If these conditions are not conformed with, the perspective can only be seen falsely. Accord ing to what has already been said, it can easily be realized that the tolerances in the position of the eye during the examination become greater the greater the principal distance. In particular, if the principal distance is at least equal to io times the mean separation of the eyes, there will no longer be a very marked difference between the objects as received individually by each of the eyes, and the binocular view of the picture will no longer cause any inconvenience.
28. Anomalies of an Exact Perspective. A perspective, traced directly on glass or resulting from correctly carried out graphical construc tion, is of necessity exact in the geometrical sense, but it may be either picturesque or defective, according to the value chosen for the principal distance and the included angle. If the eye can be placed at the viewpoint, it will obviously see an object identical with the object seen from the same viewpoint, but as soon as one moves from the normal position (and this will necessarily be the case if the principal distance is very short, or if the included angle exceeds the angle of the visual field) serious distortions will appear, especially towards the limits of the field. These distortions are due especially to the fact that the image projected on our retina is projected on to a sphere, a very different case from a plane perspective.
From whatever angle we may look at a sphere its outline always appears exactly circular. On the contrary, the plane perspective of a sphere is an ellipse, except in the case where the centre of the sphere is on the perpendicular from the viewpoint to the projection plane. As the visual ray to the centre of the sphere makes an increasing angle with this perpendicular, so the distortion also becomes greater.
Nevertheless, if one stands in front of a colonnade, all the columns appear the same diameter. If there is a difference, the columns farthest away appear somewhat smaller ; in the perspective of a colonnade seen from the front, the images of the columns become larger as one moves farther away from the principal point.
Fig. 6 (from an old paper by Moessard), showing in elevation, in plan, and in perspective a series of identical vertical cylinders, each being surmounted by a sphere, is an excellent example of anamorphosis (i.e. a perspective which is displeasing, although correct), due to the fact that an excessive angle' has been included (by means of the angular graduations given, the obliquities corresponding with different deforma tions may be seen).
In fact, the artist, painter, engraver, or draughtsman always modifies the strict laws of geometrical perspective by means of certain tricks of which the greatest masters have given resulting from the drawing on the plane of their spherical perspectives.
Notice, however, that the observer who can only see with one eye and who cannot move, though provided for by the theorists of per spective, is not found amongst Nature artists, who always judge their effects with both eyes open, and frequently move about so as to look at their picture from points far removed from the actual viewpoint ; by doing this they can correct the anomalies which would show to badly-placed spectators. This explains why pic tures in museums can be examined from very different positions, and often even abnormal positions, without appearing displeasing. Un fortunately, this wide tolerance is not found in the examination of a perspective, unless its principal distance is very great and the included angle very small.
29. Influence of Choice of Viewpoint. The choice of viewpoint affects the aspect of the p examples. He generally limits the included angle to between j50 and by choosing a principal distance somewhere between twice and three times the greatest dimension of the image. Further, even if he respects the laws of perspective whilst tracing the principal lines, he departs from them for the details, each object being represented almost as if it were seen from the front. It can almost be said that the painter only adopts the plane perspective for the placing of the different elements, the tracing of these image of each of the different objects and at the same time the ratio of the respective sizes of the images of objects situated at different distances.
Consider the case of a sphere (Fig. 7), and let us determine the perspectives from the two viewpoints 0 and V. It will be realized at once that, seen from very near, the sphere will show only a small fraction of the surface which can be seen from a farther distance away ; all the shaded zone will be seen from 0 and not from 0'. It can be seen that if we substitute for the sphere a human face seen from the front, then from the viewpoint 0' the ears will be hidden, and the mouth (the opening of which represents about a quarter of the diameter) will occupy a third of the apparent diameter and seem to be enormous.