1

«Th *

and r 6 lntersect ' n g points of the arches h i, and k l, and n o,and t ] f u ' are at t * le sarae distance from one another,or heVl 1163 B h> c k, D n, s p, F r, and G t, being the risingsone S J° t * le steps, in Figure 96, b h being the height of(j f 0 p c ^ fwo, dm of tliree, e p of four, f r of five, and° n tfi 0 S! • C ' ^ ow > these lines are raised up perpendicular°f Clrc ie A d g, it is evident that the point of intersectionPoint 6 arc ^ es h an d *> W 'H stand perpendicularly over theover d t * 16 arc ^ es h, over c > °f the arches n and o,F . the arches p,g, over e ; of the arches r and j, over

into t) ■ ^ le arc ' les t and u, over G. Now, if nails be struck•'tile t * 6 1 . nter9ect ' n g points of the said arches, and a thinA k ft 6 ^ 6nt roun d them, you may describe the arch,the n, P r b ^ ^ le edge thereof, being the mould to strike«. of the rail with.

to j, e ar ch or mould of the rail being found, as above, how*he stu ff °f which the rail is to be made, and work

Fitj S ^ Lereo f without setting it up in its due position.

t ^ strike two circles, whose diameters are

how 0 11 w an d a g, in Figure 95, and next consider intolet. lj„ nan y P' ec es you glue the rail, which in the semicircle.. N S1X > a f in the example.

F jh Jl ° w ’ divide the semicircle into six equal parts, as E F,sion' dr' S L - L D ’ anc ^ D K ’ ^ rom eac h of these points of divi-und ' A ^ <Uv ,*', nes to the centre a, as a e, a f, a m, a s, a l, a d,eq Ua i 1 ^ * le n from f raise f g perpendicular to a f, and

St N p e ° l le height of one step. Also, at the point H, raiseand i n l P® n< di cu lar to am, equal to the height of two steps ;pend;,. ] e maun er at the points s, l,d, and k, raise the per-to the ], aiS s T ’ L1r > D e, and bl, respectively equal in lengtha li n(j ^ e, 8l't of three, four, five, and six steps. Then drawfr° m oni G to b, parallel and equal to a f ; as also anotherParallel ° P ara H e l and equal to a m ; another from T to W,e< l"al to* 111 ^ e< l ua l to s A ; another from v to b, parallel andand an A > another from e to h, parallel and equal to d a ;tii e point 161 ^ rom L t° r> parallel and equal to ica. Fromto the h • A d'‘ a w the line A b, perpendicular to A e, and equaldraw t’ < ,. lt one ste P » al 80 at the points n y, w, b, n, r,l|c %htof " les R r -> Yz » wx, BO, hi, po, all equal to theT W, y B ° ae ste P, and respectively perpendicular to b g, t n,tx, Yo’ E H ’ Lp ’ an< ^ draw the hypothenuse e b, is, zn,«-pj 1 E Uo.

G to j las ' )e ' n g done, set off the width of the rail from e to d,S| errt of ° °‘ T to u > 1 to «, E to f, and L to m ; and set thePoint g a s d uar e on the line e b, till the blade touches thetlie lin e ’ ana draw the line c d. Moreover, set a square on' ira ' v tli e v ’ an< ^ w ' lere it cuts the line b g, as in the point I,® tf, y lne h i; and in like manner draw the lines p o,

a 0(] t|, e F > ar, d n m. Then the angles ~s.dc, a\h,~H p o, &c.do i'ep res eSt tl le little black spaces, as you see in the Figure,t:i ken off f\‘ t * le twisting of each piece, and what must be°i the -I 0 ® the back at the lower end, to make the twist

d 8 - Ihe lines being drawn, you are next to con-a jj — 1 manner they are to be applied in the working

6 | d«r a f t

th e y V What

d*'st lo n the piece of timber, of which you design to make the?*de tlie,? fc0 'r "ddch is represented in Figure 98, and plane one! n g to T,,*? st raight, and cut it to its bevels a c, b d, answer*

