CIHM 
 Microfiche 
 Series 
 (iMonograplis) 
 
 iCMH 
 
 Coiiection de 
 microfiches 
 (monographies) 
 
 Canadian InatHuta for Historical Mierorop iductiona / inatitiit Canadian da microropreductions liittoriquao 
 
 1994 
 
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 fifot poQV with o printod of Muotfolod i 
 
 •Ion. and ending on tho loM page mMi a pffcitad 
 
 Of iHuatfatod HnpfOMlon« 
 
 Tho last focofdad ffORM on aaoh 
 •haM eontain tha oymbol — 
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 ■■m 
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 MfflBMidultaa AiMa la 
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 pogo i|ul oonpofto uno ompfolnta 
 ou drNuotfation ot on tofniinont 
 pogo qui oomporto uno toNo 
 
 Un doo lyw bo l o t oulvonts a pp awhra Mir la 
 oarnioio imaga oa cnaqua imoroiranat ■aioii la 
 oaK la oymbolo -^ tignlflo "A SUIVRE", lo 
 ■yiiiuuM ▼ Mgnma nn • 
 
 Mapo. platao. eharta. ate., may ba flhnad at 
 d iffaton t raduetion ratioo. ThOM too lorgo to bo 
 ontifoly HMHidod hi ono oapooiiffo oro nHnod 
 beginning in tho upper loft bond oomM , loft to 
 rigjit end top to bottom, oe mony framee oa 
 rmiuHmd. The foNoMring diegreme INustrata the 
 
 Lee eortee, plenohee, tableauii, eto>, pouvent otfo 
 fNmoe A dee taux da rMuetion differ onto. 
 LofBQue lo dooument eet trop grand pour Atia 
 repreduit en un eeul oHohi. It eet flbiU i portir 
 do Iwigle euporlottr goueho, do gouoho a drollo, 
 ot do heut on bee, en prenont lo nombro 
 d •mogee neoeesebo* Lee dtagrammee euivente 
 Muotrent la m4tiiodo« 
 
 1 2 3 
 
 
 1 
 
 2 
 
 3 
 
 
 4 
 
 5 
 
 6 
 
(ANSI ofid so mr CHART N». 2) 
 
 1.0 ^ 
 
 2£ 123 
 
 U 
 
 1.1 
 
 g2 
 L8 
 
 1.25 lu 
 
 m^M ml 
 
 16 
 
 4 
 
 dEPyEDjM^GE ine 
 
 IMS tm Hobi Strart 
 
 N** York 14609 USA 
 
 (7t« 4a-0300-PhecM 
 (71«)aM-9M»-r« 
 
COMPANION 
 
 TI)THK 
 
 PUBLIC SCHOOL ARITHMETIC. 
 
 FOB THE USE OF TEACHFRS ivn nun *».. 
 
 1 &At.Jll!,K^i AXD PRIVATE NTfTDKNTS. 
 
 BY 
 
 ^H. SCOTT, B.A., 
 
 Principal or the Toronto Normal School, 
 AND 
 
 CHABLES A. BABNES, M.A., 
 
 PuBuo School Inspector. 
 
 TOBONTO: 
 
 CANADA PUBLISHING COMPANY, Limited, 
 
 190K 
 

 
PBEFldL 
 
 ToROHTo, July 34th, 1901. 
 
1 
 
 46 
 
 CONTENTS. 
 
 AmnriM ^ 
 
 (^mt II. " " "■• — 
 
 HlllT. n,« Sotmo CWWAIl, I>»o.t«,. 
 
 I HI* 
 
 1. MaaWr Worit.... 
 
 n. A|rti.».u.i«i^- —-;;-•■ •• - ■■■ ■" 
 
 III. BoauM Notation... "* 
 
 IV. Addition I "• 
 
 V. Snbtnetlon ...."..Z." "' 
 
 VI. MnItlpII«»tlon..„ J... ^ >» 
 
 VII. DiTUIon 122 
 
 VIII. Pfoblomi .....2. 127 
 
 tt. Btdnotion luid'^'i;;™;;;; ~ "2 
 
 M. Fbetof, CweolUtlon, U^ur^ ^ uZ": "® 
 
 XII. FrMtlons -•-urw and JInltlpIo, ]46 
 
 Xni. DmIumIs ...3 ^*2 
 
 XIV. PoNontngo '** 
 
 XV. Applloatiou. of P»»ont«^' "« 
 
 XVI. Piurtnenhip 180 
 
 XVn. Inrolntlon .nd ETolution ^^ 
 
 XVm. Monromtion 206 
 
 XIX. Tho ICotrlo System -^* 
 
 XX. MlwelUneoM Exewiw, ^ 
 
 |P«rt IV. • - •: 280 
 
 B«vi»w PsoBLsin. 
 
 I. Simple Rales 
 
 II. Compound Nnmbon . ^ 
 
 ua 
 
qpr 
 
 OOMTBllTt. 
 
 Pass. 
 .i 245 
 
 .. 247 
 
 .. 206 
 
 in. ATenget «nd ShMring .^.>.... 
 
 lY. Applieatlons of Simple aud Componnd Namben. 
 
 V. FfMton, MeMnres and Moltiple* 
 
 VI. Vulgar Fraetions 
 
 Vn. Oeeimals 262 
 
 Vin. Trade Diieoant 263 
 
 IX. Profit and Lou „ 264 
 
 X. Commission 266 
 
 XI. Insaranoe .....•■. - 267 
 
 Xn. Taxe* ^:. 268 
 
 XIII. Interest 269 
 
 XIV. Bank Discount 271 
 
 XV. Stocks 272 
 
 XVI. Equation of Payments ^ 273 
 
 XVn. Part-ership 274 
 
 XVm. Applications of Involution and Evolution 275 
 
 XIX. Metric System 278 
 
 XX. Work Problems 280 
 
 XXI. Clock Problems 281 
 
 XXII. Problems Involving Velocities 282 
 
 XXIII. Miscellaneous Exercises 286 
 
 Party. 
 
 A Tabu or SqvABXs, Cubks and Boots 307 
 
COMPANION TO THE PUBLIC 
 SCHOOL ARITHMETIC. 
 
 PART I. 
 
 Answera, 
 
 «.4i,'Sl^:'C'- •'*«7.U; .Uiy..,^, «^,^.rt,, .^. 
 «%:.Sr^'*~' «Urty.,.„, ,.^.u^, ,„^.,„. ^^_ 
 
 .■A^-**" '"•"♦^ •"' «'^-«w., w.,.ri,, .1^.^. 
 
 .hf..2X"2^*' '"~**"' "^-n.! -x.,.nl«, .ta^.' 
 •i/f-o^nSfef ' '»«^-'»«.- •Urh.X-l.ur, d^.,.„, ^^. 
 
 2 pt EXERaSE II. PAGE g 
 
 •Ix hnn^X^hl^^,^'^^' •Whuidred; two h„ndr«|, 
 
 1 
 
2 
 
 AUTHHBTIO. 
 
 III 
 
 Hi 
 
 
 w 
 
 
 f 
 
 
 
 
 1 
 
 ■ 
 
 r, 
 
 3. Two hundred and Are; fonr hundred and aiz; Are hundred 
 and Mvep; rtyen hundred and Are; five hundred and aer^tv 
 •even hnndfed and fifty. ^^ ^ •^•"Wt 
 
 fl. Pour thousand, seven hundred and five; five thousand, eicht 
 *',!2j'*f "»i«<»^-*hwf? nine thousand, one hundred and sS^- 
 !L^V **# *»»«««»«» wd forty-nine; tour thousand, nine hun^ 
 and five; tour thousand, two hundred and thirty-one. ^^ 
 
 fthJ:.??*** *»><"w«»d and seven; eight thousand and seventy; eight 
 J&^J' ■5'Tu?"°?"*[ ■*^*" thousand and eighty] sefrti 
 thousand and eight; nine thousand and torty-flve. 
 
 ■iT^hfJlfJ*"^""*"!? »»^^»'^-«»»ht; nine thousand and eight; 
 !;^ -?T^Iu''° J«°dred and two; one thousand, five hundred 
 fK«„-!*f •* ***'*? tliousand, seven hundred and torty-six; five 
 thousand, seven hundred and eighty-six. 
 
 t./JT *5**'**?ll?^ hundred and thirty- tour; one thousand. 
 Wv th^#""**u'^*'*y-?"J one thousand, two hundred and 
 lu^I:^J^' '""^ *j»oasand, three hundred and twenty-one; four 
 thousand, one hundred and thirty-two; eight thousand and nine! 
 iO. Nine thousMd and one; one thousand and sixty-nine; nine 
 
 it^l'tf" **°"f "f ^^J'^'V "'"« thousand, one hundwd Md 
 six ; nine thousand, six hundred and ten ; nine thousand and eights'. 
 
 EXERCISE III. PAGE 8. 
 
 1. ^orty^thousand, eight hundred and seventy-six; flfty-four 
 
 JhnZ«H *"* ^S^^*?"!^"* ' ,'** '^ thousand and seventy ; ninrty -SJ 
 thousand, one hundred and eleven. 
 
 flf*l'.PJ!?!u?!l **'°.''"*^? and eighty-nine; torty thousand and 
 hSd^ Md rii!^' ""^ '"^ '^^•"' ^""^ thousand, one 
 
 ^rJi^l^f'T'^'T thon»«wd and ninety-five; fifty-nine thousand, 
 one hundred; ninety-five thousand, one hundred and one: ttirtv- ' 
 seven thousand, six hundred and ninety-eight. ^ 
 
 • k:i®'*5* i»°>'^'«^ »°^ nineteen thousand and seventy-five- 
 eight hundred and ninty-pne thousand, tour hundred and nineS- 
 two; two hundred and ninety- tour thousand, seven hundred and 
 sixteen; tour hundred and ten thousand, one hundred and ew. 
 
 .iJLf^?^}''^^'^ and ten thousand and ten; nine hundred and 
 !«^ w ^^9"^:^ "^ J^e ; two hundred and thirty-one thouumd 
 and torty-siz; two hundred and seventeen thousand and six. 
 
 6. One million, tour hundred and seventy-six thousand, nine 
 d?tt;!^.*^ thirty-one; three million, seven hundwd^ifajty! 
 tLiH"f!?^ f'^''^ hundred and torty-two; nine hundred and 2n 
 ind SSe million, one hundred and three thousand 
 
 7. Three nailHon, ninety-one thousand and six; fonr minion 
 witiJ°T"* •».?,."^*».? °°« hundred and ninety' thZsSd,^ 
 hundred; three million, nineteen thousand and torty-sevenT 
 
"OTATIOH AMD XVUUunoV. g 
 
 million, th«e hnnd^d wd i^tUi ^LiL^*^ . ""^u •^•' »»»• 
 rixty; «Hrenty million. SThJISSTwd^ir^' "*"* '"'»*'«» •»«» 
 
 ^i.S%r;;;i^^^^ fonr hund«d 
 
 ■nd ninety-one mlUlon Ave hin^^^^^* ^}Ulon, fonr hnndred 
 •ix handrid ^nininl?4.^l^^^,,^^ ninety-one thoneand. 
 hundred and ten thouSSd JJrf t^i *'""""' *»'«rteen miUhJn, two 
 ■•Ton hundred thoS^Jnd onr ' ■*^*" **""°°' -ixty million. 
 
 EXERCISE IV. PAGE a 
 
 i. 15; 21; 34; 78; 87; 19; 91. *' 
 
 f* ???'■ ^^'' ^^^J ^0; W9; 919; 991. 
 S. 1000; 1402; 8006; 8060; 2496. 
 
 iO. 636347972. 
 
 n. 6000090148; 700000000001. 
 It. 99000037004. 
 IS. 864538217953. 
 U. 40004400414. 
 JS' 49000000068798. 
 PAGE 9. 
 
 ^. 1011; 10604; 29470; 80990. 
 S. 804016; 291704. 
 
 «. 1101001; 6004030. 
 7. 904000806. 
 *. 7707707. 
 9. 146147047. * 
 
 EXERCISE V. 
 
 ^. V; VI; Vni; IX; IV. 
 
 I* ^l^^' ^^^'- 3^f XIV. 
 
 I' ?X' ^^' ^^^'^^^i XXIV; XLIV. 
 
 3 ^A^^' ^^' XCVIII; XCIX. 
 
 6'^Si''!lV^'''^^™'<»<^'XXIX. 
 
 IXfXCIX. ' DCCLXXXIX; DCCLXXVII ; DCCLXVI ; 
 
 CML3^^!^^^' DCCCLVII; DLXXVIH ; DCCCXCIV. 
 
 MCMIV. ' "WCCLXXXIX; MDCCCXCIX; MDCCCXLIX; 
 
 '•m!io.ii«,a»;5oi,J"i,. 
 

 ii 
 
 Asmmno. 
 
 5. 4M; 
 
 4. 833; 
 
 5. 506; 
 
 6. 1111 
 
 7. 1290 
 
 8. 2222 
 
 9. 1744 
 i0. 1099 
 
 730; 040; 444; 029; 624. 
 
 4M; 888; 484. 
 
 430; 297; 844; 828; 000. 
 ; 1000; 1014; 990; 999; 1304. 
 J 1000; 1444; 1009; 1282; 1490. 
 
 ; 947; 1906; 1400; 1900; 1000. 
 
 1449; 1666; 2009; 1119. 
 i 1900; 1901; 1809. 
 
 \ ■ 
 
 VII. PAOE 10. 
 
 i. 10; 100; 1000. 
 
 f . ClIXCIX. 
 
 4..1 oui be written to the left of V and X. 
 5. X ean be Dli«9d to the left of I, V, L and C 
 9, n.*' ^' ^* °' '• ™' *' '^'' *' ^5 «• VI; 7. VII; 8, Vnij 
 
 thoJJd*nS*dirti!t''?S'm*r^ *^"»*«^ "d »l»«tf 
 
 to»tir«,,«- Inn . ??? ™? ■""• The length of the ecnator is 
 
 S'-toJit^i?' T? * ^^^ ""^ twen^?Sren tt^,S«dLd 
 
 hundred and thirty-fJir doluS. *»»''^"*^» thousand, two 
 
 9. V; X; XV; XXV; XXXV. 
 10. 100; 110; 120; 130; 200; 210; 220; 230; 300; 310; 820; 330. 
 
 ^*^**^^^"- PAOE II. 
 
 i. 76; 67;' 77; 89; 69. 
 
 f. 988; 806; 1098; 999; 098. 
 
 5. 8999; 11636; 9987; 9998; 9968. 
 
 4. 18676; 20687 j 20987; 19085; 19667 
 
 6. 204996; 225469; 196678; 187898; 214829 
 
 6. 7497. 7. 8789. 8. 7888. 9. 30888. it?. 89476 
 
▲oomoii. ^ 
 
 EXERCISE IX. PAOE U. 
 
 ^ L^' J'^'^' *-2<»lm. 4. 97 ml. S.lUwA, 0. »457eo 
 
 7. 909 yd. *. laermi. *. 786. JO. leespngiw. ••*»^"- 
 
 EXERCISE X. PAOE IS. 
 
 2. 1488; 1330; 1090; 1814; 1312; 18812. 
 
 t. 10242; 14181; 14422; 14822; 183188; 1829«S 
 
 S. 141722; 162222; 152661; 167526; 178246; 160618 
 
 4, 184264; 198698; 178467; 906676; 189806; 172498* 
 
 5. 200896; 946121; 220260; 285326; 221682- 236796 
 
 • !f?if ' *"^^' ^^^^^i 217479; 276014; 258123'. . 
 I* SJJJii ^'^ ^^^^^' ^^5 25869; 242007. " 
 f' 2SSJ' *•***' 269181; 803376; 249409; 808787. 
 9. 277929; 304164; 289089; 289446; 808648 285296 
 
 20. 868489; 802884; 281950; 266875; 368887; 301027.* 
 
 EXERCISE XI. PAGE 14. 
 
 2. 3482890; 4584711; 3328081; 6487312; 4801749 
 g. 8380666; 4164757; 4212613; 4644085; 6870413.' 
 S. 3885886; 4150872; 8515001 ; 8929106; 8462627 
 
 4. 1621900; 4312101; 6478906; 1109747; 14126889 
 
 5. 40393623; 472198044; 465850384; 80717060; 57286686 
 
 • 3^^'' !S^T' ''''^' «»011645i; 4^9. 
 7. 30970664; 6772880; 4564359; 11556690; 391M681 
 
 S. 66381127; 11813141; 12048191; 227559^972^^^ 
 
 9. 186811552; 77223388; 2918515^; 496^; W^M 
 
 20. 62637126; 661680628; 72328309^; 5t^^7S,^, 
 
 * ^ EXERCISE XII. PAliE le. 
 
 6 m^% L^^^' *"8«887. rf. 8809278. 5.5199140. 
 e. 13786. 7. 2683. 8. 10288. 9. 11947. iO. 13254. 
 
 ' EXERaSE XIII. PAGE 17. 
 
 ^87432779. «. 66751805. 5. 68318319. 4 2384473 
 
 EXERCISE XIV. PAGE 17. 
 
 B x^\ '-3" A. S\ 272 marble., rf. 168 mi. 5. 97353 ' 
 «. 1273 •nimiU.. 7. 885 tree.. *. MCXVH. i>. 4639i ^226. 
 
 1 lA .K, ^*^^SE ^- PAGE 18. 
 
 «. tlWO. 7.9870. *. 98ot. ». 208 mi. !<?. 97866. 
 
•p.-' i 
 
 Aunmnio. 
 
 •. W». 7, 144 rt. *. fiOO et. 9. 180 A. i(?. M ri»,.p, ^ 
 
 , .^, EXERCISE XVM. PAOE ft. 
 
 /. 9^1. f. 1300. S. 197796. 4. 1529482711 A mit -i.^ 
 •. 510 ml. 7. ,100. S. 1120. .. igi e'Jl'^rL "-''• 
 
 , T« . "»W:iSE XVIII. PAOEM. 
 
 I. 76 mi. f. 1100620. S. MfiOOO ^ iiTi.i«A 
 
 EXERCISE XIX. PAOE 21. 
 
 i. 1990977. t. 72720, 147720. J. iisfias j ,ili .^ 
 
 i. 86; 18; 18; 26; 64; 80; 26. 
 ». 541; 026; 888; 668; 801; 446. 
 «. 622; 432; 018; 811 ; 242; 017. 
 <. 4630; 2740; 0246; 4711; IIH; 8681. 
 S' 20082; 76464;.01236; 86380; 20142; 18106. 
 e. 14884; 10624; 96162; 26324; 62483; 884261 
 7. 24780; 16880; 16280; 86310; 44002; 86448 ' 
 S. 6232; 24414; 8440; 8117; 2^3; 46444. 
 9. 0210; 106042; 7724; 8282; 845462. 
 JO. 126668; 606072; 224; 246000; 67802. 
 
 EXERCISE XXI. PAOE 23. 
 
 i. Ill eows. g. 40 «Uekeii«. 
 S, 272 g»l. 6. 9100. 7, 204 i,W. 
 10. $1200. 
 
 EXERCISE XXII. 
 
 /. 66; 27; 23; 29; 24; 61; 26. 
 
 8. 186; 462; 193; 746; 581; 690. 
 
 5. 447; 682; 222; 647; 656; 423. 
 4. 2215; 1414; 2343; 3212; 2962; 3926. 
 
 ' S' 1846; 1254; 1265; 8812; 1524; 1018. 
 
 6. 18354; 25283; 33222; 35343; 17427; 27728 
 
 7. 105064; 107014; 302078; 304022; 177244; 312816, 
 *. 226173; 114542; 234121; 213658; 132500; 679924 
 
 9. 457022; 318234; 515265; 025223; 725675: 876899* 
 20. 491978; 261636; 294928; 680929; 281939- 577184* 
 
 * «S. 4. 118 pages. 
 *. 12U;s shMp. 9. 488 A. 
 
 PAOE 23. . 
 
i' M5{ 788. 
 9- 1808} 0886. 
 8' 23610; 6779. 
 7. 601; 479778. 
 *. 487710; 191188. 
 
 '• 3888; 42S6; S828. 
 S. 5287; 7768; 4464. 
 S. 6889; 2766; 2682. 
 '• «87; 822; 6275. 
 9. 4649; 8886; 8786. 
 
 •VBTBAOnoir. 
 
 f' 892; 112. 
 
 *' 29097; 28666. 
 
 8. 887712; 476998. 
 
 .*. 828229 r 199600. 
 
 iO. 186118; 409086. 
 
 WIV. PAQE24. 
 '. 8366; 4666; 4296. 
 4. 8267; 776; 3262. 
 «. 8167; 1444; 4474. 
 *. 4127; 2077; 6266. 
 10, 5667; 1882; 2466. 
 
 '. 32423; 7776.^^SS^ *?• ""^ ^^' 
 S. 35624 S;S !• S£f ' «^' ^««^*- 
 
 ^. 47171 25666- S* 1* S*^' **^' ^^^^^S- 
 
 7. 69094 ^: S* f • f;*^^' ^«'- 3«0646. 
 
 •«>«a, 8«>i67. 10, 6272; 30878; 484717. 
 
 ' 4W9060; 49^"'''* '^'- '•AOE 25. 
 
 ^. 88214W. 727S2f • '* '*^**"»5 «««»7. 
 
 ^ 7733440;' ^^S* ^^ ^*'^'- *««««• 
 
 e. 2714. 
 
 ^. 74. ,. 286^^' «iJS^"- ""^^^ ^»- 
 
 «"o. ». 0067316. /o. 141098, 
 / oa u EXERaSE XXVIII. PAGE 2«. 
 
 »«• *. 1432 ml. 9. 162482. 20. 168677 oow. 
 
 i ««n« . EXERCISE XXIX. PAOE 2«. 
 
 ^. 361636 min. 6 mn!L J*^ "**"• '* ♦3«1«- 
 
 *. 117993. /(I.^sZHT* '••'''<^^- *• 6300836 ft. 
 
 ^•27ct. ..2S^'!f,^* '•«»^^^. 
 
 • WW n. p. 1325 rotes. W. 3960856. 
 
7^ 
 
 il 
 
 .ail 
 
 III 
 
 \\ 
 
 <' 
 
 nnosexxxi. PAoear. 
 
 7. wrua. 8. 5 mi., 187 jrd. P. 225 mi. W. 2210. 
 EXCRdSe XXXII. PA0E28. 
 
 ». Jm. 81, Jao. 26. 7. 40 A. *. 70 d*. P. ISmarblM. 
 to, 21171, 14886, 18691. "»«»i««. 
 
 EXERCISE XXXIIi. PAOE 2t. 
 /. 6746. f . 12968. J. 1606. i. 26B8225. B. 6S29. fl. 925868. 
 r. 2584. «. 78680. ». 2166. 10. f^. /i. 28718. If . wS. 
 
 EXERCISE XXXIV. PAOE 31. 
 
 i. 6060408; 8604864; 846064; 680486; 6408604. 
 i. 1048468,' 9926482; 1750482; 19694912; 14169184. 
 
 5. 1586128; 1106984; 1416192; 1197492; 1935780. 
 4. 1726856; 1586094; 1401216; 734992; 1569984. 
 
 B. 10309862; 10363985; 13630368; 19603068; 10636892 
 
 6. 26300425; 28942092; 26308368; 28454890; 23698468* 
 
 7. 13616586; 2536972; 16549616; 6713872; 27133748 
 *. 21749956; 27156062; 8914696; 1383948; 16559056' 
 9. 1152280; 27160306; 17376320; 12682360; 6172835' 
 
 10. 22985225; 48412845; 39465480; 35404520; 88424815. 
 
 11. 28948225; 4475847>; 27394780; 24488245; 43238245 
 It. 22446384; 204. »884; 22811858; 251844206; 25180824 
 
■vumnuTKnr. 
 
 mimST' '"'•^' 'w^ois.., »««.,«», s„,„,^, 
 
 «*ft.S3r"' »«W«M, «,4««„, ,*««„„, ^,„,^^ 
 U^iiS&T" '*»•"»"' '«««W| ta4f«M17., M,«6<,4o«, 
 
 ««i.lS?l£??^,?%»««»»i »M'34U70, 425.2S.365, . 
 
 •J0Wr^^1^,JgJ«'«Wi ««««XW, 542«84l»2, 
 «»«««f^*5S*«*' ««««»! »«W024520, 
 
 f n.» **B«CISE XXXVII. PAOEM. 
 
 i' Si!?' "*"«i ""iai JWM. ^ 
 
 !• 12?' ''*'»*' "«W»i 3MW0. 
 »• 2a«7»2; 255098; 2»7«12i M7i!U 
 
 «• «0«8»; 6847S; gi4M; iggMT 
 «. aOSaU; 288315; 3W»78: Ml»u 
 r. 3.888., 384260 JZi^- 
 
 ». »M9Ml 4U2D., 484407: Oaaaoa 
 
 :=;3lS:=:|is- 
 

 #. tUes vt. «. 709 tnm. 7. SMO ■!. #. Wm hiu,. 
 ». $110406. iO. 75067 Immmm. 
 
 KiMooooH. t.nmji, 5. smsmiis. w. ommbi. 
 
 #. 17U16 in. «. 188600 tt. 7. 488040 vt. *. 8804000. 
 9. 638600 Bla. /«. 6886484 iNip«n. 
 
 exERcncxu. paoem. 
 
 i. 48060. 1.62941100. «. 66. 4. 668 et. 4.6616. 
 «. OftlB,689. 7. 04730 et. «. 847Stt. 9. 1087 ml. /0. Oiaa,66l 
 
 EXERCISE XUI. PAOEaS. 
 
 i. 173484.' #. 288180. «. 1069847. 4. 67410148. 4. 16408466 
 6.3016078061. 7.1138103116. «. 68086088. 9.60700. /i>. 14264 
 
 EXERCISE XUII. PAOESt. 
 
 i. 66066806. f. 1616. S. 63086. W. 8660001. 6. 7061388. 
 6.680618. 7. 67416 et. «. 16736810 A. 9. 708«tookt,8486thMTM 
 iO. 90608084. 
 
 EXERCISE 
 
 i. 13; 38; 48; 48. 
 S. 831; 388; 339; 803. 
 S. 117; 137; 41; 140. 
 7. 107; 131; 83; 186. 
 9. 91; 102; 81; 40. 
 
 XUV. PAQE37. 
 
 f. 984; 986; 418; 478. 
 4. 191; 149; 184; 166. 
 6. 106; 61; 81; 160. 
 «. 191; 106; 116; 01. 
 10. 671; 891; 749; 801. 
 
 EXERCISE XLV. PAOE 97. 
 
 i. 914821; 104981; 191840; 213418; 281480. 
 f. 78006; 67807; 176806; 266079; 167086. 
 S. 182023; 69816; 164672; 288810; 248561. 
 4. 183602; 106181; 208878; 168627; 140688. 
 8. 86062; 100207; 148860; 71437; 185530. 
 e. 114126; 102067; 140202; 165246; 116667. 
 
 \i in 
 
» ' 
 
 [•wlii^'SlyRT*' '"'**••»' »*««l "IWM-l, 
 
 (M.li.TSili.S"'*""**"-*' '"-^-'i «l>0e44.., 
 
 •»-»!«i7i.f •*••*' "•«»•»' •WW-I, M!W,<- 
 
 [•M«io'.Sf51ViU.^***' •'«*•»' «>"»-«i «M6as-i, 
 
 lnwSilT"' •***•»' •'"»•»' ««••». MM.I.4, ,„...„ 
 
 «M^*!i*.r^-" •^•*' •"»•»! wwM-e, 
 l^yjTi., .,«„.«, „„„^, „^.,^ ^^^ ^^^^^ 
 
 ^^^'BKCmE XLVII. PAoe mm 
 . EXERCISE XUX. PAOE am 
 
 II 
 
 *. 85«-17j 420-88; 248; 213; 1 
 
 *. 8111; 2S01; 2091; 1074.57- 
 
 ^. 1725-18; 1482-21; 1299-24; il6« 
 
 5. 1481-256; 741-595; 669-377 
 
 6. 1666-216; 941-141; 2846-36! 776 
 
 89-54. 
 1262-89. 
 
 47; 849-194. 
 1174-92; 843-664. 
 
 7. 1188-629; 965-82; 847-460 
 *. 824-106; 672-178; 582-568 , 
 9. 1168-776; 1042-626 r ISI8.40 
 
 MO; 682-774. 
 1286-121; 1577-390. 
 M9-124; 494-460. 
 
 M. 786-586; 1564-10; 801-424 
 
 2896-7; 1787-340. 
 872-706; 1^-853. 
 
 EXERCISE L. PAGE 39. 
 
 /. 1082-870; 1071-192; 1067-416 
 
 *. fla9.464; 896-578; 888 
 
 1012-964; 1048-488. 
 
 482; 880-509; 897-594 
 
I 
 
 Hh, 
 
 If 
 
 s, immi iiu-iMi iiti.4aii iitr^t uit-rat. , 
 
 4, l4H'4mi im-Mlli IMl-ati 141S>Mt| 14ir^. ^ 
 t. im-mi UM-Mli Ulf-^Mi UBi-Mlt ISU-IN. 
 
 f. i44s.iiit Mii-iMt im-mt im-mi im-m, 
 r. tm-ioii siit.iMi nM-MiiiM-iHi tm-im, 
 
 t. MM.40( tlM.|M| Mir-r4| MO-SNi tISS-tt. 
 •. MMI-t) MU.M| aMH-fSi B«»-t| 01811-11 1 ITMT-l. 
 to. MMe-0t 7mi-10| MMT-l} UtT/'it 4mi-$t BliM-8I. 
 
 i. 11560-5; 505-5; SI60.5; OSiO-5. 
 
 f. 50615; S5I16-0; MOM; 10565. 
 
 t. 11117-51 17000-45 1 17040-Mi 15165-5. 
 
 4. 10745-10I IHM-IO; 50050-15; 15601-5. 
 
 5. 17874-5; 16017-51{ 10060-14; 10831-41. 
 0. 16000-7; C1410-51 1 11600-7; 11111-10. 
 7. 15M0-10; 0007-0; 7040-50; 0054-40. • 
 «. 15110-10; 11541-50; 8007-15; 0744-U. 
 
 0. 8070-41; 4000-41; 8881-41; 1400-41. 
 10, 1070-106; 1040-06; 1410-006; 1184-480. 
 
 ExmcMiui. PAoeot. 
 
 1. 0540. f . 501636. #. 45iilS. I. 160807. S. 401. 0. 4780. 
 7. 01. «. 170. 9. 0005. iO. 
 
 UN. 
 
 1. 184 4<i. ff. 08000. $. 1040. 4. 10000 lb. S. 
 
 0.100iq. rd. 7. 887 al. «. 376 pMiont. 0.1001b. iO.Oda. 
 
 EXERdSe UV. PAOC 41. 
 i. 170 ml. f. 00004 yd. S, 10 «f . 4. 04 \m. 0. 01 b«. 
 
 0. 146 b«. 7. 144. S. 76 «. yd. ' P. 807 bbl. 10. 704 cd. 
 
 EXERCnC LV. PAOE 42. 
 i. no. f . 010. S. OS. tf. 1881484. 8. 46. 0. 87. 7. 14080. 
 S. Oil. 8. 41. 10. 38048. 
 
 EXERCISE LVI. PAQE 42. 
 
 /. 7400. f. 88. S. 631330. i. 838000. «. 15001. t. 06. 
 7. 846. 8. 119035. 9. 707601. /0. 880. 
 
 EXERCISE LVN. PAOE 43. 
 
 1. 040 ttoiw. f . 14000. a. 3880277. 4. 1340. 5. 002650. 
 e. 1706S8. 7. 868440 in. «, 80003110004. 9. 86048010. 
 10. 40100 et. 
 
i.nmm. 
 
 •■•. i. UMTIi. ii. tIMtl. 
 
 «.•». 
 
 
 «. IMfl. 
 
 
 r. fiti. #. NiM. t. iM 
 
 '• ■«•• 
 
 r. ti 
 
 t' i7«i. f. it0t. i. ti 
 
 nnatcuu. paoc4s. 
 
 ■U. 4, «1. i. f IM. #. IQ ,^ 
 
 «. ITM b«. ». 11 Mr. 10. 07^ 
 
 lb. 
 
 f. a 
 
 EXCRCISeUM. PA0e4S. 
 
 IL^•A1?^ '•*^**- ^•»'*»- '•"<•. «.Mf 
 
 ». f7ai.,MBi. i0. iM, 
 
 «»C«eul||. PAIUE4t. 
 
 J». r. 19,18. f. mwl.,.189 
 
 198, 
 
 >» Aav. 
 
 *»"«•« UV. PA0e47. 
 
 /. 81148. f. 8807 at. #, 
 
 10«t. i. 17. 4.47 
 
 y. » fiU. #. OITOT 0. 8048 tX. i/oii. *' *' •*• '• "^ •* 
 
 , iy« . «»€»€ iXVI. pAoc 4,. 
 
 '• ISOplMM. i. IOOdImm a Urn* >t a. 
 
 •wHvi 01. 9. 600 A. ». 00 bu. itf. 17 h^i 
 KXEIICBE LXVII. PAOE 4« 
 
 •. wgw w., 90 «t. 0. 88 U>. itf. ifgi. 
 
 , i«i,«,. OKwase Lxvin. paoc o, 
 
 1 1M07W. «. 148»|. J. 08877. 4.1808 
 
 •t. i. 
 
 •Wbojr.. 7.081104. #.88 A., 048. O.lSLi 
 
 M U4ai. 
 
M 
 
 . eXERCIK UUX. PAOCM. w 
 t, fite.) 408t.; S06«. f. M04e.; lOOiBe. 
 
 i. 7Mt.{ 1046«.: 8007«.| lOOMe.; 270Be. ; 40404«. 
 4. lOOOlt.; lOOOOOe.; lOlSle.; 100001c. ; 7000T70e. 
 4. ITlTte. ; 8764»e. ; 618478e. ; 87884e. ; M7O0e. 
 «. #7; $ie.M; $449.68. 7. $10.01; $676.48; $100. 
 
 t. $870.10; $470.06; $74000.07. 9. $870; $80008.07; $47100.71. 
 10. $4708.41; $10101.01; $906006.08. 
 
 EXERCISE IXX. PA0ES1. 
 
 ^^ W^fM.; 486 far.; 1500 far.; 1804 far.; 8186 fto.{ 7840 far.; 
 
 «. 80d. ; 858d. ; 1800d. ; 888J<I. ; 4488d. ; 8664d. ; 108108d. . 
 
 8. 146*.; 840a.; 1800s.; 8880a.; 877a.; aOlSi. 
 
 4. 864 far.; 4C0 ffer.; 604 far.; 679 far.; 848 far.; 8800 ter. 
 
 6, 6840 far. ;,4704 far. ; 6762 far. ; 6464 far. ; 489ia far. 
 
 8. 9d.; 180d.; 106H.; 225d.; 2604.; 690d. 
 
 7, 6a. 8d.; 14i.; 81a. 8d.; 150a. Sd.; 1474a. Id.; 416a. 8d. 
 H. £4; £38 4a. ; £98 198. ; £228 7s. 
 
 9. £3 4s.; £15 7s. 5d.; £30 18s.; £866 4s. 8d. 
 
 10. £8 16s. 8d.; £8 Os. 2id.; £47 lis. 6d.{ £82 4a. 8|d. 
 
 EXERCISE LXXI. PAOC 54. 
 
 i. 32 oa. ; 80 OS. ; 464 OS. ; 2048 OS. 
 
 ». 64000 OS.; 06800 oa.; 243200 oa.; 284016 oi; 
 
 8, 2 lb. 4 oa.; 30 lb.; 36 lb. 9 oa.; 447 lb. 1$ os. 
 
 4. 2 t. 216 lb. ; 41 1. 161 lb. ; 11 1. 949 lb. ; 24 \. 1862 lb. 9 os. 
 
 8. 84 in.; 116 in.; 351 in.; 1746 in. * 
 
 8. tod.; 12 yd. 2 ft. 8 in.; 104 yd. 1 f». 9 in. ; 496 yd. 2 ft. 10 in. 
 
 7. mi sq. in. ; 2548 sq. in. ; 6480 sq. in. ; 288 sqr in. 
 
 8. 8 sq. yd. 6 sq. ft. ; 97 sq. yd. 3 sq. ft. ; 
 
 2 sq. yd. 7 sq. ft. 89 sq. in.; 186 sq. yd. 1 sq. ft. 15 sq. In. 
 
 9. 5184 on. in.; 8640 en. in.; 15552 en. in.; 209188 en. in. 
 
 ^JJ^'P^' ^^ «»• ft. ; « cd. 8 en. ft. ; 76 cd. 36 en. ft. ; 
 754 ed. 29 en. ft. ' ' - 
 
 EXERCISE LXXII. 
 
 ,-, 14 pt.; 193 pt. ; 943 pt. 
 
 PAOESS. 
 
 1. 8pt. 
 
 f. 6gal. 8 qt.; 190 gal. 1 qt.; 71 gal.; 1220 gal. 5 pt. 
 S. 79 bn. 28 lb. ; 1702 bn. 28 lb. ; 1373 bu. 3 lb. 
 4. 94 pt.; 42 pt.; 62 pt.; 75 pt. 
 
 _ 8. 8 ind. 1 pt.; 80 gal. 2 qt. 1 pt.; 961 gal. qt. 1 pt.j 
 281 gal. 1 qt. 
 
• OOMTOVVD XOTttCM. 
 «. 425 Me.; 02100 we.; 486020 we 
 
 •d::5iUlo**«t 41 Si.''"""' ^*'>-- »«-. M 
 
 '. 1440'; 40097"; 128810"; 616651" 
 0. IV iff; 15« OO*; 2* r rt 21- 14' ii» 
 itf. 1760 Md 1866. • 
 
 *. 74 ewt. 64 lb. 8 OS.; 127t.0ewt 79lh . m» * _i -^ 
 
 i'st;»rBir:'ff---.... 
 
 ». i d. 18 £,«»?:' !■ ■ ' '* « ««• ! 2 *. 1 P*. 
 l^g-.'^f ' «•' »> •• ^'- " •• «. !«. .....,« .. ^. , .: ^ 
 
 ^«. IV 16' 42"; 126* y 84». lo « »j «« 
 
 ' • »^ 2* ; W c. yd. 22 0. ft. 069 e. in. 
 
 EXERCISE LXXV. PAGE «7 
 
 ' ^- ^' **• *• 2880; 166. 9. 78; 1680. 
 
 ^- 826; 64. 
 iO. 1120; 808. 
 
 f A*. .. EXERCISE UXVI. PAGE 57 
 
If 
 
 AsmMmo. 
 
 ;!!, 
 
 p^ 
 
 q'.. 
 
 m 
 
 mil 
 
 EXCIieiK IXXVII. PMIE56. 
 
 1. nr. f. 1801. 5. $104. 4. 8060 yd. S, flOMTi. ^ 
 «. 848 min. 7. 87 lb. 14 m. «. 16 1. P. 8000 gftl. tO. $651700 
 
 EXERCISE LXXVIII. PAOE S8. 
 
 i. 46 ». f . 00 tpiooiw. S. 108. rf. 16 iwgM. S, 43 mi. 00 rd 
 0. £110101. 7.ie9 7t.0d. «. $64.98. 9.00 yd. iO. 16 et. 
 
 EXERCISE LXXIX. PAOE M. "^^ 
 
 i. 06 gal. 2 9t. 1 pt. i. 12 gal. 2 qt. 1 pt. S. 278 bn. 86 lb. 
 tf. 88 bn. 18 lb. 5. 6 mln. 16 sm. paat 8. 0. 4 lb. 4 oa. 10 dwt. 
 7. £8 17i. low. *. 888 lb. 9. $201$. 20. 16 lb. 
 
 EXERCISE LXXX. PACE 01. 
 /. $44.70. 9. $168. S. $8778.60. rf. $184.00. 8. $2$7.46. 
 0. $168.27. 7. $17.81. *. $49.07. P. $8.66. W. $68.06. 
 
 EXERCISE LXXXI. PAOE tU 
 
 i. $290. P. $2.79. S, $7.26. rf. $811.48. S. $221.81. 0. $6.83. 
 7. $81.80. «. $49.70. P. $18.94. W. $71.91. ii. $18.64. 
 
 EXERaSE LXXXII. PAGE 03. 
 
 1.10 In.; 14 in.; 22 in.; 10 in. #.6611. «. $46. i.260boaRla. 
 5.08.40. 0. $700. 7.0266. tf. 14080 yd. 9. $1440. 
 i0. 120 ft., 40 ft. 
 
 EXERCISE LXXXm. PAOE tt. 
 
 . 1. 1234 aq. ft.; 1216 aq. ft.; 6616 aq. yd. 
 f.0A^10A.;16A.;42A.;16A.;19A. J.Waq.ft. 4. 778q.yd. 
 
 5. 28H aq. yd. fl. 200 aq. yd. 7. 112 aq. in. 8. 1066 m. ft. 
 9. 2000 aq. ft. lO, 24 aq. ft. 
 
 EXERaSE LXXXIV. J»AGE M. 
 
 1. 10 ft. 5. 64 ft. 8. 40 rd. rf. $890. 8. $160. fl. 600. 
 7. 72 ft. *. $040. 9, 360 ft. iO. 0600. 
 
 EXERaSE LXXXV. PAOE es. 
 
 1, 40 yd. 8. 00 yd. tf. 32 yd. 4. 70 yd. 5. 186 yd. 
 
 6. $67.60. 7. $18. 8. $180. «. $24. 10. $12.00. 
 
 EXERaSE LXXXVI. PAOE 6S. 
 
 1. 6; 9. t. 8. 8. 16. ^. 8. 5. 10. 6. 72 yd. 7. 48 yd. 
 ^.$68.80. 0. $88. 10. $110. 
 
•ntK* MBAMTKKIllim. 
 
 , ^ EXERdSe LXXXVtI. PAGE M. 
 
 «. 191: 028. P. MB* *4i >A -^ .^- v«».ww. , fae.20. 
 *«. ». fW, 041.50. iO. 070.20; 070.14. 
 
 ,«*»«. EXERCISE LXXXIX. PAGE M 
 
 *..10000ft. p.,800. iO.OM^ *-^*^"- 7. lOOOff.' 
 EXERCISE XC PAAF m 
 
 *. 4082 lb. tf. 040.00. 7 iMno - ^ - * ^*° "• y*^- 
 I*. 2870 eft. Mo!^Z90 ^' *' ^<» «• J^- 1 c ft. 
 
 17 
 
 80 «d. 5. «s ed. J. 30 ed. 
 
 7. 80 ft. 8.S ft. p. 8 
 
 ft. 10. 2Hft 
 
 '. $84. 3. 1210. fi. 
 
 870.20. 
 
 ^^ERCISEXai. PA0E70. 
 
 i'7ti. t. lift. ,.2^^ i 3ft ^ 
 
 y. 182 ft. 8. 40 ft. 9 
 
 80 to. i<?. 17 ft. 
 
 112 ft. 6. 18144. 
 
 '• 32 ft. t. 040.25. * 
 Itf. 4&t. 7. 1700 e. yd. *. 
 
 XCIII. PAOE 70. 
 
 81080. rf. 1120 
 
 lb. 6. 32 t. 
 
 ♦"». *. 81440. 10. m 
 *CIV. PAGE 71, 
 
 i. 882.04. f. 220Td i «aaa ^ 
 
 83 ml. 7. 15 ft fi ft"- TJ^- J- l**- '' ^ «. ft 
 
 ft- 9. 88 sq. yd. 
 EXERaSE XCV. PAGE 
 
 JO. 5 ft. 
 72, 
 
 
 EXERaSEXCVl. PAGE 
 
 i. 86120; 01280. f . 2004 ba. 
 IJiii^/*- ^'207; 316. 
 
 72. 
 
 23" »w. *. 82720. 
 0. 4(12; 034 
 
 4 -i. w M;;<r.1; f.;.*-, /• » *• "» -• > >» a. « ^ 
 
f I 
 
 .18 
 
 AUTHMBTIO. 
 
 EXERCISE XCVII. PAliE 73. 
 
 i. 30r00. f. 2M;S08. ^. 28 yd. ; 92 yd. 4, 12400; I080C 
 ^. $7S;$168. 6. $140; $462. 7. $3400; $10500. «. 80 id.; 00 id 
 
 9. $126. i0. 1240; 8787. 
 
 EXERCISE XCVni. PAGE 73. 
 
 1. $36; $48. i. 00 bn. tMUi 100 bn. peM. S. l7. 
 
 4. $7800; $11700. 3. 270; 880. 6. $20; $40; $60. 7. 80; 40; 7B 
 8. 6. 9. $420; $140; $060. 10. $10040; $3020; $2400. 
 
 EXERCISE XOX. PAOE 74. 
 
 /. $8; $10; $13. ». 170 lb. ; 102 lb. ; 134 lb. 
 
 5. 100 yd. ; 125 yd. ; 169 yd. 4. 2400 lb. ; 2200 lb. ; 1800 lb. 
 
 6. 127 lb. ; 100 lb.* 170 lb. 6. 60 mi. ; 20 ml. ; 40 mi. 
 
 7. 81 rd. ; 45 rd. ; 128 rd. 8. 256; 378; 402. 9. $400; $031; $612 
 
 10. 180 bu. ; 283 bu. ; 160 bu. 11. 32 ct. 
 li. 87 red, $4 blue, 100 white. 
 
 EXERCISE C. PAGE 75. 
 
 1. 1975. 3. 3683. S. 184019. 4. 7, 10, 9. S. 14, 11. 
 6.43,16. 7.14 1b. «. 48yr. 9. $119. 20. $7000. 
 
 EXERaSEa. PAOE 76. 
 
 1. 659 lb. 13 OJ5. g. 206 mi. 160 ids. 3. $204.70. 4. $17.82, 
 
 5. 35 ewt. 25 lb. 6. 12 lb. 9 o«. 7. 33 mi. 96 id. 8. 45. 9. $75 
 10, 24 lb. 10 o«. 
 
 EXERCISE Cll. PAGE 76. 
 
 /. $32. S. 7 ct. 5. 10 carats. 4. 40 ct. 5. 6 et. 
 
 6. 200 bu. at 75 ct., 300 bu. at 70 ct. 7. 4 ft. 3 in. 8. 139 lb. 
 9. Is. 7d. 10. 48. 9d. 
 
 EXERCISE CHI. PAGE 77. 
 
 ! 7. 272 lb., 2448 lb. S. $570940. ^. 2 o«. ^.30 ct. 6. 22 yr. 
 «. $20. 7. 7 ct. «. 46 ct. 9. $6.60. 10. 12 cants. 
 
 EXERCISE CIV. PAGE 78. 
 
 1. 2, 2, 3; 2, 2, 2, 7; 2, 2, 3, 7; 2, 3, 0. 
 
 5. 2, 2, 7, 7; 3, 7, U; 2, 2, 3, 8, 7; 2, 2, 2, 2, 2, 2, 2, 3. 
 
 a. 2, 2, 3, 73; 2, 2, 3, 79; 2, 2, 263; 3, 363. 
 
 4. 3, 5, 73; 3, 7, 63; 7, 7, 23; 2, 2, 17, 17. 
 
 5. 2, 601; 2, 607; 2, 3, 7, 29; 5, 311. 6. 797, 821. 1187. 
 ^. 9543, 2521. * 2273^ 2339, 2417. 10. 3119, 
 
 ^fll i } 
 
i. 2, 5; 8, 7. f. 8, 7; 11, w. 8, 7. 17: 2 2 a 
 ». 2» 8, 8; 8, 8, 7; 8, 7, 11, 7, 11, M, n, 17,' ij. ' *"' *"' 
 
 , ,^ EXERCISE evil. PAOEBO. 
 
 •.88; 110; 14. lo/n] m-m * '••.•8,i> 
 
 EXERCISE GVIII. PAOE 80 
 ^'^ERdSE OX. PAOEAi 
 
 EXERaSE ex. PAGE At 
 
 <«. ^f. 19 men. 9, 7 o,. /^, jjG. 
 EXERCISE CXI. PAfir «« 
 
 ^. 24; 120; 120. *. 78, eOoVwo iai^'o^o 
 
 1 I9tt o^^*^""^** CX«- PACE 83. 
 
 ^. Tiro-third.; three-flftlig. |^r^L«L. * J?' *' ** 
 
I! i 
 
 n 
 
 ■'iM 
 
 /■ : 
 
 Or, I la. i«|»NMBti a thM of 2 in. 
 , (AU tiM otter teetioM are eapoblo of itaiilw intoiMotatiou. ] 
 
 ^ *%illij££dby%." •«"> P~^ «d 7 ci tht.0 w 
 *' ^ ^ ii'I!| ^1 !1l^'*^^ P«t» «d T of tho« «• 
 <^ *• f^ *■ " •«"•' PMteMd II of tlMMuoninMiited 
 ,y^ «*• fhMtloB ia abatraet ttauybaTO a foarlh BMaaiac. 
 Sf ludt. ' if «f M in., «r tho meaaaio of 11 la. whoa IS la. In 
 ^^ ** ^^ *" *^ "'^ '***^ "^ *' of «iow aio fopiMoated 
 Obo la «TMod ia 25 ovMa parti and 7 of tlioio afo ropwaontod 
 ''• '^r:jii!;tir2J^o!i:;' .q~l I-H. ana « of th-. a- 
 "^ "%!::SS!rVt^^^ '^ -^ 17of thaaoa^ 
 ^^ '"aSiiS ^ » *" * *'^ '"^ Md T of tbaaa aio lopm. 
 
 EXERCISE CXV. PAQE M. 
 i. ♦; V; V; y. ^. V; V; V; V. 
 
 3 V} V;«; W. 4. V; V; V;H*. 
 ^. W; *♦*; W; W/. tf. Ml*; Ml»; ^W*: *lf» 
 7. *H^; '^Vi'^; *W*; M«*. 
 «. ^/i; *W*; *4H^; J^VW*. 
 ^. *W*; ^Hfi; "If"; i^VV^. 
 lt>. *i||^; ^W*; *ViVi} HIIH. 
 
J: 5: WfS^^^i.'^' *~*' ^•^^ ^^• 
 
 /<^. 7M mi. , JAlf ad. , 21*f yd. , e8A ot. 
 
 EXERCISE CXVni. PAOE 87. 
 
 ^- #H. *. OH ba. J, 
 
 «. Ulter I7 A lb. 7. 
 
 W«i. 4. mib. ^. 821ib«. 
 
 0. aOft.;Uf|. itf. $10.75 
 
 11 in.; 7 lb.: 28 
 
 oi. tf.Tigia. 
 
 ^- A; Aj ^i 
 
 «OiaSECXIX. PAOE 87. 
 
 V if* V' Ir *• ^^ W? *• tf. H; H- A 
 
 ? !!• yy* ^y « u? n; h. - * 
 
 ^<>. H;II;M 
 
 ^- «; H; A. 
 
 ^. 1; i; f. 
 
 ^^^"CBCCXX. PAOE 88. 
 »' If iff. 
 
 !• ft' H' !*• *• *5 A; A 
 
 iO. i?; II; II 
 
 f- A; ,\; A. 6. 41; A; tV. 
 
 ^. H; A; H. 
 
 EXERCISE CXXI. PAOE 88. 
 
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 EXERCISE CXXIV. PAOC M. 
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 EXERCISE CXXV. PAQE M. 
 
 i. GfMtMt, I; l,Mt, I: gfentMt. f ; 1«im», |. . • 
 
 5. OvMlert, I; leMt. i*,; gMstMt, f; ImmI, |. 
 
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 ^- A; iVj K 
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 CXXVI. PAGE to. 
 
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 ^ ,,, EXERCISE CXXIX. PAOE M 
 
 ^. II. ^. 2911 A. 3 nnTT l' «^» 
 
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 CXXXI, 
 
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 <"-XERCiaE OIXXII. PMEM. 
 
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 EXEROSe CLVN. PAOE IM. 
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 5. 1 A. 100 rd. 22 yd. 8 ft. Of in. ; 2 A. 10 Id. 
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 r. 1 ba. ft gal. ; 2 ba. pk. 4 qt. 
 
 f. fitl.; 18 gal. 1 pt. 9. 28 br. 20 min. ; hr. 26 ntn. 40 aec 
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 |M. 9. 
 
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 J ^^ ^ ^J^CISE CUWII. PAGE III 
 
 ^ 4« «,K ^^f*E CUWIIl. PAGE III 
 / 288 . ff»««C«XtV. PAGE I w 
 » RA A ,- =^*««CISE CLXXV, PAGE li« 
 
 *.»l.t,r. »U2I.m'^fJ;4Sr' ^■*" '"*"»' •^•'»i 
 
 EXEROSe CWXVII. PA0E„6. 
 
 ^- Two, and six hnnH«^*i.- ""nared and nine thonsandths 
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 twottISLd^d1L"£^ ■«» ten.th«MMuidth«; 
 
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 . ^« , «OM»C CLXXVW. PAOE tf«. 
 
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 9. MOeOOOO.000066. 
 
 EXERCnC CLXXIX. PAOE 117. 
 
 i. 961.1«; 808.081; 1110.1817; 227.06. t IflOfi lUUOA 
 
 7.181.8609. *. 170.68676. S. $608.36. itf. 8018.898. 
 EXERCISE CUXX. PAOE 117. 
 
 6. 8074.1378. C. 4678.1364. 7. 296.36187. * 41IMI 1134 
 9. 222.WA22. 20. 4683.246. *«W.«a4. 
 
 EXERCISE CUCXXI. PAOE 117. 
 
 S inf ^^;«f ^•^*^*- ^- 23288.111606. 7. .49861803 
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 ■ 
 
 EXERCISE CUUXN. PAOE IIS. 
 
 i. 4.17; UMt 14.281; mm. ^** "•• . x v ' ; 
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 «. 8.06; .7688; 8.786. 
 
 6. 4.2617; 1.2S5; .8086. 
 
 7. .675; 777.15; 784.216. 
 9. .1236; 26.1205; 2.46. 
 
 4. 70.4625; 2.621; 7.8888. 
 ». 9.8086; .125; 21,825. 
 8. 608.84; 4.725; .825. 
 10. 06.855; 4.4445; .99646. 
 
 EXERCISE CLXXXIV. PAGE 119. 
 
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 EXERCISE CUXXV. PAOE lift. 
 
 EXERCISE CUXXVi. PAOE 130. 
 
 K L^f^ ^ '• *^-^- *• »»-35 ml. rf. 1968 68. 
 5. 262.35 A. 0. .Oefai. 7 illl IM * oomo, «« 1 ^^ 
 
 EXERCISE CUawVR, PME nt 
 
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 . .«. EXERCISE CLXXXVIIi. PAGE 121. 
 
 4 io^lif'-, '• «»**«8J 85.4367610. S. .013272; 32.6770 
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 , ,^^ «BIC«e CUXXIX. PAOEI21. 
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 EXERCISE CXC. PAOE 122. 
 
 EXERCISE CXa. PAOE 122. 
 
 /|.4;40;50. «. 200; 400; 80. J. .018; 7.5; 8. 4 a4.2JKtii 
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 EXERCISE CXCII. PAOE 123. 
 
 /. 14; 19.28. i. 185000; .00002. S. 52.418: 013382 
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 EXERCISE CXail. PAOE 123. 
 
 /. 15.24. t. 850000. 5. .418. rf. 880000. 6. 024 
 
 ». 127.4. 10, .075, .0075, .00075. 
 
 f «,«^ EXERCISE CXdV. PAOE 123. 
 
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 tf.8128JW. 7.827.5. *. 810800. 5. 15.75 bu. iO. 5.2 hr. 
 EXERCISE CXCV. PAOE 124. 
 
 *• tIt; A; t; tit. <. J^. ||. A.\^. 
 
 ^. 6«V; IW; 71; 111. ,C. 5A; 2^1 A 
 , ^ ■ . EXERCISE CXCVI. PAOE 124. 
 
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 ^ ^^ EXERCISE CXCVIII. paqc ,»- 
 
 /. £I.«25; £7.«8126. l « iJlT '?^ 
 
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 6> 7.875 ed.; 7.(1875 <m. yd. 
 
 7. 27.875 gal.; 14.875 gal. 
 
 9. 8.8775*; 17.i2875*. 
 
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 «. 'MOSbu.; 5.880825 1)0. 
 «. 8.65875 d».; 2.7725 wk. 
 /«. 5.8875 m.; 24.75 gn. 
 
 f «Hi<M - EXERCISE CXCIX. PAOE 128 
 
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 EXERCISE CC PAOE 12a. 
 
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 t' iS" ly^' ^'*' ^^^ ^ 
 
 ^.5^7%, 10%; 17%; 26%. 
 
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 , « ^ EXERCISC CCV. PAGE 130. 
 
 EXERCISE CCVI. RAOE 130. 
 
 , ... . "ERCISe CCVM. PAGE 130. 
 
 1. 444 shMp. jf . $103, • 225 IwIm ^ <mo w 
 
 , ...»» "ERcise ccvm. paoe mi. 
 
 EXERCISE CCIX. PAGE 131. 
 
EXERCISE CCX. PMm 132 
 
 »• *i»w. i>. 8000 bn. JO. 14.20 
 
 6 
 
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 EXERCISE CCXK. PME 
 
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 138. 
 
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 fl. 4100 lb. 7. 03000 yd. tf. $8500. P. 1807.75. 10. $4000. 
 
 eXEROSE CCXXII. PAOE 14«. 
 
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 EXERCISE CCXXIII. PAOE 141. 
 
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 EXERaSE CCXXIV. PAOE 142. 
 
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 EXERCISE CCXXV. PAOE 143. 
 
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 EXERCISE CCXXVI. PAOE f 44. 
 
 6. $6.80. 7. $16.12. 8. $88.88. ». $18.20. m $4.6116. 
 EXERCISE CCXXVII. PAOE 144. 
 
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 EXERaSE CCXXVHI. PAOE 145. 
 
 7 i'l^'.V^' *-1?*- '•^*- '•«*• «•«*• 
 
 7. 7i%. *. 4^*. ^. Q%^ jQ gj5 
 
 EXERCISE CCXXIX. PAOE 145. 
 
 7 nA^* p*',!*''* *. Hyr. 4. 5 mo. 5. 6 mo. «. 8 mo. 
 7. 116 da. 8,li yr. *. 15$ d«. m 76 da. 
 
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 To FoKnut AH© JoNKs, Mtbeu-. 
 
 Moutreal. 
 
ccMxnr. mm ta. 
 
 (I 
 
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 exEROse ccxxxvi. pam ia«. 
 
 /. 0700. f . 02S00. 8. 03SOO. 4. 00000. *. 03900. 0. 6. 
 7. 10. 8. 0. 0. 30. iO. 10. 
 
 EXEROaC CCXXXVII. PAOE lOt. 
 .1. 0300. f. 0940. J. 0300. 4. 0100. J. 0113. 0. ft|«. 
 7. 4|ft. «. 0». 9. Oift. 
 
 EXEROSE CCXXXVIII. PAOE tSI. 
 
 /. OOIOO. f. 013810. S. 011340. rf. 010070. g. 011480. 
 «. 00. 7. 70. a. 390. 0. 000. 
 
 EXERCISE CCXXXIX. PAOE 151. 
 
 /. 010000. f. 194. 9. 010000; 720. 4.9%. 6.7%. e. 
 
 7. 0100. S. 0040. 9. 04030 
 
 EXERCISE CCXL. PAOE 102. 
 
 /. 1141. t. 88i. S. 9001. 4. H%. 6. 03400. 
 7. SO. tf. 039400. 9. 0%. /O. $6400. 
 
 EXERCISE CCXU. PAOE 102. 
 
 8i«, 
 
 0. 01438». 
 
 i. OlOOO; 0500; 0900. f. 08000; 01500; 01000; 0000; 0875; 0300. 
 
 *. 10 d». ; 6 dft. ; 4 d*. ; 3 d«. 4. 8 no. S, 
 
 10 BM». 8. 8 d*. 
 
 7. 00 days after the debt is due. *. mo. 9. 03 da 
 
 EXERCISE .CCXUI. PAOE 1SS. 
 
 /. 0mo.;3ao.;4mo. iS. 120 da. J. 4 mo. 4. 6 mo. 
 «. Ap. 88. 6. USi da. 7. 8i mo. 8. 70 da. 0. 8 mo. 
 
f-' 
 
 . — ccKuii. PAoe ia«. 
 
 BxaoK ocuiv. rMw laa. 
 
 ;.(«);.«, («)*'»J«, ,3^:=MH 
 
 ft t-l; I. f. !;.«. I. ill J:ljl**- 
 
 EXERCI8C CCXLVI. PAOE fsr 
 
 /. 861; 20SB; UBs* ftUA • ,«««, 2/^ 
 *. 5715.36, aiwliTiSS*; i* i^ ^T Ji T^ "'«*• 
 
 *. »878.e86; M.196S75; mmaoiTtMLi^ 
 EttROSE CCXLVH, PAOE IS7 
 
 j. «l hVS,%*^; 4;?4-.<^ »«i'-««. 
 
 s.s.a.2.3.S.3.8-2«x8*. /5. loj^ 
 
MBmORATHni. 
 
 nniaie ccxLVM. paoc iit. 
 
