,transcrib]'s ,notes3 ,und]scores 80 be=e & aft] a ^w or phrase indicate italics 9 ! orig9al text4 ,equal signs 80 be=e & aft] a ^w or phrase indicate bold 9 ! orig9al text4 ,small capitals h be5 conv]t$ to ,,solid capitals4 ,illu/rations h be5 mov$ s !y d n break up p>agraphs4 ,typographical errors h be5 sil5tly correct$4 ,add$ ,,index to ,,toc4 ,,/air-,,build+ ,,& ,,! ,,/eel ,,squ>e ,a ,,manual ,,( ,,practical ,,in/ruction ,,9 ,,! ,,art ,,( ,,/air-,,build+ ,,& ,,h&-,,rail+1 ,,& ,,! ,,manifold ,,uses ,,( ,,! ,,/eel ,,squ>e ,,"p ,i--,,/air-,,build+ ,by ,,fr$ ,t4 ,,hodgson ,,au?or ,,( 8,,mod]n ,,c>p5try10 8,,ar*itectural ,,draw+1 ,,self-,,taught10 ,,etc4 ,,memb] ,,( ,,ont>io ,,association ,,( ,,ar*itects ,,& ,,morris ,,williams ,,writ] ,,& ,,exp]t ,,on ,,c>p5try ,,& ,,build+ ,,"p ,,ii--,,! ,,/eel ,,squ>e ,by ,,morris ,,williams ,,illu/rat$ ,,*icago ,,am]ican ,,te*nical ,,society #aiag ,,copyright1 #aiaj1 #aiaf1 ,,by ,,am]ican ,,te*nical ,,society ,,copyright$ ,,9 ,,great ,,brita9 ,,all ,,rights ,,res]v$ ,,introduction ,on ent]+ a build+1 almo/ ! fir/ ?+ t meets ! eye is ! /aircase & unconsci\sly x is made to s]ve z an indicator ( ! quality ( ! ar*itecture4 ,if ! design is poor or ! con/ruction faulty1 ?is flaw imm$iately gives ! visitor a bad impression ( ! :ole build+4 ,fur!rmore1 /air-build+ is a r difficult subject & ! pr9ciples involv$ are v little und]/ood1 :i* is evid5c$ by ! fact t ! lay\ts z furni%$ by ar*itects 9 _! plans are (t5 improp]ly done4 ,probably m mi/akes occur 9 connection ) ! /airway ( a build+ ?an ) any o!r con/ruction feature4 ,x is ) ! idea1 !re=e1 ( giv+ a complete ?\gh simple pres5tation ( ! con/ruction me?ods z appli$ to /&>d design ( /aircases1 t ?is book has be5 prep>$4 ,! article discusses /raight & w9d+ /airs1 /airs ) well hole1 lay\ts = curv$ turns1 ! prop] proportions ( rise & wid? ( tread1 ! design ( h& rail+s & _m o!r problems1 ! solution ( :i* w be f\nd v useful4 ,c\pl$ ) ?is article is a mo/ in/ructive section on ! ,/eel ,squ>e1 conta9+ _m applications ( ?is useful in/rum5t to ro( & o!r types ( con/ruction4 ,illu/ration3 ,,greyrocks1 ,,rockport1 ,,mass4 ,frank ,*\teau ,br[n1 ,ar*itect1 ,bo/on1 ,mass4 ,,cont5ts ,,"p ,i ,,/air-,,build+ ,,page ,/air con/ruction #a ,def9itions #b ,sett+ out /airs #h ,pit*-bo>d #aj ,well-hole #ah ,lay+ out close-/r+ /air #bb ,op5-newel /airs #cb ,/airs ) curv$ turns #cd ,geometrical /airways & h&-rail+s #dc ,wrea?s #dc ,tang5t sy/em #dd ,bevels to squ>e wrea?s #fj ,h[ to put curves on face-m\ld #fh ,arrangem5t ( ris]s #gd ,,"p ,,ii ,,/eel ,,squ>e ,introductory #a ,specifications = /eel squ>e #a ,mit] & l5g? ( side ( polygon #d ,/eel squ>e 9 ro( fram+ #g ,g5]al problems #h ,heel cut ( common raft] #ac ,hips #ac ,heel cut ( hips & valleys #af ,,index #bh ,illu/ration3 ,,hall ,,& ,,p>tially ,,enclos$ ,,/aircase ,,9 ,,long ,,hall1 ,,greyrocks1 ,,rockport1 ,,mass4 ,frank ,*\teau ,br[n1 ,ar*itect1 ,bo/on1 ,mass4 ,,"p ,i ,,/air-,,build+ ,introductory4 ,9 ! foll[+ in/ructions 9 ! art ( ,/air-build+1 x is ! int5tion to adh]e closely to ! practical phases ( ! subject1 & to pres5t only su* matt] z w directly aid ! /ud5t 9 acquir+ a practical ma/]y ( ! art4 ,/air-build+1 ?\gh "o ( ! mo/ important subjects connect$ ) ! art ( build+1 is probably ! subject lea/ und]/ood by design]s & by workm5 g5]ally4 ,9 b few ( ! plans t leave ! (fices ( ,ar*itects1 are ! /airs prop]ly laid d[n2 & _m ( ! books t h be5 s5t out = ! purpose ( giv+ in/ruction 9 ! art ( build+1 h ?is common defect--t ! body ( ! /airs is laid d[n imp]fectly1 & !re=e pres5ts great difficulties 9 ! con/ruction ( ! rail4 ,! /airs are an important feature ( a build+4 ,on ent]+ a h\se !y are usually ! fir/ object to meet ! eye & claim ! att5tion4 ,if "o sees an ugly /aircase1 x w1 9 a measure1 condemn ! :ole h\se1 = ! fir/ impression produc$ w seldom be totally eradicat$ by comm5dable features t may be not$ else:]e4 ,x is extremely important1 !re=e1 t bo? design] & workman %all see t /aircases are prop]ly laid out4 ,/airways %\ld be commodi\s to asc5d--invit+ p1 z x 71 to g up4 ,:5 w9d]s are us$1 !y %\ld ext5d pa/ ! spr+ l9e ( ! cyl9d]1 s z to give prop] wid? at ! n>r[ end 7see ,fig4 #gb7 & br+ ! rail !re z ne>ly z possible to ! same pit* or slant z ! rail ov] ! squ>e /eps4 ,:5 ! hall is ( suffici5t wid?1 ! /airway %\ld n be less ?an f\r feet wide1 s t two p c conv5i5tly pass ea* o!r !reon4 ,! height ( ris] & wid? ( tread are gov]n$ by ! /aircase1 :i* is ! space all[$ = ! /airway2 b1 z a g5]al rule1 ! tread %\ld n be less ?an n9e in*es wide1 & ! ris] %\ld n be ov] eight in*es high4 ,sev5-in* ris] & elev5-in* tread w make an easy /epp+ /airway4 ,if y increase ! wid? ( ! tread1 y mu/ r$uce ! height ( ! ris]4 ,! tread & ris] toge!r %\ld n be ov] eighte5 in*es1 & n less ?an sev5te5 in*es4 ,^! dim5sions1 h[ev]1 _c always be adh]$ to1 z conditions w (t5 compel a deviation f ! rule2 = in/ance1 9 l>ge build+s1 su* z hotels1 railway depots1 or o!r public build+s1 treads are (t5 made #ah in*es wide1 hav+ ris]s ( f #b in*es to #e in*es dep?4 ,def9itions4 ,be=e proce$+ fur!r ) ! subject1 x is ess5tial t ! /ud5t make himself famili> ) a few ( ! t]ms us$ 9 /air-build+4 ,illu/ration3 ,fig4 #a4 ,illu/rat+ ,rise1 ,run1 & ,pit*4 ,! t]m rise & run is (t5 us$1 & indicates c]ta9 dim5sions ( ! /airway4 ,fig4 #a w illu/rate exactly :at is meant2 ! l9e ,a ,b %[s ! run1 or ! l5g? ov] ! floor ! /airs w occupy4 ,f ,b to ,c is ! rise1 or ! total height f top ( l[] floor to top ( upp] floor4,a ,! l9e ,d is ! pit* or l9e ( nos+s1 %[+ ! angle ( incl9ation ( ! /airs4 ,on ! ?ree l9es %[n--! run1 ! rise1 & ! pit*--dep5ds ! :ole sy/em ( /air-build+4 ,! body or /aircase is ! room or space 9 :i* ! /airway is conta9$4 ,?is may be a space includ+ ! wid? & l5g? ( ! /airway only1 9 :i* case x is call$ a close /airway1 no rail or balu/] be+ necess>y4 ,or ! /airway may be 9 a l>ge ap>tm5t1 su* z a passage or hall1 or ev5 9 a l>ge room1 op5+s be+ left 9 ! upp] floors s z to all[ road room = p]sons on ! /airway1 & to furni% communication betwe5 ! /airways & ! diff]5t /ories ( ! build+4 ,9 su* cases we h :at are kn[n z op5 /airways1 f ! fact t !y are n clos$ on bo? sides1 ! /eps %[+ _! ends at "o side1 :ile on ! o!r side !y are g5]ally plac$ aga9/ ! wall4 ,sometimes /airways are left op5 on bo? sides1 a practice n uncommon 9 hotels1 public halls1 & /eam%ips4 ,:5 su* /airs are employ$1 ! op5+s 9 ! upp] floor %\ld be well trimm$ ) joi/s or beams some:at /rong] ?an ! ord9>y joi/s us$ 9 ! same floor1 z w be expla9$ fur!r on4 ,tread4 ,?is is ! horizontal1 upp] surface ( ! /ep1 ^u :i* ! foot is plac$4 ,9 o!r words1 x is ! piece ( mat]ial t =ms ! /ep1 & is g5]ally f #a to #c in*es ?ick1 & made ( a wid? & l5g? to suit ! position = :i* x is int5d$4 ,9 small h\ses1 ! treads are usually made ( -in* /uff4 ,ris]4 ,?is is ! v]tical height ( ! /ep4 ,! ris] is g5]ally made ( ?9n] /uff ?an ! tread1 &1 z a rule1 is n s heavy4 ,its duty is to connect ! treads toge!r1 & to give ! /airs /r5g? & solidity4 ,rise & ,run4 ,?is t]m1 z already expla9$1 is us$ to indicate ! horizontal & v]tical dim5sions ( ! /airway1 ! rise mean+ ! height f ! top ( ! l[] floor to ! top ( ! second floor2 & ! run mean+ ! horizontal di/ance f ! face ( ! fir/ ris] to ! face ( ! la/ or top ris]1 or1 9 o!r words1 ! di/ance betwe5 ! face ( ! fir/ ris] & ! po9t :]e a plumb l9e f ! face ( ! top ris] w\ld /rike ! floor4 ,x is1 9 fact1 simply ! di/ance t ! treads w\ld make if put side by side & measur$ toge!r--)\t1 ( c\rse1 tak+ 9 ! nos+s4 ,suppose !re are fifte5 treads1 ea* be+ #aa in*es wide2 ?is w\ld make a run ( #ae #aa #afe in*es #ac feet #i in*es4 ,sometimes ?is di/ance is call$ ! go+ ( ! /air2 ?is1 h[ev]1 is an ,engli% t]m1 seldom us$ 9 ,am]ica1 & :5 us$1 ref]s z frequ5tly to ! l5g? ( ! s+le tread z x does to ! run ( ! /airway4 ,/r+-,bo>d4 ,?is is ! bo>d =m+ ! side ( ! /airway1 connect+ )1 & support+ ! ends ( ! /eps4 ,:]e ! /eps are h\s$1 or groov$ into ! bo>d1 x is kn[n by ! t]m h\s$ /r+2 & :5 x is cut ?r\gh = ! tread to re/ ^u1 & is mit]$ to ! ris]1 x is kn[n by ! t]m cut & mit]$ /r+4 ,! dim5sions ( ! lumb] g5]ally us$ = ! purpose 9 practical "w1 are #i in*es wid? & -in* ?ickness4 ,9 ! fir/-class /airways ! ?ickness is usually #a in*es1 = bo? front & wall /r+s4 ,illu/ration3 ,fig4 #b4 ,common ,me?od ( ,jo9+ ,ris]s & ,treads4 ,fig4 #b %[s ! mann] 9 :i* mo/ /air-build]s put _! ris]s & treads toge!r4 ,t & ,t %[ ! treads2 ,r & ,r1 ! ris]s2 ,s & ,s1 ! /r+2 ,o & ,o1 ! cove m\ld+s "u ! nos+s ,x & ,x4 ,b & ,b %[ ! blocks t hold ! treads & ris]s toge!r2 ^! blocks %\ld be f #d to #f in*es long1 & made ( v dry wood2 _! section may be f #a to #b in*es squ>e4 ,on a tread #c feet long1 ?ree ( ^! blocks %\ld be us$ at ab\t equal di/ances ap>t1 putt+ ! two outside ones ab\t #f in*es f ! /r+s4 ,!y are glu$ up tight into ! angle4 ,fir/ w>m ! blocks2 next coat two adjo9+ sides ) good1 /rong glue2 !n put !m 9 position1 & nail !m firmly to bo? tread & ris]4 ,x w be notic$ t ! ris] has a lip on ! upp] edge1 :i* ent]s into a groove 9 ! tread4 ,?is lip is g5]ally ab\t -in* long1 & may be -in* or -in* 9 ?ickness4 ,c>e mu/ be tak5 9 gett+ out ! ris]s1 t !y %all n be made too n>r[1 z all[ance mu/ be made = ! lip4 ,illu/ration3 ,fig4 #c4 ,v]tical ,section ( ,/air ,/eps4 ,illu/ration3 ,fig4 #d4 ,end ,section ( ,ris]4 ,illu/ration3 ,fig4 #e4 ,end ,section ( ,tread4 ,if ! ris] is a little too wide1 ?is w d no h>m1 z ! ov]-wid? may hang d[n bel[ ! tread2 b x mu/ be cut ! exact wid? :]e x re/s on ! /r+4 ,! treads mu/ be made ! exact wid? requir$1 be=e !y are groov$ or h ! nos+ work$ on ! out] edge4 ,! lip or tongue on ! ris] %\ld fit snugly 9 ! groove1 & %\ld bottom4 ,by foll[+ ^! la/ in/ructions & see+ t ! blocks are well glu$ 91 a good solid job w be ! result4 ,fig4 #c is a v]tical section ( /air /eps 9 :i* ! ris]s are %[n tongu$ into ! "u side ( ! tread1 z 9 ,fig4 #b1 & also ! tread tongu$ into ! face ( ! ris]4 ,?is la/ me?od is 9 g5]al use ?r\gh\t ! c\ntry4 ,! /air-build]1 :5 he has /eps ( ?is k9d to con/ruct1 ne$s to be v c>eful to secure ! exact wid? = tread & ris]1 includ+ ! tongue on ea*4 ,! usual me?od1 9 gett+ ! p>ts prep>$1 is to make a patt]n %[+ ! end section ( ea*4 ,! millman1 ) ^! patt]ns to guide him1 w be able to run ! mat]ial ?r\gh ! ma*9e )\t any dang] ( leav+ x ei!r too wide or too n>r[2 :ile1 if he is left to himself )\t patt]ns1 he is liable to make mi/akes4 ,^! patt]ns are illu/rat$ 9 ,figs4 #d & #e respectively1 &1 z %[n1 are m]ely end sections ( ris] & tread4 ,illu/ration3 ,fig4 #f4 ,side ,elevation ( ,f9i%$ ,/eps ) ,return ,nos+s & ,cove ,m\ld+4 ,illu/ration3 ,fig4 #g4 ,front ,elevation ( ,f9i%$ ,/eps4 ,fig4 #f is a side elevation ( ! /eps z f9i%$1 ) return nos+s & cove m\ld+ complete4 ,a front elevation ( ! f9i%$ /ep is %[n 9 ,fig4 #g1 ! nos+ & ris] return+ aga9/ ! base ( ! newel po/4 ,(t5 ! newel po/ projects pa/ ! ris]1 9 front2 & :5 su* is ! case1 ! ris] & nos+ are cut squ>e aga9/ ! base ( ! newel4 ,illu/ration3 ,fig4 #h4 ,portion ( a ,cut & ,mit]$ ,/r+1 ,%[+ ,me?od ( ,con/ruct+ ,/airs4 ,fig4 #h %[s a portion ( a cut & mit]$ /r+1 :i* w give an excell5t idea ( ! me?od ( con/ruction4 ,! lett] ,o %[s ! nos+1 ,f ! return nos+ ) a bracket t]m9at+ aga9/ x4 ,^! brackets are ab\t #e_/af-;in* ?ick1 & are plant$ 7nail$7 on ! /r+2 ! brackets mit] ) ! ends ( ! ris]s2 ! ends ( ! brackets :i* mit] ) ! ris]s1 are to be ! same height z ! ris]4 ,! l[] ends ( two balu/]s are %[n at ,g ,g2 & ! dovetails or mortises to receive ^! are %[n at ,e ,e4 ,g5]ally two balu/]s are plac$ on ea* tread1 z %[n2 b !re are sometimes in/ances 9 :i* ?ree are us$1 :ile 9 o!rs only "o balu/] is made use (4 ,an end portion ( a cut & mit]$ /r+ is %[n 9 ,fig4 #i1 ) "p ( ! /r+ tak5 away1 %[+ ! c>riage--a r\gh piece ( lumb] to :i* ! f9i%$ /r+ is nail$ or o!rwise fa/5$4 ,at ,c is %[n ! return nos+1 & ! mann] 9 :i* ! "w is f9i%$4 ,a r\gh bracket is sometimes nail$ on ! c>riage1 z %[n at ,d1 to support ! tread4 ,! balu/]s are %[n dovetail$ into ! ends ( ! treads1 & are ei!r glu$ or nail$ 9 place1 or bo?4 ,on ! l[] edge ( /r+1 at ,b1 is a return bead or m\ld+4 ,x w be notic$ t ! r\gh c>riage is cut 9 snugly aga9/ ! floor joi/4 ,illu/ration3 ,fig4 #i4 ,end ,portion ( ,cut & ,mit]$ ,/r+1 ) ,"p ,remov$ to ,%[ ,c>riage4 ,fig4 #aj is a plan ( ! portion ( a /airway %[n 9 ,fig4 #i4 ,"h ! position ( ! /r+1 bracket1 ris]1 & tread c be se54 ,at ! l[] /ep is %[n h[ to mit] ! ris] to ! /r+2 & at ! second /ep is %[n h[ to mit] x to ! bracket4 ,fig4 #aa %[s a quick me?od ( m>k+ ! ends ( ! treads = ! dovetails = balu/]s4 ,! templet ,a is made ( "s ?9 mat]ial1 pref]ably z9c or h>dwood4 ,! dovetails are outl9$ z %[n1 & ! int]v5+ portions ( ! mat]ial are cut away1 leav+ ! dovetail portions solid4 ,! templet is !n nail$ or screw$ to a gauge-block ,e1 :5 ! :ole is ready = use4 ,! me?od ( us+ is cle>ly indicat$ 9 ! illu/ration4 ,/r+s4 ,!re are two ma9 k9ds ( /air /r+s--wall /r+s & cut /r+s4 ,^! are divid$1 aga91 "u o!r names1 z h\s$ /r+s1 not*$ /r+s1 /av$ /r+s1 & r\gh /r+s4 ,wall /r+s are ! support]s ( ! ends ( ! treads & ris]s t are aga9/ ! wall2 ^! /r+s may be at bo? ends ( ! treads & ris]s1 or !y may be at "o end only4 ,!y may be h\s$ 7groov$7 or left solid4 ,:5 h\s$1 ! treads & ris]s are key$ into !m1 & glu$ & block$4 ,:5 left solid1 !y h a r\gh /r+ or c>riage spik$ or screw$ to !m1 to l5d additional support to ! ends ( ris]s & treads4 ,/airs made aft] ?is fa%ion are g5]ally ( a r\gh1 /rong k9d1 & are especially adapt$ = use 9 factories1 %ops1 & w>eh\ses1 :]e /r5g? & rigidity are ( m importance ?an m]e ext]nal appe>ance4 ,op5 /r+s are outside /r+s or supports1 & are cut to ! prop] angles = receiv+ ! ends ( ! treads & ris]s4 ,x is ov] a /r+ ( ?is sort t ! rail & balu/]s range2 x is also on su* a /r+ t all nos+s return2 h5ce1 9 "s localities1 an op5 /r+ is kn[n z a return /r+4 ,illu/ration3 ,fig4 #aj4 ,plan ( ,portion ( ,/air4 ,illu/ration3 ,fig4 #aa4 ,templet ,us$ to ,m>k ,dovetail ,cuts = ,balu/]s4 ,h\s$ /r+s are ^? t h grooves cut 9 !m to receive ! ends ( treads & ris]s4 ,z a g5]al ?+1 wall /r+s are h\s$4 ,! h\s+s are made f to in* deep1 & ! l9es at top ( tread & face ( ris] are made to correspond ) ! l9es ( ris] & tread :5 9 position4 ,! back l9es ( ! h\s+s are s locat$ t a tap] w$ge may be driv5 9 s z to =ce ! tread & ris] close to ! face %\ld]s1 ?us mak+ a tight jo9t4 ,r\gh /r+s are cut f undress$ plank1 & are us$ = /r5g!n+ ! /airs4 ,sometimes a comb9ation ( r\gh-cut /r+s is us$ = circul> or geometrical /airs1 &1 :5 fram$ toge!r1 =ms ! support or c>riage ( ! /airs4 ,/av$ /r+s are built up /r+s1 & are compos$ ( n>r[ pieces glu$1 nail$1 or bolt$ toge!r s z to =m a portion ( a cyl9d]4 ,^! are sometimes us$ = circul> /airs1 ?\gh 9 ord9>y practice ! circul> "p ( a /r+ is a "p ( ! ma9 /r+ b5t ar\nd a cyl9d] to give x ! "r curve4 ,not*$ /r+s are /r+s t c>ry only treads4 ,!y are g5]ally some:at n>r[] ?an ! treads1 & are h\s$ across _! entire wid?4 ,a sample ( ?is k9d ( /r+ is ! side ( a common /ep-ladd]4 ,/r+s ( ?is sort are us$ *iefly 9 cell>s1 or = /eps int5d$ = simil> purposes4 ,a ,,note4--,! measure = ! rise ( a /airway mu/ always be tak5 f ! top ( "o floor to ! top ( ! next4 ,sett+ ,out ,/airs4 ,9 sett+ out /airs1 ! fir/ ?+ to d is to asc]ta9 ! locations ( ! fir/ & la/ ris]s1 ) ! height ( ! /ory :]e9 ! /air is to be plac$4 ,^! po9ts %\ld be m>k$ out1 & ! di/ance betwe5 !m divid$ (f equally1 giv+ ! numb] ( /eps or treads requir$4 ,suppose we h betwe5 ^! two po9ts #ae feet1 or #ahj in*es4 ,if we make our treads #aj in*es wide1 we %all h #ah treads4 ,x mu/ be rememb]$ t ! numb] ( ris]s is always "o m ?an ! numb] ( treads1 s t 9 ! case be=e u !re w be #ai ris]s4 ,! height ( ! /ory is next to be exactly det]m9$1 be+ tak5 on a rod4 ,!n1 assum+ a height ( ris] suitable to ! place1 we asc]ta91 by division1 h[ (t5 ?is height ( ris] is conta9$ 9 ! height ( ! /ory2 ! quoti5t1 if !re is no rema9d]1 w be ! numb] ( ris]s 9 ! /ory4 ,%\ld !re be a rema9d] on ! fir/ division1 ! op]ation is rev]s$1 ! numb] ( in*es 9 ! height be+ made ! divid5d1 & ! be=e-f\nd quoti5t1 ! divisor4 ,! result+ quoti5t w indicate an am\nt to be add$ to ! =m] assum$ height ( ris] = a new trial height4 ,! rema9d] w n[ be less ?an 9 ! =m] division2 & if necess>y1 ! op]ation ( r$uction by division is repeat$1 until ! height ( ! ris] is obta9$ to ! ?irty-second "p ( an in*4 ,^! heights are !n set (f on ! /ory rod z exactly z possible4 ,! /ory rod is simply a dress$ or plan$ pole1 cut to a l5g? exactly correspond+ to ! height f ! top ( ! l[] floor to ! top ( ! next floor4 ,let u suppose ?is height to be #aa feet #a in*1 or #acc in*es4 ,n[1 we h #ai ris]s to place 9 ?is space1 to enable u to get up/airs2 !re=e1 if we divide #acc by #ai1 we get #g )\t any rema9d]4 ,sev5 in*es w !re=e be ! wid? or height ( ! ris]4 ,)\t figur+ ?is out1 ! workman may f9d ! exact wid? ( ! ris] by divid+ 8 /ory rod1 by means ( po9t]s1 into #ai equal p>ts1 any "o "p be+ ! prop] wid?4 ,x may be well1 at ?is po9t1 to rememb] t ! fir/ ris] mu/ always be n>r[] ?an ! o!rs1 because ! ?ickness ( ! fir/ tread mu/ be tak5 (f4 ,! wid? ( treads may also be f\nd )\t figur+1 by po9t+ (f ! run ( ! /airs into ! requir$ numb] ( p>ts2 ?