II.

Plate VII.

SECT. which point draw a line to the center of the picture, and divide that line perfpectively into the fame number of divifions, with the required foffits, as at u, v, and then transfer thofe points by lines drawn parallel to the horizon, producing the points c 2, c 3, by their interfections with the line that is drawn from the points c 1, to the center of the picture; and thofe points, c 1, c 2, and c 3, will be the centers for the fegments which produce the foffits of the ceiling, as g h, and the rest.

In Fig. 1, of the fame Plate, the ceiling is the portion or arc of a circle, but being of very faint elevation, the centers for the conftructions of the foffits, lie very low on the plate.

To find those centers, proceed as in the foregoing figure. That is, by Problem VIII. Fig. 10, Page 7, in the geometrical Section, find the center a 2, of an arc paffing through the points, S 1, P, S 2.

The points S1, S2, are the extreme width of the room, and the fummits of the nearest pilafters from which the foffits fpring; therefore, at thofe points draw the line a 1, parallel to the horizon, which will be the chord of the arch, bifect this line at a 1, through which point draw the line P, P 2, perpendicular to the horizontal line, and continue it downward as to a 2.

Then from a 1 and a 2, draw right lines to the center of the picture, for the other centers must be found in the line which is drawn from a 2 to the center of the picture.

To obtain the other centers, firft find the divifions perspectively on the fides of the room, from which the foffits spring, as the points S3, S4, S5, S 6, and at thofe divifions draw lines parallel to the horizon, or to the floor of the room; and thofe lines will cut the line that is drawn from the point a 1, to the center of the picture, and produce the interfections b 1, c, d, from all which points draw right lines perpendicular to the horizon, and where thofe lines inter

fect the line that paffes from a 2* to the center of the picture, will SECT. be the centers required for the different foffits.

In this figure, no more than two centers are given, which are a 2 and b 2; a 2 is the center for the fegment S 1, P, S 2, as already fhewn, and b 2, the center for the fegment S 3, S 4. The reft of the centers are omitted, because the lines neceffary to produce them would incumber the example, but if those which are given are well confidered, the student will have no difficulty in finding the rest, only let him remember that every line in the foffit must have its own

center.

II.

Plate IV.

IV.

In Plate IV. Fig. 2, is the representation of a building with femi- PLATE circular arches, which are drawn by compaffes, the centers are found by the process taught in the preceding instructions, given for Fig. 3, Plate VII. page 66.

The points 4 and 6 being the centers for the front of the foffits, and the points 5 and 7, the centers for the back line of the foffits of the arches.

Plate VIII. Fig. 1.

Which is drawn to a Scale of One Inch to a Foot

Represents a stool fituated parallel to the picture. The dimenfions PLATE

of which are as follows † :

The height is 1 foot 9 inches.

The width is 1 foot 6 inches.

The line which is drawn from a 2 to the center of the picture, is the indefinitive representation of the line in which the centers for all the foffits are found, for it may be confidered as the axis of the concave cylinder, of which the ceiling is a part.

+ The scale is not marked on the plate, therefore the student may exercise himself, by taking the proper measures from any common rule.

VIII.

The

* Having determined the feat of the nearest leg on the base line G, as at 1, fet on the whole width of the front of the stool, that is 1 foot 6 inches by the scale, from 1 to the point 4. Then determine the distance at which the ftool is placed beyond the picture, which is i foot 6 inches; thus from the point 1, fet off that distance by the fcale to the point 5. Then, from 5, fet off the depth of the stool, 1 foot 2 inches, to 8. Having thus determined the measures of what may be called the plan of the ftool, draw right lines from the points 1 and 4 to C, the center of the picture, and from 5 and 8, draw lines to D, the distance of the picture, and thofe points in which the lines that are drawn from 5 and 8 to D, cut or interfect the line which is drawn from the point 1 to the center C, will mark the space that lies between the picture and the object, and also the depth of the object,

Thus the space between the points 1 and e, represents the distance

* The ftool is difpofed as if standing in a room, of which a part only is feen. The lines R R, are the interfections of the floor with the fides of the room, and the line R 2, is the intersection of two of the fides which are seen.

Fig. 3. No. 2. is the representation of a square on the fame floor, on which the stool stands, therefore the center and distance of the picture are the fame with those by which the ftool is drawn.-See the explanation in Section VI. Page 245.

between