 1. •! Ill ISt 16. f. B7| Mt Ml tl. S. 1M{ tl4| IMt SIT. 
 ^. li Hi m H. i. Itt Ht ^l HVb. «. .It .Mt .Mt M. 
 7. Mil Mi; .M8t .16. «. lit ft H) |. 
 
 #. a.Mt .IMt .571 1 .MMi. /a. t.net .7V7t 'Msi .mi. 
 ■xmose ocxux. paoc im. 
 
 /. M0. f . Ml. «. MM. 4, M y4. tf. 440 yd. 4. 9M rd. 
 7. 971 ft. t. ilM. ». 144 Id. /O. MS4. 
 
 EXERCISE CO. PAOE IM. 
 
 i. 7» jrd., 35 jd. 9.320 yd., 44 yd. J. ]| in. 4. 17 rd. ^ 
 f. 1440 rails. 4. 3M rd. 7. 8090 yd. *. IS ft. 9. 221 yd. 
 10. 7712 yd. - ' 
 
 EXERCISE ecu. PAOE KM. 
 
 1. 6; 8; •( 12. f. 16; 10; 18; 21. S. 26; 24; 28; M. 
 4. 36; M; 65; 60. S. 17; 28} 2»t «7. 4. 68; 00; 07; 71. 
 7. 101; 111; IM; IM. *. A; A; Hi H- ». .1; .M; 11.0; M.8. 
 iO. .828; .48M; .2; 1.7M. . 
 
 EXERCISE CCUI. PAOE IM. 
 
 i. M; .M; 1.28; 10.04. f. 21; 0»; 7*; 7|. J. 86.8. 
 4. 6470 tq. ft. 4. 60164 aq. ft. 0. 17 ft. 7. 00 In. 8. 0.2 in. 
 ». 12 ft. 10. 16.75 In. li. 87 ft. If. 6 ft. /J, 
 
 EXERCISE CCUN. PAOE IM. 
 
 13. 14. M ft. 
 
 /. 1621 aq. yd. f . 
 
 aq. ft. 60 aq. in. S. 1144 gq. ft. 
 
 4. 210 ft. S. 3 eh. 40 1. f. (a) 2m tq. In. (4) .64 A. («) 30| iq. ft 
 7. 6A tq. ft. *. 10 rd. 9. 80 id. 10. 06O. 
 
 EXERCISE CCUV. 
 
 IM. 
 
 1. (•) IW aq. ft. (6) 818H iq. ft. («) 6A A. (d) SH A. 
 «. 60 in. S. 67 In. 4. 92 rd. 4. 4300 tq. ft. 6. 2146 aq. yd. 
 7. 1716 aq. ft. 8. 664| aq. yd.. ». 203 aq. ft. 10. 60 ft. 
 
 EXERCISE CCLV. PAOE IM. 
 
 1. 44 in.; 00 In.; 11 ft.; 61* ft.: 78* ft.; 14 ah. 961. 
 
 4. 7 In.; 17* In.; 10* ft:; 1 eb. 71* 1.; 7yd.; 21 yd. 7 In. 
 
 5. 24* aln. 4. Ill rd. 1ft. 10 In. 4. 6 ft. ». 7. 7. 41* ft. 
 S. 84 yd. 4. 12 ft. 10 In. 
 
 10. 22 in.; 83 In.; 66 In.; M In.; 110 in.; 121 In. 
 
^ s 
 
 »••. Niiiti. 
 
 *- '' ii.li fl. #. M ft. £0, |M.t». 
 
 «•••«... W "i? ? «'•,"'♦ '^'^ "'♦•!■ «. 
 
 (•)mtq. «.,«), ng 
 
 y. «*.». #. 1 
 
 f. IM.TB. «. iMMra 
 
 •«• «.» 101 iq. ia. A 
 
 ecu. PAoe 
 
 niaq.ft 
 
 •«*ft.l 
 
 iT«P M. la. a, 
 
 »»4l3rd. ».«! 
 
 Wiq.ft. 4.»aq.i%. 
 
 :i- 5:- i'i' -••'•«•'<»)«" 
 
 ft* /0. a ia 
 
 K'^isHCtte ocun. pahc 
 
 f«f. 
 
 j.ij!2.'^.1;5;;':!«U;'»;'.)«.K.u..(*,^ 
 
 *. («)M)Sfea.lD. (ft)7Mlf 
 
 •q.in. 
 
 «-4aUM.ft 
 
 /. IS4 ft. f . M 
 
 fa.(«)l«7*ea.la. (rf)i7»| 
 
 - . *■• •llOBW. W. 2641 
 
 "" CCUHI. PAIIEf«7. 
 
 Ml. In. 
 
 '. T5 ft. e. 48.8 
 iO. 1180 yd. 
 
 y?' *. M yd.; 887 
 
 •«• ft. y. «8 ft. 
 
 ■Q. yd. ^. 881 ft. 
 
 '• •• y«l. ». 880 
 
 :?.** 
 
4t 
 
 nmcm ccuiv. pase tit. 
 
 •.Ijmi,*!!. 7. ASM.,, ft. #. T»Wit,.l|. 9. l«.|.f|. 
 
 i. M fl. t0 A. f . 5 A. «. ntS •«. fl. ^. II m, ft. 
 #.7111. •.MiSaq. IB.} 4174 •,.!•. w. ii2*ft. ' 
 
 EXCRdSe CCtXVI. PAAC I7«. 
 
 * iJ?*?' /\?f?'* "•*"•'«•'*• *-M«.«3r4. <.a«Or-" 
 «. 4Meft. «. 40 Id., 90 Id. r. f.71ll 
 
 to. 
 
 #. IS ft. f . IM.II. 
 
 EXCKOSE CCUVN. PAOC If*. 
 
 i. ft2ft. f. 10.10 yd. «. 8S.04«il. 4. 8| tli. i. 00 yd. 
 0. 4Sfl. 7.414.1211. #.tl.fl8ft. P. 800* iq. ft. iO.40it.ft. 
 
 CXEROM CCLXVHI. PAOE 171. 
 
 4.10181b. 0.004. 7. lOaOOOthot. #. Stt do*. 0. IS is. 
 
 10. 40 M. 
 
 EXEKCliE CCUCIX. PAIHE 171. 
 
 «. (1) 400 em., (S) 40.00 dm., (8) 4.000 m. 
 
 i' 12 i!*^ ■•' ^^^ ^''^^^ ■■•' <•) *«^ •■• ^. HW000.484 m. 
 i. 780.48 m. J 11.08 mm. 0. 83.206 m. ; 280.10003 m. 
 
 !;'II.lS!?'* '• 27«00 timet. 0.170.80. /0.7.0870 ml. 
 11. 0006700. if. 20000 timea. 
 
 EXERCISE COXX. PAOE 174. 
 
 1. 287.0845 heetMee. 0. 37806 am. 
 
 ** 55!l!?' •"• ^ ^'^'•W aq. mm. 4. 2341700 aq. m. 5. 542 eq 
 
 ?;^^!L:"- ^•"^•^- *.38.«*-q.». 0. 02.00. ' 
 iO. 200000 iMrlelta. 
 
i. 
 
 lir 
 
 ** , ABitnccno. 
 
 WERCISE GCLXXI. PAGE If4. 
 
 € /'Jl*«* fill!""* *-^^***'- ^MW**.-. A2.«^».^ 
 «. l.««.m. 7. 80e«. #. SOOHl. ». $875.81. W. %.%. 
 
 EXERCISE CCUUH. PAOE IW. 
 
 rf i'S^'!^Stl^' '•^"ffi-*? 80.75 dg. J. 8070005.5 eg. 
 
 *. fiao.ueas. a, 8ioiBg. io» .oo60i. 
 
 EXERCISE CCLXXIII. *PAOE f7t. 
 
 /i wor VAw^ •**»• ^''•aw-- w. Met. 
 
 «. 180 mi. IS. 477 Uidm. irf. 13.44 ^ou,^ 
 
 . .. ??EW»E CCLXXiV. PAI1E177. 
 
 f tW^ -^^ •'*• • . .'• •*.' "2857; .285714; .4«57i. 
 S. .671428; .714885; .867142; .076823. 
 
 «. .8428671; .854; .88286714; .16880. 
 7. .7088; .4ltfB428S7i; .54861; .164778. 
 *. .44880768; .731168846; .1888046; .880858. 
 9. .80888085; .8870; .140766; .6060676. 
 10. .170188; .688788772; .85807866142; .20146. 
 
 EXERCISE CCLXXV. PAOE I7». 
 
 «. H fift^; 2Hi 7H. io. 4Tif ; &rh; 7,ff ; &A. 
 EXERCISE CCLXXVI. PAOE 178. 
 
 /. 6.60244. f. 2.8660841228268. S. 8.4868; 14.0686727 
 4. .32467; .32147. 5. .73231777. 6. 1.680. 6.883. 7. 33^. 420 
 *. .4675; .850648. 9. 68; 10. to. .64175; 7.805. 
 
 EXERCISE CCLXXVII. PAGE 17$. 
 
 i. 10.5. t. .42. rf. .16i; .03. 6. 38.142857. 7. £2 0.. 81 
 *. 8t.8«wt.85.31b. S. 6 mi. 82 Id. 1.6 yd. itf. 68 t. 888.8'l|». 
 
t. $3780. 
 6. .0078125. 
 
 MItOlLLAXIOrs lUBOIUS. || 
 
 . ^ pOtCWE CCLWVIII. PAOEf79. 
 
 *• A, !;♦, SjH, 6; ^,3. 
 •• 111; tt, 1; U. 1; H, 3; H, a. 
 
 fi. 7.4M. r. (.006X.M>X.(006X.O4)».00O2X.00O2 
 pui. to ^'^:7 ''* *^' ^^' *••• »-• "'^ I-'"' 1. ». 3. *c., 
 
 pijs: s^a:; St!'' '~' '««' *••' ->- »^« »-»«' h 2, 3, ^., 
 
 9. .13. 
 
 EXERCISE CCLXXIX. PAOE I7». 
 
 5. 9216 cu. ft. *. $132, $247.60, $278. 4, $m 
 
 6. 33 mi. 7. .405 hr. 8. 1«A%. A .00129. 
 
 EXERCISE CCLXXX. PAOE ISO. 
 
 i- A. *. i da. S. 81 da. i. 14.7 da. S. h 
 
 ?; i«^' /•Hi'!:- ''•-^•8«*^;B,73Ma.;CMl0da. 
 /5. 15da. W. 82hr, W. H hr. W. 8 hones. 
 
 16. A, 8A da. ; B, 8H da. ; C, 6A da. 17. A, $1.10; B, $1. 
 EXEROSC CCtXXXl. PACE 181. 
 i. 12 mia.; 24 win.; 80 mln. t. 18 min. S. IH^ min. p.rt3. 
 
 7. 24 min. part « and 4lA mip. past 6. 
 
 *' iA*Si"iLT«!Lt^*^ r* "*"• p^ '• ^*> ^^ "•*"• p^ 8. 
 
 ». 4»iV min. past 9{ 64A min. past 10; 12 o'doek. 
 JO. 23i\ min. fact 5. 
 
 EXERaSE CCUXXII. PAOE IS2. 
 
 -f iVT' "?."•?"' *• '• 1»A min. past 8. J. 31 A min. paste. 
 
 j. 120 da. ; 44 min. past 11 ; I4 min. past 12. 6. 76 da. 
 
 e. ^ min. part 6 a.m., Friday. 7. 5A min. past 5. 
 
 *. S* min. part 9 p.m. on Saturday, and 67i min. part 8 p.m. . 
 
 ». 3 p.m.. May 8. 20. 48|||f min. part 9 p.m. 
 
 EXERCISE CCLXXXIII. PAOE 182. 
 i.44fl. f. 84Aml. ^.22*. rf. 7*860. 5. 14min.»4sM 
 e-Skf. 7.88|»1. *.7*yd. P. 82H. iO. Gains n&X 
 
44 
 
 Ainmnmo. 
 
 •^.■a^ff;^ 
 
 EXpOSE COXXXIV. PAOeiM. 
 
 7. 46 Bin. *. 3 mi. p. 6 to 1. i0. 2| br. 
 
 EXERCISE CCUXXV. PAAE 184. 
 
 ».8Wfl. 7.M|,d. «.22«|. fl.2WiiiI. W.6|«J. «. eTlH. 
 EXmoSE CCUXXVI. PiUME 18S. 
 
 6.». 7. £ie«t. *. 1980. ». a br. 84 mla. iO.awib. 
 
 EXERCISE CCUXXVn. PAGE 188. 
 
 /. 144 min. f . Moa, $12.50; women. 48: bor* ts as * «r km 
 -.1022. 5.76 yd. 4. 82 dit. 7. 17 mK V^*^*^* *-^***- 
 P. 110 dien»; 140 pig.. 10. m, 
 
 EXEROSE CCUUXVIH. PAOE 188. 
 
 0, Job., 88801 TboiM., 8178} tt,i»,y, $22. lo. 56 et. 
 
 / «« . ^J?*^ CCUOWX. PAOE 187. 
 •. «, 11, 22, 28. 7. 188. *. 860. 9. 7876 sbii^lM. itf. 1501b. 
 EXERCISE CCXC PAOE 187. 
 
 *.«».0246. 4.88460. 7. 8870, 6%. *. $2.50. 9.i9i^ 
 EXERCISE CCXa. PAGE 188. 
 
 ^ EXPOSE CCxqi. PAGE 188. 
 
 /^,30ot.;B,88ct.;C,40oi. ». 160Je«p«. 5.02460 
 4. 130* see. 5. $500. 6. 80e. •r. U yd 
 *. 900 lb. «k 7 ct.; 1100 al 10 ct. 9, 248 yd. j 62 yd. 10, 8440. 
 
 EXERCISE CCXail. PAGE IS8. 
 < i.Tf"* ^••^^O. ^. Divisor, 647; Qaot., 31S8. 4 m 
 !' <g-y- ^ ' A'. «te 1. to B». .s 79 ti 6b. ^• 
 
wwitLAinovt imoitM. 
 0.«MO}07r. 7. 4fai. *. 8Wl6iH)«. «. »lir. W. 84 ml. 
 
 CCXCV. PAOEItl. 
 
 W. A, $7W.ie; B, |8Wj 0, $880,- D, leOO. 
 
 RBROSe CCXCVI. PAOE l§2. 
 
 4 il^tu • /• JUL*** »»^ W ft. iqr 13 ft. 8. 4.6 e«. ft.' . 
 
 7. fa4W. *. UBd.perhr. *. » ml., p^t 4 •.«. itf. $2X7:80. 
 
 WERCBE CCXCVn. PAOE Its. 
 «. 14.288 to 1. 7. 481 cl. 8. 8H. fl. $1.80. 10, 19oV 
 
 EXERCISE CGXCVIII. PAOE 193. 
 
 i. 272 fd. 8. m. S. 24 et.; loM. 4%. 
 
 fl.a875|t. 7.8441. *.88yr.i85,r. P. 867 k»T- 10,m^. 
 CXERCBE COtOX. PAOE 194. 
 
 ..i^^^lSioo'-^*^- *-^-*- -•^~^»>- '^•^- * 
 
 J* i2*7i"i*/r'**'J!^l' '•"**** «id width bdng equal.) 
 *. 184.7114 ill. iD. A, $1035; B, $1868; C, nm. 
 
 EXERCISE CCC. PAOE 198. 
 
 /. 2 to 6. 8. IZ^ min. past 4, or SO mia. pMt 4. 8 840 
 
 *. Stoj. *. 2ift. iO. $1800; 16 mo. -««"«• 
 
 EXEROSE CCa. PAGE 199. 
 
 «. 80. 7. Slir. «. 628 lb., 4$6 lb., 880 lb. ^ 
 
 ». moo, $1760. $1050, $700. . 10. B, by 60 yd. i« 4| min. 
 
 EXERCISE CCai. PAOE 197. 
 
 • ^■'W. 9, lit min. pMt 12. 10. $9^; $9f. 
 
I' I3lfr 
 
 m 
 
 V 
 . PART II. 
 
 Sokmon or Certain PtoMems. 
 
 lf<yfi.~In tiM followiag Mlslioiit tb* araltlplier to hmwIIt 
 wfittwi to tl» l«ft of Ike «iiltlpUMn4 Mi to to b. iwid Tims. 
 
 MEROK UU PAOE44. 
 i. Tho fMton of M »ra 6 aad 7. 
 
 As tho Iwk reiutndar to 6 iho aeeona diTtoor mwk bo 7; 
 
 Fintflaottont»(7X72)-M 3=610; 
 RwnberBsr (5X510)+2825S2. 
 S. Nambor of yMds ta flnt ptoeo b^H* »80 ; 
 Pctoo of 1 TMdof Moond ptoeo»fHe.s»Me. 
 
 EXERCBCUUI. PAIiE45. 
 
 8, Nttnbor of mon to do tiM woA la 45 da.a:60' 
 . •• " " " " " ld..«45xe0; 
 
 •• " •• * 5.d...«^«54. 
 
 Nambor dtoehw|od» (60-54) aoa^a MOB. 
 JO. Mnmbor of moa to do 1 work in 36 da.**^; 
 
 " " 1 •• 1 d».«»6X25; 
 
 «l 
 
 « 
 
 t< 
 
 41 
 
 13da.«??^. 
 12 • 
 
 iQ J. _ 8X36X25 ^. 
 12 da.ss ~ =226. 
 
 EXERCISE tXVII. PAGE 4S. 
 
 J. »i« dearths the qnanthy to bo bought to tho loartaamber 
 
 of poan* whieh tdded to 17886 pooad. wiU miAo tho fo«ilt eoatian 
 68 poaadi. 
 
 17386-r6B^255 aad 45 ramalador. 
 <^*nt% to be bea^^tss^tt— 45) Ib.=:Se lb, 
 
 46 
 
■OLUnOKl. 
 
 EXEROSC LXXVI. PAOc'sT. 
 
 10. Walfht of wool fkom 1 alMop-*? lb. 8 tm,i 
 
 '* a •* »ax(71b. 8oii.)-*lSlb.; 
 •• 380 " «(*Hxi6)lb.; 
 
 »3700 lb.»a7 ewt. 
 Vslne of 1 ewt. of woolasfW.SO; 
 
 27 " »8(27)l(19.«0)»«639.90. 
 
 f» 
 
 II 
 II 
 
 n 
 
 EXERCISE UUCVm. PAOE 88. 
 
 7. Ooit of bttUding (85-80) yd., or 5 jd,=12». 8d. ; 
 
 II 
 
 II 
 
 II 
 
 1 yd.ss — ^ — as2t. 8d. ; 
 
 76]rd.»78X(8».«d.); 
 aB£9 7t. 8d. 
 
 II 
 11 
 
 ti 
 II 
 
 EXERCISE LXXIX. PAOE 88. 
 
 5. Betwoea noon on Mondny nad 8 p.m. on Wednesdi^ an 08 
 boara. 
 
 Time gained in 8 hr.a:40 aee. ; 
 1 hr.»V eeo. j 
 58 br.»(58xV) eee.^sff min. 15 lee. 
 Tbe ekiek will sbow 8 br. 5 min. 15 aee. 
 
 9. Qnaatitj of baj eaten s(lS0X90X7xa0) lb. ; 
 
 _ 120X»X7X80 _ 
 
 20QQ •• — **• ••? 
 
 Qaaality of oiUe eaten »(190xaOX7xlO) qt. j 
 
 110X90X7X10 
 
 8£ 
 
 bn.=s5250 bn. ; 
 
 6. 
 
 Goet of 188 t. bay =8(188X8) «81344; 
 Coet of 6250 bu. o»to=8(5250X^)=81575; 
 Cost of bay and oate »$mo. 
 
 EXERCISE LXXXU. PAGE 63. 
 
 Perimeter of lot= (2X80-f 2X 144; ft.— 408 ft. j 
 Namber ei poet boleB=M'=88; 
 Cost <rf digging 1 ^e=5e. ; 
 . " " 68 " »(68X5)e.=83.40. 
 
f. Moibtr «f Mil la 1 ■l.a.BIO} 
 
 Wtighk of WIM lMdm(5X640) lb. I 
 
 Oeitof llb.>-8e.; 
 Ooil or (5X610) n».«(»x««OX«)e. 
 
 -\ 
 
 
 ' KXBicisc uaumi. paoecs. 
 
 .-.«•. of pah«(«»a-78oo) .,.ii..i!oo5:ft: 
 
 i<». A^«H. wMlli Of bo«d-l»|i«ta.^ie ta., 
 
 Am of bowd»(i8x 12X16) oq. I.. . .' 
 
 " 144 — "flt ».»a4 aq. ft. 
 
 EXERCISE LXXXIV. PAOE M. 
 
 Wl«hoflol-^ft..«ft., 
 
 Pjrimotor of lol»(2XM0+2X«0) ft.»0oo ft. j 
 Coot of foBeing 1 ft.»25e. ; 
 
 " «• ft.»(600X2S)«.«#150. 
 ADOft of fwm««f|%u»80». J 
 
 mWi of fcwi*?25i2?M.-64 Id. i 
 
 4. 
 
 10. 
 
 ^rimoter of toB»(2X WH-2xa4) >d.»fi28 id. ; 
 Coot of foMing 1 rd.8$1.2S; «•»«., 
 
 *' " 528 »d.«628X$1.26=|080. 
 
 EXERCISE LXXXV. PAOE 68. 
 
 i. Awo of ioo»=(24X15) sq. ft.= (24X16X144) .q. fa, . 
 .-. Length of e«rpet=?^^SH?lli*i„ _ 8*Xi5xl44 , ' 
 
 ^^ •« *"•"" 8X12X86 J^-^O yd. 
 
 r ,. ^ ^» Alwi of rooms (24X15) m ft • 
 
 L«»itli of o«pot to eoTo, (8X3) «,. tt.Jl jd. " ' 
 
 (^X15)«|.ft.«^Xlyd.«40^ 
 
 «< 
 
 (I 
 
i. 
 
 ■OLIJTKnit. 
 
 eXEROK UCXXVI. PAOEM. 
 
 WMth o( fooi««(18Xlt) tai.t' 
 Mb. of Uriiw la irtdtH^^il"—. 
 
 Lngth of nNMi»(S7Xia) la. ; 
 Mb. of tMfM in lmgtti«-^^i?«9. 
 
 4. 
 
 EXCRCaE LXXXVn. PAQEM. 
 
 Anm of oeiling- (94X18) iq. ft. -.!l^,q,^-, 
 
 48 aq. yd.; 
 
 OoM of plMtoring 1 iq. jd.«>l»e. ; 
 
 « "q. y<l.=»(48X10)o.«|8.12. 
 
 II 
 
 II 
 
 e. 
 
 Perimeter of rooms (2X27+8X 18) ft. =90 ft. ; 
 
 Aio» of ontlzo walbai(90XlO) tq. ft. «900 aq. ft. ; 
 
 A»o» of 8 doon»:(8X7X4) iq. ft. sM iq. ft.; 
 
 Area of 8 wiadow»-(8X6X8) oq. ft. »54 tq. ft. ; 
 
 Aim of 1 windows (1X6X4) sq. ft. »94 aq. ft. 
 Am of doon Md wiadowi» (84-1-64-1-94) aq. ft. ^m aq. ft.; 
 
 (1) Am to bo plaatond» (900-182) aq. ft. =82 aq. yd. : 
 
 (2) " " •' «(900-81) aq. ft. «9i;i.id.' 
 
 EXERCISE XC PAIUECt. 
 
 8. By dnwlng a diagmai of the fonndatioa H will bo aam Iha* 
 two of tlw waUa aro 60 ft. long and two of th«m 32 ft. loiiff. 
 
 Longtli of waUa» (2X60-1-8X82) ft.sl84 ft. ; 
 Coble eontent of walla» (2X8X184) «. ft. =2944 e. ft. j 
 
 ■=109 e. yd. 1 e. ft. 
 
 EXERaSEXCI. PAOEn. 
 
 10. No. of eorda in the pUe=mH=il06. 
 
 CoMo eontent of pUes (losx 128) e. ft. ; 
 
 '294 ft. 
 
 L«,gth«fpUe=i^i?ft.= 
 
 SX12 
 
.-^^ 
 
 JV "If 
 
 Bi- I 
 
 v; 
 
 I-«Wttjf U.. two ild..wMta- (2X60) ft. , 
 
 .-. Wldtholbittii«40fl. 
 "»CI8exCVM. PAOE73. 
 
 . . 4 Umm T»liM of ii«l»$(l88B0-lM) ; * 
 
 •eeoiid»$(8X84a<H.lflO)««06«. 
 
 P. It I. .Ortjy fooBd ihrt A «w«. 72 .. «,d B 48 •. 
 Valnoof A'ilMid-t(72X8«)} 
 " B^i " -$(72X84), 
 
 EWROSe XCVMI. PAGE 79. 
 
 «. •l+W+88=r86. 
 
 th.^^.S"^'*''*^*^'-''^^*'^-— *.t2;.»a 
 No. of ttaMt 80 If dividod«^»80; 
 
 Stefo of ftnt3raox81»8SO, 
 
 '• MOOiMl»20X88»840; 
 
 tltird<s20X88a80e. 
 
 n 
 
 BhMo Of A=B.i^x83»8420: 
 
 " B«iV*X81«8140; 
 
 C«iV*XN«8600. 
 
 
 iO Value of Om ho«.e=2 ti«K« viUu. of oll»r tt«>| 
 . . 3 timM value of other two boiuea»r8i6410} 
 
 8 •»«'w» 
 
 ▼»!«• <rf firat iioiiM»2x85470»810M0. 
 
•1 
 
 (▼■lM«f thM-MI70)-|-T«lttt <f tklf«it||tyi, 
 
 .'. i tiMM VMtat of VbMiim${§m-Vn\ tiWOi 
 
 
 II 
 
 /. 
 
 cxaicaexax. rMicf4. 
 
 " aU-S tfiBM TilM of int+«7; 
 .*. 8 Umm TAlM of trrt+87»«Sl ; 
 .-.8 •♦ " " -•(8I-7)-88«j 
 
 8 •*' 
 
 << 
 
 tyrd » 
 
 8(8+8) «f|«{ 
 r8(10+8)*-818. 
 
 S. 
 
 <4 
 
 Lragth of MoondaloiiKtb of Meond ; 
 
 «»•*- " " +»yd.; 
 third- »' •• +2Byd.+l»yd.; 
 •Il««8 timoa loBftb of M00iid+8B yd. } 
 .'.3 tlnot leagth of Moond+as yd.a444 yd. ; 
 ••8 " " •♦ -(4ii-88)yd.-8T5yd., 
 
 «*|»yd.-myd.| 
 lint , « (125+25) yd.»150yd.; 
 
 •' third -(180+10) yd.-ie» yd. 
 
 n. n Inatoftd of 5 hn. of o«t«, 5 ba. of whoat had boon booght, 
 the eoat woaM hare boon (6X83)e. mora. 
 
 Heaee. eort of 18 ba. of whea«f(fl.80+1.65)»88.45; 
 
 II 
 i< 
 II 
 
 1 
 1 
 
 II 
 II 
 
 II 
 
 o«ltsr(eB-.83)e. 
 
 =6Be.; 
 ==82e. 
 
 it. 
 
 (Bed+ White) iiiarble«al02; 
 
 (Bltte+Wblt«) •' s=lM; 
 
 .'. (Bed+Blae+White+ White) •* =391; 
 
 and (Bod+Blae+ White) • " s286; 
 
 .*. White " »I06; 
 
 Bed *• »192-ieft»87; 
 
 BhM •• »188-l«6«f4. 
 
^''Hii^ -C-tiXTl).. 
 
 «« 
 
 
 «« u 
 
 kM Immmm th« mH bv It. 
 
 £;^ 
 
 tf. 
 
 «»"C«fCIII. P4M77. 
 
 00lio(4Ib.«a|i.«l||,.; 
 
 tIb.«M«.«l««.) 
 ilb.«41«.>-_Mi.) 
 
 II 
 II 
 II 
 
 • lb. 
 lib. 
 
 ». AatlM 
 
 ■•a»IS. 
 
 !^ l i!r_'?»' ^'^y^'^fa" to 1, 4, -d It. w. 
 
 wm nniiw «it p^r mttk; 4 mm, |»; tmi M 
 
 ofl 
 " 4 
 
 " U " 
 «* 1 II 
 
 • «lt-ili; 
 
 I 
 
 I 
 
 r 
 
 441«tXtX7X7} 
 Mr»SX8X8XtX7{ 
 
 tUBixsxsxr; 
 
 H«QM, G.C.M.»SX8XTa>«i) 
 Mvaabwr of buhah In a l«id»68. 
 
 EXERCISE OX. PAOEtl. 
 
 Itf. Mud ttM O.C.M. of US80 aad 44100: 
 18880)44100 
 
 bOM 
 
 '4tt9l8S80 
 18880 
 Km* iad tbo CLO.lf . of 4410 asd Unss* 
 Thtola iMdUj fenad to to 815. 
 
fM ite«.o.M. 9t mm Mi Mint. 
 
 1 r»iKM 
 
 mm 
 Tfim 
 
 aiiM 
 
 TM 
 
 4 
 
 4 
 
 S 
 
 1 
 
 IS 
 
 a 
 
 4 
 
 imm 
 
 nam 
 
 IMS 
 
 itm 
 
 10M 
 
 IM 
 
 Th» O.O.M. of 190 Md turn i« MMlly foua to b« It. 
 
 txnianiGi. nuisai. 
 
 IMSiMXSXTXlti 
 
 i. 
 
 lTi6»lX5X7XlT| 
 - O.C.II.«tXSXT»10S. 
 
 ^^M All tte eOMMM MMMfM, foni M MHqr MriM M tlMTO 
 
 M«4iflMmi( pftaM ftMton, awkliig 1 th* im tor* of mmk MriM 
 ud MMRty tbMt tofUhw. 
 
 1, 1 
 I, 5 
 
 1, S, S, 16 
 1,7 
 
 1, t, 5, U, 7, U, SB, IM. 
 «. If th« aaalMr wUl dlr^oSOSO Md Imm 11. It wtU U wm. 
 tiOMd MMtl/ia S00»-11, or MtS. 
 
 Blatlwly, tho aiwilMr wlU !>• OMtelMd onotly in S706-17. 
 orSISl. 
 
 no 0.0.11. of 1S8S Md SOSl to 117^ .. 
 
 EXERCISE CXin. PAOEas. 
 
 9. 48e80»SX2xax2X8X8X5X7XlS. 
 Thwo eM bo t—dOj amngod into foor ooBMovtiTo nnmbofo 
 ••foUowt: 
 
 18; 7X2} 5X8; 2X2X2X8, or 18, 14, li, 16. 
 
 EXEROSECXLV. PAOEtS. 
 
 S. Ooft of SeO «Qidji>c$(600XSi) ^1437i; 
 
 Bum rMoivod for 751 ootdi»$(76|x4|) »$tm ; 
 (660-761) oo>dv«4Sa ootdo; 
 

 u .1 
 
 P 
 
 T>ny i iii ifH .i( imf Mm) 
 
 *• **;,•* f^ "^^il • irtP-l tf IM-iM, 
 
 OiOaMlit 
 
 MH 
 
 l«.-#(ltxA) 
 
 «. PM 
 
 14 kjr tiM tklii»(l~A-i)»4 
 
 Ci. MOKlti. 
 
 •ifM«(«pMl|iw|BW|||Mt||,l 
 
 I. Tte 
 
 U. tiM 
 
 »J "•!'% X, Mii -i- 
 
 •k««M »• 
 
 m. IW 
 
 PMMMt liiliiiifl by X mtil 1 ■iwM te 
 
 fM» thai iiidlMltd kgr •;-. btktotMt 
 dlatlaMM bttiTMa X tad '*«f.*' 
 
 »•. «♦, fH to •mOnimA ttmOmt wMi 
 
 I fri^AH} 7H«^i 
 
 u^ ?!!5**" *• •• n«»te «»• ■«atotl mmkm of ten. Ik* 
 
 Tht O.O.M. of snMi»» .^ fiiri, sr 
 
 Homo, tbo O.O.M. of «|it f, oad «l 
 
 loeh wtU ooateto y ta., or N In 
 
 *l*loV. 
 
 »8|+a|«10t 9thi-H^Mi 70|^t|.,f|j 
 Hmmo, ambor of kogo->l»-|-9H>Sl»ftl. 
 
 M' l-H; I-Aj |*H: 
 
 L.C.M. of H, A. Md H !• W, ©r ef; 
 NoMbor of timoo A gooo io«a4«flH-h.iO; 
 
 tt 
 (( 
 
 «4 
 
 B 
 
CUX. PAMIM. 
 
 f. Weight tt I lb, AnltUptkmim gr. i 
 llb.Tktf •tlWp.l 
 
 .MfWgr.blilltCTeitfr.i 
 fin"' III* 
 
 EXntOKCUIV. PAOe !•?. 
 
 TfaM to wtJk m 14.-1 aiB.| 
 
 ** mn ii.-(ifriix A) »ib.-m br. 17 i^tm, 
 nmoKoxvi. pam ttt. 
 
 lkr.«(M)(il)Mi.t 
 Mal.«(MxilN)f|.) 
 DMmm tb« trala com hi <«)(••) ■m.-MxMW II. » 
 
 ** •* •• •• 1 ••. wxBm j^ 
 
 7. 
 
 (I 
 
 4, 
 
 It 
 II 
 
 II 
 II 
 
 lkr.»iiate.( 
 4tBl.«(iiX11i»)ji.{ 
 te«Mia.-(41X11il)j4.| 
 
 • ■!■•■■ — jgp- yil.vun fi.; 
 
 lM.«i»]NI.; 
 
 1 aki.«(ftXII) yi.->liO0 94.; 
 it iMtor by (Itl»-11N) yC, or n y«. 
 
 EXOCIMI CiXXI. PA0Efl«. 
 J. B»t p«t MMtdt A'i bjr (A-A), or A of w«b; 
 A of wob, or i of wobaBftl 74. { 
 
 .'. tbo irob->(6X5i) yd. -tlTtf.; 
 A'o |iMl»(A of 88) y4.-18l jd. ; 
 B't pwt>-(A of SI) 74.-18I yC 
 
 UXIM 
 
 • «i 
 
 Agia», " 
 
 Tho 
 
 i. WMtb of inl Mda 
 
 ov 
 
 „_tXMi 
 " 80 
 
 Sj^^H^^S^s cjjv flBfi^^^l^X 
 
 fd.as80f4.{ 
 i4. a48f«L 
 
'■t ■> 
 
 
 4( 
 it 
 It 
 «« 
 
 II 
 fl 
 II 
 
 I 
 
 . «^^ wraoMi cuwm. Pmm tti. 
 
 ivm^ateff -♦of«h„n 
 •«« to atlihbor-* •! i o£ ihttp, 
 
 ihMpal of IM •lioo|»-i4SO tboop. 
 
 *• « }-•»•* ««««i*-(2X«a80) 11., 
 
 . „^ ^** •« H*d !■ 10 ft.»i fl.} 
 • Wp* of wM to (9X5380) fl.-(2X6a8X*) f|.-176 fl. 
 0. Ptoll^dTid 1^ WHO -tof-trto, 
 
 naMtotof m| 
 
 neoivod bj oMooi ton «f of | of ootato: 
 
 *•••»'•* t»y dt«fhlor »|ofiV '• —A " 
 
 .-. • Ml«to->$(16X750)»019000. 
 CXCROSE CIMIV. PiMHEiri. 
 S. KthoflratMdyMioldHMofMlta 
 
 th» aoMBd ioM jWio a ^«wi of 4« bi!, 
 . . I •bwit»4a9 Im. } 
 
 •wis " r^Jt.. .-. "if* *"-^'f*^ •* «^J 
 
 •■» » - (aXliOl) lm.»8Sl| lMI.:«^«|d of MOOI^ 
 
 «. Stenoflnt -ma.; 
 
 M00B(b»f«ftbe]Md; 
 
 *Mi* -mi».-HoftholM4, 
 
 •n *» C.-H of tlM ]Ml4! 
 
 •Mof tlM]uid»9Ba.; 
 
 thokttid«t4X26)..«l00«. 
 
 EWROSCCLXXV. fAOEllS. 
 
 0.aM^of^5*'^":JJiriT~' *"• ^•"'* Of «eh «i..t b. 01. 
 «» O^CM. of 9011 rt. Md 41* fd. I. fl rt. J 
 
 l^HBbot of loll OB tlW lm«»| «^*as44. 
 
 T«rf wiiBbor of lolo44«X0»ai0. 
 
cxBiaac cuwvi. paoe i is. 
 
 f. PWI A dOM fat 1 dft. ati of work: 
 
 « 
 
 II 
 
 B 
 
 II 
 
 II 
 
 9d». a| 
 
 Ids. >»# 
 Sd». «| 
 
 II 
 II 
 
 JO. 
 
 AaadB d<» fai 2 dft.»(H-i) «f ivOTk -1% of worki 
 Wotk to b* doiM>-(l~ A) «f WMk^A •! work. 
 
 Ftet A ud B do in 1 d».a(H-i) of work 
 
 ■o <*f woA 
 
 ; 
 
 Put jH to bo donoM(l~A) of work 
 
 ^11 of worit 
 
 ; 
 
 Fart of work A, B md C do in 1 da.«(H-H-i) of work- 
 
 ■*rre of work; 
 TipM for A, B ud to do M of work»l diu ; 
 
 II 
 II 
 
 II 
 II 
 
 II 
 II 
 
 II 
 II 
 
 H 
 
 I* 
 II 
 
 -Wd».j 
 "(iixW)dft.«-lHda. 
 
 11, Put A and B do in 1 dft.»A of work} 
 
 II 
 II 
 
 II 
 
 M 
 
 B 
 
 11 
 II 
 
 (I 
 
 11 
 li 
 
 -A 
 
 II 
 II 
 
 MB of A*t ■trofwth.S MB of B't ■troogfh, and 3 
 MB of C't otM^th do ia 1 day 
 
 •(A+fHi) of wofkj 
 A,BaBd<JdolBld».-4 * CA+ff^, or JJfc of work 
 C data to 1 d».-(JBt-TV), or J* of work J 
 
 TiiBO tor C to do tMk ^ work«l da 
 
 II 
 II 
 
 •4 
 II 
 
 llf 
 
 m 
 
 «i 
 II 
 
 ■Ada.; 
 «(a«XTV)da.»2lAdB. 
 
 IS. TtflMferf BMatodethaworiEvMltt. 
 
 •I 
 
 It 
 
 II 
 
 i 
 
 ■lOOkr. 
 
 aiaillarly, 
 
 part 1 " do«a ia 1 kr. «itlv M work: 
 
 II 
 
 II 
 
 1 woman 
 Iboj 
 
 II 
 II 
 
 II 
 II 
 
 
 II 
 
 H«Mo, part 1 BMB, 9 woaon, and 8*boja do la 1 hr 
 
 TIbm to do liv of work»l ki!. 
 
 »< !>■ I ih - f ill ) of work 
 'ilvofwork:^ 
 
 *i 
 
 i« 
 
 II 
 
 m 
 
 ** ^ 
 II _ 
 
 t 
 
 =*kr.} 
 
 «(aeOXf ) te.»88^ kr. 
 
i. 
 
 /. 
 
 i^(iMMiC CXCVH. PAOCtas. 
 
 •. IBMmo .8139 of li.».81SS of ?i d. 
 
 il.5:w5o2 .78ofld.IjJrf4qr. 
 
 qr. 8.00MOO Honm, £.790M5-Ut. *»M. 
 ^IBK»E CXCVni. PAm 120. 
 
 ALOSD. Ill . 
 
 x^ 
 
 fltnw, jCI lOi. 6d.s£l.0SB. 
 
 ««CISC CC PACE 129. 
 
 \aharo, tkta 
 
 «. 
 
 ». Lot 1 M« gol 
 
 1 jOQtt goto .i»o muwmt 
 
 8lM«. of 6 M Md 11 ,O.th0-«Xl d»,.+Hx.528 dtMO; 
 
 _ »11.775AafM; 
 
 H0900, 11.775 ■liom«aB#47.10{ 
 
 ^^ '11.775 •*• 
 OERCtKCa. PAQCtiw. 
 
 ttoHiOMi iom i. « mi».«(2.8xaa80) fl. 
 
 »insofi.; 
 12 *V«Mi8awii. 
 
 Coblo eontoat of stNom 9640 fl UmJ^tf^tSi' L _.^ 
 4.«fl. dooD«r9Siovt«riwiw7x ^' ****** ft- wMo, and 
 ».o n. «ioq>s(MMxiSS.lXBX4^) ea. ft.»UM5M o«. fl. 
 
 ^««CISE Cai. PAOE 117. 
 
 «. Sx|M«Miii« ooeli of tho namben m toii-tho««m,»Mk. 
 ■UMt ind tiiA o o If .,# ooKAA •«».r^ ^ ••■■"Oo«M»d»lMi, wo 
 
 mSL2 .L2 ^' "^'^' "^ ^25 ton-thooMuidtli. 
 O )8i500. 88750. 2 8125 — ««"~i«mw. 
 
 5) 4500/ 5750, 5^ 
 
 «( 
 
 <« 
 
 <« 
 
 «i 
 
 Jf 
 
 >00> 1860. 1186 
 
 9) 
 
 i80» 870. 226 
 
 *. 
 
 84, 
 
 «, 
 
 6 
 
lljli^J»»O.O.li;ii(5X0X5><5X»)li«.thoMMidlh. «* MM 
 »• L.C JI. It iMurf fa s .taU^ ^7" "*'"~**^' •» •««». 
 
 EMEROie CON. PAOe t2t. 
 
 •kw B ftMivw 1.7S ihanti 
 
 .-J^ (1+I.W+4.W6) " or6.87S 
 . . f.flS ■haitWMiMtJO} 
 
 1.50 ... 
 
 It 
 
 
 1.7Sof#M»|77 »B't 
 1.5 of •(44+T7)-$mdMN«A'i 
 
 «. OiMe MMrtMto of ifflfttsk-(».5XMXl.ia6) e. ft.; 
 
 W.U-— /^. . ■•«»»« "-(21.T6Xl.«WX1.26)e.fl.; 
 W«ifM«f(lt.5Xi.5Xl.Ui)«.fli«4a87JIb.t 
 
 *• *-"«5Xi3xnM*' 
 .-. " fll.Tliyi ««vt <«)^ fi - »l.WXl.f»Xl;a5X4aOT » 
 
 iiJXS.5Xl.lS5 
 »S«^.875 lb. 
 
 lb. 
 
 f. 
 
 ©"WOK COB. F^Mem. 
 
 iMof»0a.«B58.5».; 
 
 ^«C|89s.«c87.fta.; 
 
 W^ofa6tft.«»tlOs.| 
 
 Co* of 5S4 «. • «ta.»1479.M| 
 
 .•r.5».«ilS«$B0tS.5O; 
 
 St5ft.«#M«^BMMe{ 
 
 It 
 It 
 
 ; 
 
 7. CMlfag priee of in piaaoBBlH of IS60 
 
 " « ^ u »♦*»•' •W-WO;' 
 
 WB ^*nnr of i860 a» HOO; 
 
 Mlfaf prios Of aUsinfB. 
 
 RM pifa»t(575-790)t-«lS6. 
 ». SntdopooiM >Mofft»rlinio; 
 
 » .."'? ^^*^<tf ^<tftortto»"^offartmo; 
 
 •■^^•j tw o* "PWiiMTBfpm . 
 
 *Wof 
 
 
 II 
 
f. 
 
 eXERCISE OCXN. PAQK |3S. 
 
 fifft wmbw-jg of l«lwa.b«, 
 
 <« «« 
 
 Mworbotii 
 
 •« 
 
 H«iM,^<»fflnk " 
 
 • « (4 
 
 I* 
 
 181 
 
 100 
 "■»« •* W01«MiO; 
 
 ccxiv, PAoeiss. 
 
 Invoia* p ilm » oa 7 1 | 
 not dinmmk # Mia. 7S; 
 
 «< 
 
 Or. 
 
 # 10%« 80; 
 K«t prie««|l70. 
 
 Fiftl NiiMia4«PB| of $8753 
 
 <i 
 
 *% «t t of |87S«|870. 
 
 f* fta* «C hmM pri«o nawiaiiicaliw dadMkliic 
 is^ofHMPfcodpiiM. «—«««» 
 
 Hmm, ^ of Minted priee»8l.79; 
 
 .-. •• " *Wof|a.72»88.ao. 
 
 9. Ffert of prieo ramaistiiff aftor int diMoniit 
 
 X- 
 
 tlMdiMOVIlt 
 
 «« 
 
 «< 
 
 << 
 
 iMiof ««t. prieo; 
 
 -M of ^ of oal. priee 
 
 g7.5 
 100 
 
 of oat. prieoj 
 
 viagio diMooata/ 
 
 100 67 
 
 »88ift. 
 
f. 
 
 ^ofBKOK caw, nine iss. 
 
 . . iM of WHted i»ri««i.i|| of If { 
 
 " -WlHIolH-IMP. 
 
 ' ba.vMoo Iw 
 
 «. Chya*^ of eo«t-il.40; 
 WU-t priee to gtiii Wft»HI oi $B.«0.f7M. 
 
 «. Lon ■ ilv of 6(MftaMB54IO) 
 
 . . WJfaf l»rie«»M<2776-65.60)-|i71»^. 
 ^' . '^'"** <"> 1 l»>"'Ak of 79e.»Vo t 
 
 •'• " " " lS80OOe ** »iSSi2^ 
 
 72 
 
 EttROSE COtVIII, PAOEfSr. - 
 
 <• HI of ooot of 10 oowi»iOBO; 
 . tuniJ.L^*L ^•••'"AofWofiaMj 
 
 • 8*aii« Ptio. tegy. «-^ Of A ^ III i ^j,,,^ 
 
 «• BajrlBg prieo»^ of j,,^^ ^^ 
 
 8ellia« <« «»f|| «< u ' 
 .'. gtiii oa M of auukot prieo»^ «< <« 
 
 ^ " "^ ©f M of nuttkol prieo; 
 
 " 100 '* " ^ 100X100X80 „ 
 
 86X100 
 
 "•In por «Mit.«86A. 
 
 •'• gain OB 886 nil Ho I 
 
 .-. " 8100-^??^«> 
 86* 
 
 .'. (fAiii»S6A%» 
 
fl 
 
 ▼■iM 
 
 n. 
 
 ••» •« -(•Ki»XltXli)«.| 
 
 >(llv«ftX8tXMX»)«. 
 
 ;v 
 
 i« 
 
 
 Mki-aift 
 
 
 «< II 
 
 woo»»'^j;gt*». 
 
 #. C«M lM te« »yfc Of ■— rfttthndt 
 
 8ti wi i» tw i i w^ 
 
 _-itox 
 
 
 '■ 
 
 97 
 of 
 
 coon. PiMfa*. 
 
 «. 
 
 ifi 
 
 fffi i d o«l «( «l«t«^0»| 
 
 <i ft 
 
 QMBUty boogkt tor tio.»l lb. 
 
 MMXIOO 
 IBT 
 
 « i« « 
 
 « « i« 
 
 lo.»Alb.| 
 SOMOOXS 
 
 Sam ooUooMb-^ ol $UW 
 
 lb. 
 
 lb. 
 
 bgr •Ndiloi-#(M»-.47.8S)»|Wr.99. 
 
 10. 
 
 « e amal^ Mi=^ of vobM of goo^; 
 
 -«' • «« «« 
 
con 
 
 _gl«X»i» 
 
 •1 
 
 EXERCfSe CCXXN. PAQC f 4«. 
 
 afUme-taooaf 
 
 4. 
 
 tkvimmbumnimmM 
 
 141. 
 
 { 
 
 « <i 
 
 
 
 Urn \9 •mmmtm%{wm^fmM)*'mmM. 
 
 I 
 
 $. 
 
 " fcH"MWfc«f»10WINtW00 
 CXEROSE CCXXV. PAOC 149. 
 
 <« M (« 
 
 lOM 
 
 * *' *< M 
 
 *fl78S; 
 _lM0XlTi8 
 
 *MniaI«ff •ftor dtdnetlBr Mit of MdteeliM 
 
 JMXISSM. 
 
•• TtamfMom 
 
 *t 
 
 ** 
 
 m^xm 
 
 'N^ 
 
 IXBiaK CCUOk PMUL iU. 
 
 #. VSMfBTWMthttolirttlMltovHpriMilNri-lTr 
 
 • ti AA AM M» » . . * _ _* 
 
 i« 
 
 i« 
 
 «« 
 
 41 
 
 ih 
 
 «l 
 «( 
 
 
 eunciK ccxxxii. paoi t4«. 
 
 PriMi|wi»|iiM 
 blnwl Ilk half yr.»$ 400 
 
 InlMMt Slid half jr.»0 ae 
 
 laltiwk Srd lalf jt.i-O 441 
 
 IrtMwt 4lfc half yr.wQ 40t.05 
 
 »» 40t. 
 
 BlMpla 
 
 ialMwt»«im.Oft 
 
 II 
 
 Tha aoMpoud iataiwk fa gnattr bj $(17M 
 
 SXtV^XfOOOOa-OlOOO; 
 
 0B~10I0), or $194.00. 
 
 ixnoK ccxxmH. paoe t4«. 
 
 S, lMa«Cdfafl>iOfM 
 
 iJaatiHOM Q n» 
 Ooakof4iftCk«|70i.87S. 
 
 0. 0101 will panhaaa a dmfk for 0100; 
 
 01000 
 
 i« 
 
 << 
 
 .UOOXIOO 
 ' 101 ' 
 
 or for 01486.148B. 
 
 EXERCISE CCXXXIV. PAGE 14a. 
 
 '• 8aM.froaii^^l7faJttl7i7; 
 
 „ ^^ ^ A^Oiayaoffiaaa, •• 90x»dale of naterftj; 
 
 No. of daya batwaan Maj 1 and July 20 fa SOstarm of dfaaouak : 
 
 Intaraal a« lOBT for 00 di^ at 8»«Jft of tI» af 0067 
 
 »«ll.fii; 
 of ■ala-»0(0B7-11.52)«-0e40.40. 
 
iMk dlMo«B|H| of tIw flf fiM rtimtm^^ af ^tt talao 
 
 •'• fM« ira hwil of « 
 
 ». TIM Mit Irilt dM w 11^. ». 
 of 4^« fNM AiW. M to li9r. 
 
 irai— i»li «mmw ma. 
 
 » 
 
 .7S>B$lMe.7t. 
 
 19. Tto Mit teUt dM M J«ly n 
 
 Vo. 9i dagri ftom M^ a to Jaly 31-i74; 
 WMl OB fMia.74 lor 74 dft. • 6ft»iia. 
 
 .^ ^ ••ft»$lS.97.. 
 
 PMMoodi of Mioipfaots.74-aif .»7»$io6i.n 
 Exoase ccxxxv. pmmi •«•. 
 
 $100 olook li wettli HOIf 
 
 JiOOXlM 
 ' 100 '* 
 
 07100 
 
 « « «i 
 
 M t« u 
 
 *. Mo. of doUaw of otook fai 78 oimoo»a(7gxfl0) -atTSO 
 VolwofMOO ' * 
 
 084 
 
 * mm *' -M¥«f09oo.amo. 
 
 CCXXXVI. PAAC tot. 
 
 <f 
 
 wHl Nqr 0100 otodi 
 
 i( 
 
 » 
 
 W of 0100 Hook, or 0700 olook. 
 
 II 
 
 wUl 1W7 0100 iledki 
 
 II 
 
 %ltf of OlOO alook, or 09000 otook. 
 
 Mow 0000 olook-il ohMo. 
 .*. OaOOO " "-^RF of 1 ohu«»lo okavoo. 
 
 EXOIOK CCXXXVN. PAOE IM. 
 
 /. laomno fram fanrootiac OIMsbS* 
 
 ••• " " •• 0Ba0O=M¥ of 06«0»0. 
 
 f. booBo from IsToitiiif OUSssf?. 
 
 •'• " " " 0100=.Hf of 07-061; 
 
 1. Baoi iBTootod to i^odnoo OS fiio<»Bo«B$iao 
 
 II 
 
 II 
 
 •I 
 
 i-H>ofoiao«oMOo. 
 
ttt. 
 
 t 
 
 ▼alto if not ** 
 
 f. 
 
 Mflein. 
 
 II «i 
 
 I 
 
 B«M»,lk»tli|it|k9kl||| 
 
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 } 
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 .'. tiao for to do all tko woikiBll 4i^ 
 
 JO. 
 
 fteoflMTl 
 
 to do tiM w wfc W kr,; 
 
 I 
 
 FMI wUoii 1 Mhi 4000 fai 1 hr. m^ 
 
 (I '* * 1 h^ ** ** M^k ** 
 
 poi4 wUoh B MB oai 41 kofiAo in 1 kr.«i(^H-M) 
 
 I 
 
 •Mi 4» bofo to do oB tko 
 
 l»."4ihr. 
 
 tIaoforS 
 
 U. Part of tto work dMM bf A, Band te 1 6ar^ 
 TiMportodoMlvA, BoadOMwaol, 4«idi, oraoi, tiadt. 
 
 Homo, port doM bf A la 1 dqr«A«i^ w«rli-*Tfo of «Hk; 
 .'. tiao far A to ooMplolo tho worii-^ da.»ai| da. ;. 
 TIawiorB" ** '* -^X«|} da.«m da{ 
 
 if. Tliao for A to do tko utalo noik^ of 11 
 
 flMt of ITS* doBO br Bia 1| da.*-(l-^ of arorit 
 
 t« 
 
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 i5. Ptut whieli A and B tagethor do la 1 lir.a*M of work; 
 
 .'. part whioli B aloBO dooo la 1 kr.»(^yb-A) of work 
 
 ■■li* <rf work; 
 .'. tfaao for B to do ah tto woik^*f* hr.»88 to. 
 

 " " 1 M II 
 
 kr.l 
 hr. 
 
 TI-. lor A. B «i •• i. iw.-^jUlir.-Ur.-«7#iri.. 
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 1 
 
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 MMk Mil Mn dMiM bt gIfMi to MMrtm ttt p«pll to 
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 TtflM to 1^ 11 mlmito' 
 "15 " 
 
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 »$ «« 
 
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 tt 
 
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 ^~p ato.-ltA toto. 
 
 tiM tkm to 1«A Mto. VMk t. 
 
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 15 
 
 11 
 
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 «. Al 5 o*6look Iho bMrfi an M 
 
 MX 13 
 
 Ti«« to goto 15 ata«to< 
 
 11 
 
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 To be 8 ainato-spaeoa apart tt 
 
 ^Kb« to fais tt adaato- 
 
 ttXIS 
 
 11 
 
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 la 94 ada. paat 5. 
 
r. Att«'«lMktlMhMiiaM|t 
 
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 •PHI «MMr II or M mImU. 
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 MX IS 
 
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 TtaMfidMi te in ift.«lMxr Mt.-U Mia. 
 is 14 alB. iMl It. 
 
 #. TIatiBirlMi 
 
 «* 
 
 «• tt 
 
 «i 
 
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 i« 
 
 « 
 
 17 
 
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 •IMBfai.«t4ft.0ltt.lti 
 
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 IWBiB.«i 
 
 «i II «i 
 
 )•».■. 
 
 iHP. 9t tow ttB«l 
 
 -IN o( ft ]». «C tm* tteM«5 kr. 6A Biii* 
 
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 f. TteM is lildab Um ctodB an t aia. qpit»lS k 
 
 II 
 
 II 
 
 II 
 
 II 
 
 II II 
 
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 lur. Imnb ■sob m ^mtejr to 9 p. m* mi nftWH^. 
 
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f. fMi A fMiHr t» U ». a. M Ibf t It t a. B. Ml MiV T 
 fiM ItlMt H ■to.aim kr. I 
 
 Mikr. IMiftiMMHrlt U ^ ■. MHlf lift ». M. Miy t. 
 
 Mil l•^•. iMuAij «• Ml hr. 
 Mmt, IMH Mte. §• llM wilrt«l4lt MlB. tnt ttetf 
 
 /.l«kff. " -2g^ffl4MBia.tiw 
 
 »1» hr. «t|||i «te. 
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 I. 
 
 t 
 ft • 
 
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 fOM il (tlXtl) ttt.>>(«X«XM) n,mHH Ml. 
 
 faillttt.-iSii.t 
 
 1^ te (iixtl) Mt.-^^9 •( II t*.mm mL 
 4. TiM It aovt (MX17W) yi.»(WX«) tM.| 
 
 #. Tlat itt 
 
 -TiMt. 
 logttMi.«*ilraf Ikr.t 
 *' I.t6 Mi.-t|! of ^ of 1 kr.-14| Bte. 
 
 i. TtaM ftr A to girfB « ml.*! hr.) 
 
 *< 
 
 14 
 
 l« 
 
 4 al.-l of 1 kr.>iS hr. 
 
 7. AMidBftpi»raMliMMhollMvaltlMntooC(4H-8i)ml.p«rhr. 
 T1»« to tn^wA S ai.ail hr. ; 
 
 " 60 «i.«V of 1 h». «T4hr.; 
 OtotaBot A fott te 7i Jlr.«(7iX4«) ml.»IU ai. 
 
■■OWIMi IVr OMIf 
 
 (ANSI and ISO nsr CHART Na. 2) 
 
 1.0 
 
 122 125 
 
 \i2 
 
 
 L8 
 
 ^5 lyiii 
 
 J. 
 
 ^PPUBDJVMGE 
 
 <aM tel Main Strwl 
 
 I MS/MGE Ine 
 
 ^^ o^^-^sk^Php^r" "" 
 
 (7»«) 
 
 c4l^&jk- 
 
 2W-aMt.F« 
 
ABlTHIIinO. 
 
 tM 
 
 % 
 
 *. A rana 1760 jd. wUl* B raiis 1680 yd. rad C, 1678; 
 
 .*. B rani 1680 yd. whUe C ran* 1878 yd. ; 
 
 /.B •' 1760yd. " C '• «Ho<1678yd.,orl75Hyikj 
 
 Henee, B era bent C by (1760-17521) yd., or 7» yd. la » mil«. 
 
 9. A eu ran 1760 yd. while B ean ran 1788 yd.; 
 B " 1760 yd. " C " 1740 yd.; 
 .-.B " 1788 yd. " C " «« of 1749 yd. 
 
 or, 1727Hyd.; 
 Henee. A ean gire C (1760-1727tt)yd. or, 32|» yd. etort In • nile. 
 
 10. When the hands of a clock move correctly, they coincide every 
 66A min. To coincide every 66 niin. ^ min. must be gained. 
 Gain in 66 min.—i^ min.; 
 .*. " 1440 min.=^p of fr min.^lO^ft min. 
 
 /. 
 
 EXERCISE GCLXXXIV. PAGE 1S3. 
 
 Greater No.^-Lesa No.=365; 
 
 Greater No.— Less No.= 83; 
 
 .*. twice greater No. =365+83=448; 
 
 .'. greater No.=*|* =224; 
 
 and twice less No.=365— 83=282; 
 
 .'. le88No.=*|* =141. 
 
 t. Bate down 8treMn=7 mi. per hr. ; 
 
 .-. I' in still water= (7-U) mi. per hr.=5| mi. per hr. ; 
 .*. " np 8tream=(5i— H) mi. " =4 mi. per hr. 
 
 5. 
 
 Bate down stream per hr.=4 mi. : 
 " - " ♦* =21 mi. 
 
 up 
 
 Bate in still water+rate of stream=4 mi. per hr. 
 
 .'. twice rate of stveam=l| 
 rate of stream=-^ 
 
 4. Bate up stream per hr.=2Tmi.=4 mi. : 
 
 
 =1 mi. per hr. 
 
 
 in still water " =(4+H) mi. =54 mi. 
 down stream '* =(5i+U) mi.=7 mi. 
 Time to row 7 mi.=l hr. 
 
 " " 3imi.=|*of 1 hr.=4 hr. 
 
•0LUTI0V8. 
 
 S. 
 
 Bate down stnam per hr.s^mi. s6 ml. ' 
 
 <4 
 
 up •• •« =Vinl.= 3|inl.; 
 
 .'. nte In 11111 water+rate of stream=6 mi. per hr.; 
 
 .'. twiee rate in stlU water=9| *' *< 
 
 • «< 44 44 _.W II II ., , . 
 
 =-2 —4* mi. per hr. 
 
 $. Rate down stream per lir.=:4 distaneei; 
 
 •• up •• *« =3 " 
 
 .'. rate in still water+rate of 8tream=4 times the distanee;* 
 and *♦ " 
 
 '• — " •« =3 
 
 44 
 
 .*. twiee rate of stream=l 
 
 41 
 
 44 14 __l 
 
 44 
 
 Hence i the distanee=l mi. ; 
 .'.the distance=2 mi. 
 
 f. Bate in still water=4 mi. per hr. ; 
 
 " down streams (4Xli) mi. per hr.=Si mi. per hr. ; 
 .-. rate of stream=(5i— 4) mi. per hr.-=li mi. per hr.; 
 .-. •' np •♦ =(4-U) mi. per hr.=2| mi. per hr. 
 
 Time to retnm 1| mi. up stream=^ hr.=i hr. 
 
