526 



CARPENTRY. 



Construe- rence meets the seat of the summit of the arches. 



tive If several adjacent ribs from the same pillar rise from 



Carp entI 7- as many points in a straight line, all the seats of the 



"^<~* ' joints for each, and all the portions, will have the 



same point of concourse. What has now been said 



will be clearly seen by the following diagrams, Plate 



CXX. 



PLATE Fig. 1. shows the plan of Gothic groining, where 



CXX. the ribs spring from points in the circumference of a 



Fig- lt circle, terminating the head of each pillar ; and con- 



sequently, if the arches have several points of con- 

 course, two of these points will run too far out of 

 the diagram for their centres to be marked. 



PKOB. IV. To determine the seats of the joints, 

 draw half the sectional curve ABC between two 

 opposite pillars, upon its seat AB : divide the curve 

 AC into as many equal parts as there are to be cour- 

 ses : through the points of division draw ordinates 

 to cut the seat AB : divide BD into the same equa- 

 lity of parts respectively as BA : let e be the next 

 adjoining point to D : produce e D till it meet the 

 seat of the summit ; but if the part of concourse 

 run out to a great distance, which is not accessible, 

 pioduce e D to n ; draw n o parallel to DB, meet- 

 ing the seat of the summit at o ; divide o n in the 

 same proportion as BD ; draw lines through the cor- 

 responding point of division in o n and BD, and 

 produce them till they meet the seat of the next di- 

 agonal ef\ join g e, which produce ; but if it is 

 likewise inaccessible, proceed in the same manner, by 

 drawing a line parallel to ef, arid dividing the line 

 so drawn in the same proportion as ~ef; and draw 

 lines also through the corresponding points of divi- 

 sion, and produce them to meet the seat g h of the 

 diagonal, and the seats of the joints will be comple- 

 ted for one side. Produce g i to p, and draw lines 

 from the points of division g h, to the seat i k of the 

 next rib, tending towards p : produce i I to q, and 

 draw lines tending towards q from the points of di- 

 vision in i k, to / m ; and the seats of the joints will 

 be completed for one quarter of the groin. 

 Fig. 2. PROB. V. To find any rtb, suppose the diagonal 



rib represented by its seat AB or EB. 



Take AB, with its divisions, and place it upon 

 CD, Fig. 3 : raise ordinates upon CD, equal in 

 height to those of the half section upon EF, and 

 trace a curve through the extremities, and it will 

 form the angle rib over the seat AB. Any other 

 rib will be found in the same manner. 



Pig. 3. Instead of the rib Fig. 3. being found from its 



seat, suppose the rib F'g. 4. to be described with a 

 compass : let the curve EM, Fig. 2. be divided into 

 equal parts, and lines be drawn to meet EL parallel to 

 the base EF, and let lines be also drawn perpendicu- 

 lar to, and meeting EF: let the base GH, Fig. 4. 

 be equal to the seat AB ; and HI equal to MN : 

 Fig. 4. make the distances on GK, Fig. 4. equal to those 

 on EL, Fig. 2. : from the points of division, draw 

 lines parallel to GH, to meet the curve GI : draw 

 lines perpendicular to GH, to meet it : apply the 

 divisions to AB and BE. Fig. 2 ; and they will be 

 the points for drawing the seats of the joints. 



Another method for finding points in the seats of 

 the angles and joints is, by dividing all the seats of 



the ribs in the same proportion as in Fig. 5, which Construe- 

 is the same rib with Fig. 2: the parts are taken from tive 

 PQ, PR, Fig. 5, and applied to ST, SU, Fig. 2, J 

 which will give the directing points of the stats of ^Tlf" 

 the joints, and also of the remaining one*. Fig. 6. j?j ' g 

 is the rib corresponding to ST, the base being divi- 

 ded, as PQ or ST. 



Fig. 7- is an equilateral fan groin. In this the four i> LATB 

 trilineal spaces, formed by the four quadrants, and CXX. 

 the circle inscribed, are all in the same horizontal F'g. 7. 

 plane ; the surface within the entire circle is gene- 

 rally horizontal, but may be raised with an arched 

 concavity of any form whatever ; the curve of the 

 rib, continued through this circle to meet in the 

 centre, would have no bad efftct, and would form a 

 kind of pointed dome. 



Fig. 8. is an oblong fan groin. In this diagram, p- 9 

 the sides of the transverse arch meet at an interior 

 angle, and the line of concourse terminates by the seat 

 of the horizontal rib, the radii of which is half the 

 breadth of the building ; the four tricurvilineal spa- 

 ces, comprehended by the arcs of the opposite hori- 

 zontal ribs, and the inscribed circle, are horizontal 

 planes, and the inscribed circle may be as in the pre- 

 ceding observation. These are generally filled with 

 fan work. It may be here observed, that the sum- 

 mit lines, AB, CD, EF, GH, will not be straight 

 lines, but curves, which will run higher as they ap- 

 proach nearer to the centre. 



Cylindro-cylindric Arching. 



Fig 1. is a plan of groining and arching in three Cylindro- 

 aisles. The side aisles, AAA, BBB, are vaulted cylindric 

 with cylindric groins : the middle vault and princi- Ac 

 pal aisle, CCC, being higher than the sides, form cy- 

 lindro- cylindric arches. The principles of construe- 

 tion are shown in the following problem, so far as 

 regards the construction of the angular ribs, for lath 

 and plaster, of the cylindro-cylindnc arches. Fig. 2. FJ~ ^ 

 is a section of the wud arch. 



PROB. VI. To describe the angular rib of a cylin- 

 dro-cylindnc arch, and to range the under edge, so as 

 to range with the two sides of the said arch, Fig. 3. p,v. $. 

 Let AB be the side of the groin, corresponding to 

 de, (Fig. 1.) and BC the side corresponding to ef t 

 the diameter of the vault of the. middle aisle, the di- 

 mensions being here extended to five times that of the 

 plan, in order to prevent the confusion of lines, which 

 would take place in consequence of a smaller scale : 

 let the sides AB, BC, be placed in position, the an- 

 gle of which is here a right-angle : divide the half 

 arc, standing upon AB, into any number of points, 

 by the points of division, 1, 2, 3, 4; produce the 

 side AB to h, and the side CB to d: parallel to AB 

 draw 1 a, 2 b, 3 c, 4 d, cutting B d, at a, b, c : from 

 B, with the radii B a, B b. Be, B d, describe arcs 

 d/i, eg, bf, ae, cutting BA at e,f, g : parallel to 

 B c draw e i, j'k, g /, h m, cutting the arc upon the 

 diameter BC, at the points ', k, /, m : parallel to AB 

 draw i n, k o, Ip, m G, and parallel to BC, draw 1 ?j, 

 2o, 3/j, 4G, and through the points n, o, p, G, draw 

 a curve, which will give half the seat of the angle 

 rib: join BG> and through the points n, o,p, G, 



