entirely out of focus, nothing but the image which it reflects from the large one1. This is not bright, much light being always lost by reflection; but some of these instruments define very well, and Gregorian reflectors are still to be met with.

Another construction was invented by Cassegrain, a Frenchman, which bears his name. The smaller speculum is here replaced by a convex one, which catches the converging rays before they come to focus, and reflects them to the same place as in the Grego

rian, to which some observers have preferred it. A very large one of this construction, with a concave speculum of 4 feet, was erected at Melbourne in 1869.

A third kind, the best of all, was not only invented by Sir Isaac Newton, but executed with his own hands in 1671, and that relic is still in the Library of the Royal Society. Here the great speculum is not perforated, and the reflected rays are caught on a plane mirror near the mouth of the tube, so inclined as to turn

1 For the same reason nothing is seen of a fly, or even a finger, on or near the object-glass of a refracting telescope. Only a small loss of light is the result.

them out sideways at right angles through an opening in the tube, where they are viewed by an eye-piece. With this kind, the "Newtonian reflector," Sir W. Herschel made many of his discoveries1. But all these different reflectors went out of fashion when the achromatic telescope, which we are going to describe, came into use, though the Earl of Rosse, at a later date, constructed an enormous Newtonian of 6 feet aperture, the largest telescope in the world, but,

owing to its length and weight, not the most generally useful.

A far simpler method of disposing of the difficulty is to tilt the large mirror so as to throw the focus a little on one side, dispense with a second reflection, and view the image direct with the eye-piece, turning one's back to the object. This, which is called the "Front view," was proposed by Le Maire, and extensively employed

1 But not with the high powers sometimes absurdly ascribed to them.

by both the Herschels with their large telescopes. The image is bright, as the loss in the second reflection is avoided, but it is less perfect. It is never so perfect as when in the axis. You must have noticed in your experiments with convex lenses in the sunshine, what strange distortion there is at the focus if the lens is held awry, and though comparatively trifling in these telescopes, it is enough to spoil their perfection.

All these reflecting telescopes sprang out of the extreme unwieldiness of the long refractor, which was considered irremediable, owing to a mistake of Sir Isaac Newton's, who made as few mistakes as any man, but was wrong about this. He imagined that in all substances the dispersion bears a fixed proportion to the refraction. But this is not the case. Two kinds of glass may be found, one of which, flint glass, of which wine-glasses are made, has a stronger dispersion than the other, crown or plate glass, that is, of course, supposing they refract equally. So that if we were to combine two lenses,

one of each kind of glass, a convex and a concave, of equal foci, though of course there would be no refraction, and the rays would pass through unchanged in that respect, yet colour would be shown, because the dispersive powers would be unequal. Now what would be the converse of this? Of course, that the dispersions of the two lenses might be equal, if the refractions were unequal; that is, if the focal lengths were different, and then the rays would undergo refraction and yet be colourless. We have only to combine a concave of naturally stronger dispersion but longer focus, and therefore in this case dispersing less, with a convex of naturally weaker dispersion but shorter focus, and therefore actually dispersing as much as its companion, and the thing is done. The shorter focus, as you ought to remember (see p. 57), will prevail, and the combination will act as a convex lens and form an image which will be without colour; and thus we have got the achromatic telescope, in which an object-glass of 6 inches aperture may have a focus of 7 instead of 120 feet, and be equally colourless, you may guess how much more manageable. This beautiful discovery is due to a gentleman named Hall, about 1733, and independently, though later, to Dollond, whose telescopes were long celebrated. And it

had another almost equally important advantage. I hinted (see p. 48) that spherical surfaces, such as grinding would produce, were not capable of forming a perfect focal image. You would not be able to understand the mathematical reasoning, but you may easily satisfy yourselves of it by experiment. Take our old friend the shortfocused reading-glass, and cut a piece of card to fit into its setting and cover it up, all except a small round hole of a quarter of an inch, which we must cut out of the centre, and a little ring half as broad, to be cut from the edge all round, leaving a few bridges of card here and there to keep it in the setting of the lens. If we hold this in sunshine or candlelight, and observe carefully how the rays come to focus on another card, we shall find that the sharpest image formed by the open ring at the edge is rather nearer to the lens than that from the hole in the centre. In fact, if we can suppose the whole lens made up of narrow rings outside one another, every ring would have its own focus, just as I showed you that the colours have; and the sharpness of the general image suffers in proportion. This is called the spherical error or aberration. With the same focal length it gets worse rapidly as the aperture is increased; and therefore the old telescope-makers were obliged to reduce it, as