 44 
 44 
 
 44 
 <4 
 
 1 ml. on the eanal=i hr. ; 
 to starting plaee=(H-*) hr.=f hr. 
 
 8. 
 
 Bate per hr. up stream=2 mi. ; 
 •• down •' =6 mi.; 
 Time to go 1 mi. up and bae]c=(i+i) hr.=| hr. 
 Distance the man goes and returns in f hr.=l mi. ; 
 
 4« 
 
 2 hr.=| of 1 mi. =3 mi. 
 
 Bate down per hr.=*^*^ di»tanee. 
 
 up 
 
 the distance 
 
 .'. rate in still water+rate of streams"** distance. 
 
 and rate in still water— rate of stream= 
 
 2 
 the distance 
 3 ' 
 
Ir ' t. 
 
 AsirmiTic. 
 
 6 ' 
 
 - .'. '•« « _ 8 tia— the dliUiMia 
 
 12 ' 
 
 AgiOa, twte« nte of ■♦.^m- ^^^^^ <»l»na» 
 
 6 ' 
 
 i< 
 
 — the dirtmea 
 
 Heiiee, the nte in ttill water i. to rate of rtreem m 
 
 gtin-thedlrt.^^ thedfataiwe 
 
 • 12 ""® 12 . or M 6 to 1. 
 
 10. Brte per hr. up itreun «^ nH. 
 
 2? 
 
 «2|ml.; 
 In etiU w»ter=:(2'|+U) mi.»:z4 ml.j 
 
 Time to row Si mi. down itream-i hr. ; 
 • " " 12 mi. - .. =|Joflhr. «2ihr. 
 
 «« !( i< _12 
 
 ^51 
 
 KERCBE CCLXXXV. PAGE i«4. 
 
 /. I)lrtMceA«ted.g»inrtthewindin60min.=6 mi.; 
 
 W " «ttof6mi. 
 
 lUf of -ktlng in ejJm+rat. of window m. per hr. ; 
 
 . *_. ** ^fini' perhr.: 
 .. twice rate of wind«(10~7i) ml. perhr.; 
 ... .« » ^ lo-n .^ . _ ^ 
 2^ nu. per hr. 
 
 • a »^^ ^^^ *!• PO' hr. 
 
 *. Bam of the mtes in S aeo.* (110+88) yd.; 
 
 «< 
 
 << 
 
 perhr.=«^ofl98yd.=81mi. 
 
 Diiference of the rates in 45 sec.* (110+88) yd. ; 
 
 perhr.=-^ oflMyd.«9mi. 
 Bate of faster+rate of alowersSl mi. : 
 
 =9 mi. ; 
 .*. twice rate of fastersgo mi. • 
 
 A . *-..•• " " =Vii«l.=46mi.; 
 
 Again, twiee rate of Blower=(81— 9) ml.- 
 
 • ' * =y ml.=39 mi. 
 
tOLUTUWI. 
 
 Bum of ntM of tho timiiw per Me.» (44+40) ft.^SS yd. ; 
 DtalMio** gOM in 1 Me.aras yd. 
 .*. " " 8M«.»(8X28)yd.»2Myd. 
 
 Leagth of Mooiid tr»iii«(224-110) yd.Bll4 yd. 
 
 4. Birto p«r 4 Me.s88 yd. 
 
 Brteperhr. =?^ of 88 yd.«46 ml. 
 
 5. DUtMioo the freight ia ahoMls^ cf 88 mi. 
 
 Dietanee the exproMi g»iiM per hr.slO mi. 
 Time to gain 19 mi.si hr. ; 
 .'. time to gain ^ of 38 mi.»i^ of 38 of A hr.=i4 hr. 
 
 «. Dirtanee the train goe. in 10 eee.^ ^^^^^^^ ft.=440 ft. 
 
 i« 
 
 14 
 
 goes 
 
 44 
 
 .4 _ 10X8X5280 ^ _^ ^ 
 60X60 "— ** "• 
 440 ft. ia the anm of the length of the train and 44 ft. ; 
 
 .'. length of the trains (440-44) ft.=306 ft. 
 Or, diatanee gained by the train in 1 hr.s27 mi.s(27X5280) ft.; 
 
 .-. ' " 10 aee =^52<27X5M0 ' * 
 
 60X60 ''•^SWft. 
 
 7. Diatanoethetraingoeain20aee.«??^^l^^llZ??yd 
 
 60X60 ^* 
 
 «*V* yd. 
 
 *V* yd. ia the awn of the length of the bridge and the lensth 
 of the train; 
 
 .-. length of the bridge=(*V«-160) yd.=94| yd. 
 
 8. Diatanee the man goea in 10 8ee.= ^^^*^^^^ yd.=H^ yd. 
 Diatanee the train goea in 10 aec.=(88+^A) yd. ; 
 
 ♦• 44 t. «< ,. 60X60 -,„„.,,., 
 
 • • 1 **'• ^0~ *' (88+^) yd. 
 
 =22 mi. 
 
 9. Diatenee the man goea in 8 aee.= ^^^^^ yd.=i|* ,d. ; 
 Diatanee the train goea in ^ 8ec.= (no— a|*) yd. ; 
 
 4< 
 
 (4 
 
 •' 1 hr.=^ (llO-i*.) yd. 
 
 =23imi. 
 
' ABITHMBTIO. 
 
 to. W.I~«.tb.«M«igo..lnl5.e<..l»|^^ft..88fl., 
 
 ;; ;; i«i«. ;• w .^..-w+as) «. -44011., 
 
 »■«».=* of 440 ft. »2«4I|., 
 
 ■"•» ■•0.- (862-264) ft. «88fl.; 
 
 *i <i . .._ ^ 60X6 
 
 9 
 
 Ihr.: 
 
 ■of88ft.»6|mi. 
 
 //. Olrtanee the train goes In 10 sec.* (88+44) yd.=182 yd.; 
 
 " •' " •* ihF - flOX60X182 . „ ' 
 
 10 3^*27 mi.; 
 
 Time for train to go 180 ml.=V^ br.aO} hr. 
 
 EXERCISE CCLXXXVI. PAGE 185. 
 
 /i Length of the flnt pleee=V^ yd.=:86 yd. • 
 Cost of 1 yd. of the aeooud plece=*|4^. «01.92. ' 
 
 f . No. in ilrrt biHr =^^25+1 )=325; 
 
 No. In third bug «?2?=5? ^ 
 
 2 
 
 No. in second bags 125+50 
 
 =125; 
 =175. 
 
 5. Sum spent in 10 yi'.=$(6X700+4X500)«$6200; 
 .-. ineome for 1 yr.=$»f«* =^20. 
 
 4. £288 4s. lld.=276716 far.; 
 
 £3 17s. 10M.=8737 far.: 
 276716 far.-r87S7 far.=74 and 178 far. remaining; 
 178 far.=3s. 8id. 
 
 6. 5e.+10e.+25e.=40e. ; 
 
 No. of ea6h=^.=l7. 
 
 e. No. Is tbeG. C. M. of (365-20), (646-17) and (1140-13) ; 
 G. C. M. of 346, 629 and 1127 is 23. 
 
 7. Share of B and C=£40 28. 8d. 
 
 " A and C=£29 IDs. ; 
 .*. shares of A, B and twice C's=£60 12s 8d • 
 But, " A,BandC =£63 68. M. j ' 
 
 /. C's share=£16 6s. 
 
■OLvnoirt. 
 
 87 
 
 8. P»rimetor of lleld»2X (120+30) >d.B4950 ft. ; 
 No. of boards to go onee roandasHf ^330; 
 
 . *• " " 6 times " =6X330 «1M0. 
 
 9. No. of fonows in 16 H.^^^^-^^U; 
 Time to ploof^ 1 fanows6 min. ; 
 
 .'. " " 24 •• =(24X6)min.=2hr. 24miii. 
 
 /0. Valae of daeks=(8X7S)e. s:600e.; 
 V»lae of eliieliens=(13X50)c. a=650e. ; 
 
 12fi0o.; 
 No. of pounds booglit for 91 as 16; 
 
 $12i=12iX16=-200. 
 
 <« 
 
 <« 
 
 i. 
 
 EXERCISE CCLXXXVII. P4QE 189. 
 
 Oigsl.si e. ft.; 
 
 .'. 000 gftl.=^ c. ft. 
 
 =80 e. ft.; 
 
 No. of c. ft.=(8X6X4) e. ft.=192 e. ft. 
 Time for 80 e. ft. to enter eistom=60 min. ; 
 
 192 0. ft. 
 
 <i 
 
 . 1&2X60 
 80 
 
 min. =144 min. 
 
 f. 
 
 Sliare of boy =1 sliare; 
 " womftn=l '• +25o.; 
 " man =1 *♦ +60o.; 
 Shares of 7 boys = 7 sbares; 
 
 " 8women=8 " +200e.; 
 " 10 men = 10 *' -j-SOOe .; 
 25 " +700C.; 
 .'. 25 share8+700o.=2575e.; 
 
 .*. 25 shares=(2575— 700)o.=1875o.; 
 .*. 1 share =-4i*c.=75c. =boy's share; 
 
 1 share+25e.=$1.00 
 
 =woman's share; 
 
 1 " +50c.=$1.25 
 
 =man's share; 
 
 Money received by boys =7X75o. 
 
 =$5.25; 
 
 " •* " women =8X$1.00 
 
 =$8.00; 
 
 " " " men =10X$1.25 
 
 =$12.50. 
 
 S. L.C.M. of 250c. and 175o.=1750c. ; 
 No. of barrels to cost 1750o.=^'ye.=7. 
 
 4. Diyidend=7469X 728+19=5437451 ; 
 (5437451— 411)-r5320=1022. 
 
1^ 
 
 t." 
 
 «. No of bojii. for ao ■«! to do tlio work-MO; 
 
 *■•» " ♦• -80X9I0- 
 
 ••• " " "26mo» " « -»0xa40^j^^ 
 
 No. of working daTt |n 288 )ir.»i|«a83 
 
 y. No. of nUto.-^i??^«17 
 
 * Pri«« iwid for 1 ft..f^W-K»; 
 
 « '^*^** '•' ^ •.*80Xf76*$2280j 
 " ^•.»46XtCO«|22gO; 
 
 ftim for whieh 46 a. miw» bo ■old=8(780(H.a00^4a00)«3llOO. 
 W«« for whieh 1 a. iniut bo (Ktfd^tMftlJgo; '^**' 
 
 Bvry ti». a p|, ta i»jd thU «« |. rodilifby « ' 
 
 To lodiieo taooo to $1720 thoro miist be f dIm mM «. i^ . 
 Heaee, there wo,. (250-140) riieep^orVlo'STp ''*'''*«•• 
 '<>• Let eort of 1 Tort »i vert; 
 
 Then •' 1 eoat »l Te.t+81.26j 
 * ^ Teats^4 Teste* 
 
 . . coet of 4 Teete and 6 eoate^O Teet.+|6.26«833 2S • 
 .-. eoetofOTeet««|27; 
 .-. •• ireetsfS; 
 
 " X eoat a:t4.25; 
 
 " 12eoates86i. 
 
 EXERCISE CCUXXVIII. PAGE IBS. 
 
 i. Each time he paid N.50 he owed |8. 
 
 No. of times he paid M.50=^ ^i^. 
 
 .-.sum owed=8(i600X8)=$12800. 
 *. Costofl28g.l.=8(i28xl.70) =$217.60- 
 
 Sumtobereali«ed«:$(2i7.60+33.40)=8261: ' 
 No. of gals. 80ld=251; 
 
 Qnwtity of water added= (261-128) gal.=123 gal 
 
S. Coil of hoHM Mid 7 
 
 MW 
 
 •-$1900; 
 
 
 «< 
 
 • 
 
 •• " M 
 
 II 
 
 -$1900) 
 
 • 
 • • 
 
 I* 
 
 lb 
 
 II .1 j4 
 
 II 
 
 -IMOO; 
 
 Mkl 
 
 «i 
 
 18 
 
 II 11,9 
 
 II 
 
 »|8i00{ 
 
 
 
 t 
 • • 
 
 .MMkofSS 
 
 II 
 
 -01900; 
 
 
 
 • 
 • 
 
 . " i 
 
 eow 
 
 »N8. 
 
 Th« «(wl of lionM»0(190»-7X48)a0004; 
 .'. *' " 1 bono -006; 
 Cook of 8 hOTMO Mid 8 eowo»0(8XPa+8X48)aB0879. 
 
 4, Cort of 475 »ppl««s(0BX0)e. a670e.; 
 .'. eoit of Moond lot»(lO9O-57O)e.»40Oe.; 
 
 No. of timoo he tpont Oe.»^^' «00; 
 
 No. of opitlM 111 Mooad lot»(00X8) a790. 
 
 5. AiMOf flolds(40Xl(4X24Xl«i) iq. fl.; 
 Aroft of 1 lot= (165X08) iq. ft. ; 
 
 No.oflot.=^22<l§i><ai><i«=.24: 
 
 av. wk IWM 185X68 *■• 
 
 Prieo of 1 lotaOHf'-OTS. 
 
 8. Sam reeelTod for the tM»60X40X8t. 6d.s>£490; 
 OAiiis£(420~280)»£140. 
 
 7. No. of eofda in the plle- "^^^* ; 
 
 Valae of the wood=|(?5^^*X8.25)=007.60. 
 
 8. 28 hr. 2 min. 36 ■ee.3s82966 tee. ; 
 46 hr. 8 min. 55 ■ee'.=166185 lee. ; 
 
 The O. C. M. of 82966 see. Mid 166185 lee. is 228 eee. 
 
 a Let Henry get 1 ihAre; 
 
 then ThomM gets 8 shures; 
 end Jolm gets 40 shares. 
 40 shares. 
 Value of 40 Bhare8=il078; 
 .'. " " 1 share =t^H=$22; 
 . Henry gets $22; 
 Thomas" $(8X22), or $176; 
 John " $(40X22), or $880. 
 
f\ 
 
 4i' 
 
 to. No. of qwrti nlm^lm ^^^^m jaKt 
 
 8o« rooolTod for 90 ba.»0MO«. » 
 
 ucRdsc ccuxxM. PAoeitr. 
 
 1. Ano of roon-dSXlSXlflS) tq. |b.| 
 
 Lwnth of Con»ot»<"><»X'«) «- _ 18XHX1M . ^^ 
 
 87 MX97 " '^•"•^ y*' 
 
 Cool of Oftrpot»(MX76)o.«f27. 
 
 f. Loogthof fopo-ax4 ft.+2X(8 ft. 8 Iii.)+4X(8 ft. 8 In.) 
 
 "80 ft. 6 la. 
 
 «. Agmiato hoifffat of « bo|r.»6X(4 ft. 5 Ib.)-86 fl. 6 in. 
 
 4 b07«»4X (4 ft. 7 in.)« ie ft. 4 In . j 
 
 "8b<^=8ft. 8lB.{ 
 .-. OTonco of o boy==4 ft. 1 In. 
 
 ^' 18npplos»10e.; 
 
 .-. 8 oppleo or 2 orongos«| of lOe., or 2ie. ; 
 . . 4 orugM ui 3 lomonss2x2i«., or Se. ; 
 .*. 15 lemonaarSXSe., or ISe. 
 
 *' O.C.M. of 1069 ft. ud 1875 ft.«ll ft. , 
 
 Perimeter of fleld=r(2xl089+2X1875) ft.»4928 ft 
 
 No.^ of rail, to go 1 time roand=Mf^448. ; 
 6 time* " -6X448=2688. 
 e. 212620-2X2X2X8X5X7X11X28.; 
 Thew arranged to make 4 oonseentire nnmben beeome 
 2X2X6, 8X7, 2X11, 23. ' 
 
 7. L.C.M. of 3, 4 and 6—60: 
 .*. least namber poMible— 60+2— ^. • 
 62 is not a multiple of 7; ' ' 
 
 2X60+2=122. This is not a multiple of 7- 
 8X60+2=182. This I. a multiple of 7- 
 . . least number of marbles=lS2. ' 
 
No. of bAloo In ewai 
 
 •oLvnom. 11 
 
 #. IVriatm of lol-(Sxii04>2XM) f|.»a60 f|.t 
 Am of Mrfk«o«(OxaaO) iq. ft. .,40 m. yd , 
 
 ». Aioo of roof- (S5X 13X36X13) m. 1b. t 
 Aroo of 1 ■kiBfflo«(4x4) tq. Ib.i 
 
 /.No.of-i,.i,,o..~Xl|JpW.,,,5. 
 
 W. CbMo oontoBt of oar « (88X8X6) e. ft. ; 
 bolo-(8X8X«)o. fl., 
 . 88X8X6 ,-_ 
 8X8X1*"""* 
 Wolfht of 176 InUoo-36400 lb. { 
 .'. •• • 1 b^« -«HH lb.-180 lb. 
 
 EXERCISC CCXC. PAGE 187. 
 
 MttL^^J*^ ■*• of oquiU ilM OM fMm mart eort f of 
 •19600 Md tbo otbor { of 118600. 
 
 f of $10600»67800, ond f of |18500»$11700. 
 Coot of 180 a.»87800: 
 " 1«.»6W«660, 
 ■ad •• 180 •.»8li700; 
 
 *• 1 •.-tH|H=|90. 
 
 #. Tho L.C.1I. of 10 ft. Md 12 ft.=60 ft. 
 ^ Jn going 60 ft. tho front whool tarn. 1 time moro than tho hind 
 
 Dlstaneo In whloh the front whool tarn. 1 tin.. mor.=60 ft. ; 
 
 " •• J»* " " =(264X60)ft. 
 
 »3ml. 
 
 «. ^■8MforlOOda7.»(100X06)o. =806.; 
 
 Wage. lo.t=8(B5-76.80)=$18!20; 
 Wage, let In 1 day==(86+46)«. =|i.40; 
 No. ot day. idle to Iom 818.20=^^^ --13. 
 
 No. of day. he worked=100— 13 sgx. 
 
 rf. Perimeter of lot= (2X120+2X90) ft. =420 ft • 
 
 Cortoffeneing=(420X15)c. ^.^gg ' 
 
 Area of lot= (120X90) .q. ft. -inann „ #♦ . 
 
 Area of walk and lot=[(120+e)x(90+9)] «,. ft.Il^^.ft;; 
 
 Ijj 
 
A M ' fMWiU . 
 
 Aim tf wilkB(lSm-lMM) iq. fl. miwn •«. ft. 
 Ooil of WBlk«(tI»X9)t. ■fM.ftl.i 
 
 #. Aim of tkt 
 
 i« 
 
 «l 
 
 (tXl««XT) iq. ft.«Sll §q. ft | 
 (SXT«X7) iq. ft. -IMiq. ft.| 
 i-i(16«X7«) fq. ft. - ItH iq. ft. 
 
 No. of iq. yd.-»-W| 
 
 Wtlffht-(WXS) lb. I 
 
 ^l»X8 4.WK 
 ■ 13 '^100/ 
 
 tfMiq. ft. 
 
 -fSO.OSM. 
 
 «. IqJvMd goodsai of i of loodo* A of goodii 
 
 .'. TftlM of A of valBJorod eoods»«1680; 
 
 .'. TAlno of goqdsai^ of $1680 < 
 
 8am roo«iTod»$(84<H-a00) »$1140{ 
 Low«$(M0O-114O)»|6««0. 
 
 7. lBtor«otoatlMpriiieipftIfor4yr.»$(18W.80~1181)»f90i.f»; 
 
 •8861} 
 
 " " •• 5 yr.»i of 8906.80 
 Honoo. the priiieipftl«8( 1181-261) 
 Tho intortol on 8870 for B yr.s«8261 ; 
 
 «8870. 
 
 fl 
 
 II 
 
 100 " l]rr.»8 
 
 100X861 
 
 S. 
 
 870X8 
 Honoo, the nU^6%. 
 
 Voino of the Hnffs»8(50X8.70) 
 2 lb. 3 dwt. 8 gr.»24i ob. ; 
 Volno of the gold»8(24|X18) 
 
 B8487.80. 
 
 '^8430; 
 Oftina82.S0. 
 
 9. 60 men ore to do thd work of 150 men for (40—34) da. 
 Time for ISO menssO da. ; 
 
 II 
 
 II 
 
 60 
 
 — ~QQ~ da.=15da.; 
 
 Renee, the 60 men mnet begin work (34—15) da. after tho 
 eommeneement, or 19 da. 
 

 nOtOMOCXd. PAAC IM. 
 
 I. (•'•iMMtoiaffaflwpiylaf ltiMy4ii^jr-A«f#|flM-it«M« 
 
 8hM« o( im ■! of •MMaHMt 
 ■■■■■ *■ I af MMO-$liW; 
 (kM -|of#M90-$ll00. 
 
 '• IVo* «f kontiaA No. of oittlo't 
 
 " OAttIo -H " " 
 Hot " " -Ml 
 
 /. " " -HofSft-Wt 
 
 Md " l i0 WM» A Of <0»>5. 
 If all hud boon horaoo Um ooot woald lw?o boon •(•0X8) 
 thu IMM, or $8060. 
 
 HoBM, T»lno of 86 hoio>t»t8660| 
 
 I •• .tH|>-l86. 
 8. Ko. of bonlMlo of bftrio y^H* b^i, 
 
 VaIm of 68 lNi.»(68X46)e. »f88.0e. 
 
 Mo. of iNUlMlo of 170»1f* »54; 
 
 ValM of 64 lMi.-*(64X66)e. -089.70. 
 nmMr't fmlBi-O(a8.7O~28.O6)ai790. 
 4. No. of MrM rtpmontod by 4 iq. la.»640; 
 .-. " " " (48X80) iq. ta.-*t^l?^>l^. 
 
 —28040. 
 8' 10 ». S68 oq. rd.-]868 sq. id. ; 
 
 Aroo of 6old, 4 rd.X8 fd.»18 tq. id. ; 
 Tho 6n( 6old la ^ff tinoo m lugo m tho Moond. 
 HoBoo, tho looRth of tho im 6old to »/^fH timoo 4 tods; 
 Mid tho width " " " |/iffi •• 8 rods; 
 (•*«*X4) rd.»(12.478X4) id.s40.90 . . id.; 
 (•MHX8) id.-(:2.476X8) rd.»87.428. . id. 
 
 6. Selling priee»M of eort prieo ; 
 . '. M of ooot prio»f 60e.»i«§ of ooot prioo; 
 
 •*• -fih of eoct prio«ai60e. ; 
 
 .'. eost priee=sW of 50e.s02.50. 
 
 7. Length of wiJl^jf—j ft.=842 ft. ; 
 
 By drawing the figure, it will be seen thi^ 
 ay loiigth+2(length~24 ft.-6 ft.) =842 ft. ; 
 
 I 
 
AKiTmino. 
 
 if 
 
 .'. iMgth -Mragth— 29 ft.»171 fl.; 
 
 .'. 2Xleiigth=(171-|-39) ft.sSOO fl. 
 . .'. lengthsH* ft. slOOft. 
 
 MBd InMdtKs (100-24) ft.»70 ft. 
 
 661 
 
 iV. j^ (of ftittMr't moiw7-$128.S0)»$188.80; 
 
 .M of father'a mon«7-|85|»$128,a0; 
 .*. I of father's moiiey=t214.16|; 
 
 .'. father'* money=| of $214,161 =s|821.2S: 
 or, i of remainder=$128.50; 
 .'. remainder=$192.75; 
 .'. father's mone7=$(192.75+128.50)s|821.25. 
 
 9. Intereet for 1 yr. 9 ido.@6%=} of tIv of notes A^ of note; 
 .'. amount of note=iU of note --=9891.17 ; 
 .'. note=iff of 9391.17. =^$36*. 
 
 10. Wagea for 12 mo.=s8 8heep+9180; 
 7mo.=8ah«e|H-990; 
 5 mo.=$100; 
 1 yr. =V of 9100=9240; 
 Value of 8 aheep=9(24r;-180) ; 
 .-. •• of 1 8heep=9V=97*. 
 
 EXERCISE CCXCII. PAGE 18t. 
 
 i. In 1 day A and B earn ^fe. or 66e. ; 
 AandC " Wc or70o.; 
 BandC " Wo., or76e.; 
 66+70-I-76 
 
 II 
 It 
 
 11 
 II 
 II 
 
 II 
 
 14 
 
 (I 
 
 II 
 
 II 
 
 A, BandC " 
 
 2 
 
 -c, or 106e.; 
 
 41 
 14 
 41 
 
 •• C eama (106— 66)c., or 40o. ; 
 •♦ B " (106-70)c., or 86c.; 
 
 41 
 
 A ♦' (106— 76)o., or 30e. 
 
 g. 5 of hare's leaps=2 of hounds; 
 but the hare takes 4 leaps while the hound takes 2; 
 .'.1 hare's leap is gained erery 2 leaps of the hound; 
 .*. 80 hare's leaps is gained every (80X2) leaps, or 
 of the hound. 
 
 5. A's selling price=HI of eost to A; 
 
 160 leaps 
 
 B's 
 
 =Hlof Hlof oostto A; 
 
 HI of HI of eost to A=93166.60; 
 
 cost to A=m of m of 93166.80=92460. 
 
•oLvnoini. 
 
 4. TlM futor tnin galnt (21—16) mi., or 5 ml. per hr. 
 TlaM to gain (5X1700) yd.* (60X60) Me. ; 
 
 •• " (184+188) yd.-^;g|?£?? .ee.=130* 
 
 6X1760 "^^ 
 
 S, Valoeof hoaaesSiXTslaeof lot; 
 
 .'. 8i TAloe of lot+yalae of lotasfiTSO; 
 
 It 
 
 " =»^«|600. 
 
 6. Sinee M of eoet=8277i; 
 
 .*. m of eoet^W of $2771»8882.80; 
 .-. eoet of 1 ba.=<|fHe. =80e. 
 
 7. Distanoe tnTelled=(|f of 4X5280) ft. ; 
 
 Area ent= (2^X4840X9) Rq. ft.; 
 
 «. Coat of Migar=$(160+13) s8173; 
 
 Cost at 7e.=$140; 
 Differenee from aetaal eoat3=8(i78— 140)=:f38; 
 Eaeh poond bought at lOe. inereasea thia priee by (10— 7)e., orSo. 
 Henee, No. of pounds at lOe.s'V* =1100; 
 
 " " *• •• 7e.=2000~1100=900. 
 
 9. Divide the field in four eqnare fields by dividing the length 
 into 4 equal parts and drawing lines paraUel to the ends through 
 the points of section. 
 
 Then, ana of eaeh square fields'^}^ sq. yd.=8844 sq. yd. ; 
 .*. width of the large field=/(3844) yd. =62 yd. ; 
 .-. length •♦ •• " =(4X62) yd. =248 yd. 
 
 10. L.C.M. of f yd., 1 yd., li yd. and 11 yd.=16 yd. ; 
 .'. width of hall=15 yd.; 
 
 No. of strips I yd. wide=y ==20; 
 
 Length of each 8trip=V yd. =20 yd. ; 
 
 No. of yd. needed= (20X20) yd.=400 yd.; 
 „,, Co8t=$(400X 1.10) =$440. 
 
 EXERCISE CCXail. PAGE 189. 
 
 1. Distanee the train gains in 1 hr. =27 mi. ; 
 
 " " •* » iA 10X27X5280 ^ __' 
 
 ^® *^ 60X60 "-^^ **• J 
 
 Hence, length of train=306 ft. 
 
ABirmmo. 
 
 '• ihoi$iBO»$27t 
 
 Bam to b* dlTlded Meoidiog to eftpitml»#(460->27)af428 • 
 C»plt«l»$(4S0(H-14O0)ai8800 ; 
 A's thansH of 1428 a|829. 
 
 1641* '*' ■"•••"^^ maltlplM of th« dlTlMr »n 1641, lOM. 
 
 The O.C.M. of 1641, lOM, 1641 ud 1641 it 647. 
 fienee, the diyisor Is 547 and the quotient 8288. 
 
 4. The dilTerenee between n gain of 7« and a loas of 17* is 
 'Mr of eoat; 
 
 •'• i%of eoatstl; 
 
 5. Coet of (25 eowB+25 caiTe«)=6(427.75-|-808.60)=t781.25; 
 Coct of 25 ^Teii»$(25X5.75) =$148.75; 
 
 25 eows »6781.25-14S.75) »6687.50; 
 
 «< i< 
 
 " " leow =f"-^ 
 
 =628.50. 
 
 «. When B waa rappoaed to win he ran 1760 yd. whUe A ran 
 1738 yd.; 
 
 Henee, A'g n^ is to B's as 1788 is to 1760? 
 
 But 1760 represents | of B's aetnal rate; 
 
 .M of B's rate=1760; 
 
 .*. B's rate=1820. 
 
 Henee, A's rate is to B's as 1738 is to 1820, or as 70 to 60. 
 
 7. Noiaber A and B eaa dig=68 
 
 It 
 
 AandC 
 BandO 
 
 =66 
 =62 
 
 all togetiber " =98 
 
 L.C.M. of 36, 32, 30, 68, 66, 62 and 08=409036320 
 S. Galn=i% of 64860=$1944; 
 Let what B gets=l share; 
 Then A get8=2 shares; 
 ai^ gets=6 shares; 
 .'. 9shares=i$1944; 
 .'.1 share -$ 216=B's share; 
 and 2 shares=f 482=A'8 " 
 and 6 shares=$1296=C's " 
 
■obUTioxa. 
 
 9, 
 
 My tM«««$(nao-lo«8.75)=$88.25; 
 
 Itote on th* doU«r=S^e.=7*e. =.74*. 
 After ptgriBff tb* tax there remained 92i« of ineome; 
 •*• 100 «' lneome=fl654; 
 
 MO 
 .-. inoome=^ of $1054 =$1680. 
 
 20. Selling priee of let lot^iM of eoet; 
 
 .-. eoet of let lot=itt of gelling priee 
 =* of selling priee. 
 SeUing priee of 2nd lot=i% of eoat ; ^- 
 
 .-. eoet of 2nd lot«W of selling price=| selling priee. 
 Henee, eoet of both lots=(Hi) of selling price 
 
 =11 of selling priee 
 =2iSr times selling priee; 
 .*. log8=iV wiling priee. 
 .' . A of selling priee=$30; ^ 
 
 .-. " " =$300; 
 
 Cost of Ist l6t=H§ of $360=>$800; 
 " 2nd lot=W of $360=$460. 
 
 EXERCISE GCXCIV. PAGE 190. 
 
 1. a016=2X2X2X2X2X3X3X7=2»+2«X3«X7; 
 .-. to beeome a perfect enbe it most be multiplied by 
 
 2X3X7*, or by 294. 
 The enbe root of 2»X2«X8» X7"=2X 2X3X7=84. 
 i. Interest for 3 yr. @ 4*%=^ of principal; 
 " 2i yr. ® 6%=:^ 
 •*. ^ of first snm=:;Mr of second sum. 
 Henee, first sum is to second as 64 is to 46, or as 6 is to 6. 
 Henee, first sam=A of $1650=$900; 
 and second 8am= A of $1660=$760. 
 Selling prices: A5r of cost ; 
 
 Supposed '* •« Lll?! «« 
 
 100 
 • /112i 90 \ , _ 
 
 ••V'ioo~ioa/**'****=^' 
 
 100 
 •••«<«t=^of$46«$200. 
 
 5. 
 
,1 i- 
 
 mw 
 
 s. 
 
 AlITHMinO. 
 
 (.a01)'-(.102)- (^1+ J02) (.8oi-.io2)'=:2orKm 
 
 FUr gains ^ of oost; 
 UhfUr gaiii:s2 os. for every 14 ou. lold 
 ^4ofgooda; 
 Sam rediMd for ♦ of good.»| of m of 00^=,% of ooet ; 
 Totolgfttns^ofeoet »$240; 
 .'.eort==Wof|940 »$400. 
 6. Interest at *« for the given tUne=$(386"330)=|6; 
 • • " 851 '« *• «« SI6XI6 =:M6 
 
 .-. prinolpal " " - =$(336-96) =^. 
 Interest on $240 for 1 yr. at 8*=$19.20: 
 Time for which <19.20 Is lnterest=l yr. ; 
 
 .*. •* " •' Me H «4 _ W ,, 
 
 7^ . *i9:2o**'*y=«y- 
 
 y. Cubic content of sphet.- '— iii' e. in. • 
 
 Area of iron in end of cylinder= r [(6i)«— r"l • 
 Cubic content of eyliuder=8 t [((4) i_,i j . 
 
 .'. (6*)«-r«=6X6; ^ 
 .-. r«=6J. 
 Hence, radius of opening=| in. • 
 
 Thickness of iron=(6i-24) in.=4 in. 
 8. 2 hound's leaps»3 hare's leaps; 
 
 Nnl-Ji *K *!. "f"'^^*'*'''^®*!^^** hare's leaps; 
 Now whUe the hound takes 3 leaps the hare takes 4; 
 Hence, i leap is gained each time the hound takes 3 leaps; 
 
 .'. SOleapsare " ♦« «• <. g^^ ,, 
 
 ^' 8i+5A=13A; 
 
 Time the fire is buming=^ of 24 hr.=9 hr. 
 
 10. Since the time is inversely proportioned to the rate and ti.« 
 supposed time is f of the actual timer 
 
 theait'LJ^U;"' "^ ** « "** ~«»P^ -*« »» *» 1 -ore than 
 
■oLcnom. 
 
 Now, 1 mi. p*r br. iloiror would mbIm Uto rot* 2. 
 
 L.C.M. or8MMl2it6; 
 
 1 br. ia Um differenoe in time to walli 6 ni. ; 
 
 EXERCISE CGXCV. PAOE 1*1 . 
 
 1. ..Selling prieo per gal.=i« of $3.20=13.84. 
 After 20% has leaked away M of a g»l. remain*; 
 .'. flelling priee of M of gal.--|3.84; 
 ••• * lg*i. =W of 18.84=14.80. 
 
 '' 1ft of $2700=$27; 
 
 Interest on $(227S-f 2700) at lower rate=f (425— 27) ; 
 
 .-. interest on $100 at lower rate=f^^|^=$8; 
 
 .'. lower rate=8%; 
 and bigber rate«0%. 
 S. m of eost of Ist kind=:45e. ; 
 
 • " " " =mof45e.=36e. 
 
 " '♦2n4" =42e.; 
 
 " •' •• •• =H«of42o.=30c. 
 
 TOT 
 
 . ^ 36+30 
 
 Average eo8t= — s^o. 
 
 Gain on 33e.ssl0i«. ; 
 
 =33o. 
 
 .-. gain per eent.=i5^^=3lA. 
 
 ^- M of I of value of wbeat=|44.07; 
 
 II II __^600X4X44.07 
 
 . . =^e- ; 
 
 12X3 ♦ 
 
 5. A reeeived ff of tbe votes; B received H ; 
 .'. -A ot number of votes=124; 
 
 ••. " •• =24X124=2976. 
 
 No. wbo did not vote=3200— 2976=224. 
 
 6. L.C.M. of 4and7=28; 
 
 In 28X V ft., one wbeel turns 3 times more tban tbe otber. 
 
 Distance to turn 3 times more=88 ft. ; 
 .*. " "180 " "=60X88 ft.; 
 
 .'. rate per minute=60X88 ft.; 
 .'. " " bour =60X60X88 fft=60 mi. 
 
100 
 
 ▲BiniMITIO. 
 
 7. Time for 1 nwa to do Um work»10 tiuM tho tlao: 
 
 . ,«.. . »7tiin««tbttliiiOMid49d«.x 
 
 .-. 10 tlm- to. M«o -7tln.e.UwtI«.«d4»d. 
 
 .-. Itlme •• •• .. - u «V a«'.Ll6i d«. 
 Or, 7 mon-f-S men do 1 work In 1 time; 
 /. 7 men do A work in 1 Ume; 
 
 .*. 7 men do A work in 7 deyi; 
 
 .*. 10 men de 4i wnk i» V<}^7 , ,^ ^ 
 
 •• tf wort In -jQjjjji- d»., or 16t dn. 
 
 *. Area of perk witUn the elienmferenee of path 
 
 ^^ -(Vxi4»*)«,.3rd.j 
 
 P^ -(Vxi45«)«i.yd.; 
 
 Area of path»Vx(14»«-146«) iq. yd. 
 
 QuMtity of graTel«(AxVX294X4) o.yd. 
 
 9. In 1 da. A doe* i\ of the work; B, A; and C A 
 
 Work done by B in 1* da.-(Ux A) of work^i of work; 
 
 Henoe, if B and C worked ae long ai A, they wonld do 
 (H-*-l-A)ofwork; 
 Time todo (A+A+A) of work«l da.; 
 
 " (1+H-A) " -r±^.^ 
 20. Let D'e ehare^i share; ""•"""♦^ 
 C'i •• =i««hare; 
 B'« •• «HlofiH«li«re; 
 A'e " =iMofi«ofm8hare; 
 Henee (l+IM+iH of m+i«of H«of i|||) dm,e«W699.16; 
 or, imi 8hare-92e09.16; »«w.io, 
 
 .M >hare=H«fl of $2699.16»f600 =:D's share • 
 iM of |800=M630 ssC's " * 
 HI of fe80=:$e83 =B's « 
 Hf of $6e3=$776.16»A'8 " 
 EXERCISE CCXCVI. PAGE 192. 
 1. Let quantity raised the second yr.=l share: 
 ^^ " " " first yr.«« •' 
 
 .-. " " bothyr.=« " =3105 ba.; 
 
 _ . • •'• 1 •iMtfossilofSlOSbu. »1850bo • 
 
 <Juantity raised more the first yr.=AJ»of 1380bu.«406bn. * ' 
 
 =6Ada. 
 
•OLCnOMS. 
 
 IM 
 
 
 f . Ares of wallss^U* iq. jd.»ll2 iq. yd.atlOOS tq. ft. ; 
 Let heigbtsi height} 
 brMdthsii 
 leiigthss2 
 
 periinet«raK(4+8) heii^tsas? heights; 
 Area of w»Us3s[7X (No. of niiito of height)'] iq. ft. 
 
 =1008 aq. ft.; 
 .'. (No. of onita of height) "=144; 
 No. of unite of height=12. 
 Henee, heights 12 ft.; breadth=18 ft.; Iength=24 ft. 
 
 5. 62i Ib.srl ea. ft. of water; 
 
 7.112X621 lb.=l en. ft. of iron; 
 1 
 
 .*. 2000 lb.= - noyftoi '**' '' ^^ irons=4.5 en. ft. nearly. 
 
 4. Snm reeeired from $5000 8toelc=MJI^ of $110=$SS00; 
 •• •• •• $7600 '• =W?of $115=$8740; 
 
 14240x41 
 Ineome from $(6600+8740) =$=2=2^^=$720; 
 
 Original ineome from $5000 8toelc=$250; 
 " •• •• $7800 " =$456; 
 
 Gain in ineome=$72a-$(250+4S6)=$14. 
 
 6. Buying priee per orange={e. ; 
 Selling " " ♦• =fj.; 
 
 Gain •• *• =(l-|)o.=Ac.; 
 No. of oranges to gain i/be.=l: 
 
 4t 
 
 „ u 12000= ^^^,^^^ =8000. 
 
 6. Value of 1 lb. golfl=£46 14s. 6d.; 
 
 Value of 18 lb. gold+18 lb. silver=£896 8s. ; 
 
 Value of 18 lb. gold=£841 Is. ; 
 
 .*. Talue of 18 lb. silyer=£56 7s. ; 
 
 .-. " " los. " =5ts. 
 
 Value of 18 lb. of gold=Je841 Is. ; 
 
 Value of 18 lb. of mixture= £637 78. ; 
 
 £203 14s. 
 
 Each pound of silver reduces the value by £46 148. 6d.— £3 Is. 6d. 
 
 M . J - ,, £203 14s. ^, 
 
 No. of pounds of Bilver= ^^ .- — =4f ; 
 
 No. of pounds of gold=18— 4| =13i. 
 
IM 
 
 r. 
 
 HfoffMtl-ilHMal; 
 
 «i of (1-l-A) •ort-Hil ad; 
 MllaffprkM-IHIaotl; 
 
 O^^tt-AA o ort »m 7; 
 
 . . tiiM to row M ml. «p and Uek-tlmo to row 80 ml. down • 
 .-. rate of rowing down=H ml. per hr. 
 _, ^ =»|ml. perhr.; 
 
 Tl«etoi«w80mI.down=tlnietoiowl8B,|.BD- 
 
 . . M-e to row 80 «i. down nnd b-k-tlme to «w 48 ^i Z' 
 
 .-. rate of rowing np»H mi. per lir. * 
 
 B.t. i. ^m wi^r+mte ,f .tra^n^Jfti.'^^r'i;:; 
 
 ** '"4 mi. perlir.; 
 ..ax rateof •treuB^Sl mi. per lir.i 
 ••• " " -U -I. perhr. 
 JUtt the time pMt 8 p.m. i. repr-ented by 4; 
 
 VVi.- *• V ^ •• "• '^"^ ** rapreeented by 1; 
 
 ^the time between 8 p.m. and 1 a.m. will be repreiented by 8- 
 
 The time between 8 p.m. and 1 a.m. la 10 hr. '^^"*** "^ ^' 
 
 If 8repreaent> lOhr.; 
 
 • *. 1 will repreaent 8 hr. ao mir 
 
 Henee. the time 1. 8 hr. 20 min. pat 1 a.m., or 4 hr. 20 min. a.». 
 10. Sinee the width la | of the length; 
 
 • •• I of area»| of I a. =* a • 
 
 f a.-ia.=100«q. rd.; * 
 
 Width=(^100) rd. =10 rf . 
 
 Length=| of 10 id. =12 fd ' ' 
 
 Mwt- (484X40)0. =$217.80. 
 
 EXER 'ISE CCXCVII. PAGE 193. 
 
 '. 2X(No. of nuita of 8!de)*»48* =2804- 
 .-.( " " " )'=^=1162; 
 
 ■=1152 aq. ft. 
 
•OUJTKMm. 
 
 IM 
 
 f. 8«lliaff priM of th* lMj«$(1000X90) »|10000{ 
 
 /. •oaBilMiM-$[90M»-(188tM'9ra)]«|t00| 
 CommtMloB on $20000»#MO) 
 *' " $100«H| 
 
 S, WiiMrMnaliilBgaftortlMli(dmwiiiff(rf|3>|of OMk; 
 
 ♦• fad " " MoflofoMk; 
 *' " " 8rd " " »lof|of|ofe««li; 
 
 " *• " 4th " " -loflofloffofeMk 
 
 «M of OMk. 
 
 4. Lot the nnmber of vnita of thlekneMacthieknoM; 
 thon " «• " holffht^5X thlekaoMi 
 
 " " length»40XthlekiiOM; 
 
 .'. enbie eontont of waU=400x (thleknooi)* 
 
 B62S680A «• in. ; 
 .'. (thieknen)*a:e2668OA-^300 
 »8128.100880e25; 
 .'. thieknoMsf (8138.160890025) in. 
 sl4.e25 In. 
 
 II 
 
 5. 25.i85X13Aa25Ayi8A« 
 
 30X410 
 
 61.875XSH»61fX5if » 
 
 87 
 401X28 
 
 80X410 401X26^ 
 
 37 
 
 87 
 
 ^^=» 
 
 87 
 ^.075 
 
 6. 2 lb. of standard gold =1800$.; 
 
 .M " " •• =984.6«.; 
 
 .M " p«e " =rH of OT4.5«.«AJrtUg. 
 
 1 lb. of standard sUrersOOs.; 
 .M •• pnre ** =|f of 60s.s=*H^. J 
 
 .'. 1 lb. of gold : 1 lb. of sUrer : : HV^ : H^, or as 14.288 : 1. 
 
 112i 
 
 7. 
 
 100 
 
 of eoet priees4Se. ; 
 
 <i 
 
 i< 
 
 =40o.; 
 
 Cost of 1500 Ib.s (1500X40)0. =0600; 
 
 Soiling priee=s|it of 0600 =$730; 
 
 Bom sow >«aliBeds(800X45)e. =01%; 
 
 •• tobe *• =0(730-185) =0586; 
 
 SeUing priee per Ih.^^fUlfo. »48ie. 
 
IM 
 
 4ll«f««Ml-HlefMtl| 
 
 .*. (UHilH-^^M) or MM-isoot 
 
 .'. Mtt of SM Jdi.-HN of UMi 
 .'.ooitof 1 7d. -lit of HN of HOCN-iH. 
 
 ». LoBglh of tido of wioMO ioM-i |/ (40X IM) i«.*iO id. | 
 PorhMtor of ■qwMro flok|M(4}(M) rd. >S90 id. 
 BiMdth of iMtonffolar UU»^^^ rd. .7U id. | 
 
 P»rim«twof " •• -89Hid.; 
 
 DUroroiMO in Imgth of foiMM»9| id. : 
 
 " •• eort " " -•(Hx8l)e.-«.i0. 
 
 i0. IneooM fiom $1000 in 8ft ttoeliMflO; 
 
 " " now inTostmont »$40t 
 
 •'• tIi of now •took»f40; 
 
 .-.«•• " -1500. 
 
 Bom inrottod in 1000 " »M of OlOOO«M0Oz 
 
 .*. prieo of now stoekBlOQ. 
 
 EXERCISE CCXCVni. PAOE ItS. 
 
 /. 27 •. 48 tq. nl.»4888 m|. id. j 
 
 Toking A of 4868 aq Id. away will looro oflold oonal to » nnoio • 
 H of 4368 iq id.:.2704 aq. id. ; ^ ' 
 
 8ideofiqnMoflold»^2704id. »58id.: 
 
 Widthof flold»58id.i 
 Length '• »ftof6Sid. »84id.; 
 
 Perimeter " » (2X84-1-2X62) rd.«272 id. 
 f . Cost of 818800 etoek % 75^113735. 
 Interest on $18726 d 8%s8iooe ; 
 Total ootlnya814823; 
 Income from 818800 stoek ® 8%=s8649; 
 
 Netoatln73s814274; 
 Sum reeeired for $18800 8toeks$(i4274— 122) ; 
 .'. Belling priee of ■toeks>HII'B77|. 
 S, It is evident that lOo., the dlffeMnee between the two prices, 
 mnst be divided into two parts proportional to 20e. and SOe. 
 Smaller part=| of lOe. s«4e. ; • 
 Belling priee»(20-H)e.«24e. 
 
WlMI MH (IN-M)t. It toM for «•. { 
 
 .'. IOMOB0Otaiat.| 
 
 t MM pnr •Mil*^4> 
 
 4. IM b«lglrt«mMbtr of ■aito of bolgMi 
 Moabor of mMo of orto la ouo rido»IOtt 
 " " " . " •• oad-lltt 
 Nambor of aalto of l^i^f^^^g^it 
 
 " " " •* »««<«»-sS5i» 
 408 y 111 _„, 
 
 CiSi fc»ifii»"°J|' 
 
 .-. (liolilit)»-^^l?| 
 
 .'. holffht-lt; 
 , Loogth-W-Mt 
 
 I Bfoodth-iW-W. 
 
 TiaM for tbo int to go 8 nl.^l hr. 
 
 I. 
 
 i< 
 
 II 
 
 <i 
 
 II 
 
 19 ml.' 
 
 18 
 
 -af hr.; 
 
 Ttmo for hla to oonploto tho Joam«7«*(2H-i) hr. »^ hr. ; 
 DiBUiwo tho Mooad goot ia 8A hr.«» (8^X84) ni.-lOl nl. ; 
 " " " haa yot to go»(lS~10|) ail.»4| mi. • 
 
 «• 6a.a.(6X48SeO)Mi. ft.; 
 
 Qaaatitj of ieo» (6X486eOXi) ea. ft. ; 
 Weight of 1 ea. ft. of wat«r«1000 os. ; 
 Weight of (6X4850OXi) ea. ft. of iee^A of 6X43560XiX1000 os. 
 
 »8e75|t. 
 7. Hlof4eoet=>|U«oet; 
 Hlofi " »H| ♦• 
 i%ofH" ^^H*' 
 
 Bum neeiTed» (H+H+HI) eoet=Ui eoet ; 
 Net gaio»M eoet =$15.40; 
 
 •*• eootiSKg 
 
 .fiiOX 15.40 
 
 82 
 
 -$441. 
 
 8. A'e age ; B'e age : : 9 : 5; 
 
 .'. A'e ages| o: B'e ago; 
 Bat A'e age— 28 : B'a age— 28 t: 10 : 8; 
 
 .'. A'a age— 88aV of (B'e age— 28) ; 
 
f • 
 
 .'. (V-f ) of B*t agv^Ttl-ii, 
 
 .'. B'oag»«MorMI»aBt 
 udA'aaft^ferw »«. 
 
 1)1 
 
 1 •• ^¥M gr. I 
 
 .•.MMgr.-(4O0OXM)iqia., 
 Bbw of lMTM«^J!^^«ae7. 
 
 
 w. 
 
 s 
 
 4 
 .'.6 
 
 Mld» 
 
 II 
 
 15 bojra «k4 9 Btn-ST boji; 
 
 bogn Mid 16 wmbm-M bognt 
 
 i» 4 womra aad 8 boy» -i96bera; 
 
 16 
 
 II 
 
 II 
 
 ThM for 96 bogn to do>l work 
 ." 76 " "• 1 •• 
 
 18 
 
 II 
 
 <i 
 
 76 
 
 II 
 
 II 
 
 II 
 
 -i76 
 
 -lfiOdft.1 
 
 _ 88X160 ^. 
 
 _9xa6X16p. 
 78 •• 
 ■104 dft. 
 
 I. 
 
 EXCRCISe CCXCIX. P^ME 194. 
 
 BlBM « elr.-MtMi.«60 fk. md tbt eir.^^XdiMi.t 
 
 Aioa of •0BiielNl««.(4 of ¥x VxV) oq. fl. 
 
 <«818|tq. f|.{ 
 .*. No. of plute3s218. 
 
 A't Mlling pri««»)% of «o«t; 
 
 ;'• " " «MofMofoo.l{ 
 
 . Ul-^JSI'^*^ " -Hlof^VofMof•ort, 
 • • m of M of iVk of eoota$8786.76; 
 
 .-. eort=rtt| of W of W of I8786.76==64600. 
 R^down 8tmm per hr.=4i ml.+mte of .trMun; 
 
 f. 
 
 9, 
 
 np 
 
 II 
 
 =4i ml.— nte of akraain; 
 
 . . 4* mt.+r»te of streuB«=8 (4i ml.-mto of •Itwub) i 
 
 '*. 4Xroto of slresmssd tti. . 
 
 .*. nito of titntm^U mi. 
 
4, TiM iMBlitf af Mwk ktad mmI b9 hifttwiy piopoffltoMl to 
 Ik* priM*, <.«., to 4I». Md fOt., or M 4 to ii 
 QMuMlf al Mi.-I of IM lk.«lM lb. t 
 ** «i.«| of IM ».« M lb. 
 
 I* 
 
 Ooil of ooflM por lb.«%VVe. -Ko. ; 
 ** oUooiT " -i^WN. -lOt.i 
 51b. oUoer]r«lte.««to.| 
 71b. ooflM«Mo.-IMt.t 
 Coot of IS lb. of mlxtvro>illo.) 
 
 .-.of lib. " -Wo. -Mo. I 
 BoUlag prioo-i of Mo.««to. 
 
 Mof 
 
 • II 
 
 II 
 
 J00X85M 
 
 7. 8«B roool?o4 by orodHon-^ Of 16000-ltlMt 
 
 100 
 
 II 
 
 *• 
 
 II 
 
 I* 
 
 
 u 
 
 oai 
 
 rji of ♦ OOli— iH OOllj 
 
 .'. (MHitt) ooH-OSlSSt 
 
 .100X0190 
 
 #. Wolght of 1 •«. ft of lroii-(7.402X02.5) lb. ; 
 
 Wolght of 1 oo. ft. of eodor— ao lb. ; 
 
 SO 
 .'. Iron weighoj- ^ — - oi m oqnol bolk 9i eodor; 
 
 TbioknoM of oodorof ooortola wt.—O In. ; 
 
 iron of MHno wt. ^s-nJrr=r-. of in.».8S4 . . In. 
 
 7.402X02.6 
 
 9, Edgo of enbosf (11800025) In.»225 In.; 
 
 Length of diagon»l3B2S5 (|/8) In. ; 
 Diifertnoe In longtba»225 ( y'S— 1) in. a:i64.7114 . . In. 
 
 10. 
 
 A's loM»H of 2000 
 
 =0800 J 
 
 A't eoplt«l—0(10000— 800) s«9200; 
 B'B loaaaif of 0»)80 =^01»0 ; 
 
 B's eoplto]aBt( 10000— 1280) 
 0(0a0O+1472OX 18000) »041020 ; 
 
 »0147S0: 
 
M 
 
 ill 
 
 108 
 
 AtlTBHXTIO. 
 
 •(»200+14720+18000)«$41M0; '~'^'*^^' 
 A'i ihAres^MM of 14716 »$1086: 
 B'« •• -if««f#l716=$lW 
 C'i " -ttHlo«$47ie«Is8S. 
 
 PAOE Its. 
 
 EMEROSECCC. 
 
 \H of eo«ts:$4.32; 
 
 •••«ort=tMof$4.82=»f; 
 WIn«tW«»,dfor|S#giUB.tf,or#H, 
 
 wJ JliTlf'' '^'Jf *" •"** ^"^ •*>»•' « •*»«• •* « muit b. mixed 
 with W do., .t $»|, or 2 do., most bo mixed witli 5 do,. 
 
 K./' ®^,^^';'^°« *>»• *ri«»«le it will bo *on that the uele 
 botwMD the hMid. ii 46*. ■ *«» we ugie 
 
 ^P^ mo^be^X""^ •'^ ^"^'^^ ^' ^^"> -^-*- 
 Time to g^ 12J minute.n««a.=(mxH) min.«18A «.!«.; 
 27i " =(27iXH) mlii.«80 min. 
 
 «. fl«ningpriee=iWfcofeort; 
 
 Sappoeed eortsVil^ •• 
 ^VP«>»d waning prUi^:^^^ " +W8; 
 •*• Hi of -fi^ of eoirtss-Alk ♦• "f $18* 
 •'• (f— VWr) of eort«:$i8; 
 
 . . eort=» j^ - g fio. 
 <• A eoet of $0 giT*,a . width of 1 yd. ; 
 
 145 
 
 45X1 
 
 S. 
 
 IneroMod eoet due to 4 
 
 ■g— yd., or 5 yd. 
 Cort of 11 lb. @ 88c.=968o. : 
 
 ooet of 11 lb. of 
 
 4< 
 
 lb. of better kind» 88e. 
 poorer *' =880c. 
 
 1 lb. of " 
 
 (I 
 
 = 80e. 
 
 1 lb. of better " =(8<H-22)e.=102c. 
 rh of cost of l«t=,yj, of eott of 2nd ; 
 .*. cost of l»t=| of e^st of 2nd; 
 
•OLUTMnft. 
 
 •'•lofMttof 
 
 ted-feoit of 2iid*|0880; 
 
 ;; " ^Iof|6800»t9000; 
 Itt^l of f9600»$8280. 
 
 y. 8«»<rf*«-*(a^);«,.fl.+(23»)«.,.f»., 
 
 Lwigth of .lde«K'"W^ fl.«*Hi ft.«:28»tt ft. 
 
 *. Tho L.C.M. of ISSO and 350»:6e50* 
 Time for 176 non and 340 bojs^isao* 
 
 Hone. 86 men and 48 bojni=W mon and ^H* boy.. 
 
 . . W6 men and 912 boys»808 mon and 1006 boya- 
 
 /. 63 man =98 boys; ' 
 
 „ ^ , or2mon=r8boy8. 
 
 Henee a nan's work : boy's work : : 8 : 8. 
 
 *• ^ Areaof roomaslBsq. yd.} 
 
 A-aial«o.tofeari)etandoll.eIoth=|90.60: =^"^«»» 
 
 K-ek yard Of ^^^-^^^-^--thopH^^ (340-96)c.. orby 144c.; 
 
 Area of oil-eloth* W» tq. yd. =181 «,.yd. 
 
 T ^u - .'^*^'*'***^*^*8|)sq.yd.=80*M.yd 
 I*»«tb of ride of oarpet^C^ao*) yd ^^^ . ' 
 
 WMtb of ol|.eIoth=:?t=15* tt. 
 
 >2ift. 
 
 W. 
 
 <i 
 
 A'B profit for 6 mo.:=K1200— 960)«#840' 
 ' * " " IS mo.s$480* ' 
 
 ' ■ ^'' S^t ST* !!?** •* '"^ ^' " i«o.=$(96(H^80) =$1440. 
 Stock to prodaee fl440 in 12 mo.s«06O; 
 
 •2440 in 12 ^tr -i^^^ 
 1440 
 
 =$1600 «B's stock. 
 
 C's proflt=$(1040— 640)=i400 
 Time for $1600 to gain $800=12 mo.; \ 
 
 ^^^ 1600X400X12 
 M0X800 
 =16 mo. 
 
 <i 
 
 14 
 
 $640 
 
 (I 
 
 mo. 
 
11* 
 
 EXEROSE CCa. PAOC Itt. 
 
 i. If Um tmla pMwt 1 poi* per mlnat* the tni* tpMd per hr. 
 
 Approzlnwte ■peed«:2 ml. ; 
 
 •*• e rror** n Bi* 
 
 Now, lAr ml. is A of II mi. 
 
 «. 80X*e.«26o.; |8-26e.«f7.78; 
 Cortolllb. ofB's=We. «»H«.i 
 
 " " " A'r=(J»H+i)e. -lOAe.} 
 
 A'« ■h«re=(50X10A)o.=:$6.(»f} 
 
 B'l •* =(80X»H)e. =#2.901. 
 
 5. Interest on $1800 for 1 yr. @ 8|«a$45.0O; 
 
 Total inlereet for 12 ino.a:$i35. 
 Time for wliioh fl86*4e inierestsl2 mo. ; 
 
 112.50X12 
 
 14 
 
 $112.50 " »i 
 
 135 
 
 4. Diameter of plate^i/fe'-f 8') in.»10 in. 
 i' HI of I eo«t»ii| eoct; 
 
 HI of I eoetarfH eort; 
 .'. HI eo«t»||| eoet~|21; 
 .'. ilveoctB921; 
 
 .-. eoet»^of 121; 
 and eost of I 7(l.»ii« of *|« of |21=|8. 
 
 6. Net ineomeas^ of tIv of 8toek=$il40; 
 
 8toek=W of ^ of $1140=:r$40000: 
 CkMt of $40000 stoe]E»$36000; 
 •. •• $100 " »$HII' =190. 
 
 7. f^ dene bgr Junes in l lir.si| ef I =^; 
 John " lhr.=iof|of 1=1; 
 Charles " 1 hr.=:| of A =*; 
 
 mo.=10 mo. 
 
 (I 
 «« 
 
 u 
 
 . <« 
 
 << 
 
 all 
 
 1 hr.=/ 
 
 V. 
 
 41 
 
 8. 
 
 Time to do A of work=l hr. 
 '' all the " =3hr. 
 6X 7=85 
 8X11=33 
 2X13=^ 
 M 
 
■OLunom. Ill 
 
 Wciglit of in iMt»la|| of 1410 lb.»625 lb. ; 
 ;; "and •• -«ofl410 1b.«4«Hb.; 
 •• "8fd " =« of 1410 lb.«8W lb. 
 
 9' \h of 1st aamsTiv of 2ndaA of 3rds^ of 4th; 
 
 .'. Irt rams: I of 2Bd»2X8nl »8x4tli; 
 .'. 1st sui-H of lst,Xi of lst,+» of Ist^lSeOO; 
 
 .'. 1st smn-f of $S600a02100; 
 2iid " =|of $2100«$1760; 
 8nl " siof$2IOO»$1050; 
 4tli " «i of f2100s$700. 
 
 ^0. TimeAnmslmi.«^^„|„.«4|».in.r^ 
 
 Dittuee B runs after 4 inin.»(638e0— 4X800X44) in. 
 
 »10060in.; 
 
 'Irnln.; 
 
 1. 
 
 Time to ran 10660 in.^s—??; min. 
 
 820X44 
 
 Time for B to ran » mile=s4f min. ; 
 .-. B wins by t(4f-4|)X 270X48] in. =80 yd. 
 
 EXERCISE CCai. PAOE 197. 
 
 Afe» of tri«i«le»/(48X25XlBX4) sq. ft. 
 ^^801 .908876 so ft 
 Are* of eqoiUteral trianglea(i6xi0X |/8) sq. ft. ; 
 
 »448.404..^. ft.; 
 Diflerenee of nreaBi4i.4 . . sq. ft. 
 
 t. A*» shsre=A <tf D's; 
 
 C's " =AofA's«Aof AofD's«rl«o«D's: 
 B'« •• =(A+Tfe)ofD's=TWrofD's; 
 •*• (A+M+Tfr+ilf) of D's 8baro=03660; 
 .*. D's sbMre=if| of $3060=$2000; 
 A's ♦' =A of 02000 -1600; 
 B's " -Ail of 02000=0780; 
 C's " =Tfc of 02000=0180. 
 
