dition of the trees to their right outline without injury from constantly working over the paper. Here the vanishing points are too distant to be shown on the diagram; but the reader, from the tendency of the several lines, will easily find where they lie. In the same manner, he will find whereabout the station point is placed. BA, BA, BA, No. 2., are lines for the transference of the heights. The projection of the cornice is dotted round the leading lines of the building on the plan. The rest of the figure cannot fail of being understood and put in practice by the student who has made himself master of the preceding examples. 2443. We shall now turn to a point whereon much difference of opinion has prevailed, namely, the adjustment of what may generally be considered the best angle of vision, within which objects should be seen to obtain the most agreable representation of them. For as this angle is enlarged or decreased by viewing the objects at greater or less distances, their appearance will vary, and their delineation, in consequence, be affected thereby, and distortion of the objects will be the result. B $448. The attempt to sele 60 degrees; and others allo 2444. By the angle of vision or angle of view is understood the expansion of the lines proceeding from the eye, by the two extreme visual rays embracing the whole extent of the view, and this whether it consists of one object or of many. Let A (fig. 835.) represent the plan of a mansion; let B be the C outhouse contiguous to the mansion, and let the places of trees be at CCC and DDD. Let S be the station or point of view from which the whole is seen. Considering the mansion A as a lone object, the extreme visual rays Sa Sb form at the eye the angle aSb; then aSb is the angle of view under which that object is seen, Sa and Sh being the two extreme visual rays embracing the whole extent of the object. Again, if the outhouse B be taken as a single object, then will the extreme visual rays eS and dS form, at the eye, the angle eSd, being the magnitude of the angle under which that object is seen. So of any object, the visual rays that embrace its whole extent form the angle of view under which it is said to be seen. It is then manifest that the angle of view will be either large or small, as the eye is near to or remote from the object. Suppose both the objects A and B are to be taken into the view, with the ad Fig. 835. B dition of the trees to their right and left. Let visual rays be drawn from the trees on both 2447. Smallness of object has no relation to the angle of view; a die, or the smallest possible object, may be brought so near the eye as to give pain in looking at it, and a large extent of view may be contemplated with as much ease as a small one, by merely placing the larger one at a greater distance. If the place of the plane of delineation be at FG, then FSG will be the angle of view. If a section of the same visual rays be taken at HI, then HI will be the extent of the picture, and the angle HSI is the angle of view; but the angles FSG and HSI are the same, therefore the eye views both with equal satisfaction but in this case one must be placed at the distance SO, and the other at the distance SP. 2448. The attempt to select an angle suitable to all the cases that may occur, as the best angle of view, would be as vain as it would be absurd. Different subjects require different treatment. External subjects differ from internal ones; and the last from each other, according to circumstances. Some authors on the subject have laid it down as a rule, that the greatest distance of the eye from the picture should not exceed the width of the picture laterally, which makes the angle of view about 53 degrees; others have insisted that the distance should be less, requiring that the angle of view should not be smaller than 60 degrees; and others allow of a still larger angle. The elder Malton, and his son, to whom we are indebted for all that is valuable in this section, and whose (both of them) experience in the matter was very extended, advise that the angle of view should never exceed from 53 to 60 degrees; the former recommending an angle of 45 degrees as the best, because neither too large nor too small. The elder Malton advises to keep between the one and the other, that is, not to let the angle of view exceed 60 degrees, nor be less than 45, the first being likely to distort the objects, and the last rendering them too tame in the outline. We can add, from our own experience, that the advice is sound; for though, under very particular circumstances, it may be necessary to use a larger angle of view than 60 degrees, such a case does not frequently occur. Much must always be left to the discretion of the artist in respect to points which are to guide the angle of view he adopts. After a little experience, he will find that angle best suited to the circumstances under which his drawing is to exhibit the object or objects. 