Ir may be readily conceived that, to produce this effect, nothing is necessary but to dispose the mirrors on the circumference of a circle, in such a manner, that they shall correspond with the chords of that circle; if you then place yourself in the centre, you will see your image in all the mirrors at the same time.

REMARK.

If these mirrors are disposed according to the sides of a regular polygon, of an equal number of sides, such as a hexagon or octagon, which seem to be fittest for the purpose, and if all the mirrors are perfectly vertical and plane, they will form a sort of cabinet, which will appear of an immense extent, and in whatever part of it you place yourself, you will see your image, and immensely multiplied.

If this cabinet be illuminated in the inside, by a lustre placed in its centre, it will exhibit a very agreeable spectable, as you will see long rows of lights towards whatever side your sight is directed.

PROBLEM XXX.

To measure, by means of reflection, a vertical height, the bottom of which is inaccessible.

We shall here suppose that A B (fig. 25 pl. 7) the vertical height to be measured, is that of a tower, steeple, or such like. Place a mirror at C, in a direction perfectly horizonal; or, because this is very difficult, and as the least aberration might produce a great error in the measurement, place in Ca vessel containing water, which will reflect the

light in the same manner as a mirror. The eye which receives the reflected ray being at O, measure with care the height OD above the horizontal plane of the mirror at C; measure also D C as well as CB, if the latter is accessible, and then say : As CD, is to DO, so is CB to a fourth proportional B A, which will be the height required.

But if the bottom of the tower be not accessible, to measure the height A B, we must proceed as follows:

Having performed every part of the preceding operation, except measuring CB, which by the supposition is impossible, take another station, as c, and place there a mirror, or vessel of water: then taking your station in d, from which you can see the point A, by means of the reflected ray co2 measure c d and do. When this is done, you must employ the following proportion: As the difference between CD and cd is to CD, so is Cc, the distance between the two points of reflection, to a fourth proportional, which will be the distance B C, before unknown.

When B C is known, nothing is necessary but to make use of the proportion indicated in the first case, which will give the height A B.

We do not consider this operation as susceptible of much accuracy in practice. Methods purely geometrical, if good instruments are employed, ought always to be preferred; but we should perhaps have been considered as guilty of an omission had we taken no notice of this geometrico-catoptric speculation, though it has never perhaps been put in practice.

PROBLEM XXXI.

To measure an inaccessible height by means of its shadow.

Fix a stick in a perpendicular direction, on a plane perfectly horizontal, and measure the height of it above that plane, which we shall suppose to be exactly 6 feet. When the sun begins to sink towards the horizon in the afternoon, mark on the ground which is accessible the point C (fig. 26 pl. 8), where the shadow of the summit of the tower falls, and also the point the extremity of the shadow of the stick erected perpendicularly on the same plane: at the end of two hours, more or less, mark, as speedily as possible, the two points D and d, which will be the summits of the shadows at that period; then join the two points of the shadow of the summit of the tower, by means of a straight line, and measure their distance; measure also, in like manner, the line which joins the two points c and d of the shadow of the stick; after which you will have nothing to do but to employ the following proportion: As the length of the line cd which joins the two points of the shadow of the stick, is to the height of the stick a b, so is the length of the line CD which joins the two points of the shadow of the tower, to the height of the tower A B.

It requires only an acquaintance with the first principles of geometry to be able to perceive, merely by inspecting fig. 26, that the pyramids BAD C and bad c are similar; consequently that c d is to a b as CD to A B, which is the height required.

PROBLEM XXXII.

Of some tricks or kinds of illusion, which may be per formed by means of plane mirrors.

MANY curious tricks, capable of astonishing those who have no idea of catoptrics, may be performed by the combination of several plane mirrors. Some of these we shall here describe.

1st. To fire a pistol over your shoulder and hit a mark, with as much certainty as if you took aim at it in the usual manner. Fig 27 pl. 8.

To perform this trick, place before you a plane mirror, so disposed, that you can see in it the object you propose to hit; then rest the barrel of the pistol on your shoulder and take aim, looking at the image of the pistol in the glass as if it were the pistol itself; that is, in such a manner, that the image of the object may be concealed by the barrel of the pistol it is evident that if the pistol be then fired, you will hit the mark.

2d. To construct a box in which heavy bodies, such as a ball of lead, will appear to ascend contrary to their natural inclination.

Construct a square box, as ABCD (fig. 28), where one of the sides is supposed to be taken off, in order to shew the inside; and fix in it a board HGDC, so as to form a plane, somewhat inclined, with a serpentine groove in it of such a size, that a ball of lead can freely roll in it and descend. Then place the mirror HGFI in an inclined position, as

seen in the figure, and make an aperture opposite to it at M, in the side of the box, but so disposed that the eye, when applied to it, can see only the mirror, and not the inclined plane HD. It may be easily perceived that the image of this plane, viz HLKG, will seem to be a plane almost vertical, and that a body which rolls from G to C, along the serpentine groove, will appear to ascend in a similar direction from G to L. Hence, if the mirror is very clean, so as not to be observed, or if only a faint light be admitted into the box, which will tend to conceal the artifice, the illusion will be greater, and those not acquainted with the deception will have a good deal of difficulty to discover it.

3d. To construct a box in which objects shall be seen through one hole, different from what were seen through another, though in both cases they seem to occupy the whole box.

Provide a square box, which, on account of its right angles, is the fittest for this purpose, and divide it into four parts, by partitions perpendicular to the bottom, crossing each other in the centre. To these partitions apply plane mirrors, and make a hole in each face of the box, to look through; but disposed in such a manner, that the eye can see only the mirrors applied to the partitions, and not. the bottom of the box. In each right angle of division formed by the partitions, place some object, which, being repeated in the lateral mirrors, may form a regular representation, such as a parterre, a fortification or citadel, a pavement divided into compartments, &c. That the inside of the box may be