 S. HeUing price of first lot=01876+^ of selling price; 
 
 •' =01876; 
 
 ** =H of 01875 =02000; 
 .'. price of seeond Iot=iU of 01200=01296. 
 
 ioo**' 
 
 (< 
 
 i< 
 
lU 
 
 riff 
 
 ' 1 " Mi 
 
 '\ ^ 
 
 ABimnmo. 
 
 /. iBtofMKmlSMOOforljrr. alift-flTOi 
 
 .'.ttMliilMMtoa$(84000+14000) forl7r.«tlow«rnl»«iin0{ 
 
 " "WOO «• ly,.«« «« 41 a.^iy|Hp.|4j 
 
 #. 
 
 C<Ml priee of tlM mbttara»HI of 06e. »56e.} 
 PriM of i lb. of tum(2XM)o. nllOo. : 
 Prieo of 1 lb. of bottor kind* (110-60) 6.»«0«. 
 
 9. 
 
 $. No. of dftji' work for 1 mwi»MXNo. of men: 
 
 " 1 •'-iex(No.ofiD«,+ie), 
 
 .'. 94XNo. of mensiexNo. of iiMa+266; 
 •'. 8XNo. of iii«BaB286; 
 .*. No. of m«Da82. 
 
 7. WhonBtastthetowii, AI.*oftliow»yt|i6fo. 
 Distuoo A goM in 70 min.»(if X8) ml. aSi mi. 
 Bnl B BMOte A I of 12 mi^ from tho town; 
 
 .-. tho di»teiMe=i of tho ditton«o+(8H-8) mi • 
 .M of the diataneoKlli mi. ; ' 
 
 .-. tbo dirtuMeasI of 11* mi. si5| mi. 
 
 S. C^ityrt6iidof4tiiyr.«H*of$8880.28«|91808.26: 
 Henee, HofHofHofHof origi«a eapital»80l506 25> 
 
 .•.origlimloi^,ltia«:*|Hfof|91506.26«882600*. * 
 areamferoneo of dUas(2X9XV) ft.; 
 .-. No. of min. .•!»•«. in 11 ft.«j-JL^ «f eo min..| 
 
 =1U min.-BpMeo; 
 Honee, the time is 11| min. pMt 18. 
 
 10. (1) Interest on $120 for 1 time 3b|S; 
 •• •• $120 •♦ 2 time>»$10; 
 .*. diaeoontonflSO " 2 " =b$10; 
 
 " •• $125 " 2 " - t^26X10 , 
 
 ' 130 ""*"• 
 (2) Interest fori time=A of prineipnl; 
 
 .*. unoant for 1 " s|f « ** 
 
 .*. " " 2time8=(tt)«ofprincipiU 
 
 ={fi of principal; 
 .'. interest for ,2 times=iA'b " * •* 
 .-. diseoant for 2 times on m of prineip*l=M ot prineipal; 
 .*. diseonnt for 2 times on 8126ss8(125xM)»|^. 
 
PART III. 
 
 SugflcstkNis for TeachliHi Artthmelic. 
 
 I. NUMBER WORK. 
 
 IM tiM pupils OM •plinto, p«bblM, muMon with ralM, tie. 
 M. Wwrt i n ftwa l.t«. 
 
 (2) detoite loaMuw., and (8) namber-pietam, snd h^TSi 
 pupili iMin tli« qmbol (flgai«) for mmIi. 
 
 TIw following it ..,-,:erted M bliwkboMd ■ammafy: 
 
 • = laone. 
 
 tf^'sis. 
 
 • »' 2»two. 
 
 7a«S0T«n. 
 
 4jBsfour. 
 
 ^=8 8»oigiift. 
 
 #•#* 6=«Te. 
 
 -lO»t0a. 
 
 Hon.— Only «m fom of aomlMr-BtBtan -*-— " h. ■ - .^ ». * .^ 
 
 ^il^Ll^^ ^ ^ °' ■^*''*» "* «ibln««oii in eonnection 
 withewh number and intwduee the .ynibol. of openrtion + «.d - 
 Th«>, by obJeetB m splints, definite messures as 1 in.. 1 ft 
 etc., and by nmnber-pietures teach that ' 
 
 6+1=6. 6_5==1. 
 
 1+5=6. e_i^5 
 
 4+2=6. e_4=,2. 
 
 2+4=6. 6-2=4. 
 
 S+3=:6. 6—3=8, 
 
 If though* preferable begin with 3+3=6, ete. 
 
114 
 
 ABlmraTio. 
 
 NofMt.h<mld b« nrmUAk oiitU Um popUt Iuit* pMtoni«Kl 
 »h« op*nkioiu bj eMsUBff, MMMrittg, vie. V 
 
 TbM* teeto wiU b. flxM bj brM, f«pMt«d drill. (•) with ob- 
 J«eto, (ft) without objMts, («) h»Tlaf papils fw. pioWwn.. (4) 
 harlng paplb worii probtont. f . \-; 
 
 <Wri«i «itU th. toU !»• • •iMt.l kii»whiHi of wmbm to m 
 MoR.>(S) Tfc.piiplto»airb.«»ieto«dtaB»kliif MdadTiattwh. 
 
 4+2- J 4+f-6. f+2-6. 
 
 8-l«t 8-f«2. f-i=B2. 
 
 8+8=1 8+r«6. f+8«6. 
 
 6-2«f 6-f«:8. f-8»3. 
 
 IN. The W «iwt M« Irmm 1140L 
 
 (a) AnalyMthwe number. M in rtepn., the work b«lng eon- 
 lined to the faot. of addition and rabtrMUon ud one of the part, 
 being alway. 10. Thu., *^ 
 
 17»l(H-7=10+4+8=^14+8-10+8+4«18+4, ete. 
 (ft) The number, from 1-20 .honid now be meaenred by .oeh 
 unit. M 2, 8, 4, ete., and .ueh question, anawered, a. how many 
 time. ? inehes make 8 inehesf How many two. make 8f ete, 
 ■ IV. The W.mft u. frmm Zt-im. 
 
 By u.ii« number-pieture., definite meaeure., ete., thoM num- 
 
 5!2t'^tJ"'thu° *" ""* ^^''^''"' *^' *•"• **^°« "•'""y 
 
 87-80+7=20+17=10+104.10+7, ete. 
 
 Kow-No attoMH AooM b. Bud. to b«iA th. nambw »p tatoiBch pMU M 
 87=l»+18=16+21=13+24, ete. 
 
 II. ARABIC NOTATION AND NUMERATION. 
 I. The IMIa. 
 
 A. the number, from 1 to 9 are dereloped their .ymbol. are 
 giren and pupils learn to associate eaeh number with its symbol. 
 U. The Tens. 
 
 Have bundles of ten and single splints. 
 
 Hare pupils represent 1 splint, thus, 1. 
 
 Have pupils represent 1 bundle of ten, thus, 1. 
 
 How is the 1 lepreMuting 1 splint to be distin^shed from the 
 1 representing 1 bundle? 
 
•VOOimoXS fOB TIAOBUia. 115 
 
 The feMohtr explAin. tha this is don* by th« potition of th« V, 
 Th. 1 ftpmenting 1 bundU of toni. aiw.y. pii«^ to th. lofi oi 
 *fc« 1 ropraooBtlng 1 splint. •« •« wk oi 
 
 s^ ;'h?^ii "^^^ •".• *~"*' ^' *•" »* '•p'^"*^ ^ -how 
 
 thrnl te a bandl. of ton ud not » lingl. iplintr 
 
 Th. tMeh.r will that b. ab). to .how th. lu. of is to gir. 
 po.iUon to th. signillMnt flgnras. 
 
 Contina. to 100, m 80, 40, 60, 60, 70, 80, .te. ^ 
 
 m. CmuMm m. T«M 
 
 Thus, 26, 27, 34, 89, 47, .te. 
 
 IV. 
 
 (a) Using bondlM of ton-tens, show, in » similar way, that 
 1, -, 3, 4, etc., in th. 3rd plaee rsprsMOt hnndrmls. 
 
 (4) Combine hundrods, tsns and units together and giv. sueh 
 drill as will .nable pipils to write and read with readiness any 
 number expressed by three figures. 
 
 V. 
 
 (a) In a similar way teaeh the thousands' plaee and havemueh 
 praetiee in reading and writing numbers expressed by four figures. 
 
 (ft) Introdnee the fifth plaee, give its name, and, as before, 
 glre raneh praetiee in reading and writing numbers of five figures! 
 
 (e) Introduce the eomptete period and give praetiee in readinir 
 and writing it as before. 
 
 id) Teach the meaning of period and how many places con- 
 stitute a period. Show iaat in the two periods that haye been 
 taught that unite, tens, and hundreds occupy the same relatiye 
 positions. 
 
 HOTS.-T11. Int pariod It the unite' period , tbe .«eond one. the thouMndi' Ae. 
 The flnt period i. nerer to be eslled the hundred,- period as wme tether. a<L 
 
 VI. Lm«e Nambcrs. 
 
 (•) Teach the millions' period by giving its name and drUling 
 in reading and writing numbers of 7, 8 and 9 figures. 
 
 (ft) Continue thus giving the names and periods in order and 
 having much drill. 
 
1W flrttowlaff 4girlM of BoMMMtMa 
 M » bsMw MMM of iainmBliif 
 
 M tH thU OMtMi ft 
 
 MdNMbHtto 
 
 tlMl MMh «Hfftt bM In* 
 
 Mi 
 
 
 Th» naaU rate rapiMrato 1 mitt} the ttoT* !• 1 tm: Um nliito 
 Is 1 handnd; and the Iwga onb«, 1 thoiuMid. ^^ 
 
 A huidjr toMlMr ran biaIi* Umm for hlmielf . Then ahoald bo 
 •tloo«»l»oo«hofthoimidlrab6o,itoTOi,oiidplMoi. Itlolobo 
 ■■od in » •imUar UMuior to tho spUnto, bmidloo of ton, eto. 
 
 Non.— iBowvaKaiafBotatlMitlmHMdMAJirlod. TilifathirrMit 
 I to ■ ■jimH thM. M l H i MDim . M< i. """•••I 
 
 III. ROMAM NOTATION. 
 
 (a) Bj moons of the roodor, lot tho pnpils oboorro how th4 
 lossons from 1 to 10 are niimborod. «w m^ 
 
 Tobnlato the results as 1=1; 2«n; 8=m; 4=IV} 5«Vj eto. 
 (») Prom obsenration of those symbols teach the following':- 
 
 1. The effeet of repeating a symbol. 
 
 2. The effeet of writing a symbol of lower ralno to the left of 
 one of greater Talno. 
 
 8. The effeet of writing a symbol of lees Talne to tho right of 
 one of greater ralno. ^^ 
 
 4. How often a symbol is repeated. 
 
117 
 
 (•) TbMh kow to vMd ud write Ik* Ims m 
 
 •0, SO, M, 40, 60, 70, iO, 100, 00. 
 (») OonbiM th» tMW u« nlto m 17, M, 4a, «!•. 
 
 (•) TtMh tiM hmidff«d« dOM M 100, 900. 800, M«,4M.^. 
 
 J S!!?I?**.!I*J*"!f^ ttd Iw. M IW, laViM, t40, •««. 
 (•) CoMbiMtlMliaiidMds, tTMffiml ■rthijgirn, 466, 040, tie. 
 
 y«>..^p-.«i. -Ml .. .. ^ ^ iril_U__ BMlalMnL 
 
 7«IID0UCX0Vn. 
 •00+0+1 -MCMI. ' ,^ 
 
 IV. AOOmON. 
 I. OfH AMMm. ar Ito AMMm Takto. 
 
 P«pll» alMmld not b« glvMi wrHIra «ddlli<m natil thtjeu eon. 
 Wm Bombm without eoimtiiiff by onot. Fteiliiy in or»l odditioa 
 OM bo Moarod by (1) eomteiit driU mad (a) oomet pnetiee. 
 
 (1) Coimt by twos boffiaaiiiff with (a) t, and (») 1, «» to and 
 Jnat bayond 100. 
 
 Coaat by thma bagiiiiiiiig -'th («) a, (») 8, and («) 1, np to 
 •Bd joat bayond 100. ' » r 
 
 Traat aaeh of tha othar nnmbara np to 10 in a dmilar way. 
 
 (3) Taaah tha aam of two nnmbara, aa 7+8; 8+7. 
 
 Pny attention to tia anding, aa 17+8; 18+7; 97+8; 88+7, ata. 
 Whan a aaeond aombination ia known aa 5+0, naa thaaa in giTinc 
 driU in rapid addition aa (add from tha left) 
 7+8+6+8+7+5+8=* 
 8+7+5+7+8+5+7+8- 
 
 Whan a third aombination, aa 4+8, 8+4 is known, othar 
 azereiaaa are giran ri, 
 
 4+3+8+5+8+4+8+5+7* 
 8+4+8+5+7+8+6+4+8= 
 Aa aaeh new eombination ia learned, aa 9+8, the pnpU ahonld 
 use it aa ahown abore, thni, 
 
 9+8+8+5+H:8+8+5+4+3« 
 Thns, the pnpil is nerer called on to add eombinationa which 
 he haa not learned and thui compelled to laaort to eonnting on hia 
 Angara, or making mwdn which he connta. 
 
P«plto ■hMM b« tasfhl froM tlM b»tliu|ic t»Mffhmmmmk 
 OII««| UtM. la tiM iMl lluA. IT yil an ••TiT* T^ »»▼••■• ■■» W 
 • I. 17, It JiTtoM, hT; ' ' ' *' *'' •••.. -d .01 • .M 
 
 W Wrttt th* ^to OB tiM blMkbOMd, M 
 
 1. 7. 5, 8, », «, 4. 7, 5, J, 8, i, 7, ». •!•., 
 
 djSlSl '^ ■0«l « b. btpfto. to INrflrtlotho 
 
 Ondwllj hiwpoMo tbo tpood of pototfiif . 
 
 tbo tort igow „ 00 o^oo tbo wbolo. Tbopinrfte-MttidTthI 
 digitt 010 plaood OB tbo boord. f-Rw ■« ww •• Ibo 
 
 tJ iStBr*'*'' *" ***^ '^ •^'^ eo-bi^illoB., -p-tolly tboo. 
 
 VOffB.— 1. lariltfc*— — i— — .^^ 
 
 t. WlMo • pi*a fiyia, 
 •MMMtloM eMriac tlM dtthnltr. 
 
 fo; .iiWKoii w»«r» llW» <• oo «irtf<o^. 
 
 (1) Sbow bow tbe addends mi»t be ptoeed. 
 
 (2) CHre ezemplee for praetiee. 
 (8) Oire problem* to be eolrcd. 
 
 (b) AdHtkm wktrt ikf it mrryktg. 
 
 (1) Show the neeoMity of eanying. 
 
 (2) Show the eoBTenienee of beginning at the right hand tide. 
 
 (3) WTO ezamplee for praotiee. 
 
 (4) Oire piobleni to be aolved. 
 
] 
 
 •VMiamom mm imjumnm. up 
 
 I. l^MtH^M^f H. M tte p«pil. do » fww mmiMm. tfc„, 
 
 ' ^ S ""l^ •*•• lUlW ■•• of tlM platao. Hkvaa ..rf ..w. 
 
 MMi4 or boMlloo of q»ll»t.. "* J**^ "^^ "^ ••*••. 
 
 ij« to tho rtirt. Of iK»lo book Olid wy .«.|^ oTS^^ 
 b»ilTo.ipto»o« pHoieor43on PHo l" ^^ 
 
 klltoly^JSr^'"^**'^''^^' ""»•—• •««•«»• work' 
 
 •^ t»«»P. Thoo flod tbo ram of UiMe rams. If tho loralft 
 witk th. «i« of II tho «Id«id. Iho work to Ukrty wrir 
 
 I. Oral 
 
 V. SUBTRACTION. 
 
 It ■hevld bo ImprMMd bgr moo ikllftol drUl and pnMttoo. 
 
 (1) Cooat bMkwards bj twoo from 100. 
 
 II 
 II 
 II 
 l« 
 «l 
 
 II 
 II 
 
 II 
 II 
 
 II 
 
 throoa « 
 << II 
 
 II 
 
 foon 
 
 .11 
 
 II 
 II 
 
 00. 
 00. 
 00. 
 07. 
 100. 
 O0,ote. 
 
 ^i?*?T^ ! •*■•*•' **••*• **•• ■■«»»«»»oi»d at tho eoiitro and 
 toand tbo olroomforoBco writo number.. Lot tbo popil rabtnu»t m. 
 
 /^™' ***"*■ *** • """'»*' «» «»• clreomferonio 
 
 (8) Ptoeo the minaend ot the centre of • eiiole and the diffita 
 
 in Mj order round tho eirenmference. Let the pupil .ubtr«,t «. 
 
 the teaeher polnta to a rabtrahend. •«"». » 
 
 (4) Plaeo the digit. In any order upon the blackboard, aa 
 7, 4, 0, 6. 3, 8, 6, 2. I, 
 
 •Bd foqniro the popila to rabtraet eaeh from a f! en number aa 70 
 
 when tho digit to pointed to. » numoer, a. 70, 
 
«. 1^ •«, O. «f^ W, », «. M. H. 
 
 
 l»lh» 
 
 liplMtdvllh 
 
 (1) 
 (t) 
 
 Tkm tft ••Vital aotei of proMdiiv kM« 
 Am. taa H lylMi lO. M ipiiM,. 
 
 ^^^ A "^^ ^NH VMM 
 
 ■ • + 1 « s + iT 
 
 M - 1+4 
 
 ^™22^ "^ '^ *!?*^ ** *~ ■l***^ <» >f tokliirf ■tern 
 "bonvwinf and M„,la,M 11,11^^ •■•^ ""Immfw V mim th» 
 •■•tolir2«iIi*T'II!IlL^T^ 
 
 «• BOI ftUilW to «rt*«rtl«.^^ ^^ »-• •O.dltlCiM 
 
 .d^r^ "^ '^::!i^***'**' ^•»'«^ ■!«»«»• p^^ 
 
 IVmb ft 7 • 6 18 M 
 
 Ttt» S 5 7 a 12 2S 
 
 « « 5 4 4 1 
 
 ■t *a^- - J^ - — g^w " ■MBUr la pw i wMlt TirrtlBM i 
 
 ■iiriM" ii__ii_ .-.. 7 , ■■■■■ "^w* ■ a rMMM wg ' 
 
 th« 
 
(in) 
 
 Ala a^^M la *.-- . 
 
 ■■i^t>>y tfMit 
 
 Tk» MBiNiton* Miked it M 
 
 '^Mi • fivM MWBbtr. "■■•■• •"••■•kln»lt4«l©ii«t 
 
 V^M, fkO« tm Ilk* Ik* MM ii# SA* 'am . 
 
 "**_ H-»+(i)- • 
 
 W II mv b» M*d to ihoflw Urn. iMvl.l«i 
 Thn, diTtd* ISMIO I7 BTiT 
 
 »7»21»I10(4M 
 
 __ ^rriw «.»X7+»+(4)-M.8x.+,+,„.„, 
 
m 
 
 AKITHMICTIO. 
 
 (1) Bj Addition. The ram of the remainder and tiw rabtnthend 
 ie equal to the minuend, if the worii is eorreet. 
 
 (8) B7 Snbtraetion. When the remainder ie taken from the 
 minnend, the reaolt li the same as the rabtrahend, if the work la 
 eorreel. 
 
 VI. MULTIPLICATION. 
 
 LOral 
 
 Using splints, deflnite units in meararing, the numeral frame, 
 eto., build up the table. 
 
 Thus, 1 in.+l in.s2X 1 in.s2 iu., or 2 times 1 in. is 2 in. 
 
 2 in.+2 in.=-2x 2 in.=4 in., or 2 times 2 In. are 4 in. 
 
 S in.+3 in.=2;< H in.— 6 in., or 2 times 3 in. are d in. ; ete. 
 Then, 2X1=2; 
 
 2X2=b4; proceeding from the eoncrote to the abstract. 
 lin.+l in.+l in.+l in. =4^1 in. =4 in., or4timesl in. is4in. 
 2in.+2in.+2in.+2in.=4X2in.=8in., or 4 times 2 in. aro 8 in. 
 3in.-i-3in.+3in.+3in.s:4X3in.Bl2in.,or4times3in.arol2in. 
 Then, 4X1=4; 
 
 4X2=8, ete. . 
 Thus it will be seen that multiplication is a short methdd of 
 doing addition when the addends aro all the same. 
 
 It will also be understood why the multipUer i$ akoa^M an ah$traet 
 
 MISIMr. 
 
 Fix the table by much drill and as soon as a few of the facts 
 aro learned begin written multiplication. 
 DrtH Ejcerdees. 
 
 (1) Describe a einle; place the multiplier in the centro and 
 round the eiroumferonee range the figures, including 0, in any 
 order. Hrtc the pupils tell the product as a flgnro is pointed to. 
 
 (2) Write the figures in any order in a row upon the black- 
 board, and placing the multiplier above, have the product given 
 as a figuro is pointed to. 
 
 (3) Write the flguros as in (2) and have a pupil begin at one 
 end to state the successive products to the other. 
 
 NoTB.--Wli«ii ft pnpil faili, he sboald discover the eorreet prodnet by aainc 
 eddttlOB. 
 
 No WnUcii Miilllpllcstlons 
 (a) Shoti MtaUpUeatUm. 
 (1) Whero thero is no carrying. 
 
BvaaMntom por tbaohimo. 123 
 
 Vf^. *""" *• P*^' **»• ""»l«P»J<»«Ml aud mulilpltor mad how ia, 
 
 ThM, John and Jwum h»T» Meh 343 mubim. Bow m..* 
 have tiM7 togothorf "«w». now many 
 
 348 "SS" 
 
 848 2 
 
 (8) Whora there la eanying. 
 
 .^H^*" **^ f^ •»B>ples the eonneoUon between earryia, in 
 addition and In nraltiplieation. «irryiii, m 
 
 1618 1812 
 
 Give (1) ezamplee; (8) pfobleus. 
 
 •IwajF. be an abetraet nomber («o many time.) ; and (3) why the 
 p«.dnet »njt be of tte «.n,e denomination a. tie mnltipl llnJ 
 bv Si! '^W -^,»r»«» *^her and pnpil fton» blonderiig later on 
 wmS^ J^^^ impoeeible operaHon. as mnltlplying lengtli by 
 
 8X 7=81 8 and 7 a»e the fketora of 31 • 
 
 4X9=86 4 " » «• " •« ** 30. 
 
 7X5=86 7 " 5 " " " " 36.'^ 
 
 (8) By using numbers not greater that 18 show 
 (I) That multiplying by a number and by the factors of the 
 number produee the same results. 
 
 Thus, 17 17 17 17 
 
 -i? J 4 6 
 
 _J _§ 2 
 
 804 304 204 
 
IM 
 
 AB^mmo* 
 
 (U) TlMl II doM Bot BBAttor IB wkMi Older Urn fMtonai*«td. 
 (iii) That whan a nninber ean be reeolved into Mrena mUm o< 
 iMtOTa M 4oes »et Metier wUeh eel ie eaed. 
 
 In eonneetion with thia give mneh praetiee la anUliptyiiif bgr 
 20, 30, 40, ete., 300, 800, 400, ete., 2000, 8000, 4000, ete. 
 
 Show that the eonTeBient faetora are 10 and 2; 10 and 8; 10 
 and 4; ete.; 100 and 2; 100 and 8; 100 and 4; ete.; 1000 and 2, ete. 
 (e) Long MtUt^^tkaikm. 
 
 Uloitfate the prineiple of long malttplfeatiou, rla. : MnltlplTlng 
 the eereral parte of the multiplleand by tiie several parte of the 
 multiplier, multipliee the aggregate nraltiplieand bj the multiplier. 
 Thus the pupil will see there is a reason for what he le doing. 
 He should not be expeeted to fully reprodnee It. 
 8 » ft+8 
 _»« 2+7 
 
 72 » 2X6+2X8+7X6+7X8. 
 Multiply 862 by 23. « 
 
 28=20+3. 
 The pupil can multiply by 3 and by 20 and, henee, by 23. 
 862 
 23 
 1086 := 3 times 862. 
 7240 = 20 " 362. 
 8326 = 28 " 862. 
 Multiply 4S7 by 205. 
 
 205»200+6. 
 4S7 
 20» 
 
 2285 ~ 5 timee 457. 
 91400 = 200 «« 457. 
 98685 = 205 " 457. 
 The nselessness of putting down the O's will soon be observed 
 and it will be noticed that the correct result is found by placing 
 the first figure of each partial product under tiiat figure of the 
 multiplier by which it is obtained. 
 
 KorB.-As Mtoner »od nuMltr mn elowly HModated. Braeh drlJl ahoold be 
 bItob in doiiic » ewtain aaMmnt of miiltiplkwtioii in a c1t«ii time. A nomber, m 
 7W9M, nujr be talen and the invU reqairad to maltii>ljr siieeMdvelr by » gina 
 maltiidler (m oraMply by 2, the Mmltinc prodne* by 8. the new irodaet by S, ete.) 
 M often M poMible in the spedflad time, m one minute; or • gtrm nomber may 
 be mnitiidied raeeeedirely by a fiven mnlUpUer a flzed nomber of timea and the 
 time re«Bixed to do ttaii obaervecl. 
 
■vooMnom nm viAOHnre. i^ 
 
 In Miuieation with problwm, «»• mwl be takM to ^ ti»ith. 
 •oneei maltlpUer la oMd. ^^ to tw llirtth* 
 
 Thus, And the eott of 7 hsls 9 fS Mej, 
 
 FUji the eoel «rf T8M ttilele. it 16 «»h. •■W••^• 
 
 Ce^of7iMaftIele««t$le«»h*f7896: 
 
 «»i wS^ ^ "^ •*""*• •"~«»« a-*™. -H«i« 
 
 («) OmMv «>( a« niMt. 
 
 ■V. MMtaMnl WMi I, IMtMnOM. 
 
 to gliiiig idmIimUmU work from the bbtkhn..! .i„ . .. 
 
 1. (a) 58X53=50X56+3'=2809 
 (b) 78X78=80X76-|-a*=6084. 
 (e) 7«8X783=800X786+7"=628M» 
 
US 
 
 ABmniKTio. 
 
 ' 5f 
 
 iiii' 
 
 .i. h 
 
 3. («) 4ex44a90X4(H-«X4s2024. 
 
 (ft) iaSXl27sia0Xl2(H-8X7sl6e21. . 
 (e) lS2Xl58-*160X15(hf2X8-'94016. 
 NotiM th* number of tona is the mmm ia bolh miiltlpU«r tad 
 molUpllMnd and that the ram oi Um aaite o< th* jualtli^r aad 
 multipUeMid is ten. 
 
 8. Uss tlw ArUhmetleal eomptomaajt. 
 
 Tlis arithmstisal eomplsmant of a namber is ths diBennea 
 between the number sad tbe unit of the next raperior order. 
 
 Thus, the A.C. of 6 Is 10—6, or 4; of 78 is 100—78, or 22; 
 of 584 is 1000—584, or 416. 
 MalUply 9984 by 9906. 
 
 9964; A.C. is 16 The A.C. of the mnltipUeand snd 
 
 9996 ; A.C. i s 4 nnttipUer are mnltipUed together and 
 99800064 0064 M manj flgnres are written in the' 
 
 prodaet by placing naughts to the left as will malce'the number of 
 plaees equal to the number of flgnres ^n the multiplieand or 
 multiplier. Bet down this pro&uet. Then the A.C. of the multi- 
 plier is rabtraeted from the t.ulUplieand or riee Tersa and the 
 am^nder is written to the left of the figures alrMdy placed. 
 
 Hfvn.-iX) Tte mnltt^ter sad aoltl^iMuid ■hoidd 1i»t« tli* 
 
 ifUW. 
 
 (S) Wm flonvmlMiM namb«« wtth hmD A.O.'a ■hovld b* 
 
 It is reeommended that praetiee In sueh eontraetions as the 
 following be given advwMtd students. 
 Buohexereises areraluable in that: — 
 
 (1) They faeUitate results. 
 
 (2) They give pupils a elearer eoneeption of tiie nature of the 
 multiplteation proeess. 
 
 (3) Th^ furnish ezeellent praetiee to the pup'ls in determining 
 the relations between numbers. 
 
 I. To multiply by raeh numbers as 999, 798, 9996, ete. 
 Ex. 1. Multiply 784564 by 999. 
 
 734564000 — 1000 times the multiplicand. * 
 
 734564 » 1 
 
 
 
 it 
 (I 
 
 
 738829486 = 999 
 X. 2. Multiply 587469 by 798. 
 
 469975200 = 800 times the multiplieand. 
 1174988 = 2 
 
 468800262 = 79B 
 
 (( 
 
 It 
 
 «( 
 
iO^BtnMM tOB rlAomitd. 
 
 itt 
 
 n. To multiply la » glTwi nttinbcr of Uaoi of partUU prodaota. 
 Is. 8. MuUlply 78S649 by 860 in two linM of portua piodnets. 
 78SM9 
 (86)9 
 7O70M1 » 9 tImM tho moltlplicuid. 
 88888864 »> 40 " 9 tlniM, or 860 times tho mnlUpUewid. 
 880904481 «i809 " tho maltipUeMid. 
 
 Ex. 4. Multiply 81884S67 Iqr 64482 in tluM UaM of prodoeta. 
 81284867 
 (64X4X^) 
 89498«S08 ■> 400 tlmM tho mnltiplleuid. 
 2S90606144 = 8 '* 4timM,or82timostbemnltiplieand^ 
 8180012288 »2000 " 82, or 64000 time* the moltipHeand. 
 6234105620944 »64482 " the mnltipHeMid. 
 III. To multiply by S, 25, 125. 
 
 (1) To multiply by 6, multiply by 10 and diride the product 
 by 2. 5»10-^2. 
 
 (2) To multiply by 25, multiply by 100 and divide the prodnet 
 by 4. 2S=100-r4. 
 
 (8) To multiply by 125, multiply by 1000 and divide the product 
 by 8. 125s=1000-r-8. 
 
 VII. DIVISION. 
 L Orri OhMei^ w Uie DMalM TaMe. 
 
 The Diviaion Table is the eonvene of the Multiplieation Table 
 and ean be learned from It. ' 
 
 The pnpU should diseover similar answers to the following 
 questions in eonneotion with eaeh product in the mnltipnoiition table : 
 
 (1) How often esn 2 be taken from 6t 
 
 (2) How many 2's are there In 61 
 
 (3) How aumy times 2 make Of 
 
 (4) How often Is 2 eontained in 6t 
 
 (5) One of the fiMtors of 6 is 2, what is the othert 
 
 (6) Divide 6 into 2 equal parts. 
 
 (7) What is the half of 67 
 
 > for DfflL 
 
 (o) Describe a eirele. Place the divisor in the centre, «nd 
 rwnd tiie circumference place numbers up to 12 times the divisor. 
 Point to these and let the pupil tell instantly the quotfont and 
 
Si. I? :: 
 
 ; Hi 
 
 Mwwwr hf ulBf obJMtof of muBlMr>pi0taMt. 
 
 (6) PIm« tlM diglto ia «ty otdw apoa tiM blMkbowd with Um 
 
 J ■ ■ 
 e, 8, 7, 8, 6, 4, 8, f , •, i, 7, 6, 7, 8, 8. 
 
 Fdal to ft digit ftnd liftT* ft |ml»U dlrlde. If tkM* It ft 
 Minftliider plaa* It to thft l«ft oIHIm nrat dlgH pointed to ftnd dlrldo 
 tho romltlng mtmber, ote. 
 
 Mon.-Du«MttM lMU«lM oC tlM dMaIra tabto tlM m»lk dMiM gnkhuUly 
 dlM«VHr (1) tlurt 4hrlslra 1« tiM proMM br irMeh iMTteg glvM • ] 
 fMlortiM otter «Mir to laaaAi Mrf <« «k«k UiWmi to • ■hoM i 
 foraiag wfwal w a ta M l w tm Uw a t to — •< tto mw* aaaibMr. 
 
 Lat tlw 9Bplto atoeoTwr tto krtUr by wotkifig wtth objwto MMb ] 
 kof* owv n ««iUm bo dhridtd. iMiNt MMh bogr • 1 
 MouuMm 
 
 _S TlddM 8 muMm and ihriat tton to tto ftnt boTt 
 
 IB " than m 15 wnwIiilMi 
 
 J. ** TMklac>o<ttMM«p<*.3lviBgtbraitotb*M60iidbagr. 
 W ** th«««nMau»blMi«aMlBliig. 
 
 ISnMw • oC IftiM wrf «lvfa« thm to tlM tUsA boTt 
 
 thno u« 18 muMm iwaalalat. 
 
 T«ktac 8 ^ tbMO MiA ghtMt thoB to tbo fowth boy. 
 
 Aon MM M sMiblM tMuMac* 
 
 TkUiit 8 of thMO ud gMac thm to tlM ftftb tor. 
 
 thoM AM 5 murblM mMdalaf. 
 
 TMktiic thMO Mid flvli« ItoM to tho ilzth bor, 
 
 thoM MO BOB* noMlniac. 
 
 ■ujr to dhrktod MMBt i boya, iMiig to «wb bogr 8 HMblMf. 
 
 I 
 
 _8 
 
 16 
 8 
 
 7 
 
 _8 
 
 6 
 
 _B 
 
 
 
 • boyi, bow aoay 
 
 bwl. 
 
 If M i|mMm mo dlTtdod 0««WB7 I 
 neolTot 
 
 MauHrhiM 
 
 • " Ci|dftgtaMNMHMldflMM« 
 M ** tbonuoMnHudalac. 
 
 TiddiMr • o( toMW Md gMi« wMli boy 1. 
 that* on U mwdnlnfl oad OMh bof boo Si 
 T«klBc 6 ot thMO Hi fthrlnft iMh bogr 1, 
 tb«n no IS NBslntac and Mwb bojr baa 8. 
 TaUac 8 (rf tbaao and gMng oaeh boy 1, 
 tiMM an • fwaaMac aad oadi bar bM 4. 
 Taktec tbaaa 6 aad iMNt OMh bor 1. 
 than am BOBo lOBulnliig aad oaeh bar baa 8. 
 
 bor 
 
 _8 
 
 U 
 
 H. SiMrt DMoloft to toe Lent DMakM Metood. 
 
 Divide 88 eplii^ e^BftUy between 8 boT*. 
 Let tbe po^te dis^re? haw maaajumh bo/ wiil get by dividing 
 6 bondlee of . tea aad 8 ^pUnto. 
 
■vMB0nom poft nAOBixo. 
 
 Mm iguteff M Um UMkkMud, tktt% 
 
 S) 
 
 (M 
 
 8 
 
 JAfUt n apUBto •quOljr bRwMn 2 hqji. 
 
 As tefoTO, tiM pnptk bar* 7 IrandlM aad 3 •pi'nU. TIm luOf 
 of 6 baiidlM Is rsMllly found and After s tino tlwj And thoy amsl 
 nntis ths bundle and then they hsre 12 splinU, whish they esn 
 easily dirlde into 2 equal parts. 
 
 Hmw the figuring: 
 
 ^^ SplBtt. BpitaISi 
 
 2) 72 (20 ^ 
 
 IS 
 M 
 
 IN. Sherl DMslea by Me Ueaal Melherf. 
 
 Hon.- la workiat ptoblMU sapUs •boold iMurn that thw* an two kinds of 
 •urriaM.vls.1 (1) «lMMiawhMitlMdlTlHriauialMtrMtBiimlMruid(S) thoM 
 la wldeh tiM dhrlaor to of tlM MUM BUM M tlM dMdMid. 
 
 laoaelkirftlMMMiMatlMyshoald bo oartfaUjr tealaad to kaow tho aatnn of 
 
 tht ipintliiBt ■nil tin rmnlmtoi. 
 
 Thas. whan tho dhrtoor to aa abotraot aaaib^, tho «aotttBt and nmaindor aio 
 atwajroUkothodtirMMid. Whoa tbo divtoor to of tho mbio aamo «• tho divtdond, 
 «ko«aottoBt toahraim m anay Mmmo aad aa lad) Mm ramatadsr to of tbo mbm 
 
 IV. 
 
 Pupils should be trained in the following steps until they are 
 automatie: — 
 
 (1) See how ouuiy thaes the dirisor is eontained in the part of 
 the dividend to be eonsidered. 
 
 (2) Plaee the flgnre in the qaotieBt. 
 
 (8) Multiply the divisor by this number and plase the product 
 under the part of the dividend under eonsideration. 
 
 (4) Subtract the product from this part of the dividend. 
 (6) firing down the next figure in the dividend. 
 
 After a pupil knOws these steps there still remain two diflleulties 
 to be overcome: — 
 
 (a) To tell the quotient figure. 
 
 (6) To supply a in the quotient when the divisor is not eoo- 
 tained in the part of the dividend to be divided. 
 
UXS-67 "^ r* 
 19X9--171 
 
 81)800000(40600 
 64 
 
 ili 
 
 166 
 
 10 
 00 
 
 100 
 100 
 
 V. OMalM ky Factora. «• -WMiiv. 
 
 ffi 5f JS?"" ''^^ *?•" *^ *^* '•^" "^ »o rwMdBdtr 
 
 JL""^ -«-««-«. two 1^ .^ . i::rxs!:r wuh 
 
 de» with «y <„ auXS^.***^ " "*~*^ '^^ "* «-»*-- 
 
 Dlyide 132 by 12. 
 12)182 
 11 
 
 4 )182 
 8238 
 11 
 
 8)182 
 4)J4 
 11 
 
 6)182 
 
 11 
 
 Workiiig an ezunple In this way shows 
 2^r Of tho diTl«„r •»« the rating qnotlont dwSd ^ S 
 
•Manmn MB titcniw. 
 
 miBTm 
 
 
 B ''**•••• *« *" '•• •••II Mad S »>««~. «# •"iL 
 
 «». WMk h «i„^. ■"''*•""*«** •IMI *. IHTKto.4 If 
 (*) BabtiMt tiM Bmaladn fkr_ •!_»... 
 
 Vte foUowbiff an mrmm,t I t 
 
 75649 or, 
 8X7 
 
 ..^9548 
 
 2a8M7 
 27006693' 
 
 J6*g«7 *•'» 
 7471871 
 
 879)«^«HHHi(a487o,«*>8a081(976 
 
 **■ •▼•r. 47o?«r. 
 
 8708)M167041(* 
 
 * "mow 
 
 84704 
 
 JUUIMM. 
 
 wwwwv 
 
 iiiT 
 
VNI* 
 
 **^ thi iMif illfciuiti la iniiiM 
 
 •Hit fio«tli#folkml«f •«»•„- '™™«« » ■w»«Nr 
 
 (I) Piiplto 4» Ml iii«tniu4 tiM Mitan of 
 
 (Ill) Tbtjr kftT» M I«p.rf,rt wkUrtftMdlat •« «» Mtan of 
 lollSr*' *^ "^ *■ *'~^ '^ "**^ •*•««"•-"• « 
 
 l2^**loodmtati»oooi.ofHo. IWlaro to do^«i. -Sftf 
 tto^«««.«»l.l MtlunoU. l«.oo«p,oho».IW., nj!l^^ Z 
 
 tt»popll to tlio- dlffleolty, thoy toiMih tho wlatlon m woU. aZJ 
 
 A f«pU wlM niidontu4i tho four fttndunontol opomiiMa and 
 
 imia dtfleulty in looeUiif » «onoet loralt. 
 llooluudool.oettir,ey,lM^l^,„,,g^ 
 
 ? ^J "^"^ ** »"*• .mlrtidto In mldWon, «ibtrSten*«f 
 Ap.pariioDMbohoMionKm.iblo for oroiy ilg,^ bTSto do^; 
 
 ^./*^ Ji'T^.'ir^'**'" **• *'^ P"»^ to ttoto tho mppootkion or 
 dotam h, itoolf Mid undomdhth it to wrtto tho domwdT^ 
 
 ri«i i i^i^H^ of ' Bol. ofThroo » problom. tho wppooltion 
 
 jJouM bo writto. 00 .. to bring tho nmobor of tho ««« 'iZT M 
 tho uiowor roqairod, ot tho ond of tho stotomont ^^ 
 
■*«M«flMltkt 
 
 fIvM to lh« Bwbtr n^nd: 
 
 I. Viiid tte M pf 7 bmi. of icflf liD p.y ft^ a 
 8olutloBt-Coi| of 5 bWMlt-tSO; ux 
 
 th. prto. «f 1 bbl. w«J b, i of th. prto. «f 5 bi '^* ' *~^' 
 I bMTlii S! T?!!"* ^^ <*> •• (•) to T bbl. to 7 •!».. 
 
 •tflOOpwftoolfhwitH,. How«Mhtotlurti)«Mi.t 
 
 B«foit MMh • iimUmb to flferwi. pMlto ahMM -«-! . ^ 
 
m 
 
 if: 
 
 ^-••f IM ■«. ft..iiM, '^"^' 
 
 «W— lHl..M.«»I.MN.«).,.ft.bl^»g^,» 
 
 •«. a. taw. Ik, «* K («»x») .,. n. I, l^gj y_^ ^ 
 •<uoi«.fi. «*• "■"■• 
 
 «I«|«M IM MW« WM» Ih. ..I, piiq... ta Ik. »I.M., .1 
 
 mSHizs is'^i:ji '^■?* """-^ «*•«" •• >» 
 
 mmituigr wM. Pi^u. .ut b. N^idnt i, f,,,,, „ 
 
 IX. REoucnn-. ino tw compound num. 
 
 17mL-i5t^ ' i** ■'"^ *"*»^ "«*• 1 tqw foot! •tTr 
 1788 MMe IneliM mak* 1 evMe foot; tte. * ' 
 
 tf work«I, nothliif being mU of Bediwttoii, m *^^^ ^^'^ 
 Ix. 1. H©WBiaiiypiBto^„»tl»i«ia5qt.f 
 l«t.«2pt.; 
 Bat 6 qt.>i5 tluM 1 qtj ; 
 H«Be«, 5 qt.3K6 timea 2 pt., or 10 pt. 
 «ail*rfy, How ««y pint, fa J ,».f i, 7 ,4., ,, Ij, ^j , ^ 
 
««»t. B^ BMgr pteto ftM ikm fai I •!. 1 ii.f 
 lq».»Sp|.l 
 
 ««•». Bow Muijr qaarti M« Ikwp* te U pl.f 
 t|»l.-ilqt.| 
 SHOjSpl. 
 
 M. 4. H«waMuiyqiMifto«f»ibw»lB7pl.f 
 
 « P*.ll !>•. 
 
 t tia« Md 1 pi. oTvri 
 
 i.«27^!!!** ""^ »>" l«ftli aiHl bwmltli, orkdghl and 
 tl» bonii4«rlM of • rarfM* m« Ubm. * ~^ '•^ 
 
 X SIMMS •! SwfMM. 
 
 Tw«h tlw tMVM rMtADfl*, or obtonc Md muio. gut. thmk 
 Hare papile dniw % mmmm fool and nwk m a« i«*-.' 
 
 ':::z f<r ^.rjT" V *^--^^-^- i^t: 
 
 T>*Mt tho wiawo jafd simllMly. 
 
i 
 
 m 
 
 Bann tlw |ri|»11i mmmun m mpmn nd aktor your dfaMUou. 
 
 whfcAjirm *hittj«p,,«rt . ,,^ ft wlU b. ..Jnt^ 
 
 »-l»lf • ■qoM. yiH Mid 1 ■«««• halff •• Uttg, » i« o, thJ 
 ■qoM* Tftfds in I afMM nd. i«'"w«iw wit 
 
 toUtbMitlilsl.»i>.ere; and Ure »«« dnw • pl« «f i|, with 
 1 ineh rtpr«Mntiiiff 1 tod. By Mrfdag the pl»n off luto mum. 
 IiK^ha.. thV wUl dl«imr till* 1» «,J^ wd*^^^ 
 
 I.Miirtiilf 
 
 Show ^IMiMid then withdniwtliem. Pupil. wiU obterr* that 
 
 papU. RiT. • deflalUon. -A «>Ud I. iiything thirt uL up,"r 
 
 Show that Mllds am bonnded by MufMMa and thai &•• hava 
 length, bTMdth, and tbMoMM. ^ 
 
 X VMana aad Now R la Maaaarcd. 
 
 The anumnt of qiaee. an objeet oeenple. ia eahed ita Tohime. 
 Teaeh the tenia reetangalar eoHd and enbe. feH pnpil. the 
 tolame of a jolld i. mmar^ In enbea and t«M>h ^e ternu enblo 
 inch and enbie foot. Let thfi pnpil. dl^over the number of ineh- 
 dtee^e eubie foot will make, the numb^o* nm. of ertle hiehea. 
 !l22LrS^:fa!StL*~*^ I» .i^ mw of the allee.^ 
 w»^haaNalaia#lhaM»ba,of ertbiefawieahi theWaMa./ 
 
 Give eae problem, to tttiliaa the lufcimailoaaemrifed ^^ 
 Teaeh tiie enbie yaid in a rimilar manner. 
 
 ••, n, n.n are quantitte. that expren rahre. 
 4 oa., 7 lb., 7 lb. 8 oi. are qnantitie. that ezprsM weight. 
 8 hr., 7 min., 4 hr. 8 min. are quantities that ezprea. tima; 
 AH thaaa aaa eaUadOeaomiaate QMmtitiea. 
 
 lata, the unit iale. 
 In 4 08. the unit i. 1 o>. 
 In 6 mi. the unit i. 1 mi. 
 
■vmnmom won tiaokiito. iff 
 
 Agtin, 
 
 In 10.25 the niilto m« $i ud le. 
 
 In 7 lb. 9 OS. tlM naite »ra l Ib. and 1 oi. 
 
 In 8 ft. • la. th* imJti nw 1 ft. and i is. 
 
 i. .tlt"!!?"^ »«Mj«P.«P'~d In mom Ui.li o»o Uiid of .»Ik 
 tt ealled a ComiKraiid Donoaimite Quaatity. 
 
 Tbewuiafa wWohaOMvoiNkl li*HMi,la«l. ^a«^ 
 •ra eaUed ite DiHOMiHATioiii. '^ ' 
 
 «„.S!r'I'*!Ji?" ** «*'^" '" determining whether a denominato 
 qoantltjr la sinple or e<»Bpoond. 
 
 KEOUCTMM. 
 
 (a) By meana of qneationa almiiar to the fbllowiag, the tema. 
 Beduetion, Bedaetion Deeeeadiiig, Bednetion Aaeending, ahonld be 
 taught: 
 
 (1) In 19, how HMiiy eentt ai« theref 
 
 In 4 »., how mai^ jfoaeea are fheref 
 
 In 3 lb. 7 OB., how many ooneea are theief 
 
 (2) In 700 eta., how many dollam are theief 
 In 82 o«., how many ponndk are thwer 
 In 4S oa., how many pounds are theref 
 
 (») When examples in written redvetion are reaehed, the papil 
 Bbonld be required to write out the work in full for a time. When 
 the proeess is understood he should be shown the abbreriated form 
 in ordinary use and required to compare the new form, step by 
 ■tep, with the one used at first. 
 
 Ex. 1. Beduee 6 bu. 8 pk. 1 gal. 2 qt. to quarts. 
 lbu.»4pk.; 
 
 6 hu.^5 tines 4 pk. =20 pk. ; 
 20pk.+3pk.=28pk.; 
 lpk.=2gal.; 
 28 pk.=23 times 2 gal.B46 gal. ; 
 46 gal.+l gal.=47 gal. ; 
 1 gri.=B4 qt. ; 
 47 gal.=47 times 4 qt.=188 qt, ; 
 188 qt.+2 <^=M0 qt. 
 
AmmiMBvio. 
 
 I 
 
 8 b«. I 9k. 1 gy. 2 fk. 
 
 
 0) 
 
 47 iM. »Pk.pta.»pk.«28pk.Mr ' **•* 
 
 .4 qt « 
 
 190 qt. 
 
 ItalioaldbeqaltoelMrtotlMpntUthaiiiik i.^ ^^ 
 
 ^*I«M*I d«l»W^ III, "Uw «f C««,rtak^ 
 
 4»I««5pk.«»tli»iMWM 5tinM4iikt 
 4 " 47 qt. " M " M j; u l^'* 
 
 4qt.»lgal.; 
 4 qt. )817 «^ . 
 
 . M7 «il.«7» liM 1 gri.+i ,t.«7» frt. I «t. 
 8gal.»l]ilE.; ^. *qi. 
 
 Wtfiiwi and 1 gal. oy^. 
 
 . 817 qt.»8» pk. 1 gid. 1 0., ete. 
 817,t.«ygia.-7»gia.lqt.} 
 
 V'JMTjI. 
 
 t ^_ » pk- 1 gia., •!«. 
 
 ^ T. V. n m .. 
 
 7 6 8 7* 5 2* 
 
 ft s a ? ' " 
 
 • ' • 6 8 9 
 
 («) 
 (Ui) 
 
 9 9 9 
 
 81 29 81 
 
 9 9 9 
 14 2 1 
 
*099Mamem nm ncAoawa. 
 
 By qac^ioiM 
 
 ^ I*pll to dlMofw Why ha 
 •— »- 8 to th* tMM; ote. 
 
 1 
 
 i * ■ 
 
 » 7 5 
 
 > > 9 
 81 29 81 
 
 •iwiy. ton, wMlo to Cowmm^L^S^ £ ^^* ^^ 
 THI. e-i ho weU don. bj ^S?SJt^ J^LTtT I!^' 
 Compound Addition. ^^ "wnbew in Sinipio and 
 
 €0»iF0UNo nmTmcuew. 
 
 CoJXSTairtio^"'^ ^'^^^^ - •'««- to ti«« ui 
 
 «».T:r::'o;?:?s:<i"^\^ "-If ^ ^^-s^* «»^tion. 
 
 «MWmM» MULnPUCAmM. 
 
 a T. u. 
 
 7 S 9 
 
 7 
 
 49 36 a 
 
 M. T. U. 
 
 7 5 9 
 
 7 
 
 S8 1 3 
 
 .-?'pjrj?r.r.*r.t:rr-r'^ - -. ^ . ^ «„ 
 
 off 
 
 M. a 
 
 7 S 
 
 D. 
 9 
 
 7 
 
 49 35 63 
 
 InfiTing the fint lesson, e»re slionld be taken to n,^ th. - 
 pound MulMpUoation "«"»?P«»» 4» both Sini|»Je and Oom- 
 
140 
 
 W, Wn««TNCOIVISOR»Afi|AUTIMCTNIMIBCI|. 
 
 
 L IN«lt«r 
 
 B. T. U. 
 
 a )> 7 6 
 
 4 8 8 
 
 The papU must b* abl* to •xplaln bow 
 be geta 4 bondrede, 8 tone end 8 iwito. 
 
 M. H. D. 
 
 (Bk WHEN TNC DIVISOR IS A DCMOMINATE NUMBER. 
 latfodnee tbie by problems saeb as the foUowiiif : 
 
 1. How many yards of elotb at 8s. a yaid ean be boncfat for 
 90 s.t 
 
 I. How masy yards of elotb at as. a yard eaa be bought for £lf 
 
 What stop bad to be taken in the lattor ease whieb was not 
 taken in the fmrmert 
 
 8. How often ean yon sablraet 5s. frmn £2t 
 
 How often doee £8 eontain 6a.f 
 
 Explain the steps by whieb £2 is dirided by fie. 
 
 4. How often does £2 5s. eontain Os.t 
 
 Explain the stops in the solution. 
 
 Continue sneb examples nntU it beeomes elear that to diride 
 one denominato number by another, eaeh must be redaeed to 
 the lowest dmimnination mentioned in either. 
 
 X. SIMPLE APPLICATIONS OF THE PREVIOUS RULES. 
 
 BILLS AND ACCOUNTS. 
 
 Inteaehing this inbject, a WU neatly written and perfect in ail 
 ite details should be on the blaekboard. 
 
 The pupils should be quesUoned to eause them to diseover the 
 following: 
 
 (a) What is shown in the bill. 
 
 {h) Why eaeh itom of detail is shown. 
 
 (e) The arrangement of the various parte. 
 
 (d) The eiEeet of omitting any detail. 
 
 After soeh a bill has been earefuUy ttodied, and the details 
 tebnlsted, the pupils should be given praetlee in rulins bills, 
 filling in detaUs, ete. 
 
•TOOBtnon fOB TBAOBIWe. 141 
 
 Cn«l. OlvM IIM iMtMi Md 
 
 TBI UtOTAirOUI. 
 
 !S!!^ wMlTided into iqiuurM •eoonling to tho unit of aiZ 
 ■^Mtod. Tho pupil, will thu. iMrn tbiit S. n^itt^ L^ 
 plMod along ono .Id. of the mtu>cl« m often L tUL^ 
 ponding li««« nniU of »i««ir. to toTrido Ld STth^ """ 
 «MJ »wi of .neh *jnmio unit, of J«rl^<l!l •'••'• •• 
 
 ll«.a, unit, in tho JSTnt^Sr^^*" •on^ndtog 
 
 Length of rtetanglesia in. ; 
 Width " •« «i2 in . 
 A«»of motengle 1 in. longby 1 in. wide«l «,. ii. . 
 •' 16 in. •• "lin " «iiivi^ 1 
 
 *■ « ■ »" » » •• IM Ik. Mkcr. ™~*» «-«!..» ». 
 
 A. ta Out I Ou pupil rtoiild IM ntolmi to dm- . —t..^. 
 
 NurnlMr of npimra anita sloDg Uh leiigai=27. 
 
 row» to sudu 4m M. ft. =«L.«7_,, 
 
141 
 
 W«k» 
 
 III 
 
 ■aiUMnOtwiUfollMri 
 
 
 (•) In Cm* I th« bmmI wmbboii mlitalM is ia trmrMiir ikal 
 »«t^riJ5?5L*^ --hlplyfa,, l««th ttd width tog««k«raoM 
 
 itflTwi. How li the otlwr fonndt this It >iiM» uc^hgia^ ^ 
 It do.. »at <M»»p.l ft. pMsia to tntlTMft. p«,w«. «d gi^. « 
 •d.qiiiit.NMOii<forM.hrt.p^ •iwgiT.Mi 
 
 MARO MftHUItC. 
 
 To t«di Bo«d Mw««, hwe ..rwia b.Md. • ioot .,a». Md 
 •f Tjriou. thtokn..., M * fa, ♦ la., 1 ta., a to., 8 i»., .to 
 
 Ejptatolhrtih. boMd. i fa. thtok, i to. thiek. ud 1 In. thfok 
 
 8fa.oM4«8bo«rdft.;.l.. 
 
 OiM I. <4Mif«i «M 
 
 MMt«IMf|ie 
 
 ^ Wll. ihMld IM nqiilMd to dmw «MtMigiiI«r wild, of 
 
 rtMW «««MlM.. flMM d»o«M b. .oMUTidMl fato ««bM 
 
 «»eofifagtoft.«idt«feiiW.oort.rt..l..t«L * 
 
 18 ^Jml*^!?!;?;- **• **' ^ "• •^^^ i» •«NrtMviii» wo« 
 
 18 ft. 1^ l« It. sad 10 it. Ufbf 
 
 No. «rf.. ft. whl0hMttib.i*M.doiii.Bgth«18..ft.: 
 
 .. . «««>' =(16X18) ..ft.; 
 
 fa loom «Xl»X16X18)..ft. 
 =2880 e. ft. 
 
 a»d^«Miil1,^S* i "**•? *^ P°P"' •« "^I^*^ todmw 
 Md rabdi^ iho MUd aad Mt dowa a Mfatfoaiwll] riidw them 
 that <>« ctibie ewKeai o/ a r.clgii«F«ler <aiM ^^h.^ ly fmift(yi^nj 
 
•VMMTiom worn WAOWJI.. * ,^ 
 
 tW««rils«MMtlMStoflMl|||««||,^. ■■"••0«i«M 
 
 A« in Cm« I th« popUa tbonld 1m rmnmh^^,^ 
 
 wf?How^r«i?p's:;"^"^*»»p"*««-^«^i«fi. 
 
 No. Of., ft. SicblVLlil,'!!: «"^-(WX128)e.<; 
 ■ •" "• P***^ «> one eiid«(8X12) o. ft • 
 
 ^^•••'^•y''" to miAo (60X128) •.ft.*2»>ll^^^ ' 
 Hence, length of the pUe It 80 ft *^** 
 
 The following nirtakee an often mnde— 
 (&) The enble eontent ia diriamJt k. 4k ' 
 
 tt. Q«u.« I. «u.a ttT tiU *Sti*.^ «. ^ « -*. «4 
 
 on to do. Mwmaoivee what they are called 
 
 >«celvlag more ikM «|||«f^ ^"•••'•r 
 
S44 
 
 Bl. 1. DhrUto M miMm btlwfm Jmms «M 
 fhMlk My kitf* It am* thaa Jwm. 
 fink fflv* Fraak 10. 
 Tito wm lM«» M It b» dlTldtd tqullj bttiw ta Ftaak mi4 
 
 90 mtrt >lM- < -a»ll BUMMMt 
 JuMt' ih«r*Bi8 aaiMM} 
 Vraak't " *>i(10+ll) aaiUM^ll buuMm. , 
 
 Show thai tk* •ktfw li wd 08 ftdfi att lh« MBdiUaM flf tte 
 proMtm. 
 
 It tmaqi b« wp— t»d too oflon that impUi ■hoold bo tmliiod to 
 onmiM tholr iwalti md 0Bd wliotlior tiiojr fnlfll tho ooAditioM 
 nqoifod. 
 
 Ex. S. IMvldo 0110 MBOBff A, B MMl 0, ffhriag B 07 low tkoo A 
 who It to NOOiVO 010 BOfO Uuui C. 
 C roeoiiroi tho loost. 
 
 Estm for CaB0O; 
 
 " A-010; I 
 " B»0(10-7)-00} 
 Bxtm for A and B»085. 
 
 Sotting this Mido fiBrAaiidB, tlMMunlofttobo dhridcd 
 oqwOly MDong throo la 0(119—20), or 087. 
 007-r8>-0l0. 
 
 A roeolToa 0(89+10) . or 046. 
 B " 0(89+9), or 088. 
 C *' 0(29+0), or 089. 
 
 The pnplla riioald bo roquired to alww that theao reantta aro 
 eorreet. 
 
 I* 
 
 II* Shwfnp wiMfo Hm valto of iIm alMvoa la 
 • Ex. 8. Otrida 0100 botwoon Jamaa and Frank ao that Jamaa 
 may hare 8 timea at many aa Frank. 
 When Frank haa 01, 
 James has 08, 
 Both hare 04. 
 It is oTident that Fnmk will hare as many timea 01 and James 
 aa many times 08 as the number of timea 04 is eontidned in 0100. 
 01OO»25X04; 
 .*. Frank's shartffe=0(25Xl)»035; 
 .'.James' " »0(25X3)s:075. 
 

 Ml 
 
 
 0«l«f«fwj 
 
 AirUifHTtiMt$l,artr) 
 B f " tS.or$14t 
 
 ^J " " y " •S.orftt. 
 
 
 
 I 
 
 W. afc««ai«iMi«CMMlMiNara( 
 
 fc.«. A,B,midOUt tm nkmn$am, B Iim $18 bom ih*. 
 •• A. flow mneh Ium MMbf ^^ *■ ""^ 
 
 Bzto» for Basils ; 
 
 Extm for B and Ca«i88; 
 ■M»«tod«r to be <UTkled^(9M.88)«B$i7s 
 
 B •• $2, 
 
 out of «twy f7. 
 
 $175-r-$7»35 timM. 
 
 A hM 25 timM $1, or $35. 
 
 B " 26 " •2+$13,or|6S. 
 
 C " 25 " $H-$20, or f 120. 
 
 Be. 7. $2.40 It made op of thrM timM u muy 6e dImm *»^ 
 twiMMm«.,l0e.piMMM25c.p,eeM. How^^ijJZo*^ 
 
HI 
 
 !• f 
 
 two to* 
 ■adthiM Oe. |>lMM^ 
 «rt 9i •vwjr •)•. . 
 
 BMW*, ihM* Mt 4 tUMt I tfmitj.ivt Mat plaM, w 4 ttmnlf 
 ift Mat piMMf ' ^^^ 
 
 4 ttaM 2 tra omt piMM, or » tM MBl piMOTi 
 •ad 4 Umm t tva Mat piMw^ o» Itirt otat ptotM. 
 1IM1.-TIM "■ wMl iM ri " mmOmI m0 wllk pNtI to 
 
 Wn. 9. BftI* ffer tmrng A, B, ando, to thai B -_, , 
 tao IM tkaa S timm A'l •hara and C $17 aMia fhaa UriMB't 
 LtlAiaMhrt 1 than, 
 tkra B NMiTM t a ha wa H O, 
 •bA " e rtatw MO+»I Ti 
 an iiMhra lb •hafM-tO(H-$17{ 
 .-. 10 ahana-OOO-l-OlTvfMrf 
 
 .'. 10 •iiarM»f«^-f.fM| 
 1 ahaia-fW-MS. 
 Sam B rMalTw»SXfl5-|9O»$n0. 
 
 II 
 
 XI. FACTORS. CAMCELUTION. MEAimeS AND 
 
 MULTIPLES. 
 
 kPACTOm. 
 
