 1, 
 Oct. 15, 
 Dec. 10, 
 M*r. 13, 
 
 ITEMS. TlilB. PUODOCTS. 
 
 83GO y. Othi. = 00. 
 
 400 X 70 " = ;iOO.OO. 
 
 450 X 131 " = 58'.). 50. 
 
 (iUO X 223 '• » 1,338.00. 
 
 »1,8U0 82,227.5a 
 
 1800 ) 222750 [ 123J. 
 
 Aug. 1 + 124 days = Deo. 3. 
 
EqUATlOS OF ACCOUNTS. 
 
 I 
 
 EXPUNATIOW. 
 
 Thii method of •elation may ba osnUinnl u - 
 Riven to Solution 8, Art. 390 '^P'*"'^'^ '«> • '"•nn«i ■lm»»,to th.l 
 
 RtTLB roB PKoonoT >ri:Tnoo 
 
 SOLTION 3. 
 
 Interest method. 
 ^k^^ra> the lale.t date. .U„„U 12.h. 1889, aa tU, ,«ri 
 
 DATS. LNIliiiK^T AT 6 %. 
 
 DUB. 
 Auf,'. 1. 
 Oct. 1.5, 
 Duo. 10, 
 Mar. 12, 
 
 lf.;50 223 
 
 40o 148 
 
 ■ioO 93 
 
 600 
 
 Amount = JI,-<oo 
 Interest on 5 1,KG0 fori (Jhv at .;% 
 2y.77.i f 30 = oaj ,j^'y^_ 
 Hiidu, s Deo. 3 
 
 6.L.I}. 
 00. 
 
 8 30. 
 
 Interest, 
 
 liar. 12 
 
 £xPi.A.yATro.x. 
 
 R«ckoning the days from tliedao.latan" In. i . o 
 Mar. 12th, to tbo focal d.to ilar. I.tWe ttn ' °'' '"''■ ^'=^- ""'• 
 223. H8. 92. and day« respect vey th^ f K.""'^'^' °' ''^'' "^ ^e 
 
 Mar. 12th. 181,1. William Grant woa^d ll t, ^ "'''^ °°* ^^''''^ ""'^1 
 days, on 8400 for 148 days, S-l^O Tor y W '°*"'''' °° ^'•'•'" ^°' 223 
 on Mar. 12th, 181.1. The PribLm totnT" °' ' ""•*' ^'^^^^' "' ^-'^m 
 time should W:a. Grant JI^ Td .Westor»T; 7:: :^' '^"^''^ °' 
 receive 829.77^ interest 7-»nd ^h-h°,T '^'^' '^■''^°'' "" " «« 
 
 time at which the debt should be paid^ th 'l ""^Ik ^^''''^ ^"y'' Th« 
 
 ^7V 
 
 -'.■itv 
 
 ■■?«S:t" 
 
iia 
 
 EQUATION OF ACCuUMS. 
 
 
 BOLCTION 4. 
 
 By product method. 
 
 M»rth IMh ns th« focal date. 
 
 DUB. ITIMS. lATB. PKODPCT 
 
 Aug. 1. S.ijii X •-">3 z, 87><,U60. 
 
 Oct. 15. .100 X US r, .V».L'W). 
 
 Dec. 10. I.IO X '.):' 3 -11,100. 
 Mar. 13. _^C')j x ■ OO. 
 
 Amount Sl,>iO() Jil.KuO) 8178 f, 50. 
 
 '•"••t 'i^y. 
 
 Mar. 12. 1S91 — yg days « Dec. 3. liJO. 
 
 ExS-LkSATtOS. 
 
 The number of day« ii foniid as iu SoluUou 3. 
 
 If the debt is settled on M»r. li'tl., Id-U. \V'.lli:im Grant will lose the 
 
 •400 for 148 d.> or th. .nterc.t on Sr,V>uO for 1 day ; and on u'o tor 
 92 day. or the latorest on 841,100 for i day. Tho total !o.s of iuter st 
 « therefore the .uterest on M78,0.o for 1 day. We have then to d.t r 
 
 debt 18 du3 ^9 day. before Mar. 12ch. 1891, or Deo. 3rd. 1890 
 
 M, 
 
 it^ '^ 
 
 EXERCISE 89. 
 1. A mcrcbaut bought goo;1s as follo^^s : 
 
 Sept. 5, 1890, a bill of $2 un a credit of G mos 
 
 8 " 
 
 60 days. 
 
 Ii 
 
 300 
 
 K 
 
 Oct. 10, " 
 
 Nov. 11, " «• 8^0 
 
 Dec. 5, " " 425 for cash. 
 
 What is the average date for the payment of the whole ? 
 a. John E. Lewis purcliased goods of Isaac S. Smyth & 
 
 1889, $1,000 to be paid July 5th. $2,000 to be paid Au'^ 
 16th; the balance, $750, will become due Aug. 80th At 
 what date must a single note for the whole amount be 
 drawn, payable in 8 months, that it may become due at 
 the aterage date ? 
 
I 
 
 EQUATION OF ACCOUNTa. 
 
 211 
 
 8- Bought goods as follows : 
 
 ^^'Imt is the average date "of. '^ '^"^^ " 
 f fen ry Field. ^ . 
 
 W.ir. s 
 
 Apr. 4 
 
 • 16 
 
 May 1 
 
 ;i) .V'- :. 
 
 II 
 
 •250 00 
 loo 00 
 3u0 00 
 420 00 
 
 81070 1)0 
 
 i< 
 11 
 
 «• ^^^-'^e the following shtcMnpnf r "' 
 
 25, .. .. ^: " 420.00 
 
 Apr. i, .. .. ;^ ■'';-• «I:'50 
 
 " 12. " u 'I'^'^T 210.25 
 
 -•;• What is 1 : in Jf ^,« -'^-^ Of 80 da,, 
 whole amonnt ? '^ '"^' ^<^'- ^^e payuient of the 
 
 II 
 
 
 15, 
 July 12, 
 Aug. J8, 
 Sept. 2.-, 
 
 II 
 II 
 
 O 111 03. 
 
 ;; 90 .-lava 
 3 ino3. 
 
 $1,275.00 
 600.00 
 450.50 
 820.87 
 145.63 
 
 ?2,G92.00 
 
h 
 
 f 
 
 Ml--' 
 
 1 J 
 
 ^^^^F_Mi' 
 
 ■ •' : 
 
 ^^Hh- . 
 
 1 'i 
 
 214 
 I. 
 
 LQUATIUN UF ACCOUMS. 
 
 May 6, Mdee. @ OO days 
 
 $.000.00 
 
 II iQ^ 11 II 80 " 
 
 SUfi.lO 
 
 Juiip 10, Cash 
 
 2jO()0 
 
 July 7, MdHO. (net) 
 
 42(1.00 
 
 AuR. 14, " (ft CO days 
 
 MH.'>S 
 
 $•2,201.08 
 
 9. A young man, liavinp nionoy ailviuiceil to In Ip liim 
 pay his way through collce, roctivod : 
 
 Soi-t. 1, 1888, $75. Fib. 15, IHHO. .^SG. 
 
 Feb. 16, 1889, !=;hO. 8. i>t. 20, isno. ?! -28. 
 
 Aug. 81, 18SII, §l»5. Aug. fJO, IMH, .^17:.. 
 
 Wliat wnB the (qijattd time at wliicli Ik .-liould date a 
 single interest hearing note for the whole hum ? 
 
 10. Five ytairi from the date of the lirst loan, the above 
 mentioned note was paid, with iutcri'-st at 4%. Wlmt waa 
 the iimuunt? 
 
 11. What is the average time at which the following hillp 
 become due ? Feb. 10th, 18'.)2, l? JOO on 2 raontiis' credit ; 
 May 10th, 1892, $300 on 4 montha' credit; June 16th, 
 1892, $350; Aug. 6th, 1892, $150. 
 
 12. Find the equitable date for a single note given on 
 the following bills for merchandise: June Ist, 1895, $20, 
 July 1st, $80, Aug. Iflt, $30, Sept. Ist, $20, each on 
 2 months' credit. 
 
 18. Bought goods of Messrs Ho't & Co., as follows: Mar. 
 11th, $85, on 80 days' credit; July 20th, $95, on 2 months' 
 credit; Sept. 8th, $215, on 8 months' credit. What was 
 the average term of credit ? 
 
 ' 892. To find the extension of credit to which the 
 balance of a debt is entitled when partial payments 
 have been made before they are due. 
 
J-VUAiiuy Of dccuvMs. 
 Interest method. 
 
 Hill in drift yh,r. 12 f t! ,„, ,.1 ^ 
 
 •l.WO. 
 
 Pl-ncr; . f 1,7(0 , il,->rf) 
 
 ■■'7 - 4.:!i^ 
 
 Si'.'iS intorcil 
 "10. 
 
 Intcre., ^.Sn^O for l<J.;,,t,;;^ „,,„,, 
 
 JOjrHVATInV, 
 
 If a partial payment is made l.cfore a ■i..>,t i. i 
 
 to tLo interest of the pre payLnt '" "'" ''•''^'"^"- '"'"'-''■•''• 
 
 H., I)y paying a portion of Lis ,l,.ht t,„f m • , 
 on r,on for 64 d^.. and t>, , / ,tf "oo T 'r,' 1"" ''^ ''''^•^''•* 
 '"t-cst. A ,l„n<ld tb-nf,,.,. a ow 'm '"' f <'">•«• in all S'J.GS 
 
 "ntil tl,o interest on it amount, tl;/", 'r/".^: I''^ ''^''"-^ ^^''O. 
 be 107 days. '^' ''"' ^""^ *'"ch is shown abov« t« 
 
 NoTK.-Kqnity requires »n extension of credit 1,nt n 
 always willing to .Uow this and is not rr^rrlft; d^o s':;;',:,:" " ""^ 
 
 Solution 2. 
 
 By the product method. 
 
 nrjis. r,AV3. 
 
 8">00 X (11 = .32000 
 
 8700 X HI a 2o000 
 
 e 1,200 .^^ 
 
 Jl,740 - 81/200 = ?.-io 
 
 540 ).57;iOO( 107- lavs. 
 Sept. 12 + 107 days » Dec. 29. 
 
 ExrH.NATluN. 
 
 A similar explanation to that, given ia Solut, 
 
 "D 4, Art. Zn, may b» 
 

 
 ' 
 
 iiJ 
 
 216 
 
 EQUATION OF ACCOUNTS. 
 
 EXERCISE 90. 
 
 i t 
 
 1. P. owed me $1,800 due in 1 year. At the end of 4 
 months he paid me $500, and at the end of 7 months $300 
 on condition that I would let tho balance stand an equit- 
 able time m consideration of these pre-paymenta. What 
 was the balance, and when should it bo paid ? 
 
 . ^;o^T" "''''""^'^ * ^'^'^ "^ -"'^'^^ "'^ »0 days, amounting 
 to $2,840.75; if he pays $1,000 down, what extension 
 ought he to have on tiio balauce ? 
 
 8. A man owes $1,569.75, payable in 90 days ; 60 days 
 before it is due he pays $350.80, and 30 days later $211 89 
 more; what extension ought ho to have on the balance? 
 
 4. A person owes a debt of $1,6R0 .hie in 8 months, of 
 which he pays ^ in month..., ^ in 5 months, | G months 
 and J in 7 months. When is the remainder due ? 
 
 6. Bought a bill of goo.ls, amountinjr to $l,.'-,00 on 6 
 months' credit At the en<i of 2 months, I paid $300 on 
 account, and 2 months afterward, paid $100 on account 
 giving my note for the hWanee. For what tiine was the 
 note drawn? 
 
 6. Tho following sums are due from E. to F -—$500 at 
 the present time ; $C,00, in 80 days ; $-100. in 40 days • 
 
 «fnf °'\n"i'' '^" '' ''■^'^'''- ^'^' to-day. 'and 
 ?1,000 m 10 days, how long from the present time should 
 the rest stand, to balance the pre-paymonts ? 
 
 7. A debt of $2,000 is due in 1 year from Jan. 1st 1890 
 In consideration of the payment of $100 March 2nd. and 
 1800 April iBt. till what date should the balance be allowed 
 to stand ? 
 
 1 «n ! ''^ "" ?'^"' ''"^^ " P^^^^ ^^ ^"^y^ before it is due; 
 i. 60 days; ^. 27 days. What extension should the debtoi 
 be allowed for the payment of the balance ? 
 
',U 
 
 EQUA HON OF A CCO UNIS. 
 
 ^ I. I 
 
 9. A. sold B. a bill of good, March 12tb, on 6 monlh. 
 titled on^'lC?' '" ^'■"' ^'"'"--'^-Ji' iB 13. el. 
 
 ll..'^;i?" ° ''"" "' '-■""' •'''= ■' S »°"tl„ from Fd,. !,t 
 Ike follcAving ravracu.i „,.. r-ade- May l«t M'n i i 
 13., SaOO; and So,.. U., ..=00. W„;„'i7.„eU™e'/:e'; 
 11. Find the average term of credit, and the eauated 
 
 sTolTmS '■"'" r- ^■^"'.«f-^225duein3rdayB 
 5dD0 due m GO flays, and $7.50 due in 90 duya. 
 
 31»*.^. To fird the eqvited time for the oavm^nf nf 
 ti- inlance of an account havin, both d^S^i^^^ 
 
 fo.!o.in":^~r''" " ''' ^'^""^'^ '''"« -'^ '^^^'^ 0/ paying the 
 
 /)/■. 
 
 n. BiaRRi.F,Y in acct. ^ith UvmxY & Co. 
 
 i8;to. 
 
 May 21 j To Mdse. 3 mfig 
 ," 23 1 ■• 3^03. 
 
 June 91 " 80 da. 
 
 Cr. 
 
 
 SO' rTIf;M 1. 
 
 Interest method. 
 
 DUE. 
 
 Aug. 21 
 
 " 28 
 
 Jn.'v 9 
 
 ITE.\H, 
 
 SI CO 
 
 TIME. IVTIilil-^T 
 
 112 rla. 89.33i 
 119d,.i. oi.unl 
 
 ITR. 
 
 ^1:1 y 21 
 Ant,'. 7 
 
 69 da. I Hm^ I July 21 
 »'*10 8liU3i~ 
 
 £800 9.n:^ 
 
 8110 
 
 "EMS. I TIMB.jls.TEnEsfr 
 
 SI. 15 
 
 ?I.3.5 
 
 SSOO 
 
 $9.03| 
 
 87.0'JJ 
 Int. on 8110 for 1 day at G% = ? 0181 
 
 ^l-^y 1, 1890 + 387 days = May 23, 1891. 
 
 Notes 1.— May ist ia chosen a^ tv^- '-ra! -Inf. * 
 choseu however. ^"**- ^^^ <^*'e «"».* b« 
 
 .A 
 
 Si', 
 
 ' ".1 
 
 f. 
 
 -4 
 
 J 
 
 ■**r-J»«#»»Uij Hill rjin ■■--«/ TWtt 
 
a 
 
 lljl 
 
 a "1 
 
 11 
 
 ■ 1" 
 
 i 
 
 '218 
 
 KQVATlnS OF ACCOUNTS. 
 
 2. In thia example the halanoe of i„tere.t on May IhI i. in faror ol 
 n. Una,- oy. he,.«, ho i. enl,f.l.,l to the intor„.t .,n tlu, balance of th. 
 account for :<87 davH after May l^t. 
 
 Ha.l fho l,nl,v„cr of intcn.st l.oen on th. crrdit .i.l. of the aoconnt. w. 
 •houKl then have suMractci llm ,-jn,ar.l lin.efrom the fo,..Hl date. 
 
 Uui.B Kon rNTPiiii ,T Miniion. 
 J. Find fhp iutrrest o„ nich itnn for the time from the 
 
 focal <hitc to tin- watunh, of the rrspertir, itnn,, ,v,d .Hride 
 the hiLiiu-e of thr intnr.ts hi/ the intn;-xt of th- luilaure of 
 the ,!rms for 1 da,, or 1 mouth ; the <,nnlir„! n-ill he the. 
 nimher of </„,/., or tnonthx, ns the e„r,e m.nj be, hetween the 
 fil,uiJ.,rd date and the lime of s,lt!emeiit. 
 
 '2. When the hahmce of an aceonnt and the hihrnce of 
 interest are hoth on the same side, add the qnutient to the foeal 
 date; if on oppn,ite sides, sul>trael it: the rrsult udl be the 
 date of selllemeut. 
 
 , ^'".?r~ '; '" *"""^'"" ^^^ '"■^'""ty ot notes an,l drafts 3 days of grao. 
 
 •houia Iv ft>MoJ to th. sp.vif.ed tit.,0 of p:v^ ^lent. 
 
 Jjrr "," ''"7 1 ""^" ■' '"''"''""•"' »l'-^ transaction is understood 
 to be for oash. and the payment due at once. 
 
 Soi.rTioN 2. 
 By the product method. 
 
 Dr. 
 
 Cr. 
 
 DUB. 
 
 .\uy. 21 
 
 •• 28 
 
 July 9 
 
 rTKMSl. 
 
 DAYS. 
 
 Sr.OO 
 
 112 
 
 ?--':.o 
 
 119 
 
 f-ir.o 
 
 G9 
 
 800 
 
 DUE. 
 
 l\ray 24 
 Ani,'. 7 
 July ai 
 
 ITKMS. 
 
 n^va. 
 
 8:too 
 
 23 
 
 SlOO 
 
 98 
 
 fino 
 
 81 
 
 90700 
 C-l'JOO 
 
 <800 
 
 nionnrTS, 
 
 oono 
 
 SOl'OO 
 8100 
 
 6420O~ 
 
 110 ) J2-,9.1 ( 3S7,\ dava. 
 
 May 1, 1S90 + 387 day.j = >[ny 23, 1891. 
 
 Hi-i.f roil TUB rnopncx SlETnon. 
 
 1. Find the number of days from the focal date to the 
 maiurito oi each item. 
 
EQUATION (I I- ACCDViSlS. 
 
 211) 
 
 2. Multiply each item by iU iintnhf.r of tltiyn, ami dindr 
 the. (iijfnenre hefirr.ai the hiwik of jirmhirtH hy the lUpii'inc 
 belli. ■en the mrns of iti-ms ; the qnolicnt will he the <:<iii>itnl 
 time. 
 
 ■'J. If the (fr.'dter mim of ilnm uml the grmtrr njun of pro 
 lurtu arc lioth nn the 8iinir si,lr of llir orroiinl, add the 
 njiKited time to the focal ditr ,- if on oi'imsite sidcx Ruhtrart 
 M : the result irill he the date n!i<n the LJance of the account 
 11 ill be ciiuitably due. 
 
 EXEKCISE 01. 
 
 1. Wlien (li'l a nnto piveri in settJcinent of the foUowin;:' 
 account bogiu to bear int. n ht ? 
 
 Dr. 
 
 L. If. (lr,KM. 
 
 IS'JO. 
 July 2 
 
 TomdB. . 
 
 
 Cr. 
 
 2. When did interest be^^in on the following af^coiint, and 
 what was due on settlement, Jan 1st, 1892, intcroBt 5 % ? 
 
 Dr. 
 
 0. L. rioOSACK. 
 
 Cr. 
 
 1891. 
 Jane 17 
 Sept. 20 
 Oct. 1 
 
 To mdsa , 2 mos. 
 " 8 moa. 
 " 1 mo. 
 
 S270 
 SlOO 
 
 IH'JI. 
 
 Junu ;!0 
 Oct. 1 
 Nov. 30 
 
 By mrlso. 
 " ciisli, 
 " ml 90. 
 
 ?2.-0 
 
 SriOO 
 
 8. When is the balance of the following account due by 
 equation ? 
 
 Dr. 
 
 Frank H. Baunard. 
 
 1S«9. 
 Jan. 16 
 Feb. 28 
 
 To mdse. 
 
 
 \n^:\. 
 
 Mm 
 
 1 I5y cawh, 
 
 >:iOO 
 
 J.'iOO 
 
 ^'B!!! 
 
* f 
 
 , 
 
 
 'II 
 
 II 
 
 I } 
 
 I 
 
 ■t I as* 
 
 
 :220 
 
 EQUATION OF ACCOUNTS. 
 
 
 Benj. F. Hawkiks. 
 
 •'nn. itj TonidHo, 
 
 " 28 
 Feb. 3 
 
 " 15 
 
 Dr-J. K. S™»„^4 Co. in »cct. with Sm,th 4 C«.»». Or. 
 
 Mar.25,Ton,dse..00da. I f.-,no 
 May a) .. .. I -"^■>0 
 
 ^^^jD,sa^He,.80da.N.50 
 Oct. 31 1 .. draft. 30 da. \ ^S> 
 
 date. '• *'*'' •'^'-'^'^^'^ '""« 's *uUn^ted from tho standard 
 
 6. Wliat is the lialancfl nf fV.^ r n • 
 when due? ^^^ following account and 
 
 />r. 
 
 JnJy 20 j To sundries 
 Aut;. 10 1 " 
 
 Sept. 15 
 
 " " ''^- ^'th LocKwooD & Co. Cr. 
 
 8520 
 
 
 JoZlT "" ■""'«' '™' °f P-ii"* the following 
 
 Dr. 
 
 1891. 
 
 Georoe Jenkins. 
 
 1891. 
 
 Mar. lJTonid3o.,30da. 
 
 3moa. I S!700 IJM'iv 10 1 "■'"JT' 
 
 ^^20! :'""'«^- iSli^^:?^l^y'^^*'».2ed.. 
 
 Or, 
 
 f400 
 $540 
 »600 
 
m^rn 
 
 b.QUATlON OF ACCOUNTS. 
 
 221 
 
 8. F 
 
 due on 
 
 Dr. 
 
 'ind the equated time for the payment of the balance 
 the following accownt : 
 
 W. T. i)AWEa, 
 
 18'J2. 
 Mnr. 1 
 May 10 
 June 20 
 July 30 
 Aqjj. 14 
 
 To mdae., CO da. 
 
 90 du. 
 iiO da. 
 GO (la. 
 
 ?'.-'oo 
 
 t-llH» 
 
 SU;a 
 
 iy;fj. 
 ^.^tr. (i 
 yi.Ky in 
 
 Jwiju 2ii 
 Jiiiy 1 
 .iiig. 28 
 
 By mdiia 
 " oaah, 
 
 indao. 
 
 Or 
 
 r-2( I) 
 
 9. Average the following account : 
 PT^ Jamks Gi:kkn & Co. 
 
 1892. 
 Jan. 10 
 " 26 
 Apr. 20 
 
 To mdse., .S mos. 
 
 •SO da. 
 
 " 3 moa. 
 
 !| 1892. 
 ?4.'j0 'IJudo 1 
 
 tR'>0 ;iMar. 1 
 
 By bal. of acct. 
 " note, 3 nios. 
 " draft, 30 da. 
 
 C, 
 
 f2,:oo 
 5a(;o 
 
 10. Balance the followiiig account 
 
 ^^'•- 0. J. II.U11LT0N. 
 
 Ci, 
 
 ibmTl : 
 
 Jan. 20 To6tuidrioa,.^0aa. ,«!.-no 
 Feb. 12 " GOda.i i-ilO 
 
 Mar. 1 " BOda.i !,-:;0o 
 
 ■'an. 20 1 By re:t! .■HUto, eoda.l WH) 
 War. 1 I •• di;ut, GO da. I f.-M) 
 
 " 20! " cadi, j i^:,:. 
 
 11. Find the balance of the followino account and when 
 due : 
 
 Dr. 
 
 A. B. in acct. with C. D. 
 
 lauo. 
 
 Xag. 11 
 St>pt. 5 
 Oct. 20 
 
 For mdue. 
 For 1 horsa, 
 
 flf.O 
 i^ilO 
 
 ^i i t. ■> ; By aumirics, 
 Oct. 10 , " note, 30 da. 
 
 £175 IjNov. 1 1 •■ cash, 
 
 Cr. 
 
 §100 
 
 eiio 
 
 12. Find the balance of the following account and when 
 due: 
 
 Dr. Wm. Gorman in acct. with John Hendrib. Cr. 
 
 isno. 
 
 Feb. 10 
 May 11 
 July 26 
 
 
 1890. 
 
 ?4.50 
 
 Mar. 20 
 
 8500 
 
 July 9 
 
 «300 
 
 Sept. 15 
 
 By Bundries, Smcs. ?325 
 " draft, 60 d». , »I50 
 " cash, I $400 
 
 I \a 
 
 III 
 
 IP 
 
 i 
 
 I* 
 
f 
 
 222 
 
 tqU Alios OF ACCOUNTS. 
 
 13. When is the balance of the following account due bj 
 equation ? 
 
 Dr. Samuel Peck &. Son. Cr. 
 
 ISS'.I. 1 
 
 
 188'J. j 
 
 
 Miir. '.i To m.lae. 
 
 »''.0 
 
 Apr. 1 1 By oaBh, 
 
 SIoO 
 
 Apr. 21 ; " 
 
 Jliiii 
 
 .lune 1 1 " 
 
 U-.0 
 
 May I , •• 
 
 Sl.-.o 
 
 A"!?. M 
 
 §:i:)i) 
 
 '• ao " 
 
 S-jo 
 
 Oct. 1 " 
 
 UIKI 
 
 AUf,'. 17 '• 
 
 8-'uo 
 
 
 
 11. Find Ist, tho balanco of the fol!owin,'» account, "iuil, 
 when due by eqiuitiou : 
 
 Dr. Walter L. Paukeii. Cr. 
 
 iNS'J. 
 
 
 
 
 IHS'J. 
 
 
 
 May 11 
 
 To mdBe. 
 
 2 mo3. 
 
 IHOS.lOijJmie 1 
 
 By cash, 
 
 $124.27 
 
 July 1 
 
 «« 
 
 soda. 
 
 8'2'J.5.00 ' 
 
 Oct. 31 
 
 " 4 moa. note 
 
 
 Auf- 31 
 
 •■ 
 
 
 S'iyu.so ! 
 
 
 (no interest;, 
 
 81 (57 91 
 
 Oct. 1 
 
 « 
 
 
 C137.50 
 
 Deo. 1 
 
 " caui), 
 
 8300.05 
 
 15. Find when the following account is due by equation : 
 Dr. John Mo>:TaoMi;i;y & Co. (Jr. 
 
 iBaj. 
 
 
 IH'.iU. 
 
 
 Ueo. 15 
 
 To mdae. 
 
 8200 Jan. 2 
 
 By cash, i 8300 
 
 " 28 
 
 " 2 moa. 
 
 »;iO0 Mar. 1 
 
 " CO da. note (no 
 
 1883. 
 
 
 1 
 
 interest), ll.'^O 
 
 Jan 14 
 
 80 da. 
 
 i3C0|[ 
 
 
 
 ii 
 
 iiagmim^:vm 
 
 ^■Frjr^TT^- 
 
 ... ■/^■ni.y... i/r. ^•>■■■•.^■■" 
 
 wzmMtiT. 
 
 ^fftl 
 
AVhliAOlSQ ACCOUNT SALES. 
 
 AVERAGING ACCOUNT SALES. 
 
 228 
 
 f 
 
 i la 
 
 
 !{0:t. An account sales is an account reiulored hy a 
 cotninipsioti iii;ent. of goods Hf)l(l on account (jf a consi;;nor, 
 atid contiiins a stiitt'in.^nt of tlit; sules, attendant chur^^ob, 
 and th*^ net i)rocf'f-ds diiu the ownor. 
 
 NoTKs.— 1. Tho ch'iri:oH inclml'' frcii^lit, cartiii^c. f-torajje, tt(lvertiaiu({, 
 insnranco. ciitniiiiBsioii, tjiiaranty, etc. 
 
 2. Tho talet form the credit sido of th<; account luij the ehuTijei and 
 advances the debit side. 
 
 31>4. Guaranty is a charge made in addition to the 
 commission, for insuring the iwner against the risk of non- 
 payment in case of goods sold on credit. 
 
 liitti. The charged for transportation, cartage, adver- 
 tiaing, storage and inHurance are considered due at the 
 time of payment of tho same. 
 
 !tfM$. The commission, guaranty, and other after charges 
 of the comraission moiidiant are considered due by some 
 at the avcraije date of miles ; by others at tlie average due date 
 of sales ; while some merchants enter the commission at the 
 date the account sales is rendered. 
 
 NoTKa — 1. When the commit-, ion is httivU compared with the gross 
 Bales, either of these melhoda pnxluoo a result, which ia practicallj 
 Buliiciently accurate. 
 
 2. In this worli they will be considered due at the average duo date oV 
 the sales. 
 
 3. Of course the due date of the co.naiisaion most be a matter of 
 agroement between the parties ooncemed. 
 
 {5?>7. The method of averjiging an account sales is the 
 same as that for averaging an account having both debits 
 and credits, except in the matter of adjusting the date for 
 the commission and other charges. 
 
 
 f 
 I'- 
 
 II' 
 
 
 w 
 
 ^^•^ 'V. M.\.\''-!^: 
 
 ^PPSEjTcT 
 
 wmmtim 
 ■■-■ vx-:. 
 
 i-"..A* 
 
diLBAUJUU ACCOUM HALLS. 
 
 3»,S. To average an account sales, and find when 
 the net proceeds are due. 
 
 .-ot pro^iasT""^''''""' ""■ ^""°^'"«' *"'' fl"'* "'" ^^^ ^"f Of tho 
 
 Cak'Sr °° '^''"'-'"'"'"' '-OOO •>='"-'« of «"ur from Scott. Bros. 
 
 evLi -i. 
 
 ■luiy ill i-'UOLi.la. of U.ur, .,.:.! on. ti» ,|m 
 
 Au 
 
 " 2(1 
 Sojit, i! 
 
 July 1 
 
 ■•i.-.O 
 
 •2^0 
 
 1" 'l>i... 
 
 ;ii» .ii..., 
 
 CO d.i..., 
 
 CnAI:0E3. 
 
 ,, Fn.;::l>t 
 
 ll ^r'--- 
 
 o Stoia^t' 
 
 Coiniiur,Hion, 2J %' ou v"j,;i20. . ' 
 
 Coniiucroial balance 
 
 '• -"j 1!, 170(10 
 
 <'■') r| i.-.oooa 
 
 ;'.7^>; l.iou.oo ?j,920.00 
 
 ■l"o •..'.') 
 
 l.".oi)(3 
 1 la 00 
 
 ?77'J 00 
 1 80,11100 
 
 OI-HTION. 
 
 1. Find avera:,'e date of sales-Focal cl,.,ia, J„lv 1st. 
 
 M-K. ITEMS, IMYS. rMlCl.KST AT %. 
 
 Auu 10. $1,100. .10. *7.T,L 
 
 " ^■'- -^!"f'. 45. i,;.27J. 
 
 Bept. 19. i,,-o,,. RQ_ ,,j, ,,,j_ 
 
 ^'O''- 1- IJoO. ]-23. 23.." J. 
 
 es.irjo. «,^ai 
 
 Int. on §5,920 for 1 day at C% = j/jsj. 
 
 S''7 ISj" ^ .98J = 08 days. 
 Balos due July lat + 08 days a Sept. 7th. 
 
 •2. Find average date of charges, focal date July Ist. 
 
 Dtnt. ITEMS. DATS. tNTEREST AT 6%. 
 
 Julyl. 8450.25. 0, $ OO 
 
 Jnlyl, 30 75. a loO 
 
 Only 4. 150.00. 2. .05 
 
 Sept. 7. 148.00. 68. I'o?}*. 
 
 «779.oo. ^Tnn 
 
 Int. on 8779 for 1 day at 6 % s e.l2|f 
 ^ S1-72H -5- 8.12^ . 13 day* 
 
 Charges dne July 1 + 18 days m July 14. 
 
 ■'p^mm^m^ 
 
.....U'U 
 
 AVEUAQIHQ ACCOUNT SALES. 
 
 220 
 
 8. Averaging sales and expenses, they now stand as 
 follows : .^ocal date July Ist. 
 
 nnr. ,t.m8. b.„ pkoi^cot. du,. ,i.„.. ^.t.. raoDucT 
 JoiyU »779 18 10.127. Sept 7 15.920 68 402,.5r.o. 
 
 779 10.127 
 
 •6.141 ) 392.433 
 
 „., , Avora^io time TtidavB. 
 
 Net proceeds »o,141 dno Jnly 1 + 76 days . Sept. 16. 
 
 BULB. 
 
 1. Find the amount and the average date of tales. The date 
 of the mles will he the date of the commission and guaranty. 
 
 2. Find the atno^mt and the average date of the charge*. 
 5 3/aAe the charges the debits and tkr sales the credits 
 
 and find the average date for paying the balance. 
 
 r 
 
 
 EXERCISE 92. 
 
 1. Put the following items into the form of an account 
 sales, liud tb(> net proceeds and date of payment : 
 
 A. B- Harrison, of Alontreal, sold a corsignmont of goods 
 rom Chase cV Co.. Toronto, a^ follows: Nov. 15th. W 
 135 chests tea at $45. on 80 days ; Nov. •20th 76 sacks 
 coiTee at $28. on 2 months; Dec. 1st. 2.58 Icegs larTal 
 *4.50. 80 days ; same date 285 tubs hntter at $18.87 on 
 2 month. Paid freight Dec. l.t. $28.7.5 .■ ..,rtage, $5.40 
 storage, Dec. 10th. $7.80 ; commission. 2}%. 
 
 2. Same parties sold Sept. 1st, on 8 months. 8.620 lb 
 sugar, at $.12J; Sept. 16th, 25 chests tea, each 85 lbs . at 
 $.98 on 2 months ; October 2ud. 28 half-chests Oolong tea, 
 12 lbs each, at $105. on 2 months. The charges wer^ 
 paid October 16th, freight and cartage S8'5 mZli 
 wd guaranty 6%. " ^ ' '^°°^°^^«8ion 
 
 m 
 
 JPK: 
 
22e AVEIUQING ACCOUNT SALES. 
 
 8. Avtnig'' the four following account aalea : 
 
 BALHH. 
 
 hiirrels to Hudson A Son, 
 " '• Oiiiia. II. Kn .pp. 
 
 (^ SS/>0. cas)i, 
 (ij 8'). 75. I ni')., 
 
 " ■• •' ^ «:..H0. CO .lii , 
 
 " Vv'iii Cliirk Ac Hro.. (a r.l.t-'i, 30 il:..., 
 " Chilton Mcriiirson,^ J.'i.TS, casli. 
 
 ClI.\U<ilib. 
 
 -lit 
 
 (j'irt.i;,'ii 
 
 Ciibli advaiici d on coiisi;;iiin(mt 
 
 C'lOiiorarfd 
 
 CotamisBion, 4 % 
 
 62 .10 
 
 :iO'.)0 
 
 '.OiiOOO 
 
 6 00 
 
 137.78 
 
 in'j'ci 
 
 1 
 
 July 
 
 It' 
 
 • 1 
 
 ao 
 
 Aug. 
 
 10 
 
 Ant?. 
 
 10 
 
 July 
 
 1 
 
 SALRS. 
 
 500 barrels, 30 dii ^g 3*;. .10 
 300 " " " 7.00 
 
 COO " " » G.75 
 
 TAB01C8. 
 
 Storage, labor . ;i' i[n.-rin?e, 
 Insuranci! on ?'J,0 M a: ^ %, 
 Coiniiiis-iion oa S'.), l^'O @ 2J %, 
 
 Not proceeds duo per average, 
 
 $71.25 
 11.25 
 
 235.00 
 
 83,'MO 00 
 2,100 00 
 4,0.-.0 00 
 
 SALKd. I 
 
 Sold liennurd Barker i% Co., •^ 6 moa. : '! 
 
 l.i lihds. Cuba Bii^ar, ^.l.l-J-i Ib^. @ ICo. j| 
 
 32 balf cb.ists Oolong teft, 1,805 lbs., tare 4S0 = j 
 
 1,325, it^ 1.10, 
 
 CH.\r,OI'3. 
 
 Fire ins. on 30,000 @ IJ 'i, 
 Cooperage, wei^ihinn, labor, etc., 
 Com. and fiun'. on r'5,5.ir>.02 @ 5%, 
 Net proceeds due per average, 
 
 eoo.oo 
 
 17.37 
 276.25 
 
 9<J,400 00 
 
 317 50 
 
 $;bOs2 50 
 
 84,0.;7 52 
 l,4.'i7..50 
 
 J5, 525.02 
 
 ».5~14140 
 
 1892 
 
 
 May 
 
 10 
 
 Jane 
 
 12 
 
 ti 
 
 25 
 
 July 
 
 17 
 
 May 
 
 10 
 
 Jane 
 
 6 
 
 co.iia. 
 
 1,000 kilogrammos prunes, 60 days @ TOa, 
 2 bbls currants, 30 days, 
 1 case figs, 60 days. 
 100 bags peanuts, 30 days, 
 
 CBABnES. 
 
 Dutiss on S930 ig: 20 70. 
 Freight, storage and labor. 
 Commission on $1,612.15 at 2^ %, 
 Net prooe*is duu. 
 
 eiso.oo 
 
 S26.60 
 40.30 
 
 8700 00 
 
 85 05 
 
 69.60 
 
 757 50 
 
 91,612.15 
 
 465.80 
 
 »1,156 36 
 
 fifWB 
 
 , fy;^' 
 
 '.-"^ 
 
 
AVEHAQISQ ACCOUNT SALES. 
 
 4. Average thfl following ,iciwuut of ank's: 
 
 227 
 
 Ae:n»nt sale, of 600 hnrreU of pnrk reoivedfrnrn Conover d 
 Droivne, of Cincinnati, to he sold un llu-ir .u-munt and risk. 
 
 187-J. 
 
 Pui.i) TO DnsrHii'TioN. I li\n. 
 
 ..;) 
 
 July I FosAHon .. j Now M.mi... 
 " 14 A. Ro.'ii- .... I I'rinie Moxs. 
 
 15 
 
 18 
 
 Clay <fc Co. .. ^ KxUH i'riiiiR 
 
 10') j 87.i;i). MiU. 
 
 li'l i ll'..,t."l, (.MWll 
 
 210 
 
 n.f.d, 1 mo. 
 15 2'i, 2 mo. 
 
 9 
 
 CllAIlllK.-*. 
 
 July 3. Prcitjht on 500 bhla., it T-'ic , a 
 
 [\ •>, Cartage •• '..'..'. .'4) 50 
 
 " 28, Stora^^o and insurunco, .. I'/'o 
 
 — , Commission ou S , at ^i '..".."..'" 
 
 Total cli;ir(!ci '~ 
 
 Net procetida, due as iK:r ttvura^o, ~" 
 
 ( 
 
 
jt:'' 
 
 \:f'. 
 
 lii 
 
 228 ACCOUNTS CUHHENT. 
 
 ACCOUNTS CURRENT. 
 
 »1M». An Account Current is mi itemized recor;! of tlie 
 mercantile traiisdctioin between two parties, showiuy the 
 cash balance due at a certain date. 
 
 Notes.— 1. An Hcconnt current i« a tr.ui'^oript of the ledger account, 
 with the addition of certain details taken from the books of ori«inal 
 entry, and Is arrantJt'd in u different form. 
 
 2. Wliether tlie iltins bear interest or notdopenda on onatom or agree- 
 ment between the iiartiee. 
 
 3. It ia customary for merchants, bankcra, and brokers to render their 
 accounts at stated times, as monthly, quarterly, aemi-annaally. or 
 annually. 
 
 4. Among retail dealers, mechanics, farmers, etc., the items seldom 
 bear interest ; hence, in settling such accounts it is necessary to find only 
 the morob'^ndise balance. 
 
 5. In the illustrative example iniBrest ia calculated on the 8R0 days' 
 basis, the necessary change to 30.5 days' basia being afterwards made. 
 
 fi. In Ontario and Manitoba, interest may be recovered on open 
 Rcconnta from and after demand of payment and notice that interest 
 will 1)0 charged. 
 
 400. The Commercial or Merchandise Balance is the 
 
 ditTerencc between the debit and credit ituius. 
 
 401. The Cash Balance is the .sum required to settle nn 
 account at a given dai«> 
 
 403. To find the cash balance of an account at a given 
 
 date. 
 
 KxAin'i.R.— Find the cash balance of the following ncconnt, due on 
 July 16th, 1800, at 6% interest : 
 
 Cr. 
 
 D, 
 
 J. M. DoYi.E in acct. with R. IIiscox. 
 
 1890. I 
 llh'r. 10 To mdse , 30 da. 
 
 Apr. 1 
 May 26 
 
 cash, 
 •• note, coda. 
 
 i iSliO. 
 f0.50 1 Apr. 20 
 1000 1 May 13 
 12G0 June 1 
 
 By hal. acct. 
 " draft on 00 da. 
 " bank stock. 
 
 J.500 
 
 910 
 lOOu 
 
•.:al^- 
 
 2m. k*.' 
 
 T 
 
 I 
 
 ACCOUSIS (JUUUEHT. 
 
 BoLOTIOH. 
 
 DVI. 
 
 BATS. 
 
 rrmt 
 
 niTMntn 
 
 Apr. 
 
 1 
 
 Jaiy 38 
 
 97 
 
 IDS 
 
 -13 
 
 two 
 
 1000 
 l'2Bo» 
 
 810.61 
 IT.r.O 
 
 • 
 
 
 
 Ji'JlO 
 
 l,70f 
 
 
 
 2110 
 
 «:i-> 71 
 
 U il. of 
 
 itoraa 
 
 8470 
 
 17.-.'3 
 815. H 
 
 ODI. 
 
 Apr 20 
 A'i«- U 
 Juiji) 1 
 
 Ititerost. .il)') Jayg to )<ht, 
 iir->AH - /j r.f ,?1.3.H = S1.VJ7. Actual iutereit. 
 8170 + 815.'.'7 - 81-.VJ7. Casli bulauce. 
 
 EsPL.tN.tTION. 
 
 The third item on tlm Dr. iido in not .|.io until 13 dayi (indicated br 
 
 - I'll 'ifter the date of h ttl-n.-nt an 1 tlicref to J. M. Dovio iH ,;ntilK i 
 to the diacuiii.t ou ? 1 ,'.>f,0 for l;i 1 1 v a. Tliii amount niav either bedoduot«d 
 from tho intorost ou the Dr. M>- or u.l LI to the interest on th« Cr. 
 side %s in tlij prohlein. Similar remul.s apply to tho sncoad item ui 
 the Cr. aidu. 
 
 NoTBs.— 1. Iho reason for placim^ tlie luterost of tin i!.:(n on ita own 
 dirle. whon it becoin..') due boforo th..- time of settlemu-nt, ia becauia it ii 
 entitled to interest for the intervening^ time. 
 
 2. In like manner, if a credit extends beyond the settlem.' t, equity 
 r -quiros tlnit iiiter.'St should bo allo'.ve 1 on that item, ir.nco, Ub inter, at 
 for tliat time mnnt either hu subtiMctcd from ita own side or bo added 
 to the oppoaite. The latter ia tho more oouveuieut, a 1 therefore 
 adopted. 
 
 3. Interest tables are much used in makinj^ out accoantd curron! 
 
 4. If tho accoimt has b^.n avcra;;ed, tho amount due at a i;iv. ii dat.; 
 may be found by calculating tlio inf.jrest on the bilance of tlie ace mt 
 from the time it i. due to the date of sett! niont. If tho dat- of settle 
 meut is earlier than the uv. la-e date, subtract the inton st from the 
 balance of the account; if later than tho avera^'o date, add the int-r-st. 
 
 5. The interest metlio 1 of finding a Casa Balance is recommer.dod 
 because it -ivcs the inten-t or di,-,cou!it on each item, it i.-i readily under 
 stood, it ia more satisfactory to those to whom accounts current are sent 
 than the product metho 1, and whjn interest tablos are used it is shorter 
 than any other method, 
 
 Rule fob Interk:*! AIetuod. 
 
 1. Find tlu- ■hie dat^ of each it' in of ihe account. Then 
 
 find the interest on each item from (he date it hccomea due to 
 
 the day of set'lement. The difference hetween the nums of 
 
 the debit and the credit interests will be the balance of interett. 
 
 \i 
 
230 
 
 ACCUUNIS CUliliLST. 
 
 2. To find fhe cash balance due, when the balance of inter- 
 est and the balance of items are on the same side, take tJuir 
 »um ; when on opposite sides, take their difference. 
 
 EXERCISE 93. 
 
 1. Find the cash balauce of the following accoant, Aug. 
 6th, 1892, at 6%: 
 
 Dr. H. Meadows in acct. with J. P. Hume. Cr. 
 
 1692. 
 
 
 
 . is: 12 
 
 _ -— ., ,; — 
 
 
 
 «une 10 
 
 To mdse. 
 
 8200 
 
 i J line 15 
 
 By cash, 
 
 fioo 
 
 " HO 
 
 11 
 
 300 
 
 ■' 30 
 
 14 
 
 150 
 
 July 11 
 
 ■< 
 
 1-20 
 
 •lulv 6 
 
 It 
 
 200 
 
 " 24 
 
 II 
 
 250 
 
 ■• 30 
 
 tl 
 
 300 
 
 2. Find the cash balance of the toUowing account, Oct. 
 80th, 1892, at % : 
 
 Dr. J. S. Cakson in acct. with Jajikh Fep.ouson. Cr. 
 
 18'J2. 
 
 Jan. .5 To nijise., COda. 
 Feb 12 1 '• 30da. 
 
 Mar. 7 
 
 Apr. 15 " 60 da. 
 
 May 9 1 " " 
 
 €1»2 :,]-eb. 1 1 By bal. of acct, 
 270 i.Mar. 3'il •. cash 
 
 430 :iA|.r. 20 
 640 ' June 15 
 530 iAu-j. 1 
 
 " note, .SO Ja. 
 " cash, 
 
 S300 
 250 
 200 
 300 
 400 
 
 8. Find the cash balance of the same account at 8%. 
 
 4. Find the balance due Aug. Ist, 1892, at 8%. 
 
 6. Find the balance of the same account due Jan, 1st, 
 1898, at 6%. 
 
 6. Find Ist, the balance of the following account ; 2nd, 
 when due by equation ; Brd, oasli balance due Jan. Ist, 1888, 
 if money be worth 6% per annum. Prove the result. 
 T)r. John McMillan & Co. Cr. 
 
 18S7. 
 May 14 
 June 3 
 July 31 
 
 To mdse., 1 mo. 
 coda 
 " 2 ni08. 
 
 ?300 
 200 
 400 
 
 US87. 
 May 31 
 
 ■Inly 15 
 
 1888. 
 Jan. 1 
 
 By 2 mo. note (no 
 
 interest), ; f240 
 
 " 30 da note (no 
 
 interest), 150 
 
 caph. 
 
 100 
 
ACCOUNTS CUIiliEM. 
 
 231 
 
 7. Find the cash balance due on the following account 
 on the latest day of maturity, interest 6 % : 
 
 Dr. 
 
 W. NlCKXE. 
 
 Cr. 
 
 16S2. 
 Mar. 30 
 Apr. 2 
 July 16 
 
 IVSL'. 
 Mar. !0 
 )'ino'JO 
 
 I.IU ,Iu!v 27 
 
 By mdse. 
 
 " draft, 
 
 $180 
 9S0 
 2',i0 
 
 8. Wliat sum in cash will Huttle the following account on 
 Jan Ist, 1893, interest at i]%? 
 
 Dr. 
 
 Geo. Miij.3 & Co. 
 
 Cr 
 
 18112. 
 
 
 |l 1892. i 
 
 i 
 
 Sept 14 
 
 To mdse., 3 raos. 
 
 8125.00 :R..pt.30J Bv mdpo, 30d:t. 
 
 i f'-'.'^O 
 
 Oct. 4 
 
 coda. 
 
 410.50 Nov. 15 : "' note. 3 nios. 
 
 3i)0 
 
 Nov. 11 
 
 30 da. 
 
 217.15 " 25 
 
 " mJse. (not), 
 
 650 
 
 Deo. 12 
 
 " cash, 
 
 ■MO.O ) 
 
 
 
 9. Find cash balance of the following account due July 
 21st, 1892, interest 8%: 
 
 Dr. 
 
 Trios. McKay. 
 
 Cr. 
 
 18!»2. 
 May 22 
 ■' 29 
 June 10 
 
 To mdse., 3 mos. 
 30 da. 
 
 ?500 
 2.50 
 150 
 
 ld-.)2. 
 May 25 
 Juuo 9 
 July 2 
 
 By cash, 
 " sundries, 
 " cash, 
 
 |.S00 
 400 
 100 
 
 10. Find 1st, the balance of the followiuc? account ; 2nd, 
 when due by equation ; 3rl, the casli halance due March 1st, 
 1889, if money be worth 5 % per iumum. Prove the result. 
 r^r. S. S. Cook. Gr. 
 
 ls,SS. 
 
 
 j If-SS. 
 
 1 
 
 Aug. 31 
 
 Dy mdse., 1 mo. 
 
 ?lnO Oct, 2 
 
 By 30 da. note (no; 
 
 Sept. 5 
 
 " GO da. 
 
 L'OO 
 
 1 
 
 interest), ^100 
 
 Oct. 31 
 
 4 mo. 
 
 i;oo 
 
 " 30 
 
 " cash, ' 200 
 
 Dec. 19 
 
 " 80 da. 
 
 130 
 
 Deo. 1 
 
 " CO .i:i. note (no' 
 
 1889. 
 
 
 
 l.<s;, 
 
 i'.:t rest), 300 
 
 Jan. 1 
 
 •* Imo. 
 
 100 
 
 Jan. 25 
 
 " liiio iiccpt. (r;o 
 
 interest , r,00 
 
I r A 
 
 ACCOUNTS CURRENT. 
 
 11. Find cash balance due Jan. let. 1893, interest 6 % . 
 ^* J. Bkadfield & Co. Ck 
 
 1892. 
 Oot. 10 
 •' 1 
 
 " 18 
 
 m , i i 1892. 
 
 To mdse., uOda. 8150 |Aug. 2.5 
 
 " cash, I 350 : Sept. 20 
 
 " draft, 30 da. i 25) 
 
 12. Find the cash balance of the following account due 
 Nov. 8rd, 1893, interest 8 X : 
 
 A. B. bought of C. D., July 16tb. 1993. merchandise 
 1350; Aug. nth. $4(35; Sept. 9th. $570; Sept. 14th. 
 $850 ; Oct. 18th, $780. The former paid August 1st. $3«0 • 
 Sept. 80th, in grain $340; Oct. 6th, cash $500; Oct. 21st.' 
 $625. 
 
 13. Reduce the following memoranda to the form of an 
 account, and find the cash balance due Jan. Ist. 1889: 
 
 Aug. 1st, 1888, A. bought goods of B. amounting to S5G0 • 
 Aug. 26th. $840; Sept. 21st, $1,000; Oct. 12th, $1 370 ' 
 and Nov. l8t. $600. A. Rold E. Sept. 11th, 1888, wheat 
 amounting to $350; Oct. let, wool amounting to $760- 
 Oct. 3l8t, $400 worth of butter ; Nov. 16th, paid him §1 000 
 cash. ' 
 
 14. What is the cash balance of the following account 
 Dec. 81st, 1889, at 7 % ? 
 
 Dr. S. Morgan in acct with J. D. Bissonnk 
 
 TTl. 
 
 Cr. 
 
 1889. 
 Sept.ld 
 Oot. 1 
 
 " 23 
 
 Nov. 15 
 
 To mdse. 
 
 30 da 
 
 |i 
 
 CO 
 
 <Ia 
 
 «• 
 
 4f\ 
 
 da. 
 
 ti 
 
 ()0 
 
 da. 
 
 II 1889. 
 
 »lA'o0.1,')'Sept.25 
 
 1,051. nOilOot. 10 
 
 1.500.8,5!! •• 30 
 
 1.7i6A4 Deo 15 
 
 By mdse. 
 
 , 60 da. 
 
 81,560 50 
 
 «• 
 
 90 da. 
 
 948.30 
 
 
 40 da. 
 
 I.4Hnc,.5 
 
 
 HO da. 
 
 1,365.42 
 
ACCOUNTS CURRENT. 
 
 233 
 
 15. What is the cash balance on the following account 
 Jan. 10th, 1892 ? 
 
 Dr. W. E. Telfobd in acct with A. T. Stkwart. Cr. 
 
 By mJse., 3 ino3. i $)>Sn 
 i 810 
 
 " draft, 30 da. ! 800 
 
 16. Reduce the following transactions to the form of an 
 account bearing interest at 6 %, and find the cash balance : 
 
 Feb. nth, 1890, C. bought goods of D. amoimting to 
 $1,250; March 14th, a bill of $2,160; Apr. lO^'i, a bill of 
 $1,700; Apr. 30th, a bill of $1,070; Mav Oth. a bill of 
 $2,000. March 1st, 1890, C. sold a bill to D. of $1,(M0, 
 March 20th, a bill of $1,160; Apr. lath, a bill of $1,600; 
 May 1st, a bill of $1,340; May 21st, a bill of $1,000. 
 What was the cash balance June 10th, 1890 ? 
 
 17. What was the cash balance due July 20th, 188'J, on 
 the following account, at 7 % interest ? 
 
 C. W. Harrison in acct with L. Conodon. 
 
 Dr 
 
 Cr. 
 
 1889. 
 
 Mar. 1 
 
 " 20 
 
 Apr. 10 
 
 May 21 
 
 For mdse., 3 mos. 
 
 2 mr,3. 
 
 •• 6 mos. 
 '• 1 mo. 
 
 8500 
 750 
 410 
 600 
 
 jl ISS'J. 
 jIApr. 5 
 l! " 20 
 ,May 1 
 " 22 
 
 By mdse., 3 mos. 
 2 mos. 
 " 4 mos. 
 " cash. 
 
 5'3.>0 
 '.100 
 C^O 
 200 
 
 f 
 
 I 
 

 I 
 
 II 
 
 \ii 
 
 2S4 STORAQE. 
 
 STORAGE. 
 
 403. Storage is a provision made for keeping goods in 
 a warehouse for a time agreed upon, or for an indefinite 
 
 time, subjout to accepted conditions. 
 
 'I'lie ti "- storage is used also to desiacHto the charges for keeping tha 
 
 go 
 
 • sto.ed. 
 
 liiitcs of storage may be fixed by agrcinient of the parties 
 to the contract, but are often regulated by Boards of Trade, 
 Cliambors of Commerce, or Warehouse Compauiea, and are 
 estimated at a certain price per barrel, bale, bag, bushel, 
 etc., per storage term. 
 
 401. A storage term is the number of days for which 
 the St »age is charged. The storage terra is usually one 
 woel:, 10 days, 20 days or 80 dajs. The rates of storage 
 often vary for grains, or goods of dill'erent grades or values, 
 and also on account of diiforent modes of shipment. 
 
 405. Cash storage is a term applied to cases in which 
 the i>«yment of charges is made on each withdrawal or 
 Bhif'iuent, at the time of such withdrawal or shipment, 
 notwithstanding the fact that the owner may still have 
 goods of the same kind in store at the warehouse. 
 
 4!J6. Credit storage is a term applied to cases in which 
 sundry deposits or consignments are received, from which 
 sundry withdrawals or shipments are made, and all 
 charges adjusted at the time of final withdrawal. 
 
 40T. A grain elevator is a building erected for the 
 convenience of storing and shipping grain. 
 
 40.**. Storage receipts, especially of grains, are fre- 
 quently bought and sold under the name of " warehouse 
 receipts " or " elevator receipts," aa representing so much 
 vahie by current market reports. 
 
 NoTB. -Whpn deposits or consignments, and withdrawals or shipments, 
 ftje made at differeat times, debit is to be given for the amount of each 
 
t r^ 
 
 STORAGE. 
 
 285 
 
 deposit or consipiment, from dato to its final wit'idrawal or sliipment, 
 and credit given to the owner or consignor for lacli witlidrawal or sliip- 
 ment, from date up to the time of siitlument. 
 
 40!>. To find the average storage when goods have 
 been received at different dates, but none delivered. 
 
 KxAMri.K.— Tliero was received at a storaj^o wnriliouso: Oct. loth, 
 500 bb!s. (lour ; Oct. 21th, 120 bbls. ajiplLri ; Nov. .Otli. l2o bbl.H. i.ot.vtoes; 
 Nov. 20tli, 200 bbls. .]iiince8 ; Nov. 2.»tii, 340 bbla. ai)i)le8 The merchan- 
 dise was all deUvircJ Deo 12th. If the afora^^o cliar.'e \vai Ic. por bbl. 
 for a p*?riod of 30 days average storai^c, what was the stoni-u bill ? 
 
 ROLCMON. 
 
