CARPENTRY. 





Fig. I. 

 ig-2. 





...Im^ n< they arc built of atone or brick, <>r om- 

 Itrncted of rimber-work, lathed and plaaterfd over. 

 In thr f'.iiMHT case, a timber eenteung is made to 

 (orm the concavity, and placed in order to support 

 -roin during its erection. The criit.-ring con- 

 tints of several ribs, disposed at three or four K-.-t 

 distance, made to the si/e of the vault, which ha 

 tin- greatest opening. These ribs rest at their ex- 

 tremities upon beams supported by standards, and 

 are boarded over without any regard to the trans- 

 verse opening, which is afterwards formed by another 

 let of ribs adapted thereto, and then boarded so as 

 to meet the boarding of the first vault, which, if it 

 be of considerable breadth, must have short ribs fix- 

 ed upon its suaface, in order to sustain the board- 

 ing of the transverse opening, and thus the centering 

 will be completed. It is obvious in forming the ribs 

 for each vault, that the outer curve must be the arc 

 of a circle or ellipse within the curve of the vault, 

 and at a distance from it towards the axis equal to 

 the thickness of the boarding. In the making of 

 the ground centre, it will be necessary to find the 

 place of the angles upon the boarding of the large 

 vault, in order to ascertain the place of the ribs 

 and boarding of the transverse vault. This may be 

 done in three different methods. If two straight 

 edges are placed vertically at the angles, and ano- 

 ther straight edge or extended line be made to touch 

 the surface of the boarding, and marked at all the 

 points of contact, keeping this straight edge or line 

 always upon the edges of the two vertical straight 

 edges ; the defect of this method is, that the place 

 of the angles at the bottom can never be found, as it 

 would require the cross straight edge or line to be of 

 infinite length, and the vertical ones infinitely high. 

 A more eligible method, where there is room, is to 

 fix two ribs in the transverse part, and direct a level 

 straight edge upon the edges of these ribs, so that 

 the end may come in contact with the boards, and 

 mark the boarding in this place ; find a number of 

 points in the same manner as may be sufficient for 

 the purpose, and curves being drawn through the 

 points, will give the curves for fixing the ends of the 

 ribs. But the best method is by the following geo- 

 metrical problem. 



Fig. 1. is a cylindrical groin ; No. 1. the plan, 

 No. 2. the elevation. Such groins as this frequently 

 occur in lobbies, halls, passages, antirooms, &c. 



Fig. 2. is a cylindroido-cylindric groin ; No. 1. the 

 plan, No. 2. the elevation. It is this kind of groin- 

 ing that generally occurs in cellaring ; to construct 

 which, a centering must be formed as at Fig. 2. No. 

 3, 4, 5, and 6. No. 3. shows the cylindroidal part, 

 which is the widest opening, boarded over the whole 

 length ; then in order to fix the transverse boarding, as 

 at No. 2. the lines AB, CD, and EF, GH, No. 3. 

 must be drawn upon the boarding for the wide open- 

 ing, either by the former mechanical means, or by 

 the following geometrical process. No. 5. shows the 

 end of this boarding. If the wide opening be of 

 considerable dimensions, the shallow ribs, called jack- 

 ribs, are fixed between the lines to the height of the 

 cross-vault, and made less by the thickness of the 

 boarding, so as to come within this thickness of the 

 height of the groining. No. 4. shews the left hand 



2 



part completely boarded in ; No. 5. the end of No. Comtrue. 



. end of No. 4., shewing the face of ' 



on<- of tin- ribs of the centering, tlie tln< kn.-n of Jj^j^ 

 tlir hoarding, the jack-ribs over the boarding, and 

 the posts and endb of the beami that kupport the 

 whole. 



PROB. I. To find the mould or curve for deter- 

 mining the place of the angles upon the boarding 

 of the cylindroid, in order to fix the jack-ribs and 

 transverse bordering of the cylindric vault No. 4. 



PROB. II. Let it be proposed to find the angles p,. Air 

 of the groin on the surface of the foregoing board- CXIX. 

 ing. In order to prevent confusion of letters, we Fg. 2. 

 shall suppose the seal enlarged. Let AEM be half No ' 7> 

 the rib for the cylindroido part ; the bases AM, 

 and MN, being at right angles to each other, pro- 

 duce MA to M c ; extend the curve AE upon AM e , 

 from the equal parts or arcs A6, be, cd, rfE, to A/ 1 *, 

 f b h c , h c k d , /t d M e ; through the points of division 

 draw ordinates ; aizkef b g, h c i, k d l, M e N, equal 

 tofg, hi, kl ; MN, and through the points g, i, I, N, 

 draw a curve, which, when bent round the border- 

 ing at No. 3. from A to I, from C to I, from D to I, 

 from B to I , &c. determines the place of the angles. 



PROS. ill. To find the form of the end of the 

 boarding of the cylindric parts, in order to fit it against 

 the boarding of the cylindroido part, stretch out the 

 parts Mo, o/>, pa, i/R, of the arc MR, in the straight y\g. 9. 

 line MN r , from M to *, from s to *P, from t p to u* 1 , No. 7. 

 and from w q to N r ; draw the ordinates MA, *y, t p i t 

 tt q /, which make equal to MA, sg, ti, u I ; draw 

 the curve A^i/N, and the thing required is done. 



Centering to Gothic Groins. 



In one species of Gothic groins, the lines of con- c er , ter j n g. 

 course of the sides of the arches at the summit, cross to GotUu 

 one another in level lines parallel to, and equidistant groins, 

 from, the sides of the building. The vaulting is sup- 

 ported upon several ribs springing from the head of 

 each pillar, and terminating upon the transverse lines 

 of the ceiling at different equidistant points. The 

 surface of the vaulting lying upon, and between any 

 two adjacent ribs from middle to middle of these 

 ribs, may be considered to be a cunioid, and the ribs 

 may be considered to be sections of the cunioid. The 

 surface of the ceiling between any two adjacent ribs, 

 will therefore have this property, that a straight line 

 or edge applied everywhere level or parallel to the 

 horizon, to two given points on the surface between 

 any two ribs, will coincide entirely with the said sur- 

 face. From what has been said, it appears that the 

 seats of the joints of the arches between any two 

 ribs, will r.ieet each other in one and the same point 

 in the seats of the summits of the arches. It will 

 readily appear, that if eeveral ribs spring from the 

 top of the same pillar, each from a point in the cir- 

 cumference of a circle, or from an angle of a poly- 

 gon, that there will be as many portions of differ- 

 ent cunioids as there are pairs of adjacent ribs ; and 

 consequently the point of concourse of the seats of 

 the joints of each portion will be in the seat of the 

 summit of the arches, where a straight line drawn 

 through two adjacent points in the said circumfe-- 