 (a) Um tlM papUa' kaMrMft of iMlon (mo MaMplIoaiieB) 
 
 BiMkboard Nmmarjr: — 
 
 He flMton «mpt OM nth— i—4— *^.^ 
 
 Mi4ttoBUib«ri •■tttoMMitorj 
 
 18 
 17 
 
 PriowNuilwn. 
 (») In 
 
 £Ten 
 
 •Inilar 
 aanbon. 
 
 10 
 12 
 14 
 OoBpodto NwBbm. 
 maimer teseh the dlsttsetioB betwMn Odd ond 
 
tLfm 
 
 1. 
 
 t 
 1. 
 
 lis 
 
 ft 
 flit 
 
 IN^ Ito givw Bvater bgr tlM iMUlMl priM 
 
 iiMMr, u4 M oa ■atO » qaoitoal wkM b « 
 pria* mabup is obUlMd. 
 
 Th* VMSllM tor ttM papu it, What to th* mmUmI nth*. 
 
 ^-b^ih.ito.toH.ron2uf Twofaor iLrysj?!::; 
 
 (•) A mmter to MMUy dirtoibto by 4, If Ito two rfgW tattid 
 ■fWJJ •!•■«»■ or Mpww » nnaur txMUr *lTtolW» fc, i. 
 
 to « 2 ^ '"^ *'*'**^ ^''^''"* *^ *' " "• '*«*»* ***** •«■»• 
 
 .. J!!J. ^ ■"***' ^ "^y iifUm* by 6, If h to •»•» •■# omu, 
 diTtoibto by 8. •-■wiy 
 
 ft> ▲ MiAct toMMlly dIvtolUo by 8, if ita tteo. rffin fc|„a 
 
 /.r^ A ^* "»«»•«»•«»» •wtly dirtoibto by 8. 
 
 (7) Ainunbtrtoo»»HydlTtoflMoby8, lfl|io«i«ofltidl«lto 
 to«M*ty«vtoiblobyt. wwoifng 
 
 (8)A anaibor to oswtty dhrtotbto by U, if tiw diierwMo 
 
 difili in tbo oTon ptooM to ehhor or ezaetly dMalbto by 11. 
 Ttai, 7B601 to osMtly divtoiblo by 11, 7+6+l«*+9. 
 
 (ft) To lad an the diTteon of a aoMbw. 
 Ex. Rod all th« diTison of 960. 
 8 )860 1, 2, 4, 8 
 
 1* a, 9 
 
 1, 2, 4. 8, 8, 6, 12, 24, 8, 18, 86, T2 
 
 22180 
 
 2jM 
 
 8)46 
 
 ftJB 
 
 ft 
 
 1, 8, 4, 8, 8, 6, 12, 24, 9, 18, 86, 72, 
 
 5, 10, 80, 40, 16, 80, 60, 120, 46, 90, 180, 860. 
 
IthtiMlMlCftMll 
 
 •fa* tht MtMii pMvw a( 
 
 
 iMnrMiilfMMiilylkt 
 
 iMl«lMMi,TlB.I>ivMil^ 
 
 to^MiWilfaigtWMlUfh— to>i^4k, 
 
 . .y* '; "y^ *^ — tiM«< pwdwl of U, 4Mdftlvth» 
 
 i 
 jx|xS-ixixl-*' 
 
 f«f 
 
 (1) rM all 
 
 •*• ■•Hi of iMgih wkUk wlU MMUy -"^- 
 
 wkkk will woMlly 
 
 19ia.MSia.MSte.|Mte.| 
 
 (S) riad aU th« sbUi of , 
 
 • tq. 11.; 1« aq. ft.| M iq. ft., S7 ,,. ft., ^, 
 
 (t) rfai«llth«aaltoofTyMwU«hwUl«n«tlyaMnnik 
 
 94 ft. 
 
 riiid »U tiM aaito of toagth tlmt wtUnuetly 
 
 If 18 ft. and 
 
 Blaakboard work: 
 
 Tha 
 
 TIm 
 
 18 ft.. M ft. 
 
 of 18 ft. ara 1 ft.. 2 ft., t ft., e ft., » ft., w ft. 
 «f 84 ft. ai. 1 ft.. 3 ft., 8 fl.. 4 ft.. 6 ft., 8 ft.. 
 
 eft. 
 
 TiM maaaoraa opiaaioN to 18 ft. and 84 ft. 
 
 •«• 1 fl., 8 ft.. 8 ft. 
 
maltipl* 
 
 •ad k tiM a.0.1f. of tiM BOMlMn 
 
IV. iiiii.iipiia 
 
 w- f^ri^f^ "*^**^ ■''®'* qwnMtle. m 8 la., $5, 7 mieeMtlTvly 
 bjr 1, % t, 4, 5, •*•. * 
 
 BiMkboMd work! 
 
 SXKM910 
 8X$5»*$18 
 4Xi5afM 
 
 1X8 iB.«* 8 in. 
 SX8 la.» 6 in. 
 8X8 lA.>- 9 to. 
 4X8 in.«lS in. 
 
 1X7« T 
 
 • 1XT»U 
 
 8X7»S1 
 
 tX7s28 
 
 M«M9lM. 
 
 HnT« tteh mnHlpl* In tb* flm oolnnn mMMONd l»y 8 In : In th* 
 ■•«»d,bfiB}UilUtliiid,l>y7. 
 
 *»to«d M (1) on* or mon inUpnl timM tho glT«i nnmbtv or 
 C2t M » nnmbor width eontaUis tho giron nnmW oxMtljt. 
 
 (h) Cemmom Multiple, i 
 
 Hnvo irapUa writo anlllip^ llw«^— 
 
 ^ mitiplo. of 2 are 2. 4, «, 8, 10, 12, 14. M^ W. ^ 
 8 '• 8, 6, 0. 18, 18, 18, oto. 
 
 Vkc»kMo thoeoMm nuiMipk« MlMte^^ ▼!«., «, «, ig, ^e. 
 
 rnm Mnong the «oiamon nraltlplot of nombora ftmnd In (8) 
 
 ■•loel Iho tmnWort nnmber wWohh » common BmmpW of oneh of 
 tiw gfTon nnmbon. 
 
 Than, mnmptooof 6 mo 8, 12, 18, 91, 80, ole. 
 
 .. ..J u g^ 18^ „^ 8e, ete. 
 Tho L.C.M. of 6 and 9 is 18. 
 N. To fiBrf Mm UCJUL 
 
 (•> llit «ho >Mthod of fMolTlag tilt nua*m in prima feg^^ 
 
 Ex. 1. Find tht L.C.M. of 34, 80 and 88. 
 
 84«»X 2X2X8. 
 
 8»»8X8Xft. 
 
 855a«X7. 
 
 To ttatoin 24 IW L.C.]i. matt kwwtht pHata fatiart 2. iu 9 St 
 totontaln80,2,l,i,a«d*oton«a8ft,tt,l. B^tei^^ 
 
mwtmmam wn nAxmno. m 
 
 (^ T) M teatots. or 2, », i. 8, fl, and 7. 
 L.0.M.»SXS)(2X8X5X7»840. 
 
 qwUwto •» pri«. to «»• «oth„. »o.ootlMltho 
 
 ^uJZSTi ••''^•' •M«pl«t worind to thto wv tho mlo wUl bo 
 
 ^. a. Ftod tho L.C.M. of 18, 18, 81, 40, 80 maA M. 
 
 fC::> r ^5 ??' fff y. ■^M'^ nd s prime anmbtr that. 
 
 li Miititoid MMtljr to uj two or 
 ttwo Is Mloeted nd wkA m % 
 dlvfaor»*Mni. flMB« 
 
 la«i;'.to4. 
 toMTtiaia 
 
 •M itkit ia aootataad to ai^ 
 
 l >lfti •. «. i^. ifc! n 
 
 1. «, 
 
 A. 8> «, 5 
 
 . ^ 1. ii, i 
 M«4MMrUkatlMtfat. 
 to M priMM aaakar 
 
 *wttj^^wlUfca4hal.XJI.iatBto.d. — "'iwo 
 
 «tatt» l^JC«tX3X»>aKftN«H««il8ie. 
 
 fci. »tod tho LCM . «* 18, 18, 81, 40, 80, and 00 
 
 « >?»» W. U 
 
 nri; 
 
 1. 
 
 4 0,80,80 
 5. 
 
 1, 
 
 J. 1 
 
 L.C.lC.«;60X80aa800. 
 
 Ono of tho wuBbon, aa 00, 
 
 hartoff Mreral lietora la aatoeted. 
 
 Tho G^CM. of 80 and oatfh of tho 
 
 irtvoB Bttmbos la "aaflonod ont of 
 
 .. te annbom to tnoooajlop and all 
 
 .^ **' !;!L'** f^ *y fa t p tii ta i i a. ilioro. ThopJaTi^ 
 tho uaOian .alaatad wUU» tha L^ J|. 4»f 4ha Maaa 
 
 HI. — - 
 
 A Toiy oomoMB mittako is to speak of nao 
 
 uothor «Ma% whon «M«% la uoant. Thaa 3B 
 OtisMa. 
 
 7exaetfy 
 
in 
 
 to) 
 
 Ml. fiucnoNi. 
 
 i OOfMinON. NOTATION AND NUMEIUTION. 
 
 (X) DiTMmi of » iiiiift Into tqu] p^rto 
 
 w ?s2::i'5.':;:,"Sr ^^ •—"" »•«■»• 
 
 ytoM*-, M tod a-fcrth. of , fool; ftS^ ysio;; ^^ 
 
 mttaaoa tfeovld bo ghrmi nd ospfaOaed. Tbo torms. n^MMiii. 
 Md tewndntor, dmU U giro- ood tbol, rigSZLo ihZT 
 ThM, fa f tho 5 1«li«rtoo tho fhMrtlonol «ut «r»^ 
 
 |-H«f |-|«f 2XA=:f 
 
 it;*j '-i-f fxt«i 
 
 f+Ta»f f-f«f SXf^if 
 
 H. RCOUCTION. 
 
 lowSTtlST-r^i ^i?i "^"^ ""■'^'' ^"p"^ '"«^«». 
 
 iowo« tofOM, ote., ■henld bo iirtradaood and - 
 
 l-r 2«f 
 
 tengfat 00 loqoirod. 
 
 ahithaasV. 
 
OTMMnom worn vuMman. 
 
 m 
 
 w 
 
 /. 7«7X|«V{ 
 
 ••• 71-V+l-V. 
 
 Mnii*iillH«ffMiniriiii ftwIlMto 
 B. S. Sspivw ^ M « nizad mmbw. 
 
 (S) Um HMh npodtonta m:~ 
 
 (i) WTM.»«oollirtoa«ii»lp.rt.«»d»pw.,at«»..lMaf«f ft 
 ■■ f. 
 
 («) DWJ. • fcot Ia»o 4 «p«| pM*. |,Bd i^proTOt wio-half of ft 
 
 *. I fi.»| fl.*| fl. 
 (It) WtM*^. fool into » •qual parti ud f^wMent OM.thiid of 
 (r) I^Tidej. foot into M i^pua p«rti |«d ,,p„,^^ on^^Udrd of 
 (Ti) Wrido^. foot Into 8 «p„u pttti «d ropmoiit ono-thW of 
 
p 
 
 it! 
 
 IL 
 
 (8) Twktmtfmakmk 
 
 tmmmwit 
 
 B H HI u w 
 
 (4 
 
 (1) ExeMiaM ia wUeh om 
 (i) Oamlnc la v 
 
 <<t) l^wlw Jb ivbiah tiM 
 
 lira BnOtiple t»r M«h 
 •■• aol fiiaM to .«iie 
 
 (1) TW Daiaitkm. 
 
 (Hi) fPlattf oC f ^ » yart; eto. 
 
 (iT)Dmw«iin^^y«^. lUA of f of It; thM iBd i « tl» 
 p«ft markad off. ■ •»• 
 
 «>w»rt a aoniMmiid fnetlon with • limpi* one. 
 (2) Simpl^jriag oompoand frmottosi. 
 
 (I) toff; lot A; i of H. 
 
**rti*i «f (ill) |»*^ «i, 
 
 .'. i of i»| of 1*4. 
 Solatkm of (It) $^^J^.§ -.h. 
 
 .-. I of -t^f of n^'if^J^ma 
 
 KovBL— Onnr 
 
 '•» 
 
 I «f ♦-«. 
 
 dMNMBinator, as 
 
 1 ft 
 
 f«r4i»|of |.f.4. 
 
 I 1 
 M. Aoomim OP FiMcnoNs. 
 
 Of £2«I^?;:j.7j{*^*-<«*»«- 
 
 M iil^?' " "^ ''•"o-*-^ ^ Prime to o«. .«^er, 
 (5) Addltioii of mixed nanben, u 4|+2}«f 
 
 »*6 +l+A-fA, 
 
 TiiSarEiS^rs; 
 
▲BiraMino. 
 
 i 
 
 Ir 
 
 BfM«, aM tlM swB of tiM wbol* aaatera to Mm nm of tht 
 fnetlMM to liid tbt Mm of tiM nlmd BSMbon. 
 
 XOtl.-II Is «Mr fcr tlM taMhw to •« two feMllMM Wllh » MM 
 
 ,lX(7-».») 
 7X9 
 
 «H. 
 
 tlMtofUM 
 
 ■■•TartsMiranpf 
 
 W, SMITIIACnOM OP niACTIOMti. 
 
 (1)> BaVirMtion of fnetioM IwTiaff • oooibiob doomnlBator, m 
 
 (S) Bvbimotlon whtn ono of tbo doBomlB«ton is a nnltlplo of 
 tho ottior, M ffOM I toko A. 
 
 (!) M)toMtf«a wboB tko doaomiBotoni ai« prino to Mwh otoer, 
 M f^om I telre A. 
 
 (4) SobtiMUmi whoa iho deaomiaaton ara aot prino to oaek 
 othor, a* fioai A toko A- 
 
 (5) BvbtraotioB of mlaod auaabon. 
 'Nora.— la taUoc «m afand bm 
 
 peeMdiag wkM tlM MmMm af tiM I 
 
 Bx. 1. FhMB 7| toko 4|. 
 
 4|*4|- 4|. 
 
 2|. 
 
 This i« the method of deeompooltioa. 
 
 <») 7«»7|; 7f+4«7V. 
 • 4i*4|j 4jH-l=«J. 
 
 Thia h the method of equal addition. 
 («) 7fH>n7|. 
 4ff|=6. 
 H. 
 This is the met^ ol eomplemMitafy addition. 
 In general the laat method is the simplest. It eonsiste in 
 adding saeh a fraetton to that in the snhtoabend as will make ito 
 talae 1, and addinf the laaM fafstion to the minnend. The sab- 
 traetion eaa then be leadnj perfonned. 
 
ii0ns.H 
 
 •VMitriom worn nAomro. 
 
 m 
 
 •Mh* 
 
 7X9 
 
 ilxas "^* 
 
 V. mULTimCATION AND MVIIION OT FlUCTIONt. 
 
 or bjr di^U., th. d.n<iiZ,l^"rC.^ ''**"'• """•^' 
 AX5-|f Had AX4«||«|«i|. 
 C«~ il. Til* DMy«. f . fc,rtl^ fcy , ,,1^ ,,,,,,^ -' 
 
 the whoto nambw. "«»»iplylng the duioiniiiator by 
 
 •fawlMIe 
 
 •rmfndtti 
 
 ^ ^y^^* ««^ »h.»»fc«tk. 
 
 CmcIN. The 
 hyaftvdlM. 
 
 iadtealM tiM dhWoB of ha 
 Ite this M follows:— 
 
 iio^J SIT 'i"!!* *^.*f*** ^•«» *»»««»b« two f«tfj^ 
 Trtt f of the shorter and i of the lonnr •'"V""*' 
 
 Compere these parts. ^^ ' 
 
 It Hill be seen that I of l«i of 2, or 2-r.6. 
 
 Sliiillariy diow that I of 1=.J of 8. or 8^4. ete. 
 ^*) l~4foorthsof a^mit; 
 
 3=3 times 4 fourths of a unit 
 »12 fourths of a unit; 
 .*. i of 3=i of 12 fourths of a uuit 
 »8 fourths of a unit 
 =lof 1; 
 
 .*. iof Sasf of 1. 
 
 Kx. 1. Multiply ♦ by I. 
 
 The ranftiplier is i of 8, or 8-^4 
 ♦X8r V. 
 
it 4 til 
 
 toolttft. 
 
 ^•4ivttMkf4 
 
 H^Mt, fXf«if*arrn" 
 
 
 teWIWilHl^lM|iWll||l|Hll|lHl|lilfc»| 
 
 WW 9,—tm jNi— «■■»!■■ im 
 
 •M BMlk* lb* liMk 
 
 IrlMnrtestk* 
 
 TluM,7iX7f»lX7+iXi »S6A. 
 llfX ISf-tSX »-f |Xf«IMA. 
 
 UBC llr • IM9 DlMMMI 9V S tMMIV 
 
 «r« 
 
 -4i : 
 
 iy« 
 
 la dirldlBf a wliol* nlmlwr or » fmetimi bj ft fnwtioB yMif 
 ftra TftrloM wajt of proooodlag. 
 
 Iz. 1. mtMbfb^l; 
 
 (•) |-HftlKl}>*f|{ 
 
 •*• I'rl^ll'f" 11*^87 fofty'ttlto^U fiNty>M0M 
 
 sxf 
 
 ^••'*5TI»^¥'*-T**''NHwillw fMlfl||MlMI ^|f IjM Jftttttt^ 
 
 (» |»7-r9. 
 1^7-A. 
 
 Tliia it orldoaUy •fttriM* too nnail m f ii aoi to bo dliFMod bf 
 7 bot bj i of 7. > Smoo, fbo trao qnottontwIU bo« liMM Avorfi. 
 
 Thot, f-r|»||»|^»|X? 
 
 axiMiMMi anrff^ilM ly Om /WmMom >br«iMf If imtrtktg IJko 
 
 («) f^l=(fX|)-H(|Xf)=«-rl=H=|0|=fXf 
 
 This method depends ob the foUowteg: — 
 
 (i) Any mmber dlridod bjr 1 glToo that aambor fw faoMwI. 
 
m 
 
 
 m 
 
 **^ »iM •)•! »m 
 
 
 n. coMpux nucnoNt. 
 
 ffa>—r wM i |Hi ,towMrtio-»,belfc 
 
 i 4 t *♦ ^ 
 
 •f ftteeHaiistlM 
 
 1^ «-P-y^*. 
 
 MiUMply both tenM by 12 mhI t±*«f±» . 
 
 fa. 8. Simplify^. 
 Mvltiply both tMBM liy 18 Md 
 
 If_42-SM 
 
 '♦l*K 
 
 
m 
 
 AaiMMMne. 
 
 I 
 
 i 
 
 If, Iff m4 ft. 
 
 m TNI QMATIST ^ ^^ 
 
 Utt IM p«Hli» toowldiit •! tht 0.0.11. iTrfcito 
 Tkw, Ui tte O.C.M. of Ite. Md li. 
 " £lMito. 
 
 M M „ •Mii.t.dii. 
 
 •it.Miili. 
 
 " " •• " U. «. »i U. 
 
 i^'str* '^"''^^•^•!^^ 
 
 F[»dlh.O.C.M.of4|,H«d*|. 
 
 FIiidih,0.cil.<»f|,A»dH. 
 IW«i.d to • •o.aio. «t»«y iMi,, th^ 
 Th« O.O.M. !• Nudiij wMlo b* A. 
 
 •* tlM »»«»to» wid TO I. tut L.C.M. or tho donomtaJST 
 
 *w.i!!!![^ "^^ *'^^ •ortiJM tho O.C.M. oaetly Mid that' 
 too iOTona VH*Io»tt wo primo to 000 oaolfcor '^"'*^'^^* 
 
 16, 10 oirf » «» wholo wwWfi tad M. ,H«o to OHO oiwtoor. 
 
 ^^Y>«>i-cAiT COMMON Riu.Tif»iK or niAcno^ 
 
 JJo tiM iNipll.' toowledfo of too L.C.1I. of wi»lo Mirii«. 
 ThBo, iad tlio L.C.M. of ISd. Md M. — — ^. 
 
 ;; ;; " '•io.«,dM. 
 
 " •♦ 2i. ond J.. 4d. 
 " " " " £1 6.. Md 18.. 
 
 All iooB M tlio impU. 000 that tho MBibow wwt l« ,,a«od to 
 FlBd too L.C.M. of A Mid A. 
 
 ;; Ao«d«. 
 
 " " " "l,*«.dl. 
 
 l^ueed to a •onmott do»miin»tor, thooo booono «, « »nd A. 
 Tho L.C.M. ii rMdIlj foand to bo W, or V "» t» •»« rt. 
 
 to ^S^^^ "^ ""'*^"'' ^'^ ^•^•^- " -• 
 
 O.OJI.O» 
 
■MMifMiit fmi nuoauitt. , m 
 
 *>• !• ffl of H--H>fHx>f 
 
 Mon that liidlM««d by •(-. ■«»«• ■• ptrfwatd 
 
 ■«. a. II of U -i-l|'of A 
 -(If ol U)+(i| of A) 
 
 i.iii^oi,r:£rti^tr*^"--*-^^ 
 
 .4. "-*x»xfx* 
 
 ^^♦^* -ixixtxt 
 
 i. Tb« fffftilii *• «>®*0«i»IATl PRACnONS. * 
 
 P^ oat that wboB ibm primary mU te « ^1 rf rnf r ^»^ ^ 
 
 ^^.oid to b. . aoacint. f-tiorTST; xto?: 
 
 Ix. 1. Find tbo tml^M of I of ft tea. 
 loewt. by 5 ao la oompoiwd diTlolwi. ^^ 
 
t^' 
 
 
 
 t t f l«f£iii.44.-l«faii«MM 
 
 •i.M. 
 
 T 
 T 
 
 M11S.M. 
 
 ««. I. lipNM IS M tiM fkWilMI Of H. 
 
 •iitfltoMtit 
 
 telliiMlii. 
 
 MWMIpiMiflililll 
 
 Hmr ■Mto.MMrte 
 
 ■«.t. Whilpui«(«71to.M.to£tM.f 
 
 icr lit. §A,mtam. 
 
 hli 
 
 Bm nM.it fit tteMM 
 ;;;W.^W<(1«M. 
 
 f 
 
 AM. it|iCie711t.N. 
 
 ■x. B» 
 
 TTtAn iri. to tht iMMtiMi o( ft feoi. 
 
 l«i 
 
 ft.; 
 
 i*^* n*vt of nn ft.. . A II. ; 
 M« tr^ 9i mtt «!.- A l|.-ri ft. 
 
 to. 4. WhatfjNMMo^^f tfilltlorft 
 
 l«(4*»f«||; 
 
 |«rf»|»U; 
 Now, A It A or Mj 
 
 'HhtforH; 
 
 fof|ltHoCfof4|. 
 
vuiviii 
 
 
 -J *, . "- ■• »** ■•*• «• at tto --TH|,_ if Mten 
 
 Tkt diUlMliM 
 
 IWaadsalMv. UalM«Mbr 
 
 v'kM MOjr tb» MBtrat^r I 
 
 ■ifMM i t . Hit < ,ri i m . 
 
 «■■*» f » i^» Mr tit ••«•«■ ftwtftaa. 
 «< ^ .If, .MS «!• dMiay.; 
 
 (i) P»plh ■hpirtd kiwr tW fWIowtoiri- 
 
 (•) TkMVMtlkiMplMMtoMekpMlod. 
 
 
 (8) Pot • Boater raeh m 77777.7777 uaau th* klMkbo^M 
 

 *** AiuTCvano. 
 
 thtteftofit. *^ ••"'^'^ ■• »• "fW of Uw polat •• to 
 
 f^Mt 10 of My plM« makaa m« a# *k« ««_* vi_.. 
 
 > - «7 PI- «L; w iTSlrj? w ^ "*" n-.. -* 
 
 ■*tt*t tlntkM|>llMM,*te. ""^ ~ »•'•»•»* HfM o« 
 
 V 
 
 mmm 
 
 "« .Jr^tirs^itLjtr,"" • «-.«'• Pi- 
 ••««l»; •. 7JM thonMKltt,. • -^ ™ »«"«»••««• tlHM. 
 
 TMMk tUi M Mlom: 
 
 '•*°*"I?'. "r'".' ''°?'+'' """^wWi+T tlioiwu>dlk. 
 
 ^.. 200+60+6 
 
 ^1000 
 «7 and 206 thonsandtlu. 
 
IIMCWllOlts foil VtAOliiM. 
 
 AfilB, 7.ise»7 MilH-i toBthM- ft Inwdiadtlw-M 
 
 10 '♦"mqo 
 
 (8) Write 756 m tn-mmioM. 
 (4) WrHt 786 M tM mUUo&tlw. 
 ^^J»)^ --17 iffum •.« fMiiUMd to .spMM 914S handled 
 
 tiJUSJIf ""' **^ •^ '^•^'^ *" •«P'^ ***• '*»«»*'^ 
 
 ;f S?^ • •■ ■■'*■» ••««»?•• hwid^idi; ate. 
 its ^af "^~"" '**•* *" • ^*~* ^^* »• •«««^ •" 
 
 Is. 1. .9»M a.OOO; tie. 
 .» -A. 
 .90 »AV -A. 
 •ooo-Aft-A. 
 
 m, mEDucnoN op meomals to vulqar fractions. 
 
 »^ 1. B«4ll«« .m to . TBlgW fifMtlOB to 14. Iow«rt toriM. 
 .i7S»AMr"M«W. 
 
 •"»•»• WUIU BO tfOQble Witt ibi. If the n«tolIo« Mid BWMim. 
 
 Thoa, Ibtanptol: 
 
 .276*2 tMtliH-7 hoBdradthH-ft thoawodtlu. 
 
 _ 200-f70-t-S 
 1000 
 
tbi' 
 
 i 1) ' 
 
 (•) Dmimal Mtetfaa. 
 
 (») Tte ftmd f t fcta i priailiit of aidlftkM vi. ^i. 
 
 ••••■ <rtif ^Mair ^BA aiM^fc^^ ^••^i !^Pi^ •■ 
 
 fefi««iMri»cWM|y:- 
 
 I flMM. wAtr MMilf €M am^^ ^*^w 
 
 ^^* *-^^,f '^ 'rtU .M Will* lN*|li •» Mii 
 
 triMatte 
 
 te. L Flad tiM m of 4.8, «,ili^ li, .Mir. s 
 
 ae. «M«lf uMlir IMA*, «!,. iMsli«i 
 
 •JE I^«»«« •!• to »>• IMi. vwtiMl list 
 
 21 tko«MDdthM«» - "^ -- .| ■ 
 
 ^"^li^twr aMtbod of ■■Utagtlra *•— «---- _.^ 
 «w»Ur.rtKmldb.u.«||«8«Mriirtlo.rDJS^"!^ *" ''*^ 
 Fx. 1. From 17.8 teln I2.870. 
 
 17.800 or if^ 
 
 A« to Mblnetion of totaMn, write aalte m^^ ...li. *^ *.. 
 
 "o •• to Mko.tto ...b.r of d.ofa«d*%2rrt2r" "*"**" 
 
 nii fxpodloat for aMktac Um «MHiliM M.U. c^ . 
 
 If;: 
 
 VK MULTIPLICAtlOli m momkLB, 
 
 (a) Multiply « doolmal by a wholo owibor. 
 «x. 1. Mnltlply .7 by ». 
 
 .7«=A; 
 .-. .7X»=Ax»=:f|=«.8. 
 
9m WttHftf .tff ^ f. 
 
 lf.§««l TMfc mff t 
 
 (e) M i Him >4wi— I ^ m imkmi. 
 Is. 4. M m m t ii .10 kr 7. 
 .l*-* A Mi .7*^1 
 .-. .lii<.7-^fcxA«,^ifc«.M8. 
 
 fa.«. M mMp^ .o»17 «y .011. 
 
 (i) MnMMy • aiMi dMiMi by m dMlMd. 
 Ex. e. mOi^fy 4.70 bj .«. 
 
 4.7»»|tt Mi .8I«,«A; 
 • • *-»»X.»-ttlx*-fH||«8.W87. 
 (•) M«l«^ • mImA dcetaml bgr • mind deeinal. 
 »K. 7. Maltlpfy74tliy5.». 
 7.1t»fiiMift.0»t|; 
 
 ItwUlbetMB 
 
 ■lUnHw sBi « 1ll|i l« M id M wM« BambM Mi maMp^ in 
 
 iNi te^ MU^iter «K| MriUpHMiid tocpUMT. it wUl b. m*. 
 — » •^-> M* w anajr deeiaua i>!aeM ia th* prodotl m ia the 
 
 MiMlMpli«MdtOC«UMr. -««M 
 
 ir tk» ipnw wmU panBii oTlt. 
 
 Mijt^ 07410 by M, bgr lOM, by liiiOO. 
 
 «•«• 07.600 
 
 M» lOOOW 
 
 07.000 
 10 
 
 0IS4M 
 
 i7N0.0M 
 
 0700900.000 
 
.1 
 
 ••■I 
 
 
 jii 
 
 ll:: 
 
 H«M». *o ■«ltip<7 bgr tt iviibw 
 
 ■»>kw ia dfTWoa'oC dMlpMh! 
 
 "•«'i»<»*i*t«wMNiir 
 
 ^ i toltewfd hf 
 
 ^iviHrawlMb 
 
 "« pvim M m.prapar pia«« la th* mintiaiii 
 Otmwfc. ifcfci •. iMfcwrt,^ '""^ 
 
 (irilA. th. diTlTO . wiMito a«,bw. 
 »■■. »it 8)J«, H)m 16)M 
 
 8 • 8 -r- 
 
 fXf-H-^, ale. 
 The divlMr OM slwi^^ he anift « 
 
 *•» «• 4«*«y ]^,« l»^ 4,^,^ 
 
 (•) INvMm «f • BiM4 ^im»l by m 
 ■x. 1. DMtviMbjS. 
 
 W IHtI.I« •€ .d«|«y by . wiwto wmibw. 
 te. 2. DiTttto .me ky f. 
 
!5;i *!«••••» fcy .01. 
 
 M MX ite ' ■"••••w. 
 
 ■k. 4. ObMt .0011 bgr .MMt. 
 
 JggL- miot- • tift 
 
 .OPIMl-Jil^— if-""'- 
 
 ^- 
 
 r+lJ?4.«WI» . 11.5 
 
 ISB.lSBOMp 
 25"*" "IS"" 
 
 ^18.5 , IMP 
 
 "■•H-WH-a+swao 
 
 a>M0B6.5. 
 
 Kx. «. Dividt 1.78546 by 4M.r. 
 
 45fr)lJ^(0.0088 4567 I. not •cmuto.il. 17 .irfW. It 
 
 l.«oteo.W»odl«171lw».. Itl.«H 
 •0iitala«dial7a5lnn4ndth«. BM178M 
 
 _jBli hai^vM ta --'■^rY^Miiiiiii 
 
 ¥W.— IHTIMCTieW>WMBlfiWJC4yi^^l,lp 
 
 iV L41431M • 
 
 totMdeelaai 
 
 I^^^tii 
 
 38 
 18966 
 
 6nSMM 
 
 38166245 
 132664680 
 331M24 
 
 M.1MM5 
 6812414.1 
 
 16i»«6 
 8M0I 
 
 4860 
 
 46.00415l478MH» 
 
 88I98SS 
 
 »88166f4X 1-1-1 
 
 IIIMM 
 
 » 831662X4^3 
 
 33106 
 
 » 38166X1 
 
 18266 
 
 - II1«X4^8 
 
 668 
 
 * 881 XHl 
 
 SB 
 
 * 88X1 
 
 10 
 
 =» 3X3-».l 
 
 2 
 
 0X6+2 
 
 46.00415 
 
li 
 
 I! 
 I 
 
 1^«ipMplte 
 
 •,»• 
 
 t,ft 
 
 •• wnHMI 
 
 
 vHMMita 
 
 liW 
 
 V--- 
 
 ■f I* ■ fc l t iK if tiM 
 
 I 
 
 >>.•. INvii»tJ98||i|, 
 
 ftl Hi 
 
 4MKVt)t.f7IMt(.lMt7 
 
 0.0 Ji. or 4iM^ 
 
 
 te.0036. 
 
 
 or 
 or 1.36. 
 
■i. a. 
 A 
 
 
ITt 
 
 Bl.ft. BaiM* I to ft 4MfaMl. 
 
 |s.7777 . . . Iftiiiftltoly. 
 
 Is. t. IMM*Atoft4MlMa. 
 
 A-.lSlSU . . . iaidtoitoly. 
 
 Bx. T. ■•*«• I to ft 4mIm1. 
 • 
 
 • ixi ixix 10 " •' 
 
 I 
 
 By. 8. BftdftM A to ft dMteftl. 
 A 5 
 
 ^"ixixi"^xi|xJxioxi*"***"-"~ • • • «"<^tt*»y. 
 II 
 
 Bz. 9. BadftM A to ft 4MlaftI. 
 
 S ft 5 
 A- y ^ TXXtXWXW 
 
 " axaxsxii fxfx^xiixioxioxib 
 111 
 
 -tHH- .07164M . . . Iftddhiitoly. 
 
 Bjr cwpftHiif tliMM ttlM waaplM, \% will te dtotmd t— 
 
 (I) Thai whM thft fnMtkm b la Ito toww* tomt ftad Um 
 draMftlftfttor kftft ao fiMtor* oUmr ttaa S or ft, ttw dMhMU to iiA« 
 •ftd that thtra ftM fts mmaj ptaMi to tk* dMtofti •• tte grMtort 
 BBBlwr of tiMoo a or ft oooan fto ft taotor to too 
 
 (8) Thai vidfftr ftooUoM to tlMlr lowoot 
 iftftton ooirtftto ao S*o or ft*o ao tooton inodaoo 4oohBftlo vlikli 
 aovor tomtaito sad tiMlliM igfttoo ropoftk fma too dootaMl pot>t. 
 
 (•) Th ft tf Ip t fta ot loM totooir laiaoittowaftwhooodoaoBrfBfttora 
 kavo I'o ovi^oaad ««lMr prtoM aaaibon ao iMtom prodooo doolawl* 
 •r wUoh paito do aol lapoal aa« paito lopool aad toal tooto aw ao 
 toftajr ifWM la too paMo whioli 4o aol lopoal ao too 
 aaaritor of ttoMa 8 or ft oooaio aa a tootor of too 
 
 fa«iA».«^J>.— »u-«i^. .»^ ^J-^!^% ' -^— f TTii ■■■111 r 
 
 •ate lotto 
 
 Us 
 
1*^ *!!•.?' ^«.-* 
 
 **'» *( S| M I •* $t n 
 
 <»<k*pwiii| 
 
 in 
 
 
 
 •^•t fMa 
 
 
 
 
 A*.41«W... 
 ij*.81g|8i8... 
 
▼te.1 top«|»itft««ttii»flpMltal 
 
 ft 
 ifi 
 
 (t) •»•,«, t, It. Mi 414 •!• Ite 
 
 A^Mi 
 
 MdtiM 
 
 (4) TiMH tkt tonMr Mt Pvbi OliMlntfaii OmImIs nd Um 
 tattor an Mm OiiMiMi^ OMtaMlt. 
 
 (B) TlMlAPiMwOtiMlillif OMWftlMMMiflf aMpaiVtlM 
 laiattopwl. 
 
 («) Tkal ft Mlati eiMtiiltet DmImI MMMi cff Ura pMli, » 
 Pftil •hfak ift ftii ■ ipi rtHt. tkft t ft H i i ft i i , mdVlmmA wUtk h 
 nfmkai^ *H "Mittt nut 
 
 (I) |«.i{ .-. .i -ti. ftfP-ifti; .-. .Mi mwh' 
 
 A-.01; .-. .01-i^. Hi-i.llfj .-. .Iff -lill. 
 
 •adolh faBW^rttft tliiarWii rf w Mi ittMla^ 
 
 vti^ HmMom tkat teM M or • p««i«r •( M a 
 
 M4,«JI» 
 
MICMWOPV HMUITION TKT CNAIT 
 
 (ANSI and ISO TEST CHART No. 3) 
 
 1.0 
 
 1.1 
 
 LM 123 
 
 133 
 
 U 
 
 Itt 
 
 i 
 
 5 US 
 
 ^1 
 
 
 J. 
 
 y^PPUEa fA/K3E Ine 
 
 ia53 Cart Main StiMt 
 
 ^ W a c hoOi r . Na« Yorh I4«0> USA 
 (7t«) ai-9M»-r«i 
 
i^ 
 
 
 vn 
 
 ARITHMETIC. 
 
 This can be done as, followi:— 
 
 (i) Regard a pure eiroulatiug decimal ai a mixed one. v 
 
 Thus, .3b .38= .333, etc. 
 
 (ii) Malce a mixed circulating decimal begin to repeat at any 
 place greater than the number in the finite part. 
 Thus, .23457=. 234574= .2345745, etc. 
 
 Ex. 1. Add .3, .324, .2345 and .834567. 
 
 .3 =.3333 
 
 .324 =.32424 
 
 .2345 =.23454 
 
 .834567= .834567 
 
 (2) Having made the decimals similar, next proceed to malce 
 them OOTERMIMOUS, i.e., make the repetends 6nd at the same place 
 to the right of the point. 
 
 This is done by flndiifg the L.C.M.'of the number of places in 
 each repetend and repeating each repetend to that number of places. 
 
 Thus, the number of places in the repetenda is 1, 2, 2, and 3. 
 
 L.C.M. of 1, 2, 2, and 3 is 6. 
 
 Thus, .3 =.333333333 
 .324 =.324242424 
 .2345 =.234545454 
 .834567 =. 834567567 
 
 1.726688779 
 
 The number to be carried to the right hand column is found by 
 adding the first column of repeating figures, thus 5+5+2+3=15; 
 carry 1. 
 
 Ex. 2. From 7.9845 take 5.7856387. 
 
 7.9845 =7.984584 =7.984584584584584 
 
 fc7856387=5.7856387= 5.785638763876387 
 
 2.198945820708196 
 
 («) Multlpilcatlon and Dlviakm of Clrculatlnfl Dcclmala. 
 
 Sufficient accuracy can generally be secured by extending the 
 repetends a few places and then multiplying or dividing as in 
 ordinary decimals. 
 
 When perfect accuracy is required, the decimals must be 
 reduced to their equivalent vulgar fractions and then these are 
 multiplied or divided and the result is reduced to a circulating 
 decimal. 
 
 
SUOOEBTIOW POR TCACHIVO. 
 
 m 
 
 Ex. 1. Find the value of £.876. 
 ^•876 .876 of £1=.876 of 20..-17.600.. 
 
 12 • • «"876=178. 6d. 
 
 e.OOOd. 
 Ex. 2. Express 2.375 bu. as « compound number. 
 2.876 bu. 2.375 bu.=2 bu.+.376 of 1 bu. 
 
 j-^^^ .375 of 1 bu.=.375 of 4 pk.=1.500 pk. ^^ 
 
 2 * °' ^ I'^'—S o' 2 gal. =1 gai. 
 
 1.000 gill. •*• --^^^ **"-=2 bu. 1 pk. 1 gal. 
 
 Ex. 1. Reduce 4 cwt. 3 lb. 8 oz. to the decimal of a ton 
 
 ImH^k 8o«.=Alb. =.6 1b.; 
 
 100)3^1b. .-. 3 lb. 8 o«.=3.5 lb. 
 
 20 )4.035 cwt. 
 .20176 t. 
 
 .'.4 cwt. 3 lb. 8 02. =4.035 cwt. ; 
 
 ^•*^*>=I^cwt.= .036cwt.; 
 
 Or, 
 
 4.036 cwt.=i^ t.=.20l76 t. 
 
 4 cwt. 3 lb. 8 02.=6456 oz.; 
 
 1 t.=32000 oz. ; 
 
 .•.4cwt. 3 1b. 8o2. is AWfijoflt.; 
 a'»d M^o=. 20175. 
 
 Ex. 2. Express £2 17s. 6d. as the decimal of £5 
 £2 178. 6d.=690d. ; 
 £5=1200d.; 
 .-. •e2 178.6d. ls,^of£5. 
 
 Now, i^=.575: 
 ••• £2 178. 6d. is .575 of £5. 
 
 Ex 3 Express | of 2 qr. 14 lb. a. the decimal of A of 1 ton 
 lof2qr. 14 1b.=|of64 1b. =24 lb.; 
 A of 1 t.=A of 2000 lb.=160 lb'. 
 ••• f of 2 qr. 14 lb. is ^A- of A of 1 t. *' 
 
 Now, A\,=A=.15; 
 ••• I of 2 qr. 14 lb, is .15 of A of I t, 
 
178 
 
 ABinOIBTlO. 
 
 \h 
 
 MV. raiCENTAOE. 
 
 * "n* BcfiNrrNM. ^ 
 
 Prowni nuiy problemt mi— 
 
 (DA droTvr lo«t 7 <mt of erery 100 diMp he had; how muy 
 sheep did be lose oat of 900f ^ 
 
 (2) A merahent gained $20 on ererjr $100 he had in boaineM- 
 how mneh did he gain on $1200? 
 
 (3) A eompaogr ehMgea $2 for evenr $100 of in«irauoe; how 
 mneh would it eharge for $700 f 
 
 (4) A bojr is abaent from sehool 3 days ent of ereiy 100 sehool 
 days; how many days is he absent in 200 sehool daysf 
 
 Tell the class tlurt the nmal way of stating tbeae p»>blems 
 is to say 7 per eent. instead of 7 ont of erery 100* 
 * " •• " «0" " $100 
 
 a • » $2 •• - $100 
 
 3 " " •• 8 da. - 100 da. • 
 
 BY .00, and being a contraction is to be Written with a period. 
 
 Explain that business men compute their gains and losses at so 
 much per eent. 
 
 Also that the eymbol % is used for the words per cent. 
 
 Ask many questions as 8 is what per cent, of lOOf 
 
 8 " " '* •« «• 5or 
 8" " " •« "200f 
 8 ** •* «« «' " 25r 
 8 *• " •' «* •« 4oor 
 
 What is 5% of MOf of 200? of SOOf of 4007 
 
 «. THE RELATION OF PER CENT. TO DECIMALS. 
 
 (a) Much practice should be given in nading per cents, as 
 decimals and expressing them as such. 
 
 Thus, 5% is read as 5 hundredths and is written .05 
 11% " " "u " «. .. .. J. 
 
 25% •• «• "26 " " «« " *25* 
 
 EXAMPLRS. Write as decimals the following:— 
 
 15%, 35%, 40%, 374%, 5J%, 8*%, 150%, 1124%, «%. 
 
 (6) The converse of this should also be given, i.e., decimal* 
 Sbould be expressed as per cents. 
 
nroennoKs not nAcaan. 
 
 vm 
 
 That, .25 li rMd as liaiidradtha Md is SSft 
 .15, .20, .76, .161, .06, .061. 
 
 Tho,, 5% i. 6 handHHlth.. or .06. or ^, or A. * .' 
 
 "**-}S=*- 
 
 =/A=*. 
 
 100 •• 
 
 
 8x8ai~ioo""^*- 
 
 1=3^112*^871 -• 
 
 8X12i 100 ****• 
 
 ._2X20_^ 
 
 MOR L— A« tb» draomlaator of tha fM<iM«. l v .. 
 
 *«» of the frmrtlon -^1^^^^ l^SXS^^ *"*' *«»• *^ 
 
 by tl*d«K,alBrtor of the ndg,wfc«So,K^^^^^ *""*'**»«»» 
 
 Now l-Itwffl aowbeel«tttli«tpwe«t.«m b»e»in»^i.«^ 
 
 o) ;; •; •• v»boi%. 
 
 W * " » dMiBMl ftrMtltm. 
 <*) " " «T«lr„.fr.rtton. 
 
 The following should be memoriied:— 
 
 ml-l ^**==* «7***l. 
 
 !«*=* 40%=| #i»«-.a 
 
 20%=i 50*=i 2*Ia 
 
 26*=i ' 66|%=» ^Zzt 
 
 ^*-* 76»«| ^Izt 
 
110 
 
 AKmUfSRO. 
 
 IV. ATTLICAriON TO TVFt PROBLEMS. 
 
 a«iie«, tlMN ariM tbrM euM m foUowa :— 
 
 I. T«fMMyp«rcMt.«f«ilvMfMiillly. 
 
 II. T« IW ,Hi^ per e«H. one ••«*•, I. of an*Mi€r. 
 C^lll. TolI«llM,i«,tt,y,M.e«..«..Krc«itf HI. 
 
 now many did h* mII? 
 (•) 48«»i5/S 
 
 M of 2500 •heepsiors aheep. 
 (») Or, 43*=r.»3; 
 
 .48 of 2600 shMp»2000 ihe«pX .43=1076.00 sh««p. 
 
 C»e II. Ex. 2. A drSrer having 2500 alieep loid 1076 of tliom. 
 Wliat per eont. of his sheep did he sellf 
 (a) No. sold from 2600 sheeps 1076 ; 
 .-. ;' " - 100 " «4l*,or48; 
 .'. 48% of the sheep were sold. 
 (5) Or, 1076 sheep is Hjl of 2600 sheep; 
 
 Mid HI§»ift|of 100handredth8=43 hiindredths>e43ft. 
 III. l!x. 8. A drorer sold 1076 sheep; ihis was 48ft of 
 the number he had. How many had he at iirstf 
 
 48«=i%; 
 . . inn of the number of sheep=1076; 
 
 ••• " " •• " «W of 1076 
 
 =100X26 
 =2500. 
 
 XV. APPLICATIONS OF PERCENTAGE. 
 
 No«.-The dlfflenltjr of •pplytoc pewentM* to eommenial trMiaution. tu. 
 
 St^l™ T «>-r««««?I>INO ™ MATURE OF TM mSSiSS 
 INVOLVED. Henee, befora problems an tolvwl, MUCH CABB SROntn m 
 
 «hut«t«l, a. ter H po«lble. by «,m., bH.ta«« form,, m crtatoiTlSotol 
 
 Th. topic ta«l.«, .hould b. d,««M«l.'Sl.lnS!.lS^ISll °* •" *^*- 
 The* llhutiKtioM and nplanatiou will nmov« the dlfllenltte. .ri.i.. # 
 
mj99Mtfnmx9 worn TiACBim. in 
 
 •• TRADE OtSCOUNT. 
 
 ^J^^'^TJUr •r!j»'*»|r^« ««-»•« ^•"•'•"y ••t.logne their 
 
 A dediiotioQ i« made from thii priee to enable the ratailer i, 
 make hi. proflt^^ If the eatalofae fell Into the hand, of t^e pn . 
 
 mueh for the good.. Wherea.. if the net priee we« printed^ 
 the eatalogue, the pirohaMr would nntunilly feel that he wa. 
 
 f^rir"*??^', !"^' • ~**»^»"*' -1.0. enable, the maT" 
 faoturer or whoIe«Ie dealer to meet the lloetuation. of the market 
 by merely .hanging the rate of di«,o«nt «.d thn. the exp^U o 
 printing a new eatologne 1. avoided. «P«i.e oi 
 
 aJ^T^^"^^ ! ■^*'"^ deduction {. allowed off what remain, aftor 
 deduetingthei»r.tone. ThI. i. to indue, prompt paymentiy^I 
 
 Kn^Mf T ■ ''**'^ ^Jeduetion i. made on eertain kind, of good, 
 h^ut^thi. i. a matter of .pecinl arrangement between l^^yoTTi 
 
 DiiS^OT.^''*""' ^*^"'"'*"" '" ^"^''" " ''*^* *»» CoMMracut 
 
 Trade DiMount i. alway. reekoned at a eertain rate per cent 
 The flr.t dlecount I. deducted f„,m the ll.t prlce;Te Text one 
 from what remain.; etc. * 
 
 The final reeult i. not affected by the order in which the 
 diwount. are made. Thus, diBconnts of 40*. 10%, «„d 5% TZ 
 
 ZTIX"^ '' ''^' **' ^' *«* ■' - - tho.'of"5V.U': 
 
 M. Appncatton to Solutioa of PraMeaie. 
 
 fh.^1* L I** !I? **• *•**""* *^»« 9hen the amount of 
 the Mil and the rates of dtecomit. -™««ire or 
 
 ^t ^*' }i .*''"? i*** dlMount off a bill of |120, the rate, of 
 dUcountbeing25*, 10%, and5%. -» i •ub raie. oz 
 
ISf 
 
 Awtmrnaino, 
 
 
 BmmmI 
 
 «i 
 
 41 
 
 <i 
 
 10ft: 
 
 Ht 
 
 ToUl di«ooBnt»|(120-7e.JB)»$«.aB. 
 ji^ "• 7? "«^ «« Ml h-vliil •!•«. »• 
 
 to. t. What was tha bin for wUeii «1U waa aaaanfti^ .. 
 l^«it,tli.«t«iaf4h««,tbataf«0fta»diftT ^ 
 P*i« of bUI faaalDiuff aftar tha ftnft diaeoaat»Ab of blU. 
 
 SaaoMi •• ' m^ •« 
 " " " «wodiaooaiita*-A& " 
 
 Bniaa, ^ of tiia UU^J4. 
 
 .-. " ''-W of $114 
 
 ti 
 
 «( 
 
 ^*P^^^in^>^»h.,^tni^a»^nni^M of bill; 
 
 ^TS* " =-Afcof/AafbUl, 
 • • Mr of iM of bUlB$114; 
 
 .•.4habUl«WofWof$114 
 
 a|200. 
 
 Cm* III. T« And me rate or dtecowM IimIm nh., m 
 
 Ex. 8. What la tha rata of dJteooiit whan a bUl of $876 H 
 ■•*'l^ ^ • iMymant of $260r '^ * 
 
 Aapnnt of diaeonatasffSTS— 2S0)=s ai?y 
 «25 fa in of $876; 
 .'. rMo of diacoaiit=i||3Bi3=33|%, 
 
 Cwe IV. T« Hud • alRaia dtacavnt ri|Mliy,,t i, t,^ 
 
 Part of biU lamainliig aftar first disaonnt^^ of bUl • 
 SMo&d diwooiit at 10ft=T}v ' 
 
 .'.part of bill ramaining after leeond diMOinit=::VHr 
 «««•, •ingioiUaao«iit«<|»_^) ^ blU.^^ 
 
 «37ft. 
 
 «< 
 
•VMwnom worn TCAORma. 
 
 •.-i^of't **:J!rpS'r '^hiL^^^ — n^hi p.^ 
 
 Mtf^'t / JMwhMt boosht goods for #357 
 •SIO. Flod his ptoflt. 
 
 8*Uioc PrieosBisio 
 Cost " s:t2S7 
 Profltss IS8 
 
 ud Mid thon for 
 
 the flM« wIms per 
 
 Gain on 8o.=(8-5)o.=3«.; 
 
 " " ioo>.^?y^\. 
 
 '•» 
 
 .*. gain=60«. 
 Or, gRiii=:| of eost priee; 
 
 .'. g»in=60%. 
 
 Ill* Qlve« |||« co^ price wmI thr 
 
 CMt. to find the selll«9.pHoe. 
 
It 
 
 IM 
 
 fr 
 
 AMniflTIC. 
 
 'HI of 8c.»0c. 
 
 • II t( 
 
 I. 
 
 Nk COMMItsiON. 
 
 ""V^ •• »-»T " "ll <. th. «r^Ti Sell ^ u*!! 
 
 -.«i^« -- «-■-- '•' ^^"t,:i:t;z 
 
«l 
 
 «l 
 
 •« II 
 
 ^•r» mail, lioir«?«r. h* ukan »itk .u^ •»•-•»•«'» f». 
 
 CommlMion on $109»$2^; 
 .*. ram iBTMtMl oat of $1024»«ioO| 
 
 fooM^f 2885X100 
 
 IV. msuKANce. 
 •Bd If UTVAL CoMPAXin •'■«••, BrooK Com pAjfiig 
 
 •w inmirwl bMome memlM*. «7« P***** "•>«.• proportlot 
 
w 
 
 •* '■*^»^ «•» k.«lktf. •# Irtrt. 
 
 
 1 ]V 
 
 i 
 
 li' 
 
 
 nmoM. — -^ iM BAn or Iummm, «m| h. 
 
 ^W •!?• riM ft* tkiw MM> ^i.11 ^ 
 
 ApoIl^of$100wlUp«yfo»«*^ . 
 
 lanso '< <« 
 
 a-^WSOXlOOv 
 
V. TAWS, 
 
 W 
 
 •«-r «l.«l for ^.TjLrSTtolrTJr^' "*•*' '"»"-• TU 
 N..^ lit .•^JTJi'^^^^^^^ r- W.O .. . .^, u.. 
 
 «• wUltd a DcTT. ' • *•* '■ •» I»WMCT Tax anil 
 
 Sir-;.-'"'- •^'. xrx r*?ir; 
 
 " Sj^JIriSS;:'. •• ""*• ■"*"• """- •';•«* P»P«»r, 
 
 «» JW will b.. u„ Bat, o,?l^;^" ',«'*• •«!»««» for 
 
 b. ta^ Th. ,.';z. n: i**«^°*i^' *• f-^' •« 
 
n 
 
 P!"" 
 
 ABITRllino. 
 2. Cmm af mrtd Tmc«. 
 
 T4WTE Of the property whloh ii Uxed, (2) the matm Jd fsT^ 
 
 AMOUKT Of the tUE. ' *"" ^'' "* 
 
 Cnc I. Otven tlie 
 rate, to Hud the tax. 
 
 on fe ioll.^"^ ^' *" "" *'~^''^ "-^ '•»' 15400 1 15* mill. 
 T«zoii$l »|.015S; 
 
 W400=$(5400X .0168)=tS8.70. 
 
 value of the properly and ffce 
 
 «< <i 
 
 llie 
 
 ^^ II. Olveo the .Meseed v1«e of the preperty 
 MMwleffllietax,toflMltlierate. . '^"^ 
 
 Ex. 2. What Is the nte of tioation when $66 is the tax »««- 
 property assessed for $30Mr ««» W is the tax npon 
 
 Tax on $3500=106; 
 ••• " "W =$rffy=$.016. 
 .'. the rate is 16 mills on tae dollar. 
 
 Value of property when $.0125 is the tax=$l ; 
 
 .31.25X1 
 
 <( It 
 
 44 
 
 *l 
 
 $31.25 
 
 << <i 
 
 =$= 
 
 .0125 
 
 =$2500. 
 
 3. MWIRECT TAXES are of two Unda. cuKTttMm. >«..»... 
 
 EXCISE DUTIES. ^^ CUSTOMS DUTIES and 
 
 by law to be landed at eertain places ealled Poets of Ehtot 
 
 At eaeh port of entry the Dominion Goyemment has an 
 ejteWtehmen . called a Custom House, with one or more oSce« 
 
 inspect the goods, examine the invoices, collect the duties, etc 
 
 Ax Invoice is a statement detailing the kind and qnalit^ of the 
 arUdes shipped or sent to a parchaser or agent with tT^iTwei^t 
 or amount, and the cost of each article. Ibices are mlde^uMn 
 
».^::r:jsr r;rs'r::r "• '•' "^ •»■»-•' 
 
 I»7lllg *ltr, et«. •"•«»• BOM M» dlq»«d of WithOBt 
 
 . ^^^orx rai""^"j?t! "J- '-" *""■ '• 
 
 them. '"• '^ "^ «*n»y Impced by law npoa 
 
 rol^jeet:- «»«KWted as headings for teaching this 
 
 («)I)i«et. TAXATIOH. 
 
 (*) Indirect. 
 
 («) Direct Taxes, called Taxes. 
 
 (1) By whom leWed. 
 
 (3) On what leried. 
 
 (») For what pwpow^fc,^^ 
 
 ''^^i^"!r^'^-«»-*>"-«<iu««.thod 
 
 (») Mrect Taxes, caUed Duties. 
 
 (1) Cnstoms Daties. 
 
 (2) Bxeise Daties. 
 
 (3) By wh<nn levied. 
 
190 
 
 ▲lUTHMBTIO. 
 
 
 I:.. 
 
 Vk. INTEREST. ^ 
 
 Hon L-Imm wHIumMm tatrodoM Stoeks ImCbm lalMwt, bol m teuf 
 MtfcHM ia SiMks Mw diflealt ter «M aiuMqiwliitwl with tiM rabdMl. h to btilMvd 
 •drtoiM* to poalpHM (hair wmsktontloa oattl lateiwt hat 1mm stadtod. 
 
 Non 1— 8iaee • mw atonMBt, tlm*. mton iata^ tba ealeolatloiia In latocwt, 
 tt U awMMHTir to i^ wan •ttoatlon to thto unXtiuMm of PwvMitaa* tlua to 
 MnMo(lh*«th«s. 
 
 1. ExplMMllMM. 
 
 niostnte Int«rM« by ealliiig •ttention to what !■ pftid when m 
 honw is hired at • livery, when » house or farm is rented, when a 
 man's labor is employed. 
 
 Make elear tliat the money paid is for the UsB of the horse, or 
 the house, or the farm, or the labor. 
 
 Point out that the rent yaries with the value of the house and 
 the Mnm it is rented. 
 
 Apply this to money:— * 
 
 Instead of getting the use of a house, one who gets the use of 
 money pays for this use in proportion to the turn borrowed and 
 the MsM he has its use. 
 
 Introdnee the terms, Prineipal and Interest. 
 
 Money loaned to another is called Prikoipal. 
 
 The sum paid for ito tueAt the Imtkiuut. 
 
 Money employed by a person in his own business is ealled 
 Capital. 
 
 Interest is oomputed at a certain Bati Pbb Ckkt. per annum. 
 
 At this stage give many mental examples in finding the interest. 
 
 Introduce the term. Amount, by means of an example, as: 
 
 A borrowed $200 from B for a year at 8% per annum. How mueh 
 must A pay B at the end of the year? 
 
 Make clear how the $216 is made up, and give the term, 
 Amoumt. . 
 
 The Amouxt eonsisto of the Principal (which is constant) and 
 the Interest (which varies w'th the Principal, Bate, and Time). 
 
 When Interest is paid on the Principal only, it is called Simpub 
 Iktkrut. 
 
 When the Interest remains unpaid after it falls due, it is smne- 
 times added to the Prineipal and the Interest for the seoond period 
 is computed on this increased Prineipal. This is known aa 
 
 COMPOUm) INTXBBST. 
 
<< 
 
 II 
 
 •UOOBmOXS FOR TBAORIVO. 191 
 
 ♦, ♦, *, •tc., this nte for the period spMifled. 
 
 i .T'VtJ* rr """" If '•«*^*** •■ «j»i^«t to 4% oMh 
 
 ♦ yr., 2|*6Mh*yr., or2* oMhiyr. 
 
 Thto ia, howeror, not ttrietly Meunto. 
 
 * y»^*\tta W-W.*"*" "" •^^ •* ** '" 1 y. i. W; .t 411 per 
 2. C e ee e ef Iwtereet. 
 
 riMe, to find tke laterest or Amomit. 
 
 Interest on $1 for 1 yr. «Mw; 
 
 " « " 2iyr.=$(2iXTfc); 
 1360" 2* yr.=$(3a0X24X,f,) 
 ^ =$52.60. 
 
 Or, • Intereet for 1 yr. =t«t of $360; 
 
 .*. •' •• 2*yi'.=2iXTl»of|360 
 »9&2.50. 
 
 Interett on $350 for 2i yr.=f52.50; 
 •• ;; "♦3W " lyr.=| of •62.60; 
 
 •'•100 " lyr. =H«of|of$52.60i 
 =16; 
 .*. rste=6%. 
 Interest for 2* yr.=$62.50; 
 
 " lyr. =f of $62.60=121; 
 .'.the interest is A^ of the Principal. 
 
 iWf of Principal=Tib of Principal; 
 .-.the rate is 6*.' 
 
 be mMl ^ ""^ ""• '"" *^* ^"""^ on $360 at 6% per annnm 
 
 Or, 
 

 r 
 
 ^1^ 
 
 lit 
 
 ARlTHMCnO. 
 
 The InteiMt on $300 for 1 yr. At 6ft to $21 
 
 Tin* for whieh $21 it the intorMt oa $8M»1 yr. ; 
 
 $S2.50 
 
 «< 
 
 ^800sr~. of 1 yr. 
 
 >9«yr. 
 
 IV. («)Olveii the l^itarMl, Rate Mr cent MrfTiM* 
 
 Prineipal to giro $6 intermt in 1 yr. »$100: 
 ••• " " " W " "2iyr.^|ofil00; 
 
 ••• •^a.M- "2iyr.=^x|of$100 
 
 «f350. 
 
 Ex.6. What Priaeipal wiU waonat to $402.60 at 6 Mr wnt 
 per umoin in 2i yr.f '^ 
 
 The interest on $100 st 6ft for 2i yr.a$16* 
 .*. priaelpal whieh amonnte to $116 for 2i yr.=r$100' 
 
 ••• " " " "1402.50'' 2* yr.=$(^!^:52X100v 
 
 «$860. 
 VW. COMPOUND INTEREST. 
 
