far behind the glass as you stand before it.

James. Yes: and if I move forwards or backwards, the image behind the glass seems to approach or recede.

Tutor: Let a b (Plate 11. Fig. 15.) be the looking-glass, and a the spectator, standing opposite to it. The ray from his eye will be reflected in the same line A a, but the ray cb flowing from his foot, in order to be seen at the eye, must be reflected by the line b a.

Charles. So it will, for if r b be à line perpendicular to the glass, the incident angle will be c br, equal to the reflected angle a b x.

Tutor. And therefore the foot will appear behind the glass at D along

the line a b D, because that is the line in which the ray last approaches the eye.

James. Is that part of the glass a b intercepted by the lines A B and A D, equal exactly to half the length B D, or A C?

Tutor. It is; A a b and A B D may be supposed to form two triangles, the sides of which always bear a fixed proportion to one another; and if A B is double of a a, as, in this case it is, B D will be double of a b, or at least of that part of the glass intercepted by A B and A D.

Charles. This will hold true, I see, stand at what distance we please from the glass.

Tutor. If you walk towards a looking-glass, your image will approach, but with a double velocity,

because the two motions are equal and contrary. But if, while you stand before a looking-glass, your brother walk up to you from behind, his image will appear to you to move at the same rate as he walks, but to him the velocity of the image will appear to be double; for with regard to you, there will be but one motion, but with regard to him, there will be two equal and contrary ones.

James. If I look at the reflection of a candle in a looking-glass, I see in fact two images, one much fainter than the other, what is the reason of this?

Tutor. The same may be observed of any object that is strongly illuminated, and the reason of the double image is, that a part of the rays are immediately reflected from the upper

surface of the glass which form the faint image, while the greater part of them are reflected from the farther surface, or silvering part, and form the vivid image. To see these two images you must stand a little sideways, and not directly before the glass.

Charles. What is meant by the expression of "An image being formed behind a reflector ?"

Tutor. It is intended to denote that the reflected rays come to the eye with the same inclination as if the object itself were actually behind the reflector. If you, standing on one side of the room, see the image of your brother, who is on the other side, in the looking-glass, the image seems to be formed behind the glass, that is, the rays come to your eye

precisely in the same way as they would if your brother himself stood in that place, without the intervention

of a glass.

James. But the image in the glass is not so bright or vivid as the object.

Tutor. A plain mirror is in theory supposed to reflect all the light which falls upon it, but in practice nearly half the light is lost on account of the inaccuracy of the polish, &c.

Charles. Has it not been said, that Archimedes, at the siege of Syracuse, burned the ships of Marcellus, by a machine composed of mirrors?

Tutor. Yes: but we have no certain accounts that may be implicitly relied on. M. Buffon, about fifty or sixty years ago, burned a plank at