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Les images suivantes ont dt^ reproduites avec le plus grand soin, compte tenu de l., KURCTKOTVPKKS AND PrIMTIIIIS. I r o (0 a> e,\r iH;3, by Waihinnlon. n Primtkhs. I r ! \ i - V r COIS TENTS. Fa«»., iNTKOnJKJTION ^ . . a Ckntkk, I'ointm, and Htkakiht Lwrh t » , .10 HTIIAKIIIT lil.NK KldlTHEH 40 HiMi'i.K ci'HVKH nn CUMI-UU.ND CUUVBH. — EM.II'SK AND OvAI. .72 Compound !i . I . \ INTRODUCTION. That it in pructicuhlo to teach tlrawiiiK i» <••«' piililir Hfliooln iii no loiigor a niiUtcr of doubt ; uiid tliiit til.' Mtiiily in oiii' of ^,'rciit imluMtriftl iiiul filiicii- tioiitil viiliif, wlicii jiropi'rly tiiiinlit, no pfr-xn, who luirt nircfully invcctiKiitcil ilic miliji-ct, qucMtioMn for ii monu>nt. Tin' tlrtivvinn, liowovur, inuMt Im wiilo in itn riinnf, nitiohiil, iiinl Hyrtti'iniitic. It numt !••• niuili niort' timn Niniplit (:r)pyiny : indi'cd, it niuxt In-, in tin miiin, Homctliing wholly dittertnt froni tlnit ; iind it must ho much nioru thiui pirturt^-nnikin),', — I'vi-u >;o()d orininiil pictun'-nuikiiiK- Thorn' who think oihcrwirtc Hiully inisnpi)r('ht'nd tho woj)*^ and vahn; of one of tin* nnwt practiital studii'«. It will ho olwiTVi'd, as chariutoristii; of this course of drawiu);, both in its prinniry and udvaiu-cd ^radex, that the pioture-tdoment, an »uch, in iilmost entirrly excluded. The iiuthor is well aware, that, in j'xclud- iuR many pretty thiuf^s which have usually been con- sidered proper for drawiuR exercises, he sacrilices something of superlicial attractiveness; Init he omits them because tlie best artistic, practical, or educa- tional results cannot otherwise be produced. lie excludes them from even this primary course, because he would here lay a sound basis for more advao'cd and severer work, when pupils reach the granunar TK.WUKI/y U.iyi'AL m'\umU. Mt'iiri', wliili- tlif lUitlior U ftwnrf lliut |Mi|iiU iirt> iiiixiiiiiN to lH>|{ih wliut tuny Im> i'iillt>i| " jirxtty work," iih I'urly iix |ini«i«ili|i<, )ii> wImIu'm ii>iirli- fi-M I'Irarlv III iiiiili'i-Htuiiil tliitt iiictiiri'Miitikiiiu. no i'lir ilH tlit> piiltlii! HflioolH ur«* coiii-i'rtiiul, mImiiiM iilwuyit Imi ri"4aril)'i| uh ii HcioiHliirv tiiuttcr. lit* uImo wixlion ti-iK-liiTH til ri'iiii'iiilM'r tliiil tin- corri'i't ri'pn'Ki'ntft- tinii of any olijfrt, itit rt'iilly hc(>ii, itivolvctt priti- liplcrt of |H'rMp*>ctivrNtaiipro- tliii'iii^, ill II incri'ly inccliiiiiicul wiiy, whiit they cunnot posxilily coniprt'ht'inl. riiHtciiil of li'iuiiiiK h'lirni'rii into Hiich riitH, the author dtmireH, lirNt of nil, to tiiitko thciii ii('i|iiiiiiit«il with the hfuiiticx of piirt' form iiiul with tlic principIi'M of k"">I ,'n. Thcrffon-, it is tliiit the fxiTciNi'M in thiH prinnuy foiirHc arc priii- ci|ially Miu-li tw tlcal vvitli incn- oiitliiii> ri*pri*N<-iitatiiin, buHttil on ({I'iiiiii'ti'ical foriiiK, ami iniistratiiij^ h'lulin^ priiu'ipli'H of practical dfHign. It is only wlieii pupils have well iiiaHtt'rciI thiN Mtagc that they arc pn-pait-il to tiikf up intclligiMitly, ami in a thorough nmiincr, pcrspft'tivc, anil luoild unil ohjm't drawing. IIK.VWINU HHOIM.II UK TAIMJIIT IIV KKIICI.AU TKArllKltS. Drawing i-aii, ami hIioiiIiI, l>t> taught hy thi> rogular tt'aoher. One who umliTstamls the gi-neral prinriples of ti'iiching i!iin toai'h drawing HUcct'HHfully, without any special artistic gifts. Thousands of persons teach i rnrt' tlint IIK t<>ltr||< i«. HO fur 10 wixlioii 'lin'Ht'litft- vi'H prill- li<, which I cuiiiiot, Hit iniicli iiiK (mm I to rc|>ro> «>y cumiot IcuriDTH , to iiiikkt r priii- ^(•iitiition, g li'Uiliiif^ uii |iii|iils |in'|iar('il lULAlt f ri'nijliir |)i'ii>('i|il<-.s , witliiiut oils tcucl) ISTHiWUCItOtf. f MrittlllU'tii' MIllTDNIlfully will) \W*MM no ll|M'i'iul llUtttll'- ntittiiMl ((iflx; tiiitl tlit'rc it) iiotliiii^ a)K)Ut ilruwiii^ mo tlirticuU til iiiiixtt-r ui* xoiiii' III' lilt' I'ftitiiri'H of mutlM*- nmtiut, L<*t it| tln'ii, li«> iti'c«i|itfil um true, tliitt there In nothing ithotit ilniwin^ to prevenl uiiy perKuii of fitir riipiu'ity heroiniii^ |>ri>ll<'ii'iit enough to teiuli it iiitelli^etilly mill vvith miiiri'HM. It in cle'ir, from tin- preneiit iiioviMiieiit in fitvor of art eiliiciitioii, that the teuchiiiK of ilrit\viiii( will loon he reipiin d in ull piililii* hi'IiooIm; and it iiiiiNt, therefore, lie tiiiii^ht liy the ri'i^iiliir teucherM. Itnleeil, it in bunt, for various roiMoiiM, that it hIioiiM thiiM be tuuijht, TlIK OIUKCT OK TIIIH fniMAHV COl'liSB. Thiit Manual, with thiM-anU wliiuh lux'onipiUiy it, irt ititemleil fur a i-oui'mu of iiottriii'tion in nlate-ilrawing in primary Hchoolx. The uxercines uru «o Miinplc, ami Ml ^ruilnk(!ly pro^ruKMive, that tencliurM, though they may have liiul no pruviouH iiiHtnuition in drawing, can nnirtter them, if they cliooMe. without anniHtunce, and intelligently lead any class of young ptipiU who hnppiMi to Im under their charge. There In nc better way to teach oui-'m self than leucliing others. With the cards in the hands of the pupils, furniithiiig them good copit'H, it is not at all essential that teachers should bo extraordinarily ukilful in drawing on the blackboard. The Manual will acquaint them with all the principles involved: these principles they can explain orally to the pupils. It is the clear xetting forth of these principles that constitutes the feature of chief importance in teaching drawing. The ptqiils, with their card copii's before them, aided by the oral TMAVllt^nfl* M.tSUAL ••x|>l!ii>!itii»), iuhI l>y »)i)'h lllii!>tritti*.>ii!> (vyt*ii tli'>ui;)i llii'v Im' rtiil<') li* (III- ii'iu'lii'r limy |{ivc on thi' iMNinl, Hill ihuki' vi'ry <«nt:»fm toi-y \>t»ittvn». It i>« tliK li'u«i> I'lirlit to trMh pi>i|Mirtiitii, till- '•iiii|)l<> ll^iiri'M of |iluiii* |{i»iiiM>(ry, tli* iit'iiK i|*li"* "t |>riMii< itl •Itiai^n, lUiii to laiiiiliitri/i< the pu- pil uitli iM-uiitiliil toriiiii. To iiiiiiii'ilmti'ly lollow {\\v*v uurtlN ill tlui uppi cxcrciiii't in iIu'mk liiHikM iipply till- priiii'ipli-M of tlio itiMtriu'tioii ^Ivi'ii iti till' t'iir fully iIm' ilruwiiiK ill oiitliiiu uf objticti with ri'^uiur fuuturuit. IlKUirrTION \SU KNt.ABllKMBVT. Ti'iidicrM mIioiiIiI iiiiilto tlii'iiiNi'lvcH Hiitliiiciitly lit- iiiiliiir with tlio I'MTfiMCM, liy dniwiiiK tliciii, to Ik- iilili* to point out tlifir I'l'itturt'M rt'iulily iiml tifitrly. Wlii'ii woikiiif{ on till' hliK'klioiinl, tlit-y xlionld pro- ci'i'il nlowly, i'Xplaiiiinv( I'Uih point as tlify go ulon((, uiui rci|ttiriii|{ tint wliolt* i;Iiimn to work tiiKi-tln'r, I'Vcn tlioiigli Monit' urc oliliK*'*! t" I'xccuti' their tirivwingii vciy rnili'ly. It in iiiti'tiih'd tliut tlni fif|uri>H givnn in thi' lirnt chiiptiir of tliii MniDial hIiuII Ix* ilrawn on thi' hliu-k- lionnl liy the ti'iuhci to u niuIc of one foot for i-vi'ry Iiiilf inch of tin py. Tln'ii tlio pnpiln nn- to lopy tiii'in on their »lati'H, making thi-in of a ih>lliiiti< h! i' Mtwti'd by the teacher. Thu Hi/u of the flguri'H w ill he goviTiind hy tho »izt' of the piipiln' nliiti'M. Tliix will tt'ach nduv.tiun. It w intouded that i\w lorniM on • T* 4 ISTHOIWVriUS, - w- tiiti \iM\\* »\\vA\ iw t;«»t>ieil hy thu |»ii|))it l'^Ml) tlit* lanUt ltii> ti'iM'tiiT iiMlit iitiiiK tilt' |iri)|Hirl* MtM, or Mtttl*', wliiili (•limilil Ih< iimk Ii larger ilntit iii tin' r)i|i). TliU hIU lino'li ih» |Mi|iilN I ii/iififi III! iif. 'I'tx' iMii Icitttir*'* iif priu'tlfi*, ri'ilin'tioii iimt i'iilit.'t{iMiitn i'i>|iictf, nImmiIiI ko ttij(i'lln'r : iHith iii'' i'»M'iif iul »<• K'»hI |irt(. )(ri>B>« ill tiling iit tlii> *uini' tinii>, \vliili> tin- lulvuiH'i'iiii'iif of tlu' «lioli' rlium kvill li«> liiiin* xittiMt'iM'tory tliiiii it tun !)•< i>tlii'i'wi-rii of tlii' Mini- mil, uikI not rotiml on tlii< i-unU, ui'« iiiti>iii|i>il for lilui'kliounl i-o|iii>M. to lie tiruwii liy tin' li-uilirr iin iiitroiliictoiy I'xiT.'iKi'K to till' iiKi' of till' I'upU, or lor tlirtntioii i>xi>n-ii«*M ta iii'i>iiiii|iuiiy tlii> ruiiU. ilROMKTKlr.VI. IlKKINITIllVM. Tlii« ilfiliiitioiiH of |iluiii* Ki'oiiiftry, illiixtrutioiit of wliii'li Mv I'liiplovfil \\n u liuni^ of fri'i'liuml iliuwiiiK, mIioiiIiI I'I' nivtii to, uMil ri'|H'iUt'y, tlio yoimni'Ht liiipili. Tlii-y hIioiiIiI I)i> i>x|iluiiii'il, not mi iiiih'Ii liy \vorli>in ^oiii* ovi-r oiiri>, ami tlifii 111' tukim u^'^in from tlii« llrHt, with u ln-tti-r umlfi- Ktumliii;? uml iiirri'uxfd wkill. Wlicii tcuiliiii;,' f. Since intelligent drawing is always an expression .(f knowledge, the power of observation must be cul- tivated from the outset. Pupils must be trained to discover the features of whatever they are to draw before they begin their work. To take a simple illus- tration : When the pupils liavo learned the names of the ditten^nt straight lines and angles, the square may be given as an exercise. The teacher should draw it on the blackboard, requiring the pupils to name eacn lino as drawn, ami, when the figure is completed, to give tlie number and names of the angles it contains. After the diameters and diagonals have been drawn, tho pupils should then be required to state the effect of these lines upon the original angles, and to give (he number and Tiames of the new angles and tri- angles. Other exorcises may be treated in a similar manner. i - -V V- rk. They nor of tin' ii'V iire ox- lily iicquirt' :L'iich llieir ooiuT than ■ by logical M'oliaiul or y oiiu : the lildren iirc tl one. exprpssion lUst be cul- I trained to iH' to distinguish form, and the mind to comprehend prin- ciples: the correct .nanual rendering of the form is a simple matter, which will come by practice. In the early lessons, therefore, teachers should biy more stress 12 TEACHERS' MANUAL. iilion tlevi'lopiiiK oltsorviition and underHtaiiiling tliiin ii()()M lUciM' dexterity in exocution. It in rare, almost lUHiiduntiil, for yoiiMj,' |)Ui>il.s to draw elear unbroken lines; wliilo linos varying in thiekness must be ex- lieeted from tliem for a long time. In criticising' tlieir etVorts, form, irrespective of beauty of execution, should be maiidy considered at first. Wlien form has bc-en fairly masterctl, then teacln-rs nuiy begin to insist upon better li .'s and more careful workman- ship. One thing should thus be taken at a time. DBAWINQ 0\ THK HLACKUOAKD. Drawing on the blackboard slu>uld be practised at least once a week by all the pupils; a section working on the board every time a lesson is given, th(i others working at the same time on tli.ir slates. Vupils will be deliglited with this, while it will aftbrd them variety of practice, whicli is important. It will, in particular, allow them to make their drawings on a large scale. This work on the board may be termed the completest exemplification of freehand drawing. LKNOTH OF I-E.SSONS. Short lessons, often repeated, are better for young pupils than long ones at greater intervals. Four les- sons a week, of half an hour each, or .six of twenty minutes each, will bo a fair amount of time for chil- dren under ten years to give to drawing. After that I age the lessons may ho. longer and not so frequent, ! while new subjects may be taken up. When instruc- i tion is given at all in drawing, the lessons should be ; sufticiently fre(pient and sufficiently long to keep the INTIinhnrilDS. m aiiilin^; tliiin rare, aliimst, ir unbroken iimst Iv ox- iicisin^; tlicir f execution, len ioriu luiH ivy begin to il worknmn- ; a tinit'. ID. priictisc'd at tion working i given, tho kites. I'upils I aftbrd tlieni . It will, in •awings on a ay be ternied tid drawing. ter for yotmg is. Four les- six of twenty time for ehil- ;. After that ; so frequent, kVhen instruc- lona should be ig to keep tlio ■%* jiupiis iilivi' to tlieir work, and tliomu^'lily iuleresled. Two Hlioi't lessons a week will Mot do tliis. |''our Irs- Bons will much more than doui>li' the results, and six lessons much more than trelile tlicni. This is not only true of drawing; Imt every teacher who has trii-il tint experiment knows that it is also triu* of arithme- tic or geography, for t.-xample. In neither of tliese studies wouhl any one expecrt to nmke any satisfac- tory progres.s with only two short lessons a week. Indeed, the time would i)e regarded as, perhaps, woim- than wasted; sini^e tlie little progress actually nuide would not compensate for the disgust many of the childrtMi would .icipiire for the .study thu.s treated. If, then, drawing is to he taught at all, it should he taught in earnest, and not as a merely tolerated study. Even its decided attractiveness will not Inlly compen- sate for the lack of earnest work. Again, if any new study, whatever, is to be put into a school, it .should receive for a while, if possible, special attention, in order to emphasize its importance in the minds of tho i)upils, and to make a strong he- ginning. To begin well is half the battle. When the new study is thus once firmly established, it may then take its place with the other regular studies. Thus should the schools welcome drawing, which is destined to contribute so much towards the future prosperity and culture of the country. UrOTATIUN KXERCISKS. It is remarkable how few persons can accurately describe the true form, size, proportions, color, and character of any thing which tho eye sees. People ' i 14 TEAVIIKUS' M Ay UAL hiivi- K'''>i'nil iinprcssioiiH, wliidi, brdii^lit fo tlio ti'Ht of (li'scriptioii, lire round to In- vii-^ui' iiml alto^rctlicr iiiirt'liiililc. Dntwiiij,', i>nM'f(lfii l)y rriticixm uimI uii- iiIvkIh of copies or ohjf.tx, ill wliich Wfll-clioHPii tiTiim (Ifscrilii; (li'tiiils, tiiiiiiot fuil to wlticiito even tlio i<;is.iiiin>; powers us well us the imitutive and iirtistio. i''oi- til is purpose, lessons should also lie freijueiitly dictated by the teacher, without illustration in hooks, on cards, or on the Idackhoard. For this kind o^' instruction, artificial ohjects, hiiv- int; f^eoniotrio forms, are hetter suited than natural ohjects. For example, houses of simple proportions may thus be dictated and drawn. When such n drawing has been executed, it is then iwlviaiiblo to require the pupils capable of doing so to write a minute descri[)tion of it, giving its form, size, pro- portions, ScK. There could not possibly be a better subject for a composition, when it is desired to teacdi exactitude in the use of language. A simple illustration of the I dictation exercise is here given. I The drawing of the annexed geometrical form may be «lic- tated thus : Draw a square, jits diameters and diagonals. Halve the semi - diameters. I From each corner of the iquare, draw a straight line to I the nearest point of division on each diameter. Un the diameters of the lirst wpiare, as diagonals, draw a second .s(piare. Erase the diago- nals of the first square, and the outer divisions of its ^ lyriuiinvnas. 15 t fo tlin text. (1 iiltD^jctlicr iMiii iiinl uii- L'lioHOii torniH ;i! even tlio 1111(1 iirtiHtic. « fri'iniriitly ion in bnokx, . proportionH lien such \\ lulvitiiiblo to D to writo II m, Hizo, jiro- lic n better lired to teiKili ration of" tlio islinre given, tlip iiiinexe*- li - diiuneterH. rner of tlu) ;raight lino to of division on e lirMt s(Hiart', use tlic diago- iviaioiirt of it« ft diameters; also tlume purtM of tlie inni-r hcjiiari' wliicli K<> beliind the poiiitK of tlio star. If tlie pupils lieed what is dictated, they will pnMlu.x' the re.piir.,! |ij,„re ; if not, tiioy will draw HomethiiiK else. After the pupils have finished their work, the teii.;Iier will draw* tlio llf,'iiro eorreetly on tlio bla(lti)Oiird. Tho object, then, of dictation exercises is to mIiow that forms and words nre interehanpablo, both being niediuins for tho expression of thought; to teach IHipils to lis.) either language with equal facility; to translate and retranslato ♦rom one into tin; other. Such exorcises, beginning with siniplo geomutric forms, may bo continued, until th.) most •■laborato irregular forms can bo drawn from dictation, if tho language describing them lui nceunito and terse. Artisans have constant use for the j)ower which is m-quired from dictation exorcises. MKMOKY KXKHCISKS. J'upils sIxMild bo frequently required to produce, from memory, exercises which tliey have previously drawn. This will show tho tea.her how much of previous instruction is retained, while it is valuable simply us a means for developing the power of memory. Therefore, as soon as pupils have got a limited knowledge of forms, they should begin to reproduce these forms without sofcing the copies and witliin a specified time. It is also urged that the pupils, leaving their cards at school, b'' MASUAL. IHI.INU AM> MKAXUUISa ( With ea
  • Hciih' ill tho niiini..' prol.il.it.a. It i« cHHiiliiil tliivt tl..- first liufs of any .iriiwint,' should h- iipproxi- Miatcly oornct, otlu-rsviso tin* ninainiuK liiu-s will h.- wli.illy out of phu-c. Hnii-... wh.^n tli.' iirst propor- tiuuui linos have In-t-n drawn as n.arly .orrf.t as possible by the oy.' alon.-, pupils shoul.l U- p.rniittfd to m.-asure th.-ni, and to .orrcct th.MU if th.-y ni-cd corn-ction. Ft is to l.o distinctly undt-rstood, how-- cver, that the ninasurin.i,' is not to 1... porniitlnl until the lines have been iitli!«. nn liiii'»* at'tt'r tir^t (Iniwiiij,' iirt do not iis«> t \h ('M><'lltitll III lit' iipiirnxi- liiics will Ix' ■ iirst propor- rly I'on'fi't iw I lif pcrmittfil if tiny lU't'tl Icrstiioil, liow- I'l-iuitli'il until fc Htiiiinlit lino ilinn it;" y«'t ( than to rule >r sonu) upciMiil strai^lit, biitli >yo ami hiind, f ruler. Tlif H. Of COUISI', ,s upon a irirrli! uso a i>air of cxiift nuiy 1)1! ieiici', anil it is ^tico, it will Iju ill orliorizontal the aid of the ISTIlOlilrnnS. IT <•>'»' illoiic A Hoini'wiiat fxlfnilfd i-xpiTiiMioc in trurli- iii^, witli riiiitinui'il olisii'vation of (In- work of niuny piipiU, has niiiviiici'd th<> author that thoHc win* draw viTliiai and horizontal lint's frcidntnd, lH>>idi*s doinn thi'ir work in h'-s time. ;,'i'ni'rally tnakr their lines ninif iieiuly ii|pri^;hl und level than tlM»e who rule iheiii. Tho^e only draw well wlm draw in- teliij^ently. I'owiritiN. When vertical and hori/.ontal lines iin- drawn, the slate iir paper shouhl be k. pt in one position in front of the piijiil, its fdgu paralhd with tho ed^o id' tint de^k. When ohliipio lines uro drawn, the slate or paper may he kej)t in the Hanie position, while the hand is turnt'd so that the vision may not bo oh.structed. When cu-V(;s aro drawn, it will he bi-st to allow the slaN! or paper to he put in any position the pupil may prefer, in order that the hand nniy form the eentre of tho c!urve drawn, which can be, in fionn- cases, only when the drawing is turned sidcwise or upside down. l'Ky«'lLS AND MUUKIS. The slatu punciJH should be soft, lonij, wtdl-pointed, and held about an incli and a half from the eiul, far enough to keep the lingers from obstructing tho vision. For tho purpose of illu.strating many of the ex- orcises, and accelerating the advance of tho pujiils, ••very primary school should have a box of models, which can be procured of the publishers of this book. / Such a box would contain a sphere, cube, oblongV block, triangular prism, hexagonal prism. tit niM'IIKRS' MANUAL ...,iir, ,y\mU% r.-tim«iiliir i.yruini.l. ^ know Tln'iv irt no royal roii.l to .liawinn : an.l tliosf wl... i.rofV..H t.. otV.T Hu.h a roiul to u. umy l... h.im ,„...f.-l of a .K-mro to iniHlt-ml with a r-Kal J.unii" wliiH. iv|iri'«outH nothing. I ,. L.-- iImi tnn* tViiiiit', III ilif .liiM I'll iill^llt !<• will I"' iil'l'' lilil iiii({lit to ; iillil tlliiHi- limy !••' »"•*'* iiiiini' vvhii'h ■ <'IIAITi:U 1. CKNTUK, POINTS, AM) STHAIOIIT f.INKS Wiii;\ yomiK cliil.ln'ii \>rff\u to dniw, ti'iiih ili. m, (ii>f, tlic nu'iiiiiii^ (if till' wiinl 'ii'iitiv." l:ri|iiiri' tliiiii. I»y wiiy lit' illiiMfniti to tmiili tl ihtn- .'I' flii'ir n\nU>A with tlii' iihI of tlirir iiciicIN, Tliis ii'iitri' we will call ii point. A Point. A /»>!nf h slm/ttji jinsithiii III- /,forf, in'thmtf shi; iiiiil iiiai/ hi: tiiiliiati'il In ifi(l'nriif irni/s. Kxiiliiiii. next, til.' iiii'aiiiiiK of tlic wmds •• ri>,'Iif " mill " li.ft.'' Diiiw ii v.'iti.iil line on tin' l.|ii.klioar.l ; t)ht lliif, iiflhihitf ni'il/>.r ii/> »'»• '/""/' d')- An Oiii.Kii'K Link. — .1/' »/,li' tlHMr luiiiu'H. Tiu'U rf<|uiro tli.- i.ii|.iU ti» ,liaw tl I "„ tli.'ir HliU.'r4. witliniif ttiniiim tli.ir >liit-H. Ku.'li liiM- NJKml.l Im( tlr.iwM nmnv rwuv. until th.. iMijiilrt can im*tunlly .li«tiii>{iii.'li l.-tw-.n tl,.. ,litV.T.'iit liii.'rt; until tlioy riiii ii.Hiuntly \now tlirin wli.'ii «lniwii l>.v til.. tfiidiiT, or iiiMtiintly .In.w tin-Ill wli.-ii i.uni.'.l hy llu' tfurli.-r. A Htniinlit Hli'U lifl.l in .lilV.'Vi'iit piisitioiif. will Horvf riift-ly to illiii*- tmt.! th." mi'iiiiiiiK of tli<» wonN " liorizmitiil," " v<-r- ticiil." " ohii.iu.-." UcqiU'st til.' pupils to ii.tni.i ohj.'ct. ill tli.'si" iimVr.'iit positioiiH. V.ui\UUKUlASKn.—l''n-alM Utirs am lin>n run- nlii'f nt,h, I'll shir III til,' nam: dirrrtioii, ami arr nhr.f/s lit tl„- mnw distann; from, our another thron.jhoat thr.lr wholr. Imijth. Thr,, moij Im Htraijht or r.armd, tnrtial, ohliqur, or horixontal. uritAiuin usfis. it imll) illiin- .1 I'i'ffiiiit lih rinm Uf> ffirr f» till' •iiliii' bni'k' il liiir i.i II II' iliiini ( II). is II Mfl'llil/llf llllt Hlill.t- II till' lioaril. Iit> |iii|iiU to iriiihu tluir iiaiiv tiiiii", iii|i lictvvi'i'ii tUlltlv lllUlli* wtiiiilly 'Iniw tnii>?lit *U'\< ci'ly ti> illuK- iiitiil," " v<'r- iiitiiiii object* re lini'n run- ioii, and arn mil' another III/ liif sfruiijht il. . iJrtw Mil flu- iMiufl |>iinillfl Virtual (.\», lu'ri/oiiiil ltd, aiiil ••liiii|iii* liiii'" (ilM to ri'iHiit tliciii nil tlu'ir ttluti'H, witlimit liiriiliiK tlii-ir MJalt'D. Tliix il* Hii I'stTiim- 111 wliiili yo'i nIhiiiIiI trii|Uiiitly ii'Vi-rt. WIm'Ii tin- ^ |Mi|iil« liavii ilrawM Iwn liiii'i* |iaritllcl, rcquirk) tln-in to r. Till' pfiKil xlimilil liitv.' u Hill' |niiiit I'l-r thi* \v.irl<. ami im two lini'* mIi"|||i| Ih' all'.rMd t |iii|iiU liavi' ui'i|iiira*li.iiilil have a tliar imiliTHtaiuliii;^ of paral- li'l lini'x. 'riii'ri- iiri' two tliiiin^ ri'i|uiwiti' to mukf litii'!* paniilil : tliry niiiKt lie niile liy niili', ami tln-y tiiiiKt liavc till- HaiiK- tliii'i'tioii. U'lim, llH'iit'orf. u" want two parallel vertical, or two parallel liori/.iiiital liiu'H, it i>t not eiiou;»li to say. "Hraw two Mitiial liin'rt," or. " Draw two liori/.ontal line'.; " lor in iieitlur ease lieetl tile lilies lie drawn side liv side. Nor is it eiioiiuli when two purallel lines are wanted, -imply to draw tlu'iu tiidt' by aide; for niile bv siib' diM, not neeessarily mean tliat tlie lines must liave e\aetly tlie same dire'-tion. Ileiiee we must >iiy parallel vei- tietil lines, parullel perpendienlar lines, parallel oblitpie n rKAVllHHH' MAM'U. tth*>«. or |M»riitt«-l tM»ri»><>i)ftil tttM>«, un ttii> ••na«> M>i»y U-, If Wf wniM •!») |(i«t »liiii wi' iiM'iiii, A» ItirtlM-r |)t)>Krt>*« !• iHinlf ill Itii* •••Hir«i* of ilnmhiti, it will U' iiioro I'ti'iiilv ••'•>• wli.v ■•• MiiU'li MlrvM (m i ' "inmi tbi* ••xiifl II"' "f tirni*. Hfi' ihiil 'III' |Mi|)iU iiIhuv* linvc lutt^ iiimI ut'll- |i'>iiit)>i| |i»>ni'tU; tliry i)liuiilt| iii'vcr \m uIIhwimI in ilniMr ««llll nllllxi >)|- hllllll iM'lh'iU, To iMiltti' xlll'i' lllitt till* |>' iK'il* iin* iihviivt III ^ihhI I'oiiilitiiih, kri'|i tin III in ii l>'>\ iiiiiji'r yiHir Murii iliiirui'. ii» \>*' ilinrriltiiicil uml litki'll )l|l lit V\fr\ It'iKitM, .