\gh1 :]e ! /ud5t is qualifi$1 x is always bett] to obta9 ! wid?1 bo? ( treads & ( ris]s1 by ! simple ari?metical rules4 ,hav+ det]m9$ ! wid? ( treads & ris]s1 a pit*-bo>d %\ld be =m$1 %[+ ! angle ( incl9ation4 ,?is is done by cutt+ a piece ( ?9 bo>d or metal 9 ! %ape ( a "r-angl$ triangle1 ) its base exactly equal to ! run ( ! /ep1 & its p]p5dicul> equal to ! height ( ! ris]4 ,x is a g5]al maxim1 t ! great] ! bread? ( a /ep or tread1 ! less %\ld be ! height ( ! ris]2 &1 conv]sely1 ! less ! bread? ( a /ep1 ! great] %\ld be ! height ( ! ris]4 ,! prop] relative dim5sions ( treads & ris]s may be illu/rat$ graphically1 z 9 ,fig4 #ab4 ,illu/ration3 ,fig4 #ab4 ,graphic ,illu/ration ( ,proportional ,dim5sions ( ,treads & ,ris]s4 ,9 ! "r-angle triangle ,a ,b ,c1 make ,a ,b equal to #bd in*es1 & ,b ,c equal to #aa in*es--! /&>d proportion4 ,n[1 to f9d ! ris] correspond+ to a giv5 wid? ( tread1 f ,b1 set (f on ,a ,b ! wid? ( ! tread1 z ,b ,d2 & f ,d1 erect a p]p5dicul> ,d ,e1 meet+ ! hypot5use 9 ,e2 !n ,d ,e is ! height ( ! ris]2 & if we jo9 ,b & ,e1 ! angle ,d ,b ,e is ! angle ( incl9ation1 %[+ ! slope ( ! asc5t4 ,9 l mann]1 :]e ,b ,f is ! wid? ( ! tread1 ,f ,g is ! ris]1 & ,b ,g ! slope ( ! /air4 ,a wid? ( tread ,b ,h gives a ris] ( ! height ( ,h ,k2 & a wid? ( tread equal to ,b ,l gives a ris] equal to ,l ,m4 ,9 ! op9ion ( _m build]s1 h[ev]1 a bett] s*eme ( proportions = treads & ris]s is obta9$ by ! foll[+ me?od3 ,set d[n two sets ( numb]s1 ea* 9 ari?metical progression--! fir/ set %[+ wid?s ( tread1 increas+ by in*es2 ! o!r %[+ heights ( ris]1 decreas+ by half-in*es4 ,,treads1 ,,in*es ,,ris]s1 ,,in*es #e #i #f #h #g #h #h #g #i #g #aj #f #aa #f #ab #e #ac #e #ad #d #ae #d #af #c #ag #c #ah #b ,x w readily be se5 t ea* pair ( treads & ris]s ?us obta9$ is suitably proportion$ z to dim5sions4 ,x is seldom1 h[ev]1 t ! proportions ( treads & ris]s are entirely a matt] ( *oice4 ,! space allott$ to ! /airs usually det]m9es ?is proportion2 b ! above w be f\nd a useful /&>d1 to :i* x is desirable to approximate4 ,9 ! bett] class ( build+s1 ! numb] ( /eps is consid]$ 9 ! plan1 :i* x is ! bus9ess ( ! ,ar*itect to arrange2 & 9 su* cases1 ! height ( ! /ory rod is simply divid$ into ! numb] requir$4 ,pit*-,bo>d4 ,x w n[ be 9 ord] to describe a pit*-bo>d & ! mann] ( us+ x2 no /airs c be prop]ly built )\t ! use ( a pit*-bo>d 9 "s =m or o!r4 ,prop]ly speak+1 a pit*-bo>d1 z already expla9$1 is a ?9 piece ( mat]ial1 g5]ally p9e or %eet metal1 & is a "r-angl$ triangle 9 outl9e4 ,"o ( its sides is made ! exact height ( ! rise2 at "r angles ) ?is l9e ( rise1 ! exact wid? ( ! tread is measur$ (f2 & ! mat]ial is cut along ! hypot5use ( ! "r-angl$ triangle ?us =m$4 ,! simple/ me?od ( mak+ a pit*-bo>d is by us+ a /eel squ>e1 :i*1 ( c\rse1 e c>p5t] 9 ?is c\ntry is suppos$ to possess4 ,by means ( ?is invaluable tool1 also1 a /air /r+ c be laid out1 ! squ>e be+ appli$ to ! /r+ z %[n 9 ,fig4 #ac4 ,9 ! in/ance "h illu/rat$1 ! squ>e %[s #aj in*es = ! tread & #g in*es = ! rise4 ,illu/ration3 ,fig4 #ac4 ,/eel ,squ>e us$ z a ,pit*-,bo>d 9 ,lay+ ,out ,/air ,/r+4 ,to cut a pit*-bo>d1 aft] ! tread & rise h be5 det]m9$1 proce$ z foll[s3 ,take a piece ( ?91 cle> mat]ial1 & lay ! squ>e on ! face edge1 z %[n 9 ,fig4 #ac4 ,m>k out ! pit*-bo>d ) a %>p knife2 !n cut out ) a f9e saw1 & dress to ! knife m>ks2 nail a piece on ! l>ge/ edge ( ! pit*-bo>d = a gauge or f5ce1 & x is ready = use4 ,fig4 #ad %[s ! pit*-bo>d pure & simple2 x may be half an in* ?ick1 or1 if ( h>dwood1 may be f a qu>t]-in* to a half-in* ?ick4 ,fig4 #ae %[s ! pit*-bo>d aft] ! gauge or f5ce is nail$ on4 ,?is f5ce or gauge may be ab\t #a in*es wide & f to in* ?ick4 ,fig4 #af %[s a sectional view ( ! pit*-bo>d ) a f5ce nail$ on4 ,illu/ration3 ,fig4 #ad4 ,fig4 #ae4 ,fig4 #af4 ,%[+ ,h[ a ,pit*-,bo>d is ,made4 ,fig4 #ae %[s gauge fa/5$ to long edge2 ,fig4 #af is a sectional elevation ( complet$ bo>d4 ,9 ,fig4 #ag ! mann] ( apply+ ! pit*-bo>d is %[n4 ,r ,r ,r is ! /r+1 & ! l9e ,a %[s ! jo9t$ or /raight edge ( ! /r+4 ,! pit*-bo>d ,p is %[n 9 position1 ! l9e #h repres5ts ! /ep or tread1 & ! l9e #g %[s ! l9e ( ! ris]4 ,^! two l9es are ( c\rse at "r angles1 or1 z ! c>p5t] w\ld say2 !y are squ>e4 ,?is /r+ %[s f\r complete cuts1 & "p ( a fif? cut = treads1 & five complete cuts = ris]s4 ,! bottom ( ! /r+ at ,w is cut (f at ! l9e ( ! floor on :i* x is suppos$ to re/4 ,! l9e ,c is ! l9e ( ! fir/ ris]4 ,?is ris] is cut l[] ?an any ( ! o!r ris]s1 because1 z above expla9$1 ! ?ickness ( ! fir/ tread is always tak5 (f x2 ?us1 if ! tread is #a in*es ?ick1 ! ris] 9 ?is case w\ld only require to be #f in*es wide1 z #g-a #f4 ,! /r+ mu/ be cut s t ! l9e at ,w w be only #f in*es f ! l9e at #h1 & ^! two l9es mu/ be p>allel4 ,! fir/ ris] & tread hav+ be5 satisfactorily dealt )1 ! re/ c easily be m>k$ (f by simply slid+ ! pit*-bo>d along ! l9e ,a until ! out] end ( ! l9e #h on ! pit*-bo>d /rikes ! out] end ( ! l9e #g on ! /r+1 :5 ano!r tread & ano!r ris] are to be m>k$ (f4 ,! rema9+ ris]s & treads are m>k$ (f 9 ! same mann]4 ,illu/ration3 ,fig4 #ag4 ,%[+ ,me?od ( ,us+ ,pit*-,bo>d4 ,sometimes !re may be a little difficulty at ! top ( ! /airs1 9 fitt+ ! /r+ to ! trimm] or joi/s2 b1 z x is necess>y fir/ to become exp]t ) ! pit*-bo>d1 ! me?od ( trimm+ ! well or atta*+ ! cyl9d] to ! /r+ w be left until o!r matt]s h be5 discuss$4 ,fig4 #ah %[s a portion ( ! /airs 9 position4 ,s & ,s %[ ! /r+s1 :i* 9 ?is case are cut squ>e2 t is1 ! "p ( ! /r+ to :i* ! ris] is jo9$ is cut squ>e across1 & ! butt or end wood ( ! ris] is se54 ,9 ?is case1 also1 ! end ( ! tread is cut squ>e (f1 & flu% ) ! /r+ & ris]4 ,bo? /r+s 9 ?is in/ance are op5 /r+s4 ,usually1 9 /airs ( ?is k9d1 ! ends ( ! treads are r\nd$ (f simil>ly to ! front ( ! tread1 & ! ends project ov] ! /r+s ! same di/ance t ! front edge projects ov] ! ris]4 ,if a m\ld+ or cove is us$ "u ! nos+ 9 front1 x %\ld be c>ri$ r\nd on ! /r+ to ! back edge ( ! tread & cut (f squ>e1 = 9 ?is case ! back edge ( ! tread w be squ>e4 ,a ris] is %[n at ,r1 & x w be notic$ t x runs d[n beh9d ! tread on ! back edge1 & is ei!r nail$ or screw$ to ! tread4 ,?is is ! ,am]ican practice1 ?\gh 9 ,engl& ! ris] usually re/s on ! tread1 :i* ext5ds cle> back to /r+ z %[n at ! top tread 9 ! diagram4 ,x is mu* bett]1 h[ev]1 = g5]al purposes1 t ! ris] g beh9d ! tread1 z ?is t5ds to make ! :ole /airway mu* /rong]4 ,h\s$ /r+s are ^? :i* c>ry ! treads & ris]s )\t _! ends be+ se54 ,9 an op5 /air1 ! wall /r+ only is h\s$1 ! o!r ends ( ! treads & ris]s re/+ on a cut /r+1 & ! nos+s & m\ld+s be+ return$ z be=e describ$4 ,illu/ration3 ,fig4 #ah4 ,portion ( ,/air 9 ,position4 ,illu/ration3 ,fig4 #ai4 ,%[+ ,me?od ( ,h\s+ ,treads & ,ris]s4 ,! mann] ( h\s+ is %[n 9 ,fig4 #ai1 9 :i* ! treads ,t ,t & ! ris]s ,r ,r are %[n 9 position1 secur$ 9 place respectively by means ( w$ges ,x ,x & ,f ,f1 :i* %\ld be well cov]$ ) good glue be=e ins]tion 9 ! groove4 ,! h\s+s are g5]ally made f to in* deep1 space = ! w$ge be+ cut to suit4 ,9 "s clos$ /airs 9 :i* !re is a h\s$ /r+ betwe5 ! newels1 ! /r+ is d\ble-t5on$ into ! %anks ( bo? newels1 z %[n 9 ,fig4 #bj4 ,! /r+ 9 ?is example is made #ab in*es wide1 :i* is a v good wid? = a /r+ ( ?is k9d2 b ! ?ickness %\ld nev] be less ?an #a in*es4 ,! upp] newel is made ab\t #e feet #d in*es long f drop to top ( cap4 ,^! /r+s are g5]ally capp$ ) a subrail ( "s k9d1 on :i* ! balu/]1 if any1 is cut-mit]$ 94 ,g5]ally a groove1 ! wid? ( ! squ>e ( ! balu/]s1 is work$ on ! top ( ! subrail1 & ! balu/]s are work$ out to fit into ?is groove2 !n pieces ( ?is mat]ial1 made ! wid? ( ! groove & a little ?ick] ?an ! groove is deep1 are cut s z to fit 9 snugly betwe5 ! ends ( ! balu/]s re/+ 9 ! groove4 ,?is makes a solid job2 & ! pieces betwe5 ! balu/]s may be made ( any %ape on top1 ei!r bevel$1 r\nd$1 or m\ld$1 9 :i* case mu* is add$ to ! appe>ance ( ! /airs4 ,illu/ration3 ,fig4 #bj4 ,%[+ ,me?od ( ,connect+ ,h\s$ ,/r+ to ,newels4 ,illu/ration3 ,fig4 #ba4 ,me?od ( ,connect+ ,rail & ,/r+ to ,bottom ,newel4 ,fig4 #ba exhibits ! me?od ( atta*+ ! rail & /r+ to ! bottom newel4 ,! dott$ l9es indicate ! =m ( ! t5ons cut to fit ! mortises made 9 ! newel to receive !m4 ,fig4 #bb %[s h[ ! /r+ fits aga9/ ! newel at ! top2 also ! trimm] ,e1 to :i* ! newel po/ is fa/5$4 ,! /r+ 9 ?is case is t5on$ into ! upp] newel po/ ! same way z into ! l[] "o4 ,! op5 /r+ %[n 9 ,fig4 #bc is a portion ( a f9i%$ /r+1 %[+ nos+s & cove return$ & f9i%+ aga9/ ! face ( ! /r+4 ,along ! l[] edge ( ! /r+ is %[n a bead or m\ld+1 :]e ! pla/] is f9i%$4 ,a portion ( a /air ( ! bett] class is %[n 9 ,fig4 #bd4 ,?is is an op51 bracket$ /r+1 ) return$ nos+s & coves & scroll brackets4 ,^! brackets are made ab\t in* ?ick1 & may be 9 any desirable patt]n4 ,! end next ! ris] %\ld be mit]$ to suit2 ?is w require ! ris] to be in* long] ?an ! face ( ! /r+4 ,! upp] "p ( ! bracket %\ld run "u ! cove m\ld+2 & ! tread %\ld project ov] ! /r+ ! full in*1 s z to cov] ! bracket & make ! face ev5 = ! nos+ & ! cove m\ld+ to fit snugly aga9/ ! end ( ! tread & ! face ( ! bracket4 ,great c>e mu/ be tak5 ab\t ?is po9t1 or endless tr\ble w foll[4 ,9 a bracket$ /air ( ?is k9d1 c>e mu/ be tak5 9 plac+ ! newel po/s1 & provision mu/ be made = ! extra in* due to ! bracket4 ,! newel po/ mu/ be set out f ! /r+ in*1 & x w !n align ) ! balu/]4 ,illu/ration3 ,fig4 #bb4 ,connections ( ,/r+ & ,trimm] at ,upp] ,newel ,po/4 ,illu/ration3 ,fig4 #bc4 ,portion ( ,f9i%$ ,/r+1 ,%[+ ,return$ ,nos+s & ,coves1 also ,bead ,m\ld+4 ,illu/ration3 ,fig4 #bd4 ,portion ( ,op51 ,bracket$ ,/r+ ,/air1 ) ,return$ ,nos+s & ,coves1 ,scroll ,brackets1 & ,bead ,m\ld+4 ,we h n[ describ$ sev]al me?ods ( deal+ ) /r+s2 b !re are /ill a few o!r po9ts connect$ ) ^! memb]s1 bo? h\s$ & op51 t x w be necess>y to expla92 be=e ! "y workman c proce$ to build a fair flight ( /airs4 ,! connection ( ! wall /r+ to ! l[] & upp] floors1 & ! mann] ( affix+ ! out] or cut /r+ to ! upp] joi/ & to ! newel1 are matt]s t mu/ n be ov]look$4 ,x is ! int5tion to %[ h[ ^! ?+s are accompli%$1 & h[ ! /airs are made /rong by ! addition ( r\gh /r+s or be>+ c>riages4 ,illu/ration3 ,fig4 #be4 ,side ,elevation ( ,"p ( ,/air ) ,op51 ,cut & ,mit]$ ,/r+4 ,illu/ration3 ,fig4 #bf4 ,plan ( ,"p ( ,/air ,%[n 9 ,fig4 #be4 ,fig4 #be gives a side view ( "p ( a /air ( ! bett] class1 ) "o op51 cut & mit]$ /r+4 ,9 ,fig4 #bf1 a plan ( ?is same /airway1 ,w ,s %[s ! wall /r+2 ,r ,s1 ! r\gh /r+1 plac$ !re to give ! /ructure /r5g?2 & ,o ,s1 ! out] or cut & mit]$ /r+4 ,at ,a ,a ! ends ( ! ris]s are %[n1 & x w be notic$ t !y are mit]$ aga9/ a v]tical or ris] l9e ( ! /r+1 ?us prev5t+ ! end ( ! ris] f be+ se54 ,! o!r end ( ! ris] is 9 ! h\s+ 9 ! wall /r+4 ,! out] end ( ! tread is also mit]$ at ! nos+1 & a piece ( mat]ial made or work$ l ! nos+ is mit]$ aga9/ or return$ at ! end ( ! tread4 ,! end ( ?is return$ piece is aga9 return$ on itself back to ! /r+1 z %[n at ,n 9 ,fig4 #be4 ,! m\ld+1 :i* is -in* cove 9 ?is case1 is also return$ on itself back to ! /r+4 ,! mortises %[n at ,b ,b ,b ,b 7,fig4 #bf71 are = ! balu/]s4 ,x is always ! prop] ?+ to saw ! ends ( ! treads ready = ! balu/]s be=e ! treads are atta*$ to ! /r+2 !n1 :5 ! "t arrives to put up ! rail1 ! back ends ( ! mortises c be cut out1 :5 ! treads w be ready to receive ! balu/]s4 ,! mortises are dovetail$1 &1 ( c\rse1 ! t5ons on ! balu/]s mu/ be made to suit4 ,! treads are f9i%$ on ! b5*2 & ! return nos+s are fitt$ to !m & tack$ on1 s t !y may be tak5 (f to ins]t ! balu/]s :5 ! rail is be+ put 9 position4 ,fig4 #bg %[s ! mann] 9 :i* a wall /r+ is f9i%$ at ! foot ( ! /airs4 ,s %[s ! /r+1 ) m\ld+ wr\ght on ! upp] edge4 ,?is m\ld+ may be a simple ogee1 or may consi/ ( a numb] ( memb]s2 or x may be only a bead2 or1 aga91 ! edge ( ! /r+ may be left q pla92 ?is w be regulat$ 9 great measure by ! /yle ( f9i% 9 ! hall or o!r "p ( ! h\se 9 :i* ! /airs are plac$4 ,b %[s a portion ( a basebo>d1 ! top edge ( :i* has ! same f9i% z ! top edge ( ! /r+4 ,b & ,a toge!r %[ ! junction ( ! /r+ & base4 ,f ,f %[ blocks glu$ 9 ! angles ( ! /eps to make !m firm & solid4 ,illu/ration3 ,fig4 #bg4 ,%[+ ,h[ ,wall ,/r+ is ,f9i%$ at ,foot ( ,/air4 ,illu/ration3 ,fig4 #bh4 ,%[+ ,h[ ,wall ,/r+ is ,f9i%$ at ,top ( ,/air4 ,fig4 #bh %[s ! mann] 9 :i* ! wall /r+ ,s is f9i%$ at ! top ( ! /airs4 ,x w be notic$ t ! m\ld+ is work$ r\nd ! ease-(f at ,a to suit ! wid? ( ! base at ,b4 ,! /r+ is cut to fit ! floor & to butt aga9/ ! joi/4 ,! pla/] l9e "u ! /airs & on ! ceil+1 is also %[n4 ,illu/ration3 ,fig4 #bi4 ,%[+ ,h[ a ,cut or ,op5 ,/r+ is ,f9i%$ at ,foot ( ,/air4 ,fig4 #bi %[s a cut or op5 /r+ at ! foot ( a /airway1 & ! mann] ( deal+ ) x at its junction ) ! newel po/ ,k4 ,! po9t ( ! /r+ %\ld be mortis$ into ! newel #b in*es1 #c in*es1 or #d in*es1 z %[n by ! dott$ l9es2 & ! mortise 9 ! newel %\ld be cut ne> ! c5t]1 s t ! c5t] ( ! balu/] w be directly opposite ! c5tral l9e ( ! newel po/4 ,! prop] way to manage ?is1 is to m>k ! c5tral l9e ( ! balu/] on ! tread1 & !n make ?is l9e correspond ) ! c5tral l9e ( ! newel po/4 ,by c>eful att5tion to ?is po9t1 mu* tr\ble w be avoid$ :]e a turn$ cap is us$ to receive ! l[] "p ( ! rail4 ,! l[] ris] 9 a /air ( ?is k9d w be some:at %ort] ?an ! ones above x1 z x mu/ be cut to fit betwe5 ! newel & ! wall /r+4 ,a portion ( ! tread1 z well z ( ! ris]1 w also butt aga9/ ! newel1 z %[n at ,w4 ,if !re is no sp&rel or wall "u ! op5 /r+1 x may run d[n to ! floor z %[n by ! dott$ l9e at ,o4 ,! piece ,o is glu$ to ! /r+1 & ! m\ld+ is work$ on ! curve4 ,if !re is a wall "u ! /r+ ,s1 !n ! base ,b1 %[n by ! dott$ l9es1 w f9i% aga9/ ! /r+1 & x %\ld h a m\ld+ on its upp] edge1 ! same z t on ! l[] edge ( ! /r+1 if any1 ?is m\ld+ be+ mit]$ into ! "o on ! /r+4 ,:5 !re is a base1 ! piece ,o is ( c\rse disp5s$ )4 ,! squ>e ( ! newel %\ld run d[n by ! side ( a joi/ z %[n1 & %\ld be firmly secur$ to ! joi/ ei!r by spik+ or by "s o!r suitable device4 ,if ! joi/ runs ! o!r way1 try to get ! newel po/ aga9/ x1 if possible1 ei!r by furr+ out ! joi/ or by cutt+ a portion (f ! ?ickness ( ! newel4 ,! solidity ( a /air & ! firmness ( ! rail1 dep5d v mu* ^u ! rigidity ( ! newel po/4 ,! above sugge/ions are applicable :]e great /r5g? is requir$1 z 9 public build+s4 ,9 ord9>y "w1 ! usual me?od is to let ! newel re/ on ! floor4 ,illu/ration3 ,fig4 #cj4 ,%[+ ,h[ a ,cut or ,op5 ,/r+ is ,f9i%$ at ,top ( ,/air4 ,fig4 #cj %[s h[ ! cut /r+ is f9i%$ at ! top ( ! /airs4 ,?is illu/ration requires no explanation aft] ! in/ructions already giv54 ,?us f>1 /airs hav+ a newel only at ! bottom h be5 dealt )4 ,!re are1 h[ev]1 _m modifications ( /raight & return /airs :i* h f two to f\r or six newels4 ,9 su* cases1 ! me?ods ( treat+ /r+s at _! f9i%+ po9ts mu/ necess>ily be some:at diff]5t f ^? describ$2 b ! g5]al pr9ciples1 z %[n & expla9$1 w /ill hold good4 ,well-,hole4 ,be=e proce$+ to describe & illu/rate newel$ /airs1 x w be prop] to say some?+ ab\t ! well-hole1 or ! op5+ ?r\gh ! floors1 ?r\gh :i* ! travel] on ! /airs asc5ds or desc5ds f "o floor to ano!r4 ,fig4 #ca %[s a well-hole1 & ! mann] ( trimm+ x4 ,9 ?is in/ance ! /airs are plac$ aga9/ ! wall2 b ?is is n necess>y 9 all cases1 z ! well-hole may be plac$ 9 any "p ( ! build+4 ,! arrangem5t ( ! trimm+ v>ies accord+ z ! joi/s are at "r angles to1 or are p>allel to1 ! wall aga9/ :i* ! /airs are built4 ,9 ! =m] case 7,fig4 #ca1 ,a7 ! joi/s are cut %ort & tusk-t5on$ into ! heavy trimm] ,t ,t1 z %[n 9 ! cut4 ,?is trimm] is aga9 tusk-t5on$ into two heavy joi/s ,t ,j & ,t ,j1 :i* =m ! ends ( ! well-hole4 ,^! heavy joi/s are call$ trimm+ joi/s2 &1 z !y h to c>ry a mu* heavi] load ?an o!r joi/s on ! same floor1 !y are made mu* heavi]4 ,sometimes two or ?ree joi/s are plac$ toge!r1 side by side1 be+ bolt$ or spik$ toge!r to give !m ! desir$ unity & /r5g?4 ,9 con/ructions requir+ great /r5g?1 ! tail & head] joi/s ( a well-hole are susp5d$ on iron brackets4 ,if ! op5+ runs p>allel ) ! joi/s 7,fig4 #ca1 ,b71 ! timb] =m+ ! side ( ! well-hole %\ld be left a little heavi] ?an ! o!r joi/s1 z x w h to c>ry %ort trimm]s 7,t ,j & ,t ,j7 & ! joi/s runn+ into !m4 ,! me?od "h %[n is m p>ticul>ly adapt$ to brick build+s1 b !re is no reason :y ! same sy/em may n be appli$ to frame build+s4 ,usually 9 *eap1 frame build+s1 ! trimm]s ,t ,t are spik$ aga9/ ! ends ( ! joi/s1 & ! ends ( ! trimm]s are support$ by be+ spik$ to ! trimm+ joi/s ,t ,j1 ,t ,j4 ,?is is n v workmanlike or v secure1 & %\ld n be done1 z x is n ne>ly s /rong or durable z ! old me?od ( fram+ ! joi/s & trimm]s toge!r4 ,fig4 #cb %[s a /air ) ?ree newels & a plat=m4 ,9 ?is example1 ! fir/ tread 7,no4 #a7 /&s =w>d ( ! newel po/ two-?irds ( its wid?4 ,?is is n necess>y 9 e case1 b x is sometimes done to suit conditions 9 ! hallway4 ,! second newel is plac$ at ! twelf? ris]1 & supports ! upp] end ( ! fir/ cut /r+ & ! l[] end ( ! second cut /r+4 ,! plat=m 7#ab7 is support$ by joi/s :i* are fram$ into ! wall & are fa/5$ aga9/ a trimm] runn+ f ! wall to ! newel along ! l9e #ab4 ,?is is ! case only :5 ! second newel runs d[n to ! floor4 ,illu/ration3 ,fig4 #ca4 ,%[+ ,ways ( ,trimm+ ,well-,hole :5 ,joi/s ,run 9 ,diff]5t ,directions4 ,if ! second newel does n run to ! floor1 ! framework support+ ! plat=m w ne$ to be built on /udd+4 ,! ?ird newel /&s at ! top ( ! /airs1 & is fa/5$ to ! joi/s ( ! second floor1 or to ! trimm]1 some:at aft] ! mann] ( fa/5+ %[n 9 ,fig4 #bi4 ,9 ?is example1 ! /airs h #af ris]s & #ae treads1 ! plat=m or l&+ 7#ab7 mak+ "o tread4 ,! figure #af %[s ! floor 9 ! second /ory4 ,?is /yle ( /air w require a well-hole 9 %ape ab\t z %[n 9 ! plan2 & :]e /r5g? is requir$1 ! newel at ! top %\ld run f floor to floor1 & act z a support to ! joi/s & trimm]s on :i* ! second floor is laid4 ,p]haps ! be/ way = a beg9n] to g ab\t build+ a /airway ( ?is type1 w be to lay out ! "w on ! l[] floor 9 ! exact place :]e ! /airs are to be erect$1 mak+ ev]y?+ full size4 ,!re w be no difficulty 9 do+ ?is2 & if ! positions ( ! fir/ ris] & ! ?ree newel po/s are accurately def9$1 ! build+ ( ! /airs w be an easy matt]4 ,plumb l9es c be rais$ f ! l9es on ! floor1 & ! positions ( ! plat=m & ea* ris] ?us easily det]m9$4 ,n only is x be/ to l9e out on ! floor all /airs hav+ m ?an "o newel2 b 9 con/ruct+ any k9d ( /air x w p]haps be safe/ = a beg9n] to lay out 9 exact position on ! floor ! po9ts ov] :i* ! treads & ris]s w /&4 ,by adopt+ ?is rule1 & see+ t ! /r+s1 ris]s1 & treads correspond exactly ) ! l9es on ! floor1 _m cases ( annoyance w be avoid$4 ,_m exp]t /air-build]s1 9 fact1 adopt ?is me?od 9 _! practice1 lay+ out all /airs on ! floor1 includ+ ev5 ! c>riage /r+s1 & !y cut out all ! mat]ial f ! l9es obta9$ on ! floor4 ,by foll[+ ?is me?od1 "o c see exactly ! requirem5ts 9 ea* p>ticul> case1 & c rectify any error )\t de/roy+ valuable mat]ial4 ,illu/ration3 ,fig4 #cb4 ,/air ) ,?ree ,newels & a ,plat=m4 ,lay+ ,out4 ,9 ord] to af=d ! /ud5t a cle> idea ( :at is meant by lay+ out on ! floor1 an example ( a simple close-/r+ /air is giv54 ,9 ,fig4 #cc1 ! lett] ,f %[s ! floor l9e2 ,l is ! l&+ or plat=m2 & ,w is ! wall l9e4 ,! /air is to be #d feet wide ov] /r+s2 ! l&+1 #d feet wide2 ! height f floor to l&+1 #g feet2 & ! run f />t to f9i% ( ! /air1 #h feet #h in*es4 ,! fir/ ?