 In Oompomid Interest the interest m it falls dne at the end of 
 a stated period Is added to the prineipal and this sum beeomes the 
 piindpal for the next period; at the end of this seeond period the 
 interest on the new prineipal is added on and the amonnt forms a 
 new prineipal for the next period; ete. »« • 
 
 When the hiterest is added at the end of eaeh year, it is said 
 to be eompoundcd annnaUy; when added at the end of eaeh half 
 ZL L^rlZT^^ half-yearly; when added at the end of eaeh 
 uiree months, it is eompoanded quarterly, ete. 
 
 to And the Compmiiid Intere^ or Amovnt. 
 
 Ex. 1. A man deposited $2600 in a savings bank, the interest 
 being eompoanded half-yearly at 4ft. («) How mwh Wrt^ 
 
 k 
 
» ISO; 
 = 181; 
 = $82.02; 
 
 •UOOMTIOMi fO» TtACHWG. j^ 
 
 Lult "" •"" •' ^'^ — "-' "- (*) ^ ~b Of thl. ta 
 
 Original pHaeiiMl»92500; 
 Interwt for l.t poriod«2% of 02600 
 Prin««l»l" 2iKl •• =:|2880- 
 ?!:7*,;;2"d " «2»of'|2M0 
 
 Intorw* " 8rd " =2* of $2601 
 Amoont at hb er^Ut «|2688.02; 
 
 ^*«'««'=t(2888.02-2600)=$163.02. 
 
 Benee, 
 Amount of $1 at end of irt poriod=i|f of $1 
 
 $1 .2nd " Z^^'^I^J^J^^^P^F^^' 
 
 It 
 
 tt 
 
 II 
 
 II 
 
 II 
 
 $1 
 
 « II II 
 
 3rd 
 
 II 
 
 n 
 
 -mof(«|of$l)=(|«,.of,i 
 -ftinoipal for next period. 
 
 =(+«)• of $1; '^ 
 
 ^H^xmn =$2083.02; 
 
 "$2800'* •• "8,4 
 
IM 
 
 
 ABinmino. 
 
 rnnelpal which MBonBto to |(l.02S)'»$i; 
 
 <1878.42 ^»"!*'*^^i«»l280 ' 
 
 1. 
 
 VMI, TRUE AND BANK DfSCOUINrt. 
 
 If A owe* $212 to B, the money to be neld in i «. i* «» i^ v 
 
 being worth 6« per annam, for B would hare the nee of IhT*^ 
 
 woo ii eelled the Pbukmt Wobth of the debt. ^ 
 
 $12 i. called the Tbui Disooukt; being mthematieellT .««» 
 ft iiiiwmetime. eidled Mathimatical DigcJuOT ' ' 
 
 SSL"-?"""— -"^-•5 
 
 T«oi, o« Mathuutkui, Dimnn to tlw lnt««M «. >i. 
 ft«.nt Worth f.,tt.,l«,„to«.dtli». •" *• 
 
 Thto kind of dtoeoont, Ik. todiiii of which to <rft.li t».i^ .. 
 
 iZ^! "* "" "• «'"°' •• «"•' «■• Wnrip.1 „ 
 
 ..rf J; ..^to"«*^ '^'* " """■ *• >^"«^ ««».. 
 
 The interest on «25 for the given time and rate«t25; 
 
 di8eoantoir$350 •' •• «« «« u «i if,' 
 
 =$25; 
 
 •*• " " *• $325 " " I « _g325X26 
 
 350 
 
 Ex. 8. If $5 is allowed off a bill of $105 dn« a ».« i. 
 
iV<H»«nOM fUft tUMMlMB. 
 
 IW 
 
 l»I.tl^dl«Nm«t«tfwo6fo,emo., 
 •••o dlMomitoff $u "Wmo 
 
 ■^ori^ of Um note or bill Ita* L. ■^^"••« »»oaty «« tlw 
 borrow, |06. 'n^dm.^ 1 ^JT"^' *? '^^ «*^ *• *»•• 
 
 through. "•-•lOMly outlined Mid wr»ft,lly ewrled 
 
 payment. * noiaert d the maker fails ln 
 
 reeeiTing payment. * '^ endorw It before 
 
 A Pbotsst is a declaration made In wHtt... k. *t . 
 
 A BILL or EzOHAirOK la a w^m„ , »""*• 
 
 "««. to par . fl»e|4.d ram .( 
 
AMTMMme. 
 
 u\ 
 
 ml: 
 
 ■owy to t tUtd pmM •iUJtdlfc.pujri.ortotfc.o.j.r.ftht 
 
 Bllli of InkMif* an of tiro Uado, ▼!■., (i) lalud Bllla of 
 BMlMiifo, or Dntti, Mi« (t) Ponlffn Blllo of KnkMifo. 
 
 As iMiiAm Bill op Bxobami is om is wkUk tho dnwtr uid 
 dmoM *mMo hi tho moo oonliy. 
 
 Thio It ■ 11 % ooUod a Obavt. 
 
 ThMO MOTOfhNw Uadt of Dnfti, mD$mmd J^/to, poToUo oa 
 PtMMlotloB i mgkt 4r^, povablo tftor thioo 4ogro of gnMo i TUm 
 dr^, pograblo ■! o ooiteia tiiao oftor tho doto of th« dmft. or 
 oftor pfooentoUoa for ooooptMMo. 
 
 Aftor tho AwMf offroM to Mr tt oad writto " aoeeptod " with 
 his tigiwtiuo ud tho doto, aoron tho fteo of It. Lo 
 
 ii OM is whieh tho Dmnor and 
 
 A Voanov Bill ov 
 ooldoia 
 
 A LnnB o» OsiDiv Is a lottor or aotifloatloB iMued to pofKwa 
 tvaroUlac wd addiosssd by a hoabsr to his Ofoat, infomiiif him 
 that tho pofsoB naaod thoroia la oirtitlod to draw a eortala som of 
 nonsgr; whoa ad d i osss d to soiroial agoats oa whom tiie amaoj eaa 
 ho diawa ia saarn to salt tho ooavoaioaoo of tho t»roUor, It is 
 oallod a CofOOhUi Lnna w Gaum. 
 
 a. C sBiis Hn ii or Tnw oa 
 
 Baak Dlsooaat is oqoal to tho iatsiMt oa tho ralae of tho aoto 
 atmatoritsr. 
 
 Trao DiseoBBi to tho fartsioot oa tho sam whIeh will ameoat to 
 tho Talao of tho aoto at aiatarlty. 
 
 Baak Dlsooaat Is, honoe, gioator thaa Tnio Diseoaat hf tho 
 
 OB tho Trao Dlseoaat. 
 Caaa I. lUwoa Hm sola. 
 
 rale of 
 
 ••**!* ToaoMTO, April 17, 1901. 
 
 Tkroo moiUho aftor data, I prraiise to pay to tho order of 
 James Joaes, six hnr .red and forty-fonr -M dtilars with iatorest 
 at B% per anaam, TShie reeehrod. 
 
 JoBN Baowx. 
 
 TUs Bote was diseooated at the Imperial Baak at 711 oa 
 Majrist. 
 
•DMnnon foa nAoaiiio. 
 
 wr 
 
 flad (1) tiM teak diMMnt Md rs) Um .^ «-: ^ 
 
 •r MM 
 
 •I 
 
 N. 
 
 •r 
 
 tolMlkt 
 
 ^.^' \ ^ ■•'■rity, ft Bot« Is worth $B9ilt thm di.-i».« i 
 
 iBtMwt Ml $0021 for 45 dft. «$41^, 
 
 m. 
 
 
 OlKM the 
 
 to"* «f diMoont. F«wMe« 9115.48. Had Um 
 
 ""^ " .u;*^;^ -^-jL"* .»-»«•«'-♦'•»•. 
 
 .'. 51.82 " '< « «• 1»MX855 . 
 
 — Ij^j— d»., orSSda.; 
 
 •*. tsm of diaaoant it 56 da. 
 
 tioa of Omo m of Siaple latorMl. "odfflea- 
 C»«IV. Oit>«HI,« act „^aaMl^ tfc> ->. ^ ^ . 
 
 Not proeoodo of aotoa>^ « «« 
 •*. M of iniitority.TaiBeaii587{ 
 
 •'• ■Mtarity-Talao»W of 5687 
 -5660. 
 
f 
 
 I'! 
 
 If 
 
 HI 
 
 t. 
 
 n.tTOCKI ANOMMOgWOt. 
 
 OH) Tte tia* tl whteh til* dlTidMdi an dM. PHm* u* 
 jufMMrhMitlM dlTMrada m* wwn <Im Md nmuUly drop after th«y 
 
 (It) Tte piMpMt of a fntw* IneroaM or dooroaao is tho 
 
 (T).Tho ampviit of tho Bort, or Bmotto. ' 
 
 ConpMiloo Moally roMnr* a part of tlioir Mmlagi, iaatoad of 
 PVing thorn aU to dlvidAda, to onablo thorn to moot naforooMB 
 iomm, oto. This io oallod tho Ran, ok Bmuti. Whon tho 
 MouiBBlatod Boot to largo It add. to tho Taloo of tho 8to«k. 
 
 inotnato to prloo bat not to tho mum oxtoat. Thia teotutioii la 
 Jw!i.i****^T*^'J" tho prioo of mono,. Whon inonoy la 
 plontiftti and honoo ehoap, anoh bonda wUl tooroaoo to prloo; whon 
 "^^y,** ***^ •*** ^^^ ^^» *^ 'rtll doefoaao In prteo. 
 «# ?^"^* •'!**'»*■ •» ••wrftlo. giTon aa aeknowlodgmont 
 of dobta, boartoff flxod ratoo of totoroat, and prorldtog for tho 
 ropaymo nt of th o priaoipal al a opootood timo. 
 
 PuramioB, OB PBinnBio Stock la atoak boaring a ind 
 ratoof totoioat whioh nniat bo paid boforo a divtdond oaa bo paid 
 
 on OBDnUBT, OB DlVlBBIO 81OOK. 
 
 Watwi© Svook la itoek whioh haa boon iamiod to atoekhoMora 
 Ii^ addition to what thoy own and for whioh no payment haa boon 
 ■iOde or ia roqnirod. 
 
 AtJP^^f ^* Charter of the eompif^y forbldi tho deelartog of a 
 diTidond ozeoediDg a eertain rate per cent, of thoipar ralno of tho 
 *?? ^ '^***" ***• eompany wishea to keep the pabUe In ignoranee 
 9t h» piDsperity. ita capital itoek Is inereaaed by iaaotog additional 
 aharea to Ita present stoekholders so that a low rate of dlridond on 
 the toeroaaed stoek will prodaee as mneh Ineome aa a hich rate 
 upon the original capital atoek. Stoek so inereaaed is said to bo 
 watered. ^ 
 
••MbtoM i.«iWm Bn*«H. XU. mZTT" -- ^ 
 
 b^M.^.o.jiL^-rriSj^i:.'^ '- "^ 
 
 whom tbo ikMk ii boi«ht Md •.« to i. fc^!! ^^f^** ' '" 
 0. 0. .took wUI ooot wiJlSio. ^'^ '•~^' •• •* •' 
 
 To toll OBo ■haio of G a ^mw .« ^v _. 
 
 »w MO itook bfokon who oontnat to •.ii .*^i. ^ 
 
 2. Coooo o# StocfcOi 
 
 Tho foUowliig tWngo m la^j^ ,„ p^^,^ , -^ 
 
 (6) lu^'ri'^r.'oJt^e*^" ""' ''^-'' <*> "«• ««>«. 
 
 ^v *n.^ *" •^^ •^'^ •' "^* ^»*»»*»" 8^ worth ot 846f 
 V»hjo of $100 atook^OSAS; "" » »»f 
 
 "•860 •' =fH of $a46»01502.50. 
 

 llilMllMill»9flM,l» 
 
 ^ J;, ■J7,^»^ -^ •* «*• ■«* of ott.w» .1 itr •«! %• 
 
 MMk kovfkt fer 1197 •f ■ ot y $H»; 
 
 l»«iiillMpfln«filit 
 
 ■?iLf"*^ ** "^ ** *'***^ ■'^ ''''*^ ''^ •^ ■•^^ 
 
 TftlM of HOO Hedi-fMtMi 
 B. 9t M. tlMk It qMM •! ur. 
 
 t • 
 
 Cm^W. OlvM ito MM Immm mi «.. Pjj^lfc. 
 
 Bx.4. WlMtMMwaittMNMltdtrivtdftoafaitMliMilMOlB 
 laeoflM frott $100 itoek a$Ti| 
 
 .'. " <• $mi«oiM7»$rit 
 
 ... « « ij^^ u -^o|$74«oi». 
 
 »t. 6. A •!«• $6800 to • gloek whWi pujr. . diTldwd of 5». 
 Wlttt Is A'o tooomof 
 
 A'o toeoMiM-Tlv of $6a00«$900. 
 
 V. 
 
 «ff 
 
 unui 
 
 Sx. 9. A wko own $8000 oloek imoItoo $08 m tho k«lf- 
 yowlj dlTidoBd. Whirttothohalf.jwwiynUoofdiTidoiidt 
 iSiOO elook flvM $888 toootoo; 
 .-. $100 *• " 8W •• ,or$4*; 
 .'. tko half -Toarly nio of dlrMoBd it 4k%. 
 
 Cn«VI. Olvm Ike IncMM Mtf llM i,ite «f 
 
 toflni 
 

 • • 
 
 «« 
 
 ■l. i. ▲ ISfMll In BMk of COMIMiM alMk ^ fM iM.. 
 •• " «00-«|<rf|7-$«|, 
 
 •'.»!• Of latMwt-il ft. 
 
 T pw Mat. oa bia aoaw wk.* -Ja ^ - *' ^ ■ 
 i7 It tha iaaoBM fhw lamtiac floo t 
 
 ^^ v*^^ «•■■( asMi bmhk ^a i^^^—^^^ a- 
 
 -- "• ^»ww»^w la 
 
 •«ia. at W* » a, la p,«l«^ „ ,„,^ ^ ^,^ !'«■»*«» W Ptr 
 
 Biata II.M to th* loMmia fftmi iBTaaUag |07|; 
 
 .'. $1400 " •• " « u 1400 ,.^. 
 
 J35«f|»7*,ar$i9000. 
 
 1. 
 
 thst neltl^r A aor B woold g2n f **" *" •^ "» ■» 
 
 «x»inlBlng thia, i( bMomet arideot that If a h.# !. 
 
 lBtfir««lwi 1100 lor Otto, •"«»•»«»• B $800 and tha 
 
 iii 
 
209 
 
 k 
 
 :! 
 
 i» 
 
 ¥r 
 
 -AMmutmo. 
 
 It ttuwbteome* clear that he miwi WIT th«whnu.*. u .. 
 
 «r!k •"''*'''• «"■• •' PVmwl I. «eh . tim. tl»t Iht 1b«.m^ 
 •n tt. -.ni who« p.j„.n, h d.f.mKl wUl b. .qu Jto th! touZ. 
 <»iai.iamwlK)Mp,,TOiittop„.p,M. •«°" •» "«> intetM. 
 
 The example ean now be worked as foUowa— 
 
 "^^ T ?f ??? ^r * "??•=*»•• °- °' « fo' 1200 mo. 
 
 Number of ino.=i,Wy=n. ' ^^ 
 
 It ahonld be shown that 11 mo. is correct. 
 
 'S* T ?f 1??? ^r I «;?•=»»»* «« of II for 2100 mo. 
 
 These two deferred paymentB= " «• •• $i «« 5300 u 
 
 =A'8 gain or B's loss 
 
 The use of 1800 for 7 mo.=the nse of $1 for S600 
 
 — A*8 loss or B's gain. 
 
 mo. 
 
roootwioii. fo« TtACHnr«. ^ 
 
 •r. duoislott by kirn i^^p^J!!^^'^ P-ymeirt. •ft.rtlwy 
 P>»i«it worth of th, Mtiolprtod n«»!^ ^^ ^"••'^ « "»• 
 
 woxe»4aoo 
 
 ■jggX18a l4400 
 
 MOO )19800 ^' 
 
 a 
 
 1. 
 
 *^' »*AllTWHlSlflP. 
 
 naw. »wion to fonood is ealled • PABnrxB. 
 
 The Nw Loss in the excess of th« t«*-i i 
 tlJ^ ' """^'" P>«»« •«•' the am, of . «™ _ 
 
SM 
 
 ABITHMITIO. 
 
 •ompftny doAt nol eztond twyond the MMnnt of eapital MMh hai ia 
 tlie Arm. The l»w reqatfw the word, "Limited/' to be piaeed 
 •fter the name of the >1bem whenever ite Mme i« osed. 
 
 In the eaee of •hueholden in benki, to eeenre bill hoUien akid 
 depoaiton, the law nuUcee the liability of etoekholden doable the 
 amoont of the eapital held bj them. Thoe, the owner of Are 
 paid-ftp shaiea of one handred dollars eaoh would be Uable, in ease 
 of the bank's faUnre, to be ealled upon to pay ^$000 as weU as 
 lose the money ilready inrested. This is known as DotMt LkMUtp. 
 
 When the sereral shares of eapital have been in the business 
 for the sflMM Imtgth of Msm, the division of the gains or losses is 
 ealled atmple Partnerakip, or Pabtukkship without Tim. 
 
 When the several shares of eapital have been invested for 
 diiferent lengths of time and the gains or losses are to be divided 
 aoeording to the average investments, «.«., in proportion to the 
 several eapitals and the times for whieh they have been employed, 
 the division of the gains or losses is ealled CoMiouin> Pabtmsr- 
 
 ■HIP OB PABTNXBSinP WITH TlXK. 
 2. Slaiale rsitwiisMa. 
 
 Simple Partnership is merely an applieation of Case II of 
 Sharing. See page 144. 
 
 There are three things to be considered, (1) the capital of the 
 firm, (2) the capital of eaeh partner, and (3) the oaim ob Loes to 
 be shared. 
 
 I. Qhftm the capllal •! each partner and fhe gain nr 
 toaa, t» find each partner*a ahare aff the gain or loaa. 
 
 Ex. 1. A and B formed a partnership. A invested 18000; 
 B, $7000. They gained $4200. What share of the gain should 
 eaoh getf > 
 
 $9000 
 7000 
 
 $16000, the whole eapital. 
 
 , Sum gained by $16000=:$4200 ; 
 .'. " " " W00O=ififififtr of $4200=$2362.50==A's share. 
 .*. •' " " $7000=TW«fOf$4200=$1837.80=B'8 " 
 
 Caae II. Qhren the total capital and the ahare of each 
 parluu off the gain or loaa, to ffind the capRal each Inveated. 
 
 Ex. 2. A, B, and C formed a partnership. "Their total eapital 
 was $29000. A reoeived $246 of the gain; B, $314; and C, $440. 
 JNnd the eapital of eaeh. 
 
■VOemiOM VOB TBAOHWO. 
 
 •(8«»+814+««)«fi000j 
 
 ^ • «iWftr of l29000»|l27«o. 
 
 80ft 
 
 Wnt. «»• amoant of hi. eapitai. 
 
 ««» 00 ilwriBd la proportion to tlMir «.ni!.i t^ **" ** '«* 
 •- •q»- to. gala o, Iom mZ h? Il2^*?' ''*"*» ^ «**«- 
 ««••; and wlu»a artto.r to. ^uTnTT f^P^^lon to to. 
 
 •rj»r h. *ook ia B ^i^ J^^ZJ^.yj^ «' «000; 8 «,o. 
 took la c wito a capital of mSo avT* "^ * »*• ■«•' «»«• he 
 
 • • (08000 ** I «« t4 
 
 •«4 •' " *8aOM " , .. ;2''*!|'?=««»=A'.rtM„. 
 
 ^^^>( 9 SE aeooo 
 
 1200X S ==8000 
 138000 
 
 C'. - "=^ «' »"fl»=«1350. 
 ^" =Tl.ofOM78«|j85 
 
 «« «( 
 
 
 « 
 
 II 
 II 
 
li 
 
 I;; 
 
 ill 
 
 11 
 
 xvH. iNvoumoN ANoevouinoN. 
 
 1. T( 
 
 la doing tUt MBphMlM fte »««»«• <!fyiMt0fW «• fW POMT. 
 
 Tht dtiaitkm of powor la ofton iatmtanMj ospiMMd m tfao 
 mmbtr of tteto tbo mtmbor to ommpUod by itnlf. Tho thlid 
 powor Is BolobtalMd by mUtiiilyiaff • mmbor by Uoolf twloo but 
 bynolUplyiBfflhoiqiUtto of tbo mnbor by thomnbtr; thoftmrtli 
 iw»w ta aol obtelaod by mnltiplyliw • WM»bor by Uoolf throo 
 timoo but by multlplyiiig tho iqiuwo by tho aumbor to obtain tto 
 oabo and this onbo by tbo nnabor to obtaia ito ftwvtli powor. 
 2. T«-^ - - '^■ 
 
 (a) B»To a aambor of fMton iadiootod ao powon. 
 (») Haro powoio ospaadod into footon.. ' 
 
 (a) Boffla by oqaMrftic (1) wbolo aambert, 12) doeiaalo. 
 (8) Tolfw fraetiont. -.— _, 
 
 Mow L-CrtI atlMiUoB to • «owrwimt ww«f 
 «4th|MtlMtawUowav«ft. Tliaa, 
 
 (g);«6X(H-J«80i; 
 {7l5««7X8+i«a6jl 
 (W)««9X10+i»Si. 
 9'-Bkmrimr to mum twsmimot two Mfum. 
 85*aB80X4<H-8*»122S: 
 52=«0X54+8««82«j 
 
 ga««iox8H.a*««7a4. 
 
 (ft) Prooeod to bigber powon with (1) iHwlo nanbon. 
 (2) doeimals, (3) migar fraetioaa. 
 
 (a) Tho sqnaraa of all tho niunbors from 1 to 12 InehisiTo. 
 
 (b) Tho aqaaioa of $uj nnabor of toaa op to 10 tnis. Thna. 
 20", 30»^40«, Pr." ote. 
 
 («) Squares of freqaent oeenrrenco as 16*, !«•, 26«, ete. 
 
 Ko«.-TlM Mwnd powwof smunlwrlsealM iutrutn, Ymvm the mo- 
 d«t of «,• BUBber of imita in Um Wncth of • mpum bj lUdf I. ooul to U» 
 a«ab«rofiiiittaofuMofth«aaaai«. - -qwi w wo 
 
 •Jlil^*^ *!!!!1^'^ f MimbW I. Wdlod It. «*•, bWMM the OOMtaMd 
 
 '•"'I^ "Vwo of s wii^ muBba- la MdM • y«i^M ««ii 
 «.— Tho eab. of • whoio BMibor I. aUtod •*«9N« iiiSfc 
 
1. 
 
 «• •MM«C HOOT. 
 
 ^•▼itw Insolation in so fkr •> it .•«m . 
 
 Wm tha Mm..^ ■ : ••• •■• *•• » l» MtealadL 
 
 f »i^ ^ **•"»••*»»««* Of 45 8 i.tl«.,.^^ 
 ■«l»l*ln nloo that tlioM m»m *«- 
 
 •rini I M M i»k,. ^ • **^ '^"^ •*«»•, and (2) ly 
 P«". •4«2,. ^9^, ^1^. 
 
 **•»*»>• tto tollowias:. 
 Stneo, l>»iudO«-==Gi. 
 
 ik^. ^ ^ * "«** fa • nwpber of l or 2 
 
 nniS^'di^ """^ "^ »' • "»»»*' ^ » or 2 flguo. i. . 
 
 ^^th..q»«eof.n^t^of2ig„«.,..„^^^,3^^ 
 
 .a-^ToH^iia^'''^'^*' --»-^ 8 o, 4 «^«. ,. . 
 Ag^n. since 100«=.10000 «d 9»-=9W001 • 
 
I 
 
 .» 
 
 ^ ^ABinniino. 
 
 two flffOfM MMh Md tlMf* win • M mof IgUfM !■ IIm MMM 
 
 root M Umm an ptriods or pm of » poriod. 
 4. To MMlim FOriMt Hwrii. 
 
 40«+(2X40 4.t)S 
 
 «: \ttt 
 
 n m 10X64-6* 
 
 180- lO'-l- 10X5 
 
 10'+2X 10X6+5* 
 
 225 
 
 10»+ (2X10+5)5 
 Piom thooo eaaplot, it Is erldont tiwt <*• tqmrt of nnnmUr 
 <• ffiMK to thotqmurooftketmu^twioo theprodnet of tko tint bt tko 
 
 product of twk§ tko toM pint tko mttt ty the mntts. 
 
 *> T* <M o ■ Ill tmm Ito Tnriri 
 
 Ex. 1. Find the •qauo root of 1849. 
 
 I^-Ma Motkod. 
 
 . 1849(40+8 
 40*al000 — *— 
 
 1849^ 
 
 249 88 ~34i 
 
 (2X40+8)8- 849 S 
 
 Sqouo roei»48. Squuo rMti«43. 
 
 w- ?!"*• "T **'*** •* *•■■ '■ '»»»»*^. «»• PWt of 1849 ^nrontd 
 Ijr 49 eoiit«^j»» no p«t of tho *,«.„, «f tont, Thmo igJmZ., 
 
 18 tondiod Is 18 hundred, tlie squro root of whleh is 4 tons. 
 
 f^^?"*^. !."**•• '•^«»«*«-i»8t«is;8t««isso«JZd 
 In 24 tens, 8 times. "-""wneo 
 
 Is jS!^ **** **^ ^^"* "*•""**• *• ^' *»^ «8 mnltipUed bj 3 
 Another method of explaining sqnare root is often giten:- 
 
 l«t«^u* ^ ^ ^'^ ■9~» *•*»•«> 'rtshes to ar?«.«o them 
 STaJo^*'""* H<»^»"ydl«kswllltherebeln^Srsideof 
 
 .„ ^I^A^ ^'*'^' ***** ****** ''*" ^ ^'•*^» 40 and 50 disk, 
 in the side of the square. ^^ 
 
 ,^*?.u* »""«* • *»«"• ^"h « disks in the side and plaees 
 1800 of them In position. He has still 249 to arrange. 
 
 To proserre the sqnare already formed he mnst add diAseMally 
 to two sides as shown In the diagram. • "^wuiy 
 
•VMBOTlOHa VUR TBACHIM. 
 
 Ex.8. 
 
 On. row alonff ih^ two 
 •!«•• would telw twie* forty 
 (2X40) digki. 
 
 I 
 
 To Mwrtela how 01*07 
 rowi ho mUi plMo ho diTidot 
 80 Inio 219 ood flodo he eaa 
 ploee 8 rowi oloog oMh of 
 tho two ildct. He etill hM 
 • dtoko wbleh ore needed to 
 All io the eouOl ■qnoro. 
 
 The fonnol eolntion Js the 
 •wne M Uuu giT«r oboTo 
 under Enuuple 1. 
 
 48i636(aM 
 
 a« — 
 
 Eztnet the aqowo root of 481886. 
 
 •00.. »i52±20±4 
 
 (2X800+00)90 =- n^ *» I2I6 
 
 (2X690+4)4. ^ *^ "^ 
 
 ^ The.liur.root.694. The «,a.ro^694. 
 
 ^«2;*' ^ **"•'• •' koodreds is ten-thouwrnd. th« «.^ ^ 
 
 y^ the reoeoo gireo under Ex 1 th« «»»•». m . j. 
 In finding the teneMlguro. ^"* ** "* <«««g»rded 
 
 numini k^L^^t r"'*' ^ ««™ »» the equoro root Of . 
 
 ««^beeon.iderodi'nS:::,;^j:r:iX^;*^'"'' '^'•* ^ 
 
 Henee, the rtepe in the extrwtion of Sqnaro Boot aro:- 
 (1) Divide the nnmber into naHaiia «# ♦_ « 
 begfaming lU the deeimi^int ^*°'*' •**"^ 
 
 pJ^^^^ ^ ^"'*^ **"^ oontUned in the left-h«id period 
 
(i) »MM» Ikt »«« If Iht IWI 1Mb«. rtM 11 to ^ !■* ^ «k^ 
 
 mart U of th. and, 4»h. aih . . . oidw, <.#, th,,^ aiirt bTlS^^ 
 Ineoehporiodoowitliiffionthopotat. ' "T* ""»»•» ■««fw 
 te.-4. Bitnot Iho sqiiMt root of .4SIS. 
 
 y^n tlio BBMbor of doolnal plae«« !■ 
 •;r»ii, point off tlM dodMl into porioda of 
 two llgiuM oMh, eonntlnff from tlio point 
 •^ •«*»•* *• "qwr* root M in wliolo 
 nnnbon, plMing tlio point in tho root m 
 
 Ex 4 E,tr^,«.**"*'**^^*-*»»*P«rf«»todMatirith. 
 M. «. sxtnet tlio •qonro root of .4. 
 
 .4009o6 (.e6 ... WlMn tlM nnabor of deeimal plaees io 
 
 128 ^M »ot eirwi, make thou «Ton bj nflUing » 
 
 JS •*jJf''«<»«rt«*»ttlio«purorootMrin 
 
 2B8* , 
 
 676 
 
 .422S(.«5 
 .86 — 
 
 128 625 
 
 T* To «■■■•« oto aoMn — -' ^ • 
 
 •^^m ro«Ut will bo the torn, of th. root. ^J^L^' 
 
 l^f-K'.T6s=.866...; |/A=»/.»=.Ma6... 
 «. ApM«o«Iom or Tkcory. 
 
<S) Hf iiki If vial 
 whtoh to Ml a pMfMt 
 
 tu 
 
 ■^** Mllilrti^lo 
 
 '» M thai tba 
 
 ■(Vkta 
 
 (I) Tw flad Iha rida af a MM.ii. -^ ^^ 
 
 tli. .id«, aad Iha JSTa^i^T^' '^^ "* ""^ *^ 
 
 {!} X 5S «-«**««'• euila, whan tha am 1. 1,..''^ 
 twoawfl^B. ^"'"'•''••^•^♦ri^lfl-wl.a.lfcaalhar 
 
 «M.€UK||OOT. 
 
 aamban. «» »r aa || a»pllat la tha ««»«• of whola 
 
 '■Taatfctfca^MiaiafOifcaBaat-^.^.^^^^^,, 
 •JSLS^.T^ """ •' *• 72»a.d «.al^ ^, ,.^ ^^ 
 
 . 4 »4X4X4a64; .-. 64«4X4X4«4«. .t. 
 
 BxpWiithat2i.lliaeubanwtof8.ai.iK \I ' 
 
 I!«pWn I*, th« tha» l^two^^J: S ,'Ji^ T'^ "' ^' 
 "xrt of a number, (1) by pladLT W^ ♦! i»<«wtlug tha «nba 
 wi-f I a. an Indix. '^^^ ^ **'*"• **»• »»»«>•'. «d (2) by 
 
 That, ^8=2; ^27=3; f 64«4j 
 
 O', 8*«2; 27»«3'; 64»«4' 
 3^ Ta wcwtoai h^ „„ . „ 
 
 a.^!'|Ji;ir^^ S^^64; 5-I25I 8.«21«; 7.«848. 
 
ttetitotf ■ 
 
 •f IdlfUtea 
 
 •f 1. 1, w a 
 
 QnvwMli, th* mN fMl of ft Mmhtr «f i i. m • 41.1*. 1. . 
 BiMkir of 1 ilfii. ' •"■«»•«».■.•»• i%ll»s|M| 
 
 ;^•fc• trto of • wnrtwr of 1 lg«„ I, p^of 4, », Of • Wmo.. 
 BMoot to MMrtaia kow aoajr ^hwoo tkoro wUl bo to tko oabo 
 
 JEToTi^^J^S-^ •• ^' "^"^ *■•*»• ~»* "^ 
 
 iMio MO poriodi ud port of o ported. 
 
 4. To 
 
 •6*-«14116; 
 .'. C141IS-«*-(8IH-S)* 
 
 M-i 
 
 Urn 
 
 Mm 
 
 §M0« 
 
 TBS m 
 
 SB* 
 
 8USB 
 
 St! 
 
 . jo4± 
 
 M«XlH.tXSOX»*+ft* 
 
 «41« - S!t»XW;^WX80X5«+5* 
 » 80«+(8X80« +8X80X6 +5«)6 
 
 wot o poiftot oubo hoTlDf 4, 0, or 6 ploeoo eoniito of 
 
 ^ To IM o ■! t il l tnm Ro cabs. 
 
 Ex. 1. Find tho eabo root <tf 614125. 
 
 614126(604-8 
 « 612000* 
 
 103126 
 
 80* 
 Trial diriior 8X80*s= 19200 
 3X80X5 a 1200 
 5»« » 
 
 204a{X6s 103125 
 
fit 
 
 At fNtiMl Mto la tu 
 
 IMl«fwfcMllttlMt. 
 
 Urn 
 
 ItlMMi 
 
 bfIS 
 
 •M miInI. hi^ ^1 T?.^ ^^ »••• Of • Wmbtr •! BOM ttea 
 
 •lit p«loi| fcrt .U tofOf. lU pftotlpl. a. amlt^^i^r 
 
 • 614115 
 
 M 18M0 tlMlB 
 
 •l. S. yiB4 tto milw root ofHTMllS. 
 
 • 4 MOO 
 
 ItfOf 
 Iff 
 Vi 5 17101 
 
 J*« awibw It iopMttid lato 1 poriodo. 
 Tlo frortoti «ibo to tht 1,11 iMiBd poflod ta i fUt Jn»^ ■ M 
 TOO, tho Bost period. •«••«»»• iMMtador aaats 
 
 •nd tho product wbtnJ^'f^ iSS ' f*' *" ■»»«P'»«> bj 4 
 Noxt Mt down throo timet S4 uid »1im« ♦!— ^ *i. 
 

 
 • ii 
 
 toifaiMiiktiMi — 
 
 *-\ 
 
 
 fa 
 
 ft MHkirtf iht««MiiiH it • ._, 
 •faMM.,««4MlMlitfthtaii,fih,Mi,«le.Trr 
 
 rr^ 7.S" ■■••■■••••••■• •tofawi n ■■n fct «i 
 
 MMttai fto« tkt potel. -^Mwr 
 
 •«.«. ffad t hf»to wtit oi ,9mm. 
 
 •^1 
 
 m 
 
 ■ MaitM 
 
 Si!iii[ 
 nu t 
 
 
 msm 
 
 F •■■■•■■83 . t , 
 (•) tt bolk tofSM mn tntl tsbw, tunwi tht «alw mm iif 
 
 lllW|9 fey iMpMltoHb ^^ ••^^^^ W «» ■» W 9 
 
«l 
 
 •1 
 
 l« 
 
 II 
 
 •• 
 
 II 
 
 •1 
 
 II 
 
 1* 
 
 II 
 
 l( 
 
 II 
 
 1 
 
 I 
 
 «l 
 
 II 
 
 m, 
 
 II 
 
 
 II 
 
 tu 
 
 " " " M II s 11 T^^Tr J* 
 " " " «l II f II tl „ •* 
 
 -^{•to. 
 
 Ite Mte fMl •! ft MNKkw hf tmiili^ II iaio 
 
 
 (4) loiaithadalfc»o|,f . JSJ*^^^ 
 m ^Uliil /taalalHaa. 
 
 (1) *»*ii*ttatl4a««atabMrhaBltiMW.«*iii*.-*i.-i 
 
 .^^yj!!-?^ *^ «»tB i l o aa of a l>oiy. wkaa tha aaMt 
 
 aai dl>Mafc» of a •too.. «B, .,. ^; ''^ "^ •■*^ •*»«'^ 
 
 XVM. MDHSUUTION. 
 
 I. INK MCTANWLI AND SOIMM. 
 Baa pagw 185 aad 141. 
 
 N. YMt MKAUCUNMMM. 
 
 LTha 
 
 Dwwpafallalofiam.. Ha^a p«pItadniwotha««f Tarfaaartaa. 
 
 l»l taa parpaadiaalar diiaaa«« batwaan tha panllal akha. 
 
2I« 
 
 If 
 
 A«ITlfMinc< 
 
 Show by flguts slailar te 
 ABCDtlMrt.TwjrpM.U^ogn« 
 ■MJ b« eluuigid iato • iMteng 1« 
 
 **^ l«agth is that of the 
 
 A 'I PMiUslognuB and whoM biMdth 
 
 •Wtwi. of tho iMwllolotrtt, HJ^'J*^'^''^ '^"». or 
 diiM-rioMof tlip«S^^ "•«M«a.»t. uo too 
 
 to 
 
 TW. J. twrtod mid., t||. B«,ungi., *p.ge 141. 
 m. THE TRUNOLE. 
 
 1. Tho 
 
 :•» («) Dmw trianglM 
 and giro toe longto of 
 on« of the tides, hsTo 
 
 pvpils draw toe llgoro 
 showing toe otoer di- 
 iBensioii to enable the 
 C«*l. (Uvm the leiMliri.r . «. "*•*»»>• determined. 
 
 >- «fW imeZwr , r^^ •^ ■•»« lid tint ■er p.-^i-i rf^ 
 
 ■»" m* •ppoaiu angle on that bu» «• «k^ t^ r^r' -Niinei 
 «l«l Ihe «» ef the wHele. ^* •^^ '"^"^ «• 
 
 In tMoWng tois Case, toe following order is .u«»..i^ 
 
 (•) Bight angled triangles "«'"«•' « •uggested.— 
 
 (i) Aeute "II 
 
 (e) Obtneo '* <i 
 
 If it is made elear toat tha ti4.»»i. . .. .- 
 parallelogram of toe same bwL ^SLI *^' *^ "•• of a 
 diffleulty wito tola Case^ ■''""^•' *»»•" '^H be no 
 
•vaaKniom for tbacbimo. 
 
 117 
 
 CMC II. QlvM lfc« ««■ Md M* 
 to IM tfie cllMr. 
 
 ««m and thi. l^eom,. Cm. U of th. p.nUl.loS«r 
 
 IV. TIUKZOIO. 
 
 CMUMrJnMi iMtd ce«- 
 
 H»v« papik take mien and dnw trapesolds of ..ftlinill 
 .ion., M d»w . tr.p.«,ld th. pa«|,.j .W^ Wni 2^^^^ .?' 
 Io«« r..p.etir.ly, ^ the dtat^ic. b.tw..n thon."'? to 
 
 P««««. •«llfc«««toiicek«|,««, !!,«•, to ftad the ««^^ 
 
 and the pen*»dle«l.r helZl gir^!" "" ^'"'^ *' **»• »^ 
 Th. «rM Mn b. roMUly found. 
 
 Another w^ta to tiUwh.Ifth.wMB of th. «».«#*-« * 
 on. Iwing on th. lonmr .Id. u.^ m^ Zl^ «« toowrtwiflw 
 
 *•« of oM triugh -"xia 1^ 
 
 g— ^. IB. al60«l. In.; 
 Amof the othertriMgle=l»|i? «,. „. ^^ ^ ,„ . 
 .-. Me. of taipe«>id=(150+90) «,. In.=240 «,. ln. 
 
 I». «240 Ml. In. 
 
 Or M»a of both trimnglMas!2>ll? ^ 
 
 m4 fhm 
 
 II. QIVC|I the •!«• MM Ihe MM «« M^ _ - 
 
 81«,2^ 
 
 . 2X667 
 
 ' 42 
 
 •'.perpendlealu>height»27 ft. 
 
 »27; 
 
i'-\ 
 
 V.TIIK 
 
 ■ — ••• i^iw vvvpi VNS V^HBHHHK flRttflftvBA ^^^^^h^k^^A^ 
 
 H.T* popu. point <mt the iii«tiii«ii.eiits iiaetMuy to^S^ 
 tlwir MMM to be foond. ^^^^ *" •aww 
 
 nB^' *l.i^.^? *• ■ *»!**'«»• ACI.48yd. leng; BPimd 
 
 trnpeaiiuB. 
 
 Are. of triMgl. A B C«^^ «,. ,d.=408 «,. yd. 
 A D C«— ^ eq. yd.=486 eq. yd. 
 .-. «e» of A B C D=(4a8+466) .q. yd.^884 eq. yd. 
 Or. «e.of ABCD=(*§fLV-5fi?) .q. yd. 
 
 _ 48x3e ■^ ^# 
 
 *— f «!. yd.*864 .q. yd. 
 a.goMl, to flM4 Ihe mnh of tlie IcngUi. of the jirrnniiBf lwi. 
 
 ;^2i.'**5«!r** •• "" •^"**~. «•"-«« 
 
 to. 2. JH» aUgoul of • ttaiwiinm ■wuoring 1 aen b 88 rd 
 this diagoma from the opposite angles. 
 
■UOOtWlOW >0« TEAOHIHO. 
 
 Aim Of trftpMinm»H^lfHS.£L£!! ^ 
 VLTNEanCLC. 
 
 S10 
 
 I. 
 
 Jl^T"^ •""• ■-»• "-^ tM « h . „^.. ... . ^,,^ 
 
 "-"t'^S",.^.'""-' «'- • -^ tor »d,„ ^, 
 
 (a) OiT«n the diAmat«i> a# ♦k* , T •* * •• i Bll>i» » »- 
 
 «»I»»rp knife cut the triangle, ti^ iT^K J*"'** '^•» ^^^ • 
 . .Ufht margui to co^ lie ««' ,^ «»e cheumference W^ 
 into seml-dnile. Md fit the tri^S't^ ^f "•^*^*^ ^^ «»«!• 
 
 wiMgies together m •howa in^fce 
 
^ifffiMB. TIm nor* BniMfmw 11m trimgiM an, th* mw BMrly 
 th« agvvt wUl ftppmsiBMto » iMtang to. 
 
 Th« length of tiM 9wtugl« la eTMMtly hiOf tiM elf«unf«i«iM» 
 of tho einlo and ito broadth la lialf tho dlanotor, or ndioa. 
 
 Hanoa, tho nmnbar of nnlia of ana la found by maltiplylttf tho 
 anmbar of eorraapondinf nnlta la naif tha elnnmfoMnaa br tba 
 wuBbar In tha radlna. 
 
 2 ' 
 
 iex 
 
 >»»•. 
 
 ""^TT^**^ «««wla«. •!• cHw. M tiM «MMl».»r tlM«lfeai. 
 wvofa.diagtlM.Na«<tlMdi«l*. '""•"'~^'«****«*»»*^* 
 
 CmoN. OlMailMara^tofMiiMMMM. 
 
 Ex. 1. TIm area of a olrele is 3850 iq. In. ; And Ita radios. 
 Sinea, VXr'«38S0; 
 
 .*. r'»A ofi8850=1228; 
 .*. r=Vl226« 36. 
 Qonoe, radioaBsSS in. 
 
 IN. T«fM|lMAiw«r«i 
 
 Ex. 2. A road rans round a elrealar ahmbbery; tha diauetor 
 
 of tho shrubbery is 478 ft. and tho width of tho road la 19 ft.: And 
 the area of the road. 
 
 Badiua of shmbberysH' ft. arssg ft. . 
 
 Badins of road and shrabberya (230+19) ft.s:2S8 ft. • 
 Area of large cirele^:: ( Vx 268«) sq. ft. ; 
 " •* smaU •• »(VX239') sq. ft.; 
 
 .;* area of road=CVx(268«-239»)] sq. fl. 
 
 =CVX (268+239, (268-239)] sq. ft. 
 =(VX497X19) sq. ft.«29678 sq. ft. 
 
 im. THE momWMOLED TRMNQUL 
 
 1. •«Ka «M MiMiiioa and the aaaMa of the aHMa. 
 
 Do thia by drawiLg right-angled trianglea of Tartous aiaea and 
 al ipea «* glf» nanMa to the aidea. Then hare pupihi draw othen 
 a? ! name tte rite. 
 
 * ^~2J^!L2L««~« •«•»•«'»•«*«"»-*•• *fi- te MM «■■ 
 
tn 
 
 Tot,.ehUii.,ietBCDBFOh..i, ** 
 
 ■Vuwe*. BCHiam ,*«*,*. ^~7* •hb*I to tho nun of ths «»» 
 
 n» MIoirlac b - - "^ """^ *>» «»»weh«i. 
 
 « to.. •'T^ti?^'**;'^ « to. «d 4 1,., „ 5 to. ^ 
 Vk« j^,r^ '""to. indigta. •■•«o 
 
 (» f»'+l>')'-(.«-l,t>«+f«.M. ^^ 
 
39a 
 
 ABITIMITIO. 
 
 I. OlvM IIM kM« mi 
 
 
 Ex. 1. find tlM hypotlMovM of m ri|^t-Mi|^«d trin^ 
 bM0 Mid pwptndteiilw M« 40 la. ud 42 la. mpMUTtly. 
 (TlM iiMwor* of Um lijpotlManM)*a40**H3*; 
 .'. tho IMMBM of tho h7polb«aaMm/(40*+42*)*68; 
 .*. loagth ot lqrpothoanMaB58 ia. 
 
 ClMli. OIVMllM 
 
 
 Ex.3. TliohjpotlMa«Mof»riglit-MigI«dtrlMigIolt73Ia.lOBff 
 and (he bote la 56 la. lonf; Had the toagth of (ho porpoadleolar. 
 (Tho moMmro of tho porpondlealor) 'sTS*— 65' ; 
 .'. (ho moMmro of (he porpoBdienlara>^(78*— 55*)k48{ 
 .*. (bi* l«ig(h 9i tiM perpeodIeulMr»48 la. 
 
 Com III. mvm mm^bim aUtm ^ i 
 find llie Iwiatfl oTIfce 
 
 Kz. 8. Tho boM and porpoadleolar <rf a rlgh(-aai^od (rlaa^ 
 are reopeettT^, 65 la. aad 48 ia. ; iBad (he leBg(h of (ho per- 
 peadlealar from (he ri8^(-aagle apon (he h7po(heaaM. 
 
 Long(h of h7p<^eaasea^(56*-H8') ia.»78 la. 
 Twloo (ho area of (he (rlaagloa (65X48) n. la. ; 
 
 Atao, * " " " «(pX78)iq.la.; 
 
 .'. pX78a65X48; 
 
 .•.p=?5gS-Ws 
 
 Leng(h of perpoadlealar^seH la. 
 gj^^ VIII. SIMILAR SURFACES. 
 
 I. Tcecli Mm DeitallMii. 
 
 By drawiagi show (ha( similar sarfaees mart be of (he same 
 shape. Tkas, elrolos, squares, aad eqnila(eral (riangles are sfaaUar. 
 Show (ha( whoa (hey are reedlineal they are (1) eqoiaagolar aad 
 (2) have (he sides aboa( the equal angles proportional. 
 
 Ulostrate (his by drawing numy parallelograms aad reotaaglea. 
 of (ho same shi^ bo( of diiferea( sisos. 
 
^OQQEammu won Tuxmam. m 
 
 _?• »U« by dnwrlM rt«|i« «--_^ . . 
 
 ■•MUM •»• •• 1 to 4, or M 1« to a» 
 
 . •«• aivM MO M 1 to 4 or M 1* to 2' 
 
 .-. " " «.i. ., * " " "»xaomiii.j 
 
 " " 5 «« «' I. »X20 , ' 
 
 orMmia. ""s""""-' 
 
 StaM. ^ 'niE CVUNOER. 
 
 1* Teach tke fftlhliin. 
 
 Of the um. ^. CttL feT^ J '^^ "* •*"^- 
 whleh is equally 4,-*^. #«»»/. «J. ?''^ •"•*•«» •^'7 part of 
 the ciminSL. " • "^'^ "»• *»W»g the Z^ ^ 
 
: 
 
 
 ' 
 
 fiNl ikow iMv to ii4 tkt MM •! «to nrftd MuteM. 
 
 TUt ii MH iMtfiljrdoM bgr ratllBc ft ahMl o( papOT to II Mm. 
 ramdnfteM. 0» fwwfftlifc. pft|», i, »« to W ft iMtoMlT 
 •M dfaMmlm of wUth i« •qoftl to tte ttnimftuftn «C tto 
 •rUadtr uaA th* olfair to oqiftl to ito Mght. 
 
 HMMt,tteftnftoftht«ttmdMfffiMtoteradl9MftltMyiBC 
 tlM Builwr of ftftito is tko •Immtofonoo by m Mwbor of lUw 
 «aito to tho loaglh to flad tho ftftabor of mfiopoadlftg ftaito of 
 
 TljototoliwtotoiftaBowboiorilyfo«.dbjrlhoi»pllwfcooft» 
 And too ftNft of tho boaadlac aiioloo. 
 
 a. ONoft too <■■■■ ! ■-, to Itoi too Cutoe C ili 't 
 
 ■z. 1. Find too onMe oontont of o eyliador H to. to mdlu 
 oad 1 ft. to longth. 
 
 ANft of OBO ond-[Vx(W)»] iq. to.»88* iq. to. 
 
 It lo oTldoBt that ft Moek from this eyllndor 1 tooh doof^wUI 
 eoBtfttn 881 o. to. Tho eyUndor it IS to. doop, honoo, tho e«Mo 
 oontont la (18X88i) o. to., or 488 e. to. 
 
 Ex. a. Find too nombor of onble foot of Iron In n wator pipo 
 8 ft. in diamotor, 18 ft. long, tho Iron botog 1 to. thielc. 
 
 Thia la to bo found bj eonpttttoff tho enblo oontont of fwo 
 
 oyllndora, one tho wholo ejllndor aa though It woio aolld, and tho 
 
 othor tho eylindrieal oponing, nnd thon taking ono ftom the other. 
 
 Thua, onble oontont of a aolld eyllndor^CUX («)•»] e. ft. 
 
 " " "too oponing »[18X (H)« » ] e. ft. 
 
 Qnantity of iron In eylindor^dSXfftX^X » ) o. ft. 
 
 »9| 0. ft. 
 Tho popator waj of doing thia onnpto la ttrooneoiro tho pipo 
 to bo ont open and flattened ont. Thia la inaoonxato for the 
 roaatting ahapo la not a roatoa^ilar aoUd, the upper and lower 
 aarfaooa not being «f too aamo are*. 
 
 4. Qlvaa Ifeo ceMc eeiilaaft ^irt ^^ ^^^^^^- «^ — - «>— .».--- 
 
 """ - ■ "^^i^^ ^^ ^^ Hi^HMMiit le inM nw ottw* 
 
 Sz. 8. Find tho radlna of a eylindor 28 to. long whieh eontftins 
 
 1782 e. in 
 
 Cubic eontonts(28Xr*X w ) e. ia.a»1788 e. in. t 
 
 ... ,.- J^.Vi 
 
 •*. r**j**4^» 
 Henoe, radinaaci^ in. 
 
I. 
 
 II 
 
 OWl 
 
 ft«i «nmlM th« oih«r fMM TIim. .- . 
 
 »^ 2r;r'jrsi5u* sat ^ssr^iii^ •*- -!— 
 
 odg* 
 
 telM 
 
 ««• 2 fl. 8 to. MMl tUuit Jitlght I. 8 ft. 6 fa^ 
 
 Am«r4f^.(4X?|XW)^ ft..lH.,.ft., 
 Totol mrf«Ma2ft} aq. ft. 
 
 «d rid,. •! right «^t^tL.?2^X? '^****'*"^^ 
 
 T— rt. <>>««««• to do thl.«SiLoJliS^^*f*^*^' 
 
 ^jh. t.. ^ ^,^ jss^^s:^^^ 
 
 ber of oorr-pondtog «lt. «f •.SelSir^ wiU bo tb. .«». 
 
 •ovS .' JJ::tut%to*'of*^^ :^ t"**^ *^ -«^ 
 
 high. ""*•"*"•' ^^•^"'S'WMdM ft. bylSft. Midli28ft. 
 
 Ar«»ofbMo=(15X18)«,.ft.s 
 Cttb.o contentcrCix 15X18X28) «. ft.=.a070 o. ft. 
 
If'! 
 
 Uk 
 
 ), a •into/ Mid tQ tkt 
 
 thitby 
 Call rttiBlioB to th« 
 ti^^riag to » prist. 
 
 BmMf ft MM to ft Mild bMnd«d by ft tinfttor ptoM tarn, i1m 
 bftM, ftftd ft Mr?»d teM tapmrlaff tnm th* •ImiBtevaM of tiM 
 bftMtoftpoial. 
 
 8ho# thftt ft MM Mftjr b* ptojMtod bjr w?ri?iaf ft rifM-ftSftod 
 totoagto ftbMt OM oUhft ildM raelMloff Um rigkt-ftagto. ^^ 
 
 a. OlvM IM «MMtoM •« MM taM ftftd IM atoM MtoM to AM IM 
 
 If ft ptoM of pftpw bft Ml to flt tlM «arvftd MrfJt ftad Umb 
 •prMd mt, It will form ft MHor of ft eirato. . 
 
 Ex. 1. Find tlM totftl MrfftM of ft MM 7 In. ia ndlM aad 18 
 la. in slant hoif^t. • 
 
 Thownrod aarftea, tlia Motof of a aiiato, awy ba wppoaad to 
 bo aaada np of trlaaglM tha •am of tha baaM of wUab is Jm eir- 
 eaatfafaaM of tha baM of tha aoM and tha altltada of whiah to 
 tha alaat halght. 
 
 CiianflnfaMaM of baaa-* ( Vx 14) in. «44 la, ; 
 
 Araa of annrad saifiMaK—i? gq. la. * 
 
 m 
 
 Araa of baM«(Vx7«) tq. In.. 
 Total araasB0SO oq. la. 
 
 ^806 iq. la. 
 »1S4 aq. In. 
 
 S. CRvM tht baM aad oMtad*. to IhMl Hm anMe Mataal a« a Mao. 
 
 To Ulnstrato thto proaora a hollow ejrUndar and a hollow aoM 
 of tha wma aiM of baM m tha and of tha eylladar, and of aqnal 
 altltnda. Than proMad m la tha eaM of tha pyramid. It wiU ba 
 found that tha evble Mntont of tha eylindar to Jnat thbbb tIaMa 
 that of tha mm. 
 
 Ex. 1. What to tha Tolnma of tha largaat pooibla eona tnmad 
 
 fraoi a eoble blMk of wood whoM adga to lOi in. r 
 
 Diamator of MnaslOi in. ; 
 
 ATM of baM of eona«r[Vx (5i)«] sq. in. s=86| «}. in. ; 
 Altltnda of Mnesio} in. ; 
 
 Volumo of Mna«(iXl04X86#) c. in.=303A «u. In. 
 
f.Ti« 
 
 
 •VMlljdfatutfroM 
 
 ItttktpMitlMI 
 
 ApolatwItUB 
 
 Bammt • 9phtn to a tolid, liMiid«4 b* » mmd MiteM .mm 
 
 ^ ^l^ft* ftm rmMm, H Hat ^ ^mm ma »^ 
 
 •n»rasiflMtol7 d«twmiB«d M followit— T^ 
 
 •mc.. of th. .I««tor f.- . rubb., -•■brJSnLJ.nf « 2l 
 
 •limd •«&•• of . hMUiphtw to J«rt twto. th. M«i «f »U pliil 
 
 ?J?!: !?***.T **'*? *>^ ^»* ^ P*rt of tho otho, bomtoah.., >»^ 
 •ttwrti tho twtiio to tbo tMk Mid wind it onwad vna^^TirjL!!! 
 
 Tho nainbor of onite of wwila pi«,. f^e* »,•; 
 
 ft 
 it 
 
 II 
 II 
 
 II II 
 II II 
 
 
 
II 
 
 •r Miti •« MM tllw* -4 r ff* I 
 •• •♦ 11 k^i_»^ ' - r- 1 
 
 ^ I. BMP MMli liMi to mm ii ft ZiCJ'' 
 V tkt iiN Wtaf 1 to. tktokt 
 
 •c «. te. of toM«|x V (•*-A*)-iau|. 
 
 l«to. fai 
 
 II 
 
 
 •f Ikt 
 
 jni«i«- tk^i^^p^L^T::^^^ .I.UM 
 
 • iJ^"' •*~''''!^ '•''*~ •* *^ w**^ with •d«, , ,- MiJ 
 CoapMt Um TofauM of footoMolar Moek 1 1b h» a t. i-. 
 
 ..^zi^,ts!!::.'^'^'^^'-''^^f'^^^ 
 
 ''•llfM «rf • 01*010 .ttdo of tho .iM .Mrtorlid « u •.'^IZJ^ 
 
 Woifhl or t»d ophow-^'xM OO..UI •«. 
 ■>• >• Tho teoodth of rootoagnlor 
 
 ■•torW « In. to dkMiolof. 
 
 b;^ b^oat. Of ..^^-.iiir:;^::^ '^^^"^t 
 
 Hoio, C»— MO of bftadthy t 
 
 ofbreodth)*»]2*X8; 
 "■•-wo of bfoodth-12X1.44225«U.80Ti 
 »•* br wdt h - 17.387 ft. 
 
«»• TNI IKTMC SVtfM. 
 
 •fWtliMt mA 
 
 ••■••• •■• MtMa utea^irf Mate .^ I ».. r^r "^ ^■■■' •■■■•••• 
 
 (<) IVm MiAiint or Wii«bv— 
 
Aammmo. 
 
 u 
 
 Li 
 
 (•) T«Mh Llaeftr U-Mon inl. 
 
 W B«fla with tlM B«ki«. Show that lO^dMioMtiM «BnW 1 
 »^, ««1 that 10 e4nti»«tm imOn 1 d-imtr., •»! inS^Li 
 100 •tntim«trM auUw a bmIm. ^^ 
 
 ^i'L^'* Pfl»"»"~«i» 2, 8, 4, 6, .te., deeimetrM ud •»»« 
 Meh of thM* In •MtimHTM. If thfj .ndewtwd dteimiUt hat* 
 »!»«• wprMMd abo a« ai«ti««. 
 
 (d) Show h, measaring that 10 milUmatrM aaka a etaftlmatM 
 •ad one* mora «•• wdo«tloii to flz the wlati^ i«,gthi of tho 
 aMMono alioadj taofht. ^ ^ * "" 
 
 ♦ i*^'^***"**"P'*»«^*»y»««w»ringtothodekamotro:thoa 
 tott. h«rto«et« and kUo«.t« and vm in oaeh ea.. ma»y »«^ 
 IWDhloim in rodnotion to fix tho ralativo longtlw of thMo aoanuw. 
 r^L^1S!i '^^^ "•^'^ "d ^^ OS for fntnio 
 oweot a ttraigfat road or stroot for this pnrpoae. 
 ,.„y ^* ^.1« "■»• ""J" no attempt to infer the meanlan of the 
 
 done after Long Mearare is weU onderstood. 
 
 XX. MISCELLANEOUS EXERCISES. 
 
 See Ffege 178. 
 
 -,- _ •». WOBLCMS ON WORK. 
 
 (I) ^ow the relation between the time of doing a work and 
 the part done in one nnit of time. 
 
 1 dl^'^te* '^'^ **" ^^*"' *" ^ *"•' ^'•"^ *«'"*■ *»»• to 
 
 ti™?2«?ir*?'* '•^***" ^*^**" **»• P^ ^*»« to «• »»»» of 
 Wme and the time neeesMuy to eomplete the work. 
 
 woA^^'donef' *'^* !• *me in 1 da., in what time ean the whole 
 
 ''l?*!???J?!''»*«lda.; 
 
 I" •• »fda.«Uda. 
 (8) Show how to And the amount of work done by a number of 
 men in a unit of time. "«»«wr oi 
 
 (4) A|>ply theoe prinelples to solving problems. See page 74. 
 
 I". CLOCK PROBLEMS. 
 (1) By meana pf a eloek or wateh show that the mtnute.hand 
 more. 12 times as fast as the hour-hand. It moves over 00 
 
■vooMnom fob nuoHiiia. 
 
 «.• «tojjl..h«4l to Wb, thorn Into tho podtteTC^ ^ 
 
 (4) Now ooloiiloto tho tlmo loqaiiod. 
 
 Bx. 1. 8oo pogo 78. 
 
 Ex. 2. What I. tho woond timo oftor four that tho hand, of a 
 wateh an 2 miaato-opaooo a|iartr 
 
 (1) At low thoy aio 20 ■ila..ipaeoo apart. 
 
 (2) Thooo 20 inIii..apaeoo mwt bo gainod and 2 morot-li^noo 
 22 iBln.-tpoeoo nnit bo gainod. * ^^' 
 
 In S^^!^'"^^ •" "^^ to 22 timo. l,»r mln. of timo, or 
 Honoe, tho timo ia 24 min. paat 4 
 
 «.^viht!X1 "" *^ **"• '^' ' *'•'*'• '-"^ -'•'«'•»» 
 
 (1) At 7 tho hands an 85 min.-spaeoo ilpart. 
 
 (2) Whonatrightanglo.thojanl5miB...p«^ap,rt; honoo. 
 20 min.-«paeoo moot bo gainod. ^^ ^^' 
 
 2lA'i^ «*»-P^ «• «^»e<l in 20 timo. lA mm. of timo, or 
 Boneo, tho timo i. 21^- min. paat 7. 
 
 Eat.4. What I. tho tot timo aftor 6 that tho hand, of a wateh 
 form an anglo of 72't ^""^ 
 
 TTaH of tho eirevmfennoo; 
 
 .*. 72'»i of 80 min...paoo.al2 miB.-q>ae«.; 
 
 (1) At 6 tho hand, an 25 min.-qiaeo. apart. 
 