\|(|Hlill| Ktiliii- IMM- i)f |Ih> |Mi|)il«, t'riMii ilitv >•• *liiy. tti »liiii|M'h lIn' |m'I|i iln, it>>iittt till' tVt>rk uIm'Ii' it will l|i>l lll-tlllll till' '•r lliloj, N\ lt||> iHit uinnI iiiiiti-riitl) it U iiii|Hm>iili|i' to ijniu ra|)ii|lv iiimI w.ll, • Till' |M'iii'il >liiiiili| III' III M aliiiiit ail iiH li iiitil It liall I'l'iilll til)' |liiitlt, iMhI no Ik III tllllt the lliilnl will lint I'tMih* lintwiMMi till' vyi' iiiiil tliM K|mi'i< ulii'i'i' tlir lint* U III li>' ili'awii. iilMtriii'liiiu till' vi'iiiii. Wlii'ii ili-ii\viii}i •tr.iinlii iitii'o III ilirti'i'i'iit liiivrtioiin, iii« liori/oiitjil, vrrtii'tkl, itml iil>lii|iii'. iii»ti>ui| nntii'iiiii^ till' xluti' III- |iiiiii'i'. turn till' liiiml, OIwitvi' tlii">i' two tliiiii^i: t'hvuvM ki'i'p till- liiuiil jiihI IIii^ii'm in ii |Hi«i- timi of I'ri'riliiiii } iii'Vi'i' lit till' liaml obitruit tlin hiu'lt. Itiiiw till' Hliort('«r liin ' witli tin* Pn-'frx itmii't ilniHi' •iiiini'wiiir ' • ;• 1 It.i with tin- ii.iinl, lifting the \»ri'.t joint; tin* iii'xt j^nuli' ilniw wifli tlu' lori-uriii, iiiii'i till' I'lliow jiiiiit ; tliiw lonj^i'i* yi't, wliirli will ii'«imll,v III' oil fill' liliii'Uliimnl. ilniw with tin- wlmlw arm. ii^iir,' tin- ■*1iimiIc1i r jciinf, < ►iTu-iinnallv. in iliaw- iii',' a ^''t'V \»\t>fi liori/oiital liin' i>ii tin- lilai'ltliiianl. it • «• HTH tin HI' /./,V>i* Uil A« liirfltcr »)(. it will U' fi!.' "|Hih llif m IIIdI Hi'll* >wi'<| |i» ilriMV •nil lliitt llii> |i tin til in II irilxiii'tl uimI •• UIM* nf |Im> ••iii'iN, )titiiiix I'tiil, \\ ifli« ' rit|*i)ll,v iiimI li mill It liall iiM>l will init Ir till' lint' \n It iliivi'lioiiK, 111 ol' hii'iiiii^ VI' till'*!' two X ill II |iii«i. *l)ttrii)'t till- I'.'i'r-* iImim' ! III. lining tin- Ill' liiri'-uriii. . wlii.li will li till- uIimIi- illy, ill liniw- liii-kliiiiii' to I'lirry lit" IhhIv f^^t\^^m\ it> IIm' Hiu' i<* •Iniuii. Ii i< iN->i, wlii'it ilmwiiiu ti vi'rtb'iil Uiit* on till' ^t|,t••kl•^M^^I, ••» •IihuI tlini'tly in rrniil .if wln-rt- •Iim IliM- K III Ih- ilrtwh. uiili till' >lit>' |iiirti.klly turiitit iin»itr'U (In- In'UkI. uii'l dir i-inniuli uwuy '■' '•'' •'"' liiiii'l, wltiti till' iiriii io i-kti'iiilitl. fitll I'Huilv i-.trr>iitt{ »liM rruyoii iliiwii. N'l-vtr ilmw ti liitf with ii ,i''rky iiMiviiiM lit, liiit iilwiiy» with Ik iiiiitxi'iii iii"ti"ii. iii-'l • litw i'iiiMi((li t->r till' t-yi' til I'l'lliiw. IMVUll.M. »IU.\ll.ar I.INKt A.Mi -M.IM.IM. Ill** \hn\\ I'll ill' lilllI'MiiMII'l II MIIMill Iim- 1 1;, iiinl iliviili' it iiitu t» |n:ii piirtN. Kxpliiiii tliiit till' ili'iiliiiK iiiiuk >* ill tin- I'l'iitrii 111' till' Iim*. Iliaw itii- •itlnr litii* i'Jh iiikI iliviili' it into iiiiii ■ ■'|iiiil iiuil"; llr-t. l-y 'livi-Iinu it iii'n two i>i|iiiil {iiii'to, iiinl llii'ii I'lii h "I iIk' lialvi>>« into twii )itlii>ri'i|iiiti |iui-tx. Ilriiw iinollii'i- Iim- (.'ti. ami iliviili' it into tliri-u t>i|iiul |iiii-u. Miviilin;; a Iim- into tlii-i' ri|iiiil piirt-* i^* nior<' ilillii'iilt than iliMiliiiif it into two ri|ii:il |>art^. I>raw aiiotlu'r Iim* (4). mill iliviili- it into Hi\ i>i|iiai paitM ; llmt, liy -liviiljn^ it into two i>i|iiai pail*, ami linn i-aili ot' I ill' lialvi-- into tliii-f i"pial pail-. Wliilf tin- ttailn-r ilraWH tln-Ni- lini'M on tin- Itlai-klioavil, tin- |iiipil<« ilioiilil iliMW iini'H ol' a nivi'ii |i-nutli on tln-ir «l:iti-N, ami -liviili- llii-ni into lialvi-1. i|iiai'ti-i--«, tliinU. ami r^ivtlnt, follow iii^' till- li-aflii'f. lAai'tni-H-* in tin- ilivi- of .skill in determining deUiiito distances and [iroportions. Youiifj; childr(!ii, unless they have recoivod posit-ve instruction, seldom have any clear idea of tlie length of an inch, a foot, a yard, or mile, though they may have heard the words used liundreds of times. If (plestioned, they fretpUMitly give answers that astonish the (pn'stioner. Suppose, furtiier, that it is retpiired to draw a line, lint of no particular length, and to divide it into five, seven, eiuveii, thirteen, or any other prime numher of equal parts. In that case, having drawn a line, divide it into fouretpial [tarts, and then add one pait, to make five ; or divide it into eight equal parts, and then erase oiio, heaving seven, if that is the iiumlier retpiired. That is, first draw a lino, and divide it into a composite numher of parts, then add or erase, as may lie required. Th.is is not, of course, a suitable exercise for the youngest pupils. Frequently iisk the jnipils how they would procei'd to divide a line into any dosignatcid number of equal parts. If, for example, the number is six, the answer should be: Divide the line into two etpial parts; IK i tile.'*!' cill'Iv iuilts in f'ri'i' llicil UCIIDIII- tifc will ill' I to I'l.irrcct ll> tllC I1M< it with llii'ir II this iiiiiii- h other Ics- prci' of .-kill tortious, voil posit'vc [■ tlio length h they nmy f times. If hilt iistoiiish (Iriiw a line, it into five. 1! number of ,wn ii line. M one pait. il parts, and the iiiimher 1(1 divide it ,(ld or erase, L', a suitable uld proeeed ber of (Mjual the answer (|ual parts ; sn/Aiaiir 7./,va..v. -» then divide eiuli part int.. three e(iMal parts, j,'"^'"^ MX. foMIIIMM) STUAIlilir 1.IM:.S. A>I. As soon as the pupils have anpiired a knowledge of straight lim's, tiiey should begin to eoiul.ine them. Draw on the l>laekboard a vertical line of delinitt^ length, say twelve inehes. and ^ u. then reipiire the pupils to draw a similar line, say lour inehes long, on their slates. At this stage, tho linos should all be drawn of definite lengths. Having first been drawn by the aid of the eye ahuie, they should afterwards all be e.orreeted by the seale. Such practieo is tho begin- ning of the study of jn-oportion. Having drawn the vertieal line, next draw a hori- zontal line of the same leiigtli ; draw it from the lower end and to the right of the vortical line. The two linos, thus united, form what ehildren will eall a corner, but \\iiat we will eall an angle. This j.ar- tieular angle (l>) is culled a right anglo, not, hr.w- ever, beeauso it ojtens to the right. Bight Angles. A riff fit nnrj/r /.s' furmfi f>i/ thi- wi'iflu;/ of fii'o Hfvnyjlit, or ritj/it, flncK j>nrj>cii.>itinii. iiiiiy 111- <>lili(|iic, Itiit one line is ncv" r s ml to lie viTtii'iil to uiiDtliiT. U'licii ji rl^lit iinglc '!■'•< 1 II l'"i'i I oil ii sl.itc l»y tlic mci'tiiig of !i vcr- lii'iil liiiM ;iimI ii Inirizoiiliil line, it will rciiijiin ii ri},'lit !m^'l(■, l|ioiii;Ji I III. sliitK 1h( piirfly tunicil nroiind. ami ilii' lines ln'coine oMi(|Mc. Wlieii 11 Unite is liaif opi'ii. it forms u ri'^ht im^'le : the l)liii|e is iiei'iien- (iirliliil- to tlie lliillille, in wlmtever Jiosition tile knife liMiy lie lield. while llie liiuiille is |>cr|icii III' till! VCI'ti- I'vpliiiii tliiit II' li'ft is Ills.. ;tt'iiijiiii4 till' II' lii>ri/iiiit:il 'il ; ami ymi I point, or at lit ill) on the (/ offint fines ! \'] Woillil 111- j n-,'1'1'. j arioiiH wiiys. (t cnil. draw i a liori/oiital 1 yillMUIIT l.ist.s. n liti.-: from it-* riirlil .'nil. drnw a vortinil liin' ilnwii- wiu-ds; alsn. IVoii. aliovr. draw a vi'rtiial lim' l.. jnin till- ri',dit iiid III' till' liiiri/i.iital liiu'. A'^'ain. ili"i" ;iii oiilii|iii' Inif ; iind. |ii'rin'iiili(iiliir to its icntri'. draw aiiotlirr wliirli «ill maKi' two ri^lit aiiKl'''* "" ''"■ ''''^^ iiliiii|iii' liiii', as sliown at V. I'iii>ils ri'pi'at on ilii' r slatr>. Acute AdkIbh. Ami ninilelesK flnni ii riijlit iniijlr is (in iKldr iiin//i\ l)rawii n^lit aiijilf, and. midway 1m- Iwi'cii till' two liiii's, (ira« all iililii|iii' liiii! mi'ctiiigtlu' lirst two in the inriirr. orvi'rti'x.oftli('iiii},'l''at(r. Tliis(>l.lii;ui' liiii' di villi's till' rii^'lit an^lc, and inalii's two sliarpir fDrm-rs of it. 'I'licsi' sliurpcr corners iviv callrd ai'iiti' anj,di's, l.t'caiisc tliry arc sliarpt-r, or more iiointcd, than a riglit alible. ObtuHs AnKlea. .1/; iiinjli'. i/irnfrr tlmu n rli//tf iiHi/lii '.">■ iiilli'd (III iilitiisr inn/fi: Tliirt figure at II shows wliat is mt'ant by "gn-ati-r than a right angle." Draw a Imri/ontal line as ill I ; tlii'ii ail oliliipii' line, joining tlic horizinital lim' at j its I'l'iiti'i' : and tlii'ii a tliird lint', prriiriidiciilar tn tin- >l'('Olld iilM'. 'I'll'' ll!li"ll "f i the 1 iiiiu' ]iiit> I'linu- iii:f ai'iiti' j I 88 rh.MUlKllS' MAM AL aii^l<- and oim' olitiisi! iiii^'lr ; tlic t'oriiiii- to llio ri<»lit lit' tin- iihliijtic liiii', the Iivtlcr to llic Icl'f. Tlii' union ol' tlit- two ol)lji|ui' linos forms two rij^lit im^jlcs. Tims (Iniw till' (litVrrcnt ungli's lit viirioiis po.si- tions, ami r('i|uii'f tlic pupils to naino t1ii> uncles, until tlicy can readily rciogni/e tlicin, liowi-vcr tlii-y nniy he drawn. Also rci|uirf llic pupils to makf the dift'crcnt anj^dcs, hy placing two «tii'k.H in dilfcriMit positions. Kxplain (^Icarly that an iinj^lc is tin- iliffi'i'i'iii'i'. in tlircrtimi of two liih's, and not tlie lines tlicnist'lvi'S, nor the spacn botwccMi tlicin. An anj;!i' is fornifd when two lines tend towards each other, thouf^h they do not extend far enou;,'h to meet. Good drawing niodtds are the Itesiohjects with wliiidi to illustrate the principles of giHiinetrieal drawing. The following letters drawn with single lines illustrate the dilVerent angles. Tietlers K. I"*, II, L, contain right angles. Letters M,N, V. \V, Z, eontain acute angles, Ijctters A. K, X, Y, contain acute and ohtusti angles. rr i-v ^M • lOMniNINfi SllJAKJlIT LINKS. ■TItlANMJI.KH. A trianrfle is afir/iirr liavimj thri>r stniif/lit siitrs, enclosiiiff f/iri'r aii;//rs. J A BiKbt-anKled Trianxle. i A ri'jht-diiffliul /ri r left. Til.' •ijjiil unifies. iri<»us |)08i- III, liowcvcr pupils III two .stii'ks y tliiit iiii ;lt',«i. \', Z, coiitiiiii tti'is A. K. I* iiiid <)1)tiis(t ANfll.KS. alijlit siiii's. fS (Ulf//vS It 1(1 ot" u vcr- Sill.MUIir USKS. '_".> ticiil liii-' to til.' imkI of u liori/ontiil line. Dniw mi ol.lic|l|c lilM', joillih},' till- otIliT ciul.-. of tlif lines. 'I'lu-'so tlim- lines will jjive ii tliree-,-iile«l lij,'iiri-, as iit .1, wliicli is CUlleil a triiUi:j;le, lie.-illise it Illls tlli-ii' aiij,'les: iinil a ri','lit-:iii;,'letl trian},'lc. l.e- eaiisc one of the aii^leH is a ii>,'lit an;,'le. Here is a eiirious fact ahoiit tiiaiit^h's; The three im!,'les are always .•-iiial to two liglit aiit,'les. If one is a right angle, as in the present instanee. then the other two will he etpial to a right angle. Th'.s may he easily illustrated with paj.e. Cut paper into triangles of various sha[ies ; then eut oil" the corners of any one of the triangles, ami lay them si.le by side, .so that the points will he elose together, when they will be foiin.l exactly to till tlie space of two right angles. Mark the eorner.s before they are eut off; otherwise, the right corner.H may not be laiil together. An Equilateral Trlanglo. .1// v.qidlaterol trinm/h /his t/nrr i-'iiial sI. Draw a )it>ri/.()ntd liiu>, ami mark it** rcntri'. Fnnii tlii.-t rciiirc ilraw a vit- tiiiil line u|)\vanlH. .Fuin tlif ciid of till' virtical line Id tin- t-nds of lliu Iiori/Diital lint' l)y two ohli<|U«^ linen, (W ill \i. ICrasc tlic vertical lim-, wlicii an isosceles triaii^jle will remain, 'i'lie j^ wonl isosceles means liaving equal loRS, as this triangle has two equal si.les. An equi- lateral trianjjle is an isosceles trianj^le; hut all isos- celes triangles are not ecjuilateral. A Boalene Triangle. A srnfpur f)'!a>if/li' fins no tiro of its siilrs fjiiii/. Draw three strainht linos of unequal lenj,'tli, uniting' their ends, as at M. The word sca- M. leno moans limping- This triangle can be placed on no one of its sides without leaning to the right (U- left. rOMIlININf! STKAKiHT MNES, UECTANWJULAU KKiUUE.S. Aiii/ f>/iirr Ii'iriii;/ four strtth/Jit sidrs and four riijht innilrs is rolird a rertaiDj/r. A Square. ,( s'/ii'irr is !aw II ri;,'lit ivn'^If Kpciiing to tlio r'\\i\\t, wiMi till' lioi'iiCDiital ainl vi'i'tii'al lincH nf tin' HaiiH' li'ii^lli. I''i'lilii|ui' lilies coiiiutHiih the oppoHiti' lUiKlt'H, Hit in v. A |iii|iilK to ti'll liow iiiuriy mi^,'lt"* uimI tri- imnltM IIP' now coiitiiiiuMl in llio H<|iiiiri'. ami t" nivc tin' iiuiiic of fiuli. IfiiviiiK'li'iiwn II Ktiiiiiri' iw li"for«', tlividf ifn lioii- zontiil Mif!:'H into tlin-t' i-qnul imrt!*. mill tlifn ilriiw vcrtinil liiii's ronni'itiiiK iln> piiint'^ of division as in Q. Ni'Xt, ilivi.lr tin- verticiil sitlcB of tlio Hqimro into tlirt'd oqiiiil purtf, and tlien draw **• liorizontal linen ecnnectinK' tlie points „f division. Tlio sijuaro will tiuis bu dividml into iiimt Binaller miuarcH. It will now bo woll for tlie pupils to divide the sipiare by a larger miinber of vertical, li..ri/.ontal. and oblique lines. TIk- obli.pu, liii.-« should be drawn parallel with the dianc.als, whilo Mi«^ other lini's will bo paralU'l witl' t(<'.' shloH . Illicit"* mill tri- III till' K<|iiiiri'. finll. iviil<' itrt lioi'i- • i><|iiiil (lurtH, Ill's ('l)nlll'<'till^ * ill Q. Next, of tllP «<]Ulll't> iiiil tiu'ii ilniw \i\\i tlie points I! tlivitU'il into 10 wpII for till' •gor mimlMT of . Till' oi>liiH'.o tb<> *liiig(>'.»lit, wit'' ti".' Hir!<, lodd. r HTItMUin I.ISKS. IVi ▲ IquW* oonMruoUd on tU SUgdlltU. Draw two lincN of ('(|Uikl Irti^lli, one horir.ontul, tile otlit-r vertical, ami itohhIii); at tlnir ctntrcM. Draw otiit'r lin«>M coiuu'ctinK tlii> i'liiiM of till* iirnt two liiii'M, ami tlif rt'Hult will Ik' a »<(|iiurc, U.M in it. It will III- well for the pnpilH to prartirti- drawing; M]uaro)« in clilV)>n>nt ponitioiiH. An Oblong. An ofihtiff h'lH four riijlit itnf/li:i, but imhj its o/t/ttinite sidfs lire of I'l/tial I c mi til. Drawa liori/oiitui line; from it."* fi>(U, draw dowiiwanlH two viTtica! liiu'x, of ciiual Icii^tli, ^- liiit It'MH t'liin tilt' I' ri/.ontal linu ; foiinect till! lower ctiil.s of till' vcrtii'al liner* liy a Hueond horizontal line, and tliu re.>tiilt will lie an ol)- long, as ill S. Frei|nently requiru the |iu|iil to point out thu difttironcu bvtwucn the ohlong and the H(iiiare, CoMUIMNO 8TUAI(iltT LI^K^<. — OHLiguK FunrKEH. A Bhombui. A RhomhuH huH four equal »iden, hilt its aiiyles an- not riijht anijhs (T). It will he observed, that in the preMcnt inwtunce, while two of the t. Hides are horizontal, the other two are oblique. Of course the rhombus, like all other geometrical fig- uru8, may be drawn in any position, without change \ M t^:.i<■ltKNs' .t/.i.v(/,tA. of t'|ii4riii-ti-i'. It io ii'it iM>i't.«i«ary that any <'l it^ ftiiii>f4 .ImmiIiI lx> liori/.iiiitiki, ii4 it im not iii-rrnKiiry ill, it ,iii\ <>r ilti' MJil I' tt xi|mirf xliniilil Im>. Tlif |iii' piU kIiomM Im> |Vi|l|i|i'i| til iiillllUol till' i'IioimImim witli till- Ki|nill'i', UIhI |Milht mil tllc illtlilrliri' lictWi'iM^ IIk' i\v iIm' xi|ii.iri' liiiH t'liiir <'>|iiul kjiIi-h, So ItiiH till' i'Iiiii|ri iiinl lli<* itii^li'M. Ill- till' ili'liiiilioii wliiili it« iiiti-iiili'il {'"I till' mil' IIIU3' In' laUi'ii till' till' iitln r. All li){iin>)« liivviii({ tour htnii^lit hIiIi'i* an' rallril i|iia |tii|iilM will learn an readily to iliittiii- ynifh ami ih'scriln' three nr I'liiir, iih they will learn one iiloiie. 'I'liirt involves a valiial)li' |iriiii'i|ili' in teaehillK. The ]iu|iils having ilrawii a rhninhiH, let them iliviih< it into any mi' iher of limilar lij,Miri"<. ii-i they iliviih il the sr|uan'. A Rhomboid. A llhonihniit fiiT.i j'oiif sldv.s ; wtlir oj' its tnii/ffS mr. ri'j/if ttntf/in, miil oii/if till' nnjiiisifr sliirs ni'i' fi/iiiif (V). ^" The termination <>-/W nioaiiM like; heme rhomhoiil meaiiH like, or re»eni- hliii),', a ihomhiis, Kei|iiiie the |iii|>ils to 'ontraHt tho yrU.MUlll I.ISHH, .'lA iiiiy I'l itrt , iiiM-fitKary . Til- |>ii. i|||l>ll« will) rlVVt'iu till' ■>|llul xilli'M. ^Iit \\\\)i\v* ; tiiMMinnli-. « lit'rt'>.i«m'v, I)' nii>{lt>H, rtr Hill' IIIU}' Im' iiri' rikllril llUtl'i' tlliUI I K'""""'*'"'* y III ilistin- r' will li-iini ii'iiiri|il(' in tlit'iii iliviilii Ili'V iliviilril I hiiH font .1, (/;/(/ iiii/i/ uli/r.i II iw lilt ion o-i-i/ ■, iir ri'Hi'in- •ontruHt till' rhoiiil I Willi till- rli'iniliU". iil-i> wiili ilu' i-IiImhh. uh'I j |Miiiil out llii> ri'»fiHl)liiiM'>-K iukI iIm- ilitVi-r«>in'i'< iMiiiniu llif tlii-i'i' llunt')'". TIm' |iM|iil^. Iiiiviiii: ili-itwii II iliMiii- liiiiil. oliuiilil III' ri'i|iiirii| !•• i|i\i'li' it iiil>* miv iimihIm i III -Miiil.ir li;.'iiii V It will !'•• wi'll »•• ImiIIi laljiil |iiinilli'l'",'niiii''. Iii'iuii»i' ilii'.v liiiV"' lliiir M|i|i'i-iii' »ii|i'« i'i|iiiil iiml jiaiiilli t. Till' ti iiilii'rwiiii U Hiixiiiii'- ti. iiii|iri'i»« iiii iIh' mhii'I- nl till' |ill|iil« ll" llfllll.V II- liiCKililf till' ililVi'Ti'llt li'lIM". Ill |iliiiii' Ki'uiiiitiiiiil lluMii'x. mill l-i liivi' inlililioiiut viii'ivt.v I" llif in-tinrii «ill lln'l u '"i"'!' «iili it'« Iwit I'luU tml lii>{itlii r, I.I' xt'rvii'i-, wln-n ii.»iil ifi tin- |nllii\vin« iiiiiiiiii'i : l.i't ilii'i'i' piipiU tali.' Inlil nl' tli. n.nl. 1 iuh Willi 'iiu' limiil. iiinl iImh. at ii'i|iU'-t Im'I'I till' I'linl 111 III I'lnn a riwlif-aii^iliil triaiiuli-. an i'<|iii- lali'i-al Iriiiiiijif. 'If aiiyii|iil» talii' liiiM ol' tlu' ronl. uiiil. in u Hiniilar iiiaiiinr. I"i'ni ililViiiiit l>iiir-»iiliil li'^iircK. Fivi' iiupili niiil.l fiiiin till' iM'iitapiii, xis pii- ],\U till- lii'xa^'i'ii. ami ^.l mi. All tln' ll;;uii'» Inniii'il iiv till' Hjinii' I'linl WHiilil liavi' tlii> hiiiiii- liiKlain'c ai-ininil tlii'iii, iiiid Hii wunltl Ih- iHiiiM'iiini'lriral. Till' jiriMi'ilin^; I'ViniiiM slmiilil ln' fairly nmlri- hIiiihI Ity till' impil' lu'l'iri' tln'V ailvaiui' lartliir. It In not lUH'c'HMiry tliut tliry i*ln>ulil Im' uMi' to draw ilir liKiircM uccumti'ly ; lait tin y sIiouM In- abli' Ici ;;iM' tlii'ir naIlll'^<, anil tii ili'sn-ilii' tlicni with n'ailiiii'H>*. TiarliiTK ran iiirna"!' tin- lovi' iil'llu'ir inijiilM I'm' lliiir work by ilrawinn for llu'iii tlif ninipli' oiitliin's of oltji'i'tn wiiiili riiiiii' iiiiiliT tlirinlaily uliMiviitinii in tin' tltt nA'HHMf*' MlSIAh ...|,.H.|r.H,n, ..r ti. ih.' vlHnUy Hi«m|'I- r..ini.. •»• ,H....l m .irulrfl.i IMM-. UI..I .xlul.ihhn III.- «.'..m..irk' r.u.f.ir.- ..r til.. |.r.-.-...|iiii» .■«..r.i..-. will.H.nr i.M.v..ry l,.ii.h..r. •|'.-.Ml..r« Ik .liiUiM t.r tliut tl>.-yi»» »-..in|.n'l»"h.l tl liMII, Kvi-ry prinmry H.ti.M.tr.>..m «1i'Mi1.I Ih- Hii|.|.li.a witli n J.t .if i-iiiiiurv mIi'h.I h.'mU.U 'n..- I'l"'!'!* ""' v..ry nm-lnl f..r lixinK i" «•'" "'''"'- "»" >'"""« I*"!"'* II liii.ittl-'l«" •••' «'">ii>''»<'''' l'"''"^- Tl.i. iMM.k in HiM-iully .UiKii.Ml f.-r lli- " t i.-m-H. vTH la nhow tli.Mii how tu .■s..fiito tliM .ImwiiiK". uihI lu.i t.. iii-trii.t otl.oM. Tli.y ur.. ...xiHM'ti.l t.. ..x|.luiii ..vry tliin« in liUiKuiiK" "•v" "'"f" I'ii""!"^'- "'='" ''"'♦ „f tl'f l...nL tluit y..»i.K .liiMn'M may !..■ al.l- .l.Mily t.. .....l.-r^taiMl tl... tl.ii.KH tuuKl.t. TJii-y hIu.uI.I not, liowm-r. lull into tli.. .-rrorof i*ii|.iH.sin«tliut rlMl-livn, ,.v.-ii M"it.- V.M.i.K rl.il.lnii. .•ui.i...t 1'.' r.u.l.ly '"'"I" '" ,M.,l.-r«tiii..l' tlu' i.u-ui.itiK of l.'"i« «-..r.ls ..r -n.-i.till.' wnnU. Inruu..- tli.-y iiri. long or Hoifntill. . WlwiH-vr tl„. m.-.u.iu« of Mi.li wor.ls, loroxiUiipl.MiH ixtihmhIu- „1,^,, ,..,uilat..nil. rl.o.nlM.i.l, \* vi.il.jy illiHtnit..!, .iiil- .livi. .an iih.l. THtun.l tlu- wonl ' li'* f'ulily uh tlioy can „„a.-rst.in.l tl..- nimininu ..f ri«lit, l.-ft, mpmn-. iin.l will i»rni«, I'Mii- •• |{i'))iiii'lrlu ■iir liM'Vi'fjf iiki iki tlii« ivi'h I'll till' |iiitiM>ini|»li' imnlit n» 'III iH 'I iitfiifimj \\r*t !•» »«'•• tii'Mof foriiiM ilriiw tlii'in llllllll, til''!"!- i-iiiit|>r«li<*tHl ii|i|iliti| with ' luiHli'lit iin* i'<)llllt< ]MI|lillt IMt'llf Iflicll* rawing'*, iiii't I'll to i'\|ilskill iiir tliuti Hiikt i. aJ.lc rli'iuly y^ Hlioiiltl not) lint I'liilili'fii, ulily iniiilt' to t, or Hrifutilltt Wlu'iii'vcr iiM j)t'r|H'iitlii'- iHtriitid, (liil- ly UM tlii'y can |iiart'. iiiul will hrttMuiii ustn. a: tiikf prt-l.' Ill «i-iiti« i.iiily ii..m| ill timliiiirf .lr.k«i".U. if tl"'-'- >*'"• ♦'■'"'' ^""''' ,.x,„..,. tiM'i Iv<- ••>..llv uii'l . U'trly. imi-I I»'»v.. tli.'lr |iii|til» I'lirii »•» il" il»* *»»»''• |>.i|.i|. -Iio.il.l tjruw rn..|u.nily "ii »!••• Mn- hi»"iir.l. k tiling tli.y HI" ul«iiy»y iii'ii'v 'I"'' '••«il'l>''' ""•' "" olli.r-. wImm. tlu.y iM-uiii U> .Iruw. «lioiil.l l-niii wiili huliiiul ol.j.M t*. mi.l not with »..v.'rn «.'oiii.'tri.Mil foriii*. Hut i'urMfiil I'xnmimiti'iii of r.'-iilt- in Kiiropr, .lunii« tli.< li».t twi'Mtv yur-. hIiow* timt tli- fninuT in not tli- |«.,t wuy to lM.«"in, tl.ou«li it iii.»y I." lit" l""t w;iy to ..n.l ; uii.l .•.iH..ially it i« not tin. lM.».t wiiy to Im^hiii wlii'ii till' iiim i-* to i.ro■'•"' •"•""•" '""' •'"'" ''"' '""""" ""'""" "'"'"'' '"" iniiinly. in iv romiilMvl.oiit un.l lalioi-ioin way to mi-Ii ri'Kiilt-*. Of ••<»iirm« ii liiiiitiul iiiiioiint of .liiiwin« fi < n.Umv, for tl..- -ak.- of vuri.'ty, i- not only tu 1... p..- - „„ii...l, l.nt .•n.o.imK.Ml. at all tiin.H.* Tl... im.,.iI-| I ,1, ..v.'ii lit tlu. outsi't, .houl.l li.' ina.lr acinaint.-.l with tl. ..in.'tri.iil foriiin ami t.Tin^ tlmt th.y nmy i.ft.r- wunU Ik- iil.l.'. nn.l.r>itan.lin>.'ly, to .l.K.rilir aii' UAMAL foniH till" iirtisim. in piirticiiliir, riin liavo no rli-iir a]>|)i'i'iiat inn nl liis wurk. A^'iiin, it is ciiMtniry Imtli in I'Xpcrit'iici' ami \>< tlif |irinci|il(.'s i)t' ;,'(>imI ti'acliiiij? to .sU[>iiosr tliat pupils fan ilraw. with any flcjjrcc of accuracy, a coiu- poMhil cnivc, like tlic o^cc, or tin' dclicatdy- wiivini,' lines wliicli arc seen in the I'oruis of niitural ulijcts, wlicii tlicy arc nnaMc to draw a ,strait,'lit line; or to suppose tliey can draw, with any de- gree of accura(!y, such irregular forms as those of iiniunils and trees, whose proportions can only he f,'U((ssed, when they cannot draw regular, syniuietrical forms, whoso exact proportions aro known; or that they can draw ohjccts from nature, involving tin' dif- iiculties of shade antl perspective, wluui they cannot drau from Hat copies, without shade or perspective, those symmetrical forms whi(di always Inive bccMi, and still are, so extensively employed in practical design. IIcucu it is that this course of drawing begins with geometrical forms illustrated hy models; gives pre- cedence to that which has delinite proportions, and so permits the drawings to ho veritied hy actual meas- urement ; puts tho symmetrical before the unsym- metrical; and works with Hat copies, making tln^ pupils familiar with pure form, and teaching the principles of practical design, before taking natural objects, which involve perspective, light, and shadow. Qui-.srioNS. — WImt is a point >. Dt'scrilH" tl>« ditTcrcnt kinds of straij;lit lines. WImt is the ditrorcncc hctwccn a viTticiil and 11 iicrpfiidicular line f WImt two tlnn;,'s aro rcnuisitc to nmku VO 111) I'Iriir • and til till- tlial pupils K-y, 11 ciiiii- (Icliciitcly- s III' iii'tiiriil { u fitniij^lit itli liny di'- as those of ■an only Ih- synmu'trical \vn ; or tliat vin}^ tilt' dit- they cuuiiot perspective, ive been, and tieal design. ; begins with i ; gives piv- 'tion.s, and so actual ineas- the uiisyni- making the ;eaeliiiig the king natural and shadow. ! (JitTcront kind.') II a vcrtii'iil iind i|uisitc to iimku .S77M /'.///' /./AA.'.S. yu liiK'^ imnilli'l '. Wliiil is -aid How would voii divi.lf n liiir iiii<> sis .■.imil purls ' Into M'vcn > Wlmt i.s iiii iinnie <■ Di'MTJk' tin- .lillriviil klmls of iiii-k's? WIml is ii liiaii«lo ? UcMMil).' lliu dill'cmit kiihU of liiiiii;;ii's '. Uliat is llif dimTiiire ImIwccii an isosiuli's tiiaii«le mid an iM|iiilai.Tai tiiiin-lr ' Bciwiuii a .iiiad- rilateral and a rcctan},'le >. Hctwirn ii squar.; an.l a riiomliiis ' Bilwi'cn an oldon;; and n rlioinlioid ' What is tin: diainetcr uf a siinaro >. lis dia;;onal > How sliould diawiii^; always \\r taii^lit ' What is said of ^ivint: . Inldrni Ujii- UMhr.ical words? Mow doi's this course of diiiwiub' Iji'giu '■ Why dots it so hcaiii '. CHAITKll 11. STUAlCIIT-hINK FKil'KKS. TiiK pupils, hiivin^? Ix-fDim' f'aniiliiir witli tlu' prrccd- iii<^ cxcrfiscs, sliDiilil lii'^jiu to (Iniw iVoin furds, tiinlcr til.' ilircitidii of the tcairlicr. Tims lar tlicy liavo l>ffn t;iii!,'Iit rnlurtioii, since tlu-y were rcipiircd to iiiiiko tlicir (Irawiiijjs sinallcr tlian flw ti'aclii'i's Maiklioanl copies. Tlie canl exen'ises will teach tliein iiilnnjc- iiii'iif, since tliey slioiiM lie leipiircil to make tlieir ilnvwin^js much hir«er than the card copies. These two modes of practice, />i/ rii/iiiti"ii -K.VKK<:ISK 1. Vertioal, Horizontal, Oblique, and Parallel Lines. Draw verti?;al lines the whole h'ngth ot' the .slate ; then, heginning at one end, di- vide them into (Hjual parts, first of indefinite length, next of definite length, as one inch, an inch and a half, &c. Draw horizontal and ohliijue lines, ilividing them in a similar manner. Afterwards draw vertical, horizontal, and ohliciue lines, and divide them ^ ,s n/A in II I- 1. 