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C0N"TENT3. 1 irithmotic **"■ 5 Algebra . . 19 Statics and Hydrostatics 43 Dliemistry 65 Eiiglisli Literature 79 EiigliBli Grammar . . 83 Geography ... 96 Paoi. 6 19 43 66 70 83 95 niNTS AND ANSWERS TO INTERMEDIATE EXAMINATION PAPERS. -:(o): Jlrithmelif.-^rio. I. 1. Amount of debts 2 X $21,735 = 513,470; .105 103^ •* '00 100' ""^ *^^P'^'''^ = ^43,470 ; .•. capital ^f.-ja of ,285> of «43,470, -$40,000. Hence y( •. share - ,2 of §40,000 =-- $524,000- and lis " - 5 of $40,0U0=?iilG,000.' 2. No change* Sotfrr.w"'?.^'"'""''^ '^'^'"'^^ *°S«th«r -^ter going 803 feet, the L. C. M. of the number of feet in tlxe circum ferenco of each wlieel ; ^-'icum- .-. time required =~^2i><«0 minutea. = Ijfff minutes. 4 ''^^24^/.00004or^2^5^^y^^^^ #'•81 + ^.03 r.03(r27T# I) __4-24x.ll5 3-M •=1— 6X.116 6 aiNTS ANJ> AA'SVVJSKS, IN i, 1M'KK,MEJ)JATK RXA =(3iXf)Xf>j MINATIONm, 6. Area of end — r^js/ox^M J'<'7.'i^' cubic incJio Araa of inside of end Cubic contents of hollow Quantity of iron V\'eight of iron — (.5-K8X8) S(ju;iro inches. = (iiliXSjX«X«) cubic inches-. = 724],', cubic iiiche*!. ~2iH2'^ cubio iijohes *^. J^«t;=the zntm-cst of .$1 for the fuurti. of a yea. then (1 + ?-)^ ==1.08; ' ■■•1 + '= V'l'Oi'^l.OJf).... . S. f5. 03 (nearly). a The sum of the velocities ^ ^^^ + ^^0 .J ■ teotper second =90 foot. ,120 I 150 10 = 27 feet. The difference (( (( (f The velocity of fastor=?^t^7 ■ 2 <• «< sIowej:=' ~* , The rate per hour can easily be obtained fro.u these ^4,., 3^«<^«'" 6 1,000000,000000 is an English billion Th. , correspond till the place of hundred of ..ill '^'''"'' in Enghsh notation the ...p.. is e:;:dt:;::;r^^ 3. Co^ of one-half wheat per bushel = ] oo ^f g. g. ^. Costor.he.,^f,erhushel = ^^:;|S:S:50 .cost oi two bushels = ^2. 50 • .-.loss on 12.50=^.10 ; * .-. Joss on $100= ^-^^ X ^-l^ __ «. 2 50 "~^*' fir^ r!;;;:nwLSr ^f ^ P-^-^y-^l^OOO) to eldest son, Sec j^^ ^"' -^^"^^s ''^ property +4000; .3rd, .S'18000. 5. Since the areas of similar surfaces nro fn .n 1, .u ^V s,uares of their like dnuensions! we h^ve ' '''" "^ ^S'' : flength of 2nd)'^ : ; $500: §320 ; .'.length uf 2nd-- J^^~>[320 * ^ "'00 48x4 = -g - = 38f. 6. Interest on $3!)55 for G months=:f 138.421. __ <5 3955 X 100 ■tiiuount of stock sold Money necessary to buy Sum to be paid 98l = ^4000. 100 ~ " ==^3900. -'<3300+.$138.42|. -<^««4038.42^. 8 HINTS *»„ „,WEM, miEEMBBu™ BXAMm^ONS, Ii5 days i, S773 SlsKo ?8 F ";,'°"'',' ^ *"" '""' ^^ /o • 8. 18^]^ hom-s. — ,^,iuche3. V ^ c ~ ~ = :)04.7808 =332. 544 ••• weight of cufcting8-=,'i,:i7^ of 572^8308 of ij^f os. 10. .4m. 11141 feet per second. Solidity of spliero Solidity of cube ^0. 3. ton-bnSr' '^'^ '"""°" *^^"*^ ^'-"-"^ -^ '^-ty one 17.0000001008006. 2 Resolve 171G85800 into its prime factors : one of tneae wm be found to be 29. As 29 is not a factor of Jl H the first two numbers it must be one of the third 3. #4500. 4. A's investment=$560a h'l- 1 mo. B's " =$7400 " " ' C's " -^1814000" " C'sgain --»«1710-($430 + 1^550) --^iV^O. frtNTS AND ANTnaRS, IVIEKMEDIATK KX AMINATJOM?, O/iijHal required to gain 8730-=,S14G00 for J mo, " " " $i30-$'^i50xI4GOO » it :. mm put in by A 730 =68000 ; _o8000-GC00 ^ =$500. StTnilavly B's sum is found to be §G00. th 2| oz. fi Tf ho has 16 parts of the good article, he m(xM fpur f'ftl'ta of the inferior with them and sells the whulij for 22 rwcts, But the four parts of the infcri.ir cost tho «an.e a« 4 paHs of the better, hence he sold Vd\ parts for 22 j,art«». From this his gain is found to be 14^%. To g/iin 20%' wJittt ho cells for 22 must cost 18^. Then cost of tho itiKrod* i«mt.9 bein^ 20 and 1(5 what portion of each must I.o takor. to fwHrt tt mixture worth 18^. This is easily fumid tg bo 7 7- 10 in. Jl ^t '"*°"''* ^"'* * *'^''*'^'" *^^"'« ** (i^i -8;% »• ai012.60. fJ/oOor ^62. 50. Tu terest at 2|% =|62. 50 8x02,50 « " " 8%=§ -=^200. Hence the principal is ^950-$200 or '^"im. The time is easily found to be '.S\ yearu. 0. Sum left after gaining !^14=| of money + %H. $8=i(|of money I )gJ4j-( $8 = .^ of money |-$19,^ . I of money =.^il9,i Hence his money =$48. I of money =| of money + ^r'i 10 HI.N1S AVI, ,«„.«„,_ ,.V,BRM«„,ATE BUr.S- ,,„,.,,. and o......,„,;:;;;:;:;:;:rr,: ;:--'"-'"■"■■- Ana. 101. 1 iJ''^i #0. 4. •• iU men, S hnvs jn<7 <1 „;,.i.. „ -y* •• 10 men, 8 boys, and 6 mrls , M ir ri But 3 men, 8 boys, and G girls ,',' I ••• 7 men clear (jj-^) of field in 1 d.Jy And 1 man clears (J„--^>7 nr M ^p r 1 1 • , •• U men, and 2 boys clear (i-i ' j'i " Butllmenclear|^.ffi,Minlday "^ " And 1 boy clears ^,, of field in 1 day In a similar manner it may be fo.mrl f i, ^ t , , »ield in 3 day. ^ '^ "''''* ^ S"-I clears ^ j^ of Hence 3 men, 5 boys, and 4 girls do (A4 ."^ 4- * ^ p , >n 1 day, &c. ^t^^^tjj +jig) of work Ans.» lOff. 3. The machine cost $40 before the duty was paid 4. Sin^^of child's sliare==2(>y^ of brothers share) •• * children's share8 = 8x 100^ 9B ri ^^^^^^^ _ °4 , f'^ ^ TtftT of brother's share Ana SSiSnn u-n, , ~ '« 'brothers' shares. Ans. e4800=a child's share and ^-450.a brother's share 5. Cost of 8ugar=-2000 x 8 cents-) $13 = !^173. Cost at 7cts. =$140 The difference between the tpfnni „ ^ cents, viz. |33, arises from Iviiif ^ 7' ""' '^'' ^°«* ^'* ' lb. more than 7 cts. ^ '^'^'* ^ P''''* ^^ 3 cts. per 1^ niSTS AND ANSWERS, tXTEUMKDIATE J£XA UINATIO.VS. J, Number of lbs. at lOcts- ^/^-.:= HOOlbs. Number at 7ct8 = <)Oo lbs. 7. Amount of note at the end of year .-■: 400 x $1. 10 = S440 Interest on $390 for 9 mos. = S440-$390 = $50 From this the rate per annum can be found. Ans. 17^V7%. 8. He buys 80000 stock. He receives $800 for his dividend bum received ==8o970-|-$300 = .«!(J270 Sum expended ^^(;]35 + ^^ of 86135 -$0504.45. l^oss =<>i>04.45— $G270=$294.45 9. 23o8^2i^\h. 10. A overtakes B 61/, yds. from the corner where B Btiu-tou : 3 tiinea. ilo. 5. 1. -3 ; -1. 2. Suppose the vulgar fraction to be in its lowest terms Ihe division IS carried on by successively multiplying the numen.tor by 10. The factors of 10 are 2 and o' "^Henc If the denominator contains no factors but 2 or 5, or powers of hese the decimal will terminate; if it has othe' I tor than these, it will be a repeating decimal. 3. and But and 12 bales and 21 casks fill ^ of cave, 4 '< 7 '< 1 <( ' -^ " 35 " t\ecave. 18 " 40 u 2 bales occupy the same space as 6 casks, 1 bale occupies " " 2^ 18 bales occupy " «< se^ Hence it would hold (45 + 40) casks, ov (18 + 10) bales. m il!! 4 i ^ T^=-^m cost price, 1 V 10 7 1(17 6. Total sum realized ^^"""^^Z^W^^o. ,, Sumrea].edat9% -^^^^ + 183 + ^§ag)of cost ^° — T?ff of C»St, (folS— loo) of co8t=824.50 Ans. $7000. Face of Ist note=$(ioo of 375)_.qoo,2 Present value of 2nd note=.s;,;8l>. g + i^sT^''''* Face of 2nd note=$(i,'^Q of 384/,'^) =$302.25 cts. nearly. Si"«e {t2^-(t^ + ^2^)j of sum=«50, .-. sum=$l48824i Sum realized =£30400000. Total interest paid =£1830000, :.100 X 1830000 9. 7. average rate=£- =6-3 30400000 Interest paid on each £ of l8t=£y' of 2nd P4 . •• the lowest rate is paid on the second. «.Sxnce216(co.toflo.ofgold^costofloz.ofsilver) =£637 78. +£2g9 is. •.costoflo2.ofgld + costofloz.ofsilver=^'^'*^ 83. 216 =£4 3s. .. co«t of 1 oz. of 8ilver=£43.s. -fSlTslO^d. P =5s. l|d. W. 15J per «.«. „, „i„ . 8,j ^^^ ^^^^ ^^ ^^^^ Mi' HINTS AND ANSWERS, INTERMEPIATE EXAMINATIONS. M 6. 13 1. See Kirkland and Scott's Elementary Arithmetic, Art. 141. Ana. 27. 2. L. C. M. of 2, 3, 4, 5, 6=(;0 ; GO + 1=01. This number is not divisible by 7 ; we must, hence, find the least multiijle of GO, wliich increased by 1 is exactly divi- sible by 7. Ans. 301 peaches. 3. Each time he draws off ^% of the wine then in the cask. Part remaining = ^^^ of ^^ of ^7 of £^ of 20 gal. = 4.802 gal., etc. ^ 4. If he owns .?t00 stock his tax is 4 cents and his income IS reduced to $3.90, and when the tax is iloubled, to S3.0'> But when flOO stock yields 83.90 net-incomo, he is making"* per cent, on his investment ; what per cent, is he making when $100 stock yields liim ^3.92 net-income ? 392 X 4 Percent. = 39G Q 05 5. By Alligation it is readily shown that 11 men, 8 women and 8 boys would receive on an average Si. 10 per day Hence number employed = 22 men + 16 women + IG boys. 6. Is.; 6f%. 7. 7 min. 14 //J'j. sec. past 11. 8. 20 per cent. 9. Water displaced by 1 oz. silver = 2304 „ :„ , . ,, 15000 ^' '"• ^ ' " " sold = ^^^ ,. in. iLxcess of water displaced by 1 oz. silver = ^ig-i^o.s^ c. in. Water displaced by alloy = 1.3.824 c in. " gold = 12.96c. in.' Excess of water displaced by alloy = .804 c. in. Hence, number of ounces of silver = .804 -r = 12f Number of oz. of gold = 1371. 1008 14 HINTS AXD AysWEK.S, INTEKUKDIAT« K 10. Number of grains required = Sy.tt .-. cost =. ^ i' ^17 60 ' 480 ~ = $1.44376. KXAMIiNATIONg. 'li fio. 7. 3. Seo H. Smith's ArithiMtic, Art.42. 6. 7W00000000070000 0070000007 6. Ths word two »l,„uld bo three. (1) Evety „„„W of W or ,„o.„ «,„,, garaoda,,„a,eupofa„„„Wofthousand.f," the uu„„,er of .,„„d,.