 (2) 18 min. -.paeoo mnrt bo gainod. 
 
 (1) Tho hand, an 25 min.>q>aee. apart. 
 
 (2) Tho hoar-hand i. a eortain dirtanoe fnm 5. 
 
 th f iJ*"* "»to-'i»nd i. tho Mmo diotanoo from 5 and 12 timot 
 that dirtanee from 12. ' 
 
 (4) Honoo, 13 timo. that dirtanoo»2S min.-qtaeoo; 
 •'. <meo thi^ di.taneoa>i|| BiQ,. 
 
r.^'^'l^ ta (»-i«) mln.-wp^ p«t IS. or a»A 
 a.-qMMt pMt IS. ^ " 
 
 *tot is StA Mia. |NMt. fl. 
 
 IV. MOMJEMt MVOLVMQ m«ClTV. X -. ^ 
 
 CfeM I. OIVMI IIW - 
 
 ft. 
 
 »I1?U* wT ""^ '^^ I** ••*»« to n-a to • nrtt ef 45 
 
 IB (WXeO) Me. the dtrtMM «mi««(46X6880) ft.. 
 ••• " 1 •• " •« *t ^ 46X8880 
 
 mllM p., iKmr, tok. to •«« . bridf. M4 ,«dk Wf ^^ 
 Tim. to moT* (SOX IfW) y4.»(eOXM) m.. ; 
 
 ••• " " " (804-184) yd. «»*X»OX(» ^ ^„ ^ 
 
 ' ' 30X1760 ■"••■■•• •••• 
 
 V. FIMWIIS WVOLVINO ll««|^ 
 
 By mMas of muy «im^>Im allow 
 
 (l)tt^ the Willi of two wmbmn aditod to tiMir dlffBioiiM sItm 
 
 (8) tlMt tiw differmeo of two BooibentyMn from thoir ram 
 flv^ • remainder eqn»I to lw*of tl# «ia«ir wuiiber. 
 »i>fi» 4 
 
 18 
 
 SX» 
 8X5 
 
 « 14+4=: 
 
 » 14—4^ 
 
 10 
 
 Problems ihonld not be gIvMi until the foreee •IbetiniP a boet 
 ^ ""SS?f^I^'^:i SiKiwthe following by raehq'nitS:! 
 ^H«J2?SJ2^"' !S?? •»»«»•* to more itow» . lemnf " 
 HowdothMefbreeetlllMttlieboatlagoingr * "TT"* 
 
 tho 
 
 il!^?** *!?« ^ -^^^ to the ««• <tf two nito.. Tiiu. 
 
 Ta'^'n'?* *» •«» r*" •«» «»• «*• of the .troMi 
 (8) The mto np etreftm Is the dlflbienee of tho 
 
 Mmo. two nitee. 
 
 to twtoe hie rato of iowia« In stQI water. «««« » •««« 
 
 \ 
 
tvooMnom worn nMrnxan. 
 *•*• d©wa p«r liooraB4 ml. 
 
 "^"Tf ft •Sf^'-' - -f.-4 1. 
 
 . ■ — «8ml.| 
 
 .\SXnitoofttr.»laU.i 
 
 Brt» In itm watOT pM liaw-gml..8 aU.. 
 • • »*• o« b«* «p rtiwu««(j_H) «l.-« ml. ; 
 
 Time to row 4f nl. up •tn«n»^»8 hr. 
 
 i* 
 
 nMOfSMrtiMm. Had lito »to «f rowing In iffll wrter 
 
 ««» " as-l " " i< «i 
 
 «rf^*S^!L*t?^ th. roimd trip he .p«id. I of the ti«e in 
 •mag down and t ia rowing baak. 
 
 i <rf leo niin.sB40 Bin. 
 
 Brte per how dowB rtieam=« of « nU.«» ml. 
 «P " «|bU. -Sail. 
 
 H«iee, rate in atUI water«s?±?Bil. a-6 ml. 
 
 Bx. 4. A boat'a erew eaa row over a eooiee of li ml >imtn.t 
 
 wew take in the nnial cti^ of the rfyer f • «•«• mw 
 
 Bate np etream per hr.=(«xU) ml.»7i ml. 
 
 Bi^^etreamK2 *' ; 
 .*. rate in still waters»i " • 
 •'• nte in nmal atate of riTer«9 " 
 Heuee, time to row 9 ml.sdO min. ; 
 
 1* J— iBin.«84 min. 
 
 f f 
 
in 
 
 *■■ 
 
 Hi ' 
 
 X 
 
 1. A boy HdM nwad • ««W «0 rod. Um* and 48 m<i. .m. 
 
 How BUT lOda will lui tm^m^t t« 1 ^^ ** '*^ '^•^ 
 
 2. A room is 64 ft. lone and 27 ft wld« w«- i _... 
 4. A hM $8120 wJUeh is |084 mon th^ » k« m r, ^ 
 
 7. In ft sehool thore sm 818 aeholftr. ; 177 m«i |w«. «,. 
 giri. occupy two rooms, in one thowaroas hLT ^^' ''^^ 
 
 8. A boy eanght 178 Ush and another eaiurht 2flO W«. « 
 
 mast taa flrst gat from the seeoiid that WI?»«K ^*^ ""^ 
 nmnbarf Aiw. 42 fish. "^^^ ""* »^ "»y »»▼• •« aqaal 
 
 ». A drorer bought 10431 sheap; he sold 67M «ui *k v. . 
 10. A is worth 815687; B $578 lass than A: C 8047 ««^ ♦k 
 
 li»Ta thay all f Aim. 87418. ^**"*'' ^'^ »«w»h 
 
•troounom vok nAcinro. 
 
 A»«. 914000 «»h ••^••"75 to B. How««di li«d M«h tiMnt 
 M. A told • hone to B and toftin^.! «i«a « 
 IK A •"**"♦'*• ^'w* did the lione eost Af Am mmi 
 « foUowt: J«,., «1972r»lh tiliL J*^ "^ "*»»'»>• 'W'* 
 •8M17. F,^ ^ ^ ^ ^^; 2:;.<J^J3^ ^i^^ 
 
 Wl An. WM. ""•""»• "•» "■Mil h* llMui A did D 
 
 ♦21^. H.wm»hdidh.«„,'";;ri;'i2"'^- *~™* 
 
Uti 
 
 
 «• « «MMfM$S.40ad«7. WhtlwmteMnilattMBMth 
 of J«i}utteao^b«g|iiSMiTiiMdft7t Ara.|M.M. 
 
 S7. A BMB Mnlac W.» por daj of » hn., toti 17 kow»4»» 
 WMk. What did kit —nlngt tmomnt to for that WMk of 6 d^t"^ 
 AiiB.l9.S0. ^ 
 
 M 5:> ""**'*«* •'^•««»«'»M««*W«poroo»t tad ioM II 
 for 17000. What did ho gaiaf Axa. $360. 
 
 ». AttMo»ra««ltawookaiidp»7«|27pornoiithforbe«id. 
 How moeh ou ho mto In a yoarf 1 y».«i2 iiioaths»oa wooks. 
 Am. $018. 
 
 80. What aaaiber is that to whioh if 17be addod tho mattwUl 
 bo 1ft tioMO 138f Am. 1808. 
 
 81. Flad tho dlfforoaoo ia tho ooot of 87S honos at ^^.80 oaek 
 and 488 oatUo at tM.10 oaob. Ana. $1466.80. 
 
 82. A iamor oiahaagod 1840 ha. of whoat at $1.10 por ha. 
 for 164 bU. ioar at $8.80 por bM. aad tho balaaoo ia eaab. How 
 naeh oath ahoald ho rooolvot Am. $016.80. 
 
 88. riad tho dlfforoaoo la tho Talao of two faran oao of 800 
 aeros at $74aa aoro aad tho othor 188 aeios at $130poraora. Am. 
 $0000. 
 
 84. What la tho difloreaoo botwooa tho Talaas of JB4 bonos at 
 $188 oaeh aad 168 eattio at $64 oaehf Avs. $84. 
 
 80. Flad a anaOwr nioh that whoa tho aam of tho odd aaaboia 
 botwooa 68 aad 78 la takoa frooi It tho romalador wiU bo 80 Uaos 
 886. Am. 7760. 
 
 86. What aambor la that from whieh If 47 tlmos 18 bo takoa 
 tho roBiaindor wlU bo 80 tlaaoa 187t A>8. 0688. * 
 
 87. If I bay eofloo for 68e., toa for 88e. aad battor for 127o., 
 aad (Ito a $0 blU la paymoat. What ehaago ahoald I rooolTot 
 Am. $8.10. 
 
 88. 898 aoros of whoat ia Maaltoba yielded 82 bn. per aero, 
 whieh aold at 40e. a ba. What warn the Talae of the eropf Am. 
 $8278.40. *^ 
 
 88. A ftaaer aoU 284 oattle at $04 oaeh aad thea boaght 960 
 wreo of land at $20 aa aere, borrowing tho balaaee to pay for it. 
 Bxm aiaeh did ho borrowf Am. $9024. 
 
 40. A MmthoiB tradar sold 678 bales of eotKm 
 
 at 88e. a lb. Wkat did ho got for itf Aira. $64047.48 
 
 of 417Ib.ea6h 
 
tut 
 
 ■**: ^ /^""^ bOHirt tfaow fg, aiflM, k. a^ .. , 
 
 •rti. Aw. $|»3r ^ '"'•*^- «»dU«tatia 
 
 «. Floor ami boa^t mi.t.. I _. ^ ^^ *•*• 
 
 «»▼•» Am. #4006. -» •"• ^^ WW «« ttMi B. WhaldidD 
 
 Am. 0U80. '^^ * y**^" mo«tliM=«2 w«Mka. 
 
 «. DlTld* the modmt of 784 Mid 848 Iw th. At&.. . 
 784 ud 480. Am. 784. "" *** "^ »• dMwwiee be»w»Mi 
 
 80. 281 rntneMa 81788.80 in aif^ek Wfc.* ^^ . 
 • d«7f Am. 81.28. "•^••«. Wbat doM MMh Mm la 
 
 fi8bt hand digit.. ^, 2M0 • "' ^' ^8 by the pwduet of thoi, 
 82. Mud the nmalmtor whmi «m ^.^ _* - 
 
 AM.. 8880688 brio.. ^* **** •^ ^'^ •xpoitwif 
 
WMMh. fladtiM 
 
 W. iMliWkMMite 
 
 •MtafMMh. Aat.tlM. 
 
 mMvH9ihtn^tm «l«llptrMi*ndtbtiMlatiiiS 
 MM. Wkaldldtefyat An. 91T7W. 
 
 07. ▲ MMivkut teofhl flow for $1061^0 at |6.M por bkl. ud 
 MM U to g«ia Mo. oa oMk bU., flad tho aubor of bU. aad tho 
 total fda. Aaa.lMbU.} $77.10. 
 
 M. HM hoMM ooil fttM, a» wkiit nto mul oMh bo ioM to 
 Ida 911.5^ por koidr Am. flfiO. 
 
 M. lCBllip|j4178Bbgr6MoaddiTtdotboi»rodaotbfS> 5X7X9. 
 Aai. 41798. 
 
 99. A firall doalor boagbt 9 bU. of a|»pIoo at 99.19 por bU. 
 1Mb bbl. ooatalaod 999 apidM, wblob bo wM at 9 for 9o. Bow 
 BMMb did bo gala? Am. 9*1.99. 
 
 91. A Maa boagbt 99 naa at 9«9 oaeb; 4 diod aad bo mM tba 
 not M M to gala 990 oa'tbo tnuMOtloa. Had tbo Mlllac prteo 
 ofoatb. Am. 999. 
 
 01* A aun aold 119 bU. of floar for 99111 aad galaod 91179. 
 Flad tbo eoot por bbl. Am. 918. 
 
 98. Wbat io tbo naallaot aaaibor dMdblo by 9 wbSdi addod to 
 4991 BukM tbo aaa dlTialblo bf llf Am. 99. 
 
 94. Aoortaia aambor laeroaood bj4979 aau tbo mm aialtipltod 
 bj 417 ghrw 8948419 for prodaot. Wballatboaaiaborf Am.4981. 
 
 80. Wbat ia tbo loaot aanbor wbleb talmi froai 299488 looToa a 
 romalador of wbiob 84 Is aa onet dlTlM>rf Am. 09. 
 
 99. TbodlTidfadit84X0X10X84aBdtbodlTiMrex7X88X108. 
 Fiad tbo quotient. Am. 2. 
 
 87. 1 aoU my bomo for 94000; TiUago lots for 9000; Loaa Co. 
 stoek for 91100; fnraitaro for 91000; and roeoiro ia payment 
 99000 ia easb aad tbo balaaM in N. W. lands at 92.00 per Mre. 
 How many aeres do I getf Ams. 480 serM. 
 
 08. Find tbo amount of tbo following Mil :— 
 147 eorte bard wood ® 90.70 per eord; 
 
 200 
 
 «i 
 
 soft 
 
 <i 
 
 9 94.25 
 
 i( 
 
 II 
 
 4 ear loads of slabs 19 eords OMb 9 98.70 por oord; 
 819 toM hard OMl # 90.10 per ton ; 
 
 089 
 
 soft 
 
 9 98.80 
 
 11 II 
 
 88182.70. 
 
Mri. for lb. .MUMf Aiw.$i. """'^ **^ « *• pojr p« 
 
 ww>ot$i»,..fc. How««vfc»todldkoortlf AwirSl 
 •hUdf Aii^ $7.10/^ •"^- ^^* «• Ifco ooot f or oooh 
 
 •• '^ -^r •^ « * •• ft.-17«8 0. 1..f !Sr2S f» "^ "^ 
 
 77. A fnUt growor la (klifbraia nMk^ •^iwwwTT^ 
 Aw. $84. "•"««»• Prioo of tho oottio p«, |„|Mlf 
 
 •102.40? Aw. 7ae. ^ ""^ ' J-^* wM it to g«bi 
 
 »l«»re.eortmotol«yrtthowB.^, AlTlSii ^^* 
 
 ist' T.''r'*'*^«»--^^ Si^*' SSS r' s? 
 
 «M 1» Mlir Aw. 00 loti. "waoy. How nwny Jot, 
 
•4. How BMur bmfhtit of wlMit ot Tte. « Im .k^u .^ -^ 
 
 •i.HowBMvbMfholiolwkirt tlHi. »b«.*o^h•-l-L 
 >Mohlloirtraa,ft4lilMooof4MBUoof AnJlifcir^ 
 •i. II « lb. of to. oool Hi.g§, whrt oaoMl of bailor ■« 10. 
 
 ^^w. ruid lb. ,.tao of am lb. of wb.it 1 no. . b.. a... 
 
 gt« forie fbo of bottor of 80 lb. oorti M Mo. lb. f ^J. . 
 
 *f* ^ ■•■ bo^fh* » oofoo at 106 por oorot bo mM ma hm 
 
 ~p^i2ji«i.oi4i»iorim4. H<r»':s^i;sr.2?^ 
 
 •»4ft»18o. How awob did ho fofai to 7 wooktf Mim^ 
 
 M. find tbo aaooat of fbo ftollowtoff biUt— 
 
 nCb«. polBlooo«40o.obo.| 
 lMbtt.tanip««15e.»b..| 
 
 170b..pooo«8te.ob«. AW.H70.7*. 
 
 »•. A BMB ooM 147i bbl. of iow for tlion SM bM ».ax 
 
 "i» ••ri^»»M.*»-«Obbl..l 16.50 porwiu^^ 
 bU. did bo ioU tbo lOMlBdort Ai». lIT ^'«««^P«f 
 
 0010 not ft ]oi« of 047.25 por aofo. Howmiob loioMr oorodU 
 B looolTo tbftn A poldf Am. 000.75. "^ '^ I»« ••'• «< 
 
 «^. »wr«ii..ydldbo.ellftitogrtborfor06S6f AmImm 
 
 06. Whftt immbor Ii tbol to whieh If 847 ond 4 ttmoo 047 h« 
 «ldod «»d 187 ond 4 ttmo. 187 bo tako. fnTtb. iZlt ^ 
 renaiiidor wUl bo 01647 Axo. 8564. ' 
 
 • 06. A ftomor rftloed 518 ba. wbMil to 1806 and twioo u mnA 
 tol890.ondtol000oi««d»Mtotbo^^^^^^^^^ 
 
 tbo ^aliio of ftU al $1^ per bB.f Asa. 03840, 
 
 otbortwojoora. Wbotwao 
 
»~» — «a^H OK (M Of 79 lb. MMh Aft TIfa « IK w i^^^ 
 
 ^•MJ^«f«i.lNi,of«ow. A».l08r • ""**** 
 
 Iw. Ataftll* droirtr paid tasiiu #«* mmi. .« m^. 
 
 ikamamk^ .M «. V^* ** •"« *^ »^ tt » gala of 19714 >|im» 
 
 109. If iottrIgt4.79abbl. •nd«i»pleit2 40.KM k 
 
 l«. •« b. bwight for 9848.20 to L^(S ^;!^ ^v' ^'^^ "^ 
 Aw. 49 bbL^loeh. »»*•▼• «» «»• .uabo, of oMhr 
 
 99.79 for • pair of ^ooto- 917 wfT/T-it. *® '*" • ■•^J 
 i-i' w ooon, 917.79 f6r elothot, and 99.89 fcr 
 
mm, ■•vaM^bv.afvhwiaifrt. viiipi^lh^hm. AM. 
 
 MqralMt. BMrMBrM.<lMMfimMMf Am. ml^ 
 
 lit. ▲flMWbMfll4IMl.«f«0MiMMHi*»fy.tli». 
 
 ■IIMMthi lMplfiat|6.MtMk,M«MMpatMMi 
 ■MfskMpdMtelMyf AM.197MMP. 
 
 U4. MbM.ofTlMfWMrt|IM. If HwMMM»tMt.»gy. 
 m4 Ihtf* «wt M fia. te s bM., MwBMh wm gyMdff Am. 
 
 Bmt 
 
 ."t,i^ •»2?*^ ^^•'Hrh* tow. lote ft» fTIM, aM iold tll« w 
 i^aMlOtlllOMik. HowBHjMlWMUf AM.Mloto. 
 
 lit. If 40 tq. fDd* i|^ UMd wUl fraiMt U b«. oC mtig, 
 wtat wUl b« tte vfthM of tht Mop gromi m IT mum al M. » h.. f 
 
 Am. 1010. 
 
 117. lMM1000lNi.ofwkMlfor|tNtn4tlraglMl|N. Ul 
 kad MM U to f^a IM, whm ihMM I g*l pw M.t AM. $IJ». 
 
 lit. Bow MB7 bbl. of anilM MBtaUUiiff t Iw. Mth «l 40t. a 
 M. wUl bt oqaal la valao to It bozM of omagM oaoh ooatainlac 
 ttt omafw allt for lOo.f Am.4»Vbl. ^^ 
 
 lit. Bov wuaj bU. of oagar of tOO lb. oath wofth to. a lb. 
 ■■■I bo givra for tt bbl. of toar al ti.4t por bM. aad ttS.40 
 oaibf Am. 15 bbl. 
 
 ItO. AfMMrioM144tba.ofoatouttta.aba.aadiMoN«d 
 la pagrmoat ttM fl. of laaibor at to. a fool aad pigi al tt.00 oaofe. 
 Bow BiMwy pifi 4M ho gttr Am. Itplfi. 
 
 Itl. A toM ooatotnioff 48 aoiM jrtoMod tt ba. por Mro. Tio 
 giala WM MM at t6e. a bn. aad tho moaor iaWitod la thoop at 
 t0.tO oooh. Bow naay thoop wort boaghtt Am. 1M thoop. 
 
 Itl. A doator boaght tM bn. of whoat tt 18 ba. for ttt.60 aad 
 aoM it at 11 ba. tor tlt.8G. Bow mneh did ho fainf Am. ttlO. 
 
 m. Tho taiallMr of two nnmbort it eoataiood 48 ttpM ia tt4 
 aad tho larior aambor it 21 tioMt tho tiaaUor. Had tho ptodoot 
 of tho two a a ab o rs. Am. 748. 
 
^* A MM hmn Ml lb. ml ^mmm lu. m> ■« ■> 
 IIT. lrt«d th, firtlowlH t^ tod Ml. «« of Ih, ..^.^ 
 
 » — X P I ^ IMAWI 
 
 llMftXV'M^ UHtxi 
 
 isSiSrxSE iSSxtHi^ 
 
 UMSOrn UM067l»Xt-»^ 
 
 II. COMRHMO NUNBEIIS. 
 
 ^•■4 8 ft. Ugh. am .Mwy w«to wlU bp Itftf ^. iM 
 
 4. A temn told sm bmm of tnH rnnnghtm I ot 
 Bpw an, bnhtto did h» MUf Am. m b«. ^^ ^' 
 
 •M ft boj walk in Ml honrf Am. 1 ml. 280 roda ■»«"«■ 
 
li. 
 
 ». U*<ipw«igktaffllM.16dwt.6(Ml£8fc.«W.,whiit 
 lMpttldforoMwdfllUoffl7<M.10<lwft. Ugr.f Am. <• la. Hd. 
 
 t0. Tht lalltad* of, Brutford la 4r 21' ST, ud of Qitlm irar 
 Ijr. H«w M^r dmiMt to^wbM Borth of Bfutfoidf A«a.V 
 
 11. If in lb. S 00. IS dwt. M fr. of gold bo aado iaio 14 
 otftUMBto of etaia woighl. How mob wUl ono onMMit noicbt 
 Am. 8 lb. 8 00. 18 dwt. 90 gr. ^^ 
 
 •418.80. Wbtftdidlgtlporooidr Am. $«.80. 
 
 18. A limor bw 111 b«. 2 pk. 4 0. of wbort wbleb bo widioo 
 
 topattobiftwblobbold2hi.lpk.4qt.omb. Howmuiyboii 
 WlU bo roqolMdr Am. 47 bofi. 
 
 14. How lo»t wUl It tiAo » mil to walk 147840 yd. ot 8 «flii 
 uboort Am.98bo«n. 
 
 18. If obiiar foot to bod at balf.paat 8 p.m. and goto ap M 
 7a.M. »>w loag la bo lb bodt Am. 10 br. 80 ada. 
 
 18. Fi«BialM.ofTlmftt«oatatolag81gi|1.2atu.Sgm lot. 
 woio tafcon oat, and 800. wara aartid. BowjMAatm lolalMd 
 totbaboRolf Am.l8gal. 24t. 
 
 17. How Buaj lb. oa. dr. Amir. wt. am tiMt la 4 lb. 4 oa. 
 10dwt.Tiogrf 18dnaaa»toa. Am. 8 lb. 8 oa. 8| dr. 
 
 18. Malt^ «a diftnoMa botwoon 17 nUoa and 18 aU. 819 
 M. iyd. 1 ft. 8 to, by 27. Am. 27 ariloa. 
 
 18. Tboioaio880pQato(ta«hidiagtbo8oaitbooBdof tboioad) 
 
 aia tba poanr Am. 8 roda. 
 
 20. A batehor boagbt 2 1. 8 ewt. of boof at 8180 a taa aad aoU 
 tt at 2 lb. for 280. How WMb did bo gafaif Am. 8144. 
 
 21. How laaiiy atopa wiU « bum tako to trafolltog 80 ■!. a^ 
 4S0 jd., allowtoc 2 ft. 8 la. to oaab atopt Am. 42780 atopa. 
 
 22. Had tbo ooat of 28 lb. 14 oa. of qatotoo wboa 8102!88 la 
 paid fto 8 lb. 8 oa. Am.880B.82|. w«^ » 
 
 28. A ooUar 42 ft. kmg aod 24 ft. wldo la floodod to tbo doptb 
 ofStoeboo. Bowataaybarralaof watorara tboro tottf 1 bbl.- 
 BligaUoaa. Am.lS8»bbl. 
 
 " ' wbleb 
 
 by a tigbt board 
 betb aldoa at 16o. 
 
 anoloaad 
 
 Mwa 8 ft. 8 to. blgb. Ftod tbo eoat of fi«fW 
 pwtq. yd. Am. 888.76. 
 

 Am. 1171, 
 
 (i>M p«v MvAf 
 
 
 S7. K 
 
 779 
 
 lm.isn«. ft. 
 
 M «ir, Md 1 «. ft. cC 
 
 sr.:r*'«'^ -. *» -^ ^ n. ., -.•;5i:i;;.^i 
 
 ». Bow mamy b«. of whN* wffl woigli m aMh m IM 1m af 
 ». »io« » pUo of iwod 18 ft. k»t. 4 ft. wMo. 4 ft. high 
 
 1 od. 64 0. ft. i« mM •! ono timo «ad M 
 l> tho rmaiador worth at 16.40 » eoidf 
 
 •• ft. a* •Mlkoff.'^Wbat 
 All. 18.00 
 
 117 da^ later! Ams. Doe. nth. ■twwnia 
 
 H. aw «aay ttawa wlU • wlMol 6 ft. e to. alroMofomaoo 
 «mto||otoff4niloof Am.l|MOttoMo. «wmmoiwioo 
 
 81. 7 ewt. 10 lb. of 
 
 Mf» b tOw to oaoiiaafo Ite 1 
 
 Alli.lOd. 
 
 •I !•. Od. a lb. Had tho ptioo of tho 
 
 621b. 
 •ofw por lb. 
 
 wttb ioda aaoh oontatotof 1 i,. ft., tbo aodi wh 
 iOt. P« tondnd. Am. 11.40. 
 
 •*. A barrel of iow wolgha IM lb. If 1 
 ••* ■•*• 100 lb. of floor, bow maaj bbl. oaa 
 
 MidlOfl.wido 
 «* toUooattoc 
 
 bo. of wbaalt Am. 100 bbl 
 
 ba. and 1 pk. of 
 boaMdofkoaMi 
 
 85. Wha» le »bo ooai of 15 lolala eaah 6 to. by 4 to. aad 
 
 long at IM per X. board 
 
 118.00. 
 
 lift. 
 
 a roe- 
 
 86. How maaj torn of wire wtU It roqairo •« Mmmmm a m 
 
 .9iiwU|^aiid8ft. ofwIreweIihtoffllb.r Am. 1 ton 18001b. 
 m. AVERAQES AND SNAIH!^. 
 
 l.n» aeoim »ido by a eMe al eriehot weio 10, 5, 14. 0.45 
 W. 81. 0, 0, W. J flirt the .foraio .««. of oaA brtt;,.' 'iJ: S' 
 
 ^\t i^*^ii?* 2J*1- ^ ■* "•• •"»•"« 7 lb. at le. a lb. 
 ^" ^' «» !*• What waa tho avoiaio priee por Ib.t Am. 
 
 » V' 
 
AimniiTiQ. 
 
 P 
 
 Hi' 
 
 «iA -^ *T^ ^«»I «»fta«l fl»to hi, .„«„ «q,„^ to, 
 WTdVtteb. Mt. ed. • digr, for th. ilwi 4a divi UMy »«»n««d 
 lO^.dv. WlHUwMtli«.T«»fetortheU»tl4diutf . 
 Tbtal npMMf for 06 6ity i» K8». and foi 42 dari it ia lAll^ 
 
 4. Tlio ftvoraco nambor of rans made by 11 men tA oriekot waa 
 12. TlMl0oftlieaiwhofokoa*iiiador«ipo««Toly22,8,7,4. W. 
 0, 21, 0, 0, 90. Find t|M Mora of tho 11th nan. Amu. 87 rau. 
 
 6. A ftomar paya a rant of $0 an aera for 100 aerM, 90.00 par 
 aera for 120 aoraa, and #8.80 par aera for IN) aerea. What ia the 
 avelfage rant par aeraf Am. 86.82i. 
 
 «, Three eehoola edneate 70, 88 and 81 ehiiaran at an aTaram 
 eoat annoaUy of £2 lOe., £8 lOs. and £8 16.., respeetiTely; they 
 ara naited and an annual sa^ng la made of £141 Oa. Find the 
 avaiage eoet atternnloa. Am. £2. 
 
 7. Divide 88608 among three boys in the proportion of 1. 4. 6. 
 Am. 1888, 61818, 8106|. * ' 
 
 8. Divide an aetata of 8874 aeiaa among A, B and 0; givingB 4 
 timea A'a ahara aod 9 times A's. Axa. A, 24X ae; B, 864 ae; 
 
 8. An examiner wiahea to mark 8 questions in the pioportioB 
 of 0, 8 and 12. The sam of the marks is 100. How must ha die- 
 tribute themf Am. 80, 48 and 72. 
 
 10. A bag eontaina a eertain number of sereraigns, three timea 
 •e many aUUiags and four timea aa many penee. The whole aum 
 •BMunts to £060. How many eoins ara thera of eaeh Uadf Am. 
 460 SOT., 1440s. and 1980d. 
 
 11. A, B and C have 6300, B has twiee ss mueh as A, and the 
 diffsienee between the aharea of A and C is 63.92, C's being the 
 IPMtor. Find the shara of eaeh. Avs. A, 649.02; B, 696.04; 
 V, 603*94. 
 
 12. A sum of money is divided among A, B and C. C geta 
 twiee aa mueh aa A; A and B get 6200; B and C get 6240. How 
 mueh doeeaaeh gatt Am. A, 640; B, 6160; C, 680. 
 
 U. Divide 681 aamog persons giving two of them eaeh 62.00 
 leaa than eaeh of the othen. 
 
 iJd£r(27695o)+6ili^." «"««»«•«»• ^ ^*rfbuted 
 
 •86~0a«617.20 for eaeh of ttireei 
 6(l7.ao-8.60)-614.70 ' ihw! 
 
■■▼WW rmmuatM. 
 
 9*7 
 
 C, 1229 M. ^^ A, JMBae.; B, 7»1 m.; 
 
 IV. APPUUTIONS OF SMIPU AND COMraUND 
 
 MM !■■■■■ ■!■ " 
 
 «wa M »e. M l». Aim. BaUuim $6.00. 
 
 •««165yd.ofoiUtoo»|7e..,d. Ant. |84;2r^ • * • '^•' 
 
 4. Ifake Mt th« following bIU:-.16 qaim «f »«•» .t « ^ . 
 
 . . length of io«m«(8160~-3«) f|,««i «. 
 
US 
 
 8. T^lad tlM ra^ar tf m m ^ i X> 
 
 "o^ 10 fl. 6 In. wM. «d iTlTiJl^-J^^ 
 
 M ft. wid, «ul 10 II. wI^JtJTS ** l"^ *• ft- >^ 
 
 •^ 1^ .«. ft. I. «i4« JToilSJf,'*' *** •«• ft- « « •^^ 
 
 -iSSrt'pSj^l^^^ 1^0 „. ft., 
 
 10* A noon 11 ft. kuh t«u— 1JA .4 ^ 
 
 "wuNlthtitHwif iS.78ftr ^^ »» ■•««li*l to t» 
 » hi tr2L?»*V*l*!i~« *• ft- « to, wid. .wl 10 ft wrt, 
 
 ■«»i»p.i«ift.oi«.Sd,ii;J^'tiS^ ^•'^ 
 
 M. A bo«d tone, 9 ». ,^^ ^ '^• 
 
 ^^rm^ .q. ft.;^^<J^J^.^'iJ^£;i«fxgi .^^ ft., 
 
 Ho. of •OMttlBf»10eo^j|3,^jj 
 
■■■*»"*ft»ei«.iq««»,, indite hdfit. •/«.••. n. 
 
 ...sy?*'.-*"*"^'"^ !■««.. ft. = 11^ „-.-.-. 
 
 ^*.-i..ft.,i#.h«Hkfc..i..«.i;';^j^ ^. 
 
 f^i^^Hl^tl^ '^ o-.; iBd th. wight «f 
 
 «~o»u on out .eft 1 in. d.,p. Aw. IM t. tW lb. 
 
 »7. A steMt IMD ft. l«Dg aitd 40 ft wU. «i.^ *i«im. - 
 
 «( « 
 
1 
 
 AMtftnamo. 
 ». A NMrroir Is S80 ft. kny 199 f|. ,^|^ md 4i ft d-wT^ 
 
 How m^gr M,k. 8 In.lof 4« !«. wiTwinTJaal^ tfS; 
 pftTMMat !• 8 ft. wid«r "qw»«i IT tM 
 
 — •» tq. m. or nirtMti /. BimDar fiqiUMd is W7r ^^ 
 
 80 jd. long ud S6 yd. wids for $1190. ud Uw oChor fl«^ 1!!! 
 «d60,d wid.fo,W800. WWh I. JtSLt^^^ 
 how modi p«r«i.3rd.f Aw. Tho j^tor; ««. P'*'*'^*"**^ 
 
 JlftissJiti'::^^ 
 
 ■wo • n. uuek, feow may Uooks 8 In. long 4 in wkU nad 9 in 
 tUokasabooatoiitotitf No aUowwo. for wasts 
 
 Cabl-loojrtwitof^WoJ -(W72X88)e.Ia. 
 oaonuIlbloeks(8X4X9) a in . 
 .-. >aaibor of Woeks-iriO ifs. ' 
 
 W. A p«id m ft. by 180 ft. ta aoToiod wtth lo. 8 In thUk 
 flad^wrtiirtiatenso£a»leo!fl6 ft iSwITiJik T^ 
 
 85. A taetangalar eistora Is U ft. long and 8 ft. wide fnrfd^ 
 «OM««a«li: «d ti« wrtsr I. 7 ft. d^Tp. How mi^tot^S 
 wrtorsfothMolattooistora. AHS.21ton.. '^ ""^r *«»• •* 
 
 88. A street 80 rods long and 80 ft. wide !• to be dotmI «l«i. 
 
» ft. wM. «d 4'ii. ikSr. "iS!;;;^ ^^ -^ » ft. ki» 
 
 ..**•"««. to. ©f Iron „«lgfc^^ * 
 
 j^ •'»•••«». o*^ ir?i. w%!"- •* '^'^ •^ 
 
 ^* ^ flUUI fldZ^ t^*m anil 
 
 «»to to 4 b«. of P.M SSTiJSlir,!^ ^J!'''*'*^ ot mm. of 
 •^ •« worth mTpJ^T;!^^ Iftt. 
 
 •LlOpwlHi.- '^"^' ''^^•^"^•I*- worth porbu.f A». 
 
 »-.^ What wSnr:!?^ ^tisn^^.t'S: ^' '^'^-^ 
 
 a« mw* I, ttrt ,« »,.f^^^f'- •"«•"»• ~W tor »4S». 
 
•'•¥ . 
 
 I Ml 
 
 4t. Bmt ttMir iign tM ilMtt teM Jim in to OMMmt ilk 
 40. If ihtft iM i ftMM ia ft baadlt ni 5 taaOM far ft ^iit 
 
 M« TB llftM ftM MM M^ Urania bftltft, WhftI it Mm IWMiBiit 
 
 wwllifttMt. ft^int JUlSvllMJO. 
 
 4lb.loft. WfcittotfcftWltoriwrtfcftlMt,«ib.f A»ft.$n.7f. 
 
 M.Ijyi««lMol»t<5.tftpMi«,<„mhiWifti60..> 
 ^••^ft. Wka*to«ytilBMlMb(lohftr Am. 91.10. 
 
 MnpnT Aaft.M«Ui. 
 
 laleuwiUb»i«vdradforl»i.«f»»u««idr AmTwi. ^^ 
 
 M. A ftoiipa^ Blasts lb. 6 ••. 10 dwt, of tilfw into lift 
 
 bft««*ftjMwtli^ >|iid thft wHght of .ftA W. AW. 4 lb. 
 
 S6. AbamlofbeefwdglitaoOlb. Rad tte TalM of tht bMl 
 aMB nooifOi 1 A. 4 Oft. Mlf . Am,$un. 
 
 •«. ft, iftd fho loaglk of ft lit If ibo wkMh it • H. 
 
 ift^J!|ifi!!iaf A** ■"■**•' ■«. ft. to 1 i^r 1441 lomoi of 
 
 W. A li«Of oold M tau bMlqr ftad S7 bft. oftto for $HM 
 
 f^MMBffMi.9orbtt.aMioforbftrbgrtkftBfwoftto. Had tbo rnloo 
 ofoftohporba; "^ 
 
 " ^* 22!! !??^^?«*-<«*-«N-(«7Xa8)o.«0107.80: 
 
 lo.*".^!^,^^.:*;..^'^ •*• * '-^ ^ ''• ^ «»• ^ «• ^ 
 
 ». »» foio wbool of ft oftRiaso i, g ft. |, olmimfW^aoo •»« 
 
 ^ LT^^T* ■?•••««-»«»•«»« «• to fotot4 •!. 
 MO Id. Flad tho oinaaitoioaoo of ibo hlad irhori. 
 
 «te . . 4 an. UO fd.wiSOTM fl. t 
 
*•" ■• •■• MMiMw wkaa fth« «^ ^- . .:-" .'** ^■•* 
 
 
 itiiTidtiifiaf 
 
 its. 
 
 
 «*.«»Wlf AMI. lit fy. 10 
 
 
 «wih«ifc.«^.f Aii^$ia.n 
 
 tlMBllk 
 
 ^ ■«. A tabw 9T bo. Md B tk« mL mvHi. a *«« « w^ 
 
 ▼oloooftlMloModHlMiif Am. 
 
 im.M. 
 
 »i* Sn id. bt divMid to fito 
 
 *• ^ '•■^ •* * IIWOM teod iMOkkavt mm^ -^ ^.^ — 
 •■• •••■ WOOMB 4^. ThA kill - r«. .. TI^ ^^ •'" ■••* 
 
 __^T '■" '■•• *■• ••« WOO $ll.t7. Bow — 
 
 ii.to 
 
 «P»«t.,Olldtfco«OddiiioI. OfwrnloP. W.-i.wji^ 
 
 fi~^ *~*^^ •* '^^ *-• p»r goiio. «2t: lift; 
 
 Am. $6.80, 
 
 ^. If 8 tefktTi avt worth 4 goooo, uid 
 
 oUdmu. 
 
 u* worth 10 
 
 •MbokodtDrttoiJngFor Am. 
 
 40 
 
 •fooolo^lS. 
 
 ooA Mort ho rooolTo to holMioo tho otooool. Am. 88Sr 
 
 80. A owB boji 80 lb. oofEM ot 94o 
 
 lb., oad oftor aUxfaiff thon mUs 40 lb. i^ S8e 
 
 o lb. o«d 80 lb. ot 88o. 
 
 • lb. AtwhotfolM 
 
 He .rtl tho rooMjodo, to «,. hlio f*«. lo^f li. 80, 
 ^'S?Xl*"L*'.'*r *• I^ W*. • too- for 114 loo2^ B 
 
 tOokUttOS 
 
 dad hb 
 
 ioUy 
 
 l«Mf. Kft 
 
It 
 
 Isf 
 
 i«(M«.lt.«rti|fw. AMt.0lNtS7ilb. 
 
 fl. Bam aMjr fiUMM of wattr wUl ft «lMwn ImM wkow Ml- 
 
 |>j^(Mlli). Ttopl«ktiwfcWith.tlrt««li»iiitl,tta. 
 74. Twrnrtgr-Mfw mm w wni » Mitola mm la U int. BaA 
 
 Biiil (M.ei for ftll»li«. ter MMh pw ii^ ; 
 .*. 4yi]r WHJt—t(l.ll-.U)-fi.to. 
 
 telf aC il a* ilt. pM ba. At nhat lala par ka. aaal ka aaO Iha 
 iwiala«arlaialBllB.»lm.oatiawlWa«aaatllrf • 
 Hia talal |aia-iOMOXlla.«<IMi 
 
 Oa faia aaTHOf-SBMx la.«SMt 
 
 Gala aa Sai " » mm! 
 
 Oaia «• 3Bd half par ka.»#M»a-160f»lSS. 
 IttinafpriaaMTtB. 
 
 >, (S«-17A) ll.»4A ft.«rfMBaiad»r. 
 
 W. A awa la to wetlTa N» aad a rateh lor IS Bwrtta' warli. 
 Attto ama rata lio faoaivaa $9M aad 9 watthoo for T aMmtka' 
 mm. riad tka Talaa of tha watah. -'««-' 
 
 i!^!Lfy^ ^.y» «.<W •^ t watalwat fat T mm^ h> 
 
 aM»rthal»oont«iee 
 
A iiki 1.:? «.: zz"'::: ^ts^'iIm ^' •'^^•^•^ 
 
 MM) .-. th« sM* •! tniin iSi u^ IStV* ^'^'^I •>*• tolf tk« 
 
 •ttttlydlTWW. 1^481 ^^^^^'^■■■^•'*%»^ 
 •1. Aa •MMi mutm M m«. .^^ w«__ ^^ * 
 
 ^•••'•^fc-N.f.i-^lg.,.. A«..„^ 
 
 «• 07.10 • 
 
 «. A tMpwtw •«» n. JO . d«y. Hta 
 wttk. Hawlo«»winittol»te«ir;|8i2f 
 
 fc* WA b. «^ •(»»-7.J0). A». 5S wrt, 
 tr. B»«r flttaj feti boMd mmmm 4w ''•■"• 
 
 « ft. 1«« 5 Im wM. «id T fa. ttwT JS.l!IS ft "^ •~**^ 
 •8. A«M«MrtoldMb«.©f whtirtMidlBliB •#^*. 
 
If 
 
 ■I fit tMk ■ktf* tttl* ^V . 
 
 toft 
 
 «I.M 
 
 thM»f 
 
 M^^dw It I, tkt mmK It T Md tkt tlOM Is «| If tte «Mli«il 
 ItlMliiilhtmMkw. Aat.4nM. 
 
 M. A 
 
 pMaititrt.tatMkf 
 
 4nM. 
 
 t* ft 9itil tf !••. tftifti „ 
 
 ht ttu ti ft mil jc «t. «Mk i» n«hm 
 
 nSurssfjs!!^iS.^^^ 
 
 » 
 
 of 
 
 • •tl|lfJ0,A«BiO|li.tl,BtaiOillii. Whil#iA 
 If thift > ftfti t M i M iiif AMi.ttA.M. 
 
 V. rncmt. mmiiiB ano Muuma. 
 
 1. fM tte pitet iMltit t( MNM ftirf SUM tai MltiiHy 
 
 i« 
 
 «• <i 
 
 tC ltl«t*XS«X7* 
 
 Xl'XT't 
 7,17,lir,tl;14. 
 
 •• ■""^ itixTixifxtfxii ' ^»- "«>• 
 
 ' S* WhftI mutbtr mltliiM by 144X17 wiU ght tkt piototi tf 
 •l4XMX74t Aw. 1181. ^^ 
 
 4. ABs ft Igftft to llM rifM of MMh of Um ftll«irli« 
 ntftitiftf ■uibtr mgr bo oaoMtfy dlvitiblo 
 aS719;871t. A«t. 47M; MS 1 1871»7; 87110 
 
 8. Afls ft Iffftio to tht right of toth of tho foUowiac 
 
 — 4fl| i86f 
 
 totfto 
 
 tho rtmtttat aaitbor MaoHy 4ivlttblo by 11:-^4I8| ITItt 
 S478. Am. 74188, 17381, 78880. M7a0. 
 
 8. Ptt t Mi too whioh of tho f oUowing 
 
 •It piiBiot— IM, 
 
 Wff, «1», 4398, nil, 987, 498, ITW tmd SU. Jkxm, ttt. ilft 
 897, 488. — ^ ^ , 
 
jgagjggg*"-,,, ^ 
 
 
 jywjltowrtf 
 
 <!.» Wn ft. tai «»»', 
 
 oiniUMMtef thMi. Aw. lift, 
 •i Hi) ■■Im al IMi MVM •* MA ^ ^^^■""'•^■■yiitiM 
 
 ?•* •» ihplit thMi iato iMt •« tte ^- — - - - y * ■•:• ?^ 
 
 ••iitwillfctfcmf 
 
 ilM«fMi,tM. Am. 
 
 triMf. 
 
 i^.2ti?J2;?::S2 j;*t '^ -^ 
 
 14. 
 
 tk« llM.M4»t .* M 
 
 — ^i«» miiMi wbM froM vkitk if tr k* «.w. a.^ 
 
 
 •oBtaimie 
 
 ^•*«^««4xaiiiirtwiT.. A»riiIS. ^^ 
 
 It. riad ftll MM iaiMfBl diviMM«# iM ' . 
 
 •. ^ ". «. i*. «^>^1!?Sl''2- Jn*,,*' '' »• *• •' ^' 
 
 AM.Uft. "•**'*^'^«^»>«.l>«. lft.il,. 
 
 I 
 
 ^'! 
 
^.' 
 
 ». fted Hm MMllwl tW of MMMf thU^^ k* ««UM t^ 
 
 ofS4«.tto.«rMt. A». ##727 ^** ""^ 
 
 f Id. • fai. art BaltiylM. An.ltft. "-.-■■•ptf. 
 
 »•• "^ »••«*»«■»•«»», diTlfcd team taiMmlm 
 ». Thm toll. Mrik. M iirtwnl. ot «, 7 u4 1 mb. •»_ 
 
 H^. AM.«Bta. |HwtlOp.B. ■ ^"™«"«>«»" 
 
 ^. MX .U tt. Wty, tM .I.MBWtlTMrt.1^ ■- nW .rt 
 
 H.C.F^««, tt. M«». - «« «. H ,. 4. ^ ^ „. „. 
 
 t^xzxsa^ »« -v w.^.,. »d «.pto» 
 
 •«-!?». "a^. »"i, Si "'*"-•' <»»«.". .»to, I. « 
 
 •JLJ^ i:?"' "."^ ;"""*" '•«»»!«>• only teto, of th. 
 
mxttxi£?4jiiS:**''-<'>«-Hc.r.xixixix»xrxii- 
 ■* to ^-""y- •*-*- ■'■'*» •• *, tu iMte. to th. M 
 
 MX7XUXtXlt««M0M. 
 H.C.F. of 1980 Sm ^^ *^' ^ ••^J^ *^W« by 
 
 tti^fc? will's JSSuJTK ina!!!f l!L'^^ 
 
^ ^ umnnie. 
 
 p»r nl. ^- 
 
 $(UHfSlA}S${!''' ••*^ <• 1«* -i.! -1 p.r .i.- 
 
 •. Two MM, A Md B, tlMt to mOk toWMil tMh «lk« lkii» 
 
 •A ai. ud tht ilhMr II ml. piw kr. if y^- .J^ Miw^ 
 ^•^ Whrt P«t of • twl. » lb. t ^ b 1 ^ 8, ,^ 1^ ^ 
 
 A <^«hMB ^ • inoAt of fA pw bM. B»ir ■•A did hTilZ! 
 lMwkiifth*wIdf A]m.flM. "■■•■•WW. 
 
 «• IM fMagMT t M MNMi at to tiM tliMr. Hib " 
 
 MiliMt la tb» 
 
 fcr win they b*«pwl!a 12 d... If tbty tinwl 1. ihrtoZ; 
 Hon, itartiiiff ^ tht (MM plMM al lb« mum tin*. 
 
 f!S "f^^ «*»", W "i-TWl. Of m 
 
 d». It to 81 Mi. 
 15. 
 
 te 1 (tagr !• >i% 
 
 ,4MrBgo«i 
 
 OlTid* the diSmsM b«lw««iM Md M by lh» 
 
Si; 
 
A* A at A wtti flf« • 
 at. Wk«i If ikt iwgMi 
 
 1. Atlte 
 l.7Sf 
 
 
 ¥. 
 
 Ills. 
 
 MHlIfllfMP 
 
 wi tS.hir^**''** **^''^ '^ «« tt tot • Ui9»l«. 
 taB Ml li .UXttmYf , » W J«. 
 
 iL-l!!!i^**^*i??* "^ •■ *^ *^ *• '^'^ was -a. 
 
 BMrfv«ite|»lteaniift.r ▲M.M.Smi. 
 
 -.*• t !IS *^ •" ^ •* ^*^» *••**•»•« tt i^fJO pw 
 W. aM ^<fHw wrt 1 $.71 pwhi. AwMik4iik»M*r» 
 ■1l«iliii «^ tew Muqr te. tei l» itM iw MM Ht mm i„ 
 
 ^^_?J? •* • ""^ •* ""^ i»«i«*h «^ «|»l it MM MM 
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 ttit»iifa«f«.aM 
 
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 M. ^« for* «ht^ cc « bvggjr k 11.28 fl. fowi mM 
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 tMumm tMxmm 
 
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 -Iff. 
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 «epil$.« 
 
 fen. iyM.IMI.7t. 
 
 ^«lk«tf ih» 
 
 II. 
 
 •^1?''*i^^- ^ 
 
 .fMf. 
 
 «Bi*f 
 
i 
 
 
 t, A 
 
 tf fotdt •* 20ft, iSft Md Mft of, lad tte 
 
 nil, US «ai !•« «*M8.tft off; 
 
 UH prloo««MM. 
 
 4. .toif gM4t in »•« m% Md lafft off, ud «te 
 -MMNuitid lo $mM, Hod tho liol prioo. Am, UTS. 
 
 ft. Tbt Ml prioo of as tevoloo •( foodo woo tlM».9t, tfeo w„- 
 okooortoftafbooaoltowid 16ft, Ullaad ion off. WfenlwMtho 
 
 Mft, Mft and l»ft off«a6.74ft «ff: 
 Hoiieo,M.Mftofliolpiioo«fltMJB. Am. il«M. 
 
 f. Whol lo tho Mft l ilu i bokwooB asft off Md iftft wd Mft 
 «f» AM. lift. "m»»«MW» 
 
 ^^.T^*" ?• ^Ir^ *•*««• M* tod »ft off Olid »« 
 »ad 15ft Off. Am. Mo — 
 
 8. Iboofhi 3g0 jd. oCoMh te o«m ti» ltol|»ioo MNr «». 
 
 74*d, tl 15ft OM Itft off Md •• odMHOBOl 5ft bolM ftllMMi 
 
 foroooh. flikltlioooiioeiliooloau Aw. «74.41. 
 ^ 1 boBght oppioo 0* d l oo oM i M of 15ft Md mft off. fhoHol 
 prioo wao 51.35 por Vbl. Bow wumf borate did I b«y it tto dh- 
 ooinrt o ai o M i i i d to 5llS.55f 
 
 1. AaioioliMtlMi7aM5 7d.ofoBkfor58SO;lMo^ir855«d oi 
 •1.10 por yd. Mdtbo Met 01400. por yd. Had tho goia or looo ft 
 
 fai!t1<J?ft.'^**-*®^***^-'*^"*^'*»^^»"*-^- ^ 
 
 9. If I bay two lola of too, oao at 51.00 por lb. aad tho ottor 
 at 576 por owt. How nuut I alz thorn to soil «t 55o. a ft. «ad 
 fain 10ft f 
 
 _,.**^'*P^ wlftoatgafai=s50c. » lb. ; lo«a on lot, 109. a %.: 
 iWloaSBdlSo. alb.; prapotttoa ia adxtaM 8 of lot to 8 of Sad! 
 

 ■• m. • bwkal, 9Mt 
 
 •• ■§« ynit far HO. Bmt 
 
 MB.5^bwMs 
 
 •. •• *« 
 
 «< 
 
 mi 
 
 IttM-BdTi-iM) k«.«iikii 
 
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 prim, WUiAm9 9^% 
 
 ZM^IL'^JllTit.'^:^^^ 
 
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 *b* tttaU 
 
 li| 
 
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 «fttegMte. 
 
 >««ikU«r'tMlltM 
 
 
 ♦w^l Hin (f+B)%9t 
 
 7. % 
 
 
 1^ 
 
 tethtMUaiat 
 
 • lb. 
 
 ktofOa ftoBkta 
 
 Aftor 
 

 «fltft 
 
 V 
 
 li«imaiiat.ftfi. StotoigMiift 
 Mi tft^ hnr Mgrfi. 4li to hi^ 
 
 «. rn i w iii o ii. 
 
 ilitowiig|tfe n i| l i jn. im tUMJi. 
 
 tUSJI. ffMltoratotftMMiMlM. An. ail. 
 
 t. A mmiIhIm ■ iw hart wM rlM m s if alMlii tf i|ft, 
 
 ■fc i lM . AM.il4IJt. 
 
 4. «to M* ymtit •( aO* tMN IMM.4I •!!» yiytaff |M.fS 
 Mi H% 9 »mm\ m \ 9t u WkM tnuf th* mmhuiI ti tit 
 
 .79| .'.I 
 
 m%'^%mm%im%9ti 
 
 If ■■■■ i M tf , >tw MMF liMh i h — I bBylWt. »tt 
 
 t. A MMhMl MM taariwr OB •• 
 
 fiMMii la fotii M 4ft MmdnlM. WImImmM 
 tolatwlf 
 
 •"^ •■▼^^■^^•f^ ^ 9iOTl*OTMMBM* 
 
 r. A mmiIiMm iMWhMl MM liM lb. «( tufagri al Mt. • Ik. 
 
 Mi f Hii B l i tMlii M t f kM <iM». Wll«lMtoo(MMBi«lM«i 
 
 nl MMlMi fM tuinyv-ltfO} $110 ghrM III.M mm. 
 
 M W. 
 
 of • 
 
 •. A ■ W I MfcMlM IMNlMM wm |i.M IMgbl, 
 ■Hrfim , Mi M«ii tH.li ♦» ttoiMfilfM M Ito M< 
 
 iililifMtor. **-""' iiitffiilin jl iff. 
 
 m 
 
 Ml 
 
 at 
 
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 IMMO, lift 9imimm9HMi .', m 
 
 •* le. • lb. 
 
 
•Itft. 
 
 MMtfl 
 «« u 
 
 Vnri 
 
 mMIMMI. 
 
 •MkH 
 
 
 t. A 
 
 XklNMRANCi. 
 
 
 
 •»•«••••. fMtktmit. Am. fill. ^^ 
 
 a. iMwwd 
 
 •MJB. fladthtvilM 
 
 MHoftto 
 
 iwi0l|||flMM«|t*ll. ""-I[|B||||._'_ 
 
 MaCtktiloM. - ^^ 
 
 '"rs tkt 
 
 •f tt» H ow»M it| 
 
 •f iMif. 
 
 ill'i*'"***""''**^* '"•imm 
 
 OftttYlOM 
 
 0. A 
 
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 n IH. 
 
 
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 TW 
 
 tela. 
 
 itffftlnbvilM 
 
 §«( 
 
 •. Ai 
 tHIllte 
 
 sr^*» 
 
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 •mil. HiikvMitettMl 
 
 IHI 
 
 lUm^i 
 
 Vfaidtte 
 
 ■JJ^HwMai, faMMiat «.a© tor tk* ptM^ 
 
 nMitaii«>fri8&-l.00)«$l7tJ»{ 4^« *# wnit . m— ■■ 
 
 BaMkowMl tf ft 
 
 isiMoiti'l^l^ 
 
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 miti 
 
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 1. Tko oool of Mliaff ft oOool ho«o 10 ko poM ky • It! of 
 St Bllli OB tkt Mltff «tt ItfWt wktlmo tkt -^ I IT 
 Am. iiiMM. 
 
 t. It ft iMM*t p topo iti It 
 Hwt Itt ktttHI 
 itIMfllif 
 
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 If tkt MMIf 
 
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 •. Tkotti It tun J0| wktl io tkt tutiiMBl It 
 
 It gift titj 
 
 •t gNt 
 
 't 
 
 flitt for ttlftvlit, ItStt for oikor ^HMTTIir^ j- J^mI 
 
 6. ▲ turn wortk tlOOOt la ntod hy tko ntiiwEi al | of Ho 
 irahM. Tkt ffttt tf tnatios it 8 aOli o» tkt Mlio. Vlai tkt 
 ptM. 
 
 tAi of I of tiooot«ttt.at. 
 
Cfte 
 
 
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 f. I Mm 
 
 MlfMMtia 
 
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 tM»«aiii 
 
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MnuinoN im cnmt 
 
 (ANSI and no TEST CHART No. 2) 
 
 1.0 
 
 
 ift 
 
 1.1 
 
 Ut 122 
 
 18 
 
 llii iJ^ 
 
 .^ 
 
 ^PPUED IS4<3E Ine 
 
 ««3 CM* Moln SlTMl 
 
 Mm York 14aM USA 
 
 (7t(0 4K-O900-nieM 
 
i 
 
 ▲KITRlimO. 
 
 «. A friend loMied n* 9488.50 at 9%, whieh I k«i>t tUl it 
 •mounted to #472.77. How long did I koep It. Axt. 4 mo. \^ 
 
 7. $1800 wu borrowed Jan. lit, 1909. at 0« per miniim. 
 What aom wUl repay the deU on October 20thf Ani. 91872. 
 
 8. At what rate per cent, will a giTtn ram doable Itaelf in 30 
 yearef Axa. 8i%. 
 
 9. A maa borrowed a certain snm May 11th, 1898, at 6%, and 
 on Feb. 27th, 1900, paid 9637.10, whieh was the amount dne. 
 How much did he borrowt 
 
 Time 1| years; rate 6%; amoont of 9100 for ffiren time and 
 
 100 
 B9110.80; .*. amount borrowedsj^^ of 9637.10s:9675. 
 
 rate: 
 
 10. I loaned Mr. Jones a sum of money July 7th, 1897, at 8% 
 simple interest, and on Nor. 30th, 1900, he |>aid the interest dne, 
 whieh was 9188.60. How much did I loan himf 
 
 Interest on 9100 for Sfyr. @ 8%=927.20. Am. 9675. 
 
 11. Pind the eompound interest on 92080 in 3 yr. at 4« per 
 annum. Aks. 9259.71. 
 
 12. What principal will amount to N250 in 2 years at 5% com- 
 pound interestr Ams. 93854.875. 
 
 13. What is the difference between the simple and* compound 
 interest on 91500 for 8 yr. at 6« f Ans. 916.524. 
 
 14. What is the amount of 92000 for U yr. at 6S per annum, 
 payable half yearly r 
 
 There will be 3 payments at 8«; Amount=s9[2000 (1.03)fl= 
 92185.45. 
 
 15. Rnd the compound interest on 98000 for 2 years at 85(. 
 payable half yearly. Ams. 95d0.58. 
 
 16. *1nd the amount of 91700 for 2f yr. at4% per annum com- 
 pound interest. 
 
 Amonnt=9(1700xmxiWx|«|)=$1893.88. 
 
 17. Pind the amount of 96282 in 2 yr. at 3i% per annum eom- 
 pound interest. 
 
 Amount=9[6282X (1.035) »]=96729.4355. 
 
 18. What principal will amount to 98279 fn 2i yr. at 3« com- 
 pound interestr 
 
 ' Principal=9[8279Xi«fX«fX^] 
 
 ■ =9C8279X(i«§)«Xf«f]=97688.482. 
 
^*ynM raonain. 
 
 m 
 
 It 8 Jf •^ "•"* •'"'• ^' *«»' *» »^«»>«' 31.t. iwo! 
 •'. diirennees9l6.82. 
 
 WV. BANK DISCOUNT. 
 
 2. «7M. , 
 
 S. A note for $1314, dated Jm i.i ibqo i 
 aad i. di«oanfd Feb. 12ttr»t S* PtoTil'T^"! *" ' "'^• 
 The note ie lenUv due J^rnZu '^^J^* diwount. 
 
 4. A note for *6M dtM Oet. t3th to, m ^ . j*»-**'»- 
 
 5. For what sum must a 70 dav n^f. w j 
 
 «> that when dieeoanted at 1 ui 11*?^ ''"'°°* ^"^•'^* 
 $673.90f ^** •' ** '*»• Proeeede wiU be 
 
 oountedf ««». was f40.60. At what rate was it dls- 
 
 Time 58 days; interest N0.60. 
 
 Interest on glOO toi. mha^ - glOOX365X40.« > ^ 
 
 08X1829 — "•**• AHi.14%. 
 
 i )| 
 
7. Tlw fM* of a BOU to 1960; dO* Fkb. Mh, INOt ttet « 
 dV»; fait««tl5*; dkeouated Ftb. 20kh. 1000, •I6«. IIbTiZ 
 
 Aiaoaiit of not* ^en duo in 00 dayiai072.28t 
 I>i«»oant off Wr2.2i .t 6« for 8lT^^ j 
 Pioeeod.=0C072.23-U.046)»0060.28i. 
 
 8. I widi to «M $8294.20 for 2 mo. For wImI muB most I kIto 
 »y note that wlien diMoontMl at tho buk at 12ft per aiumn I 
 .hiUl roeelT. llut wBowt. Day. of gnM,e not tdien. 
 
 Fnoe of notes W of 03224.20»08200. 
 
 Ti.««-.^*v s. . ToBOOTO, Dee. 28rd, 1900. 
 
 !1^ ^ • "' *^*'' ****^ *»""'*"*> ^^^i*" with intend 
 j!o!^. '^*^ ""• ^' •» •»' »o ^y of g»ee. iTd 
 
 d JIS' tl;**" ^ • '^ ^- -•*• «»t wiH yield 0,482 wh«i 
 FMeofnote-*ofTl»offMeofnote=01482. Am. flOOO. 
 
 XV. sToacs. 
 
 .i 191 f 1*11!^ ••^xi •*«*»*y ♦*«• ■»»«- •' B«k of OiMo .teek 
 at 121; brokerage, J*. 
 
