The head of the sash depends on the cutting of a hollow cylinder, so that the side contained between the two cylin drical surfaces, that stand upon the exterior and interior sides of the plane of the sash, may be every where perpen dicular to these surfaces, and to follow the true shape of the elevation of the window, and thus the angles will be easily moulded. But in order that there may be no variation of the mouldings in a circular sash frame, it is necessary that both the radial and circular bars, as well as the head, should be moulded upon the same principle as a hand rail, viz. by means of face and falling moulds ; the face mould for the radial bars will be as before observed, and the fall ing mould will be a parallel slip of wood, straight in the edges, in breadth equal to the thickness of the bar. The falling moulds of the other parts must be made according to the development oldie cy lindrical surfaces.
In fig. 1. ABC, Plate CCCXXXVII. is the elevation of the head of the sash, and ADC the plan of, the same. Bi sect the arc ABC in B : draw BE perpendicular to AC, cutting the concave side of the plan at D : draw DG paral lel to AC, and AG parallel to BE. Bisect the arc AB at 3, and draw 3 c parallel to BE, cutting GD at c, and the curve AD ate : draw the straight line A 3 K : draw All making any angle with AK, and 3 1 parallel to All : make All equal to AG, and 3 I equal to cc': draw the straight line IIIK : join 13K, and produce 131( to L: draw AL perpen dicula• to 131,, and join HI,. Divide the arc All into any number of equal parts as here, into 6 : draw 1 a, 2 b, 3 c, &c. parallel to BF, cutting the inside of the head of the sash at a, b, c, Sec. the inside of the plan at a, b, c, &c. and the straight line GD at a, b, c, &c. From the points a, 6, c, &c. draw ad, GU, cc', &c. perpendicular to AL, cutting IlL at b', c', &c. and AL at g, h, i, &c.: perpendicular to III, draw a' a" , 146" , cc", &c. Make a' a" , b' b", c" , re spectively equal to ga, hb, ic, acc., and through the points cc" b" c" &c. draw the curve a" b" c" d" j" : draw also the straight line p,q, r, parallel to AH, cutting AL at g, HL draw rs, perpendicular to IIL ; make rs equal to glz ; draw LB' perpendicular to IlL, and make LB' equal to LB; join I Is, sa" and B' f" , which will comple the concave edge of the fact: mould. In the same manner, by transferring the perpendiculars between AL, and the convex side AB respectively, to the perpendiculars upon 111,, we shall have the points through which the convex edge of the face mould must pass, then tracing through the points so found, will complete the face mould R.
To draw the falling mould S. Fig. 2, for the convex side of the rail. Extend the arc AB, Fig. 1. with the divisions to the straight fine AB, Fig. 2. and mark the extremities A, B, and the divisions 1, 2, 3, Stc. Draw the lines AA', 1 a, 2 b, 3 c, &c. perpendicular to All. From Fig. 1, transfer the distances G A, al, cc', &c. to Figui e 2. upon A A',1 a, 2 b, 3 c, Su.. and draw the curve A a b c d c B will give one edge of the falling mould S; the lower edge will be found in the same manner.
To find the falling mould T, Fip.. 3. for the concave side. From Fig. 1. extend p a, a b, b c, &c. to f, to Fig. 3. and place them upon PF, from P to a. a to b, b to c, &c. per pendicular to PF draw P 1, a m. b n. &c. From Fig. 1. transfer the perpendiculars g r,g a' h b',i c, &c. to Fig 3. upon P I, a m,b n, c o, Ecc. and draw the curve /mnopg r. From Fiv. 2. transfer AA', 1 a, 2 b, 3 c, &c. to Fig. 3. up Ste. and draw the curve a bcd eF which gives the upper edge of the falling mould T. The under edge of 'I' will be found in the same manner from the un der edge of S. The upper line in n o p 9 r coincides with the top of the stuff, when the mould '1' is bent round, and the space between the curves a b c e I!, and / m r. 0 1t q r, shews the waste of stuff at the acute angle of the piece.
Fig. 4. shews the application of the face mould R to the plank ; the plane U shews the upper face of the plank ; the plane V the edge ; and the plane NV the lower face of the plank ; so that the two sides and the edge of the plank shew as if they were stretched out it one plane.
To apply the moulds in order to square the stuff, that is, to make it stand over the plane, and opposite to its eleva tion, when set up in due position : Apply the mould first to the top of the plank at U, so that the chord line of the con cave arc of the mould may coincide with AB, the edge of the plank, then draw the form of the mould upon the plane U ; let g be one of the extremities of the chord ; draw g I: perpendicular to AB, cutting the orris line CD at h ; make the angle B gi equal to the angle LHA, Fig. I. and the angle h f in the plane NV equal to LYE, Fig. 1. make hf equal to h and drawf e parallel to CD. Then apply the mould to the plane NV, so that the face may coincide therewith, and the chord with the line CD, and the point that was at g may now coincide with f ; then draw the form of the mould upon the plane NV ; proceed to cut out the head in the same manner as directed for a hand rail.