«,,, .e„,. and units indicated by«.eh«uro,i„thesep,ace,i„thenu.„bor I 1000 „ exactly divisible by 8 any „„„,he, of tho7 -ds ..„ be also divisible by 8, .0 if the nit; represented by the three right hand figures is « -tlyd. ib,eby8thewhol,n„„bt„u ;■ divuable by 8. (2) 3384.=2'x 3^x47, 8272 = 2^x11x47, 7567=7 X 23 X 47 ; .-. H. (J. F^47and L. C.M.=2^x3'^x7xllx23x47 = 11582928. (3) 8280604200=2' x 3' . 6' x 7. x U . J3 x 23 x 29 32340=2'x3x6x7-xll 2622520=2'x3-x6x7'xllxl3. hence, a, the other number n.„.t contain all tLe facto, found niNTH AND AN.SWKUS, INTERMEDIATE EXAMINATIONS. 15 i" the H. 0. F. us well as those of the L. 0. M. not found :n the number given, tho other number must be 2^ X 3 X 5^ X 7^ X 11 X 23 X 2!) ^107853900. 7. Elementary Arithmetic, Ait. 141. Since the denominator of a pure ropetend of 3 figures is 991), the denominator must be 999 or a submultiple of thia number, as 111 or 37. 8. (a)ix --^^y^'^-q 401238 'MS-^ 1000099^ 1 -'^1000099* 213845 2319 103(5832 ^''^ 285124 +2Wr.21504d4=^"¥AVy'^'\VaWir. - 9. (a) 1=1 1-2-3- 1_ 1-2-3- l-2-3=0-;iG06666 1 :«=!• 0466066 ;=0- 0093333 :=*0- 0015555 1-2-3- 1_ 1-2-3- 1 •-=0- 0002222 1 j:2T37T.=0- 0000277 1-2 -3 .=0 00000308 l-724475~' (h) $21.75. Mo. 8. deal with co.n,,o.,ndcd numbu i Tho c„ ^„^„^, ^,^,j^^ Elo.n. Arith. irt. i';y"'"^"^«- ^^eo K.rkland and Scott'. 3. 7089740 X 990993=7080748 x aOOOOOO ^7, = 7089748000000-53828236 = 7080094171704. denominator can be L-u.,.f.II,»i ^ ., ^ ^ » 'ina os m the 5. (a) 7396. (i) 100191, 100009, -091091, 0069, 1100. 6. 8 per cent. 7. (b) $178. 11. 8. o^%(near]y.) 9. Amount of bond Jany. Ut 1882=800 x $1.06=f 848 Sum paid for bond July Ut l881=$-?lL_j.«tq nr Proceeds from a note of $1 for 03 days at Sy^^P^i ■'■ ^^""^ «f "i« "ote=-.#(8192VT X mW m a^- ^ =^836.37.... 10. (6; yards. BINTS AND ANSWBUS, INTiiUMKDUTJ!: JiXA?IINAT10N8. 17 1. 39840. ^0. 9. 968793(;-4852 (144)(12)(1728) UG2552,'{7«224 1395062853808S ^167407542404250 i39C242T470012r04256 S*G Key to H. S. Aritli., p. I, for a similar aiample. 8. (b) $14595.70. 5. J, B, and C do |» of the work. It can readily be found tliat A does Jg, B ^%, and G A of rhe work ; .'. ^ gets ^§ of .«159.70=$G9|g ; A' " A of §159.70=$34|3; ^' .» ^'15 of $159.70=$56iV5. 6. Selling price of a yard to gain 20% = $0.84. lof^rJ^^ shrinkage each yard bought contained ( o» of ^^^of J)sq. yd.=fisjsq. yd. ^^""^ Hence the selling price of 1 sq. yd. =:-- 22§fJ of 86.84. =§4.22 (nearly). 7. If of a year. capitair'"""^^^" '''''^■'^^^"^ ""' ^^^"-^ °' --^ °^ ••• (^A of /xr + fVir of T?7T + fnl of ^n^) of capital =$1736*- .-. Capital =$35000. 9. 109. I I 10. 2 inches. "''"^""^^^^'^-'-'•^-KnU.KKX.M........ lu 3. " Wluw, wo mulfi,,ly on« intoyer « Lvanotl. .,• ; dcscnbo t].o operafi.a tin,. • wfn/wo di .^ ' """'' (2) = x.._(2^, .''■k-+2,"=,..-_5,,.,.^,^«. (3) =l«"V(."--^)l(X-(,..._,„^,v:(.„._^^,_ etc. (2) Dividing bv Hnrnn..'„ ^. , 4.1.^+2.^.0. '^"''^'""^*^'°^-«^'«t> for quotient, (3) (•c''+a;^'-2)-f(a-2+x-a-_2) 6. Hamblin Smith's Algebra, j.ago 70. .+o 20 HINTS AM. AN,SWKKS, iNT.KM.m.VTK EXAMINATIONS. 7. Ha,nblin Snuth's Algebra, ,..«o 104. Arran,n„. in or- ' der of mchces we have x'^-4.'v-+4,..-.M>.-12c-^'+.„-ep^ Th« square root of first term... and since twice fir«t into lecond »-«t-_ - 4. . ; .-. second tenn ,„ust be -^2.,f, and third tern, -square root of 9.-^. ; henco square root = .3.__j^,,^3_^-,,^ 8. Haniblin Snuth's Algebra, page 58. (1) Equation =x!^— 1 = 4+ ^"-1 ; ^^^. --^^ ^ a; = 81. (2) Tile liist equation may bo writt(!ii :— whence c(ay+bx^:,y)=^.y^^,^,j_^,^^ . diVKluig the second equation by tins we have :' =4; X1J al>o c y'a/; • this value of ., being substituted in the given equations, we find x= ^ac, and y= ^fc 9. Let A's daily jjart--.-^, B's=^^ - and the remainder after 4 days=| ; ^ y 10 • 30 3 •'• -y -4' wli«»ce y .. 48 days and x =24 days. NATIONS. ranging in or- 'st into second nd third tern) =4; uations, we =24 days. HINTS AND ANSUKUS, IXTKKMKDIATK K.VA.MINAi ,uNS o, Jllgebni -No. 2 1. See Hamblin Smith's Algebra, Arts. 260-272 Sec al o Mathematical Notes in this month's Examiner. 2. See Examiner for June, Let in-l)n(n+l) be the product of any three consecutive integers. And (m-l)m(m+l) be the product of any other three con-, secutive integers. The difference of these products=(«'^-l)u- (m-' - !)„,. «vhich is evidently divisible by the difference of the middle integers. 3. (^+aXx+b)(x+c){x+d)=:t^>+(a+b+c+d0^ + (<'^+^<^+<^d+bc+bd+cd)r^ + (abc+abd+acd+bcd)x+abcd Coefficient of x=2. 6. 10+2. 6. 14 +2. 10. 14 + G. 10. 14=1408. 4. ix+y+z)3 . •• l=l+3x-«(l - x)+3y:'(l - y)+3zHl - z)+Q^y. 0=3(a;H3/H22) - Z{x^+y^+^^)+Q;,cyz.) =3 — 3+6x(/z ; . '. xyz=zQ, 5. Dmdend=(a^+6HcHc^'0.cH(a* + 6^+c--+d»)yf 22'"'VTS AXi) ANSWK "S, INTERMKDIATE EXAMlNATlOXg. A]gohra.~C„nfinued. 6 Hamblin Smith's Al^'ebra, Art. l.m The H. C. F. of (1) and (2) is eytleMy aU+e. ^'^ 7. Hamblin Smith's Algebra Arts. 145, 149, 158. Adopting the meaning given in Art. 158, viz. : that f repre- s^ents the quotient resulting from tl,e divi.sion of a by 6, let ,—?; then, since by the nature of division, a quotient, when there is no remainder, is such a quantity, that, if it be mul tiphed by the divisor, the product is the dividend. We hrve," a=hq; and mct=iahq; ina a mh ' h ^0. M. of denominators=r._/,)(,_,)^,.,). ,,,.^^^ ^^ (a-6)(6-c)(c-a,) In numerator let a=,, and it vanishes, therefore, a-h is a factor ; szmdarly , - e, and e - a are factors ; hence, numer tor=m(a-b)ib-cKc-a). Letting a=0. /,^i ,_o ^, " , *j, 1 rri 1 , ML, ( — «, we iina w—i. The whole expression is thorefore==l. 8. In £+(a*-6^;a6 (6 - rt)6c+(o - a)ac+(a - bjab =('^+f>+c). (3) Reduce each term to a mixed number md 2 n,n u ^ 'fV ■'' - o^=(cc+6 _ 2a)(x+a--2b) which i^vm two root,* each equal to h{a+h '')• 2tUINT8 ANO AN «*VKUS, INTJ. '-, 'M-KUA.l.;.>,ArB KXAM,.VATiON8. (41 If applying th a r h ^";7=7-=«tc.;tiicn''= ^-f:2,+s.:.&o. +(■) 7— :=« + /) )-, .'•■I from whicl aiul 1 i 111; and .V iu;iy be written d ly oanily ho ohtui.iod, tl: (r^) <^wn by syiiunotry, ' I'M tJio valuoa of ■"+^i=fj+°" •1-2 <-'•;/-'(-■,) -18: a; J./* 7±v^4!rr' 4!»-, 72 » 7±n 2 =9 or -2. «=*+ — = 9; x^ 9J=-8; Thf ' + 7 x'^=:2 or I «='i or 1. reinaininir roots may be may he found by equating J+ to— 2 KXAMI.VATI0N8. (a+b+c)\ ' tlie valuos of a ^18; x^ + -v; to— 2 1 i niNTS ANU ANHWKU., rNrKHMKUUTK KX AM,> A n- .N... .^, 4To. :j. I. a ~ a — a \a _ l ) ivr r ,„^ ■^'^- '^"w if TO-n >a «,ver), '«! otlier caaos may l)o * ~ I, ia diviail)lo by « ) |. proved in a similar nianiKir. iJ. Take for example tlu, .xi„..«.io„x^ + p,. ,, ,,^ ,. ,,^,j ,^^ where 72 does not contain ;»• nnd wHl i.^, c -e. whatever value n.a.t:;ltf''i;'r ^^! ^ ^px'+qxir, is dividUa by x4-l ifH,, .„„, r n l '^o^mcrmtsofthedivideMdarecim,! and ofoj>j,n.ifr. sh/u, Ina«,rnilarmannoritmaybo .hown that the i^xnr.^.sion Bible bv x^l J respoei,vely; it is, therefore, divi- thll fr ; '""''^ '"'•^ ^' '"•'^^^^' numerically .reate,^ than the other by assigning certain values to . and ,. 4. By means of the formula r.'-/=(:,_^) fe'4-x^-L,.^ the expression reduces to ^'^ ^ +-^2/+ 2/';, {h + c~2a) (a'+b^Tc^IIIJr-l^Ta) 6. The iquare roots are "-''_?' ^ , ? 3 7 4' 4 '7 ' a 3- The le.sults may be '^■'•K BXAMmATIONfc expressed by -t | "_ •'^ _ ?/ ) '''••'^"™""" notice that the rolt-L"'., lain,.,) I • ^^ "■""'>■ ■» »•>• .nd _^''»'^2„_ . _ ""'3. ^^21 •3--,The„,„„e„„t.,f;;i,thel«tte™, ""' 3 X., must equ.1 _ ?. . . , , 6- ■• ''""snr. must t. „i„^ tj„ '""'"+'• ^""^'-~ive„„™He™: Which =.„(„_,,3 +1, l:p;e.;el'H;;tt""'=^'+^''+'' , 23' := (11 f, 2). = 4x Jl xtijT '"'^' =*"• a « + --- — « . '■^ . « = J«±^«Mc-M) «/, Here ax + cy-^},^ = cx+by + a,; By symmetry (c-&) ^+ (6_„) By elmination, we have- ^ '^ ®- y — (b^iS^~7r~7^\ / — i X — jy -^<^^ ~ab-ac~hc (^ a) - (c - b) (a~c)^ y. + 6^+c^r«,Z7c- ,^. ^ -=a;=2, by synimetry, «"t ax + cy+ bz^a' -(- b' ^_ ^^ - 3a6c. Adding these equations, wo have^ MX.VATIONi. 1} y ^'•isily he oh. 5rst term is s, s the last term nust be miniu. 'umbers : H =3GJ. 28 + ] ::^629 - » ac-he ac~hc ry «. Siuca x=a2+6Hc8-a6-a.-6r=y^e The interest of $1 in 4 per cenU. is $ . - , «1 Let f« be invested in the 4 per ccnts/and 075 — aV* Then »■• ?/ 4A , or 10 The erj nation reduced becomes -•■'+(.'+f=;x!-3„(,„=0, which gives — 0,andtc-~ „ , ,„ — ^U. 4. 1. It is obvious that hx^cy must be on« «f .i. ^ and that ..+«.,+,. ,.„, be divi.,! tr,:. ^'Llr^:;: formnig the division the remainder wiJl be | 1 -J'l'^S' \ ^ , which must be equal to zero, in order that !l,« A' ■^- "^ '^ ' leave no remainder. "'^ '^'^''^"" "I'^y ^^2. K^ any function of ., say, ..+,^,,,^, ,, ,,,,^^ The coefficients of the dividend are, 1, p, ^, ^, " quotient are, 1, a + ;i, a^^ „„, _ and the remainder is ,3^ . ..T/+'' Dn.de ^-6.M 11..-G by ..--3, Coeffs. of fiividend 1 _6 ' H __ti ":!^' multiplying each of these^bv 3 .nJ , r ceediiig one, we have, ^ ' "^ *^^^'"S the .uo- I. 3-C, -9| U, 0, The remained is 27Z5^%flQ'J^'- "^ *^^ ^"^tient. ^n the question, the.