JOINERY. 



215 



riatrr. perpendiculars. A curve being traced through the 

 V"^ points, gives the form of the cap. The section, No. 

 1. is used in any kind of rail whatever. 



Fig. 5. shows the section of a rail in a circular form. 

 The sections of rails also form elliptic figures. 

 . 6. Fig. 6. is-another form, called a toad's back rail, to 



be executed in the beat houses. The top is generally 

 cross bended, with coloured wood. 



To draw the scroll for terminating the hand rail of a 

 . 7. geometrical stair at the bottom. I,ct A B, Fig. 7- be the 

 breadth given ; draw AE perpendicular to AB ; divide 

 AB into eleven equal parts, and make AE equal to one 

 of these parts. Join BE ; bisect AB in C, and BE in 

 lake CD equal to CF ; draw DG perpendicular to 

 AB ; from F, .with the radius FE or FB, describe an 

 arc cutting DG at G. Draw GH perpendicular to BE, 

 cutting BE at O. Draw the diagonals DOK and IOI. 

 perpendicular to DOK. Draw IK parallel to BA ; KL 

 parallel to I D, and so on to meet trie diagonals. From 

 D as a centre, with the distance DB, describe the arc 

 BG. From I as a centre, with the distance IG, de- 

 scribe |he arc GE. from K as a centre, with the dis- 

 tance KE, describe the arc EH. From L as a centre, 

 with the distance LH, describe the arc HP. Proceed 

 in the same manner, and complete the remaining three 

 quarters, which will complete the outside of the scroll. 

 Make BR equal to the breadth of the rail, viz. about 

 two inches and a quarter. Then, with the centre D, 

 and distance DR, describe the arc -h the cen- 



tre I, and the distance IS, describe the arc ST ; and with 

 the centre T, and distance KT, describe the arc TU, 

 which will complete the scroll. 



T>f 9. Fig. 8. Shews the construction of the curtail step, 



which is that under the scroll, abed represents the 

 veneer which covers the risrr : ie nosing of the 



cover, or lioriiontal part of the step ; i k I the face of 

 the string-board ; and m n o the projection of the not- 

 ing. 



, . Fig. 9. Shews the cover-board for the curtail step ; 



abed and rj'gk in dotted lines represent the plan 

 of the scroll ; opqrt the nosing of the curtail step: 

 IMV t the nosings and the end* of the risers. The 

 circle I, 8, 3, tec. is described from the centre of the 

 scroll, and divided into equal parts, equal to the 

 distances of the balutter* from centre to centre ; and 

 lines are drawn to the centre of the scroll, in order to 

 ascertain the middle of the balusters, by givin 

 gular gradation to the spaces. The whole of 

 ral lines in this and in F ig. 9- are drawn from the same 

 centres as the scroll. 



Three height* from the base being given on the sur- 

 face of a cylinder, or through three given points on its 

 surface, to find a section of the cylinder, the heights 

 of these points from the base being given. 



TLtir Lf and 2. PI the 



xix. base of the cylinder, and -he seats of the three 



1^. 1. i 2. noint*. of which the heights are a 6 c. Draw At) 



and CE perpendicular to the chord AC ; make AD 

 equal to a, BG equal to A, and CE equal to c. Pro- 

 duce C \ and ED to meet each other in F. Drw BH 

 parallel to CF, and GH parallel to EF; and join FH 

 and produce it to I, if necessary. In CF take any point 

 K, and draw KI perpendicular to CF, and KL per- 

 pendicular to EF, cutting EF at M. About K as a 

 . . -.re describe the arc M N. cutting CF at N, and draw 

 N I I mm F, with the distance FI, describe an arc 

 t L, and join 1 L. In the arc ABC take any number 

 of points, from which draw lines parallel to FI, meet- 

 From these point* in the chord CF 

 draw lines parallel to CE to meet EF. From these 



F'S- 



* * , 



points draw lines parallel to FL, equal in length to the Joinery. 

 lines parallel to FI ; and through the extremities draw ~~~~~ ~~* 

 the curve EPD, which is the section of the cylinder TE x ,x 

 required. The angle which the section now found 

 makes with the plane AC ED, is equal to the angle 

 CM. 



Fig. 1. No. 1. is the plan of a part of a geometrical 

 stair with winders and flyers below and above, with the 

 rail marked upon the plan. No. 2. is the falling mould, 

 found in the following manner. ABC is the semicir- 

 cumference of ABC, No. 1. extended in a straight line ; 

 AD and CE are each in length equal to the breadth of 

 one of the flyers extended in the same line ; EF, per- 

 pendicular to ED, is the height of twelve steps, viz. 

 equal to the heights of all the windows and two of the 

 flyers. Draw A I perpendicular to AD ; make A I and 

 FG each equal to the height of a step. Draw GH per- 

 pendicular to FG, and make GH equal to the breadth 

 of one of the flyers. Join FH, HI, and ID. Draw 

 BK perpendicular to AC, cutting HI at L. Make l.M at 

 the discretion of the workman ; through M draw OMP, 

 meeting ID in P, and produce FH to O. Make Pa, 

 P 6, O c, O d each equal to 1 D or H F. Divide a P into 

 any number of equal parti, beginning at a, and P 6 in- 

 to the same number of equal parts, beginning at P ; 

 and draw lines through the corresponding points of di- 

 . and they will form a parabolic curve. Divide 

 cO and o D in the same manner, and form another pa 

 rabolic curve ; and thus the curves and the straight line 

 a d will form the under edge of the falling mould. 

 Make M N equal to the thickness of the falling mould, 

 and through the point N draw the up|H-r edge parallel 

 to the lower edge, and thus complete the boundaries of 

 the falling mould. 



Make AV any distance, at the discretion of the work- 

 man, say * inches. Produce BM to K. cutting the up- 

 per edge of the falling mould at X. Bi-cct 14V in Q. 

 Draw QR and V\V parallel to BX. cutting the upper 

 edge of the falling mould at R and \V. 



Draw KTS parallel to EV. Make KT, TS, respec- 

 tively equal to tit}. <)\'. Draw TU and SY parallel to 

 KM. cutting the under edge of the falling mould at U 

 and V 



As one of the joints of the rail piece generally stands 

 over the middle of the semicircular plan, and the other 

 joint not over the place where the straight and circular 

 parts meet, but three or four inches advanced into the 

 straight part, in order to make a Wronger joint, by using 

 straight bolls or screws instead of circular ones ; in 

 laying down the plan of the rail for the face mould, we 

 most first lay down the circular quarter, and then ;idd 

 the straight part, which is shewn l>y AN' in the con- 

 struction of the falling mould. It is obvious that the 

 falling mould depends in some measure on the fancy of 

 the workman. The reason of raising it above the line 

 I, is, because if the rail were made the same heipht 

 above the step* over the circular part of the plan as 

 over the straight part, it would approach nearer to the 

 nosings of the steps of the winders than to those of the 

 flyers. It is evident that the ends of the steps might 

 be so narrow in the circular part, as even to cause 

 the rail to coincide with the nosings of the winders, while 

 the under side of the rail would be two feet and upwards 

 from the nosings, supposing the rail to be one height 

 throughout, both in the straight and circular parts; 

 the height being supposed to be regulated from tin- 

 top. The curves a ft and c d are entirely at the fancy 

 of the workman} some making them longer and some 

 shorter. Fig. i. 



In No. 3. the construction of the falling mould make N*. 3. 



