We have already seen, that, in order to possess perfect symmetry, an object must consist of two parts in complete contact, one of which is an inverted image of the other. But in order that an object possessing perfect symmetry may appear perfectly symmetrical, four conditions are required. The two halves of the object must be so placed with respect to the eye of the observer, that no part of the one half shall conceal any part of the other; that whatever parts of the one half are seen, the corresponding parts of the other must also be seen; and that the corresponding parts of both halves, and both halves themselves, must subtend the same angle at the eye. When we stand before a looking-glass, and hold out one hand so as to touch it, the hand will be found to conceal various parts of its image; and, in some positions of the eye, the whole image will be concealed, so that a symmetrical picture cannot possibly be formed by the union of the two. If the eye is placed so obliquely to the looking-glass, that the hand no longer interferes with its image, it will still be seen, that parts of the hand which are not directly visible, are visible in its reflected image, and therefore that a symmetrical picture cannot be created by the union of two parts apparently dissimilar. If the eye of the observer is placed near his hand, so that he can see distinctly both the hand and its image, the angular magnitude of his hand is much greater than that of its image; and therefore, when the two are united, they cannot form a symmetrical object. This will be better understood from Fig. 15. When the eye is placed at ε, the object =M N O P= is obviously nearer than its image _m n o p_, and must therefore appear larger; and this difference in their apparent magnitudes will increase as the eye rises above the plane of the mirror =A E=. As the eye approaches to =E=, the distances of the object and its image approach to an equality; and when the eye is at =E=, the object =M N O P=, and its image _m n o p_, are situated at exactly the same distance from the eye, and therefore have the same angular magnitude. Hence it follows, that when they are united, they will form a perfectly symmetrical combination. [Illustration: FIG. 15.] When the eye is placed in the plane of both the mirrors, the field of view arising from the multiplication of the sector =A O B=, Fig. 14, will be perfectly circular; but as the eye rises above the plane of both the mirrors, this circle will become a sort of ellipse, becoming more and more eccentric as the eye comes in front of the mirrors, or rises in the direction =E ε=. If the observer were infinitely distant, these figures would be correct ellipses; but as the eye, particularly when the mirrors are broad, must be nearly twice as far from the last reflected sector as from the sector seen by direct vision, the field of view, and consequently every pattern which it contains, must be distorted and destitute of beauty, from this cause alone.