* of dividonc,:.e,V^,,,_,,_, and the remainder is ,.5_^, \ , , 1' -8, 12,-18, 20, -30; Therefore, the coefft. of the quotient are, .n, ^' r^' - 4.-34, -ik;. Ihe remainder i8 obtained by writing 4 . let '!+''-«' _ i -«. and pontine the proce,,, a. in the method of undinff the H C v ^ a iniiKt 0; a ) a ,/ - which «'— C» »?l2— 6c2 a ac ,3 > a'^—e' mab- ~bc'~m' *''' («'-c'-a6)M=6ci. tdding the lao- the quotient. a'^so — t. 10, ad of as. = —494. f, the remain- 3> and aa .;r iji UBual way; % as in the >mainder, ,i ~ which HINTS AND AKSWEIW, INTBKMfc„IATE i.:XAM,^.^Tr.,^s. .„, SubstitiUing the valu« of . ^ 4. In Arithuietic a fractiun i^ any part or parts of a unH or whole ; in Algebra, any cj.„.„tity ^ is called a fraction, al- antlunotioal fraction. The Afecbnuoal fraction" Jn,t „,,,„» S7Jr TLt;'r '■^' ': ■' '" "« """"""^^ ''^ « -■• vmcu oy o. ling dofinitioji, however tlii-Mii,rl. fi ^;eraUtyofA,,ehra,n.h.ae;thato;rA:;t:^^^^^^^^ J^ In the second term of the denominator, .-36c should Fraction = ^±^^'^''(tzS)z:^{2h~c)A^h^\ '»(Hc){a-(6+c)-a6(2/H^+6'' + 6'j 6. If a>6, then a-6>0, and a3-2r,6+/>2>o a 6 mean ; hence 4«cx-=6^.^ or 6^ =4," ''^"'''' ""^ ^'^^ We may obtain the same result bv 'extractin,. f). root, and equating the remainder to tero or '/ ''""'" thus :-If it be a complete square it is ' " "'"^^ '"''''''^ Thp ^,fr"' ^"^ « "^' '''■ *'=^^''' '-»« before. + 0^:+^!:""" .s ^«+6^+(12-a)..+ (56-6)^+(06 ^c).> It is obvious that .«, 0.«, and 64, are the first second an-^ fourth terms of the square. second, and HINTS AND AN.WKU.S, .Ntk.^,,:.,, VTK KX AMiVATIOXS. S.-PPOSO ™ to bo tho cooff. of the third tenn, then, FY'^n t„. ,,^o , , , i, „„, ,, ,^,^,„^ and b, »,„.„,o.^, „elt,.„. . „„, X^ i,,^, "i'^r^^t' d the numr vanishes • ■ „ ; • r , ^ei a— <>, and -ns the only ..t.. tl... .e J l^^Zr^U'^l^iZ, (c-a) ; the nun.eraror must therefore =:..(c -6) (V-c)/; \ To find m let x = 0, a=l anrl ^ o i „ cMc— a). found to be = l Therefn!: T^ ' ^'"'^ ' = ^ *"^' '" '« form = l. ^i^^^efore .the expression in its simplest 8. (1) Equation = -4+ 1^ +0 Ji x + 1^' .^ + 2' 114 10 ;, Ac. whence .__ {ox + 1) {2x + 7) (x + ix:^^)' (2) Multiply each side of the eouation by Mx + 2)^ ^^^ we have 8 + 2(x + 2y = 17(,o + 2). ' ^ ^ ' ^ q,.,drat.c e^u:.t,an c.m,„, luve ,„„r. dia,. two i-oot.. If Uio eqmthn is »ati.H«l l,y i.i.,r„ tin,, „. 1 i-o^+c-0, chanpox into - and we 10. Lot u-^-width of itjith, tliun a~2,- h o of Hio inner loctangle, ' ^^"^ "° "^« «'^l«» (a-2..)(A-2,<0=.arou of inner rectun^lo ; /. a6 - (a-2a;) (6-2.0=area of iKiihJltJki'lIi^fl 1. See note at end of Examimcr fur Juno Whon.as.-»+6,.y4 ,y-. is divided by ..4-™ t,,, , • , =<~^ny~^my+c.f ; if the.uantityrdivS'b] •"""'" der must^O ; equate it to Jo and find y' '""""• l4^ Al5:'t:i''^ ^'-^- ^- ^«' -'^^"-ter-s Ex.:!:r '^'^' ^^"^ '^^ '^^-^^^^^ -^ ^ ^•"^"- --'^er of the 3. (1) x» + «W a;*--a* a;- — «» X*— a* 2 a x^ — a* n n »2"+' 0" + »•' —a' "O-I W" _«3 fA'llOVs, lluUH of X, it oroforo, truo on that thoir X and we ocals of the ro the sides r rectangle, ,'lo ; ro mail) dor lis remain - xUiun tor's Jer of tiic Multiplyiny, wo have— (2) Product of 2 factors = «»-„' » henco,^:'^±^+l^^ ) 3^)^ ,' (2;/-f.'fe)f(2j/f.'is)a 5. Hamblin Smith's Algebra, Arts. 127, ICS. ' The followiiiir iiK.fli,,,! „t r t easier than the ordinary n.otho.l : ' ^^ ''' "^^''" Write the coell's. , inscrfiiu, n'c i wanting. ' "''"^'^'"''^ Os where powers of x are 2 '»-ll ft H) 18jT^Ororo"r8lT:(i)xO. (3) 22_£1_0-(.J-T(2HT3J 44^^ (4) i yi ^ ^ 0+81... /r^ a 022__0_j)9..(2)-(5).(r,) 1 ^^ 2 9..(r>U-ii..(7) _2_ 1__0-. 9.. (4) ^~-l_3 (4) + (7) find .inoe this expression canimt he ro,nlvf,l ,•■,,„ • , , tors .t mu»t be the Highest C„,„ ^ , '" t" vT;'"" r !4 fllNTS .\\|( AN SWKiis, I.vr|.;i(.M(.;i» R E.VAMIVATI()N3. Change . into « and «i„,plify ; ,,, ,,,,,_ ^l^dividing Uy I, valMo of oxproH«sion required = 7. Hainblin Smith's Algebra, Art. 223. Expression =(,6^4- //^ J,..'.' I ,m". . , , „ ,„ J.^,.=4, wiil he an identity, nine, in that ease. the. v'l No value of ,n can make the expression an equation. 9. (1) -+l'Z^_^+^'-7_ .•{.,■117 •^+7 a'-fS y''fl2.r + 35 a'-l 7 ' x-l-5 __llj:2^ ^ •^■'' 117 .-.^•=7. Dividing (I) by.,, C2)'by;';;tnd (3)b;,f ^ have- 3-^ I ' 1-' ' HI>'TS AND ANSWKUS, INTKltM KI>1. ;.\.\.\1IN.V! r^N3. 35 a»6 !=■ 1 .'/ 1 J .(«;; .-.2-^- _...(4)-(5;..(r) .•.,^--=—3. S:c., (3) When rediicoil tho ociiiation bocnnies— — (a + J") («—'••+•'■) =--- {h—<:+x)(b-^x). (4) x= bi c Cib^—biC, y- -((,(•. iixb^ — '^i^a * ''11*2 — cij^,^ If -^=^=-?-, then a^fea — "2'-'n«iC2-"«2Ci, ^'if^, =^o.^Ci ; <'2 "2 '^i in this case, x and y assume the form , and their val- ues are indetevminafe. It will be fi)Uiid, in fact, that, in this case, there are not two iudupeudeut equations, one of them being only a multiple of the other ; for let— =- ^= ?= m ; «2 ^2 '■'2 then «! =ma2, ?>i =m&2)«i = ""'2 ! and, therefore, llie last equation becomes »i(rt2;'.-f /'ia;)=fliCo, whicli i- identical with the second equation. There being then only one e(juation between x and y, if wo give any value to x or (/, there will be a corresponding value for y or x. 10. V-'^' + 7-'- + = V^'^ + 4.f— 5— 2 ; Squaring and simplifying, we havo— 7a;''+22x=-129 ; .:x^ 3 or— 6}. ' If 3 be substituted tor x, it does not satisfy the condi- tions of the equation. The reason is that, x'^+7x+6, and ^'+ 4x — 5, are the squares of— ^/./•2+ 7.1+ C, and — /Jj^+i'x—-^, as well as of the same quantities with + signs ; thus squarinc; both sides of tho e^uatiijus introduces a new condition, and a .30 HINTS AND ANSWEKS, INTKUMEWATK KXAMINATiONS. new value of the unknown quantity corresponding to it, which had no place before. Here 3 is the value which corresponds to the suppositiqn thai — l/a;H7x+C=— ^xH4a;— 5— 2. ItHlionld be particularly renienibercHl, that since +ax +/.1. equal to -«x^-A in the nndtiplication and evolution of quantities new values are always introduced, which if not a^aui excluded by the nature of the question, will appear in the fanal equation. So. 7. 1. +{a-3b + 3c), and-(3/>-a-3c). 3. Answered in a preceding number. 4. Multiply the quantities together and in the product make such substitution as will make each of the three factor, identical to x + y. X~y ' divide this expression by *HJ/^ we obtain the required ex' pression : ^•"-y" ..•^-1/ VTiONS. ; to it, which corresijonds since +ax i evolution hich, if not 1 appear in («i + Oa product !e factor? ired ex 'ftP-Im 7. HlHtn AND ANSWEKS, INTERMEDIATE EXAMINATI0N8. it^ + px' + px + l {x^ + i) + 2r.c{j' + 1) ii7 X+1 X+1 = x'—..: + l + t)x = x'' + {p—l)x + L ■^ -f /«^ + qx^ + qj?- '^-px + 1 = (,.;^ + 1) +j>x(.r' + 1) + rya;»(ie + J ), which M djvisihle by x + l. H, Putai=— />and the expression becomes zero. ThertJ- fore, 4 + 6 JH a factor, and from synanetry, /> + t', and ^'-fa nmttfc filrto ho factors ; and since the expression is of throw diiMUKsiotiH, tlie factors =}a{a + 6)(/) + c)(c + a) where tn in ^% nuiHwriyal r|uantity. To ;-.c-' + !=,;_! ^^-. or c— tt6'''=0, and c;-?/:=o, whence ad=bc. tho product ,fcrsl;„X''' """"'" '"""'"• "o-v liie 12 IS found i„ the usual „,a,m„r. ^ >«« + * + «. 7- Hamblin s„it|,., .4,g„^^^_ ^^.^.^^^ ^^^ The H.C.F.i, evident,, .i^,.h,„„,_„^^^^.^ « __ c e h ~(l ~ ~f~ =^' Again, a"=6»a;», etc. =:etc. ; . a^'+c» + e»+ a etc,=etc. ; oce. . . . hdf~'. ~^''' ^__^,n . ATIOJS3. I, 272. licos, either I) page 26, therefore rs. Now xpressioii 3 another + 6 + c. [. is HINTS AND ANSWERS, INTERMEDIATE EXAMINATIONS. 39 ace. hdf. a" + t;" + e''4- 9. Sin( '>"+ci" + c" + ice a, 6, c are sides of a t.riangle, ((H-6>c, .-. ac + 6c>c'^ ••• «'M-?/' + c^<2(rt6-|-6c+ca). Again since any positive quantity is greater than 0, we have {a-hf>0, or a'+lr:>2ab c^ + a^y2ca; 10 a) ?rLl+2^zl+4 _ „ 11..--18 + 36 • ' ^ x-1 ^ . ^-2 - "Tl^^Zis ~ 5 1+ 2 ^ 4 . 36_ sc-l x-2 V ^ Ii,._i8; 1 2 30 2 _ x-i^x^2~\l^ ■18 , which can be solved by the ordinary methods. (2) y'a; = \/x + \ - yjITT; square and simplify. .3, V^i^V2a2 +^262 ^^ x2-l ~26 » «♦+! 2aH262 «*— 2x^ + 1" x*+l_2 aH26' a' + 6» 2x« ~ 2a'-26-' ~ a'^^ft^* x*+ 2*" + 1 _ a" xHl x»— 1 a J' 'a -6* 11 40 Hmr» „„ .«,„,„,, ,™a.„„UT. .x„„.„,o«^ ■Sto. 9. 1- Aiiegalivc quantity iuu.lies fl.it rt ■• . ••^- («) -216; (b)2a'~3ah + 4b\ 4. (1) Write -2a for 6 + c or -r2./x.N t i. , pre8«ion becomes zero • oZ,l • If ^ "" ^' ^"'^ *^« *''^- the exprLiot is :;,;/;,;'''■' -^^^^^ ■:^J- factors, and since ^-.. T.ee.pr:::ri:;x.:^;:::;-r--"*^e «.(2,, + (, + c)(2i+,+„j(2 , ,2,rrt ^"'"=''""^ »"•■■" t^^"»d=3 (^) isiniilar to tlio aliove. 5. HamM,„s,„itl,.,Alj.b,^, ^,,t ,2„ L CM. of „Uxe/:lTe "'atd t ■ /" *»-"«■'<' 'ho separately. "'"^ ""* ^'IfeWaical quantitie. e. Hambhn Smith', Algebra, Art. 148 ^""^ 2ab ~ which beinff=]ast *f>rm - = 2a6* ' ° -asr vorm, expression = 0, ITIONS. ftlXTS AND ANSWERS, INTKUMKUIATE BXAMlNATlONtJ. 