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, VOL. III.-F

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. Mr. Buffon, about fifty or sixty years ago, burned a plank at the distance of seventy feet, with forty plain mirrors.

James. I do not see how they can act as burning glasses.

Tutor. A plain mirror reflects the light and heat coming from the sun, and will illuminate and heat any substance on which they are thrown, in the same manner as if the sun shone upon it. Two mirrors will reflect on it a double quantity of heat; and if 40 or 100 mirrors could be so placed as to reflect from each the heat

coming from the sun, or any particular substance, they would increase the heat 40 or 100 times.

CONVERSATION XI.

Of Concave Mirrors-their Uses-how they act.

James. To what uses are concave mirrors applied?

Tutor. They are chiefly used in reflecting telescopes; that is, in telescopes adapted to viewing the heavenly bodies. And as you like to look at Jupiter's little moons, and Saturn's ring, through my telescope, it may be worth your while to take some pains to know by what means this pleasure is afforded you.

Charles. I shall not object to any attention necessary to comprehend the principles on which these instruments are formed.

Tutor. A B (Plate 11. Fig. 16.) represents a concave mirror, and a, b, c, d, e, f, three parallel rays of light falling upon it. c is the centre of concavity, that is, one leg of your compasses being placed on c, and then open them to the

length c d, and the other leg will touch the mirror A B in all its parts.

James. Then all the lines drawn from c to the glass will be equal to one another, as c b, c d, and cƒ?

Tutor. They will: and there is another property belonging to them; they are all perpendicular to the glass, in the parts where they touch.

Charles. That is c b and c f are perpendicular to the glass at b and f, as well as c d at d.

Tutor. Yes, they are:-c d is an incident ray, but as it passes through the centre of concavity, it will be reflected back in the same line, that is, as it makes no angle of incidence, so there will be no angle of reflection: a b is an incident ray, and I want to know what will be the direction of the reflected ray?

Charles. Since cb is perpendicular to the glass at b, the angle of incidence is a b c; and as the angle of reflection is always equal to the angle of incidence, I must make another angle, as cbm, equal to a b c,* and then the line b m is that in which the incident ray will move after reflection.

*To make an angle c bm, equal to another given one, as a b c. From b as a centre with any radius b x, describe the arc xo, which will cut cb in z, take the distance x z in your compasses, and set off with it z o, and then draw the line bom, and the angle m b c is equal to the angle abc.

Tutor. Can you, James, tell me how to find the line in which the incident ray ef will move after reflection?

James. Yes: I will make the angle cf m equal to c f e, and the line fm will be that in which the reflected ray will move; therefore ef is reflected to the same point m as a b was.

Tutor. If, instead of two incident rays, any number were drawn parallel to c d, they would every one be reflected to the same point m; and that point which is called the focus of parallel rays is distant from the mirror equal to half the radius c d.

James. Then we may easily find the point, without the trouble of drawing the angles, merely by dividing the radius of concavity into two equal parts.

Tutor. You may.-The rays, as we have already observed, which proceed from any point of a celestial object, may be esteemed parallel at the earth, and therefore the image of that point will be formed at m.

Charles. Do you mean that all the rays flowing from a point of a star, and falling upon such a mirror, will be reflected to the point m, where the image of the star will appear?

Tutor. I do, if there be any thing at the point m, to receive the image.

James. Will not the same rule hold with regard to terrestrial objects?

Tutor. No: for the rays which proceed from