As the eye must necessarily be placed above a line perpendicular to the plane A B O at the point O, it will see a portion of the object situated below that perpendicular continued to the object. Thus, in [Fig. 16], if the eye is placed at e above E, and if M N is the object placed at the distance P O, then the eye at e will observe the portion P Oʹ of the object situated below the axis P O E, and this portion, which may be called the aberration, will vary with the height E e of the eye, and with the distance O P of the object.
Fig. 17.
Let us now suppose E e and O P to be constant, and that a polygonal figure is formed by some line placed at the point Q of the object M N. Then if P Q is very great compared with P Oʹ, the polygonal figure will be tolerably regular, though all its angles will exhibit an imperfect junction, and its lower half will be actually, though not very perceptibly, less than its upper half. But if Q approaches to P, P Oʹ remaining the same, so that P Oʹ bears a considerable ratio to P Q, then the polygonal figure will lose all symmetry, the upper sectors being decidedly the largest, and the lowest sectors the smallest. When Q arrives near P, the aberration becomes enormous, and the figure is so distorted, that it can no longer be recognised as a polygon.
The deviation from symmetry, therefore, arising from the removal of the object from the extremity of the reflectors, increases as the object approaches to the centre of the luminous sectors or the circular field, and this deviation becomes so perceptible, that an eye accustomed to observe and admire the symmetry of the combined objects, will instantly perceive it, even when the distance of the object or P O is less than the twentieth part of an inch. When the object is very distant, the defect of symmetry is so enormous, that though the object is seen by direct vision, and in some of the sectors, it is entirely invisible in the rest.
The principle which we have now explained is of primary importance in the construction of the Kaleidoscope, and it is only by a careful attention to it that the instrument can be constructed so as to give to an experienced and fastidious eye that high delight which it never fails to derive from the exhibition of forms perfectly symmetrical.
From these observations it follows, that a picture possessed of mathematical symmetry, cannot be produced unless the object is placed exactly at the extremity of the reflectors, and that even when this condition is complied with, the object itself must consist of lines all lying in the same plane, and in contact with the reflectors. Hence it is obvious, that objects whose thickness is perceptible, cannot give mathematically symmetrical patterns, for one side of them must always be at a certain distance from O. The deviation in this case is, however, so small, that it can scarcely be perceived in objects of moderate thickness.
In the simple form of the Kaleidoscope, the production of symmetrical patterns is limited to objects which can be placed close to the aperture A O B; but it will be seen in the sequel of this treatise, that this limitation may be removed by an optical contrivance, which extends indefinitely the use and application of the instrument.