Parastasis I.
Plane specula may be made to multiply the images of one object.
A wonderful, and, so far as I know, a new property, is exhibited by two specula, so constructed that they may be opened and shut like a book. If they are placed upon any plane, in which there is a semicircle divided into degrees, in such a manner that the point where the specula meet is in the centre of the circle, and the edge of each speculum stands upon the diameter of the semicircle, one image only will be visible, and there will appear two things, namely, a real one, without the specula, and another formed by reflexion behind them,[21] and so on, as in the following table, where the first column shows the inclination of the specula, and the second the figure which is produced:—
| Angle of Specula. | Effect produced. |
|---|---|
| 180° | one image and one object, |
| *120° | two images and one object, |
| 90° | four images, |
| *72° | a pentagon and five forms, |
| 60° | a hexagon and six forms, |
| *51³/₇° | a heptagon and seven forms, |
| 45° | an octagon and eight forms, |
| *40° | an enneagon and nine forms, |
| 36° | a decagon and ten forms, |
| *32⁸/₁₁° | an endecagon and eleven forms, |
| 30° | a dodecagon and twelve forms, |
and so on, ad infinitum, the polygon formed by reflexion having always as many sides as the number of times that the angle of the specula is contained in 360°.
The combination of plane mirrors, which Kircher describes in the preceding extract, is precisely the same as that which is given by Baptista Porta. The latter, indeed, only mentions, that the number of images increases by the diminution of the angle, whereas Kircher gives the number of images produced at different angles, and enumerates the regular polygons which are thus formed.
It must be quite obvious to any person who attends to Kircher’s description, that the idea never once occurred to him of producing beautiful and symmetrical forms by means of plane mirrors. His sole object was to multiply a given regular form a certain number of times; and he never imagined that, when the mirrors were placed at the angles marked with an asterisk, there could be no symmetry in the figure, and no union of the two last reflected images, unless in the case where a regular object was placed, either by design or by accident, in a position symmetrically related to both the reflectors.
In Kircher’s mirrors the eye was placed in front of them. The object therefore was much nearer the eye than the images, and the light of the different reflected images was not only extremely unequal, but the difference in their angular magnitude was such that they could not possibly be united into a symmetrical whole. From the accidental circumstance of his using lines upon paper as an object, the distortion of the pictures arising from the erroneous position of the eye was prevented; but if the same combination of mirrors were applied to the object-plates of the Kaleidoscope, it would be found utterly incapable of producing any of the fine forms which are peculiar to that instrument.
If it were necessary to prove that Kircher and his pupils were entirely ignorant of the positions of the eye and the object which are necessary to the production of a picture, symmetrical in all its parts, and uniformly illuminated, and that they went no farther than the mere multiplication of forms that were previously regular and symmetrical, we would refer the reader to Schottus’ Magia Universalis Naturæ et Artis, printed at Wurtzbourg in 1657, where he repeats, almost word for word, the description of Kircher, and adds the following curious observation:—“But it is not only the objects placed in the semicircle in the angle of the glasses that are seen and multiplied, but also those which are more distant; for example, a wall, with its windows, and in this case the multiplication produced by the mirrors will create an immense public place, adorned with edifices and palaces.” This passage shows, in the clearest manner, not only that the multiplication of an object, independent of the union of the multiplied objects into a symmetrical whole, was all that Kircher and his followers proposed to accomplish; but also that they were entirely unacquainted with the effects produced by varying the distance of the object from the mirrors. If any person should doubt the accuracy of this observation, we would request him to take Kircher’s two mirrors, to direct them to a “wall with its windows,” either by Kircher’s method, or even by any other way that he chooses, and to contemplate “the public place adorned with edifices and with palaces.” He will see heaps of windows and of walls, some of the heaps being much larger than others; and some being farther from, and others nearer to, the centre; and some being dark, and others luminous; while all of them are disunited. Let him now take a Telescopic Kaleidoscope, and direct it to the same object; he will instantly perceive the most perfect order arise out of confusion, and he will not scruple to acknowledge, that no two things in nature can be more different than the effects which are produced by these two combinations of mirrors.