4_[ a contrary if positive, ependently tity. nd the ex- ;or, and by and since ire all the -3. {pxy px-p^) • tions see find the lantities a + b) , (x")^-l and -— = x^—l 1 " ..'ill 1 Q (3) Resolve into factors and simplify. Result=l. 7. (1) Expression=..-2-2+ * + 2(x - -^)-l + 2. the square root of which is evidently = 3: — - + 1. X . (2) Expression="; + 2 + ^C- !=(' + ') + ('/. " the square root of which is=''- + - • V '■>■' V-2 8. Dividing the numerators by tlic corresponding denomi- nators, we see that x + y + z is a factor of each term, and, therefore, when x + i/4-« = 0, the whole = 0. _1 1 1 x+1 x + 2'^x—4: 9. (1) Dividing numerators by denominators, and then dividing by 2, we have— .•■ + 3 'x--9' _ J^ x-3' from which we find x=l, (2) Taking the reciprocals of each equation and dividing, we have — 125 2 3_13 3 413 y'^x~2' z'^y~^* z'^x~ 3' from whicli x, y, z can be found by the ordinary method of elimination. 42 iUS l\-i A.NO AYS WfiilS, I.NTBlUIEUXATli EXAMINATIONS. 10. L«t x=tho clistance,'^'=,H.„rs of J ^ ''« 4.V =hourfaof 5, but^''~^ 7 2,r + l 2 == f,— +^ whence 2x = 29 miles. NATIONS. 2x~l = 29 miles. HINTS AND /.?;.SWKRS, INTERMEPTATK KXAMTNATIONS. 43 (Statics ani ^)i)bro)3latic0.--^lo. I. SToTB.— The refrronccH are to Kirkkud's Elementary Stattc8. 1. Statics, pacres 4 and 7. 2. Statics, page 1(58. Let a ho one force, and 2a the other, then as in ex. 2, page 16, of Statics, we have, 3. The con^•ol^se of tlio Polygon of forces. Form a quad- rilateral, of which the giv^n prensiiro is one aide. Any three lines equal in magnitude and parallel indirection to the other sides, will be the components. 4. If tlie resultant be reversed the three forces are in -jquilibrimn. Resolve all the forces vertically and horUmtMy liud we have hP^f2-\Q=in i^V:i+i^v/3 =15V"3. from which P and Q can easily be determined. 5. Resolve the weiglit of beam AB into 50 lbs. acting at A, und. 50 lbs. acting at B, and the weight of the beam £into 50 lbs. acting at 0, and 50 lbs. acting at B. Let F be the force acting along the beam AB, and Q the force acting along the beam €B. Resolve P and ^ vertically a«d horizontally, and we have iPV2"-^Q =0, andiPV~2+ig/3 =200; ^ V3 + 1 Now regolve Q vertically and horizontally, and we get the pressure and thrust at C. ''^' B EXAMI.SATIOAS, 200 Similarly we find thru.sf,a^,/>-. 7.50 lU'osh'ire " -12^.2 «• Statics, payea 4!> aii.l HI. ^'-'t « bo tho tension of tl.cHtri,. n , ;^'^-'^'^"taIly, and we ... Jl^ ,„, ,"' /"'"''^■' / ^•^'•^'"'"y-and the reactions of tho vertij,! .11 ," T^"^^'^''^}'- 1V.k1„co /'■ Let ^C'=a and ■""' ^'''^''^ ^'■'' '^'^T ".eet in ■'■ ^ = '/■(^^•i -I) 7. Statics, pages 70 and 74 -":.^it.:t:t:i;rr"'"-'- ^ »< Area of inscribed cirJleJ™?. Let .(^--distance of , wo iirt, of ; then ments igle thu 45 Af^IiC-^a, then l\ KO^^-^Q.CF^Q {a- CE), Binco f'A' --('A' ; If, when tho woiglits are rovorsud, the fulcmn must he p aced at a ch.stance x from C; wo have (IF being the weight or j^ IS) . , ^ (^.CE-PJJF Q-P W-fP+Q ~lV+P+\,''' i\o. 2. The rfiferencea are to Hainl.lin Smitli's Hydrostatics. 1. Hydrostatics, Arts. 18— 2T, 24. The pressure at any point of a fluid is measured by the pressure wliich would bo produced upon a unit of surface, If the whTjle of that uait were pressed unin,rn,ly, witli a ,.res aure equal to that which it is proposed to measure. Uli lbs. 2. Tho wliole or resultant pressure is equal to the weight of a column of the liquid liaving the plane area f..r base and the vertical depth of the centre of gravity of the plane area for height. 6 X 10 in.=area of plane area ; depth of centre gravity=5 inches ; hence, G x 10 x 5 x i-O-'o ^^j^^i^ pressure. 3. Hydrostatics, Art. 61. Let x-w«ight of cylinder, FT^weight of equal bulk of water t^en, x + m^^W- and, x^^W; X Or thus : Since cylinder rises one-sixth of its axis when one pound ig removed, therefore, Ibs.-weight of volume of water equal in bulk to volume of cvlindfir ■ and whon -ei-Jit is removed, it has a tHrd of axis immersed,' therefote, weight =i of 6 lbs. ^%^lro«tatic., Am. .1] ,,„Nfi. cork weighs. 24; " """3 f''<.„ i volunu. „t y>f ,1,'iitta |„>,vli;, ,voi-|, 7>. .,,^ ,. ,, '"-tee, tho .,..,„„ „,,„^,„^,.^ ^^^^^,, ,, Uieroh.ro ..f fhe ball H ..f ■ '"'^^ the level in the cLsK. I , ' '""'""■>' ^" ^-'^ ^"t^" that *his scale will only gi -e 1; " '/'' " '"!"' ^^'^ ''^"^^^ vortical. ^ ^'"^ '^'"''''^ ^'^^''Jta "iien the tube is TVt ' ^^'"^=>vt. of cork; then Since - -,,, , sp.gr ■""^^•'•' behave JL^O , ^^^ loO+w 112^ :2i'^ ~~r~ Jt V=.-volujne, we htva a Lot x-wt. „f „,ip ,„_i ^^_ "> X r X r.ll* n.e.iupri,e,li„„M,,,,iacl.,,,,„,iooM,,,. loSH. n of tlioii lilt (1 t Mil- jorK, C'alJ ■olllJl 11' ut Mi; 10, . and IH'i'pen- h.d tube h case, t if the ivitlent ube is ive huvo >8. I us, UlNW ANU ANSVVKUS, INTEU.ME.MATK KXAMlNAlluNi*. 47 1. Statics Art. 10. 2. Statics, Arts. 29 ;ind 32. Lot tlie fnrco of SOll.s. intersect tlio diroction of P i„ C, tlitn the .Iiroctioi. of the pressure on th.. p.dnt B n.u.st pass tliro,,^']. the point (Statics Art. ;u. Fron, 15 dr.vw B D at riglit angles t<, li A, nuuitin- the direction of |> in 1>. J he triangle 13 D C has its sides parallel t.> the direction o the three forces whi.h keej, the rod A li at re«t. and ar-j Iion.fore proportional to then,. B C D is an e.pnlateral triangle and since B D is jjarallel and proportional to tho aUlbs., therefore each of tho other two forces i.s also nUibs. 3. For the general working of such problems, see Statics page 32. ' In this case 1 and 4, 2 and 5 are opposite; tho problem then reduces to three forces, each equal to 3, and makii... angles of GO' with each other. The counter- balannn-. force IS o. ' 4. Statics, Arts. 58 and 54. 5. Take moments about the edge of the table. G. Statics, Art. 108. 7 Take, for example, the case in which there are 4 pulleys. Take moments ab.,uJ the point wliero the strin<^ passing over tho first pulley is fastened t.. the rod and let r~ distance required from this point then, by the principle of moments, we have P(2* - 1) x^o P + 2. 2P + 4. 2-'P + G. 2"P. Or (2'-l)ic=.2.2+4.2-'+G.2^ From which :..: can easily be found. If there are n pulleys, we have ^2" -J. ..2.2 + 4.2^ + 0. OH r2'-2A"~/ The right-hand member is a series of quantities in .,eo,,,.. tncal progression, having their co-elUcicnts in Arithmeti.al 48 "*""""' "^>''«"' -'-«.'.™ „«,»„,„,, Statics, articles 123 and lao "le lower liiiige . assi H ' ^'r'«'''' ^"'^ "'-^^ "irust on t-o. The forLC ; 2 V;" /r^^^-'*-- of these t'-"Slo thu.sfor.no.l at ^ 4 1 ''V'"" "^''^^^ "^ "- ««-<1000+ 10X2000 3 Denfli.fn 1(1000 I- 2000r=^^ 3.DepthofC.,rav.,offa.«ts,„arolwsurface.8Ji„ T/. , second " ,< ^ •If 10 be the weight of i.»,;f « . ~x+2k 3X8JX81„= "(:^-2 1';' ""'""•• r ''•™ Then proa,,„e „„ „„,„ half of „ .i,,e„2„.„.« , _„., ■> ecual to tlw weight of water , Z, "'* ' °' "'"'* «*'2 = a,'), ; ••• "---=a'^ I^-e«sur.onWerhalf=2«.a/«"'4'^^ ATIONsr. ' be learned ' St betaken ■ horizontal thrust on s of these (les of the and since !e = 8|in. 30. 12 in. 2 be the I'st find f which HINTS ^ND ANBWEM, INTKRft.i:)aATB EA AMINATIOXS. 49 Hence, preflBure on sides : pressure on base ' • So^-Ss ,4-. Or thus :— "^ ^' -'s+h- S. G, of \TOter-l, and of mercury=13|, and «;=weight of unit of water ■ then we Jiave, Pressure on upper half of side = 2a. a.'\o = a' w. (( II lower << due to water = 2ci2.a.-^. =2r»»M» 3a II mercury = 13i. 2a. Pressnre_on Bides ^4(ft3-f-2aM- 13.1 a V 33 ^ ^ ' ~ iW'+THa')w~~ ^29' -lir di-spli d .w. Pressure on base 5. By the weight of the TOlnnio < The S. Gr. of the diamond is less than that of the weights andsmceapparem wt. of diamonds = wt. of airdisp'd4-rea1 vvt' of diamonds = constant wt., Then, the heavier the air the les.s will be the apparent wt of the diamonds and, therefore, the better for the buyer. 6. The principle of Archimedes is ' ' that a bod, nnmcrscl in Let a; = weight of gold in crown ; then w— a; = weight of silver ; hence -..r 4- (w 3,') - *" • 11 •• ''~20' .*. gold . silver : ; 11 • 9 7. 13.39 lbs. 8. Let X be the amount of this pressure ; tho air in the upper part of the tube will liave a j.ressure rcj.resented by ,^xand .his, together with the height <.f the mercurial colnnm 302 wil bethe pressure exerted in tho interior of the tube on the level of the mercury in tho bath, which is equal to the atmospheric pressure, that i.s J 5,. + 302 = r, from which r = 755»i,TO. i 3 ^- i-t a bo t].e den«ity of the ai. at ii.st f?3 .< ^^ alter turns Then.^, = (;o),^^.^^__^^,jj^3^_ " ^ " ' "T^f^ "' '''" '^■^'^'^"•^^''^^^ f-'" pump w.t>, barrel ui 1 foot capacity ^ ::arS.r"*-^"-^^^ after 5 turn. Sin.ilar]y, (), the quantity oxl^au.ted from the oth =-m~iOd, ^^"''^ the other pump Uence, 10. P^ 10^0,7, ^l-_(j.o)5 J) Let ^^=20 foet AG:^17 feet .4i)=10feet Let P be the greatest licight, and lot 4P~:r pressure of aVin BQ^ ])p==iq_Z^' But pressure in 5QK^=33, if we assume that ^' the water barometer stands at 33 feet, .'• pressure DQ=z-^2z~^^ (33— ar) ^ IG— X =-^3 ; Here there is no greatest heiifht „„H+T, . - flows out. ^ ' "^ *^® «'ater (2) When the range of piston is BO. 20~x) (33-;,.