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• and supposing the secton of the moulding which stands in: the line of concourse of the obtuse angle to be given, it isrequired to find the section of the other, so as to mitre in aplane bisecting the remaining right angle of the solid. Thetrihedral will thus consist of three plane angles, two of whichare right angles, and the other obtuse.

Make an angle equal to that formed by the sides of theobtuse-angled plane of the solid ; let one of the legs be called: the mitre-line, and the other the raking-line ; draw the posi-I tion of the moulding at the point of concourse in respect of; the mitre-line without the angle ; take any number of pointsin the curve of the moulding ; through these points drawlines parallel to the mitre-line; also draw lines throughj the same points parallel to the raking-line : draw a line per-! pendicular to the mitre-line, cutting the other parallels ati right angles ; take the perpendicular, thus cut into severalportions by the parallels of the mitre, and transfer it uponany part of the raking-line, marking all the points of sec-tion : through the points of section, draw lines at rightangles to the raking-line, to cut its respective parallels;through the points of section of the parallels and perpendi-culars of the raking-line, draw a curve, which will be thesection of the moulding.

Theraking-mouldings in pediments depend upon this. Theraking-line is the top of the tympanum ; the mitre-line, theangle of the building ; and the line of concourse of the ob-J tuse angle of the solid, the level returning cornice, at right

j angles to the tympanum, or plane of the front of the

; building.

| The same is also applicable to a hollow trihedral, such as! the inside of a room, of which the two vertical planes are atright angles to each other, the legs of the one plane forminga right angle, and those of the other an obtuse, angle; andconsequently the ceiling, which is the third side of the trihe-dral, will be inclined to the horizon, like the exterior side ofi a pediment, or triangular roof, with this difference, that the\ surface of the former is opposed to the floor, and the latter; to the sky. Open pediments are not now in use, otherwise itmight be shown how the return mouldings were to be formed :j if, however, the above general description is well understood,j the reader cannot be at a loss to apply the principle to find-j ing the section of such return moulding in an open pedimentalso. This, however, will be noticed under the articleMoulding.

In a trihedral solid, with two of its planes at right anglesto the third, as in the preceding case, let the two planes makean acute angle instead of an obtuse one ; then the other twoi angles of the solid will be both right angled, as also each ofI the planes forming the acute angle : now supposing onei moulding to be placed in the line of concourse of the acutej angle of the solid, and another in the line of concourse ofI one of the right angles ; then if these mitre together upon aI plane, passing along the line of concourse of the planes whichj form the remaining right angle of the solid, they will showI the principle of the formation of the angle-bars of a bow-j window, consisting of three or more vertical planes. Asthe angle-bar stands in the concourse of two of the verticalplanes, suppose those two planes to be cut by a third planeat right angles to their line of concourse, and the solid thus' formed again divided in halves by a plane passing along the; concourse of the two vertical planes, bisecting the angle-bar,

| or the angle of their inclination, two equal trihedrals will bej formed, each having one acute angle and two right angles :j and the mouldings formed on the two legs of the front plane1 will be those required to mitre together. One of thesemouldings will be half of the angle-bar, and the other halfof the horizontal-bar.

The section of the horizontal-bar being given, to find thatof the angle-bar, —Lay down the horizontal side of the tri-hedral, viz., that side which is contained by the acute angle;then calling one of the legs the mitre-line, and the other thesash-line; draw half the section of the horizontal bar per-pendicular to the sash line, with the surface of the mouldingopposed to the mitre line; take any number of points in thecurve of the moulding, and draw lines through them perpen- Idicular to the sash-line, cutting it in as many points; takethe length of the intercepted line between the extreme points,and transfer it upon a line perpendicular to the mitre-line,with the several points of division from the mitre-line towardsthe section of the horizontal-bar; through the several pointsof division in the said perpendicular, draw lines parallel tothe mitre-line ; again, through the several points of divisionin the curve of the section of the horizontal-bar, draw linesparallel to the sash-line, cutting the respective lines parallelto the mitre-line, and the points of intersection will give thesection of half the angle-bar, by drawing a curve throughthem. The counter part being drawn on the other side ofthe mitre-line, the whole section of the angle-bar will becomplete.

The reader will perceive that this principle is similar tothe former, both depending upon the trihedral, or solid angle,consisting of three plane angles. The mitre passes throughone of the lines of concourse, and a moulding along each ofthe two others. In both cases, that which is perpendicularto the other two is laid down.

A circular sash-frame in a circular wall, is a solid ofdouble curvature ; its formation, therefore, depends upon thesection of a cylinder, and the covering of any portion ofthe cylinder.

The gluing up of the arecular bars depends upon thedevelopment of any portion of a cylindric surface.

The radial bars are portions of different ellipses, whichintersect each other in one common line of concourse, orconjugate axis, being the sections of a cylinder at differentinclinations, all passing through a line at right angles tothe axis.

Two of the sides of these bars are plane surfaces, and theother two curved surfaces are cylindrical; consequently theyterminate the plane surfaces in curved lines, which are por-tions of elliptical figures. j

The head of the sash is generally got out of the solid inhalves, or in four pieces, according to the size of the window,and when put together, ought to be so formed, that one con-cave surface may saddle upon a cylinder of a radius equal tothat of the inner circle, which forms the plan, while the outersurface is everywhere equidistant from the cylindric surface! iand that the other concave surface may coincide with theconvex surface of another cylinder, whose radius is equal tothat required to describe the interior curve of the sash-head,while the outer surface is everywhere equally distant fro®the cylindric surface. i

An enlarged or diminished cornice has its parts, in heigh*and in projection, of the same proportions as those of another,already given. Here it is only necessary to suppose theheight or projection given; thus, take one of them as theheight to be given, and find a fourth proportional to the fid" jlowing three measures, placed in order, viz., the heightthe given cornice, the height of the required cornice, and the Hprojection of the given cornice; then divide the height o*the required cornice in the same proportion as the heigh*of the given one, and the projection of the one required, ®the same proportion as the projection of that given. . I

The drawing of the flutes of a diminished pilaster, wi*h I

curved sides, depends also upon the division of a line in *h 8 i