Chap. XXIV.

MASONRY.

1455

in the same manner with the radii 96, 10, 11, a 12 of the plan. Through the points G,<?,c,6,a, C, draw a curve, which will express the edge of the trompe foreshortened: tohave this curve without foreshortening, take the breadth of the line G C on the plan;being the result of a plane cutting a cone parallel to the opposite sides, it will be aparabola.

To draw the profile represented in the development, which indicates the section of thetrompe taken on the axis L G, on the plan: first make the base line, L. F, equal to L G ;then from the point F raise a perpendicular, F G, equal to I G on the elevation, anddraw the oblique line L G, which gives the inclination and real length of the linepassing through the middle of the key: then set off En from the plan from L to o,raise the perpendicular on, which gives the vertical projection of the circle terminatingthe trompillion. In like manner set off LE from the plan from L to C, and raise theperpendicular C E, representing the projection of the quarter circle, E C, on the elevation :having then set off on this line the heights 17 d, 18c, 196, and 20a, from C to d,c,b,and a, draw these points to L, the summit of the cone; the indefinite lines will representthe joints of the intrados, to terminate which, and to indicate the curve at the edgeof the trompe, set off the points E, 11, 9, 7, 5, from the plan, from C to 13, 14, 15, and 16,through which raise the perpendiculars, cutting the joints of the intrados in the pointsa,b,c,d, through which and the point CG draw a curve which terminates these joints,and shows the edge foreshortened.

Development of the Moulds for the Intrados and Joints . — The intrados of the trompebeing oblique in two directions, cannot be wholly expressed either on the plan, elevation,or section: to find their elongation, it must be remembered, that the length of a line in-clined to the plane of projection depends on the difference of the perpendicular distancefrom its two extremities to this plane, which gives in every case a right-angled triangle,whose vertical and horizontal projections give the two sides forming the right angle ; sothat the hypotenuse of this triangle always presents the real length of the foreshortenedline.

In the figures which represent this trompe, the projection of the joints of the intradosof the plan, and the heights given by the elevation or the profile, express the sides oftriangles which answer to each joint, represented as foreshortened; thus, to have their reallength, we raise, from the points d,c, 6, and a of the joints shown on the plan, perpendicularsto each of the lines which represent them : the corresponding heights are set off at d,p,c,q,b , r,a,s ; then through the points/),<7,r,s lines are drawn to L, which give the true lengthof the joints of the intrados prolonged to the point of the cone: knowing these lengths andthe chords Gd,dc,cb,ba, and a C of the centre of the developed face forming the edgeof the trompe, we obtain the three sides of the triangles forming the moulds of the intradosprolonged to the summit of the cone, and they are united in the development, where theyare indicated by the letters L ,d, G for the half key, and Lcd,Lc6, La6, LCa.

The moulds of the joint are placed on the corresponding lines of the intrados to obtaina greater solidity : they are of equal width, and their lower angle is a right angle, that isto say, perpendicular to the slopes of the intrados, so that it only remains to find theelongation produced by the obliquity of the joint of the intrados with the face. To obtainthis elongation, take on the plan the length of the line "Lg , which represents the projectionof the diagonal of the joint mould of the key, indicated on the elevation by dg ; set off thislength from G to 21 on the horizontal line passing through g, and take the distance ina right line from I to 21, which gives the length of the diagonal required; with thislength, from the point L describe an indefinite arc, intersecting another, described fromthe point d with a radius equal to dg, taken on the development of the curve formingone of the two edges of the trompe, on the elevation ; having then drawn a parallel toL d, to mark the width of the joint, till it intersects dg prolonged, cut off by a line drawnfrom g the point of the mould intercepted by the level joint. To have the direction ofthis line, take the length L d on the plan, with which, from the point L of the develop-ment, describe the arc of a circle, intersected at the point 23 by another described fromthe point d, with a radius equal to the perpendicular height of the point d above thehorizontal line I C on the elevation.

To have the mould of the joint, indicated on the plan by Lc, and on the elevation by ch,take, as in the preceding, the length L6, which indicates the projection of the diagonalof this joint; set it off from 24 to 25 on a horizontal line of the elevation passingthrough h, to have the distance 1,25, which will be the length of the prolongation of thediagonal: with this length as a radius, from the point L of the development describe anindefinite arc, intersected by another, described from the point c, with a radius equal tothe joint of the head, ch, of the centre of the face prolonged: from the point of intersection,h, draw a parallel to L c, to determine the breadth of the joint, terminated by a perpen-dicular raised from the point 3, which forms the section of the base. The two othermoulds of the joints are found in the same manner: it is sufficient to draw on thestones which form the voussoirs the bevels which give the angles of the intrados with