^ " J7=:x— =33; , •■• a' = llorf). Honce ^/'^.T 1 feof or f, + riNATXONS. I'St, fter 6 turns " 3 " imp ter 5 turne. B other pump Er Q' D »ton is at niSm AMI. ANSWERS, IN'TRRMEDIATE EXAMIN..\TIr,X3, ^^j i^o. 5. TlfK ItKJTEIlKNOKS ARK TO KuUvLAXd's Stat JCS I. At'l, 10, If tAnn. 13 represented by 1ft Hin .Jill., 24 in., or 2ft. 2 Apt, 2«'}, und Ajipondix, pno-i IG8. \ \ \ \ \ \ r.«t ^/l-2.,; JC'=.„, -, and .1D = « ; then the sides c cJie .mt.yjo y|(//> V ,: i,,,3scnt the f,.rces. Since {\uf^ (''V^/i «^ tiR, H„ /j is a right .-.ngle, and its side« are i.» th« Viiiiuuf'i, ^'3, 1 ; tlierefore the angle ACU is .'JO" and (itnm(iiH3UiiY C'AB=loO''. ' 3. T\m umy be understood from the anahigous case of the action of fcho wind in propelling a vessel ; see exam,,le .'} page 33, ' ' 4. Hm ©Xrttnple 4, page 84. Avmi,f tmngle=3(;=area of square. Take momenta, about vmm ,4 triangle ; and if x=distance of C. G from f ho vertex, w« Imvtf— " 0O4-3(J> = 8x3G-fl5x36; x--=lli. 5. Art«, H<}, 88, 6. Ait«, J 05, lOfi. 7. Lot i'=:the power, and TT^the weight. When pLano is smooth, P= \ '2 IV Wlien plane is rough, F~^''Jjr I! 52 HINT. ,,n A^SWKKS, INTEKMK.UTK EXAMIXAXIOXS. •> = K2- V2) = -2!»2!). 8. Let AB ho thelovov i.wi r* n 3t ...1=^. then r/; = 10-^ .-ma, X. lake moments about 6' nn-1 ,.-. le have ut C, and we iV3.r/'=.UlO-,,.)0. 9. In the figure, exan.ple 4, page G3. f.on. i." d.aw L'.V p.. pendici^irto .lo. ' per- In this case, R^== ^^, 2 Tak e moments about J, and wo have-^. IF ■■AG = 2AK^Ay. Since angle .4 (r'Z? = anWe ^ V/' . • w ^^. then .„„„ ,,«.„„^,„ ^^,, , „,,;,,,,; ;;;,^;^;7^ |To. 6. The Rkkkkkxcek ah. to KrRrctAxn'.s Statics. 1. Arts. 16, 23, and Appendix pa.o i«4, (1). .'AT10\8. he ftilrviiia ; it C, and wo iw IJ\ per. and vl^= lelt.o46'; ^s. HIXTS AN.> AX^WEKS, INTLKMUIUA I C EX. lINATIcN. II ^/3 the sides of trianole ^r/f are in the ratio of P IP j^- /", or as 2, 1, /.3, therefore the angle I>CK=. BAC=^GO\ 3. Art, 42. Resolving vertically and horizontally, we have- Sum of vertical fnrccs-20 i 70,. p,^,^ " horizontal " =20, 3-10^//. resultant « -^ ^/(„..| z/.; =.14..;,.{.8 j.,^ 54 HINTS AND ANSWERS, INTEKMEDIATE EXAMINATIONS. 4. WJien t]u-eo forces keep a body at rest cacl, one is equ' anl opposite to t].e resultant of the otl.er two ; then see L. T AB = 2r, :. AE=^^y3; since angle G'OJS'=GfC!a -30' and GE=hGO'. :. IIG+aE={(GC+GO) = ^; Taking moments about A, we have— 50r/3+10;!V3 =^Fr,(y3+l); .-./''- 69 -73725. 5 Let 1V=wt wliich placed on the end will be on the point of overturning the beam. Taking moments about the prop adjacent to W 4Tr=]40; .-. >r- 35. C. Let AFB bo the rod, of which F is tho fulcrum, and let the 8oz. be placed at A, and the 7 ..:-. at R fATIONS. 1 5 x 8, C. G. lies between A and i'. Let a: = di3lanL0 of C.G. hum A. Taking moments about F 42=40+ WX5-X); 2= jr(5-x) (1). Interchange the weiglits and let F, be the new fulcrum. Taking momenta about i'\ we have 8x5i'v = 7x5}-J+/r(5[f-x); .-.50 =0QW- 17 ny (2). From these equations W^=2oz. '•«;=4 inches, 7. Neither gains nor loses. 8. The weight =22tbs, Let a; = perpendiculai; distance of i(,t from AB. and y= " «• « « ^^ Taking moments about AB. 22x='^-^^^ 4 . - 9/231 Taking moments about AG^ 22y_ 5^231, 10 .•.V=-i^-?y=.345. 44 9 Art. 110. W 2x60x3-1014. 10" i 60 i.iNTS ANO AN.SWm:s, IXT«RMJi„IATK KXAMINAXIONH. 10. Let a - length of beam. ^-distance of C.G. from the lower eml of the beam. ft :=:wt. of beam, ii— reaction of the llior, and J'^friction of the beam on tlie floor Reaction of the wall=- 2' Friction alontr «' —^ . ~4' 4 4 • ■" Taking moments about the foot of the wall (1) •(2), From these equations o— "(^^ + ^ n^S) '" 25 . ur the seg. ments by the centre of gravity are as 43:57 nearly. ilo. 7. Thb Rekkhknoes ake ro H.mb.in Smith's IIv^bosxatics 1. Art. 21. The pressure at any point of a fluid is measurP,! h.. fi, sure equal to that which it :s proposed to measure "^ 2. Arts. 23, 92. IGibs. 3. The pressure of a fluid on any surfar^ ,•« . 1 x .^ weight of „ co.u„,„ „„„„„,,, ^rbtofvZri': '': to the area of the surfac- -- ' - -■• .""'"^^« equal uid tl "le altitude equal to the HINT8 AND A.VSWiJIlS, r.VlKRMeKI.VTR KXAMIWTioNS. 5" depth of the centre of gravity of the; surface be.ow the sur- face of the fluid. Let AC a - length of side of cube. then ^ if =- ft v/2=length diagonal of side, and A D = a ^f3 = length diagonal of cube. From B draw BF perpendicular to AD. AF may be found by similar triangle-., or as follows r AB' - BD'=AF'' - FD'^{AF^-FD){AF- ED) ^a^'3^AF~FI)); :. AF-FD=-^\-= ''-^ ay/3 V3 AF+F.D=a^3=-% AF 2rt a Distance of C. G. of upper side, AB, from. A^\ AF By symmetry, distance of C. G. of lower side from D a a V3' .-. distance of 0. G. of lower side from ^=-a V3 "-=^ ^"' • ^ V3 ^/3 C8 II/NTS AXD ANSWERS, INTEIIMEDIATE EXAMIXATIOVS. l'>it A is a below surface of water ; therefore, disUuico of C. G. of upper side below surface =--«+-?- - ^2a (I <( or, lower << (t lower side V3+2 4 Art 05. NV t. of iron in water =:(j.7]ba. VVt. of iron + wt. of wood 5 -Jibs.'in water ; twoen wrr''^/"r^ "P--1B =1.4lbs.= ditrerence be. twcen Mt. of wood and wt. of equal bulk of water • .-.wt. of equal bulk of water=71b3 + 1.41bs.=:8.41bs. Hence S. G. = -?- — ? 8.4 0' 5 S- G. of cliain = 2000 153"' t-_v(jl. of brass ; and «i=vol. of rj'.Id J then 7. 8. + 19. 3.,=--°%, + ,, ). from which we find vol. brass: vol. ^old; : 9529 -8006 6. Art G7. Wt. of metal=l4.85 grains. When the metal is placed in the lower cup 2.03 grams aTbefore! '' "'"' "" ""*"'""' ''"' '' *^" ""'" ''""^^ therefore wt. of water displaced = 2.03 grams j hence S. G. of metal = -~^ — T qi u 2.03 ~'-^^ 7. Art. 80. In the first case a litre of air=. J^^ x 1.293 grams, second " « -!,^x 1.293 « ~a-\ , =:8.4Ibs. HINTS AND ANSWBKS, INTEKMEDIAIE EXAMINATIONS. 5,, change in weight ==-^^J~x 1.293 - .Ol>5 granis. 8. Art. 71. Wt. of cork=:^wt. of WiiterdiBi)liiced+wt of airdispkcocl ; hence as the air disi.hico.l by the cork diniiiiislies, the water displaced must increase ; that is, the cork will sink in the water. 9. Art. 86. Air, like otlior fluids, transmits pressure equally in all directions; therefore, in this case, a iiressure of 771b3. ia transmitted to every 3.5 .s(j. in. of the receiver : pressure on every sq. in =77-i-3.5 = 221bs. total pressure in air chauiber=(22 + 15)lb8.=:371b8. 10. 15 lbs. pressuie -- column of water — -^^ ^ ^^ == 34.56ft. high. ^^^ and since the volume varies inversely as the pressure, we have — 34.56: (600+ 34. 56) ::2: a;; .'. a;-=36| J cubic inches. ilcr. 8. Note— The references are to Kirkland's Statics. 1. The force of gravity diminishes slowly from the pole to the equator. A mass of matter which would compress a spring with a force equal to that of l'J4lbs. at the equator, would act upon it with a force of lO.olbs. .-it the poles. This difference would not, of course, be perceived by the ordinary raoae of weighing by the balance, as both weights of the body would be similarly and equally affected. 2. Articles 2, 8, 9, 10, and note, page 20. 3. Article 23, and Appendix T, no "INTa ANI, A.VSWKRH, INTI' 4. Thorosnlhuuofauytwo-oftho 'tMKMrATE RXAMlNATrONH. posite to (hoothurf. >rce. "rces is equal uud op. the para] lulo^nun. The J iT V p? " ^*' '""^ -""'Ploto 5. On each post tlio rosi.ltai.t prosHure is '>()() n towards the oeutro of the drclu. *' "''*'"« 2P(;> = 62^-28' = 80x24- 8- Let P, g. ^be the forces; then we haveP^g..^.. and ^ = g, fro,n which the required ratio is found. 9. Produce the wei^lit hack\v-irr1« +;i7 •. point 0. From B druv /?).?! /* """^^^ ^ ^^ the three sides of the t^^l'sCD^ '"'''' '' ^^' *^-' ^^e and direction the threefo^f J ,7"";^ in magnitude rest. ADk bisected in ''%'^^!"^'^ ^'^^ t^e rod BA at 30Mshaifth.h,;;:;t:3e'^^i;;;r^,^t ;^'^t^^*^ *^« i^^^^/> is equilateral, and hence V "' !•"''' "if *"^^«J« = DC,= r, = 50 lbs. ' ' ' '''°*^°" ^^ ^^« l""ge, 10. See Ex. 5, pagt; 26. , U)il uiid op. fin'l 14 an.i 1<1 COIllpJoto !,' fit 120' is tlio 14, and imi'iii AM, ANaWKRM, INIEKAIUUUTK KXAMINATIO.N8. Ul i\0. 9. (The refeiouuea uro Kirkhin.l's Statica.) 1. Art. 29. 2. When tho woigl.t is vertically over tho centre .,f fI,o Btieot, complete the i,u.allelugrann,f which the adjacent .sides are eac ..5 One of the .lia.onals <.f this parand..,.. the wu th .,t the street 50 feet, and the othJr, which cut at right angles, is f..uud t., he 20 x/r Now, if the weights 20 I/O-, tensi And «i II = 1, - 8, i« -iJi) ; 35 :J0 4/0 20 4/0 ^ _J4 3. Art. 38. Let AB be the .iven force. From A draw AC, making an angle of 00" with AB ; and from B let faU vhicTTifjSr"' ^'';.'" ^'' ^^^""^^'^^^^ *'-' -tangle h ch Al, BD are adjacent sides. The adjacent sides of this rectangle terminating in A are the rcjuired forces. 