1 .V i: >'/'v uhkn. 4t li tliu jirrciMl- curils, \inilcr I'V liavo lii'tu iri'd to iiiiilvn s liliu'kliouril licm riiliinjr- I luiiUc tlii'ir )l)ii's. Tlu'so / I III ndoriju- V t'sscntiiil to tllel liineB. lines tlu> f tlu' slate ; t one cntl, two e.pial parts, and then eaeh part into I line e.pial parts. Frequently. i)elore the i)ni)ils l.e^'in to draw IVoni a eard, the teaehi-r shotdd re.piirr them, as a . la^s and under his direction, to analyze the copy, and ^'et a clear understanding of its features. Thus t<. analyze each copy would consuin- too much time, nor is such an analysis of each copy essi'ntial to a dear nnder- htanding of the exereise.s, as each feature is usually „ften repeated in the dift'ereut exercises; hut the preliminary analysis should r.-ceive cpiite fre.pnnt attention. Many elahorate .Irawings heeome easy of execution the moment analysis has n.ade Ui.own their elementary lines or forms. .Vgain. tiiis analyzing process shows how much of the previous instruction has heeii retained, while it also tends to develop the perceptive powers of the pupils. CaKI>-KxEU< ISK II. Right-Line Figures. Having placed a canl in the liamls of each member of the class, conduct the analyzing exercises after tho following manner : — FOKM (1. 7Vvfc//cr. — What lines in this figure? ^„.s.„vT. — Vertical, horizontal, and ohliipie lines. 7V,„.//c»-. — Into how many parts is tho vertical line divided '.' 42 lEMIIKHS' MAS UAL, h AitHii'ft'. — Four. 'I'l'itr/ii-r. — Hiiit of division, draw a lioi'i/oiital line ol' tin- f*iiuu' li'ji^tli as tlic vi'i'lical lini', oni- lialf to till' rinlil I'nK' t" tin- li'l't, of till' vcifical liiii'. yV,/. ./„,■. — What is tin- iianu' of tlic tiij;iirc drawn on the vertical and lioii/.nntai liin's ? Aiisim: — A Mpian-. Tioi'lnr. — How is it drawn'.' Aiimni'. — On itH diaK""iilf' Tiiiflin: — Wliat is tin- diaj^onal of a si|uarr'.' Aiixwi'i: — A strai^lit line connect ini; o|i|icpsiif an- gles of a s(|inire, ami dividing the siinan- into two equal rif^lit-aii^lcd triangles. Ti'iii'liri: — How many diugornds can a si|inii'o have '! Ausirn: — Two. Triir/iii: — When drawn, flow do tliey divide the w|uan> ? Aiisiri)'. — Into four e(|iial rif^ht-anf;led tiian|,'les. Tiiif/,,r. — How do yon olitain the ]ioints for this j sqmire V I Aiisirrr. — I>y dividing; each half of the vertical f. and horizontal lines into two equal parts. Triir/in: — How do you then coniplete tliesi|uare V Aiisirri: — l>y drawing obliqut! lines to eonneet the [joints of division. It is not to he expecteil that young children will give answers correctly as here set down. The fore- going is presented only as a suggestivi- mode of con- <» 4 » rt til lll'ilW lIlIM ic, iiiiil ili\ iili' it irts. 'riii'iiiii^Ii vir4iiiii. draw ii III' tlh- tuinxr rticiil liiii', niic- lil, iiiH'-lialt' III dtiial liiii'. Wliat i.-^ till' ;iirc drawn nii tiid li(ii'i/.i>iital s(|niU't>. ow is it drawn'.' a t^i|uari' '.' Ij,' ci|(|insitt' aii- Hiiai'if ill I" Iwn ciiii a si|iiai'u lioy dividf the ' fK'd tiiuMfilt's. ]M lints for this of I lie virtical •tH. ('to tlu' Hiiuure V I ti> ('(iniu'ft tilt' i;^ <'Iiildron will iwn. 'I'lu' t'ore- • miidi' niiilio ourli aiiswi-r a comi.l.N' Htatcni.'iit. Do this at tini.'s in th.- analysis of f.inii>: Thus : — 7;„,./,,.,.._ Wlifvt is tilt' diiiK'oiiid 'if a s.iuaif.' /'„/,//. —Tho tliaK'onal of a s.piaiv is a straij^iit lint' fomifftiiif,' t)i)iuisiti' an^lfs of th,: s.iuaiv, ami tlividiiiK if into two ftiual n«lit-aiiK'li'd tnani;lfs. 7V,„./,,,, —How niiiny tliugonals tan a s-iuarc havt'? l'„inl. — A »,'""als. Mii.h import aiiff is justly attafli.-l to this iiiodf of aiiswfriii«, fsiifcially hy small .diihUvn. It is not only a h.-ttfr test of thfir kmnvlftlj,'.', hut trains them to flt'ar statfim-nt. To i-ractist- it constantly, how- over, wotdd ht'fomt' Wfarisonif. and would foiisuiiif ttto niiifh tinu'. l.',„j;^, /,. — Draw a vertical lim-. tlivi.h. it into thinls; throU!:!li the upi-fr iioint of division, draw a liori/ontal lint> ftiual to twt)-tliirdst)f thf vfrtical line ; antl tluMi fomplftt* thf iinuro hy tlrawing thf ohlitiuf liiifs. KniiM ,-. — Draw a square. I'intl tht* mi.hlif of thf ujiptT sidu, untl, l'rt>m this point, thaw a Vfrtital liif upwards, (".lual tt. t.m-half oftlif k-ngth t.f tht; sith- of thf stpiart'. From thf uppt- r futl t)f thf vertical liiif. draw ohlitpit! lines tlt)wnwar.ls to the Ifft and right, striking the uppfr corners of thf s-iuare. and projftt- ■\ ^4 TKACIIKHS' MASVAI.. \ . , .^lijjlitly lu'yoriil. Draw tlio pncalli'l nhlicjiit' lines, .,riiw II Miiiiiiro uiul iN diiiK'nivIx. IIiilvc t'licii M<'mi- tlio Humc ccntro. Wiirii tlic pupils lire drawing from tlio cards, and after tin- first liiif to lie drawn lias lu'cn sidcctcd, statu liow lonjj tlio line is to bo made on tlie Hlntps. Wlien they have drawn the lino of the desijTiiated leiif^tli, and in the position it lias on the .-ard, then the tciu'her should draw it on the hiaekhoard. Thus proceed with each line. In this way the teacher's drawinj,' will eonlirm the work of the class, and not serve as a ropy. In this way, too, the meml>ers of the class will he kept together, and instructed as one pupil. The aim should ho to work with a good degree of riipidity, though the Hgures may not he accurately i'xecuted at first. At this stage pupils should begin to draw lioth from memory and dictation. That is memory ilrawing, when the [uipils ure required to reproduce, without definite instructions, forms which they have previously driiwii. as they might, in this ca.se, he required to draw frinn memory an equilateral triangle, a sipiare on its diamclcis an ohiong, a rhombus, or a rhom- hoid. The teacher would simply direct the drawing of any one of these figures, and the pupils would execute it from memory. That is dictation drawing, when the teacher dictates, but does not draw, the lines for the composition of a new figure. The V » il» *"> '1 nlili(im< linoM, i({i nals. Iliilvt* [toiiits of (liviM- 10 (lottl'tl lillOH. ric H(|tmu'H, lic- tlio <-uri]s, mill 11 sclt'ctt'd, stivto ■ ulates. Wlu'M ignutfil Icn^'tli, lie .'iml, tlli'll •khoiinl. TliiiM y the tuiK^lii'r'H class, iiud not , tlio inenilnTs and iiistnictiMl r» work with a IguroH may imt draw liotli from •mory drawiiifj, rndiK'o, without liav*' prtn'ioitaly bo required to angle, a siiuaro lus, or a rhom- ict tho drawing pupils would tation drawing, not draw, tho V lijruro. The ) V r* /"» i SlHAWin-USK yiUVHKS 4ft pupils draw. f..llowing th.- words of th- t...uluT. TuU«' tjgiuf A, for <'xampl('. Tho ti-afhcr dictatt-s lhu«, whiK- thf pupils fx.c\iti' : •' Draw a vcrtii-al lint- fouf inchi'M in length; mark its v.vw- tre. and from it, to the right, draw a horizontal line two imhes in length From the end of this horizontal line. draw downwards a vertieal lino two inehoH in length.'' This illustrateH the general mode ■*• of conducting dictation exercises. The teacher must be very particular about the words used. The memory exercises show whether the forms, and the modes of tlrawing them, have been clearly and permanently lixed in the minds of the [tupils. Of course the memory i-s greatly strengthened thereby. The dictation exercises show the perfect interchange- ability of words with lines ami forms : thai a form ' can be drawn from words us well as from a t. 4«( TKAVllKHs' MASCAL Tliirt ffivi'M two conct'iitrif M|imn'M. IIilvin^{ tlivi'l^'tl tliii hIiIi'h III' till' tiiidr M|tl;irit into lour |i;irfM, ciiiini'tt fli« piiintn III (livii-iiiii \>y nlilii|tii' liiH'H imriillfl with tin- wiilrn ut' liio imiir ^ i)ii|iil« to iini\ly/«' lifforo tlit-y lii't{ii» '" ilriiw it. Ziii-ZAii MoiLlMNd. — Draw ^ two iiiinillil linri/.oiitivl liiuK, ..I Hutlioifiit i.i.Ktli to nllow tliiTc or inon- hiiuiui'm to ill- ilriiwii lii'twi'fii thfiii. Divi.lr til.' ujipiT silk- of »'iu'h H(|iiur<' into two cqiml partn, nint, from tlio poiiitrt of division, draw tliu oMinim liii<'«- Ailil a line aluivf ami a liiic below, jiarallul with the Hi.l.-H of till' Htjiiari's. ('ARii-KxKit( iHi; iV. A Pioture-Frame. Draw an oblong, with its wiilth fiiual to two-thiriln of itM hciglit. Divitli" its wiilth into nix I'liual parts; draw tin! vertical lines 1 '-' and .'» 4 ; and then th<' horizontal lines f) and 7 S, forming sipiares at tlie corners of tho ol)l')ng. Draw the diagonals of the ^^^__^_^^^_ small Hiinares; then add the hliort vertical and horizontal lines, which divid.' each side of tho frame into two ciiual parts. 1 > / K. tin III 1,1. \K nui'itt:s. i; Iiiviii^ iliviil<>il !• oiittr Miimrii I, I'liiini'i t til*' inn )>,v t draw ii virliial liin' of till' rr(|iiirid iciii^lli, — two inilii*. I'nri'Xiiniidi'; lii<'iidr;iw iVohi ciicii rnd a liori/.onlal line to till' right, twii:<' a^ long. C'oiiipli't*' till' ohloiig, and draw its diaiiH'ti-rH. 'I'Ih' liiiglil of tlu' roof is (>(|iial to one-half of tho height of the olilong. It should |iroje(t sliglitly at eacli end. Notiee that the horizontal diameter of the ohlong giveK tho tojw of the door iind of the lower windows. Add the windows imd chimneys. Cahd-Kxkiicisk VT. Oonoentrlo Bquirca. Draw a si|uare on its diame- ters. Using the diameter> of tho first Hquaro for the diagonals of a second s<|uare. draw tlie Becond square inside the lirst. Divide the senii- Miameter.H of the first square into two parts, and, through the points of division, draw a third sipiare. Krase the dotted lines. 1 m UAtllKlif Mi MM.. Vnscr.sruv Swi aickh i.ukxhi. l|nuiz..NtAi.i,v, i — I»raw t«..i..trullrl l.on/...iiiul I...... ..I' .u.y .U^hhhUmI | iHiKtli. ""'I 'I'vi'l- »!"• iiit«TVi-nii.« «l»ivv int.. i..iii..n». | Dniw «h.. .liiu«.-t..r* ..f tl..^ m,i.ar.-. un-l tli.n .l.vi.l.. ...mI, H..n.i-.liunM.t.T int.. tw. i.irl.. Tl.r...,«li tl.r ,,oi„tK of .liviM-.i, ..„ ll... m-...i-.l.um..t.T-. .Imw ofT.-r ,.,uun'H. Km.»« tli.m.. piirt.. of lli.. diuin.t.-r.* ..f IUm lur«.T ..i-mn-- wl.ifl. lull witi.i:. H..- Humll.r m,uur.'.. TIk'h.- rl«lit-liiM' llu'tifM iiiv I'lit u|.j.lio«ili..iiH ..r |,n.vio.i. 1.-..!.". II' '•<•>■ "f »''••'•* *■•'»« """' "'" "••* uii.h-M.KMl l.y tl.- impil-, r-IW HuMi. I., th.m.- .-s.-r- ciHfM wh.Ti« tluy w'l.- lliHt .Iriiwu uii.l .xplmn**!. ('Ann-KxKiiri»K VU. A Pour-polnud Bt.r fornn»n n.ia itji ilianiotiTH. Iliilvf tlio 51'iiii- .liiiuietcrs, thiit ii* ilividf tlirin t into two iMjUiil imrtH, itml cm tla'pointfof «livi»i* tlit; liiHt H(|imr«', tlrikw uu isow«'lej. | triftn^l*, with itH niH'\ in ii coriiiT of tlio flrHt miimr.'. Knt- tiM- fli-Ht M|Uiin- uiul its diunH-tiTH. i.wlhat.Ml l.y ,l„tt.a lines in tlu- o^.y. m<\ tl.er. is IrH h iout- ixiiiitiMl »tiir , Cull til. uti.'.iti..!! of tho l.upil« to tho «ynun..tru-id urrann'-nu'nt of the linen .ilH.ut the eei.tre ot tho H.inure. Show them that when they have drawn one I i 4 OIII/liNTAII^ any ititi> i><|iiiiri^> 1. 1 tlii'ii iliviilx 'riimngh tin- ••rx, «lmw uiWif miintt'r>» rif tlif uullir i«i|imr<>». iH.|tlii:«iii not tit tlHWt' V%"T' tn •nd IlO«9«tM lun* "f luiy ili'll- I tlu'i) iM \i* liilvi" tho si'Mii- d it* (lividf tlii-rn j ill jnirti*, iinil "ii liviHitiii miiHtnK't I finli Hiii"' <>* tl>" I raw lilt iiO«f»ilH!» li itrt iipi'S in (» Ir- lifHt K.|Uiirt'. ers, iiiilivatiMl l>y u Ih Iffl » «u»ir- ) tho xyiiiim'truNil lu) i:t'iifie of til" \' luive ilruwu ono 1 lllio lll.y MlllftI .iiltW fi'Hllill "tll'T llIM'* liuviiiK ill*' ii.iiin» |..mitioii witli rif*T iif tin- hnimri'. ilmw !i liiu' vijiwiinU, •■•jutil to .ii>!-httif of til" »iil»' of tht ■<(i»aic. Kroiii till' to|t of thic liiir, draw iIh- iiiinT oliliiiuf liiicM of tin- roof, ami tlioii tin* lUitur purallii oliliijii.' liiici'. Xotici- tliat tin- r.Hif i>ro- j«'ct« ln-yonil tliu ci l.'H of tlii< liointo. Miiki- tlio titiiiuu'y iiM lilyli iw till' riiln<' of tlu' roof. Hn tli<- otiicr niilf of till- riHif. tiraw tlu' lioiizmilal atxi vi'i-ti.al liiUH fi.niiiii>,' tin- |iroj.'.ti<.ii tor flu- window, I)ivii'iii>; tlm oitlf of liii- nwif into four •■<|iiul l>artn wiil «ivi> jioiiifs wIhtu IIh' liin- i<\' tin- ^'ulilc hiriki' tilt- rocif. 'I'lu- ImhIv of tiir |ii>i< li l* fiirnii'il I'y a M|uai>' iliawn <»ii oiH-liulf of tin- lifi>{lit (.f tho HJilr of tlif Iioii-.('. Till- roof i.f tin- porth in half as hi^'h aft the l"i'ly of tlic ponh, und pr-ji'itK Nli>,'liHy li.-yonl thi- l'"dy, l»lvid.' tl.c ii{'|i<->- liidf of til.' Iiody t>f tho jKm-h into four partH. Thf iowcr window of tin- liody of thi- liouxf is h:ilf tlo- lifijrht \ IKAVHUHi*' W.I.V/'.I/. i.r tin- li-'M*''. wfill.- llu' wi.hli ..f tlif wfii.L.w I- liikir 'tf it» ImIkIiI. 'I'll'' |nr wmhImw iir<' ii litllf li""« «lt*ii ••»"""• ••• <'"' '"*'■' '*''•'• ilow. It i« ii«>t •■> '»' 'Xi l""t 'I'l'* viitiiiiii iliiMnii Mill .il llr«» rt'iulily iiiMi|irtlit'ii will ptriiiit. Cakd-Kxkih l-K, IX. Brcot Orott. Praw a Hipiitn, iumI iliMrinin(( niio* H(|iiari>>*. KiiiKf tln' rfiilrul «<(piiiri' mill null rinlii(( niiH* ' tllf iM'lltl'ul ciicli citriKi' r wiiiiIh. t'rii»<' lire i|(ili<'i| ill •l|i ill tllf loii- ll|l'tilll)-M i'llllol ni-<'il wIm'Ii tllf llnttfd lillfH of ifii, tliiit tlit'sf itiilllN, ilUfll liM ill uiidWfr Wfll I A OroM forniad of fiM Hijumm. I»niw u >M|iiftr«' irti »t» tliuiiiflf r«. Divitlo ciuli of if« niilcH intit i'oiir i'<|iiul |iurt> Divitif till' «'Mii-i|tiiil part*. Con* IM>rt til)' |M)iiiti* )if iliviiiiih UM ill tin- lopy, uimiiit? to iiuikf till- ihtfr«fitiii(i{ liiit'< iif tllf i'M«M iiiPi't itt till) pointit lit ijivixioii oil tllf iliiiiiiftfix. Ill iitlifr wiiriU, (oiiiifft llif |K)inti« of itiviitiiiii liy iililiijiif jliii'ii, MO ikM to form Hvp obliqiiM iii|uur«fii itiNidt) tin- lirxt i«i|uari>. ('MII>-l!xKllt'M|.: XI. Two OblJDiii m • Bquar*. Driiw II «i|iiurf, ami ilivido itn KidfM into thirds. Tliriiii((li the jKiintH of division, dmw two vfitiful mid two lioiizoiitiil liiifs, iiiitkiti^ iiitif >t<|imrf:4. In fiu'li foruf r Hqiiuri', draw a di- a^oiiul, with itn nidf towards tllf fftiti'f of tllf largf s(|iiaro. I<»( «'IiiIm of tllf diai^oiialf, wliicli art' jmriillfl. Tlif tfadifr can tmHily modify tlii* t'Xfrcisf, and iiiakf a dictation lc^. uii, l>y adding othfr lini'rt parallel or oliliijue to tlioMc ali-fady drawn. r.'.» TKACUKH.S' MANUAL. Caud-Kxkim rsK. XII. 1 A OrOB« with iU AnKles aU Acute. Draw a square, and .livid.- »'a.-h of its sid.'s into thirds. Tlirou^li the points of division, draw horizontal and j vortical lines, fonninf,' "'»" snialliT squares. Divitle each side of the inner square into halves. In eaeh corner s(iuare, draw a diagonal, with its si.h^ to the centre of tlie large sfjuare. ^roni each end of each diagonal, draw a line to the nearest point of division on the inner square. Oaku-Kxkkcisk \1U. Bigbt-Iiine MouldingB. FouM ". — Draw two pai- allel horizontal lines, at any .riven .iistance apart. Divide the .space between them into squares, and .Iraw the diago- nals of the squares. Add a horizontal line above, an.l another below. Form /'. — Draw two Iwri- zontal lines, at any given dis- tance apart. Divide the intervening space into squares, and draw their .Uagonals. D.vide each halt ol semi-diagonal into two equal parts, and, through the points of division, draw the inner s.iuar.'s. Add ii horizontal line above, and one below. > lit A ui II T- 1, is'k: Fi'ir It /. ^ m ute. its sides into 1 tlu' points of lorizontal ami Ibnning niii" Divitlo t'licli (r sqiuirc into coriu'r s(iiuirt', I witli its side iolar)^es(iuurf. fcadulia'^onal, on on tlio inntT Draw two pai- 1 lined, at any apart. Divide vot'U them into raw the diago- uares. Add a le above, and Draw two hori- t any given dis- ing space into )ivide each half ts, and, through r scjuares. Add V. l-'niiM <•. — 1 >raw two horizontal lines, at any definite distance apart, and divide the spai-e l.etween th.^m into squares. Draw their diameters ami diagonals. Di- vide each semi-diameter into two ei|ual parts; and. from the points of division, ilraw lino to the sides of the s(|nares. — these lines to he parallel with the di- agonals. Adil a horizontal line ahove. and one helow. A r.\ What is the nse of the ilotted lines in the ciipies > ami what is to 1)0 done with them ! 6* CM APTKK III SIMPLE CUUVES. Ik the pupils have been interested in the prece.lii.); exercisen, they will he nm.-h more intereste.l .n the oneH which follow. It is rare to f....! ch.hlren that do not like to draw. As «oo:. as they acquire a litt e skill in the use of their pen.^ils, they delifiht to apply it in every direction. While they shoul.l he allowed great freedom in the exercise of their skill, the tea.her Hhould frequently require them to submit the.r uue- p,.,ident work for inspection, in order that the faults may be pointed out and corrected. A Curve. A nirved line is n In,. n-Uirh rha„rs Its direction at t'iwri/ point. Curved lines are of diflerent kinds. A SiMi'i-K CriivE. — yl s!)ii]d<'. curve henils reijiddrl;/, and, if continued, irifl form a rirrh: All simple euvvea, less than a circle, are but parts of a circle. The curves at A are simple curves. The teacher should have suitabl.- ..l.je.ts U>x the I m TKACIIKUS' .\tA,\L'AL linrpiisc ot illustrating the diflcrt'iit WrniU of ciirvcH. In till' set of nioih'ls for priiiisiry schools, thcri' is a ilisK witli wliifii tlif various fcatiiros of the tinrlc. or parts of cirrlcs, nv.iy Ix' iilustratcil. Hiivin;,' (Iriiwn several simi»li' curves on the lioaril. and pxi)lain<'(l thcin to tlie pupils, require tbo latter to draw from memory a rij^lit unRle, and then to connect the two ends of the lines forminjj tlii' alible hy a simple curve, as at I». Tliis figure is called a tiuadrant, i>ec,ause it is ()iM'-(iuaiter of a circle. Kepeatinn till! curve to tlie left, we have a semi-circle (C), or one-half of a circle. Kej)eat- ing the lines below, w(( have the complete circle (I)), with O. its liorizontal and vertical di- ameters. To draw a semi-circle (('), begin by drawing a liori/.ontal line ; at the centre of this, draw a perpendicular, ecjual to one- half of the horizontal line. Connect the ends of these D. line.s by a sinijde curve. To draw a circle (D), begin by drawing two of its diame- ters, tlie same as for a square ; then connect tlie ends of these lines by foiir simple curves, which will form, when all drawn, one continuous simple curve, or circle. It is not to be expected, at fir.st, tluit pupils will, in this way, draw a circle with any great degree of HISII'LK VVRVKS. iiis of ciirvcrt. tlnTc is II disk ■\ti'\i', or parts III till' liniiril, ii'<' till* latter mill then to UK till' aiigl<> Iraiit, IfL'iuiUHi! Kt'licatiiiK O. 1(1 vertical . ids of thcsi' 1»^ cvirvo. To ) of its (liamc- iiiect the ends icli will form, jrve, or circK'. it pupils will, cat dt'grei' of ( acfiiracy. Iiidfed, it is not Iutc given so imuli as an i-xtTiMsi' to be copied liy the pupils, us for tlie purpose of showing tliem the completion of a simiile curve. — showing that all simple curves, if continued, will form lireies. When a curve is drawn on a Rtraight lino, as ;il K, the straiglit line is called the Itase of the curve, while the dis- tanco of the i-urve from its Imse is called tlie altitiiile. or heighl. B. of the curve. The dotted line in K shows the alti- tude of the curve at its centre. It is important that pupils have a clear idea of the hase and alti- tude of a curve. The hase is a straight line connecting the ends of a curve : it may he vertical, lior- izoiital, or oblique, as shown at V. *"• \Vc do not say a vertical curve, or a horizon- tal curve, or an oblique curve ; but we descrilie curves by their base lines, as " a simple curve on a vertical base." or, "a simple curve on a horizontal base," &c. The altitude of a curve, or of any point of a curve, is its perpendicular dis- tance from the base. It will be remembered that perpendicular does not necessarily mean vertical. Hence every curve has altitude, whether its base line be horizontal, vertical, or oblique. If a curve has a vertical base, tlu' distance of the curve from its base is called tlie altitude or height of the curve, just as if t had a horizontal base. When we simply speak of the altitude of a curve, we mean its greatest altitude; ftH IKM tlEKS' MASUAL. l.iit WO may him-hU of itw altitude at any point, Lesiilrs till- hinlu'st, jirovidi'd w fli'siRnatf tlui point. Draw on the l.la.^klioar.l .-irvi's with vi-rtiiMil. hori- Koiital, and ohliquo hanoH, and witli their c^ntrcH at dil^ViTiit iiltitnd.'M, until pupils have a clear eonipru- liensioi: of the terms; for these terms will be fre- quently used in sueceeding exercises. In the page of skeleton letters will Xw found some good forms for hlacklward copies. As the letters afford the simplest combinations of straight lines and curves, and as the forms are familiar, no definite proportions need be given here : they will be reiwlily discovered. If the subsequent exercises should be interspersed with the drawing of these letters, it will give a pleas- ing variety to the work. Not too much of the same thing at one time. A Cnun.K. — A rlrc/e in a plune fig- ure houndeil hij n. nirvi'd lliin, mffed its chrniiifi-ri'nre, every part of irfiich ia e'/ml/i/ Jlst'int from a point within, jj, called its centre (ii). This is the strict mathematical definition of a cir- cle, and makes it consist of the spacio ench.sed by the curved line. A Radiis. — A radius of a circle Is a sfrai;//it line drawn from its centre to the cirruniference (H). When we wish to speak of more than ^^ one radius, we say radii. A circle may have an unlimited number of radii; that is, you may point, iK'niilfH |)oiiit. verticttl. liori- u'ir centrcH at I cl«'!ir coinpri!- 18 will be frf- !)(• found Homi' le lottoM affbnl ties and curvnH, litp proportiotiH lily discovered. )e iiiteri^persed ill give a pleas- Bh of the «ame iH a plane fig- line., mlfad its rt of which is point within, inition of a cir- enclosod l»y the Ins of a circle •awn from its •rencc, (H). sale of more than i'. A eirclo may that is, you may SDtl'l.h: rdltVKS r.<» 6i» IK.UIIhns- M.XSVAI,. unlimiti'il mmibor (Iniw liny number of riulii. suid yet thoro run Ix- am' iniirt' tiriiwn iil'ti-rwanU. DlAMKTKR OK .\ I'lUrr-K. — .1 iH'iiiirtrr of n I Irrlr is II xti'iiiijht lliii; th'inni f/iriiiiij/i till' niih'i' mill turn If iiii/ fill- lininiif'i'i'iK'i' "II f"if^i siilr.t (])). Ailiiuii'trrof'arir.lfisiiiiiilo lip of two milii riinninK in op- poHitd ilirt'ftionf'. TIkip may l><) ivn uiilimitr.l numl>fia;,'e of the word might 1"' ilhi>trated hy a ring. In llu* one case, the whole (tf the penny wouhl represent the cinile ; in the otlu'r case, the circle would he repre- sented by the ring. Thus 'he distincli.m l«etweeu the two usages of the word would 1 learly seen. Tin' pupils should 111' reipiired to name objects which are circiilar in form. They would doul>th'ss mention wheels, hoops, plates, &c. ; ipiite likely they would also mention balLs, oranges, pencils, &c.. because thost! objects have the elenicnt of rcMindness. .\t this point, thiTcfore. it woidd be well to give some special attention to the wonl "round." It is a long time before children learn, without sonui special instruction, the exact force of this common word. Various ob- jects they can only de-crib" as round, though their forms nuiy n, tlu-y n-inlily It'iirii to ii.>n' tlif woriU wliiili f)nu'»l.v «'Xi»r<'i.ft tlu-i«(» tliHtiiictiotiH C.viili-KxKHrMl-: XIV, lo«oHb»d and C«rouimor»b«) Wf ilri'W tli<< cinlt' oil itrt liorixoiitui »ihI vcrtiiul (liiiiiM'td'ri* : we will losv draw II cii' Ic ill a K(|u;uf, Muviiix iliiiwii ii H<|iiiiri', with t-t 'liiiiiK'tir-i iinil iliiip>iiuln, iiiiu'k «>ii tlif •Iiii^oimiIh i»iiiiitH iIukiikIi wlii'li III'- ••irilt< hIu.uI.I [k h(|n!uv, and lim.liiiiK tlio Hcpiaf ■, i.-« said t^. l>. in- Hcnlwd. Knis.' til.' dotted liiK'i*. KmUM /'. .1 ' '■'•'/'' lii'finnHi't'ihi'il i(f)i>iit " S/iiiifi:— Draw a s.iiian' ; tln'ii, uii .-aidi Mf of tl|. .^r>* of tl:." H.|Uan'. tlicy nIidiiIiI for'ii om .■iidli':*^ Miiii.lt' iiiivf or .'indf. Wlifii u «'ir.l<' i-* thus drawn arot'iiil a s(|u«rt', it i.i waid to bo cirniin- ^(!ril>t'd. FoiiM .. .1 (i/olir. — Draw ii sqimn* und it» diam.'t.-ra; th.'ii an iiis.ril.cd .irclc. Divide each (..■mi-diaiii.'ti'r and »'Ul1i iiuarti-r Mi thu circle into four i<> iliMtiiirtiiiiiit II, llii'v fiulily lob*. Wheal. .J Cirrff in- fiimr. — III i» If (l») Wf ilrcw liivfixoulul uiitl tj'rn : w«» will ■li' ill ii c«|iiiuf. ii Hi|iiiirf, MJth uitil iliiipiiiuU, IiiXI'ImiIm i»iiiiitM li tin- ciri'It' 1(1 till' i'ihIk «J' raw till' iiirvi'H .Iniwii iu*iili' u salil I.. III- >i(t 'I S/imrr. — li' .xijntirt', 'h'liw rvi'H iiri' iinit«'«l lioiiltl f'or'ii iiiit' It'll II rinli' i.-« I to be cirruni- iqiian* und it» Diviilc cufh circle into four ^Itin! jmrld. Throui^li tlin |H)iPt» ul' tlivi»l»ri, .Ifttw th« iiiiM'r t'lirvf^. KouM il. A MVir/'/, — . l»rii« n w|iiiiri', willi it* ilU ttiiM-ti-rit ttiitl .liii({uiiitU ; itiiil tlii'ii iui iii»i'rili*Ml rin-i*'. I>iv(t|c till- 4«>ini-r tliroii^tli tlii* iiitM>r ptiiutit of iliviitioii. KriiHt' tin- tlotfcil liiin-n. I Cakii-Kxkummk XV. K Croii wlt»» Auitt«i. itlKht. Acuta. »nd ObluM. - fwl Moulding. Druw II («|Huri', uml tlivi'l*' it into iiiiio t>i|uiil Hinullt-r MiuurcM. Divide I'iiih Midi' of till' iniii-r i«|iitu'i> into two (•(|iiid jhiHh. Fri'iii I'rtrli jioiiit of division oii till' iiiiiur Mqimri', druw ohlimui liiii'M to tlif jioiiitj* of division uii thf rorriHpi}iidiiij{ i«id' of the liirK'* i>(|iiiir<-, KiiK.T, Kit Kkv. \Jini.i»iNiirt*, j Hiid, from till- [lointM of divinion, diiiw liuri/niitiil liios diviiliny 'dl the Hijuari!*. Divido tlif ui»|H'r Htdi- of «>a<'li i«i|iiur(' into four ••i|ual |iu,rt(i, and, from tln-u (lointK of division, druw vi-rticid liio's tlirouijli tlot squiirc'K, dividiiim?iW'li of the lirnt 8«|Uiir( >t int*> sixtL'tMi Kiiiidlfr si|imrifi. Dniw tlic liiu'.'* formiuj; tln' frot as hIiowu. If llu' linjtdit ure. uiifortiiiuili-lv without 1K.it II KHH' MAS If 4 1. fiinU, »li»'i» tli.« ti'ftilHT inu«t Kiv.« fur«li.r vi-rl.ul ix|»li»- tiulMMi. »t illicfrut.- ..II til- iM.iir.l. A.I.I u li..ri/..ii»ul liiM- uIh.v.'. iiii.l in».»thiT Im-Iow. 'riii* u ..II.' "l" »li.' iii..<'t |h.|.iili»r. iw li in •.»•' »t ♦•••' <'l«l«'»t. ornimifiitiil form.* t.vi>r iiivt.iiic'l. fAnn-KxriuiMK XVI. HoaattM oompoicil of •ImpU OurvM. KoMM II. — Driiw 11 *qinw ..ii ltd iliuint'fcrs, iiiul ui|)i tin* .littH.itiiilH. ThIiik I'li.li Hi'iiii- .|iitK.iiiul UN 11 I'liH.', tlriiw u HJiii- ii|i« .urvc 1.11 I'luli Hi.K'. Aim I.) niitki' all of till' ciirvtm ttlik»«. Ki.uM /'. — l>ruw li in|iiui.' .in itH tliuiiu'ti'M. r»>iiiK <'»