 The stuwvge of 500 bbls. for ,"8 Jays = 20,000 l)bk. stcrtd for 1 day 
 
 '• 120 " 49 •' = .-).ss:) ' 
 
 125 " 37 " = \r.i; " " " •• 
 
 200 •« 22 " = -l.lOO " " " •• 
 
 340 " 18 " = (;,)20 " 
 
 M 
 N 
 M 
 
 .00.02.) bbls. Bt.)P-d for 1 day. 
 60,025 bbls. for 1 day = li^Ifa = l.t'.Hii bbl=>. fur 30 bys 
 1,GC7J bbls. @ 4c. a bbl. = SCO, 70, stora;^e bill. 
 
 BULE. 
 
 Multiply the nvmher of articles of each receipt Iry the 
 numbrr of days hetwi'.m the time of its dcjiosit and withdrawal 
 and divide the sum of these products hy the. Nnmlier of d^iys 
 in the storage term. TJie quotient will be the average storage 
 for that term. 
 
 EXERCISE 94. 
 
 1. There was received at a warohonse : May 15th, 2,500 
 bush, wheat ; June 8th, '2,500 bush, oats ; July 21th, 3,500 
 bush, barley; July SOtli, 5,000 bush. corn, if nil of this 
 was shipped August 20th, what was the btornge hill, the 
 charge beiug l^c. per bushel per term of 30 days average 
 storage ? 
 
 2. A farmer received for pasture: April 30th, 12 head 
 of cattle; May 15th, 14 head of cattle; ^^:^y 23r:l, 27 head 
 of cattle ; June 9th, 5 head of cattle ; Juik- 80th, 8 Load of 
 cattle ; July 16th, 40 head of cattle. All were delivered 
 
.I> 
 
 >2;)0 STORAQK. 
 
 July 25th, and the charnoa wero 75o. per head for each 
 weok of 7 diiya' avera;^o piiBtura^jo. How much was his 
 hill ? 
 
 3. The follnwiri}^ produce was rccoivod at a warfliouBo : 
 Oct. IDtli, 'JM) l.l)ln. Hour; Oct. 27tli, IGO hhla. potatoes; 
 Nov. 'ind. tiK) 1»1)1h. np[il.s ; Nov. 21lh, CO i>l)lH. onions; 
 Dec. (')lli. IHO bl)lH. llour. Tlie merchandise was all 
 delivered Dec. 8th. Wliat was tlit; storn^^e hill, the cliarf^o 
 beiii^ 'l\ii. per hbl. per term of !30 days '} 
 
 no. To find the average storage when goods have 
 been received and delivered at different times. 
 
 ExAUiLK.— A wiiri'lumsi'inini roooivud ami ilelivorod tlio following: 
 
 UKCKIVCI). OBLIVEUKn. 
 
 Jan. lit, aOO bbla. Fob. 9, 1">0 bbla. 
 
 Feb. 21, 200 " Mar. 18, 200 " 
 
 Miir 8, 150 '• Apr. 4, 150 " 
 
 Apr. 21, 400 " May 7, 5.00 " 
 
 Whnt wiHt \y.M for stora<;e at 2o. a bbl., for a porioil of 30 days average 
 Btorago, a sottloim'ut liaviii>; beon mado May 7th? 
 
 First Method. 
 
 Solution. 
 
 From Jan. 19 to Fob 9=21 <la.; ;i0() bl)l. stored for 21 da. = 6,300 for 1 da. 
 
 Fob. 9 l.'iO bbl. delivered. 
 
 From Feb. 9 to I"( b. 24 = 15 du.; l.'.O bbl. reni'g for 15 da. = 2,250 •• 
 
 l'\b. 21 .. 200 received. 
 
 From Feb. 24 t > Mar. 8 = 12da.; :!:iO bbl. stored for 12 da. = 4,200 " 
 
 Jlar. 8 l.">0 bbl. received. 
 
 From Mar. 8 to :\Iar. 18 s 10 da. ; 500 bbl stored for lOda. = 5,000 " 
 
 Mar. IS 200 bbl. delivered. 
 
 From 'S\\r. 13 to Apr. 4 = 17 da ; 300 bbl. stored for 17 da a 5,100 •• 
 
 .\pr. 4 150 bbl. delivered. 
 
 From Apr. 4 to Apr. 21 = 17 da. ; \hO bbl. rem'f^ for 17 da a 2,650 •• 
 
 Apr. 21 401) bbl. received. 
 
 From Apr. 21 to May 7 - 16 da ; 5,j0 bbl. sttyred for 16da a 8,800 •• 
 
 May 7 650 bbl delivered. 
 
 Total 34,200 •♦ 
 
 8,4200 bbl. for 1 day a u^ „ 1,140 bbl. for 80 da. 
 1,140 bbl. @ 2o. a bbl. = S22.80 Cost of storage. 
 
aiOUAUK. 
 
 2i}7 
 
 hdi.r. 
 
 1. Multiply the number of bnrrrh, hairs, etc., ly the num- 
 ber of diii/» between the date of thiir receipt and the date of 
 the next receipt or del iter;/ ; add the number ofarlirlnt of nurh 
 next receipt, or subtract the number of such dcHrcri/, <ih the 
 case may be, and so proceed to the time of the final dclinry. 
 
 2. Divide the sum of the products thus found by the number 
 of days in the storage term, and the quulient will be the A rerage 
 Storage for that term. 
 
 Second method. 
 
 HOLUTION. 
 
 DELIVKRF.D. 
 Fob. 9, l.Wbbl. X H7 
 
 KEOBITED. 
 
 J»n. 19, 800 bbl. x I OS 
 
 Fob. 24, 200 hbl. X 72 
 
 Mar. 8, 150 bbl. x CO 
 
 Apl. 21, 400 bbl. X 10 
 
 .32,400 
 It.lOO 
 
 9,000 
 
 O.IOO 
 C2,200 
 2M,000 
 81,200 
 
 :to = 1,140 
 
 1.3,0ri0 
 Mar. 18, 200 bbl. x r,0 = 10,00:j 
 Apl. 4, 150 bbl. X 3;» = 4,!).'iO 
 May 7, 650 bbl. x a 0,000 
 
 28,000 
 
 84,200 
 1,140 bbl. i<^ 2c. per bbl. as 822.80. Coat of Btoraxo. 
 
 EXERCISE 95. 
 
 1. Wliat will be the storage charge, at 4c. per hbl., for a 
 term of thirty days averago, on the following; transaction '? 
 
 IIK(JKIVKI). DKMV.'.IiM). 
 
 18H9.— Juno 12, 200 bbla., pot.itooH. 1989.— ,Jiiin' 17, 7.0 bbU. potitor-s. 
 
 " " 20, 150 " apples. " " 25, 125 " 
 
 " July 18, CO •' turnipB. " " .SO, 90 " Rpj;l( a. 
 
 '• Aug. 2, 90 " onions. " July 5, OO " 
 
 " " 25, 40 " turnips. 
 
 " Aug. 9, 20 " 
 
 •• " 15, 90 " onioua. 
 
 2. What will be the storage charge, at 4Jc. per bill., for 
 a term of thirty days average, in the followin;^' transaction ? 
 
 BECEIVED. DELIVEUKD. 
 
 1889 — Feb. 8, 180 bbl8. flour. 1889. -Mar. 1, 100 bbls. apples. 
 
 " 27, 100 " apples. " " 28, 190 " flour. 
 
 '• Mar. 8, fiO " potatoes. " Apr. 15, CO '• potatoe* 
 
 " " 13, 300 " flour. " " " GO " flour. 
 
 •' 29, 2:',0 " 
 
 fff 
 
288 
 
 STURAQE. 
 
 8. What is the storage on the following accouut to Deo. 
 SlBt, 1889, at 2ic. per bbl., for 30 days ? 
 
 BECKIVKO. 
 
 1889.— Aug. 17, 2rj0 bblg. rndse. 
 •* " 26, 00 •• " 
 
 " Bciit 19, iiOO •• 
 " Oct. 12, 300 " " 
 
 •' Nov, 18, 200 " 
 " Doc. 17, 400 " " 
 
 OSLIVRRED. 
 
 1889 —Aut;. 23, 200 bbli. mdse. 
 
 Sipt.25. 210 " •' 
 
 Oct. 13. 300 " •* 
 
 " Nov. 20. l.'.O •• •• 
 
 " I'eo. 26, C60 " •« 
 
 411. To find the Cash Storage on goods received 
 and delivered at different dates, when charges vary. 
 
 i:xAMrLK.~At a warehouise there was received aud delivered 
 merobaudise as follows : 
 
 RECKITEO. 
 
 Jan. 3, 150 bbl. 
 Jan. 20, 200 bbl. 
 Feb. 1, 300 bbl. 
 
 OBUTEREO. 
 
 Jan. 23, 250 bbl. 
 Mar. 1, 400 bbl. 
 
 How much muf-t be paid for storage ou the above, at 
 the rate of 5c. per bbl. for the fivfit 10 davs, or part thereof, 
 and 8c. per bbl, for each subsoqueut 10 days, or part 
 thereof ? 
 
 SOLHTIOS. 
 
 Dat*. Receipt* and Delheritt, 
 Jan 8, rcc<.'ived 150 bbl. 
 " 20, " 200 '• 
 
 330 bbl. in store. 
 
 Jan. 23, delivered 250 bbl. I }^ ^^}- ^^f,^ ^0 da. or 2 terms, 8c. = «12, 
 1 100 " " 8 da. or 1 term, 6c. =s 6, 
 
 100 bbl remaining. 
 Feb. 1, received ;!00 bbl. 
 
 00 
 00 
 
 400 bbl. in storp. 
 (1001 
 1300 
 
 Mai. 1. deUvered 400 bbl. | ,J°^^^.'- ^^!^.^ ^ ^••. °' * ^^'' J4°- « »1J-JJ 
 
 28 " 3 •■ lie. 
 Total cost of storage. 
 
 164.00 
 
 ZV'.M 
 
 ■ M^ -.M 
 
STORAOJs. 
 
 2dk 
 
 W^ 
 
 ErERCiSE 96. 
 
 account nt tLo rate of 5 centn per l.bl. for the first lOda s' 
 or part thereof, un.l Scouts per hbl. for each Hub=e, '' u 
 10 days, or part thereof? -^ ,u. .u 
 
 BECEIVKIJ. 
 
 Ib89.— May 7, 35u bbl. dour. 18S'J 
 
 " 26. 160 '• " 
 '* Juno 16, 200 " •• •• 
 
 I'l'MVlltPD. 
 
 - Mav 2i;, '.',-0 bbl. tlour. 
 June 1, 100 " '« 
 
 " y, 100 " 
 
 " 3o, ■.',",:( " .. 
 
 1889. 
 •• 
 
 II 
 
 II 
 
 th« 'J^ '''''^*' ^""^ '^'^''''''' ""' ^ '^^''^^"^ warehouse on 
 the following account were as follows : 
 
 BECEIVRD. 
 
 DEMVKIIEU. 
 
 " 25, ino *• '• •• ., ... ,.„ 
 
 8ept. 12, aO « " 11 « » , "!• " " 
 
 ' ' bept. 10, .">0 " <« 
 
 •* 20, dL 
 
 What was the total storage paid, the rate b.i.K. 5 cer.ts 
 quent 10 days, or part thereof ? 
 8. Find the cash storage on the following st.-rage .account .• 
 
 RECErVEC, 
 
 1889.-8ept. 2, 100 bbl. 
 
 " " 25, 200 " 
 
 Oct. 19, 350 " 
 
 " •' 31, InO .1 
 
 " Not. 7. 200 >* 
 
 t>r.!.i\EV.ED. 
 
 188'J.— St'i^t, 20, 100 bbl. 
 
 •' 30, 100 " 
 
 " Oct. 10, 100 •• 
 
 " 20, 100 " 
 
 " " 30, 100 " 
 
 Nov. 20, the n-mainder. 
 
 The contract required the payment of 6c. ner bbl for th. 
 present term of 80 days or fraction thereof a^:d3::pe 
 
 theteor ' '^"''' *''" °^ '^ ^*^y^ °' f^^°*^«" 
 
 i 
 
 ii 
 
 i 
 
240 
 
 UlSCELLASLUUS. 
 
 MISCELLANEOUS. 
 
 EXERCISE 97. 
 
 1. The interest on 81,805, loaned on May 13th, at 6\% 
 per annum ia $37.905 ; on what day was the money 
 returned ? 
 
 2. A Bum of monej* at simple interest has in four and 
 one-half years amounted to §735, the rate of interest 
 being 5 per cunt, per annum ; what was the sura at first, 
 and in how many years more will it amount to $1,140 ? 
 
 8. I am offered a house that rents for §27 per month, at 
 such a price that, after paying $67.20 taxes, and other 
 yearly expenses amounting to $24.85, my net income will 
 be 8 J % on my investment. What is the price asked for 
 the house ? 
 
 4. In order to engage in business, I borrowed $3,750 at 
 6 %, and kept it until it amounted to $4,571.25. How long 
 did I keep the money ? 
 
 5. October 12th, 1889, I purchased 2,700 bushels of 
 wheat, at $1.05 per bushel, and afterwards sold it at f 
 profit of 6 %. On what date was tl j wheat sold, if my gain 
 was equivalent to 10 % iutercr^t on my investment ? 
 
 6. December 11th, 1888, a lumlxr dealer borrowea 
 money and bought shingles at $4.50 per M. ; September 
 17th, IKBO, he sold the sliingles a-Ml paid his dibt, and 8 % 
 interest, amounting to §3,162 GO. How many thousand 
 shingles did ho buy ? 
 
 7. I loaned a bridge builder $17,500 for seven years, at 
 10% per annum, compound interest payable quarterly, and 
 took a bond and mortgage to secure the debt and its interest. 
 Nothing having been paid until the end of the seven years, 
 how much was required in full settlement? 
 
MISCELLANEOUS. 
 
 24] 
 
 8. Harry is ten, and Fred seven yo;u3 old. If 7 % com- 
 pound iiitorcist invo.sttii'MitH can bo sOiUirod by their father, 
 for what anaounts must niich iiivc.stiufuta be inado in order 
 that at tho ago of twenty-one the boya may o icb have 
 !jil2,500? 
 
 9. The day Ghari'.'S was six years old, his father deiiosited 
 for him fn a n-iviii^a hank such a sum of lumify that, at 
 4% interest, coinpoundfl ijuarterly, theio will be $7,500 tc 
 his credit on tho day he atlaiud liis n. ijirity. What flum 
 was deposited '? 
 
 10. Having purchased July l.'jth 1,150 barrels of pork, 
 at $1(5 per barrel, on four mouths' credit, the dealer, thirty 
 days later, sold it at !?l7.r)0 per barrel, receiving; therefor i 
 six months' note without inti rrst. When the purchase 
 money became due, he diseountid the note on a lasis of 7 %, 
 and paid his debt. How much was |.;aiued '? 
 
 11. I loaned a friend a sura of money for uino months, 
 atG%per annum, and w the loan was due ho paid 
 $851.50 in cash, which was 75 ',o of tlio amouut duo me ; 
 the remainder was paid sit months, tifteon days later, with 
 interest at the rate of 10%. Find tlie amount paid at tinal 
 Btttlement. 
 
 12. Having bought a mill for $12,000, I paid cash 
 $4,000 on delivery, and gave a bond and mortgage fur 
 eight years without interest to secure the balance ; to 
 secure the interest, which was to be paid semi-annually, at 
 the rate of 7% per annum, I gave sixteen non-interest 
 bearing notes, without grace, for $"280 each, one maturing 
 at the end of each six months for the eight years. If the 
 four of the notes first maturing were paid when due, and 
 no other payment was made until the mortgage bccaiat 
 due, how much was required for full settlement ? 
 
 3 ! 
 
 If 
 
 si 
 
24i 
 
 UlSCELLANKOUa, 
 
 18. The discount on S/JG'- 50 
 fijid the rate of inttrest. 
 
 )r nine months is $16.50 : 
 
 14. Bought 5,000 l.nshel' l* ,v at at $1.25 a hushol.pay. 
 ■hie in six months ; 1 i ,ir -dii f^ i realized for it at $1.20 
 cash, and put the inont. .t u* u terost at 10%. At the 
 api-ointed time I pni.l f,y the vi ofit; did I gain or lose 
 by the trnnsactii^n, and u( ,' !, n ;, ? 
 
 lo. Jones loaned ?2,-i;.»0 
 amounted to $J,UOO. F> .^U.d li 
 
 ii% S'un! 
 
 ,r< \K: 
 
 n. crest, until it 
 the loan made ? 
 
 16. A man inv' sted $16,<\.">0 -'n Im- 
 
 iind at the end 
 of three ytara. three moi is. ^- ,'i.]^, - <;22,8,S0, which 
 sum included investment and gains. What yearly per 
 cent, of inNjrest did his invealnient pay ? 
 
 17. Sold pn invoice of crockery on two months' credit; 
 the hii! \>a paid three month:., eighteen days, after the date 
 of pur. ,,<.^e, with interest at 8 %, by a check for |1,0G3.45. 
 How much was tlje interest ? 
 
 18. A bond, bearin- interest at 8 %, and dated H^., lat, 
 1881, was settled in full November KUh, 1889, by the pay 
 ment of $17,685. For what face amount was the bond 
 given ? 
 
 IP. What sum will be due January 18th, 1892, on a debt 
 of $5,100, dated March 17th, 1885. bearing interest at 7 % 
 per annum, payable semi-annually, if the first five pay- 
 ments were made when due and no eubsequent payments 
 Wore made ? 
 
 20. A merchant sold a stock of glassware on one month's 
 credit; the bill was not paid until three months, twenty- 
 one days after it became due, at which time the seller 
 received a draft for $J.716.21 for the bill, and interest 
 thereon at the rate of &%. Find the selling price of the 
 goods. 
 
 .wm- 'wwmm^m^mm: 
 
"T^ -'^^^ 
 
 MlSCKLLAShOUS, 
 
 2-19 
 
 21. A tradesman who is m,,ly to allow 5% per auu.m 
 npou„d .nterent for ready n.oney. is .nkod oj. Ht' 
 for two years. If ho ch,ir,..d $110.25 in his bMI wl.l 
 ought tho readv money price to have boon? ' 
 
 witf tltoT"''''L^''''' ''''^ ^''-'^^ •'* 7i - i°'"^«t. aoJ 
 ?7 500, maturing m t.h,o months wit'uut interest l.i 
 
 purcnase. if the n.>:y < r-'v (5 <v j,,*,;^ ,, ,,f. 
 
 (l-iJ Ita nMr«i,»» *^ " ^ >» /o inr,.-r. :u after m.ituritv. 
 
 <i.-i lU purchaser gam or lus«. and how much ? 
 
 at?o«,f ^*°''^"',*"'"^''' 6.000 .vardB of Ax- inster carpet 
 
 flol It nt $ ,.15 per yard, g.vi„. a credit of two mon'hs- 
 at tl e e,p.rat.on of the two months he a.ticin.t. i the pav- 
 ment of h.B own paper. geUin, a di.seount .^J of 10 "^ per 
 annum. How much did he gain by the transaction ? 
 
 24. On the 20th of March. 1889. I borrowed $in .'00 at 
 6%mterosf on April 5tb. I loune.i ^o.OOO of the' mo^ey 
 nnUl December 20th, 1889. at 8- April 15th. I „archn 
 w h he rema ,or a claim for §J0.000, dn. Ai.n.st l.t 
 
 M .h^ .,ot bcn,g paid at maturUy. was e.^.nded uutd 
 the ?.,.000 became due. at the rate of fl -. How inu^h 
 
 20. If po be allowed off a bill of $ 120 dno in six months 
 bow much .hou d be allowed off the same bill due in tw Iv^ 
 months, reckonmg true discount ? 
 
 ihouldl^/ll? '^T^''''' °" ^115 for a ^iven time, what 
 ihould be the true discount off $115 for the same time ? 
 
 
244 
 
 MISCELLANEOUS. 
 
 J ! 
 
 f •. 
 
 Kk 
 
 28. If $10 be allowed off a bill of $110 due eight montha 
 hence, what should be the hill from which the same sum is 
 allowed as four months' discount ? 
 
 29. How much may bo gained by hiring money at 5 % to 
 pay a debt of $6,400, due in eight months, allowing the 
 present worth of this debt to bo reckoned by deducting 5% 
 per annum discount ? 
 
 80. The discount on a certain sum due nine months hence 
 is $20, aud the interest on the same sum for the same time 
 is $20.75. Find the sum and the rate of interest. 
 
 81. Having bought goods to the amountof $2,431.80 cash, 
 I gave my 60-day note in settlement. If discount be at 
 7 %, what should have been the face of the note ? 
 
 82. A note dated September Ist, 1889, payable in 90 days, 
 with interest at 7^%, was discounted twenty-one days after 
 date, at 10 %. If the proceeds were $6'J0.52, what must 
 have been the face? 
 
 83. If, on a note made for $700, bearing interest at 6 %, 
 and dated January 1st, 1889, $50 is paid on the first of 
 every month, commencing February Ist, following the date, 
 what is due January 1st, 1890 ? 
 
 34. F. J. Eamsay & Co. bought goods of John Hope & Co. 
 as follows : July Ist, $150, at three montha ; July 20th, 
 $200, at four months ; August Idth, $300, at two months ; 
 and October 4th, $250 at four mouths. Find the equated 
 time of payment, and what would be due on the account 
 March 15th following, at 6% interest. 
 
 86. I owe $480 payable in ninety days, and $320 pay- 
 able in sixty days. Mj creditor consents to an extension 
 of time to one year, and offers to take my note for the 
 
MISCELLANEOUS. 
 
 245 
 
 whole amount on interest at 6 % from the equated time or 
 a note for the true present worth of both debts, on interest 
 from date. How much will I gain if I choose the latter 
 condition ? 
 
 36. I sell goods to A. at different times, and for different 
 lerma of crodit, us follows : 
 
 Sept. 12, 1859, a bill on thirty duys' 
 
 Oct. 7, 
 Nov. 16, " 
 Dec. 20, " 
 Jan. 25, 1860, 
 Feb. 21, " 
 
 « 
 
 crodit, for $180 
 300 
 150 
 
 " 350 
 
 130 
 llf) 
 
 thirty 
 
 sixty 
 
 ninety 
 
 thirty 
 
 thirty 
 
 ^ If I take his note in settlement; at what time should 
 interest commeMoe ? 
 
 37. A person owes $350. ,iue in three months, and $750 
 due in SIX months ; but at the end of two - months he pavs' 
 *200. and three months afterwards, $500. When is the 
 remainder due ? 
 
 38 A note for $1,000. dated April 1st, 1889, payable 
 on demand, with interest at 7%, bears the following 
 endorsements : May 6th, $200 ; July 5th, $225.37 ; Octo- 
 ber 18th, $322. What is due Jiuuiary 1st, 1880 ? 
 
 39. Bought goods to the amount of $10,000, of which 
 $2,C00 was to be paid in one month ; $2,000 in two 
 months; $-1,000 in three moitlis, and the balance in six 
 months. If a note is given for the whole amount, how 
 long should it run ? 
 
 40. Four notes, made by J. Simpson, and parable as 
 follows: $o60, duo September 10th, 1883; $800 due 
 October 15th, 1888; $1,100, due December 1st, 1888- 
 $900, due February 1st. 1889, were exchanged for a sin^^le 
 note. W^hen will it fall due ? ** 
 
 fig 
 
246 
 
 msCELLANEO VS. 
 
 41. Asa May has given three notes ; one for $300. due 
 May 1st ; one for $350, due June 15th ; and one for $550, 
 due August Ist. Desiring to exchange them for two notes 
 of $600 each, he makes one payable June 15th ; when 
 should the other fall due ? 
 
 42. Bought a bill of goods amounting to $1,200, on six 
 months' credit. Paid cash on account $100; at the end 
 of three months paid $300 more; and two months after- 
 wards paid $400, giving a note for the balance. For what 
 time was the note drawn ? 
 
 43. A note for $885.25, dated July 1st, 1888. payable on 
 demand, with interest at 6^%, bears the following endorse- 
 ments : August 20th, $157.50 ; September 2l8t, $180 25 • 
 October 6th, $200; December 1st, $80. What is due 
 January 1st, 1889 ? 
 
 44. On a bill of goods bought March Ist, amounting to 
 $1,500, on eight months' credit, the following payments 
 were made: May 1st, $350; August 1st, $500 ; September 
 1st, $150. What is the equated time for the payment of 
 the balance ? 
 
 I 
 
 46. A note for $618.75, dated April 17th, 1888, payable 
 on demand, bears the following ei -^orsements : June 5th 
 $126.50 ; August 20th, $127.25 ; November 17th, $210.' 
 What is due January 1st, 1889, reckoning interest at 6 %? 
 
 46. Bought of A. T. Stewart & Co., the following bills 
 of goods on five months' credit: February 10th, 1888 
 $900 ; March 15th, 1888, $2,000 ; May 10th, 1888, $750 • 
 June 12th, 1888, §2,000. Find the present worth of a 
 note drawn July 1st, in payment of the whole, discounted 
 at 6%. 
 
MISCELLANEO VS. 
 
 247 
 
 
 47. Bought goods at different dates, as follows : 
 
 Aug. 16, amounting to $475, on 6 months' credit. 
 Sept. 10, " 600, " 6 
 
 Oct. 5, « 750, .. 4 
 
 Nov. 1, « 450, '. 3 
 
 What sum will equitably discharge the whole debt 
 ^ovemb(.r 10th, allowing true discount at 7% ? 
 
 48. Purchased merchandise of W. Duncan & Co.. as 
 follows : 
 
 Jan, 1, a bill amounting to $375.50, on i months' credit 
 
 Jan- 20. " 168.75, 5 
 
 ^^^•4. « 386.25, 4 
 
 ^^^-n, " 144.60, 5 
 
 ^P>^- 7- ** 386.90, 3 « 
 
 What is the present worth of a note made May Ist, ir 
 payment of the whole, discounted at 6%? 
 
 M 
 

 248 
 
 PEiiCEaiAGE. 
 
 1% 
 
 \i 
 
 
 I 
 
 u 
 
 \ 
 
 ■h 
 
 PERCENTAGE. 
 
 STOCKS. 
 
 413* Stocks represent tlie cuiiital or property of incor- 
 porated companies. 
 
 413. An Incorporated Company is a^^ association 
 autliorized by law to transact business, i nd having the 
 Bame rights and obligations as ;. single individual. 
 
 414* A Share is one of the equal parts into which the 
 
 capital stock of a corporation is divided. 
 
 Note. — Tlie par value of ft share varies in different companies. It is 
 asually JilOO. anil will be ao ret^arded in this work unless othorwi.se stated. 
 BharoB of 650 and §25 are called half sto;;k and quarter-stock respectively. 
 
 4 IS* A Certificate of Stock is a paper issued by a cor- 
 poration specifying the numher of shares to which the 
 holder is entitled, and the par value of each share. 
 
 416. The par value of a stock is the sum named in the 
 certificate. 
 
 417. The Market Value of stock is the sum for which 
 it can bo sold. 
 
 Note. — When shares sell tor tnoir nomutdl valne, they are at pur; 
 wl"3n they sell for more, th .-y are above pir. at a premium, or rtt an 
 adrniire ; when they sell for loss, they are iloic par, or at a discoimt. 
 
 When stocks sell at par they are quoted at IQO ; when at 6% above par 
 tlicy are quoted at 10-5 ; when at 10% discount they are quocod at 90. 
 
 4IJS. A Dividend is a sum divided among the stock- 
 holders from the net profits of the company, and is a 
 certain percentage computed on the par value of the stock. 
 
 Note. — Companies sometimes declare a Scrip Dividend, entitling th» 
 holder to the sum named payable .'a stock at par value. 
 
STOCKS. 
 
 249 
 
 419. A Preferred Stock is one which is entitled 
 annually to a state! per cent, dividend out of the net 
 profits before the common stock dividend id declared. 
 
 4 20. A Stock Broker is one who buys and sells stocks 
 for others, on a commission called brokerage which is 
 always a certain percentage computed on the par value of 
 the stock purchased or sold. 
 
 '121. A Stock Jobber is one who buys and sells stocks 
 on his own account. 
 
 422. An Instalment is a payment of part of the capital. 
 
 423. An Assessment is a sum required of stnokholdera 
 to meet the losses or the business expenses of the company. 
 
 424. The Gross Earnings of a company are its entire 
 receipts from its ordinary Imsiness. 
 
 42.1. The Net Earnings is the remainder after all 
 expenses are deducted. 
 
 42«. A Bond or Debenture is a written agreement to 
 pay a sum of money, with a fixed rate of interest, at or 
 before a specified time. The term is applied to tlie Dominion, 
 Provincial, County, Township, City, Town, Village, Railroad 
 Bonds, etc. 
 
 Note. — BovAa or Debentnroa are mrned fro'.i the cori<orationg who 
 ibsuo tlicrn, the rate of interest tliey bear, the date at which tlicy are 
 payable or from a combi ..tiou of any of these. 
 
 ]5onds are also known, First Mortga-o, Secoud JIortga;;o, etc.. Income 
 Bonds, Consols, Sinking Fund, etc. 
 
 427. Coupon Bonds are those having sniali certificates 
 attached representinL; the different inshihaeuta of inten st 
 payable tit the times specified, and which are to be cut off 
 when paid, as a receipt. 
 
 Note. — 1. Bonds are also iesned without coupons, in what is known aa 
 the registered form. In t...s case the bond ia only payable to the regis- 
 tered owner, or bis assif,'nee, and the interest is paid by cheque or in cash 
 to the owner or to his attorney. 
 
 ii 
 
-r- 
 
 it 
 it 
 
 If 
 II ^ 
 
 250 
 
 STOCKS. 
 
 2. Bonds are somatimes issued with oonpona attached payable to 
 bearur. but the principal of which may or may not be registered at tht 
 choice of the owner. 
 
 428. The principal United States government bonds 
 are tbe 4J's of 91, redeemable at the option of the govern- 
 ment after Sept. 1st, 1891 ; 4's of 1907, redeemable at the 
 option of the Government after July Ist, 1907 ; Refunding 
 Certiiicates of the denomination of $10, bearing interest 
 at 4 %, and convertible at any time with accrued interest, 
 into 4% bonds; Currency B's, issued to aid in the 
 construction of Pacific railroads, payable in thirty years 
 after date, and maturing at different dates from 1895 to 
 1899. 
 
 Consols are the leading funded securities of the English 
 Government, bearing 3 % interest, payable half-yearly, and 
 redeemable only at the pleasure of the Government. 
 
 The funded debt of France bears the title of Rentes, 
 bearing usually, interest at the rate of 5 %. 
 
 The German Empire has a funded debt bearing 4% 
 interest, known as 4 %, Imperial bonds. 
 
 The funded debt of Austria is known as the Austrian 
 Consols, the largest part of which bears 5 % interest. 
 
 Russia has a debt which bears a nominal interest of 6 %, 
 or "5 J %. The bonds are known as Oriental Loans, and 
 are below par. 
 
 The bonds in Italy are called Rentes, and bear interest 
 of 8%, or S-J^ 
 
 ! 1 
 
 If i 
 
 I; 4 
 
 ui 
 
STOCK KXcaA^QE. 
 
 251 
 
 STOCK EXCHANGE. 
 
 429. Stock Exchanges are associations organized for 
 buying and selling stocks, bonds, and other similar securities. 
 
 430. Quotations are usually made at so much per cent. 
 on the basis of a par value of $100 per share. 
 
 431. Stocks are usually bought or sold either "cash " 
 " regular way," " seller three," " buyer three." 
 
 NoTK.-l. AatockBold "ea»h " is ddivorable the day sold, a stock sold 
 "regular way " is deliverable next day, or if bought " regular way" is to 
 be paid for the next day. " StUer three " meana deliverable on either 
 of three days at the option of the seller. " Iiu,jcr three" means the 
 buyer can demand delivery within three days, but must take and pay for 
 it the third day. 
 
 2. Quotations are termed "flat" when the aocru<?d interest is included 
 in the price named. 
 
 8. Transactions on any of the above terms carry no interest. 
 4. If the option is over three days, interest on the selling value of the 
 ■took is paid by the buyer to the seller. 
 
 6. One day's notice is required of intention to terminate an option of 
 ft longer period than three days. 
 
 6. Should the stock pay a dividend during the pendency of a contract 
 the dividend belongs to the purchaser of the stock, unless otherwise 
 previously agreed. 
 
 432. Margin is cash or other security deposited with 
 a broker on account of either the purchase or sale of 
 securities, and to protect the broker against loss, in case the 
 market price of the securities, bought or sold, varies so as 
 to be against the interests of the customer. It is usuiiUy 
 10% of the par value of the stock. 
 
 NoTK — 1. Brokers oha/ge interest on the amount furnished by them 
 for " carrying the stock." 
 
I 
 
 lA 
 
 
 >r 
 
 if 
 
 252 
 
 STOCK EXCHANOE. 
 
 2, The margin deposited with the broker ia simply to protect the 
 broker a^^ainst losinr; any money Eihiiulil the etock move in tho wrong 
 direction. In case of the stock so doin;;, tlio margin must be made good by 
 the deposit of an additional amount, otherwise the broker will sell the 
 Htock to protect himHolf from losing any of tho money be has advanced 
 It is nsually 10% of the par value of the stock. 
 
 4itii. 1. A Ee,ir 13 an operator who is "short" of stock. 
 He wislics to l>uy at a lower rate, and tries to depress the 
 price of the stock of which he is "short." 
 
 2. A Bull i8 an operator who is holding stock for an 
 advance. J Je is said to bo "long" of stock. Bulls try to 
 advance the price of tlie stock of which they are " long." 
 
 8. Collaterals. Stocks, bonds, notes, or other value 
 given in pledge as security, when money is borrowed. 
 
 4. Hyphothecating Stocks and bonds, is depositing 
 them as collaterals. 
 
 5. B. C " between calls." The sale not taking place on 
 the call of the 6t'.>ck but after the first call and before the 
 second call. 
 
 6. Short. When one has sold stock which he does not 
 own hophig to realize a profit by buying it at lower prices, 
 he is said to be ** short." 
 
 7. A "Put" is a contract which secures to the holder 
 the privilege of delivering to the person named therein a 
 numl)or of shares of stock at a Bpecified price per share, 
 within a limited time (usually thirty days), without the 
 obligation to deliver it. The holder of a "put" is not required 
 to pay interest. 
 
 8. A "Call" is a contract which secures to the holder 
 the privilege of buying a jiumber of shares of stock at a 
 specified price, within a limited time without the obligation 
 to purchase it. The holder of the "call " must pay inter- 
 est on the purchase price of the stocks to the day of 
 delivery. 
 
STOCK EXCUANQB. 
 
 253 
 
 9. A "Spread" is a contract which secures to the holder 
 he privilege of either buying or soHing within a lin.ited 
 
 w^ \ Z ^V- ' "''"'"'' °^ '^'''^'' ^^ " «P^<^'!fi«^J price, 
 without the ohl,gati.,u3 of takil.^r or delivering it. 
 
 10. A "Straddle " is a contract whi,.h secures to the holder 
 he privilege of either buying or Helling, within a liuiited 
 
 ^me a number of shares of stock, not only at the price 
 mentioned in the contract, but, also at tbe market price of 
 the stock, at the date the privilege wad purchased. 
 
 11. Puts. Calls. Spreads and Straddles, are privileges 
 not recognized by the Stock ExcLan-o. 
 
 12. Cover, to "cover one's shorts." Where stock has 
 been sold short and the seller buys it in to realize his profit 
 or to protect himself from loss, or to make his dehvery he 
 18 said to be " covering short sales." 
 
 13. Ex..Div. or Ex-Dividend. When the price of 
 stock does not include, and the stock does not carry to the 
 buyer a recently declared dividend. 
 
 14. Difference. When the price at which a stock is 
 bargained and the price of the stock on the day of del'verv 
 are not the same, the broker a.^ainst whom the variation 
 exists, frequently pays the " ditierence " in money, instead 
 Of furnisning or receiving the stock. 
 
 15. Watering: Stock is increasing the number of shares 
 of an incorporated company without a corresponding 
 increase of their value. This is usually done in the 
 re-organization of a railroad or in the consolidation of two 
 or more railroads. 
 
 16. A "Comer" is produced when one or more operators 
 <nvnmg or controlling all the stock of a company are able 
 to purchase still more for either immediate or future 
 delivery, from one who is " short." When they demand the 
 stock, the sellers are unable to find it in the market. 
 
 \% 
 
 i i 
 •I 
 
264 
 
 STOCK EXCHANOK. 
 
 17. Brokerage. The usual brokerage for buying and 
 selling; stocks iB J %, and is calculated on the par value of 
 the Rtock. 
 
 •!« I. Given number of shares, the par value of a 
 share. To find the stock, or vice versa. 
 
 KxAJiPi,B 1,— What utnount of stock is rcprosontod by 40 ahana of 
 Bank of Montroal stock, par vahio t'200 per share ? 
 
 Sdi.dtion. 
 40 sliaros at 5200 oaoh m 6200 x 40 ■ 8«,0(i() stock. 
 
 Example 2. — llow many shares, par value 8200 oach, are represented 
 by 18,000 Bank of Montroal stock 7 
 
 Snr.rTioN. 
 8200 x= value of 1 share. 
 .-. »8,U0O = " " »,%o^<t „ 40 shares. 
 
 ExAifi'i.E 8.— What is tlic par value of a share, when 40 sbarea of 
 Bank of Montreal stock reprcsont 88,000 stock? 
 
 SoLtmo.v. 
 40 sliares reproaeut 88,000 stock 
 .'. 1 s'lare represents >{^ ■ 9200 stock. 
 
 EXERCISE 9& 
 
 What amount of stock is reprepented hv — 
 
 1. 120 shares Western Asauranoa, par value 340 per sharat 
 
 2. C(i " I{..iik o£ Montreal, 
 
 ■'•■ 200 " " Toronto, 
 
 4. 150 " " Commerce, 
 
 6- 175 " " Hamilton, 
 
 G. 240 " Imperial Bank, 
 
 7. 98 " Dominion Bank, 
 
 . 75 " Standard Bank, 
 
 f200 
 
 8200 
 
 850 
 
 $100 
 
 8100 
 
 S50 
 
 850 
 
 Find the par value of a share when — 
 
 9. 40 shares Imperial Bank represent 84,000 stock f 
 
 10. 7u *■ Merchants' Bank " 87.500 " 
 
 11. 90 " Ontario Bank " 89,000 " 
 
 12. 120 " standard Bank " $6,000 " 
 
 13. 300 «• Westflm Assnranoe Oo. 812,000 *• 
 
 14. 70 " Imp. S. & Invest. " $7,000 " 
 
 15. 80 " B. & L. Association " 82,000 *• 
 
 16. 110 " Dominion Telecraph " 85,500 " 
 
STOCK EXCUANQE. 
 
 How 
 
 many sharea 
 
 Mo 
 
 ---- roprcsentod by— 
 
 18. fO.COO 
 
 19. 17,525 
 
 20. 82,CJ0 
 ai. 8.1,160 
 92, ?;j,i75 
 
 2."1. £.J75 
 24. 8(1,100 
 
 11 
 «< 
 
 Batik of .^[a^f,^e;ll, 
 Lon. .t Cui. L, ,v A., 
 W.stiTii Asiiir.uioo Co., 
 U ink of Toronto, 
 B. .t L .Vsaociation, 
 North. West Lm.iCo., 
 Inipuriiil JUnk, 
 
 «."0. 
 
 .*10. 
 
 8100. 
 
 given, and 4e vlirsa '""''"''^'"» "" '"= ^n^«. being' 
 
 SoLCTtOn. 
 
 Coit of 1 sliaro 
 CO shares 
 
 ;l -1 + ^ 
 
 8121) 
 
 87,275. 
 
 . •''■T.UTIO.V. 
 
 Be.Jjn-pnco 1 sharo =. S121 _ ^ ^ jj.,f,j 
 OOsharoJ = Sl20,> x 1 » .^7 215 
 
 Soi.rno.'i. 
 60 sbarcg cost $•7,273 
 
 .'. i BUaro costs Il''l£ « 51211 
 
 »12Ii - ^ brokc^rago = §121 . market vaiae 
 
 SOLCIIO.V. 
 
 60 Bhares sold for S7,245 
 :. 1 share sol-l for V.--^± = 512O} 
 
 •1201 + fi . rokera'.L SI21 = market value 
 - be l^^^ S^V;^^^ °' ^— B*-^ " 121 
 
 Soi/UTIO!f. 
 
 Cost of 1 ohare = |121 + 81^ $12U 
 «7.274^ $121) = GO shares Ana. 
 
•256 
 
 SIOCK EXCUASUIi. 
 
 ExA«ri,B8.-lIow many Hl.nr.M H u.k of Co.nmorce Btock ftt 131 
 muht 1 Hell to realizu »7,'.'1.'», Im.lu rim" i ..? 
 
 SoLDTlON. 
 
 J7,'-'1j t l-"i =» t;0 Hliarod. Ajw. 
 
 exe:«cise 99. 
 
 Find the amoutit of canh rniuircl to p irohnso— 
 
 BllUUH. 
 
 UAlt. VM.. 
 
 Ul'.OK. 
 
 
 tillMiK.S. 
 
 sun. Vlli. 
 
 nnoK 
 
 1. 70 
 
 IIU 
 
 i ".■,. 
 
 '.». 
 
 i:i5 
 
 11 i 
 
 i '%• 
 
 2. "'O 
 
 75 
 
 t "- 
 
 10. 
 
 16 
 
 B'i 
 
 i%- 
 
 3. liO 
 
 :!.•» 
 
 4 ■;.'- 
 
 11. 
 
 l:to 
 
 'j:!f 
 
 }%. 
 
 4. i'OO 
 
 110 
 
 i '.o- 
 
 11. 
 
 21)0 
 
 7--t 
 
 i '/o- 
 
 6. 45 
 
 220 
 
 4 %• 
 
 i:«. 
 
 75 
 
 si; J 
 
 4%- 
 
 C. 90 
 
 206 
 
 i%- 
 
 U. 
 
 170 
 
 l-.".'i 
 
 i% 
 
 7. 110 
 
 10'. 
 
 i'o- 
 
 15 
 
 800 
 
 26 li 
 
 4%. 
 
 8. 31) 
 
 80 
 
 i VG- 
 
 16. 
 
 ;ii'.f» 
 
 tin 
 
 !%• 
 
 Find the cash received fioia the sale of— 
 
 bum;, s 
 
 MAB. VAI- 
 
 ii:;iiK 
 
 SHVIU'.H, 
 
 MAK. VAL. 
 
 BnoK. 
 
 17. 
 
 I'.O ' 
 
 96 
 
 1 \',. 
 
 2'). 200 
 
 lioi 
 
 1 f>/ 
 
 18 
 
 70 
 
 47 
 
 !»., ' o. 
 
 2(i. H 
 
 'm\ 
 
 4%- 
 
 I'J. 
 
 200 
 
 i;;5 
 
 i Vc 
 
 27. IJO 
 
 2605 
 
 4%- 
 
 20. 
 
 U6 
 
 120 
 
 i%- 
 
 2-A. :i6 
 
 \rM\ 
 
 4%' 
 
 21. 
 
 US 
 
 110 
 
 1 o/ 
 
 29. 45 
 
 75i 
 
 }%• 
 
 2'2. 
 
 2."0 
 
 80 
 
 h-fo- 
 
 30. 160 
 
 378 
 
 i7o. 
 
 23. 
 
 36 
 
 84 
 
 i%- 
 
 31. 2i0 
 
 1454 
 
 i'-i- 
 
 24. 
 
 87 
 
 120 
 
 i%. 
 
 32. 60 
 
 75S 
 
 4%. 
 
 Fin 
 
 lI the 
 
 market valuo of the stock when— 
 
 
 
 BHABES 
 
 
 nnoK. 
 
 BHARBS. 
 
 
 BBOX. 
 
 83. 
 
 30 cost 83,615 
 
 *%• 
 
 41. 70 sold for «5,600 
 
 \%' 
 
 84 
 
 40 
 
 " 2,405 
 
 *%. 
 
 42. 84 
 
 " 6,720 
 
 !%• 
 
 85. 
 
 50 
 
 " 3,795 
 
 4%- 
 
 43. 100 
 
 •• 7,525 
 
 i%. 
 
 3C. 
 
 60 
 
 '• 7,215 
 
 i%- 
 
 44. 60 
 
 " 4,890 
 
 4%. 
 
 n^ 
 
 80 
 
 •• 6.410 
 
 *%■ 
 
 45. 48 
 
 «• 3,8.=J8 
 
 l%- 
 
 88. 
 
 120 
 
 " 14,520 
 
 J%- 
 
 46. 56 
 
 " 3,962 
 
 t%- 
 
 89. 
 
 360 
 
 " 2!-,245 
 
 1 n' 
 8 /O" 
 
 47. 75 
 
 •• 4,500 
 
 J%- 
 
 40. 
 
 90 
 
 " 6,750 
 
 i%- 
 
 48. 80 
 
 7,270 
 
 »%• 
 
STVCK MXCHJtfOa. 
 
 Ut 
 
 How many shares may be bought for — 
 
 COIIT. 
 
 4l». S 13. 155 
 
 60. »'J,760 
 
 SI. tSfilO 
 
 5'i. tlS.GUO 
 
 MS J%. 
 
 140 it 
 
 85 i%. 
 
 coHr. 
 
 .vi. »i,'j2;j 
 61. 9:i,h:,o 
 <»• 912.029 
 66. 94, IM 
 
 iu«. TAU Bnu«. 
 80 4%. 
 
 210 
 
 be 
 
 How many aharea mutt be sold to realiz 
 
 a. p. tun. TAL. BIIOK. 
 
 67. 18.605 121} jTi. 
 
 68. 110.245 85J Jivi. 
 6'j. 8I.:ju 90 j%. 
 60. 11.360 87i J%. 
 
 ■• P. lUa. TAL. 
 
 61. ?U,755 220 
 62 «'^\ 100 9t>t 
 
 63. 'ii.i.iC 130 J 
 
 64 iiOMH no 
 
 4'^ 
 
 nBOB. 
 iff. 
 
 <iafl. Given the number of shares or amiunt of stock 
 held and xate per cent of dividend to ft-id income, oi 
 vice versa. 
 
 ExAMPLi 1.— What Income will bo ilcrivod from 60 iharea Ci. T. K 
 Stock paying 6 % dividends? 
 
 Solution. 
 
 Inoomo from 1 sbaro is 96 
 
 " 60 shares is 8i"> x (30 m J,360. 
 
 ExiMPu 2.— What would :v stocklioid. r, w',o owm «t.000 Bank oi 
 Comineroe Stock, receive from a 5 % dividend ? 
 
 Solution. 
 $4,000 stock = 40 shares 
 40 shares at 85 income per share = 8200. 
 
 ExAMPLB 3.— What number of shares does a i)er3oo hold who 
 f«';«iveH f 300 income, from a 6 % dividend ? 
 
 Ror.rTiDN. 
 16 income is derived from 1 share 
 •■• »300 '• •• 300 + 6 » 60 shares. 
 
 KxAMPLK 4,— Wlmt amount of stock must be held to obtain KOt 
 inccime frcm a 4 % dividend ? 
 
 SOLCTIOH. 
 
 •4 income is derived from 1 share 
 •'• '^'W " " 200 + 4 « 50 zh^T^ 
 
 50 shares = 50 X 100 = $6,000 stocl . 
 
 .% '^ 
 
268 
 
 STOCK EXCHANGE. 
 
 ExAimJi 6.— What is the rate per cent, dividend wUen 40 sharet 
 
 yitid an income of 9'J407 
 
 Solution. 
 
 40 Bhares yield an income of $240 
 1 share yields an income of 90 
 ,-. rate per cent, dividend is 6 %. 
 
 Example C— »300 income is derived from 83.750 stock; find the 
 
 nto por cent, of dividend. 
 
 Solution. 
 
 $3,750 stock = 37 J shares 
 
 87J Hliares yield an income of $300 
 
 ;, 1 share yields an income of , = »o 
 ,*. rate per cent, dividend « 8 %. 
 
 EXERCISE 100. 
 
 TNTiat income will be derived from — 
 
 8HABV.S. 
 
 DIV. 
 
 SB&BBS. 
 
 nrv. 
 
 
 ■HIRP.S. 
 
 Drv. 
 
 1. 70 
 
 6%. 
 
 5. 120 
 
 3%. 
 
 9. 
 
 131 
 
 5i%. 
 
 2. 120 
 
 6i%. 
 
 6. no 
 
 3J%. 
 
 10. 
 
 145 
 
 6%. 
 
 fi. 150 
 
 4J%. 
 
 7. 75 
 
 9%. 
 
 11. 
 
 C4 
 
 7%- 
 
 4. 05 
 
 8%. 
 
 8. 126 
 
 8J%. 
 
 12. 
 
 87 
 
 8i%. 
 
 What iucorac ^^ill be derived from— 
 
 
 
 
 STOCK. 
 
 DIV. 
 
 STOCK. 
 
 DIV. 
 
 
 STOCK. 
 
 err. 
 
 13. «5,000 
 
 7%. 
 
 17. SS.OOO 
 
 0%. 
 
 21. 
 
 $4,100 
 
 5h% 
 
 n. 88,750 
 
 3%. 
 
 18. 84,500 
 
 n%- 
 
 22. 
 
 82,225 
 
 e%. 
 
 15. 84,101 
 
 4%. 
 
 19. 89,160 
 
 6J%. 
 
 23. 
 
 Si,.:iO 
 
 8i% 
 
 J(i. S3,(520 
 
 6%. 
 
 20 84,375 
 
 8%. 
 
 24. 
 
 83,200 
 
 6%. 
 
 What number of shares and vrbat stock must be held to 
 •btain — 
 
 i.NTOiir. 
 25. 83L>'> 
 20. 84-20 
 
 27. 8600 
 
 28. S-"'0 
 
 or>. 
 
 6%. 
 5*- 
 
 4%. 
 
 INCOKB. 
 
 S9. ?04 
 
 80. $240 
 
 81. 8520 
 32. *3r.O 
 
 DIV. 
 
 8i%. 
 4i%. 
 
 8S. 
 
 B4. 
 
 85. 
 86. 
 
 8150 
 
 8i:.0 
 8160 
 83 to 
 
 
STOCK EXCHANQE. 
 
 What is the rate per cent, of dividend when- 
 
 259 
 
 EHAIUU. 
 
 87. 60 
 
 88. 
 89. 
 40. 
 41. 
 
 CO 
 90 
 75 
 84 
 
 tNCOMB. 
 
 yield »275. 
 •• 8300. 
 
 •' 8n0. 
 " 8170. 
 
 ■BAD I a. 
 
 42. 36 
 4.3. 42 
 
 44. 80 
 
 45. r,4 
 40. 120 
 
 What is the rate per cent, of dividend when— 
 
 iNcom. 
 
 yield $196. 
 " »189. 
 " ».500. 
 " f351. 
 " 8900. 
 
 47. 
 48. 
 19. 
 60. 
 61. 
 
 STOCK 
 
 #3,500 
 88,640 
 82,250 
 84,000 
 82,300 
 
 I.VCOMK. 
 
 yields $246. 
 " i-183. 
 " 8223. 
 " 8380. 
 " 1116. 
 
 02. 
 63. 
 64. 
 66. 
 56. 
 
 STOCK, 
 
 $4,500 
 
 88.G00 
 83,275 
 84,125 
 
 iNoom. 
 
 yields 8135. 
 
 " 8453. 
 
 " 8301. 
 
 " 8131. 
 
 $330. 
 
 437, Given cash invested, market value of stock and 
 rate per cent, dividend to find income, or vice versa 
 
 ExAMPLK 1.- What income will be derived from investing S6 315 in 
 the 6 pM cents at 106. brokerase i % ? mvestmg 86.316 in 
 
 6316 ^ ^^r™'" 
 
 j^ « Number of shares bongh*. Art. 485. 
 
 6315 
 105i 
 
 X 6 a 8360. Income. Art. 436. 
 
 DMA f,^"!^"^/''^^** '""" """'^ ^ '""^^^''^ *° «^°«" " income of 
 8880 from the f. per oents at 105, brokerage J % 1 
 
 ariO Solution. 
 
 -g = 60, Nnmber of shares held. Art. 4.36. 
 
 105J X 60 - 86,316, Cash invested. .'. m. 
 
 EXERCISE 101. 
 1. What income is derived from investing— 
 
 CASH. 
 
 84,210 
 
 85,716 
 ? 1,683 
 83,524 
 815,025 
 17,9.38 
 7. 324,050 
 
 ?• tio.isg 
 
 1. 
 
 s. 
 
 3. 
 4. 
 6. 
 6. 
 
 BATS. 
 
 6% 
 
 41% 
 
 3% 
 
 e% 
 
 7% 
 8% 
 9% 
 7*% 
 
 UAR.VAI.. BROK. 
 
 1(15 
 95 
 70 
 110 
 150 
 220 
 240 
 140 
 
 i%. 
 
 i%. 
 i%. 
 i%. 
 i%. 
 i% 
 
 CASH. 
 
 9. 88,510 
 10. 8.i,311 
 11- ?2.3,070 
 
 12. 1f27.:i20 
 
 13. S.J.OIO 
 M. ? 13.025 
 15. 815,785 
 
 If*' $n,ooo 
 
 BATE. MAB. VAT>. 
 
 4% 
 6i% 
 
 H% 
 
 H% 
 
 7% 
 
 10% 
 
 lOOJ 
 
 llOi 
 96 
 8,5 } 
 
 140 
 
 130 
 
 225 
 
 7n 
 
 . BROK 
 
 4 %• 
 
 8 A3- 
 k%- 
 i%- 
 
 i%- 
 i%- 
 i%. 
 
"rf! 
 
 260 
 
 STOCK EXCUANQE. 
 
 * J 
 
 2. What amount of cash must be invested in order to 
 
 derive an- 
 
 — 
 
 
 
 
 
 
 
 
 iNCosra. 
 
 RATI. 
 
 inM.ra,. 
 
 BROS. 
 
 
 nrooMK. 
 
 RATB. 
 
 UAR. VAIk 
 
 nROB. 
 
 1. 8200 
 
 6% 
 
 105 
 
 i'/o. 
 
 9 
 
 8:520 
 
 4% 
 
 lOi-.J 
 
 i%- 
 
 a. 9-270 
 
 44% 
 
 95 
 
 i%. 
 
 10. 
 
 82';4 
 
 6i% 
 
 llOi 
 
 \% 
 
 8. »72 
 
 3J% 
 
 70 
 
 k"^ 
 
 11. 
 
 81.500 
 
 f-i% 
 
 9ti 
 
 *%• 
 
 4. »192 
 
 6% 
 
 110 
 
 i%- 
 
 12. 
 
 8112 
 
 34% 
 
 8.H 
 
 i%. 
 
 5. $700 
 
 7% 
 
 150 
 
 i%- 
 
 13. 
 
 8288 
 
 8% 
 
 140 
 
 i% 
 
 8. 9288 
 
 8% 
 
 220 
 
 i%. 
 
 14. 
 
 8700 
 
 7% 
 
 i:!0 
 
 i%- 
 
 7. »900 
 
 9% 
 
 210 
 
 i%. 
 
 15. 
 
 8700 
 
 10% 
 
 225 
 
 4%- 
 
 8. «540 
 
 u% 
 
 140 
 
 J%- 
 
 16. 
 
 8360 
 
 44% 
 
 76 
 
 4%- 
 
 4:iH. To find the per cent, of income from a given 
 investment without regard to its maturity. 
 
 ExAMPia.— What per cent, of my investment shall I aeoara by 
 puroh»8ing Ontario Bank stocl; at 105, paying 7 % dividends 7 
 
 SOLUTIOH. 
 
 On 8105 inveatment, 87 income is derived. 
 
 '• 81 " lis " 
 
 » 8100 " 100 X rSs ■ 86§ iuoome is derived. 
 
 .-. rate per cent » 6i %• 
 
 48». To find how stock must be bought, which pays 
 a given per cent dividend, to realize a specified per 
 cent, on the investment. 
 
 EZA1IPI.K-— At what price must I bay stock which pays 6 % dividend 
 to realise 8 % on my investment? 
 
 Solution. 
 Since the income derived from 1 share is $6, 86 mast therefore be 8% 
 of my investment for 1 share. 
 
 8 % of purchase price of 1 share = 86 
 ■ 100 % " " " s 1^ X 6 =t 875. Ans. 
 
 EXERCISE 102. 
 
 What per cent, of my investment will be derived from 
 investing in the — 
 
 1. 4 per cents at 120. 5. 8 per cents at 125. 9 
 
 2^ 5 •• 80. 6. 9 " 175. 10. 
 
 s] 6 " 110- 7. 10 " 225. 11. 
 
 4' 3^ - 90. 8. 12 " 240. 12. 
 
 3J per cents at 70. 
 4J " 76. 
 
 54 " 110. 
 
 6 " 90. 
 
STOCK EXCHANQE. 
 
 At what price must I buy stock which pays — 
 
 13. 6 % dividends to realize 9 % on my investment? 
 
 361 
 
 14. 
 