 80X«21^(w!*"==*^"^+*>*^"^*' .-. «oet of 80 .haieas 
 
 2. What anm mnet I inyeiit in 5% stoek at 108 to yield an 
 ioeome of fT20f ' " 
 
 014^?^"**"* ^ ^^'^^ •*" •"'' •'• »»^^««»* to yi»M 0720» 
 
 8. What iaeome wUl I derive from 00240 invested in 6% etoek 
 
 06240^Soo.'~" *"''•**"* W04=06; .'. ineome from inverting 
 
 4. A man bought bank stoek at Zi% diseoont, and sold at 4f % 
 
 premium, and gained 0900 by the transaetion. Find the par value 
 of the stoek. 
 
 ^ is gained from $100 stoek; .'. 0060 is gained from 012000 
 
'* *' 2iidi^$8800 . 
 
 ^« l«t Is bettor l^fNO 
 
 •. - WM» Mt, riroUd r taw IWBjht It to rttlh. «»f 
 
 «rte=jj of *118=M2. 
 wJi "■"«*'•*** "^ •»». "-tat pH« m.* 1 .rti to „U, 
 
 10. 8oIdsloek«tl7ift dlMonnt and vmII.^ ia« 
 Find th. »,. Of ffl»oa.t «^ rS,^ "" "-^"■•taT. 
 ^JrtW-jrt «U.f.,»Wl, H«of ««„rt,^»,, ... ,^^. 
 
 XVI. EQUATION OF PAYMENTS. 
 2. A man lends $10000 in four sums. He Mt« a« #«. *<mww. 
 
 J. A mereliMit parehMed goods on April Ist. iwo, «. foHowst 
 -•TOO on 2 mo.; $1000 on 3 mo., and •1400 on « m! ^!!II 
 What ,. the e^naled lime of P.yme'ntrAtr*^™!,'^- :T^' 
 
 ^^^tillr ^TJ«»« -^^ «>• •q«*~i tim. tor's. 
 p»7mMit of the whole majr I keep the bateaeef 
 
ir 
 
 taia Miw 2rilftr«'i."d;;.'"5X'. *«•«?• ""^ "^ »• 
 
 *MI. PARTNERSHIP. 
 
 ba. B Mill, c Mil. 9 h« t SL ' . . * *«• J «»d 'or •▼•ly 9» 
 
 *. A bogma bailneis witb $4500 ud !• joIbmI hw n »t«v aimaa 
 *■ A,BniiCjoliiiii|Mrtiwnhip. The eM>It«l i. «»itoii-»-i 
 
nmww raoBtnrs. 
 oJJLTJ^'.'^ PMtiimbip «tth . mpiui of nana, »« 
 
 A»»MSO; B-»!»Tg. 
 
 10. A mui left bis propwty to hi* ehildnn in tlie followin* 
 •hoaM M«li raMiref A». |»12, $4608, $8456. 
 XVIII. APPLICATION OF INVOLUTION AND EVOLUTION. 
 
 ic)t^ ' ^"^ 21^^^182X6X24. AN., (a) 210; (») 2^2; 
 
 ^ feJin^ir.»SJ;r;r" '' -• ^ -i- «»• «-^ «». oo., ^ 
 
 P*rimrtOT«216 rt.; .-. 2I6X68|«.=$148.60. 
 ing 37 -. 156 sq. rd. What will f neing it eort «t W.ri per rf f 
 
 4. A boKt in efOMing a rirer 786 yd. wide luuU^i ^ tk- 
 
 (i'tw+jts') ,d.-m ,4. 
 
M.teiNrt>dti.*.wli.||»..„^g,M^,^^, Urn. 
 
 i. A pil« of wood in tho tarn ot • wttMnter aottd te la m 
 wM.. Be 11. Ugh «d 2W ft. fc^g. IflTwiyTth^^ 
 fb. whl would bo Uio l.«gth7o«* «lf7 AW. W ^ •* ' 
 
 MMofltofMoor Am. 748 oq. ft. a* ,q. la. »'«•«•»• 
 
 •K *1A'!?' «• 880 «*. loBf aWO ft. wldooad IS ft. doOD- And 
 
 I>*pUi of Noorfolr-r ( ^tt»XM80xaS40X12) ft.»A880 ft 
 
 12. Find tho T>ltto of 4^fi625X8ri9W8-4». Am. 4060 
 18. Find tlio mine of 8^409«-r4^827S. Am. 4 
 
 ^^ij.ft.-«26«,.ft.,«,rf^afo»ofb.o,ddo«2Bft. Am. 
 
 «n^ M"tn**liriK 'i?* **'*^ •*"*• «»* •« bo dmwn In . 
 •qmo, 00 in. on oneh oldo. 
 
 Aion o? «liolo=(28*X V)«,. |n.«2464 oq. In. 
 ^16^^. ho« fa Mod toj«on « ..^, ^ ta th. l«.gtl» of 
 
 lWiM=(/i840=9) yd.=80.24 ,d. 
 ^J1^^Th• Tolnmo of • oubloni bloek fa 80898.467 0. ft. Find Ito 
 
 •aeO^M^'*^'"^* «•' •«^«C«X(I94»).] oq. ft.. 
 m^'l Sri!*'^ii"*^"! 6 ~. 48 m. 8* ^. How .any 
 '••^^"'•^ 8« 3«>- «* W yd. longor thM tho fw«of f 
 
tVf 
 
 SM» of TMMl-tr(iaxUX197t)] l0.»ia la. 
 
 fiu^of !I!l!lr?* ***"'■•' • ••^^ •'•^ *^ •^"••'^ ""• 
 
 814* of elrtw«-[f (mSQX^] ft.-M ft. 
 
 tog 63 ae. 894 aq. yd. •! H at. m fcr.f 
 
 PoriatUr-aooi ]rd. Am. 19Hl». 
 «. A tqaM* U\A mbUIb* 8 m. 121 sq. yd.; Mraditr teM ia 
 
 tS* !SL t.'f;^^* !1"'^"* * ••• ^^ ■^- y*- "-'•. «d to M 
 ya. wldtr. Flad ito Itnglh. 
 
 .^ ^,2l!ft •' •^•'* ^ *■* ««M-lil yd. ; MM of Snd>-7 m. S81 m 
 
 ■84161 
 .'. I«iictb»(3il6i 
 
 . width 
 -rl77) ]rd.*-198 yd 
 
 ». A aqiiu* plot ooatftliu 8S4464 iq. yd. What will be tht 
 MMOf ft rMtMgalw field whOM lencth !• three timee ud breadth 
 twiee aa moehr "— •» 
 
 Areaa(8X3X8844e4) sq. yd.»4»46784 aq. yd. 
 
 24. The am «f « laeee of a eobe ii 87i eq. ft., find ita wei«hl 
 Mramiiiff that a ea. ft. weighs 1648 o>. " weif ai 
 
 U.SS) £.^mM'A.^''' • • -• ••»*•"* **•«» «»• ft- 5 a««x 
 
 25. By what nambermiut the foUowing be nmltiplied to make 
 then perfeet aqvarear ^*^ 
 
 775; S80; 42888, and972. Fteton of 778* fBX S) XSl •• «.«... 
 JSSittSAyf'^^' the other n««bS'^^''*Af jlf," aS"" 
 
 26. What is the area of aa Isoaeeles triangle whose base is 12 
 ft. aad eaeh of the equal sides 10 ft.? Am. 48 sq. ft. 
 
 27. Find the area of a triangle whose sides are 409 ft.. 169 ft. 
 and 510 ft. long. Am. 80600 sq. ft. 
 
 28. By what number mnst the sqoare of 126 be mnltiplied to 
 beemne a perfset enbe t 
 
 196*s2X3X3X7X3X3X8X7a:2*X8'X3X7«- hMM thmw«^ 
 tipUer is 2X3'X7, or 126. '^ * ""• ^^^^ ' »«^. »• »d. 
 
 39. Find tte largest pofieet square oontalned ia 8016 
 The fketors are 2»X8«X7} .-. highest sq. No.-144. * 
 
 t , f 
 
 r' * r 
 
ABmuino. 
 M8Wi4. ft • "* "*•* *• »«P*MMlr. Am. 
 
 ^ixim^***) ">=WH lb. '^ 
 
 XIX. METRIC SVSTEM. 
 
 alnamfmaMt Am. I9M timn. ™huk ?«■.!« 
 
7. How BBMy litrM Mmalii after takinc 8M7 •.! f M»r . -..w 
 
 MBurm^ir 2.75 hi. aw. 235.09 1. "*" • '"^ 
 
 ^M lilfi"'^ **' ""^^ ~^ •»• '«"•. how many hoetollti^ 
 •oiUd ba bonciit tor 78 francf An. IMVi HI. '^••"''^ 
 
 I« J^:«r!lli"'* "'^^'^ •' ^••*^ *» • '*»«««»lw plot 1.225 K». 
 looff and 606 m. wida. Ana. 68.11 ha. •*«*». 
 
 •ud ovarlakaa ft at 10 «I». piurt 2 p.«.f Ana. 07.00 Km. 
 
 14. H tha Intareat on 068.20 fr. tor 3 yaara is 127 88 fr wt^A 
 tha rata of tntaraat. /•«• w i^.W i*. Ffod 
 
 "^*(b5^ *»' * *^' 127.86)%«7.5» naarly. 
 
 U^Jf wiJ^^ •"f **' •**«*"« *• «-^« "• !»•' «• ».. tod S 
 langth In kilomatrea. Akb. .3125 Km. .«»»««» 
 
 rodlf e?' ^ "'• **•*'* ^•*'^ ^^••'^- «»«» «»• i^- »» -«.. 
 
 «8l}2.l^**^'ir^'^/4:^^W {iS»3^-^^«-».«»X11860- 
 
 17. Howaianyframaaratherainllb.aTolr.t Am. 451.61. 
 
 l!: I 
 
• ^■•"•-•Mlit.fi.i 
 
 ^•liit tf i">«" ^^^y Xfl.25-W4.l57. 
 
 •»•««»• ■•ttJr ^^ ^^ ••" ••»«^nl»f 18 hMtMM 
 
 XX. WORK mOBLCMi. 
 
 Jijmn do the work in ii T, * f/.'"ill^» »«»»» *« «»«•»> Uf 
 
 A 
 
 B •«» do the work in 24 d. . a . . i- * *^ *° «» 
 
 8. ▲ eaa eiit ft floid of gnUn In 94 h» n t ,« ^ 
 
 «7 hf. They work together STi hr ^LJ Jk I"-** *"' •"^ ^ »» 
 How long did A JT^Z^tl ***•" ^ *"*^- **- ''•A. 
 
 wo44^S,t.iJU'hr*Als.i4 £:'• «- '- A to do ^;, 
 
UTIIV 
 
 • ift. »wfcrt4tai.,«U4Ad»lfc«wo»kf «-^»» 
 
 A««IB4oAtoi4a.|llAtolil.. Am.l9«^ 
 
 •■f IciMbw to 4. Ik. „ ",' ''*^«~»<"UUl>,fo,iUlwMk. 
 XXI. CLOCK fHOBLEMS. 
 
 Tim. for on. .look to smia l| min. o» th. oibor-i d. • 
 
 ••• " * •• " zi> " «?^i'a, 
 
 *««•«»« St noon. How i^n. w .J^ " * "• ^V •»• 
 
 1i< 
 
AKlTHMinO. 
 
 Wh«t I. th. tru, tl«..wh.n th. wi^h rtow. 12 o'cl^rS^iJi 
 
 96 uiD. on tho w»t«h»100 mint true tiuoi 
 .'.(12X60) " " ♦♦ «« _.12X60X100 . 
 
 " M — n>H.tnMtIiM«>12ibr. 
 
 8. At what time Is the muntter of mlnatet PMt ft mi»i t^ a ^ 
 the number of ainntea to e? •«««»» PM» o equal to f of 
 
 No. of mm. part 6«| of (flO^No. of mto. part 6). Ak.. 8.2«. 
 24 h ®°' °'«'^ «»^»« * n»»n. in « da. and another lom 1 min in 
 Time to differ If min.=l da.; .-. time to differ 16 mln.«9 da 
 
 £.t^iS? :^::'^^^Zn't:''^'^r:^^ ^r- 
 
 The hand, are 15 mfn. apart and will be togrther In 19Ar 
 min. ; dietanee walk»d In 60 mln- ^Q^^*^ 
 
 16A 
 
 yd.s4 ml. 
 
 8. I looked at my wateh between 8 and 9 o'eloek .»<! .i«. 
 between 9 and 10. and foand the hand. had^g^Tee. ^iSl 
 time wa. It when I looked flrrt at my watehf ^ 
 
 mov^*^ViSr;n^!sL7n*iss£r'o?^^^ !S;Sd"tS;i^*^;?»»- 
 
 paw. once), or 60 mIn...Dil8er Th^V f^^^ ^* ?*• <*» «»J« 
 han^ H of the dteUnce. *mS*hr -hand ±f^j!^ii "d min.- 
 
 JA sMeee. Thi. I. the dlrtMoo the m?n*?««^ *' *? •^•■' •' 
 flrtt looked; .-. It ha. SaliS 4iA "5!"***"? ^" ahead when 1 
 
 did I flrat look? Ana. 9A min. p,JlS: *•"*••• -^^ ''^at time 
 
 XXII. PROBLEMS INVOLVING VELOCITIES 
 
 ft Lt ?*:r *" "^, ^' '^•^ ^' • ^^^--'J "d take. 10 leap, of 7 
 ft. each in 6 oeeonj., the honnd take. 12 leap. of »fk 44^ ! 
 
 a^cond-. How long before the honnd w;7Si:i'LIi*lLr*^' 
 
 
 gain. 15S 
 
 41 
 
 810 
 
 II II 
 
 18 
 
 <i 
 If 
 
nniir nwunn. jg, 
 
 L,\*^ .'»" ^:..""f T^ •••'nmpli POM i. « «,., „„, 
 
 ic » .. 2nd " 3| 8ec.=a7fl.irM>ii 
 
 2nd 
 2nd •* 
 
 3| 8ec.=(176-lo6|) yd. 
 1 hr. =45 mi. 
 
 8. A ean ran 400 yd. in 42 see.; B, 500 yd. in 56 m« mo- 
 A »!rj^^. . to come out even with A in a 200 yd. raeef 
 
 5. A man in a boggy goes (H miles per hr. and starts at 8 . m 
 A boy on a bieyele starts 1 hr. 50 min. iVter and overtLVes the m^n 
 •tnoon. At what rate did the boy ridef "^•"•^w ««« man 
 
 2* s:roM2sri?£""-=^ '^'^' *^* ^-^ ^ ^ -^^^ m 
 
 ■ee. ; and that it passed completely over the dlstancTLtw J« ^ 
 Mrtjuw. a. t»l. gjy, to (S71-1M) ,« -io, rt. , 
 
 m;~. ^g,"^:, 
 
 nod It. nto ,»r boor in th. 2od taXf o/ th. journey 
 
 tor ttTa.'S ESteSv^S^ffi,** ? ^J^ *• «"« ilf ..d . n,I. 
 
 whi^h trs r/oi .^:i «i-r .r.'-.jr ir.r 
 
 Howta-g win I. t.k. th. f«. tnuo ,. .„ruk,TS ^T 
 
 Brt. of «Mt tnln p., h,.=M Bl., tta. t. giu» 00 Bl.= 
 
 60 
 45-25 
 
 i, 
 ill 
 
 hr.s=8 hr. 
 
^ AnmcBTio. 
 
 l«ngth of trains (792-840) yd.^SSS yd. 
 
 10. A »«n Ma low 8 mi. »n hr. in stm wi^er. How lone wiU 
 flows 1 mi. por lur.f Axt. 9 hr. ^^^ 
 
 «i.^'-i;^ir42Tr "" ""• ^"^ * ^'-^ ^^ **• -^ ^^^ ^^ 
 
 12. A boat run. 24 mi. down wbcwm in U hr. and 15 m! an 
 rtjjjam in tl»e «m. time. Affc., running down for 9" , how W 
 will it be in returning r Ahb. 14flir. '-.aowwng 
 
 A^tiT'^V^'"^^'''^'^'^' How much rtnrt ew 
 AgireBinami. nMie;#nd7etwinb7 44 7d.r 
 
 fMterarriTeelhr.aheiid of the other. Find the distmiee truTeUed 
 76 S"^\«"''\lf .*^ '"^' tr.in=(2X26+26) mi.; tim/to gri,; 
 76 mi.=V hr.=18 hr.; distance tiaveUed=(15X30) iS7=4£> mi! 
 
 16. A train running 80 mi. per hr. OTertakee a man going 5 ml 
 •n hr. and p.^ him in 18 see. Find the length of thltrSn. 
 Distarn^ «S-»^^ taUn in 1 hr.=26 mi.; diatance gained by 
 
 traininl8««.=li^5^ya.=220yd.;lengthoftrain«220yd 
 
 W. Aeanwalkl0mi.in2ihr.;B,llmi.in2*hr. Theyrtart 
 to walk a race of 55 mi. Which will win and by how much timet 
 
 A walks 10 mi. in 2i hr.. or 55 mi. in 121 hr • B mlir> 11 ».i 
 In 2i^hr., or 55 mi. in 12^ hr.; .-. A win's by '(f2jlSa/ir"i 
 
 17. A train going 40 mi. an hr. takes 18 see. to pass another 
 
 DUrtance trareUed by train in 18 sec.=l«^^???ft., „ io56 
 ft. ; length of trains (1066-192) ft.=864 ft. 
 
BITIBW FWXBLBW. 
 
 jnm« to go 1 ml. down stnam ud lM«ksr/x^i\ v 
 Wrtanee gone down and biik i^A h!J ^l^ii!*^ ^'^ 
 
 « 
 
 41 
 
 12 hr. »-jp ml.»64 ml. 
 
 DisUnoe the man goes in 15.8eo.=22 yd.; 
 
 " •* train " " i h, , 60Xgbx(4184.22> ^ 
 
 15X1760 "i.^Wml. 
 
 Will. MISCELLANEOUS EXERaSES. 
 
 1. SimpUfy °*-^ ot lg*4.2i A-;-2Hx2 ^ , 
 
 lofTf-ftf-r-ait .«Airi. i. 
 
 2. A train 264 ft. lour takes in .^^ «^ 
 
 3. I buy three town lots whose aamt i. «- ♦ 
 
 "Mooad ud kw 4« OB a„ Udrtlft .!,!? "»««.«» on the 
 tt. TiUa,,ot «di lot. "•'*^- "y "iota gmin i. »B«. Find 
 
 pigs did Jie bay f '^ '^^ '^- ^ow many 
 
 half^5V;n*S?4jc'"*«^.«t' J' «o»e«h; loss of 10% on 2nd 
 =41|e., or tS on M p1^*' -. net gain on each pig=66|e.-jS,! 
 
 5. Show that the prodaet of 72 and M t. ti... «-^j . 
 L.C.M. and G.C.M. •«'-»»<» W is the prodnet of their 
 
 *!. *:*ii"**** ^ *^^ *®^^« J » «J°"6 one eontalninff 224 .«>«. . ^ 
 the other a reotangnlar field of 314 »^^ TZTZT^^ ^' "** 
 
 «!««• at 12 miles w^A^ifl; ^1 ,^ ^ '^^•« '»'"^ »• 
 -^ amesanjur. Another round the rwjtangular field in 
 
 •HI 
 
^ ABirmiKTio. 
 
 Ji*'!!'!^'**^* "»**»»•«»• Pw h«ir of »b, tad bw. If 
 tt^rfr rid. of «!. ,^t«„. ta tb. ««. « th. S 7iil 
 
 41 *%.•' *J"»'«*W «i. ; .*. sldM of netaiicl«»rm and ia\ ^ . 
 r. s, 8, «, m4 7, iHiliit kBowii 10 b. iMtoFi of . ii,m1«tt, wbrt 
 
 Tm^." ""^ " •""' ^ '• •• "• '*• "• «• «. i'^ 
 
 »«*. WAI^W to. p„a.y, „a «<»«■„»«.(» pj^,"" 
 
 10. nnd tiM paWlt-r preM Ml Um m^ Vt 10400 aoplM of • 
 
 26)o.«b28A«. total proflt»(10400X28A)e.»%440. »'""*^^*n— 
 
 11. A reetangalar eittera 4i f|. long when foU oontaint 2M o 
 ft. of water. If the b««dth and deptt «. the nJ^^^^L 
 
 ^.Z^ ftt* *"• *"'"• "' *^* •*^" ^r?^ (^o M)!2 
 
 Bwedth and depth, e«,h=^@) ft.«2i ft.; .-. 46i «,. f|. 
 to be lined. Ahs. $12.96. 
 
 -qui^rtTetc.M.^"''-"'*^''^'^'^ 
 
 18 . A boy does in 4 day. what a man doee in 8 days, but a man 
 geta $1.40 per d^rand a boy $1.00. How much wii i mJ^ 
 if he employs 7 boy* for 12 days instead of menf 
 
 7 men will do the work in 9 da. : eosfcsiSfi 20. 7 »wm. ^it ^ 
 the worlc in 12.; eost«$84.00; sa^iSSi ' ^ *^ ^" ^« 
 
 14. If I bny O.T.B stock at 1224. I get $7 per share of $100, 
 bm if I innMt in mining rtook at 106, 1 get $6i per $100 to. 
 
fttriBV noBunit. 
 
 itr 
 
 Th. totmtr laTMtawnt glTM m* $lA mor» iMom* thu thmUHUt. 
 Find tlM UBoniit lavMled. 
 
 15. A biuiknr't diMonnt on $4920 for 2i jMn !• |61S. What 
 will b* tiM tra* dlMouat on $18400 for 8 j-n at mubo mU. and 
 nrnplo interostf 
 
 t ^^•.5K^Vi8SS4S&. *^ *"• "^^^ "^ •^"^ '•' » ^• 
 
 16. nnd a nnmbar whoao aqnaro la aqnal to tho aam of tho 
 aqnaroa of 1892 and 080; alM> one whoae aqnaro !■ aqn^l^ tha 
 diffaronoa of tha aqnaraa of 1480 and 876, and anbtraet tha ona 
 from the other. 
 
 li*"1608; 2nd=1168; d!irerenee=340. 
 
 17. A man meeta 5 beggars and he diTidet a certain ram amonc 
 fonr of them in the proportion of 1, 2, 3, 4, with the nnderatanding 
 ttat eaeh mnat give the «fth A of hi. Shaw. The fifth get. $6.25. 
 Find the diare of eaeh of the other.. 
 
 18. A mna 800 yd. in 3 min.; B, 1100 yd. in 4 mln. How 
 
 f!?.*^ "™* •"• «*^ "»• •"»•' *o »wl» the winnlnff poet 
 together In a mOe raeef ^ *^ 
 
 0, MiJS! *"*•*"•* "^* ' ®' *"•*••'• ^ ""* *«^ *"»»• ••^ 
 
 19. A man haa an income of $1660 from capital in 4% atoek. 
 5**r »L!? f 11» "d bay. bond, which pay 5%; find the price 
 of the bond, in order that hie income may be $1700. 
 
 He haa $41500 of 4% rtoek; he Mil. at 119 and leallaM aAuasR. 
 bond. ma.t«$84000 to glre $1700 Income; ."."rilrSr^ 
 
 20. A note for $24680 drawn March 14th at 9 mo. wa. dlMonnted 
 atabMlkMayl2th«t8j«. Find the net proce«l.. 
 
 «^ £m%S **?»«»*» ^» ^»- ; »»«"* diMonnt i« I of 8i« of $24630 
 or $478,835; hence net PWeed.«$(24580-478 Sj)=««6l!S: 
 
 «J!:#I*%""*t.'*'^!!''*^**"'**"P*'"i»WW- Rndthe 
 cct of fencing It at 15c. a yd. Axs. $132. 
 
 A n^;/J°^** • *»'-■"•« ««M? AB i.48rd. long; BC. 20rd • 
 AC, 62 rd.} and the perpendicnlar from D on AcTi^ ri iLs 
 theTmIiiaofth.flaMat$80anac. Aw. $680. 
 
V.off of#of|ol«««b««lil«t-4000 1«.iMl. A1I..M00 
 
 84. Whrt i« til* weiidit of « eiwUw bnui nl«to SO In i« 
 
 rjifpX-r - ' "•"""•' --'" -i.^i::2 
 
 number, and to BuUn the rirLi i.n»C:.7l!l!' V** ^'«*»«^ •»*• 
 by 2«xil», or 48?!^ "^ """**' * ^•''••^ ^^» multiply 
 
 26. Two raiu of money are dlTided amonc A. B end C- .^i. 
 
 80. Abu iBTMt. «a8«00, P«t la S« rtck rt 88 «n« watta B» 
 ^wv bond. « IIH. H. wi*.. to grt th. „«,. ,..^*;j* 
 
MTiBW nomuau. m 
 
 M. Th. iwlfhto of .vua l«lta of tow Mid rtlw bttaf •• Wji 
 
 WMiiti, hMl«diii« iatoml at 6%, of $8941.85 •••b? Whrt wm 
 tlweMliTBlnooftiwftomf Am. 8114881. "-^wmi 
 
 88. A e. In. of ifoa woiglii 100 dr. I b»TO an lion i«4 * f. In 
 *i«»fr.wlikbwlgl».i4»dr. Find It. tonfUi. Ti.^ ^ 
 tK.flL'*!!!"**'^ on n mm of money for 4 yr. Is 8281^. and 
 
 «oo.w«mtorort on diMoant for 4 jr. ; .*. mtostfift ; mm 81185. 
 
 IV "•/,"^*»~*''o«»»«rttof mixod groon and bkwk tMo of 48 
 
 b. and 42 lb. ron^Toly. Tbo p,opoS«« of blaST to\^ to 
 
 ^J!^V\''^^'^^- What will now bo ibop««^ 
 tlonaofblask and groon toat «• fwwpor 
 
 «ia*ti **».** *?***H black and romalnder 161 creon* M »# a9» 
 
 bik!^i6a'2(5GrS?tb'JSi^^ now%\Tf^',b*t52|l^ 
 Dia«K, (16H-20H-20) lb.*67i lb. ^preen; honeo. proportion 12:18! 
 
 tow dtooonnt how mneh moro will bo paid than If 6« from tho 
 iMipIe amount to dodnetedf 
 
 ^RW. of Ut»811060; P.W. of 2nd«811022.876; difforonoo- 
 
 87. The aoeonnta of a eompany show that when 54ft of tho 
 reoolpt. aro UMd for working oxponnoa, 10ft for rMorro fond, and 
 6ft proforonoo diridond paid on 81.000,000 of eapital. 8180MO 
 
 ;s:f"prL,5ra"'^^^^*-«----i-p^ 
 
 -860000; ^tho racelpt. aro W of 8(120000+60000); w iSSoK^ 
 eapital ia -^ of 8120000+81000000, or 86800000. 
 
 SI ^' I^mZ*"? "'''^' thearwiof the top. aio20.q. ft. and 
 81 •«. fl. i«WO«tlT.ly. Aho.ethatiUtoth.toll«4ii^TOM 
 
*ik» T Mia. to in tlM Sad. Md tha mam m^ 
 
 ^•Ptti of .Mh. V*^ *•**••* *^ **»P- '»^»» 
 
 M ^ \SrZ^^ Jr i«T«*fa»g »««y to O.T.B. bond. jM«to, 
 uJ^mS'JSirm mI^} £* "S* «^ Hft ln««, , 
 
 .-. pri<« of goS bSd^»'.8tt! •^' ^"'•'»<»'-8xw.88;-«a: 
 
 first WM 16 ft. lonff and 14 ffc -iHTrVv *^ . '^P*'^* '^^ 
 hoightTS r^n.,* ^* ^•'^»»o'*«<»rtw« $20.1(1. Il,»d tho 
 
44. UIlMjrOOihMMof mUwiijelo«ktl|t9ptrakan,«idlOO 
 aoi* at HI p«r tliMt, and I i«mIt0 78t. • thu* half>jMrly m • 
 
 tflTMMd, WlMl % p«r UBOB do I NMlT»r 
 
 46. I wlahtoluiTtM iDeom* of |18«0 por umam. I Mm IbtmI 
 to Oitjr Gm Co. itoek M 871 Md pajliiff 8 % dlTldond, or la Bank 
 ■took wklok If MUlng al 8833 and pajing a diridoad of 7|« oa 
 oaoh ahan of 8100. How maeh mora would I noalra to loTaat la 
 tho latUr than tho fomorf 
 
 A JS.*'!^!?? '••«»'[!»"» WJ*? WMO Ineomo b got from 8S3580. 
 
 fMNOO. Addltioiial oxpondltua In lattor Is 8S830. 
 
 46. A bodj whan wolfhod In ono aeala of a falao balanoa 
 walffhs 81 OS. and In anotlmr 87* os. What would a monhant 
 gain ft hy salUnc g oods wi th saeh a sealof 
 
 8* £r*or'»|f»*r'^'**^**" •■"' ** •"• «^" (^^^) o».- 
 
 47. A oinular yard 940 ft. In diaa otor has a elraular plot In tha 
 oentM whoso radius is 88 yd. A driraway Is oonstruotod around 
 tha outside of tho plot and Is 34 ft. wide. Had tha eoot of eon- 
 stmetion at 2Te. por sq. yd. - 
 
 48. A room Is 85 ft. long and 15 ft. wido and has a somlefioular 
 bow 90 ft. long thrown out on ono sido; And tho aroa of tho wholo 
 
 -♦ftyATSTT^iBf^'I? •^v"; ' •^ <»! ••mldfoular pari 
 "SsJT^.ft. * **• **•' ''^®** "Wi»(87o+167|) sqTft. 
 
 «. Throe boys, A, B and C, start In a 8 ml. raee; A goea 
 82 yd. while B goes 80 yd. and C 22 yd. How tmt from tho 
 
 winning post win B and C be when A reaehesitt Am. B. 880 yd. s 
 •ndC, 1660 yd. ' '^ 
 
 50. ^InTosts a eertain sum In 2|ft stoek at 60; B luTosts aa 
 equal amount at 89| and his ineome is 625 more; And the amouni 
 invested by each. Ava. 6128700. 
 
 51, An ornament of gold and rilTor contains He. In, and weighs 
 64ios. A e. in. of gold weighs lOi OS. and of sUTor 51 08. Bow 
 nuah gold Is there In tha omamentff 
 
 ii 
 
X "• i -» »»»tht 186 pig.; h. .old I Of t^rt li» »«.*t. 
 
 66. DiTid. $18900 bttWMii John Mid Jubm m fth.« *i^ ^ . 
 IntWMt on John', for 8 tmh at 4« »ni il w "*^ *** ■^"P'* 
 
 ^ M« gt. It and Jm,- A of the ««,; John'.. $10000, J«i..» 
 
 ino Ij.U.M. of 08. 86. 40n4OO* • ^nA_« ^«<^ ^ 
 
 *jr «^ « »d «, wui*i2;.'S^X.' ^S**;!*SL° 4S:'" 
 
MTlwl ft at $IM vt iq. yd. { th« wM»f pftp«i«d »! !••. p«r m. 
 •t wia», 4 jq. Iilfa. 
 
 ». A TMd aMMai* nadt •£ itMl MnNuid* A of u laak !■ 
 warn wMtbmr and Matratto A la •©« waathtr; vkal la tha Itm 
 iMWtt of a ftaaa wlOih .^Mawa M ia. ■»!• I. hot thaa I. a«M 
 
 iJjHJjjrfcl .'. tIv cf tlM Baamira»8i la. | ,*. tha foaaa 
 
 ei. A raetongnlar plaoo of laad 18 la. loag lOi la. wido and 
 SA la. thtek !i BMltad. Flad how many eubaa 2i la. aaah waj 
 oaa ba mada frma It aad how uaay A la. aaah way aar U mada 
 from tha raflBaladarf Aira. 8A aad 7525. 
 
 •9. Thara ara ISO ba. of frala la two bias, and » I bla than 
 aia 15 ba. laaa than f aa naah aa thara ara la f . othar. How 
 Biaay be. ara thara la tha anallar biaf 
 
 Aiii?*45*tal!"* *" **'■*' **'""*^ *' ^•* ^ **■• *■ ^"l^' WB-W6 ba. 
 
 68. If M a. la. of gonpowdar watfh 1 lb., flad tha dlamatar of 
 a hollow iphara that wlU hold 11 lb. 
 
 |XVXH«880J.-. r.4.28«8... A»8. 8.6738 .. . 
 
 64. A boaght 16 aows aad 120 shaap for 8M6, tha aafaaali of 
 tha aame Mod aoatiag a uniform priea. Ha told th«m for 8488.50. 
 falalBf 7*% on tha oowa and 6* on tha shaap. Elad tha aoat of 
 oaah par haad. 
 
 Total gain !■ 831.50; 6% gain on all is 827 BO Bahm liC «« 
 Talaa of aow. is 8(81.jib-275i)), or W.w'^^i. 815.oSr5' Jl.wj! 
 
 a. Thara Is a mixtnrs of rinegar and watar In tha proportion 
 of 08 parta of Tinagar and 7 parts of watar. How maah watar 
 mast ba addad so that in 25 qt. of tha mixtara thaw may ba 2 ot 
 of watarf ^ 
 
 was HP qt. The new mixture Is H§t qt. Henea. the flnt 
 mixture has been Inereased by A of ItseiT 
 
 .V ^J »«y*w horses for 8225, and sell one so as to loae4« and 
 the other so as to gain 5«. If on the whole, I neither gain nor 
 loae, what did eaeh horse eostf 
 
 4* of prioe of lst»5% of priee of saeond* • nwU* »* i.« 
 
 i of prise of sooond. A»i. 8125 "JlOO; ' * * '^''^ •* *■*" 
 
!!!. rtrJT^ -h^ iMiv. twit. M .Mb M ft •widTwdTUii 
 
 Aw. A BM. WTM.lOi ft woBftft, $a6S.tS, ft .hM, $I7».41. 
 
 «I Jd 'l^ir**^; ""I!?*' *! ^^'^^ »V ». and th, ,»otl.«t ..lu. 
 JW bgr 17. Th« prodoet !• th«ii diTkbd by SOO, .nd 8S to ftddted 
 
 •«n«i«y tod. 80 «l. ft. bimr, ftftd tbftt tbft .iprtw fti« fa JrJ!^ 
 "^l"JL*^"» ?;• ~-.f •-^i b, on. ft. by tb. JZ.^ 
 
 .f 60. ftiid 7.1 b. ^.if. to wiof ^ !»««•••«» A fflT. Corn 
 
 T2. Tb. poimlfttloii of ft wrtftUi town to.,w.„ ftt ft ^rtftbi »t. 
 Pjrjj.ftt.p.,ftn««n. Now It I. 1»«4«1. Von, j^^^ 
 
 160000X(H.»t.)*-im4«lj »t.«5«.^.. 21^16. 
 
 W. Gold wftlgb. 10.8 tliDM. ftftd Mpp., 8.80 tlm« „ mn^h ft. 
 
 wfttor. How mft»y time. M bwvy ft. wfttw I. ft cola oofttftfaZ n 
 pwti of gold, ud 1 part of copper. wiuftuuag u 
 
 No. of tim..-(UX10.8+lX8.80)+12«18.4S25. 
 
 74. Tb. tro. dfawunt on ft mm of money for on. wftr a 6« i, 
 
 •L'!!!^!!^*^''™**' *»»'*^'»''«»"»«rfon..bJfS2a 
 ■adtb.oth.r]»K#eft. Fl^tb««ttt. ""**«<«»»*». 
 
uniw ruomuan. 
 
 A--ilf ) of ■Uia$l I MM te tilftTft.fO. 
 
 7S. My iwrM Md IIm omb^j i0 It m« legMlMr worlk Ii6.6fl. 
 If I siMBd 13I* of Bjr nmi«j, mi4 mU Um pwM for 4 !!• t»1m, 
 I steU ttea hftv* 167.25. Find Um tiUm of my pvrw. 
 
 I moBoj u4 i T»lno of punw aro worth $97.90 1 hoiiM, | nonoy 
 M4l I T»lM of parM MO worth I9.SS; bonoo, moaoy and 4 tinoo 
 
 ™J •'^l'"'^*? '^rt'* W4| I tItMO nUM of paiM la worth 
 fr JO. Am. 18.00. 
 
 n. A mtM pvrehMod » farm for 03000, and affrtod to pay 
 priaalpal and lotoroat la 4 oqnal aanoal InatalaMuta. InUioal 
 boiag 9% por auaM, what waa tho aaattal payamitt 
 
 01 pold ywurly anomiti to O ^'/^j' ' ^ •♦•W^Oi 
 
 DoM amoanta to 0C300OX (1.00)«L or 08787.40071 aaaaal pay- 
 ■MBt la 0(8787.48074-4.8740), or M.n. ■« poy 
 
 77. A ottba of load, whoao odgo la 10 la., la wholly lamorMd 
 
 to a oylladrloal tab pwUy flllod with water, whoM latorua 
 
 diamotor la 10 la. How mnoh will It ralao tho wator la tht tab* 
 
 Aioo of bottom of tab«-(Vxi00) aq. la.: hoooo. dooth tho 
 wator wlU rlao la [1000+ (Vx 100)] la.7or zH ll: ' ^^ 
 
 78. A, B aad C form a eompaoy. A'a atoek la to trada 8 mo. 
 aad ho elalma i^ of tho gala; B'a atoek la mo. la tradoi aad 
 advaaooa 08094 for 4 mo., aad alalam half tho profit. How n > 
 do A aad B ooatrlbntof 
 
 Tho proOta ar. A. A "J *• "fP^'^'y; .'. A', atoa. 
 •2^-0079, B> atoek»0 ^y^^ «01190. 
 
 79. A toa morehaat mtoaa 40 lb. of taa • 40e. por poaad, with 
 00 lb. • 37«. por poaad, aad aoUa tho mtotaro • 40e. porpoaad, 
 What por eaat. profit dooa ho makaf Ana. 88^. 
 
 80. Dhrldo 09400 latotwo porta, Mieh that tho aaaaal latoioat 
 oa tho flrat part d 84«, addod to that oa tho aaeoad % OiK may 
 oqoal that oa tho wholo ram ® 5^% . 
 
 81. A boat's erow eaa row 10 mi. dowa stroam to tha aame timo 
 that they eaa row 7 ml. op It. If their rate of rowlag U Oi ml. 
 an hr. la atiU water, what is the reloelty of the stream f 
 
 The rate la $tm water Is to the rate of tkt ttmm aa 11 to 4t 
 
 4yRX — •• •* ■■I 
 
 , rate of atream i»-jp ml. per hr., or lif mi. 
 

 ^ uimnno. 
 
 lOOXrom lOOXmi 
 
 W. A eonleftl tout, whOM tluit heiirht I. 19 m 
 ■q. yd. of euiTM to n^a it w«- u ***' '^^''^ «« 
 
 the lent coil^riS.^ *;,. t^ ""'"^ ««'"»'» ^<^ »»«• «oor of 
 
 a*. I buy two horsM for $260. If I mU tha H^ -* - . - 
 8», Md the seeond ftt • Ion of «« t « **•""*•*» gmin of 
 w« the price of Jh holler ' ""* *^" **' '^ 
 
 Of (S«!!:;<i;^«;2)%-1^^ 
 
 woo*Llr ■fiTj:jJ?i2.r'^"« "*~^""- ® ^^^ ^^> «« i» ^ 
 
 Mt» of U, wmmtaioiif Am. «s •"'"''»"• wl"* wm tt» 
 
 the seeond mui wnUdngf . "» » eee. At what rate la 
 
 (362-264) ft. AH8. 6» nTier hr ^' T"* "»« »«* «• 
 
 HeiSTtfel;- c» ij?^j^r*"Hermi?r-''^'';r «» «»• ^jh>jo. 
 
 $2.86. ^ women. Her money was (10X26-16)e., or 
 
 88. From the first of two cannon, 36 shells am tk«»-« k.# 
 the second is ready for firimr fih-.11 ^ thrown befors 
 
 proportion of 87r^m the ^ ^tLT.^"""^ 'T *^*^ *" «"• 
 
 requires as mnch wX f^ ?!i. " **" T*"^' "^^ ««««»« 
 AM 1. powaer for 3 chaises as the first 6otm a«. ^ 
 
S^' ^Si^ Ti'^ '*' • wiJl 80 ft. long, 12 ft. high u.d 24 ft 
 thiek, •Uowing 6»« of tho gpM. for (ho mortarf Aw. 84M0. 
 
 90. A ^rm eoti 81 timot m mueh m a honao. Bt Miiinir ti.* 
 •1. Ctonlato corrootly to 7 plMot of doelmal. tho t»I«o of 
 
 i-a+ro+EOl+OXO""**- 
 
 1.2.3.4.6 
 1 
 
 1.2.3.4.5.0 
 1 
 
 -j;^=.50000000 
 
 -.04186066 
 =.00838333 
 
 [».00138888 
 
 i:2JX6i:7-.00018841 
 
 1 
 
 r=r%=s.00002480 
 
 l>a.3.4.5.6.7.8 
 1 
 
 l.a.3.4.5.6.7.8.9 
 1 
 
 «=.00000275 
 
 1.2.M.S.6.7.8.0.10 
 I 
 
 ;».00000027 
 
 T2jAlJjJJJoJi='^^f*000002 
 
 .7182818 
 92. In firing at a targ«t A hits it twice out of three shot. B 
 torn ime. out of four, and C fonr time, ont of five. The tCt^iJ. 
 
 many hit. eaeh made and the total number of riwt. fired 
 
w t 
 
 ABITBlflTIO. 
 
 w eqiul balk of water, while tin weigh. 7.44 time., and le!i U ^ 
 time, •. mueh m eqnal bulk, of water. Find th. noXr S 
 pound, of eaeh metal in 766 lb. of the oomponntf 
 
 ib.lf4-?o!!i3%^r'7S: »L*?ti^-,??SnTii-i-^. Of 
 
 thel^e^or^eTr Zle" ^i.."r^^^ ^^ 
 
 T *'!L?v ^^^^ ^"^ *^**** «»^« »• W46 for a notoof t860 
 Intjrert being charged 2 8%, when wa. the note dne? 
 
 Jnii?ii2."' '" ''"'*' ♦"* *"»»• ^*«««* o» WO i. 80 day.. Ah.. 
 
 97. The map of a eonntiy i. drawn on a wale of A of an ineh 
 ^^' r^*«^*°"«»*»»Pwillr.pre.ent360^.^.r^''^ 
 86000 a. i. represented by (HmXTiT)«q. in. Ahs. «.,.,„. 
 
 98. A number of men ean be formed either into a Mild mhi.*. 
 
 :J :«*;;. 'rn''""' ' '^^ l».ving970meninrL?ri; 
 of^h .ide. ^How many men are there in each aide of the «,lid 
 
 Numbers ,/ {OX [2X970+2 (970-18)]} =186 
 
 36c^ J?!^^ "" **^* ""*; "' **•' ^'^^ reapectiTcly at a2c.. 
 ^:L ^ th ' ^'. ?: ^ "'^'^ ^'^^ '^'^^ oontatoing 6 fb 
 
 of ^K ?J^ '^' ^*^ **''^ '^""^'y mu.t be taken that the n^ 
 of the mixture may be 38o. a lb. f 
 
 In tv* ».?-*„__ ^M-^*"* saw Qinerenee. Menee, thero are 39 lb. 
 
 32 
 36 
 
 42 
 
 in the mixture. 
 
100. Two 60gg«d whMls work togothor, thmw Mag It oogt on 
 
 OM and 97 on Uio other. Tho largor whool ia«koi 80 rorolatfona 
 in f of a minato. How ofton dooo tho Bmallor torn in 8 Moondat 
 
 No. of reTolntionss{|x~r^«34. 
 
 40 
 
 101. A box with • lid is nude of material 1 ineh thiek. If the 
 internal dimeniiona are 8 ft. hjr 2 ft. by 1 ft. 6 in. And the num- 
 ber of eubie inehes of the material. 
 
 Cubie eontent of interior of box= (36X24X17) e. in.» 14688 
 e. in.; enbie eontent of entire bozs(88X 26X19) e. in.«18772 e. 
 in. Am. 4084 e. in. 
 
 102. The Freneh 20-frai>e pieee weigh* 6.40161 grams (a gram 
 »15.482S5 grains) and is A pure gold. The sorerelgn is H toe, 
 weighs 128.274 grains, and is worth $4.8666. How mMTis tho 
 20-frane pieee worthf 
 
 Value of (H of m.274)gr. of pure goldBt4.8666; weight of 
 pure gold in 20 fr.s(A of 6.40161X15.48286) gr. Am. $3.85 . , . 
 
 108. If 76 men and 59 boys ean do as mneh work in 299 days as 
 40 men and 83 boys ean do in 067 days, bow many men will do as 
 mueh work in a day as 15 boysf 
 
 The work of (299X76) men and (289X09) boys equals the work 
 
 of (567X40) men and (557X88) boys. Henee, the work of 15 
 
 «■ _■■ 15X444 _ 
 
 boys^—sjg— menaeo noa. 
 
 104. Find the eost of polishing a marble pillar 2 ft. 4 in. la 
 diameter, and 18 ft. long, at $1.25 per sq. yd. Am. 818i. 
 
 105. A bought goods at 06.70 on 4 months' credit, and sold 
 them immediately at 06.12 on sueh a term of eredit as made his 
 immediate gain 6i%. Bedceniag interest at 4% per annum, how 
 long eredit did A givet 
 
 If eash had been paid, the goods would hsTO been sold for 
 06.08; time for 4e. iatoreet on 06.08 at 4 « is 60 days. 
 
 106. A bar of gold weighing 196 lb. 10 os. 10 dwt. is eased in 
 lead weig^iing 24 lb. 14 os. Find the weight of the whole in 
 aToirdupois. 
 
 196 lb. 10 08. iO dwt.=1134000 gr.=:162 lb. Am. 186.875 lb. 
 
 107. A person haTing a eertain earn of money to invest finds 
 that an inyestment in 5 per eent. stock at 117| will yield him 029 
 nu>re interest ssnually than an inrestment in 3 per eent. stoek at 
 99|. Broker^pt being i%f how mueh mosey has he to iaTostf 
 
 OXsnm 8Xwir 
 117i i«i 
 
 »$29. Ans. 02890.50. 
 
108. A boogftt 900 m. of elokh in ■ .« i«i <. 
 
 M «M A «»i o .- ^.TT "•'•■'• •»* ■WO It In Toronto ak 
 
 th-i ; Jr ?!"^' •' • P*do.triMi elnb wolko m aaiiT mUoo m 
 
 whon h.„, up by on. ^^^IJ^n^ b^ .?,,. irjoJ^J 
 
 111. Tho wm of $640 i. to bo diridod among 200 ponont oon 
 •tating of mon, women and chlldron. The .1^^^*!^: 
 wimion'. jnd ohUdron'. riu^e. «• proportloiL to thf "t^l 
 6, 4, and 8, bat the indiyidoal ahaw. n# V«»;» « nm»bero 
 
 are proportional to the nnXaTTl lS?ih ™^"S '"^^ 
 women and ohildren. ""**'*'»'' ^- ^nd tho nwnbo, <rf «•„, 
 
 T^emw^^e 0^. the iromen, tMO j and the ehUdiM. tl86 
 
 l«to*^. otll^'-Thi.'^ao.eTtU^^ "ti^- ^"^ 
 
 mneh water wiU th* II!.!? !v ^^''^ ""•*' '^°« "^ ^^ 
 
 At r^J *^ T**' *^~ ««peotlvely eontalnf 
 
 Of wini; .?«!e1nd of'St ^iATjti'^r * ? *» «-' 
 
 of the third. A of A of JL«# ia* , * **' ^® «»*• ? •"* the end 
 
 WU«, 2.71 i,*^* ^A^'i« Sii^Lllth ^JS. "^^ 
 
 113. The ram of the ages of A and B it now AO «..*. —^ t« 
 
n-i »t ~" •'~>»«y ta Prt o«t «t eonponnd intoiMt for 4 yr. 
 
 8iwiX(1.04)»X(1.06)«-t745». Am. #62800. 
 •Md. booflit U« ttoek. H« obtaintd 1000 1m. stock Uum btfon, 
 
 j1 ^.Tl^m: s^""" ""•** "*»"*3^ ** »»• »''«<»*»Jy »»^» 
 
 &. oawo^*'^'^"'*^"^' ^•'•«<*k-H«rf (Irtrtoek-IOOO). 
 
 110. AwetMifalwMlMI.li«Biii«r«Ion«H».Ieiigthl.liMi»a,ed 
 hM ite thtekneM bMn diminlshedf -«r P»r ••«. 
 
 ofiiru»l^:jro?JSl4'.*?t?'^^''"«^»^' dImi«.tioBl.M 
 
 -««11I'. ^ iT"**' *• '*«"*'«> to -"PPly • K« of furibto mttel 
 eoniirting of 8 purto by weight of bitmoth, 6 of 1*«|, and 8 of tin 
 m»e ^y bi«nnth h. Hm i» rtook i. « idloy oonsIrtUig of 9 p^ 
 bi.«ath, 4 l«id. Mid 8 tin. How mnoh lUloy mnrt ii uk.^ 
 how omeh iMd and tin mart he add to flJl the ozderf 
 
 118. If the mMrafbetarer makes a profit of 10*, the wholesale 
 de^er one of 15«, and the shopkeeper one of 20», what was the 
 eojt^to the manuflKrtnrer of an article bon|ht et a diop for 
 
 ill of HI of lit of cost»875.90. Am. |50. 
 
 119. A train 100 yd. long Is orerteklng another 160 yd. Ions on 
 » parallel track. The first is going at the nto of 40 mUes an hour 
 ud the second at the rato of 18. Find how long a person in the 
 long train wUl see the other whUe passing it. 
 
 mt 180X80X60 
 
 ""' 22X1760 ^'•-laHf sec. 
 
 lao. A trader in London owes a debt of 1000 pistoles to one in 
 C»««. Knd what be gains by sending it to him through Franee 
 fhe exehanges being £1*25.4 fnncs; 19 francs^l Spanish pistole* 
 4 SpMidi ]^Mk>lm=a, ^ * 
 
lli 
 
 inST 
 
 •Vul Ui wdghl to MMlT liT^Jrl! ^ 5* •• «». of 001^ iu» 
 
 ^l!^' i. ^ 1" !*~*«» iHl 5 ft. • fa,, fa. UiJ^Tk^^^ 
 Wat U la. tUok, «Bd the thieknow of tho bottom: ^'**" 
 8|MM« oeeaplod b7 water is ^QQ<>X1728 . 
 
 5ixM5<Bi *■•'**•**»• Aw. 2 fa,. 
 
 ■«ii«dir«^Zf JSTLi. th ;;h^ .^" they »ot. fa. th. 
 
 8«m of ntof pe, i,^ - «>Xfl0xl7e 
 
 53aOXli »*•'*«> ml. J 
 IMenneo " " « « ^ <»X60X176 , 
 
 . _ "6280X6" ""•*a* al. 
 A«i. 62 nl. tad 28 mi. 
 
 MM Miriuw»<rv2/ ^. '^ •»»««. It« neeipts for the yeu 
 •re f8176000. Iti woridnc ozMnM* »«» m« !« ^v .^ 
 
 •MOOO beIl^r retftfaMd m rewrre foadf '^^^ 
 
 65oS?!* iS..*!Ha!"* *• •^«* <»' 8l76000-4i* of 11600000- 
 
 126. A oM IMP .field fa, 16 d«yt. and B l« 12 day. Th. 
 
 -ii'^'ni T"" """•'"» ■■'•. I«t'7 br rtug, imi pirtly br 
 
to ti hr., 
 Mi. 
 
 Bil»bf naiilOaU.Mrhr.i tiMtlMMitk* 
 udjdwk OB tmta « to. , £ta^W^Uild iTu^ 
 
 ^"'m IT^ *! *^,*^ of • WHlta frMta. is to hold Si 
 pi. If ^diMMtonofitooadoMolOiii. Mdeta. iMPootiMly 
 iod^tto lioifl.1 of tlM fcartw. tlM c»l. being 277.874^!^^^' 
 
 of the wood it i in. When the box ia enptj it weicha 8 lb end 
 • ;;^*»JJ^«»'^-««»itwelgh.251b. CoTi^theiSliti'w^ 
 
 Cable content of box it 1886 e. to., end of send le llfiS'a in . 
 
 1». A mnn naning et the rete of 10 mi. per hr. toweids 
 • potot where mtonte-gnns ere diseherging, flnds that 18 mto. 45 
 see. elapee between his hearing the let and 90th reporta. Find 
 the Teloeity of aonnd. 
 
 180. Aboilderaella a hooae to B for $3480 at a loss of 19« n 
 iJril'' Ftol S's'^ga'ln':'*" *^ '^^ ^" '^-- ""^ "^"^^ 
 AlJwSr **** **• **"*" •^^ •»*«'•«»»»» i»t(361(^-2430). 
 
 life for W960.50, paying annnal preminms of $80. At the end of 
 8 7P., Mid, jnst before the ftmrth premiom is to be paid. B dies 
 hajrtogneTer repaid anything. What snn» mnst A haTe tent B in 
 
 ^r«^ ""''^^."!' ***''• •"^'^ **» '^""P ^^'-^W. together 
 with^5* oompoond interest on the sum lent and on the pr«Sttms 
 
 Sum (1.05)--f.80[(1.06)«+(1.06)-+1.05]=2«S0.60. An.. $2820. 
 
 132. ProTo that the diiterenee of any two nnmben composed of 
 
 the same digits is divisible by ». ««'niposed of 
 
 shown for any other ammgemintSttwSito. ^^"^^^'^^ 
 
fai Mfw. Bliiolal 
 to tut. WkMnte 
 
 m. Ab •fnl mU ft 
 
 •OMMJ— te a am tka *»* *tntlgtln«M 
 
 I1«4tl»frtt«f4I««mrtftU«wd«ftditta.7 ^^ • 
 
 ('"^*"^**- *»«^»». 
 
 U6. I booflit thraoffii a Imkwr la Toronto • bill of •mIi.i.m 
 o. OU-gow for £600, poying tb. bmk., |2»16.^ tor |? Tt^ 
 quotoUim WM tb. bUI pnmbMod, lOlowlng «ft fbr bmL«f 
 Co.lofbUlofX60Ul.W016.27; AiToJImT^ 
 
 boU.* rtrik. tb. t.rg«t four Moood. .ftor b. •m\\mZltu^ 
 
 MmoforbiOltoao totM»«nr«*^^^^""**^* H»»«o, 
 
 660 yd. |?lj lyr JJiToO^ftfVri;^.^*"*' •'^ *~^^ *^ 
 
 W. In balMlag > bow, A poM 81 tlmw m im.h #«. yntirri.! « 
 
 IM. A^ to wmlk from P to Q at Mi. rut. of 4 ml. ui br 
 w»d 1 br. aftonrvd. B .t»»s from P ud ov.rtakJ A I» d kV 
 WjJbJ^onB«i^^g»b,.b.for.A. JSd^rdlil'j!:; 
 
 To sj?nr^^!.r .jii s«:^'aJ?. JoV- ^ ^ "•*• 
 
 180. A is 12 yr. old« tbu B. Sboald Uiey botb lir. 8 yr 
 long.r.B'..g.wiIltb.nb.AofA'.. Find tbeZonlJ* Ji 
 
 A* ^'* '•S*.? y* *••■•• to to B'. at tbat tim. u 10 !■ Aa 7 w.«^ 
 
^ iSi^i ■^* "^ *"^ •* ^»~*y' "^ •" i^- •«»*»• ftiii 
 
 01 WMir. Bow MMh »Hl bt t tiMfan td frm MMk Mtk to tka 
 olhw thot tho mlsluo mr bo of oqMl .tmgtht •""••"• 
 
 Tbo ooBloate oC tooh Mik bmI bo I bnadv oad I' wmft^ 
 Hti-t. f of 8 gy. of btwkiy «ort bo tokol ^iTiJr^ 
 
 Ml. A eoBteMtor oadortokM to osoooto ■ oortoia work ia a 
 jJfoatUao. Ho omiOojrt 86 moa, who work » br. dolly. WbMi I 
 
 2 tbo tlmo bot osplrod, bo flado that oaly f of tbo work i. doao. 
 
 •w^r^^ "*" """ *** "^'^ *"''***^ 11 hr. • day to falfll bio 
 • ^Su. nS^*^n '■ *!»^«-W noa worklaff » br. daily do I of a 
 
 y2o*'wi;?ii?s'tf:;s?'s?. TS""^ " '- ^^ - -• ♦ 
 
 1«. Tbtoo moa form a partaoribip, witb a oapltal ^88200. 
 tl!^J^ *" *«^«"«>»B',12b.o., aad C'tlS mo., aadattbo 
 
 ^^mJ^^**' ^ r**'^ W40 of tbo taia, B 8800 «,d C 
 f«w. flad oaeb ponoa'o ttoak. 
 
 A'i Jtoekoara. 840 poraio.,B'., 8861, aad C, 8881. Hoaoo. 
 ^ *^ iwj *** ***• "^^^i •*•• ^•- A, 8860; B, 81800; C, 8640. 
 
 « *?*v^* J **?*."*• *»P o* • Pl<»<»* wMi in. oboTo tbo wator bat 
 fo«ed bytb. wiad tbo plant loaa«l oTor aad wm «,ba..r.«l T. 
 
 «totMooof8ft.flromjrbofolt«toodoroot. Plad tbo doptb of tbo 
 67* tar^" •' '^•P«»+9)*-8e-«(Moa.uro of doptb)-. Ajw. 
 
 144. A morebaat boagbt 600 lb. of logar and 80 lb. of too 
 Tbo eort of tbo -ngor por lb. wm 16|« tbat of tbo tw. Ho .old 
 
 S*o!f •Iw *T *' *** "^ **»• "W •* • ««^ o* 26* wd gUnod 
 84.26 on tbo wbolo tnuiMotion. find tbo .oiling priooo por lb • 
 
 146. A ailrojd train trarol. * of tbe dirtanoo at tbo rato of 
 M mi. per br., tbo next I of tbo dirtanco at tbo rate of 36 mi. per 
 
 hr. and tbo remaining distaaeo at th« rate of 40 mi. per br. Wbal 
 iBtboaToragoratoinmi. perbr.f 
 
 rA?fliyy^ !? ^J^- •"* •^b ■••Won 1 ml., It wiU iwralro 
 G^A+A) of an br. to mn 8 mi. ; 3Hp(A+A+A)" Sm.^SS! 
 
ImTl ^ *^ ^t -^ oii* •• lb. wl. to " 
 m 1 
 
 tni • 
 
 14S. A MMibw of m«i Md wooMa Mra«4 Mft im t^h bu 
 f^Miff ^.M. ud mA #Mwi $1.80. Hikl tb«» b«U • ■•» 
 ■« M 7 Bon froMM th« wliol* maber of womob wo«ld haim 
 •«|d ttj «m. « IM wbolo .«b.r of ««i. IS^CmS 
 
 Wllh tho addltioMa Bwnbor of am nd womb tho tatel «i«. 
 owMd irwdd bo $117. Tho moof'om hall pfiJJrjKirlSf 
 
 14». A dlteh hM to bo miido S60 ft. loBff, 10 ft. wido ol thotoD 
 
 boiBff 4ft . Find tho uabor of e. jd. to bo ozoorotod. 
 
 By dnwiof o diagrui of a eraoowetion, itwUl botoon thMtbo 
 dopthwttl bo H ft. ; No. of 0. yd»(8eox *-^X»)4.a7-»0W. 
 
 ISO. AdooIorboiiffhtlOOoiiiiMloforflOO: eolToo««Si,luBboA 
 Jli, and tnrkoyt® fi. How maay animal* won tltoio of oadiUadf 
 
 li 
 
 2i 
 
 2:0 
 0:1 
 
 1 lamb and ItariMyaToragotlMoh. Robm' 
 i ealto^ 1 Iamb iad T toAo^;*^??! 
 •JJ*' Bono*, at 100 anlmalt aw MoSwd! 
 20 oaltwi, 10 lambs and 70 tarkoys w3l Xi 
 tt!« aTorago. ' •' • 
 
 ^2^r lolutloa. ao 17 calToa, 1« lamhi and 97 t«r}Ety> maybf 
 
 6:1 
 
K 
 
 k 
 
 PAIirV. A 
 
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A«» 
 
110 
 
 AMITOMBTIO. 
 
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 tlllli74« 
 MI19HM 
 U4171M 
 
 fu mm 
 
 oomioo 
 
 ttjiraoM 
 mnmm 
 
 •ninaasiTSiiof-SnS 
 £12!!! »'»r4M 7'4anS 
 '"*™' S-S!!i! riaim 
 
 714Tlirej»OT5m7 
 
 aasmr' 
 
 SS4«i»:MMn 7-seo74i 
 7*soaMi 
 
 ifiSflStlS-S^K 7-5US71 
 
 — pww« Taum 
 
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 — -«^7'fi9nii 
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 471 
 
 471 
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 477 
 478 
 479 
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 Mngnn.-aami 
 
 lUaMONfiSS 
 
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 rmm 
 
 7 
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■qVABIS, OtTBU, AMD MOOTC. 
 
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