Fig. 2, shews the angle formed by two ranges of buildings, each of which has a different vanishing point. N 0 is the per. pendicular edge of the angle ; N Q 0, and N P 0, shew the two faces, each of which is intersected by streets of various breadths. In both instances the specta tor's eye is supposed to be situated near two-thirds up the two buildings ; that is to say, about X on one face, and about W on the other. This produces a mixed effect, seldom to be found in reality ; though in some cases, where streets lying on a declivity, and joining others with less deviation from the level, this will be pro duced. The mode of proving the due direction of lines in perspective, such as X Q, and W P, which appear like the bands or fillets that separate the different stories of edifice, is very simple ; name• ly, all horizontal lines in buildings that decline from the plane of a picture, and tend towards some vanishing point, will, when above the spectator's eye, appear to descend towards that point, as from N to Q but when below the spectator's eye, they will appear to rise as 0 Q. The tri angle 0 Q N being more acute will give a more direct view of the houses, and ap pear to recede less from the eye than N P Q, which is more obtuse, and makes every house appear narrower.
Fig. 3, shews the front of a house, I H G, which, when thrown into per spective by the vanishing point, Q, being made high, and several rays proceeding from opqrst to k being carried too high, give an mare appearance to the front, as shewn by the outlines I F L M, in which it will be seen that a rude and unpleasant disproportion is given in every part. Nor is this even the manner in which the house would appear when seen from above, or below it ; on the principle of a bird's eye view. The places of the seve ral doors and windows being ascertained, the several lines, opqrs t, intersect the ground-line 1' M in those parts which cor respond with the places of the doors ; whose heights are ascertained or deter mined by the line S Q, equal at S F to their height in the original front I 11F G.
The windows being over the doors, must be under the same perpendiculars in both cases ; their depth is determined by taking the measurements on the line I S, and drawing rays to the point Q. This figure is given chiefly with the inten tion of spewing the immense dispropor. tions which are generated by a false placing of the point to which the rays proceed; and which point is always form. ed to advantage rather below than above the centre of a picture. When the horizon is too much raised, numberless distortions take place.
Fig. 4, gives the ground plan of a gal lery, R S V T, which is to be shewn in perspective with its several standards, and the pitch of the awning on the ground lines V X and W X. Here II cl) becomes the horizontal line, on which X is the va. nishing point, and c1) the point to which the- rays It (/), 9 0,10 0, and W 4), being drawn, cut V X in the places marked 4, 3, 2, 1, respectively, and give the si tuations of the standards for the right side. The places for those on the left side are found by drawing the lines 4, 5,; 6, 3; 7, 2; 8, 1; all parallel to W V. In this instance all the intervals, R, 9; 9, 10; 10, W; and W, V; being equal, the proximate superior ray will always give that parallel : thus the ray of R cuts X W exactly at the point 6, which gives the line 6, 3, parallel to 7, 2; and so of all in succession. The lines Y Z and
W V are parallel ; they determine the height of the front standards, and by means of the lines Y X and Z X cut the other standards at their proper heights. Their descent towards X skew them to be above the line n 4), which is level with the spectator's eye. The summits of the couples are ascertained by the line A X. They will all have their centres over the centres of the lines 5, 4 ; 6, 3 ; 7, 2 ; and 8, 1 : ascertained by drawing a line from B to X.
Fig. 5, exhibits the wall of a monaste ry, supported in some parts by reinforce ments, or pillars, betWeen which the wall is less substantial. The measurement of the pillars and of the intervals is given on the base-line AB, while G F spews the horizon and line of sight. The rays from a, c, e, and g, shew the places where the several divisions take place on the ground-line A E„ and shew the projec tions of b, d, f, h. The upper line is also determined by CD, and the crosses in like manner are made to diminish towards the vanishing point F. The small mark at A in the middle of the wall's thickness, as shewn by the shaded part, gives rule for each projection of. the several pillars, as shewn by the shaded parts : their sum mits and bases will, however, have their fronts, i. e. the parts parallel with C A, terminated by horizontal lines parallel with A B. We must once more impress, that all fronting horizontals in nature must be so represented in perspective, provided they do not extend beyond 60'; also, that in every instance perpendicu lars in nature are so delineated in per spective.
* The reader will have seen, that the base-line, and the depth below it, give the measure of the figure when obliqued. To render this more perfectly intelligible, let us say that it were necessary to place the square W, V, 13, Tin perspective be tween W, V and X (fig. 4). This being a square is readily done ; the more so, as it is proximate to the line ; because the quadrant T W is so readily acted upon ; \V V being equal to V T. But say that it were needful to place the line T K (fig. 4) in perspective on the line V X. Draw the quadrant T, W ; and the quad rant K, 10 ; the line W, 1, drawn to 402 will shew the place of 1', and the line 8, 2, will shew the place of K : therefore the line T K will be found in perspective be tween the points 1 and 2 on the line V X. Thus any line or object may be re presented ; observing that the distance at which it stands below the base-line must be measured on the baseline; when, by drawing rays to the horizontal line, (whereon all the vanishing • points must rest) its place on the oblique line, or scite, will be determined. Some authors on this subject have directed that the back ground should be limited by a semicircle, describing the half-horizon, and that all the vanishing points ought to be placed thereon. This, however well it may an swer in a panoramic point of view, cab never be so appropriate as the horizontal line, in a picture which includes only the sixth part of a circle.
What has been said relates entirely to mathematical perspective, and forms the basis of architectural design, and governs (though rather occultly) every kind of landscape painting : with regard to the perspective of living objects, and of va ried nature, that can only be acquired by attention to models, and to the real figures.