  • «'ini-.liaiiu>t<>rx. |.',,,tM ,/. _[)m\v II H.|uar<'. with its .liuinHiTu iiml ,liii«..iiul^. Widiiii til.' m|iiurt., ilruw uii iiiHcril..'.! I'ircU); UHiiijj .-ai-li Hi.tni-tliiiinft.T of tho ciwlw tt« ft | biiM', .liiiw a Kiiiiplf fiii've on cttcli «iilf. J Cahi>-Kxkk«mmk XVll. An Elght-polnt«rl>iil ixjilu' (III II Imri/iiiitiil la itiH' iif itii' imt, iiriiitiiK'iititl lurrM. imw n i«<|iinri' on nml uilil the '\tm (•iK-li Ht'iiii- itnc, (Iriiw It Him- lull MJilt*. Aim Im> trurvuH uliki*. >rnw li ii<|iiui-(' oil 'hiiiK<'iK'l> '*«'ii>i- huM i.nii»ll .•|imr<'. ioii on ihf i'orit-|M>iMlinK ^i.|.. ol' 111.' Iur«<' »\mr'\ V»\uu III.' .|ii»intlt»-« ol III »»"»• m|iiitri- IW .liiiuoiiiiU. ilriiw un iniMi' ■'i|iuii'i', |{iiii.iiil"'i' tliiil ill.' Imi« «liiili 'If' 'l"i''''l i" tlif .'.ipy ntv «lwny« to !..• •'I'Um'il. KiiKT Mnrf.i»i\ "|"'»«'«- into llv.' ixjuul i>uit»<, i.ii.l, I1..111 til.' iiointH .»r .li\i«ion. .liuw lioii/untiil liin"« tliroii^li nil of tli.» H.|.iur.>«. Pivi.l.' tli.- iipi-r -i'l" „f ,',M'li H.|iiiin' into llv |uiil piU'tH. uimI. iVom lli- points r.f .livinion. .Iriivv v.'iti.iil liif'* .livi.lini{ <'u.li of III.' iiirn.' H inner jiiirts, I !anu' as .\ in Card- K.xercisc XVI., ilhistrali-s iwo principli s -iv\i i.'Msi; XIX. LozenKO MouldicK. — Siinplo Uurvci on a Square, and Simplo Uui'ves in iv Square. Kidt.M II. — I)ra\v thi. , (,r more M|uan's, united hoii/un- taliy. Draw their diaup'ter.-. wlio>e points ot' intersection will ,i;ive the centres of the s(pnires. < )n each upper aiid lower >ide of each sipuire, as a liase, ilraw a senii-i-ircle throujjh the centre. .Add a horizontal line aI>ove, and an- other helow. Komi //. Srini-rirr/rs, or Siiiiji/n ('in-i'i.'n, oti, a S/idnr. — Draw a sijuare on its diameters. Using the lar},'er part of these diameters as diaj^onal.s, draw an inner scpiarc On each sidt- of the inner sipiare, draw a semi-circlo. Erase all hut the inner .square and the semicircles. l"'oitM ('. Siiii/ile (Uiri'cs in a S'/ikh'i: — Draw a square and its diagonal.s. ])ivid(' each si'urvo ilrawn through the centre of the s(piare. Draw tho three corresponding curves. Ci.s Th:.\' IIF.IIS' MAMM- rour-polnted Star, Outline. l)riiw ii >. On I'lifli Mtlf of tlif iiui.'V s.nmiv. ilniw an isos.M'l.'s U-v.w^h: witli i'"* iil>cv in tlli- .■.■l.tlT of til.- .ni- v.'sitondinj,' si.lc "f tli- hiV'A'' Kviis." all i'x«'''l'' '•"• S(iiiavlate or l.lack^ourd t..ay thus ho V. iiud tlivitlo ,n.>, 1)11 I'lifli r siiniirt'. ilf^^v Illicit', \vitli i'^ tn- nf till- (iil- ot' till' lill'iii' all I'Xi'i'pt tlic iiiv iiiid its ili- tlii», as ii base. lioiisf, without )iiH. 'I'liis is a • rhiss aiialy!*is. atinK Form for imtal lines at Ww lore vertit-al lint'S, •iiiinR a serifs of )unl may tlms l)c SIMPLE CI UVK^. m .•oVfiHMl with s.|naivs. I)ivi4.' .•a.h si.l>"'f \ihli' sipiares and irosscs. The same vesnlt nniy he ivaehi'cl in tliis way. avoid- m-^ the lirst series of stpnirfs. Draw a sipnire. or an ohluii^'. of deihiite size: an ol.lon-. for rxaiiiple. fonr in.'hes hy six. Divith' the sides into .Mpnd parts, an ineh or two inches Ion?, for in-tanec l!ci.'innin,i,' with the points of division neaiv-t tlic corners, con- nect all thf points hy ohlicpic Inics. lorniin.u' a scries of ohrKpn" s(pnircs. Finish as in the lirst mode. Dire.'t the attention of pupils to similar forms to he found in cari)et:i, wall papers, &c. ro ■ILMUIKlis' St A SUM,. Ueml-oiroloB and BtnilRht Lines for oovorlns HurrucoR. I'iMU :i x'rics (irsi|ii;»ri's t(» 111) tln' sl;it(' or Idai'li- liDiinl. IHviilc ciii'Ii niili' (>r I'iicli siinarr into I'lmr .(jUiil ii.irts. Oil till' two iciitiiil imrts . of fiicli si(l'. ilriivv II scnii-i'irt'lc, tcisilin^ iiltiTii.itrly li>- j£ wiinU iiiiil tVoiii tlif niitri' of till' scjuari". ('AI!I»-KxKIII MI". XXII. Forms for Bopotltion, composed of Simple Curves. KoiiM ('. — l>ri\\v two pur- iillrl lii,ii/i>iital lines of any Icnj^lli, ami at any Kivcn dis- tant-.' apart. Diviili' thi'spaco lu'twi't'ii tlii'iii into s(pian's. Diaw till' ilia<,'oiials of tlio s(piari's, and divide I'lvcli .scmi-dia^'onal into two fcjual parts. Conncot tlio opposito oiids of caib diaj^onal l-y simple curvi'.s drawn tlirough tin- divi.-ions of tlio otlur diagonal of tlic same square. Add a horizontal line aliove, and another Ix low. Yoixsi /,._r)niw a series of squares, united horizon- tally, as in A. Draw their diameters and diagonals. Conneet the ends of the horizontiil diameters to tho *'ii(ls of the vertical diameters by seini-eircles drawn thiou:Ji theeentresnf the squares. TaUiiigeaeh half of the vertical lines which se^iarate the sipiares as ft base, \ oriDB HurracoR. x'rics (if si|ii;»ri'H shiH' III' liliii-l\- 'iviilc ciu'li Hiilt' (inarr iiiti» lour [s. Oil till' two liirts of oacli V a scmi-i'irclt', iiltiTii.iti'ly I"- I t'ri)in the niitii- I. Iniple Curvei. - 1 >iiiw t\V(» psir- al liiu'.t t'C any t any j^'ivcn dis- Diviili' till' .HpacH II iiitii si|iiaii's. iajiKiials of tlio I (liviilo oarli 1 into two (Mjiial oct tlio opposito •h i\\i\^o\ui\ \>y ilivi>ioiif". of tint AiM a liorizonlal ,, united liorizon- < and diayonids. (liamcterd to tho mi-i'irclcs drawn Uiiigcaidi half i)f ipiari's a.s a buso, >/.»//•/./•; rr/.'fA.v, t* draw 1.11 raidi mdf of tlii'l-aM' ^iinp!.' iurv<-<. to iinlto Willi till' s.'ini-cirrli-v Add a liori/mital linr aLov. and aiiotlnr Im-1'>w. I.',,, .J, ,.. _ Dniw ii scrii'S of Miuaivs. a> in lln' last two ••xcri'isi's. Draw lliiir diami'li'i>. < >ii carli side of ca.di .Hqiiarc, as a l.asr, draw a -.iiii-ciirli- tlimn^di tlic I'Liitiv of the siinaiv. Tlim draw a einle. pa»mj; till i^h the ends of the diameters. As an addition to these exenises. draw a similar M-riis of sipiares ahove. and another l.elow. eaeh nnilid with the lirst series. Till these sipiaivs. in the .same manner as the lirst were lilled. with mrves. If they are correetly drawn, they will in liuli ease form an involved s.'ries of i^erfeet eirele.s. ( )iiiit the paral- lel horizontal lines. These exercises for eoveriiiK a surface will be found ^r„od ones for the pupils to practise fre(|neiitly. Much of what has been learned in previous lessons will be brought into use. The pupils should be jki- mittod to cover their slates with su.di forms, and also to draw them with many repetitions on the blackboard. If a slate is tilled with them carefully, tb.re oiij,'ht to be considerable improvement between tiie iii>t and the last linos drawn. (iuKSTiONS. — Dcscrik- a curve. A simple curve. A «iiiail- rmit. A semi-circle. What are the tVaturcs i.f a circle > What is the base of a curve? The altitmie ? Wh:>t i> n chonl ? An arc ' What is the .liirevenee hetween the iiiatheinatical aii.l tho iK.piilar use of the word "circle" ? How shimM .letiiations ho ^.iveii to chil.lrcin What of the wor,l " ruun.l " ' AVhcii is a eiiele said to he circumscrihed ahoiU a .-quaiv 7 Inscriheil in a M,aare ? What is meant hy " foil " >■ Trefoil ^ U.uuieto'.l < CHAI'TKi: IV. ( ..Mi'di Nil ( Tuvr.s -Tin; kllii'sk and oval. Tins ruvwc liMvc'cliMit ultli siini-lfciirvi's; tliiit is. Willi .'iii'vi's struck Ib^iii one n.iitiv. iiml liiiviii^-, I'on- sr.|iic.|itly. tl.csiimi' ilr;,Mvc ,.f ciirvatmv in ov.-ry part. All s!iii|ilc .'urvi's arc par^- "f circles, iiiid, if cniitiii- ucil tar cii .'i^'li. Iicioiuf circles. A circle, therefore, is 1)1 t ail elKliess siinjile curve. A coliipnllllensr is II jihllir fh/lirr /loiniifrif III/ a ('itiii/iiiiniit riirrr sfriir/: froiii firn rnifrfs (A). There are many curious things to l.e said ahout the ellipse, [t is the f.u-m a circle appears to tidie when viewed ol.- and a circle is always viewed thus, except when til!) eye is directly opposite its centre. Draw a circle on the l.hudd.oard : step to one aide and view it, and the circle will apparently l.e- .•ouie an ellipse. Draw a circl i a .slate : turn the slate from tho eye, and view the .-ircle : it ; AND OVAL. Lirvt'H; tlint in, I liiivin^', fnii- iii ovcry part, md, if foiitin- rolc, thcrcfort', |inuiiil I'lirvi' i>* liroiiyliiiiil its nidi fi.iin tWH rt'll, till' (ll'f,'Vf(' iiit, us ill tln' [IS in tlu' "Viil : lirection, us in tii/iifc hninxlril. in:/: from tn-n s tliinfjs to I'c is tin' t'linn u icn vi('\vi'il <>1>- (1 tllllS, CXCt'llt centre. Druw to one sitlo iiDDarcntly 1»'- u .sluli' : tnrn thf circlf : it ro.i//'or,v/> <:rt{yh:s. *■> will liirn tali.i tin- form <>!' un .11 ipso. Hold ;i lio..p in u vi'itii'ul position, wii'i its cMitro diri'.'tly in front of tin' vyr : \\u- Imop will then 1m. scimi as u rinlc, — its ri'id foini. Tnrn tin- lioop from tin' "•ye, iind its form will m.priir to Imv.' .■Iiun'_'id t'. lliat of :in cliipsc. Tin' farther tlir I p is tnrned tVoni tiie eye. the liutter will heeoine tiie ellipse, until its two sides nn'r!,'e in one, iind only a strai),dil line is se.^n. TaUi' u round stiek : ent it uim-oss. ol.li.pn'ly and e\enl.\ : ilie shape of tlio section or scurf will l.e that of an .'llip^e. The more ol.li.pn-ly tin' sti.'k is ent. the ^nater will hi' tin' length of the section compared with its l.nadth ; hut it will always l.e an ellipse. A disk or cone atVords the hest means for illnstriit- in;; the ellipse; hut. if the jiroper models nre want in;,', th.' teacher can. hy usins the moiles ,,f illu>trati..n just described, familiarize the pupils with the » \Uit 'form of the (dlipse. It is essential that they sln.nld he.-ome perfectly familiar with this curve, w it is so freipii'iitly einph.yed hy hotli artists and artisans, 'i'o draw a coin', with an ohIi(|Ue view of its base. lii>t draw an ellijise, and then add a vertical and twoohliijue liin's. as shown at 1'.. The ohli.pie lines hIiouM not be drawn to tin' ends of the Iotijj diame- ter, but tanj,'ent to tlie _ eiirve. l'>e particidar to ^■ observe this. Erase the diameters. Draw several 74 7>.ir»A7,-.s' W I V/',0, cimi'H, \i\v'mg a in«irf or h'** i>\<\'u\\u' vii'w <>f Mio t)!iM.. llUi^tniti- witli II iiiiHlt'l. Tilt !••■ ail' iiiaiiv \;nialioii^ in tin- f'lnii i»f tlii' flli|>'<'. Hiiirc il.H r flml tlif two centres of an el- lipsc iilnii ly ilniwn, tlien draw fronj an end of tin- sliort iliami'ter two ol)li(pie lines, on i eilher sid". to the lon,^' diameter; eaeli o»' tlii'sr ..hli.pie lines lmvin« ii lei.jjth eipial to one-lialf of tin- lonjj diiinn- ter. Where the oldiipie lines toiu-li the ionj,' diani-- ter will 1m; the two centres, or Jjrl, of the ellipse. N(.w take any point in the circumferenee of the el- lipse, and draw a line iVom tliat point to each enntro of the ellipse: and these two linos iinitod will e(pial the length of the Ion},' diunieter. If that .liaineler is two feet, for exaniph', the two lines will meaHurf two feet. If these two oblique lines do not eipnd the len^'th of the lont,' diameter, then it follows that the ellipse is not i-orreelly drawn. liarge ellipses, of dilVerent proi>ortionH, should he drawn on the blackhoard. from time to time, f..r the pupils to study. This can be easily rliiM'ly lis to a|iiir<>iirli •IT its I'lirni. it irt'H. ■r, ami its Hlmrf, lli|isi> into two U'tiTH, liiset'tiiiK I'llipHc into four iciitrt'H of ail I'l- aii I'liil of tin- on I'itlii'i- sill". i> oi)lii|iii' liiH's tin* h>ufi iliiinn- tlii' ioii^ iliann- , of tlio I'liipst'. trt'nrn of till' I'l- it to encli o«ntro initpil will t'linal f tliat iliaini'li-r I's will nu-asuii- L's do not *-i|nal n it follows tliut ■tions, nlionlil l>i' to tinii", for tin- y iliiiic. Take a I'liil ; stick two voMi>ni:sn vvii vkh. W \ j»Ins into ttii- MarKlioanl. lU a Ii-ss ilixtaiiii a|.ait limn tin- li'n','tli ul till' lliriM^l; pnl a liin]. o\. r .a. Ii |.iii. wlii'ii tli«' tiiirail will liuiiK loo^ily; |»i'f.Hs a rva.von u;,'aiuHt tilt' tliri'ail until it i" ivmli ri'l tani ; t'nii fanv tin cravon ai'oiiinl, toiiiliiiiK' tin- lihu'klioaril. aii'l niakinj,' an i-Ilipsr. If an illipsi' is iii|uiri'il liavinj; iliann't/i'rs of ilrii- iiilr li'iif^tli, as a Ion;,' iliain.'tiT of tliiri- fi'it ainl II .-liort tliiiini'tiT of two flit, iliaw tin' iliannlii', iinil linil tin' iiiitri's of tin- illips... as uln-inly ilcsfiMlifil. I'liu'iuji an <'n»l of tlir tlif.ail at larli of thi'sc ci'iitii's. witli slark i'iioiij,'li to allow tin- cravon, wlifii pri'ssi'i] a;,'ainst tin- tliri'ail. to touch an ciiii of tin- nliort (lianii'tiT, draw tin' flli|isi'. wlicn its lioiindary-litn) will pass tliroiiv'li tlif ••mis of l.olli diaini'liTs. ami lie of tlic n'i|niri'd proportions. |{y diawinj,' tin- cUipsf in tliis nninmr. tin' cliildnn will nnvlily puncivt? wlnvt is nicunt wln-n it is «aiil, that tliii fUipsi' is a coinponnd riirvi', struck from two cciitri's. As the two [lins, or two centres, are brought nearer and neiuvr together, tlioy will readily perceive that the ellipse approaches nearer and nearer a circle, while it never becomes a circle until the two loops are placed over onu pin and the curve is struck from one centre. Literally no figuro can have two centres. Children need not be taught all that is here said about the ellipse before they begin to draw it. Indeed, it is best for them to acipiire a knowledge of its fea- tures along with their drawing, and so acquire that knowledge gradually. They should, however, have a di.stimt idea of the form of an ellijtse before thoy begin to draw one freehand. This they can obtain by 7»l THAVUkHs' W.I.Vf .W. vhvvlug; n • i» 111.1.1.1. Ill .itli. !• "I 111'' III"! tw.. .ii-.'K. til.- .'.v.- iiiiiHt Im' tliri-.-rl.v ..|.|M.'it.- ll;- tnu- vinxtrv, or iM.iiit wli. r.- tliM twu iliiHwt.'f* iiitt'r»'«-<'t. 'r.i .Iniw mi i-llipi..' IVi-i-liaii.l. i»». «f A. 1m «iii l.y (IruwiiiK IV v.-rti.iil liii«' l'.>r tlu" truu^v.-r**-. »r I..11K (li.im.-t.T. Divi.l.' thU liii«' !•»»•> »^v.» .-.iiml |.iirt-< i tlll'nll;{h til.' lioitlt .if «livi«i.>ll. .Imw ;l l|..li/.nllllll lilL' foi- til.- xli'.rt iliiim.-t.-r, Imviiiy "ii.'-lialf tin- l.-tiKtli ..t' till- Icii^ ili.iiiu-t.-r. Tliv..unli til- i'IhU of thm- .liiim- i.ti-rn. .Imw til.' lM,iiii.li(iy-liii.' of tli.; .llipsf. S.-.- tliat IH iiurt <.f tins lM.u!,.l.in-lii>o \* Hlr.UKl'' ! ♦*•■'* '• ""- \vh.-iv iiiiiU." u "liiup til -i, ; tliiit .-lull .|iiiirt.i »( tlxi ..lli|wliii.« tlii'HimH'Hlia|..- Ill th.- otlx-r tlii-t-c-.|iuui.rH. ll.-.iuiv.,' tlh- pupiU t.) .Iniw til- ^iinii- oil flu-ir nliit.-, iiiiikiiiK till- loiiK' iliiiiiu-t.-r f..iir incl.t'S for i-xiiiiii>l.-, aii.l till* sliort .liaiiH'ttT t\v.) in. hex. After Bevt rtil «-nii)»('«, with til.' j)ro|n>rtioii»< 1 X - (<"'•' ''.V \\M>), lik.' III.' "in' »t A, liiivo 1h-(-ii tliiiwii. thi-ii iliiuv iitlii-ix, with tlilVi-n-iit )ii'nii(iitii)iis. iiiiil ill .lilV.T.iil lM).Hiti..iii», UK at ('. It.-.iuin- tho pupili* t.i r.pr..- .lucc thi-m on their xhit.--*. Tilt' piilh of th.- t'iu-th iihoiit thi- sun is nil .'llii-. Th.- SUM i^ in <•>..• -f ;♦« »";'l l,„t. w.-r.' an .Uil's.' drawn ..n th.' hla.khoar.1 1uivm.« tho sam.- pr..porti.Mis ns th.' ..rhit of th.- .-avth. it wonl.l 1m . p.-rhai>-.. inip..ssil.h< for th.- unaidcl cyo to ti-ll it from a triu- .'in-le. r»j( till iiftiiiil I till- I yi' iniiMt »r |M)iMt wlit'i't' t A. Ill i^iii l>y VIT*I', "t llltl(( i'(|iml |i:ii'l-* ; liiii'i/iiiitiil line ' tlif ItriKtli lit' itH ftu'i; iiklMiiinl liuvhiK cciiitlt, it wi.iiM III eyo to tfll it T7 iiil.l vtnii'nrst* i:i uvas. An- AuTixr't I'MKrif;, — l»ii»w uii "W wliiM'f t)it> rtilor i" iioiiitlly |iliti-i'«l. A .■.lilii'iiliil I'aiiiti'C w;m oiiff (ixkiil Willi wit I' III- iiiixi'l I'i" lolor-'. •• Witli liniiiiN fir," lt< ii|iliiiini. D. UH lit I). ii •'"• liori/.oiiiiil lim-. Uf ii I'usf, imrt of wliosc iMtniiiliiiy-liii" is u !.ini|ili' cuiv.', tlif otlii'i- piirf an "Uipxc It will Iw HiTii that thf lon« diaiiK't.T dividi-n tho oval into two Pfiuiil .similar imrts, and that tin- »jiiof >i!iiiil>n' l>arts. " Eijnal " n-fiTw to the arcu, or Hurfacf ; "simihir"* nl'i-rs to thf slmiH'. Hi-nco two <'(|iial figur«'» may have diiVcivnt hIiuih-s; whilf two similar V -J fi tflWHUUM' MASirAL Muutf* miiy lukV"' ilirt'iTfiit unnw. A« tin* two |»iirti« v\' llif oviil, nli'ii .liviili.l \l I"' aliki' ill ImiIIi ri'>«|M'i ti4, it i« lun "ury to «|i'M.'nlM> tlii'iii II* njiiikl similar jiiirf *. Kitlu-r iliiiiiit'tt'r •»!' uii I'lliiiM', Nvliifli U xonit'tiiiuH I'ullfil lui iiviil, l»iit |. hot itit oViil. .livi.li'-t it \u\i> two i.|iml MJiniiar piirtit. It IM not fuMUnliul to UII oMll lllUt III* ImHIImIiU>-I.II«» Ih' ill |>iirt a •Inlf, iukI mi «lliii«' in purt. lik" !'■ On tlif otliiT liiiiiil, it limy !»• llt I HJiniiiir [uxtin, liiiiiiMlaiy-l'iirt I |iurt, liki> t>. iiMi'il ftliolly iii^ irNot'ilitVi'ii lit 'li'iiruii t'llipMc, rvit. It i* only ■'UK i iliitl iiii* ,1 Kiiiiilur |iiiil'<, I>ia\v "11 til'- tlli'il ovuIm, Utiil lir wlutiM, Do tliciii with liny if tlii'y gft tlid n ilciir foiiipn- tllM OVttI, tllD.ilt hIioiiIiI III' iilili' ;fly, iiU'l toroii- vovcr, 'lroj» tin* itly by wiiy "f 1)^ ciirvcjt art' tit nine* tlii'iii ciirv- I'ir ('(iinpoMitiiin. to till' piir|M(Hii rt'viow of tlii'so I T0 i» info f«.i VUMI'OL'Mt UUHVl." Millal. Pmw u viTtii'iil liiM', uihI i|ivi .'<|itil |iurtH. On lli>' ii|i|H'r Imll ilr roue |Miiihi|, likf |>iirti» of u:i uviil. CAIiU-KxKUCrHK XXI i I. Uouf'UlM*. KlU, Top. An II«>l'K-iitrul vfiti.ul line, uikI li'iilt' it into tlii'i'>' I'ljiiiil I'lirtt. Draw the lioii- 1 fi'iif.il liiifM, uimI titt-ri tl.o nidi' I >u'«, iiiiikiiiK ill'" width of tin- ;;liiKM i'(|iiul to iinc-tliint of itt height. 'I'Im' tliickni>>H of tin* fruiit« i>t )H|iiitl to otic-Hixtli r! tlu' wtiltli of till' ^liiHi« ; whili> tiio top uiias.-, .Iraw a .<■....-.■..■.•.• t,,,..„,,l, ,1... toi, «!■ tlK v..rtieani,.u.. Hum j-mnts ,„,,, ,1 n.ls of tlH- l.ovi/.ontal lin.s .Inuv o ...,.1. ,|,„.s totlM. l.ott..n. of tlu. v.rti.al line. A.M tlu- l,,,iut at tlH. to,., au.l th. sligl.t cams at th- npi-r ends of till' ol>li» [vw ii scnii-i'iifli' I'. Krniu Jioiiits 111', (Inuv olvliiiiu' line-. A«M tli«' rvert iit till' njiiMT tical liiii! of any ree equal i»ai'ts. (Irawiihori/.initiil ical lint'. Divide . into lialvt's. and, a vi'i-y sliiirt lim-i- ic horiznntal lines, ruling till' straiglit Kintal lines at tlie it losiJ tlian atliinl veH, the remaiuiag ' bottom. I Form. al line, and divide x\ iiavts. Thron.u'li n, draw the lonjiest •qual to two-tliirds line. Upon this st the figure. The ivcle ; the acorn a e whole is an oval. I COMPOUND UUIIVKS 81 CARD-ExKUCiaK XXIV. Lemon and Barrel. - The FUip»e lUustrated. TiKMOv. — Firnt draw an ellipsi', with its short diameter about (wo-tbinlH ot the length of the bug diam- eter. .\dd the jioints t'nrmin;; the ends nf the iemou. ' Haukei-. — 'litis is a gooi figure for rlass-analysis i)efbrc drawing. Thus, lor exam- ple : — Trnrfii'i: — Wli.'it lines arc seen iu this iiguie ? J'lt/iif. — J^tiaight lines and curves. Tiiir/it')'. — What is the position of the straight lines? I'lijiU. — Vertieal. Tc'ukrr. — If vertieal, what else must they be, as they are side by side ? Piij>l/. — \\m]M. Tnu'her. — What do they represent in this drawing? I'lqiil. — Hoops on a barrel. Teacher. — liut hoDjts are eireular: tlieae lines are straight. How is that ? /'uj)i/. — When a hoop is turned so we cannot see through it, then it iooks like a straight line. Tcdclicr. — Is that the position of the hoops on this barrel ? Pupil.— Yc». Ti'dchcr. — If youiiold a hoop with its centre oppo- .site the eye, with each point of the hoop at the same distance from the eye, what will its shape appear to be? Piijiil. — A circle; and that is its real shape Tiar/tvr. — What is a circle? 82 tkaviikhh' manual. /.„/;//.__ A simi.U- .•nrvo. It is struck i'roin oiio .MMitri,', uikI ImmmIs ;ililic ill all l>iii„„//.._ Into two .M]nal similar parts. ^ T,;,r/irr. — Wliy do you say i''/iiid and ,sv/»(/"r . /V,,,7 _ 15,.causi; " eipial" n-fcrs to area on.y; '• similar" to shape only. Two iifjures may he equal in area, hut of ditt'erent shap.'s; or they may he simi- lar in sliape, hut of ditVerent area-. 2\,,(rf,n: — \low does the conjugate, or short tliam- eter divitle the ellipse? />„,,//. _ Into two equal simihir parts. 2' „,,•/( ,;c. — How do hoth diameters divide tlie ellipse '.' l>„niL — Into' four eiiual similar parts. ^ 7V„rA,r.— ITow (h) the diameters divide eaeh other i riinil. — Into halves. Ti-Airher. — How do you tiiid the two toei, or eeiitres, of the ellip.se? ,. ,. i /j„.,//._|5y drawing an ohli(jue line from an end of the short diameter, on either side, to the long diam- eter, the ohlique lin.^ heing eijual to one-halt ot the lon.r diameter. Tln^ points where the ohlique hues toudi the long diameter are the foci of the ellipse. 2V,„.//t'/-.— On what does the shape of the ellipse debend ? , , , .- ..^ t P„IjII — On the difference m the length ot its diam- eters. lick i'rom iiiio >li(iucly, wliat roiii two foci- awing siiiipW". Ifs of tlu; bar- er long (liivni- to iiri'ii only ; iiiiiy Ih» ciiual )' iniiy 1)1' J-imi- j or sliort (liivni- | i ts. j ■rs (livitlf the j tH. idcfUfhotlu'r? ' I I foi-i, or fciitrcs, j (' from an fnd the long (liani- one-lialf of tho le oblique lines ■ the ellipse. ! of the ellipse igth of its (liani- ( o.yfrou.VD vun vks. 83 Tfiiflin: — The less the (liH'ereiiec '.' — I'lijiil. — The more nearly the ellipse comcf. to iieing il I'll' le. Tiuflii'i: — The greater the ilitlcrencc '.' — I'djiil. — The more nearly it comes to ln'inj,' a straight line. Ti'dvlit'r. — How nnuiy shapes nniy an ellipse luive".' I'lijiil. — .