CHAPTER V.

ON THE EFFECTS PRODUCED UPON THE SYMMETRY OF THE PICTURE BY VARYING THE POSITION OF THE OBJECT.

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HAVING ascertained the proper position of the eye, we shall now proceed to determine the position of the object. If the object is placed within the reflectors at any point D, Fig. 16, between their object end o, and their eye a perfectly symmetrical picture will obviously be formed from it; but the centre of this picture will not be at o, centre of the luminous sectors, but at the point D, where the object is placed, or its projection d, so that we shall have a circular luminous field enclosing an eccentric circular pattern. Such a position of the object is therefore entirely unfit for the production of a symmetrical picture, unless the object should be such as wholly to exclude the view of the circular field, formed by the reflected images of the aper

ture A O B.

As the point D approaches to o, the centre d of the symmetrical picture will approach to o, and when D coincides with o, the centre of the picture will be at o, and all the images of the object placed in the plane A O B will be similarly disposed in all the sectors which compose the circular field of view. Hence we may conclude, that a perfectly symmetrical pattern cannot be exhibited in the circular field

of view, when the object is placed between o and E, or anywhere within the reflectors. If the eye could be placed

exactly at the angular point E, so that every point of the line E O should be projected upon o, then the images would be symmetrically arranged round o; but this is obviously impossible, for the object would, in such circumstances, cease to become visible when this coincidence took place. But independent of the eccentricity of the pattern, the position of the object within the mirrors prevents that motion of the objects, without which a variation of the pattern cannot be produced. An object between the reflectors must always be exposed to view, and we cannot restrict our view to one-half, one-third, or one-fourth of it, as when we have it in our power to move the objects across the aperture, or the aperture over the objects.

Another evil arising from the placing of the objects within the mirrors, is, that we are prevented from giving them the proper degree of illumination which is so essential to the distinctness of the last reflexions. The portions of

the mirrors, too, beyond the objects, or those between D and o, are wholly unnecessary, as they are not concerned in the formation of the picture. Hence it follows, that the effects of the Kaleidoscope cannot be produced by any combination of mirrors, in which the objects are placed within them.

Let us now consider what will happen, by removing the object beyond the plane passing through AO B. In this case the pattern will lose its symmetry from two causes. In the first place, it is manifest, as already explained, that as the eye is necessarily raised a little above the point E, and also above the planes A O E, BO E, it must see through the aperture A Oв a portion of the object situated below both of these planes. This part of the object will therefore appear to project beyond the point, or below the plane where the direct and reflected images meet. If we suppose, therefore, that all the reflected images were symmetrical, the whole picture would lose its symmetry in consequence of the irregularity of the sector A O B seen by direct vision. But this supposition is not correct; for since the image m'n, Fig. 3, seen by direct vision does not coincide with the first reflected images mn', nm', it is clear that all the other images will likewise be incoincident, and, therefore, that the figure formed by their combination must lose its symmetry, and, consequently, its beauty.

As the eye must necessarily be placed above a line perpendicular to the plane ABO 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 O' of the object situated below the axis PO E, and this portion,

which may be called the abberration, will vary with the height Ee of the eye, and with the distance OP of the object.

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 of the object м N. Then if P Q is very great compared with P o', 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 o' remaining the same, so that P O' 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

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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.