+ to det]m9e is ! dim5sions ( ! treads & ris]s4 ,! wid] ! tread1 ! l[] mu/ be ! ris]1 z /at$ be=e4 ,no def9ite dim5sions = treads & ris]s c be giv51 z ! /eps h to be arrang$ to meet ! v>i\s difficulties t may occur 9 ! work+ out ( ! con/ruction2 b a common rule is ?is3 ,make ! wid? ( ! tread1 plus twice ! rise1 equal to #bd in*es4 ,?is w give1 = an #h-;in* tread1 an #h-;in* rise2 = a #i-;in* tread1 a #g-;in* rise2 = a #aj-;in* tread1 a #g-;in* rise1 & s on4 ,hav+ ! height 7#g feet7 & ! run ( ! flight 7#h feet #h-;in*es71 take a rod ab\t "o in* squ>e1 & m>k on x ! height f floor to l&+ 7#g feet71 & ! l5g? ( ! go+ or run ( ! flight 7#h feet #h in*es74 ,consid] n[ :at are ! dim5sions :i* c be giv5 to ! treads & ris]s1 rememb]+ t !re w be "o m ris] ?an ! numb] ( treads4 ,m>k (f on ! rod ! l&+1 =m+ ! la/ tread4 ,if twelve ris]s are desir$1 divide ! height 7namely1 #g feet7 by #ab1 :i* gives #g in*es z ! rise ( ea* /ep4 ,!n divide ! run 7namely1 #h feet #h in*es7 by #aa1 & ! wid? ( ! tread is f\nd to be #i in*es4 ,great c>e mu/ be tak5 9 mak+ ! pit*-bo>d = m>k+ (f ! treads & ris]s on ! /r+4 ,! pit*-bo>d may be made f dry h>dwood ab\t -in* ?ick4 ,"o end & "o side mu/ be p]fectly squ>e to ea* o!r2 on ! "o1 ! wid? ( ! tread is set (f1 & on ! o!r ! height ( ! ris]4 ,connect ! two po9ts ?us obta9$1 & saw ! wood on ?is l9e4 ,! addition ( a gauge-piece along ! longe/ side ( ! triangul> piece1 completes ! pit*-bo>d1 z 0 illu/rat$ 9 ,fig4 #ae4 ,! l5g? ( ! wall & out] /r+ c be asc]ta9$ by means ( ! pit*-bo>d4 ,"o side & "o edge ( ! wall /r+ mu/ be squ>$2 b ! out] /r+ mu/ be tru$ all r\nd4 ,on ! /r+s1 m>k ! positions ( ! treads & ris]s by us+ ! pit*-bo>d z already expla9$ 7,fig4 #ag74 ,/r+s are usually made #aa in*es wide1 b may be made #ab in*es wide if necess>y = /r5g?4 ,illu/ration3 ,fig4 #cc4 ,me?od ( ,lay+ ,out a ,simple1 ,close-,/r+ ,/air4 ,aft] ! wid?s ( ris]s & treads h be5 det]m9$1 & ! /r+ is ready to lay out1 apply ! pit*-bo>d1 m>k+ ! fir/ ris] ab\t #i in*es f ! end2 & numb] ea* /ep 9 succession4 ,! ?ickness ( ! treads & ris]s c be drawn by us+ ?9 /rips ( h>dwood made ! wid? ( ! h\s+ requir$4 ,n[ all[ = ! w$ges "u ! treads & beh9d ! ris]s1 & ?us f9d ! exact wid? ( ! h\s+1 :i* %\ld be ab\t -in* deep2 ! treads & ris]s w require to be made #a in*es long] ?an %[n 9 ! plan1 to all[ = ! h\s+s at bo? ends4 ,be=e putt+ ! /air toge!r1 be sure t x c be tak5 into ! h\se & put 9 position )\t tr\ble4 ,if = any reason x _c be put 9 aft] be+ put toge!r1 !n ! p>ts mu/ be assembl$1 w$g$1 & glu$ up at ! spot4 ,x is ess5tial 9 lay+ out a plan on ! floor1 t ! exact positions ( ! fir/ & la/ ris]s be asc]ta9$1 & ! height ( ! /ory :]e9 ! /air is to be plac$4 ,!n draw a plan ( ! hall or o!r room 9 :i* ! /airs w be locat$1 includ+ surr\nd+ or adjo9+ p>ts ( ! room to ! ext5t ( t5 or twelve feet f ! place assign$ = ! foot ( ! /air4 ,all ! doorways1 bran*+ passages1 or w9d[s :i* c possibly come 9 contact ) ! /air f its comm5cem5t to its expect$ t]m9ation or l&+1 mu/ be not$4 ,! sket* mu/ necess>ily include a portion ( ! entrance hall 9 "o "p1 & ( ! lobby or l&+ 9 ano!r1 & on x mu/ be laid out all ! l9es ( ! /air f ! fir/ to ! la/ ris]4 ,! height ( ! /ory mu/ next be exactly det]m9$ & tak5 on ! rod2 !n1 assum+ a height ( ris]s suitable to ! place1 a trial is made by division 9 ! mann] previ\sly expla9$1 to asc]ta9 h[ (t5 ?is height is conta9$ 9 ! height ( ! /ory4 ,! quoti5t1 if !re is no rema9d]1 w be ! numb] ( ris]s requir$4 ,%\ld !re be a rema9d] on ! fir/ division1 ! op]ation is rev]s$1 ! numb] ( in*es 9 ! height be+ made ! divid5d & ! be=e-f\nd quoti5t ! divisor2 & ! op]ation ( r$uction by division is c>ri$ on till ! height ( ! ris] is obta9$ to ! ?irty-second "p ( an in*4 ,^! heights are !n set (f z exactly z possible on ! /ory rod1 z %[n 9 ,fig4 #cc4 ,! next op]ation is to %[ ! ris]s on ! sket*4 ,?is ! workman w f9d no tr\ble 9 arrang+1 & no arbitr>y rule c be giv54 ,a "p ( ! =ego+ may appe> to be repetition2 b x is n1 = x mu/ be rememb]$ t sc>cely any two flights ( /airs are alike 9 run1 rise1 or pit*1 & any dep>ture 9 any "o dim5sion f ^! conditions leads to a new s]ies ( dim5sions t mu/ be dealt ) indep5d5tly4 ,! pr9ciple laid d[n1 h[ev]1 applies to all /raight flights ( /airs2 & ! /ud5t :o has foll[$ closely & reta9$ ! pi? ( :at has be5 said1 w1 if he has a fair k ( ! use ( tools1 be fairly equipp$ = lay+ out & con/ruct+ a pla91 /raight /air ) a /raight rail4 ,pla9 /airs may h "o plat=m1 or sev]al2 & !y may turn to ! "r or to ! left1 or1 ris+ f a plat=m or l&+1 may run 9 an opposite direction f _! />t+ po9t4 ,:5 two flights are necess>y = a /ory1 x is desirable t ea* flight %\ld consi/ ( ! same numb] ( /eps2 b ?is1 ( c\rse1 w dep5d on ! =m ( ! /aircase1 ! situation & height ( doors1 & o!r ob/acles to be pass$ "u or ov]1 z ! case may be4 ,9 ,fig4 #cb1 a /air is %[n ) a s+le plat=m or l&+ & ?ree newels4 ,! fir/ "p ( ?is /air corresponds1 9 numb] ( ris]s1 ) ! /air %[n 9 ,fig4 #cc2 ! second newel runs d[n to ! floor1 & helps to su/a9 ! l&+4 ,?is newel may simply be a #d by #d-;in* po/1 or ! :ole space may be inclos$ ) ! sp&rel ( ! /air4 ,! second flight />ts f ! plat=m j z ! fir/ flight />ts f ! l[] floor1 & bo? flights may be atta*$ to ! newels 9 ! mann] %[n 9 ,fig4 #bi4 ,! bottom tread 9 ,fig4 #cb is r\nd$ (f aga9/ ! squ>e ( ! newel po/2 b ?is _c well be if ! /airs />t f ! l&+1 z ! tread w\ld project too f> onto ! plat=m4 ,sometimes1 9 high-class /airs1 provision is made = ! fir/ tread to project well onto ! l&+4 ,if !re are m plat=ms ?an "o1 ! pr9ciples ( con/ruction w be ! same2 s t :5ev] ! /ud5t grasps ! full conditions gov]n+ ! con/ruction ( a s+le-plat=m /air1 he w be prep>$ to lay out & con/ruct ! body ( any /air hav+ "o or m l&+s4 ,! me?od ( lay+ out1 mak+1 & sett+ up a h&-rail w be describ$ lat]4 ,/airs =m$ ) treads ea* ( equal wid? at bo? ends1 are nam$ /raight flights2 b /airs hav+ treads wid] at "o end ?an ! o!r are kn[n by v>i\s names1 z w9d+ /airs1 dog-legg$ /airs1 circul> /airs1 or elliptical /airs4 ,a tread ) p>allel sides1 hav+ ! same wid? at ea* end1 is call$ a fly]2 :ile "o hav+ "o wide end & "o n>r[1 is call$ a w9d]4 ,^! t]ms w (t5 be made use ( 9 :at foll[s4 ,! elevation & plan ( ! /air %[n 9 ,fig4 #cd may be call$ a dog-legg$ /air ) ?ree w9d]s & six fly]s4 ,! fly]s1 h[ev]1 may be ext5d$ to any numb]4 ,! h\s$ /r+s to receive ! w9d]s are %[n4 ,^! /r+s %[ exactly ! mann] ( con/ruction4 ,! %ort] /r+1 9 ! corn] f #a to #d1 :i* is %[n 9 ! plan to conta9 ! h\s+ ( ! fir/ w9d] & half ( ! second1 is put up fir/1 ! treads be+ level$ by aid ( a _s level2 & ! long] upp] /r+ is put 9 place aft]w>ds1 butt+ snugly aga9/ ! l[] /r+ 9 ! corn]4 ,x is !n fa/5$ firmly to ! wall4 ,! w9d]s are cut snugly ar\nd ! newel po/1 & well nail$4 ,_! ris]s w /& "o above ano!r on ! po/2 & ! /raight /r+ above ! w9d]s w ent] ! po/ on a l9e ) ! top edge ( ! upp]mo/ w9d]4 ,illu/ration3 ,fig4 #cd4 ,elevation & ,plan ( ,dog-,legg$ ,/air ) ,?ree ,w9d]s & ,six ,fly]s4 ,plat=m /airs are (t5 con/ruct$ s t "o flight w run 9 a direction opposite to t ( ! o!r flight1 z %[n 9 ,fig4 #ce4 ,9 cases ( ?is k9d1 ! l&+ or plat=m requires to h a l5g? m ?an d\ble t ( ! treads1 9 ord] t bo? flights may h ! same wid?4 ,sometimes1 h[ev]1 & = v>i\s reasons1 ! upp] flight is made a little n>r[] ?an ! l[]2 b ?is exp$i5t %\ld be avoid$ :5ev] possible1 z its adoption unbalances ! /airs4 ,9 ! example be=e u1 elev5 treads1 n includ+ ! l&+1 run 9 "o direction2 :ile f\r treads1 includ+ ! l&+1 run 9 ! opposite direction2 or1 z workm5 put x1 ! /air 8returns on itself40 ,! elevation %[n 9 ,fig4 #cf illu/rates ! mann] 9 :i* ! "w is execut$4 ,! v>i\s p>ts are %[n z foll[s3 ,illu/ration3 ,fig4 #ce4 ,plan ( ,plat=m ,/air ,return+ on ,itself4 ,illu/ration3 ,fig4 #cg is a section ( ! top l&+1 ) balu/] & rail4 ,illu/ration3 ,fig4 #ch is "p ( ! long newel1 %[+ mortises = ! /r+s4 ,illu/ration3 ,fig4 #cf4 ,elevation ,%[+ ,con/ruction ( ,plat=m ,/air ( :i* ,plan is ,giv5 9 ,fig4 #ce4 ,illu/ration3 ,fig4 #cg4 ,section ( ,top ,l&+1 ,balu/]1 & ,rail4 ,illu/ration3 ,fig4 #ci repres5ts "p ( ! bottom newel1 %[+ ! /r+1 m\ld+ on ! outside1 & cap4 ,illu/ration3 ,fig4 #dj is a section ( ! top /r+ enl>g$4 ,fig4 #da is ! newel at ! bottom1 z cut out to receive bottom /ep4 ,x mu/ be rememb]$ t !re is a cove "u ea* tread4 ,?is may be nail$ 9 aft] ! /airs are put toge!r1 & x adds greatly to ! appe>ance4 ,we may /ate t /airs %\ld h c>riage pieces fix$ f floor to floor1 "u ! /airs1 to support !m4 ,^! may be not*$ "u ! /eps2 or r\gh brackets may be nail$ to ! side ( ! c>riage1 & c>ri$ "u ea* ris] & tread4 ,!re is also a fram$ sp&rel :i* helps mat]ially to c>ry ! weight1 makes a s\nd job1 & adds greatly to ! appe>ance4 ,?is sp&rel may be made ( #a-;in* mat]ial1 ) panels & m\ld+s on ! front side1 z %[n 9 ,fig4 #cf4 ,! jo9t betwe5 ! top & bottom rails ( ! sp&rel at ! angle1 %\ld be made z %[n 9 ,fig4 #db ) a cross-tongue1 & glu$ & fa/5$ ) long screws4 ,fig4 #dc is simply "o ( ! panels %[+ ! mit]s on ! m\ld+ & ! %ape ( ! sections4 ,z !re is a conv5i5t space "u ! l&+1 x is commonly us$ = a closet4 ,illu/ration3 ,fig4 #ch4 ,/r+ ,mortises 9 ,long ,newel4 ,illu/ration3 ,fig4 #ci4 ,mortises 9 ,l[] ,newel = ,/r+1 ,outside ,m\ld+1 & ,cap4 ,illu/ration3 ,fig4 #dj4 ,enl>g$ ,section ( ,top ,/r+4 ,illu/ration3 ,fig4 #da4 ,newel ,cut to ,receive ,bottom ,/ep4 ,9 sett+ out /airs1 n only ! proportions ( treads & ris]s mu/ be consid]$1 b also ! mat]ial available4 ,z ?is mat]ial runs1 z a rule1 9 c]ta9 sizes1 x is be/ to "w s z to con=m to x z ne>ly z possible4 ,9 ord9>y /airs1 #aa by #a-;in* common /ock is us$ = /r+s & treads1 & #g-;in* by -in* /ock = ris]s2 9 /airs ( a bett] class1 wid] & ?ick] mat]ial may be us$4 ,! rails are set at v>i\s heights2 #b feet #h in*es may be tak5 z an av]age height on ! /airs1 & #c feet #a in* on l&+s1 ) two balu/]s to ea* /ep4 ,9 ,fig4 #cf1 all ! newels & balu/]s are %[n squ>e2 b x is mu* bett]1 & is ! m common practice1 to h !m turn$1 z ?is gives ! /airs a mu* m arti/ic appe>ance4 ,! sp&rel "u ! /r+ ( ! /airway %[s a /yle 9 :i* _m /airs are f9i%$ 9 hallways & o!r simil> places4 ,pla/] is sometimes us$ in/ead ( ! panel "w1 b is n ne>ly s good z woodwork4 ,! door "u ! l&+ may op5 into a closet1 or may lead to a cell>way1 or ?r\gh to "s o!r room4 ,9 /airs ) w9d]s1 ! wid? ( a w9d] %\ld1 if possible1 be ne>ly ! wid? ( ! regul> tread1 at a di/ance ( #ad in*es f ! n>r[ end1 s t ! l5g? ( ! /ep 9 walk+ up or d[n ! /airs may n be int]rupt$2 & = ?is reason & sev]al o!rs1 x is always be/ to h ?ree w9d]s only 9 ea* qu>t]-turn4 ,above all1 avoid a f\r-w9d] turn1 z ?is makes a breakneck /air1 :i* is m difficult to con/ruct & inconv5i5t to use4 ,illu/ration3 ,fig4 #db4 ,%[+ ,me?od ( ,jo9+ ,sp&rel ,rails1 ) ,cross-,tongue ,glu$ & ,screw$4 ,illu/ration3 ,fig4 #dc4 ,panel 9 ,sp&rel1 ,%[+ ,mit]s on ,m\ld+1 & ,%ape ( ,section4 ,bullnose ,tread4 ,no o!r /air1 p]haps1 looks s well at ! />t+ po9t z "o hav+ a bullnose /ep4 ,9 ,fig4 #dd are %[n a plan & elevation ( a flight ( /airs hav+ a bullnose tread4 ,! me?od ( obta9+ ! l9es & sett+ out ! body ( ! /airs1 is ! same z has already be5 expla9$ = o!r /airs1 ) ! exception ( ! fir/ two /eps1 :i* are made ) circul> ends1 z %[n 9 ! plan4 ,^! circul> ends are work$ out z h]eaft] describ$1 & are atta*$ to ! newel & /r+ z %[n4 ,! example %[s an op51 cut /r+ ) brackets4 ,! sp&rel "u ! /r+ conta9s %ort panels1 & makes a v h&some f9i%4 ,! newels & balu/]s 9 ?is case are turn$1 & ! latt] h cutwork panels betwe5 !m4 ,illu/ration3 ,fig4 #dd4 ,elevation & ,plan ( ,/air ) ,bullnose ,tread4 ,illu/ration3 ,fig4 #de4 ,section ?r\gh ,bullnose ,/ep4 ,bullnose /eps are usually built up ) a ?ree-piece block1 z %[n 9 ,fig4 #de1 :i* is a section ?r\gh ! /ep indicat+ ! blocks1 tread1 & ris]4 ,fig4 #df is a plan %[+ h[ ! v5e] ( ! ris] is prep>$ be=e be+ b5t into position4 ,! block ,a indicates a w$ge :i* is glu$ & driv5 home aft] ! v5e] is put 9 place4 ,?is tight5s up ! "w & makes x s\nd & cle>4 ,figs4 #dg & #dh %[ o!r me?ods ( =m+ bullnose /eps4 ,illu/ration3 ,fig4 #df4 ,plan ,%[+ ,prep>ation ( ,v5e] be=e ,b5d+ into ,position4 ,fig4 #di is ! side elevation ( an op5-/r+ /air ) bullnose /eps at ! bottom2 :ile ,fig4 #ej is a view %[+ ! l[] end ( ! /r+1 & ! mann] 9 :i* x is prep>$ = fix+ to ! blocks ( ! /ep4 ,fig4 #ea is a section ?r\gh ! /r+1 %[+ ! bracket1 cove1 & projection ( tread ov] same4 ,illu/ration3 ,fig4 #dg4 ,fig4 #dh4 ,me?ods ( ,=m+ ,bullnose ,/eps4 ,illu/ration3 ,fig4 #di4 ,side ,elevation ( ,op5-,/r+ ,/air ) ,bullnose ,/eps4 ,figs4 #eb & #ec %[ respectively a plan & v]tical section ( ! bottom "p ( ! /air4 ,! blocks are %[n at ! ends ( ! /eps 7,fig4 #ec71 ) ! v5e]$ p>ts ( ! ris]s go+ r\nd !m2 also ! position :]e ! /r+ is fix$ to ! blocks 7,fig4 #eb72 & ! t5on ( ! newel is m>k$ on ! upp] /ep4 ,! section 7,fig4 #ec7 %[s ! mann] 9 :i* ! blocks are built up & ! newel t5on$ into !m4 ,! newel1 ,fig4 #di1 is r an elaborate affair1 be+ c>v$ at ! base & on ! body1 & hav+ a c>v$ rosette plant$ 9 a small1 sunk5 panel on ?ree sides1 ! rail butt+ aga9/ ! f\r? side4 ,op5-,newel ,/airs4 ,be=e leav+ ! subject ( /raight & dog-legg$ /airs1 ! /ud5t %\ld be made famili> ) at lea/ "o example ( an op5-newel /air4 ,z ! same pr9ciples ( con/ruction gov]n all /yles ( op5-newel /airs1 a s+le example w be suffici5t4 ,! /ud5t mu/1 ( c\rse1 und]/& t he himself is ! greate/ factor 9 plann+ /airs ( ?is type2 t ! sett+ out & design+ w g5]ally devolve on him4 ,by ex]cis+ a little ?\ght & =esight1 he c s arrange 8 plan t a m9imum ( bo? labor & mat]ial w be requir$4 ,illu/ration3 ,fig4 #ej4 ,l[] ,end ( ,/r+ to ,connect ) ,bullnose ,/ep4 ,illu/ration3 ,fig4 #ea4 ,section ?r\gh ,/r+4 ,fig4 #ed %[s a plan ( an op5-newel /air hav+ two l&+s & clos$ /r+s1 %[n 9 elevation 9 ,fig4 #ee4 ,! dott$ l9es %[ ! c>riage timb]s & trimm]s1 also ! l9es ( ris]s2 :ile ! treads are %[n by full l9es4 ,x w be notic$ t ! /r+s & trimm]s at ! fir/ l&+ are fram$ into ! %ank ( ! second newel po/1 :i* runs d[n to ! floor2 :ile ! top newel drops bel[ ! fascia1 & has a turn$ & c>v$ drop4 ,?is drop hangs bel[ bo? ! fascia & ! /r+4 ,! l9es ( treads & ris]s are %[n by dott$ l9es & cros%at*$ sections4 ,! position ( ! c>riage timb]s is %[n bo? 9 ! l&+s & 9 ! runs ( ! /airs1 ! project+ ends ( ^! timb]s be+ suppos$ to be re/+ on ! wall4 ,a scale ( ! plan & elevation is atta*$ to ! plan4 ,9 ,fig4 #ee1 a /ory rod is %[n at ! "r1 ) ! numb] ( ris]s spac$ (f !reon4 ,! design ( ! newels1 sp&rel1 fram+1 & panel+ is %[n4 ,illu/ration3 ,fig4 #eb4 ,plan ( ,bottom ,"p ( ,bullnose ,/air4 ,illu/ration3 ,fig4 #ec4 ,v]tical ,section ?r\gh ,bottom ,"p ( ,bullnose ,/air4 ,only ! c5tral c>riage timb]s are %[n 9 ,fig4 #ed2 b 9 a /air ( ?is wid?1 !re ought to be two o!r timb]s1 n s heavy1 p]haps1 z ! c5tral "o1 yet /rong en\gh to be ( s]vice 9 l5d+ additional /r5g? to ! /airway1 & also to help c>ry ! la?s & pla/] or ! panel+ :i* may be necess>y 9 complet+ ! "u side or s(fit4 ,! /r+s be+ clos$1 ! butts ( _! balu/]s mu/ re/ on a subrail :i* caps ! upp] edge ( ! out] /r+4 ,illu/ration3 ,fig4 #ed4 ,plan ( ,op5-,newel ,/air1 ) ,two ,l&+s & ,clos$ ,/r+s4 ,! fir/ newel %\ld pass ?r\gh ! l[] floor1 &1 to insure solidity1 %\ld be secur$ by bolts to a joi/1 z %[n 9 ! elevation4 ,! rail is atta*$ to ! newels 9 ! usual mann]1 ) h&rail bolts or o!r suitable device4 ,! upp] newel %\ld be made fa/ to ! joi/s z %[n1 ei!r by bolts or 9 "s o!r effici5t mann]4 ,! int]m$iate newels are left squ>e on ! %ank bel[ ! /airs1 & may be fa/5$ 9 ! floor bel[ ei!r by mortise & t5on or by mak+ use ( jo9t bolts4 ,illu/ration3 ,fig4 #ee4 ,elevation ( ,op5-,newel ,/air ,%[n 9 ,plan 9 ,fig4 #ed4 ,ev]y?+ ab\t a /air %\ld be made solid & s\nd2 & e jo9t %\ld set firmly & closely2 or a %aky1 rickety1 squeaky /air w be ! result1 :i* is an abom9ation4 ,/airs ) ,curv$ ,turns4 ,suffici5t examples ( /airs hav+ angles ( great] or less degree at ! turn or *ange ( direction1 to enable ! /ud5t to build any /air ( ?is class1 h n[ be5 giv54 ,!re are1 h[ev]1 o!r types ( /airs 9 common use1 ^: turns are curv$1 & 9 :i* newels are employ$ only at ! foot1 & sometimes at ! f9i% ( ! flight4 ,^! curv$ turns may be any "p ( a circle1 accord+ to ! requirem5ts ( ! case1 b turns ( a qu>t]-circle or half-circle are ! m common4 ,! /r+ =m+ ! curve is call$ a cyl9d]1 or "p ( a cyl9d]1 z ! case may be4 ,! radius ( ?is circle or cyl9d] may be any l5g?1 accord+ to ! space assign$ = ! /air4 ,! op5+ ar\nd :i* ! /air w9ds is call$ ! well-hole4 ,illu/ration3 ,fig4 #ef4 ,/air ,s]v+ = ,two ,flights1 ) ,mid-,floor ,l&+4 ,fig4 #ef %[s a portion ( a /airway hav+ a well-hole ) a #g-;in* radius4 ,?is /air is r peculi>1 z x %[s a qu>t]-space l&+1 & a qu>t]-space hav+ ?ree w9d]s4 ,! reason = ?is is ! fact t ! l&+ is on a level ) ! floor ( ano!r room1 into :i* a door op5s f ! l&+4 ,?is is a problem v (t5 met ) 9 practical "w1 :]e ! ma9 /air is (t5 made to d ! "w ( two flights because ( "o floor be+ s mu* l[] ?an ano!r4 ,a curv$ /air1 sometimes call$ a geometrical /air1 is %[n 9 ,fig4 #eg1 conta9+ sev5 w9d]s 9 ! cyl9d] or well-hole1 ! fir/ & la/ align+ ) ! diamet]4 ,9 ,fig4 #eh is %[n ano!r example ( ?is k9d ( /air1 conta9+ n9e w9d]s 9 ! well-hole1 ) a circul> wall-/r+4 ,x is n (t5 t /airs are built 9 ?is fa%ion1 z mo/ /airs hav+ a circul> well-hole f9i% aga9/ ! wall 9 a mann] simil> to t %[n 9 ,fig4 #eg4 ,illu/ration3 ,fig4 #eg4 ,geometrical ,/air ) ,sev5 ,w9d]s4 ,sometimes1 h[ev]1 ! workman w be confront$ ) a plan su* z %[n 9 ,fig4 #eh2 & he %\ld "k h[ to lay out ! wall-/r+4 ,9 ! elevation1 ,fig4 #eh1 ! /r+ is %[n to be /raight1 simil> to ! /r+ ( a common /raight flight4 ,?is results f hav+ an equal wid? 9 ! w9d]s along ! wall-/r+1 &1 z we h ( necessity an equal wid? 9 ! ris]s1 ! developm5t ( ! /r+ is m]ely a /raight piece ( bo>d1 z 9 an ord9>y /raight flight4 ,9 lay+ out ! /r+1 all we h to d is to make a common pit*-bo>d1 &1 ) x z a templet1 m>k ! l9es ( ! treads & ris]s on a /raight piece ( bo>d1 z %[n at #a1 #b1 #c1 #d1 etc4 ,if y c manage to b5d ! /r+ )\t k]f+ 7groov+71 x w be all ! bett]2 if n1 ! k]fs 7grooves7 mu/ be p>allel to ! rise4 ,y c set out ) a /raight edge1 full size1 on a r\gh plat=m1 j z %[n 9 ! diagram2 & :5 ! /r+ is b5t & set 9 place1 ! ris]s & w9d]s w h _! correct positions4 ,to b5d ^! /r+s or o!rwise prep>e !m = fa/5+ aga9/ ! wall1 p]haps ! easie/ way is to saw ! /r+ ) a f9e saw1 across ! face1 mak+ p>allel grooves4 ,?is me?od ( b5d+ is call$ k]f+1 above ref]r$ to4 ,! k]fs or grooves mu/ be cut p>allel to ! l9es ( ! ris]s1 s z to be v]tical :5 ! /r+ is 9 place4 ,?is me?od1 h[ev]--h&y ?