In order to explain the effects produced upon the symmetry of the picture by a variation in the position of the eye, we must suppose the object to be placed at a small distance from the end of the mirror. This position is represented in Fig. 13, where =A E= is a section of the mirror in the direction of its length; =M N O P= an object placed at a distance from the extremity =A= of the mirror, and _m n o p_, its image seen by an eye to the right hand of =E=, and which, by the principles of catoptrics, will be similar to the object and similarly situated with respect to the mirror =A E=. Now, if the eye is placed at ε, it will see distinctly the whole object =M N O P=, but it will only see the portion _n r s o_ of the image cut off by drawing the line =ε A _r_= through the extremity of the mirror, so that there cannot be a symmetrical form produced by observing at the same time the object =M N O P= and this portion of its image; and the deviation from symmetry will be still greater, if =M N O P= is brought nearer the line =B A=, for the image _m n o p_ will be entirely included between the lines =A _r_= and =A B=, so that no part whatever of the image will be visible to an eye at =ε=. As the eye of the observer moves from ε to _e_, the line =ε A _r_= will move into the position =_e_ A _x_=, and when it has reached the point =e=, the whole of the image _m n o p_ will be visible. The symmetry, therefore, arising from the simultaneous contemplation of the object and its image will be improved; but it will still be imperfect, as the image will appear to be distant from the plane of the mirror, only by the space _m x_, while the distance of the object is =M _x_=. As the eye moves from =_e_= to =E=, the line =_e_ A _x_= will move into =E A B=, and the object and its image will seem to be placed at the equal distances =M B=, =_m_ B= from the plane of the mirror, and will therefore form a symmetrical combination. When the object is moved, and arrives at =B A= the image will touch the object, and they will form one perfect and united whole, whatever be the shape of the line =M P=. Hence we conclude, _that when an object is placed at a little distance from the extremity of a plain mirror, its image formed by reflexion from the mirror cannot unite with the object in forming a conjoined and symmetrical picture, unless the eye is in the plane of the mirror_. [Illustration: FIG. 14.]