\n emlless numher. Tiiicln'i: — lint what may In- said of nny point in the lioiindary-line of any ellipse'.' I'lipil. — ■That, if a line he drawn from this jioint to eaeii of the foci, or centres, the two lines united will he cijual to tin long diameter. Trin'hi'i: — In drawing an ellipse freehand, what is to he observed ? I'lijii/. — Xot to nnike any i)art straight, imr any part a circle, nor a sharp turn anywhere. Ti'drlicr. — Ls iteverprop(;rN)<;all an ellipse an oval? Puiill. — No; for an oval is always egg-sliaped : one end is always larger than the other, wliich is not true of an I'llipse. The short diameter of the cival never divides it into two equal similar parts; but the short diiuneter always divides the ellipse in that way. It is not expected th..t the teaelnr will follow ex- actly thi.; mode of ainilysis. The manner ot' putting the questions, and their number, must be adapted to tl'.e <'apiicity of the nupils. .Vfter th(! prelimimiry analysi.s. bringing out nmny or few of the characteristics of the ellipse, proceed to draw the barrel thus : — Draw an ellipse, with its short diameter about two- thirds of the long diameter. On either side of the centre of tlu long diameter, mark ofi' a distance e(pnvl to one-half of the short diameter; ilivi'ie wluit re- mains into iialves, and. through the points of division, I H4 TKAciiya^^' .u.i.v'.i/.. .U,,,v tl... lu.a.Is of tlu. l-anvl. Draw tlu- ..n.l-l.no,.H. ,„,Ui.„ th.-ir wi.1.1. ...,.-l t., ..n.-I.alf of .... .,.a.. .,,,„:., ,,v .I." l:-t divisions. D.v.lo t ... s,u..o ,„.,,,„„„ tl... .....l-l.-r i..to four ...V.'il l-'^'-t'* ; ••'' ^^ „,„ ,,„„« i.. tlu. .■•■Mtr.., a.ul tlu, other Lo-'PH .-, tl,. otliur points of division. Boitle. — Ovoid Form. I )ni\v II vertical lii..',ivi..l.livi.l.' it \ i„to tluve ...lual parts. At ti... I'ot- i ton., iiii.l throuKh th.. i.pp.'r po.i.t of .Uvisioii, ilrasv liori/.oiitiil lii."'-, luvvii.^; a lei.Ktl. .■«l'"il •" «">.'-y judgment of eye. Tl... teu.:l.- Vr will draw then, thus on the hliickhoard, and will then re- quire the pupils to dniw tl.eui on their 8lat..s without deli- „___^_^^-^ iiito ;irop(U'tious heiug giv<.|i. Draw the full outline of each grap.' at tirst, an.l th.... erase the parts which should not show. 10 «>ii<'l>'*. of till" riJlilfO ll> till- SIilU'H jiartH ; dniw llliops (til tilt' , iviul tlivitlf it . At tlic I'ot- • ui>iii'r pi'iiit. ,ri/,itiitiil liiii'f, 111 to uiu'-tliinl Dviiw the I'l"- licli is !iii iiviil I mid the iii'di ipeB) and 'Em- I, wliuli is oviil whii'li iUH' I'liip- i'«t,' ('■). whifli ) 1)1' diiiwii l>y yi.. Tlio toiidi- liciii thus on tliu id will tluni ri'- ils to dmw them i.s witliout dfli- ,iis lu'itif: ^,'ivt'ii. it tiiHt, iind thfu I i.'OSt POUND VVKVKH. «■> .M, Mi. — Tilt" vcrticid iiml Imri/oiital dotted lines artM'(|ual in ifn^^l') ^^''''''' '•"' I""""'' is hfiiily onc-tliinl of the widtli of till' lii.rizoiital line. It will Ix* :>o- scvvimI that tlic curves foriiiinjf tlie handle hiive ii semi-elliptical char- acter. This is a favorite curve with Xatiire and with de.^i<;iiers. Oahi)-1Cxeiccisk XXVI. Bosette of Ovoid Forms. Draw a square, its diainete-s and diagonal ; ar.d then an inscrihed circle. Di- vide each diameter into six eqiial parts, and, on the central divisions, draw the inner circle, which will thus have a diam- eter eiiual t(j one-third of the diaiiH'ter of the larj^'e nwXv. On i'ach part of the iliameters and diagonals, between the two circles, draw an oval, making eight in all, and touching one another. (iiiKsrioNS. — What is w f()m))oiin(l oiii'vu? Ad dlipsc f What is tlic sliapc of a circle when viewed oli!i(|ueiy >. Wliat aiv the diameters of an ellipse ealled ' ll«w .lees eiieh divide llie el- lipse ' What is meant hy the foci of an elliiise '> How can tliey be toiind >. How can you draw an elliitse of «ivon proiiortions < What is an oval ' How do its diameters divide it f Of what may its houndary line he .omposed ? What is meant by " enial " nntl "similar" when applied to ti^'uies '. •■ I OHAI'TKU V. roMl'OUNl) (TRVEa, itHVRUsMo <'ri:vES. — tiik ixiek. — AnsTitArr • IJHVKS. Tiik ri>ni|Miun will now iittcnd to those curves wliicli Ufit only cliiiiige their direcliou irregularly, Itut reverse it, turuiiig from the right to the left, from the left to the right, and never enclosing space, The two parts of this form of the ccujpouiid curve may each he a simple curve struck from one uii( tions of rhe curve we coiiiinHisid in itself, A^ruiii. cacii M';j!nieiit of the reversed ciirvf iii.iy iie '.juiie ditVci'.'iit from any one of the eoninound uurvee) winch lia\c yet heeu de^c^il(ed. It may '-"' «f '""■^' ** eharactir that it y iiiey hand without tlse aid of iuHtrunieiit-. Tu thj«i last varii'ty heloii;4 the tirst thrse curve.s shown at T 'i'he first curve at (' i.s eaUed the <^gee, and .-otnetiuus tlio " line nf beauty." li» two icgments are alike. The tle^jree of curvature o1 each U greatest at the noint of its f,'reatest iilutJide, and grown le.s.H u and losf- from tlu*.' jiojut- Ah v/f niijuoach the ]Hinit where the eurve changes its direction, it beeonicN nearly u straijjht line. Each s.-jruicnt. therefore. is a iinely-graduated oomjiound cinve : and, the two segments unite wit'iout any siuMen chan<.;e of direction in the eurve. Let this be earefidly noted and remembered. Where the segments ot the compound curve at P. unite, th.- direction of the eurve is instantly and completely reversed. This 9mm mwm 88 TKAVtl Kits' HAS UAL iniikiM 11 Honu'wlidi <1iHa>jrpOftlih' impii'K.tioii iipnti tlio (•>•<•; l.iil, wIhti- the HfjjiiH'iits ol" tlif lirnt (MmiM.iiiMl .iirvf lit (; miiti', tlicri- i* no hui'Ii iil)ruiit cliuiiKf <>f ilircftioii, iiiul llu" iiniiivsHidii niiidc upon tlic «•>■•• in .•..iiscqiMiitly a^ivi'iil'l.-. Thin is HoiiictliiiiK to l>o ..l.s.Tvnl ill ilriiwiiin voiiipoiiinl curvcH tiTi'luvii« stop until till' oilier i-nd is rrarluil. Set' tliiil tln-rc is no miililun cliaiiH" ol' .lin'ction in tin* furvc. Till- si'cond iinil tliird ciirvi'H sliown at V arc inodi- lloations ol' tin- ogee. In tlit! hi-coiuI, tln' iippiT cud of tin- iippi'V Hi'Kiiii'nt. and tho lower end of the lower HeRmeiit. are drawn fuller tlian the other puts ; wliilo just the reverse is triiv in the third. I5ut ohserve, that as ill the oKi-e, so in these eurves, there is no «udden «;hair;,'« of directioi.. In drawing these curvei*, proeeed as with the ogee. To draw the fourth form in (\ whieh is a uni n of straight and curved lines, first, draw a vertical'Iine. Divide this line into four equal parts. and.throuK'i the central [loiiit of division, draw a horizontal line eipial to one-fourth of the vertical line. Draw tl urves and straight lines as shown. Ol'servo that the straight line* so run into the ciirve>. that it is iuijios- sii.le to tell where the former terminate, and the lat- ter liegin. This is as it .should be, if wc would have our lilies l.eatitiful. Were tho points of junction <«ion iipnii tlio IrHt i'iiiii|iiiiitii' ivc'liiiinl, if Wf iiHl iMijiils !ir<' i\v !i stnii^'lit liiiK iit oiit't'iid ' CCIltl'l' of tlic I'lid Ih rt'nclicd. lirt'ctioii in tho lit (' arc inoili- ic upiiiT end of 1(1 of till! lower ■r pirts; wliilo 15ut ((llHlTVf, 't'8, there is no in these ciirvt'», h is a nni 11 of 11 vcrticiil'lino. ml. throu^'h tin- mtiil line t'(iuiii raw till' curvi'M I'rvo that thf hat it is iiiij^js- i', and thi' hit- wo would have ts of juiit'tioii VOMPOISU VUHVKS. W eiinily diMtiiiKiiiHlml.K', the •■IV-.l w.Mild Im- imiHi h-: h |il,;i>iii«. lift tlii'^ |.riiMi|»leof lii-ftiity he reiiinnlMnd. In I) wi' hiivf lit her vii- ricticH of the rcvcrsiMl IhuhI- riirve. 'I'lie hiisc is divided into third-* inxtead of lialven. To draw fhesi' lurvi-s. pioct'cd 114 with tlu' np'i'. hraw the whole liiH' witliDiit (*ti.|>iiinf,', and iiiiil< ' altrupt eliaiij^e in its direetiiiii. It will tliiiM ho seen how u. eiiHV it is to prodiiee a nreat variety of reversetl curves hy ehaiiKiiiK ^'"' divisions of the hiwe line, or hy niodifyin-,' the eiirviiture of the separate se<,'iiieiits, I'lipils should fiei|iieiitly draw these curves and inoditieatioiiH of theiii. The eontoiir of articles of glassware, crockery, &»;., is usually composed of curves like these. Reversed Curves applied to Vaaea, fto. A Vask. — Draw a vertical line of any i;iven leii;;th, ami divide it into three ecpiiil parts. Through llie extremi- ties of this line, draw two horizontal lines eijual to one third of the vertical line, ami extendinn equally on either side of the vi-rtical line. These hcri/.ontal lines will give the width of the top ami hottom ot the vase. IMJ IK-iCUNHH' HANI A I.. Join till' tinU "I Oic liuriisontiil liiu's, nivinn in i.l.F'>h)t »*« till' nt'oiiiotririil liiiHi liir llu> ili»i^'ii, IHvidc iIm> liist vtM'tiful liiK" into tlMi'iln, lunl, tlirnunh tin niiiitr (ll*'i»lonH, timw the iiirv.- /> in I). 'I'lu' IwikIiIi, ••t' CO iiwc. niij;Iit liiivt' lii'i'ii Iftkt'ii 1»?!«m or ymftnT, I'mw tin' vt'rtiiul liiii"'. itml iliviilt- tlii'ni iiH in tin' lii'l I'X- 1'H'iHt'. I'hf t•nl■^■l' '■ in I' lor • 111- contour of tilt' viiHc. A'ld tlio liori/oiititl iihi- lot' till! tottoni. Ri>i|iiii'<' till' piipils, ux'm^ the HUinr I'liivc. !•> iliiiw kiIht \ ii^cs of ililVrli'Ilt \\i(|lll>. A Fitobar. Dniu iIk' viTtiriil lini'.t, aiul iliviili' tlii'in iim in tlir lant two cxcrrisos, For tln' contour of tlio jiitclior. nsi' ciirvi' '/ in I*. AiM tlic liiinillc anil tlic liottom. Any otliiT j)i'"'>i>rlii'ns tliiiii tliinls may I"' t.ikrii, jirovidi'il tin' ri'siiltiiif,' (li'sitrn is* urai-cfnl. whic'li will ili'iMiid lai'K'i'ly "ii till' ihiiwiii^; of tlii^ rnrvM. It will tliiis 111' si'i'ii liow .xinijilr is tlic iiumIi' of ili'«i},'niiiK '!"' lontours of vasi>s, artii'li'H of tiilili'-wari', «■ n'lvinn .III iil'F'ihj* i^'ii, I)iviil(' lilt' roii^h till ii|i|i)>r Till' liri'iKltli, "f r gri'ikt^T. •ortital lini'*. iiitti IH ill till' !:!■<( I'S- rlll'M' (■ ill I' t'nr r III.' viiMc. A'ltl III liiii- r.>i- tin- ii> pupils, iiHiii)* \i\ til ilniw III liiT lent \\i(|lll>. ■ vertical lini'M, tlii'in iiM in till' •rciscs. I''i>r tilt' tliii pitclicr. iiHt« 1 I). A.M tliH lie liottoiii. Any tiiiiis tliiiii lliinlM en, proviili'il till' l■si^ll is j;riU'ot'iiI. Ii'ImikI liii'ticly "II I' is till' iiiimIi' lit' •li's (if tiil>l<'-\vuri>, VhMt>offSh I I HthS, \t\ Siv. KiU'iiiiriiut' till' piipiU tti t'M'iii'**' iIh'ii' iiivi'iUiuu ill ill-vising iii'w I'.iriiis. 'rhtirv Im yi-t rniMu •noii^li Im' tin' inipi'iiNinii'iil of fOinilKill «T«irki'l',V. Tilis impliivrlinill KHI-I lii'^ill Willi till' cii'^iilioii III" till' piiiilii' tiisti'. muliiiijj; lulv tllill^;s iinsiilulilf. With tlii< ili'iiiuml f^r licUi'r witrk will ••••iH>' IIm- lii'ttir work. r>iiiully it »'t»*fK iih lumi' t» iii.ilii' an "liji'i f lii'tuitit'n! tliaii tmiiald* it Innui'ly. Iwdviili'd ulwayx tliut tin- wiirKiiiiin liii'* liisti'. wliitli )m I'llucaMoii hIioiiM ^iv'- liim. 1 1' ili"' wiirUinun is iMjt al»l»> to (liftf iiiKuisIi hctw n what i* liiaiitil'iil ami Wlnil i« not. it i?< iiiipoKHilili' I'll- liiiii, I'Mi'pl I'.V imri' BtH'iiltiit, to iiitiUc any tliiiit;? lii'imtirul. It would Im'u Miinl man sl•('ill^^ llcin'i- tin' ni'i'i'Hxity of I'lluraiiiiK till- pi'oplc, us II wlioli', to a Just appri'ciiitioii "I' pure form, wliiili lii's at tin' roiimlafinii of nil licanly. WIii'ii ill.' lonn itHt'lf in uiinrari'fiil, liiii' lliii»i"l line with a strai^'ht line. It will he rea that eaeli curvi"! m TKAi'llKNti' MAfllM.. lltic, KM il ii|»|inmi')iMi« till' virtinil lliif. tlmnKf* it. ilirit'tiiMi li-t uml II'**} mill, wlifii if iiniti-.* with till' vt'rtiml liin-. it tukf* tin- kuiih' tlin-i- ( tlim, mill fo woiilil ii«>t < Mt iM-nw* i». Ii-'wi-vt-r tut itiimci], Tlii« i^ .iilli"! tli- tuiiK»'iitiul iiui'Hi of M nirvt'il liiii' with » "tminlit lim'. 'I'hf riiXM \» niiiih iniiri' pl«u»iiiU ihiiii ii wftmt iitiitiii, um ;if I'", whi-rt' thfriirvi'vi'ii li'ii«»li. "iii'l 'liviil'' it into tlirri' ti|iinl [mitM. MuUf tlii- Inn-i- *'. /.i.iitiii lim- I'liniil t'< two piirtx. Uriiw till- .|iuiilmiitH «i»riii.,'iii;,' iVi.iii '.'. ami ,i'>iiiinK •!••' '•i"'l'» of till' hiiri/'ifittil liiii'. Hraw tin' I'luninMinil nirviH from I, mill tlii'ii tin- M'lni-eirclo frnni tin- ti|.|ii r imls 1)1' till' iiiiinlrmitM. DetaiU of Ornkmant. Uniw II viTtii'ivl liin'. iin-l diviili' it iiitii two i'i|iiiil piirts. MiiUi' the \i\>\»'t liori/oiitiil iiH', wliiili hIiouIiI 1h' ilmwii u'xt, n|iiiil to till' vcrtiiiil iiiH'. All of <1"' I'urvi'H mil I'ompouiiil, I'xri'pt thi' two Hhurtfwt. Mollify tin' linuii' l.y ii'Vi'iHin^ a part or all of lh(! curvoH. 1/.. iful tlii's rfmn^ix* I, wIm'ii it niiiii'M ilif Miiiii)' iliri'i- iM If, Imwi'VtT I'lir h•ll^••llHltl imioii li^lit liiii', 'I'Im' 11 X4>t'(iiit union, n* I liiii-, it'i'Diitiiiinil, rt'ii|n r i'imIh at. vt-rtii'ivl line. iiU'l ktti two ('i|uiil |iurtH. i u|i|K>r liDri/'Hitikl I hIioiiIiI Im' ilniwti ill to till' ViTtical of till' riirvi'H an* , i'Xi:t'j)t tilt' two MoiliCy till' linuro 11^; ti part or all of %^ a^ :(' IMAGE EVALUATION TEST TARGET (MT-3) i^o w ^^ .<•, '^ ^ /^,^ ^ 1.0 I.I 1.25 ''■' !||28 32 1.4 |||L5 IIIM |Z0 1.6 ^ <^ /¥' ^. ^ /. -ew/ 'em c-i ^ On ■%' ^# r Photographic Coiporation 23 WEST WAIN STREET WEBSTER, NV 1 4580 (716) 872-4303 # '^ *% V A ^1-^ 1^ <> ■%'■ m s f/j "^ 1% \ \ 4 >> CIHM/ICMH Microfiche Series. CIHM/ICMH Collection de microfiches. Canadian Institute for Historical Microreproductions / Institut canadien de microreproductions historiques COMPOUSn VUKVKS. 08 Caud-Kxkk'Isk XXVII. Simple AbstrftOt Curves Balanced. Dnivv I 1'. uMil .livi.l.- it i nto thirds. Tlirovigh till' liiwcr point iion, ilrivw .'{ 4, fquivl tu twit-tiiinls of 1 2. Diiiw tluMiottcil hoiindiiry-liue, mill tlii'M tlif other horizontal liut's. Driiw tlic ciirvfs wliich iiiiitf with the vi'rticiil lino at its silk's ; sec tliiit thi-y hal- iiiK!!' each other. Erase the Jotted lines. The lines in this exercise nii>,'lit he u.sed as the construction-lines for drawing a leaf; the st 'in beiuK at 2, the tip at 1, while the veins would follow th.' halanced curves. (See card- exercise 10, second series.) Balanced Abstract Curves. For a, div'ide the base- line into thirds ; for ft, into fourths. Ueginning at the top, draw through the upper divisions first, and draw from one end of the hasu- line to the other without stopping. See that tho curves on one si(h^ of the hase-line are like those on the opposite side. Erase the dotted lines. m ri< A VII Kits' in AN If A I.. ('Aiti.-I'xKiirrsr. XXVTII. Abitraot Ourveii. - Junction of Curved and Straight Linei. l"iivt(lriiw tlifci'iitnil liin- 1 2. iui a little less. J)raw 1 •'», - G. Tlirough the upper division of the central line, draw ,'i 4. Througli jioints t3 and 4, draw the curves forming the outli.ie of tlio vase. The line forming the lip of the vase is to be added abov(! 1 2. Draw the parallel lines in the jjositions shown, the up|ier one at the bottom through the centre of the ' lower thir.l of tlu.' vase, and the shortest one on ytj TKACIIKIIH M.iMAL ; a VU.S 1.". n-t at it. -ntr... Nan.ty ,nay I • .,,,.•, I l.y ,.U-.n« tlH..n u..ar to^otlu-r .u o„.. i.-it, ilikI till' r.vi'iHi- ill aiiiithiT. t will I t».ut tiui n,nt..ur of tlii. v... ,h u Hli.l.t niiMlilinvtion of the curves at l),in tl..M.a.lv part t.f thirt i'liaptt'V. ('AiH)-KxK.uni«K XXXT. Flow.r.For«.-Flow.r.Va...-0«« Curve Applied. FiiuM »/. — Kor H'l" rtow- or-fonn. l-nin >'>' -awi.»K a viTtii'al liiii' of any n'lvvu length. Divide it into four eiiual partH. Throujj:!! the upper eiul of tlu^ vertieal line, draw a horizontal line of the same lengtli, one-half to th« ri^ht, one-half to tlie lett. igi^^l^HM^Bv Draw Htrai^^ht li.u's, nnit" ;,., the en.ls of the horizontal lines to the lower en.l o 'the vertical line. Halve thene last hues, ami. irough each point of .livi.ion, draw a eompon..- ...we' with the ogee eharaeter, the upper seg^m temling inwanls. the lower segment outwanls. ).. W the i. ner eompouml eurves from the endH of the lllrizontal li.ai to the lower .livi.ion in the vert.cal li„e. Alia the short upper curves. FouM /. - l)nt.v u vertical line, of any given length, .,,1 j»cr tliinl. irt'tTcnt piirtrt •icty iiiiiy '»•' r ill t»iu' ii''iti tlii«« viifto II* u tlu! I'luly piirt irve Applied. I'.ir thin rtow- liy drawing »)t' iiiiy Kiv>-ii it into t'ltiir 'riiroujjth tilt* 10 verticiil \\w, itivl line of tliti Kiif-liiiir to tln! X to till' It't't- it liiit's, uiiit- tliu lowiT IMItl lust lilH'!*, iiK'l- v\v u coiiipotiml upptT segiui'iit utwiinls. l^rivw h.. »'iid« of the 1 in the vrticiil my piven length, Make the top of width of tl-.e bowl voMi'ouxit rrn i-f:s: t«7 Mill* part and ii hiilf, luid one part iind a lialf from tin- top. Malic *hi' width of fill' Itiitloiii Millie a-t {Kreatext svidth of the liDwI. l''oUM »'. — Driiwti vertieiil line, of any niven Icnjfth. and divid ' it into thirds. Throin,di the hiwer end of the vertieal line, draw a hori/ontai Hiic, making it ei|iial to two-thirdft of tlu' vertical line. From the upper division of tho vertical line, draw ohliipui Mtrainlit lines to the ends of the liorizoiitiil line, On these ohiiipic lines, draw the conipniind curves fi)riiiiii^{ the hell. Add the liandle on the iip|ier third of the vertical line, and the touguu htdow. C.vuiJ-K.yKiiti.sK XXX II. Four-pointed Stsr and SQuaree. I)raw two straight lines of any given eipial length, ono hori/ontal, oiu^ vertical, uiiil hisecting each other. Divide ea<'li half of each line into twoecjual parts. Through the points of division, draw lines forming a sipiare, iuiviug its sides parallel with the jirst lines drawn. (Joiinect the same points of division by oI)li(pu' lines, forming a second sipiaro within the first. Divide tlie sides of the first sipiare into three equal parts. On the Cc'ntral part, draw isosceles tri- angles, with their apexes ut the cads of tin; first two lines drawn. Add the circle, which will test the accuracy of the drawing. 98 TKACIIKIIS' MAMIAL <;auI)-Kxk.im:imk XXXIII. Vui>.— The ORa« Ourva Appllad. Diinv ;i vcrliiiil lint'. QiiiirfiT it. I'liroti^li cncli i'IkI, oii«>- liiilf us lonn us the Vfrticiil liiii', iintl cxtt'iitliiij; tivii|i' till' liiHt- ilriiwu veitinii lines into two i'(|iiul piirts; ami, thiDiiuli t'licli point dl' division, ilniw a >'<>in- |ioiMitl tuivc, liaviiiK' till' ot,'i'f iliariirttT, to coiiii«Mt tliP end of till' liorizintal line al.ov.' with tin- uiitl of tlu) liorizontal lino li"lovv. Make tlie altitudf of the curve at ;li<' ceiitie of each se^'lllent <(|iial to one-half of one-r.nirtli of the vase'n liei^ht. Add tho hottoni, nialiin^ the widtli of that and the width of the hands e(|nal to oiic-foiirth of one-fourth of the vase's heiglit. (;ai{u-Kxkk(;ise XXXIV. A Hosette oompoaed of a Olroto and BeRinsnts of Clrolei. Draw a. square, its diameters ami diat^onals. Divide the diameters into six equal parts, and, throuj,'h the inner points of division, draw a eircile. Draw ohlicpiu lines to form tho other diagonals of the four small H(piares. Divide tliese last lines into thrtH! equal jiarts. Using the last linv's us bases, draw on their inner roiigli )'m'1i 111 liii<> oiii'- Ii(« vt-rtiriil lljj to tile I'itluT niili'. rtinil lines, r tin' Imri- |i> the liiHt- H iiitio two ii'du^Ii caoli liiw II <'i)in- coniu'ft tilt' li till' fiiil iiltitiiilt' ut' t t-qiiiil to ;. A(l«l tlio In- wiiltli of iirtli of tilt' ta of Olrolea. ill.-*. Diviili! Ihroiii^li tlio )i-ii,w oblii|Uti four small equal jiarts. tlit'ir iiiiiiT i COMPOUXn I tttiK.S. 1(1 1 niil***. -.impl.' .iirv.s, to .oiiMii t r i,i|» .,| tli,. •lium vU'tn ot llio larj^ti ii<|Miir)>, aiiij Witii their K'eatiMt uUifiuli' at till' eeutle, ami tourliili^' ||i . eirfuiiifert'iMi' of fho .jii I.' alriMuly tlrawD, I-Vom tlir aiiKlei* of tlu< larKC *|uure, mill fi'uiit till' eiiiU of it.H ill. iiiiictent, draw Hiiii|)lc ciirvtH to the points of ilivJMioii on tile iliayoiiuls of the Miiail M|uare(<, «|iiur«'i». Diviili- tiicli xiilf «•!' ill" >*f''<'i- mil H.iuuri' int. ttwociinnl part ». |»raw an iilili.|in' liiu- lr<>m llif (•.•iitriil point of ii «>il ..ii.li ».i.lf to fii.'li an«l.'Oii tlit> i.ppoHitf nidi- iaw a Minilar liorizontal line tlirouuli tin- low.T 'Mnl of til.' v.Ttical lin.-. ^^_^___^^^__ Draw vi-rtii'al lim-'* coniu-ctiny \ tin. ..n.l-* of tin. l.ori/ontnl lin-.. Divi.l.' lim' 7 H ' into four ..p"^! I''>'»- l'"'"'" ^''" '''^^'' '""^ ^"^'' ^'"""'' VUMI'nCSh Vt'Ht^.s. m i» rtiiu with nil'. mill miiIhII- |iial »«|iiiirt'K. il' llif or'i^i- ii'i|iinl piirtH. iiii- Irxiii tilt" lliviKJDll oil UIIKIi- oil till' tlii> M]iiurc. At till' »«iiiikn- tu tl"»l tl'f III Uw: I •_'. i^tli. iiimI t of ll»» KltllH' ii'llUlll it" I '•'. till' llrf>l Vl'l'tirill lllli' illltMM, Draw II liiiii/oiitiii liin loiuiii tinx llir ii|>|m r i-ihN III' tlii'si' two viTtii'ul liiii'H, iiikI tniimiin iIm' ihIui' of till- limimt. Kroiii tin- ciiiU i.f tin- Imri/itnlul Iiih', timw iililii|Uii liiM'w for till' niiif. Hw ilmt ilif roof |iiiiji'ftH mimfwlmt. Ailil tl Iiiiimfy, '.». <•. MuKi- llii- wimloWK mill iliior two-tliii'iU uw wiili- iiwuiii'-fnuitli of till' wiiltli of till' liiHMi'. Miikf tliM liiiulit of till' ii|i|iiT wimlowH li littli- li'Hi tliiiii till' lifiirlit of tliii k'wi'r wiiiilowM. Fiiiinlt. t'.\HI|.r,XKU. tSK XX Will. A. JuR. -The Rlllpua AppU»- ji-rtiii^ to till' Hiiiiiii tliHtmii'i- ■ III I'lirll -^idi' of llic VlTticill liiii'. I'HiiiK tlii'Ki' two liiit'H uH till' ilimiii-ti'i'H of mi rlli|Hf, ilmw till- I'liip.ti'. Muilify tlii' i'lli|)si' to fiii'iii tile liiidy of till* jit({ ; mill tlic limiill'' mnl mrk. ('.\iiii-l''\KK( isi: XXXiX. A Vase. - VivlaUoni of tho Okbo Curve. Drnw 1 L', ami iliviili- it into tliirii^. Uiiiw .'I I, (•i|iiul to two-tliirds of tin- vcrtiial liiir hriiw ipMii|Ui' liiii'i«, juiiiiiig the I'lid.s of tlii' 1i(iii/oii;;il line «it!i 'In- m TKVHKHh' V4.Vr.IA. iHttliMU "I lltf vi'riii'iil liiitt. TliiMUKh tUv |Niiiiia >t|' >liUKiri/<»iihil lihi'*. i)t tiHii'li iIm' nli|l<|l||t Ii||»«, |>ruW till' I' iiiiiii:iiiu liorijiiirilitl liiii'it | iiiiki* IIm' l)Uf iM'urlv i>i|iiiil !'• itiii'iialt <>!' tlitt llt•i^||t III iIm>viiiii>. FihUti l>y ('iiri'dilly IrikMiii^ ill MM|Hniit| t'lirvi'N wllirll Intlll llli' fitlllolll' III' till' N.tii'. Mil* tliiit till' I'lirvi'w iiiiiki' II liiMtiitil'iil jiiiirtiiiii Willi ilii- •truiclit liiti>» iit •1 It. '{'Ill' ii|i|ii'i' riirvi"* itii' li hliu'lit viiriatioi) nl' iIh' ■ i({r>>. till) |ii\U'r iii-({llli'lltn lii'ili^ li ll'llli- illlli'r tllllll till* ii|i|ii'r uiii'>«. t'\iii>-l'!xr.t(ri»K. XI.. Tti« Orumli k'ikii- hi'uwilii-HtiilViit'tlii-lliiKltrMt. Till' ii|i|M'i- mill lower liiH'fi III' till' lliii.; lU'i' I'liiniiofii'il III I'liin- |iiiuiiil I'lirvi'A, liiul till' I'llj^i- lai'lln'Ht I'liiiM till- xtitl)' i.'4 u M'i'tii'iil liiH'. I'll!' iiiiiiih-jiii'k iiciil|ii"H iiliiiilt iilir-li'llllll III' till' Wllolf llll^ (MI'I'll ill tlii>« \ii'W). hniw till- liinii iit till' ii|i|M't' I'i'jiit-liiiiiil niriii r ill wliicli till' liiii'K rui'iiiiii^ till' jiK'k lii'i' iiliu'i'il, ItH • iiil^lltluU lilnl lliuilM'tlMfl, with tun |iUI".ilfl liiii-M on I'lU'li ftiili', will n'wi- till- oiitliiii' ul" till' luH'H. Tliu iliaillrti'l't mill ilillitolillN In In- tlirh I'l'itKi'il. |M>l||ta itl* rlhlll IllM', •, hi titlh'li hriiH ill)' ul lihi'it I itrly i>i|ii(ii lifiuht ot' y vnrvUiWy IIdI rlirVfH oil I III' ttll> III' rllI'VI'l* lilt lillI'M Itl iilll III' till' liilli'i' tliuu ii'llitKllrNt. ■t-r lint'* III' I'll III' I Olll- till- I'll^i' ittull" i* Ik iiniiiii-jiii'k -liMiiih 111' I'll ill tlii" ' tnl'lll lit mil riiriii'i' lii I. \l» I liiii')« lilt nil's. 'I'llL' VUMl'itV.Xh VI HVttik Oftrlyiiiii rorma. I>rikw II vi'rtiriil litii', III' any i:ivinK(li. |)|vii|i> It iittil nix )'(|I|||I |il||-t>>. TliMii^li tilt' ri'hirul |i>>ihl III' iliuKiiin, ilriiM 11 liiin/iiti- likl IhiM twiHihirilH UN liiiiK ikM till- vcrtii'iil line, ami iliviilii it into >ilx i'i|iiul purtM. Oil lliiKii iwii liiii'i. iM iliitiiii-li*ri«, iiiiiMtriii't lui nil- liMi((, iiinl ilrusv itt iliii^- iiiiiiIh. With till' I'liiU mill nit|im of tliti olil'jiiKit itM liiiMfM, ilriiw i.iiii|ili' riirvf^ iIiiiiiikIi till- outiT poiiitM iii'diviiiiiiii till till* iliuiiiftiTK. hraw HJiiiiiitr riirvrx. iiiiiiii'itiiiK' tin- ailjiii'tiit i'IhU nl till' iliaiiii'ti'i-'* mill ti'iiiliijj; iiiwuril". Mr.iw ullii"* niinilur mm'*, ti'iiiliii>{ iriwunlK, ami fniiiii'itiiiK •!'" ailjiu'ciit iMiiiiti III' iiiti'i'M'i'tii r tlif la-l iiii'M'h with tlui tlia^iiimlii. Kraxi' tin- ilntli'il liiifi. ami tliimi' (mitu t>r till' llrnt mirio* dl' iiirvi'H wliiili |ii|.