 4% 
 
 
 6% 
 
 
 
 15. 
 
 5% 
 
 
 6% 
 
 
 
 16. 
 
 8% 
 
 
 4J% 
 
 
 
 17. 
 
 3i% 
 
 
 5% 
 
 
 
 18. 
 
 ^% 
 
 
 H% 
 
 
 
 19. 
 
 7% 
 
 
 4-0 
 
 
 
 20. 
 
 9% 
 
 
 10% 
 
 
 
 440. To find the per cent, income derived from 
 investing in bonds or debentures payable in a given 
 time. 
 
 Example. — What per cent, incomo will be received if 
 Dominion 6'b at 120, payable at par in 16 years ? 
 
 I buy 
 
 SoiiCTION 1. 
 
 Coat price of 8100 of bonds = 8120 
 Belling " " " = §100 
 
 par valae. 
 
 Loss in 16 years = ^'20 
 " 1 year = 81J 
 Income each year from ^i.OO of bonds « 86 
 .*. Gain each year on $100 of bonds = S6 - $1} s 94} 
 On 9120 invested, the income cleared = 94| 
 
 :. On 9100 •• " ■ 11 X 100 = 93j| 
 
 .*. 9dJ2 IB derived from the investment. 
 
 BOLCTION 2. 
 
 BeeeiptB of |100 of bonds s flOO par valne at end of 16 yean 
 Income " " = 96. f 6 per year for 16 years 
 
 Total receipts 
 Cost 
 
 = 9106 at end of 16 yean 
 s 120 
 
 .'. Gain on 9120 investment a 976 for IG yean 
 100 " = 93§J for 1 year 
 
 •'• ^31 % of interest is derived from the investment. 
 
 441. To find howbr>nds must be bought, which have 
 several years to run, and which pay a given per cent 
 dividend, to realize a specified per cent on the invest- 
 ment 
 
262 
 
 STOCK EXOHANOK. 
 
 I ; 
 
 i' 
 
 lliii 
 
 BzAKFU.— At what price must 6 % bonds, payable in 10 years, b« 
 bosglit BO U to realizo 5 % on the investment 7 
 
 Solution 1. 
 
 By simple interest. 
 
 Amount of $100 of bonds in 10 yrs. at 6 % ■! 8160. 
 In or-ler to realize 5 % on the investment we can afford to pay tba 
 fresent \vorth of |1'">0 due in 10 years, reckoning interest at 5 %. 
 Press nt worth of $160 for 10 yrs. at 5 % « ^g x 160 = 8106|. 
 We can thereforp afford to pay IJO63 for 8100 of bonds. 
 
 SOLDTION 2. 
 
 By compound interest. 
 
 If 86 inoomo be invested at compound interest as soon as received each 
 year at 6%, the incoTiie at the end of 10 years will amount to 875.467 
 (see Table of Annuities). 
 
 .-. Amount of 8100 of bonds at end of 10 years = 8175.467, and tb* 
 present worth of this amount for 10 years at 5 %, compound interest ■ 
 1176.467 ■^ I1.C289 -t- b |107.72 + Ans. 
 
 I 
 
 I' 
 
 
 EXERCISE 103. 
 
 1. What per cent, of the investment is received as 
 income by purchasing C P. R. 5'a at 105, payable at par 
 in twenty years? 
 
 2. What per cent, income will be received if I buy 
 Dominion 4'b at 112, payable at par in sixteen years ? 
 
 3. Bought Intercolonial Railway bonds at 90, bearing 
 4 % interest, having twenty-five years to run. Wiiat per 
 Cfut. will be realized if they are paid at par at maturity ? 
 
 4. What per cent, income will be gained from 8 % bonds, 
 bought at 80, and payable at par in twenty years ? 
 
 6. In 1882, intercolonial 6*8, due at par in 1930, were 
 bought for 108. What interest will this pay ? 
 
STOCK EXCHANQE. 
 
 MS 
 
 6. If I pay 108 for Dominion 4*3, having fifteen years to 
 run, what per cent, will I receiv- if I ke.^p them till they 
 mature, and they are paid at par ? 
 
 7. At what price must 6 % debeiittins, payable at par in 
 eight years, be brou.^ht to realize I f. ou the inveatment? 
 
 8. Bouj^ht railroad bonds payable in 'ive years, and 
 expect to realize 7 % on the investment. What did I pay ? 
 
 9. What must I pay for 5 % debentures, which mature in 
 fifteen years, that my investment may yield 4 % ? (Both 
 simple and compound interest). 
 
 10. What shall I pay for a bond of $500 having twelve 
 years to run, with interest at G %, in order to make it an 
 8% investment? (Both methods). 
 
 11. What must be paid for a $600 debenture, due in five 
 years, with interest annually at i %, so a3 to realize 6 % 
 on the investment ? 
 
 EXERCISE 104. 
 
 1. What income will $10,650 invested in Dominion 8}'b 
 at 97 1 yield, brokerage ^ % ? 
 
 2. If 1548,000 is invested, ^ in 5% stock, at 95|, and ^ 
 in 6% stock at 112, brokerage ^"^ in each case, what 
 annual income is secured ? 
 
 3. A farm which rents for $111.15 per aanam, is so!.] 
 for $8,229, and the proceeds invested in 5% bonds at 105, 
 brokerage | %. Is the yearly iucom-a increased or diiniu- 
 ishcd, and how much '? 
 
 4. How much must a gentleman invest for his dau^'ntcr 
 in 7% bonds, sellini^ at 95, to secure to her a semi-anniud 
 income of $315 ? 
 
264 
 
 STOCK EXCHANGE. 
 
 I 
 
 \i^m 
 
 6. Bought 800 shares of Michi^^an Central at 101 ; held 
 them twenty days, paying interest at 7 % on the purchase- 
 money, and sold them at 102|. Deducting interest, and 
 brokerage |%, for purchase and sale, what was the net 
 profit ? 
 
 6. A man bought 100 shares Canadian Pacific at 79|, 
 and sold the same at 82f . What was the gain, less I % 
 brokerage ? 
 
 7. Governments yielding $240 income a year at 4% 
 interest, were sold at 108, and the proceeds invested inland 
 at $76 an acre. How many acres were bought ? 
 
 8. Which is the r investment, R. R. stock at 25% 
 discount, and paj-ing a semi-annual dividend of 4%, or 
 money loaned at 10%, interest payable annually? What 
 per cent, better ? 
 
 9. What per cent, of his money will a man obtain by 
 investing in 6% stock at 108, at a discount of 16 %? 
 
 10. If stock paying 10% dividends is at a i)ro!uium of 
 12} %, what per cent, of income will be realized on an 
 investment in it '? 
 
 11. Which will yield the better income, 8% bonds at 
 110, or 5*8 at 75 ; 6*8 at 70, or G's at 80? 
 
 12. Which is the more profitable, and how much, to 
 buy B. «fe L H. 7'8 at 105, or 6% bonds, at 84? 
 
 13. If a man buys stock at 17% above par, what per 
 cent does he receive on his investment, if the stock pays a 
 dividend of 8^ % on its par value ($100) ? 
 
 14. A man bought 8 shares of stock at lOSj, and after 
 keeping it eleven months received a dividend of $7 a share, 
 and sold the stock then at 109J. What per cent, did he 
 receive on his investment ? 
 
 M' 
 
STOCK EXCUANOE. 
 
 265 
 
 16. How manj sharee of Dominion Telegraph stock at 
 84J, can bo bought for $12,000, brokerage i%? 
 
 16. Bought Oct. 12th, 400 G. W. R. at 42J, and 200 
 Michigan Central at 92^ ; Nov. 10th, sold the form r at 
 42J, and the latter at 93\. What was my gain, money 
 being worth 6%? 
 
 17. Which would be the better investment, §12,120 in 
 Michigan Central at 84, paying 3 % annual dividends, or 
 the same invested in Canada Bank stock at 2,020, paying 
 16 % every two months ? 
 
 18. On 84 shares of stock two semi-annual dividends were 
 declared, one at 5%, the other at 4%, the investment paid 
 10%. What did the stock cost ? 
 
 19. A man's income from $2,000 worth of stock is $75 
 semi-annually. What is the per cent, per annum ? 
 
 20. At what per cent, discount must 6% stock be bought, 
 that the investment may pay 9%? 
 
 21. If a stock yields 15 % per annum, what is its value 
 when money is worth 8 % ? 
 
 22. Which is the more profitable investment, a stock at 
 120, paying 8 % annually, or a 20-year bond at 90, paying 
 € % annually ? 
 
 23. At what price must 6% bonds, payable in eight 
 years, be bought to realize 4 % on the investment. 
 
 24. How many shares of a half stock, standing at 5 % 
 above par, should be given in exchange for 700 shares of 
 the stock of an express company, at 25 % below par ? 
 
 25. A man subscribed for 300 shares of stock in a manu- 
 facturing company, the par value of which was placed at 
 $50 per share; but. after paying three instalments, 
 amounting to 75 % of the par value, a dividend of 3% was 
 declared. How much will he receive, and at what rate per 
 cent, on the actual cosit 9 
 
266 
 
 STOCK EXCHANGE. 
 
 I.'?! 
 
 •f 
 
 i ! 
 
 .Yt'H'. 
 
 26. The «rosa earnings of a stock company with a 
 capital of §3,500,000 are $120,000; their expenses are 
 60% of their gross earnings. What per cent, dividend can 
 they declare, after putting aside $28,000 aa a surplus ? 
 
 27. The receipts of a mining company in one year are 
 $170,000, clear of all expensos. The company has a capital 
 of $500,000, divided into buares of §10 each, reserving 
 $50,000 as a contingent fund. What rate of dividend can 
 it declare for the year? what per mouth? and how much 
 can be paid on each share of stock ? 
 
 28. March 4th, deposited with my broker §600 margin, 
 for purchasing 50 shares Canada Pacific R. R. stock at 92^.' 
 The stock was sold March 28th at 96J. Allowing 6% 
 interest on the deposit, and charging 6 % interest on the 
 purchase, and J% brokerage, what was the net profit on 
 the transaction ? 
 
 29. Sold " short " through my broker 200 shares Michi- 
 gan Central at 90, and "covered" my "short "at SGf. 
 Allowing J % commission for buying and selling, what was 
 my net profit ? 
 
 80. May 6th, I bought through my broker 800 shares of 
 a certain stock at 93^, depositing with him §3,000 as 
 " margin," for his security against loss by a fall of price. 
 On the first of the following month, he sold them for my 
 account at 95. How much does he owe me besides the 
 $3,000, if he charges i% brokerage for each transaction, 
 mterest at 6% (for the exact number of days) on the laoney 
 used in excess of my deposit ? 
 
 81. Three companies, A, B, andO, are to Se consolidated 
 on the basis of the relative market values of tl'eir st"'jk. 
 Thus, A'a capital $1,000,000, Market value 100;.;; 
 B's " §1,500,000, " 50-,; 
 
 C's " $025,000, " 40".'.' 
 
STOCK EXCIlASOE. 
 
 267 
 
 The capital of the consolidated company is to be 
 §2,000,000, in 20,000 shares of $100 each. Wliat propor- 
 tion and what amount of the capital should be allotted to 
 each of tho old companies ; and how much ytock in the 
 new company should the holder of 1 eharo of ilie ttock 
 of each of the old companies be entitled to ? 
 
 82. A customer deposited $500 margin with a broker 
 November 23rd, who purchased for him 50 shares Michigan 
 Central at 80. Uq sold the same stock November 30th, at 
 98. What was the gain, brokerage ^%? 
 
 83. Aug. 30th, a broker purchased for the account of a 
 customer 300 shares of Railroad Htock at 78. He deposited 
 as a margin $8,000. On Sept. 22nd ,the stock was sold at 
 74i. What was the loss ? Interest G%, and commission 
 
 8 /O' 
 
 84. May 10th, a speculator deposited with his broker 
 $5,000 as a margin, and directed him to purchase for his 
 account 600 shares L ominion Saving & Loan, preferred at 
 90|. May 20th, the stock was sold at 94J. What was the 
 gain ? Interest 6 %, brokerage i %. 
 
 . 85. Sept. 10th, I deposited with my broker $5,000 as 
 margin, and he purchased for me 200 shares, C. P. R. at 
 DO}, 200 shares, Lon. & Can. L. & A. (half stock) at 122;}, 
 and 200 shares Intercolonial Railway Stock at 49|. The 
 stocks on Sept. 30th were quoted as follows : C. P. K. 80|, 
 Lon. & Can. L. & A., 120^, Intercolonial Railway 41^ 
 How much should I have deposited with my broker to make 
 my margin of 10 % good, and to cover commission of ^ % 
 for buying and selling, and interest at 6%? If I had been 
 unable to have made an additional deposit. !uul the broker 
 had " sold me out," what would have beeu my loss ? 
 
 k'. 
 
 .■i>.. 
 
EXCUA^O£. 
 
 EXCHANGE. 
 
 f 1 
 
 Ivi 
 
 4-ia. Exchange is the syetora by which morchautfl in 
 fli^taiit places discharge their dehta to each other without 
 the transmission of money. 
 
 Suppose for oxamplo that A. of Toronto owes 13. of Halifax 82,000 for 
 grain, anfl C. of Halifax owes 1). of Toronto »'.>,or)0 for ,lrv f;o(.ds. The 
 two d. bts may be discbar^f-d by means of ono draft or 1. I of exchange 
 without the transmission of money. Tims H. of Halifax .iraws on A. of 
 Toronto for «2,()00 and soils the draft to C. of n,ilif.«. who remits it to 
 D. of Toronto, D. of Toronto presents the (haft to A. of Toronto for 
 acceptance or payment, and thus both d.bts are cancellud. Thoro is in 
 effect a setting ofif or exchantje of ono debt for the other. 
 
 44». A Bill of Exchange is a written order, drawn 
 by one party on another, to pay a specified sum of money 
 to a party named tlierein, or to his order, or to bearer. 
 
 4-14. Bills of Excliange are of two kinds, viz. : Inland 
 or Domestic, and Foreign. 
 
 445. An Inland Bill of Exchange is one which is 
 drawn and made payable in the same country. 
 
 440. A Foreign Bill of Exchange is one which is 
 drawn in one country and made payable in another 
 country. 
 
 447. Inland Bills of Exci;anj^e are usually called Drafts, 
 and are distinguished as Time Drafts and Sight Drafts. 
 
 44.S. A Sight Draft is one which is made payable upon 
 prc-£f.iitation or on demand. 
 
 44«. A Time Draft is one which is made payable at a 
 certain specified thno after date or after time of presenta- 
 tion for acceptance. 
 
 *^f :f 1 
 
 -«fi"':-.-i:T,-,*v .i^jL.r al^.-j: .'^.■i.TL^'}Ut-m^9y. .\?.;', 
 
 .rw^'^i^ysmr^iti 
 
KXVIUNQE. 
 
 26i) 
 
 4HO* A Bill of Exchange is negotiable when it may be 
 Iransferred from one peraou to another by eudorrfoinent or 
 ftBBignment. 
 
 451. Tht' Rate of Exchange ia the rate por cent, which 
 b computeil on the Hill of Exchaiigo. 
 
 452. Thu Course of Exchange is the current price 
 paid in one place for billa of exchanfjn on another place. 
 This price viiriea, liccordina to the reiaUve conditions ol 
 trade and commercial credit at the two places, between which 
 oxchange ia made. 
 
 ThecourMof exchange betwoea two ooDntries, depends in their relative 
 •mount of indebtoiliiess to erich other ; und these, in turti are lai-^ely 
 depeudunt on " the balance of trade," or comparative amuani of exports 
 and imports. Tbae, if the United States owes Oroat Britain more than 
 Great Britain o«7e8 the Unitt3 1 f^tates, which is likely to be the case if it 
 has imported from Groat Jki'.^in more than it has exported thither, 
 exchange on that country will bo Ln demand, anJ will cousc juently 
 command a premium. If, on the otiier hanl. the balaii.;:> ot trade is in 
 favor of the Unitud States — that ia, if the exports exceed the imports, — 
 Great Britain will bo indebted to the Unite 1 States, the supply of bills 
 on Great Britain will more than meet the demand, and exchange will 
 fall below par. 
 
 The premium for exchange on any country can not long exceed the 
 OOflt of shipping specie thither; for meroiiaiUs will transmit coin to pay 
 their indebtedness abroad, if it is cheaper so to do than to buy exchange. 
 
 453. The Par of Exchanere is the estimated value of 
 the coins of one country as compareii with thode of another, 
 and is either intrinsic or commercial. 
 
 454. The Intrinsic Par of Exchange is the comparative 
 value of the coins of different countries, as determined by 
 their weight and purity. 
 
 Thus, according to the mint regulations of Great Britain ind France, 
 £1 sterling is eqoal to 2'> fr. 20 cent., which is said to be the par between 
 London and Paris. £s.uhange between the two countries is said to be at 
 par whoa billa are negotiated at this rata; that is, when a bill for £100 
 drawn in L-ondoa ia worth 2,520 francs in Paris, and ouiivursdy. When 
 
 n TV-cMlRITCgEJSHCVin 
 
i 
 
MICROCOPY RESOLUTION TEST CHART 
 
 (ANSI and ISO TEST CHART No. 2) 
 
 1.0 
 
 I.I 
 
 1.25 
 
 12.8 
 
 1.4 
 
 2.5 
 
 1 2.2 
 2.0 
 
 1.8 
 
 J /APPLIED INA^GE Inc 
 
 ST. 1653 Easl Wam St'eel 
 
 ^S Rochester, New York U609 uSA 
 
 SB (716) «82 - 0300 - Phone 
 
 ^ (716) 288 - 5989 - Fo» 
 
270 
 
 EXCUANOE. 
 
 £1 in London bnyB a bill on Paris for more than 26 fr. 20 cent., tbe 
 excLan<;eis said to bo in favor of London and against Paris; when £1 in 
 London will not bay a bill on Paris for 2i>fr. 20 cent., exchange is againrt 
 London and in favor of Paris. 
 
 Exchange is made to diverge from par by any discrepancy between 
 the actual weight or fineness of tho coins and the mint standard, and by 
 the variations in the f.emand and supply of bills of exchange. 
 
 455. The Commercial Par of Exchange i8 the com- 
 parative value of the coma of different countries, as deter- 
 mined by their nominal or market price. 
 
 Note.— The intrinsic par is always the same while the coins remain 
 unchanged ; but the commercial par, being determmed by coramorcial 
 usage, fluctuates. 
 
 456. When exchange sells for more than the face of the 
 draft, it in above par, or at a premium, and below par, 
 or at a discount, when sold fo, less than its face. 
 
 f'3»£- ■ll'< . 
 
liiLA:iD OA DOMEHilC EXCHANQE. 
 
 271 
 
 INLAND OR DOMESTIC EXCHANGE. 
 
 457. To find the cost of a draft at sight. 
 
 ExAMrLE 1.— ITow mucli must be paid for a sight draft of (1,000, 
 on the Bank of Montreal, at a premium of 1 J % ? 
 
 Solution. 
 91 + ?.015 = 81.015, course of exchange 
 :. 81 costs 81.01.5 
 ;. 81,000 cost 51.015 X 1,000 = 81,015. Ana. 
 
 KxAMPLK 2. — How much mast be paid for a sight draft of |600, on 
 tie Bfl»k of Ottawa, at a discount of 1 %? 
 
 Solution. 
 91 — 8.01 = 8.99, course of exchange 
 .■. 81 costs 8.99 
 /. 8600 cost 8.99 x 600 a $591. Ana. 
 
 45S. To find the cost of a time draft. 
 
 E-^CAMPLK 1.— What will bo the oo'st of the following draft, exchange 
 on Hamilton beinj; in Toronto at 2J % premium ? 
 
 $600. Toronto, July 18th, 1889. 
 
 Seventy days after sight, pay to J. S. Carson, or order, 
 six hundred dollars, value received, and charge the same Lo 
 my account. 
 
 J.VMK8 FeUGUBCN, 
 
 To Bank of Montreal, Hamilton. 
 
 Solution. 
 ■IJ + 8.0225 = ttl.0225, course of exchange 
 
 .012, bank discount of 81 for 73 da, at 6% (legal rate) 
 81.010 J, cost of exchange of 81 
 81 ooit 81.0105 
 'J600 " 81.0105 X COO = SOOO.SO. 
 

 i: 
 
 n 
 
 1 
 
 27'J 
 
 IWLASD OR DOilESTIC KXCIIASaH. 
 
 ExAsrpi-E 2.— Find the cost of a 60 days' draft on the Bank at 
 Quebec, Toronto, (or J'JOO, at a discount of 2J %. 
 
 SoLniioN. 
 
 11 - 8.025 a J.975, coarao of exchange 
 
 .0104 + , bank di.scount of 91 (<53 da.), at 6 % (legal rate) 
 8.904I), coat of exciiaii^e of 81 
 «1 cost i.WAC 
 :. 8000 " 8.0016 X 900 = 58C3.14. 
 
 EXERCISE 105. 
 
 1. Find the cost of a draft on Montreal for $1,100, at ^ of 
 1 % premium. 
 
 2. Find tbe cost of a drjift on Winnipeg for $1,350, at i 
 of 1 % discount. 
 
 3. What is the cost of a draft on Chatham for $1,800, at 
 li% premium? 
 
 4. Exchanged $600 in bank notes for gold at 5 % premium. 
 How n> -"i. iid I receive ? 
 
 6. Sold $375 uncurrent money at 2^ % discount. How 
 much did I receive ? How much did I lose ? 
 
 6. What was the cost of a bill for $210 on Belleville, pur- 
 chased at 1^% premium ? 
 
 7. Required the amount to pay for a draft to be remitted 
 to Hart & Denton, Kingston, for $1,250, exchange at |% 
 discount. 
 
 8. Shipped goods to Winnipeg, and received a draft for 
 ' $2,500, which gave me a profit of 20% ; sold the draft at 
 
 4J % premium. How much did I gain by both transac- 
 tions ? 
 
 9. Bought goods for $1,250, and sold them at a profit of 
 25%; purchased a draft on Fredricton with the proceeds, 
 at a discount of J%,. What was the amount of the draft f 
 
 I '• 
 
LWLAND OR DOMESTIC KXCHANOE. 278 
 
 10. A commission merchant sold goods, the net proceeds 
 of which were $2,750. How lar^'e a draft cnn he buy tc 
 remit to his consio .Jf },« pays 2^% premium for the 
 draft ? How large a draft if he purchases at 2^ % discount J 
 
 11. Find the cost of a draft for $1,600, payable 30 days 
 after sight, when exchange ia J of 1 % premium, and interest 
 6%. 
 
 12. Find the cost of a draft for $9r)0, payable in 80 days, 
 when exchange is at par and interest 4 J %. 
 
 13. Find the cost of a draft for SoOO, payable 60 days 
 after sight, when exchange is i of 1 % discount, and inter- 
 est 7 %. 
 
 14. Find the cost of a draft for $1,200, pn able in 90 
 days after sight, when exchange is ^ of 1 % premium, and 
 interest 7 %. 
 
 15. Find the cost of a draft for $810, payable in 90 days 
 when exchange is at i of 1 % premium, and interest 5J%. ' 
 
 16. Find the cost of a draft for $725, payable in 60 days 
 when exchange is at i of 1 % discount, and interest 6 %. 
 
 17. What must be paid in Toronto for a draft on Victoria 
 at 90 days, for $4,800, the course of exchange being 
 
 18. A firm in Toronto bought a 60 days' draft on Mon- 
 ireal for $2,500, at f % premium, 6 % interest. What did 
 the draft cost ? 
 
 19. A broker in Montreal bought a 90 days' draft on 
 Halifax for $1,299 at i% discount. He paid i % additional 
 for brokerage. How much did he pay for the draft ? 
 
 20. A commission merchant in Winnipeg sold for a firm 
 in Hamilton a consignment of cotton. The sales amounted 
 to $12 240, and his commission was 5 -J^ on the sales. He 
 bought and remitted a 30 days' draft at f % discount for the 
 proceeds due the firm. How much did the draft cost ? 
 
! 
 
 274 
 
 INLAND OR DOMESTIC iiXCh^NaE. 
 
 4S1>. To find the face of a draft at sight. 
 
 BxAMPLB 1.— I p«id 16*9.86 for a MRht dr»ft on the Bank of Com- 
 meroa, Winnipeg, at m pnmiom of f %. What wae the amount of itt 
 faca? 
 
 BOLUTIOH. 
 
 •1 + t.OOTS ■ I1.007S, ooanu of exohauge 
 91.0076 it paid for 11 face 
 
 MM 41 A •l tA 
 
 tl 
 
 •653.86 
 
 1.0076 
 ,652.86 
 
 10076 
 .'. Faoa of draft ■ I64S. 
 
 ExiMPLB a. — A. oommiMion merchant in BeJleyille wishei to remit 
 to his employer at Halifax a tight draft purchased with |7 ,202.70 What 
 it tb« face of the draft, exchange ^t | % discount 7 
 
 Solution. 
 |1 - 9.00635 s $.99375, course of exchange 
 9.09376 it paid for 91 fM* 
 ... 1 
 
 91 " - 
 
 * .99376 
 
 97.202.70 " 
 
 /. Face of draft = 97.248. 
 
 -7,202.70 „ 
 .99375 
 
 4«0. To find the face of a time draft 
 
 EXAMPM 1.— The cost in London of a 70 days' draft on Ottawa, 
 axohange } % premium, was 9797.40. What was the face of the draft 1 
 
 Solution. 
 •1 + 9.00876 ■ 91.00876. course of exchange 
 
 .012, bank discount of 91 for 73 da. at 6% 
 9.99676 ■ cost of 91 
 9.99676 is paid for 91 face 
 •1 " •• 
 
 ♦799.40 " •• 
 .*. Faoe of draft 
 
 '.99675 
 
 ,797.40 H 
 
 .99676 
 9800. 
 
INLAND OH DuMJOmU KXCUAHQU. 
 
 276 
 
 ExAMPLB 3. — A commission tnerchant in .~tratford wiahea to remit 
 to his employer in Montreal 8987.10 by n. araft at 30 days. Wlmt i« tha 
 face of the dntfi which b« oan purchase with this sum, ezchantie being 
 at a disGoont of } % ? 
 
 Solution. 
 
 II - 9.0075 ■ %:.i<iin, ooarao of axchanjjs 
 
 .0u5 1 ^ , bank diMuunt for 88 da. at 6 % 
 
 8.9871 »: co,,t o' 01 
 
 9.9371 is paid for «1 i'ac« 
 
 .'.M71 
 9H7.10 .. 
 .'.'>71 
 Faoa of draft = ti.OOO. 
 
 91 
 
 •9S7.10 
 
 
 40I. To find the rate of exchange on a sight draft. 
 
 ExiiMPLB 1.— The cost of a sight draft on Winnipeg for |1,'J00 was 
 11,213.50. Find the rate of exchange. 
 
 SOLOTION. 
 
 Gost a 91.213.60 
 
 Face ■ 91,200.00 
 
 Fremiam 
 
 913.60 
 91.200 was purchased at a premium of 913.60 
 
 91 " " •• ft^^5? 
 
 1,200 
 
 * 1,200 
 .'. Rate of exchange = 1^ % premium. 
 
 9100 
 
 - W| 
 
 ExAMPU a.— The cost of a sight draft on Victoria for $600 wae 
 9694.75. What was the rate of exchange ? 
 
 SOLCTIOM. 
 
 Faoe s 9G0O.0O 
 
 Cost = 9594.76 
 
 Discount a 95.26 
 9600 was porohased at a discount of 95.25 
 II M M i< « 5.26 
 
 600 
 
 9100 
 
 .5.26 X 100 
 9 ^^ » 
 
 Bate of exchange 
 
 600 
 \% discount. 
 
276 
 
 INLAND Uli DOMESTIC KXCHANQE. 
 
 E i 
 
 409. To find the rate of exchange on a time draft. 
 
 KxAuriM 1 —The cost in CoUinf^wood of a 70 daya' draft for 91,000 
 U |1,(M(>. Interuat being 6 %, what was the rate of itxohange 7 
 
 BOLUTIOM. 
 
 Cott $1,030 
 
 Face $.1000 
 
 Freininm, lesi interest S20 
 
 Interest for 73 da. at C % 812 
 
 Full premium .. .. J32 
 
 91,000 wuB puroliduud at a premium of W 
 
 •J U H U 
 
 •100 " •• •• 
 
 1.000 
 .32 X 100 
 
 .'. Rate of exchange 
 
 1,000 
 3| % premium. 
 
 •H 
 
 EziMPLi 2.— The cost in Quebec of a 70 days' draft for t6,000 is 
 |S,910. Interest being 6%, what is the rate of exchange 7 
 
 BOLDTION. 
 
 Cott 96,000 
 
 Faoe to.OlO 
 
 Disconnt, plus interest 
 Interest for 73 da . . 
 Fall discount.. .. 
 
 »90 
 872 
 
 818 
 
 96,000 was purchased at a discount of 
 |1 •• i< •• 8 
 
 918 
 
 18 
 
 6,000 
 
 9100 
 
 9ii.iy22 = 9A 
 
 .'. Kate of exchange 
 
 6,000 
 ^% disoount. 
 
 EXERCISE 106. 
 
 H 
 
 1. A sight draft was purchased for $550.62, exchange 
 being at a premium of 8^ % ; what was the face ? 
 
 2. What is the face of a sight draft bought for $7,600 
 at a premium of $2.50 ? ($2.50 on $1,000 - i%.) 
 
 jr.' 
 hi 
 
ISLAND OH DOUESTIC KXCUASQK. 
 
 277 
 
 8. Find the largest draft payahl.' ao days after date that 
 can he houghi for $4,985.00, exchange being at a rremium 
 of i%. 
 
 4. What per cent, of its face is the cost of a HO (Jays' 
 draft, if exchange is 1 % premium, and interest is allowed 
 
 at4%? 
 
 6. Find the face of a 60 days' draft, bought for $620.76, 
 if exchange is §2.60 diacouut, and interest «%. 
 
 6. Find the face of a draft, payable 60 days after date, 
 that can be boiif,'lit for $1,1'25, when exchange is at ^ of 
 1 % discount, and interest 5^ %. 
 
 7. Find the face of a draft, payable 80 days after date, 
 that -an he bought for §520, when exchange is at J of 1 ^ 
 premium, p.nd interest 4%. 
 
 8. Find the face of a draft, payable 60 days after sight, 
 tb t can be bought for $1,250, when exchange* is at ^ of 
 1% premium, and interest 1%. 
 
 9. Find the face of a draft, payable 80 days after sight, 
 that can be bought for §274, when exchange is at par, and 
 interest 6 %, 
 
 10. Find the face of a draft, payable 90 days after date, 
 that can be bought for $10,000, when exchange is at par, 
 and interest 4^ %. 
 
 11. A flommigsion merchant in Detroit wishes to remit 
 to his employer in St. Louis, $512.86 by draft at 60 days ; 
 what is the face of the draft which he can purchase with 
 this sum, exchange b- mg at 2^ % discount ? 
 
 12. An agent in Halifax having §1,824.74 due his em- 
 ployer, is instructed to purchase with the same a draft 
 drawn at 30 days ; what will be the face of tlie draft, ex- 
 change being at 1J% premium ? 
 
278 
 
 ISl.ASD OR DOUKSriC EXCUASQK. 
 
 I 
 
 \\ 
 
 18. My agent in Winnipop; sftlls a house and lot for 
 $7,600, on coiniuiHHion of 1^%, and remits to roc the 
 proceedn in a draft purchased at ^ % premium ; what bulu 
 do I receive fro a the sale of my property ? 
 
 14. The Merchants' Bank of New York having declared 
 a dividend of 61%, a 8i;)ckhohler in Toronto drew on the 
 bank for the sum due him, and sold tue draft at a pre- 
 mium of 1 J %, thus realizing; $509.75 from his dividend; 
 t'ow many aharefl did he own ? 
 
 16. A man io O^-en Sound has $4,800 due him in 
 Quebec ; how much more will he realize by making a 
 ira't for this sum on Quebec and soiling it at \% dis- 
 90unt, than by having a draft on Owen Sound remitted to 
 bim, purchased in Quebec for this sum at f % premium ? 
 
 16. A man in Brantford purchased a draft on Montreal 
 for $5,820, drxwu at 60 da.vs, paying $5,141.78; what was 
 ihe course of exchange ? 
 
 17. An agen^ owing his principal $5,05U. 20, was directed 
 10 buy a draft with tliin amount, and remit it. Tlie prin- 
 Bipal received $4,960 ; what was the rate of exchange ? 
 
 18. Sight exchange on Toronto for $6,000 cost $5 076; 
 wha^ wcs the course of exchange? 
 
POU£ION KXCUANQM. 
 
 279 
 
 FOREIGN EXCHANGE. 
 
 i 
 
 468. Foreign Exchange is the exchange which is 
 carritd on between different countrios, and is diHtinguished 
 A8 direct and circuitous. 
 
 Exohanye with Europe is efToot«d mainly through the f.Tt^t ttnanoial 
 oentros, London, Parii, Antwp p, Herliu, Hamburg, Frankfort, uiil 
 Amateruam, 
 
 464. Direct Exchange is confined to the two places 
 between which the money is to be remitted. 
 
 40.1. There are always two methods of transmitting 
 mon(n- between two places. Thus^ if A. is to receive moLey 
 from B., 
 
 let. A. may draw on B. and sell the draft ; 
 2nc B. may remit a draft made in favor of A. 
 
 S*"^ {)!)•-■ !ierBon in said to draw on another person when h« ia tbe 
 makf a draft ^ddresoed to that person. 
 
 4AP A set of cchange is a bill usually drawn in tripli- 
 eftt» ,mi heariiig the same date, payable to t*- 3 same party, 
 
 eseed thfct when one of the hi. .s is paid the 
 'me void. 
 
 sject of drawing Bills of Exchange in sets of 
 provide against losa in transmitting from one 
 another. The bills are sometimes sent jy 
 I *e9 or by th» same route at different dates. 
 Some mer< i*- ^ send omy the first and second and pre- 
 serve the thir« 
 
 and 
 
 oth. 
 
 The 
 three '«i 
 country 
 different 
 
'2U0 
 
 roUtAUN KXailASGB. 
 
 SET '^F EXCHAf^GE. 
 
 (1.) 
 ^^'^^ Toronto, July 23. 1889. 
 
 Sixty rlavH after Bicht of this First cf Exchan-e (Second 
 an.l fhird of tht- hame tenor and date unpaid), pay to the 
 --■'iu- of II. E. Ciark. Ono Thousand Pounds Sterling 
 valut' received, and charge the same to account of 
 
 „ . John MoDonald & Co. 
 
 To Brown. Nt,i, ley & Co., 
 
 London, Ensland. 
 No. 17U. 
 
 (2.) 
 ^^'^^' Toronto, July 23, 1689. 
 
 Sixty days after P'ght of this Second of Exchange (First 
 and Tliird of the same tenor and date unpaid), pay to the 
 order of H. E. Clarke. One Thousand Pounds Sterling 
 value received, and cliarge the same to account of 
 
 rr„ u a. . , . John Donald & Co. 
 
 To Brown, Shipley <fe Co., 
 
 London, England. 
 No. 179. 
 
 (8.) 
 
 ^'^'°^- TouoNTo. July 23, 1889. 
 
 Sixty days after sight of this Third of Exchange (First 
 and Second of the same tenor and date unpaid), pav to the 
 order of H. E. Chiike, One Thousand Pound> Sterling, 
 value received, and charge the same to account of 
 
 m ,, n, . . -^o^N McDonald & Co. 
 
 To Brown, Shipley & Co., 
 
 London, England. 
 No. 179. 
 
 iir-v 
 
yOHKlON HXCUASUi:. 
 
 281 
 
 in 
 
 4«7. Forfign Bills -if Exc i, uise a-.< usuiillv .li;i\v 
 tbjciintiioy of the country in v> i.-li thev :,"c |mi ,,.1. 
 Ihu8 -liafts on EiikI..,.,! are UH.n.lly .l.awn in poiuuls, 
 :^liilhiij^.s, and peiico ; on 1- nmcy, Hcl-iura, and Switzer- 
 land, in francs ; on Gerimin> in murks, etc. 
 
 4«.S. Foreign Bills of Exrhange aro usu.illv drawn at 
 »i«ht a days;, or at sixty (t!3 dayn) davh' sight. 
 
 4«». Quotations for T iays refer to Hi^'ht exc!ian;,'t-. on 
 the theory that 3 dayH' gracu are allowed on siKl.t .hufts, 
 thougii custom varies in this re.jjcct. 
 
 470. Sight drafts are fre.iu.'ntlv called "short" 
 exclmage, and 60 day drafts, "long" exchan^'e. 
 
 '■■•^"Long" exclianjre is Hold at a rate l.clow that for 
 "Su, ft "exchange, suthcient to equalize the differctice in 
 interest between the dateH of maturity of the two claasos of 
 bills, the banker having the use of the money from the 
 time the draft is drawn till it is paid. 
 
 47a. A Letter of Credit is a draff, made hv a hanker 
 in one country, addressed to foreign bankers, hy which the 
 holder may draw funds at different places to any amount 
 not exceeding the limits of the letter of credit. 
 
 47a. Exchan;^e on Enj^land (sterlitig exchan^'6) is 
 quoted by giving the value of £1 in dollais and cents. 
 
 ThuH, when exchange is 4.84, a draft of Mi will cost 
 14.8-1 ; of i'lOO, $ 184. 
 
 474. By Act of Parliament the value of the pound 
 sterling was fixed at $4J (yf=$10). This is much below 
 its intrinsic value, which is now iixed at $4,863. 'flj« rales 
 ©f exchange usually quoted in commercial papers are 
 
il 
 
 :) 
 
 282 
 
 FOREIGN KXCHANOE. 
 
 calculated at a certain per cent, on the old par of 
 exchange- 
 Exchange is at par between Great Britain and Canada 
 when the old par of exchange is at a premium of 9^ per 
 cent., for $4^ increased by 9^ per cent., equals $4.86§. 
 
 475. Sterling quotations usually range between 4.80 
 and 4.91 (t. e. $4.80 to $4.91 to the £ sterling). Two 
 quotations are mentioned for each kind of exchange, and 
 indicate the highest and lowest price paid on the 
 same day. Thus GO days' sterling 4.8G @ 4.87, means 
 that tiie lowest quotation to the £ was $4.86, and the 
 highest $4.87. 
 
 Qnntations are frequently given with reference to the old 
 par of exchange. Thus 60 days' sterling 9J to !>^ means 
 that the old par of exchange {£1 » $4f) rangtti from 
 9J % to 9^ % jiremium, i. e. tiie lowest course of exchange 
 is $4i X 1.09^ ; the highest, $4* x 1.09^. 
 
 476. Exchange on France, Belgium, and Switzerland, 
 is quoted by giving the valuo of >;i in francs and centimes. 
 Thus, when exchange is 5.27 i, U will buy 5 frani;^ and 
 27i centimes. 
 
 477. Exchange on Amsterdam, (Netherlands), is quoted 
 by giving the value of one guilder or florin in Canadian 
 currency. 
 
 The intrinsic par value of one guilder is 40^^ cents. 
 
 478. Exchange on Germany is quoted by giving the 
 value of 4 marks (reichsmarks) in cents. 
 
 The intrinsic par value of 1 mark is 23^ cents. 
 
FOhElON EXCUANOE. 
 
 288 
 
 
 a B o u tcS hC «^ a tf:^ o 0,3 g g 3 a S,fe al; 3 o .ffS 
 
284 
 
 FOBEIO:^ EXCHANGE. 
 
 4»0. To find the cost of a foreign bill of exchange. 
 
 BxAHFLB 1.— How much must be paid in Toronto for a bill of 
 exohan^o on Liverpool for £1,-00, exchange being quoted at $-1.80J to the 
 £ sterling ? 
 
 SOLCTIO.N. 
 
 Cost of £1 = :i.«.i 
 
 £1,200 = 84.8i!J X 1,'JOO = 1*5,841. Ana. 
 ExAMPLK 2.— How much must bo paid in Haniiltou lor a drufl on 
 Paris for 2,072 franoa, exchange being quoted at 6.18 ? 
 
 SOLDTIOS. 
 
 6.18 
 
 1 
 
 2,072 
 
 francs = 81 
 
 franc = S- 
 
 ,18 
 
 francs = s":^— = S400. Ana. 
 6.18 
 
 EXAMPI.H 3.— What will be tho cost in Montreal of the following 
 bill of exchange on Liverpool, at 9^ % premium 7 
 
 £432. Montreal, July 22n(l, 1889. 
 
 At sight of this first of exchange (second ami third of 
 same tenor and date unpaid), pay to the order of W. R. 
 Telford, Montreal, four hundred and thirty-two pounds, 
 value received, and charge the same to the account of, 
 
 J. P. Hume & Co. 
 To Alex. Grant & Son., 
 
 Liverpool, England. 
 
 SOLUTIOH. 
 
 £9 = $40 X 1.095 
 ,40 X 1.095 
 
 £1 
 
 £432 
 
 V 
 
 ,40 X 1.095 X 432 
 I _ 
 
 s $2,102.40 Ans. 
 
 Explanation. 
 
 Since exchange on 
 
 Liverpool is at 9J% 
 
 preuiium, £9 will cost 
 
 840 X 1.095. Art. 475. 
 
 Ifir 
 
 EXERCISE 107. 
 
 1. Sold to a broker 480 English sovereigns at 4.86. I 
 was paid in currency when gold was quoted at 1.05^. How 
 much did I receive ? 
 
FOUEION EXCHANGE. 
 
 281 
 
 2. An importer rurchased a lull of exchange on London, 
 at 3 days' sight, for i;488 IGs. Gd., at 4.85^. What wai 
 the cost? 
 
 8. Find the cost of a hill of exchange on Manchester, 
 for £'485 128. 6d. at the par value. 
 
 4. An exporter sold a draft for £540 8s. on Liverpool, 
 payable in London, at 4.84. brokerage k%- What were the' 
 proceeds ? 
 
 5. What is the cost in Kingston of a bill on London, 
 Eng., for ^£425 68. 8d., at 9J% premium ? 
 
 6. How much will a draft on Berlin for 2,400 marks 
 cost, exchange being quoted at 94 1 ? 
 
 7. Bought a bill of exchange on Paris for 3,760.20 francs, 
 v?hen exchange was 5.22^. What did the bill cost ? 
 
 8. What is the cost in Toronto of a bill of exchange on 
 St. Petersburg for 8000 roubles at 1^% premium, the par 
 of exchange being $.754 for 1 rouble ? 
 
 9. What is the cost of a bill of exchange on New York 
 for $7,200, at f% premium ? 
 
 10. Bought at par, 260 rupees of India, 560 Austrian 
 florins, and 480 crowns of Denmark. How much did I 
 pay for all ? 
 
 11. Sold a bill of exchange on Amsterdam for 1,440 
 guilders. Exchange 89|. What was the sum obtained ? 
 
 12. Sold exchange on Geneva, through a broker, for 
 8,000 francs at 60 days' sight. What were the proceeds of 
 the draft, exchange being 5.20f, brokerage ^%? 
 
 13. What will it coat to remit 8,750 francs to Antwerp 
 at par value ? 
 
 14. What were the proceeds of a draft, sold through a 
 broker, for 8,748 marks (Reichsmarks), at 94f , brokerage 
 
286 
 
 FOIiEION EXCUANQE. 
 
 J i: 
 
 16. What are the proceeds of a draft on Paris for 12,420 
 francs, at 5.19}, brokerage on exchange ^%7 
 
 4SI. To find the course of exchange. 
 
 EzAMFU 1.— The oo8t of a bill of exchange on Liverpool for £500, 
 including a brokeraxe of i %, waa »2,443.05. What waa the quotation T 
 
 Solution. 
 100% + t%- 100^%. 
 100J% of cost of bill a »2, 143.06 
 
 ^ 2,143.05 X 100 ^ j2^4Q 
 
 .'. Coat of bin 
 
 ,-. £500 are worth 
 £1 is worth 
 
 lOOi 
 
 N.88, ooarao of exchange. 
 
 •2,440 
 2,440 
 600 
 
 BxAMPLK 2.— The cost of a bill of ejohange on Hamburjj for 4,400 
 marks, including brokerage of \ %, waa %\fibl.i'i. What was the coorte 
 of exchange on Hamburg? 
 
 SOLUTIOH. 
 
 100% + l%= I00i%. 
 loot % of cost of bill = 11,067.32 
 /. Ck»t of bill . tl.057.32 x 100 -. ^^ 
 
 .'. 4,400 marks are worth 91,056 
 1 mark is worth 21c. 
 24c. X 4 = 96o. = course of exchange. Art. 478. 
 
 EXERCISE 108. 
 
 Find the course of exchange of a bill. 
 
 1. Face £6,000, 
 
 2. " £2,000, 
 
 8. " 3,200 marks. 
 
 4. " 800 " 
 
 5. " 1,000 guilders, 
 
 6. " 3,600 " 
 
 7. " 1,854 francs, 
 
 8. •' 366.20 " 
 
 9. " 2,200 reiohsmarks, 
 10. " 5,500 • " 
 
 Cost S24,2S0 60, Brokerage \ %. 
 
 " 89,732.16, » ^%, 
 
 " J765.66. " J%. 
 
 8184.23, " J%. 
 
 " 8646.61, •' J%, 
 
 " 81,680.75, " 1%. 
 
 '• 8360.45, " J%. 
 
 872.09, " 1%. 
 
 " 8528.66, " i%. 
 
 » 81,321.66, " \%. 
 
 11. A draft on Dublin for £860 cost |1,786. 
 vas the course of exchange ? 
 
 What 
 
OREIGN EXCUAHUE ^g^ 
 
 12 The cost in currency, whon «ol.l was at 104^ for a 
 !;^;1Z^^^^^^^ *^ ^-^-^«- ^^- - the conrse 
 
 Of bXager** '" ^'^ ""^^ °^ ^^"^^''^'«- -'--" 
 
 An'tt'er?fortq.^''"'^'"' ^l '''^'''''' ''' ^ ''^^^ on 
 of elehange ? '""^ "^^ ^^'^^ ""''''' ^^ ^^^ — 
 
 8 2f^ 1 °^f «fa*°t paid $765 for a bill of exchange for 
 8,200 marks on Frankfort. What wa« t!>e course of 
 exchange, no charges for brokerage bein^r ma.ie ? 
 
 482. To find the Face of a Foreign Bill of Exchange 
 
 oiunange was 4.88. What was the fac« of th« bill t 
 Solution. 
 W.88 s cost of £1 
 
 II „ .. jej_ 
 
 4.88 
 
 91194.04 
 
 pll94.90 
 
 4.M3 
 = £244 178. Od. 
 
 = £244.875. 
 
 Pace of bill. 
 
 -!,.„ T^" *"~'^^ °°'* °' ■* ^'" °* exchange on Bremen was 8670 
 when exchange waa 95. What was tho face of the bill ? ' 
 
 SoLtrrio.w. 
 
 ».95 . cost of 4 marks. (Art. 478). 
 
 •1 » " _i 
 
 •95 
 
 »670 s •• ^x67Q „ 
 .95 
 
 = 2,400 marks. : 'aoe of bUl. 
 
 -h^ ?^" ^-"^^ *^* °^ * ^"' "' «°1"'° on Paris waa 86.-0 
 when exchange was at 6.18. What was tl,e face of the bill ? ' 
 
 SoLtrrioN. 
 •1 « cost of 5.18 francs. 
 1600 B •• 5.18x500 " 
 
 = 2,590 francs, Face of biJl, 
 
2B8 
 
 hvumaa exchanqe. 
 
 ^1 
 
 lii 
 
 >l 
 
 EXERCISE 109. 
 
 1. A bill of exchanj^e on Montreal, coat Jei25 in Bir- 
 mingham, England, exchange b^ing at 8% premium for 
 sterling ; required the faco of the bill ? 
 
 2. Bought a bill of exchange on London, when exchange 
 wa.8 4.90 and gold 1()-2|. I paid $37,668.75 in currency. 
 What was the face of the bill ? 
 
 3. An agent remitted to his principal a draft on Toronto 
 from Amsterdam at J % brokerage, exchange being at 40. 
 The cost of the draft in Amsterdam, including brokerage, 
 was 960 guilders. What was the face of the draft? 
 
 4. A broker invested $1,158 in Paris francs at par. How 
 many francs did he purchase ? 
 
 6. What will be the face of a bill on Hamburg, exchange 
 being quoted at 94^ and the coat of the draft $756 ? 
 
 6. An agent in Boston, having $7,536.80 due bii 
 employer in England, is directed to remit by a bill on 
 Liverpool. What is the face of the bill which he can pur- 
 chase for this money, exchange being at 31 % premium ? 
 
 7. A merchant in Chatham has 9,087 guilders, 10 stivers, 
 due him in Amsterdam, and requests the remittance by draft. 
 What sum will he receive, exchange on Canada being in 
 Amsterdam at 2^ guilders for $1 ? (1 guilder - 20 stivers.) 
 
 8. What is the face of a 3 days' draft on Brem , that 
 was purchased in Hamilton for $3,261.60, exchange rf4|? 
 
 9. A trader in London, Eng., wishes to invest £2,500 in 
 merchandise in Lisbon. If he remits to his correspondent 
 at Lisbon a bill purchased for this sum at the rate of 
 64id. sterling, per milree. What sum in the currency of 
 Portugal will the agent receive ? 
 
 10. G. B. Smith & Co., Toronto, instructed their agent 
 at Berlin to draw on them for a bill of goods of 4,500 
 mark-, exchange at 97*, brokerage i%. What did they 
 pay in Canadian money for the goods ? 
 
if'ORKjaa ExcuANoa. 
 
 289 
 
 FOREIGN CIRCUITOUS EXCHANGE. 
 
 in*?h!'c^?!f fj? "' !"''*"^*^ '' *"« P^°-- of find- 
 "i„ ineco=t of exchange between two places 7 romJH.^ 
 
 be made ti.ro„,b „„e or „„„ u,.er,„o,£rpl,;ees "°" 
 
 If A. is to transmit to C. thioLK^h B Isf A .« 
 «aw on J3.. Srd. L. may draw o,i A., and remit to'C 
 
 •tiveis. and hencerPaHs^f ^r . "? "' *''' '"^ °^ ^1 cents for 10 
 
 SoLvinos. 
 28 stivers = 3 francs ,. ^ stivers = 1 frano 
 21 cents = 10 stivers .-. ,j cents = l lu "^ 
 _ 6,400 X 28 
 
 6.400 francs 
 
 6,400 X 28 .. 
 5 ■tiveri 
 
 stivers 
 
 o 
 
 . 6.400 X 28 X 21 
 
 3 X 10 
 - »1,058.40. Ans. 
 
 oenta 
 
1 
 
 11 i 
 
 yoHKias asvuANOa. 
 
 EXVI^NATIOM. 
 
 To rednc« fntnoa to •tiveri, multiply by M, beoauM »her« are M ''«"«>• 
 M many Mtivors aa there are fraiios. 
 
 To rednoe Bkiveri tc centa, multiply by f^, beoauae tber* arc f^ tmea 
 M many oeota aa there are stivera. 
 
 KzAHBUi 3. — A Montreal merchant remits 6.:,88U tibrina to 
 AniRterdam by way of London add Paris, at a time when the excLan;4« 
 of Montreal on London ia •4.886 for i:i, uf London on Paria is 35.4 
 francs for £1, and of Paria on Amsterdam ia 212 francs for 100 florins ; 
 I per cent, brokerage being paid in London and in Paria. Uow many 
 dollara will purchase the bill of exchange ? 
 
 SoLDTION. 
 
 212 
 
 Vioo 1(10 ; 
 1 „ 100 ;\ 
 
 100/ 
 •4.886 m £1. 
 CC,880 X 212 X 801 ^^^^^ 
 100 X 80(J 
 
 ,. 66,8^0 X 212 X 801 x 801 
 
 100 dorina a ,12 franoa 
 
 tfi 4 franca ■ £1 
 
 Pi? X L^"»Vnu.c. - 1 florin. 
 
 V25.4 
 
 1 frano. 
 
 66,680 florins x 
 66,880 X 212 X 801 
 
 fr«"oa 
 
 100 X 800 
 , 66,880 X 212 X 801 x 801 
 ' 100 X 800 X 26.4 X 800 
 
 100 X BOO X 26.4 X 800 
 ^ -55,880 x2l'i X 801 x 8 01 x 4 886 
 
 100 )r'80O X 25.4 X 800 
 = •22,»10.G34 + Aua. 
 
 C- 
 
 Vi( 
 
 13 ^ lOOU 
 100 100/ 
 
 Explanation. 
 
 212 
 
 Too luo ' 
 
 timea aa many franco aa there are florins. 
 
 To reduce florins to franci, multiply by ^^ x -— i, because there are 
 
 To rednoe franca to t, multiply by f JL X — „M. because there 
 
 \2o.4 100 / 
 
 are (—L. x —i \ times as many £ as there are francs. 
 \2o 4 100 / 
 
 To reduce £ to •, multiply by 4.335, because there are 4.685 times aa 
 many I as there are £. 
 
 ExAMPLi 8. — A banker in New York remits $3,000 to Liyerpoo , by 
 arbitration, as followa : First to Paris at 5 francs H) centimes per •] ; 
 tlienoe to Hamburg at 186 francs per 100 marcs ; thence to Amsterdam 
 at 35 ativera per 2 marcs ; thciioo to Liverpool at 220 stivers per £1 
 .orling. How mnoh sterling money will he have in liunk at I'iverpool, 
 and what will be his gain over direct exchan<;e at 10 % iiroiniutn ? 
 
/ 
 
 ronmun Lxcudsom 
 
 291 
 
 220 itiveii m £1 
 
 - "iwc* - as stive™ 
 
 IM frm. - 100 marc* 
 
 S /rau.'H to oeut ■ |1 
 
 9300U ■ 
 
 3. OO P X 540 , 
 
 100 
 ii.UOO X 540 X 100 
 
 100 X 185 
 
 S.OOO x^40 X 100 X 83 
 
 100 X lac X 2 
 
 luarcii. 
 
 ■tiven 
 
 §3,000 m £1^* X A K fH 
 
 • ^'tf» ■ 1 niiftr. 
 
 . '^ stiver! m 1 luara 
 f?! niiirca m I fr»uo. 
 
 {♦S <r.HiC« m »1, 
 
 8,01). X r.jo , 
 •• •• — , — frano*. 
 
 .. .. ''^W '^ 510 X 100 
 100 X 186 
 . 8,000 X .540 X 10<t X 85 
 100 X 18S x"3 ' 
 » £ ?.000_x^6JOj<_t^O_x 36 
 
 100 X 186 X a X a-jo 
 
 - £6'j(j llg. ad. Ciroaitoui exohaat 
 
 uurua 
 
 •tivem 
 
 SAVi l it, 9d. 
 £82 18d. 6d. 
 
 Direct oxcliau| 
 Oaia. Ana. 
 
 EXERMSE Iia 
 
 1. When exchange at New York on Paria is 5 franca 16 
 centimes per $1, and at Paria on Hamburg ^ francs per 
 marc banco, what will be the arbitrated price in New York 
 of 7,680 marc baucos of ilamburj? 
 
 2. The exchange at Paria upon London is at the rate of 
 '2.5 franca 70 centimes for il sterling, and the excbange at 
 Vienna upon Paris is at the rate of 40^ Austrian florins for 
 20 franco: find how many Austrian fiorina should be paid 
 at Vienna for a ^£60 note. 
 
 3. An agent in Boston, having $7,536.10 due his 
 e.i;ployer in England, is directed to remit by a bill on 
 Liverpool. What is the face of the bill which he can 
 purchase for this money, exchange being a* ,1 * 
 premium ? 
 
./-- 
 
 292 
 
 rOHEiaS KXCUANOE. 
 
 lit 
 
 4. Bills on Araaterdam, bou^'ht in London at 12 florina 
 16 cents per £l sterling, are sold in Paris at 67^ florins for 
 120 francs. What is the course of exchange botwoen London 
 and Paris? 
 
 6. If at Philadelphia, exchange on Liverpool is at 9| % 
 premium, and at Liverpool on Paris 26 francs 86 oentim s 
 per A'l ; what is the arbitrateil course of exchange betwerii 
 Philadolphitt and Paria, throui^'h Liverpool ? 
 
 6. A resident at Naples having a bequest of $8,720 
 made him in J^oston, ordors the remittance to be made to 
 his agent in London. w!)o remits the proceeds to Naples, 
 reserving his coiumisKion of i % on the draft sent. If 
 exchange on Loudon is 9% in Boston, and the rutebetwoeii 
 London and Naples is ^1 for 6 scudi, how much does the 
 man realize from his bequest ? 
 
