Page:On the Fourfold Root, and On the Will in Nature.djvu/109

 the sense, in which it is to be understood, can only be gathered from its connection with the rest. An object subtending the same visual angle may in fact be small and near, or large and far off; and it is only when we have previously ascertained its size, that the visual angle enables us to recognise its distance: and conversely, its size, when its distance is known to us. Linear perspective is based upon the fact that the visual angle diminishes as the distance increases, and its principles may here be easily deduced. As our sight ranges equally in all directions, we see everything in reality as from the interior of a hollow sphere, of which our eye occupies the centre. Now in the first place, an infinite number of intersecting circles pass through the centre of this sphere in all directions, and the angles measured by the divisions of these circles are the possible angles of vision. In the second place, the sphere itself modifies its size according to the length of radius we give to it; therefore we may also imagine it as consisting of an infinity of concentric, transparent spheres. As all radii diverge, these concentric spheres augment in size in proportion to their distance from us, and the degrees of their sectional circles increase correspondingly: therefore the true size of the objects which occupy them likewise increases. Thus objects are larger or smaller according to the size of the spheres of which they occupy similar portions say—10°—while their visual angle remains unchanged in both cases, leaving it therefore undecided, whether the 10° occupied by a given object belong to a sphere of 2 miles, or of 10 feet diameter. Conversely, if the size of the object has been ascertained, the number of degrees occupied by it will diminish in proportion to the distance and the size of the sphere to which we refer it, and all its outlines will contract in similar proportion. From this ensues the fundamental law of all perspective; for, as objects and the intervals between them must necessarily