<4 umliT tlm wu'oml HiTit" Tin- witltli ol" tlm horilir I* ••iii>-linll' of oiiu-Nixtl' "i' till' vcriii'til (liuiiititfr. ('Allli-KxKUriHK \MI. DoK-tooth Moiitcling. Ii.terUolnK rorma. Draw tw<» Miiiiart'^ lyiiij^ i tiiiuliiiij,' rai'Ii ntln-r. l)iaw ltii> iljiiiii- •'ti'i'H uinl diaKKiials ; ailil llu- >lij'lit iiiili'iitatimiii at tlio I'liUd of I'ui'h iliaiiii'tiT. Kium- I In' lliiHlK'tl'^•^ and i 104 V>.IC7/r;/.'>' M.\y('A!.. ilraw ;i i.!U"ill<'l liii<' aliovti and Ixi.w, ax in oiImt iiiniililin^s. Draw a .-(luiirc ami its «lia)i- uiials. Cut ntV a Irillo IVoiu tin- (■nils ()(' cacli (lia^; iiial. ( )ii <'a<'li side of wliat remains "t" ''ach (liaKiMial, as a l>asc, draw a siii'plf <'i>vv<', liaviii;,' ail alti- tiidi' fi[\\:\\ to oiH'-tliird of tlic scini-dia^oiial. Iii>idi' tln'M* curves, draw similar jiiiraliid .•iirvcs. Draw oacli band lull, and tluui erase the iM>r- lions wliieli ilo not sliow lieeausi^ of tlie interla<-in|,'. Draw a see<)nidc of tlie sijuare, draw a senii-.'irele, joining tlio eorneis of tlie square, and passing tlivongh its centre. i'lu'U draw an ii.scrilted cinde. Inside these curves. draw similar i.arall.d curves, except that the curvcM parallel with the senii-cindes must he drawn on a part ,,f each semi-dia!,'.)nal as a base. l>r.iw tlu! hands full, and then erase the parts which do not show hecans(! of the interhving. (iiKSTioNS. — \Vli:\t is a rcvorscil vww > Its si'^liK'nts * What iniiv lie tlio < liariicter of oiioh se>;nuMU ' M'li it is nioaiit \,y u liiuiil-cinve '. l)»tiil)o llic o'^ve. How slioulil tlio reversed ciuvc ili.ui-e its .liivction to !).■ l.fuutil'ul ? How should it 1»; .liiiwn' How >li<)ul(l ii eiuie inn into a straic^ht line for the iunctic!! to ho heautifiil ? How c ui tlic sliapo of the reversnl cnirvc he rctulilv niodifie.l ? For wliat is this rnrve nuicli used ' Wluit are ahstVaet euives ? \Vhnt is the tangential union nl strai-ht and curvi'd lines ? Wliat of it? What lines should he draw^. iirst,— the Ion-, or sh.rt? the left, or right? How are interlaeiii)' forms hest drawn ' IIS in dIImt 11(1 itfl (liajt- illilll' tllCM' ilar i>arallt'l ruse tlic )Hir- itrrlafiiig. s. On oiich joining tlio ;li its centre. liicsc iMirvcs. ,t till' curvi's ivn on ii part V till! liand.s () not slioNV Its srj;Mii'nts t \\'\) It is mount jlil tlio rcVLTSfil w should it 1)0 ■;lit line for tin; o( the reversal ve much usnl ' entiiil union nI lines shoulil liu ;;ht? How i\n; CHAITKIJ VI. l'UA("ri(AL DKSKiN. liKOMI'.TKK'AI, I'AITKUNS, 1 1.1.1 S m.VTI.N (J S V MMKTKV, ItlU'KTITlO.N, IIAI.AM K. IM'.riiSK. ItliKADril. SoMK of the pri'vions oxcroisfs iUustrati- fninlann-n- tal principlo.s of practiciil dcsiyn. Miit as tln-rt* were, at tin; beginning, so nniiiy otln'r tilings tn teaeli. it was thovight he.st to deter all systenuilic explanation of design until the pupils eaine to tin- second series of cards. It will not l)e di.licnlt. even tor ipiite young clii!dr(>n, to understand the principles wliidi will now lie discussed and illustrated. A knowledge of these prineiples will give an additior.al charm to draw- ing : it will enable the pupils to begin at once and intelligently, to make original designs. Though these prininples of design will be found so easy of comprehension, like the fundaun-ntal principles of arithmetic, yet their applications can be madt! sullici- ently difficult to test the ability of the hand, eye, and taste, which have been tliorougldy trained. Perhaps it nuvy be thought, at the lirst glaiice. that sor.ie of the drawings on the card.>- in this series are too elaborate for young children ; but, if they have been fairly instructed in the preceding exercises, and are now made ac(]uainted with the principles of de- sign which these drawings illustrate, their execution will be found none too ditficult, if we would secure 105 100 m. it: UK US' M.IMAL. gdoil irsiilts. Wliiit may at lirst .strike tlic inipilH as intricate will, cvi-n to tiicin. apjicar siinidc ciimi^li. till' iiiiiini'iil the iiriiii'iplcs coiitrDJliiig tlii> df^igii arc nnilfi'.Htonil. SYMMinUKAI, VUKANUKMKNT AltOI'T A OKNTHK. First of all, tt'ucli tlie pupils what is meant hy sym- metrical :irrant,'i'meiit al)i«nt a centre. This re(inires, that whiitever is done in one part of a (lesi>;n .shall lie done in all correspondins^ parts. When a line, for example, is aiMod in one part, or removed, lines in all other parts havin;; the same relation to the centre of the desij^n mnst i)e added or removed. The mo- ment a line is uilded without its corresponding; lines, the design is spoiled, hecause there is a violation of the principle of symmetry. There must he no super- fluous lines. On the other hand, every timo a new line, with all its corresponding lines, is added to a figure, a new design is ]troducet' II n line, for )ve(l, lines in to tlic centre d. Tlie mo- unding lines, I violation of id' no snpep- tinic a new i added to a ' new desifiii 'ss beantifnl, lens, that an •king tlie dif- nn))er of less jvered by an- niany or few, ly iixed law : istration will young or so liis drawing witli tile law I'U.iCTlr.M. ///■..s/'/.V. m A CroBs, aiuatratniK Syinmutriool Arrttnucniotil about the Centre of a 3qunre. Draw tilt' lignre at A on the lilacklioard. reiiniring the pupils to draw it with you, on their slates. Tho exercise may he conducted somewhat after the following manner: — Tiiir/ifi: — Draw a f^quan' on its diagonals ; add its di- ameters, all in liglit line. J'u/iI/k. — We have. _ Thi^ puitil."* will indicate tinit tiiey have completed their work hy raising their hands, or in any other way the teacher may direct. Ti'iif/ii-r. — Mark tin* centre of the npjier half of the u(>p(T left-hand side, as you see that I have. J'kjiI/s. — We have. Thia will give what is seen at ({ in R Having explained what is meant by symmetrical arrangement about a centre, pro- Tfir/ii-r. — IIow many other nnvrks can be made, having just the same position with reference to the centre of the square '.' Pupils, — Seven. 1((M TE.WUKItS' MANUAL. •<•* 'riioii>,'li tliii* miiy 111" tlii'ir first lt'H*«on in symmo- tiy. s.iin- i.r tlx- |>(i|>ils. iifViTrliclcss, will «ivf tho ront'cl iili>\vi'l'. T'lir/irr. — Miikf the seven luWitionul inarkn. I'it/ii/s. — We liavH. Tliis will give what is seen at h ill B, lesstbe lioavy t'n at h ' obliiiuc liiif. ii- | yi't certainly : n by any oiio art of putting inga a teai'hor il heavy linen. iciMi at C, less rhe upper Ict't- hanil litavv line. „f,i/s. — We have, and it >,Mves us a cross. The result may he seen at A, less the foiistruetioii lines. It is a simple eomhination of straight lines; but, hecan.se the lines are .symnu'trieally arranged about a eeiitre, the effect is pleasing. A Kosette, lUustratinK Symmotrioal Arrannement about the Centre of a Square. Here, at D, we have another simple illustration of the prineiple of .symmetri- eal arrangement about the centre of a .sipiare. The form may he used for a blackboard lesson in this wise: — Tfiir/ir,: — Draw a scpiare on its diameters ; adil the di- agonals. Thns. From the upper end of the upper left-hand semi-diagonal, mark ott' one-eighth of its length. Thus. What does Bymni''try now recpiire? Fujjils. — That the same length be KKirl^cd otV 10 no 'Ih.ti Ums' M.l.\(AL tVniii .ii'li I'lnl »( til'' «liii^,'i)iiiil,-<, Wf Imvo iiiurkfti it •'»V. . , Ti'iiohi')'. — Knnn lit" uii|u'r t'lul ot tin- vcrtiriil tliaiin'tcr. m:irl» "tV ..n.-ci^'litli of tlu^ Ifiintli of itn lialt'. riiiiM. Wliiit ilors syiuniftr.v in>w rr(|iiin>? I'li/iHs. — 'I'lial llif Miini- IfiiHtli I"' miirlu'il olT \v»[n catli riid <'l' ilf ih ■•.in'tcrs. Ti'iu'lirr. — Oil til" uii|MT niilc of tlic iipiHT li-ft- liainl Miiiii-ilia^roiial. an a liasc. licj^iiiiiinK at tin- jioint of (livi>*ioti, ai«l ifrmiiiatiii^; tit tlin ccntri' of tlio H(|iiarf. iliaw a siin|ilc curve. TIiuh. (Seen at '/ ill v..) t'li/ilh. — Wi' liavr tirawn it. Ti'iiihi'i: — Wliat (loi'H syiiiiiu'trv now rfmiirc? I'„f)i/s. — That .M'Vi'ii other similar liiifs hi' ilrawii, havinj,' thi" saim- relation to the I'l'iitrc of the Mciuare. Tror/ii'i:- Draw thriii acconlinnly. I'liiil/s. — We liave. (Seen at /> in E, h's8 the short eiirve.) Trurhi'i'. — From the upper point of ilivisioii on the vertical diameter, draw u curve fending from the diameter, to toiidi tlio lirst drawn curve a litile helnw itH centre. Tims. (Seen at h in K.) What does symmetry now require? /',tf,l/s. — Tliat seven otlier simihir curves in' drawn in tlie .seven corresponding parts of the sipiare. IV'irlirr. — Draw them accord- ingly; then draw the sides of the .s(piiire in lieavy line, and erase the diameters and diagonals. The final result ia shown ; D, less the dotted lines. •o nmrktMl it till' VITtii'llI I'liKtIi of itH ri'i|uin> '.' llllU'l<«'il •'•1" ' ll|)|HT li't't- nt tilt* ]Miint iitrt' ot tliH (Stu'ii lit '/ rciiiiiri'? fs be drawn, till- s(|iiiiro. vv<«. (Scfii lit it ciirvi',) 11 tllf llJipiT I till" vt'itiiiil mvt' It'iiiliiiK to tolH'll tllK , litilv below (Sct'ii lit h ill nunt'try now seven otlier Iriiwii in tlio l» jmrts of tlie rtlu'niacfonl- le sides of tlie lie, and eiiise iS till! dotted I'ltWrWAI. ItKSlUS. Ill At tinier* i'ei|iiii-e tile ]>ii|iiis, win n uoi'kin^ in tliin Wliy, to llUlke tlieir Uliswers iiilll|>lete .Hlllh'llielits, UH expliiineil ill tdiapter two. I'niiii the illiistnitioiiH wliiili iiiive now lieen >iiveii, it will lie seen tllilt tlli'< Jirineiple ol' desi;,'!! — .xyniine- trieal arraiif^enieKt al'oiit ti ceiitrc — in co eiwily eoiii- pndieiided and so easily ohserveil in piiictiie, tliat it can l)e taiifjlit to yonn^ cliildn n almost at tlic outset of tlieir drawing; career. \'oii will often llnd, in (^ivin>{ IcHMons from tlic Idaelihoard, ax just illustrated, that attention paid to this prineiple will greatly ahiid),'e yoiir lahor, whih the pupils will niaiiifi'st iii- ereased delight in their work. Voii will often llnd, nlso, that attention paid to this priiu-iph' will he of servicH- in H'^''">? dietation lessons. .\j,'aiii, pupils, when drawing from copies on the cards, will he },'reat- ly helped hy a ktiowledj^e of this pri;ici|ih' of .symmet- rical arran^ji'ineiit. .\ iK'sigii. which would otherwi.se appear to them intricate and ditliciilt of execution, in tliscovered to he (piiti! tho reverwo when vii>w«'d in the light of tliis knowledge. It i.s soon, tliat if two or three ditVercnt lines can he drawn, in themselves sim- ple, then the whole design, which is hut a coiiihina- tioii of these two or three liuew, can be quite us readi- ly drawn. Symmetry is, indeed, the ki'y which unlocks many of the secrets of de.dgn and drawing. See that your jiupils, wlien they examine the draw- ings on tlieir slates, do not look at them ohiiipuly ; for, if they look at them thus, the drawings are di.s- torted, and tliey fail to see them a.s they arc, and heiico cannot tell whether they are correct or not. The eye iiiust he directly opposite the (lentro of the drawing. ih TKAL'IIKUs' MAXIM. 8rnim«trloftl Arrannemant about th* Oantr* of an ffiquU UMral Trlkiiile. liii (or tin* l^'i'oini'trii-al lia^i^. liikr. tliM tiiiK*. itii i>)|iiiliilcral tnah^l*-. Iliiving limwii tlic tiiaii^'li', ImhccI t'lirli hIiIc; t'l'nm I'uili (loitit ut' hiHi'i'tiitii. iliaw it Htrai^lit liiH' to tin- opjio.-iti' aiinl"'. Til*' lii"''* will 'roi*" cai'li otliiT at tile rtaiiii' |Hiiht. jj- — — till' ci'iitrc ol' the iriaiijjii'. This will nivi' six li^jiit triunj;h's Hyinnutiiiullv ai- riinni'd iiroiiml tin- cciitro of tin' lar},M' triangle Coii- iH-ct llif iM'iitri's of till- siili-< of tlic nri;;iiial tiiannlc liy Htniinlit liiu'w. AiM tin' ciin-id liiuH as at I-'. ^'oll ininlit stoji lu'H', fiT till' < r- fi'i't. Take aiiotliiT stt'|i, how- ever, iiiitl udil the furvt'd lines us ut (i ; ulwo the outer strai^iht lines paralh-l with the inner trianjjle. Ilrase the (l<>tte'^ // , //■ '>C'' V A of an Bqiil* |uaii> for till' ". Ink). tlii'« Till tnaii^l)-. till' triiiiiuli'. ; iViilM t'lirll inn. ilniw Ik till- OpIKwitl) ■5 will rriiKH Mitiiii' |Hiiiit, till' ti-iiiii^li'. iictiiiiill.v ar- ;iii;^li'. Cmi- iiial tiiaii^lc ics UK at !■'. licrt', I'cr till' I'triiully i>i'i- HT Mtl'lP, liow- ! curvi'il liiH'H II till' iiiiti'i- parailrl with I'. i'!nisi' till' 111-^ yoiiolitiiiii rmi iiii^lit, ill . taki' aniitliiT III. II it Wiis Kiiiii aiiis in itsrll'. iwtli, i|uiti' a 1 an- ri'iiilily ;n at Cr 11)11- I'HACTHM, /(A..s/»;.V. Il:i tiiiim tint mil' at I-', wliili- liirtliiT aiiiily.^it nmuiIiI ili'<* I'loHi' iitlnTH roritaiiii'il in V, 8ymni«trlo*l ArranRflnient about th« Uantra of * Cirola. Draw ariri:li' on it.-« lioi'i/.i)n- tiil ami vertical ilianii'ton* ; itilii two otluT iliaini'ti'i'?<, linr, ami ri'ipiirin^ till' pupils til iiild all till' rorri'spomlin^ lines. l''or iitlii'r t'xainpli's of synimi'friral arranj^i'iiii'iit iiliout till' ri'iitri' of a sipiai'r, lirrli'. lii'.\aj.;on. pi'iita- f^on. anil trianj;l(', si'o tlii' di'si^'iis .\, I'.. ('. D, K. in till' ui'xt rliaptiT, wlii-ri' a roiiM-ntional Ifat i> tin' priin;ipal I'leint'iit. From tini" to tinii' n-vii'W llii' piipiN in thr pr.ini- pli's explained in tlie tirst series of iupI-. w 114 rHAVIIKH/f MA.St AL ANfK nK I'AHT-. 111.. II. xt tliiiiK i» will '»' wfll for yon to tfiu'li your {.tipil^ in th. ii»-uiiiii« of Hymmrtricttl urrim^i'in.'iit on tui iixkthiit Im, on it .tniiulit liio-. Tlii* ri'«|iiiri'» Liilun.'.- of imrtx. — timt tin- rinlit hulf of u .If^Kn ^1 1,1 Im. Iikr 111.' I.'fi. Wli.ii you liiivo >.yniiiM'tri.-Hl urruMKi'mt'iit iilniut u .•.•iitn-. any ^.^rlli^{Ilt liii.- .Iiii«ii tliroiiK'li till- .•.•Mtn< will .livi.l.' tli.- «l.'xi«n Into \\\» •'.|iittl |.intH, wlii.li will alwiiy* I..- juMt iilik.'. \M. wli.'ii you liiivf nyiinnftri.iil urruiiK«'ii»''iit "" i"' »""•• tlif ilf-iKii iiiu^t 111- .livi.l.'.l on til.' u.\i?'. otlnTwino tlio |mrt-< will !»• mi-.|iml nn.l iinlik.'. In tin- lii^t .■ui«-. if til.- HV"! n.tii.iil uiiunK.'ni.'nt U ul)out tli.< cftifro <.f II triun«l.-, tli.n ii liiu- < Iriiwn inuHt bo tliri.o or »'\\ tini.'.-. .Iriiwn ; if iil'out ill.- .•.■iitr.' -.f ii H.|imiv, it niii^t 1m- f.Mir ..I- .'iKlit tiin.r- .Iruwii ; if alHuit tin- n-ii- Iri- of II iM'iilii^jon. it iniiHt l.f liv.- .>r l.-n tiiiifn .Iniwii ; if aliout tln'.vntiiM.f iiriirl.s it must 1..' .Iniwn iw niiiny lim.'sus tli" .iirl.- .un Im- aivi.l.'.l into partH. Ilk., "til.. ..11.. in wlii.li 111.- llrM lint' of tli.- kIv.-ii kin.l iH.'mwii. IJut ill tin- m.'.oii.I .•an.', wln-u a lim- lia-* 1m...|i on.... .iiawn. it .an only I"' 'Iniwii a Mv..n.l lim.., till! Hf.'onil lint' luilaii.iiiK tin- lir^*!- 'I'll.' larK'f I'iU't "f •'"• «'X''»'<'i'«»''< i'» t'lf "''••"H'l i**'""''"* of iimlH illnHtrat.' f-yinno'tri.'.il arniii«.'ni.'nt on mi uxi^. Ka.li .'f til.- l.u.U, f.if..xain|.l.-, at l>, in Kx.T.'is.- I., s.Ton.l s..ri..s. i^ syiiiin..tri.ally ;.iTanK'f lln- Hl'ian- wlii.li ..n.loM..K it. Ol.- M-m- that tliiH liiM- alon.. will .livi.l.^ tlu' I'U.l into two ,.,|nal partn; not ho with th.' ros..tt..^ at ,i, in tin' Ham.' .'Xi'ii^is... 1 n Kxi-r.-iiii' II.. ><''on.l MTii-x. we hav "1 ASf8. — MAI.- ti) ti'ui'li your urruiii;)'in<>iit 'I'IiIm ri'i|iiir)'M I' <)|' It nyiiiiin'triiul It line ilrii«u *\\iu into Iwii t iiliki>. Kilt it on nil nxiM, iillliTwiHO till' the tiint <'i(.«f, lilt tilt' rt'iitrii iiiMt 1«> thrill' 1(1" 11 HI|lllU't', it iiImiiiI till' n-ii- tiiiii'H ilmwii ; he ilniwii ii!4 li'il iiitii |iartH, Ik- ^ivfii kiml I'll li line liii^ 11 M't'iiiul tiiiii', Hocniid Hi'rit'H Hi'ini'iit on uii ; /<, in KxtTi'is.' pil on till' vrr- ilnst'H it. «>i>- II' luul into two s lit (f, in till' srrii-s, w»' liiivi' I'N.irrn it. in>:>mx IIA It U'lod ilhi«tniti'>!i of j-vniiiii'triiiil iirriin^ji'iHi-nt oit nv. HHin. I'oitihiiM'il witli MyiiiiiM'lrii'iil itrritn^i'iiii'iil itlMiiit H ri'niri'. Hin'li Mi'|)itriiti< ImhI Im Myiniiti'lriiiilly iir- ntiiKi'il oil nil itxii : utiito tlir ilini^n, t'ciii>it|ir.ii'tii'iti iiiirpoNrH, titki- tin- iti'xiitit mt » unit, uml ri" ( |)i'.it it all iiiili'llniti' iimitlti'i' of tiiiirx. I'itlo'r in ii liori- I iioiititl or ill It viTtiriil ilirt'i'lioii. Tliii* it iloin- in itri'liiti'i'tiiral ilt'i'orittion, In tlii' ili'siKH)« fur i'iir|MtK. Hiiij all kiiiilN of oriiaiiH'nti'il ti'Xtili- faliricM, ami in I'ltvi-rinn MnCaii'H yi'iiiTally. Ofti'ii a fi'W lini'H uri- aidliil for till' |Mir|ioMi' of iinitiii^ tin- ri'pititioni of tin- ori^iniil unit. Sonii>tinii'H ilir unit itm-lf may liaM- liltli' or no licjiiity: yit. if ri'iii-ati'il virticaliy or lior- izoiitallv, till' n-milt iiiroincH viTy |)li'a."tin>;. Kxinj.r (., MtHHiml HfrifH, iliiiHtruti'Mliorizontal ri'iii'iition; wliilo KxiTrii*!' v., Nitinn m-ritm, illuKtrati'M vi-rtii'iil ri'|it'tifiiin. riKI'OMK AVI> MUKAinil. Wlii'H tim vyf I'iiIIh iipon a ilf»*i>,'n wliicli proiliiics tlii.- ijiiii'tiii;,', a),'rii'alili' I'llV-it. ii* ilf- nomimitcil njiom'. \f flicn- i* it lark of rt'ixwf. tlim till' I'yi- fi'i'ls iiii|K'lli'i| to wiimlrr ovi'r till' iii'«i;{n. or olf it. fimliiit,' no ivst. 'I'ln- .■^I'lisation ih ilrcidi'illy iiiii'omfortaMi'. Tims tlii'i'i' is no vvs\ for tlir i-m- wlii'ii looking u|ioti a I'lirpi't wliich Iium only >.traij,'lit. Iiaralli'I liiu's; l.iit it litis im|ii'l|t'(l to follow llir IIih'm Ittt IKAVHUNif M.iSfAl.. Iiltln*r i»Ht1 »1ii!l>««r ai •^»•» 'J*** t*nm\ fntfocfari' irth»»r Rlrnitflit lii»-i« i!r.tMiiiK iIm' rtr»». ni«l liif wiui U'riiiK |iii.|.'iit y '*( »*»'• ••>■•• I" •lli»li»l"l>"'' *'• '•i»»»"»'l "1 |.urull. I "triiinht lim-*, 'li.' .I< •inn ••.Mi«w!* .mly ..f .011. .•.•iitri.' .ir. I.'", tli.i- ilx' t • ' '"y »( th" lyn i* i'» inov.' r..tiii.l iunl r.Miii.l, loiloAiiiu tli.' .in'lM*. TliU t |i.h.y i- .limliii.lM'il, or miM- iilto«i'tl»'r, wIm-ii lli- . ir> li* i»r<' iri»»ny u lf« ttruinlit lim-. rn ..r.l<'r. llu-ii, llii»t u tUmi«ii muy Imv.- r.'p.>».'. tlii-rf inii«» I"' HO l"MK, iiiiii>t<'rrn|ttiil liin'* i piU""- tivi'ly loii« lor ihf i»i««' of tli.« .l.'»i«iii. •itlur ..triii«lii I or .iirvnl i iHif tli.'iv niiiHt Im- u .Im- I.iiiiitioii ..» liiM'", ctmiKlit uii'l .iirv.-.l. v.rti.ul. Iion/oiilul. uihI ol.lii|ii«. Willi.' .iff.'mptiiiK, how.'vi-r. lo Mtxm n*- i |»o»i', uvoiil ail iiii.lii'' iiiiiltii»liiiiti.Mi »( \U\f*; \'«t ti<*> ' iiiiiiiy liiif^ toiiCiiM' iiiitl ilt'.lioy tin- ftVi'il. Mfi', »•»•■ lliiir llii-n- arc "oiim' liin* '"•i.li niort' pioiiiiin'iit llnih I otlii'ri*, — ntort' proiiiiiK-iit l.y rriiwoii ol' tlnir I'lintli. uiiil not of llfir n\/.,: ul llii* ^Hi«.' of .lrawiii«; I'or. if l|„.ri. Ill- It Mi.liliiifM, iIk' 'I'^i^ii will la.U i.r.'u.llli. j —it wiP not pli'iiM- lit till- lirnt Kluiu-f. uiiU m> will ii"t * lliviti- flirflllT illHlMTtioll, lloWrVtT IIUl'll ii* 'I'-tllll- ! ininlit iilfiiM' wlii'ii iivi'i'fnlly "tuilif'l. l'mNlMI'l.i:!» (IK DKHIUN liKltlVKIl KUOM NATI IH^. \ 'r'ti' ).tint'iiili'- of iiriifti.iil ili'MKii ari" ili-rivi'il liom ! tt «iua> ol" luituiv, .•Kpr.iiilly fioii u Mtii.ly of tli.' i VK.:,.tai.li. .rl.l, — of lliirt-ern, frultit, l.-ttVfK. vim-. WhiMi WM .■xtiiiiiiii' flowi'i-K. w.' tlii'l th.'ir pi-tulH hvui- m.'tri.iilly iu.iiiiK«'«l iiliout .fiitriH ; wliili- I'luli p'tal. .•oiiHi.lir.".! liy itH.'lf, ix Kyiinii.-tri.nlly urniiiK.-il on an iixiH, WIh-11 wi' oxuuiiiif I.-uv.'h, wi- liiul tliut r, wIm'H iIm' I'M. lirtvt- rt»|M»i'. \\\%>* ii-iiiii|iiiru' iitlii'c i.truinlii iiiiiiiiiiiiiii)it <>r iitn/Diitikl, itml til Mfi'iirM ri'- line* ; fiif t'Mt I'lM'l. Sfl', Inn. llUllliltl'tit lIllMI I' tlicir liii«ili. Iinwiii^:'. I'i>r. it' I lu.'U l>ri'ai|llt. Ihll il>t lli-tuil" ItOM X ATI UK. ic (lirivi'fl Iritiii \ Ntinly of till . Ifiivf". villi". ifir pctiilK nym- liilf cii'li I»tal. urriiiiK<'' lol"'. 'riii*. of I'tttiwi'. i* imJy tw«» iif til" K"'i"*rttl f^nn <»l" iln' l»*(»f. ••••! "►!' i»« tli'fdlU. Tliiii. ••«>. 'Ill llli<|ll«' liuw, wliili* MMiu* tirit iiri> Ml irn-Kiilur llii-yi'iiiiiMit Ih< iluaitilii'^l, ittul III'', tlitf rori', 'Hllfl iiin'iiiiil'iii*. IihI'-i'iI. imtiirM iiKiK itll IWriiiKi I'Ut, wliili' xln' 'I'M'* tliix, xlif p«liim>t A iliH'iilcil |)n>fi'ri'iii')' f'lr tin- i«yiiiiiii'tririil. Till' luw III' nviiiiiiitriral (li'V>lit|iiiii'iit on itti uxi"* ImliU I nil', ill ili«' iiiuiii, of uiiiiiuil loriiiK. 'I'liii' tlii< liMiiiitii 11^111" t'ointi^tit III' two )'i|iiul. Miiiiilur imrtn. tlio ohi* liuliiiH'inu till' otlnr. Wliut \n tiiH' of tlMMi- iiifMliictM of niitiir' tliiit tiiii III' Bliiilii'il liy till' iiiiiiiili'il lyr, in foiiiiil to !..■ i.||iiiiily trill' of till' iiiii-riioropir worlil. KxiimiiH' •iiow-tli»ki'» iniili'i' Ik iiiii'roi«i«i|ii- ; the rryitiiU i-xliiMt u urviit vu- rii'fy 'if ••liiiriiiiin{ roriiii* ; yi't I'urh ip» »yiiiiiii'irira!ly iirriiiiKi'il, uliiiowt with Ki'omitririil pri'iiHioii, uhoiit ii ri'titri'. Ill ilinfriliiitiiiy lii-r lint"* of >{rowfIi. iiafiiri' i^ alw» olmi'ivaiit of lni'iullli ami ii'poKi'. Kxaiiiiin' th'' "tiiu- tiiri" of II h'lif. ThiTt! uri' thi' rilm. or only u niiiliili, UH till' i'U«t' muy hi'. Mtroiiyly il'-lliifil ; tlnn ronii' tlir vi'iiiM. h'HN HtnniKly ili'llin'«l. itml tivliiir- fill'' l>y vi'iiih'tH, ami i-vitii IIiht triwinKH. What iM trill' of till' ii'af. it tri f tin' tr it a wli'.h'. Stiiiiiliii« I'l'iii'utli thi' tri'i>. ami InokiiiK "p. wi' hi'hold tin- lai'Hi' iiramhi'M intowhifh tlm trunk iliviih'H; tlii'ii follow thi' minor MuhdiviMioiit. ilowii to twi^M ami nx TKACIIKliS' MANUAL. leavi'M: tliis is ii coinltiiiivtioii wliich givos at omc bri'iidth as tlic rcstilt of tlm gi-iicral fcaiuri's. and rojiosi as tlio rt'sult of the aiMcd iniiior IVaturt's, All is harmoiiioiis ami agrt'i'al)lt'. Rcijuirc your pupils to hring into school Icavi's, flowers, sliclls, insects, tliat tlii'ir ibrnis may l>e stiulieil in connection with the lessons in tlrawintJ. Require them to bring tin) greatest variety possil)le, not only to be eomiiared with one another, Itut to bo drawn rapidly. The study of art and the study of nature will thus go hand in hand, ai\d each will help the other. When there is an intimate c .nneetion be- tween two things, they can both be learned together, as easily as either can be learned alone, and often- times with less eft'ort. OKIfJINAF, DKSKi.V.S »Y TlIK I'UPIL.S. Guided by the principles which have now been ex- plained, the [)upils will be able to construct original geometrical designs, with both I'ase and understand- ing. They should be permitted, therefore (for hard- ly more than permission will be, necessary), to exercise their inventive powers in this manner. They can use the construction lines employed in the copies, anil dr.iw upon these, as a basis, lines wliich will give new combinations ; or they can modiiy the construction lines themselves, by dividing them differ- ently, or by adding new ones. In devising their new geometrical designs, they will be limited by the al- phabet of lines, straight and curved : they will have nothing to do with natural forms, except to follow the general principles deduced from a study of these .- givi's ivt oiii'o tViit.iu'es, anil iiior I'ciiturf.s, HcllOol 1('IVV»'S, )ri)is iniiy !>•' ; ill tlrawiiig. riety possililc, lu;r, Itut to 1)0 the study of L'licli will liclp CJimcction be- riuitl togotluT, :ie, iviul oftt'ii- uriLH. now l)ef n ox- itnit't original il uiidcrstand- forc (tor Imrd- noncssary), to tlii.s niannor. iploycd in the is, lini's svliicli an niodiiy tlin ig tliom diffcr- sing their nt-w ed by the al- thoy will have it to follow the tudy of these PRAVTWAh ltt:swy. 11» forms. Farther idoiig, tlie direct use to be made of these forms in iiraetical design will be explained and illustrated. Ins|iect the designs originated by the pupils: eriti- eise kindly; commend whenever ynu can. Do nnt judge their productions by a high standard. Too many lines will be, perhai)s. their greatest defect at lirst. destroying the breadth of the design. With the hints here given, teachers can make the succeeding exercises very agreeable work for their pu- pils. When drawing is taught, not simply as an ex- ercise of copying forms, but as suggested in this chap- ter, it becomes an exercise which cultivates, in a wonderful degree, tlie observing and inventive powers on the one hand,"while it imparts skill in the visible expression of knowledge on thr horizon- tal, bisecting each other. Di- vide each into si.\ ey two horizontal and two vi'r- tical liiu's, thus forming live eijual sijuares. Draw the diagonals of the four outer scjuares, indicating the position of the leaves of the buds to be drawn. On each diameter of the inner square, draw two com- j)0und curves, and. in ea