 7. A merchant of Toronto wishes to transmit 2,400 
 marcB banr > to Hamhiirs. He linds exchange between 
 Toronto and Hamburj,' to' be 85 cents for 1 marc. The 
 exchange between Toronto and London is $4.83 for .£1 ; 
 that between London und Purls is 26 francs for £1 ; and 
 that of Paris on Haiubur;:; is 47 fruncs for 25 marcs. By 
 what way sliould the Toronto merchant remit ? 
 
 8. A person in London owes another in St. Petersburg 
 920 roubles, whifh must be remitted through Paris. He 
 pays the requisite mm to his broker, at a time when the 
 exchange between London and Paris is 25.15 francs for A'l, 
 and between Paris and St. Petersburg 1.2 francs for 1 
 rouble. The remittance is delayed until the rates are 25.35 
 francs for £1 and 1.16 francs for 1 rouble. What does the 
 broker gain or lose by the delay ? 
 
 9. A merchant in New York wishes to pay £3,000 in 
 London. Exchange on Lr ,. i at par; on Paris, 5 
 
 ^ ' 
 
 1 .*i 1 ■<! 
 
^lihlUH iCUdSUK. 
 
 288 
 
 'f oxcl„,j •.. betweeu Lod.lou and 
 
 I y.»;3 f , are equivalent to 1 
 
 ^ tb Uer. t. .^4 Austrian florins, 
 
 to 12.8 V.-aetian ducatH,— if » 
 
 o'H '1 Yen. « l.oou .iiicatH, will 
 
 ^.rem- by*,yor ?ari8, Berlin, 
 
 o i^iaict- . ipposiiig a ducat to be 
 
 10. When the CO 
 Paris i.s l/jd. p..r f 
 Prussian thaler, a. 
 and 'Jr, Au^rian t 
 London merchaiit . 
 it be more ad van tag 
 and Vienna, or dir^rf 
 equivuluiit to 4g. 2.1 
 
 .^m3-"J*^. 
 
2U4 
 
 [IIO. 
 
 RATIO. 
 
 4h:1. Ratio \n the rf!ntion }»etween two roer ' rs of tlio 
 Baiuti (Icmnuination, oxpna-^oil by tlio quotient ui tlie firat 
 diviiied bv Uio Hocond. 
 
 Thus the ratio of D to 6 is (9*6); tiie ratio of 6 to 'J is 
 (fi + '.)). 
 
 tHil. Thf Sign of ratio is the colon ( :). 
 
 TiM' ratio of U to 6 is ic ir.issed 9 : 0, or 9 ♦ 6, or aa n 
 fraction |. 
 
 4h7. The Terms of a nitio aru the numbers compared. 
 
 4HH. The Antecedent is tho first term, or the divilond, 
 or, if exproHsed ne a fruction, tho numerator. 
 
 4.S1I. The Consequent is the ecoond terra, or the 
 divisor, or, if oxprcsaetj as a fr., lion, the dononunator. 
 
 41MK The two terra h together fo»"ra a couplet 
 
 4111. A Direct Ratio is the quoti»Mit of the autecedent 
 divided by the consi<jupnt 
 
 4«2. An Inverse Ratio or Reciprocal Ratio is the 
 
 quotient of the conseqiuMit divided by the antecedent. 
 
 4J»». Ritios are compared by comparing the fractions 
 by which they are repro^iiitcd. 
 
 4»4. Eatios are compounded ])y multiplying together 
 the fractions by which tliey are represented, and expressing 
 
 the resulting fraction as a ratio 
 
 ThuH th** ratio compounded of 3 : 6 and 7 : 9, is | x ^ ■ 
 
 II 
 
 21 : 15. 
 
/ 
 
 tmi-uHTios. 
 
 196 
 
 PROPORTION. 
 
 4»5. Proportion cotiRifltfl in tho equality of two rntios. 
 
 Foi example, th< ratio of 37 ydi. to jrdi. ia V - 8 ; tl.o ratio of 
 874 ot.. to laj eta. i. JJ* . 8 wid. th«refora. th« ratio of «7 ydi to 
 
 9 ydf. ia equ.il to tlm ratio of ;t7J ota. to laj ots.. ainoe jftoh ratio ia # /wl 
 ton. ' 
 
 Thia in . iprcHBod thna •.—21 yda. : !» ydM. . 87i ota. : I24 eta. or 37 ydm. • 
 » yda. :: 874 cU : 12J eta., tlv .louble col-n i::) b...in^. nsod in»to,«l of lh« 
 
 12^ ctH. 
 
 iii(iuof equality («), or it may be exprMaod '^l-l^ 
 
 V yda 
 
 4»«. Tlie arithmntio test of proportion ia, therefore, 
 that the two fractions ropreaonting the ratios must be 
 equal. 
 Since ,•, » I tlierofora 6 : 13 :: 4 : 8. 
 
 4«>7. The two terms fi and 8 are called the extremes. 
 The two terms 12 and 1 are called the means. 
 
 6 is called the;!r«f proportional. 13 ie called the Hcorui proportional. 4 
 la Oftlled the third proportional, and 8 ia called ih%fo;irth proportioual. ' 
 
 4»H. Where the two means are the same number, that 
 number is said to be a mean proportional between the two 
 extremes. 
 
 Thue. in the proportion 4 : 6 :: 6 : 9, 6 is the mean pro- 
 portional between 4 and 9. 
 
 4»9. When two quantities are connected in such a way, 
 that, when the lirst is increased any number of times, the 
 second is increased the same number of times, they are 
 said to be in direct proportion. 
 
i; 
 
 ^i 
 
 W 
 
 
 296 PROPORTION. 
 
 For example, if 1 lb. of snsar cost 8 ots. 
 
 3 lb8. will oost 3 times 8 ot«. 
 8 " " 3 " s " 
 
 4 " " 4 M 3 u 
 
 etc., eto. 
 
 That U. if we inoreaM the weight any nnmber of times we inoreaw 
 the coet the same nnmber of times. t.«., thu oost of the inear ii directlg 
 proportional to iU weight and vice rerta. 
 
 Hence, I lb. : 7 lbs. :: 8 cts. : 7 times 8 ota. 
 
 liOO. When two quantities are connected in such a way, 
 that, when the first ie increased any number of times, the 
 second is decreased the same number of times, they are 
 said to be in inverse proportion. 
 
 For example, if one man can do n piece of work in 13 dayi, 
 9 B-en will do the work in 12 days + 3 
 
 • " " 12 days + 3 
 
 * " " 12 days + 4 
 etc., etc. 
 
 That is, if we incre(ue the nnmber of men any number of times, we 
 decrease the time the same nnmber of times, i.e., the number of men 
 required to do the work ie inversely proportional to the nnmber of daya 
 and vies vtrta. ' 
 
 Henoa, 1 man : 4 man :; V days ; 12 lays. 
 
 501. The student will obtain from the foregoing illus- 
 trations the following principles. 
 
 i. The product of extremes is equal to the product of the 
 tnenns. 
 
 2. Hence, the product of the extremes, divided by either 
 mean, will give the other mean. 
 
 8. The product of the means, divided by either extreme 
 tcill give the other ertrcme. 
 
 ! I 
 
SIMPLE PBOPOliTION. 
 
 297 
 
 SIMPLE PROPORTION. 
 
 «02. A Simple Proportion is an expressioa of equality 
 between two simple ratios.* 
 
 ExAMri.!, l._Find the term omitted in the foUowing prcport.on 
 a : 16 :; no. required : 48. " r r 
 
 8OL0TION. 
 
 8 X 48 + 16 M 9, no. required. Principle 2. 
 Example 2— If 5 lbs. of sagar cost 60 ota, find the cost of U Iba. 
 
 SOLUTION. 
 
 Her* more require more, {i.e., more weight requires more cost) hcnc* 
 me ooat is directly proportional to the weight. 
 
 .-. 6 lbs. : 11 lbs. :: 60 cts. : required coat. 
 :. required oost » "^6<> « $1.32 Ans Principle 8. 
 
 Example 3.— If 3 men can do a piece of work in 26 days, how 
 long will it take 5 men to do the same work ? 
 
 SOLnTIOK. 
 
 Here more requires leu (i.e., more men require less time to do the seiin* 
 work) hence, the time is inversely proportional to the number of men. 
 
 .-. 3 men : 6 mem :: time reqiiiro.l for 6 men : 25 days (time reouiu'd 
 for 8 men). 
 
 time required for 6 men 
 
 3x25 
 o 
 
 or, 
 
 ■■ 15 days Ana. Principle 3. 
 
 S men : 8 men :: 36 days (time required for 3 men) : no. of u'lvg 
 required, 
 
 .. no. days required » ?4^ = 15 daya. Principle S 
 o ^ 
 
 Example 4.— If 6 men can do a piece of work in 12 davs, in \c!,at 
 time will 4 man do the same work* 
 
 SOLUIION. 
 
 Here U$t requires more {i.e, lois men require more time tn do the same 
 quantity of work), hence the time is invenehj proportional to the numb t 
 of man. 
 
 aiiM), 
 
 8 men : 4 men :: time r(>q:!:r,.,1 for 4 men ; 12 (time rLquireiJ for e 
 
 time required for 4 men = "liii^ « IS days, Ans. l'riaci'.,le t. 
 
1 
 
 li 
 
 ^98 SIMPLE PROPORTION. 
 
 *i ^"^' \Z" *I" *!""" "' '"^ ~"^''''* "" °' '^•«f«"'»* denomination.. 
 they must be reduced to the siune denomination. 
 
 3 If the odd term is a compound number rodnoe U to its lowert unit. 
 8. If the divi.or and dividend contain factor, common to both, cancel 
 
 EXERCISE IIL 
 
 Find the term omitted, and represented by x, in each of 
 the following proportions : 
 
 1. h:52«20:*. 6. »176.35:9, :;|.^ 
 
 a. 12 : X » 1 ; 144. 7. 4j yd. : .r vd. :: m : &27i. 
 
 3.x: 20:: 1-20: 60. 8. x : 9.01 = -16.05 : 5 36 * 
 
 i. m : M - X : 8. . 1,5.05. 
 
 «.aj5:r.2.6::6:* 9.9:01-5:35. 
 
 10. I yd. : xyd. :: »i : »5. 
 
 11. If 12 gallons of wine cost $30, what will 63 gallons 
 cost ? 
 
 12. If 9 bush, of wheat make 2 bbl. of flour, how many 
 barrels of Hour will 100 buah. liiake ? 
 
 18. If 6J bush, of oats cost $3, what will 9i bush, cost ? 
 
 14. Wh It will 87.6 yd. of cloth cost, if IJ y,l. cost |.42 ? 
 
 15. If by selling $1,600 worth of dry goods I gain 
 $275.40, what amount must 1 sell to gain $CoOO ? 
 
 Ifi. What will Hi ,. of tea cost, if 3 lb. 12 oz. cost 
 $3.oO ? 
 
 17. If a speculator in grain gain $26.32 by investing 
 $326, how much would he gaiu by inve.stiiig $2,275 ? 
 
 18. In canning 5 lb. of raspberries 3 lb. sugar are needed, 
 how many pounds sugar for 88 lb. of berries ? 
 
 19. If with the money I have, I can buy 84 lb. of coffee 
 at 25e a lb., how many pounds can I buy for the same 
 moiiev at SOp n lb 9 
 
I 
 
 SIMPLE I'liOl'UliilOS. 
 
 2!>Ji 
 
 20. If wall paper ho 20 inclies wide, I slmll need 7 rolI« 
 to paper a room. How many roll- will s'dU^e if the paper 
 be 24 inches wide ? If 30 inehen wide '} 
 
 21. If $750 will yicl.l C-I-iO interest in a certain timo 
 what interest will $000 yield in the same time ? 
 
 2-2. A man, whose step measurfs J vard, connta ] 200 
 steps from his house to his office. Ilmv ninny steps 'wil! 
 his eon have to take, whose stop mca.HnreH I yd ? 
 
 23. If each man on board ship consumes daily U !>, 
 bread, their bread will last 5} .-months. How much will 
 each man get per day if it is to last ij] months ? 
 
 24. The rate of two pfritstrians is as 5 : 4. How manv 
 miles will the first travel in the Fame time in which the 
 secoud travels 84^ miles ? 
 
 25. At tlK- rate of $180 for vV acre, what will 5 aci. m 
 cost ? 
 
 26. The heat produced by a cubic yard of beech-wood 
 18 to that produced by a cu. yd. of pine as 9:7. How 
 many cu. yd. of boech-wood are needed to produce the 
 beat of 50 cu. yd. of jjine ? 
 
 27. If U yards of velvet cost $5i, what will 9 yd. cost ? 
 
 28. A farmer sowed bush, of buckwheat on 2| acres 
 How much would be need for a field conta. ing 4^ acres V 
 
 29. I of a sum of money is $8U0, huw mucii is | of it ? 
 
600 
 
 coMfoumu mo^oiinoa. 
 
 COMPOUND PROPORTION. 
 
 ,n i 
 
 a08. A Compound Proportion is an expression of 
 equality between two ratios, one or both of which are com- 
 pound. 
 
 Thu8 3:4| ..,.„„. 
 
 6:9/ .. 14 : J8 18 a proportion composed of a cotnponnd and a 
 
 ■imple ratio, and may bo expressed. 3 x 6 : 4 x 9 :: 14 : 28, equivalent 
 to a simple proportion, 18 : 36 :: 14 : 28. 
 
 504. The terms of a proporti ui have not only the 
 relations of magnitude, but also the relations of cause and 
 effect 
 
 505. Causes, in proportion, are considered as things 
 that produce a certain result: as, men at work, money 
 lent, horses, time, etc. 
 
 50«. Effects are the result of causes : as, work done, 
 inte'est drawn, cost, distance travelled. 
 
 i><>7. Every problem in proportion may be considered 
 as a comparison of two causes and t .vo effecL ; these causes 
 and eflfects being themselves either simple or co>aipound. 
 
 Thus if 4 tons of hay as a cause, will bring, when sold, 82 i as an effect. 
 12 tons, when sold, as a cause, will bring $72 as an efeet. Or, if 6 horses 
 »« a cause, draw 10 tons aa an effect, 9 horses as a cau<ie, will draw 15 tons 
 as an effect. 
 
 ^ SOM. S^ivre like causes produce like cfccts, the ratio of two 
 like cnu.'ft'x must equal the ratio of two like effects produced by 
 these causes. 
 
 Ji^^^SKl. 
 
i 
 
 I 
 
 COUFOUSD PROPOHIWN. 
 
 80.1 
 
 Hence every question in proportion must give oue of tbr 
 following statetnents : 
 
 1st cau3e : 2nd cause : : let effect : 2n(l effect. 
 or iBt effect : 2uii etl'oct :: 1st cause : 2ud cause. 
 
 ExAUPLB 1. — If 4 horses consume 24 bashels of oata in 12 days, 
 how many bu^ihela will 20 horsos oat in 16 days 7 
 
 BOLUTIOM. 
 
 Ist canse : 2nd canso ;: Ist effect : 2nd effect. 
 
 4 horses : 20 liortieB 
 lays 
 20 X k; X 2J 
 
 12 days : IG days } ■-* {^^ ^^uah- : No. bush, required. 
 
 160 bush Ans. Prin. 3 
 
 .'. No. bush, required » 
 
 4 X 12 
 
 Es.tMPLR 2.— If 2 workrao-i dig a ditoh 21 yards long and 3 feet 
 widt-. Hud 2 feet deep, in 5 days, liow Ion;,' will it take 3 workmen to di^; a 
 ditoii yO yarda Ion;,', 4 fett vride, and 3 feet deep? 
 
 Solution. 
 l.st ca ise : 2nd cause •; Ist e. feet : 2nd effect. 
 
 30 vards. 
 
 ! workmen : 3 workmen 
 
 ) ( 21 >ard3 
 
 5 days : No days required \ " \ t f^ 
 
 4 feet. 
 8 feet. 
 
 Here one part of the means is missinu, and it may be found by 
 dividing the pi-oduot of the extremes by the product of the given parts of 
 the means. 
 
 , 2 X 5 X 30 X 4 X :^ 
 
 Hence, required time = ^ 
 
 3 X 24 X 3 X 2 
 
 = 8J days. Ans. Prin. 2. 
 
 EXERCISE 112. 
 
 Find the term omitted and represented by x in the fol- 
 lowing proportions. 
 
 « = »^ 40:*. S. .6: xU 136:48. 
 
 3:4f 
 
 480: X) 
 30: 16f 
 
 84 : 31. 
 
 4. 
 
 14: 12/ 
 
 7 : 28) .. 
 13: zf" 
 
 156:54. 
 60:80, 
 3, 
 8. 
 
 6. Five clerks use 25 quires of paper in 8 days. At the 
 s:irao rate, how much paper will 6 clerks use in 10 days ' 
 
802 
 
 COMPOUND PROPORTION. 
 
 6. Six lamps consume 2 gallons of petroleum in 8 days. 
 How many lamps will cou^ume 8 gallons in 12 days ? 
 
 7. Two workmen dig a ditch of 24 yds. in length and 
 8 ft. in width in 5 dpys. How long will it take 8 workmen 
 to dig a ditch 30 yds. long and 4 ft. wide ? 
 
 8. Eight persons spend $296 on a journey of 7 days. 
 How long will $300 last 7 persons at that rate? 
 
 9. If a block of marble 5 ft. long, 8 ft. wide, 2 ft. thick, 
 weighs 4,850 lb., what will a block weigh measuring 7 ft. in 
 length, 4 ft. in width, and 8 ft. in thickness ? 
 
 10. Ten cwt. of merchandise cost $2^ freight for 245 
 miles. What will 5 cwt. cost for 210 miles ? 
 
 11. If $700 at interest amounts to $770 in 15 months, 
 what sum must be put at the same rate to amount to $845 
 in the same time '? 
 
 12. From the milk of 20 cows, each giving 18 qts. daily, 
 16^ cheeses of 50 lb. each are made in 42 days. How 
 many cows, giving but 16 qts. daily, will be needed to make 
 
 • 88 cheeses of 60 lb. each in 28 days ? 
 
 13. Being asked to find the number of bricks in a wall 
 10 ft. high, 922 ft. long, and 16 in. thick, I found that 
 a part of the wall, 4 ft. high, 4 ft. long, and 16 in. thick, 
 contained 448 bricks. How many in the whole wall ? 
 
 14. If $760 gain $202.50 in 4 years 6 months, what sum 
 will gain $15, .52 in 1 year 6 months ? 
 
 16. If it require 1,200 yds. of cloth J wide to clothe 600 
 men, how many yards which is | wide will clothe 960 men ? 
 
 16. If by travelling 6 hours a day at the rate of 4J miles 
 an hour, a man perform a journey of 540 milea in 20 days, 
 in how many days, travelliug 9 hours a day at the rate of 
 4| miles an hour, will ho travel 600 miles ? 
 
i 
 
 I 
 
 t 
 I 
 
 COMPOUND FHOPOMTION. 
 
 K)3 
 
 17. What sum of money will produce $300 in 8 montbB, 
 if $800 produce $70 iu 15 months ? 
 
 18. How many days will 21 men reqtiire to dip; a ditch 
 80 ft. long, 8 ft. wide, and 8 ft. deep, if 7 men can dig a 
 ditch 60 ft. long, 8 ft. wide, and 6 ft. deep, in 12 days ? 
 
 19. How many men will bo required to din; a cellar 45 ft. 
 long, 84.6 ft. wide, and 12.8 ft. deep, in 12 days of 8.2 
 hours each, if 6 men can dig a similar one 22.5 ft. lonj,', 
 17.8 wide, and 10.25 ft. deep, in 3 days of 10.25 hours each ? 
 
 20. If a bin 8 ft. long. [\ ft. wide, ann 2.J ft. deep hold 
 67J bush., how deep luuat another bin he made, that ip 
 18 f long and 85- ft. wide, to hold 450 hush. ? 
 
 21. How long should A. lend B. $1,175, to balance loans 
 from B. to A. of $100 for 8 months, $ 100 for 2 montliH, and 
 $600 for 6 months ? How much should A. lend B. for 10 
 months, to balance these loans ? 
 
if I 
 
 
 i: I 
 
 li:li 
 
 iU4 
 
 viamiiiuuvM tHo.foHnou. 
 
 DISTRIBUTIVE PROPORTION. 
 
 «0». Distributive or Partitive Proportion is ih, 
 
 metliod of d.v.li,,^- rt number, or quantity, into parte which 
 are proportioiiiil to given numbers. 
 
 «IO. Tlie principle of this rule can be applied to the 
 solution of numerous questions of a practical nature, such 
 as determining the protitH and losses of partners in trade 
 apportioning' shares of participators of prize money, finding 
 the relative proportion of ingredients requisite to form a 
 given quantity of a com}.ound. apportioning taxes, sehool 
 rates, averaging, etc. 
 
 Example l._Divido 8600 amons A. B. G. and D.. «, th*t thali 
 •ham may b^ in the proportion of 3. 4, 6 and 6. 
 
 SurrioN 1. 
 8 + 4 + 5 + 6 =18 
 
 18:3 :: f OO : A.'s share 
 18:4 :: StJOO : B. 'a share 
 18 : 6 : : ?(;00 : O.'h slmre 
 18: 6 :: JiiOO : D.a sbaro 
 
 A.'s share =i 8HiO 
 H.'d share = il6i\ 
 C.'s share = §1C6| 
 U. s auare = 8200. 
 
 r.XPI.ANAnoN. 
 
 Altogether there are 18 shares, of which A. gets 3 B 4 C 6 D fl and 
 the probiunuhen becomes: If 18 shan. represent 50OO wh.'tis' represented 
 
 ^.^l Z" ■ "' ' ""' ' '''"''' ' "^y « "'-•'=" ' '^"^-^ «'va rise to 
 the preceding proportions. 
 
 BOWJTION 2. 
 
 A. 3 shares 
 
 B. 4 " 
 
 C. 6 •• 
 P. 6 " 
 
 Total IS'sharei. 
 
 18 shares m $600 
 .'. 1 share E tsia 
 
 A. gets 3 shares = ^ x 8 » 9100 
 
 B. fjets 4 shares » ^ x 4 a 8133J, 
 
 pto 
 
i 
 
 A. 8 sharM 
 D. 4 " 
 
 C. 6 " 
 
 D. 6 " 
 
 mSTRlBVTlVE rnurOHTION. 
 
 Hi'LOTIOIl 8. 
 
 A. K'ts A "' *''» wliole and /. ^ of »C00 
 B- (i«'* A of the vrholo and .•. ,\ of JCOO 
 eta 
 
 808 
 
 • 100 
 
 ToUl 18 aharei. 
 
 The Btndeat ii reooinmendod to nu either tho second or third method 
 of ■oliition 
 
 EzAMPU 3 -Divide »2,(J00 amorif,' A., B.. C., no (liut B. may h»v« 
 •dOO more than A., and C. faoo ni..ro tliun B. 
 
 Solution. 
 A.'e Bimre m A.'i share 
 B.'s sliaro = A.'e share + ' lOO 
 O.'b Bliare a A.'b gli are + S:;oo + f'iOO 
 Total 3 8 titiicH A.V share + «bOO 
 .% 8 times A.'b Blmro + 8800 » 8i'.000 
 A 8 " " a ?l,200 
 
 /. A.'b share = 8100 
 
 B.'c share a '•HO + $:V)ii m |700 
 O.'b Hharc a $700 -«- 8 00 a (900. 
 
 EXERCISE tl3. 
 
 1. Divide f 60 into two parts proportional to 11 and 9. 
 
 2. Divide $2,500 into parts pn i^ortionii! to 2, 3, 7, 8. 
 
 8. Divide $8,470 into parts proportional to ^, J, ^and ^. 
 
 4. Gunpowder is made of saltpetre, sulphur and charcoal 
 In parts proportional to 75, 10 and 16 ; how many pounds 
 of each are contained in 12 cwt. of gunpowder ? 
 
 5. The sides of a triangle are as 3, 4, 5, and the sum of 
 the lengths of the sides is 480 yards : find the sides. 
 
 6. Divide $040 among A., B. and C, so that A. may have 
 three times as much as B., and C. as much as A. and B. 
 together. 
 
 7. Divide the number 682 into 4 such parts that the 
 ■econd may be twice the first, the third 21 more than the 
 Becond, and the fourth 54 more than tho first. 
 
 «■■■ 
 
1 
 
 m-^ 
 
 n^' 
 
 
 t 
 
 
 
 
 
 i 
 
 
 \ 
 
 * 
 
 i 
 
 :i '■ 
 
 I ■ 
 
 l| , 
 
 
 V' 
 
 1 
 
 I'll • 
 
 
 . 
 
 
 
 
 I 
 
 
 
 
 i 
 
 
 i 
 
 
 
 
 i! 
 
 
 
 
 { 
 
 
 ■ ; 
 
 
 w 
 
 
 
 1 
 
 i I 
 
 1 
 
 i^ 
 
 |; 
 
 I! , 
 
 1 ^ t 
 
 t 
 
 ) 
 
 i 
 
 
 
 
 I 
 
 i • 
 
 if 
 
 
 ; 1 
 
 
 1 ' 
 
 j] 
 
 
 t • 
 
 
 1 
 
 ■ : 
 
 ' 
 
 
 i 
 
 
 ■ i ^ 
 
 '•i 
 
 f 1 . 
 
 
 u Z 
 
 |Bt . 
 
 '^f [ 
 
 'Si 
 
 t f ( ■" 
 
 ... r 
 
 iiil 
 
 L 
 
 "^H^H 
 
 eo«< 
 
 DlSTHlUVnVK PHUl'O li 1 1 ' >S 
 
 H. If G. has twice nu tnucli money iiB li., and if $12 be 
 taken from A.'s monty, it will bo equal Id J of B.'h ; how 
 mucli Ims encli, the r<um of thuir inonnyH boini? $♦> 15 ? 
 
 9. A man ii;ft his property to be divided anioiiR his 8 
 Hons in proportion to tliiir a<^OH, wliich are 21, 18, and 12 
 years. The nliare of the youngest is $1,-110. What wa* 
 the value of the property? 
 
 10. A., B , C, and 1). coiutnoncod bufliness with a capita* 
 of $18,500 ; A. invested $SUO less than B., and C. invested 
 $1,000 more than A., and D. $UUO loan than C. ; how mutih 
 did each invest? 
 
 11. rivide 560 into parts, so that the second may br 4 
 times the tirst. 
 
 12. A force of police 1,921 stronfr i^ to be distributeu 
 among i towns in proportion to the number of inhabitants 
 in each; the population bein;? 4,150, 12,150, 21,U00, and 
 29,050 respectively. Determmd the number of men sent 
 to each. 
 
 13. Divide 450 shares of stock among 8 persons, in pro- 
 portion to the number of shares owned by each ; A. holds 
 400, B. 200, and 0. 300; how many shares will each 
 receive ? 
 
 14. A piece of land of 200 acres is to be divided among 
 4 persons, in proportion to their rentals from surrounding 
 property. Supposing these rents to be j£500, £850, £800, 
 and £90, how many acres must be allotted to each ? 
 
 16. If 9 of A.'s money, and 5 of B.'s equal $900, and \ 
 of B.'s is twice f of A.'s, what sum has each ? 
 
 16. A father divided $18,500 among 8 children, so that 
 the portion of the second was greater by one-half than tbai 
 of the first, and ^ the first was equal to i of the thud ; 
 what was the share of each ? 
 
 ^^^ 
 
PAhiskusuii-. 
 
 ao7 
 
 PARTNERSHIP, 
 
 Sll. A Partnership is lui nf-Hociation of two or mort 
 persons, who coinbino llioir cnpittil, Hkill or lahor, or all of 
 them, for the purpose of carrying' on rfome lawful ItiiHitusH. 
 and for particii)ivting in tlu; profits or Iohhob arisiii}^ there- 
 from, according to the tertiis of thuir aureemout. 
 
 5H8« The husinesB association is called a Firm, Home, 
 or Company .- and each iu(hvidiial of the addociatioa is 
 called a Partner. 
 
 •'tis* Partiiers may be claBsiliud as — 
 
 1. Active partiurs. 
 
 2. Silent or dormant partneri. 
 8. Nominal partners. 
 
 4. Special partners. 
 
 914. An Active Partner is one who has an interest in 
 the business, and is known to the public as a partner. 
 
 51S. A Silent or Dormant Partner is one who has an 
 
 interest in the business, but is uukuowu to the .c as a 
 partner. 
 
 510. A Nominal Partner is one who allows his name 
 to be used for the benefit of the firm, without having any 
 pecuniary interest in its business. 
 
 517. A Special Partner is one who is held liable for 
 only a specified amount. 
 
008 
 
 PAHiaaHiimt. 
 
 t%lH, In an on^nary piirtnorship, each mcmher is liablt 
 to the full extent of his m<aiiB for the liabilitieB of the 
 firm ; but in a joint stock compauy, each slmreholtlor is 
 liable only for the amount of his unpaid capital. This 
 exj)Iain9 the meaning of the term "Limited," which is 
 addcil to the uainefl of companies, as for exaiuple, " The 
 Canada Publishing Co." (Limited). 
 
 5I1>. Capital is tli" money or property invested in the 
 biisineM. 
 
 ffao. The Resources or Assets of a firm consist of 
 the property it owns and the debts duo the firm. 
 
 521. The Liabilities of a firm embrace all the debts 
 or obligations due by the firm to its creditors. 
 
 532. The Investment is the aggregate of the money 
 or property jointly contributed by the partners. 
 
 H2li* The Net Capital is the excess of the Assets or 
 Resources over all Liabilities. 
 
 5a4. The Net Insolvency is the amount which the 
 lialtilities exceed the rusuurces. 
 
 sa.l. The Net Investment of a firm is the difference 
 between the total sum invested and the total withdrawals. 
 
 520. The Net Gain is the excess of the gains over 
 the lossca, during i. certain time. 
 
 527. The Net Loss is the excess of the losses over 
 the gains, during a certain time. 
 
 528. A Partnership Settlement is an adjustment of 
 the partners' accounts setting forth the net invoatment, 
 liabilities assumed, withdrawals, gains, losses, and ^ .sowing 
 his net capital or net insolvency at closing or settiing the 
 partnership's interests. 
 
 f^m^ 
 
PARTSKRSUIP. 
 
 30l> 
 
 029. To divide the Gain or Loss, when each part- 
 ner's capital has been employed for the same period of 
 time. 
 
 EXAJOU.— A. and B formoil a pnrtncrHhip; A. farniihed l.i.OOO, 
 B. IB.OOO; they «aine<l -.'JOOO, aii.l »^'rc-^>.l to •haro tli.> proflt or \oa» ia 
 proportion »o khu onpital ot each ; what wan «M>h piituor'i Kbar«7 
 
 HoLi-Tri)-*. 
 
 ,1.000 
 = ,'.,u(iO 
 
 Total " a $H,000 
 
 .". A. farnishfis J'!!} or ) of (Mpital. 
 
 " " l;::iJorj 
 
 .'. A.'r ttl.aro of gkin a g of Ji.ooO :3 JTr.O. 
 
 B''« " = S of y2,UU0 a 81.260. 
 
 or, 
 
 ToUl gain (S-'.OOfl) ^ j';?j or ^ .f raivital a .2.- „f oapi|»L 
 
 .•. A.'e sliaro of tjuiu = Sil.ooo x .2'> - *7.')0. 
 
 B.'i " a 95,UuO < .25 -. »1.3.'/ 
 
 A.'i oapitiil 
 n.'s " 
 
 EXERCISE 114. 
 
 1. A. and B. hny a Btore which roots for $or^0 a year ; 
 k. advance<l $3,500, B. $1,800; how much rent should 
 each receive ? 
 
 2. A. and B. form a partnership, A. furnishing' $'2,'J00 
 mkI B. $'2,500: they lose .^800; what is each one's <!iare 
 of the lc3s ? 
 
 3. A. put .$7,500, and B. §f5.000into a land speculation : 
 md A.'s share of the loss was .:?i-2.") ; what was B.'s share? 
 
 4. Two men formed a partnership, the former furnisiiing 
 5 times as much capital as the latter : thoy gained .$12, .'^OO ; 
 ^hat was each one's share of the gain ? 
 
 5. The net Kxins of A., B., and C. for a year are $12,800; 
 A. furnishes $2.5,000, B. $lb,000, and C. $15,000; how 
 »bould the profit be divided ? 
 
mi: 
 
 t •! 
 
 i 
 
 M 
 
 -inv 
 
 810 
 
 PARTNERSHIP. 
 
 6. X., Y. and Z. bought a Bliip on speculation ; X. put in 
 $30,000, Y, $20,000, and Z., $15,000: they sold it at a loss 
 of $7 ■:>'.' , ■;vi.iit was each man's share of the '-^ss ? 
 
 7. A.. B., C, ar ■. D. form a partnership with a capital 
 of $..7,000; A. f .rnishing .$10,000, B. 12,000, C. $5,000, 
 and 1). the rem.Jnder ; they gain 15 % of the joint stock ;' 
 what ip each partner's share of ^lie profit ? 
 
 8. A., B. and C. entered into partnership ; A. famishing 
 }, B. J, and C. the rest of the capital. On winding up the 
 husin.s.s, C.'s share of the profit was $4,518; what were 
 the respective dividends of A. and B. ? 
 
 9. A. invested $12,000 and B. $8,000 in a business. 
 A.'s share of the gain or Iosh is to be 5 and B.'b ^. At the 
 Close of the year their resources are $25,000 in goods and 
 ca.h, and liabilities $15,000; what is the net capital, and 
 what each partner's share of the gain or loss? 
 
 10. Four persons enga',-e in the lumber trade, and hivest 
 jointly $22,500; at the expiration of a certain time A 'b 
 Bhare of the gain is $2,000, B.'s $2,800.75, C.'s $1,085.25, 
 and D.'s $1,014 ; how much capital did each put in ? 
 
 11. Three persons enter into partnership for the manu- 
 facture of coal oil, with a joint capital of $ 18,840. A. puts 
 in $3 as often as B. i.uts in $5, and as often as C. puts in 
 17. Their annual gain is equal to C.'s stock ; how much 
 is eacV' partner's gain ? 
 
 12. A., B. and C. are employed to do a piece of work 
 for $26.45. A. and B. together are supposed to do f of the 
 work. A. and C. ,\, and B. and C. H, and are paid pro- 
 portionally ; how much must each receive ? 
 
 13. Three men trade in company. A. furnishes S8 000 
 and B. $12,000. Their gain is $1,680, of which C.'s share 
 u $800 ; required, C.'s stock, and A.'s and B.'s gain 
 
 !^^^^^^5y^-^T3TT>k^!T^^T^ 
 
 ^:';v' 
 
cARTKEJiSUIP. 
 
 811 
 
 14. Sis persons are to share among them $6,300 ; A. ia 
 to have | of it, B. ^, C. t, D. is to liave as much na A. ana 
 C. together, and the n^miiiniler is to be dividtil botwci n E. 
 and F. in the ratio of 3 to 5. How much does each receive ? 
 
 16. A., B. and C. form a company for the manufacture 
 of woollen cloths. A. puts in i- 10,000, B. $12,800, and C. 
 $3,200. C. is allowed $1,500 a year for personal attention 
 to the business ; their expenses for labor, clerk hire, and 
 other incidentals for 1 year are $;]. 100, and their receipts 
 during the same time are $9,400. Wliat is A/s, B.'s and 
 C.'s income respectively from the busiuesB ? 
 
 530. To divide the gain or loss according to the 
 amount of capital invested and time it is employed 
 
 Example.— A.. B. and C. are partners in a business; A. invested 
 ♦3,0")0 for four years, B. iuvesteil 55,000 for three years, and C. invested 
 •4,500 for two years. IIow should a uain of §18,000 be divided ? 
 
 Solution. 
 A.'b investment of 93,000 for i yrs. = an investment of Sl'i.OOO for 1 yr. 
 B.'b " 85,000 for 3 yrs = " $15,000 " 
 
 C.'b " 84,500 for 2 yrs. = " } 9,000 •• 
 
 Total investment « 836,000 " 
 A furnishes i\ of investment .-. his gain = ,«, of 818,000 = 80,000. 
 B' " A " .-. " = A of 818,000 = 87,500. 
 
 C- " A " .-. •• = A of 618,000 = S4,.';00. 
 
 or, 
 Total gain ($18,000) = H?H or i of investment = .5 of investment. 
 .-. A.'s share of gain = 812,000 x .5 = 80.000, 
 B.' " . 815,000 X .5 = «7,.500. 
 
 C " a 9 9,000 X .5 « 84,500. 
 
 RULE. 
 
 Multiply each partner's capitd bit the time it if. emplf^i/fd, 
 consider these products as their respective capitals and pro- 
 ceed at in Art. 5Sf) 
 
»■! 
 
 
 
 m 
 
 tjia 
 
 PABINKRSUIP. 
 
 EXERCISE t15. 
 
 1. A., B. and C. form a partnership; A. furnishing 
 $8,000 for 9 months, B §3,400 for 10 months, and C. 
 $2,800 for 15 months; they lose |3,200; what ia each 
 man's share of the loss ? 
 
 2. January 1st, 188!>, A., B. and 0. form a partnership ; 
 
 A. puts in §3,000, but after six months withdrew $2,000 '; 
 
 B. puts in $6,000, and adds $500 after 4 months ; G. puts 
 in $4,000 for the year; they gain 5^3,600; what is the 
 share of each ? 
 
 3. Three men hire a pasture for $175. A. put in 20 cows 
 for 7 months, B. 120 sheep for 5 months, and C. 24 horses 
 for 8 months ; 5 sheep being considered equal to 1 cow, 
 and 4 horses equal to 5 cows ; how much should each pay ? 
 
 4. A. and B. are pnrtners, A. putting in $4,500 and B. 
 $2,500; after 6 months they take in C, who furnished 
 $10,000 ; their gain for the year was $5,000 ; what was 
 the of each ? 
 
 5. > , ^. and Z. formed a partnership; X. puttinf^ in 
 $8,000 for 1 year, Y. $4,500 for 8 months, and Z. $5})c0 
 for 6 months; they lost $4,000; what was each man's 
 share of the loss ? 
 
 6. A. and B. formed a partnership and divided the gain 
 or loss in proportion to their average investments. A. put 
 in $C,000 for 12 months, and afterwards $4,000 for 6 
 mouths. He withdrew $3,000 for 4 months, then $0,000 
 for 2 mouths, before the close of the partnership. B. put 
 in $7,000 for 12 months, then 6,000 for 8 months. He 
 withdrew $4,000 for 5 months, then $8,000 for 2 months. 
 They gained $4,560 ; what was each partner's share ? 
 
 7. A., B. and G. began business Jan. Isfc, when A. put 
 in $7,500, and July 1st he put in $2,500 more ; B. put in 
 
 'i»d«!^M^siii»>«K»ir«nFt 
 
.J ,-.v 
 
 i 
 
 PAIiTSERSHlP. 
 
 313 
 
 Jan. 1st $12 000, and l\n.y Ist withdrew $4,000 ; C. pi t in 
 Jan. 1st $10,000, Aug. l-,t ho acMed §3,000. au.l Oct. Ui he 
 withdr. w $7,000. At the close of the year the profit was 
 $_8,o()() ; how mucb ought each to hnve, the gains being 
 divided according to their avenige iiiveatmeut ? 
 
 8. Howard & Salter commencod business with a capital 
 of which Howard furnished $2 to Snlter's $1. At the end 
 of 3 months, Howard withdrew half of his capifal, and 
 Salter increased his 25%. At the end of 9 montlis,' th.-y 
 had $3,150 to divide. What was the share of each ? 
 
 9. Mills, Ross and Mo Adams, haviii^' been in partner- 
 ship for one year, under an agmm-nt to divide the profit 
 proportionally to their respective sliiuea of capital, have 
 made $2, 103. On the first day of the year, each put in 
 $10,000 ; but Eoss in 4 months withdrew 20% of his sliare, 
 and M.'Adams at the end of six months put in $2,000 more.' 
 Find each partner's share of the profit. 
 
 10. E. E. Walker and John Lawson engaged in a lumber 
 business on January 1st. 18S9. Mr. Walker investrd 
 $6,000. and Mr. Lawson investeci $o,000. On Marcli Ist, 
 Mr. Lawson trade an additional investment of $;5,0()0, and 
 Mr. Walkrr withdrew $1,500. July 1st, Mr. Walker 
 invested $2,'.'00, and Mr. Lawson witiwlrew $:5,Ono. 'I l,o 
 profits for the year were $-1,620. What was eacii partner's 
 average inv( stment and share of the profits, if the ])xoUUi 
 were divided in proportion to the capital invested and the 
 time it was employed ? 
 
 11. S. Morgan, J. R. Street and R. C. Cheswrinht formed 
 a co-partnership, and invested respectively, $9,(;<'0, $8,100 
 and $7,200. At the end of four months, Mr Mor-an 
 invested $2,000, Mr. Street $1,400, and Mr. Cheswrigbt 
 $800. The net profits for the year were $12,600. What 
 was each partner's share, the gains and losses being divide] 
 in proportion to their average investments ? 
 
 wmm 
 
 'lix'-.U. jr.*A,. 
 
 y-srujiz 
 
 -i^ • 
 
,i 
 
 tl'i 
 
 
 314 
 
 PARTNEliSIIIP. 
 
 12. Three men take an interest in a coal mine. B. 
 invfBts his capital for 4 months, and claims ^^ of the pro- 
 fits ; C.'s cajiital is in 8 montlis ; and D. invests $6,000 
 for 6 months, and claims | of the promts ; how much did 
 ii. and C. put in? 
 
 18. A. and ]i. are partners. A.'s capital is to B.'s as 6 
 to 8 ; at tlio end of 1 months A. witiidraws ^ of his capital, 
 and B. f of his ; at the end of the year their whole ga'n is 
 $4,000 ; how much helongs to each ? 
 
 14. Three men ttigago in trade. A.'s money was in 10 
 months, for which tie received $ 156 of the profits ; B.'s was 
 in 8 months, for which Im received $342.20 of the profits ; 
 and C.'b was in 12 montlis, for which he received $750 of 
 the profits. Their whole capital invested was $14,345 ; 
 how much was the capital of each ? 
 
 15. A., B. and L. engage in manufacturing shoes. A. 
 puts in $1,920 for six months ; B. a sum not specified for 
 12 months ; and C. $1,280 for a timo not sp-'cifud. A. 
 received $2, 100 for his stock and profits, B. $ 1,800 for his, 
 and C. $2,080 for his. Required, B.'s stock and C.'s time ? 
 
 16. B. commenced business with a cai)ital of $15,000. 
 Three mouths afterward C. entored into partnership with 
 him, and put in 125 acres of land. At the close of the 
 year their profits were $4,500, of which C. was entitled to 
 $1,800 ; what was the value of the land per acre ? 
 
 17. B., C. and D. form a manufacturing company, with 
 capitals of $15,800, $25,000, and $30,000 respectively. 
 After 4 months, B. draws out $1,200, and in two months 
 more he draws out $1,500 more, and four months after- 
 wards puts in $1 ,000. G. draws nut $2,000 at the end of 
 6 months, and $1,500 more 4 months afterwards, and a 
 month later puts in $800. D. puts in $1,800 at the end of 
 
PARTKKIiSUlP. 
 
 S15 
 
 7 months, and 8 months after draws out $5,000 If tlioir 
 gain at the eud of 18 montlis bu $15,000, how much sliould 
 each receive ? 
 
 18. July Ist, 1886, A. and B. coramrnp ,1 businesa with a 
 capital of $7,500, for wliicli A. furnishe.] i and B. tho 
 remainder; May It^t, 1887, B. invested l?l,5()(), and A. with- 
 drew $000 ; Oct. 1st, 1887, they admitted C. as a iKirtm r, 
 with an investment of $-l,50i) ; Jan. Ist, ls88, eacli jiai-tuer 
 invested $1,000, and on Jan. 1st, 18^1), yacli [.aitner with- 
 drew $500. On closing Inisine.ss, Oct. 1st, 1889, it is found 
 that a net loss of $3,000 has been sustained. Find eacli 
 partner's proportion of the loss. 
 
 19. Gih^^on and Montague dissolved a three-years part- 
 nership Aug. 1st, 1888, having resources of $16,500, and 
 liabilities of $2,! 50. At first Gibson invested $2,750, and 
 Montague $2,500; at the end of the first year Gibson drew 
 out $1,500, and Montague invested $3,000; six months 
 later each invested $1,200. No interest account being 
 kept, what has been the gain or loss, and the share of .ach 
 partner, if apportioned according to average iuvestineut-i ? 
 
 20. Day, Scott and Garruthers, each invested $15,500 in 
 a business that gave the firm a profit of $21,000 in one 
 year. Nin- months before dissolution, Day i)icreased his 
 invcstmeni $:$,()00, and Scott and Carrnth.-rs eacli with- 
 drew $3,000; six months before dissohition, Scott invested 
 $2,000, and Day and Carruthi;rs each drew out $-2,()00; 
 three months before dissolution, Carruthv^rs invested 
 $1,000, and Day and Scott each drew out $1,000. If no 
 interest account was kept, and the gain be divided according 
 to average investment, what is each partner's share ? 
 
 21. A. and B. formed a eo-partncr.ship for 3 years. A.. 
 investing $7,200, and B. investing $5,400. At the end 
 of 6 months A. increased his investment by $1,500, 
 
 m 
 
816 
 
 PARTNEBSHIP. 
 
 and B. withdrew $900 ; one year before the expiration 
 of the partnership, each withdrew $1,000, and six monthi 
 later each invested $500. The net loss was $2,400. How 
 much F'lould bo sustained by each, if the partners receive 
 credit for interpat at the rate of 6 % on all investments, 
 and are charged interest on all sums drawn out, and the 
 loss be sustained in proportion to average investment ? 
 
 22. April Ist, 1881, Craig and Cowan commenced business 
 as partners, Crai;,' investing $8,000, and Cowan $6,000 ; 
 six months later each increased his investment $1,500; and 
 on Jan. Ist, 1885, Allan wan admitted as a partner with an 
 investment of !$2,400. On Oct. 1st, 1885, each partner drew 
 out $1,500 ; on Apr. Ist, 1886, Craig and Cowan each drew 
 out $1,000, and AIIlu invested .'?(),000. On Jan. Isi, 1889, 
 it warf found that a net gain of $37,500 had been realized. 
 What was the share of each, if by agiooment Craig, at final 
 settlement, was to be allowed $1,200 per yenr for keeping 
 the books of the concern ? 
 
 
 531. To find the net gam or loss, the net resources 
 or the liabilities of a partnership. 
 
 F.YAMPT.K 1, — A. and B. oomracnced business with a capital of 
 ?10,000 cash ; merchandise as por inventory, 95,000 ; bills payable, SI, 500. 
 At the end of the year they had cash $6,500 ; merchandise as per inven- 
 lory, 95,400; bills receivable, 93,200; Jubt» owed by firm, 9G50. What 
 was the net gain or loss of the firm ? 
 
 S 
 
 OLCTIOS. 
 
 ASSETS AT COMMENCBMENT. | 
 
 Cash .. 910,000 I 
 
 M'dso 5.0 00 i 
 
 Total Assets 915,000 ' 
 
 Liabilities l.'OO | 
 
 Net Capital 913,500 j 
 
 Net gain » 914,450 - 
 
 ASSETS AT CL0S8. 
 
 Cash 96,500 
 
 M'dse 6,400 
 
 Bills receivable .. .. 8,'JOO 
 
 Total Assets 915,100 
 
 Liabilities 650 
 
 Net Capital 9U.460 
 
 $13,500 = ?I,950. 
 
PARTNERSHIP. g-_ 
 
 ErAMPLi a.-A. and II. .re part.iers, A. sharinR § of the cain or 
 loe. w.a H J. A. invests »5,000. and H. S2,3.^0. At the en,l of the yc*i 
 thmr peaourocs and liabilitioa are as follows : merchandise on htnd ai 
 per inventory, ga.OOO; real estate. 87.000; cash on hand and in bmk, 
 • 1532; due on personal accoants, «l.f,.10.25; bills receivable. 91 000 • 
 bills payable. »800 ; owing by the firm to sundry persons $4,471 6» 
 What IB the amount of not resouroea belonging to each partner ? 
 
 Solution. 
 nsorncKs. 
 
 M'd-JO. on Imiiil 82, 001. 00 
 
 Beal estate 7 ooq aq 
 
 Cash on hand and in bank .. l,53a.00 
 
 Personal account 1.040.25 
 
 Bills receivable 1000.00 
 
 Bills payable J'iOO.OO 
 
 Personal accounts 4,471.00 ?r, 271.89 
 
 Present worth 87,900.56 
 
 Less investments 7,H.j0.00 
 
 Total net gain ~uioM 
 
 I of Sr,50 50 = nciM, A.'s sl:are of gain. 
 i of ?5.30.56 m ?is;i.52. n.'.s '• 
 
 A.'s investment a« 85,Ono.OO 
 
 A.'s gain.. .. s 307.01 
 
 A.'s present worth 85,367.04 
 
 B.'s investment = 82,3.50.00 
 B.'s gain . . . . . ib;j.52 
 
 B.'s present worth J?2^533.62 
 
 Present worth iia before .. .. 87,900.56 
 
 «»2. To find each partner's interest, when eacii 
 partner is allowed to withdraw a certain sum, and when 
 no interest account is kept. 
 
 ExAMPLK.— A. and B. are partners, each Invested 86.000, and 
 »greed to share the gains and losses equally. A. drew out 81,200 and B 
 11,000. Required their gains at the end of the year, their booki 
 •bowing the following result : 
 
818 
 
 PARTNERSHIP. 
 
 BtsonaoM. 
 
 OmL 17.000 
 
 Mdaa. per {nventory . . 7,200 
 
 Bills receivable 3,400 
 
 Debtaduu firm as per lodger 6,000 I 
 Total retiource* .. .. 921,t>U0 I 
 
 Net capital at oloaing, UifiOO - 14.600 
 A. invested 96,000 
 
 A. withdrew 1,200 
 
 A.'b credit balance 84.800 
 
 B. invested fO.OOO 
 B. withdrew 1,000 
 
 "" »5,000 
 
 LUniUTIKI. 
 
 Debt! firm owe aa per ledger W 000 
 
 Bills payable « 1,600 
 
 Total liabilitioa 94,600 
 
 917,000 
 
 B.'s credit balance 
 
 Net gain of firm . . 
 A.'s i uet gain ^^ 93,600 
 B.si " - 93,600 
 
 99.800 
 97,200 
 
 PROOF. 
 
 A. InTested.. .. .. .. 86,000 
 
 A. withdrew 1,200 
 
 94,800 
 
 A.'8 i netga,,; S.COO 
 
 A.'s net capital at closing (18,100 
 
 B. invested 96,000 
 
 B. withdrew 
 
 B.'b } net Rain 
 
 B.'b net capital at closing 
 
 $8,400 + S8,600 3> $17,000, firm's net capital. 
 
 1.000 
 
 t.5,noo 
 
 3,(ji^ 
 98,600 
 
 i-i)i 
 
 53S. To find each partner's interest, when one or 
 more partners are allowed a fixed salary and no interest 
 arcoimt is kept. 
 
 ExAifPLE. — A., B. and C. entered into partnership January Ist, 
 1899. A. invested 914,000, B. 914,000, and G. 928,000. A. to share i of 
 the gains and losses, B. ^, and C. }. A. was to receive a salary of 91,000 
 per yoar. B. 91,200. and C. S600 for BerTioes. A. drew out 91.300, B. 
 9900, and G. 91,800. What was each partner's interest in the firm Jan- 
 nary Ist, 1R90, when their resources were 8108.000, and their liabilities 
 927.000? 
 
i 
 
 000 
 
 600 
 SOO 
 
 000 
 000 
 000 
 ()|,0 
 600 
 
 or 
 
 :st 
 
 iBt, 
 
 : of 
 
 000 
 B. 
 
 an- 
 
 tiea 
 
 PARTSKliSUU: y^y 
 
 SOLOIIUM. 
 
 ffT"'":."" iioH.ooo 
 
 ^**'"''"" _a7,ooo 
 
 Firm's net c:ii>ital 181000 
 
 A.'« investiueiil 914,000 
 
 *«"«f'''»ry _um 
 
 815,000 
 ijeag iiinonnt witliJrawn .. L.'JOO 
 
 A.'a credit balntica H3 700 
 
 B. '8 investment .. ,. .. fU.ooo 
 B.8 salary I'^oo 
 
 |1">,..'00 
 Less amount withdrawn .. <jOO 
 
 B. 'a credit balance 614,300 
 
 C.'b investment 828,000 
 
 O.B salary (;oo 
 
 828,000 
 Less amoant withdrawn .. 1,800 
 
 8-'';.800 854,800 
 
 Firm's net gain ^:^ 
 
 A.'a credit bal. 813.700 I n.'soredit bal. ?M,H00 1 O.'a crHit bal. 826 800 
 A. '8 t gam . . 6,550 U.'s i gain . . ,5.550 i O.'a i t;..!,, . . is'lOO 
 A.'a net capital |20.25U I B.'s net capital .?L'0,«,^0 i C. n«t oap.Ul 8^9:^) 
 
 PKOor. 
 
 A.'a net capital %\lO,->r,Q 
 
 B.'8 " 20,850 
 
 O.'s " 39,tiOO 
 
 Firm's net capital ?Rl,(HiO 
 
 5»4. To find each partner's interest at the end of 
 the year or close of partnership when amounts with- 
 drawn are averaged, and interest is charged and 
 allowed. 
 
 EXAMPU.— A. and B. entered into partnership January ist 1889 
 and agreed to ahare the gains or losses eqaally. A. invested 86 and 
 B 87,250; each partner was allowed 6% on hia investment and' wa« 
 chwi«d 6% for the sums withdrawn. A. drew aa follow«: M..rcV. U% 
 8300; July 9th. 8250; September 10th, S'-'OO; December 18th 8150.' 
 B. drew. AprU 17th. JICO ; August 4th, 8400 ; November 23rd' f25a 
 What was each partner's interest in the buainess Januarv ist. 1890 thtiv 
 T »Dd liabilities being aa foUowa : 
 
 <AJ i"-' 
 
 sw^^ 
 
8-20 
 
 PAIiTNEIiSUlP. 
 
 KE80UR0Et< 
 
 Cash »!.«"« 
 
 I'orBonril <lobti due firm .. 8,<i()0 
 
 Dills rcoiivablo 700 
 
 M'die. as per inventory .. 13,000 
 
 O. P. H. Uailwiiy Stuck . . 3,00> 
 
 Total run .urcus .. ..SJi1,'>00 
 
 TcrBonal (l.btH Ann 0W8 . . 16,750 
 
 HilUpayal.lu _ 2r)0 
 
 Total liabilitie* Jfi.OOO 
 
 Finn's net capital 
 
 I'JO.-OO 
 120,^00 
 
 From 
 
 fioirttoN. 
 A.'s r.m.mt withdrawn »000 ; uvora^o date July 7th. From July 7th 
 to Janmuy Ut = 17B days. 
 
 B.'a amount withdrawn »750; average date Au-ust 37th. 
 Auj-Uflt 27tli to January Ist ■ 127 days. 
 
 A.'s invistimnt 
 
 Less witlidriwn 
 
 Int. on iii\\v,tnient for 1 year .. 
 Less int. on §'.tOi) for IT'^ da. at f.% 
 
 ecooo.oo 
 
 '.(OD.O) ^5,100.00 
 
 t;ii;o.oo 
 
 •2iV.'?3 
 
 333.G7 
 
 A.'s credit balance »5,J;i:i.07 
 
 B.'s invi'f<tnii!iit •• 
 
 Less witlidrawn 
 
 Int. on invcattnent for 1 y(!iir .. 
 Lf^.^ int. on :750 for 127 da. ot G% 
 
 B. '8 credit balance 
 
 Firm's net capital 
 
 A.'s credit balance 
 
 U.'s " 
 
 Firm's net u'ain 
 
 87,2.')0.00 
 
 7:.0_00 Sn.r.OO.OO 
 
 ' 6i;i5.00 
 
 15.6G 419.34 
 .. .. 86,019.34' 
 
 520,500.00 
 
 ^.5,i:!:!.07 
 C'Jl'.cU ^_12.3.V1.01 
 
 A.'b credit balancu 
 A.'sjyain.. .. 
 A.'b net capital .. 
 
 8."j,i;i:?.r)7 ( B.'s credit balance.. ..86,919.34 
 
 4,073.1'.).i 
 
 B.'b i f^ain 
 B.'a net capital 
 
 ..?'I.'.07 101 
 Firm's net capital §20,")00. 
 
 4,073. i.; J 
 «10.992.83i 
 
 EXERCISE 118. 
 
 1 At the expiration of a year from the commencoTnent 
 of their business, Baker, Morgan & Co.. after taking an 
 account of stock, find the amount of merchanaise, aa per 
 inventory, to be $17,450; cash on hand, $10,250; debts 
 due the firm, $11,300; amount of firm's indebtedness, 
 
 U.iW'r*' J, 
 
 4? '■^:.y.'»'J^:;,r...- 
 
■I :. 
 
 y^e^^M4^.j:^..Mm 
 
 pauhhEUsuip. 
 
