From f and g draw lines parallel with a e, for the sides of the figure ; draw the line e F to a perpendicular let fall from the horizontal line at r to M. From F draw a line to any part of the horizontal line, as to L, and draw from xi a line to meet this in L. To f draw the line f h, and to d the line I ; then from h and i raise perpendiculars to intersect F 1., and from the points of intersection draw the lines p I and r k ; thus will be obtained the perspective outline of the cube klfagoe. If the cube had not been viewed directly opposite one of its angles, the points of distance would not on each side have coincided with the vanishing points, and the vanishing points would have been best obtained as tor the triangular prism, fig. 12.
The procedure of a parallelopiped, is essentially the same as for a cube. To put a cylinder into perspective, first pro ceed as for a cube or parallelopiped, draw on the perspective of each, and such an ellipse as it will admit ; let the longer or conjugate axes be equal, and join the opposite extremities of these axes by two parallel lines, as shown in Figure 14. (laving thus obtained the perspective of the cylinder, it only remains to erase the lines which belong to the cube or parallelopiped.
Of shadows, and description for drawing perspective.— Having now shown the mode of putting into perspective those elementary forms which enter into the composition of drawings of every description, we shall be obliged to be con cise with the remainder of the subject. The student must be aware how much difference of position affiicts the visual appearance of objects. And that by a proper attention to this circumstance, the few rules which have been given, may be applied to subjects of considerable complication. To acquire a knowledge of the principles of perspective, it is recommended not merely to compare the plates with the printed page, but to copy the diagrams, and, for the sake of greater perspicuity, to do this on as large a scale as may be convenient. some treatise especially devoted to the subject may be perused, and perhaps Brook Taylor's and Idatton's may be the best ; tor although these authors will require considerable attention, they have the merit of being sure guides.
With respect to shadows, the proper distribution of which give such life to perspective drawings, it may be useful to remark, that the shadow cast by any object, covers the pre cise space which that object would prevent the eye from seeing, if the eye were in the place of the luminous body.
The position, therefore, of the luminous body must always be ascertained, and the shadow to be assigned to any object in a picture, will be a perspective view of the space which the eye would be prevented from seeing, if in the place of the luminous body. A few experiments with a candle at night will be an easy mode of gaining a little acquaintance with this subject ; it must, however, be observed, that the shadow from a candle is every way larger than that part of the object which intercepts the rays ; but in point of breadth, this never happens with the shadows of the sun. The reason is, that the rays from the candle considerably diverge, while those from the sun, on account of the immense distance of that luminary, have no perceptible deviation from parallelism. It must be remembered also, that strong reflections from surrounding objects will diminish the intensity of shades, and that not only the quantity of light which falls on an object, but the quantity which can be reflected to the eye, must be considered.
As it frequently happens that persons have occasion to draw in perspective, who have acquired no theoretical know ledge of the art ; for the use of such, a great variety of machines have been constructed. Most of these machines are on optical principles ; the camera obs,•n•a, which we have already described, is one of them, and the camera Incida is another. In praise of the latter, much has lately been said ; but although it must be admitted to be a very portable and beautiful instrument, the acquisition of the proper art of using it is extremely difficult to all, and to some impossible. Its chief use will be, that of affording the means of contem plating the real perspective appearance of objects, and per haps to obtain the position of a few points ; but for very minute delineation, it is of little value. Fur general use we may venture to recommend an instrument described by Fer guson, to whom the knowledge of it was communicated by Dr. Bevis. It has the advantage of other machines in two points ; it may be constructed at a small expense by any tolerably skilful artisan in wood, and the use of it will con stantly tend to render the practice of perspective drawing more easy, by the manner in which it produces the measure of surtlices or angles. It will therefore, better than most other instruments for the same purpose, supply the want of a more extended essay.