any terrestrial object, however remote, cannot be esteemed strictly parallel, they therefore come diverging; and will not be converged to a single point, at the distance of half the radius of the mirror's concavity from the reflecting surface; but in separate points, at a little greater distance from the mirror than half the radius. Charles. Can you explain this by a figure? Tutor. I will endeavour to do so. Let A B (Plate 11. Fig. 17.) be a concave mirror, and M E any remote object, from every part of which rays will proceed to every point of the mirror; that is, from the point м rays will flow to every point of the mirror, and so they will from E, and from every point between these extremities. Let us see where the rays that proceed from M to A, C, and B will be reflected, or, in other words, where the image of the point м will be formed.

James. Will all the rays that proceed from м, to different parts of the glass, be reflected to a single point?

Tutor. Yes, they will, and the difficulty is to find that point: I will take only three rays, to prevent confusion, viz. m a, m c, M B ; and c is the centre of concavity of the glass.

Charles. Then if I draw c A, that line will be perpendicular to the glass at the point a: the angle м A C is now given, and it is the angle of incidence.

James. And you must make another equal to it, as you did before.

Tutor. Very well; make ca x equal to м A c, and extend the line A x to any length you please.

Now you have an angle м c c made with the ray M c, and the perpendicular c c, which is another angle of incidence.

Charles. I will make the angle of reflection ccx equal to it, and the line ez being produced, cuts the line ax in a particular point, which I will call m.

Tutor. Draw now the perpendicular c B, and you have with it, and the ray м B, the angle of incidence м B C: make another angle equal to it, as its angle of reflection.

James. There it is c B u, and I find the line Bu meets the other lines at the point m.

Tutor. Then m is the point in which all the reflected rays of м will converge; of course the image of the extremity M of the arrow E M will be formed at m. Now the same might be shown of every other part of the object м E, the image of which will be represented by e m, which you see is at a greater distance from the glass than half c c, or radius.

Charles. The image is inverted also, and less than the object.

CONVERSATION XII.

Of Concave Mirrors, and Experiments on them.

Tutor. If you understand what we conversed on yesterday, and what you have yourselves done, you will easily see how the image is formed by the large concave mirror of the reflecting telescope, when we come to examine the construction of that instrument. In a concave mirror, the image is less than the object, when the object is more remote from the mirror than c, the centre of concavity, and in that case the image is between the object and mirror.

James. Suppose the object be placed in the centre c.

Tutor. Then the image and object will coincide and if the object is placed nearer to the glass than the centre c, then the image will be more remote, and bigger than the object.

Charles. I should like to see this illustrated by an experiment.

Tutor. Well here is a large concave mirror: place yourself before it, beyond the centre of the concavity; and with a little care in adjusting your position, you will see an inverted image of yourself in the air between you and the mirror, and of a less size than you are.

When you see the image, extend your hand gently towards the glass, and the hand of the image will advance to meet it, till they both meet in the centre of the glass's concavity. If you carry your hand still farther, the hand of the image will pass by it, and come between it and the body now move your hand to either side, and the image of it will move towards the other.

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James. Is there any rule for finding the distance at which the image of an object is formed from the mirror?

Tutor. If you know the radius of the mirror's concavity, and also the distance of the object from the glass,

"Multiply the distance and radius together, and divide the product by double the distance less by the radius, and the quotient is the distance required."

Tell me at what distance the image of an object will be, suppose the radius of the concavity of the mirror be 12 inches, and the object be at 18 inches from it.

James. I multiply 18 by 12, which is equal to 216; this I divide by double 18 or 36 less by 12, that is 24; but 216 divided by 24 gives 9, which is the number of inches required.

Tutor. You may vary this example, in order to impress the rule on your memory; and I will show you another experiment. I take this bottle partly full of water, and corked, and place

it opposite the concave mirror, and beyond the focus, that it may appear to be reversed: now stand a little farther distant than the bottle, and you will see the bottle inverted in the air, and the water which is in the lower part of the bottle will appear to be in the upper.-I will invert the bottle, and uncork it, and whilst the water is running out, the image will appear to be filling, but when the bottle is empty, the illusion is at an end.

Charles. Are concave mirrors ever used as burning-glasses?

Tutor. Since it is the property of these mirrors to cause parallel rays to converge to a focus, and since the rays of the sun are considered as parallel, they are very useful as burningglasses, and the principal focus is the burning point.

James. Is the image formed by a concave mirror always before it?

Tutor. In all cases, except when the object is nearer to the mirror than the principal focus. Charles. Is the image then behind the mirror?

Tutor. It is; and farther behind the mirror than the object is before it. Let A c (Plate III. Fig. 18.) be a mirror, and x z the object between the centre K of the glass, and the glass itself; and the image ar y will be behind the glass erect, curved, and magnified, and of