{joina - A “ ’

'g also 7 anc ^ KDA > Figure 97, and both ends'thereofthat CUt t0 t ‘ l(1 ra king-joint of the rail, proceed thus :S ' v,; rs to . P ai- t of the raking-arch in Figure 95, which an-a ^d lay j t le nrst length of the rail, as a A in the arch a u,tl^ 0tl t ' le u PP er s 'de of Figure 98, from l to h, andtgur e g* ar< '] 1 Hi, then take Ec, equal to G h, or up, int ^d 8 tfi] ie ’ an d set it on the line bd from h to m, Figure 98,** Dquai to ;^ Uare str °k e at pleasure from m to g ; also take1 ! > or T o, &c., Figure 97, and set it on the line

A;

from m to g, and draw the line hg, which represents theback of the rail when it is worked, and is equal to E d, or G»or N o, &c., Figure 97. This being done, represent the lowerend of the rail hg ki at right angles to h g; as also the upperend Icon at right angles to l c, and baste out the inward archc m square from the upper side abed, as mg; and take athin lath, and bend it close to the side thereof, from c to g,whereon strike a line along the edge of the lath, and so thelines Ih and eg are your guides in backing the rail ; which,when done, turn the piece upside-down, and with the mouldstrike an arch equal to Ih, from a to k, and baste out the sideto the lines Ih and o k; then you have one side and the backsquared, which is the greatest difficulty in the formation of atwisted rail, because the two other sides are found by gaugingfrom them.

“ Note. —If the triangles in Figure 97, and lines whereonthey stand, be supposed to be raised up perpendicularly, thenwill the lines a b, b l, tz, w x, b c, h i, and po, join toeach other, and produce one line perpendicularly over A,equal to seven risings or heights of the steps. But in work-ing a rail of this kind, you have need of but one triangle,abc sd, because they are all equal, and of but one effect inworking, they being drawn only to satisfy the curious in thenature of the thing.”

He finds the moulds for elliptical staircases in a similarmanner, viz., by finding an arch line divided into equal parts,so that each of them may be equal to the hypothenuse of thepitch-board, and the distance of the points of division in suc-cession respectively equal to the heights of the steps; thisprinciple is to be understood in all staircases where the stepsar.e equally divided at the well-hole, whatever be the form ofthe plan : but in elliptic staircases the degree of twist isdifferent, and therefore requires a pitch-board to be made forevery portion.

It is hardly possible to conceive any method so distantfrom principle as what is here shown : the squaring of thewreath is altogether guessed at, not to mention the greatdisadvantage in making the rail in so many pieces. If therifil were really executed, the above method would then be aproperty ; but the moulds never can be obtained from anyconstruction in piano upon the same consideration. It israther astonishing that any attempt should be made at demon-stration, for the support of a method so entirely destitute ofprinciple as the above.

“ How to form the arch or mould to the hand-rail of a pairof stairs that sweeps two steps, so as to stand perpendicularlyover its ground, and the manner of squaring the same, with-out setting it up in its position.

“ First : draw Figure 99, to represent the ground-work ofthe rail, whose arch, g c, consists of two different arches, onewhereof is a quarter of a circle, the other a quarter of anoval. A b (equal to a c, equal to C D, equal to B d) is equalto one-third of a step : and n is the centre to the arch c b ;also, b f is equal to two-thirds of a step, and f g is equal toone step and two-thirds ; by means of which, and B F, is thearch g b described. G k represents the straight part of therail to one step, and the arch h d is drawn by gauging fromthe arch G C; that is, it is drawn parallel to it, and thestraight part IH is found by gauging from kg, or is drawnparallel to it.

Figure 100, “ shows the manner of drawing the rake orarch of the rail, which is done thus : draw i l equal to g kof Figure 99, and represent the tread of the steps as before,by pricked lines. Then divide that part of the ground-workof the rail which belongs to each step into any number ofequal parts, as a f into five, and F K into four. This beingdone, draw ab,bc, od, in Figure 101, to represent the