4. The outer cords evidently make angles of 45° with the horizon, and 90° with each other. Resolve each of th hine cords along each of the outer cords, and we get 100+50+50^ This force makes an angle of 45° with the vertical Id horizonta ines. Resolve vertically and horizonfln" The X": "'^^ "'"^^'^'^^ ^^^^^ "^'^^ T^- vertical com- 2 / 150+50 4/r\ ,_ ^ V 72^= ;-(150+50 4/r)4/r=334. There is 18 cwt. =1800 Ihs actMi<- -Imv- ,..>. ^ x, ,, , . ,„„„ — ''•' •^•»f^'''fe aowiivvards ; theiwiore the 8train=1800-334=1466 lbs. '-^'«*we, 62 HI^X« AND ANSWKUS, INTKUMK,.,AT.; KXA.ii.vrio.N-.S. enouJf:;d:!:rfujV''' '":'""•" ^^'" ^^PP- evident . Dy dranmy tlie tigu,e uad carefully examining it. / 6. Art. 63. ^ 7. 12cwt. 8. 304 lbs. Mo. 10. (The referei..o.s are to Kirkiand'H Statics.) i. Arts. 2, 18, 20. a ^ZZ ^- .^ie'^^ f ^'^^'; ""^ ^ ^-*- ^e have then ti-a. r.eet;:;;:rr;:r ;:;;:^ force requu-ed, then by the triangle of lUr^ " ' ^' '^' J\ _ .'{00 lbs 3. The fourth force will li.. ..,„... i, i • direction by GA. '^'P^'^-^fntod .n magnitude and 4. Ex. 2, pa,cre 32. Resolving vertically and horizo„|,dIy we find fh tude of the resultant = 52-44 • the df.' T . " '"'''"'"• ant cannot be found without 'a 1 '^ '^' '''''^^■ . ^ ,. '"'^^^'^"'^ -^ '-'"'^^J^'^Iy*' "f trigonometry. o. xtesolvinf vpr(-i(>'iii,, .... i i • braic ™„. Of «r:vr ■:r„:;;!„,';;:ir:'' 'i:'^'>__r r r'^'°- hence the resultant will bo lu.K. .i . 2 ' and .ts .nagnitude= ^^ "'^''"" "^" ^-"'^-^ 6 and 7 J Since the horizontal comr onont-l ./- i .i , = v/3, the adjacent an^le is he J^''*;.?'^^ force 6 makes an ^^\^ ^^''^ ~ ''' ^^^■*- ^8) ; the lino the resultant will there o.; [ ""« «^'»« horizontal angle of 90^ " ""^'^'^ "'"» ^^^e force 6 au VTIO.N.S. •ear evident lining it. '.) ' have then is 20 feet, • i' be the itutle and le maorni- o le result- nometry. the alge- algebraic 2 "' and 7 ; >thonuso J«); the >i'izontal 'CG 6 an HINTS AXn ANSWERS, INTERMEDIATE EXAMINATIpNS. G3 6. The wt. will divide the rope into two parts of 6 feet each. If the parallelogram of which these two parts are adjacent sides be completed, the diagonal will evidently be G Hence if the wt. were 6 cwt, each of its components would be G cwt ; but the wt. is 1 cwt., each of its components is 1 cwt., that IS, the tension is 1 cwt. 7. Arts. Dl, 52, 63, 50. 8. Take moments about the point of the lever which the finger supports, and wehave Px>2=--10xGoz. ■■• P=48oz. The finger has to support the G oz. , and the 48 oz. , or 64oz. the^'ra^ih"' '"" *'' '"' "'" *'" ^"'^^^^^ '''^ ' « '^'^ ^rom 10, Art. 50, 45, 46. "* 11. Distance from the side of squares '73840. c< St til 8ti reti in niu gaa in a gre; agi Buol, 8 Of A HfSfBJ AMU ANSWERS, INTERMKDIATE EXAMINATIONS. m I. llimno, pntjoa 140, hV?. Mo,a. mi,,ut i« the smallest propovtion by w^.„,., ;, «^mch m «l«,„ont enters into or is ev, ellor] .• V" (X) In mixiug oxygen and nitrogen in their nrmp,- „ -i Proporti,m«, «dther change of voluni. nurhelT,, ^ '•'"' rnultiplos thereof "oimng weiglits, nor any .__ W n, „.rt ,„ tl,o p.,,p„rti„„ ,n „l,ich they are o„„e.i„<„, g^tou,,',!?" ';"';'"«"'y" » ^-I'loyed to indicate ,l„. LJi';t''''"« '''"■■"'* ■-j-"i.-ofth„ G(J >^'NT.S .NT) .KSW^,,,,, INTKI^MKLUTK EXAMINATIONS. to...^:^ V t r ^^ cube Of hydrogen, .tthe standar4 be borne i;^':r^i:r^""^"^^^^^^ *'^^^" *^''^ «- to calculation a. a ;Zn:;^"i:;r relative volinue-wei"ht of .1,1 ; • "" '^"^'^'"I'l^S the 16- that of n '"-'^^^*^;'^^h^«ri»«bein^r35.o; that of uxv.ren if. that of nitrogen, 14; the actual weier is formed (CuO). '^' ^. (1) Koscoe, p. J8. (2) 4,1,1 ■,;,>, , .i and boil; „e Le 2,^^^^y„^ ^l':"*-" '-''■>' oxide)-fH2. ^^■'^"-^^"1^2^>2(lJotassi.' 7wcic NATIONS. the standard, ij griunnie; a with a sliarj) pr()l)ably nu I tlii.s one to 'ss for ujQ in xanijile, the ■t of oxygon, litre of (>ar']i 18. pressure, ths, and 1-/ ;ht, we find y is known: nore atoms 1 presented ). 'ertedj .lO »t'e or less ion of an wit]) the (re,OJ; ic;->f'-.ash 'I' 7Ji,>cic 4. Towards the end of the last cfnt,,,. i • • The mercury eomb.ned witl, tl.e „,y..e'„ . 'T ' ■^- li... subject „iU be ,„„„,,,, „ „„^, ,„„__^, , ^^^_ 9. 126 ' ••• 1 ton yields Jlii tons nitric acid 2HCH-Zn=ZnCl, + H,. 1 litre of hydrogen weighs .0806 gramme. .0^)6 1000 «« «i -'oOj<^^ 089(5 1060~ "''i'""!®. 1 cubic centimetre 250 (( are dissolved ; "^ . .■.taev„lvi„g2»-»« „ 06 260... „3 grammes of zinc are dissolved. ^^ oo,..bi„i„g „„„.,, w !„"' ;::,'"" "; I»'^-'r:;:;i;::- (i8 HINTS A.VO ANSWERS, INTEKMKWATE RXAMINATiONS. ZT"1 ^ ?.^' '* ^ "^' "^" ^"''' "^ ■■' ^^i^d element, l.avi„. wo boruls «....e and two latent, cabined witb and s;tisfyi " 1. See Examiner No. 2. The molecule of water (H,0; is 18 gr.im« Hence 18 grams of water yiek! 2 grams nf ..drogen 1 " Jill " ^"d 1 " .8889 - oxy.<>n .« gh 089J6 ,rams. Then wlut volume would .lui " ml < 'f Jiydrogeij c w. upy ? ^ "'* Ther..uHi.l2t3.28cc. of hydrogen ajic icM.'aa ce. of oxygen 2. (2). 2MuO,-j.'>.a,SO,=2MnSO,+2H,0+20 ItisusuaUo say that the Manganese Dioxide let. by Catalysrs winch refers to the phenomena which takes ph'e when effects are brought about by the mere presen e o ubstan.o w^^^^^^^^ undergoes no perceptible'chan " { this case the KCIO, .s decon.posed at a much low^r tem- perature than would be required if MnO «.„ yeUhaM„0. is found, iX^^CT ITT' '"' state a. at the com,ue„o.„e„t. It u.iy, Zl" ^ZZ t.mp„rary alteration. We know that this MnO i^Zlllt H.MnO,), and .t is possible that when heated witt KCIO state of the higher ox.Je which is immediately decomposed the oxjgon being evolved and the MnO, leturiiin" f?!,' onginal state. This same etlect is noti/ed If So Z mixed with C„0, Fe.O,, &o., «„ of which .re k,™ t'o be susceptible of higher oxidation. The oxides of iS™ 1/ ne.u„„, .Vc. , on the con,,,,.,, „,,;,,, j„ „„j ,,^,^ fc-^^er o'xWef ni vo] un; aci( hyo s'.VTiONS. lilst in cnrDou Tient, liavinir ■nd satisfyidg roffen. id 760 rain., 20, ie acta by takes }uiioe esence of a lange. Ii, ower teni" ■esent, and the same undergo a is capable janic acid th KCIO3, iss into the :omposed, iiig to its ^ClOg be 'wn to be inc. mag- do not facilitate the deconxposition of the Pota.siun. Cliloratl 8. Cold sulphuric acid has no action on copper When heated, the action u.' du, copper on the sulphuric »( !d, IS in-.^bably lirst of all "'pjuuic Cru + H,.S04=CuS04 + H.,. But the lij-drogen never escapes, for at"the moment of its H, + H^,S(),=MH.,() I so,. So that the gas actually e^•olvcd is sulphur dioxide Nitnc Acid is what is called an o^udhh., aneM that is it readily gives ud nart of \i^ - . '' ■ "' ** ment and imi , V "^^■^'"" ^'^ '"^'^ oxidizable do- nieni, ana IS tJuis broken up. Zinc mm-,!, „,.,.,. ri . • . acul gives the following reaitio^f" "'' '^'"^^ '"^^'^'^ 4Zn+10IlXO3=4Zn(XO3),+]VH^I,^O3+3H,O ' With moderately dilute col.l nitric acid we have •- 4Zn^-10HN(),=4.Zn(X<),), + x„O+oI-l,() ' With somewhat less dilute nitric aci.i, we ..et •_ 3Zn+8HN03=3Zn(N03), + 2XO+5HoO Concentrated nitric acid dissolves zinc but sli.htlv H nitrate being very sparingly soluble in nitric acicl''' ^ cHo. 5. 1. ^^/f«^«n. -Water dissolves a trace of hydrogen- 100 volumes take up 1.03 volumes of the -.is its ZTf^ I unailected by the temperature of the s:iv;nt ' '""^ ^^^^Carhon dioxide combines with water, forming carbonic CO.+H.O^^H^COg. Ammonia combines with w')f,.r- f , • hydrato. "^' ^""""^' ammonium iv oxides, NH3-f-H„o = ]s-ii r m. 70 Hl.vr.-i AN/) A\ WKli f'tlrhtm carl)oiuile.~\\ 'vn;:;MKi.rATEEXAMryATzoN». tity uf calcium carbonatu, about 'dtvv dissolves a V ■«ry small quan- Hcid. ZT carhonate, about 2 grains in a gallon "''^"'•''^^'''^^""'•^-- -t^-vate., forming nitrou. Sodhm a.id rofa..in,n eacl. rcp-ac- one atom of th. T Na2+2H,0--r.o>T.^On4-iT 0+0^=003. ^'" ^'"''' ^''''^"" ^^'"^"^«; Sulphur bunipil in ru-, S+O.isO,. '^-''" "'^'^^ ^^"Ji'J^u^- cli<.xide; Phmphorm bur.ied in Oxyrren ryivo^ Pi. 1 ido ; P2 + 0,,=^l».,.0^. ^'^ ^ *• Phosphorus pentox- results, but distinct intclio ^ greemsl.-gray powder but also by stirring sonLf tl ';; ' " "r"^"!^ ^^r' quantity of water, when the 1, •„, I . -o"«iclt.able quickly to the bott/nn of tiLtlljrr^T /' ^^"" '^" more slowly subsides and o<^^ T ' ^'°^'*^"^' ^"^I'hur heat the .u;stance ^^'r " 'V. '""^^^^ ^•^>'- ^--■ mixture beeon.e p2 ^ f j^" ^ "^"^ "^ ^-^^ glass; the Cool and remove the ."h" f '"" '" ^^ ^'^"^* *'"^^- When exanuned ^i^l :: "f ^"'f ^^"^^ ^-^ the tabe. or sulphur ean be fef "t h' •' "^ - P-tieles of iron longer separable by n^^^i J^ ^ ^^^^^ ^ "" Phur have chemically combined u 1 " '""'* «"^- iroii sulphite. ''^ ^''""^^ =^ "'^^^' sui.stanc., ao int ■^Nv ATIONS. sJiiall qimn- 1(H1. liiij,' nitrous of tlio hy. ,' t]it' liydx'i). 1 flioxide ; '■ dioxide ; us pentox- » ; Na^ + O ibout two- ly powder 1 he easily -'iiig glass, ii«idtiable iron fall i" sulphur or. No^\■ :lass ; the •rt time. ;he tube. -iS of iron r are no and sul- i^As tunes, ai«9 ATO ,«»WE„., ..VrERMEnUTE EX,, 1,NAT„™. -, ;i-,..:ir;,::-,^^r:::„:rc;:;;;rzL:^:rt Lovever, the nnxture is fa-cd, the three solids di appc-t -'1 -e sudd.nly oonvu-ted into an enonuous vol ol gaseous n, u'ter, the new substances produced possess "." l-;es .tany di.Inct .on. those oi ti. .L, ::;Zrr 4. Roscoe, page !)2. (l).