JOI
84
JOI
its angular points or in its whole breadth, supposing boththe wreath and the mould to be set up in the true pitch.
He has invented a method of tracing the mitre-cap for thehand-rail, as used in dog-legged staircases, from a givensection of the rail.
He has invented a method of gradating the steps, so as toform a regular surface upon the soffit at the junction of theflyers and winders ; this not only gives an easy turn to theskirting, but permits the rail to be kept at a uniform dis-tance from the nosings of the steps.
He was the firet that showed a development of the plank,in order to apply the face-mould, and to range the two sidesin the cylindric or prismatic surfaces, according to the planof the rail.
In the article Hand-Railing, he has shown a more regularmethod of describing the spiral lines of the scroll, by findingthe centres in a fret or right-angled guilloche ; so that thedifference of any two adjoining sides of the fret will bealways the same. In order to describe the scroll with com-passes, he also invented the method of regulating the differ-ence of radii of a scroll by a line of sines; as had formerlybeen done by a line of tangents, in order to trace the scrollby hand.
He was the inventor, and the first that showed themethod of getting the scroll out of the solid, without gluingany part.
The method of capping an iron rail was never practisedwith certainty until his invention appeared in the Carpenter’sGuide.
He was the inventor of the method of springing theplank, by making its plane of inclination to rest upon threevertical sections of the wreath, viz., one at each end and onein the middle, being obtained by three heights taken fromthe falling-mduld. By this means the thickness of the railis ascertained with certainty, and will never exceed 24 incheswhere the rail is intended to be 2 inches deep, and 2| inchesbroad ; whereas, by former methods, the plank would requireto be 6 or 8, or even 10 inches thick.
No author before him ever regulated the pitch of theplank by the falling-mould, but by the height of the stepsonly ; by this he obtained an immense saving of stuff.
He also invented the method of cutting the veneers inthickness, so that the rail may come off squared from thecylinder.
He was the first author that showed the method of scribingdown the skirting upon stairs, however irregular the stepsmight be in respect of each other.
He also invented a method for squaring the bars for thehead of a sash in a circular wall ; no method had been evershown before by which such work might be executed.
He invented, and was the first to show, a method for theformation of a circular architrave in a circular wall.
Besides Price ’s method of raking mouldings, he added thatfor the angle-bars of a polygonal window, such as tire usedin shop fronts.
He improved the method of proportioning mouldings, byshowing how the projections were to be found in the sameratio with the heights, which had been neglected by otherwriters.
He was the first that treated upon hinging, and thehanging of doors and shutters, and the various kinds offolding joints.
In Figure 176, No. 1, aiicdefghi is half the ground-plan of a continued rail, viz., where the risers are equal toeach other, .as are likewise the heads.
Figure 177 shows the falling-mould, and the developmentbelow it, to the quadrant efgei; and because the risers
and treads are all equal, the edges of the falling-mould Wittbe straight lines parallel to each other : ef g hi, No. 2, is a °orthographic projection of the quarter of the rail, corre'sponding to efgh l, No. 1; in No. 2, draw lt parallel toA i, No. 1; make the angle vlm, No. 2, equal to the ang'®which the edge of the falling-mould makes with the base 0the development in Figure 177; through i draw kn parall®to L M ; through N draw NM perpendicular to L M ; throug 11L draw l k parallel to M N ; then m n or l k will be the thick'ness of stuff necessary, according to the method given bjPrice and Swan.
a b e defg hi, No. 3, is a projection of the rail to t* 1whole semi-circumference. We shall now show the thickne® 3of stuff according to Pain . It will be recollected that h efinds the pitch of the rail by the diameter or semi-diainetC’and the rise of the steps in the semi-circumference or quart®*accordingly; suppose, then, there are eight steps in the se!D Kcircle, now w y is the diameter, and y x the rise of eig nsteps ; therefore join w x, and you have the line of seed 0 ®of the cutting-plane : through a draw r s parallel to w x, o nthrough i draw qt, also parallel to wx: draw TS and Qperpendicular to war; then the breadth Q r or t s, and t®length qt or r s of the rectangle qr s t, will be respective ”the thickness and length of the stuff. ^
The projection of the upper half of No. 3 is equal 8**^similar, and similarly situated to No. 2 ; the lower ha"No. 3 is equal and similar to the upper part when reverse >the lower part at abed showing the soffit, and the upp e "fg h i, the back or top of the rail. ,|
Figure 178 shows the projection for a quarter of the r® ’upon a plane parallel to one of the radii : this shows ®^equal thickness to that shown at No. 3, Figure 176, the p' tebeing obtained from the radius, and the height of the st®rin a quarter of the circumference. ^
Figure 179 shows the method of finding the face-W° u , gaccording to the first invention of Nicholson, shown in , )0Carpenter’s New Guide, where the cutting plane ofcylinder is perpendicular to the plane of the chord of the r .and passes through the upper corners of the sections at ®^ (J |end. Figure 180 shows the projection upon a plane P il,ll |,],to the chord of the plan, agreeable to the face-m oU 0Figure 179. All these projections are made agreeableone pitch-board, Figure 177. c |i
We shall now show the quantity of stuff according to e .^method. Figure 181 is a development of the plank, s ' lOrt ,j,0fthe application of the face-mould according to Price , tog® 1 ^
with the thickness, the length, and breadth of the P. ge iThe particular measures are to be taken from the subjo 1scale.
Ft. In.
} 1 5 .{
which reduced toinches, gives 17-
The lengthmeasuresThe breadthThe thickness 0 6
By these measures we obtain 867 solid inches l0quantity of stuff required by Price ’s method.
J --!- - j ---- # A« \t>
Figure 182 is a development of the plank according 1pitch and face-mould required by Pain ’s method, for a ' vsemi-circumference.
In.
which reduced toinches, gives 34.
44
The lengthmeasuresThe breadthThe thickness
JL L. All.
} 210 {