 321 
 
 750 
 
 2.')0 
 
 000 
 
 ;.uo 
 
 7tl. 
 
 rom 
 
 9.R4 
 
 i.v.;.j 
 
 2.83i 
 
 nent 
 J an 
 
 per 
 lebta 
 aess, 
 
 $15,600. Make out a stattMnent, sbowinR the resourcea 
 and liabilities of tbe firm, with net capital and gain ; and 
 find each partner's share of tbe litter, the respective 
 shares of capital being as follows: J. iiakor, $8,000; S. 
 Morgan, $5,000 ; and J. Murray, $3,000. 
 
 2. A. put $10,000 into a partnorsbip and B. $5,000. 
 Thoy agreed to divide tbe t^iiin or loss in proportion to 
 their original investments, and to keep no interest account. 
 During the year A. withdrew ;?80r> an 1 U. $500; what was 
 the net capital of eiM'li at the close of the year, their 
 resources bein;,' $25,800 and th>-ir liabilities $18,500 ? 
 What per cent of their investm •nt was the gain or loss ? 
 
 3. J)uff, Fry & Rowat became partners, each investing 
 $15,1 00, and eacb to have one-thinl of tin gaim or sustain 
 one-third of tbe lonsea. Dull withdrew $2,100 during tbe 
 time of tbe partnership, Fry $1,800, and Uowat $2,0(;0. 
 At close of business their resources were : cash, $3,5i0 ; 
 m'lse., $1 1,785; notes, acceptances, and accounts receiv- 
 able, $U), 250 ; real estate, $28,500. They owed on their 
 outstanding notes $8,125, and on sundry personal accounts, 
 $1,1)50. riml til!' pi'csi'ot worth of e.uh partuer at closing. 
 
 4. A , B., and C forme 1 a paitnersbip ; A. put in $5,000, 
 B. $1,IHK). i.ad C. $2,500. A. witlidrew $1,000, B. $800, 
 and C. $5U0. They a^^ifed to share the gain or loss in 
 proportion to their original investments, no interest 
 account being kept. At the close, what was eacb partner's 
 share of gain or loss, and the net capital of eacb, as shown 
 by tbe following statement : 
 
 BEBOUBCXS. 
 
 Cash in bank 18.475 
 
 Mdse. per inventory 6,i'i0 
 
 Bills receivable 4,225 
 
 Debts due firm _3,1.j0 
 
 Total resourcea f 10,00' 
 
 LUBILTTrei. 
 
 Bills payable 18,000 
 
 Eont, etc 700 
 
 Debtsflrmowe 2..300 
 
 Total liabilities «0,000 
 
i t 
 
 -3m^^.m^i:^M^ 
 
 3J2 /'.(A/'.V/iA'.v//// 
 
 r>. At till! liiuu of closiiit; lni.iiiu;s«, ihc lesourct'^ ut 
 a llrm were: casli, .;y3l.5U; mdso., per invfutury, 
 $ia,ll»fi.25 ; notes ami accounts clue it, $8,164; iiitert'st 
 on same, §211.50; real eHtate, $! 1.150. The tiri.i a d, 
 on its notes, acceptancos and lulls outstainliii^. $7,14*2. 
 and interest on the same, $818.50; ami tliere was an unpaid 
 mortgage on the real estate of $2,500, with interest fu'cruid 
 thereon of $88.50. If the invented capital was $22,5(10, 
 what was the net solvency or net insolvency of the iimi at 
 closing, and how much has been the net Knin or net loss ? 
 
 6. The firm of A. & B. formed a partnership Jan. Ist 
 for 1 .ve;ir, investing $8,000 each. They were to have 6% 
 interest on their capital and be charged 6 % on sums with- 
 drawn. The gains or losses were to be shared equally. 
 April 4th, A. drew out $500, July lOili, $400, and Sept. 
 5th, $200. B. drew out May 6th, $700. Aug. 12th, $o()0, 
 and Oct. 4th, $400. What wad each j^artner's net capital 
 on closing, the net gains being $3,650? 
 
 7. JohuHtou and Atkinson became partners April Ist, 
 1888, under an agreement that each should be allowed 
 6% flimplo interest on all investments, and th:;t, on final 
 settlement, Johnston should be allowed 10% of the net gains, 
 before other division, for superintending the business, but 
 that otherwisie the ^' .ins and losoen bo divided in propor- 
 tion to average inveHtment. April Ist, 1888, Atkinson 
 invested $18,000, and Johnston, $4,000; Jan. let, 1889, 
 Atkinson withdrew $5,000, and Johnston invested $3,000; 
 Aug. Ist, 1889, Atkinson withdrew $1,500 ; Deo. Ist, 1889, 
 the partners agreed upon a dissoluti m of the partnership, 
 having resources and liabilities as follows : 
 
 RES00RCK8. LUBU.mBS. 
 
 Cash on hand « 1,101 06 Bills payable %i,biQ 00 
 
 Accounts receivable.. 10,405 50 Outstanding accouiita . . l,24tj 60 
 
 Bills receivable 2,550 00 Rentdue WOO 00 
 
 Interest 287 41 
 
 Mdee., as per inventory 9,716 65 
 
 -.••■■Miiiiimpi 
 
l|./*,V^'.;i5wr.'5j 
 
 i 
 
 PAliTSt.HSUlP. 
 
 828 
 
 If, of the accoiintB recoivablf, only HO"', itrovi- to be ;,'i>o.l, 
 whnt liafl boen the net Rftin or loss '? Wlint ban bfcii tlie 
 gain or loss of eacb partiur? WbiU in tho (irin'ri net 
 inaolveucy nt diHSolufinti ? What ifl the net iusolvoncy of 
 each ? 
 
 8. A., n., and C. forniod a co-piutn- r^liip for 2 years, 
 invostin):; •■qu'-' •'Uinfl, with ilie n_;ri'omi;nt (hat each hIuiU 
 ret-oive interest ine rato of % ou all buiiis inverittd, be 
 chargeii iiitcnst at tin same rnto on all sums withdrawn, 
 and the f:;aiiis or Ioshch -;lin\vn ou final wcttlonu'iit be app .r- 
 tiont'd accordinRto avera^^enet iiivi;stinoat. Three nnufhs 
 after the formation of the partnoruhip A. drew out ?l,20(), 
 and six monthfi later B. and C each drew out §1,000, and 
 A. invested $G,000 ; at tho end of the firnt year eiidi drew 
 out $500 On closing the allii -i of the firm, tho followin^^ 
 Btatemont was made: net Rnin, $]5,(n)0; present worth, 
 $75,000. What was the original inve.-luiont of e;ich ? 
 What was the present worth of each at the time of the 
 dissolution ? What wat* each jiartuer'a share of tho gmn f 
 
 9. A. and B. became partners for one year ; A. invr-ting 
 I of the capital, and B. J; the agreement being that the 
 gains or losses aliall be apporfioned according to average 
 net investment, and that each partner bo allowed 6% 
 interest per annum on all investments, and be charged 
 interest at that rate ou all suras withdrawn. At ihe end of 
 the year the firm had as resources: mdse., per inventory, 
 $21,460 ; real estate, $15,000 ; cash, $1,950 • bills 
 receivable, $18,146.50 ; interest accrued on the same, 
 $519.25; accounts due it. $11,218.50; store furniture, 
 $l,3iO; delivery wagons and horses, $2,100. The liabilities 
 were : mortgage on real estate. $7,000 ; interest on same 
 accrued, $210 ; notes outstanding, $26,950 ; interest 
 accrued on same, $811.75. The firm owes H. W. Darling 
 & Co., Toronto. $33,560. It is found that 33^% of th^ 
 
 
i: 
 
 SJ 
 
 6 -] 
 
 If ' >. 
 
 i ! 
 
 
 ii 
 
 824 
 
 PARTNERSHIP. 
 
 accounts due the firm are uncollectable. If the firm's /osset 
 during the year have been $12,000, how much was invested 
 by each partner? What is the present worth or net 
 insolvency of the firm, and of each partner, at closing ? 
 
 10. Sills and Jones became partners July Ist, 1886, under 
 a 3-year'a contract, which provided that Sills should have 
 $1,500 each year for superintending saU-s, and that Jones 
 should have $1,000 each year for keeping the books of the 
 concern, and that these salaries should be adjusted at the 
 end of each year, and before other apportionment of gains 
 or losses was made. July 1st, 1886, each invested $12,500. 
 Six mouths later, each increased liis investment $5,000. 
 July 1st, 1887, Sills drew out §3,600 and Jones drew out 
 $3,000. Oct. 1st, 1837, Sills withdrew $1,000 and Jones 
 invested $2,000. July 1st, 1888, each drew out $1,500. At 
 the e.xpiration of the time of the contract, the resources 
 exceeded all liabilities by $17,280. What was the gain of 
 each, iind the present worth of each ? 
 
 11. A. and B. comm iicod business as partners. A. 
 invested $20,000, and B. $10,000, A. sharing! and B. J of 
 the gains and losses. No interest account was kept. A. 
 drew out $1,700, and B. $2,150. Their assets at the close 
 of the year consisted of — cash, $4,200 ; bills receivable, 
 $8,800; mdse., $26,000; and personal debts, $16,000. 
 10% of the personal debts are considered bad. Their 
 liabilities are— bills payable, $3,250; personal accounts, 
 $11,250. If B. should retire from the firm, how much 
 ought he to receive ? 
 
 12. On January 1st, 1889, A. E. Brock, W. McMaster and 
 H. Crawford entered into a co-partnership. Brock was to 
 invest ^ of the capital and share | of the gains. McMaster 
 was to invest f of the capital and share f of the gains, 
 and Crawford was to invest i of the capital and share | of 
 

 ^ ^RTNEHSHIP. 
 
 825 
 
 the gains. IntereBt at the rate of 10% per annum was to 
 be allowed to each partner should he invest more than his 
 proportion; and interest, at the same rate, was to be 
 char-,'od each partner if he failod to invest his proportion. 
 A settlement was made at the end of the year, and the net 
 gain was $3,600. Find Brock's and McMaster's net 
 interest, and Crawford's insolvency Jan. Ist, 18i)0, the 
 following being a statement of each partner's account. 
 
 Dr. 
 
 A. E. Brock. 
 
 1889.— April 23, Drew out g3.U0d 
 
 " June 16, " 1,000 
 
 " Aug. 17, " _1,800 
 
 " Total withdrawn 50,400 
 
 Cr. 
 
 1889 — Jan. 1, Invested fe:J2,(it)() 
 
 " Mar. 18, " 4,800 
 
 " Oct. 20. '• 6,000 
 
 " Total investment 942,800 
 
 Dr. 
 
 W. MoMaster. 
 
 1889.— July 28, Drew out SI, -200 1889,— Jan. 1, Invested 
 •• Dec. 4, " 1,000 
 
 " Total withdrawn 
 
 52,800 
 
 Dr. 
 
 H. Crawford. 
 
 1889 ^Mar. 30, Drew out $12,000 
 " Sept. 5, " 8,000 
 
 ■ Total withdrawn 820,000 
 
 Cr. 
 
 S-'},000 
 
 21, " 3,000 
 
 May 17, " 1,200 
 
 Total investment 928,800 
 
 Cr 
 
 1889.— Jan. 1, Invested J12.000 
 
 Aug. 3, " 1,200 
 
 " Total invested 913,200 
 
M 
 
 W 
 
 
 •' I 
 
 826 
 
 BAKK&UPTCY. 
 
 BANKRUPTCY. 
 
 535. Bankruptcy is the formal acknowledgement in 
 accordance with the law, by a person or firm, of inability 
 to pay indebtedness. 
 
 536. A Bankrupt is a persrn who is insolvent, or 
 unable to pay his debts. 
 
 537. After the assets of a bankrupt have been applied 
 to meet bis liabilities, he still remains liable for them unless 
 discharged, or unless a compromise has been eflfected with 
 his creditors. 
 
 S3S. The Assets of a bankrupt are his entire property. 
 
 589. The Liabilities of a bankrupt are the debts and 
 obligations due by bim to his creditors. 
 
 540. The Net Proceeds are the assets less the expense 
 of settlement. They are divided among the creditors 
 according to their claims. 
 
 The claims of a certain class of creditors, aa employees and others, are 
 paid in full up to a certain amount. Theae are oaUed "Preferred Credi- 
 tors." 
 
 541. An AssigTiee is a person appointed in accordance 
 with the law, to take charge of the bankrupt's property, to 
 make collections of debts duo the estate, and after deduct- 
 ing the expenses of the assignment, to pay such proportion 
 of the debts due the creditors as the available assets will 
 allow. 
 
BANKIWPTCY. 
 
 827 
 
 942. To find each creditor's dividend, the liabilities 
 and net proceeds being given. 
 
 ExAUFLB. — A merchant failing in bnaineaa gave the following 
 statement of his asBets and liabilities : Asseta, oash, $5,474 ; real estate, 
 93,000; mercbandide, 84,000; personal accoonts, 91,900. Liabilities, 
 bills payable, 92,400 ; dae B. £. Walker & Oo , 96.000 ; dae A. Boyle 
 & Co, (17,500. The expenses of assignment were 9430. How maoh did 
 each creditor receive 7 
 
 Solution. 
 
 LUBILmU. 
 
 Bills payable . , , . 
 R. E. Walker & Oo. , 
 
 A. Boyle <k Co 
 
 Total 
 
 ASSSTB. 
 
 Cash 95,474 
 
 Real estate 8,000 
 
 Mdse 4,000 
 
 Personal accounts.. .. 1,900 
 
 Total 914,374 
 
 Less expenses I'iO 
 
 Net assets 913,944 
 
 813,944 + ^24,900 = .56, or 50%, rate on dollar. 
 
 92,400 X .56 = 91,344 on bills payable. 
 
 95,000 X .56 = 82,S00 to R. E. Walker <k Oa 
 917,500 X .60 a §9,800 to A. Boyle A Co. 
 
 12,400 
 
 6,000 
 
 17.500 
 
 124,900 
 
 924,900 
 
 918,944 
 
 EXERCISE 117. 
 
 1. A bankrupt owes A. $6,600, B. $4,600, and D. $8,800; 
 his assets are $5,950, and the expenses of settling $1,700 ; 
 what per cent, and how much will each creditor receive ? 
 
 2. J. Gould & Co. failed with liabilities amounting to 
 $800,000. The assets of the firm were $186,294. How 
 much should each creditor receive on the dollar, and what 
 sum was allowed J. P. Hume & Co., whose claim was 
 $17,814, tde expenses of settling being $6,294 ? 
 
 8. J. Wild & Co., went into bankruptcy, owing $48,500, 
 and having $13,300 assets; the expense of settling was 6 % 
 of the amount distributed to creditors. What per cent, and 
 how much did a creditor receive on $8,350 ? 
 
 * xt J«W'-. 
 
 -rsrai iLvrfi' • ' 
 
S28 
 
 BANKRUPTCY. 
 
 4. A grain firm failed with liabilities amounting to 
 $24,600. The assets were: cash, $1,080; real estate, 
 $8,250; notes on hand, $1,170. The expenses of settling 
 were 2% of the assets. How much should W. H. Hull & Co. 
 receive, whose claim against the firm was $0,308.50 ? 
 
 6. A manufacturer failed, owing A. $12,260, B. $18,850, 
 and 0. $14,560 ; his assets were $28,350, and the expenses 
 of settling were $1,250. He owed $850 to employees who 
 were to be paid in full ; what per cent, and how much did 
 the other creditors receive ? 
 
 6. The real estate of a bankrupt firm was sold by an 
 assignee for $24,000, goods in store for $12,24-1. There 
 were collected on notes due the firm $4,214, and on personal 
 accounts $5,346. The total liabilities of the firm were 
 $54,067.50, and the expenses of settling $1,850. How 
 much on the dollar can be paid, and what should Howard 
 Bros, receive, whose claim is $12,430 ? 
 
 7. A. Reid's claim against a bankrupt firm was $7,200, 
 and J. Taylor's 70 % of that of A. Eeid's. After the expenses 
 of the assignment were deductt'd from the assets, there 
 remained $18,260. The total liabilities were $24,480. 
 How much did A. Eeid and J. Taylor respectively receive ? 
 
 8. A firm failed with lial)ilities amounting to $26,126. 
 The assets of the firm exclusive of real estate were $1,521 .25. 
 The assignee obtained for a warehouse and three building 
 lots the sum of $15,675. The expenses for settling the 
 bankruptcy was $237.50. W. Alexander's claim against 
 the firm was $3,642 ; J. Moblo's, $3,191 ; R. A. Harrison's, 
 $2,897; D. McGregor's, $2,383.50; W. Ayer's, $1,982. 
 How much did each of these creditors receive ? 
 
 ISi^^^ 
 
i 
 
 dUxSUIIIIiiS, 
 
 829 
 
 ANNUITIES. 
 
 S43> An Annuity is a specified sum of money paid 
 annually, or at equal periods as, half-yei ily, quarterly, etc., 
 to continue a given number of years, for life, or for ever. 
 
 JS44. A Certain Annuity is one wliich begins and ends 
 at a fixed time. 
 
 545. A Perpetual Annuity or Perpetuity is one which 
 continues for ever. 
 
 540. A Contingent Annuity ia one whose time of 
 commencement or ending, or both, is uncertain, and which 
 depends upon some unforeseen event, as the death of an 
 individual, or his arrival at a certain age. Life insurance, 
 pensions, dowers, leases, etc., belong to this cla^e oi 
 incomes. 
 
 547. An Annuity in Possession or an Immediate 
 Annuity is one that begins immediately. 
 
 54S. A Deferred Annuity or an Annuity in Reversion 
 
 is oue that begins at some future time, it may be at some 
 specified time, or at the occurrence of some event. 
 
 549. An Annuity in Arrears or Forborne is one on 
 which the payments were not made when due. 
 
 550. The Amount or Final Value of an annuity is 
 the sum to which all its payments with interest on each, 
 will amount at its termination. 
 
880 
 
 ANNUITIES. 
 
 I 
 
 asi. The Present value c*^ an Annuity is the bxhx 
 which at the given rate of interest, will amount to its final 
 yalue. 
 
 Non 1.— The present valae of a deferred annuity is that principal 
 which will atnonnt, at the time the reversion expires, to what will then 
 be the present value of the annuity. 
 
 3. The present value of a perpetual annuity is the sum whose interest 
 equals the annuity. 
 
 8. Annuities and their values are computed by simple interest or by 
 
 oom pound interest. 
 
 mple interest ? 
 
 
 SOUJTION. 
 
 &NMUITT. 
 
 INT. AMT. 
 
 »500 + 
 
 ?120 « »620 
 
 600 + 
 
 90 = 690 
 
 600 + 
 
 60 = 660 
 
 600 -«■ 
 
 80 = 630 
 
 600 + 
 
 = 500 
 
 Amount 82,800 
 
 S5S. To find the amount of an annuity at simple 
 interest when the time and rate are given. 
 
 EzAMPLB. — What is the amount of 9600 annuity for 6 years at 6 % 
 
 EXFLUdTION. 
 
 The interest on 9600 for 1 year at 6% 
 ■t 930. The first annuity is not due 
 until the end of the first year, and 
 hence draws interest for only 4 years m 
 9120. The second is not due until the 
 end of the second year, and hence draws 
 interest for only 8 years, eto. 
 
 S53. To find the present worth of an annuity at 
 simple interest. 
 
 ExAHFLB. — What is the present value of an annuity of 9600 for 
 6 years, when money is worth 6 % simple interest ? 
 
 Solution. 
 By the preceding example the final value of the annuity ia 92,800. The 
 present worth of 9^,800 due in 6 years at 6 % a ^gj of 93.800 m 92163.846i. 
 
 EXERCISE 118. 
 
 1. What is the amount of an annuity of $160 for 8 years, 
 when money is worth 6 % simple interest ? 
 
ANNUITIES. 
 
 881 
 
 2. A man works for 1 year and 6 months at $20 per 
 mouth, payable monthly ; and those wages remain unpaid 
 until the expiration of the whole time of service. How 
 much is due to the workman, allowing simple interest at 
 the rate of 6 % per annum ? 
 
 8. A father deposits $50 a year for his son, commencing 
 on the son's 10th birthday. What amount will the son 
 have on his 2l8t birthday, if the payments draw simple 
 interest at the rate of 8 % per annum ? 
 
 4. A lady has $300 a year left to her for 10 years. What 
 is its present cash value, at 7 % snnple interest ? 
 
 6. What is the present worth of an annuity of $600 for 
 4 years, money being worth 6% simple interest ? 
 
 6. How much will an annuity of $100 amount to in 
 6 years at 8 % simple interest ? 
 
 7. An annuity of $200 for 12 years is in reversion for 
 < years. What is its present worth, simple interest at 6 % ? 
 
\i''' 
 
 332 
 
 AMiUll'lKS AT COUtOUHD lUIEIiKST. 
 
 ANNUITIES AT COMPOUND INTEREST. 
 
 551. The labor of computing the viilues of annuitieB at 
 compound interest is greatly dinnnirfhed by the use of the 
 following tables. The tables are always used in practice. 
 
 Tabm 1. 
 Amount of $1 annuity at compound interest, from 1 year 
 to -10, inclusive. 
 
 Tri. 
 
 3%. 
 
 34%. 
 
 i%. 
 
 5%. 
 
 6%. 
 
 7%. 
 
 Yr» 
 
 1 
 
 1.000 00(J 
 
 l.OOOOOO 
 
 1000 000 
 
 1.000 000 
 
 1.0(10 iflO 
 
 1.000 000 
 
 I 
 
 a 
 
 8.030 0(X) 
 
 8.03r> W» 
 
 2010 000 
 
 2.0.-* 000 
 
 9.01,0 tH>i 
 
 9.070 0(0 
 
 a 
 
 3 
 
 8.090 NO 
 
 3.100 22.) 
 
 3 121 000 
 
 3.1.32 .300 
 
 a. 1.^3 (HI) 
 
 8.211 !M) 
 
 3 
 
 « 
 
 4.183 '27 
 
 4.214 9-13 
 
 4.216 40t 
 
 4310 12.) 
 
 4.374 010 
 
 4.439 913 
 
 4 
 
 B 
 
 8.309 136 
 
 A,.H69 4a6 
 
 5.416 3?3 
 
 8525 031 
 
 6.CS7 093 
 
 6.750 73'J 
 
 B 
 
 e 
 
 6.468 410 
 
 6S50 1fiB 
 
 0.638 97S 
 
 6.801 913 
 
 0975 319 
 
 7.153 891 
 
 • 
 
 7 
 
 7.6G2 4r.2 
 
 7.77!) 408 
 
 T.898 2-J4 
 
 8.142 008 
 
 8.39.) 838 
 
 8.03 J 021 
 
 7 
 
 8 
 
 8.8'JJ im 
 
 OO.-il 687 
 
 9.214 226 
 
 9.r)49 KO 
 
 9.697 468 
 
 10.2.39 W13 
 
 8 
 
 9 
 
 10.15'J liHi 
 
 103'18 196 
 
 10.583 795 
 
 11026 564 
 
 11.491 310 
 
 11.977 989 
 
 9 
 
 10 
 
 U.463S7>J 
 
 11.731 393 
 
 19.006 107 
 
 12.577 8'j3 
 
 13.160 795 
 
 13,810 448 
 
 10 
 
 11 
 
 18^7 796 
 
 13 141 999 
 
 13.480 3.')1 
 
 14.206 7R7 
 
 14.971 6 13 
 
 15.783 599 
 
 11 
 
 18 
 
 14.1P3 030 
 
 14.601 903 
 
 15 02'. 805 
 
 15.917 127 
 
 16.869 941 
 
 17.88S 4.51 
 
 la 
 
 13 
 
 15.617 7'jO 
 
 1C.113 030 
 
 10 620 833 
 
 17.712 983 
 
 18.1S2 138 
 
 20.110 Gl.l 
 
 13 
 
 14 
 
 17.0a6 324 
 
 1?.C76 986 
 
 13.2(11 911 
 
 19.398 fi;t2 
 
 91.013 060 
 
 22.550 4NH 
 
 14 
 
 IB 
 
 laSOS 014 
 
 19295 681 
 
 80 023 588 
 
 81.078 50- 
 
 170 
 
 96.199 022 
 
 IB 
 
 16 
 
 901S6 881 
 
 90971 030 
 
 21.824 531 
 
 93.6.57 492 
 
 25. >70 528 
 
 27.888 051 
 
 16 
 
 17 
 
 91.761 SS.'f 
 
 82.70.-. 016 
 
 2-i.6'.)7 512 
 
 23.840 306 
 
 28 J 2 880 
 
 30.840 217 
 
 17 
 
 18 
 
 23.114 435 
 
 21.499 691 
 
 21015 413 
 
 2.S.132 3.15 
 
 30 J05 053 
 
 33.999 033 
 
 18 
 
 19 
 
 25.110 868 
 
 90357 180 
 
 27.071 229 
 
 30.5;i9 (JO I 
 
 33 7,59 999 
 
 37.378 9 5 
 
 19 
 
 ao 
 
 28.870 374 
 
 98.279 688 
 
 89.778 079 
 
 33 065 954 
 
 36 -85 591 
 
 40 095 492 
 
 20 
 
 21 
 
 2S 676 486 
 
 30.289 471 
 
 Sl.rfiO 203 
 
 35.719 2.32 
 
 39 )92 727 
 
 44.865 177 
 
 21 
 
 aa 
 
 30..'>3i) 7hU 
 
 32.;f28 '.m 
 
 31.217 070 
 
 38.5115 214 
 
 44 392 290 
 
 49.005 739 
 
 2a 
 
 83 
 
 32.1.'2 8..4 
 
 34.100 11 J 
 
 36.017 S,S9 
 
 41 430 475 
 
 4<J 993 828 
 
 5,3,4:i0 141 
 
 23 
 
 84 
 
 31.420 470 
 
 36.0GIJ o23 
 
 39 082 004 
 
 44 301 999 
 
 60.815 577 
 
 53 170 671 
 
 84 
 
 88 
 
 36.459 804 
 
 38.949 857 
 
 41.645 908 
 
 47.737 09B 
 
 64.864 519 
 
 63.219 030 
 
 aB 
 
 86 
 
 38.r>53 042 
 
 41.313 109 
 
 44.311 748 
 
 01.113 454 
 
 59.156 383 
 
 68 678 470 
 
 ao 
 
 87 
 
 40.709 634 
 
 43.759 OeO 
 
 47.084 214 
 
 Bi.&?J 126 
 
 63 705 766 
 
 74 483 823 
 
 87 
 
 88 
 
 42.930 923 
 
 46.290 627 
 
 49.967 583 
 
 BX. I'la 583 
 
 6'<.528 112 
 
 80 697 691 
 
 as 
 
 89 
 
 45.2 IS HjO 
 
 48.910 799 
 
 52.966 286 
 
 63.322 71-3 
 
 73 639 798 
 
 87318 629 
 
 89 
 
 SO 
 
 47.07fi 416 
 
 61.693 677 
 
 66.064 938 
 
 60.438 848 
 
 79.058 186 
 
 94.460 786 
 
 30 
 
 81 
 
 50.002 678 
 
 54.429 471 
 
 69,188 335 
 
 70.760 790 
 
 84.801 677 
 
 102.073 041 
 
 31 
 
 33 
 
 52.302 75 J 
 
 57.334 603 
 
 62701 469 
 
 73 2<i8 829 
 
 90.800 778 
 
 110.218 1.54 
 
 33 
 
 83 
 
 50.077 &41 
 
 00.341 210 
 
 66.209 .'527 
 
 80.063 771 
 
 97.343 165 
 
 118 933 25 
 
 33 
 
 34 
 
 57.730 177 
 
 63.453 iri2 
 
 OO.aW 909 
 
 85.0C0 959 
 
 104.1,H3 755 
 
 128.238 76. 
 
 34 
 
 SB 
 
 60.463 osa 
 
 66.674 013 
 
 73.052 235 
 
 90.320 307 
 
 1U.431 780 
 
 13&936 878 
 
 SB 
 
 86 
 
 63.371 944 
 
 TO.007 603 
 
 77.,-i98 314 
 
 95.836 323 
 
 119 120 867 
 
 148.913 460 
 
 38 
 
 37 
 38 
 88 
 40 
 
 66.171 223 
 
 73.437 «•'■•? 
 
 .11 ';■¥>. 2 'A 
 
 10! fiSS 130 
 
 !27.2(V8 119 
 
 1003.17 400 
 
 37 
 
 60.159 449 
 
 77028 89.5 
 
 85.970 3.J6 
 
 107.709 546 
 
 135.904 206 
 
 172 561 020 
 
 38 
 
 72.234 233 
 
 80.794 900 
 
 90.409 150 
 
 114.095 023 
 
 145.058 458 
 
 186.610 292 
 
 39 
 
 75.401 960 
 
 84.660 r8 
 
 96.095 616 
 
 190.799 Hi 
 
 154.761 966 
 
 199.635 112 
 
 40 
 
ANNUITIES AT COUFOUND INIKULST. 
 
 888 
 
 TlBLI 9. 
 
 nrtS. Present worth of $1 annuity at compound interest, 
 from 1 year to 40, inclusive. 
 
 Tr» 
 
 8^ 
 
 3i%. 
 
 4%. 
 
 5%. 
 
 6%. 
 
 7% 
 
 
 ^r. 
 
 1 
 
 oro) wi 
 
 O'.iCC 1^1 
 
 O'Jfil XH 
 
 0.9"2 S-il 
 
 9 13 W:) 
 
 9,11 
 
 .■.79 
 
 1 
 
 a 
 
 i.yi 1 470 
 
 1 KV.i r.'.n 
 
 1 i-HO (^5 
 
 l.\v.i tin 
 
 l.Kt3 393 
 
 1 -in 
 
 017 
 
 a 
 
 3 
 
 isis oil 
 
 2, SOI fi;7 
 
 2.77.') "91 
 
 2.7-.ii -.1 iH 
 
 2I-.73 012 
 
 '2 021 
 
 311 
 
 3 
 
 4 
 
 3.717 O'.iS 
 
 3.1)73 079 
 
 3.0JJ Kr, 
 
 a.', 15 '.jt 
 
 3- Hi". lUC 
 
 8 3-7 
 
 2 '.1 
 
 4 
 
 5 
 
 4.579 707 
 
 4..'J15 053 
 
 4.451 >)ia 
 
 4.329 477 
 
 4 212 364 
 
 4 luO 19,-. 
 
 6 
 
 6 
 
 6.417 191 
 
 6.32S Sj3 
 
 5.213 m 
 
 6-07-. 6>a 
 
 4.917 .'J24 
 
 4,7'.'; 
 
 .-,37 
 
 e 
 
 7 
 
 C 2 ;.) i!S3 
 
 Gill 5)4 
 
 0(1 2 'M 
 
 B.7-0 :v. i 
 
 8 :--2 381 
 
 .', ;i -.1 
 
 ■j^i* 
 
 7 
 
 e 
 
 7 W.I fM 
 
 0. 7.1 U.W 
 
 07 J 715 
 
 lii' J J 
 
 2 19 7 1 1 
 
 .'■.•.•71 
 
 •> r. 
 
 8 
 
 e 
 
 7.7-r. 109 
 
 7. 1-' 7 IW7 
 
 7 Ml 11 .'2 
 
 7 1 1 12 
 
 On 11 (-.•Ji 
 
 5.-1 
 
 22. 
 
 9 
 
 10 
 
 8U(i 9u3 
 
 6.316 0O3 
 
 8.110 b'jC 
 
 t.Tii 73.) 
 
 7,3i>i .V)7 
 
 7.i).a 
 
 577 
 
 10 
 
 ■a 
 
 «.2o2 034 
 
 8001 551 
 
 KS'VI 477 
 
 s.T'c. m 
 
 7 "^n: H75 
 
 7 41s mo 
 
 11 
 
 ^V 
 
 , j.'.r.i 001 
 
 9.(V,;) :'..il 
 
 0.3k.> 071 
 
 8 -0.: :.'i 
 
 8.:k1 814 
 
 7.9 i 2 
 
 071 
 
 la 
 
 I'u-.ii >x,r, 
 
 10.:i fi 73S 
 
 9.9H"i Cl) 
 
 9:.9.! ..7J 
 
 H.S.V2 i;s3 
 
 S,:i-.7 
 
 RH 
 
 13 
 
 iV 
 
 n■^■<^, .)7j 
 
 li.MI :V20 
 
 10. .VU 123 
 
 9.h'.'- Oil 
 
 9.2,' 1 9-.1 
 
 8.7 l,'. 
 
 1.-.2 
 
 14 
 
 IS 
 
 ll.'JJ7 %ii 
 
 11.017 411 
 
 ll.ll,t 3.S7 
 
 10.379 03.i 
 
 9 712 249 
 
 9 1 7 
 
 K9.M 
 
 15 
 
 16 
 
 12,V,l 103 
 
 13.001 117 
 
 n.er,2 200 
 
 lO.-*.?? 770 
 
 in.M', s',!,', 
 
 9.44r 
 
 (■ .;) 
 
 16 
 
 17 
 
 13,ir,il 118 
 
 I2&-1I 331 
 
 iS.Kw rxy 
 
 11-271 o.y. 
 
 li i7r 2<V) 
 
 9.7.-.:i 
 
 21 »; 
 
 17 
 
 18 
 
 13 7 .3 ,^13 
 
 13 119 r.s'i 
 
 l-l.r,:,:) ±17 
 
 ll.iV-i --7 
 
 1 •.■■-; mi 
 
 100.9 
 
 1)70 
 
 18 
 
 19 
 
 14.3i) T.» 
 
 13 7u9 KI7 
 
 n.i:3 9:11 
 
 12.>.; .iji 
 
 n.i:H na 
 
 10 XV, 
 
 Cj'h 
 
 19 
 
 ao 
 
 14.677 475 
 
 14.213 403 
 
 i3..5'J0 :jW 
 
 12.402 210 
 
 11.409 i'Jl 
 
 10.59.1 
 
 '*97 
 
 ao 
 
 ai 
 
 15 n.'! 0-21 
 
 14 697 974 
 
 14 0'29 160 
 
 12-21 1.03 
 
 11.7ri 077 
 
 10,'<.T, 
 
 VVT 
 
 ai 
 
 aa 
 
 lj.<*;« 917 
 
 \r,.\r.7 12.-. 
 
 ll.l.'Jl 115 
 
 M.I .i 003 
 
 12 ■11! .'>><2 
 
 11 i.-: 
 
 2a 
 
 aa 
 
 S3 
 
 16 U3 008 
 
 15<'..M 410 
 
 14 S.')C. 8i3 
 
 IS is, ,•■.71 
 
 12 .13 379 
 
 1 : •J 2 
 
 1^7 
 
 33 
 
 a* 
 
 1C.H3J 513 
 
 1iVm:,8 30-) 
 
 15.2 WH 
 
 13 7, .s c.ij 
 
 12 .").'! 3,'>,S 
 
 11 1'," 
 
 :.i4 
 
 84 
 
 86 
 
 17.413 148 
 
 16.481 515 
 
 15.0J2 O13O 
 
 11.0J3 945 
 
 12 783 3.i6 
 
 llC-i 
 
 .■)fv) 
 
 as 
 
 ae 
 
 17 876 fWa 
 
 10.890 3';3 
 
 15 9K2 769 
 
 11 ;7:-) 1-) 
 
 13 on icfl 
 
 11,K2- 
 
 779 
 
 36 
 
 27 
 
 ir,.:i27 031 
 
 17,2s.') 305 
 
 16 3-29 r.s6 
 
 MC.i:! .131 
 
 l:i2! 1 .^;i 
 
 11. ',.■-', 
 
 7.19 
 
 a? 
 
 as 
 
 18.7i;i HM 
 
 17.007 019 
 
 Ifi Oii.l 1 (VI 
 
 11.-9-1 127 
 
 13 ,ii llil 
 
 12 1.17 
 
 111 
 
 33 
 
 as 
 
 19.1 AS 4.J5 
 
 ia035 707 
 
 16 9-^1 715 
 
 ir> 111 on 
 
 13.V.ilt 721 
 
 12 -277 
 
 671 
 
 29 
 
 30 
 
 19.000 441 
 
 18.3^ 045 
 
 17.292 0:i3 
 
 l,x:(72 451 
 
 13.701 S31 
 
 12.119 
 
 Oil 
 
 30 
 
 31 
 
 aOOOO 428 
 
 18 736 276 
 
 17..''.8-i 491 
 
 15..''.92 811 
 
 13 029 086 
 
 12.-3! 
 
 81! 
 
 31 
 
 3a 
 
 20.3a« Ti.O 
 
 19 008 b65 
 
 17.873 5-i2 
 
 15.8 e 077 
 
 II.OSI 013 
 
 12 c, 1, 
 
 ",.-j ', 
 
 32 
 
 33 
 
 2(>,7f.l 7il3 
 
 19 300 21)3 
 
 1M.1I7 010 
 
 16-0112 -.19 
 
 H 2:vi 2:ti) 
 
 12 7.:i 
 
 7.11 
 
 33 
 
 34 
 
 21.1.U 637 
 
 19.700 6H1 
 
 l.s.dl r.w 
 
 10 192 21)4 
 
 ll,:i'.w 141 
 
 12. -nM 
 
 U'.l 
 
 34 
 
 35 
 
 21.487 320 
 
 90 000 661 
 
 13.6&1 013 
 
 16.374 194 
 
 14.498 246 
 
 12.917 
 
 072 
 
 35 
 
 "'f 
 
 V" 32 9.53 
 
 2il.29) 494 
 
 18.918 2Ha 
 
 16.540 R-2 
 
 14 620 987 
 
 13.03-. 
 
 20<^ 
 
 36 
 
 
 k....;7 23J 
 
 2i).J7ii 53) 
 
 19. H2 579 
 
 16.711 .;-7 
 
 14 7 M 7S0 
 
 13 117 
 
 (07 
 
 37 
 
 ■ J 
 
 2J; , ,2 402 
 
 a0.d41 087 
 
 19 307 .SC4 
 
 16 867 >•'■■! 
 
 14. MO 019 
 
 13 1;>3 473 
 
 38 
 
 3* 
 
 9n m ai.'j 
 
 21.103 500 
 
 19 5H1 4S6 
 
 17.017 Oil 
 
 14.919 075 
 
 13.201 
 
 928. 
 
 33 
 
 4^ 
 
 "iu 114 773 
 
 aijssoTS 
 
 19.793 774 
 
 17.169 086 
 
 15.046 297 
 
 13.331 
 
 709 
 
 40 
 
r 
 
 , 
 
 ,1 
 
 
 Ul 
 
 i 
 
 \\h 
 
 }■ 
 
 i^ 
 
 ..i 
 
 884 
 
 ANNUITIES AT COUPOVND INTMliHST. 
 
 «5«. To find the final value of an annuity Dy 
 compound interest. 
 
 KxAMFLB 1.— What ia the final value of an annuity of 1600 for 6 
 
 yeara at 6 % 
 
 SoLnTios. 
 
 By Tablo 1 the final value of an annuity of 
 
 »1. at 6% for 6 yoara ■ »6.fl019l8. 
 .-. final val.10 of an annuity of $500 - 6.801013 x 500 - «3100.U566. 
 Note— When payments are made half-ycwrly. take from the table 
 double the tinio, and ) tho rate. 
 
 5«7. To find the present value of an Annuity. 
 
 ExAMi'LU.— What ia tho pro>iOiit worth of an annuity of 8500 for 8 
 
 years at G %. 
 
 Solution. 
 
 By Tablo 2 the preeent worth of an annuity ol 91 for 6 years at «% U 
 84.212."»r).l, 
 
 .-. The p. w. of an annuity of «500 - »4.ai2304 x .^ m = «2106 182. 
 
 55H. To find the present worth of an annuity in 
 reversion. 
 
 Example.— Wl ' '" ♦tie present worth of an annuity in reversion of 
 8500 at 6%, which bet;i"8 in 4 years, and then terminates after 6 y. art. 
 
 Solution. 
 
 The p. w. of an annuity of 
 
 $1, at 6 % for 10 yrs. « »7.360037. 
 .. 4 yra. a |i3.40510a. 
 
 • The present worth of an annuity of SI to 
 begin in 4 years, and then to cont.nne 6 years = p.8" m\. the dlfTereno* 
 .-. p.w. of 8500 = 3 89ll!Sl x 500 » 81917.4905. 
 
 55». To find the present worth of a perpetual annuity. 
 
 Example l.-A perpetual scholarship of 8150 per year is established 
 at Queen'a University. What sum must be invested at 6% to yield thlf 
 
 income. 
 
 Solution. 
 
 6 % of the investment « 8150. 
 .•. the investment = 4« x 100 - 83,000 Ana. 
 Example 2.— What is the present worth of a perpetual annoity ol 
 $300 iu arrears for 20 years, ahv^wins 5% compound interest. 
 
 Solution. 
 There U now due the amount of »300 for 20 years at 5% compound 
 interest, together with the present worth of the perpetual annuity of 
 8300. 
 
ASNUITIBS AT COMl'QUND hSTUHJiST. 836 
 
 The p. w. of the pirpotnal annuity of 
 
 »300, by Kx.uiiple 1 ■ H» X 100 ■ 16,000. 
 Amoant of annuity of 
 
 •1 for 20 yeari at 6% ■ »33 Ofi.'OSi. (Table 1). 
 
 1300 " ■ »:i;<.ot;.M»54 K 800 - i'mi.isnr 
 
 .: total present worth « 99'J19 780'i + 16,000 m »15'J19.786a. Aju. 
 
 EXERCISE It9. 
 
 1, Money being worth %, liow much mut bo prosentod 
 to a college, to insure $50 a year forever, for an annual 
 prize ? 
 
 2. Aperaon left $5,000 fir tlie poor of hia native town. 
 How great was the perpetuity realized from it, at %? 
 
 :j. What ia the final value of an annual pension of $150 
 for 15 years at 4%eorapouncl interest ? 
 
 4. A widow ia entitled to $110 a year for 18 years, at 
 10% aemi-annual compound interest: what ia ita tiua) 
 value ? 
 
 6. An annuity of $350 was left to A., and one of $550 to 
 B., by the same peraon ; both were to run 12 years. Al- 
 lowing compound interest, at 6%, by how much would tiie 
 amount of A.'a exceed that of B.'a in the given time ? 
 
 6. Ilow miich will an annuity of $100 amount to, in 8 
 years, at 8% simple interest? How much at 6% com- 
 pound iii^erest ? 
 
 7. A soldier 67 years old, having a penaion of §80 a 
 year, agreed to aell it for caah at 10 % leas than ita pre^^ent 
 value, compound interest being allowed at 7 %. Uow much 
 should he receive, his expectation of life beinj^ 74 years of 
 age? 
 
 8. A lawyer collected for a client an annuity of $700, in 
 arrears fur 4 years, the legal rate of intereat being 6%. He 
 charged 15 % on the amount collected. At this rate, how 
 much greater would have been hia fee had he been able tf 
 eolleot compound interest ? 
 
^m^iW'j^:^ 
 
 m^^^ 
 
 836 
 
 ASSVITIKS AT COMPOUND INTEREST. 
 
 9. A clerk iavea from \m Hillary |50 l very year, and puti 
 it in a savings bank which allows interest com i^nu, idee 
 annually at 6%. If be draws uo checks on the bank, bow 
 much will he have there at the end of 10 years ? 
 
 10. \ iHWHon agod 64 has a life annuity of $400. What 
 
 is it:4 present value, allowitif^ co'upoimd interest at 4%, bis 
 oxpictatioii nl life bcin^ 19 years? 
 
 11. At the age of 20, and ovi-ry year after, a y.>ung man 
 places $200 at coiapound interest at 5%. How much will 
 be have at the a^;e of 30 ? At the age of 40 ? 
 
 12. IIow much a year must bt iuvewted for a boy 11 
 years old, tlia^ the hihih tluid invented, with compound in- 
 terest at 5 %, may make a total of $10,OuO by the tim(^ he 
 becomea of n':;e ? 
 
 13. What ia the preaoiit worth of an annuity of $500 for 
 8 years, at 1 % compound iulerertt? 
 
 14. What ia the present worth of an annuity of $3,00C 
 for 20 years at 3 % compound inten st? 
 
 16. What is the preHent worth of an annuity in reveraion 
 of $1,000, at6%coiup )und intiu-est, which b^i^'inRin 8 .year* 
 and then terminates in 8 yearri ? 
 
 li'i. The reversion of a lease of $450 per y^'r at 5%, 
 begins in 3 yoaiH and continues IG ^.jars. W^.'tt ia its 
 present worth ? 
 
 17. A father bequeathed to bis son, 11 ye'iis of age, a 
 6 % amiuity of $1,000, to begin in 3 years and continue 10 
 years. Wliat would be the amount when the son was 21 
 years old ? What is its present worth ? 
 
 18. What is the present worth of a perpetual annuity of 
 $250, in arrears for 10 years, allowing 8 %, compound in- 
 terest ? 
 
 19. What is the present worth of a perpetuity of $600 in 
 •rrears for 30 years, allowing compound interest at 6 % ? 
 
iiXMlNO FUifDa. 
 
 S87 
 
 SINKING FUNDS. 
 
 ffOO. Sinking Funds are sums of ranney set apart at 
 regular iotervalH for the payment of iudebtedness. 
 
 961* Sinking Fund Bonds are socuritiea iaaucd by 
 :orporations, based on the pledge of a apocial income, 
 which is funded for their rediiuption. 
 
 S63. To find what sum f ust be set apart annually, 
 as a sinking fund, to pay a debt in a given time. 
 
 ExAMir.K.— The Town of Wondstock borrowed JJO.OOO to build * 
 SiKh School, and a,jreed to pay S % compound intoroat. Whsit Bum muB» 
 be let apart annaully, ai a linking fund, to pay the debt in 12 yean T 
 
 SOLUTIOH. 
 
 Amount of 
 
 •1 at 6% compound int<3ro3t for 13 years m $1.795868. 
 
 .', $20,000 - $i.7'.<-''")C X 20,000 - f.^-^.on.ia. 
 
 Amount of annual payment of $1 for 12 yoara at 5% a |16.917127. Art.SM 
 /. amount necessary to pay a debt of 
 $.5,917.13 will require 835,917.12 -^ 15.917127 » $L',256.M. Ans. 
 
 RULB. 
 
 Divide the amnnnt of the debt at its maturity at compound 
 interi'st, by the amount '>f an annuity of $1 for the ijiven time 
 and rate, and the quotient will he the sinking fund required. 
 
 50». To find the number of years required to pay a 
 given debt, by a given annual sinking fund. 
 
 ExAMPi.!. — Tie Town of Port Hope built a Court ilouse at a cost 
 at $16,000, and raised 1(1,300 a year to pay for it. Allowing a % compound 
 mtareat, how many years will it require to cancel the debt T 
 
I 
 
 n 
 
 l! 
 
 f > 
 
 888 
 
 aiSKIKO FUNDS. 
 
 BOLUTIOM. 
 
 A sinking fund of 91,800 has a present worth of 916,000 for a ocrtavn 
 time at 6%. 
 
 .-. A sinking fund of »1 has a present worth of ^^^ « f 11.638461, tax 
 the required time at 6 %■ 
 
 Looking in Table 3, Art. 666, in the colamn 6 %, we find the nearest 
 nnmber less than 11.638461, to be 11.469421, tha present worth of 91 
 annuity for 20 years. 
 
 20 years is therefore the number of whole years required. 
 
 Af^ain : 
 The amount of the debt 915,000 at 6 % compound interest 
 
 fop20years -948,107 40 
 
 The amount of a sinking fund 91,300 at 6% compound 
 
 Interest ■ t7,8?1.27 
 
 Balance due at end of 20 years m 9286.11 
 
 BTTLS. 
 
 L' ^ide the debt by the given sinking fund, and the quotient 
 will be the present worth of $1 annuity for the given time. 
 
 Look for this number in Table S, Art. 655, in the column 
 denoting the given rate, and opposite in the column of time 
 will be found the number of whole years. 
 
 Notes 1. — If the exact nnmber is not found in the oolamn, take the 
 years standing opposite the next smaller number. 
 
 3. To ascertain the balance due at the end of the number of whole 
 years, find the difference between the amount of the debt, at the given 
 rate, for the time taken, and the amount of the sinking fund for the same 
 time and rate. 
 
 EXERCISE 120. 
 
 1. If a railroad company sets apart an annual sinking 
 fund of $20,000, and loans it at 5 % compound interest. 
 What will be its amount in 12 years ? 
 
 2. What will be the amount in 15 years of a sinking 
 fund of $12,000, yielding 4% compound interest ? 
 
 8. What sum must be set apart annually to rebuild a 
 bridge costing $80,000, estimated to la^it 17 years, allowmg 
 6 % compound interest ? 
 
SlSKISa FUNDS. 
 
 339 
 
 4. A railroad company bou<^ht $10%000 worth of rolling 
 Btock, payable in 6 years with 6 % couipoimil interest ; what 
 sum must be set apart annually as a sinking fund to dis- 
 charge the debt ? 
 
 5. A man bays a farm for $5,000, and a,!j;rees to pay for 
 it in six equal annual infitalments. What is the amount of 
 each payment, money being worth 5 % compound interest ? 
 
 0. A railroad company issued sinking fund bonds at 6% 
 fci $200,000, payable in 10 years. If at compound interest, 
 what sum must be set apart annually to meet interest and 
 principal when due ? 
 
 7. What would be the amount in 10 years, at 6% simple 
 interest ? 
 
 8. If the funded secnrities were drawing an annual 
 income of 4% compound interest, by how mu..h would the 
 amount necessary to meet principiil and interest at 6% be 
 reduced ? 
 
 9. With the above reduction, what sura would be needed 
 annually as a sinking fund to pay the amount when due at 
 4%. 
 
 10. A man buys a farm for $6,000, and agrees to pay 
 $700 each year until paid, allowing 6 % compound interest, 
 both on the debt and on the payments. How many 
 number of whole years will he be in paying for the farm ? 
 What is the balance then due ? 
 
 11. A village built a school- house costing $12,000, and 
 raised $1,700 a year to pay for it ; allowing 6% compound 
 interest. How many whole years will it reqmre to cancel 
 the debt ? What wiU be the balance then due? 
 
i 
 
 
 
 , < 
 
 m 
 
 It 
 
 S40 
 
 aUOUND BEHXa. 
 
 GROUND RENTS. 
 
 564. Ground Rents is a term applied to leaBf>« of 
 
 building lots, the reut of which is considered eqaal to the 
 interest on the valuation of the land. The payment is 
 generally secured by a claim on the boilding erected on the 
 land occupied. 
 
 565. When the party who rents the ground has the 
 privilege of purchasing it, the Ground Rent is said to be 
 redeemable ; otherwise, it is irredeemable. The rentor 
 of the land usually erects buildings thereon in his own 
 right and pays a specified sum quarterly, semi-annually, 
 or yearly, for the use of the ground. In some cities the 
 issue of irredeemable ground rents is prohibited. 
 
 50G. Building lots are sometimes sold at bo much per 
 foot frontage ground rent. Thus, a lot valued at |4,000, 
 with a frontage of 20 feet, drawing interest at 8 %, is said 
 to be worth $16 per foot. The interest on $4,000 for 
 1 year at 8% is $820, which, being divided by 20, the num- 
 ber of feet on the front, gives $16 as the price. 
 
 When a 6% ground rent yields the owner $180 per year, 
 the value of the ground is estimated at $3,000, since $180 
 is the interest on $8,000 for 1 year at 6 %. 
 
 EXERCISE 12U 
 
 1. What ia the capitalized valne of gronnd, which at 
 5 % ground rent, yields the owner $600 per year ? 
 
OROUND RENTS. 841 
 
 2. What will be received as ground rent for a . viuued 
 at $5,000, leased at a ground rent of 8 % ? 
 
 8. What is the ground rent price per foot frontage of a 
 lot 80 feet front, valued at $12,000 and paying a ground 
 rent of 7 %. 
 
 4. If $192 be received yearly from a ground rent bought 
 for $3,840, what is the rate per cent, ground rent ? 
 
 6. I bouftht three lots, each 25 feet front and 140 feet 
 in depth, at §50 per foot frontage, and leased them at 
 4^ % ground rent. What income do I receive from my 
 investment ? 
 
 6. A real estate owner sold a giound rent of $75 at 6 %. 
 What did he receive for it ? 
 
 7. The annual income received on a 6% ground rent 
 was $540. If the ground rent be sold at its value and the 
 proceeds applied to the purchase of a mining stock at $50 
 per share, how man; shares can be bought ? 
 
 8. Find the present worth of a ground rent of 8 % on a 
 lot valued at $4,500, to commence in 8 years and to then 
 continue 15 years, if money be worth 6 % co lound 
 interest. 
 

 
 
 1 
 
 j 
 
 
 1 
 
 ! 
 
 ' 
 
 1 
 
 
 ( 
 
 
 1 
 
 > Si 
 
 if 
 
 S42 
 
 UFJi JUSUHANCE. 
 
 LIFE INSURANCE. 
 
 567* Life Insurance is a contract by which a com* 
 
 pany (the insurer), in consideration of certain payments, 
 agrees to pay to the heirs of a person, when he dies, or to 
 himself, if hving at a specified age, a certain sum of 
 money. 
 
 li^S, The principal kinds of policies issued by Life 
 Insurance Companies are the following : Ordinary Life 
 Limited Payment Life, Endowment, and Annuity. 
 
 5«». An Ordinary Life Policy is one on which a 
 certain premium is to he paid every year until the death 
 of the insured, wlien the policy becomes payable to the 
 persons named in the policy as the beneficiaries. 
 
 570. A Limited Payment Life Policy is one on which 
 the premium is paid annually for a certain number of 
 years, fixed upon at the time of insuring, o: until the 
 death of the insured, should that occur prior to the end of 
 the selected period. The policy is payable on the death of 
 the insured. 
 
 571. An Endowment Policy ia one which is payable 
 to the person insured, if he survives a certain number of 
 years, or to his heirs, if he should die before the expiration 
 of such period, in consideration of certain regular payment 
 from the person insured, 
 
 572. An Annuity Policy ia one which secures to the 
 holder the payment of a certain sum of money every year 
 during his life-time. It is secured by a single payment. 
 
 {578. A Non-Forfeiting Policy is one which does not 
 become void on account of non-payment of premium. 
 
 574. The Surrender Value of a policy is the amount 
 of cash which the Company will pay the holder on the 
 surrender of the policy. It is the legai reserve less a 
 certain per cent, for expenses. 
 
LIFE INSURASCB. 
 
 843 
 
 575. The Reserve of Life hnuranoe Policies is the 
 present value of the amount to he paid at death loss the 
 present value of all the net premiums to be paid in the 
 future. 
 
 570* The Reserve Fund of a Life Insurance Com- 
 pany is that sum on hand which invested at a given rate 
 of interest together with future premiums on existing 
 policies, should be sui&oient to meet all obligations as they 
 become due. It is the sum of the separate reserves of the 
 several policies outstanding. 
 
 577. The Premium is the sum paid for the insurance 
 of a person's life. It is paid annually, semi-annually, or 
 quarterly. 
 
 578. The Premium consists of three elements: 1st. 
 The Reserve, or that portion of each premium which musl 
 be kept and improved by interest, to pay the policy at ita 
 certain maturity. 
 
 2nd, An • stimated amount for each man's share ol 
 the annual losses of the company. 
 
 3rd. Loading, or a certain per cent, to be added to th« 
 net premium to cover the general expenses of the business, 
 and to provide against unusual contingencies. 
 
 57». The Sum Insured is the sum which is payable 
 by the company upon the conditions mentioned in the 
 contract. 
 
 5SO. Tables of Mortality are tables showing the aver- 
 age rate of deaths in every ten thousand persons. 
 
 581. Expectation is the average number of years 
 which a person of a certain age is expected to live, based 
 on a Table of Mortality. 
 
 582. The Rates of premium for Life Insurance, aa 
 fixed by different companies, are based on the probabilities 
 of life, determined by a table of mortality, and the probable 
 rates of interest which money will bear, and a lending or 
 margin for expenses. 
 
844 
 
 LIFE INSUEANCS. 
 