^iCu+r,HN()3 = 3Cu(xXO,)3-f3n,. (2) SH^ f.2IIN03=2KO-i .tlJ^O. 8. Ammonium car])onate CNFT ^ nn i a-. . Hvn • * ^""'''^> U^n.,;„o(>.j and Citric acid Hi>()3, give Annnonium nihvite Nil NO /i ' ,^"^' acid. ' ^^^^4^'-':i' •■^iid Carbonic It resembles oxygen : ,^^J1) In rekindling a glowing chip of wood when plunged (2) In supporting combustion with nearly equal energy It differs from oxyuen ; (1) By being nuich more soluble in water. (2) In extingui;dung a feeble flame of sulphur. (3) It does not form red fumes with nitrogen dioxide i^yjj (4) It is not ab3o:l,od by potassium pyrogallate. 72 HINTS Avu A.-.SWKU,S, INTKUMKDUTK EXAMINATIONS. (5) V/hon i.h„s,,l,nTnH is inmied in it. the ..sidiml ^aa is of tl.o sa,no vul.MMo as the original gas. ^ glass rod n.to nitric -id .,.: hdd it „. t,.o l...tt J 'repeat MS several tunes, and shaking np .ach tin.e. N.,;/! t tie barunn cldoride, a white precipUate will appear, sho v ' the presence of sulphuric acid. ^ 10. Add hydrochloric acid, and filtnr. each oir^" ''"""*' " '^'^"^"""^^^ ^""^^"- directly with NH4+IIC1=NH,C1, .S + 0o==S02. (2) ^^J^^n compounds are split up into their elements or into less complex cump..nents. «^"aents, or HgO = Hg-i-0. KH4K03=:^,0+2H2O. anothl'r l^'^'"/'"' ^^^^"^^'"^ or group of elcn.ents displaces dnoiliur ...ement or gr.nip of eicnuiits. 2HCl + Ko^2K01-| H2. CuSC)j+Fe=i'e:-()4 + Cn. (1) When elements or groups of elements in one bodv ar^ CuCl24-II,S = CuS + 2HCl. KiV(), + H.80, - I:H,S0,4 IIKOg. (r.) Vvhcn t],o elements of a compound are re-arranW an in tlie conversion of starch into sugar. T 'i nol i exun.ple of tliis in inorganic ci^omistry """ ^'""^ noNs. id mil gas is 8ti]])luir iji ttlo ; dip a 'le ; repeat New ;i(ld a .r, allowing y be classi- ectly with uients, or HINTS ASU ANSWKK.S, IMEUMKOIATR KXAMZ.VAT.VVR. ,3 So. 6. TLo ann^vors to nearly all the questions on Oherniatrv will ;>e_f..u.,d.„thet..p...edin,n«n.^...^ produced by the ovapon^tiou ^^ir'u^ ^^d^'^'^r^'"" vaouuni. On removin.r fl,, r "''"'^'- '" '^ escaped fro.n tl^^; "^ ^.^ir^l 'l^ "^"^^ -^^- ^ioxideand carb.n d.ox^e ti:^" , ^t^r^^^^'^'^ur bon dtoxide was elFocted at a teu.pera ure , ^^^f l ?" a pressure of 4 to G atnioHplK.v.s This inn 1 K ' ^* was tlien passed along a tube ab ut L ' "''^'" '^'"^'^^^ in. with the air-p^aip ; 1^;;^^^ puuipsthe carbon dioxide soli lit ^n ;'"';"';; ''■''' *'" of this tube a second and si' tul "' ^' ?*"'" wbich a current of oxygen et 1 " ' T'''' *^""^'^ be passed. o^uiij, vtstej, can displaces body are another ran/p-j^i, ao good 41 0. 7. 1. Set TxAMixKR for Oct(jber. 2. See iiXAMiNBK, page 204. pLorcttod hydrogen „ , ,1",. , '"",'"■' "'"""'■ I'''"" I'.iitained in the -loi.! „r ,„I 1". '"" «"'"'' »"■ cess yields an ino,\ofou- ^nr, : ■»^^'^^'-'.. Ihis pro. ^JKO*i i ii U— ii., mO , ; H. 74 HINTS .N„ VVSWEHS. mTEKMKUIATB BXAMIN. rU.NS. 5. 39-04 parts hy ui'/.^ht , f ,. < -Kliun^ Hn.1 7-01 pLoM ,.•,''; r'"''' f'^''-'^-^' yi-M tlio ,u,..st, aodiuui will '''""' ''^'''"'" "'" yiold the lea«t. '"'"" "^'•'''' ""^ I^^t'^-^ium v.ill 0. '';^""ExAM;.N,.Kfo,y,vomber,p. 2f)l. 7. .Sou E.VAMiNKii, r»ii"( ''"n \\\ '» -ir, nitn,,ua will be Fn th' \'^'" '"'^^'"'^ '« »'•""* two vol.nnos of hycu'Cn T , ^ '^'^ oo„.b,.Htion ..f ii^iuui^en and onij vo imw. ^.p waor ,,,,,1 „,„„i„g „u„i. „.,„U,„«I ,i ,;7f" "•"■" '■■- «-M.i:u.».i.,M „f „a. c,„„;,„.i.L„ „;:;■:;„';"'"'' ^'^ '"" toriuetlKids of obtaining }..,-). AMiN^K, present number ' "^ ""' '"'" ^'^*"^' ^'^^ ^^- Oxy^'on inay be obtained from vvater- (It By electrolysis. (2) IJy passii.g stean. and chlorine throurrh n ^ w porcelain tube : t.m.ugh a red-hot 2H,0 + 2Cl, = 4HClfO„. S>- Ihe impurities of water are either ^l^ • organic. Suspended matter mav be 7 "\'"^^g'''"'« : (2) See EXAMIXKH for May, pa^e 158 "' ''y «If 'ation. iO. In 1772, Rutherford discovered nif,. Priestly discovered oxvgen Fn l^i T "'"' "'^^ "' ^'^^ air consists of a mixture of* ih -^'^voisier proved tJiat 1 volume of oxy- irand /"r' '""'/^ *^- P-portion of ..^ainderofthis^-j::.^,tz;:^''-'"- ^-- ^l^AirisaW.n/.....,.Jll^^^^^^^^^^ other gases, as proved by the follow ing':;;:^:;^:?^"' '^"' (1) On nuxing oxygen and nitrogen in th.ir " serial ]>roportions, neither cjC'f ^'"'''^' i^eat,norolectn.;yresu^:''"''^'^''^^""^"- ?-nf' }KU-tH of u vohuno of lithium will Jtussiuiu will ^Ji'ir is burnt luir dioxide. 'Jiibustioii (if •xyi^en pure >t, lnuvevur, ii;i' gave the :or, see Ex- a red-hot 'ganic; (2) ■ tiltmtion. u in 1774, ft'ved that portion of Tlie re- ur Miller. ygen, and Lis : ^' prouei' ume, nor vi/., us 4 of nitro'-en to o..,. ,,f „ ' acd, ,ro„, alur.to„, „„„„„, ,,„ ^J:';:;;;"-"'*--"'^ '■"P'-rio 'lii-„„gl, tl,„ burm, a, t,,,' '"''.'" " *"" P""''"'"- nnd ...ch ,l,„vi„» pV^idl 1,: " "' "'""' ""«"»'-b- liKvted, +1 • '^ P'linuo becomes tho centi-o ,,f ,. r i- throwing out its luminous puls.n , radiation, Tlie .sparks laat, however j^, f '^'"'^" ^'^ '''^•^''y ^li'-^otion. n-entthecha;coai:;ir;;;;r";''^^ particles succeed whir}, h "x^;^^on. 00,,.^ although the s ikJl . ' '""'"^ "' ^"••"' --«1 J-'"-N spaiks are evanescent, the light is continuous ^- Koscoe, page 4f). w^NWcs- of the rws.vn/. ,/ . , "■7. 11. Deducting 3 per cent, from m grams, we have 145i grams. From every 100 parts of puro calcium carbonate we obtain 44 parts by weight of carbon dioxide, and therefore from 14oo grams of carbonate we got (i4-02 parts of carbon dioxide., l^ut a litre of carbon dioxide weighs 22 criths or 1071o gi-ams, and in U4 02 grams there are 04 02 .- J •9713 ^ ;}2 -4 'IONS. ims of sul- ?, MnO., equations ■ill precip- tala of the ddition of im belong dioxide, le volui.ie >f carbon probably HINTS ANT) ANSWERS, INTERMRUFATE EXAMINATIONS. 77 litres at O'C, and TOO mm. pressure, which at 745 mm. and 15°C. will be increased to 34 '8 litres : 32-4x760 X 288 745 X 273 which is therefore the volume obtained. 34-8 gaseous Lve 145| :)nate we herefore : carbon ' 10712 .3-32-4 ^. I mtms AND ANSWEKS, INTEHMEmATE >,\AM1A ATiOftB, I. nm nr,f,e« to Canto I., Taylor's ed., where tlu,- cuunivu,. 'm of the 8penseri,ui stanza is fully explained, and «.>,„« of tl»0 wr»f<)f« named. i/i»ibjc Tetrameter. 2- See flnalysifl of each canto at the be-innin'> of t!)« „„tc« W tlwfc canto, Taylor's ed. '« '"tt«t &> Hyo notes, Stanza 16, Canto in. 7- A») o/;;>c/irc writer pictures and describes mtv.-ard ///> M }>|*re«,ml by the sense or realized by the inm,ination. lU, «t*«-'U* *hno8t exclusively on sceiies apparent to an ..rdinatY o >»«rv«r *nd does not trou])Ie himself with the jrroat world of th..Hiiht wUhin. The .nhjective writer on the other hm^ imtmlnfihe ontwanl sense, dcscnbes the variou.. f.elini mil tU>,it^hta which it occasions in the mind. H. TMuK the lines in order, the first is an example of (f^, V>n'>rm, Of the fi,;ure by which is meant the saviu^ of fh»fc ^mh «j|pe»ri, foolish, yet is to the point ; other oxan.i^leH ar.^ Cn,«| knulness." " A pious fraud," etc. The second in m "*'"i'7 *; Metonymy, the eflect being put fur the cuu*.. ; dm Uurd Hi AUUeraiion the fourth of I'Uunusia Ho. 2. 2. fn the Spenserian stanioii Scott refers metar,hoi ically to th« prominont qualities set forth by the incidents in the c^nto of wUwh a forms the introduction ; it also serves to .o„n««t tho (WJitiment of the preceding canto «it}i that (,f the follow. »ng Sanuiel Johnson w^e are indebted f«i- the Rmhl^ ajui tlie Idln In Scotland,Henry Mackenfrio and a number of crfJiers con- ducted tho i/i,Tor (175!)j and tlio Lou.uger CJ7(■;o^ in tlie aid ormances iden was tumbling diminu- al sense. I St. 12, go. 4. 1. Note the following diiicrences between proeo and poetry : — (a) They differ in form. 1. As to the words employed. 2. As to the arrangement of words. 3. Poetiy permits the largest possible use of figures of speech. 4. Poetry has generally a certain nu^de of presen- tation peculiar to itself into which the words are thrown. This is called versification. {h) They differ as to the mitimmi- 82 HINT« ANO AN8WKKS, INTKHMKnXATE KXAMINATIONS. In poetry this is alway« n.ore elevated, more im lussK.ned, and n.ore imaginative. -i>e MiUe^, ' liheioric, a Bred to no business, &c.~.Hysteron Proteron. The order of thon.ht is reversed, and ti.at is p„i first which should come laat. ITIONS. I, more im- ~Ue Mille'a ' hat is puJ 83 B1NT8 A^'I, ANSWERS, INTERMBnUTR EXAMINATIONS. English (grammar. -ila I '•b'li , lue special terms, crepn «/d <./.•; ^ ^«-, etc., ma,^ boy, cow, Lm eir / f'^'/^'^^«' ^'"J/" o. See Mason, art. 170, etc (another r>irH-) T i . I ^ ^"^""^'^^ ^o'^'es him ^''' allfL'"" ';""' ""'■"'• ""™ "« --^ »P-W"? 0. m^f i, generally „Be,l i„«te,„l of ,„,,„ „,. ,,,,;„;. (1) After adjectives in tlio siiperlativ.. 3- Gouerally after .svrwe. 10. (d) TJie antecedent of flimr ;„ i i ".e,U„ «.o singular n„,;Lr „,„;'■ ' "'"^'^ «-"■ wl.ich i. 2. See Art. 83. 4. See Art. 402. 