Vanishing point:, in every position, were known to Guido ; and Gravesande not only understood the use of vanishing points, the use of directors also, in the repre sentation of a point, prior to the appearance of any thing published by Brook Taylor; but the latter has extended his theory not only to vanishing points, but to the vanishing lines of planes in every situation, which, when once ascer tained, the representation of an object is found by the same means in each plane, con:equently with the same facility. Hamilton seems to be the first writer who introduced the Within the last few years, writers on perspective have been so numerous, that it is impossible, as indeed it is un necessary, to enumerate them.
We shall now proceed to describe the art of perspective, in such a manner as will, we trust, be found a very way of acquiring a general knowledge of the subject. Let the strident place himself in a darkened chamber, and then let him make a small hole, not larger than a pea, in the dour or window, opposite to sonic remarkable oljects, such as ur trees, the distance of which should be at least equal to their height, and may, with propriety, he two or three times that distance; and the experiment will be most agreeably conducted, when the sun shines strongly on the surfaces facing the hole. If a sheet of paper, or any white screen, be placed within the room before the hole, an image of the external objects opposite the aperture will be depicted upon it. image will be beautiful, although the outline of the objects will not be very well defined, nor their colours very distinct, for rea-ons which the study of optics will fully explain. The instruction, however, to be derived from the experiment, will, tbr the present object, he the same. It will be observed that the images of all objects are inverted ; and, to understand this, the stud.mt must be reminded of the rectilinear motion of light. The image on the screen can, of course, be formed only by those rays of light which enter the chamber at the aperture, and it will be admitted that the rays from the top of the external objects cannot proceed in a right line to the screen, unless they proceed to the bottom of the screen, and the objects on the left hand will be on the right of the image. That the lays of light from the objects cross each other at the aperture, and spread afterwards as they advance, may be proved by varying the distance of the screen ; the size of the image upon which is enlarged by drawing it hack, and lessened by placing it nearer the aper tore. The student must further be informed, that if he could trace the image on the screen exactly as it is there • delineated, he would, on reversing the screen, have an out line of the external objects in accurate perspective. As the proportions of the several parts, therefou e. are not altered by the inverted position of the image, they may be contemplated and compared with the original objects. as if no inversion took place. Suppose the front of a single house to be paral lel to the surface of the screen, and its centre very mat ly opposite to the centre of the aperture, its image upon the screen will be of the same shape as the front itself is known to have, and its dimensions will he obtained by a rule easily discoverable ; the image will be very nearly as much less than the original as the distance between the original and the aperture. This estimate of the proportion between the
image and the object, would not require the (pant:\ ing term nearly, but would be correct, if the aperture were exactly opposite the centre of the front of the house ; but we have supposed the aperture to he nearer one side of the building than the other. in order that the rays from the nearest gable of the house may pass through the aperture. This being attended to, there will be an image of the gable end upon the screen ; and the size and shape of this part of the image must be particularly noticed. It will he food. that, though the gable may be in reality as broad as the front, its image is extremely narrow ; that its ground-line, instead of being level with that of the front, inclines more and more towards the top as it recedes from the eye. and that the further edge of the inclined roof inclines to this line with a greater degree of inclination than the original is known to have : thus, besides the narrowness in point of breadth, the height of the most distant corner of the gable is in the image shorter than the hithermost corner. This visual contraction of surfaces is called fore-shortening.
To understand how it happens, let the student suppose a thread stretched from any given point in the most distant angle or vertical edge of the gable to its image on the screen, or spot on which it would 11111 by taking a rectilinear course; let another line be supposed to be drawn fr4un an opposite point of the nearest angle of the gable, and it will he, per ceived that as these lines, like the rays of light, cross the aperture, they will, at the screen, furm but a very narrow opening; and as the breadth of the image cannot be greater than this opening, the breadth of the gable must be iheon siderable on the screen, It will be obvious at the same time, that the more nearly the gable is taken in front, the greater will he the breadth of its image, while that of the apparent extent ()Nile front will be proportionally eontra..ted. The incli. , nation &lithe ground-line of the gable will be explained. by sup posing lines to be drawn from 'the four corners or limits of the gable, to their respective places on the screen ; for the line which bounds the further side of the gable. must have a less image on the screen than the hithermost, because it is more distant. and at an intermediate distance, any vertical line in the gable must have an intermediate height ; therefore, there practice of setting the radial, or parallel of the original line from the vanishing, point, upon the vanishing line, and the original line front the intersecting point upon the intersecting line. in order to a.leertain the representation of any point, or any part or parts of the original line, and to find the origi nals from the representations given. This author is the first who has applied the harmonic:II division of lines to perspec tive. Noble's Perspective contains several inventions ; par ticularly his methods of drawing indefinite representations to inaccessible vanishing points, both by scales and other means. Thomas Alalton's treatise on this subject is also an able performance.