Angle of Specula. 36°

*32°
30°

Effect produced.

a decagon and ten forms,

an endecagon and eleven forms,
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

From the

possibly be united into a symmetrical whole. 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.

work, entitled, New Improvements in Planting and Garden ing, published in 1717, this author has drawn and described Kircher's apparatus as an invention of his own; and, instead of having in any respect improved it, he has actually deteriorated it, in so far as he has made the breadth of the mirrors greater than their height. An exact copy of the mirrors used by Bradley is shown in Fig. 55, from which it will be at once seen, that it is precisely the same as Kircher's, shown in Fig. 54. We are far from saying that Bradley stole the invention from Kircher, or that Kircher stole it from Baptista Porta, or that Baptista Porta stole it from the ancients. There is reason, on the contrary, to think that the apparatus had been entirely forgotten, in the long intervals which elapsed between these different authors, and there can be no doubt that each of them added some little improvement to the instrument of their predecessors. Baptista Porta saw the superiority of two mirrors, as a multiplying machine, to a greater number used by the ancients. Kircher showed the relation between the number

merit of noticing, that figures upon paper, which had a certain degree of irregularity, like those in Fig. 56, could still form a regular figure.

In order that the reader may fully understand Bradley's method of using the mirrors, we shall give it in his own words :

"We must choose two pieces of looking-glass (says he), of equal bigness, of the figure of a long square, five inches in length, and four in breadth; they must be covered on the back with paper or silk, to prevent rubbing off the silver, which would else be too apt to crack off by frequent This covering for the back of the glasses must be so put on, that nothing of it may appear about the edges on the bright side.

use.

"The glasses being thus prepared, they must be laid face to face, and hinged together, so that they may be made to open and shut at pleasure, like the leaves of a book; and now the glasses being thus fitted for our purpose, I shall proceed to explain the use of them.

"Draw a large circle upon paper; divide it into three, four, five, six, seven, or eight equal parts; which being done, we may draw in every one of the divisions a figure, at our pleasure, either for garden-plats or fortifications; as, for example, in Fig. 55, we see a circle divided into six parts, and upon the division marked F is drawn part of a design for a garden. Now, to see that design entire, which is yet confused, we must place our glasses upon the paper, and open them to the sixth part of the circle, i.e., one of them must stand upon the line b, to the centre, and the other must be opened exactly to the point c; so shall we