 588. Expectation of Life. 
 
 The following table showa the number living, the num- 
 be dying and the expectatiau or duration of life of eaTh 
 
 irirm;'T;ht"*^' '-- ''- ^-^^-^ ^^p-^- 
 
 ***- | ^^'°8- I Dying.j Expootatlon. I Age. I Uvln., I n^„„ l"^ 
 
 -• * "ving. Dying. Expectation, 
 
 ■ A innnnn /•_/> I TT *"' ' 
 
 11 
 
 Vi 
 13 
 14 
 19 
 16 
 17 
 1§ 
 19 
 30 
 91 
 
 3a 
 
 33 
 
 34 
 
 3.1 
 
 36 
 
 37 
 
 3§ 
 
 39 
 
 80 
 
 81 
 
 83 
 
 83 
 
 84 
 
 39 
 
 86 
 
 37 
 
 3» 
 
 30 
 
 40 
 
 41 
 
 43 
 
 43 
 
 44 
 
 4.1 
 
 46 
 
 47 
 
 '£§ 
 
 49 
 
 SO 
 
 5t 
 
 .13 
 
 53 
 
 S4 
 
 lO 100000 
 
 9dG,00 
 
 97978 
 
 97307 
 
 9(i6;jfl 
 
 95965 
 
 95293 
 
 94620 
 
 93946 
 
 93208 
 
 92553 
 
 91905 
 
 91219 
 
 90529 
 
 89835 I 
 
 89137 
 
 88134 
 
 87726 
 
 87012 
 
 86292 
 
 83565 
 
 84831 
 
 84089 
 
 83339 
 
 82581 
 
 81814 
 
 81038 
 
 80253 
 
 79458 
 
 78653 
 
 77H38 
 
 77012 
 
 76173 
 
 76316 
 
 74435 
 
 73526 
 
 72582 
 
 71601 
 
 70580 
 
 G9517 
 
 68409 
 
 676 
 674 
 672 
 671 
 671 
 671 
 672 
 673 
 676 
 677 
 680 
 683 
 686 
 690 
 694 
 698 
 703 
 708 
 714 
 720 
 727 
 734 
 742 
 760 
 768 
 767 
 776 
 785 
 795 
 805 
 815 
 826 
 839 
 857 
 881 
 909 
 944 
 981 
 1021 
 1063 
 1108 
 1156 
 
 67253 1207 
 66046 1261 
 647S5 ! 1316 
 
 48.36 
 
 47.68 
 
 47 01 
 
 46.33 
 
 45.64 
 
 44.96 
 
 44.27 
 
 43.58 
 
 4288 
 
 42.19 
 
 41.49 
 
 40.79 
 
 40.09 
 
 89.39 
 
 88.68 
 
 87.98 
 
 87.27 
 
 86.66 
 
 85.86 
 
 85 16 
 
 84 48 
 
 33.72 
 
 83.01 
 
 82.30 
 
 81.58 
 
 30.87 
 
 30.16 
 
 29.44 
 
 28.72 
 
 28.00 
 
 27.28 
 
 86.56 
 
 25.84 
 
 25.12 
 
 24.40 
 
 23 69 
 
 22 97 
 
 22.27 
 
 21.56 
 
 20.87 
 
 SO. 18 
 
 19.50 
 
 18.82 
 
 18 16 
 
 17.50 
 
 5.1 
 
 56 
 
 57 
 
 5§ 
 
 59 
 
 60 
 
 61 
 
 63 
 
 63 
 
 61 
 
 65 
 
 66 
 
 67 
 
 68 
 
 69 
 
 70 
 
 71 
 
 73 
 
 73 
 
 71 
 
 75 I 
 
 76 
 
 77 
 
 78 
 
 79 
 
 80 
 
 81 
 
 83 
 
 83 
 
 84 
 
 85 
 
 86 
 
 87 
 
 88 
 
 89 
 
 90 
 
 91 
 
 93 
 
 93 
 
 94 
 
 95 
 
 96 
 
 »7 
 
 98 
 
 99 
 
 1376 
 1436 
 1497 
 1561 
 1627 
 
 63409 
 
 62094 
 
 60658 
 
 59161 
 
 67600 
 
 65973 j 1698 
 
 64275 1770 
 62.-,05 1811 
 60661 1917 
 48744 1990 
 46754 2001 
 44693 2123 
 42505 2191 
 40371 2246 
 
 38128 
 
 35837 
 
 33510 
 
 31159 
 
 28797 
 
 26439 
 
 24100 
 
 21797 
 
 19548 
 
 17369 
 
 2291 
 
 2327 
 
 2351 
 
 2362 
 
 2358 
 
 2339 
 
 2303 
 
 2249 
 
 2179 
 
 2092 
 
 15277 1987 
 
 13290 
 
 11424 
 
 9694 
 
 8112 
 
 6085 
 
 5417 
 
 4306 
 
 3348 
 
 2637 
 
 1864 
 
 1319 
 
 892 
 
 570 
 
 839 
 
 184 
 
 89 
 
 87 
 
 13 
 
 4 
 
 1 
 
 1806 
 1730 
 1582 
 1427 
 1268 
 
 nil 
 
 958 
 
 811 
 
 673 
 
 546 
 
 427 
 
 322 
 
 231 
 
 166 
 
 96 
 
 62 
 
 24 
 
 9 
 
 8 
 
 1 
 
 lo.'ia 
 
 16.22 
 15.69 
 14.97 
 14.37 
 13.77 
 13.18 
 12.61 
 12.06 
 11.51 
 10.97 
 10.46 
 9.96 
 9.47 
 9.00 
 8.54 
 8.10 
 7.67 
 7.26 
 6.86 
 6.48 
 6.11 
 6.76 
 6.42 
 6.09 
 4.78 
 4.48 
 4.18 
 8.90 
 8.63 
 8.86 
 8.10 
 3.84 
 2.69 
 S.35 
 
 a.ii 
 
 1.89 
 1.67 
 1.47 
 1.28 
 1.18 
 0.99 
 0.89 
 0.76 
 0.60 
 
LU'K ISSUIiASCE. 
 
 846 
 
 a»4* 
 
 Table of Rates. 
 
 RATES FOR WHOLE LIFE INSURANCE. 
 Pbimidmii to Insure 81,000 patabu ai Dsatu, with PRorm. 
 
 
 
 
 Annu 1.1 
 
 Annui 
 
 Auiiiial 
 
 .Vunuiil 
 
 <K*- 
 
 Annual 
 
 Siniile 
 
 Premium 
 
 ' Prcnuumi 
 
 Premium! 
 
 Premiums . 
 
 
 rruiuiunu 
 
 Proiuiums 
 
 for 
 
 for 
 
 for 
 
 f r ^•• 
 
 . 
 
 
 
 5 Years. 
 
 10 Years 
 
 15 Years. 
 
 ao Yfars. 
 
 ! 
 
 ! 30 
 
 '10 
 
 17.80 
 
 265.17 
 
 60.22 
 
 35.03 
 
 26.96 
 
 23.10 
 
 31 
 
 18.20 
 
 270.07 
 
 61.34 
 
 35.(i;) 
 
 27.46 
 
 23. -.0 1 31 
 
 'i'J 
 
 18.G2 
 
 275.11 
 
 62.50 
 
 3t;.38 
 
 28.00 
 
 24 05 1 33 
 
 43 
 
 19.06 
 
 280.38 
 
 63.71 
 
 37.09 
 
 28.55 
 
 24.54 1 33 
 
 *i4 
 
 1951 
 
 28.-). 79 
 
 64.95 
 
 87.82 
 
 29.13 
 
 25.04 ! 3t 
 
 •i.-s 
 
 19,99 
 
 291.39 
 
 66.24 
 
 38.68 
 
 29.72 
 
 2.').55 
 
 39 
 
 36 
 
 20.49 
 
 21)7.17 
 
 67.67 
 
 89.37 
 
 30.31 
 
 26.09 
 
 ! 36 
 
 a 7 
 
 21.01 
 
 SOU. 15 
 
 69.94 
 
 40.18 
 
 80.97 
 
 26.65 37 
 
 38 
 
 21.66 
 
 30;).32 
 
 70.36 
 
 41.02 
 
 81.64 
 
 27.23 
 
 38 
 
 39 
 
 22.13 
 
 81.'-..70 
 
 71.83 
 
 41.90 
 
 32.32 
 
 27.N3 
 
 3» 
 
 »o 
 
 22.73 
 
 822.28 
 
 73.35 
 
 42.80 
 
 83.03 
 
 28.45 
 
 30 
 
 31 
 
 23.36 
 
 829.08 
 
 74.92 
 
 43.73 
 
 83.76 
 
 20.10 
 
 31 
 
 33 
 
 24.02 
 
 836.10 
 
 76.55 
 
 44.70 
 
 84.52 
 
 20.78 
 
 33 
 
 33 
 
 24.71 
 
 843.33 
 
 78.22 
 
 45.70 
 
 3531 
 
 30.48 
 
 33 
 
 34 
 
 25.44 
 
 8.50.81 
 
 "0 95 
 
 46.73 
 
 36.13 
 
 31.21 
 
 34 
 
 39 
 
 20 21 
 
 858.53 
 
 ei.74 
 
 47.80 
 
 86.98 
 
 31.97 
 
 Mi 
 
 36 
 
 27.01 
 
 8G().50 
 
 83.59 
 
 48.1)0 
 
 37.87 
 
 32.77 
 
 36 
 
 37 
 
 27.86 
 
 874.73 
 
 85.50 
 
 60.05 
 
 38.79 
 
 33.60 
 
 37 
 
 3§ 
 
 28.76 
 
 883.23 
 
 87 48 
 
 61.24 
 
 39.75 
 
 31 17 
 
 38 
 
 39 
 
 29.71 
 
 892.02 
 
 89.53 
 
 62.48 
 
 40.76 
 
 3.-) 30 
 
 39 
 
 lO 
 
 30.71 
 
 401.10 
 
 91.67 
 
 63.77 
 
 4181 
 
 3i;.3;i 
 
 lO 
 
 41 
 
 31.78 
 
 410.43 
 
 93.84 
 
 65.12 
 
 42.02 
 
 37.37 
 
 11 
 
 43 
 
 82.91 
 
 420.19 
 
 9013 
 
 60.5;i 
 
 44.08 
 
 38.45 
 
 13 
 
 ts 
 
 34.11 
 
 430.22 
 
 98.50 
 
 58.01 
 
 45.30 
 
 39. .-.8 
 
 43 
 
 14 
 
 35.39 
 
 440.54 
 
 100.116 
 
 51). .'■.5 
 
 46.59 
 
 40.78 
 
 44 
 
 14 
 
 36.74 
 
 451.13 
 
 103.51 
 
 61.15 
 
 47.93 
 
 42.04 
 
 49 
 
 46 
 
 3S.17 
 
 461.96 
 
 106.13 
 
 62.82 
 
 49.33 
 
 43.37 
 
 46 
 
 47 
 
 j\i OV 
 
 472.99 
 
 108 81 
 
 64.53 
 
 60.79 
 
 44.76 
 
 47 
 
 4§ 
 
 ii.2t! ; 
 
 484.23 
 
 111.57 
 
 66.31 
 
 52.32 
 
 4C,.22 
 
 48 
 
 49 
 
 i2.93 ; 
 
 495.66 
 
 114.39 
 
 68.01 
 
 63.00 
 
 47.75 
 
 49 
 
 ■^O 
 
 ^i.ir 
 
 507.27 
 
 117.28 
 
 70.05 
 
 65.56 
 
 40.37 
 
 90 
 
 .'SI 
 
 46.56 
 
 619.06 
 
 120.24 
 
 72.01 
 
 57 30 
 
 51.07 
 
 91 
 
 .'i'i 
 
 48.53 
 
 631.01 
 
 123.28 
 
 74.05 
 
 59.11 
 
 52.S0 
 
 93 
 
 !i3 
 
 60.61 
 
 643.10 
 
 126,38 
 
 76.16 
 
 61.00 
 
 54.75 
 
 93 
 
 94 
 
 62.81 
 
 655 33 
 
 129.55 
 
 78.33 
 
 63.00 
 
 5<i.7.") 
 
 91 
 
 93 
 
 65.14 
 
 667.70 
 
 132.79 
 
 80.61 
 
 65.01> 
 
 58..-I0 
 
 99 
 
 96 
 
 67.61 
 
 680.17 
 
 130.11 1 
 
 82.07 
 
 67.29 
 
 61.11 
 
 96 
 
 97 
 
 60.22 
 
 692.74 
 
 139.5 1 
 
 85.43 
 
 69.01 
 
 63 40 
 
 97 
 
 ^n 
 
 63.00 
 
 (lO.vJl 
 
 143 00 
 
 88.00 
 
 72.07 
 
 60.03 
 
 98 
 
 sj» 
 
 65.'J4 
 
 618.17 
 
 140.58 
 
 90.09 
 
 74.68 
 
 68.74 99 
 
 'iO 
 
 69.07 
 
 630.98 
 
 1.50.26 
 
 93.51 
 
 77.44 
 
 71.03 GO 
 
S46 
 
 LJF£ IMiUJiANVJi. 
 
 
 SHS, RATES FOR ENDOWMENT IN8UKANCE. 
 
 Airanu. PRimvira to Insuu 11 ,000. Pat4bli a D«*th ot tM 
 Expiration or thb foixownro T«bm», with PRoriTi. 
 
 Age. 
 
 no 
 'it 
 
 tl3 
 94 
 'in 
 
 tie 
 ar 
 
 28 
 
 39 
 
 30 
 
 31 
 
 39 
 
 33 
 
 34 
 
 itH 
 
 8« 
 
 3V 
 
 38 
 
 89 
 
 40 
 
 41 
 
 49 
 
 43 
 
 44 
 
 49 
 
 4<t 
 
 4T 
 
 18 
 
 49 
 
 .50 
 
 51 
 
 39 
 
 A3 
 
 «4 
 
 SS 
 
 56 
 
 57 
 
 59 
 
 59 
 
 60 
 
 10 Teaw. M Tear*. 
 
 95. S3 
 
 Oy.39 
 
 <Jo.l5 
 
 95.61 
 
 95.58 
 
 95.05 
 
 95.73 
 
 95.81 
 
 95.89 
 
 95.98 
 
 9fi.08 
 
 90. 13 
 
 90 -JS 
 
 96;i9 
 
 90 50 
 
 90 03 
 
 96.70 
 
 90.90 
 
 97 05 
 97.23 
 97.13 
 97.06 
 97.94 
 98.'?5 
 
 98 02 
 99.02 
 9947 
 90.96 
 
 100.50 
 
 101.08 
 
 101.72 
 
 102.41 
 
 103 17 
 
 104.00 
 
 104.90 
 
 105.89 
 
 100.97 
 
 108.16 
 
 109.47 
 
 110.91 
 
 112.50 
 
 61.63 
 
 6170 
 
 6177 
 
 61.85 
 
 6194 
 
 62.03 
 
 62.12 
 
 6222 
 
 62.33 
 
 62.44 
 
 02 55 
 
 02.08 
 
 02 81 
 
 62.95 
 
 63.11 
 
 63 28 
 
 63 40 
 83.67 
 03.90 
 64.16 
 64.46 
 
 64 80 
 05.18 
 05.01 
 ilO.lO 
 60.03 
 67.23 
 67.87 
 08.58 
 69.35 
 70.19 
 71.12 
 72.12 
 73.22 
 74.42 
 76.74 
 
 flOYMu-i. 
 
 45.02 
 
 46 10 
 
 45.19 
 
 45.29 
 
 45 39 
 
 45.50 
 
 45.61 
 
 45.74 
 
 45 87 
 
 40.01 
 
 40.10 
 
 40 32 
 
 4650 
 
 46.09 
 
 40.90 
 
 47.14 
 
 47.10 
 
 47.09 
 
 4801 
 
 48.37 
 
 48 77 
 
 49.22 
 
 49.72 
 
 50 28 
 
 5091 
 
 61.00 
 
 52.30 
 
 63.18 
 
 64.09 
 
 66.07 
 
 50.15 
 
 as Tean. 
 
 85.31 
 
 86.41 
 
 85.52 
 
 35 03 
 
 35.70 
 
 85.89 
 
 86.04 
 
 86.19 
 
 86.86 
 
 36.54 
 
 36.74 
 
 36.96 
 
 37.20 
 
 87.46 
 
 87.74 
 
 88 06 
 
 38.40 
 
 88.78 
 
 89.20 
 
 89.67 
 
 40.19 
 
 40.77 
 
 41.41 
 
 42.12 
 
 42.91 
 
 43.77 
 
 • • • • 
 
 • • ■ • 
 
 • • a • 
 
 SO Tean. 
 
 39.10 
 29.22 
 
 29 36 
 29.50 
 29.66 
 29.83 
 30.02 
 30.23 
 
 30 14 
 80.07 
 80.93 
 3121 
 31.63 
 31.86 
 !I2.23 
 .•i2.63 
 83.07 
 33.56 
 84.09 
 34.68 
 83.38 
 
 • • ■ • 
 
 • • • • 
 
 • • • • 
 
 as Tean. 
 
 24.94 
 
 25 10 
 
 35.27 
 
 25.40 
 
 26.66 
 
 25.87 
 
 36.11 
 
 36.86 
 
 26.64 
 
 26.94 
 
 27.27 
 
 37.63 
 
 28.01 
 
 28.44 
 
 38 90 
 
 Si940 
 
 Afl» 
 
 9« 
 
 91 
 
 99 
 
 93 
 
 94 
 
 93 
 
 96 
 
 97 
 
 98 
 
 99 
 
 30 
 
 31 
 
 39 
 
 83 
 
 84 
 
 »a 
 
 86 
 
 37 
 
 38 
 
 89 
 
 40 
 
 41 
 
 49 
 
 48 
 
 44 
 
 43 
 
 46 
 
 47 
 
 48 
 
 49 
 
 30 
 
 31 
 
 39 
 
 33 
 
 34 
 
 33 
 
 36 
 
 37 
 
 38 
 
 39 
 
LIFE ISSURASOK. 
 
 847 
 
 EXERCISE 122. 
 
 1. Find *^ie amount of proraiura for an ordinary life 
 policy of ^4,000, issued to a person 40 yoarB of age. (Art. 
 588.) 
 
 2. Find Iho annual prerainin for a 10-payraent life policy 
 of $5,000, issued to a person 85 years of age. (Art. 685.) 
 
 8. When 40 years of agi\ a p<TSon took out a 20-year 
 endowment policy of $ 10.000. He survived the endowment 
 period. How much less di.l he receive than ho paid as 
 premiums, not reckoning interest ? 
 
 4. The annual premium, wit^iout profits, on a life policy 
 of $5,000 at the age of 35 is $111. How much would be 
 necessary to invest at 6 % interest to secure the payment of 
 the annual pri luium ? 
 
 6 Ur. A., age 30, insures his life for $10,000, ordinary 
 life plan, with profits. How much must he place in trust 
 BO that the interest at 5 % will be sufficient to pay the 
 premiums on the policy ? 
 
 6. A single premium for an insurance of $1,000, without 
 profits, for "a person 32 years of age, is $300. What would 
 be the excess of the insurance over the amount produced 
 by placing the money at coiupoand interest at 4 %, supposing 
 the insured to live 20 years ? 
 
 7. Mr. A , aged 36, insured his life for $5,000, and paid 
 an annual premium of §135 ; supposing he died at the age 
 of 68, how much did the premiums he paid exceed the face 
 of his policy, money being worth 6 % compound interest ? 
 
 8. Mr. A., at the age of 35, takes out a 20-year endow- 
 ment policy for $3,000 and pays an annual premium of 
 $141. By what amount will the premiums exceed the face 
 of the policy at the end of the endowment period, money 
 bemg worth 6 % compound interest ? 
 
848 
 
 MiaCKLLANKoVS. 
 
 MISCELLANEOUS 
 
 EXERCISE 123. 
 
 I. 
 
 1. Which is the better investment, % $3,000 7% bond, 
 or a house which rents for $240 a year, taxes being $30.60, 
 and annual repairs $40 ? 
 
 2. A person exchanges 250 shares of 6 % stock, at 70, 
 for stock bearing 8%, at 120; what is the dilierence in 
 his income ? 
 
 8. A gentleman baa been receiving 12 % on bis capital 
 in Canada. He goes to England to reside, and invests it in 
 the 8 per cents, at 94f, and his income in England is 
 je2,400. What was his income in Canada, the £ being equal 
 to $4.86| ? 
 
 3 1 
 
 4. Find the alteration in income occasioned by shifting 
 £3,200 stock from tlie 3 per cents, at 86g, to 4 per cent, 
 stock at 114J : the brokerage being J%. 
 
 6. Suppose a railroad stock, actually worth $100 a share, 
 to be •• watered " by the issue of a stock dividend of 20 % 
 to tli( stockholders, what would the watered stock be 
 worth ? 
 
 6. A person bought stock at 95J, and after receiving the 
 half yearly dividend at the rate of 7% per annum, 
 sold out at 92| and made a profit of $37.60. How ' ich 
 stock did ho buy ? 
 
 7. At whnt price must U. S. 4^*8 be bought, to yield 
 the interest on the investment that 5 % bonds will at 110 ? 
 
 What amount of the latter bonds (par value) must be 
 ■old at 109, leaving brokerage out of account, that with 
 the proceeds a suflScient amount of 4^'a may be bought, at 
 par, to yield a semi-annual income of $364.60 ? 
 
UlSCHLLANKOVa. 
 
 84U 
 
 3. 
 
 i 
 
 2 
 
 8. A person invcata the proceeds of a note for $9,607.60 
 due 16 months hence, discounted (true discount) at 4^ %, 
 in 6% stock at 91, brokerage ^%. Find his net annual 
 income from this investment after deducting an income 
 tax of 2J%. 
 
 9. The present income of a railway company would 
 justify H dividend of 8|%, if there were no preference 
 shares ; but as $1,200,000 of the stock consists of such 
 shares, which are guaranteed 6% per annum, the ordinary 
 eliareholders receive only 8%. What is the whole amount 
 of stock ? 
 
 10. A gentleman has $25,000 of Bank of Commerce 
 stock which pays a dividend of 8%. When money is 
 worth 7 % he sella out, and invests in Bank of Toronto 
 stock at 205, which pays a dividend of 12 %. What 
 difference in his inoorae after allowing his agent ^ % com- 
 mission fur each transaction ? 
 
 11. A man invests $19,450 in Bank of Montreal stock 
 at 194, and $iy,8.j0 in Bank of Toronto stock at 198, pay- 
 ing; Ilia broker in each case i% on the amount of stock 
 purchased. If the former pays a half-yearly dividend of 
 6^%, and the latter a half-yearly dividend of 6^%, find 
 his total income for the half-year. 
 
 12. A man invested a certain sum in Bank of Commerce 
 stock, which is at 120, and pays 4^ % half-yearly dividends ; 
 and 62J per cent, more than that sum in Dominion Bank 
 stock, which is at 130, and pays 4J % half-yearly dividends ; 
 his income from both investments is $222.50. Find the 
 amount of money invested in each kind of stock. 
 
 n. 
 
 1. Jan. Ist, 1889, three persons began basinesa. A. 
 put in $1,200, B. put in $500, and May Ist $800 more, 
 C. put in $700, and July Ist $400 more. At the end of 
 the year the profits were $875. How shall it be divided ? 
 
! 
 
 860 
 
 UtSCELLANEOUS. 
 
 2. A. B. and C. commence business; A. pats ' 260 
 firkins of butter, B. imts in $2,500. and C. |4.100. .heir 
 profits amounted to $2,210, of which A. took $560. How 
 much was his butter a pound, and to how much were B. and 
 C. eutitlod ? 
 
 8. A building worth f 28,.';00 is insured in the iEtna for 
 $3,2(10, in the Western for $ 1,200, and in the Mutual for 
 $G,f.OO. It having been partially destroyed, the damage is 
 set at :? 10,500. What nhould t^ach company pay ? 
 
 4. A. had $8,800 at uitor. i for fiO diivn ; B. had $4,100 
 at interest for 46 days ; and C. hal ^' t/JfO at interest for 
 70 days. They received $16;: interest money. What did 
 each get, and what was tbo rate fer c .ut? 
 
 6. A. and B. formed a puiliurphij; Jnu. Ist, 1889. A. 
 put in $0,(100, and at the end of 8 months $900 more, and 
 at the end of 10 months drew out $600 ; B. put in $9,000, 
 and 8 months after $1,500 more, and drew out $500 Dec. 
 Ist. At the end of the year the net profits were $8,900. 
 Faid the share of each. 
 
 6. Two persons coramei;ce trad« with the same amoui !; 
 of money. The first man t-pends 48 % of his money yearly, 
 and the second spends a sum ( qual to 25 % of what both had 
 at first. At the end of the year thf^y both together had 
 $8,iG8. How much had each at the end of the year ? 
 
 7. A. commenced business with a capital of $10,000, on 
 the 1st of January, 1889 ; on the 1st of May, B. entered 
 into partnership with him, and put in 1,500 barrels of flour. 
 On the first of January, 1890 their profits were $5,100, of 
 which B. was entitled to $2,100. What was the value of 
 the flour per barrel ? 
 
 8. Three person i formed a partnership, with a capital of 
 $4,600. The first man's stock was in trade 8 months and 
 
UtSCKLLAShOUS. 
 
 mi 
 
 t. 
 
 gnuif^d $752; the Bfcoml man 
 monthfl ami Kiiiiitd :J^('.0() ; au( 
 in 16 months and gaiueil $i) iO 
 Block? 
 
 s Bt )i'k W113 in trdle I'i 
 
 iio Diir I 
 
 li^ a took 
 
 iiM man iiaa m 
 Wl;at was each man's 
 
 9. Thrte men enROged in the manufacture of pails; A. 
 jiut in $<2,550 for R months ; B., a sum not specified for 12 
 rauntiiB ; C, $1.'»H0 for a time not spocitiel. A. ri'Cfived 
 for his stock and !)rolit ?:J,i:lO; 13., $1,'200 for las; C, 
 $l,48r> for hid. Required, li.'a Hlock and O.'s time. 
 
 1(1. Oil the Ist of Jaiiuiiry, IHAU, .Tamos Wilson oponod a 
 haniwfire store wi-h a stock of i?l7,200; on the Ist of 
 April, Joseph Brooks entered into partnership with him, 
 and advanced .*;i'2.onO; on tlio Ist of July, Abraham Miller 
 put in goods to tliH amount of $ir»,000; on the IhI of 
 Jauuiiry, 1890, wlicn the b;:lanco bhect was cxhihiud, there 
 appcfired a net profit of $8,0ti(). To how much was oach 
 i);irtner entitled ? 
 
 11. A., B. and 0. engaged in business, A. puts in $400 
 at first, and $400 more at the end of (5 months ; B. [luta in 
 $iH)(i at first, anl withdraws ono-thirtl of his capital at the 
 end of 6 mouths ; C. [uts in sji-iOO at th(* end of every 
 months. At the end of two years they have Rained 
 $0,700. What share of the profits should C. receive in 
 addiiion to 25 % of the total profit for managing the 
 business ? 
 
 12. A., B. and C. formed a partnership for 2 years ; A. 
 put in $10,000, B. $5,000, and C $2,500; it was agreed 
 that C. should receive $1,500 a year for superintending the 
 business. A. drew out $1,000 at the end of each quarter 
 for one year, and at the end of 13 months put in $15,000 
 more ; B. withdrew $600 at the end of each quarter. At 
 the time of settlement the net gain was $22,500. Required 
 efvch one's share. 
 
9ffil 
 
 MISCELLANEOUS. 
 
 !-; 
 
 m. 
 
 1. A draft on Winnipeg bought at f % premium for 
 $12,000, was sent to an agent to pay for cotton purchased 
 at 2} % commission ; what was the value of the cotton ? 
 
 2. A commission merchant in Peterborough wishes to 
 remit to his employer in Belleville $512,136 by draft at 60 
 days ; what is the face of the draft that he can purchane 
 with this sum, exchange being at 2^ % discount, interest 
 7%? 
 
 3. Shipped to Liverpool, 2,000 barrels of flour, which cost 
 in Montreal $4.50 per barrel ; it was sold at £1 18s. 6d. 
 per barrel, when the premium was 8^ % ; how much v as 
 the gain ? 
 
 4. A grain dealer bought 10,000 bushels of corn, at 88f 
 cts. a bushel. He sent it to London, where it brought 
 28s. 9d. a quarter, when tlie premium was 9^%; the 
 cost of transportation was 12^ cts. per bushel ; how much 
 was gained ? 
 
 5. A person in Barrie ■; oeived £1,000 sterling, from 
 England, when the premiuici was 9%. He put it out at 
 interest for 9 months, 18 days at 6 % per annum ; to 
 how much did it amount ? 
 
 6. A merchant sent his agent in London 425 bales of 
 cotton weighing 856 lbs. apiece, which cost him 9^ cents 
 a lb. ; the agent paid §d. a lb. for freight, i643 for car- 
 tage, sold it at 8d. a lb., and charged 2^% commission. 
 If the merchant sells a bill of exchange for the amount, 
 at 10^%, will he make or lose by the operation. Ho* 
 mi-ich ? 
 
UlSCELLANEOVS. 
 
 869 
 
 7. Received from my correspondent in New York $6,150 
 U. S. currency, with instructions to deduct m; commission 
 at 2^%, and invest the remainder in Canadian Tweedi 
 worth $1.03^ per yard. How many yards should I send 
 him, gold being quoted at 116 ? 
 
 8. An importer bought 1,566 yards of silk, at 68. 6d. 
 per yard ; paid £,1 128. for freight, 25% duties, and remitted 
 a bill on London at 9J % premium ; how must he sell it 
 per yard on 6 months, m order to make 12^%, allowing 
 7 % interest ? 
 
 9. Exchange between Paris and Amsterdam being at 
 the rate of 2 francs 20 centimes to the guilder, that 
 between London and Paris at the rate of 26 francs 80 
 centimes to the £, and that from New York on London at 
 9i % premium, what will be the cost of a remittance for 
 1,000 guilders from New York to Amsterdam by bills of 
 exchange through London and Paris ? 
 
 10. A merchant in Toronto wishes to pay ^£3,000 in 
 London. Exchange on London is 9\% premium ; on 
 Paris, 5 francs 25 centimes por $1 ; and on Amsterdam, 
 40 cents to a guilder. The exchange between France and 
 England at the same time is 25 francs to £\, and that of 
 Amsterdam on England 12^ guilders to ;fil. Which is 
 the most advantageous, the direct exchange, or through 
 Paris, or through Amsterdam ? 
 
 11. A Hamilton merchant, owing 2,400 florins in Ams- 
 terdam, can buy exchange on that citv for 41^, Is it 
 better for him to do so, or to remit to London, and thence 
 to Amsterdam,— exchange on London being 4.87 in Ham- 
 ilton, exchange on Amsterdam being 12 florins to the 
 pound sterling in London, and brokerage for purchasing 
 the exchange in London being \ oi 1 % ? 
 
864 
 
 MISCELLANEOUS. 
 
 12. A banker in Toronto remits $10,000 to Liverpool as 
 follows : First to Paris, at 5 francs 40 centimes per $1 ; 
 thence to Hamburg, at 185 franca per 100 marcs ; thence 
 to Amsterdam, at 17 J stivers per marc ; thence to Liver- 
 pool, at 220 stivers per £ sterling; how much sterling 
 money will he have in bank at Liverpool, and what will be 
 his gain over direct exchange at 10 % premium ? 
 
 'I 
 
 l! 
 
 I 
 
 IV. 
 
 1. Allowing 6% compound interest on an annuity of 
 $200 which is in arrears 20 yeara, what is its present 
 amount ? 
 
 2. What is the prwRent worth of an annuity of $500 for 
 7 years, at 6 % compound interest ? 
 
 3. Find the annuity whose amount for 25 years is 
 $16,459.35, allowing compound interest at 6 %- 
 
 4. The present worth of an annuity to be continued 10 
 years at 6 %, compound interest, compounded annually, is 
 $7,360.08. What is the annuity ? 
 
 6. A man bought a farm for $4,500, and agreed to pay 
 principal and interest in 4 equal annual instalments ; how 
 much was the annual payment, interest being 6 % ? 
 
 6. A man bought a piece of property for $10,000, and 
 agreed to pay principal and interest in 8 equal annual in- 
 stalments. How much was the annual payment, interest 
 being 7 % ? 
 
 7. A father bequeathed his son, 11 years of age, » 6% 
 annuity of $is,600, to begin in 3 years and continue iO 
 years ; what would be the amount when the son was 21 
 years old ? 
 
MlSC£LLANhOUS. 
 
 355 
 
 m 
 
 8. A man took out a life i-olicy for $3,000, at the rate of 
 $21.50 per $1,000. What sum must he depoaif in a savings 
 bank, the compound hiterest of which, at 5%, payable 
 aemi-aunually, shall discharge hia annual premium? 
 
 9. A man died leaving :?.3,000 to be divided between 
 his three sons, aged 13, 15, and 16 years respectively, 
 in such a proportion that the share of each baiiig put at 
 simple interest at 6%, thould amount to the suirjo aum 
 when they should arrive at the age of 21. IIow much was 
 each on j's share ? 
 
 10. A man paid annually $10 for tobacco from the age 
 of 14 until he was 50, when he died, he left $1,000 for 
 his heirs. What sum rai'^ht he have left them iial he 
 dispensed with tobacco, and loaned the muuuv thus siived 
 at the end of each year at 6 % compound interest ? 
 
 11. A mortgage of $1,000, repayable in 5 years at $200 
 a year with interest at Q'< on the unpiiid principal, is sold ; 
 what is its value allowir ; i !- purchaser 8% for his money? 
 
 12. L mortgage on a fiu-in is payable in four equal 
 annu.l iristalments of §1,000 each. When the first instal- 
 ment falls ilue the mortgagn- offers in part payment $2,000 
 in 6% municipal debv^iturts upon which interest is due, 
 and which mature in one year. What balance in cash 
 should the mortgagor demand in exchange for the mort- 
 gage, money bcirjg ~crtb 10 '5!;? 
 
866 
 
 POWERS AND ROOTS. 
 
 POWERS AND ROOTS. 
 
 ■^A. ri\ 
 
 580« A Power of a nutnber is the number itself, or the 
 product of equal factors, each of which is that number. 
 
 Thus, 8 is a power of 2, since 8-2x2x2. 
 
 SH7» The First Power is the number itself. 
 
 fiHH, The Second Power is the product of a number 
 taken twice ns a factor, and is called a Square. 
 
 Thus, 16 is the square of 4, since 16 = 4 x 4. 
 
 58». The Third Power is the product of a number 
 taken three times as a factor, and is called a Cube. 
 
 Thus, 125 is the cube of 6, since 125 - 6 x 5 x 6. 
 
 ff90. A Root is one of the equal factors of a number. 
 
 KoTB. — Boots are named from the namber of equal factors they 
 OOntain, 
 
 591* The Square Root is one of the two equal factors 
 of a number. 
 
 Thus, 7 is the square root of 49, since 49 - 7 x 7. 
 
 593. The Cube Root is one of the three equal factors 
 of a number. 
 
 Thus, 7 is the cube root of 813, since 343 =■ 7 x 7 x 7. 
 
 5W». The Radical Sign is the character V, which, 
 placed before a number, indicates that its root is to be 
 found. 
 
 59-1. The Index of the root is the figure placed above 
 the raciiL-al sign to denote what root is to be taken. When 
 no index is written, the index 2 is always understood. 
 
 Note. — The names of the roots are derived from the corresponding 
 pawerB, and are denoted by the indices of the radical sign. 
 
 Thus V^ denotes the square root of 9, the V^ denotes the cube root 
 of 9, etc. 
 
 595. A Perfect Square is one whose exact square root 
 ean be found ; as 9, 16, 36, etc. 
 
 596. A Perfect Cube is one whose exact cube root can 
 be found ; as 27, 64. 216, fttc. 
 
SQUARE ROOT. 
 
 867 
 
 SQUARE ROOT. 
 
 (197. Extracting the Square Root of a number is the 
 process of finding one of the two equal factors of a number. 
 
 Noia— The stadent shoald memorize the sqaares of the first nine 
 digits 
 The sqaares of 1, 3, 8, 4, 6, 6, 7, 8, 9, are respectively 1, 4, 9, 16, 25, 36, 
 
 49, 64, 81. 
 
 S9H, To extract the square root of a number. 
 
 ExAUPLi 1. — Extract the sqaare root of 6,635. 
 Paocbss. 
 
 146 
 
 66 j 25 (76 
 49 
 725 
 
 725 
 
 EZPLAKATION or THB MbTHOO. 
 
 Separate the given number into periods of two figarea each, beginning 
 at the anits' figure. 
 
 Find the greatest square in tlie first period (56), which is 49, and place 
 it under 66, also write the root of 49, which is 7, as tho first figure in the 
 fequired root. 
 
 Subtract 49 from 66, and to the remainder (7) affix the next period (25), 
 giving 735 for a dividend. At the left of the dividend (725), write twio« 
 the root already found (7), which gives 14. 
 
 Divide 72 by 14, which gives a quotient (5). 
 
 Affix 5 to 14, giving 145,also place 5, as the second figure of the root. 
 
 Multiply 145 by 5, giving 723, which subtracted from the dividend {725), 
 leaves no remainder. 
 
 75 is the required root. 
 
 EzAiiPi.1 2.— Extract the square root of 6,838,226. 
 Process. 
 
 
 6 1 83 1 82 1 25 (2616 
 4 
 
 46 
 
 283 
 276 
 
 621 
 6325 
 
 782 
 521 
 
 26125 
 20126 
 

 I; 
 *! 
 
 t I 
 ■ .1 
 
 \ 
 
 fi' 
 
 HI 
 
 858 
 
 SQUARE ROOT. 
 
 Ectlasatioh of thr Method. 
 
 Separate the)<ivon number into periods of two flj^urea eaoh, commencing 
 «t the unite' fii^ure. 
 
 Find the greatest square in the flrat period (G). which is 4, and place it 
 ondcr 6 also write the root of 4, which is 2, as the first figure of the 
 required root. 
 
 Subtract 4 from 6, and to the remainder (2) affix the next period (88;, 
 giving 283 as t)ie divid'.nd. 
 
 At the left of the dividend (283), write twice the root already foand (3), 
 which gives 4. 
 
 Divide 28 by 4, which gives 7 as a quotient. 
 
 Affix 7 to 4, giving 47, also place 7 as the second fi^juro of the root, and 
 multiply 47 by 7, which gives 329, a number greater than the dividend 
 (283), showing that 7 is too lar;^o El number. 
 
 We next try 6 as the second figure of the root. 
 
 Affix to 4, giving 40 ; and place 6 as the second figure of the root. 
 
 Multiply 46 by 6, giviiif^ 276, which subtracted from the dividend 288, 
 leaves a remainder 7, to which affix the next period (82), giving ai the 
 next dividend 782. 
 
 Multiply the part of the root already found (26) by 2, obtaining 63, 
 which place to the left of the dividend 782. 
 
 Divide 78 by 52, which gives a quotient of 1. 
 
 Affix 1 to 62, giving 521, also place 1 as the third figure of the root. 
 
 Multiply 521 by 1 and subtract from the dividend 782, after which pro- 
 ceed as before. 
 
 NoiEB 1. — If there is a remainder after the root of the last period is 
 found, annex periods of ciphers, and proceed as before. The figures of the 
 root thus obtained will be deeimalt. 
 
 2. If the trial divisor ia not contained in the dividend, annex a cipher 
 both to the root and to the divisor, and bring down the next period. 
 
 3. It sometimes happens that the remainder is larger than the divisor ; 
 but it does not neoesaarily follow that the figure in the root is too smalL 
 
 599. To extract the squa-e root of a decimal. 
 
 BCLB. 
 
 Bi'gin at the units' place, and proceed towards the left and 
 
 right, to separate into periods of two figures each, then 
 
 extract the root at in whole numbers. 
 
 NoTBS 1 —The left hand period in vihoU numberB may have but one 
 figure ; but in decimals, eaoh period must have tteo figures. Hence, if tlie 
 number of decimals is odd, a cipher must be annexed to complete the 
 period 
 
HQUAliE HOOT. 
 
 859 
 
 3. It muat be kept in mind that no period shoold contain ftn inte^^or 
 ftnd decimal, and that, if there is an odd number of decimal places in the 
 giren number, the last period must be completed by annexing a cipher. 
 
 600. To extract the square root of a fraction. 
 
 BDIil. 
 
 Reduce the fraction to its timplest form and find theaqiuirt 
 root of each term aeparatcly. 
 
 NoTKS 1. — If the denominator of the given fraction, when rednoed, ii 
 an imperfect square, reduce the fraction to a decimal, and proceed a* 
 above. 
 
 2. Mixed numbers should be reduced to improper fractions, or the 
 fractional part to a decimal. 
 
 EXERCISE 123. 
 
 Find the square root of — 
 
 1. 36864. 5. 344036. 9. 679131. 
 
 i. 81225. 6. 258Utl4. 10. 734449. 
 
 8. 168921. 7. 896lt00. 11. 820836. 
 
 4. 313631. 8. 499849. 13. 850C25. 
 
 Find one of the two equal factors of — 
 
 17. 6838226. 20. 290356226. 
 
 18. 9048064. 31. 3196944. 
 
 19. 688587ft. 33. 19228226. 
 
 Extract the square root of — 
 
 36. .0961. 80. 28867. 84. 8819.34 
 
 37. 16.21. SI. 33489. So. 1.3386M. 
 
 38. 22.09. 83. 4.2849. 86. 226.8036. 
 29. .0004. 8S. 17.3066. 87. .00001024. 
 
 Extract the square root of — 
 
 43. 6. 46. 3. 50. 20^. 
 
 43 .6. 47. .08. 6i. 153J. 
 
 44 .05. 48. 26. 62. 1^ 
 45. ,005. 49. .03. 63. 23.1. 
 
 Find the square root of — 
 
 68. f 61. m. G4. A- 
 
 69. f 62. |§§f. 65. 171|. 
 60. |. 68. '4mf ''S 1115- 
 
 18. 906289. 
 
 14. 1081600. 
 
 15. 1177225. 
 
 16. 1231321. 
 
 88. 44502241. 
 34. 61685316. 
 26. 1795811801. 
 
 88. 6416.96. 
 
 8S. 50.1264. 
 
 40. .00720801. 
 
 41. 2'jU.22529G. 
 
 54. 8}. 
 
 55. 35J. 
 
 56. 27f. 
 
 57. 36|. 
 
 67. I 
 
 68. Bf 
 
 69. 33}|. 
 
• t 
 
 M 
 
 
 %.' 
 
 f 
 
 ••♦- 
 
 i 
 
 r'^ 
 
 
 -.3'- 
 
 ':\\ 
 
 860 CXJBE ROOT, 
 
 CUBE ROOT. 
 
 601. Extracting the Cube Root of a namber ie the 
 process of finding one of the three equal factors of tht 
 number. 
 
 NoTi.-The itadent should memorize the onbea of the firat nine digiu 
 
 uTbU^ "*' ^' ^' '• *• *• "' '•*••*" "'I-Otively 1, 8. 27, 64. IM. 316 
 
 602. To find the cube root of a number, 
 
 EzAHPU — Find the onbe root of 32768. 
 Fbocxii. 
 
 1. n. III. 
 
 8 
 
 
 82 1 7 
 27 
 
 9 
 
 2700 
 184 
 
 676S 
 
 
 23a4 
 
 6768 
 
 82 is the cube root. 
 
 EZPLANATIOM OT IHB MeTHOD. 
 
 Pirrt separate the given number into period* of three fleurei eMh. 
 beginning at the unite' figure. ^^ 
 
 Then take the nearest perfect cube not greater than 82, which is 27. 
 and set down its cube root, which is 8 in column II., in line with 82768 
 
 Then subtract 27 from 82, and to the remainder (6) annex the next 
 period (768), giving 6768. 
 
 . S"ov^n*°* ' ""*"• ^^^ ^"* *^'""* (^' °' ^^^ «^*' "^''^y 'oond. which 
 !• (8 X 8) 9 m column I , and 3 times the square of the root (8) already found, 
 which gives (8x8x8) 37, with two cipliers annexed to it, in column III 
 each opposite 6768. ** 
 
 Divide 5768 by 2700, which gives a quotient of 2. 
 
 Place 2 in column II., opposite 9. 
 
 ,,^^ ^■L')fn°°!/°"'^' ^' '°°'*'P'y *^'' ^y '^' "^d place the product 
 184 under 2700, add and multiply their sum, 2884 by «, and place their 
 product 6768 under 6768. and subtract. As there is no remainder 82768 
 ie a perfect cube 
 
 The figures in column II. taken in order give the onbe root 32. 
 
CUBE HOOT. 
 
 861 
 
 I the 
 
 r the 
 
 iiglta 
 S,91« 
 
 I 37, 
 
 768. 
 next 
 
 hioh 
 and, 
 III.. 
 
 lao« 
 
 heir 
 2768 
 
 EzAMru 3.— EztrMt Iba onbs root of 133016337383. 
 Pnocsu. 
 L IL III. 
 
 4 
 
 U 9 
 
 147 
 
 
 123 1 616 1 837 1 381 
 
 4800 T.D. 
 1161 
 
 8961" C D. 
 81 
 
 720300 T.D. 
 8856 
 
 68616 
 
 63649 
 4966837 
 
 729166 0-I>. 
 86 
 
 73804800 T.D, 
 
 119104 
 73923904 CD. 
 
 4371936 
 69139138S 
 
 691391233 
 
 1488 
 
 EZPLANATIOR OV TBI MbTBOD. 
 
 Separate the j^ven number into periods of three flgaren. each beginninff 
 at the unite' flgore. 
 
 Then aa in Example 1, take the nearest perfect cube not greater than 
 122, which ia 64, and aet down its cube root which is 4 in oolumn II., in 
 line with the given number. 
 
 Subtract 64 from 133, and to tha remainder (68) annex Iha next period 
 (616), giying 68615. 
 
 Next place 8 timea 4 (the first figure of the root), that is 12 in column I j 
 and S timea 4x4 (the square of 4), which equals 48 in column III ; 
 •^ach in line with 68615, and annex two ciphers to 48 giving 4800. 
 
 Divide 58816 by 4800, and a quotient 19 is obtained. 
 
 Vow 9 ia the largest number we can have aa a fi^;ure of the root, and 
 w« thoreftre use l», placing it in column II. opposite 13. 
 
 Read "3 as one number 129. Multiply 129 by 9, and place the product 
 y.--, ".'ii:»r 4800, to which it is then added, giving as a result 6901. 
 
 Mai.ij :j t.mi by '}, and place the product 6^649 under 68616 and sob- 
 tract, and 10 ;ho re ir under 4966 annex the next period 327. 
 
 Nfl ;t place tha ».i,i,.rg of 9, which ia 81, under 6961. add the three 
 unn:l. -t or.nneoted by the bracket, and to their anm 7203 annex two 
 ciphera. 
 
 Then t .a ■«• C timea 49 (the part of the root already found), wh oh la 
 147, in oolumn X., :ri the position indicated in the solution. 
 
 Divide 4966327 by 720300, aod a quotient 6 is obtained. Place 6 ia 
 oolumn II. opposite 147. 
 
I 
 
 45 
 
 i 
 
 
 8t'>2 
 
 CUliK ROOT. 
 
 Head 147-6 at one number 1476. Multiply 1476 by 6, and add th« pr^ 
 dnot 8856 to 720300. Multiply their mm 729H6 by 6. and plac« their 
 prodact 4374936 in the poeition niven in the nolntion, etc. 
 
 The attention ol the gtulent in dlreoteil tlrat to the method of obtain- 
 ing the number! in colnmn 1. from those in column II; 19 ■ 4 x 1; 
 147 •■ 49 x S; 1498 a 490 X 3 ; eto. 
 
 Second, to the formation of tho following numben : 
 
 11(1 - 129 X 9j 8656 • 1476 x 6; 119104 - 14888 x 8. 
 
 Third, to the formation of trial divisore marked T.D. 
 
 Foartb, to the formation of completo divisorB marked 0.1>. 
 
 NoTBB 1.— If there i« a remaimler after the root of the last period ii 
 found, annex period* of ciphcn, and proceed as before. The root fl«ttre« 
 Ihns obtained will be decimaU. 
 
 2. If a trial divisor is not contained in the dividend, put a eipher in the 
 root, iico ciphtrt on the right of the divieor, and bring down the next 
 period. 
 
 8. If the prodact of the diviaor completed into the figure last placed in 
 the root axceedt the dividend, the root figure ii too large. Sometimes the 
 remainder is larger than the divisor completed ; but it does not necessarily 
 follow that the root figure is too iniaH. 
 
 603. To extract the cube root of a decimal 
 
 BULK. 
 
 Begin at the units' place, and proceed both toward th« left 
 and riiiht to $eparate into periods of three , figures each, then 
 extract the root as in xchole numbers. 
 
 Nora.— The Uft hand period in tehole nutnber$ may have but ojm or (wo 
 flgnres, bat iu decimaU each period must have three figures. Hence, 
 ciphers mast be annexed to the right of the decimal to complete the 
 periods, when neoesaary. 
 
 604. To extract the cube root of a fraction. 
 
 BULK. 
 
 Reduce the fraction to its lowest terms, then extract the root 
 of its numerator and denominator. 
 
 Noras 1— When the denominator is not a perfect eubt, the fraction 
 ihould be reduced to a decimal, and the root of the decimal be found as 
 
 •bore. 
 i. A mixed number should be reduced to an improper fraction. 
 
 ^_ 
 
CUUK HOOT. 
 
 M8 
 
 EXERCISE 124. 
 
 Find the cube root ol — 
 
 1. 6859. 
 S. 1-'167. 
 
 4. wmai. 
 
 6. 6S45239. 
 
 Extract the cube root of — 
 
 10 
 
 11. 
 
 I412lt;7848. 
 1805409391. 
 
 la. 
 
 IS. 
 
 83413fl2.'576. 
 23.)7-i43059. 
 
 Find the cube root of — 
 
 16. 
 17. 
 
 830.584. 
 .970299. 
 
 18. 1.092727. 
 
 19. .002197. 
 
 7. 49037S9«. 
 
 8. 0';»i()l25. 
 
 9. 92U714178. 
 
 14. 
 15. 
 
 8i;i(SS05,378. 
 4065JaU788. 
 
 90. .000176016. 
 21. .007045378. 
 
 Find the cube root of the following numbers carrying 
 incomi)lete roots to three or five decimal places, as may be 
 re<j aired : 
 
 ^ 1- 24 01. 20 .001. 28. §. 80 J 
 
 «»• a. 28. .03. 27 .009. 99. f. »l. ^. 
 
i 
 
MICROCOPY RESOLUTION TEST CHART 
 
 (ANSI and ISO TEST CHART No. 2) 
 
 1.0 
 
 I.I 
 
 1.25 
 
 l£ ■£ 12.2 
 
 1^ 
 
 2.0 
 
 1.6 
 
 A /APPLIED INA^GE Inc 
 
 sir. !653 Eost Main Streel 
 
 ~^ Rochester. Ne« York 14609 USA 
 
 JS (716) 482 - 0300 - Phone 
 
 ^S (716) 288 - 5989 - Fa» 
 
i( 
 
 864 
 
 PRACTICAL MENSURATION. 
 
 'i 
 
 .1 
 
 ^g H 
 
 PRACTICAL MENSURATION. 
 
 i; 
 
 liii 
 
 fl:: 
 
 605< Mensuration treats of the measorement of lines, 
 Burfaces and solids. 
 
 606. Lines are measured by expressing their length in 
 inches, feet, yards, etc. (Linear Measure), or in links, 
 •hains, etc. (Surveyors' Measure.) 
 
 607« A Surface is that which has length and breadth 
 
 only. 
 
 &0S» Surfaces are measured by expressing the number 
 of times they contain the units of surface measure, i.«., the 
 sq. inch, eq. yard, etc. (Square Measure), or the sq. 'ink, 
 pq. chain (Surveyors' Square Measure). 
 
 609* If a straight edge laid anywhere upon a surface 
 touches at every point, the surface is a plane surface. 
 
 •10. A Polygon is a plane surface bounded by straight 
 lines. 
 
 All. The Area of a plane surface is the space enclosed 
 by the lines which bonnd «» 
 
 612. A polygon takes its name from the number of 
 sides which bound it, thus : 
 
 (^OOO 
 
 Mangla. Qtwdri lateral Pentagon. Hexagon. Heptagon Octagon 
 
g UADRILA TERALS. 
 
 865 
 
 QUADRILATERALS. 
 
 613. A Right Angle ia an angle formed by 
 two lines perpendicular to each other. 
 
 614. Parallel Lines are lines in the same PN. 
 plane, which being produced both ways never meet, and 
 which are therefore the same distance apart throughout 
 their entire length. 
 
 615. Quadrilaterals are of three kinds, as follows: 
 
 tJ ZZ\ 
 
 t-kraiitilogram. 
 
 Trapuzoid. 
 
 Trapezium. 
 
 616. A Parallelogram has its opposite sides parallel; 
 ft Trapezoid has only two aides parallel ; a Trapezium has 
 has no two sides parallel. 
 
 617. Parallelograms are of four kinds, as follows : 
 
 a o 
 
 Square. 
 
 Rectangle. 
 
 Rhomboid. 
 
 RhouibuB. 
 
 61«. A Square has all its sides equal and all its angles 
 right angles; a Rectangle has its opposite sides equal, 
 and all its angles right angles ; a Rhomboid has its op- 
 posite sides equal, and none of its angles right angles; a 
 Rhombus has all its sides equal and none of its angler 
 right angles. 
 
866 
 
 Q UADRILA TERALS. 
 
 * f. 
 
 019. The Altitude of a parallelogram or trapezoid it 
 the perpendicular distance between the parallel sidea. 
 
 620. The Diagonal of a quadrilateral is a straight line 
 joining two opposite corners. 
 
 621. To find the area of a rectangle or square. 
 
 ExAMPLK 1.— Find the area of the reotftngle whose sides *re 
 8 inches and 5 inches in len^ith. 
 
 SoLnTio-:. 
 6 sq. in. X 3 a> 15 aq in. 
 
 EzVIiA^lTION. 
 
 Ans, In the figure A B D, let A B b« 
 B 6 inches, and A D he 8 inches. Let 
 A B he divided into 6 equal parts, 
 each 1 inch in length, and let A D be 
 divided into 3 equal divisions each, 
 _ 1 inch in length. Draw through these 
 
 divisions the lines represented in the 
 figure. The whole figure will then be divided into squares, each of vhose 
 sides is 1 inch in length, and hence each square is a tquare inch. In laoh 
 horizontal row there are 5 square inches, and in the three horizontal j ^p 
 there will be 3 times 6 square inches, or 16 square inches, and henc m 
 solution, 6 sq. in. X 3 « 15 sq. in. 
 
 Example 2.— Find the area of a square whose side is 8 inch**. 
 
 SOLOTIOK. EXPWNATION. 
 
 8 sq. in X 8 » 64 sq. in. Ans. Same as Example I. 
 
 BVhM. 
 
 Multiply the length by the breadth and the result icill he the 
 area. 
 
 Notes 1.— The student will observe that the rule is only a shortened 
 form of expressing the longer rule. Multiply the measure of the length 
 expressed in units of square measure by the measure of the breadth. 
 
 2. All the following rules will be expressed in a shortened form. 
 
 The converse of the preceding rule must be true : 
 If the area of a rectangle be divided by a side, the quotient 
 will be the other side, or if the square root of th* area of • 
 square be extracted^ the result will be the length of a side. 
 
QUADRILATERALS. 
 
 8f)7 
 
 622. To find the area of a rhomboid or rhombus, the 
 leng^th of a pair of opposite sides and the perpendicular 
 distance between them being given. 
 
 Example.— Find the area of a rhomboid, ona pair of whose 
 oppoBife sides are 10 feet in length, and the diatanco b,- wieu them C feet. 
 
 SOLCTION. Ejj-lanation 
 
 10 Bq. ft. X 6 » 60 sq. fl. An«. It ig prov-jd in lluclfd, Book I, pro- 
 position 33. that tho area of a parr\i. 
 lelogram ia eqnal to tho area of a reotan^iie on the same base, and of the 
 ■ame altitude, and hence the solution n'ven. 
 
 hULp;. 
 
 Multiply the length oj onn of the purallel aid, by the per- 
 pendicular distance between them. 
 
 62». To find the area of a trapezoid, the lengths of 
 the parallel sides and the perpendicular distance 
 between them being given. 
 
 ExAMPLB.— Find the area of a trapezoid, the lengths of the parallel 
 ■ides being 6 feet and 10 feet, and the perpendicular distance between 
 them 6 feet. 
 
 SoLUTrON. 
 
 (6ft. + 10ft.) + a - 8 ft. 8 sq. ft. X 6 = 40 sq. ft. 
 
 Ana. 
 
 BT7LB. 
 
 Multiply one-half the mm of th< parallel oidet bj, im p/>r. 
 yeadicuLar dittance between them. 
 
4d8 
 
 TRIANQLE3. 
 
 is 
 
 II 
 
 TRIANGLES. 
 
 034. A Triangle is the space enclosed by three straight 
 lines. 
 
 62J5. Triangles are named according to their sides, and 
 also according to their angles, as follows : 
 
 EquilaterAl. Iioioeles. SMien*. Bight-angled. 
 