2449. Example VII. The principles upon which we delineate any of the interior parts of a building are in no wise different from those used for the representation of their external views, for it is of course immaterial whether we represent the external faces of their sides, or those which form their internal faces; the only difficulty which arises in making an internal view being that which arises from the inability, on account of the restricted distance under which they are in reality viewed, of placing the station point at such a distance as to take in a sufficient quantity of the objects to be represented. A person placed in a room can of course only see the whole of one and part of another wall; in short, in every direction he cannot see comfortably more than, as we have above mentioned, forty, or, at the most, fifty, degrees of the objects around him. On this account, and for the purpose of showing more than in reality can be seen, it is customary, and perhaps justifiable, in order to give a more comprehensive view of the interior to be delineated, to place the station point of the spectator out of the room or place, supposing one or more of its sides to be removed. This is, in fact, a delusion, as is every view of an interior possessing any merit that has come under our notice. But for picturesque delineation, it is not only one which is necessary, but one without the practice whereof no satisfactory representation can be given of an interior whose dimensions are not very extended. The section whereon we are now engaged is not supposed to be a treatise on Perspective, but merely a concise developement of its principles so as to give the reader such a general knowledge of the subject as may enable him to pursue it, if he please, from the hints it affords. With this apology for not producing to him a more complicated, though not less useful subject, we proceed. 2450. Fig. 836. (No. 1.) represents the plan of a staircase one third the size used for the purposes of the delineation; YZ (No. 1.) is the plane of the picture, O is its centre. From the data, therefore, there will be no difficulty of obtaining the vanishing points of the sides Ya and ab. The diagram is not encumbered with the visual rays necessary for the delineation, which we are to suppose drawn and transferred to their proper places on No. 3., wherein HH is the horizontal line. No. 2. is a longitudinal section of the staircase, wherein are shown the rising and descending steps, and the dotted line cd gives the section of the vaulted ceiling over the staircase. It will be immediately seen that the ends of the steps will be determined by visual lines, notwithstanding the ascent and descent of them, because either is determined by referring to any lines of height, which may be obtained from the plan and section, by which the portions seen of the flights will be immediately found and transferred to their respective places on the picture. With these observations we leave the diagram for the exercise, on a larger scale than here given, of the ingenuity of the student. 2451. Example VIII. The last perspective example to be submitted is that of a cornice (fig. 837.), wherein the contrivance of the elder Malton is used for finding the places of the modillions and the other parts. 2452. Let EM, FN, GO (No. 1.) represent the angles of a building in perspective, LMNO being the lower horizontal line of the cornice, whose geometrical elevation and profile are shown in No. 2. Make MQ equal to mq the depth of the cornice, supposing the edge EQ to be in the plane of projection; draw PQRS, &c., the lines of the top of the cornice, to their respective vanishing points. Make QT, QT' in RQ, PQ, produced equal to the perspective projection of the cornice qt. Then place the depths of the various mouldings along MQ, and fix the lengths of their projections on the lines drawn to the vanishing points through those in EQ, an operation which may be much facilitated by drawing MT, MT, by which, in many places, the points of the mouldings are at once determined, as in the case of the top and bottom of the fillets of the ovolo; and very often, if the drawing is not on a very large scale, mt and its perspective images MT, MT, &c. will enable the eye to proportion the mouldings. Thus the perspective projections MQT, MQT' of the sections of the cornice by the planes of the sides EN, EL, supposed to be prolonged or extended, may be found; and it is manifest that lines through the points of these sections to the proper vanishing points will give the perspective forms of the cornice mouldings as they would appear. 2453. The lines found will by their intersections supply the mitre MQU; but where the scale is large, it is better to obtain mitre sections at each principal angle of the building as shown by the lines MQU, NRX, &c. The planes of the mitres form, of course, angles of forty-five degrees with the sides of the building itself, consequently the vanishing points of QU, RX, &c. may be found by bisecting perspectively the right angles found, or by drawing on the plan lines parallel to the diagonal lines or mitres from the station point to intersect the picture. If these, indeed, are found in the first place, there would be no necessity to draw the square sections MQT, MQT, inasmuch as lines drawn from the mouldings intersecting the mitre sections to the vanishing points will at once form the perspective representation of the cornice. In practice, this is the usual mode of proceeding, because a skilful draughtsman can pretty well proportion by his eye most mouldings as seen in perspective; but where great accuracy is required, the method of proceeding by square sections is recommended, because, from the great foreshortening of the diagonal line, the smallest inaccuracy of intersection on it will cause very large errors in the mouldings. When the diagonal sections alone are used, it is clear that the geometrical profile, No. 2., will not be the same as that formed by the oblique section of the cornice: this last must therefore be obtained from a plan and elevation of the mouldings as shown in No. 3. 