JOINERY. 



^VUKiy. - 



_-- ^ therefore v- = 



at/* , 



-j x* ; whence we infer 

 c o* 



\ui. that the curve is an hyperbola ; and if a and c become 



Ki ' ' l d* d 



equal, we should then have y' = -:- x', or _y = -=- x, 



and consequently, in this case, the projection of the in- 

 tersection of th<- two surfaces would be straight lines, 

 and would form the figure of a groin ; and if A and d were 



equal, we should have y' =: - - -| **, which 



i* a case that would more frequently occur in practice. 



Binoplc 3. $-* s - Suppose the generating figure of the one pri-m 

 to be a semi-ellipse, ef which the greater axis is the 

 base, and the generating figure of the other to be a se- 

 micircle; and that the rectangle described by the great- 

 er axis of the former, and the rectangle described by 

 the diameter of the Utter, are in the plane of projec- 

 tion. 



f..-. >>. Lt APDC, Fig. 22. be the half of the generating fi- 



gure of the elliptic-prism, or semi-cylindroid, and 

 A'P'D'C' be half of the generating figure of the semi- 



r' nder. Make CA = o, CB = r, CDs*, and BP = j; 

 = c, C'B' = z, CD' = d, and BT' = y. 

 Then, from the property of the ellipse, in the figure 

 APDC, we have : A*: : (a + x) (a s) : r ; whence 



z'). 



Therefore :' = a- r- ** 



Again, from the property of the circle in the figure 

 A'PD'C, we have y = (rf -f z) </ r) = (f 



whence * = d 1 -y*, therefore a* TJ- ** = /* s* ; 



whence y* = rf 1 a* 4. j~ **. Wlience we infer that 



the curve i* an hyperbola. 



This example i* exceedingly useful in groined arches. 



> 

 Let y = o, then will o = rf 1 a + **, whence i = 



^(tf f), which it half of the greater axis of the 

 curve. Suppose y infinite, then will y'=.^ *', or 



,y = 4-*, therefore*:*:: y : s, that it GF: FE::t: y; 



whence GE U an asymptote to the curve. If a = 4, a* 

 is generally the case, we thall have y' = f o 1 + * ; 

 and in this case, if y = o, we shall have j* = a* 

 rf* = (a + d) (a-~d); therefore this particular value 

 ' will be a mean proportional between the sum and 

 fofthr two radii. 



Of the tariotii F-rmt of Jwolt f,,r Opart and Sh*tlert, 

 Mtf oftkt Mtltiodt of Hinging them lofttkrr. 



The form* of joint* for folding and hinging i* essen- 

 tial to the beauty of the work. > - ought to 

 be to made, at to preserve the uniformity of the door 

 or shutter on both sides ; and to exclude at much air 

 at possible from rushing through between the edges of 

 the two bodies to be hinged, and thereby rendering 

 the apartment* cold* in winter. 



In the joints of doors which are to be hinged toge- 

 ther, both angle* of one of the bodies are usually bead- 

 ed, in order to conceal the open space which would 

 be seen from every point of view ; and to preserve the 

 regularity of the work, the hinges employed to couple 

 them together are made exactly to the size of the bead, 



tot. an. r.\aj i. 



on the side on which the knuckle is to be placed ; so Joinery. ^ 

 that, when they are hung, the knuckles of the hinges ^ "V" 1 *' 

 and the wooden bead forms one continued staff or cy- 

 linder. 



Plate CCCXXXIV. Fig. 1. Nos. 1. and 2, is a section PLATE 

 of part of the door style and part of the hanging style cccxxxiv. 

 at the joint. In this the centre of the bead on each **& * 

 side is in the line of the straight pirt of the joint from 

 the opposite side. To form the joint exactly, let C be the 

 centre of the bead, AG part of the joint in a line with 

 the edge of the same, join AC, and draw AB perpendi- 

 cular to AC ; the other part BH is perpendicular to 

 EF, the face of the door or hanging style. This joint 

 will be found sufficient for many purposes, and may be 

 hung with common hinges, and, being crooked, will 

 brenk the current of air. 



Fig. 2. Nos. 1 . and 2. is a plane joint, beaded alike on Fig. ?. 

 both sides. Here, as the plane of the joint is a tangent 

 to the cylindrical surfaces of both beads, the margin will 

 be alike on both sides, and therefore affords no check 

 in preventing the cold air from rushing through the 

 aperture or seam into the apartment. Another inconve- 

 nience is, that the hinge which is to connect the two 

 bodies must not be made in the usual manner, but in 

 the form shewn in No. 3, where the bodies are hinged 

 together. 



!. In Nos. 1. and 2. the plane of the joint from Fig. 3. 

 the one side is directed to the axis of the bead on the 

 other. This joint is upon the same principle as Fig. 1. 

 and therefore may also be hinged with common hinges, 

 at at No. 3. where the two parts are coupled together. 

 These forms of Figs. 1 . and 3. are applicable to those 

 case* where a part ef the margin is concealed on one 

 side of the door. 



Fig. 4. In Nos. I . and 2. the beads are of the tame size Fig. 4. 

 on both tides, and are exactly opposite to each other, 

 and the joint it broken by indenting a part which ter- 

 minate* by a plane directed to the axis of the two op- 

 posite bead*. This form is not only beautiful and 

 strong, but tends to* make the apartment comfortable, 

 and the hinges only require to be of the common form. 

 No. 3. shews the two parts hinged together. 



Fig. 5. In Nos. I. and 2. the beads are placed alike on Fig. 5. 

 both sides, but not on the same piece as in Fig. 4 ; and 

 though the uniformity is preserved, the bead which 

 projects the whole of it* thickness is weakened. 



Fig. 6. Shews the method of hinging shutters and con- Fig. 6. 

 cealing the hinges. A is the inside bead of the sash frame, 

 B the inside lining, C part of the style of the shutter. 

 To find the form of the joint, let af be the face of the 

 shutter perpendicular to a r, the face of the inside li- 

 ning. Bisect the angle y a r by the straight line a a ; 

 then, taking any point r in the centre, draw d d per- 

 pendicular to a a, cutting a a at c ; and c it the centre 

 of the hinge. From c describe an arc a m, which must 

 be hollowed out of the inside lining of the sash, from 

 the whole height of the shutter ; and the internal right 

 angle must be cut out of the edge of the shutter to the 

 breadth of the hinge, in order to make way for the 

 hinge in the act of opening and shutting. Here the 

 toil* of the hinges are shewn of different lengths, in 

 order to strengthen them. 



Fig. ?. 1* a joint with concealed hinges intended for a Pig. 1, 

 door; and here, a* the door it sufficiently thick, the 

 emN of the hinges are of equal lengths, and are conceal- 

 ed in the thickness of the wood. 



Fig. 8. Is the method of hinging shutters in the com- fig, g. 

 mou way, where the hinge it let it* whole thickness 