 636. An Equilateral Triangle has its three sides equal. 
 
 627. An Isosceles Triangle has only two sides equa\. 
 
 628. A Scalene Triangle has all of its sides unequal. 
 
 629. A Right Angled Triangle has one of its angjea *. 
 right angle. 
 
 «»0. The Base of a triangle is any 
 side oi a triangle upon which a perpen- 
 dicular is let fall from the opposite 
 
 angle. 
 
 6.31. The Altitude of a triangle is the 
 length of the perpendicular let fall from 
 an angle on the opposite side or the 
 opposite side produced. 
 
 NoTK. — Dotted lines represent the al tit ale. 
 
 632. To find the area of a triangle. 
 
 ExAMPLK 1.— Find the area of a triangle whose base is Id feet, a»' 
 
 whose altitude is 9 feet. 
 
 Solution. 
 
 (16 sq. ft ■{• 2) X 9 = 72 sq. ft. 
 
TRIANGLES. 
 
 mid 
 
 r 
 
 KXi'LANATFON. 
 
 It ii proved in Enohd, Book I, proposition 41. that the area of a 
 <tian){Ie i3 half the area of a p-vr.illola^ram oa ''he same bajt and of th« 
 tame altitude, hence the solation givna. 
 
 BtTLB. 
 
 Multiply one-half the base by the altitude. 
 
 The *- 'lowing rule is also necessary when three sides are 
 iSiven. 
 
 From half the sum of the tides subtract each side separately ; 
 then multiply half the sum and the three remainders together, 
 and extract the square root of the product. 
 
 Etahplb 2.— What is the area of a triangle whose aides are 12 feet, 
 16 feet, and 18 feet? 
 
 Solution. 
 (12 + 16 + 18) -f 3 a 23 
 23-18-6 23 X 6 X 7 X 11 - 8.85S. 
 
 23 - 16 » 7 
 
 33 - 12 a 11 V 8858 a 94.1 so. ft. An.. 
 
 683. It is proved in Euclid, Book 1, proposition 47, that 
 
 in any right angled triangle the area of the square described 
 
 on the side opposite the right angle, is equal to the sum of the 
 
 ir'as of the squares described on the tides containing the light 
 
 i.ngle. 
 
 In the accompanying figure, if 
 ABC by a triangle having a right 
 jbHgle at C, the area of the square 
 described on A B is equal to the sum 
 of the areas of the squares described 
 on A C and B 0, 
 
 A B, the side opposite the right angle, is called the 
 hypothenuse ; B G the bass ; and A C the perpendicular. 
 
 Hence, the square on the hypothenuse - square or. the 
 base + the square on the perpendicular. 
 
r i: 
 
 1^ 
 
 
 ; i' 
 
 il 
 
 (I 
 
 t 
 
 870 
 
 ruusoL&s. 
 
 ExAMPLB 1.— If the base of a right an^le.l triant'lc be a *.»st, and 
 the pcri mdicular be 6 feet, what is the length of the hypotbeu*^ • 
 
 Solution. 
 In the preoedin'i fi'^ure, 
 
 ■q. ou A 1! = 8 X 8 + 6 X (3 
 
 = lOOBIJ.lt. 
 
 .•. A B = Vloo = 10 ft. An«. 
 
 ExA«rpi.« 2.— The hypothenuHB of a ri-jht anijled triangle is 35 fnet 
 and the perpendicular is 'J8 feet, tiiid the base. 
 
 Solution 
 85 X 35 s» Bq. on tho base + 28 X 28 
 /. pq. on the baae = 35 x 35 - 28 x 23 » 441 
 ;. the baae a V'i'^^ " ^^ ''" '^"^■ 
 
 es-l. To find the area of a trapezium. 
 
 A trapezium may be divided into two triangles oy joining 
 two opposite corners, aud hence it is only necesBary loiiiid 
 the areas of the two triangles and to take their sum. 
 
 Example.— rind the area of a trapezium whose sides are 10 feet, 
 11 feet, 12 feet, and 16 feet, the length of the line joining opposiVo corners 
 
 l)oiug 13 feet. 
 
 boLurioN. 
 
 Arta A B C s= V 18 x 7 Vo"xl •• * ■ 49 
 
 " ACD = >yi9irsrx tjin = 04.06. 
 
 (Art. Gi2.) 
 Area A B C D » 61.48 + 04.06 a: 
 
 125.54 »q. ft. Ana 
 
t<jLHjO.\i>. 
 
 an 
 
 FOLVGONS. 
 
 ^*^ fo find the area of a regular polygon containing 
 more than four sides. 
 
 MidlijUy the mriindur (-vuii of all the Hides} of the base 
 
 h one-lhdt the perpendicular distance from tUectitre to one 
 of the sidea. 
 
 EiAMPLi.— What ia tlie urea of ti he.ii'.^on, side 8 (t-.t. thu perptu- 
 dicular diutauce from the centre to ono uf tlie aiil.s btin;! (3.<J28 •»• feet. 
 
 Perimeter 
 Are* 
 
 S(vi,crioN. 
 8 ft. X = 4-; ft 
 48 8qft. X '--!!:? = 1G(;.272 + »(]. ft. 
 
 Tiw urea of an liitcral triangle equals the sijiire of 
 
 a side uiultiplieJ Ly .i;j3, and the urea of a hexat,'uii, wiiich 
 is made I'.j. of 6 eqiiihiteral triaui^if.-, is thtroiore 6 x .433 
 ti.'uns tHt aquare of a side. 
 
 * h 
 
872 
 
 ■rUK CIliCLE. 
 
 THE CIRCLE. 
 
 636« A Circle is a plane figure bounded 
 by a curve line callpd the circumference, 
 «very poiut of which is equally distant from 
 a p'^int called the centre. 
 
 637. The Diameter of a circle is a line drawn through 
 the centre, and terminated at both ende by the circum* 
 ference. 
 
 63S. A Radius is a straip;ht line drawn from the centre 
 to the circumference and is equal to half the diameter. 
 
 Noil —From tbo definition of a circle, it follows that all the radii an 
 tquul ; also, that all diameten are equal. 
 
 6311* Principles. ' The circumference «■ tfui iametf^ 
 8.1416 nearly. 
 
 2. Therefore the diameter ■ the circumference + H I'Hd 
 nearly. 
 
 8. The area of a cuck >=■ the st^uare of the radius x 3.1416 
 nearly. 
 
 4.. The area of a circle « the circumference x half the 
 radius. 
 
 6. Therefore the radius of a circle - iq. root of (the area 
 ♦ S.1416) nearly. 
 
 KoiE. The fraotion S^ it oommonly need in place of the decimal 
 
 t.l416, and ia near anoagh for common practical operations, and will be 
 Bsed ill this work. 
 
TfMt/ 
 
 THE CincLH. 
 
 KxAicrui 1. What it the circi:in(eraii(.<i of • circle wboM 
 
 8/8 
 
 fK'llUI It 
 
 dUm tMt t 
 
 8oi,cri«!f. 
 
 7 ft. X 2 » 1. ft diamet.-r, 
 14 ft. X 8^ = 44 ft. Aur (Prin. l.) 
 
 EzAHru 9. Thecircmuference of a circle ii 176 fuet. What is t;i« 
 
 BOLUTIO!*. 
 
 i76 + 3^ = r,r, It. Am. (Prin. 8.) 
 
 HxuouL a. Wtiat ia tlie area of a circle whose diamoto; is 14 feet T 
 
 SuLCTIO.N 1. 
 
 14 ft. -(■ 2 3 7 ft. the radini, 
 7x7x3^ = 154 sq. ft. Am. (Prin. 8.) 
 
 Solution 2. 
 
 14 ft. X 3;^ 3 44 ft. the circumference. (Prin. 1.) 
 14 ft. + 2 =7 ft. the ra.liua. 
 
 44 X } - 154 aq. t. Ana. (Prin. 4.) 
 
 RxAMPLE 4. The area of a circle ia Glti square feet. Find the rudici, 
 diameter, and oiroumfereuoe. 
 
 SOLDTIOit. 
 
 Radins = ^/GiJ'^~^ =, li ::. (Prin. fl.j 
 14 f*. X 2 » 29 ft. the d ameter. 
 CS ft. X »^ ■ 88 ft. tue oircumfereaoe. If tin. 14 
 
 9. 
 
 I 
 
if 
 
 874 
 
 UlSCKLLASKOUa 
 
 MISCELLANEOUS. 
 
 EXERCISE 128. 
 
 1. How may acres in a piece of woodland 220 yards in 
 length and 40 roda in width f 
 
 2. How many square miles in a township 6 miles and 
 40 chains square? 
 
 8. How many square feet in a floor 20 feet lone and 5 
 yards wide? 
 
 4. Find the surfaon of a pane of glass measuring 87i 
 inches long and 28 inches wide. 
 
 6. How many square yards ir the four walls of a room 
 If) ft. 6 in. high and 80 feet in compass ? 
 
 6. A rectan;,'ular pavement, oO ft. 9 in. long anJ 12 ft. 
 6 in.^ wide, was laid with a central line of stone 6 feot wido 
 at C\75 a rwnnmg forit ; the sides were flanked with brick 
 at h) cents per square yard. What did the paving cost ? 
 
 7. How many square feet in a surface 24 feet long 20 feet 
 wide? How many in another surface of half these 
 dimensions ? 
 
 8. Two flelds contain 10 acres each ; one is in the form 
 of a square, the other is 4 times as long as it is wide 
 What would be the difference in expense of fencing them 
 at $2.26 per rod ? 
 
 9. If the fence were built ^ feet high, of boards 8 inches 
 wide, the lower one raised 2 inches above the ground, and a 
 space of 8 mches between the boards, bow many square feet 
 of boards would be required for both fields ? 
 
10. How many more fur imo than loi c other? 
 
 376 
 
 11 A piece of hind contftitiitiR 2 acres is 5 tinoH ha hmg 
 tB it i« broad. What ia its length iind breiidtli '? 
 
 12. How many bricks 8 inches long and 4 inches wide will 
 pave a yard that is 100 f<- by 60 ? 
 
 18. What will it oosi ave a roadway 80 feot Iour and 
 IB feot wide, at $1.50 per sqiiavo yard? 
 
 14. I have a box witliout a lid; it is 8 feet lonj?, 4 ieet 
 wide, and 8 feet deep, interior dimensions, flow many 
 squar ^ feet of zinc will it take to line the bottom and side^ 
 of the box ? 
 
 16. Find the area of a rhomboid whose length ii l ji. 
 I ft. 6 iii., and whose width ia 2 ft. 8 in. 
 
 16. Tlie base of a rhombus is 10 ft. 6 in., and its altitude 
 8 feet What ia its area ? 
 
 17. xiow many acres in a piece of land in :he form of a 
 rhomboid, the base being 8.75 ch. and altitude 6 ch. ? 
 
 18. A man bought a farm 198 rods long and 150 rods 
 wide, and agreed to give $32 an »cre. What did the farm 
 cost? 
 
 19. A certain rectangular piece of land measures 1,000 
 links by 100. How many acres does it contain ? 
 
 20. How many square feet in a board 18 feet long 18 
 inches wide at one end and 25 inches wide at the other 
 end? 
 
 21. Required the area of a trapezoid whose parallel aides 
 are 178 and 146 feet, and the altitude 69 feet. 
 
!-;:i 
 
 i 
 
 II 
 
 I 
 
 876 
 
 MISCELLANEOUS. 
 
 22. One side of a quadrilateral field measures 88 rods ; 
 the side opposite and parallel to it measures 26 rods, and 
 the distance between the two sides is 10 rods. Find the 
 area. 
 
 28. The parallel sides of a trapezoid measure respectively 
 8| feet and 6 inches ; the perpendicular distance between 
 them is 2 feet. What is the area ? 
 
 24. Find the area of a trapezium whose diagonal is 168, 
 and one perpendicular 42, the other £6. 
 
 26. Find the area of a trapezium whose diagonal is 
 85 ft. 6 in., and the perpendiculars to this diagonal 9 feet 
 and 12^ feet. 
 
 26. How many acres ito a quadrilateral field whoso 
 diagonal is 80 rods, and the perpendiculars to this diagonal 
 20.458 and 50.832 rods. ? 
 
 27. What is the base of a triangle whose area is 166 
 square feet, and its altitude 12 feet ? 
 
 28. What is the base of a triangle whose area is 144 
 acres and its altitude 60 rods ? 
 
 29. Find the base of a triangle whose area is 6,280 
 square yards, and altitude 240 yards. 
 
 80. What is the area of a triangle whose three sides are 
 18,14, and 16 feet? 
 
 81. What is the area in acres of a triangular field whos« 
 three sides measure Ivspectively 47, 58, and 69 rods ? 
 
 82. What is the area of a triangle whose base is 24 feet 
 and altitude 16 feet ? 
 
 88. The base of a triangle is 28 inches and the altitude 
 16 inches ; what is the area ? 
 
 mmk 
 
MISCELLANEOUS. 
 
 377 
 
 84. A board 16 feet long is 22 inchea wide at one end, 
 and tapers to a point ; what is the value at 4^ cents a 
 square foot ? 
 
 35. Find the area of a triangle whose base is 12 ft. 6 in. 
 and altitude 6 ft. 9 in. 
 
 36. Whose base is 25.01 chains and altitude 18.14 
 chains. 
 
 87. What is the cost of a triangular piece of land whose 
 base is 16.48 ch. and altitude 9.67 ch. at $60 an acre ? 
 
 88. At $.40 a square yard, find the cost of paving a 
 triangular court, its base being 105 feet, aud its altitude 
 21 yards ? 
 
 89. Find the area of a circular pond, its circumference 
 being 200 chains. 
 
 40. The distance around a circalar park is 1^ miles. 
 How many acres does it contain ? 
 
 41. How much land in a circular garden that requires 
 84 rods of fencing to inclose it ? 
 
 42. Find the diflference in cost at 87^ cts. per rod between 
 fencing a square field of 10 acres and a rectangular field 
 82 rods wide of the same area. 
 
 48. Draw a square containing 81 square inches ; inscribe 
 a circle in this square. What is the superficies of this 
 circle in square inches ? 
 
 44. A cow is tethered to a post driven in the centre of a 
 lot 100 feet square ; the tether is just long enough for her 
 to reach the fence. How much of the surface of the field 
 h she unable to crop ? 
 
878 
 
 MISCELLANEOUS. 
 
 46. If the diameter of an iron column is 3 ft. 5 in., what 
 is the circumference ? If the girth of a tree la 5 ft. 9 in., 
 what must be its diameter ? 
 
 46. If the equatorial diameter of the earth is 7,926 
 miles, how long in miles and rods is the equator ? 
 
 47. The distance from the centre of the hub of a wheel 
 to the outer edge of the felly is 16 inches. How long must 
 the tire be ? 
 
 48. If the length of an oar from the thole-pin to the end 
 of the blade is 6 feet, how many feet would the end of the 
 blade travel in the water during 6.000 strokes, each 
 describinr; an arc of GO® ? (60° » 1 of the circumference.) 
 
 49. If the circumference of a circular pond is 628 318 
 rods, what part of a mile must I row to pass from shore to 
 shore across the centre of the pond ? 
 
 60. If a horse is tethered to the middle post of a fence, 
 from which he can graze out into the field in a curved line 
 78.539314 feet long, how long is the tether ? 
 
 61. What will be the circumference of the largest circle 
 that can be drawn on a sheet of paper 12 inches wide aud 
 18 inches long ? 
 
sol.lhs. 
 
 •M9 
 
 SOLIDS. 
 
 «40. A Solid is tliat which has low^th, breadth, ami 
 thickness. 
 
 Oil. A Prism is a solid whose bases are similar. C(|nal. 
 and parallel polygons, and whose sides are parallelo-^'raius. 
 
 6-42. Prisms take tlieir names from tlie forms of tlicir 
 bases, as tridNr/ulxr, r<rtatviul,i>\ pcnta^ioiud, Ii<'.r.i;i,»i>il, etc. 
 
 OUJ. A Cube is a rectangular prism whoso faces are all 
 equal squares. 
 
 644. A Cylinder is a circular body of uniform diameter 
 whose ends are equal and parallel circles. 
 
 645. The Altitude of a jirism or cylinder is the perpen- 
 dicular distance between its bases. 
 
 Triangular lu-ism. Rectangular prism. Pentag.jual prism. HcxaKOiial prism, 
 
 Cube 
 
-T' 
 
 880 
 
 SOLIDS. 
 
 646* To find the convex surface of a prism or cylinder 
 
 Bnppoae a blook of the shape of one of the preceding prisms to hare 
 been fitted with a piece of paper so as to Rsactty cover its conves snrface. 
 Now if the paper be nii rolled it will be found to be the shape of a rect- 
 angle, one side being equal to the hei^Iit. and the other tide eqnal to 
 the perimeter of the base. Hence, the following rale. 
 
 BULB. 
 
 1. Multiply the perimeter Caum of all the $ide$J of th • 
 base by the altitude. 
 
 2. To find the entire surface, add the area of the baset 
 to the convex surface. 
 
 ExAMPLB 1. Find the convex surfaoe and also the entire surface at 
 a rectangular prism whose ends are b inches by 7 inches, and whost 
 altitude is 12 inches. 
 
 SoLunoM 
 
 Perimeter of the base s (6 -)■ 7 -f 6 + 7) in. s 24 in. 
 Altitude 3 12 in. 
 .'. Convex surface = 21 sq. in. x 12 = 28S sq, In. 
 Again, area of base = 7 aq. in. x 5 a 35 si;. in. 
 .-. Entire surface m b5 aq. in. + 35 sq. in. + 288 sq. in. s 358 sq. in 
 
 Example 3. Find entire surface of a cylinder the diameter oi 
 whose base is 14 inches, and whose altitude is 20 inches. 
 
 Solution. 
 
 Perimeter of base = 14 x 3f = 44 in. 
 .*. Convex surface = 44 sq. m x 20 = 880 sq. in. 
 Again, area of base = 7 x 7 x 3| « 154 sq. in. 
 .-. Entire surface » (154 + 154 + 880) sq. in. = 1188 sq. in. 
 
 647* To find the volume of a pristn or cylinder. 
 
 BCLB. 
 
 Multiply the area of the base by the altitude. 
 
 ExAUPLK. 1. Find the volume of a rectangular prism whose bast 
 is 4 inches by 6 inches, and altitude 10 inches. 
 
 SOLCTIOH. 
 
 Area of base s 6 sq. in. x 4 s 24 sq. in. 
 Volume = 24 cub. in. x 10 = 240 cub in. 
 
 #::'l 
 
SOLIDS. 
 
 881 
 
 EzPI.U(iTIO!l. 
 
 The base can be divided into 24 eqao-os eacL side of which i. 1 inch 
 
 to the base It can be dmded in 24 small blocks, corresponding to the 
 M ^/l""ff •"*°/h'°'' the base can be divided, each of those smaU 
 b ocks will therefore be 1 inch lon«. 1 inch wide, and 1 inch in thickness. 
 Uence he part cu off will contain 24 cubic inches. 10 such pieces can be 
 ont ofif the whole block, and the whole block therefore contains 
 24 cub. in. x 10 « 240 cub. in. 
 
 ExAMPW. 2. What is the volame of a triangular prism whose 
 base is an equilateral triangle each side 8 inches, and whoae altitude it 
 12 incneB 7 
 
 SotUTIO!!. 
 
 Area of base 
 Volume 
 
 Vl2 X 4 X 4 X 4 
 
 27.712 cub. in. x 12 
 
 27.'12 + sq.in. 
 .332 541 cub. in. 
 
 . EXAMFLB. 3. Find the volume of a cylinder, the diameter of whos« 
 base IS 14 incliea and altitude 20 inches. 
 
 SoLnriON. 
 Area of base » 7 x 7 x .3,f ■ 154 sq. in. 
 Volume s 154 cub. In x 20 = 3030 onb. to. 
 
 64H. A Pyramid ia a solid whose hrtse ia a polygon and 
 whose sides terminate in a point called the vertex. 
 
 «49. A Cone is a solid which has a circle for its base, 
 and terminates in a point called the vertex. 
 
 650. The Altitude of a pyramid or cone ia the perpen- 
 dicular distance fr' the base to the vertex. 
 
 65!. The Slant eight of a pyramid ia the distance 
 from the vertex to the middle point of any side of the base. 
 
 658. A Frustrum of a pyramid or cone ia the part 
 which is left after the top ia cut off by a plane parallel to 
 the baae. 
 
 653. The Altitude of a frustrum is the perpendicular 
 distance between its ends. 
 
882 
 
 SOLID-. 
 
 «5-l. Tlie Slant Height of a frustrum of a pyrami^l in 
 the distance hftwecii the middle points of two parallel 
 sides of one of its faces. 
 
 I'yramul. 
 
 Co 11^ 
 
 Fnistiuiiiiif ;i iiyniiiiid. Frubtniui of a coiio. 
 
 «55. To find the convex surface of a pyramid or 
 cone. 
 
 r.ULE. 
 
 1. Multiphj the pcnmdcr hi/ uiw -half the shint liei<iht. 
 
 2. To lind the entire snrfaee ad'l the arm of the linne to the 
 area of the ei>nvex surface. 
 
 EXAMILK 1. - Find the entire surface ..f a i)yranii(l who^e base is n 
 square aide •> inches, ami whose slant lieij^lit is lU incliL-s^ 
 
 SOLITION. 
 
 Perimetei of base = 1'") in- 
 Convex surfuce ^ l''i S'i- i"- < ^'- = >^^ *1- *"• 
 Areii of basf = -1 -il- in- ■■ > = 1'' *!• '"• 
 .-. Entire surface = i-O :- ir.) sq. in. = '.n; s.]. in. 
 
 Ex-UUXK 2. — I-'ind untire surface of a cone, the tliameVer of the base 
 ' ing 1-1 inches, and slant hei^^hc :!U inches. 
 
 ScjLL'TION. 
 
 Perimeter of base = 11 in. x 31- - -U in. 
 
 Convex surface = 11 sq. in x -i'- - <')00 scj. in. 
 
 Area of base = 7 x 7 x :U = l.'.lsq. in. 
 
 Entire surface = ('>;0 -r ir)l) s<i. in. ^ 811 sq. m. 
 
 «5«. To find convex surface of a frustrum of a cone 
 or pyramid. 
 
 nrLE. 
 
 1. Midtipln one-half the sum of the perimeters of the ends 
 by the slant height. 
 
 2. To find the entire surface, add the areas of the ends to 
 the area of the con rex surf tee. 
 
SOLIDS. 
 
 aH3 
 
 J 
 
 iJxAMi'iK — Find entire siirfucf (,f tlio iru-f ri-.ni .'f m c<\\-- the 
 (liaiuc'turs of wiiosf < p:Is arc 7 inc!u - and 14 iaciu -. :in.i wli.,-,' >l,uit 
 luM;i;t is -Jo inolicH. 
 
 Solution. 
 iVrmictcrof euils = Tin. x :»i -^ •.'■_' in., ami 1 I in. •. :;l -- Mill. 
 LoiivuX iui-face = I. "Jki. in. •. -JO ^ t;i;o m.;, ■;; 
 
 Area (if Miiiailffend ='■.:' v ;;; = ;ix', -.j, in. 
 Area of i:a-_,.|- eiiil ^ 7 ■: 7 ■, :;; == l.".!,-). in. 
 Lmirij snrfa>e = (OCO + :j.-ii + l.'.lisj. in. ^ svj', .^j. in. 
 
 C57. To find the volume of a cent or pyramid. 
 
 I. ("I.;;. 
 Miiltiphi (ircit ()/ till },'isi- liji inr-liiiril th< 'iititii'i- . 
 
 Kx.vMrLF.. — Fniil volume of a conLs wliost' bii<.- is 1 [ inciied in 
 dianictcr. ami whosi' altiuulc is 21 inclius. 
 
 .Soi.rrioN. 
 7x7 X ;U (area of l>.'.-;^'i •: 
 
 - 12:;j 'iih. 
 
 fi.l.H. To find the volume of the frustrum of a rone or 
 nyramid. 
 
 iiri.!:. 
 (.1 -r (I i \ .1 X (/) X // X .ij, iflwri' 'A ' stai)i-< I'or (he 
 ari'tt :'f tlic binii'v end, 'n' for tlir arci of tlh! s,iinih', tinl, 
 (iitil ' It ' jhr the ])erj>cn'Ucul(ir hciiiltt. 
 
 JIx.iMi'Li:.— "i''inil the voJunK' i_)f the fi'ustruin of a conr. wliosu eml 
 diameters are 7 f and 11 feet, and whoso allitiule is 12 feet. 
 
 Soi.i-r.'oN. 
 Area of smaller and = " -Ik ifi = :isi, Si]. ft. 
 Area of liir^,'er end = 7 ■. 7 x :i! = lU ^ j. ft 
 Volume = (l.Jl - 3SA t- \ l-M -- ;WJI ■: 12 ■ K = lU7>i cnb. ft. 
 
 <S*>1>. A Sphere or Globe i.s a solid tonuiuated by a 
 curve surlace, every part of wliieli is 
 equally distaut from a point within, 
 called the centre. 
 
 <><iO. The Diameter of a sphere is a 
 fetrai^ht line (irnwii tluvumii irs centre 
 and terminated at both ends by the sur- 
 face. 
 
f^ 
 
 8a4 SOLIDS. 
 
 OOI. A Hemisphere is one-balf a aphere. 
 
 tt03. The Radius of a sphere is a straight line drawn 
 from its ceutre to any point in its surfuce. 
 
 603. To find the surface of a sphere. 
 
 BCU. 
 
 Multiply the square of the diameter by 3f. 
 
 EzAKn.!.— What is ihe surface of a sphere wboM diMn<>lei tt 
 
 feet? 
 
 80LUTI0!<. 
 
 7 X 7 X 8f a 151 3q. ft. Ana. 
 
 ttG4. To find the volume of a sphere. 
 
 BCLa. 
 
 Multiply the cube of the diumeter by 3|, and divide the 
 result by 6. 
 
 ExAMPLi. — What ia the volume of a sphere whoae diameter it 
 
 »feet? 
 
 Solution. 
 
 7x7x7 (onbe of the diameter) x 3> x i » 179| cab. ft. 
 
CI!iii.UNS ASH Bi^iS. 
 
 Sbft 
 
 CISTERNS AND BINS. 
 
 t* 
 
 he 
 
 II 
 
 6«5. To find the number of gallons in a cistern. 
 
 BDUI, 
 
 Find the volume in cubic inches and divide the reeuU by 231. 
 
 NoT«.— There are 38] oubio inohes in one |.;allon. 
 
 Example.— Find the number of gallons in a roctanKnlar ciatem, 
 A (eet by 6 feet, and 3 feet doep. 
 
 SoLcnoN. 
 Volume a (8 X 6 X 3) cub. ft. » (8 X 6 X 3) x 1728 cab. in. 
 .. No gallons » 8 x 6 x 3 x 1,728 + 231 a 1.077f J gal. 
 
 <J«G. To find the number of bushels ux wheat in a bin 
 or pile. 
 
 RniiX. 
 
 Find the volume in cubic inches and divide the result by 
 9Jo0.4S. 
 
 NoTK. — There are 2160 i2 onbic inches in one bushel. 
 
 ExAMPia.— How many bushelo of grain in a bin 4 feet by 6 feei 
 and 8 feet deep 1 
 
 HoLtrrio-N. 
 Volume at 4 X 6 x 8 X 1,728 oub. in 
 .-. No. bushela « 4 x 6 x 4 x 1,738 -*• 3UU.43 ■ £8 bush, naarly 
 
 M '.. 
 
A86 
 
 QAUQISQ or CASKS. 
 
 GAUGING OP CASKS. 
 
 607. Gauging is tho process of ilndin;^ the capacity oi 
 
 volume of casks and other vessels. 
 
 NoTK.— A oaik is eqniTahnt Ui a oylinder, having the lama langta and 
 a diameter eqaal to the meai, diameter of the oaak. 
 
 tt6M. To find the mean diameter of a cask (nearly). 
 
 Add to the head diameter §. or, if the etavei are but lUtU 
 curved, f of the difference between the head and bung 
 diameters. 
 
 669. To find the volume of the cask in gallons. 
 
 BULK. 
 
 Multiply the square of the mean diameter by the length 
 {both in inches), and this product by .0034. 
 
 ExxMPLi. — How many gallons in a cask whose head diamuter is 
 M inches, bang diameter 80 inches, and length 34 inches 7 
 
 
 
 SoLnxioN. 
 
 
 
 
 Mmn diameter 
 
 « 
 
 {24 + (30 - 24) 
 
 x|} 
 
 n 
 
 28 in. 
 
 Capacity 
 
 
 28 X 26 X 34 X 
 fcXi-RClSE 128. 
 
 .0034 
 
 
 90.65 gat 
 
 1. What is the solidity of a triangular prism whow 
 length is 12 feet, and one of the equal sides of one of it* 
 equilateral ends is 3 feet ? 
 
 2. How many gallons of water would a cylindrical boiler 
 sontain if 25 inches high and 12 inches in diameter ? 
 
OAVQlNii OF CASKS. 
 
 381 
 
 8. Find the cubic inches 
 
 the 
 
 
 inches m the lar^^'est cone that can ue 
 cut from a cylinder 2 ft. 6 in. higli and 14 iuch.a in 
 diameter. 
 
 4. A sphere 8 inches in diameter is placed in a cubical box 
 whoBo interior dimensions are 8 inches. How much vacant 
 ■pace is left ? 
 
 5. I have a cylindrical tank which contains IGOgallouH , 
 it is 6 ft. 5 in. ia diamoter. How deep is it ? 
 
 6. How many square feet of canvas will be required to 
 cover a cylinder 16^ feet in circumfeiance and 26 feet 
 long ? 
 
 7. How many square inches of surface in a stove pipe 22 
 Inchos in circumference and 12 feet lo.:,' ? 
 
 8. What is the convex surface of a log 26 feet ir. circum- 
 ference and 18 feet long ? 
 
 9. What is the convex surface of a cylinder 3 feet long 
 and U feet in diameter ? What is its entire surface ? 
 
 10. What are the contents of a log 16 feet long and 2 
 feet in diameter ? 
 
 11. The standard liquid gallon is 231 rubio inches; how 
 many gallona in a can 22 inches in diaraeter and 3 feet 
 high ? 
 
 12. How many cunic feet in a trianp;ular prism, the area 
 of whose base is 920 square feet and height 20 feet ? 
 
 18. Wliat are the contents of a quadrangular prism 
 whose length is 25 centimeters, and the base a rectangle 3 
 by 6 centimeters ? 
 
 14. What is the lateral surface of a regular pyramid 
 whose slant height is 16 feet, and whose base is 80 feet 
 square ? 
 
 16. What is the surface of a pyramid whose base is an 
 equilateral triangle measuring 4 feet on each side, and slant 
 height 16 feet ? 
 
I 
 
 ? 
 
 « 
 
 1' 
 
 Ui mi 
 
 m 
 
 il 
 
 888 
 
 QAVaiKQ OF CASKS. 
 
 16. What is the convex Burfaco of a rono, the dinmeter 
 of wboBc base is 7 feet and its Bhiiit height 12 fcit ? 
 
 17. What iH the entire Burface of a triangular pyramid 
 whoae Blant height in 25 feut, and each side of the base 10 
 feet? 
 
 18. What is the entire surface of a rij^ht cone, tho 
 diamotor of the base ami Vm mhiui hei;^ht being each 40 
 feet '? 
 
 1.'. Find the cubic foot in a log 80 feet long and 2 feet in 
 diameter at the hirger and 1 fl. 10 in. at the smaller end. 
 
 20. Find the cubic contents of a pyramid, base 300 feet 
 square, and altitudo 80 feet. 
 
 21. How many cubic .ot in a circular mound 48 feet 
 high, and liavinp; a diamotor of 8fi fuet iit the top, and a 
 cireunifcrence of 471.21 feet at tlie bottom ? 
 
 22. How many cubic miles in the earili, supposing it to 
 be a perfect eplii re 8,000 miles in diameter ? 
 
 23. How miiny barrel- of oil in a tank GO feet in diameter 
 if the oil is 5 feet deep ? (40 gal. tu the barrel.) 
 
 21. A mouuiuent in the form of a square pyramid, is 2 
 ft. 10 in. square at bnse, and 11 feut high ; at 175 jiounds 
 to a cubic foot what is its weight ? 
 
 25. Wiuit are the content-* of a round log whoso length 
 is 20 feet, diaraetoi" of larger end 12 inches, and smaller 
 end inches ? 
 
 26. The altitude of a frustrum of a pyramid is 27 feet, the 
 ends are 4 feet and 3 feet square ; what is its solidity ? 
 
 27. W'hat are the contents of a pyramid whose base is 
 144 b(iuare feet, and its altitude 33 feet ? 
 
 28. Find the solidity of a sphere whose diameter is 13 
 
 inches. 
 
 .rAr>»^ 
 
QAUUISG UF CASKS. 
 
 389 
 
 29. What are tlio cojitentjj «)f a on., the area of whoae 
 base IB 1,803 mi. foot, tuul itd iiltitu.lu 3(» ftvt •? 
 
 80. Find the convex aurfiico of a frustnuu of n con« 
 whose Hlfuit height is 15 feet, th(!circiinjrorouce of tlie lowei 
 base 80 feet, and of the ui)i)or base Hi feet. 
 
 81. , nat will it cost to gild a ball 12 inched in diameter, 
 at 10 cents u square inch ? 
 
 82. The atandanl bushel of the United Statos is IH| 
 inches in diameter and 8 inches deep ; how many cubic 
 inches does it contain ? 
 
 88. IIow many square yards in the convex surface of a 
 fruHtrum of a pyramid, whose bases are heptagons, each 
 side of the lower base being 8 feet, and of the upper base 4 
 feet, and the slant height 55 feet ? 
 
 84. Find the contents in gallons of a cask whose length 
 is 64 inches, its bung diameter 42, and head diameter 86 
 inches. 
 
 35. Required the contents in gallons of a rectangular 
 ■istern 4J feet long, 3^ feet wide, and G feet deep. 
 
 86. What are the contents in gallons of a cask 36 inches 
 long, its head diameter 26 inches, and bung diameter 82 
 inches ? 
 
 87. How many gallons in a cask whose head diameter is 
 24 inches, bung diameter 30 inches, and its length 34 
 inches ? 
 
 88. What is the volume of a cask whose length ia 40 
 inches the diameters 21 and 30 in. respectively ? 
 
 89. How many gallons in a cask of slight curvature, 3 
 ft. 6 in. long, the head diameter being 20 inches, the bung 
 diameter 31 inches ? 
 
1 
 
 i 
 
 !l 
 
 li 
 
 in 
 
 In 
 
 it 
 
 890 
 
 MKASUUJiMENT OF CAUPETINQ. 
 
 MEASUREMENT OF CARPETING. 
 
 6TO. Carpet is sold by the linear yard, and is of various 
 widths. The more common widths are 27 inches and 
 86 inches. 
 
 071. In determining the number of yards of carpet that 
 will be required to cover a room, it is first necessary to 
 decide whether the strips of carpeting shall run lengthwise 
 of the room or crosswise. Economy in matching usually 
 decides this. 
 
 07a. In determining the length of each strip of carpet, 
 allowance must be made for waste in matching. 
 
 67-^. To find the number of yards of carpeting 
 required for a room of given dimensions. 
 
 ExAMPLB 1.— How many yards of carpet 27 inches wide will bt 
 required for a rectanj,'nlar room 21 foot long and 18 feet wide, if the strips 
 run lengtliwise and no wuste in matching ? 
 
 Solution. 
 18 ft. = 216 in. 
 
 21G -^ 27 = 8, No. strips of carpet. 
 1 strip is 21 ft. or 7 yds. lon^^. 
 8 strips aro, 7 yds x 8 = 56 yds. Ana. 
 
 EzAMPLB 2. — How many yards of carpet 36 inches wide will be 
 required for a rectangular room 20 feet 6 inches long, and 16 feet 9 inches 
 wide, if the strips rna crosswise, and 4 inches per strip be allowed for 
 matching 7 
 
 Solution. 
 16 ft. 9 in. = 201 in. 
 
 201 in. -r 36 in. = 5 times and 21 in. remaining. 
 .•. It will take 6 strips of carpet. 
 
 Length of each atrip = 20 ft. 6 in. + 4 in. = :0 ft. 10 In. 
 1 strip is 20 ft. 10 in. long. 
 .-. 6 strips are, 20 ft. 10 in. x 6 as 125 ft. or 41| yds. Ans. 
 
UEASVREMENT OF CAJiFEIINQ. 
 
 891 
 
 EXERCiSE 127. 
 
 1. A rectangular room 26 ft. 8 in. long, and IG ft. 6 in 
 wide, is to be covered with carpet 1 yard wide. Which 
 way of the room should the strips run that there may be 
 the least turned under or cut olT from one side of a breadth ? 
 
 2. In No. 1, if the strips were 16 ft. 6 in. long, how many 
 strips would be required ? 
 
 8. In No. 1, if the strips were 26 ft. 3 in. long, how many 
 wonld be required. 
 
 4. In No. 1, if the strips were 16 ft. 6 in. long, and there 
 was no waste in matching, how many yards would it take ? 
 
 6. In No. 1, if the strips were 26 ft. 3 in. long, and there 
 were no waste in matching, how many yards would it take ? 
 
 6. How many yards of carpeting 27 inches wide will be 
 required for a room 17 ft. 6 in. by 15 ft. 5 in., if the strips 
 run crosswise, and 7 inches be wasted in matching each 
 ■trip ? 
 
 7. A room is 15 feet by 17 ft. 6 in., and the carpet is | of a 
 yard wide. "What must be the length of the strips to have 
 the least waste ? How many stnus will be required ? 
 
 8. In No. 7, how many yaras oi carpet would be required if 
 there were a waste of 8 inches in matching each strip, except 
 the first ? Why should there be no waste in the first strip ? 
 
 9. Find the cost of carpeting a room 22 ft. 8 in. by 13 ft. 
 4 in. if the carpeting be 27 inches wide, and cost $1.80 per 
 yard, there being a waste of 8 inches per strip in matching, 
 the strips running lengthwise. 
 
 10. A parlor 20 feet by 17 feet is carpeted with a carpet 
 1 yard wide, at $1.20 per yard, surrounded with a carpet 
 border 1 foot wide, at 76 cents a yard. Find the total cost. 
 
i 
 
 i 
 
 [if, 
 
 rii 
 
 ■:S 
 
 892 
 
 MEASUREMENT OF CARPETINO. 
 
 11. Find the coat of carpeting a room 28 ft. 10 in. loog, 
 by 17 ft. 8 in. wide, with carpet J of a yard wide, at $1.80 
 per yard, if the strips run lengthwise of the room, and 
 9 inches per strip be wasted in matching. 
 
 12. Find the cost of the carpet for a stair of 17-12 inch 
 steps, each rising 8 inches, at 90 cents a yard. 
 
 18. Find the cost of the stair carpet at $1.20 a yard, 
 for a flight of stairs of 22 steps, 11 inches wide, with 7 inches 
 rise, allowing 1 yard extra at the top. 
 
 14. Find the cost of covering t floor of a hall 24 feet 
 long by 8 feet wide, with oil -cloth 4 feet wide, no waste in 
 matching. 
 
MEASUREMENT OF WALL PAPER. 
 
 81^3 
 
 MEASUREMENT OF WALL PAPER. 
 
 «74. Wall paper is sold by the roll, any part of a roll 
 being counted as a whole roll. 
 
 675. Canadian and American wall papers are 18 inches 
 wide, and have 8 yards in a roll. For convenience wall 
 paper is done up in double rolls of 16 yards. 
 
 «7«. In estimating the number of rolls necessary for 
 a certain room, paper-hangers ascertain the height of the 
 room and its perimeter, making an allowiiuce in the peri- 
 meter of 8 feet for each door or window. 
 
 677. The exact cost of papering a room can be ascer- 
 tained only by taking account of the number of rolls of 
 paper actually used in doing the work. 
 
 «7». To find the number of rolls of paper required 
 for a room. 
 
 Example 1._How many rolls of wall paper will be required for 
 the wa-.3 of a rectangular room 20 feet by 16 feet, with a 12 foot ceiling 
 there being one door 3 feet 8 inches wide, and 3 windows each 4 feet 
 S inches wide 7 
 
 SoLnrioN. 
 
 Perimeter of room ia (20 ft. + 16 ft.) x 2 =72 ft. 
 
 Width of door, 3 ft. 8 in. 
 
 Width of 2 windows {* ft. 2 in.) x 2 = 8 ft. 4 in. 12 ft 
 Perimeter after deducting width of door and windows a 60 ft 
 60 ft. = 720 inches. 
 720 in. -J- 18 in. (width of paper) s 40. number of strips. 
 1 strip is 12 ft. long. 
 .". 40 strips are 480 ft. or 160 yds. long. 
 
 160 yards ^ 8 yds. (No. yds. in a roll) . 20, No. of rolls. Anfc 
 
;} 
 
 :ii i- 
 
 ' I t 
 
 il 
 
 394 
 
 MEASUREMENT OF WALL PAPER. 
 
 Example 2.— Find the cost of the wall paper at 80 cents a roll 
 and bordering at 7 centi> a yard for a room 18 feet 9 inches long by 16 
 feet 6 inches wide, with the ceiling 10 feet 9 inches above the base 
 boards, allowing for 2 doors each 3 feet 8 inches wide, and 3 windows 
 each 8 feet 6 inches wide, also an allowance of 9 inches on each strip for 
 matching. (In reckoning the cost of the bordering no allowauoe is made 
 (or the doors and windows ) 
 
 Solution. 
 Perimeter of room is (18 ft. 9 in. + 16 ft 5 in.) x 2 = 70 ft. 4 in. 
 Width of doors (3 ft. 8 in.) x 2 = 7 ft. 4 in. 
 Width of windows (3 ft. 6 in.) x 8 = 10 ft. in. 17 ft. 10 in. 
 Perimeter of room after deducting width of doors and windows ■ 
 82 ft. 6 in. 
 
 62 ft. 6 in. B 630 in. 
 630 in. -5- 18 in. = 35, No. of strips. 
 To allow for raatchin he paper will out into strips of 
 (10 ft 9 in. + 9 in.) = il ft. 6 in. in length. 
 
 One roll will practically cut into 2 strips. 
 .-. No. of rolls = 35 -f 2 = 17i 
 .'. It will take 18 rolls 
 
 1 roll is worth 80 cents 
 .•. 18 rolls are worth 80 cents x 
 70 ft. 4 in. = 24 yds. nearly 
 1 yard is worth 7 cents 
 :. 24 yds. are worth 7 cents x 24 
 
 18 = 814.40, Cost of wall paper. 
 
 81.68, Cost of border. 
 916.C8. Total cost. 
 
 EXERCISE 128. 
 
 1. How many strips of paper will go around a room 18 
 feet by 24 feet ? 
 
 2. How many strips of paper are required for a room 80 
 feet by 24, if there are 4 windows and 2 doors ? (Art. 676.) 
 
 8. How many rolls will paper a ceiling 24 feet by 18 feet ? 
 
 4. How many double rolls are required for a hall 21 feet 
 long and 13 feet high, with a cornice 1 foot deep ? 
 
 6. Find the cost of the paper for a room 86 feet by 
 24 feet and 11 feet high, with a cornice 1 foot deep, and a 
 wainscoting 2 feet deep, at 50 coats pe- -able roll. 
 
 » 
 
MEASUIiEAIENT OF WALL PAPER. 395 
 
 6. How many double rolls of wall paper will be requiret^ 
 for a room 18 ft. 6 in. by 15 ft. 4 in., the ceiling 8 feet above 
 tbe base-boards, allowance being made for 1 door 3 ft. 8 in. 
 wide and 2 windows each 4 feet wide ? 
 
 7. If a roll of paper cuts into two strips, and 10 strips 
 be allowed for doors and windows, find the cost of papering 
 a room 24 ft. 8 in. long by 16 feet wide with paper at 45 
 cents a roll and bordering at 7 cents a yard, the hanging 
 of the paper costing 16 cents a roll, 
 
 8. Find the cost of paper lor a hall 72 feet by 44 feet, 14 
 feet high, below the cornire, allowing for 8 windows each 
 4 ft. 2 in. wide and 2 doors each 3 ft. 8 in. wide, the paper 
 costing 45 cents per double roll. 
 
 9. With paper at li per roll, and border at 8 
 cents a yard, what is the co.-. of paper and border for a 
 room 24 feet by 20 feet and 12^ feet high, with cornice 
 6 inches deep, there being 5 opuuings of an average width 
 of 3 feet ? 
 
 10. If the paper-lianger charges $3, and the paper costs 
 80 cents a double roll and the border 4 cents a yard, find 
 the cost of papering a room 18 ft. 9 in. long, IG ft. 8 in. 
 wide, with a ceiling 13 ft. 6 in. high, allowing for two 
 doors, each 3 ft. Kin. wide, and 3 win^lows, each 4ft. 2 in. 
 wide ; also for a base-board 18 inches deep. 
 
ii 
 
 896 ilEASUREUEST OF SAW-LOGS. 
 
 MEASUREMENT OF SAW-LOGS. 
 
 679. TABLE OP LUMBEU AND LOG MEASUREMENT. 
 
 Showing net proceeds (fractions of feet omitted) of logs in 1 inob 
 boards, deducting saw kerf and slabs. The length will be found in the 
 left hand column, and the diameter in inches on the head of the o'her 
 columns. 
 
 
 US n 
 
 
 Diam. 
 10 
 
 
 Diam, 
 U 
 
 
 
 Diam. 
 12 
 
 Diam. 
 18 
 
 »S b9 (9 ^9 bS I 
 
 »si-'i-'oocooDa-jasoiincn*»Miotoi-'>-'oooaDOo~io»o> 
 
 
 i^<no>occ'-coi-'bCicoi(^ui09->ixccoi->bscoi^c>ia>-4aDroo 
 
 ocox<x>ao'-40»C3o:uii^i;^ii^cetsbsi-<^ovcoaoaci-jo>a3u< 
 
 oaoa>i^ts::bvit3oaoaoi(»>-'WJ>('booaos:4'u<o^c;i(o 
 
 ^? ^fcp* "^ V. w v.* l*^ '-^' X,' 'J,' '^1 
 
 5? -p C! c> w tc 
 
 >t^Mcuwcuc»o:e»ts.ot.st<3tototSM>-'i->»-'i-> 
 
 Q -i? "X C5 0> W tsD O '^ 'OC 35 l! W bD I-" OJ ac ^ Cl ijk 
 
 Oioio>u<eni».i*>i».i».iu,^4^cu:ocu03Coc»t£tctSb9tetoi-'i->i-> 
 
 «JWl^t0l-'«C0005*'0>l-'Oa03i«iWt0O00-4tn>i>-bBOO-]3> 
 
 c-.oi^(Xtoa»Oi^aDtsc:o><*xt<so30i(^(xt4a30i(^xtoa30 
 
 Diam. 
 14 
 
 Diam. 
 16 
 
 Diam 
 16 
 
 Diam 
 17 
 
 Diam. 
 18 
 
 Diam. 
 19 
 
 Diam. 
 20 
 
UEASUIiKMENT OF SAfF-LOOS. 
 
 897 
 
 
 r. 
 
 aob 
 tiio 
 her 
 
 Ol iC >- to -J r: !*• tS O V- -J " 
 
 ^ ;; ■— -- -1 — . ~ 1-5 c 3C -J :,i w ►- o X 
 ►- w ti -J -.c p- tc 1 1 -o tc ►- w ai -4 at o 
 
 9° S^ 
 
 L)iam. 
 21 
 
 
 
 •- a c; -u »- «s M .i. ic c a r- »- ►- tr -j in ic o x •-• o; >- o -3 li li 
 
 Piam, 
 
 23 
 
 o -a ii- tc © -q ci li o ~J -' tc o -] oi ic Q -o ai ti c -1 ?^ (3 c -1 iS 
 
 Diatn. 
 24 
 
 
 Diam, 
 25 
 
 © O O «C tC to «C 06 a OC -J -J «3 ;r. C5 ~. r: i ' i.-i i-i 
 
 Oc i;i re "^ r', tc o c& C5 1-; CD -T tc tc c^ i: © -^ .u I— ' 
 OCXOtGROD^C^OC2CaC^0>O)C;iCnCnv'ii(k^i^ 
 
 1-1 )^ i£k 1^ OS cc CO o: 
 
 ' ■ X -■• C*5 CO C". iO ^ 
 
 i«^ W C0 Cd w cc tc 
 
 t-»h-h-©©O5Ot0'r^00aiX*3»4«*3Os0i05CnC;iili*ifc*k|t*ti;t0Ci: i-'lHr 
 «o CT li so a; M o ii t- to oj ic ;o o M to cs « «o ci cc ts C3 1; S C-. u «n 
 
 ic o o M o Ci li to c; ea o-j i<i> © c. w>-©©uoc". t«:c»q;;© ^i 
 
 Diam, 
 20 
 
 Diarn. 
 
 iotiia"-i-'^©©©tc»toxor-^'<l-ocvC!OswsiCTifc)Uo;i>: 
 to crs ts 00 ui ►- X *. S ^ u- o 3-. lo to -.1 tc X *. P-. <i £. o ~ cc o =: 
 
 05O4»00tSOiOi«-XMC;©*>.XlC.C-. ©*.»bSCS©ii.O0l*C-. O 
 
 Diam. 
 28 
 
 n- ; ; v; tc 'c I* I— ^ 
 © --. t« a- *' •-- "J :*; 
 c. ~J X to o h> ci w.; 
 
 — 0©tOtOXXX^-J--T5^©CTCntn> 
 tOiii-'-OWOC. MXi(^OC:iCX^®: 
 •*- C>i OS *3 X X © © IC tC W »*-■ -I -?; "J X t 
 
 Ci (t. i«- W tc W IC li h- >— © © O O to X X X -J "3 C. 3V U> i-1 ii J» ,;» 
 lOtOJJi(»U.tOC:>(-liOXC-. i(»li©»JtnWl-'X05W^:0-Jf;? 
 
 Diam, 
 29 
 
 Diim. 
 
 iwt^ssit't^tsciii-iioxw. it»iwO"~jmwi-'X05W^:0-jf;c 
 
 " 
 
 
 ■ 
 
 Oi !• w f. ,i- It. :,: w tc 141 !-■ t- © c © to to X X -1 ~1 0-. C5 tn tn ii >u. 
 *- -J >t- c^ i-i 1— cv ic -^i -c X SB © ,;- O en i— C". ri ^j li X iu iO *. & ?■ 
 ©*.X i;a tC©^-C. ©i<»tD*.©ii»-JtSl'i©4.©iJXtCMW© 
 
 Diara. 
 31 
 
 *j *j c o; C'l 4n **k tu w w ^^ t3 h-i H- o o o CD » X -o "J oi c c-t cn 4». Diam. 
 ?^ ^ ^- •■; x^ 1* ^ J^ r3 i^ T^ !E^ ^ ''t !J !^ 55 w oc 5^ po Co a; ic cr- w CO I on 
 
 •u 
 
 C;>O^X©©H^tCCA5lt.;U«©^X©©H^tO 
 
 Wi*»Cn©^X©© 
 
 
 
 
 
 
 
 'O 
 
 © 
 © 
 
 © X X -3 -a © OS 
 
 It. to ifc. X W X CO 
 © fl t* © OS *, I-" 
 
 
 X X -J -3 rv 
 
 © *. to w X 
 
 M ►- ©-J J*» 
 
 0-. 
 
 yi en *. i(k DC 
 ^ to -J M c: 
 
 X ai bs o X 
 
 ■ji M ij 
 
 r- s; o 
 
 iT tC © 
 
 t— » H-< © 
 
 tn O i. 
 
 ^1 tw 
 
 X © 
 
 O © © X a ^ © -. 
 tC©i-'iii©>t-Xic 
 l»»Xl-S©©*,X^- 
 
 -'wi»t»»;v:«h5ic,*-t-'©©©©x-j«.3©©cn 
 
 *.l^-©©1.*'©iOXtC©H-C;f©,i-XtC»4h-»© 
 
 4.XtO©OviXH-cn©tc©©rf»^H-cn©tCt 
 
 Diam 
 33 
 
 Diam 
 34 
 
 tCtCIC-^l-'l-iMI-'M 
 
 K- ^©©©xx-^c-. 
 © © ito- X ti ~ ~ ■ " 
 
 ©^ Vi Ct ;i- iJ i; I 
 
 - _ - - - _ _- - - © *. X ic r: ^ — a tc © © — X tc © © 
 
 tC ti IC tC IC tC tC U. tC ti tC H- tC *— IC f— Iw ^ — ^ h- H- ^ H* H- ►- >— 
 
 ' f" - © © © © X -.1 -J r: © Diara 
 
 I tC to tC to 14 I 
 
 ICCbSh- — ^© t;X-4-J©©iTlf^lt.COlOtO^©®© T. CC '^ "^ 0> 
 
 I i<k © © tC X 
 
 X 14 Oi © to © © W 
 
 It- © © ti X *■ © © 
 
 -JOUkXi-ittxto©©^;©©*. 
 lO X it. © © :i I .t- © © to X It. © 
 
 Diam. 
 
 ■.u'< 
 
i I 
 I 
 
 tl 
 
 I \ 
 
 i I 
 
 
 V'i 
 
 
 ' i 
 
 ;Ui 
 
 ^ 
 
 H 
 
 ■ T 
 
 
 ; ' 
 
 Mm 
 
 ■ ^ 
 
 :' ■; 
 
 B^P 1 
 
 > H 
 
 *■•■ 
 
 ii^ - 
 
 " 
 
 y 
 
 Wtmt 
 
 " ■ 
 
 •''i^ 
 
 ^J^^^^^Ul 
 
 ! 
 
 898 
 
 JiMASUHKMKST OF SAW-LOOS. 
 
 6MO. In some parts of Caiia.Ia saw-lo^s are bouRht and 
 Bold by the Stantlunl, in otiier parts witli referunce to the 
 number of feet of inch lumber which they will produce. 
 
 6»l. A Standard Log is 12 feet long and 21 inches in 
 diameter, and will produce 1,085 ftet of inch lumber. 
 
 «N2. The measurement of a l(»g is always taken at the 
 small end and between the bark. 
 
 iiH'.i. To find the number of standards in a given 
 number of saw-logs. 
 
 Example 1.— How many Btandarda are there in i saw-logs, caob 
 12 feet long, the diameters of which are 16 Inches, 20 ir ^hes, 23 inches, 
 and 25 inches respectively 7 
 
 Solution. 
 
 16» = 256 
 2'j« = 400 
 22« = 484 
 25« = 625 
 Sum = 1,705 
 1,766 + 21* a 1,705 -^ 441 = 4. No. standard. Ans. 
 
 Examile 2.— How many standards are there in 5 logs, each 16 feel 
 long, the diameters of which are 18, 20, 21. 24, and SO inches respec- 
 tively ? 
 
 BOLDTION. 
 
 18' = 3-24 
 20^ = -100 
 21^ = 441 
 242 = 57t; 
 30- = 900 
 Sum = 2,641 
 
 2,641 -J- 441 = 6 nearly. No. of standards 12 feet long. 
 16 = IJ times 12 
 .*. No. of standards = 6 x IJ = 8. Ans. 
 
 EXERCISE 129. 
 
 1. How many standards are there in 6 saw-logs, each 
 12 feet long, the diameters of which are 12, 16, 20, 26, 26 
 and 28 inches respectively ? 
 
 .uf-^^.'M :-^--^ 
 
 
MtASUlihillC:^!' OF SAii'-LOOS. 
 
 8ug 
 
 2. How many etandards are there in 5 loj^s, each 18 
 feet long, the diaiut^ters of which are 14, '20, 22, 24 and 30 
 inches respectively ? 
 
 8. What is the side of the largest square i»iece of tiiubei 
 which can be sawn from a lo„', tlie diameter of which is 
 28 inches ? 
 
 4. P'rom the Table, Art. 679. tind out the quantity of inch 
 lumber that can be sawn ; oin the following : 
 
 3 Iof,'8 10 feet long, diameters 15, 20 and 32 inches respeclivoly. 
 2 " 14 " " 18 and 24 
 
 4 " 16 •* " 16, 20, 22 and 80 •• •< 
 a " 18 '• " 20 and 26 " «• 
 
 6. A man wishes a piece of timber 18 inches square, 
 what is the diameter of the smallest log from which it may 
 be H»wa r 
 
f 
 
 i 
 
 llfl 
 
 ' f 
 
 400 
 
 iltASlj'HKMKNT OF LVMIihB 
 
 MEASUREMENT OF LUMBEK. 
 
 OH4. Lumber, as the term is used here, includeB all 
 kinds of snwed boards, plank, scantling, joists, etc. 
 