2454. Instead of finding the square section made by the plane FNGO at the angle OG, it may be drawn on the plane TQM, where it is more readily found by producing the lines whereby the section TQM was obtained; so the lines TT", MO are set out in perspective equal to the projection of the break of the building ON: moreover by the line T"O" we may obtain the mouldings of the cornice on the face of the wall GH as produced or prolonged to T"O", and conversely the cornice in perspective may be drawn from this imaginary section, if it be previously found. Where vanishing points Fig. 837. a. C D are at an inconvenient distance in draw- is this. Let A (fig. 837 a.) be the vanishing point, CDB a segment B Fig. 837. b. a vanishing line for such bisection; and if CD be bisected, and a ruler applied to join CD, it will, by the application of a square on CD, give the vanishing line for the new bisection. Fig. 837. b. 2455. Our next care is to find the vanishing point of the raking mouldings, which may be found from what has already been said, and a perspective section must be made of these mouldings by means of any vertical plane where most convenient; but the best place is through the apex of the pediment, which, as it could not, for want of room, be done in the present example, is taken through the line oo, No. 2., passing through the extreme left angle of the tympanum of the pediment. 2456. As the mouldings of the pediment (fig. 837.) here are of the same depth and projection as in the horizontal parts, they will not, when inclined, coincide with the diagonal section of the horizontal cornice at OS; hence that section, if found in perspective at OS, cannot be used for drawing the perspective representation of the pediment cornice, except for the bead or fillet above the corona, which, from the construction of the pediment, will coincide at this mitre, as we may see in No. 2.; whence it may also be seen that the point does not coincide with t. X'z cannot, therefore, in the perspective representation, be drawn through X, the point answering tot in the diagonal section NRX. OO' in the line OH is to be made in perspective equal to mo, No. 2., and the whole depth oo, and those of the several mouldings on the oblique section, being set upon EQ produced, they are to be transferred to 00' by means of the vanishing points. The distance O'I is the perspective distance of the projection qt of the cornice as before, and is most readily obtained from the section O"T", which is transferred to the plane OʻI, and will be easily comprehended from the figure; the quantity of projection of each raking moulding of the pediment is equal to that of the same moulding where horizontal. Thus the perspective representation of an oblique section made by a plane passing through oo, No. 2., is obtained, and the mouldings are then drawn to the vanishing point through the various points, the line IX cutting TX in the point corresponding to r, No. 2. As to the modillions, their representations are found with less confusion by planning them apart and using visual rays; but if no plan is used, the following method, invented by the elder Malton, may be adopted: 2457. Draw BC, the line intersecting the plane of the sofite of the corona, Nos. 2. and 3., through the proper point in MQ at right angles to it, and draw ry to the vanishing point. Produce the line corresponding to A in No. 3. to A in zy, and transfer A to 1 in BC, so as to be proportional to it in respect of the whole extent. Then set off the proportional widths and intervals of the modiflions, as shown on Nos. 2. and 3. on BC, and transfer them by means of the same proportioning point by which z was transferred to 1; and from the points 2, 3, 4, 5, 6, &c. in ry thus obtained, draw on the perspective of the sofite by the use of the vanishing point the lines representing the tops of the modillions corresponding to 2, 3, 4, &c., No. 2. The cymatium round them and the inner angle of the sofite may be drawn by the eye, or where great accuracy is required, the mitre or diagonal sections may be determined as for the principal mouldings already described. At the backs of the modillions the verticals are to be determined either by means of visual rays from a plan, or through the medium of intersections of the perspective lines of the upper parts of them on the sofite, which is as much as can be requisite for guiding us to a correct delineation. The same process is to be used for the modillions on the other sides. D 9 A B R E The following is an easy method for dividing vanishing lines in perspective. Let AB, CD be the perspective representation of two parallels, no matter in what plane, It is required to divide the given portion of AB on one of them so that its parts shall be the perspective representation of equal portions of the real line (or in any assigned ratio). Draw BE parallel to CD and equal to AB, and divide it into the required number of equal parts or of parts in the desired proportion beginning at E. Join AE and produce it to meet CD in F. From F draw lines to each of the points of division PQRS of the line AE, and they will cut AB in the required points of subdivision p q r s. F Fig. 837. e SECT. III. SHADOWS. 2458. Sciography, or the doctrine of shadows, is a branch of the science of projection, and some preparation has been made for its introduction here in Sect. VI. Chap. I. (1110, et. seq.) on Descriptive Geometry, which, if well understood, will remove all difficulty in comprehending the subject of this section. 2459. The reader will understand that in this work, which is strictly architectural, the only source of light to be considered is the sun, whose rays, owing to his great distance, are apparently parallel and rectilineal. It is moreover to be premised, that such parts of any body as may be immediately opposed to the rays of light are technically said to be in |