  • i:Hled. 'I'lu' »«trai>,'lit liiicf* vixi- lile in till iunnin<,' pattern are drawn on the dia^'mials "f the s(iuare», Kraso the dotted lines. 'I'hiH is a sanip'e o'" the miillnche. an orininiental form which was used hy thi very earliest historic na- (i,,im, — us l»y the Assyrians, for instanc". Its pe- culiar feature c I, "» <>, ^^^^—-^^^^^ Pqi'fll to three-fourths oi 1 li. TnHTtir^^th^n^i-'^t curves .'J li, 4 '2, balancing them : ! I'HACIICAL l)h:si(/X. \Jt mtlonkliaed. - Draw Hvt' J one '.inotlier ill tlii'in witli 1, as II, ill tilt' ^^l, wiirt lillfil. sidu-liiu'H. i\v livi'siiiiart's. utliiT liorizDii- 1 with n'jM'ivtcd in /), last ciird- jliiiiK lioriziMi- >8 construction JCUtlMl tlowiTs. la, Balanced. , and 42. those .'st 1, and the lottoni. art! all otht-r two iiaiV' •s. KcniundxT \\f tht'curvi'.s. divide it into Afak.- .'M, n (), burths oi 1 li. balunLinf; them ! ••.|ually on rach sidf of tin- v.-rti.al lim-. Draw l»u' ninipit' iiirvt's nprinKinn from r> and Oto join tin- cnrvt'it (ir«t drawn. Divide 1 I'i into four I'ijual part:*. hIi-o I -l. From thi- central points t.f division, draw tin- simple curves to the eentre of the vert leal line; and. from the points of division neiirest t. draw tin- tulip- shaped eurves terminating' at the lowest point ..f di- vision on the vertical line. Draw the spirals, with their ends joining; the ends of a liori/.nntal line drawn two-thirds of Olio p'Uft of the vertical line ahove 'J. See tliivt all the lines run gracefully into one another. <'AUI>K.\KKniSK VIM. Simple and Oom;le spiral, because its I-Jll ruAvnimti' n axial 1 l.rfiulili iii'ii'iixfi* Jihiriirinly with i>iuh rt'Vcliifion : if in uUo iiillcil till' All liimi, ami wiw llic llrM to tl.-lim- itK iliamrtiT* iwiirft. It" all u|iri;,'lit lyliinliT, or tin- roimd trmiU of a tree, III- woiiinl witli a niiiuli' laytT of roril. ami, it a |ii'iNoii llicfi take lioM of till- t'liil of III il, ami iiii- wiiiil it l>.v walking anniinl I lie tylimlir or tnc kt'i|i- iii^ till' I'onl all tlic wliili- taut, liin patli will Im' that of ail iM|iial>li' H|iiram). ''''"''' *'""' '"' ""^''""^ '^ ri'voliitioii III' will ihircaM- liis distamt' from tlir ryl- Imli-r liyjiiHt tlitMiiriiinfi'ifiHc of tlii' i yliiiilcr. 'I'liiH !iiay Ik' illiiHtratnl. in a Hiiiall way, l>y usiiiK a miiihI pi'iiiil ami tlin iut. To const nict till- first fiiriii of tlic Hiiiiai I, ilraw two xtraij^lit lim*)*, ii ami n ", rnmsiiij; catli otlnr at ri),'lit- annlt'H. At till' poi'.it of iiitfi- si'ttioii, (haw a iiiall rinlc to ropi'CHciit "'• • I'liil of a lyliii- ill'y (IV V • cil'clc irt callfil till- .., ; Hiiiral. Let tilt' Mpira' "i tin- horizontal liiu' .. i<"*'* tin- I I, vertical iiiii' almvr at 1. tin- , hoiizoiital line (lift) at 'J. tin- vn-tical liiii' Inflow at I :\, the Iioiizoiital lim' (ri^ht) at 1. Tlu' tipin's 1. 1'. I i{, t. imliiatc that the distam'.' of tlic spire from tin- I eye of thi' spiral at those jioiiits is, rfspcctivcly. (Mpial I to oiK-foiirlh. two-fourths, thrt'o-foiirtlis. ami the 1 wlioh'. of the vi>lulinas. I 'J? till' part <>\' tlic icviiiiitioii a 'ciiiii|iliiilicil. I'lic iIim- tuni'M f'rnm t> to 4 in tliiTt'lori'. I'ltual to tin- cirniiii* rcroiicc .»t' till* «;ircli', nr woiiM Ih> in an actual illiiHtratiiiii witli a cviiinlcr ami curil, IScliirc lic^iiiiiiiig til iliaw llic Kpiial itni'lt', mark uii tlic Imrixoiital uii! vertical line* the |HiintH tliinii^'li wliicli the spiral Ik to pass. Willi tlicHe puJntK lixcil. the ciiive can lie ipiite rcailily drawii. Wlien the Hpiral is liniMlicil, the circle may he eraneil, as that loriiiH no part nf it. hraw a spiral witliniit the aid of a circle. Alter tin* points have hcen marked as dii'iM ted, on the Imri/.oiit.d and virtiial lims. other horizontal and vertical lines, similur to those in ,1, may he drawn through the points in assist in tliecoii« striiction ot' the spiral, it' it is a larj^e nne. The spiral should he IVci|iient!y drawn tor practice. Ill tlio Hi'i-oiul vari"ty, or variahle spiral seen ?it ; at the smaller end. Tin' person who unwinds the cord will liiid, that, with each suc- ceeding revolution, he increases more rapiilly his dis- tance from the cone, his path In inj; that »( the va- riahle spiral (•! ). To construct a spiral of thfs character, draw two straijL^lit liiu's, « and ,/'. crossing each other at rij^lit- ant^les ate. Draw twii other straij,'lil lines, >■ and f. crossing each other at right-angles at c also : hut iiiaku tlio angle o <• .s- slightly smaller than the angle .v I' />. negitining at any point on the line d to I'iK rn ^rll^:l,•s• mam m.. tli.< li^lit ..r til.' Iiii- /. ./, i\n ut 'I ixt .•xiiinp!.-. 'Iriiw till- liii«> >i I; piirullfl Willi tlif liiu* /< /. I'Mm tlu> |H»iiit l>, wlittrt* till' liiiK (I A ti)iii'li(>H till' iii>lii|Mi' liiif ^ l>li<|iM' liiH- x. tlruw a vi'iti.'iil lint' ilowiiwiinU iiiilil It lull. Iu'>« f 111 < . 'I'll"'* I'l'"- J— ,.,.,.,1 Willi tin- i«trniKlit liiu'H. Sliiitiii« IV.Mii »'. .iniw III.' Kpiriil llin-iiKli tli.' pnintH wlii'if llii- v.Tti.'iil iin.l Ih.rizoiiliil liii<'« iiit'■ ilriiwii ill a niiiiiiK'r Hiiiiiliir l<» tlu> tllHt. ('.Vltll-KXKIHIMK IX. AIISTIIAIT ri ItVKH. II.M.ANt KM SI'lltAI, I'OUM. !);iA\v till' .'.'iitial iiii.' I '-', lui'l 'lividi' it into l'"iii- fi|iiul |milH. Tlirniiuli 111.' lowiT |)oiiit of ilivi!*i Iiiiw tho liorizoiitiil liiH- .'5 I. iiiiiluiiK it I'ljiiiil l"> iMii'-lialf 'if t .'. A liltlo Ih'Iow lilt' fi'iiti" "f '•"■ iiIt|H'r fmirlli of till' v.-i'tiial lint', .Imw .". (■». of till' .■<;iiii'' li'iiKtli 11-* .14. Diviil.'.'l \ into four i'i|miiI iiiiits, ami ." <> into nix i'i|larliiiK tlii-iii from "i uii.l *'., iiml lininli l»y a.l.liiig tilt' siiiiiU «iiiv«!<. xtiinptf. 'Iruw tlli-l witli thf tlic point 1), A tOlll'llOM till* uw /< (/ piiritl- II, l''ri)iii lli« tilt' lint* ti r Miiiiilur to It A I, KOKM. Ii* it into four riiii>in,'li tin- livijiii'M. tiriiw i<> .'t I. inaliin}; ill' ..r I ;. A cfiitru ic vfr'ictil lint', .Hitniinttttoii. i'lilra* ^uunli'il ii^ain'^t it, tli<' t-yt) i'ii»ily ln'rnn»'x iti'i'iiMtitniiMl tn an iTMr in II iiirv»« lit' tliii rlinraitiT, uihI at liii.t . annot i-viii ilctt'i't it. Ily vicwiit)^ tlic I'liivi' in all piiMititinn, tin- liability to i-rror i* lr»H(>iifi|, .\i» a pri'liininiiry Wimii, it will ill' wi'II to (,'ivi' till' lljjiiri' Hitli all tlm minor lini'H oniitti'ij. Atti-rwaril' ilraw it loniplitf. Tin- spiral ii« a niont iliffliuli nirvi' to ilruw well j nml, iiH it Im of tin- llrMt ronM'i|iifn«'i> in ntlni-il draw- ing, it xlioiilil tlnrifor- lie niinli prarti^f.l. Winn oni' ran ilraw fin- npiral n-ailily ami wi-ll, he will havii liiit littlt> triMiltli- with otluT I'lirvi't. V,\iiiATli)NH. — F)ruw the lljjnri- in a nviTHnl position. Alrto ilraw it twioi> uInivi* ti horizontal liiii> pii','li '.', anil twioc Im-Iow the horixontikl liin* in a ruveriti'il pimition. 3qu«ra Boiattoi Rapaatad. FoitM n. — Draw a liorizun- tal lini>; on tlii:' ronMtruiit two equal HijUuri'M at a xli^^lit diH- tuiKM' upart. Aiiil tht>ir diugo- nal.s and diaini'tiTM. Ni-xt draw till' Hhort ohliipu' lines, tliosp Htarting innw the einU of the ilianieturM to he drawn par- allel with the diagoimls. Add the cnrven, a horizontal line uhove, and another helow. FuKM I). — Draw two 8»iuurL'», their diagonuU and i'M tHAVHKHM' MASUiak .nrtnH'itr«. i«* ii> »■'""' " lit-* rib' a rin'l" in •!»•!» ii.|tiar<'. Miikf fit" .liumi'lir i»f tin- xinftlU-r .iftl.- w Irillo iiH'ri' tliiui •mt"«liir.l -.1 tin- itit|)li< ^■llrvt•^ tnii. Iiinij «lii' riniiiiilVr <• <•! tlir iihht lirtUn. A.lr .l.'.'oriitinK iir.'liit.Mtiir.', til.' iiro.ln itllcr ••irfli"» i» ifti-n uf iIm> •liuiin'ffr* liy l< n| till' ihlKT iHinillil Itnt ir«« f<>r blink* ^1' ill tlu' « ■IlHIlt of pMld r'Ht oriiuiiK'li*''! ly iiHi'il, in till' (riniiiiitf, tlicy pjlcftfH til lllVVl' I'ojiU', livilizt'tl IK r«'i»«)ti'Ht, «)l" o orimiiu'iit in lor ili'i-iirittiiiK III, iHittrry, ii»- lon* nrMtriirily j»ivt'ii ill (Jiinl- HHUHHCH li gri>iit timiout. growth •»r iJif vim. I iiitii it ffiii Im' iMiaily niixiiflpii for a Viirit'ty ••! |Mir|N»irii. Itiit till' I'lMiiitrii'o wliirli imvi< I'lirrii'il Ki>oiiiirfi>t'tioii itri> Ihom. wliiTi- till' .Moliiiiiiiiii'ilaii ri'tirfiott pri'VuiU t''iirl>i |H*oplii uni tliiiM i'iMii|M'lli>i| to rily ii|miii Ki'<)iiii>triinil oriiiiini-iit itloiu', Mori'p>i|iii> iliaiun, in |>iirtii'iilur, hIicmk what i'Xi|Mi> ri'«iilt. iiiuy Im- nl.. Itkiiiitil iroiii lliM iiHi> of .mil lim | ii„u..riul, wIh-u till' lih.s itri' ••oiiibiiitMl nil oriliiig to thi> |iriiii>i|ili>. ..t iiutiiri', mill yi-t wiilioiit iiiiy utti-initf to ii'|iri'Miiit. «'viii r«'iiii»ld^', iiiitiutil toriim. (jrRRriiiNo —Ari' ihi' primipli* oi prMciiial lUnlKri Itunl in tiii>lvriiilii(iii* tliux ( oi Mill' .l.'.iaM iiH'liKliiiK mliff'. ' How HUH ihi' pilmi- |ili' of •uiiiiii-iiiiril iirniiiiri iniiu nlH)ui u .fiiiri! Im' ti>i't| in lilark- iMdinl lcM<.«>ii«f In (lit'UlioM li'KMini' How iItniiu'iiiriil iirrunuiinunl niMmt It venUvi Wh.it io >iti WIml U ,iiii| of KioliU't- rKul uriittniint ( ; M iIk- MuiiumiiKiluii ivIlKJon ( iii CHAPTEU VIT. PRACTICAL DESIGN. LEAVK9, HUDS, FI.OWKKS, rONVRNTIONAMZEP. With two or tlivcc minor cxcoptioiis, all of the pro- c.MliiiK ..x.>rei8i>8, wl.id. have illu>*tnite.l principles of ,l...sigi. in any way, have consistcil of g.'onu'trical pat- terns, or outUn." representations of artificial ol.jects. We now conio to exercises which not only illustrate the principles of . K, illustrate tbe power of repetition in nnndiers on form: CODventionol Leaves Bymmetrioally arran«ed about the Centra of ao Equilateral Triangle. The Power of 3. Draw an e.piilateral triangle. Divide oacb side into balves; and, from eacb point of division, draw si line to tbe opposite angle. Tbis will divide tbe triangle into six equal i)art8. In eaib tbird, draw a conventional leaf, as seen in tbe copy (A). Add tbe curves near tbe centre. Observe tbat in making eacb of tbeso live designs, A, I>, V, a. 1), K, we bave used tbe same elements; modifying tlnin just enougb to adapt tbem to tbe spaces to be filled. Tbe leaf-form \vbi<;b lias been used is, of course, U bigldy ccmventional one. Require your pupils to make new designs, by com- bining, in a similiar manner, tbe leaves and otber forma given on tbe cards. Tbis is one of tbe Hrst steps in design, putting old forms into new combina- tions, and will bo found exceedingly pleasant and profitable for tbe pupils. Wben a pupil bas made a new design on bis slate, permit bim to reproduce it on tbe blackboard tbat tbe wbolo scbool may see it. Tben require bim to tell bow ho drew bis design, and describe tbe principles wbicb it illustrates. For tbe pupils to de.scril)e, in a like manner, any of tbe card-exercises will be very serviceable in giving tbem a command of language. 134 TKACUKHH ' MA y UA L. Conventional liOaves •ymmetrtoally arranged about the Centre of a Square. The Power of 4. Dniw !i s'luari", its »liiiint;ter.s und dingnnal:*. Add t*triiight liiii's coiiiu'rting the ••lids ol' tlu' diimu'tiTH, and divide tliciu into thirds. In ciich t|iiiirtfr of tlio wtjimrp, di'uw ii I'onvi-ntiunul leaf, an M'cn iit I{. Add the curves ni'iir the centre, the outer points of the triiiiiguhir forms fulling on the centres of the semi-diiiineters. nt!i^oii. In ' TE.WIIKUS' .MAMAL. V'ou will Kooii lind tliiit the imitils wlio draw bcHt (III not iilwiiys succiu<(l licst in original designs. Miinuiil skill and inventive {lower are not always united in e(|ual proportions ; lienet^ it will soinetimes happen that a pnpil, discouraged by his poor inaininl »'xeeution, wi'l takct heart again when he begins origi- nal design, becausti he succeeds so well. OblonR RoMtt« of Irregular Oonventional liOavea. Draw un oblong, making its width two-thirds of its lengtli. This can be done by drawing the vertical line 5 (), dividing it into thirds, and then drawing 1 T) and r» 2, each ecjual to one of tlie thirds. In the same manner, draw .'5 4. Then add 1 .'I, 2 4, and draw 7 H through the centre. On the diameters, draw four ogee curve.s, drawing each curve from one end of the diameter to the other without stopping. Next draw the slightly curved lines which form the midribs of the leaves, and then the (Mirves forming the lobe.s. Now draw the two short curves which meet on eiwdi semi-diameter at a distance from the centre of the oblong ecpial to one-half of a short semi-diameter. Where these curves meet, add the lierries as seen in the cop}', two on ciich sliort senii- dianietcr, and three on e.ach long semi-diameter. Variation. — Draw a .scpiure rosette as in the pre- ceding exercise; then add the berries, two on eacii semi-diameter. VHAVTWAl. hKSKjy. 1»7 ili<» (Iniw bi'st iiiial (Icsigim. o not always 'ill H()iii(;tiinea [Kior maiiual • l)t'giiis origi- lal liOavea. two-ill ir« Is of (1111 bc^ (lone •crtical litit; 5 :o tliinlt), mid I ') ami r. 2, of tlic tliirdn. ficr, draw .'{ 4. 4, and draw coiitro. On aw lour ogee leli curve from lout stopping, licli form tlic irves fonning eurvcs wliich net' from the If of a short nect, add tlie li sliort seiiii- liametcr. as in the pre- two on each Square Rosette of Irrejiular Conventional Leavei Draw a wquan' and its diaimtcrs. and on the latter draw four ogi'e curves. Next (haw the four slightly curved lines which form the midribs of the leaves ; then add the curves forming the lobes. Ob- serve that while each leaf is slightly irregular, the four are just alike and aymm"tiicully arranged about the centre of the S(juare. IjOtuB-Flower Boiette, Square. Draw a s.iuare, its diagonals and diameters. Par- allel with the diagonals, draw tlie lines which form the out- lines of the lily or lotus-flow- ers. Draw the central leaf of each, and finish according to the copy. This can be easily used for a blackboard lesson. The lotus-tlower is an Egyp- tian ornament, symbolic of the Nile, source of fruitfulness and plenty. Vauiation. — Instead of drawing tlie lotus flow- ers oil the semi-diameters, draw them on the semi- diagonals, lie certain to retain the general charac- t(!riatic of the flower. i:tH rh:.t(IIKUs' M.tMAL Lotui-Flower Rosette, Obloug. Draw tlio lino 1 2, and (liv'dc it into tlirco <>i|uul piirts. Miiko till' i>i)(!s (if till' oliliiiig vi|Uiil to two-tliiriiti lit' 1 '2. (.Vitn|'!eto the oblong, anil draw itH diagonalH and short dianu'trr. Conni'ct tlic rnds nt" tilt! diaini'ters liy straight lineM, and divide thorn* into fiiurthH. Parallel with till' diai'iinals, ilraw the linos tbrniiii>; tin- outliiii's of tho lotus-tlowors. Adapt each flowor to tho space to ho lilli'd. This illustrates Hymmetrical arrangement around the centre of an ohiong, and will «ervo for a hlikklioard lesaoii by the teacher. Blackboard and Charts. See that 3'iiu iiiaki- only a proper uao of the black- liiianl. If yiiu attempt to teacli a class wholly from that, making your hiaiklioanl copies take tho place of all printed copies, then it is absolutely essen- tial that you he abh- to draw both rapidly and beauti- fully. The development of taste is one of the chief objects of drawing: that cannot be secured unless the pupils have beautiful copies, models, to look upon and to draw, — the more beautiful the better. Scarc'ly any one can draw with suflicient rapidity and beauty to pr.iviile such c()]iies wholly from the blackboard. Hut this is not all. When pupils draw from luipies on the black iioard, if the class is large, only a few of to thn>o ei|uul (' I'lu'.X (if tilt' two-til iriiy (if I tlu> nbluii^, Lliu^oiinlH lUid Connect tlic (liainctiTH hy 1(1 divide tlu'sc I'ariilUI with tt'iiw tlio lincH itlincM of tlu^ IV Hpnco to bo Hrriuigt>Mit>nt rill Hurve for ii of the bla(!k- Hs wholly from tivko the place lolutely e.sxcn- lly and beiinti- e of the chief ired unless the look upon and :ter. S(!arc>ly ty and beauty blackboard. aw from cuipies , only a few of I'llACTICAI. //A.'.S/'/.V. l:J!» the whole numlier can obtain a ^"""l *''''*^' "^ •'"' copy, — tlie few wild sit directly iu front. For those who nit to the right or to the left, every line, except vertical ones, is foresh(irtene(l ; that is. the fore <>v front view does not give the true h-ngth of the line, bei;aiise it is seen iibli(pu'ly. Thus, a sipnire appearn to bo an oblong; a circle, an ellipse; all but vertical lines are distorted; forms which may lie, in reality, beautiful, lose all their beauty. While, therefore, only a few of those having good vision can »oe the blackboard copy as it is, others having defective vi.s- ion cannot see it at all becau.so of the distance. These sauio grave objections hold against drawing from churta, and so they are forbidden to be used iu the best European schools. Hence it is absolutely essential, if pupils are to make satisfactory progress in drawing, that each one should have beautiful copies placed in his hands ; and, in addition to these, there must be beautiful models, and alw.iys rle r^:.iriii-:uy mash.h,. tit^cHuT. tf'uili itll lit oiiw liow to draw tin- nivcii tiff- lilt', Mpiir till' iiiil liliitlilioiinl t'litiit'ly new i'X<'r< ifti-w, tliui* <'oni|U'll- iiij; the iMipilM to oImitvi' ciirt'l'iilly every Htcp you liikc, mill to rcpi'iit tin- HiiiiiK litter you. Also, lor tlie purpoHe of verifying tlietiition exurciHOH, you tnuHt use the liliu'klxniril; otlierwisu you must tul«e time to exiimiiio the work of euch pupil 'V[iiirutely, however lurj;«! the cIiihh miiy he. Thin limited umu of tlio hlaekhoiinl, iiiid thin only, hiin the iipproviil of the lie«t experience. Kemeiiiher that several thiiiHH, in the way of din- eipliue, are to be aimed at, and the moile of instruc- tion miint l)fl mnditied accordingly. (!AKn-KxEKCISK X. OonventionallBad Lekf, Drawtho vertical lino 1 2, and divide it into thirds. Make il 4 ('([ual to two-thirdn of 1 '2. Draw the dotted curves forming the boundary-line, and then the other horizondtl linos. Next draw the curves from the endu of the liori/oiital lines to the verticaliine. Finish. This is the conventionalized form of no parti(;ular leaf. Observe that it is built oil tho abstriv<;t curves in Card-exercise XXVII., of tho First Series. This illiiHtrato.s Hymmutriial arranRoment on an axis. r PHACIHAI. UK'^liiS Itl till- j,'iv('ii Wff- y, mill n'Mtniiii wi-ll to n\v»' on tlllH riinipfll- very Htcji you Alrto, for till' , you tniut UHi> tiiko tiiiu* to •utcly, liowcvfr h1 Ui*0 of 1 1 If pprovttl of tliL' lie way of (liM- imIc of inntrui'- I' it into tliinls. :o two-tliirils of dottf'il furvcM ixliiry-liiio, iiiul orizontal liiius, virvi'S from tin' i/oiit;il liui'.s to Finish. Tliis lali/.t'd form of f. Observe that ubstriuit curves t Series. This I ail axis. Caki)-I''xku»m»k XI, I Ofooui riow«r, Oon**ntlon»Jl««d Draw th.« vrti-al line I L'. ami .livi.l<< it into He^•en , «M|ual parts. Draw .» l ainl '» (i e(|iuil to four of I he^e |u»rtH. Join tliM entU of thiwi horizon- tal lines l»y vortical lines, uinl draw 7 H throu^'i the sec- iMid point of division from the top. Draw the lonK <'urvcH of the tlower llrst, and then the shorter ones. Here we have another illnatratioii of sym- nietrical arran^jiiujent on an axis. Cakd-Exkkcisr XIL OoDTolvulus Bud, OonTontlori»lt«ed. Divide the vertical line I 2 into thirds. Make .1 I equal to one -third of 1 2. Sketch lightly an unbroken boundary-line of tho whole bud; and then finish as in tho copy. Obser>-e that one of the curves passes through the up- per point of division on the vertical line. Froni the ne- cessity of the case, tho drawing of the spiral portion of the bud cannot bo perfectly symmetrical above the cup. IKAVUhmt' MAMAL <.'AKI».KxK.lt( IHK XIII. ■prtxorOonvolvului, Convantlonaliiad. f>rnw fv viTfi.vil lino (,f „|,y ^Jv,.,, |,.|,j{t)i, ahtt Imlvf it. Muk,. 1 'J „,j,,«| to tlinc-lourtl' or tilt' v.Tliciil liiif, mill .1 I vi^ at) fii tliri'c- foiirtliH of I 'J, Uruw tilt" ^»iHi tunc* Iroiu till' i u|i|M'r thinl, liniw tlni o|mii oomllti. Front flic i-fntrt' <«f 1 -', tlruw live l('uvi"«, !ilw» two iiiiopciifil !iimIm. Si'« thiit till" |Mi{iiU iiinko their Uruwiuyd mucli l(ir((«'r tliiui tho ropy. C'aki)-Kxki«;.mk XIV. l)"»l»n fVom the Oonvot* uiu* Flowtr. l)raw 11 ^<^n^l'•l'. itn (liiiini'tcrH iiinl difigoiiuls. In tin- npfu'r qiiurti'r of till! h* yivcn in tin- '•<'j>y, — 'Wliicli \* tliu Bjinii' lis the flowi'r in the lu-t ox<'n'i>n', — uiul I'pi'at ill I'iicb of tlif otlicr tlircc quarter?*. Make tin- lifit;lit of till' taivx at tin- liam* of till! Huwi'r ttliout ont'-fourtli of tin- Ki'mi-iiiunifti'r. I'HAtflVAL itKfluX. 149 I It'iiKth, aiwl t 'J I'H'.in] til tlifl viTlital ', JttI U> tliri'o- I'niw fill' It till' I'liil iif r« iif 1 1', or l>tl tllC liiWiT iir half of till' I' till' ii\\y% or ; aiitl, oil il)i> oin fin iitri* l(>|M'llCll iltlllx. It iiiucli ltirj{t'r iw«r. itH iliatnoroni [ii llui iiiiiH'r |iiiir<', on till) iw Ii ri>iivoi« given ill tlii> till! H!inu> nx la-t t'xi'nini', eui'b of tlio it. Miiki' till' X III tllu liJlHU L-uu-Uiunicti. iu tlf.i«ii I* t»» •nki' II f'ttin iilri'Utly tlrnwii.uriil mi iinf it m t.i.|iinHiiii« ,t iii'W <;iinil>in!»tioii. I'ii|iilit of nil UK'>« l"Vi' tu ilo ttiiit, wliifli iit uii I'Xfriiftt' piirti}' iii ilrii«iiiu iiinl imrtly in iiivi'iitin^. l)o iM)f forxi't to roqiiiro tlio |tn|iii», fMiii tiiiii' to tiini', to iiiialyzti ilin tiir-Kxi-.KrlrtR XV. Symmetr'CM Moroiqua Ornkmeni. I>ruw II viTticiil lini> of any uivt-n Ifiitfth. iiiwl l(' tiirvci. Muku ul! tliu eurvtH as gro^-eful m poasubk'. Vakiation, — HiiYiii){ drawn tlii« fij»Mr(' iih given, ri'iieat it on tliu lower side of •"> Kxmti inr, XVT. Mur«« I'fiitri' of imm'Ii ohli* <>f ilio »)|tiitri', ilrikw Ik liiit> |M'r- ;>i, ami '>iii>-tliirii({i>r. •)n tlii< liiii>, uml tliK Niilo of ilii> «|iiiir'i* III tliti liiitt cunl-fxirii^t'. liiMiili' I III' Ni|utiri-, ilruw Ik nmt'tto, lik" 'I ill <'urili'X<'r- I ii4o I. 'riiiM illuHtriUiM li<>«v I'ikMy n tliiii}{ it it to coiiiliiiu* Kiv«>ii utiitN mill iiiuku now f thi> Mi|iitir)'i*. Diviti** tlicHC iliuiiH'ti'rH unw- iii^ its IoIk'h «.» tmirli i-itlicr xiilf »( tlic H«|iiiir«'. Kmli of the Htiiull liiili'M tukurt up oiii-Mixtli, uml ••adi of tlm Hiiiiill iliuiiioml Hliuiit'H two-»ixtli»i, of u biJu of a, mjuure. . ,•:.. I lv^-o*,J r ^HJVnVAL I/Aa/U.V. iiri • CroMk IW II liiiti ptT- till' fu\o, itml [ur. < >n tliU niiU* of tli)> h<* fonn ant'U |U»rf, ilriiw It ill fiinl'i'Xi'r- illuHtriitiM liow it in to ciiiiil>iiii< rrafolll Fornn. I 'J, mill ii|Miti it i|uui'i''<, loiicliiii^ Pmw ill" liori- I of till' Mt|iiuri'i«. iint'tcrH iktiil till' iif till' r«|llurcM 1 piirtM. Diiiw vn wliii'li iiifir- ovcr mill iiiiiliT iiiiti'ly. iiw tliriM* wjimriM I ll>ut', not lll'')\V- (' 8i|iuin'. I'imli , tiiiil «'iu:h of tilt) »i Ju of » tttiuure. CJanm-Kxkni iMK XVtfl. ■oftunnUl N*9«lllion. -Trafbil r>>rmii, »ii(t InUrUalng. |<'iii(M II. — |)rn\v liiiir -i|iiiui •• iiiiitiil lioii/iiiiiiilly, uml itild llii'ir vi't'tiiiil iliiiiiK- (■•r*. I itt^lifM' iliitiiii'tirit. ilmw Iri'fiMl lt'(»vin, i\t ill till' ••■•p.v Mritw i\ liori/iiiiiitl liiti' uIhivi', iiiiotlicr Ih'Iiiu, FnitM /), — Draw fitiii M)iiiiri'4, iiiiiliMl Imri/. iiitully I'ill lltfMf M|iiitri>M with iiiti'r- I u'iiig jiiii'it, M ill II, liiitt I'unl- i'ru\s' it Imri/H'iitiil lint) iihovr iumI lii'liiw. |iivii|i> till' ii|)|M'i- liiiii/.oiiiiu liiii> into lmlvi'4; on t'lu'li liitif loiiNtriiit ii Mi|iiiiri', uml nil it witli It tri'foil Ifuf, nn ill tlii> copy, Tn cuiiipli'tK till' lllnllliliti^, ill'ikW Ii liiil'i/oiiliil lllio uIhiVi'. Hqu«r« IloMtta of Uooyantlonal L«»vm, ancl MouldlnR. I 'raw till! Mpiuri', itN iliu^iiiiulH uml (liiiiiiiti'rH. Muki' till' iliuiiK tor of tlif cir* • It' lit till' ri'llll'i' ''i|lial to illll'- tolll'tll of till' iliuilll'tlT of tliu M|Uuro. 1)i'a\v I lie coinpoiiiiil rllI'VcM oil till' iliuKullul(«. Nl'Xt ilruw till' lt'uvi'« nil tlu' iliuiiu'- tiTH, uml lliiir«li liy ilriiwiii^ till' iiiurKiiiH of till' otlit'i- ll'UVI'M. Mlllil' tiic Miillll of tlii> iiiniililiii^ Im'Idw till' i-iMfttt' I'ipiul tu oiii'-tliii-tl of «. '>iil(' of till* Hi|iiuri'. § 14U TKACIIKHS' MANUAL. Vaimation 1. — Draw til rec sfiuiircrt uiiiti-d liori- /...iitiilly, and iill tliciu in a siiuilar muuii.