\gh x may be--is n a good "o1 inasmu* z ! saw groove w %[ m or less 9 ! f9i%$ "w4 ,illu/ration3 ,fig4 #eh4 ,plan ( ,circul> ,/air & ,lay\t ( ,wall ,/r+ = ,same4 ,ano!r me?od is to build up or /ave ! /r+4 ,!re are sev]al ways ( do+ ?is4 ,9 "o1 comp>atively n>r[ pieces are cut to ! requir$ curve or to portions ( x1 & are fa/5$ toge!r1 edge to edge1 ) glue & screws1 until ! necess>y wid? is obta9$ 7see ,fig4 #ei74 ,! head+ jo9ts may be ei!r butt$ or bevel$1 ! latt] be+ /rong]1 & %\ld be cross-tongu$4 ,fig4 #fj %[s a me?od t may be foll[$ :5 a wide /r+ is requir$1 or a piece curv$ 9 ! direction ( its wid? is ne$$ = any purpose4 ,! pieces are /epp$ ov] ea* o!r to suit ! desir$ curve2 & ?\gh %[n squ>e-edg$ 9 ! figure1 !y are usually cut bevel$1 z !n1 by rev]s+ !m1 two may be cut out ( a batt54 ,illu/ration3 ,fig4 #ei4 ,fig4 #fj4 ,me?ods ( ,build+ ,up ,/r+s4 ,panels & quick sweeps = simil> purposes are obta9$ 9 ! mann] %[n 9 ,fig4 #fa1 by jo9+ up n>r[ bo>ds edge to edge at a suitable bevel to give ! desir$ curve4 ,! int]nal curve is frequ5tly work$ approximately1 be=e glu+ up4 ,! num]\s jo9ts incid5tal to ^! me?ods limit _! uses to pa9t$ or unimportant "w4 ,illu/ration3 ,fig4 #fa4 ,build+ ,up a ,curv$ ,panel or ,quick ,sweep4 ,9 ,fig4 #fb is %[n a wrea?-piece or curv$ portion ( ! outside /r+ ris+ ar\nd ! cyl9d] at ! half-space4 ,?is is =m$ by r$uc+ a %ort piece ( /r+ to a v5e] betwe5 ! spr++s2 b5d+ x ^u a cyl9d] made to fit ! plan2 !n1 :5 x is secur$ 9 position1 fill+ up ! back ( ! v5e] ) /aves glu$ across x2 &1 f9ally1 glu+ a piece ( canvas ov] ! :ole4 ,! appe>ance ( ! wrea?-piece aft] x has be5 built up & remov$ f ! cyl9d] is indicat$ 9 ,fig4 #fc4 ,! canvas back has be5 omitt$ to %[ ! /av+2 & ! c\nt]-w$ge key us$ = connect+ ! wrea?-piece ) ! /r+ is %[n4 ,! wrea?-piece is1 at ?is /age1 ready = m>k+ ! outl9es ( ! /eps4 ,fig4 #fb also %[s ! drum or %ape ar\nd :i* /r+s may be b5t1 :e!r ! /r+s are =m$ ( v5e]s1 /av$1 or k]f$4 ,ano!r drum or %ape is %[n 9 ,fig4 #fd4 ,9 ?is1 a portion ( a cyl9d] is =m$ 9 ! mann] cle>ly indicat$2 & ! /r+1 be+ set out on a v5e] bo>d suffici5tly ?9 to b5d easily1 is laid d[n r\nd ! curve1 su* a numb] ( pieces ( l ?ickness be+ !n add$ z w make ! requir$ ?ickness ( ! /r+4 ,9 work+ ?is me?od1 glue is introduc$ betwe5 ! v5e]s1 :i* are !n quickly /ra9$ d[n to ! curv$ piece ) h& screws4 ,a /r+ ( almo/ any l5g? c be =m$ 9 ?is way1 by glu+ a few feet at a "t1 & :5 t dries1 remov+ ! cyl9drical curve & glu+ d[n m1 until ! :ole is complet$4 ,sev]al o!r me?ods w sugge/ !mselves to ! workman1 ( build+ up good1 solid1 circul> /r+s4 ,illu/ration3 ,fig4 #fb4 ,wrea?-,piece ,b5t ar\nd ,cyl9d]4 ,illu/ration3 ,fig4 #fc4 ,complet$ ,wrea?-,piece ,remov$ f ,cyl9d]4 ,illu/ration3 ,fig4 #fd4 ,ano!r ,drum or ,%ape = ,build+ ,curv$ ,/r+s4 ,illu/ration3 ,fig4 #fe4 ,lay+ ,out ,treads & ,ris]s ar\nd a ,drum4 ,"o me?od ( lay+ out ! treads & ris]s ar\nd a cyl9d] or drum1 is %[n 9 ,fig4 #fe4 ,! l9e ,d %[s ! curve ( ! rail4 ,! l9es %[+ treads & ris]s may be m>k$ (f on ! cyl9d]1 or !y may be m>k$ (f aft] ! v5e] is b5t ar\nd ! drum or cyl9d]4 ,!re are v>i\s me?ods ( mak+ inside cyl9d]s or wells1 & ( fa/5+ same to /r+s4 ,"o me?od is %[n 9 ,fig4 #ff4 ,?is gives a /rong jo9t :5 prop]ly made4 ,x w be notic$ t ! cyl9d] is not*$ out on ! back2 ! two blocks %[n at ! back ( ! (fsets are w$ges driv5 9 to secure ! cyl9d] 9 place1 & to drive x up tight to ! /r+s4 ,fig4 #fg %[s an #h-;in* well-hole ) cyl9d] complete2 also ! me?od ( trimm+ & f9i%+ same4 ,! cyl9d]1 too1 is %[n 9 su* a mann] t its con/ruction w be readily und]/ood4 ,/airs hav+ a cyl9drical or circul> op5+ always require a weight support und]nea? !m4 ,?is support1 :i* is g5]ally made ( r\gh lumb]1 is call$ ! c>riage1 because x is suppos$ to c>ry any reasonable load t may be plac$ ^u ! /airway4 ,fig4 #fh %[s ! "u side ( a half-space /air hav+ a c>riage b5ea? x4 ,! timb]s m>k$ ,s are ( r\gh /uff1 & may be #b-;in* by #f-;in* or ( great] dim5sions4 ,if !y are cut to fit ! ris]s & treads1 !y w require to be at lea/ #b-;in* by #h-;in*4 ,9 prep>+ ! r\gh c>riage = ! w9d]s1 x w be be/ to let ! back edge ( ! tread project beyond ! back ( ! ris] s t x =ms a l$ge z %[n "u ,c 9 ,fig4 #fi4 ,!n fix ! cross-c>riage pieces "u ! w9d]s1 ) ! back edge ab\t flu% ) ! backs ( ris]s1 secur+ "o end to ! well ) screws1 & ! o!r to ! wall /r+ or ! wall4 ,n[ cut %ort pieces1 m>k$ ,o ,o 7,fig4 #fh71 & fix !m tightly 9 betwe5 ! cross-c>riage & ! back ( ! ris] z at ,b ,b 9 ! section1 ,fig4 #fi4 ,^! c>riages %\ld be ( #c-;in* by #b-;in* mat]ial4 ,n[ get a piece ( wood1 #a-;in* by #c-;in*1 & cut pieces ,c ,c to fit tightly betwe5 ! top back edge ( ! w9d]s 7or ! l$ge7 & ! pieces m>k$ ,b ,b 9 section4 ,?is me?od makes a v s\nd & /rong job ( ! w9d]s2 & if ! /uff is r\ghly plan$1 & blocks are glu$ on ea* side ( ! %ort cross-pieces ,o ,o ,o1 x is next to impossible = ! w9d]s ev] to spr+ or squeak4 ,:5 ! weight is c>ri$ 9 ?is mann]1 ! pla/]] w h v little tr\ble 9 la?+ s t a graceful s(fit w be made "u ! /airs4 ,illu/ration3 ,fig4 #ff4 ,"o ,me?od ( ,mak+ an ,inside ,well4 ,illu/ration3 ,fig4 #fg4 ,con/ruction & ,trimm+ ( #h-;,in* ,well-,hole4 ,! mann] ( plac+ ! ma9 /r+]s ( ! c>riage ,s ,s1 is %[n at ,a1 ,fig4 #fi4 ,fig4 #fh %[s a complete half-space /air2 "o-half ( ?is1 f9i%$ z %[n1 w answ] well = a qu>t]-space /air4 ,illu/ration3 ,fig4 #fh4 ,"u ,side ( ,half-,space ,/air1 ) ,c>riages & ,cross-,c>riages4 ,ano!r me?od ( =m+ a c>riage = a /air is %[n 9 ,fig4 #gj4 ,?is is a peculi> b v h&some /air1 inasmu* z ! fir/ & ! la/ f\r /eps are p>allel1 b ! rema9d] balance or dance4 ,! treads are numb]$ 9 ?is illu/ration2 & ! plan ( ! h&rail is %[n ext5d+ f ! scroll at ! bottom ( ! /airs to ! l&+ on ! second /ory4 ,! trimm] ,t at ! top ( ! /airs is also %[n2 & ! r\gh /r+s or c>riages1 ,r ,s1 ,r ,s1 ,r ,s1 are repres5t$ by dott$ l9es4 ,?is plan repres5ts a /air ) a curtail /ep1 & a scroll h&rail re/+ ov] ! curve ( ! curtail /ep4 ,?is type ( /air is n n[ mu* 9 vogue 9 ?is c\ntry1 ?\gh x is adopt$ occasionally 9 "s ( ! l>g] cities4 ,! use ( heavy newel po/s in/ead ( curtail /eps1 is ! prevail+ /yle at pres5t4 ,9 lay+ out geometrical /airs1 ! /eps are arrang$ on pr9ciples already describ$4 ,! well-hole 9 ! c5t] is fir/ laid d[n & ! /eps arrang$ ar\nd x4 ,9 circul> /airs ) an op5 well-hole1 ! h&rail be+ on ! inn] side1 ! wid? ( tread = ! /eps %\ld be set (f at ab\t #ah in*es f ! h&rail1 ?is giv+ an approximately uni=m rate ( progress = anyone asc5d+ or desc5d+ ! /airway4 ,9 /airs ) ! rail on ! outside1 z sometimes occurs1 x w be suffici5t if ! treads h ! prop] wid? at ! middle po9t ( _! l5g?4 ,:]e a flight ( /airs w likely be subject to great /ress & we>1 ! c>riages %\ld be made mu* heavi] ?an indicat$ 9 ! =ego+ figures2 & !re may be cases :5 x w be necess>y to use iron bolts 9 ! sides ( ! r\gh /r+s 9 ord] to give !m great] /r5g?4 ,?is necessity1 h[ev]1 w arise only 9 ! case ( /airs built 9 public build+s1 *ur*es1 halls1 factories1 w>eh\ses1 or o!r build+s ( a simil> k9d4 ,sometimes1 ev5 9 h\se /airs x may be wise to /r5g!n ! treads & ris]s by spik+ pieces ( bo>d to ! r\gh /r+1 ends up1 fitt+ !m snugly aga9/ ! "u side ( ! tread & ! back ( ! ris]4 ,! me?od ( do+ ?is is %[n 9 ,fig4 #ga1 9 :i* ! lett] ,o %[s ! pieces nail$ to ! /r+4 ,illu/ration3 ,fig4 #fi4 ,me?od ( ,re9=c+ ,/air4 ,illu/ration3 ,fig4 #gj4 ,plan ,%[+ ,"o ,me?od ( ,con/ruct+ ,c>riage & ,trimm+ ,w9d+ ,/air4 ,types ( ,/airs 9 ,common ,use4 ,9 ord] to make ! /ud5t famili> ) types ( /airs 9 g5]al use at ! pres5t day1 plans ( a few ( ^? mo/ likely to be met ) w n[ be giv54 ,fig4 #gb is a plan ( a /raight /air1 ) an ord9>y cyl9d] at ! top provid$ = a return rail on ! l&+4 ,x also %[s a /ret*-out /r+] at ! />t+4 ,fig4 #gc is a plan ( a /air ) a l&+ & return /eps4 ,fig4 #gd is a plan ( a /air ) an acute angul> l&+ & cyl9d]4 ,fig4 #ge illu/rates ! same k9d ( /air z ,fig4 #gd1 ! angle1 h[ev]1 be+ obtuse4 ,fig4 #gf exhibits a /air hav+ a half-turn ) two ris]s on l&+s4 ,fig4 #gg is a plan ( a qu>t]-space /air ) f\r w9d]s4 ,fig4 #gh %[s a /air simil> to ,fig4 #gg1 b ) six w9d]s4 ,illu/ration3 ,fig4 #ga4 ,re9=c+ ,treads & ,ris]s by ,blocks ,nail$ to ,/r+4 ,illu/ration3 ,fig4 #gb4 ,plan ( ,/raight ,/air ) ,cyl9d] at ,top = ,return ,rail4 ,illu/ration3 ,fig4 #gc4 ,plan ( ,/air ) ,l&+ & ,return ,/eps4 ,fig4 #gi %[s a /air hav+ five danc+ w9d]s4 ,fig4 #hj is a plan ( a half-space /air hav+ five danc+ w9d]s & a qu>t]-space l&+4 ,fig4 #ha %[s a half-space /air ) danc+ w9d]s all ar\nd ! cyl9d]4 ,fig4 #hb %[s a geometrical /air hav+ w9d]s all ar\nd ! cyl9d]4 ,fig4 #hc %[s ! plan & elevation ( /airs :i* turn ar\nd a c5tral po/4 ,?is k9d ( /air is frequ5tly us$ 9 l>ge /ores & 9 clubh\ses & o!r simil> places1 & has a v graceful appe>ance4 ,x is n v difficult to build if prop]ly plann$4 ,! only =m ( /air n %[n :i* ! /ud5t may be call$ ^u to build1 w\ld v likely be "o hav+ an elliptical plan2 b1 z ?is =m is s seldom us$--be+ f\nd1 9 fact1 only 9 public build+s or great mansions--x r>ely falls to ! lot ( ! ord9>y workman to be call$ ^u to design or con/ruct a /airway ( ?is type4 ,illu/ration3 ,fig4 #gd4 ,plan ( ,/air ) ,acute-,angle ,l&+ & ,cyl9d]4 ,illu/ration3 ,fig4 #ge4 ,plan ( ,/air ) ,obtuse-,angle ,l&+ & ,cyl9d]4 ,illu/ration3 ,fig4 #gf4 ,half-,turn ,/air ) ,two ,ris]s on ,l&+s4 ,illu/ration3 ,fig4 #gg4 ,qu>t]-,space ,/air ) ,f\r ,w9d]s4 ,illu/ration3 ,fig4 #gh4 ,qu>t]-,space ,/air ) ,six ,w9d]s4 ,illu/ration3 ,fig4 #gi4 ,/air ) ,five ,danc+ ,w9d]s4 ,illu/ration3 ,fig4 #hj4 ,half-,space ,/air ) ,five ,danc+ ,w9d]s & ,qu>t]-,space ,l&+ ,illu/ration3 ,fig4 #ha4 ,half-,space ,/air ) ,danc+ ,w9d]s all ar\nd ,cyl9d]4 ,,geometrical ,,/airways ,,& ,,h&-,,rail+ ,! t]m geometrical is appli$ to /airways hav+ any k9d ( curve = a plan4 ,! rails ov] ! /eps are made cont9u\s f "o /ory to ano!r4 ,! result+ w9d+ or twi/+ pieces are call$ wrea?s4 ,illu/ration3 ,fig4 #hb4 ,geometrical ,/air ) ,w9d]s all ,ar\nd ,cyl9d]4 ,wrea?s4 ,! con/ruction ( wrea?s is bas$ on a few geometrical problems--namely1 ! projection ( /raight & curv$ l9es into an oblique plane2 & ! f9d+ ( ! angle ( incl9ation ( ! plane into :i* ! l9es & curves are project$4 ,?is angle is call$ ! bevel1 & by its use ! wrea? is made to twi/4 ,illu/ration3 ,fig4 #hc4 ,plan & ,elevation ( ,/airs ,turn+ ar\nd a ,c5tral ,po/4 ,9 ,fig4 #hd is %[n an obtuse-angle plan2 9 ,fig4 #he1 an acute-angle plan2 & 9 ,fig4 #hf1 a semicircle enclos$ )9 /raight l9es4 ,projection4 ,a k ( h[ to project ! l9es & curves 9 ea* ( ^! plans into an oblique plane1 & to f9d ! angle ( incl9ation ( ! plane1 w enable ! /ud5t to con/ruct any & all k9ds ( wrea?s4 ,! /raight l9es a1 b1 c1 d 9 ! plan1 ,fig4 #hf1 are kn[n z tang5ts2 & ! curve1 ! c5tral l9e ( ! plan wrea?4 ,! /raight l9e across f n to n is ! diamet]2 & ! p]p5dicul> l9e f x to ! l9es c & b is ! radius4 ,a tang5t l9e may be def9$ z a l9e t\*+ a curve )\t cutt+ x1 & is made use ( 9 h&rail+ to squ>e ! jo9ts ( ! wrea?s4 ,tang5t ,sy/em4 ,! tang5t sy/em ( h&rail+ takes its "n f ! use made ( ! tang5ts = ?is purpose4 ,9 ,fig4 #hf1 x is %[n t ! jo9ts connect+ ! c5tral l9e ( rail ) ! plan rails w ( ! /raight flights1 are plac$ "r at ! spr++2 t is1 !y are 9 l9e ) ! diamet] ( ! semicircle1 & squ>e to ! side tang5ts a & d4 ,! c5t] jo9t ( ! cr[n tang5ts is %[n to be squ>e to tang5ts b & c4 ,:5 ^! l9es are project$ into an oblique plane1 ! jo9ts ( ! wrea?s c be made to butt squ>e by apply+ ! bevel to !m4 ,all h&rail wrea?s are assum$ to re/ on an oblique plane :ile asc5d+ ar\nd a well-hole1 ei!r 9 connect+ two flights or 9 connect+ "o flight to a l&+1 z ! case may be4 ,9 ! simple/ cases ( con/ruction1 ! wrea? re/s on an incl9$ plane t incl9es 9 "o direction only1 to ei!r side ( ! well-hole2 :ile 9 o!r cases x re/s on a plane t incl9es to two sides4 ,illu/ration3 ,fig4 #hd4 ,obtuse-,angle ,plan4 ,fig4 #hg illu/rates :at is meant by a plane incl9+ 9 "o direction4 ,x w be notic$ t ! l[] "p ( ! figure is a reproduction ( ! quadrant enclos$ by ! tang5ts a & b 9 ,fig4 #hf4 ,! quadrant1 ,fig4 #hg1 repres5ts a c5tral l9e ( a wrea? t is to asc5d f ! jo9t on ! plan tang5t a ! height ( h above ! tang5t b4 ,illu/ration3 ,fig4 #he4 ,acute-,angle ,plan4 ,illu/ration3 ,fig4 #hf4 ,semicircul> ,plan4 ,9 ,fig4 #hh1 a view ( ,fig4 #hg is giv5 9 :i* ! tang5ts a & b are %[n 9 plan1 & also ! quadrant repres5t+ ! plan c5tral l9e ( a wrea?4 ,! curv$ l9e ext5d+ f a to h 9 ?is figure repres5ts ! developm5t ( ! c5tral l9e ( ! plan wrea?1 &1 z %[n1 x re/s on an oblique plane incl9+ to "o side only--namely1 to ! side ( ! plan tang5t a4 ,! jo9ts are made squ>e to ! develop$ tang5ts a & m ( ! incl9$ plane2 x is = ?is purpose only t tang5ts are made use ( 9 wrea? con/ruction4 ,!y are %[n 9 ! figure to consi/ ( two l9es1 a & m1 :i* are two adjo9+ sides ( a develop$ section 79 ?is case1 ( a squ>e prism71 ! section be+ ! assum$ incl9$ plane :]eon ! wrea? re/s 9 its asc5t f a to h4 ,! jo9t at h1 if made squ>e to ! tang5t m1 w be a true1 squ>e butt-jo9t2 s also w be ! jo9t at a1 if made squ>e to ! tang5t a4 ,9 practical "w x w be requir$ to f9d ! correct geometrical angle betwe5 ! two develop$ tang5ts a & m2 & "h1 aga91 x may be obs]v$ t ! f9d+ ( ! correct angle betwe5 ! two develop$ tang5ts is ! ess5tial purpose ( e tang5t sy/em ( h&rail+4 ,illu/ration3 ,fig4 #hg4 ,illu/rat+ ,plane ,incl9$ 9 ,"o ,direction ,only4 ,illu/ration3 ,fig4 #hh4 ,plan ,l9e ( ,rail ,project$ into ,oblique ,plane ,incl9$ to ,"o ,side ,only4 ,9 ,fig4 #hi is %[n ! geometrical solution--! "o necess>y to f9d ! angle betwe5 ! tang5ts z requir$ on ! face-m\ld to squ>e ! jo9ts ( ! wrea?4 ,! figure is %[n to be simil> to ,fig4 #hg1 except t x has an additional portion m>k$ 8,section40 ,?is section is ! true %ape ( ! oblique plane :]eon ! wrea? asc5ds1 a view ( :i* is giv5 9 ,fig4 #hh4 ,x w be obs]v$ t "o side ( x is ! develop$ tang5t m2 ano!r side1 ! develop$ tang5t a 7 a74 ,! angle betwe5 ! two z "h pres5t$ is ! "o requir$ on ! face-m\ld to squ>e ! jo9ts4 ,9 ?is example1 ,fig4 #hi1 ow+ to ! plane be+ oblique 9 "o direction only1 ! %ape ( ! section is f\nd by m]ely draw+ ! tang5t a at "r angles to ! tang5t m1 mak+ x equal 9 l5g? to ! level tang5t a 9 ! plan4 ,by draw+ l9es p>allel to a & m respectively1 ! =m ( ! section w be f\nd1 its outl9es be+ ! projections ( ! plan l9es2 & ! angle betwe5 ! two tang5ts1 z already said1 is ! angle requir$ on ! face-m\ld to squ>e ! jo9ts ( ! wrea?4 ,! solution "h pres5t$ w enable ! /ud5t to f9d ! correct direction ( ! tang5ts z requir$ on ! face-m\ld to squ>e jo9ts1 9 all cases ( practical "w :]e "o tang5t ( a wrea? is level & ! o!r tang5t is incl9$1 a condition usually met ) 9 level-l&+ /airways4 ,fig4 #ij exhibits a condition ( tang5ts :]e ! two are equally incl9$4 ,! plan "h also is tak5 f ,fig4 #hf4 ,! incl9ation ( ! tang5ts is made equal to ! incl9ation ( tang5t b 9 ,fig4 #hf1 z %[n at m 9 ,figs4 #hg1 #hh1 & #hi4 ,illu/ration3 ,fig4 #hi4 ,f9d+ ,angle betwe5 ,tang5ts4 ,9 ,fig4 #ia1 a view ( ,fig4 #ij is giv51 %[+ cle>ly ! incl9ation ( ! tang5ts c & d ov] & above ! plan tang5ts c & d4 ,! c5tral l9e ( ! wrea? is %[n ext5d+ along ! sectional plane1 ov] & above its plan l9es1 f "o jo9t to ! o!r1 &1 at ! jo9ts1 made squ>e to ! incl9$ tang5ts c & d4 ,x is evid5t f ! view "h giv51 t ! condition necess>y to squ>e ! jo9t at ea* end w\ld be to f9d ! true angle betwe5 ! tang5ts c & d1 :i* w\ld give ! correct direction to ea* tang5t4 ,9 ,fig4 #ib is %[n h[ to f9d ?is angle correctly z requir$ on ! face-m\ld to squ>e ! jo9ts4 ,9 ?is figure is %[n ! same plan z 9 ,figs4 #ij & #ia1 & ! same incl9ation to ! tang5ts z 9 ,fig4 #ij1 s t1 except = ! portion m>k$ 8,section10 x w\ld be simil> to ,fig4 #ij4 ,to f9d ! correct angle = ! tang5ts ( ! face-m\ld1 draw ! l9e m f d1 squ>e to ! incl9$ l9e ( ! tang5ts c d2 revolve ! bottom incl9$ tang5t c to cut l9e m 9 n1 :]e ! jo9t is %[n fix$2 & f ?is po9t draw ! l9e c to w4 ,! int]section ( ?is l9e ) ! upp] tang5t d =ms ! correct angle z requir$ on ! face-m\ld4 ,by draw+ ! jo9ts squ>e to ^! two l9es1 !y w butt squ>e ) ! rail t is to connect ) !m1 or to ! jo9t ( ano!r wrea? t may belong to ! cyl9d] or well-hole4 ,illu/ration3 ,fig4 #ij4 ,two ,tang5ts ,equally ,incl9$4 ,illu/ration3 ,fig4 #ia4 ,plan ,l9es ,project$ into ,oblique ,plane ,incl9$ to ,two ,sides4 ,illu/ration3 ,fig4 #ib4 ,f9d+ ,angle betwe5 ,tang5ts4 ,fig4 #ic is ano!r view ( ^! tang5ts 9 position plac$ ov] & above ! plan tang5ts ( ! well-hole4 ,x w be obs]v$ t ?is figure is made up ( ,figs4 #hh & #ia comb9$4 ,fig4 #hh1 z "h pres5t$1 is %[n to connect ) a level-l&+ rail at a4 ,! jo9t hav+ be5 made squ>e to ! level tang5t1 a w butt squ>e to a squ>e end ( ! level rail4 ,! jo9t at h is %[n to connect ! two wrea?s & is made squ>e to ! incl9$ tang5t m ( ! l[] wrea?1 & also squ>e to ! incl9$ tang5t c ( ! upp] wrea?2 ! two tang5ts1 align+1 gu>antee a squ>e butt-jo9t4 ,! upp] jo9t is made squ>e to ! tang5t d1 :i* is "h %[n to align ) ! rail ( ! connect+ flight2 ! jo9t w consequ5tly butt squ>e to ! end ( ! rail ( ! flight above4 ,! view giv5 9 ?is diagram is t ( a wrea? />t+ f a level l&+1 & w9d+ ar\nd a well-hole1 connect+ ! l&+ ) a flight ( /airs lead+ to a second /ory4 ,x is pres5t$ to elucidate ! use made ( tang5ts to squ>e ! jo9ts 9 wrea? con/ruction4 ,! wrea? is %[n to be 9 two sections1 "o ext5d+ f ! level-l&+ rail at a to a jo9t 9 ! c5t] ( ! well-hole at h1 ?is section hav+ "o level tang5t a & "o incl9$ tang5t m2 ! o!r section is %[n to ext5d f h to n1 :]e x is butt-jo9t$ to ! rail ( ! flight above4 ,illu/ration3 ,fig4 #ic4 ,lay+ ,out ,l9e ( ,wrea? to ,/>t f ,level-,l&+ ,rail4 ,w9d ar\nd ,well-,hole1 & ,connect at ,l&+ ) ,flight to ,upp] ,/ory4 ,?is figure cle>ly %[s t ! jo9t at a ( ! bottom wrea?