159. The subject of this exercise (Plate XXIX) is a com memorative chapel of the Denticular Doric Order, and is to be drawn at the size.indicated-13" x18'. This is the first of three exercises where a dome plays an important part in the exterior effect of an edifice. In any study, in elevation, of a building employing a dome or cylindrical story, it must be remembered that, in perspective, that portion which is circular in plan looks considerably smaller with reference to the square base from which it springs, than it does in any elevation,—on account of the differ ence in plan between a square, and a circle which is contained within such a square;—in other words, the 'circle remains of the same diameter if seen from any point; while an object square in plan, seen from any other position than in direct elevation, has its width considerably increased by the projecting corners.
160. The plan of the chapel is a square, having on the side of the principal faCade, a projection formed by two columns placed upon pedestals and enclosing an arch whose proportions are like those of Fig. n, this projection being crowned by a pediment. The opposite side has a semi-circular projection, in which is located a niche in which the altar may be placed.
161. The entablature surrounds the entire building, but the triglyphs are found only beneath the projecting pediment of the main facade. The building itself is surmounted by a low attic in the form of a plain parapet, above which are two steps forming a base for the domical roof.
162." The interior of the chapel is a square with its floor raised three steps above the exterior level. In the corners are pilasters forty parts in width and fifteen in projection; these pilas ters, and also the entablature which surmounts them, are repetitions of the exterior order. The ceiling is a semi-circular vault or dome.
163. At the side of the facade is indicated the commencement of a retaining wall, with a grille, which might be continued to enclose a plot of land. • 164. Exercise R is a circular temple (Plate XXX, and plan Fig. 29) with a pedimented porch or portico, showing the use of the order set upon a dado around the interior walls. The ceiling is domical, with an opening in the center, and is ornamented on the under side by a series of recessed panels called caissons or coffers. This plate, like the one preceding. is to be drawn at the size of 13X18 inches.
165. Plate XXX shows an Ionic portico or porch attached to an edifice circular in form. The circular hall is six entablatures twenty parts in diameter, and the thickness of the wall is fifty parts. The perimeter of the hall is divided by pilasters of a smaller order than that on the exterior into twelve bays, as shown in the plan in Fig. 29. The difference in size is due to the pedestal, ninety parts in height, on which the pilasters are placed.
The scale for this interior order is obtained by dividing the total height of the pilaster and its entablature into five parts (each part representing one entablature of the interior order).
166. This circular hall is covered by a spherical cupola or dome, divided into caissons or coffers, the drawing of which consti tutes the most interesting part of this exercise; it will therefore be explained as clearly as possible. It is illustrated on Plate XXX.
167. The projection of the interior pilasters being ten parts (at the scale of that order) from the face of the wall, the interior diameter of the springing of the cupola is six entablatures. Draw
a half plan of the cupola, dividing its circumference into twelve equal parts and then draw the radii; lay off on each one of these' radii, outside the circumference, the profile of a rib and the two coffers one on each side of the rib, each eighteen parts wide, and the two coffers seven parts each and three parts in depth. Next draw in on the plan two semi-circles, one of three entablatures and three parts radius, the other of three entablatures six parts radius. Having thus established the whole profile of the springing of the cupola, draw from each division a radius to the center; then show above this plan, centering on the same axis, the section of the cupola, whose center will be found forty parts below the first hori zontal course. This height of forty parts forms a conge with an astragal above the cornice. The cupola is divided into five rows of caissons whose height is relative to their width. Notice that the first band above the astragal is fifteen wide; draw the vertical line from the point A (section) to the point A (plan); draw the quarter circle A which intersects at E and F the lines of the rib. Take from the plan the width EF and lay it off from A to B along the curve on the section, thus obtaining the height of the first row of caissons. From the point B (section) draw a vertical to the (plan) and draw the quarter circle through B' in plan intersecting . the radii at G and H. This distance (G II) laid off along the curve from B to 0 shows the width of the second horizontal band. Now project the point C (section) to C' (plan) and draw the quarter circle C' on which C' D' will give the height of the second row of caissons which will be laid off from C to D along the curve in the section. Continue this operation up to the fifth row of caissons. As to the widths of the coffers, they are found on the plan of each row of caissons and consequently diminish gradu ally with them. The profile of the caissons is formed in the section in this way and their location is found in plan. From each angle of the profile of the caisson draw a horizontal line through the section; this will give the horizontal lines on which all the points of intersection will be found in projecting the verticals from the corresponding points in the plan. Thus, from the point I (plan) which is found on the upper line of the topmost row of caissons, draw a vertical up to the point I (section) which is on the corresponding line in the section; from the point J (plan), which is found on the lower line of the same row of caissons, draw a vertical to the point J (section). Thus the circle I (plan) is ren. resented in the section by the horizontal line I; the circle J, in the plan, by the horizontal J in section, the circles L, M, and N in plan by the horizontals K, L, M, and N of the section. The points of intersection of the radiating ribs in plan with the circu lar segment I, should be projected vertically to the horizontal I in the section. Those of the circle J, to the horizontal J; those of the circles K, L, M, and N, to the corresponding horizontals in the section. In this manner on each horizontal of the section, are found the points by means of which the curves of the bands may be drawn.