-r. Cdii- tiniu! tilt" niouldin),' l»c'low Hio rosottes. Vaimation' 2. — 1 raw lli" wiuaro, its diagonals an-KxKU<'isr. XIX. Toy Oburoh. Draw a square, and divide it into nine iM|u:d small squares. Erase tlie right two of the upper three. l)i- vide the right and left sides of the renmining upper S(iuaru into thirds, and the top into fourths. Through tin- lower points of division on the sides, and the outer points of divis- ion on the top, draw the in- dining sides of the spire. The window occupies one-half the width of the square. Draw the vertical and liorizontal lines belonging to the spire and body of the church; then add the lines for the roof, door, and windows. Draw the lower lines of the roof before the upper lines; observe that the ridge is level with the bottom of the spire. cfl united linri- inuiMKT. ("on- ', its (liiigoniils (H'litrf. TluMi, rvi's on the tli- UIkI tllf ll'llVfH line (Mjuul HiiiiiU raso t)ie right pper three. 1 Ji- lt and left sides ling upper stjuare imd the top into rough tin- lower isiou on the sides, r points of divis- top, draw the in- s of the spire. dth of the square, nea belonging to hen add the lines Draw the lower ues; observe that F the spire. l'HA cue A L UK.SIUS. 14( ('AUI>-K.\Klt/'.• .V. U!) Kxt.'iid 1 L' liiilf fxtrcinity dniw . Tliis liiHt liii.' II wliii'li iidtl tlit> ^ al'ovc tlie li't't I'Clltrc Id'lli'lltll II to wlicrt' llif u'ciinlinj; ti> tlic If iiiiidi', us silvtM'. )ii. II. 1 StraiRht Lines. il divide it iiitii aliovf tilt' lower iw ."> 4 equal to if 1 2. Draw the per, wliidi oceiipy If of 1 2, inaUint,' :lie neck eiiual to 1 '_'. On the low- verticid line, draw , forniinf? the out- udy <»f the hottle, cnrvos .s])rin^'in<,' Candleitiok, Candle, and Eztingui«her. Draw the central vertical line, aud divide it into foureiinal piirts. 'riiroii;;h tin' lower jioint of division, dniw 1 'J a little longer tliiin three- foiirtlis of till- vertical line, and extending to the sann' distance on each side of it. >rake .'5 4 ei|iial to one-half of 1 2. The top of the socket reaches to the centre of the Vertical line, while the wick occupies the upper half of the upper fourth. Uraw the curves care- fiiilv, most of them lieinj,' compound. I^raw tlie outer curve of the handle iiefore drawing the inner. See that thi' sides of the extinguisher have the same slope. In this exercise hut few exact ineasiirenieiits are given: it will, therefore, he a good one for the liest pupils to draw on the Idackhoard from tin- hook. QcKsrioNs. — Wliat is Miiii of I'onvciuioniili/.i il r(irn> ' Wlioii is it |)ro|inr to imitate Niitiirc exncily ! Wlmt is mm- tioiioil as tlif first step in original iloicri > How c:iii tlif \ 3nt degrees of L)l)j('('t9 hIiouIiI •niiinentwli it'll (leiisiiig ett't'ct, ndaptetl to the been selected, uotlier a sprij;. be sometliiii^,' , to be viewed iliiite diftereiit from all sides, but cannot be n. tberefore, is ;, for example. * of the room. , the ornament finials, eorl)els. I is good that ion must never lament to con- < 'AKn-KxKU<'IHK X X H I. Aoorn and Cupi OonventionalUed. Draw a vertical line, and divide it into three equal parts. Through the upper point of division, draw 1 - slightly longer than one-third of the vertical line. Above this, draw the outline of the acorn ; below it, draw its cup, de.scending nearly to the sec- ond point of division on the vertical line. The outline of the cup is a semi-circle. .\dd the empty cups, making them like the full cup. Variations. — Draw the figure as given in the copy; then fill the sida cups with acorns of the same sliapo aa the acorn in the upper cup, Card-Kxkkoise XXIV. Aooms and Iieavea Coaventionaliaad. Draw the ac(U'n» as in the last exercise, and then ••ontiniie the central vertical line down- wards until its length is doubled. Draw two oak-leaves springing symmetrically up- wards from the bottom of the vertical line, and touching the sides of the acorns. There arc different varieties of the oak- tree, and of course tney have leaves somewhat different l.VJ ill tnrin rh:.ic/iKns' mamai. 1 1' it oiiii l>i' tloiic, rn|Uc.-»t tlw piipiln to l.riiiK' ill woiiK- y. ('Altl)-KxRIUISK XXV. Olover-IiOftf Uonventlonaliaed. Draw a viTticul liiK' ami liiilvc it. On tin- iiiiptT liaif, as ii iiiiilril', ni\v an (•(|iiilatcriil ti-iaii}.;l(', .and from ha (ciitn! ilraw a straij^bt lino to carli aii!.?lf. On tlic.-c Hiicm V .■oinpoiinil leaf like tin- one in (llilNV as iiiiih'ili tlu'copy. Draw two stvai;,'lit liiit-s bisecting •■aclj other at ri<,'lit aii},'l('s. Divide oaeli into tliiids, and. tliroii>,'li tlie points of division nearest tlie coininoii centre of tlie two lines, draw a cirele. On each of the outer parts of the lines, draw a single lohe of the elover-leat\ thus ohtainini,' the etVeet of the four-leaved sham- rock. A<,'aiii. ilraw two eipial lines, one horizontal, the other vertical, hiseetinj,' each other. Divide each into four eipial parts. On the upper half of the vertical line, draw a complete clover leaf pointing upwards; on tlie lower lialf, draw a seeond pointing downwards. I'lt.wiicAi. hksiux. \:i\ \i' |nii»iln to ad i'oin|)aru Iniw tlic t|) 1()ln'. ilniw loWlT IoIpCS. ■ l>rii\v ;iii (', .iiiiil tVuin straight lino 1 tlic^f lini'H ■ till- one in icli other at and. thron<,di nil cclltri' of of tin- outer le eliiver-leaf, eaved sliaiii- irizontal, thn ide eaeh into f tlie vertieal ng upwards ; I downwards. Oil e;irli eiel ..f tile horizontal line, di'aw a single lol.e of till) leaf. The re.y. I'.et weell each pair, draw a cin.pie-roi! tlower, that is. a llower having live leaver ; or draw a hiiiwli of spheres which shall represent tlu' hall of s I of the llower. ITti TKAVIIKNS' W.I.V/ .1/-. CAiii»-KxKK«;iHK XXVII. Wina-Olui. ICuvinpf (|nul to two of tlu»»c i»iirtH, r» (1 to one of tlio purtit, uiiil 7 tn, hiwe, Vakiations. — With tlif Kunu) proportional divistion of tli(> vertical lint- ii gn-ut variety of Mliupes iniiy bo ohtiiiiit'*. Draw parallel horizontal donhh' lines near the lip. and lictweeii them draw a star repi-ated around the glass. Tile star may \m composed of four straight lines cros.s- iiig one another at a common centre, the alternate lines mutually perpeiidicidar. See that the pupils, when they examine their draw- ings, do not look at them oldiiindy. They should holil them directly in front of the eye, and turn them around. I'liless rrcipiently reminded, they will neglect to do this. f'N.ivw.n. hhsnis. IM > four into foiirei|uiil parts; on each part, coniitruct a nquare, and till it iiH the larm* xcjuare wan tuh-a. CAHn-KXKRf!I«K XXIX. AMU*. Draw the central vertical line, und divide it into six eijuai partH. Make 1 'J, 3 4, equal to two-thirds of the ver- tical line, imd draw the sides ot" the iiiu^. Draw the hori- zontal lines, the lower one of the upper group through the upper point of division on the vertical line, tho upper ono of tilt! lower group through the lower point of division, and tlie single one through the central point of division. - servo that the tlutings towards the hottoin t )i>ii>|i i'i|iiill to 'HM-lllll'l rl«rill lillf, Willi itp« Kr»'(l»t'»t [ifo- jiM-iloii fruni !!»<• ui»\i inwanU tlii> top. Notice tli«- liMii/.i.iituI Wui'* Irfin wliivli I|»k lmn liuuill<' tliii'lc ami I'liiiiiity. ,\iitiivi'hl tliiM, N'viiuilov. — Divi'lf tlti- ichtrul vi'i'tirtil !int< iiiln (|iiitrtcrH, uikI iitaki' llh> wi'tili llii> littler lii'tiiitM tlio xitiiH', hilt iiiii'it|iiiii. t'vuii-KxKiM iMi: XXX. MAple-Lvitr UonvcntloDnIlsed. I^raw u vi'i'fii'Ml liin'. univii(li' IiiIm'K. Coiiipliti' till' Ii'iil' iiH hlmwii. XotiiM! timt fli>' I'lirvcM vvltlirll cllflosi' till' liilx-f* of tlir Ii'llf iihviiVH luiiil oiitwanlM rrmii tin- iHMitroof till* IoIh' ; alsotliat tin- tint's at lilt' jiiiiftioii of tlio loht'n iiowlitTi' form uii- )j;lt'x hilt Inivi' a roiiinlt'il Hliupi'. Ut'iiirirf tins piijiiN to (iriiw this ]c;if ri'i.ni tiiiif to tiiiii", until tlu'v i-aii riiniilv ilraw it iV.oii iiK-iuorv. i'MACnCil. hUf'lUS. IW N«iti<'<' titi r'lli' »|>riiiK«. till' lllll tilK ■'I • tllK llUtllilc t*lit tliim. irul lino iiilo I* till) Mttltll', |M-, |tfiijt'rlillg iiimI I'otloiii, fliinl-*. MitUc \vo-tliinlf« of hivi)li> I mil, tlit'oii^'li ivi'^ioii. ili'iiw if (IS »li(ivvii. I'lirvcH witicli iif till- li'iii mix IViiiii till' rtlso tliiit tin- icri' form jiii- re tlu! |iiii>iN litil tlii'v rail OAHIi-KXKHriHK XXXI. Uriiw u li.iriftiiitiil un.l h xiIi.uI liiii< of tin- unni" yiviMi liii(;lli, liiitfiviit<> I'Kfh ill* tU'wU I'liitf till' ixdhtu •if ilivinioii, tliiu foriiiiiit; n i«|ii;ih- oil ItM tliii^oiiiilK. Witliiii till' itt|imrf, ilruw ii tri'foil ; witliiii tin- tn f'lil. ii iiirvi'<|iiil;tti'iiil triaiiKl''. Oil till- oiltfr lliil'ii of tin viTtirul uiul li)iri«»iit>il liiit'x, .Iniw vi'Utiiiuiilizi'il muplt-lfiivi ■>, li.iviiiK slir |>i"- |iiirtiiMiiinuUlii«iK>(i| iliiMiiiu ill tli«- Uwt ainl-txi'wiM'. C'AKi»-KxKHrii*»', XXXll. OonTei>Uon»li«ed rorm ; Simple LeaVM MJd Flow^ri. l>iii\v till' \. itiral liii" I Ii, iK'*l (livido it into four i'i|iiiii j>;iit^. .Muiii' ."> I. r» 0, ciiiiiil tu oiit-liuH of till' verti- cal liMf. •"> > to Ih! ilravvii tliriMi)fli tln' iippi-r point of ilivjoion oil till* vcrtiiiil line Draw llr^t tlii> iiii'lrilis luul !iii!S of tin- liMVi-.t, mid th«>ti tlii'ir iu;tt'i,'iii». I >i':uv tin- llowvr lit tliii to|>, uimI lastly till- littlv tiri'li'.H at till" Itottoin. rfpri'Sfnt- •iij; till' lit'rricK. M i m TKdVIIIHHI' Mi, MAI. Cudi-KKKNi Mr. XX Mil. 0i«l<' It into lliinU. Muk«> t 'J ami .'( t iMlHitl to, iMIil TlO a little ji-M tlutii, tMi)-tliir ' By wliiit iiii' you to Ih- kuIiIiiI in KiUctiiiK ilil- (■(•niil lurmi* lur tin' |iiir|ioii' I By u»i' ' 1(1 Flowari, I, utui itki' t '.' nml I n little ll'KM till' VrrticttI A anil 4 «t. II t. ilmw l)i« Ig tllf CI'll- It'lkVt'ii lUlit fiiiU of 1 '2, iiiiitl ctirvfrt lltlllM- t)l' till' ■I ikt a r liort rti», itinl iiiiiti) , IVitiii M 4 to II till' poilltrt iiH'iirtiiri'iiU'iit llllll |H>lllll'llt .'UllVl'lltlullull/Cll ill M'U'ctiiiK ilil- I lluw nIiiiuIiI I Hy u»i.' ' «'HAI'TKU IX, KOHMM OK I.KAVKM AND I'LOWKIW. uTimV 'tf MnTAMV. 1 1 liii- ulri'U'ly l'i'«'ii nftlil, tliut Niitiir«« oftt-ii ImiUU ii|Miii iiitirki'il gi'iiiiH'trii'tkl i'oniiK. In il< ii* f irri'ttnlttr, Imt umiully tin' ri'ViTwi in d^fiu'rul uiitliiik'.!. 'I'llllt tllim U trill' of li'UVi'* UlliI (loWlTi, will III- Nl't'll I'rniii till' I'Xi'rrini'fi wliirli miiiH'iliiiti'ly full'iw. Aiiimin li'tivii«, notiiK liuM' till- t(i'iii'rikl fiiriii tif till' I'llijwi', iitlu'rw of tln' •iviil, otliiTM of till' Iriuiiuli'. wliili' oiIhtk liri' llUull'llnl M|M>ll till' |H'lltllJ{oll. AlllollK (loWI'fK, ■ iliiTi' ii II Ic -s viiriity of I'oniid, niiici' tlnir jii'tiilH uri' imiiully iirriiiiKi'i' nyiniiu'trii'iilly unMiinl u I'l'iiti'ii, i |{ii|iii'st iiuli |iii|iil {<> \>r\\ni I" Hrliool till' li'uf of { uiiy iii'»i«iiiiti'il till', xlinili, llowiT : u-. tlir iiiii|ili'. roKi', lily. Kii'li |miiil liiiviiij? in liin IuuhI iln' "n"'" I viirii'ty of Itiuf, pmci'i'il to yivf u h-nnoii mi itn form I ami Hlriifturi', toai'liiiin lit tin' hiiiiii< tiiiu' liotli lioluiiy iiinl till' iniiirilili'H of piin'ticul ili'^in'i- I'or ii »ri'oiii| ! lt>«Muii, tttk't tint muno U'lif, Ixit mill luiotlior, uinl ti-mli till' impilrt to . wliiih lii'loti); to a flower. Hki'AL. — This is one of the leaves lomposlii;,' tlic enlvx. (^oitoi.i.A. — This consists of the usually dclicatilv ruloird (lower-leaves inside the ealyx. I'lCTALS. — These are leaves of tint eondla. SrAMKNS. — These are the sli'iidcr parts toiind next iiisidi' the eoi'olla. I'iRTIl,. — This is the central jiurt of ilic llower wiiliin the HtHinens. F1.0WKU IN I'l.AN ANI> Kl.KVATlON. — The first is the llower as seen when vi^ rd directly from ahovc ; the second iis seen when it is viewed from ono side. Caku-Kxkkcisk XXXTV. Syringa-IJeaf slifttitly Conventionalized. Draw a. verticiil lino forming tlio midrib offlio Innf. and dividt! it into fivo equal ptirts. Tiirotigh' tliti second point of divi.sion from tlie bot- tom, draw a horizontal line ono-lialf iis long as the verticil line. Add the veins joining the midrib. Around the whole, draw the .serrate margin of the leaf. The apex of th(! leaf is acuminate ; the base obtuse. The whole leaf is slightly con- ventionalized, making it symmetrical. As a whole, the leaf is oval, inclining to the ellipse. With the proportions thus given, the pupils can readily draw the leaf many times larger than in the copy. 14* U\-l Tt:.{riih:/,'s' MAS'C.l/.. Cakd-Kxkhcihk XXXV. OatniP'Iieaf, allKhtly Conv«ntionallied. Draw ii viTticivl liiiu t'ormiii^ tlit! miilril) iiml potiolo of tlio leaf, and iliviilo it into thirds. Throiigli the lowi-r point of division, draw a hori- zontal lino two-thirds as lon^ as the vertical lint!. Add tlm veins. Around the whole, draw tho i-ronati- margin of the leaf. Thu base of the leaf is cordate, or lieart- ^■^■^■^■■■■^■B shaped ; its apex itcttte. .'he I petiole, or leaf-stalk, occupies one-half of the lower i third of th(! vertical line. As a whole, th.' leaf is de- i cidely oval. i Cakd-K-kkucisk XXXV I. German Ivy-Leaf, sliKbtly Conventionalized. Draw a vertical line forming the midrib and petiole of the leaf, and divide it into three equal parts. Through the points of division and through the lower end of the line, draw horizontal lines, tiie upper and lower a little more tiian half, the central a little less than half, as long as the vertical line. Add the side ribs, and, around the whole, draw the margin of the leaf. The margin is .uitire ; the leaf yOR}fli OF LEAVES ASh FUtWKHS. Hi:i lied. > iiiid ])uti()l(t livido it iiitii I the lower , draw a hori- lirdH as long ,0. Add i\w tho wIjoK', !• margin of base of tin.' , or lit'urt- afuti'. ."111! uf tlio lower lie leaf is de- lalized. I) and petiole livide it into Througli the and through he line, draw lie uppcu' and •0 than half, tie less than the vertical ide ribs, and, le, draw the ;ire ; the leaf ftve-lobed, with sinuHes very siiallow. As a whole, the loaf is pimtagoiial. Cahi)-Kxkk(;isk XXXVII. Ooosaberry-Leaf, sliKhtly Conventionaltaed. Draw a vertical lino forming the midrib and petiole of the leaf, and divide it into thirds. Just below tho upper point of division, draw a hori- zontal lino not quite as long iia tho vertical line. Add the other ribs and tho vein.s, and around tho whole draw the margin of tho leaf. The leaf is five-lobed, sinuses deep, nuvrgin unevenly serrate. Cauo-Exeroisk XXXVIII. Strawberry-Iieaf, alishtly Conventionaliaed. Draw a vertical line forming the petiole of the and the midrib of the cen- tral leaflet. Divido this line into thirds, and, through the upper point of division, draw a horizontal line as long as the vertical line. Draw the midribs of the right and left leaflets, and add the veins for all three. Finish by drawing the coarsely serrate margin of each leaflet. leaf I — ■"" ' I 1U4 TK.tVllKHS' MANUAL. A li'jnf, sliRhtly OonventionallEed. Draw the vertirul lim-, forming tlio midrib, iiiitl (lividt* it into thirds. Just iibovc tlie centre, draw a hori- zontal line, making it eiiiial to two-thirds of tlu' vortical line. Add the other horizontal lines, ont; below and two above, by j udgment of eye. Then draw the lines forniinj^ the veins, and, around their ends, draw the margin of the leaf. This leaf is just onouKh conventionalized to make it symmetri.'al. As it is a simple leaf, the midrib is the axis. CurraDt Leaf, slightly Conventionalized. Hr.aw the vertictal line, forminR the midrib of the leaf, and divide it into four e(iual parts. Through tlu! upper point of division, draw the horizontal line, making it equal to three-fourths of tho vertical line; tlirough th( lower point of division, draw a second horizontal line, making it a little shorter than the first. Add the lines forming the veins, and. around their ends, draw the margin of tl-e pentagonal leaf. Tiiis leaf is, also, just enough conventionalized to make it symmetrical' on its midrib, which is the axis. FOUMS OF LEAVFS A.\H tUtWt.lls. I )>o Bed. u midrib, iiiid tliirils. diiHt 5, draw ii liori- ing it c'cjuiil to «' verticivl line, orizontal linos, two above, by e. Tben draw ing tlie veins, t'ir endn, draw \w leaf. Uized to inako ", tlie midrib is aalized. midrib of tluf le it into four Through tlu; ' division, draw line, making it -fourths of the through till! ■ division, draw ori/ontal line, tie shorter than dd the lines ends, draw tlie ventionalized to lich is the axis. Hawthorn-Leaf, »llKhtly Oonventlonallaed, Draw the vertieiii line, forming th e midrib, and divide it into four f(iual parts. Through the central point of division, draw the upper hori- zontal line, making it a little longer than one-half of the vertical line; and, through the lower point of division, draw a set l.cli.w liie centre, draw the lines forming the ribs; and, around these, draw the contour of the leaf, making the breadth a tritht greater than its height. Use these ditt'c^rent leaves not on the cards, for black- board lessons, anuf und tint ini of tlie central leaflet. Dividt; tln'H lino into four ocjiial piirtH. Make tlio nii(lril)8 of tlio ri^jlit and left Jcaflctn about two- tliirds OS long as tlie niidribH of the central leaflet. The breadth of each leaflet in a little le8!i than one-half uf itn length. The margin is en- tire. This is a compound leaf, each leaflet ellij)tical; general outline of the whole triangular. Cakd-Exbrcihk XL. Boae-Laaf, illRbtljr OonventlonallHed. Draw a vertical line for the rachia, and mark the points of junction made by the leaflets with it. Draw the midribs of the leaflets, and flnish. Kach leaflet is elliptical: the whole leaf, in its general outline, might be called the same. This is a compound leaf, whicli is quite a different thing from a lobed leiif. Sometimes, however, it is no easy matter to distinguish one from the other. 1 FOItM.S Of I.K.xyhS AM> hUtWhllS. h\ Used. 'tiiiUt of tlie ilril> of (lip Divido tluH i|iiul piirtH. of tlio rij,'lit ivliout two- tlie midribs t'iirtet. Tlio li'iUV't irt a I'-lialf of it» rgiii is en- it elliptical ; ed. (1 niiirk tlio iniule by the l)r.aw tlio eafluts, and luaflct is ole h'af, in i, might be This is a ich is quite om a lobed however, it the other. «'ntaKo- iial, cimiiie-foil, or five-leaved. At li \\A' hiive the i-levation of the flower, or the Hide view. At (■ we have the bud; and ut (/ the eouipound leaf. It will he Keen, that the snaigin of the natural leaflet is ser- rate, and not entire, as given in the last exercise, where the loaf is slightly cou- vi'iitionali/.ed. Observe how syinnietrieally the live large jietals of the corolla at a, also the flvo small petals of th*) calyx, making ten in all, are arranged about the centre of the flower. The ten little stamens near the (^entro have the same symmetrical arrangement. Observe, also, how symmetrically the leaflets of the compound leaf at d are arranged on an axis, that is, on the ratOiis from which the leaflets spring. As the i)upils draw tlie leaves and flowers, q\iestion them about their forms and parts. Do this until they are perfectly familiar with the terms used. At the same time question them, also, about the jirin- ciples of design to be learned from these natural forms. You can readily make this a very interesting exercise. In tho same way .shells and insects nlay bo drawn, and lessons in design learned from them. ICS •SHMmnUS' MANVAL. (Aiiii-KxiJii'im.; X lill. Oran«'a-BIU Flower, Iiaaf, ^nd Bud from Natur*. At a we liiivo the plan r»f tin- llowi-r; iit l> tlin cli'- viitioii ; lit (/ tlic h'lif ; (it /■ tlm lm li'ut'; lit t !*]llk|)tt ({ivi'M •riiiii''-< hill. |ii'titai^i)tial, 'I'liki' iMitirtt ciil (irraiij^c- UIIll StUIIII'IIH of tilt' HkW- ri' tlic Ifiil' at at il ill till' niitl Hiin|il<', yiiiiMt'tricully H riu'liij*. iiy sliiiiiltl hn I (HTtaiii <>x- ntli (Irawiiijr 111' jH'iicil of villl'M. flTIIS, ill iirawiii^', di/.c(l, all till) <|uii'k<'ii till) iiiciT art of III', and tliu8 I'll^jo ill till* ncr ill which tor, usi's lier lines, I'oviTH U' laws that miiiithi'ol»'>M'il ill [iriu'tual .h'sinii. if wi- woiiM sn-iiri' th.' ha|»|»it'Ht I'fli'.'ts. Thus, in n irrfain .h'^'r.-i'. to iiiiiti' hotiiiiy, ilrawiiiK- in»ut«!d, and do thoy miito taii(,'«'ntially, or othcrwisi'V As you proceed, thrro will ''c such (piestioiis as these: What lessons in syniinetrical arrangement ahoiit a centre, aloiiK an axis, are to hu learned from simple leaves, compound haves, from the petals and stamens of flowers V What lessons in radiation I'lom a parent stem arc to he learned Irom deeply-lohed and compound leaves and from tlower- nnihcls? What lessons in continuous development foriovcring irrcjjular and other surfaces can vines, trailing, climhing, twiniiiK, and axillary iiitlorcsceiice, teach us? What lessons in hrcadth, in repose, can we learn from all? Nature lias a ivady response for each of these i|Uestions, whenever we choose to inter- rogate her in a proper manner. lUit, while she is answering the ipiestioiis put hy the student of art, she can, at the same time, answer many «>f the (piestions put by the student of science. 170 TKAt'ltKHS' ilASVAL Tiiu i'X<aK<* art* )(ivi>ti for tMWh* iTn wlio liikVH a<-i|ulrtMl noinu mUiII hi tirnwin^;. to juit oil iIk' •miirtl ni|>in* im-n-Iy an «uj(mmtivx<>rciiioM ulihili tenulicrt* iiiuy urn* to inuki* tlicir drnw- iiig-leMf.!)!)!! iiiturvMtiiig to thi-ir |iii|iilM. Tlic M, un* ■iiii|>I<> illuMtnUioiiH cf how tlic f<*inH III 111. Il>«t.m rul''!' *>'"■■">•. *•"• "I"'"" "' '"• ■Ihl, ,yM.m I- ih, unly ...m,.«h«n,lvt t.mr,. .,| In.irua.n.. u. a«*m« .ccc.,lM. •.. Ar,..rlcun »cI..m,N. Tl.r cur,. I, ... *f*>M *- 1.1 ihB n.u-.t ..Jv..n...l 0*.' .1 »^ - hluh .cIuh.I. The ) • nnnin^eH A Primary Cour««. An Inter Mediate CourHe, A /[irammar CourHO, A HlKh School Oourie. TIIK I'KIMAKV cmUNK. ThiH c.mr.c c...,iH., ..f * Munualfor ll.« u^c „t lf.ul.fr,, i.. wlml, lli« ,ln.pWclc...i-ni, ..( tl.f .i...ly »re PHpta.ned u.ul in..,tr..UHl 1^ .!..• m.«t f»mili..r l.-..' ..-.'I .■^..-..l.l"i ..ul tw,. scri.-, ..( C»r +.» | i— w ■ ■•* llli: (.KAMMAK COL'RSE. This course consists i>( : — /•'inf. I'"ouR Hooks in 1''kk|'.iianii Outlink Dkawinc anh Dksicn. The exercises in tliesc books arc more advanced tlian those in the Intermediate Course; and by a wide variety of orna- mental, conventional, and natural forms, and reprpsrntatioiis of his- torical ornau.ent, pupils are taught a j;reat deal aljout the art of past ..i|{cr., and also the principles of guod IJcsi^n. Sfifliii/. FoiK Hooks in (;i;omi;thi( al l)RA\viN(i. These l>ooks form the basis for I'erspective, Model and Object, and Mechanical I>r:nvin«. I he exercises consist of problems in I'lane (ieometry, the uorkint; of which teadies pupils the exact meaninf; of words and terms: and by the rare rc(|uired to execute the problems they are trained to accural y of \vorkm.->nship. T/iik/. Two ItooKs in Mohel and Oii.ihi t Drawing;. The exercises in tlicse Ixioks arc all in outline; and pupils arc tauKht in a thorouKJi manner how to draw from objects. The exercises are of such a character, that tiie pupil's t.iste will be cultivated while acfpiir- ing skill in ilrawi:;;;. /•'oiirt/i. Two Hooks in I'kksit.ctivk Di.awinc. These books teiich the elements of I'arallel and Anqubr I'erspective. Kach of these divisions is accompanied by a M.inual for teachers, containilm all the exercises in the books, ,ind many more iK-sidcs. 'Vice of the Books. S5 Cents each. As above set forth, the (irammar Course comprises twelve books; and with an allowance of an hour and a half to two hours per week to drawiiiK. pupils can easily go throuKli three of these books in a year ; imd when pupils have linished this (irammar Course, they will be able to draw in outline wluitever they can see and understand. Where pupils in ;;rainuuir schools have received no previous instruc- tion in I'rcehanil Drawiiii;. the f,rst Kmdin- of the instruction must be jiri visional. Till'. HK.ii .SCHOOL corusr.. This c( urse consists of adv.nnced work in I'e. pectivp, Mode! and Object DrawiuR, or Mechanical Dr.iwins;, according to the t.astes of pupils. As in the previous courses,