--ow+ to ! tang5t a be+ level & !re=e align+ ) ! level rail ( ! l&+--w be a true butt-jo9t2 & t ! jo9t at h1 :i* connects ! two wrea?s1 w also be a true butt-jo9t1 ow+ to x be+ made squ>e to ! tang5t m ( ! bottom wrea? & to ! tang5t c ( ! upp] wrea?1 bo? tang5ts hav+ ! same incl9ation2 also ! jo9t at n w butt squ>e to ! rail ( ! flight above1 ow+ to x be+ made squ>e to ! tang5t d1 :i* is %[n to h ! same incl9ation z ! rail ( ! flight adjo9+4 ,z previ\sly /at$1 ! use made ( tang5ts is to squ>e ! jo9ts ( ! wrea?s2 & 9 ?is diagram x is cle>ly %[n t ! way !y c be made ( use is by giv+ ea* tang5t its true direction4 ,h[ to f9d ! true direction1 or ! angle betwe5 ! tang5ts a & m %[n 9 ?is diagram1 0 demon/rat$ 9 ,fig4 #hi2 & h[ to f9d ! direction ( ! tang5ts c & d 0 %[n 9 ,fig4 #ib4 ,illu/ration3 ,fig4 #id4 ,tang5ts ,unfold$ to ,f9d ,_! ,incl9ation4 ,fig4 #id is pres5t$ to help fur!r t[>d an und]/&+ ( ! tang5ts4 ,9 ?is diagram !y are unfold$2 t is1 !y are /ret*$ out = ! purpose ( f9d+ ! incl9ation ( ea* "o ov] & above ! plan tang5ts4 ,! side plan tang5t a is %[n /ret*$ out to ! floor l9e1 & its elevation a is a level l9e4 ,! side plan tang5t d is also /ret*$ out to ! floor l9e1 z %[n by ! arc n m4 ,by ?is process ! plan tang5ts are n[ 9 "o /raight l9e on ! floor l9e1 z %[n f w to m4 ,^u ea* "o1 erect a p]p5dicul> l9e z %[n1 & f m measure to n1 ! height ! wrea? is to asc5d ar\nd ! well-hole4 ,9 practice1 ! numb] ( ris]s 9 ! well-hole w det]m9e ?is height4 ,illu/ration3 ,fig4 #ie4 ,well-,hole ,connect+ ,two ,flights1 ) ,two ,wrea?-,pieces1 ,ea* ,conta9+ ,portions ( ,unequal ,pit*4 ,n[1 f po9t n1 draw a few treads & ris]s z %[n2 & along ! nos+ ( ! /eps1 draw ! pit*-l9e2 cont9ue ?is l9e ov] ! tang5ts d1 c1 & m1 d[n to :]e x connects ) ! bottom level tang5t1 z %[n4 ,?is gives ! pit* or incl9ation to ! tang5ts ov] & above ! well-hole4 ,! same l9e is %[n 9 ,fig4 #ic1 fold$ ar\nd ! well-hole1 f n1 :]e x connects ) ! flight at ! upp] end ( ! well-hole1 to a1 :]e x connects ) ! level-l&+ rail at ! bottom ( ! well-hole4 ,x w be obs]v$ t ! upp] portion1 f jo9t n to jo9t h1 ov] ! tang5ts c & d1 co9cides ) ! pit*-l9e ( ! same tang5ts z pres5t$ 9 ,fig4 #ib1 :]e !y are us$ to f9d ! true angle betwe5 ! tang5ts z x is requir$ on ! face-m\ld to squ>e ! jo9ts ( ! wrea? at h4 ,9 ,fig4 #hi ! same pit* is %[n giv5 to tang5t m z 9 ,fig4 #id2 & 9 bo? figures ! pit* is %[n to be ! same z t ov] & above ! upp] connect+ tang5ts c & d1 :i* is a necess>y condition :]e a jo9t1 z %[n at h 9 ,figs4 #ic & #id1 is to connect two pieces ( wrea? z 9 ?is example4 ,9 ,fig4 #id are %[n ! two face-m\lds = ! wrea?s1 plac$ ^u ! pit*-l9e ( ! tang5ts ov] ! well-hole4 ,! angles betwe5 ! tang5ts ( ! face-m\lds h be5 f\nd 9 ?is figure by ! same me?od z 9 ,figs4 #hi & #ib1 :i*1 if comp>$ ) ! pres5t figure1 w be f\nd to correspond1 except+ only ! curves ( ! face-m\lds 9 ,fig4 #id4 ,! =ego+ explanation ( ! tang5ts w give ! /ud5t a fairly good idea ( ! use made ( tang5ts 9 wrea? con/ruction4 ,! treatm5t1 h[ev]1 w\ld n be complete if left (f at ?is po9t1 z x %[s h[ to h&le tang5ts "u only two conditions--namely1 fir/1 :5 "o tang5t incl9es & ! o!r is level1 z at a & m2 second1 :5 bo? tang5ts incl9e1 z %[n at c & d4 ,illu/ration3 ,fig4 #if4 ,f9d+ ,angle betwe5 ,tang5ts = ,bottom ,wrea? ( ,fig4 #ie4 ,illu/ration3 ,fig4 #ig4 ,f9d+ ,angle betwe5 ,tang5ts = ,upp] ,wrea? ( ,fig4 #ie4 ,9 ,fig4 #ie is %[n a well-hole connect+ two flights1 :]e two portions ( unequal pit* occur 9 bo? pieces ( wrea?4 ,! fir/ piece ov] ! tang5ts a & b is %[n to ext5d f ! squ>e end ( ! /raight rail ( ! bottom flight1 to ! jo9t 9 ! c5t] ( ! well-hole1 ! bottom tang5t a 9 ?is wrea? incl9+ m ?an ! upp] tang5t b4 ,! o!r piece ( wrea? is %[n to connect ) ! bottom "o at ! jo9t h 9 ! c5t] ( ! well-hole1 & to ext5d ov] tang5ts c & d to connect ) ! rail ( ! upp] flight4 ,! relative incl9ation ( ! two tang5ts 9 ?is wrea?1 is ! rev]se ( t ( ! two tang5ts ( ! l[] wrea?4 ,9 ! l[] piece1 ! bottom tang5t a1 z previ\sly /at$1 incl9es consid]ably m ?an does ! upp] tang5t b2 :ile 9 ! upp] piece1 ! bottom tang5t c incl9es consid]ably less ?an ! upp] tang5t d4 ,! "q may arise3 ,:at causes ?is8 ,is x = v>iation 9 ! incl9ation ( ! tang5ts ov] ! well-hole8 ,x is simply ow+ to ! tang5ts be+ us$ 9 h&rail+ to squ>e ! jo9ts4 ,! incl9ation ( ! bottom tang5t a ( ! bottom wrea? is cle>ly %[n 9 ! diagram to be det]m9$ by ! incl9ation ( ! bottom flight4 ,! jo9t at a is made squ>e to bo? ! /raight rail ( ! flight & to ! bottom tang5t ( ! wrea?2 ! rail & tang5t1 !re=e1 mu/ be equally incl9$1 o!rwise ! jo9t w n be a true butt-jo9t4 ,! same rem>ks apply to ! jo9t at #e1 :]e ! upp] wrea? is %[n jo9t$ to ! /raight rail ( ! upp] flight4 ,9 ?is case1 tang5t d mu/ be fix$ to incl9e con=mably to ! incl9ation ( ! upp] rail2 o!rwise ! jo9t at #e w n be a true butt-jo9t4 ,illu/ration3 ,fig4 #ih4 ,diagram ( ,tang5ts & ,face-,m\ld = ,/air ) ,well-,hole at ,upp] ,l&+4 ,! same pr9ciple is appli$ 9 det]m9+ ! pit* or incl9ation ov] ! cr[n tang5ts b & c4 ,ow+ to ! necessity ( jo9t+ ! two wrea?s1 z %[n at h1 ^! two tang5ts mu/ h ! same incl9ation1 & !re=e mu/ be fix$1 z %[n f #b to #d1 ov] ! cr[n ( ! well-hole4 ,! tang5ts z "h pres5t$ are ^? ( ! elevation1 n ( ! face-m\ld4 ,tang5t a is ! elevation ( ! side plan tang5t a2 tang5ts b & c are %[n to be ! elevations ( ! plan tang5ts b & c2 s1 also1 is ! tang5t d ! elevation ( ! side plan tang5t d4 ,illu/ration3 ,fig4 #ii4 ,draw+ ,m\ld :5 ,"o ,tang5t ,is ,level & ,"o ,incl9$ ov] ,"r-,angl$ ,plan4 ,if ?is diagram 7 fold$1 z ,fig4 #id 0 %[n to be 9 ,fig4 #ic1 ! tang5ts ( ! elevation--namely1 a1 b1 c1 d--w\ld /& ov] & above ! plan tang5ts a1 b1 c1 d ( ! well-hole4 ,9 practical "w1 ?is diagram mu/ be drawn full size4 ,x gives ! correct l5g? to ea* tang5t z requir$ on ! face-m\ld1 & furni%es also ! data = ! lay\t ( ! m\ld4 ,fig4 #if %[s h[ to f9d ! angle betwe5 ! tang5ts ( ! face-m\ld = ! bottom wrea?1 :i*1 z %[n 9 ,fig4 #ie1 is to span ov] ! fir/ plan quadrant a b4 ,! elevation tang5ts a & b1 z %[n1 w be ! tang5ts ( ! m\ld4 ,to f9d ! angle betwe5 ! tang5ts1 draw ! l9e a h 9 ,fig4 #if2 & f a1 measure to #b ! l5g? ( ! bottom tang5t a 9 ,fig4 #ie2 ! l5g? f #b to h1 ,fig4 #if1 w equal ! l5g? ( ! upp] tang5t b1 ,fig4 #ie4 ,f #b to #a1 measure a di/ance equal to #b-a 9 ,fig4 #ie1 ! latt] be+ f\nd by dropp+ a p]p5dicul> f w to meet ! tang5t b ext5d$4 ,^u #a1 erect a p]p5dicul> l9e2 & plac+ ! divid]s on #b1 ext5d to a2 turn ov] to ! p]p5dicul> at a2 connect ?is po9t ) #b1 & ! l9e w be ! bottom tang5t z requir$ on ! face-m\ld4 ,! upp] tang5t w be ! l9e #b-;h1 & ! angle betwe5 ! two l9es is %[n at #b4 ,make ! jo9t at h squ>e to #b-;h1 & at a squ>e to a-#b4 ,illu/ration3 ,fig4 #ajj4 ,plan ( ,curv$ ,/eps & ,/r+] at ,bottom ( ,/air4 ,! m\ld z x appe>s 9 ,fig4 #if is complete1 except ! curve1 :i* is comp>atively a small matt] to put on1 z w be %[n fur!r on4 ,! ma9 ?+ is to f9d ! angle betwe5 ! tang5ts1 :i* is %[n at #b1 to give !m ! direction to squ>e ! jo9ts4 ,9 ,fig4 #ig is %[n h[ to f9d ! angle betwe5 ! tang5ts c & d %[n 9 ,fig4 #ie1 z requir$ on ! face-m\ld4 ,on ! l9e h-#e1 make h-#d equal to ! l5g? ( ! bottom tang5t ( ! wrea?1 z %[n at h-#d 9 ,fig4 #ie2 & #d-e equal to ! l5g? ( ! upp] tang5t d4 ,measure f #d ! di/ance %[n at #d-f 9 ,fig4 #ie1 & place x f #d to #f z %[n 9 ,fig4 #ig2 ^u #f erect a p]p5dicul> l9e4 ,n[ place ! divid]s on #d2 ext5d to h2 turn ov] to cut ! p]p5dicul> 9 h2 connect ?is po9t ) #d1 & ! angle %[n at #d w be ! angle requir$ to squ>e ! jo9ts ( ! wrea? z %[n at h & #e1 :]e ! jo9t at #e is %[n drawn squ>e to ! l9e #d-e1 & ! jo9t at h squ>e to ! l9e #d h4 ,fig4 #ih is a diagram ( tang5ts & face-m\ld = a /airway hav+ a well-hole at ! top l&+4 ,! tang5ts 9 ?is example w be two equally incl9$ tang5ts = ! bottom wrea?2 & = ! top wrea?1 "o incl9$ & "o level1 ! latt] align+ ) ! level rail ( ! l&+4 ,illu/ration3 ,fig4 #aja4 ,f9d+ ,angle betwe5 ,tang5ts = ,squ>+ ,jo9ts ( ,ramp$ ,wrea?4 ,! face-m\ld1 z "h pres5t$1 w fur!r help t[>d an und]/&+ ( ! lay\t ( face-m\lds z %[n 9 ,figs4 #if & #ig4 ,x w be obs]v$ t ! pit* ( ! bottom rail is cont9u$ f a to b1 a condition caus$ by ! necessity ( jo9t+ ! wrea? to ! end ( ! /raight rail at a1 ! jo9t be+ made squ>e to bo? ! /raight rail & ! bottom tang5t a4 ,f b a l9e is drawn to d1 :i* is a fix$ po9t det]m9$ by ! numb] ( ris]s 9 ! well-hole4 ,f po9t d1 ! level tang5t d #e is drawn 9 l9e ) ! level rail ( ! l&+2 ?us ! pit*-l9e ( ! tang5ts ov] ! well-hole is f\nd1 &1 z 0 %[n 9 ! explanation ( ,fig4 #ie1 ! tang5ts z "h pres5t$ w be ^? requir$ on ! face-m\ld to squ>e ! jo9ts ( ! wrea?4 ,9 ,fig4 #ih ! tang5ts ( ! face-m\ld = ! bottom wrea? are %[n to be a & b4 ,to place tang5t a 9 position on ! face-m\ld1 x is revolv$1 z %[n by ! arc1 to m1 cutt+ a l9e previ\sly drawn f w squ>e to ! tang5t b ext5d$4 ,!n1 by connect+ m to b1 ! bottom tang5t is plac$ 9 position on ! face-m\ld4 ,! jo9t at m is to be made squ>e to x2 & ! jo9t at c1 ! o!r end ( ! m\ld1 is to be made squ>e to ! tang5t b4 ,illu/ration3 ,fig4 #ajb4 ,bottom ,/eps ) ,obtuse-,angle ,plan4 ,illu/ration3 ,fig4 #ajc4 ,develop+ ,face-,m\ld1 ,obtuse-,angle ,plan4 ,! upp] piece ( wrea? 9 ?is example is %[n to h tang5t c incl9+1 ! incl9ation be+ ! same z t ( ! upp] tang5t b ( ! bottom wrea?1 s t ! jo9t at c1 :5 made squ>e to bo? tang5ts1 w butt squ>e :5 put toge!r4 ,! tang5t d is %[n to be level1 s t ! jo9t at #e1 :5 squ>$ ) x1 w butt squ>e ) ! squ>e end ( ! level-l&+ rail4 ,! level tang5t is %[n revolv$ to its position on ! face-m\ld1 z f #e to #b4 ,9 ?is la/ position1 x w be obs]v$ t its angle ) ! incl9$ tang5t c is a "r angle2 & x %\ld be rememb]$ t 9 e simil> case :]e "o tang5t incl9es & "o is level ov] a squ>e-angle plan tang5t1 ! angle betwe5 ! two tang5ts w be a "r angle on ! face-m\ld4 ,a k ( ?is pr9ciple w enable ! /ud5t to draw ! m\ld = ?is wrea?1 z %[n 9 ,fig4 #ii1 by m]ely draw+ two l9es p]p5dicul> to ea* o!r1 z d #e & d c1 equal respectively to ! level tang5t d #e & ! incl9$ tang5t c 9 ,fig4 #ih4 ,! jo9t at #e is to be made squ>e to d #e2 & t at c1 to d c4 ,comp>+ ?is figure ) ! face-m\ld z %[n = ! upp] wrea? 9 ,fig4 #ih1 x w be obs]v$ t bo? are alike4 ,9 practical "w ! /air-build] is (t5 call$ ^u to deal ) cases 9 :i* ! conditions ( tang5ts diff] f all ! examples ?us f> giv54 ,an in/ance ( ?is sort is %[n 9 ,fig4 #ajj1 9 :i* ! angles betwe5 ! tang5ts on ! plan are acute4 ,9 all ! prec$+ examples1 ! tang5ts on ! plan 7 at "r angles2 t is1 !y 7 squ>e to "o ano!r4 ,illu/ration3 ,fig4 #ajd4 ,cutt+ ,wrea? f ,plank4 ,illu/ration3 ,fig4 #aje4 ,wrea? ,twi/$1 ,ready to be ,m\ld$4 ,fig4 #ajj is a plan ( a few curv$ /eps plac$ at ! bottom ( a /airway ) a curv$ /r+]1 :i* is /ruck f a c5t] o4 ,! plan tang5ts a & b are %[n to =m an acute angle ) ea* o!r4 ,! rail above a plan ( ?is design is usually ramp$ at ! bottom end1 :]e x int]sects ! newel po/1 &1 :5 s treat$1 ! bottom tang5t a w h to be level4 ,illu/ration3 ,fig4 #ajf4 ,twi/$ ,wrea? ,rais$ to ,position1 ) ,sides ,plumb4 ,9 ,fig4 #aja is %[n h[ to f9d ! angle betwe5 ! tang5ts on ! face-m\ld t gives !m ! correct direction = squ>+ ! jo9ts ( ! wrea? :5 x is det]m9$ to h x ramp$4 ,?is figure mu/ be drawn full size4 ,usually an ord9>y draw+-bo>d w answ] ! purpose4 ,^u ! bo>d1 reproduce ! plan ( ! tang5ts & curve ( ! c5t] l9e ( rail z %[n 9 ,fig4 #ajj4 ,measure ! height ( #e ris]s1 z %[n 9 ,fig4 #aja1 f ! floor l9e to #e2 & draw ! pit* ( ! flight adjo9+ ! wrea?1 f #e to ! floor l9e4 ,f ! newel1 draw ! dott$ l9e to w1 squ>e to ! floor l9e2 f w1 draw ! l9e w m1 squ>e to ! pit*-l9e b4 ,n[ take ! l5g? ( ! bottom level tang5t on a trammel1 or on divid]s if l>ge en\gh1 & ext5d x f n to m1 cutt+ ! l9e drawn previ\sly f w1 at m4 ,connect m to n z %[n by ! l9e a4 ,! int]section ( ?is l9e ) b det]m9es ! angle betwe5 ! two tang5ts a & b ( ! face-m\ld1 :i* gives !m ! correct direction z requir$ on ! face-m\ld = squ>+ ! jo9ts4 ,! jo9t at m is made squ>e to tang5t a2 & ! jo9t at #e1 to tang5t b4 ,illu/ration3 ,fig4 #ajg4 ,f9d+ ,bevel1 ,bottom ,tang5t ,incl9$1 ,top ,"o ,level4 ,illu/ration3 ,fig4 #ajh4 ,application ( ,bevels 9 ,fitt+ ,wrea? to ,rail4 ,9 ,fig4 #ajb is pres5t$ an example ( a few /eps at ! bottom ( a /airway 9 :i* ! tang5ts ( ! plan =m an obtuse angle ) ea* o!r4 ,! curve ( ! c5tral l9e ( ! rail 9 ?is case w be less ?an a quadrant1 &1 z %[n1 is /ruck f ! c5t] o1 ! curve cov]+ ! ?ree fir/ /eps f ! newel to ! spr++4 ,9 ,fig4 #ajc is %[n h[ to develop ! tang5ts ( ! face-m\ld4 ,reproduce ! tang5ts & curve ( ! plan 9 full size4 ,fix po9t #c at a height equal to #c ris]s f ! floor l9e2 at ?is po9t place ! pit*-bo>d ( ! flight to det]m9e ! pit* ov] ! curve z %[n f #c ?r\gh b to ! floor l9e4 ,f ! newel1 draw a l9e to w1 squ>e to ! floor l9e2 & f w1 squ>e to ! pit*-l9e b1 draw ! l9e w m2 connect m to n4 ,?is la/ l9e is ! developm5t ( ! bottom plan tang5t a2 & ! l9e b is ! developm5t ( ! plan tang5t b2 & ! angle betwe5 ! two l9es a & b w give ea* l9e its true direction z requir$ on ! face-m\ld = squ>+ ! jo9ts ( ! wrea?1 z %[n at m to connect squ>e ) ! newel1 & at #c to connect squ>e to ! rail ( ! connect+ flight4 ,illu/ration3 ,fig4 #aji4 ,face-,m\ld & ,bevel = ,wrea?1 ,bottom ,tang5t ,level1 ,top ,"o ,incl9$4 ,! wrea? 9 ?is example foll[s ! nos+ l9e ( ! /eps )\t be+ ramp$ z x 0 9 ! examples %[n 9 ,figs4 #ajj & #aja4 ,9 ^? figures ! bottom tang5t a 0 level1 :ile 9 ,fig4 #ajc x incl9es equal to ! pit* ( ! upp] tang5t b & ( ! flight adjo9+4 ,9 o!r words1 ! me?od %[n 9 ,fig4 #aja is appli$ to a con/ruction 9 :i* ! wrea? is ramp$2 :ile 9 ,fig4 #ajc ! me?od is applicable to a wrea? foll[+ ! nos+ l9e all along ! curve to ! newel4 ,! /air-build] is suppos$ to "k h[ to con/ruct a wrea? "u bo? conditions1 z ! conditions are usually det]m9$ by ! ,ar*itect4 ,illu/ration3 ,fig4 #aaj4 ,f9d+ ,bevels = ,wrea? ) ,two ,equally ,incl9$ ,tang5ts4 ,! =ego+ examples cov] all conditions ( tang5ts t are likely to turn up 9 practice1 &1 if cle>ly und]/ood1 w enable ! /ud5t to lay out ! face-m\lds = all k9ds ( curves4 ,bevels to ,squ>e ! ,wrea?s4 ,! next process 9 ! con/ruction ( a wrea? t ! h&rail] w be call$ ^u to p]=m1 is to f9d ! bevels t w1 by be+ appli$ to ea* end ( x1 give ! correct angle to squ>e or twi/ x :5 w9d+ ar\nd ! well-hole f "o flight to ano!r flight1 or f a flight to a l&+1 z ! case may be4 ,illu/ration3 ,fig4 #aaa4 ,application ( ,bevels to ,wrea? ,asc5d+ on ,plane ,incl9$ ,equally 9 ,two ,directions4 ,illu/ration3 ,fig4 #aab4 ,f9d+ ,bevel ,:]e ,upp] ,tang5t ,incl9es ,m ,?an ,l[] ,"o4 ,! wrea? is fir/ cut f ! plank squ>e to its surface z %[n 9 ,fig4 #ajd4 ,aft] ! application ( ! bevels1 x is twi/$1 z %[n 9 ,fig4 #aje1 ready to be m\ld$2 & :5 9 position1 asc5d+ f "o end ( ! curve to ! o!r end1 ov] ! incl9$ plane ( ! section ar\nd ! well-hole1 its sides w be plumb1 z %[n 9 ,fig4 #ajf at b4 ,9 ?is figure1 z also 9 ,fig4 #aje1 ! wrea? a lies 9 a horizontal position 9 :i* its sides appe> to be out ( plumb z mu* z ! bevels are out ( plumb4 ,9 ! upp] "p ( ! figure1 ! wrea? b is %[n plac$ 9 its position ^u ! plane ( ! section1 :]e its sides are se5 to be plumb4 ,x is evid5t1 z %[n 9 ! relative position ( ! wrea? 9 ?is figure1 t1 if ! bevel is ! correct angle ( ! plane ( ! section :]eon ! wrea? b re/s 9 its asc5t ov] ! well-hole1 ! wrea? w 9 t case h its sides plumb all along :5 9 position4 ,x is = ?is purpose t ! bevels are ne$$4 ,illu/ration3 ,fig4 #aac4 ,f9d+ ,bevel ,:]e ,upp] ,tang5t ,incl9es ,less ,?an ,l[] ,"o4 ,a me?od ( f9d+ ! bevels = all wrea?s 7:i* is consid]$ r difficult7 w n[ be expla9$3 ,fir/ ,case4 ,9 ,fig4 #ajg is %[n a case :]e ! bottom tang5t ( a wrea? is incl9+1 & ! top "o level1 simil> to ! top wrea? %[n 9 ,fig4 #ih4 ,x has already be5 not$ t ! plane ( ! section = ?is k9d ( wrea? incl9es to "o side only2 !re=e "o bevel only w be requir$ to squ>e x1 :i* is %[n at d1 ,fig4 #ajg4 ,a view ( ?is plane is giv5 9 ,fig4 #ajh2 & ! bevel d1 z !re %[n1 indicates ! angle ( ! incl9ation1 :i* also is ! bevel requir$ to squ>e ! end d ( ! wrea?4 ,! bevel is %[n appli$ to ! end ( ! l&+ rail 9 exactly ! same mann] 9 :i* x is to be appli$ to ! end ( ! wrea?4 ,! true bevel = ?is wrea? is f\nd at ! upp] angle ( ! pit*-bo>d4 ,at ! end a1 z already /at$1 no bevel is requir$1 ow+ to ! plane incl9+ 9 "o direction only4 ,fig4 #aji %[s a face-m\ld & bevel = a wrea? ) ! bottom tang5t level & ! top tang5t incl9+1 su* z ! piece at ! bottom connect+ ) ! l&+ rail 9 ,fig4 #id4 ,illu/ration3 ,fig4 #aad4 ,f9d+ ,bevel ,:]e ,tang5ts ,incl9e ,equally ov] ,obtuse-,angle ,plan4 ,illu/ration3 ,fig4 #aae4 ,same ,plan z 9 ,fig4 #aad1 b ) ,bottom ,tang5t ,level4 ,second ,case4 ,x may be requir$ to f9d ! bevels = a wrea? hav+ two equally incl9$ tang5ts4 ,an example ( ?is k9d also is %[n 9 ,fig4 #id1 :]e bo? ! tang5ts c & d ( ! upp] wrea? incl9e equally4 ,two bevels are requir$ 9 ?is case1 because ! plane ( ! section is incl9$ 9 two directions2 b1 ow+ to ! incl9ations be+ alike1 x foll[s t ! two w be ! same4 ,!y are to be appli$ to bo? ends ( ! wrea?1 &1 z %[n 9 ,fig4 #aje1 9 ! same direction--namely1 t[>d ! inside ( ! wrea? = ! bottom end1 & t[>d ! outside = ! upp] end4 ,illu/ration3 ,fig4 #aaf4 ,f9d+ ,bevels = ,wrea? ( ,fig4 #aae4 ,9 ,fig4 #aaj ! me?od ( f9d+ ! bevels is %[n4 ,a l9e is drawn f w to c1 squ>e to ! pit* ( ! tang5ts1 & turn$ ov] to ! gr\nd l9e at h1 :i* po9t is connect$ to a z %[n4 ,! bevel is at h4 ,to %[ t equal tang5ts h equal bevels1 ! l9e m is drawn1 hav+ ! same incl9ation z ! bottom tang5t c1 b 9 ano!r direction4 ,place ! divid]s on o1 & turn to t\* ! l9es d & m1 z %[n by ! semicircle4 ,! l9e f o to n is equal to ! side plan tang5t w a1 & bo? ! bevels "h %[n are equal to ! "o already f\nd4 ,!y repres5t ! angle ( incl9ation ( ! plane :]eon ! wrea? asc5ds1 a view ( :i* is giv5 9 ,fig4 #aaa1 :]e ! plane is %[n to incl9e equally 9 two directions4 ,at bo? ends is %[n a section ( a rail2 & ! bevels are appli$ to %[ h[1 by means ( !m1 ! wrea? is squ>$ or twi/$ :5 w9d+ ar\nd ! well-hole & asc5d+ ^u ! plane ( ! section4 ,! view giv5 9 ?is figure w enable ! /ud5t to und]/& ! nature ( ! bevels f\nd 9 ,fig4 #aaj = a wrea? hav+ two equally incl9$ tang5ts2 also = all o!r wrea?s ( equally incl9$ tang5ts1 9 t e wrea? 9 su* case is assum$ to re/ ^u an incl9$ plane 9 its asc5t ov] ! well-hole1 ! bevel 9 e case be+ ! angle ( ! incl9$ plane4 ,illu/ration3 ,fig4 #aag4 ,upp] ,tang5t ,incl9$4 ,l[] ,tang5t ,level1 ,ov] ,acute-,angle ,plan4 ,?ird ,case4 ,9 ?is example1 two unequal tang5ts are giv51 ! upp] tang5t incl9+ m ?an ! bottom "o4 ,! me?od %[n 9 ,fig4 #aaj to f9d ! bevels = a wrea? ) two equal tang5ts1 is applicable to all conditions ( v>iation 9 ! incl9ation ( ! tang5ts4 ,9 ,fig4 #aab is %[n a case :]e ! upp] tang5t d incl9es m ?an ! bottom "o c4 ,! me?od 9 all cases is to cont9ue ! l9e ( ! upp] tang5t d1 ,fig4 #aab1 to ! gr\nd l9e z %[n at n2 f n1 draw a l9e to a1 :i* w be ! horizontal trace ( ! plane4 ,n[1 f o1 draw a l9e p>allel to a n1 z %[n f o to d1 ^u d1 erect a p]p5dicul> l9e to cut ! tang5t d1 z %[n1 at m2 & draw ! l9e m u o4 ,make u o equal to ! l5g? ( ! plan tang5t z %[n by ! arc f o4 ,put "o leg ( ! divid]s on u2 ext5d to t\* ! upp] tang5t d1 & turn ov] to #a2 connect #a to o2 ! bevel at #a is to be appli$ to tang5t d4 ,aga9 place ! divid]s on u2 ext5d to ! l9e h1 & turn ov] to #b z %[n2 connect #b to o1 & ! bevel %[n at #b w be ! "o to apply to ! bottom tang5t c4 ,x w be obs]v$ t ! l9e h repres5ts ! bottom tang5t4 ,x is ! same l5g? & has ! same incl9ation4 ,an example ( ?is k9d ( wrea? 0 %[n 9 ,fig4 #ie1 :]e ! upp] tang5t d is %[n to incl9e m ?an ! bottom tang5t c 9 ! top piece ext5d+ f h to #e4 ,bevel #a1 f\nd 9 ,fig4 #aab1 is ! real bevel = ! end #e2 & bevel #b1 = ! end h ( ! wrea? %[n f h to #e 9 ,fig4 #ie4 ,illu/ration3 ,fig4 #aah4 ,f9d+ ,bevels = ,wrea? ( ,plan1 ,fig4 #aag4 ,f\r? ,case4 ,9 ,fig4 #aac is %[n h[ to f9d ! bevels = a wrea? :5 ! upp] tang5t incl9es less ?an ! bottom tang5t4 ,?is example is ! rev]se ( ! prec$+ "o2 x is ! condition ( tang5ts f\nd 9 ! bottom piece ( wrea? %[n 9 ,fig4 #ie4 ,to f9d ! bevel1 cont9ue ! upp] tang5t b to ! gr\nd l9e1 z %[n at n2 connect n to a1 :i* w be ! horizontal trace ( ! plane4 ,f o1 draw a l9e p>allel to n a1 z %[n f o to d2 ^u d1 erect a p]p5dicul> l9e to cut ! cont9u$ portion ( ! upp] tang5t b 9 m2 f m1 draw ! l9e m u o across z %[n4 ,n[ place ! divid]s on u2 ext5d to t\* ! upp] tang5t1 & turn ov] to #a1 connect #a to o2 ! bevel at #a w be ! "o to apply to ! tang5t b at h1 :]e ! two wrea?s are %[n connect$ 9 ,fig4 #ie4 ,aga9 place ! divid]s on u2 ext5d to t\* ! l9e c2 turn ov] to #b2 connect #b to o2 ! bevel at #b is to be appli$ to ! bottom tang5t a at ! jo9t :]e x is %[n to connect ) ! rail ( ! flight4 ,fif? ,case4 ,9 ?is case we h two equally incl9$ tang5ts ov] an obtuse-angle plan4 ,9 ,fig4 #ajb is %[n a plan ( ?is k9d2 & 9 ,fig4 #ajc1 ! developm5t ( ! face-m\ld4 ,9 ,fig4 #aad is %[n h[ to f9d ! bevel4 ,f a1 draw a l9e to a1 squ>e to ! gr\nd l9e4 ,place ! divid]s on a2 ext5d to t\* ! pit* ( tang5ts1 & turn ov] z %[n to m2 connect m to a4 ,! bevel at m w be ! only "o requir$ = ?is wrea?1 b x w h to be appli$ to bo? ends1 ow+ to ! two tang5ts be+ incl9$4 ,six? ,case4 ,9 ?is case we h "o tang5t incl9+ & "o tang5t level1 ov] an acute-angle plan4 ,illu/ration3 ,fig4 #aai4 ,lay+ ,out ,curves on ,face-,m\ld ) ,p9s & ,/r+4 ,9 ,fig4 #aae is %[n ! same plan z 9 ,fig4 #aad2 b 9 ?is case ! bottom tang5t a is to be a level tang5t4 ,probably ?is condition is ! mo/ commonly met ) 9 wrea? con/ruction at ! pres5t "t4 ,a small curve is consid]$ to add to ! appe>ance ( ! /air & rail2 & consequ5tly x has become almo/ a 8fad0 to h a little curve or /ret*-out at ! bottom ( ! /airway1 & 9 mo/ cases ! rail is ramp$ to int]sect ! newel at "r angles in/ead ( at ! pit* ( ! flight4 ,9 su* a case1 ! bottom tang5t a w h to be a level tang5t1 z %[n at a 9 ,fig4 #aae1 ! pit* ( ! flight be+ ov] ! plan tang5t b only4 ,to f9d ! bevels :5 tang5t b incl9es & tang5t a is level1 make a c 9 ,fig4 #aaf equal to a c 9 ,fig4 #aae4 ,?is l9e w be ! base ( ! two bevels4 ,^u a1 erect ! l9e a w m at "r angles to a c2 make a w equal to o w 9 ,fig4 #aae2 connect w & c2 ! bevel at w w be ! "o to apply to tang5t b at n :]e ! wrea? is jo9$ to ! rail ( ! flight4 ,aga91 make a m 9 ,fig4 #aaf equal ! di/ance %[n 9 ,fig4 #aae betwe5 w & m1 :i* is ! full height ov] :i* tang5t b is incl9$2 connect m to c 9 ,fig4 #aaf1 & at m is ! bevel to be appli$ to ! level tang5t a4 ,illu/ration3 ,fig4 #abj4 ,simple ,me?od ( ,draw+ ,curves on ,face-,m\ld4 ,illu/ration3 ,fig4 #aba4 ,tang5ts1 ,bevels1 ,m\ld-,curves1 etc41 f ,bottom ,wrea? ( ,fig4 #ie1 ,9 :i* ,upp] ,tang5t ,incl9es ,less ?an ,l[] ,"o4 ,sev5? ,case4 ,9 ?is case1 illu/rat$ 9 ,fig4 #aag1 ! upp] tang5t b is %[n to incl9e1 & ! bottom tang5t a to be level1 ov] an acute-angle plan4 ,! plan "h is ! same z t 9 ,fig4 #ajj1 :]e a curve is %[n to /ret* out f ! l9e ( ! /raight /r+] at ! bottom ( a flight to a newel1 & is l>ge en\gh to conta9 five treads1 :i* are gracefully r\nd$ to cut ! curve ( ! c5tral l9e ( rail 9 #a1 #b1 #c1 #d4 ,?is curve also may be us$ to connect a l&+ rail to a flight1 ei!r at top or bottom1 :5 ! plan is acute-angl$1 z w be %[n fur!r on4 ,illu/ration3 ,fig4 #abb4 ,develop$ ,section ( ,plane ,incl9+ ,unequally 9 ,two ,directions4 ,illu/ration3 ,fig4 #abc4 ,arrang+ ,ris]s ar\nd ,well-,hole on ,level ,l&+ ,/air1 ) ,radius ( ,c5tral ,l9e ( ,rail ,"o-,half ,wid? ( ,tread4 ,to f9d ! bevels--= !re w be two bevels necess>y = ?is wrea?1 ow+ to "o tang5t b be+ incl9$ & ! o!r tang5t a be+ level--make a c1 ,fig4 #aah1 equal to a c 9 ,fig4 #aag1 :i* is a l9e drawn squ>e to ! gr\nd l9e f ! newel & %[n 9 all prec$+ figures to h be5 us$ = ! base ( a triangle conta9+ ! bevel4 ,make a w 9 ,fig4 #aah equal to w o 9 ,fig4 #aag1 :i* is a l9e drawn squ>e to ! incl9$ tang5t b f w2 connect w & c 9 ,fig4 #aah4 ,! bevel %[n at w w be ! "o to be appli$ to ! jo9t #e on tang5t b1 ,fig4 #aag4 ,aga91 make a m 9 ,fig4 #aah equal to ! di/ance %[n 9 ,fig4 #aag betwe5 ! l9e repres5t+ ! level tang5t & ! l9e m #e1 :i* is ! height t tang5t b is %[n to rise2 connect m to c 9 ,fig4 #aah2 ! bevel %[n at m is to be appli$ to ! end t int]sects ) ! newel z %[n at m 9 ,fig4 #aag4 ,! wrea? is %[n develop$ 9 ,fig4 #aja = ?is case2 s t1 ) ,fig4 #ajj = plan1 ,fig4 #aja = ! developm5t ( ! wrea?1 & ,figs4 #aag & #aah = f9d+ ! bevels1 ! me?od ( h&l+ any simil> case 9 practical "w c be f\nd4 ,h[ to ,put ! ,curves on ! ,face-,m\ld4 ,x has be5 %[n h[ to f9d ! angle betwe5 ! tang5ts ( ! face-m\ld1 & t ! angle is = ! purpose ( squ>+ ! jo9ts at ! ends ( ! wrea?4 ,9 ,fig4 #aai is %[n h[ to lay out ! curves by means ( p9s & a /r+--a v common practice among /air-build]s4 ,9 ?is example ! face-m\ld has equal tang5ts z %[n at c & d4 ,! angle betwe5 ! two tang5ts is %[n at m z x w be requir$ on ! face-m\ld4 ,9 ?is figure a l9e is drawn f m p>allel to ! l9e drawn f h1 :i* is m>k$ 9 ! diagram z 8,direct+ ,ord9ate ( ,section40 ,! l9e drawn f m w conta9 ! m9or axes2 & a l9e drawn ?r\gh ! corn] ( ! section at #c w conta9 ! major axes ( ! ellipses t w con/itute ! curves ( ! m\ld4 ,illu/ration3 ,fig4 #abd4 ,arrangem5t ( ,ris]s ,ar\nd ,well-,hole ) ,radius ,l>g] ,?an ,"o-,half ,wid? ( ,tread4 ,illu/ration3 ,fig4 #abe4 ,arrangem5t ( ,ris]s ar\nd ,well-,hole1 ) ,ris]s ,spac$ ,full ,wid? ( ,tread4 ,illu/ration3 ,fig4 #abf4 ,plan ( ,/air ,%[n 9 ,fig4 #abc4 ,illu/ration3 ,fig4 #abg4 ,plan ( ,/air ,%[n 9 ,fig4 #abd4 ,illu/ration3 ,fig4 #abh4 ,plan ( ,/air ,%[n 9 ,fig4 #abe4 ,illu/ration3 ,fig4 #abi4 ,draw+ ,face-,m\ld = ,wrea? f ,pit*-,bo>d4 ,! major is to be drawn squ>e to ! m9or1 z %[n4 ,place1 f po9t #c1 ! circle %[n on ! m9or1 at ! same di/ance z ! circle 9 ! plan is fix$ f ! po9t o4 ,! diamet] ( ?is circle indicates ! wid? ( ! curve at ?is po9t ,! wid? at ea* end is det]m9$ by ! bevels4 ,! di/ance a b1 z %[n ^u ! long edge ( ! bevel1 is equal to ! wid? ( ! m\ld1 & is ! hypot5use ( a "r-angl$ triangle ^: base is ! wid? ( ! rail4 ,by plac+ ?is dim5sion on ea* side ( n1 z %[n at b & b1 & on ea* side ( h on ! o!r end ( ! m\ld1 z %[n also at b & b1 we obta9 ! po9ts b #b b on ! inside ( ! curve1 & ! po9ts b #a b on ! outside4 ,x w n[ be necess>y to f9d ! elliptical curves t w conta9 ^! po9ts2 & be=e ?is c be done1 ! exact l5g? ( ! m9or & major axes respectively mu/ be det]m9$4 ,! l5g? ( ! m9or axis = ! inside curve w be ! di/ance %[n f #c to #b2 & its l5g? = ! outside w be ! di/ance %[n f #c to #a4 ,to f9d ! l5g? ( ! major axis = ! inside1 take ! l5g? ( half ! m9or = ! inside on ! divid]s3 place "o leg on b1 ext5d to cut ! major 9 z1 cont9ue to ! m9or z %[n at k4 ,! di/ance f b to k w be ! l5g? ( ! semi-major axis = ! inside curve4 ,illu/ration3 ,fig4 #acj4 ,developm5t ( ,face-,m\ld = ,wrea? ,connect+ ,rail ( ,flight ) ,level-,l&+ ,rail4 ,to draw ! curve1 ! po9ts or foci :]e ! p9s are to be fix$ mu/ be f\nd on ! major axis4 ,to f9d ^! po9ts1 take ! l5g? ( b k 7:i* is1 z previ\sly f\nd1 ! exact l5g? ( ! semi-major = ! inside curve7 on ! divid]s2 fix "o leg at #b1 & describe ! arc ,y1 cutt+ ! major :]e ! p9s are %[n fix$1 at o & o4 ,n[ take a piece ( /r+ long en\gh to =m a loop ar\nd ! two & ext5d+1 :5 tight1 to #b1 :]e ! p5cil is plac$2 &1 keep+ ! /r+ tight1 sweep ! curve f b to b4 ,illu/ration3 ,fig4 #aca4 ,arrang+ ,ris]s 9 ,qu>t]-,turn betwe5 ,two ,flights4 ,! same me?od1 = f9d+ ! major & foci = ! outside curve1 is %[n 9 ! diagram4 ,! l9e drawn f b on ! outside ( ! jo9t at n1 to w1 is ! semi-major = ! outside curve2 & ! po9ts :]e ! outside p9s are %[n on ! major w be ! foci4 ,illu/ration3 ,fig4 #acb4 ,arrangem5t ( ,ris]s ar\nd ,qu>t]-,turn ,giv+ ,tang5ts ,equal ,pit* ) ,connect+ ,flight4 ,illu/ration3 ,fig4 #acc4 ,f9d+ ,bevel = ,wrea? ( ,plan1 ,fig4 #acb4 ,to draw ! curves ( ! m\ld accord+ to ?is me?od1 :i* is a sci5tific "o1 may seem a complicat$ problem2 b once x is und]/ood1 x becomes v simple4 ,a simpl] way to draw !m1 h[ev]1 is %[n 9 ,fig4 #abj4 ,! wid? on ! m9or & at ea* end w h to be det]m9$ by ! me?od j expla9$ 9 connection ) ,fig4 #aai4 ,9 ,fig4 #abj1 ! po9ts b at ! ends1 & ! po9ts 9 :i* ! circumf]5ce ( ! circle cuts ! m9or axis1 w be po9ts conta9$ 9 ! curves1 z already expla9$4 ,n[ take a flexible la?2 b5d x to t\* b1 z1 & b = ! inside curve1 & b1 w1 & b = ! outside curve4 ,?is me?od is h&y :]e ! curve is comp>atively flat1 z 9 ! example "h %[n2 b :]e ! m\ld has a %>p curvature1 z 9 case ( ! "o %[n 9 ,fig4 #aja1 ! me?od %[n 9 ,fig4 #aai mu/ be adh]$ to4 ,illu/ration3 ,fig4 #acd4 ,well-,hole ) ,ris] 9 ,c5t]4 ,tang5ts ( ,face-,m\ld1 & ,c5tral ,l9e ( ,rail1 ,develop$4 ,) a cle> k ( ! above two me?ods1 ! /ud5t w be able to put curves on any m\ld4 ,! m\ld %[n 9 ^! two diagrams1 ,figs4 #aai & #abj1 is = ! upp] wrea?1 ext5d+ f h to n 9 ,fig4 #id4 ,a practical h&rail] w\ld draw only :at is %[n 9 ,fig4 #abj4 ,he w\ld take ! l5g?s ( tang5ts f ,fig4 #id1 & place !m z %[n at h m & m n4 ,by comp>+ ,fig4 #abj ) ! tang5ts ( ! upp] wrea? 9 ,fig4 #id1 x w be easy = ! /ud5t to und]/& ! rema9+ l9es %[n 9 ,fig4 #abj4 ,! bevels are %[n appli$ to ! m\ld 9 ,fig4 #aje1 to give x ! twi/4 ,9 ,fig4 #ajf1 is %[n h[1 aft] ! rail is twi/$ & plac$ 9 position ov] & above ! quadrant c d 9 ,fig4 #id1 its sides w be plumb4 ,illu/ration3 ,fig4 #ace4 ,arrangem5t ( ,ris]s 9 ,/air ) ,obtuse-,angle ,plan4 ,illu/ration3 ,fig4 #acf4 ,arrangem5t ( ,ris]s 9 ,obtuse-,angle ,plan1 ,giv+ ,equal ,pit* ov] ,tang5ts & ,flights4 ,face-,m\ld ,develop$4 ,9 ,fig4 #aba are %[n ! tang5ts tak5 f ! bottom wrea? 9 ,fig4 #ie4 ,x 0 %[n h[ to develop ! section & f9d ! angle = ! tang5ts 9 ! face-m\ld1 9 ,fig4 #aac4 ,! me?od %[n 9 ,fig4 #aai = putt+ on ! curves1 w\ld be ! mo/ suitable4 ,illu/ration3 ,fig4 #acg4 ,arrangem5t ( ,ris]s 9 ,flight ) ,curve at ,l&+4 ,fig4 #aba is pres5t$ m = ! purposes ( /udy ?an z a me?od ( con/ruction4 ,x conta9s all ! l9es made use ( to f9d ! develop$ section ( a plane incl9+ unequally 9 two diff]5t directions1 z %[n 9 ,fig4 #abb4 ,illu/ration3 ,fig4 #ach4 ,developm5t ( ,face-,m\lds = ,plan1 ,fig4 #acg4 ,arrangem5t ( ,ris]s 9 & ar\nd ,well-,hole4 ,an important matt] 9 wrea? con/ruction is to h a k ( h[ to arrange ! ris]s 9 & ar\nd a well-hole4 ,a great deal ( labor & mat]ial is sav$ ?r\gh x2 also a f> bett] appe>ance to ! f9i%$ rail may be secur$4 ,9 level-l&+ /airways1 ! easie/ example is ! "o %[n 9 ,fig4 #abc1 9 :i* ! radius ( ! c5tral l9e ( rail is made equal to "o-half ! wid? ( a tread4 ,9 ! diagram ! radius is %[n to be #e in*es1 & ! treads #aj in*es4 ,! ris]s are plac$ 9 ! spr++1 z at a & a4 ,! elevation ( ! tang5ts by ?is arrangem5t w be1 z %[n1 "o level & "o incl9$1 = ea* piece ( wrea?4 ,:5 9 ?is position1 !re is no tr\ble 9 f9d+ ! angle ( ! tang5t z requir$ on ! face-m\ld1 ow+ to t angle1 z 9 e su* case1 be+ a "r angle1 z %[n at w2 also no special bevel w h to be f\nd1 because ! upp] bevel ( ! pit*-bo>d conta9s ! angle requir$4 ,! same results are obta9$ 9 ! example %[n 9 ,fig4 #abd1 9 :i* ! radius ( ! well-hole is l>g] ?an half ! wid? ( a tread1 by plac+ ! ris] a at a di/ance f c equal to half ! wid? ( a tread1 in/ead ( at ! spr++ z 9 ! prec$+ example4 ,9 ,fig4 #abe is %[n a case :]e ! ris]s are plac$ at a di/ance f c equal to a full tread1 ! effect 9 respect to ! tang5ts ( ! face-m\ld & bevel be+ ! same z 9 ! two prec$+ examples4 ,9 ,fig4 #abf is %[n ! plan ( ,fig4 #abc2 9 ,fig4 #abg1 ! plan ( ,fig4 #abd2 & 9 ,fig4 #abh1 ! plan ( ,fig4 #abe4 ,= ! wrea?s %[n 9 all ^! figures1 !re w be no necessity ( spr++ ! plank1 :i* is a t]m us$ 9 h&rail+ to d5ote ! twi/+ ( ! wrea?2 & no o!r bevel ?an ! "o at ! upp] end ( ! pit*-bo>d w be requir$4 ,?is type ( wrea?1 also1 is ! "o t is requir$ at ! top ( a l&+ :5 ! rail ( ! flight int]sects ) a level-l&+ rail4 ,9 ,fig4 #abi is %[n a v simple me?od ( draw+ ! face-m\ld = ?is wrea? f ! pit*-bo>d4 ,make a c equal to ! radius ( ! plan c5tral l9e ( rail z %[n at ! curve 9 ,fig4 #acj4 ,f :]e l9e c c cuts ! long side ( ! pit*-bo>d1 ! l9e c a is drawn at "r angles to ! long edge1 & is made equal to ! l5g? ( ! plan tang5t a c1 ,fig4 #acj4 ,! curve is drawn by means ( p9s & /r+ or a trammel4 ,9 ,fig4 #aca is %[n a qu>t]-turn betwe5 two flights4 ,! correct me?od ( plac+ ! ris]s 9 & ar\nd ! curve1 is to put ! la/ "o 9 ! fir/ flight & ! fir/ "o 9 ! second flight "o-half a /ep f ! int]section ( ! cr[n tang5ts4 ,by ?is arrangem5t1 z %[n 9 ,fig4 #acb1 ! pit*-l9e ( ! tang5ts w equal ! pit* ( ! connect+ flight1 ?us secur+ ! second easie/ condition ( tang5ts = ! face-m\ld--namely1 z %[n1 two equal tang5ts4 ,= ?is wrea?1 only "o bevel w be ne$$1 & x is made up ( ! radius ( ! plan c5tral l9e ( ! rail o c1 ,fig4 #aca1 = base1 & ! l9e #a-b1 ,fig4 #acb1 = altitude1 z %[n 9 ,fig4 #acc4 ,! bevel %[n 9 ?is figure has be5 previ\sly expla9$ 9 ,figs4 #aje & #ajf4 ,x is to be appli$ to bo? ends ( ! wrea?4 ,! example %[n 9 ,fig4 #acd is ( a well-hole hav+ a ris] 9 ! c5t]4 ,if ! radius ( ! plan c5tral l9e ( rail is made equal to "o-half a tread1 ! pit* ( tang5ts w be ! same z ( ! flights adjo9+1 ?us secur+ two equal tang5ts = ! two sections ( wrea?4 ,9 ?is figure ! tang5ts ( ! face-m\ld are develop$1 & also ! c5tral l9e ( ! rail1 z %[n ov] & above ea* quadrant & ^u ! pit*-l9e ( tang5ts4 ,! same me?od may be employ$ 9 /airways hav+ obtuse-angle & acute-angle plans1 z %[n 9 ,fig4 #ace1 9 :i* two flights are plac$ at an obtuse angle to ea* o!r4 ,if ! ris]s %[n at a & a are plac$ "o-half a tread f c1 ?is w produce 9 ! elevation a pit*-l9e ov] ! tang5ts equal to t ov] ! flights adjo9+1 z %[n 9 ,fig4 #acf1 9 :i* also is %[n ! face-m\ld = ! wrea? t w span ov] ! curve f "o flight to ano!r4 ,9 ,fig4 #acg is %[n a flight hav+ ! same curve at a l&+4 ,! same arrangem5t is adh]$ to respect+ ! plac+ ( ! ris]s1 z %[n at a & a4 ,9 ,fig4 #ach is %[n h[ to develop ! face-m\lds4 ,illu/ration3 ,,f9i%$ ,,ro( ,,truss ,,9 ,,fir/ ,,presbyt]ian ,,*ur*1 ,,syracuse1 ,n4 ,y4 ,tracy ,sw>tw\t1 ,ar*itects2 ,ballantyne ,evans1 ,associat$4 ,reproduc$ by c\rtesy ( 8,! ,ar*itectural ,review40 ,,"p ,,ii ,,! ,,/eel ,,squ>e ,introductory4 ,! ,/&>d ,/eel ,squ>e has a blade #bd in*es long & #b in*es wide1 & a tongue f #ad to #ah in*es long & #a in*es wide4 ,! blade is at "r angles to ! tongue4 ,! face ( ! squ>e is %[n 9 ,fig4 #a4 ,x is always /amp$ ) ! manufactur]'s "n & numb]4 ,! rev]se is ! back 7see ,fig4 #b74 ,! long] arm is ! blade2 ! %ort] arm1 ! tongue4 ,9 ! c5t] ( ! tongue1 on ! face side1 w be f\nd two p>allel l9es divid$ into spaces 7see ,fig4 #a72 ?is is ! octagon scale4 ,! spaces w be f\nd numb]$ #aj1 #bj1 #cj1 #dj1 #ej1 #fj1 & #gj1 :5 ! tongue is #ah in*es long4 ,to draw an octagon ( #h in*es squ>e1 draw an #h in* squ>e & !n draw a p]p5dicul> & a horizontal l9e ?r\gh its c5t]4 ,to f9d ! l5g? ( ! octagon side1 place "o po9t ( a compass on any ( ! ma9 divisions ( ! scale1 & ! o!r po9t ( ! compass on ! eigh? subdivision2 !n /ep ?is l5g? (f on ea* side ( ! c5t] l9es on ! side ( ! squ>e1 :i* w give ! po9ts f :i* to draw ! octagon l9es4 ,! diamet] ( ! octagon mu/ equal 9 in*es ! numb] ( spaces tak5 f ! squ>e4 ,on ! opposite side ( ! tongue1 9 ! c5t]1 w be f\nd ! brace rule 7see ,fig4 #c74 ,! fractions d5ote ! rise & run ( ! brace1 & ! decimals ! l5g?4 ,= example1 a brace ( #cf in*es run & #cf in*es rise1 has a l5g? ( #ej4ia in*es2 a brace ( #db in*es run & #db in*es rise1 has a l5g? ( #ei4dj in*es2 etc4 ,illu/ration3 ,fig4 #a4 ,face ,side ( ,tongue ( ,/eel ,squ>e1 ,%[+ ,octagon ,scale4 ,illu/ration3 ,fig4 #b4 ,back ( ,blade ( ,/eel ,squ>e1 ,%[+ ,raft] ,table4 ,illu/ration3 ,fig4 #c4 ,back ( ,tongue ( ,/eel ,squ>e1 ,%[+ ,brace ,measure4 ,illu/ration3 ,fig4 #d4 ,back ( ,blade ( ,/eel ,squ>e1 ,%[+ ,essex ,bo>d ,measure4 ,on ! back ( ! blade 7,fig4 #d7 w be f\nd ! bo>d measure1 :]e eight p>allel l9es runn+ along ! l5g? ( ! blade are %[n & divid$ at e in* by cross-l9es4 ,"u #ab1 on ! out] edge ( ! blade1 w be f\nd ! v>i\s l5g?s ( ! bo>ds1 z #h1 #i1 #aj1 #aa1 #ab1 etc4 ,= example1 take a bo>d #ad feet long & #i in*es wide4 ,to f9d ! cont5ts1 look "u #ab1 & f9d #ad2 !n foll[ ?is space along to ! cross-l9e "u #i1 ! wid? ( ! bo>d2 & "h is f\nd #aj feet #f in*es1 d5ot+ ! cont5ts ( a bo>d #ad feet long & #i in*es wide4 ,to ,f9d ! ,mit] & ,l5g? ( ,side = any ,polygon1 ) ! ,/eel ,squ>e4 ,9 ,fig4 #e is %[n a p5tagon figure4 ,! mit]s ( ! p5tagon /& at #gb degrees ) ea* o!r1 & are f\nd by divid+ #cfj by #e1 ! numb] ( sides 9 ! p5tagon4 ,b ! angle :5 appli$ to ! squ>e to obta9 ! mit]1 is only "o-half ( #gb1 or #cf degrees1 & int]sects ! blade at #h-bc_/cb1 z %[n 9 ,fig4 #e4 ,illu/ration3 ,fig4 #e4 ,use ( ,/eel ,squ>e to ,f9d ,mit] & ,side ( ,p5tagon4 ,by squ>+ up f #f on ! tongue1 int]sect+ ! degree l9e at a1 ! c5t] a is det]m9$ ei!r = ! inscrib$ or ! circumscrib$ diamet]1 ! radii be+ a b & a c1 respectively4 ,! l5g? ( ! sides w be #h-bc_/cb in*es to ! foot4 ,illu/ration3 ,fig4 #f4 ,use ( ,/eel ,squ>e to ,f9d ,mit] & ,side ( ,hexagon4 ,if ! l5g? ( ! inscrib$ diamet] be #h feet1 !n ! sides w\ld be #h #h-bc_/cb in*es4 ,! figures to use = o!r polygons are z foll[s3 ,triangle #bj-be_/cb ,squ>e #ab ,hexagon #g ,nonagon #d ,decagon #c ,9 ,fig4 #f ! same process is us$ 9 f9d+ ! mit] & side ( ! hexagon polygon4 ,to f9d ! degree l9e1 #cfj is divid$ by #f1 ! numb] ( sides1 z foll[s3 #cfj #f #fj2 & #fj #b #cj degrees4 ,n[1 f #ab on tongue1 draw a l9e mak+ an angle ( #cj degrees ) ! tongue4 ,x w cut ! blade 9 #g z %[n2 & f #g to m1 ! heel ( ! squ>e1 w be ! l5g? ( ! side4 ,f #f on tongue1 erect a l9e to cut ! degree l9e 9 c2 & ) c z c5t]1 describe a circle hav+ ! radius ( c #g2 & ar\nd ! circle1 complete ! hexagon by tak+ ! l5g? #g m ) ! compass = ea* side1 z %[n4 ,illu/ration3 ,fig4 #g4 ,use ( ,/eel ,squ>e to ,f9d ,mit] & ,side ( ,octagon4 ,9 ,fig4 #g ! same process is %[n appli$ to ! octagon4 ,! degree l9e 9 all ! polygons is f\nd by divid+ #cfj by ! numb] ( sides 9 ! figure3 #cfj #h #de2 & #de #b #bb degrees4 ,?is gives ! degree l9e = ! octagon4 ,complete ! process z 0 describ$ = ! o!r polygons4 ,by us+ ! foll[+ figures = ! v>i\s polygons1 ! mit] l9es may be f\nd2 b 9 ^! figures no acc\nt is tak5 ( ! relative size ( sides to ! foot z 9 ! figures prec$+3 ,triangle #g 94 & #d 94 ,p5tagon #aa #h ,hexagon #d #g ,heptagon #ab #f ,octagon #ag #g ,nonagon #bb #i ,decagon #i #c ,! mit] is to be drawn along ! l9e ( ! fir/ column1 z %[n = ! triangle 9 ,fig4 #h1 & = ! hexagon 9 ,fig4 #i4 ,9 ,fig4 #aj is %[n a diagram = f9d+ degrees on ! squ>e4 ,= example1 if a pit* ( #ce degrees is requir$1 use #h-ac_/cb on tongue & #ab on blade2 if #de degrees1 use #ab on tongue & #ab on blade2 etc4 ,illu/ration3 ,fig4 #h4 ,use ( ,squ>e to ,f9d ,mit] ( ,equilat]al ,triangle4 ,9 ,fig4 #aa is %[n ! relative l5g? ( run = a raft] & a hip1 ! raft] be+ #ab in*es & ! hip #ag in*es4 ,! reason1 z %[n 9 ?is diagram1 :y #ag is tak5 = ! run ( ! hip1 in/ead ( #ab z = ! common raft]1 is t ! seats ( ! common raft] & hip d n run p>allel ) ea* o!r1 b div]ge 9 ro(s ( equal pit* at an angle ( #de degrees2 !re=e1 #ag in*es tak5 on ! run ( ! hip is equal to only #ab in*es :5 tak5 on t ( ! common raft]1 z %[n by ! dott$ l9e f heel to heel ( ! two squ>es 9 ,fig4 #aa4 ,illu/ration3 ,fig4 #i4 ,use ( ,squ>e to ,f9d ,mit] ( ,hexagon4 ,9 ,fig4 #ab is %[n h[ o!r figures on ! squ>e may be f\nd = corn]s t deviate f ! #de degrees4 ,x is %[n t = a p5tagon1 :i* makes a #cf-;degree angle ) ! plate1 ! figure to be us$ on ! squ>e = run is #ad in*es2 = a hexagon1 :i* makes a #cj-;degree angle ) ! plate1 ! figure w be #ac in*es2 & = an octagon1 :i* makes an angle ( #bb degrees ) ! plate1 ! figure to use on ! squ>e = run ( hip to correspond to ! run ( ! common raft]s1 w be #ac in*es4 ,x w be obs]v$ t ! height 9 ea* case is #i in*es4 ,illu/ration3 ,fig4 #aj4 ,diagram = ,f9d+ ,pit*es ( ,v>i\s ,degrees by ,means ( ! ,/eel ,squ>e4 ,fig4 #ac illu/rates a me?od ( f9d+ ! relative height ( a hip or valley p] foot run to t ( ! common raft]4 ,! squ>e is %[n plac$ ) #ab on blade & #i on tongue = ! common raft]2 & %[s t = ! hip ! rise is only #f-g_/af in*es4 ,illu/ration3 ,fig4 #aa4 ,squ>e ,appli$ to ,det]m9e ,relative ,l5g? ( ,run = ,raft] & ,hip4 ,! ,/eel ,squ>e z ,appli$ 9 ,ro( ,fram+4 ,ro( fram+ at pres5t is z simple z x possibly c be1 s t any attempt at a new me?od w\ld be sup]flu\s4 ,!re may1 h[ev]1 be a c]ta9 way ( pres5t+ ! subject t w c>ry ) x almo/ ! weight assign$ to a new !ory1 mak+ :at is already simple /ill m simple4 ,! /eel squ>e is a mighty factor 9 ro( fram+1 & )\t d\bt ! greate/ tool 9 practical pot5cy t ev] 0 inv5t$ = ! c>p5t]4 ,) its use ! l5g?s & bevels ( e piece ( timb] t goes into ! con/ruction ( ! mo/ intricate design ( ro(1 c easily be obta9$1 & t ) b v little k ( l9es4 ,illu/ration3 ,fig4 #ab4 ,use ( ,squ>e to ,det]m9e ,l5g? ( ,run = ,raft]s on ,corn]s ,o!r ?an #de4 ,9 ro(s ( equal pit*1 z illu/rat$ 9 ,fig4 #ad1 ! /eel squ>e is all t is requir$ if "o prop]ly und]/&s h[ to h&le x4 ,:at is meant by a pit* ( a ro(1 is ! numb] ( in*es x rises to ! foot ( run4 ,illu/ration3 ,fig4 #ac4 ,me?od ( ,f9d+ ,relative ,height ( ,hip or ,valley p] ,foot ( ,run to t ( ,common ,raft]4 ,9 ,fig4 #ae is %[n ! /eel squ>e ) figures repres5t+ ! v>i\s pit*es to ! foot ( run4 ,= ! -pit* ro(1 ! figures z %[n1 f #ab on tongue to #ab on blade1 are ^? to be us$ on ! /eel squ>e = ! common raft]2 & = pit*1 ! figures to be us$ on ! squ>e w be #ab & #i1 z %[n4 ,illu/ration3 ,fig4 #ad4 ,diagram to ,illu/rate ,use ( ,/eel ,squ>e ,9 ,lay+ ,out ,timb]s ( ,ro(s ( ,equal ,pit*4 ,to und]/& ?is figure1 x is necess>y only to keep 9 m9d t ! pit* ( a ro( is reckon$ f ! span4 ,s9ce ! run 9 ea* pit* z %[n is #ab in*es1 ! span is two times #ab in*es1 :i* equals #bd in*es2 h5ce1 #ab on blade to repres5t ! foot run1 & #ab on tongue to repres5t ! rise ov] ! span1 w be ! figures on ! squ>e = a -pit* ro(4 ,= ! pit*1 ! figures are %[n to be #ab on tongue & #i on blade1 #i be+ ( ! span1 #bd in*es4 ,! same rule applies to all ! pit*es4 ,! pit* is %[n to rise #d in*es to ! foot ( run1 because #d in*es is ( ! span1 #bd in*es1 ! pit* is %[n to rise #h in*es to ! foot ( run1 because #h in*es is ( ! span1 #bd in*es2 etc4 ,illu/ration3 ,fig4 #ae4 ,/eel ,squ>e ,giv+ ,v>i\s ,pit*es to ,foot ( ,run4 ,! ro( ref]r$ to 9 ,figs4 #af & #ag is to rise #i in*es to ! foot ( run2 x is !re=e a -pit* ro(4 ,= all ! common raft]s1 ! figures to be us$ on ! squ>e w be #ab on blade to repres5t ! run1 & #i on tongue to repres5t ! rise to ! foot ( run2 & = all ! hips & valleys1 #ag on blade to repres5t ! run1 & #i on tongue to repres5t ! rise ( ! ro( to ! foot ( run4 ,:y #ag repres5ts ! run = all ! hips & valleys1 w be und]/ood by exam9+ ,fig4 #ai1 9 :i* #ag is %[n to be ! diagonal ( a foot squ>e4 ,9 equal-pit* ro(s ! corn]s are squ>e1 & ! plan ( ! hip or valley w always be a diagonal ( a squ>e corn] z %[n at #a1 #b1 #c1 & #e 9 ,fig4 #ad4 ,9 ,fig4 #ah are %[n pit*1 pit* & pit* ov] a squ>e corn]4 ,! figures to be us$ on ! squ>e = ! hip1 w be #ag = run 9 ea* case4 ,= ! pit*1 ! figures to be us$ w\ld be #ag in*es run & #d in*es rise1 to correspond ) ! #ab in*es run & #d in*es rise ( ! common raft]4 ,= ! pit*1 ! figures to be us$ = hip w\ld be #ag in*es run & #i in*es rise1 to correspond ) ! #ab in*es run & #i in*es rise ( ! common raft]2 & = ! pit*1 ! figures to be us$ on ! squ>e w be #ag in*es run & #ab in*es rise1 to correspond ) ! #ab in*es run & #ab in*es rise ( ! common raft]4 ,illu/ration3 ,fig4 #af4 ,me?od ( ,lay+ ,out ,common ,raft]s ( a -,pit* ,ro(4 ,x w be obs]v$ f above1 t 9 all cases :]e ! plan ( ! hip or valley is a diagonal ( a squ>e1 ! figures to be us$ on ! squ>e = run w be #ag in*es2 & = ! rise1 :atev] ! ro( rises to ! foot ( run4 ,x %\ld also be rememb]$ t ?is is ! condition 9 all ro(s ( equal pit*1 :]e ! angle ( ! hip or valley is a #de-;degree angle1 or1 9 o!r words1 :]e we h ! diagonal ( a squ>e4 ,x has be5 %[n 9 ,fig4 #ab h[ o!r figures = o!r plan angles may be f\nd2 & t 9 ea* case ! figures = run v>y accord+ to ! plan angle ( ! hip or valley1 :ile ! figure = ! height 9 ea* case is simil>4 ,illu/ration3 ,fig4 #ag4 ,me?od ( ,lay+ ,out ,hips & ,valleys ( a -,pit* ,ro(4 ,9 ,fig4 #ad are %[n a v>iety ( runs = common raft]s1 b all h ! same pit*2 !y rise #i in*es to ! foot ( run4 ,! ma9 ro( is %[n to h a span ( #bg feet1 :i* makes ! run ( ! common raft] #ac feet #f in*es4 ,! run ( ! front w+ is %[n to be #aj feet #d in*es2 & ! run ( ! small gable at ! left corn] ( ! front1 is %[n to be #h feet4 ,! div]sity exhibit$ 9 ! runs1 & especially ! fractional "p ( a foot %[n 9 two ( !m1 w af=d an opportunity to treat ( ! ma9 difficulties 9 lay+ out ro( timb]s 9 ro(s ( equal pit*4 ,let x be det]m9$ to h a rise ( #i in*es to ! foot ( run2 & 9 ?is connection x may be well to rememb] t ! proportional rise to ! foot run = ro(s ( equal pit* makes n ! lea/ diff]5ce 9 ! me?od ( treatm5t4 ,to lay out ! common raft]s = ! ma9 ro(1 :i* has a run ( #ac feet #f in*es1 proce$ z %[n 9 ,fig4 #af4 ,take #ab on ! blade & #i on ! tongue1 & /ep #ac times along ! raft] timb]4 ,?is w give ! l5g? ( raft] = #ac feet ( run4 ,9 ?is example1 h[ev]1 !re is ano!r #f in*es ( run to cov]4 ,= ?is additional l5g?1 take #f in*es on ! blade 7x be+ a foot run7 = run1 & take ( #i on ! tongue 7:i* is #d in*es71 & /ep "o "t4 ,?is1 9 addition to :at has already be5 f\nd by /epp+ #ac times ) #ab & #i1 w give ! full l5g? ( ! raft]4 ,illu/ration3 ,fig4 #ah4 ,me?od ( ,lay+ ,out ,hips & ,raft]s = ,ro(s or ,v>i\s ,pit*es ov] ,squ>e ,corn]4 ,! squ>e ) #ab on blade & #i on tongue w give ! heel & plumb cuts4 ,ano!r me?od ( f9d+ ! l5g? ( raft] = ! #f in*es is %[n 9 ,fig4 #af1 :]e ! squ>e is %[n appli$ to ! raft] timb] = ! plumb cut4 ,squ>e ,no4 #a is %[n appli$ ) #ab on blade & #i on tongue = ! l5g? ( ! #ac feet4 ,squ>e f ?is cut1 measure #f in*es1 ! additional in*es 9 ! run2 & to ?is po9t move ! squ>e1 hold+ x on ! side ( ! raft] timb] ) #ab on blade & #i on tongue1 z = a full foot run4 ,x w be obs]v$ t ?is me?od is easily adapt$ to f9d any fractional "p ( a foot 9 ! l5g? ( raft]s4 ,9 ! front gable1 ,fig4 #ad1 ! fractional "p ( a foot is #d in*es to be add$ to #aj feet ( run2 !re=e1 9 t case1 ! l9e %[n measur$ to #f in*es 9 ,fig4 #af w\ld measure only #d in*es = ! front gable4 ,heel ,cut ( ,common ,raft]4 ,9 ,fig4 #af is also %[n a me?od to lay out ! heel cut ( a common raft]4 ,! squ>e is %[n appli$ ) #ab on blade & #i on tongue2 & f :]e ! #ab on ! squ>e int]sects ! edge ( ! raft] timb]1 a l9e is drawn squ>e to ! blade z %[n by ! dott$ l9e f #ab to a4 ,!n ! ?ickness ( ! "p ( ! raft] t is to project beyond ! plate to hold ! cornice1 is gaug$ to int]sect ! dott$ l9e at a2 & f a1 ! heel cut is drawn ) ! squ>e hav+ #ab on blade & #i on tongue1 m>k+ along ! blade = ! cut4 ,! common raft] = ! front w+1 :i* is %[n to h a run ( #aj feet #d in*es1 is laid out precisely ! same1 except t = ?is raft] ! squ>e ) #ab on blade & #i on tongue w h to be /epp$ along ! raft] timb] only #aj times = ! #aj feet ( run2 & = ! fractional "p ( a foot 7#d in*es7 :i* is 9 ! run1 ei!r ( ! two me?ods already %[n = ! ma9 raft] may be us$4 ,! proportional figures to be us$ on ! squ>e = ! #d in*es w be #d on blade & #b on tongue2 & if ! second me?od is us$1 make ! addition to ! l5g? ( raft] = #aj feet1 by draw+ a l9e #d in*es squ>e f ! tongue ( squ>e ,no4 #a 7see ,fig4 #af71 in/ead ( #f in*es z !re %[n = ! ma9 raft]4 ,hips4 ,?ree ( ! hips are %[n 9 ,fig4 #ad to ext5d f ! plate to ! ridge-pole2 !y are m>k$ 9 ! figure z #a1 #b1 & #c respectively1 & are %[n 9 plan to be diagonals ( a squ>e measur+ #ac feet #f in*es by #ac feet #f in*es2 !y make an angle1 !re=e1 ( #de degrees ) ! plate4 ,9 ,fig4 #ah x has be5 %[n t a hip /&+ at an angle ( #de degrees ) ! plate w h a run ( #ag in*es = e foot run ( ! common raft]4 ,!re=e1 to lay out ! hips1 ! figures on ! squ>e w be #ag = run & #i = rise2 & by /epp+ #ac times along ! hip raft] timb]1 ! l5g? ( hip = #ac feet ( run is obta9$4 ,! l5g? = ! additional #f in*es 9 ! run may be f\nd by squ>+ a di/ance ( #h in*es1 z %[n 9 ,fig4 #ag1 f ! tongue ( ! squ>e1 & mov+ squ>e ,no4 #a along ! edge ( ! timb]1 hold+ ! blade on #ag & tongue on #i1 & m>k+ ! plumb cut :]e ! dott$ l9e is %[n4 ,9 ,fig4 #ah is %[n h[ to f9d ! relative run l5g? ( a portion ( a hip to correspond to t ( a fractional "p ( a foot 9 ! l5g? ( ! common raft]4 ,f #ab in*es1 measure along ! run ( ! common raft] #f in*es1 & drop a l9e to cut ! diagonal l9e 9 m4 ,f m to a1 along ! diagonal l9e1 w be ! relative run l5g? ( ! "p ( hip to correspond ) #f in*es run ( ! common raft]1 & x measures #h in*es4 ,illu/ration3 ,fig4 #ai4 ,diagram ,%[+ ,relative ,l5g?s ( ,run = ,hips & ,common ,raft]s ,9 ,equal-,pit* ,ro(s4 ,illu/ration3 ,fig4 #bj4 ,me?od ( ,det]m9+ ,run ( ,valley = ,additional ,run 9 ,common ,raft]4 ,! same results may be obta9$ by ! foll[+ me?od ( figur+3 ,z #ab 3 #ag 33 #f #f #ab 7#ajb -------- #h - #f #h ,9 ,fig4 #ai is %[n a #ab-;in* squ>e1 ! diagonal m be+ #ag in*es4 ,by draw+ l9es f ! base a b to cut ! diagonal l9e1 ! "p ( ! hip to correspond to t ( ! common raft] w be indicat$ on ! l9e #ag4 ,9 ?is figure x is %[n t a #f-;in* run on a b1 :i* repres5ts ! run ( a foot ( a common raft]1 w h a correspond+ l5g? ( #h in*es run on ! l9e #ag1 :i* repres5ts ! plan l9e ( ! hip or valley 9 all equal-pit* ro(s4 ,9 ! front gable1 ,fig4 #ad1 x is %[n t ! run ( ! common raft] is #aj feet #d in*es4 ,to f9d ! l5g? ( ! common raft]1 take #ab on blade & #i on tongue1 & /ep #aj times along ! raft] timb]2 & = ! fractional "p ( a foot 7#d in*es71 proce$ z 0 %[n 9 ,fig4 #af = ! raft] ( ! ma9 ro(2 b 9 ?is case measure out squ>e to ! tongue ( squ>e ,no4 #a1 #d in*es in/ead ( #f in*es4 ,illu/ration3 ,fig4 #ba4 ,corn] ( ,squ>e ,build+1 ,%[+ ,plan ,l9es ( ,plates & ,hip4 ,fig4 #bb4 ,corn] ( ,squ>e ,build+1 ,%[+ ,plan ,l9es ( ,plates & ,valley4 ,! additional l5g? = ! fractional #d in*es run c also be f\nd by tak+ #d in*es on blade & #c in*es on tongue ( squ>e1 & /epp+ "o "t2 ?is1 9 addition to ! l5g? obta9$ by /epp+ #aj times along ! raft] timb] ) #ab on blade & #i on tongue1 w give ! full l5g? ( ! raft] = a run ( #aj feet #d in*es4 ,illu/ration3 ,fig4 #bc4 ,use ( ,squ>e to ,det]m9e ,heel ,cut ( ,valley4 ,9 ! int]section ( ?is ro( ) ! ma9 ro(1 !re are %[n to be two valleys ( diff]5t l5g?s4 ,! long "o ext5ds f ! plate at n 7,fig4 #ad7 to ! ridge ( ! ma9 ro( at m2 x has !re=e a run ( #ac feet #f in*es4 ,= ! l5g?1 proce$ z = ! hips1 by tak+ #ag on blade ( ! squ>e & #i on tongue1 & /epp+ #ac times = ! l5g? ( ! #ac feet2 & = ! fractional #f in*es1 proce$ precisely z %[n 9 ,fig4 #ag = ! hip1 by squ>+ out f ! tongue ( squ>e ,no4 #a1 #h in*es2 ?is1 9 addition to ! l5g? obta9$ = ! #ac feet1 w give ! full l5g? ( ! long valley n m4 ,! l5g? ( ! %ort valley a c1 z %[n1 ext5ds ov] ! run ( #aj feet #d in*es1 & butts aga9/ ! side ( ! long valley at c4 ,by tak+ #ag on blade & #i on tongue1 & /epp+ along ! raft] timb] #aj times1 ! l5g? = ! #aj feet is f\nd2 & = ! #d in*es1 measure #e in*es squ>e f ! tongue ( squ>e ,no4 #a1 9 ! mann] %[n 9 ,fig4 #ag1 :]e ! #h in*es is %[n add$ = ! #f in*es additional run ( ! ma9 ro( = ! hips4 ,illu/ration3 ,fig4 #bd4 ,/eel ,squ>e ,appli$ to ,f9d+ ,bevel = ,fitt+ ,top ( ,hip or ,valley to ,ridge4 ,! l5g? #e is f\nd z %[n 9 ,fig4 #bj1 by measur+ #d in*es f a to m along ! run ( common raft] = "o foot4 ,^u m erect a l9e to cut ! seat ( ! valley at c2 f c to a w be ! run ( ! valley to correspond ) #d in*es run ( ! common raft]1 & x w measure #e in*es4 ,h[ to ,treat ! ,heel ,cut ( ,hips & ,valleys4 ,hav+ f\nd ! l5g?s ( ! hips & valleys to correspond to ! common raft]s1 x w be necess>y to f9d also ! ?ickness ( ea* above ! plate to correspond to ! ?ickness ! common raft] w be above ! plate4 ,9 ,fig4 #ba is %[n a corn] ( a squ>e build+1 %[+ ! plates & ! plan l9es ( a hip4 ,! l5g? ( ! hip1 z already f\nd1 w cov] ! span f ! ridge to ! corn] #b2 b ! sides ( ! hip int]sect ! plates at #c & #c respectively2 !re=e ! di/ance f #b to #a1 z %[n 9 ?is diagram1 is measur$ backw>ds f a to #a 9 ! mann] %[n 9 ,fig4 #ag2 !n a plumb l9e is drawn ?r\gh #a to m1 p>allel to ! plumb cut a-#ag4 ,f m to o on ?is l9e1 measure ! same ?ickness z t ( ! common raft]2 & ?r\gh o draw ! heel cut to a z %[n4 ,9 l mann] ! ?ickness ( ! valley above ! plate is f\nd2 b z ! valley z %[n 9 ! plan figure1 ,fig4 #bb1 projects beyond po9t #b be=e x int]sects ! outside ( ! plates1 ! di/ance f #b to #a 9 ! case ( ! valley w h to be measur$ outw>ds f #b1 z %[n f #b to #a 9 ,fig4 #bc2 & at ! po9t ?us f\nd ! ?ickness ( ! valley is to be measur$ to correspond ) t ( ! common raft] z %[n at m n4 ,illu/ration3 ,fig4 #be4 ,/eel ,squ>e ,appli$ to ,jack ,raft] to ,f9d ,bevel = ,fitt+ aga9/ ,side ( ,hip or ,valley4 ,9 ,fig4 #bd is %[n ! /eel squ>e appli$ to a hip or valley timb] to cut ! bevel t w fit ! top end aga9/ ! ridge4 ,! figures on ! squ>e are #ag & #ai4 ,! #ag repres5ts ! l5g? ( ! plan l9e ( ! hip or valley = a foot ( run1 :i*1 z 0 %[n 9 previ\s figures1 w always be #ag in*es 9 ro(s ( equal pit*1 :]e ! plan l9es /& at #de degrees to ! plates & squ>e to ea* o!r4 ,! #ai tak5 on ! blade repres5ts ! actual l5g? ( a hip or valley t w span ov] a run ( #ag in*es4 ,! bevel is m>k$ along ! blade4 ,! cut across ! back ( ! %ort valley to fit x aga9/ ! side ( ! long valley1 w be a squ>e cut ow+ to ! two plan l9es be+ at "r angles to ea* o!r4 ,9 ,fig4 #be is %[n ! /eel squ>e appli$ to a jack raft] to cut ! back bevel1 to fit x aga9/ ! side ( a hip or valley4 ,! figures on ! squ>e are #ab on tongue & #ae on blade1 ! #ab repres5t+ a foot run ( a common raft]1 & ! #ae ! l5g? ( a raft] t w span ov] a foot run2 m>k+ along ! blade w give ! bevel4 ,illu/ration3 ,fig4 #bf4 ,f9d+ ,l5g? to ,%ort5 ,raft]s = ,jacks p] ,foot ( ,run4 ,! rule 9 e case to f9d ! back bevel = jacks 9 ro(s ( equal pit*1 is to take #ab on ! tongue to repres5t ! foot run1 & ! l5g? ( ! raft] = a foot ( run on ! blade1 m>k+ along ! blade 9 ea* case = ! bevel4 ,9 a -pit* ro(1 :i* is ! mo/ common 9 all p>ts ( ! c\ntry1 ! l5g? ( raft] = a foot ( run w be #ag in*es2 h5ce x w be well to rememb] t #ab on tongue & #ag on blade1 m>k+ along ! blade1 w give ! bevel to fit a jack aga9/ a hip or a valley 9 a -pit* ro(4 ,9 a ro( hav+ a rise ( #i in*es to ! foot ( run1 su* z ! "o "u consid]ation1 ! l5g? ( raft] = "o foot ( run w be #ae in*es4 ,! squ>e z %[n 9 ,fig4 #be1 ) #ab on tongue & #ae on blade1 w give ! bevel by m>k+ along ! blade4 ,to f9d ! l5g? ( a raft] = a foot ( run = any o!r pit*1 place ! two-foot rule diagonally f #ab on ! blade ( ! squ>e to ! figure on tongue repres5t+ ! rise ( ! ro( to ! foot ( run2 ! rule w give ! l5g? ( ! raft] t w span ov] "o foot ( run4 ,illu/ration3 ,fig4 #bg4 ,f9d+ ,l5g? ( ,jack ,raft] 9 -,pit* ,ro(4 ,illu/ration3 ,fig4 #bh4 ,f9d+ ,l5g? ( ,jack ,raft] 9 -,pit* ,ro(4 ,! l5g? ( raft] = a foot ( run w also det]m9e ! diff]5ce 9 l5g?s ( jacks4 ,= example1 if a ro( rises #ab in*es to "o foot ( run1 ! raft] ov] ?is span has be5 f\nd to be #ag in*es2 ?is1 !re=e1 is ! numb] ( in*es ea* jack is %ort5$ 9 "o foot ( run4 ,if ! rise ( ! ro( is #h in*es to ! foot ( run1 ! l5g? ( ! raft] is f\nd = "o foot ( run1 by plac+ ! rule diagonally f #ab on tongue to #h on blade1 :i* gives #ad in*es1 z %[n 9 ,fig4 #bf4 ,?is1 !re=e1 w be ! numb] ( in*es ! jacks are to be %ort5$ 9 a ro( ris+ #h in*es to ! foot ( run4 ,if ! jacks are plac$ #bd in*es f c5t] to c5t]1 !n multiply #ad by #b #bi in*es4 ,9 ,fig4 #bg is %[n h[ to f9d ! l5g? ) ! /eel squ>e4 ,! squ>e is plac$ on ! jack timb] raft] ) ! figures t h be5 us$ to cut ! common raft]4 ,9 ,fig4 #bg1 #ab on blade & #ab on tongue 7 ! figures us$ to cut ! common raft]1 ! ro( be+ pit*1 ris+ #ab in*es to ! foot ( run4 ,9 ! diagram x is %[n h[ to f9d ! l5g? ( a jack raft] if plac$ #af in*es f c5t] to c5t]4 ,! me?od is to move ! squ>e z %[n along ! l9e ( ! blade until ! blade measures #af in*es2 ! tongue !n w\ld be z %[n f w to m1 & ! l5g? ( ! jack w\ld be f #ab on blade to m on tongue1 on ! edge ( ! jack raft] timb] z %[n4 ,?is latt] me?od becomes conv5i5t :5 ! space betwe5 jacks is less ?an #ah in*es2 b if us$ :5 ! space is m ?an #ah in*es x w become necess>y to use two squ>es2 o!rwise ! tongue z %[n at m w\ld n rea* ! edge ( ! timb]4 ,illu/ration3 ,fig4 #bi4 ,me?od ( ,det]m9+ ,l5g? ( ,jacks ,betwe5 ,hips & ,valleys2 also ,bevels = ,jacks1 ,hips1 & ,valleys4 ,9 ,fig4 #bh ! same me?od is %[n = f9d+ ! l5g? ( a jack raft] = a ro( ris+ #i in*es to ! foot ( run1 ) ! jacks plac$ #ah in*es c5t] to c5t]4 ,! squ>e 9 ?is diagram is %[n plac$ on ! jack raft] timb] ) #ab on blade & #i on tongue2 !n x is mov$ =w>d along ! l9e ( ! blade to w4 ,! blade1 :5 9 ?is latt] position1 w measure #ah in*es4 ,! tongue w meet ! edge ( ! timb] at m1 & ! di/ance f m on tongue to #ab on blade w indicate ! l5g? ( a jack1 or1 9 o!r words1 w %[ ! l5g? ea* jack is %ort5$ :5 plac$ #ah in*es betwe5 c5t]s 9 a ro( hav+ a pit* ( #i in*es to ! foot ( run4 ,illu/ration3 ,fig4 #cj4 ,me?od ( ,f9d+ ,bevels = ,all ,timb]s 9 ,ro(s ( ,equal ,pit*4 ,illu/ration3 ,fig4 #ca4 ,me?od ( ,f9d+ ,bevel #e1 ,fig4 #cj1 = ,fitt+ ,hip or ,valley ,aga9/ ,ridge :5 n ,back$4 ,:5 jacks are plac$ betwe5 hips & valleys z %[n at #a1 #b1 #c1 #d1 etc41 9 ,fig4 #ad1 a bett] me?od ( treatm5t is %[n 9 ,fig4 #bi1 :]e ! slope ( ! ro( is project$ into ! horizontal plane4 ,! di/ance f ! plate 9 ?is figure to ! ridge m1 equals ! l5g? ( ! common raft] = ! ma9 ro(4 ,on ! plate a n n is made equal to a n n 9 ,fig4 #ad4 ,by draw+ a figure l ?is to a scale ( "o in* to "o foot1 ! l5g? ( all ! jacks c be measur$ & also ! l5g?s ( ! hip & ! two valleys4 ,x also gives ! bevels = ! jacks1 z well z ! bevel to fit ! hip & valley aga9/ ! ridge2 b ?is la/ bevel mu/ be appli$ to ! hip & valley :5 back$4 ,x has be5 %[n be=e1 t ! figures to be us$ on ! squ>e = ?is bevel :5 ! timb] is left squ>e on back z is ! cu/om 9 con/ruction1 are ! l5g? ( a foot run ( a hip or valley1 :i* is #ag1 on tongue1 & ! l5g? ( a hip or valley t w span ov] #ag in*es run1 on blade--! blade giv+ ! bevel4 ,fig4 #cj conta9s all ! bevels or cuts t h be5 treat$ ^u s f>1 &1 if correctly und]/ood1 w enable any "o to frame any ro( ( equal pit*4 ,9 ?is figure x is %[n t #ab in*es run & #i in*es rise w give bevels #a & #b1 :i* are ! plumb & heel cuts ( raft]s ( a ro( ris+ #i in*es to ! foot ( run4 ,by tak+ ^! figures1 !re=e1 on ! squ>e1 #i in*es on ! tongue & #ab in*es on ! blade1 m>k+ along ! tongue w give ! plumb cut1 & m>k+ along ! blade w give ! heel cut4 ,illu/ration3 ,fig4 #cb4 ,me?od ( ,f9d+ ,back ,bevel #f1 ,fig4 #cj1 = ,jack ,raft]s1 & ,bevel #g1 = ,ro(-,bo>d4 ,illu/ration3 ,fig4 #cc4 ,det]m9+ ,mit] ,cut = ,ro(-,bo>d4 ,bevels #c & #d are ! plumb & heel cuts = ! hip1 & are %[n to h ! l5g? ( ! seat ( hip = "o foot run1 :i* is #ag in*es4 ,by tak+ #ag in*es1 !re=e1 on ! blade1 & #i in*es on ! tongue1 m>k+ along ! tongue = ! plumb cut1 & along ! blade = ! heel cut1 ! plumb & heel cuts are f\nd4 ,bevel #e1 :i* is to fit ! hip or valley aga9/ ! ridge :5 n back$1 is %[n f o w1 ! l5g? ( ! hip = "o foot ( run1 :i* is #ai in*es1 & f o s1 :i* always 9 ro(s ( equal pit* w be #ag in*es & equal 9 l5g? to ! seat ( a hip or valley = "o foot ( run4 ,^! figures1 !re=e1 tak5 on ! squ>e1 #ai on ! blade1 & #ag on ! tongue1 w give ! bevel by m>k+ along ! blade z %[n 9 ,fig4 #ca1 :]e ! squ>e is %[n appli$ to ! hip timb] ) #ai on blade & #ag on tongue1 ! blade %[+ ! cut4 ,bevels #f & #g 9 ,fig4 #cj are %[n =m$ ( ! l5g? ( ! raft] = "o foot ( run1 :i* is #ae in*es1 & ! run ( ! raft]1 :i* is #ab in*es4 ,^! figures are appli$ on ! squ>e1 z %[n 9 ,fig4 #cb1 to a jack raft] timb]2 tak+ #ae on ! blade & #ab on ! tongue1 m>k+ along ! blade w give ! back bevel = ! jack raft]s1 & m>k+ along ! tongue w give ! face cut ( ro(-bo>ds to fit along ! hip or valley4 ,illu/ration3 ,fig4 #cd4 ,lay+ ,out ,timb]s ( ,"o-half ,gable ( -,pit* ,ro(4 ,x is %[n 9 ,fig4 #cj1 also1 t by tak+ ! l5g? ( raft] #ae in*es on blade1 & rise ( ro( #i in*es on tongue1 bevel #h w give ! mit] cut = ! ro(-bo>ds4 ,9 ,fig4 #cc ! squ>e is %[n appli$ to a ro(-bo>d ) #ae on blade1 :i* is ! l5g? ( ! raft] to "o foot ( run1 & ) #i on tongue1 :i* is ! rise ( ! ro( to ! foot run2 m>k+ along ! tongue w give ! mit] = ! bo>ds4 ,illu/ration3 ,fig4 #ce4 ,f9d+ ,back+ ( ,hip 9 ,gable ,ro(4 ,o!r uses may be made ( ^! figures1 z %[n 9 ,fig4 #cd1 :i* is "o-half ( a gable ( a ro( ris+ #i in*es to ! foot run4 ,! squ>es at ! bottom & ! top w give ! plumb & heel cuts ( ! common raft]4 ,! same figures on ! squ>e appli$ to ! /udd+1 m>k+ along ! tongue = ! cut1 w give ! bevel to fit ! /udd+ aga9/ ! raft]2 & by m>k+ along ! blade we obta9 ! cut = ! bo>ds t run across ! gable4 ,by tak+ #ai on blade1 :i* is ! l5g? ( ! hip = "o foot ( run1 & tak+ on ! tongue ! rise ( ! ro( to ! foot ( run1 :i* is #i in*es1 & apply+ ^! z %[n 9 ,fig4 #ce1 we obta9 ! back+ ( ! hip by m>k+ along ! tongue ( ! two squ>es1 z %[n4 ,x w be obs]v$ f :at has be5 said1 t 9 ro(s ( equal pit* ! figure #ab on ! blade1 & :atev] numb] ( in*es ! ro( rises to ! foot run on ! tongue1 w give ! plumb & heel cuts = ! common raft]2 & t by tak+ #ag on ! blade in/ead ( #ab1 & tak+ on ! tongue ! figure repres5t+ ! rise ( ! ro( to ! foot run1 ! plumb & heel cuts are f\nd = ! hips & valleys4 ,by tak+ ! l5g? ( ! common raft] = "o foot ( run on blade1 & ! run #ab on tongue1 m>k+ along ! blade w give ! back bevel = ! jack to fit ! hip or valley1 & m>k+ along ! tongue w give ! bevel to cut ! ro(-bo>ds to fit ! l9e ( hip or valley ^u ! ro(4 ,) ?is k ( :at figures to use1 & :y !y are us$1 x w be an easy matt] = anyone to lay out all raft]s = equal-pit* ro(s4 ,illu/ration3 ,fig4 #cf4 ,lay+ ,out ,timb]s ( ,ro( ) ,two ,unequal ,pit*es4 ,9 ,fig4 #cf is %[n a plan ( a ro( ) two unequal pit*es4 ,! ma9 ro( is %[n to h a rise ( #ab in*es to ! foot run4 ,! front w+ is %[n to h a run ( #f feet & to rise #ab feet2 x has ?us a pit* ( #bd in*es to ! foot run4 ,!re=e #ab on blade ( ! squ>e & #ab on tongue w give ! plumb & heel cuts = ! ma9 ro(1 & by /epp+ #ab times along ! raft] timb] ! l5g? ( ! raft] is f\nd4 ,! figures on ! squ>e to f9d ! heel & plumb cuts = ! raft] 9 ! front w+1 w be #ab run & #bd rise1 & by /epp+ #f times 7! numb] ( feet 9 ! run ( ! raft]71 ! l5g? w be f\nd ov] ! run ( #f feet1 & x w measure #ac feet #f in*es4 ,if1 9 place ( /epp+ along ! timb]1 ! diagonal ( #ab & #bd is multipli$ by #f1 ! numb] ( feet 9 ! run1 ! l5g? may be f\nd ev5 to a great] exactitude4 ,_m c>p5t]s use ?is me?od ( fram+2 & to ^? :o h confid5ce 9 _! ability to figure correctly1 x is a sav+ ( "t1 &1 z be=e said1 w result 9 a m accurate measurem5t2 b ! bett] & m sci5tific me?od ( fram+ is to "w to a scale ( "o in*1 z has already be5 expla9$4 ,illu/ration3 ,fig4 #cg4 ,f9d+ ,l5g? ( ,raft] = ,front ,w+ 9 ,ro( ,%[n 9 ,fig4 #cf4 ,accord+ to t me?od1 ! diagonal ( a foot ( run1 & ! numb] ( in*es to ! foot run ! ro( is ris+1 measur$ to a scale1 w give ! exact l5g?4 ,= example1 ! ma9 ro( 9 ,fig4 #cf is ris+ #ab in*es to a foot ( run4 ,! diagonal ( #ab & #ab is #ag in*es1 :i*1 consid]$ z a scale ( "o in* to a foot1 w give #ag feet1 & ?is w be ! exact l5g? ( ! raft] = a ro( ris+ #ab in*es to ! foot run & hav+ a run ( #ab feet4 ,illu/ration3 ,fig4 #ch4 ,lay+ ,out ,timb]s ( ,ro( ,%[n 9 ,fig4 #cf1 by ,project+ ,slope ( ,ro( into ,horizontal ,plane4 ,! l5g? ( ! raft] = ! front w+1 :i* has a run ( #f feet & a rise ( #ab feet1 may be obta9$ by plac+ ! rule z %[n 9 ,fig4 #cg f #f on blade to #ab on tongue1 :i* w give a l5g? ( #ac in*es4 ,if ! scale be consid]$ z "o in* to a foot1 ?is w equal #ac feet #f in*es1 :i* w be ! exact l5g? ( a common raft] ris+ #bd in*es to ! foot run & hav+ a run ( #f feet4 ,x w be obs]v$ t ! plan l9es ( ! valleys 9 ?is figure 9 respect to "o ano!r deviate f =m+ a "r angle4 ,9 equal-pit* ro(s ! plan l9es are always at "r angles to ea* o!r1 & !re=e ! diagonal ( #ab & #ab1 :i* is #ag in*es1 w be ! relative foot run ( valleys & hips 9 equal-pit* ro(s4 ,9 ,fig4 #cf is %[n h[ to f9d ! figures to use on ! squ>e = valleys & hips :5 deviat+ f ! "r angle4 ,a l9e is drawn at a di/ance ( #ab in*es f ! plate & p>allel to x1 cutt+ ! valley 9 m z %[n4 ,! "p ( ! valley f m to ! plate w measure #ac in*es1 :i* is ! figure t is to be us$ on ! squ>e to obta9 ! l5g? & cuts ( ! valleys4 ,illu/ration3 ,fig4 #ci4 ,me?od ( ,f9d+ ,l5g? & ,cuts ( ,octagon ,hips ,int]sect+ a ,ro(4 ,x w be obs]v$ t ?is equals ! l5g? ( ! common raft] z f\nd by ! squ>e & rule 9 ,fig4 #cg4 ,9 t figure is %[n #ab on tongue & #f on blade4 ,! #ab "h repres5ts ! rise1 & ! #f ! run ( ! front ro(4 ,if ! #ab be tak5 to repres5t ! run ( ! ma9 ro(1 & ! #f to repres5t ! run ( ! front ro(1 !n1 ! diagonal #ac w indicate ! l5g? ( ! seat ( ! valley = #ab feet ( run1 & !re=e = "o foot x w be #ac in*es4 ,n[1 by tak+ #ac on ! blade = run1 & #ab in*es on ! tongue = rise1 & /epp+ along ! valley raft] timb] #ab times1 ! l5g? ( ! valley w be f\nd4 ,! blade w give ! heel cut1 & ! tongue ! plumb cut4 ,9 ,fig4 #ch is %[n ! slope ( ! ro( project$ into ! horizontal plane4 ,by draw+ a figure bas$ on a scale ( "o in* to "o foot1 all ! timb]s on ! slope ( ! ro( c be measur$4 ,bevel #b1 %[n 9 ?is figure1 is to fit ! valleys aga9/ ! ridge4 ,by draw+ a l9e f w squ>e to ! seat ( ! valley to m1 mak+ w #b equal 9 l5g? to ! l5g? ( ! valley1 z %[n1 & by connect+ #b & m1 ! bevel at #b is f\nd1 :i* w fit ! valleys aga9/ ! ridge1 z %[n at #c & #c 9 ,fig4 #cf4 ,illu/ration3 ,fig4 #dj4 ,%[+ ,h[ ,cornice ,affects ,valleys & ,plates 9 ,ro( ) ,unequal ,pit*es4 ,9 ,fig4 #ci1 is %[n h[ to f9d ! l5g? & cuts ( octagon hips int]sect+ a ro(4 ,9 ,fig4 #cf1 half ! plan ( ! octagon is %[n to be inside ( ! plate1 & ! hips o1 z1 o int]sect ! slope ( ! ro(4 ,9 ,fig4 #ci1 ! l9es bel[ x y are ! plan l9es2 & ^? above1 ! elevation4 ,f z1 o1 o1 9 ! plan1 draw l9es to x y1 z %[n f o to m & f z to m2 f m & m1 draw ! elevation l9es to ! apex o1 int]sect+ ! l9e ( ! ro( 9 d & c4 ,f d & c1 draw ! l9es d v & c a p>allel to x y2 f c1 drop a l9e to int]sect ! plan l9e a o 9 c4 ,make a w equal 9 l5g? to a o ( ! elevation1 & connect w c2 measure f w to n ! full height ( ! octagon z %[n f x y to ! apex o2 & connect c n4 ,! l5g? f w to c is t ( ! two hips %[n at o o 9 ,fig4 #cf1 bo? be+ equal hips int]sect+ ! ro( at an equal di/ance f ! plate4 ,! bevel at w is ! top bevel1 & ! bevel at c w fit ! ro(4 ,aga91 drop a l9e f d to int]sect ! plan l9e a z 9 d4 ,make a #b equal to v o 9 ! elevation1 & connect #b d4 ,measure f #b to b ! full height ( ! t[] z %[n f x y to ! apex o 9 ! elevation1 & connect d b4 ,! l5g? #b d repres5ts ! l5g? ( ! hip z %[n 9 ,fig4 #cf2 ! bevel at #b is t ( ! top2 & ! bevel at d1 ! "o t w fit ! foot ( ! hip to ! int]sect+ ro(4 ,:5 a cornice ( any consid]able wid? runs ar\nd a ro( ( ?is k9d1 x affects ! plates & ! angle ( ! valleys z %[n 9 ,fig4 #dj4 ,9 ?is figure are %[n ! same valleys z 9 ,fig4 #cf2 b1 ow+ to ! wid? ( ! cornice1 ! foot ( ea* has be5 mov$ ! di/ance a b along ! plate ( ! ma9 ro(4 ,:y ?is is done is %[n 9 ! draw+ to be caus$ by ! necessity = ! valleys to int]sect ! corn]s c c ( ! cornice4 ,! plates are also affect$ z %[n 9 ,fig4 #da1 :]e ! plate ( ! n>r[ ro( is %[n to be mu* high] ?an ! plate ( ! ma9 ro(4 ,! bevels %[n at #c1 ,fig4 #dj1 are to fit ! valleys aga9/ ! ridge4 ,illu/ration3 ,fig4 #da4 ,%[+ ,relative ,position ( ,plates 9 ,ro( ) ,two ,unequal ,pit*es4 ,illu/ration3 ,fig4 #db4 ,me?od ( ,f9d+ ,bevels = ,purl9s 9 ,equal-,pit* ,ro(s4 ,9 ,fig4 #db is %[n a v simple me?od ( f9d+ ! bevels = purl9s 9 equal-pit* ro(s4 ,draw ! plan ( ! corn] z %[n1 & a l9e f m to o2 measure f o ! l5g? x y1 repres5t+ ! common raft]1 to w2 f w draw a l9e to m2 ! bevel %[n at #b w fit ! top face ( ! purl94 ,aga91 f o1 describe an arc to cut ! seat ( ! valley1 & cont9ue same ar\nd to ,s2 connect ,s m2 ! bevel at #c w be ! side bevel4 ,,index ,,"p ,,page ,b ,bevel ,i1 #dd ,bevels1 application ( 9 fitt+ wrea?s to rail ,i1 #eh ,bevels to squ>e wrea?s ,i1 #fj ,bottom /eps ) obtuse-angle plan ,i1 #ef ,bullnose /air ,i1 #cc ,bullnose /eps ,i1 #cb ,bullnose tread ,i1 #bi ,c ,c>riage ,i1 #af ,c>riage pieces ,i1 #bh ,circul> /airs ,i1 #be ,close /airway ,i1 #b ,cove ,i1 #bh ,curv$ /eps & /r+]1 plan ( ,i1 #ed ,cyl9d] ,i1 #ce ,d ,dog-legg$ /airs ,i1 #be ,f ,face-m\ld ,i1 #fh ,face-m\ld develop+ 7obtuse-angle plan7 ,i1 #ef ,fly] ,i1 #be ,foci ,i1 #gj ,g ,geometrical /air ,i1 #dd ,geometrical /airways & h&rail+ ,i1 #dc ,k ,k]f+ ,i1 #cf ,n ,newel po/ ,i1 #ad ,o ,op5-newel /airs ,i1 #cb ,p ,pit*-bo>d ,i1 #aj ,plan l9es ,i1 #dh ,plat=m ,i1 #bj ,plat=m /airs ,i1 #bf ,projection ,i1 #dd ,q ,qu>t]-space /air ) six w9d]s ,i1 #dc ,quick sweep ,i1 #cg ,r ,rail1 plan l9e ( ,i1 #df ,rise & rim ,i1 #c ,ris] ,i1 #c arrangem5t ( ,i1 #gd ,r\gh brackets ,i1 #bh ,s ,spr++ ! plank ,i1 #gd ,/air ) five danc+ w9d]s ,i1 #dc ,/air-build+ ,i1 #a-ge def9itions ,i1 #b introductory ,i1 #a lay+ out ,i1 #bb op5-newel /airs ,i1 #cb plat=m ,i1 #bj /airs ) curv$ turns ,i1 #cd /r+s ,i1 #g h\s$ ,i1 #g not*$ ,i1 #h op5 ,i1 #g r\gh ,i1 #g /av$ ,i1 #h well hole ,i1 #ah ,/airs1 plans & elevation turn+ ar\nd c5tral po/ ,i1 #dd ,/airs1 sett+ ( ,i1 #h ,/airs1 types ( 9 common use ,i1 #da ,/eel squ>e ,,ii1 #a-bg appli$ 9 ro( fram+ ,,ii1 #g appli$ to jack raft] ,,ii1 #ag back ,,ii1 #a back ( blade1 %[+ essex bo>d measure ,,ii1 #c back ( blade1 %[+ raft] table ,,ii1 #b back ( tongue1 %[+ brace measure ,,ii1 #c bevels1 me?od ( f9d+ = all timb]s 9 ro(s ( equal pit* ,,ii1 #bj blade ,,ii1 #a bo>d measure ,,ii1 #a brace rule ,,ii1 #a common raft]s1 me?od ( lay+ out ,,ii1 #aa face ,,ii1 #a face side ( tongue1 %[+ octagon scale ,,ii1 #b f9d+ back+ ( hip 9 gable ro( ,,ii1 #bb f9d+ l5g? ( raft] = front w+ 9 ro( %[n 9 ,fig4 #cf ,,ii1 #bd f9d+ l5g? to %ort5 raft]s = jacks p] foot ( run ,,ii1 #ah giv+ v>i\s pit*es to foot ( run ,,ii1 #aj heel cut ( common raft] ,,ii1 #ac hips ,,ii1 #ac hips & raft]s = ro(s ( v>i\s pit*es ov] squ>e corn]1 me?od ( lay+ out ,,ii1 #ab hips & valleys1 h[ to treat ! heel cut ( ,,ii1 #af hips & valleys ( a -pit* ro(1 me?od ( lay+ out ,,ii1 #aa jack raft]1 f9d+ l5g? ( ,,ii1 #ah jacks betwe5 hips & valleys1 me?od ( det]m9+ l5g? ,,ii1 #ai lay+ out timb]s ( "o-half gable ( -pit* ro( ,,ii1 #bb lay+ out timb]s ( ro( ) two unequal pit*es ,,ii1 #bc me?od ( f9d+ bevels = purl9s 9 equal-pit* ro(s ,,ii1 #bg me?od ( f9d+ l5g? & cuts ( octagon hips int]sect+ a ro( ,,ii1 #be octagon scale ,,ii1 #a rise & run ,,ii1 #a tongue ,,ii1 #a use ( to f9d mit] ( equilat]al triangle ,,ii1 #f use ( to f9d mit] ( hexagon ,,ii1 #g use ( to f9d mit] & side ( p5tagon1 hexagon & octagon ,,ii1 #d1 #e ,/ory rod ,i1 #h ,/raight flights ,i1 #be ,/r+-bo>d ,i1 #c ,/r+s ,i1 #g h\s$ ,i1 #g me?ods ( build+ up ,i1 #cg not*$ ,i1 #h op5 ,i1 #g r\gh ,i1 #g /av$ ,i1 #h ,t ,tang5t incl9$-l[] tang5t level ,i1 #fc ,tang5t sy/em ,i1 #dd ,tang5ts & face-m\ld1 diagram ( ,i1 #ec ,tang5ts unfold$ ,i1 #ej ,tread ,i1 #c ,treads & ris]s1 h\s+ ( ,i1 #ac ,trimm+ joi/s ,i1 #ai ,twi/$ wrea? rais$ to position ,i1 #eg ,w ,well-hole ,i1 #ah ,well-hole connect+ two flights ,i1 #ea ,w9d] ,i1 #be ,w9d+ /airs ,i1 #be ,wrea?1 cutt+ f plank ,i1 #eg ,wrea? ) two equally incl9$ tang5ts1 f9d+ bevels = ,i1 #ei ,wrea? twi/$1 ready to be m\ld$ ,i1 #eg ,wrea?s ,i1 #dd