6. (a) See Art. 202. |To. 2. 84 7. In (/') Loving is a verbal noun, (c) Loving is an afljoctivc; (^)P.espocting is a participle ;! Jf="''taining is a verbal noun. (OSpc^King is a participle used absolutely. See Art. W Pa,...i fro„, Lat. pangere to fasten fix • Fro pangero, the Low Taf f '"■^^on, nx . From Pli«Plete is - that of r state of fulness havin,. no deficiency " it shouh n f v, co^^red^Good usage however, permiLfirm^^^^^ rt»; 'n.srs ..v.v,. .,,wEn,s, i.v.khmkdiate KXAmvArio.s. S i^ ll!7' '7 '"" "'^J"'^ ^'^^ verb should 1.0 pJurtl ,'^; It the antecedent. „f wJu. he T f].,. (.) *-;*«»"l'Joc.,„ra .i„,ul„,. .,„a oo„„„eWby„„r tlio vorb «l,„iil,l be «iiij.ulai- "10 ilH a Kit ler form ,.f il, . •'-'„<»JU Who should 1)0 whom becuuso th^ ^u- .• '■°- '"":;: T"? , ''''°„'"«"'"™ « '«<- after certain WMI,,,,-^ l"'-™-, "without its sign "t„" » J<.-,n,„Tow. In Early E,i.rli,l, '• t.. w;". a no,,,., t^ r„™;'t, !;iv™...*TbbS Mcdc..s^;ear.«H Grammar, Art l.)0) ^'^'''^'^"^ ^«r/yfo^.«i "Toisaprepositioi^- .V,^a^o.,o-n,a>d.^o together for a nonn. 10. ^- is in the Subjunctive mood. Art. 195 rhere is an adverb of place TJu^selr^i, in the Objective case after deemed P-. ,s objective complement to deemed. Trf 301 ('•) Pageant-Metonymy. ^0"glive....Jaine,s-ExcIamation. You --E„al]...; dS T T''"^'' ''" ^^'^ '^^•"•''^l- uii..,^c -Dehiute fur li.deii.ute pronoun. HINTS /\|. AN.SWRKS, INTKiiMKnUTB KXAMINA rIO^S. ^J Thc> mean, .disflainecl— IJy|,i»ilage. Tower -Synecildclie. (rf) Quaint, Lat. axjnitus, known, litjstage, oh and sede.o. The 'li' is prosthetic, Tl has no connection with hostis, an enemy. Ho. 4. THT:; i;bkeHJSNCES AKB TO MA30.> is OUAMMAB. 1. Arts. 52 and 53. i^'or alms, summons, eaves, riches see art. 00 ; fur dir' Banns, costs and iveeds are plural. 2. Art. 288. Connectives include all words which serve to join sen- tences wliether principal or subordinate, and tluia include Relative pronouns and Relative adverbs as wollusconjuiutions. 8. Arts. 114, 115, 4. Arts. 33, 200, 183, 247, 227, 5. A Phrase is two or more word.s correctly put together but not making a statement. Thus, A man of wisdom will succeed ; of wisdom in a phrase. ThiH is made at the i)lace where we carry on our business ; at the place where we carry on our business is a phrase. A clause is a subordinate sentenca Art. 313. 6. See F relimlnwry Notice, page 3 7. (a) Such should be followed by as in tne clause with wliich it is connected except when the clause ex- presses a consequence, when that is employed. Hence ivhich should be replaced by as. {b) Since either is singular (art, 175) its predicate should be .si'igular. Hence are is incorrect, it should be is. (c) Supply ^/if. bofor^ propagating, ororait o/l>df--i\j vic€t Art. 470. IMAGE EVALUATION TEST TARGET (MT-3) "^< (A 7a 1.0 I.I 11.25 !ri^ IIM 1114 as, lliio Ul us 1.4 1.8 1.6 V] <^ /i / cW OS. Hiotographic Sciences Corporation 33 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 ■£" iV :\ \ ''\ «>.^ ^\%\ ^^ ^ .ts •1^\ ^ i I (rf) 7mfan«.v is a rep.titiou of as soon as and hP„co should bo oiwittcd. ' "''''' (e) TJus «entonc. co,itai,.s the "and t.Aic7." error ihi« error is f,.und when the words "and 7/.A;VV' -en.ph.,od'• 't.sused HI oertanr combinations to form adverbs and prepositions, as beneath, below, beside, &c An,-u.s ir.uid-book, Art. Ma. HINTS AND ANSW ■,H^, 1 N ! KK.MEDIATK KXAMINATIONfl. q„ Bo. 5. fNoTB. — TnE Rrfkrevcks aw; to AI a son's Cham mar. 1. Comnare tlie exproaions : " Tho ki.ij.f.s pictuvo " -.v.u] "The pictnro of the kitiu;' D;AVof theLord." Tlie Lord's L»iiy ' aMil "The 2. For the thres relations expressed by the objective case, see arts. 79 and 80. 3. Arts. ;88 and 105. Tt is so called from usually occur- ring in subordinate sentences. 6. (a) James "vorks better than he does. (6) John loves James htlter thmi him. (c) John, than whom a truer friend never lived, died. (d) The house, wliicli you purchased, und irhich Ilhought so cheap, catiyht Hi-c. (e) James is as good as I an- at algebra. {g) Robert considers him r/s ijoml d.-. me. (h) John is the older, hut James is //(,.- n-i^er man. (t) JFoultl thai wars would cease. 0") He drove .sj,';t'//-/uv/,/ of cattle to market yesterday, 8. (a) Other should be f.-llowed by tliun. The sentence should be "with ho aid but the notes," or '' with ho other aid thau the notes. " (&) No should be nut. (c) It is not correct to say " wo had read." It should be " we m;w«W sooner road," &c. (d) Our most caruful writers, when speak inj,' of inan- imate objects, use " of which " instead of " ivhose. " «»«";" How c.„„„,u,fi,.„.,,„,„^„,., <«*-• when opeakin- in hvlk. (9) Rend ^'ofarcrcomhunf," fo ,„al-o fi corrosnond fn fi , ''""'^'^'^ ^^'e construction respond to the fanner part of the sentence 0. Co.t..as^,W. and the par.n. beco.es evi- that gallant pa,,(i,„e. » r*«(i,a,„I,„rion,I„„tive to cut. ';;, '". °'"""''-"" "• «'*- «"'. an,l hy ,™, g„„, "-„,„, ,»„.Mod a negative „Iati,e. '■''"! """t "•"'* l-r-ly „«on„e R„„„iok', ""::;:::::;—'" -^— «... Aghast is fro„, A. S. ;,r.fau to terrify C'<>itZ(^-See Art. 242, note Z^/-^-;' The. i«i,„..rantl, inserted owin. to confu sion with isle, a word of F.. . i • • ° " ''tr' """"• ^'~- "-—■•.- onhe.„t Unkind ; «n means not. ^"'''"^-"^h'tR no meaning. hich We can- >"," Ac. ? jf numbers^ oTisfruction ^ntence. icornea evi- '■« »"e/< with fne gram- 'edicative oderick's ) applied HINT. ANX, A.N.swKit«, INTKUMEOUXK KXAMi.VAT,, .Vs. „ .m,olf ; '. AM ,,,„ „,„„.. „.„,, u„ .„„„„,„.„« „„t to include M(jses. (^) Let I make a covenant is certainly not Englisi,. (/') "I shall ittenipt neither tn pulhate iior deny." (0 Th,s sentence is faulty in that the pronoun, "they" •B us,Hl in a slovenly .nanner. Any rendering which will ...ake .t clear that the antecedent of ''they" ,. "population" and not "priests" will improve it. onize Its I confu- dand is le root &0. 7. 1. ih) flirme-nc'.at, mu-se'-am, ,•..,•,,,,'. ar.tif'-i-cn; nl-ly'. 5. (c) (1) Auburn is in th. Nominative of Address, being the name of the thin- addressed. (2) Plato is also in the Nominative of Address (3J John is the Possessive case, John is the nauie of the owner of the coat. (4) Chair.ann is in the Objective case, being what Mason calls the Objective complemeiU. See Art. 395 (6) Af, '<" is in the IVi.minati jootive couiplement. See Art ve case, being the Sub- >m. i i I'VonniiativocaseinEn.rJish W 1^1. Uiaik remarks on this " Of « ">««*»./. But the "' ~™. " »1"»>.I<1 - held t„ I ' '""' f'"""""' '""' be held t,„,„ .n a,„„o ,„„,,„,,, rectify even SJielJey's bold, ' lest til ore be No.«oJaceleftfor^Aonand«.e/' The grannaatical law has so slight a hold f K . :;:;r-^ ~-::r::: W This may be justified o„ the ground that th • ^n ellipsis, and th-.f ., , • *^''^ " " There ^. . ^""'' ^^'^ statements. W l>a,r, says that this is incorrect H« be correct to say << two p::LandT'^^"^' - W pounds, but JthlC^tn^^ struct, what is meant is tlut th. ' * '"■"-tion of two .„,, , ! """^'"^'-^^ <^«"^- r„) Th- ■ • ^^*"'"^«t'ie same as four W 1 his IS incorrect TJ,«. • '«« loui. "vio» nuke, f„u>' Tr"""""""""""ake„ "-.beH.„,„a„;..if;;,:^;::«„*-a„eof, VATI0N8. phrase ' thia truction. iriiUy agreed I'ase is in the I the relative ''tvhich." e, it should ms must be ipated from Who would »oId that a ifficient to lakesptare *vo names "ten made UXWTH KHU AUrwweiW, I.VTERMEDIATK EXAMINA/^y**, {,3 lent .r ' ." r '";";;:;;' /;"- >* connects two .„..r^,^, ■ y' f "H-t tlie watcli.naii, ,rf„> told nu< (.hm< had beou « «r., At school I studied ,eon..try, ./..// 10. (a) Whom should },o wlio. (See Mason, Art. iVM } (/') Thi- J» comet. Wh.„n is the ol.ject of th. l^h love, rhesrntoneein full being '"IVy w^ho,,* tr»« !4"d« love die vounc. " (c) Th:* IM correct. Him is used leHexively. »(ff « ^ilhf" would bo better than "pillar's" hai tht, htU^F ,n»y be allowed for the sako of ll^ «^||„ »A (StH! MiBoii, Art. 78. ' t there is itements. ig." it would * poiuids the ab. cal com- )ur. ^o taken -ne of J, t] M C tc ^ ^^ '■^^^^•-'«<^k with B; A looks Houth;R,„oHh currents, which from f J, . r , "-'' ^°"'"'l '>y th.» |.<,I,ir wc..,wa aj"j::it 'r:itt: irrr-' 3. The anti-trade winds, which blow in a ri;. *• 4. See Sullivan's General Geography. 5. The climate of a country is if^ rrm^.v te.nperature,nu.i.tur.and^;:.;^:;:;:::;::" " "^"" ^'^ ^.ri::;tJ:r^ *^^" *'^^ ^'-- '^^ 'M^lace depend. The chief modifiers of this Ll^s• are the following • (U AU- tude, 2j Prevaiiin'. winds H^ Ono.., '"""^'"g • (1) Alt.. u ^ ^ »>nms, i^n) Ucean currents (4) l*,;,v;,.. ity of mountain ranges, Ac. ^ * '"' 6. 11 lir. 2 min, 3i sec. "^e Dntch alreal ^W '^ Xrt:X7"'"t' ^^^'^ this mixed race In 181o r fi -^ descendants of igrated n.^ain and again until tinallv ,. '^'f "'^^^ ^hoy o,„. to the North of the vl I l /^ *^? ^"'"'^ "^^ *''"''• '»'>'>de the V A{ the same meridian under the sun. %B \M I NATIONS. rs. Rfi mill. 4 see. inovt) forward in ut from tho time same meridiuii iifter completing minutes moro to % r