1454

THEORY AND PRACTICE OF ENGINEERING.

Hook II.

To construct a Trompe in an Angle raking with a salient Angle. — This is a prolongation ofthe preceding problem, cut by two vertical planes forming a right angle. The word

trompe , which has been so frequently madeuse of, is a peculiar feature in French archi-tecture of the time of Philibert Delorme ,who describes it as signifying a projectingvault supported in the air, and derived fromthe shell called the sea-trumpet; or becauseit is deceptive, its construction beinghidden. It is variously used, both on ex-terior and interior angles, in niches, or inround towers projected to contain a staircase:

19 l 20t

Fig.

Fig. 2393.

TROMPE OS AN ANGLE.

that called the Trompe de Montpellier was one of the most celebrated. Having dividedthe voussoirs on the quarter circle, E C, of the elevation, whose projection is seen on the planat EC, and transformed to this line the divisions of the quarter circle, by others parallel to theaxis G L, we must draw through the points a, b, c, d the point L, representing the apex of thecone on the plan, right lines from no, which indicate the projection of the circle, formingthe trompillion to G C, indicating the projection of one of the faces of the angle. Theselines will show’ on the plan the joints of the several voussoirs which form the trompe, andthe face of their intrados: to obtain their elevation, draw from the point L indefinite lines,passing through the points of division of the circle deba. To determine their extre-mity and height, observe that this trompe being formed by a right cone, whose axis G Lis level, if w'e prolong the side L C to the intersection of the perpendicular G M, with theaxis L G, the angle of the trompe raised perpendicularly above G will be in the middleof a semicircle, whose radius will be G^I, and which will be the base of a cone prolongedto the line G M : thus the height of the angle G should be equal to the radius; whence itresults, that to have the extremities of the joints of the intrados, which terminates at theedge of the trompe, we must draw through the points d,c,6,a of the plan, lines parallel toG M, which will indicate the radii of the semicircles in which the extremities of thesejoints are found. Then from the point I at the summit of the cone, on the elevation, with aradius equal to 5 d6 of the plan of projection, make the section, which will cut thejoint 4 d, prolonged in d: from the same point, I, with a radius equal to 7r, make mothersection, which will cut the joint 3 c prolonged in c: the points b and a may be obtained