 0»5. A foot of lumber, or a board foot, is the unit of 
 measurement. It is 1 foot long, 1 foot wide, and 1 inch 
 thick. 
 
 686. The term scautling is given to lumber 8 or 4 
 inches wide, and from 2 to 4 inobes thick. 
 
 Joist is usually from 2 to 4 inches thick, and from 6 to 
 16 inches wide. 
 
 Lumber heavier tlian joist or scantling is called timber, 
 A broad piece of lumltor thicker than a board, — usually 
 from 1^ to 4 inchee thick, is called a plank. 
 
 6>47. All liinil)er less than one inch in thickness is con- 
 sidered inch lumber in measuring. 
 
 QHH. In iiif ahiirinrr the width of a board a fraction 
 greater than a half inch is called a half, and if loss than a 
 half it is rejected. Thus a board 5 J inches wide would be 
 considered 6 inchea wide, a board 9J inches wide would be 
 considered 9 inches wiao. 
 
 6H1>. The price of lumber is usually quoted at a certain 
 rate per thousand feet, board measure. 
 
 61>0. To find the number of board feet or feet of 
 lumber in a board, plank, joist, etc. 
 
 ExAMPLK 1. — Find the number of feet of lumber in a board H fcc» 
 long, 12 inches wide, and 1 inch thick. 
 
 Solution. 
 (14 X 12 X 1) -f 12 = 14 feet. Ana. 
 
 
measui{i:mest of lumber. ^qj 
 
 KiAMPM a. -Find U.0 nnmber of feet of luml-or in m pUu* I« ««., 
 «M«. 14 inchei wido. and U iaclie. thick. 
 
 (16 X U X 3) + 12 m j.; foe». Am. 
 
 RULI. 
 
 Multiply the trnglh in feet I,,, the width and thickn,'.^ in 
 v,chcs, and divide the product hy 12, and the result will bt 
 the number of board Jut of lumber. 
 
 
 EXERCISE 130. 
 
 1. Find the number of feet of lumber in 24 boards 14 
 feet long and 10 inches wide. 
 
 2. Find the cost of iifty 2-inch plank 16 feet long and 
 10 inches wide at $18 per thousand. 
 
 8. How many square feet are there in the surface of a 
 board IG feet by 9 inches ? 
 
 4. How many feet of lumber are there in a board 12 
 feet long, incliea wide and 1 inch thick ? 
 
 6. How many feet of lumber are there in the followin^t 
 bill ?-24 joists 16 feet by 10 inches, 2 inches thick • 210 
 pieces of sidinn;, 12 feet long, 4 inches wido, f inch tliick • 
 14 beams 20 feet long, and 9 inches square; 16 scantling' 
 2 inches by 4 inches, 16 feefc long. 
 
 6 How many feet of lumber in a 140 pieces of siding 
 each 12 feet long, 6 iuchoi wid.. and I inch thick ? 
 
 7. How much lumber is there in eighty 2x4 scantling 
 14 feet long ? ^ 
 
 8. Find the cost of 2,250 feet of lumber at $20 ner 
 thousand. *^ 
 
-/ 
 
 .1 1 
 
 402 
 
 iltUSUHKUENf OF LUilUhli, 
 
 9. Find the coat of IJ inch flooring required to lay • 
 aoor 42 feet by 24 feet at $24 per tliousaud. 
 
 10. Find the coat of flooring a bridge 820 yards long by 
 20 feet wide with 8 inch oali planks, at $22 per thoinaad. 
 
 11. If 2 X 4 studs are used, and they are placed 16 inchea 
 apart, from centre to centre, how many feet of lumber are 
 there in the studding of a wall 20 feet long and 12 feet 
 high ? 
 
 12. How many 12 foot boards 6 inches wide arc required 
 to put a wainscoting 3 feet high around a kitciuii 12 ftet 
 by 16 feet, allowing for 2 doors, each 8^ feet wide ? 
 
 18. Find the cost of the lumber for two floor!^ of a house 
 24 feet long and 18 feet wide, if the lower fl.' r in IJ inches 
 thick, and the upper floor 1 inch, at $20 a thousand. 
 
 14. A barn is 61 feet long and 40 foot wile, and 20 feet 
 high to the eaves; the gables are 8 feet lii«b, and the 
 rafters 22 feet, 6 inches long. Find the number of feet of 
 uicu c - ;nl8 nccsbiiry to inclose the two aides, allowing for 
 two doors 12 leet by 16 feet. 
 
 16. In No. 5, find the number of feet of lumber in the 
 ends and gables. 
 
 16. In No. 5, find the number of feet of lumber required 
 to sheet the roof. 
 
 17. In No. 5, find the cost of the lumber for the doors at 
 $20 a thousand. 
 
 18. In No. 6, find the cost of the 2 inch plank needed for 
 the floor at $24 a thousand. 
 
 19. If 4 X 5 rafters are used, and they are placed 30 
 inches apart, from centre to centre, how many feet of 
 lumber are there in the 20 foot rafters of a double roof 40 
 feet long ? 
 
 .:f 
 
MUdSUIiEMJiSl Ut /,, .UilER, 
 
 ll>:i 
 
 20. Fiiul the price of th.; followiuti bill of lumber m $.ii 
 per thousand : — 
 
 120 'iiiich plank 10 inched wide, 11 feet long, 
 125 boanls 10 inclit's \viil(>, 1«» feet long. 
 8<) 2 X t-iiich sc!intliii>,', ' \ f'-tt long. 
 50 3 X 1-inch " I. " 
 
 120 8 X 10-iuch joist, 10 f. ;t long. 
 
 21. How many feet of hunber are tliore in the 2 x Mncli 
 -tuilg of a partition wall 32 foot lon^^ and 14 fot-t hij^ii ? 
 
 NoTK.— Tho stii'lH of partition walls aru u.<ui»lly pUoo.l l-i iaohun \\\n\n 
 from centre i> ocntrs. 
 
 22. IIow many 12-foot Htrips '1\ inches wido will lay a 
 walk 1 feet wide and ^() yard.n lung, allowing half an inch 
 l)t iwecn the atripa ? 
 
 23. If lumber 10 inches wide is useil in shectiuj,' the roof 
 in No. 19, and tho boards are placed two inches apart, allow- 
 ing for a t-rojoction of one foot at each end, how many feet 
 of lumber will be required ? 
 
 2-4. How many feet of lumber arc there in the 12-inch 
 base board of a square 10 uci« held ? 
 
 26. Find the cost of tlio lumber for the dressed door 
 facings of 18 doors, each 7 feet high and 2 feet 8 inches 
 wide, the facings being 6 inches wide, ut $30 per thousand 
 feet. 
 
^'^^^'nmCW 
 
 mz 
 
 
 ■!*r;'- 
 
 It ' i 
 
 jfl: 
 
 i 
 
 ll' 
 
 H 
 
 i 
 
 n 
 
 ; J ffil 
 
 404 MEASUIiEMENI OF SIIINGLINa. 
 
 MEASUREMENT OF SHINGLING. 
 
 691. Shingles are sold by the bunch, each bunch £ n- 
 tains a quarter thousand. A bunch of shingles is 2^ iaclips 
 wide, and has 25 courses on each side. Dealers ■•Ul oot 
 Bell a part of a bunch. 
 
 692. Ordinary shingles have an average width of 4 
 inches, and are generally laid 4 inches to the weather. 
 
 693. Allowing for waste, 1000 shingles will cover a 
 surface of 100 square feet (a square of shingling), 4 inches 
 to the weather ; laid 4^ inches to the weather, 900 shingles 
 are required. 
 
 EXERCISE 131. 
 
 1. How many shingles are there in 24 bunches ? 
 
 2. How many bunches are there in 15^ thousiiud? 
 8. How many thousand are there in 48 bunches ? 
 
 4. Laid 4 inches to the weather, how many square 
 inches are covered by the exposed part of one shingle ? 
 6. How many shingles are required for a roof having a 
 
 surface of 2,400 square feet ? 
 
 6. How many bunches of shingles will shingle a roof 
 
 82 feet by 24 feet ? 
 
 7. How many shingles are required for a double roof 86 
 feet long, with SiO-foot rafters ? 
 
 8. Find the cost of laying a double roof 48 feet long, 
 rafters 24 feet long, with shingles 4 inches to the weathi^x 
 at $3.20 per thousand. 
 
 9. Find the cost of shingles for a double roof 86 feet 
 long, rafters 21 feet long, at 60 cents a bunch, if the shingle* 
 are laid ^ inches to the weather. 
 
 10. At $3.60 per thousand, find the cost of the shingles 
 for a roof of a building 60 feet long, 40 feet wide, having a 
 gable 12 feet high, and the rafters having an 18-inch heeL 
 
 'V .• 
 
if'^'T^i^.i 
 
 FENCING. 
 
 4U5 
 
 FENCING. 
 
 EXERCISE 132. 
 
 1. How many fence posts are required for a fence 80 
 rotls long, if the posts are placed 8 feet apart ? 
 
 2. How many posts are required for a fence around a 
 field 40 rods square, if they are placed 8 feet apart ? 
 
 8. How many posts are required for a square 10-acre 
 f aid, if they are placed 8 feet apart ? 
 
 4. Find the cost of the posts for a fencfc around a garaen 
 plot 2'jO yards by 220 yards, if the posts are placed 6 feet 
 apart and cost 10 cents each. 
 
 5. In No. 4, how many 2x4 scantling, 12 feet long will 
 be required for the 2 stringers of the fence ? 
 
 6. In No. 3, find the cost of 2 x 4 scantling, 16 feet long, 
 that will be required for the 2 stringers of the fence, if tha 
 lumber is worth $18 por thousand. 
 
 7. How many feet oi lamoer are required for a 10-inch 
 base board around the field in No. 2 ? 
 
 8. How many 2-inch pickets are required for a fence 40 
 rods long, if the pickets are placed 2 inches apart ? 
 
 9. How many 2^-inch pickets, placed 2 inches apart, are 
 required for a fence around a garden 200 yards by 150 
 yard3 ? 
 
 10. How much lumber is there in a common board fence 
 40 rods long, consisting of 5 rounds of 6-inch boards ? 
 
JT'^rs 
 
 ■-i.^^A.t^^^i:^^-^ ':^^^^ 
 
 406 
 
 FENCINO. 
 
 11. What will it cost to fence 5 miles o: railway, both 
 Bides, with 6 rounds of 6-inch boards, at $12 per thousand 
 feet? 
 
 12. What will it cost at $10 per thousand to fence a field 
 40 rods by 60 rods with 1 round of 12-inch boards, and 5 
 of 6-inch boards ? 
 
 13. What will be the cost per mile to fence a railway 
 with 5 strands of barbed wire, which weighs 1 lb. per rod, 
 at 8 cents a pound ? 
 
 14. Find the cost of a quarter mile of fence with the posts 
 8 feet apart, a 12-inch base, a 2 x 4 rail at top, and 4 strands 
 of barbed wire ; the posts cost 10 cents eacli, the lumber 
 f 12 per thousand, and the wire at 7 cents a pound. ^A 
 pound atretches 16^ feet.) 
 
 ! 'I 
 
 t i. .\ 
 
 
 
tf*tm 
 
 MKASUliEMENT OF PAINTING, ETC. 
 
 407 
 
 MEASUREMENT OF PAINTING, KALSO- 
 MINING AND PAVING. 
 
 604. The unit of measurement of painting, kalsomining, 
 and paving is the square yard. 
 
 EXERCISE 133. 
 
 i. How many square yards of painting are there in a 
 floor 30 feet by 28 feet ? 
 
 2. Find the cost of kalsomining the ceiling of a hall 64 
 feet long and 36 feet wide, at 20 cents a square yard. 
 
 8. What will it cost to paint a close board fence 6 feet 
 high around a lot 36 yards long by 24 yards wide V 
 
 4. What will it cost to paint a house 36 feet by 30 feet, 
 which bas an average height of 18 feet, at 18 cents a 
 square yard ? 
 
 5. Wbat will it cost to kalsomine a room 20 feet by 18 
 feet and 10 feet high, at 7. cents a square yard ? 
 
 6. Find the cost of painting a double roof 44 feet long 
 by 24 feet, at 12 cents a square yard. 
 
 7. What will it cost to tuckpoint the front of a brick 
 bouse 36 feet long and 22 feet high, allowing for half the 
 openings which form one quarter of the surface, $1.25 per 
 square yard ? 
 
 8. Find the cost of paving a street half a mile long and 
 60 feet wide, at 30 cents a square yard. 
 
 9. Find the cost of paving a street one-eighth of a mile 
 long and 1^ chains wide, at 25 cents per square yard. 
 
 10. A circular plot of ground, 4 chains in diameter, has 
 a walk 8 feet wide, formed around the outer edge. Find 
 the cost of gravelling the walk, at 15 cents a square yard. 
 
 ! I 
 
I.,i 
 
 JhA^ 
 
 408 MEASUIiEMENI OF LAlUliHi AND PLA6IKlU.Sa. 
 
 MEASUREMENT OF LATHING AND 
 PLASi'ERING. 
 
 695* Laths are sold by the buiich. There are 50 laths 
 in a bunch, each lath being 4 feet long and IJ inches wide. 
 They are usually laid about three-eights of an inch apart. 
 
 696* Allowing for waste, contractora reckon that a 
 bunch of laths will cover 3 square yards of surface. 
 
 697. Lathing and plastering are estimated by the square 
 yard. Only one-half the surface of openings is allowed. 
 
 69S. To find the cost of lathing and plastering a 
 room of given dimensions. 
 
 ExAMPLK. — A rectangular room 24 feet by 18 ft. 9 in., and 10 ft. 
 10 in. high. The base board is 10 iuchea hi£;h ; there are two doora 8 feet 
 by 4 ft. 3 in. each, and three windows 6 ft. 4 in. by 4 feet each. Find ths 
 cost of lathing and plastering the walls and ceiling at 30 cents a square 
 yard. 
 
 Solution. 
 
 Perimeter of room ■ (2tft. + 18 ft. 9 in.) x 2 a. 85 ft. 
 
 Height of walls aboTC base board - 10 ft. 10 in. - 10 in. = 10 ft. 
 
 6 in. 
 
 855 sq. ft. 
 
 450 sq. ft. 
 
 1,305 sq. ft. 
 
 Area of walls s 85 ft. 6 in. x 10 ft. s 
 
 Area of ceiling a 24 ft. x 18 ft. 9 in. = 
 
 Total ^oss area s 
 
 Area of 2 doors = (8 ft. x4 ft.Sin.) x 2 = 68 sq.ft. 
 
 Area of 3 windows «= (b ft. 4 in. x 4 ft.) x 3 = 76 ag. ft. 
 
 Total area of *oors and windows = 144 sq. ft. 
 
 Half of 144 sq. ft. is allowed ■ 72 sq. ft. 
 
 Net area to be lathed and plastered s 1,233 sq.ft. 
 
 1,233 sq.ft. = 137 sq. yds. 
 
 1 sq. yd. is worth iiO cents. 
 
 137 sq. yds. urn wuriii 30 cents x 137 a> S41.10. Ana. 
 
MKASUREMBNT OF LATHING AND PLASTKHISO. 40i> 
 
 EXERCISE 134. 
 
 1. Includinj? one of the spaces between the latha, how 
 many square inches does one lath cover ? 
 
 2. How many square feet will a bunch of laths cover? 
 
 3. How many bunches of laths will be required for a wall 
 86 feet long and 12 feet high '? 
 
 4. How many hunches of laths will be required for the 
 ceiling of a room 32 feet by 28 feet '? 
 
 6. How many bunches of laths are required for the walls 
 and ceiling of a room 15 feet by 18 f«et, and 9 feet higli? 
 
 6. How many bunches of laths are required for a hall 84 
 feet long, 52 feet wide, and 21 feet hii^'ti, allowing for 4 
 doors and 10 windows, each having an average surface of 
 82 square feet. Art. 696. 
 
 7. At 80 cents a bunch, find the cost of the laths for a 
 room 20 feet by 24 feet and 15 feet high, there being 3 
 windows and 2 doors, each 8 feet by 4 feet. 
 
 8. At 25 cents a bunch, find the cost of the laths for a 
 room 24 feet by 16 feet and 10 feet high, allowing for a 
 door 8 feet by 3 ft. 6 in., and a window 7 feet by 4 feet. 
 
 9. How many square yards of plastering are there in 
 the ceiling of a room 60 teet bv 32 feet ? 
 
 10. How many square yards of plastering are there in 
 the walls and ceiling of a room 36 feet by 24 feet and 12 
 feet high ? 
 
 11. Allowing for an 18-inch base-board, find the number 
 of yards of plastering in a room 36 feet by 30 feet and 14 
 feet high. 
 
41U MEASUUEilENT OF LAIUINQ AND PLASTERING. 
 
 12. Find the cost of plastering the ceiling of a room 36 
 feet by 82 feet, at 9 cents per square yard. 
 
 18. Find the cost of plastering the walls and ceiling of a 
 room 18 feet by 24 feet, 12 feet high, at 12J cents a square 
 yard. 
 
 14. At 15 cents a square yard, find the cost of plastering 
 the walls and ceiling of a room 21 feet long, 14 feet wide, 
 and 12 feet high, with 4 openings, each 8 feet by 4 feet. 
 
 15. At 12^ cents a square yard, find the cost of plaster- 
 ing a room 20 feet by 16 feet and 12 feet high, with an 18- 
 inch base, and having 4 openings, averaging 82 square feet 
 each. 
 
 16. Find the cost of lathing and plastering a room 16 
 feet by 18 feet and 12 feet high, with laths at 80 cents a 
 bunch, and plastering at 15 cents a square yard. 
 
 17. Find the cost of cementing a circular cistern 8 feet 
 in diameter and 9 feet high, at 8 cents per square foot. 
 
 
 I 111 
 
 ii 
 
MEASUIiEMKNT OF SIUNE-WORK. 
 
 411 
 
 MEASUREMENT OF STONE-WORK. 
 
 61>0. A cord of stone is of the same size as a core" of 
 wood. In estimating stone-work no smaller part than 
 quarter-oords is allowed. 
 
 700. A cord of stone will make about 100 cubic feet 
 of wall. 
 
 TOl. In estimating the cost of mason-work, it is 
 customary to take the outside measureraent of the wall, 
 and make no allowance for openings, except they are large. 
 
 702. It takes about throe bushels of lime and a cubic 
 yard of sand to lay a cord of sto.ie. 
 
 703. Stone-work is usually estimated by the perch. 
 
 704. A perch of stone-work is 1 rod long, 1 J feet thick, 
 and 1 foot high. It contains 24 f cubic feet. 
 
 EXERCISE 135. 
 
 1. How many cubic feet of stone are there in a pile 38 
 feet long, 6 feet wide, and 4 feet high ? 
 
 2. How many cubic feet of stone are there in wagon-box 
 9 feet long, 8J feet wide, and IJ feet high ? What part of 
 a cord does it contain ? 
 
 8. How many cords of stone are there in a pile 20 feet 
 long, 8 feet wide, and 8 feet high ? 
 
 4. In No. 3, how many cubic feet of wall will the stone 
 build ? 
 
 5. How many cords of stone will build a wall 200 feet 
 long, 6 feet high, and 8 feet thick ? 
 
 6. How many cords of stone will build a wall 60 yards 
 long, 6 feet high, and 18 inches thick ? How many perch 
 of Btone-work in the wall ? 
 
412 
 
 MEASl/HKMKUT UF SXOiSK-HunK. 
 
 If 
 
 ( ' 
 
 7. Find the cost of the stone in a wall 42 feet long, 
 8 feet high, 18 inchefa thick, at |6 per cord. 
 
 8. IJow many cordj of atone are required for a cellar 
 86 feet long, 80 feet «*: .e, if the wall be built 8 feet high, 
 and two feet thick ? Find the cost of the mason work at 
 60 cents a perch. 
 
 9. How many cords of stone are required for the founda- 
 tion of a bank barn 60 feet long, by S*} feet riuc. if the 
 foundation wall be 7 feet high and 3 feet thick ? Find the 
 cost of building the foundation at 60 cents a perch. 
 
 10. At 60 cents per perch, what is the cost of the stone- 
 work for the basement of a house which haa an outside 
 perimeter of 160 feet, the wall being 8 feet high and 20 
 inches thick ? 
 
 11. How much lime and sand will be required for the 
 mortar of an 18-inch wall 8 feet high, under a house 40 
 feet by 30 feet ? 
 
 12. In No. 9, find the cost of the material at $6 per 
 cord for the stone, 30 cents a bushel for the lime, and 
 $1.20 per cubic yard for the sand. 
 
 18. A stone house is 36 feet by 24 feet ; the cellar walls 
 are 9 feet high and 3 feet thick ; the walls of the ground 
 floor are 12 feet higli and 2 feet thick; the wall., of the 
 second floor are 8 feet high and 18 inches thick ; the gable 
 walls are 7 feet high and 12 inches thick ; find— 
 
 1st. Number of perches of mason work in the building, 
 and cost of labour at $1.10 a perch. 
 
 2nd. Cost of the stone at $5 a cord. 
 
 3rd. Cost of the lime at 85 cents a bushel. 
 
 4th. Cost of the sand at $1.10 per cubic yard. 
 
 4^ 
 
4*VA.- 
 
 UKASUliKilEST Of liJUCK-HUIiK. 
 
 41P 
 
 MEASUREMENT OF BRICK-WORK. 
 
 TOtl. Bricks vary so much in size an.l style, that to give 
 the exact dimensions of the differoiit styles is im|iractical)Ie. 
 Ordinary bricks are 8 inches long, 4 incius wide, and 2J 
 inches thick. 
 
 TOO. It is sufficiently accurate, in making an estimate 
 of the number of brick needed for a certain work, to reckon 
 20 bricks to the cubic foot laid dry. 
 
 707. In half-brick walls, such as in veneering wooden 
 houses, each brick, with the mortar required to lay it, has 
 an external surface of 8J x 3, or for aliout every 25 
 square inches of surface. 
 
 70S. In single-brick walls, ^ach brick, with the mortar 
 required to lay it, has an external surface of -IJ x 3, or one 
 brick is required for about every 18 square inches of 
 surface. 
 
 700. In a brick-arul-a half vf&W, a brick is required for 
 about every 8f square inches. 
 
 710. In double-brick walls, a brick is required for about 
 every 6J square inches of surface. 
 
 711. In estimating material, corners are measured 
 once, and allowance is made for doors and windows 
 
 In estimating labor, the corners are measured twice, 
 that is, the outside measurement is taken, and allowance 
 ie usually made for one-half the openings. 
 
 EXERCISE 136. 
 
 1. A pile of ordinary bricks is 8 feet 6 inches high, 14 
 
 feet long, and 15 feet wide. What is the pile worth at $8 
 per thousand ? 
 
I ' 
 
 li 
 
 n. 
 
 V. 
 
 ill 
 
 fl 
 
 If 
 
 III 
 
 414 
 
 MHASUREMKSr Olf UUICKWOUK. 
 
 2. IIow many bricks aro tlicro in a wall 36 foot loug, 
 12 feet high, hnd lialf a brick thick ? 
 
 3. How many brickn are required to veneer the front of 
 
 a house 18 fctt wide and 25 feet hi^;h? 
 
 4. How many bricks are require I for a einglo brick 
 partition between two houses, 40 feet deep and 24 feet hi.^h ? 
 
 5. How many bricks aro roiiuired to build a house iiO 
 feet by 24 feet, and 18 feet high, with single brick walla ? 
 
 6. How many bricks are rcpiirod for a double brick wall 
 of a basement, 48 feet by 32 i'eot, and 10 feet high ? 
 
 7. What will it cost to lay the brick of a house 40 feet 
 by 32 feet, and 21 feet bif^h, with a Dat roof and double 
 walls, at $2.75 per thousand ? 
 
 8. Find the cost of the brick in the wall around a 
 garden. 400 "eet by 200 feet, 6 feet high, and a b-ick and a 
 Lalf thick at :?7 per thousand. 
 
 9. At $8 per thousand, find the cost of the brick in the 
 front walls of a terrace block, 120 feet long and 22 feet 
 hi^h. There are 6 doo" ch 8 feet by 3,J, and 20 
 windows, each 8 feet by 4 ib.^, the wall being a brick an I a 
 half thick. 
 
 10. How many bricks will be required for a house 40 
 feet by 30 feet ; the basement walls are 8 feet high and 
 2 brick thick, one door 4 feet by 6 feet ; the ground floor 
 is 11 feet between the floors, and the walls a brick and a 
 half thick, 2 doors and 4 windows, each 8 feet by 3J feet ; 
 the second floor is 10 feet high between the floors, and the 
 the walls one brick thick, 6 windows, each 8 feet by 3^ 
 feet ; the gables are 10 feet high and half a brick thick. 
 
^_L!5Kr_ 
 
 Mh JhIC ^VSn-.M Ur- .1/A.J.N? hi. \il:\ r. 
 
 15 
 
 THE METRIC SYSTEM OF MEASUREMENl. 
 
 "Tl'..' r.'.il tH'irlnnlni.' -f exact kiiowli'iltti . or ■^i irim-. lu ■« in m>a"iirini.'. mil 
 
 thf failhril uhs.-IVil iii nature U :il«:l>« uC 'U]u. .1 in llKilsUliliu- —Har,. 
 
 lllllllllirillllllLillllllllalllllllllllltftl 
 
 This enfravliii.' is a /J\ ;wc.'r-t' (exiict 9lzi'\ ur the t.iitli iJiii .1' u MIU'Rh. 
 The hiru'i' whiteaiicl-hhuk -<in.iri-< lit top shdw lis (llvlshjii inici ID Ciir-.nutre;, 
 each dl' which is siil)-(livliiiil iiit.i IM Miiltmclrc^. as mIihwii iit h..tt..iii hy the smiill 
 whitf ami Illicit -^trllJS. A cniEpletu Metre can he easily eoiijlriK'ted Irjin this 
 llli;-'lr:<ti')ii. 
 
 712. The Metric Syst«.m (pronounced Mtt-ric) is a sys- 
 tem of weights and measures expressed in tln' decimal 
 scale. It is now legal in ni'arly all eivilizt-d OMUiiirit's. It 
 was Ifgali/i in Canada hy Act of Domini'in Parliametu in 
 1886 (chap, lol, sec. 21), and all er»nn-acts l)ased ujxin it ai'o 
 now enlbfcihle at law. It was legalized in the United States 
 in iSt'ji;, and copies of llic standard metre furni-^hcd to all the 
 States. This system of measurement is used in all countries 
 for scientific purposes on account of its exactP"ss, and in 
 many countries it is used for ordinary puryioses. Since 18 JO 
 the metric measures have been the only ones in common use 
 in France. 
 
 713, The Standard Metre, which is the i)asis of the 
 Metric System cf Measurement, is a liar of platinum ."'.i.37 
 inches long This lengtli Avas chosen because it was supposed 
 
 to be one ten-mil ii-nth (in .' , '-r .0'y)0001) of a quarter of 
 
 the earth's circumterence measured by a line parsing 
 through Paris, France, from the equator to the pok . The 
 
1 .^ 
 
 . , 
 
 
 
 I 
 
 'i. 
 
 
 I.'! 
 
 416 
 
 MA/A7C Sy:>ri.]/ or M1:A.SL A/-.\/J:.\7. 
 
 ori^'iiiHl bar. or metre, was made by Uorda in 1795 at I'aris 
 where it is carefully pivserved, aecurate copies beiii*; fui' 
 nislH.d to the governments ofall civilized nations Its leiiLnl, 
 being nearly 3 ft. 33 in, the metre may be remembered as 
 the rule of the three threes. 
 
 714. The Standards used in a general scheme of meas- 
 urenicnt are called Units. Thus, the Metre in France 
 ("nils tiie foundation and starting-point of everv measure i„ 
 exi>tence. 
 
 715. All the Units of measures are derived in a simi.le 
 nanner from the Metre. Thus : 
 
 The Metre is the unit ol '.ength. It is a bar .i'j.'M 
 Inches long. 
 
 The Ar (or Are) is the uni. of Land Measure. It is a 
 sciuarc whose side is 10 metres. 1 Ar = lia.G sq. yds. 
 
 The Litre (Le.-ter) is the unit of Capacity.'* It is a 
 
 cubic decinu'tor; th;it is, a cube whose edge is a decimetre 
 long. A Litre = 1.7(; jdnt. 
 
 The Gram is the mat of Weight. It is the w(ii,ri,r ,,r a 
 cubic centimetre of water. 
 
 Aotla- terms us.a |„ tlic Mitrio SysUm are derived tVo.i, tl..' ..,.,U 1 „|i. 
 (liiji.pi.i^r the liiial "me ' 111 'Vr<7«//;jf," etc. 
 
 716. The Metre is sub-divided always into tenths, 
 hundredths, thousandths, c\:c., or decimal parts, thus : 
 
 Decimetre (dm) Latin decern, ten = ,Vor .1 metre (m) 
 Centimetre (cm) " centum, hundrr.l = ,ii, or .01 metre. 
 Millimetre (mm) " mille, thousand=,oW or .001 " 
 
 „„n?''^ "",'"?"' """' '""■"■ •''="">"l"a»ons are formed by prefixing /atm 
 m men, I, deei. cenn milli.) and ,vriti,„- ,.,e a..breviatlu„s (dm, cm. mm.Ww/I./ 
 »"/w)r^""' '^""'•''■"'"'•""'"•"'^'nes .ire accented on the first syll„lde tlms. 
 
 Tiierefore ■ \ metre=10decimotre.<== 100 centimetres=l()Ou mm. 
 
 1 decimetre = 10 centimeties= 100 mm. 
 
 1 ceutimetro = 10 mm. 
 
METBIC sys/£A/ Oh MhAHU/HArfNT. 
 
 
 7. Multiples of the Metre ar« aa follows: 
 Decametre (Dm) .iie«k lJ»k«. teu-lu metres 
 Hectom.tre (Hn.) " ifekaton. hundred- i.k) metre. 
 Kilometre (Knw " Kilioi. ,houHa„d-lu«. „^.r.r 
 Myrlametr.,Mm) •' Myrm. ten ihou««nd«lu . ,!,,„ 
 Metfameire (MKm> - MeKa, miUion-l.CKW.uu, metre-! 
 
 718. A person wfiu wi^lud to buy 125 metres of,, j, 
 would not ask for "1 hectometre, 2 decametres, 5 nutrcH " 
 any more than a Ik)ston merchant would tell a person who 
 owes him e25.9G that his bill is 2 eagles, 6 dollars. 9 diuies 
 6 cents. 
 
 719. Comparative Lengths are as follows.- 
 
 Inches. Feet. Yards. 
 
 1 Metre- 89 37079 8.280809-2 l.uw:i.;38i 
 
 1 Decimetre- 3.9:C08 .S2mH','J .iou;i.i;J3 
 
 ICeut.metre- .3y371 m2B)9 .oioctt.i3 
 
 1 Millimetre- .03937 .0032a09 .001093*; 
 
 720. The Metre, like the yard-stick, is used iri nieasur- 
 Ing .-.oth and short di.srances; the Kilometre is used in 
 measuring' \ouix distances. 
 
 721. .^iPce, in the .Metric System, 10, luu, 1000, etc., units 
 of a lower denominatioi. make a unit of a higher denomin-i- 
 tion, It Ibilows that any one ot the metric measures mav be 
 expressed m terras ..r another measure by simplv movirff 
 the decimal point to the right or left. 
 
 1. Anumhrr is ndwrd to a LOWER denomination by re- 
 moving the decimal points as many places to the RIGHT a, there 
 are ciphers in the multiplier. * 
 
 «.J' ^/•"7*«.'-"/«<^"^''rf to a HIGHER denomination hy re- 
 movinn the decimal point as many places to the LP FT ^h '--r^ 
 are ciphers in the divisor. ' '" "'° 
 
 Thus 12,465.687- may be written as Kilo-metres by 
 observmg that Milli-metres are changed to metres by mov- 
 
418 
 
 MBTJilC SYSTEM OF MEASUREMENT. 
 
 i *. 
 
 
 cm. 
 
 
 1 decimetre, " 
 
 dm. 
 
 dm. 
 
 
 1 metre, " 
 
 m. 
 
 m. 
 
 
 1 dekametre, " 
 
 Dm. 
 
 Dm. 
 
 
 1 hektometre, " 
 
 Hm. 
 
 Hm. 
 
 
 1 Kilometre, " 
 
 Km. 
 
 Km. 
 
 
 1 Myriametre, " 
 
 Mm. 
 
 ing the point three places to the left, and metres are changed 
 to Kilo-metres by carrying the point three places further, 
 making in all six places. 
 
 Therefore 1 2, 4 66, 68 7 """^ - 12.465687^ 
 
 RULE. — First count the number of places needed to convert 
 the given measures into terms of the principal unit; then the 
 number needed to convert the principal into the required units. 
 
 Before adding or subtracting, the quantities must be 
 written in the same unit of measure. 
 
 722. MEASURES OF LENGTH. 
 
 10 millimetres, marked mm. are 1 centimetre, marked cm. 
 
 10 centimetres, " 
 
 10 decimetres, " 
 
 10 metres, " 
 
 10 dekametres, " 
 
 10 hektometres, " 
 
 10 Kilometres, " 
 
 723. To Reduce 3.825 m. to cm. 
 
 Solution. — To reduce metres to centimetres, multiply 
 by 100. Write 3825, and place the decimal point between 
 2 and 5, two orders farther to the right tlian it is in 3.825. 
 Aus. 382.5 cm. 
 
 724. To Reduce 1025.5 m. to Km. 
 
 SoLaTiON. — To reduce metres to kilometres, divide by 
 1000. Write 10255, and place the decimal point between 1 
 and 0, three orders farther to the left than it is in 1025.5. 
 Ans. 1.0255 Km. 
 
 725. To Reduce 2.15 Dm. to centimetres. 
 
 Solution. — To reduce dekametres to centimetres, mul- 
 tiply 10 X 100 = 1000. Write 215 and annex a -^ipher. Ans. 
 
 2150 cm. 
 
 LAND OR SQUARE MEASURE. 
 
 726. TtiQ Are is the unit of Land measure (or Area). It 
 is legal at 119.6 sq. yds. The Are is the principal unit of 
 
UE THIC aVSTHM OF MEASUhEMENT. 
 
 surface of small plots of land. The area of a farm is ex 
 pressed m Hektars ; of a country in square Kilometres; 
 
 Table. 
 100 centiares, marked ca., are 1 Are, marked a. 
 ''^ ^"-^^ " a., » I hektar " Ha. 
 
 727. An Are is lOu square metres, marked ml The 
 Hektar is nearly 2^ acres C2. 17). 
 
 728. t^r measuring other surfaces, squares of the metre 
 and us subdi visions are used. 
 
 1. Eeduce 397.8 a. to hektars. A.-3.978 Ha. 
 
 ^•^ *• *o square metres. A.— 360 m». 
 
 MEASURES OF CAPACITY. 
 
 1 l^^i ^"^l ^l'.''^'' *^' ""'' '^ '^J^^^^i'i'- ^' i^ legal at 
 1.0567 quarts, Liquid measure. 
 
 Table. 
 
 10 centilitres, marked cl., are 1 decilitre, marked dl 
 decilitres, " dl.. " i litre. '• ? " 
 
 lures .. 1., . 1 dekalitre '• Dl 
 
 10 dekalitres, " Dl.. " i hektolitie " HI. 
 
 heHoL^'Th'T''''"'™""^^' ''^'^ ""'^ '""^ ^itr« -"'I ^he 
 hektoh re. The lure is very nearly a quart ; it is u.ed in 
 
 measunng milk, wine, etc., in moderate qua.uities. ^ T " 
 
 h ktoli re IS about 2 bu. ^ pk. ; it is used in measurin.^ 
 
 grain, fruu, roots, etc. in large quantities. 
 
 731. For measuring wood the Stere is used ; it is a cubic 
 metre ( = 35.316 cub. ft.) 
 
 MEASURES OF WEIGHT. 
 
 15.432 grains Troy. 
 
:-li 
 
 420 
 
 ■«i 
 
 ill 
 
 i'M 
 
 733. 
 
 METRIC SYSTEM OF MEASUREMENT. 
 
 Table. 
 
 eg., * 
 
 ' 1 decigram 
 
 11 
 
 dg. 
 
 dg., ' 
 
 ' 1 gram, 
 
 (1 
 
 g. 
 
 B- 
 
 ' 1 dekagram, 
 
 <i 
 
 Dg. 
 
 Dg., ' 
 
 ' 1 hektOKram, 
 
 ■ 1 
 
 Hg. 
 
 Hg., ' 
 
 ' 1 kilogram, 
 
 11 
 
 Kg. 
 
 Kg., ' 
 
 ' 1 myriagram, 
 
 11 
 
 Mg. 
 
 Mr., ' 
 
 ' 1 quintal, 
 
 11 
 
 Q. 
 
 10 milligrams, marked mg., are 1 centigram, marked eg. 
 
 10 centigrams, " 
 
 10 decigrams " 
 
 10 grams, " 
 
 10 dekagrams, *' 
 
 10 hektograms, " 
 
 10 kilograms, " 
 
 10 myriagrams, " 
 
 10 quintals or 1000 kilograms are 1 Metric ton, marked M.l*. 
 
 734. The weights com- 
 monly used are the 
 Gram, Kilogrram, and 
 Metric ten. The Gram 
 
 is used in mixing medi- 
 cines, in weighing the 
 precious metals, and in 
 all cases where great ex- 
 actness is required. The 
 Kilogram, ( comuionly 
 called the "Kilo"), is the 
 usual weight for Grocer- 
 ies and coarse articles 
 generally ; it is very 
 nearly 2\ Q)S. Avoir. The 
 metric ton is used for 
 weighing hay and other 
 heavy articles; it is about 
 204 ft)3. more th.in our 
 ton. 
 
 1 Kilogram =1000 ct.iius, (exact size), 
 commonly called the " Kilo." 
 
 735. Legal and Approximate Values are as follows: 
 
 Denomination. Legal Value. Approximate Value. 
 
 Metre 89.37 inches 8 ft. 8i inches. 
 
 Centimetre 39371 " finch. 
 
 Kilometre 62137 mile | mile. 
 
 Square Metre 1.196 sq. yards 10^ sq. feet. 
 
Mh TRIC HYSTEM OF MEASUkhMErfT. 
 
 Legral and Approximate Values (continued) 
 
 Denomination. Le .ai Value. Approximate Value. 
 
 Hek.ar...:::::::::;:::;::J^?:2,r;^-; ^^..rod. 
 
 Cubic Metre 1.3. g cub. yds .-i ' \^T^- 
 
 ^^■^ 27o9cord. ^-i cub. feet. 
 
 Y ■ i cord. 
 
 ■^"'■® 1.051)7 quarts. ... f 1 A liquid quart. 
 
 f l'^""*™ 2.am bushels ■ ^ ^2Zr^- . 
 
 Oram 15.132 «r. Troy ^ b-,'. 4 ,,k. 
 
 or.,w ^ «. :.""^ 2i pounds. 
 
 J3-'«r. Troy. 
 
 OlHtb. 
 
 Metric Ton (or toi.neau) . .220J.6 tb. 
 
 Stere . 
 
 .0.27,^9) cord... 
 
 IT. 204 n.s. 
 
 i cord. 
 
 exa"' J'' "'" "'"" " ""'' '" =°'""* '"« f°»™'n« 
 
 737. MISCELLANEOUS EXAMPLES. 
 
 1. How many yards, feet, etc.. in 
 4 M.? 
 
 Solution. - In one metre there are 
 89.87 in. ; in 4 metres there are 4 times 
 89.37 in., which are 157 48 in. ; 157 43 in 
 reduced to integers cf higher denomina- 
 tions are 4 yds. 1 ft. 1.48 in. 
 
 OPERAIIOS. 
 
 39.37 
 4 
 
 12)157.48 
 
 3)13 ft. 1.48 in. 
 
 4 yds. 
 
 OPERATION. 
 
 Ift 
 
 2. What is the value of 
 36 ftg. in kilograms ? 
 
 Solution.— In one kilogram 
 there are 2.2046 fts ; in 36 ths. 
 there are as many kilograms as 
 2.2016 are contained times in 86, 
 which are 16.329+. 
 
 2.2046)36.0000(1 6.32-J + 
 
 13 9540 
 13 2276 
 
 7:iG40 
 661.^8 
 
 65020 
 44092 
 
 20l>280 
 198414 
 
 3. What is the value 
 
 4. How many hektars 
 
 of 20 Km. ? 
 in 160 acres? 
 
 12.4274 mile* 
 64.75 + Ha. 
 
422 
 
 M ETHIC SYSTEM Ol' MEASUREMENT. 
 
 ni. 
 
 1* 
 
 5. What is the value of 49 m. ? 9 rd. 4 yd. 3.] 3 In. 
 
 6. How many hektolitres in 42 bu. ? 14.8 + HI. 
 
 7. How many square yards in a roll of paper 9 m. long 
 and 5 m. wide? 5-382 sq. yd. 
 
 8. The five-cent piece weighs 5 grams; how much will 
 100 such pieces weigh? 5 Kg. 
 
 9. Ten litres of a certain liquid weigh 92 Kg. ; what is the 
 weight of a decilitre ? -92 Kg. 
 
 10. One hektogram of goods costs §5.35 ; what costs one 
 kilogram ? ^53.50 
 
 11. A piece of money weighs 10 g.; how many such pieces 
 in a bag weighing 1 Kg. ? 1^^^ 
 
 12 A hcktolitre of wheat costs 86.25 ; what is the price ol 
 a dekalitre ? ^-^-^ 
 
 13. A hektolitre of wine costs $25.10 ; what is the price 
 of a litre? ^^ol 
 
 14. A kilogram of wool costs ^1.875 ; what Is the cost of 
 100 kilograms ? ^187.50 
 
 15. A litre of wine weighs 880 g. ; what is the weight of 
 a hektolitre? 88 Kg. 
 
 16. Add 45 kilograms, 4 hektograms, 5 dekagrams; 35 
 kilograms, 8 dekagrams, 7 grams; and 45 hektograms, 4 
 grams. 85.041 Kg. 
 
 17. A wine merchant sold 1270 litres, 487 litres, 1503 
 litres, 1000 litres, and 2345 litres ; how many hektolitres did 
 he sell ? 66.65 HI. 
 
 18. A vase, weighing 24.67 hektolitres, contains 18.79 
 hektolitres of liquid ; what is the weight of the empty 
 vase ? 5.88 HI. 
 
 19. From a barrel containing 117 litres of wine, 42.75 
 litres leaked out ; how much remained ? 104.25 1- 
 
A13TRIG SYSTEM OF MEASUREMENT. 
 
 (23 
 
 20. How much will 1:55.00 m. of cloth cost at $1.10 a 
 "'etre? i;i.-.7.J% 
 
 21. A grocer bought ;i84.1 Kg. of sugar at 19 cents a kilo- 
 gram ; hov,- much did it cost ? $730.r)j 
 
 22. Bought 2') hogsheads of wine, of 2J.") litres each, at the 
 rate of $.l.")f) a litre ; how much did it cost ? $S77..-)0 
 
 2:5. What is the cost of 21 pieces of cloth of l-.' ni. cacii, at 
 $r).r.Oa metre? $.^.018.58 
 
 2 L I have an article that sells for 2G cents a pound ; how 
 much is it worth a kilogram ? $.."')7;5 + 
 
 2."). A man bought 25 lbs. of tea at $1.80 a pound; he 
 exchanged it for five times its weight in coffee, which he 
 sold at ^M a kilogram ; did he gain or lose by the bargain, 
 and how much ? $.376 + 
 
 20. How many metres of carpeting, .75 m. wide, will cover 
 a floor 8 m. long and 5 m. wide ? 53 33 + m. 
 
 27. I paid $13 for a barrel of vinegar contaming 140 1. ; 
 I lost 22 1. by leakage, and sold the remainder at 20 cents a 
 litre; how much did I gain? 810.60 
 
1 
 
 42t INSTITUTE OF GUARTERED ACCOCXTAXTS. 
 
 INSTITUTE OF CHARTERED ACCOUNTANTS. 
 
 i 
 
 , I 
 
 Pt 
 
 ORGANIZATION. 
 
 738. This Institute, which re- 
 ceived its charter from the Ontario. 
 Legislature in 1883, comprises in 
 its membership the leading Account- 
 ants of Canada. The chief aim 
 of the Institute is to raise the 
 standard of accountancy ; and in 
 order to increase the knowledge, 
 skill and proficiency of its members, 
 it is empowered to establish classes, lectures and examinations ; 
 to prescribe tests of compettncy ; to grant diplomas entitling 
 members to use the distinguishing letters RCA. (Fellow of the 
 Chartered Accountants) ; and to affiliate with any other similar 
 bodies for mutual benefit 
 
 AFFILIATION. 
 
 739. Business Colleges and other Educational institutions 
 having a department devoted to the study of Accounts may 
 become affiliated with the Institute, and may conduct the Inter- 
 mediate Examinations in connection therewith, on terms fixert 
 from time to time by the Council 
 
ISSTITVTE OF CHARTERED ACCOUXTAXTS 425 
 
 740. StudentS~at- Accounts, of the age of i6 years or 
 over, are admitted to registration under two classes: (1) 
 Primary Students and (2) Intermediate Students or Book-keepers. 
 Such Students are entitled to attend the meetings of the Institute 
 and take part in discussion of papers. Students may form an 
 Association for the better advancement of their studies and pro- 
 fessional knowledge, and for making recommendations to the 
 Council affecting their joint interests. 
 
 741. The Primary Examination required of students on 
 entrance comprises Business Composition and Correspondence, 
 Spelling and Punctuation, Arithmetic, Penmanship, Elementary 
 Book-keeping, Common Latin Terms and Roots, British and 
 Canadian History, Geogri^phy, Stenography (the last optional). 
 This examination may be conducted in any affiliated institution, 
 or the Council may waive this examination or. studeiitj showing 
 that they have passed one equivalent, or have had practical ex- 
 perience at accounts which may be deemrd t .bivalent. The 
 object of the Primary Examination is to reasonably ensure that 
 future candidates for membership shall be men of good general 
 education, the Council holding the view that the comparatively 
 slow progress made hitherto, towards obtaining recognition from 
 the public of the claims of accountancy to be considered as a 
 profession, has been due in no small measure to the superficial 
 character of the education deemed to be necessary to fit a man 
 for intelligently undertaking the duties of an accountant, or even 
 of a book-keeper (understood in the sense of one versed in one 
 branch only of accountancy). While it may be true that every 
 accountant will find his own level, on the ground of natural 
 ability alone, it is equally certain that the accountant who has 
 had the initial advantage of a good general education, supple- 
 mented by a judicious course of special training for his calling or 
 profession, will out-distance the accountant who has not had 
 these advantages, everything else being equal. 
 
426 
 
 INSTITUTE OFCHARTELID ACCOUNTANTS. 
 
 Ik 
 
 1 •■ 
 
 ;;. 
 
 . 
 
 
 » 
 
 
 1 
 
 
 h' 
 
 .«4i 
 
 742. The Intermediate Examination is open to any one 
 who has registered as a Student-at-Accounts, 19 years of age or 
 over, after one year from passing the Primary or equivalent 
 Examination The Intermediate Examination comprises Mer- 
 cantile Arithmetic, Negotiable Instruments, Book-keeping, 
 Auditing, Shareholders' and Partners' Accounts, Insolvency. 
 This examination may be held in affiliated institutions. Every 
 person passing the Intermediate Examination is entitled to a 
 Certificate to that effect, and setting forth in suitable terms his 
 attainments as a book-keeper. The Intermediate Examinations 
 are intended to afford to students who desire to take up account- 
 ancy as a profession, an opportunity to test their general pro- 
 gress in professional knowledge, to enable the Council to form an 
 estimate of their capabilities, and to advise upon and direct, so 
 far as may be, their course of preparation for the Final Examin- 
 ation, which qualifies for admission to membership as an Asso- 
 ciate. There is the further intention to provide recognition of the 
 attainments of those candidates who do not purpose attempting 
 the Final Examinations, but desire to have the Certificate of the 
 Institute of competency to undertake the duties of a book keeper. 
 The scope of the Intermediate Examinations, therefore, will, 
 generally speaking, be limited to a thorough comprehension of 
 the duties of one required to undertake the duties of chief book- 
 keeper in a first-class business. 
 
 743. Final Examinations. Any person who has passed 
 the Intermediate may apply for membership in the Institute, 
 and if of the age of 21 or over, the Council will set a Final 
 Examination comprising Book-keeping, Auditing, Insolvency, 
 Joint Stock Companies, Mercantile Law, Partnerships and 
 Executorships. This Final Examination shall be held in Toronto, 
 and any who pass, upon being admitted to the Institute by ballot 
 shall receive a Certificate of membership, and right to use the 
 appellation "Chartered Accountant," and to be styled 
 " Associate." 
 
IXSTITL'TE OF CHAHTERED ACCOUSTASTS 
 
 " K. C. A 
 
 744. A Chartered Accountant who has been in continuous 
 practice as such for three years after admission as a menfber 
 may be admitted a " Fellow of the Chartered Accountants *' 
 upon passing the tests, viz. : (1) Known standing and reputa- 
 tion as a Public Accountant, and (•-') a thesis upon some subject 
 to be approved by the Council. Upon passing these tests a 
 "Diploma of Fellowship " is issued to the candidate, giving him 
 the right to use the letters " F.C A " 
 
 745. Every Commercial Student should aim to secure 
 membership in this Institute of Chartered Accountants, and 
 to pass through the various grades above outlined till tho 
 goal is reached — the high honors and privileges of a " Fellow 
 of the Chartered Accountants," upon whom the stamp of this 
 honorable Institute is placed in the letters "F.C.A." In order 
 to help our readers to reach this end, the above informatiou 
 is given and the following Examination Papers are quoted. 
 
l-i 
 
 if 
 
 428 
 
 MERCASTir.K AHITllMETIV. 
 
 MERCANTILE ARITHMETIC. 
 
 Problflms set for Candidates In Intermediate Examination, 
 Institute of Chartered Accountants, May, 1897. 
 
 1 A nail manufacturer has 3 grades of nails which ho wants to 
 net hini i^r keg. «2.75. 82.80, «2.8o. He desires to make a list of 
 prices to sell at 60,4. 10.^, 5,v discount to net the above prices. 
 Give the list prices and show how it is worked out. 
 
 2 A Trustee invests 84.000 in Ontario Bank stock at 80, paying 
 67 and 81.000 in Dominion Bank stock at 200 paying 10^, After 
 tw°o -ears he sells the former at 86 and the Utter at 180. What 
 rate 'of interest has he received during the period of investment 
 and how has the value of the capital changed ? 
 
 3. Convert £855 59. lOd. into currency, exchange being 9.78. 
 
 4. Convert 8750 into Francs, Sterling exchange being at 9^, 25^ 
 Francs representing £1 Sterling. 
 
 0. Find the e«iuated time of paying the balance of the following 
 account on ' xsis of 360 days to the year. Interest 6%. 
 
 1896 
 
 1896 
 Jan. .'• 
 Jan. 2. 
 Mar. 1 
 Mar. 14 
 Apr. 9 
 May 7 
 
 .lods 4, m, 
 " 2;ra, 
 " 1 m, 
 " Net, 
 " 3 m, 
 " 2 tn. 
 
 8175 
 
 75 
 125 
 
 60 
 200 
 100 
 
 8726 
 8315 
 
 Feb. 
 Mar. 
 
 Apr. 
 May 
 
 9 
 2 
 
 3 
 
 7 
 
 By Cash, 
 By Cash, 
 
 By Cash, 
 By Cash, 
 Balance, 
 
 8100 
 50 
 
 60 
 200 
 315 
 
 8725 
 
 May 7th, Balance, 
 
 Adjust the interest and state what amount is due in Cash 
 
 May 7th. 
 
 6 A merchant has a line of tweeds which he is selling in oO yd. 
 ends, for 875 per end, a profit of 25% on cost. His cl<-rk, m order 
 to make quick cash sales, sells for 15% cash discuant. 
 advance over cost did he net 1 
 
 >^hat 
 
MUltGA STILB A HITIIMII'IC. 
 
 420 
 
 7. A n'lte of 8*j'H), dated April ls», IMT., j.iy,kl)lo July 1st 
 (without grace) with interest at (i i w.8 (lisc'iuiiu-d May 1st at 8%. 
 Find the proceeds. Iiiturust on basi'j of \ii'A) lUys to the yeitr. 
 
 8. A Board of Schoil Trustejs desire to issue Dohentures to tho 
 amount of 82, 5(X). Interest 5^ payaKle aniiu:Uly Ist JiiUUrtry each 
 year, the whole amount with interest to be paid in live ei|ual annual 
 payments. Divide the amount into live debentures, one t<> mature 
 each yoar. 
 
 Find the face amount of each debenture numheriiijj theni 1, 2, 3, 
 4, 5, and the amount of coupms duo each yei»r. 
 
 0. A merchant haa ti chests (of 30 lbs. each) of Tea at the fol- 
 lowing prices : — 
 
 1 at 80c. per lb. 
 
 1 " 7.">c. 
 
 1 " oUc. 
 
 1 " COc. 
 
 1 " 2.")f. 
 
 1 " 2()o. 
 
 He de.sires to make 1 chest of a blend containing all these grades 
 to sell at 81.00 per lb. which will give him an advance over costs of 
 100%. Find how many pounds of each ho must use. 
 
 10. If the profits are divided in proportion to the capital invested 
 and tho time it was employed, at the end of a year what would be 
 each partner's average investmert atid share of the protits from the 
 following account*. Net profit 850* *. 
 
 Jno. Roberts Harry Jones 
 
 Dr. Cr. Dr. Cr 
 
 Apr. 1, 82,000 I 1 J in. 84,000 
 I 1 Aug. 3,UX» 
 
 May 1, 8:iOO I Jan. 1, 82,(«)0 
 I Sept. 1, I.IKKJ 
 
 Problems set for Candidates in Intermediate Examination, 
 Institute of Cliartered Accountants, Nov. 1895. 
 
 MERCANTILE ARITHMHTIC. 
 
 snrt of wino at 82 per sallon. and another 
 
 1. A merchant b-'.ys ,•> 
 at 81.50 per gallon. At what price must he sell a blu.id of 7 pirts 
 of the former and 3 parts of the latter to realize 20 per cent, profit ? 
 
430 
 
 MEHCANTILb ARITIIiiETIC. 
 
 % 
 
 'Am 
 
 2. Tou manage an eiUte, and reoeive as your remuneration 5 p«r 
 cent, of the net amount paid tu the bonetioiarieH. Taxna, rei>airM and 
 ■undry expensea in a given year are isl540. Your oomtnisaioni amount 
 to 9350. Find the gruai revenue of the eitate. 
 
 3. Find the present value of 83,250 due 3 yeara ami (t month* hviioe 
 at 4 per cent, per annum. Show working. 
 
 4. Average the following account : 
 
 Jan. 20. -Merchandise, 30 days ?l.»«> 00 
 
 27.— " 4 months lOt) o;> 
 
 Feb. 15.— " net 150 <H) 
 
 Cr. ?<4(H) 00 
 
 Feb. 10.— Cash 75 00 
 
 Balance !?;}25 00 
 
 5. A certain stock pays a semi-annual dividend <>f 3^ per cent. 
 What is it worth to an investor who wants a return of 4^ per cent, 
 per annum upon his investment ? 
 
 0. Convert $,1000 into sterling at ten and on^-half per cent. 
 
 7. Find the cost of papering a room 30 x 22 feet, and 12 feet high, 
 with paper 18 inches broad, costinyr eighty cents per roll of 12 yards, 
 deducting 20 yards of paper for window and door spaces. 
 
 8. k merchant imiwrts aa follows : 
 
 850 yards sheeting at 5 cents ; 
 
 1,400 yards flannel at 13 cents. 
 The duty on sheeting is 20 per cent, ad k'il., and 5 cen.s per lb. (9 
 yards to 2 lbs.) ; the duty on flannel is 30 por cent. (4 yards to the lb.) 
 Packages are charged at S-'t. Freight 8t). 50. Cartage 81. Find the 
 cost per yard of each laid 'Iotv: in his warehouse. 
 
 9. An insolvent estate realized, after payment of expenses, $1,840.72. 
 The claims to rank are as follows : A, .93, lOO.tiO ; B, §1,347.85 ; C, 
 ?890.96 ; D, §870.42 ; E, 8391.80 ; F, 8102 ; G, 884.58. Prepare a 
 dividend sheet showing the rate per cent, and the amount coming to 
 each. 
 
 10. You are being charged interest monthly at 7 per cent, per 
 annum on an overdraft at your bankers. They offer to discount your 
 bills at three months at 0| per cent, per cmnum. Which is the more 
 profitable transaction, and by how much } 
 
 ■■ItllllMI^ 
 
FICHE 6 NOT REQUIRED 
 
FICHE 7 NOT REQUIRED