Father Zahn mentions something more singular than what is related by Wolf of the artist of Dresden, for he says that an engineer of Vienna, in the year 1699, made a mirror of paste-board, covered on the inside with straw cemented to it, which was so powerful as to fuse all metals.

Concave mirrors of a considerable diameter, and which produce the same effect as the preceding, may be procured at present at much less expence. For this advantage we are indebted to M. de Bernieres, one of the controllers general of bridges and causeways, who discovered a method of giving the figure of any curve to glass mirrors; an invention which, besides its utility in optics, may be applied to various purposes in the arts. The concave mirrors which he constructed, were round pieces of glass bent into a spherical form; concave on one side and convex on the other, and silvered on the convex side. M. de Bernieres constructed one for the king of France, of 3 feet 6 inches in diameter, which was presented to his majesty in 1757. Forged iron exposed to its focus was fused in two seconds silver ran in such a manner that when dropped into water it extended itself in the form of a spider's web; flint became vitrified, &c.

These mirrors have considerable advantage over those of metal. Their reflection from the posterior surface, notwithstanding the loss of rays, occasioned by their passage through the first surface is still more lively than that from the best polished metallic surface; besides, they are not subject, like metallic mirrors, to lose their polish by the contact of the air, always charged with vapours which corrode metal, but which make no impression on glass :

in a word, nothing is necessary, but to preserve them from moisture, which destroys the silvering.

PROBLEM XXXVII.

Some properties of concave mirrors, in regard to vision, or the formation of images.

I. IF an object be placed between a concave mirror and its focus, its image is seen within the mirror, and more magnified the nearer the object is to the focus; so that when the object is in the focus itself, it seems to occupy the whole capacity of the mirror, and nothing is seen distinct.

If the object, placed in the focus, be a luminous body, the rays which proceed from it, after being reflected by the mirror, proceed parallel to each other, so that they form a cylinder of light, extended to a very great distance, and almost without diminution. This column of light, if the observer stands on one side, will be easily perceived when it is dark; and at the distance of more than a hundred paces from the mirror, if a book be held before this light, it may be read.

II. If the object be placed between the focus and the centre, and if the eye be either beyond the centre, or between the centre and the focus, it cannot be distinctly perceived, as the rays reflected by the mirror are convergent. But if the object be strongly illuminated, or if it be a luminous body itself, such as a candle, by the union of its rays there will be formed, beyond the centre, an image in an inverted situation, which will be painted on a piece of paper or cloth at the proper distance, or

which, to an eye placed beyond it, will appear suspended in the air.

III. The case will be nearly the same when the object is beyond the centre, in regard to the mirror: an inverted image of the object will be painted then between the focus and the centre; and this image will approach the centre in proportion as the object itself approaches it; or will approach the focus as the object removes from it.

In regard to the place where the image will be painted in both these cases, it may be found by the following rule.

Let ACS (fig. 33 pl. 9) be the axis of the mirror, indefinitely produced; F the focus, C the centre, and O the place of the object, between the centre and the focus. If F be taken a third proportional to F O and F C, it will represent the distance at which the image of the point placed in O will be painted.

If the object be in w, by employing the same proportion, with the proper changes, that is by making FO a third proportional to F and F C, as in, the image of it will be found in O.

In the last place, if the object be between the focus and the glass, the place where it will be observed within the mirror, may be found by making F to FA, as F A to Fo.

REMARKS.

ist. This property which concave mirrors have, of forming between the centre and the focus, or beyond the centre, an image of the objects presented to them, is one of those which excite the greatest surprise in persons not acquainted with this

theory. For if a man advance towards a large concave mirror, presenting a sword to it, when he comes to the proper distance, he will see a sword blade, with the point turned towards him, dart itself from the mirror; if he retires the image of the blade will retire; if he advances in such a manner that the point shall be between the centre and the focus, the image of the sword will cross the real sword as if two people were engaged in fighting.

2d. If, instead of a sword blade, the hand be presented at a certain distance; you will see a hand formed in the air in an inverted situation; which will approach the real hand, when the latter approaches the centre, so that they will seem to meet each other.

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3d. If you place yourself a little beyond the centre of the mirror, and then look directly into it, you will see beyond the centre the image of face inverted. If you then continue to approach, this phantastic image will approach also, so that you can kiss it.

4th. If a nosegay be suspended in an inverted situation (fig. 34 pl. 9), between the centre and the focus, a little below the axis, and if it be concealed from the view of the spectator, by means of a piece of black pasteboard, an upright image of the nosegay will be formed above the pasteboard, and will excite the greater astonishment, as the object which produces it is not seen; for this reason those not acquainted with the deception will take it for a real object, and attempt to touch it *.

* Curious spectres, and appearances, formed in this manner, have of late years been exhibited as shows to spectators in London.

5th. If a concave mirror be placed at the end of a hall, at an inclination nearly equal to 45°, and if a print or drawing be laid on a table before the mirror, with the bottom part turned towards it, the figures in the print or drawing will be seen greatly magnified; and if a proper arrangement be made, so as to favour the illusion, that is if the mirror be concealed, and only a small hole left for looking through, you will imagine that you see the objects themselves.

On this principle are constructed what are called Optical boxes, which are now very common: the method of constructing them will be found in the following problem.

PROBLEM XXXVIII.

To construct an optical box or chamber, in which objects are seen much larger than the box itself.

PROVIDE a square box, of a size proper to contain the concave mirror you intend to employ; that is to say, let each side be a little less than the focal distance of the mirror; and cover the top of it with transparent parchment, or white silk, or glass made smooth, but not polished.

Apply the mirror to one of the vertical sides of the box, and on the opposite side place a coloured print or drawing, representing a landscape, or seaport, or buildings, &c. The print ought to be introduced into the box by means of a slit, so that it can be drawn out, and another substituted in its place at pleasure.

At the top of the side opposite to the mirror, a round hole or aperture must be made, for the pur